%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP216^3 : TPTP v9.2.1. Bugfixed v9.2.1.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n007.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 09:05:05 AM UTC 2026
% Result : Theorem 18.75s 7.45s
% Output : Refutation 18.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 18 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 38 ( 23 equ; 0 cnn)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 74 ( 11 ~; 0 |; 0 &; 63 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Number of types : 306 ( 305 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 2601 (2598 usr; 163 con; 0-8 aty)
% Number of variables : 28 ( 12 ^; 16 !; 0 ?; 28 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
rat: $tType ).
thf(type_def_6,type,
int: $tType ).
thf(type_def_8,type,
nat: $tType ).
thf(type_def_9,type,
a: $tType ).
thf(type_def_10,type,
heap_T6362127782908069795rray_a: $tType ).
thf(type_def_11,type,
list_a: $tType ).
thf(type_def_12,type,
assn: $tType ).
thf(type_def_13,type,
produc3658429121746597890et_nat: $tType ).
thf(type_def_14,type,
set_nat: $tType ).
thf(type_def_15,type,
heap_e7401611519738050253t_unit: $tType ).
thf(type_def_16,type,
produc2732055786443039994et_nat: $tType ).
thf(type_def_17,type,
set_Product_prod_o_o: $tType ).
thf(type_def_18,type,
set_Pr1261947904930325089at_nat: $tType ).
thf(type_def_19,type,
set_o: $tType ).
thf(type_def_20,type,
code_integer: $tType ).
thf(type_def_21,type,
produc8923325533196201883nteger: $tType ).
thf(type_def_22,type,
num: $tType ).
thf(type_def_23,type,
product_prod_int_int: $tType ).
thf(type_def_24,type,
code_natural: $tType ).
thf(type_def_25,type,
produc7822875418678951345atural: $tType ).
thf(type_def_26,type,
product_prod_nat_nat: $tType ).
thf(type_def_27,type,
product_unit: $tType ).
thf(type_def_28,type,
set_Pr1932065953672099015od_o_o: $tType ).
thf(type_def_29,type,
set_Pr4329608150637261639at_nat: $tType ).
thf(type_def_30,type,
set_Pr457366540195662369at_nat: $tType ).
thf(type_def_31,type,
produc5835291356934675326atural: $tType ).
thf(type_def_32,type,
option_num: $tType ).
thf(type_def_33,type,
product_prod_num_num: $tType ).
thf(type_def_34,type,
produc6271795597528267376eger_o: $tType ).
thf(type_def_35,type,
set_in8474487674441654202_int_o: $tType ).
thf(type_def_36,type,
option6357759511663192854e_term: $tType ).
thf(type_def_37,type,
set_Pr8914822823351560561eger_o: $tType ).
thf(type_def_38,type,
produc6241069584506657477e_term: $tType ).
thf(type_def_39,type,
set_Pr1457143144315775327_nat_o: $tType ).
thf(type_def_40,type,
produc3925858234332021118et_nat: $tType ).
thf(type_def_41,type,
set_Pr8208987589773510107_nat_o: $tType ).
thf(type_def_42,type,
set_Pr5050529186185961540_int_o: $tType ).
thf(type_def_43,type,
produc8551481072490612790e_term: $tType ).
thf(type_def_44,type,
set_nat_nat_o: $tType ).
thf(type_def_45,type,
set_se9180647916752606350_nat_o: $tType ).
thf(type_def_46,type,
set_int: $tType ).
thf(type_def_47,type,
set_op3165557761946182707t_unit: $tType ).
thf(type_def_48,type,
option_Product_unit: $tType ).
thf(type_def_49,type,
set_option_set_nat: $tType ).
thf(type_def_50,type,
option_set_nat: $tType ).
thf(type_def_51,type,
set_Product_unit: $tType ).
thf(type_def_52,type,
set_set_o: $tType ).
thf(type_def_53,type,
set_set_Code_integer: $tType ).
thf(type_def_54,type,
set_Code_integer: $tType ).
thf(type_def_55,type,
set_set_int: $tType ).
thf(type_def_56,type,
set_set_list_nat: $tType ).
thf(type_def_57,type,
set_list_nat: $tType ).
thf(type_def_58,type,
set_set_nat: $tType ).
thf(type_def_59,type,
set_se7394616247590735609nt_int: $tType ).
thf(type_def_60,type,
set_Pr1872883991513573699nt_int: $tType ).
thf(type_def_61,type,
set_se124295367203800706nteger: $tType ).
thf(type_def_62,type,
set_Pr1281608226676607948nteger: $tType ).
thf(type_def_63,type,
set_se5120235452707311462et_nat: $tType ).
thf(type_def_64,type,
set_Pr8536935166611901872et_nat: $tType ).
thf(type_def_65,type,
set_se8543413830569400298et_nat: $tType ).
thf(type_def_66,type,
set_Pr3286484037609594932et_nat: $tType ).
thf(type_def_67,type,
set_se2364587433798273647nt_int: $tType ).
thf(type_def_68,type,
set_Pr9222295170931077689nt_int: $tType ).
thf(type_def_69,type,
set_se7855581050983116737at_nat: $tType ).
thf(type_def_70,type,
set_se5479201105039950375at_nat: $tType ).
thf(type_def_71,type,
set_set_Product_unit: $tType ).
thf(type_def_72,type,
set_option_o: $tType ).
thf(type_def_73,type,
option_o: $tType ).
thf(type_def_74,type,
set_se3372686590935047281atural: $tType ).
thf(type_def_75,type,
set_Pr7564037697178849041atural: $tType ).
thf(type_def_76,type,
set_num: $tType ).
thf(type_def_77,type,
set_op687863988967635939nteger: $tType ).
thf(type_def_78,type,
set_option_int: $tType ).
thf(type_def_79,type,
set_option_nat: $tType ).
thf(type_def_80,type,
set_option_num: $tType ).
thf(type_def_81,type,
set_op4508134149509766951at_nat: $tType ).
thf(type_def_82,type,
set_op239864471688321678it_nat: $tType ).
thf(type_def_83,type,
set_Pr4811707699266497531nteger: $tType ).
thf(type_def_84,type,
set_Pr6496905503482889930er_int: $tType ).
thf(type_def_85,type,
set_Pr8986988648414616686er_nat: $tType ).
thf(type_def_86,type,
set_Pr3948176798113811640et_nat: $tType ).
thf(type_def_87,type,
set_Pr8415741480598773322nteger: $tType ).
thf(type_def_88,type,
set_Pr958786334691620121nt_int: $tType ).
thf(type_def_89,type,
set_Pr3448869479623346877nt_nat: $tType ).
thf(type_def_90,type,
set_Pr2406931829603198446nteger: $tType ).
thf(type_def_91,type,
set_Pr7995236796853374141at_int: $tType ).
thf(type_def_92,type,
set_Pr8693737435421807431at_nat: $tType ).
thf(type_def_93,type,
set_Pr1354866905816374718it_nat: $tType ).
thf(type_def_94,type,
set_rat: $tType ).
thf(type_def_95,type,
multis2468970476368604999at_nat: $tType ).
thf(type_def_96,type,
option8057788054806935849nteger: $tType ).
thf(type_def_97,type,
option7428179582072448501nteger: $tType ).
thf(type_def_98,type,
option_Code_integer: $tType ).
thf(type_def_99,type,
option_nat_o: $tType ).
thf(type_def_100,type,
option_int: $tType ).
thf(type_def_101,type,
option_nat: $tType ).
thf(type_def_102,type,
option8956607266484857688it_nat: $tType ).
thf(type_def_103,type,
produc8664842809031399944it_nat: $tType ).
thf(type_def_104,type,
produc7773217078559923341nt_int: $tType ).
thf(type_def_105,type,
produc3832618445565238089e_term: $tType ).
thf(type_def_106,type,
produc7360885484439884007_nat_o: $tType ).
thf(type_def_107,type,
produc1908205239877642774nteger: $tType ).
thf(type_def_108,type,
produc998928222018024388e_term: $tType ).
thf(type_def_109,type,
produc4962441903510821572_nat_o: $tType ).
thf(type_def_110,type,
produc6907119039986491712_nat_o: $tType ).
thf(type_def_111,type,
produc2285326912895808259nt_int: $tType ).
thf(type_def_112,type,
produc1821397396195235155e_term: $tType ).
thf(type_def_113,type,
product_prod_o_o: $tType ).
thf(type_def_114,type,
produc2256096406371053034er_int: $tType ).
thf(type_def_115,type,
produc6433947425880249742er_nat: $tType ).
thf(type_def_116,type,
produc6756470014200349799atural: $tType ).
thf(type_def_117,type,
produc3981471736659609608atural: $tType ).
thf(type_def_118,type,
produc6714399278180371524it_nat: $tType ).
thf(type_def_119,type,
option3216581401566546698it_nat: $tType ).
thf(type_def_120,type,
produc2963269191615333738nteger: $tType ).
thf(type_def_121,type,
product_prod_int_nat: $tType ).
thf(type_def_122,type,
produc2591615631378489102nteger: $tType ).
thf(type_def_123,type,
product_prod_nat_int: $tType ).
thf(type_def_124,type,
option5403585828896915703atural: $tType ).
thf(type_def_125,type,
produc3843707927480180839at_nat: $tType ).
thf(type_def_126,type,
set_nat_o: $tType ).
thf(type_def_127,type,
produc4193628355235574503at_nat: $tType ).
thf(type_def_128,type,
produc1319942482725812455at_nat: $tType ).
thf(type_def_129,type,
list_nat: $tType ).
thf(type_def_130,type,
set_se8531188866349061887nteger: $tType ).
thf(type_def_131,type,
set_set_set_int: $tType ).
thf(type_def_132,type,
set_set_set_list_nat: $tType ).
thf(type_def_133,type,
set_set_set_nat: $tType ).
thf(type_def_134,type,
set_se5158245632345848097at_nat: $tType ).
thf(type_def_135,type,
set_se7118615804146677933t_unit: $tType ).
thf(type_def_136,type,
array_a: $tType ).
thf(type_def_137,type,
typerep: $tType ).
thf(type_def_138,type,
heap_T5738788834812785303t_unit: $tType ).
thf(type_def_139,type,
list_char: $tType ).
thf(type_def_140,type,
produc2867611627572283311it_nat: $tType ).
thf(type_def_141,type,
produc3911288613690379145it_nat: $tType ).
thf(type_def_142,type,
list_int: $tType ).
thf(type_def_143,type,
option_set_o: $tType ).
thf(type_def_144,type,
option_set_int: $tType ).
thf(type_def_145,type,
option8963830502488799655at_nat: $tType ).
thf(type_def_146,type,
option1583680563626158861at_nat: $tType ).
thf(type_def_147,type,
option_assn: $tType ).
thf(type_def_148,type,
set_Pr8834758594704517033_o_int: $tType ).
thf(type_def_149,type,
set_Pr2101469702781467981_o_nat: $tType ).
thf(type_def_150,type,
set_Pr903927857289325719_int_o: $tType ).
thf(type_def_151,type,
set_Pr3149072824959771635_nat_o: $tType ).
thf(type_def_152,type,
set_Pr6558897299634722526_nat_o: $tType ).
thf(type_def_153,type,
option5190343406534369742et_nat: $tType ).
thf(type_def_154,type,
option2651255830984564193nteger: $tType ).
thf(type_def_155,type,
option936205604648967762et_nat: $tType ).
thf(type_def_156,type,
option4624381673175914239nt_int: $tType ).
thf(type_def_157,type,
produc6576344331059438605e_term: $tType ).
thf(type_def_158,type,
produc7819656566062154093et_nat: $tType ).
thf(type_def_159,type,
set_Pr7040061329075590551_o_num: $tType ).
thf(type_def_160,type,
set_Pr6777250647868329861it_nat: $tType ).
thf(type_def_161,type,
set_Pr2352657477744078772atural: $tType ).
thf(type_def_162,type,
set_Pr8387461105917469447nt_num: $tType ).
thf(type_def_163,type,
set_Pr6200539531224447659at_num: $tType ).
thf(type_def_164,type,
set_Pr633603713510679705it_nat: $tType ).
thf(type_def_165,type,
set_Pr7477759153910077568at_num: $tType ).
thf(type_def_166,type,
set_Pr8551490117392284871at_nat: $tType ).
thf(type_def_167,type,
sum_sum_nat_nat: $tType ).
thf(type_def_168,type,
option4256020574406277085nt_int: $tType ).
thf(type_def_169,type,
option8051342751916580710nteger: $tType ).
thf(type_def_170,type,
option2860828798490689354et_nat: $tType ).
thf(type_def_171,type,
option7541221861074943443nt_int: $tType ).
thf(type_def_172,type,
option4927543243414619207at_nat: $tType ).
thf(type_def_173,type,
option8699557107911914541at_nat: $tType ).
thf(type_def_174,type,
option_rat: $tType ).
thf(type_def_175,type,
option8137458692691377843t_unit: $tType ).
thf(type_def_176,type,
set_op3940070208846178154it_nat: $tType ).
thf(type_def_177,type,
set_Pr5142436192348053284it_nat: $tType ).
thf(type_def_178,type,
set_op989438649584373901at_nat: $tType ).
thf(type_def_179,type,
set_Pr5564308138774400199at_nat: $tType ).
thf(type_def_180,type,
set_in3461395444621081367e_term: $tType ).
thf(type_def_181,type,
set_Pr7604974323444597168e_term: $tType ).
thf(type_def_182,type,
set_Pr4532377907799695533_nat_o: $tType ).
thf(type_def_183,type,
set_Pr3642885161833720865e_term: $tType ).
thf(type_def_184,type,
set_Pr7909803484932130503_nat_o: $tType ).
thf(type_def_185,type,
set_Pr7717912310451564380at_nat: $tType ).
thf(type_def_186,type,
set_Pr1625285437083415874at_nat: $tType ).
thf(type_def_187,type,
set_Pr2539167527615954998at_nat: $tType ).
thf(type_def_188,type,
set_Pr552903133987017116at_nat: $tType ).
thf(type_def_189,type,
set_Co726186806682698383nteger: $tType ).
thf(type_def_190,type,
set_assn: $tType ).
thf(type_def_191,type,
set_Pr5889264611543340172t_unit: $tType ).
thf(type_def_192,type,
set_Pr4334478416066269672t_unit: $tType ).
thf(type_def_193,type,
set_Pr8497134830871917726it_int: $tType ).
thf(type_def_194,type,
set_Pr1763845938948868674it_nat: $tType ).
thf(type_def_195,type,
set_Pr5094982260447487303t_unit: $tType ).
thf(type_def_196,type,
produc8763457246119570046nteger: $tType ).
thf(type_def_197,type,
produc8731074985263844745atural: $tType ).
thf(type_def_198,type,
produc1945540942535730339e_term: $tType ).
thf(type_def_199,type,
produc7248412053542808358at_nat: $tType ).
thf(type_def_200,type,
produc4471711990508489141at_nat: $tType ).
thf(type_def_201,type,
produc8187290932660736981e_term: $tType ).
thf(type_def_202,type,
produc4972180933644002618e_term: $tType ).
thf(type_def_203,type,
produc989692990947075319atural: $tType ).
thf(type_def_204,type,
produc4928098042776334183_nat_o: $tType ).
thf(type_def_205,type,
produc4499399687821757879e_term: $tType ).
thf(type_def_206,type,
product_prod_o_int: $tType ).
thf(type_def_207,type,
product_prod_o_nat: $tType ).
thf(type_def_208,type,
produc6653097349344004940it_nat: $tType ).
thf(type_def_209,type,
product_prod_int_o: $tType ).
thf(type_def_210,type,
produc4166570645942440679at_nat: $tType ).
thf(type_def_211,type,
product_prod_nat_o: $tType ).
thf(type_def_212,type,
product_prod_nat_num: $tType ).
thf(type_def_213,type,
produc3313772616054891654at_nat: $tType ).
thf(type_def_214,type,
produc2501202720802129403nt_int: $tType ).
thf(type_def_215,type,
produc824974754969098637nteger: $tType ).
thf(type_def_216,type,
produc5657529347773406293et_nat: $tType ).
thf(type_def_217,type,
produc6830853553727218525et_nat: $tType ).
thf(type_def_218,type,
produc2432570611225516007nt_int: $tType ).
thf(type_def_219,type,
produc3334582477557816039nteger: $tType ).
thf(type_def_220,type,
produc8111630337999740517et_nat: $tType ).
thf(type_def_221,type,
produc1219242969750017639nt_int: $tType ).
thf(type_def_222,type,
produc652263959640188542_nat_o: $tType ).
thf(type_def_223,type,
produc859450856879609959at_nat: $tType ).
thf(type_def_224,type,
produc2714363965264676845at_nat: $tType ).
thf(type_def_225,type,
produc366245978424229472at_nat: $tType ).
thf(type_def_226,type,
produc2087150632810049441at_nat: $tType ).
thf(type_def_227,type,
produc1906917888121415911at_nat: $tType ).
thf(type_def_228,type,
produc7369051934464679207_set_o: $tType ).
thf(type_def_229,type,
produc6491284506569428743nteger: $tType ).
thf(type_def_230,type,
produc2115011035271226405et_int: $tType ).
thf(type_def_231,type,
produc2934264451710624999od_o_o: $tType ).
thf(type_def_232,type,
produc732395585841259969at_nat: $tType ).
thf(type_def_233,type,
produc7299876168958306407at_nat: $tType ).
thf(type_def_234,type,
set_Code_natural: $tType ).
thf(type_def_235,type,
set_Pr3451248702717554689st_nat: $tType ).
thf(type_def_236,type,
set_Pr7549493975000385137at_nat: $tType ).
thf(type_def_237,type,
set_Pr698032948827214833st_nat: $tType ).
thf(type_def_238,type,
set_Pr7705059561495379578_nat_o: $tType ).
thf(type_def_239,type,
set_Pr1628540301243981434e_term: $tType ).
thf(type_def_240,type,
set_Pr4208978187861016310_nat_o: $tType ).
thf(type_def_241,type,
set_Pr9020418513037773311e_term: $tType ).
thf(type_def_242,type,
set_Pr7309386651551657097e_term: $tType ).
thf(type_def_243,type,
set_Pr5488025237498180813et_nat: $tType ).
thf(type_def_244,type,
produc6237349844158694175nteger: $tType ).
thf(type_def_245,type,
produc382792921321436433nt_int: $tType ).
thf(type_def_246,type,
produc3295550550304853304nteger: $tType ).
thf(type_def_247,type,
produc3346328345660746739nteger: $tType ).
thf(type_def_248,type,
produc6691574917238108761nteger: $tType ).
thf(type_def_249,type,
produc8299537390109905600et_nat: $tType ).
thf(type_def_250,type,
produc4130039061994950697nteger: $tType ).
thf(type_def_251,type,
produc5219672859094816389atural: $tType ).
thf(type_def_252,type,
produc5665947927044467078nt_int: $tType ).
thf(type_def_253,type,
produc5111566536631596683et_nat: $tType ).
thf(type_def_254,type,
produc6025053409261769070rm_int: $tType ).
thf(type_def_255,type,
produc759720530913461378nt_int: $tType ).
thf(type_def_256,type,
produc7172142986261921671rm_int: $tType ).
thf(type_def_257,type,
produc6162884466328367972nteger: $tType ).
thf(type_def_258,type,
produc3776562785724475560_o_int: $tType ).
thf(type_def_259,type,
produc8065447618272157327et_nat: $tType ).
thf(type_def_260,type,
produc5577056076408194680rm_int: $tType ).
thf(type_def_261,type,
produc5966032636589952099nteger: $tType ).
thf(type_def_262,type,
produc7142191362829087448er_num: $tType ).
thf(type_def_263,type,
produc1828647624359046049st_nat: $tType ).
thf(type_def_264,type,
produc1540777390238407569at_nat: $tType ).
thf(type_def_265,type,
produc4575160907756185873st_nat: $tType ).
thf(type_def_266,type,
product_prod_o_num: $tType ).
thf(type_def_267,type,
produc2900562427881843919it_nat: $tType ).
thf(type_def_268,type,
product_prod_int_num: $tType ).
thf(type_def_269,type,
produc3839731585411834681it_nat: $tType ).
thf(type_def_270,type,
produc9082142974458947146at_num: $tType ).
thf(type_def_271,type,
ref_array_a: $tType ).
thf(type_def_272,type,
ref_Product_unit: $tType ).
thf(type_def_273,type,
set_in2553536192574375378_nat_o: $tType ).
thf(type_def_274,type,
set_in2260935666578096390nteger: $tType ).
thf(type_def_275,type,
set_in1345054734626228863atural: $tType ).
thf(type_def_276,type,
set_in6154042108061588260nt_int: $tType ).
thf(type_def_277,type,
set_na3661387095409732706nteger: $tType ).
thf(type_def_278,type,
set_na2454399383705037859atural: $tType ).
thf(type_def_279,type,
set_na7251125088705586816nt_int: $tType ).
thf(type_def_280,type,
set_Pr9591959067864425nteger: $tType ).
thf(type_def_281,type,
set_Pr7322412474522714716atural: $tType ).
thf(type_def_282,type,
set_Pr3770298976803184519nt_int: $tType ).
thf(type_def_283,type,
set_Pr2072254264782222413at_nat: $tType ).
thf(type_def_284,type,
set_Pr5070339090747523585at_nat: $tType ).
thf(type_def_285,type,
set_Pr1604112560894399303at_nat: $tType ).
thf(type_def_286,type,
set_Pr1425283071195816930_int_o: $tType ).
thf(type_def_287,type,
set_Pr606876518868980121eger_o: $tType ).
thf(type_def_288,type,
set_Pr1230246726286442933_nat_o: $tType ).
thf(type_def_289,type,
set_Pr8959645425803247153_nat_o: $tType ).
thf(type_def_290,type,
set_Pr6358892174463501804_int_o: $tType ).
thf(type_def_291,type,
set_Pr5582243495563764594_nat_o: $tType ).
thf(type_def_292,type,
set_Pr7010166363911110284_nat_o: $tType ).
thf(type_def_293,type,
set_mu2057375006010111271at_nat: $tType ).
thf(type_def_294,type,
char: $tType ).
thf(type_def_295,type,
set_Pr7577011563204128103nteger: $tType ).
thf(type_def_296,type,
set_Pr2522554150109002629et_int: $tType ).
thf(type_def_297,type,
set_Pr7140365069852192003e_term: $tType ).
thf(type_def_298,type,
set_Pr2560585780119916871nt_int: $tType ).
thf(type_def_299,type,
set_Pr8634505666381077339nt_int: $tType ).
thf(type_def_300,type,
set_Pr6418322821503574069e_term: $tType ).
thf(type_def_301,type,
set_Pr5052581263052047815nteger: $tType ).
thf(type_def_302,type,
set_Pr1722956316086891245nteger: $tType ).
thf(type_def_303,type,
set_Pr2161125870931222855_nat_o: $tType ).
thf(type_def_304,type,
set_Pr7928877670098842301et_nat: $tType ).
thf(type_def_305,type,
set_Pr3444600963470892981et_nat: $tType ).
thf(type_def_306,type,
set_Pr719794911490849221et_nat: $tType ).
thf(type_def_307,type,
set_Pr4675205556198584599e_term: $tType ).
thf(type_def_308,type,
set_Pr4708930517165415495nt_int: $tType ).
thf(type_def_309,type,
set_Pr4577759397028426247_set_o: $tType ).
thf(type_def_310,type,
set_Pr7459493094073627847at_nat: $tType ).
thf(func_def_0,type,
set_Pr3444600963470892981et_nat: $tType ).
thf(func_def_1,type,
produc5657529347773406293et_nat: $tType ).
thf(func_def_2,type,
set_Pr1722956316086891245nteger: $tType ).
thf(func_def_3,type,
produc824974754969098637nteger: $tType ).
thf(func_def_4,type,
set_Pr4708930517165415495nt_int: $tType ).
thf(func_def_5,type,
produc2432570611225516007nt_int: $tType ).
thf(func_def_6,type,
set_Pr7928877670098842301et_nat: $tType ).
thf(func_def_7,type,
produc6830853553727218525et_nat: $tType ).
thf(func_def_8,type,
set_Pr6418322821503574069e_term: $tType ).
thf(func_def_9,type,
produc8187290932660736981e_term: $tType ).
thf(func_def_10,type,
set_Pr4675205556198584599e_term: $tType ).
thf(func_def_11,type,
set_se5120235452707311462et_nat: $tType ).
thf(func_def_12,type,
set_Pr8634505666381077339nt_int: $tType ).
thf(func_def_13,type,
produc4499399687821757879e_term: $tType ).
thf(func_def_14,type,
set_Pr1230246726286442933_nat_o: $tType ).
thf(func_def_15,type,
option2860828798490689354et_nat: $tType ).
thf(func_def_16,type,
set_Pr7705059561495379578_nat_o: $tType ).
thf(func_def_17,type,
set_Pr8536935166611901872et_nat: $tType ).
thf(func_def_18,type,
produc2501202720802129403nt_int: $tType ).
thf(func_def_19,type,
produc4193628355235574503at_nat: $tType ).
thf(func_def_20,type,
set_Pr1457143144315775327_nat_o: $tType ).
thf(func_def_21,type,
produc4962441903510821572_nat_o: $tType ).
thf(func_def_22,type,
produc2732055786443039994et_nat: $tType ).
thf(func_def_23,type,
set_Pr7459493094073627847at_nat: $tType ).
thf(func_def_24,type,
produc1319942482725812455at_nat: $tType ).
thf(func_def_25,type,
set_Pr5564308138774400199at_nat: $tType ).
thf(func_def_26,type,
set_se124295367203800706nteger: $tType ).
thf(func_def_27,type,
set_Pr606876518868980121eger_o: $tType ).
thf(func_def_28,type,
produc1906917888121415911at_nat: $tType ).
thf(func_def_29,type,
option8051342751916580710nteger: $tType ).
thf(func_def_30,type,
set_Pr1628540301243981434e_term: $tType ).
thf(func_def_31,type,
set_Pr1281608226676607948nteger: $tType ).
thf(func_def_32,type,
set_Pr8914822823351560561eger_o: $tType ).
thf(func_def_33,type,
produc998928222018024388e_term: $tType ).
thf(func_def_34,type,
produc989692990947075319atural: $tType ).
thf(func_def_35,type,
produc1908205239877642774nteger: $tType ).
thf(func_def_36,type,
set_se2364587433798273647nt_int: $tType ).
thf(func_def_37,type,
set_Pr6358892174463501804_int_o: $tType ).
thf(func_def_38,type,
option7541221861074943443nt_int: $tType ).
thf(func_def_39,type,
set_Pr7309386651551657097e_term: $tType ).
thf(func_def_40,type,
set_Pr9222295170931077689nt_int: $tType ).
thf(func_def_41,type,
set_Pr5050529186185961540_int_o: $tType ).
thf(func_def_42,type,
set_se8543413830569400298et_nat: $tType ).
thf(func_def_43,type,
set_Pr2161125870931222855_nat_o: $tType ).
thf(func_def_44,type,
set_Pr8959645425803247153_nat_o: $tType ).
thf(func_def_45,type,
produc1821397396195235155e_term: $tType ).
thf(func_def_46,type,
produc2285326912895808259nt_int: $tType ).
thf(func_def_47,type,
option5190343406534369742et_nat: $tType ).
thf(func_def_48,type,
set_Pr7140365069852192003e_term: $tType ).
thf(func_def_49,type,
produc3295550550304853304nteger: $tType ).
thf(func_def_50,type,
set_Pr4208978187861016310_nat_o: $tType ).
thf(func_def_51,type,
set_Pr3286484037609594932et_nat: $tType ).
thf(func_def_52,type,
produc4928098042776334183_nat_o: $tType ).
thf(func_def_53,type,
set_Pr8208987589773510107_nat_o: $tType ).
thf(func_def_54,type,
set_Pr719794911490849221et_nat: $tType ).
thf(func_def_55,type,
produc1945540942535730339e_term: $tType ).
thf(func_def_56,type,
produc4130039061994950697nteger: $tType ).
thf(func_def_57,type,
produc7172142986261921671rm_int: $tType ).
thf(func_def_58,type,
produc6907119039986491712_nat_o: $tType ).
thf(func_def_59,type,
produc3925858234332021118et_nat: $tType ).
thf(func_def_60,type,
set_Pr5070339090747523585at_nat: $tType ).
thf(func_def_61,type,
set_Pr2072254264782222413at_nat: $tType ).
thf(func_def_62,type,
produc8111630337999740517et_nat: $tType ).
thf(func_def_63,type,
produc5577056076408194680rm_int: $tType ).
thf(func_def_64,type,
produc2087150632810049441at_nat: $tType ).
thf(func_def_65,type,
produc2714363965264676845at_nat: $tType ).
thf(func_def_66,type,
produc8731074985263844745atural: $tType ).
thf(func_def_67,type,
produc8763457246119570046nteger: $tType ).
thf(func_def_68,type,
set_Pr7604974323444597168e_term: $tType ).
thf(func_def_69,type,
produc5966032636589952099nteger: $tType ).
thf(func_def_70,type,
set_se7394616247590735609nt_int: $tType ).
thf(func_def_71,type,
produc5219672859094816389atural: $tType ).
thf(func_def_72,type,
set_Pr1425283071195816930_int_o: $tType ).
thf(func_def_73,type,
produc6576344331059438605e_term: $tType ).
thf(func_def_74,type,
set_Pr3642885161833720865e_term: $tType ).
thf(func_def_75,type,
set_Pr552903133987017116at_nat: $tType ).
thf(func_def_76,type,
set_Pr1625285437083415874at_nat: $tType ).
thf(func_def_77,type,
option4256020574406277085nt_int: $tType ).
thf(func_def_78,type,
set_Pr9020418513037773311e_term: $tType ).
thf(func_def_79,type,
set_Pr1872883991513573699nt_int: $tType ).
thf(func_def_80,type,
set_Pr1604112560894399303at_nat: $tType ).
thf(func_def_81,type,
set_Pr5052581263052047815nteger: $tType ).
thf(func_def_82,type,
produc3911288613690379145it_nat: $tType ).
thf(func_def_83,type,
produc2867611627572283311it_nat: $tType ).
thf(func_def_84,type,
set_in8474487674441654202_int_o: $tType ).
thf(func_def_85,type,
set_Pr633603713510679705it_nat: $tType ).
thf(func_def_86,type,
set_op989438649584373901at_nat: $tType ).
thf(func_def_87,type,
option1583680563626158861at_nat: $tType ).
thf(func_def_88,type,
produc3832618445565238089e_term: $tType ).
thf(func_def_89,type,
produc7773217078559923341nt_int: $tType ).
thf(func_def_90,type,
set_Pr8551490117392284871at_nat: $tType ).
thf(func_def_91,type,
set_Pr6777250647868329861it_nat: $tType ).
thf(func_def_92,type,
option7428179582072448501nteger: $tType ).
thf(func_def_93,type,
set_se5479201105039950375at_nat: $tType ).
thf(func_def_94,type,
produc7299876168958306407at_nat: $tType ).
thf(func_def_95,type,
produc6756470014200349799atural: $tType ).
thf(func_def_96,type,
produc3334582477557816039nteger: $tType ).
thf(func_def_97,type,
set_Pr7010166363911110284_nat_o: $tType ).
thf(func_def_98,type,
produc3839731585411834681it_nat: $tType ).
thf(func_def_99,type,
set_Pr7322412474522714716atural: $tType ).
thf(func_def_100,type,
option8699557107911914541at_nat: $tType ).
thf(func_def_101,type,
set_op239864471688321678it_nat: $tType ).
thf(func_def_102,type,
set_op3940070208846178154it_nat: $tType ).
thf(func_def_103,type,
produc4166570645942440679at_nat: $tType ).
thf(func_def_104,type,
produc2900562427881843919it_nat: $tType ).
thf(func_def_105,type,
set_Pr4329608150637261639at_nat: $tType ).
thf(func_def_106,type,
produc6691574917238108761nteger: $tType ).
thf(func_def_107,type,
produc4471711990508489141at_nat: $tType ).
thf(func_def_108,type,
set_na2454399383705037859atural: $tType ).
thf(func_def_109,type,
set_in1345054734626228863atural: $tType ).
thf(func_def_110,type,
produc6237349844158694175nteger: $tType ).
thf(func_def_111,type,
set_se9180647916752606350_nat_o: $tType ).
thf(func_def_112,type,
option8956607266484857688it_nat: $tType ).
thf(func_def_113,type,
option3216581401566546698it_nat: $tType ).
thf(func_def_114,type,
produc5111566536631596683et_nat: $tType ).
thf(func_def_115,type,
produc8299537390109905600et_nat: $tType ).
thf(func_def_116,type,
produc3843707927480180839at_nat: $tType ).
thf(func_def_117,type,
set_Pr1354866905816374718it_nat: $tType ).
thf(func_def_118,type,
produc3776562785724475560_o_int: $tType ).
thf(func_def_119,type,
set_Pr457366540195662369at_nat: $tType ).
thf(func_def_120,type,
set_Pr5142436192348053284it_nat: $tType ).
thf(func_def_121,type,
produc6025053409261769070rm_int: $tType ).
thf(func_def_122,type,
set_Pr2352657477744078772atural: $tType ).
thf(func_def_123,type,
produc8065447618272157327et_nat: $tType ).
thf(func_def_124,type,
set_Pr8693737435421807431at_nat: $tType ).
thf(func_def_125,type,
set_Pr2560585780119916871nt_int: $tType ).
thf(func_def_126,type,
produc8664842809031399944it_nat: $tType ).
thf(func_def_127,type,
produc732395585841259969at_nat: $tType ).
thf(func_def_128,type,
produc6714399278180371524it_nat: $tType ).
thf(func_def_129,type,
set_Pr1932065953672099015od_o_o: $tType ).
thf(func_def_130,type,
produc3981471736659609608atural: $tType ).
thf(func_def_131,type,
produc5835291356934675326atural: $tType ).
thf(func_def_132,type,
produc3346328345660746739nteger: $tType ).
thf(func_def_133,type,
set_Pr4532377907799695533_nat_o: $tType ).
thf(func_def_134,type,
produc859450856879609959at_nat: $tType ).
thf(func_def_135,type,
produc1219242969750017639nt_int: $tType ).
thf(func_def_136,type,
set_in3461395444621081367e_term: $tType ).
thf(func_def_137,type,
set_Pr9591959067864425nteger: $tType ).
thf(func_def_138,type,
option936205604648967762et_nat: $tType ).
thf(func_def_139,type,
produc2934264451710624999od_o_o: $tType ).
thf(func_def_140,type,
set_Pr7577011563204128103nteger: $tType ).
thf(func_def_141,type,
set_Pr3948176798113811640et_nat: $tType ).
thf(func_def_142,type,
produc6162884466328367972nteger: $tType ).
thf(func_def_143,type,
set_na3661387095409732706nteger: $tType ).
thf(func_def_144,type,
set_in2260935666578096390nteger: $tType ).
thf(func_def_145,type,
produc4972180933644002618e_term: $tType ).
thf(func_def_146,type,
produc6241069584506657477e_term: $tType ).
thf(func_def_147,type,
set_se3372686590935047281atural: $tType ).
thf(func_def_148,type,
set_in2553536192574375378_nat_o: $tType ).
thf(func_def_149,type,
produc6491284506569428743nteger: $tType ).
thf(func_def_150,type,
produc3658429121746597890et_nat: $tType ).
thf(func_def_151,type,
set_Pr7477759153910077568at_num: $tType ).
thf(func_def_152,type,
set_Pr2539167527615954998at_nat: $tType ).
thf(func_def_153,type,
set_Pr7717912310451564380at_nat: $tType ).
thf(func_def_154,type,
produc366245978424229472at_nat: $tType ).
thf(func_def_155,type,
produc3313772616054891654at_nat: $tType ).
thf(func_def_156,type,
produc5665947927044467078nt_int: $tType ).
thf(func_def_157,type,
produc382792921321436433nt_int: $tType ).
thf(func_def_158,type,
option5403585828896915703atural: $tType ).
thf(func_def_159,type,
option2651255830984564193nteger: $tType ).
thf(func_def_160,type,
set_Pr3451248702717554689st_nat: $tType ).
thf(func_def_161,type,
set_Pr3770298976803184519nt_int: $tType ).
thf(func_def_162,type,
produc8551481072490612790e_term: $tType ).
thf(func_def_163,type,
set_Pr6558897299634722526_nat_o: $tType ).
thf(func_def_164,type,
set_se5158245632345848097at_nat: $tType ).
thf(func_def_165,type,
set_Pr5488025237498180813et_nat: $tType ).
thf(func_def_166,type,
set_Pr2522554150109002629et_int: $tType ).
thf(func_def_167,type,
set_Pr7564037697178849041atural: $tType ).
thf(func_def_168,type,
set_Pr4811707699266497531nteger: $tType ).
thf(func_def_169,type,
option6357759511663192854e_term: $tType ).
thf(func_def_170,type,
produc6653097349344004940it_nat: $tType ).
thf(func_def_171,type,
produc9082142974458947146at_num: $tType ).
thf(func_def_172,type,
produc7248412053542808358at_nat: $tType ).
thf(func_def_173,type,
produc759720530913461378nt_int: $tType ).
thf(func_def_174,type,
set_Pr5094982260447487303t_unit: $tType ).
thf(func_def_175,type,
set_Pr7909803484932130503_nat_o: $tType ).
thf(func_def_176,type,
set_mu2057375006010111271at_nat: $tType ).
thf(func_def_177,type,
set_op4508134149509766951at_nat: $tType ).
thf(func_def_178,type,
set_na7251125088705586816nt_int: $tType ).
thf(func_def_179,type,
set_in6154042108061588260nt_int: $tType ).
thf(func_def_180,type,
option8963830502488799655at_nat: $tType ).
thf(func_def_181,type,
produc1828647624359046049st_nat: $tType ).
thf(func_def_182,type,
set_Pr698032948827214833st_nat: $tType ).
thf(func_def_183,type,
set_Pr7549493975000385137at_nat: $tType ).
thf(func_def_184,type,
produc652263959640188542_nat_o: $tType ).
thf(func_def_185,type,
option8057788054806935849nteger: $tType ).
thf(func_def_186,type,
set_se7855581050983116737at_nat: $tType ).
thf(func_def_187,type,
set_Pr2406931829603198446nteger: $tType ).
thf(func_def_188,type,
set_Pr8415741480598773322nteger: $tType ).
thf(func_def_189,type,
set_Pr8986988648414616686er_nat: $tType ).
thf(func_def_190,type,
set_Pr6496905503482889930er_int: $tType ).
thf(func_def_191,type,
produc7819656566062154093et_nat: $tType ).
thf(func_def_192,type,
produc2115011035271226405et_int: $tType ).
thf(func_def_193,type,
produc7822875418678951345atural: $tType ).
thf(func_def_194,type,
produc8923325533196201883nteger: $tType ).
thf(func_def_195,type,
set_Pr4577759397028426247_set_o: $tType ).
thf(func_def_196,type,
set_Pr1763845938948868674it_nat: $tType ).
thf(func_def_197,type,
set_Pr8497134830871917726it_int: $tType ).
thf(func_def_198,type,
set_Pr4334478416066269672t_unit: $tType ).
thf(func_def_199,type,
set_Pr5889264611543340172t_unit: $tType ).
thf(func_def_200,type,
set_Pr5582243495563764594_nat_o: $tType ).
thf(func_def_201,type,
set_Co726186806682698383nteger: $tType ).
thf(func_def_202,type,
produc7360885484439884007_nat_o: $tType ).
thf(func_def_203,type,
multis2468970476368604999at_nat: $tType ).
thf(func_def_204,type,
set_set_set_list_nat: $tType ).
thf(func_def_205,type,
option4927543243414619207at_nat: $tType ).
thf(func_def_206,type,
option4624381673175914239nt_int: $tType ).
thf(func_def_207,type,
set_se8531188866349061887nteger: $tType ).
thf(func_def_208,type,
set_se7118615804146677933t_unit: $tType ).
thf(func_def_209,type,
produc4575160907756185873st_nat: $tType ).
thf(func_def_210,type,
produc1540777390238407569at_nat: $tType ).
thf(func_def_211,type,
set_Pr6200539531224447659at_num: $tType ).
thf(func_def_212,type,
set_Pr1261947904930325089at_nat: $tType ).
thf(func_def_213,type,
set_Pr7995236796853374141at_int: $tType ).
thf(func_def_214,type,
set_Pr8387461105917469447nt_num: $tType ).
thf(func_def_215,type,
set_Pr3448869479623346877nt_nat: $tType ).
thf(func_def_216,type,
set_Pr958786334691620121nt_int: $tType ).
thf(func_def_217,type,
produc2591615631378489102nteger: $tType ).
thf(func_def_218,type,
produc2963269191615333738nteger: $tType ).
thf(func_def_219,type,
produc7142191362829087448er_num: $tType ).
thf(func_def_220,type,
produc6433947425880249742er_nat: $tType ).
thf(func_def_221,type,
produc2256096406371053034er_int: $tType ).
thf(func_def_222,type,
produc7369051934464679207_set_o: $tType ).
thf(func_def_223,type,
set_option_set_nat: $tType ).
thf(func_def_224,type,
set_op687863988967635939nteger: $tType ).
thf(func_def_225,type,
set_op3165557761946182707t_unit: $tType ).
thf(func_def_226,type,
set_nat_nat_o: $tType ).
thf(func_def_227,type,
option8137458692691377843t_unit: $tType ).
thf(func_def_228,type,
set_set_list_nat: $tType ).
thf(func_def_229,type,
set_Pr3149072824959771635_nat_o: $tType ).
thf(func_def_230,type,
set_Pr903927857289325719_int_o: $tType ).
thf(func_def_231,type,
set_Pr7040061329075590551_o_num: $tType ).
thf(func_def_232,type,
set_Pr2101469702781467981_o_nat: $tType ).
thf(func_def_233,type,
set_Pr8834758594704517033_o_int: $tType ).
thf(func_def_234,type,
produc6271795597528267376eger_o: $tType ).
thf(func_def_235,type,
set_set_set_nat: $tType ).
thf(func_def_236,type,
set_set_set_int: $tType ).
thf(func_def_237,type,
set_set_Code_integer: $tType ).
thf(func_def_238,type,
heap_T5738788834812785303t_unit: $tType ).
thf(func_def_239,type,
heap_T6362127782908069795rray_a: $tType ).
thf(func_def_240,type,
set_set_Product_unit: $tType ).
thf(func_def_241,type,
heap_e7401611519738050253t_unit: $tType ).
thf(func_def_242,type,
product_prod_num_num: $tType ).
thf(func_def_243,type,
product_prod_nat_num: $tType ).
thf(func_def_244,type,
product_prod_nat_nat: $tType ).
thf(func_def_245,type,
product_prod_nat_int: $tType ).
thf(func_def_246,type,
product_prod_int_num: $tType ).
thf(func_def_247,type,
product_prod_int_nat: $tType ).
thf(func_def_248,type,
product_prod_int_int: $tType ).
thf(func_def_249,type,
set_Product_prod_o_o: $tType ).
thf(func_def_250,type,
sum_sum_nat_nat: $tType ).
thf(func_def_251,type,
set_option_num: $tType ).
thf(func_def_252,type,
set_option_nat: $tType ).
thf(func_def_253,type,
set_option_int: $tType ).
thf(func_def_254,type,
option_set_nat: $tType ).
thf(func_def_255,type,
option_set_int: $tType ).
thf(func_def_256,type,
option_Code_integer: $tType ).
thf(func_def_257,type,
option_Product_unit: $tType ).
thf(func_def_258,type,
option_nat_o: $tType ).
thf(func_def_259,type,
set_list_nat: $tType ).
thf(func_def_260,type,
product_prod_nat_o: $tType ).
thf(func_def_261,type,
product_prod_int_o: $tType ).
thf(func_def_262,type,
product_prod_o_num: $tType ).
thf(func_def_263,type,
product_prod_o_nat: $tType ).
thf(func_def_264,type,
product_prod_o_int: $tType ).
thf(func_def_265,type,
set_set_nat: $tType ).
thf(func_def_266,type,
set_set_int: $tType ).
thf(func_def_267,type,
set_Code_natural: $tType ).
thf(func_def_268,type,
set_Code_integer: $tType ).
thf(func_def_269,type,
option_assn: $tType ).
thf(func_def_270,type,
ref_Product_unit: $tType ).
thf(func_def_271,type,
set_Product_unit: $tType ).
thf(func_def_272,type,
set_option_o: $tType ).
thf(func_def_273,type,
set_nat_o: $tType ).
thf(func_def_274,type,
option_set_o: $tType ).
thf(func_def_275,type,
ref_array_a: $tType ).
thf(func_def_276,type,
product_prod_o_o: $tType ).
thf(func_def_277,type,
set_assn: $tType ).
thf(func_def_278,type,
set_set_o: $tType ).
thf(func_def_279,type,
option_rat: $tType ).
thf(func_def_280,type,
option_num: $tType ).
thf(func_def_281,type,
option_nat: $tType ).
thf(func_def_282,type,
option_int: $tType ).
thf(func_def_283,type,
list_char: $tType ).
thf(func_def_284,type,
list_nat: $tType ).
thf(func_def_285,type,
list_int: $tType ).
thf(func_def_286,type,
set_rat: $tType ).
thf(func_def_287,type,
set_num: $tType ).
thf(func_def_288,type,
set_nat: $tType ).
thf(func_def_289,type,
set_int: $tType ).
thf(func_def_290,type,
code_natural: $tType ).
thf(func_def_291,type,
code_integer: $tType ).
thf(func_def_292,type,
product_unit: $tType ).
thf(func_def_293,type,
option_o: $tType ).
thf(func_def_294,type,
array_a: $tType ).
thf(func_def_295,type,
list_a: $tType ).
thf(func_def_296,type,
typerep: $tType ).
thf(func_def_297,type,
assn: $tType ).
thf(func_def_298,type,
set_o: $tType ).
thf(func_def_299,type,
char: $tType ).
thf(func_def_300,type,
rat: $tType ).
thf(func_def_301,type,
num: $tType ).
thf(func_def_302,type,
nat: $tType ).
thf(func_def_303,type,
int: $tType ).
thf(func_def_304,type,
a: $tType ).
thf(func_def_305,type,
archim2889992004027027881ng_rat: rat > int ).
thf(func_def_306,type,
archim3151403230148437115or_rat: rat > int ).
thf(func_def_307,type,
archimedean_frac_rat: rat > rat ).
thf(func_def_308,type,
archim7778729529865785530nd_rat: rat > int ).
thf(func_def_309,type,
array_make_a: nat > ( nat > a ) > heap_T6362127782908069795rray_a ).
thf(func_def_310,type,
array_new_a: nat > a > heap_T6362127782908069795rray_a ).
thf(func_def_311,type,
array_of_list_a: list_a > heap_T6362127782908069795rray_a ).
thf(func_def_312,type,
rep_assn: assn > produc3658429121746597890et_nat > $o ).
thf(func_def_313,type,
in_range: produc3658429121746597890et_nat > $o ).
thf(func_def_314,type,
in_range_rel: produc3658429121746597890et_nat > produc3658429121746597890et_nat > $o ).
thf(func_def_315,type,
one_assn_raw: produc3658429121746597890et_nat > $o ).
thf(func_def_316,type,
one_assn_raw_rel: produc3658429121746597890et_nat > produc3658429121746597890et_nat > $o ).
thf(func_def_317,type,
proper: ( produc3658429121746597890et_nat > $o ) > $o ).
thf(func_def_318,type,
pure_assn: $o > assn ).
thf(func_def_319,type,
relH: set_nat > heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit > $o ).
thf(func_def_320,type,
times_assn_raw: ( produc3658429121746597890et_nat > $o ) > ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o ).
thf(func_def_321,type,
times_assn_raw_rel: produc2732055786443039994et_nat > produc2732055786443039994et_nat > $o ).
thf(func_def_322,type,
wand_assn: assn > assn > assn ).
thf(func_def_323,type,
wand_raw: ( produc3658429121746597890et_nat > $o ) > ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o ).
thf(func_def_324,type,
wand_raw_rel: produc2732055786443039994et_nat > produc2732055786443039994et_nat > $o ).
thf(func_def_325,type,
bNF_Cardinal_ctwo: set_Product_prod_o_o ).
thf(func_def_326,type,
bNF_Cardinal_czero_o: set_Product_prod_o_o ).
thf(func_def_327,type,
bNF_Ca3793111618940312692of_nat: set_nat > set_Pr1261947904930325089at_nat ).
thf(func_def_328,type,
bNF_Ca8331644756375544342r_on_o: set_o > set_Product_prod_o_o > $o ).
thf(func_def_329,type,
bNF_Ca8665028551170535155natLeq: set_Pr1261947904930325089at_nat ).
thf(func_def_330,type,
bNF_re2555365631850037877_int_o: ( ( ( int > $o ) > int > $o ) > ( ( int > $o ) > int > $o ) > $o ) > ( ( ( int > int > $o ) > int > int > $o ) > ( ( int > int > $o ) > int > int > $o ) > $o ) > ( ( ( int > $o ) > int > $o ) > ( int > int > $o ) > int > int > $o ) > ( ( ( int > $o ) > int > $o ) > ( int > int > $o ) > int > int > $o ) > $o ).
thf(func_def_331,type,
bNF_re5051145820034318685nt_int: ( ( ( int > $o ) > int > int ) > ( ( int > $o ) > int > int ) > $o ) > ( ( ( int > int > $o ) > int > int > int ) > ( ( int > int > $o ) > int > int > int ) > $o ) > ( ( ( int > $o ) > int > int ) > ( int > int > $o ) > int > int > int ) > ( ( ( int > $o ) > int > int ) > ( int > int > $o ) > int > int > int ) > $o ).
thf(func_def_332,type,
bNF_re615132412071444453_nat_o: ( ( ( int > $o ) > nat > $o ) > ( ( int > $o ) > nat > $o ) > $o ) > ( ( ( int > int > $o ) > int > nat > $o ) > ( ( int > int > $o ) > int > nat > $o ) > $o ) > ( ( ( int > $o ) > nat > $o ) > ( int > int > $o ) > int > nat > $o ) > ( ( ( int > $o ) > nat > $o ) > ( int > int > $o ) > int > nat > $o ) > $o ).
thf(func_def_333,type,
bNF_re3161894838932316637_int_o: ( ( ( int > int ) > int > $o ) > ( ( int > int ) > int > $o ) > $o ) > ( ( ( int > int > int ) > int > int > $o ) > ( ( int > int > int ) > int > int > $o ) > $o ) > ( ( ( int > int ) > int > $o ) > ( int > int > int ) > int > int > $o ) > ( ( ( int > int ) > int > $o ) > ( int > int > int ) > int > int > $o ) > $o ).
thf(func_def_334,type,
bNF_re4659646225794970589_nat_o: ( ( ( int > int ) > nat > $o ) > ( ( int > int ) > nat > $o ) > $o ) > ( ( ( int > int > int ) > int > nat > $o ) > ( ( int > int > int ) > int > nat > $o ) > $o ) > ( ( ( int > int ) > nat > $o ) > ( int > int > int ) > int > nat > $o ) > ( ( ( int > int ) > nat > $o ) > ( int > int > int ) > int > nat > $o ) > $o ).
thf(func_def_335,type,
bNF_re3491090157995142405_int_o: ( ( ( nat > $o ) > int > $o ) > ( ( nat > $o ) > int > $o ) > $o ) > ( ( ( int > nat > $o ) > int > int > $o ) > ( ( int > nat > $o ) > int > int > $o ) > $o ) > ( ( ( nat > $o ) > int > $o ) > ( int > nat > $o ) > int > int > $o ) > ( ( ( nat > $o ) > int > $o ) > ( int > nat > $o ) > int > int > $o ) > $o ).
thf(func_def_336,type,
bNF_re5539255234643219293nt_int: ( ( ( nat > $o ) > int > int ) > ( ( nat > $o ) > int > int ) > $o ) > ( ( ( int > nat > $o ) > int > int > int ) > ( ( int > nat > $o ) > int > int > int ) > $o ) > ( ( ( nat > $o ) > int > int ) > ( int > nat > $o ) > int > int > int ) > ( ( ( nat > $o ) > int > int ) > ( int > nat > $o ) > int > int > int ) > $o ).
thf(func_def_337,type,
bNF_re1550856938216548981_nat_o: ( ( ( nat > $o ) > nat > $o ) > ( ( nat > $o ) > nat > $o ) > $o ) > ( ( ( int > nat > $o ) > int > nat > $o ) > ( ( int > nat > $o ) > int > nat > $o ) > $o ) > ( ( ( nat > $o ) > nat > $o ) > ( int > nat > $o ) > int > nat > $o ) > ( ( ( nat > $o ) > nat > $o ) > ( int > nat > $o ) > int > nat > $o ) > $o ).
thf(func_def_338,type,
bNF_re4919612610145136063nteger: ( ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer ) > $o ) > ( ( ( code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( ( num > code_integer ) > num > code_integer ) > $o ) > ( ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( ( code_integer > code_integer ) > ( num > code_integer ) > num > code_integer ) > $o ).
thf(func_def_339,type,
bNF_re1890273300020150979nt_num: ( ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( nat > num ) > $o ) > ( ( ( code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( ( int > nat ) > int > num ) > $o ) > ( ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( ( nat > num ) > ( int > nat ) > int > num ) > $o ).
thf(func_def_340,type,
bNF_re8134695817916415679nteger: ( ( code_integer > code_integer ) > ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > $o ) > ( ( ( num > code_integer ) > num > code_integer ) > ( ( code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > $o ) > ( ( code_integer > code_integer ) > ( num > code_integer ) > num > code_integer ) > ( ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > $o ).
thf(func_def_341,type,
bNF_re5979881370344185769nteger: ( ( code_integer > code_integer ) > ( code_integer > code_integer ) > $o ) > ( ( ( num > code_integer ) > num > code_integer ) > ( ( num > code_integer ) > num > code_integer ) > $o ) > ( ( code_integer > code_integer ) > ( num > code_integer ) > num > code_integer ) > ( ( code_integer > code_integer ) > ( num > code_integer ) > num > code_integer ) > $o ).
thf(func_def_342,type,
bNF_re5190287125156074331nt_num: ( ( code_integer > code_integer ) > ( int > nat ) > $o ) > ( ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( int > num ) > $o ) > ( ( code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( ( int > nat ) > int > num ) > $o ).
thf(func_def_343,type,
bNF_re5469402333911078061nt_num: ( ( code_integer > code_integer ) > ( nat > num ) > $o ) > ( ( ( num > code_integer ) > num > code_integer ) > ( ( int > nat ) > int > num ) > $o ) > ( ( code_integer > code_integer ) > ( num > code_integer ) > num > code_integer ) > ( ( nat > num ) > ( int > nat ) > int > num ) > $o ).
thf(func_def_344,type,
bNF_re6724329528997265415nteger: ( ( code_integer > code_integer ) > ( num > code_integer ) > $o ) > ( ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( num > code_integer ) > $o ) > ( ( code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( ( num > code_integer ) > num > code_integer ) > $o ).
thf(func_def_345,type,
bNF_re1900612664124570461_int_o: ( ( int > int > $o ) > ( int > int > $o ) > $o ) > ( ( ( int > int ) > int > int > $o ) > ( ( int > int ) > int > int > $o ) > $o ) > ( ( int > int > $o ) > ( int > int ) > int > int > $o ) > ( ( int > int > $o ) > ( int > int ) > int > int > $o ) > $o ).
thf(func_def_346,type,
bNF_re8651060166502312541_int_o: ( ( int > int > $o ) > ( int > int > $o ) > $o ) > ( ( int > int > $o ) > ( int > int > $o ) > $o ) > ( ( int > int > $o ) > int > int > $o ) > ( ( int > int > $o ) > int > int > $o ) > $o ).
thf(func_def_347,type,
bNF_re7462748251485907171nt_int: ( ( int > int > $o ) > ( int > int > $o ) > $o ) > ( ( int > int > int ) > ( int > int > int ) > $o ) > ( ( int > int > $o ) > int > int > int ) > ( ( int > int > $o ) > int > int > int ) > $o ).
thf(func_def_348,type,
bNF_re2446162618891206493_nat_o: ( ( int > int > $o ) > ( int > int > $o ) > $o ) > ( ( int > nat > $o ) > ( int > nat > $o ) > $o ) > ( ( int > int > $o ) > int > nat > $o ) > ( ( int > int > $o ) > int > nat > $o ) > $o ).
thf(func_def_349,type,
bNF_re4984751527058004117nt_int: ( ( int > int > int ) > ( int > int > int ) > $o ) > ( ( ( int > int ) > int > int > int ) > ( ( int > int ) > int > int > int ) > $o ) > ( ( int > int > int ) > ( int > int ) > int > int > int ) > ( ( int > int > int ) > ( int > int ) > int > int > int ) > $o ).
thf(func_def_350,type,
bNF_re1313934062736347107_int_o: ( ( int > int > int ) > ( int > int > int ) > $o ) > ( ( int > int > $o ) > ( int > int > $o ) > $o ) > ( ( int > int > int ) > int > int > $o ) > ( ( int > int > int ) > int > int > $o ) > $o ).
thf(func_def_351,type,
bNF_re4332408551980016867_nat_o: ( ( int > int > int ) > ( int > int > int ) > $o ) > ( ( int > nat > $o ) > ( int > nat > $o ) > $o ) > ( ( int > int > int ) > int > nat > $o ) > ( ( int > int > int ) > int > nat > $o ) > $o ).
thf(func_def_352,type,
bNF_re62019127700022579nt_rat: ( ( int > int > product_prod_int_int ) > ( int > int > rat ) > $o ) > ( ( ( int > int ) > int > int > product_prod_int_int ) > ( ( int > int ) > int > int > rat ) > $o ) > ( ( int > int > product_prod_int_int ) > ( int > int ) > int > int > product_prod_int_int ) > ( ( int > int > rat ) > ( int > int ) > int > int > rat ) > $o ).
thf(func_def_353,type,
bNF_re7908124382625962333_nat_o: ( ( int > nat > $o ) > ( int > nat > $o ) > $o ) > ( ( ( int > int ) > int > nat > $o ) > ( ( int > int ) > int > nat > $o ) > $o ) > ( ( int > nat > $o ) > ( int > int ) > int > nat > $o ) > ( ( int > nat > $o ) > ( int > int ) > int > nat > $o ) > $o ).
thf(func_def_354,type,
bNF_re2655111580231008093_int_o: ( ( int > nat > $o ) > ( int > nat > $o ) > $o ) > ( ( int > int > $o ) > ( int > int > $o ) > $o ) > ( ( int > nat > $o ) > int > int > $o ) > ( ( int > nat > $o ) > int > int > $o ) > $o ).
thf(func_def_355,type,
bNF_re7395152722673581539nt_int: ( ( int > nat > $o ) > ( int > nat > $o ) > $o ) > ( ( int > int > int ) > ( int > int > int ) > $o ) > ( ( int > nat > $o ) > int > int > int ) > ( ( int > nat > $o ) > int > int > int ) > $o ).
thf(func_def_356,type,
bNF_re5673586069474677853_nat_o: ( ( int > nat > $o ) > ( int > nat > $o ) > $o ) > ( ( int > nat > $o ) > ( int > nat > $o ) > $o ) > ( ( int > nat > $o ) > int > nat > $o ) > ( ( int > nat > $o ) > int > nat > $o ) > $o ).
thf(func_def_357,type,
bNF_re2535741173671728349_nat_o: ( ( int > $o ) > ( int > $o ) > $o ) > ( ( nat > $o ) > ( nat > $o ) > $o ) > ( ( int > $o ) > nat > $o ) > ( ( int > $o ) > nat > $o ) > $o ).
thf(func_def_358,type,
bNF_re3014639844587090765_int_o: ( ( int > int ) > ( int > int ) > $o ) > ( ( int > int > $o ) > ( int > int > $o ) > $o ) > ( ( int > int ) > int > int > $o ) > ( ( int > int ) > int > int > $o ) > $o ).
thf(func_def_359,type,
bNF_re724639330072410579nt_int: ( ( int > int ) > ( int > int ) > $o ) > ( ( int > int > int ) > ( int > int > int ) > $o ) > ( ( int > int ) > int > int > int ) > ( ( int > int ) > int > int > int ) > $o ).
thf(func_def_360,type,
bNF_re949775918795716016nt_rat: ( ( int > int ) > ( int > int ) > $o ) > ( ( int > int > product_prod_int_int ) > ( int > int > rat ) > $o ) > ( ( int > int ) > int > int > product_prod_int_int ) > ( ( int > int ) > int > int > rat ) > $o ).
thf(func_def_361,type,
bNF_re6033114333830760525_nat_o: ( ( int > int ) > ( int > int ) > $o ) > ( ( int > nat > $o ) > ( int > nat > $o ) > $o ) > ( ( int > int ) > int > nat > $o ) > ( ( int > int ) > int > nat > $o ) > $o ).
thf(func_def_362,type,
bNF_re9099949428469764705nt_num: ( ( int > nat ) > ( int > nat ) > $o ) > ( ( int > num ) > ( int > num ) > $o ) > ( ( int > nat ) > int > num ) > ( ( int > nat ) > int > num ) > $o ).
thf(func_def_363,type,
bNF_re8894579221946749965nteger: ( ( int > nat ) > ( num > code_integer ) > $o ) > ( ( int > num ) > ( num > code_integer ) > $o ) > ( ( int > nat ) > int > num ) > ( ( num > code_integer ) > num > code_integer ) > $o ).
thf(func_def_364,type,
bNF_re2724346968851715293_int_o: ( ( nat > $o ) > ( nat > $o ) > $o ) > ( ( int > $o ) > ( int > $o ) > $o ) > ( ( nat > $o ) > int > $o ) > ( ( nat > $o ) > int > $o ) > $o ).
thf(func_def_365,type,
bNF_re7183634743573646861nt_int: ( ( nat > $o ) > ( nat > $o ) > $o ) > ( ( int > int ) > ( int > int ) > $o ) > ( ( nat > $o ) > int > int ) > ( ( nat > $o ) > int > int ) > $o ).
thf(func_def_366,type,
bNF_re2697311982885662685_nat_o: ( ( nat > $o ) > ( nat > $o ) > $o ) > ( ( nat > $o ) > ( nat > $o ) > $o ) > ( ( nat > $o ) > nat > $o ) > ( ( nat > $o ) > nat > $o ) > $o ).
thf(func_def_367,type,
bNF_re2163612987331707565nteger: ( ( nat > num ) > ( code_integer > code_integer ) > $o ) > ( ( ( int > nat ) > int > num ) > ( ( num > code_integer ) > num > code_integer ) > $o ) > ( ( nat > num ) > ( int > nat ) > int > num ) > ( ( code_integer > code_integer ) > ( num > code_integer ) > num > code_integer ) > $o ).
thf(func_def_368,type,
bNF_re3846787885862361009nt_num: ( ( nat > num ) > ( nat > num ) > $o ) > ( ( ( int > nat ) > int > num ) > ( ( int > nat ) > int > num ) > $o ) > ( ( nat > num ) > ( int > nat ) > int > num ) > ( ( nat > num ) > ( int > nat ) > int > num ) > $o ).
thf(func_def_369,type,
bNF_re2439920061672227847nteger: ( ( num > code_integer ) > ( code_integer > code_integer ) > $o ) > ( ( num > code_integer ) > ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > $o ) > ( ( num > code_integer ) > num > code_integer ) > ( ( code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > $o ).
thf(func_def_370,type,
bNF_re1151383970801924621nt_num: ( ( num > code_integer ) > ( int > nat ) > $o ) > ( ( num > code_integer ) > ( int > num ) > $o ) > ( ( num > code_integer ) > num > code_integer ) > ( ( int > nat ) > int > num ) > $o ).
thf(func_def_371,type,
bNF_re6097285183634142137nteger: ( ( num > code_integer ) > ( num > code_integer ) > $o ) > ( ( num > code_integer ) > ( num > code_integer ) > $o ) > ( ( num > code_integer ) > num > code_integer ) > ( ( num > code_integer ) > num > code_integer ) > $o ).
thf(func_def_372,type,
bNF_re1551779926989065179nt_nat: ( $o > $o > $o ) > ( int > nat > $o ) > ( $o > int ) > ( $o > nat ) > $o ).
thf(func_def_373,type,
bNF_re916649866902569443nt_rat: ( $o > $o > $o ) > ( int > rat > $o ) > ( $o > int ) > ( $o > rat ) > $o ).
thf(func_def_374,type,
bNF_re4863541036035986956nteger: ( $o > $o > $o ) > ( nat > code_integer > $o ) > ( $o > nat ) > ( $o > code_integer ) > $o ).
thf(func_def_375,type,
bNF_re549935744578960347at_int: ( $o > $o > $o ) > ( nat > int > $o ) > ( $o > nat ) > ( $o > int ) > $o ).
thf(func_def_376,type,
bNF_re552426215088010623at_nat: ( $o > $o > $o ) > ( nat > nat > $o ) > ( $o > nat ) > ( $o > nat ) > $o ).
thf(func_def_377,type,
bNF_re9140668191856290695at_rat: ( $o > $o > $o ) > ( nat > rat > $o ) > ( $o > nat ) > ( $o > rat ) > $o ).
thf(func_def_378,type,
bNF_re5635613845597506580nteger: ( $o > $o > $o ) > ( rat > code_integer > $o ) > ( $o > rat ) > ( $o > code_integer ) > $o ).
thf(func_def_379,type,
bNF_re233381100644094435at_int: ( $o > $o > $o ) > ( rat > int > $o ) > ( $o > rat ) > ( $o > int ) > $o ).
thf(func_def_380,type,
bNF_re235871571153144711at_nat: ( $o > $o > $o ) > ( rat > nat > $o ) > ( $o > rat ) > ( $o > nat ) > $o ).
thf(func_def_381,type,
bNF_re8824113547921424783at_rat: ( $o > $o > $o ) > ( rat > rat > $o ) > ( $o > rat ) > ( $o > rat ) > $o ).
thf(func_def_382,type,
bNF_re9137223911888007311n_assn: ( assn > assn > $o ) > ( ( assn > assn ) > ( assn > assn ) > $o ) > ( assn > assn > assn ) > ( assn > assn > assn ) > $o ).
thf(func_def_383,type,
bNF_re3650450707543776735t_assn: ( assn > assn > $o ) > ( ( nat > assn ) > ( nat > assn ) > $o ) > ( assn > nat > assn ) > ( assn > nat > assn ) > $o ).
thf(func_def_384,type,
bNF_re1143782165119297793n_assn: ( assn > assn > $o ) > ( assn > assn > $o ) > ( assn > assn ) > ( assn > assn ) > $o ).
thf(func_def_385,type,
bNF_re5822757241383739566nteger: ( assn > code_integer > $o ) > ( ( assn > assn ) > ( code_integer > code_integer ) > $o ) > ( assn > assn > assn ) > ( code_integer > code_integer > code_integer ) > $o ).
thf(func_def_386,type,
bNF_re2102180915162216137nteger: ( assn > code_integer > $o ) > ( ( nat > assn ) > ( nat > code_integer ) > $o ) > ( assn > nat > assn ) > ( code_integer > nat > code_integer ) > $o ).
thf(func_def_387,type,
bNF_re4134162077946812779nteger: ( assn > code_integer > $o ) > ( assn > code_integer > $o ) > ( assn > assn ) > ( code_integer > code_integer ) > $o ).
thf(func_def_388,type,
bNF_re7882741803053012379nt_int: ( assn > int > $o ) > ( ( assn > assn ) > ( int > int ) > $o ) > ( assn > assn > assn ) > ( int > int > int ) > $o ).
thf(func_def_389,type,
bNF_re185025794348816359at_int: ( assn > int > $o ) > ( ( nat > assn ) > ( nat > int ) > $o ) > ( assn > nat > assn ) > ( int > nat > int ) > $o ).
thf(func_def_390,type,
bNF_re2927800259774540553sn_int: ( assn > int > $o ) > ( assn > int > $o ) > ( assn > assn ) > ( int > int ) > $o ).
thf(func_def_391,type,
bNF_re4386305596031132807at_nat: ( assn > nat > $o ) > ( ( assn > assn ) > ( nat > nat ) > $o ) > ( assn > assn > assn ) > ( nat > nat > nat ) > $o ).
thf(func_def_392,type,
bNF_re8560028565313717551at_nat: ( assn > nat > $o ) > ( ( nat > assn ) > ( nat > nat ) > $o ) > ( assn > nat > assn ) > ( nat > nat > nat ) > $o ).
thf(func_def_393,type,
bNF_re6742580585434904145sn_nat: ( assn > nat > $o ) > ( assn > nat > $o ) > ( assn > assn ) > ( nat > nat ) > $o ).
thf(func_def_394,type,
bNF_re967558844708792991at_rat: ( assn > rat > $o ) > ( ( assn > assn ) > ( rat > rat ) > $o ) > ( assn > assn > assn ) > ( rat > rat > rat ) > $o ).
thf(func_def_395,type,
bNF_re6138836914430330175at_rat: ( assn > rat > $o ) > ( ( nat > assn ) > ( nat > rat ) > $o ) > ( assn > nat > assn ) > ( rat > nat > rat ) > $o ).
thf(func_def_396,type,
bNF_re9003240792272343649sn_rat: ( assn > rat > $o ) > ( assn > rat > $o ) > ( assn > assn ) > ( rat > rat ) > $o ).
thf(func_def_397,type,
bNF_re7789648203153440174n_assn: ( code_integer > assn > $o ) > ( ( code_integer > code_integer ) > ( assn > assn ) > $o ) > ( code_integer > code_integer > code_integer ) > ( assn > assn > assn ) > $o ).
thf(func_def_398,type,
bNF_re2546461910754330953t_assn: ( code_integer > assn > $o ) > ( ( nat > code_integer ) > ( nat > assn ) > $o ) > ( code_integer > nat > code_integer ) > ( assn > nat > assn ) > $o ).
thf(func_def_399,type,
bNF_re1475883931861434731r_assn: ( code_integer > assn > $o ) > ( code_integer > assn > $o ) > ( code_integer > code_integer ) > ( assn > assn ) > $o ).
thf(func_def_400,type,
bNF_re122555440370955213nteger: ( code_integer > code_integer > $o ) > ( ( code_integer > code_integer ) > ( code_integer > code_integer ) > $o ) > ( code_integer > code_integer > code_integer ) > ( code_integer > code_integer > code_integer ) > $o ).
thf(func_def_401,type,
bNF_re5462749793222359603nteger: ( code_integer > code_integer > $o ) > ( ( nat > code_integer ) > ( nat > code_integer ) > $o ) > ( code_integer > nat > code_integer ) > ( code_integer > nat > code_integer ) > $o ).
thf(func_def_402,type,
bNF_re4341081746073172381nteger: ( code_integer > code_integer > $o ) > ( ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > code_integer > $o ) > ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer ) > $o ).
thf(func_def_403,type,
bNF_re3370092614548195229nteger: ( code_integer > code_integer > $o ) > ( code_integer > ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > $o ) > ( code_integer > code_integer ) > ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > $o ).
thf(func_def_404,type,
bNF_re1062419521925302741nteger: ( code_integer > code_integer > $o ) > ( code_integer > code_integer > $o ) > ( code_integer > code_integer ) > ( code_integer > code_integer ) > $o ).
thf(func_def_405,type,
bNF_re8304916493157054650nt_int: ( code_integer > int > $o ) > ( ( code_integer > code_integer ) > ( int > int ) > $o ) > ( code_integer > code_integer > code_integer ) > ( int > int > int ) > $o ).
thf(func_def_406,type,
bNF_re6766650671887726929at_int: ( code_integer > int > $o ) > ( ( nat > code_integer ) > ( nat > int ) > $o ) > ( code_integer > nat > code_integer ) > ( int > nat > int ) > $o ).
thf(func_def_407,type,
bNF_re8127238762813979689er_num: ( code_integer > int > $o ) > ( ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > num > $o ) > ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( int > num ) > $o ).
thf(func_def_408,type,
bNF_re2888858428391045491er_int: ( code_integer > int > $o ) > ( code_integer > int > $o ) > ( code_integer > code_integer ) > ( int > int ) > $o ).
thf(func_def_409,type,
bNF_re2891348898900095767er_nat: ( code_integer > int > $o ) > ( code_integer > nat > $o ) > ( code_integer > code_integer ) > ( int > nat ) > $o ).
thf(func_def_410,type,
bNF_re3981674901896804262at_nat: ( code_integer > nat > $o ) > ( ( code_integer > code_integer ) > ( nat > nat ) > $o ) > ( code_integer > code_integer > code_integer ) > ( nat > nat > nat ) > $o ).
thf(func_def_411,type,
bNF_re4269568176766901913at_nat: ( code_integer > nat > $o ) > ( ( nat > code_integer ) > ( nat > nat ) > $o ) > ( code_integer > nat > code_integer ) > ( nat > nat > nat ) > $o ).
thf(func_def_412,type,
bNF_re7119966052990372301er_num: ( code_integer > nat > $o ) > ( ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > num > $o ) > ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( nat > num ) > $o ).
thf(func_def_413,type,
bNF_re5201166830993046715er_nat: ( code_integer > nat > $o ) > ( code_integer > nat > $o ) > ( code_integer > code_integer ) > ( nat > nat ) > $o ).
thf(func_def_414,type,
bNF_re1758498617148825349er_num: ( code_integer > nat > $o ) > ( code_integer > num > $o ) > ( code_integer > code_integer ) > ( nat > num ) > $o ).
thf(func_def_415,type,
bNF_re166502229267952730nteger: ( code_integer > num > $o ) > ( ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > code_integer > $o ) > ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( num > code_integer ) > $o ).
thf(func_def_416,type,
bNF_re7350422212947406738nteger: ( code_integer > num > $o ) > ( code_integer > code_integer > $o ) > ( code_integer > code_integer ) > ( num > code_integer ) > $o ).
thf(func_def_417,type,
bNF_re2976496150901874110at_rat: ( code_integer > rat > $o ) > ( ( code_integer > code_integer ) > ( rat > rat ) > $o ) > ( code_integer > code_integer > code_integer ) > ( rat > rat > rat ) > $o ).
thf(func_def_418,type,
bNF_re1167376069379428009at_rat: ( code_integer > rat > $o ) > ( ( nat > code_integer ) > ( nat > rat ) > $o ) > ( code_integer > nat > code_integer ) > ( rat > nat > rat ) > $o ).
thf(func_def_419,type,
bNF_re4698098036185532619er_rat: ( code_integer > rat > $o ) > ( code_integer > rat > $o ) > ( code_integer > code_integer ) > ( rat > rat ) > $o ).
thf(func_def_420,type,
bNF_re6321650412969554871eger_o: ( int > code_integer > $o ) > ( ( int > $o ) > ( code_integer > $o ) > $o ) > ( int > int > $o ) > ( code_integer > code_integer > $o ) > $o ).
thf(func_def_421,type,
bNF_re398004352372739002nteger: ( int > code_integer > $o ) > ( ( int > int ) > ( code_integer > code_integer ) > $o ) > ( int > int > int ) > ( code_integer > code_integer > code_integer ) > $o ).
thf(func_def_422,type,
bNF_re4711666741709854504_nat_o: ( int > code_integer > $o ) > ( ( nat > $o ) > ( nat > $o ) > $o ) > ( int > nat > $o ) > ( code_integer > nat > $o ) > $o ).
thf(func_def_423,type,
bNF_re6574881592172037608er_o_o: ( int > code_integer > $o ) > ( $o > $o > $o ) > ( int > $o ) > ( code_integer > $o ) > $o ).
thf(func_def_424,type,
bNF_re3379532845092657523nteger: ( int > code_integer > $o ) > ( int > code_integer > $o ) > ( int > int ) > ( code_integer > code_integer ) > $o ).
thf(func_def_425,type,
bNF_re3804157879324367682nt_int: ( int > code_integer > $o ) > ( int > int > $o ) > ( int > int ) > ( code_integer > int ) > $o ).
thf(func_def_426,type,
bNF_re1831474436612530402atural: ( int > code_integer > $o ) > ( nat > code_natural > $o ) > ( int > nat ) > ( code_integer > code_natural ) > $o ).
thf(func_def_427,type,
bNF_re2807294637932363402at_nat: ( int > code_integer > $o ) > ( nat > nat > $o ) > ( int > nat ) > ( code_integer > nat ) > $o ).
thf(func_def_428,type,
bNF_re6718328864250387230um_num: ( int > code_integer > $o ) > ( num > num > $o ) > ( int > num ) > ( code_integer > num ) > $o ).
thf(func_def_429,type,
bNF_re2342410721167621787atural: ( int > code_natural > $o ) > ( ( int > int ) > ( code_natural > code_natural ) > $o ) > ( int > int > int ) > ( code_natural > code_natural > code_natural ) > $o ).
thf(func_def_430,type,
bNF_re5484556299188842761atural: ( int > code_natural > $o ) > ( int > code_natural > $o ) > ( int > int ) > ( code_natural > code_natural ) > $o ).
thf(func_def_431,type,
bNF_re3403563459893282935_int_o: ( int > int > $o ) > ( ( int > $o ) > ( int > $o ) > $o ) > ( int > int > $o ) > ( int > int > $o ) > $o ).
thf(func_def_432,type,
bNF_re711492959462206631nt_int: ( int > int > $o ) > ( ( int > int ) > ( int > int ) > $o ) > ( int > int > int ) > ( int > int > int ) > $o ).
thf(func_def_433,type,
bNF_re157797125943740599nt_int: ( int > int > $o ) > ( ( int > product_prod_int_int ) > ( int > product_prod_int_int ) > $o ) > ( int > int > product_prod_int_int ) > ( int > int > product_prod_int_int ) > $o ).
thf(func_def_434,type,
bNF_re3461391660133120880nt_rat: ( int > int > $o ) > ( ( int > product_prod_int_int ) > ( int > rat ) > $o ) > ( int > int > product_prod_int_int ) > ( int > int > rat ) > $o ).
thf(func_def_435,type,
bNF_re3376528473927230327_nat_o: ( int > int > $o ) > ( ( nat > $o ) > ( nat > $o ) > $o ) > ( int > nat > $o ) > ( int > nat > $o ) > $o ).
thf(func_def_436,type,
bNF_re5089333283451836215nt_o_o: ( int > int > $o ) > ( $o > $o > $o ) > ( int > $o ) > ( int > $o ) > $o ).
thf(func_def_437,type,
bNF_re1784066744496875891nteger: ( int > int > $o ) > ( code_integer > code_integer > $o ) > ( int > code_integer ) > ( int > code_integer ) > $o ).
thf(func_def_438,type,
bNF_re343602593470180162er_int: ( int > int > $o ) > ( code_integer > int > $o ) > ( int > code_integer ) > ( int > int ) > $o ).
thf(func_def_439,type,
bNF_re8934335040747510510er_rat: ( int > int > $o ) > ( code_integer > rat > $o ) > ( int > code_integer ) > ( int > rat ) > $o ).
thf(func_def_440,type,
bNF_re6290619412732081552atural: ( int > int > $o ) > ( code_natural > produc7822875418678951345atural > $o ) > ( int > code_natural ) > ( int > produc7822875418678951345atural ) > $o ).
thf(func_def_441,type,
bNF_re982302072995117890nteger: ( int > int > $o ) > ( int > code_integer > $o ) > ( int > int ) > ( int > code_integer ) > $o ).
thf(func_def_442,type,
bNF_re4712519889275205905nt_int: ( int > int > $o ) > ( int > int > $o ) > ( int > int ) > ( int > int ) > $o ).
thf(func_def_443,type,
bNF_re4079880299697760445nt_rat: ( int > int > $o ) > ( int > rat > $o ) > ( int > int ) > ( int > rat ) > $o ).
thf(func_def_444,type,
bNF_re3715656647883201625at_nat: ( int > int > $o ) > ( nat > nat > $o ) > ( int > nat ) > ( int > nat ) > $o ).
thf(func_def_445,type,
bNF_re7626690874201225453um_num: ( int > int > $o ) > ( num > num > $o ) > ( int > num ) > ( int > num ) > $o ).
thf(func_def_446,type,
bNF_re6250860962936578807nt_int: ( int > int > $o ) > ( product_prod_int_int > product_prod_int_int > $o ) > ( int > product_prod_int_int ) > ( int > product_prod_int_int ) > $o ).
thf(func_def_447,type,
bNF_re2214769303045360666nt_rat: ( int > int > $o ) > ( product_prod_int_int > rat > $o ) > ( int > product_prod_int_int ) > ( int > rat ) > $o ).
thf(func_def_448,type,
bNF_re1382721322319792878nteger: ( int > int > $o ) > ( rat > code_integer > $o ) > ( int > rat ) > ( int > code_integer ) > $o ).
thf(func_def_449,type,
bNF_re3396611533439285437at_int: ( int > int > $o ) > ( rat > int > $o ) > ( int > rat ) > ( int > int ) > $o ).
thf(func_def_450,type,
bNF_re2763971943861839977at_rat: ( int > int > $o ) > ( rat > rat > $o ) > ( int > rat ) > ( int > rat ) > $o ).
thf(func_def_451,type,
bNF_re5416042074812042131at_nat: ( int > nat > $o ) > ( ( int > int ) > ( nat > nat ) > $o ) > ( int > int > int ) > ( nat > nat > nat ) > $o ).
thf(func_def_452,type,
bNF_re4343356799547411545nt_nat: ( int > nat > $o ) > ( int > nat > $o ) > ( int > int ) > ( nat > nat ) > $o ).
thf(func_def_453,type,
bNF_re151304249936775380nteger: ( int > num > $o ) > ( nat > code_integer > $o ) > ( int > nat ) > ( num > code_integer ) > $o ).
thf(func_def_454,type,
bNF_re7315484114762210078nteger: ( int > num > $o ) > ( num > code_integer > $o ) > ( int > num ) > ( num > code_integer ) > $o ).
thf(func_def_455,type,
bNF_re7661208983170134443at_rat: ( int > rat > $o ) > ( ( int > int ) > ( rat > rat ) > $o ) > ( int > int > int ) > ( rat > rat > rat ) > $o ).
thf(func_def_456,type,
bNF_re4480299549022435433nt_rat: ( int > rat > $o ) > ( int > rat > $o ) > ( int > int ) > ( rat > rat ) > $o ).
thf(func_def_457,type,
bNF_re7367609096550055590nteger: ( nat > code_integer > $o ) > ( ( nat > nat ) > ( code_integer > code_integer ) > $o ) > ( nat > nat > nat ) > ( code_integer > code_integer > code_integer ) > $o ).
thf(func_def_458,type,
bNF_re1599192376174140603nteger: ( nat > code_integer > $o ) > ( nat > code_integer > $o ) > ( nat > nat ) > ( code_integer > code_integer ) > $o ).
thf(func_def_459,type,
bNF_re8763372240999575301nteger: ( nat > code_integer > $o ) > ( num > code_integer > $o ) > ( nat > num ) > ( code_integer > code_integer ) > $o ).
thf(func_def_460,type,
bNF_re1639080489988575423ural_o: ( nat > code_natural > $o ) > ( ( nat > $o ) > ( code_natural > $o ) > $o ) > ( nat > nat > $o ) > ( code_natural > code_natural > $o ) > $o ).
thf(func_def_461,type,
bNF_re2895713572246619415_nat_o: ( nat > code_natural > $o ) > ( ( nat > $o ) > ( nat > $o ) > $o ) > ( nat > nat > $o ) > ( code_natural > nat > $o ) > $o ).
thf(func_def_462,type,
bNF_re88643428490162567atural: ( nat > code_natural > $o ) > ( ( nat > nat ) > ( code_natural > code_natural ) > $o ) > ( nat > nat > nat ) > ( code_natural > code_natural > code_natural ) > $o ).
thf(func_def_463,type,
bNF_re2785088596696291543al_o_o: ( nat > code_natural > $o ) > ( $o > $o > $o ) > ( nat > $o ) > ( code_natural > $o ) > $o ).
thf(func_def_464,type,
bNF_re5252274238750452962nteger: ( nat > code_natural > $o ) > ( int > code_integer > $o ) > ( nat > int ) > ( code_natural > code_integer ) > $o ).
thf(func_def_465,type,
bNF_re3704215830270325841atural: ( nat > code_natural > $o ) > ( nat > code_natural > $o ) > ( nat > nat ) > ( code_natural > code_natural ) > $o ).
thf(func_def_466,type,
bNF_re7333046803109187065at_nat: ( nat > code_natural > $o ) > ( nat > nat > $o ) > ( nat > nat ) > ( code_natural > nat ) > $o ).
thf(func_def_467,type,
bNF_re5864104203909894035nt_int: ( nat > int > $o ) > ( ( nat > nat ) > ( int > int ) > $o ) > ( nat > nat > nat ) > ( int > int > int ) > $o ).
thf(func_def_468,type,
bNF_re6022984109467102297at_int: ( nat > int > $o ) > ( nat > int > $o ) > ( nat > nat ) > ( int > int ) > $o ).
thf(func_def_469,type,
bNF_re4935368626670024657nteger: ( nat > nat > $o ) > ( ( int > int ) > ( code_integer > code_integer ) > $o ) > ( nat > int > int ) > ( nat > code_integer > code_integer ) > $o ).
thf(func_def_470,type,
bNF_re4785983289428654063nt_int: ( nat > nat > $o ) > ( ( int > int ) > ( int > int ) > $o ) > ( nat > int > int ) > ( nat > int > int ) > $o ).
thf(func_def_471,type,
bNF_re578469030762574527_nat_o: ( nat > nat > $o ) > ( ( nat > $o ) > ( nat > $o ) > $o ) > ( nat > nat > $o ) > ( nat > nat > $o ) > $o ).
thf(func_def_472,type,
bNF_re3692170009638431535atural: ( nat > nat > $o ) > ( ( nat > nat ) > ( code_natural > code_natural ) > $o ) > ( nat > nat > nat ) > ( nat > code_natural > code_natural ) > $o ).
thf(func_def_473,type,
bNF_re1345281282404953727at_nat: ( nat > nat > $o ) > ( ( nat > nat ) > ( nat > nat ) > $o ) > ( nat > nat > nat ) > ( nat > nat > nat ) > $o ).
thf(func_def_474,type,
bNF_re4705727531993890431at_o_o: ( nat > nat > $o ) > ( $o > $o > $o ) > ( nat > $o ) > ( nat > $o ) > $o ).
thf(func_def_475,type,
bNF_re4051817429369991249n_assn: ( nat > nat > $o ) > ( assn > assn > $o ) > ( nat > assn ) > ( nat > assn ) > $o ).
thf(func_def_476,type,
bNF_re1831131418152741254nteger: ( nat > nat > $o ) > ( assn > code_integer > $o ) > ( nat > assn ) > ( nat > code_integer ) > $o ).
thf(func_def_477,type,
bNF_re4792267480158271317sn_int: ( nat > nat > $o ) > ( assn > int > $o ) > ( nat > assn ) > ( nat > int ) > $o ).
thf(func_def_478,type,
bNF_re4794757950667321593sn_nat: ( nat > nat > $o ) > ( assn > nat > $o ) > ( nat > assn ) > ( nat > nat ) > $o ).
thf(func_def_479,type,
bNF_re4159627890580825857sn_rat: ( nat > nat > $o ) > ( assn > rat > $o ) > ( nat > assn ) > ( nat > rat ) > $o ).
thf(func_def_480,type,
bNF_re2692373401909853574r_assn: ( nat > nat > $o ) > ( code_integer > assn > $o ) > ( nat > code_integer ) > ( nat > assn ) > $o ).
thf(func_def_481,type,
bNF_re1236659899165691067nteger: ( nat > nat > $o ) > ( code_integer > code_integer > $o ) > ( nat > code_integer ) > ( nat > code_integer ) > $o ).
thf(func_def_482,type,
bNF_re3514700588913618570er_int: ( nat > nat > $o ) > ( code_integer > int > $o ) > ( nat > code_integer ) > ( nat > int ) > $o ).
thf(func_def_483,type,
bNF_re3517191059422668846er_nat: ( nat > nat > $o ) > ( code_integer > nat > $o ) > ( nat > code_integer ) > ( nat > nat ) > $o ).
thf(func_def_484,type,
bNF_re2882060999336173110er_rat: ( nat > nat > $o ) > ( code_integer > rat > $o ) > ( nat > code_integer ) > ( nat > rat ) > $o ).
thf(func_def_485,type,
bNF_re6101645755646507080atural: ( nat > nat > $o ) > ( code_natural > produc7822875418678951345atural > $o ) > ( nat > code_natural ) > ( nat > produc7822875418678951345atural ) > $o ).
thf(func_def_486,type,
bNF_re4153400068438556298nteger: ( nat > nat > $o ) > ( int > code_integer > $o ) > ( nat > int ) > ( nat > code_integer ) > $o ).
thf(func_def_487,type,
bNF_re2976995220195273813atural: ( nat > nat > $o ) > ( int > code_natural > $o ) > ( nat > int ) > ( nat > code_natural ) > $o ).
thf(func_def_488,type,
bNF_re6650684261131312217nt_int: ( nat > nat > $o ) > ( int > int > $o ) > ( nat > int ) > ( nat > int ) > $o ).
thf(func_def_489,type,
bNF_re6653174731640362493nt_nat: ( nat > nat > $o ) > ( int > nat > $o ) > ( nat > int ) > ( nat > nat ) > $o ).
thf(func_def_490,type,
bNF_re6018044671553866757nt_rat: ( nat > nat > $o ) > ( int > rat > $o ) > ( nat > int ) > ( nat > rat ) > $o ).
thf(func_def_491,type,
bNF_re2605341659958429177atural: ( nat > nat > $o ) > ( nat > code_natural > $o ) > ( nat > nat ) > ( nat > code_natural ) > $o ).
thf(func_def_492,type,
bNF_re5653821019739307937at_nat: ( nat > nat > $o ) > ( nat > nat > $o ) > ( nat > nat ) > ( nat > nat ) > $o ).
thf(func_def_493,type,
bNF_re341483209202555957um_num: ( nat > nat > $o ) > ( num > num > $o ) > ( nat > num ) > ( nat > num ) > $o ).
thf(func_def_494,type,
bNF_re6830278522597306478at_int: ( nat > nat > $o ) > ( product_prod_nat_nat > int > $o ) > ( nat > product_prod_nat_nat ) > ( nat > int ) > $o ).
thf(func_def_495,type,
bNF_re4553819317763231286nteger: ( nat > nat > $o ) > ( rat > code_integer > $o ) > ( nat > rat ) > ( nat > code_integer ) > $o ).
thf(func_def_496,type,
bNF_re3377414469519948801atural: ( nat > nat > $o ) > ( rat > code_natural > $o ) > ( nat > rat ) > ( nat > code_natural ) > $o ).
thf(func_def_497,type,
bNF_re5334775905295391749at_int: ( nat > nat > $o ) > ( rat > int > $o ) > ( nat > rat ) > ( nat > int ) > $o ).
thf(func_def_498,type,
bNF_re5337266375804442025at_nat: ( nat > nat > $o ) > ( rat > nat > $o ) > ( nat > rat ) > ( nat > nat ) > $o ).
thf(func_def_499,type,
bNF_re4702136315717946289at_rat: ( nat > nat > $o ) > ( rat > rat > $o ) > ( nat > rat ) > ( nat > rat ) > $o ).
thf(func_def_500,type,
bNF_re3590448190763046039at_rat: ( nat > rat > $o ) > ( ( nat > nat ) > ( rat > rat ) > $o ) > ( nat > nat > nat ) > ( rat > rat > rat ) > $o ).
thf(func_def_501,type,
bNF_re5790763769214331825at_rat: ( nat > rat > $o ) > ( nat > rat > $o ) > ( nat > nat ) > ( rat > rat ) > $o ).
thf(func_def_502,type,
bNF_re5031869190687302234nteger: ( num > code_integer > $o ) > ( code_integer > ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > $o ) > ( num > code_integer ) > ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > $o ).
thf(func_def_503,type,
bNF_re5202476307641864082nteger: ( num > code_integer > $o ) > ( code_integer > code_integer > $o ) > ( num > code_integer ) > ( code_integer > code_integer ) > $o ).
thf(func_def_504,type,
bNF_re6324211044263125204er_nat: ( num > int > $o ) > ( code_integer > nat > $o ) > ( num > code_integer ) > ( int > nat ) > $o ).
thf(func_def_505,type,
bNF_re2881542830418903838er_num: ( num > int > $o ) > ( code_integer > num > $o ) > ( num > code_integer ) > ( int > num ) > $o ).
thf(func_def_506,type,
bNF_re7876454716742015248nteger: ( num > num > $o ) > ( ( num > int ) > ( num > code_integer ) > $o ) > ( num > num > int ) > ( num > num > code_integer ) > $o ).
thf(func_def_507,type,
bNF_re8402795839162346335um_int: ( num > num > $o ) > ( ( num > int ) > ( num > int ) > $o ) > ( num > num > int ) > ( num > num > int ) > $o ).
thf(func_def_508,type,
bNF_re6741283560065411407nteger: ( num > num > $o ) > ( code_integer > code_integer > $o ) > ( num > code_integer ) > ( num > code_integer ) > $o ).
thf(func_def_509,type,
bNF_re6501075790457514782nteger: ( num > num > $o ) > ( int > code_integer > $o ) > ( num > int ) > ( num > code_integer ) > $o ).
thf(func_def_510,type,
bNF_re5324670942214232297atural: ( num > num > $o ) > ( int > code_natural > $o ) > ( num > int ) > ( num > code_natural ) > $o ).
thf(func_def_511,type,
bNF_re1822329894187522285nt_int: ( num > num > $o ) > ( int > int > $o ) > ( num > int ) > ( num > int ) > $o ).
thf(func_def_512,type,
bNF_re1824820364696572561nt_nat: ( num > num > $o ) > ( int > nat > $o ) > ( num > int ) > ( num > nat ) > $o ).
thf(func_def_513,type,
bNF_re1189690304610076825nt_rat: ( num > num > $o ) > ( int > rat > $o ) > ( num > int ) > ( num > rat ) > $o ).
thf(func_def_514,type,
bNF_re6129422230220670146nteger: ( num > num > $o ) > ( nat > code_integer > $o ) > ( num > nat ) > ( num > code_integer ) > $o ).
thf(func_def_515,type,
bNF_re4953017381977387661atural: ( num > num > $o ) > ( nat > code_natural > $o ) > ( num > nat ) > ( num > code_natural ) > $o ).
thf(func_def_516,type,
bNF_re822976182286467729at_int: ( num > num > $o ) > ( nat > int > $o ) > ( num > nat ) > ( num > int ) > $o ).
thf(func_def_517,type,
bNF_re825466652795518005at_nat: ( num > num > $o ) > ( nat > nat > $o ) > ( num > nat ) > ( num > nat ) > $o ).
thf(func_def_518,type,
bNF_re190336592709022269at_rat: ( num > num > $o ) > ( nat > rat > $o ) > ( num > nat ) > ( num > rat ) > $o ).
thf(func_def_519,type,
bNF_re5228765855967844073nt_int: ( product_prod_int_int > product_prod_int_int > $o ) > ( ( product_prod_int_int > product_prod_int_int ) > ( product_prod_int_int > product_prod_int_int ) > $o ) > ( product_prod_int_int > product_prod_int_int > product_prod_int_int ) > ( product_prod_int_int > product_prod_int_int > product_prod_int_int ) > $o ).
thf(func_def_520,type,
bNF_re7145576690424134365nt_int: ( product_prod_int_int > product_prod_int_int > $o ) > ( product_prod_int_int > product_prod_int_int > $o ) > ( product_prod_int_int > product_prod_int_int ) > ( product_prod_int_int > product_prod_int_int ) > $o ).
thf(func_def_521,type,
bNF_re7627151682743391978at_rat: ( product_prod_int_int > rat > $o ) > ( ( product_prod_int_int > product_prod_int_int ) > ( rat > rat ) > $o ) > ( product_prod_int_int > product_prod_int_int > product_prod_int_int ) > ( rat > rat > rat ) > $o ).
thf(func_def_522,type,
bNF_re8279943556446156061nt_rat: ( product_prod_int_int > rat > $o ) > ( product_prod_int_int > rat > $o ) > ( product_prod_int_int > product_prod_int_int ) > ( rat > rat ) > $o ).
thf(func_def_523,type,
bNF_re717283939379294677_int_o: ( product_prod_nat_nat > int > $o ) > ( ( product_prod_nat_nat > $o ) > ( int > $o ) > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( int > int > $o ) > $o ).
thf(func_def_524,type,
bNF_re7408651293131936558nt_int: ( product_prod_nat_nat > int > $o ) > ( ( product_prod_nat_nat > product_prod_nat_nat ) > ( int > int ) > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > ( int > int > int ) > $o ).
thf(func_def_525,type,
bNF_re6644619430987730960nt_o_o: ( product_prod_nat_nat > int > $o ) > ( $o > $o > $o ) > ( product_prod_nat_nat > $o ) > ( int > $o ) > $o ).
thf(func_def_526,type,
bNF_re7400052026677387805at_int: ( product_prod_nat_nat > int > $o ) > ( product_prod_nat_nat > int > $o ) > ( product_prod_nat_nat > product_prod_nat_nat ) > ( int > int ) > $o ).
thf(func_def_527,type,
bNF_re4202695980764964119_nat_o: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( ( product_prod_nat_nat > $o ) > ( product_prod_nat_nat > $o ) > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > $o ).
thf(func_def_528,type,
bNF_re3099431351363272937at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( ( product_prod_nat_nat > product_prod_nat_nat ) > ( product_prod_nat_nat > product_prod_nat_nat ) > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > $o ).
thf(func_def_529,type,
bNF_re3666534408544137501at_o_o: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( $o > $o > $o ) > ( product_prod_nat_nat > $o ) > ( product_prod_nat_nat > $o ) > $o ).
thf(func_def_530,type,
bNF_re2241393799969408733at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > product_prod_nat_nat ) > ( product_prod_nat_nat > product_prod_nat_nat ) > $o ).
thf(func_def_531,type,
bNF_re8417623677625516633nteger: ( product_unit > product_unit > $o ) > ( code_integer > code_integer > $o ) > ( product_unit > code_integer ) > ( product_unit > code_integer ) > $o ).
thf(func_def_532,type,
bNF_re5641277236161133866atural: ( product_unit > product_unit > $o ) > ( code_natural > produc7822875418678951345atural > $o ) > ( product_unit > code_natural ) > ( product_unit > produc7822875418678951345atural ) > $o ).
thf(func_def_533,type,
bNF_re8422471777688076791nt_int: ( product_unit > product_unit > $o ) > ( int > int > $o ) > ( product_unit > int ) > ( product_unit > int ) > $o ).
thf(func_def_534,type,
bNF_re4307939118855507134nteger: ( rat > code_integer > $o ) > ( ( rat > rat ) > ( code_integer > code_integer ) > $o ) > ( rat > rat > rat ) > ( code_integer > code_integer > code_integer ) > $o ).
thf(func_def_535,type,
bNF_re2328245411608324299nteger: ( rat > code_integer > $o ) > ( rat > code_integer > $o ) > ( rat > rat ) > ( code_integer > code_integer ) > $o ).
thf(func_def_536,type,
bNF_re6252345487650389919atural: ( rat > code_natural > $o ) > ( ( rat > rat ) > ( code_natural > code_natural ) > $o ) > ( rat > rat > rat ) > ( code_natural > code_natural > code_natural ) > $o ).
thf(func_def_537,type,
bNF_re4433268865704509537atural: ( rat > code_natural > $o ) > ( rat > code_natural > $o ) > ( rat > rat ) > ( code_natural > code_natural ) > $o ).
thf(func_def_538,type,
bNF_re8876735282041863595nt_int: ( rat > int > $o ) > ( ( rat > rat ) > ( int > int ) > $o ) > ( rat > rat > rat ) > ( int > int > int ) > $o ).
thf(func_def_539,type,
bNF_re5838490730811218025at_int: ( rat > int > $o ) > ( rat > int > $o ) > ( rat > rat ) > ( int > int ) > $o ).
thf(func_def_540,type,
bNF_re4357912360536923287at_nat: ( rat > nat > $o ) > ( ( rat > rat ) > ( nat > nat ) > $o ) > ( rat > rat > rat ) > ( nat > nat > nat ) > $o ).
thf(func_def_541,type,
bNF_re5469327641083423665at_nat: ( rat > nat > $o ) > ( rat > nat > $o ) > ( rat > rat ) > ( nat > nat ) > $o ).
thf(func_def_542,type,
bNF_re6603079268895015599at_rat: ( rat > rat > $o ) > ( ( rat > rat ) > ( rat > rat ) > $o ) > ( rat > rat > rat ) > ( rat > rat > rat ) > $o ).
thf(func_def_543,type,
bNF_re5606270390558447553at_rat: ( rat > rat > $o ) > ( rat > rat > $o ) > ( rat > rat ) > ( rat > rat ) > $o ).
thf(func_def_544,type,
bNF_We2654380646378065620so_o_o: set_Pr1932065953672099015od_o_o ).
thf(func_def_545,type,
bNF_We5258908940166488438at_nat: set_Pr4329608150637261639at_nat ).
thf(func_def_546,type,
bNF_We8182288985678559134_o_nat: set_Pr457366540195662369at_nat ).
thf(func_def_547,type,
basic_7565498685090299632nteger: ( code_integer > nat ) > ( code_integer > nat ) > produc8923325533196201883nteger > nat ).
thf(func_def_548,type,
basic_8185638495112405971atural: ( code_natural > nat ) > ( produc7822875418678951345atural > nat ) > produc5835291356934675326atural > nat ).
thf(func_def_549,type,
basic_1872990034501187214nt_int: ( int > nat ) > ( int > nat ) > product_prod_int_int > nat ).
thf(func_def_550,type,
binomial: nat > nat > nat ).
thf(func_def_551,type,
gbinom8545251970709558553nteger: code_integer > nat > code_integer ).
thf(func_def_552,type,
gbinomial_int: int > nat > int ).
thf(func_def_553,type,
gbinomial_nat: nat > nat > nat ).
thf(func_def_554,type,
gbinomial_rat: rat > nat > rat ).
thf(func_def_555,type,
bit_and_int_rel: product_prod_int_int > product_prod_int_int > $o ).
thf(func_def_556,type,
bit_and_not_num: num > num > option_num ).
thf(func_def_557,type,
bit_and_not_num_rel: product_prod_num_num > product_prod_num_num > $o ).
thf(func_def_558,type,
bit_concat_bit: nat > int > int > int ).
thf(func_def_559,type,
bit_or_not_num_neg: num > num > num ).
thf(func_def_560,type,
bit_or3848514188828904588eg_rel: product_prod_num_num > product_prod_num_num > $o ).
thf(func_def_561,type,
bit_ri7632146776885996613nteger: code_integer > code_integer ).
thf(func_def_562,type,
bit_ri7919022796975470100ot_int: int > int ).
thf(func_def_563,type,
bit_ri6519982836138164636nteger: nat > code_integer > code_integer ).
thf(func_def_564,type,
bit_ri631733984087533419it_int: nat > int > int ).
thf(func_def_565,type,
bit_se3949692690581998587nteger: code_integer > code_integer > code_integer ).
thf(func_def_566,type,
bit_se2773287842338716102atural: code_natural > code_natural > code_natural ).
thf(func_def_567,type,
bit_se725231765392027082nd_int: int > int > int ).
thf(func_def_568,type,
bit_se727722235901077358nd_nat: nat > nat > nat ).
thf(func_def_569,type,
bit_se3928097537394005634nteger: nat > code_integer > code_integer ).
thf(func_def_570,type,
bit_se2751692689150723149atural: nat > code_natural > code_natural ).
thf(func_def_571,type,
bit_se8568078237143864401it_int: nat > int > int ).
thf(func_def_572,type,
bit_se8570568707652914677it_nat: nat > nat > nat ).
thf(func_def_573,type,
bit_se1345352211410354436nteger: nat > code_integer > code_integer ).
thf(func_def_574,type,
bit_se168947363167071951atural: nat > code_natural > code_natural ).
thf(func_def_575,type,
bit_se2159334234014336723it_int: nat > int > int ).
thf(func_def_576,type,
bit_se2161824704523386999it_nat: nat > nat > nat ).
thf(func_def_577,type,
bit_se2119862282449309892nteger: nat > code_integer ).
thf(func_def_578,type,
bit_se943457434206027407atural: nat > code_natural ).
thf(func_def_579,type,
bit_se2000444600071755411sk_int: nat > int ).
thf(func_def_580,type,
bit_se2002935070580805687sk_nat: nat > nat ).
thf(func_def_581,type,
bit_se1080825931792720795nteger: code_integer > code_integer > code_integer ).
thf(func_def_582,type,
bit_se9127793120404214118atural: code_natural > code_natural > code_natural ).
thf(func_def_583,type,
bit_se1409905431419307370or_int: int > int > int ).
thf(func_def_584,type,
bit_se1412395901928357646or_nat: nat > nat > nat ).
thf(func_def_585,type,
bit_se7788150548672797655nteger: nat > code_integer > code_integer ).
thf(func_def_586,type,
bit_se6611745700429515170atural: nat > code_natural > code_natural ).
thf(func_def_587,type,
bit_se545348938243370406it_int: nat > int > int ).
thf(func_def_588,type,
bit_se547839408752420682it_nat: nat > nat > nat ).
thf(func_def_589,type,
bit_se2793503036327961859nteger: nat > code_integer > code_integer ).
thf(func_def_590,type,
bit_se1617098188084679374atural: nat > code_natural > code_natural ).
thf(func_def_591,type,
bit_se7879613467334960850it_int: nat > int > int ).
thf(func_def_592,type,
bit_se7882103937844011126it_nat: nat > nat > nat ).
thf(func_def_593,type,
bit_se1745604003318907178nteger: nat > code_integer > code_integer ).
thf(func_def_594,type,
bit_se569199155075624693atural: nat > code_natural > code_natural ).
thf(func_def_595,type,
bit_se2923211474154528505it_int: nat > int > int ).
thf(func_def_596,type,
bit_se2925701944663578781it_nat: nat > nat > nat ).
thf(func_def_597,type,
bit_se8260200283734997820nteger: nat > code_integer > code_integer ).
thf(func_def_598,type,
bit_se7083795435491715335atural: nat > code_natural > code_natural ).
thf(func_def_599,type,
bit_se4203085406695923979it_int: nat > int > int ).
thf(func_def_600,type,
bit_se4205575877204974255it_nat: nat > nat > nat ).
thf(func_def_601,type,
bit_se3222712562003087583nteger: code_integer > code_integer > code_integer ).
thf(func_def_602,type,
bit_se2046307713759805098atural: code_natural > code_natural > code_natural ).
thf(func_def_603,type,
bit_se6526347334894502574or_int: int > int > int ).
thf(func_def_604,type,
bit_se6528837805403552850or_nat: nat > nat > nat ).
thf(func_def_605,type,
bit_se9216721137139052372nteger: code_integer > nat > $o ).
thf(func_def_606,type,
bit_se8040316288895769887atural: code_natural > nat > $o ).
thf(func_def_607,type,
bit_se1146084159140164899it_int: int > nat > $o ).
thf(func_def_608,type,
bit_se1148574629649215175it_nat: nat > nat > $o ).
thf(func_def_609,type,
bit_take_bit_num: nat > num > option_num ).
thf(func_def_610,type,
bit_un7362597486090784418nd_num: num > num > option_num ).
thf(func_def_611,type,
bit_un4731106466462545111um_rel: product_prod_num_num > product_prod_num_num > $o ).
thf(func_def_612,type,
bit_un6697907153464112080or_num: num > num > num ).
thf(func_def_613,type,
bit_un4773296044027857193um_rel: product_prod_num_num > product_prod_num_num > $o ).
thf(func_def_614,type,
bit_un2480387367778600638or_num: num > num > option_num ).
thf(func_def_615,type,
bit_un2901131394128224187um_rel: product_prod_num_num > product_prod_num_num > $o ).
thf(func_def_616,type,
boolea5643492148547655015nteger: ( code_integer > code_integer > code_integer ) > ( code_integer > code_integer > code_integer ) > ( code_integer > code_integer ) > code_integer > code_integer > $o ).
thf(func_def_617,type,
boolea5469654029284665142ra_int: ( int > int > int ) > ( int > int > int ) > ( int > int ) > int > int > $o ).
thf(func_def_618,type,
boolea2445317508997433345nteger: ( code_integer > code_integer > code_integer ) > ( code_integer > code_integer > code_integer ) > ( code_integer > code_integer ) > code_integer > code_integer > ( code_integer > code_integer > code_integer ) > $o ).
thf(func_def_619,type,
boolea8527374999097803216ff_int: ( int > int > int ) > ( int > int > int ) > ( int > int ) > int > int > ( int > int > int ) > $o ).
thf(func_def_620,type,
code_Nat: code_integer > code_natural ).
thf(func_def_621,type,
code_Neg: num > code_integer ).
thf(func_def_622,type,
code_Pos: num > code_integer ).
thf(func_def_623,type,
code_Suc: code_natural > code_natural ).
thf(func_def_624,type,
code_bit_cut_integer: code_integer > produc6271795597528267376eger_o ).
thf(func_def_625,type,
code_cr_integer: int > code_integer > $o ).
thf(func_def_626,type,
code_cr_natural: nat > code_natural > $o ).
thf(func_def_627,type,
code_divmod_abs: code_integer > code_integer > produc8923325533196201883nteger ).
thf(func_def_628,type,
code_divmod_integer: code_integer > code_integer > produc8923325533196201883nteger ).
thf(func_def_629,type,
code_dup: code_integer > code_integer ).
thf(func_def_630,type,
code_int_of_integer: code_integer > int ).
thf(func_def_631,type,
code_integer_of_int: int > code_integer ).
thf(func_def_632,type,
code_integer_of_nat: nat > code_integer ).
thf(func_def_633,type,
code_i5400310926305786745atural: code_natural > code_integer ).
thf(func_def_634,type,
code_integer_of_num: num > code_integer ).
thf(func_def_635,type,
code_nat_of_integer: code_integer > nat ).
thf(func_def_636,type,
code_nat_of_natural: code_natural > nat ).
thf(func_def_637,type,
code_natural_of_nat: nat > code_natural ).
thf(func_def_638,type,
code_n4118661773612635043nteger: code_integer > code_natural ).
thf(func_def_639,type,
code_negative: num > code_integer ).
thf(func_def_640,type,
code_num_of_integer: code_integer > num ).
thf(func_def_641,type,
code_pcr_integer: int > code_integer > $o ).
thf(func_def_642,type,
code_pcr_natural: nat > code_natural > $o ).
thf(func_def_643,type,
code_positive: num > code_integer ).
thf(func_def_644,type,
code_size_nat: code_natural > nat ).
thf(func_def_645,type,
code_sub: num > num > code_integer ).
thf(func_def_646,type,
comple7280212863790966717_int_o: set_in8474487674441654202_int_o > ( int > option6357759511663192854e_term ) > product_prod_int_int > $o ).
thf(func_def_647,type,
comple797978290332539892eger_o: set_Pr8914822823351560561eger_o > ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o ).
thf(func_def_648,type,
comple1647972170925272290_nat_o: set_Pr1457143144315775327_nat_o > ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o ).
thf(func_def_649,type,
comple4401490224799119198_nat_o: set_Pr8208987589773510107_nat_o > ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o ).
thf(func_def_650,type,
comple2375672059646964807_int_o: set_Pr5050529186185961540_int_o > ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o ).
thf(func_def_651,type,
comple1675732732025788397_nat_o: set_nat_nat_o > nat > nat > $o ).
thf(func_def_652,type,
comple8322679762649017525_nat_o: set_se9180647916752606350_nat_o > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ).
thf(func_def_653,type,
complete_Inf_Inf_int: set_int > int ).
thf(func_def_654,type,
complete_Inf_Inf_nat: set_nat > nat ).
thf(func_def_655,type,
comple5564859526659248602t_unit: set_op3165557761946182707t_unit > option_Product_unit ).
thf(func_def_656,type,
comple3446467376476514063et_nat: set_option_set_nat > option_set_nat ).
thf(func_def_657,type,
comple2584293577114468500t_unit: set_Product_unit > product_unit ).
thf(func_def_658,type,
comple3063163877087187839_set_o: set_set_o > set_o ).
thf(func_def_659,type,
comple1256288197631046732nteger: set_set_Code_integer > set_Code_integer ).
thf(func_def_660,type,
comple3628384868704368283et_int: set_set_int > set_int ).
thf(func_def_661,type,
comple184543376406953807st_nat: set_set_list_nat > set_list_nat ).
thf(func_def_662,type,
comple7806235888213564991et_nat: set_set_nat > set_nat ).
thf(func_def_663,type,
comple2057271477292249724nt_int: set_se7394616247590735609nt_int > set_Pr1872883991513573699nt_int ).
thf(func_def_664,type,
comple141797230998674821nteger: set_se124295367203800706nteger > set_Pr1281608226676607948nteger ).
thf(func_def_665,type,
comple8400030738448405097et_nat: set_se5120235452707311462et_nat > set_Pr8536935166611901872et_nat ).
thf(func_def_666,type,
comple8712884055654468845et_nat: set_se8543413830569400298et_nat > set_Pr3286484037609594932et_nat ).
thf(func_def_667,type,
comple6065809805536145394nt_int: set_se2364587433798273647nt_int > set_Pr9222295170931077689nt_int ).
thf(func_def_668,type,
comple1930127330929219688at_nat: set_se7855581050983116737at_nat > set_Pr1261947904930325089at_nat ).
thf(func_def_669,type,
comple6751905152567503566at_nat: set_se5479201105039950375at_nat > set_Pr4329608150637261639at_nat ).
thf(func_def_670,type,
comple7216939928495492468t_unit: set_set_Product_unit > set_Product_unit ).
thf(func_def_671,type,
comple8902563120744349527_int_o: set_in8474487674441654202_int_o > ( int > option6357759511663192854e_term ) > product_prod_int_int > $o ).
thf(func_def_672,type,
comple6692557002573936782eger_o: set_Pr8914822823351560561eger_o > ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o ).
thf(func_def_673,type,
comple5542144468884744060_nat_o: set_Pr1457143144315775327_nat_o > ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o ).
thf(func_def_674,type,
comple2736776311324672504_nat_o: set_Pr8208987589773510107_nat_o > ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o ).
thf(func_def_675,type,
comple7735192718774405345_int_o: set_Pr5050529186185961540_int_o > ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o ).
thf(func_def_676,type,
comple3592611370556534995_nat_o: set_nat_nat_o > nat > nat > $o ).
thf(func_def_677,type,
comple493620192902636699_nat_o: set_se9180647916752606350_nat_o > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ).
thf(func_def_678,type,
complete_Sup_Sup_o: set_o > $o ).
thf(func_def_679,type,
complete_Sup_Sup_int: set_int > int ).
thf(func_def_680,type,
complete_Sup_Sup_nat: set_nat > nat ).
thf(func_def_681,type,
comple4490649148004324043tion_o: set_option_o > option_o ).
thf(func_def_682,type,
comple7481738165189995200t_unit: set_op3165557761946182707t_unit > option_Product_unit ).
thf(func_def_683,type,
comple8455683388168444585et_nat: set_option_set_nat > option_set_nat ).
thf(func_def_684,type,
comple4687483117567863418t_unit: set_Product_unit > product_unit ).
thf(func_def_685,type,
comple90263536869209701_set_o: set_set_o > set_o ).
thf(func_def_686,type,
comple739944243200306918nteger: set_set_Code_integer > set_Code_integer ).
thf(func_def_687,type,
comple3221217463730067765et_int: set_set_int > set_int ).
thf(func_def_688,type,
comple8404747032580312297st_nat: set_set_list_nat > set_list_nat ).
thf(func_def_689,type,
comple7399068483239264473et_nat: set_set_nat > set_nat ).
thf(func_def_690,type,
comple5772984051336441366nt_int: set_se7394616247590735609nt_int > set_Pr1872883991513573699nt_int ).
thf(func_def_691,type,
comple1324685164916153887nteger: set_se124295367203800706nteger > set_Pr1281608226676607948nteger ).
thf(func_def_692,type,
comple5063570841203093763et_nat: set_se5120235452707311462et_nat > set_Pr8536935166611901872et_nat ).
thf(func_def_693,type,
comple4849024849677941639et_nat: set_se8543413830569400298et_nat > set_Pr3286484037609594932et_nat ).
thf(func_def_694,type,
comple6871990601243273356nt_int: set_se2364587433798273647nt_int > set_Pr9222295170931077689nt_int ).
thf(func_def_695,type,
comple4956303571586142718atural: set_se3372686590935047281atural > set_Pr7564037697178849041atural ).
thf(func_def_696,type,
comple5685304695842803022at_nat: set_se7855581050983116737at_nat > set_Pr1261947904930325089at_nat ).
thf(func_def_697,type,
comple4364388969068068532at_nat: set_se5479201105039950375at_nat > set_Pr4329608150637261639at_nat ).
thf(func_def_698,type,
comple3349607820504768346t_unit: set_set_Product_unit > set_Product_unit ).
thf(func_def_699,type,
nth_item_rel: nat > nat > $o ).
thf(func_def_700,type,
adjust_div: product_prod_int_int > int ).
thf(func_def_701,type,
divmod_nat: nat > nat > product_prod_nat_nat ).
thf(func_def_702,type,
eucl_rel_int: int > int > product_prod_int_int > $o ).
thf(func_def_703,type,
unique5706413561485394159nteger: produc8923325533196201883nteger > $o ).
thf(func_def_704,type,
unique6319869463603278526ux_int: product_prod_int_int > $o ).
thf(func_def_705,type,
unique6322359934112328802ux_nat: product_prod_nat_nat > $o ).
thf(func_def_706,type,
unique3479559517661332726nteger: num > num > produc8923325533196201883nteger ).
thf(func_def_707,type,
unique5052692396658037445od_int: num > num > product_prod_int_int ).
thf(func_def_708,type,
unique5055182867167087721od_nat: num > num > product_prod_nat_nat ).
thf(func_def_709,type,
unique4921790084139445826nteger: num > produc8923325533196201883nteger > produc8923325533196201883nteger ).
thf(func_def_710,type,
unique5024387138958732305ep_int: num > product_prod_int_int > product_prod_int_int ).
thf(func_def_711,type,
unique5026877609467782581ep_nat: num > product_prod_nat_nat > product_prod_nat_nat ).
thf(func_def_712,type,
euclid6377331345833325938nteger: code_integer > nat ).
thf(func_def_713,type,
euclid5200926497590043453atural: code_natural > nat ).
thf(func_def_714,type,
euclid4774559944035922753ze_int: int > nat ).
thf(func_def_715,type,
euclid4777050414544973029ze_nat: nat > nat ).
thf(func_def_716,type,
euclid6289375185220004616nteger: code_integer > code_integer ).
thf(func_def_717,type,
euclid5112970336976722131atural: code_natural > code_natural ).
thf(func_def_718,type,
euclid3395696857347342551nt_int: int > int ).
thf(func_def_719,type,
euclid3398187327856392827nt_nat: nat > nat ).
thf(func_def_720,type,
comm_s8582702949713902594nteger: code_integer > nat > code_integer ).
thf(func_def_721,type,
comm_s7406298101470620109atural: code_natural > nat > code_natural ).
thf(func_def_722,type,
comm_s4660882817536571857er_int: int > nat > int ).
thf(func_def_723,type,
comm_s4663373288045622133er_nat: nat > nat > nat ).
thf(func_def_724,type,
comm_s4028243227959126397er_rat: rat > nat > rat ).
thf(func_def_725,type,
semiri3624122377584611663nteger: nat > code_integer ).
thf(func_def_726,type,
semiri2447717529341329178atural: nat > code_natural ).
thf(func_def_727,type,
semiri1406184849735516958ct_int: nat > int ).
thf(func_def_728,type,
semiri1408675320244567234ct_nat: nat > nat ).
thf(func_def_729,type,
semiri773545260158071498ct_rat: nat > rat ).
thf(func_def_730,type,
inverse_inverse_rat: rat > rat ).
thf(func_def_731,type,
finite_card_o: set_o > nat ).
thf(func_def_732,type,
finite4902975817058060853nteger: set_Code_integer > nat ).
thf(func_def_733,type,
finite_card_int: set_int > nat ).
thf(func_def_734,type,
finite_card_list_nat: set_list_nat > nat ).
thf(func_def_735,type,
finite_card_nat: set_nat > nat ).
thf(func_def_736,type,
finite711546835091564841at_nat: set_Pr1261947904930325089at_nat > nat ).
thf(func_def_737,type,
finite3771342082235030671at_nat: set_Pr4329608150637261639at_nat > nat ).
thf(func_def_738,type,
finite410649719033368117t_unit: set_Product_unit > nat ).
thf(func_def_739,type,
finite1340570857867686763nteger: set_set_Code_integer > nat ).
thf(func_def_740,type,
finite_card_set_int: set_set_int > nat ).
thf(func_def_741,type,
finite2364142230527598318st_nat: set_set_list_nat > nat ).
thf(func_def_742,type,
finite_card_set_nat: set_set_nat > nat ).
thf(func_def_743,type,
finite4356350796350151305at_nat: set_se7855581050983116737at_nat > nat ).
thf(func_def_744,type,
finite22775419188893461t_unit: set_set_Product_unit > nat ).
thf(func_def_745,type,
finite_finite_o: set_o > $o ).
thf(func_def_746,type,
finite6017078050557962740nteger: set_Code_integer > $o ).
thf(func_def_747,type,
finite_finite_int: set_int > $o ).
thf(func_def_748,type,
finite8100373058378681591st_nat: set_list_nat > $o ).
thf(func_def_749,type,
finite_finite_nat: set_nat > $o ).
thf(func_def_750,type,
finite_finite_num: set_num > $o ).
thf(func_def_751,type,
finite6785661671136154180nteger: set_op687863988967635939nteger > $o ).
thf(func_def_752,type,
finite1345302120164226195on_int: set_option_int > $o ).
thf(func_def_753,type,
finite5523153139673422903on_nat: set_option_nat > $o ).
thf(func_def_754,type,
finite6231397076622260609on_num: set_option_num > $o ).
thf(func_def_755,type,
finite6732403688824079472at_nat: set_op4508134149509766951at_nat > $o ).
thf(func_def_756,type,
finite6292238467249657455it_nat: set_op239864471688321678it_nat > $o ).
thf(func_def_757,type,
finite1445617369574913404t_unit: set_op3165557761946182707t_unit > $o ).
thf(func_def_758,type,
finite4151335170723375381et_nat: set_Pr3286484037609594932et_nat > $o ).
thf(func_def_759,type,
finite6120865539452801872od_o_o: set_Product_prod_o_o > $o ).
thf(func_def_760,type,
finite2154694888287295812nteger: set_Pr4811707699266497531nteger > $o ).
thf(func_def_761,type,
finite818523575018126227er_int: set_Pr6496905503482889930er_int > $o ).
thf(func_def_762,type,
finite4996374594527322935er_nat: set_Pr8986988648414616686er_nat > $o ).
thf(func_def_763,type,
finite2970523954037356441et_nat: set_Pr3948176798113811640et_nat > $o ).
thf(func_def_764,type,
finite1525696360262406931nteger: set_Pr8415741480598773322nteger > $o ).
thf(func_def_765,type,
finite2998713641127702882nt_int: set_Pr958786334691620121nt_int > $o ).
thf(func_def_766,type,
finite7176564660636899590nt_nat: set_Pr3448869479623346877nt_nat > $o ).
thf(func_def_767,type,
finite1154042800025562295nteger: set_Pr2406931829603198446nteger > $o ).
thf(func_def_768,type,
finite1999359929226648326at_int: set_Pr7995236796853374141at_int > $o ).
thf(func_def_769,type,
finite6177210948735845034at_nat: set_Pr1261947904930325089at_nat > $o ).
thf(func_def_770,type,
finite4392333629123659920at_nat: set_Pr8693737435421807431at_nat > $o ).
thf(func_def_771,type,
finite6446286893012251551it_nat: set_Pr1354866905816374718it_nat > $o ).
thf(func_def_772,type,
finite4343798906461161616at_nat: set_Pr4329608150637261639at_nat > $o ).
thf(func_def_773,type,
finite4290736615968046902t_unit: set_Product_unit > $o ).
thf(func_def_774,type,
finite_finite_rat: set_rat > $o ).
thf(func_def_775,type,
finite6931041176100689706nteger: set_set_Code_integer > $o ).
thf(func_def_776,type,
finite6197958912794628473et_int: set_set_int > $o ).
thf(func_def_777,type,
finite7047420756378620717st_nat: set_set_list_nat > $o ).
thf(func_def_778,type,
finite1152437895449049373et_nat: set_set_nat > $o ).
thf(func_def_779,type,
finite9047747110432174090at_nat: set_se7855581050983116737at_nat > $o ).
thf(func_def_780,type,
finite1772178364199683094t_unit: set_set_Product_unit > $o ).
thf(func_def_781,type,
finite_fold_int_int: ( int > int > int ) > int > set_int > int ).
thf(func_def_782,type,
finite_fold_nat_int: ( nat > int > int ) > int > set_nat > int ).
thf(func_def_783,type,
finite_fold_nat_nat: ( nat > nat > nat ) > nat > set_nat > nat ).
thf(func_def_784,type,
finite3745491028973389255at_nat: ( nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ) > set_Pr1261947904930325089at_nat > set_nat > set_Pr1261947904930325089at_nat ).
thf(func_def_785,type,
finite8124994865635982712et_nat: ( produc3925858234332021118et_nat > set_Pr8536935166611901872et_nat > set_Pr8536935166611901872et_nat ) > set_Pr8536935166611901872et_nat > set_Pr3286484037609594932et_nat > set_Pr8536935166611901872et_nat ).
thf(func_def_786,type,
finite7641027033760462367nteger: ( produc8923325533196201883nteger > set_Pr1281608226676607948nteger > set_Pr1281608226676607948nteger ) > set_Pr1281608226676607948nteger > set_Pr4811707699266497531nteger > set_Pr1281608226676607948nteger ).
thf(func_def_787,type,
finite2494574492299216512et_nat: ( produc3658429121746597890et_nat > set_Pr3286484037609594932et_nat > set_Pr3286484037609594932et_nat ) > set_Pr3286484037609594932et_nat > set_Pr3948176798113811640et_nat > set_Pr3286484037609594932et_nat ).
thf(func_def_788,type,
finite5333674244414288180nt_int: ( product_prod_int_int > set_Pr1872883991513573699nt_int > set_Pr1872883991513573699nt_int ) > set_Pr1872883991513573699nt_int > set_Pr958786334691620121nt_int > set_Pr1872883991513573699nt_int ).
thf(func_def_789,type,
finite1318812335397358250nt_int: ( product_prod_int_int > set_Pr9222295170931077689nt_int > set_Pr9222295170931077689nt_int ) > set_Pr9222295170931077689nt_int > set_Pr958786334691620121nt_int > set_Pr9222295170931077689nt_int ).
thf(func_def_790,type,
finite3179781904389220718at_nat: ( set_Pr1261947904930325089at_nat > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat ) > set_Pr4329608150637261639at_nat > set_se7855581050983116737at_nat > set_Pr4329608150637261639at_nat ).
thf(func_def_791,type,
comp_C3959375555751086581er_num: ( ( code_integer > code_integer ) > code_integer > code_integer ) > ( ( ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > num ) > code_integer > code_integer ) > ( ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > num ) > code_integer > code_integer ).
thf(func_def_792,type,
comp_C2822359487432382964nteger: ( ( code_integer > code_integer ) > code_integer > code_integer ) > ( code_integer > code_integer > code_integer ) > code_integer > code_integer > code_integer ).
thf(func_def_793,type,
comp_C5301300457492916725nteger: ( ( code_integer > code_integer ) > num > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( ( code_integer > code_integer ) > code_integer > code_integer ) > ( code_integer > code_integer ) > num > produc8923325533196201883nteger > produc8923325533196201883nteger ).
thf(func_def_794,type,
comp_C9104104092898552938er_num: ( ( code_integer > code_integer ) > num > code_integer ) > ( ( code_integer > num ) > code_integer > code_integer ) > ( code_integer > num ) > num > code_integer ).
thf(func_def_795,type,
comp_C3983183376822107068nteger: ( ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( ( code_integer > code_integer ) > code_integer > code_integer ) > ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ).
thf(func_def_796,type,
comp_C8797469213163452608nteger: ( ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).
thf(func_def_797,type,
comp_C8645541002826910333er_num: ( ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( num > code_integer > code_integer ) > num > produc8923325533196201883nteger > produc8923325533196201883nteger ).
thf(func_def_798,type,
comp_C5076291335850163704nteger: ( ( code_integer > code_integer ) > code_integer ) > ( code_integer > code_integer > code_integer ) > code_integer > code_integer ).
thf(func_def_799,type,
comp_C8127656796141369388er_int: ( ( code_integer > nat ) > num > num ) > ( ( code_integer > int ) > code_integer > nat ) > ( code_integer > int ) > num > num ).
thf(func_def_800,type,
comp_i6226780894115828703_nat_o: ( ( int > $o ) > int > $o ) > ( ( product_prod_nat_nat > $o ) > int > $o ) > ( product_prod_nat_nat > $o ) > int > $o ).
thf(func_def_801,type,
comp_int_o_int_o_int: ( ( int > $o ) > int > $o ) > ( int > int > $o ) > int > int > $o ).
thf(func_def_802,type,
comp_i1993086638917920293nt_int: ( ( int > $o ) > int > int ) > ( int > int > $o ) > int > int > int ).
thf(func_def_803,type,
comp_int_o_nat_o_int: ( ( int > $o ) > nat > $o ) > ( int > int > $o ) > int > nat > $o ).
thf(func_def_804,type,
comp_i5098556425753098485_o_int: ( ( int > int ) > int > $o ) > ( int > int > int ) > int > int > $o ).
thf(func_def_805,type,
comp_i1129928922100200191nt_int: ( ( int > int ) > int > int ) > ( int > int > int ) > int > int > int ).
thf(func_def_806,type,
comp_i4411980392712547921_o_int: ( ( int > int ) > nat > $o ) > ( int > int > int ) > int > nat > $o ).
thf(func_def_807,type,
comp_i1790862786758963855nt_int: ( ( int > product_prod_int_int ) > int > product_prod_int_int ) > ( int > int > product_prod_int_int ) > int > int > product_prod_int_int ).
thf(func_def_808,type,
comp_i118865614814752126nt_int: ( ( int > product_prod_int_int ) > int > rat ) > ( ( int > product_prod_int_int ) > int > product_prod_int_int ) > ( int > product_prod_int_int ) > int > rat ).
thf(func_def_809,type,
comp_i1302866070986779890at_int: ( ( int > product_prod_int_int ) > int > rat ) > ( int > int > product_prod_int_int ) > int > int > rat ).
thf(func_def_810,type,
comp_i929186717396404458nt_int: ( ( int > rat ) > int > product_prod_int_int ) > ( int > int > rat ) > int > int > product_prod_int_int ).
thf(func_def_811,type,
comp_i5271019637457297241nt_int: ( ( int > rat ) > int > rat ) > ( ( int > product_prod_int_int ) > int > rat ) > ( int > product_prod_int_int ) > int > rat ).
thf(func_def_812,type,
comp_i8258899369942393943at_int: ( ( int > rat ) > int > rat ) > ( int > int > rat ) > int > int > rat ).
thf(func_def_813,type,
comp_nat_o_int_o_int: ( ( nat > $o ) > int > $o ) > ( int > nat > $o ) > int > int > $o ).
thf(func_def_814,type,
comp_n3090169619561918849nt_int: ( ( nat > $o ) > int > int ) > ( int > nat > $o ) > int > int > int ).
thf(func_def_815,type,
comp_n5656820349209612572_nat_o: ( ( nat > $o ) > nat > $o ) > ( ( nat > $o ) > nat > $o ) > ( nat > $o ) > nat > $o ).
thf(func_def_816,type,
comp_nat_o_nat_o_int: ( ( nat > $o ) > nat > $o ) > ( int > nat > $o ) > int > nat > $o ).
thf(func_def_817,type,
comp_n3323228797031117228um_num: ( ( nat > code_integer ) > int > code_integer ) > ( ( num > num ) > nat > code_integer ) > ( num > num ) > int > code_integer ).
thf(func_def_818,type,
comp_n4765151935410462062um_int: ( ( nat > nat ) > int > num ) > ( ( num > int ) > nat > nat ) > ( num > int ) > int > num ).
thf(func_def_819,type,
comp_P3928908779438215820nteger: ( ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).
thf(func_def_820,type,
comp_P286844350285437056_nat_o: ( ( product_prod_nat_nat > $o ) > int > $o ) > ( ( product_prod_nat_nat > $o ) > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > $o ) > int > $o ).
thf(func_def_821,type,
comp_P9039549498699531069at_nat: ( ( product_prod_nat_nat > $o ) > int > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > int > $o ).
thf(func_def_822,type,
comp_P1872448293794610368at_nat: ( ( product_prod_nat_nat > product_prod_nat_nat ) > int > int ) > ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > product_prod_nat_nat > int > int ).
thf(func_def_823,type,
comp_s518380907012905326o_assn: ( ( set_o > assn ) > set_set_o > assn ) > ( ( $o > assn ) > set_o > assn ) > ( $o > assn ) > set_set_o > assn ).
thf(func_def_824,type,
comp_s262121120021782499nteger: ( ( set_o > code_integer ) > set_set_o > code_integer ) > ( ( $o > code_integer ) > set_o > code_integer ) > ( $o > code_integer ) > set_set_o > code_integer ).
thf(func_def_825,type,
comp_s6084864194472624150_o_nat: ( ( set_o > nat ) > set_set_o > nat ) > ( ( $o > nat ) > set_o > nat ) > ( $o > nat ) > set_set_o > nat ).
thf(func_def_826,type,
comp_s1265507639253661726_o_rat: ( ( set_o > rat ) > set_set_o > rat ) > ( ( $o > rat ) > set_o > rat ) > ( $o > rat ) > set_set_o > rat ).
thf(func_def_827,type,
comp_s3531641609786562035r_assn: ( ( set_Code_integer > assn ) > set_set_Code_integer > assn ) > ( ( code_integer > assn ) > set_Code_integer > assn ) > ( code_integer > assn ) > set_set_Code_integer > assn ).
thf(func_def_828,type,
comp_s8484400498494363538nteger: ( ( set_Code_integer > code_integer ) > set_set_Code_integer > code_integer ) > ( ( code_integer > code_integer ) > set_Code_integer > code_integer ) > ( code_integer > code_integer ) > set_set_Code_integer > code_integer ).
thf(func_def_829,type,
comp_s9045439038509510147er_rat: ( ( set_Code_integer > rat ) > set_set_Code_integer > rat ) > ( ( code_integer > rat ) > set_Code_integer > rat ) > ( code_integer > rat ) > set_set_Code_integer > rat ).
thf(func_def_830,type,
comp_s4595925057662634336t_assn: ( ( set_int > assn ) > set_set_int > assn ) > ( ( int > assn ) > set_int > assn ) > ( int > assn ) > set_set_int > assn ).
thf(func_def_831,type,
comp_s7646638485285982975nteger: ( ( set_int > code_integer ) > set_set_int > code_integer ) > ( ( int > code_integer ) > set_int > code_integer ) > ( int > code_integer ) > set_set_int > code_integer ).
thf(func_def_832,type,
comp_s4088261402702255472nt_rat: ( ( set_int > rat ) > set_set_int > rat ) > ( ( int > rat ) > set_int > rat ) > ( int > rat ) > set_set_int > rat ).
thf(func_def_833,type,
comp_o_o_o: ( $o > $o ) > ( $o > $o ) > $o > $o ).
thf(func_def_834,type,
comp_o_o_nat: ( $o > $o ) > ( nat > $o ) > nat > $o ).
thf(func_def_835,type,
comp_o8022916681612831582at_nat: ( $o > $o ) > ( product_prod_nat_nat > $o ) > product_prod_nat_nat > $o ).
thf(func_def_836,type,
comp_C2931745410781319416nteger: ( code_integer > code_integer > code_integer ) > ( code_integer > code_integer ) > code_integer > code_integer > code_integer ).
thf(func_def_837,type,
comp_C3662112809048933045er_num: ( code_integer > code_integer > code_integer ) > ( num > code_integer ) > num > code_integer > code_integer ).
thf(func_def_838,type,
comp_C95226695241045696nteger: ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( ( code_integer > code_integer ) > code_integer ) > ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ).
thf(func_def_839,type,
comp_C1593894019821074884nteger: ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).
thf(func_def_840,type,
comp_C6617437204949736321er_num: ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( num > code_integer ) > num > produc8923325533196201883nteger > produc8923325533196201883nteger ).
thf(func_def_841,type,
comp_C8462447471145125178sn_nat: ( code_integer > assn ) > ( nat > code_integer ) > nat > assn ).
thf(func_def_842,type,
comp_C7449957260575251196nteger: ( code_integer > code_integer ) > ( code_integer > code_integer ) > code_integer > code_integer ).
thf(func_def_843,type,
comp_C6974050283906349679er_nat: ( code_integer > code_integer ) > ( nat > code_integer ) > nat > code_integer ).
thf(func_def_844,type,
comp_C3531382070062128313er_num: ( code_integer > code_integer ) > ( num > code_integer ) > num > code_integer ).
thf(func_def_845,type,
comp_C1043215000170864188nteger: ( code_integer > code_integer ) > ( produc8923325533196201883nteger > code_integer ) > produc8923325533196201883nteger > code_integer ).
thf(func_def_846,type,
comp_C5046419837055054490nt_int: ( code_integer > int ) > ( int > code_integer ) > int > int ).
thf(func_def_847,type,
comp_C5048910307564104766nt_nat: ( code_integer > int ) > ( nat > code_integer ) > nat > int ).
thf(func_def_848,type,
comp_C4049556595663050210at_nat: ( code_integer > nat ) > ( nat > code_integer ) > nat > nat ).
thf(func_def_849,type,
comp_C2277306503614464128nteger: ( code_integer > produc8923325533196201883nteger ) > ( produc8923325533196201883nteger > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ).
thf(func_def_850,type,
comp_C8086623346886033437it_nat: ( code_integer > product_unit ) > ( nat > code_integer ) > nat > product_unit ).
thf(func_def_851,type,
comp_C3733001951728184298at_nat: ( code_integer > rat ) > ( nat > code_integer ) > nat > rat ).
thf(func_def_852,type,
comp_int_int_o_int: ( int > int > $o ) > ( int > int ) > int > int > $o ).
thf(func_def_853,type,
comp_int_int_int_int: ( int > int > int ) > ( int > int ) > int > int > int ).
thf(func_def_854,type,
comp_int_int_int_nat: ( int > int > int ) > ( nat > int ) > nat > int > int ).
thf(func_def_855,type,
comp_i87437609017934369nt_int: ( int > int > product_prod_int_int ) > ( int > int ) > int > int > product_prod_int_int ).
thf(func_def_856,type,
comp_int_int_rat_int: ( int > int > rat ) > ( int > int ) > int > int > rat ).
thf(func_def_857,type,
comp_int_nat_o_int: ( int > nat > $o ) > ( int > int ) > int > nat > $o ).
thf(func_def_858,type,
comp_int_assn_int: ( int > assn ) > ( int > int ) > int > assn ).
thf(func_def_859,type,
comp_int_assn_nat: ( int > assn ) > ( nat > int ) > nat > assn ).
thf(func_def_860,type,
comp_i1585864551200866970er_int: ( int > code_integer ) > ( int > int ) > int > code_integer ).
thf(func_def_861,type,
comp_i1588355021709917246er_nat: ( int > code_integer ) > ( nat > int ) > nat > code_integer ).
thf(func_def_862,type,
comp_int_int_int: ( int > int ) > ( int > int ) > int > int ).
thf(func_def_863,type,
comp_int_int_nat: ( int > int ) > ( nat > int ) > nat > int ).
thf(func_def_864,type,
comp_i4330622015127193916nt_int: ( int > int ) > ( product_prod_int_int > int ) > product_prod_int_int > int ).
thf(func_def_865,type,
comp_int_nat_int: ( int > nat ) > ( int > int ) > int > nat ).
thf(func_def_866,type,
comp_int_nat_nat: ( int > nat ) > ( nat > int ) > nat > nat ).
thf(func_def_867,type,
comp_int_num_int: ( int > num ) > ( int > int ) > int > num ).
thf(func_def_868,type,
comp_i5941103828406351439nt_int: ( int > product_prod_int_int ) > ( product_prod_int_int > int ) > product_prod_int_int > product_prod_int_int ).
thf(func_def_869,type,
comp_i1108739374719436894at_int: ( int > product_prod_nat_nat ) > ( int > int ) > int > product_prod_nat_nat ).
thf(func_def_870,type,
comp_int_rat_int: ( int > rat ) > ( int > int ) > int > rat ).
thf(func_def_871,type,
comp_int_rat_nat: ( int > rat ) > ( nat > int ) > nat > rat ).
thf(func_def_872,type,
comp_nat_nat_nat_nat: ( nat > nat > nat ) > ( nat > nat ) > nat > nat > nat ).
thf(func_def_873,type,
comp_nat_o_nat: ( nat > $o ) > ( nat > nat ) > nat > $o ).
thf(func_def_874,type,
comp_nat_assn_nat: ( nat > assn ) > ( nat > nat ) > nat > assn ).
thf(func_def_875,type,
comp_n3898172953802868194er_nat: ( nat > code_integer ) > ( nat > nat ) > nat > code_integer ).
thf(func_def_876,type,
comp_nat_int_int: ( nat > int ) > ( int > nat ) > int > int ).
thf(func_def_877,type,
comp_nat_int_nat: ( nat > int ) > ( nat > nat ) > nat > int ).
thf(func_def_878,type,
comp_n8698576032424989604at_nat: ( nat > multis2468970476368604999at_nat ) > ( nat > nat ) > nat > multis2468970476368604999at_nat ).
thf(func_def_879,type,
comp_nat_nat_int: ( nat > nat ) > ( int > nat ) > int > nat ).
thf(func_def_880,type,
comp_nat_nat_nat: ( nat > nat ) > ( nat > nat ) > nat > nat ).
thf(func_def_881,type,
comp_nat_num_int: ( nat > num ) > ( int > nat ) > int > num ).
thf(func_def_882,type,
comp_nat_num_nat: ( nat > num ) > ( nat > nat ) > nat > num ).
thf(func_def_883,type,
comp_n9025697279074352746it_nat: ( nat > product_unit ) > ( nat > nat ) > nat > product_unit ).
thf(func_def_884,type,
comp_nat_rat_nat: ( nat > rat ) > ( nat > nat ) > nat > rat ).
thf(func_def_885,type,
comp_n6909714581898973814er_num: ( num > code_integer ) > ( num > num ) > num > code_integer ).
thf(func_def_886,type,
comp_num_int_num: ( num > int ) > ( num > num ) > num > int ).
thf(func_def_887,type,
comp_num_nat_num: ( num > nat ) > ( num > num ) > num > nat ).
thf(func_def_888,type,
comp_num_num_int: ( num > num ) > ( int > num ) > int > num ).
thf(func_def_889,type,
comp_num_num_nat: ( num > num ) > ( nat > num ) > nat > num ).
thf(func_def_890,type,
comp_num_num_num: ( num > num ) > ( num > num ) > num > num ).
thf(func_def_891,type,
comp_n6731957995704128387um_num: ( num > option_num ) > ( num > num ) > num > option_num ).
thf(func_def_892,type,
comp_o7188567781464924208nteger: ( option8057788054806935849nteger > option7428179582072448501nteger ) > ( option_Code_integer > option8057788054806935849nteger ) > option_Code_integer > option7428179582072448501nteger ).
thf(func_def_893,type,
comp_o8860755393669798242_nat_o: ( option_nat_o > nat > $o ) > ( ( nat > $o ) > option_nat_o ) > ( nat > $o ) > nat > $o ).
thf(func_def_894,type,
comp_option_o_o_o: ( option_o > $o ) > ( $o > option_o ) > $o > $o ).
thf(func_def_895,type,
comp_o9011007105448239796nteger: ( option_Code_integer > option7428179582072448501nteger ) > ( option_Code_integer > option_Code_integer ) > option_Code_integer > option7428179582072448501nteger ).
thf(func_def_896,type,
comp_o5321900959263616553on_num: ( option_Code_integer > option_Code_integer ) > ( option_num > option_Code_integer ) > option_num > option_Code_integer ).
thf(func_def_897,type,
comp_o2446264010603541305nt_int: ( option_int > int ) > ( int > option_int ) > int > int ).
thf(func_def_898,type,
comp_o4663963155070737957at_nat: ( option_nat > nat ) > ( nat > option_nat ) > nat > nat ).
thf(func_def_899,type,
comp_o3128663659858294251on_int: ( option_nat > option_num ) > ( option_int > option_nat ) > option_int > option_num ).
thf(func_def_900,type,
comp_o6878144249584144265on_num: ( option_num > nat ) > ( option_num > option_num ) > option_num > nat ).
thf(func_def_901,type,
comp_o6342398210560591875um_num: ( option_num > num ) > ( num > option_num ) > num > num ).
thf(func_def_902,type,
comp_o8931257242830428707on_num: ( option_num > option_num ) > ( option_num > option_num ) > option_num > option_num ).
thf(func_def_903,type,
comp_o279924169626513613it_nat: ( option8956607266484857688it_nat > produc8664842809031399944it_nat ) > ( produc8664842809031399944it_nat > option8956607266484857688it_nat ) > produc8664842809031399944it_nat > produc8664842809031399944it_nat ).
thf(func_def_904,type,
comp_P1875353012086385820e_term: ( produc7773217078559923341nt_int > int > option6357759511663192854e_term ) > ( produc3832618445565238089e_term > produc7773217078559923341nt_int ) > produc3832618445565238089e_term > int > option6357759511663192854e_term ).
thf(func_def_905,type,
comp_P5363713469694551954e_term: ( produc7773217078559923341nt_int > product_prod_int_int ) > ( produc3832618445565238089e_term > produc7773217078559923341nt_int ) > produc3832618445565238089e_term > product_prod_int_int ).
thf(func_def_906,type,
comp_P8312345242777556868_nat_o: ( produc7360885484439884007_nat_o > nat > $o ) > ( ( nat > $o ) > produc7360885484439884007_nat_o ) > ( nat > $o ) > nat > $o ).
thf(func_def_907,type,
comp_P1075760313067033319_o_int: ( produc7360885484439884007_nat_o > nat > $o ) > ( int > produc7360885484439884007_nat_o ) > int > nat > $o ).
thf(func_def_908,type,
comp_P8650103696410638905e_term: ( produc1908205239877642774nteger > produc6241069584506657477e_term > option6357759511663192854e_term ) > ( produc998928222018024388e_term > produc1908205239877642774nteger ) > produc998928222018024388e_term > produc6241069584506657477e_term > option6357759511663192854e_term ).
thf(func_def_909,type,
comp_P1663382703091044646e_term: ( produc1908205239877642774nteger > produc8923325533196201883nteger ) > ( produc998928222018024388e_term > produc1908205239877642774nteger ) > produc998928222018024388e_term > produc8923325533196201883nteger ).
thf(func_def_910,type,
comp_P4355506512671352436_nat_o: ( produc2732055786443039994et_nat > produc3658429121746597890et_nat > $o ) > ( produc4962441903510821572_nat_o > produc2732055786443039994et_nat ) > produc4962441903510821572_nat_o > produc3658429121746597890et_nat > $o ).
thf(func_def_911,type,
comp_P9183373265949749025_nat_o: ( produc2732055786443039994et_nat > produc3925858234332021118et_nat ) > ( produc4962441903510821572_nat_o > produc2732055786443039994et_nat ) > produc4962441903510821572_nat_o > produc3925858234332021118et_nat ).
thf(func_def_912,type,
comp_P1110778729668777324_nat_o: ( produc3925858234332021118et_nat > produc3658429121746597890et_nat > $o ) > ( produc6907119039986491712_nat_o > produc3925858234332021118et_nat ) > produc6907119039986491712_nat_o > produc3658429121746597890et_nat > $o ).
thf(func_def_913,type,
comp_P5089495125153697957_nat_o: ( produc3925858234332021118et_nat > produc3658429121746597890et_nat ) > ( produc6907119039986491712_nat_o > produc3925858234332021118et_nat ) > produc6907119039986491712_nat_o > produc3658429121746597890et_nat ).
thf(func_def_914,type,
comp_P8577347034251779110e_term: ( produc2285326912895808259nt_int > produc8551481072490612790e_term > option6357759511663192854e_term ) > ( produc1821397396195235155e_term > produc2285326912895808259nt_int ) > produc1821397396195235155e_term > produc8551481072490612790e_term > option6357759511663192854e_term ).
thf(func_def_915,type,
comp_P4057098934159210662e_term: ( produc2285326912895808259nt_int > product_prod_int_int ) > ( produc1821397396195235155e_term > produc2285326912895808259nt_int ) > produc1821397396195235155e_term > product_prod_int_int ).
thf(func_def_916,type,
comp_P2137996956111167876_o_o_o: ( product_prod_o_o > $o ) > ( $o > product_prod_o_o ) > $o > $o ).
thf(func_def_917,type,
comp_P7111796090210262324nteger: ( produc8923325533196201883nteger > code_integer ) > ( code_integer > produc8923325533196201883nteger ) > code_integer > code_integer ).
thf(func_def_918,type,
comp_P3107242062624629507er_int: ( produc8923325533196201883nteger > code_integer ) > ( int > produc8923325533196201883nteger ) > int > code_integer ).
thf(func_def_919,type,
comp_P3109732533133679783er_nat: ( produc8923325533196201883nteger > code_integer ) > ( nat > produc8923325533196201883nteger ) > nat > code_integer ).
thf(func_def_920,type,
comp_P3428181540658402820nteger: ( produc8923325533196201883nteger > code_integer ) > ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > produc8923325533196201883nteger > code_integer ).
thf(func_def_921,type,
comp_P659088277599099894t_unit: ( produc8923325533196201883nteger > code_integer ) > ( product_unit > produc8923325533196201883nteger ) > product_unit > code_integer ).
thf(func_def_922,type,
comp_P2475326853202991862er_nat: ( produc2256096406371053034er_int > code_integer ) > ( nat > produc2256096406371053034er_int ) > nat > code_integer ).
thf(func_def_923,type,
comp_P8345930540558018757nt_nat: ( produc2256096406371053034er_int > int ) > ( nat > produc2256096406371053034er_int ) > nat > int ).
thf(func_def_924,type,
comp_P5700178199414968986er_nat: ( produc6433947425880249742er_nat > code_integer ) > ( nat > produc6433947425880249742er_nat ) > nat > code_integer ).
thf(func_def_925,type,
comp_P1337767177661389325at_nat: ( produc6433947425880249742er_nat > nat ) > ( nat > produc6433947425880249742er_nat ) > nat > nat ).
thf(func_def_926,type,
comp_P3067963646784605345atural: ( produc7822875418678951345atural > produc7822875418678951345atural ) > ( produc5835291356934675326atural > produc7822875418678951345atural ) > produc5835291356934675326atural > produc7822875418678951345atural ).
thf(func_def_927,type,
comp_P4943825737035310295atural: ( produc7822875418678951345atural > produc6756470014200349799atural ) > ( produc5835291356934675326atural > produc7822875418678951345atural ) > produc5835291356934675326atural > produc6756470014200349799atural ).
thf(func_def_928,type,
comp_P5589825499870570807al_int: ( produc5835291356934675326atural > code_natural ) > ( int > produc5835291356934675326atural ) > int > code_natural ).
thf(func_def_929,type,
comp_P5592315970379621083al_nat: ( produc5835291356934675326atural > code_natural ) > ( nat > produc5835291356934675326atural ) > nat > code_natural ).
thf(func_def_930,type,
comp_P210409258367696578t_unit: ( produc5835291356934675326atural > code_natural ) > ( product_unit > produc5835291356934675326atural ) > product_unit > code_natural ).
thf(func_def_931,type,
comp_P8475394669922486716al_int: ( produc5835291356934675326atural > produc7822875418678951345atural ) > ( int > produc5835291356934675326atural ) > int > produc7822875418678951345atural ).
thf(func_def_932,type,
comp_P8477885140431536992al_nat: ( produc5835291356934675326atural > produc7822875418678951345atural ) > ( nat > produc5835291356934675326atural ) > nat > produc7822875418678951345atural ).
thf(func_def_933,type,
comp_P7610810914149544718atural: ( produc5835291356934675326atural > produc7822875418678951345atural ) > ( produc5835291356934675326atural > produc5835291356934675326atural ) > produc5835291356934675326atural > produc7822875418678951345atural ).
thf(func_def_934,type,
comp_P5756991293874479000atural: ( produc5835291356934675326atural > produc7822875418678951345atural ) > ( produc3981471736659609608atural > produc5835291356934675326atural ) > produc3981471736659609608atural > produc7822875418678951345atural ).
thf(func_def_935,type,
comp_P1945487127105810045t_unit: ( produc5835291356934675326atural > produc7822875418678951345atural ) > ( product_unit > produc5835291356934675326atural ) > product_unit > produc7822875418678951345atural ).
thf(func_def_936,type,
comp_P2097125496263478628t_unit: ( produc6714399278180371524it_nat > option3216581401566546698it_nat ) > ( heap_e7401611519738050253t_unit > produc6714399278180371524it_nat ) > heap_e7401611519738050253t_unit > option3216581401566546698it_nat ).
thf(func_def_937,type,
comp_P6870028373966156406er_nat: ( produc2963269191615333738nteger > code_integer ) > ( nat > produc2963269191615333738nteger ) > nat > code_integer ).
thf(func_def_938,type,
comp_P59025373045620805nt_nat: ( produc2963269191615333738nteger > int ) > ( nat > produc2963269191615333738nteger ) > nat > int ).
thf(func_def_939,type,
comp_P6651465171681656048nt_int: ( product_prod_int_int > int ) > ( int > product_prod_int_int ) > int > int ).
thf(func_def_940,type,
comp_P6653955642190706324nt_nat: ( product_prod_int_int > int ) > ( nat > product_prod_int_int ) > nat > int ).
thf(func_def_941,type,
comp_P5356232565778667509nt_int: ( product_prod_int_int > int ) > ( product_prod_int_int > product_prod_int_int ) > product_prod_int_int > int ).
thf(func_def_942,type,
comp_P6796073005956588617t_unit: ( product_prod_int_int > int ) > ( product_unit > product_prod_int_int ) > product_unit > int ).
thf(func_def_943,type,
comp_P5335556815845735580at_int: ( product_prod_int_int > rat ) > ( int > product_prod_int_int ) > int > rat ).
thf(func_def_944,type,
comp_P5648219952011055433nt_int: ( product_prod_int_int > rat ) > ( product_prod_int_int > product_prod_int_int ) > product_prod_int_int > rat ).
thf(func_def_945,type,
comp_P645145991195131448nt_nat: ( product_prod_int_nat > int ) > ( nat > product_prod_int_nat ) > nat > int ).
thf(func_def_946,type,
comp_P8869164316148852700at_nat: ( product_prod_int_nat > nat ) > ( nat > product_prod_int_nat ) > nat > nat ).
thf(func_def_947,type,
comp_P5461341465284484122er_nat: ( produc2591615631378489102nteger > code_integer ) > ( nat > produc2591615631378489102nteger ) > nat > code_integer ).
thf(func_def_948,type,
comp_P9144323761349829517at_nat: ( produc2591615631378489102nteger > nat ) > ( nat > produc2591615631378489102nteger ) > nat > nat ).
thf(func_def_949,type,
comp_P8963773574283657272nt_nat: ( product_prod_nat_int > int ) > ( nat > product_prod_nat_int ) > nat > int ).
thf(func_def_950,type,
comp_P7964419862382602716at_nat: ( product_prod_nat_int > nat ) > ( nat > product_prod_nat_int ) > nat > nat ).
thf(func_def_951,type,
comp_P7507668834397697393_o_int: ( product_prod_nat_nat > int > $o ) > ( int > product_prod_nat_nat ) > int > int > $o ).
thf(func_def_952,type,
comp_P1029605119844863363nt_int: ( product_prod_nat_nat > int > int ) > ( int > product_prod_nat_nat ) > int > int > int ).
thf(func_def_953,type,
comp_P1289042343629989734_o_int: ( product_prod_nat_nat > $o ) > ( int > product_prod_nat_nat ) > int > $o ).
thf(func_def_954,type,
comp_P1955610211387027840at_nat: ( product_prod_nat_nat > nat ) > ( nat > product_prod_nat_nat ) > nat > nat ).
thf(func_def_955,type,
comp_P2980510830910040157t_unit: ( product_prod_nat_nat > nat ) > ( product_unit > product_prod_nat_nat ) > product_unit > nat ).
thf(func_def_956,type,
comp_P7428279379633703887at_int: ( product_prod_nat_nat > product_prod_nat_nat ) > ( int > product_prod_nat_nat ) > int > product_prod_nat_nat ).
thf(func_def_957,type,
comp_P864883071962432936um_num: ( product_prod_num_num > num ) > ( num > product_prod_num_num ) > num > num ).
thf(func_def_958,type,
comp_P3887058762840424708atural: ( produc3981471736659609608atural > produc7822875418678951345atural ) > ( produc5835291356934675326atural > produc3981471736659609608atural ) > produc5835291356934675326atural > produc7822875418678951345atural ).
thf(func_def_959,type,
comp_P230220204662055659atural: ( produc6756470014200349799atural > produc7822875418678951345atural ) > ( produc5835291356934675326atural > produc6756470014200349799atural ) > produc5835291356934675326atural > produc7822875418678951345atural ).
thf(func_def_960,type,
comp_P3118722334806803912t_unit: ( produc8664842809031399944it_nat > option8956607266484857688it_nat ) > ( heap_e7401611519738050253t_unit > produc8664842809031399944it_nat ) > heap_e7401611519738050253t_unit > option8956607266484857688it_nat ).
thf(func_def_961,type,
comp_P756492639069434009er_nat: ( product_unit > code_integer ) > ( nat > product_unit ) > nat > code_integer ).
thf(func_def_962,type,
comp_P7645380973975430442t_unit: ( product_unit > product_unit ) > ( product_unit > product_unit ) > product_unit > product_unit ).
thf(func_def_963,type,
comp_rat_nat_nat: ( rat > nat ) > ( nat > rat ) > nat > nat ).
thf(func_def_964,type,
comp_r4727614531642239972nt_int: ( rat > rat ) > ( product_prod_int_int > rat ) > product_prod_int_int > rat ).
thf(func_def_965,type,
comp_rat_rat_rat: ( rat > rat ) > ( rat > rat ) > rat > rat ).
thf(func_def_966,type,
fun_upd_o_o: ( $o > $o ) > $o > $o > $o > $o ).
thf(func_def_967,type,
fun_upd_o_int: ( $o > int ) > $o > int > $o > int ).
thf(func_def_968,type,
fun_upd_o_nat: ( $o > nat ) > $o > nat > $o > nat ).
thf(func_def_969,type,
fun_upd_o_option_num: ( $o > option_num ) > $o > option_num > $o > option_num ).
thf(func_def_970,type,
fun_up1288979561775348147it_nat: ( $o > option8956607266484857688it_nat ) > $o > option8956607266484857688it_nat > $o > option8956607266484857688it_nat ).
thf(func_def_971,type,
fun_up8056716234270145717nteger: ( code_integer > code_integer > code_integer ) > code_integer > ( code_integer > code_integer ) > code_integer > code_integer > code_integer ).
thf(func_def_972,type,
fun_up8139772397987072257nteger: ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > code_integer > ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).
thf(func_def_973,type,
fun_up8355007323143964473nteger: ( code_integer > code_integer ) > code_integer > code_integer > code_integer > code_integer ).
thf(func_def_974,type,
fun_up6566892301432185865nteger: ( code_integer > option_Code_integer ) > code_integer > option_Code_integer > code_integer > option_Code_integer ).
thf(func_def_975,type,
fun_up2923169431403285008atural: ( code_natural > option5403585828896915703atural ) > code_natural > option5403585828896915703atural > code_natural > option5403585828896915703atural ).
thf(func_def_976,type,
fun_upd_int_o: ( int > $o ) > int > $o > int > $o ).
thf(func_def_977,type,
fun_upd_int_int: ( int > int ) > int > int > int > int ).
thf(func_def_978,type,
fun_upd_int_nat: ( int > nat ) > int > nat > int > nat ).
thf(func_def_979,type,
fun_upd_int_num: ( int > num ) > int > num > int > num ).
thf(func_def_980,type,
fun_up8666045135305973159on_int: ( int > option_int ) > int > option_int > int > option_int ).
thf(func_def_981,type,
fun_up4328768054909231765on_num: ( int > option_num ) > int > option_num > int > option_num ).
thf(func_def_982,type,
fun_up6992348036167380867it_nat: ( int > option8956607266484857688it_nat ) > int > option8956607266484857688it_nat > int > option8956607266484857688it_nat ).
thf(func_def_983,type,
fun_upd_nat_o: ( nat > $o ) > nat > $o > nat > $o ).
thf(func_def_984,type,
fun_up3904115110581602988nteger: ( nat > code_integer ) > nat > code_integer > nat > code_integer ).
thf(func_def_985,type,
fun_upd_nat_int: ( nat > int ) > nat > int > nat > int ).
thf(func_def_986,type,
fun_upd_nat_nat: ( nat > nat ) > nat > nat > nat > nat ).
thf(func_def_987,type,
fun_up1493157387958331631on_nat: ( nat > option_nat ) > nat > option_nat > nat > option_nat ).
thf(func_def_988,type,
fun_up2201401324907169337on_num: ( nat > option_num ) > nat > option_num > nat > option_num ).
thf(func_def_989,type,
fun_up4116053422210368295it_nat: ( nat > option8956607266484857688it_nat ) > nat > option8956607266484857688it_nat > nat > option8956607266484857688it_nat ).
thf(func_def_990,type,
fun_upd_nat_set_nat: ( nat > set_nat ) > nat > set_nat > nat > set_nat ).
thf(func_def_991,type,
fun_up1844922938552261878nteger: ( num > code_integer ) > num > code_integer > num > code_integer ).
thf(func_def_992,type,
fun_up8025039454679724718on_num: ( product_prod_nat_nat > option_num ) > product_prod_nat_nat > option_num > product_prod_nat_nat > option_num ).
thf(func_def_993,type,
fun_up3996838528606387100it_nat: ( product_prod_nat_nat > option8956607266484857688it_nat ) > product_prod_nat_nat > option8956607266484857688it_nat > product_prod_nat_nat > option8956607266484857688it_nat ).
thf(func_def_994,type,
fun_up3286109336741039636on_num: ( produc3843707927480180839at_nat > option_num ) > produc3843707927480180839at_nat > option_num > produc3843707927480180839at_nat > option_num ).
thf(func_def_995,type,
fun_up5549328659429834498it_nat: ( produc3843707927480180839at_nat > option8956607266484857688it_nat ) > produc3843707927480180839at_nat > option8956607266484857688it_nat > produc3843707927480180839at_nat > option8956607266484857688it_nat ).
thf(func_def_996,type,
fun_up4695802795598371002on_num: ( product_unit > option_num ) > product_unit > option_num > product_unit > option_num ).
thf(func_def_997,type,
fun_up1973317344121680296it_nat: ( product_unit > option8956607266484857688it_nat ) > product_unit > option8956607266484857688it_nat > product_unit > option8956607266484857688it_nat ).
thf(func_def_998,type,
id_nat_o: ( nat > $o ) > nat > $o ).
thf(func_def_999,type,
id_num_Code_integer: ( num > code_integer ) > num > code_integer ).
thf(func_def_1000,type,
id_Pro496765588584934260nteger: ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > produc8923325533196201883nteger > produc8923325533196201883nteger ).
thf(func_def_1001,type,
id_o: $o > $o ).
thf(func_def_1002,type,
id_Code_integer: code_integer > code_integer ).
thf(func_def_1003,type,
id_int: int > int ).
thf(func_def_1004,type,
id_nat: nat > nat ).
thf(func_def_1005,type,
id_num: num > num ).
thf(func_def_1006,type,
id_option_nat_o: option_nat_o > option_nat_o ).
thf(func_def_1007,type,
id_option_o: option_o > option_o ).
thf(func_def_1008,type,
id_option_int: option_int > option_int ).
thf(func_def_1009,type,
id_option_nat: option_nat > option_nat ).
thf(func_def_1010,type,
id_option_num: option_num > option_num ).
thf(func_def_1011,type,
id_Pro3923183700162330716nt_int: produc7773217078559923341nt_int > produc7773217078559923341nt_int ).
thf(func_def_1012,type,
id_Pro1379270990444177765nteger: produc1908205239877642774nteger > produc1908205239877642774nteger ).
thf(func_def_1013,type,
id_Pro1297863087923562825et_nat: produc2732055786443039994et_nat > produc2732055786443039994et_nat ).
thf(func_def_1014,type,
id_Pro1888964116897856973et_nat: produc3925858234332021118et_nat > produc3925858234332021118et_nat ).
thf(func_def_1015,type,
id_Pro5422067691592394322nt_int: produc2285326912895808259nt_int > produc2285326912895808259nt_int ).
thf(func_def_1016,type,
id_Pro2309048762231606924nteger: produc8923325533196201883nteger > produc8923325533196201883nteger ).
thf(func_def_1017,type,
id_Pro4381231610383771306nt_int: product_prod_int_int > product_prod_int_int ).
thf(func_def_1018,type,
id_Pro1159712480615372887it_nat: produc8664842809031399944it_nat > produc8664842809031399944it_nat ).
thf(func_def_1019,type,
id_Product_unit: product_unit > product_unit ).
thf(func_def_1020,type,
id_rat: rat > rat ).
thf(func_def_1021,type,
id_set_nat_o: set_nat_o > set_nat_o ).
thf(func_def_1022,type,
id_set_o: set_o > set_o ).
thf(func_def_1023,type,
id_set_int: set_int > set_int ).
thf(func_def_1024,type,
id_set_nat: set_nat > set_nat ).
thf(func_def_1025,type,
id_set_num: set_num > set_num ).
thf(func_def_1026,type,
map_fu1335501423231535891nteger: ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( num > code_integer ) > ( ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > num ) > code_integer > code_integer ).
thf(func_def_1027,type,
map_fu6423247683660063826nteger: ( code_integer > code_integer ) > ( ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).
thf(func_def_1028,type,
map_fu2576242048321985878nteger: ( code_integer > code_integer ) > ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).
thf(func_def_1029,type,
map_fu5082455417554595470nteger: ( code_integer > code_integer ) > ( code_integer > code_integer ) > ( code_integer > code_integer ) > code_integer > code_integer ).
thf(func_def_1030,type,
map_fu5423760287386111952nt_nat: ( code_integer > code_integer ) > ( int > nat ) > ( code_integer > int ) > code_integer > nat ).
thf(func_def_1031,type,
map_fu603974984455542859nteger: ( code_integer > code_integer ) > ( num > code_integer ) > ( code_integer > num ) > code_integer > code_integer ).
thf(func_def_1032,type,
map_fu2496120808607739376eger_o: ( code_integer > int ) > ( ( int > $o ) > code_integer > $o ) > ( int > int > $o ) > code_integer > code_integer > $o ).
thf(func_def_1033,type,
map_fu8272188784021352819nteger: ( code_integer > int ) > ( ( int > int ) > code_integer > code_integer ) > ( int > int > int ) > code_integer > code_integer > code_integer ).
thf(func_def_1034,type,
map_fu186220595405829473_nat_o: ( code_integer > int ) > ( ( nat > $o ) > nat > $o ) > ( int > nat > $o ) > code_integer > nat > $o ).
thf(func_def_1035,type,
map_fu6957801986076833569nt_o_o: ( code_integer > int ) > ( $o > $o ) > ( int > $o ) > code_integer > $o ).
thf(func_def_1036,type,
map_fu2599414010547811884nteger: ( code_integer > int ) > ( int > code_integer ) > ( int > int ) > code_integer > code_integer ).
thf(func_def_1037,type,
map_fu1051355602067684763atural: ( code_integer > int ) > ( nat > code_natural ) > ( int > nat ) > code_integer > code_natural ).
thf(func_def_1038,type,
map_fu6539832666145259331at_nat: ( code_integer > int ) > ( nat > nat ) > ( int > nat ) > code_integer > nat ).
thf(func_def_1039,type,
map_fu1227494855608507351um_num: ( code_integer > int ) > ( num > num ) > ( int > num ) > code_integer > num ).
thf(func_def_1040,type,
map_fu6256889081107267320ural_o: ( code_natural > nat ) > ( ( nat > $o ) > code_natural > $o ) > ( nat > nat > $o ) > code_natural > code_natural > $o ).
thf(func_def_1041,type,
map_fu6244533035418998608_nat_o: ( code_natural > nat ) > ( ( nat > $o ) > nat > $o ) > ( nat > nat > $o ) > code_natural > nat > $o ).
thf(func_def_1042,type,
map_fu6549440983881763648atural: ( code_natural > nat ) > ( ( nat > nat ) > code_natural > code_natural ) > ( nat > nat > nat ) > code_natural > code_natural > code_natural ).
thf(func_def_1043,type,
map_fu4892316939951275536at_o_o: ( code_natural > nat ) > ( $o > $o ) > ( nat > $o ) > code_natural > $o ).
thf(func_def_1044,type,
map_fu2787874002554666395nteger: ( code_natural > nat ) > ( int > code_integer ) > ( nat > int ) > code_natural > code_integer ).
thf(func_def_1045,type,
map_fu1239815594074539274atural: ( code_natural > nat ) > ( nat > code_natural ) > ( nat > nat ) > code_natural > code_natural ).
thf(func_def_1046,type,
map_fu226235371393106610at_nat: ( code_natural > nat ) > ( nat > nat ) > ( nat > nat ) > code_natural > nat ).
thf(func_def_1047,type,
map_fu7831380289885515383nt_rat: ( int > int ) > ( ( int > product_prod_int_int ) > int > rat ) > ( int > int > product_prod_int_int ) > int > int > rat ).
thf(func_def_1048,type,
map_fun_int_int_o_o: ( int > int ) > ( $o > $o ) > ( int > $o ) > int > $o ).
thf(func_def_1049,type,
map_fu2180209013632630320nt_int: ( int > int ) > ( product_prod_int_int > product_prod_int_int ) > ( int > product_prod_int_int ) > int > product_prod_int_int ).
thf(func_def_1050,type,
map_fu3424225382358772769nt_rat: ( int > int ) > ( product_prod_int_int > rat ) > ( int > product_prod_int_int ) > int > rat ).
thf(func_def_1051,type,
map_fu6531859369801489698at_rat: ( int > int ) > ( rat > rat ) > ( int > rat ) > int > rat ).
thf(func_def_1052,type,
map_fu1717202910479192016nteger: ( int > nat ) > ( code_integer > code_integer ) > ( nat > code_integer ) > int > code_integer ).
thf(func_def_1053,type,
map_fu3669222299741785344at_num: ( int > nat ) > ( nat > num ) > ( nat > nat ) > int > num ).
thf(func_def_1054,type,
map_fu2609383839613498790nt_num: ( int > num ) > ( int > num ) > ( num > int ) > int > num ).
thf(func_def_1055,type,
map_fu229184005524548567nteger: ( int > num ) > ( num > code_integer ) > ( num > num ) > int > code_integer ).
thf(func_def_1056,type,
map_fu434086159418415080_int_o: ( int > product_prod_nat_nat ) > ( ( product_prod_nat_nat > $o ) > int > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > int > int > $o ).
thf(func_def_1057,type,
map_fu4960017516451851995nt_int: ( int > product_prod_nat_nat ) > ( ( product_prod_nat_nat > product_prod_nat_nat ) > int > int ) > ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > int > int > int ).
thf(func_def_1058,type,
map_fu4826362097070443709at_o_o: ( int > product_prod_nat_nat ) > ( $o > $o ) > ( product_prod_nat_nat > $o ) > int > $o ).
thf(func_def_1059,type,
map_fu3667384564859982768at_int: ( int > product_prod_nat_nat ) > ( product_prod_nat_nat > int ) > ( product_prod_nat_nat > product_prod_nat_nat ) > int > int ).
thf(func_def_1060,type,
map_fu8224359078269604234nteger: ( nat > nat ) > ( ( int > int ) > code_integer > code_integer ) > ( nat > int > int ) > nat > code_integer > code_integer ).
thf(func_def_1061,type,
map_fu6981160461238011112atural: ( nat > nat ) > ( ( nat > nat ) > code_natural > code_natural ) > ( nat > nat > nat ) > nat > code_natural > code_natural ).
thf(func_def_1062,type,
map_fun_nat_nat_o_o: ( nat > nat ) > ( $o > $o ) > ( nat > $o ) > nat > $o ).
thf(func_def_1063,type,
map_fu6290471996055670595nteger: ( nat > nat ) > ( int > code_integer ) > ( nat > int ) > nat > code_integer ).
thf(func_def_1064,type,
map_fu4742413587575543474atural: ( nat > nat ) > ( nat > code_natural ) > ( nat > nat ) > nat > code_natural ).
thf(func_def_1065,type,
map_fu8361869985550671104nt_nat: ( nat > num ) > ( int > nat ) > ( num > int ) > nat > nat ).
thf(func_def_1066,type,
map_fu1090464068875036027nteger: ( nat > num ) > ( num > code_integer ) > ( num > num ) > nat > code_integer ).
thf(func_def_1067,type,
map_fu1235460277957925907nteger: ( num > code_integer ) > ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer ) > num > produc8923325533196201883nteger > produc8923325533196201883nteger ).
thf(func_def_1068,type,
map_fu5269526691104299083nteger: ( num > code_integer ) > ( code_integer > code_integer ) > ( code_integer > code_integer ) > num > code_integer ).
thf(func_def_1069,type,
map_fu8479170043890205655nt_num: ( num > code_integer ) > ( int > num ) > ( code_integer > int ) > num > num ).
thf(func_def_1070,type,
map_fu7479816331989151099at_num: ( num > code_integer ) > ( nat > num ) > ( code_integer > nat ) > num > num ).
thf(func_def_1071,type,
map_fu8223014087597717000nteger: ( num > code_integer ) > ( num > code_integer ) > ( code_integer > num ) > num > code_integer ).
thf(func_def_1072,type,
map_fu6891787308814931657nteger: ( num > num ) > ( ( num > int ) > num > code_integer ) > ( num > num > int ) > num > num > code_integer ).
thf(func_def_1073,type,
map_fu8638147718074629079nteger: ( num > num ) > ( int > code_integer ) > ( num > int ) > num > code_integer ).
thf(func_def_1074,type,
map_fu1707080289169145046at_o_o: ( product_prod_nat_nat > product_prod_nat_nat ) > ( $o > $o ) > ( product_prod_nat_nat > $o ) > product_prod_nat_nat > $o ).
thf(func_def_1075,type,
map_fu4333342158222067775at_rat: ( rat > product_prod_int_int ) > ( ( product_prod_int_int > product_prod_int_int ) > rat > rat ) > ( product_prod_int_int > product_prod_int_int > product_prod_int_int ) > rat > rat > rat ).
thf(func_def_1076,type,
map_fu5673905371560938248nt_rat: ( rat > product_prod_int_int ) > ( product_prod_int_int > rat ) > ( product_prod_int_int > product_prod_int_int ) > rat > rat ).
thf(func_def_1077,type,
fun_max_strict: set_Pr4329608150637261639at_nat ).
thf(func_def_1078,type,
fun_max_weak: set_Pr4329608150637261639at_nat ).
thf(func_def_1079,type,
fun_min_strict: set_Pr4329608150637261639at_nat ).
thf(func_def_1080,type,
fun_min_weak: set_Pr4329608150637261639at_nat ).
thf(func_def_1081,type,
fun_pair_leq: set_Pr8693737435421807431at_nat ).
thf(func_def_1082,type,
fun_pair_less: set_Pr8693737435421807431at_nat ).
thf(func_def_1083,type,
fun_re7357418987779152907at_nat: produc4193628355235574503at_nat > $o ).
thf(func_def_1084,type,
fun_re2478310338295953701at_nat: produc1319942482725812455at_nat > $o ).
thf(func_def_1085,type,
gcd_Gcd_nat: set_nat > nat ).
thf(func_def_1086,type,
gcd_Lcm_nat: set_nat > nat ).
thf(func_def_1087,type,
bezw: nat > nat > product_prod_int_int ).
thf(func_def_1088,type,
bezw_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).
thf(func_def_1089,type,
gcd_gcd_int: int > int > int ).
thf(func_def_1090,type,
gcd_gcd_nat: nat > nat > nat ).
thf(func_def_1091,type,
gcd_lcm_nat: nat > nat > nat ).
thf(func_def_1092,type,
gcd_nat_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).
thf(func_def_1093,type,
abs_abs_Code_integer: code_integer > code_integer ).
thf(func_def_1094,type,
abs_abs_int: int > int ).
thf(func_def_1095,type,
abs_abs_rat: rat > rat ).
thf(func_def_1096,type,
group_Code_integer: ( code_integer > code_integer > code_integer ) > code_integer > ( code_integer > code_integer ) > $o ).
thf(func_def_1097,type,
group_int: ( int > int > int ) > int > ( int > int ) > $o ).
thf(func_def_1098,type,
group_rat: ( rat > rat > rat ) > rat > ( rat > rat ) > $o ).
thf(func_def_1099,type,
minus_8373710615458151222nteger: code_integer > code_integer > code_integer ).
thf(func_def_1100,type,
minus_7197305767214868737atural: code_natural > code_natural > code_natural ).
thf(func_def_1101,type,
minus_minus_int: int > int > int ).
thf(func_def_1102,type,
minus_4286766774447292334at_nat: multis2468970476368604999at_nat > multis2468970476368604999at_nat > multis2468970476368604999at_nat ).
thf(func_def_1103,type,
minus_minus_nat: nat > nat > nat ).
thf(func_def_1104,type,
minus_minus_rat: rat > rat > rat ).
thf(func_def_1105,type,
minus_minus_set_o: set_o > set_o > set_o ).
thf(func_def_1106,type,
minus_2355218937544613996nteger: set_Code_integer > set_Code_integer > set_Code_integer ).
thf(func_def_1107,type,
minus_minus_set_int: set_int > set_int > set_int ).
thf(func_def_1108,type,
minus_7954133019191499631st_nat: set_list_nat > set_list_nat > set_list_nat ).
thf(func_def_1109,type,
minus_minus_set_nat: set_nat > set_nat > set_nat ).
thf(func_def_1110,type,
minus_minus_set_num: set_num > set_num > set_num ).
thf(func_def_1111,type,
minus_1356011639430497352at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
thf(func_def_1112,type,
minus_3314409938677909166at_nat: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat ).
thf(func_def_1113,type,
minus_6452836326544984404t_unit: set_Product_unit > set_Product_unit > set_Product_unit ).
thf(func_def_1114,type,
minus_minus_set_rat: set_rat > set_rat > set_rat ).
thf(func_def_1115,type,
one_one_assn: assn ).
thf(func_def_1116,type,
one_one_Code_integer: code_integer ).
thf(func_def_1117,type,
one_one_Code_natural: code_natural ).
thf(func_def_1118,type,
one_one_int: int ).
thf(func_def_1119,type,
one_one_nat: nat ).
thf(func_def_1120,type,
one_one_rat: rat ).
thf(func_def_1121,type,
plus_p5714425477246183910nteger: code_integer > code_integer > code_integer ).
thf(func_def_1122,type,
plus_p4538020629002901425atural: code_natural > code_natural > code_natural ).
thf(func_def_1123,type,
plus_plus_int: int > int > int ).
thf(func_def_1124,type,
plus_p7104986032573967614at_nat: multis2468970476368604999at_nat > multis2468970476368604999at_nat > multis2468970476368604999at_nat ).
thf(func_def_1125,type,
plus_plus_nat: nat > nat > nat ).
thf(func_def_1126,type,
plus_plus_num: num > num > num ).
thf(func_def_1127,type,
plus_plus_rat: rat > rat > rat ).
thf(func_def_1128,type,
sgn_sgn_Code_integer: code_integer > code_integer ).
thf(func_def_1129,type,
sgn_sgn_int: int > int ).
thf(func_def_1130,type,
sgn_sgn_rat: rat > rat ).
thf(func_def_1131,type,
times_times_assn: assn > assn > assn ).
thf(func_def_1132,type,
times_3573771949741848930nteger: code_integer > code_integer > code_integer ).
thf(func_def_1133,type,
times_2397367101498566445atural: code_natural > code_natural > code_natural ).
thf(func_def_1134,type,
times_times_int: int > int > int ).
thf(func_def_1135,type,
times_times_nat: nat > nat > nat ).
thf(func_def_1136,type,
times_times_num: num > num > num ).
thf(func_def_1137,type,
times_times_rat: rat > rat > rat ).
thf(func_def_1138,type,
uminus_uminus_nat_o: ( nat > $o ) > nat > $o ).
thf(func_def_1139,type,
uminus_uminus_o: $o > $o ).
thf(func_def_1140,type,
uminus1351360451143612070nteger: code_integer > code_integer ).
thf(func_def_1141,type,
uminus_uminus_int: int > int ).
thf(func_def_1142,type,
uminus2952777764628376836t_unit: product_unit > product_unit ).
thf(func_def_1143,type,
uminus_uminus_rat: rat > rat ).
thf(func_def_1144,type,
uminus804700908173204444nteger: set_Code_integer > set_Code_integer ).
thf(func_def_1145,type,
uminus1532241313380277803et_int: set_int > set_int ).
thf(func_def_1146,type,
uminus5710092332889474511et_nat: set_nat > set_nat ).
thf(func_def_1147,type,
uminus5944136376168626660t_unit: set_Product_unit > set_Product_unit ).
thf(func_def_1148,type,
uminus2201863774496077783et_rat: set_rat > set_rat ).
thf(func_def_1149,type,
zero_z3403309356797280102nteger: code_integer ).
thf(func_def_1150,type,
zero_z2226904508553997617atural: code_natural ).
thf(func_def_1151,type,
zero_zero_int: int ).
thf(func_def_1152,type,
zero_z1048942125864253310at_nat: multis2468970476368604999at_nat ).
thf(func_def_1153,type,
zero_zero_nat: nat ).
thf(func_def_1154,type,
zero_zero_rat: rat ).
thf(func_def_1155,type,
groups4406642042086082107nteger: ( $o > code_integer ) > set_o > code_integer ).
thf(func_def_1156,type,
groups8505340233167759370_o_int: ( $o > int ) > set_o > int ).
thf(func_def_1157,type,
groups8507830703676809646_o_nat: ( $o > nat ) > set_o > nat ).
thf(func_def_1158,type,
groups7872700643590313910_o_rat: ( $o > rat ) > set_o > rat ).
thf(func_def_1159,type,
groups879477027807139574nteger: ( code_integer > code_integer ) > set_Code_integer > code_integer ).
thf(func_def_1160,type,
groups7234854612051535045er_int: ( code_integer > int ) > set_Code_integer > int ).
thf(func_def_1161,type,
groups7237345082560585321er_nat: ( code_integer > nat ) > set_Code_integer > nat ).
thf(func_def_1162,type,
groups6602215022474089585er_rat: ( code_integer > rat ) > set_Code_integer > rat ).
thf(func_def_1163,type,
groups7873554091576472773nteger: ( int > code_integer ) > set_int > code_integer ).
thf(func_def_1164,type,
groups4538972089207619220nt_int: ( int > int ) > set_int > int ).
thf(func_def_1165,type,
groups4541462559716669496nt_nat: ( int > nat ) > set_int > nat ).
thf(func_def_1166,type,
groups3906332499630173760nt_rat: ( int > rat ) > set_int > rat ).
thf(func_def_1167,type,
groups4396056296759096172at_nat: ( list_nat > nat ) > set_list_nat > nat ).
thf(func_def_1168,type,
groups7501900531339628137nteger: ( nat > code_integer ) > set_nat > code_integer ).
thf(func_def_1169,type,
groups6325495683096345652atural: ( nat > code_natural ) > set_nat > code_natural ).
thf(func_def_1170,type,
groups3539618377306564664at_int: ( nat > int ) > set_nat > int ).
thf(func_def_1171,type,
groups6857163185585827899at_nat: ( nat > multis2468970476368604999at_nat ) > set_nat > multis2468970476368604999at_nat ).
thf(func_def_1172,type,
groups3542108847815614940at_nat: ( nat > nat ) > set_nat > nat ).
thf(func_def_1173,type,
groups2906978787729119204at_rat: ( nat > rat ) > set_nat > rat ).
thf(func_def_1174,type,
groups5442708359310287027nteger: ( num > code_integer ) > set_num > code_integer ).
thf(func_def_1175,type,
groups196832835297161892nteger: ( product_prod_nat_nat > code_integer ) > set_Pr1261947904930325089at_nat > code_integer ).
thf(func_def_1176,type,
groups977919841031483927at_nat: ( product_prod_nat_nat > nat ) > set_Pr1261947904930325089at_nat > nat ).
thf(func_def_1177,type,
groups342789780944988191at_rat: ( product_prod_nat_nat > rat ) > set_Pr1261947904930325089at_nat > rat ).
thf(func_def_1178,type,
groups8766797177574957219it_nat: ( product_unit > nat ) > set_Product_unit > nat ).
thf(func_def_1179,type,
groups2416162284031854641er_int: ( set_set_Code_integer > int ) > set_se8531188866349061887nteger > int ).
thf(func_def_1180,type,
groups1080061135233207040nt_int: ( set_set_int > int ) > set_set_set_int > int ).
thf(func_def_1181,type,
groups7004213669654646580at_int: ( set_set_list_nat > int ) > set_set_set_list_nat > int ).
thf(func_def_1182,type,
groups7084729577923612836at_int: ( set_set_nat > int ) > set_set_set_nat > int ).
thf(func_def_1183,type,
groups1759609815103008563at_int: ( set_se7855581050983116737at_nat > int ) > set_se5158245632345848097at_nat > int ).
thf(func_def_1184,type,
groups9212676010950626495it_int: ( set_set_Product_unit > int ) > set_se7118615804146677933t_unit > int ).
thf(func_def_1185,type,
groups1402912129352969042nteger: ( $o > code_integer ) > set_o > code_integer ).
thf(func_def_1186,type,
groups4556407284786078405_o_nat: ( $o > nat ) > set_o > nat ).
thf(func_def_1187,type,
groups3921277224699582669_o_rat: ( $o > rat ) > set_o > rat ).
thf(func_def_1188,type,
groups910942671188738463nteger: ( code_integer > code_integer ) > set_Code_integer > code_integer ).
thf(func_def_1189,type,
groups288081504127972206er_int: ( code_integer > int ) > set_Code_integer > int ).
thf(func_def_1190,type,
groups290571974637022482er_nat: ( code_integer > nat ) > set_Code_integer > nat ).
thf(func_def_1191,type,
groups8878813951405302554er_rat: ( code_integer > rat ) > set_Code_integer > rat ).
thf(func_def_1192,type,
groups926780983652909934nteger: ( int > code_integer ) > set_int > code_integer ).
thf(func_def_1193,type,
groups2983280209131991357nt_int: ( int > int ) > set_int > int ).
thf(func_def_1194,type,
groups2985770679641041633nt_nat: ( int > nat ) > set_int > nat ).
thf(func_def_1195,type,
groups2350640619554545897nt_rat: ( int > rat ) > set_int > rat ).
thf(func_def_1196,type,
groups555127423416065298nteger: ( nat > code_integer ) > set_nat > code_integer ).
thf(func_def_1197,type,
groups1983926497230936801at_int: ( nat > int ) > set_nat > int ).
thf(func_def_1198,type,
groups1986416967739987077at_nat: ( nat > nat ) > set_nat > nat ).
thf(func_def_1199,type,
groups1351286907653491341at_rat: ( nat > rat ) > set_nat > rat ).
thf(func_def_1200,type,
groups3328076802468863542at_rat: ( product_prod_nat_nat > rat ) > set_Pr1261947904930325089at_nat > rat ).
thf(func_def_1201,type,
groups5301882518646026715o_assn: ( $o > assn ) > set_o > assn ).
thf(func_def_1202,type,
groups7694694392188491536nteger: ( $o > code_integer ) > set_o > code_integer ).
thf(func_def_1203,type,
groups3502327434004483295_o_int: ( $o > int ) > set_o > int ).
thf(func_def_1204,type,
groups3504817904513533571_o_nat: ( $o > nat ) > set_o > nat ).
thf(func_def_1205,type,
groups2869687844427037835_o_rat: ( $o > rat ) > set_o > rat ).
thf(func_def_1206,type,
groups1304777262505850412r_assn: ( code_integer > assn ) > set_Code_integer > assn ).
thf(func_def_1207,type,
groups3674199335183972705nteger: ( code_integer > code_integer ) > set_Code_integer > code_integer ).
thf(func_def_1208,type,
groups3188404863801439024er_int: ( code_integer > int ) > set_Code_integer > int ).
thf(func_def_1209,type,
groups3190895334310489300er_nat: ( code_integer > nat ) > set_Code_integer > nat ).
thf(func_def_1210,type,
groups2555765274223993564er_rat: ( code_integer > rat ) > set_Code_integer > rat ).
thf(func_def_1211,type,
groups7882442080178216443t_assn: ( int > assn ) > set_int > assn ).
thf(func_def_1212,type,
groups3827104343326376752nteger: ( int > code_integer ) > set_int > code_integer ).
thf(func_def_1213,type,
groups1705073143266064639nt_int: ( int > int ) > set_int > int ).
thf(func_def_1214,type,
groups1707563613775114915nt_nat: ( int > nat ) > set_int > nat ).
thf(func_def_1215,type,
groups1072433553688619179nt_rat: ( int > rat ) > set_int > rat ).
thf(func_def_1216,type,
groups6906906614972039071t_assn: ( nat > assn ) > set_nat > assn ).
thf(func_def_1217,type,
groups3455450783089532116nteger: ( nat > code_integer ) > set_nat > code_integer ).
thf(func_def_1218,type,
groups2279045934846249631atural: ( nat > code_natural ) > set_nat > code_natural ).
thf(func_def_1219,type,
groups705719431365010083at_int: ( nat > int ) > set_nat > int ).
thf(func_def_1220,type,
groups708209901874060359at_nat: ( nat > nat ) > set_nat > nat ).
thf(func_def_1221,type,
groups73079841787564623at_rat: ( nat > rat ) > set_nat > rat ).
thf(func_def_1222,type,
groups1396258611060191006nteger: ( num > code_integer ) > set_num > code_integer ).
thf(func_def_1223,type,
groups4075276357253098568at_int: ( product_prod_nat_nat > int ) > set_Pr1261947904930325089at_nat > int ).
thf(func_def_1224,type,
groups4077766827762148844at_nat: ( product_prod_nat_nat > nat ) > set_Pr1261947904930325089at_nat > nat ).
thf(func_def_1225,type,
groups5360233303959380816t_assn: ( product_unit > assn ) > set_Product_unit > assn ).
thf(func_def_1226,type,
groups8185359811944078981nteger: ( product_unit > code_integer ) > set_Product_unit > code_integer ).
thf(func_def_1227,type,
groups8984663225794451456it_rat: ( product_unit > rat ) > set_Product_unit > rat ).
thf(func_def_1228,type,
groups6963733262650904763o_assn: ( set_o > assn ) > set_set_o > assn ).
thf(func_def_1229,type,
groups8987389756002350576nteger: ( set_o > code_integer ) > set_set_o > code_integer ).
thf(func_def_1230,type,
groups4868773677410035043_o_nat: ( set_o > nat ) > set_set_o > nat ).
thf(func_def_1231,type,
groups4233643617323539307_o_rat: ( set_o > rat ) > set_set_o > rat ).
thf(func_def_1232,type,
groups4245288774754739042r_assn: ( set_Code_integer > assn ) > set_set_Code_integer > assn ).
thf(func_def_1233,type,
groups1474571732273379991nteger: ( set_Code_integer > code_integer ) > set_set_Code_integer > code_integer ).
thf(func_def_1234,type,
groups5409254039008640018er_rat: ( set_Code_integer > rat ) > set_set_Code_integer > rat ).
thf(func_def_1235,type,
groups5950967880310095793t_assn: ( set_int > assn ) > set_set_int > assn ).
thf(func_def_1236,type,
groups8770619586034088166nteger: ( set_int > code_integer ) > set_set_int > code_integer ).
thf(func_def_1237,type,
groups5800339274786551393nt_rat: ( set_int > rat ) > set_set_int > rat ).
thf(func_def_1238,type,
groups12625163056032370o_assn: ( $o > assn ) > set_o > assn ).
thf(func_def_1239,type,
groups2836416601086271911nteger: ( $o > code_integer ) > set_o > code_integer ).
thf(func_def_1240,type,
groups5320751605702587254_o_int: ( $o > int ) > set_o > int ).
thf(func_def_1241,type,
groups5323242076211637530_o_nat: ( $o > nat ) > set_o > nat ).
thf(func_def_1242,type,
groups4688112016125141794_o_rat: ( $o > rat ) > set_o > rat ).
thf(func_def_1243,type,
groups980104329299799381r_assn: ( code_integer > assn ) > set_Code_integer > assn ).
thf(func_def_1244,type,
groups7219916603568234122nteger: ( code_integer > code_integer ) > set_Code_integer > code_integer ).
thf(func_def_1245,type,
groups4891613008741529892t_assn: ( int > assn ) > set_int > assn ).
thf(func_def_1246,type,
groups8661743855124024409nteger: ( int > code_integer ) > set_int > code_integer ).
thf(func_def_1247,type,
groups5744458235038148136nt_int: ( int > int ) > set_int > int ).
thf(func_def_1248,type,
groups5746948705547198412nt_nat: ( int > nat ) > set_int > nat ).
thf(func_def_1249,type,
groups5111818645460702676nt_rat: ( int > rat ) > set_int > rat ).
thf(func_def_1250,type,
groups3916077543535352520t_assn: ( nat > assn ) > set_nat > assn ).
thf(func_def_1251,type,
groups8290090294887179773nteger: ( nat > code_integer ) > set_nat > code_integer ).
thf(func_def_1252,type,
groups4745104523137093580at_int: ( nat > int ) > set_nat > int ).
thf(func_def_1253,type,
groups4747594993646143856at_nat: ( nat > nat ) > set_nat > nat ).
thf(func_def_1254,type,
groups4112464933559648120at_rat: ( nat > rat ) > set_nat > rat ).
thf(func_def_1255,type,
groups4561878855575611511st_nat: list_nat > nat ).
thf(func_def_1256,type,
nO_MAT8252062027627875367nteger: code_integer > code_integer > $o ).
thf(func_def_1257,type,
nO_MAT8427913294028938742er_int: code_integer > int > $o ).
thf(func_def_1258,type,
nO_MAT8430403764537989018er_nat: code_integer > nat > $o ).
thf(func_def_1259,type,
nO_MAT7795273704451493282er_rat: code_integer > rat > $o ).
thf(func_def_1260,type,
nO_MATCH_int_int: int > int > $o ).
thf(func_def_1261,type,
nO_MATCH_int_nat: int > nat > $o ).
thf(func_def_1262,type,
nO_MATCH_int_rat: int > rat > $o ).
thf(func_def_1263,type,
nO_MATCH_nat_int: nat > int > $o ).
thf(func_def_1264,type,
nO_MATCH_nat_nat: nat > nat > $o ).
thf(func_def_1265,type,
nO_MATCH_nat_rat: nat > rat > $o ).
thf(func_def_1266,type,
nO_MATCH_rat_rat: rat > rat > $o ).
thf(func_def_1267,type,
the_int: ( int > $o ) > int ).
thf(func_def_1268,type,
defaul566961228789861419t_unit: product_unit ).
thf(func_def_1269,type,
undefined_array_a: array_a ).
thf(func_def_1270,type,
undefi8805113437130903861t_unit: heap_e7401611519738050253t_unit ).
thf(func_def_1271,type,
undefined_num: num ).
thf(func_def_1272,type,
undefi2974082611360736373t_unit: product_unit ).
thf(func_def_1273,type,
arrays_Product_unit: heap_e7401611519738050253t_unit > typerep > nat > list_nat ).
thf(func_def_1274,type,
lim_Product_unit: heap_e7401611519738050253t_unit > nat ).
thf(func_def_1275,type,
refs_Product_unit: heap_e7401611519738050253t_unit > typerep > nat > nat ).
thf(func_def_1276,type,
heap_T1488828001306802186rray_a: ( heap_e7401611519738050253t_unit > option3216581401566546698it_nat ) > heap_T6362127782908069795rray_a ).
thf(func_def_1277,type,
heap_T6183433275982383450t_unit: ( heap_e7401611519738050253t_unit > option8956607266484857688it_nat ) > heap_T5738788834812785303t_unit ).
thf(func_def_1278,type,
heap_T4142866422068808505t_unit: ( product_unit > nat ) > heap_T5738788834812785303t_unit > nat ).
thf(func_def_1279,type,
heap_T3039585018531920163rray_a: heap_T6362127782908069795rray_a > heap_T6362127782908069795rray_a > $o ).
thf(func_def_1280,type,
heap_T499439718319394433t_unit: heap_T5738788834812785303t_unit > heap_T5738788834812785303t_unit > $o ).
thf(func_def_1281,type,
heap_T7971689983404357896rray_a: ( array_a > $o ) > array_a > heap_T6362127782908069795rray_a ).
thf(func_def_1282,type,
heap_T4208721593536448476t_unit: ( product_unit > $o ) > product_unit > heap_T5738788834812785303t_unit ).
thf(func_def_1283,type,
heap_T2407400398799471159rray_a: heap_T6362127782908069795rray_a > ( array_a > heap_T6362127782908069795rray_a ) > heap_T6362127782908069795rray_a ).
thf(func_def_1284,type,
heap_T7324619625323989613t_unit: heap_T6362127782908069795rray_a > ( array_a > heap_T5738788834812785303t_unit ) > heap_T5738788834812785303t_unit ).
thf(func_def_1285,type,
heap_T7158140910958840029rray_a: heap_T5738788834812785303t_unit > ( product_unit > heap_T6362127782908069795rray_a ) > heap_T6362127782908069795rray_a ).
thf(func_def_1286,type,
heap_T2633723481742716231t_unit: heap_T5738788834812785303t_unit > ( product_unit > heap_T5738788834812785303t_unit ) > heap_T5738788834812785303t_unit ).
thf(func_def_1287,type,
heap_T5830633491639066771rray_a: heap_T6362127782908069795rray_a > heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit > array_a > nat > $o ).
thf(func_def_1288,type,
heap_T6553295506729943825t_unit: heap_T5738788834812785303t_unit > heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit > product_unit > nat > $o ).
thf(func_def_1289,type,
heap_T5591663578999710211rray_a: heap_T6362127782908069795rray_a > heap_e7401611519738050253t_unit > option3216581401566546698it_nat ).
thf(func_def_1290,type,
heap_T875086893843062177t_unit: heap_T5738788834812785303t_unit > heap_e7401611519738050253t_unit > option8956607266484857688it_nat ).
thf(func_def_1291,type,
heap_T7685628758766326643rray_a: ( heap_e7401611519738050253t_unit > $o ) > ( heap_e7401611519738050253t_unit > produc6714399278180371524it_nat ) > heap_T6362127782908069795rray_a ).
thf(func_def_1292,type,
heap_T8440541562793052209t_unit: ( heap_e7401611519738050253t_unit > $o ) > ( heap_e7401611519738050253t_unit > produc8664842809031399944it_nat ) > heap_T5738788834812785303t_unit ).
thf(func_def_1293,type,
heap_T7473999186002612558rray_a: ( heap_e7401611519738050253t_unit > produc6714399278180371524it_nat ) > heap_T6362127782908069795rray_a ).
thf(func_def_1294,type,
heap_T6927113302350381334t_unit: ( heap_e7401611519738050253t_unit > produc8664842809031399944it_nat ) > heap_T5738788834812785303t_unit ).
thf(func_def_1295,type,
heap_T1552190017797416154rray_a: list_char > heap_T6362127782908069795rray_a ).
thf(func_def_1296,type,
heap_T2927564422264180874t_unit: list_char > heap_T5738788834812785303t_unit ).
thf(func_def_1297,type,
heap_T4896204969850773234rray_a: array_a > heap_T6362127782908069795rray_a ).
thf(func_def_1298,type,
heap_T7507251653302230130t_unit: product_unit > heap_T5738788834812785303t_unit ).
thf(func_def_1299,type,
heap_T6932021131025641745rray_a: heap_T6362127782908069795rray_a > heap_e7401611519738050253t_unit > $o ).
thf(func_def_1300,type,
heap_T584514906347983379t_unit: heap_T5738788834812785303t_unit > heap_e7401611519738050253t_unit > $o ).
thf(func_def_1301,type,
heap_T2055650868554030641rray_a: ( heap_e7401611519738050253t_unit > array_a ) > heap_T6362127782908069795rray_a ).
thf(func_def_1302,type,
heap_T560649228465745139t_unit: ( heap_e7401611519738050253t_unit > product_unit ) > heap_T5738788834812785303t_unit ).
thf(func_def_1303,type,
heap_T531568236820715630rray_a: nat > option3216581401566546698it_nat > option3216581401566546698it_nat ).
thf(func_def_1304,type,
heap_T3616969660504097270t_unit: nat > option8956607266484857688it_nat > option8956607266484857688it_nat ).
thf(func_def_1305,type,
heap_T6578553156929092987rray_a: produc2867611627572283311it_nat > produc2867611627572283311it_nat > $o ).
thf(func_def_1306,type,
heap_T996182799752388649t_unit: produc3911288613690379145it_nat > produc3911288613690379145it_nat > $o ).
thf(func_def_1307,type,
heap_T4328122439115681491rray_a: array_a > heap_T6362127782908069795rray_a ).
thf(func_def_1308,type,
heap_T4284346855313245393t_unit: product_unit > heap_T5738788834812785303t_unit ).
thf(func_def_1309,type,
heap_Time_wait: nat > heap_T5738788834812785303t_unit ).
thf(func_def_1310,type,
if_assn: $o > assn > assn > assn ).
thf(func_def_1311,type,
if_Code_integer: $o > code_integer > code_integer > code_integer ).
thf(func_def_1312,type,
if_Code_natural: $o > code_natural > code_natural > code_natural ).
thf(func_def_1313,type,
if_Hea5896630067203373929rray_a: $o > heap_T6362127782908069795rray_a > heap_T6362127782908069795rray_a > heap_T6362127782908069795rray_a ).
thf(func_def_1314,type,
if_Hea8138950348631371857t_unit: $o > heap_T5738788834812785303t_unit > heap_T5738788834812785303t_unit > heap_T5738788834812785303t_unit ).
thf(func_def_1315,type,
if_int: $o > int > int > int ).
thf(func_def_1316,type,
if_list_int: $o > list_int > list_int > list_int ).
thf(func_def_1317,type,
if_mul8430962117462786573at_nat: $o > multis2468970476368604999at_nat > multis2468970476368604999at_nat > multis2468970476368604999at_nat ).
thf(func_def_1318,type,
if_nat: $o > nat > nat > nat ).
thf(func_def_1319,type,
if_num: $o > num > num > num ).
thf(func_def_1320,type,
if_option_num: $o > option_num > option_num > option_num ).
thf(func_def_1321,type,
if_opt7017092727090204112it_nat: $o > option3216581401566546698it_nat > option3216581401566546698it_nat > option3216581401566546698it_nat ).
thf(func_def_1322,type,
if_opt1729522071442692626it_nat: $o > option8956607266484857688it_nat > option8956607266484857688it_nat > option8956607266484857688it_nat ).
thf(func_def_1323,type,
if_opt6227717841141446553t_unit: $o > option_Product_unit > option_Product_unit > option_Product_unit ).
thf(func_def_1324,type,
if_option_set_o: $o > option_set_o > option_set_o > option_set_o ).
thf(func_def_1325,type,
if_option_set_int: $o > option_set_int > option_set_int > option_set_int ).
thf(func_def_1326,type,
if_option_set_nat: $o > option_set_nat > option_set_nat > option_set_nat ).
thf(func_def_1327,type,
if_opt7704869406773131885at_nat: $o > option8963830502488799655at_nat > option8963830502488799655at_nat > option8963830502488799655at_nat ).
thf(func_def_1328,type,
if_opt5121585740920863443at_nat: $o > option1583680563626158861at_nat > option1583680563626158861at_nat > option1583680563626158861at_nat ).
thf(func_def_1329,type,
if_Pro5737122678794959658eger_o: $o > produc6271795597528267376eger_o > produc6271795597528267376eger_o > produc6271795597528267376eger_o ).
thf(func_def_1330,type,
if_Pro6119634080678213985nteger: $o > produc8923325533196201883nteger > produc8923325533196201883nteger > produc8923325533196201883nteger ).
thf(func_def_1331,type,
if_Pro3027730157355071871nt_int: $o > product_prod_int_int > product_prod_int_int > product_prod_int_int ).
thf(func_def_1332,type,
if_Pro6206227464963214023at_nat: $o > product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ).
thf(func_def_1333,type,
if_rat: $o > rat > rat > rat ).
thf(func_def_1334,type,
if_set_int: $o > set_int > set_int > set_int ).
thf(func_def_1335,type,
abs_Integ: product_prod_nat_nat > int ).
thf(func_def_1336,type,
neg: num > int ).
thf(func_def_1337,type,
pos: num > int ).
thf(func_def_1338,type,
rep_Integ: int > product_prod_nat_nat ).
thf(func_def_1339,type,
dup: int > int ).
thf(func_def_1340,type,
intrel: product_prod_nat_nat > product_prod_nat_nat > $o ).
thf(func_def_1341,type,
nat2: int > nat ).
thf(func_def_1342,type,
pcr_int: product_prod_nat_nat > int > $o ).
thf(func_def_1343,type,
ring_11222124179247155820nteger: set_Code_integer ).
thf(func_def_1344,type,
ring_1_Ints_int: set_int ).
thf(func_def_1345,type,
ring_1_Ints_rat: set_rat ).
thf(func_def_1346,type,
ring_18347121197199848620nteger: int > code_integer ).
thf(func_def_1347,type,
ring_1_of_int_int: int > int ).
thf(func_def_1348,type,
ring_1_of_int_rat: int > rat ).
thf(func_def_1349,type,
sub: num > num > int ).
thf(func_def_1350,type,
inf_inf_assn: assn > assn > assn ).
thf(func_def_1351,type,
inf_inf_Product_unit: product_unit > product_unit > product_unit ).
thf(func_def_1352,type,
inf_inf_set_nat: set_nat > set_nat > set_nat ).
thf(func_def_1353,type,
sup_su600977994968626096_int_o: ( ( int > option6357759511663192854e_term ) > product_prod_int_int > $o ) > ( ( int > option6357759511663192854e_term ) > product_prod_int_int > $o ) > ( int > option6357759511663192854e_term ) > product_prod_int_int > $o ).
thf(func_def_1354,type,
sup_su234547053653886311eger_o: ( ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o ) > ( ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o ) > ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o ).
thf(func_def_1355,type,
sup_su6535292691877529429_nat_o: ( ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o ) > ( ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o ) > ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o ).
thf(func_def_1356,type,
sup_su1630790145277462993_nat_o: ( ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o ) > ( ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o ) > ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o ).
thf(func_def_1357,type,
sup_su4182031696650224058_int_o: ( ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o ) > ( ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o ) > ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o ).
thf(func_def_1358,type,
sup_sup_nat_nat_o: ( nat > nat > $o ) > ( nat > nat > $o ) > nat > nat > $o ).
thf(func_def_1359,type,
sup_su7519161239522478338_nat_o: ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ) > ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ) > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ).
thf(func_def_1360,type,
sup_sup_assn: assn > assn > assn ).
thf(func_def_1361,type,
sup_sup_option_assn: option_assn > option_assn > option_assn ).
thf(func_def_1362,type,
sup_su7717485023253700007t_unit: option_Product_unit > option_Product_unit > option_Product_unit ).
thf(func_def_1363,type,
sup_su3598758113090618626et_nat: option_set_nat > option_set_nat > option_set_nat ).
thf(func_def_1364,type,
sup_su2273273666271716065at_nat: option1583680563626158861at_nat > option1583680563626158861at_nat > option1583680563626158861at_nat ).
thf(func_def_1365,type,
sup_sup_Product_unit: product_unit > product_unit > product_unit ).
thf(func_def_1366,type,
sup_sup_set_o: set_o > set_o > set_o ).
thf(func_def_1367,type,
sup_su848401254843788991nteger: set_Code_integer > set_Code_integer > set_Code_integer ).
thf(func_def_1368,type,
sup_sup_set_int: set_int > set_int > set_int ).
thf(func_def_1369,type,
sup_sup_set_list_nat: set_list_nat > set_list_nat > set_list_nat ).
thf(func_def_1370,type,
sup_sup_set_nat: set_nat > set_nat > set_nat ).
thf(func_def_1371,type,
sup_sup_set_num: set_num > set_num > set_num ).
thf(func_def_1372,type,
sup_su3298353300217089135nt_int: set_Pr1872883991513573699nt_int > set_Pr1872883991513573699nt_int > set_Pr1872883991513573699nt_int ).
thf(func_def_1373,type,
sup_su4591284015454442744nteger: set_Pr1281608226676607948nteger > set_Pr1281608226676607948nteger > set_Pr1281608226676607948nteger ).
thf(func_def_1374,type,
sup_su8975264963432250076et_nat: set_Pr8536935166611901872et_nat > set_Pr8536935166611901872et_nat > set_Pr8536935166611901872et_nat ).
thf(func_def_1375,type,
sup_su7128418612487073120et_nat: set_Pr3286484037609594932et_nat > set_Pr3286484037609594932et_nat > set_Pr3286484037609594932et_nat ).
thf(func_def_1376,type,
sup_su3382966977382714213nt_int: set_Pr9222295170931077689nt_int > set_Pr9222295170931077689nt_int > set_Pr9222295170931077689nt_int ).
thf(func_def_1377,type,
sup_su5769328420594410459od_o_o: set_Product_prod_o_o > set_Product_prod_o_o > set_Product_prod_o_o ).
thf(func_def_1378,type,
sup_su6189057272928884437_o_int: set_Pr8834758594704517033_o_int > set_Pr8834758594704517033_o_int > set_Pr8834758594704517033_o_int ).
thf(func_def_1379,type,
sup_su8679140417860611193_o_nat: set_Pr2101469702781467981_o_nat > set_Pr2101469702781467981_o_nat > set_Pr2101469702781467981_o_nat ).
thf(func_def_1380,type,
sup_su7481598572368468931_int_o: set_Pr903927857289325719_int_o > set_Pr903927857289325719_int_o > set_Pr903927857289325719_int_o ).
thf(func_def_1381,type,
sup_su6024340866399070445nt_int: set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int ).
thf(func_def_1382,type,
sup_su8514424011330797201nt_nat: set_Pr3448869479623346877nt_nat > set_Pr3448869479623346877nt_nat > set_Pr3448869479623346877nt_nat ).
thf(func_def_1383,type,
sup_su503371503184139039_nat_o: set_Pr3149072824959771635_nat_o > set_Pr3149072824959771635_nat_o > set_Pr3149072824959771635_nat_o ).
thf(func_def_1384,type,
sup_su3837419291706048657at_int: set_Pr7995236796853374141at_int > set_Pr7995236796853374141at_int > set_Pr7995236796853374141at_int ).
thf(func_def_1385,type,
sup_su6327502436637775413at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
thf(func_def_1386,type,
sup_su5921324857680904370_nat_o: set_Pr6558897299634722526_nat_o > set_Pr6558897299634722526_nat_o > set_Pr6558897299634722526_nat_o ).
thf(func_def_1387,type,
sup_su5525570899277871387at_nat: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat ).
thf(func_def_1388,type,
sup_su793286257634532545t_unit: set_Product_unit > set_Product_unit > set_Product_unit ).
thf(func_def_1389,type,
sup_sup_set_rat: set_rat > set_rat > set_rat ).
thf(func_def_1390,type,
sup_su3642409539654194069at_nat: set_se7855581050983116737at_nat > set_se7855581050983116737at_nat > set_se7855581050983116737at_nat ).
thf(func_def_1391,type,
lattic8265883725875713057ax_nat: set_nat > nat ).
thf(func_def_1392,type,
lattic7826324295020591184_F_nat: ( nat > nat > nat ) > nat > set_nat > nat ).
thf(func_def_1393,type,
quotie2291698863146621601nteger: ( int > int > $o ) > ( int > code_integer ) > ( code_integer > int ) > ( int > code_integer > $o ) > $o ).
thf(func_def_1394,type,
quotie743640454666494480atural: ( nat > nat > $o ) > ( nat > code_natural ) > ( code_natural > nat ) > ( nat > code_natural > $o ) > $o ).
thf(func_def_1395,type,
append_int: list_int > list_int > list_int ).
thf(func_def_1396,type,
append_nat: list_nat > list_nat > list_nat ).
thf(func_def_1397,type,
butlast_nat: list_nat > list_nat ).
thf(func_def_1398,type,
drop_nat: nat > list_nat > list_nat ).
thf(func_def_1399,type,
filter_nat: ( nat > $o ) > list_nat > list_nat ).
thf(func_def_1400,type,
fold_nat_nat: ( nat > nat > nat ) > list_nat > nat > nat ).
thf(func_def_1401,type,
last_nat: list_nat > nat ).
thf(func_def_1402,type,
linord2614967742042102400et_nat: set_nat > list_nat ).
thf(func_def_1403,type,
cons_int: int > list_int > list_int ).
thf(func_def_1404,type,
cons_nat: nat > list_nat > list_nat ).
thf(func_def_1405,type,
nil_int: list_int ).
thf(func_def_1406,type,
nil_nat: list_nat ).
thf(func_def_1407,type,
map_nat_nat: ( nat > nat ) > list_nat > list_nat ).
thf(func_def_1408,type,
set_int2: list_int > set_int ).
thf(func_def_1409,type,
set_nat2: list_nat > set_nat ).
thf(func_def_1410,type,
nth_int: list_int > nat > int ).
thf(func_def_1411,type,
nth_nat: list_nat > nat > nat ).
thf(func_def_1412,type,
take_nat: nat > list_nat > list_nat ).
thf(func_def_1413,type,
upt: nat > nat > list_nat ).
thf(func_def_1414,type,
upto: int > int > list_int ).
thf(func_def_1415,type,
upto_rel: product_prod_int_int > product_prod_int_int > $o ).
thf(func_def_1416,type,
eps_Opt_nat: ( nat > $o ) > option_nat ).
thf(func_def_1417,type,
eps_Opt_num: ( num > $o ) > option_num ).
thf(func_def_1418,type,
eps_Op6423059015816587746et_nat: ( produc3925858234332021118et_nat > $o ) > option5190343406534369742et_nat ).
thf(func_def_1419,type,
eps_Op9034888937550303799nteger: ( produc8923325533196201883nteger > $o ) > option2651255830984564193nteger ).
thf(func_def_1420,type,
eps_Op1141264490366522080it_nat: ( produc6714399278180371524it_nat > $o ) > option3216581401566546698it_nat ).
thf(func_def_1421,type,
eps_Op2013419657081471078et_nat: ( produc3658429121746597890et_nat > $o ) > option936205604648967762et_nat ).
thf(func_def_1422,type,
eps_Op2446201859369042517nt_int: ( product_prod_int_int > $o ) > option4624381673175914239nt_int ).
thf(func_def_1423,type,
eps_Op3393321821070424684it_nat: ( produc8664842809031399944it_nat > $o ) > option8956607266484857688it_nat ).
thf(func_def_1424,type,
eps_Op994234036888646909at_nat: ( set_Pr1261947904930325089at_nat > $o ) > option8963830502488799655at_nat ).
thf(func_def_1425,type,
biject576505603616484041nt_int: set_Pr1872883991513573699nt_int > $o ).
thf(func_def_1426,type,
biject9051520373387432658nteger: set_Pr1281608226676607948nteger > $o ).
thf(func_def_1427,type,
biject1468766312547416318et_nat: set_Pr8536935166611901872et_nat > $o ).
thf(func_def_1428,type,
biject2615096655818420098et_nat: set_Pr3286484037609594932et_nat > $o ).
thf(func_def_1429,type,
biject383251550997737151nt_int: set_Pr9222295170931077689nt_int > $o ).
thf(func_def_1430,type,
bijective_nat_nat: set_Pr1261947904930325089at_nat > $o ).
thf(func_def_1431,type,
biject3388518990857851981at_nat: set_Pr4329608150637261639at_nat > $o ).
thf(func_def_1432,type,
dflt_None_set_o: set_o > option_set_o ).
thf(func_def_1433,type,
dflt_None_set_int: set_int > option_set_int ).
thf(func_def_1434,type,
dflt_None_set_nat: set_nat > option_set_nat ).
thf(func_def_1435,type,
dflt_N6592383573632408824at_nat: set_Pr1261947904930325089at_nat > option8963830502488799655at_nat ).
thf(func_def_1436,type,
dflt_N3208751546879591902at_nat: set_Pr4329608150637261639at_nat > option1583680563626158861at_nat ).
thf(func_def_1437,type,
map_mmupd_o_num: ( $o > option_num ) > set_o > num > $o > option_num ).
thf(func_def_1438,type,
map_mm4340940675810032635it_nat: ( $o > option8956607266484857688it_nat ) > set_o > produc8664842809031399944it_nat > $o > option8956607266484857688it_nat ).
thf(func_def_1439,type,
map_mmupd_int_num: ( int > option_num ) > set_int > num > int > option_num ).
thf(func_def_1440,type,
map_mm5942422175790858651it_nat: ( int > option8956607266484857688it_nat ) > set_int > produc8664842809031399944it_nat > int > option8956607266484857688it_nat ).
thf(func_def_1441,type,
map_mmupd_nat_num: ( nat > option_num ) > set_nat > num > nat > option_num ).
thf(func_def_1442,type,
map_mm4316137065318800191it_nat: ( nat > option8956607266484857688it_nat ) > set_nat > produc8664842809031399944it_nat > nat > option8956607266484857688it_nat ).
thf(func_def_1443,type,
map_mm6272435474268545910at_num: ( product_prod_nat_nat > option_num ) > set_Pr1261947904930325089at_nat > num > product_prod_nat_nat > option_num ).
thf(func_def_1444,type,
map_mm8925508573636269924it_nat: ( product_prod_nat_nat > option8956607266484857688it_nat ) > set_Pr1261947904930325089at_nat > produc8664842809031399944it_nat > product_prod_nat_nat > option8956607266484857688it_nat ).
thf(func_def_1445,type,
map_mm2124855372588256220at_num: ( produc3843707927480180839at_nat > option_num ) > set_Pr4329608150637261639at_nat > num > produc3843707927480180839at_nat > option_num ).
thf(func_def_1446,type,
map_mm6227321356191524810it_nat: ( produc3843707927480180839at_nat > option8956607266484857688it_nat ) > set_Pr4329608150637261639at_nat > produc8664842809031399944it_nat > produc3843707927480180839at_nat > option8956607266484857688it_nat ).
thf(func_def_1447,type,
pairself_int_int: ( int > int ) > product_prod_int_int > product_prod_int_int ).
thf(func_def_1448,type,
pairse3534876335208825186e_term: ( int > option6357759511663192854e_term ) > product_prod_int_int > produc6576344331059438605e_term ).
thf(func_def_1449,type,
pairse4825235148789309005nteger: ( nat > code_integer ) > product_prod_nat_nat > produc8923325533196201883nteger ).
thf(func_def_1450,type,
pairself_nat_int: ( nat > int ) > product_prod_nat_nat > product_prod_int_int ).
thf(func_def_1451,type,
pairself_nat_nat: ( nat > nat ) > product_prod_nat_nat > product_prod_nat_nat ).
thf(func_def_1452,type,
pairself_nat_set_nat: ( nat > set_nat ) > product_prod_nat_nat > produc7819656566062154093et_nat ).
thf(func_def_1453,type,
pairse6848479906795794847e_term: produc7773217078559923341nt_int > produc7773217078559923341nt_int > $o ).
thf(func_def_1454,type,
rel_of5543720577181062686nt_int: ( ( int > option6357759511663192854e_term ) > option4624381673175914239nt_int ) > ( produc7773217078559923341nt_int > $o ) > set_Pr1872883991513573699nt_int ).
thf(func_def_1455,type,
rel_of7835217753297429671nteger: ( ( produc6241069584506657477e_term > option6357759511663192854e_term ) > option2651255830984564193nteger ) > ( produc1908205239877642774nteger > $o ) > set_Pr1281608226676607948nteger ).
thf(func_def_1456,type,
rel_of7774016450764239315et_nat: ( ( produc3658429121746597890et_nat > $o ) > option5190343406534369742et_nat ) > ( produc2732055786443039994et_nat > $o ) > set_Pr8536935166611901872et_nat ).
thf(func_def_1457,type,
rel_of4838799251197538391et_nat: ( ( produc3658429121746597890et_nat > $o ) > option936205604648967762et_nat ) > ( produc3925858234332021118et_nat > $o ) > set_Pr3286484037609594932et_nat ).
thf(func_def_1458,type,
rel_of8306664904814525588nt_int: ( ( produc8551481072490612790e_term > option6357759511663192854e_term ) > option4624381673175914239nt_int ) > ( produc2285326912895808259nt_int > $o ) > set_Pr9222295170931077689nt_int ).
thf(func_def_1459,type,
rel_of_nat_nat: ( nat > option_nat ) > ( product_prod_nat_nat > $o ) > set_Pr1261947904930325089at_nat ).
thf(func_def_1460,type,
rel_of6563097375766832824at_nat: ( set_Pr1261947904930325089at_nat > option8963830502488799655at_nat ) > ( produc3843707927480180839at_nat > $o ) > set_Pr4329608150637261639at_nat ).
thf(func_def_1461,type,
set_to1653371902132773855nt_int: set_Pr1872883991513573699nt_int > ( int > option6357759511663192854e_term ) > option4624381673175914239nt_int ).
thf(func_def_1462,type,
set_to680829756418416360nteger: set_Pr1281608226676607948nteger > ( produc6241069584506657477e_term > option6357759511663192854e_term ) > option2651255830984564193nteger ).
thf(func_def_1463,type,
set_to2047380710992656148et_nat: set_Pr8536935166611901872et_nat > ( produc3658429121746597890et_nat > $o ) > option5190343406534369742et_nat ).
thf(func_def_1464,type,
set_to6040779677306527128et_nat: set_Pr3286484037609594932et_nat > ( produc3658429121746597890et_nat > $o ) > option936205604648967762et_nat ).
thf(func_def_1465,type,
set_to6585427216324510421nt_int: set_Pr9222295170931077689nt_int > ( produc8551481072490612790e_term > option6357759511663192854e_term ) > option4624381673175914239nt_int ).
thf(func_def_1466,type,
set_to_map_o_num: set_Pr7040061329075590551_o_num > $o > option_num ).
thf(func_def_1467,type,
set_to3023635543527487849it_nat: set_Pr6777250647868329861it_nat > $o > option8956607266484857688it_nat ).
thf(func_def_1468,type,
set_to6264436334439079987nteger: set_Pr4811707699266497531nteger > code_integer > option_Code_integer ).
thf(func_def_1469,type,
set_to6039658477269176016atural: set_Pr2352657477744078772atural > code_natural > option5403585828896915703atural ).
thf(func_def_1470,type,
set_to_map_int_int: set_Pr958786334691620121nt_int > int > option_int ).
thf(func_def_1471,type,
set_to_map_int_num: set_Pr8387461105917469447nt_num > int > option_num ).
thf(func_def_1472,type,
set_to_map_nat_nat: set_Pr1261947904930325089at_nat > nat > option_nat ).
thf(func_def_1473,type,
set_to_map_nat_num: set_Pr6200539531224447659at_num > nat > option_num ).
thf(func_def_1474,type,
set_to785951348762482001it_nat: set_Pr633603713510679705it_nat > nat > option8956607266484857688it_nat ).
thf(func_def_1475,type,
set_to5081529003106763492at_num: set_Pr7477759153910077568at_num > product_prod_nat_nat > option_num ).
thf(func_def_1476,type,
set_to4447731662395764663at_nat: set_Pr4329608150637261639at_nat > set_Pr1261947904930325089at_nat > option8963830502488799655at_nat ).
thf(func_def_1477,type,
the_default_num: num > option_num > num ).
thf(func_def_1478,type,
the_de8559148246674365659it_nat: produc6714399278180371524it_nat > option3216581401566546698it_nat > produc6714399278180371524it_nat ).
thf(func_def_1479,type,
the_de2487931475039285041it_nat: produc8664842809031399944it_nat > option8956607266484857688it_nat > produc8664842809031399944it_nat ).
thf(func_def_1480,type,
the_default_set_o: set_o > option_set_o > set_o ).
thf(func_def_1481,type,
the_default_set_int: set_int > option_set_int > set_int ).
thf(func_def_1482,type,
the_default_set_nat: set_nat > option_set_nat > set_nat ).
thf(func_def_1483,type,
the_de3668382347305825784at_nat: set_Pr1261947904930325089at_nat > option8963830502488799655at_nat > set_Pr1261947904930325089at_nat ).
thf(func_def_1484,type,
the_de6830073021511528542at_nat: set_Pr4329608150637261639at_nat > option1583680563626158861at_nat > set_Pr4329608150637261639at_nat ).
thf(func_def_1485,type,
uncurry_int_int_int: ( int > int > int ) > product_prod_int_int > int ).
thf(func_def_1486,type,
uncurr7650761721940715016nt_int: ( int > int > product_prod_int_int ) > product_prod_int_int > product_prod_int_int ).
thf(func_def_1487,type,
uncurr7511940902602773877_nat_o: ( nat > nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > product_prod_nat_nat > $o ).
thf(func_def_1488,type,
uncurr8011562610307062878at_nat: ( nat > nat > product_prod_nat_nat > product_prod_nat_nat ) > product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ).
thf(func_def_1489,type,
uncurry_nat_nat_nat: ( nat > nat > nat ) > product_prod_nat_nat > nat ).
thf(func_def_1490,type,
add_ms2612439473150266591at_nat: product_prod_nat_nat > multis2468970476368604999at_nat > multis2468970476368604999at_nat ).
thf(func_def_1491,type,
ms_strict: set_Pr8551490117392284871at_nat ).
thf(func_def_1492,type,
ms_weak: set_Pr8551490117392284871at_nat ).
thf(func_def_1493,type,
pw_leq: multis2468970476368604999at_nat > multis2468970476368604999at_nat > $o ).
thf(func_def_1494,type,
set_ms8126754132646256062at_nat: multis2468970476368604999at_nat > set_Pr1261947904930325089at_nat ).
thf(func_def_1495,type,
suc: nat > nat ).
thf(func_def_1496,type,
compow_nat_nat: nat > ( nat > nat ) > nat > nat ).
thf(func_def_1497,type,
case_nat_option_num: option_num > ( nat > option_num ) > nat > option_num ).
thf(func_def_1498,type,
semiri4939895301339042750nteger: nat > code_integer ).
thf(func_def_1499,type,
semiri3763490453095760265atural: nat > code_natural ).
thf(func_def_1500,type,
semiri1314217659103216013at_int: nat > int ).
thf(func_def_1501,type,
semiri1316708129612266289at_nat: nat > nat ).
thf(func_def_1502,type,
semiri681578069525770553at_rat: nat > rat ).
thf(func_def_1503,type,
semiri4055485073559036834nteger: ( code_integer > code_integer ) > nat > code_integer > code_integer ).
thf(func_def_1504,type,
semiri2879080225315754349atural: ( code_natural > code_natural ) > nat > code_natural > code_natural ).
thf(func_def_1505,type,
semiri8420488043553186161ux_int: ( int > int ) > nat > int > int ).
thf(func_def_1506,type,
semiri8422978514062236437ux_nat: ( nat > nat ) > nat > nat > nat ).
thf(func_def_1507,type,
semiri7787848453975740701ux_rat: ( rat > rat ) > nat > rat > rat ).
thf(func_def_1508,type,
size_s1564113455978345259t_unit: heap_T5738788834812785303t_unit > nat ).
thf(func_def_1509,type,
size_size_list_int: list_int > nat ).
thf(func_def_1510,type,
size_size_list_nat: list_nat > nat ).
thf(func_def_1511,type,
size_size_num: num > nat ).
thf(func_def_1512,type,
size_size_option_num: option_num > nat ).
thf(func_def_1513,type,
size_s6797157356856800118it_nat: option3216581401566546698it_nat > nat ).
thf(func_def_1514,type,
size_s8766407808098229740it_nat: option8956607266484857688it_nat > nat ).
thf(func_def_1515,type,
nat_list_decode: nat > list_nat ).
thf(func_def_1516,type,
nat_list_decode_rel: nat > nat > $o ).
thf(func_def_1517,type,
nat_list_encode: list_nat > nat ).
thf(func_def_1518,type,
nat_list_encode_rel: list_nat > list_nat > $o ).
thf(func_def_1519,type,
nat_prod_decode: nat > product_prod_nat_nat ).
thf(func_def_1520,type,
nat_prod_decode_aux: nat > nat > product_prod_nat_nat ).
thf(func_def_1521,type,
nat_pr5047031295181774490ux_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).
thf(func_def_1522,type,
nat_prod_encode: product_prod_nat_nat > nat ).
thf(func_def_1523,type,
nat_set_decode: nat > set_nat ).
thf(func_def_1524,type,
nat_set_encode: set_nat > nat ).
thf(func_def_1525,type,
nat_sum_decode: nat > sum_sum_nat_nat ).
thf(func_def_1526,type,
nat_triangle: nat > nat ).
thf(func_def_1527,type,
bitM: num > num ).
thf(func_def_1528,type,
inc: num > num ).
thf(func_def_1529,type,
nat_of_num: num > nat ).
thf(func_def_1530,type,
neg_nu8804712462038260780nteger: code_integer > code_integer ).
thf(func_def_1531,type,
neg_numeral_dbl_int: int > int ).
thf(func_def_1532,type,
neg_numeral_dbl_rat: rat > rat ).
thf(func_def_1533,type,
neg_nu7757733837767384882nteger: code_integer > code_integer ).
thf(func_def_1534,type,
neg_nu3811975205180677377ec_int: int > int ).
thf(func_def_1535,type,
neg_nu3179335615603231917ec_rat: rat > rat ).
thf(func_def_1536,type,
neg_nu5831290666863070958nteger: code_integer > code_integer ).
thf(func_def_1537,type,
neg_nu5851722552734809277nc_int: int > int ).
thf(func_def_1538,type,
neg_nu5219082963157363817nc_rat: rat > rat ).
thf(func_def_1539,type,
neg_nu2435721316971906650nteger: code_integer > $o ).
thf(func_def_1540,type,
neg_nu7441568979088483369um_int: int > $o ).
thf(func_def_1541,type,
neg_nu6808929389511037909um_rat: rat > $o ).
thf(func_def_1542,type,
neg_nu5755505904847501662nteger: num > num > code_integer ).
thf(func_def_1543,type,
neg_numeral_sub_int: num > num > int ).
thf(func_def_1544,type,
neg_numeral_sub_rat: num > num > rat ).
thf(func_def_1545,type,
bit0: num > num ).
thf(func_def_1546,type,
bit1: num > num ).
thf(func_def_1547,type,
one: num ).
thf(func_def_1548,type,
case_num_option_num: option_num > ( num > option_num ) > ( num > option_num ) > num > option_num ).
thf(func_def_1549,type,
size_num: num > nat ).
thf(func_def_1550,type,
num_of_nat: nat > num ).
thf(func_def_1551,type,
numera6620942414471956472nteger: num > code_integer ).
thf(func_def_1552,type,
numera5444537566228673987atural: num > code_natural ).
thf(func_def_1553,type,
numeral_numeral_int: num > int ).
thf(func_def_1554,type,
numeral_numeral_nat: num > nat ).
thf(func_def_1555,type,
numeral_numeral_rat: num > rat ).
thf(func_def_1556,type,
pred_numeral: num > nat ).
thf(func_def_1557,type,
ring_16219924574208605041nteger: code_integer > $o ).
thf(func_def_1558,type,
ring_1_iszero_int: int > $o ).
thf(func_def_1559,type,
ring_1_iszero_rat: rat > $o ).
thf(func_def_1560,type,
sqr: num > num ).
thf(func_def_1561,type,
bind_num_num: option_num > ( num > option_num ) > option_num ).
thf(func_def_1562,type,
bind_n6186876254402743274it_nat: option_num > ( num > option3216581401566546698it_nat ) > option3216581401566546698it_nat ).
thf(func_def_1563,type,
bind_n550516262659884002it_nat: option_num > ( num > option8956607266484857688it_nat ) > option8956607266484857688it_nat ).
thf(func_def_1564,type,
bind_P7816469540982926368at_num: option3216581401566546698it_nat > ( produc6714399278180371524it_nat > option_num ) > option_num ).
thf(func_def_1565,type,
bind_P1787608729393679550it_nat: option3216581401566546698it_nat > ( produc6714399278180371524it_nat > option3216581401566546698it_nat ) > option3216581401566546698it_nat ).
thf(func_def_1566,type,
bind_P3087804342168909838it_nat: option3216581401566546698it_nat > ( produc6714399278180371524it_nat > option8956607266484857688it_nat ) > option8956607266484857688it_nat ).
thf(func_def_1567,type,
bind_P4387644102537648098at_num: option8956607266484857688it_nat > ( produc8664842809031399944it_nat > option_num ) > option_num ).
thf(func_def_1568,type,
bind_P1106314856888375420it_nat: option8956607266484857688it_nat > ( produc8664842809031399944it_nat > option3216581401566546698it_nat ) > option3216581401566546698it_nat ).
thf(func_def_1569,type,
bind_P7351952464966851536it_nat: option8956607266484857688it_nat > ( produc8664842809031399944it_nat > option8956607266484857688it_nat ) > option8956607266484857688it_nat ).
thf(func_def_1570,type,
combine_options_num: ( num > num > num ) > option_num > option_num > option_num ).
thf(func_def_1571,type,
combin3867838909898076099it_nat: ( produc6714399278180371524it_nat > produc6714399278180371524it_nat > produc6714399278180371524it_nat ) > option3216581401566546698it_nat > option3216581401566546698it_nat > option3216581401566546698it_nat ).
thf(func_def_1572,type,
combin4318129983670048329it_nat: ( produc8664842809031399944it_nat > produc8664842809031399944it_nat > produc8664842809031399944it_nat ) > option8956607266484857688it_nat > option8956607266484857688it_nat > option8956607266484857688it_nat ).
thf(func_def_1573,type,
none_o: option_o ).
thf(func_def_1574,type,
none_int: option_int ).
thf(func_def_1575,type,
none_nat: option_nat ).
thf(func_def_1576,type,
none_num: option_num ).
thf(func_def_1577,type,
none_P3773570700014501484nt_int: option4256020574406277085nt_int ).
thf(func_def_1578,type,
none_P4442379456014020469nteger: option8051342751916580710nteger ).
thf(func_def_1579,type,
none_P199884684680593241et_nat: option2860828798490689354et_nat ).
thf(func_def_1580,type,
none_P4972525538344268765et_nat: option5190343406534369742et_nat ).
thf(func_def_1581,type,
none_P1286213070022356066nt_int: option7541221861074943443nt_int ).
thf(func_def_1582,type,
none_P2587165478634041381it_nat: option3216581401566546698it_nat ).
thf(func_def_1583,type,
none_P5556105721700978146at_nat: option4927543243414619207at_nat ).
thf(func_def_1584,type,
none_P9117596204409417319it_nat: option8956607266484857688it_nat ).
thf(func_def_1585,type,
none_P5811896708078067656at_nat: option8699557107911914541at_nat ).
thf(func_def_1586,type,
none_Product_unit: option_Product_unit ).
thf(func_def_1587,type,
none_set_o: option_set_o ).
thf(func_def_1588,type,
none_set_int: option_set_int ).
thf(func_def_1589,type,
none_set_nat: option_set_nat ).
thf(func_def_1590,type,
none_s625347054029921090at_nat: option8963830502488799655at_nat ).
thf(func_def_1591,type,
none_s6518873173954064040at_nat: option1583680563626158861at_nat ).
thf(func_def_1592,type,
some_nat_o: ( nat > $o ) > option_nat_o ).
thf(func_def_1593,type,
some_o: $o > option_o ).
thf(func_def_1594,type,
some_assn: assn > option_assn ).
thf(func_def_1595,type,
some_Code_integer: code_integer > option_Code_integer ).
thf(func_def_1596,type,
some_int: int > option_int ).
thf(func_def_1597,type,
some_nat: nat > option_nat ).
thf(func_def_1598,type,
some_num: num > option_num ).
thf(func_def_1599,type,
some_P7455497367792166888nt_int: produc7773217078559923341nt_int > option4256020574406277085nt_int ).
thf(func_def_1600,type,
some_P1462369734362851057nteger: produc1908205239877642774nteger > option8051342751916580710nteger ).
thf(func_def_1601,type,
some_P1630309045189364437et_nat: produc2732055786443039994et_nat > option2860828798490689354et_nat ).
thf(func_def_1602,type,
some_P750831030444334937et_nat: produc3925858234332021118et_nat > option5190343406534369742et_nat ).
thf(func_def_1603,type,
some_P2355398578364412894nt_int: produc2285326912895808259nt_int > option7541221861074943443nt_int ).
thf(func_def_1604,type,
some_P6772290148444788224nteger: produc8923325533196201883nteger > option2651255830984564193nteger ).
thf(func_def_1605,type,
some_P5671840033927537686atural: produc7822875418678951345atural > option5403585828896915703atural ).
thf(func_def_1606,type,
some_P6105628898608307625it_nat: produc6714399278180371524it_nat > option3216581401566546698it_nat ).
thf(func_def_1607,type,
some_P624177172695371229et_nat: produc3658429121746597890et_nat > option936205604648967762et_nat ).
thf(func_def_1608,type,
some_P4184893108420464158nt_int: product_prod_int_int > option4624381673175914239nt_int ).
thf(func_def_1609,type,
some_P7363390416028606310at_nat: product_prod_nat_nat > option4927543243414619207at_nat ).
thf(func_def_1610,type,
some_P1914260805536162275it_nat: produc8664842809031399944it_nat > option8956607266484857688it_nat ).
thf(func_def_1611,type,
some_P131194445498448716at_nat: produc3843707927480180839at_nat > option8699557107911914541at_nat ).
thf(func_def_1612,type,
some_Product_unit: product_unit > option_Product_unit ).
thf(func_def_1613,type,
some_rat: rat > option_rat ).
thf(func_def_1614,type,
some_set_o: set_o > option_set_o ).
thf(func_def_1615,type,
some_set_int: set_int > option_set_int ).
thf(func_def_1616,type,
some_set_nat: set_nat > option_set_nat ).
thf(func_def_1617,type,
some_s147305329494351046at_nat: set_Pr1261947904930325089at_nat > option8963830502488799655at_nat ).
thf(func_def_1618,type,
some_s5890477192898017836at_nat: set_Pr4329608150637261639at_nat > option1583680563626158861at_nat ).
thf(func_def_1619,type,
some_s8043159101241848530t_unit: set_Product_unit > option8137458692691377843t_unit ).
thf(func_def_1620,type,
case_o1441893360019914891nteger: ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ) > option8057788054806935849nteger > produc8923325533196201883nteger > produc8923325533196201883nteger ).
thf(func_def_1621,type,
case_o7134296353695833103nteger: ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > option_Code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).
thf(func_def_1622,type,
case_o43118980978444458nteger: $o > ( code_integer > $o ) > option_Code_integer > $o ).
thf(func_def_1623,type,
case_option_o_int: $o > ( int > $o ) > option_int > $o ).
thf(func_def_1624,type,
case_option_o_nat: $o > ( nat > $o ) > option_nat > $o ).
thf(func_def_1625,type,
case_option_o_num: $o > ( num > $o ) > option_num > $o ).
thf(func_def_1626,type,
case_o2169478532838437047it_nat: $o > ( produc6714399278180371524it_nat > $o ) > option3216581401566546698it_nat > $o ).
thf(func_def_1627,type,
case_o2686588417244861013it_nat: $o > ( produc8664842809031399944it_nat > $o ) > option8956607266484857688it_nat > $o ).
thf(func_def_1628,type,
case_option_o_rat: $o > ( rat > $o ) > option_rat > $o ).
thf(func_def_1629,type,
case_o4401850862724306899et_nat: $o > ( set_nat > $o ) > option_set_nat > $o ).
thf(func_def_1630,type,
case_o9049918639272118855nteger: code_integer > ( code_integer > code_integer ) > option_Code_integer > code_integer ).
thf(func_def_1631,type,
case_o356765784539232260er_num: code_integer > ( num > code_integer ) > option_num > code_integer ).
thf(func_def_1632,type,
case_o5621594795226839503al_num: code_natural > ( num > code_natural ) > option_num > code_natural ).
thf(func_def_1633,type,
case_o8314599424437789472it_nat: array_a > ( produc6714399278180371524it_nat > array_a ) > option3216581401566546698it_nat > array_a ).
thf(func_def_1634,type,
case_o8180226181140434498it_nat: heap_e7401611519738050253t_unit > ( produc6714399278180371524it_nat > heap_e7401611519738050253t_unit ) > option3216581401566546698it_nat > heap_e7401611519738050253t_unit ).
thf(func_def_1635,type,
case_o2566993838309857162it_nat: heap_e7401611519738050253t_unit > ( produc8664842809031399944it_nat > heap_e7401611519738050253t_unit ) > option8956607266484857688it_nat > heap_e7401611519738050253t_unit ).
thf(func_def_1636,type,
case_option_int_num: int > ( num > int ) > option_num > int ).
thf(func_def_1637,type,
case_option_nat_num: nat > ( num > nat ) > option_num > nat ).
thf(func_def_1638,type,
case_o1134687144775446439it_nat: nat > ( produc6714399278180371524it_nat > nat ) > option3216581401566546698it_nat > nat ).
thf(func_def_1639,type,
case_o5424514124273913701it_nat: nat > ( produc8664842809031399944it_nat > nat ) > option8956607266484857688it_nat > nat ).
thf(func_def_1640,type,
case_option_num_int: num > ( int > num ) > option_int > num ).
thf(func_def_1641,type,
case_option_num_nat: num > ( nat > num ) > option_nat > num ).
thf(func_def_1642,type,
case_option_num_num: num > ( num > num ) > option_num > num ).
thf(func_def_1643,type,
case_o4484465799723439917n_assn: option_assn > ( assn > option_assn ) > option_assn > option_assn ).
thf(func_def_1644,type,
case_o6005452278849405969um_num: option_num > ( num > option_num ) > option_num > option_num ).
thf(func_def_1645,type,
case_o8555119740594961093it_nat: option3216581401566546698it_nat > ( produc6714399278180371524it_nat > option3216581401566546698it_nat ) > option3216581401566546698it_nat > option3216581401566546698it_nat ).
thf(func_def_1646,type,
case_o5699750240967658439it_nat: option3216581401566546698it_nat > ( produc8664842809031399944it_nat > option3216581401566546698it_nat ) > option8956607266484857688it_nat > option3216581401566546698it_nat ).
thf(func_def_1647,type,
case_o3886096569520666655it_nat: option8956607266484857688it_nat > ( produc6714399278180371524it_nat > option8956607266484857688it_nat ) > option3216581401566546698it_nat > option8956607266484857688it_nat ).
thf(func_def_1648,type,
case_o2963978774867076333it_nat: option8956607266484857688it_nat > ( produc8664842809031399944it_nat > option8956607266484857688it_nat ) > option8956607266484857688it_nat > option8956607266484857688it_nat ).
thf(func_def_1649,type,
case_o2985186191577459077t_unit: option_Product_unit > ( product_unit > option_Product_unit ) > option_Product_unit > option_Product_unit ).
thf(func_def_1650,type,
case_o4054078431260844265et_nat: option_set_nat > ( set_nat > option_set_nat ) > option_set_nat > option_set_nat ).
thf(func_def_1651,type,
case_o9080059180780454917at_nat: option1583680563626158861at_nat > ( set_Pr4329608150637261639at_nat > option1583680563626158861at_nat ) > option1583680563626158861at_nat > option1583680563626158861at_nat ).
thf(func_def_1652,type,
case_o9196786658626276042it_nat: product_unit > ( produc8664842809031399944it_nat > product_unit ) > option8956607266484857688it_nat > product_unit ).
thf(func_def_1653,type,
map_op3563471509957180299nteger: ( ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ) > option8057788054806935849nteger > option7428179582072448501nteger ).
thf(func_def_1654,type,
map_op6424164270877473355_nat_o: ( ( nat > $o ) > nat > $o ) > option_nat_o > option_nat_o ).
thf(func_def_1655,type,
map_option_o_o: ( $o > $o ) > option_o > option_o ).
thf(func_def_1656,type,
map_op370346339404370627nteger: ( code_integer > code_integer > code_integer ) > option_Code_integer > option8057788054806935849nteger ).
thf(func_def_1657,type,
map_op9146685272036663823nteger: ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > option_Code_integer > option7428179582072448501nteger ).
thf(func_def_1658,type,
map_op3669829223712506439nteger: ( code_integer > code_integer ) > option_Code_integer > option_Code_integer ).
thf(func_def_1659,type,
map_option_int_int: ( int > int ) > option_int > option_int ).
thf(func_def_1660,type,
map_option_int_nat: ( int > nat ) > option_int > option_nat ).
thf(func_def_1661,type,
map_option_int_num: ( int > num ) > option_int > option_num ).
thf(func_def_1662,type,
map_option_nat_nat: ( nat > nat ) > option_nat > option_nat ).
thf(func_def_1663,type,
map_option_nat_num: ( nat > num ) > option_nat > option_num ).
thf(func_def_1664,type,
map_op2849635639313731588nteger: ( num > code_integer ) > option_num > option_Code_integer ).
thf(func_def_1665,type,
map_option_num_num: ( num > num ) > option_num > option_num ).
thf(func_def_1666,type,
map_op6598675229099881181it_nat: ( num > produc6714399278180371524it_nat ) > option_num > option3216581401566546698it_nat ).
thf(func_def_1667,type,
map_op8118133509425879471it_nat: ( num > produc8664842809031399944it_nat ) > option_num > option8956607266484857688it_nat ).
thf(func_def_1668,type,
map_op8228268515680064275at_num: ( produc6714399278180371524it_nat > num ) > option3216581401566546698it_nat > option_num ).
thf(func_def_1669,type,
map_op6002829699023054091it_nat: ( produc6714399278180371524it_nat > produc6714399278180371524it_nat ) > option3216581401566546698it_nat > option3216581401566546698it_nat ).
thf(func_def_1670,type,
map_op674526153330701057it_nat: ( produc6714399278180371524it_nat > produc8664842809031399944it_nat ) > option3216581401566546698it_nat > option8956607266484857688it_nat ).
thf(func_def_1671,type,
map_op2731889312448867759at_num: ( produc8664842809031399944it_nat > num ) > option8956607266484857688it_nat > option_num ).
thf(func_def_1672,type,
map_op7916408704904942447it_nat: ( produc8664842809031399944it_nat > produc6714399278180371524it_nat ) > option8956607266484857688it_nat > option3216581401566546698it_nat ).
thf(func_def_1673,type,
map_op8673683442680995229it_nat: ( produc8664842809031399944it_nat > produc8664842809031399944it_nat ) > option8956607266484857688it_nat > option8956607266484857688it_nat ).
thf(func_def_1674,type,
size_option_num: ( num > nat ) > option_num > nat ).
thf(func_def_1675,type,
size_o5312321843473198183it_nat: ( produc6714399278180371524it_nat > nat ) > option3216581401566546698it_nat > nat ).
thf(func_def_1676,type,
size_o29782932136985253it_nat: ( produc8664842809031399944it_nat > nat ) > option8956607266484857688it_nat > nat ).
thf(func_def_1677,type,
the_nat_o: option_nat_o > nat > $o ).
thf(func_def_1678,type,
the_o: option_o > $o ).
thf(func_def_1679,type,
the_int2: option_int > int ).
thf(func_def_1680,type,
the_nat: option_nat > nat ).
thf(func_def_1681,type,
the_num: option_num > num ).
thf(func_def_1682,type,
the_Pr5856008525237892824it_nat: option3216581401566546698it_nat > produc6714399278180371524it_nat ).
thf(func_def_1683,type,
the_Pr7776125533777466484it_nat: option8956607266484857688it_nat > produc8664842809031399944it_nat ).
thf(func_def_1684,type,
these_o: set_option_o > set_o ).
thf(func_def_1685,type,
these_int: set_option_int > set_int ).
thf(func_def_1686,type,
these_nat: set_option_nat > set_nat ).
thf(func_def_1687,type,
these_num: set_option_num > set_num ).
thf(func_def_1688,type,
these_6645423997822192641it_nat: set_op3940070208846178154it_nat > set_Pr5142436192348053284it_nat ).
thf(func_def_1689,type,
these_8061402112538453438at_nat: set_op4508134149509766951at_nat > set_Pr1261947904930325089at_nat ).
thf(func_def_1690,type,
these_3407724651694999947it_nat: set_op239864471688321678it_nat > set_Pr1354866905816374718it_nat ).
thf(func_def_1691,type,
these_1872268174106123684at_nat: set_op989438649584373901at_nat > set_Pr4329608150637261639at_nat ).
thf(func_def_1692,type,
these_Product_unit: set_op3165557761946182707t_unit > set_Product_unit ).
thf(func_def_1693,type,
these_set_nat: set_option_set_nat > set_set_nat ).
thf(func_def_1694,type,
bot_bo1403522918969695512_int_o: ( int > option6357759511663192854e_term ) > product_prod_int_int > $o ).
thf(func_def_1695,type,
bot_bo3000040243691356879eger_o: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o ).
thf(func_def_1696,type,
bot_bo3790638025767943357_nat_o: ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o ).
thf(func_def_1697,type,
bot_bo5580076615179976505_nat_o: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o ).
thf(func_def_1698,type,
bot_bo8662317086119403298_int_o: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o ).
thf(func_def_1699,type,
bot_bot_nat_nat_o: nat > nat > $o ).
thf(func_def_1700,type,
bot_bo394778441745866138_nat_o: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ).
thf(func_def_1702,type,
bot_bot_assn: assn ).
thf(func_def_1703,type,
bot_bot_nat: nat ).
thf(func_def_1704,type,
bot_bot_option_num: option_num ).
thf(func_def_1705,type,
bot_bot_Product_unit: product_unit ).
thf(func_def_1706,type,
bot_bot_set_o: set_o ).
thf(func_def_1707,type,
bot_bo3990330152332043303nteger: set_Code_integer ).
thf(func_def_1708,type,
bot_bot_set_int: set_int ).
thf(func_def_1709,type,
bot_bot_set_list_nat: set_list_nat ).
thf(func_def_1710,type,
bot_bot_set_nat: set_nat ).
thf(func_def_1711,type,
bot_bot_set_num: set_num ).
thf(func_def_1712,type,
bot_bot_set_option_o: set_option_o ).
thf(func_def_1713,type,
bot_bo2519760366563279686on_int: set_option_int ).
thf(func_def_1714,type,
bot_bo5009843511495006442on_nat: set_option_nat ).
thf(func_def_1715,type,
bot_bo725063100934353204on_num: set_option_num ).
thf(func_def_1716,type,
bot_bo8185009268211221974it_nat: set_op3940070208846178154it_nat ).
thf(func_def_1717,type,
bot_bo3414888551220300179at_nat: set_op4508134149509766951at_nat ).
thf(func_def_1718,type,
bot_bo1172055076661450530it_nat: set_op239864471688321678it_nat ).
thf(func_def_1719,type,
bot_bo1471150103859235065at_nat: set_op989438649584373901at_nat ).
thf(func_def_1720,type,
bot_bo2792743115866486943t_unit: set_op3165557761946182707t_unit ).
thf(func_def_1721,type,
bot_bo5650944848895983264et_nat: set_option_set_nat ).
thf(func_def_1722,type,
bot_bo4508923176915781079nt_int: set_Pr1872883991513573699nt_int ).
thf(func_def_1723,type,
bot_bo5443222936135328352nteger: set_Pr1281608226676607948nteger ).
thf(func_def_1724,type,
bot_bo5635537948650799172et_nat: set_Pr8536935166611901872et_nat ).
thf(func_def_1725,type,
bot_bo1481135142794719944et_nat: set_Pr3286484037609594932et_nat ).
thf(func_def_1726,type,
bot_bo572930865798478029nt_int: set_Pr9222295170931077689nt_int ).
thf(func_def_1727,type,
bot_bo7073875226086086771od_o_o: set_Product_prod_o_o ).
thf(func_def_1728,type,
bot_bo6799815435448350781_o_int: set_Pr8834758594704517033_o_int ).
thf(func_def_1729,type,
bot_bo66526543525301729_o_nat: set_Pr2101469702781467981_o_nat ).
thf(func_def_1730,type,
bot_bo6361524548789211024it_nat: set_Pr5142436192348053284it_nat ).
thf(func_def_1731,type,
bot_bo8092356734887935275_int_o: set_Pr903927857289325719_int_o ).
thf(func_def_1732,type,
bot_bo1796632182523588997nt_int: set_Pr958786334691620121nt_int ).
thf(func_def_1733,type,
bot_bo4286715327455315753nt_nat: set_Pr3448869479623346877nt_nat ).
thf(func_def_1734,type,
bot_bo1114129665703605383_nat_o: set_Pr3149072824959771635_nat_o ).
thf(func_def_1735,type,
bot_bo8833082644685343017at_int: set_Pr7995236796853374141at_int ).
thf(func_def_1736,type,
bot_bo2099793752762293965at_nat: set_Pr1261947904930325089at_nat ).
thf(func_def_1737,type,
bot_bo5454027612061941066_nat_o: set_Pr6558897299634722526_nat_o ).
thf(func_def_1738,type,
bot_bo5327735625951526323at_nat: set_Pr8693737435421807431at_nat ).
thf(func_def_1739,type,
bot_bo7193250159860175667at_nat: set_Pr5564308138774400199at_nat ).
thf(func_def_1740,type,
bot_bo5696401558416705618it_nat: set_Pr1354866905816374718it_nat ).
thf(func_def_1741,type,
bot_bo228742789529271731at_nat: set_Pr4329608150637261639at_nat ).
thf(func_def_1742,type,
bot_bo3957492148770167129t_unit: set_Product_unit ).
thf(func_def_1743,type,
bot_bot_set_rat: set_rat ).
thf(func_def_1744,type,
bot_bo9204850693367297629nteger: set_set_Code_integer ).
thf(func_def_1745,type,
bot_bot_set_set_int: set_set_int ).
thf(func_def_1746,type,
bot_bo3886227569956363488st_nat: set_set_list_nat ).
thf(func_def_1747,type,
bot_bot_set_set_nat: set_set_nat ).
thf(func_def_1748,type,
bot_bo3083307316010499117at_nat: set_se7855581050983116737at_nat ).
thf(func_def_1749,type,
bot_bo6284674557190688313t_unit: set_set_Product_unit ).
thf(func_def_1750,type,
ord_less_o: $o > $o > $o ).
thf(func_def_1751,type,
ord_le6747313008572928689nteger: code_integer > code_integer > $o ).
thf(func_def_1752,type,
ord_le5570908160329646204atural: code_natural > code_natural > $o ).
thf(func_def_1753,type,
ord_less_int: int > int > $o ).
thf(func_def_1754,type,
ord_less_nat: nat > nat > $o ).
thf(func_def_1755,type,
ord_less_num: num > num > $o ).
thf(func_def_1756,type,
ord_le7113747843092208513nteger: option_Code_integer > option_Code_integer > $o ).
thf(func_def_1757,type,
ord_less_option_int: option_int > option_int > $o ).
thf(func_def_1758,type,
ord_less_option_nat: option_nat > option_nat > $o ).
thf(func_def_1759,type,
ord_less_option_num: option_num > option_num > $o ).
thf(func_def_1760,type,
ord_less_option_rat: option_rat > option_rat > $o ).
thf(func_def_1761,type,
ord_le361264281704409273t_unit: product_unit > product_unit > $o ).
thf(func_def_1762,type,
ord_less_rat: rat > rat > $o ).
thf(func_def_1763,type,
ord_less_set_o: set_o > set_o > $o ).
thf(func_def_1764,type,
ord_le1307284697595431911nteger: set_Code_integer > set_Code_integer > $o ).
thf(func_def_1765,type,
ord_less_set_int: set_int > set_int > $o ).
thf(func_def_1766,type,
ord_less_set_nat: set_nat > set_nat > $o ).
thf(func_def_1767,type,
ord_less_set_num: set_num > set_num > $o ).
thf(func_def_1768,type,
ord_le7866589430770878221at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ).
thf(func_def_1769,type,
ord_le2604355607129572851at_nat: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o ).
thf(func_def_1770,type,
ord_le8056459307392131481t_unit: set_Product_unit > set_Product_unit > $o ).
thf(func_def_1771,type,
ord_less_set_rat: set_rat > set_rat > $o ).
thf(func_def_1772,type,
ord_less_set_set_nat: set_set_nat > set_set_nat > $o ).
thf(func_def_1773,type,
ord_le2124322318746777828_int_o: ( ( int > option6357759511663192854e_term ) > product_prod_int_int > $o ) > ( ( int > option6357759511663192854e_term ) > product_prod_int_int > $o ) > $o ).
thf(func_def_1774,type,
ord_le4340812435750786203eger_o: ( ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o ) > ( ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o ) > $o ).
thf(func_def_1775,type,
ord_le6753239538765779593_nat_o: ( ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o ) > ( ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o ) > $o ).
thf(func_def_1776,type,
ord_le8000401564054156549_nat_o: ( ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o ) > ( ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o ) > $o ).
thf(func_def_1777,type,
ord_le5643404153117327598_int_o: ( ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o ) > ( ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o ) > $o ).
thf(func_def_1778,type,
ord_le6558929396352911974_nat_o: ( list_nat > list_nat > $o ) > ( list_nat > list_nat > $o ) > $o ).
thf(func_def_1779,type,
ord_le1520216061033275535_nat_o: ( list_nat > $o ) > ( list_nat > $o ) > $o ).
thf(func_def_1780,type,
ord_le2646555220125990790_nat_o: ( nat > nat > $o ) > ( nat > nat > $o ) > $o ).
thf(func_def_1781,type,
ord_less_eq_nat_o: ( nat > $o ) > ( nat > $o ) > $o ).
thf(func_def_1782,type,
ord_le7226304311989208114_nat_o: ( produc2732055786443039994et_nat > produc2732055786443039994et_nat > $o ) > ( produc2732055786443039994et_nat > produc2732055786443039994et_nat > $o ) > $o ).
thf(func_def_1783,type,
ord_le1658592502415435381_nat_o: ( produc2732055786443039994et_nat > $o ) > ( produc2732055786443039994et_nat > $o ) > $o ).
thf(func_def_1784,type,
ord_le1598226405681992910_int_o: ( product_prod_int_int > product_prod_int_int > $o ) > ( product_prod_int_int > product_prod_int_int > $o ) > $o ).
thf(func_def_1785,type,
ord_le8369615600986905444_int_o: ( product_prod_int_int > $o ) > ( product_prod_int_int > $o ) > $o ).
thf(func_def_1786,type,
ord_le5604493270027003598_nat_o: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > $o ).
thf(func_def_1787,type,
ord_le704812498762024988_nat_o: ( product_prod_nat_nat > $o ) > ( product_prod_nat_nat > $o ) > $o ).
thf(func_def_1788,type,
ord_le3935385432712749774_nat_o: ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ) > ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ) > $o ).
thf(func_def_1789,type,
ord_less_eq_o: $o > $o > $o ).
thf(func_def_1790,type,
ord_le3102999989581377725nteger: code_integer > code_integer > $o ).
thf(func_def_1791,type,
ord_le1926595141338095240atural: code_natural > code_natural > $o ).
thf(func_def_1792,type,
ord_less_eq_int: int > int > $o ).
thf(func_def_1793,type,
ord_less_eq_nat: nat > nat > $o ).
thf(func_def_1794,type,
ord_less_eq_num: num > num > $o ).
thf(func_def_1795,type,
ord_le1736525451366464988on_int: option_int > option_int > $o ).
thf(func_def_1796,type,
ord_le5914376470875661696on_nat: option_nat > option_nat > $o ).
thf(func_def_1797,type,
ord_le6622620407824499402on_num: option_num > option_num > $o ).
thf(func_def_1798,type,
ord_le2406147912482264968on_rat: option_rat > option_rat > $o ).
thf(func_def_1799,type,
ord_le2843612097646854710et_nat: option_set_nat > option_set_nat > $o ).
thf(func_def_1800,type,
ord_le3221252021190050221t_unit: product_unit > product_unit > $o ).
thf(func_def_1801,type,
ord_less_eq_rat: rat > rat > $o ).
thf(func_def_1802,type,
ord_le567748327753481079e_term: set_in3461395444621081367e_term > set_in3461395444621081367e_term > $o ).
thf(func_def_1803,type,
ord_le7106919388332126736e_term: set_Pr7604974323444597168e_term > set_Pr7604974323444597168e_term > $o ).
thf(func_def_1804,type,
ord_le2965882846123202637_nat_o: set_Pr4532377907799695533_nat_o > set_Pr4532377907799695533_nat_o > $o ).
thf(func_def_1805,type,
ord_le4129093240937979009e_term: set_Pr3642885161833720865e_term > set_Pr3642885161833720865e_term > $o ).
thf(func_def_1806,type,
ord_less_eq_set_o: set_o > set_o > $o ).
thf(func_def_1807,type,
ord_le7084787975880047091nteger: set_Code_integer > set_Code_integer > $o ).
thf(func_def_1808,type,
ord_less_eq_set_int: set_int > set_int > $o ).
thf(func_def_1809,type,
ord_le6045566169113846134st_nat: set_list_nat > set_list_nat > $o ).
thf(func_def_1810,type,
ord_less_eq_set_nat: set_nat > set_nat > $o ).
thf(func_def_1811,type,
ord_less_eq_set_num: set_num > set_num > $o ).
thf(func_def_1812,type,
ord_le135402666524580259nt_int: set_Pr1872883991513573699nt_int > set_Pr1872883991513573699nt_int > $o ).
thf(func_def_1813,type,
ord_le3745675095661657703_nat_o: set_Pr7909803484932130503_nat_o > set_Pr7909803484932130503_nat_o > $o ).
thf(func_def_1814,type,
ord_le653643898420964396nteger: set_Pr1281608226676607948nteger > set_Pr1281608226676607948nteger > $o ).
thf(func_def_1815,type,
ord_le4763372923235995152et_nat: set_Pr8536935166611901872et_nat > set_Pr8536935166611901872et_nat > $o ).
thf(func_def_1816,type,
ord_le5966269811547037844et_nat: set_Pr3286484037609594932et_nat > set_Pr3286484037609594932et_nat > $o ).
thf(func_def_1817,type,
ord_le8725513860283290265nt_int: set_Pr9222295170931077689nt_int > set_Pr9222295170931077689nt_int > $o ).
thf(func_def_1818,type,
ord_le192195778054999463od_o_o: set_Product_prod_o_o > set_Product_prod_o_o > $o ).
thf(func_def_1819,type,
ord_le3982295392052344841_o_int: set_Pr8834758594704517033_o_int > set_Pr8834758594704517033_o_int > $o ).
thf(func_def_1820,type,
ord_le6472378536984071597_o_nat: set_Pr2101469702781467981_o_nat > set_Pr2101469702781467981_o_nat > $o ).
thf(func_def_1821,type,
ord_le3725938330318615451nteger: set_Pr4811707699266497531nteger > set_Pr4811707699266497531nteger > $o ).
thf(func_def_1822,type,
ord_le719211969347571306er_int: set_Pr6496905503482889930er_int > set_Pr6496905503482889930er_int > $o ).
thf(func_def_1823,type,
ord_le3209295114279298062er_nat: set_Pr8986988648414616686er_nat > set_Pr8986988648414616686er_nat > $o ).
thf(func_def_1824,type,
ord_le6478268328230966961atural: set_Pr7564037697178849041atural > set_Pr7564037697178849041atural > $o ).
thf(func_def_1825,type,
ord_le2202040463148982292atural: set_Pr2352657477744078772atural > set_Pr2352657477744078772atural > $o ).
thf(func_def_1826,type,
ord_le8090042543978450200et_nat: set_Pr3948176798113811640et_nat > set_Pr3948176798113811640et_nat > $o ).
thf(func_def_1827,type,
ord_le5274836691491929335_int_o: set_Pr903927857289325719_int_o > set_Pr903927857289325719_int_o > $o ).
thf(func_def_1828,type,
ord_le2638047946463454698nteger: set_Pr8415741480598773322nteger > set_Pr8415741480598773322nteger > $o ).
thf(func_def_1829,type,
ord_le2843351958646193337nt_int: set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int > $o ).
thf(func_def_1830,type,
ord_le5333435103577920093nt_nat: set_Pr3448869479623346877nt_nat > set_Pr3448869479623346877nt_nat > $o ).
thf(func_def_1831,type,
ord_le7519981659162375251_nat_o: set_Pr3149072824959771635_nat_o > set_Pr3149072824959771635_nat_o > $o ).
thf(func_def_1832,type,
ord_le5852610332322655630nteger: set_Pr2406931829603198446nteger > set_Pr2406931829603198446nteger > $o ).
thf(func_def_1833,type,
ord_le656430383953171549at_int: set_Pr7995236796853374141at_int > set_Pr7995236796853374141at_int > $o ).
thf(func_def_1834,type,
ord_le3146513528884898305at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ).
thf(func_def_1835,type,
ord_le3050193496395145148at_nat: set_Pr7717912310451564380at_nat > set_Pr7717912310451564380at_nat > $o ).
thf(func_def_1836,type,
ord_le3218026494883419554at_nat: set_Pr1625285437083415874at_nat > set_Pr1625285437083415874at_nat > $o ).
thf(func_def_1837,type,
ord_le5919393503700438654_nat_o: set_Pr6558897299634722526_nat_o > set_Pr6558897299634722526_nat_o > $o ).
thf(func_def_1838,type,
ord_le7094820750414311574at_nat: set_Pr2539167527615954998at_nat > set_Pr2539167527615954998at_nat > $o ).
thf(func_def_1839,type,
ord_le2145644191787020796at_nat: set_Pr552903133987017116at_nat > set_Pr552903133987017116at_nat > $o ).
thf(func_def_1840,type,
ord_le1268244103169919719at_nat: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o ).
thf(func_def_1841,type,
ord_le3507040750410214029t_unit: set_Product_unit > set_Product_unit > $o ).
thf(func_def_1842,type,
ord_less_eq_set_rat: set_rat > set_rat > $o ).
thf(func_def_1843,type,
ord_le1914454125413604393nteger: set_set_Code_integer > set_set_Code_integer > $o ).
thf(func_def_1844,type,
ord_le4403425263959731960et_int: set_set_int > set_set_int > $o ).
thf(func_def_1845,type,
ord_le1068707526560357548st_nat: set_set_list_nat > set_set_list_nat > $o ).
thf(func_def_1846,type,
ord_le6893508408891458716et_nat: set_set_nat > set_set_nat > $o ).
thf(func_def_1847,type,
ord_le2077887516847798113at_nat: set_se7855581050983116737at_nat > set_se7855581050983116737at_nat > $o ).
thf(func_def_1848,type,
ord_le3674001228145610605t_unit: set_set_Product_unit > set_set_Product_unit > $o ).
thf(func_def_1849,type,
ord_max_Code_integer: code_integer > code_integer > code_integer ).
thf(func_def_1850,type,
ord_max_Code_natural: code_natural > code_natural > code_natural ).
thf(func_def_1851,type,
ord_max_int: int > int > int ).
thf(func_def_1852,type,
ord_max_nat: nat > nat > nat ).
thf(func_def_1853,type,
ord_max_rat: rat > rat > rat ).
thf(func_def_1854,type,
ord_min_Code_integer: code_integer > code_integer > code_integer ).
thf(func_def_1855,type,
ord_min_Code_natural: code_natural > code_natural > code_natural ).
thf(func_def_1856,type,
ord_min_int: int > int > int ).
thf(func_def_1857,type,
ord_min_nat: nat > nat > nat ).
thf(func_def_1858,type,
ord_min_num: num > num > num ).
thf(func_def_1859,type,
ord_min_rat: rat > rat > rat ).
thf(func_def_1860,type,
ord_min_set_nat: set_nat > set_nat > set_nat ).
thf(func_def_1861,type,
top_to6513043852502318900_int_o: ( int > option6357759511663192854e_term ) > product_prod_int_int > $o ).
thf(func_def_1862,type,
top_to8112647782992986859eger_o: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o ).
thf(func_def_1863,type,
top_to7190503160269336793_nat_o: ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o ).
thf(func_def_1864,type,
top_to2428096842796733269_nat_o: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o ).
thf(func_def_1865,type,
top_to6261655714344447806_int_o: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o ).
thf(func_def_1866,type,
top_top_nat_nat_o: nat > nat > $o ).
thf(func_def_1867,type,
top_to8903224817164384382_nat_o: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ).
thf(func_def_1868,type,
top_top_assn: assn ).
thf(func_def_1869,type,
top_top_option_assn: option_assn ).
thf(func_def_1870,type,
top_to4322782652514146083t_unit: option_Product_unit ).
thf(func_def_1871,type,
top_to2336371874512884450et_int: option_set_int ).
thf(func_def_1872,type,
top_to4826455019444611206et_nat: option_set_nat ).
thf(func_def_1873,type,
top_to7662761140297458691t_unit: option8137458692691377843t_unit ).
thf(func_def_1874,type,
top_top_Product_unit: product_unit ).
thf(func_def_1875,type,
top_to3804862627464599871nteger: set_Co726186806682698383nteger ).
thf(func_def_1876,type,
top_top_set_nat_o: set_nat_o ).
thf(func_def_1877,type,
top_top_set_o: set_o ).
thf(func_def_1878,type,
top_top_set_assn: set_assn ).
thf(func_def_1879,type,
top_to4645266643341252675nteger: set_Code_integer ).
thf(func_def_1880,type,
top_top_set_int: set_int ).
thf(func_def_1881,type,
top_top_set_nat: set_nat ).
thf(func_def_1882,type,
top_top_set_num: set_num ).
thf(func_def_1883,type,
top_to5929521628599800467nteger: set_op687863988967635939nteger ).
thf(func_def_1884,type,
top_to6430115241214627170on_int: set_option_int ).
thf(func_def_1885,type,
top_to8920198386146353926on_nat: set_option_nat ).
thf(func_def_1886,type,
top_to4635417975585700688on_num: set_option_num ).
thf(func_def_1887,type,
top_to7137183367772546234it_nat: set_op3940070208846178154it_nat ).
thf(func_def_1888,type,
top_to3251141154256563319at_nat: set_op4508134149509766951at_nat ).
thf(func_def_1889,type,
top_to6632602878615679294it_nat: set_op239864471688321678it_nat ).
thf(func_def_1890,type,
top_to2690860209552263555t_unit: set_op3165557761946182707t_unit ).
thf(func_def_1891,type,
top_to2069137843433766899nt_int: set_Pr1872883991513573699nt_int ).
thf(func_def_1892,type,
top_to7512759353274530428nteger: set_Pr1281608226676607948nteger ).
thf(func_def_1893,type,
top_to1599102959340997728et_nat: set_Pr8536935166611901872et_nat ).
thf(func_def_1894,type,
top_to8753217654552796900et_nat: set_Pr3286484037609594932et_nat ).
thf(func_def_1895,type,
top_to3181862456159035625nt_int: set_Pr9222295170931077689nt_int ).
thf(func_def_1896,type,
top_to3995162779041354868it_nat: set_Pr5142436192348053284it_nat ).
thf(func_def_1897,type,
top_to4366644338036079209nt_int: set_Pr958786334691620121nt_int ).
thf(func_def_1898,type,
top_to6856727482967805965nt_nat: set_Pr3448869479623346877nt_nat ).
thf(func_def_1899,type,
top_to876157113852465980t_unit: set_Pr5889264611543340172t_unit ).
thf(func_def_1900,type,
top_to2179722763343057421at_int: set_Pr7995236796853374141at_int ).
thf(func_def_1901,type,
top_to4669805908274784177at_nat: set_Pr1261947904930325089at_nat ).
thf(func_def_1902,type,
top_to8544742955230171288t_unit: set_Pr4334478416066269672t_unit ).
thf(func_def_1903,type,
top_to3484027333181043534it_int: set_Pr8497134830871917726it_int ).
thf(func_def_1904,type,
top_to5974110478112770290it_nat: set_Pr1763845938948868674it_nat ).
thf(func_def_1905,type,
top_to4082048134677576814it_nat: set_Pr1354866905816374718it_nat ).
thf(func_def_1906,type,
top_to1835807148980544151t_unit: set_Pr5094982260447487303t_unit ).
thf(func_def_1907,type,
top_to6833984726390702231at_nat: set_Pr4329608150637261639at_nat ).
thf(func_def_1908,type,
top_to1996260823553986621t_unit: set_Product_unit ).
thf(func_def_1909,type,
top_top_set_rat: set_rat ).
thf(func_def_1910,type,
top_top_set_set_o: set_set_o ).
thf(func_def_1911,type,
top_top_set_set_int: set_set_int ).
thf(func_def_1912,type,
top_top_set_set_nat: set_set_nat ).
thf(func_def_1913,type,
top_to7629004291339433233at_nat: set_se7855581050983116737at_nat ).
thf(func_def_1914,type,
top_to1754375979021635447at_nat: set_se5479201105039950375at_nat ).
thf(func_def_1915,type,
top_to1767297665138865437t_unit: set_set_Product_unit ).
thf(func_def_1916,type,
power_power_assn: assn > nat > assn ).
thf(func_def_1917,type,
power_8256067586552552935nteger: code_integer > nat > code_integer ).
thf(func_def_1918,type,
power_7079662738309270450atural: code_natural > nat > code_natural ).
thf(func_def_1919,type,
power_power_int: int > nat > int ).
thf(func_def_1920,type,
power_power_nat: nat > nat > nat ).
thf(func_def_1921,type,
power_power_rat: rat > nat > rat ).
thf(func_def_1922,type,
produc6137756002093451184nteger: ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > produc8763457246119570046nteger ).
thf(func_def_1923,type,
produc2252593628808123835atural: ( code_natural > option6357759511663192854e_term ) > produc7822875418678951345atural > produc8731074985263844745atural ).
thf(func_def_1924,type,
produc4510790414113558107e_term: ( int > option6357759511663192854e_term ) > ( int > option6357759511663192854e_term ) > produc1945540942535730339e_term ).
thf(func_def_1925,type,
produc4305682042979456191nt_int: ( int > option6357759511663192854e_term ) > product_prod_int_int > produc7773217078559923341nt_int ).
thf(func_def_1926,type,
produc3209952032786966637at_nat: ( nat > nat > nat ) > produc7248412053542808358at_nat > produc4471711990508489141at_nat ).
thf(func_def_1927,type,
produc5701653931590357335_nat_o: ( nat > $o ) > ( nat > $o ) > produc7360885484439884007_nat_o ).
thf(func_def_1928,type,
produc6915061378690470669e_term: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8187290932660736981e_term ).
thf(func_def_1929,type,
produc8603105652947943368nteger: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > produc1908205239877642774nteger ).
thf(func_def_1930,type,
produc3831813291587773865atural: ( produc4972180933644002618e_term > option6357759511663192854e_term ) > produc7822875418678951345atural > produc989692990947075319atural ).
thf(func_def_1931,type,
produc7368190662567826135_nat_o: ( produc3658429121746597890et_nat > $o ) > ( produc3658429121746597890et_nat > $o ) > produc4928098042776334183_nat_o ).
thf(func_def_1932,type,
produc2245416461498447860et_nat: ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > produc2732055786443039994et_nat ).
thf(func_def_1933,type,
produc5001842942810119800et_nat: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > produc3925858234332021118et_nat ).
thf(func_def_1934,type,
produc8124735558134971759e_term: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > ( produc8551481072490612790e_term > option6357759511663192854e_term ) > produc4499399687821757879e_term ).
thf(func_def_1935,type,
produc5700946648718959541nt_int: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > produc2285326912895808259nt_int ).
thf(func_def_1936,type,
product_Pair_o_o: $o > $o > product_prod_o_o ).
thf(func_def_1937,type,
product_Pair_o_int: $o > int > product_prod_o_int ).
thf(func_def_1938,type,
product_Pair_o_nat: $o > nat > product_prod_o_nat ).
thf(func_def_1939,type,
produc6677183202524767010eger_o: code_integer > $o > produc6271795597528267376eger_o ).
thf(func_def_1940,type,
produc1086072967326762835nteger: code_integer > code_integer > produc8923325533196201883nteger ).
thf(func_def_1941,type,
produc8805100893531834658er_int: code_integer > int > produc2256096406371053034er_int ).
thf(func_def_1942,type,
produc8807591364040884934er_nat: code_integer > nat > produc6433947425880249742er_nat ).
thf(func_def_1943,type,
produc3574140220909816553atural: code_natural > code_natural > produc7822875418678951345atural ).
thf(func_def_1944,type,
produc6639722614265839536atural: code_natural > produc7822875418678951345atural > produc5835291356934675326atural ).
thf(func_def_1945,type,
produc1733996804261680252it_nat: array_a > produc6653097349344004940it_nat > produc6714399278180371524it_nat ).
thf(func_def_1946,type,
produc584006145561248582it_nat: heap_e7401611519738050253t_unit > nat > produc6653097349344004940it_nat ).
thf(func_def_1947,type,
produc7507926704131184380et_nat: heap_e7401611519738050253t_unit > set_nat > produc3658429121746597890et_nat ).
thf(func_def_1948,type,
product_Pair_int_o: int > $o > product_prod_int_o ).
thf(func_def_1949,type,
produc220428336201996578nteger: int > code_integer > produc2963269191615333738nteger ).
thf(func_def_1950,type,
product_Pair_int_int: int > int > product_prod_int_int ).
thf(func_def_1951,type,
product_Pair_int_nat: int > nat > product_prod_int_nat ).
thf(func_def_1952,type,
produc4348348721325984599at_nat: multis2468970476368604999at_nat > multis2468970476368604999at_nat > produc4166570645942440679at_nat ).
thf(func_def_1953,type,
product_Pair_nat_o: nat > $o > product_prod_nat_o ).
thf(func_def_1954,type,
produc9072146812819927750nteger: nat > code_integer > produc2591615631378489102nteger ).
thf(func_def_1955,type,
product_Pair_nat_int: nat > int > product_prod_nat_int ).
thf(func_def_1956,type,
product_Pair_nat_nat: nat > nat > product_prod_nat_nat ).
thf(func_def_1957,type,
product_Pair_nat_num: nat > num > product_prod_nat_num ).
thf(func_def_1958,type,
produc3378006678175723489it_nat: nat > option3216581401566546698it_nat > produc2867611627572283311it_nat ).
thf(func_def_1959,type,
produc638857205735767105it_nat: nat > option8956607266484857688it_nat > produc3911288613690379145it_nat ).
thf(func_def_1960,type,
produc487386426758144856at_nat: nat > product_prod_nat_nat > produc7248412053542808358at_nat ).
thf(func_def_1961,type,
produc5463602008962177208at_nat: nat > set_Pr1261947904930325089at_nat > produc3313772616054891654at_nat ).
thf(func_def_1962,type,
product_Pair_num_num: num > num > product_prod_num_num ).
thf(func_def_1963,type,
produc5950683997804057413e_term: option6357759511663192854e_term > option6357759511663192854e_term > produc6576344331059438605e_term ).
thf(func_def_1964,type,
produc8406175334058502835nt_int: produc7773217078559923341nt_int > produc7773217078559923341nt_int > produc2501202720802129403nt_int ).
thf(func_def_1965,type,
produc7954516348491987909nteger: produc1908205239877642774nteger > produc1908205239877642774nteger > produc824974754969098637nteger ).
thf(func_def_1966,type,
produc1940133919992309389et_nat: produc2732055786443039994et_nat > produc2732055786443039994et_nat > produc5657529347773406293et_nat ).
thf(func_def_1967,type,
produc8599840265553166229et_nat: produc3925858234332021118et_nat > produc3925858234332021118et_nat > produc6830853553727218525et_nat ).
thf(func_def_1968,type,
produc7601053194514725023nt_int: produc2285326912895808259nt_int > produc2285326912895808259nt_int > produc2432570611225516007nt_int ).
thf(func_def_1969,type,
produc4911887526399440471nteger: produc8923325533196201883nteger > produc8923325533196201883nteger > produc3334582477557816039nteger ).
thf(func_def_1970,type,
produc1272419604612767874atural: produc7822875418678951345atural > code_natural > produc3981471736659609608atural ).
thf(func_def_1971,type,
produc4480994950612372183atural: produc7822875418678951345atural > produc7822875418678951345atural > produc6756470014200349799atural ).
thf(func_def_1972,type,
produc8199053930788261021et_nat: produc3658429121746597890et_nat > produc3658429121746597890et_nat > produc8111630337999740517et_nat ).
thf(func_def_1973,type,
produc3646306378393792727nt_int: product_prod_int_int > product_prod_int_int > produc1219242969750017639nt_int ).
thf(func_def_1974,type,
produc855456346497908590_nat_o: product_prod_nat_nat > $o > produc652263959640188542_nat_o ).
thf(func_def_1975,type,
produc6161850002892822231at_nat: product_prod_nat_nat > product_prod_nat_nat > produc859450856879609959at_nat ).
thf(func_def_1976,type,
produc8824474337961625893at_nat: produc3313772616054891654at_nat > produc3313772616054891654at_nat > produc2714363965264676845at_nat ).
thf(func_def_1977,type,
produc3585720979125124569at_nat: produc366245978424229472at_nat > produc366245978424229472at_nat > produc2087150632810049441at_nat ).
thf(func_def_1978,type,
produc2335810615602371415at_nat: produc3843707927480180839at_nat > produc3843707927480180839at_nat > produc1906917888121415911at_nat ).
thf(func_def_1979,type,
produc7133225469290080770it_nat: product_unit > produc6653097349344004940it_nat > produc8664842809031399944it_nat ).
thf(func_def_1980,type,
produc5838405689764958487_set_o: set_o > set_o > produc7369051934464679207_set_o ).
thf(func_def_1981,type,
produc7443773368509356479nteger: set_Code_integer > set_Code_integer > produc6491284506569428743nteger ).
thf(func_def_1982,type,
produc6363374080413544029et_int: set_int > set_int > produc2115011035271226405et_int ).
thf(func_def_1983,type,
produc4532415448927165861et_nat: set_nat > set_nat > produc7819656566062154093et_nat ).
thf(func_def_1984,type,
produc763777882069021527od_o_o: set_Product_prod_o_o > set_Product_prod_o_o > produc2934264451710624999od_o_o ).
thf(func_def_1985,type,
produc8517790099723286449at_nat: set_Product_prod_o_o > set_Pr1261947904930325089at_nat > produc732395585841259969at_nat ).
thf(func_def_1986,type,
produc5245064249948416855at_nat: set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat > produc4193628355235574503at_nat ).
thf(func_def_1987,type,
produc3149970401713881818at_nat: set_Pr1261947904930325089at_nat > nat > produc366245978424229472at_nat ).
thf(func_def_1988,type,
produc2922128104949294807at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > produc3843707927480180839at_nat ).
thf(func_def_1989,type,
produc9060074326276436823at_nat: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > produc1319942482725812455at_nat ).
thf(func_def_1990,type,
produc7462898802507495127at_nat: set_se7855581050983116737at_nat > set_se7855581050983116737at_nat > produc7299876168958306407at_nat ).
thf(func_def_1991,type,
produc1318478031590598990nt_int: set_in3461395444621081367e_term > ( ( int > option6357759511663192854e_term ) > set_Pr958786334691620121nt_int ) > set_Pr1872883991513573699nt_int ).
thf(func_def_1992,type,
produc7256824055837167575nteger: set_Pr7604974323444597168e_term > ( ( produc6241069584506657477e_term > option6357759511663192854e_term ) > set_Pr4811707699266497531nteger ) > set_Pr1281608226676607948nteger ).
thf(func_def_1993,type,
produc7016705354093686019et_nat: set_Pr4532377907799695533_nat_o > ( ( produc3658429121746597890et_nat > $o ) > set_Pr3286484037609594932et_nat ) > set_Pr8536935166611901872et_nat ).
thf(func_def_1994,type,
produc8052021730408606599et_nat: set_Pr4532377907799695533_nat_o > ( ( produc3658429121746597890et_nat > $o ) > set_Pr3948176798113811640et_nat ) > set_Pr3286484037609594932et_nat ).
thf(func_def_1995,type,
produc5808185664642557892nt_int: set_Pr3642885161833720865e_term > ( ( produc8551481072490612790e_term > option6357759511663192854e_term ) > set_Pr958786334691620121nt_int ) > set_Pr9222295170931077689nt_int ).
thf(func_def_1996,type,
product_Sigma_o_o: set_o > ( $o > set_o ) > set_Product_prod_o_o ).
thf(func_def_1997,type,
product_Sigma_o_int: set_o > ( $o > set_int ) > set_Pr8834758594704517033_o_int ).
thf(func_def_1998,type,
product_Sigma_o_nat: set_o > ( $o > set_nat ) > set_Pr2101469702781467981_o_nat ).
thf(func_def_1999,type,
produc5882431272649516420nteger: set_Code_integer > ( code_integer > set_Code_integer ) > set_Pr4811707699266497531nteger ).
thf(func_def_2000,type,
produc4258167722180586323er_int: set_Code_integer > ( code_integer > set_int ) > set_Pr6496905503482889930er_int ).
thf(func_def_2001,type,
produc4260658192689636599er_nat: set_Code_integer > ( code_integer > set_nat ) > set_Pr8986988648414616686er_nat ).
thf(func_def_2002,type,
produc6231535905537262655atural: set_Code_natural > ( code_natural > set_Pr7564037697178849041atural ) > set_Pr2352657477744078772atural ).
thf(func_def_2003,type,
product_Sigma_int_o: set_int > ( int > set_o ) > set_Pr903927857289325719_int_o ).
thf(func_def_2004,type,
produc4896867201705524051nteger: set_int > ( int > set_Code_integer ) > set_Pr8415741480598773322nteger ).
thf(func_def_2005,type,
produc1453890548195736866nt_int: set_int > ( int > set_int ) > set_Pr958786334691620121nt_int ).
thf(func_def_2006,type,
produc1456381018704787142nt_nat: set_int > ( int > set_nat ) > set_Pr3448869479623346877nt_nat ).
thf(func_def_2007,type,
produc2622961094310184599t_unit: set_int > ( int > set_Product_unit ) > set_Pr5889264611543340172t_unit ).
thf(func_def_2008,type,
produc6850429418872557834st_nat: set_list_nat > ( list_nat > set_list_nat ) > set_Pr3451248702717554689st_nat ).
thf(func_def_2009,type,
produc7466890150575444730at_nat: set_list_nat > ( list_nat > set_nat ) > set_Pr7549493975000385137at_nat ).
thf(func_def_2010,type,
product_Sigma_nat_o: set_nat > ( nat > set_o ) > set_Pr3149072824959771635_nat_o ).
thf(func_def_2011,type,
produc4525213641468679415nteger: set_nat > ( nat > set_Code_integer ) > set_Pr2406931829603198446nteger ).
thf(func_def_2012,type,
produc454536836294682310at_int: set_nat > ( nat > set_int ) > set_Pr7995236796853374141at_int ).
thf(func_def_2013,type,
produc5227933103413159546st_nat: set_nat > ( nat > set_list_nat ) > set_Pr698032948827214833st_nat ).
thf(func_def_2014,type,
produc457027306803732586at_nat: set_nat > ( nat > set_nat ) > set_Pr1261947904930325089at_nat ).
thf(func_def_2015,type,
produc1809337555817847783at_nat: set_nat > ( nat > set_Pr1261947904930325089at_nat ) > set_Pr7717912310451564380at_nat ).
thf(func_def_2016,type,
produc396409126344608333at_nat: set_nat > ( nat > set_Pr4329608150637261639at_nat ) > set_Pr1625285437083415874at_nat ).
thf(func_def_2017,type,
produc5506539147108004339t_unit: set_nat > ( nat > set_Product_unit ) > set_Pr4334478416066269672t_unit ).
thf(func_def_2018,type,
produc8445815324708537221_nat_o: set_Pr3286484037609594932et_nat > ( produc3925858234332021118et_nat > set_Pr4532377907799695533_nat_o ) > set_Pr7705059561495379578_nat_o ).
thf(func_def_2019,type,
produc552098293437506509e_term: set_Pr4811707699266497531nteger > ( produc8923325533196201883nteger > set_Pr7604974323444597168e_term ) > set_Pr1628540301243981434e_term ).
thf(func_def_2020,type,
produc5879417536264718849_nat_o: set_Pr3948176798113811640et_nat > ( produc3658429121746597890et_nat > set_Pr4532377907799695533_nat_o ) > set_Pr4208978187861016310_nat_o ).
thf(func_def_2021,type,
produc4529769248912663762e_term: set_Pr958786334691620121nt_int > ( product_prod_int_int > set_in3461395444621081367e_term ) > set_Pr9020418513037773311e_term ).
thf(func_def_2022,type,
produc5327145186146221532e_term: set_Pr958786334691620121nt_int > ( product_prod_int_int > set_Pr3642885161833720865e_term ) > set_Pr7309386651551657097e_term ).
thf(func_def_2023,type,
produc203973861852599583_nat_o: set_Pr1261947904930325089at_nat > ( product_prod_nat_nat > set_o ) > set_Pr6558897299634722526_nat_o ).
thf(func_def_2024,type,
produc7672662199629908489at_nat: set_Pr1261947904930325089at_nat > ( product_prod_nat_nat > set_nat ) > set_Pr2539167527615954998at_nat ).
thf(func_def_2025,type,
produc1095920968030776047at_nat: set_Pr4329608150637261639at_nat > ( produc3843707927480180839at_nat > set_nat ) > set_Pr552903133987017116at_nat ).
thf(func_def_2026,type,
produc6872886531786962417it_int: set_Product_unit > ( product_unit > set_int ) > set_Pr8497134830871917726it_int ).
thf(func_def_2027,type,
produc6875377002296012693it_nat: set_Product_unit > ( product_unit > set_nat ) > set_Pr1763845938948868674it_nat ).
thf(func_def_2028,type,
produc6121607364029222536t_unit: set_Product_unit > ( product_unit > set_Product_unit ) > set_Pr5094982260447487303t_unit ).
thf(func_def_2029,type,
produc105401717395143638et_nat: set_set_nat > ( set_nat > set_set_nat ) > set_Pr5488025237498180813et_nat ).
thf(func_def_2030,type,
produc7726050920695093128at_nat: set_se7855581050983116737at_nat > ( set_Pr1261947904930325089at_nat > set_se7855581050983116737at_nat ) > set_Pr4329608150637261639at_nat ).
thf(func_def_2031,type,
product_Unity: product_unit ).
thf(func_def_2032,type,
produc7131893314732144953nt_int: ( ( int > option6357759511663192854e_term ) > int > option6357759511663192854e_term ) > produc7773217078559923341nt_int > produc7773217078559923341nt_int ).
thf(func_def_2033,type,
produc6067946493426971951nt_int: ( ( int > option6357759511663192854e_term ) > produc8551481072490612790e_term > option6357759511663192854e_term ) > produc7773217078559923341nt_int > produc2285326912895808259nt_int ).
thf(func_def_2034,type,
produc2515316116081422825nteger: ( ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc6241069584506657477e_term > option6357759511663192854e_term ) > produc1908205239877642774nteger > produc1908205239877642774nteger ).
thf(func_def_2035,type,
produc1442628905706551930et_nat: ( ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o ) > produc2732055786443039994et_nat > produc2732055786443039994et_nat ).
thf(func_def_2036,type,
produc3198230245617193214et_nat: ( ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > produc3925858234332021118et_nat ).
thf(func_def_2037,type,
produc6919319362177967663nt_int: ( ( produc8551481072490612790e_term > option6357759511663192854e_term ) > int > option6357759511663192854e_term ) > produc2285326912895808259nt_int > produc7773217078559923341nt_int ).
thf(func_def_2038,type,
produc7277921532047535397nt_int: ( ( produc8551481072490612790e_term > option6357759511663192854e_term ) > produc8551481072490612790e_term > option6357759511663192854e_term ) > produc2285326912895808259nt_int > produc2285326912895808259nt_int ).
thf(func_def_2039,type,
produc3207347198985423705nteger: ( code_integer > int > option6357759511663192854e_term ) > produc8923325533196201883nteger > produc6237349844158694175nteger ).
thf(func_def_2040,type,
produc5167107986097539517nt_int: ( code_integer > int > option6357759511663192854e_term ) > produc382792921321436433nt_int > produc7773217078559923341nt_int ).
thf(func_def_2041,type,
produc7628915689858001394nteger: ( code_integer > produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > produc3295550550304853304nteger ).
thf(func_def_2042,type,
produc5215714788235631558nteger: ( code_integer > produc6241069584506657477e_term > option6357759511663192854e_term ) > produc3346328345660746739nteger > produc1908205239877642774nteger ).
thf(func_def_2043,type,
produc7528800376889492689nteger: ( code_integer > produc3658429121746597890et_nat > $o ) > produc8923325533196201883nteger > produc6691574917238108761nteger ).
thf(func_def_2044,type,
produc4644964300586701942et_nat: ( code_integer > produc3658429121746597890et_nat > $o ) > produc8299537390109905600et_nat > produc3925858234332021118et_nat ).
thf(func_def_2045,type,
produc7602971101079744739nteger: ( code_integer > produc8551481072490612790e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > produc4130039061994950697nteger ).
thf(func_def_2046,type,
produc7725767832589379507nt_int: ( code_integer > produc8551481072490612790e_term > option6357759511663192854e_term ) > produc382792921321436433nt_int > produc2285326912895808259nt_int ).
thf(func_def_2047,type,
produc3195571438000033749nteger: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ).
thf(func_def_2048,type,
produc8323928115967317034atural: ( code_natural > int > option6357759511663192854e_term ) > produc5835291356934675326atural > produc5219672859094816389atural ).
thf(func_def_2049,type,
produc7347430915296828978nt_int: ( code_natural > int > option6357759511663192854e_term ) > produc5665947927044467078nt_int > produc7773217078559923341nt_int ).
thf(func_def_2050,type,
produc7618241212158389867et_nat: ( code_natural > produc3658429121746597890et_nat > $o ) > produc5111566536631596683et_nat > produc3925858234332021118et_nat ).
thf(func_def_2051,type,
produc4623092060929046819atural: ( code_natural > code_natural ) > produc5835291356934675326atural > produc5835291356934675326atural ).
thf(func_def_2052,type,
produc2895628470685950711rm_int: ( int > int > option6357759511663192854e_term ) > product_prod_int_int > produc6025053409261769070rm_int ).
thf(func_def_2053,type,
produc7862092043137183022nt_int: ( int > int > option6357759511663192854e_term ) > produc759720530913461378nt_int > produc7773217078559923341nt_int ).
thf(func_def_2054,type,
produc7344697412356995344rm_int: ( int > produc6241069584506657477e_term > option6357759511663192854e_term ) > product_prod_int_int > produc7172142986261921671rm_int ).
thf(func_def_2055,type,
produc5502177047915545527nteger: ( int > produc6241069584506657477e_term > option6357759511663192854e_term ) > produc6162884466328367972nteger > produc1908205239877642774nteger ).
thf(func_def_2056,type,
produc1933289243015553937_o_int: ( int > produc3658429121746597890et_nat > $o ) > product_prod_int_int > produc3776562785724475560_o_int ).
thf(func_def_2057,type,
produc5259063908904861543et_nat: ( int > produc3658429121746597890et_nat > $o ) > produc8065447618272157327et_nat > produc3925858234332021118et_nat ).
thf(func_def_2058,type,
produc212012705979908097rm_int: ( int > produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > produc5577056076408194680rm_int ).
thf(func_def_2059,type,
produc9204274687749184420nt_int: ( int > produc8551481072490612790e_term > option6357759511663192854e_term ) > produc759720530913461378nt_int > produc2285326912895808259nt_int ).
thf(func_def_2060,type,
produc2355237562570658114nt_int: ( int > int ) > product_prod_int_int > product_prod_int_int ).
thf(func_def_2061,type,
produc9020447175693601247nteger: ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > produc8923325533196201883nteger > produc5966032636589952099nteger ).
thf(func_def_2062,type,
produc6499014454317279255nteger: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ).
thf(func_def_2063,type,
produc4047920161794714618e_term: ( code_integer > produc8923325533196201883nteger ) > produc3295550550304853304nteger > produc1908205239877642774nteger ).
thf(func_def_2064,type,
produc7166930624044334813nteger: ( code_integer > produc8923325533196201883nteger ) > produc8923325533196201883nteger > produc3346328345660746739nteger ).
thf(func_def_2065,type,
produc898583841617791278_nat_o: ( code_integer > produc3658429121746597890et_nat ) > produc6691574917238108761nteger > produc3925858234332021118et_nat ).
thf(func_def_2066,type,
produc7246245855585345468nteger: ( code_integer > produc3658429121746597890et_nat ) > produc8923325533196201883nteger > produc8299537390109905600et_nat ).
thf(func_def_2067,type,
produc8992176017387436671e_term: ( code_integer > product_prod_int_int ) > produc6237349844158694175nteger > produc7773217078559923341nt_int ).
thf(func_def_2068,type,
produc6067092816631456265e_term: ( code_integer > product_prod_int_int ) > produc4130039061994950697nteger > produc2285326912895808259nt_int ).
thf(func_def_2069,type,
produc3535056655957556987nteger: ( code_integer > product_prod_int_int ) > produc8923325533196201883nteger > produc382792921321436433nt_int ).
thf(func_def_2070,type,
produc4463282112584876420nt_int: ( int > int ) > product_prod_int_int > product_prod_int_int ).
thf(func_def_2071,type,
produc552091674517523435e_term: ( int > produc8923325533196201883nteger ) > produc7172142986261921671rm_int > produc1908205239877642774nteger ).
thf(func_def_2072,type,
produc2935421404040714269er_int: ( int > produc8923325533196201883nteger ) > product_prod_int_int > produc6162884466328367972nteger ).
thf(func_def_2073,type,
produc3447581998352395295_nat_o: ( int > produc3658429121746597890et_nat ) > produc3776562785724475560_o_int > produc3925858234332021118et_nat ).
thf(func_def_2074,type,
produc9121118195053341018at_int: ( int > produc3658429121746597890et_nat ) > product_prod_int_int > produc8065447618272157327et_nat ).
thf(func_def_2075,type,
produc3260485439724623344e_term: ( int > product_prod_int_int ) > produc6025053409261769070rm_int > produc7773217078559923341nt_int ).
thf(func_def_2076,type,
produc189803804368834042e_term: ( int > product_prod_int_int ) > produc5577056076408194680rm_int > produc2285326912895808259nt_int ).
thf(func_def_2077,type,
produc6100211334659168315nt_int: ( int > product_prod_int_int ) > product_prod_int_int > produc759720530913461378nt_int ).
thf(func_def_2078,type,
produc7418200839687411156nteger: ( num > code_integer ) > produc7142191362829087448er_num > produc8923325533196201883nteger ).
thf(func_def_2079,type,
produc969530845752564945_nat_o: ( produc3925858234332021118et_nat > produc3925858234332021118et_nat ) > produc2732055786443039994et_nat > produc2732055786443039994et_nat ).
thf(func_def_2080,type,
produc1515462096303866701_nat_o: ( produc3925858234332021118et_nat > produc3658429121746597890et_nat ) > produc2732055786443039994et_nat > produc3925858234332021118et_nat ).
thf(func_def_2081,type,
produc717174245515237944e_term: ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > produc1908205239877642774nteger > produc1908205239877642774nteger ).
thf(func_def_2082,type,
produc4464772112783624294atural: ( produc7822875418678951345atural > produc7822875418678951345atural ) > produc5835291356934675326atural > produc5835291356934675326atural ).
thf(func_def_2083,type,
produc1304257963789341151atural: ( produc7822875418678951345atural > produc3658429121746597890et_nat ) > produc5835291356934675326atural > produc5111566536631596683et_nat ).
thf(func_def_2084,type,
produc7977970570655791143e_term: ( produc7822875418678951345atural > product_prod_int_int ) > produc5219672859094816389atural > produc7773217078559923341nt_int ).
thf(func_def_2085,type,
produc5167862320620071534atural: ( produc7822875418678951345atural > product_prod_int_int ) > produc5835291356934675326atural > produc5665947927044467078nt_int ).
thf(func_def_2086,type,
produc7714581247149323085_nat_o: ( produc3658429121746597890et_nat > produc3925858234332021118et_nat ) > produc3925858234332021118et_nat > produc2732055786443039994et_nat ).
thf(func_def_2087,type,
produc8750854537940449737_nat_o: ( produc3658429121746597890et_nat > produc3658429121746597890et_nat ) > produc3925858234332021118et_nat > produc3925858234332021118et_nat ).
thf(func_def_2088,type,
produc7011684061226097695e_term: ( product_prod_int_int > product_prod_int_int ) > produc7773217078559923341nt_int > produc7773217078559923341nt_int ).
thf(func_def_2089,type,
produc4973430039190721449e_term: ( product_prod_int_int > product_prod_int_int ) > produc2285326912895808259nt_int > produc2285326912895808259nt_int ).
thf(func_def_2090,type,
produc9098658269643458507_int_o: ( produc7773217078559923341nt_int > $o ) > ( int > option6357759511663192854e_term ) > product_prod_int_int > $o ).
thf(func_def_2091,type,
produc1217013493180205570eger_o: ( produc1908205239877642774nteger > $o ) > ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o ).
thf(func_def_2092,type,
produc5101573711933517782_nat_o: ( produc2732055786443039994et_nat > $o ) > ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o ).
thf(func_def_2093,type,
produc6216949301066131538_nat_o: ( produc3925858234332021118et_nat > $o ) > ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o ).
thf(func_def_2094,type,
produc730925184835016917_int_o: ( produc2285326912895808259nt_int > $o ) > ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o ).
thf(func_def_2095,type,
produc1016772743285680337nt_int: ( product_prod_int_int > int ) > int > int > int ).
thf(func_def_2096,type,
produc8249235968001453780nt_int: ( product_prod_int_int > product_prod_int_int ) > int > int > product_prod_int_int ).
thf(func_def_2097,type,
produc3704529784387675049_nat_o: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > nat > nat > product_prod_nat_nat > $o ).
thf(func_def_2098,type,
produc3610074571335452306at_nat: ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > nat > nat > product_prod_nat_nat > product_prod_nat_nat ).
thf(func_def_2099,type,
produc8871627978511607229at_nat: ( product_prod_nat_nat > nat ) > nat > nat > nat ).
thf(func_def_2100,type,
produc7926200574084438792nt_int: ( int > int > int ) > product_prod_int_int > int ).
thf(func_def_2101,type,
produc297006045350968285nt_int: ( int > int > product_prod_int_int ) > product_prod_int_int > product_prod_int_int ).
thf(func_def_2102,type,
produc4780622933104268256_nat_o: ( nat > nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > product_prod_nat_nat > $o ).
thf(func_def_2103,type,
produc1854806715440696265at_nat: ( nat > nat > product_prod_nat_nat > product_prod_nat_nat ) > product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ).
thf(func_def_2104,type,
produc6557683772455589876at_nat: ( nat > nat > nat ) > product_prod_nat_nat > nat ).
thf(func_def_2105,type,
produc2558449545302689196_int_o: ( ( int > option6357759511663192854e_term ) > product_prod_int_int > $o ) > produc7773217078559923341nt_int > $o ).
thf(func_def_2106,type,
produc5122537100556696953nt_int: ( ( int > option6357759511663192854e_term ) > product_prod_int_int > produc7773217078559923341nt_int ) > produc7773217078559923341nt_int > produc7773217078559923341nt_int ).
thf(func_def_2107,type,
produc8646739037753556108_set_o: ( ( int > option6357759511663192854e_term ) > product_prod_int_int > set_o ) > produc7773217078559923341nt_int > set_o ).
thf(func_def_2108,type,
produc4111701587417901774et_int: ( ( int > option6357759511663192854e_term ) > product_prod_int_int > set_int ) > produc7773217078559923341nt_int > set_int ).
thf(func_def_2109,type,
produc8289552606927098482et_nat: ( ( int > option6357759511663192854e_term ) > product_prod_int_int > set_nat ) > produc7773217078559923341nt_int > set_nat ).
thf(func_def_2110,type,
produc5154663461364529269at_nat: ( ( int > option6357759511663192854e_term ) > product_prod_int_int > set_Pr1261947904930325089at_nat ) > produc7773217078559923341nt_int > set_Pr1261947904930325089at_nat ).
thf(func_def_2111,type,
produc2845945524848125740at_o_o: ( ( nat > $o ) > ( nat > $o ) > $o ) > produc7360885484439884007_nat_o > $o ).
thf(func_def_2112,type,
produc6253627499356882019eger_o: ( ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o ) > produc1908205239877642774nteger > $o ).
thf(func_def_2113,type,
produc6512950862096126219nteger: ( ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > produc1908205239877642774nteger ) > produc1908205239877642774nteger > produc1908205239877642774nteger ).
thf(func_def_2114,type,
produc2373554395599118147_set_o: ( ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_o ) > produc1908205239877642774nteger > set_o ).
thf(func_def_2115,type,
produc5700143819190870999et_int: ( ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_int ) > produc1908205239877642774nteger > set_int ).
thf(func_def_2116,type,
produc654622801845291899et_nat: ( ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_nat ) > produc1908205239877642774nteger > set_nat ).
thf(func_def_2117,type,
produc838355143741117751_nat_o: ( ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o ) > produc2732055786443039994et_nat > $o ).
thf(func_def_2118,type,
produc2377985495875741467et_nat: ( ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > produc2732055786443039994et_nat ) > produc2732055786443039994et_nat > produc2732055786443039994et_nat ).
thf(func_def_2119,type,
produc1437786849005270451_nat_o: ( ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o ).
thf(func_def_2120,type,
produc4058941399401191971et_nat: ( ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > produc3925858234332021118et_nat ) > produc3925858234332021118et_nat > produc3925858234332021118et_nat ).
thf(func_def_2121,type,
produc7715693535893868691_set_o: ( ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > set_o ) > produc3925858234332021118et_nat > set_o ).
thf(func_def_2122,type,
produc4627640435386541703et_int: ( ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > set_int ) > produc3925858234332021118et_nat > set_int ).
thf(func_def_2123,type,
produc8805491454895738411et_nat: ( ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > set_nat ) > produc3925858234332021118et_nat > set_nat ).
thf(func_def_2124,type,
produc1573362020775583542_int_o: ( ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o ) > produc2285326912895808259nt_int > $o ).
thf(func_def_2125,type,
produc8492565224438309093nt_int: ( ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > produc2285326912895808259nt_int ) > produc2285326912895808259nt_int > produc2285326912895808259nt_int ).
thf(func_def_2126,type,
produc2066375834425727024eger_o: ( code_integer > code_integer > $o ) > produc8923325533196201883nteger > $o ).
thf(func_def_2127,type,
produc7469247390737344965nteger: ( code_integer > code_integer > code_integer ) > produc8923325533196201883nteger > code_integer ).
thf(func_def_2128,type,
produc1553301316500091796er_int: ( code_integer > code_integer > int ) > produc8923325533196201883nteger > int ).
thf(func_def_2129,type,
produc1555791787009142072er_nat: ( code_integer > code_integer > nat ) > produc8923325533196201883nteger > nat ).
thf(func_def_2130,type,
produc7336495610019696514er_num: ( code_integer > code_integer > num ) > produc8923325533196201883nteger > num ).
thf(func_def_2131,type,
produc9125791028180074456eger_o: ( code_integer > code_integer > produc6271795597528267376eger_o ) > produc8923325533196201883nteger > produc6271795597528267376eger_o ).
thf(func_def_2132,type,
produc6916734918728496179nteger: ( code_integer > code_integer > produc8923325533196201883nteger ) > produc8923325533196201883nteger > produc8923325533196201883nteger ).
thf(func_def_2133,type,
produc4281629032016041417nteger: ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > produc3346328345660746739nteger > produc8923325533196201883nteger ).
thf(func_def_2134,type,
produc8282080750456430313atural: ( code_natural > code_natural > produc6756470014200349799atural ) > produc7822875418678951345atural > produc6756470014200349799atural ).
thf(func_def_2135,type,
produc7358226366420480123ural_o: ( code_natural > produc7822875418678951345atural > $o ) > produc5835291356934675326atural > $o ).
thf(func_def_2136,type,
produc6302656368764539796atural: ( code_natural > produc7822875418678951345atural > produc7822875418678951345atural ) > produc5835291356934675326atural > produc7822875418678951345atural ).
thf(func_def_2137,type,
produc6785097126449100389atural: ( code_natural > produc7822875418678951345atural > produc3981471736659609608atural ) > produc5835291356934675326atural > produc3981471736659609608atural ).
thf(func_def_2138,type,
produc8767961711439910440rray_a: ( array_a > produc6653097349344004940it_nat > array_a ) > produc6714399278180371524it_nat > array_a ).
thf(func_def_2139,type,
produc7016084256669755260t_unit: ( array_a > produc6653097349344004940it_nat > heap_e7401611519738050253t_unit ) > produc6714399278180371524it_nat > heap_e7401611519738050253t_unit ).
thf(func_def_2140,type,
produc6028340861379781217at_nat: ( array_a > produc6653097349344004940it_nat > nat ) > produc6714399278180371524it_nat > nat ).
thf(func_def_2141,type,
produc8915672860170107321it_nat: ( array_a > produc6653097349344004940it_nat > option3216581401566546698it_nat ) > produc6714399278180371524it_nat > option3216581401566546698it_nat ).
thf(func_def_2142,type,
produc3495058329975564393it_nat: ( array_a > produc6653097349344004940it_nat > option8956607266484857688it_nat ) > produc6714399278180371524it_nat > option8956607266484857688it_nat ).
thf(func_def_2143,type,
produc2025300630104146186rray_a: ( heap_e7401611519738050253t_unit > nat > array_a ) > produc6653097349344004940it_nat > array_a ).
thf(func_def_2144,type,
produc9092781844693468442t_unit: ( heap_e7401611519738050253t_unit > nat > heap_e7401611519738050253t_unit ) > produc6653097349344004940it_nat > heap_e7401611519738050253t_unit ).
thf(func_def_2145,type,
produc4278983685114131267at_nat: ( heap_e7401611519738050253t_unit > nat > nat ) > produc6653097349344004940it_nat > nat ).
thf(func_def_2146,type,
produc921929042997482327it_nat: ( heap_e7401611519738050253t_unit > nat > option3216581401566546698it_nat ) > produc6653097349344004940it_nat > option3216581401566546698it_nat ).
thf(func_def_2147,type,
produc7488178964372371019it_nat: ( heap_e7401611519738050253t_unit > nat > option8956607266484857688it_nat ) > produc6653097349344004940it_nat > option8956607266484857688it_nat ).
thf(func_def_2148,type,
produc1863717115126956122t_unit: ( heap_e7401611519738050253t_unit > nat > product_unit ) > produc6653097349344004940it_nat > product_unit ).
thf(func_def_2149,type,
produc4947309494688390418_int_o: ( int > int > $o ) > product_prod_int_int > $o ).
thf(func_def_2150,type,
produc8211389475949308722nt_int: ( int > int > int ) > product_prod_int_int > int ).
thf(func_def_2151,type,
produc4245557441103728435nt_int: ( int > int > product_prod_int_int ) > product_prod_int_int > product_prod_int_int ).
thf(func_def_2152,type,
produc6382697403170970154_nat_o: ( list_nat > list_nat > $o ) > produc1828647624359046049st_nat > $o ).
thf(func_def_2153,type,
produc7308574044827705018_nat_o: ( list_nat > nat > $o ) > produc1540777390238407569at_nat > $o ).
thf(func_def_2154,type,
produc1728318271963197120er_int: ( nat > int > produc2256096406371053034er_int ) > product_prod_nat_int > produc2256096406371053034er_int ).
thf(func_def_2155,type,
produc1486167065449562675at_int: ( nat > int > product_prod_nat_int ) > product_prod_nat_int > product_prod_nat_int ).
thf(func_def_2156,type,
produc5265810065896090426_nat_o: ( nat > list_nat > $o ) > produc4575160907756185873st_nat > $o ).
thf(func_def_2157,type,
produc8739625826339149834_nat_o: ( nat > nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > product_prod_nat_nat > $o ).
thf(func_def_2158,type,
produc27273713700761075at_nat: ( nat > nat > product_prod_nat_nat > product_prod_nat_nat ) > product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ).
thf(func_def_2159,type,
produc6081775807080527818_nat_o: ( nat > nat > $o ) > product_prod_nat_nat > $o ).
thf(func_def_2160,type,
produc6840382203811409530at_int: ( nat > nat > int ) > product_prod_nat_nat > int ).
thf(func_def_2161,type,
produc2761476792215241774st_nat: ( nat > nat > list_nat ) > product_prod_nat_nat > list_nat ).
thf(func_def_2162,type,
produc6842872674320459806at_nat: ( nat > nat > nat ) > product_prod_nat_nat > nat ).
thf(func_def_2163,type,
produc39701218431283661nteger: ( nat > nat > produc8923325533196201883nteger ) > product_prod_nat_nat > produc8923325533196201883nteger ).
thf(func_def_2164,type,
produc9191653645064861724er_int: ( nat > nat > produc2256096406371053034er_int ) > product_prod_nat_nat > produc2256096406371053034er_int ).
thf(func_def_2165,type,
produc4146132627719282624er_nat: ( nat > nat > produc6433947425880249742er_nat ) > product_prod_nat_nat > produc6433947425880249742er_nat ).
thf(func_def_2166,type,
produc675454393454366620nteger: ( nat > nat > produc2963269191615333738nteger ) > product_prod_nat_nat > produc2963269191615333738nteger ).
thf(func_def_2167,type,
produc3625529712395680143nt_nat: ( nat > nat > product_prod_int_nat ) > product_prod_nat_nat > product_prod_int_nat ).
thf(func_def_2168,type,
produc303800833217521984nteger: ( nat > nat > produc2591615631378489102nteger ) > product_prod_nat_nat > produc2591615631378489102nteger ).
thf(func_def_2169,type,
produc7671697017840204687at_int: ( nat > nat > product_prod_nat_int ) > product_prod_nat_nat > product_prod_nat_int ).
thf(func_def_2170,type,
produc2626176000494625587at_nat: ( nat > nat > product_prod_nat_nat ) > product_prod_nat_nat > product_prod_nat_nat ).
thf(func_def_2171,type,
produc8197505143624133779at_nat: ( nat > nat > set_Pr1261947904930325089at_nat ) > product_prod_nat_nat > set_Pr1261947904930325089at_nat ).
thf(func_def_2172,type,
produc478579273971653890on_num: ( nat > num > option_num ) > product_prod_nat_num > option_num ).
thf(func_def_2173,type,
produc1908958340173245860_nat_o: ( nat > set_Pr1261947904930325089at_nat > produc3313772616054891654at_nat > $o ) > produc3313772616054891654at_nat > produc3313772616054891654at_nat > $o ).
thf(func_def_2174,type,
produc7997411485876045171_nat_o: ( nat > set_Pr1261947904930325089at_nat > $o ) > produc3313772616054891654at_nat > $o ).
thf(func_def_2175,type,
produc9203276081649983901et_nat: ( produc3925858234332021118et_nat > ( produc3658429121746597890et_nat > $o ) > produc2732055786443039994et_nat ) > produc4962441903510821572_nat_o > produc2732055786443039994et_nat ).
thf(func_def_2176,type,
produc5068368601420144385nteger: ( produc8923325533196201883nteger > ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc1908205239877642774nteger ) > produc998928222018024388e_term > produc1908205239877642774nteger ).
thf(func_def_2177,type,
produc1198152457851389869atural: ( produc7822875418678951345atural > code_natural > produc5835291356934675326atural ) > produc3981471736659609608atural > produc5835291356934675326atural ).
thf(func_def_2178,type,
produc5206072795621629085et_nat: ( produc3658429121746597890et_nat > ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat ) > produc6907119039986491712_nat_o > produc3925858234332021118et_nat ).
thf(func_def_2179,type,
produc3478612561300218621nt_int: ( product_prod_int_int > ( int > option6357759511663192854e_term ) > produc7773217078559923341nt_int ) > produc3832618445565238089e_term > produc7773217078559923341nt_int ).
thf(func_def_2180,type,
produc199769199162113789nt_int: ( product_prod_int_int > ( produc8551481072490612790e_term > option6357759511663192854e_term ) > produc2285326912895808259nt_int ) > produc1821397396195235155e_term > produc2285326912895808259nt_int ).
thf(func_def_2181,type,
produc6590410687421337004_nat_o: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > produc859450856879609959at_nat > $o ).
thf(func_def_2182,type,
produc7830147906768200158_nat_o: ( produc3313772616054891654at_nat > produc3313772616054891654at_nat > $o ) > produc2714363965264676845at_nat > $o ).
thf(func_def_2183,type,
produc8701595406162815018_nat_o: ( produc366245978424229472at_nat > produc366245978424229472at_nat > $o ) > produc2087150632810049441at_nat > $o ).
thf(func_def_2184,type,
produc1561160019221259564_nat_o: ( produc3843707927480180839at_nat > produc3843707927480180839at_nat > $o ) > produc1906917888121415911at_nat > $o ).
thf(func_def_2185,type,
produc6568152436032731486t_unit: ( product_unit > produc6653097349344004940it_nat > heap_e7401611519738050253t_unit ) > produc8664842809031399944it_nat > heap_e7401611519738050253t_unit ).
thf(func_def_2186,type,
produc5629734405777326591at_nat: ( product_unit > produc6653097349344004940it_nat > nat ) > produc8664842809031399944it_nat > nat ).
thf(func_def_2187,type,
produc875294279294635931it_nat: ( product_unit > produc6653097349344004940it_nat > option3216581401566546698it_nat ) > produc8664842809031399944it_nat > option3216581401566546698it_nat ).
thf(func_def_2188,type,
produc1230459020282432263it_nat: ( product_unit > produc6653097349344004940it_nat > option8956607266484857688it_nat ) > produc8664842809031399944it_nat > option8956607266484857688it_nat ).
thf(func_def_2189,type,
produc5075907435489727646t_unit: ( product_unit > produc6653097349344004940it_nat > product_unit ) > produc8664842809031399944it_nat > product_unit ).
thf(func_def_2190,type,
produc6247414631856714078_nat_o: ( set_nat > set_nat > $o ) > produc7819656566062154093et_nat > $o ).
thf(func_def_2191,type,
produc7110675705651593384_nat_o: ( set_Pr1261947904930325089at_nat > nat > produc366245978424229472at_nat > $o ) > produc366245978424229472at_nat > produc366245978424229472at_nat > $o ).
thf(func_def_2192,type,
produc3595121349294487249_nat_o: ( set_Pr1261947904930325089at_nat > nat > $o ) > produc366245978424229472at_nat > $o ).
thf(func_def_2193,type,
produc1971064617671185730_nat_o: ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > produc3843707927480180839at_nat > $o ) > produc3843707927480180839at_nat > produc3843707927480180839at_nat > $o ).
thf(func_def_2194,type,
produc410239310623530412_nat_o: ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ) > produc3843707927480180839at_nat > $o ).
thf(func_def_2195,type,
produc3999165221712921880at_int: ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > int ) > produc3843707927480180839at_nat > int ).
thf(func_def_2196,type,
produc4001655692221972156at_nat: ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > nat ) > produc3843707927480180839at_nat > nat ).
thf(func_def_2197,type,
produc1491100424724016556_nat_o: ( set_se7855581050983116737at_nat > set_se7855581050983116737at_nat > $o ) > produc7299876168958306407at_nat > $o ).
thf(func_def_2198,type,
produc6230002227079971283nt_int: produc7773217078559923341nt_int > int > option6357759511663192854e_term ).
thf(func_def_2199,type,
produc6972895793295859523_nat_o: produc7360885484439884007_nat_o > nat > $o ).
thf(func_def_2200,type,
produc7822682618958472924nteger: produc1908205239877642774nteger > produc6241069584506657477e_term > option6357759511663192854e_term ).
thf(func_def_2201,type,
produc180342877477747464et_nat: produc2732055786443039994et_nat > produc3658429121746597890et_nat > $o ).
thf(func_def_2202,type,
produc995936583742144908et_nat: produc3925858234332021118et_nat > produc3658429121746597890et_nat > $o ).
thf(func_def_2203,type,
produc6816164490631068361nt_int: produc2285326912895808259nt_int > produc8551481072490612790e_term > option6357759511663192854e_term ).
thf(func_def_2204,type,
product_fst_o_o: product_prod_o_o > $o ).
thf(func_def_2205,type,
product_fst_o_int: product_prod_o_int > $o ).
thf(func_def_2206,type,
product_fst_o_nat: product_prod_o_nat > $o ).
thf(func_def_2207,type,
product_fst_o_num: product_prod_o_num > $o ).
thf(func_def_2208,type,
produc1440270732834495325it_nat: produc2900562427881843919it_nat > $o ).
thf(func_def_2209,type,
produc8508995932063986495nteger: produc8923325533196201883nteger > code_integer ).
thf(func_def_2210,type,
produc8630172574501217550er_int: produc2256096406371053034er_int > code_integer ).
thf(func_def_2211,type,
produc8632663045010267826er_nat: produc6433947425880249742er_nat > code_integer ).
thf(func_def_2212,type,
produc1861665112190112313nteger: produc3346328345660746739nteger > code_integer ).
thf(func_def_2213,type,
produc497848011034438852atural: produc5835291356934675326atural > code_natural ).
thf(func_def_2214,type,
produc491454361838572648it_nat: produc6714399278180371524it_nat > array_a ).
thf(func_def_2215,type,
produc2838810277069100634it_nat: produc6653097349344004940it_nat > heap_e7401611519738050253t_unit ).
thf(func_def_2216,type,
product_fst_int_o: product_prod_int_o > int ).
thf(func_def_2217,type,
produc45500017171379470nteger: produc2963269191615333738nteger > int ).
thf(func_def_2218,type,
product_fst_int_int: product_prod_int_int > int ).
thf(func_def_2219,type,
product_fst_int_nat: product_prod_int_nat > int ).
thf(func_def_2220,type,
product_fst_int_num: product_prod_int_num > int ).
thf(func_def_2221,type,
product_fst_nat_o: product_prod_nat_o > nat ).
thf(func_def_2222,type,
produc8897218493789310642nteger: produc2591615631378489102nteger > nat ).
thf(func_def_2223,type,
product_fst_nat_int: product_prod_nat_int > nat ).
thf(func_def_2224,type,
product_fst_nat_nat: product_prod_nat_nat > nat ).
thf(func_def_2225,type,
product_fst_nat_num: product_prod_nat_num > nat ).
thf(func_def_2226,type,
produc5854401122675660893it_nat: produc3839731585411834681it_nat > nat ).
thf(func_def_2227,type,
product_fst_num_num: product_prod_num_num > num ).
thf(func_def_2228,type,
produc1609452848092598666_nat_o: produc4962441903510821572_nat_o > produc3925858234332021118et_nat ).
thf(func_def_2229,type,
produc1117956856558811858e_term: produc998928222018024388e_term > produc8923325533196201883nteger ).
thf(func_def_2230,type,
produc4353917038236142998atural: produc3981471736659609608atural > produc7822875418678951345atural ).
thf(func_def_2231,type,
produc1537665297809786051atural: produc6756470014200349799atural > produc7822875418678951345atural ).
thf(func_def_2232,type,
produc8046704426453032966_nat_o: produc6907119039986491712_nat_o > produc3658429121746597890et_nat ).
thf(func_def_2233,type,
produc217921407547260247e_term: produc3832618445565238089e_term > product_prod_int_int ).
thf(func_def_2234,type,
produc6335124012134732001e_term: produc1821397396195235155e_term > product_prod_int_int ).
thf(func_def_2235,type,
produc1179527155093393624at_num: produc9082142974458947146at_num > product_prod_nat_nat ).
thf(func_def_2236,type,
produc4530234641508181270it_nat: produc8664842809031399944it_nat > product_unit ).
thf(func_def_2237,type,
produc6011863565407846595at_nat: produc3843707927480180839at_nat > set_Pr1261947904930325089at_nat ).
thf(func_def_2238,type,
produc3162348030201620241nt_int: produc7773217078559923341nt_int > product_prod_int_int ).
thf(func_def_2239,type,
produc6795044007072221829_nat_o: produc7360885484439884007_nat_o > nat > $o ).
thf(func_def_2240,type,
produc7856867400915047194nteger: produc1908205239877642774nteger > produc8923325533196201883nteger ).
thf(func_def_2241,type,
produc5374455773327741254et_nat: produc2732055786443039994et_nat > produc3925858234332021118et_nat ).
thf(func_def_2242,type,
produc4011572625026189258et_nat: produc3925858234332021118et_nat > produc3658429121746597890et_nat ).
thf(func_def_2243,type,
produc7328097813583171335nt_int: produc2285326912895808259nt_int > product_prod_int_int ).
thf(func_def_2244,type,
product_snd_o_o: product_prod_o_o > $o ).
thf(func_def_2245,type,
product_snd_o_int: product_prod_o_int > int ).
thf(func_def_2246,type,
product_snd_o_nat: product_prod_o_nat > nat ).
thf(func_def_2247,type,
product_snd_o_num: product_prod_o_num > num ).
thf(func_def_2248,type,
produc5978051280710547099it_nat: produc2900562427881843919it_nat > produc8664842809031399944it_nat ).
thf(func_def_2249,type,
produc6174133586879617921nteger: produc8923325533196201883nteger > code_integer ).
thf(func_def_2250,type,
produc1514845087660660048er_int: produc2256096406371053034er_int > int ).
thf(func_def_2251,type,
produc1517335558169710324er_nat: produc6433947425880249742er_nat > nat ).
thf(func_def_2252,type,
produc7955729907432593271nteger: produc3346328345660746739nteger > produc8923325533196201883nteger ).
thf(func_def_2253,type,
produc6591912806276919810atural: produc5835291356934675326atural > produc7822875418678951345atural ).
thf(func_def_2254,type,
produc6991280839920081578it_nat: produc6714399278180371524it_nat > produc6653097349344004940it_nat ).
thf(func_def_2255,type,
produc2594868675584459928it_nat: produc6653097349344004940it_nat > nat ).
thf(func_def_2256,type,
product_snd_int_o: product_prod_int_o > $o ).
thf(func_def_2257,type,
produc2153544567185597776nteger: produc2963269191615333738nteger > code_integer ).
thf(func_def_2258,type,
product_snd_int_int: product_prod_int_int > int ).
thf(func_def_2259,type,
product_snd_int_nat: product_prod_int_nat > nat ).
thf(func_def_2260,type,
product_snd_int_num: product_prod_int_num > num ).
thf(func_def_2261,type,
product_snd_nat_o: product_prod_nat_o > $o ).
thf(func_def_2262,type,
produc1781891006948753140nteger: produc2591615631378489102nteger > code_integer ).
thf(func_def_2263,type,
product_snd_nat_int: product_prod_nat_int > int ).
thf(func_def_2264,type,
product_snd_nat_nat: product_prod_nat_nat > nat ).
thf(func_def_2265,type,
product_snd_nat_num: product_prod_nat_num > num ).
thf(func_def_2266,type,
produc8417671938598930591it_nat: produc3839731585411834681it_nat > produc8664842809031399944it_nat ).
thf(func_def_2267,type,
product_snd_num_num: product_prod_num_num > num ).
thf(func_def_2268,type,
produc6803565743942592456_nat_o: produc4962441903510821572_nat_o > produc3658429121746597890et_nat > $o ).
thf(func_def_2269,type,
produc1152141638515386128e_term: produc998928222018024388e_term > produc6241069584506657477e_term > option6357759511663192854e_term ).
thf(func_def_2270,type,
produc7455300194457530885atural: produc6756470014200349799atural > produc7822875418678951345atural ).
thf(func_def_2271,type,
produc1838968430882301508_nat_o: produc6907119039986491712_nat_o > produc3658429121746597890et_nat > $o ).
thf(func_def_2272,type,
produc6373639247523685013e_term: produc3832618445565238089e_term > int > option6357759511663192854e_term ).
thf(func_def_2273,type,
produc6847057335086834975e_term: produc1821397396195235155e_term > produc8551481072490612790e_term > option6357759511663192854e_term ).
thf(func_def_2274,type,
produc8847702614181477910at_num: produc9082142974458947146at_num > num ).
thf(func_def_2275,type,
produc8604850587836428116it_nat: produc8664842809031399944it_nat > produc6653097349344004940it_nat ).
thf(func_def_2276,type,
produc2937545259423399429at_nat: produc3843707927480180839at_nat > set_Pr1261947904930325089at_nat ).
thf(func_def_2277,type,
produc5538323210962509403atural: ( produc7822875418678951345atural > produc5835291356934675326atural ) > ( code_natural > produc7822875418678951345atural > produc5835291356934675326atural ) > produc7822875418678951345atural > produc5835291356934675326atural ).
thf(func_def_2278,type,
product_Abs_unit: $o > product_unit ).
thf(func_def_2279,type,
product_Rep_unit: product_unit > $o ).
thf(func_def_2280,type,
inc_shift: code_natural > code_natural > code_natural ).
thf(func_def_2281,type,
iterat8892046348760725948atural: code_natural > ( code_natural > produc7822875418678951345atural > produc5835291356934675326atural ) > code_natural > produc7822875418678951345atural > produc5835291356934675326atural ).
thf(func_def_2282,type,
log: code_natural > code_natural > code_natural ).
thf(func_def_2283,type,
log_rel: produc7822875418678951345atural > produc7822875418678951345atural > $o ).
thf(func_def_2284,type,
minus_shift: code_natural > code_natural > code_natural > code_natural ).
thf(func_def_2285,type,
next: produc7822875418678951345atural > produc5835291356934675326atural ).
thf(func_def_2286,type,
range: code_natural > produc7822875418678951345atural > produc5835291356934675326atural ).
thf(func_def_2287,type,
split_seed: produc7822875418678951345atural > produc6756470014200349799atural ).
thf(func_def_2288,type,
abs_Rat: product_prod_int_int > rat ).
thf(func_def_2289,type,
fract: int > int > rat ).
thf(func_def_2290,type,
frct: product_prod_int_int > rat ).
thf(func_def_2291,type,
rep_Rat: rat > product_prod_int_int ).
thf(func_def_2292,type,
normalize: product_prod_int_int > product_prod_int_int ).
thf(func_def_2293,type,
of_int: int > rat ).
thf(func_def_2294,type,
pcr_rat: product_prod_int_int > rat > $o ).
thf(func_def_2295,type,
positive: rat > $o ).
thf(func_def_2296,type,
quotient_of: rat > product_prod_int_int ).
thf(func_def_2297,type,
ratrel: product_prod_int_int > product_prod_int_int > $o ).
thf(func_def_2298,type,
ref_change_array_a: ( array_a > array_a ) > ref_array_a > heap_T6362127782908069795rray_a ).
thf(func_def_2299,type,
ref_ch7259622376331601608t_unit: ( product_unit > product_unit ) > ref_Product_unit > heap_T5738788834812785303t_unit ).
thf(func_def_2300,type,
ref_get_array_a: heap_e7401611519738050253t_unit > ref_array_a > array_a ).
thf(func_def_2301,type,
ref_get_Product_unit: heap_e7401611519738050253t_unit > ref_Product_unit > product_unit ).
thf(func_def_2302,type,
ref_lookup_array_a: ref_array_a > heap_T6362127782908069795rray_a ).
thf(func_def_2303,type,
ref_lo7930775386976318366t_unit: ref_Product_unit > heap_T5738788834812785303t_unit ).
thf(func_def_2304,type,
ref_set_array_a: ref_array_a > array_a > heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit ).
thf(func_def_2305,type,
ref_set_Product_unit: ref_Product_unit > product_unit > heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit ).
thf(func_def_2306,type,
refine_Imp_assert: $o > heap_T5738788834812785303t_unit ).
thf(func_def_2307,type,
domain452967906960104687nteger: ( int > code_integer > $o ) > int > $o ).
thf(func_def_2308,type,
domainp_int_int: ( int > int > $o ) > int > $o ).
thf(func_def_2309,type,
domain8128281535334753374atural: ( nat > code_natural > $o ) > nat > $o ).
thf(func_def_2310,type,
domainp_nat_nat: ( nat > nat > $o ) > nat > $o ).
thf(func_def_2311,type,
field_o: set_Product_prod_o_o > set_o ).
thf(func_def_2312,type,
field_Code_integer: set_Pr4811707699266497531nteger > set_Code_integer ).
thf(func_def_2313,type,
field_int: set_Pr958786334691620121nt_int > set_int ).
thf(func_def_2314,type,
field_nat: set_Pr1261947904930325089at_nat > set_nat ).
thf(func_def_2315,type,
field_4706345496283612622at_nat: set_Pr8693737435421807431at_nat > set_Pr1261947904930325089at_nat ).
thf(func_def_2316,type,
field_2862844103579723188at_nat: set_Pr5564308138774400199at_nat > set_Pr4329608150637261639at_nat ).
thf(func_def_2317,type,
field_3145993188331922222at_nat: set_Pr4329608150637261639at_nat > set_se7855581050983116737at_nat ).
thf(func_def_2318,type,
id_on_o: set_o > set_Product_prod_o_o ).
thf(func_def_2319,type,
id_on_int: set_int > set_Pr958786334691620121nt_int ).
thf(func_def_2320,type,
id_on_nat: set_nat > set_Pr1261947904930325089at_nat ).
thf(func_def_2321,type,
id_on_2554058798563519774at_nat: set_Pr1261947904930325089at_nat > set_Pr8693737435421807431at_nat ).
thf(func_def_2322,type,
id_on_7869290023980668164at_nat: set_Pr4329608150637261639at_nat > set_Pr5564308138774400199at_nat ).
thf(func_def_2323,type,
id_on_6713504163309144702at_nat: set_se7855581050983116737at_nat > set_Pr4329608150637261639at_nat ).
thf(func_def_2324,type,
inv_image_nat_nat: set_Pr1261947904930325089at_nat > ( nat > nat ) > set_Pr1261947904930325089at_nat ).
thf(func_def_2325,type,
inv_im6750873321330482877at_nat: set_Pr1261947904930325089at_nat > ( set_Pr1261947904930325089at_nat > nat ) > set_Pr4329608150637261639at_nat ).
thf(func_def_2326,type,
inv_im4437241714082187487at_nat: set_Pr4329608150637261639at_nat > ( nat > set_Pr1261947904930325089at_nat ) > set_Pr1261947904930325089at_nat ).
thf(func_def_2327,type,
inv_im7023619800666061458at_nat: set_Pr4329608150637261639at_nat > ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ) > set_Pr4329608150637261639at_nat ).
thf(func_def_2328,type,
relcom967497705283160040nteger: ( int > int > $o ) > ( int > code_integer > $o ) > int > code_integer > $o ).
thf(func_def_2329,type,
relcom1729257228895983867atural: ( nat > nat > $o ) > ( nat > code_natural > $o ) > nat > code_natural > $o ).
thf(func_def_2330,type,
total_on_o: set_o > set_Product_prod_o_o > $o ).
thf(func_def_2331,type,
total_on_int: set_int > set_Pr958786334691620121nt_int > $o ).
thf(func_def_2332,type,
total_on_nat: set_nat > set_Pr1261947904930325089at_nat > $o ).
thf(func_def_2333,type,
total_3592101749530773125at_nat: set_Pr1261947904930325089at_nat > set_Pr8693737435421807431at_nat > $o ).
thf(func_def_2334,type,
total_1513685709984341995at_nat: set_Pr4329608150637261639at_nat > set_Pr5564308138774400199at_nat > $o ).
thf(func_def_2335,type,
total_7212417256332265445at_nat: set_se7855581050983116737at_nat > set_Pr4329608150637261639at_nat > $o ).
thf(func_def_2336,type,
algebr932160517623751201me_int: int > int > $o ).
thf(func_def_2337,type,
algebr934650988132801477me_nat: nat > nat > $o ).
thf(func_def_2338,type,
divide6298287555418463151nteger: code_integer > code_integer > code_integer ).
thf(func_def_2339,type,
divide5121882707175180666atural: code_natural > code_natural > code_natural ).
thf(func_def_2340,type,
divide_divide_int: int > int > int ).
thf(func_def_2341,type,
divide_divide_nat: nat > nat > nat ).
thf(func_def_2342,type,
divide_divide_rat: rat > rat > rat ).
thf(func_def_2343,type,
dvd_dvd_assn: assn > assn > $o ).
thf(func_def_2344,type,
dvd_dvd_Code_integer: code_integer > code_integer > $o ).
thf(func_def_2345,type,
dvd_dvd_Code_natural: code_natural > code_natural > $o ).
thf(func_def_2346,type,
dvd_dvd_int: int > int > $o ).
thf(func_def_2347,type,
dvd_dvd_nat: nat > nat > $o ).
thf(func_def_2348,type,
dvd_dvd_rat: rat > rat > $o ).
thf(func_def_2349,type,
modulo364778990260209775nteger: code_integer > code_integer > code_integer ).
thf(func_def_2350,type,
modulo8411746178871703098atural: code_natural > code_natural > code_natural ).
thf(func_def_2351,type,
modulo_modulo_int: int > int > int ).
thf(func_def_2352,type,
modulo_modulo_nat: nat > nat > nat ).
thf(func_def_2353,type,
unit_f2748546683901255202or_nat: nat > nat ).
thf(func_def_2354,type,
zero_n356916108424825756nteger: $o > code_integer ).
thf(func_def_2355,type,
zero_n8403883297036319079atural: $o > code_natural ).
thf(func_def_2356,type,
zero_n2684676970156552555ol_int: $o > int ).
thf(func_def_2357,type,
zero_n2687167440665602831ol_nat: $o > nat ).
thf(func_def_2358,type,
zero_n2052037380579107095ol_rat: $o > rat ).
thf(func_def_2359,type,
collec2839945811840875229_nat_o: ( ( int > produc7360885484439884007_nat_o ) > $o ) > set_in2553536192574375378_nat_o ).
thf(func_def_2360,type,
collec8221555239282056977nteger: ( ( int > produc8923325533196201883nteger ) > $o ) > set_in2260935666578096390nteger ).
thf(func_def_2361,type,
collec5961276329923387678atural: ( ( int > produc5835291356934675326atural ) > $o ) > set_in1345054734626228863atural ).
thf(func_def_2362,type,
collec2229320974926845999nt_int: ( ( int > product_prod_int_int ) > $o ) > set_in6154042108061588260nt_int ).
thf(func_def_2363,type,
collec7299664631084759149nteger: ( ( nat > produc8923325533196201883nteger ) > $o ) > set_na3661387095409732706nteger ).
thf(func_def_2364,type,
collec3197714919839585474atural: ( ( nat > produc5835291356934675326atural ) > $o ) > set_na2454399383705037859atural ).
thf(func_def_2365,type,
collec8414850927317488011nt_int: ( ( nat > product_prod_int_int ) > $o ) > set_na7251125088705586816nt_int ).
thf(func_def_2366,type,
collec492036462967229448nteger: ( ( product_unit > produc8923325533196201883nteger ) > $o ) > set_Pr9591959067864425nteger ).
thf(func_def_2367,type,
collec3282430933710331751atural: ( ( product_unit > produc5835291356934675326atural ) > $o ) > set_Pr7322412474522714716atural ).
thf(func_def_2368,type,
collec2513708037538135334nt_int: ( ( product_unit > product_prod_int_int ) > $o ) > set_Pr3770298976803184519nt_int ).
thf(func_def_2369,type,
collect_o: ( $o > $o ) > set_o ).
thf(func_def_2370,type,
collect_Code_integer: ( code_integer > $o ) > set_Code_integer ).
thf(func_def_2371,type,
collect_int: ( int > $o ) > set_int ).
thf(func_def_2372,type,
collect_list_nat: ( list_nat > $o ) > set_list_nat ).
thf(func_def_2373,type,
collect_nat: ( nat > $o ) > set_nat ).
thf(func_def_2374,type,
collect_num: ( num > $o ) > set_num ).
thf(func_def_2375,type,
collect_option_num: ( option_num > $o ) > set_option_num ).
thf(func_def_2376,type,
collec8141831914148684149it_nat: ( option3216581401566546698it_nat > $o ) > set_op3940070208846178154it_nat ).
thf(func_def_2377,type,
collec5742531119322951597it_nat: ( option8956607266484857688it_nat > $o ) > set_op239864471688321678it_nat ).
thf(func_def_2378,type,
collec506566255779805410nt_int: ( produc7773217078559923341nt_int > $o ) > set_Pr1872883991513573699nt_int ).
thf(func_def_2379,type,
collec5110290359514967890_nat_o: ( produc7360885484439884007_nat_o > $o ) > set_Pr7909803484932130503_nat_o ).
thf(func_def_2380,type,
collec6950949345391930603nteger: ( produc1908205239877642774nteger > $o ) > set_Pr1281608226676607948nteger ).
thf(func_def_2381,type,
collec5543584681430388431et_nat: ( produc2732055786443039994et_nat > $o ) > set_Pr8536935166611901872et_nat ).
thf(func_def_2382,type,
collec1402215087704437587et_nat: ( produc3925858234332021118et_nat > $o ) > set_Pr3286484037609594932et_nat ).
thf(func_def_2383,type,
collec1790188477890212312nt_int: ( produc2285326912895808259nt_int > $o ) > set_Pr9222295170931077689nt_int ).
thf(func_def_2384,type,
collec7766031446232907142nteger: ( produc8923325533196201883nteger > $o ) > set_Pr4811707699266497531nteger ).
thf(func_def_2385,type,
collec1991479681304692691atural: ( produc5835291356934675326atural > $o ) > set_Pr2352657477744078772atural ).
thf(func_def_2386,type,
collec213857154873943460nt_int: ( product_prod_int_int > $o ) > set_Pr958786334691620121nt_int ).
thf(func_def_2387,type,
collec1570431334306492044st_nat: ( produc1828647624359046049st_nat > $o ) > set_Pr3451248702717554689st_nat ).
thf(func_def_2388,type,
collec8096645339561496572at_nat: ( produc1540777390238407569at_nat > $o ) > set_Pr7549493975000385137at_nat ).
thf(func_def_2389,type,
collec1907656820224499068st_nat: ( produc4575160907756185873st_nat > $o ) > set_Pr698032948827214833st_nat ).
thf(func_def_2390,type,
collec3392354462482085612at_nat: ( product_prod_nat_nat > $o ) > set_Pr1261947904930325089at_nat ).
thf(func_def_2391,type,
collec7088162979684241874at_nat: ( produc859450856879609959at_nat > $o ) > set_Pr8693737435421807431at_nat ).
thf(func_def_2392,type,
collec2088441199205367000at_nat: ( produc2714363965264676845at_nat > $o ) > set_Pr2072254264782222413at_nat ).
thf(func_def_2393,type,
collec1461227866750739596at_nat: ( produc2087150632810049441at_nat > $o ) > set_Pr5070339090747523585at_nat ).
thf(func_def_2394,type,
collec223960383693904210at_nat: ( produc1906917888121415911at_nat > $o ) > set_Pr5564308138774400199at_nat ).
thf(func_def_2395,type,
collec6662362479098859352et_nat: ( produc7819656566062154093et_nat > $o ) > set_Pr5488025237498180813et_nat ).
thf(func_def_2396,type,
collec6321179662152712658at_nat: ( produc3843707927480180839at_nat > $o ) > set_Pr4329608150637261639at_nat ).
thf(func_def_2397,type,
collec2601550354786890194at_nat: ( produc7299876168958306407at_nat > $o ) > set_Pr1604112560894399303at_nat ).
thf(func_def_2398,type,
collect_rat: ( rat > $o ) > set_rat ).
thf(func_def_2399,type,
collec574505750873337192nteger: ( set_Code_integer > $o ) > set_set_Code_integer ).
thf(func_def_2400,type,
collect_set_int: ( set_int > $o ) > set_set_int ).
thf(func_def_2401,type,
collect_set_nat: ( set_nat > $o ) > set_set_nat ).
thf(func_def_2402,type,
collec5514110066124741708at_nat: ( set_Pr1261947904930325089at_nat > $o ) > set_se7855581050983116737at_nat ).
thf(func_def_2403,type,
collec9208119312383884190nteger: ( set_set_Code_integer > $o ) > set_se8531188866349061887nteger ).
thf(func_def_2404,type,
collect_set_set_int: ( set_set_int > $o ) > set_set_set_int ).
thf(func_def_2405,type,
collec4691811733418234273st_nat: ( set_set_list_nat > $o ) > set_set_set_list_nat ).
thf(func_def_2406,type,
collect_set_set_nat: ( set_set_nat > $o ) > set_set_set_nat ).
thf(func_def_2407,type,
collec6698286964019821996at_nat: ( set_se7855581050983116737at_nat > $o ) > set_se5158245632345848097at_nat ).
thf(func_def_2408,type,
collec4600646233855244344t_unit: ( set_set_Product_unit > $o ) > set_se7118615804146677933t_unit ).
thf(func_def_2409,type,
image_7670822187664137143_int_o: ( ( ( int > option6357759511663192854e_term ) > product_prod_int_int > $o ) > produc7773217078559923341nt_int > $o ) > set_in8474487674441654202_int_o > set_Pr1425283071195816930_int_o ).
thf(func_def_2410,type,
image_5214523798439755767eger_o: ( ( ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o ) > produc1908205239877642774nteger > $o ) > set_Pr8914822823351560561eger_o > set_Pr606876518868980121eger_o ).
thf(func_def_2411,type,
image_1033581555836824229_nat_o: ( ( ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o ) > produc2732055786443039994et_nat > $o ) > set_Pr1457143144315775327_nat_o > set_Pr1230246726286442933_nat_o ).
thf(func_def_2412,type,
image_8189751627993580965_nat_o: ( ( ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o ) > set_Pr8208987589773510107_nat_o > set_Pr8959645425803247153_nat_o ).
thf(func_def_2413,type,
image_7631425643974863415_int_o: ( ( ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o ) > produc2285326912895808259nt_int > $o ) > set_Pr5050529186185961540_int_o > set_Pr6358892174463501804_int_o ).
thf(func_def_2414,type,
image_7708985414016646955nt_int: ( ( int > option6357759511663192854e_term ) > set_Pr1872883991513573699nt_int ) > set_in3461395444621081367e_term > set_se7394616247590735609nt_int ).
thf(func_def_2415,type,
image_7429393840292777309_nat_o: ( ( nat > nat > $o ) > product_prod_nat_nat > $o ) > set_nat_nat_o > set_Pr5582243495563764594_nat_o ).
thf(func_def_2416,type,
image_nat_o_nat_o: ( ( nat > $o ) > nat > $o ) > set_nat_o > set_nat_o ).
thf(func_def_2417,type,
image_2770089787918713472nt_int: ( ( produc7773217078559923341nt_int > $o ) > set_Pr1872883991513573699nt_int ) > set_Pr1425283071195816930_int_o > set_se7394616247590735609nt_int ).
thf(func_def_2418,type,
image_2691561895000378432nteger: ( ( produc1908205239877642774nteger > $o ) > set_Pr1281608226676607948nteger ) > set_Pr606876518868980121eger_o > set_se124295367203800706nteger ).
thf(func_def_2419,type,
image_3321512208570918720et_nat: ( ( produc2732055786443039994et_nat > $o ) > set_Pr8536935166611901872et_nat ) > set_Pr1230246726286442933_nat_o > set_se5120235452707311462et_nat ).
thf(func_def_2420,type,
image_8138495846740763712et_nat: ( ( produc3925858234332021118et_nat > $o ) > set_Pr3286484037609594932et_nat ) > set_Pr8959645425803247153_nat_o > set_se8543413830569400298et_nat ).
thf(func_def_2421,type,
image_7643917626522560896nt_int: ( ( produc2285326912895808259nt_int > $o ) > set_Pr9222295170931077689nt_int ) > set_Pr6358892174463501804_int_o > set_se2364587433798273647nt_int ).
thf(func_def_2422,type,
image_3218922492622835021nteger: ( ( produc6241069584506657477e_term > option6357759511663192854e_term ) > set_Pr1281608226676607948nteger ) > set_Pr7604974323444597168e_term > set_se124295367203800706nteger ).
thf(func_def_2423,type,
image_4127253568139551288et_nat: ( ( produc3658429121746597890et_nat > $o ) > set_Pr8536935166611901872et_nat ) > set_Pr4532377907799695533_nat_o > set_se5120235452707311462et_nat ).
thf(func_def_2424,type,
image_1916054815030244540et_nat: ( ( produc3658429121746597890et_nat > $o ) > set_Pr3286484037609594932et_nat ) > set_Pr4532377907799695533_nat_o > set_se8543413830569400298et_nat ).
thf(func_def_2425,type,
image_5111841350319496619nt_int: ( ( produc8551481072490612790e_term > option6357759511663192854e_term ) > set_Pr9222295170931077689nt_int ) > set_Pr3642885161833720865e_term > set_se2364587433798273647nt_int ).
thf(func_def_2426,type,
image_7124889717316225246at_nat: ( ( product_prod_nat_nat > $o ) > set_Pr1261947904930325089at_nat ) > set_Pr5582243495563764594_nat_o > set_se7855581050983116737at_nat ).
thf(func_def_2427,type,
image_4902389024228248874at_nat: ( ( produc3843707927480180839at_nat > $o ) > set_Pr4329608150637261639at_nat ) > set_Pr7010166363911110284_nat_o > set_se5479201105039950375at_nat ).
thf(func_def_2428,type,
image_6226802281960588479_nat_o: ( ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ) > produc3843707927480180839at_nat > $o ) > set_se9180647916752606350_nat_o > set_Pr7010166363911110284_nat_o ).
thf(func_def_2429,type,
image_o_o: ( $o > $o ) > set_o > set_o ).
thf(func_def_2430,type,
image_o_int: ( $o > int ) > set_o > set_int ).
thf(func_def_2431,type,
image_o_nat: ( $o > nat ) > set_o > set_nat ).
thf(func_def_2432,type,
image_o_option_o: ( $o > option_o ) > set_o > set_option_o ).
thf(func_def_2433,type,
image_o_option_num: ( $o > option_num ) > set_o > set_option_num ).
thf(func_def_2434,type,
image_5849929686412825643it_nat: ( $o > option8956607266484857688it_nat ) > set_o > set_op239864471688321678it_nat ).
thf(func_def_2435,type,
image_4415570909310888640t_unit: ( $o > option_Product_unit ) > set_o > set_op3165557761946182707t_unit ).
thf(func_def_2436,type,
image_966425688229763753et_nat: ( $o > option_set_nat ) > set_o > set_option_set_nat ).
thf(func_def_2437,type,
image_o_Product_unit: ( $o > product_unit ) > set_o > set_Product_unit ).
thf(func_def_2438,type,
image_6491638074533506790nteger: ( $o > set_Code_integer ) > set_o > set_set_Code_integer ).
thf(func_def_2439,type,
image_o_set_int: ( $o > set_int ) > set_o > set_set_int ).
thf(func_def_2440,type,
image_o_set_nat: ( $o > set_nat ) > set_o > set_set_nat ).
thf(func_def_2441,type,
image_2177946750938214461nteger: ( code_integer > code_integer > code_integer ) > set_Code_integer > set_Co726186806682698383nteger ).
thf(func_def_2442,type,
image_4470545334726330049nteger: ( code_integer > code_integer ) > set_Code_integer > set_Code_integer ).
thf(func_def_2443,type,
image_948535463418740880er_int: ( code_integer > int ) > set_Code_integer > set_int ).
thf(func_def_2444,type,
image_951025933927791156er_nat: ( code_integer > nat ) > set_Code_integer > set_nat ).
thf(func_def_2445,type,
image_8960079959263999889nteger: ( code_integer > option_Code_integer ) > set_Code_integer > set_op687863988967635939nteger ).
thf(func_def_2446,type,
image_7182656606676592809t_unit: ( code_integer > product_unit ) > set_Code_integer > set_Product_unit ).
thf(func_def_2447,type,
image_2291390168754192375nteger: ( code_integer > set_Code_integer ) > set_Code_integer > set_set_Code_integer ).
thf(func_def_2448,type,
image_3530315724569248802atural: ( code_natural > set_Pr7564037697178849041atural ) > set_Code_natural > set_se3372686590935047281atural ).
thf(func_def_2449,type,
image_int_o: ( int > $o ) > set_int > set_o ).
thf(func_def_2450,type,
image_1587234942943678608nteger: ( int > code_integer ) > set_int > set_Code_integer ).
thf(func_def_2451,type,
image_int_int: ( int > int ) > set_int > set_int ).
thf(func_def_2452,type,
image_int_nat: ( int > nat ) > set_int > set_nat ).
thf(func_def_2453,type,
image_int_num: ( int > num ) > set_int > set_num ).
thf(func_def_2454,type,
image_int_option_int: ( int > option_int ) > set_int > set_option_int ).
thf(func_def_2455,type,
image_int_option_num: ( int > option_num ) > set_int > set_option_num ).
thf(func_def_2456,type,
image_7905038228067148555it_nat: ( int > option8956607266484857688it_nat ) > set_int > set_op239864471688321678it_nat ).
thf(func_def_2457,type,
image_1735198859854722016t_unit: ( int > option_Product_unit ) > set_int > set_op3165557761946182707t_unit ).
thf(func_def_2458,type,
image_2293489338514188681et_nat: ( int > option_set_nat ) > set_int > set_option_set_nat ).
thf(func_def_2459,type,
image_259982842891744372_nat_o: ( int > produc7360885484439884007_nat_o ) > set_int > set_Pr7909803484932130503_nat_o ).
thf(func_def_2460,type,
image_5194296484788039592nteger: ( int > produc8923325533196201883nteger ) > set_int > set_Pr4811707699266497531nteger ).
thf(func_def_2461,type,
image_6835604608220425009atural: ( int > produc5835291356934675326atural ) > set_int > set_Pr2352657477744078772atural ).
thf(func_def_2462,type,
image_5705468584675977158nt_int: ( int > product_prod_int_int ) > set_int > set_Pr958786334691620121nt_int ).
thf(func_def_2463,type,
image_5846526143423701914t_unit: ( int > product_unit ) > set_int > set_Product_unit ).
thf(func_def_2464,type,
image_75573793354812870nteger: ( int > set_Code_integer ) > set_int > set_set_Code_integer ).
thf(func_def_2465,type,
image_int_set_int: ( int > set_int ) > set_int > set_set_int ).
thf(func_def_2466,type,
image_int_set_nat: ( int > set_nat ) > set_int > set_set_nat ).
thf(func_def_2467,type,
image_2516384619306764229at_nat: ( multis2468970476368604999at_nat > multis2468970476368604999at_nat ) > set_mu2057375006010111271at_nat > set_mu2057375006010111271at_nat ).
thf(func_def_2468,type,
image_nat_o: ( nat > $o ) > set_nat > set_o ).
thf(func_def_2469,type,
image_1215581382706833972nteger: ( nat > code_integer ) > set_nat > set_Code_integer ).
thf(func_def_2470,type,
image_nat_int: ( nat > int ) > set_nat > set_int ).
thf(func_def_2471,type,
image_nat_nat: ( nat > nat ) > set_nat > set_nat ).
thf(func_def_2472,type,
image_nat_num: ( nat > num ) > set_nat > set_num ).
thf(func_def_2473,type,
image_nat_option_nat: ( nat > option_nat ) > set_nat > set_option_nat ).
thf(func_def_2474,type,
image_nat_option_num: ( nat > option_num ) > set_nat > set_option_num ).
thf(func_def_2475,type,
image_5028743614110135983it_nat: ( nat > option8956607266484857688it_nat ) > set_nat > set_op239864471688321678it_nat ).
thf(func_def_2476,type,
image_1497621718204147004t_unit: ( nat > option_Product_unit ) > set_nat > set_op3165557761946182707t_unit ).
thf(func_def_2477,type,
image_1085372205585808685et_nat: ( nat > option_set_nat ) > set_nat > set_option_set_nat ).
thf(func_def_2478,type,
image_4272405876590741764nteger: ( nat > produc8923325533196201883nteger ) > set_nat > set_Pr4811707699266497531nteger ).
thf(func_def_2479,type,
image_8172478253469051731er_int: ( nat > produc2256096406371053034er_int ) > set_nat > set_Pr6496905503482889930er_int ).
thf(func_def_2480,type,
image_3126957236123472631er_nat: ( nat > produc6433947425880249742er_nat ) > set_nat > set_Pr8986988648414616686er_nat ).
thf(func_def_2481,type,
image_4072043198136622805atural: ( nat > produc5835291356934675326atural ) > set_nat > set_Pr2352657477744078772atural ).
thf(func_def_2482,type,
image_8879651038713332435nteger: ( nat > produc2963269191615333738nteger ) > set_nat > set_Pr8415741480598773322nteger ).
thf(func_def_2483,type,
image_2667626500211843362nt_int: ( nat > product_prod_int_int ) > set_nat > set_Pr958786334691620121nt_int ).
thf(func_def_2484,type,
image_6845477519721040070nt_nat: ( nat > product_prod_int_nat ) > set_nat > set_Pr3448869479623346877nt_nat ).
thf(func_def_2485,type,
image_8507997478476487799nteger: ( nat > produc2591615631378489102nteger ) > set_nat > set_Pr2406931829603198446nteger ).
thf(func_def_2486,type,
image_1668272788310788806at_int: ( nat > product_prod_nat_int ) > set_nat > set_Pr7995236796853374141at_int ).
thf(func_def_2487,type,
image_5846123807819985514at_nat: ( nat > product_prod_nat_nat ) > set_nat > set_Pr1261947904930325089at_nat ).
thf(func_def_2488,type,
image_8730104196221521654t_unit: ( nat > product_unit ) > set_nat > set_Product_unit ).
thf(func_def_2489,type,
image_2385391725447763818nteger: ( nat > set_Code_integer ) > set_nat > set_set_Code_integer ).
thf(func_def_2490,type,
image_nat_set_int: ( nat > set_int ) > set_nat > set_set_int ).
thf(func_def_2491,type,
image_nat_set_nat: ( nat > set_nat ) > set_nat > set_set_nat ).
thf(func_def_2492,type,
image_7178329752028323786at_nat: ( nat > set_Pr1261947904930325089at_nat ) > set_nat > set_se7855581050983116737at_nat ).
thf(func_def_2493,type,
image_1087905878993176368at_nat: ( nat > set_Pr4329608150637261639at_nat ) > set_nat > set_se5479201105039950375at_nat ).
thf(func_def_2494,type,
image_8379761247532268670nteger: ( num > code_integer ) > set_num > set_Code_integer ).
thf(func_def_2495,type,
image_num_num: ( num > num ) > set_num > set_num ).
thf(func_def_2496,type,
image_num_option_num: ( num > option_num ) > set_num > set_option_num ).
thf(func_def_2497,type,
image_option_num_num: ( option_num > num ) > set_option_num > set_num ).
thf(func_def_2498,type,
image_5549452628634654015it_nat: ( option3216581401566546698it_nat > produc6714399278180371524it_nat ) > set_op3940070208846178154it_nat > set_Pr5142436192348053284it_nat ).
thf(func_def_2499,type,
image_1237920015125996135it_nat: ( option8956607266484857688it_nat > produc8664842809031399944it_nat ) > set_op239864471688321678it_nat > set_Pr1354866905816374718it_nat ).
thf(func_def_2500,type,
image_4217645046469565813e_term: ( produc7773217078559923341nt_int > int > option6357759511663192854e_term ) > set_Pr1872883991513573699nt_int > set_in3461395444621081367e_term ).
thf(func_def_2501,type,
image_3108077152341812517nt_int: ( produc7773217078559923341nt_int > product_prod_int_int ) > set_Pr1872883991513573699nt_int > set_Pr958786334691620121nt_int ).
thf(func_def_2502,type,
image_4436781500471753239e_term: ( produc1908205239877642774nteger > produc6241069584506657477e_term > option6357759511663192854e_term ) > set_Pr1281608226676607948nteger > set_Pr7604974323444597168e_term ).
thf(func_def_2503,type,
image_3141030398089242942nteger: ( produc1908205239877642774nteger > produc8923325533196201883nteger ) > set_Pr1281608226676607948nteger > set_Pr4811707699266497531nteger ).
thf(func_def_2504,type,
image_2517677226577294348_nat_o: ( produc2732055786443039994et_nat > produc3658429121746597890et_nat > $o ) > set_Pr8536935166611901872et_nat > set_Pr4532377907799695533_nat_o ).
thf(func_def_2505,type,
image_4557310310409863807et_nat: ( produc2732055786443039994et_nat > produc3925858234332021118et_nat ) > set_Pr8536935166611901872et_nat > set_Pr3286484037609594932et_nat ).
thf(func_def_2506,type,
image_6802380912191114376_nat_o: ( produc3925858234332021118et_nat > produc3658429121746597890et_nat > $o ) > set_Pr3286484037609594932et_nat > set_Pr4532377907799695533_nat_o ).
thf(func_def_2507,type,
image_4390311411407041927et_nat: ( produc3925858234332021118et_nat > produc3658429121746597890et_nat ) > set_Pr3286484037609594932et_nat > set_Pr3948176798113811640et_nat ).
thf(func_def_2508,type,
image_8189767104526903093et_nat: ( produc3925858234332021118et_nat > set_Pr8536935166611901872et_nat ) > set_Pr3286484037609594932et_nat > set_se5120235452707311462et_nat ).
thf(func_def_2509,type,
image_142517975987106933e_term: ( produc2285326912895808259nt_int > produc8551481072490612790e_term > option6357759511663192854e_term ) > set_Pr9222295170931077689nt_int > set_Pr3642885161833720865e_term ).
thf(func_def_2510,type,
image_3915291023682402351nt_int: ( produc2285326912895808259nt_int > product_prod_int_int ) > set_Pr9222295170931077689nt_int > set_Pr958786334691620121nt_int ).
thf(func_def_2511,type,
image_7896445794123959606_o_o_o: ( product_prod_o_o > $o ) > set_Product_prod_o_o > set_o ).
thf(func_def_2512,type,
image_5860565421610830622_int_o: ( product_prod_o_int > $o ) > set_Pr8834758594704517033_o_int > set_o ).
thf(func_def_2513,type,
image_7072963285496371238nt_int: ( product_prod_o_int > int ) > set_Pr8834758594704517033_o_int > set_int ).
thf(func_def_2514,type,
image_8105710389281276538_nat_o: ( product_prod_o_nat > $o ) > set_Pr2101469702781467981_o_nat > set_o ).
thf(func_def_2515,type,
image_4888532181312399726at_nat: ( product_prod_o_nat > nat ) > set_Pr2101469702781467981_o_nat > set_nat ).
thf(func_def_2516,type,
image_8863890952250787504_num_o: ( product_prod_o_num > $o ) > set_Pr7040061329075590551_o_num > set_o ).
thf(func_def_2517,type,
image_5849890305759347266_nat_o: ( produc2900562427881843919it_nat > $o ) > set_Pr6777250647868329861it_nat > set_o ).
thf(func_def_2518,type,
image_6316824473203919795nteger: ( produc8923325533196201883nteger > code_integer ) > set_Pr4811707699266497531nteger > set_Code_integer ).
thf(func_def_2519,type,
image_5715966689554962722nteger: ( produc8923325533196201883nteger > set_Pr1281608226676607948nteger ) > set_Pr4811707699266497531nteger > set_se124295367203800706nteger ).
thf(func_def_2520,type,
image_8194678751871465133atural: ( produc5835291356934675326atural > code_natural ) > set_Pr2352657477744078772atural > set_Code_natural ).
thf(func_def_2521,type,
image_3837677093542026988atural: ( produc5835291356934675326atural > produc7822875418678951345atural ) > set_Pr2352657477744078772atural > set_Pr7564037697178849041atural ).
thf(func_def_2522,type,
image_4799632500972785611it_nat: ( produc6714399278180371524it_nat > option3216581401566546698it_nat ) > set_Pr5142436192348053284it_nat > set_op3940070208846178154it_nat ).
thf(func_def_2523,type,
image_15228131989405757et_nat: ( produc3658429121746597890et_nat > set_Pr3286484037609594932et_nat ) > set_Pr3948176798113811640et_nat > set_se8543413830569400298et_nat ).
thf(func_def_2524,type,
image_5561579847027142576nt_o_o: ( product_prod_int_o > $o ) > set_Pr903927857289325719_int_o > set_o ).
thf(func_def_2525,type,
image_90517134139374612_o_int: ( product_prod_int_o > int ) > set_Pr903927857289325719_int_o > set_int ).
thf(func_def_2526,type,
image_5042161079198086560nt_int: ( product_prod_int_int > int ) > set_Pr958786334691620121nt_int > set_int ).
thf(func_def_2527,type,
image_2653370878348428101nt_int: ( product_prod_int_int > product_prod_int_int ) > set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int ).
thf(func_def_2528,type,
image_5963362749323609783nt_int: ( product_prod_int_int > set_Pr1872883991513573699nt_int ) > set_Pr958786334691620121nt_int > set_se7394616247590735609nt_int ).
thf(func_def_2529,type,
image_815654828163180973nt_int: ( product_prod_int_int > set_Pr9222295170931077689nt_int ) > set_Pr958786334691620121nt_int > set_se2364587433798273647nt_int ).
thf(func_def_2530,type,
image_2855239504505064772at_int: ( product_prod_int_nat > int ) > set_Pr3448869479623346877nt_nat > set_int ).
thf(func_def_2531,type,
image_2857729975014115048at_nat: ( product_prod_int_nat > nat ) > set_Pr3448869479623346877nt_nat > set_nat ).
thf(func_def_2532,type,
image_4873634598471238286um_int: ( product_prod_int_num > int ) > set_Pr8387461105917469447nt_num > set_int ).
thf(func_def_2533,type,
image_7478392465989118804at_o_o: ( product_prod_nat_o > $o ) > set_Pr3149072824959771635_nat_o > set_o ).
thf(func_def_2534,type,
image_8629803608462650132_o_nat: ( product_prod_nat_o > nat ) > set_Pr3149072824959771635_nat_o > set_nat ).
thf(func_def_2535,type,
image_4670507518961241924nt_int: ( product_prod_nat_int > int ) > set_Pr7995236796853374141at_int > set_int ).
thf(func_def_2536,type,
image_4672997989470292200nt_nat: ( product_prod_nat_int > nat ) > set_Pr7995236796853374141at_int > set_nat ).
thf(func_def_2537,type,
image_202211252889950930er_int: ( product_prod_nat_int > produc2256096406371053034er_int ) > set_Pr7995236796853374141at_int > set_Pr6496905503482889930er_int ).
thf(func_def_2538,type,
image_9117352539549038149at_int: ( product_prod_nat_int > product_prod_nat_int ) > set_Pr7995236796853374141at_int > set_Pr7995236796853374141at_int ).
thf(func_def_2539,type,
image_2972642778337070200_nat_o: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > set_Pr1261947904930325089at_nat > set_Pr5582243495563764594_nat_o ).
thf(func_def_2540,type,
image_3693632289388996572_nat_o: ( product_prod_nat_nat > $o ) > set_Pr1261947904930325089at_nat > set_o ).
thf(func_def_2541,type,
image_2483585944268220136at_int: ( product_prod_nat_nat > int ) > set_Pr1261947904930325089at_nat > set_int ).
thf(func_def_2542,type,
image_2486076414777270412at_nat: ( product_prod_nat_nat > nat ) > set_Pr1261947904930325089at_nat > set_nat ).
thf(func_def_2543,type,
image_1023191801488348454on_num: ( product_prod_nat_nat > option_num ) > set_Pr1261947904930325089at_nat > set_option_num ).
thf(func_def_2544,type,
image_4198897800814241419at_nat: ( product_prod_nat_nat > option4927543243414619207at_nat ) > set_Pr1261947904930325089at_nat > set_op4508134149509766951at_nat ).
thf(func_def_2545,type,
image_5755308894823448084it_nat: ( product_prod_nat_nat > option8956607266484857688it_nat ) > set_Pr1261947904930325089at_nat > set_op239864471688321678it_nat ).
thf(func_def_2546,type,
image_7548311901266006551t_unit: ( product_prod_nat_nat > option_Product_unit ) > set_Pr1261947904930325089at_nat > set_op3165557761946182707t_unit ).
thf(func_def_2547,type,
image_7383884694314771602et_nat: ( product_prod_nat_nat > option_set_nat ) > set_Pr1261947904930325089at_nat > set_option_set_nat ).
thf(func_def_2548,type,
image_5669961043262023647nteger: ( product_prod_nat_nat > produc8923325533196201883nteger ) > set_Pr1261947904930325089at_nat > set_Pr4811707699266497531nteger ).
thf(func_def_2549,type,
image_6418031315350042158er_int: ( product_prod_nat_nat > produc2256096406371053034er_int ) > set_Pr1261947904930325089at_nat > set_Pr6496905503482889930er_int ).
thf(func_def_2550,type,
image_1372510298004463058er_nat: ( product_prod_nat_nat > produc6433947425880249742er_nat ) > set_Pr1261947904930325089at_nat > set_Pr8986988648414616686er_nat ).
thf(func_def_2551,type,
image_7125204100594322862nteger: ( product_prod_nat_nat > produc2963269191615333738nteger ) > set_Pr1261947904930325089at_nat > set_Pr8415741480598773322nteger ).
thf(func_def_2552,type,
image_1990417195239315453nt_int: ( product_prod_nat_nat > product_prod_int_int ) > set_Pr1261947904930325089at_nat > set_Pr958786334691620121nt_int ).
thf(func_def_2553,type,
image_6168268214748512161nt_nat: ( product_prod_nat_nat > product_prod_int_nat ) > set_Pr1261947904930325089at_nat > set_Pr3448869479623346877nt_nat ).
thf(func_def_2554,type,
image_6753550540357478226nteger: ( product_prod_nat_nat > produc2591615631378489102nteger ) > set_Pr1261947904930325089at_nat > set_Pr2406931829603198446nteger ).
thf(func_def_2555,type,
image_991063483338260897at_int: ( product_prod_nat_nat > product_prod_nat_int ) > set_Pr1261947904930325089at_nat > set_Pr7995236796853374141at_int ).
thf(func_def_2556,type,
image_5168914502847457605at_nat: ( product_prod_nat_nat > product_prod_nat_nat ) > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
thf(func_def_2557,type,
image_4566292076127975857et_nat: ( product_prod_nat_nat > produc7819656566062154093et_nat ) > set_Pr1261947904930325089at_nat > set_Pr5488025237498180813et_nat ).
thf(func_def_2558,type,
image_6169909464789311569t_unit: ( product_prod_nat_nat > product_unit ) > set_Pr1261947904930325089at_nat > set_Product_unit ).
thf(func_def_2559,type,
image_5061345727057949854et_int: ( product_prod_nat_nat > set_int ) > set_Pr1261947904930325089at_nat > set_set_int ).
thf(func_def_2560,type,
image_15824709712370754et_nat: ( product_prod_nat_nat > set_nat ) > set_Pr1261947904930325089at_nat > set_set_nat ).
thf(func_def_2561,type,
image_5423882813909314213at_nat: ( product_prod_nat_nat > set_Pr1261947904930325089at_nat ) > set_Pr1261947904930325089at_nat > set_se7855581050983116737at_nat ).
thf(func_def_2562,type,
image_4504471508743443926um_nat: ( product_prod_nat_num > nat ) > set_Pr6200539531224447659at_num > set_nat ).
thf(func_def_2563,type,
image_5261730836495542980at_nat: ( produc3839731585411834681it_nat > nat ) > set_Pr633603713510679705it_nat > set_nat ).
thf(func_def_2564,type,
image_7255662321850427333et_nat: ( produc4962441903510821572_nat_o > produc2732055786443039994et_nat ) > set_Pr7705059561495379578_nat_o > set_Pr8536935166611901872et_nat ).
thf(func_def_2565,type,
image_8159590125932948193nteger: ( produc998928222018024388e_term > produc1908205239877642774nteger ) > set_Pr1628540301243981434e_term > set_Pr1281608226676607948nteger ).
thf(func_def_2566,type,
image_4501728140019976901et_nat: ( produc6907119039986491712_nat_o > produc3925858234332021118et_nat ) > set_Pr4208978187861016310_nat_o > set_Pr3286484037609594932et_nat ).
thf(func_def_2567,type,
image_1292712855239066845nt_int: ( produc3832618445565238089e_term > produc7773217078559923341nt_int ) > set_Pr9020418513037773311e_term > set_Pr1872883991513573699nt_int ).
thf(func_def_2568,type,
image_1640129903684976221nt_int: ( produc1821397396195235155e_term > produc2285326912895808259nt_int ) > set_Pr7309386651551657097e_term > set_Pr9222295170931077689nt_int ).
thf(func_def_2569,type,
image_7418169580930627696at_nat: ( produc9082142974458947146at_num > product_prod_nat_nat ) > set_Pr7477759153910077568at_num > set_Pr1261947904930325089at_nat ).
thf(func_def_2570,type,
image_3455408117458022631it_nat: ( produc8664842809031399944it_nat > option8956607266484857688it_nat ) > set_Pr1354866905816374718it_nat > set_op239864471688321678it_nat ).
thf(func_def_2571,type,
image_3500134854233901558_nat_o: ( produc3843707927480180839at_nat > $o ) > set_Pr4329608150637261639at_nat > set_o ).
thf(func_def_2572,type,
image_3196035031069704014at_int: ( produc3843707927480180839at_nat > int ) > set_Pr4329608150637261639at_nat > set_int ).
thf(func_def_2573,type,
image_3198525501578754290at_nat: ( produc3843707927480180839at_nat > nat ) > set_Pr4329608150637261639at_nat > set_nat ).
thf(func_def_2574,type,
image_8464016542990802060on_num: ( produc3843707927480180839at_nat > option_num ) > set_Pr4329608150637261639at_nat > set_option_num ).
thf(func_def_2575,type,
image_140351626946063738it_nat: ( produc3843707927480180839at_nat > option8956607266484857688it_nat ) > set_Pr4329608150637261639at_nat > set_op239864471688321678it_nat ).
thf(func_def_2576,type,
image_8585598761158579761t_unit: ( produc3843707927480180839at_nat > option_Product_unit ) > set_Pr4329608150637261639at_nat > set_op3165557761946182707t_unit ).
thf(func_def_2577,type,
image_934083234596377592et_nat: ( produc3843707927480180839at_nat > option_set_nat ) > set_Pr4329608150637261639at_nat > set_option_set_nat ).
thf(func_def_2578,type,
image_7082456443403096939t_unit: ( produc3843707927480180839at_nat > product_unit ) > set_Pr4329608150637261639at_nat > set_Product_unit ).
thf(func_def_2579,type,
image_3160451284896210088et_nat: ( produc3843707927480180839at_nat > set_nat ) > set_Pr4329608150637261639at_nat > set_set_nat ).
thf(func_def_2580,type,
image_7979982168039674559at_nat: ( produc3843707927480180839at_nat > set_Pr1261947904930325089at_nat ) > set_Pr4329608150637261639at_nat > set_se7855581050983116737at_nat ).
thf(func_def_2581,type,
image_3815118110082124069nteger: ( product_unit > code_integer ) > set_Product_unit > set_Code_integer ).
thf(func_def_2582,type,
image_873079544045703924it_int: ( product_unit > int ) > set_Product_unit > set_int ).
thf(func_def_2583,type,
image_875570014554754200it_nat: ( product_unit > nat ) > set_Product_unit > set_nat ).
thf(func_def_2584,type,
image_5965367930834091826on_num: ( product_unit > option_num ) > set_Product_unit > set_option_num ).
thf(func_def_2585,type,
image_5022536681399171104it_nat: ( product_unit > option8956607266484857688it_nat ) > set_Product_unit > set_op239864471688321678it_nat ).
thf(func_def_2586,type,
image_7094380055901048587t_unit: ( product_unit > option_Product_unit ) > set_Product_unit > set_op3165557761946182707t_unit ).
thf(func_def_2587,type,
image_8089323762101378259nteger: ( product_unit > produc8923325533196201883nteger ) > set_Product_unit > set_Pr4811707699266497531nteger ).
thf(func_def_2588,type,
image_220848230107539526atural: ( product_unit > produc5835291356934675326atural ) > set_Product_unit > set_Pr2352657477744078772atural ).
thf(func_def_2589,type,
image_4103462098156874993nt_int: ( product_unit > product_prod_int_int ) > set_Product_unit > set_Pr958786334691620121nt_int ).
thf(func_def_2590,type,
image_7281959405765017145at_nat: ( product_unit > product_prod_nat_nat ) > set_Product_unit > set_Pr1261947904930325089at_nat ).
thf(func_def_2591,type,
image_405062704495631173t_unit: ( product_unit > product_unit ) > set_Product_unit > set_Product_unit ).
thf(func_def_2592,type,
image_rat_rat: ( rat > rat ) > set_rat > set_rat ).
thf(func_def_2593,type,
image_838307146230912995et_nat: ( set_nat > option_set_nat ) > set_set_nat > set_option_set_nat ).
thf(func_def_2594,type,
image_1744818337813142478_int_o: ( set_Pr1872883991513573699nt_int > ( int > option6357759511663192854e_term ) > product_prod_int_int > $o ) > set_se7394616247590735609nt_int > set_in8474487674441654202_int_o ).
thf(func_def_2595,type,
image_3377504002992083726eger_o: ( set_Pr1281608226676607948nteger > ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o ) > set_se124295367203800706nteger > set_Pr8914822823351560561eger_o ).
thf(func_def_2596,type,
image_6856364241397052896_nat_o: ( set_Pr8536935166611901872et_nat > ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o ) > set_se5120235452707311462et_nat > set_Pr1457143144315775327_nat_o ).
thf(func_def_2597,type,
image_1071233342602175200_nat_o: ( set_Pr3286484037609594932et_nat > ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o ) > set_se8543413830569400298et_nat > set_Pr8208987589773510107_nat_o ).
thf(func_def_2598,type,
image_5684251269295653582_int_o: ( set_Pr9222295170931077689nt_int > ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o ) > set_se2364587433798273647nt_int > set_Pr5050529186185961540_int_o ).
thf(func_def_2599,type,
image_6923511907955291850_nat_o: ( set_Pr1261947904930325089at_nat > nat > nat > $o ) > set_se7855581050983116737at_nat > set_nat_nat_o ).
thf(func_def_2600,type,
image_6898982319499645995at_nat: ( set_Pr1261947904930325089at_nat > set_Pr4329608150637261639at_nat ) > set_se7855581050983116737at_nat > set_se5479201105039950375at_nat ).
thf(func_def_2601,type,
image_6595146019508340652_nat_o: ( set_Pr4329608150637261639at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ) > set_se5479201105039950375at_nat > set_se9180647916752606350_nat_o ).
thf(func_def_2602,type,
insert_o: $o > set_o > set_o ).
thf(func_def_2603,type,
insert_Code_integer: code_integer > set_Code_integer > set_Code_integer ).
thf(func_def_2604,type,
insert_int: int > set_int > set_int ).
thf(func_def_2605,type,
insert_list_nat: list_nat > set_list_nat > set_list_nat ).
thf(func_def_2606,type,
insert_nat: nat > set_nat > set_nat ).
thf(func_def_2607,type,
insert_num: num > set_num > set_num ).
thf(func_def_2608,type,
insert_option_o: option_o > set_option_o > set_option_o ).
thf(func_def_2609,type,
insert_option_int: option_int > set_option_int > set_option_int ).
thf(func_def_2610,type,
insert_option_nat: option_nat > set_option_nat > set_option_nat ).
thf(func_def_2611,type,
insert_option_num: option_num > set_option_num > set_option_num ).
thf(func_def_2612,type,
insert7468008629046257882it_nat: option3216581401566546698it_nat > set_op3940070208846178154it_nat > set_op3940070208846178154it_nat ).
thf(func_def_2613,type,
insert6842972033726296599at_nat: option4927543243414619207at_nat > set_op4508134149509766951at_nat > set_op4508134149509766951at_nat ).
thf(func_def_2614,type,
insert2007652293347934600it_nat: option8956607266484857688it_nat > set_op239864471688321678it_nat > set_op239864471688321678it_nat ).
thf(func_def_2615,type,
insert6833468608972679677at_nat: option8699557107911914541at_nat > set_op989438649584373901at_nat > set_op989438649584373901at_nat ).
thf(func_def_2616,type,
insert2866144167138965411t_unit: option_Product_unit > set_op3165557761946182707t_unit > set_op3165557761946182707t_unit ).
thf(func_def_2617,type,
insert6281397740311767046et_nat: option_set_nat > set_option_set_nat > set_option_set_nat ).
thf(func_def_2618,type,
insert750232675644355261nt_int: produc7773217078559923341nt_int > set_Pr1872883991513573699nt_int > set_Pr1872883991513573699nt_int ).
thf(func_def_2619,type,
insert4245756632806152262nteger: produc1908205239877642774nteger > set_Pr1281608226676607948nteger > set_Pr1281608226676607948nteger ).
thf(func_def_2620,type,
insert8297122186708525866et_nat: produc2732055786443039994et_nat > set_Pr8536935166611901872et_nat > set_Pr8536935166611901872et_nat ).
thf(func_def_2621,type,
insert3111075074545270702et_nat: produc3925858234332021118et_nat > set_Pr3286484037609594932et_nat > set_Pr3286484037609594932et_nat ).
thf(func_def_2622,type,
insert984290209421517107nt_int: produc2285326912895808259nt_int > set_Pr9222295170931077689nt_int > set_Pr9222295170931077689nt_int ).
thf(func_def_2623,type,
insert6201435330877294327od_o_o: product_prod_o_o > set_Product_prod_o_o > set_Product_prod_o_o ).
thf(func_def_2624,type,
insert3770363720049103139_o_int: product_prod_o_int > set_Pr8834758594704517033_o_int > set_Pr8834758594704517033_o_int ).
thf(func_def_2625,type,
insert7948214739558299847_o_nat: product_prod_o_nat > set_Pr2101469702781467981_o_nat > set_Pr2101469702781467981_o_nat ).
thf(func_def_2626,type,
insert8656458676507137553_o_num: product_prod_o_num > set_Pr7040061329075590551_o_num > set_Pr7040061329075590551_o_num ).
thf(func_def_2627,type,
insert6915099157023601407it_nat: produc2900562427881843919it_nat > set_Pr6777250647868329861it_nat > set_Pr6777250647868329861it_nat ).
thf(func_def_2628,type,
insert4913895101485356395nteger: produc8923325533196201883nteger > set_Pr4811707699266497531nteger > set_Pr4811707699266497531nteger ).
thf(func_def_2629,type,
insert6505218763252461998atural: produc5835291356934675326atural > set_Pr2352657477744078772atural > set_Pr2352657477744078772atural ).
thf(func_def_2630,type,
insert412334881326329105_int_o: product_prod_int_o > set_Pr903927857289325719_int_o > set_Pr903927857289325719_int_o ).
thf(func_def_2631,type,
insert5033312907999012233nt_int: product_prod_int_int > set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int ).
thf(func_def_2632,type,
insert9211163927508208941nt_nat: product_prod_int_nat > set_Pr3448869479623346877nt_nat > set_Pr3448869479623346877nt_nat ).
thf(func_def_2633,type,
insert696035827602270839nt_num: product_prod_int_num > set_Pr8387461105917469447nt_num > set_Pr8387461105917469447nt_num ).
thf(func_def_2634,type,
insert2233377226759017069_nat_o: product_prod_nat_o > set_Pr3149072824959771635_nat_o > set_Pr3149072824959771635_nat_o ).
thf(func_def_2635,type,
insert4033959196097957677at_int: product_prod_nat_int > set_Pr7995236796853374141at_int > set_Pr7995236796853374141at_int ).
thf(func_def_2636,type,
insert8211810215607154385at_nat: product_prod_nat_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
thf(func_def_2637,type,
insert8920054152555992091at_num: product_prod_nat_num > set_Pr6200539531224447659at_num > set_Pr6200539531224447659at_num ).
thf(func_def_2638,type,
insert2528233410557839625it_nat: produc3839731585411834681it_nat > set_Pr633603713510679705it_nat > set_Pr633603713510679705it_nat ).
thf(func_def_2639,type,
insert2126339615020983374_nat_o: produc652263959640188542_nat_o > set_Pr6558897299634722526_nat_o > set_Pr6558897299634722526_nat_o ).
thf(func_def_2640,type,
insert2790150385885543546at_num: produc9082142974458947146at_num > set_Pr7477759153910077568at_num > set_Pr7477759153910077568at_num ).
thf(func_def_2641,type,
insert5050368324300391991at_nat: produc859450856879609959at_nat > set_Pr8693737435421807431at_nat > set_Pr8693737435421807431at_nat ).
thf(func_def_2642,type,
insert398606708087465655at_nat: produc1906917888121415911at_nat > set_Pr5564308138774400199at_nat > set_Pr5564308138774400199at_nat ).
thf(func_def_2643,type,
insert5940566491043231800it_nat: produc8664842809031399944it_nat > set_Pr1354866905816374718it_nat > set_Pr1354866905816374718it_nat ).
thf(func_def_2644,type,
insert9069300056098147895at_nat: produc3843707927480180839at_nat > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat ).
thf(func_def_2645,type,
insert_Product_unit: product_unit > set_Product_unit > set_Product_unit ).
thf(func_def_2646,type,
insert_rat: rat > set_rat > set_rat ).
thf(func_def_2647,type,
insert9200635055090092081at_nat: set_Pr1261947904930325089at_nat > set_se7855581050983116737at_nat > set_se7855581050983116737at_nat ).
thf(func_def_2648,type,
set_fo1959793692361082170t_assn: ( nat > assn > assn ) > nat > nat > assn > assn ).
thf(func_def_2649,type,
set_fo1084959871951514735nteger: ( nat > code_integer > code_integer ) > nat > nat > code_integer > code_integer ).
thf(func_def_2650,type,
set_fo9131927060563008058atural: ( nat > code_natural > code_natural ) > nat > nat > code_natural > code_natural ).
thf(func_def_2651,type,
set_fo2581907887559384638at_int: ( nat > int > int ) > nat > nat > int > int ).
thf(func_def_2652,type,
set_fo4497565046347964853at_nat: ( nat > multis2468970476368604999at_nat > multis2468970476368604999at_nat ) > nat > nat > multis2468970476368604999at_nat > multis2468970476368604999at_nat ).
thf(func_def_2653,type,
set_fo2584398358068434914at_nat: ( nat > nat > nat ) > nat > nat > nat > nat ).
thf(func_def_2654,type,
set_fo1949268297981939178at_rat: ( nat > rat > rat ) > nat > nat > rat > rat ).
thf(func_def_2655,type,
set_fo3699595496184130361el_nat: produc4471711990508489141at_nat > produc4471711990508489141at_nat > $o ).
thf(func_def_2656,type,
set_or8904488021354931149Most_o: $o > $o > set_o ).
thf(func_def_2657,type,
set_or7959216805967363635t_assn: assn > assn > set_assn ).
thf(func_def_2658,type,
set_or189985376899183464nteger: code_integer > code_integer > set_Code_integer ).
thf(func_def_2659,type,
set_or1266510415728281911st_int: int > int > set_int ).
thf(func_def_2660,type,
set_or1269000886237332187st_nat: nat > nat > set_nat ).
thf(func_def_2661,type,
set_or7049704709247886629st_num: num > num > set_num ).
thf(func_def_2662,type,
set_or5692540242118139586t_unit: product_unit > product_unit > set_Product_unit ).
thf(func_def_2663,type,
set_or633870826150836451st_rat: rat > rat > set_rat ).
thf(func_def_2664,type,
set_or266616469461849773_set_o: set_o > set_o > set_set_o ).
thf(func_def_2665,type,
set_or370866239135849197et_int: set_int > set_int > set_set_int ).
thf(func_def_2666,type,
set_or4548717258645045905et_nat: set_nat > set_nat > set_set_nat ).
thf(func_def_2667,type,
set_or2784603332384507286at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_se7855581050983116737at_nat ).
thf(func_def_2668,type,
set_or4049648398082403068at_nat: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > set_se5479201105039950375at_nat ).
thf(func_def_2669,type,
set_or269330187037242274t_unit: set_Product_unit > set_Product_unit > set_set_Product_unit ).
thf(func_def_2670,type,
set_or7139685690850216873Than_o: $o > $o > set_o ).
thf(func_def_2671,type,
set_or8404916559141939852nteger: code_integer > code_integer > set_Code_integer ).
thf(func_def_2672,type,
set_or4662586982721622107an_int: int > int > set_int ).
thf(func_def_2673,type,
set_or4665077453230672383an_nat: nat > nat > set_nat ).
thf(func_def_2674,type,
set_or1222409239386451017an_num: num > num > set_num ).
thf(func_def_2675,type,
set_or4663484573592751262t_unit: product_unit > product_unit > set_Product_unit ).
thf(func_def_2676,type,
set_or4029947393144176647an_rat: rat > rat > set_rat ).
thf(func_def_2677,type,
set_or3540276404033026485et_nat: set_nat > set_nat > set_set_nat ).
thf(func_def_2678,type,
set_ord_atLeast_nat: nat > set_nat ).
thf(func_def_2679,type,
set_ord_atMost_o: $o > set_o ).
thf(func_def_2680,type,
set_ord_atMost_assn: assn > set_assn ).
thf(func_def_2681,type,
set_or9101266186257409494nteger: code_integer > set_Code_integer ).
thf(func_def_2682,type,
set_ord_atMost_int: int > set_int ).
thf(func_def_2683,type,
set_ord_atMost_nat: nat > set_nat ).
thf(func_def_2684,type,
set_ord_atMost_num: num > set_num ).
thf(func_def_2685,type,
set_or8621721900777396692t_unit: product_unit > set_Product_unit ).
thf(func_def_2686,type,
set_ord_atMost_rat: rat > set_rat ).
thf(func_def_2687,type,
set_ord_atMost_set_o: set_o > set_set_o ).
thf(func_def_2688,type,
set_or58775011639299419et_int: set_int > set_set_int ).
thf(func_def_2689,type,
set_or4236626031148496127et_nat: set_nat > set_set_nat ).
thf(func_def_2690,type,
set_or2762583123196137896at_nat: set_Pr1261947904930325089at_nat > set_se7855581050983116737at_nat ).
thf(func_def_2691,type,
set_or4071486571221009422at_nat: set_Pr4329608150637261639at_nat > set_se5479201105039950375at_nat ).
thf(func_def_2692,type,
set_or2827140217781692084t_unit: set_Product_unit > set_set_Product_unit ).
thf(func_def_2693,type,
set_or2715278749043346189nteger: code_integer > code_integer > set_Code_integer ).
thf(func_def_2694,type,
set_or6656581121297822940st_int: int > int > set_int ).
thf(func_def_2695,type,
set_or6659071591806873216st_nat: nat > nat > set_nat ).
thf(func_def_2696,type,
set_or1716231572884733764Than_o: $o > $o > set_o ).
thf(func_def_2697,type,
set_or4266950643985792945nteger: code_integer > code_integer > set_Code_integer ).
thf(func_def_2698,type,
set_or5832277885323065728an_int: int > int > set_int ).
thf(func_def_2699,type,
set_or5834768355832116004an_nat: nat > nat > set_nat ).
thf(func_def_2700,type,
set_or2392100141987894638an_num: num > num > set_num ).
thf(func_def_2701,type,
set_or5199638295745620268an_rat: rat > rat > set_rat ).
thf(func_def_2702,type,
set_or8625682525731655386et_nat: set_nat > set_nat > set_set_nat ).
thf(func_def_2703,type,
set_or1210151606488870762an_nat: nat > set_nat ).
thf(func_def_2704,type,
set_ord_lessThan_o: $o > set_o ).
thf(func_def_2705,type,
set_or5754767410780653050nteger: code_integer > set_Code_integer ).
thf(func_def_2706,type,
set_ord_lessThan_int: int > set_int ).
thf(func_def_2707,type,
set_ord_lessThan_nat: nat > set_nat ).
thf(func_def_2708,type,
set_ord_lessThan_num: num > set_num ).
thf(func_def_2709,type,
set_or8708608758551125680t_unit: product_unit > set_Product_unit ).
thf(func_def_2710,type,
set_ord_lessThan_rat: rat > set_rat ).
thf(func_def_2711,type,
set_or3489638696441961371_set_o: set_o > set_set_o ).
thf(func_def_2712,type,
set_or5935648273017318783et_int: set_int > set_set_int ).
thf(func_def_2713,type,
set_or890127255671739683et_nat: set_nat > set_set_nat ).
thf(func_def_2714,type,
set_or5243998310507771012at_nat: set_Pr1261947904930325089at_nat > set_se7855581050983116737at_nat ).
thf(func_def_2715,type,
set_or2137699863726836970at_nat: set_Pr4329608150637261639at_nat > set_se5479201105039950375at_nat ).
thf(func_def_2716,type,
set_or3324826255835560848t_unit: set_Product_unit > set_set_Product_unit ).
thf(func_def_2717,type,
char2: $o > $o > $o > $o > $o > $o > $o > $o > char ).
thf(func_def_2718,type,
integer_of_char: char > code_integer ).
thf(func_def_2719,type,
sum_Inl_nat_nat: nat > sum_sum_nat_nat ).
thf(func_def_2720,type,
sum_Inr_nat_nat: nat > sum_sum_nat_nat ).
thf(func_def_2721,type,
syntax5678989248478167196nt_int: int > int > $o ).
thf(func_def_2722,type,
syntax5084084251851430274at_nat: multis2468970476368604999at_nat > multis2468970476368604999at_nat > $o ).
thf(func_def_2723,type,
syntax4682126007086162916at_nat: nat > nat > $o ).
thf(func_def_2724,type,
syntax3730441303064801268at_rat: rat > rat > $o ).
thf(func_def_2725,type,
time_fails_array_a: heap_T6362127782908069795rray_a > heap_e7401611519738050253t_unit > $o ).
thf(func_def_2726,type,
time_f8834461667527620124t_unit: heap_T5738788834812785303t_unit > heap_e7401611519738050253t_unit > $o ).
thf(func_def_2727,type,
time_t490086488869527696rray_a: heap_T6362127782908069795rray_a > heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit ).
thf(func_def_2728,type,
time_t3350536682685678164t_unit: heap_T5738788834812785303t_unit > heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit ).
thf(func_def_2729,type,
time_the_res_array_a: heap_T6362127782908069795rray_a > heap_e7401611519738050253t_unit > array_a ).
thf(func_def_2730,type,
time_t2745601220510131320t_unit: heap_T5738788834812785303t_unit > heap_e7401611519738050253t_unit > product_unit ).
thf(func_def_2731,type,
time_time_array_a: heap_T6362127782908069795rray_a > heap_e7401611519738050253t_unit > nat ).
thf(func_def_2732,type,
time_t4224138285095624986t_unit: heap_T5738788834812785303t_unit > heap_e7401611519738050253t_unit > nat ).
thf(func_def_2733,type,
transi2905341329935302413cl_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
thf(func_def_2734,type,
transi6264000038957366511cl_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
thf(func_def_2735,type,
type_d8366093980585677751er_int: ( code_integer > int ) > ( int > code_integer ) > set_int > $o ).
thf(func_def_2736,type,
type_d4410041424927559462al_nat: ( code_natural > nat ) > ( nat > code_natural ) > set_nat > $o ).
thf(func_def_2737,type,
type_d6188575255521822967unit_o: ( product_unit > $o ) > ( $o > product_unit ) > set_o > $o ).
thf(func_def_2738,type,
accp_list_nat: ( list_nat > list_nat > $o ) > list_nat > $o ).
thf(func_def_2739,type,
accp_nat: ( nat > nat > $o ) > nat > $o ).
thf(func_def_2740,type,
accp_P8928870874622223812nt_int: ( produc7773217078559923341nt_int > produc7773217078559923341nt_int > $o ) > produc7773217078559923341nt_int > $o ).
thf(func_def_2741,type,
accp_P6019419558468335806at_nat: ( produc4471711990508489141at_nat > produc4471711990508489141at_nat > $o ) > produc4471711990508489141at_nat > $o ).
thf(func_def_2742,type,
accp_P1862375125659990705et_nat: ( produc2732055786443039994et_nat > produc2732055786443039994et_nat > $o ) > produc2732055786443039994et_nat > $o ).
thf(func_def_2743,type,
accp_P8126237942716283194atural: ( produc7822875418678951345atural > produc7822875418678951345atural > $o ) > produc7822875418678951345atural > $o ).
thf(func_def_2744,type,
accp_P5801069581201407417et_nat: ( produc3658429121746597890et_nat > produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o ).
thf(func_def_2745,type,
accp_P1096762738010456898nt_int: ( product_prod_int_int > product_prod_int_int > $o ) > product_prod_int_int > $o ).
thf(func_def_2746,type,
accp_P4275260045618599050at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > $o ).
thf(func_def_2747,type,
accp_P8948468358075348838it_nat: ( produc2867611627572283311it_nat > produc2867611627572283311it_nat > $o ) > produc2867611627572283311it_nat > $o ).
thf(func_def_2748,type,
accp_P414730952086964626it_nat: ( produc3911288613690379145it_nat > produc3911288613690379145it_nat > $o ) > produc3911288613690379145it_nat > $o ).
thf(func_def_2749,type,
accp_P3113834385874906142um_num: ( product_prod_num_num > product_prod_num_num > $o ) > product_prod_num_num > $o ).
thf(func_def_2750,type,
finite2416775604798480986nteger: set_Pr7577011563204128103nteger ).
thf(func_def_2751,type,
finite_psubset_int: set_Pr2522554150109002629et_int ).
thf(func_def_2752,type,
finite_psubset_nat: set_Pr5488025237498180813et_nat ).
thf(func_def_2753,type,
finite469560695537375940at_nat: set_Pr4329608150637261639at_nat ).
thf(func_def_2754,type,
less_than: set_Pr1261947904930325089at_nat ).
thf(func_def_2755,type,
lex_pr7234932505866811047nt_int: set_Pr7140365069852192003e_term > set_Pr2560585780119916871nt_int > set_Pr8634505666381077339nt_int ).
thf(func_def_2756,type,
lex_pr3763927252266284464nteger: set_Pr6418322821503574069e_term > set_Pr5052581263052047815nteger > set_Pr1722956316086891245nteger ).
thf(func_def_2757,type,
lex_pr4722427456421979612et_nat: set_Pr2161125870931222855_nat_o > set_Pr7928877670098842301et_nat > set_Pr3444600963470892981et_nat ).
thf(func_def_2758,type,
lex_pr5340572901959109728et_nat: set_Pr2161125870931222855_nat_o > set_Pr719794911490849221et_nat > set_Pr7928877670098842301et_nat ).
thf(func_def_2759,type,
lex_pr4548132154224949661nt_int: set_Pr4675205556198584599e_term > set_Pr2560585780119916871nt_int > set_Pr4708930517165415495nt_int ).
thf(func_def_2760,type,
lex_prod_nat_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr8693737435421807431at_nat ).
thf(func_def_2761,type,
lex_pr4265550801952275104at_nat: set_Pr1261947904930325089at_nat > set_Pr4329608150637261639at_nat > set_Pr2072254264782222413at_nat ).
thf(func_def_2762,type,
lex_pr1951919194703979714at_nat: set_Pr4329608150637261639at_nat > set_Pr1261947904930325089at_nat > set_Pr5070339090747523585at_nat ).
thf(func_def_2763,type,
lex_pr8000699672184251119at_nat: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > set_Pr5564308138774400199at_nat ).
thf(func_def_2764,type,
max_ext_o: set_Product_prod_o_o > set_Pr4577759397028426247_set_o ).
thf(func_def_2765,type,
max_ext_Code_integer: set_Pr4811707699266497531nteger > set_Pr7577011563204128103nteger ).
thf(func_def_2766,type,
max_ext_int: set_Pr958786334691620121nt_int > set_Pr2522554150109002629et_int ).
thf(func_def_2767,type,
max_ext_nat: set_Pr1261947904930325089at_nat > set_Pr5488025237498180813et_nat ).
thf(func_def_2768,type,
max_ex8135407076693332796at_nat: set_Pr8693737435421807431at_nat > set_Pr4329608150637261639at_nat ).
thf(func_def_2769,type,
max_ex8833738776070432290at_nat: set_Pr5564308138774400199at_nat > set_Pr7459493094073627847at_nat ).
thf(func_def_2770,type,
max_ex4535816423174879388at_nat: set_Pr4329608150637261639at_nat > set_Pr1604112560894399303at_nat ).
thf(func_def_2771,type,
max_extp_nat: ( nat > nat > $o ) > set_nat > set_nat > $o ).
thf(func_def_2772,type,
max_ex4864111882549613972at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ).
thf(func_def_2773,type,
max_ex4845989503969680116at_nat: ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ) > set_se7855581050983116737at_nat > set_se7855581050983116737at_nat > $o ).
thf(func_def_2774,type,
measure_nat: ( nat > nat ) > set_Pr1261947904930325089at_nat ).
thf(func_def_2775,type,
measur1827424007717751593at_nat: ( set_Pr1261947904930325089at_nat > nat ) > set_Pr4329608150637261639at_nat ).
thf(func_def_2776,type,
min_ex6901939911449802026at_nat: set_Pr8693737435421807431at_nat > set_Pr4329608150637261639at_nat ).
thf(func_def_2777,type,
mlex_prod_nat: ( nat > nat ) > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
thf(func_def_2778,type,
mlex_p3502713205431853936at_nat: ( set_Pr1261947904930325089at_nat > nat ) > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat ).
thf(func_def_2779,type,
pred_nat: set_Pr1261947904930325089at_nat ).
thf(func_def_2780,type,
same_f6662725367016992042nt_int: ( ( int > option6357759511663192854e_term ) > $o ) > ( ( int > option6357759511663192854e_term ) > set_Pr2560585780119916871nt_int ) > set_Pr8634505666381077339nt_int ).
thf(func_def_2781,type,
same_f8038803414157382067nteger: ( ( produc6241069584506657477e_term > option6357759511663192854e_term ) > $o ) > ( ( produc6241069584506657477e_term > option6357759511663192854e_term ) > set_Pr5052581263052047815nteger ) > set_Pr1722956316086891245nteger ).
thf(func_def_2782,type,
same_f1912051055550046943et_nat: ( ( produc3658429121746597890et_nat > $o ) > $o ) > ( ( produc3658429121746597890et_nat > $o ) > set_Pr7928877670098842301et_nat ) > set_Pr3444600963470892981et_nat ).
thf(func_def_2783,type,
same_f7251492184213700963et_nat: ( ( produc3658429121746597890et_nat > $o ) > $o ) > ( ( produc3658429121746597890et_nat > $o ) > set_Pr719794911490849221et_nat ) > set_Pr7928877670098842301et_nat ).
thf(func_def_2784,type,
same_f5472592420709775776nt_int: ( ( produc8551481072490612790e_term > option6357759511663192854e_term ) > $o ) > ( ( produc8551481072490612790e_term > option6357759511663192854e_term ) > set_Pr2560585780119916871nt_int ) > set_Pr4708930517165415495nt_int ).
thf(func_def_2785,type,
same_fst_nat_nat: ( nat > $o ) > ( nat > set_Pr1261947904930325089at_nat ) > set_Pr8693737435421807431at_nat ).
thf(func_def_2786,type,
member2790140394383616496nteger: ( code_integer > code_integer ) > set_Co726186806682698383nteger > $o ).
thf(func_def_2787,type,
member8845023287901829240e_term: ( int > option6357759511663192854e_term ) > set_in3461395444621081367e_term > $o ).
thf(func_def_2788,type,
member7306185171444233115_nat_o: ( int > produc7360885484439884007_nat_o ) > set_in2553536192574375378_nat_o > $o ).
thf(func_def_2789,type,
member2248416676132969167nteger: ( int > produc8923325533196201883nteger ) > set_in2260935666578096390nteger > $o ).
thf(func_def_2790,type,
member3292482584629245920atural: ( int > produc5835291356934675326atural ) > set_in1345054734626228863atural > $o ).
thf(func_def_2791,type,
member254662033361028077nt_int: ( int > product_prod_int_int ) > set_in6154042108061588260nt_int > $o ).
thf(func_def_2792,type,
member1326526067935671339nteger: ( nat > produc8923325533196201883nteger ) > set_na3661387095409732706nteger > $o ).
thf(func_def_2793,type,
member528921174545443716atural: ( nat > produc5835291356934675326atural ) > set_na2454399383705037859atural > $o ).
thf(func_def_2794,type,
member6440191985751670089nt_int: ( nat > product_prod_int_int ) > set_na7251125088705586816nt_int > $o ).
thf(func_def_2795,type,
member4242434998011752849e_term: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > set_Pr7604974323444597168e_term > $o ).
thf(func_def_2796,type,
member6576561426505652726_nat_o: ( produc3658429121746597890et_nat > $o ) > set_Pr4532377907799695533_nat_o > $o ).
thf(func_def_2797,type,
member3222579708246209666e_term: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > set_Pr3642885161833720865e_term > $o ).
thf(func_def_2798,type,
member2006080708140975699_nat_o: ( product_prod_nat_nat > $o ) > set_Pr5582243495563764594_nat_o > $o ).
thf(func_def_2799,type,
member2837767709637065162nteger: ( product_unit > produc8923325533196201883nteger ) > set_Pr9591959067864425nteger > $o ).
thf(func_def_2800,type,
member4946248492122881829atural: ( product_unit > produc5835291356934675326atural ) > set_Pr7322412474522714716atural > $o ).
thf(func_def_2801,type,
member5541948317052402408nt_int: ( product_unit > product_prod_int_int ) > set_Pr3770298976803184519nt_int > $o ).
thf(func_def_2802,type,
member_o: $o > set_o > $o ).
thf(func_def_2803,type,
member_Code_integer: code_integer > set_Code_integer > $o ).
thf(func_def_2804,type,
member_Code_natural: code_natural > set_Code_natural > $o ).
thf(func_def_2805,type,
member_int: int > set_int > $o ).
thf(func_def_2806,type,
member_list_nat: list_nat > set_list_nat > $o ).
thf(func_def_2807,type,
member_nat: nat > set_nat > $o ).
thf(func_def_2808,type,
member_num: num > set_num > $o ).
thf(func_def_2809,type,
member_option_o: option_o > set_option_o > $o ).
thf(func_def_2810,type,
member_option_int: option_int > set_option_int > $o ).
thf(func_def_2811,type,
member_option_nat: option_nat > set_option_nat > $o ).
thf(func_def_2812,type,
member_option_num: option_num > set_option_num > $o ).
thf(func_def_2813,type,
member3517700364412436275it_nat: option3216581401566546698it_nat > set_op3940070208846178154it_nat > $o ).
thf(func_def_2814,type,
member3954567711264315760at_nat: option4927543243414619207at_nat > set_op4508134149509766951at_nat > $o ).
thf(func_def_2815,type,
member5596548051065438575it_nat: option8956607266484857688it_nat > set_op239864471688321678it_nat > $o ).
thf(func_def_2816,type,
member4288423094740844502at_nat: option8699557107911914541at_nat > set_op989438649584373901at_nat > $o ).
thf(func_def_2817,type,
member1378114217278917244t_unit: option_Product_unit > set_op3165557761946182707t_unit > $o ).
thf(func_def_2818,type,
member8989860449721436141et_nat: option_set_nat > set_option_set_nat > $o ).
thf(func_def_2819,type,
member6538663773838357324e_term: produc1945540942535730339e_term > set_Pr7140365069852192003e_term > $o ).
thf(func_def_2820,type,
member7034335876925520548nt_int: produc7773217078559923341nt_int > set_Pr1872883991513573699nt_int > $o ).
thf(func_def_2821,type,
member6786453453753086846e_term: produc8187290932660736981e_term > set_Pr6418322821503574069e_term > $o ).
thf(func_def_2822,type,
member4164122664394876845nteger: produc1908205239877642774nteger > set_Pr1281608226676607948nteger > $o ).
thf(func_def_2823,type,
member8781333585448626064_nat_o: produc4928098042776334183_nat_o > set_Pr2161125870931222855_nat_o > $o ).
thf(func_def_2824,type,
member6124377750444531601et_nat: produc2732055786443039994et_nat > set_Pr8536935166611901872et_nat > $o ).
thf(func_def_2825,type,
member1996754912294343701et_nat: produc3925858234332021118et_nat > set_Pr3286484037609594932et_nat > $o ).
thf(func_def_2826,type,
member8796044733138646368e_term: produc4499399687821757879e_term > set_Pr4675205556198584599e_term > $o ).
thf(func_def_2827,type,
member7618704894036264090nt_int: produc2285326912895808259nt_int > set_Pr9222295170931077689nt_int > $o ).
thf(func_def_2828,type,
member7466972457876170832od_o_o: product_prod_o_o > set_Product_prod_o_o > $o ).
thf(func_def_2829,type,
member7847949116333733898_o_int: product_prod_o_int > set_Pr8834758594704517033_o_int > $o ).
thf(func_def_2830,type,
member2802428098988154798_o_nat: product_prod_o_nat > set_Pr2101469702781467981_o_nat > $o ).
thf(func_def_2831,type,
member157494554546826820nteger: produc8923325533196201883nteger > set_Pr4811707699266497531nteger > $o ).
thf(func_def_2832,type,
member8280416476884352090atural: produc7822875418678951345atural > set_Pr7564037697178849041atural > $o ).
thf(func_def_2833,type,
member2108296798382401941atural: produc5835291356934675326atural > set_Pr2352657477744078772atural > $o ).
thf(func_def_2834,type,
member6260224972018164377et_nat: produc3658429121746597890et_nat > set_Pr3948176798113811640et_nat > $o ).
thf(func_def_2835,type,
member4489920277610959864_int_o: product_prod_int_o > set_Pr903927857289325719_int_o > $o ).
thf(func_def_2836,type,
member5262025264175285858nt_int: product_prod_int_int > set_Pr958786334691620121nt_int > $o ).
thf(func_def_2837,type,
member216504246829706758nt_nat: product_prod_int_nat > set_Pr3448869479623346877nt_nat > $o ).
thf(func_def_2838,type,
member6689249552917799696at_nat: produc4166570645942440679at_nat > set_Pr8551490117392284871at_nat > $o ).
thf(func_def_2839,type,
member6310962623043647828_nat_o: product_prod_nat_o > set_Pr3149072824959771635_nat_o > $o ).
thf(func_def_2840,type,
member4262671552274231302at_int: product_prod_nat_int > set_Pr7995236796853374141at_int > $o ).
thf(func_def_2841,type,
member8440522571783428010at_nat: product_prod_nat_nat > set_Pr1261947904930325089at_nat > $o ).
thf(func_def_2842,type,
member4085533954029916580nt_int: produc2501202720802129403nt_int > set_Pr8634505666381077339nt_int > $o ).
thf(func_def_2843,type,
member2446009503569356342nteger: produc824974754969098637nteger > set_Pr1722956316086891245nteger > $o ).
thf(func_def_2844,type,
member6341495586645257982et_nat: produc5657529347773406293et_nat > set_Pr3444600963470892981et_nat > $o ).
thf(func_def_2845,type,
member4763271486408492550et_nat: produc6830853553727218525et_nat > set_Pr7928877670098842301et_nat > $o ).
thf(func_def_2846,type,
member6582457606847315088nt_int: produc2432570611225516007nt_int > set_Pr4708930517165415495nt_int > $o ).
thf(func_def_2847,type,
member335077259223437328nteger: produc3334582477557816039nteger > set_Pr5052581263052047815nteger > $o ).
thf(func_def_2848,type,
member6099555550032318734et_nat: produc8111630337999740517et_nat > set_Pr719794911490849221et_nat > $o ).
thf(func_def_2849,type,
member8566619992076573584nt_int: produc1219242969750017639nt_int > set_Pr2560585780119916871nt_int > $o ).
thf(func_def_2850,type,
member2200362271989506215_nat_o: produc652263959640188542_nat_o > set_Pr6558897299634722526_nat_o > $o ).
thf(func_def_2851,type,
member8206827879206165904at_nat: produc859450856879609959at_nat > set_Pr8693737435421807431at_nat > $o ).
thf(func_def_2852,type,
member4107301959146914710at_nat: produc2714363965264676845at_nat > set_Pr2072254264782222413at_nat > $o ).
thf(func_def_2853,type,
member3480088626692287306at_nat: produc2087150632810049441at_nat > set_Pr5070339090747523585at_nat > $o ).
thf(func_def_2854,type,
member6009668390874684176at_nat: produc1906917888121415911at_nat > set_Pr5564308138774400199at_nat > $o ).
thf(func_def_2855,type,
member3421417852355157663it_nat: produc8664842809031399944it_nat > set_Pr1354866905816374718it_nat > $o ).
thf(func_def_2856,type,
member9116954335612470352_set_o: produc7369051934464679207_set_o > set_Pr4577759397028426247_set_o > $o ).
thf(func_def_2857,type,
member4307123515891402160nteger: produc6491284506569428743nteger > set_Pr7577011563204128103nteger > $o ).
thf(func_def_2858,type,
member2572552093476627150et_int: produc2115011035271226405et_int > set_Pr2522554150109002629et_int > $o ).
thf(func_def_2859,type,
member8277197624267554838et_nat: produc7819656566062154093et_nat > set_Pr5488025237498180813et_nat > $o ).
thf(func_def_2860,type,
member444158400953824016od_o_o: produc2934264451710624999od_o_o > set_Pr1932065953672099015od_o_o > $o ).
thf(func_def_2861,type,
member4095101504841534314at_nat: produc732395585841259969at_nat > set_Pr457366540195662369at_nat > $o ).
thf(func_def_2862,type,
member8757157785044589968at_nat: produc3843707927480180839at_nat > set_Pr4329608150637261639at_nat > $o ).
thf(func_def_2863,type,
member1466754251312161552at_nat: produc1319942482725812455at_nat > set_Pr7459493094073627847at_nat > $o ).
thf(func_def_2864,type,
member4300370950623927696at_nat: produc7299876168958306407at_nat > set_Pr1604112560894399303at_nat > $o ).
thf(func_def_2865,type,
member_Product_unit: product_unit > set_Product_unit > $o ).
thf(func_def_2866,type,
member_rat: rat > set_rat > $o ).
thf(func_def_2867,type,
member_set_o: set_o > set_set_o > $o ).
thf(func_def_2868,type,
member1834298987299537450nteger: set_Code_integer > set_set_Code_integer > $o ).
thf(func_def_2869,type,
member_set_int: set_int > set_set_int > $o ).
thf(func_def_2870,type,
member_set_list_nat: set_list_nat > set_set_list_nat > $o ).
thf(func_def_2871,type,
member_set_nat: set_nat > set_set_nat > $o ).
thf(func_def_2872,type,
member2643936169264416010at_nat: set_Pr1261947904930325089at_nat > set_se7855581050983116737at_nat > $o ).
thf(func_def_2873,type,
member5877623283571906838t_unit: set_Product_unit > set_set_Product_unit > $o ).
thf(func_def_2874,type,
h: heap_e7401611519738050253t_unit ).
thf(func_def_2875,type,
xs: list_a ).
thf(func_def_2894,type,
sP0: ( option3216581401566546698it_nat > option8956607266484857688it_nat > $o ) > option3216581401566546698it_nat > option8956607266484857688it_nat > $o ).
thf(func_def_2895,type,
sP1: ( option3216581401566546698it_nat > option8956607266484857688it_nat > $o ) > option3216581401566546698it_nat > option8956607266484857688it_nat > $o ).
thf(func_def_2896,type,
sP2: ( option_num > option3216581401566546698it_nat > $o ) > option3216581401566546698it_nat > option_num > $o ).
thf(func_def_2897,type,
sP3: ( option_num > option3216581401566546698it_nat > $o ) > option_num > option3216581401566546698it_nat > $o ).
thf(func_def_2898,type,
sP4: ( option8956607266484857688it_nat > option3216581401566546698it_nat > $o ) > option3216581401566546698it_nat > option8956607266484857688it_nat > $o ).
thf(func_def_2899,type,
sP5: ( option8956607266484857688it_nat > option3216581401566546698it_nat > $o ) > option8956607266484857688it_nat > option3216581401566546698it_nat > $o ).
thf(func_def_2900,type,
sP6: ( option3216581401566546698it_nat > option3216581401566546698it_nat > $o ) > option3216581401566546698it_nat > option3216581401566546698it_nat > $o ).
thf(func_def_2901,type,
sP7: ( option3216581401566546698it_nat > option3216581401566546698it_nat > $o ) > option3216581401566546698it_nat > option3216581401566546698it_nat > $o ).
thf(func_def_2902,type,
sP8: ( option3216581401566546698it_nat > option_num > $o ) > option3216581401566546698it_nat > option_num > $o ).
thf(func_def_2903,type,
sP9: ( option3216581401566546698it_nat > option_num > $o ) > option3216581401566546698it_nat > option_num > $o ).
thf(func_def_2904,type,
sK10: ( option3216581401566546698it_nat > option8956607266484857688it_nat > $o ) > option3216581401566546698it_nat > option8956607266484857688it_nat > produc6714399278180371524it_nat ).
thf(func_def_2905,type,
sK11: ( option3216581401566546698it_nat > option8956607266484857688it_nat > $o ) > option3216581401566546698it_nat > option8956607266484857688it_nat > produc8664842809031399944it_nat ).
thf(func_def_2906,type,
sK12: heap_T6362127782908069795rray_a > heap_e7401611519738050253t_unit > produc6653097349344004940it_nat ).
thf(func_def_2907,type,
sK13: heap_T6362127782908069795rray_a > heap_e7401611519738050253t_unit > array_a ).
thf(func_def_2908,type,
sK14: ( option_num > option3216581401566546698it_nat > $o ) > option3216581401566546698it_nat > option_num > produc6714399278180371524it_nat ).
thf(func_def_2909,type,
sK15: ( option_num > option3216581401566546698it_nat > $o ) > option3216581401566546698it_nat > option_num > num ).
thf(func_def_2910,type,
sK16: heap_T6362127782908069795rray_a > heap_e7401611519738050253t_unit > produc6653097349344004940it_nat ).
thf(func_def_2911,type,
sK17: heap_T6362127782908069795rray_a > heap_e7401611519738050253t_unit > array_a ).
thf(func_def_2912,type,
sK18: ( option8956607266484857688it_nat > option3216581401566546698it_nat > $o ) > option3216581401566546698it_nat > option8956607266484857688it_nat > produc6714399278180371524it_nat ).
thf(func_def_2913,type,
sK19: ( option8956607266484857688it_nat > option3216581401566546698it_nat > $o ) > option3216581401566546698it_nat > option8956607266484857688it_nat > produc8664842809031399944it_nat ).
thf(func_def_2914,type,
sK20: option3216581401566546698it_nat > produc6714399278180371524it_nat ).
thf(func_def_2915,type,
sK21: option3216581401566546698it_nat > produc6714399278180371524it_nat ).
thf(func_def_2916,type,
sK22: heap_T6362127782908069795rray_a > heap_T6362127782908069795rray_a > heap_e7401611519738050253t_unit ).
thf(func_def_2917,type,
sK23: ( option3216581401566546698it_nat > option3216581401566546698it_nat > $o ) > option3216581401566546698it_nat > option3216581401566546698it_nat > produc6714399278180371524it_nat ).
thf(func_def_2918,type,
sK24: ( option3216581401566546698it_nat > option3216581401566546698it_nat > $o ) > option3216581401566546698it_nat > option3216581401566546698it_nat > produc6714399278180371524it_nat ).
thf(func_def_2919,type,
sK25: ( option3216581401566546698it_nat > option_num > $o ) > option3216581401566546698it_nat > option_num > num ).
thf(func_def_2920,type,
sK26: ( option3216581401566546698it_nat > option_num > $o ) > option3216581401566546698it_nat > option_num > produc6714399278180371524it_nat ).
thf(func_def_2921,type,
sK27: option3216581401566546698it_nat > produc6714399278180371524it_nat ).
thf(f18102,plain,
$false,
inference(equality_resolution,[status(thm)],[f18075]) ).
thf(f18075,plain,
! [X0: heap_e7401611519738050253t_unit,X1: list_a] :
( ( heap_T5591663578999710211rray_a @ ( array_of_list_a @ xs ) @ h )
!= ( heap_T5591663578999710211rray_a @ ( array_of_list_a @ X1 ) @ X0 ) ),
inference(equality_proxy_clausification,[status(thm)],[f18074]) ).
thf(f18074,plain,
! [X0: heap_e7401611519738050253t_unit,X1: list_a] :
( ( ( heap_T5591663578999710211rray_a @ ( array_of_list_a @ X1 ) @ X0 )
= ( heap_T5591663578999710211rray_a @ ( array_of_list_a @ xs ) @ h ) )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f18073]) ).
thf(f18073,plain,
! [X0: heap_e7401611519738050253t_unit,X1: list_a] :
( $true
= ( ( heap_T5591663578999710211rray_a @ ( array_of_list_a @ X1 ) @ X0 )
!= ( heap_T5591663578999710211rray_a @ ( array_of_list_a @ xs ) @ h ) ) ),
inference(beta_eta_normalization,[status(thm)],[f18058]) ).
thf(f18058,plain,
! [X0: heap_e7401611519738050253t_unit,X1: list_a] :
( $true
= ( ^ [Y0: heap_T6362127782908069795rray_a,Y1: heap_e7401611519738050253t_unit] :
( ( heap_T5591663578999710211rray_a @ Y0 @ Y1 )
!= ( heap_T5591663578999710211rray_a @ ( array_of_list_a @ xs ) @ h ) )
@ ( array_of_list_a @ X1 )
@ X0 ) ),
inference(definition_unfolding,[status(thm)],[f18020,f18051]) ).
thf(f18051,plain,
( heap_T6932021131025641745rray_a
= ( ^ [Y0: heap_T6362127782908069795rray_a,Y1: heap_e7401611519738050253t_unit] :
( ( heap_T5591663578999710211rray_a @ Y0 @ Y1 )
!= ( heap_T5591663578999710211rray_a @ ( array_of_list_a @ xs ) @ h ) ) ) ),
inference(definition_unfolding,[status(thm)],[f18035,f18008]) ).
thf(f18008,plain,
( none_P2587165478634041381it_nat
= ( heap_T5591663578999710211rray_a @ ( array_of_list_a @ xs ) @ h ) ),
inference(cnf_transformation,[status(thm)],[f17922]) ).
thf(f17922,plain,
( none_P2587165478634041381it_nat
= ( heap_T5591663578999710211rray_a @ ( array_of_list_a @ xs ) @ h ) ),
inference(flattening,[status(thm)],[f8004]) ).
thf(f8004,negated_conjecture,
~ ( ( none_P2587165478634041381it_nat
!= ( heap_T5591663578999710211rray_a @ ( array_of_list_a @ xs ) @ h ) ) ),
inference(negated_conjecture,[status(cth)],[f8003]) ).
thf(f8003,conjecture,
( none_P2587165478634041381it_nat
!= ( heap_T5591663578999710211rray_a @ ( array_of_list_a @ xs ) @ h ) ),
file('/export/starexec/sandbox2/tmp/tmp.rG2Hh59idJ/DTF2THF_32404.p',conj_0) ).
thf(f18035,plain,
( heap_T6932021131025641745rray_a
= ( ^ [Y0: heap_T6362127782908069795rray_a,Y1: heap_e7401611519738050253t_unit] :
( ( heap_T5591663578999710211rray_a @ Y0 @ Y1 )
!= none_P2587165478634041381it_nat ) ) ),
inference(cnf_transformation,[status(thm)],[f12854]) ).
thf(f12854,plain,
( heap_T6932021131025641745rray_a
= ( ^ [Y0: heap_T6362127782908069795rray_a,Y1: heap_e7401611519738050253t_unit] :
( ( heap_T5591663578999710211rray_a @ Y0 @ Y1 )
!= none_P2587165478634041381it_nat ) ) ),
inference(fool_elimination,[status(thm)],[f12853]) ).
thf(f12853,plain,
( heap_T6932021131025641745rray_a
= ( ^ [X0: heap_T6362127782908069795rray_a,X1: heap_e7401611519738050253t_unit] :
( ( heap_T5591663578999710211rray_a @ X0 @ X1 )
!= none_P2587165478634041381it_nat ) ) ),
inference(rectify,[status(thm)],[f13]) ).
thf(f13,axiom,
( heap_T6932021131025641745rray_a
= ( ^ [X10: heap_T6362127782908069795rray_a,X1: heap_e7401611519738050253t_unit] :
( none_P2587165478634041381it_nat
!= ( heap_T5591663578999710211rray_a @ X10 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.rG2Hh59idJ/DTF2THF_32404.p',fact_12_success__def) ).
thf(f18020,plain,
! [X0: heap_e7401611519738050253t_unit,X1: list_a] :
( $true
= ( heap_T6932021131025641745rray_a @ ( array_of_list_a @ X1 ) @ X0 ) ),
inference(cnf_transformation,[status(thm)],[f13216]) ).
thf(f13216,plain,
! [X0: heap_e7401611519738050253t_unit,X1: list_a] :
( $true
= ( heap_T6932021131025641745rray_a @ ( array_of_list_a @ X1 ) @ X0 ) ),
inference(fool_elimination,[status(thm)],[f13215]) ).
thf(f13215,plain,
! [X0: heap_e7401611519738050253t_unit,X1: list_a] : ( heap_T6932021131025641745rray_a @ ( array_of_list_a @ X1 ) @ X0 ),
inference(rectify,[status(thm)],[f46]) ).
thf(f46,axiom,
! [X8: heap_e7401611519738050253t_unit,X17: list_a] : ( heap_T6932021131025641745rray_a @ ( array_of_list_a @ X17 ) @ X8 ),
file('/export/starexec/sandbox2/tmp/tmp.rG2Hh59idJ/DTF2THF_32404.p',fact_45_success__of__listI) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP216^3 : TPTP v9.2.1. Bugfixed v9.2.1.
% 0.00/0.14 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.21/0.37 % Computer : n007.cluster.edu
% 0.21/0.37 % Model : x86_64 x86_64
% 0.21/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.37 % Memory : 8042.1875MB
% 0.21/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.21/0.37 % CPULimit : 300
% 0.21/0.37 % WCLimit : 300
% 0.21/0.38 % DateTime : Thu Feb 26 05:09:38 EST 2026
% 0.21/0.38 % CPUTime :
% 0.21/0.38 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.29/0.48 ---- Original DTF file ---
% 0.29/0.48 thf(spec,logic,$$dhol).
% 0.29/0.48 %------------------------------------------------------------------------------
% 0.29/0.48 % File : ITP216^3 : TPTP v9.2.1. Bugfixed v9.2.1.
% 0.29/0.48 % Domain : Interactive Theorem Proving
% 0.29/0.48 % Problem : Sledgehammer problem Time_Reasoning 00074_002979
% 0.29/0.48 % Version : [Des22] axioms.
% 0.29/0.48 % English :
% 0.29/0.48
% 0.29/0.48 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.29/0.48 % : [Des22] Desharnais (2022), Email to Geoff Sutcliffe
% 0.29/0.48 % Source : [Des22]
% 0.29/0.48 % Names : 0029_Time_Reasoning_00074_002979 [Des22]
% 0.29/0.48
% 0.29/0.48 % Status : Theorem
% 0.29/0.48 % Rating : ? v9.2.1
% 0.29/0.48 % Syntax : Number of formulae : 10879 (4924 unt;2876 typ; 0 def)
% 0.29/0.48 % Number of atoms : 20486 (10777 equ; 0 cnn)
% 0.29/0.48 % Maximal formula atoms : 48 ( 2 avg)
% 0.29/0.48 % Number of connectives : 81663 (2054 ~; 295 |;1214 &;71318 @)
% 0.29/0.48 % ( 0 <=>;6782 =>; 0 <=; 0 <~>)
% 0.29/0.48 % Maximal formula depth : 25 ( 5 avg)
% 0.29/0.48 % Number of types : 306 ( 305 usr)
% 0.29/0.48 % Number of type conns : 14872 (14872 >; 0 *; 0 +; 0 <<)
% 0.29/0.48 % Number of symbols : 2574 (2571 usr; 164 con; 0-8 aty)
% 0.29/0.48 % Number of variables : 21351 (3365 ^;17684 !; 302 ?;21351 :)
% 0.29/0.48 % SPC : TH0_THM_EQU_NAR
% 0.29/0.48
% 0.29/0.48 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.29/0.48 % from the van Emde Boas Trees session in the Archive of Formal
% 0.29/0.48 % proofs -
% 0.29/0.48 % www.isa-afp.org/browser_info/current/AFP/Van_Emde_Boas_Trees
% 0.29/0.48 % 2022-02-17 16:14:06.785
% 0.29/0.48 % Bugfixes : Added ()s around negated sides of equations.
% 0.29/0.48 %------------------------------------------------------------------------------
% 0.29/0.48 % Could-be-implicit typings (305)
% 0.29/0.48 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__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_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_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_J_J,type,
% 0.29/0.48 set_Pr3444600963470892981et_nat: $tType ).
% 0.29/0.48
% 0.29/0.48 thf(ty_n_t__Product____Type__Oprod_It__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_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_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_J,type,
% 0.29/0.48 produc5657529347773406293et_nat: $tType ).
% 0.29/0.48
% 0.29/0.48 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_Mt__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J_J,type,
% 0.29/0.48 set_Pr1722956316086891245nteger: $tType ).
% 0.29/0.48
% 0.29/0.48 thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_Mt__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J,type,
% 0.29/0.48 produc824974754969098637nteger: $tType ).
% 0.29/0.48
% 0.29/0.48 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Int__Oint_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_Mt__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Int__Oint_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J_J,type,
% 0.29/0.48 set_Pr4708930517165415495nt_int: $tType ).
% 0.29/0.48
% 0.29/0.48 thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Int__Oint_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_Mt__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Int__Oint_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
% 0.29/0.48 produc2432570611225516007nt_int: $tType ).
% 0.29/0.48
% 0.29/0.48 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__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_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_J,type,
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% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001_062_I_062_It__Int__Oint_M_Eo_J_M_062_It__Int__Oint_Mt__Int__Oint_J_J_001_062_I_062_It__Int__Oint_M_Eo_J_M_062_It__Int__Oint_Mt__Int__Oint_J_J_001_062_I_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_M_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J_J_001_062_I_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_M_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
% 0.29/0.49 bNF_re5051145820034318685nt_int: ( ( ( int > $o ) > int > int ) > ( ( int > $o ) > int > int ) > $o ) > ( ( ( int > int > $o ) > int > int > int ) > ( ( int > int > $o ) > int > int > int ) > $o ) > ( ( ( int > $o ) > int > int ) > ( int > int > $o ) > int > int > int ) > ( ( ( int > $o ) > int > int ) > ( int > int > $o ) > int > int > int ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001_062_I_062_It__Int__Oint_M_Eo_J_M_062_It__Nat__Onat_M_Eo_J_J_001_062_I_062_It__Int__Oint_M_Eo_J_M_062_It__Nat__Onat_M_Eo_J_J_001_062_I_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_M_062_It__Int__Oint_M_062_It__Nat__Onat_M_Eo_J_J_J_001_062_I_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_M_062_It__Int__Oint_M_062_It__Nat__Onat_M_Eo_J_J_J,type,
% 0.29/0.49 bNF_re615132412071444453_nat_o: ( ( ( int > $o ) > nat > $o ) > ( ( int > $o ) > nat > $o ) > $o ) > ( ( ( int > int > $o ) > int > nat > $o ) > ( ( int > int > $o ) > int > nat > $o ) > $o ) > ( ( ( int > $o ) > nat > $o ) > ( int > int > $o ) > int > nat > $o ) > ( ( ( int > $o ) > nat > $o ) > ( int > int > $o ) > int > nat > $o ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001_062_I_062_It__Int__Oint_Mt__Int__Oint_J_M_062_It__Int__Oint_M_Eo_J_J_001_062_I_062_It__Int__Oint_Mt__Int__Oint_J_M_062_It__Int__Oint_M_Eo_J_J_001_062_I_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J_M_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_J_001_062_I_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J_M_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_J,type,
% 0.29/0.49 bNF_re3161894838932316637_int_o: ( ( ( int > int ) > int > $o ) > ( ( int > int ) > int > $o ) > $o ) > ( ( ( int > int > int ) > int > int > $o ) > ( ( int > int > int ) > int > int > $o ) > $o ) > ( ( ( int > int ) > int > $o ) > ( int > int > int ) > int > int > $o ) > ( ( ( int > int ) > int > $o ) > ( int > int > int ) > int > int > $o ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001_062_I_062_It__Int__Oint_Mt__Int__Oint_J_M_062_It__Nat__Onat_M_Eo_J_J_001_062_I_062_It__Int__Oint_Mt__Int__Oint_J_M_062_It__Nat__Onat_M_Eo_J_J_001_062_I_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J_M_062_It__Int__Oint_M_062_It__Nat__Onat_M_Eo_J_J_J_001_062_I_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J_M_062_It__Int__Oint_M_062_It__Nat__Onat_M_Eo_J_J_J,type,
% 0.29/0.49 bNF_re4659646225794970589_nat_o: ( ( ( int > int ) > nat > $o ) > ( ( int > int ) > nat > $o ) > $o ) > ( ( ( int > int > int ) > int > nat > $o ) > ( ( int > int > int ) > int > nat > $o ) > $o ) > ( ( ( int > int ) > nat > $o ) > ( int > int > int ) > int > nat > $o ) > ( ( ( int > int ) > nat > $o ) > ( int > int > int ) > int > nat > $o ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001_062_I_062_It__Nat__Onat_M_Eo_J_M_062_It__Int__Oint_M_Eo_J_J_001_062_I_062_It__Nat__Onat_M_Eo_J_M_062_It__Int__Oint_M_Eo_J_J_001_062_I_062_It__Int__Oint_M_062_It__Nat__Onat_M_Eo_J_J_M_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_J_001_062_I_062_It__Int__Oint_M_062_It__Nat__Onat_M_Eo_J_J_M_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_J,type,
% 0.29/0.49 bNF_re3491090157995142405_int_o: ( ( ( nat > $o ) > int > $o ) > ( ( nat > $o ) > int > $o ) > $o ) > ( ( ( int > nat > $o ) > int > int > $o ) > ( ( int > nat > $o ) > int > int > $o ) > $o ) > ( ( ( nat > $o ) > int > $o ) > ( int > nat > $o ) > int > int > $o ) > ( ( ( nat > $o ) > int > $o ) > ( int > nat > $o ) > int > int > $o ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001_062_I_062_It__Nat__Onat_M_Eo_J_M_062_It__Int__Oint_Mt__Int__Oint_J_J_001_062_I_062_It__Nat__Onat_M_Eo_J_M_062_It__Int__Oint_Mt__Int__Oint_J_J_001_062_I_062_It__Int__Oint_M_062_It__Nat__Onat_M_Eo_J_J_M_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J_J_001_062_I_062_It__Int__Oint_M_062_It__Nat__Onat_M_Eo_J_J_M_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
% 0.29/0.49 bNF_re5539255234643219293nt_int: ( ( ( nat > $o ) > int > int ) > ( ( nat > $o ) > int > int ) > $o ) > ( ( ( int > nat > $o ) > int > int > int ) > ( ( int > nat > $o ) > int > int > int ) > $o ) > ( ( ( nat > $o ) > int > int ) > ( int > nat > $o ) > int > int > int ) > ( ( ( nat > $o ) > int > int ) > ( int > nat > $o ) > int > int > int ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001_062_I_062_It__Nat__Onat_M_Eo_J_M_062_It__Nat__Onat_M_Eo_J_J_001_062_I_062_It__Nat__Onat_M_Eo_J_M_062_It__Nat__Onat_M_Eo_J_J_001_062_I_062_It__Int__Oint_M_062_It__Nat__Onat_M_Eo_J_J_M_062_It__Int__Oint_M_062_It__Nat__Onat_M_Eo_J_J_J_001_062_I_062_It__Int__Oint_M_062_It__Nat__Onat_M_Eo_J_J_M_062_It__Int__Oint_M_062_It__Nat__Onat_M_Eo_J_J_J,type,
% 0.29/0.49 bNF_re1550856938216548981_nat_o: ( ( ( nat > $o ) > nat > $o ) > ( ( nat > $o ) > nat > $o ) > $o ) > ( ( ( int > nat > $o ) > int > nat > $o ) > ( ( int > nat > $o ) > int > nat > $o ) > $o ) > ( ( ( nat > $o ) > nat > $o ) > ( int > nat > $o ) > int > nat > $o ) > ( ( ( nat > $o ) > nat > $o ) > ( int > nat > $o ) > int > nat > $o ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Code____Numeral__Ointeger_M_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_J_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001_062_I_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_M_062_It__Code____Numeral__Ointeger_M_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_J_J_001_062_I_062_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_M_062_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_J,type,
% 0.29/0.49 bNF_re4919612610145136063nteger: ( ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer ) > $o ) > ( ( ( code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( ( num > code_integer ) > num > code_integer ) > $o ) > ( ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( ( code_integer > code_integer ) > ( num > code_integer ) > num > code_integer ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Code____Numeral__Ointeger_M_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_J_001_062_It__Nat__Onat_Mt__Num__Onum_J_001_062_I_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_M_062_It__Code____Numeral__Ointeger_M_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_J_J_001_062_I_062_It__Int__Oint_Mt__Nat__Onat_J_M_062_It__Int__Oint_Mt__Num__Onum_J_J,type,
% 0.29/0.49 bNF_re1890273300020150979nt_num: ( ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( nat > num ) > $o ) > ( ( ( code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( ( int > nat ) > int > num ) > $o ) > ( ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( ( nat > num ) > ( int > nat ) > int > num ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001_062_It__Code____Numeral__Ointeger_M_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_J_001_062_I_062_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_M_062_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_J_001_062_I_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_M_062_It__Code____Numeral__Ointeger_M_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_J_J,type,
% 0.29/0.49 bNF_re8134695817916415679nteger: ( ( code_integer > code_integer ) > ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > $o ) > ( ( ( num > code_integer ) > num > code_integer ) > ( ( code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > $o ) > ( ( code_integer > code_integer ) > ( num > code_integer ) > num > code_integer ) > ( ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001_062_I_062_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_M_062_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_J_001_062_I_062_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_M_062_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_J,type,
% 0.29/0.49 bNF_re5979881370344185769nteger: ( ( code_integer > code_integer ) > ( code_integer > code_integer ) > $o ) > ( ( ( num > code_integer ) > num > code_integer ) > ( ( num > code_integer ) > num > code_integer ) > $o ) > ( ( code_integer > code_integer ) > ( num > code_integer ) > num > code_integer ) > ( ( code_integer > code_integer ) > ( num > code_integer ) > num > code_integer ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_It__Code____Numeral__Ointeger_M_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_J_001_062_It__Int__Oint_Mt__Num__Onum_J,type,
% 0.29/0.49 bNF_re5190287125156074331nt_num: ( ( code_integer > code_integer ) > ( int > nat ) > $o ) > ( ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( int > num ) > $o ) > ( ( code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( ( int > nat ) > int > num ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001_062_It__Nat__Onat_Mt__Num__Onum_J_001_062_I_062_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_M_062_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_J_001_062_I_062_It__Int__Oint_Mt__Nat__Onat_J_M_062_It__Int__Oint_Mt__Num__Onum_J_J,type,
% 0.29/0.49 bNF_re5469402333911078061nt_num: ( ( code_integer > code_integer ) > ( nat > num ) > $o ) > ( ( ( num > code_integer ) > num > code_integer ) > ( ( int > nat ) > int > num ) > $o ) > ( ( code_integer > code_integer ) > ( num > code_integer ) > num > code_integer ) > ( ( nat > num ) > ( int > nat ) > int > num ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001_062_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_001_062_It__Code____Numeral__Ointeger_M_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_J_001_062_It__Num__Onum_Mt__Code____Numeral__Ointeger_J,type,
% 0.29/0.49 bNF_re6724329528997265415nteger: ( ( code_integer > code_integer ) > ( num > code_integer ) > $o ) > ( ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( num > code_integer ) > $o ) > ( ( code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( ( num > code_integer ) > num > code_integer ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_001_062_I_062_It__Int__Oint_Mt__Int__Oint_J_M_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_J_001_062_I_062_It__Int__Oint_Mt__Int__Oint_J_M_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_J,type,
% 0.29/0.49 bNF_re1900612664124570461_int_o: ( ( int > int > $o ) > ( int > int > $o ) > $o ) > ( ( ( int > int ) > int > int > $o ) > ( ( int > int ) > int > int > $o ) > $o ) > ( ( int > int > $o ) > ( int > int ) > int > int > $o ) > ( ( int > int > $o ) > ( int > int ) > int > int > $o ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J,type,
% 0.29/0.49 bNF_re8651060166502312541_int_o: ( ( int > int > $o ) > ( int > int > $o ) > $o ) > ( ( int > int > $o ) > ( int > int > $o ) > $o ) > ( ( int > int > $o ) > int > int > $o ) > ( ( int > int > $o ) > int > int > $o ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_001_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J,type,
% 0.29/0.49 bNF_re7462748251485907171nt_int: ( ( int > int > $o ) > ( int > int > $o ) > $o ) > ( ( int > int > int ) > ( int > int > int ) > $o ) > ( ( int > int > $o ) > int > int > int ) > ( ( int > int > $o ) > int > int > int ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_001_062_It__Int__Oint_M_062_It__Nat__Onat_M_Eo_J_J_001_062_It__Int__Oint_M_062_It__Nat__Onat_M_Eo_J_J,type,
% 0.29/0.49 bNF_re2446162618891206493_nat_o: ( ( int > int > $o ) > ( int > int > $o ) > $o ) > ( ( int > nat > $o ) > ( int > nat > $o ) > $o ) > ( ( int > int > $o ) > int > nat > $o ) > ( ( int > int > $o ) > int > nat > $o ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J_001_062_I_062_It__Int__Oint_Mt__Int__Oint_J_M_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J_J_001_062_I_062_It__Int__Oint_Mt__Int__Oint_J_M_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
% 0.29/0.49 bNF_re4984751527058004117nt_int: ( ( int > int > int ) > ( int > int > int ) > $o ) > ( ( ( int > int ) > int > int > int ) > ( ( int > int ) > int > int > int ) > $o ) > ( ( int > int > int ) > ( int > int ) > int > int > int ) > ( ( int > int > int ) > ( int > int ) > int > int > int ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J,type,
% 0.29/0.49 bNF_re1313934062736347107_int_o: ( ( int > int > int ) > ( int > int > int ) > $o ) > ( ( int > int > $o ) > ( int > int > $o ) > $o ) > ( ( int > int > int ) > int > int > $o ) > ( ( int > int > int ) > int > int > $o ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Int__Oint_M_062_It__Nat__Onat_M_Eo_J_J_001_062_It__Int__Oint_M_062_It__Nat__Onat_M_Eo_J_J,type,
% 0.29/0.49 bNF_re4332408551980016867_nat_o: ( ( int > int > int ) > ( int > int > int ) > $o ) > ( ( int > nat > $o ) > ( int > nat > $o ) > $o ) > ( ( int > int > int ) > int > nat > $o ) > ( ( int > int > int ) > int > nat > $o ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J_001_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Rat__Orat_J_J_001_062_I_062_It__Int__Oint_Mt__Int__Oint_J_M_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J_J_001_062_I_062_It__Int__Oint_Mt__Int__Oint_J_M_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Rat__Orat_J_J_J,type,
% 0.29/0.49 bNF_re62019127700022579nt_rat: ( ( int > int > product_prod_int_int ) > ( int > int > rat ) > $o ) > ( ( ( int > int ) > int > int > product_prod_int_int ) > ( ( int > int ) > int > int > rat ) > $o ) > ( ( int > int > product_prod_int_int ) > ( int > int ) > int > int > product_prod_int_int ) > ( ( int > int > rat ) > ( int > int ) > int > int > rat ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_M_062_It__Nat__Onat_M_Eo_J_J_001_062_It__Int__Oint_M_062_It__Nat__Onat_M_Eo_J_J_001_062_I_062_It__Int__Oint_Mt__Int__Oint_J_M_062_It__Int__Oint_M_062_It__Nat__Onat_M_Eo_J_J_J_001_062_I_062_It__Int__Oint_Mt__Int__Oint_J_M_062_It__Int__Oint_M_062_It__Nat__Onat_M_Eo_J_J_J,type,
% 0.29/0.49 bNF_re7908124382625962333_nat_o: ( ( int > nat > $o ) > ( int > nat > $o ) > $o ) > ( ( ( int > int ) > int > nat > $o ) > ( ( int > int ) > int > nat > $o ) > $o ) > ( ( int > nat > $o ) > ( int > int ) > int > nat > $o ) > ( ( int > nat > $o ) > ( int > int ) > int > nat > $o ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_M_062_It__Nat__Onat_M_Eo_J_J_001_062_It__Int__Oint_M_062_It__Nat__Onat_M_Eo_J_J_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J,type,
% 0.29/0.49 bNF_re2655111580231008093_int_o: ( ( int > nat > $o ) > ( int > nat > $o ) > $o ) > ( ( int > int > $o ) > ( int > int > $o ) > $o ) > ( ( int > nat > $o ) > int > int > $o ) > ( ( int > nat > $o ) > int > int > $o ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_M_062_It__Nat__Onat_M_Eo_J_J_001_062_It__Int__Oint_M_062_It__Nat__Onat_M_Eo_J_J_001_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J,type,
% 0.29/0.49 bNF_re7395152722673581539nt_int: ( ( int > nat > $o ) > ( int > nat > $o ) > $o ) > ( ( int > int > int ) > ( int > int > int ) > $o ) > ( ( int > nat > $o ) > int > int > int ) > ( ( int > nat > $o ) > int > int > int ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_M_062_It__Nat__Onat_M_Eo_J_J_001_062_It__Int__Oint_M_062_It__Nat__Onat_M_Eo_J_J_001_062_It__Int__Oint_M_062_It__Nat__Onat_M_Eo_J_J_001_062_It__Int__Oint_M_062_It__Nat__Onat_M_Eo_J_J,type,
% 0.29/0.49 bNF_re5673586069474677853_nat_o: ( ( int > nat > $o ) > ( int > nat > $o ) > $o ) > ( ( int > nat > $o ) > ( int > nat > $o ) > $o ) > ( ( int > nat > $o ) > int > nat > $o ) > ( ( int > nat > $o ) > int > nat > $o ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_M_Eo_J_001_062_It__Int__Oint_M_Eo_J_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Nat__Onat_M_Eo_J,type,
% 0.29/0.49 bNF_re2535741173671728349_nat_o: ( ( int > $o ) > ( int > $o ) > $o ) > ( ( nat > $o ) > ( nat > $o ) > $o ) > ( ( int > $o ) > nat > $o ) > ( ( int > $o ) > nat > $o ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J,type,
% 0.29/0.49 bNF_re3014639844587090765_int_o: ( ( int > int ) > ( int > int ) > $o ) > ( ( int > int > $o ) > ( int > int > $o ) > $o ) > ( ( int > int ) > int > int > $o ) > ( ( int > int ) > int > int > $o ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J,type,
% 0.29/0.49 bNF_re724639330072410579nt_int: ( ( int > int ) > ( int > int ) > $o ) > ( ( int > int > int ) > ( int > int > int ) > $o ) > ( ( int > int ) > int > int > int ) > ( ( int > int ) > int > int > int ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J_001_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Rat__Orat_J_J,type,
% 0.29/0.49 bNF_re949775918795716016nt_rat: ( ( int > int ) > ( int > int ) > $o ) > ( ( int > int > product_prod_int_int ) > ( int > int > rat ) > $o ) > ( ( int > int ) > int > int > product_prod_int_int ) > ( ( int > int ) > int > int > rat ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Int__Oint_M_062_It__Nat__Onat_M_Eo_J_J_001_062_It__Int__Oint_M_062_It__Nat__Onat_M_Eo_J_J,type,
% 0.29/0.49 bNF_re6033114333830760525_nat_o: ( ( int > int ) > ( int > int ) > $o ) > ( ( int > nat > $o ) > ( int > nat > $o ) > $o ) > ( ( int > int ) > int > nat > $o ) > ( ( int > int ) > int > nat > $o ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_It__Int__Oint_Mt__Num__Onum_J_001_062_It__Int__Oint_Mt__Num__Onum_J,type,
% 0.29/0.49 bNF_re9099949428469764705nt_num: ( ( int > nat ) > ( int > nat ) > $o ) > ( ( int > num ) > ( int > num ) > $o ) > ( ( int > nat ) > int > num ) > ( ( int > nat ) > int > num ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_001_062_It__Int__Oint_Mt__Num__Onum_J_001_062_It__Num__Onum_Mt__Code____Numeral__Ointeger_J,type,
% 0.29/0.49 bNF_re8894579221946749965nteger: ( ( int > nat ) > ( num > code_integer ) > $o ) > ( ( int > num ) > ( num > code_integer ) > $o ) > ( ( int > nat ) > int > num ) > ( ( num > code_integer ) > num > code_integer ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Int__Oint_M_Eo_J_001_062_It__Int__Oint_M_Eo_J,type,
% 0.29/0.49 bNF_re2724346968851715293_int_o: ( ( nat > $o ) > ( nat > $o ) > $o ) > ( ( int > $o ) > ( int > $o ) > $o ) > ( ( nat > $o ) > int > $o ) > ( ( nat > $o ) > int > $o ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Int__Oint_Mt__Int__Oint_J,type,
% 0.29/0.49 bNF_re7183634743573646861nt_int: ( ( nat > $o ) > ( nat > $o ) > $o ) > ( ( int > int ) > ( int > int ) > $o ) > ( ( nat > $o ) > int > int ) > ( ( nat > $o ) > int > int ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Nat__Onat_M_Eo_J,type,
% 0.29/0.49 bNF_re2697311982885662685_nat_o: ( ( nat > $o ) > ( nat > $o ) > $o ) > ( ( nat > $o ) > ( nat > $o ) > $o ) > ( ( nat > $o ) > nat > $o ) > ( ( nat > $o ) > nat > $o ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Nat__Onat_Mt__Num__Onum_J_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001_062_I_062_It__Int__Oint_Mt__Nat__Onat_J_M_062_It__Int__Oint_Mt__Num__Onum_J_J_001_062_I_062_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_M_062_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_J,type,
% 0.29/0.49 bNF_re2163612987331707565nteger: ( ( nat > num ) > ( code_integer > code_integer ) > $o ) > ( ( ( int > nat ) > int > num ) > ( ( num > code_integer ) > num > code_integer ) > $o ) > ( ( nat > num ) > ( int > nat ) > int > num ) > ( ( code_integer > code_integer ) > ( num > code_integer ) > num > code_integer ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Nat__Onat_Mt__Num__Onum_J_001_062_It__Nat__Onat_Mt__Num__Onum_J_001_062_I_062_It__Int__Oint_Mt__Nat__Onat_J_M_062_It__Int__Oint_Mt__Num__Onum_J_J_001_062_I_062_It__Int__Oint_Mt__Nat__Onat_J_M_062_It__Int__Oint_Mt__Num__Onum_J_J,type,
% 0.29/0.49 bNF_re3846787885862361009nt_num: ( ( nat > num ) > ( nat > num ) > $o ) > ( ( ( int > nat ) > int > num ) > ( ( int > nat ) > int > num ) > $o ) > ( ( nat > num ) > ( int > nat ) > int > num ) > ( ( nat > num ) > ( int > nat ) > int > num ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001_062_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_001_062_It__Code____Numeral__Ointeger_M_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_J,type,
% 0.29/0.49 bNF_re2439920061672227847nteger: ( ( num > code_integer ) > ( code_integer > code_integer ) > $o ) > ( ( num > code_integer ) > ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > $o ) > ( ( num > code_integer ) > num > code_integer ) > ( ( code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_001_062_It__Int__Oint_Mt__Num__Onum_J,type,
% 0.29/0.49 bNF_re1151383970801924621nt_num: ( ( num > code_integer ) > ( int > nat ) > $o ) > ( ( num > code_integer ) > ( int > num ) > $o ) > ( ( num > code_integer ) > num > code_integer ) > ( ( int > nat ) > int > num ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_001_062_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_001_062_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_001_062_It__Num__Onum_Mt__Code____Numeral__Ointeger_J,type,
% 0.29/0.49 bNF_re6097285183634142137nteger: ( ( num > code_integer ) > ( num > code_integer ) > $o ) > ( ( num > code_integer ) > ( num > code_integer ) > $o ) > ( ( num > code_integer ) > num > code_integer ) > ( ( num > code_integer ) > num > code_integer ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001_Eo_001_Eo_001t__Int__Oint_001t__Nat__Onat,type,
% 0.29/0.49 bNF_re1551779926989065179nt_nat: ( $o > $o > $o ) > ( int > nat > $o ) > ( $o > int ) > ( $o > nat ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001_Eo_001_Eo_001t__Int__Oint_001t__Rat__Orat,type,
% 0.29/0.49 bNF_re916649866902569443nt_rat: ( $o > $o > $o ) > ( int > rat > $o ) > ( $o > int ) > ( $o > rat ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001_Eo_001_Eo_001t__Nat__Onat_001t__Code____Numeral__Ointeger,type,
% 0.29/0.49 bNF_re4863541036035986956nteger: ( $o > $o > $o ) > ( nat > code_integer > $o ) > ( $o > nat ) > ( $o > code_integer ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001_Eo_001_Eo_001t__Nat__Onat_001t__Int__Oint,type,
% 0.29/0.49 bNF_re549935744578960347at_int: ( $o > $o > $o ) > ( nat > int > $o ) > ( $o > nat ) > ( $o > int ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001_Eo_001_Eo_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.29/0.49 bNF_re552426215088010623at_nat: ( $o > $o > $o ) > ( nat > nat > $o ) > ( $o > nat ) > ( $o > nat ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001_Eo_001_Eo_001t__Nat__Onat_001t__Rat__Orat,type,
% 0.29/0.49 bNF_re9140668191856290695at_rat: ( $o > $o > $o ) > ( nat > rat > $o ) > ( $o > nat ) > ( $o > rat ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001_Eo_001_Eo_001t__Rat__Orat_001t__Code____Numeral__Ointeger,type,
% 0.29/0.49 bNF_re5635613845597506580nteger: ( $o > $o > $o ) > ( rat > code_integer > $o ) > ( $o > rat ) > ( $o > code_integer ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001_Eo_001_Eo_001t__Rat__Orat_001t__Int__Oint,type,
% 0.29/0.49 bNF_re233381100644094435at_int: ( $o > $o > $o ) > ( rat > int > $o ) > ( $o > rat ) > ( $o > int ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001_Eo_001_Eo_001t__Rat__Orat_001t__Nat__Onat,type,
% 0.29/0.49 bNF_re235871571153144711at_nat: ( $o > $o > $o ) > ( rat > nat > $o ) > ( $o > rat ) > ( $o > nat ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001_Eo_001_Eo_001t__Rat__Orat_001t__Rat__Orat,type,
% 0.29/0.49 bNF_re8824113547921424783at_rat: ( $o > $o > $o ) > ( rat > rat > $o ) > ( $o > rat ) > ( $o > rat ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Assertions__Oassn_001t__Assertions__Oassn_001_062_It__Assertions__Oassn_Mt__Assertions__Oassn_J_001_062_It__Assertions__Oassn_Mt__Assertions__Oassn_J,type,
% 0.29/0.49 bNF_re9137223911888007311n_assn: ( assn > assn > $o ) > ( ( assn > assn ) > ( assn > assn ) > $o ) > ( assn > assn > assn ) > ( assn > assn > assn ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Assertions__Oassn_001t__Assertions__Oassn_001_062_It__Nat__Onat_Mt__Assertions__Oassn_J_001_062_It__Nat__Onat_Mt__Assertions__Oassn_J,type,
% 0.29/0.49 bNF_re3650450707543776735t_assn: ( assn > assn > $o ) > ( ( nat > assn ) > ( nat > assn ) > $o ) > ( assn > nat > assn ) > ( assn > nat > assn ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Assertions__Oassn_001t__Assertions__Oassn_001t__Assertions__Oassn_001t__Assertions__Oassn,type,
% 0.29/0.49 bNF_re1143782165119297793n_assn: ( assn > assn > $o ) > ( assn > assn > $o ) > ( assn > assn ) > ( assn > assn ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Assertions__Oassn_001t__Code____Numeral__Ointeger_001_062_It__Assertions__Oassn_Mt__Assertions__Oassn_J_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 0.29/0.49 bNF_re5822757241383739566nteger: ( assn > code_integer > $o ) > ( ( assn > assn ) > ( code_integer > code_integer ) > $o ) > ( assn > assn > assn ) > ( code_integer > code_integer > code_integer ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Assertions__Oassn_001t__Code____Numeral__Ointeger_001_062_It__Nat__Onat_Mt__Assertions__Oassn_J_001_062_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J,type,
% 0.29/0.49 bNF_re2102180915162216137nteger: ( assn > code_integer > $o ) > ( ( nat > assn ) > ( nat > code_integer ) > $o ) > ( assn > nat > assn ) > ( code_integer > nat > code_integer ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Assertions__Oassn_001t__Code____Numeral__Ointeger_001t__Assertions__Oassn_001t__Code____Numeral__Ointeger,type,
% 0.29/0.49 bNF_re4134162077946812779nteger: ( assn > code_integer > $o ) > ( assn > code_integer > $o ) > ( assn > assn ) > ( code_integer > code_integer ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Assertions__Oassn_001t__Int__Oint_001_062_It__Assertions__Oassn_Mt__Assertions__Oassn_J_001_062_It__Int__Oint_Mt__Int__Oint_J,type,
% 0.29/0.49 bNF_re7882741803053012379nt_int: ( assn > int > $o ) > ( ( assn > assn ) > ( int > int ) > $o ) > ( assn > assn > assn ) > ( int > int > int ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Assertions__Oassn_001t__Int__Oint_001_062_It__Nat__Onat_Mt__Assertions__Oassn_J_001_062_It__Nat__Onat_Mt__Int__Oint_J,type,
% 0.29/0.49 bNF_re185025794348816359at_int: ( assn > int > $o ) > ( ( nat > assn ) > ( nat > int ) > $o ) > ( assn > nat > assn ) > ( int > nat > int ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Assertions__Oassn_001t__Int__Oint_001t__Assertions__Oassn_001t__Int__Oint,type,
% 0.29/0.49 bNF_re2927800259774540553sn_int: ( assn > int > $o ) > ( assn > int > $o ) > ( assn > assn ) > ( int > int ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Assertions__Oassn_001t__Nat__Onat_001_062_It__Assertions__Oassn_Mt__Assertions__Oassn_J_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.29/0.49 bNF_re4386305596031132807at_nat: ( assn > nat > $o ) > ( ( assn > assn ) > ( nat > nat ) > $o ) > ( assn > assn > assn ) > ( nat > nat > nat ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Assertions__Oassn_001t__Nat__Onat_001_062_It__Nat__Onat_Mt__Assertions__Oassn_J_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.29/0.49 bNF_re8560028565313717551at_nat: ( assn > nat > $o ) > ( ( nat > assn ) > ( nat > nat ) > $o ) > ( assn > nat > assn ) > ( nat > nat > nat ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Assertions__Oassn_001t__Nat__Onat_001t__Assertions__Oassn_001t__Nat__Onat,type,
% 0.29/0.49 bNF_re6742580585434904145sn_nat: ( assn > nat > $o ) > ( assn > nat > $o ) > ( assn > assn ) > ( nat > nat ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Assertions__Oassn_001t__Rat__Orat_001_062_It__Assertions__Oassn_Mt__Assertions__Oassn_J_001_062_It__Rat__Orat_Mt__Rat__Orat_J,type,
% 0.29/0.49 bNF_re967558844708792991at_rat: ( assn > rat > $o ) > ( ( assn > assn ) > ( rat > rat ) > $o ) > ( assn > assn > assn ) > ( rat > rat > rat ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Assertions__Oassn_001t__Rat__Orat_001_062_It__Nat__Onat_Mt__Assertions__Oassn_J_001_062_It__Nat__Onat_Mt__Rat__Orat_J,type,
% 0.29/0.49 bNF_re6138836914430330175at_rat: ( assn > rat > $o ) > ( ( nat > assn ) > ( nat > rat ) > $o ) > ( assn > nat > assn ) > ( rat > nat > rat ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Assertions__Oassn_001t__Rat__Orat_001t__Assertions__Oassn_001t__Rat__Orat,type,
% 0.29/0.49 bNF_re9003240792272343649sn_rat: ( assn > rat > $o ) > ( assn > rat > $o ) > ( assn > assn ) > ( rat > rat ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Code____Numeral__Ointeger_001t__Assertions__Oassn_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001_062_It__Assertions__Oassn_Mt__Assertions__Oassn_J,type,
% 0.29/0.49 bNF_re7789648203153440174n_assn: ( code_integer > assn > $o ) > ( ( code_integer > code_integer ) > ( assn > assn ) > $o ) > ( code_integer > code_integer > code_integer ) > ( assn > assn > assn ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Code____Numeral__Ointeger_001t__Assertions__Oassn_001_062_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J_001_062_It__Nat__Onat_Mt__Assertions__Oassn_J,type,
% 0.29/0.49 bNF_re2546461910754330953t_assn: ( code_integer > assn > $o ) > ( ( nat > code_integer ) > ( nat > assn ) > $o ) > ( code_integer > nat > code_integer ) > ( assn > nat > assn ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Code____Numeral__Ointeger_001t__Assertions__Oassn_001t__Code____Numeral__Ointeger_001t__Assertions__Oassn,type,
% 0.29/0.49 bNF_re1475883931861434731r_assn: ( code_integer > assn > $o ) > ( code_integer > assn > $o ) > ( code_integer > code_integer ) > ( assn > assn ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 0.29/0.49 bNF_re122555440370955213nteger: ( code_integer > code_integer > $o ) > ( ( code_integer > code_integer ) > ( code_integer > code_integer ) > $o ) > ( code_integer > code_integer > code_integer ) > ( code_integer > code_integer > code_integer ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001_062_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J_001_062_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J,type,
% 0.29/0.49 bNF_re5462749793222359603nteger: ( code_integer > code_integer > $o ) > ( ( nat > code_integer ) > ( nat > code_integer ) > $o ) > ( code_integer > nat > code_integer ) > ( code_integer > nat > code_integer ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Code____Numeral__Ointeger_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,
% 0.29/0.49 bNF_re4341081746073172381nteger: ( code_integer > code_integer > $o ) > ( ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > code_integer > $o ) > ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_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,type,
% 0.29/0.49 bNF_re3370092614548195229nteger: ( code_integer > code_integer > $o ) > ( code_integer > ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > $o ) > ( code_integer > code_integer ) > ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 0.29/0.49 bNF_re1062419521925302741nteger: ( code_integer > code_integer > $o ) > ( code_integer > code_integer > $o ) > ( code_integer > code_integer ) > ( code_integer > code_integer ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Code____Numeral__Ointeger_001t__Int__Oint_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001_062_It__Int__Oint_Mt__Int__Oint_J,type,
% 0.29/0.49 bNF_re8304916493157054650nt_int: ( code_integer > int > $o ) > ( ( code_integer > code_integer ) > ( int > int ) > $o ) > ( code_integer > code_integer > code_integer ) > ( int > int > int ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Code____Numeral__Ointeger_001t__Int__Oint_001_062_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J_001_062_It__Nat__Onat_Mt__Int__Oint_J,type,
% 0.29/0.49 bNF_re6766650671887726929at_int: ( code_integer > int > $o ) > ( ( nat > code_integer ) > ( nat > int ) > $o ) > ( code_integer > nat > code_integer ) > ( int > nat > int ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Code____Numeral__Ointeger_001t__Int__Oint_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__Num__Onum,type,
% 0.29/0.49 bNF_re8127238762813979689er_num: ( code_integer > int > $o ) > ( ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > num > $o ) > ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( int > num ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Code____Numeral__Ointeger_001t__Int__Oint_001t__Code____Numeral__Ointeger_001t__Int__Oint,type,
% 0.29/0.49 bNF_re2888858428391045491er_int: ( code_integer > int > $o ) > ( code_integer > int > $o ) > ( code_integer > code_integer ) > ( int > int ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Code____Numeral__Ointeger_001t__Int__Oint_001t__Code____Numeral__Ointeger_001t__Nat__Onat,type,
% 0.29/0.49 bNF_re2891348898900095767er_nat: ( code_integer > int > $o ) > ( code_integer > nat > $o ) > ( code_integer > code_integer ) > ( int > nat ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Code____Numeral__Ointeger_001t__Nat__Onat_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.29/0.49 bNF_re3981674901896804262at_nat: ( code_integer > nat > $o ) > ( ( code_integer > code_integer ) > ( nat > nat ) > $o ) > ( code_integer > code_integer > code_integer ) > ( nat > nat > nat ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Code____Numeral__Ointeger_001t__Nat__Onat_001_062_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.29/0.49 bNF_re4269568176766901913at_nat: ( code_integer > nat > $o ) > ( ( nat > code_integer ) > ( nat > nat ) > $o ) > ( code_integer > nat > code_integer ) > ( nat > nat > nat ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Code____Numeral__Ointeger_001t__Nat__Onat_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__Num__Onum,type,
% 0.29/0.49 bNF_re7119966052990372301er_num: ( code_integer > nat > $o ) > ( ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > num > $o ) > ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( nat > num ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Code____Numeral__Ointeger_001t__Nat__Onat_001t__Code____Numeral__Ointeger_001t__Nat__Onat,type,
% 0.29/0.49 bNF_re5201166830993046715er_nat: ( code_integer > nat > $o ) > ( code_integer > nat > $o ) > ( code_integer > code_integer ) > ( nat > nat ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Code____Numeral__Ointeger_001t__Nat__Onat_001t__Code____Numeral__Ointeger_001t__Num__Onum,type,
% 0.29/0.49 bNF_re1758498617148825349er_num: ( code_integer > nat > $o ) > ( code_integer > num > $o ) > ( code_integer > code_integer ) > ( nat > num ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Code____Numeral__Ointeger_001t__Num__Onum_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,
% 0.29/0.49 bNF_re166502229267952730nteger: ( code_integer > num > $o ) > ( ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > code_integer > $o ) > ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( num > code_integer ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Code____Numeral__Ointeger_001t__Num__Onum_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 0.29/0.49 bNF_re7350422212947406738nteger: ( code_integer > num > $o ) > ( code_integer > code_integer > $o ) > ( code_integer > code_integer ) > ( num > code_integer ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Code____Numeral__Ointeger_001t__Rat__Orat_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001_062_It__Rat__Orat_Mt__Rat__Orat_J,type,
% 0.29/0.49 bNF_re2976496150901874110at_rat: ( code_integer > rat > $o ) > ( ( code_integer > code_integer ) > ( rat > rat ) > $o ) > ( code_integer > code_integer > code_integer ) > ( rat > rat > rat ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Code____Numeral__Ointeger_001t__Rat__Orat_001_062_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J_001_062_It__Nat__Onat_Mt__Rat__Orat_J,type,
% 0.29/0.49 bNF_re1167376069379428009at_rat: ( code_integer > rat > $o ) > ( ( nat > code_integer ) > ( nat > rat ) > $o ) > ( code_integer > nat > code_integer ) > ( rat > nat > rat ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Code____Numeral__Ointeger_001t__Rat__Orat_001t__Code____Numeral__Ointeger_001t__Rat__Orat,type,
% 0.29/0.49 bNF_re4698098036185532619er_rat: ( code_integer > rat > $o ) > ( code_integer > rat > $o ) > ( code_integer > code_integer ) > ( rat > rat ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Code____Numeral__Ointeger_001_062_It__Int__Oint_M_Eo_J_001_062_It__Code____Numeral__Ointeger_M_Eo_J,type,
% 0.29/0.49 bNF_re6321650412969554871eger_o: ( int > code_integer > $o ) > ( ( int > $o ) > ( code_integer > $o ) > $o ) > ( int > int > $o ) > ( code_integer > code_integer > $o ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Code____Numeral__Ointeger_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 0.29/0.49 bNF_re398004352372739002nteger: ( int > code_integer > $o ) > ( ( int > int ) > ( code_integer > code_integer ) > $o ) > ( int > int > int ) > ( code_integer > code_integer > code_integer ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Code____Numeral__Ointeger_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Nat__Onat_M_Eo_J,type,
% 0.29/0.49 bNF_re4711666741709854504_nat_o: ( int > code_integer > $o ) > ( ( nat > $o ) > ( nat > $o ) > $o ) > ( int > nat > $o ) > ( code_integer > nat > $o ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Code____Numeral__Ointeger_001_Eo_001_Eo,type,
% 0.29/0.49 bNF_re6574881592172037608er_o_o: ( int > code_integer > $o ) > ( $o > $o > $o ) > ( int > $o ) > ( code_integer > $o ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Code____Numeral__Ointeger_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
% 0.29/0.49 bNF_re3379532845092657523nteger: ( int > code_integer > $o ) > ( int > code_integer > $o ) > ( int > int ) > ( code_integer > code_integer ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Code____Numeral__Ointeger_001t__Int__Oint_001t__Int__Oint,type,
% 0.29/0.49 bNF_re3804157879324367682nt_int: ( int > code_integer > $o ) > ( int > int > $o ) > ( int > int ) > ( code_integer > int ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Code____Numeral__Ointeger_001t__Nat__Onat_001t__Code____Numeral__Onatural,type,
% 0.29/0.49 bNF_re1831474436612530402atural: ( int > code_integer > $o ) > ( nat > code_natural > $o ) > ( int > nat ) > ( code_integer > code_natural ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Code____Numeral__Ointeger_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.29/0.49 bNF_re2807294637932363402at_nat: ( int > code_integer > $o ) > ( nat > nat > $o ) > ( int > nat ) > ( code_integer > nat ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Code____Numeral__Ointeger_001t__Num__Onum_001t__Num__Onum,type,
% 0.29/0.49 bNF_re6718328864250387230um_num: ( int > code_integer > $o ) > ( num > num > $o ) > ( int > num ) > ( code_integer > num ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Code____Numeral__Onatural_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J,type,
% 0.29/0.49 bNF_re2342410721167621787atural: ( int > code_natural > $o ) > ( ( int > int ) > ( code_natural > code_natural ) > $o ) > ( int > int > int ) > ( code_natural > code_natural > code_natural ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Code____Numeral__Onatural_001t__Int__Oint_001t__Code____Numeral__Onatural,type,
% 0.29/0.49 bNF_re5484556299188842761atural: ( int > code_natural > $o ) > ( int > code_natural > $o ) > ( int > int ) > ( code_natural > code_natural ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_062_It__Int__Oint_M_Eo_J_001_062_It__Int__Oint_M_Eo_J,type,
% 0.29/0.49 bNF_re3403563459893282935_int_o: ( int > int > $o ) > ( ( int > $o ) > ( int > $o ) > $o ) > ( int > int > $o ) > ( int > int > $o ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Int__Oint_Mt__Int__Oint_J,type,
% 0.29/0.49 bNF_re711492959462206631nt_int: ( int > int > $o ) > ( ( int > int ) > ( int > int ) > $o ) > ( int > int > int ) > ( int > int > int ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_062_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
% 0.29/0.49 bNF_re157797125943740599nt_int: ( int > int > $o ) > ( ( int > product_prod_int_int ) > ( int > product_prod_int_int ) > $o ) > ( int > int > product_prod_int_int ) > ( int > int > product_prod_int_int ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_062_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Int__Oint_Mt__Rat__Orat_J,type,
% 0.29/0.49 bNF_re3461391660133120880nt_rat: ( int > int > $o ) > ( ( int > product_prod_int_int ) > ( int > rat ) > $o ) > ( int > int > product_prod_int_int ) > ( int > int > rat ) > $o ).
% 0.29/0.49
% 0.29/0.49 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,
% 0.29/0.49 bNF_re3376528473927230327_nat_o: ( int > int > $o ) > ( ( nat > $o ) > ( nat > $o ) > $o ) > ( int > nat > $o ) > ( int > nat > $o ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_Eo_001_Eo,type,
% 0.29/0.49 bNF_re5089333283451836215nt_o_o: ( int > int > $o ) > ( $o > $o > $o ) > ( int > $o ) > ( int > $o ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 0.29/0.49 bNF_re1784066744496875891nteger: ( int > int > $o ) > ( code_integer > code_integer > $o ) > ( int > code_integer ) > ( int > code_integer ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Code____Numeral__Ointeger_001t__Int__Oint,type,
% 0.29/0.49 bNF_re343602593470180162er_int: ( int > int > $o ) > ( code_integer > int > $o ) > ( int > code_integer ) > ( int > int ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Code____Numeral__Ointeger_001t__Rat__Orat,type,
% 0.29/0.49 bNF_re8934335040747510510er_rat: ( int > int > $o ) > ( code_integer > rat > $o ) > ( int > code_integer ) > ( int > rat ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Code____Numeral__Onatural_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J,type,
% 0.29/0.49 bNF_re6290619412732081552atural: ( int > int > $o ) > ( code_natural > produc7822875418678951345atural > $o ) > ( int > code_natural ) > ( int > produc7822875418678951345atural ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
% 0.29/0.49 bNF_re982302072995117890nteger: ( int > int > $o ) > ( int > code_integer > $o ) > ( int > int ) > ( int > code_integer ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint,type,
% 0.29/0.49 bNF_re4712519889275205905nt_int: ( int > int > $o ) > ( int > int > $o ) > ( int > int ) > ( int > int ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint_001t__Rat__Orat,type,
% 0.29/0.49 bNF_re4079880299697760445nt_rat: ( int > int > $o ) > ( int > rat > $o ) > ( int > int ) > ( int > rat ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.29/0.49 bNF_re3715656647883201625at_nat: ( int > int > $o ) > ( nat > nat > $o ) > ( int > nat ) > ( int > nat ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Num__Onum_001t__Num__Onum,type,
% 0.29/0.49 bNF_re7626690874201225453um_num: ( int > int > $o ) > ( num > num > $o ) > ( int > num ) > ( int > num ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 0.29/0.49 bNF_re6250860962936578807nt_int: ( int > int > $o ) > ( product_prod_int_int > product_prod_int_int > $o ) > ( int > product_prod_int_int ) > ( int > product_prod_int_int ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Rat__Orat,type,
% 0.29/0.49 bNF_re2214769303045360666nt_rat: ( int > int > $o ) > ( product_prod_int_int > rat > $o ) > ( int > product_prod_int_int ) > ( int > rat ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Rat__Orat_001t__Code____Numeral__Ointeger,type,
% 0.29/0.49 bNF_re1382721322319792878nteger: ( int > int > $o ) > ( rat > code_integer > $o ) > ( int > rat ) > ( int > code_integer ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Rat__Orat_001t__Int__Oint,type,
% 0.29/0.49 bNF_re3396611533439285437at_int: ( int > int > $o ) > ( rat > int > $o ) > ( int > rat ) > ( int > int ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Rat__Orat_001t__Rat__Orat,type,
% 0.29/0.49 bNF_re2763971943861839977at_rat: ( int > int > $o ) > ( rat > rat > $o ) > ( int > rat ) > ( int > rat ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Nat__Onat_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.29/0.49 bNF_re5416042074812042131at_nat: ( int > nat > $o ) > ( ( int > int ) > ( nat > nat ) > $o ) > ( int > int > int ) > ( nat > nat > nat ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Nat__Onat_001t__Int__Oint_001t__Nat__Onat,type,
% 0.29/0.49 bNF_re4343356799547411545nt_nat: ( int > nat > $o ) > ( int > nat > $o ) > ( int > int ) > ( nat > nat ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Num__Onum_001t__Nat__Onat_001t__Code____Numeral__Ointeger,type,
% 0.29/0.49 bNF_re151304249936775380nteger: ( int > num > $o ) > ( nat > code_integer > $o ) > ( int > nat ) > ( num > code_integer ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Num__Onum_001t__Num__Onum_001t__Code____Numeral__Ointeger,type,
% 0.29/0.49 bNF_re7315484114762210078nteger: ( int > num > $o ) > ( num > code_integer > $o ) > ( int > num ) > ( num > code_integer ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Rat__Orat_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Rat__Orat_Mt__Rat__Orat_J,type,
% 0.29/0.49 bNF_re7661208983170134443at_rat: ( int > rat > $o ) > ( ( int > int ) > ( rat > rat ) > $o ) > ( int > int > int ) > ( rat > rat > rat ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Rat__Orat_001t__Int__Oint_001t__Rat__Orat,type,
% 0.29/0.49 bNF_re4480299549022435433nt_rat: ( int > rat > $o ) > ( int > rat > $o ) > ( int > int ) > ( rat > rat ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Code____Numeral__Ointeger_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 0.29/0.49 bNF_re7367609096550055590nteger: ( nat > code_integer > $o ) > ( ( nat > nat ) > ( code_integer > code_integer ) > $o ) > ( nat > nat > nat ) > ( code_integer > code_integer > code_integer ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Code____Numeral__Ointeger_001t__Nat__Onat_001t__Code____Numeral__Ointeger,type,
% 0.29/0.49 bNF_re1599192376174140603nteger: ( nat > code_integer > $o ) > ( nat > code_integer > $o ) > ( nat > nat ) > ( code_integer > code_integer ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Code____Numeral__Ointeger_001t__Num__Onum_001t__Code____Numeral__Ointeger,type,
% 0.29/0.49 bNF_re8763372240999575301nteger: ( nat > code_integer > $o ) > ( num > code_integer > $o ) > ( nat > num ) > ( code_integer > code_integer ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Code____Numeral__Onatural_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Code____Numeral__Onatural_M_Eo_J,type,
% 0.29/0.49 bNF_re1639080489988575423ural_o: ( nat > code_natural > $o ) > ( ( nat > $o ) > ( code_natural > $o ) > $o ) > ( nat > nat > $o ) > ( code_natural > code_natural > $o ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Code____Numeral__Onatural_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Nat__Onat_M_Eo_J,type,
% 0.29/0.49 bNF_re2895713572246619415_nat_o: ( nat > code_natural > $o ) > ( ( nat > $o ) > ( nat > $o ) > $o ) > ( nat > nat > $o ) > ( code_natural > nat > $o ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Code____Numeral__Onatural_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J,type,
% 0.29/0.49 bNF_re88643428490162567atural: ( nat > code_natural > $o ) > ( ( nat > nat ) > ( code_natural > code_natural ) > $o ) > ( nat > nat > nat ) > ( code_natural > code_natural > code_natural ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Code____Numeral__Onatural_001_Eo_001_Eo,type,
% 0.29/0.49 bNF_re2785088596696291543al_o_o: ( nat > code_natural > $o ) > ( $o > $o > $o ) > ( nat > $o ) > ( code_natural > $o ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Code____Numeral__Onatural_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
% 0.29/0.49 bNF_re5252274238750452962nteger: ( nat > code_natural > $o ) > ( int > code_integer > $o ) > ( nat > int ) > ( code_natural > code_integer ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Code____Numeral__Onatural_001t__Nat__Onat_001t__Code____Numeral__Onatural,type,
% 0.29/0.49 bNF_re3704215830270325841atural: ( nat > code_natural > $o ) > ( nat > code_natural > $o ) > ( nat > nat ) > ( code_natural > code_natural ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Code____Numeral__Onatural_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.29/0.49 bNF_re7333046803109187065at_nat: ( nat > code_natural > $o ) > ( nat > nat > $o ) > ( nat > nat ) > ( code_natural > nat ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Int__Oint_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Int__Oint_Mt__Int__Oint_J,type,
% 0.29/0.49 bNF_re5864104203909894035nt_int: ( nat > int > $o ) > ( ( nat > nat ) > ( int > int ) > $o ) > ( nat > nat > nat ) > ( int > int > int ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Int__Oint_001t__Nat__Onat_001t__Int__Oint,type,
% 0.29/0.49 bNF_re6022984109467102297at_int: ( nat > int > $o ) > ( nat > int > $o ) > ( nat > nat ) > ( int > int ) > $o ).
% 0.29/0.49
% 0.29/0.49 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__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 0.29/0.49 bNF_re4935368626670024657nteger: ( nat > nat > $o ) > ( ( int > int ) > ( code_integer > code_integer ) > $o ) > ( nat > int > int ) > ( nat > code_integer > code_integer ) > $o ).
% 0.29/0.49
% 0.29/0.49 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,
% 0.29/0.49 bNF_re4785983289428654063nt_int: ( nat > nat > $o ) > ( ( int > int ) > ( int > int ) > $o ) > ( nat > int > int ) > ( nat > int > int ) > $o ).
% 0.29/0.49
% 0.29/0.49 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,
% 0.29/0.49 bNF_re578469030762574527_nat_o: ( nat > nat > $o ) > ( ( nat > $o ) > ( nat > $o ) > $o ) > ( nat > nat > $o ) > ( nat > nat > $o ) > $o ).
% 0.29/0.49
% 0.29/0.49 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__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J,type,
% 0.29/0.49 bNF_re3692170009638431535atural: ( nat > nat > $o ) > ( ( nat > nat ) > ( code_natural > code_natural ) > $o ) > ( nat > nat > nat ) > ( nat > code_natural > code_natural ) > $o ).
% 0.29/0.49
% 0.29/0.49 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,
% 0.29/0.49 bNF_re1345281282404953727at_nat: ( nat > nat > $o ) > ( ( nat > nat ) > ( nat > nat ) > $o ) > ( nat > nat > nat ) > ( nat > nat > nat ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001_Eo_001_Eo,type,
% 0.29/0.49 bNF_re4705727531993890431at_o_o: ( nat > nat > $o ) > ( $o > $o > $o ) > ( nat > $o ) > ( nat > $o ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Assertions__Oassn_001t__Assertions__Oassn,type,
% 0.29/0.49 bNF_re4051817429369991249n_assn: ( nat > nat > $o ) > ( assn > assn > $o ) > ( nat > assn ) > ( nat > assn ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Assertions__Oassn_001t__Code____Numeral__Ointeger,type,
% 0.29/0.49 bNF_re1831131418152741254nteger: ( nat > nat > $o ) > ( assn > code_integer > $o ) > ( nat > assn ) > ( nat > code_integer ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Assertions__Oassn_001t__Int__Oint,type,
% 0.29/0.49 bNF_re4792267480158271317sn_int: ( nat > nat > $o ) > ( assn > int > $o ) > ( nat > assn ) > ( nat > int ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Assertions__Oassn_001t__Nat__Onat,type,
% 0.29/0.49 bNF_re4794757950667321593sn_nat: ( nat > nat > $o ) > ( assn > nat > $o ) > ( nat > assn ) > ( nat > nat ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Assertions__Oassn_001t__Rat__Orat,type,
% 0.29/0.49 bNF_re4159627890580825857sn_rat: ( nat > nat > $o ) > ( assn > rat > $o ) > ( nat > assn ) > ( nat > rat ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Code____Numeral__Ointeger_001t__Assertions__Oassn,type,
% 0.29/0.49 bNF_re2692373401909853574r_assn: ( nat > nat > $o ) > ( code_integer > assn > $o ) > ( nat > code_integer ) > ( nat > assn ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 0.29/0.49 bNF_re1236659899165691067nteger: ( nat > nat > $o ) > ( code_integer > code_integer > $o ) > ( nat > code_integer ) > ( nat > code_integer ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Code____Numeral__Ointeger_001t__Int__Oint,type,
% 0.29/0.49 bNF_re3514700588913618570er_int: ( nat > nat > $o ) > ( code_integer > int > $o ) > ( nat > code_integer ) > ( nat > int ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Code____Numeral__Ointeger_001t__Nat__Onat,type,
% 0.29/0.49 bNF_re3517191059422668846er_nat: ( nat > nat > $o ) > ( code_integer > nat > $o ) > ( nat > code_integer ) > ( nat > nat ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Code____Numeral__Ointeger_001t__Rat__Orat,type,
% 0.29/0.49 bNF_re2882060999336173110er_rat: ( nat > nat > $o ) > ( code_integer > rat > $o ) > ( nat > code_integer ) > ( nat > rat ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Code____Numeral__Onatural_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J,type,
% 0.29/0.49 bNF_re6101645755646507080atural: ( nat > nat > $o ) > ( code_natural > produc7822875418678951345atural > $o ) > ( nat > code_natural ) > ( nat > produc7822875418678951345atural ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
% 0.29/0.49 bNF_re4153400068438556298nteger: ( nat > nat > $o ) > ( int > code_integer > $o ) > ( nat > int ) > ( nat > code_integer ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Int__Oint_001t__Code____Numeral__Onatural,type,
% 0.29/0.49 bNF_re2976995220195273813atural: ( nat > nat > $o ) > ( int > code_natural > $o ) > ( nat > int ) > ( nat > code_natural ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Int__Oint_001t__Int__Oint,type,
% 0.29/0.49 bNF_re6650684261131312217nt_int: ( nat > nat > $o ) > ( int > int > $o ) > ( nat > int ) > ( nat > int ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Int__Oint_001t__Nat__Onat,type,
% 0.29/0.49 bNF_re6653174731640362493nt_nat: ( nat > nat > $o ) > ( int > nat > $o ) > ( nat > int ) > ( nat > nat ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Int__Oint_001t__Rat__Orat,type,
% 0.29/0.49 bNF_re6018044671553866757nt_rat: ( nat > nat > $o ) > ( int > rat > $o ) > ( nat > int ) > ( nat > rat ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat_001t__Code____Numeral__Onatural,type,
% 0.29/0.49 bNF_re2605341659958429177atural: ( nat > nat > $o ) > ( nat > code_natural > $o ) > ( nat > nat ) > ( nat > code_natural ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.29/0.49 bNF_re5653821019739307937at_nat: ( nat > nat > $o ) > ( nat > nat > $o ) > ( nat > nat ) > ( nat > nat ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Num__Onum_001t__Num__Onum,type,
% 0.29/0.49 bNF_re341483209202555957um_num: ( nat > nat > $o ) > ( num > num > $o ) > ( nat > num ) > ( nat > num ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint,type,
% 0.29/0.49 bNF_re6830278522597306478at_int: ( nat > nat > $o ) > ( product_prod_nat_nat > int > $o ) > ( nat > product_prod_nat_nat ) > ( nat > int ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Rat__Orat_001t__Code____Numeral__Ointeger,type,
% 0.29/0.49 bNF_re4553819317763231286nteger: ( nat > nat > $o ) > ( rat > code_integer > $o ) > ( nat > rat ) > ( nat > code_integer ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Rat__Orat_001t__Code____Numeral__Onatural,type,
% 0.29/0.49 bNF_re3377414469519948801atural: ( nat > nat > $o ) > ( rat > code_natural > $o ) > ( nat > rat ) > ( nat > code_natural ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Rat__Orat_001t__Int__Oint,type,
% 0.29/0.49 bNF_re5334775905295391749at_int: ( nat > nat > $o ) > ( rat > int > $o ) > ( nat > rat ) > ( nat > int ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Rat__Orat_001t__Nat__Onat,type,
% 0.29/0.49 bNF_re5337266375804442025at_nat: ( nat > nat > $o ) > ( rat > nat > $o ) > ( nat > rat ) > ( nat > nat ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Rat__Orat_001t__Rat__Orat,type,
% 0.29/0.49 bNF_re4702136315717946289at_rat: ( nat > nat > $o ) > ( rat > rat > $o ) > ( nat > rat ) > ( nat > rat ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Rat__Orat_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Rat__Orat_Mt__Rat__Orat_J,type,
% 0.29/0.49 bNF_re3590448190763046039at_rat: ( nat > rat > $o ) > ( ( nat > nat ) > ( rat > rat ) > $o ) > ( nat > nat > nat ) > ( rat > rat > rat ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Rat__Orat_001t__Nat__Onat_001t__Rat__Orat,type,
% 0.29/0.49 bNF_re5790763769214331825at_rat: ( nat > rat > $o ) > ( nat > rat > $o ) > ( nat > nat ) > ( rat > rat ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Num__Onum_001t__Code____Numeral__Ointeger_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,type,
% 0.29/0.49 bNF_re5031869190687302234nteger: ( num > code_integer > $o ) > ( code_integer > ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > $o ) > ( num > code_integer ) > ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Num__Onum_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 0.29/0.49 bNF_re5202476307641864082nteger: ( num > code_integer > $o ) > ( code_integer > code_integer > $o ) > ( num > code_integer ) > ( code_integer > code_integer ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Num__Onum_001t__Int__Oint_001t__Code____Numeral__Ointeger_001t__Nat__Onat,type,
% 0.29/0.49 bNF_re6324211044263125204er_nat: ( num > int > $o ) > ( code_integer > nat > $o ) > ( num > code_integer ) > ( int > nat ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Num__Onum_001t__Int__Oint_001t__Code____Numeral__Ointeger_001t__Num__Onum,type,
% 0.29/0.49 bNF_re2881542830418903838er_num: ( num > int > $o ) > ( code_integer > num > $o ) > ( num > code_integer ) > ( int > num ) > $o ).
% 0.29/0.49
% 0.29/0.49 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__Code____Numeral__Ointeger_J,type,
% 0.29/0.49 bNF_re7876454716742015248nteger: ( num > num > $o ) > ( ( num > int ) > ( num > code_integer ) > $o ) > ( num > num > int ) > ( num > num > code_integer ) > $o ).
% 0.29/0.49
% 0.29/0.49 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,
% 0.29/0.49 bNF_re8402795839162346335um_int: ( num > num > $o ) > ( ( num > int ) > ( num > int ) > $o ) > ( num > num > int ) > ( num > num > int ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Num__Onum_001t__Num__Onum_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 0.29/0.49 bNF_re6741283560065411407nteger: ( num > num > $o ) > ( code_integer > code_integer > $o ) > ( num > code_integer ) > ( num > code_integer ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Num__Onum_001t__Num__Onum_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
% 0.29/0.49 bNF_re6501075790457514782nteger: ( num > num > $o ) > ( int > code_integer > $o ) > ( num > int ) > ( num > code_integer ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Num__Onum_001t__Num__Onum_001t__Int__Oint_001t__Code____Numeral__Onatural,type,
% 0.29/0.49 bNF_re5324670942214232297atural: ( num > num > $o ) > ( int > code_natural > $o ) > ( num > int ) > ( num > code_natural ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Num__Onum_001t__Num__Onum_001t__Int__Oint_001t__Int__Oint,type,
% 0.29/0.49 bNF_re1822329894187522285nt_int: ( num > num > $o ) > ( int > int > $o ) > ( num > int ) > ( num > int ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Num__Onum_001t__Num__Onum_001t__Int__Oint_001t__Nat__Onat,type,
% 0.29/0.49 bNF_re1824820364696572561nt_nat: ( num > num > $o ) > ( int > nat > $o ) > ( num > int ) > ( num > nat ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Num__Onum_001t__Num__Onum_001t__Int__Oint_001t__Rat__Orat,type,
% 0.29/0.49 bNF_re1189690304610076825nt_rat: ( num > num > $o ) > ( int > rat > $o ) > ( num > int ) > ( num > rat ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Num__Onum_001t__Num__Onum_001t__Nat__Onat_001t__Code____Numeral__Ointeger,type,
% 0.29/0.49 bNF_re6129422230220670146nteger: ( num > num > $o ) > ( nat > code_integer > $o ) > ( num > nat ) > ( num > code_integer ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Num__Onum_001t__Num__Onum_001t__Nat__Onat_001t__Code____Numeral__Onatural,type,
% 0.29/0.49 bNF_re4953017381977387661atural: ( num > num > $o ) > ( nat > code_natural > $o ) > ( num > nat ) > ( num > code_natural ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Num__Onum_001t__Num__Onum_001t__Nat__Onat_001t__Int__Oint,type,
% 0.29/0.49 bNF_re822976182286467729at_int: ( num > num > $o ) > ( nat > int > $o ) > ( num > nat ) > ( num > int ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Num__Onum_001t__Num__Onum_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.29/0.49 bNF_re825466652795518005at_nat: ( num > num > $o ) > ( nat > nat > $o ) > ( num > nat ) > ( num > nat ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Num__Onum_001t__Num__Onum_001t__Nat__Onat_001t__Rat__Orat,type,
% 0.29/0.49 bNF_re190336592709022269at_rat: ( num > num > $o ) > ( nat > rat > $o ) > ( num > nat ) > ( num > rat ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
% 0.29/0.49 bNF_re5228765855967844073nt_int: ( product_prod_int_int > product_prod_int_int > $o ) > ( ( product_prod_int_int > product_prod_int_int ) > ( product_prod_int_int > product_prod_int_int ) > $o ) > ( product_prod_int_int > product_prod_int_int > product_prod_int_int ) > ( product_prod_int_int > product_prod_int_int > product_prod_int_int ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 0.29/0.49 bNF_re7145576690424134365nt_int: ( product_prod_int_int > product_prod_int_int > $o ) > ( product_prod_int_int > product_prod_int_int > $o ) > ( product_prod_int_int > product_prod_int_int ) > ( product_prod_int_int > product_prod_int_int ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Rat__Orat_001_062_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Rat__Orat_Mt__Rat__Orat_J,type,
% 0.29/0.49 bNF_re7627151682743391978at_rat: ( product_prod_int_int > rat > $o ) > ( ( product_prod_int_int > product_prod_int_int ) > ( rat > rat ) > $o ) > ( product_prod_int_int > product_prod_int_int > product_prod_int_int ) > ( rat > rat > rat ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Rat__Orat_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Rat__Orat,type,
% 0.29/0.49 bNF_re8279943556446156061nt_rat: ( product_prod_int_int > rat > $o ) > ( product_prod_int_int > rat > $o ) > ( product_prod_int_int > product_prod_int_int ) > ( rat > rat ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_001_062_It__Int__Oint_M_Eo_J,type,
% 0.29/0.49 bNF_re717283939379294677_int_o: ( product_prod_nat_nat > int > $o ) > ( ( product_prod_nat_nat > $o ) > ( int > $o ) > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( int > int > $o ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001_062_It__Int__Oint_Mt__Int__Oint_J,type,
% 0.29/0.49 bNF_re7408651293131936558nt_int: ( product_prod_nat_nat > int > $o ) > ( ( product_prod_nat_nat > product_prod_nat_nat ) > ( int > int ) > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > ( int > int > int ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001_Eo_001_Eo,type,
% 0.29/0.49 bNF_re6644619430987730960nt_o_o: ( product_prod_nat_nat > int > $o ) > ( $o > $o > $o ) > ( product_prod_nat_nat > $o ) > ( int > $o ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint,type,
% 0.29/0.49 bNF_re7400052026677387805at_int: ( product_prod_nat_nat > int > $o ) > ( product_prod_nat_nat > int > $o ) > ( product_prod_nat_nat > product_prod_nat_nat ) > ( int > int ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J,type,
% 0.29/0.49 bNF_re4202695980764964119_nat_o: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( ( product_prod_nat_nat > $o ) > ( product_prod_nat_nat > $o ) > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 0.29/0.49 bNF_re3099431351363272937at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( ( product_prod_nat_nat > product_prod_nat_nat ) > ( product_prod_nat_nat > product_prod_nat_nat ) > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_Eo_001_Eo,type,
% 0.29/0.49 bNF_re3666534408544137501at_o_o: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( $o > $o > $o ) > ( product_prod_nat_nat > $o ) > ( product_prod_nat_nat > $o ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.29/0.49 bNF_re2241393799969408733at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > product_prod_nat_nat ) > ( product_prod_nat_nat > product_prod_nat_nat ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Ounit_001t__Product____Type__Ounit_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 0.29/0.49 bNF_re8417623677625516633nteger: ( product_unit > product_unit > $o ) > ( code_integer > code_integer > $o ) > ( product_unit > code_integer ) > ( product_unit > code_integer ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Ounit_001t__Product____Type__Ounit_001t__Code____Numeral__Onatural_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J,type,
% 0.29/0.49 bNF_re5641277236161133866atural: ( product_unit > product_unit > $o ) > ( code_natural > produc7822875418678951345atural > $o ) > ( product_unit > code_natural ) > ( product_unit > produc7822875418678951345atural ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Ounit_001t__Product____Type__Ounit_001t__Int__Oint_001t__Int__Oint,type,
% 0.29/0.49 bNF_re8422471777688076791nt_int: ( product_unit > product_unit > $o ) > ( int > int > $o ) > ( product_unit > int ) > ( product_unit > int ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Rat__Orat_001t__Code____Numeral__Ointeger_001_062_It__Rat__Orat_Mt__Rat__Orat_J_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 0.29/0.49 bNF_re4307939118855507134nteger: ( rat > code_integer > $o ) > ( ( rat > rat ) > ( code_integer > code_integer ) > $o ) > ( rat > rat > rat ) > ( code_integer > code_integer > code_integer ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Rat__Orat_001t__Code____Numeral__Ointeger_001t__Rat__Orat_001t__Code____Numeral__Ointeger,type,
% 0.29/0.49 bNF_re2328245411608324299nteger: ( rat > code_integer > $o ) > ( rat > code_integer > $o ) > ( rat > rat ) > ( code_integer > code_integer ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_BNF__Def_Orel__fun_001t__Rat__Orat_001t__Code____Numeral__Onatural_001_062_It__Rat__Orat_Mt__Rat__Orat_J_001_062_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J,type,
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% 0.29/0.49 thf(sy_c_Finite__Set_Ofinite_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J,type,
% 0.29/0.49 finite2970523954037356441et_nat: set_Pr3948176798113811640et_nat > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Finite__Set_Ofinite_001t__Product____Type__Oprod_It__Int__Oint_Mt__Code____Numeral__Ointeger_J,type,
% 0.29/0.49 finite1525696360262406931nteger: set_Pr8415741480598773322nteger > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Finite__Set_Ofinite_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 0.29/0.49 finite2998713641127702882nt_int: set_Pr958786334691620121nt_int > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Finite__Set_Ofinite_001t__Product____Type__Oprod_It__Int__Oint_Mt__Nat__Onat_J,type,
% 0.29/0.49 finite7176564660636899590nt_nat: set_Pr3448869479623346877nt_nat > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Finite__Set_Ofinite_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J,type,
% 0.29/0.49 finite1154042800025562295nteger: set_Pr2406931829603198446nteger > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Finite__Set_Ofinite_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Int__Oint_J,type,
% 0.29/0.49 finite1999359929226648326at_int: set_Pr7995236796853374141at_int > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Finite__Set_Ofinite_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.29/0.49 finite6177210948735845034at_nat: set_Pr1261947904930325089at_nat > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Finite__Set_Ofinite_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 0.29/0.49 finite4392333629123659920at_nat: set_Pr8693737435421807431at_nat > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Finite__Set_Ofinite_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 0.29/0.49 finite6446286893012251551it_nat: set_Pr1354866905816374718it_nat > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Finite__Set_Ofinite_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 0.29/0.49 finite4343798906461161616at_nat: set_Pr4329608150637261639at_nat > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Finite__Set_Ofinite_001t__Product____Type__Ounit,type,
% 0.29/0.49 finite4290736615968046902t_unit: set_Product_unit > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Finite__Set_Ofinite_001t__Rat__Orat,type,
% 0.29/0.49 finite_finite_rat: set_rat > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Finite__Set_Ofinite_001t__Set__Oset_It__Code____Numeral__Ointeger_J,type,
% 0.29/0.49 finite6931041176100689706nteger: set_set_Code_integer > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Finite__Set_Ofinite_001t__Set__Oset_It__Int__Oint_J,type,
% 0.29/0.49 finite6197958912794628473et_int: set_set_int > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Finite__Set_Ofinite_001t__Set__Oset_It__List__Olist_It__Nat__Onat_J_J,type,
% 0.29/0.49 finite7047420756378620717st_nat: set_set_list_nat > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Finite__Set_Ofinite_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.29/0.49 finite1152437895449049373et_nat: set_set_nat > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Finite__Set_Ofinite_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 0.29/0.49 finite9047747110432174090at_nat: set_se7855581050983116737at_nat > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Finite__Set_Ofinite_001t__Set__Oset_It__Product____Type__Ounit_J,type,
% 0.29/0.49 finite1772178364199683094t_unit: set_set_Product_unit > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Finite__Set_Ofold_001t__Int__Oint_001t__Int__Oint,type,
% 0.29/0.49 finite_fold_int_int: ( int > int > int ) > int > set_int > int ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Finite__Set_Ofold_001t__Nat__Onat_001t__Int__Oint,type,
% 0.29/0.49 finite_fold_nat_int: ( nat > int > int ) > int > set_nat > int ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Finite__Set_Ofold_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.29/0.49 finite_fold_nat_nat: ( nat > nat > nat ) > nat > set_nat > nat ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Finite__Set_Ofold_001t__Nat__Onat_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 0.29/0.49 finite3745491028973389255at_nat: ( nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ) > set_Pr1261947904930325089at_nat > set_nat > set_Pr1261947904930325089at_nat ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Finite__Set_Ofold_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_001t__Set__Oset_It__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_J,type,
% 0.29/0.49 finite8124994865635982712et_nat: ( produc3925858234332021118et_nat > set_Pr8536935166611901872et_nat > set_Pr8536935166611901872et_nat ) > set_Pr8536935166611901872et_nat > set_Pr3286484037609594932et_nat > set_Pr8536935166611901872et_nat ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Finite__Set_Ofold_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Set__Oset_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J,type,
% 0.29/0.49 finite7641027033760462367nteger: ( produc8923325533196201883nteger > set_Pr1281608226676607948nteger > set_Pr1281608226676607948nteger ) > set_Pr1281608226676607948nteger > set_Pr4811707699266497531nteger > set_Pr1281608226676607948nteger ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Finite__Set_Ofold_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_001t__Set__Oset_It__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,
% 0.29/0.49 finite2494574492299216512et_nat: ( produc3658429121746597890et_nat > set_Pr3286484037609594932et_nat > set_Pr3286484037609594932et_nat ) > set_Pr3286484037609594932et_nat > set_Pr3948176798113811640et_nat > set_Pr3286484037609594932et_nat ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Finite__Set_Ofold_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Set__Oset_It__Product____Type__Oprod_I_062_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
% 0.29/0.49 finite5333674244414288180nt_int: ( product_prod_int_int > set_Pr1872883991513573699nt_int > set_Pr1872883991513573699nt_int ) > set_Pr1872883991513573699nt_int > set_Pr958786334691620121nt_int > set_Pr1872883991513573699nt_int ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Finite__Set_Ofold_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Set__Oset_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Int__Oint_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
% 0.29/0.49 finite1318812335397358250nt_int: ( product_prod_int_int > set_Pr9222295170931077689nt_int > set_Pr9222295170931077689nt_int ) > set_Pr9222295170931077689nt_int > set_Pr958786334691620121nt_int > set_Pr9222295170931077689nt_int ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Finite__Set_Ofold_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
% 0.29/0.49 finite3179781904389220718at_nat: ( set_Pr1261947904930325089at_nat > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat ) > set_Pr4329608150637261639at_nat > set_se7855581050983116737at_nat > set_Pr4329608150637261639at_nat ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001_062_I_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_Mt__Num__Onum_J,type,
% 0.29/0.49 comp_C3959375555751086581er_num: ( ( code_integer > code_integer ) > code_integer > code_integer ) > ( ( ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > num ) > code_integer > code_integer ) > ( ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > num ) > code_integer > code_integer ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Code____Numeral__Ointeger,type,
% 0.29/0.49 comp_C2822359487432382964nteger: ( ( code_integer > code_integer ) > code_integer > code_integer ) > ( code_integer > code_integer > code_integer ) > code_integer > code_integer > code_integer ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001_062_It__Num__Onum_M_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_J_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 0.29/0.49 comp_C5301300457492916725nteger: ( ( code_integer > code_integer ) > num > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( ( code_integer > code_integer ) > code_integer > code_integer ) > ( code_integer > code_integer ) > num > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001_062_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_001_062_It__Code____Numeral__Ointeger_Mt__Num__Onum_J,type,
% 0.29/0.49 comp_C9104104092898552938er_num: ( ( code_integer > code_integer ) > num > code_integer ) > ( ( code_integer > num ) > code_integer > code_integer ) > ( code_integer > num ) > num > code_integer ).
% 0.29/0.49
% 0.29/0.49 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_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 0.29/0.49 comp_C3983183376822107068nteger: ( ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( ( code_integer > code_integer ) > code_integer > code_integer ) > ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 0.29/0.49
% 0.29/0.49 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,
% 0.29/0.49 comp_C8797469213163452608nteger: ( ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 0.29/0.49
% 0.29/0.49 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__Num__Onum,type,
% 0.29/0.49 comp_C8645541002826910333er_num: ( ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( num > code_integer > code_integer ) > num > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 0.29/0.49 comp_C5076291335850163704nteger: ( ( code_integer > code_integer ) > code_integer ) > ( code_integer > code_integer > code_integer ) > code_integer > code_integer ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001_062_It__Code____Numeral__Ointeger_Mt__Nat__Onat_J_001_062_It__Num__Onum_Mt__Num__Onum_J_001_062_It__Code____Numeral__Ointeger_Mt__Int__Oint_J,type,
% 0.29/0.49 comp_C8127656796141369388er_int: ( ( code_integer > nat ) > num > num ) > ( ( code_integer > int ) > code_integer > nat ) > ( code_integer > int ) > num > num ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001_062_It__Int__Oint_M_Eo_J_001_062_It__Int__Oint_M_Eo_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J,type,
% 0.29/0.49 comp_i6226780894115828703_nat_o: ( ( int > $o ) > int > $o ) > ( ( product_prod_nat_nat > $o ) > int > $o ) > ( product_prod_nat_nat > $o ) > int > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001_062_It__Int__Oint_M_Eo_J_001_062_It__Int__Oint_M_Eo_J_001t__Int__Oint,type,
% 0.29/0.49 comp_int_o_int_o_int: ( ( int > $o ) > int > $o ) > ( int > int > $o ) > int > int > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001_062_It__Int__Oint_M_Eo_J_001_062_It__Int__Oint_Mt__Int__Oint_J_001t__Int__Oint,type,
% 0.29/0.49 comp_i1993086638917920293nt_int: ( ( int > $o ) > int > int ) > ( int > int > $o ) > int > int > int ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001_062_It__Int__Oint_M_Eo_J_001_062_It__Nat__Onat_M_Eo_J_001t__Int__Oint,type,
% 0.29/0.49 comp_int_o_nat_o_int: ( ( int > $o ) > nat > $o ) > ( int > int > $o ) > int > nat > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Int__Oint_M_Eo_J_001t__Int__Oint,type,
% 0.29/0.49 comp_i5098556425753098485_o_int: ( ( int > int ) > int > $o ) > ( int > int > int ) > int > int > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Int__Oint_Mt__Int__Oint_J_001t__Int__Oint,type,
% 0.29/0.49 comp_i1129928922100200191nt_int: ( ( int > int ) > int > int ) > ( int > int > int ) > int > int > int ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Nat__Onat_M_Eo_J_001t__Int__Oint,type,
% 0.29/0.49 comp_i4411980392712547921_o_int: ( ( int > int ) > nat > $o ) > ( int > int > int ) > int > nat > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001_062_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001t__Int__Oint,type,
% 0.29/0.49 comp_i1790862786758963855nt_int: ( ( int > product_prod_int_int ) > int > product_prod_int_int ) > ( int > int > product_prod_int_int ) > int > int > product_prod_int_int ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001_062_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Int__Oint_Mt__Rat__Orat_J_001_062_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
% 0.29/0.49 comp_i118865614814752126nt_int: ( ( int > product_prod_int_int ) > int > rat ) > ( ( int > product_prod_int_int ) > int > product_prod_int_int ) > ( int > product_prod_int_int ) > int > rat ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001_062_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Int__Oint_Mt__Rat__Orat_J_001t__Int__Oint,type,
% 0.29/0.49 comp_i1302866070986779890at_int: ( ( int > product_prod_int_int ) > int > rat ) > ( int > int > product_prod_int_int ) > int > int > rat ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001_062_It__Int__Oint_Mt__Rat__Orat_J_001_062_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001t__Int__Oint,type,
% 0.29/0.49 comp_i929186717396404458nt_int: ( ( int > rat ) > int > product_prod_int_int ) > ( int > int > rat ) > int > int > product_prod_int_int ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001_062_It__Int__Oint_Mt__Rat__Orat_J_001_062_It__Int__Oint_Mt__Rat__Orat_J_001_062_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
% 0.29/0.49 comp_i5271019637457297241nt_int: ( ( int > rat ) > int > rat ) > ( ( int > product_prod_int_int ) > int > rat ) > ( int > product_prod_int_int ) > int > rat ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001_062_It__Int__Oint_Mt__Rat__Orat_J_001_062_It__Int__Oint_Mt__Rat__Orat_J_001t__Int__Oint,type,
% 0.29/0.49 comp_i8258899369942393943at_int: ( ( int > rat ) > int > rat ) > ( int > int > rat ) > int > int > rat ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Int__Oint_M_Eo_J_001t__Int__Oint,type,
% 0.29/0.49 comp_nat_o_int_o_int: ( ( nat > $o ) > int > $o ) > ( int > nat > $o ) > int > int > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Int__Oint_Mt__Int__Oint_J_001t__Int__Oint,type,
% 0.29/0.49 comp_n3090169619561918849nt_int: ( ( nat > $o ) > int > int ) > ( int > nat > $o ) > int > int > int ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Nat__Onat_M_Eo_J,type,
% 0.29/0.49 comp_n5656820349209612572_nat_o: ( ( nat > $o ) > nat > $o ) > ( ( nat > $o ) > nat > $o ) > ( nat > $o ) > nat > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Nat__Onat_M_Eo_J_001t__Int__Oint,type,
% 0.29/0.49 comp_nat_o_nat_o_int: ( ( nat > $o ) > nat > $o ) > ( int > nat > $o ) > int > nat > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001_062_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J_001_062_It__Int__Oint_Mt__Code____Numeral__Ointeger_J_001_062_It__Num__Onum_Mt__Num__Onum_J,type,
% 0.29/0.49 comp_n3323228797031117228um_num: ( ( nat > code_integer ) > int > code_integer ) > ( ( num > num ) > nat > code_integer ) > ( num > num ) > int > code_integer ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Int__Oint_Mt__Num__Onum_J_001_062_It__Num__Onum_Mt__Int__Oint_J,type,
% 0.29/0.49 comp_n4765151935410462062um_int: ( ( nat > nat ) > int > num ) > ( ( num > int ) > nat > nat ) > ( num > int ) > int > num ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_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_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,
% 0.29/0.49 comp_P3928908779438215820nteger: ( ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_001_062_It__Int__Oint_M_Eo_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J,type,
% 0.29/0.49 comp_P286844350285437056_nat_o: ( ( product_prod_nat_nat > $o ) > int > $o ) > ( ( product_prod_nat_nat > $o ) > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > $o ) > int > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_001_062_It__Int__Oint_M_Eo_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.29/0.49 comp_P9039549498699531069at_nat: ( ( product_prod_nat_nat > $o ) > int > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > int > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001_062_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.29/0.49 comp_P1872448293794610368at_nat: ( ( product_prod_nat_nat > product_prod_nat_nat ) > int > int ) > ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > product_prod_nat_nat > int > int ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001_062_It__Set__Oset_I_Eo_J_Mt__Assertions__Oassn_J_001_062_It__Set__Oset_It__Set__Oset_I_Eo_J_J_Mt__Assertions__Oassn_J_001_062_I_Eo_Mt__Assertions__Oassn_J,type,
% 0.29/0.49 comp_s518380907012905326o_assn: ( ( set_o > assn ) > set_set_o > assn ) > ( ( $o > assn ) > set_o > assn ) > ( $o > assn ) > set_set_o > assn ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001_062_It__Set__Oset_I_Eo_J_Mt__Code____Numeral__Ointeger_J_001_062_It__Set__Oset_It__Set__Oset_I_Eo_J_J_Mt__Code____Numeral__Ointeger_J_001_062_I_Eo_Mt__Code____Numeral__Ointeger_J,type,
% 0.29/0.49 comp_s262121120021782499nteger: ( ( set_o > code_integer ) > set_set_o > code_integer ) > ( ( $o > code_integer ) > set_o > code_integer ) > ( $o > code_integer ) > set_set_o > code_integer ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001_062_It__Set__Oset_I_Eo_J_Mt__Nat__Onat_J_001_062_It__Set__Oset_It__Set__Oset_I_Eo_J_J_Mt__Nat__Onat_J_001_062_I_Eo_Mt__Nat__Onat_J,type,
% 0.29/0.49 comp_s6084864194472624150_o_nat: ( ( set_o > nat ) > set_set_o > nat ) > ( ( $o > nat ) > set_o > nat ) > ( $o > nat ) > set_set_o > nat ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001_062_It__Set__Oset_I_Eo_J_Mt__Rat__Orat_J_001_062_It__Set__Oset_It__Set__Oset_I_Eo_J_J_Mt__Rat__Orat_J_001_062_I_Eo_Mt__Rat__Orat_J,type,
% 0.29/0.49 comp_s1265507639253661726_o_rat: ( ( set_o > rat ) > set_set_o > rat ) > ( ( $o > rat ) > set_o > rat ) > ( $o > rat ) > set_set_o > rat ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001_062_It__Set__Oset_It__Code____Numeral__Ointeger_J_Mt__Assertions__Oassn_J_001_062_It__Set__Oset_It__Set__Oset_It__Code____Numeral__Ointeger_J_J_Mt__Assertions__Oassn_J_001_062_It__Code____Numeral__Ointeger_Mt__Assertions__Oassn_J,type,
% 0.29/0.49 comp_s3531641609786562035r_assn: ( ( set_Code_integer > assn ) > set_set_Code_integer > assn ) > ( ( code_integer > assn ) > set_Code_integer > assn ) > ( code_integer > assn ) > set_set_Code_integer > assn ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001_062_It__Set__Oset_It__Code____Numeral__Ointeger_J_Mt__Code____Numeral__Ointeger_J_001_062_It__Set__Oset_It__Set__Oset_It__Code____Numeral__Ointeger_J_J_Mt__Code____Numeral__Ointeger_J_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 0.29/0.49 comp_s8484400498494363538nteger: ( ( set_Code_integer > code_integer ) > set_set_Code_integer > code_integer ) > ( ( code_integer > code_integer ) > set_Code_integer > code_integer ) > ( code_integer > code_integer ) > set_set_Code_integer > code_integer ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001_062_It__Set__Oset_It__Code____Numeral__Ointeger_J_Mt__Rat__Orat_J_001_062_It__Set__Oset_It__Set__Oset_It__Code____Numeral__Ointeger_J_J_Mt__Rat__Orat_J_001_062_It__Code____Numeral__Ointeger_Mt__Rat__Orat_J,type,
% 0.29/0.49 comp_s9045439038509510147er_rat: ( ( set_Code_integer > rat ) > set_set_Code_integer > rat ) > ( ( code_integer > rat ) > set_Code_integer > rat ) > ( code_integer > rat ) > set_set_Code_integer > rat ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001_062_It__Set__Oset_It__Int__Oint_J_Mt__Assertions__Oassn_J_001_062_It__Set__Oset_It__Set__Oset_It__Int__Oint_J_J_Mt__Assertions__Oassn_J_001_062_It__Int__Oint_Mt__Assertions__Oassn_J,type,
% 0.29/0.49 comp_s4595925057662634336t_assn: ( ( set_int > assn ) > set_set_int > assn ) > ( ( int > assn ) > set_int > assn ) > ( int > assn ) > set_set_int > assn ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001_062_It__Set__Oset_It__Int__Oint_J_Mt__Code____Numeral__Ointeger_J_001_062_It__Set__Oset_It__Set__Oset_It__Int__Oint_J_J_Mt__Code____Numeral__Ointeger_J_001_062_It__Int__Oint_Mt__Code____Numeral__Ointeger_J,type,
% 0.29/0.49 comp_s7646638485285982975nteger: ( ( set_int > code_integer ) > set_set_int > code_integer ) > ( ( int > code_integer ) > set_int > code_integer ) > ( int > code_integer ) > set_set_int > code_integer ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001_062_It__Set__Oset_It__Int__Oint_J_Mt__Rat__Orat_J_001_062_It__Set__Oset_It__Set__Oset_It__Int__Oint_J_J_Mt__Rat__Orat_J_001_062_It__Int__Oint_Mt__Rat__Orat_J,type,
% 0.29/0.49 comp_s4088261402702255472nt_rat: ( ( set_int > rat ) > set_set_int > rat ) > ( ( int > rat ) > set_int > rat ) > ( int > rat ) > set_set_int > rat ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001_Eo_001_Eo_001_Eo,type,
% 0.29/0.49 comp_o_o_o: ( $o > $o ) > ( $o > $o ) > $o > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001_Eo_001_Eo_001t__Nat__Onat,type,
% 0.29/0.49 comp_o_o_nat: ( $o > $o ) > ( nat > $o ) > nat > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001_Eo_001_Eo_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.29/0.49 comp_o8022916681612831582at_nat: ( $o > $o ) > ( product_prod_nat_nat > $o ) > product_prod_nat_nat > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Code____Numeral__Ointeger,type,
% 0.29/0.49 comp_C2931745410781319416nteger: ( code_integer > code_integer > code_integer ) > ( code_integer > code_integer ) > code_integer > code_integer > code_integer ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Num__Onum,type,
% 0.29/0.49 comp_C3662112809048933045er_num: ( code_integer > code_integer > code_integer ) > ( num > code_integer ) > num > code_integer > code_integer ).
% 0.29/0.49
% 0.29/0.49 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_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 0.29/0.49 comp_C95226695241045696nteger: ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( ( code_integer > code_integer ) > code_integer ) > ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 0.29/0.49
% 0.29/0.49 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,
% 0.29/0.49 comp_C1593894019821074884nteger: ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 0.29/0.49
% 0.29/0.49 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__Num__Onum,type,
% 0.29/0.49 comp_C6617437204949736321er_num: ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( num > code_integer ) > num > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001t__Assertions__Oassn_001t__Nat__Onat,type,
% 0.29/0.49 comp_C8462447471145125178sn_nat: ( code_integer > assn ) > ( nat > code_integer ) > nat > assn ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 0.29/0.49 comp_C7449957260575251196nteger: ( code_integer > code_integer ) > ( code_integer > code_integer ) > code_integer > code_integer ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Nat__Onat,type,
% 0.29/0.49 comp_C6974050283906349679er_nat: ( code_integer > code_integer ) > ( nat > code_integer ) > nat > code_integer ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Num__Onum,type,
% 0.29/0.49 comp_C3531382070062128313er_num: ( code_integer > code_integer ) > ( num > code_integer ) > num > code_integer ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 0.29/0.49 comp_C1043215000170864188nteger: ( code_integer > code_integer ) > ( produc8923325533196201883nteger > code_integer ) > produc8923325533196201883nteger > code_integer ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001t__Int__Oint_001t__Int__Oint,type,
% 0.29/0.49 comp_C5046419837055054490nt_int: ( code_integer > int ) > ( int > code_integer ) > int > int ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001t__Int__Oint_001t__Nat__Onat,type,
% 0.29/0.49 comp_C5048910307564104766nt_nat: ( code_integer > int ) > ( nat > code_integer ) > nat > int ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.29/0.49 comp_C4049556595663050210at_nat: ( code_integer > nat ) > ( nat > code_integer ) > nat > nat ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 0.29/0.49 comp_C2277306503614464128nteger: ( code_integer > produc8923325533196201883nteger ) > ( produc8923325533196201883nteger > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001t__Product____Type__Ounit_001t__Nat__Onat,type,
% 0.29/0.49 comp_C8086623346886033437it_nat: ( code_integer > product_unit ) > ( nat > code_integer ) > nat > product_unit ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001t__Rat__Orat_001t__Nat__Onat,type,
% 0.29/0.49 comp_C3733001951728184298at_nat: ( code_integer > rat ) > ( nat > code_integer ) > nat > rat ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001_062_It__Int__Oint_M_Eo_J_001t__Int__Oint,type,
% 0.29/0.49 comp_int_int_o_int: ( int > int > $o ) > ( int > int ) > int > int > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001_062_It__Int__Oint_Mt__Int__Oint_J_001t__Int__Oint,type,
% 0.29/0.49 comp_int_int_int_int: ( int > int > int ) > ( int > int ) > int > int > int ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001_062_It__Int__Oint_Mt__Int__Oint_J_001t__Nat__Onat,type,
% 0.29/0.49 comp_int_int_int_nat: ( int > int > int ) > ( nat > int ) > nat > int > int ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001_062_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001t__Int__Oint,type,
% 0.29/0.49 comp_i87437609017934369nt_int: ( int > int > product_prod_int_int ) > ( int > int ) > int > int > product_prod_int_int ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001_062_It__Int__Oint_Mt__Rat__Orat_J_001t__Int__Oint,type,
% 0.29/0.49 comp_int_int_rat_int: ( int > int > rat ) > ( int > int ) > int > int > rat ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001_062_It__Nat__Onat_M_Eo_J_001t__Int__Oint,type,
% 0.29/0.49 comp_int_nat_o_int: ( int > nat > $o ) > ( int > int ) > int > nat > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Assertions__Oassn_001t__Int__Oint,type,
% 0.29/0.49 comp_int_assn_int: ( int > assn ) > ( int > int ) > int > assn ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Assertions__Oassn_001t__Nat__Onat,type,
% 0.29/0.49 comp_int_assn_nat: ( int > assn ) > ( nat > int ) > nat > assn ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Code____Numeral__Ointeger_001t__Int__Oint,type,
% 0.29/0.49 comp_i1585864551200866970er_int: ( int > code_integer ) > ( int > int ) > int > code_integer ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Code____Numeral__Ointeger_001t__Nat__Onat,type,
% 0.29/0.49 comp_i1588355021709917246er_nat: ( int > code_integer ) > ( nat > int ) > nat > code_integer ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint,type,
% 0.29/0.49 comp_int_int_int: ( int > int ) > ( int > int ) > int > int ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Int__Oint_001t__Nat__Onat,type,
% 0.29/0.49 comp_int_int_nat: ( int > int ) > ( nat > int ) > nat > int ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Int__Oint_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 0.29/0.49 comp_i4330622015127193916nt_int: ( int > int ) > ( product_prod_int_int > int ) > product_prod_int_int > int ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Nat__Onat_001t__Int__Oint,type,
% 0.29/0.49 comp_int_nat_int: ( int > nat ) > ( int > int ) > int > nat ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.29/0.49 comp_int_nat_nat: ( int > nat ) > ( nat > int ) > nat > nat ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Num__Onum_001t__Int__Oint,type,
% 0.29/0.49 comp_int_num_int: ( int > num ) > ( int > int ) > int > num ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 0.29/0.49 comp_i5941103828406351439nt_int: ( int > product_prod_int_int ) > ( product_prod_int_int > int ) > product_prod_int_int > product_prod_int_int ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint,type,
% 0.29/0.49 comp_i1108739374719436894at_int: ( int > product_prod_nat_nat ) > ( int > int ) > int > product_prod_nat_nat ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Rat__Orat_001t__Int__Oint,type,
% 0.29/0.49 comp_int_rat_int: ( int > rat ) > ( int > int ) > int > rat ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Rat__Orat_001t__Nat__Onat,type,
% 0.29/0.49 comp_int_rat_nat: ( int > rat ) > ( nat > int ) > nat > rat ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat,type,
% 0.29/0.49 comp_nat_nat_nat_nat: ( nat > nat > nat ) > ( nat > nat ) > nat > nat > nat ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001_Eo_001t__Nat__Onat,type,
% 0.29/0.49 comp_nat_o_nat: ( nat > $o ) > ( nat > nat ) > nat > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Assertions__Oassn_001t__Nat__Onat,type,
% 0.29/0.49 comp_nat_assn_nat: ( nat > assn ) > ( nat > nat ) > nat > assn ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Code____Numeral__Ointeger_001t__Nat__Onat,type,
% 0.29/0.49 comp_n3898172953802868194er_nat: ( nat > code_integer ) > ( nat > nat ) > nat > code_integer ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Int__Oint_001t__Int__Oint,type,
% 0.29/0.49 comp_nat_int_int: ( nat > int ) > ( int > nat ) > int > int ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Int__Oint_001t__Nat__Onat,type,
% 0.29/0.49 comp_nat_int_nat: ( nat > int ) > ( nat > nat ) > nat > int ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Nat__Onat,type,
% 0.29/0.49 comp_n8698576032424989604at_nat: ( nat > multis2468970476368604999at_nat ) > ( nat > nat ) > nat > multis2468970476368604999at_nat ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Nat__Onat_001t__Int__Oint,type,
% 0.29/0.49 comp_nat_nat_int: ( nat > nat ) > ( int > nat ) > int > nat ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.29/0.49 comp_nat_nat_nat: ( nat > nat ) > ( nat > nat ) > nat > nat ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Num__Onum_001t__Int__Oint,type,
% 0.29/0.49 comp_nat_num_int: ( nat > num ) > ( int > nat ) > int > num ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Num__Onum_001t__Nat__Onat,type,
% 0.29/0.49 comp_nat_num_nat: ( nat > num ) > ( nat > nat ) > nat > num ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Product____Type__Ounit_001t__Nat__Onat,type,
% 0.29/0.49 comp_n9025697279074352746it_nat: ( nat > product_unit ) > ( nat > nat ) > nat > product_unit ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Rat__Orat_001t__Nat__Onat,type,
% 0.29/0.49 comp_nat_rat_nat: ( nat > rat ) > ( nat > nat ) > nat > rat ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001t__Num__Onum_001t__Code____Numeral__Ointeger_001t__Num__Onum,type,
% 0.29/0.49 comp_n6909714581898973814er_num: ( num > code_integer ) > ( num > num ) > num > code_integer ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001t__Num__Onum_001t__Int__Oint_001t__Num__Onum,type,
% 0.29/0.49 comp_num_int_num: ( num > int ) > ( num > num ) > num > int ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001t__Num__Onum_001t__Nat__Onat_001t__Num__Onum,type,
% 0.29/0.49 comp_num_nat_num: ( num > nat ) > ( num > num ) > num > nat ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001t__Num__Onum_001t__Num__Onum_001t__Int__Oint,type,
% 0.29/0.49 comp_num_num_int: ( num > num ) > ( int > num ) > int > num ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001t__Num__Onum_001t__Num__Onum_001t__Nat__Onat,type,
% 0.29/0.49 comp_num_num_nat: ( num > num ) > ( nat > num ) > nat > num ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001t__Num__Onum_001t__Num__Onum_001t__Num__Onum,type,
% 0.29/0.49 comp_num_num_num: ( num > num ) > ( num > num ) > num > num ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001t__Num__Onum_001t__Option__Ooption_It__Num__Onum_J_001t__Num__Onum,type,
% 0.29/0.49 comp_n6731957995704128387um_num: ( num > option_num ) > ( num > num ) > num > option_num ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001t__Option__Ooption_I_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001t__Option__Ooption_I_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_J_001t__Option__Ooption_It__Code____Numeral__Ointeger_J,type,
% 0.29/0.49 comp_o7188567781464924208nteger: ( option8057788054806935849nteger > option7428179582072448501nteger ) > ( option_Code_integer > option8057788054806935849nteger ) > option_Code_integer > option7428179582072448501nteger ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001t__Option__Ooption_I_062_It__Nat__Onat_M_Eo_J_J_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Nat__Onat_M_Eo_J,type,
% 0.29/0.49 comp_o8860755393669798242_nat_o: ( option_nat_o > nat > $o ) > ( ( nat > $o ) > option_nat_o ) > ( nat > $o ) > nat > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001t__Option__Ooption_I_Eo_J_001_Eo_001_Eo,type,
% 0.29/0.49 comp_option_o_o_o: ( option_o > $o ) > ( $o > option_o ) > $o > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001t__Option__Ooption_It__Code____Numeral__Ointeger_J_001t__Option__Ooption_I_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_J_001t__Option__Ooption_It__Code____Numeral__Ointeger_J,type,
% 0.29/0.49 comp_o9011007105448239796nteger: ( option_Code_integer > option7428179582072448501nteger ) > ( option_Code_integer > option_Code_integer ) > option_Code_integer > option7428179582072448501nteger ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001t__Option__Ooption_It__Code____Numeral__Ointeger_J_001t__Option__Ooption_It__Code____Numeral__Ointeger_J_001t__Option__Ooption_It__Num__Onum_J,type,
% 0.29/0.49 comp_o5321900959263616553on_num: ( option_Code_integer > option_Code_integer ) > ( option_num > option_Code_integer ) > option_num > option_Code_integer ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001t__Option__Ooption_It__Int__Oint_J_001t__Int__Oint_001t__Int__Oint,type,
% 0.29/0.49 comp_o2446264010603541305nt_int: ( option_int > int ) > ( int > option_int ) > int > int ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001t__Option__Ooption_It__Nat__Onat_J_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.29/0.49 comp_o4663963155070737957at_nat: ( option_nat > nat ) > ( nat > option_nat ) > nat > nat ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001t__Option__Ooption_It__Nat__Onat_J_001t__Option__Ooption_It__Num__Onum_J_001t__Option__Ooption_It__Int__Oint_J,type,
% 0.29/0.49 comp_o3128663659858294251on_int: ( option_nat > option_num ) > ( option_int > option_nat ) > option_int > option_num ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001t__Option__Ooption_It__Num__Onum_J_001t__Nat__Onat_001t__Option__Ooption_It__Num__Onum_J,type,
% 0.29/0.49 comp_o6878144249584144265on_num: ( option_num > nat ) > ( option_num > option_num ) > option_num > nat ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001t__Option__Ooption_It__Num__Onum_J_001t__Num__Onum_001t__Num__Onum,type,
% 0.29/0.49 comp_o6342398210560591875um_num: ( option_num > num ) > ( num > option_num ) > num > num ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001t__Option__Ooption_It__Num__Onum_J_001t__Option__Ooption_It__Num__Onum_J_001t__Option__Ooption_It__Num__Onum_J,type,
% 0.29/0.49 comp_o8931257242830428707on_num: ( option_num > option_num ) > ( option_num > option_num ) > option_num > option_num ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001t__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 0.29/0.49 comp_o279924169626513613it_nat: ( option8956607266484857688it_nat > produc8664842809031399944it_nat ) > ( produc8664842809031399944it_nat > option8956607266484857688it_nat ) > produc8664842809031399944it_nat > produc8664842809031399944it_nat ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_I_062_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_062_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_J,type,
% 0.29/0.49 comp_P1875353012086385820e_term: ( produc7773217078559923341nt_int > int > option6357759511663192854e_term ) > ( produc3832618445565238089e_term > produc7773217078559923341nt_int ) > produc3832618445565238089e_term > int > option6357759511663192854e_term ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_I_062_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_062_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_J,type,
% 0.29/0.49 comp_P5363713469694551954e_term: ( produc7773217078559923341nt_int > product_prod_int_int ) > ( produc3832618445565238089e_term > produc7773217078559923341nt_int ) > produc3832618445565238089e_term > product_prod_int_int ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_I_062_It__Nat__Onat_M_Eo_J_M_062_It__Nat__Onat_M_Eo_J_J_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Nat__Onat_M_Eo_J,type,
% 0.29/0.49 comp_P8312345242777556868_nat_o: ( produc7360885484439884007_nat_o > nat > $o ) > ( ( nat > $o ) > produc7360885484439884007_nat_o ) > ( nat > $o ) > nat > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_I_062_It__Nat__Onat_M_Eo_J_M_062_It__Nat__Onat_M_Eo_J_J_001_062_It__Nat__Onat_M_Eo_J_001t__Int__Oint,type,
% 0.29/0.49 comp_P1075760313067033319_o_int: ( produc7360885484439884007_nat_o > nat > $o ) > ( int > produc7360885484439884007_nat_o ) > int > nat > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_M_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_J,type,
% 0.29/0.49 comp_P8650103696410638905e_term: ( produc1908205239877642774nteger > produc6241069584506657477e_term > option6357759511663192854e_term ) > ( produc998928222018024388e_term > produc1908205239877642774nteger ) > produc998928222018024388e_term > produc6241069584506657477e_term > option6357759511663192854e_term ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_M_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_J,type,
% 0.29/0.49 comp_P1663382703091044646e_term: ( produc1908205239877642774nteger > produc8923325533196201883nteger ) > ( produc998928222018024388e_term > produc1908205239877642774nteger ) > produc998928222018024388e_term > produc8923325533196201883nteger ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_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_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__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_M_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_J,type,
% 0.29/0.49 comp_P4355506512671352436_nat_o: ( produc2732055786443039994et_nat > produc3658429121746597890et_nat > $o ) > ( produc4962441903510821572_nat_o > produc2732055786443039994et_nat ) > produc4962441903510821572_nat_o > produc3658429121746597890et_nat > $o ).
% 0.29/0.49
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% 0.29/0.49 comp_P8869164316148852700at_nat: ( product_prod_int_nat > nat ) > ( nat > product_prod_int_nat ) > nat > nat ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J_001t__Code____Numeral__Ointeger_001t__Nat__Onat,type,
% 0.29/0.49 comp_P5461341465284484122er_nat: ( produc2591615631378489102nteger > code_integer ) > ( nat > produc2591615631378489102nteger ) > nat > code_integer ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.29/0.49 comp_P9144323761349829517at_nat: ( produc2591615631378489102nteger > nat ) > ( nat > produc2591615631378489102nteger ) > nat > nat ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Int__Oint_J_001t__Int__Oint_001t__Nat__Onat,type,
% 0.29/0.49 comp_P8963773574283657272nt_nat: ( product_prod_nat_int > int ) > ( nat > product_prod_nat_int ) > nat > int ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Int__Oint_J_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.29/0.49 comp_P7964419862382602716at_nat: ( product_prod_nat_int > nat ) > ( nat > product_prod_nat_int ) > nat > nat ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Int__Oint_M_Eo_J_001t__Int__Oint,type,
% 0.29/0.49 comp_P7507668834397697393_o_int: ( product_prod_nat_nat > int > $o ) > ( int > product_prod_nat_nat ) > int > int > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Int__Oint_Mt__Int__Oint_J_001t__Int__Oint,type,
% 0.29/0.49 comp_P1029605119844863363nt_int: ( product_prod_nat_nat > int > int ) > ( int > product_prod_nat_nat ) > int > int > int ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_Eo_001t__Int__Oint,type,
% 0.29/0.49 comp_P1289042343629989734_o_int: ( product_prod_nat_nat > $o ) > ( int > product_prod_nat_nat ) > int > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.29/0.49 comp_P1955610211387027840at_nat: ( product_prod_nat_nat > nat ) > ( nat > product_prod_nat_nat ) > nat > nat ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat_001t__Product____Type__Ounit,type,
% 0.29/0.49 comp_P2980510830910040157t_unit: ( product_prod_nat_nat > nat ) > ( product_unit > product_prod_nat_nat ) > product_unit > nat ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint,type,
% 0.29/0.49 comp_P7428279379633703887at_int: ( product_prod_nat_nat > product_prod_nat_nat ) > ( int > product_prod_nat_nat ) > int > product_prod_nat_nat ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Num__Onum_Mt__Num__Onum_J_001t__Num__Onum_001t__Num__Onum,type,
% 0.29/0.49 comp_P864883071962432936um_num: ( product_prod_num_num > num ) > ( num > product_prod_num_num ) > num > num ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_Mt__Code____Numeral__Onatural_J_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J,type,
% 0.29/0.49 comp_P3887058762840424708atural: ( produc3981471736659609608atural > produc7822875418678951345atural ) > ( produc5835291356934675326atural > produc3981471736659609608atural ) > produc5835291356934675326atural > produc7822875418678951345atural ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J,type,
% 0.29/0.49 comp_P230220204662055659atural: ( produc6756470014200349799atural > produc7822875418678951345atural ) > ( produc5835291356934675326atural > produc6756470014200349799atural ) > produc5835291356934675326atural > produc7822875418678951345atural ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_001t__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J,type,
% 0.29/0.49 comp_P3118722334806803912t_unit: ( produc8664842809031399944it_nat > option8956607266484857688it_nat ) > ( heap_e7401611519738050253t_unit > produc8664842809031399944it_nat ) > heap_e7401611519738050253t_unit > option8956607266484857688it_nat ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001t__Product____Type__Ounit_001t__Code____Numeral__Ointeger_001t__Nat__Onat,type,
% 0.29/0.49 comp_P756492639069434009er_nat: ( product_unit > code_integer ) > ( nat > product_unit ) > nat > code_integer ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001t__Product____Type__Ounit_001t__Product____Type__Ounit_001t__Product____Type__Ounit,type,
% 0.29/0.49 comp_P7645380973975430442t_unit: ( product_unit > product_unit ) > ( product_unit > product_unit ) > product_unit > product_unit ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001t__Rat__Orat_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.29/0.49 comp_rat_nat_nat: ( rat > nat ) > ( nat > rat ) > nat > nat ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001t__Rat__Orat_001t__Rat__Orat_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 0.29/0.49 comp_r4727614531642239972nt_int: ( rat > rat ) > ( product_prod_int_int > rat ) > product_prod_int_int > rat ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ocomp_001t__Rat__Orat_001t__Rat__Orat_001t__Rat__Orat,type,
% 0.29/0.49 comp_rat_rat_rat: ( rat > rat ) > ( rat > rat ) > rat > rat ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ofun__upd_001_Eo_001_Eo,type,
% 0.29/0.49 fun_upd_o_o: ( $o > $o ) > $o > $o > $o > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ofun__upd_001_Eo_001t__Int__Oint,type,
% 0.29/0.49 fun_upd_o_int: ( $o > int ) > $o > int > $o > int ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ofun__upd_001_Eo_001t__Nat__Onat,type,
% 0.29/0.49 fun_upd_o_nat: ( $o > nat ) > $o > nat > $o > nat ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ofun__upd_001_Eo_001t__Option__Ooption_It__Num__Onum_J,type,
% 0.29/0.49 fun_upd_o_option_num: ( $o > option_num ) > $o > option_num > $o > option_num ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ofun__upd_001_Eo_001t__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
% 0.29/0.49 fun_up1288979561775348147it_nat: ( $o > option8956607266484857688it_nat ) > $o > option8956607266484857688it_nat > $o > option8956607266484857688it_nat ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ofun__upd_001t__Code____Numeral__Ointeger_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 0.29/0.49 fun_up8056716234270145717nteger: ( code_integer > code_integer > code_integer ) > code_integer > ( code_integer > code_integer ) > code_integer > code_integer > code_integer ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ofun__upd_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,type,
% 0.29/0.49 fun_up8139772397987072257nteger: ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > code_integer > ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ofun__upd_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 0.29/0.49 fun_up8355007323143964473nteger: ( code_integer > code_integer ) > code_integer > code_integer > code_integer > code_integer ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ofun__upd_001t__Code____Numeral__Ointeger_001t__Option__Ooption_It__Code____Numeral__Ointeger_J,type,
% 0.29/0.49 fun_up6566892301432185865nteger: ( code_integer > option_Code_integer ) > code_integer > option_Code_integer > code_integer > option_Code_integer ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ofun__upd_001t__Code____Numeral__Onatural_001t__Option__Ooption_It__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J,type,
% 0.29/0.49 fun_up2923169431403285008atural: ( code_natural > option5403585828896915703atural ) > code_natural > option5403585828896915703atural > code_natural > option5403585828896915703atural ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ofun__upd_001t__Int__Oint_001_Eo,type,
% 0.29/0.49 fun_upd_int_o: ( int > $o ) > int > $o > int > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ofun__upd_001t__Int__Oint_001t__Int__Oint,type,
% 0.29/0.49 fun_upd_int_int: ( int > int ) > int > int > int > int ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ofun__upd_001t__Int__Oint_001t__Nat__Onat,type,
% 0.29/0.49 fun_upd_int_nat: ( int > nat ) > int > nat > int > nat ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ofun__upd_001t__Int__Oint_001t__Num__Onum,type,
% 0.29/0.49 fun_upd_int_num: ( int > num ) > int > num > int > num ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ofun__upd_001t__Int__Oint_001t__Option__Ooption_It__Int__Oint_J,type,
% 0.29/0.49 fun_up8666045135305973159on_int: ( int > option_int ) > int > option_int > int > option_int ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ofun__upd_001t__Int__Oint_001t__Option__Ooption_It__Num__Onum_J,type,
% 0.29/0.49 fun_up4328768054909231765on_num: ( int > option_num ) > int > option_num > int > option_num ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ofun__upd_001t__Int__Oint_001t__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
% 0.29/0.49 fun_up6992348036167380867it_nat: ( int > option8956607266484857688it_nat ) > int > option8956607266484857688it_nat > int > option8956607266484857688it_nat ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ofun__upd_001t__Nat__Onat_001_Eo,type,
% 0.29/0.49 fun_upd_nat_o: ( nat > $o ) > nat > $o > nat > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ofun__upd_001t__Nat__Onat_001t__Code____Numeral__Ointeger,type,
% 0.29/0.49 fun_up3904115110581602988nteger: ( nat > code_integer ) > nat > code_integer > nat > code_integer ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ofun__upd_001t__Nat__Onat_001t__Int__Oint,type,
% 0.29/0.49 fun_upd_nat_int: ( nat > int ) > nat > int > nat > int ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ofun__upd_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.29/0.49 fun_upd_nat_nat: ( nat > nat ) > nat > nat > nat > nat ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ofun__upd_001t__Nat__Onat_001t__Option__Ooption_It__Nat__Onat_J,type,
% 0.29/0.49 fun_up1493157387958331631on_nat: ( nat > option_nat ) > nat > option_nat > nat > option_nat ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ofun__upd_001t__Nat__Onat_001t__Option__Ooption_It__Num__Onum_J,type,
% 0.29/0.49 fun_up2201401324907169337on_num: ( nat > option_num ) > nat > option_num > nat > option_num ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ofun__upd_001t__Nat__Onat_001t__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
% 0.29/0.49 fun_up4116053422210368295it_nat: ( nat > option8956607266484857688it_nat ) > nat > option8956607266484857688it_nat > nat > option8956607266484857688it_nat ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ofun__upd_001t__Nat__Onat_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.29/0.49 fun_upd_nat_set_nat: ( nat > set_nat ) > nat > set_nat > nat > set_nat ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ofun__upd_001t__Num__Onum_001t__Code____Numeral__Ointeger,type,
% 0.29/0.49 fun_up1844922938552261878nteger: ( num > code_integer ) > num > code_integer > num > code_integer ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ofun__upd_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Option__Ooption_It__Num__Onum_J,type,
% 0.29/0.49 fun_up8025039454679724718on_num: ( product_prod_nat_nat > option_num ) > product_prod_nat_nat > option_num > product_prod_nat_nat > option_num ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ofun__upd_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
% 0.29/0.49 fun_up3996838528606387100it_nat: ( product_prod_nat_nat > option8956607266484857688it_nat ) > product_prod_nat_nat > option8956607266484857688it_nat > product_prod_nat_nat > option8956607266484857688it_nat ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ofun__upd_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__Option__Ooption_It__Num__Onum_J,type,
% 0.29/0.49 fun_up3286109336741039636on_num: ( produc3843707927480180839at_nat > option_num ) > produc3843707927480180839at_nat > option_num > produc3843707927480180839at_nat > option_num ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ofun__upd_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
% 0.29/0.49 fun_up5549328659429834498it_nat: ( produc3843707927480180839at_nat > option8956607266484857688it_nat ) > produc3843707927480180839at_nat > option8956607266484857688it_nat > produc3843707927480180839at_nat > option8956607266484857688it_nat ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ofun__upd_001t__Product____Type__Ounit_001t__Option__Ooption_It__Num__Onum_J,type,
% 0.29/0.49 fun_up4695802795598371002on_num: ( product_unit > option_num ) > product_unit > option_num > product_unit > option_num ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Ofun__upd_001t__Product____Type__Ounit_001t__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
% 0.29/0.49 fun_up1973317344121680296it_nat: ( product_unit > option8956607266484857688it_nat ) > product_unit > option8956607266484857688it_nat > product_unit > option8956607266484857688it_nat ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Oid_001_062_It__Nat__Onat_M_Eo_J,type,
% 0.29/0.49 id_nat_o: ( nat > $o ) > nat > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Oid_001_062_It__Num__Onum_Mt__Code____Numeral__Ointeger_J,type,
% 0.29/0.49 id_num_Code_integer: ( num > code_integer ) > num > code_integer ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Oid_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,type,
% 0.29/0.49 id_Pro496765588584934260nteger: ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Oid_001_Eo,type,
% 0.29/0.49 id_o: $o > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Oid_001t__Code____Numeral__Ointeger,type,
% 0.29/0.49 id_Code_integer: code_integer > code_integer ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Oid_001t__Int__Oint,type,
% 0.29/0.49 id_int: int > int ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Oid_001t__Nat__Onat,type,
% 0.29/0.49 id_nat: nat > nat ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Oid_001t__Num__Onum,type,
% 0.29/0.49 id_num: num > num ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Oid_001t__Option__Ooption_I_062_It__Nat__Onat_M_Eo_J_J,type,
% 0.29/0.49 id_option_nat_o: option_nat_o > option_nat_o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Oid_001t__Option__Ooption_I_Eo_J,type,
% 0.29/0.49 id_option_o: option_o > option_o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Oid_001t__Option__Ooption_It__Int__Oint_J,type,
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% 0.29/0.49 thf(sy_c_Fun_Oid_001t__Option__Ooption_It__Nat__Onat_J,type,
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% 0.29/0.49 thf(sy_c_Fun_Oid_001t__Option__Ooption_It__Num__Onum_J,type,
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% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Oid_001t__Set__Oset_I_Eo_J,type,
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% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Oid_001t__Set__Oset_It__Int__Oint_J,type,
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% 0.29/0.49
% 0.29/0.49 thf(sy_c_Fun_Oid_001t__Set__Oset_It__Nat__Onat_J,type,
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% 0.29/0.49
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% 0.29/0.49
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% 0.29/0.49 thf(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Int__Oint_001_Eo_001_Eo,type,
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% 0.29/0.49 thf(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Int__Oint_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
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% 0.29/0.49 thf(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Nat__Onat_001t__Nat__Onat_001t__Num__Onum,type,
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% 0.29/0.49 thf(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Num__Onum_001t__Int__Oint_001t__Num__Onum,type,
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% 0.29/0.49 thf(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001_062_It__Int__Oint_Mt__Int__Oint_J,type,
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% 0.29/0.49 map_fu4826362097070443709at_o_o: ( int > product_prod_nat_nat ) > ( $o > $o ) > ( product_prod_nat_nat > $o ) > int > $o ).
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% 0.29/0.49 thf(sy_c_Fun_Omap__fun_001t__Nat__Onat_001t__Nat__Onat_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J,type,
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% 0.29/0.50 case_option_int_num: int > ( num > int ) > option_num > int ).
% 0.29/0.50
% 0.29/0.50 thf(sy_c_Option_Ooption_Ocase__option_001t__Nat__Onat_001t__Num__Onum,type,
% 0.29/0.50 case_option_nat_num: nat > ( num > nat ) > option_num > nat ).
% 0.29/0.50
% 0.29/0.50 thf(sy_c_Option_Ooption_Ocase__option_001t__Nat__Onat_001t__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 0.29/0.50 case_o1134687144775446439it_nat: nat > ( produc6714399278180371524it_nat > nat ) > option3216581401566546698it_nat > nat ).
% 0.29/0.50
% 0.29/0.50 thf(sy_c_Option_Ooption_Ocase__option_001t__Nat__Onat_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 0.29/0.50 case_o5424514124273913701it_nat: nat > ( produc8664842809031399944it_nat > nat ) > option8956607266484857688it_nat > nat ).
% 0.29/0.50
% 0.29/0.50 thf(sy_c_Option_Ooption_Ocase__option_001t__Num__Onum_001t__Int__Oint,type,
% 0.29/0.50 case_option_num_int: num > ( int > num ) > option_int > num ).
% 0.29/0.50
% 0.29/0.50 thf(sy_c_Option_Ooption_Ocase__option_001t__Num__Onum_001t__Nat__Onat,type,
% 0.29/0.50 case_option_num_nat: num > ( nat > num ) > option_nat > num ).
% 0.29/0.50
% 0.29/0.50 thf(sy_c_Option_Ooption_Ocase__option_001t__Num__Onum_001t__Num__Onum,type,
% 0.29/0.50 case_option_num_num: num > ( num > num ) > option_num > num ).
% 0.29/0.50
% 0.29/0.50 thf(sy_c_Option_Ooption_Ocase__option_001t__Option__Ooption_It__Assertions__Oassn_J_001t__Assertions__Oassn,type,
% 0.29/0.50 case_o4484465799723439917n_assn: option_assn > ( assn > option_assn ) > option_assn > option_assn ).
% 0.29/0.50
% 0.29/0.50 thf(sy_c_Option_Ooption_Ocase__option_001t__Option__Ooption_It__Num__Onum_J_001t__Num__Onum,type,
% 0.29/0.50 case_o6005452278849405969um_num: option_num > ( num > option_num ) > option_num > option_num ).
% 0.29/0.50
% 0.29/0.50 thf(sy_c_Option_Ooption_Ocase__option_001t__Option__Ooption_It__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_001t__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 0.29/0.50 case_o8555119740594961093it_nat: option3216581401566546698it_nat > ( produc6714399278180371524it_nat > option3216581401566546698it_nat ) > option3216581401566546698it_nat > option3216581401566546698it_nat ).
% 0.29/0.50
% 0.29/0.50 thf(sy_c_Option_Ooption_Ocase__option_001t__Option__Ooption_It__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 0.29/0.50 case_o5699750240967658439it_nat: option3216581401566546698it_nat > ( produc8664842809031399944it_nat > option3216581401566546698it_nat ) > option8956607266484857688it_nat > option3216581401566546698it_nat ).
% 0.29/0.50
% 0.29/0.50 thf(sy_c_Option_Ooption_Ocase__option_001t__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_001t__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 0.29/0.50 case_o3886096569520666655it_nat: option8956607266484857688it_nat > ( produc6714399278180371524it_nat > option8956607266484857688it_nat ) > option3216581401566546698it_nat > option8956607266484857688it_nat ).
% 0.29/0.50
% 0.29/0.50 thf(sy_c_Option_Ooption_Ocase__option_001t__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 0.29/0.50 case_o2963978774867076333it_nat: option8956607266484857688it_nat > ( produc8664842809031399944it_nat > option8956607266484857688it_nat ) > option8956607266484857688it_nat > option8956607266484857688it_nat ).
% 0.29/0.50
% 0.29/0.50 thf(sy_c_Option_Ooption_Ocase__option_001t__Option__Ooption_It__Product____Type__Ounit_J_001t__Product____Type__Ounit,type,
% 0.29/0.50 case_o2985186191577459077t_unit: option_Product_unit > ( product_unit > option_Product_unit ) > option_Product_unit > option_Product_unit ).
% 0.29/0.50
% 0.29/0.50 thf(sy_c_Option_Ooption_Ocase__option_001t__Option__Ooption_It__Set__Oset_It__Nat__Onat_J_J_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.29/0.50 case_o4054078431260844265et_nat: option_set_nat > ( set_nat > option_set_nat ) > option_set_nat > option_set_nat ).
% 0.29/0.50
% 0.29/0.50 thf(sy_c_Option_Ooption_Ocase__option_001t__Option__Ooption_It__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
% 0.29/0.50 case_o9080059180780454917at_nat: option1583680563626158861at_nat > ( set_Pr4329608150637261639at_nat > option1583680563626158861at_nat ) > option1583680563626158861at_nat > option1583680563626158861at_nat ).
% 0.29/0.50
% 0.29/0.50 thf(sy_c_Option_Ooption_Ocase__option_001t__Product____Type__Ounit_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 0.29/0.50 case_o9196786658626276042it_nat: product_unit > ( produc8664842809031399944it_nat > product_unit ) > option8956607266484857688it_nat > product_unit ).
% 0.29/0.50
% 0.29/0.50 thf(sy_c_Option_Ooption_Omap__option_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,type,
% 0.29/0.50 map_op3563471509957180299nteger: ( ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ) > option8057788054806935849nteger > option7428179582072448501nteger ).
% 0.29/0.50
% 0.29/0.50 thf(sy_c_Option_Ooption_Omap__option_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Nat__Onat_M_Eo_J,type,
% 0.29/0.50 map_op6424164270877473355_nat_o: ( ( nat > $o ) > nat > $o ) > option_nat_o > option_nat_o ).
% 0.29/0.50
% 0.29/0.50 thf(sy_c_Option_Ooption_Omap__option_001_Eo_001_Eo,type,
% 0.29/0.50 map_option_o_o: ( $o > $o ) > option_o > option_o ).
% 0.29/0.50
% 0.29/0.50 thf(sy_c_Option_Ooption_Omap__option_001t__Code____Numeral__Ointeger_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 0.29/0.50 map_op370346339404370627nteger: ( code_integer > code_integer > code_integer ) > option_Code_integer > option8057788054806935849nteger ).
% 0.29/0.50
% 0.29/0.50 thf(sy_c_Option_Ooption_Omap__option_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,type,
% 0.29/0.50 map_op9146685272036663823nteger: ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > option_Code_integer > option7428179582072448501nteger ).
% 0.29/0.50
% 0.29/0.50 thf(sy_c_Option_Ooption_Omap__option_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 0.29/0.50 map_op3669829223712506439nteger: ( code_integer > code_integer ) > option_Code_integer > option_Code_integer ).
% 0.29/0.50
% 0.29/0.50 thf(sy_c_Option_Ooption_Omap__option_001t__Int__Oint_001t__Int__Oint,type,
% 0.29/0.50 map_option_int_int: ( int > int ) > option_int > option_int ).
% 0.29/0.50
% 0.29/0.50 thf(sy_c_Option_Ooption_Omap__option_001t__Int__Oint_001t__Nat__Onat,type,
% 0.29/0.50 map_option_int_nat: ( int > nat ) > option_int > option_nat ).
% 0.29/0.50
% 0.29/0.50 thf(sy_c_Option_Ooption_Omap__option_001t__Int__Oint_001t__Num__Onum,type,
% 0.29/0.50 map_option_int_num: ( int > num ) > option_int > option_num ).
% 0.29/0.50
% 0.29/0.50 thf(sy_c_Option_Ooption_Omap__option_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.29/0.50 map_option_nat_nat: ( nat > nat ) > option_nat > option_nat ).
% 0.29/0.50
% 0.29/0.50 thf(sy_c_Option_Ooption_Omap__option_001t__Nat__Onat_001t__Num__Onum,type,
% 0.29/0.50 map_option_nat_num: ( nat > num ) > option_nat > option_num ).
% 0.29/0.50
% 0.29/0.50 thf(sy_c_Option_Ooption_Omap__option_001t__Num__Onum_001t__Code____Numeral__Ointeger,type,
% 0.29/0.50 map_op2849635639313731588nteger: ( num > code_integer ) > option_num > option_Code_integer ).
% 0.29/0.50
% 0.29/0.50 thf(sy_c_Option_Ooption_Omap__option_001t__Num__Onum_001t__Num__Onum,type,
% 0.29/0.50 map_option_num_num: ( num > num ) > option_num > option_num ).
% 0.29/0.50
% 0.29/0.50 thf(sy_c_Option_Ooption_Omap__option_001t__Num__Onum_001t__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 0.29/0.50 map_op6598675229099881181it_nat: ( num > produc6714399278180371524it_nat ) > option_num > option3216581401566546698it_nat ).
% 0.29/0.50
% 0.29/0.50 thf(sy_c_Option_Ooption_Omap__option_001t__Num__Onum_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 0.29/0.50 map_op8118133509425879471it_nat: ( num > produc8664842809031399944it_nat ) > option_num > option8956607266484857688it_nat ).
% 0.29/0.50
% 0.29/0.50 thf(sy_c_Option_Ooption_Omap__option_001t__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_001t__Num__Onum,type,
% 0.29/0.50 map_op8228268515680064275at_num: ( produc6714399278180371524it_nat > num ) > option3216581401566546698it_nat > option_num ).
% 0.29/0.50
% 0.29/0.50 thf(sy_c_Option_Ooption_Omap__option_001t__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_001t__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 0.29/0.50 map_op6002829699023054091it_nat: ( produc6714399278180371524it_nat > produc6714399278180371524it_nat ) > option3216581401566546698it_nat > option3216581401566546698it_nat ).
% 0.29/0.50
% 0.29/0.50 thf(sy_c_Option_Ooption_Omap__option_001t__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 0.29/0.50 map_op674526153330701057it_nat: ( produc6714399278180371524it_nat > produc8664842809031399944it_nat ) > option3216581401566546698it_nat > option8956607266484857688it_nat ).
% 0.29/0.50
% 0.29/0.50 thf(sy_c_Option_Ooption_Omap__option_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_001t__Num__Onum,type,
% 0.29/0.50 map_op2731889312448867759at_num: ( produc8664842809031399944it_nat > num ) > option8956607266484857688it_nat > option_num ).
% 0.29/0.50
% 0.29/0.50 thf(sy_c_Option_Ooption_Omap__option_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_001t__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
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% 0.29/0.50
% 0.29/0.50 thf(sy_c_Option_Ooption_Omap__option_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 0.29/0.50 map_op8673683442680995229it_nat: ( produc8664842809031399944it_nat > produc8664842809031399944it_nat ) > option8956607266484857688it_nat > option8956607266484857688it_nat ).
% 0.29/0.50
% 0.29/0.50 thf(sy_c_Option_Ooption_Osize__option_001t__Num__Onum,type,
% 0.29/0.50 size_option_num: ( num > nat ) > option_num > nat ).
% 0.29/0.50
% 0.29/0.50 thf(sy_c_Option_Ooption_Osize__option_001t__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
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% 0.29/0.50
% 0.29/0.50 thf(sy_c_Option_Ooption_Osize__option_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
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% 0.29/0.50
% 0.29/0.50 thf(sy_c_Option_Ooption_Othe_001_062_It__Nat__Onat_M_Eo_J,type,
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% 0.29/0.50
% 0.29/0.50 thf(sy_c_Option_Ooption_Othe_001_Eo,type,
% 0.29/0.50 the_o: option_o > $o ).
% 0.29/0.50
% 0.29/0.50 thf(sy_c_Option_Ooption_Othe_001t__Int__Oint,type,
% 0.29/0.50 the_int2: option_int > int ).
% 0.29/0.50
% 0.29/0.50 thf(sy_c_Option_Ooption_Othe_001t__Nat__Onat,type,
% 0.29/0.50 the_nat: option_nat > nat ).
% 0.29/0.50
% 0.29/0.50 thf(sy_c_Option_Ooption_Othe_001t__Num__Onum,type,
% 0.29/0.50 the_num: option_num > num ).
% 0.29/0.50
% 0.29/0.50 thf(sy_c_Option_Ooption_Othe_001t__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
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% 0.29/0.50
% 0.29/0.50 thf(sy_c_Option_Ooption_Othe_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
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% 0.29/0.50
% 0.29/0.50 thf(sy_c_Option_Othese_001_Eo,type,
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% 0.29/0.50
% 0.29/0.50 thf(sy_c_Option_Othese_001t__Int__Oint,type,
% 0.29/0.50 these_int: set_option_int > set_int ).
% 0.29/0.50
% 0.29/0.50 thf(sy_c_Option_Othese_001t__Nat__Onat,type,
% 0.29/0.50 these_nat: set_option_nat > set_nat ).
% 0.29/0.50
% 0.29/0.50 thf(sy_c_Option_Othese_001t__Num__Onum,type,
% 0.29/0.50 these_num: set_option_num > set_num ).
% 0.29/0.50
% 0.29/0.50 thf(sy_c_Option_Othese_001t__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
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% 0.29/0.50 thf(sy_c_Option_Othese_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
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% 0.29/0.50
% 0.29/0.50 thf(sy_c_Option_Othese_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
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% 0.29/0.50 thf(sy_c_Option_Othese_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
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% 0.29/0.50
% 0.29/0.50 thf(sy_c_Option_Othese_001t__Product____Type__Ounit,type,
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% 0.29/0.51 ( ( heap_T5591663578999710211rray_a @ F @ H2 )
% 0.29/0.51 = ( heap_T5591663578999710211rray_a @ G @ H2 ) )
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% 0.29/0.51 % Heap_eqI
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% 0.29/0.51 ( ! [H2: heap_e7401611519738050253t_unit] :
% 0.29/0.51 ( ( heap_T875086893843062177t_unit @ F @ H2 )
% 0.29/0.51 = ( heap_T875086893843062177t_unit @ G @ H2 ) )
% 0.29/0.51 => ( F = G ) ) ).
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% 0.29/0.51 % Heap_eqI
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% 0.29/0.51 ( ~ ( P @ H3 )
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% 0.29/0.51 ( ~ ( P @ H3 )
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% 0.29/0.51 % successI
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% 0.29/0.51 % success_def
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% 0.29/0.51 ( ( heap_T875086893843062177t_unit @ F2 @ H )
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% 0.29/0.51 % success_def
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% 0.29/0.51 ( ( heap_T3039585018531920163rray_a @ X @ Y )
% 0.29/0.51 => ( ( ( heap_T5591663578999710211rray_a @ X @ H3 )
% 0.29/0.51 != none_P2587165478634041381it_nat )
% 0.29/0.51 => ( ( heap_T5591663578999710211rray_a @ X @ H3 )
% 0.29/0.51 = ( heap_T5591663578999710211rray_a @ Y @ H3 ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % Heap_ordE
% 0.29/0.51 thf(fact_15_Heap__ordE,axiom,
% 0.29/0.51 ! [X: heap_T5738788834812785303t_unit,Y: heap_T5738788834812785303t_unit,H3: heap_e7401611519738050253t_unit] :
% 0.29/0.51 ( ( heap_T499439718319394433t_unit @ X @ Y )
% 0.29/0.51 => ( ( ( heap_T875086893843062177t_unit @ X @ H3 )
% 0.29/0.51 != none_P9117596204409417319it_nat )
% 0.29/0.51 => ( ( heap_T875086893843062177t_unit @ X @ H3 )
% 0.29/0.51 = ( heap_T875086893843062177t_unit @ Y @ H3 ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % Heap_ordE
% 0.29/0.51 thf(fact_16_Heap__ordI,axiom,
% 0.29/0.51 ! [X: heap_T6362127782908069795rray_a,Y: heap_T6362127782908069795rray_a] :
% 0.29/0.51 ( ! [H2: heap_e7401611519738050253t_unit] :
% 0.29/0.51 ( ( ( heap_T5591663578999710211rray_a @ X @ H2 )
% 0.29/0.51 = none_P2587165478634041381it_nat )
% 0.29/0.51 | ( ( heap_T5591663578999710211rray_a @ X @ H2 )
% 0.29/0.51 = ( heap_T5591663578999710211rray_a @ Y @ H2 ) ) )
% 0.29/0.51 => ( heap_T3039585018531920163rray_a @ X @ Y ) ) ).
% 0.29/0.51
% 0.29/0.51 % Heap_ordI
% 0.29/0.51 thf(fact_17_Heap__ordI,axiom,
% 0.29/0.51 ! [X: heap_T5738788834812785303t_unit,Y: heap_T5738788834812785303t_unit] :
% 0.29/0.51 ( ! [H2: heap_e7401611519738050253t_unit] :
% 0.29/0.51 ( ( ( heap_T875086893843062177t_unit @ X @ H2 )
% 0.29/0.51 = none_P9117596204409417319it_nat )
% 0.29/0.51 | ( ( heap_T875086893843062177t_unit @ X @ H2 )
% 0.29/0.51 = ( heap_T875086893843062177t_unit @ Y @ H2 ) ) )
% 0.29/0.51 => ( heap_T499439718319394433t_unit @ X @ Y ) ) ).
% 0.29/0.51
% 0.29/0.51 % Heap_ordI
% 0.29/0.51 thf(fact_18_execute__bind_I2_J,axiom,
% 0.29/0.51 ! [F: heap_T6362127782908069795rray_a,H3: heap_e7401611519738050253t_unit,G: array_a > heap_T6362127782908069795rray_a] :
% 0.29/0.51 ( ( ( heap_T5591663578999710211rray_a @ F @ H3 )
% 0.29/0.51 = none_P2587165478634041381it_nat )
% 0.29/0.51 => ( ( heap_T5591663578999710211rray_a @ ( heap_T2407400398799471159rray_a @ F @ G ) @ H3 )
% 0.29/0.51 = none_P2587165478634041381it_nat ) ) ).
% 0.29/0.51
% 0.29/0.51 % execute_bind(2)
% 0.29/0.51 thf(fact_19_execute__bind_I2_J,axiom,
% 0.29/0.51 ! [F: heap_T6362127782908069795rray_a,H3: heap_e7401611519738050253t_unit,G: array_a > heap_T5738788834812785303t_unit] :
% 0.29/0.51 ( ( ( heap_T5591663578999710211rray_a @ F @ H3 )
% 0.29/0.51 = none_P2587165478634041381it_nat )
% 0.29/0.51 => ( ( heap_T875086893843062177t_unit @ ( heap_T7324619625323989613t_unit @ F @ G ) @ H3 )
% 0.29/0.51 = none_P9117596204409417319it_nat ) ) ).
% 0.29/0.51
% 0.29/0.51 % execute_bind(2)
% 0.29/0.51 thf(fact_20_execute__bind_I2_J,axiom,
% 0.29/0.51 ! [F: heap_T5738788834812785303t_unit,H3: heap_e7401611519738050253t_unit,G: product_unit > heap_T6362127782908069795rray_a] :
% 0.29/0.51 ( ( ( heap_T875086893843062177t_unit @ F @ H3 )
% 0.29/0.51 = none_P9117596204409417319it_nat )
% 0.29/0.51 => ( ( heap_T5591663578999710211rray_a @ ( heap_T7158140910958840029rray_a @ F @ G ) @ H3 )
% 0.29/0.51 = none_P2587165478634041381it_nat ) ) ).
% 0.29/0.51
% 0.29/0.51 % execute_bind(2)
% 0.29/0.51 thf(fact_21_execute__bind_I2_J,axiom,
% 0.29/0.51 ! [F: heap_T5738788834812785303t_unit,H3: heap_e7401611519738050253t_unit,G: product_unit > heap_T5738788834812785303t_unit] :
% 0.29/0.51 ( ( ( heap_T875086893843062177t_unit @ F @ H3 )
% 0.29/0.51 = none_P9117596204409417319it_nat )
% 0.29/0.51 => ( ( heap_T875086893843062177t_unit @ ( heap_T2633723481742716231t_unit @ F @ G ) @ H3 )
% 0.29/0.51 = none_P9117596204409417319it_nat ) ) ).
% 0.29/0.51
% 0.29/0.51 % execute_bind(2)
% 0.29/0.51 thf(fact_22_the__default_Osimps_I2_J,axiom,
% 0.29/0.51 ! [X: produc6714399278180371524it_nat] :
% 0.29/0.51 ( ( the_de8559148246674365659it_nat @ X @ none_P2587165478634041381it_nat )
% 0.29/0.51 = X ) ).
% 0.29/0.51
% 0.29/0.51 % the_default.simps(2)
% 0.29/0.51 thf(fact_23_the__default_Osimps_I2_J,axiom,
% 0.29/0.51 ! [X: num] :
% 0.29/0.51 ( ( the_default_num @ X @ none_num )
% 0.29/0.51 = X ) ).
% 0.29/0.51
% 0.29/0.51 % the_default.simps(2)
% 0.29/0.51 thf(fact_24_the__default_Osimps_I2_J,axiom,
% 0.29/0.51 ! [X: produc8664842809031399944it_nat] :
% 0.29/0.51 ( ( the_de2487931475039285041it_nat @ X @ none_P9117596204409417319it_nat )
% 0.29/0.51 = X ) ).
% 0.29/0.51
% 0.29/0.51 % the_default.simps(2)
% 0.29/0.51 thf(fact_25_raise__bind,axiom,
% 0.29/0.51 ! [E: list_char,F: product_unit > heap_T5738788834812785303t_unit] :
% 0.29/0.51 ( ( heap_T2633723481742716231t_unit @ ( heap_T2927564422264180874t_unit @ E ) @ F )
% 0.29/0.51 = ( heap_T2927564422264180874t_unit @ E ) ) ).
% 0.29/0.51
% 0.29/0.51 % raise_bind
% 0.29/0.51 thf(fact_26_raise__bind,axiom,
% 0.29/0.51 ! [E: list_char,F: product_unit > heap_T6362127782908069795rray_a] :
% 0.29/0.51 ( ( heap_T7158140910958840029rray_a @ ( heap_T2927564422264180874t_unit @ E ) @ F )
% 0.29/0.51 = ( heap_T1552190017797416154rray_a @ E ) ) ).
% 0.29/0.51
% 0.29/0.51 % raise_bind
% 0.29/0.51 thf(fact_27_raise__bind,axiom,
% 0.29/0.51 ! [E: list_char,F: array_a > heap_T5738788834812785303t_unit] :
% 0.29/0.51 ( ( heap_T7324619625323989613t_unit @ ( heap_T1552190017797416154rray_a @ E ) @ F )
% 0.29/0.51 = ( heap_T2927564422264180874t_unit @ E ) ) ).
% 0.29/0.51
% 0.29/0.51 % raise_bind
% 0.29/0.51 thf(fact_28_raise__bind,axiom,
% 0.29/0.51 ! [E: list_char,F: array_a > heap_T6362127782908069795rray_a] :
% 0.29/0.51 ( ( heap_T2407400398799471159rray_a @ ( heap_T1552190017797416154rray_a @ E ) @ F )
% 0.29/0.51 = ( heap_T1552190017797416154rray_a @ E ) ) ).
% 0.29/0.51
% 0.29/0.51 % raise_bind
% 0.29/0.51 thf(fact_29_heap_Oleq__refl,axiom,
% 0.29/0.51 ! [X: heap_T5738788834812785303t_unit] : ( heap_T499439718319394433t_unit @ X @ X ) ).
% 0.29/0.51
% 0.29/0.51 % heap.leq_refl
% 0.29/0.51 thf(fact_30_heap_Oleq__refl,axiom,
% 0.29/0.51 ! [X: heap_T6362127782908069795rray_a] : ( heap_T3039585018531920163rray_a @ X @ X ) ).
% 0.29/0.51
% 0.29/0.51 % heap.leq_refl
% 0.29/0.51 thf(fact_31_heap_Oleq__trans,axiom,
% 0.29/0.51 ! [X: heap_T5738788834812785303t_unit,Y: heap_T5738788834812785303t_unit,Z: heap_T5738788834812785303t_unit] :
% 0.29/0.51 ( ( heap_T499439718319394433t_unit @ X @ Y )
% 0.29/0.51 => ( ( heap_T499439718319394433t_unit @ Y @ Z )
% 0.29/0.51 => ( heap_T499439718319394433t_unit @ X @ Z ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % heap.leq_trans
% 0.29/0.51 thf(fact_32_heap_Oleq__trans,axiom,
% 0.29/0.51 ! [X: heap_T6362127782908069795rray_a,Y: heap_T6362127782908069795rray_a,Z: heap_T6362127782908069795rray_a] :
% 0.29/0.51 ( ( heap_T3039585018531920163rray_a @ X @ Y )
% 0.29/0.51 => ( ( heap_T3039585018531920163rray_a @ Y @ Z )
% 0.29/0.51 => ( heap_T3039585018531920163rray_a @ X @ Z ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % heap.leq_trans
% 0.29/0.51 thf(fact_33_heap_Oleq__antisym,axiom,
% 0.29/0.51 ! [X: heap_T5738788834812785303t_unit,Y: heap_T5738788834812785303t_unit] :
% 0.29/0.51 ( ( heap_T499439718319394433t_unit @ X @ Y )
% 0.29/0.51 => ( ( heap_T499439718319394433t_unit @ Y @ X )
% 0.29/0.51 => ( X = Y ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % heap.leq_antisym
% 0.29/0.51 thf(fact_34_heap_Oleq__antisym,axiom,
% 0.29/0.51 ! [X: heap_T6362127782908069795rray_a,Y: heap_T6362127782908069795rray_a] :
% 0.29/0.51 ( ( heap_T3039585018531920163rray_a @ X @ Y )
% 0.29/0.51 => ( ( heap_T3039585018531920163rray_a @ Y @ X )
% 0.29/0.51 => ( X = Y ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % heap.leq_antisym
% 0.29/0.51 thf(fact_35_success__ifI,axiom,
% 0.29/0.51 ! [C: $o,T: heap_T5738788834812785303t_unit,H3: heap_e7401611519738050253t_unit,E: heap_T5738788834812785303t_unit] :
% 0.29/0.51 ( ( C
% 0.29/0.51 => ( heap_T584514906347983379t_unit @ T @ H3 ) )
% 0.29/0.51 => ( ( ~ C
% 0.29/0.51 => ( heap_T584514906347983379t_unit @ E @ H3 ) )
% 0.29/0.51 => ( heap_T584514906347983379t_unit @ ( if_Hea8138950348631371857t_unit @ C @ T @ E ) @ H3 ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % success_ifI
% 0.29/0.51 thf(fact_36_success__ifI,axiom,
% 0.29/0.51 ! [C: $o,T: heap_T6362127782908069795rray_a,H3: heap_e7401611519738050253t_unit,E: heap_T6362127782908069795rray_a] :
% 0.29/0.51 ( ( C
% 0.29/0.51 => ( heap_T6932021131025641745rray_a @ T @ H3 ) )
% 0.29/0.51 => ( ( ~ C
% 0.29/0.51 => ( heap_T6932021131025641745rray_a @ E @ H3 ) )
% 0.29/0.51 => ( heap_T6932021131025641745rray_a @ ( if_Hea5896630067203373929rray_a @ C @ T @ E ) @ H3 ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % success_ifI
% 0.29/0.51 thf(fact_37_success__guardI,axiom,
% 0.29/0.51 ! [P: heap_e7401611519738050253t_unit > $o,H3: heap_e7401611519738050253t_unit,F: heap_e7401611519738050253t_unit > produc8664842809031399944it_nat] :
% 0.29/0.51 ( ( P @ H3 )
% 0.29/0.51 => ( heap_T584514906347983379t_unit @ ( heap_T8440541562793052209t_unit @ P @ F ) @ H3 ) ) ).
% 0.29/0.51
% 0.29/0.51 % success_guardI
% 0.29/0.51 thf(fact_38_success__guardI,axiom,
% 0.29/0.51 ! [P: heap_e7401611519738050253t_unit > $o,H3: heap_e7401611519738050253t_unit,F: heap_e7401611519738050253t_unit > produc6714399278180371524it_nat] :
% 0.29/0.51 ( ( P @ H3 )
% 0.29/0.51 => ( heap_T6932021131025641745rray_a @ ( heap_T7685628758766326643rray_a @ P @ F ) @ H3 ) ) ).
% 0.29/0.51
% 0.29/0.51 % success_guardI
% 0.29/0.51 thf(fact_39_success__assertI,axiom,
% 0.29/0.51 ! [P: product_unit > $o,X: product_unit,H3: heap_e7401611519738050253t_unit] :
% 0.29/0.51 ( ( P @ X )
% 0.29/0.51 => ( heap_T584514906347983379t_unit @ ( heap_T4208721593536448476t_unit @ P @ X ) @ H3 ) ) ).
% 0.29/0.51
% 0.29/0.51 % success_assertI
% 0.29/0.51 thf(fact_40_success__assertI,axiom,
% 0.29/0.51 ! [P: array_a > $o,X: array_a,H3: heap_e7401611519738050253t_unit] :
% 0.29/0.51 ( ( P @ X )
% 0.29/0.51 => ( heap_T6932021131025641745rray_a @ ( heap_T7971689983404357896rray_a @ P @ X ) @ H3 ) ) ).
% 0.29/0.51
% 0.29/0.51 % success_assertI
% 0.29/0.51 thf(fact_41_fails__bind,axiom,
% 0.29/0.51 ! [M2: heap_T5738788834812785303t_unit,F: product_unit > heap_T5738788834812785303t_unit,H3: heap_e7401611519738050253t_unit] :
% 0.29/0.51 ( ( time_f8834461667527620124t_unit @ ( heap_T2633723481742716231t_unit @ M2 @ F ) @ H3 )
% 0.29/0.51 = ( ~ ( time_f8834461667527620124t_unit @ M2 @ H3 )
% 0.29/0.51 => ( time_f8834461667527620124t_unit @ ( F @ ( time_t2745601220510131320t_unit @ M2 @ H3 ) ) @ ( time_t3350536682685678164t_unit @ M2 @ H3 ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % fails_bind
% 0.29/0.51 thf(fact_42_fails__bind,axiom,
% 0.29/0.51 ! [M2: heap_T6362127782908069795rray_a,F: array_a > heap_T5738788834812785303t_unit,H3: heap_e7401611519738050253t_unit] :
% 0.29/0.51 ( ( time_f8834461667527620124t_unit @ ( heap_T7324619625323989613t_unit @ M2 @ F ) @ H3 )
% 0.29/0.51 = ( ~ ( time_fails_array_a @ M2 @ H3 )
% 0.29/0.51 => ( time_f8834461667527620124t_unit @ ( F @ ( time_the_res_array_a @ M2 @ H3 ) ) @ ( time_t490086488869527696rray_a @ M2 @ H3 ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % fails_bind
% 0.29/0.51 thf(fact_43_fails__bind,axiom,
% 0.29/0.51 ! [M2: heap_T5738788834812785303t_unit,F: product_unit > heap_T6362127782908069795rray_a,H3: heap_e7401611519738050253t_unit] :
% 0.29/0.51 ( ( time_fails_array_a @ ( heap_T7158140910958840029rray_a @ M2 @ F ) @ H3 )
% 0.29/0.51 = ( ~ ( time_f8834461667527620124t_unit @ M2 @ H3 )
% 0.29/0.51 => ( time_fails_array_a @ ( F @ ( time_t2745601220510131320t_unit @ M2 @ H3 ) ) @ ( time_t3350536682685678164t_unit @ M2 @ H3 ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % fails_bind
% 0.29/0.51 thf(fact_44_fails__bind,axiom,
% 0.29/0.51 ! [M2: heap_T6362127782908069795rray_a,F: array_a > heap_T6362127782908069795rray_a,H3: heap_e7401611519738050253t_unit] :
% 0.29/0.51 ( ( time_fails_array_a @ ( heap_T2407400398799471159rray_a @ M2 @ F ) @ H3 )
% 0.29/0.51 = ( ~ ( time_fails_array_a @ M2 @ H3 )
% 0.29/0.51 => ( time_fails_array_a @ ( F @ ( time_the_res_array_a @ M2 @ H3 ) ) @ ( time_t490086488869527696rray_a @ M2 @ H3 ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % fails_bind
% 0.29/0.51 thf(fact_45_success__of__listI,axiom,
% 0.29/0.51 ! [Xs: list_a,H3: heap_e7401611519738050253t_unit] : ( heap_T6932021131025641745rray_a @ ( array_of_list_a @ Xs ) @ H3 ) ).
% 0.29/0.51
% 0.29/0.51 % success_of_listI
% 0.29/0.51 thf(fact_46_success__tapI,axiom,
% 0.29/0.51 ! [F: heap_e7401611519738050253t_unit > product_unit,H3: heap_e7401611519738050253t_unit] : ( heap_T584514906347983379t_unit @ ( heap_T560649228465745139t_unit @ F ) @ H3 ) ).
% 0.29/0.51
% 0.29/0.51 % success_tapI
% 0.29/0.51 thf(fact_47_success__tapI,axiom,
% 0.29/0.51 ! [F: heap_e7401611519738050253t_unit > array_a,H3: heap_e7401611519738050253t_unit] : ( heap_T6932021131025641745rray_a @ ( heap_T2055650868554030641rray_a @ F ) @ H3 ) ).
% 0.29/0.51
% 0.29/0.51 % success_tapI
% 0.29/0.51 thf(fact_48_success__heapI,axiom,
% 0.29/0.51 ! [F: heap_e7401611519738050253t_unit > produc8664842809031399944it_nat,H3: heap_e7401611519738050253t_unit] : ( heap_T584514906347983379t_unit @ ( heap_T6927113302350381334t_unit @ F ) @ H3 ) ).
% 0.29/0.51
% 0.29/0.51 % success_heapI
% 0.29/0.51 thf(fact_49_success__heapI,axiom,
% 0.29/0.51 ! [F: heap_e7401611519738050253t_unit > produc6714399278180371524it_nat,H3: heap_e7401611519738050253t_unit] : ( heap_T6932021131025641745rray_a @ ( heap_T7473999186002612558rray_a @ F ) @ H3 ) ).
% 0.29/0.51
% 0.29/0.51 % success_heapI
% 0.29/0.51 thf(fact_50_success__ureturnI,axiom,
% 0.29/0.51 ! [X: product_unit,H3: heap_e7401611519738050253t_unit] : ( heap_T584514906347983379t_unit @ ( heap_T4284346855313245393t_unit @ X ) @ H3 ) ).
% 0.29/0.51
% 0.29/0.51 % success_ureturnI
% 0.29/0.51 thf(fact_51_success__ureturnI,axiom,
% 0.29/0.51 ! [X: array_a,H3: heap_e7401611519738050253t_unit] : ( heap_T6932021131025641745rray_a @ ( heap_T4328122439115681491rray_a @ X ) @ H3 ) ).
% 0.29/0.51
% 0.29/0.51 % success_ureturnI
% 0.29/0.51 thf(fact_52_execute__guard_I2_J,axiom,
% 0.29/0.51 ! [P: heap_e7401611519738050253t_unit > $o,H3: heap_e7401611519738050253t_unit,F: heap_e7401611519738050253t_unit > produc6714399278180371524it_nat] :
% 0.29/0.51 ( ( P @ H3 )
% 0.29/0.51 => ( ( heap_T5591663578999710211rray_a @ ( heap_T7685628758766326643rray_a @ P @ F ) @ H3 )
% 0.29/0.51 = ( some_P6105628898608307625it_nat @ ( F @ H3 ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % execute_guard(2)
% 0.29/0.51 thf(fact_53_execute__guard_I2_J,axiom,
% 0.29/0.51 ! [P: heap_e7401611519738050253t_unit > $o,H3: heap_e7401611519738050253t_unit,F: heap_e7401611519738050253t_unit > produc8664842809031399944it_nat] :
% 0.29/0.51 ( ( P @ H3 )
% 0.29/0.51 => ( ( heap_T875086893843062177t_unit @ ( heap_T8440541562793052209t_unit @ P @ F ) @ H3 )
% 0.29/0.51 = ( some_P1914260805536162275it_nat @ ( F @ H3 ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % execute_guard(2)
% 0.29/0.51 thf(fact_54_combine__options__simps_I1_J,axiom,
% 0.29/0.51 ! [F: produc6714399278180371524it_nat > produc6714399278180371524it_nat > produc6714399278180371524it_nat,Y: option3216581401566546698it_nat] :
% 0.29/0.51 ( ( combin3867838909898076099it_nat @ F @ none_P2587165478634041381it_nat @ Y )
% 0.29/0.51 = Y ) ).
% 0.29/0.51
% 0.29/0.51 % combine_options_simps(1)
% 0.29/0.51 thf(fact_55_combine__options__simps_I1_J,axiom,
% 0.29/0.51 ! [F: num > num > num,Y: option_num] :
% 0.29/0.51 ( ( combine_options_num @ F @ none_num @ Y )
% 0.29/0.51 = Y ) ).
% 0.29/0.51
% 0.29/0.51 % combine_options_simps(1)
% 0.29/0.51 thf(fact_56_combine__options__simps_I1_J,axiom,
% 0.29/0.51 ! [F: produc8664842809031399944it_nat > produc8664842809031399944it_nat > produc8664842809031399944it_nat,Y: option8956607266484857688it_nat] :
% 0.29/0.51 ( ( combin4318129983670048329it_nat @ F @ none_P9117596204409417319it_nat @ Y )
% 0.29/0.51 = Y ) ).
% 0.29/0.51
% 0.29/0.51 % combine_options_simps(1)
% 0.29/0.51 thf(fact_57_combine__options__simps_I2_J,axiom,
% 0.29/0.51 ! [F: produc6714399278180371524it_nat > produc6714399278180371524it_nat > produc6714399278180371524it_nat,X: option3216581401566546698it_nat] :
% 0.29/0.51 ( ( combin3867838909898076099it_nat @ F @ X @ none_P2587165478634041381it_nat )
% 0.29/0.51 = X ) ).
% 0.29/0.51
% 0.29/0.51 % combine_options_simps(2)
% 0.29/0.51 thf(fact_58_combine__options__simps_I2_J,axiom,
% 0.29/0.51 ! [F: num > num > num,X: option_num] :
% 0.29/0.51 ( ( combine_options_num @ F @ X @ none_num )
% 0.29/0.51 = X ) ).
% 0.29/0.51
% 0.29/0.51 % combine_options_simps(2)
% 0.29/0.51 thf(fact_59_combine__options__simps_I2_J,axiom,
% 0.29/0.51 ! [F: produc8664842809031399944it_nat > produc8664842809031399944it_nat > produc8664842809031399944it_nat,X: option8956607266484857688it_nat] :
% 0.29/0.51 ( ( combin4318129983670048329it_nat @ F @ X @ none_P9117596204409417319it_nat )
% 0.29/0.51 = X ) ).
% 0.29/0.51
% 0.29/0.51 % combine_options_simps(2)
% 0.29/0.51 thf(fact_60_option_Oinject,axiom,
% 0.29/0.51 ! [X2: num,Y2: num] :
% 0.29/0.51 ( ( ( some_num @ X2 )
% 0.29/0.51 = ( some_num @ Y2 ) )
% 0.29/0.51 = ( X2 = Y2 ) ) ).
% 0.29/0.51
% 0.29/0.51 % option.inject
% 0.29/0.51 thf(fact_61_option_Oinject,axiom,
% 0.29/0.51 ! [X2: produc8664842809031399944it_nat,Y2: produc8664842809031399944it_nat] :
% 0.29/0.51 ( ( ( some_P1914260805536162275it_nat @ X2 )
% 0.29/0.51 = ( some_P1914260805536162275it_nat @ Y2 ) )
% 0.29/0.51 = ( X2 = Y2 ) ) ).
% 0.29/0.51
% 0.29/0.51 % option.inject
% 0.29/0.51 thf(fact_62_not__None__eq,axiom,
% 0.29/0.51 ! [X: option3216581401566546698it_nat] :
% 0.29/0.51 ( ( X != none_P2587165478634041381it_nat )
% 0.29/0.51 = ( ? [Y3: produc6714399278180371524it_nat] :
% 0.29/0.51 ( X
% 0.29/0.51 = ( some_P6105628898608307625it_nat @ Y3 ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % not_None_eq
% 0.29/0.51 thf(fact_63_not__None__eq,axiom,
% 0.29/0.51 ! [X: option_num] :
% 0.29/0.51 ( ( X != none_num )
% 0.29/0.51 = ( ? [Y3: num] :
% 0.29/0.51 ( X
% 0.29/0.51 = ( some_num @ Y3 ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % not_None_eq
% 0.29/0.51 thf(fact_64_not__None__eq,axiom,
% 0.29/0.51 ! [X: option8956607266484857688it_nat] :
% 0.29/0.51 ( ( X != none_P9117596204409417319it_nat )
% 0.29/0.51 = ( ? [Y3: produc8664842809031399944it_nat] :
% 0.29/0.51 ( X
% 0.29/0.51 = ( some_P1914260805536162275it_nat @ Y3 ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % not_None_eq
% 0.29/0.51 thf(fact_65_not__Some__eq,axiom,
% 0.29/0.51 ! [X: option3216581401566546698it_nat] :
% 0.29/0.51 ( ( ! [Y3: produc6714399278180371524it_nat] :
% 0.29/0.51 ( X
% 0.29/0.51 != ( some_P6105628898608307625it_nat @ Y3 ) ) )
% 0.29/0.51 = ( X = none_P2587165478634041381it_nat ) ) ).
% 0.29/0.51
% 0.29/0.51 % not_Some_eq
% 0.29/0.51 thf(fact_66_not__Some__eq,axiom,
% 0.29/0.51 ! [X: option_num] :
% 0.29/0.51 ( ( ! [Y3: num] :
% 0.29/0.51 ( X
% 0.29/0.51 != ( some_num @ Y3 ) ) )
% 0.29/0.51 = ( X = none_num ) ) ).
% 0.29/0.51
% 0.29/0.51 % not_Some_eq
% 0.29/0.51 thf(fact_67_not__Some__eq,axiom,
% 0.29/0.51 ! [X: option8956607266484857688it_nat] :
% 0.29/0.51 ( ( ! [Y3: produc8664842809031399944it_nat] :
% 0.29/0.51 ( X
% 0.29/0.51 != ( some_P1914260805536162275it_nat @ Y3 ) ) )
% 0.29/0.51 = ( X = none_P9117596204409417319it_nat ) ) ).
% 0.29/0.51
% 0.29/0.51 % not_Some_eq
% 0.29/0.51 thf(fact_68_combine__options__simps_I3_J,axiom,
% 0.29/0.51 ! [F: num > num > num,A: num,B: num] :
% 0.29/0.51 ( ( combine_options_num @ F @ ( some_num @ A ) @ ( some_num @ B ) )
% 0.29/0.51 = ( some_num @ ( F @ A @ B ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % combine_options_simps(3)
% 0.29/0.51 thf(fact_69_combine__options__simps_I3_J,axiom,
% 0.29/0.51 ! [F: produc8664842809031399944it_nat > produc8664842809031399944it_nat > produc8664842809031399944it_nat,A: produc8664842809031399944it_nat,B: produc8664842809031399944it_nat] :
% 0.29/0.51 ( ( combin4318129983670048329it_nat @ F @ ( some_P1914260805536162275it_nat @ A ) @ ( some_P1914260805536162275it_nat @ B ) )
% 0.29/0.51 = ( some_P1914260805536162275it_nat @ ( F @ A @ B ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % combine_options_simps(3)
% 0.29/0.51 thf(fact_70_mem__Collect__eq,axiom,
% 0.29/0.51 ! [A: produc3843707927480180839at_nat,P: produc3843707927480180839at_nat > $o] :
% 0.29/0.51 ( ( member8757157785044589968at_nat @ A @ ( collec6321179662152712658at_nat @ P ) )
% 0.29/0.51 = ( P @ A ) ) ).
% 0.29/0.51
% 0.29/0.51 % mem_Collect_eq
% 0.29/0.51 thf(fact_71_mem__Collect__eq,axiom,
% 0.29/0.51 ! [A: product_prod_nat_nat,P: product_prod_nat_nat > $o] :
% 0.29/0.51 ( ( member8440522571783428010at_nat @ A @ ( collec3392354462482085612at_nat @ P ) )
% 0.29/0.51 = ( P @ A ) ) ).
% 0.29/0.51
% 0.29/0.51 % mem_Collect_eq
% 0.29/0.51 thf(fact_72_mem__Collect__eq,axiom,
% 0.29/0.51 ! [A: $o,P: $o > $o] :
% 0.29/0.51 ( ( member_o @ A @ ( collect_o @ P ) )
% 0.29/0.51 = ( P @ A ) ) ).
% 0.29/0.51
% 0.29/0.51 % mem_Collect_eq
% 0.29/0.51 thf(fact_73_mem__Collect__eq,axiom,
% 0.29/0.51 ! [A: int,P: int > $o] :
% 0.29/0.51 ( ( member_int @ A @ ( collect_int @ P ) )
% 0.29/0.51 = ( P @ A ) ) ).
% 0.29/0.51
% 0.29/0.51 % mem_Collect_eq
% 0.29/0.51 thf(fact_74_mem__Collect__eq,axiom,
% 0.29/0.51 ! [A: nat,P: nat > $o] :
% 0.29/0.51 ( ( member_nat @ A @ ( collect_nat @ P ) )
% 0.29/0.51 = ( P @ A ) ) ).
% 0.29/0.51
% 0.29/0.51 % mem_Collect_eq
% 0.29/0.51 thf(fact_75_mem__Collect__eq,axiom,
% 0.29/0.51 ! [A: list_nat,P: list_nat > $o] :
% 0.29/0.51 ( ( member_list_nat @ A @ ( collect_list_nat @ P ) )
% 0.29/0.51 = ( P @ A ) ) ).
% 0.29/0.51
% 0.29/0.51 % mem_Collect_eq
% 0.29/0.51 thf(fact_76_Collect__mem__eq,axiom,
% 0.29/0.51 ! [A2: set_Pr4329608150637261639at_nat] :
% 0.29/0.51 ( ( collec6321179662152712658at_nat
% 0.29/0.51 @ ^ [X3: produc3843707927480180839at_nat] : ( member8757157785044589968at_nat @ X3 @ A2 ) )
% 0.29/0.51 = A2 ) ).
% 0.29/0.51
% 0.29/0.51 % Collect_mem_eq
% 0.29/0.51 thf(fact_77_Collect__mem__eq,axiom,
% 0.29/0.51 ! [A2: set_Pr1261947904930325089at_nat] :
% 0.29/0.51 ( ( collec3392354462482085612at_nat
% 0.29/0.51 @ ^ [X3: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X3 @ A2 ) )
% 0.29/0.51 = A2 ) ).
% 0.29/0.51
% 0.29/0.51 % Collect_mem_eq
% 0.29/0.51 thf(fact_78_Collect__mem__eq,axiom,
% 0.29/0.51 ! [A2: set_o] :
% 0.29/0.51 ( ( collect_o
% 0.29/0.51 @ ^ [X3: $o] : ( member_o @ X3 @ A2 ) )
% 0.29/0.51 = A2 ) ).
% 0.29/0.51
% 0.29/0.51 % Collect_mem_eq
% 0.29/0.51 thf(fact_79_Collect__mem__eq,axiom,
% 0.29/0.51 ! [A2: set_int] :
% 0.29/0.51 ( ( collect_int
% 0.29/0.51 @ ^ [X3: int] : ( member_int @ X3 @ A2 ) )
% 0.29/0.51 = A2 ) ).
% 0.29/0.51
% 0.29/0.51 % Collect_mem_eq
% 0.29/0.51 thf(fact_80_Collect__mem__eq,axiom,
% 0.29/0.51 ! [A2: set_nat] :
% 0.29/0.51 ( ( collect_nat
% 0.29/0.51 @ ^ [X3: nat] : ( member_nat @ X3 @ A2 ) )
% 0.29/0.51 = A2 ) ).
% 0.29/0.51
% 0.29/0.51 % Collect_mem_eq
% 0.29/0.51 thf(fact_81_Collect__mem__eq,axiom,
% 0.29/0.51 ! [A2: set_list_nat] :
% 0.29/0.51 ( ( collect_list_nat
% 0.29/0.51 @ ^ [X3: list_nat] : ( member_list_nat @ X3 @ A2 ) )
% 0.29/0.51 = A2 ) ).
% 0.29/0.51
% 0.29/0.51 % Collect_mem_eq
% 0.29/0.51 thf(fact_82_Collect__cong,axiom,
% 0.29/0.51 ! [P: nat > $o,Q: nat > $o] :
% 0.29/0.51 ( ! [X4: nat] :
% 0.29/0.51 ( ( P @ X4 )
% 0.29/0.51 = ( Q @ X4 ) )
% 0.29/0.51 => ( ( collect_nat @ P )
% 0.29/0.51 = ( collect_nat @ Q ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % Collect_cong
% 0.29/0.51 thf(fact_83_Collect__cong,axiom,
% 0.29/0.51 ! [P: list_nat > $o,Q: list_nat > $o] :
% 0.29/0.51 ( ! [X4: list_nat] :
% 0.29/0.51 ( ( P @ X4 )
% 0.29/0.51 = ( Q @ X4 ) )
% 0.29/0.51 => ( ( collect_list_nat @ P )
% 0.29/0.51 = ( collect_list_nat @ Q ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % Collect_cong
% 0.29/0.51 thf(fact_84_option_Odistinct_I1_J,axiom,
% 0.29/0.51 ! [X2: produc6714399278180371524it_nat] :
% 0.29/0.51 ( none_P2587165478634041381it_nat
% 0.29/0.51 != ( some_P6105628898608307625it_nat @ X2 ) ) ).
% 0.29/0.51
% 0.29/0.51 % option.distinct(1)
% 0.29/0.51 thf(fact_85_option_Odistinct_I1_J,axiom,
% 0.29/0.51 ! [X2: num] :
% 0.29/0.51 ( none_num
% 0.29/0.51 != ( some_num @ X2 ) ) ).
% 0.29/0.51
% 0.29/0.51 % option.distinct(1)
% 0.29/0.51 thf(fact_86_option_Odistinct_I1_J,axiom,
% 0.29/0.51 ! [X2: produc8664842809031399944it_nat] :
% 0.29/0.51 ( none_P9117596204409417319it_nat
% 0.29/0.51 != ( some_P1914260805536162275it_nat @ X2 ) ) ).
% 0.29/0.51
% 0.29/0.51 % option.distinct(1)
% 0.29/0.51 thf(fact_87_option_OdiscI,axiom,
% 0.29/0.51 ! [Option: option3216581401566546698it_nat,X2: produc6714399278180371524it_nat] :
% 0.29/0.51 ( ( Option
% 0.29/0.51 = ( some_P6105628898608307625it_nat @ X2 ) )
% 0.29/0.51 => ( Option != none_P2587165478634041381it_nat ) ) ).
% 0.29/0.51
% 0.29/0.51 % option.discI
% 0.29/0.51 thf(fact_88_option_OdiscI,axiom,
% 0.29/0.51 ! [Option: option_num,X2: num] :
% 0.29/0.51 ( ( Option
% 0.29/0.51 = ( some_num @ X2 ) )
% 0.29/0.51 => ( Option != none_num ) ) ).
% 0.29/0.51
% 0.29/0.51 % option.discI
% 0.29/0.51 thf(fact_89_option_OdiscI,axiom,
% 0.29/0.51 ! [Option: option8956607266484857688it_nat,X2: produc8664842809031399944it_nat] :
% 0.29/0.51 ( ( Option
% 0.29/0.51 = ( some_P1914260805536162275it_nat @ X2 ) )
% 0.29/0.51 => ( Option != none_P9117596204409417319it_nat ) ) ).
% 0.29/0.51
% 0.29/0.51 % option.discI
% 0.29/0.51 thf(fact_90_option_Oexhaust,axiom,
% 0.29/0.51 ! [Y: option3216581401566546698it_nat] :
% 0.29/0.51 ( ( Y != none_P2587165478634041381it_nat )
% 0.29/0.51 => ~ ! [X22: produc6714399278180371524it_nat] :
% 0.29/0.51 ( Y
% 0.29/0.51 != ( some_P6105628898608307625it_nat @ X22 ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % option.exhaust
% 0.29/0.51 thf(fact_91_option_Oexhaust,axiom,
% 0.29/0.51 ! [Y: option_num] :
% 0.29/0.51 ( ( Y != none_num )
% 0.29/0.51 => ~ ! [X22: num] :
% 0.29/0.51 ( Y
% 0.29/0.51 != ( some_num @ X22 ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % option.exhaust
% 0.29/0.51 thf(fact_92_option_Oexhaust,axiom,
% 0.29/0.51 ! [Y: option8956607266484857688it_nat] :
% 0.29/0.51 ( ( Y != none_P9117596204409417319it_nat )
% 0.29/0.51 => ~ ! [X22: produc8664842809031399944it_nat] :
% 0.29/0.51 ( Y
% 0.29/0.51 != ( some_P1914260805536162275it_nat @ X22 ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % option.exhaust
% 0.29/0.51 thf(fact_93_split__option__ex,axiom,
% 0.29/0.51 ( ( ^ [P2: option3216581401566546698it_nat > $o] :
% 0.29/0.51 ? [X5: option3216581401566546698it_nat] : ( P2 @ X5 ) )
% 0.29/0.51 = ( ^ [P3: option3216581401566546698it_nat > $o] :
% 0.29/0.51 ( ( P3 @ none_P2587165478634041381it_nat )
% 0.29/0.51 | ? [X3: produc6714399278180371524it_nat] : ( P3 @ ( some_P6105628898608307625it_nat @ X3 ) ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % split_option_ex
% 0.29/0.51 thf(fact_94_split__option__ex,axiom,
% 0.29/0.51 ( ( ^ [P2: option_num > $o] :
% 0.29/0.51 ? [X5: option_num] : ( P2 @ X5 ) )
% 0.29/0.51 = ( ^ [P3: option_num > $o] :
% 0.29/0.51 ( ( P3 @ none_num )
% 0.29/0.51 | ? [X3: num] : ( P3 @ ( some_num @ X3 ) ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % split_option_ex
% 0.29/0.51 thf(fact_95_split__option__ex,axiom,
% 0.29/0.51 ( ( ^ [P2: option8956607266484857688it_nat > $o] :
% 0.29/0.51 ? [X5: option8956607266484857688it_nat] : ( P2 @ X5 ) )
% 0.29/0.51 = ( ^ [P3: option8956607266484857688it_nat > $o] :
% 0.29/0.51 ( ( P3 @ none_P9117596204409417319it_nat )
% 0.29/0.51 | ? [X3: produc8664842809031399944it_nat] : ( P3 @ ( some_P1914260805536162275it_nat @ X3 ) ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % split_option_ex
% 0.29/0.51 thf(fact_96_split__option__all,axiom,
% 0.29/0.51 ( ( ^ [P2: option3216581401566546698it_nat > $o] :
% 0.29/0.51 ! [X5: option3216581401566546698it_nat] : ( P2 @ X5 ) )
% 0.29/0.51 = ( ^ [P3: option3216581401566546698it_nat > $o] :
% 0.29/0.51 ( ( P3 @ none_P2587165478634041381it_nat )
% 0.29/0.51 & ! [X3: produc6714399278180371524it_nat] : ( P3 @ ( some_P6105628898608307625it_nat @ X3 ) ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % split_option_all
% 0.29/0.51 thf(fact_97_split__option__all,axiom,
% 0.29/0.51 ( ( ^ [P2: option_num > $o] :
% 0.29/0.51 ! [X5: option_num] : ( P2 @ X5 ) )
% 0.29/0.51 = ( ^ [P3: option_num > $o] :
% 0.29/0.51 ( ( P3 @ none_num )
% 0.29/0.51 & ! [X3: num] : ( P3 @ ( some_num @ X3 ) ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % split_option_all
% 0.29/0.51 thf(fact_98_split__option__all,axiom,
% 0.29/0.51 ( ( ^ [P2: option8956607266484857688it_nat > $o] :
% 0.29/0.51 ! [X5: option8956607266484857688it_nat] : ( P2 @ X5 ) )
% 0.29/0.51 = ( ^ [P3: option8956607266484857688it_nat > $o] :
% 0.29/0.51 ( ( P3 @ none_P9117596204409417319it_nat )
% 0.29/0.51 & ! [X3: produc8664842809031399944it_nat] : ( P3 @ ( some_P1914260805536162275it_nat @ X3 ) ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % split_option_all
% 0.29/0.51 thf(fact_99_combine__options__cases,axiom,
% 0.29/0.51 ! [X: option3216581401566546698it_nat,P: option3216581401566546698it_nat > option3216581401566546698it_nat > $o,Y: option3216581401566546698it_nat] :
% 0.29/0.51 ( ( ( X = none_P2587165478634041381it_nat )
% 0.29/0.51 => ( P @ X @ Y ) )
% 0.29/0.51 => ( ( ( Y = none_P2587165478634041381it_nat )
% 0.29/0.51 => ( P @ X @ Y ) )
% 0.29/0.51 => ( ! [A3: produc6714399278180371524it_nat,B2: produc6714399278180371524it_nat] :
% 0.29/0.51 ( ( X
% 0.29/0.51 = ( some_P6105628898608307625it_nat @ A3 ) )
% 0.29/0.51 => ( ( Y
% 0.29/0.51 = ( some_P6105628898608307625it_nat @ B2 ) )
% 0.29/0.51 => ( P @ X @ Y ) ) )
% 0.29/0.51 => ( P @ X @ Y ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % combine_options_cases
% 0.29/0.51 thf(fact_100_combine__options__cases,axiom,
% 0.29/0.51 ! [X: option3216581401566546698it_nat,P: option3216581401566546698it_nat > option_num > $o,Y: option_num] :
% 0.29/0.51 ( ( ( X = none_P2587165478634041381it_nat )
% 0.29/0.51 => ( P @ X @ Y ) )
% 0.29/0.51 => ( ( ( Y = none_num )
% 0.29/0.51 => ( P @ X @ Y ) )
% 0.29/0.51 => ( ! [A3: produc6714399278180371524it_nat,B2: num] :
% 0.29/0.51 ( ( X
% 0.29/0.51 = ( some_P6105628898608307625it_nat @ A3 ) )
% 0.29/0.51 => ( ( Y
% 0.29/0.51 = ( some_num @ B2 ) )
% 0.29/0.51 => ( P @ X @ Y ) ) )
% 0.29/0.51 => ( P @ X @ Y ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % combine_options_cases
% 0.29/0.51 thf(fact_101_combine__options__cases,axiom,
% 0.29/0.51 ! [X: option3216581401566546698it_nat,P: option3216581401566546698it_nat > option8956607266484857688it_nat > $o,Y: option8956607266484857688it_nat] :
% 0.29/0.51 ( ( ( X = none_P2587165478634041381it_nat )
% 0.29/0.51 => ( P @ X @ Y ) )
% 0.29/0.51 => ( ( ( Y = none_P9117596204409417319it_nat )
% 0.29/0.51 => ( P @ X @ Y ) )
% 0.29/0.51 => ( ! [A3: produc6714399278180371524it_nat,B2: produc8664842809031399944it_nat] :
% 0.29/0.51 ( ( X
% 0.29/0.51 = ( some_P6105628898608307625it_nat @ A3 ) )
% 0.29/0.51 => ( ( Y
% 0.29/0.51 = ( some_P1914260805536162275it_nat @ B2 ) )
% 0.29/0.51 => ( P @ X @ Y ) ) )
% 0.29/0.51 => ( P @ X @ Y ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % combine_options_cases
% 0.29/0.51 thf(fact_102_combine__options__cases,axiom,
% 0.29/0.51 ! [X: option_num,P: option_num > option3216581401566546698it_nat > $o,Y: option3216581401566546698it_nat] :
% 0.29/0.51 ( ( ( X = none_num )
% 0.29/0.51 => ( P @ X @ Y ) )
% 0.29/0.51 => ( ( ( Y = none_P2587165478634041381it_nat )
% 0.29/0.51 => ( P @ X @ Y ) )
% 0.29/0.51 => ( ! [A3: num,B2: produc6714399278180371524it_nat] :
% 0.29/0.51 ( ( X
% 0.29/0.51 = ( some_num @ A3 ) )
% 0.29/0.51 => ( ( Y
% 0.29/0.51 = ( some_P6105628898608307625it_nat @ B2 ) )
% 0.29/0.51 => ( P @ X @ Y ) ) )
% 0.29/0.51 => ( P @ X @ Y ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % combine_options_cases
% 0.29/0.51 thf(fact_103_combine__options__cases,axiom,
% 0.29/0.51 ! [X: option_num,P: option_num > option_num > $o,Y: option_num] :
% 0.29/0.51 ( ( ( X = none_num )
% 0.29/0.51 => ( P @ X @ Y ) )
% 0.29/0.51 => ( ( ( Y = none_num )
% 0.29/0.51 => ( P @ X @ Y ) )
% 0.29/0.51 => ( ! [A3: num,B2: num] :
% 0.29/0.51 ( ( X
% 0.29/0.51 = ( some_num @ A3 ) )
% 0.29/0.51 => ( ( Y
% 0.29/0.51 = ( some_num @ B2 ) )
% 0.29/0.51 => ( P @ X @ Y ) ) )
% 0.29/0.51 => ( P @ X @ Y ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % combine_options_cases
% 0.29/0.51 thf(fact_104_combine__options__cases,axiom,
% 0.29/0.51 ! [X: option_num,P: option_num > option8956607266484857688it_nat > $o,Y: option8956607266484857688it_nat] :
% 0.29/0.51 ( ( ( X = none_num )
% 0.29/0.51 => ( P @ X @ Y ) )
% 0.29/0.51 => ( ( ( Y = none_P9117596204409417319it_nat )
% 0.29/0.51 => ( P @ X @ Y ) )
% 0.29/0.51 => ( ! [A3: num,B2: produc8664842809031399944it_nat] :
% 0.29/0.51 ( ( X
% 0.29/0.51 = ( some_num @ A3 ) )
% 0.29/0.51 => ( ( Y
% 0.29/0.51 = ( some_P1914260805536162275it_nat @ B2 ) )
% 0.29/0.51 => ( P @ X @ Y ) ) )
% 0.29/0.51 => ( P @ X @ Y ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % combine_options_cases
% 0.29/0.51 thf(fact_105_combine__options__cases,axiom,
% 0.29/0.51 ! [X: option8956607266484857688it_nat,P: option8956607266484857688it_nat > option3216581401566546698it_nat > $o,Y: option3216581401566546698it_nat] :
% 0.29/0.51 ( ( ( X = none_P9117596204409417319it_nat )
% 0.29/0.51 => ( P @ X @ Y ) )
% 0.29/0.51 => ( ( ( Y = none_P2587165478634041381it_nat )
% 0.29/0.51 => ( P @ X @ Y ) )
% 0.29/0.51 => ( ! [A3: produc8664842809031399944it_nat,B2: produc6714399278180371524it_nat] :
% 0.29/0.51 ( ( X
% 0.29/0.51 = ( some_P1914260805536162275it_nat @ A3 ) )
% 0.29/0.51 => ( ( Y
% 0.29/0.51 = ( some_P6105628898608307625it_nat @ B2 ) )
% 0.29/0.51 => ( P @ X @ Y ) ) )
% 0.29/0.51 => ( P @ X @ Y ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % combine_options_cases
% 0.29/0.51 thf(fact_106_combine__options__cases,axiom,
% 0.29/0.51 ! [X: option8956607266484857688it_nat,P: option8956607266484857688it_nat > option_num > $o,Y: option_num] :
% 0.29/0.51 ( ( ( X = none_P9117596204409417319it_nat )
% 0.29/0.51 => ( P @ X @ Y ) )
% 0.29/0.51 => ( ( ( Y = none_num )
% 0.29/0.51 => ( P @ X @ Y ) )
% 0.29/0.51 => ( ! [A3: produc8664842809031399944it_nat,B2: num] :
% 0.29/0.51 ( ( X
% 0.29/0.51 = ( some_P1914260805536162275it_nat @ A3 ) )
% 0.29/0.51 => ( ( Y
% 0.29/0.51 = ( some_num @ B2 ) )
% 0.29/0.51 => ( P @ X @ Y ) ) )
% 0.29/0.51 => ( P @ X @ Y ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % combine_options_cases
% 0.29/0.51 thf(fact_107_combine__options__cases,axiom,
% 0.29/0.51 ! [X: option8956607266484857688it_nat,P: option8956607266484857688it_nat > option8956607266484857688it_nat > $o,Y: option8956607266484857688it_nat] :
% 0.29/0.51 ( ( ( X = none_P9117596204409417319it_nat )
% 0.29/0.51 => ( P @ X @ Y ) )
% 0.29/0.51 => ( ( ( Y = none_P9117596204409417319it_nat )
% 0.29/0.51 => ( P @ X @ Y ) )
% 0.29/0.51 => ( ! [A3: produc8664842809031399944it_nat,B2: produc8664842809031399944it_nat] :
% 0.29/0.51 ( ( X
% 0.29/0.51 = ( some_P1914260805536162275it_nat @ A3 ) )
% 0.29/0.51 => ( ( Y
% 0.29/0.51 = ( some_P1914260805536162275it_nat @ B2 ) )
% 0.29/0.51 => ( P @ X @ Y ) ) )
% 0.29/0.51 => ( P @ X @ Y ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % combine_options_cases
% 0.29/0.51 thf(fact_108_success__effectE,axiom,
% 0.29/0.51 ! [C: heap_T5738788834812785303t_unit,H3: heap_e7401611519738050253t_unit] :
% 0.29/0.51 ( ( heap_T584514906347983379t_unit @ C @ H3 )
% 0.29/0.51 => ~ ! [R: product_unit,H4: heap_e7401611519738050253t_unit,N: nat] :
% 0.29/0.51 ~ ( heap_T6553295506729943825t_unit @ C @ H3 @ H4 @ R @ N ) ) ).
% 0.29/0.51
% 0.29/0.51 % success_effectE
% 0.29/0.51 thf(fact_109_success__effectE,axiom,
% 0.29/0.51 ! [C: heap_T6362127782908069795rray_a,H3: heap_e7401611519738050253t_unit] :
% 0.29/0.51 ( ( heap_T6932021131025641745rray_a @ C @ H3 )
% 0.29/0.51 => ~ ! [R: array_a,H4: heap_e7401611519738050253t_unit,N: nat] :
% 0.29/0.51 ~ ( heap_T5830633491639066771rray_a @ C @ H3 @ H4 @ R @ N ) ) ).
% 0.29/0.51
% 0.29/0.51 % success_effectE
% 0.29/0.51 thf(fact_110_effect__success,axiom,
% 0.29/0.51 ! [C: heap_T5738788834812785303t_unit,H3: heap_e7401611519738050253t_unit,H5: heap_e7401611519738050253t_unit,R2: product_unit,N2: nat] :
% 0.29/0.51 ( ( heap_T6553295506729943825t_unit @ C @ H3 @ H5 @ R2 @ N2 )
% 0.29/0.51 => ( heap_T584514906347983379t_unit @ C @ H3 ) ) ).
% 0.29/0.51
% 0.29/0.51 % effect_success
% 0.29/0.51 thf(fact_111_effect__success,axiom,
% 0.29/0.51 ! [C: heap_T6362127782908069795rray_a,H3: heap_e7401611519738050253t_unit,H5: heap_e7401611519738050253t_unit,R2: array_a,N2: nat] :
% 0.29/0.51 ( ( heap_T5830633491639066771rray_a @ C @ H3 @ H5 @ R2 @ N2 )
% 0.29/0.51 => ( heap_T6932021131025641745rray_a @ C @ H3 ) ) ).
% 0.29/0.51
% 0.29/0.51 % effect_success
% 0.29/0.51 thf(fact_112_effect__raiseE,axiom,
% 0.29/0.51 ! [X: list_char,H3: heap_e7401611519738050253t_unit,H5: heap_e7401611519738050253t_unit,R2: product_unit,N2: nat] :
% 0.29/0.51 ~ ( heap_T6553295506729943825t_unit @ ( heap_T2927564422264180874t_unit @ X ) @ H3 @ H5 @ R2 @ N2 ) ).
% 0.29/0.51
% 0.29/0.51 % effect_raiseE
% 0.29/0.51 thf(fact_113_effect__raiseE,axiom,
% 0.29/0.51 ! [X: list_char,H3: heap_e7401611519738050253t_unit,H5: heap_e7401611519738050253t_unit,R2: array_a,N2: nat] :
% 0.29/0.51 ~ ( heap_T5830633491639066771rray_a @ ( heap_T1552190017797416154rray_a @ X ) @ H3 @ H5 @ R2 @ N2 ) ).
% 0.29/0.51
% 0.29/0.51 % effect_raiseE
% 0.29/0.51 thf(fact_114_the__default_Osimps_I1_J,axiom,
% 0.29/0.51 ! [Uu2: num,X: num] :
% 0.29/0.51 ( ( the_default_num @ Uu2 @ ( some_num @ X ) )
% 0.29/0.51 = X ) ).
% 0.29/0.51
% 0.29/0.51 % the_default.simps(1)
% 0.29/0.51 thf(fact_115_the__default_Osimps_I1_J,axiom,
% 0.29/0.51 ! [Uu2: produc8664842809031399944it_nat,X: produc8664842809031399944it_nat] :
% 0.29/0.51 ( ( the_de2487931475039285041it_nat @ Uu2 @ ( some_P1914260805536162275it_nat @ X ) )
% 0.29/0.51 = X ) ).
% 0.29/0.51
% 0.29/0.51 % the_default.simps(1)
% 0.29/0.51 thf(fact_116_Heap__cases,axiom,
% 0.29/0.51 ! [F: heap_T6362127782908069795rray_a,H3: heap_e7401611519738050253t_unit] :
% 0.29/0.51 ( ! [X4: array_a,H4: produc6653097349344004940it_nat] :
% 0.29/0.51 ( ( heap_T5591663578999710211rray_a @ F @ H3 )
% 0.29/0.51 != ( some_P6105628898608307625it_nat @ ( produc1733996804261680252it_nat @ X4 @ H4 ) ) )
% 0.29/0.51 => ( ( heap_T5591663578999710211rray_a @ F @ H3 )
% 0.29/0.51 = none_P2587165478634041381it_nat ) ) ).
% 0.29/0.51
% 0.29/0.51 % Heap_cases
% 0.29/0.51 thf(fact_117_Heap__cases,axiom,
% 0.29/0.51 ! [F: heap_T5738788834812785303t_unit,H3: heap_e7401611519738050253t_unit] :
% 0.29/0.51 ( ! [X4: product_unit,H4: produc6653097349344004940it_nat] :
% 0.29/0.51 ( ( heap_T875086893843062177t_unit @ F @ H3 )
% 0.29/0.51 != ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ X4 @ H4 ) ) )
% 0.29/0.51 => ( ( heap_T875086893843062177t_unit @ F @ H3 )
% 0.29/0.51 = none_P9117596204409417319it_nat ) ) ).
% 0.29/0.51
% 0.29/0.51 % Heap_cases
% 0.29/0.51 thf(fact_118_successE,axiom,
% 0.29/0.51 ! [F: heap_T5738788834812785303t_unit,H3: heap_e7401611519738050253t_unit] :
% 0.29/0.51 ( ( heap_T584514906347983379t_unit @ F @ H3 )
% 0.29/0.51 => ~ ! [R: product_unit,H4: produc6653097349344004940it_nat] :
% 0.29/0.51 ( ( heap_T875086893843062177t_unit @ F @ H3 )
% 0.29/0.51 != ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ R @ H4 ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % successE
% 0.29/0.51 thf(fact_119_successE,axiom,
% 0.29/0.51 ! [F: heap_T6362127782908069795rray_a,H3: heap_e7401611519738050253t_unit] :
% 0.29/0.51 ( ( heap_T6932021131025641745rray_a @ F @ H3 )
% 0.29/0.51 => ~ ! [R: array_a,H4: produc6653097349344004940it_nat] :
% 0.29/0.51 ( ( heap_T5591663578999710211rray_a @ F @ H3 )
% 0.29/0.51 != ( some_P6105628898608307625it_nat @ ( produc1733996804261680252it_nat @ R @ H4 ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % successE
% 0.29/0.51 thf(fact_120_execute__heap,axiom,
% 0.29/0.51 ! [F: heap_e7401611519738050253t_unit > produc6714399278180371524it_nat] :
% 0.29/0.51 ( ( heap_T5591663578999710211rray_a @ ( heap_T7473999186002612558rray_a @ F ) )
% 0.29/0.51 = ( comp_P2097125496263478628t_unit @ some_P6105628898608307625it_nat @ F ) ) ).
% 0.29/0.51
% 0.29/0.51 % execute_heap
% 0.29/0.51 thf(fact_121_execute__heap,axiom,
% 0.29/0.51 ! [F: heap_e7401611519738050253t_unit > produc8664842809031399944it_nat] :
% 0.29/0.51 ( ( heap_T875086893843062177t_unit @ ( heap_T6927113302350381334t_unit @ F ) )
% 0.29/0.51 = ( comp_P3118722334806803912t_unit @ some_P1914260805536162275it_nat @ F ) ) ).
% 0.29/0.51
% 0.29/0.51 % execute_heap
% 0.29/0.51 thf(fact_122_some__opt__sym__eq__trivial,axiom,
% 0.29/0.51 ! [X: num] :
% 0.29/0.51 ( ( eps_Opt_num
% 0.29/0.51 @ ( ^ [Y4: num,Z2: num] : ( Y4 = Z2 )
% 0.29/0.51 @ X ) )
% 0.29/0.51 = ( some_num @ X ) ) ).
% 0.29/0.51
% 0.29/0.51 % some_opt_sym_eq_trivial
% 0.29/0.51 thf(fact_123_some__opt__sym__eq__trivial,axiom,
% 0.29/0.51 ! [X: produc8664842809031399944it_nat] :
% 0.29/0.51 ( ( eps_Op3393321821070424684it_nat
% 0.29/0.51 @ ( ^ [Y4: produc8664842809031399944it_nat,Z2: produc8664842809031399944it_nat] : ( Y4 = Z2 )
% 0.29/0.51 @ X ) )
% 0.29/0.51 = ( some_P1914260805536162275it_nat @ X ) ) ).
% 0.29/0.51
% 0.29/0.51 % some_opt_sym_eq_trivial
% 0.29/0.51 thf(fact_124_success__newI,axiom,
% 0.29/0.51 ! [N2: nat,X: a,H3: heap_e7401611519738050253t_unit] : ( heap_T6932021131025641745rray_a @ ( array_new_a @ N2 @ X ) @ H3 ) ).
% 0.29/0.51
% 0.29/0.51 % success_newI
% 0.29/0.51 thf(fact_125_success__makeI,axiom,
% 0.29/0.51 ! [N2: nat,F: nat > a,H3: heap_e7401611519738050253t_unit] : ( heap_T6932021131025641745rray_a @ ( array_make_a @ N2 @ F ) @ H3 ) ).
% 0.29/0.51
% 0.29/0.51 % success_makeI
% 0.29/0.51 thf(fact_126_mmupd__in__upd,axiom,
% 0.29/0.51 ! [K: produc3843707927480180839at_nat,K2: set_Pr4329608150637261639at_nat,M2: produc3843707927480180839at_nat > option_num,V: num] :
% 0.29/0.51 ( ( member8757157785044589968at_nat @ K @ K2 )
% 0.29/0.51 => ( ( map_mm2124855372588256220at_num @ M2 @ K2 @ V @ K )
% 0.29/0.51 = ( some_num @ V ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % mmupd_in_upd
% 0.29/0.51 thf(fact_127_mmupd__in__upd,axiom,
% 0.29/0.51 ! [K: product_prod_nat_nat,K2: set_Pr1261947904930325089at_nat,M2: product_prod_nat_nat > option_num,V: num] :
% 0.29/0.51 ( ( member8440522571783428010at_nat @ K @ K2 )
% 0.29/0.51 => ( ( map_mm6272435474268545910at_num @ M2 @ K2 @ V @ K )
% 0.29/0.51 = ( some_num @ V ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % mmupd_in_upd
% 0.29/0.51 thf(fact_128_mmupd__in__upd,axiom,
% 0.29/0.51 ! [K: $o,K2: set_o,M2: $o > option_num,V: num] :
% 0.29/0.51 ( ( member_o @ K @ K2 )
% 0.29/0.51 => ( ( map_mmupd_o_num @ M2 @ K2 @ V @ K )
% 0.29/0.51 = ( some_num @ V ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % mmupd_in_upd
% 0.29/0.51 thf(fact_129_mmupd__in__upd,axiom,
% 0.29/0.51 ! [K: nat,K2: set_nat,M2: nat > option_num,V: num] :
% 0.29/0.51 ( ( member_nat @ K @ K2 )
% 0.29/0.51 => ( ( map_mmupd_nat_num @ M2 @ K2 @ V @ K )
% 0.29/0.51 = ( some_num @ V ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % mmupd_in_upd
% 0.29/0.51 thf(fact_130_mmupd__in__upd,axiom,
% 0.29/0.51 ! [K: int,K2: set_int,M2: int > option_num,V: num] :
% 0.29/0.51 ( ( member_int @ K @ K2 )
% 0.29/0.51 => ( ( map_mmupd_int_num @ M2 @ K2 @ V @ K )
% 0.29/0.51 = ( some_num @ V ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % mmupd_in_upd
% 0.29/0.51 thf(fact_131_mmupd__in__upd,axiom,
% 0.29/0.51 ! [K: produc3843707927480180839at_nat,K2: set_Pr4329608150637261639at_nat,M2: produc3843707927480180839at_nat > option8956607266484857688it_nat,V: produc8664842809031399944it_nat] :
% 0.29/0.51 ( ( member8757157785044589968at_nat @ K @ K2 )
% 0.29/0.51 => ( ( map_mm6227321356191524810it_nat @ M2 @ K2 @ V @ K )
% 0.29/0.51 = ( some_P1914260805536162275it_nat @ V ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % mmupd_in_upd
% 0.29/0.51 thf(fact_132_mmupd__in__upd,axiom,
% 0.29/0.51 ! [K: product_prod_nat_nat,K2: set_Pr1261947904930325089at_nat,M2: product_prod_nat_nat > option8956607266484857688it_nat,V: produc8664842809031399944it_nat] :
% 0.29/0.51 ( ( member8440522571783428010at_nat @ K @ K2 )
% 0.29/0.51 => ( ( map_mm8925508573636269924it_nat @ M2 @ K2 @ V @ K )
% 0.29/0.51 = ( some_P1914260805536162275it_nat @ V ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % mmupd_in_upd
% 0.29/0.51 thf(fact_133_mmupd__in__upd,axiom,
% 0.29/0.51 ! [K: $o,K2: set_o,M2: $o > option8956607266484857688it_nat,V: produc8664842809031399944it_nat] :
% 0.29/0.51 ( ( member_o @ K @ K2 )
% 0.29/0.51 => ( ( map_mm4340940675810032635it_nat @ M2 @ K2 @ V @ K )
% 0.29/0.51 = ( some_P1914260805536162275it_nat @ V ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % mmupd_in_upd
% 0.29/0.51 thf(fact_134_mmupd__in__upd,axiom,
% 0.29/0.51 ! [K: nat,K2: set_nat,M2: nat > option8956607266484857688it_nat,V: produc8664842809031399944it_nat] :
% 0.29/0.51 ( ( member_nat @ K @ K2 )
% 0.29/0.51 => ( ( map_mm4316137065318800191it_nat @ M2 @ K2 @ V @ K )
% 0.29/0.51 = ( some_P1914260805536162275it_nat @ V ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % mmupd_in_upd
% 0.29/0.51 thf(fact_135_mmupd__in__upd,axiom,
% 0.29/0.51 ! [K: int,K2: set_int,M2: int > option8956607266484857688it_nat,V: produc8664842809031399944it_nat] :
% 0.29/0.51 ( ( member_int @ K @ K2 )
% 0.29/0.51 => ( ( map_mm5942422175790858651it_nat @ M2 @ K2 @ V @ K )
% 0.29/0.51 = ( some_P1914260805536162275it_nat @ V ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % mmupd_in_upd
% 0.29/0.51 thf(fact_136_option_Ocollapse,axiom,
% 0.29/0.51 ! [Option: option3216581401566546698it_nat] :
% 0.29/0.51 ( ( Option != none_P2587165478634041381it_nat )
% 0.29/0.51 => ( ( some_P6105628898608307625it_nat @ ( the_Pr5856008525237892824it_nat @ Option ) )
% 0.29/0.51 = Option ) ) ).
% 0.29/0.51
% 0.29/0.51 % option.collapse
% 0.29/0.51 thf(fact_137_option_Ocollapse,axiom,
% 0.29/0.51 ! [Option: option_num] :
% 0.29/0.51 ( ( Option != none_num )
% 0.29/0.51 => ( ( some_num @ ( the_num @ Option ) )
% 0.29/0.51 = Option ) ) ).
% 0.29/0.51
% 0.29/0.51 % option.collapse
% 0.29/0.51 thf(fact_138_option_Ocollapse,axiom,
% 0.29/0.51 ! [Option: option8956607266484857688it_nat] :
% 0.29/0.51 ( ( Option != none_P9117596204409417319it_nat )
% 0.29/0.51 => ( ( some_P1914260805536162275it_nat @ ( the_Pr7776125533777466484it_nat @ Option ) )
% 0.29/0.51 = Option ) ) ).
% 0.29/0.51
% 0.29/0.51 % option.collapse
% 0.29/0.51 thf(fact_139_not__Some__eq2,axiom,
% 0.29/0.51 ! [V: option8051342751916580710nteger] :
% 0.29/0.51 ( ( ! [X3: produc6241069584506657477e_term > option6357759511663192854e_term,Y3: produc8923325533196201883nteger] :
% 0.29/0.51 ( V
% 0.29/0.51 != ( some_P1462369734362851057nteger @ ( produc8603105652947943368nteger @ X3 @ Y3 ) ) ) )
% 0.29/0.51 = ( V = none_P4442379456014020469nteger ) ) ).
% 0.29/0.51
% 0.29/0.51 % not_Some_eq2
% 0.29/0.51 thf(fact_140_not__Some__eq2,axiom,
% 0.29/0.51 ! [V: option5190343406534369742et_nat] :
% 0.29/0.51 ( ( ! [X3: produc3658429121746597890et_nat > $o,Y3: produc3658429121746597890et_nat] :
% 0.29/0.51 ( V
% 0.29/0.51 != ( some_P750831030444334937et_nat @ ( produc5001842942810119800et_nat @ X3 @ Y3 ) ) ) )
% 0.29/0.51 = ( V = none_P4972525538344268765et_nat ) ) ).
% 0.29/0.51
% 0.29/0.51 % not_Some_eq2
% 0.29/0.51 thf(fact_141_not__Some__eq2,axiom,
% 0.29/0.51 ! [V: option2860828798490689354et_nat] :
% 0.29/0.51 ( ( ! [X3: produc3658429121746597890et_nat > $o,Y3: produc3925858234332021118et_nat] :
% 0.29/0.51 ( V
% 0.29/0.51 != ( some_P1630309045189364437et_nat @ ( produc2245416461498447860et_nat @ X3 @ Y3 ) ) ) )
% 0.29/0.51 = ( V = none_P199884684680593241et_nat ) ) ).
% 0.29/0.51
% 0.29/0.51 % not_Some_eq2
% 0.29/0.51 thf(fact_142_not__Some__eq2,axiom,
% 0.29/0.51 ! [V: option7541221861074943443nt_int] :
% 0.29/0.51 ( ( ! [X3: produc8551481072490612790e_term > option6357759511663192854e_term,Y3: product_prod_int_int] :
% 0.29/0.51 ( V
% 0.29/0.51 != ( some_P2355398578364412894nt_int @ ( produc5700946648718959541nt_int @ X3 @ Y3 ) ) ) )
% 0.29/0.51 = ( V = none_P1286213070022356066nt_int ) ) ).
% 0.29/0.51
% 0.29/0.51 % not_Some_eq2
% 0.29/0.51 thf(fact_143_not__Some__eq2,axiom,
% 0.29/0.51 ! [V: option4256020574406277085nt_int] :
% 0.29/0.51 ( ( ! [X3: int > option6357759511663192854e_term,Y3: product_prod_int_int] :
% 0.29/0.51 ( V
% 0.29/0.51 != ( some_P7455497367792166888nt_int @ ( produc4305682042979456191nt_int @ X3 @ Y3 ) ) ) )
% 0.29/0.51 = ( V = none_P3773570700014501484nt_int ) ) ).
% 0.29/0.51
% 0.29/0.51 % not_Some_eq2
% 0.29/0.51 thf(fact_144_not__Some__eq2,axiom,
% 0.29/0.51 ! [V: option3216581401566546698it_nat] :
% 0.29/0.51 ( ( ! [X3: array_a,Y3: produc6653097349344004940it_nat] :
% 0.29/0.51 ( V
% 0.29/0.51 != ( some_P6105628898608307625it_nat @ ( produc1733996804261680252it_nat @ X3 @ Y3 ) ) ) )
% 0.29/0.51 = ( V = none_P2587165478634041381it_nat ) ) ).
% 0.29/0.51
% 0.29/0.51 % not_Some_eq2
% 0.29/0.51 thf(fact_145_not__Some__eq2,axiom,
% 0.29/0.51 ! [V: option8956607266484857688it_nat] :
% 0.29/0.51 ( ( ! [X3: product_unit,Y3: produc6653097349344004940it_nat] :
% 0.29/0.51 ( V
% 0.29/0.51 != ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ X3 @ Y3 ) ) ) )
% 0.29/0.51 = ( V = none_P9117596204409417319it_nat ) ) ).
% 0.29/0.51
% 0.29/0.51 % not_Some_eq2
% 0.29/0.51 thf(fact_146_effect__assertI,axiom,
% 0.29/0.51 ! [P: product_unit > $o,X: product_unit,H5: heap_e7401611519738050253t_unit,H3: heap_e7401611519738050253t_unit,R2: product_unit,N2: nat] :
% 0.29/0.51 ( ( P @ X )
% 0.29/0.51 => ( ( H5 = H3 )
% 0.29/0.51 => ( ( R2 = X )
% 0.29/0.51 => ( ( N2 = one_one_nat )
% 0.29/0.51 => ( heap_T6553295506729943825t_unit @ ( heap_T4208721593536448476t_unit @ P @ X ) @ H3 @ H5 @ R2 @ N2 ) ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % effect_assertI
% 0.29/0.51 thf(fact_147_effect__assertI,axiom,
% 0.29/0.51 ! [P: array_a > $o,X: array_a,H5: heap_e7401611519738050253t_unit,H3: heap_e7401611519738050253t_unit,R2: array_a,N2: nat] :
% 0.29/0.51 ( ( P @ X )
% 0.29/0.51 => ( ( H5 = H3 )
% 0.29/0.51 => ( ( R2 = X )
% 0.29/0.51 => ( ( N2 = one_one_nat )
% 0.29/0.51 => ( heap_T5830633491639066771rray_a @ ( heap_T7971689983404357896rray_a @ P @ X ) @ H3 @ H5 @ R2 @ N2 ) ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % effect_assertI
% 0.29/0.51 thf(fact_148_fun__comp__eq__conv,axiom,
% 0.29/0.51 ! [F: code_integer > code_integer,G: num > code_integer,Fg: num > code_integer] :
% 0.29/0.51 ( ( ( comp_C3531382070062128313er_num @ F @ G )
% 0.29/0.51 = Fg )
% 0.29/0.51 = ( ! [X3: num] :
% 0.29/0.51 ( ( F @ ( G @ X3 ) )
% 0.29/0.51 = ( Fg @ X3 ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % fun_comp_eq_conv
% 0.29/0.51 thf(fact_149_fun__comp__eq__conv,axiom,
% 0.29/0.51 ! [F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer,Fg: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 0.29/0.51 ( ( ( comp_C1593894019821074884nteger @ F @ G )
% 0.29/0.51 = Fg )
% 0.29/0.51 = ( ! [X3: code_integer] :
% 0.29/0.51 ( ( F @ ( G @ X3 ) )
% 0.29/0.51 = ( Fg @ X3 ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % fun_comp_eq_conv
% 0.29/0.51 thf(fact_150_fun__comp__eq__conv,axiom,
% 0.29/0.51 ! [F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer > code_integer,Fg: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 0.29/0.51 ( ( ( comp_C8797469213163452608nteger @ F @ G )
% 0.29/0.51 = Fg )
% 0.29/0.51 = ( ! [X3: code_integer] :
% 0.29/0.51 ( ( F @ ( G @ X3 ) )
% 0.29/0.51 = ( Fg @ X3 ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % fun_comp_eq_conv
% 0.29/0.51 thf(fact_151_fun__comp__eq__conv,axiom,
% 0.29/0.51 ! [F: nat > num,G: int > nat,Fg: int > num] :
% 0.29/0.51 ( ( ( comp_nat_num_int @ F @ G )
% 0.29/0.51 = Fg )
% 0.29/0.51 = ( ! [X3: int] :
% 0.29/0.51 ( ( F @ ( G @ X3 ) )
% 0.29/0.51 = ( Fg @ X3 ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % fun_comp_eq_conv
% 0.29/0.51 thf(fact_152_comp__cong__right,axiom,
% 0.29/0.51 ! [X: num > code_integer,Y: num > code_integer,F: code_integer > code_integer] :
% 0.29/0.51 ( ( X = Y )
% 0.29/0.51 => ( ( comp_C3531382070062128313er_num @ F @ X )
% 0.29/0.51 = ( comp_C3531382070062128313er_num @ F @ Y ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % comp_cong_right
% 0.29/0.51 thf(fact_153_comp__cong__right,axiom,
% 0.29/0.51 ! [X: code_integer > code_integer,Y: code_integer > code_integer,F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 0.29/0.51 ( ( X = Y )
% 0.29/0.51 => ( ( comp_C1593894019821074884nteger @ F @ X )
% 0.29/0.51 = ( comp_C1593894019821074884nteger @ F @ Y ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % comp_cong_right
% 0.29/0.51 thf(fact_154_comp__cong__right,axiom,
% 0.29/0.51 ! [X: code_integer > code_integer > code_integer,Y: code_integer > code_integer > code_integer,F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 0.29/0.51 ( ( X = Y )
% 0.29/0.51 => ( ( comp_C8797469213163452608nteger @ F @ X )
% 0.29/0.51 = ( comp_C8797469213163452608nteger @ F @ Y ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % comp_cong_right
% 0.29/0.51 thf(fact_155_comp__cong__right,axiom,
% 0.29/0.51 ! [X: int > nat,Y: int > nat,F: nat > num] :
% 0.29/0.51 ( ( X = Y )
% 0.29/0.51 => ( ( comp_nat_num_int @ F @ X )
% 0.29/0.51 = ( comp_nat_num_int @ F @ Y ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % comp_cong_right
% 0.29/0.51 thf(fact_156_comp__cong__left,axiom,
% 0.29/0.51 ! [X: code_integer > code_integer,Y: code_integer > code_integer,F: num > code_integer] :
% 0.29/0.51 ( ( X = Y )
% 0.29/0.51 => ( ( comp_C3531382070062128313er_num @ X @ F )
% 0.29/0.51 = ( comp_C3531382070062128313er_num @ Y @ F ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % comp_cong_left
% 0.29/0.51 thf(fact_157_comp__cong__left,axiom,
% 0.29/0.51 ! [X: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,Y: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,F: code_integer > code_integer] :
% 0.29/0.51 ( ( X = Y )
% 0.29/0.51 => ( ( comp_C1593894019821074884nteger @ X @ F )
% 0.29/0.51 = ( comp_C1593894019821074884nteger @ Y @ F ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % comp_cong_left
% 0.29/0.51 thf(fact_158_comp__cong__left,axiom,
% 0.29/0.51 ! [X: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,Y: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,F: code_integer > code_integer > code_integer] :
% 0.29/0.51 ( ( X = Y )
% 0.29/0.51 => ( ( comp_C8797469213163452608nteger @ X @ F )
% 0.29/0.51 = ( comp_C8797469213163452608nteger @ Y @ F ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % comp_cong_left
% 0.29/0.51 thf(fact_159_comp__cong__left,axiom,
% 0.29/0.51 ! [X: nat > num,Y: nat > num,F: int > nat] :
% 0.29/0.51 ( ( X = Y )
% 0.29/0.51 => ( ( comp_nat_num_int @ X @ F )
% 0.29/0.51 = ( comp_nat_num_int @ Y @ F ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % comp_cong_left
% 0.29/0.51 thf(fact_160_bex2I,axiom,
% 0.29/0.51 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,S2: set_Pr4329608150637261639at_nat,P: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o] :
% 0.29/0.51 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ B ) @ S2 )
% 0.29/0.51 => ( ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ B ) @ S2 )
% 0.29/0.51 => ( P @ A @ B ) )
% 0.29/0.51 => ? [A3: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 0.29/0.51 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A3 @ B2 ) @ S2 )
% 0.29/0.51 & ( P @ A3 @ B2 ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % bex2I
% 0.29/0.51 thf(fact_161_bex2I,axiom,
% 0.29/0.51 ! [A: nat,B: nat,S2: set_Pr1261947904930325089at_nat,P: nat > nat > $o] :
% 0.29/0.51 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ S2 )
% 0.29/0.51 => ( ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ S2 )
% 0.29/0.51 => ( P @ A @ B ) )
% 0.29/0.51 => ? [A3: nat,B2: nat] :
% 0.29/0.51 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A3 @ B2 ) @ S2 )
% 0.29/0.51 & ( P @ A3 @ B2 ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % bex2I
% 0.29/0.51 thf(fact_162_bex2I,axiom,
% 0.29/0.51 ! [A: produc6241069584506657477e_term > option6357759511663192854e_term,B: produc8923325533196201883nteger,S2: set_Pr1281608226676607948nteger,P: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o] :
% 0.29/0.51 ( ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ A @ B ) @ S2 )
% 0.29/0.51 => ( ( ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ A @ B ) @ S2 )
% 0.29/0.51 => ( P @ A @ B ) )
% 0.29/0.51 => ? [A3: produc6241069584506657477e_term > option6357759511663192854e_term,B2: produc8923325533196201883nteger] :
% 0.29/0.51 ( ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ A3 @ B2 ) @ S2 )
% 0.29/0.51 & ( P @ A3 @ B2 ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % bex2I
% 0.29/0.51 thf(fact_163_bex2I,axiom,
% 0.29/0.51 ! [A: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat,S2: set_Pr3286484037609594932et_nat,P: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o] :
% 0.29/0.51 ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ A @ B ) @ S2 )
% 0.29/0.51 => ( ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ A @ B ) @ S2 )
% 0.29/0.51 => ( P @ A @ B ) )
% 0.29/0.51 => ? [A3: produc3658429121746597890et_nat > $o,B2: produc3658429121746597890et_nat] :
% 0.29/0.51 ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ A3 @ B2 ) @ S2 )
% 0.29/0.51 & ( P @ A3 @ B2 ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % bex2I
% 0.29/0.51 thf(fact_164_bex2I,axiom,
% 0.29/0.51 ! [A: produc3658429121746597890et_nat > $o,B: produc3925858234332021118et_nat,S2: set_Pr8536935166611901872et_nat,P: ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o] :
% 0.29/0.51 ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ A @ B ) @ S2 )
% 0.29/0.51 => ( ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ A @ B ) @ S2 )
% 0.29/0.51 => ( P @ A @ B ) )
% 0.29/0.51 => ? [A3: produc3658429121746597890et_nat > $o,B2: produc3925858234332021118et_nat] :
% 0.29/0.51 ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ A3 @ B2 ) @ S2 )
% 0.29/0.51 & ( P @ A3 @ B2 ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % bex2I
% 0.29/0.51 thf(fact_165_bex2I,axiom,
% 0.29/0.51 ! [A: produc8551481072490612790e_term > option6357759511663192854e_term,B: product_prod_int_int,S2: set_Pr9222295170931077689nt_int,P: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o] :
% 0.29/0.51 ( ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ A @ B ) @ S2 )
% 0.29/0.51 => ( ( ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ A @ B ) @ S2 )
% 0.29/0.51 => ( P @ A @ B ) )
% 0.29/0.51 => ? [A3: produc8551481072490612790e_term > option6357759511663192854e_term,B2: product_prod_int_int] :
% 0.29/0.51 ( ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ A3 @ B2 ) @ S2 )
% 0.29/0.51 & ( P @ A3 @ B2 ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % bex2I
% 0.29/0.51 thf(fact_166_bex2I,axiom,
% 0.29/0.51 ! [A: int > option6357759511663192854e_term,B: product_prod_int_int,S2: set_Pr1872883991513573699nt_int,P: ( int > option6357759511663192854e_term ) > product_prod_int_int > $o] :
% 0.29/0.51 ( ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ A @ B ) @ S2 )
% 0.29/0.51 => ( ( ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ A @ B ) @ S2 )
% 0.29/0.51 => ( P @ A @ B ) )
% 0.29/0.51 => ? [A3: int > option6357759511663192854e_term,B2: product_prod_int_int] :
% 0.29/0.51 ( ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ A3 @ B2 ) @ S2 )
% 0.29/0.51 & ( P @ A3 @ B2 ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % bex2I
% 0.29/0.51 thf(fact_167_pairself_Ocases,axiom,
% 0.29/0.51 ! [X: produc7773217078559923341nt_int] :
% 0.29/0.51 ~ ! [F3: int > option6357759511663192854e_term,A3: int,B2: int] :
% 0.29/0.51 ( X
% 0.29/0.51 != ( produc4305682042979456191nt_int @ F3 @ ( product_Pair_int_int @ A3 @ B2 ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % pairself.cases
% 0.29/0.51 thf(fact_168_fails__array__new,axiom,
% 0.29/0.51 ! [N2: nat,X: a,H3: heap_e7401611519738050253t_unit] :
% 0.29/0.51 ~ ( time_fails_array_a @ ( array_new_a @ N2 @ X ) @ H3 ) ).
% 0.29/0.51
% 0.29/0.51 % fails_array_new
% 0.29/0.51 thf(fact_169_timeFrame_Ocases,axiom,
% 0.29/0.51 ! [X: produc2867611627572283311it_nat] :
% 0.29/0.51 ( ! [N: nat,R: array_a,H2: heap_e7401611519738050253t_unit,N3: nat] :
% 0.29/0.51 ( X
% 0.29/0.51 != ( produc3378006678175723489it_nat @ N @ ( some_P6105628898608307625it_nat @ ( produc1733996804261680252it_nat @ R @ ( produc584006145561248582it_nat @ H2 @ N3 ) ) ) ) )
% 0.29/0.51 => ~ ! [N: nat] :
% 0.29/0.51 ( X
% 0.29/0.51 != ( produc3378006678175723489it_nat @ N @ none_P2587165478634041381it_nat ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % timeFrame.cases
% 0.29/0.51 thf(fact_170_timeFrame_Ocases,axiom,
% 0.29/0.51 ! [X: produc3911288613690379145it_nat] :
% 0.29/0.51 ( ! [N: nat,R: product_unit,H2: heap_e7401611519738050253t_unit,N3: nat] :
% 0.29/0.51 ( X
% 0.29/0.51 != ( produc638857205735767105it_nat @ N @ ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ R @ ( produc584006145561248582it_nat @ H2 @ N3 ) ) ) ) )
% 0.29/0.51 => ~ ! [N: nat] :
% 0.29/0.51 ( X
% 0.29/0.51 != ( produc638857205735767105it_nat @ N @ none_P9117596204409417319it_nat ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % timeFrame.cases
% 0.29/0.51 thf(fact_171_execute__assert_I1_J,axiom,
% 0.29/0.51 ! [P: array_a > $o,X: array_a,H3: heap_e7401611519738050253t_unit] :
% 0.29/0.51 ( ( P @ X )
% 0.29/0.51 => ( ( heap_T5591663578999710211rray_a @ ( heap_T7971689983404357896rray_a @ P @ X ) @ H3 )
% 0.29/0.51 = ( some_P6105628898608307625it_nat @ ( produc1733996804261680252it_nat @ X @ ( produc584006145561248582it_nat @ H3 @ one_one_nat ) ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % execute_assert(1)
% 0.29/0.51 thf(fact_172_execute__assert_I1_J,axiom,
% 0.29/0.51 ! [P: product_unit > $o,X: product_unit,H3: heap_e7401611519738050253t_unit] :
% 0.29/0.51 ( ( P @ X )
% 0.29/0.51 => ( ( heap_T875086893843062177t_unit @ ( heap_T4208721593536448476t_unit @ P @ X ) @ H3 )
% 0.29/0.51 = ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ X @ ( produc584006145561248582it_nat @ H3 @ one_one_nat ) ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % execute_assert(1)
% 0.29/0.51 thf(fact_173_execute__tap,axiom,
% 0.29/0.51 ! [F: heap_e7401611519738050253t_unit > array_a,H3: heap_e7401611519738050253t_unit] :
% 0.29/0.51 ( ( heap_T5591663578999710211rray_a @ ( heap_T2055650868554030641rray_a @ F ) @ H3 )
% 0.29/0.51 = ( some_P6105628898608307625it_nat @ ( produc1733996804261680252it_nat @ ( F @ H3 ) @ ( produc584006145561248582it_nat @ H3 @ one_one_nat ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % execute_tap
% 0.29/0.51 thf(fact_174_execute__tap,axiom,
% 0.29/0.51 ! [F: heap_e7401611519738050253t_unit > product_unit,H3: heap_e7401611519738050253t_unit] :
% 0.29/0.51 ( ( heap_T875086893843062177t_unit @ ( heap_T560649228465745139t_unit @ F ) @ H3 )
% 0.29/0.51 = ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ ( F @ H3 ) @ ( produc584006145561248582it_nat @ H3 @ one_one_nat ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % execute_tap
% 0.29/0.51 thf(fact_175_option_Osel,axiom,
% 0.29/0.51 ! [X2: num] :
% 0.29/0.51 ( ( the_num @ ( some_num @ X2 ) )
% 0.29/0.51 = X2 ) ).
% 0.29/0.51
% 0.29/0.51 % option.sel
% 0.29/0.51 thf(fact_176_option_Osel,axiom,
% 0.29/0.51 ! [X2: produc8664842809031399944it_nat] :
% 0.29/0.51 ( ( the_Pr7776125533777466484it_nat @ ( some_P1914260805536162275it_nat @ X2 ) )
% 0.29/0.51 = X2 ) ).
% 0.29/0.51
% 0.29/0.51 % option.sel
% 0.29/0.51 thf(fact_177_option_Oexpand,axiom,
% 0.29/0.51 ! [Option: option3216581401566546698it_nat,Option2: option3216581401566546698it_nat] :
% 0.29/0.51 ( ( ( Option = none_P2587165478634041381it_nat )
% 0.29/0.51 = ( Option2 = none_P2587165478634041381it_nat ) )
% 0.29/0.51 => ( ( ( Option != none_P2587165478634041381it_nat )
% 0.29/0.51 => ( ( Option2 != none_P2587165478634041381it_nat )
% 0.29/0.51 => ( ( the_Pr5856008525237892824it_nat @ Option )
% 0.29/0.51 = ( the_Pr5856008525237892824it_nat @ Option2 ) ) ) )
% 0.29/0.51 => ( Option = Option2 ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % option.expand
% 0.29/0.51 thf(fact_178_option_Oexpand,axiom,
% 0.29/0.51 ! [Option: option_num,Option2: option_num] :
% 0.29/0.51 ( ( ( Option = none_num )
% 0.29/0.51 = ( Option2 = none_num ) )
% 0.29/0.51 => ( ( ( Option != none_num )
% 0.29/0.51 => ( ( Option2 != none_num )
% 0.29/0.51 => ( ( the_num @ Option )
% 0.29/0.51 = ( the_num @ Option2 ) ) ) )
% 0.29/0.51 => ( Option = Option2 ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % option.expand
% 0.29/0.51 thf(fact_179_option_Oexpand,axiom,
% 0.29/0.51 ! [Option: option8956607266484857688it_nat,Option2: option8956607266484857688it_nat] :
% 0.29/0.51 ( ( ( Option = none_P9117596204409417319it_nat )
% 0.29/0.51 = ( Option2 = none_P9117596204409417319it_nat ) )
% 0.29/0.51 => ( ( ( Option != none_P9117596204409417319it_nat )
% 0.29/0.51 => ( ( Option2 != none_P9117596204409417319it_nat )
% 0.29/0.51 => ( ( the_Pr7776125533777466484it_nat @ Option )
% 0.29/0.51 = ( the_Pr7776125533777466484it_nat @ Option2 ) ) ) )
% 0.29/0.51 => ( Option = Option2 ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % option.expand
% 0.29/0.51 thf(fact_180_effect__def,axiom,
% 0.29/0.51 ( heap_T5830633491639066771rray_a
% 0.29/0.51 = ( ^ [C2: heap_T6362127782908069795rray_a,H: heap_e7401611519738050253t_unit,H6: heap_e7401611519738050253t_unit,R3: array_a,N4: nat] :
% 0.29/0.51 ( ( heap_T5591663578999710211rray_a @ C2 @ H )
% 0.29/0.51 = ( some_P6105628898608307625it_nat @ ( produc1733996804261680252it_nat @ R3 @ ( produc584006145561248582it_nat @ H6 @ N4 ) ) ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % effect_def
% 0.29/0.51 thf(fact_181_effect__def,axiom,
% 0.29/0.51 ( heap_T6553295506729943825t_unit
% 0.29/0.51 = ( ^ [C2: heap_T5738788834812785303t_unit,H: heap_e7401611519738050253t_unit,H6: heap_e7401611519738050253t_unit,R3: product_unit,N4: nat] :
% 0.29/0.51 ( ( heap_T875086893843062177t_unit @ C2 @ H )
% 0.29/0.51 = ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ R3 @ ( produc584006145561248582it_nat @ H6 @ N4 ) ) ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % effect_def
% 0.29/0.51 thf(fact_182_effectI,axiom,
% 0.29/0.51 ! [C: heap_T6362127782908069795rray_a,H3: heap_e7401611519738050253t_unit,R2: array_a,H5: heap_e7401611519738050253t_unit,N2: nat] :
% 0.29/0.51 ( ( ( heap_T5591663578999710211rray_a @ C @ H3 )
% 0.29/0.51 = ( some_P6105628898608307625it_nat @ ( produc1733996804261680252it_nat @ R2 @ ( produc584006145561248582it_nat @ H5 @ N2 ) ) ) )
% 0.29/0.51 => ( heap_T5830633491639066771rray_a @ C @ H3 @ H5 @ R2 @ N2 ) ) ).
% 0.29/0.51
% 0.29/0.51 % effectI
% 0.29/0.51 thf(fact_183_effectI,axiom,
% 0.29/0.51 ! [C: heap_T5738788834812785303t_unit,H3: heap_e7401611519738050253t_unit,R2: product_unit,H5: heap_e7401611519738050253t_unit,N2: nat] :
% 0.29/0.51 ( ( ( heap_T875086893843062177t_unit @ C @ H3 )
% 0.29/0.51 = ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ R2 @ ( produc584006145561248582it_nat @ H5 @ N2 ) ) ) )
% 0.29/0.51 => ( heap_T6553295506729943825t_unit @ C @ H3 @ H5 @ R2 @ N2 ) ) ).
% 0.29/0.51
% 0.29/0.51 % effectI
% 0.29/0.51 thf(fact_184_map__mmupd__def,axiom,
% 0.29/0.51 ( map_mm2124855372588256220at_num
% 0.29/0.51 = ( ^ [M: produc3843707927480180839at_nat > option_num,K3: set_Pr4329608150637261639at_nat,V2: num,K4: produc3843707927480180839at_nat] : ( if_option_num @ ( member8757157785044589968at_nat @ K4 @ K3 ) @ ( some_num @ V2 ) @ ( M @ K4 ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % map_mmupd_def
% 0.29/0.51 thf(fact_185_map__mmupd__def,axiom,
% 0.29/0.51 ( map_mm6272435474268545910at_num
% 0.29/0.51 = ( ^ [M: product_prod_nat_nat > option_num,K3: set_Pr1261947904930325089at_nat,V2: num,K4: product_prod_nat_nat] : ( if_option_num @ ( member8440522571783428010at_nat @ K4 @ K3 ) @ ( some_num @ V2 ) @ ( M @ K4 ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % map_mmupd_def
% 0.29/0.51 thf(fact_186_map__mmupd__def,axiom,
% 0.29/0.51 ( map_mmupd_o_num
% 0.29/0.51 = ( ^ [M: $o > option_num,K3: set_o,V2: num,K4: $o] : ( if_option_num @ ( member_o @ K4 @ K3 ) @ ( some_num @ V2 ) @ ( M @ K4 ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % map_mmupd_def
% 0.29/0.51 thf(fact_187_map__mmupd__def,axiom,
% 0.29/0.51 ( map_mmupd_nat_num
% 0.29/0.51 = ( ^ [M: nat > option_num,K3: set_nat,V2: num,K4: nat] : ( if_option_num @ ( member_nat @ K4 @ K3 ) @ ( some_num @ V2 ) @ ( M @ K4 ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % map_mmupd_def
% 0.29/0.51 thf(fact_188_map__mmupd__def,axiom,
% 0.29/0.51 ( map_mmupd_int_num
% 0.29/0.51 = ( ^ [M: int > option_num,K3: set_int,V2: num,K4: int] : ( if_option_num @ ( member_int @ K4 @ K3 ) @ ( some_num @ V2 ) @ ( M @ K4 ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % map_mmupd_def
% 0.29/0.51 thf(fact_189_map__mmupd__def,axiom,
% 0.29/0.51 ( map_mm6227321356191524810it_nat
% 0.29/0.51 = ( ^ [M: produc3843707927480180839at_nat > option8956607266484857688it_nat,K3: set_Pr4329608150637261639at_nat,V2: produc8664842809031399944it_nat,K4: produc3843707927480180839at_nat] : ( if_opt1729522071442692626it_nat @ ( member8757157785044589968at_nat @ K4 @ K3 ) @ ( some_P1914260805536162275it_nat @ V2 ) @ ( M @ K4 ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % map_mmupd_def
% 0.29/0.51 thf(fact_190_map__mmupd__def,axiom,
% 0.29/0.51 ( map_mm8925508573636269924it_nat
% 0.29/0.51 = ( ^ [M: product_prod_nat_nat > option8956607266484857688it_nat,K3: set_Pr1261947904930325089at_nat,V2: produc8664842809031399944it_nat,K4: product_prod_nat_nat] : ( if_opt1729522071442692626it_nat @ ( member8440522571783428010at_nat @ K4 @ K3 ) @ ( some_P1914260805536162275it_nat @ V2 ) @ ( M @ K4 ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % map_mmupd_def
% 0.29/0.51 thf(fact_191_map__mmupd__def,axiom,
% 0.29/0.51 ( map_mm4340940675810032635it_nat
% 0.29/0.51 = ( ^ [M: $o > option8956607266484857688it_nat,K3: set_o,V2: produc8664842809031399944it_nat,K4: $o] : ( if_opt1729522071442692626it_nat @ ( member_o @ K4 @ K3 ) @ ( some_P1914260805536162275it_nat @ V2 ) @ ( M @ K4 ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % map_mmupd_def
% 0.29/0.51 thf(fact_192_map__mmupd__def,axiom,
% 0.29/0.51 ( map_mm4316137065318800191it_nat
% 0.29/0.51 = ( ^ [M: nat > option8956607266484857688it_nat,K3: set_nat,V2: produc8664842809031399944it_nat,K4: nat] : ( if_opt1729522071442692626it_nat @ ( member_nat @ K4 @ K3 ) @ ( some_P1914260805536162275it_nat @ V2 ) @ ( M @ K4 ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % map_mmupd_def
% 0.29/0.51 thf(fact_193_map__mmupd__def,axiom,
% 0.29/0.51 ( map_mm5942422175790858651it_nat
% 0.29/0.51 = ( ^ [M: int > option8956607266484857688it_nat,K3: set_int,V2: produc8664842809031399944it_nat,K4: int] : ( if_opt1729522071442692626it_nat @ ( member_int @ K4 @ K3 ) @ ( some_P1914260805536162275it_nat @ V2 ) @ ( M @ K4 ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % map_mmupd_def
% 0.29/0.51 thf(fact_194_map__mmupdE,axiom,
% 0.29/0.51 ! [M2: produc3843707927480180839at_nat > option_num,K2: set_Pr4329608150637261639at_nat,V: num,K: produc3843707927480180839at_nat,X: num] :
% 0.29/0.51 ( ( ( map_mm2124855372588256220at_num @ M2 @ K2 @ V @ K )
% 0.29/0.51 = ( some_num @ X ) )
% 0.29/0.51 => ( ( ~ ( member8757157785044589968at_nat @ K @ K2 )
% 0.29/0.51 => ( ( M2 @ K )
% 0.29/0.51 != ( some_num @ X ) ) )
% 0.29/0.51 => ~ ( ( member8757157785044589968at_nat @ K @ K2 )
% 0.29/0.51 => ( X != V ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % map_mmupdE
% 0.29/0.51 thf(fact_195_map__mmupdE,axiom,
% 0.29/0.51 ! [M2: product_prod_nat_nat > option_num,K2: set_Pr1261947904930325089at_nat,V: num,K: product_prod_nat_nat,X: num] :
% 0.29/0.51 ( ( ( map_mm6272435474268545910at_num @ M2 @ K2 @ V @ K )
% 0.29/0.51 = ( some_num @ X ) )
% 0.29/0.51 => ( ( ~ ( member8440522571783428010at_nat @ K @ K2 )
% 0.29/0.51 => ( ( M2 @ K )
% 0.29/0.51 != ( some_num @ X ) ) )
% 0.29/0.51 => ~ ( ( member8440522571783428010at_nat @ K @ K2 )
% 0.29/0.51 => ( X != V ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % map_mmupdE
% 0.29/0.51 thf(fact_196_map__mmupdE,axiom,
% 0.29/0.51 ! [M2: $o > option_num,K2: set_o,V: num,K: $o,X: num] :
% 0.29/0.51 ( ( ( map_mmupd_o_num @ M2 @ K2 @ V @ K )
% 0.29/0.51 = ( some_num @ X ) )
% 0.29/0.51 => ( ( ~ ( member_o @ K @ K2 )
% 0.29/0.51 => ( ( M2 @ K )
% 0.29/0.51 != ( some_num @ X ) ) )
% 0.29/0.51 => ~ ( ( member_o @ K @ K2 )
% 0.29/0.51 => ( X != V ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % map_mmupdE
% 0.29/0.51 thf(fact_197_map__mmupdE,axiom,
% 0.29/0.51 ! [M2: nat > option_num,K2: set_nat,V: num,K: nat,X: num] :
% 0.29/0.51 ( ( ( map_mmupd_nat_num @ M2 @ K2 @ V @ K )
% 0.29/0.51 = ( some_num @ X ) )
% 0.29/0.51 => ( ( ~ ( member_nat @ K @ K2 )
% 0.29/0.51 => ( ( M2 @ K )
% 0.29/0.51 != ( some_num @ X ) ) )
% 0.29/0.51 => ~ ( ( member_nat @ K @ K2 )
% 0.29/0.51 => ( X != V ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % map_mmupdE
% 0.29/0.51 thf(fact_198_map__mmupdE,axiom,
% 0.29/0.51 ! [M2: int > option_num,K2: set_int,V: num,K: int,X: num] :
% 0.29/0.51 ( ( ( map_mmupd_int_num @ M2 @ K2 @ V @ K )
% 0.29/0.51 = ( some_num @ X ) )
% 0.29/0.51 => ( ( ~ ( member_int @ K @ K2 )
% 0.29/0.51 => ( ( M2 @ K )
% 0.29/0.51 != ( some_num @ X ) ) )
% 0.29/0.51 => ~ ( ( member_int @ K @ K2 )
% 0.29/0.51 => ( X != V ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % map_mmupdE
% 0.29/0.51 thf(fact_199_map__mmupdE,axiom,
% 0.29/0.51 ! [M2: produc3843707927480180839at_nat > option8956607266484857688it_nat,K2: set_Pr4329608150637261639at_nat,V: produc8664842809031399944it_nat,K: produc3843707927480180839at_nat,X: produc8664842809031399944it_nat] :
% 0.29/0.51 ( ( ( map_mm6227321356191524810it_nat @ M2 @ K2 @ V @ K )
% 0.29/0.51 = ( some_P1914260805536162275it_nat @ X ) )
% 0.29/0.51 => ( ( ~ ( member8757157785044589968at_nat @ K @ K2 )
% 0.29/0.51 => ( ( M2 @ K )
% 0.29/0.51 != ( some_P1914260805536162275it_nat @ X ) ) )
% 0.29/0.51 => ~ ( ( member8757157785044589968at_nat @ K @ K2 )
% 0.29/0.51 => ( X != V ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % map_mmupdE
% 0.29/0.51 thf(fact_200_map__mmupdE,axiom,
% 0.29/0.51 ! [M2: product_prod_nat_nat > option8956607266484857688it_nat,K2: set_Pr1261947904930325089at_nat,V: produc8664842809031399944it_nat,K: product_prod_nat_nat,X: produc8664842809031399944it_nat] :
% 0.29/0.51 ( ( ( map_mm8925508573636269924it_nat @ M2 @ K2 @ V @ K )
% 0.29/0.51 = ( some_P1914260805536162275it_nat @ X ) )
% 0.29/0.51 => ( ( ~ ( member8440522571783428010at_nat @ K @ K2 )
% 0.29/0.51 => ( ( M2 @ K )
% 0.29/0.51 != ( some_P1914260805536162275it_nat @ X ) ) )
% 0.29/0.51 => ~ ( ( member8440522571783428010at_nat @ K @ K2 )
% 0.29/0.51 => ( X != V ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % map_mmupdE
% 0.29/0.51 thf(fact_201_map__mmupdE,axiom,
% 0.29/0.51 ! [M2: $o > option8956607266484857688it_nat,K2: set_o,V: produc8664842809031399944it_nat,K: $o,X: produc8664842809031399944it_nat] :
% 0.29/0.51 ( ( ( map_mm4340940675810032635it_nat @ M2 @ K2 @ V @ K )
% 0.29/0.51 = ( some_P1914260805536162275it_nat @ X ) )
% 0.29/0.51 => ( ( ~ ( member_o @ K @ K2 )
% 0.29/0.51 => ( ( M2 @ K )
% 0.29/0.51 != ( some_P1914260805536162275it_nat @ X ) ) )
% 0.29/0.51 => ~ ( ( member_o @ K @ K2 )
% 0.29/0.51 => ( X != V ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % map_mmupdE
% 0.29/0.51 thf(fact_202_map__mmupdE,axiom,
% 0.29/0.51 ! [M2: nat > option8956607266484857688it_nat,K2: set_nat,V: produc8664842809031399944it_nat,K: nat,X: produc8664842809031399944it_nat] :
% 0.29/0.51 ( ( ( map_mm4316137065318800191it_nat @ M2 @ K2 @ V @ K )
% 0.29/0.51 = ( some_P1914260805536162275it_nat @ X ) )
% 0.29/0.51 => ( ( ~ ( member_nat @ K @ K2 )
% 0.29/0.51 => ( ( M2 @ K )
% 0.29/0.51 != ( some_P1914260805536162275it_nat @ X ) ) )
% 0.29/0.51 => ~ ( ( member_nat @ K @ K2 )
% 0.29/0.51 => ( X != V ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % map_mmupdE
% 0.29/0.51 thf(fact_203_map__mmupdE,axiom,
% 0.29/0.51 ! [M2: int > option8956607266484857688it_nat,K2: set_int,V: produc8664842809031399944it_nat,K: int,X: produc8664842809031399944it_nat] :
% 0.29/0.51 ( ( ( map_mm5942422175790858651it_nat @ M2 @ K2 @ V @ K )
% 0.29/0.51 = ( some_P1914260805536162275it_nat @ X ) )
% 0.29/0.51 => ( ( ~ ( member_int @ K @ K2 )
% 0.29/0.51 => ( ( M2 @ K )
% 0.29/0.51 != ( some_P1914260805536162275it_nat @ X ) ) )
% 0.29/0.51 => ~ ( ( member_int @ K @ K2 )
% 0.29/0.51 => ( X != V ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % map_mmupdE
% 0.29/0.51 thf(fact_204_success__bind__executeI,axiom,
% 0.29/0.51 ! [F: heap_T6362127782908069795rray_a,H3: heap_e7401611519738050253t_unit,X: array_a,H5: heap_e7401611519738050253t_unit,N2: nat,G: array_a > heap_T5738788834812785303t_unit] :
% 0.29/0.51 ( ( ( heap_T5591663578999710211rray_a @ F @ H3 )
% 0.29/0.51 = ( some_P6105628898608307625it_nat @ ( produc1733996804261680252it_nat @ X @ ( produc584006145561248582it_nat @ H5 @ N2 ) ) ) )
% 0.29/0.51 => ( ( heap_T584514906347983379t_unit @ ( G @ X ) @ H5 )
% 0.29/0.51 => ( heap_T584514906347983379t_unit @ ( heap_T7324619625323989613t_unit @ F @ G ) @ H3 ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % success_bind_executeI
% 0.29/0.51 thf(fact_205_success__bind__executeI,axiom,
% 0.29/0.51 ! [F: heap_T5738788834812785303t_unit,H3: heap_e7401611519738050253t_unit,X: product_unit,H5: heap_e7401611519738050253t_unit,N2: nat,G: product_unit > heap_T5738788834812785303t_unit] :
% 0.29/0.51 ( ( ( heap_T875086893843062177t_unit @ F @ H3 )
% 0.29/0.51 = ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ X @ ( produc584006145561248582it_nat @ H5 @ N2 ) ) ) )
% 0.29/0.51 => ( ( heap_T584514906347983379t_unit @ ( G @ X ) @ H5 )
% 0.29/0.51 => ( heap_T584514906347983379t_unit @ ( heap_T2633723481742716231t_unit @ F @ G ) @ H3 ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % success_bind_executeI
% 0.29/0.51 thf(fact_206_success__bind__executeI,axiom,
% 0.29/0.51 ! [F: heap_T6362127782908069795rray_a,H3: heap_e7401611519738050253t_unit,X: array_a,H5: heap_e7401611519738050253t_unit,N2: nat,G: array_a > heap_T6362127782908069795rray_a] :
% 0.29/0.51 ( ( ( heap_T5591663578999710211rray_a @ F @ H3 )
% 0.29/0.51 = ( some_P6105628898608307625it_nat @ ( produc1733996804261680252it_nat @ X @ ( produc584006145561248582it_nat @ H5 @ N2 ) ) ) )
% 0.29/0.51 => ( ( heap_T6932021131025641745rray_a @ ( G @ X ) @ H5 )
% 0.29/0.51 => ( heap_T6932021131025641745rray_a @ ( heap_T2407400398799471159rray_a @ F @ G ) @ H3 ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % success_bind_executeI
% 0.29/0.51 thf(fact_207_success__bind__executeI,axiom,
% 0.29/0.51 ! [F: heap_T5738788834812785303t_unit,H3: heap_e7401611519738050253t_unit,X: product_unit,H5: heap_e7401611519738050253t_unit,N2: nat,G: product_unit > heap_T6362127782908069795rray_a] :
% 0.29/0.51 ( ( ( heap_T875086893843062177t_unit @ F @ H3 )
% 0.29/0.51 = ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ X @ ( produc584006145561248582it_nat @ H5 @ N2 ) ) ) )
% 0.29/0.51 => ( ( heap_T6932021131025641745rray_a @ ( G @ X ) @ H5 )
% 0.29/0.51 => ( heap_T6932021131025641745rray_a @ ( heap_T7158140910958840029rray_a @ F @ G ) @ H3 ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % success_bind_executeI
% 0.29/0.51 thf(fact_208_Eps__Opt__eq__Some__implies,axiom,
% 0.29/0.51 ! [P: num > $o,X: num] :
% 0.29/0.51 ( ( ( eps_Opt_num @ P )
% 0.29/0.51 = ( some_num @ X ) )
% 0.29/0.51 => ( P @ X ) ) ).
% 0.29/0.51
% 0.29/0.51 % Eps_Opt_eq_Some_implies
% 0.29/0.51 thf(fact_209_Eps__Opt__eq__Some__implies,axiom,
% 0.29/0.51 ! [P: produc8664842809031399944it_nat > $o,X: produc8664842809031399944it_nat] :
% 0.29/0.51 ( ( ( eps_Op3393321821070424684it_nat @ P )
% 0.29/0.51 = ( some_P1914260805536162275it_nat @ X ) )
% 0.29/0.51 => ( P @ X ) ) ).
% 0.29/0.51
% 0.29/0.51 % Eps_Opt_eq_Some_implies
% 0.29/0.51 thf(fact_210_Eps__Opt__eq__Some,axiom,
% 0.29/0.51 ! [P: num > $o,X: num] :
% 0.29/0.51 ( ! [X6: num] :
% 0.29/0.51 ( ( P @ X )
% 0.29/0.51 => ( ( P @ X6 )
% 0.29/0.51 => ( X6 = X ) ) )
% 0.29/0.51 => ( ( ( eps_Opt_num @ P )
% 0.29/0.51 = ( some_num @ X ) )
% 0.29/0.51 = ( P @ X ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % Eps_Opt_eq_Some
% 0.29/0.51 thf(fact_211_Eps__Opt__eq__Some,axiom,
% 0.29/0.51 ! [P: produc8664842809031399944it_nat > $o,X: produc8664842809031399944it_nat] :
% 0.29/0.51 ( ! [X6: produc8664842809031399944it_nat] :
% 0.29/0.51 ( ( P @ X )
% 0.29/0.51 => ( ( P @ X6 )
% 0.29/0.51 => ( X6 = X ) ) )
% 0.29/0.51 => ( ( ( eps_Op3393321821070424684it_nat @ P )
% 0.29/0.51 = ( some_P1914260805536162275it_nat @ X ) )
% 0.29/0.51 = ( P @ X ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % Eps_Opt_eq_Some
% 0.29/0.51 thf(fact_212_option_Oexhaust__sel,axiom,
% 0.29/0.51 ! [Option: option3216581401566546698it_nat] :
% 0.29/0.51 ( ( Option != none_P2587165478634041381it_nat )
% 0.29/0.51 => ( Option
% 0.29/0.51 = ( some_P6105628898608307625it_nat @ ( the_Pr5856008525237892824it_nat @ Option ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % option.exhaust_sel
% 0.29/0.51 thf(fact_213_option_Oexhaust__sel,axiom,
% 0.29/0.51 ! [Option: option_num] :
% 0.29/0.51 ( ( Option != none_num )
% 0.29/0.51 => ( Option
% 0.29/0.51 = ( some_num @ ( the_num @ Option ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % option.exhaust_sel
% 0.29/0.51 thf(fact_214_option_Oexhaust__sel,axiom,
% 0.29/0.51 ! [Option: option8956607266484857688it_nat] :
% 0.29/0.51 ( ( Option != none_P9117596204409417319it_nat )
% 0.29/0.51 => ( Option
% 0.29/0.51 = ( some_P1914260805536162275it_nat @ ( the_Pr7776125533777466484it_nat @ Option ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % option.exhaust_sel
% 0.29/0.51 thf(fact_215_effect__assertE,axiom,
% 0.29/0.51 ! [P: product_unit > $o,X: product_unit,H3: heap_e7401611519738050253t_unit,H5: heap_e7401611519738050253t_unit,R2: product_unit,N2: nat] :
% 0.29/0.51 ( ( heap_T6553295506729943825t_unit @ ( heap_T4208721593536448476t_unit @ P @ X ) @ H3 @ H5 @ R2 @ N2 )
% 0.29/0.51 => ~ ( ( P @ X )
% 0.29/0.51 => ( ( R2 = X )
% 0.29/0.51 => ( ( H5 = H3 )
% 0.29/0.51 => ( N2 != one_one_nat ) ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % effect_assertE
% 0.29/0.51 thf(fact_216_effect__assertE,axiom,
% 0.29/0.51 ! [P: array_a > $o,X: array_a,H3: heap_e7401611519738050253t_unit,H5: heap_e7401611519738050253t_unit,R2: array_a,N2: nat] :
% 0.29/0.51 ( ( heap_T5830633491639066771rray_a @ ( heap_T7971689983404357896rray_a @ P @ X ) @ H3 @ H5 @ R2 @ N2 )
% 0.29/0.51 => ~ ( ( P @ X )
% 0.29/0.51 => ( ( R2 = X )
% 0.29/0.51 => ( ( H5 = H3 )
% 0.29/0.51 => ( N2 != one_one_nat ) ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % effect_assertE
% 0.29/0.51 thf(fact_217_comp__apply,axiom,
% 0.29/0.51 ( comp_C3531382070062128313er_num
% 0.29/0.51 = ( ^ [F2: code_integer > code_integer,G2: num > code_integer,X3: num] : ( F2 @ ( G2 @ X3 ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % comp_apply
% 0.29/0.51 thf(fact_218_comp__apply,axiom,
% 0.29/0.51 ( comp_C1593894019821074884nteger
% 0.29/0.51 = ( ^ [F2: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,G2: code_integer > code_integer,X3: code_integer] : ( F2 @ ( G2 @ X3 ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % comp_apply
% 0.29/0.51 thf(fact_219_comp__apply,axiom,
% 0.29/0.51 ( comp_C8797469213163452608nteger
% 0.29/0.51 = ( ^ [F2: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G2: code_integer > code_integer > code_integer,X3: code_integer] : ( F2 @ ( G2 @ X3 ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % comp_apply
% 0.29/0.51 thf(fact_220_comp__apply,axiom,
% 0.29/0.51 ( comp_nat_num_int
% 0.29/0.51 = ( ^ [F2: nat > num,G2: int > nat,X3: int] : ( F2 @ ( G2 @ X3 ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % comp_apply
% 0.29/0.51 thf(fact_221_prod_Oinject,axiom,
% 0.29/0.51 ! [X1: produc6241069584506657477e_term > option6357759511663192854e_term,X2: produc8923325533196201883nteger,Y1: produc6241069584506657477e_term > option6357759511663192854e_term,Y2: produc8923325533196201883nteger] :
% 0.29/0.51 ( ( ( produc8603105652947943368nteger @ X1 @ X2 )
% 0.29/0.51 = ( produc8603105652947943368nteger @ Y1 @ Y2 ) )
% 0.29/0.51 = ( ( X1 = Y1 )
% 0.29/0.51 & ( X2 = Y2 ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % prod.inject
% 0.29/0.51 thf(fact_222_prod_Oinject,axiom,
% 0.29/0.51 ! [X1: produc3658429121746597890et_nat > $o,X2: produc3658429121746597890et_nat,Y1: produc3658429121746597890et_nat > $o,Y2: produc3658429121746597890et_nat] :
% 0.29/0.51 ( ( ( produc5001842942810119800et_nat @ X1 @ X2 )
% 0.29/0.51 = ( produc5001842942810119800et_nat @ Y1 @ Y2 ) )
% 0.29/0.51 = ( ( X1 = Y1 )
% 0.29/0.51 & ( X2 = Y2 ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % prod.inject
% 0.29/0.51 thf(fact_223_prod_Oinject,axiom,
% 0.29/0.51 ! [X1: produc3658429121746597890et_nat > $o,X2: produc3925858234332021118et_nat,Y1: produc3658429121746597890et_nat > $o,Y2: produc3925858234332021118et_nat] :
% 0.29/0.51 ( ( ( produc2245416461498447860et_nat @ X1 @ X2 )
% 0.29/0.51 = ( produc2245416461498447860et_nat @ Y1 @ Y2 ) )
% 0.29/0.51 = ( ( X1 = Y1 )
% 0.29/0.51 & ( X2 = Y2 ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % prod.inject
% 0.29/0.51 thf(fact_224_prod_Oinject,axiom,
% 0.29/0.51 ! [X1: produc8551481072490612790e_term > option6357759511663192854e_term,X2: product_prod_int_int,Y1: produc8551481072490612790e_term > option6357759511663192854e_term,Y2: product_prod_int_int] :
% 0.29/0.51 ( ( ( produc5700946648718959541nt_int @ X1 @ X2 )
% 0.29/0.52 = ( produc5700946648718959541nt_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_225_prod_Oinject,axiom,
% 0.29/0.52 ! [X1: int > option6357759511663192854e_term,X2: product_prod_int_int,Y1: int > option6357759511663192854e_term,Y2: product_prod_int_int] :
% 0.29/0.52 ( ( ( produc4305682042979456191nt_int @ X1 @ X2 )
% 0.29/0.52 = ( produc4305682042979456191nt_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_226_old_Oprod_Oinject,axiom,
% 0.29/0.52 ! [A: produc6241069584506657477e_term > option6357759511663192854e_term,B: produc8923325533196201883nteger,A4: produc6241069584506657477e_term > option6357759511663192854e_term,B3: produc8923325533196201883nteger] :
% 0.29/0.52 ( ( ( produc8603105652947943368nteger @ A @ B )
% 0.29/0.52 = ( produc8603105652947943368nteger @ A4 @ B3 ) )
% 0.29/0.52 = ( ( A = A4 )
% 0.29/0.52 & ( B = B3 ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % old.prod.inject
% 0.29/0.52 thf(fact_227_old_Oprod_Oinject,axiom,
% 0.29/0.52 ! [A: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat,A4: produc3658429121746597890et_nat > $o,B3: produc3658429121746597890et_nat] :
% 0.29/0.52 ( ( ( produc5001842942810119800et_nat @ A @ B )
% 0.29/0.52 = ( produc5001842942810119800et_nat @ A4 @ B3 ) )
% 0.29/0.52 = ( ( A = A4 )
% 0.29/0.52 & ( B = B3 ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % old.prod.inject
% 0.29/0.52 thf(fact_228_old_Oprod_Oinject,axiom,
% 0.29/0.52 ! [A: produc3658429121746597890et_nat > $o,B: produc3925858234332021118et_nat,A4: produc3658429121746597890et_nat > $o,B3: produc3925858234332021118et_nat] :
% 0.29/0.52 ( ( ( produc2245416461498447860et_nat @ A @ B )
% 0.29/0.52 = ( produc2245416461498447860et_nat @ A4 @ B3 ) )
% 0.29/0.52 = ( ( A = A4 )
% 0.29/0.52 & ( B = B3 ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % old.prod.inject
% 0.29/0.52 thf(fact_229_old_Oprod_Oinject,axiom,
% 0.29/0.52 ! [A: produc8551481072490612790e_term > option6357759511663192854e_term,B: product_prod_int_int,A4: produc8551481072490612790e_term > option6357759511663192854e_term,B3: product_prod_int_int] :
% 0.29/0.52 ( ( ( produc5700946648718959541nt_int @ A @ B )
% 0.29/0.52 = ( produc5700946648718959541nt_int @ A4 @ B3 ) )
% 0.29/0.52 = ( ( A = A4 )
% 0.29/0.52 & ( B = B3 ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % old.prod.inject
% 0.29/0.52 thf(fact_230_old_Oprod_Oinject,axiom,
% 0.29/0.52 ! [A: int > option6357759511663192854e_term,B: product_prod_int_int,A4: int > option6357759511663192854e_term,B3: product_prod_int_int] :
% 0.29/0.52 ( ( ( produc4305682042979456191nt_int @ A @ B )
% 0.29/0.52 = ( produc4305682042979456191nt_int @ A4 @ B3 ) )
% 0.29/0.52 = ( ( A = A4 )
% 0.29/0.52 & ( B = B3 ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % old.prod.inject
% 0.29/0.52 thf(fact_231_execute__bind_I1_J,axiom,
% 0.29/0.52 ! [F: heap_T6362127782908069795rray_a,H3: heap_e7401611519738050253t_unit,X: array_a,H5: heap_e7401611519738050253t_unit,N2: nat,G: array_a > heap_T6362127782908069795rray_a] :
% 0.29/0.52 ( ( ( heap_T5591663578999710211rray_a @ F @ H3 )
% 0.29/0.52 = ( some_P6105628898608307625it_nat @ ( produc1733996804261680252it_nat @ X @ ( produc584006145561248582it_nat @ H5 @ N2 ) ) ) )
% 0.29/0.52 => ( ( heap_T5591663578999710211rray_a @ ( heap_T2407400398799471159rray_a @ F @ G ) @ H3 )
% 0.29/0.52 = ( heap_T531568236820715630rray_a @ N2 @ ( heap_T5591663578999710211rray_a @ ( G @ X ) @ H5 ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % execute_bind(1)
% 0.29/0.52 thf(fact_232_execute__bind_I1_J,axiom,
% 0.29/0.52 ! [F: heap_T6362127782908069795rray_a,H3: heap_e7401611519738050253t_unit,X: array_a,H5: heap_e7401611519738050253t_unit,N2: nat,G: array_a > heap_T5738788834812785303t_unit] :
% 0.29/0.52 ( ( ( heap_T5591663578999710211rray_a @ F @ H3 )
% 0.29/0.52 = ( some_P6105628898608307625it_nat @ ( produc1733996804261680252it_nat @ X @ ( produc584006145561248582it_nat @ H5 @ N2 ) ) ) )
% 0.29/0.52 => ( ( heap_T875086893843062177t_unit @ ( heap_T7324619625323989613t_unit @ F @ G ) @ H3 )
% 0.29/0.52 = ( heap_T3616969660504097270t_unit @ N2 @ ( heap_T875086893843062177t_unit @ ( G @ X ) @ H5 ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % execute_bind(1)
% 0.29/0.52 thf(fact_233_execute__bind_I1_J,axiom,
% 0.29/0.52 ! [F: heap_T5738788834812785303t_unit,H3: heap_e7401611519738050253t_unit,X: product_unit,H5: heap_e7401611519738050253t_unit,N2: nat,G: product_unit > heap_T6362127782908069795rray_a] :
% 0.29/0.52 ( ( ( heap_T875086893843062177t_unit @ F @ H3 )
% 0.29/0.52 = ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ X @ ( produc584006145561248582it_nat @ H5 @ N2 ) ) ) )
% 0.29/0.52 => ( ( heap_T5591663578999710211rray_a @ ( heap_T7158140910958840029rray_a @ F @ G ) @ H3 )
% 0.29/0.52 = ( heap_T531568236820715630rray_a @ N2 @ ( heap_T5591663578999710211rray_a @ ( G @ X ) @ H5 ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % execute_bind(1)
% 0.29/0.52 thf(fact_234_execute__bind_I1_J,axiom,
% 0.29/0.52 ! [F: heap_T5738788834812785303t_unit,H3: heap_e7401611519738050253t_unit,X: product_unit,H5: heap_e7401611519738050253t_unit,N2: nat,G: product_unit > heap_T5738788834812785303t_unit] :
% 0.29/0.52 ( ( ( heap_T875086893843062177t_unit @ F @ H3 )
% 0.29/0.52 = ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ X @ ( produc584006145561248582it_nat @ H5 @ N2 ) ) ) )
% 0.29/0.52 => ( ( heap_T875086893843062177t_unit @ ( heap_T2633723481742716231t_unit @ F @ G ) @ H3 )
% 0.29/0.52 = ( heap_T3616969660504097270t_unit @ N2 @ ( heap_T875086893843062177t_unit @ ( G @ X ) @ H5 ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % execute_bind(1)
% 0.29/0.52 thf(fact_235_prod__cases3,axiom,
% 0.29/0.52 ! [Y: produc1908205239877642774nteger] :
% 0.29/0.52 ~ ! [A3: produc6241069584506657477e_term > option6357759511663192854e_term,B2: code_integer,C3: code_integer] :
% 0.29/0.52 ( Y
% 0.29/0.52 != ( produc8603105652947943368nteger @ A3 @ ( produc1086072967326762835nteger @ B2 @ C3 ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % prod_cases3
% 0.29/0.52 thf(fact_236_prod__cases3,axiom,
% 0.29/0.52 ! [Y: produc3925858234332021118et_nat] :
% 0.29/0.52 ~ ! [A3: produc3658429121746597890et_nat > $o,B2: heap_e7401611519738050253t_unit,C3: set_nat] :
% 0.29/0.52 ( Y
% 0.29/0.52 != ( produc5001842942810119800et_nat @ A3 @ ( produc7507926704131184380et_nat @ B2 @ C3 ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % prod_cases3
% 0.29/0.52 thf(fact_237_prod__cases3,axiom,
% 0.29/0.52 ! [Y: produc2732055786443039994et_nat] :
% 0.29/0.52 ~ ! [A3: produc3658429121746597890et_nat > $o,B2: produc3658429121746597890et_nat > $o,C3: produc3658429121746597890et_nat] :
% 0.29/0.52 ( Y
% 0.29/0.52 != ( produc2245416461498447860et_nat @ A3 @ ( produc5001842942810119800et_nat @ B2 @ C3 ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % prod_cases3
% 0.29/0.52 thf(fact_238_prod__cases3,axiom,
% 0.29/0.52 ! [Y: produc2285326912895808259nt_int] :
% 0.29/0.52 ~ ! [A3: produc8551481072490612790e_term > option6357759511663192854e_term,B2: int,C3: int] :
% 0.29/0.52 ( Y
% 0.29/0.52 != ( produc5700946648718959541nt_int @ A3 @ ( product_Pair_int_int @ B2 @ C3 ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % prod_cases3
% 0.29/0.52 thf(fact_239_prod__cases3,axiom,
% 0.29/0.52 ! [Y: produc7773217078559923341nt_int] :
% 0.29/0.52 ~ ! [A3: int > option6357759511663192854e_term,B2: int,C3: int] :
% 0.29/0.52 ( Y
% 0.29/0.52 != ( produc4305682042979456191nt_int @ A3 @ ( product_Pair_int_int @ B2 @ C3 ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % prod_cases3
% 0.29/0.52 thf(fact_240_prod__cases4,axiom,
% 0.29/0.52 ! [Y: produc2732055786443039994et_nat] :
% 0.29/0.52 ~ ! [A3: produc3658429121746597890et_nat > $o,B2: produc3658429121746597890et_nat > $o,C3: heap_e7401611519738050253t_unit,D: set_nat] :
% 0.29/0.52 ( Y
% 0.29/0.52 != ( produc2245416461498447860et_nat @ A3 @ ( produc5001842942810119800et_nat @ B2 @ ( produc7507926704131184380et_nat @ C3 @ D ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % prod_cases4
% 0.29/0.52 thf(fact_241_prod__induct3,axiom,
% 0.29/0.52 ! [P: produc1908205239877642774nteger > $o,X: produc1908205239877642774nteger] :
% 0.29/0.52 ( ! [A3: produc6241069584506657477e_term > option6357759511663192854e_term,B2: code_integer,C3: code_integer] : ( P @ ( produc8603105652947943368nteger @ A3 @ ( produc1086072967326762835nteger @ B2 @ C3 ) ) )
% 0.29/0.52 => ( P @ X ) ) ).
% 0.29/0.52
% 0.29/0.52 % prod_induct3
% 0.29/0.52 thf(fact_242_prod__induct3,axiom,
% 0.29/0.52 ! [P: produc3925858234332021118et_nat > $o,X: produc3925858234332021118et_nat] :
% 0.29/0.52 ( ! [A3: produc3658429121746597890et_nat > $o,B2: heap_e7401611519738050253t_unit,C3: set_nat] : ( P @ ( produc5001842942810119800et_nat @ A3 @ ( produc7507926704131184380et_nat @ B2 @ C3 ) ) )
% 0.29/0.52 => ( P @ X ) ) ).
% 0.29/0.52
% 0.29/0.52 % prod_induct3
% 0.29/0.52 thf(fact_243_prod__induct3,axiom,
% 0.29/0.52 ! [P: produc2732055786443039994et_nat > $o,X: produc2732055786443039994et_nat] :
% 0.29/0.52 ( ! [A3: produc3658429121746597890et_nat > $o,B2: produc3658429121746597890et_nat > $o,C3: produc3658429121746597890et_nat] : ( P @ ( produc2245416461498447860et_nat @ A3 @ ( produc5001842942810119800et_nat @ B2 @ C3 ) ) )
% 0.29/0.52 => ( P @ X ) ) ).
% 0.29/0.52
% 0.29/0.52 % prod_induct3
% 0.29/0.52 thf(fact_244_prod__induct3,axiom,
% 0.29/0.52 ! [P: produc2285326912895808259nt_int > $o,X: produc2285326912895808259nt_int] :
% 0.29/0.52 ( ! [A3: produc8551481072490612790e_term > option6357759511663192854e_term,B2: int,C3: int] : ( P @ ( produc5700946648718959541nt_int @ A3 @ ( product_Pair_int_int @ B2 @ C3 ) ) )
% 0.29/0.52 => ( P @ X ) ) ).
% 0.29/0.52
% 0.29/0.52 % prod_induct3
% 0.29/0.52 thf(fact_245_prod__induct3,axiom,
% 0.29/0.52 ! [P: produc7773217078559923341nt_int > $o,X: produc7773217078559923341nt_int] :
% 0.29/0.52 ( ! [A3: int > option6357759511663192854e_term,B2: int,C3: int] : ( P @ ( produc4305682042979456191nt_int @ A3 @ ( product_Pair_int_int @ B2 @ C3 ) ) )
% 0.29/0.52 => ( P @ X ) ) ).
% 0.29/0.52
% 0.29/0.52 % prod_induct3
% 0.29/0.52 thf(fact_246_prod__induct4,axiom,
% 0.29/0.52 ! [P: produc2732055786443039994et_nat > $o,X: produc2732055786443039994et_nat] :
% 0.29/0.52 ( ! [A3: produc3658429121746597890et_nat > $o,B2: produc3658429121746597890et_nat > $o,C3: heap_e7401611519738050253t_unit,D: set_nat] : ( P @ ( produc2245416461498447860et_nat @ A3 @ ( produc5001842942810119800et_nat @ B2 @ ( produc7507926704131184380et_nat @ C3 @ D ) ) ) )
% 0.29/0.52 => ( P @ X ) ) ).
% 0.29/0.52
% 0.29/0.52 % prod_induct4
% 0.29/0.52 thf(fact_247_timeFrame_Osimps_I2_J,axiom,
% 0.29/0.52 ! [N2: nat] :
% 0.29/0.52 ( ( heap_T531568236820715630rray_a @ N2 @ none_P2587165478634041381it_nat )
% 0.29/0.52 = none_P2587165478634041381it_nat ) ).
% 0.29/0.52
% 0.29/0.52 % timeFrame.simps(2)
% 0.29/0.52 thf(fact_248_timeFrame_Osimps_I2_J,axiom,
% 0.29/0.52 ! [N2: nat] :
% 0.29/0.52 ( ( heap_T3616969660504097270t_unit @ N2 @ none_P9117596204409417319it_nat )
% 0.29/0.52 = none_P9117596204409417319it_nat ) ).
% 0.29/0.52
% 0.29/0.52 % timeFrame.simps(2)
% 0.29/0.52 thf(fact_249_Pair__inject,axiom,
% 0.29/0.52 ! [A: produc6241069584506657477e_term > option6357759511663192854e_term,B: produc8923325533196201883nteger,A4: produc6241069584506657477e_term > option6357759511663192854e_term,B3: produc8923325533196201883nteger] :
% 0.29/0.52 ( ( ( produc8603105652947943368nteger @ A @ B )
% 0.29/0.52 = ( produc8603105652947943368nteger @ A4 @ B3 ) )
% 0.29/0.52 => ~ ( ( A = A4 )
% 0.29/0.52 => ( B != B3 ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % Pair_inject
% 0.29/0.52 thf(fact_250_Pair__inject,axiom,
% 0.29/0.52 ! [A: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat,A4: produc3658429121746597890et_nat > $o,B3: produc3658429121746597890et_nat] :
% 0.29/0.52 ( ( ( produc5001842942810119800et_nat @ A @ B )
% 0.29/0.52 = ( produc5001842942810119800et_nat @ A4 @ B3 ) )
% 0.29/0.52 => ~ ( ( A = A4 )
% 0.29/0.52 => ( B != B3 ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % Pair_inject
% 0.29/0.52 thf(fact_251_Pair__inject,axiom,
% 0.29/0.52 ! [A: produc3658429121746597890et_nat > $o,B: produc3925858234332021118et_nat,A4: produc3658429121746597890et_nat > $o,B3: produc3925858234332021118et_nat] :
% 0.29/0.52 ( ( ( produc2245416461498447860et_nat @ A @ B )
% 0.29/0.52 = ( produc2245416461498447860et_nat @ A4 @ B3 ) )
% 0.29/0.52 => ~ ( ( A = A4 )
% 0.29/0.52 => ( B != B3 ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % Pair_inject
% 0.29/0.52 thf(fact_252_Pair__inject,axiom,
% 0.29/0.52 ! [A: produc8551481072490612790e_term > option6357759511663192854e_term,B: product_prod_int_int,A4: produc8551481072490612790e_term > option6357759511663192854e_term,B3: product_prod_int_int] :
% 0.29/0.52 ( ( ( produc5700946648718959541nt_int @ A @ B )
% 0.29/0.52 = ( produc5700946648718959541nt_int @ A4 @ B3 ) )
% 0.29/0.52 => ~ ( ( A = A4 )
% 0.29/0.52 => ( B != B3 ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % Pair_inject
% 0.29/0.52 thf(fact_253_Pair__inject,axiom,
% 0.29/0.52 ! [A: int > option6357759511663192854e_term,B: product_prod_int_int,A4: int > option6357759511663192854e_term,B3: product_prod_int_int] :
% 0.29/0.52 ( ( ( produc4305682042979456191nt_int @ A @ B )
% 0.29/0.52 = ( produc4305682042979456191nt_int @ A4 @ B3 ) )
% 0.29/0.52 => ~ ( ( A = A4 )
% 0.29/0.52 => ( B != B3 ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % Pair_inject
% 0.29/0.52 thf(fact_254_prod__cases,axiom,
% 0.29/0.52 ! [P: produc1908205239877642774nteger > $o,P4: produc1908205239877642774nteger] :
% 0.29/0.52 ( ! [A3: produc6241069584506657477e_term > option6357759511663192854e_term,B2: produc8923325533196201883nteger] : ( P @ ( produc8603105652947943368nteger @ A3 @ B2 ) )
% 0.29/0.52 => ( P @ P4 ) ) ).
% 0.29/0.52
% 0.29/0.52 % prod_cases
% 0.29/0.52 thf(fact_255_prod__cases,axiom,
% 0.29/0.52 ! [P: produc3925858234332021118et_nat > $o,P4: produc3925858234332021118et_nat] :
% 0.29/0.52 ( ! [A3: produc3658429121746597890et_nat > $o,B2: produc3658429121746597890et_nat] : ( P @ ( produc5001842942810119800et_nat @ A3 @ B2 ) )
% 0.29/0.52 => ( P @ P4 ) ) ).
% 0.29/0.52
% 0.29/0.52 % prod_cases
% 0.29/0.52 thf(fact_256_prod__cases,axiom,
% 0.29/0.52 ! [P: produc2732055786443039994et_nat > $o,P4: produc2732055786443039994et_nat] :
% 0.29/0.52 ( ! [A3: produc3658429121746597890et_nat > $o,B2: produc3925858234332021118et_nat] : ( P @ ( produc2245416461498447860et_nat @ A3 @ B2 ) )
% 0.29/0.52 => ( P @ P4 ) ) ).
% 0.29/0.52
% 0.29/0.52 % prod_cases
% 0.29/0.52 thf(fact_257_prod__cases,axiom,
% 0.29/0.52 ! [P: produc2285326912895808259nt_int > $o,P4: produc2285326912895808259nt_int] :
% 0.29/0.52 ( ! [A3: produc8551481072490612790e_term > option6357759511663192854e_term,B2: product_prod_int_int] : ( P @ ( produc5700946648718959541nt_int @ A3 @ B2 ) )
% 0.29/0.52 => ( P @ P4 ) ) ).
% 0.29/0.52
% 0.29/0.52 % prod_cases
% 0.29/0.52 thf(fact_258_prod__cases,axiom,
% 0.29/0.52 ! [P: produc7773217078559923341nt_int > $o,P4: produc7773217078559923341nt_int] :
% 0.29/0.52 ( ! [A3: int > option6357759511663192854e_term,B2: product_prod_int_int] : ( P @ ( produc4305682042979456191nt_int @ A3 @ B2 ) )
% 0.29/0.52 => ( P @ P4 ) ) ).
% 0.29/0.52
% 0.29/0.52 % prod_cases
% 0.29/0.52 thf(fact_259_surj__pair,axiom,
% 0.29/0.52 ! [P4: produc1908205239877642774nteger] :
% 0.29/0.52 ? [X4: produc6241069584506657477e_term > option6357759511663192854e_term,Y5: produc8923325533196201883nteger] :
% 0.29/0.52 ( P4
% 0.29/0.52 = ( produc8603105652947943368nteger @ X4 @ Y5 ) ) ).
% 0.29/0.52
% 0.29/0.52 % surj_pair
% 0.29/0.52 thf(fact_260_surj__pair,axiom,
% 0.29/0.52 ! [P4: produc3925858234332021118et_nat] :
% 0.29/0.52 ? [X4: produc3658429121746597890et_nat > $o,Y5: produc3658429121746597890et_nat] :
% 0.29/0.52 ( P4
% 0.29/0.52 = ( produc5001842942810119800et_nat @ X4 @ Y5 ) ) ).
% 0.29/0.52
% 0.29/0.52 % surj_pair
% 0.29/0.52 thf(fact_261_surj__pair,axiom,
% 0.29/0.52 ! [P4: produc2732055786443039994et_nat] :
% 0.29/0.52 ? [X4: produc3658429121746597890et_nat > $o,Y5: produc3925858234332021118et_nat] :
% 0.29/0.52 ( P4
% 0.29/0.52 = ( produc2245416461498447860et_nat @ X4 @ Y5 ) ) ).
% 0.29/0.52
% 0.29/0.52 % surj_pair
% 0.29/0.52 thf(fact_262_surj__pair,axiom,
% 0.29/0.52 ! [P4: produc2285326912895808259nt_int] :
% 0.29/0.52 ? [X4: produc8551481072490612790e_term > option6357759511663192854e_term,Y5: product_prod_int_int] :
% 0.29/0.52 ( P4
% 0.29/0.52 = ( produc5700946648718959541nt_int @ X4 @ Y5 ) ) ).
% 0.29/0.52
% 0.29/0.52 % surj_pair
% 0.29/0.52 thf(fact_263_surj__pair,axiom,
% 0.29/0.52 ! [P4: produc7773217078559923341nt_int] :
% 0.29/0.52 ? [X4: int > option6357759511663192854e_term,Y5: product_prod_int_int] :
% 0.29/0.52 ( P4
% 0.29/0.52 = ( produc4305682042979456191nt_int @ X4 @ Y5 ) ) ).
% 0.29/0.52
% 0.29/0.52 % surj_pair
% 0.29/0.52 thf(fact_264_old_Oprod_Oexhaust,axiom,
% 0.29/0.52 ! [Y: produc1908205239877642774nteger] :
% 0.29/0.52 ~ ! [A3: produc6241069584506657477e_term > option6357759511663192854e_term,B2: produc8923325533196201883nteger] :
% 0.29/0.52 ( Y
% 0.29/0.52 != ( produc8603105652947943368nteger @ A3 @ B2 ) ) ).
% 0.29/0.52
% 0.29/0.52 % old.prod.exhaust
% 0.29/0.52 thf(fact_265_old_Oprod_Oexhaust,axiom,
% 0.29/0.52 ! [Y: produc3925858234332021118et_nat] :
% 0.29/0.52 ~ ! [A3: produc3658429121746597890et_nat > $o,B2: produc3658429121746597890et_nat] :
% 0.29/0.52 ( Y
% 0.29/0.52 != ( produc5001842942810119800et_nat @ A3 @ B2 ) ) ).
% 0.29/0.52
% 0.29/0.52 % old.prod.exhaust
% 0.29/0.52 thf(fact_266_old_Oprod_Oexhaust,axiom,
% 0.29/0.52 ! [Y: produc2732055786443039994et_nat] :
% 0.29/0.52 ~ ! [A3: produc3658429121746597890et_nat > $o,B2: produc3925858234332021118et_nat] :
% 0.29/0.52 ( Y
% 0.29/0.52 != ( produc2245416461498447860et_nat @ A3 @ B2 ) ) ).
% 0.29/0.52
% 0.29/0.52 % old.prod.exhaust
% 0.29/0.52 thf(fact_267_old_Oprod_Oexhaust,axiom,
% 0.29/0.52 ! [Y: produc2285326912895808259nt_int] :
% 0.29/0.52 ~ ! [A3: produc8551481072490612790e_term > option6357759511663192854e_term,B2: product_prod_int_int] :
% 0.29/0.52 ( Y
% 0.29/0.52 != ( produc5700946648718959541nt_int @ A3 @ B2 ) ) ).
% 0.29/0.52
% 0.29/0.52 % old.prod.exhaust
% 0.29/0.52 thf(fact_268_old_Oprod_Oexhaust,axiom,
% 0.29/0.52 ! [Y: produc7773217078559923341nt_int] :
% 0.29/0.52 ~ ! [A3: int > option6357759511663192854e_term,B2: product_prod_int_int] :
% 0.29/0.52 ( Y
% 0.29/0.52 != ( produc4305682042979456191nt_int @ A3 @ B2 ) ) ).
% 0.29/0.52
% 0.29/0.52 % old.prod.exhaust
% 0.29/0.52 thf(fact_269_one__reorient,axiom,
% 0.29/0.52 ! [X: code_integer] :
% 0.29/0.52 ( ( one_one_Code_integer = X )
% 0.29/0.52 = ( X = one_one_Code_integer ) ) ).
% 0.29/0.52
% 0.29/0.52 % one_reorient
% 0.29/0.52 thf(fact_270_one__reorient,axiom,
% 0.29/0.52 ! [X: assn] :
% 0.29/0.52 ( ( one_one_assn = X )
% 0.29/0.52 = ( X = one_one_assn ) ) ).
% 0.29/0.52
% 0.29/0.52 % one_reorient
% 0.29/0.52 thf(fact_271_one__reorient,axiom,
% 0.29/0.52 ! [X: rat] :
% 0.29/0.52 ( ( one_one_rat = X )
% 0.29/0.52 = ( X = one_one_rat ) ) ).
% 0.29/0.52
% 0.29/0.52 % one_reorient
% 0.29/0.52 thf(fact_272_one__reorient,axiom,
% 0.29/0.52 ! [X: nat] :
% 0.29/0.52 ( ( one_one_nat = X )
% 0.29/0.52 = ( X = one_one_nat ) ) ).
% 0.29/0.52
% 0.29/0.52 % one_reorient
% 0.29/0.52 thf(fact_273_one__reorient,axiom,
% 0.29/0.52 ! [X: int] :
% 0.29/0.52 ( ( one_one_int = X )
% 0.29/0.52 = ( X = one_one_int ) ) ).
% 0.29/0.52
% 0.29/0.52 % one_reorient
% 0.29/0.52 thf(fact_274_comp__eq__dest__lhs,axiom,
% 0.29/0.52 ! [A: code_integer > code_integer,B: num > code_integer,C: num > code_integer,V: num] :
% 0.29/0.52 ( ( ( comp_C3531382070062128313er_num @ A @ B )
% 0.29/0.52 = C )
% 0.29/0.52 => ( ( A @ ( B @ V ) )
% 0.29/0.52 = ( C @ V ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % comp_eq_dest_lhs
% 0.29/0.52 thf(fact_275_comp__eq__dest__lhs,axiom,
% 0.29/0.52 ! [A: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,B: code_integer > code_integer,C: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,V: code_integer] :
% 0.29/0.52 ( ( ( comp_C1593894019821074884nteger @ A @ B )
% 0.29/0.52 = C )
% 0.29/0.52 => ( ( A @ ( B @ V ) )
% 0.29/0.52 = ( C @ V ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % comp_eq_dest_lhs
% 0.29/0.52 thf(fact_276_comp__eq__dest__lhs,axiom,
% 0.29/0.52 ! [A: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,B: code_integer > code_integer > code_integer,C: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,V: code_integer] :
% 0.29/0.52 ( ( ( comp_C8797469213163452608nteger @ A @ B )
% 0.29/0.52 = C )
% 0.29/0.52 => ( ( A @ ( B @ V ) )
% 0.29/0.52 = ( C @ V ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % comp_eq_dest_lhs
% 0.29/0.52 thf(fact_277_comp__eq__dest__lhs,axiom,
% 0.29/0.52 ! [A: nat > num,B: int > nat,C: int > num,V: int] :
% 0.29/0.52 ( ( ( comp_nat_num_int @ A @ B )
% 0.29/0.52 = C )
% 0.29/0.52 => ( ( A @ ( B @ V ) )
% 0.29/0.52 = ( C @ V ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % comp_eq_dest_lhs
% 0.29/0.52 thf(fact_278_comp__eq__elim,axiom,
% 0.29/0.52 ! [A: code_integer > code_integer,B: num > code_integer,C: code_integer > code_integer,D2: num > code_integer] :
% 0.29/0.52 ( ( ( comp_C3531382070062128313er_num @ A @ B )
% 0.29/0.52 = ( comp_C3531382070062128313er_num @ C @ D2 ) )
% 0.29/0.52 => ! [V3: num] :
% 0.29/0.52 ( ( A @ ( B @ V3 ) )
% 0.29/0.52 = ( C @ ( D2 @ V3 ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % comp_eq_elim
% 0.29/0.52 thf(fact_279_comp__eq__elim,axiom,
% 0.29/0.52 ! [A: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,B: code_integer > code_integer,C: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,D2: code_integer > code_integer] :
% 0.29/0.52 ( ( ( comp_C1593894019821074884nteger @ A @ B )
% 0.29/0.52 = ( comp_C1593894019821074884nteger @ C @ D2 ) )
% 0.29/0.52 => ! [V3: code_integer] :
% 0.29/0.52 ( ( A @ ( B @ V3 ) )
% 0.29/0.52 = ( C @ ( D2 @ V3 ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % comp_eq_elim
% 0.29/0.52 thf(fact_280_comp__eq__elim,axiom,
% 0.29/0.52 ! [A: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,B: code_integer > code_integer,C: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,D2: code_integer > code_integer > code_integer] :
% 0.29/0.52 ( ( ( comp_C1593894019821074884nteger @ A @ B )
% 0.29/0.52 = ( comp_C8797469213163452608nteger @ C @ D2 ) )
% 0.29/0.52 => ! [V3: code_integer] :
% 0.29/0.52 ( ( A @ ( B @ V3 ) )
% 0.29/0.52 = ( C @ ( D2 @ V3 ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % comp_eq_elim
% 0.29/0.52 thf(fact_281_comp__eq__elim,axiom,
% 0.29/0.52 ! [A: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,B: code_integer > code_integer > code_integer,C: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,D2: code_integer > code_integer] :
% 0.29/0.52 ( ( ( comp_C8797469213163452608nteger @ A @ B )
% 0.29/0.52 = ( comp_C1593894019821074884nteger @ C @ D2 ) )
% 0.29/0.52 => ! [V3: code_integer] :
% 0.29/0.52 ( ( A @ ( B @ V3 ) )
% 0.29/0.52 = ( C @ ( D2 @ V3 ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % comp_eq_elim
% 0.29/0.52 thf(fact_282_comp__eq__elim,axiom,
% 0.29/0.52 ! [A: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,B: code_integer > code_integer > code_integer,C: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,D2: code_integer > code_integer > code_integer] :
% 0.29/0.52 ( ( ( comp_C8797469213163452608nteger @ A @ B )
% 0.29/0.52 = ( comp_C8797469213163452608nteger @ C @ D2 ) )
% 0.29/0.52 => ! [V3: code_integer] :
% 0.29/0.52 ( ( A @ ( B @ V3 ) )
% 0.29/0.52 = ( C @ ( D2 @ V3 ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % comp_eq_elim
% 0.29/0.52 thf(fact_283_comp__eq__elim,axiom,
% 0.29/0.52 ! [A: nat > num,B: int > nat,C: nat > num,D2: int > nat] :
% 0.29/0.52 ( ( ( comp_nat_num_int @ A @ B )
% 0.29/0.52 = ( comp_nat_num_int @ C @ D2 ) )
% 0.29/0.52 => ! [V3: int] :
% 0.29/0.52 ( ( A @ ( B @ V3 ) )
% 0.29/0.52 = ( C @ ( D2 @ V3 ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % comp_eq_elim
% 0.29/0.52 thf(fact_284_comp__eq__dest,axiom,
% 0.29/0.52 ! [A: code_integer > code_integer,B: num > code_integer,C: code_integer > code_integer,D2: num > code_integer,V: num] :
% 0.29/0.52 ( ( ( comp_C3531382070062128313er_num @ A @ B )
% 0.29/0.52 = ( comp_C3531382070062128313er_num @ C @ D2 ) )
% 0.29/0.52 => ( ( A @ ( B @ V ) )
% 0.29/0.52 = ( C @ ( D2 @ V ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % comp_eq_dest
% 0.29/0.52 thf(fact_285_comp__eq__dest,axiom,
% 0.29/0.52 ! [A: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,B: code_integer > code_integer,C: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,D2: code_integer > code_integer,V: code_integer] :
% 0.29/0.52 ( ( ( comp_C1593894019821074884nteger @ A @ B )
% 0.29/0.52 = ( comp_C1593894019821074884nteger @ C @ D2 ) )
% 0.29/0.52 => ( ( A @ ( B @ V ) )
% 0.29/0.52 = ( C @ ( D2 @ V ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % comp_eq_dest
% 0.29/0.52 thf(fact_286_comp__eq__dest,axiom,
% 0.29/0.52 ! [A: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,B: code_integer > code_integer,C: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,D2: code_integer > code_integer > code_integer,V: code_integer] :
% 0.29/0.52 ( ( ( comp_C1593894019821074884nteger @ A @ B )
% 0.29/0.52 = ( comp_C8797469213163452608nteger @ C @ D2 ) )
% 0.29/0.52 => ( ( A @ ( B @ V ) )
% 0.29/0.52 = ( C @ ( D2 @ V ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % comp_eq_dest
% 0.29/0.52 thf(fact_287_comp__eq__dest,axiom,
% 0.29/0.52 ! [A: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,B: code_integer > code_integer > code_integer,C: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,D2: code_integer > code_integer,V: code_integer] :
% 0.29/0.52 ( ( ( comp_C8797469213163452608nteger @ A @ B )
% 0.29/0.52 = ( comp_C1593894019821074884nteger @ C @ D2 ) )
% 0.29/0.52 => ( ( A @ ( B @ V ) )
% 0.29/0.52 = ( C @ ( D2 @ V ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % comp_eq_dest
% 0.29/0.52 thf(fact_288_comp__eq__dest,axiom,
% 0.29/0.52 ! [A: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,B: code_integer > code_integer > code_integer,C: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,D2: code_integer > code_integer > code_integer,V: code_integer] :
% 0.29/0.52 ( ( ( comp_C8797469213163452608nteger @ A @ B )
% 0.29/0.52 = ( comp_C8797469213163452608nteger @ C @ D2 ) )
% 0.29/0.52 => ( ( A @ ( B @ V ) )
% 0.29/0.52 = ( C @ ( D2 @ V ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % comp_eq_dest
% 0.29/0.52 thf(fact_289_comp__eq__dest,axiom,
% 0.29/0.52 ! [A: nat > num,B: int > nat,C: nat > num,D2: int > nat,V: int] :
% 0.29/0.52 ( ( ( comp_nat_num_int @ A @ B )
% 0.29/0.52 = ( comp_nat_num_int @ C @ D2 ) )
% 0.29/0.52 => ( ( A @ ( B @ V ) )
% 0.29/0.52 = ( C @ ( D2 @ V ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % comp_eq_dest
% 0.29/0.52 thf(fact_290_comp__assoc,axiom,
% 0.29/0.52 ! [F: code_integer > code_integer,G: num > code_integer,H3: num > num] :
% 0.29/0.52 ( ( comp_n6909714581898973814er_num @ ( comp_C3531382070062128313er_num @ F @ G ) @ H3 )
% 0.29/0.52 = ( comp_C3531382070062128313er_num @ F @ ( comp_n6909714581898973814er_num @ G @ H3 ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % comp_assoc
% 0.29/0.52 thf(fact_291_comp__assoc,axiom,
% 0.29/0.52 ! [F: nat > num,G: int > nat,H3: int > int] :
% 0.29/0.52 ( ( comp_int_num_int @ ( comp_nat_num_int @ F @ G ) @ H3 )
% 0.29/0.52 = ( comp_nat_num_int @ F @ ( comp_int_nat_int @ G @ H3 ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % comp_assoc
% 0.29/0.52 thf(fact_292_comp__assoc,axiom,
% 0.29/0.52 ! [F: code_integer > code_integer,G: code_integer > code_integer,H3: num > code_integer] :
% 0.29/0.52 ( ( comp_C3531382070062128313er_num @ ( comp_C7449957260575251196nteger @ F @ G ) @ H3 )
% 0.29/0.52 = ( comp_C3531382070062128313er_num @ F @ ( comp_C3531382070062128313er_num @ G @ H3 ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % comp_assoc
% 0.29/0.52 thf(fact_293_comp__assoc,axiom,
% 0.29/0.52 ! [F: num > num,G: nat > num,H3: int > nat] :
% 0.29/0.52 ( ( comp_nat_num_int @ ( comp_num_num_nat @ F @ G ) @ H3 )
% 0.29/0.52 = ( comp_num_num_int @ F @ ( comp_nat_num_int @ G @ H3 ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % comp_assoc
% 0.29/0.52 thf(fact_294_comp__assoc,axiom,
% 0.29/0.52 ! [F: nat > num,G: nat > nat,H3: int > nat] :
% 0.29/0.52 ( ( comp_nat_num_int @ ( comp_nat_num_nat @ F @ G ) @ H3 )
% 0.29/0.52 = ( comp_nat_num_int @ F @ ( comp_nat_nat_int @ G @ H3 ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % comp_assoc
% 0.29/0.52 thf(fact_295_comp__assoc,axiom,
% 0.29/0.52 ! [F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer,H3: num > code_integer] :
% 0.29/0.52 ( ( comp_C6617437204949736321er_num @ ( comp_C1593894019821074884nteger @ F @ G ) @ H3 )
% 0.29/0.52 = ( comp_C6617437204949736321er_num @ F @ ( comp_C3531382070062128313er_num @ G @ H3 ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % comp_assoc
% 0.29/0.52 thf(fact_296_comp__assoc,axiom,
% 0.29/0.52 ! [F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer,H3: code_integer > code_integer] :
% 0.29/0.52 ( ( comp_C1593894019821074884nteger @ ( comp_C1593894019821074884nteger @ F @ G ) @ H3 )
% 0.29/0.52 = ( comp_C1593894019821074884nteger @ F @ ( comp_C7449957260575251196nteger @ G @ H3 ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % comp_assoc
% 0.29/0.52 thf(fact_297_comp__assoc,axiom,
% 0.29/0.52 ! [F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer > code_integer,H3: code_integer > code_integer] :
% 0.29/0.52 ( ( comp_C1593894019821074884nteger @ ( comp_C8797469213163452608nteger @ F @ G ) @ H3 )
% 0.29/0.52 = ( comp_C8797469213163452608nteger @ F @ ( comp_C2931745410781319416nteger @ G @ H3 ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % comp_assoc
% 0.29/0.52 thf(fact_298_comp__assoc,axiom,
% 0.29/0.52 ! [F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,G: ( code_integer > code_integer ) > code_integer,H3: code_integer > code_integer > code_integer] :
% 0.29/0.52 ( ( comp_C8797469213163452608nteger @ ( comp_C95226695241045696nteger @ F @ G ) @ H3 )
% 0.29/0.52 = ( comp_C1593894019821074884nteger @ F @ ( comp_C5076291335850163704nteger @ G @ H3 ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % comp_assoc
% 0.29/0.52 thf(fact_299_comp__assoc,axiom,
% 0.29/0.52 ! [F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G: ( code_integer > code_integer ) > code_integer > code_integer,H3: code_integer > code_integer > code_integer] :
% 0.29/0.52 ( ( comp_C8797469213163452608nteger @ ( comp_C3983183376822107068nteger @ F @ G ) @ H3 )
% 0.29/0.52 = ( comp_C8797469213163452608nteger @ F @ ( comp_C2822359487432382964nteger @ G @ H3 ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % comp_assoc
% 0.29/0.52 thf(fact_300_comp__def,axiom,
% 0.29/0.52 ( comp_C3531382070062128313er_num
% 0.29/0.52 = ( ^ [F2: code_integer > code_integer,G2: num > code_integer,X3: num] : ( F2 @ ( G2 @ X3 ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % comp_def
% 0.29/0.52 thf(fact_301_comp__def,axiom,
% 0.29/0.52 ( comp_C1593894019821074884nteger
% 0.29/0.52 = ( ^ [F2: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,G2: code_integer > code_integer,X3: code_integer] : ( F2 @ ( G2 @ X3 ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % comp_def
% 0.29/0.52 thf(fact_302_comp__def,axiom,
% 0.29/0.52 ( comp_C8797469213163452608nteger
% 0.29/0.52 = ( ^ [F2: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G2: code_integer > code_integer > code_integer,X3: code_integer] : ( F2 @ ( G2 @ X3 ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % comp_def
% 0.29/0.52 thf(fact_303_comp__def,axiom,
% 0.29/0.52 ( comp_nat_num_int
% 0.29/0.52 = ( ^ [F2: nat > num,G2: int > nat,X3: int] : ( F2 @ ( G2 @ X3 ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % comp_def
% 0.29/0.52 thf(fact_304_timeFrame_Oelims,axiom,
% 0.29/0.52 ! [X: nat,Xa: option3216581401566546698it_nat,Y: option3216581401566546698it_nat] :
% 0.29/0.52 ( ( ( heap_T531568236820715630rray_a @ X @ Xa )
% 0.29/0.52 = Y )
% 0.29/0.52 => ( ! [R: array_a,H2: heap_e7401611519738050253t_unit,N3: nat] :
% 0.29/0.52 ( ( Xa
% 0.29/0.52 = ( some_P6105628898608307625it_nat @ ( produc1733996804261680252it_nat @ R @ ( produc584006145561248582it_nat @ H2 @ N3 ) ) ) )
% 0.29/0.52 => ( Y
% 0.29/0.52 != ( some_P6105628898608307625it_nat @ ( produc1733996804261680252it_nat @ R @ ( produc584006145561248582it_nat @ H2 @ ( plus_plus_nat @ X @ N3 ) ) ) ) ) )
% 0.29/0.52 => ~ ( ( Xa = none_P2587165478634041381it_nat )
% 0.29/0.52 => ( Y != none_P2587165478634041381it_nat ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % timeFrame.elims
% 0.29/0.52 thf(fact_305_timeFrame_Oelims,axiom,
% 0.29/0.52 ! [X: nat,Xa: option8956607266484857688it_nat,Y: option8956607266484857688it_nat] :
% 0.29/0.52 ( ( ( heap_T3616969660504097270t_unit @ X @ Xa )
% 0.29/0.52 = Y )
% 0.29/0.52 => ( ! [R: product_unit,H2: heap_e7401611519738050253t_unit,N3: nat] :
% 0.29/0.52 ( ( Xa
% 0.29/0.52 = ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ R @ ( produc584006145561248582it_nat @ H2 @ N3 ) ) ) )
% 0.29/0.52 => ( Y
% 0.29/0.52 != ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ R @ ( produc584006145561248582it_nat @ H2 @ ( plus_plus_nat @ X @ N3 ) ) ) ) ) )
% 0.29/0.52 => ~ ( ( Xa = none_P9117596204409417319it_nat )
% 0.29/0.52 => ( Y != none_P9117596204409417319it_nat ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % timeFrame.elims
% 0.29/0.52 thf(fact_306_execute__bind__eq__SomeI,axiom,
% 0.29/0.52 ! [F: heap_T6362127782908069795rray_a,H3: heap_e7401611519738050253t_unit,X: array_a,H5: heap_e7401611519738050253t_unit,N2: nat,G: array_a > heap_T6362127782908069795rray_a,Y: array_a,H7: heap_e7401611519738050253t_unit,N5: nat] :
% 0.29/0.52 ( ( ( heap_T5591663578999710211rray_a @ F @ H3 )
% 0.29/0.52 = ( some_P6105628898608307625it_nat @ ( produc1733996804261680252it_nat @ X @ ( produc584006145561248582it_nat @ H5 @ N2 ) ) ) )
% 0.29/0.52 => ( ( ( heap_T5591663578999710211rray_a @ ( G @ X ) @ H5 )
% 0.29/0.52 = ( some_P6105628898608307625it_nat @ ( produc1733996804261680252it_nat @ Y @ ( produc584006145561248582it_nat @ H7 @ N5 ) ) ) )
% 0.29/0.52 => ( ( heap_T5591663578999710211rray_a @ ( heap_T2407400398799471159rray_a @ F @ G ) @ H3 )
% 0.29/0.52 = ( some_P6105628898608307625it_nat @ ( produc1733996804261680252it_nat @ Y @ ( produc584006145561248582it_nat @ H7 @ ( plus_plus_nat @ N2 @ N5 ) ) ) ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % execute_bind_eq_SomeI
% 0.29/0.52 thf(fact_307_execute__bind__eq__SomeI,axiom,
% 0.29/0.52 ! [F: heap_T6362127782908069795rray_a,H3: heap_e7401611519738050253t_unit,X: array_a,H5: heap_e7401611519738050253t_unit,N2: nat,G: array_a > heap_T5738788834812785303t_unit,Y: product_unit,H7: heap_e7401611519738050253t_unit,N5: nat] :
% 0.29/0.52 ( ( ( heap_T5591663578999710211rray_a @ F @ H3 )
% 0.29/0.52 = ( some_P6105628898608307625it_nat @ ( produc1733996804261680252it_nat @ X @ ( produc584006145561248582it_nat @ H5 @ N2 ) ) ) )
% 0.29/0.52 => ( ( ( heap_T875086893843062177t_unit @ ( G @ X ) @ H5 )
% 0.29/0.52 = ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ Y @ ( produc584006145561248582it_nat @ H7 @ N5 ) ) ) )
% 0.29/0.52 => ( ( heap_T875086893843062177t_unit @ ( heap_T7324619625323989613t_unit @ F @ G ) @ H3 )
% 0.29/0.52 = ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ Y @ ( produc584006145561248582it_nat @ H7 @ ( plus_plus_nat @ N2 @ N5 ) ) ) ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % execute_bind_eq_SomeI
% 0.29/0.52 thf(fact_308_execute__bind__eq__SomeI,axiom,
% 0.29/0.52 ! [F: heap_T5738788834812785303t_unit,H3: heap_e7401611519738050253t_unit,X: product_unit,H5: heap_e7401611519738050253t_unit,N2: nat,G: product_unit > heap_T6362127782908069795rray_a,Y: array_a,H7: heap_e7401611519738050253t_unit,N5: nat] :
% 0.29/0.52 ( ( ( heap_T875086893843062177t_unit @ F @ H3 )
% 0.29/0.52 = ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ X @ ( produc584006145561248582it_nat @ H5 @ N2 ) ) ) )
% 0.29/0.52 => ( ( ( heap_T5591663578999710211rray_a @ ( G @ X ) @ H5 )
% 0.29/0.52 = ( some_P6105628898608307625it_nat @ ( produc1733996804261680252it_nat @ Y @ ( produc584006145561248582it_nat @ H7 @ N5 ) ) ) )
% 0.29/0.52 => ( ( heap_T5591663578999710211rray_a @ ( heap_T7158140910958840029rray_a @ F @ G ) @ H3 )
% 0.29/0.52 = ( some_P6105628898608307625it_nat @ ( produc1733996804261680252it_nat @ Y @ ( produc584006145561248582it_nat @ H7 @ ( plus_plus_nat @ N2 @ N5 ) ) ) ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % execute_bind_eq_SomeI
% 0.29/0.52 thf(fact_309_execute__bind__eq__SomeI,axiom,
% 0.29/0.52 ! [F: heap_T5738788834812785303t_unit,H3: heap_e7401611519738050253t_unit,X: product_unit,H5: heap_e7401611519738050253t_unit,N2: nat,G: product_unit > heap_T5738788834812785303t_unit,Y: product_unit,H7: heap_e7401611519738050253t_unit,N5: nat] :
% 0.29/0.52 ( ( ( heap_T875086893843062177t_unit @ F @ H3 )
% 0.29/0.52 = ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ X @ ( produc584006145561248582it_nat @ H5 @ N2 ) ) ) )
% 0.29/0.52 => ( ( ( heap_T875086893843062177t_unit @ ( G @ X ) @ H5 )
% 0.29/0.52 = ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ Y @ ( produc584006145561248582it_nat @ H7 @ N5 ) ) ) )
% 0.29/0.52 => ( ( heap_T875086893843062177t_unit @ ( heap_T2633723481742716231t_unit @ F @ G ) @ H3 )
% 0.29/0.52 = ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ Y @ ( produc584006145561248582it_nat @ H7 @ ( plus_plus_nat @ N2 @ N5 ) ) ) ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % execute_bind_eq_SomeI
% 0.29/0.52 thf(fact_310_timeFrame_Osimps_I1_J,axiom,
% 0.29/0.52 ! [N2: nat,R2: product_unit,H3: heap_e7401611519738050253t_unit,N5: nat] :
% 0.29/0.52 ( ( heap_T3616969660504097270t_unit @ N2 @ ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ R2 @ ( produc584006145561248582it_nat @ H3 @ N5 ) ) ) )
% 0.29/0.52 = ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ R2 @ ( produc584006145561248582it_nat @ H3 @ ( plus_plus_nat @ N2 @ N5 ) ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % timeFrame.simps(1)
% 0.29/0.52 thf(fact_311_heap__def,axiom,
% 0.29/0.52 ( heap_T6927113302350381334t_unit
% 0.29/0.52 = ( ^ [F2: heap_e7401611519738050253t_unit > produc8664842809031399944it_nat] : ( heap_T6183433275982383450t_unit @ ( comp_P3118722334806803912t_unit @ some_P1914260805536162275it_nat @ F2 ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % heap_def
% 0.29/0.52 thf(fact_312_option_Osplit__sel,axiom,
% 0.29/0.52 ! [P: int > $o,F1: int,F22: num > int,Option: option_num] :
% 0.29/0.52 ( ( P @ ( case_option_int_num @ F1 @ F22 @ Option ) )
% 0.29/0.52 = ( ( ( Option = none_num )
% 0.29/0.52 => ( P @ F1 ) )
% 0.29/0.52 & ( ( Option
% 0.29/0.52 = ( some_num @ ( the_num @ Option ) ) )
% 0.29/0.52 => ( P @ ( F22 @ ( the_num @ Option ) ) ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % option.split_sel
% 0.29/0.52 thf(fact_313_option_Osplit__sel,axiom,
% 0.29/0.52 ! [P: option_num > $o,F1: option_num,F22: num > option_num,Option: option_num] :
% 0.29/0.52 ( ( P @ ( case_o6005452278849405969um_num @ F1 @ F22 @ Option ) )
% 0.29/0.52 = ( ( ( Option = none_num )
% 0.29/0.52 => ( P @ F1 ) )
% 0.29/0.52 & ( ( Option
% 0.29/0.52 = ( some_num @ ( the_num @ Option ) ) )
% 0.29/0.52 => ( P @ ( F22 @ ( the_num @ Option ) ) ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % option.split_sel
% 0.29/0.52 thf(fact_314_option_Osplit__sel,axiom,
% 0.29/0.52 ! [P: num > $o,F1: num,F22: num > num,Option: option_num] :
% 0.29/0.52 ( ( P @ ( case_option_num_num @ F1 @ F22 @ Option ) )
% 0.29/0.52 = ( ( ( Option = none_num )
% 0.29/0.52 => ( P @ F1 ) )
% 0.29/0.52 & ( ( Option
% 0.29/0.52 = ( some_num @ ( the_num @ Option ) ) )
% 0.29/0.52 => ( P @ ( F22 @ ( the_num @ Option ) ) ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % option.split_sel
% 0.29/0.52 thf(fact_315_option_Osplit__sel__asm,axiom,
% 0.29/0.52 ! [P: int > $o,F1: int,F22: num > int,Option: option_num] :
% 0.29/0.52 ( ( P @ ( case_option_int_num @ F1 @ F22 @ Option ) )
% 0.29/0.52 = ( ~ ( ( ( Option = none_num )
% 0.29/0.52 & ~ ( P @ F1 ) )
% 0.29/0.52 | ( ( Option
% 0.29/0.52 = ( some_num @ ( the_num @ Option ) ) )
% 0.29/0.52 & ~ ( P @ ( F22 @ ( the_num @ Option ) ) ) ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % option.split_sel_asm
% 0.29/0.52 thf(fact_316_option_Osplit__sel__asm,axiom,
% 0.29/0.52 ! [P: option_num > $o,F1: option_num,F22: num > option_num,Option: option_num] :
% 0.29/0.52 ( ( P @ ( case_o6005452278849405969um_num @ F1 @ F22 @ Option ) )
% 0.29/0.52 = ( ~ ( ( ( Option = none_num )
% 0.29/0.52 & ~ ( P @ F1 ) )
% 0.29/0.52 | ( ( Option
% 0.29/0.52 = ( some_num @ ( the_num @ Option ) ) )
% 0.29/0.52 & ~ ( P @ ( F22 @ ( the_num @ Option ) ) ) ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % option.split_sel_asm
% 0.29/0.52 thf(fact_317_option_Osplit__sel__asm,axiom,
% 0.29/0.52 ! [P: num > $o,F1: num,F22: num > num,Option: option_num] :
% 0.29/0.52 ( ( P @ ( case_option_num_num @ F1 @ F22 @ Option ) )
% 0.29/0.52 = ( ~ ( ( ( Option = none_num )
% 0.29/0.52 & ~ ( P @ F1 ) )
% 0.29/0.52 | ( ( Option
% 0.29/0.52 = ( some_num @ ( the_num @ Option ) ) )
% 0.29/0.52 & ~ ( P @ ( F22 @ ( the_num @ Option ) ) ) ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % option.split_sel_asm
% 0.29/0.52 thf(fact_318_one__natural_Orsp,axiom,
% 0.29/0.52 one_one_nat = one_one_nat ).
% 0.29/0.52
% 0.29/0.52 % one_natural.rsp
% 0.29/0.52 thf(fact_319_timeFrame_Opelims,axiom,
% 0.29/0.52 ! [X: nat,Xa: option3216581401566546698it_nat,Y: option3216581401566546698it_nat] :
% 0.29/0.52 ( ( ( heap_T531568236820715630rray_a @ X @ Xa )
% 0.29/0.52 = Y )
% 0.29/0.52 => ( ( accp_P8948468358075348838it_nat @ heap_T6578553156929092987rray_a @ ( produc3378006678175723489it_nat @ X @ Xa ) )
% 0.29/0.52 => ( ! [R: array_a,H2: heap_e7401611519738050253t_unit,N3: nat] :
% 0.29/0.52 ( ( Xa
% 0.29/0.52 = ( some_P6105628898608307625it_nat @ ( produc1733996804261680252it_nat @ R @ ( produc584006145561248582it_nat @ H2 @ N3 ) ) ) )
% 0.29/0.52 => ( ( Y
% 0.29/0.52 = ( some_P6105628898608307625it_nat @ ( produc1733996804261680252it_nat @ R @ ( produc584006145561248582it_nat @ H2 @ ( plus_plus_nat @ X @ N3 ) ) ) ) )
% 0.29/0.52 => ~ ( accp_P8948468358075348838it_nat @ heap_T6578553156929092987rray_a @ ( produc3378006678175723489it_nat @ X @ ( some_P6105628898608307625it_nat @ ( produc1733996804261680252it_nat @ R @ ( produc584006145561248582it_nat @ H2 @ N3 ) ) ) ) ) ) )
% 0.29/0.52 => ~ ( ( Xa = none_P2587165478634041381it_nat )
% 0.29/0.52 => ( ( Y = none_P2587165478634041381it_nat )
% 0.29/0.52 => ~ ( accp_P8948468358075348838it_nat @ heap_T6578553156929092987rray_a @ ( produc3378006678175723489it_nat @ X @ none_P2587165478634041381it_nat ) ) ) ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % timeFrame.pelims
% 0.29/0.52 thf(fact_320_timeFrame_Opelims,axiom,
% 0.29/0.52 ! [X: nat,Xa: option8956607266484857688it_nat,Y: option8956607266484857688it_nat] :
% 0.29/0.52 ( ( ( heap_T3616969660504097270t_unit @ X @ Xa )
% 0.29/0.52 = Y )
% 0.29/0.52 => ( ( accp_P414730952086964626it_nat @ heap_T996182799752388649t_unit @ ( produc638857205735767105it_nat @ X @ Xa ) )
% 0.29/0.52 => ( ! [R: product_unit,H2: heap_e7401611519738050253t_unit,N3: nat] :
% 0.29/0.52 ( ( Xa
% 0.29/0.52 = ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ R @ ( produc584006145561248582it_nat @ H2 @ N3 ) ) ) )
% 0.29/0.52 => ( ( Y
% 0.29/0.52 = ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ R @ ( produc584006145561248582it_nat @ H2 @ ( plus_plus_nat @ X @ N3 ) ) ) ) )
% 0.29/0.52 => ~ ( accp_P414730952086964626it_nat @ heap_T996182799752388649t_unit @ ( produc638857205735767105it_nat @ X @ ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ R @ ( produc584006145561248582it_nat @ H2 @ N3 ) ) ) ) ) ) )
% 0.29/0.52 => ~ ( ( Xa = none_P9117596204409417319it_nat )
% 0.29/0.52 => ( ( Y = none_P9117596204409417319it_nat )
% 0.29/0.52 => ~ ( accp_P414730952086964626it_nat @ heap_T996182799752388649t_unit @ ( produc638857205735767105it_nat @ X @ none_P9117596204409417319it_nat ) ) ) ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % timeFrame.pelims
% 0.29/0.52 thf(fact_321_add__right__cancel,axiom,
% 0.29/0.52 ! [B: multis2468970476368604999at_nat,A: multis2468970476368604999at_nat,C: multis2468970476368604999at_nat] :
% 0.29/0.52 ( ( ( plus_p7104986032573967614at_nat @ B @ A )
% 0.29/0.52 = ( plus_p7104986032573967614at_nat @ C @ A ) )
% 0.29/0.52 = ( B = C ) ) ).
% 0.29/0.52
% 0.29/0.52 % add_right_cancel
% 0.29/0.52 thf(fact_322_add__right__cancel,axiom,
% 0.29/0.52 ! [B: rat,A: rat,C: rat] :
% 0.29/0.52 ( ( ( plus_plus_rat @ B @ A )
% 0.29/0.52 = ( plus_plus_rat @ C @ A ) )
% 0.29/0.52 = ( B = C ) ) ).
% 0.29/0.52
% 0.29/0.52 % add_right_cancel
% 0.29/0.52 thf(fact_323_add__right__cancel,axiom,
% 0.29/0.52 ! [B: nat,A: nat,C: nat] :
% 0.29/0.52 ( ( ( plus_plus_nat @ B @ A )
% 0.29/0.52 = ( plus_plus_nat @ C @ A ) )
% 0.29/0.52 = ( B = C ) ) ).
% 0.29/0.52
% 0.29/0.52 % add_right_cancel
% 0.29/0.52 thf(fact_324_add__right__cancel,axiom,
% 0.29/0.52 ! [B: int,A: int,C: int] :
% 0.29/0.52 ( ( ( plus_plus_int @ B @ A )
% 0.29/0.52 = ( plus_plus_int @ C @ A ) )
% 0.29/0.52 = ( B = C ) ) ).
% 0.29/0.52
% 0.29/0.52 % add_right_cancel
% 0.29/0.52 thf(fact_325_add__left__cancel,axiom,
% 0.29/0.52 ! [A: multis2468970476368604999at_nat,B: multis2468970476368604999at_nat,C: multis2468970476368604999at_nat] :
% 0.29/0.52 ( ( ( plus_p7104986032573967614at_nat @ A @ B )
% 0.29/0.52 = ( plus_p7104986032573967614at_nat @ A @ C ) )
% 0.29/0.52 = ( B = C ) ) ).
% 0.29/0.52
% 0.29/0.52 % add_left_cancel
% 0.29/0.52 thf(fact_326_add__left__cancel,axiom,
% 0.29/0.52 ! [A: rat,B: rat,C: rat] :
% 0.29/0.52 ( ( ( plus_plus_rat @ A @ B )
% 0.29/0.52 = ( plus_plus_rat @ A @ C ) )
% 0.29/0.52 = ( B = C ) ) ).
% 0.29/0.52
% 0.29/0.52 % add_left_cancel
% 0.29/0.52 thf(fact_327_add__left__cancel,axiom,
% 0.29/0.52 ! [A: nat,B: nat,C: nat] :
% 0.29/0.52 ( ( ( plus_plus_nat @ A @ B )
% 0.29/0.52 = ( plus_plus_nat @ A @ C ) )
% 0.29/0.52 = ( B = C ) ) ).
% 0.29/0.52
% 0.29/0.52 % add_left_cancel
% 0.29/0.52 thf(fact_328_add__left__cancel,axiom,
% 0.29/0.52 ! [A: int,B: int,C: int] :
% 0.29/0.52 ( ( ( plus_plus_int @ A @ B )
% 0.29/0.52 = ( plus_plus_int @ A @ C ) )
% 0.29/0.52 = ( B = C ) ) ).
% 0.29/0.52
% 0.29/0.52 % add_left_cancel
% 0.29/0.52 thf(fact_329_Heap_Oinject,axiom,
% 0.29/0.52 ! [X: heap_e7401611519738050253t_unit > option8956607266484857688it_nat,Ya: heap_e7401611519738050253t_unit > option8956607266484857688it_nat] :
% 0.29/0.52 ( ( ( heap_T6183433275982383450t_unit @ X )
% 0.29/0.52 = ( heap_T6183433275982383450t_unit @ Ya ) )
% 0.29/0.52 = ( X = Ya ) ) ).
% 0.29/0.52
% 0.29/0.52 % Heap.inject
% 0.29/0.52 thf(fact_330_Heap__execute,axiom,
% 0.29/0.52 ! [F: heap_T6362127782908069795rray_a] :
% 0.29/0.52 ( ( heap_T1488828001306802186rray_a @ ( heap_T5591663578999710211rray_a @ F ) )
% 0.29/0.52 = F ) ).
% 0.29/0.52
% 0.29/0.52 % Heap_execute
% 0.29/0.52 thf(fact_331_Heap__execute,axiom,
% 0.29/0.52 ! [F: heap_T5738788834812785303t_unit] :
% 0.29/0.52 ( ( heap_T6183433275982383450t_unit @ ( heap_T875086893843062177t_unit @ F ) )
% 0.29/0.52 = F ) ).
% 0.29/0.52
% 0.29/0.52 % Heap_execute
% 0.29/0.52 thf(fact_332_add__right__imp__eq,axiom,
% 0.29/0.52 ! [B: multis2468970476368604999at_nat,A: multis2468970476368604999at_nat,C: multis2468970476368604999at_nat] :
% 0.29/0.52 ( ( ( plus_p7104986032573967614at_nat @ B @ A )
% 0.29/0.52 = ( plus_p7104986032573967614at_nat @ C @ A ) )
% 0.29/0.52 => ( B = C ) ) ).
% 0.29/0.52
% 0.29/0.52 % add_right_imp_eq
% 0.29/0.52 thf(fact_333_add__right__imp__eq,axiom,
% 0.29/0.52 ! [B: rat,A: rat,C: rat] :
% 0.29/0.52 ( ( ( plus_plus_rat @ B @ A )
% 0.29/0.52 = ( plus_plus_rat @ C @ A ) )
% 0.29/0.52 => ( B = C ) ) ).
% 0.29/0.52
% 0.29/0.52 % add_right_imp_eq
% 0.29/0.52 thf(fact_334_add__right__imp__eq,axiom,
% 0.29/0.52 ! [B: nat,A: nat,C: nat] :
% 0.29/0.52 ( ( ( plus_plus_nat @ B @ A )
% 0.29/0.52 = ( plus_plus_nat @ C @ A ) )
% 0.29/0.52 => ( B = C ) ) ).
% 0.29/0.52
% 0.29/0.52 % add_right_imp_eq
% 0.29/0.52 thf(fact_335_add__right__imp__eq,axiom,
% 0.29/0.52 ! [B: int,A: int,C: int] :
% 0.29/0.52 ( ( ( plus_plus_int @ B @ A )
% 0.29/0.52 = ( plus_plus_int @ C @ A ) )
% 0.29/0.52 => ( B = C ) ) ).
% 0.29/0.52
% 0.29/0.52 % add_right_imp_eq
% 0.29/0.52 thf(fact_336_add__left__imp__eq,axiom,
% 0.29/0.52 ! [A: multis2468970476368604999at_nat,B: multis2468970476368604999at_nat,C: multis2468970476368604999at_nat] :
% 0.29/0.52 ( ( ( plus_p7104986032573967614at_nat @ A @ B )
% 0.29/0.52 = ( plus_p7104986032573967614at_nat @ A @ C ) )
% 0.29/0.52 => ( B = C ) ) ).
% 0.29/0.52
% 0.29/0.52 % add_left_imp_eq
% 0.29/0.52 thf(fact_337_add__left__imp__eq,axiom,
% 0.29/0.52 ! [A: rat,B: rat,C: rat] :
% 0.29/0.52 ( ( ( plus_plus_rat @ A @ B )
% 0.29/0.52 = ( plus_plus_rat @ A @ C ) )
% 0.29/0.52 => ( B = C ) ) ).
% 0.29/0.52
% 0.29/0.52 % add_left_imp_eq
% 0.29/0.52 thf(fact_338_add__left__imp__eq,axiom,
% 0.29/0.52 ! [A: nat,B: nat,C: nat] :
% 0.29/0.52 ( ( ( plus_plus_nat @ A @ B )
% 0.29/0.52 = ( plus_plus_nat @ A @ C ) )
% 0.29/0.52 => ( B = C ) ) ).
% 0.29/0.52
% 0.29/0.52 % add_left_imp_eq
% 0.29/0.52 thf(fact_339_add__left__imp__eq,axiom,
% 0.29/0.52 ! [A: int,B: int,C: int] :
% 0.29/0.52 ( ( ( plus_plus_int @ A @ B )
% 0.29/0.52 = ( plus_plus_int @ A @ C ) )
% 0.29/0.52 => ( B = C ) ) ).
% 0.29/0.52
% 0.29/0.52 % add_left_imp_eq
% 0.29/0.52 thf(fact_340_ab__semigroup__add__class_Oadd_Oleft__commute,axiom,
% 0.29/0.52 ! [B: multis2468970476368604999at_nat,A: multis2468970476368604999at_nat,C: multis2468970476368604999at_nat] :
% 0.29/0.52 ( ( plus_p7104986032573967614at_nat @ B @ ( plus_p7104986032573967614at_nat @ A @ C ) )
% 0.29/0.52 = ( plus_p7104986032573967614at_nat @ A @ ( plus_p7104986032573967614at_nat @ B @ C ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % ab_semigroup_add_class.add.left_commute
% 0.29/0.52 thf(fact_341_ab__semigroup__add__class_Oadd_Oleft__commute,axiom,
% 0.29/0.52 ! [B: rat,A: rat,C: rat] :
% 0.29/0.52 ( ( plus_plus_rat @ B @ ( plus_plus_rat @ A @ C ) )
% 0.29/0.52 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % ab_semigroup_add_class.add.left_commute
% 0.29/0.52 thf(fact_342_ab__semigroup__add__class_Oadd_Oleft__commute,axiom,
% 0.29/0.52 ! [B: nat,A: nat,C: nat] :
% 0.29/0.52 ( ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C ) )
% 0.29/0.52 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % ab_semigroup_add_class.add.left_commute
% 0.29/0.52 thf(fact_343_ab__semigroup__add__class_Oadd_Oleft__commute,axiom,
% 0.29/0.52 ! [B: int,A: int,C: int] :
% 0.29/0.52 ( ( plus_plus_int @ B @ ( plus_plus_int @ A @ C ) )
% 0.29/0.52 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % ab_semigroup_add_class.add.left_commute
% 0.29/0.52 thf(fact_344_ab__semigroup__add__class_Oadd_Ocommute,axiom,
% 0.29/0.52 ( plus_p7104986032573967614at_nat
% 0.29/0.52 = ( ^ [A5: multis2468970476368604999at_nat,B4: multis2468970476368604999at_nat] : ( plus_p7104986032573967614at_nat @ B4 @ A5 ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % ab_semigroup_add_class.add.commute
% 0.29/0.52 thf(fact_345_ab__semigroup__add__class_Oadd_Ocommute,axiom,
% 0.29/0.52 ( plus_plus_rat
% 0.29/0.52 = ( ^ [A5: rat,B4: rat] : ( plus_plus_rat @ B4 @ A5 ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % ab_semigroup_add_class.add.commute
% 0.29/0.52 thf(fact_346_ab__semigroup__add__class_Oadd_Ocommute,axiom,
% 0.29/0.52 ( plus_plus_nat
% 0.29/0.52 = ( ^ [A5: nat,B4: nat] : ( plus_plus_nat @ B4 @ A5 ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % ab_semigroup_add_class.add.commute
% 0.29/0.52 thf(fact_347_ab__semigroup__add__class_Oadd_Ocommute,axiom,
% 0.29/0.52 ( plus_plus_int
% 0.29/0.52 = ( ^ [A5: int,B4: int] : ( plus_plus_int @ B4 @ A5 ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % ab_semigroup_add_class.add.commute
% 0.29/0.52 thf(fact_348_add_Oright__cancel,axiom,
% 0.29/0.52 ! [B: rat,A: rat,C: rat] :
% 0.29/0.52 ( ( ( plus_plus_rat @ B @ A )
% 0.29/0.52 = ( plus_plus_rat @ C @ A ) )
% 0.29/0.52 = ( B = C ) ) ).
% 0.29/0.52
% 0.29/0.52 % add.right_cancel
% 0.29/0.52 thf(fact_349_add_Oright__cancel,axiom,
% 0.29/0.52 ! [B: int,A: int,C: int] :
% 0.29/0.52 ( ( ( plus_plus_int @ B @ A )
% 0.29/0.52 = ( plus_plus_int @ C @ A ) )
% 0.29/0.52 = ( B = C ) ) ).
% 0.29/0.52
% 0.29/0.52 % add.right_cancel
% 0.29/0.52 thf(fact_350_add_Oleft__cancel,axiom,
% 0.29/0.52 ! [A: rat,B: rat,C: rat] :
% 0.29/0.52 ( ( ( plus_plus_rat @ A @ B )
% 0.29/0.52 = ( plus_plus_rat @ A @ C ) )
% 0.29/0.52 = ( B = C ) ) ).
% 0.29/0.52
% 0.29/0.52 % add.left_cancel
% 0.29/0.52 thf(fact_351_add_Oleft__cancel,axiom,
% 0.29/0.52 ! [A: int,B: int,C: int] :
% 0.29/0.52 ( ( ( plus_plus_int @ A @ B )
% 0.29/0.52 = ( plus_plus_int @ A @ C ) )
% 0.29/0.52 = ( B = C ) ) ).
% 0.29/0.52
% 0.29/0.52 % add.left_cancel
% 0.29/0.52 thf(fact_352_add_Oassoc,axiom,
% 0.29/0.52 ! [A: multis2468970476368604999at_nat,B: multis2468970476368604999at_nat,C: multis2468970476368604999at_nat] :
% 0.29/0.52 ( ( plus_p7104986032573967614at_nat @ ( plus_p7104986032573967614at_nat @ A @ B ) @ C )
% 0.29/0.52 = ( plus_p7104986032573967614at_nat @ A @ ( plus_p7104986032573967614at_nat @ B @ C ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % add.assoc
% 0.29/0.52 thf(fact_353_add_Oassoc,axiom,
% 0.29/0.52 ! [A: rat,B: rat,C: rat] :
% 0.29/0.52 ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 0.29/0.52 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % add.assoc
% 0.29/0.52 thf(fact_354_add_Oassoc,axiom,
% 0.29/0.52 ! [A: nat,B: nat,C: nat] :
% 0.29/0.52 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 0.29/0.52 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % add.assoc
% 0.29/0.52 thf(fact_355_add_Oassoc,axiom,
% 0.29/0.52 ! [A: int,B: int,C: int] :
% 0.29/0.52 ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 0.29/0.52 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % add.assoc
% 0.29/0.52 thf(fact_356_group__cancel_Oadd2,axiom,
% 0.29/0.52 ! [B5: multis2468970476368604999at_nat,K: multis2468970476368604999at_nat,B: multis2468970476368604999at_nat,A: multis2468970476368604999at_nat] :
% 0.29/0.52 ( ( B5
% 0.29/0.52 = ( plus_p7104986032573967614at_nat @ K @ B ) )
% 0.29/0.52 => ( ( plus_p7104986032573967614at_nat @ A @ B5 )
% 0.29/0.52 = ( plus_p7104986032573967614at_nat @ K @ ( plus_p7104986032573967614at_nat @ A @ B ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % group_cancel.add2
% 0.29/0.52 thf(fact_357_group__cancel_Oadd2,axiom,
% 0.29/0.52 ! [B5: rat,K: rat,B: rat,A: rat] :
% 0.29/0.52 ( ( B5
% 0.29/0.52 = ( plus_plus_rat @ K @ B ) )
% 0.29/0.52 => ( ( plus_plus_rat @ A @ B5 )
% 0.29/0.52 = ( plus_plus_rat @ K @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % group_cancel.add2
% 0.29/0.52 thf(fact_358_group__cancel_Oadd2,axiom,
% 0.29/0.52 ! [B5: nat,K: nat,B: nat,A: nat] :
% 0.29/0.52 ( ( B5
% 0.29/0.52 = ( plus_plus_nat @ K @ B ) )
% 0.29/0.52 => ( ( plus_plus_nat @ A @ B5 )
% 0.29/0.52 = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % group_cancel.add2
% 0.29/0.52 thf(fact_359_group__cancel_Oadd2,axiom,
% 0.29/0.52 ! [B5: int,K: int,B: int,A: int] :
% 0.29/0.52 ( ( B5
% 0.29/0.52 = ( plus_plus_int @ K @ B ) )
% 0.29/0.52 => ( ( plus_plus_int @ A @ B5 )
% 0.29/0.52 = ( plus_plus_int @ K @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % group_cancel.add2
% 0.29/0.52 thf(fact_360_group__cancel_Oadd1,axiom,
% 0.29/0.52 ! [A2: multis2468970476368604999at_nat,K: multis2468970476368604999at_nat,A: multis2468970476368604999at_nat,B: multis2468970476368604999at_nat] :
% 0.29/0.52 ( ( A2
% 0.29/0.52 = ( plus_p7104986032573967614at_nat @ K @ A ) )
% 0.29/0.52 => ( ( plus_p7104986032573967614at_nat @ A2 @ B )
% 0.29/0.52 = ( plus_p7104986032573967614at_nat @ K @ ( plus_p7104986032573967614at_nat @ A @ B ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % group_cancel.add1
% 0.29/0.52 thf(fact_361_group__cancel_Oadd1,axiom,
% 0.29/0.52 ! [A2: rat,K: rat,A: rat,B: rat] :
% 0.29/0.52 ( ( A2
% 0.29/0.52 = ( plus_plus_rat @ K @ A ) )
% 0.29/0.52 => ( ( plus_plus_rat @ A2 @ B )
% 0.29/0.52 = ( plus_plus_rat @ K @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % group_cancel.add1
% 0.29/0.52 thf(fact_362_group__cancel_Oadd1,axiom,
% 0.29/0.52 ! [A2: nat,K: nat,A: nat,B: nat] :
% 0.29/0.52 ( ( A2
% 0.29/0.52 = ( plus_plus_nat @ K @ A ) )
% 0.29/0.52 => ( ( plus_plus_nat @ A2 @ B )
% 0.29/0.52 = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % group_cancel.add1
% 0.29/0.52 thf(fact_363_group__cancel_Oadd1,axiom,
% 0.29/0.52 ! [A2: int,K: int,A: int,B: int] :
% 0.29/0.52 ( ( A2
% 0.29/0.52 = ( plus_plus_int @ K @ A ) )
% 0.29/0.52 => ( ( plus_plus_int @ A2 @ B )
% 0.29/0.52 = ( plus_plus_int @ K @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % group_cancel.add1
% 0.29/0.52 thf(fact_364_add__mono__thms__linordered__semiring_I4_J,axiom,
% 0.29/0.52 ! [I: rat,J: rat,K: rat,L: rat] :
% 0.29/0.52 ( ( ( I = J )
% 0.29/0.52 & ( K = L ) )
% 0.29/0.52 => ( ( plus_plus_rat @ I @ K )
% 0.29/0.52 = ( plus_plus_rat @ J @ L ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % add_mono_thms_linordered_semiring(4)
% 0.29/0.52 thf(fact_365_add__mono__thms__linordered__semiring_I4_J,axiom,
% 0.29/0.52 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.29/0.52 ( ( ( I = J )
% 0.29/0.52 & ( K = L ) )
% 0.29/0.52 => ( ( plus_plus_nat @ I @ K )
% 0.29/0.52 = ( plus_plus_nat @ J @ L ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % add_mono_thms_linordered_semiring(4)
% 0.29/0.52 thf(fact_366_add__mono__thms__linordered__semiring_I4_J,axiom,
% 0.29/0.52 ! [I: int,J: int,K: int,L: int] :
% 0.29/0.52 ( ( ( I = J )
% 0.29/0.52 & ( K = L ) )
% 0.29/0.52 => ( ( plus_plus_int @ I @ K )
% 0.29/0.52 = ( plus_plus_int @ J @ L ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % add_mono_thms_linordered_semiring(4)
% 0.29/0.52 thf(fact_367_Heap_Oexhaust,axiom,
% 0.29/0.52 ! [Y: heap_T5738788834812785303t_unit] :
% 0.29/0.52 ~ ! [X4: heap_e7401611519738050253t_unit > option8956607266484857688it_nat] :
% 0.29/0.52 ( Y
% 0.29/0.52 != ( heap_T6183433275982383450t_unit @ X4 ) ) ).
% 0.29/0.52
% 0.29/0.52 % Heap.exhaust
% 0.29/0.52 thf(fact_368_execute_Osimps,axiom,
% 0.29/0.52 ! [F: heap_e7401611519738050253t_unit > option3216581401566546698it_nat] :
% 0.29/0.52 ( ( heap_T5591663578999710211rray_a @ ( heap_T1488828001306802186rray_a @ F ) )
% 0.29/0.52 = F ) ).
% 0.29/0.52
% 0.29/0.52 % execute.simps
% 0.29/0.52 thf(fact_369_execute_Osimps,axiom,
% 0.29/0.52 ! [F: heap_e7401611519738050253t_unit > option8956607266484857688it_nat] :
% 0.29/0.52 ( ( heap_T875086893843062177t_unit @ ( heap_T6183433275982383450t_unit @ F ) )
% 0.29/0.52 = F ) ).
% 0.29/0.52
% 0.29/0.52 % execute.simps
% 0.29/0.52 thf(fact_370_option_Osimps_I5_J,axiom,
% 0.29/0.52 ! [F1: int,F22: num > int,X2: num] :
% 0.29/0.52 ( ( case_option_int_num @ F1 @ F22 @ ( some_num @ X2 ) )
% 0.29/0.52 = ( F22 @ X2 ) ) ).
% 0.29/0.52
% 0.29/0.52 % option.simps(5)
% 0.29/0.52 thf(fact_371_option_Osimps_I5_J,axiom,
% 0.29/0.52 ! [F1: option_num,F22: num > option_num,X2: num] :
% 0.29/0.52 ( ( case_o6005452278849405969um_num @ F1 @ F22 @ ( some_num @ X2 ) )
% 0.29/0.52 = ( F22 @ X2 ) ) ).
% 0.29/0.52
% 0.29/0.52 % option.simps(5)
% 0.29/0.52 thf(fact_372_option_Osimps_I5_J,axiom,
% 0.29/0.52 ! [F1: num,F22: num > num,X2: num] :
% 0.29/0.52 ( ( case_option_num_num @ F1 @ F22 @ ( some_num @ X2 ) )
% 0.29/0.52 = ( F22 @ X2 ) ) ).
% 0.29/0.52
% 0.29/0.52 % option.simps(5)
% 0.29/0.52 thf(fact_373_option_Osimps_I4_J,axiom,
% 0.29/0.52 ! [F1: int,F22: num > int] :
% 0.29/0.52 ( ( case_option_int_num @ F1 @ F22 @ none_num )
% 0.29/0.52 = F1 ) ).
% 0.29/0.52
% 0.29/0.52 % option.simps(4)
% 0.29/0.52 thf(fact_374_option_Osimps_I4_J,axiom,
% 0.29/0.52 ! [F1: option_num,F22: num > option_num] :
% 0.29/0.52 ( ( case_o6005452278849405969um_num @ F1 @ F22 @ none_num )
% 0.29/0.52 = F1 ) ).
% 0.29/0.52
% 0.29/0.52 % option.simps(4)
% 0.29/0.52 thf(fact_375_option_Osimps_I4_J,axiom,
% 0.29/0.52 ! [F1: num,F22: num > num] :
% 0.29/0.52 ( ( case_option_num_num @ F1 @ F22 @ none_num )
% 0.29/0.52 = F1 ) ).
% 0.29/0.52
% 0.29/0.52 % option.simps(4)
% 0.29/0.52 thf(fact_376_option_Ocase__eq__if,axiom,
% 0.29/0.52 ( case_option_int_num
% 0.29/0.52 = ( ^ [F12: int,F23: num > int,Option3: option_num] : ( if_int @ ( Option3 = none_num ) @ F12 @ ( F23 @ ( the_num @ Option3 ) ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % option.case_eq_if
% 0.29/0.52 thf(fact_377_option_Ocase__eq__if,axiom,
% 0.29/0.52 ( case_o6005452278849405969um_num
% 0.29/0.52 = ( ^ [F12: option_num,F23: num > option_num,Option3: option_num] : ( if_option_num @ ( Option3 = none_num ) @ F12 @ ( F23 @ ( the_num @ Option3 ) ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % option.case_eq_if
% 0.29/0.52 thf(fact_378_option_Ocase__eq__if,axiom,
% 0.29/0.52 ( case_option_num_num
% 0.29/0.52 = ( ^ [F12: num,F23: num > num,Option3: option_num] : ( if_num @ ( Option3 = none_num ) @ F12 @ ( F23 @ ( the_num @ Option3 ) ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % option.case_eq_if
% 0.29/0.52 thf(fact_379_accp_Ocases,axiom,
% 0.29/0.52 ! [R2: product_prod_nat_nat > product_prod_nat_nat > $o,A: product_prod_nat_nat] :
% 0.29/0.52 ( ( accp_P4275260045618599050at_nat @ R2 @ A )
% 0.29/0.52 => ! [Y6: product_prod_nat_nat] :
% 0.29/0.52 ( ( R2 @ Y6 @ A )
% 0.29/0.52 => ( accp_P4275260045618599050at_nat @ R2 @ Y6 ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % accp.cases
% 0.29/0.52 thf(fact_380_accp_Ocases,axiom,
% 0.29/0.52 ! [R2: product_prod_int_int > product_prod_int_int > $o,A: product_prod_int_int] :
% 0.29/0.52 ( ( accp_P1096762738010456898nt_int @ R2 @ A )
% 0.29/0.52 => ! [Y6: product_prod_int_int] :
% 0.29/0.52 ( ( R2 @ Y6 @ A )
% 0.29/0.52 => ( accp_P1096762738010456898nt_int @ R2 @ Y6 ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % accp.cases
% 0.29/0.52 thf(fact_381_accp_Ocases,axiom,
% 0.29/0.52 ! [R2: produc2732055786443039994et_nat > produc2732055786443039994et_nat > $o,A: produc2732055786443039994et_nat] :
% 0.29/0.52 ( ( accp_P1862375125659990705et_nat @ R2 @ A )
% 0.29/0.52 => ! [Y6: produc2732055786443039994et_nat] :
% 0.29/0.52 ( ( R2 @ Y6 @ A )
% 0.29/0.52 => ( accp_P1862375125659990705et_nat @ R2 @ Y6 ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % accp.cases
% 0.29/0.52 thf(fact_382_accp_Ocases,axiom,
% 0.29/0.52 ! [R2: list_nat > list_nat > $o,A: list_nat] :
% 0.29/0.52 ( ( accp_list_nat @ R2 @ A )
% 0.29/0.52 => ! [Y6: list_nat] :
% 0.29/0.52 ( ( R2 @ Y6 @ A )
% 0.29/0.52 => ( accp_list_nat @ R2 @ Y6 ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % accp.cases
% 0.29/0.52 thf(fact_383_accp_Ocases,axiom,
% 0.29/0.52 ! [R2: nat > nat > $o,A: nat] :
% 0.29/0.52 ( ( accp_nat @ R2 @ A )
% 0.29/0.52 => ! [Y6: nat] :
% 0.29/0.52 ( ( R2 @ Y6 @ A )
% 0.29/0.52 => ( accp_nat @ R2 @ Y6 ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % accp.cases
% 0.29/0.52 thf(fact_384_accp_Osimps,axiom,
% 0.29/0.52 ( accp_P4275260045618599050at_nat
% 0.29/0.52 = ( ^ [R3: product_prod_nat_nat > product_prod_nat_nat > $o,A5: product_prod_nat_nat] :
% 0.29/0.52 ? [X3: product_prod_nat_nat] :
% 0.29/0.52 ( ( A5 = X3 )
% 0.29/0.52 & ! [Y3: product_prod_nat_nat] :
% 0.29/0.52 ( ( R3 @ Y3 @ X3 )
% 0.29/0.52 => ( accp_P4275260045618599050at_nat @ R3 @ Y3 ) ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % accp.simps
% 0.29/0.52 thf(fact_385_accp_Osimps,axiom,
% 0.29/0.52 ( accp_P1096762738010456898nt_int
% 0.29/0.52 = ( ^ [R3: product_prod_int_int > product_prod_int_int > $o,A5: product_prod_int_int] :
% 0.29/0.52 ? [X3: product_prod_int_int] :
% 0.29/0.52 ( ( A5 = X3 )
% 0.29/0.52 & ! [Y3: product_prod_int_int] :
% 0.29/0.52 ( ( R3 @ Y3 @ X3 )
% 0.29/0.52 => ( accp_P1096762738010456898nt_int @ R3 @ Y3 ) ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % accp.simps
% 0.29/0.52 thf(fact_386_accp_Osimps,axiom,
% 0.29/0.52 ( accp_P1862375125659990705et_nat
% 0.29/0.52 = ( ^ [R3: produc2732055786443039994et_nat > produc2732055786443039994et_nat > $o,A5: produc2732055786443039994et_nat] :
% 0.29/0.52 ? [X3: produc2732055786443039994et_nat] :
% 0.29/0.52 ( ( A5 = X3 )
% 0.29/0.52 & ! [Y3: produc2732055786443039994et_nat] :
% 0.29/0.52 ( ( R3 @ Y3 @ X3 )
% 0.29/0.52 => ( accp_P1862375125659990705et_nat @ R3 @ Y3 ) ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % accp.simps
% 0.29/0.52 thf(fact_387_accp_Osimps,axiom,
% 0.29/0.52 ( accp_list_nat
% 0.29/0.52 = ( ^ [R3: list_nat > list_nat > $o,A5: list_nat] :
% 0.29/0.52 ? [X3: list_nat] :
% 0.29/0.52 ( ( A5 = X3 )
% 0.29/0.52 & ! [Y3: list_nat] :
% 0.29/0.52 ( ( R3 @ Y3 @ X3 )
% 0.29/0.52 => ( accp_list_nat @ R3 @ Y3 ) ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % accp.simps
% 0.29/0.52 thf(fact_388_accp_Osimps,axiom,
% 0.29/0.52 ( accp_nat
% 0.29/0.52 = ( ^ [R3: nat > nat > $o,A5: nat] :
% 0.29/0.52 ? [X3: nat] :
% 0.29/0.52 ( ( A5 = X3 )
% 0.29/0.52 & ! [Y3: nat] :
% 0.29/0.52 ( ( R3 @ Y3 @ X3 )
% 0.29/0.52 => ( accp_nat @ R3 @ Y3 ) ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % accp.simps
% 0.29/0.52 thf(fact_389_accpI,axiom,
% 0.29/0.52 ! [R2: product_prod_nat_nat > product_prod_nat_nat > $o,X: product_prod_nat_nat] :
% 0.29/0.52 ( ! [Y5: product_prod_nat_nat] :
% 0.29/0.52 ( ( R2 @ Y5 @ X )
% 0.29/0.52 => ( accp_P4275260045618599050at_nat @ R2 @ Y5 ) )
% 0.29/0.52 => ( accp_P4275260045618599050at_nat @ R2 @ X ) ) ).
% 0.29/0.52
% 0.29/0.52 % accpI
% 0.29/0.52 thf(fact_390_accpI,axiom,
% 0.29/0.52 ! [R2: product_prod_int_int > product_prod_int_int > $o,X: product_prod_int_int] :
% 0.29/0.52 ( ! [Y5: product_prod_int_int] :
% 0.29/0.52 ( ( R2 @ Y5 @ X )
% 0.29/0.52 => ( accp_P1096762738010456898nt_int @ R2 @ Y5 ) )
% 0.29/0.52 => ( accp_P1096762738010456898nt_int @ R2 @ X ) ) ).
% 0.29/0.52
% 0.29/0.52 % accpI
% 0.29/0.52 thf(fact_391_accpI,axiom,
% 0.29/0.52 ! [R2: produc2732055786443039994et_nat > produc2732055786443039994et_nat > $o,X: produc2732055786443039994et_nat] :
% 0.29/0.52 ( ! [Y5: produc2732055786443039994et_nat] :
% 0.29/0.52 ( ( R2 @ Y5 @ X )
% 0.29/0.52 => ( accp_P1862375125659990705et_nat @ R2 @ Y5 ) )
% 0.29/0.52 => ( accp_P1862375125659990705et_nat @ R2 @ X ) ) ).
% 0.29/0.52
% 0.29/0.52 % accpI
% 0.29/0.52 thf(fact_392_accpI,axiom,
% 0.29/0.52 ! [R2: list_nat > list_nat > $o,X: list_nat] :
% 0.29/0.52 ( ! [Y5: list_nat] :
% 0.29/0.52 ( ( R2 @ Y5 @ X )
% 0.29/0.52 => ( accp_list_nat @ R2 @ Y5 ) )
% 0.29/0.52 => ( accp_list_nat @ R2 @ X ) ) ).
% 0.29/0.52
% 0.29/0.52 % accpI
% 0.29/0.52 thf(fact_393_accpI,axiom,
% 0.29/0.52 ! [R2: nat > nat > $o,X: nat] :
% 0.29/0.52 ( ! [Y5: nat] :
% 0.29/0.52 ( ( R2 @ Y5 @ X )
% 0.29/0.52 => ( accp_nat @ R2 @ Y5 ) )
% 0.29/0.52 => ( accp_nat @ R2 @ X ) ) ).
% 0.29/0.52
% 0.29/0.52 % accpI
% 0.29/0.52 thf(fact_394_accp__induct,axiom,
% 0.29/0.52 ! [R2: product_prod_nat_nat > product_prod_nat_nat > $o,A: product_prod_nat_nat,P: product_prod_nat_nat > $o] :
% 0.29/0.52 ( ( accp_P4275260045618599050at_nat @ R2 @ A )
% 0.29/0.52 => ( ! [X4: product_prod_nat_nat] :
% 0.29/0.52 ( ( accp_P4275260045618599050at_nat @ R2 @ X4 )
% 0.29/0.52 => ( ! [Y6: product_prod_nat_nat] :
% 0.29/0.52 ( ( R2 @ Y6 @ X4 )
% 0.29/0.52 => ( P @ Y6 ) )
% 0.29/0.52 => ( P @ X4 ) ) )
% 0.29/0.52 => ( P @ A ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % accp_induct
% 0.29/0.52 thf(fact_395_accp__induct,axiom,
% 0.29/0.52 ! [R2: product_prod_int_int > product_prod_int_int > $o,A: product_prod_int_int,P: product_prod_int_int > $o] :
% 0.29/0.52 ( ( accp_P1096762738010456898nt_int @ R2 @ A )
% 0.29/0.52 => ( ! [X4: product_prod_int_int] :
% 0.29/0.52 ( ( accp_P1096762738010456898nt_int @ R2 @ X4 )
% 0.29/0.52 => ( ! [Y6: product_prod_int_int] :
% 0.29/0.52 ( ( R2 @ Y6 @ X4 )
% 0.29/0.52 => ( P @ Y6 ) )
% 0.29/0.52 => ( P @ X4 ) ) )
% 0.29/0.52 => ( P @ A ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % accp_induct
% 0.29/0.52 thf(fact_396_accp__induct,axiom,
% 0.29/0.52 ! [R2: produc2732055786443039994et_nat > produc2732055786443039994et_nat > $o,A: produc2732055786443039994et_nat,P: produc2732055786443039994et_nat > $o] :
% 0.29/0.52 ( ( accp_P1862375125659990705et_nat @ R2 @ A )
% 0.29/0.52 => ( ! [X4: produc2732055786443039994et_nat] :
% 0.29/0.52 ( ( accp_P1862375125659990705et_nat @ R2 @ X4 )
% 0.29/0.52 => ( ! [Y6: produc2732055786443039994et_nat] :
% 0.29/0.52 ( ( R2 @ Y6 @ X4 )
% 0.29/0.52 => ( P @ Y6 ) )
% 0.29/0.52 => ( P @ X4 ) ) )
% 0.29/0.52 => ( P @ A ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % accp_induct
% 0.29/0.52 thf(fact_397_accp__induct,axiom,
% 0.29/0.52 ! [R2: list_nat > list_nat > $o,A: list_nat,P: list_nat > $o] :
% 0.29/0.52 ( ( accp_list_nat @ R2 @ A )
% 0.29/0.52 => ( ! [X4: list_nat] :
% 0.29/0.52 ( ( accp_list_nat @ R2 @ X4 )
% 0.29/0.52 => ( ! [Y6: list_nat] :
% 0.29/0.52 ( ( R2 @ Y6 @ X4 )
% 0.29/0.52 => ( P @ Y6 ) )
% 0.29/0.52 => ( P @ X4 ) ) )
% 0.29/0.52 => ( P @ A ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % accp_induct
% 0.29/0.52 thf(fact_398_accp__induct,axiom,
% 0.29/0.52 ! [R2: nat > nat > $o,A: nat,P: nat > $o] :
% 0.29/0.52 ( ( accp_nat @ R2 @ A )
% 0.29/0.52 => ( ! [X4: nat] :
% 0.29/0.52 ( ( accp_nat @ R2 @ X4 )
% 0.29/0.52 => ( ! [Y6: nat] :
% 0.29/0.52 ( ( R2 @ Y6 @ X4 )
% 0.29/0.52 => ( P @ Y6 ) )
% 0.29/0.52 => ( P @ X4 ) ) )
% 0.29/0.52 => ( P @ A ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % accp_induct
% 0.29/0.52 thf(fact_399_accp__downward,axiom,
% 0.29/0.52 ! [R2: product_prod_nat_nat > product_prod_nat_nat > $o,B: product_prod_nat_nat,A: product_prod_nat_nat] :
% 0.29/0.52 ( ( accp_P4275260045618599050at_nat @ R2 @ B )
% 0.29/0.52 => ( ( R2 @ A @ B )
% 0.29/0.52 => ( accp_P4275260045618599050at_nat @ R2 @ A ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % accp_downward
% 0.29/0.52 thf(fact_400_accp__downward,axiom,
% 0.29/0.52 ! [R2: product_prod_int_int > product_prod_int_int > $o,B: product_prod_int_int,A: product_prod_int_int] :
% 0.29/0.52 ( ( accp_P1096762738010456898nt_int @ R2 @ B )
% 0.29/0.52 => ( ( R2 @ A @ B )
% 0.29/0.52 => ( accp_P1096762738010456898nt_int @ R2 @ A ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % accp_downward
% 0.29/0.52 thf(fact_401_accp__downward,axiom,
% 0.29/0.52 ! [R2: produc2732055786443039994et_nat > produc2732055786443039994et_nat > $o,B: produc2732055786443039994et_nat,A: produc2732055786443039994et_nat] :
% 0.29/0.52 ( ( accp_P1862375125659990705et_nat @ R2 @ B )
% 0.29/0.52 => ( ( R2 @ A @ B )
% 0.29/0.52 => ( accp_P1862375125659990705et_nat @ R2 @ A ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % accp_downward
% 0.29/0.52 thf(fact_402_accp__downward,axiom,
% 0.29/0.52 ! [R2: list_nat > list_nat > $o,B: list_nat,A: list_nat] :
% 0.29/0.52 ( ( accp_list_nat @ R2 @ B )
% 0.29/0.52 => ( ( R2 @ A @ B )
% 0.29/0.52 => ( accp_list_nat @ R2 @ A ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % accp_downward
% 0.29/0.52 thf(fact_403_accp__downward,axiom,
% 0.29/0.52 ! [R2: nat > nat > $o,B: nat,A: nat] :
% 0.29/0.52 ( ( accp_nat @ R2 @ B )
% 0.29/0.52 => ( ( R2 @ A @ B )
% 0.29/0.52 => ( accp_nat @ R2 @ A ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % accp_downward
% 0.29/0.52 thf(fact_404_not__accp__down,axiom,
% 0.29/0.52 ! [R4: product_prod_nat_nat > product_prod_nat_nat > $o,X: product_prod_nat_nat] :
% 0.29/0.52 ( ~ ( accp_P4275260045618599050at_nat @ R4 @ X )
% 0.29/0.52 => ~ ! [Z3: product_prod_nat_nat] :
% 0.29/0.52 ( ( R4 @ Z3 @ X )
% 0.29/0.52 => ( accp_P4275260045618599050at_nat @ R4 @ Z3 ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % not_accp_down
% 0.29/0.52 thf(fact_405_not__accp__down,axiom,
% 0.29/0.52 ! [R4: product_prod_int_int > product_prod_int_int > $o,X: product_prod_int_int] :
% 0.29/0.52 ( ~ ( accp_P1096762738010456898nt_int @ R4 @ X )
% 0.29/0.52 => ~ ! [Z3: product_prod_int_int] :
% 0.29/0.52 ( ( R4 @ Z3 @ X )
% 0.29/0.52 => ( accp_P1096762738010456898nt_int @ R4 @ Z3 ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % not_accp_down
% 0.29/0.52 thf(fact_406_not__accp__down,axiom,
% 0.29/0.52 ! [R4: produc2732055786443039994et_nat > produc2732055786443039994et_nat > $o,X: produc2732055786443039994et_nat] :
% 0.29/0.52 ( ~ ( accp_P1862375125659990705et_nat @ R4 @ X )
% 0.29/0.52 => ~ ! [Z3: produc2732055786443039994et_nat] :
% 0.29/0.52 ( ( R4 @ Z3 @ X )
% 0.29/0.52 => ( accp_P1862375125659990705et_nat @ R4 @ Z3 ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % not_accp_down
% 0.29/0.52 thf(fact_407_not__accp__down,axiom,
% 0.29/0.52 ! [R4: list_nat > list_nat > $o,X: list_nat] :
% 0.29/0.52 ( ~ ( accp_list_nat @ R4 @ X )
% 0.29/0.52 => ~ ! [Z3: list_nat] :
% 0.29/0.52 ( ( R4 @ Z3 @ X )
% 0.29/0.52 => ( accp_list_nat @ R4 @ Z3 ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % not_accp_down
% 0.29/0.52 thf(fact_408_not__accp__down,axiom,
% 0.29/0.52 ! [R4: nat > nat > $o,X: nat] :
% 0.29/0.52 ( ~ ( accp_nat @ R4 @ X )
% 0.29/0.52 => ~ ! [Z3: nat] :
% 0.29/0.52 ( ( R4 @ Z3 @ X )
% 0.29/0.52 => ( accp_nat @ R4 @ Z3 ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % not_accp_down
% 0.29/0.52 thf(fact_409_accp__induct__rule,axiom,
% 0.29/0.52 ! [R2: product_prod_nat_nat > product_prod_nat_nat > $o,A: product_prod_nat_nat,P: product_prod_nat_nat > $o] :
% 0.29/0.52 ( ( accp_P4275260045618599050at_nat @ R2 @ A )
% 0.29/0.52 => ( ! [X4: product_prod_nat_nat] :
% 0.29/0.52 ( ( accp_P4275260045618599050at_nat @ R2 @ X4 )
% 0.29/0.52 => ( ! [Y6: product_prod_nat_nat] :
% 0.29/0.52 ( ( R2 @ Y6 @ X4 )
% 0.29/0.52 => ( P @ Y6 ) )
% 0.29/0.52 => ( P @ X4 ) ) )
% 0.29/0.52 => ( P @ A ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % accp_induct_rule
% 0.29/0.52 thf(fact_410_accp__induct__rule,axiom,
% 0.29/0.52 ! [R2: product_prod_int_int > product_prod_int_int > $o,A: product_prod_int_int,P: product_prod_int_int > $o] :
% 0.29/0.52 ( ( accp_P1096762738010456898nt_int @ R2 @ A )
% 0.29/0.52 => ( ! [X4: product_prod_int_int] :
% 0.29/0.52 ( ( accp_P1096762738010456898nt_int @ R2 @ X4 )
% 0.29/0.52 => ( ! [Y6: product_prod_int_int] :
% 0.29/0.52 ( ( R2 @ Y6 @ X4 )
% 0.29/0.52 => ( P @ Y6 ) )
% 0.29/0.52 => ( P @ X4 ) ) )
% 0.29/0.52 => ( P @ A ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % accp_induct_rule
% 0.29/0.52 thf(fact_411_accp__induct__rule,axiom,
% 0.29/0.52 ! [R2: produc2732055786443039994et_nat > produc2732055786443039994et_nat > $o,A: produc2732055786443039994et_nat,P: produc2732055786443039994et_nat > $o] :
% 0.29/0.52 ( ( accp_P1862375125659990705et_nat @ R2 @ A )
% 0.29/0.52 => ( ! [X4: produc2732055786443039994et_nat] :
% 0.29/0.52 ( ( accp_P1862375125659990705et_nat @ R2 @ X4 )
% 0.29/0.52 => ( ! [Y6: produc2732055786443039994et_nat] :
% 0.29/0.52 ( ( R2 @ Y6 @ X4 )
% 0.29/0.52 => ( P @ Y6 ) )
% 0.29/0.52 => ( P @ X4 ) ) )
% 0.29/0.52 => ( P @ A ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % accp_induct_rule
% 0.29/0.52 thf(fact_412_accp__induct__rule,axiom,
% 0.29/0.52 ! [R2: list_nat > list_nat > $o,A: list_nat,P: list_nat > $o] :
% 0.29/0.52 ( ( accp_list_nat @ R2 @ A )
% 0.29/0.52 => ( ! [X4: list_nat] :
% 0.29/0.52 ( ( accp_list_nat @ R2 @ X4 )
% 0.29/0.52 => ( ! [Y6: list_nat] :
% 0.29/0.52 ( ( R2 @ Y6 @ X4 )
% 0.29/0.52 => ( P @ Y6 ) )
% 0.29/0.52 => ( P @ X4 ) ) )
% 0.29/0.52 => ( P @ A ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % accp_induct_rule
% 0.29/0.52 thf(fact_413_accp__induct__rule,axiom,
% 0.29/0.52 ! [R2: nat > nat > $o,A: nat,P: nat > $o] :
% 0.29/0.52 ( ( accp_nat @ R2 @ A )
% 0.29/0.52 => ( ! [X4: nat] :
% 0.29/0.52 ( ( accp_nat @ R2 @ X4 )
% 0.29/0.52 => ( ! [Y6: nat] :
% 0.29/0.52 ( ( R2 @ Y6 @ X4 )
% 0.29/0.52 => ( P @ Y6 ) )
% 0.29/0.52 => ( P @ X4 ) ) )
% 0.29/0.52 => ( P @ A ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % accp_induct_rule
% 0.29/0.52 thf(fact_414_fun_Omap__comp,axiom,
% 0.29/0.52 ! [G: num > num,F: nat > num,V: int > nat] :
% 0.29/0.52 ( ( comp_num_num_int @ G @ ( comp_nat_num_int @ F @ V ) )
% 0.29/0.52 = ( comp_nat_num_int @ ( comp_num_num_nat @ G @ F ) @ V ) ) ).
% 0.29/0.52
% 0.29/0.52 % fun.map_comp
% 0.29/0.52 thf(fact_415_fun_Omap__comp,axiom,
% 0.29/0.52 ! [G: code_integer > code_integer,F: num > code_integer,V: num > num] :
% 0.29/0.52 ( ( comp_C3531382070062128313er_num @ G @ ( comp_n6909714581898973814er_num @ F @ V ) )
% 0.29/0.52 = ( comp_n6909714581898973814er_num @ ( comp_C3531382070062128313er_num @ G @ F ) @ V ) ) ).
% 0.29/0.52
% 0.29/0.52 % fun.map_comp
% 0.29/0.52 thf(fact_416_fun_Omap__comp,axiom,
% 0.29/0.52 ! [G: code_integer > code_integer,F: code_integer > code_integer,V: num > code_integer] :
% 0.29/0.52 ( ( comp_C3531382070062128313er_num @ G @ ( comp_C3531382070062128313er_num @ F @ V ) )
% 0.29/0.52 = ( comp_C3531382070062128313er_num @ ( comp_C7449957260575251196nteger @ G @ F ) @ V ) ) ).
% 0.29/0.52
% 0.29/0.52 % fun.map_comp
% 0.29/0.52 thf(fact_417_fun_Omap__comp,axiom,
% 0.29/0.52 ! [G: nat > num,F: int > nat,V: int > int] :
% 0.29/0.52 ( ( comp_nat_num_int @ G @ ( comp_int_nat_int @ F @ V ) )
% 0.29/0.52 = ( comp_int_num_int @ ( comp_nat_num_int @ G @ F ) @ V ) ) ).
% 0.29/0.52
% 0.29/0.52 % fun.map_comp
% 0.29/0.52 thf(fact_418_fun_Omap__comp,axiom,
% 0.29/0.52 ! [G: nat > num,F: nat > nat,V: int > nat] :
% 0.29/0.52 ( ( comp_nat_num_int @ G @ ( comp_nat_nat_int @ F @ V ) )
% 0.29/0.52 = ( comp_nat_num_int @ ( comp_nat_num_nat @ G @ F ) @ V ) ) ).
% 0.29/0.52
% 0.29/0.52 % fun.map_comp
% 0.29/0.52 thf(fact_419_fun_Omap__comp,axiom,
% 0.29/0.52 ! [G: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,F: code_integer > code_integer,V: num > code_integer] :
% 0.29/0.52 ( ( comp_C6617437204949736321er_num @ G @ ( comp_C3531382070062128313er_num @ F @ V ) )
% 0.29/0.52 = ( comp_C6617437204949736321er_num @ ( comp_C1593894019821074884nteger @ G @ F ) @ V ) ) ).
% 0.29/0.52
% 0.29/0.52 % fun.map_comp
% 0.29/0.52 thf(fact_420_fun_Omap__comp,axiom,
% 0.29/0.52 ! [G: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,F: code_integer > code_integer,V: code_integer > code_integer] :
% 0.29/0.52 ( ( comp_C1593894019821074884nteger @ G @ ( comp_C7449957260575251196nteger @ F @ V ) )
% 0.29/0.52 = ( comp_C1593894019821074884nteger @ ( comp_C1593894019821074884nteger @ G @ F ) @ V ) ) ).
% 0.29/0.52
% 0.29/0.52 % fun.map_comp
% 0.29/0.52 thf(fact_421_fun_Omap__comp,axiom,
% 0.29/0.52 ! [G: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,F: ( code_integer > code_integer ) > code_integer,V: code_integer > code_integer > code_integer] :
% 0.29/0.52 ( ( comp_C1593894019821074884nteger @ G @ ( comp_C5076291335850163704nteger @ F @ V ) )
% 0.29/0.52 = ( comp_C8797469213163452608nteger @ ( comp_C95226695241045696nteger @ G @ F ) @ V ) ) ).
% 0.29/0.52
% 0.29/0.52 % fun.map_comp
% 0.29/0.52 thf(fact_422_fun_Omap__comp,axiom,
% 0.29/0.52 ! [G: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,F: code_integer > code_integer > code_integer,V: code_integer > code_integer] :
% 0.29/0.52 ( ( comp_C8797469213163452608nteger @ G @ ( comp_C2931745410781319416nteger @ F @ V ) )
% 0.29/0.52 = ( comp_C1593894019821074884nteger @ ( comp_C8797469213163452608nteger @ G @ F ) @ V ) ) ).
% 0.29/0.52
% 0.29/0.52 % fun.map_comp
% 0.29/0.52 thf(fact_423_fun_Omap__comp,axiom,
% 0.29/0.52 ! [G: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,F: ( code_integer > code_integer ) > code_integer > code_integer,V: code_integer > code_integer > code_integer] :
% 0.29/0.52 ( ( comp_C8797469213163452608nteger @ G @ ( comp_C2822359487432382964nteger @ F @ V ) )
% 0.29/0.52 = ( comp_C8797469213163452608nteger @ ( comp_C3983183376822107068nteger @ G @ F ) @ V ) ) ).
% 0.29/0.52
% 0.29/0.52 % fun.map_comp
% 0.29/0.52 thf(fact_424_comp__cong,axiom,
% 0.29/0.52 ! [F: code_integer > code_integer,G: num > code_integer,X: num,F4: code_integer > code_integer,G3: num > code_integer,X7: num] :
% 0.29/0.52 ( ( ( F @ ( G @ X ) )
% 0.29/0.52 = ( F4 @ ( G3 @ X7 ) ) )
% 0.29/0.52 => ( ( comp_C3531382070062128313er_num @ F @ G @ X )
% 0.29/0.52 = ( comp_C3531382070062128313er_num @ F4 @ G3 @ X7 ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % comp_cong
% 0.29/0.52 thf(fact_425_comp__cong,axiom,
% 0.29/0.52 ! [F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer,X: code_integer,F4: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,G3: code_integer > code_integer,X7: code_integer] :
% 0.29/0.52 ( ( ( F @ ( G @ X ) )
% 0.29/0.52 = ( F4 @ ( G3 @ X7 ) ) )
% 0.29/0.52 => ( ( comp_C1593894019821074884nteger @ F @ G @ X )
% 0.29/0.52 = ( comp_C1593894019821074884nteger @ F4 @ G3 @ X7 ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % comp_cong
% 0.29/0.52 thf(fact_426_comp__cong,axiom,
% 0.29/0.52 ! [F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer,X: code_integer,F4: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G3: code_integer > code_integer > code_integer,X7: code_integer] :
% 0.29/0.52 ( ( ( F @ ( G @ X ) )
% 0.29/0.52 = ( F4 @ ( G3 @ X7 ) ) )
% 0.29/0.52 => ( ( comp_C1593894019821074884nteger @ F @ G @ X )
% 0.29/0.52 = ( comp_C8797469213163452608nteger @ F4 @ G3 @ X7 ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % comp_cong
% 0.29/0.52 thf(fact_427_comp__cong,axiom,
% 0.29/0.52 ! [F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer > code_integer,X: code_integer,F4: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,G3: code_integer > code_integer,X7: code_integer] :
% 0.29/0.52 ( ( ( F @ ( G @ X ) )
% 0.29/0.52 = ( F4 @ ( G3 @ X7 ) ) )
% 0.29/0.52 => ( ( comp_C8797469213163452608nteger @ F @ G @ X )
% 0.29/0.52 = ( comp_C1593894019821074884nteger @ F4 @ G3 @ X7 ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % comp_cong
% 0.29/0.52 thf(fact_428_comp__cong,axiom,
% 0.29/0.52 ! [F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer > code_integer,X: code_integer,F4: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G3: code_integer > code_integer > code_integer,X7: code_integer] :
% 0.29/0.52 ( ( ( F @ ( G @ X ) )
% 0.29/0.52 = ( F4 @ ( G3 @ X7 ) ) )
% 0.29/0.52 => ( ( comp_C8797469213163452608nteger @ F @ G @ X )
% 0.29/0.52 = ( comp_C8797469213163452608nteger @ F4 @ G3 @ X7 ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % comp_cong
% 0.29/0.52 thf(fact_429_comp__cong,axiom,
% 0.29/0.52 ! [F: nat > num,G: int > nat,X: int,F4: nat > num,G3: int > nat,X7: int] :
% 0.29/0.52 ( ( ( F @ ( G @ X ) )
% 0.29/0.52 = ( F4 @ ( G3 @ X7 ) ) )
% 0.29/0.52 => ( ( comp_nat_num_int @ F @ G @ X )
% 0.29/0.52 = ( comp_nat_num_int @ F4 @ G3 @ X7 ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % comp_cong
% 0.29/0.52 thf(fact_430_curryI,axiom,
% 0.29/0.52 ! [F: produc1908205239877642774nteger > $o,A: produc6241069584506657477e_term > option6357759511663192854e_term,B: produc8923325533196201883nteger] :
% 0.29/0.52 ( ( F @ ( produc8603105652947943368nteger @ A @ B ) )
% 0.29/0.52 => ( produc1217013493180205570eger_o @ F @ A @ B ) ) ).
% 0.29/0.52
% 0.29/0.52 % curryI
% 0.29/0.52 thf(fact_431_curryI,axiom,
% 0.29/0.52 ! [F: produc3925858234332021118et_nat > $o,A: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat] :
% 0.29/0.52 ( ( F @ ( produc5001842942810119800et_nat @ A @ B ) )
% 0.29/0.52 => ( produc6216949301066131538_nat_o @ F @ A @ B ) ) ).
% 0.29/0.52
% 0.29/0.52 % curryI
% 0.29/0.52 thf(fact_432_curryI,axiom,
% 0.29/0.52 ! [F: produc2732055786443039994et_nat > $o,A: produc3658429121746597890et_nat > $o,B: produc3925858234332021118et_nat] :
% 0.29/0.52 ( ( F @ ( produc2245416461498447860et_nat @ A @ B ) )
% 0.29/0.52 => ( produc5101573711933517782_nat_o @ F @ A @ B ) ) ).
% 0.29/0.52
% 0.29/0.52 % curryI
% 0.29/0.52 thf(fact_433_curryI,axiom,
% 0.29/0.52 ! [F: produc2285326912895808259nt_int > $o,A: produc8551481072490612790e_term > option6357759511663192854e_term,B: product_prod_int_int] :
% 0.29/0.52 ( ( F @ ( produc5700946648718959541nt_int @ A @ B ) )
% 0.29/0.52 => ( produc730925184835016917_int_o @ F @ A @ B ) ) ).
% 0.29/0.52
% 0.29/0.52 % curryI
% 0.29/0.52 thf(fact_434_curryI,axiom,
% 0.29/0.52 ! [F: produc7773217078559923341nt_int > $o,A: int > option6357759511663192854e_term,B: product_prod_int_int] :
% 0.29/0.52 ( ( F @ ( produc4305682042979456191nt_int @ A @ B ) )
% 0.29/0.52 => ( produc9098658269643458507_int_o @ F @ A @ B ) ) ).
% 0.29/0.52
% 0.29/0.52 % curryI
% 0.29/0.52 thf(fact_435_curryE,axiom,
% 0.29/0.52 ! [F: produc1908205239877642774nteger > $o,A: produc6241069584506657477e_term > option6357759511663192854e_term,B: produc8923325533196201883nteger] :
% 0.29/0.52 ( ( produc1217013493180205570eger_o @ F @ A @ B )
% 0.29/0.52 => ( F @ ( produc8603105652947943368nteger @ A @ B ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % curryE
% 0.29/0.52 thf(fact_436_curryE,axiom,
% 0.29/0.52 ! [F: produc3925858234332021118et_nat > $o,A: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat] :
% 0.29/0.52 ( ( produc6216949301066131538_nat_o @ F @ A @ B )
% 0.29/0.52 => ( F @ ( produc5001842942810119800et_nat @ A @ B ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % curryE
% 0.29/0.52 thf(fact_437_curryE,axiom,
% 0.29/0.52 ! [F: produc2732055786443039994et_nat > $o,A: produc3658429121746597890et_nat > $o,B: produc3925858234332021118et_nat] :
% 0.29/0.52 ( ( produc5101573711933517782_nat_o @ F @ A @ B )
% 0.29/0.52 => ( F @ ( produc2245416461498447860et_nat @ A @ B ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % curryE
% 0.29/0.52 thf(fact_438_curryE,axiom,
% 0.29/0.52 ! [F: produc2285326912895808259nt_int > $o,A: produc8551481072490612790e_term > option6357759511663192854e_term,B: product_prod_int_int] :
% 0.29/0.52 ( ( produc730925184835016917_int_o @ F @ A @ B )
% 0.29/0.52 => ( F @ ( produc5700946648718959541nt_int @ A @ B ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % curryE
% 0.29/0.52 thf(fact_439_curryE,axiom,
% 0.29/0.52 ! [F: produc7773217078559923341nt_int > $o,A: int > option6357759511663192854e_term,B: product_prod_int_int] :
% 0.29/0.52 ( ( produc9098658269643458507_int_o @ F @ A @ B )
% 0.29/0.52 => ( F @ ( produc4305682042979456191nt_int @ A @ B ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % curryE
% 0.29/0.52 thf(fact_440_curryD,axiom,
% 0.29/0.52 ! [F: produc1908205239877642774nteger > $o,A: produc6241069584506657477e_term > option6357759511663192854e_term,B: produc8923325533196201883nteger] :
% 0.29/0.52 ( ( produc1217013493180205570eger_o @ F @ A @ B )
% 0.29/0.52 => ( F @ ( produc8603105652947943368nteger @ A @ B ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % curryD
% 0.29/0.52 thf(fact_441_curryD,axiom,
% 0.29/0.52 ! [F: produc3925858234332021118et_nat > $o,A: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat] :
% 0.29/0.52 ( ( produc6216949301066131538_nat_o @ F @ A @ B )
% 0.29/0.52 => ( F @ ( produc5001842942810119800et_nat @ A @ B ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % curryD
% 0.29/0.52 thf(fact_442_curryD,axiom,
% 0.29/0.52 ! [F: produc2732055786443039994et_nat > $o,A: produc3658429121746597890et_nat > $o,B: produc3925858234332021118et_nat] :
% 0.29/0.52 ( ( produc5101573711933517782_nat_o @ F @ A @ B )
% 0.29/0.52 => ( F @ ( produc2245416461498447860et_nat @ A @ B ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % curryD
% 0.29/0.52 thf(fact_443_curryD,axiom,
% 0.29/0.52 ! [F: produc2285326912895808259nt_int > $o,A: produc8551481072490612790e_term > option6357759511663192854e_term,B: product_prod_int_int] :
% 0.29/0.52 ( ( produc730925184835016917_int_o @ F @ A @ B )
% 0.29/0.52 => ( F @ ( produc5700946648718959541nt_int @ A @ B ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % curryD
% 0.29/0.52 thf(fact_444_curryD,axiom,
% 0.29/0.52 ! [F: produc7773217078559923341nt_int > $o,A: int > option6357759511663192854e_term,B: product_prod_int_int] :
% 0.29/0.52 ( ( produc9098658269643458507_int_o @ F @ A @ B )
% 0.29/0.52 => ( F @ ( produc4305682042979456191nt_int @ A @ B ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % curryD
% 0.29/0.52 thf(fact_445_in__lex__prod,axiom,
% 0.29/0.52 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,A4: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat,R2: set_Pr4329608150637261639at_nat,S: set_Pr4329608150637261639at_nat] :
% 0.29/0.52 ( ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ ( produc2922128104949294807at_nat @ A @ B ) @ ( produc2922128104949294807at_nat @ A4 @ B3 ) ) @ ( lex_pr8000699672184251119at_nat @ R2 @ S ) )
% 0.29/0.52 = ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ A4 ) @ R2 )
% 0.29/0.52 | ( ( A = A4 )
% 0.29/0.52 & ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ B @ B3 ) @ S ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % in_lex_prod
% 0.29/0.52 thf(fact_446_in__lex__prod,axiom,
% 0.29/0.52 ! [A: set_Pr1261947904930325089at_nat,B: nat,A4: set_Pr1261947904930325089at_nat,B3: nat,R2: set_Pr4329608150637261639at_nat,S: set_Pr1261947904930325089at_nat] :
% 0.29/0.52 ( ( member3480088626692287306at_nat @ ( produc3585720979125124569at_nat @ ( produc3149970401713881818at_nat @ A @ B ) @ ( produc3149970401713881818at_nat @ A4 @ B3 ) ) @ ( lex_pr1951919194703979714at_nat @ R2 @ S ) )
% 0.29/0.52 = ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ A4 ) @ R2 )
% 0.29/0.52 | ( ( A = A4 )
% 0.29/0.52 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ B @ B3 ) @ S ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % in_lex_prod
% 0.29/0.52 thf(fact_447_in__lex__prod,axiom,
% 0.29/0.52 ! [A: nat,B: set_Pr1261947904930325089at_nat,A4: nat,B3: set_Pr1261947904930325089at_nat,R2: set_Pr1261947904930325089at_nat,S: set_Pr4329608150637261639at_nat] :
% 0.29/0.52 ( ( member4107301959146914710at_nat @ ( produc8824474337961625893at_nat @ ( produc5463602008962177208at_nat @ A @ B ) @ ( produc5463602008962177208at_nat @ A4 @ B3 ) ) @ ( lex_pr4265550801952275104at_nat @ R2 @ S ) )
% 0.29/0.52 = ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ A4 ) @ R2 )
% 0.29/0.52 | ( ( A = A4 )
% 0.29/0.52 & ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ B @ B3 ) @ S ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % in_lex_prod
% 0.29/0.52 thf(fact_448_in__lex__prod,axiom,
% 0.29/0.52 ! [A: nat,B: nat,A4: nat,B3: nat,R2: set_Pr1261947904930325089at_nat,S: set_Pr1261947904930325089at_nat] :
% 0.29/0.52 ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A @ B ) @ ( product_Pair_nat_nat @ A4 @ B3 ) ) @ ( lex_prod_nat_nat @ R2 @ S ) )
% 0.29/0.52 = ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ A4 ) @ R2 )
% 0.29/0.52 | ( ( A = A4 )
% 0.29/0.52 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ B @ B3 ) @ S ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % in_lex_prod
% 0.29/0.52 thf(fact_449_in__lex__prod,axiom,
% 0.29/0.52 ! [A: produc6241069584506657477e_term > option6357759511663192854e_term,B: produc8923325533196201883nteger,A4: produc6241069584506657477e_term > option6357759511663192854e_term,B3: produc8923325533196201883nteger,R2: set_Pr6418322821503574069e_term,S: set_Pr5052581263052047815nteger] :
% 0.29/0.52 ( ( member2446009503569356342nteger @ ( produc7954516348491987909nteger @ ( produc8603105652947943368nteger @ A @ B ) @ ( produc8603105652947943368nteger @ A4 @ B3 ) ) @ ( lex_pr3763927252266284464nteger @ R2 @ S ) )
% 0.29/0.52 = ( ( member6786453453753086846e_term @ ( produc6915061378690470669e_term @ A @ A4 ) @ R2 )
% 0.29/0.52 | ( ( A = A4 )
% 0.29/0.52 & ( member335077259223437328nteger @ ( produc4911887526399440471nteger @ B @ B3 ) @ S ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % in_lex_prod
% 0.29/0.52 thf(fact_450_in__lex__prod,axiom,
% 0.29/0.52 ! [A: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat,A4: produc3658429121746597890et_nat > $o,B3: produc3658429121746597890et_nat,R2: set_Pr2161125870931222855_nat_o,S: set_Pr719794911490849221et_nat] :
% 0.29/0.52 ( ( member4763271486408492550et_nat @ ( produc8599840265553166229et_nat @ ( produc5001842942810119800et_nat @ A @ B ) @ ( produc5001842942810119800et_nat @ A4 @ B3 ) ) @ ( lex_pr5340572901959109728et_nat @ R2 @ S ) )
% 0.29/0.52 = ( ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ A @ A4 ) @ R2 )
% 0.29/0.52 | ( ( A = A4 )
% 0.29/0.52 & ( member6099555550032318734et_nat @ ( produc8199053930788261021et_nat @ B @ B3 ) @ S ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % in_lex_prod
% 0.29/0.52 thf(fact_451_in__lex__prod,axiom,
% 0.29/0.52 ! [A: produc3658429121746597890et_nat > $o,B: produc3925858234332021118et_nat,A4: produc3658429121746597890et_nat > $o,B3: produc3925858234332021118et_nat,R2: set_Pr2161125870931222855_nat_o,S: set_Pr7928877670098842301et_nat] :
% 0.29/0.52 ( ( member6341495586645257982et_nat @ ( produc1940133919992309389et_nat @ ( produc2245416461498447860et_nat @ A @ B ) @ ( produc2245416461498447860et_nat @ A4 @ B3 ) ) @ ( lex_pr4722427456421979612et_nat @ R2 @ S ) )
% 0.29/0.52 = ( ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ A @ A4 ) @ R2 )
% 0.29/0.52 | ( ( A = A4 )
% 0.29/0.52 & ( member4763271486408492550et_nat @ ( produc8599840265553166229et_nat @ B @ B3 ) @ S ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % in_lex_prod
% 0.29/0.52 thf(fact_452_in__lex__prod,axiom,
% 0.29/0.52 ! [A: produc8551481072490612790e_term > option6357759511663192854e_term,B: product_prod_int_int,A4: produc8551481072490612790e_term > option6357759511663192854e_term,B3: product_prod_int_int,R2: set_Pr4675205556198584599e_term,S: set_Pr2560585780119916871nt_int] :
% 0.29/0.52 ( ( member6582457606847315088nt_int @ ( produc7601053194514725023nt_int @ ( produc5700946648718959541nt_int @ A @ B ) @ ( produc5700946648718959541nt_int @ A4 @ B3 ) ) @ ( lex_pr4548132154224949661nt_int @ R2 @ S ) )
% 0.29/0.52 = ( ( member8796044733138646368e_term @ ( produc8124735558134971759e_term @ A @ A4 ) @ R2 )
% 0.29/0.52 | ( ( A = A4 )
% 0.29/0.52 & ( member8566619992076573584nt_int @ ( produc3646306378393792727nt_int @ B @ B3 ) @ S ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % in_lex_prod
% 0.29/0.52 thf(fact_453_in__lex__prod,axiom,
% 0.29/0.52 ! [A: int > option6357759511663192854e_term,B: product_prod_int_int,A4: int > option6357759511663192854e_term,B3: product_prod_int_int,R2: set_Pr7140365069852192003e_term,S: set_Pr2560585780119916871nt_int] :
% 0.29/0.52 ( ( member4085533954029916580nt_int @ ( produc8406175334058502835nt_int @ ( produc4305682042979456191nt_int @ A @ B ) @ ( produc4305682042979456191nt_int @ A4 @ B3 ) ) @ ( lex_pr7234932505866811047nt_int @ R2 @ S ) )
% 0.29/0.52 = ( ( member6538663773838357324e_term @ ( produc4510790414113558107e_term @ A @ A4 ) @ R2 )
% 0.29/0.52 | ( ( A = A4 )
% 0.29/0.52 & ( member8566619992076573584nt_int @ ( produc3646306378393792727nt_int @ B @ B3 ) @ S ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % in_lex_prod
% 0.29/0.52 thf(fact_454_rewriteR__comp__comp2,axiom,
% 0.29/0.52 ! [G: int > nat,H3: int > int,R1: nat > nat,R22: int > nat,F: nat > num,L: nat > num] :
% 0.29/0.52 ( ( ( comp_int_nat_int @ G @ H3 )
% 0.29/0.52 = ( comp_nat_nat_int @ R1 @ R22 ) )
% 0.29/0.52 => ( ( ( comp_nat_num_nat @ F @ R1 )
% 0.29/0.52 = L )
% 0.29/0.52 => ( ( comp_int_num_int @ ( comp_nat_num_int @ F @ G ) @ H3 )
% 0.29/0.52 = ( comp_nat_num_int @ L @ R22 ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % rewriteR_comp_comp2
% 0.29/0.52 thf(fact_455_rewriteR__comp__comp2,axiom,
% 0.29/0.52 ! [G: nat > nat,H3: int > nat,R1: int > nat,R22: int > int,F: nat > num,L: int > num] :
% 0.29/0.52 ( ( ( comp_nat_nat_int @ G @ H3 )
% 0.29/0.52 = ( comp_int_nat_int @ R1 @ R22 ) )
% 0.29/0.52 => ( ( ( comp_nat_num_int @ F @ R1 )
% 0.29/0.52 = L )
% 0.29/0.52 => ( ( comp_nat_num_int @ ( comp_nat_num_nat @ F @ G ) @ H3 )
% 0.29/0.52 = ( comp_int_num_int @ L @ R22 ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % rewriteR_comp_comp2
% 0.29/0.52 thf(fact_456_rewriteR__comp__comp2,axiom,
% 0.29/0.52 ! [G: num > code_integer,H3: num > num,R1: code_integer > code_integer,R22: num > code_integer,F: code_integer > code_integer,L: code_integer > code_integer] :
% 0.29/0.52 ( ( ( comp_n6909714581898973814er_num @ G @ H3 )
% 0.29/0.52 = ( comp_C3531382070062128313er_num @ R1 @ R22 ) )
% 0.29/0.52 => ( ( ( comp_C7449957260575251196nteger @ F @ R1 )
% 0.29/0.52 = L )
% 0.29/0.52 => ( ( comp_n6909714581898973814er_num @ ( comp_C3531382070062128313er_num @ F @ G ) @ H3 )
% 0.29/0.52 = ( comp_C3531382070062128313er_num @ L @ R22 ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % rewriteR_comp_comp2
% 0.29/0.52 thf(fact_457_rewriteR__comp__comp2,axiom,
% 0.29/0.52 ! [G: code_integer > code_integer,H3: num > code_integer,R1: num > code_integer,R22: num > num,F: code_integer > code_integer,L: num > code_integer] :
% 0.29/0.52 ( ( ( comp_C3531382070062128313er_num @ G @ H3 )
% 0.29/0.52 = ( comp_n6909714581898973814er_num @ R1 @ R22 ) )
% 0.29/0.52 => ( ( ( comp_C3531382070062128313er_num @ F @ R1 )
% 0.29/0.52 = L )
% 0.29/0.52 => ( ( comp_C3531382070062128313er_num @ ( comp_C7449957260575251196nteger @ F @ G ) @ H3 )
% 0.29/0.52 = ( comp_n6909714581898973814er_num @ L @ R22 ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % rewriteR_comp_comp2
% 0.29/0.52 thf(fact_458_rewriteR__comp__comp2,axiom,
% 0.29/0.52 ! [G: code_integer > code_integer,H3: num > code_integer,R1: code_integer > code_integer,R22: num > code_integer,F: code_integer > code_integer,L: code_integer > code_integer] :
% 0.29/0.52 ( ( ( comp_C3531382070062128313er_num @ G @ H3 )
% 0.29/0.52 = ( comp_C3531382070062128313er_num @ R1 @ R22 ) )
% 0.29/0.52 => ( ( ( comp_C7449957260575251196nteger @ F @ R1 )
% 0.29/0.52 = L )
% 0.29/0.52 => ( ( comp_C3531382070062128313er_num @ ( comp_C7449957260575251196nteger @ F @ G ) @ H3 )
% 0.29/0.52 = ( comp_C3531382070062128313er_num @ L @ R22 ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % rewriteR_comp_comp2
% 0.29/0.52 thf(fact_459_rewriteR__comp__comp2,axiom,
% 0.29/0.52 ! [G: nat > num,H3: int > nat,R1: nat > num,R22: int > nat,F: num > num,L: nat > num] :
% 0.29/0.52 ( ( ( comp_nat_num_int @ G @ H3 )
% 0.29/0.52 = ( comp_nat_num_int @ R1 @ R22 ) )
% 0.29/0.52 => ( ( ( comp_num_num_nat @ F @ R1 )
% 0.29/0.52 = L )
% 0.29/0.52 => ( ( comp_nat_num_int @ ( comp_num_num_nat @ F @ G ) @ H3 )
% 0.29/0.52 = ( comp_nat_num_int @ L @ R22 ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % rewriteR_comp_comp2
% 0.29/0.52 thf(fact_460_rewriteR__comp__comp2,axiom,
% 0.29/0.52 ! [G: code_integer > code_integer,H3: code_integer > code_integer,R1: code_integer > code_integer,R22: code_integer > code_integer,F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,L: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 0.29/0.52 ( ( ( comp_C7449957260575251196nteger @ G @ H3 )
% 0.29/0.52 = ( comp_C7449957260575251196nteger @ R1 @ R22 ) )
% 0.29/0.52 => ( ( ( comp_C1593894019821074884nteger @ F @ R1 )
% 0.29/0.52 = L )
% 0.29/0.52 => ( ( comp_C1593894019821074884nteger @ ( comp_C1593894019821074884nteger @ F @ G ) @ H3 )
% 0.29/0.52 = ( comp_C1593894019821074884nteger @ L @ R22 ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % rewriteR_comp_comp2
% 0.29/0.52 thf(fact_461_rewriteR__comp__comp2,axiom,
% 0.29/0.52 ! [G: code_integer > code_integer,H3: num > code_integer,R1: code_integer > code_integer,R22: num > code_integer,F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,L: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 0.29/0.52 ( ( ( comp_C3531382070062128313er_num @ G @ H3 )
% 0.29/0.52 = ( comp_C3531382070062128313er_num @ R1 @ R22 ) )
% 0.29/0.52 => ( ( ( comp_C1593894019821074884nteger @ F @ R1 )
% 0.29/0.52 = L )
% 0.29/0.52 => ( ( comp_C6617437204949736321er_num @ ( comp_C1593894019821074884nteger @ F @ G ) @ H3 )
% 0.29/0.52 = ( comp_C6617437204949736321er_num @ L @ R22 ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % rewriteR_comp_comp2
% 0.29/0.52 thf(fact_462_rewriteR__comp__comp2,axiom,
% 0.29/0.52 ! [G: code_integer > code_integer,H3: code_integer > code_integer,R1: ( code_integer > code_integer ) > code_integer,R22: code_integer > code_integer > code_integer,F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,L: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 0.29/0.52 ( ( ( comp_C7449957260575251196nteger @ G @ H3 )
% 0.29/0.52 = ( comp_C5076291335850163704nteger @ R1 @ R22 ) )
% 0.29/0.52 => ( ( ( comp_C95226695241045696nteger @ F @ R1 )
% 0.29/0.52 = L )
% 0.29/0.52 => ( ( comp_C1593894019821074884nteger @ ( comp_C1593894019821074884nteger @ F @ G ) @ H3 )
% 0.29/0.52 = ( comp_C8797469213163452608nteger @ L @ R22 ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % rewriteR_comp_comp2
% 0.29/0.52 thf(fact_463_rewriteR__comp__comp2,axiom,
% 0.29/0.52 ! [G: ( code_integer > code_integer ) > code_integer,H3: code_integer > code_integer > code_integer,R1: code_integer > code_integer,R22: code_integer > code_integer,F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,L: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 0.29/0.52 ( ( ( comp_C5076291335850163704nteger @ G @ H3 )
% 0.29/0.52 = ( comp_C7449957260575251196nteger @ R1 @ R22 ) )
% 0.29/0.52 => ( ( ( comp_C1593894019821074884nteger @ F @ R1 )
% 0.29/0.52 = L )
% 0.29/0.52 => ( ( comp_C8797469213163452608nteger @ ( comp_C95226695241045696nteger @ F @ G ) @ H3 )
% 0.29/0.52 = ( comp_C1593894019821074884nteger @ L @ R22 ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % rewriteR_comp_comp2
% 0.29/0.52 thf(fact_464_rewriteL__comp__comp2,axiom,
% 0.29/0.52 ! [F: num > num,G: nat > num,L1: nat > num,L2: nat > nat,H3: int > nat,R2: int > nat] :
% 0.29/0.52 ( ( ( comp_num_num_nat @ F @ G )
% 0.29/0.52 = ( comp_nat_num_nat @ L1 @ L2 ) )
% 0.29/0.52 => ( ( ( comp_nat_nat_int @ L2 @ H3 )
% 0.29/0.52 = R2 )
% 0.29/0.52 => ( ( comp_num_num_int @ F @ ( comp_nat_num_int @ G @ H3 ) )
% 0.29/0.52 = ( comp_nat_num_int @ L1 @ R2 ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % rewriteL_comp_comp2
% 0.29/0.52 thf(fact_465_rewriteL__comp__comp2,axiom,
% 0.29/0.52 ! [F: code_integer > code_integer,G: code_integer > code_integer,L1: code_integer > code_integer,L2: code_integer > code_integer,H3: num > code_integer,R2: num > code_integer] :
% 0.29/0.52 ( ( ( comp_C7449957260575251196nteger @ F @ G )
% 0.29/0.52 = ( comp_C7449957260575251196nteger @ L1 @ L2 ) )
% 0.29/0.52 => ( ( ( comp_C3531382070062128313er_num @ L2 @ H3 )
% 0.29/0.52 = R2 )
% 0.29/0.52 => ( ( comp_C3531382070062128313er_num @ F @ ( comp_C3531382070062128313er_num @ G @ H3 ) )
% 0.29/0.52 = ( comp_C3531382070062128313er_num @ L1 @ R2 ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % rewriteL_comp_comp2
% 0.29/0.52 thf(fact_466_rewriteL__comp__comp2,axiom,
% 0.29/0.52 ! [F: nat > num,G: nat > nat,L1: num > num,L2: nat > num,H3: int > nat,R2: int > num] :
% 0.29/0.52 ( ( ( comp_nat_num_nat @ F @ G )
% 0.29/0.52 = ( comp_num_num_nat @ L1 @ L2 ) )
% 0.29/0.52 => ( ( ( comp_nat_num_int @ L2 @ H3 )
% 0.29/0.52 = R2 )
% 0.29/0.52 => ( ( comp_nat_num_int @ F @ ( comp_nat_nat_int @ G @ H3 ) )
% 0.29/0.52 = ( comp_num_num_int @ L1 @ R2 ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % rewriteL_comp_comp2
% 0.29/0.52 thf(fact_467_rewriteL__comp__comp2,axiom,
% 0.29/0.52 ! [F: code_integer > code_integer,G: num > code_integer,L1: code_integer > code_integer,L2: num > code_integer,H3: num > num,R2: num > code_integer] :
% 0.29/0.52 ( ( ( comp_C3531382070062128313er_num @ F @ G )
% 0.29/0.52 = ( comp_C3531382070062128313er_num @ L1 @ L2 ) )
% 0.29/0.52 => ( ( ( comp_n6909714581898973814er_num @ L2 @ H3 )
% 0.29/0.52 = R2 )
% 0.29/0.52 => ( ( comp_C3531382070062128313er_num @ F @ ( comp_n6909714581898973814er_num @ G @ H3 ) )
% 0.29/0.52 = ( comp_C3531382070062128313er_num @ L1 @ R2 ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % rewriteL_comp_comp2
% 0.29/0.52 thf(fact_468_rewriteL__comp__comp2,axiom,
% 0.29/0.52 ! [F: nat > num,G: int > nat,L1: nat > num,L2: int > nat,H3: int > int,R2: int > nat] :
% 0.29/0.52 ( ( ( comp_nat_num_int @ F @ G )
% 0.29/0.52 = ( comp_nat_num_int @ L1 @ L2 ) )
% 0.29/0.52 => ( ( ( comp_int_nat_int @ L2 @ H3 )
% 0.29/0.52 = R2 )
% 0.29/0.52 => ( ( comp_nat_num_int @ F @ ( comp_int_nat_int @ G @ H3 ) )
% 0.29/0.52 = ( comp_nat_num_int @ L1 @ R2 ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % rewriteL_comp_comp2
% 0.29/0.52 thf(fact_469_rewriteL__comp__comp2,axiom,
% 0.29/0.52 ! [F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer,L1: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,L2: code_integer > code_integer,H3: code_integer > code_integer,R2: code_integer > code_integer] :
% 0.29/0.52 ( ( ( comp_C1593894019821074884nteger @ F @ G )
% 0.29/0.52 = ( comp_C1593894019821074884nteger @ L1 @ L2 ) )
% 0.29/0.52 => ( ( ( comp_C7449957260575251196nteger @ L2 @ H3 )
% 0.29/0.52 = R2 )
% 0.29/0.52 => ( ( comp_C1593894019821074884nteger @ F @ ( comp_C7449957260575251196nteger @ G @ H3 ) )
% 0.29/0.52 = ( comp_C1593894019821074884nteger @ L1 @ R2 ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % rewriteL_comp_comp2
% 0.29/0.52 thf(fact_470_rewriteL__comp__comp2,axiom,
% 0.29/0.52 ! [F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer,L1: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,L2: code_integer > code_integer,H3: num > code_integer,R2: num > code_integer] :
% 0.29/0.52 ( ( ( comp_C1593894019821074884nteger @ F @ G )
% 0.29/0.52 = ( comp_C1593894019821074884nteger @ L1 @ L2 ) )
% 0.29/0.52 => ( ( ( comp_C3531382070062128313er_num @ L2 @ H3 )
% 0.29/0.52 = R2 )
% 0.29/0.52 => ( ( comp_C6617437204949736321er_num @ F @ ( comp_C3531382070062128313er_num @ G @ H3 ) )
% 0.29/0.52 = ( comp_C6617437204949736321er_num @ L1 @ R2 ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % rewriteL_comp_comp2
% 0.29/0.52 thf(fact_471_rewriteL__comp__comp2,axiom,
% 0.29/0.52 ! [F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer,L1: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,L2: code_integer > code_integer > code_integer,H3: num > code_integer,R2: num > code_integer > code_integer] :
% 0.29/0.52 ( ( ( comp_C1593894019821074884nteger @ F @ G )
% 0.29/0.52 = ( comp_C8797469213163452608nteger @ L1 @ L2 ) )
% 0.29/0.52 => ( ( ( comp_C3662112809048933045er_num @ L2 @ H3 )
% 0.29/0.52 = R2 )
% 0.29/0.52 => ( ( comp_C6617437204949736321er_num @ F @ ( comp_C3531382070062128313er_num @ G @ H3 ) )
% 0.29/0.52 = ( comp_C8645541002826910333er_num @ L1 @ R2 ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % rewriteL_comp_comp2
% 0.29/0.52 thf(fact_472_rewriteL__comp__comp2,axiom,
% 0.29/0.52 ! [F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer,L1: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,L2: code_integer > code_integer > code_integer,H3: code_integer > code_integer,R2: code_integer > code_integer > code_integer] :
% 0.29/0.52 ( ( ( comp_C1593894019821074884nteger @ F @ G )
% 0.29/0.52 = ( comp_C8797469213163452608nteger @ L1 @ L2 ) )
% 0.29/0.52 => ( ( ( comp_C2931745410781319416nteger @ L2 @ H3 )
% 0.29/0.52 = R2 )
% 0.29/0.52 => ( ( comp_C1593894019821074884nteger @ F @ ( comp_C7449957260575251196nteger @ G @ H3 ) )
% 0.29/0.52 = ( comp_C8797469213163452608nteger @ L1 @ R2 ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % rewriteL_comp_comp2
% 0.29/0.52 thf(fact_473_rewriteL__comp__comp2,axiom,
% 0.29/0.52 ! [F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer > code_integer,L1: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,L2: code_integer > code_integer,H3: code_integer > code_integer,R2: code_integer > code_integer] :
% 0.29/0.52 ( ( ( comp_C8797469213163452608nteger @ F @ G )
% 0.29/0.52 = ( comp_C1593894019821074884nteger @ L1 @ L2 ) )
% 0.29/0.52 => ( ( ( comp_C7449957260575251196nteger @ L2 @ H3 )
% 0.29/0.52 = R2 )
% 0.29/0.52 => ( ( comp_C8797469213163452608nteger @ F @ ( comp_C2931745410781319416nteger @ G @ H3 ) )
% 0.29/0.52 = ( comp_C1593894019821074884nteger @ L1 @ R2 ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % rewriteL_comp_comp2
% 0.29/0.52 thf(fact_474_rewriteR__comp__comp,axiom,
% 0.29/0.52 ! [G: num > code_integer,H3: num > num,R2: num > code_integer,F: code_integer > code_integer] :
% 0.29/0.52 ( ( ( comp_n6909714581898973814er_num @ G @ H3 )
% 0.29/0.52 = R2 )
% 0.29/0.52 => ( ( comp_n6909714581898973814er_num @ ( comp_C3531382070062128313er_num @ F @ G ) @ H3 )
% 0.29/0.52 = ( comp_C3531382070062128313er_num @ F @ R2 ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % rewriteR_comp_comp
% 0.29/0.52 thf(fact_475_rewriteR__comp__comp,axiom,
% 0.29/0.52 ! [G: int > nat,H3: int > int,R2: int > nat,F: nat > num] :
% 0.29/0.52 ( ( ( comp_int_nat_int @ G @ H3 )
% 0.29/0.52 = R2 )
% 0.29/0.52 => ( ( comp_int_num_int @ ( comp_nat_num_int @ F @ G ) @ H3 )
% 0.29/0.52 = ( comp_nat_num_int @ F @ R2 ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % rewriteR_comp_comp
% 0.29/0.52 thf(fact_476_rewriteR__comp__comp,axiom,
% 0.29/0.52 ! [G: nat > nat,H3: int > nat,R2: int > nat,F: nat > num] :
% 0.29/0.52 ( ( ( comp_nat_nat_int @ G @ H3 )
% 0.29/0.52 = R2 )
% 0.29/0.52 => ( ( comp_nat_num_int @ ( comp_nat_num_nat @ F @ G ) @ H3 )
% 0.29/0.52 = ( comp_nat_num_int @ F @ R2 ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % rewriteR_comp_comp
% 0.29/0.52 thf(fact_477_rewriteR__comp__comp,axiom,
% 0.29/0.52 ! [G: code_integer > code_integer,H3: num > code_integer,R2: num > code_integer,F: code_integer > code_integer] :
% 0.29/0.52 ( ( ( comp_C3531382070062128313er_num @ G @ H3 )
% 0.29/0.52 = R2 )
% 0.29/0.52 => ( ( comp_C3531382070062128313er_num @ ( comp_C7449957260575251196nteger @ F @ G ) @ H3 )
% 0.29/0.52 = ( comp_C3531382070062128313er_num @ F @ R2 ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % rewriteR_comp_comp
% 0.29/0.52 thf(fact_478_rewriteR__comp__comp,axiom,
% 0.29/0.52 ! [G: nat > num,H3: int > nat,R2: int > num,F: num > num] :
% 0.29/0.52 ( ( ( comp_nat_num_int @ G @ H3 )
% 0.29/0.52 = R2 )
% 0.29/0.52 => ( ( comp_nat_num_int @ ( comp_num_num_nat @ F @ G ) @ H3 )
% 0.29/0.52 = ( comp_num_num_int @ F @ R2 ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % rewriteR_comp_comp
% 0.29/0.52 thf(fact_479_rewriteR__comp__comp,axiom,
% 0.29/0.52 ! [G: code_integer > code_integer,H3: code_integer > code_integer,R2: code_integer > code_integer,F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 0.29/0.52 ( ( ( comp_C7449957260575251196nteger @ G @ H3 )
% 0.29/0.52 = R2 )
% 0.29/0.52 => ( ( comp_C1593894019821074884nteger @ ( comp_C1593894019821074884nteger @ F @ G ) @ H3 )
% 0.29/0.52 = ( comp_C1593894019821074884nteger @ F @ R2 ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % rewriteR_comp_comp
% 0.29/0.52 thf(fact_480_rewriteR__comp__comp,axiom,
% 0.29/0.52 ! [G: code_integer > code_integer,H3: num > code_integer,R2: num > code_integer,F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 0.29/0.52 ( ( ( comp_C3531382070062128313er_num @ G @ H3 )
% 0.29/0.52 = R2 )
% 0.29/0.52 => ( ( comp_C6617437204949736321er_num @ ( comp_C1593894019821074884nteger @ F @ G ) @ H3 )
% 0.29/0.52 = ( comp_C6617437204949736321er_num @ F @ R2 ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % rewriteR_comp_comp
% 0.29/0.52 thf(fact_481_rewriteR__comp__comp,axiom,
% 0.29/0.52 ! [G: code_integer > code_integer > code_integer,H3: code_integer > code_integer,R2: code_integer > code_integer > code_integer,F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 0.29/0.52 ( ( ( comp_C2931745410781319416nteger @ G @ H3 )
% 0.29/0.52 = R2 )
% 0.29/0.52 => ( ( comp_C1593894019821074884nteger @ ( comp_C8797469213163452608nteger @ F @ G ) @ H3 )
% 0.29/0.52 = ( comp_C8797469213163452608nteger @ F @ R2 ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % rewriteR_comp_comp
% 0.29/0.52 thf(fact_482_rewriteR__comp__comp,axiom,
% 0.29/0.52 ! [G: ( code_integer > code_integer ) > code_integer,H3: code_integer > code_integer > code_integer,R2: code_integer > code_integer,F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 0.29/0.52 ( ( ( comp_C5076291335850163704nteger @ G @ H3 )
% 0.29/0.52 = R2 )
% 0.29/0.52 => ( ( comp_C8797469213163452608nteger @ ( comp_C95226695241045696nteger @ F @ G ) @ H3 )
% 0.29/0.52 = ( comp_C1593894019821074884nteger @ F @ R2 ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % rewriteR_comp_comp
% 0.29/0.52 thf(fact_483_rewriteR__comp__comp,axiom,
% 0.29/0.52 ! [G: ( code_integer > code_integer ) > code_integer > code_integer,H3: code_integer > code_integer > code_integer,R2: code_integer > code_integer > code_integer,F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 0.29/0.52 ( ( ( comp_C2822359487432382964nteger @ G @ H3 )
% 0.29/0.52 = R2 )
% 0.29/0.52 => ( ( comp_C8797469213163452608nteger @ ( comp_C3983183376822107068nteger @ F @ G ) @ H3 )
% 0.29/0.52 = ( comp_C8797469213163452608nteger @ F @ R2 ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % rewriteR_comp_comp
% 0.29/0.52 thf(fact_484_rewriteL__comp__comp,axiom,
% 0.29/0.52 ! [F: num > num,G: nat > num,L: nat > num,H3: int > nat] :
% 0.29/0.52 ( ( ( comp_num_num_nat @ F @ G )
% 0.29/0.52 = L )
% 0.29/0.52 => ( ( comp_num_num_int @ F @ ( comp_nat_num_int @ G @ H3 ) )
% 0.29/0.52 = ( comp_nat_num_int @ L @ H3 ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % rewriteL_comp_comp
% 0.29/0.52 thf(fact_485_rewriteL__comp__comp,axiom,
% 0.29/0.52 ! [F: code_integer > code_integer,G: code_integer > code_integer,L: code_integer > code_integer,H3: num > code_integer] :
% 0.29/0.52 ( ( ( comp_C7449957260575251196nteger @ F @ G )
% 0.29/0.52 = L )
% 0.29/0.52 => ( ( comp_C3531382070062128313er_num @ F @ ( comp_C3531382070062128313er_num @ G @ H3 ) )
% 0.29/0.52 = ( comp_C3531382070062128313er_num @ L @ H3 ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % rewriteL_comp_comp
% 0.29/0.52 thf(fact_486_rewriteL__comp__comp,axiom,
% 0.29/0.52 ! [F: nat > num,G: nat > nat,L: nat > num,H3: int > nat] :
% 0.29/0.52 ( ( ( comp_nat_num_nat @ F @ G )
% 0.29/0.52 = L )
% 0.29/0.52 => ( ( comp_nat_num_int @ F @ ( comp_nat_nat_int @ G @ H3 ) )
% 0.29/0.52 = ( comp_nat_num_int @ L @ H3 ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % rewriteL_comp_comp
% 0.29/0.52 thf(fact_487_rewriteL__comp__comp,axiom,
% 0.29/0.52 ! [F: code_integer > code_integer,G: num > code_integer,L: num > code_integer,H3: num > num] :
% 0.29/0.52 ( ( ( comp_C3531382070062128313er_num @ F @ G )
% 0.29/0.52 = L )
% 0.29/0.52 => ( ( comp_C3531382070062128313er_num @ F @ ( comp_n6909714581898973814er_num @ G @ H3 ) )
% 0.29/0.52 = ( comp_n6909714581898973814er_num @ L @ H3 ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % rewriteL_comp_comp
% 0.29/0.52 thf(fact_488_rewriteL__comp__comp,axiom,
% 0.29/0.52 ! [F: nat > num,G: int > nat,L: int > num,H3: int > int] :
% 0.29/0.52 ( ( ( comp_nat_num_int @ F @ G )
% 0.29/0.52 = L )
% 0.29/0.52 => ( ( comp_nat_num_int @ F @ ( comp_int_nat_int @ G @ H3 ) )
% 0.29/0.52 = ( comp_int_num_int @ L @ H3 ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % rewriteL_comp_comp
% 0.29/0.52 thf(fact_489_rewriteL__comp__comp,axiom,
% 0.29/0.52 ! [F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer,L: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,H3: num > code_integer] :
% 0.29/0.52 ( ( ( comp_C1593894019821074884nteger @ F @ G )
% 0.29/0.52 = L )
% 0.29/0.52 => ( ( comp_C6617437204949736321er_num @ F @ ( comp_C3531382070062128313er_num @ G @ H3 ) )
% 0.29/0.52 = ( comp_C6617437204949736321er_num @ L @ H3 ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % rewriteL_comp_comp
% 0.29/0.52 thf(fact_490_rewriteL__comp__comp,axiom,
% 0.29/0.52 ! [F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer,L: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,H3: code_integer > code_integer] :
% 0.29/0.52 ( ( ( comp_C1593894019821074884nteger @ F @ G )
% 0.29/0.52 = L )
% 0.29/0.52 => ( ( comp_C1593894019821074884nteger @ F @ ( comp_C7449957260575251196nteger @ G @ H3 ) )
% 0.29/0.52 = ( comp_C1593894019821074884nteger @ L @ H3 ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % rewriteL_comp_comp
% 0.29/0.52 thf(fact_491_rewriteL__comp__comp,axiom,
% 0.29/0.52 ! [F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,G: ( code_integer > code_integer ) > code_integer,L: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,H3: code_integer > code_integer > code_integer] :
% 0.29/0.52 ( ( ( comp_C95226695241045696nteger @ F @ G )
% 0.29/0.52 = L )
% 0.29/0.52 => ( ( comp_C1593894019821074884nteger @ F @ ( comp_C5076291335850163704nteger @ G @ H3 ) )
% 0.29/0.52 = ( comp_C8797469213163452608nteger @ L @ H3 ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % rewriteL_comp_comp
% 0.29/0.52 thf(fact_492_rewriteL__comp__comp,axiom,
% 0.29/0.52 ! [F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer > code_integer,L: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,H3: code_integer > code_integer] :
% 0.29/0.52 ( ( ( comp_C8797469213163452608nteger @ F @ G )
% 0.29/0.52 = L )
% 0.29/0.52 => ( ( comp_C8797469213163452608nteger @ F @ ( comp_C2931745410781319416nteger @ G @ H3 ) )
% 0.29/0.52 = ( comp_C1593894019821074884nteger @ L @ H3 ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % rewriteL_comp_comp
% 0.29/0.52 thf(fact_493_rewriteL__comp__comp,axiom,
% 0.29/0.52 ! [F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G: ( code_integer > code_integer ) > code_integer > code_integer,L: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,H3: code_integer > code_integer > code_integer] :
% 0.29/0.52 ( ( ( comp_C3983183376822107068nteger @ F @ G )
% 0.29/0.52 = L )
% 0.29/0.52 => ( ( comp_C8797469213163452608nteger @ F @ ( comp_C2822359487432382964nteger @ G @ H3 ) )
% 0.29/0.52 = ( comp_C8797469213163452608nteger @ L @ H3 ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % rewriteL_comp_comp
% 0.29/0.52 thf(fact_494_type__copy__map__cong0,axiom,
% 0.29/0.52 ! [M3: num > code_integer,G: num > num,X: num,N6: code_integer > code_integer,H3: num > code_integer,F: code_integer > code_integer] :
% 0.29/0.52 ( ( ( M3 @ ( G @ X ) )
% 0.29/0.52 = ( N6 @ ( H3 @ X ) ) )
% 0.29/0.52 => ( ( comp_n6909714581898973814er_num @ ( comp_C3531382070062128313er_num @ F @ M3 ) @ G @ X )
% 0.29/0.52 = ( comp_C3531382070062128313er_num @ ( comp_C7449957260575251196nteger @ F @ N6 ) @ H3 @ X ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % type_copy_map_cong0
% 0.29/0.52 thf(fact_495_type__copy__map__cong0,axiom,
% 0.29/0.52 ! [M3: int > nat,G: int > int,X: int,N6: nat > nat,H3: int > nat,F: nat > num] :
% 0.29/0.52 ( ( ( M3 @ ( G @ X ) )
% 0.29/0.52 = ( N6 @ ( H3 @ X ) ) )
% 0.29/0.52 => ( ( comp_int_num_int @ ( comp_nat_num_int @ F @ M3 ) @ G @ X )
% 0.29/0.52 = ( comp_nat_num_int @ ( comp_nat_num_nat @ F @ N6 ) @ H3 @ X ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % type_copy_map_cong0
% 0.29/0.52 thf(fact_496_type__copy__map__cong0,axiom,
% 0.29/0.52 ! [M3: code_integer > code_integer,G: num > code_integer,X: num,N6: num > code_integer,H3: num > num,F: code_integer > code_integer] :
% 0.29/0.52 ( ( ( M3 @ ( G @ X ) )
% 0.29/0.52 = ( N6 @ ( H3 @ X ) ) )
% 0.29/0.52 => ( ( comp_C3531382070062128313er_num @ ( comp_C7449957260575251196nteger @ F @ M3 ) @ G @ X )
% 0.29/0.52 = ( comp_n6909714581898973814er_num @ ( comp_C3531382070062128313er_num @ F @ N6 ) @ H3 @ X ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % type_copy_map_cong0
% 0.29/0.52 thf(fact_497_type__copy__map__cong0,axiom,
% 0.29/0.52 ! [M3: code_integer > code_integer,G: code_integer > code_integer,X: code_integer,N6: code_integer > code_integer,H3: code_integer > code_integer,F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 0.29/0.52 ( ( ( M3 @ ( G @ X ) )
% 0.29/0.52 = ( N6 @ ( H3 @ X ) ) )
% 0.29/0.52 => ( ( comp_C1593894019821074884nteger @ ( comp_C1593894019821074884nteger @ F @ M3 ) @ G @ X )
% 0.29/0.52 = ( comp_C1593894019821074884nteger @ ( comp_C1593894019821074884nteger @ F @ N6 ) @ H3 @ X ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % type_copy_map_cong0
% 0.29/0.52 thf(fact_498_type__copy__map__cong0,axiom,
% 0.29/0.52 ! [M3: code_integer > code_integer,G: code_integer > code_integer,X: code_integer,N6: ( code_integer > code_integer ) > code_integer,H3: code_integer > code_integer > code_integer,F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 0.29/0.52 ( ( ( M3 @ ( G @ X ) )
% 0.29/0.52 = ( N6 @ ( H3 @ X ) ) )
% 0.29/0.52 => ( ( comp_C1593894019821074884nteger @ ( comp_C1593894019821074884nteger @ F @ M3 ) @ G @ X )
% 0.29/0.52 = ( comp_C8797469213163452608nteger @ ( comp_C95226695241045696nteger @ F @ N6 ) @ H3 @ X ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % type_copy_map_cong0
% 0.29/0.52 thf(fact_499_type__copy__map__cong0,axiom,
% 0.29/0.52 ! [M3: code_integer > code_integer > code_integer,G: code_integer > code_integer,X: code_integer,N6: code_integer > code_integer > code_integer,H3: code_integer > code_integer,F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 0.29/0.52 ( ( ( M3 @ ( G @ X ) )
% 0.29/0.52 = ( N6 @ ( H3 @ X ) ) )
% 0.29/0.52 => ( ( comp_C1593894019821074884nteger @ ( comp_C8797469213163452608nteger @ F @ M3 ) @ G @ X )
% 0.29/0.52 = ( comp_C1593894019821074884nteger @ ( comp_C8797469213163452608nteger @ F @ N6 ) @ H3 @ X ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % type_copy_map_cong0
% 0.29/0.52 thf(fact_500_type__copy__map__cong0,axiom,
% 0.29/0.52 ! [M3: code_integer > code_integer > code_integer,G: code_integer > code_integer,X: code_integer,N6: ( code_integer > code_integer ) > code_integer > code_integer,H3: code_integer > code_integer > code_integer,F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 0.29/0.52 ( ( ( M3 @ ( G @ X ) )
% 0.29/0.52 = ( N6 @ ( H3 @ X ) ) )
% 0.29/0.52 => ( ( comp_C1593894019821074884nteger @ ( comp_C8797469213163452608nteger @ F @ M3 ) @ G @ X )
% 0.29/0.52 = ( comp_C8797469213163452608nteger @ ( comp_C3983183376822107068nteger @ F @ N6 ) @ H3 @ X ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % type_copy_map_cong0
% 0.29/0.52 thf(fact_501_type__copy__map__cong0,axiom,
% 0.29/0.52 ! [M3: ( code_integer > code_integer ) > code_integer,G: code_integer > code_integer > code_integer,X: code_integer,N6: code_integer > code_integer,H3: code_integer > code_integer,F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 0.29/0.52 ( ( ( M3 @ ( G @ X ) )
% 0.29/0.52 = ( N6 @ ( H3 @ X ) ) )
% 0.29/0.52 => ( ( comp_C8797469213163452608nteger @ ( comp_C95226695241045696nteger @ F @ M3 ) @ G @ X )
% 0.29/0.52 = ( comp_C1593894019821074884nteger @ ( comp_C1593894019821074884nteger @ F @ N6 ) @ H3 @ X ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % type_copy_map_cong0
% 0.29/0.52 thf(fact_502_type__copy__map__cong0,axiom,
% 0.29/0.52 ! [M3: ( code_integer > code_integer ) > code_integer > code_integer,G: code_integer > code_integer > code_integer,X: code_integer,N6: code_integer > code_integer > code_integer,H3: code_integer > code_integer,F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 0.29/0.52 ( ( ( M3 @ ( G @ X ) )
% 0.29/0.52 = ( N6 @ ( H3 @ X ) ) )
% 0.29/0.52 => ( ( comp_C8797469213163452608nteger @ ( comp_C3983183376822107068nteger @ F @ M3 ) @ G @ X )
% 0.29/0.52 = ( comp_C1593894019821074884nteger @ ( comp_C8797469213163452608nteger @ F @ N6 ) @ H3 @ X ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % type_copy_map_cong0
% 0.29/0.52 thf(fact_503_type__copy__map__cong0,axiom,
% 0.29/0.52 ! [M3: nat > nat,G: int > nat,X: int,N6: int > nat,H3: int > int,F: nat > num] :
% 0.29/0.52 ( ( ( M3 @ ( G @ X ) )
% 0.29/0.52 = ( N6 @ ( H3 @ X ) ) )
% 0.29/0.52 => ( ( comp_nat_num_int @ ( comp_nat_num_nat @ F @ M3 ) @ G @ X )
% 0.29/0.52 = ( comp_int_num_int @ ( comp_nat_num_int @ F @ N6 ) @ H3 @ X ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % type_copy_map_cong0
% 0.29/0.52 thf(fact_504_comp__apply__eq,axiom,
% 0.29/0.52 ! [F: code_integer > code_integer,G: num > code_integer,X: num,H3: code_integer > code_integer,K: num > code_integer] :
% 0.29/0.52 ( ( ( F @ ( G @ X ) )
% 0.29/0.52 = ( H3 @ ( K @ X ) ) )
% 0.29/0.52 => ( ( comp_C3531382070062128313er_num @ F @ G @ X )
% 0.29/0.52 = ( comp_C3531382070062128313er_num @ H3 @ K @ X ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % comp_apply_eq
% 0.29/0.52 thf(fact_505_comp__apply__eq,axiom,
% 0.29/0.52 ! [F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer,X: code_integer,H3: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,K: code_integer > code_integer] :
% 0.29/0.52 ( ( ( F @ ( G @ X ) )
% 0.29/0.52 = ( H3 @ ( K @ X ) ) )
% 0.29/0.52 => ( ( comp_C1593894019821074884nteger @ F @ G @ X )
% 0.29/0.52 = ( comp_C1593894019821074884nteger @ H3 @ K @ X ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % comp_apply_eq
% 0.29/0.52 thf(fact_506_comp__apply__eq,axiom,
% 0.29/0.52 ! [F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer,X: code_integer,H3: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,K: code_integer > code_integer > code_integer] :
% 0.29/0.52 ( ( ( F @ ( G @ X ) )
% 0.29/0.52 = ( H3 @ ( K @ X ) ) )
% 0.29/0.52 => ( ( comp_C1593894019821074884nteger @ F @ G @ X )
% 0.29/0.52 = ( comp_C8797469213163452608nteger @ H3 @ K @ X ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % comp_apply_eq
% 0.29/0.52 thf(fact_507_comp__apply__eq,axiom,
% 0.29/0.52 ! [F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer > code_integer,X: code_integer,H3: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,K: code_integer > code_integer] :
% 0.29/0.52 ( ( ( F @ ( G @ X ) )
% 0.29/0.52 = ( H3 @ ( K @ X ) ) )
% 0.29/0.52 => ( ( comp_C8797469213163452608nteger @ F @ G @ X )
% 0.29/0.52 = ( comp_C1593894019821074884nteger @ H3 @ K @ X ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % comp_apply_eq
% 0.29/0.52 thf(fact_508_comp__apply__eq,axiom,
% 0.29/0.52 ! [F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer > code_integer,X: code_integer,H3: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,K: code_integer > code_integer > code_integer] :
% 0.29/0.52 ( ( ( F @ ( G @ X ) )
% 0.29/0.52 = ( H3 @ ( K @ X ) ) )
% 0.29/0.52 => ( ( comp_C8797469213163452608nteger @ F @ G @ X )
% 0.29/0.52 = ( comp_C8797469213163452608nteger @ H3 @ K @ X ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % comp_apply_eq
% 0.29/0.52 thf(fact_509_comp__apply__eq,axiom,
% 0.29/0.52 ! [F: nat > num,G: int > nat,X: int,H3: nat > num,K: int > nat] :
% 0.29/0.52 ( ( ( F @ ( G @ X ) )
% 0.29/0.52 = ( H3 @ ( K @ X ) ) )
% 0.29/0.52 => ( ( comp_nat_num_int @ F @ G @ X )
% 0.29/0.52 = ( comp_nat_num_int @ H3 @ K @ X ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % comp_apply_eq
% 0.29/0.52 thf(fact_510_add_Oright__commute,axiom,
% 0.29/0.52 ! [A: multis2468970476368604999at_nat,B: multis2468970476368604999at_nat,C: multis2468970476368604999at_nat] :
% 0.29/0.52 ( ( plus_p7104986032573967614at_nat @ ( plus_p7104986032573967614at_nat @ A @ B ) @ C )
% 0.29/0.52 = ( plus_p7104986032573967614at_nat @ ( plus_p7104986032573967614at_nat @ A @ C ) @ B ) ) ).
% 0.29/0.52
% 0.29/0.52 % add.right_commute
% 0.29/0.52 thf(fact_511_add_Oright__commute,axiom,
% 0.29/0.52 ! [A: rat,B: rat,C: rat] :
% 0.29/0.52 ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 0.29/0.52 = ( plus_plus_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ).
% 0.29/0.52
% 0.29/0.52 % add.right_commute
% 0.29/0.52 thf(fact_512_add_Oright__commute,axiom,
% 0.29/0.52 ! [A: nat,B: nat,C: nat] :
% 0.29/0.52 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 0.29/0.52 = ( plus_plus_nat @ ( plus_plus_nat @ A @ C ) @ B ) ) ).
% 0.29/0.52
% 0.29/0.52 % add.right_commute
% 0.29/0.52 thf(fact_513_add_Oright__commute,axiom,
% 0.29/0.52 ! [A: int,B: int,C: int] :
% 0.29/0.52 ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 0.29/0.52 = ( plus_plus_int @ ( plus_plus_int @ A @ C ) @ B ) ) ).
% 0.29/0.52
% 0.29/0.52 % add.right_commute
% 0.29/0.52 thf(fact_514_add__less__cancel__right,axiom,
% 0.29/0.52 ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.29/0.52 ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ C ) @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 0.29/0.52 = ( ord_le6747313008572928689nteger @ A @ B ) ) ).
% 0.29/0.52
% 0.29/0.52 % add_less_cancel_right
% 0.29/0.52 thf(fact_515_add__less__cancel__right,axiom,
% 0.29/0.52 ! [A: rat,C: rat,B: rat] :
% 0.29/0.52 ( ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 0.29/0.52 = ( ord_less_rat @ A @ B ) ) ).
% 0.29/0.52
% 0.29/0.52 % add_less_cancel_right
% 0.29/0.52 thf(fact_516_add__less__cancel__right,axiom,
% 0.29/0.52 ! [A: nat,C: nat,B: nat] :
% 0.29/0.52 ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 0.29/0.52 = ( ord_less_nat @ A @ B ) ) ).
% 0.29/0.52
% 0.29/0.52 % add_less_cancel_right
% 0.29/0.52 thf(fact_517_add__less__cancel__right,axiom,
% 0.29/0.52 ! [A: int,C: int,B: int] :
% 0.29/0.52 ( ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 0.29/0.52 = ( ord_less_int @ A @ B ) ) ).
% 0.29/0.52
% 0.29/0.52 % add_less_cancel_right
% 0.29/0.52 thf(fact_518_add__less__cancel__left,axiom,
% 0.29/0.52 ! [C: code_integer,A: code_integer,B: code_integer] :
% 0.29/0.52 ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ C @ A ) @ ( plus_p5714425477246183910nteger @ C @ B ) )
% 0.29/0.52 = ( ord_le6747313008572928689nteger @ A @ B ) ) ).
% 0.29/0.52
% 0.29/0.52 % add_less_cancel_left
% 0.29/0.52 thf(fact_519_add__less__cancel__left,axiom,
% 0.29/0.52 ! [C: rat,A: rat,B: rat] :
% 0.29/0.52 ( ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 0.29/0.52 = ( ord_less_rat @ A @ B ) ) ).
% 0.29/0.52
% 0.29/0.52 % add_less_cancel_left
% 0.29/0.52 thf(fact_520_add__less__cancel__left,axiom,
% 0.29/0.52 ! [C: nat,A: nat,B: nat] :
% 0.29/0.52 ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 0.29/0.52 = ( ord_less_nat @ A @ B ) ) ).
% 0.29/0.52
% 0.29/0.52 % add_less_cancel_left
% 0.29/0.52 thf(fact_521_add__less__cancel__left,axiom,
% 0.29/0.52 ! [C: int,A: int,B: int] :
% 0.29/0.52 ( ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 0.29/0.52 = ( ord_less_int @ A @ B ) ) ).
% 0.29/0.52
% 0.29/0.52 % add_less_cancel_left
% 0.29/0.52 thf(fact_522_add__less__imp__less__right,axiom,
% 0.29/0.52 ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.29/0.52 ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ C ) @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 0.29/0.52 => ( ord_le6747313008572928689nteger @ A @ B ) ) ).
% 0.29/0.52
% 0.29/0.52 % add_less_imp_less_right
% 0.29/0.52 thf(fact_523_add__less__imp__less__right,axiom,
% 0.29/0.52 ! [A: rat,C: rat,B: rat] :
% 0.29/0.52 ( ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 0.29/0.52 => ( ord_less_rat @ A @ B ) ) ).
% 0.29/0.52
% 0.29/0.52 % add_less_imp_less_right
% 0.29/0.52 thf(fact_524_add__less__imp__less__right,axiom,
% 0.29/0.52 ! [A: nat,C: nat,B: nat] :
% 0.29/0.52 ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 0.29/0.52 => ( ord_less_nat @ A @ B ) ) ).
% 0.29/0.52
% 0.29/0.52 % add_less_imp_less_right
% 0.29/0.52 thf(fact_525_add__less__imp__less__right,axiom,
% 0.29/0.52 ! [A: int,C: int,B: int] :
% 0.29/0.52 ( ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 0.29/0.52 => ( ord_less_int @ A @ B ) ) ).
% 0.29/0.52
% 0.29/0.52 % add_less_imp_less_right
% 0.29/0.52 thf(fact_526_add__less__imp__less__left,axiom,
% 0.29/0.52 ! [C: code_integer,A: code_integer,B: code_integer] :
% 0.29/0.52 ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ C @ A ) @ ( plus_p5714425477246183910nteger @ C @ B ) )
% 0.29/0.52 => ( ord_le6747313008572928689nteger @ A @ B ) ) ).
% 0.29/0.52
% 0.29/0.52 % add_less_imp_less_left
% 0.29/0.52 thf(fact_527_add__less__imp__less__left,axiom,
% 0.29/0.52 ! [C: rat,A: rat,B: rat] :
% 0.29/0.52 ( ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 0.29/0.52 => ( ord_less_rat @ A @ B ) ) ).
% 0.29/0.52
% 0.29/0.52 % add_less_imp_less_left
% 0.29/0.52 thf(fact_528_add__less__imp__less__left,axiom,
% 0.29/0.52 ! [C: nat,A: nat,B: nat] :
% 0.29/0.52 ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 0.29/0.52 => ( ord_less_nat @ A @ B ) ) ).
% 0.29/0.52
% 0.29/0.52 % add_less_imp_less_left
% 0.29/0.52 thf(fact_529_add__less__imp__less__left,axiom,
% 0.29/0.52 ! [C: int,A: int,B: int] :
% 0.29/0.52 ( ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 0.29/0.52 => ( ord_less_int @ A @ B ) ) ).
% 0.29/0.52
% 0.29/0.52 % add_less_imp_less_left
% 0.29/0.52 thf(fact_530_add__strict__right__mono,axiom,
% 0.29/0.52 ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.29/0.52 ( ( ord_le6747313008572928689nteger @ A @ B )
% 0.29/0.52 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ C ) @ ( plus_p5714425477246183910nteger @ B @ C ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % add_strict_right_mono
% 0.29/0.52 thf(fact_531_add__strict__right__mono,axiom,
% 0.29/0.52 ! [A: rat,B: rat,C: rat] :
% 0.29/0.52 ( ( ord_less_rat @ A @ B )
% 0.29/0.52 => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % add_strict_right_mono
% 0.29/0.52 thf(fact_532_add__strict__right__mono,axiom,
% 0.29/0.52 ! [A: nat,B: nat,C: nat] :
% 0.29/0.52 ( ( ord_less_nat @ A @ B )
% 0.29/0.52 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % add_strict_right_mono
% 0.29/0.52 thf(fact_533_add__strict__right__mono,axiom,
% 0.29/0.52 ! [A: int,B: int,C: int] :
% 0.29/0.52 ( ( ord_less_int @ A @ B )
% 0.29/0.52 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % add_strict_right_mono
% 0.29/0.52 thf(fact_534_add__strict__left__mono,axiom,
% 0.29/0.52 ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.29/0.52 ( ( ord_le6747313008572928689nteger @ A @ B )
% 0.29/0.52 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ C @ A ) @ ( plus_p5714425477246183910nteger @ C @ B ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % add_strict_left_mono
% 0.29/0.52 thf(fact_535_add__strict__left__mono,axiom,
% 0.29/0.52 ! [A: rat,B: rat,C: rat] :
% 0.29/0.52 ( ( ord_less_rat @ A @ B )
% 0.29/0.52 => ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % add_strict_left_mono
% 0.29/0.52 thf(fact_536_add__strict__left__mono,axiom,
% 0.29/0.52 ! [A: nat,B: nat,C: nat] :
% 0.29/0.52 ( ( ord_less_nat @ A @ B )
% 0.29/0.52 => ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % add_strict_left_mono
% 0.29/0.52 thf(fact_537_add__strict__left__mono,axiom,
% 0.29/0.52 ! [A: int,B: int,C: int] :
% 0.29/0.52 ( ( ord_less_int @ A @ B )
% 0.29/0.52 => ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % add_strict_left_mono
% 0.29/0.52 thf(fact_538_add__strict__mono,axiom,
% 0.29/0.52 ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 0.29/0.52 ( ( ord_le6747313008572928689nteger @ A @ B )
% 0.29/0.52 => ( ( ord_le6747313008572928689nteger @ C @ D2 )
% 0.29/0.52 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ C ) @ ( plus_p5714425477246183910nteger @ B @ D2 ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % add_strict_mono
% 0.29/0.52 thf(fact_539_add__strict__mono,axiom,
% 0.29/0.52 ! [A: rat,B: rat,C: rat,D2: rat] :
% 0.29/0.52 ( ( ord_less_rat @ A @ B )
% 0.29/0.52 => ( ( ord_less_rat @ C @ D2 )
% 0.29/0.52 => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D2 ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % add_strict_mono
% 0.29/0.52 thf(fact_540_add__strict__mono,axiom,
% 0.29/0.52 ! [A: nat,B: nat,C: nat,D2: nat] :
% 0.29/0.52 ( ( ord_less_nat @ A @ B )
% 0.29/0.52 => ( ( ord_less_nat @ C @ D2 )
% 0.29/0.52 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D2 ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % add_strict_mono
% 0.29/0.52 thf(fact_541_add__strict__mono,axiom,
% 0.29/0.52 ! [A: int,B: int,C: int,D2: int] :
% 0.29/0.52 ( ( ord_less_int @ A @ B )
% 0.29/0.52 => ( ( ord_less_int @ C @ D2 )
% 0.29/0.52 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D2 ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % add_strict_mono
% 0.29/0.52 thf(fact_542_add__mono__thms__linordered__field_I1_J,axiom,
% 0.29/0.52 ! [I: code_integer,J: code_integer,K: code_integer,L: code_integer] :
% 0.29/0.52 ( ( ( ord_le6747313008572928689nteger @ I @ J )
% 0.29/0.52 & ( K = L ) )
% 0.29/0.52 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ I @ K ) @ ( plus_p5714425477246183910nteger @ J @ L ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % add_mono_thms_linordered_field(1)
% 0.29/0.52 thf(fact_543_add__mono__thms__linordered__field_I1_J,axiom,
% 0.29/0.52 ! [I: rat,J: rat,K: rat,L: rat] :
% 0.29/0.52 ( ( ( ord_less_rat @ I @ J )
% 0.29/0.52 & ( K = L ) )
% 0.29/0.52 => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % add_mono_thms_linordered_field(1)
% 0.29/0.52 thf(fact_544_add__mono__thms__linordered__field_I1_J,axiom,
% 0.29/0.52 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.29/0.52 ( ( ( ord_less_nat @ I @ J )
% 0.29/0.52 & ( K = L ) )
% 0.29/0.52 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % add_mono_thms_linordered_field(1)
% 0.29/0.52 thf(fact_545_add__mono__thms__linordered__field_I1_J,axiom,
% 0.29/0.52 ! [I: int,J: int,K: int,L: int] :
% 0.29/0.52 ( ( ( ord_less_int @ I @ J )
% 0.29/0.52 & ( K = L ) )
% 0.29/0.52 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % add_mono_thms_linordered_field(1)
% 0.29/0.52 thf(fact_546_add__mono__thms__linordered__field_I2_J,axiom,
% 0.29/0.52 ! [I: code_integer,J: code_integer,K: code_integer,L: code_integer] :
% 0.29/0.52 ( ( ( I = J )
% 0.29/0.52 & ( ord_le6747313008572928689nteger @ K @ L ) )
% 0.29/0.52 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ I @ K ) @ ( plus_p5714425477246183910nteger @ J @ L ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % add_mono_thms_linordered_field(2)
% 0.29/0.52 thf(fact_547_add__mono__thms__linordered__field_I2_J,axiom,
% 0.29/0.52 ! [I: rat,J: rat,K: rat,L: rat] :
% 0.29/0.52 ( ( ( I = J )
% 0.29/0.52 & ( ord_less_rat @ K @ L ) )
% 0.29/0.52 => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % add_mono_thms_linordered_field(2)
% 0.29/0.52 thf(fact_548_add__mono__thms__linordered__field_I2_J,axiom,
% 0.29/0.52 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.29/0.52 ( ( ( I = J )
% 0.29/0.52 & ( ord_less_nat @ K @ L ) )
% 0.29/0.52 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % add_mono_thms_linordered_field(2)
% 0.29/0.52 thf(fact_549_add__mono__thms__linordered__field_I2_J,axiom,
% 0.29/0.52 ! [I: int,J: int,K: int,L: int] :
% 0.29/0.52 ( ( ( I = J )
% 0.29/0.52 & ( ord_less_int @ K @ L ) )
% 0.29/0.52 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % add_mono_thms_linordered_field(2)
% 0.29/0.52 thf(fact_550_add__mono__thms__linordered__field_I5_J,axiom,
% 0.29/0.52 ! [I: code_integer,J: code_integer,K: code_integer,L: code_integer] :
% 0.29/0.52 ( ( ( ord_le6747313008572928689nteger @ I @ J )
% 0.29/0.52 & ( ord_le6747313008572928689nteger @ K @ L ) )
% 0.29/0.52 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ I @ K ) @ ( plus_p5714425477246183910nteger @ J @ L ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % add_mono_thms_linordered_field(5)
% 0.29/0.52 thf(fact_551_add__mono__thms__linordered__field_I5_J,axiom,
% 0.29/0.52 ! [I: rat,J: rat,K: rat,L: rat] :
% 0.29/0.52 ( ( ( ord_less_rat @ I @ J )
% 0.29/0.52 & ( ord_less_rat @ K @ L ) )
% 0.29/0.52 => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % add_mono_thms_linordered_field(5)
% 0.29/0.52 thf(fact_552_add__mono__thms__linordered__field_I5_J,axiom,
% 0.29/0.52 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.29/0.52 ( ( ( ord_less_nat @ I @ J )
% 0.29/0.52 & ( ord_less_nat @ K @ L ) )
% 0.29/0.52 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % add_mono_thms_linordered_field(5)
% 0.29/0.52 thf(fact_553_add__mono__thms__linordered__field_I5_J,axiom,
% 0.29/0.52 ! [I: int,J: int,K: int,L: int] :
% 0.29/0.52 ( ( ( ord_less_int @ I @ J )
% 0.29/0.52 & ( ord_less_int @ K @ L ) )
% 0.29/0.52 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % add_mono_thms_linordered_field(5)
% 0.29/0.52 thf(fact_554_success__returnI,axiom,
% 0.29/0.52 ! [X: product_unit,H3: heap_e7401611519738050253t_unit] : ( heap_T584514906347983379t_unit @ ( heap_T7507251653302230130t_unit @ X ) @ H3 ) ).
% 0.29/0.52
% 0.29/0.52 % success_returnI
% 0.29/0.52 thf(fact_555_success__returnI,axiom,
% 0.29/0.52 ! [X: array_a,H3: heap_e7401611519738050253t_unit] : ( heap_T6932021131025641745rray_a @ ( heap_T4896204969850773234rray_a @ X ) @ H3 ) ).
% 0.29/0.52
% 0.29/0.52 % success_returnI
% 0.29/0.52 thf(fact_556_fails__return,axiom,
% 0.29/0.52 ! [X: product_unit,H3: heap_e7401611519738050253t_unit] :
% 0.29/0.52 ~ ( time_f8834461667527620124t_unit @ ( heap_T7507251653302230130t_unit @ X ) @ H3 ) ).
% 0.29/0.52
% 0.29/0.52 % fails_return
% 0.29/0.52 thf(fact_557_fails__return,axiom,
% 0.29/0.52 ! [X: array_a,H3: heap_e7401611519738050253t_unit] :
% 0.29/0.52 ~ ( time_fails_array_a @ ( heap_T4896204969850773234rray_a @ X ) @ H3 ) ).
% 0.29/0.52
% 0.29/0.52 % fails_return
% 0.29/0.52 thf(fact_558_add_Oright__assoc,axiom,
% 0.29/0.52 ! [A: multis2468970476368604999at_nat,B: multis2468970476368604999at_nat,C: multis2468970476368604999at_nat] :
% 0.29/0.52 ( ( plus_p7104986032573967614at_nat @ ( plus_p7104986032573967614at_nat @ A @ B ) @ C )
% 0.29/0.52 = ( plus_p7104986032573967614at_nat @ A @ ( plus_p7104986032573967614at_nat @ B @ C ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % add.right_assoc
% 0.29/0.52 thf(fact_559_add_Oright__assoc,axiom,
% 0.29/0.52 ! [A: rat,B: rat,C: rat] :
% 0.29/0.52 ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 0.29/0.52 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % add.right_assoc
% 0.29/0.52 thf(fact_560_add_Oright__assoc,axiom,
% 0.29/0.52 ! [A: nat,B: nat,C: nat] :
% 0.29/0.52 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 0.29/0.52 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % add.right_assoc
% 0.29/0.52 thf(fact_561_add_Oright__assoc,axiom,
% 0.29/0.52 ! [A: int,B: int,C: int] :
% 0.29/0.52 ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 0.29/0.52 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % add.right_assoc
% 0.29/0.52 thf(fact_562_nat__add__left__cancel__less,axiom,
% 0.29/0.52 ! [K: nat,M2: nat,N2: nat] :
% 0.29/0.52 ( ( ord_less_nat @ ( plus_plus_nat @ K @ M2 ) @ ( plus_plus_nat @ K @ N2 ) )
% 0.29/0.52 = ( ord_less_nat @ M2 @ N2 ) ) ).
% 0.29/0.52
% 0.29/0.52 % nat_add_left_cancel_less
% 0.29/0.52 thf(fact_563_less__option__Some,axiom,
% 0.29/0.52 ! [X: code_integer,Y: code_integer] :
% 0.29/0.52 ( ( ord_le7113747843092208513nteger @ ( some_Code_integer @ X ) @ ( some_Code_integer @ Y ) )
% 0.29/0.52 = ( ord_le6747313008572928689nteger @ X @ Y ) ) ).
% 0.29/0.52
% 0.29/0.52 % less_option_Some
% 0.29/0.52 thf(fact_564_less__option__Some,axiom,
% 0.29/0.52 ! [X: rat,Y: rat] :
% 0.29/0.52 ( ( ord_less_option_rat @ ( some_rat @ X ) @ ( some_rat @ Y ) )
% 0.29/0.52 = ( ord_less_rat @ X @ Y ) ) ).
% 0.29/0.52
% 0.29/0.52 % less_option_Some
% 0.29/0.52 thf(fact_565_less__option__Some,axiom,
% 0.29/0.52 ! [X: num,Y: num] :
% 0.29/0.52 ( ( ord_less_option_num @ ( some_num @ X ) @ ( some_num @ Y ) )
% 0.29/0.52 = ( ord_less_num @ X @ Y ) ) ).
% 0.29/0.52
% 0.29/0.52 % less_option_Some
% 0.29/0.52 thf(fact_566_less__option__Some,axiom,
% 0.29/0.52 ! [X: nat,Y: nat] :
% 0.29/0.52 ( ( ord_less_option_nat @ ( some_nat @ X ) @ ( some_nat @ Y ) )
% 0.29/0.52 = ( ord_less_nat @ X @ Y ) ) ).
% 0.29/0.52
% 0.29/0.52 % less_option_Some
% 0.29/0.52 thf(fact_567_less__option__Some,axiom,
% 0.29/0.52 ! [X: int,Y: int] :
% 0.29/0.52 ( ( ord_less_option_int @ ( some_int @ X ) @ ( some_int @ Y ) )
% 0.29/0.52 = ( ord_less_int @ X @ Y ) ) ).
% 0.29/0.52
% 0.29/0.52 % less_option_Some
% 0.29/0.52 thf(fact_568_fold__atLeastAtMost__nat_Opelims,axiom,
% 0.29/0.52 ! [X: nat > nat > nat,Xa: nat,Xb: nat,Xc: nat,Y: nat] :
% 0.29/0.52 ( ( ( set_fo2584398358068434914at_nat @ X @ Xa @ Xb @ Xc )
% 0.29/0.52 = Y )
% 0.29/0.52 => ( ( accp_P6019419558468335806at_nat @ set_fo3699595496184130361el_nat @ ( produc3209952032786966637at_nat @ X @ ( produc487386426758144856at_nat @ Xa @ ( product_Pair_nat_nat @ Xb @ Xc ) ) ) )
% 0.29/0.52 => ~ ( ( ( ( ord_less_nat @ Xb @ Xa )
% 0.29/0.52 => ( Y = Xc ) )
% 0.29/0.52 & ( ~ ( ord_less_nat @ Xb @ Xa )
% 0.29/0.52 => ( Y
% 0.29/0.52 = ( set_fo2584398358068434914at_nat @ X @ ( plus_plus_nat @ Xa @ one_one_nat ) @ Xb @ ( X @ Xa @ Xc ) ) ) ) )
% 0.29/0.52 => ~ ( accp_P6019419558468335806at_nat @ set_fo3699595496184130361el_nat @ ( produc3209952032786966637at_nat @ X @ ( produc487386426758144856at_nat @ Xa @ ( product_Pair_nat_nat @ Xb @ Xc ) ) ) ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % fold_atLeastAtMost_nat.pelims
% 0.29/0.52 thf(fact_569_fold__atLeastAtMost__nat_Opsimps,axiom,
% 0.29/0.52 ! [F: nat > nat > nat,A: nat,B: nat,Acc: nat] :
% 0.29/0.52 ( ( accp_P6019419558468335806at_nat @ set_fo3699595496184130361el_nat @ ( produc3209952032786966637at_nat @ F @ ( produc487386426758144856at_nat @ A @ ( product_Pair_nat_nat @ B @ Acc ) ) ) )
% 0.29/0.52 => ( ( ( ord_less_nat @ B @ A )
% 0.29/0.52 => ( ( set_fo2584398358068434914at_nat @ F @ A @ B @ Acc )
% 0.29/0.52 = Acc ) )
% 0.29/0.52 & ( ~ ( ord_less_nat @ B @ A )
% 0.29/0.52 => ( ( set_fo2584398358068434914at_nat @ F @ A @ B @ Acc )
% 0.29/0.52 = ( set_fo2584398358068434914at_nat @ F @ ( plus_plus_nat @ A @ one_one_nat ) @ B @ ( F @ A @ Acc ) ) ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % fold_atLeastAtMost_nat.psimps
% 0.29/0.52 thf(fact_570_in__measure,axiom,
% 0.29/0.52 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,F: set_Pr1261947904930325089at_nat > nat] :
% 0.29/0.52 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ ( measur1827424007717751593at_nat @ F ) )
% 0.29/0.52 = ( ord_less_nat @ ( F @ X ) @ ( F @ Y ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % in_measure
% 0.29/0.52 thf(fact_571_in__measure,axiom,
% 0.29/0.52 ! [X: nat,Y: nat,F: nat > nat] :
% 0.29/0.52 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( measure_nat @ F ) )
% 0.29/0.52 = ( ord_less_nat @ ( F @ X ) @ ( F @ Y ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % in_measure
% 0.29/0.52 thf(fact_572_less__add__one,axiom,
% 0.29/0.52 ! [A: code_integer] : ( ord_le6747313008572928689nteger @ A @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) ) ).
% 0.29/0.52
% 0.29/0.52 % less_add_one
% 0.29/0.52 thf(fact_573_less__add__one,axiom,
% 0.29/0.52 ! [A: rat] : ( ord_less_rat @ A @ ( plus_plus_rat @ A @ one_one_rat ) ) ).
% 0.29/0.52
% 0.29/0.52 % less_add_one
% 0.29/0.52 thf(fact_574_less__add__one,axiom,
% 0.29/0.52 ! [A: nat] : ( ord_less_nat @ A @ ( plus_plus_nat @ A @ one_one_nat ) ) ).
% 0.29/0.52
% 0.29/0.52 % less_add_one
% 0.29/0.52 thf(fact_575_less__add__one,axiom,
% 0.29/0.52 ! [A: int] : ( ord_less_int @ A @ ( plus_plus_int @ A @ one_one_int ) ) ).
% 0.29/0.52
% 0.29/0.52 % less_add_one
% 0.29/0.52 thf(fact_576_add__mono1,axiom,
% 0.29/0.52 ! [A: code_integer,B: code_integer] :
% 0.29/0.52 ( ( ord_le6747313008572928689nteger @ A @ B )
% 0.29/0.52 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) @ ( plus_p5714425477246183910nteger @ B @ one_one_Code_integer ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % add_mono1
% 0.29/0.52 thf(fact_577_add__mono1,axiom,
% 0.29/0.52 ! [A: rat,B: rat] :
% 0.29/0.52 ( ( ord_less_rat @ A @ B )
% 0.29/0.52 => ( ord_less_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( plus_plus_rat @ B @ one_one_rat ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % add_mono1
% 0.29/0.52 thf(fact_578_add__mono1,axiom,
% 0.29/0.52 ! [A: nat,B: nat] :
% 0.29/0.52 ( ( ord_less_nat @ A @ B )
% 0.29/0.52 => ( ord_less_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( plus_plus_nat @ B @ one_one_nat ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % add_mono1
% 0.29/0.52 thf(fact_579_add__mono1,axiom,
% 0.29/0.52 ! [A: int,B: int] :
% 0.29/0.52 ( ( ord_less_int @ A @ B )
% 0.29/0.52 => ( ord_less_int @ ( plus_plus_int @ A @ one_one_int ) @ ( plus_plus_int @ B @ one_one_int ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % add_mono1
% 0.29/0.52 thf(fact_580_add__lessD1,axiom,
% 0.29/0.52 ! [I: nat,J: nat,K: nat] :
% 0.29/0.52 ( ( ord_less_nat @ ( plus_plus_nat @ I @ J ) @ K )
% 0.29/0.52 => ( ord_less_nat @ I @ K ) ) ).
% 0.29/0.52
% 0.29/0.52 % add_lessD1
% 0.29/0.52 thf(fact_581_add__less__mono,axiom,
% 0.29/0.52 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.29/0.52 ( ( ord_less_nat @ I @ J )
% 0.29/0.52 => ( ( ord_less_nat @ K @ L )
% 0.29/0.52 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % add_less_mono
% 0.29/0.52 thf(fact_582_not__add__less1,axiom,
% 0.29/0.52 ! [I: nat,J: nat] :
% 0.29/0.52 ~ ( ord_less_nat @ ( plus_plus_nat @ I @ J ) @ I ) ).
% 0.29/0.52
% 0.29/0.52 % not_add_less1
% 0.29/0.52 thf(fact_583_less__option__None,axiom,
% 0.29/0.52 ! [X: option_num] :
% 0.29/0.52 ~ ( ord_less_option_num @ X @ none_num ) ).
% 0.29/0.52
% 0.29/0.52 % less_option_None
% 0.29/0.52 thf(fact_584_less__option__None__Some__code,axiom,
% 0.29/0.52 ! [X: num] : ( ord_less_option_num @ none_num @ ( some_num @ X ) ) ).
% 0.29/0.52
% 0.29/0.52 % less_option_None_Some_code
% 0.29/0.52 thf(fact_585_less__option__None__Some,axiom,
% 0.29/0.52 ! [X: num] : ( ord_less_option_num @ none_num @ ( some_num @ X ) ) ).
% 0.29/0.52
% 0.29/0.52 % less_option_None_Some
% 0.29/0.52 thf(fact_586_less__option__None__is__Some,axiom,
% 0.29/0.52 ! [X: option_num] :
% 0.29/0.52 ( ( ord_less_option_num @ none_num @ X )
% 0.29/0.52 => ? [Z3: num] :
% 0.29/0.52 ( X
% 0.29/0.52 = ( some_num @ Z3 ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % less_option_None_is_Some
% 0.29/0.52 thf(fact_587_fold__atLeastAtMost__nat_Osimps,axiom,
% 0.29/0.52 ( set_fo2584398358068434914at_nat
% 0.29/0.52 = ( ^ [F2: nat > nat > nat,A5: nat,B4: nat,Acc2: nat] : ( if_nat @ ( ord_less_nat @ B4 @ A5 ) @ Acc2 @ ( set_fo2584398358068434914at_nat @ F2 @ ( plus_plus_nat @ A5 @ one_one_nat ) @ B4 @ ( F2 @ A5 @ Acc2 ) ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % fold_atLeastAtMost_nat.simps
% 0.29/0.52 thf(fact_588_fold__atLeastAtMost__nat_Oelims,axiom,
% 0.29/0.52 ! [X: nat > nat > nat,Xa: nat,Xb: nat,Xc: nat,Y: nat] :
% 0.29/0.52 ( ( ( set_fo2584398358068434914at_nat @ X @ Xa @ Xb @ Xc )
% 0.29/0.52 = Y )
% 0.29/0.52 => ( ( ( ord_less_nat @ Xb @ Xa )
% 0.29/0.52 => ( Y = Xc ) )
% 0.29/0.52 & ( ~ ( ord_less_nat @ Xb @ Xa )
% 0.29/0.52 => ( Y
% 0.29/0.52 = ( set_fo2584398358068434914at_nat @ X @ ( plus_plus_nat @ Xa @ one_one_nat ) @ Xb @ ( X @ Xa @ Xc ) ) ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % fold_atLeastAtMost_nat.elims
% 0.29/0.52 thf(fact_589_less__add__eq__less,axiom,
% 0.29/0.52 ! [K: nat,L: nat,M2: nat,N2: nat] :
% 0.29/0.52 ( ( ord_less_nat @ K @ L )
% 0.29/0.52 => ( ( ( plus_plus_nat @ M2 @ L )
% 0.29/0.52 = ( plus_plus_nat @ K @ N2 ) )
% 0.29/0.52 => ( ord_less_nat @ M2 @ N2 ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % less_add_eq_less
% 0.29/0.52 thf(fact_590_trans__less__add2,axiom,
% 0.29/0.52 ! [I: nat,J: nat,M2: nat] :
% 0.29/0.52 ( ( ord_less_nat @ I @ J )
% 0.29/0.52 => ( ord_less_nat @ I @ ( plus_plus_nat @ M2 @ J ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % trans_less_add2
% 0.29/0.52 thf(fact_591_trans__less__add1,axiom,
% 0.29/0.52 ! [I: nat,J: nat,M2: nat] :
% 0.29/0.52 ( ( ord_less_nat @ I @ J )
% 0.29/0.52 => ( ord_less_nat @ I @ ( plus_plus_nat @ J @ M2 ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % trans_less_add1
% 0.29/0.52 thf(fact_592_add__less__mono1,axiom,
% 0.29/0.52 ! [I: nat,J: nat,K: nat] :
% 0.29/0.52 ( ( ord_less_nat @ I @ J )
% 0.29/0.52 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % add_less_mono1
% 0.29/0.52 thf(fact_593_not__add__less2,axiom,
% 0.29/0.52 ! [J: nat,I: nat] :
% 0.29/0.52 ~ ( ord_less_nat @ ( plus_plus_nat @ J @ I ) @ I ) ).
% 0.29/0.52
% 0.29/0.52 % not_add_less2
% 0.29/0.52 thf(fact_594_less__numeral__extra_I4_J,axiom,
% 0.29/0.52 ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ one_one_Code_integer ) ).
% 0.29/0.52
% 0.29/0.52 % less_numeral_extra(4)
% 0.29/0.52 thf(fact_595_less__numeral__extra_I4_J,axiom,
% 0.29/0.52 ~ ( ord_less_rat @ one_one_rat @ one_one_rat ) ).
% 0.29/0.52
% 0.29/0.52 % less_numeral_extra(4)
% 0.29/0.52 thf(fact_596_less__numeral__extra_I4_J,axiom,
% 0.29/0.52 ~ ( ord_less_nat @ one_one_nat @ one_one_nat ) ).
% 0.29/0.52
% 0.29/0.52 % less_numeral_extra(4)
% 0.29/0.52 thf(fact_597_less__numeral__extra_I4_J,axiom,
% 0.29/0.52 ~ ( ord_less_int @ one_one_int @ one_one_int ) ).
% 0.29/0.52
% 0.29/0.52 % less_numeral_extra(4)
% 0.29/0.52 thf(fact_598_mlex__iff,axiom,
% 0.29/0.52 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,F: set_Pr1261947904930325089at_nat > nat,R4: set_Pr4329608150637261639at_nat] :
% 0.29/0.52 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ ( mlex_p3502713205431853936at_nat @ F @ R4 ) )
% 0.29/0.52 = ( ( ord_less_nat @ ( F @ X ) @ ( F @ Y ) )
% 0.29/0.52 | ( ( ( F @ X )
% 0.29/0.52 = ( F @ Y ) )
% 0.29/0.52 & ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ R4 ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % mlex_iff
% 0.29/0.52 thf(fact_599_mlex__iff,axiom,
% 0.29/0.52 ! [X: nat,Y: nat,F: nat > nat,R4: set_Pr1261947904930325089at_nat] :
% 0.29/0.52 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( mlex_prod_nat @ F @ R4 ) )
% 0.29/0.52 = ( ( ord_less_nat @ ( F @ X ) @ ( F @ Y ) )
% 0.29/0.52 | ( ( ( F @ X )
% 0.29/0.52 = ( F @ Y ) )
% 0.29/0.52 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ R4 ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % mlex_iff
% 0.29/0.52 thf(fact_600_mlex__less,axiom,
% 0.29/0.52 ! [F: set_Pr1261947904930325089at_nat > nat,X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,R4: set_Pr4329608150637261639at_nat] :
% 0.29/0.52 ( ( ord_less_nat @ ( F @ X ) @ ( F @ Y ) )
% 0.29/0.52 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ ( mlex_p3502713205431853936at_nat @ F @ R4 ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % mlex_less
% 0.29/0.52 thf(fact_601_mlex__less,axiom,
% 0.29/0.52 ! [F: nat > nat,X: nat,Y: nat,R4: set_Pr1261947904930325089at_nat] :
% 0.29/0.52 ( ( ord_less_nat @ ( F @ X ) @ ( F @ Y ) )
% 0.29/0.52 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( mlex_prod_nat @ F @ R4 ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % mlex_less
% 0.29/0.52 thf(fact_602_pairself_Opelims,axiom,
% 0.29/0.52 ! [X: int > option6357759511663192854e_term,Xa: product_prod_int_int,Y: produc6576344331059438605e_term] :
% 0.29/0.52 ( ( ( pairse3534876335208825186e_term @ X @ Xa )
% 0.29/0.52 = Y )
% 0.29/0.52 => ( ( accp_P8928870874622223812nt_int @ pairse6848479906795794847e_term @ ( produc4305682042979456191nt_int @ X @ Xa ) )
% 0.29/0.52 => ~ ! [A3: int,B2: int] :
% 0.29/0.52 ( ( Xa
% 0.29/0.52 = ( product_Pair_int_int @ A3 @ B2 ) )
% 0.29/0.52 => ( ( Y
% 0.29/0.52 = ( produc5950683997804057413e_term @ ( X @ A3 ) @ ( X @ B2 ) ) )
% 0.29/0.52 => ~ ( accp_P8928870874622223812nt_int @ pairse6848479906795794847e_term @ ( produc4305682042979456191nt_int @ X @ ( product_Pair_int_int @ A3 @ B2 ) ) ) ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % pairself.pelims
% 0.29/0.52 thf(fact_603_execute__return,axiom,
% 0.29/0.52 ! [X: array_a] :
% 0.29/0.52 ( ( heap_T5591663578999710211rray_a @ ( heap_T4896204969850773234rray_a @ X ) )
% 0.29/0.52 = ( comp_P2097125496263478628t_unit @ some_P6105628898608307625it_nat
% 0.29/0.52 @ ^ [H: heap_e7401611519738050253t_unit] : ( produc1733996804261680252it_nat @ X @ ( produc584006145561248582it_nat @ H @ one_one_nat ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % execute_return
% 0.29/0.52 thf(fact_604_execute__return,axiom,
% 0.29/0.52 ! [X: product_unit] :
% 0.29/0.52 ( ( heap_T875086893843062177t_unit @ ( heap_T7507251653302230130t_unit @ X ) )
% 0.29/0.52 = ( comp_P3118722334806803912t_unit @ some_P1914260805536162275it_nat
% 0.29/0.52 @ ^ [H: heap_e7401611519738050253t_unit] : ( produc7133225469290080770it_nat @ X @ ( produc584006145561248582it_nat @ H @ one_one_nat ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % execute_return
% 0.29/0.52 thf(fact_605_same__fstI,axiom,
% 0.29/0.52 ! [P: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > $o,X: produc6241069584506657477e_term > option6357759511663192854e_term,Y7: produc8923325533196201883nteger,Y: produc8923325533196201883nteger,R4: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > set_Pr5052581263052047815nteger] :
% 0.29/0.52 ( ( P @ X )
% 0.29/0.52 => ( ( member335077259223437328nteger @ ( produc4911887526399440471nteger @ Y7 @ Y ) @ ( R4 @ X ) )
% 0.29/0.52 => ( member2446009503569356342nteger @ ( produc7954516348491987909nteger @ ( produc8603105652947943368nteger @ X @ Y7 ) @ ( produc8603105652947943368nteger @ X @ Y ) ) @ ( same_f8038803414157382067nteger @ P @ R4 ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % same_fstI
% 0.29/0.52 thf(fact_606_same__fstI,axiom,
% 0.29/0.52 ! [P: ( produc3658429121746597890et_nat > $o ) > $o,X: produc3658429121746597890et_nat > $o,Y7: produc3658429121746597890et_nat,Y: produc3658429121746597890et_nat,R4: ( produc3658429121746597890et_nat > $o ) > set_Pr719794911490849221et_nat] :
% 0.29/0.52 ( ( P @ X )
% 0.29/0.52 => ( ( member6099555550032318734et_nat @ ( produc8199053930788261021et_nat @ Y7 @ Y ) @ ( R4 @ X ) )
% 0.29/0.52 => ( member4763271486408492550et_nat @ ( produc8599840265553166229et_nat @ ( produc5001842942810119800et_nat @ X @ Y7 ) @ ( produc5001842942810119800et_nat @ X @ Y ) ) @ ( same_f7251492184213700963et_nat @ P @ R4 ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % same_fstI
% 0.29/0.52 thf(fact_607_same__fstI,axiom,
% 0.29/0.52 ! [P: ( produc3658429121746597890et_nat > $o ) > $o,X: produc3658429121746597890et_nat > $o,Y7: produc3925858234332021118et_nat,Y: produc3925858234332021118et_nat,R4: ( produc3658429121746597890et_nat > $o ) > set_Pr7928877670098842301et_nat] :
% 0.29/0.52 ( ( P @ X )
% 0.29/0.52 => ( ( member4763271486408492550et_nat @ ( produc8599840265553166229et_nat @ Y7 @ Y ) @ ( R4 @ X ) )
% 0.29/0.52 => ( member6341495586645257982et_nat @ ( produc1940133919992309389et_nat @ ( produc2245416461498447860et_nat @ X @ Y7 ) @ ( produc2245416461498447860et_nat @ X @ Y ) ) @ ( same_f1912051055550046943et_nat @ P @ R4 ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % same_fstI
% 0.29/0.52 thf(fact_608_same__fstI,axiom,
% 0.29/0.52 ! [P: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > $o,X: produc8551481072490612790e_term > option6357759511663192854e_term,Y7: product_prod_int_int,Y: product_prod_int_int,R4: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > set_Pr2560585780119916871nt_int] :
% 0.29/0.52 ( ( P @ X )
% 0.29/0.52 => ( ( member8566619992076573584nt_int @ ( produc3646306378393792727nt_int @ Y7 @ Y ) @ ( R4 @ X ) )
% 0.29/0.52 => ( member6582457606847315088nt_int @ ( produc7601053194514725023nt_int @ ( produc5700946648718959541nt_int @ X @ Y7 ) @ ( produc5700946648718959541nt_int @ X @ Y ) ) @ ( same_f5472592420709775776nt_int @ P @ R4 ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % same_fstI
% 0.29/0.52 thf(fact_609_same__fstI,axiom,
% 0.29/0.52 ! [P: ( int > option6357759511663192854e_term ) > $o,X: int > option6357759511663192854e_term,Y7: product_prod_int_int,Y: product_prod_int_int,R4: ( int > option6357759511663192854e_term ) > set_Pr2560585780119916871nt_int] :
% 0.29/0.52 ( ( P @ X )
% 0.29/0.52 => ( ( member8566619992076573584nt_int @ ( produc3646306378393792727nt_int @ Y7 @ Y ) @ ( R4 @ X ) )
% 0.29/0.52 => ( member4085533954029916580nt_int @ ( produc8406175334058502835nt_int @ ( produc4305682042979456191nt_int @ X @ Y7 ) @ ( produc4305682042979456191nt_int @ X @ Y ) ) @ ( same_f6662725367016992042nt_int @ P @ R4 ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % same_fstI
% 0.29/0.52 thf(fact_610_zero__less__two,axiom,
% 0.29/0.52 ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ one_one_Code_integer ) ).
% 0.29/0.52
% 0.29/0.52 % zero_less_two
% 0.29/0.52 thf(fact_611_zero__less__two,axiom,
% 0.29/0.52 ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ).
% 0.29/0.52
% 0.29/0.52 % zero_less_two
% 0.29/0.52 thf(fact_612_zero__less__two,axiom,
% 0.29/0.52 ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ).
% 0.29/0.52
% 0.29/0.52 % zero_less_two
% 0.29/0.52 thf(fact_613_zero__less__two,axiom,
% 0.29/0.52 ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ one_one_int ) ).
% 0.29/0.52
% 0.29/0.52 % zero_less_two
% 0.29/0.52 thf(fact_614_is__num__normalize_I1_J,axiom,
% 0.29/0.52 ! [A: rat,B: rat,C: rat] :
% 0.29/0.52 ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 0.29/0.52 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % is_num_normalize(1)
% 0.29/0.52 thf(fact_615_is__num__normalize_I1_J,axiom,
% 0.29/0.52 ! [A: int,B: int,C: int] :
% 0.29/0.52 ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 0.29/0.52 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % is_num_normalize(1)
% 0.29/0.52 thf(fact_616_add_Osafe__commute,axiom,
% 0.29/0.52 ! [X: multis2468970476368604999at_nat,Y: multis2468970476368604999at_nat,A: multis2468970476368604999at_nat,B: multis2468970476368604999at_nat] :
% 0.29/0.52 ( ( syntax5084084251851430274at_nat @ ( plus_p7104986032573967614at_nat @ X @ Y ) @ A )
% 0.29/0.52 => ( ( plus_p7104986032573967614at_nat @ A @ B )
% 0.29/0.52 = ( plus_p7104986032573967614at_nat @ B @ A ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % add.safe_commute
% 0.29/0.52 thf(fact_617_add_Osafe__commute,axiom,
% 0.29/0.52 ! [X: rat,Y: rat,A: rat,B: rat] :
% 0.29/0.52 ( ( syntax3730441303064801268at_rat @ ( plus_plus_rat @ X @ Y ) @ A )
% 0.29/0.52 => ( ( plus_plus_rat @ A @ B )
% 0.29/0.52 = ( plus_plus_rat @ B @ A ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % add.safe_commute
% 0.29/0.52 thf(fact_618_add_Osafe__commute,axiom,
% 0.29/0.52 ! [X: nat,Y: nat,A: nat,B: nat] :
% 0.29/0.52 ( ( syntax4682126007086162916at_nat @ ( plus_plus_nat @ X @ Y ) @ A )
% 0.29/0.52 => ( ( plus_plus_nat @ A @ B )
% 0.29/0.52 = ( plus_plus_nat @ B @ A ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % add.safe_commute
% 0.29/0.52 thf(fact_619_add_Osafe__commute,axiom,
% 0.29/0.52 ! [X: int,Y: int,A: int,B: int] :
% 0.29/0.52 ( ( syntax5678989248478167196nt_int @ ( plus_plus_int @ X @ Y ) @ A )
% 0.29/0.52 => ( ( plus_plus_int @ A @ B )
% 0.29/0.52 = ( plus_plus_int @ B @ A ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % add.safe_commute
% 0.29/0.52 thf(fact_620_bijective__def,axiom,
% 0.29/0.52 ( biject3388518990857851981at_nat
% 0.29/0.52 = ( ^ [R5: set_Pr4329608150637261639at_nat] :
% 0.29/0.52 ( ! [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat,Z4: set_Pr1261947904930325089at_nat] :
% 0.29/0.52 ( ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ Y3 ) @ R5 )
% 0.29/0.52 & ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ Z4 ) @ R5 ) )
% 0.29/0.52 => ( Y3 = Z4 ) )
% 0.29/0.52 & ! [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat,Z4: set_Pr1261947904930325089at_nat] :
% 0.29/0.52 ( ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ Z4 ) @ R5 )
% 0.29/0.52 & ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ Y3 @ Z4 ) @ R5 ) )
% 0.29/0.52 => ( X3 = Y3 ) ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % bijective_def
% 0.29/0.52 thf(fact_621_bijective__def,axiom,
% 0.29/0.52 ( bijective_nat_nat
% 0.29/0.52 = ( ^ [R5: set_Pr1261947904930325089at_nat] :
% 0.29/0.52 ( ! [X3: nat,Y3: nat,Z4: nat] :
% 0.29/0.52 ( ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y3 ) @ R5 )
% 0.29/0.52 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Z4 ) @ R5 ) )
% 0.29/0.52 => ( Y3 = Z4 ) )
% 0.29/0.52 & ! [X3: nat,Y3: nat,Z4: nat] :
% 0.29/0.52 ( ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Z4 ) @ R5 )
% 0.29/0.52 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y3 @ Z4 ) @ R5 ) )
% 0.29/0.52 => ( X3 = Y3 ) ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % bijective_def
% 0.29/0.52 thf(fact_622_bijective__def,axiom,
% 0.29/0.52 ( biject9051520373387432658nteger
% 0.29/0.52 = ( ^ [R5: set_Pr1281608226676607948nteger] :
% 0.29/0.52 ( ! [X3: produc6241069584506657477e_term > option6357759511663192854e_term,Y3: produc8923325533196201883nteger,Z4: produc8923325533196201883nteger] :
% 0.29/0.52 ( ( ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X3 @ Y3 ) @ R5 )
% 0.29/0.52 & ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X3 @ Z4 ) @ R5 ) )
% 0.29/0.52 => ( Y3 = Z4 ) )
% 0.29/0.52 & ! [X3: produc6241069584506657477e_term > option6357759511663192854e_term,Y3: produc6241069584506657477e_term > option6357759511663192854e_term,Z4: produc8923325533196201883nteger] :
% 0.29/0.52 ( ( ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X3 @ Z4 ) @ R5 )
% 0.29/0.52 & ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ Y3 @ Z4 ) @ R5 ) )
% 0.29/0.52 => ( X3 = Y3 ) ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % bijective_def
% 0.29/0.52 thf(fact_623_bijective__def,axiom,
% 0.29/0.52 ( biject2615096655818420098et_nat
% 0.29/0.52 = ( ^ [R5: set_Pr3286484037609594932et_nat] :
% 0.29/0.52 ( ! [X3: produc3658429121746597890et_nat > $o,Y3: produc3658429121746597890et_nat,Z4: produc3658429121746597890et_nat] :
% 0.29/0.52 ( ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X3 @ Y3 ) @ R5 )
% 0.29/0.52 & ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X3 @ Z4 ) @ R5 ) )
% 0.29/0.52 => ( Y3 = Z4 ) )
% 0.29/0.52 & ! [X3: produc3658429121746597890et_nat > $o,Y3: produc3658429121746597890et_nat > $o,Z4: produc3658429121746597890et_nat] :
% 0.29/0.52 ( ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X3 @ Z4 ) @ R5 )
% 0.29/0.52 & ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ Y3 @ Z4 ) @ R5 ) )
% 0.29/0.52 => ( X3 = Y3 ) ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % bijective_def
% 0.29/0.52 thf(fact_624_bijective__def,axiom,
% 0.29/0.52 ( biject1468766312547416318et_nat
% 0.29/0.52 = ( ^ [R5: set_Pr8536935166611901872et_nat] :
% 0.29/0.52 ( ! [X3: produc3658429121746597890et_nat > $o,Y3: produc3925858234332021118et_nat,Z4: produc3925858234332021118et_nat] :
% 0.29/0.52 ( ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X3 @ Y3 ) @ R5 )
% 0.29/0.52 & ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X3 @ Z4 ) @ R5 ) )
% 0.29/0.52 => ( Y3 = Z4 ) )
% 0.29/0.52 & ! [X3: produc3658429121746597890et_nat > $o,Y3: produc3658429121746597890et_nat > $o,Z4: produc3925858234332021118et_nat] :
% 0.29/0.52 ( ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X3 @ Z4 ) @ R5 )
% 0.29/0.52 & ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ Y3 @ Z4 ) @ R5 ) )
% 0.29/0.52 => ( X3 = Y3 ) ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % bijective_def
% 0.29/0.52 thf(fact_625_bijective__def,axiom,
% 0.29/0.52 ( biject383251550997737151nt_int
% 0.29/0.52 = ( ^ [R5: set_Pr9222295170931077689nt_int] :
% 0.29/0.52 ( ! [X3: produc8551481072490612790e_term > option6357759511663192854e_term,Y3: product_prod_int_int,Z4: product_prod_int_int] :
% 0.29/0.52 ( ( ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X3 @ Y3 ) @ R5 )
% 0.29/0.52 & ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X3 @ Z4 ) @ R5 ) )
% 0.29/0.52 => ( Y3 = Z4 ) )
% 0.29/0.52 & ! [X3: produc8551481072490612790e_term > option6357759511663192854e_term,Y3: produc8551481072490612790e_term > option6357759511663192854e_term,Z4: product_prod_int_int] :
% 0.29/0.52 ( ( ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X3 @ Z4 ) @ R5 )
% 0.29/0.52 & ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ Y3 @ Z4 ) @ R5 ) )
% 0.29/0.52 => ( X3 = Y3 ) ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % bijective_def
% 0.29/0.52 thf(fact_626_bijective__def,axiom,
% 0.29/0.52 ( biject576505603616484041nt_int
% 0.29/0.52 = ( ^ [R5: set_Pr1872883991513573699nt_int] :
% 0.29/0.52 ( ! [X3: int > option6357759511663192854e_term,Y3: product_prod_int_int,Z4: product_prod_int_int] :
% 0.29/0.52 ( ( ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X3 @ Y3 ) @ R5 )
% 0.29/0.52 & ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X3 @ Z4 ) @ R5 ) )
% 0.29/0.52 => ( Y3 = Z4 ) )
% 0.29/0.52 & ! [X3: int > option6357759511663192854e_term,Y3: int > option6357759511663192854e_term,Z4: product_prod_int_int] :
% 0.29/0.52 ( ( ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X3 @ Z4 ) @ R5 )
% 0.29/0.52 & ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ Y3 @ Z4 ) @ R5 ) )
% 0.29/0.52 => ( X3 = Y3 ) ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % bijective_def
% 0.29/0.52 thf(fact_627_ssubst__Pair__rhs,axiom,
% 0.29/0.52 ! [R2: set_Pr1261947904930325089at_nat,S: set_Pr1261947904930325089at_nat,R4: set_Pr4329608150637261639at_nat,S3: set_Pr1261947904930325089at_nat] :
% 0.29/0.52 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ R2 @ S ) @ R4 )
% 0.29/0.52 => ( ( S3 = S )
% 0.29/0.52 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ R2 @ S3 ) @ R4 ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % ssubst_Pair_rhs
% 0.29/0.52 thf(fact_628_ssubst__Pair__rhs,axiom,
% 0.29/0.52 ! [R2: nat,S: nat,R4: set_Pr1261947904930325089at_nat,S3: nat] :
% 0.29/0.52 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ R2 @ S ) @ R4 )
% 0.29/0.52 => ( ( S3 = S )
% 0.29/0.52 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ R2 @ S3 ) @ R4 ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % ssubst_Pair_rhs
% 0.29/0.52 thf(fact_629_ssubst__Pair__rhs,axiom,
% 0.29/0.52 ! [R2: produc6241069584506657477e_term > option6357759511663192854e_term,S: produc8923325533196201883nteger,R4: set_Pr1281608226676607948nteger,S3: produc8923325533196201883nteger] :
% 0.29/0.52 ( ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ R2 @ S ) @ R4 )
% 0.29/0.52 => ( ( S3 = S )
% 0.29/0.52 => ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ R2 @ S3 ) @ R4 ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % ssubst_Pair_rhs
% 0.29/0.52 thf(fact_630_ssubst__Pair__rhs,axiom,
% 0.29/0.52 ! [R2: produc3658429121746597890et_nat > $o,S: produc3658429121746597890et_nat,R4: set_Pr3286484037609594932et_nat,S3: produc3658429121746597890et_nat] :
% 0.29/0.52 ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ R2 @ S ) @ R4 )
% 0.29/0.52 => ( ( S3 = S )
% 0.29/0.52 => ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ R2 @ S3 ) @ R4 ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % ssubst_Pair_rhs
% 0.29/0.52 thf(fact_631_ssubst__Pair__rhs,axiom,
% 0.29/0.52 ! [R2: produc3658429121746597890et_nat > $o,S: produc3925858234332021118et_nat,R4: set_Pr8536935166611901872et_nat,S3: produc3925858234332021118et_nat] :
% 0.29/0.52 ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ R2 @ S ) @ R4 )
% 0.29/0.52 => ( ( S3 = S )
% 0.29/0.52 => ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ R2 @ S3 ) @ R4 ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % ssubst_Pair_rhs
% 0.29/0.52 thf(fact_632_ssubst__Pair__rhs,axiom,
% 0.29/0.52 ! [R2: produc8551481072490612790e_term > option6357759511663192854e_term,S: product_prod_int_int,R4: set_Pr9222295170931077689nt_int,S3: product_prod_int_int] :
% 0.29/0.52 ( ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ R2 @ S ) @ R4 )
% 0.29/0.52 => ( ( S3 = S )
% 0.29/0.52 => ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ R2 @ S3 ) @ R4 ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % ssubst_Pair_rhs
% 0.29/0.52 thf(fact_633_ssubst__Pair__rhs,axiom,
% 0.29/0.52 ! [R2: int > option6357759511663192854e_term,S: product_prod_int_int,R4: set_Pr1872883991513573699nt_int,S3: product_prod_int_int] :
% 0.29/0.52 ( ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ R2 @ S ) @ R4 )
% 0.29/0.52 => ( ( S3 = S )
% 0.29/0.52 => ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ R2 @ S3 ) @ R4 ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % ssubst_Pair_rhs
% 0.29/0.52 thf(fact_634_add__is__0,axiom,
% 0.29/0.52 ! [M2: nat,N2: nat] :
% 0.29/0.52 ( ( ( plus_plus_nat @ M2 @ N2 )
% 0.29/0.52 = zero_zero_nat )
% 0.29/0.52 = ( ( M2 = zero_zero_nat )
% 0.29/0.52 & ( N2 = zero_zero_nat ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % add_is_0
% 0.29/0.52 thf(fact_635_Nat_Oadd__0__right,axiom,
% 0.29/0.52 ! [M2: nat] :
% 0.29/0.52 ( ( plus_plus_nat @ M2 @ zero_zero_nat )
% 0.29/0.52 = M2 ) ).
% 0.29/0.52
% 0.29/0.52 % Nat.add_0_right
% 0.29/0.52 thf(fact_636_not__gr__zero,axiom,
% 0.29/0.52 ! [N2: nat] :
% 0.29/0.52 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N2 ) )
% 0.29/0.52 = ( N2 = zero_zero_nat ) ) ).
% 0.29/0.52
% 0.29/0.52 % not_gr_zero
% 0.29/0.52 thf(fact_637_add__0,axiom,
% 0.29/0.52 ! [A: code_integer] :
% 0.29/0.52 ( ( plus_p5714425477246183910nteger @ zero_z3403309356797280102nteger @ A )
% 0.29/0.52 = A ) ).
% 0.29/0.52
% 0.29/0.52 % add_0
% 0.29/0.52 thf(fact_638_add__0,axiom,
% 0.29/0.52 ! [A: multis2468970476368604999at_nat] :
% 0.29/0.52 ( ( plus_p7104986032573967614at_nat @ zero_z1048942125864253310at_nat @ A )
% 0.29/0.52 = A ) ).
% 0.29/0.52
% 0.29/0.52 % add_0
% 0.29/0.52 thf(fact_639_add__0,axiom,
% 0.29/0.52 ! [A: rat] :
% 0.29/0.52 ( ( plus_plus_rat @ zero_zero_rat @ A )
% 0.29/0.52 = A ) ).
% 0.29/0.52
% 0.29/0.52 % add_0
% 0.29/0.52 thf(fact_640_add__0,axiom,
% 0.29/0.52 ! [A: nat] :
% 0.29/0.52 ( ( plus_plus_nat @ zero_zero_nat @ A )
% 0.29/0.52 = A ) ).
% 0.29/0.52
% 0.29/0.52 % add_0
% 0.29/0.52 thf(fact_641_add__0,axiom,
% 0.29/0.52 ! [A: int] :
% 0.29/0.52 ( ( plus_plus_int @ zero_zero_int @ A )
% 0.29/0.52 = A ) ).
% 0.29/0.52
% 0.29/0.52 % add_0
% 0.29/0.52 thf(fact_642_zero__eq__add__iff__both__eq__0,axiom,
% 0.29/0.52 ! [X: nat,Y: nat] :
% 0.29/0.52 ( ( zero_zero_nat
% 0.29/0.52 = ( plus_plus_nat @ X @ Y ) )
% 0.29/0.52 = ( ( X = zero_zero_nat )
% 0.29/0.52 & ( Y = zero_zero_nat ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % zero_eq_add_iff_both_eq_0
% 0.29/0.52 thf(fact_643_add__eq__0__iff__both__eq__0,axiom,
% 0.29/0.52 ! [X: nat,Y: nat] :
% 0.29/0.52 ( ( ( plus_plus_nat @ X @ Y )
% 0.29/0.52 = zero_zero_nat )
% 0.29/0.52 = ( ( X = zero_zero_nat )
% 0.29/0.52 & ( Y = zero_zero_nat ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % add_eq_0_iff_both_eq_0
% 0.29/0.52 thf(fact_644_add__cancel__right__right,axiom,
% 0.29/0.52 ! [A: code_integer,B: code_integer] :
% 0.29/0.52 ( ( A
% 0.29/0.52 = ( plus_p5714425477246183910nteger @ A @ B ) )
% 0.29/0.52 = ( B = zero_z3403309356797280102nteger ) ) ).
% 0.29/0.52
% 0.29/0.52 % add_cancel_right_right
% 0.29/0.52 thf(fact_645_add__cancel__right__right,axiom,
% 0.29/0.52 ! [A: multis2468970476368604999at_nat,B: multis2468970476368604999at_nat] :
% 0.29/0.52 ( ( A
% 0.29/0.52 = ( plus_p7104986032573967614at_nat @ A @ B ) )
% 0.29/0.52 = ( B = zero_z1048942125864253310at_nat ) ) ).
% 0.29/0.52
% 0.29/0.52 % add_cancel_right_right
% 0.29/0.52 thf(fact_646_add__cancel__right__right,axiom,
% 0.29/0.52 ! [A: rat,B: rat] :
% 0.29/0.52 ( ( A
% 0.29/0.52 = ( plus_plus_rat @ A @ B ) )
% 0.29/0.52 = ( B = zero_zero_rat ) ) ).
% 0.29/0.52
% 0.29/0.52 % add_cancel_right_right
% 0.29/0.52 thf(fact_647_add__cancel__right__right,axiom,
% 0.29/0.52 ! [A: nat,B: nat] :
% 0.29/0.52 ( ( A
% 0.29/0.52 = ( plus_plus_nat @ A @ B ) )
% 0.29/0.52 = ( B = zero_zero_nat ) ) ).
% 0.29/0.52
% 0.29/0.52 % add_cancel_right_right
% 0.29/0.52 thf(fact_648_add__cancel__right__right,axiom,
% 0.29/0.52 ! [A: int,B: int] :
% 0.29/0.52 ( ( A
% 0.29/0.52 = ( plus_plus_int @ A @ B ) )
% 0.29/0.52 = ( B = zero_zero_int ) ) ).
% 0.29/0.52
% 0.29/0.52 % add_cancel_right_right
% 0.29/0.52 thf(fact_649_add__cancel__right__left,axiom,
% 0.29/0.52 ! [A: code_integer,B: code_integer] :
% 0.29/0.52 ( ( A
% 0.29/0.52 = ( plus_p5714425477246183910nteger @ B @ A ) )
% 0.29/0.52 = ( B = zero_z3403309356797280102nteger ) ) ).
% 0.29/0.52
% 0.29/0.52 % add_cancel_right_left
% 0.29/0.52 thf(fact_650_add__cancel__right__left,axiom,
% 0.29/0.52 ! [A: multis2468970476368604999at_nat,B: multis2468970476368604999at_nat] :
% 0.29/0.52 ( ( A
% 0.29/0.52 = ( plus_p7104986032573967614at_nat @ B @ A ) )
% 0.29/0.52 = ( B = zero_z1048942125864253310at_nat ) ) ).
% 0.29/0.52
% 0.29/0.52 % add_cancel_right_left
% 0.29/0.52 thf(fact_651_add__cancel__right__left,axiom,
% 0.29/0.52 ! [A: rat,B: rat] :
% 0.29/0.52 ( ( A
% 0.29/0.52 = ( plus_plus_rat @ B @ A ) )
% 0.29/0.52 = ( B = zero_zero_rat ) ) ).
% 0.29/0.52
% 0.29/0.52 % add_cancel_right_left
% 0.29/0.52 thf(fact_652_add__cancel__right__left,axiom,
% 0.29/0.52 ! [A: nat,B: nat] :
% 0.29/0.52 ( ( A
% 0.29/0.52 = ( plus_plus_nat @ B @ A ) )
% 0.29/0.52 = ( B = zero_zero_nat ) ) ).
% 0.29/0.52
% 0.29/0.52 % add_cancel_right_left
% 0.29/0.52 thf(fact_653_add__cancel__right__left,axiom,
% 0.29/0.52 ! [A: int,B: int] :
% 0.29/0.52 ( ( A
% 0.29/0.52 = ( plus_plus_int @ B @ A ) )
% 0.29/0.52 = ( B = zero_zero_int ) ) ).
% 0.29/0.52
% 0.29/0.52 % add_cancel_right_left
% 0.29/0.52 thf(fact_654_add__cancel__left__right,axiom,
% 0.29/0.52 ! [A: code_integer,B: code_integer] :
% 0.29/0.52 ( ( ( plus_p5714425477246183910nteger @ A @ B )
% 0.29/0.52 = A )
% 0.29/0.52 = ( B = zero_z3403309356797280102nteger ) ) ).
% 0.29/0.52
% 0.29/0.52 % add_cancel_left_right
% 0.29/0.52 thf(fact_655_add__cancel__left__right,axiom,
% 0.29/0.52 ! [A: multis2468970476368604999at_nat,B: multis2468970476368604999at_nat] :
% 0.29/0.52 ( ( ( plus_p7104986032573967614at_nat @ A @ B )
% 0.29/0.52 = A )
% 0.29/0.52 = ( B = zero_z1048942125864253310at_nat ) ) ).
% 0.29/0.52
% 0.29/0.52 % add_cancel_left_right
% 0.29/0.52 thf(fact_656_add__cancel__left__right,axiom,
% 0.29/0.52 ! [A: rat,B: rat] :
% 0.29/0.52 ( ( ( plus_plus_rat @ A @ B )
% 0.29/0.52 = A )
% 0.29/0.52 = ( B = zero_zero_rat ) ) ).
% 0.29/0.52
% 0.29/0.52 % add_cancel_left_right
% 0.29/0.52 thf(fact_657_add__cancel__left__right,axiom,
% 0.29/0.52 ! [A: nat,B: nat] :
% 0.29/0.52 ( ( ( plus_plus_nat @ A @ B )
% 0.29/0.52 = A )
% 0.29/0.52 = ( B = zero_zero_nat ) ) ).
% 0.29/0.52
% 0.29/0.52 % add_cancel_left_right
% 0.29/0.52 thf(fact_658_add__cancel__left__right,axiom,
% 0.29/0.52 ! [A: int,B: int] :
% 0.29/0.52 ( ( ( plus_plus_int @ A @ B )
% 0.29/0.52 = A )
% 0.29/0.52 = ( B = zero_zero_int ) ) ).
% 0.29/0.52
% 0.29/0.52 % add_cancel_left_right
% 0.29/0.52 thf(fact_659_add__cancel__left__left,axiom,
% 0.29/0.52 ! [B: code_integer,A: code_integer] :
% 0.29/0.52 ( ( ( plus_p5714425477246183910nteger @ B @ A )
% 0.29/0.52 = A )
% 0.29/0.52 = ( B = zero_z3403309356797280102nteger ) ) ).
% 0.29/0.52
% 0.29/0.52 % add_cancel_left_left
% 0.29/0.52 thf(fact_660_add__cancel__left__left,axiom,
% 0.29/0.52 ! [B: multis2468970476368604999at_nat,A: multis2468970476368604999at_nat] :
% 0.29/0.52 ( ( ( plus_p7104986032573967614at_nat @ B @ A )
% 0.29/0.52 = A )
% 0.29/0.52 = ( B = zero_z1048942125864253310at_nat ) ) ).
% 0.29/0.52
% 0.29/0.52 % add_cancel_left_left
% 0.29/0.52 thf(fact_661_add__cancel__left__left,axiom,
% 0.29/0.52 ! [B: rat,A: rat] :
% 0.29/0.52 ( ( ( plus_plus_rat @ B @ A )
% 0.29/0.52 = A )
% 0.29/0.52 = ( B = zero_zero_rat ) ) ).
% 0.29/0.52
% 0.29/0.52 % add_cancel_left_left
% 0.29/0.52 thf(fact_662_add__cancel__left__left,axiom,
% 0.29/0.52 ! [B: nat,A: nat] :
% 0.29/0.52 ( ( ( plus_plus_nat @ B @ A )
% 0.29/0.52 = A )
% 0.29/0.52 = ( B = zero_zero_nat ) ) ).
% 0.29/0.52
% 0.29/0.52 % add_cancel_left_left
% 0.29/0.52 thf(fact_663_add__cancel__left__left,axiom,
% 0.29/0.52 ! [B: int,A: int] :
% 0.29/0.52 ( ( ( plus_plus_int @ B @ A )
% 0.29/0.52 = A )
% 0.29/0.52 = ( B = zero_zero_int ) ) ).
% 0.29/0.52
% 0.29/0.52 % add_cancel_left_left
% 0.29/0.52 thf(fact_664_double__zero__sym,axiom,
% 0.29/0.52 ! [A: code_integer] :
% 0.29/0.52 ( ( zero_z3403309356797280102nteger
% 0.29/0.52 = ( plus_p5714425477246183910nteger @ A @ A ) )
% 0.29/0.52 = ( A = zero_z3403309356797280102nteger ) ) ).
% 0.29/0.52
% 0.29/0.52 % double_zero_sym
% 0.29/0.52 thf(fact_665_double__zero__sym,axiom,
% 0.29/0.52 ! [A: rat] :
% 0.29/0.52 ( ( zero_zero_rat
% 0.29/0.52 = ( plus_plus_rat @ A @ A ) )
% 0.29/0.52 = ( A = zero_zero_rat ) ) ).
% 0.29/0.52
% 0.29/0.52 % double_zero_sym
% 0.29/0.52 thf(fact_666_double__zero__sym,axiom,
% 0.29/0.52 ! [A: int] :
% 0.29/0.52 ( ( zero_zero_int
% 0.29/0.52 = ( plus_plus_int @ A @ A ) )
% 0.29/0.52 = ( A = zero_zero_int ) ) ).
% 0.29/0.52
% 0.29/0.52 % double_zero_sym
% 0.29/0.52 thf(fact_667_add_Oright__neutral,axiom,
% 0.29/0.52 ! [A: code_integer] :
% 0.29/0.52 ( ( plus_p5714425477246183910nteger @ A @ zero_z3403309356797280102nteger )
% 0.29/0.52 = A ) ).
% 0.29/0.52
% 0.29/0.52 % add.right_neutral
% 0.29/0.52 thf(fact_668_add_Oright__neutral,axiom,
% 0.29/0.52 ! [A: multis2468970476368604999at_nat] :
% 0.29/0.52 ( ( plus_p7104986032573967614at_nat @ A @ zero_z1048942125864253310at_nat )
% 0.29/0.52 = A ) ).
% 0.29/0.52
% 0.29/0.52 % add.right_neutral
% 0.29/0.52 thf(fact_669_add_Oright__neutral,axiom,
% 0.29/0.52 ! [A: rat] :
% 0.29/0.52 ( ( plus_plus_rat @ A @ zero_zero_rat )
% 0.29/0.52 = A ) ).
% 0.29/0.52
% 0.29/0.52 % add.right_neutral
% 0.29/0.52 thf(fact_670_add_Oright__neutral,axiom,
% 0.29/0.52 ! [A: nat] :
% 0.29/0.52 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 0.29/0.52 = A ) ).
% 0.29/0.52
% 0.29/0.52 % add.right_neutral
% 0.29/0.52 thf(fact_671_add_Oright__neutral,axiom,
% 0.29/0.52 ! [A: int] :
% 0.29/0.52 ( ( plus_plus_int @ A @ zero_zero_int )
% 0.29/0.52 = A ) ).
% 0.29/0.52
% 0.29/0.52 % add.right_neutral
% 0.29/0.52 thf(fact_672_add__gr__0,axiom,
% 0.29/0.52 ! [M2: nat,N2: nat] :
% 0.29/0.52 ( ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ M2 @ N2 ) )
% 0.29/0.52 = ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 0.29/0.52 | ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % add_gr_0
% 0.29/0.52 thf(fact_673_less__one,axiom,
% 0.29/0.52 ! [N2: nat] :
% 0.29/0.52 ( ( ord_less_nat @ N2 @ one_one_nat )
% 0.29/0.52 = ( N2 = zero_zero_nat ) ) ).
% 0.29/0.52
% 0.29/0.52 % less_one
% 0.29/0.52 thf(fact_674_some__opt__eq__trivial,axiom,
% 0.29/0.52 ! [X: num] :
% 0.29/0.52 ( ( eps_Opt_num
% 0.29/0.52 @ ^ [Y3: num] : ( Y3 = X ) )
% 0.29/0.52 = ( some_num @ X ) ) ).
% 0.29/0.52
% 0.29/0.52 % some_opt_eq_trivial
% 0.29/0.52 thf(fact_675_some__opt__eq__trivial,axiom,
% 0.29/0.52 ! [X: produc8664842809031399944it_nat] :
% 0.29/0.52 ( ( eps_Op3393321821070424684it_nat
% 0.29/0.52 @ ^ [Y3: produc8664842809031399944it_nat] : ( Y3 = X ) )
% 0.29/0.52 = ( some_P1914260805536162275it_nat @ X ) ) ).
% 0.29/0.52
% 0.29/0.52 % some_opt_eq_trivial
% 0.29/0.52 thf(fact_676_zero__less__double__add__iff__zero__less__single__add,axiom,
% 0.29/0.52 ! [A: code_integer] :
% 0.29/0.52 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ A @ A ) )
% 0.29/0.52 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 0.29/0.52
% 0.29/0.52 % zero_less_double_add_iff_zero_less_single_add
% 0.29/0.52 thf(fact_677_zero__less__double__add__iff__zero__less__single__add,axiom,
% 0.29/0.52 ! [A: rat] :
% 0.29/0.52 ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ A ) )
% 0.29/0.52 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 0.29/0.52
% 0.29/0.52 % zero_less_double_add_iff_zero_less_single_add
% 0.29/0.52 thf(fact_678_zero__less__double__add__iff__zero__less__single__add,axiom,
% 0.29/0.52 ! [A: int] :
% 0.29/0.52 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
% 0.29/0.52 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 0.29/0.52
% 0.29/0.52 % zero_less_double_add_iff_zero_less_single_add
% 0.29/0.52 thf(fact_679_double__add__less__zero__iff__single__add__less__zero,axiom,
% 0.29/0.52 ! [A: code_integer] :
% 0.29/0.52 ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ A ) @ zero_z3403309356797280102nteger )
% 0.29/0.52 = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 0.29/0.52
% 0.29/0.52 % double_add_less_zero_iff_single_add_less_zero
% 0.29/0.52 thf(fact_680_double__add__less__zero__iff__single__add__less__zero,axiom,
% 0.29/0.52 ! [A: rat] :
% 0.29/0.52 ( ( ord_less_rat @ ( plus_plus_rat @ A @ A ) @ zero_zero_rat )
% 0.29/0.52 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 0.29/0.52
% 0.29/0.52 % double_add_less_zero_iff_single_add_less_zero
% 0.29/0.52 thf(fact_681_double__add__less__zero__iff__single__add__less__zero,axiom,
% 0.29/0.52 ! [A: int] :
% 0.29/0.52 ( ( ord_less_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
% 0.29/0.52 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 0.29/0.52
% 0.29/0.52 % double_add_less_zero_iff_single_add_less_zero
% 0.29/0.52 thf(fact_682_less__add__same__cancel2,axiom,
% 0.29/0.52 ! [A: code_integer,B: code_integer] :
% 0.29/0.52 ( ( ord_le6747313008572928689nteger @ A @ ( plus_p5714425477246183910nteger @ B @ A ) )
% 0.29/0.52 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B ) ) ).
% 0.29/0.52
% 0.29/0.52 % less_add_same_cancel2
% 0.29/0.52 thf(fact_683_less__add__same__cancel2,axiom,
% 0.29/0.52 ! [A: rat,B: rat] :
% 0.29/0.52 ( ( ord_less_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 0.29/0.52 = ( ord_less_rat @ zero_zero_rat @ B ) ) ).
% 0.29/0.52
% 0.29/0.52 % less_add_same_cancel2
% 0.29/0.52 thf(fact_684_less__add__same__cancel2,axiom,
% 0.29/0.52 ! [A: nat,B: nat] :
% 0.29/0.52 ( ( ord_less_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 0.29/0.52 = ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% 0.29/0.52
% 0.29/0.52 % less_add_same_cancel2
% 0.29/0.52 thf(fact_685_less__add__same__cancel2,axiom,
% 0.29/0.52 ! [A: int,B: int] :
% 0.29/0.52 ( ( ord_less_int @ A @ ( plus_plus_int @ B @ A ) )
% 0.29/0.52 = ( ord_less_int @ zero_zero_int @ B ) ) ).
% 0.29/0.52
% 0.29/0.52 % less_add_same_cancel2
% 0.29/0.52 thf(fact_686_less__add__same__cancel1,axiom,
% 0.29/0.52 ! [A: code_integer,B: code_integer] :
% 0.29/0.52 ( ( ord_le6747313008572928689nteger @ A @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 0.29/0.52 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B ) ) ).
% 0.29/0.52
% 0.29/0.52 % less_add_same_cancel1
% 0.29/0.52 thf(fact_687_less__add__same__cancel1,axiom,
% 0.29/0.52 ! [A: rat,B: rat] :
% 0.29/0.52 ( ( ord_less_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 0.29/0.52 = ( ord_less_rat @ zero_zero_rat @ B ) ) ).
% 0.29/0.52
% 0.29/0.52 % less_add_same_cancel1
% 0.29/0.52 thf(fact_688_less__add__same__cancel1,axiom,
% 0.29/0.52 ! [A: nat,B: nat] :
% 0.29/0.52 ( ( ord_less_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 0.29/0.52 = ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% 0.29/0.52
% 0.29/0.52 % less_add_same_cancel1
% 0.29/0.52 thf(fact_689_less__add__same__cancel1,axiom,
% 0.29/0.52 ! [A: int,B: int] :
% 0.29/0.52 ( ( ord_less_int @ A @ ( plus_plus_int @ A @ B ) )
% 0.29/0.52 = ( ord_less_int @ zero_zero_int @ B ) ) ).
% 0.29/0.52
% 0.29/0.52 % less_add_same_cancel1
% 0.29/0.52 thf(fact_690_add__less__same__cancel2,axiom,
% 0.29/0.52 ! [A: code_integer,B: code_integer] :
% 0.29/0.52 ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ B )
% 0.29/0.52 = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 0.29/0.52
% 0.29/0.52 % add_less_same_cancel2
% 0.29/0.52 thf(fact_691_add__less__same__cancel2,axiom,
% 0.29/0.52 ! [A: rat,B: rat] :
% 0.29/0.52 ( ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 0.29/0.52 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 0.29/0.52
% 0.29/0.52 % add_less_same_cancel2
% 0.29/0.52 thf(fact_692_add__less__same__cancel2,axiom,
% 0.29/0.53 ! [A: nat,B: nat] :
% 0.29/0.53 ( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 0.29/0.53 = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 0.29/0.53
% 0.29/0.53 % add_less_same_cancel2
% 0.29/0.53 thf(fact_693_add__less__same__cancel2,axiom,
% 0.29/0.53 ! [A: int,B: int] :
% 0.29/0.53 ( ( ord_less_int @ ( plus_plus_int @ A @ B ) @ B )
% 0.29/0.53 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 0.29/0.53
% 0.29/0.53 % add_less_same_cancel2
% 0.29/0.53 thf(fact_694_add__less__same__cancel1,axiom,
% 0.29/0.53 ! [B: code_integer,A: code_integer] :
% 0.29/0.53 ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ B @ A ) @ B )
% 0.29/0.53 = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 0.29/0.53
% 0.29/0.53 % add_less_same_cancel1
% 0.29/0.53 thf(fact_695_add__less__same__cancel1,axiom,
% 0.29/0.53 ! [B: rat,A: rat] :
% 0.29/0.53 ( ( ord_less_rat @ ( plus_plus_rat @ B @ A ) @ B )
% 0.29/0.53 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 0.29/0.53
% 0.29/0.53 % add_less_same_cancel1
% 0.29/0.53 thf(fact_696_add__less__same__cancel1,axiom,
% 0.29/0.53 ! [B: nat,A: nat] :
% 0.29/0.53 ( ( ord_less_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 0.29/0.53 = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 0.29/0.53
% 0.29/0.53 % add_less_same_cancel1
% 0.29/0.53 thf(fact_697_add__less__same__cancel1,axiom,
% 0.29/0.53 ! [B: int,A: int] :
% 0.29/0.53 ( ( ord_less_int @ ( plus_plus_int @ B @ A ) @ B )
% 0.29/0.53 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 0.29/0.53
% 0.29/0.53 % add_less_same_cancel1
% 0.29/0.53 thf(fact_698_some__opt__false__trivial,axiom,
% 0.29/0.53 ( ( eps_Op1141264490366522080it_nat
% 0.29/0.53 @ ^ [Uu: produc6714399278180371524it_nat] : $false )
% 0.29/0.53 = none_P2587165478634041381it_nat ) ).
% 0.29/0.53
% 0.29/0.53 % some_opt_false_trivial
% 0.29/0.53 thf(fact_699_some__opt__false__trivial,axiom,
% 0.29/0.53 ( ( eps_Opt_num
% 0.29/0.53 @ ^ [Uu: num] : $false )
% 0.29/0.53 = none_num ) ).
% 0.29/0.53
% 0.29/0.53 % some_opt_false_trivial
% 0.29/0.53 thf(fact_700_some__opt__false__trivial,axiom,
% 0.29/0.53 ( ( eps_Op3393321821070424684it_nat
% 0.29/0.53 @ ^ [Uu: produc8664842809031399944it_nat] : $false )
% 0.29/0.53 = none_P9117596204409417319it_nat ) ).
% 0.29/0.53
% 0.29/0.53 % some_opt_false_trivial
% 0.29/0.53 thf(fact_701_zero__reorient,axiom,
% 0.29/0.53 ! [X: code_integer] :
% 0.29/0.53 ( ( zero_z3403309356797280102nteger = X )
% 0.29/0.53 = ( X = zero_z3403309356797280102nteger ) ) ).
% 0.29/0.53
% 0.29/0.53 % zero_reorient
% 0.29/0.53 thf(fact_702_zero__reorient,axiom,
% 0.29/0.53 ! [X: multis2468970476368604999at_nat] :
% 0.29/0.53 ( ( zero_z1048942125864253310at_nat = X )
% 0.29/0.53 = ( X = zero_z1048942125864253310at_nat ) ) ).
% 0.29/0.53
% 0.29/0.53 % zero_reorient
% 0.29/0.53 thf(fact_703_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_704_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_705_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_706_fun_Omap__ident,axiom,
% 0.29/0.53 ! [T: num > code_integer] :
% 0.29/0.53 ( ( comp_C3531382070062128313er_num
% 0.29/0.53 @ ^ [X3: code_integer] : X3
% 0.29/0.53 @ T )
% 0.29/0.53 = T ) ).
% 0.29/0.53
% 0.29/0.53 % fun.map_ident
% 0.29/0.53 thf(fact_707_option_Odisc__eq__case_I2_J,axiom,
% 0.29/0.53 ! [Option: option3216581401566546698it_nat] :
% 0.29/0.53 ( ( Option != none_P2587165478634041381it_nat )
% 0.29/0.53 = ( case_o2169478532838437047it_nat @ $false
% 0.29/0.53 @ ^ [Uu: produc6714399278180371524it_nat] : $true
% 0.29/0.53 @ Option ) ) ).
% 0.29/0.53
% 0.29/0.53 % option.disc_eq_case(2)
% 0.29/0.53 thf(fact_708_option_Odisc__eq__case_I2_J,axiom,
% 0.29/0.53 ! [Option: option_num] :
% 0.29/0.53 ( ( Option != none_num )
% 0.29/0.53 = ( case_option_o_num @ $false
% 0.29/0.53 @ ^ [Uu: num] : $true
% 0.29/0.53 @ Option ) ) ).
% 0.29/0.53
% 0.29/0.53 % option.disc_eq_case(2)
% 0.29/0.53 thf(fact_709_option_Odisc__eq__case_I2_J,axiom,
% 0.29/0.53 ! [Option: option8956607266484857688it_nat] :
% 0.29/0.53 ( ( Option != none_P9117596204409417319it_nat )
% 0.29/0.53 = ( case_o2686588417244861013it_nat @ $false
% 0.29/0.53 @ ^ [Uu: produc8664842809031399944it_nat] : $true
% 0.29/0.53 @ Option ) ) ).
% 0.29/0.53
% 0.29/0.53 % option.disc_eq_case(2)
% 0.29/0.53 thf(fact_710_option_Odisc__eq__case_I1_J,axiom,
% 0.29/0.53 ! [Option: option3216581401566546698it_nat] :
% 0.29/0.53 ( ( Option = none_P2587165478634041381it_nat )
% 0.29/0.53 = ( case_o2169478532838437047it_nat @ $true
% 0.29/0.53 @ ^ [Uu: produc6714399278180371524it_nat] : $false
% 0.29/0.53 @ Option ) ) ).
% 0.29/0.53
% 0.29/0.53 % option.disc_eq_case(1)
% 0.29/0.53 thf(fact_711_option_Odisc__eq__case_I1_J,axiom,
% 0.29/0.53 ! [Option: option_num] :
% 0.29/0.53 ( ( Option = none_num )
% 0.29/0.53 = ( case_option_o_num @ $true
% 0.29/0.53 @ ^ [Uu: num] : $false
% 0.29/0.53 @ Option ) ) ).
% 0.29/0.53
% 0.29/0.53 % option.disc_eq_case(1)
% 0.29/0.53 thf(fact_712_option_Odisc__eq__case_I1_J,axiom,
% 0.29/0.53 ! [Option: option8956607266484857688it_nat] :
% 0.29/0.53 ( ( Option = none_P9117596204409417319it_nat )
% 0.29/0.53 = ( case_o2686588417244861013it_nat @ $true
% 0.29/0.53 @ ^ [Uu: produc8664842809031399944it_nat] : $false
% 0.29/0.53 @ Option ) ) ).
% 0.29/0.53
% 0.29/0.53 % option.disc_eq_case(1)
% 0.29/0.53 thf(fact_713_option_Ocase__distrib,axiom,
% 0.29/0.53 ! [H3: int > int,F1: int,F22: num > int,Option: option_num] :
% 0.29/0.53 ( ( H3 @ ( case_option_int_num @ F1 @ F22 @ Option ) )
% 0.29/0.53 = ( case_option_int_num @ ( H3 @ F1 )
% 0.29/0.53 @ ^ [X3: num] : ( H3 @ ( F22 @ X3 ) )
% 0.29/0.53 @ Option ) ) ).
% 0.29/0.53
% 0.29/0.53 % option.case_distrib
% 0.29/0.53 thf(fact_714_option_Ocase__distrib,axiom,
% 0.29/0.53 ! [H3: int > option_num,F1: int,F22: num > int,Option: option_num] :
% 0.29/0.53 ( ( H3 @ ( case_option_int_num @ F1 @ F22 @ Option ) )
% 0.29/0.53 = ( case_o6005452278849405969um_num @ ( H3 @ F1 )
% 0.29/0.53 @ ^ [X3: num] : ( H3 @ ( F22 @ X3 ) )
% 0.29/0.53 @ Option ) ) ).
% 0.29/0.53
% 0.29/0.53 % option.case_distrib
% 0.29/0.53 thf(fact_715_option_Ocase__distrib,axiom,
% 0.29/0.53 ! [H3: int > num,F1: int,F22: num > int,Option: option_num] :
% 0.29/0.53 ( ( H3 @ ( case_option_int_num @ F1 @ F22 @ Option ) )
% 0.29/0.53 = ( case_option_num_num @ ( H3 @ F1 )
% 0.29/0.53 @ ^ [X3: num] : ( H3 @ ( F22 @ X3 ) )
% 0.29/0.53 @ Option ) ) ).
% 0.29/0.53
% 0.29/0.53 % option.case_distrib
% 0.29/0.53 thf(fact_716_option_Ocase__distrib,axiom,
% 0.29/0.53 ! [H3: option_num > int,F1: option_num,F22: num > option_num,Option: option_num] :
% 0.29/0.53 ( ( H3 @ ( case_o6005452278849405969um_num @ F1 @ F22 @ Option ) )
% 0.29/0.53 = ( case_option_int_num @ ( H3 @ F1 )
% 0.29/0.53 @ ^ [X3: num] : ( H3 @ ( F22 @ X3 ) )
% 0.29/0.53 @ Option ) ) ).
% 0.29/0.53
% 0.29/0.53 % option.case_distrib
% 0.29/0.53 thf(fact_717_option_Ocase__distrib,axiom,
% 0.29/0.53 ! [H3: option_num > option_num,F1: option_num,F22: num > option_num,Option: option_num] :
% 0.29/0.53 ( ( H3 @ ( case_o6005452278849405969um_num @ F1 @ F22 @ Option ) )
% 0.29/0.53 = ( case_o6005452278849405969um_num @ ( H3 @ F1 )
% 0.29/0.53 @ ^ [X3: num] : ( H3 @ ( F22 @ X3 ) )
% 0.29/0.53 @ Option ) ) ).
% 0.29/0.53
% 0.29/0.53 % option.case_distrib
% 0.29/0.53 thf(fact_718_option_Ocase__distrib,axiom,
% 0.29/0.53 ! [H3: option_num > num,F1: option_num,F22: num > option_num,Option: option_num] :
% 0.29/0.53 ( ( H3 @ ( case_o6005452278849405969um_num @ F1 @ F22 @ Option ) )
% 0.29/0.53 = ( case_option_num_num @ ( H3 @ F1 )
% 0.29/0.53 @ ^ [X3: num] : ( H3 @ ( F22 @ X3 ) )
% 0.29/0.53 @ Option ) ) ).
% 0.29/0.53
% 0.29/0.53 % option.case_distrib
% 0.29/0.53 thf(fact_719_option_Ocase__distrib,axiom,
% 0.29/0.53 ! [H3: num > int,F1: num,F22: num > num,Option: option_num] :
% 0.29/0.53 ( ( H3 @ ( case_option_num_num @ F1 @ F22 @ Option ) )
% 0.29/0.53 = ( case_option_int_num @ ( H3 @ F1 )
% 0.29/0.53 @ ^ [X3: num] : ( H3 @ ( F22 @ X3 ) )
% 0.29/0.53 @ Option ) ) ).
% 0.29/0.53
% 0.29/0.53 % option.case_distrib
% 0.29/0.53 thf(fact_720_option_Ocase__distrib,axiom,
% 0.29/0.53 ! [H3: num > option_num,F1: num,F22: num > num,Option: option_num] :
% 0.29/0.53 ( ( H3 @ ( case_option_num_num @ F1 @ F22 @ Option ) )
% 0.29/0.53 = ( case_o6005452278849405969um_num @ ( H3 @ F1 )
% 0.29/0.53 @ ^ [X3: num] : ( H3 @ ( F22 @ X3 ) )
% 0.29/0.53 @ Option ) ) ).
% 0.29/0.53
% 0.29/0.53 % option.case_distrib
% 0.29/0.53 thf(fact_721_option_Ocase__distrib,axiom,
% 0.29/0.53 ! [H3: num > num,F1: num,F22: num > num,Option: option_num] :
% 0.29/0.53 ( ( H3 @ ( case_option_num_num @ F1 @ F22 @ Option ) )
% 0.29/0.53 = ( case_option_num_num @ ( H3 @ F1 )
% 0.29/0.53 @ ^ [X3: num] : ( H3 @ ( F22 @ X3 ) )
% 0.29/0.53 @ Option ) ) ).
% 0.29/0.53
% 0.29/0.53 % option.case_distrib
% 0.29/0.53 thf(fact_722_case__optionE,axiom,
% 0.29/0.53 ! [P: $o,Q: produc6714399278180371524it_nat > $o,X: option3216581401566546698it_nat] :
% 0.29/0.53 ( ( case_o2169478532838437047it_nat @ P @ Q @ X )
% 0.29/0.53 => ( ( ( X = none_P2587165478634041381it_nat )
% 0.29/0.53 => ~ P )
% 0.29/0.53 => ~ ! [Y5: produc6714399278180371524it_nat] :
% 0.29/0.53 ( ( X
% 0.29/0.53 = ( some_P6105628898608307625it_nat @ Y5 ) )
% 0.29/0.53 => ~ ( Q @ Y5 ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % case_optionE
% 0.29/0.53 thf(fact_723_case__optionE,axiom,
% 0.29/0.53 ! [P: $o,Q: num > $o,X: option_num] :
% 0.29/0.53 ( ( case_option_o_num @ P @ Q @ X )
% 0.29/0.53 => ( ( ( X = none_num )
% 0.29/0.53 => ~ P )
% 0.29/0.53 => ~ ! [Y5: num] :
% 0.29/0.53 ( ( X
% 0.29/0.53 = ( some_num @ Y5 ) )
% 0.29/0.53 => ~ ( Q @ Y5 ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % case_optionE
% 0.29/0.53 thf(fact_724_case__optionE,axiom,
% 0.29/0.53 ! [P: $o,Q: produc8664842809031399944it_nat > $o,X: option8956607266484857688it_nat] :
% 0.29/0.53 ( ( case_o2686588417244861013it_nat @ P @ Q @ X )
% 0.29/0.53 => ( ( ( X = none_P9117596204409417319it_nat )
% 0.29/0.53 => ~ P )
% 0.29/0.53 => ~ ! [Y5: produc8664842809031399944it_nat] :
% 0.29/0.53 ( ( X
% 0.29/0.53 = ( some_P1914260805536162275it_nat @ Y5 ) )
% 0.29/0.53 => ~ ( Q @ Y5 ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % case_optionE
% 0.29/0.53 thf(fact_725_combine__options__def,axiom,
% 0.29/0.53 ( combin4318129983670048329it_nat
% 0.29/0.53 = ( ^ [F2: produc8664842809031399944it_nat > produc8664842809031399944it_nat > produc8664842809031399944it_nat,X3: option8956607266484857688it_nat,Y3: option8956607266484857688it_nat] :
% 0.29/0.53 ( case_o2963978774867076333it_nat @ Y3
% 0.29/0.53 @ ^ [Z4: produc8664842809031399944it_nat] :
% 0.29/0.53 ( case_o2963978774867076333it_nat @ ( some_P1914260805536162275it_nat @ Z4 )
% 0.29/0.53 @ ^ [Aa: produc8664842809031399944it_nat] : ( some_P1914260805536162275it_nat @ ( F2 @ Z4 @ Aa ) )
% 0.29/0.53 @ Y3 )
% 0.29/0.53 @ X3 ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % combine_options_def
% 0.29/0.53 thf(fact_726_combine__options__def,axiom,
% 0.29/0.53 ( combine_options_num
% 0.29/0.53 = ( ^ [F2: num > num > num,X3: option_num,Y3: option_num] :
% 0.29/0.53 ( case_o6005452278849405969um_num @ Y3
% 0.29/0.53 @ ^ [Z4: num] :
% 0.29/0.53 ( case_o6005452278849405969um_num @ ( some_num @ Z4 )
% 0.29/0.53 @ ^ [Aa: num] : ( some_num @ ( F2 @ Z4 @ Aa ) )
% 0.29/0.53 @ Y3 )
% 0.29/0.53 @ X3 ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % combine_options_def
% 0.29/0.53 thf(fact_727_less__option__def,axiom,
% 0.29/0.53 ( ord_le7113747843092208513nteger
% 0.29/0.53 = ( ^ [X3: option_Code_integer] :
% 0.29/0.53 ( case_o43118980978444458nteger @ $false
% 0.29/0.53 @ ^ [Y3: code_integer] :
% 0.29/0.53 ( case_o43118980978444458nteger @ $true
% 0.29/0.53 @ ^ [Z4: code_integer] : ( ord_le6747313008572928689nteger @ Z4 @ Y3 )
% 0.29/0.53 @ X3 ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % less_option_def
% 0.29/0.53 thf(fact_728_less__option__def,axiom,
% 0.29/0.53 ( ord_less_option_rat
% 0.29/0.53 = ( ^ [X3: option_rat] :
% 0.29/0.53 ( case_option_o_rat @ $false
% 0.29/0.53 @ ^ [Y3: rat] :
% 0.29/0.53 ( case_option_o_rat @ $true
% 0.29/0.53 @ ^ [Z4: rat] : ( ord_less_rat @ Z4 @ Y3 )
% 0.29/0.53 @ X3 ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % less_option_def
% 0.29/0.53 thf(fact_729_less__option__def,axiom,
% 0.29/0.53 ( ord_less_option_num
% 0.29/0.53 = ( ^ [X3: option_num] :
% 0.29/0.53 ( case_option_o_num @ $false
% 0.29/0.53 @ ^ [Y3: num] :
% 0.29/0.53 ( case_option_o_num @ $true
% 0.29/0.53 @ ^ [Z4: num] : ( ord_less_num @ Z4 @ Y3 )
% 0.29/0.53 @ X3 ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % less_option_def
% 0.29/0.53 thf(fact_730_less__option__def,axiom,
% 0.29/0.53 ( ord_less_option_nat
% 0.29/0.53 = ( ^ [X3: option_nat] :
% 0.29/0.53 ( case_option_o_nat @ $false
% 0.29/0.53 @ ^ [Y3: nat] :
% 0.29/0.53 ( case_option_o_nat @ $true
% 0.29/0.53 @ ^ [Z4: nat] : ( ord_less_nat @ Z4 @ Y3 )
% 0.29/0.53 @ X3 ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % less_option_def
% 0.29/0.53 thf(fact_731_less__option__def,axiom,
% 0.29/0.53 ( ord_less_option_int
% 0.29/0.53 = ( ^ [X3: option_int] :
% 0.29/0.53 ( case_option_o_int @ $false
% 0.29/0.53 @ ^ [Y3: int] :
% 0.29/0.53 ( case_option_o_int @ $true
% 0.29/0.53 @ ^ [Z4: int] : ( ord_less_int @ Z4 @ Y3 )
% 0.29/0.53 @ X3 ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % less_option_def
% 0.29/0.53 thf(fact_732_zero__less__iff__neq__zero,axiom,
% 0.29/0.53 ! [N2: nat] :
% 0.29/0.53 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.53 = ( N2 != zero_zero_nat ) ) ).
% 0.29/0.53
% 0.29/0.53 % zero_less_iff_neq_zero
% 0.29/0.53 thf(fact_733_gr__implies__not__zero,axiom,
% 0.29/0.53 ! [M2: nat,N2: nat] :
% 0.29/0.53 ( ( ord_less_nat @ M2 @ N2 )
% 0.29/0.53 => ( N2 != zero_zero_nat ) ) ).
% 0.29/0.53
% 0.29/0.53 % gr_implies_not_zero
% 0.29/0.53 thf(fact_734_not__less__zero,axiom,
% 0.29/0.53 ! [N2: nat] :
% 0.29/0.53 ~ ( ord_less_nat @ N2 @ zero_zero_nat ) ).
% 0.29/0.53
% 0.29/0.53 % not_less_zero
% 0.29/0.53 thf(fact_735_gr__zeroI,axiom,
% 0.29/0.53 ! [N2: nat] :
% 0.29/0.53 ( ( N2 != zero_zero_nat )
% 0.29/0.53 => ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 0.29/0.53
% 0.29/0.53 % gr_zeroI
% 0.29/0.53 thf(fact_736_add_Ogroup__left__neutral,axiom,
% 0.29/0.53 ! [A: code_integer] :
% 0.29/0.53 ( ( plus_p5714425477246183910nteger @ zero_z3403309356797280102nteger @ A )
% 0.29/0.53 = A ) ).
% 0.29/0.53
% 0.29/0.53 % add.group_left_neutral
% 0.29/0.53 thf(fact_737_add_Ogroup__left__neutral,axiom,
% 0.29/0.53 ! [A: rat] :
% 0.29/0.53 ( ( plus_plus_rat @ zero_zero_rat @ A )
% 0.29/0.53 = A ) ).
% 0.29/0.53
% 0.29/0.53 % add.group_left_neutral
% 0.29/0.53 thf(fact_738_add_Ogroup__left__neutral,axiom,
% 0.29/0.53 ! [A: int] :
% 0.29/0.53 ( ( plus_plus_int @ zero_zero_int @ A )
% 0.29/0.53 = A ) ).
% 0.29/0.53
% 0.29/0.53 % add.group_left_neutral
% 0.29/0.53 thf(fact_739_add_Ocomm__neutral,axiom,
% 0.29/0.53 ! [A: code_integer] :
% 0.29/0.53 ( ( plus_p5714425477246183910nteger @ A @ zero_z3403309356797280102nteger )
% 0.29/0.53 = A ) ).
% 0.29/0.53
% 0.29/0.53 % add.comm_neutral
% 0.29/0.53 thf(fact_740_add_Ocomm__neutral,axiom,
% 0.29/0.53 ! [A: multis2468970476368604999at_nat] :
% 0.29/0.53 ( ( plus_p7104986032573967614at_nat @ A @ zero_z1048942125864253310at_nat )
% 0.29/0.53 = A ) ).
% 0.29/0.53
% 0.29/0.53 % add.comm_neutral
% 0.29/0.53 thf(fact_741_add_Ocomm__neutral,axiom,
% 0.29/0.53 ! [A: rat] :
% 0.29/0.53 ( ( plus_plus_rat @ A @ zero_zero_rat )
% 0.29/0.53 = A ) ).
% 0.29/0.53
% 0.29/0.53 % add.comm_neutral
% 0.29/0.53 thf(fact_742_add_Ocomm__neutral,axiom,
% 0.29/0.53 ! [A: nat] :
% 0.29/0.53 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 0.29/0.53 = A ) ).
% 0.29/0.53
% 0.29/0.53 % add.comm_neutral
% 0.29/0.53 thf(fact_743_add_Ocomm__neutral,axiom,
% 0.29/0.53 ! [A: int] :
% 0.29/0.53 ( ( plus_plus_int @ A @ zero_zero_int )
% 0.29/0.53 = A ) ).
% 0.29/0.53
% 0.29/0.53 % add.comm_neutral
% 0.29/0.53 thf(fact_744_comm__monoid__add__class_Oadd__0,axiom,
% 0.29/0.53 ! [A: code_integer] :
% 0.29/0.53 ( ( plus_p5714425477246183910nteger @ zero_z3403309356797280102nteger @ A )
% 0.29/0.53 = A ) ).
% 0.29/0.53
% 0.29/0.53 % comm_monoid_add_class.add_0
% 0.29/0.53 thf(fact_745_comm__monoid__add__class_Oadd__0,axiom,
% 0.29/0.53 ! [A: multis2468970476368604999at_nat] :
% 0.29/0.53 ( ( plus_p7104986032573967614at_nat @ zero_z1048942125864253310at_nat @ A )
% 0.29/0.53 = A ) ).
% 0.29/0.53
% 0.29/0.53 % comm_monoid_add_class.add_0
% 0.29/0.53 thf(fact_746_comm__monoid__add__class_Oadd__0,axiom,
% 0.29/0.53 ! [A: rat] :
% 0.29/0.53 ( ( plus_plus_rat @ zero_zero_rat @ A )
% 0.29/0.53 = A ) ).
% 0.29/0.53
% 0.29/0.53 % comm_monoid_add_class.add_0
% 0.29/0.53 thf(fact_747_comm__monoid__add__class_Oadd__0,axiom,
% 0.29/0.53 ! [A: nat] :
% 0.29/0.53 ( ( plus_plus_nat @ zero_zero_nat @ A )
% 0.29/0.53 = A ) ).
% 0.29/0.53
% 0.29/0.53 % comm_monoid_add_class.add_0
% 0.29/0.53 thf(fact_748_comm__monoid__add__class_Oadd__0,axiom,
% 0.29/0.53 ! [A: int] :
% 0.29/0.53 ( ( plus_plus_int @ zero_zero_int @ A )
% 0.29/0.53 = A ) ).
% 0.29/0.53
% 0.29/0.53 % comm_monoid_add_class.add_0
% 0.29/0.53 thf(fact_749_zero__neq__one,axiom,
% 0.29/0.53 zero_z3403309356797280102nteger != one_one_Code_integer ).
% 0.29/0.53
% 0.29/0.53 % zero_neq_one
% 0.29/0.53 thf(fact_750_zero__neq__one,axiom,
% 0.29/0.53 zero_zero_rat != one_one_rat ).
% 0.29/0.53
% 0.29/0.53 % zero_neq_one
% 0.29/0.53 thf(fact_751_zero__neq__one,axiom,
% 0.29/0.53 zero_zero_nat != one_one_nat ).
% 0.29/0.53
% 0.29/0.53 % zero_neq_one
% 0.29/0.53 thf(fact_752_zero__neq__one,axiom,
% 0.29/0.53 zero_zero_int != one_one_int ).
% 0.29/0.53
% 0.29/0.53 % zero_neq_one
% 0.29/0.53 thf(fact_753_plus__nat_Oadd__0,axiom,
% 0.29/0.53 ! [N2: nat] :
% 0.29/0.53 ( ( plus_plus_nat @ zero_zero_nat @ N2 )
% 0.29/0.53 = N2 ) ).
% 0.29/0.53
% 0.29/0.53 % plus_nat.add_0
% 0.29/0.53 thf(fact_754_add__eq__self__zero,axiom,
% 0.29/0.53 ! [M2: nat,N2: nat] :
% 0.29/0.53 ( ( ( plus_plus_nat @ M2 @ N2 )
% 0.29/0.53 = M2 )
% 0.29/0.53 => ( N2 = zero_zero_nat ) ) ).
% 0.29/0.53
% 0.29/0.53 % add_eq_self_zero
% 0.29/0.53 thf(fact_755_less__numeral__extra_I1_J,axiom,
% 0.29/0.53 ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ one_one_Code_integer ).
% 0.29/0.53
% 0.29/0.53 % less_numeral_extra(1)
% 0.29/0.53 thf(fact_756_less__numeral__extra_I1_J,axiom,
% 0.29/0.53 ord_less_rat @ zero_zero_rat @ one_one_rat ).
% 0.29/0.53
% 0.29/0.53 % less_numeral_extra(1)
% 0.29/0.53 thf(fact_757_less__numeral__extra_I1_J,axiom,
% 0.29/0.53 ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 0.29/0.53
% 0.29/0.53 % less_numeral_extra(1)
% 0.29/0.53 thf(fact_758_less__numeral__extra_I1_J,axiom,
% 0.29/0.53 ord_less_int @ zero_zero_int @ one_one_int ).
% 0.29/0.53
% 0.29/0.53 % less_numeral_extra(1)
% 0.29/0.53 thf(fact_759_raise__def,axiom,
% 0.29/0.53 ( heap_T1552190017797416154rray_a
% 0.29/0.53 = ( ^ [S4: list_char] :
% 0.29/0.53 ( heap_T1488828001306802186rray_a
% 0.29/0.53 @ ^ [Uu: heap_e7401611519738050253t_unit] : none_P2587165478634041381it_nat ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % raise_def
% 0.29/0.53 thf(fact_760_raise__def,axiom,
% 0.29/0.53 ( heap_T2927564422264180874t_unit
% 0.29/0.53 = ( ^ [S4: list_char] :
% 0.29/0.53 ( heap_T6183433275982383450t_unit
% 0.29/0.53 @ ^ [Uu: heap_e7401611519738050253t_unit] : none_P9117596204409417319it_nat ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % raise_def
% 0.29/0.53 thf(fact_761_guard__def,axiom,
% 0.29/0.53 ( heap_T7685628758766326643rray_a
% 0.29/0.53 = ( ^ [P3: heap_e7401611519738050253t_unit > $o,F2: heap_e7401611519738050253t_unit > produc6714399278180371524it_nat] :
% 0.29/0.53 ( heap_T1488828001306802186rray_a
% 0.29/0.53 @ ^ [H: heap_e7401611519738050253t_unit] : ( if_opt7017092727090204112it_nat @ ( P3 @ H ) @ ( some_P6105628898608307625it_nat @ ( F2 @ H ) ) @ none_P2587165478634041381it_nat ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % guard_def
% 0.29/0.53 thf(fact_762_guard__def,axiom,
% 0.29/0.53 ( heap_T8440541562793052209t_unit
% 0.29/0.53 = ( ^ [P3: heap_e7401611519738050253t_unit > $o,F2: heap_e7401611519738050253t_unit > produc8664842809031399944it_nat] :
% 0.29/0.53 ( heap_T6183433275982383450t_unit
% 0.29/0.53 @ ^ [H: heap_e7401611519738050253t_unit] : ( if_opt1729522071442692626it_nat @ ( P3 @ H ) @ ( some_P1914260805536162275it_nat @ ( F2 @ H ) ) @ none_P9117596204409417319it_nat ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % guard_def
% 0.29/0.53 thf(fact_763_pos__add__strict,axiom,
% 0.29/0.53 ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.29/0.53 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 0.29/0.53 => ( ( ord_le6747313008572928689nteger @ B @ C )
% 0.29/0.53 => ( ord_le6747313008572928689nteger @ B @ ( plus_p5714425477246183910nteger @ A @ C ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % pos_add_strict
% 0.29/0.53 thf(fact_764_pos__add__strict,axiom,
% 0.29/0.53 ! [A: rat,B: rat,C: rat] :
% 0.29/0.53 ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.29/0.53 => ( ( ord_less_rat @ B @ C )
% 0.29/0.53 => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % pos_add_strict
% 0.29/0.53 thf(fact_765_pos__add__strict,axiom,
% 0.29/0.53 ! [A: nat,B: nat,C: nat] :
% 0.29/0.53 ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.29/0.53 => ( ( ord_less_nat @ B @ C )
% 0.29/0.53 => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % pos_add_strict
% 0.29/0.53 thf(fact_766_pos__add__strict,axiom,
% 0.29/0.53 ! [A: int,B: int,C: int] :
% 0.29/0.53 ( ( ord_less_int @ zero_zero_int @ A )
% 0.29/0.53 => ( ( ord_less_int @ B @ C )
% 0.29/0.53 => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % pos_add_strict
% 0.29/0.53 thf(fact_767_canonically__ordered__monoid__add__class_OlessE,axiom,
% 0.29/0.53 ! [A: nat,B: nat] :
% 0.29/0.53 ( ( ord_less_nat @ A @ B )
% 0.29/0.53 => ~ ! [C3: nat] :
% 0.29/0.53 ( ( B
% 0.29/0.53 = ( plus_plus_nat @ A @ C3 ) )
% 0.29/0.53 => ( C3 = zero_zero_nat ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % canonically_ordered_monoid_add_class.lessE
% 0.29/0.53 thf(fact_768_add__pos__pos,axiom,
% 0.29/0.53 ! [A: code_integer,B: code_integer] :
% 0.29/0.53 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 0.29/0.53 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 0.29/0.53 => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % add_pos_pos
% 0.29/0.53 thf(fact_769_add__pos__pos,axiom,
% 0.29/0.53 ! [A: rat,B: rat] :
% 0.29/0.53 ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.29/0.53 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 0.29/0.53 => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % add_pos_pos
% 0.29/0.53 thf(fact_770_add__pos__pos,axiom,
% 0.29/0.53 ! [A: nat,B: nat] :
% 0.29/0.53 ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.29/0.53 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.29/0.53 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % add_pos_pos
% 0.29/0.53 thf(fact_771_add__pos__pos,axiom,
% 0.29/0.53 ! [A: int,B: int] :
% 0.29/0.53 ( ( ord_less_int @ zero_zero_int @ A )
% 0.29/0.53 => ( ( ord_less_int @ zero_zero_int @ B )
% 0.29/0.53 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % add_pos_pos
% 0.29/0.53 thf(fact_772_add__neg__neg,axiom,
% 0.29/0.53 ! [A: code_integer,B: code_integer] :
% 0.29/0.53 ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 0.29/0.53 => ( ( ord_le6747313008572928689nteger @ B @ zero_z3403309356797280102nteger )
% 0.29/0.53 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ zero_z3403309356797280102nteger ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % add_neg_neg
% 0.29/0.53 thf(fact_773_add__neg__neg,axiom,
% 0.29/0.53 ! [A: rat,B: rat] :
% 0.29/0.53 ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.29/0.53 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 0.29/0.53 => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % add_neg_neg
% 0.29/0.53 thf(fact_774_add__neg__neg,axiom,
% 0.29/0.53 ! [A: nat,B: nat] :
% 0.29/0.53 ( ( ord_less_nat @ A @ zero_zero_nat )
% 0.29/0.53 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 0.29/0.53 => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % add_neg_neg
% 0.29/0.53 thf(fact_775_add__neg__neg,axiom,
% 0.29/0.53 ! [A: int,B: int] :
% 0.29/0.53 ( ( ord_less_int @ A @ zero_zero_int )
% 0.29/0.53 => ( ( ord_less_int @ B @ zero_zero_int )
% 0.29/0.53 => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % add_neg_neg
% 0.29/0.53 thf(fact_776_add__less__zeroD,axiom,
% 0.29/0.53 ! [X: code_integer,Y: code_integer] :
% 0.29/0.53 ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ X @ Y ) @ zero_z3403309356797280102nteger )
% 0.29/0.53 => ( ( ord_le6747313008572928689nteger @ X @ zero_z3403309356797280102nteger )
% 0.29/0.53 | ( ord_le6747313008572928689nteger @ Y @ zero_z3403309356797280102nteger ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % add_less_zeroD
% 0.29/0.53 thf(fact_777_add__less__zeroD,axiom,
% 0.29/0.53 ! [X: rat,Y: rat] :
% 0.29/0.53 ( ( ord_less_rat @ ( plus_plus_rat @ X @ Y ) @ zero_zero_rat )
% 0.29/0.53 => ( ( ord_less_rat @ X @ zero_zero_rat )
% 0.29/0.53 | ( ord_less_rat @ Y @ zero_zero_rat ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % add_less_zeroD
% 0.29/0.53 thf(fact_778_add__less__zeroD,axiom,
% 0.29/0.53 ! [X: int,Y: int] :
% 0.29/0.53 ( ( ord_less_int @ ( plus_plus_int @ X @ Y ) @ zero_zero_int )
% 0.29/0.53 => ( ( ord_less_int @ X @ zero_zero_int )
% 0.29/0.53 | ( ord_less_int @ Y @ zero_zero_int ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % add_less_zeroD
% 0.29/0.53 thf(fact_779_zero__less__one,axiom,
% 0.29/0.53 ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ one_one_Code_integer ).
% 0.29/0.53
% 0.29/0.53 % zero_less_one
% 0.29/0.53 thf(fact_780_zero__less__one,axiom,
% 0.29/0.53 ord_less_rat @ zero_zero_rat @ one_one_rat ).
% 0.29/0.53
% 0.29/0.53 % zero_less_one
% 0.29/0.53 thf(fact_781_zero__less__one,axiom,
% 0.29/0.53 ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 0.29/0.53
% 0.29/0.53 % zero_less_one
% 0.29/0.53 thf(fact_782_zero__less__one,axiom,
% 0.29/0.53 ord_less_int @ zero_zero_int @ one_one_int ).
% 0.29/0.53
% 0.29/0.53 % zero_less_one
% 0.29/0.53 thf(fact_783_not__one__less__zero,axiom,
% 0.29/0.53 ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ zero_z3403309356797280102nteger ) ).
% 0.29/0.53
% 0.29/0.53 % not_one_less_zero
% 0.29/0.53 thf(fact_784_not__one__less__zero,axiom,
% 0.29/0.53 ~ ( ord_less_rat @ one_one_rat @ zero_zero_rat ) ).
% 0.29/0.53
% 0.29/0.53 % not_one_less_zero
% 0.29/0.53 thf(fact_785_not__one__less__zero,axiom,
% 0.29/0.53 ~ ( ord_less_nat @ one_one_nat @ zero_zero_nat ) ).
% 0.29/0.53
% 0.29/0.53 % not_one_less_zero
% 0.29/0.53 thf(fact_786_not__one__less__zero,axiom,
% 0.29/0.53 ~ ( ord_less_int @ one_one_int @ zero_zero_int ) ).
% 0.29/0.53
% 0.29/0.53 % not_one_less_zero
% 0.29/0.53 thf(fact_787_execute__ureturn,axiom,
% 0.29/0.53 ! [X: array_a] :
% 0.29/0.53 ( ( heap_T5591663578999710211rray_a @ ( heap_T4328122439115681491rray_a @ X ) )
% 0.29/0.53 = ( comp_P2097125496263478628t_unit @ some_P6105628898608307625it_nat
% 0.29/0.53 @ ^ [H: heap_e7401611519738050253t_unit] : ( produc1733996804261680252it_nat @ X @ ( produc584006145561248582it_nat @ H @ zero_zero_nat ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % execute_ureturn
% 0.29/0.53 thf(fact_788_execute__ureturn,axiom,
% 0.29/0.53 ! [X: product_unit] :
% 0.29/0.53 ( ( heap_T875086893843062177t_unit @ ( heap_T4284346855313245393t_unit @ X ) )
% 0.29/0.53 = ( comp_P3118722334806803912t_unit @ some_P1914260805536162275it_nat
% 0.29/0.53 @ ^ [H: heap_e7401611519738050253t_unit] : ( produc7133225469290080770it_nat @ X @ ( produc584006145561248582it_nat @ H @ zero_zero_nat ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % execute_ureturn
% 0.29/0.53 thf(fact_789_less__imp__add__positive,axiom,
% 0.29/0.53 ! [I: nat,J: nat] :
% 0.29/0.53 ( ( ord_less_nat @ I @ J )
% 0.29/0.53 => ? [K5: nat] :
% 0.29/0.53 ( ( ord_less_nat @ zero_zero_nat @ K5 )
% 0.29/0.53 & ( ( plus_plus_nat @ I @ K5 )
% 0.29/0.53 = J ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % less_imp_add_positive
% 0.29/0.53 thf(fact_790_tap__def,axiom,
% 0.29/0.53 ( heap_T560649228465745139t_unit
% 0.29/0.53 = ( ^ [F2: heap_e7401611519738050253t_unit > product_unit] :
% 0.29/0.53 ( heap_T6183433275982383450t_unit
% 0.29/0.53 @ ^ [H: heap_e7401611519738050253t_unit] : ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ ( F2 @ H ) @ ( produc584006145561248582it_nat @ H @ one_one_nat ) ) ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % tap_def
% 0.29/0.53 thf(fact_791_double__eq__0__iff,axiom,
% 0.29/0.53 ! [A: code_integer] :
% 0.29/0.53 ( ( ( plus_p5714425477246183910nteger @ A @ A )
% 0.29/0.53 = zero_z3403309356797280102nteger )
% 0.29/0.53 = ( A = zero_z3403309356797280102nteger ) ) ).
% 0.29/0.53
% 0.29/0.53 % double_eq_0_iff
% 0.29/0.53 thf(fact_792_double__eq__0__iff,axiom,
% 0.29/0.53 ! [A: rat] :
% 0.29/0.53 ( ( ( plus_plus_rat @ A @ A )
% 0.29/0.53 = zero_zero_rat )
% 0.29/0.53 = ( A = zero_zero_rat ) ) ).
% 0.29/0.53
% 0.29/0.53 % double_eq_0_iff
% 0.29/0.53 thf(fact_793_double__eq__0__iff,axiom,
% 0.29/0.53 ! [A: int] :
% 0.29/0.53 ( ( ( plus_plus_int @ A @ A )
% 0.29/0.53 = zero_zero_int )
% 0.29/0.53 = ( A = zero_zero_int ) ) ).
% 0.29/0.53
% 0.29/0.53 % double_eq_0_iff
% 0.29/0.53 thf(fact_794_add__0__iff,axiom,
% 0.29/0.53 ! [B: code_integer,A: code_integer] :
% 0.29/0.53 ( ( B
% 0.29/0.53 = ( plus_p5714425477246183910nteger @ B @ A ) )
% 0.29/0.53 = ( A = zero_z3403309356797280102nteger ) ) ).
% 0.29/0.53
% 0.29/0.53 % add_0_iff
% 0.29/0.53 thf(fact_795_add__0__iff,axiom,
% 0.29/0.53 ! [B: rat,A: rat] :
% 0.29/0.53 ( ( B
% 0.29/0.53 = ( plus_plus_rat @ B @ A ) )
% 0.29/0.53 = ( A = zero_zero_rat ) ) ).
% 0.29/0.53
% 0.29/0.53 % add_0_iff
% 0.29/0.53 thf(fact_796_add__0__iff,axiom,
% 0.29/0.53 ! [B: nat,A: nat] :
% 0.29/0.53 ( ( B
% 0.29/0.53 = ( plus_plus_nat @ B @ A ) )
% 0.29/0.53 = ( A = zero_zero_nat ) ) ).
% 0.29/0.53
% 0.29/0.53 % add_0_iff
% 0.29/0.53 thf(fact_797_add__0__iff,axiom,
% 0.29/0.53 ! [B: int,A: int] :
% 0.29/0.53 ( ( B
% 0.29/0.53 = ( plus_plus_int @ B @ A ) )
% 0.29/0.53 = ( A = zero_zero_int ) ) ).
% 0.29/0.53
% 0.29/0.53 % add_0_iff
% 0.29/0.53 thf(fact_798_verit__sum__simplify,axiom,
% 0.29/0.53 ! [A: code_integer] :
% 0.29/0.53 ( ( plus_p5714425477246183910nteger @ A @ zero_z3403309356797280102nteger )
% 0.29/0.53 = A ) ).
% 0.29/0.53
% 0.29/0.53 % verit_sum_simplify
% 0.29/0.53 thf(fact_799_verit__sum__simplify,axiom,
% 0.29/0.53 ! [A: multis2468970476368604999at_nat] :
% 0.29/0.53 ( ( plus_p7104986032573967614at_nat @ A @ zero_z1048942125864253310at_nat )
% 0.29/0.53 = A ) ).
% 0.29/0.53
% 0.29/0.53 % verit_sum_simplify
% 0.29/0.53 thf(fact_800_verit__sum__simplify,axiom,
% 0.29/0.53 ! [A: rat] :
% 0.29/0.53 ( ( plus_plus_rat @ A @ zero_zero_rat )
% 0.29/0.53 = A ) ).
% 0.29/0.53
% 0.29/0.53 % verit_sum_simplify
% 0.29/0.53 thf(fact_801_verit__sum__simplify,axiom,
% 0.29/0.53 ! [A: nat] :
% 0.29/0.53 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 0.29/0.53 = A ) ).
% 0.29/0.53
% 0.29/0.53 % verit_sum_simplify
% 0.29/0.53 thf(fact_802_verit__sum__simplify,axiom,
% 0.29/0.53 ! [A: int] :
% 0.29/0.53 ( ( plus_plus_int @ A @ zero_zero_int )
% 0.29/0.53 = A ) ).
% 0.29/0.53
% 0.29/0.53 % verit_sum_simplify
% 0.29/0.53 thf(fact_803_dbl__inc__simps_I2_J,axiom,
% 0.29/0.53 ( ( neg_nu5831290666863070958nteger @ zero_z3403309356797280102nteger )
% 0.29/0.53 = one_one_Code_integer ) ).
% 0.29/0.53
% 0.29/0.53 % dbl_inc_simps(2)
% 0.29/0.53 thf(fact_804_dbl__inc__simps_I2_J,axiom,
% 0.29/0.53 ( ( neg_nu5219082963157363817nc_rat @ zero_zero_rat )
% 0.29/0.53 = one_one_rat ) ).
% 0.29/0.53
% 0.29/0.53 % dbl_inc_simps(2)
% 0.29/0.53 thf(fact_805_dbl__inc__simps_I2_J,axiom,
% 0.29/0.53 ( ( neg_nu5851722552734809277nc_int @ zero_zero_int )
% 0.29/0.53 = one_one_int ) ).
% 0.29/0.53
% 0.29/0.53 % dbl_inc_simps(2)
% 0.29/0.53 thf(fact_806_disjE__realizer2,axiom,
% 0.29/0.53 ! [P: $o,Q: num > $o,X: option_num,R4: int > $o,F: int,G: num > int] :
% 0.29/0.53 ( ( case_option_o_num @ P @ Q @ X )
% 0.29/0.53 => ( ( P
% 0.29/0.53 => ( R4 @ F ) )
% 0.29/0.53 => ( ! [Q2: num] :
% 0.29/0.53 ( ( Q @ Q2 )
% 0.29/0.53 => ( R4 @ ( G @ Q2 ) ) )
% 0.29/0.53 => ( R4 @ ( case_option_int_num @ F @ G @ X ) ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % disjE_realizer2
% 0.29/0.53 thf(fact_807_disjE__realizer2,axiom,
% 0.29/0.53 ! [P: $o,Q: num > $o,X: option_num,R4: option_num > $o,F: option_num,G: num > option_num] :
% 0.29/0.53 ( ( case_option_o_num @ P @ Q @ X )
% 0.29/0.53 => ( ( P
% 0.29/0.53 => ( R4 @ F ) )
% 0.29/0.53 => ( ! [Q2: num] :
% 0.29/0.53 ( ( Q @ Q2 )
% 0.29/0.53 => ( R4 @ ( G @ Q2 ) ) )
% 0.29/0.53 => ( R4 @ ( case_o6005452278849405969um_num @ F @ G @ X ) ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % disjE_realizer2
% 0.29/0.53 thf(fact_808_disjE__realizer2,axiom,
% 0.29/0.53 ! [P: $o,Q: num > $o,X: option_num,R4: num > $o,F: num,G: num > num] :
% 0.29/0.53 ( ( case_option_o_num @ P @ Q @ X )
% 0.29/0.53 => ( ( P
% 0.29/0.53 => ( R4 @ F ) )
% 0.29/0.53 => ( ! [Q2: num] :
% 0.29/0.53 ( ( Q @ Q2 )
% 0.29/0.53 => ( R4 @ ( G @ Q2 ) ) )
% 0.29/0.53 => ( R4 @ ( case_option_num_num @ F @ G @ X ) ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % disjE_realizer2
% 0.29/0.53 thf(fact_809_set__to__map__def,axiom,
% 0.29/0.53 ( set_to4447731662395764663at_nat
% 0.29/0.53 = ( ^ [S5: set_Pr4329608150637261639at_nat,K4: set_Pr1261947904930325089at_nat] :
% 0.29/0.53 ( eps_Op994234036888646909at_nat
% 0.29/0.53 @ ^ [V2: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ K4 @ V2 ) @ S5 ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % set_to_map_def
% 0.29/0.53 thf(fact_810_set__to__map__def,axiom,
% 0.29/0.53 ( set_to_map_nat_nat
% 0.29/0.53 = ( ^ [S5: set_Pr1261947904930325089at_nat,K4: nat] :
% 0.29/0.53 ( eps_Opt_nat
% 0.29/0.53 @ ^ [V2: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ K4 @ V2 ) @ S5 ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % set_to_map_def
% 0.29/0.53 thf(fact_811_set__to__map__def,axiom,
% 0.29/0.53 ( set_to680829756418416360nteger
% 0.29/0.53 = ( ^ [S5: set_Pr1281608226676607948nteger,K4: produc6241069584506657477e_term > option6357759511663192854e_term] :
% 0.29/0.53 ( eps_Op9034888937550303799nteger
% 0.29/0.53 @ ^ [V2: produc8923325533196201883nteger] : ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ K4 @ V2 ) @ S5 ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % set_to_map_def
% 0.29/0.53 thf(fact_812_set__to__map__def,axiom,
% 0.29/0.53 ( set_to6040779677306527128et_nat
% 0.29/0.53 = ( ^ [S5: set_Pr3286484037609594932et_nat,K4: produc3658429121746597890et_nat > $o] :
% 0.29/0.53 ( eps_Op2013419657081471078et_nat
% 0.29/0.53 @ ^ [V2: produc3658429121746597890et_nat] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ K4 @ V2 ) @ S5 ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % set_to_map_def
% 0.29/0.53 thf(fact_813_set__to__map__def,axiom,
% 0.29/0.53 ( set_to2047380710992656148et_nat
% 0.29/0.53 = ( ^ [S5: set_Pr8536935166611901872et_nat,K4: produc3658429121746597890et_nat > $o] :
% 0.29/0.53 ( eps_Op6423059015816587746et_nat
% 0.29/0.53 @ ^ [V2: produc3925858234332021118et_nat] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ K4 @ V2 ) @ S5 ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % set_to_map_def
% 0.29/0.53 thf(fact_814_set__to__map__def,axiom,
% 0.29/0.53 ( set_to6585427216324510421nt_int
% 0.29/0.53 = ( ^ [S5: set_Pr9222295170931077689nt_int,K4: produc8551481072490612790e_term > option6357759511663192854e_term] :
% 0.29/0.53 ( eps_Op2446201859369042517nt_int
% 0.29/0.53 @ ^ [V2: product_prod_int_int] : ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ K4 @ V2 ) @ S5 ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % set_to_map_def
% 0.29/0.53 thf(fact_815_set__to__map__def,axiom,
% 0.29/0.53 ( set_to1653371902132773855nt_int
% 0.29/0.53 = ( ^ [S5: set_Pr1872883991513573699nt_int,K4: int > option6357759511663192854e_term] :
% 0.29/0.53 ( eps_Op2446201859369042517nt_int
% 0.29/0.53 @ ^ [V2: product_prod_int_int] : ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ K4 @ V2 ) @ S5 ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % set_to_map_def
% 0.29/0.53 thf(fact_816_K__record__comp,axiom,
% 0.29/0.53 ! [C: code_integer,F: num > code_integer] :
% 0.29/0.53 ( ( comp_C3531382070062128313er_num
% 0.29/0.53 @ ^ [X3: code_integer] : C
% 0.29/0.53 @ F )
% 0.29/0.53 = ( ^ [X3: num] : C ) ) ).
% 0.29/0.53
% 0.29/0.53 % K_record_comp
% 0.29/0.53 thf(fact_817_K__record__comp,axiom,
% 0.29/0.53 ! [C: produc8923325533196201883nteger > produc8923325533196201883nteger,F: code_integer > code_integer] :
% 0.29/0.53 ( ( comp_C1593894019821074884nteger
% 0.29/0.53 @ ^ [X3: code_integer] : C
% 0.29/0.53 @ F )
% 0.29/0.53 = ( ^ [X3: code_integer] : C ) ) ).
% 0.29/0.53
% 0.29/0.53 % K_record_comp
% 0.29/0.53 thf(fact_818_K__record__comp,axiom,
% 0.29/0.53 ! [C: produc8923325533196201883nteger > produc8923325533196201883nteger,F: code_integer > code_integer > code_integer] :
% 0.29/0.53 ( ( comp_C8797469213163452608nteger
% 0.29/0.53 @ ^ [X3: code_integer > code_integer] : C
% 0.29/0.53 @ F )
% 0.29/0.53 = ( ^ [X3: code_integer] : C ) ) ).
% 0.29/0.53
% 0.29/0.53 % K_record_comp
% 0.29/0.53 thf(fact_819_K__record__comp,axiom,
% 0.29/0.53 ! [C: num,F: int > nat] :
% 0.29/0.53 ( ( comp_nat_num_int
% 0.29/0.53 @ ^ [X3: nat] : C
% 0.29/0.53 @ F )
% 0.29/0.53 = ( ^ [X3: int] : C ) ) ).
% 0.29/0.53
% 0.29/0.53 % K_record_comp
% 0.29/0.53 thf(fact_820_pred__equals__eq2,axiom,
% 0.29/0.53 ! [R4: set_Pr4329608150637261639at_nat,S2: set_Pr4329608150637261639at_nat] :
% 0.29/0.53 ( ( ( ^ [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ Y3 ) @ R4 ) )
% 0.29/0.53 = ( ^ [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ Y3 ) @ S2 ) ) )
% 0.29/0.53 = ( R4 = S2 ) ) ).
% 0.29/0.53
% 0.29/0.53 % pred_equals_eq2
% 0.29/0.53 thf(fact_821_pred__equals__eq2,axiom,
% 0.29/0.53 ! [R4: set_Pr1261947904930325089at_nat,S2: set_Pr1261947904930325089at_nat] :
% 0.29/0.53 ( ( ( ^ [X3: nat,Y3: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y3 ) @ R4 ) )
% 0.29/0.53 = ( ^ [X3: nat,Y3: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y3 ) @ S2 ) ) )
% 0.29/0.53 = ( R4 = S2 ) ) ).
% 0.29/0.53
% 0.29/0.53 % pred_equals_eq2
% 0.29/0.53 thf(fact_822_pred__equals__eq2,axiom,
% 0.29/0.53 ! [R4: set_Pr1281608226676607948nteger,S2: set_Pr1281608226676607948nteger] :
% 0.29/0.53 ( ( ( ^ [X3: produc6241069584506657477e_term > option6357759511663192854e_term,Y3: produc8923325533196201883nteger] : ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X3 @ Y3 ) @ R4 ) )
% 0.29/0.53 = ( ^ [X3: produc6241069584506657477e_term > option6357759511663192854e_term,Y3: produc8923325533196201883nteger] : ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X3 @ Y3 ) @ S2 ) ) )
% 0.29/0.53 = ( R4 = S2 ) ) ).
% 0.29/0.53
% 0.29/0.53 % pred_equals_eq2
% 0.29/0.53 thf(fact_823_pred__equals__eq2,axiom,
% 0.29/0.53 ! [R4: set_Pr3286484037609594932et_nat,S2: set_Pr3286484037609594932et_nat] :
% 0.29/0.53 ( ( ( ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3658429121746597890et_nat] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X3 @ Y3 ) @ R4 ) )
% 0.29/0.53 = ( ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3658429121746597890et_nat] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X3 @ Y3 ) @ S2 ) ) )
% 0.29/0.53 = ( R4 = S2 ) ) ).
% 0.29/0.53
% 0.29/0.53 % pred_equals_eq2
% 0.29/0.53 thf(fact_824_pred__equals__eq2,axiom,
% 0.29/0.53 ! [R4: set_Pr8536935166611901872et_nat,S2: set_Pr8536935166611901872et_nat] :
% 0.29/0.53 ( ( ( ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3925858234332021118et_nat] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X3 @ Y3 ) @ R4 ) )
% 0.29/0.53 = ( ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3925858234332021118et_nat] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X3 @ Y3 ) @ S2 ) ) )
% 0.29/0.53 = ( R4 = S2 ) ) ).
% 0.29/0.53
% 0.29/0.53 % pred_equals_eq2
% 0.29/0.53 thf(fact_825_pred__equals__eq2,axiom,
% 0.29/0.53 ! [R4: set_Pr9222295170931077689nt_int,S2: set_Pr9222295170931077689nt_int] :
% 0.29/0.53 ( ( ( ^ [X3: produc8551481072490612790e_term > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X3 @ Y3 ) @ R4 ) )
% 0.29/0.53 = ( ^ [X3: produc8551481072490612790e_term > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X3 @ Y3 ) @ S2 ) ) )
% 0.29/0.53 = ( R4 = S2 ) ) ).
% 0.29/0.53
% 0.29/0.53 % pred_equals_eq2
% 0.29/0.53 thf(fact_826_pred__equals__eq2,axiom,
% 0.29/0.53 ! [R4: set_Pr1872883991513573699nt_int,S2: set_Pr1872883991513573699nt_int] :
% 0.29/0.53 ( ( ( ^ [X3: int > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X3 @ Y3 ) @ R4 ) )
% 0.29/0.53 = ( ^ [X3: int > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X3 @ Y3 ) @ S2 ) ) )
% 0.29/0.53 = ( R4 = S2 ) ) ).
% 0.29/0.53
% 0.29/0.53 % pred_equals_eq2
% 0.29/0.53 thf(fact_827_dbl__inc__def,axiom,
% 0.29/0.53 ( neg_nu5831290666863070958nteger
% 0.29/0.53 = ( ^ [X3: code_integer] : ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ X3 @ X3 ) @ one_one_Code_integer ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % dbl_inc_def
% 0.29/0.53 thf(fact_828_dbl__inc__def,axiom,
% 0.29/0.53 ( neg_nu5219082963157363817nc_rat
% 0.29/0.53 = ( ^ [X3: rat] : ( plus_plus_rat @ ( plus_plus_rat @ X3 @ X3 ) @ one_one_rat ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % dbl_inc_def
% 0.29/0.53 thf(fact_829_dbl__inc__def,axiom,
% 0.29/0.53 ( neg_nu5851722552734809277nc_int
% 0.29/0.53 = ( ^ [X3: int] : ( plus_plus_int @ ( plus_plus_int @ X3 @ X3 ) @ one_one_int ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % dbl_inc_def
% 0.29/0.53 thf(fact_830_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_831_fails__wait,axiom,
% 0.29/0.53 ! [X: nat,H3: heap_e7401611519738050253t_unit] :
% 0.29/0.53 ~ ( time_f8834461667527620124t_unit @ ( heap_Time_wait @ X ) @ H3 ) ).
% 0.29/0.53
% 0.29/0.53 % fails_wait
% 0.29/0.53 thf(fact_832_Euclid__induct,axiom,
% 0.29/0.53 ! [P: nat > nat > $o,A: nat,B: nat] :
% 0.29/0.53 ( ! [A3: nat,B2: nat] :
% 0.29/0.53 ( ( P @ A3 @ B2 )
% 0.29/0.53 = ( P @ B2 @ A3 ) )
% 0.29/0.53 => ( ! [A3: nat] : ( P @ A3 @ zero_zero_nat )
% 0.29/0.53 => ( ! [A3: nat,B2: nat] :
% 0.29/0.53 ( ( P @ A3 @ B2 )
% 0.29/0.53 => ( P @ A3 @ ( plus_plus_nat @ A3 @ B2 ) ) )
% 0.29/0.53 => ( P @ A @ B ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % Euclid_induct
% 0.29/0.53 thf(fact_833_Ints__odd__less__0,axiom,
% 0.29/0.53 ! [A: code_integer] :
% 0.29/0.53 ( ( member_Code_integer @ A @ ring_11222124179247155820nteger )
% 0.29/0.53 => ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ A ) @ zero_z3403309356797280102nteger )
% 0.29/0.53 = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % Ints_odd_less_0
% 0.29/0.53 thf(fact_834_Ints__odd__less__0,axiom,
% 0.29/0.53 ! [A: rat] :
% 0.29/0.53 ( ( member_rat @ A @ ring_1_Ints_rat )
% 0.29/0.53 => ( ( ord_less_rat @ ( plus_plus_rat @ ( plus_plus_rat @ one_one_rat @ A ) @ A ) @ zero_zero_rat )
% 0.29/0.53 = ( ord_less_rat @ A @ zero_zero_rat ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % Ints_odd_less_0
% 0.29/0.53 thf(fact_835_Ints__odd__less__0,axiom,
% 0.29/0.53 ! [A: int] :
% 0.29/0.53 ( ( member_int @ A @ ring_1_Ints_int )
% 0.29/0.53 => ( ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ A ) @ A ) @ zero_zero_int )
% 0.29/0.53 = ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % Ints_odd_less_0
% 0.29/0.53 thf(fact_836_num__of__nat__plus__distrib,axiom,
% 0.29/0.53 ! [M2: nat,N2: nat] :
% 0.29/0.53 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 0.29/0.53 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.53 => ( ( num_of_nat @ ( plus_plus_nat @ M2 @ N2 ) )
% 0.29/0.53 = ( plus_plus_num @ ( num_of_nat @ M2 ) @ ( num_of_nat @ N2 ) ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % num_of_nat_plus_distrib
% 0.29/0.53 thf(fact_837_divides__aux__eq,axiom,
% 0.29/0.53 ! [Q3: code_integer,R2: code_integer] :
% 0.29/0.53 ( ( unique5706413561485394159nteger @ ( produc1086072967326762835nteger @ Q3 @ R2 ) )
% 0.29/0.53 = ( R2 = zero_z3403309356797280102nteger ) ) ).
% 0.29/0.53
% 0.29/0.53 % divides_aux_eq
% 0.29/0.53 thf(fact_838_divides__aux__eq,axiom,
% 0.29/0.53 ! [Q3: nat,R2: nat] :
% 0.29/0.53 ( ( unique6322359934112328802ux_nat @ ( product_Pair_nat_nat @ Q3 @ R2 ) )
% 0.29/0.53 = ( R2 = zero_zero_nat ) ) ).
% 0.29/0.53
% 0.29/0.53 % divides_aux_eq
% 0.29/0.53 thf(fact_839_divides__aux__eq,axiom,
% 0.29/0.53 ! [Q3: int,R2: int] :
% 0.29/0.53 ( ( unique6319869463603278526ux_int @ ( product_Pair_int_int @ Q3 @ R2 ) )
% 0.29/0.53 = ( R2 = zero_zero_int ) ) ).
% 0.29/0.53
% 0.29/0.53 % divides_aux_eq
% 0.29/0.53 thf(fact_840_sgn__pos,axiom,
% 0.29/0.53 ! [A: code_integer] :
% 0.29/0.53 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 0.29/0.53 => ( ( sgn_sgn_Code_integer @ A )
% 0.29/0.53 = one_one_Code_integer ) ) ).
% 0.29/0.53
% 0.29/0.53 % sgn_pos
% 0.29/0.53 thf(fact_841_sgn__pos,axiom,
% 0.29/0.53 ! [A: rat] :
% 0.29/0.53 ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.29/0.53 => ( ( sgn_sgn_rat @ A )
% 0.29/0.53 = one_one_rat ) ) ).
% 0.29/0.53
% 0.29/0.53 % sgn_pos
% 0.29/0.53 thf(fact_842_sgn__pos,axiom,
% 0.29/0.53 ! [A: int] :
% 0.29/0.53 ( ( ord_less_int @ zero_zero_int @ A )
% 0.29/0.53 => ( ( sgn_sgn_int @ A )
% 0.29/0.53 = one_one_int ) ) ).
% 0.29/0.53
% 0.29/0.53 % sgn_pos
% 0.29/0.53 thf(fact_843_abs__add__one__gt__zero,axiom,
% 0.29/0.53 ! [X: code_integer] : ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( abs_abs_Code_integer @ X ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % abs_add_one_gt_zero
% 0.29/0.53 thf(fact_844_abs__add__one__gt__zero,axiom,
% 0.29/0.53 ! [X: rat] : ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ one_one_rat @ ( abs_abs_rat @ X ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % abs_add_one_gt_zero
% 0.29/0.53 thf(fact_845_abs__add__one__gt__zero,axiom,
% 0.29/0.53 ! [X: int] : ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ ( abs_abs_int @ X ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % abs_add_one_gt_zero
% 0.29/0.53 thf(fact_846_map__option__case,axiom,
% 0.29/0.53 ( map_option_num_num
% 0.29/0.53 = ( ^ [F2: num > num] :
% 0.29/0.53 ( case_o6005452278849405969um_num @ none_num
% 0.29/0.53 @ ^ [X3: num] : ( some_num @ ( F2 @ X3 ) ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % map_option_case
% 0.29/0.53 thf(fact_847_add__neg__numeral__special_I7_J,axiom,
% 0.29/0.53 ( ( plus_plus_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) )
% 0.29/0.53 = zero_zero_int ) ).
% 0.29/0.53
% 0.29/0.53 % add_neg_numeral_special(7)
% 0.29/0.53 thf(fact_848_add__neg__numeral__special_I7_J,axiom,
% 0.29/0.53 ( ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.29/0.53 = zero_z3403309356797280102nteger ) ).
% 0.29/0.53
% 0.29/0.53 % add_neg_numeral_special(7)
% 0.29/0.53 thf(fact_849_add__neg__numeral__special_I7_J,axiom,
% 0.29/0.53 ( ( plus_plus_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.29/0.53 = zero_zero_rat ) ).
% 0.29/0.53
% 0.29/0.53 % add_neg_numeral_special(7)
% 0.29/0.53 thf(fact_850_add__neg__numeral__special_I8_J,axiom,
% 0.29/0.53 ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 0.29/0.53 = zero_zero_int ) ).
% 0.29/0.53
% 0.29/0.53 % add_neg_numeral_special(8)
% 0.29/0.53 thf(fact_851_add__neg__numeral__special_I8_J,axiom,
% 0.29/0.53 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer )
% 0.29/0.53 = zero_z3403309356797280102nteger ) ).
% 0.29/0.53
% 0.29/0.53 % add_neg_numeral_special(8)
% 0.29/0.53 thf(fact_852_add__neg__numeral__special_I8_J,axiom,
% 0.29/0.53 ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat )
% 0.29/0.53 = zero_zero_rat ) ).
% 0.29/0.53
% 0.29/0.53 % add_neg_numeral_special(8)
% 0.29/0.53 thf(fact_853_dbl__dec__simps_I3_J,axiom,
% 0.29/0.53 ( ( neg_nu7757733837767384882nteger @ one_one_Code_integer )
% 0.29/0.53 = one_one_Code_integer ) ).
% 0.29/0.53
% 0.29/0.53 % dbl_dec_simps(3)
% 0.29/0.53 thf(fact_854_dbl__dec__simps_I3_J,axiom,
% 0.29/0.53 ( ( neg_nu3179335615603231917ec_rat @ one_one_rat )
% 0.29/0.53 = one_one_rat ) ).
% 0.29/0.53
% 0.29/0.53 % dbl_dec_simps(3)
% 0.29/0.53 thf(fact_855_dbl__dec__simps_I3_J,axiom,
% 0.29/0.53 ( ( neg_nu3811975205180677377ec_int @ one_one_int )
% 0.29/0.53 = one_one_int ) ).
% 0.29/0.53
% 0.29/0.53 % dbl_dec_simps(3)
% 0.29/0.53 thf(fact_856_neg__equal__iff__equal,axiom,
% 0.29/0.53 ! [A: int,B: int] :
% 0.29/0.53 ( ( ( uminus_uminus_int @ A )
% 0.29/0.53 = ( uminus_uminus_int @ B ) )
% 0.29/0.53 = ( A = B ) ) ).
% 0.29/0.53
% 0.29/0.53 % neg_equal_iff_equal
% 0.29/0.53 thf(fact_857_neg__equal__iff__equal,axiom,
% 0.29/0.53 ! [A: code_integer,B: code_integer] :
% 0.29/0.53 ( ( ( uminus1351360451143612070nteger @ A )
% 0.29/0.53 = ( uminus1351360451143612070nteger @ B ) )
% 0.29/0.53 = ( A = B ) ) ).
% 0.29/0.53
% 0.29/0.53 % neg_equal_iff_equal
% 0.29/0.53 thf(fact_858_neg__equal__iff__equal,axiom,
% 0.29/0.53 ! [A: rat,B: rat] :
% 0.29/0.53 ( ( ( uminus_uminus_rat @ A )
% 0.29/0.53 = ( uminus_uminus_rat @ B ) )
% 0.29/0.53 = ( A = B ) ) ).
% 0.29/0.53
% 0.29/0.53 % neg_equal_iff_equal
% 0.29/0.53 thf(fact_859_add_Oinverse__inverse,axiom,
% 0.29/0.53 ! [A: int] :
% 0.29/0.53 ( ( uminus_uminus_int @ ( uminus_uminus_int @ A ) )
% 0.29/0.53 = A ) ).
% 0.29/0.53
% 0.29/0.53 % add.inverse_inverse
% 0.29/0.53 thf(fact_860_add_Oinverse__inverse,axiom,
% 0.29/0.53 ! [A: code_integer] :
% 0.29/0.53 ( ( uminus1351360451143612070nteger @ ( uminus1351360451143612070nteger @ A ) )
% 0.29/0.53 = A ) ).
% 0.29/0.53
% 0.29/0.53 % add.inverse_inverse
% 0.29/0.53 thf(fact_861_add_Oinverse__inverse,axiom,
% 0.29/0.53 ! [A: rat] :
% 0.29/0.53 ( ( uminus_uminus_rat @ ( uminus_uminus_rat @ A ) )
% 0.29/0.53 = A ) ).
% 0.29/0.53
% 0.29/0.53 % add.inverse_inverse
% 0.29/0.53 thf(fact_862_abs__idempotent,axiom,
% 0.29/0.53 ! [A: int] :
% 0.29/0.53 ( ( abs_abs_int @ ( abs_abs_int @ A ) )
% 0.29/0.53 = ( abs_abs_int @ A ) ) ).
% 0.29/0.53
% 0.29/0.53 % abs_idempotent
% 0.29/0.53 thf(fact_863_abs__idempotent,axiom,
% 0.29/0.53 ! [A: code_integer] :
% 0.29/0.53 ( ( abs_abs_Code_integer @ ( abs_abs_Code_integer @ A ) )
% 0.29/0.53 = ( abs_abs_Code_integer @ A ) ) ).
% 0.29/0.53
% 0.29/0.53 % abs_idempotent
% 0.29/0.53 thf(fact_864_abs__idempotent,axiom,
% 0.29/0.53 ! [A: rat] :
% 0.29/0.53 ( ( abs_abs_rat @ ( abs_abs_rat @ A ) )
% 0.29/0.53 = ( abs_abs_rat @ A ) ) ).
% 0.29/0.53
% 0.29/0.53 % abs_idempotent
% 0.29/0.53 thf(fact_865_neg__equal__zero,axiom,
% 0.29/0.53 ! [A: int] :
% 0.29/0.53 ( ( ( uminus_uminus_int @ A )
% 0.29/0.53 = A )
% 0.29/0.53 = ( A = zero_zero_int ) ) ).
% 0.29/0.53
% 0.29/0.53 % neg_equal_zero
% 0.29/0.53 thf(fact_866_neg__equal__zero,axiom,
% 0.29/0.53 ! [A: code_integer] :
% 0.29/0.53 ( ( ( uminus1351360451143612070nteger @ A )
% 0.29/0.53 = A )
% 0.29/0.53 = ( A = zero_z3403309356797280102nteger ) ) ).
% 0.29/0.53
% 0.29/0.53 % neg_equal_zero
% 0.29/0.53 thf(fact_867_neg__equal__zero,axiom,
% 0.29/0.53 ! [A: rat] :
% 0.29/0.53 ( ( ( uminus_uminus_rat @ A )
% 0.29/0.53 = A )
% 0.29/0.53 = ( A = zero_zero_rat ) ) ).
% 0.29/0.53
% 0.29/0.53 % neg_equal_zero
% 0.29/0.53 thf(fact_868_equal__neg__zero,axiom,
% 0.29/0.53 ! [A: int] :
% 0.29/0.53 ( ( A
% 0.29/0.53 = ( uminus_uminus_int @ A ) )
% 0.29/0.53 = ( A = zero_zero_int ) ) ).
% 0.29/0.53
% 0.29/0.53 % equal_neg_zero
% 0.29/0.53 thf(fact_869_equal__neg__zero,axiom,
% 0.29/0.53 ! [A: code_integer] :
% 0.29/0.53 ( ( A
% 0.29/0.53 = ( uminus1351360451143612070nteger @ A ) )
% 0.29/0.53 = ( A = zero_z3403309356797280102nteger ) ) ).
% 0.29/0.53
% 0.29/0.53 % equal_neg_zero
% 0.29/0.53 thf(fact_870_equal__neg__zero,axiom,
% 0.29/0.53 ! [A: rat] :
% 0.29/0.53 ( ( A
% 0.29/0.53 = ( uminus_uminus_rat @ A ) )
% 0.29/0.53 = ( A = zero_zero_rat ) ) ).
% 0.29/0.53
% 0.29/0.53 % equal_neg_zero
% 0.29/0.53 thf(fact_871_neg__equal__0__iff__equal,axiom,
% 0.29/0.53 ! [A: int] :
% 0.29/0.53 ( ( ( uminus_uminus_int @ A )
% 0.29/0.53 = zero_zero_int )
% 0.29/0.53 = ( A = zero_zero_int ) ) ).
% 0.29/0.53
% 0.29/0.53 % neg_equal_0_iff_equal
% 0.29/0.53 thf(fact_872_neg__equal__0__iff__equal,axiom,
% 0.29/0.53 ! [A: code_integer] :
% 0.29/0.53 ( ( ( uminus1351360451143612070nteger @ A )
% 0.29/0.53 = zero_z3403309356797280102nteger )
% 0.29/0.53 = ( A = zero_z3403309356797280102nteger ) ) ).
% 0.29/0.53
% 0.29/0.53 % neg_equal_0_iff_equal
% 0.29/0.53 thf(fact_873_neg__equal__0__iff__equal,axiom,
% 0.29/0.53 ! [A: rat] :
% 0.29/0.53 ( ( ( uminus_uminus_rat @ A )
% 0.29/0.53 = zero_zero_rat )
% 0.29/0.53 = ( A = zero_zero_rat ) ) ).
% 0.29/0.53
% 0.29/0.53 % neg_equal_0_iff_equal
% 0.29/0.53 thf(fact_874_neg__0__equal__iff__equal,axiom,
% 0.29/0.53 ! [A: int] :
% 0.29/0.53 ( ( zero_zero_int
% 0.29/0.53 = ( uminus_uminus_int @ A ) )
% 0.29/0.53 = ( zero_zero_int = A ) ) ).
% 0.29/0.53
% 0.29/0.53 % neg_0_equal_iff_equal
% 0.29/0.53 thf(fact_875_neg__0__equal__iff__equal,axiom,
% 0.29/0.53 ! [A: code_integer] :
% 0.29/0.53 ( ( zero_z3403309356797280102nteger
% 0.29/0.53 = ( uminus1351360451143612070nteger @ A ) )
% 0.29/0.53 = ( zero_z3403309356797280102nteger = A ) ) ).
% 0.29/0.53
% 0.29/0.53 % neg_0_equal_iff_equal
% 0.29/0.53 thf(fact_876_neg__0__equal__iff__equal,axiom,
% 0.29/0.53 ! [A: rat] :
% 0.29/0.53 ( ( zero_zero_rat
% 0.29/0.53 = ( uminus_uminus_rat @ A ) )
% 0.29/0.53 = ( zero_zero_rat = A ) ) ).
% 0.29/0.53
% 0.29/0.53 % neg_0_equal_iff_equal
% 0.29/0.53 thf(fact_877_add_Oinverse__neutral,axiom,
% 0.29/0.53 ( ( uminus_uminus_int @ zero_zero_int )
% 0.29/0.53 = zero_zero_int ) ).
% 0.29/0.53
% 0.29/0.53 % add.inverse_neutral
% 0.29/0.53 thf(fact_878_add_Oinverse__neutral,axiom,
% 0.29/0.53 ( ( uminus1351360451143612070nteger @ zero_z3403309356797280102nteger )
% 0.29/0.53 = zero_z3403309356797280102nteger ) ).
% 0.29/0.53
% 0.29/0.53 % add.inverse_neutral
% 0.29/0.53 thf(fact_879_add_Oinverse__neutral,axiom,
% 0.29/0.53 ( ( uminus_uminus_rat @ zero_zero_rat )
% 0.29/0.53 = zero_zero_rat ) ).
% 0.29/0.53
% 0.29/0.53 % add.inverse_neutral
% 0.29/0.53 thf(fact_880_neg__less__iff__less,axiom,
% 0.29/0.53 ! [B: int,A: int] :
% 0.29/0.53 ( ( ord_less_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) )
% 0.29/0.53 = ( ord_less_int @ A @ B ) ) ).
% 0.29/0.53
% 0.29/0.53 % neg_less_iff_less
% 0.29/0.53 thf(fact_881_neg__less__iff__less,axiom,
% 0.29/0.53 ! [B: code_integer,A: code_integer] :
% 0.29/0.53 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) )
% 0.29/0.53 = ( ord_le6747313008572928689nteger @ A @ B ) ) ).
% 0.29/0.53
% 0.29/0.53 % neg_less_iff_less
% 0.29/0.53 thf(fact_882_neg__less__iff__less,axiom,
% 0.29/0.53 ! [B: rat,A: rat] :
% 0.29/0.53 ( ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) )
% 0.29/0.53 = ( ord_less_rat @ A @ B ) ) ).
% 0.29/0.53
% 0.29/0.53 % neg_less_iff_less
% 0.29/0.53 thf(fact_883_minus__add__distrib,axiom,
% 0.29/0.53 ! [A: int,B: int] :
% 0.29/0.53 ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 0.29/0.53 = ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % minus_add_distrib
% 0.29/0.53 thf(fact_884_minus__add__distrib,axiom,
% 0.29/0.53 ! [A: code_integer,B: code_integer] :
% 0.29/0.53 ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 0.29/0.53 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % minus_add_distrib
% 0.29/0.53 thf(fact_885_minus__add__distrib,axiom,
% 0.29/0.53 ! [A: rat,B: rat] :
% 0.29/0.53 ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 0.29/0.53 = ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % minus_add_distrib
% 0.29/0.53 thf(fact_886_minus__add__cancel,axiom,
% 0.29/0.53 ! [A: int,B: int] :
% 0.29/0.53 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( plus_plus_int @ A @ B ) )
% 0.29/0.53 = B ) ).
% 0.29/0.53
% 0.29/0.53 % minus_add_cancel
% 0.29/0.53 thf(fact_887_minus__add__cancel,axiom,
% 0.29/0.53 ! [A: code_integer,B: code_integer] :
% 0.29/0.53 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 0.29/0.53 = B ) ).
% 0.29/0.53
% 0.29/0.53 % minus_add_cancel
% 0.29/0.53 thf(fact_888_minus__add__cancel,axiom,
% 0.29/0.53 ! [A: rat,B: rat] :
% 0.29/0.53 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( plus_plus_rat @ A @ B ) )
% 0.29/0.53 = B ) ).
% 0.29/0.53
% 0.29/0.53 % minus_add_cancel
% 0.29/0.53 thf(fact_889_add__minus__cancel,axiom,
% 0.29/0.53 ! [A: int,B: int] :
% 0.29/0.53 ( ( plus_plus_int @ A @ ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B ) )
% 0.29/0.53 = B ) ).
% 0.29/0.53
% 0.29/0.53 % add_minus_cancel
% 0.29/0.53 thf(fact_890_add__minus__cancel,axiom,
% 0.29/0.53 ! [A: code_integer,B: code_integer] :
% 0.29/0.53 ( ( plus_p5714425477246183910nteger @ A @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) )
% 0.29/0.53 = B ) ).
% 0.29/0.53
% 0.29/0.53 % add_minus_cancel
% 0.29/0.53 thf(fact_891_add__minus__cancel,axiom,
% 0.29/0.53 ! [A: rat,B: rat] :
% 0.29/0.53 ( ( plus_plus_rat @ A @ ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ B ) )
% 0.29/0.53 = B ) ).
% 0.29/0.53
% 0.29/0.53 % add_minus_cancel
% 0.29/0.53 thf(fact_892_abs__zero,axiom,
% 0.29/0.53 ( ( abs_abs_Code_integer @ zero_z3403309356797280102nteger )
% 0.29/0.53 = zero_z3403309356797280102nteger ) ).
% 0.29/0.53
% 0.29/0.53 % abs_zero
% 0.29/0.53 thf(fact_893_abs__zero,axiom,
% 0.29/0.53 ( ( abs_abs_rat @ zero_zero_rat )
% 0.29/0.53 = zero_zero_rat ) ).
% 0.29/0.53
% 0.29/0.53 % abs_zero
% 0.29/0.53 thf(fact_894_abs__zero,axiom,
% 0.29/0.53 ( ( abs_abs_int @ zero_zero_int )
% 0.29/0.53 = zero_zero_int ) ).
% 0.29/0.53
% 0.29/0.53 % abs_zero
% 0.29/0.53 thf(fact_895_abs__eq__0,axiom,
% 0.29/0.53 ! [A: code_integer] :
% 0.29/0.53 ( ( ( abs_abs_Code_integer @ A )
% 0.29/0.53 = zero_z3403309356797280102nteger )
% 0.29/0.53 = ( A = zero_z3403309356797280102nteger ) ) ).
% 0.29/0.53
% 0.29/0.53 % abs_eq_0
% 0.29/0.53 thf(fact_896_abs__eq__0,axiom,
% 0.29/0.53 ! [A: rat] :
% 0.29/0.53 ( ( ( abs_abs_rat @ A )
% 0.29/0.53 = zero_zero_rat )
% 0.29/0.53 = ( A = zero_zero_rat ) ) ).
% 0.29/0.53
% 0.29/0.53 % abs_eq_0
% 0.29/0.53 thf(fact_897_abs__eq__0,axiom,
% 0.29/0.53 ! [A: int] :
% 0.29/0.53 ( ( ( abs_abs_int @ A )
% 0.29/0.53 = zero_zero_int )
% 0.29/0.53 = ( A = zero_zero_int ) ) ).
% 0.29/0.53
% 0.29/0.53 % abs_eq_0
% 0.29/0.53 thf(fact_898_abs__0__eq,axiom,
% 0.29/0.53 ! [A: code_integer] :
% 0.29/0.53 ( ( zero_z3403309356797280102nteger
% 0.29/0.53 = ( abs_abs_Code_integer @ A ) )
% 0.29/0.53 = ( A = zero_z3403309356797280102nteger ) ) ).
% 0.29/0.53
% 0.29/0.53 % abs_0_eq
% 0.29/0.53 thf(fact_899_abs__0__eq,axiom,
% 0.29/0.53 ! [A: rat] :
% 0.29/0.53 ( ( zero_zero_rat
% 0.29/0.53 = ( abs_abs_rat @ A ) )
% 0.29/0.53 = ( A = zero_zero_rat ) ) ).
% 0.29/0.53
% 0.29/0.53 % abs_0_eq
% 0.29/0.53 thf(fact_900_abs__0__eq,axiom,
% 0.29/0.53 ! [A: int] :
% 0.29/0.53 ( ( zero_zero_int
% 0.29/0.53 = ( abs_abs_int @ A ) )
% 0.29/0.53 = ( A = zero_zero_int ) ) ).
% 0.29/0.53
% 0.29/0.53 % abs_0_eq
% 0.29/0.53 thf(fact_901_abs__add__abs,axiom,
% 0.29/0.53 ! [A: code_integer,B: code_integer] :
% 0.29/0.53 ( ( abs_abs_Code_integer @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) )
% 0.29/0.53 = ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % abs_add_abs
% 0.29/0.53 thf(fact_902_abs__add__abs,axiom,
% 0.29/0.53 ! [A: rat,B: rat] :
% 0.29/0.53 ( ( abs_abs_rat @ ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) )
% 0.29/0.53 = ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % abs_add_abs
% 0.29/0.53 thf(fact_903_abs__add__abs,axiom,
% 0.29/0.53 ! [A: int,B: int] :
% 0.29/0.53 ( ( abs_abs_int @ ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) )
% 0.29/0.53 = ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % abs_add_abs
% 0.29/0.53 thf(fact_904_abs__1,axiom,
% 0.29/0.53 ( ( abs_abs_Code_integer @ one_one_Code_integer )
% 0.29/0.53 = one_one_Code_integer ) ).
% 0.29/0.53
% 0.29/0.53 % abs_1
% 0.29/0.53 thf(fact_905_abs__1,axiom,
% 0.29/0.53 ( ( abs_abs_rat @ one_one_rat )
% 0.29/0.53 = one_one_rat ) ).
% 0.29/0.53
% 0.29/0.53 % abs_1
% 0.29/0.53 thf(fact_906_abs__1,axiom,
% 0.29/0.53 ( ( abs_abs_int @ one_one_int )
% 0.29/0.53 = one_one_int ) ).
% 0.29/0.53
% 0.29/0.53 % abs_1
% 0.29/0.53 thf(fact_907_abs__minus__cancel,axiom,
% 0.29/0.53 ! [A: int] :
% 0.29/0.53 ( ( abs_abs_int @ ( uminus_uminus_int @ A ) )
% 0.29/0.53 = ( abs_abs_int @ A ) ) ).
% 0.29/0.53
% 0.29/0.53 % abs_minus_cancel
% 0.29/0.53 thf(fact_908_abs__minus__cancel,axiom,
% 0.29/0.53 ! [A: code_integer] :
% 0.29/0.53 ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ A ) )
% 0.29/0.53 = ( abs_abs_Code_integer @ A ) ) ).
% 0.29/0.53
% 0.29/0.53 % abs_minus_cancel
% 0.29/0.53 thf(fact_909_abs__minus__cancel,axiom,
% 0.29/0.53 ! [A: rat] :
% 0.29/0.53 ( ( abs_abs_rat @ ( uminus_uminus_rat @ A ) )
% 0.29/0.53 = ( abs_abs_rat @ A ) ) ).
% 0.29/0.53
% 0.29/0.53 % abs_minus_cancel
% 0.29/0.53 thf(fact_910_sgn__1,axiom,
% 0.29/0.53 ( ( sgn_sgn_int @ one_one_int )
% 0.29/0.53 = one_one_int ) ).
% 0.29/0.53
% 0.29/0.53 % sgn_1
% 0.29/0.53 thf(fact_911_sgn__1,axiom,
% 0.29/0.53 ( ( sgn_sgn_Code_integer @ one_one_Code_integer )
% 0.29/0.53 = one_one_Code_integer ) ).
% 0.29/0.53
% 0.29/0.53 % sgn_1
% 0.29/0.53 thf(fact_912_sgn__1,axiom,
% 0.29/0.53 ( ( sgn_sgn_rat @ one_one_rat )
% 0.29/0.53 = one_one_rat ) ).
% 0.29/0.53
% 0.29/0.53 % sgn_1
% 0.29/0.53 thf(fact_913_map__option__eq__Some,axiom,
% 0.29/0.53 ! [F: produc8664842809031399944it_nat > num,Xo: option8956607266484857688it_nat,Y: num] :
% 0.29/0.53 ( ( ( map_op2731889312448867759at_num @ F @ Xo )
% 0.29/0.53 = ( some_num @ Y ) )
% 0.29/0.53 = ( ? [Z4: produc8664842809031399944it_nat] :
% 0.29/0.53 ( ( Xo
% 0.29/0.53 = ( some_P1914260805536162275it_nat @ Z4 ) )
% 0.29/0.53 & ( ( F @ Z4 )
% 0.29/0.53 = Y ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % map_option_eq_Some
% 0.29/0.53 thf(fact_914_map__option__eq__Some,axiom,
% 0.29/0.53 ! [F: num > produc8664842809031399944it_nat,Xo: option_num,Y: produc8664842809031399944it_nat] :
% 0.29/0.53 ( ( ( map_op8118133509425879471it_nat @ F @ Xo )
% 0.29/0.53 = ( some_P1914260805536162275it_nat @ Y ) )
% 0.29/0.53 = ( ? [Z4: num] :
% 0.29/0.53 ( ( Xo
% 0.29/0.53 = ( some_num @ Z4 ) )
% 0.29/0.53 & ( ( F @ Z4 )
% 0.29/0.53 = Y ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % map_option_eq_Some
% 0.29/0.53 thf(fact_915_map__option__eq__Some,axiom,
% 0.29/0.53 ! [F: produc8664842809031399944it_nat > produc8664842809031399944it_nat,Xo: option8956607266484857688it_nat,Y: produc8664842809031399944it_nat] :
% 0.29/0.53 ( ( ( map_op8673683442680995229it_nat @ F @ Xo )
% 0.29/0.53 = ( some_P1914260805536162275it_nat @ Y ) )
% 0.29/0.53 = ( ? [Z4: produc8664842809031399944it_nat] :
% 0.29/0.53 ( ( Xo
% 0.29/0.53 = ( some_P1914260805536162275it_nat @ Z4 ) )
% 0.29/0.53 & ( ( F @ Z4 )
% 0.29/0.53 = Y ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % map_option_eq_Some
% 0.29/0.53 thf(fact_916_map__option__eq__Some,axiom,
% 0.29/0.53 ! [F: num > num,Xo: option_num,Y: num] :
% 0.29/0.53 ( ( ( map_option_num_num @ F @ Xo )
% 0.29/0.53 = ( some_num @ Y ) )
% 0.29/0.53 = ( ? [Z4: num] :
% 0.29/0.53 ( ( Xo
% 0.29/0.53 = ( some_num @ Z4 ) )
% 0.29/0.53 & ( ( F @ Z4 )
% 0.29/0.53 = Y ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % map_option_eq_Some
% 0.29/0.53 thf(fact_917_None__eq__map__option__iff,axiom,
% 0.29/0.53 ! [F: produc6714399278180371524it_nat > produc6714399278180371524it_nat,X: option3216581401566546698it_nat] :
% 0.29/0.53 ( ( none_P2587165478634041381it_nat
% 0.29/0.53 = ( map_op6002829699023054091it_nat @ F @ X ) )
% 0.29/0.53 = ( X = none_P2587165478634041381it_nat ) ) ).
% 0.29/0.53
% 0.29/0.53 % None_eq_map_option_iff
% 0.29/0.53 thf(fact_918_None__eq__map__option__iff,axiom,
% 0.29/0.53 ! [F: num > produc6714399278180371524it_nat,X: option_num] :
% 0.29/0.53 ( ( none_P2587165478634041381it_nat
% 0.29/0.53 = ( map_op6598675229099881181it_nat @ F @ X ) )
% 0.29/0.53 = ( X = none_num ) ) ).
% 0.29/0.53
% 0.29/0.53 % None_eq_map_option_iff
% 0.29/0.53 thf(fact_919_None__eq__map__option__iff,axiom,
% 0.29/0.53 ! [F: produc8664842809031399944it_nat > produc6714399278180371524it_nat,X: option8956607266484857688it_nat] :
% 0.29/0.53 ( ( none_P2587165478634041381it_nat
% 0.29/0.53 = ( map_op7916408704904942447it_nat @ F @ X ) )
% 0.29/0.53 = ( X = none_P9117596204409417319it_nat ) ) ).
% 0.29/0.53
% 0.29/0.53 % None_eq_map_option_iff
% 0.29/0.53 thf(fact_920_None__eq__map__option__iff,axiom,
% 0.29/0.53 ! [F: produc6714399278180371524it_nat > num,X: option3216581401566546698it_nat] :
% 0.29/0.53 ( ( none_num
% 0.29/0.53 = ( map_op8228268515680064275at_num @ F @ X ) )
% 0.29/0.53 = ( X = none_P2587165478634041381it_nat ) ) ).
% 0.29/0.53
% 0.29/0.53 % None_eq_map_option_iff
% 0.29/0.53 thf(fact_921_None__eq__map__option__iff,axiom,
% 0.29/0.53 ! [F: produc8664842809031399944it_nat > num,X: option8956607266484857688it_nat] :
% 0.29/0.53 ( ( none_num
% 0.29/0.53 = ( map_op2731889312448867759at_num @ F @ X ) )
% 0.29/0.53 = ( X = none_P9117596204409417319it_nat ) ) ).
% 0.29/0.53
% 0.29/0.53 % None_eq_map_option_iff
% 0.29/0.53 thf(fact_922_None__eq__map__option__iff,axiom,
% 0.29/0.53 ! [F: produc6714399278180371524it_nat > produc8664842809031399944it_nat,X: option3216581401566546698it_nat] :
% 0.29/0.53 ( ( none_P9117596204409417319it_nat
% 0.29/0.53 = ( map_op674526153330701057it_nat @ F @ X ) )
% 0.29/0.53 = ( X = none_P2587165478634041381it_nat ) ) ).
% 0.29/0.53
% 0.29/0.53 % None_eq_map_option_iff
% 0.29/0.53 thf(fact_923_None__eq__map__option__iff,axiom,
% 0.29/0.53 ! [F: num > produc8664842809031399944it_nat,X: option_num] :
% 0.29/0.53 ( ( none_P9117596204409417319it_nat
% 0.29/0.53 = ( map_op8118133509425879471it_nat @ F @ X ) )
% 0.29/0.53 = ( X = none_num ) ) ).
% 0.29/0.53
% 0.29/0.53 % None_eq_map_option_iff
% 0.29/0.53 thf(fact_924_None__eq__map__option__iff,axiom,
% 0.29/0.53 ! [F: produc8664842809031399944it_nat > produc8664842809031399944it_nat,X: option8956607266484857688it_nat] :
% 0.29/0.53 ( ( none_P9117596204409417319it_nat
% 0.29/0.53 = ( map_op8673683442680995229it_nat @ F @ X ) )
% 0.29/0.53 = ( X = none_P9117596204409417319it_nat ) ) ).
% 0.29/0.53
% 0.29/0.53 % None_eq_map_option_iff
% 0.29/0.53 thf(fact_925_None__eq__map__option__iff,axiom,
% 0.29/0.53 ! [F: num > num,X: option_num] :
% 0.29/0.53 ( ( none_num
% 0.29/0.53 = ( map_option_num_num @ F @ X ) )
% 0.29/0.53 = ( X = none_num ) ) ).
% 0.29/0.53
% 0.29/0.53 % None_eq_map_option_iff
% 0.29/0.53 thf(fact_926_map__option__is__None,axiom,
% 0.29/0.53 ! [F: produc6714399278180371524it_nat > produc6714399278180371524it_nat,Opt: option3216581401566546698it_nat] :
% 0.29/0.53 ( ( ( map_op6002829699023054091it_nat @ F @ Opt )
% 0.29/0.53 = none_P2587165478634041381it_nat )
% 0.29/0.53 = ( Opt = none_P2587165478634041381it_nat ) ) ).
% 0.29/0.53
% 0.29/0.53 % map_option_is_None
% 0.29/0.53 thf(fact_927_map__option__is__None,axiom,
% 0.29/0.53 ! [F: num > produc6714399278180371524it_nat,Opt: option_num] :
% 0.29/0.53 ( ( ( map_op6598675229099881181it_nat @ F @ Opt )
% 0.29/0.53 = none_P2587165478634041381it_nat )
% 0.29/0.53 = ( Opt = none_num ) ) ).
% 0.29/0.53
% 0.29/0.53 % map_option_is_None
% 0.29/0.53 thf(fact_928_map__option__is__None,axiom,
% 0.29/0.53 ! [F: produc8664842809031399944it_nat > produc6714399278180371524it_nat,Opt: option8956607266484857688it_nat] :
% 0.29/0.53 ( ( ( map_op7916408704904942447it_nat @ F @ Opt )
% 0.29/0.53 = none_P2587165478634041381it_nat )
% 0.29/0.53 = ( Opt = none_P9117596204409417319it_nat ) ) ).
% 0.29/0.53
% 0.29/0.53 % map_option_is_None
% 0.29/0.53 thf(fact_929_map__option__is__None,axiom,
% 0.29/0.53 ! [F: produc6714399278180371524it_nat > num,Opt: option3216581401566546698it_nat] :
% 0.29/0.53 ( ( ( map_op8228268515680064275at_num @ F @ Opt )
% 0.29/0.53 = none_num )
% 0.29/0.53 = ( Opt = none_P2587165478634041381it_nat ) ) ).
% 0.29/0.53
% 0.29/0.53 % map_option_is_None
% 0.29/0.53 thf(fact_930_map__option__is__None,axiom,
% 0.29/0.53 ! [F: produc8664842809031399944it_nat > num,Opt: option8956607266484857688it_nat] :
% 0.29/0.53 ( ( ( map_op2731889312448867759at_num @ F @ Opt )
% 0.29/0.53 = none_num )
% 0.29/0.53 = ( Opt = none_P9117596204409417319it_nat ) ) ).
% 0.29/0.53
% 0.29/0.53 % map_option_is_None
% 0.29/0.53 thf(fact_931_map__option__is__None,axiom,
% 0.29/0.53 ! [F: produc6714399278180371524it_nat > produc8664842809031399944it_nat,Opt: option3216581401566546698it_nat] :
% 0.29/0.53 ( ( ( map_op674526153330701057it_nat @ F @ Opt )
% 0.29/0.53 = none_P9117596204409417319it_nat )
% 0.29/0.53 = ( Opt = none_P2587165478634041381it_nat ) ) ).
% 0.29/0.53
% 0.29/0.53 % map_option_is_None
% 0.29/0.53 thf(fact_932_map__option__is__None,axiom,
% 0.29/0.53 ! [F: num > produc8664842809031399944it_nat,Opt: option_num] :
% 0.29/0.53 ( ( ( map_op8118133509425879471it_nat @ F @ Opt )
% 0.29/0.53 = none_P9117596204409417319it_nat )
% 0.29/0.53 = ( Opt = none_num ) ) ).
% 0.29/0.53
% 0.29/0.53 % map_option_is_None
% 0.29/0.53 thf(fact_933_map__option__is__None,axiom,
% 0.29/0.53 ! [F: produc8664842809031399944it_nat > produc8664842809031399944it_nat,Opt: option8956607266484857688it_nat] :
% 0.29/0.53 ( ( ( map_op8673683442680995229it_nat @ F @ Opt )
% 0.29/0.53 = none_P9117596204409417319it_nat )
% 0.29/0.53 = ( Opt = none_P9117596204409417319it_nat ) ) ).
% 0.29/0.53
% 0.29/0.53 % map_option_is_None
% 0.29/0.53 thf(fact_934_map__option__is__None,axiom,
% 0.29/0.53 ! [F: num > num,Opt: option_num] :
% 0.29/0.53 ( ( ( map_option_num_num @ F @ Opt )
% 0.29/0.53 = none_num )
% 0.29/0.53 = ( Opt = none_num ) ) ).
% 0.29/0.53
% 0.29/0.53 % map_option_is_None
% 0.29/0.53 thf(fact_935_option_Omap__disc__iff,axiom,
% 0.29/0.53 ! [F: produc6714399278180371524it_nat > produc6714399278180371524it_nat,A: option3216581401566546698it_nat] :
% 0.29/0.53 ( ( ( map_op6002829699023054091it_nat @ F @ A )
% 0.29/0.53 = none_P2587165478634041381it_nat )
% 0.29/0.53 = ( A = none_P2587165478634041381it_nat ) ) ).
% 0.29/0.53
% 0.29/0.53 % option.map_disc_iff
% 0.29/0.53 thf(fact_936_option_Omap__disc__iff,axiom,
% 0.29/0.53 ! [F: num > produc6714399278180371524it_nat,A: option_num] :
% 0.29/0.53 ( ( ( map_op6598675229099881181it_nat @ F @ A )
% 0.29/0.53 = none_P2587165478634041381it_nat )
% 0.29/0.53 = ( A = none_num ) ) ).
% 0.29/0.53
% 0.29/0.53 % option.map_disc_iff
% 0.29/0.53 thf(fact_937_option_Omap__disc__iff,axiom,
% 0.29/0.53 ! [F: produc8664842809031399944it_nat > produc6714399278180371524it_nat,A: option8956607266484857688it_nat] :
% 0.29/0.53 ( ( ( map_op7916408704904942447it_nat @ F @ A )
% 0.29/0.53 = none_P2587165478634041381it_nat )
% 0.29/0.53 = ( A = none_P9117596204409417319it_nat ) ) ).
% 0.29/0.53
% 0.29/0.53 % option.map_disc_iff
% 0.29/0.53 thf(fact_938_option_Omap__disc__iff,axiom,
% 0.29/0.53 ! [F: produc6714399278180371524it_nat > num,A: option3216581401566546698it_nat] :
% 0.29/0.53 ( ( ( map_op8228268515680064275at_num @ F @ A )
% 0.29/0.53 = none_num )
% 0.29/0.53 = ( A = none_P2587165478634041381it_nat ) ) ).
% 0.29/0.53
% 0.29/0.53 % option.map_disc_iff
% 0.29/0.53 thf(fact_939_option_Omap__disc__iff,axiom,
% 0.29/0.53 ! [F: produc8664842809031399944it_nat > num,A: option8956607266484857688it_nat] :
% 0.29/0.53 ( ( ( map_op2731889312448867759at_num @ F @ A )
% 0.29/0.53 = none_num )
% 0.29/0.53 = ( A = none_P9117596204409417319it_nat ) ) ).
% 0.29/0.53
% 0.29/0.53 % option.map_disc_iff
% 0.29/0.53 thf(fact_940_option_Omap__disc__iff,axiom,
% 0.29/0.53 ! [F: produc6714399278180371524it_nat > produc8664842809031399944it_nat,A: option3216581401566546698it_nat] :
% 0.29/0.53 ( ( ( map_op674526153330701057it_nat @ F @ A )
% 0.29/0.53 = none_P9117596204409417319it_nat )
% 0.29/0.53 = ( A = none_P2587165478634041381it_nat ) ) ).
% 0.29/0.53
% 0.29/0.53 % option.map_disc_iff
% 0.29/0.53 thf(fact_941_option_Omap__disc__iff,axiom,
% 0.29/0.53 ! [F: num > produc8664842809031399944it_nat,A: option_num] :
% 0.29/0.53 ( ( ( map_op8118133509425879471it_nat @ F @ A )
% 0.29/0.53 = none_P9117596204409417319it_nat )
% 0.29/0.53 = ( A = none_num ) ) ).
% 0.29/0.53
% 0.29/0.53 % option.map_disc_iff
% 0.29/0.53 thf(fact_942_option_Omap__disc__iff,axiom,
% 0.29/0.53 ! [F: produc8664842809031399944it_nat > produc8664842809031399944it_nat,A: option8956607266484857688it_nat] :
% 0.29/0.53 ( ( ( map_op8673683442680995229it_nat @ F @ A )
% 0.29/0.53 = none_P9117596204409417319it_nat )
% 0.29/0.53 = ( A = none_P9117596204409417319it_nat ) ) ).
% 0.29/0.53
% 0.29/0.53 % option.map_disc_iff
% 0.29/0.53 thf(fact_943_option_Omap__disc__iff,axiom,
% 0.29/0.53 ! [F: num > num,A: option_num] :
% 0.29/0.53 ( ( ( map_option_num_num @ F @ A )
% 0.29/0.53 = none_num )
% 0.29/0.53 = ( A = none_num ) ) ).
% 0.29/0.53
% 0.29/0.53 % option.map_disc_iff
% 0.29/0.53 thf(fact_944_neg__less__0__iff__less,axiom,
% 0.29/0.53 ! [A: int] :
% 0.29/0.53 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 0.29/0.53 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 0.29/0.53
% 0.29/0.53 % neg_less_0_iff_less
% 0.29/0.53 thf(fact_945_neg__less__0__iff__less,axiom,
% 0.29/0.53 ! [A: code_integer] :
% 0.29/0.53 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ zero_z3403309356797280102nteger )
% 0.29/0.53 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 0.29/0.53
% 0.29/0.53 % neg_less_0_iff_less
% 0.29/0.53 thf(fact_946_neg__less__0__iff__less,axiom,
% 0.29/0.53 ! [A: rat] :
% 0.29/0.53 ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ zero_zero_rat )
% 0.29/0.53 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 0.29/0.53
% 0.29/0.53 % neg_less_0_iff_less
% 0.29/0.53 thf(fact_947_neg__0__less__iff__less,axiom,
% 0.29/0.53 ! [A: int] :
% 0.29/0.53 ( ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 0.29/0.53 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 0.29/0.53
% 0.29/0.53 % neg_0_less_iff_less
% 0.29/0.53 thf(fact_948_neg__0__less__iff__less,axiom,
% 0.29/0.53 ! [A: code_integer] :
% 0.29/0.53 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ A ) )
% 0.29/0.53 = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 0.29/0.53
% 0.29/0.53 % neg_0_less_iff_less
% 0.29/0.53 thf(fact_949_neg__0__less__iff__less,axiom,
% 0.29/0.53 ! [A: rat] :
% 0.29/0.53 ( ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ A ) )
% 0.29/0.53 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 0.29/0.53
% 0.29/0.53 % neg_0_less_iff_less
% 0.29/0.53 thf(fact_950_neg__less__pos,axiom,
% 0.29/0.53 ! [A: int] :
% 0.29/0.53 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ A )
% 0.29/0.53 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 0.29/0.53
% 0.29/0.53 % neg_less_pos
% 0.29/0.53 thf(fact_951_neg__less__pos,axiom,
% 0.29/0.53 ! [A: code_integer] :
% 0.29/0.53 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 0.29/0.53 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 0.29/0.53
% 0.29/0.53 % neg_less_pos
% 0.29/0.53 thf(fact_952_neg__less__pos,axiom,
% 0.29/0.53 ! [A: rat] :
% 0.29/0.53 ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ A )
% 0.29/0.53 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 0.29/0.53
% 0.29/0.53 % neg_less_pos
% 0.29/0.53 thf(fact_953_less__neg__neg,axiom,
% 0.29/0.53 ! [A: int] :
% 0.29/0.53 ( ( ord_less_int @ A @ ( uminus_uminus_int @ A ) )
% 0.29/0.53 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 0.29/0.53
% 0.29/0.53 % less_neg_neg
% 0.29/0.53 thf(fact_954_less__neg__neg,axiom,
% 0.29/0.53 ! [A: code_integer] :
% 0.29/0.53 ( ( ord_le6747313008572928689nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 0.29/0.53 = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 0.29/0.53
% 0.29/0.53 % less_neg_neg
% 0.29/0.53 thf(fact_955_less__neg__neg,axiom,
% 0.29/0.53 ! [A: rat] :
% 0.29/0.53 ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ A ) )
% 0.29/0.53 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 0.29/0.53
% 0.29/0.53 % less_neg_neg
% 0.29/0.53 thf(fact_956_ab__left__minus,axiom,
% 0.29/0.53 ! [A: int] :
% 0.29/0.53 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ A )
% 0.29/0.53 = zero_zero_int ) ).
% 0.29/0.53
% 0.29/0.53 % ab_left_minus
% 0.29/0.53 thf(fact_957_ab__left__minus,axiom,
% 0.29/0.53 ! [A: code_integer] :
% 0.29/0.53 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 0.29/0.53 = zero_z3403309356797280102nteger ) ).
% 0.29/0.53
% 0.29/0.53 % ab_left_minus
% 0.29/0.53 thf(fact_958_ab__left__minus,axiom,
% 0.29/0.53 ! [A: rat] :
% 0.29/0.53 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ A )
% 0.29/0.53 = zero_zero_rat ) ).
% 0.29/0.53
% 0.29/0.53 % ab_left_minus
% 0.29/0.53 thf(fact_959_add_Oright__inverse,axiom,
% 0.29/0.53 ! [A: int] :
% 0.29/0.53 ( ( plus_plus_int @ A @ ( uminus_uminus_int @ A ) )
% 0.29/0.53 = zero_zero_int ) ).
% 0.29/0.53
% 0.29/0.53 % add.right_inverse
% 0.29/0.53 thf(fact_960_add_Oright__inverse,axiom,
% 0.29/0.53 ! [A: code_integer] :
% 0.29/0.53 ( ( plus_p5714425477246183910nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 0.29/0.53 = zero_z3403309356797280102nteger ) ).
% 0.29/0.53
% 0.29/0.53 % add.right_inverse
% 0.29/0.53 thf(fact_961_add_Oright__inverse,axiom,
% 0.29/0.53 ! [A: rat] :
% 0.29/0.53 ( ( plus_plus_rat @ A @ ( uminus_uminus_rat @ A ) )
% 0.29/0.53 = zero_zero_rat ) ).
% 0.29/0.53
% 0.29/0.53 % add.right_inverse
% 0.29/0.53 thf(fact_962_zero__less__abs__iff,axiom,
% 0.29/0.53 ! [A: code_integer] :
% 0.29/0.53 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ A ) )
% 0.29/0.53 = ( A != zero_z3403309356797280102nteger ) ) ).
% 0.29/0.53
% 0.29/0.53 % zero_less_abs_iff
% 0.29/0.53 thf(fact_963_zero__less__abs__iff,axiom,
% 0.29/0.53 ! [A: rat] :
% 0.29/0.53 ( ( ord_less_rat @ zero_zero_rat @ ( abs_abs_rat @ A ) )
% 0.29/0.53 = ( A != zero_zero_rat ) ) ).
% 0.29/0.53
% 0.29/0.53 % zero_less_abs_iff
% 0.29/0.53 thf(fact_964_zero__less__abs__iff,axiom,
% 0.29/0.53 ! [A: int] :
% 0.29/0.53 ( ( ord_less_int @ zero_zero_int @ ( abs_abs_int @ A ) )
% 0.29/0.53 = ( A != zero_zero_int ) ) ).
% 0.29/0.53
% 0.29/0.53 % zero_less_abs_iff
% 0.29/0.53 thf(fact_965_abs__neg__one,axiom,
% 0.29/0.53 ( ( abs_abs_int @ ( uminus_uminus_int @ one_one_int ) )
% 0.29/0.53 = one_one_int ) ).
% 0.29/0.53
% 0.29/0.53 % abs_neg_one
% 0.29/0.53 thf(fact_966_abs__neg__one,axiom,
% 0.29/0.53 ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.29/0.53 = one_one_Code_integer ) ).
% 0.29/0.53
% 0.29/0.53 % abs_neg_one
% 0.29/0.53 thf(fact_967_abs__neg__one,axiom,
% 0.29/0.53 ( ( abs_abs_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.29/0.53 = one_one_rat ) ).
% 0.29/0.53
% 0.29/0.53 % abs_neg_one
% 0.29/0.53 thf(fact_968_case__map__option,axiom,
% 0.29/0.53 ! [G: code_integer,H3: code_integer > code_integer,F: num > code_integer,X: option_num] :
% 0.29/0.53 ( ( case_o9049918639272118855nteger @ G @ H3 @ ( map_op2849635639313731588nteger @ F @ X ) )
% 0.29/0.53 = ( case_o356765784539232260er_num @ G @ ( comp_C3531382070062128313er_num @ H3 @ F ) @ X ) ) ).
% 0.29/0.53
% 0.29/0.53 % case_map_option
% 0.29/0.53 thf(fact_969_case__map__option,axiom,
% 0.29/0.53 ! [G: produc8923325533196201883nteger > produc8923325533196201883nteger,H3: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,F: code_integer > code_integer,X: option_Code_integer] :
% 0.29/0.53 ( ( case_o7134296353695833103nteger @ G @ H3 @ ( map_op3669829223712506439nteger @ F @ X ) )
% 0.29/0.53 = ( case_o7134296353695833103nteger @ G @ ( comp_C1593894019821074884nteger @ H3 @ F ) @ X ) ) ).
% 0.29/0.53
% 0.29/0.53 % case_map_option
% 0.29/0.53 thf(fact_970_case__map__option,axiom,
% 0.29/0.53 ! [G: produc8923325533196201883nteger > produc8923325533196201883nteger,H3: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,F: code_integer > code_integer > code_integer,X: option_Code_integer] :
% 0.29/0.53 ( ( case_o1441893360019914891nteger @ G @ H3 @ ( map_op370346339404370627nteger @ F @ X ) )
% 0.29/0.53 = ( case_o7134296353695833103nteger @ G @ ( comp_C8797469213163452608nteger @ H3 @ F ) @ X ) ) ).
% 0.29/0.53
% 0.29/0.53 % case_map_option
% 0.29/0.53 thf(fact_971_case__map__option,axiom,
% 0.29/0.53 ! [G: num,H3: nat > num,F: int > nat,X: option_int] :
% 0.29/0.53 ( ( case_option_num_nat @ G @ H3 @ ( map_option_int_nat @ F @ X ) )
% 0.29/0.53 = ( case_option_num_int @ G @ ( comp_nat_num_int @ H3 @ F ) @ X ) ) ).
% 0.29/0.53
% 0.29/0.53 % case_map_option
% 0.29/0.53 thf(fact_972_case__map__option,axiom,
% 0.29/0.53 ! [G: int,H3: num > int,F: num > num,X: option_num] :
% 0.29/0.53 ( ( case_option_int_num @ G @ H3 @ ( map_option_num_num @ F @ X ) )
% 0.29/0.53 = ( case_option_int_num @ G @ ( comp_num_int_num @ H3 @ F ) @ X ) ) ).
% 0.29/0.53
% 0.29/0.53 % case_map_option
% 0.29/0.53 thf(fact_973_case__map__option,axiom,
% 0.29/0.53 ! [G: option_num,H3: num > option_num,F: num > num,X: option_num] :
% 0.29/0.53 ( ( case_o6005452278849405969um_num @ G @ H3 @ ( map_option_num_num @ F @ X ) )
% 0.29/0.53 = ( case_o6005452278849405969um_num @ G @ ( comp_n6731957995704128387um_num @ H3 @ F ) @ X ) ) ).
% 0.29/0.53
% 0.29/0.53 % case_map_option
% 0.29/0.53 thf(fact_974_case__map__option,axiom,
% 0.29/0.53 ! [G: num,H3: num > num,F: num > num,X: option_num] :
% 0.29/0.53 ( ( case_option_num_num @ G @ H3 @ ( map_option_num_num @ F @ X ) )
% 0.29/0.53 = ( case_option_num_num @ G @ ( comp_num_num_num @ H3 @ F ) @ X ) ) ).
% 0.29/0.53
% 0.29/0.53 % case_map_option
% 0.29/0.53 thf(fact_975_dbl__inc__simps_I4_J,axiom,
% 0.29/0.53 ( ( neg_nu5851722552734809277nc_int @ ( uminus_uminus_int @ one_one_int ) )
% 0.29/0.53 = ( uminus_uminus_int @ one_one_int ) ) ).
% 0.29/0.53
% 0.29/0.53 % dbl_inc_simps(4)
% 0.29/0.53 thf(fact_976_dbl__inc__simps_I4_J,axiom,
% 0.29/0.53 ( ( neg_nu5831290666863070958nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.29/0.53 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.29/0.53
% 0.29/0.53 % dbl_inc_simps(4)
% 0.29/0.53 thf(fact_977_dbl__inc__simps_I4_J,axiom,
% 0.29/0.53 ( ( neg_nu5219082963157363817nc_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.29/0.53 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.29/0.53
% 0.29/0.53 % dbl_inc_simps(4)
% 0.29/0.53 thf(fact_978_abs__sgn__eq__1,axiom,
% 0.29/0.53 ! [A: code_integer] :
% 0.29/0.53 ( ( A != zero_z3403309356797280102nteger )
% 0.29/0.53 => ( ( abs_abs_Code_integer @ ( sgn_sgn_Code_integer @ A ) )
% 0.29/0.53 = one_one_Code_integer ) ) ).
% 0.29/0.53
% 0.29/0.53 % abs_sgn_eq_1
% 0.29/0.53 thf(fact_979_abs__sgn__eq__1,axiom,
% 0.29/0.53 ! [A: rat] :
% 0.29/0.53 ( ( A != zero_zero_rat )
% 0.29/0.53 => ( ( abs_abs_rat @ ( sgn_sgn_rat @ A ) )
% 0.29/0.53 = one_one_rat ) ) ).
% 0.29/0.53
% 0.29/0.53 % abs_sgn_eq_1
% 0.29/0.53 thf(fact_980_abs__sgn__eq__1,axiom,
% 0.29/0.53 ! [A: int] :
% 0.29/0.53 ( ( A != zero_zero_int )
% 0.29/0.53 => ( ( abs_abs_int @ ( sgn_sgn_int @ A ) )
% 0.29/0.53 = one_one_int ) ) ).
% 0.29/0.53
% 0.29/0.53 % abs_sgn_eq_1
% 0.29/0.53 thf(fact_981_dbl__dec__simps_I2_J,axiom,
% 0.29/0.53 ( ( neg_nu3811975205180677377ec_int @ zero_zero_int )
% 0.29/0.53 = ( uminus_uminus_int @ one_one_int ) ) ).
% 0.29/0.53
% 0.29/0.53 % dbl_dec_simps(2)
% 0.29/0.53 thf(fact_982_dbl__dec__simps_I2_J,axiom,
% 0.29/0.53 ( ( neg_nu7757733837767384882nteger @ zero_z3403309356797280102nteger )
% 0.29/0.53 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.29/0.53
% 0.29/0.53 % dbl_dec_simps(2)
% 0.29/0.53 thf(fact_983_dbl__dec__simps_I2_J,axiom,
% 0.29/0.53 ( ( neg_nu3179335615603231917ec_rat @ zero_zero_rat )
% 0.29/0.53 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.29/0.53
% 0.29/0.53 % dbl_dec_simps(2)
% 0.29/0.53 thf(fact_984_sgn__neg,axiom,
% 0.29/0.53 ! [A: int] :
% 0.29/0.53 ( ( ord_less_int @ A @ zero_zero_int )
% 0.29/0.53 => ( ( sgn_sgn_int @ A )
% 0.29/0.53 = ( uminus_uminus_int @ one_one_int ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % sgn_neg
% 0.29/0.53 thf(fact_985_sgn__neg,axiom,
% 0.29/0.53 ! [A: code_integer] :
% 0.29/0.53 ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 0.29/0.53 => ( ( sgn_sgn_Code_integer @ A )
% 0.29/0.53 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % sgn_neg
% 0.29/0.53 thf(fact_986_sgn__neg,axiom,
% 0.29/0.53 ! [A: rat] :
% 0.29/0.53 ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.29/0.53 => ( ( sgn_sgn_rat @ A )
% 0.29/0.53 = ( uminus_uminus_rat @ one_one_rat ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % sgn_neg
% 0.29/0.53 thf(fact_987_minus__equation__iff,axiom,
% 0.29/0.53 ! [A: int,B: int] :
% 0.29/0.53 ( ( ( uminus_uminus_int @ A )
% 0.29/0.53 = B )
% 0.29/0.53 = ( ( uminus_uminus_int @ B )
% 0.29/0.53 = A ) ) ).
% 0.29/0.53
% 0.29/0.53 % minus_equation_iff
% 0.29/0.53 thf(fact_988_minus__equation__iff,axiom,
% 0.29/0.53 ! [A: code_integer,B: code_integer] :
% 0.29/0.53 ( ( ( uminus1351360451143612070nteger @ A )
% 0.29/0.53 = B )
% 0.29/0.53 = ( ( uminus1351360451143612070nteger @ B )
% 0.29/0.53 = A ) ) ).
% 0.29/0.53
% 0.29/0.53 % minus_equation_iff
% 0.29/0.53 thf(fact_989_minus__equation__iff,axiom,
% 0.29/0.53 ! [A: rat,B: rat] :
% 0.29/0.53 ( ( ( uminus_uminus_rat @ A )
% 0.29/0.53 = B )
% 0.29/0.53 = ( ( uminus_uminus_rat @ B )
% 0.29/0.53 = A ) ) ).
% 0.29/0.53
% 0.29/0.53 % minus_equation_iff
% 0.29/0.53 thf(fact_990_equation__minus__iff,axiom,
% 0.29/0.53 ! [A: int,B: int] :
% 0.29/0.53 ( ( A
% 0.29/0.53 = ( uminus_uminus_int @ B ) )
% 0.29/0.53 = ( B
% 0.29/0.53 = ( uminus_uminus_int @ A ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % equation_minus_iff
% 0.29/0.53 thf(fact_991_equation__minus__iff,axiom,
% 0.29/0.53 ! [A: code_integer,B: code_integer] :
% 0.29/0.53 ( ( A
% 0.29/0.53 = ( uminus1351360451143612070nteger @ B ) )
% 0.29/0.53 = ( B
% 0.29/0.53 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % equation_minus_iff
% 0.29/0.53 thf(fact_992_equation__minus__iff,axiom,
% 0.29/0.53 ! [A: rat,B: rat] :
% 0.29/0.53 ( ( A
% 0.29/0.53 = ( uminus_uminus_rat @ B ) )
% 0.29/0.53 = ( B
% 0.29/0.53 = ( uminus_uminus_rat @ A ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % equation_minus_iff
% 0.29/0.53 thf(fact_993_same__sgn__abs__add,axiom,
% 0.29/0.53 ! [B: code_integer,A: code_integer] :
% 0.29/0.53 ( ( ( sgn_sgn_Code_integer @ B )
% 0.29/0.53 = ( sgn_sgn_Code_integer @ A ) )
% 0.29/0.53 => ( ( abs_abs_Code_integer @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 0.29/0.53 = ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % same_sgn_abs_add
% 0.29/0.53 thf(fact_994_same__sgn__abs__add,axiom,
% 0.29/0.53 ! [B: rat,A: rat] :
% 0.29/0.53 ( ( ( sgn_sgn_rat @ B )
% 0.29/0.53 = ( sgn_sgn_rat @ A ) )
% 0.29/0.53 => ( ( abs_abs_rat @ ( plus_plus_rat @ A @ B ) )
% 0.29/0.53 = ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % same_sgn_abs_add
% 0.29/0.53 thf(fact_995_same__sgn__abs__add,axiom,
% 0.29/0.53 ! [B: int,A: int] :
% 0.29/0.53 ( ( ( sgn_sgn_int @ B )
% 0.29/0.53 = ( sgn_sgn_int @ A ) )
% 0.29/0.53 => ( ( abs_abs_int @ ( plus_plus_int @ A @ B ) )
% 0.29/0.53 = ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % same_sgn_abs_add
% 0.29/0.53 thf(fact_996_sgn__minus__1,axiom,
% 0.29/0.53 ( ( sgn_sgn_int @ ( uminus_uminus_int @ one_one_int ) )
% 0.29/0.53 = ( uminus_uminus_int @ one_one_int ) ) ).
% 0.29/0.53
% 0.29/0.53 % sgn_minus_1
% 0.29/0.53 thf(fact_997_sgn__minus__1,axiom,
% 0.29/0.53 ( ( sgn_sgn_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.29/0.53 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.29/0.53
% 0.29/0.53 % sgn_minus_1
% 0.29/0.53 thf(fact_998_sgn__minus__1,axiom,
% 0.29/0.53 ( ( sgn_sgn_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.29/0.53 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.29/0.53
% 0.29/0.53 % sgn_minus_1
% 0.29/0.53 thf(fact_999_option_Omap__ident,axiom,
% 0.29/0.53 ! [T: option_num] :
% 0.29/0.53 ( ( map_option_num_num
% 0.29/0.53 @ ^ [X3: num] : X3
% 0.29/0.53 @ T )
% 0.29/0.53 = T ) ).
% 0.29/0.53
% 0.29/0.53 % option.map_ident
% 0.29/0.53 thf(fact_1000_abs__of__neg,axiom,
% 0.29/0.53 ! [A: int] :
% 0.29/0.53 ( ( ord_less_int @ A @ zero_zero_int )
% 0.29/0.53 => ( ( abs_abs_int @ A )
% 0.29/0.53 = ( uminus_uminus_int @ A ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % abs_of_neg
% 0.29/0.53 thf(fact_1001_abs__of__neg,axiom,
% 0.29/0.53 ! [A: code_integer] :
% 0.29/0.53 ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 0.29/0.53 => ( ( abs_abs_Code_integer @ A )
% 0.29/0.53 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % abs_of_neg
% 0.29/0.53 thf(fact_1002_abs__of__neg,axiom,
% 0.29/0.53 ! [A: rat] :
% 0.29/0.53 ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.29/0.53 => ( ( abs_abs_rat @ A )
% 0.29/0.53 = ( uminus_uminus_rat @ A ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % abs_of_neg
% 0.29/0.53 thf(fact_1003_abs__sgn__eq,axiom,
% 0.29/0.53 ! [A: code_integer] :
% 0.29/0.53 ( ( ( A = zero_z3403309356797280102nteger )
% 0.29/0.53 => ( ( abs_abs_Code_integer @ ( sgn_sgn_Code_integer @ A ) )
% 0.29/0.53 = zero_z3403309356797280102nteger ) )
% 0.29/0.53 & ( ( A != zero_z3403309356797280102nteger )
% 0.29/0.53 => ( ( abs_abs_Code_integer @ ( sgn_sgn_Code_integer @ A ) )
% 0.29/0.53 = one_one_Code_integer ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % abs_sgn_eq
% 0.29/0.53 thf(fact_1004_abs__sgn__eq,axiom,
% 0.29/0.53 ! [A: rat] :
% 0.29/0.53 ( ( ( A = zero_zero_rat )
% 0.29/0.53 => ( ( abs_abs_rat @ ( sgn_sgn_rat @ A ) )
% 0.29/0.53 = zero_zero_rat ) )
% 0.29/0.53 & ( ( A != zero_zero_rat )
% 0.29/0.53 => ( ( abs_abs_rat @ ( sgn_sgn_rat @ A ) )
% 0.29/0.53 = one_one_rat ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % abs_sgn_eq
% 0.29/0.53 thf(fact_1005_abs__sgn__eq,axiom,
% 0.29/0.53 ! [A: int] :
% 0.29/0.53 ( ( ( A = zero_zero_int )
% 0.29/0.53 => ( ( abs_abs_int @ ( sgn_sgn_int @ A ) )
% 0.29/0.53 = zero_zero_int ) )
% 0.29/0.53 & ( ( A != zero_zero_int )
% 0.29/0.53 => ( ( abs_abs_int @ ( sgn_sgn_int @ A ) )
% 0.29/0.53 = one_one_int ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % abs_sgn_eq
% 0.29/0.53 thf(fact_1006_abs__one,axiom,
% 0.29/0.53 ( ( abs_abs_Code_integer @ one_one_Code_integer )
% 0.29/0.53 = one_one_Code_integer ) ).
% 0.29/0.53
% 0.29/0.53 % abs_one
% 0.29/0.53 thf(fact_1007_abs__one,axiom,
% 0.29/0.53 ( ( abs_abs_rat @ one_one_rat )
% 0.29/0.53 = one_one_rat ) ).
% 0.29/0.53
% 0.29/0.53 % abs_one
% 0.29/0.53 thf(fact_1008_abs__one,axiom,
% 0.29/0.53 ( ( abs_abs_int @ one_one_int )
% 0.29/0.53 = one_one_int ) ).
% 0.29/0.53
% 0.29/0.53 % abs_one
% 0.29/0.53 thf(fact_1009_map__option_Ocompositionality,axiom,
% 0.29/0.53 ! [F: code_integer > code_integer,G: num > code_integer,Option: option_num] :
% 0.29/0.53 ( ( map_op3669829223712506439nteger @ F @ ( map_op2849635639313731588nteger @ G @ Option ) )
% 0.29/0.53 = ( map_op2849635639313731588nteger @ ( comp_C3531382070062128313er_num @ F @ G ) @ Option ) ) ).
% 0.29/0.53
% 0.29/0.53 % map_option.compositionality
% 0.29/0.53 thf(fact_1010_map__option_Ocompositionality,axiom,
% 0.29/0.53 ! [F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer,Option: option_Code_integer] :
% 0.29/0.53 ( ( map_op9146685272036663823nteger @ F @ ( map_op3669829223712506439nteger @ G @ Option ) )
% 0.29/0.53 = ( map_op9146685272036663823nteger @ ( comp_C1593894019821074884nteger @ F @ G ) @ Option ) ) ).
% 0.29/0.53
% 0.29/0.53 % map_option.compositionality
% 0.29/0.53 thf(fact_1011_map__option_Ocompositionality,axiom,
% 0.29/0.53 ! [F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer > code_integer,Option: option_Code_integer] :
% 0.29/0.53 ( ( map_op3563471509957180299nteger @ F @ ( map_op370346339404370627nteger @ G @ Option ) )
% 0.29/0.53 = ( map_op9146685272036663823nteger @ ( comp_C8797469213163452608nteger @ F @ G ) @ Option ) ) ).
% 0.29/0.53
% 0.29/0.53 % map_option.compositionality
% 0.29/0.53 thf(fact_1012_map__option_Ocompositionality,axiom,
% 0.29/0.53 ! [F: nat > num,G: int > nat,Option: option_int] :
% 0.29/0.53 ( ( map_option_nat_num @ F @ ( map_option_int_nat @ G @ Option ) )
% 0.29/0.53 = ( map_option_int_num @ ( comp_nat_num_int @ F @ G ) @ Option ) ) ).
% 0.29/0.53
% 0.29/0.53 % map_option.compositionality
% 0.29/0.53 thf(fact_1013_map__option_Ocompositionality,axiom,
% 0.29/0.53 ! [F: num > num,G: num > num,Option: option_num] :
% 0.29/0.53 ( ( map_option_num_num @ F @ ( map_option_num_num @ G @ Option ) )
% 0.29/0.53 = ( map_option_num_num @ ( comp_num_num_num @ F @ G ) @ Option ) ) ).
% 0.29/0.53
% 0.29/0.53 % map_option.compositionality
% 0.29/0.53 thf(fact_1014_option_Omap__comp,axiom,
% 0.29/0.53 ! [G: code_integer > code_integer,F: num > code_integer,V: option_num] :
% 0.29/0.53 ( ( map_op3669829223712506439nteger @ G @ ( map_op2849635639313731588nteger @ F @ V ) )
% 0.29/0.53 = ( map_op2849635639313731588nteger @ ( comp_C3531382070062128313er_num @ G @ F ) @ V ) ) ).
% 0.29/0.53
% 0.29/0.53 % option.map_comp
% 0.29/0.53 thf(fact_1015_option_Omap__comp,axiom,
% 0.29/0.53 ! [G: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,F: code_integer > code_integer,V: option_Code_integer] :
% 0.29/0.53 ( ( map_op9146685272036663823nteger @ G @ ( map_op3669829223712506439nteger @ F @ V ) )
% 0.29/0.53 = ( map_op9146685272036663823nteger @ ( comp_C1593894019821074884nteger @ G @ F ) @ V ) ) ).
% 0.29/0.53
% 0.29/0.53 % option.map_comp
% 0.29/0.53 thf(fact_1016_option_Omap__comp,axiom,
% 0.29/0.53 ! [G: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,F: code_integer > code_integer > code_integer,V: option_Code_integer] :
% 0.29/0.53 ( ( map_op3563471509957180299nteger @ G @ ( map_op370346339404370627nteger @ F @ V ) )
% 0.29/0.53 = ( map_op9146685272036663823nteger @ ( comp_C8797469213163452608nteger @ G @ F ) @ V ) ) ).
% 0.29/0.53
% 0.29/0.53 % option.map_comp
% 0.29/0.53 thf(fact_1017_option_Omap__comp,axiom,
% 0.29/0.53 ! [G: nat > num,F: int > nat,V: option_int] :
% 0.29/0.53 ( ( map_option_nat_num @ G @ ( map_option_int_nat @ F @ V ) )
% 0.29/0.53 = ( map_option_int_num @ ( comp_nat_num_int @ G @ F ) @ V ) ) ).
% 0.29/0.53
% 0.29/0.53 % option.map_comp
% 0.29/0.53 thf(fact_1018_option_Omap__comp,axiom,
% 0.29/0.53 ! [G: num > num,F: num > num,V: option_num] :
% 0.29/0.53 ( ( map_option_num_num @ G @ ( map_option_num_num @ F @ V ) )
% 0.29/0.53 = ( map_option_num_num @ ( comp_num_num_num @ G @ F ) @ V ) ) ).
% 0.29/0.53
% 0.29/0.53 % option.map_comp
% 0.29/0.53 thf(fact_1019_map__option_Ocomp,axiom,
% 0.29/0.53 ! [F: code_integer > code_integer,G: num > code_integer] :
% 0.29/0.53 ( ( comp_o5321900959263616553on_num @ ( map_op3669829223712506439nteger @ F ) @ ( map_op2849635639313731588nteger @ G ) )
% 0.29/0.53 = ( map_op2849635639313731588nteger @ ( comp_C3531382070062128313er_num @ F @ G ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % map_option.comp
% 0.29/0.53 thf(fact_1020_map__option_Ocomp,axiom,
% 0.29/0.53 ! [F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer] :
% 0.29/0.53 ( ( comp_o9011007105448239796nteger @ ( map_op9146685272036663823nteger @ F ) @ ( map_op3669829223712506439nteger @ G ) )
% 0.29/0.53 = ( map_op9146685272036663823nteger @ ( comp_C1593894019821074884nteger @ F @ G ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % map_option.comp
% 0.29/0.53 thf(fact_1021_map__option_Ocomp,axiom,
% 0.29/0.53 ! [F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer > code_integer] :
% 0.29/0.53 ( ( comp_o7188567781464924208nteger @ ( map_op3563471509957180299nteger @ F ) @ ( map_op370346339404370627nteger @ G ) )
% 0.29/0.53 = ( map_op9146685272036663823nteger @ ( comp_C8797469213163452608nteger @ F @ G ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % map_option.comp
% 0.29/0.53 thf(fact_1022_map__option_Ocomp,axiom,
% 0.29/0.53 ! [F: nat > num,G: int > nat] :
% 0.29/0.53 ( ( comp_o3128663659858294251on_int @ ( map_option_nat_num @ F ) @ ( map_option_int_nat @ G ) )
% 0.29/0.53 = ( map_option_int_num @ ( comp_nat_num_int @ F @ G ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % map_option.comp
% 0.29/0.53 thf(fact_1023_map__option_Ocomp,axiom,
% 0.29/0.53 ! [F: num > num,G: num > num] :
% 0.29/0.53 ( ( comp_o8931257242830428707on_num @ ( map_option_num_num @ F ) @ ( map_option_num_num @ G ) )
% 0.29/0.53 = ( map_option_num_num @ ( comp_num_num_num @ F @ G ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % map_option.comp
% 0.29/0.53 thf(fact_1024_minus__less__iff,axiom,
% 0.29/0.53 ! [A: int,B: int] :
% 0.29/0.53 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ B )
% 0.29/0.53 = ( ord_less_int @ ( uminus_uminus_int @ B ) @ A ) ) ).
% 0.29/0.53
% 0.29/0.53 % minus_less_iff
% 0.29/0.53 thf(fact_1025_minus__less__iff,axiom,
% 0.29/0.53 ! [A: code_integer,B: code_integer] :
% 0.29/0.53 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 0.29/0.53 = ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ A ) ) ).
% 0.29/0.53
% 0.29/0.53 % minus_less_iff
% 0.29/0.53 thf(fact_1026_minus__less__iff,axiom,
% 0.29/0.53 ! [A: rat,B: rat] :
% 0.29/0.53 ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ B )
% 0.29/0.53 = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ A ) ) ).
% 0.29/0.53
% 0.29/0.53 % minus_less_iff
% 0.29/0.53 thf(fact_1027_less__minus__iff,axiom,
% 0.29/0.53 ! [A: int,B: int] :
% 0.29/0.53 ( ( ord_less_int @ A @ ( uminus_uminus_int @ B ) )
% 0.29/0.53 = ( ord_less_int @ B @ ( uminus_uminus_int @ A ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % less_minus_iff
% 0.29/0.53 thf(fact_1028_less__minus__iff,axiom,
% 0.29/0.53 ! [A: code_integer,B: code_integer] :
% 0.29/0.53 ( ( ord_le6747313008572928689nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 0.29/0.53 = ( ord_le6747313008572928689nteger @ B @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % less_minus_iff
% 0.29/0.53 thf(fact_1029_less__minus__iff,axiom,
% 0.29/0.53 ! [A: rat,B: rat] :
% 0.29/0.53 ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ B ) )
% 0.29/0.53 = ( ord_less_rat @ B @ ( uminus_uminus_rat @ A ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % less_minus_iff
% 0.29/0.53 thf(fact_1030_is__num__normalize_I8_J,axiom,
% 0.29/0.53 ! [A: int,B: int] :
% 0.29/0.53 ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 0.29/0.53 = ( plus_plus_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % is_num_normalize(8)
% 0.29/0.53 thf(fact_1031_is__num__normalize_I8_J,axiom,
% 0.29/0.53 ! [A: code_integer,B: code_integer] :
% 0.29/0.53 ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 0.29/0.53 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % is_num_normalize(8)
% 0.29/0.53 thf(fact_1032_is__num__normalize_I8_J,axiom,
% 0.29/0.53 ! [A: rat,B: rat] :
% 0.29/0.53 ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 0.29/0.53 = ( plus_plus_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % is_num_normalize(8)
% 0.29/0.53 thf(fact_1033_add_Oinverse__distrib__swap,axiom,
% 0.29/0.53 ! [A: int,B: int] :
% 0.29/0.53 ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 0.29/0.53 = ( plus_plus_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % add.inverse_distrib_swap
% 0.29/0.53 thf(fact_1034_add_Oinverse__distrib__swap,axiom,
% 0.29/0.53 ! [A: code_integer,B: code_integer] :
% 0.29/0.53 ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 0.29/0.53 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % add.inverse_distrib_swap
% 0.29/0.53 thf(fact_1035_add_Oinverse__distrib__swap,axiom,
% 0.29/0.53 ! [A: rat,B: rat] :
% 0.29/0.53 ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 0.29/0.53 = ( plus_plus_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % add.inverse_distrib_swap
% 0.29/0.53 thf(fact_1036_group__cancel_Oneg1,axiom,
% 0.29/0.53 ! [A2: int,K: int,A: int] :
% 0.29/0.53 ( ( A2
% 0.29/0.53 = ( plus_plus_int @ K @ A ) )
% 0.29/0.53 => ( ( uminus_uminus_int @ A2 )
% 0.29/0.53 = ( plus_plus_int @ ( uminus_uminus_int @ K ) @ ( uminus_uminus_int @ A ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % group_cancel.neg1
% 0.29/0.53 thf(fact_1037_group__cancel_Oneg1,axiom,
% 0.29/0.53 ! [A2: code_integer,K: code_integer,A: code_integer] :
% 0.29/0.53 ( ( A2
% 0.29/0.53 = ( plus_p5714425477246183910nteger @ K @ A ) )
% 0.29/0.53 => ( ( uminus1351360451143612070nteger @ A2 )
% 0.29/0.53 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ K ) @ ( uminus1351360451143612070nteger @ A ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % group_cancel.neg1
% 0.29/0.53 thf(fact_1038_group__cancel_Oneg1,axiom,
% 0.29/0.53 ! [A2: rat,K: rat,A: rat] :
% 0.29/0.53 ( ( A2
% 0.29/0.53 = ( plus_plus_rat @ K @ A ) )
% 0.29/0.53 => ( ( uminus_uminus_rat @ A2 )
% 0.29/0.53 = ( plus_plus_rat @ ( uminus_uminus_rat @ K ) @ ( uminus_uminus_rat @ A ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % group_cancel.neg1
% 0.29/0.53 thf(fact_1039_one__neq__neg__one,axiom,
% 0.29/0.53 ( one_one_int
% 0.29/0.53 != ( uminus_uminus_int @ one_one_int ) ) ).
% 0.29/0.53
% 0.29/0.53 % one_neq_neg_one
% 0.29/0.53 thf(fact_1040_one__neq__neg__one,axiom,
% 0.29/0.53 ( one_one_Code_integer
% 0.29/0.53 != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.29/0.53
% 0.29/0.53 % one_neq_neg_one
% 0.29/0.53 thf(fact_1041_one__neq__neg__one,axiom,
% 0.29/0.53 ( one_one_rat
% 0.29/0.53 != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.29/0.53
% 0.29/0.53 % one_neq_neg_one
% 0.29/0.53 thf(fact_1042_map__option__cong,axiom,
% 0.29/0.53 ! [X: option_num,Y: option_num,F: num > num,G: num > num] :
% 0.29/0.53 ( ( X = Y )
% 0.29/0.53 => ( ! [A3: num] :
% 0.29/0.53 ( ( Y
% 0.29/0.53 = ( some_num @ A3 ) )
% 0.29/0.53 => ( ( F @ A3 )
% 0.29/0.53 = ( G @ A3 ) ) )
% 0.29/0.53 => ( ( map_option_num_num @ F @ X )
% 0.29/0.53 = ( map_option_num_num @ G @ Y ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % map_option_cong
% 0.29/0.53 thf(fact_1043_option_Osimps_I9_J,axiom,
% 0.29/0.53 ! [F: num > produc8664842809031399944it_nat,X2: num] :
% 0.29/0.53 ( ( map_op8118133509425879471it_nat @ F @ ( some_num @ X2 ) )
% 0.29/0.53 = ( some_P1914260805536162275it_nat @ ( F @ X2 ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % option.simps(9)
% 0.29/0.53 thf(fact_1044_option_Osimps_I9_J,axiom,
% 0.29/0.53 ! [F: produc8664842809031399944it_nat > num,X2: produc8664842809031399944it_nat] :
% 0.29/0.53 ( ( map_op2731889312448867759at_num @ F @ ( some_P1914260805536162275it_nat @ X2 ) )
% 0.29/0.53 = ( some_num @ ( F @ X2 ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % option.simps(9)
% 0.29/0.53 thf(fact_1045_option_Osimps_I9_J,axiom,
% 0.29/0.53 ! [F: produc8664842809031399944it_nat > produc8664842809031399944it_nat,X2: produc8664842809031399944it_nat] :
% 0.29/0.53 ( ( map_op8673683442680995229it_nat @ F @ ( some_P1914260805536162275it_nat @ X2 ) )
% 0.29/0.53 = ( some_P1914260805536162275it_nat @ ( F @ X2 ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % option.simps(9)
% 0.29/0.53 thf(fact_1046_option_Osimps_I9_J,axiom,
% 0.29/0.53 ! [F: num > num,X2: num] :
% 0.29/0.53 ( ( map_option_num_num @ F @ ( some_num @ X2 ) )
% 0.29/0.53 = ( some_num @ ( F @ X2 ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % option.simps(9)
% 0.29/0.53 thf(fact_1047_option_Osimps_I8_J,axiom,
% 0.29/0.53 ! [F: produc6714399278180371524it_nat > produc6714399278180371524it_nat] :
% 0.29/0.53 ( ( map_op6002829699023054091it_nat @ F @ none_P2587165478634041381it_nat )
% 0.29/0.53 = none_P2587165478634041381it_nat ) ).
% 0.29/0.53
% 0.29/0.53 % option.simps(8)
% 0.29/0.53 thf(fact_1048_option_Osimps_I8_J,axiom,
% 0.29/0.53 ! [F: produc6714399278180371524it_nat > num] :
% 0.29/0.53 ( ( map_op8228268515680064275at_num @ F @ none_P2587165478634041381it_nat )
% 0.29/0.53 = none_num ) ).
% 0.29/0.53
% 0.29/0.53 % option.simps(8)
% 0.29/0.53 thf(fact_1049_option_Osimps_I8_J,axiom,
% 0.29/0.53 ! [F: produc6714399278180371524it_nat > produc8664842809031399944it_nat] :
% 0.29/0.53 ( ( map_op674526153330701057it_nat @ F @ none_P2587165478634041381it_nat )
% 0.29/0.53 = none_P9117596204409417319it_nat ) ).
% 0.29/0.53
% 0.29/0.53 % option.simps(8)
% 0.29/0.53 thf(fact_1050_option_Osimps_I8_J,axiom,
% 0.29/0.53 ! [F: num > produc6714399278180371524it_nat] :
% 0.29/0.53 ( ( map_op6598675229099881181it_nat @ F @ none_num )
% 0.29/0.53 = none_P2587165478634041381it_nat ) ).
% 0.29/0.53
% 0.29/0.53 % option.simps(8)
% 0.29/0.53 thf(fact_1051_option_Osimps_I8_J,axiom,
% 0.29/0.53 ! [F: num > produc8664842809031399944it_nat] :
% 0.29/0.53 ( ( map_op8118133509425879471it_nat @ F @ none_num )
% 0.29/0.53 = none_P9117596204409417319it_nat ) ).
% 0.29/0.53
% 0.29/0.53 % option.simps(8)
% 0.29/0.53 thf(fact_1052_option_Osimps_I8_J,axiom,
% 0.29/0.53 ! [F: produc8664842809031399944it_nat > produc6714399278180371524it_nat] :
% 0.29/0.53 ( ( map_op7916408704904942447it_nat @ F @ none_P9117596204409417319it_nat )
% 0.29/0.53 = none_P2587165478634041381it_nat ) ).
% 0.29/0.53
% 0.29/0.53 % option.simps(8)
% 0.29/0.53 thf(fact_1053_option_Osimps_I8_J,axiom,
% 0.29/0.53 ! [F: produc8664842809031399944it_nat > num] :
% 0.29/0.53 ( ( map_op2731889312448867759at_num @ F @ none_P9117596204409417319it_nat )
% 0.29/0.53 = none_num ) ).
% 0.29/0.53
% 0.29/0.53 % option.simps(8)
% 0.29/0.53 thf(fact_1054_option_Osimps_I8_J,axiom,
% 0.29/0.53 ! [F: produc8664842809031399944it_nat > produc8664842809031399944it_nat] :
% 0.29/0.53 ( ( map_op8673683442680995229it_nat @ F @ none_P9117596204409417319it_nat )
% 0.29/0.53 = none_P9117596204409417319it_nat ) ).
% 0.29/0.53
% 0.29/0.53 % option.simps(8)
% 0.29/0.53 thf(fact_1055_option_Osimps_I8_J,axiom,
% 0.29/0.53 ! [F: num > num] :
% 0.29/0.53 ( ( map_option_num_num @ F @ none_num )
% 0.29/0.53 = none_num ) ).
% 0.29/0.53
% 0.29/0.53 % option.simps(8)
% 0.29/0.53 thf(fact_1056_same__sgn__sgn__add,axiom,
% 0.29/0.53 ! [B: code_integer,A: code_integer] :
% 0.29/0.53 ( ( ( sgn_sgn_Code_integer @ B )
% 0.29/0.53 = ( sgn_sgn_Code_integer @ A ) )
% 0.29/0.53 => ( ( sgn_sgn_Code_integer @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 0.29/0.53 = ( sgn_sgn_Code_integer @ A ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % same_sgn_sgn_add
% 0.29/0.53 thf(fact_1057_same__sgn__sgn__add,axiom,
% 0.29/0.53 ! [B: rat,A: rat] :
% 0.29/0.53 ( ( ( sgn_sgn_rat @ B )
% 0.29/0.53 = ( sgn_sgn_rat @ A ) )
% 0.29/0.53 => ( ( sgn_sgn_rat @ ( plus_plus_rat @ A @ B ) )
% 0.29/0.53 = ( sgn_sgn_rat @ A ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % same_sgn_sgn_add
% 0.29/0.53 thf(fact_1058_same__sgn__sgn__add,axiom,
% 0.29/0.53 ! [B: int,A: int] :
% 0.29/0.53 ( ( ( sgn_sgn_int @ B )
% 0.29/0.53 = ( sgn_sgn_int @ A ) )
% 0.29/0.53 => ( ( sgn_sgn_int @ ( plus_plus_int @ A @ B ) )
% 0.29/0.53 = ( sgn_sgn_int @ A ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % same_sgn_sgn_add
% 0.29/0.53 thf(fact_1059_Ints__add,axiom,
% 0.29/0.53 ! [A: rat,B: rat] :
% 0.29/0.53 ( ( member_rat @ A @ ring_1_Ints_rat )
% 0.29/0.53 => ( ( member_rat @ B @ ring_1_Ints_rat )
% 0.29/0.53 => ( member_rat @ ( plus_plus_rat @ A @ B ) @ ring_1_Ints_rat ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % Ints_add
% 0.29/0.53 thf(fact_1060_Ints__add,axiom,
% 0.29/0.53 ! [A: int,B: int] :
% 0.29/0.53 ( ( member_int @ A @ ring_1_Ints_int )
% 0.29/0.53 => ( ( member_int @ B @ ring_1_Ints_int )
% 0.29/0.53 => ( member_int @ ( plus_plus_int @ A @ B ) @ ring_1_Ints_int ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % Ints_add
% 0.29/0.53 thf(fact_1061_success__lookupI,axiom,
% 0.29/0.53 ! [R2: ref_Product_unit,H3: heap_e7401611519738050253t_unit] : ( heap_T584514906347983379t_unit @ ( ref_lo7930775386976318366t_unit @ R2 ) @ H3 ) ).
% 0.29/0.53
% 0.29/0.53 % success_lookupI
% 0.29/0.53 thf(fact_1062_success__lookupI,axiom,
% 0.29/0.53 ! [R2: ref_array_a,H3: heap_e7401611519738050253t_unit] : ( heap_T6932021131025641745rray_a @ ( ref_lookup_array_a @ R2 ) @ H3 ) ).
% 0.29/0.53
% 0.29/0.53 % success_lookupI
% 0.29/0.53 thf(fact_1063_Ints__1,axiom,
% 0.29/0.53 member_Code_integer @ one_one_Code_integer @ ring_11222124179247155820nteger ).
% 0.29/0.53
% 0.29/0.53 % Ints_1
% 0.29/0.53 thf(fact_1064_Ints__1,axiom,
% 0.29/0.53 member_rat @ one_one_rat @ ring_1_Ints_rat ).
% 0.29/0.53
% 0.29/0.53 % Ints_1
% 0.29/0.53 thf(fact_1065_Ints__1,axiom,
% 0.29/0.53 member_int @ one_one_int @ ring_1_Ints_int ).
% 0.29/0.53
% 0.29/0.53 % Ints_1
% 0.29/0.53 thf(fact_1066_Ints__nonzero__abs__less1,axiom,
% 0.29/0.53 ! [X: code_integer] :
% 0.29/0.53 ( ( member_Code_integer @ X @ ring_11222124179247155820nteger )
% 0.29/0.53 => ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ X ) @ one_one_Code_integer )
% 0.29/0.53 => ( X = zero_z3403309356797280102nteger ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % Ints_nonzero_abs_less1
% 0.29/0.53 thf(fact_1067_Ints__nonzero__abs__less1,axiom,
% 0.29/0.53 ! [X: rat] :
% 0.29/0.53 ( ( member_rat @ X @ ring_1_Ints_rat )
% 0.29/0.53 => ( ( ord_less_rat @ ( abs_abs_rat @ X ) @ one_one_rat )
% 0.29/0.53 => ( X = zero_zero_rat ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % Ints_nonzero_abs_less1
% 0.29/0.53 thf(fact_1068_Ints__nonzero__abs__less1,axiom,
% 0.29/0.53 ! [X: int] :
% 0.29/0.53 ( ( member_int @ X @ ring_1_Ints_int )
% 0.29/0.53 => ( ( ord_less_int @ ( abs_abs_int @ X ) @ one_one_int )
% 0.29/0.53 => ( X = zero_zero_int ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % Ints_nonzero_abs_less1
% 0.29/0.53 thf(fact_1069_sgn__if,axiom,
% 0.29/0.53 ( sgn_sgn_int
% 0.29/0.53 = ( ^ [X3: int] : ( if_int @ ( X3 = zero_zero_int ) @ zero_zero_int @ ( if_int @ ( ord_less_int @ zero_zero_int @ X3 ) @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % sgn_if
% 0.29/0.53 thf(fact_1070_sgn__if,axiom,
% 0.29/0.53 ( sgn_sgn_Code_integer
% 0.29/0.53 = ( ^ [X3: code_integer] : ( if_Code_integer @ ( X3 = zero_z3403309356797280102nteger ) @ zero_z3403309356797280102nteger @ ( if_Code_integer @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ X3 ) @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % sgn_if
% 0.29/0.53 thf(fact_1071_sgn__if,axiom,
% 0.29/0.53 ( sgn_sgn_rat
% 0.29/0.53 = ( ^ [X3: rat] : ( if_rat @ ( X3 = zero_zero_rat ) @ zero_zero_rat @ ( if_rat @ ( ord_less_rat @ zero_zero_rat @ X3 ) @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % sgn_if
% 0.29/0.53 thf(fact_1072_sgn__1__neg,axiom,
% 0.29/0.53 ! [A: int] :
% 0.29/0.53 ( ( ( sgn_sgn_int @ A )
% 0.29/0.53 = ( uminus_uminus_int @ one_one_int ) )
% 0.29/0.53 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 0.29/0.53
% 0.29/0.53 % sgn_1_neg
% 0.29/0.53 thf(fact_1073_sgn__1__neg,axiom,
% 0.29/0.53 ! [A: code_integer] :
% 0.29/0.53 ( ( ( sgn_sgn_Code_integer @ A )
% 0.29/0.53 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.29/0.53 = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 0.29/0.53
% 0.29/0.53 % sgn_1_neg
% 0.29/0.53 thf(fact_1074_sgn__1__neg,axiom,
% 0.29/0.53 ! [A: rat] :
% 0.29/0.53 ( ( ( sgn_sgn_rat @ A )
% 0.29/0.53 = ( uminus_uminus_rat @ one_one_rat ) )
% 0.29/0.53 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 0.29/0.53
% 0.29/0.53 % sgn_1_neg
% 0.29/0.53 thf(fact_1075_abs__not__less__zero,axiom,
% 0.29/0.53 ! [A: code_integer] :
% 0.29/0.53 ~ ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ zero_z3403309356797280102nteger ) ).
% 0.29/0.53
% 0.29/0.53 % abs_not_less_zero
% 0.29/0.53 thf(fact_1076_abs__not__less__zero,axiom,
% 0.29/0.53 ! [A: rat] :
% 0.29/0.53 ~ ( ord_less_rat @ ( abs_abs_rat @ A ) @ zero_zero_rat ) ).
% 0.29/0.53
% 0.29/0.53 % abs_not_less_zero
% 0.29/0.53 thf(fact_1077_abs__not__less__zero,axiom,
% 0.29/0.53 ! [A: int] :
% 0.29/0.53 ~ ( ord_less_int @ ( abs_abs_int @ A ) @ zero_zero_int ) ).
% 0.29/0.53
% 0.29/0.53 % abs_not_less_zero
% 0.29/0.53 thf(fact_1078_abs__of__pos,axiom,
% 0.29/0.53 ! [A: code_integer] :
% 0.29/0.53 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 0.29/0.53 => ( ( abs_abs_Code_integer @ A )
% 0.29/0.53 = A ) ) ).
% 0.29/0.53
% 0.29/0.53 % abs_of_pos
% 0.29/0.53 thf(fact_1079_abs__of__pos,axiom,
% 0.29/0.53 ! [A: rat] :
% 0.29/0.53 ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.29/0.53 => ( ( abs_abs_rat @ A )
% 0.29/0.53 = A ) ) ).
% 0.29/0.53
% 0.29/0.53 % abs_of_pos
% 0.29/0.53 thf(fact_1080_abs__of__pos,axiom,
% 0.29/0.53 ! [A: int] :
% 0.29/0.53 ( ( ord_less_int @ zero_zero_int @ A )
% 0.29/0.53 => ( ( abs_abs_int @ A )
% 0.29/0.53 = A ) ) ).
% 0.29/0.53
% 0.29/0.53 % abs_of_pos
% 0.29/0.53 thf(fact_1081_neg__eq__iff__add__eq__0,axiom,
% 0.29/0.53 ! [A: int,B: int] :
% 0.29/0.53 ( ( ( uminus_uminus_int @ A )
% 0.29/0.53 = B )
% 0.29/0.53 = ( ( plus_plus_int @ A @ B )
% 0.29/0.53 = zero_zero_int ) ) ).
% 0.29/0.53
% 0.29/0.53 % neg_eq_iff_add_eq_0
% 0.29/0.53 thf(fact_1082_neg__eq__iff__add__eq__0,axiom,
% 0.29/0.53 ! [A: code_integer,B: code_integer] :
% 0.29/0.53 ( ( ( uminus1351360451143612070nteger @ A )
% 0.29/0.53 = B )
% 0.29/0.53 = ( ( plus_p5714425477246183910nteger @ A @ B )
% 0.29/0.53 = zero_z3403309356797280102nteger ) ) ).
% 0.29/0.53
% 0.29/0.53 % neg_eq_iff_add_eq_0
% 0.29/0.53 thf(fact_1083_neg__eq__iff__add__eq__0,axiom,
% 0.29/0.53 ! [A: rat,B: rat] :
% 0.29/0.53 ( ( ( uminus_uminus_rat @ A )
% 0.29/0.53 = B )
% 0.29/0.53 = ( ( plus_plus_rat @ A @ B )
% 0.29/0.53 = zero_zero_rat ) ) ).
% 0.29/0.53
% 0.29/0.53 % neg_eq_iff_add_eq_0
% 0.29/0.53 thf(fact_1084_eq__neg__iff__add__eq__0,axiom,
% 0.29/0.53 ! [A: int,B: int] :
% 0.29/0.53 ( ( A
% 0.29/0.53 = ( uminus_uminus_int @ B ) )
% 0.29/0.53 = ( ( plus_plus_int @ A @ B )
% 0.29/0.53 = zero_zero_int ) ) ).
% 0.29/0.53
% 0.29/0.53 % eq_neg_iff_add_eq_0
% 0.29/0.53 thf(fact_1085_eq__neg__iff__add__eq__0,axiom,
% 0.29/0.53 ! [A: code_integer,B: code_integer] :
% 0.29/0.53 ( ( A
% 0.29/0.53 = ( uminus1351360451143612070nteger @ B ) )
% 0.29/0.53 = ( ( plus_p5714425477246183910nteger @ A @ B )
% 0.29/0.53 = zero_z3403309356797280102nteger ) ) ).
% 0.29/0.53
% 0.29/0.53 % eq_neg_iff_add_eq_0
% 0.29/0.53 thf(fact_1086_eq__neg__iff__add__eq__0,axiom,
% 0.29/0.53 ! [A: rat,B: rat] :
% 0.29/0.53 ( ( A
% 0.29/0.53 = ( uminus_uminus_rat @ B ) )
% 0.29/0.53 = ( ( plus_plus_rat @ A @ B )
% 0.29/0.53 = zero_zero_rat ) ) ).
% 0.29/0.53
% 0.29/0.53 % eq_neg_iff_add_eq_0
% 0.29/0.53 thf(fact_1087_add_Oinverse__unique,axiom,
% 0.29/0.53 ! [A: int,B: int] :
% 0.29/0.53 ( ( ( plus_plus_int @ A @ B )
% 0.29/0.53 = zero_zero_int )
% 0.29/0.53 => ( ( uminus_uminus_int @ A )
% 0.29/0.53 = B ) ) ).
% 0.29/0.53
% 0.29/0.53 % add.inverse_unique
% 0.29/0.53 thf(fact_1088_add_Oinverse__unique,axiom,
% 0.29/0.53 ! [A: code_integer,B: code_integer] :
% 0.29/0.53 ( ( ( plus_p5714425477246183910nteger @ A @ B )
% 0.29/0.53 = zero_z3403309356797280102nteger )
% 0.29/0.53 => ( ( uminus1351360451143612070nteger @ A )
% 0.29/0.53 = B ) ) ).
% 0.29/0.53
% 0.29/0.53 % add.inverse_unique
% 0.29/0.53 thf(fact_1089_add_Oinverse__unique,axiom,
% 0.29/0.53 ! [A: rat,B: rat] :
% 0.29/0.53 ( ( ( plus_plus_rat @ A @ B )
% 0.29/0.53 = zero_zero_rat )
% 0.29/0.53 => ( ( uminus_uminus_rat @ A )
% 0.29/0.53 = B ) ) ).
% 0.29/0.53
% 0.29/0.53 % add.inverse_unique
% 0.29/0.53 thf(fact_1090_ab__group__add__class_Oab__left__minus,axiom,
% 0.29/0.53 ! [A: int] :
% 0.29/0.53 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ A )
% 0.29/0.53 = zero_zero_int ) ).
% 0.29/0.53
% 0.29/0.53 % ab_group_add_class.ab_left_minus
% 0.29/0.53 thf(fact_1091_ab__group__add__class_Oab__left__minus,axiom,
% 0.29/0.53 ! [A: code_integer] :
% 0.29/0.53 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 0.29/0.53 = zero_z3403309356797280102nteger ) ).
% 0.29/0.53
% 0.29/0.53 % ab_group_add_class.ab_left_minus
% 0.29/0.53 thf(fact_1092_ab__group__add__class_Oab__left__minus,axiom,
% 0.29/0.53 ! [A: rat] :
% 0.29/0.53 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ A )
% 0.29/0.53 = zero_zero_rat ) ).
% 0.29/0.53
% 0.29/0.53 % ab_group_add_class.ab_left_minus
% 0.29/0.53 thf(fact_1093_add__eq__0__iff,axiom,
% 0.29/0.53 ! [A: int,B: int] :
% 0.29/0.53 ( ( ( plus_plus_int @ A @ B )
% 0.29/0.53 = zero_zero_int )
% 0.29/0.53 = ( B
% 0.29/0.53 = ( uminus_uminus_int @ A ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % add_eq_0_iff
% 0.29/0.53 thf(fact_1094_add__eq__0__iff,axiom,
% 0.29/0.53 ! [A: code_integer,B: code_integer] :
% 0.29/0.53 ( ( ( plus_p5714425477246183910nteger @ A @ B )
% 0.29/0.53 = zero_z3403309356797280102nteger )
% 0.29/0.53 = ( B
% 0.29/0.53 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % add_eq_0_iff
% 0.29/0.53 thf(fact_1095_add__eq__0__iff,axiom,
% 0.29/0.53 ! [A: rat,B: rat] :
% 0.29/0.53 ( ( ( plus_plus_rat @ A @ B )
% 0.29/0.53 = zero_zero_rat )
% 0.29/0.53 = ( B
% 0.29/0.53 = ( uminus_uminus_rat @ A ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % add_eq_0_iff
% 0.29/0.53 thf(fact_1096_zero__neq__neg__one,axiom,
% 0.29/0.53 ( zero_zero_int
% 0.29/0.53 != ( uminus_uminus_int @ one_one_int ) ) ).
% 0.29/0.53
% 0.29/0.53 % zero_neq_neg_one
% 0.29/0.53 thf(fact_1097_zero__neq__neg__one,axiom,
% 0.29/0.53 ( zero_z3403309356797280102nteger
% 0.29/0.53 != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.29/0.53
% 0.29/0.53 % zero_neq_neg_one
% 0.29/0.53 thf(fact_1098_zero__neq__neg__one,axiom,
% 0.29/0.53 ( zero_zero_rat
% 0.29/0.53 != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.29/0.53
% 0.29/0.53 % zero_neq_neg_one
% 0.29/0.53 thf(fact_1099_less__minus__one__simps_I4_J,axiom,
% 0.29/0.53 ~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 0.29/0.53
% 0.29/0.53 % less_minus_one_simps(4)
% 0.29/0.53 thf(fact_1100_less__minus__one__simps_I4_J,axiom,
% 0.29/0.53 ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.29/0.53
% 0.29/0.53 % less_minus_one_simps(4)
% 0.29/0.53 thf(fact_1101_less__minus__one__simps_I4_J,axiom,
% 0.29/0.53 ~ ( ord_less_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.29/0.53
% 0.29/0.53 % less_minus_one_simps(4)
% 0.29/0.53 thf(fact_1102_less__minus__one__simps_I2_J,axiom,
% 0.29/0.53 ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 0.29/0.53
% 0.29/0.53 % less_minus_one_simps(2)
% 0.29/0.53 thf(fact_1103_less__minus__one__simps_I2_J,axiom,
% 0.29/0.53 ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ).
% 0.29/0.53
% 0.29/0.53 % less_minus_one_simps(2)
% 0.29/0.53 thf(fact_1104_less__minus__one__simps_I2_J,axiom,
% 0.29/0.53 ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat ).
% 0.29/0.53
% 0.29/0.53 % less_minus_one_simps(2)
% 0.29/0.53 thf(fact_1105_option_Omap__sel,axiom,
% 0.29/0.53 ! [A: option_num,F: num > num] :
% 0.29/0.53 ( ( A != none_num )
% 0.29/0.53 => ( ( the_num @ ( map_option_num_num @ F @ A ) )
% 0.29/0.53 = ( F @ ( the_num @ A ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % option.map_sel
% 0.29/0.53 thf(fact_1106_Ints__double__eq__0__iff,axiom,
% 0.29/0.53 ! [A: code_integer] :
% 0.29/0.53 ( ( member_Code_integer @ A @ ring_11222124179247155820nteger )
% 0.29/0.53 => ( ( ( plus_p5714425477246183910nteger @ A @ A )
% 0.29/0.53 = zero_z3403309356797280102nteger )
% 0.29/0.53 = ( A = zero_z3403309356797280102nteger ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % Ints_double_eq_0_iff
% 0.29/0.53 thf(fact_1107_Ints__double__eq__0__iff,axiom,
% 0.29/0.53 ! [A: rat] :
% 0.29/0.53 ( ( member_rat @ A @ ring_1_Ints_rat )
% 0.29/0.53 => ( ( ( plus_plus_rat @ A @ A )
% 0.29/0.53 = zero_zero_rat )
% 0.29/0.53 = ( A = zero_zero_rat ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % Ints_double_eq_0_iff
% 0.29/0.53 thf(fact_1108_Ints__double__eq__0__iff,axiom,
% 0.29/0.53 ! [A: int] :
% 0.29/0.53 ( ( member_int @ A @ ring_1_Ints_int )
% 0.29/0.53 => ( ( ( plus_plus_int @ A @ A )
% 0.29/0.53 = zero_zero_int )
% 0.29/0.53 = ( A = zero_zero_int ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % Ints_double_eq_0_iff
% 0.29/0.53 thf(fact_1109_less__minus__one__simps_I3_J,axiom,
% 0.29/0.53 ~ ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 0.29/0.53
% 0.29/0.53 % less_minus_one_simps(3)
% 0.29/0.53 thf(fact_1110_less__minus__one__simps_I3_J,axiom,
% 0.29/0.53 ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.29/0.53
% 0.29/0.53 % less_minus_one_simps(3)
% 0.29/0.53 thf(fact_1111_less__minus__one__simps_I3_J,axiom,
% 0.29/0.53 ~ ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.29/0.53
% 0.29/0.53 % less_minus_one_simps(3)
% 0.29/0.53 thf(fact_1112_less__minus__one__simps_I1_J,axiom,
% 0.29/0.53 ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% 0.29/0.53
% 0.29/0.53 % less_minus_one_simps(1)
% 0.29/0.53 thf(fact_1113_less__minus__one__simps_I1_J,axiom,
% 0.29/0.53 ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ zero_z3403309356797280102nteger ).
% 0.29/0.53
% 0.29/0.53 % less_minus_one_simps(1)
% 0.29/0.53 thf(fact_1114_less__minus__one__simps_I1_J,axiom,
% 0.29/0.53 ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ zero_zero_rat ).
% 0.29/0.53
% 0.29/0.53 % less_minus_one_simps(1)
% 0.29/0.53 thf(fact_1115_sgn__1__pos,axiom,
% 0.29/0.53 ! [A: code_integer] :
% 0.29/0.53 ( ( ( sgn_sgn_Code_integer @ A )
% 0.29/0.53 = one_one_Code_integer )
% 0.29/0.53 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 0.29/0.53
% 0.29/0.53 % sgn_1_pos
% 0.29/0.53 thf(fact_1116_sgn__1__pos,axiom,
% 0.29/0.53 ! [A: rat] :
% 0.29/0.53 ( ( ( sgn_sgn_rat @ A )
% 0.29/0.53 = one_one_rat )
% 0.29/0.53 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 0.29/0.53
% 0.29/0.53 % sgn_1_pos
% 0.29/0.53 thf(fact_1117_sgn__1__pos,axiom,
% 0.29/0.53 ! [A: int] :
% 0.29/0.53 ( ( ( sgn_sgn_int @ A )
% 0.29/0.53 = one_one_int )
% 0.29/0.53 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 0.29/0.53
% 0.29/0.53 % sgn_1_pos
% 0.29/0.53 thf(fact_1118_Ints__odd__nonzero,axiom,
% 0.29/0.53 ! [A: code_integer] :
% 0.29/0.53 ( ( member_Code_integer @ A @ ring_11222124179247155820nteger )
% 0.29/0.53 => ( ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ A )
% 0.29/0.53 != zero_z3403309356797280102nteger ) ) ).
% 0.29/0.53
% 0.29/0.53 % Ints_odd_nonzero
% 0.29/0.53 thf(fact_1119_Ints__odd__nonzero,axiom,
% 0.29/0.53 ! [A: rat] :
% 0.29/0.53 ( ( member_rat @ A @ ring_1_Ints_rat )
% 0.29/0.53 => ( ( plus_plus_rat @ ( plus_plus_rat @ one_one_rat @ A ) @ A )
% 0.29/0.53 != zero_zero_rat ) ) ).
% 0.29/0.53
% 0.29/0.53 % Ints_odd_nonzero
% 0.29/0.53 thf(fact_1120_Ints__odd__nonzero,axiom,
% 0.29/0.53 ! [A: int] :
% 0.29/0.53 ( ( member_int @ A @ ring_1_Ints_int )
% 0.29/0.53 => ( ( plus_plus_int @ ( plus_plus_int @ one_one_int @ A ) @ A )
% 0.29/0.53 != zero_zero_int ) ) ).
% 0.29/0.53
% 0.29/0.53 % Ints_odd_nonzero
% 0.29/0.53 thf(fact_1121_execute__lookup,axiom,
% 0.29/0.53 ! [R2: ref_array_a,H3: heap_e7401611519738050253t_unit] :
% 0.29/0.53 ( ( heap_T5591663578999710211rray_a @ ( ref_lookup_array_a @ R2 ) @ H3 )
% 0.29/0.53 = ( some_P6105628898608307625it_nat @ ( produc1733996804261680252it_nat @ ( ref_get_array_a @ H3 @ R2 ) @ ( produc584006145561248582it_nat @ H3 @ one_one_nat ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % execute_lookup
% 0.29/0.53 thf(fact_1122_execute__lookup,axiom,
% 0.29/0.53 ! [R2: ref_Product_unit,H3: heap_e7401611519738050253t_unit] :
% 0.29/0.53 ( ( heap_T875086893843062177t_unit @ ( ref_lo7930775386976318366t_unit @ R2 ) @ H3 )
% 0.29/0.53 = ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ ( ref_get_Product_unit @ H3 @ R2 ) @ ( produc584006145561248582it_nat @ H3 @ one_one_nat ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % execute_lookup
% 0.29/0.53 thf(fact_1123_fails__assert_H,axiom,
% 0.29/0.53 ! [P: $o,H3: heap_e7401611519738050253t_unit] :
% 0.29/0.53 ( ( time_f8834461667527620124t_unit @ ( refine_Imp_assert @ P ) @ H3 )
% 0.29/0.53 = ( ~ P ) ) ).
% 0.29/0.53
% 0.29/0.53 % fails_assert'
% 0.29/0.53 thf(fact_1124_add_Ogroup__axioms,axiom,
% 0.29/0.53 group_int @ plus_plus_int @ zero_zero_int @ uminus_uminus_int ).
% 0.29/0.53
% 0.29/0.53 % add.group_axioms
% 0.29/0.53 thf(fact_1125_add_Ogroup__axioms,axiom,
% 0.29/0.53 group_Code_integer @ plus_p5714425477246183910nteger @ zero_z3403309356797280102nteger @ uminus1351360451143612070nteger ).
% 0.29/0.53
% 0.29/0.53 % add.group_axioms
% 0.29/0.53 thf(fact_1126_add_Ogroup__axioms,axiom,
% 0.29/0.53 group_rat @ plus_plus_rat @ zero_zero_rat @ uminus_uminus_rat ).
% 0.29/0.53
% 0.29/0.53 % add.group_axioms
% 0.29/0.53 thf(fact_1127_num__of__nat__double,axiom,
% 0.29/0.53 ! [N2: nat] :
% 0.29/0.53 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.53 => ( ( num_of_nat @ ( plus_plus_nat @ N2 @ N2 ) )
% 0.29/0.53 = ( bit0 @ ( num_of_nat @ N2 ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % num_of_nat_double
% 0.29/0.53 thf(fact_1128_Ints__nonzero__abs__ge1,axiom,
% 0.29/0.53 ! [X: code_integer] :
% 0.29/0.53 ( ( member_Code_integer @ X @ ring_11222124179247155820nteger )
% 0.29/0.53 => ( ( X != zero_z3403309356797280102nteger )
% 0.29/0.53 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( abs_abs_Code_integer @ X ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % Ints_nonzero_abs_ge1
% 0.29/0.53 thf(fact_1129_Ints__nonzero__abs__ge1,axiom,
% 0.29/0.53 ! [X: rat] :
% 0.29/0.53 ( ( member_rat @ X @ ring_1_Ints_rat )
% 0.29/0.53 => ( ( X != zero_zero_rat )
% 0.29/0.53 => ( ord_less_eq_rat @ one_one_rat @ ( abs_abs_rat @ X ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % Ints_nonzero_abs_ge1
% 0.29/0.53 thf(fact_1130_Ints__nonzero__abs__ge1,axiom,
% 0.29/0.53 ! [X: int] :
% 0.29/0.53 ( ( member_int @ X @ ring_1_Ints_int )
% 0.29/0.53 => ( ( X != zero_zero_int )
% 0.29/0.53 => ( ord_less_eq_int @ one_one_int @ ( abs_abs_int @ X ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % Ints_nonzero_abs_ge1
% 0.29/0.53 thf(fact_1131_map__conv__bind__option,axiom,
% 0.29/0.53 ( map_option_num_num
% 0.29/0.53 = ( ^ [F2: num > num,X3: option_num] : ( bind_num_num @ X3 @ ( comp_n6731957995704128387um_num @ some_num @ F2 ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % map_conv_bind_option
% 0.29/0.53 thf(fact_1132_nat__add__left__cancel__le,axiom,
% 0.29/0.53 ! [K: nat,M2: nat,N2: nat] :
% 0.29/0.53 ( ( ord_less_eq_nat @ ( plus_plus_nat @ K @ M2 ) @ ( plus_plus_nat @ K @ N2 ) )
% 0.29/0.53 = ( ord_less_eq_nat @ M2 @ N2 ) ) ).
% 0.29/0.53
% 0.29/0.53 % nat_add_left_cancel_le
% 0.29/0.53 thf(fact_1133_less__eq__option__None__code,axiom,
% 0.29/0.53 ! [X: option_num] : ( ord_le6622620407824499402on_num @ none_num @ X ) ).
% 0.29/0.53
% 0.29/0.53 % less_eq_option_None_code
% 0.29/0.53 thf(fact_1134_le__zero__eq,axiom,
% 0.29/0.53 ! [N2: nat] :
% 0.29/0.53 ( ( ord_less_eq_nat @ N2 @ zero_zero_nat )
% 0.29/0.53 = ( N2 = zero_zero_nat ) ) ).
% 0.29/0.53
% 0.29/0.53 % le_zero_eq
% 0.29/0.53 thf(fact_1135_add__le__cancel__left,axiom,
% 0.29/0.53 ! [C: rat,A: rat,B: rat] :
% 0.29/0.53 ( ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 0.29/0.53 = ( ord_less_eq_rat @ A @ B ) ) ).
% 0.29/0.53
% 0.29/0.53 % add_le_cancel_left
% 0.29/0.53 thf(fact_1136_add__le__cancel__left,axiom,
% 0.29/0.53 ! [C: nat,A: nat,B: nat] :
% 0.29/0.53 ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 0.29/0.53 = ( ord_less_eq_nat @ A @ B ) ) ).
% 0.29/0.53
% 0.29/0.53 % add_le_cancel_left
% 0.29/0.53 thf(fact_1137_add__le__cancel__left,axiom,
% 0.29/0.53 ! [C: int,A: int,B: int] :
% 0.29/0.53 ( ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 0.29/0.53 = ( ord_less_eq_int @ A @ B ) ) ).
% 0.29/0.53
% 0.29/0.53 % add_le_cancel_left
% 0.29/0.53 thf(fact_1138_add__le__cancel__right,axiom,
% 0.29/0.53 ! [A: rat,C: rat,B: rat] :
% 0.29/0.53 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 0.29/0.53 = ( ord_less_eq_rat @ A @ B ) ) ).
% 0.29/0.53
% 0.29/0.53 % add_le_cancel_right
% 0.29/0.53 thf(fact_1139_add__le__cancel__right,axiom,
% 0.29/0.53 ! [A: nat,C: nat,B: nat] :
% 0.29/0.53 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 0.29/0.53 = ( ord_less_eq_nat @ A @ B ) ) ).
% 0.29/0.53
% 0.29/0.53 % add_le_cancel_right
% 0.29/0.53 thf(fact_1140_add__le__cancel__right,axiom,
% 0.29/0.53 ! [A: int,C: int,B: int] :
% 0.29/0.53 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 0.29/0.53 = ( ord_less_eq_int @ A @ B ) ) ).
% 0.29/0.53
% 0.29/0.53 % add_le_cancel_right
% 0.29/0.53 thf(fact_1141_neg__le__iff__le,axiom,
% 0.29/0.53 ! [B: code_integer,A: code_integer] :
% 0.29/0.53 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) )
% 0.29/0.53 = ( ord_le3102999989581377725nteger @ A @ B ) ) ).
% 0.29/0.53
% 0.29/0.53 % neg_le_iff_le
% 0.29/0.53 thf(fact_1142_neg__le__iff__le,axiom,
% 0.29/0.53 ! [B: rat,A: rat] :
% 0.29/0.53 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) )
% 0.29/0.53 = ( ord_less_eq_rat @ A @ B ) ) ).
% 0.29/0.53
% 0.29/0.53 % neg_le_iff_le
% 0.29/0.53 thf(fact_1143_neg__le__iff__le,axiom,
% 0.29/0.53 ! [B: int,A: int] :
% 0.29/0.53 ( ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) )
% 0.29/0.53 = ( ord_less_eq_int @ A @ B ) ) ).
% 0.29/0.53
% 0.29/0.53 % neg_le_iff_le
% 0.29/0.53 thf(fact_1144_less__eq__option__Some,axiom,
% 0.29/0.53 ! [X: set_nat,Y: set_nat] :
% 0.29/0.53 ( ( ord_le2843612097646854710et_nat @ ( some_set_nat @ X ) @ ( some_set_nat @ Y ) )
% 0.29/0.53 = ( ord_less_eq_set_nat @ X @ Y ) ) ).
% 0.29/0.53
% 0.29/0.53 % less_eq_option_Some
% 0.29/0.53 thf(fact_1145_less__eq__option__Some,axiom,
% 0.29/0.53 ! [X: rat,Y: rat] :
% 0.29/0.53 ( ( ord_le2406147912482264968on_rat @ ( some_rat @ X ) @ ( some_rat @ Y ) )
% 0.29/0.53 = ( ord_less_eq_rat @ X @ Y ) ) ).
% 0.29/0.53
% 0.29/0.53 % less_eq_option_Some
% 0.29/0.53 thf(fact_1146_less__eq__option__Some,axiom,
% 0.29/0.53 ! [X: num,Y: num] :
% 0.29/0.53 ( ( ord_le6622620407824499402on_num @ ( some_num @ X ) @ ( some_num @ Y ) )
% 0.29/0.53 = ( ord_less_eq_num @ X @ Y ) ) ).
% 0.29/0.53
% 0.29/0.53 % less_eq_option_Some
% 0.29/0.53 thf(fact_1147_less__eq__option__Some,axiom,
% 0.29/0.53 ! [X: nat,Y: nat] :
% 0.29/0.53 ( ( ord_le5914376470875661696on_nat @ ( some_nat @ X ) @ ( some_nat @ Y ) )
% 0.29/0.53 = ( ord_less_eq_nat @ X @ Y ) ) ).
% 0.29/0.53
% 0.29/0.53 % less_eq_option_Some
% 0.29/0.53 thf(fact_1148_less__eq__option__Some,axiom,
% 0.29/0.53 ! [X: int,Y: int] :
% 0.29/0.53 ( ( ord_le1736525451366464988on_int @ ( some_int @ X ) @ ( some_int @ Y ) )
% 0.29/0.53 = ( ord_less_eq_int @ X @ Y ) ) ).
% 0.29/0.53
% 0.29/0.53 % less_eq_option_Some
% 0.29/0.53 thf(fact_1149_less__eq__option__Some__None,axiom,
% 0.29/0.53 ! [X: num] :
% 0.29/0.53 ~ ( ord_le6622620407824499402on_num @ ( some_num @ X ) @ none_num ) ).
% 0.29/0.53
% 0.29/0.53 % less_eq_option_Some_None
% 0.29/0.53 thf(fact_1150_bind__runit,axiom,
% 0.29/0.53 ! [X: option_num] :
% 0.29/0.53 ( ( bind_num_num @ X @ some_num )
% 0.29/0.53 = X ) ).
% 0.29/0.53
% 0.29/0.53 % bind_runit
% 0.29/0.53 thf(fact_1151_bind__runit,axiom,
% 0.29/0.53 ! [X: option8956607266484857688it_nat] :
% 0.29/0.53 ( ( bind_P7351952464966851536it_nat @ X @ some_P1914260805536162275it_nat )
% 0.29/0.53 = X ) ).
% 0.29/0.53
% 0.29/0.53 % bind_runit
% 0.29/0.53 thf(fact_1152_add__le__same__cancel1,axiom,
% 0.29/0.53 ! [B: code_integer,A: code_integer] :
% 0.29/0.53 ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ B @ A ) @ B )
% 0.29/0.53 = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 0.29/0.53
% 0.29/0.53 % add_le_same_cancel1
% 0.29/0.53 thf(fact_1153_add__le__same__cancel1,axiom,
% 0.29/0.53 ! [B: rat,A: rat] :
% 0.29/0.53 ( ( ord_less_eq_rat @ ( plus_plus_rat @ B @ A ) @ B )
% 0.29/0.53 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 0.29/0.53
% 0.29/0.53 % add_le_same_cancel1
% 0.29/0.53 thf(fact_1154_add__le__same__cancel1,axiom,
% 0.29/0.53 ! [B: nat,A: nat] :
% 0.29/0.53 ( ( ord_less_eq_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 0.29/0.53 = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% 0.29/0.53
% 0.29/0.53 % add_le_same_cancel1
% 0.29/0.53 thf(fact_1155_add__le__same__cancel1,axiom,
% 0.29/0.53 ! [B: int,A: int] :
% 0.29/0.53 ( ( ord_less_eq_int @ ( plus_plus_int @ B @ A ) @ B )
% 0.29/0.53 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 0.29/0.53
% 0.29/0.53 % add_le_same_cancel1
% 0.29/0.53 thf(fact_1156_add__le__same__cancel2,axiom,
% 0.29/0.53 ! [A: code_integer,B: code_integer] :
% 0.29/0.53 ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ B )
% 0.29/0.53 = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 0.29/0.53
% 0.29/0.53 % add_le_same_cancel2
% 0.29/0.53 thf(fact_1157_add__le__same__cancel2,axiom,
% 0.29/0.53 ! [A: rat,B: rat] :
% 0.29/0.53 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 0.29/0.53 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 0.29/0.53
% 0.29/0.53 % add_le_same_cancel2
% 0.29/0.53 thf(fact_1158_add__le__same__cancel2,axiom,
% 0.29/0.53 ! [A: nat,B: nat] :
% 0.29/0.53 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 0.29/0.53 = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% 0.29/0.53
% 0.29/0.53 % add_le_same_cancel2
% 0.29/0.53 thf(fact_1159_add__le__same__cancel2,axiom,
% 0.29/0.53 ! [A: int,B: int] :
% 0.29/0.53 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ B )
% 0.29/0.53 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 0.29/0.53
% 0.29/0.53 % add_le_same_cancel2
% 0.29/0.53 thf(fact_1160_le__add__same__cancel1,axiom,
% 0.29/0.53 ! [A: code_integer,B: code_integer] :
% 0.29/0.53 ( ( ord_le3102999989581377725nteger @ A @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 0.29/0.53 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B ) ) ).
% 0.29/0.53
% 0.29/0.53 % le_add_same_cancel1
% 0.29/0.53 thf(fact_1161_le__add__same__cancel1,axiom,
% 0.29/0.53 ! [A: rat,B: rat] :
% 0.29/0.53 ( ( ord_less_eq_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 0.29/0.53 = ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ).
% 0.29/0.53
% 0.29/0.53 % le_add_same_cancel1
% 0.29/0.53 thf(fact_1162_le__add__same__cancel1,axiom,
% 0.29/0.53 ! [A: nat,B: nat] :
% 0.29/0.53 ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 0.29/0.53 = ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% 0.29/0.53
% 0.29/0.53 % le_add_same_cancel1
% 0.29/0.53 thf(fact_1163_le__add__same__cancel1,axiom,
% 0.29/0.53 ! [A: int,B: int] :
% 0.29/0.53 ( ( ord_less_eq_int @ A @ ( plus_plus_int @ A @ B ) )
% 0.29/0.53 = ( ord_less_eq_int @ zero_zero_int @ B ) ) ).
% 0.29/0.53
% 0.29/0.53 % le_add_same_cancel1
% 0.29/0.53 thf(fact_1164_le__add__same__cancel2,axiom,
% 0.29/0.53 ! [A: code_integer,B: code_integer] :
% 0.29/0.53 ( ( ord_le3102999989581377725nteger @ A @ ( plus_p5714425477246183910nteger @ B @ A ) )
% 0.29/0.53 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B ) ) ).
% 0.29/0.53
% 0.29/0.53 % le_add_same_cancel2
% 0.29/0.53 thf(fact_1165_le__add__same__cancel2,axiom,
% 0.29/0.53 ! [A: rat,B: rat] :
% 0.29/0.53 ( ( ord_less_eq_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 0.29/0.53 = ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ).
% 0.29/0.53
% 0.29/0.53 % le_add_same_cancel2
% 0.29/0.53 thf(fact_1166_le__add__same__cancel2,axiom,
% 0.29/0.53 ! [A: nat,B: nat] :
% 0.29/0.53 ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 0.29/0.53 = ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% 0.29/0.53
% 0.29/0.53 % le_add_same_cancel2
% 0.29/0.53 thf(fact_1167_le__add__same__cancel2,axiom,
% 0.29/0.53 ! [A: int,B: int] :
% 0.29/0.53 ( ( ord_less_eq_int @ A @ ( plus_plus_int @ B @ A ) )
% 0.29/0.53 = ( ord_less_eq_int @ zero_zero_int @ B ) ) ).
% 0.29/0.53
% 0.29/0.53 % le_add_same_cancel2
% 0.29/0.53 thf(fact_1168_double__add__le__zero__iff__single__add__le__zero,axiom,
% 0.29/0.53 ! [A: code_integer] :
% 0.29/0.53 ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ A @ A ) @ zero_z3403309356797280102nteger )
% 0.29/0.53 = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 0.29/0.53
% 0.29/0.53 % double_add_le_zero_iff_single_add_le_zero
% 0.29/0.53 thf(fact_1169_double__add__le__zero__iff__single__add__le__zero,axiom,
% 0.29/0.53 ! [A: rat] :
% 0.29/0.53 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ A ) @ zero_zero_rat )
% 0.29/0.53 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 0.29/0.53
% 0.29/0.53 % double_add_le_zero_iff_single_add_le_zero
% 0.29/0.53 thf(fact_1170_double__add__le__zero__iff__single__add__le__zero,axiom,
% 0.29/0.53 ! [A: int] :
% 0.29/0.53 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
% 0.29/0.53 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 0.29/0.53
% 0.29/0.53 % double_add_le_zero_iff_single_add_le_zero
% 0.29/0.53 thf(fact_1171_zero__le__double__add__iff__zero__le__single__add,axiom,
% 0.29/0.53 ! [A: code_integer] :
% 0.29/0.53 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ A @ A ) )
% 0.29/0.53 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 0.29/0.53
% 0.29/0.53 % zero_le_double_add_iff_zero_le_single_add
% 0.29/0.53 thf(fact_1172_zero__le__double__add__iff__zero__le__single__add,axiom,
% 0.29/0.53 ! [A: rat] :
% 0.29/0.53 ( ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ A ) )
% 0.29/0.53 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 0.29/0.53
% 0.29/0.53 % zero_le_double_add_iff_zero_le_single_add
% 0.29/0.53 thf(fact_1173_zero__le__double__add__iff__zero__le__single__add,axiom,
% 0.29/0.53 ! [A: int] :
% 0.29/0.53 ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
% 0.29/0.53 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 0.29/0.53
% 0.29/0.53 % zero_le_double_add_iff_zero_le_single_add
% 0.29/0.53 thf(fact_1174_neg__0__le__iff__le,axiom,
% 0.29/0.53 ! [A: code_integer] :
% 0.29/0.53 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ A ) )
% 0.29/0.53 = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 0.29/0.53
% 0.29/0.53 % neg_0_le_iff_le
% 0.29/0.53 thf(fact_1175_neg__0__le__iff__le,axiom,
% 0.29/0.53 ! [A: rat] :
% 0.29/0.53 ( ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ A ) )
% 0.29/0.53 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 0.29/0.53
% 0.29/0.53 % neg_0_le_iff_le
% 0.29/0.53 thf(fact_1176_neg__0__le__iff__le,axiom,
% 0.29/0.53 ! [A: int] :
% 0.29/0.53 ( ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 0.29/0.53 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 0.29/0.53
% 0.29/0.53 % neg_0_le_iff_le
% 0.29/0.53 thf(fact_1177_neg__le__0__iff__le,axiom,
% 0.29/0.53 ! [A: code_integer] :
% 0.29/0.53 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ zero_z3403309356797280102nteger )
% 0.29/0.53 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 0.29/0.53
% 0.29/0.53 % neg_le_0_iff_le
% 0.29/0.53 thf(fact_1178_neg__le__0__iff__le,axiom,
% 0.29/0.53 ! [A: rat] :
% 0.29/0.53 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ zero_zero_rat )
% 0.29/0.53 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 0.29/0.53
% 0.29/0.53 % neg_le_0_iff_le
% 0.29/0.53 thf(fact_1179_neg__le__0__iff__le,axiom,
% 0.29/0.53 ! [A: int] :
% 0.29/0.53 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 0.29/0.53 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 0.29/0.53
% 0.29/0.53 % neg_le_0_iff_le
% 0.29/0.53 thf(fact_1180_less__eq__neg__nonpos,axiom,
% 0.29/0.53 ! [A: code_integer] :
% 0.29/0.53 ( ( ord_le3102999989581377725nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 0.29/0.53 = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 0.29/0.53
% 0.29/0.53 % less_eq_neg_nonpos
% 0.29/0.53 thf(fact_1181_less__eq__neg__nonpos,axiom,
% 0.29/0.53 ! [A: rat] :
% 0.29/0.53 ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ A ) )
% 0.29/0.53 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 0.29/0.53
% 0.29/0.53 % less_eq_neg_nonpos
% 0.29/0.53 thf(fact_1182_less__eq__neg__nonpos,axiom,
% 0.29/0.53 ! [A: int] :
% 0.29/0.53 ( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ A ) )
% 0.29/0.53 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 0.29/0.53
% 0.29/0.53 % less_eq_neg_nonpos
% 0.29/0.53 thf(fact_1183_neg__less__eq__nonneg,axiom,
% 0.29/0.53 ! [A: code_integer] :
% 0.29/0.53 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 0.29/0.53 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 0.29/0.53
% 0.29/0.53 % neg_less_eq_nonneg
% 0.29/0.53 thf(fact_1184_neg__less__eq__nonneg,axiom,
% 0.29/0.53 ! [A: rat] :
% 0.29/0.53 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ A )
% 0.29/0.53 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 0.29/0.53
% 0.29/0.53 % neg_less_eq_nonneg
% 0.29/0.53 thf(fact_1185_neg__less__eq__nonneg,axiom,
% 0.29/0.53 ! [A: int] :
% 0.29/0.53 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ A )
% 0.29/0.53 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 0.29/0.53
% 0.29/0.53 % neg_less_eq_nonneg
% 0.29/0.53 thf(fact_1186_abs__of__nonneg,axiom,
% 0.29/0.53 ! [A: code_integer] :
% 0.29/0.53 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.29/0.53 => ( ( abs_abs_Code_integer @ A )
% 0.29/0.53 = A ) ) ).
% 0.29/0.53
% 0.29/0.53 % abs_of_nonneg
% 0.29/0.53 thf(fact_1187_abs__of__nonneg,axiom,
% 0.29/0.53 ! [A: rat] :
% 0.29/0.53 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.29/0.53 => ( ( abs_abs_rat @ A )
% 0.29/0.53 = A ) ) ).
% 0.29/0.53
% 0.29/0.53 % abs_of_nonneg
% 0.29/0.53 thf(fact_1188_abs__of__nonneg,axiom,
% 0.29/0.53 ! [A: int] :
% 0.29/0.53 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.29/0.53 => ( ( abs_abs_int @ A )
% 0.29/0.53 = A ) ) ).
% 0.29/0.53
% 0.29/0.53 % abs_of_nonneg
% 0.29/0.53 thf(fact_1189_abs__le__self__iff,axiom,
% 0.29/0.53 ! [A: code_integer] :
% 0.29/0.53 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ A )
% 0.29/0.53 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 0.29/0.53
% 0.29/0.53 % abs_le_self_iff
% 0.29/0.53 thf(fact_1190_abs__le__self__iff,axiom,
% 0.29/0.53 ! [A: rat] :
% 0.29/0.53 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ A )
% 0.29/0.53 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 0.29/0.53
% 0.29/0.53 % abs_le_self_iff
% 0.29/0.53 thf(fact_1191_abs__le__self__iff,axiom,
% 0.29/0.53 ! [A: int] :
% 0.29/0.53 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ A )
% 0.29/0.53 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 0.29/0.53
% 0.29/0.53 % abs_le_self_iff
% 0.29/0.53 thf(fact_1192_abs__le__zero__iff,axiom,
% 0.29/0.53 ! [A: code_integer] :
% 0.29/0.53 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ zero_z3403309356797280102nteger )
% 0.29/0.53 = ( A = zero_z3403309356797280102nteger ) ) ).
% 0.29/0.53
% 0.29/0.53 % abs_le_zero_iff
% 0.29/0.53 thf(fact_1193_abs__le__zero__iff,axiom,
% 0.29/0.53 ! [A: rat] :
% 0.29/0.53 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ zero_zero_rat )
% 0.29/0.53 = ( A = zero_zero_rat ) ) ).
% 0.29/0.53
% 0.29/0.53 % abs_le_zero_iff
% 0.29/0.53 thf(fact_1194_abs__le__zero__iff,axiom,
% 0.29/0.53 ! [A: int] :
% 0.29/0.53 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ zero_zero_int )
% 0.29/0.53 = ( A = zero_zero_int ) ) ).
% 0.29/0.53
% 0.29/0.53 % abs_le_zero_iff
% 0.29/0.53 thf(fact_1195_abs__of__nonpos,axiom,
% 0.29/0.53 ! [A: code_integer] :
% 0.29/0.53 ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 0.29/0.53 => ( ( abs_abs_Code_integer @ A )
% 0.29/0.53 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % abs_of_nonpos
% 0.29/0.53 thf(fact_1196_abs__of__nonpos,axiom,
% 0.29/0.53 ! [A: rat] :
% 0.29/0.53 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.29/0.53 => ( ( abs_abs_rat @ A )
% 0.29/0.53 = ( uminus_uminus_rat @ A ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % abs_of_nonpos
% 0.29/0.53 thf(fact_1197_abs__of__nonpos,axiom,
% 0.29/0.53 ! [A: int] :
% 0.29/0.53 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.29/0.53 => ( ( abs_abs_int @ A )
% 0.29/0.53 = ( uminus_uminus_int @ A ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % abs_of_nonpos
% 0.29/0.53 thf(fact_1198_ord__eq__le__eq__trans,axiom,
% 0.29/0.53 ! [A: set_nat,B: set_nat,C: set_nat,D2: set_nat] :
% 0.29/0.53 ( ( A = B )
% 0.29/0.53 => ( ( ord_less_eq_set_nat @ B @ C )
% 0.29/0.53 => ( ( C = D2 )
% 0.29/0.53 => ( ord_less_eq_set_nat @ A @ D2 ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % ord_eq_le_eq_trans
% 0.29/0.53 thf(fact_1199_ord__eq__le__eq__trans,axiom,
% 0.29/0.53 ! [A: rat,B: rat,C: rat,D2: rat] :
% 0.29/0.53 ( ( A = B )
% 0.29/0.53 => ( ( ord_less_eq_rat @ B @ C )
% 0.29/0.53 => ( ( C = D2 )
% 0.29/0.53 => ( ord_less_eq_rat @ A @ D2 ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % ord_eq_le_eq_trans
% 0.29/0.53 thf(fact_1200_ord__eq__le__eq__trans,axiom,
% 0.29/0.53 ! [A: num,B: num,C: num,D2: num] :
% 0.29/0.53 ( ( A = B )
% 0.29/0.53 => ( ( ord_less_eq_num @ B @ C )
% 0.29/0.53 => ( ( C = D2 )
% 0.29/0.53 => ( ord_less_eq_num @ A @ D2 ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % ord_eq_le_eq_trans
% 0.29/0.53 thf(fact_1201_ord__eq__le__eq__trans,axiom,
% 0.29/0.53 ! [A: nat,B: nat,C: nat,D2: nat] :
% 0.29/0.53 ( ( A = B )
% 0.29/0.53 => ( ( ord_less_eq_nat @ B @ C )
% 0.29/0.53 => ( ( C = D2 )
% 0.29/0.53 => ( ord_less_eq_nat @ A @ D2 ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % ord_eq_le_eq_trans
% 0.29/0.53 thf(fact_1202_ord__eq__le__eq__trans,axiom,
% 0.29/0.53 ! [A: int,B: int,C: int,D2: int] :
% 0.29/0.53 ( ( A = B )
% 0.29/0.53 => ( ( ord_less_eq_int @ B @ C )
% 0.29/0.53 => ( ( C = D2 )
% 0.29/0.53 => ( ord_less_eq_int @ A @ D2 ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % ord_eq_le_eq_trans
% 0.29/0.53 thf(fact_1203_accp__subset,axiom,
% 0.29/0.53 ! [R12: product_prod_nat_nat > product_prod_nat_nat > $o,R23: product_prod_nat_nat > product_prod_nat_nat > $o] :
% 0.29/0.53 ( ( ord_le5604493270027003598_nat_o @ R12 @ R23 )
% 0.29/0.53 => ( ord_le704812498762024988_nat_o @ ( accp_P4275260045618599050at_nat @ R23 ) @ ( accp_P4275260045618599050at_nat @ R12 ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % accp_subset
% 0.29/0.53 thf(fact_1204_accp__subset,axiom,
% 0.29/0.53 ! [R12: product_prod_int_int > product_prod_int_int > $o,R23: product_prod_int_int > product_prod_int_int > $o] :
% 0.29/0.53 ( ( ord_le1598226405681992910_int_o @ R12 @ R23 )
% 0.29/0.53 => ( ord_le8369615600986905444_int_o @ ( accp_P1096762738010456898nt_int @ R23 ) @ ( accp_P1096762738010456898nt_int @ R12 ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % accp_subset
% 0.29/0.53 thf(fact_1205_accp__subset,axiom,
% 0.29/0.53 ! [R12: produc2732055786443039994et_nat > produc2732055786443039994et_nat > $o,R23: produc2732055786443039994et_nat > produc2732055786443039994et_nat > $o] :
% 0.29/0.53 ( ( ord_le7226304311989208114_nat_o @ R12 @ R23 )
% 0.29/0.53 => ( ord_le1658592502415435381_nat_o @ ( accp_P1862375125659990705et_nat @ R23 ) @ ( accp_P1862375125659990705et_nat @ R12 ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % accp_subset
% 0.29/0.53 thf(fact_1206_accp__subset,axiom,
% 0.29/0.53 ! [R12: list_nat > list_nat > $o,R23: list_nat > list_nat > $o] :
% 0.29/0.53 ( ( ord_le6558929396352911974_nat_o @ R12 @ R23 )
% 0.29/0.53 => ( ord_le1520216061033275535_nat_o @ ( accp_list_nat @ R23 ) @ ( accp_list_nat @ R12 ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % accp_subset
% 0.29/0.53 thf(fact_1207_accp__subset,axiom,
% 0.29/0.53 ! [R12: nat > nat > $o,R23: nat > nat > $o] :
% 0.29/0.53 ( ( ord_le2646555220125990790_nat_o @ R12 @ R23 )
% 0.29/0.53 => ( ord_less_eq_nat_o @ ( accp_nat @ R23 ) @ ( accp_nat @ R12 ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % accp_subset
% 0.29/0.53 thf(fact_1208_le__some__optE,axiom,
% 0.29/0.53 ! [M2: set_nat,X: option_set_nat] :
% 0.29/0.53 ( ( ord_le2843612097646854710et_nat @ ( some_set_nat @ M2 ) @ X )
% 0.29/0.53 => ~ ! [M4: set_nat] :
% 0.29/0.53 ( ( X
% 0.29/0.53 = ( some_set_nat @ M4 ) )
% 0.29/0.53 => ~ ( ord_less_eq_set_nat @ M2 @ M4 ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % le_some_optE
% 0.29/0.53 thf(fact_1209_le__some__optE,axiom,
% 0.29/0.53 ! [M2: rat,X: option_rat] :
% 0.29/0.53 ( ( ord_le2406147912482264968on_rat @ ( some_rat @ M2 ) @ X )
% 0.29/0.53 => ~ ! [M4: rat] :
% 0.29/0.53 ( ( X
% 0.29/0.53 = ( some_rat @ M4 ) )
% 0.29/0.53 => ~ ( ord_less_eq_rat @ M2 @ M4 ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % le_some_optE
% 0.29/0.53 thf(fact_1210_le__some__optE,axiom,
% 0.29/0.53 ! [M2: num,X: option_num] :
% 0.29/0.53 ( ( ord_le6622620407824499402on_num @ ( some_num @ M2 ) @ X )
% 0.29/0.53 => ~ ! [M4: num] :
% 0.29/0.53 ( ( X
% 0.29/0.53 = ( some_num @ M4 ) )
% 0.29/0.53 => ~ ( ord_less_eq_num @ M2 @ M4 ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % le_some_optE
% 0.29/0.53 thf(fact_1211_le__some__optE,axiom,
% 0.29/0.53 ! [M2: nat,X: option_nat] :
% 0.29/0.53 ( ( ord_le5914376470875661696on_nat @ ( some_nat @ M2 ) @ X )
% 0.29/0.53 => ~ ! [M4: nat] :
% 0.29/0.53 ( ( X
% 0.29/0.53 = ( some_nat @ M4 ) )
% 0.29/0.53 => ~ ( ord_less_eq_nat @ M2 @ M4 ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % le_some_optE
% 0.29/0.53 thf(fact_1212_le__some__optE,axiom,
% 0.29/0.53 ! [M2: int,X: option_int] :
% 0.29/0.53 ( ( ord_le1736525451366464988on_int @ ( some_int @ M2 ) @ X )
% 0.29/0.53 => ~ ! [M4: int] :
% 0.29/0.53 ( ( X
% 0.29/0.53 = ( some_int @ M4 ) )
% 0.29/0.53 => ~ ( ord_less_eq_int @ M2 @ M4 ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % le_some_optE
% 0.29/0.53 thf(fact_1213_pred__subset__eq2,axiom,
% 0.29/0.53 ! [R4: set_Pr4329608150637261639at_nat,S2: set_Pr4329608150637261639at_nat] :
% 0.29/0.53 ( ( ord_le3935385432712749774_nat_o
% 0.29/0.53 @ ^ [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ Y3 ) @ R4 )
% 0.29/0.53 @ ^ [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ Y3 ) @ S2 ) )
% 0.29/0.53 = ( ord_le1268244103169919719at_nat @ R4 @ S2 ) ) ).
% 0.29/0.53
% 0.29/0.53 % pred_subset_eq2
% 0.29/0.53 thf(fact_1214_pred__subset__eq2,axiom,
% 0.29/0.53 ! [R4: set_Pr1261947904930325089at_nat,S2: set_Pr1261947904930325089at_nat] :
% 0.29/0.53 ( ( ord_le2646555220125990790_nat_o
% 0.29/0.53 @ ^ [X3: nat,Y3: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y3 ) @ R4 )
% 0.29/0.53 @ ^ [X3: nat,Y3: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y3 ) @ S2 ) )
% 0.29/0.53 = ( ord_le3146513528884898305at_nat @ R4 @ S2 ) ) ).
% 0.29/0.53
% 0.29/0.53 % pred_subset_eq2
% 0.29/0.53 thf(fact_1215_pred__subset__eq2,axiom,
% 0.29/0.53 ! [R4: set_Pr1281608226676607948nteger,S2: set_Pr1281608226676607948nteger] :
% 0.29/0.53 ( ( ord_le4340812435750786203eger_o
% 0.29/0.53 @ ^ [X3: produc6241069584506657477e_term > option6357759511663192854e_term,Y3: produc8923325533196201883nteger] : ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X3 @ Y3 ) @ R4 )
% 0.29/0.53 @ ^ [X3: produc6241069584506657477e_term > option6357759511663192854e_term,Y3: produc8923325533196201883nteger] : ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X3 @ Y3 ) @ S2 ) )
% 0.29/0.53 = ( ord_le653643898420964396nteger @ R4 @ S2 ) ) ).
% 0.29/0.53
% 0.29/0.53 % pred_subset_eq2
% 0.29/0.53 thf(fact_1216_pred__subset__eq2,axiom,
% 0.29/0.53 ! [R4: set_Pr3286484037609594932et_nat,S2: set_Pr3286484037609594932et_nat] :
% 0.29/0.54 ( ( ord_le8000401564054156549_nat_o
% 0.29/0.54 @ ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3658429121746597890et_nat] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X3 @ Y3 ) @ R4 )
% 0.29/0.54 @ ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3658429121746597890et_nat] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X3 @ Y3 ) @ S2 ) )
% 0.29/0.54 = ( ord_le5966269811547037844et_nat @ R4 @ S2 ) ) ).
% 0.29/0.54
% 0.29/0.54 % pred_subset_eq2
% 0.29/0.54 thf(fact_1217_pred__subset__eq2,axiom,
% 0.29/0.54 ! [R4: set_Pr8536935166611901872et_nat,S2: set_Pr8536935166611901872et_nat] :
% 0.29/0.54 ( ( ord_le6753239538765779593_nat_o
% 0.29/0.54 @ ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3925858234332021118et_nat] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X3 @ Y3 ) @ R4 )
% 0.29/0.54 @ ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3925858234332021118et_nat] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X3 @ Y3 ) @ S2 ) )
% 0.29/0.54 = ( ord_le4763372923235995152et_nat @ R4 @ S2 ) ) ).
% 0.29/0.54
% 0.29/0.54 % pred_subset_eq2
% 0.29/0.54 thf(fact_1218_pred__subset__eq2,axiom,
% 0.29/0.54 ! [R4: set_Pr9222295170931077689nt_int,S2: set_Pr9222295170931077689nt_int] :
% 0.29/0.54 ( ( ord_le5643404153117327598_int_o
% 0.29/0.54 @ ^ [X3: produc8551481072490612790e_term > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X3 @ Y3 ) @ R4 )
% 0.29/0.54 @ ^ [X3: produc8551481072490612790e_term > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X3 @ Y3 ) @ S2 ) )
% 0.29/0.54 = ( ord_le8725513860283290265nt_int @ R4 @ S2 ) ) ).
% 0.29/0.54
% 0.29/0.54 % pred_subset_eq2
% 0.29/0.54 thf(fact_1219_pred__subset__eq2,axiom,
% 0.29/0.54 ! [R4: set_Pr1872883991513573699nt_int,S2: set_Pr1872883991513573699nt_int] :
% 0.29/0.54 ( ( ord_le2124322318746777828_int_o
% 0.29/0.54 @ ^ [X3: int > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X3 @ Y3 ) @ R4 )
% 0.29/0.54 @ ^ [X3: int > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X3 @ Y3 ) @ S2 ) )
% 0.29/0.54 = ( ord_le135402666524580259nt_int @ R4 @ S2 ) ) ).
% 0.29/0.54
% 0.29/0.54 % pred_subset_eq2
% 0.29/0.54 thf(fact_1220_less__eq__option__def,axiom,
% 0.29/0.54 ( ord_le2843612097646854710et_nat
% 0.29/0.54 = ( ^ [X3: option_set_nat,Y3: option_set_nat] :
% 0.29/0.54 ( case_o4401850862724306899et_nat @ $true
% 0.29/0.54 @ ^ [Z4: set_nat] : ( case_o4401850862724306899et_nat @ $false @ ( ord_less_eq_set_nat @ Z4 ) @ Y3 )
% 0.29/0.54 @ X3 ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % less_eq_option_def
% 0.29/0.54 thf(fact_1221_less__eq__option__def,axiom,
% 0.29/0.54 ( ord_le2406147912482264968on_rat
% 0.29/0.54 = ( ^ [X3: option_rat,Y3: option_rat] :
% 0.29/0.54 ( case_option_o_rat @ $true
% 0.29/0.54 @ ^ [Z4: rat] : ( case_option_o_rat @ $false @ ( ord_less_eq_rat @ Z4 ) @ Y3 )
% 0.29/0.54 @ X3 ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % less_eq_option_def
% 0.29/0.54 thf(fact_1222_less__eq__option__def,axiom,
% 0.29/0.54 ( ord_le6622620407824499402on_num
% 0.29/0.54 = ( ^ [X3: option_num,Y3: option_num] :
% 0.29/0.54 ( case_option_o_num @ $true
% 0.29/0.54 @ ^ [Z4: num] : ( case_option_o_num @ $false @ ( ord_less_eq_num @ Z4 ) @ Y3 )
% 0.29/0.54 @ X3 ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % less_eq_option_def
% 0.29/0.54 thf(fact_1223_less__eq__option__def,axiom,
% 0.29/0.54 ( ord_le5914376470875661696on_nat
% 0.29/0.54 = ( ^ [X3: option_nat,Y3: option_nat] :
% 0.29/0.54 ( case_option_o_nat @ $true
% 0.29/0.54 @ ^ [Z4: nat] : ( case_option_o_nat @ $false @ ( ord_less_eq_nat @ Z4 ) @ Y3 )
% 0.29/0.54 @ X3 ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % less_eq_option_def
% 0.29/0.54 thf(fact_1224_less__eq__option__def,axiom,
% 0.29/0.54 ( ord_le1736525451366464988on_int
% 0.29/0.54 = ( ^ [X3: option_int,Y3: option_int] :
% 0.29/0.54 ( case_option_o_int @ $true
% 0.29/0.54 @ ^ [Z4: int] : ( case_option_o_int @ $false @ ( ord_less_eq_int @ Z4 ) @ Y3 )
% 0.29/0.54 @ X3 ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % less_eq_option_def
% 0.29/0.54 thf(fact_1225_zero__le,axiom,
% 0.29/0.54 ! [X: nat] : ( ord_less_eq_nat @ zero_zero_nat @ X ) ).
% 0.29/0.54
% 0.29/0.54 % zero_le
% 0.29/0.54 thf(fact_1226_add__mono__thms__linordered__semiring_I3_J,axiom,
% 0.29/0.54 ! [I: rat,J: rat,K: rat,L: rat] :
% 0.29/0.54 ( ( ( ord_less_eq_rat @ I @ J )
% 0.29/0.54 & ( K = L ) )
% 0.29/0.54 => ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_mono_thms_linordered_semiring(3)
% 0.29/0.54 thf(fact_1227_add__mono__thms__linordered__semiring_I3_J,axiom,
% 0.29/0.54 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.29/0.54 ( ( ( ord_less_eq_nat @ I @ J )
% 0.29/0.54 & ( K = L ) )
% 0.29/0.54 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_mono_thms_linordered_semiring(3)
% 0.29/0.54 thf(fact_1228_add__mono__thms__linordered__semiring_I3_J,axiom,
% 0.29/0.54 ! [I: int,J: int,K: int,L: int] :
% 0.29/0.54 ( ( ( ord_less_eq_int @ I @ J )
% 0.29/0.54 & ( K = L ) )
% 0.29/0.54 => ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_mono_thms_linordered_semiring(3)
% 0.29/0.54 thf(fact_1229_add__mono__thms__linordered__semiring_I2_J,axiom,
% 0.29/0.54 ! [I: rat,J: rat,K: rat,L: rat] :
% 0.29/0.54 ( ( ( I = J )
% 0.29/0.54 & ( ord_less_eq_rat @ K @ L ) )
% 0.29/0.54 => ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_mono_thms_linordered_semiring(2)
% 0.29/0.54 thf(fact_1230_add__mono__thms__linordered__semiring_I2_J,axiom,
% 0.29/0.54 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.29/0.54 ( ( ( I = J )
% 0.29/0.54 & ( ord_less_eq_nat @ K @ L ) )
% 0.29/0.54 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_mono_thms_linordered_semiring(2)
% 0.29/0.54 thf(fact_1231_add__mono__thms__linordered__semiring_I2_J,axiom,
% 0.29/0.54 ! [I: int,J: int,K: int,L: int] :
% 0.29/0.54 ( ( ( I = J )
% 0.29/0.54 & ( ord_less_eq_int @ K @ L ) )
% 0.29/0.54 => ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_mono_thms_linordered_semiring(2)
% 0.29/0.54 thf(fact_1232_add__mono__thms__linordered__semiring_I1_J,axiom,
% 0.29/0.54 ! [I: rat,J: rat,K: rat,L: rat] :
% 0.29/0.54 ( ( ( ord_less_eq_rat @ I @ J )
% 0.29/0.54 & ( ord_less_eq_rat @ K @ L ) )
% 0.29/0.54 => ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_mono_thms_linordered_semiring(1)
% 0.29/0.54 thf(fact_1233_add__mono__thms__linordered__semiring_I1_J,axiom,
% 0.29/0.54 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.29/0.54 ( ( ( ord_less_eq_nat @ I @ J )
% 0.29/0.54 & ( ord_less_eq_nat @ K @ L ) )
% 0.29/0.54 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_mono_thms_linordered_semiring(1)
% 0.29/0.54 thf(fact_1234_add__mono__thms__linordered__semiring_I1_J,axiom,
% 0.29/0.54 ! [I: int,J: int,K: int,L: int] :
% 0.29/0.54 ( ( ( ord_less_eq_int @ I @ J )
% 0.29/0.54 & ( ord_less_eq_int @ K @ L ) )
% 0.29/0.54 => ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_mono_thms_linordered_semiring(1)
% 0.29/0.54 thf(fact_1235_add__mono,axiom,
% 0.29/0.54 ! [A: rat,B: rat,C: rat,D2: rat] :
% 0.29/0.54 ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.54 => ( ( ord_less_eq_rat @ C @ D2 )
% 0.29/0.54 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D2 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_mono
% 0.29/0.54 thf(fact_1236_add__mono,axiom,
% 0.29/0.54 ! [A: nat,B: nat,C: nat,D2: nat] :
% 0.29/0.54 ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.54 => ( ( ord_less_eq_nat @ C @ D2 )
% 0.29/0.54 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D2 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_mono
% 0.29/0.54 thf(fact_1237_add__mono,axiom,
% 0.29/0.54 ! [A: int,B: int,C: int,D2: int] :
% 0.29/0.54 ( ( ord_less_eq_int @ A @ B )
% 0.29/0.54 => ( ( ord_less_eq_int @ C @ D2 )
% 0.29/0.54 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D2 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_mono
% 0.29/0.54 thf(fact_1238_add__left__mono,axiom,
% 0.29/0.54 ! [A: rat,B: rat,C: rat] :
% 0.29/0.54 ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.54 => ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_left_mono
% 0.29/0.54 thf(fact_1239_add__left__mono,axiom,
% 0.29/0.54 ! [A: nat,B: nat,C: nat] :
% 0.29/0.54 ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.54 => ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_left_mono
% 0.29/0.54 thf(fact_1240_add__left__mono,axiom,
% 0.29/0.54 ! [A: int,B: int,C: int] :
% 0.29/0.54 ( ( ord_less_eq_int @ A @ B )
% 0.29/0.54 => ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_left_mono
% 0.29/0.54 thf(fact_1241_less__eqE,axiom,
% 0.29/0.54 ! [A: nat,B: nat] :
% 0.29/0.54 ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.54 => ~ ! [C3: nat] :
% 0.29/0.54 ( B
% 0.29/0.54 != ( plus_plus_nat @ A @ C3 ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % less_eqE
% 0.29/0.54 thf(fact_1242_add__right__mono,axiom,
% 0.29/0.54 ! [A: rat,B: rat,C: rat] :
% 0.29/0.54 ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.54 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_right_mono
% 0.29/0.54 thf(fact_1243_add__right__mono,axiom,
% 0.29/0.54 ! [A: nat,B: nat,C: nat] :
% 0.29/0.54 ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.54 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_right_mono
% 0.29/0.54 thf(fact_1244_add__right__mono,axiom,
% 0.29/0.54 ! [A: int,B: int,C: int] :
% 0.29/0.54 ( ( ord_less_eq_int @ A @ B )
% 0.29/0.54 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_right_mono
% 0.29/0.54 thf(fact_1245_le__iff__add,axiom,
% 0.29/0.54 ( ord_less_eq_nat
% 0.29/0.54 = ( ^ [A5: nat,B4: nat] :
% 0.29/0.54 ? [C2: nat] :
% 0.29/0.54 ( B4
% 0.29/0.54 = ( plus_plus_nat @ A5 @ C2 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % le_iff_add
% 0.29/0.54 thf(fact_1246_add__le__imp__le__left,axiom,
% 0.29/0.54 ! [C: rat,A: rat,B: rat] :
% 0.29/0.54 ( ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 0.29/0.54 => ( ord_less_eq_rat @ A @ B ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_le_imp_le_left
% 0.29/0.54 thf(fact_1247_add__le__imp__le__left,axiom,
% 0.29/0.54 ! [C: nat,A: nat,B: nat] :
% 0.29/0.54 ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 0.29/0.54 => ( ord_less_eq_nat @ A @ B ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_le_imp_le_left
% 0.29/0.54 thf(fact_1248_add__le__imp__le__left,axiom,
% 0.29/0.54 ! [C: int,A: int,B: int] :
% 0.29/0.54 ( ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 0.29/0.54 => ( ord_less_eq_int @ A @ B ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_le_imp_le_left
% 0.29/0.54 thf(fact_1249_add__le__imp__le__right,axiom,
% 0.29/0.54 ! [A: rat,C: rat,B: rat] :
% 0.29/0.54 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 0.29/0.54 => ( ord_less_eq_rat @ A @ B ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_le_imp_le_right
% 0.29/0.54 thf(fact_1250_add__le__imp__le__right,axiom,
% 0.29/0.54 ! [A: nat,C: nat,B: nat] :
% 0.29/0.54 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 0.29/0.54 => ( ord_less_eq_nat @ A @ B ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_le_imp_le_right
% 0.29/0.54 thf(fact_1251_add__le__imp__le__right,axiom,
% 0.29/0.54 ! [A: int,C: int,B: int] :
% 0.29/0.54 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 0.29/0.54 => ( ord_less_eq_int @ A @ B ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_le_imp_le_right
% 0.29/0.54 thf(fact_1252_accp__subset__induct,axiom,
% 0.29/0.54 ! [D3: product_prod_nat_nat > $o,R4: product_prod_nat_nat > product_prod_nat_nat > $o,X: product_prod_nat_nat,P: product_prod_nat_nat > $o] :
% 0.29/0.54 ( ( ord_le704812498762024988_nat_o @ D3 @ ( accp_P4275260045618599050at_nat @ R4 ) )
% 0.29/0.54 => ( ! [X4: product_prod_nat_nat,Z3: product_prod_nat_nat] :
% 0.29/0.54 ( ( D3 @ X4 )
% 0.29/0.54 => ( ( R4 @ Z3 @ X4 )
% 0.29/0.54 => ( D3 @ Z3 ) ) )
% 0.29/0.54 => ( ( D3 @ X )
% 0.29/0.54 => ( ! [X4: product_prod_nat_nat] :
% 0.29/0.54 ( ( D3 @ X4 )
% 0.29/0.54 => ( ! [Z5: product_prod_nat_nat] :
% 0.29/0.54 ( ( R4 @ Z5 @ X4 )
% 0.29/0.54 => ( P @ Z5 ) )
% 0.29/0.54 => ( P @ X4 ) ) )
% 0.29/0.54 => ( P @ X ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % accp_subset_induct
% 0.29/0.54 thf(fact_1253_accp__subset__induct,axiom,
% 0.29/0.54 ! [D3: product_prod_int_int > $o,R4: product_prod_int_int > product_prod_int_int > $o,X: product_prod_int_int,P: product_prod_int_int > $o] :
% 0.29/0.54 ( ( ord_le8369615600986905444_int_o @ D3 @ ( accp_P1096762738010456898nt_int @ R4 ) )
% 0.29/0.54 => ( ! [X4: product_prod_int_int,Z3: product_prod_int_int] :
% 0.29/0.54 ( ( D3 @ X4 )
% 0.29/0.54 => ( ( R4 @ Z3 @ X4 )
% 0.29/0.54 => ( D3 @ Z3 ) ) )
% 0.29/0.54 => ( ( D3 @ X )
% 0.29/0.54 => ( ! [X4: product_prod_int_int] :
% 0.29/0.54 ( ( D3 @ X4 )
% 0.29/0.54 => ( ! [Z5: product_prod_int_int] :
% 0.29/0.54 ( ( R4 @ Z5 @ X4 )
% 0.29/0.54 => ( P @ Z5 ) )
% 0.29/0.54 => ( P @ X4 ) ) )
% 0.29/0.54 => ( P @ X ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % accp_subset_induct
% 0.29/0.54 thf(fact_1254_accp__subset__induct,axiom,
% 0.29/0.54 ! [D3: produc2732055786443039994et_nat > $o,R4: produc2732055786443039994et_nat > produc2732055786443039994et_nat > $o,X: produc2732055786443039994et_nat,P: produc2732055786443039994et_nat > $o] :
% 0.29/0.54 ( ( ord_le1658592502415435381_nat_o @ D3 @ ( accp_P1862375125659990705et_nat @ R4 ) )
% 0.29/0.54 => ( ! [X4: produc2732055786443039994et_nat,Z3: produc2732055786443039994et_nat] :
% 0.29/0.54 ( ( D3 @ X4 )
% 0.29/0.54 => ( ( R4 @ Z3 @ X4 )
% 0.29/0.54 => ( D3 @ Z3 ) ) )
% 0.29/0.54 => ( ( D3 @ X )
% 0.29/0.54 => ( ! [X4: produc2732055786443039994et_nat] :
% 0.29/0.54 ( ( D3 @ X4 )
% 0.29/0.54 => ( ! [Z5: produc2732055786443039994et_nat] :
% 0.29/0.54 ( ( R4 @ Z5 @ X4 )
% 0.29/0.54 => ( P @ Z5 ) )
% 0.29/0.54 => ( P @ X4 ) ) )
% 0.29/0.54 => ( P @ X ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % accp_subset_induct
% 0.29/0.54 thf(fact_1255_accp__subset__induct,axiom,
% 0.29/0.54 ! [D3: list_nat > $o,R4: list_nat > list_nat > $o,X: list_nat,P: list_nat > $o] :
% 0.29/0.54 ( ( ord_le1520216061033275535_nat_o @ D3 @ ( accp_list_nat @ R4 ) )
% 0.29/0.54 => ( ! [X4: list_nat,Z3: list_nat] :
% 0.29/0.54 ( ( D3 @ X4 )
% 0.29/0.54 => ( ( R4 @ Z3 @ X4 )
% 0.29/0.54 => ( D3 @ Z3 ) ) )
% 0.29/0.54 => ( ( D3 @ X )
% 0.29/0.54 => ( ! [X4: list_nat] :
% 0.29/0.54 ( ( D3 @ X4 )
% 0.29/0.54 => ( ! [Z5: list_nat] :
% 0.29/0.54 ( ( R4 @ Z5 @ X4 )
% 0.29/0.54 => ( P @ Z5 ) )
% 0.29/0.54 => ( P @ X4 ) ) )
% 0.29/0.54 => ( P @ X ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % accp_subset_induct
% 0.29/0.54 thf(fact_1256_accp__subset__induct,axiom,
% 0.29/0.54 ! [D3: nat > $o,R4: nat > nat > $o,X: nat,P: nat > $o] :
% 0.29/0.54 ( ( ord_less_eq_nat_o @ D3 @ ( accp_nat @ R4 ) )
% 0.29/0.54 => ( ! [X4: nat,Z3: nat] :
% 0.29/0.54 ( ( D3 @ X4 )
% 0.29/0.54 => ( ( R4 @ Z3 @ X4 )
% 0.29/0.54 => ( D3 @ Z3 ) ) )
% 0.29/0.54 => ( ( D3 @ X )
% 0.29/0.54 => ( ! [X4: nat] :
% 0.29/0.54 ( ( D3 @ X4 )
% 0.29/0.54 => ( ! [Z5: nat] :
% 0.29/0.54 ( ( R4 @ Z5 @ X4 )
% 0.29/0.54 => ( P @ Z5 ) )
% 0.29/0.54 => ( P @ X4 ) ) )
% 0.29/0.54 => ( P @ X ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % accp_subset_induct
% 0.29/0.54 thf(fact_1257_le__numeral__extra_I4_J,axiom,
% 0.29/0.54 ord_le3102999989581377725nteger @ one_one_Code_integer @ one_one_Code_integer ).
% 0.29/0.54
% 0.29/0.54 % le_numeral_extra(4)
% 0.29/0.54 thf(fact_1258_le__numeral__extra_I4_J,axiom,
% 0.29/0.54 ord_less_eq_rat @ one_one_rat @ one_one_rat ).
% 0.29/0.54
% 0.29/0.54 % le_numeral_extra(4)
% 0.29/0.54 thf(fact_1259_le__numeral__extra_I4_J,axiom,
% 0.29/0.54 ord_less_eq_nat @ one_one_nat @ one_one_nat ).
% 0.29/0.54
% 0.29/0.54 % le_numeral_extra(4)
% 0.29/0.54 thf(fact_1260_le__numeral__extra_I4_J,axiom,
% 0.29/0.54 ord_less_eq_int @ one_one_int @ one_one_int ).
% 0.29/0.54
% 0.29/0.54 % le_numeral_extra(4)
% 0.29/0.54 thf(fact_1261_subrelI,axiom,
% 0.29/0.54 ! [R2: set_Pr4329608150637261639at_nat,S: set_Pr4329608150637261639at_nat] :
% 0.29/0.54 ( ! [X4: set_Pr1261947904930325089at_nat,Y5: set_Pr1261947904930325089at_nat] :
% 0.29/0.54 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X4 @ Y5 ) @ R2 )
% 0.29/0.54 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X4 @ Y5 ) @ S ) )
% 0.29/0.54 => ( ord_le1268244103169919719at_nat @ R2 @ S ) ) ).
% 0.29/0.54
% 0.29/0.54 % subrelI
% 0.29/0.54 thf(fact_1262_subrelI,axiom,
% 0.29/0.54 ! [R2: set_Pr1261947904930325089at_nat,S: set_Pr1261947904930325089at_nat] :
% 0.29/0.54 ( ! [X4: nat,Y5: nat] :
% 0.29/0.54 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Y5 ) @ R2 )
% 0.29/0.54 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Y5 ) @ S ) )
% 0.29/0.54 => ( ord_le3146513528884898305at_nat @ R2 @ S ) ) ).
% 0.29/0.54
% 0.29/0.54 % subrelI
% 0.29/0.54 thf(fact_1263_subrelI,axiom,
% 0.29/0.54 ! [R2: set_Pr1281608226676607948nteger,S: set_Pr1281608226676607948nteger] :
% 0.29/0.54 ( ! [X4: produc6241069584506657477e_term > option6357759511663192854e_term,Y5: produc8923325533196201883nteger] :
% 0.29/0.54 ( ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X4 @ Y5 ) @ R2 )
% 0.29/0.54 => ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X4 @ Y5 ) @ S ) )
% 0.29/0.54 => ( ord_le653643898420964396nteger @ R2 @ S ) ) ).
% 0.29/0.54
% 0.29/0.54 % subrelI
% 0.29/0.54 thf(fact_1264_subrelI,axiom,
% 0.29/0.54 ! [R2: set_Pr3286484037609594932et_nat,S: set_Pr3286484037609594932et_nat] :
% 0.29/0.54 ( ! [X4: produc3658429121746597890et_nat > $o,Y5: produc3658429121746597890et_nat] :
% 0.29/0.54 ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X4 @ Y5 ) @ R2 )
% 0.29/0.54 => ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X4 @ Y5 ) @ S ) )
% 0.29/0.54 => ( ord_le5966269811547037844et_nat @ R2 @ S ) ) ).
% 0.29/0.54
% 0.29/0.54 % subrelI
% 0.29/0.54 thf(fact_1265_subrelI,axiom,
% 0.29/0.54 ! [R2: set_Pr8536935166611901872et_nat,S: set_Pr8536935166611901872et_nat] :
% 0.29/0.54 ( ! [X4: produc3658429121746597890et_nat > $o,Y5: produc3925858234332021118et_nat] :
% 0.29/0.54 ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X4 @ Y5 ) @ R2 )
% 0.29/0.54 => ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X4 @ Y5 ) @ S ) )
% 0.29/0.54 => ( ord_le4763372923235995152et_nat @ R2 @ S ) ) ).
% 0.29/0.54
% 0.29/0.54 % subrelI
% 0.29/0.54 thf(fact_1266_subrelI,axiom,
% 0.29/0.54 ! [R2: set_Pr9222295170931077689nt_int,S: set_Pr9222295170931077689nt_int] :
% 0.29/0.54 ( ! [X4: produc8551481072490612790e_term > option6357759511663192854e_term,Y5: product_prod_int_int] :
% 0.29/0.54 ( ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X4 @ Y5 ) @ R2 )
% 0.29/0.54 => ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X4 @ Y5 ) @ S ) )
% 0.29/0.54 => ( ord_le8725513860283290265nt_int @ R2 @ S ) ) ).
% 0.29/0.54
% 0.29/0.54 % subrelI
% 0.29/0.54 thf(fact_1267_subrelI,axiom,
% 0.29/0.54 ! [R2: set_Pr1872883991513573699nt_int,S: set_Pr1872883991513573699nt_int] :
% 0.29/0.54 ( ! [X4: int > option6357759511663192854e_term,Y5: product_prod_int_int] :
% 0.29/0.54 ( ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X4 @ Y5 ) @ R2 )
% 0.29/0.54 => ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X4 @ Y5 ) @ S ) )
% 0.29/0.54 => ( ord_le135402666524580259nt_int @ R2 @ S ) ) ).
% 0.29/0.54
% 0.29/0.54 % subrelI
% 0.29/0.54 thf(fact_1268_le__minus__iff,axiom,
% 0.29/0.54 ! [A: code_integer,B: code_integer] :
% 0.29/0.54 ( ( ord_le3102999989581377725nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 0.29/0.54 = ( ord_le3102999989581377725nteger @ B @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % le_minus_iff
% 0.29/0.54 thf(fact_1269_le__minus__iff,axiom,
% 0.29/0.54 ! [A: rat,B: rat] :
% 0.29/0.54 ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ B ) )
% 0.29/0.54 = ( ord_less_eq_rat @ B @ ( uminus_uminus_rat @ A ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % le_minus_iff
% 0.29/0.54 thf(fact_1270_le__minus__iff,axiom,
% 0.29/0.54 ! [A: int,B: int] :
% 0.29/0.54 ( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ B ) )
% 0.29/0.54 = ( ord_less_eq_int @ B @ ( uminus_uminus_int @ A ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % le_minus_iff
% 0.29/0.54 thf(fact_1271_minus__le__iff,axiom,
% 0.29/0.54 ! [A: code_integer,B: code_integer] :
% 0.29/0.54 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 0.29/0.54 = ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ A ) ) ).
% 0.29/0.54
% 0.29/0.54 % minus_le_iff
% 0.29/0.54 thf(fact_1272_minus__le__iff,axiom,
% 0.29/0.54 ! [A: rat,B: rat] :
% 0.29/0.54 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B )
% 0.29/0.54 = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ A ) ) ).
% 0.29/0.54
% 0.29/0.54 % minus_le_iff
% 0.29/0.54 thf(fact_1273_minus__le__iff,axiom,
% 0.29/0.54 ! [A: int,B: int] :
% 0.29/0.54 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B )
% 0.29/0.54 = ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ A ) ) ).
% 0.29/0.54
% 0.29/0.54 % minus_le_iff
% 0.29/0.54 thf(fact_1274_le__imp__neg__le,axiom,
% 0.29/0.54 ! [A: code_integer,B: code_integer] :
% 0.29/0.54 ( ( ord_le3102999989581377725nteger @ A @ B )
% 0.29/0.54 => ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % le_imp_neg_le
% 0.29/0.54 thf(fact_1275_le__imp__neg__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 @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % le_imp_neg_le
% 0.29/0.54 thf(fact_1276_le__imp__neg__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 @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % le_imp_neg_le
% 0.29/0.54 thf(fact_1277_exists__leI,axiom,
% 0.29/0.54 ! [N2: nat,P: nat > $o] :
% 0.29/0.54 ( ( ! [N7: nat] :
% 0.29/0.54 ( ( ord_less_nat @ N7 @ N2 )
% 0.29/0.54 => ~ ( P @ N7 ) )
% 0.29/0.54 => ( P @ N2 ) )
% 0.29/0.54 => ? [N3: nat] :
% 0.29/0.54 ( ( ord_less_eq_nat @ N3 @ N2 )
% 0.29/0.54 & ( P @ N3 ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % exists_leI
% 0.29/0.54 thf(fact_1278_nat__le__iff__add,axiom,
% 0.29/0.54 ( ord_less_eq_nat
% 0.29/0.54 = ( ^ [M: nat,N4: nat] :
% 0.29/0.54 ? [K4: nat] :
% 0.29/0.54 ( N4
% 0.29/0.54 = ( plus_plus_nat @ M @ K4 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % nat_le_iff_add
% 0.29/0.54 thf(fact_1279_trans__le__add2,axiom,
% 0.29/0.54 ! [I: nat,J: nat,M2: nat] :
% 0.29/0.54 ( ( ord_less_eq_nat @ I @ J )
% 0.29/0.54 => ( ord_less_eq_nat @ I @ ( plus_plus_nat @ M2 @ J ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % trans_le_add2
% 0.29/0.54 thf(fact_1280_trans__le__add1,axiom,
% 0.29/0.54 ! [I: nat,J: nat,M2: nat] :
% 0.29/0.54 ( ( ord_less_eq_nat @ I @ J )
% 0.29/0.54 => ( ord_less_eq_nat @ I @ ( plus_plus_nat @ J @ M2 ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % trans_le_add1
% 0.29/0.54 thf(fact_1281_add__le__mono1,axiom,
% 0.29/0.54 ! [I: nat,J: nat,K: nat] :
% 0.29/0.54 ( ( ord_less_eq_nat @ I @ J )
% 0.29/0.54 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_le_mono1
% 0.29/0.54 thf(fact_1282_add__le__mono,axiom,
% 0.29/0.54 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.29/0.54 ( ( ord_less_eq_nat @ I @ J )
% 0.29/0.54 => ( ( ord_less_eq_nat @ K @ L )
% 0.29/0.54 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_le_mono
% 0.29/0.54 thf(fact_1283_le__Suc__ex,axiom,
% 0.29/0.54 ! [K: nat,L: nat] :
% 0.29/0.54 ( ( ord_less_eq_nat @ K @ L )
% 0.29/0.54 => ? [N: nat] :
% 0.29/0.54 ( L
% 0.29/0.54 = ( plus_plus_nat @ K @ N ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % le_Suc_ex
% 0.29/0.54 thf(fact_1284_add__leD2,axiom,
% 0.29/0.54 ! [M2: nat,K: nat,N2: nat] :
% 0.29/0.54 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M2 @ K ) @ N2 )
% 0.29/0.54 => ( ord_less_eq_nat @ K @ N2 ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_leD2
% 0.29/0.54 thf(fact_1285_add__leD1,axiom,
% 0.29/0.54 ! [M2: nat,K: nat,N2: nat] :
% 0.29/0.54 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M2 @ K ) @ N2 )
% 0.29/0.54 => ( ord_less_eq_nat @ M2 @ N2 ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_leD1
% 0.29/0.54 thf(fact_1286_le__add2,axiom,
% 0.29/0.54 ! [N2: nat,M2: nat] : ( ord_less_eq_nat @ N2 @ ( plus_plus_nat @ M2 @ N2 ) ) ).
% 0.29/0.54
% 0.29/0.54 % le_add2
% 0.29/0.54 thf(fact_1287_le__add1,axiom,
% 0.29/0.54 ! [N2: nat,M2: nat] : ( ord_less_eq_nat @ N2 @ ( plus_plus_nat @ N2 @ M2 ) ) ).
% 0.29/0.54
% 0.29/0.54 % le_add1
% 0.29/0.54 thf(fact_1288_add__leE,axiom,
% 0.29/0.54 ! [M2: nat,K: nat,N2: nat] :
% 0.29/0.54 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M2 @ K ) @ N2 )
% 0.29/0.54 => ~ ( ( ord_less_eq_nat @ M2 @ N2 )
% 0.29/0.54 => ~ ( ord_less_eq_nat @ K @ N2 ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_leE
% 0.29/0.54 thf(fact_1289_abs__le__D1,axiom,
% 0.29/0.54 ! [A: code_integer,B: code_integer] :
% 0.29/0.54 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 0.29/0.54 => ( ord_le3102999989581377725nteger @ A @ B ) ) ).
% 0.29/0.54
% 0.29/0.54 % abs_le_D1
% 0.29/0.54 thf(fact_1290_abs__le__D1,axiom,
% 0.29/0.54 ! [A: rat,B: rat] :
% 0.29/0.54 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 0.29/0.54 => ( ord_less_eq_rat @ A @ B ) ) ).
% 0.29/0.54
% 0.29/0.54 % abs_le_D1
% 0.29/0.54 thf(fact_1291_abs__le__D1,axiom,
% 0.29/0.54 ! [A: int,B: int] :
% 0.29/0.54 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 0.29/0.54 => ( ord_less_eq_int @ A @ B ) ) ).
% 0.29/0.54
% 0.29/0.54 % abs_le_D1
% 0.29/0.54 thf(fact_1292_abs__ge__self,axiom,
% 0.29/0.54 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ A @ ( abs_abs_Code_integer @ A ) ) ).
% 0.29/0.54
% 0.29/0.54 % abs_ge_self
% 0.29/0.54 thf(fact_1293_abs__ge__self,axiom,
% 0.29/0.54 ! [A: rat] : ( ord_less_eq_rat @ A @ ( abs_abs_rat @ A ) ) ).
% 0.29/0.54
% 0.29/0.54 % abs_ge_self
% 0.29/0.54 thf(fact_1294_abs__ge__self,axiom,
% 0.29/0.54 ! [A: int] : ( ord_less_eq_int @ A @ ( abs_abs_int @ A ) ) ).
% 0.29/0.54
% 0.29/0.54 % abs_ge_self
% 0.29/0.54 thf(fact_1295_less__eq__option__None,axiom,
% 0.29/0.54 ! [X: option_num] : ( ord_le6622620407824499402on_num @ none_num @ X ) ).
% 0.29/0.54
% 0.29/0.54 % less_eq_option_None
% 0.29/0.54 thf(fact_1296_less__eq__option__None__is__None,axiom,
% 0.29/0.54 ! [X: option_num] :
% 0.29/0.54 ( ( ord_le6622620407824499402on_num @ X @ none_num )
% 0.29/0.54 => ( X = none_num ) ) ).
% 0.29/0.54
% 0.29/0.54 % less_eq_option_None_is_None
% 0.29/0.54 thf(fact_1297_bind__eq__Some__conv,axiom,
% 0.29/0.54 ! [F: option_num,G: num > option_num,X: num] :
% 0.29/0.54 ( ( ( bind_num_num @ F @ G )
% 0.29/0.54 = ( some_num @ X ) )
% 0.29/0.54 = ( ? [Y3: num] :
% 0.29/0.54 ( ( F
% 0.29/0.54 = ( some_num @ Y3 ) )
% 0.29/0.54 & ( ( G @ Y3 )
% 0.29/0.54 = ( some_num @ X ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % bind_eq_Some_conv
% 0.29/0.54 thf(fact_1298_bind__eq__Some__conv,axiom,
% 0.29/0.54 ! [F: option8956607266484857688it_nat,G: produc8664842809031399944it_nat > option_num,X: num] :
% 0.29/0.54 ( ( ( bind_P4387644102537648098at_num @ F @ G )
% 0.29/0.54 = ( some_num @ X ) )
% 0.29/0.54 = ( ? [Y3: produc8664842809031399944it_nat] :
% 0.29/0.54 ( ( F
% 0.29/0.54 = ( some_P1914260805536162275it_nat @ Y3 ) )
% 0.29/0.54 & ( ( G @ Y3 )
% 0.29/0.54 = ( some_num @ X ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % bind_eq_Some_conv
% 0.29/0.54 thf(fact_1299_bind__eq__Some__conv,axiom,
% 0.29/0.54 ! [F: option_num,G: num > option8956607266484857688it_nat,X: produc8664842809031399944it_nat] :
% 0.29/0.54 ( ( ( bind_n550516262659884002it_nat @ F @ G )
% 0.29/0.54 = ( some_P1914260805536162275it_nat @ X ) )
% 0.29/0.54 = ( ? [Y3: num] :
% 0.29/0.54 ( ( F
% 0.29/0.54 = ( some_num @ Y3 ) )
% 0.29/0.54 & ( ( G @ Y3 )
% 0.29/0.54 = ( some_P1914260805536162275it_nat @ X ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % bind_eq_Some_conv
% 0.29/0.54 thf(fact_1300_bind__eq__Some__conv,axiom,
% 0.29/0.54 ! [F: option8956607266484857688it_nat,G: produc8664842809031399944it_nat > option8956607266484857688it_nat,X: produc8664842809031399944it_nat] :
% 0.29/0.54 ( ( ( bind_P7351952464966851536it_nat @ F @ G )
% 0.29/0.54 = ( some_P1914260805536162275it_nat @ X ) )
% 0.29/0.54 = ( ? [Y3: produc8664842809031399944it_nat] :
% 0.29/0.54 ( ( F
% 0.29/0.54 = ( some_P1914260805536162275it_nat @ Y3 ) )
% 0.29/0.54 & ( ( G @ Y3 )
% 0.29/0.54 = ( some_P1914260805536162275it_nat @ X ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % bind_eq_Some_conv
% 0.29/0.54 thf(fact_1301_bind_Obind__lzero,axiom,
% 0.29/0.54 ! [F: produc6714399278180371524it_nat > option3216581401566546698it_nat] :
% 0.29/0.54 ( ( bind_P1787608729393679550it_nat @ none_P2587165478634041381it_nat @ F )
% 0.29/0.54 = none_P2587165478634041381it_nat ) ).
% 0.29/0.54
% 0.29/0.54 % bind.bind_lzero
% 0.29/0.54 thf(fact_1302_bind_Obind__lzero,axiom,
% 0.29/0.54 ! [F: produc6714399278180371524it_nat > option_num] :
% 0.29/0.54 ( ( bind_P7816469540982926368at_num @ none_P2587165478634041381it_nat @ F )
% 0.29/0.54 = none_num ) ).
% 0.29/0.54
% 0.29/0.54 % bind.bind_lzero
% 0.29/0.54 thf(fact_1303_bind_Obind__lzero,axiom,
% 0.29/0.54 ! [F: produc6714399278180371524it_nat > option8956607266484857688it_nat] :
% 0.29/0.54 ( ( bind_P3087804342168909838it_nat @ none_P2587165478634041381it_nat @ F )
% 0.29/0.54 = none_P9117596204409417319it_nat ) ).
% 0.29/0.54
% 0.29/0.54 % bind.bind_lzero
% 0.29/0.54 thf(fact_1304_bind_Obind__lzero,axiom,
% 0.29/0.54 ! [F: num > option3216581401566546698it_nat] :
% 0.29/0.54 ( ( bind_n6186876254402743274it_nat @ none_num @ F )
% 0.29/0.54 = none_P2587165478634041381it_nat ) ).
% 0.29/0.54
% 0.29/0.54 % bind.bind_lzero
% 0.29/0.54 thf(fact_1305_bind_Obind__lzero,axiom,
% 0.29/0.54 ! [F: num > option_num] :
% 0.29/0.54 ( ( bind_num_num @ none_num @ F )
% 0.29/0.54 = none_num ) ).
% 0.29/0.54
% 0.29/0.54 % bind.bind_lzero
% 0.29/0.54 thf(fact_1306_bind_Obind__lzero,axiom,
% 0.29/0.54 ! [F: num > option8956607266484857688it_nat] :
% 0.29/0.54 ( ( bind_n550516262659884002it_nat @ none_num @ F )
% 0.29/0.54 = none_P9117596204409417319it_nat ) ).
% 0.29/0.54
% 0.29/0.54 % bind.bind_lzero
% 0.29/0.54 thf(fact_1307_bind_Obind__lzero,axiom,
% 0.29/0.54 ! [F: produc8664842809031399944it_nat > option3216581401566546698it_nat] :
% 0.29/0.54 ( ( bind_P1106314856888375420it_nat @ none_P9117596204409417319it_nat @ F )
% 0.29/0.54 = none_P2587165478634041381it_nat ) ).
% 0.29/0.54
% 0.29/0.54 % bind.bind_lzero
% 0.29/0.54 thf(fact_1308_bind_Obind__lzero,axiom,
% 0.29/0.54 ! [F: produc8664842809031399944it_nat > option_num] :
% 0.29/0.54 ( ( bind_P4387644102537648098at_num @ none_P9117596204409417319it_nat @ F )
% 0.29/0.54 = none_num ) ).
% 0.29/0.54
% 0.29/0.54 % bind.bind_lzero
% 0.29/0.54 thf(fact_1309_bind_Obind__lzero,axiom,
% 0.29/0.54 ! [F: produc8664842809031399944it_nat > option8956607266484857688it_nat] :
% 0.29/0.54 ( ( bind_P7351952464966851536it_nat @ none_P9117596204409417319it_nat @ F )
% 0.29/0.54 = none_P9117596204409417319it_nat ) ).
% 0.29/0.54
% 0.29/0.54 % bind.bind_lzero
% 0.29/0.54 thf(fact_1310_add__decreasing,axiom,
% 0.29/0.54 ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.29/0.54 ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 0.29/0.54 => ( ( ord_le3102999989581377725nteger @ C @ B )
% 0.29/0.54 => ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ A @ C ) @ B ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_decreasing
% 0.29/0.54 thf(fact_1311_add__decreasing,axiom,
% 0.29/0.54 ! [A: rat,C: rat,B: rat] :
% 0.29/0.54 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.29/0.54 => ( ( ord_less_eq_rat @ C @ B )
% 0.29/0.54 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_decreasing
% 0.29/0.54 thf(fact_1312_add__decreasing,axiom,
% 0.29/0.54 ! [A: nat,C: nat,B: nat] :
% 0.29/0.54 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 0.29/0.54 => ( ( ord_less_eq_nat @ C @ B )
% 0.29/0.54 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ B ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_decreasing
% 0.29/0.54 thf(fact_1313_add__decreasing,axiom,
% 0.29/0.54 ! [A: int,C: int,B: int] :
% 0.29/0.54 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.29/0.54 => ( ( ord_less_eq_int @ C @ B )
% 0.29/0.54 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ B ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_decreasing
% 0.29/0.54 thf(fact_1314_add__increasing,axiom,
% 0.29/0.54 ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.29/0.54 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.29/0.54 => ( ( ord_le3102999989581377725nteger @ B @ C )
% 0.29/0.54 => ( ord_le3102999989581377725nteger @ B @ ( plus_p5714425477246183910nteger @ A @ C ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_increasing
% 0.29/0.54 thf(fact_1315_add__increasing,axiom,
% 0.29/0.54 ! [A: rat,B: rat,C: rat] :
% 0.29/0.54 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.29/0.54 => ( ( ord_less_eq_rat @ B @ C )
% 0.29/0.54 => ( ord_less_eq_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_increasing
% 0.29/0.54 thf(fact_1316_add__increasing,axiom,
% 0.29/0.54 ! [A: nat,B: nat,C: nat] :
% 0.29/0.54 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.29/0.54 => ( ( ord_less_eq_nat @ B @ C )
% 0.29/0.54 => ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_increasing
% 0.29/0.54 thf(fact_1317_add__increasing,axiom,
% 0.29/0.54 ! [A: int,B: int,C: int] :
% 0.29/0.54 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.29/0.54 => ( ( ord_less_eq_int @ B @ C )
% 0.29/0.54 => ( ord_less_eq_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_increasing
% 0.29/0.54 thf(fact_1318_add__decreasing2,axiom,
% 0.29/0.54 ! [C: code_integer,A: code_integer,B: code_integer] :
% 0.29/0.54 ( ( ord_le3102999989581377725nteger @ C @ zero_z3403309356797280102nteger )
% 0.29/0.54 => ( ( ord_le3102999989581377725nteger @ A @ B )
% 0.29/0.54 => ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ A @ C ) @ B ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_decreasing2
% 0.29/0.54 thf(fact_1319_add__decreasing2,axiom,
% 0.29/0.54 ! [C: rat,A: rat,B: rat] :
% 0.29/0.54 ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 0.29/0.54 => ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.54 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_decreasing2
% 0.29/0.54 thf(fact_1320_add__decreasing2,axiom,
% 0.29/0.54 ! [C: nat,A: nat,B: nat] :
% 0.29/0.54 ( ( ord_less_eq_nat @ C @ zero_zero_nat )
% 0.29/0.54 => ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.54 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ B ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_decreasing2
% 0.29/0.54 thf(fact_1321_add__decreasing2,axiom,
% 0.29/0.54 ! [C: int,A: int,B: int] :
% 0.29/0.54 ( ( ord_less_eq_int @ C @ zero_zero_int )
% 0.29/0.54 => ( ( ord_less_eq_int @ A @ B )
% 0.29/0.54 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ B ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_decreasing2
% 0.29/0.54 thf(fact_1322_add__increasing2,axiom,
% 0.29/0.54 ! [C: code_integer,B: code_integer,A: code_integer] :
% 0.29/0.54 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 0.29/0.54 => ( ( ord_le3102999989581377725nteger @ B @ A )
% 0.29/0.54 => ( ord_le3102999989581377725nteger @ B @ ( plus_p5714425477246183910nteger @ A @ C ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_increasing2
% 0.29/0.54 thf(fact_1323_add__increasing2,axiom,
% 0.29/0.54 ! [C: rat,B: rat,A: rat] :
% 0.29/0.54 ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.29/0.54 => ( ( ord_less_eq_rat @ B @ A )
% 0.29/0.54 => ( ord_less_eq_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_increasing2
% 0.29/0.54 thf(fact_1324_add__increasing2,axiom,
% 0.29/0.54 ! [C: nat,B: nat,A: nat] :
% 0.29/0.54 ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 0.29/0.54 => ( ( ord_less_eq_nat @ B @ A )
% 0.29/0.54 => ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_increasing2
% 0.29/0.54 thf(fact_1325_add__increasing2,axiom,
% 0.29/0.54 ! [C: int,B: int,A: int] :
% 0.29/0.54 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.29/0.54 => ( ( ord_less_eq_int @ B @ A )
% 0.29/0.54 => ( ord_less_eq_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_increasing2
% 0.29/0.54 thf(fact_1326_add__nonneg__nonneg,axiom,
% 0.29/0.54 ! [A: code_integer,B: code_integer] :
% 0.29/0.54 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.29/0.54 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 0.29/0.54 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_nonneg_nonneg
% 0.29/0.54 thf(fact_1327_add__nonneg__nonneg,axiom,
% 0.29/0.54 ! [A: rat,B: rat] :
% 0.29/0.54 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.29/0.54 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.29/0.54 => ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_nonneg_nonneg
% 0.29/0.54 thf(fact_1328_add__nonneg__nonneg,axiom,
% 0.29/0.54 ! [A: nat,B: nat] :
% 0.29/0.54 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.29/0.54 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.29/0.54 => ( ord_less_eq_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_nonneg_nonneg
% 0.29/0.54 thf(fact_1329_add__nonneg__nonneg,axiom,
% 0.29/0.54 ! [A: int,B: int] :
% 0.29/0.54 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.29/0.54 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.29/0.54 => ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_nonneg_nonneg
% 0.29/0.54 thf(fact_1330_add__nonpos__nonpos,axiom,
% 0.29/0.54 ! [A: code_integer,B: code_integer] :
% 0.29/0.54 ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 0.29/0.54 => ( ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger )
% 0.29/0.54 => ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ zero_z3403309356797280102nteger ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_nonpos_nonpos
% 0.29/0.54 thf(fact_1331_add__nonpos__nonpos,axiom,
% 0.29/0.54 ! [A: rat,B: rat] :
% 0.29/0.54 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.29/0.54 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 0.29/0.54 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_nonpos_nonpos
% 0.29/0.54 thf(fact_1332_add__nonpos__nonpos,axiom,
% 0.29/0.54 ! [A: nat,B: nat] :
% 0.29/0.54 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 0.29/0.54 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 0.29/0.54 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_nonpos_nonpos
% 0.29/0.54 thf(fact_1333_add__nonpos__nonpos,axiom,
% 0.29/0.54 ! [A: int,B: int] :
% 0.29/0.54 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.29/0.54 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 0.29/0.54 => ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_nonpos_nonpos
% 0.29/0.54 thf(fact_1334_add__nonneg__eq__0__iff,axiom,
% 0.29/0.54 ! [X: code_integer,Y: code_integer] :
% 0.29/0.54 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X )
% 0.29/0.54 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y )
% 0.29/0.54 => ( ( ( plus_p5714425477246183910nteger @ X @ Y )
% 0.29/0.54 = zero_z3403309356797280102nteger )
% 0.29/0.54 = ( ( X = zero_z3403309356797280102nteger )
% 0.29/0.54 & ( Y = zero_z3403309356797280102nteger ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_nonneg_eq_0_iff
% 0.29/0.54 thf(fact_1335_add__nonneg__eq__0__iff,axiom,
% 0.29/0.54 ! [X: rat,Y: rat] :
% 0.29/0.54 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 0.29/0.54 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 0.29/0.54 => ( ( ( plus_plus_rat @ X @ Y )
% 0.29/0.54 = zero_zero_rat )
% 0.29/0.54 = ( ( X = zero_zero_rat )
% 0.29/0.54 & ( Y = zero_zero_rat ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_nonneg_eq_0_iff
% 0.29/0.54 thf(fact_1336_add__nonneg__eq__0__iff,axiom,
% 0.29/0.54 ! [X: nat,Y: nat] :
% 0.29/0.54 ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 0.29/0.54 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 0.29/0.54 => ( ( ( plus_plus_nat @ X @ Y )
% 0.29/0.54 = zero_zero_nat )
% 0.29/0.54 = ( ( X = zero_zero_nat )
% 0.29/0.54 & ( Y = zero_zero_nat ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_nonneg_eq_0_iff
% 0.29/0.54 thf(fact_1337_add__nonneg__eq__0__iff,axiom,
% 0.29/0.54 ! [X: int,Y: int] :
% 0.29/0.54 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.29/0.54 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.29/0.54 => ( ( ( plus_plus_int @ X @ Y )
% 0.29/0.54 = zero_zero_int )
% 0.29/0.54 = ( ( X = zero_zero_int )
% 0.29/0.54 & ( Y = zero_zero_int ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_nonneg_eq_0_iff
% 0.29/0.54 thf(fact_1338_add__nonpos__eq__0__iff,axiom,
% 0.29/0.54 ! [X: code_integer,Y: code_integer] :
% 0.29/0.54 ( ( ord_le3102999989581377725nteger @ X @ zero_z3403309356797280102nteger )
% 0.29/0.54 => ( ( ord_le3102999989581377725nteger @ Y @ zero_z3403309356797280102nteger )
% 0.29/0.54 => ( ( ( plus_p5714425477246183910nteger @ X @ Y )
% 0.29/0.54 = zero_z3403309356797280102nteger )
% 0.29/0.54 = ( ( X = zero_z3403309356797280102nteger )
% 0.29/0.54 & ( Y = zero_z3403309356797280102nteger ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_nonpos_eq_0_iff
% 0.29/0.54 thf(fact_1339_add__nonpos__eq__0__iff,axiom,
% 0.29/0.54 ! [X: rat,Y: rat] :
% 0.29/0.54 ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 0.29/0.54 => ( ( ord_less_eq_rat @ Y @ zero_zero_rat )
% 0.29/0.54 => ( ( ( plus_plus_rat @ X @ Y )
% 0.29/0.54 = zero_zero_rat )
% 0.29/0.54 = ( ( X = zero_zero_rat )
% 0.29/0.54 & ( Y = zero_zero_rat ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_nonpos_eq_0_iff
% 0.29/0.54 thf(fact_1340_add__nonpos__eq__0__iff,axiom,
% 0.29/0.54 ! [X: nat,Y: nat] :
% 0.29/0.54 ( ( ord_less_eq_nat @ X @ zero_zero_nat )
% 0.29/0.54 => ( ( ord_less_eq_nat @ Y @ zero_zero_nat )
% 0.29/0.54 => ( ( ( plus_plus_nat @ X @ Y )
% 0.29/0.54 = zero_zero_nat )
% 0.29/0.54 = ( ( X = zero_zero_nat )
% 0.29/0.54 & ( Y = zero_zero_nat ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_nonpos_eq_0_iff
% 0.29/0.54 thf(fact_1341_add__nonpos__eq__0__iff,axiom,
% 0.29/0.54 ! [X: int,Y: int] :
% 0.29/0.54 ( ( ord_less_eq_int @ X @ zero_zero_int )
% 0.29/0.54 => ( ( ord_less_eq_int @ Y @ zero_zero_int )
% 0.29/0.54 => ( ( ( plus_plus_int @ X @ Y )
% 0.29/0.54 = zero_zero_int )
% 0.29/0.54 = ( ( X = zero_zero_int )
% 0.29/0.54 & ( Y = zero_zero_int ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_nonpos_eq_0_iff
% 0.29/0.54 thf(fact_1342_not__one__le__zero,axiom,
% 0.29/0.54 ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ zero_z3403309356797280102nteger ) ).
% 0.29/0.54
% 0.29/0.54 % not_one_le_zero
% 0.29/0.54 thf(fact_1343_not__one__le__zero,axiom,
% 0.29/0.54 ~ ( ord_less_eq_rat @ one_one_rat @ zero_zero_rat ) ).
% 0.29/0.54
% 0.29/0.54 % not_one_le_zero
% 0.29/0.54 thf(fact_1344_not__one__le__zero,axiom,
% 0.29/0.54 ~ ( ord_less_eq_nat @ one_one_nat @ zero_zero_nat ) ).
% 0.29/0.54
% 0.29/0.54 % not_one_le_zero
% 0.29/0.54 thf(fact_1345_not__one__le__zero,axiom,
% 0.29/0.54 ~ ( ord_less_eq_int @ one_one_int @ zero_zero_int ) ).
% 0.29/0.54
% 0.29/0.54 % not_one_le_zero
% 0.29/0.54 thf(fact_1346_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 0.29/0.54 ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ one_one_Code_integer ).
% 0.29/0.54
% 0.29/0.54 % linordered_nonzero_semiring_class.zero_le_one
% 0.29/0.54 thf(fact_1347_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 0.29/0.54 ord_less_eq_rat @ zero_zero_rat @ one_one_rat ).
% 0.29/0.54
% 0.29/0.54 % linordered_nonzero_semiring_class.zero_le_one
% 0.29/0.54 thf(fact_1348_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 0.29/0.54 ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 0.29/0.54
% 0.29/0.54 % linordered_nonzero_semiring_class.zero_le_one
% 0.29/0.54 thf(fact_1349_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 0.29/0.54 ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 0.29/0.54
% 0.29/0.54 % linordered_nonzero_semiring_class.zero_le_one
% 0.29/0.54 thf(fact_1350_zero__less__one__class_Ozero__le__one,axiom,
% 0.29/0.54 ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ one_one_Code_integer ).
% 0.29/0.54
% 0.29/0.54 % zero_less_one_class.zero_le_one
% 0.29/0.54 thf(fact_1351_zero__less__one__class_Ozero__le__one,axiom,
% 0.29/0.54 ord_less_eq_rat @ zero_zero_rat @ one_one_rat ).
% 0.29/0.54
% 0.29/0.54 % zero_less_one_class.zero_le_one
% 0.29/0.54 thf(fact_1352_zero__less__one__class_Ozero__le__one,axiom,
% 0.29/0.54 ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 0.29/0.54
% 0.29/0.54 % zero_less_one_class.zero_le_one
% 0.29/0.54 thf(fact_1353_zero__less__one__class_Ozero__le__one,axiom,
% 0.29/0.54 ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 0.29/0.54
% 0.29/0.54 % zero_less_one_class.zero_le_one
% 0.29/0.54 thf(fact_1354_add__mono__thms__linordered__field_I4_J,axiom,
% 0.29/0.54 ! [I: code_integer,J: code_integer,K: code_integer,L: code_integer] :
% 0.29/0.54 ( ( ( ord_le3102999989581377725nteger @ I @ J )
% 0.29/0.54 & ( ord_le6747313008572928689nteger @ K @ L ) )
% 0.29/0.54 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ I @ K ) @ ( plus_p5714425477246183910nteger @ J @ L ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_mono_thms_linordered_field(4)
% 0.29/0.54 thf(fact_1355_add__mono__thms__linordered__field_I4_J,axiom,
% 0.29/0.54 ! [I: rat,J: rat,K: rat,L: rat] :
% 0.29/0.54 ( ( ( ord_less_eq_rat @ I @ J )
% 0.29/0.54 & ( ord_less_rat @ K @ L ) )
% 0.29/0.54 => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_mono_thms_linordered_field(4)
% 0.29/0.54 thf(fact_1356_add__mono__thms__linordered__field_I4_J,axiom,
% 0.29/0.54 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.29/0.54 ( ( ( ord_less_eq_nat @ I @ J )
% 0.29/0.54 & ( ord_less_nat @ K @ L ) )
% 0.29/0.54 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_mono_thms_linordered_field(4)
% 0.29/0.54 thf(fact_1357_add__mono__thms__linordered__field_I4_J,axiom,
% 0.29/0.54 ! [I: int,J: int,K: int,L: int] :
% 0.29/0.54 ( ( ( ord_less_eq_int @ I @ J )
% 0.29/0.54 & ( ord_less_int @ K @ L ) )
% 0.29/0.54 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_mono_thms_linordered_field(4)
% 0.29/0.54 thf(fact_1358_add__mono__thms__linordered__field_I3_J,axiom,
% 0.29/0.54 ! [I: code_integer,J: code_integer,K: code_integer,L: code_integer] :
% 0.29/0.54 ( ( ( ord_le6747313008572928689nteger @ I @ J )
% 0.29/0.54 & ( ord_le3102999989581377725nteger @ K @ L ) )
% 0.29/0.54 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ I @ K ) @ ( plus_p5714425477246183910nteger @ J @ L ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_mono_thms_linordered_field(3)
% 0.29/0.54 thf(fact_1359_add__mono__thms__linordered__field_I3_J,axiom,
% 0.29/0.54 ! [I: rat,J: rat,K: rat,L: rat] :
% 0.29/0.54 ( ( ( ord_less_rat @ I @ J )
% 0.29/0.54 & ( ord_less_eq_rat @ K @ L ) )
% 0.29/0.54 => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_mono_thms_linordered_field(3)
% 0.29/0.54 thf(fact_1360_add__mono__thms__linordered__field_I3_J,axiom,
% 0.29/0.54 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.29/0.54 ( ( ( ord_less_nat @ I @ J )
% 0.29/0.54 & ( ord_less_eq_nat @ K @ L ) )
% 0.29/0.54 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_mono_thms_linordered_field(3)
% 0.29/0.54 thf(fact_1361_add__mono__thms__linordered__field_I3_J,axiom,
% 0.29/0.54 ! [I: int,J: int,K: int,L: int] :
% 0.29/0.54 ( ( ( ord_less_int @ I @ J )
% 0.29/0.54 & ( ord_less_eq_int @ K @ L ) )
% 0.29/0.54 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_mono_thms_linordered_field(3)
% 0.29/0.54 thf(fact_1362_add__le__less__mono,axiom,
% 0.29/0.54 ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 0.29/0.54 ( ( ord_le3102999989581377725nteger @ A @ B )
% 0.29/0.54 => ( ( ord_le6747313008572928689nteger @ C @ D2 )
% 0.29/0.54 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ C ) @ ( plus_p5714425477246183910nteger @ B @ D2 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_le_less_mono
% 0.29/0.54 thf(fact_1363_add__le__less__mono,axiom,
% 0.29/0.54 ! [A: rat,B: rat,C: rat,D2: rat] :
% 0.29/0.54 ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.54 => ( ( ord_less_rat @ C @ D2 )
% 0.29/0.54 => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D2 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_le_less_mono
% 0.29/0.54 thf(fact_1364_add__le__less__mono,axiom,
% 0.29/0.54 ! [A: nat,B: nat,C: nat,D2: nat] :
% 0.29/0.54 ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.54 => ( ( ord_less_nat @ C @ D2 )
% 0.29/0.54 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D2 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_le_less_mono
% 0.29/0.54 thf(fact_1365_add__le__less__mono,axiom,
% 0.29/0.54 ! [A: int,B: int,C: int,D2: int] :
% 0.29/0.54 ( ( ord_less_eq_int @ A @ B )
% 0.29/0.54 => ( ( ord_less_int @ C @ D2 )
% 0.29/0.54 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D2 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_le_less_mono
% 0.29/0.54 thf(fact_1366_add__less__le__mono,axiom,
% 0.29/0.54 ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 0.29/0.54 ( ( ord_le6747313008572928689nteger @ A @ B )
% 0.29/0.54 => ( ( ord_le3102999989581377725nteger @ C @ D2 )
% 0.29/0.54 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ C ) @ ( plus_p5714425477246183910nteger @ B @ D2 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_less_le_mono
% 0.29/0.54 thf(fact_1367_add__less__le__mono,axiom,
% 0.29/0.54 ! [A: rat,B: rat,C: rat,D2: rat] :
% 0.29/0.54 ( ( ord_less_rat @ A @ B )
% 0.29/0.54 => ( ( ord_less_eq_rat @ C @ D2 )
% 0.29/0.54 => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D2 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_less_le_mono
% 0.29/0.54 thf(fact_1368_add__less__le__mono,axiom,
% 0.29/0.54 ! [A: nat,B: nat,C: nat,D2: nat] :
% 0.29/0.54 ( ( ord_less_nat @ A @ B )
% 0.29/0.54 => ( ( ord_less_eq_nat @ C @ D2 )
% 0.29/0.54 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D2 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_less_le_mono
% 0.29/0.54 thf(fact_1369_add__less__le__mono,axiom,
% 0.29/0.54 ! [A: int,B: int,C: int,D2: int] :
% 0.29/0.54 ( ( ord_less_int @ A @ B )
% 0.29/0.54 => ( ( ord_less_eq_int @ C @ D2 )
% 0.29/0.54 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D2 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_less_le_mono
% 0.29/0.54 thf(fact_1370_le__minus__one__simps_I2_J,axiom,
% 0.29/0.54 ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ).
% 0.29/0.54
% 0.29/0.54 % le_minus_one_simps(2)
% 0.29/0.54 thf(fact_1371_le__minus__one__simps_I2_J,axiom,
% 0.29/0.54 ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat ).
% 0.29/0.54
% 0.29/0.54 % le_minus_one_simps(2)
% 0.29/0.54 thf(fact_1372_le__minus__one__simps_I2_J,axiom,
% 0.29/0.54 ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 0.29/0.54
% 0.29/0.54 % le_minus_one_simps(2)
% 0.29/0.54 thf(fact_1373_le__minus__one__simps_I4_J,axiom,
% 0.29/0.54 ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.29/0.54
% 0.29/0.54 % le_minus_one_simps(4)
% 0.29/0.54 thf(fact_1374_le__minus__one__simps_I4_J,axiom,
% 0.29/0.54 ~ ( ord_less_eq_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.29/0.54
% 0.29/0.54 % le_minus_one_simps(4)
% 0.29/0.54 thf(fact_1375_le__minus__one__simps_I4_J,axiom,
% 0.29/0.54 ~ ( ord_less_eq_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 0.29/0.54
% 0.29/0.54 % le_minus_one_simps(4)
% 0.29/0.54 thf(fact_1376_abs__ge__zero,axiom,
% 0.29/0.54 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ A ) ) ).
% 0.29/0.54
% 0.29/0.54 % abs_ge_zero
% 0.29/0.54 thf(fact_1377_abs__ge__zero,axiom,
% 0.29/0.54 ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( abs_abs_rat @ A ) ) ).
% 0.29/0.54
% 0.29/0.54 % abs_ge_zero
% 0.29/0.54 thf(fact_1378_abs__ge__zero,axiom,
% 0.29/0.54 ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( abs_abs_int @ A ) ) ).
% 0.29/0.54
% 0.29/0.54 % abs_ge_zero
% 0.29/0.54 thf(fact_1379_abs__triangle__ineq,axiom,
% 0.29/0.54 ! [A: code_integer,B: code_integer] : ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( plus_p5714425477246183910nteger @ A @ B ) ) @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % abs_triangle_ineq
% 0.29/0.54 thf(fact_1380_abs__triangle__ineq,axiom,
% 0.29/0.54 ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( plus_plus_rat @ A @ B ) ) @ ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % abs_triangle_ineq
% 0.29/0.54 thf(fact_1381_abs__triangle__ineq,axiom,
% 0.29/0.54 ! [A: int,B: int] : ( ord_less_eq_int @ ( abs_abs_int @ ( plus_plus_int @ A @ B ) ) @ ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % abs_triangle_ineq
% 0.29/0.54 thf(fact_1382_abs__leI,axiom,
% 0.29/0.54 ! [A: code_integer,B: code_integer] :
% 0.29/0.54 ( ( ord_le3102999989581377725nteger @ A @ B )
% 0.29/0.54 => ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 0.29/0.54 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % abs_leI
% 0.29/0.54 thf(fact_1383_abs__leI,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 @ ( uminus_uminus_rat @ A ) @ B )
% 0.29/0.54 => ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % abs_leI
% 0.29/0.54 thf(fact_1384_abs__leI,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 @ ( uminus_uminus_int @ A ) @ B )
% 0.29/0.54 => ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % abs_leI
% 0.29/0.54 thf(fact_1385_abs__le__D2,axiom,
% 0.29/0.54 ! [A: code_integer,B: code_integer] :
% 0.29/0.54 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 0.29/0.54 => ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 0.29/0.54
% 0.29/0.54 % abs_le_D2
% 0.29/0.54 thf(fact_1386_abs__le__D2,axiom,
% 0.29/0.54 ! [A: rat,B: rat] :
% 0.29/0.54 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 0.29/0.54 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 0.29/0.54
% 0.29/0.54 % abs_le_D2
% 0.29/0.54 thf(fact_1387_abs__le__D2,axiom,
% 0.29/0.54 ! [A: int,B: int] :
% 0.29/0.54 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 0.29/0.54 => ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 0.29/0.54
% 0.29/0.54 % abs_le_D2
% 0.29/0.54 thf(fact_1388_abs__le__iff,axiom,
% 0.29/0.54 ! [A: code_integer,B: code_integer] :
% 0.29/0.54 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 0.29/0.54 = ( ( ord_le3102999989581377725nteger @ A @ B )
% 0.29/0.54 & ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % abs_le_iff
% 0.29/0.54 thf(fact_1389_abs__le__iff,axiom,
% 0.29/0.54 ! [A: rat,B: rat] :
% 0.29/0.54 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 0.29/0.54 = ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.54 & ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % abs_le_iff
% 0.29/0.54 thf(fact_1390_abs__le__iff,axiom,
% 0.29/0.54 ! [A: int,B: int] :
% 0.29/0.54 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 0.29/0.54 = ( ( ord_less_eq_int @ A @ B )
% 0.29/0.54 & ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % abs_le_iff
% 0.29/0.54 thf(fact_1391_abs__ge__minus__self,axiom,
% 0.29/0.54 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ ( abs_abs_Code_integer @ A ) ) ).
% 0.29/0.54
% 0.29/0.54 % abs_ge_minus_self
% 0.29/0.54 thf(fact_1392_abs__ge__minus__self,axiom,
% 0.29/0.54 ! [A: rat] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ ( abs_abs_rat @ A ) ) ).
% 0.29/0.54
% 0.29/0.54 % abs_ge_minus_self
% 0.29/0.54 thf(fact_1393_abs__ge__minus__self,axiom,
% 0.29/0.54 ! [A: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ ( abs_abs_int @ A ) ) ).
% 0.29/0.54
% 0.29/0.54 % abs_ge_minus_self
% 0.29/0.54 thf(fact_1394_mono__nat__linear__lb,axiom,
% 0.29/0.54 ! [F: nat > nat,M2: nat,K: nat] :
% 0.29/0.54 ( ! [M5: nat,N: nat] :
% 0.29/0.54 ( ( ord_less_nat @ M5 @ N )
% 0.29/0.54 => ( ord_less_nat @ ( F @ M5 ) @ ( F @ N ) ) )
% 0.29/0.54 => ( ord_less_eq_nat @ ( plus_plus_nat @ ( F @ M2 ) @ K ) @ ( F @ ( plus_plus_nat @ M2 @ K ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % mono_nat_linear_lb
% 0.29/0.54 thf(fact_1395_nat__geq__1__eq__neqz,axiom,
% 0.29/0.54 ! [X: nat] :
% 0.29/0.54 ( ( ord_less_eq_nat @ one_one_nat @ X )
% 0.29/0.54 = ( X != zero_zero_nat ) ) ).
% 0.29/0.54
% 0.29/0.54 % nat_geq_1_eq_neqz
% 0.29/0.54 thf(fact_1396_bind__split__asm,axiom,
% 0.29/0.54 ! [P: option3216581401566546698it_nat > $o,M2: option3216581401566546698it_nat,F: produc6714399278180371524it_nat > option3216581401566546698it_nat] :
% 0.29/0.54 ( ( P @ ( bind_P1787608729393679550it_nat @ M2 @ F ) )
% 0.29/0.54 = ( ~ ( ( ( M2 = none_P2587165478634041381it_nat )
% 0.29/0.54 & ~ ( P @ none_P2587165478634041381it_nat ) )
% 0.29/0.54 | ? [X3: produc6714399278180371524it_nat] :
% 0.29/0.54 ( ( M2
% 0.29/0.54 = ( some_P6105628898608307625it_nat @ X3 ) )
% 0.29/0.54 & ~ ( P @ ( F @ X3 ) ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % bind_split_asm
% 0.29/0.54 thf(fact_1397_bind__split__asm,axiom,
% 0.29/0.54 ! [P: option_num > $o,M2: option3216581401566546698it_nat,F: produc6714399278180371524it_nat > option_num] :
% 0.29/0.54 ( ( P @ ( bind_P7816469540982926368at_num @ M2 @ F ) )
% 0.29/0.54 = ( ~ ( ( ( M2 = none_P2587165478634041381it_nat )
% 0.29/0.54 & ~ ( P @ none_num ) )
% 0.29/0.54 | ? [X3: produc6714399278180371524it_nat] :
% 0.29/0.54 ( ( M2
% 0.29/0.54 = ( some_P6105628898608307625it_nat @ X3 ) )
% 0.29/0.54 & ~ ( P @ ( F @ X3 ) ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % bind_split_asm
% 0.29/0.54 thf(fact_1398_bind__split__asm,axiom,
% 0.29/0.54 ! [P: option8956607266484857688it_nat > $o,M2: option3216581401566546698it_nat,F: produc6714399278180371524it_nat > option8956607266484857688it_nat] :
% 0.29/0.54 ( ( P @ ( bind_P3087804342168909838it_nat @ M2 @ F ) )
% 0.29/0.54 = ( ~ ( ( ( M2 = none_P2587165478634041381it_nat )
% 0.29/0.54 & ~ ( P @ none_P9117596204409417319it_nat ) )
% 0.29/0.54 | ? [X3: produc6714399278180371524it_nat] :
% 0.29/0.54 ( ( M2
% 0.29/0.54 = ( some_P6105628898608307625it_nat @ X3 ) )
% 0.29/0.54 & ~ ( P @ ( F @ X3 ) ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % bind_split_asm
% 0.29/0.54 thf(fact_1399_bind__split__asm,axiom,
% 0.29/0.54 ! [P: option3216581401566546698it_nat > $o,M2: option_num,F: num > option3216581401566546698it_nat] :
% 0.29/0.54 ( ( P @ ( bind_n6186876254402743274it_nat @ M2 @ F ) )
% 0.29/0.54 = ( ~ ( ( ( M2 = none_num )
% 0.29/0.54 & ~ ( P @ none_P2587165478634041381it_nat ) )
% 0.29/0.54 | ? [X3: num] :
% 0.29/0.54 ( ( M2
% 0.29/0.54 = ( some_num @ X3 ) )
% 0.29/0.54 & ~ ( P @ ( F @ X3 ) ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % bind_split_asm
% 0.29/0.54 thf(fact_1400_bind__split__asm,axiom,
% 0.29/0.54 ! [P: option_num > $o,M2: option_num,F: num > option_num] :
% 0.29/0.54 ( ( P @ ( bind_num_num @ M2 @ F ) )
% 0.29/0.54 = ( ~ ( ( ( M2 = none_num )
% 0.29/0.54 & ~ ( P @ none_num ) )
% 0.29/0.54 | ? [X3: num] :
% 0.29/0.54 ( ( M2
% 0.29/0.54 = ( some_num @ X3 ) )
% 0.29/0.54 & ~ ( P @ ( F @ X3 ) ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % bind_split_asm
% 0.29/0.54 thf(fact_1401_bind__split__asm,axiom,
% 0.29/0.54 ! [P: option8956607266484857688it_nat > $o,M2: option_num,F: num > option8956607266484857688it_nat] :
% 0.29/0.54 ( ( P @ ( bind_n550516262659884002it_nat @ M2 @ F ) )
% 0.29/0.54 = ( ~ ( ( ( M2 = none_num )
% 0.29/0.54 & ~ ( P @ none_P9117596204409417319it_nat ) )
% 0.29/0.54 | ? [X3: num] :
% 0.29/0.54 ( ( M2
% 0.29/0.54 = ( some_num @ X3 ) )
% 0.29/0.54 & ~ ( P @ ( F @ X3 ) ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % bind_split_asm
% 0.29/0.54 thf(fact_1402_bind__split__asm,axiom,
% 0.29/0.54 ! [P: option3216581401566546698it_nat > $o,M2: option8956607266484857688it_nat,F: produc8664842809031399944it_nat > option3216581401566546698it_nat] :
% 0.29/0.54 ( ( P @ ( bind_P1106314856888375420it_nat @ M2 @ F ) )
% 0.29/0.54 = ( ~ ( ( ( M2 = none_P9117596204409417319it_nat )
% 0.29/0.54 & ~ ( P @ none_P2587165478634041381it_nat ) )
% 0.29/0.54 | ? [X3: produc8664842809031399944it_nat] :
% 0.29/0.54 ( ( M2
% 0.29/0.54 = ( some_P1914260805536162275it_nat @ X3 ) )
% 0.29/0.54 & ~ ( P @ ( F @ X3 ) ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % bind_split_asm
% 0.29/0.54 thf(fact_1403_bind__split__asm,axiom,
% 0.29/0.54 ! [P: option_num > $o,M2: option8956607266484857688it_nat,F: produc8664842809031399944it_nat > option_num] :
% 0.29/0.54 ( ( P @ ( bind_P4387644102537648098at_num @ M2 @ F ) )
% 0.29/0.54 = ( ~ ( ( ( M2 = none_P9117596204409417319it_nat )
% 0.29/0.54 & ~ ( P @ none_num ) )
% 0.29/0.54 | ? [X3: produc8664842809031399944it_nat] :
% 0.29/0.54 ( ( M2
% 0.29/0.54 = ( some_P1914260805536162275it_nat @ X3 ) )
% 0.29/0.54 & ~ ( P @ ( F @ X3 ) ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % bind_split_asm
% 0.29/0.54 thf(fact_1404_bind__split__asm,axiom,
% 0.29/0.54 ! [P: option8956607266484857688it_nat > $o,M2: option8956607266484857688it_nat,F: produc8664842809031399944it_nat > option8956607266484857688it_nat] :
% 0.29/0.54 ( ( P @ ( bind_P7351952464966851536it_nat @ M2 @ F ) )
% 0.29/0.54 = ( ~ ( ( ( M2 = none_P9117596204409417319it_nat )
% 0.29/0.54 & ~ ( P @ none_P9117596204409417319it_nat ) )
% 0.29/0.54 | ? [X3: produc8664842809031399944it_nat] :
% 0.29/0.54 ( ( M2
% 0.29/0.54 = ( some_P1914260805536162275it_nat @ X3 ) )
% 0.29/0.54 & ~ ( P @ ( F @ X3 ) ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % bind_split_asm
% 0.29/0.54 thf(fact_1405_bind__split,axiom,
% 0.29/0.54 ! [P: option3216581401566546698it_nat > $o,M2: option3216581401566546698it_nat,F: produc6714399278180371524it_nat > option3216581401566546698it_nat] :
% 0.29/0.54 ( ( P @ ( bind_P1787608729393679550it_nat @ M2 @ F ) )
% 0.29/0.54 = ( ( ( M2 = none_P2587165478634041381it_nat )
% 0.29/0.54 => ( P @ none_P2587165478634041381it_nat ) )
% 0.29/0.54 & ! [V2: produc6714399278180371524it_nat] :
% 0.29/0.54 ( ( M2
% 0.29/0.54 = ( some_P6105628898608307625it_nat @ V2 ) )
% 0.29/0.54 => ( P @ ( F @ V2 ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % bind_split
% 0.29/0.54 thf(fact_1406_bind__split,axiom,
% 0.29/0.54 ! [P: option_num > $o,M2: option3216581401566546698it_nat,F: produc6714399278180371524it_nat > option_num] :
% 0.29/0.54 ( ( P @ ( bind_P7816469540982926368at_num @ M2 @ F ) )
% 0.29/0.54 = ( ( ( M2 = none_P2587165478634041381it_nat )
% 0.29/0.54 => ( P @ none_num ) )
% 0.29/0.54 & ! [V2: produc6714399278180371524it_nat] :
% 0.29/0.54 ( ( M2
% 0.29/0.54 = ( some_P6105628898608307625it_nat @ V2 ) )
% 0.29/0.54 => ( P @ ( F @ V2 ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % bind_split
% 0.29/0.54 thf(fact_1407_bind__split,axiom,
% 0.29/0.54 ! [P: option8956607266484857688it_nat > $o,M2: option3216581401566546698it_nat,F: produc6714399278180371524it_nat > option8956607266484857688it_nat] :
% 0.29/0.54 ( ( P @ ( bind_P3087804342168909838it_nat @ M2 @ F ) )
% 0.29/0.54 = ( ( ( M2 = none_P2587165478634041381it_nat )
% 0.29/0.54 => ( P @ none_P9117596204409417319it_nat ) )
% 0.29/0.54 & ! [V2: produc6714399278180371524it_nat] :
% 0.29/0.54 ( ( M2
% 0.29/0.54 = ( some_P6105628898608307625it_nat @ V2 ) )
% 0.29/0.54 => ( P @ ( F @ V2 ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % bind_split
% 0.29/0.54 thf(fact_1408_bind__split,axiom,
% 0.29/0.54 ! [P: option3216581401566546698it_nat > $o,M2: option_num,F: num > option3216581401566546698it_nat] :
% 0.29/0.54 ( ( P @ ( bind_n6186876254402743274it_nat @ M2 @ F ) )
% 0.29/0.54 = ( ( ( M2 = none_num )
% 0.29/0.54 => ( P @ none_P2587165478634041381it_nat ) )
% 0.29/0.54 & ! [V2: num] :
% 0.29/0.54 ( ( M2
% 0.29/0.54 = ( some_num @ V2 ) )
% 0.29/0.54 => ( P @ ( F @ V2 ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % bind_split
% 0.29/0.54 thf(fact_1409_bind__split,axiom,
% 0.29/0.54 ! [P: option_num > $o,M2: option_num,F: num > option_num] :
% 0.29/0.54 ( ( P @ ( bind_num_num @ M2 @ F ) )
% 0.29/0.54 = ( ( ( M2 = none_num )
% 0.29/0.54 => ( P @ none_num ) )
% 0.29/0.54 & ! [V2: num] :
% 0.29/0.54 ( ( M2
% 0.29/0.54 = ( some_num @ V2 ) )
% 0.29/0.54 => ( P @ ( F @ V2 ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % bind_split
% 0.29/0.54 thf(fact_1410_bind__split,axiom,
% 0.29/0.54 ! [P: option8956607266484857688it_nat > $o,M2: option_num,F: num > option8956607266484857688it_nat] :
% 0.29/0.54 ( ( P @ ( bind_n550516262659884002it_nat @ M2 @ F ) )
% 0.29/0.54 = ( ( ( M2 = none_num )
% 0.29/0.54 => ( P @ none_P9117596204409417319it_nat ) )
% 0.29/0.54 & ! [V2: num] :
% 0.29/0.54 ( ( M2
% 0.29/0.54 = ( some_num @ V2 ) )
% 0.29/0.54 => ( P @ ( F @ V2 ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % bind_split
% 0.29/0.54 thf(fact_1411_bind__split,axiom,
% 0.29/0.54 ! [P: option3216581401566546698it_nat > $o,M2: option8956607266484857688it_nat,F: produc8664842809031399944it_nat > option3216581401566546698it_nat] :
% 0.29/0.54 ( ( P @ ( bind_P1106314856888375420it_nat @ M2 @ F ) )
% 0.29/0.54 = ( ( ( M2 = none_P9117596204409417319it_nat )
% 0.29/0.54 => ( P @ none_P2587165478634041381it_nat ) )
% 0.29/0.54 & ! [V2: produc8664842809031399944it_nat] :
% 0.29/0.54 ( ( M2
% 0.29/0.54 = ( some_P1914260805536162275it_nat @ V2 ) )
% 0.29/0.54 => ( P @ ( F @ V2 ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % bind_split
% 0.29/0.54 thf(fact_1412_bind__split,axiom,
% 0.29/0.54 ! [P: option_num > $o,M2: option8956607266484857688it_nat,F: produc8664842809031399944it_nat > option_num] :
% 0.29/0.54 ( ( P @ ( bind_P4387644102537648098at_num @ M2 @ F ) )
% 0.29/0.54 = ( ( ( M2 = none_P9117596204409417319it_nat )
% 0.29/0.54 => ( P @ none_num ) )
% 0.29/0.54 & ! [V2: produc8664842809031399944it_nat] :
% 0.29/0.54 ( ( M2
% 0.29/0.54 = ( some_P1914260805536162275it_nat @ V2 ) )
% 0.29/0.54 => ( P @ ( F @ V2 ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % bind_split
% 0.29/0.54 thf(fact_1413_bind__split,axiom,
% 0.29/0.54 ! [P: option8956607266484857688it_nat > $o,M2: option8956607266484857688it_nat,F: produc8664842809031399944it_nat > option8956607266484857688it_nat] :
% 0.29/0.54 ( ( P @ ( bind_P7351952464966851536it_nat @ M2 @ F ) )
% 0.29/0.54 = ( ( ( M2 = none_P9117596204409417319it_nat )
% 0.29/0.54 => ( P @ none_P9117596204409417319it_nat ) )
% 0.29/0.54 & ! [V2: produc8664842809031399944it_nat] :
% 0.29/0.54 ( ( M2
% 0.29/0.54 = ( some_P1914260805536162275it_nat @ V2 ) )
% 0.29/0.54 => ( P @ ( F @ V2 ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % bind_split
% 0.29/0.54 thf(fact_1414_mlex__leq,axiom,
% 0.29/0.54 ! [F: set_Pr1261947904930325089at_nat > nat,X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,R4: set_Pr4329608150637261639at_nat] :
% 0.29/0.54 ( ( ord_less_eq_nat @ ( F @ X ) @ ( F @ Y ) )
% 0.29/0.54 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ R4 )
% 0.29/0.54 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ ( mlex_p3502713205431853936at_nat @ F @ R4 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % mlex_leq
% 0.29/0.54 thf(fact_1415_mlex__leq,axiom,
% 0.29/0.54 ! [F: nat > nat,X: nat,Y: nat,R4: set_Pr1261947904930325089at_nat] :
% 0.29/0.54 ( ( ord_less_eq_nat @ ( F @ X ) @ ( F @ Y ) )
% 0.29/0.54 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ R4 )
% 0.29/0.54 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( mlex_prod_nat @ F @ R4 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % mlex_leq
% 0.29/0.54 thf(fact_1416_bind__eq__None__conv,axiom,
% 0.29/0.54 ! [A: option3216581401566546698it_nat,F: produc6714399278180371524it_nat > option3216581401566546698it_nat] :
% 0.29/0.54 ( ( ( bind_P1787608729393679550it_nat @ A @ F )
% 0.29/0.54 = none_P2587165478634041381it_nat )
% 0.29/0.54 = ( ( A = none_P2587165478634041381it_nat )
% 0.29/0.54 | ( ( F @ ( the_Pr5856008525237892824it_nat @ A ) )
% 0.29/0.54 = none_P2587165478634041381it_nat ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % bind_eq_None_conv
% 0.29/0.54 thf(fact_1417_bind__eq__None__conv,axiom,
% 0.29/0.54 ! [A: option_num,F: num > option3216581401566546698it_nat] :
% 0.29/0.54 ( ( ( bind_n6186876254402743274it_nat @ A @ F )
% 0.29/0.54 = none_P2587165478634041381it_nat )
% 0.29/0.54 = ( ( A = none_num )
% 0.29/0.54 | ( ( F @ ( the_num @ A ) )
% 0.29/0.54 = none_P2587165478634041381it_nat ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % bind_eq_None_conv
% 0.29/0.54 thf(fact_1418_bind__eq__None__conv,axiom,
% 0.29/0.54 ! [A: option8956607266484857688it_nat,F: produc8664842809031399944it_nat > option3216581401566546698it_nat] :
% 0.29/0.54 ( ( ( bind_P1106314856888375420it_nat @ A @ F )
% 0.29/0.54 = none_P2587165478634041381it_nat )
% 0.29/0.54 = ( ( A = none_P9117596204409417319it_nat )
% 0.29/0.54 | ( ( F @ ( the_Pr7776125533777466484it_nat @ A ) )
% 0.29/0.54 = none_P2587165478634041381it_nat ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % bind_eq_None_conv
% 0.29/0.54 thf(fact_1419_bind__eq__None__conv,axiom,
% 0.29/0.54 ! [A: option3216581401566546698it_nat,F: produc6714399278180371524it_nat > option_num] :
% 0.29/0.54 ( ( ( bind_P7816469540982926368at_num @ A @ F )
% 0.29/0.54 = none_num )
% 0.29/0.54 = ( ( A = none_P2587165478634041381it_nat )
% 0.29/0.54 | ( ( F @ ( the_Pr5856008525237892824it_nat @ A ) )
% 0.29/0.54 = none_num ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % bind_eq_None_conv
% 0.29/0.54 thf(fact_1420_bind__eq__None__conv,axiom,
% 0.29/0.54 ! [A: option_num,F: num > option_num] :
% 0.29/0.54 ( ( ( bind_num_num @ A @ F )
% 0.29/0.54 = none_num )
% 0.29/0.54 = ( ( A = none_num )
% 0.29/0.54 | ( ( F @ ( the_num @ A ) )
% 0.29/0.54 = none_num ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % bind_eq_None_conv
% 0.29/0.54 thf(fact_1421_bind__eq__None__conv,axiom,
% 0.29/0.54 ! [A: option8956607266484857688it_nat,F: produc8664842809031399944it_nat > option_num] :
% 0.29/0.54 ( ( ( bind_P4387644102537648098at_num @ A @ F )
% 0.29/0.54 = none_num )
% 0.29/0.54 = ( ( A = none_P9117596204409417319it_nat )
% 0.29/0.54 | ( ( F @ ( the_Pr7776125533777466484it_nat @ A ) )
% 0.29/0.54 = none_num ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % bind_eq_None_conv
% 0.29/0.54 thf(fact_1422_bind__eq__None__conv,axiom,
% 0.29/0.54 ! [A: option3216581401566546698it_nat,F: produc6714399278180371524it_nat > option8956607266484857688it_nat] :
% 0.29/0.54 ( ( ( bind_P3087804342168909838it_nat @ A @ F )
% 0.29/0.54 = none_P9117596204409417319it_nat )
% 0.29/0.54 = ( ( A = none_P2587165478634041381it_nat )
% 0.29/0.54 | ( ( F @ ( the_Pr5856008525237892824it_nat @ A ) )
% 0.29/0.54 = none_P9117596204409417319it_nat ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % bind_eq_None_conv
% 0.29/0.54 thf(fact_1423_bind__eq__None__conv,axiom,
% 0.29/0.54 ! [A: option_num,F: num > option8956607266484857688it_nat] :
% 0.29/0.54 ( ( ( bind_n550516262659884002it_nat @ A @ F )
% 0.29/0.54 = none_P9117596204409417319it_nat )
% 0.29/0.54 = ( ( A = none_num )
% 0.29/0.54 | ( ( F @ ( the_num @ A ) )
% 0.29/0.54 = none_P9117596204409417319it_nat ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % bind_eq_None_conv
% 0.29/0.54 thf(fact_1424_bind__eq__None__conv,axiom,
% 0.29/0.54 ! [A: option8956607266484857688it_nat,F: produc8664842809031399944it_nat > option8956607266484857688it_nat] :
% 0.29/0.54 ( ( ( bind_P7351952464966851536it_nat @ A @ F )
% 0.29/0.54 = none_P9117596204409417319it_nat )
% 0.29/0.54 = ( ( A = none_P9117596204409417319it_nat )
% 0.29/0.54 | ( ( F @ ( the_Pr7776125533777466484it_nat @ A ) )
% 0.29/0.54 = none_P9117596204409417319it_nat ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % bind_eq_None_conv
% 0.29/0.54 thf(fact_1425_add__neg__nonpos,axiom,
% 0.29/0.54 ! [A: code_integer,B: code_integer] :
% 0.29/0.54 ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 0.29/0.54 => ( ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger )
% 0.29/0.54 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ zero_z3403309356797280102nteger ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_neg_nonpos
% 0.29/0.54 thf(fact_1426_add__neg__nonpos,axiom,
% 0.29/0.54 ! [A: rat,B: rat] :
% 0.29/0.54 ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.29/0.54 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 0.29/0.54 => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_neg_nonpos
% 0.29/0.54 thf(fact_1427_add__neg__nonpos,axiom,
% 0.29/0.54 ! [A: nat,B: nat] :
% 0.29/0.54 ( ( ord_less_nat @ A @ zero_zero_nat )
% 0.29/0.54 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 0.29/0.54 => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_neg_nonpos
% 0.29/0.54 thf(fact_1428_add__neg__nonpos,axiom,
% 0.29/0.54 ! [A: int,B: int] :
% 0.29/0.54 ( ( ord_less_int @ A @ zero_zero_int )
% 0.29/0.54 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 0.29/0.54 => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_neg_nonpos
% 0.29/0.54 thf(fact_1429_add__nonneg__pos,axiom,
% 0.29/0.54 ! [A: code_integer,B: code_integer] :
% 0.29/0.54 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.29/0.54 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 0.29/0.54 => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_nonneg_pos
% 0.29/0.54 thf(fact_1430_add__nonneg__pos,axiom,
% 0.29/0.54 ! [A: rat,B: rat] :
% 0.29/0.54 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.29/0.54 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 0.29/0.54 => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_nonneg_pos
% 0.29/0.54 thf(fact_1431_add__nonneg__pos,axiom,
% 0.29/0.54 ! [A: nat,B: nat] :
% 0.29/0.54 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.29/0.54 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.29/0.54 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_nonneg_pos
% 0.29/0.54 thf(fact_1432_add__nonneg__pos,axiom,
% 0.29/0.54 ! [A: int,B: int] :
% 0.29/0.54 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.29/0.54 => ( ( ord_less_int @ zero_zero_int @ B )
% 0.29/0.54 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_nonneg_pos
% 0.29/0.54 thf(fact_1433_add__nonpos__neg,axiom,
% 0.29/0.54 ! [A: code_integer,B: code_integer] :
% 0.29/0.54 ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 0.29/0.54 => ( ( ord_le6747313008572928689nteger @ B @ zero_z3403309356797280102nteger )
% 0.29/0.54 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ zero_z3403309356797280102nteger ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_nonpos_neg
% 0.29/0.54 thf(fact_1434_add__nonpos__neg,axiom,
% 0.29/0.54 ! [A: rat,B: rat] :
% 0.29/0.54 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.29/0.54 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 0.29/0.54 => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_nonpos_neg
% 0.29/0.54 thf(fact_1435_add__nonpos__neg,axiom,
% 0.29/0.54 ! [A: nat,B: nat] :
% 0.29/0.54 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 0.29/0.54 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 0.29/0.54 => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_nonpos_neg
% 0.29/0.54 thf(fact_1436_add__nonpos__neg,axiom,
% 0.29/0.54 ! [A: int,B: int] :
% 0.29/0.54 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.29/0.54 => ( ( ord_less_int @ B @ zero_zero_int )
% 0.29/0.54 => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_nonpos_neg
% 0.29/0.54 thf(fact_1437_add__pos__nonneg,axiom,
% 0.29/0.54 ! [A: code_integer,B: code_integer] :
% 0.29/0.54 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 0.29/0.54 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 0.29/0.54 => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_pos_nonneg
% 0.29/0.54 thf(fact_1438_add__pos__nonneg,axiom,
% 0.29/0.54 ! [A: rat,B: rat] :
% 0.29/0.54 ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.29/0.54 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.29/0.54 => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_pos_nonneg
% 0.29/0.54 thf(fact_1439_add__pos__nonneg,axiom,
% 0.29/0.54 ! [A: nat,B: nat] :
% 0.29/0.54 ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.29/0.54 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.29/0.54 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_pos_nonneg
% 0.29/0.54 thf(fact_1440_add__pos__nonneg,axiom,
% 0.29/0.54 ! [A: int,B: int] :
% 0.29/0.54 ( ( ord_less_int @ zero_zero_int @ A )
% 0.29/0.54 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.29/0.54 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_pos_nonneg
% 0.29/0.54 thf(fact_1441_add__strict__increasing,axiom,
% 0.29/0.54 ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.29/0.54 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 0.29/0.54 => ( ( ord_le3102999989581377725nteger @ B @ C )
% 0.29/0.54 => ( ord_le6747313008572928689nteger @ B @ ( plus_p5714425477246183910nteger @ A @ C ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_strict_increasing
% 0.29/0.54 thf(fact_1442_add__strict__increasing,axiom,
% 0.29/0.54 ! [A: rat,B: rat,C: rat] :
% 0.29/0.54 ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.29/0.54 => ( ( ord_less_eq_rat @ B @ C )
% 0.29/0.54 => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_strict_increasing
% 0.29/0.54 thf(fact_1443_add__strict__increasing,axiom,
% 0.29/0.54 ! [A: nat,B: nat,C: nat] :
% 0.29/0.54 ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.29/0.54 => ( ( ord_less_eq_nat @ B @ C )
% 0.29/0.54 => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_strict_increasing
% 0.29/0.54 thf(fact_1444_add__strict__increasing,axiom,
% 0.29/0.54 ! [A: int,B: int,C: int] :
% 0.29/0.54 ( ( ord_less_int @ zero_zero_int @ A )
% 0.29/0.54 => ( ( ord_less_eq_int @ B @ C )
% 0.29/0.54 => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_strict_increasing
% 0.29/0.54 thf(fact_1445_add__strict__increasing2,axiom,
% 0.29/0.54 ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.29/0.54 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.29/0.54 => ( ( ord_le6747313008572928689nteger @ B @ C )
% 0.29/0.54 => ( ord_le6747313008572928689nteger @ B @ ( plus_p5714425477246183910nteger @ A @ C ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_strict_increasing2
% 0.29/0.54 thf(fact_1446_add__strict__increasing2,axiom,
% 0.29/0.54 ! [A: rat,B: rat,C: rat] :
% 0.29/0.54 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.29/0.54 => ( ( ord_less_rat @ B @ C )
% 0.29/0.54 => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_strict_increasing2
% 0.29/0.54 thf(fact_1447_add__strict__increasing2,axiom,
% 0.29/0.54 ! [A: nat,B: nat,C: nat] :
% 0.29/0.54 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.29/0.54 => ( ( ord_less_nat @ B @ C )
% 0.29/0.54 => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_strict_increasing2
% 0.29/0.54 thf(fact_1448_add__strict__increasing2,axiom,
% 0.29/0.54 ! [A: int,B: int,C: int] :
% 0.29/0.54 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.29/0.54 => ( ( ord_less_int @ B @ C )
% 0.29/0.54 => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_strict_increasing2
% 0.29/0.54 thf(fact_1449_discrete,axiom,
% 0.29/0.54 ( ord_le6747313008572928689nteger
% 0.29/0.54 = ( ^ [A5: code_integer] : ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ A5 @ one_one_Code_integer ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % discrete
% 0.29/0.54 thf(fact_1450_discrete,axiom,
% 0.29/0.54 ( ord_less_nat
% 0.29/0.54 = ( ^ [A5: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ A5 @ one_one_nat ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % discrete
% 0.29/0.54 thf(fact_1451_discrete,axiom,
% 0.29/0.54 ( ord_less_int
% 0.29/0.54 = ( ^ [A5: int] : ( ord_less_eq_int @ ( plus_plus_int @ A5 @ one_one_int ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % discrete
% 0.29/0.54 thf(fact_1452_le__minus__one__simps_I1_J,axiom,
% 0.29/0.54 ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ zero_z3403309356797280102nteger ).
% 0.29/0.54
% 0.29/0.54 % le_minus_one_simps(1)
% 0.29/0.54 thf(fact_1453_le__minus__one__simps_I1_J,axiom,
% 0.29/0.54 ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ zero_zero_rat ).
% 0.29/0.54
% 0.29/0.54 % le_minus_one_simps(1)
% 0.29/0.54 thf(fact_1454_le__minus__one__simps_I1_J,axiom,
% 0.29/0.54 ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% 0.29/0.54
% 0.29/0.54 % le_minus_one_simps(1)
% 0.29/0.54 thf(fact_1455_le__minus__one__simps_I3_J,axiom,
% 0.29/0.54 ~ ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.29/0.54
% 0.29/0.54 % le_minus_one_simps(3)
% 0.29/0.54 thf(fact_1456_le__minus__one__simps_I3_J,axiom,
% 0.29/0.54 ~ ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.29/0.54
% 0.29/0.54 % le_minus_one_simps(3)
% 0.29/0.54 thf(fact_1457_le__minus__one__simps_I3_J,axiom,
% 0.29/0.54 ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 0.29/0.54
% 0.29/0.54 % le_minus_one_simps(3)
% 0.29/0.54 thf(fact_1458_dense__eq0__I,axiom,
% 0.29/0.54 ! [X: rat] :
% 0.29/0.54 ( ! [E2: rat] :
% 0.29/0.54 ( ( ord_less_rat @ zero_zero_rat @ E2 )
% 0.29/0.54 => ( ord_less_eq_rat @ ( abs_abs_rat @ X ) @ E2 ) )
% 0.29/0.54 => ( X = zero_zero_rat ) ) ).
% 0.29/0.54
% 0.29/0.54 % dense_eq0_I
% 0.29/0.54 thf(fact_1459_abs__minus__le__zero,axiom,
% 0.29/0.54 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( abs_abs_Code_integer @ A ) ) @ zero_z3403309356797280102nteger ) ).
% 0.29/0.54
% 0.29/0.54 % abs_minus_le_zero
% 0.29/0.54 thf(fact_1460_abs__minus__le__zero,axiom,
% 0.29/0.54 ! [A: rat] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( abs_abs_rat @ A ) ) @ zero_zero_rat ) ).
% 0.29/0.54
% 0.29/0.54 % abs_minus_le_zero
% 0.29/0.54 thf(fact_1461_abs__minus__le__zero,axiom,
% 0.29/0.54 ! [A: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( abs_abs_int @ A ) ) @ zero_zero_int ) ).
% 0.29/0.54
% 0.29/0.54 % abs_minus_le_zero
% 0.29/0.54 thf(fact_1462_success__changeI,axiom,
% 0.29/0.54 ! [F: product_unit > product_unit,R2: ref_Product_unit,H3: heap_e7401611519738050253t_unit] : ( heap_T584514906347983379t_unit @ ( ref_ch7259622376331601608t_unit @ F @ R2 ) @ H3 ) ).
% 0.29/0.54
% 0.29/0.54 % success_changeI
% 0.29/0.54 thf(fact_1463_success__changeI,axiom,
% 0.29/0.54 ! [F: array_a > array_a,R2: ref_array_a,H3: heap_e7401611519738050253t_unit] : ( heap_T6932021131025641745rray_a @ ( ref_change_array_a @ F @ R2 ) @ H3 ) ).
% 0.29/0.54
% 0.29/0.54 % success_changeI
% 0.29/0.54 thf(fact_1464_semiring__norm_I6_J,axiom,
% 0.29/0.54 ! [M2: num,N2: num] :
% 0.29/0.54 ( ( plus_plus_num @ ( bit0 @ M2 ) @ ( bit0 @ N2 ) )
% 0.29/0.54 = ( bit0 @ ( plus_plus_num @ M2 @ N2 ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % semiring_norm(6)
% 0.29/0.54 thf(fact_1465_field__le__epsilon,axiom,
% 0.29/0.54 ! [X: rat,Y: rat] :
% 0.29/0.54 ( ! [E2: rat] :
% 0.29/0.54 ( ( ord_less_rat @ zero_zero_rat @ E2 )
% 0.29/0.54 => ( ord_less_eq_rat @ X @ ( plus_plus_rat @ Y @ E2 ) ) )
% 0.29/0.54 => ( ord_less_eq_rat @ X @ Y ) ) ).
% 0.29/0.54
% 0.29/0.54 % field_le_epsilon
% 0.29/0.54 thf(fact_1466_convex__bound__lt,axiom,
% 0.29/0.54 ! [X: code_integer,A: code_integer,Y: code_integer,U: code_integer,V: code_integer] :
% 0.29/0.54 ( ( ord_le6747313008572928689nteger @ X @ A )
% 0.29/0.54 => ( ( ord_le6747313008572928689nteger @ Y @ A )
% 0.29/0.54 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ U )
% 0.29/0.54 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ V )
% 0.29/0.54 => ( ( ( plus_p5714425477246183910nteger @ U @ V )
% 0.29/0.54 = one_one_Code_integer )
% 0.29/0.54 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ U @ X ) @ ( times_3573771949741848930nteger @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % convex_bound_lt
% 0.29/0.54 thf(fact_1467_convex__bound__lt,axiom,
% 0.29/0.54 ! [X: rat,A: rat,Y: rat,U: rat,V: rat] :
% 0.29/0.54 ( ( ord_less_rat @ X @ A )
% 0.29/0.54 => ( ( ord_less_rat @ Y @ A )
% 0.29/0.54 => ( ( ord_less_eq_rat @ zero_zero_rat @ U )
% 0.29/0.54 => ( ( ord_less_eq_rat @ zero_zero_rat @ V )
% 0.29/0.54 => ( ( ( plus_plus_rat @ U @ V )
% 0.29/0.54 = one_one_rat )
% 0.29/0.54 => ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ U @ X ) @ ( times_times_rat @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % convex_bound_lt
% 0.29/0.54 thf(fact_1468_convex__bound__lt,axiom,
% 0.29/0.54 ! [X: int,A: int,Y: int,U: int,V: int] :
% 0.29/0.54 ( ( ord_less_int @ X @ A )
% 0.29/0.54 => ( ( ord_less_int @ Y @ A )
% 0.29/0.54 => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 0.29/0.54 => ( ( ord_less_eq_int @ zero_zero_int @ V )
% 0.29/0.54 => ( ( ( plus_plus_int @ U @ V )
% 0.29/0.54 = one_one_int )
% 0.29/0.54 => ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ U @ X ) @ ( times_times_int @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % convex_bound_lt
% 0.29/0.54 thf(fact_1469_Ints__eq__abs__less1,axiom,
% 0.29/0.54 ! [X: code_integer,Y: code_integer] :
% 0.29/0.54 ( ( member_Code_integer @ X @ ring_11222124179247155820nteger )
% 0.29/0.54 => ( ( member_Code_integer @ Y @ ring_11222124179247155820nteger )
% 0.29/0.54 => ( ( X = Y )
% 0.29/0.54 = ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ X @ Y ) ) @ one_one_Code_integer ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % Ints_eq_abs_less1
% 0.29/0.54 thf(fact_1470_Ints__eq__abs__less1,axiom,
% 0.29/0.54 ! [X: rat,Y: rat] :
% 0.29/0.54 ( ( member_rat @ X @ ring_1_Ints_rat )
% 0.29/0.54 => ( ( member_rat @ Y @ ring_1_Ints_rat )
% 0.29/0.54 => ( ( X = Y )
% 0.29/0.54 = ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X @ Y ) ) @ one_one_rat ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % Ints_eq_abs_less1
% 0.29/0.54 thf(fact_1471_Ints__eq__abs__less1,axiom,
% 0.29/0.54 ! [X: int,Y: int] :
% 0.29/0.54 ( ( member_int @ X @ ring_1_Ints_int )
% 0.29/0.54 => ( ( member_int @ Y @ ring_1_Ints_int )
% 0.29/0.54 => ( ( X = Y )
% 0.29/0.54 = ( ord_less_int @ ( abs_abs_int @ ( minus_minus_int @ X @ Y ) ) @ one_one_int ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % Ints_eq_abs_less1
% 0.29/0.54 thf(fact_1472_nat0__intermed__int__val,axiom,
% 0.29/0.54 ! [N2: nat,F: nat > int,K: int] :
% 0.29/0.54 ( ! [I2: nat] :
% 0.29/0.54 ( ( ord_less_nat @ I2 @ N2 )
% 0.29/0.54 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( plus_plus_nat @ I2 @ one_one_nat ) ) @ ( F @ I2 ) ) ) @ one_one_int ) )
% 0.29/0.54 => ( ( ord_less_eq_int @ ( F @ zero_zero_nat ) @ K )
% 0.29/0.54 => ( ( ord_less_eq_int @ K @ ( F @ N2 ) )
% 0.29/0.54 => ? [I2: nat] :
% 0.29/0.54 ( ( ord_less_eq_nat @ I2 @ N2 )
% 0.29/0.54 & ( ( F @ I2 )
% 0.29/0.54 = K ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % nat0_intermed_int_val
% 0.29/0.54 thf(fact_1473_diff__diff__left,axiom,
% 0.29/0.54 ! [I: nat,J: nat,K: nat] :
% 0.29/0.54 ( ( minus_minus_nat @ ( minus_minus_nat @ I @ J ) @ K )
% 0.29/0.54 = ( minus_minus_nat @ I @ ( plus_plus_nat @ J @ K ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % diff_diff_left
% 0.29/0.54 thf(fact_1474_nat__1__eq__mult__iff,axiom,
% 0.29/0.54 ! [M2: nat,N2: nat] :
% 0.29/0.54 ( ( one_one_nat
% 0.29/0.54 = ( times_times_nat @ M2 @ N2 ) )
% 0.29/0.54 = ( ( M2 = one_one_nat )
% 0.29/0.54 & ( N2 = one_one_nat ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % nat_1_eq_mult_iff
% 0.29/0.54 thf(fact_1475_nat__mult__eq__1__iff,axiom,
% 0.29/0.54 ! [M2: nat,N2: nat] :
% 0.29/0.54 ( ( ( times_times_nat @ M2 @ N2 )
% 0.29/0.54 = one_one_nat )
% 0.29/0.54 = ( ( M2 = one_one_nat )
% 0.29/0.54 & ( N2 = one_one_nat ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % nat_mult_eq_1_iff
% 0.29/0.54 thf(fact_1476_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 0.29/0.54 ! [A: multis2468970476368604999at_nat] :
% 0.29/0.54 ( ( minus_4286766774447292334at_nat @ A @ A )
% 0.29/0.54 = zero_z1048942125864253310at_nat ) ).
% 0.29/0.54
% 0.29/0.54 % cancel_comm_monoid_add_class.diff_cancel
% 0.29/0.54 thf(fact_1477_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 0.29/0.54 ! [A: code_integer] :
% 0.29/0.54 ( ( minus_8373710615458151222nteger @ A @ A )
% 0.29/0.54 = zero_z3403309356797280102nteger ) ).
% 0.29/0.54
% 0.29/0.54 % cancel_comm_monoid_add_class.diff_cancel
% 0.29/0.54 thf(fact_1478_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 0.29/0.54 ! [A: rat] :
% 0.29/0.54 ( ( minus_minus_rat @ A @ A )
% 0.29/0.54 = zero_zero_rat ) ).
% 0.29/0.54
% 0.29/0.54 % cancel_comm_monoid_add_class.diff_cancel
% 0.29/0.54 thf(fact_1479_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 0.29/0.54 ! [A: nat] :
% 0.29/0.54 ( ( minus_minus_nat @ A @ A )
% 0.29/0.54 = zero_zero_nat ) ).
% 0.29/0.54
% 0.29/0.54 % cancel_comm_monoid_add_class.diff_cancel
% 0.29/0.54 thf(fact_1480_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 0.29/0.54 ! [A: int] :
% 0.29/0.54 ( ( minus_minus_int @ A @ A )
% 0.29/0.54 = zero_zero_int ) ).
% 0.29/0.54
% 0.29/0.54 % cancel_comm_monoid_add_class.diff_cancel
% 0.29/0.54 thf(fact_1481_diff__zero,axiom,
% 0.29/0.54 ! [A: multis2468970476368604999at_nat] :
% 0.29/0.54 ( ( minus_4286766774447292334at_nat @ A @ zero_z1048942125864253310at_nat )
% 0.29/0.54 = A ) ).
% 0.29/0.54
% 0.29/0.54 % diff_zero
% 0.29/0.54 thf(fact_1482_diff__zero,axiom,
% 0.29/0.54 ! [A: code_integer] :
% 0.29/0.54 ( ( minus_8373710615458151222nteger @ A @ zero_z3403309356797280102nteger )
% 0.29/0.54 = A ) ).
% 0.29/0.54
% 0.29/0.54 % diff_zero
% 0.29/0.54 thf(fact_1483_diff__zero,axiom,
% 0.29/0.54 ! [A: rat] :
% 0.29/0.54 ( ( minus_minus_rat @ A @ zero_zero_rat )
% 0.29/0.54 = A ) ).
% 0.29/0.54
% 0.29/0.54 % diff_zero
% 0.29/0.54 thf(fact_1484_diff__zero,axiom,
% 0.29/0.54 ! [A: nat] :
% 0.29/0.54 ( ( minus_minus_nat @ A @ zero_zero_nat )
% 0.29/0.54 = A ) ).
% 0.29/0.54
% 0.29/0.54 % diff_zero
% 0.29/0.54 thf(fact_1485_diff__zero,axiom,
% 0.29/0.54 ! [A: int] :
% 0.29/0.54 ( ( minus_minus_int @ A @ zero_zero_int )
% 0.29/0.54 = A ) ).
% 0.29/0.54
% 0.29/0.54 % diff_zero
% 0.29/0.54 thf(fact_1486_zero__diff,axiom,
% 0.29/0.54 ! [A: multis2468970476368604999at_nat] :
% 0.29/0.54 ( ( minus_4286766774447292334at_nat @ zero_z1048942125864253310at_nat @ A )
% 0.29/0.54 = zero_z1048942125864253310at_nat ) ).
% 0.29/0.54
% 0.29/0.54 % zero_diff
% 0.29/0.54 thf(fact_1487_zero__diff,axiom,
% 0.29/0.54 ! [A: nat] :
% 0.29/0.54 ( ( minus_minus_nat @ zero_zero_nat @ A )
% 0.29/0.54 = zero_zero_nat ) ).
% 0.29/0.54
% 0.29/0.54 % zero_diff
% 0.29/0.54 thf(fact_1488_diff__0__right,axiom,
% 0.29/0.54 ! [A: code_integer] :
% 0.29/0.54 ( ( minus_8373710615458151222nteger @ A @ zero_z3403309356797280102nteger )
% 0.29/0.54 = A ) ).
% 0.29/0.54
% 0.29/0.54 % diff_0_right
% 0.29/0.54 thf(fact_1489_diff__0__right,axiom,
% 0.29/0.54 ! [A: rat] :
% 0.29/0.54 ( ( minus_minus_rat @ A @ zero_zero_rat )
% 0.29/0.54 = A ) ).
% 0.29/0.54
% 0.29/0.54 % diff_0_right
% 0.29/0.54 thf(fact_1490_diff__0__right,axiom,
% 0.29/0.54 ! [A: int] :
% 0.29/0.54 ( ( minus_minus_int @ A @ zero_zero_int )
% 0.29/0.54 = A ) ).
% 0.29/0.54
% 0.29/0.54 % diff_0_right
% 0.29/0.54 thf(fact_1491_diff__self,axiom,
% 0.29/0.54 ! [A: code_integer] :
% 0.29/0.54 ( ( minus_8373710615458151222nteger @ A @ A )
% 0.29/0.54 = zero_z3403309356797280102nteger ) ).
% 0.29/0.54
% 0.29/0.54 % diff_self
% 0.29/0.54 thf(fact_1492_diff__self,axiom,
% 0.29/0.54 ! [A: rat] :
% 0.29/0.54 ( ( minus_minus_rat @ A @ A )
% 0.29/0.54 = zero_zero_rat ) ).
% 0.29/0.54
% 0.29/0.54 % diff_self
% 0.29/0.54 thf(fact_1493_diff__self,axiom,
% 0.29/0.54 ! [A: int] :
% 0.29/0.54 ( ( minus_minus_int @ A @ A )
% 0.29/0.54 = zero_zero_int ) ).
% 0.29/0.54
% 0.29/0.54 % diff_self
% 0.29/0.54 thf(fact_1494_mult_Oright__neutral,axiom,
% 0.29/0.54 ! [A: code_integer] :
% 0.29/0.54 ( ( times_3573771949741848930nteger @ A @ one_one_Code_integer )
% 0.29/0.54 = A ) ).
% 0.29/0.54
% 0.29/0.54 % mult.right_neutral
% 0.29/0.54 thf(fact_1495_mult_Oright__neutral,axiom,
% 0.29/0.54 ! [A: assn] :
% 0.29/0.54 ( ( times_times_assn @ A @ one_one_assn )
% 0.29/0.54 = A ) ).
% 0.29/0.54
% 0.29/0.54 % mult.right_neutral
% 0.29/0.54 thf(fact_1496_mult_Oright__neutral,axiom,
% 0.29/0.54 ! [A: rat] :
% 0.29/0.54 ( ( times_times_rat @ A @ one_one_rat )
% 0.29/0.54 = A ) ).
% 0.29/0.54
% 0.29/0.54 % mult.right_neutral
% 0.29/0.54 thf(fact_1497_mult_Oright__neutral,axiom,
% 0.29/0.54 ! [A: nat] :
% 0.29/0.54 ( ( times_times_nat @ A @ one_one_nat )
% 0.29/0.54 = A ) ).
% 0.29/0.54
% 0.29/0.54 % mult.right_neutral
% 0.29/0.54 thf(fact_1498_mult_Oright__neutral,axiom,
% 0.29/0.54 ! [A: int] :
% 0.29/0.54 ( ( times_times_int @ A @ one_one_int )
% 0.29/0.54 = A ) ).
% 0.29/0.54
% 0.29/0.54 % mult.right_neutral
% 0.29/0.54 thf(fact_1499_mult__1,axiom,
% 0.29/0.54 ! [A: code_integer] :
% 0.29/0.54 ( ( times_3573771949741848930nteger @ one_one_Code_integer @ A )
% 0.29/0.54 = A ) ).
% 0.29/0.54
% 0.29/0.54 % mult_1
% 0.29/0.54 thf(fact_1500_mult__1,axiom,
% 0.29/0.54 ! [A: assn] :
% 0.29/0.54 ( ( times_times_assn @ one_one_assn @ A )
% 0.29/0.54 = A ) ).
% 0.29/0.54
% 0.29/0.54 % mult_1
% 0.29/0.54 thf(fact_1501_mult__1,axiom,
% 0.29/0.54 ! [A: rat] :
% 0.29/0.54 ( ( times_times_rat @ one_one_rat @ A )
% 0.29/0.54 = A ) ).
% 0.29/0.54
% 0.29/0.54 % mult_1
% 0.29/0.54 thf(fact_1502_mult__1,axiom,
% 0.29/0.54 ! [A: nat] :
% 0.29/0.54 ( ( times_times_nat @ one_one_nat @ A )
% 0.29/0.54 = A ) ).
% 0.29/0.54
% 0.29/0.54 % mult_1
% 0.29/0.54 thf(fact_1503_mult__1,axiom,
% 0.29/0.54 ! [A: int] :
% 0.29/0.54 ( ( times_times_int @ one_one_int @ A )
% 0.29/0.54 = A ) ).
% 0.29/0.54
% 0.29/0.54 % mult_1
% 0.29/0.54 thf(fact_1504_add__diff__cancel__right_H,axiom,
% 0.29/0.54 ! [A: multis2468970476368604999at_nat,B: multis2468970476368604999at_nat] :
% 0.29/0.54 ( ( minus_4286766774447292334at_nat @ ( plus_p7104986032573967614at_nat @ A @ B ) @ B )
% 0.29/0.54 = A ) ).
% 0.29/0.54
% 0.29/0.54 % add_diff_cancel_right'
% 0.29/0.54 thf(fact_1505_add__diff__cancel__right_H,axiom,
% 0.29/0.54 ! [A: code_integer,B: code_integer] :
% 0.29/0.54 ( ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ B )
% 0.29/0.54 = A ) ).
% 0.29/0.54
% 0.29/0.54 % add_diff_cancel_right'
% 0.29/0.54 thf(fact_1506_add__diff__cancel__right_H,axiom,
% 0.29/0.54 ! [A: rat,B: rat] :
% 0.29/0.54 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 0.29/0.54 = A ) ).
% 0.29/0.54
% 0.29/0.54 % add_diff_cancel_right'
% 0.29/0.54 thf(fact_1507_add__diff__cancel__right_H,axiom,
% 0.29/0.54 ! [A: nat,B: nat] :
% 0.29/0.54 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 0.29/0.54 = A ) ).
% 0.29/0.54
% 0.29/0.54 % add_diff_cancel_right'
% 0.29/0.54 thf(fact_1508_add__diff__cancel__right_H,axiom,
% 0.29/0.54 ! [A: int,B: int] :
% 0.29/0.54 ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
% 0.29/0.54 = A ) ).
% 0.29/0.54
% 0.29/0.54 % add_diff_cancel_right'
% 0.29/0.54 thf(fact_1509_add__diff__cancel__right,axiom,
% 0.29/0.54 ! [A: multis2468970476368604999at_nat,C: multis2468970476368604999at_nat,B: multis2468970476368604999at_nat] :
% 0.29/0.54 ( ( minus_4286766774447292334at_nat @ ( plus_p7104986032573967614at_nat @ A @ C ) @ ( plus_p7104986032573967614at_nat @ B @ C ) )
% 0.29/0.54 = ( minus_4286766774447292334at_nat @ A @ B ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_diff_cancel_right
% 0.29/0.54 thf(fact_1510_add__diff__cancel__right,axiom,
% 0.29/0.54 ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.29/0.54 ( ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A @ C ) @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 0.29/0.54 = ( minus_8373710615458151222nteger @ A @ B ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_diff_cancel_right
% 0.29/0.54 thf(fact_1511_add__diff__cancel__right,axiom,
% 0.29/0.54 ! [A: rat,C: rat,B: rat] :
% 0.29/0.54 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 0.29/0.54 = ( minus_minus_rat @ A @ B ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_diff_cancel_right
% 0.29/0.54 thf(fact_1512_add__diff__cancel__right,axiom,
% 0.29/0.54 ! [A: nat,C: nat,B: nat] :
% 0.29/0.54 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 0.29/0.54 = ( minus_minus_nat @ A @ B ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_diff_cancel_right
% 0.29/0.54 thf(fact_1513_add__diff__cancel__right,axiom,
% 0.29/0.54 ! [A: int,C: int,B: int] :
% 0.29/0.54 ( ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 0.29/0.54 = ( minus_minus_int @ A @ B ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_diff_cancel_right
% 0.29/0.54 thf(fact_1514_add__diff__cancel__left_H,axiom,
% 0.29/0.54 ! [A: multis2468970476368604999at_nat,B: multis2468970476368604999at_nat] :
% 0.29/0.54 ( ( minus_4286766774447292334at_nat @ ( plus_p7104986032573967614at_nat @ A @ B ) @ A )
% 0.29/0.54 = B ) ).
% 0.29/0.54
% 0.29/0.54 % add_diff_cancel_left'
% 0.29/0.54 thf(fact_1515_add__diff__cancel__left_H,axiom,
% 0.29/0.54 ! [A: code_integer,B: code_integer] :
% 0.29/0.54 ( ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ A )
% 0.29/0.54 = B ) ).
% 0.29/0.54
% 0.29/0.54 % add_diff_cancel_left'
% 0.29/0.54 thf(fact_1516_add__diff__cancel__left_H,axiom,
% 0.29/0.54 ! [A: rat,B: rat] :
% 0.29/0.54 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ A )
% 0.29/0.54 = B ) ).
% 0.29/0.54
% 0.29/0.54 % add_diff_cancel_left'
% 0.29/0.54 thf(fact_1517_add__diff__cancel__left_H,axiom,
% 0.29/0.54 ! [A: nat,B: nat] :
% 0.29/0.54 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ A )
% 0.29/0.54 = B ) ).
% 0.29/0.54
% 0.29/0.54 % add_diff_cancel_left'
% 0.29/0.54 thf(fact_1518_add__diff__cancel__left_H,axiom,
% 0.29/0.54 ! [A: int,B: int] :
% 0.29/0.54 ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ A )
% 0.29/0.54 = B ) ).
% 0.29/0.54
% 0.29/0.54 % add_diff_cancel_left'
% 0.29/0.54 thf(fact_1519_add__diff__cancel__left,axiom,
% 0.29/0.54 ! [C: multis2468970476368604999at_nat,A: multis2468970476368604999at_nat,B: multis2468970476368604999at_nat] :
% 0.29/0.54 ( ( minus_4286766774447292334at_nat @ ( plus_p7104986032573967614at_nat @ C @ A ) @ ( plus_p7104986032573967614at_nat @ C @ B ) )
% 0.29/0.54 = ( minus_4286766774447292334at_nat @ A @ B ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_diff_cancel_left
% 0.29/0.54 thf(fact_1520_add__diff__cancel__left,axiom,
% 0.29/0.54 ! [C: code_integer,A: code_integer,B: code_integer] :
% 0.29/0.54 ( ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ C @ A ) @ ( plus_p5714425477246183910nteger @ C @ B ) )
% 0.29/0.54 = ( minus_8373710615458151222nteger @ A @ B ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_diff_cancel_left
% 0.29/0.54 thf(fact_1521_add__diff__cancel__left,axiom,
% 0.29/0.54 ! [C: rat,A: rat,B: rat] :
% 0.29/0.54 ( ( minus_minus_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 0.29/0.54 = ( minus_minus_rat @ A @ B ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_diff_cancel_left
% 0.29/0.54 thf(fact_1522_add__diff__cancel__left,axiom,
% 0.29/0.54 ! [C: nat,A: nat,B: nat] :
% 0.29/0.54 ( ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 0.29/0.54 = ( minus_minus_nat @ A @ B ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_diff_cancel_left
% 0.29/0.54 thf(fact_1523_add__diff__cancel__left,axiom,
% 0.29/0.54 ! [C: int,A: int,B: int] :
% 0.29/0.54 ( ( minus_minus_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 0.29/0.54 = ( minus_minus_int @ A @ B ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_diff_cancel_left
% 0.29/0.54 thf(fact_1524_diff__add__cancel,axiom,
% 0.29/0.54 ! [A: code_integer,B: code_integer] :
% 0.29/0.54 ( ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ B )
% 0.29/0.54 = A ) ).
% 0.29/0.54
% 0.29/0.54 % diff_add_cancel
% 0.29/0.54 thf(fact_1525_diff__add__cancel,axiom,
% 0.29/0.54 ! [A: rat,B: rat] :
% 0.29/0.54 ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ B )
% 0.29/0.54 = A ) ).
% 0.29/0.54
% 0.29/0.54 % diff_add_cancel
% 0.29/0.54 thf(fact_1526_diff__add__cancel,axiom,
% 0.29/0.54 ! [A: int,B: int] :
% 0.29/0.54 ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
% 0.29/0.54 = A ) ).
% 0.29/0.54
% 0.29/0.54 % diff_add_cancel
% 0.29/0.54 thf(fact_1527_add__diff__cancel,axiom,
% 0.29/0.54 ! [A: code_integer,B: code_integer] :
% 0.29/0.54 ( ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ B )
% 0.29/0.54 = A ) ).
% 0.29/0.54
% 0.29/0.54 % add_diff_cancel
% 0.29/0.54 thf(fact_1528_add__diff__cancel,axiom,
% 0.29/0.54 ! [A: rat,B: rat] :
% 0.29/0.54 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 0.29/0.54 = A ) ).
% 0.29/0.54
% 0.29/0.54 % add_diff_cancel
% 0.29/0.54 thf(fact_1529_add__diff__cancel,axiom,
% 0.29/0.54 ! [A: int,B: int] :
% 0.29/0.54 ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
% 0.29/0.54 = A ) ).
% 0.29/0.54
% 0.29/0.54 % add_diff_cancel
% 0.29/0.54 thf(fact_1530_minus__diff__eq,axiom,
% 0.29/0.54 ! [A: int,B: int] :
% 0.29/0.54 ( ( uminus_uminus_int @ ( minus_minus_int @ A @ B ) )
% 0.29/0.54 = ( minus_minus_int @ B @ A ) ) ).
% 0.29/0.54
% 0.29/0.54 % minus_diff_eq
% 0.29/0.54 thf(fact_1531_minus__diff__eq,axiom,
% 0.29/0.54 ! [A: code_integer,B: code_integer] :
% 0.29/0.54 ( ( uminus1351360451143612070nteger @ ( minus_8373710615458151222nteger @ A @ B ) )
% 0.29/0.54 = ( minus_8373710615458151222nteger @ B @ A ) ) ).
% 0.29/0.54
% 0.29/0.54 % minus_diff_eq
% 0.29/0.54 thf(fact_1532_minus__diff__eq,axiom,
% 0.29/0.54 ! [A: rat,B: rat] :
% 0.29/0.54 ( ( uminus_uminus_rat @ ( minus_minus_rat @ A @ B ) )
% 0.29/0.54 = ( minus_minus_rat @ B @ A ) ) ).
% 0.29/0.54
% 0.29/0.54 % minus_diff_eq
% 0.29/0.54 thf(fact_1533_Nat_Oadd__diff__assoc,axiom,
% 0.29/0.54 ! [K: nat,J: nat,I: nat] :
% 0.29/0.54 ( ( ord_less_eq_nat @ K @ J )
% 0.29/0.54 => ( ( plus_plus_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 0.29/0.54 = ( minus_minus_nat @ ( plus_plus_nat @ I @ J ) @ K ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % Nat.add_diff_assoc
% 0.29/0.54 thf(fact_1534_Nat_Oadd__diff__assoc2,axiom,
% 0.29/0.54 ! [K: nat,J: nat,I: nat] :
% 0.29/0.54 ( ( ord_less_eq_nat @ K @ J )
% 0.29/0.54 => ( ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I )
% 0.29/0.54 = ( minus_minus_nat @ ( plus_plus_nat @ J @ I ) @ K ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % Nat.add_diff_assoc2
% 0.29/0.54 thf(fact_1535_Nat_Odiff__diff__right,axiom,
% 0.29/0.54 ! [K: nat,J: nat,I: nat] :
% 0.29/0.54 ( ( ord_less_eq_nat @ K @ J )
% 0.29/0.54 => ( ( minus_minus_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 0.29/0.54 = ( minus_minus_nat @ ( plus_plus_nat @ I @ K ) @ J ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % Nat.diff_diff_right
% 0.29/0.54 thf(fact_1536_zle__add1__eq__le,axiom,
% 0.29/0.54 ! [W: int,Z: int] :
% 0.29/0.54 ( ( ord_less_int @ W @ ( plus_plus_int @ Z @ one_one_int ) )
% 0.29/0.54 = ( ord_less_eq_int @ W @ Z ) ) ).
% 0.29/0.54
% 0.29/0.54 % zle_add1_eq_le
% 0.29/0.54 thf(fact_1537_diff__ge__0__iff__ge,axiom,
% 0.29/0.54 ! [A: code_integer,B: code_integer] :
% 0.29/0.54 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( minus_8373710615458151222nteger @ A @ B ) )
% 0.29/0.54 = ( ord_le3102999989581377725nteger @ B @ A ) ) ).
% 0.29/0.54
% 0.29/0.54 % diff_ge_0_iff_ge
% 0.29/0.54 thf(fact_1538_diff__ge__0__iff__ge,axiom,
% 0.29/0.54 ! [A: rat,B: rat] :
% 0.29/0.54 ( ( ord_less_eq_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 0.29/0.54 = ( ord_less_eq_rat @ B @ A ) ) ).
% 0.29/0.54
% 0.29/0.54 % diff_ge_0_iff_ge
% 0.29/0.54 thf(fact_1539_diff__ge__0__iff__ge,axiom,
% 0.29/0.54 ! [A: int,B: int] :
% 0.29/0.54 ( ( ord_less_eq_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 0.29/0.54 = ( ord_less_eq_int @ B @ A ) ) ).
% 0.29/0.54
% 0.29/0.54 % diff_ge_0_iff_ge
% 0.29/0.54 thf(fact_1540_zero__comp__diff__simps_I1_J,axiom,
% 0.29/0.54 ! [A: code_integer,B: code_integer] :
% 0.29/0.54 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( minus_8373710615458151222nteger @ A @ B ) )
% 0.29/0.54 = ( ord_le3102999989581377725nteger @ B @ A ) ) ).
% 0.29/0.54
% 0.29/0.54 % zero_comp_diff_simps(1)
% 0.29/0.54 thf(fact_1541_zero__comp__diff__simps_I1_J,axiom,
% 0.29/0.54 ! [A: rat,B: rat] :
% 0.29/0.54 ( ( ord_less_eq_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 0.29/0.54 = ( ord_less_eq_rat @ B @ A ) ) ).
% 0.29/0.54
% 0.29/0.54 % zero_comp_diff_simps(1)
% 0.29/0.54 thf(fact_1542_zero__comp__diff__simps_I1_J,axiom,
% 0.29/0.54 ! [A: int,B: int] :
% 0.29/0.54 ( ( ord_less_eq_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 0.29/0.54 = ( ord_less_eq_int @ B @ A ) ) ).
% 0.29/0.54
% 0.29/0.54 % zero_comp_diff_simps(1)
% 0.29/0.54 thf(fact_1543_diff__gt__0__iff__gt,axiom,
% 0.29/0.54 ! [A: code_integer,B: code_integer] :
% 0.29/0.54 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( minus_8373710615458151222nteger @ A @ B ) )
% 0.29/0.54 = ( ord_le6747313008572928689nteger @ B @ A ) ) ).
% 0.29/0.54
% 0.29/0.54 % diff_gt_0_iff_gt
% 0.29/0.54 thf(fact_1544_diff__gt__0__iff__gt,axiom,
% 0.29/0.54 ! [A: rat,B: rat] :
% 0.29/0.54 ( ( ord_less_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 0.29/0.54 = ( ord_less_rat @ B @ A ) ) ).
% 0.29/0.54
% 0.29/0.54 % diff_gt_0_iff_gt
% 0.29/0.54 thf(fact_1545_diff__gt__0__iff__gt,axiom,
% 0.29/0.54 ! [A: int,B: int] :
% 0.29/0.54 ( ( ord_less_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 0.29/0.54 = ( ord_less_int @ B @ A ) ) ).
% 0.29/0.54
% 0.29/0.54 % diff_gt_0_iff_gt
% 0.29/0.54 thf(fact_1546_zero__comp__diff__simps_I2_J,axiom,
% 0.29/0.54 ! [A: code_integer,B: code_integer] :
% 0.29/0.54 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( minus_8373710615458151222nteger @ A @ B ) )
% 0.29/0.54 = ( ord_le6747313008572928689nteger @ B @ A ) ) ).
% 0.29/0.54
% 0.29/0.54 % zero_comp_diff_simps(2)
% 0.29/0.54 thf(fact_1547_zero__comp__diff__simps_I2_J,axiom,
% 0.29/0.54 ! [A: rat,B: rat] :
% 0.29/0.54 ( ( ord_less_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 0.29/0.54 = ( ord_less_rat @ B @ A ) ) ).
% 0.29/0.54
% 0.29/0.54 % zero_comp_diff_simps(2)
% 0.29/0.54 thf(fact_1548_zero__comp__diff__simps_I2_J,axiom,
% 0.29/0.54 ! [A: int,B: int] :
% 0.29/0.54 ( ( ord_less_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 0.29/0.54 = ( ord_less_int @ B @ A ) ) ).
% 0.29/0.54
% 0.29/0.54 % zero_comp_diff_simps(2)
% 0.29/0.54 thf(fact_1549_le__add__diff__inverse,axiom,
% 0.29/0.54 ! [B: code_integer,A: code_integer] :
% 0.29/0.54 ( ( ord_le3102999989581377725nteger @ B @ A )
% 0.29/0.54 => ( ( plus_p5714425477246183910nteger @ B @ ( minus_8373710615458151222nteger @ A @ B ) )
% 0.29/0.54 = A ) ) ).
% 0.29/0.54
% 0.29/0.54 % le_add_diff_inverse
% 0.29/0.54 thf(fact_1550_le__add__diff__inverse,axiom,
% 0.29/0.54 ! [B: rat,A: rat] :
% 0.29/0.54 ( ( ord_less_eq_rat @ B @ A )
% 0.29/0.54 => ( ( plus_plus_rat @ B @ ( minus_minus_rat @ A @ B ) )
% 0.29/0.54 = A ) ) ).
% 0.29/0.54
% 0.29/0.54 % le_add_diff_inverse
% 0.29/0.54 thf(fact_1551_le__add__diff__inverse,axiom,
% 0.29/0.54 ! [B: nat,A: nat] :
% 0.29/0.54 ( ( ord_less_eq_nat @ B @ A )
% 0.29/0.54 => ( ( plus_plus_nat @ B @ ( minus_minus_nat @ A @ B ) )
% 0.29/0.54 = A ) ) ).
% 0.29/0.54
% 0.29/0.54 % le_add_diff_inverse
% 0.29/0.54 thf(fact_1552_le__add__diff__inverse,axiom,
% 0.29/0.54 ! [B: int,A: int] :
% 0.29/0.54 ( ( ord_less_eq_int @ B @ A )
% 0.29/0.54 => ( ( plus_plus_int @ B @ ( minus_minus_int @ A @ B ) )
% 0.29/0.54 = A ) ) ).
% 0.29/0.54
% 0.29/0.54 % le_add_diff_inverse
% 0.29/0.54 thf(fact_1553_le__add__diff__inverse2,axiom,
% 0.29/0.54 ! [B: code_integer,A: code_integer] :
% 0.29/0.54 ( ( ord_le3102999989581377725nteger @ B @ A )
% 0.29/0.54 => ( ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ B )
% 0.29/0.54 = A ) ) ).
% 0.29/0.54
% 0.29/0.54 % le_add_diff_inverse2
% 0.29/0.54 thf(fact_1554_le__add__diff__inverse2,axiom,
% 0.29/0.54 ! [B: rat,A: rat] :
% 0.29/0.54 ( ( ord_less_eq_rat @ B @ A )
% 0.29/0.54 => ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ B )
% 0.29/0.54 = A ) ) ).
% 0.29/0.54
% 0.29/0.54 % le_add_diff_inverse2
% 0.29/0.54 thf(fact_1555_le__add__diff__inverse2,axiom,
% 0.29/0.54 ! [B: nat,A: nat] :
% 0.29/0.54 ( ( ord_less_eq_nat @ B @ A )
% 0.29/0.54 => ( ( plus_plus_nat @ ( minus_minus_nat @ A @ B ) @ B )
% 0.29/0.54 = A ) ) ).
% 0.29/0.54
% 0.29/0.54 % le_add_diff_inverse2
% 0.29/0.54 thf(fact_1556_le__add__diff__inverse2,axiom,
% 0.29/0.54 ! [B: int,A: int] :
% 0.29/0.54 ( ( ord_less_eq_int @ B @ A )
% 0.29/0.54 => ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
% 0.29/0.54 = A ) ) ).
% 0.29/0.54
% 0.29/0.54 % le_add_diff_inverse2
% 0.29/0.54 thf(fact_1557_mult__cancel__left1,axiom,
% 0.29/0.54 ! [C: code_integer,B: code_integer] :
% 0.29/0.54 ( ( C
% 0.29/0.54 = ( times_3573771949741848930nteger @ C @ B ) )
% 0.29/0.54 = ( ( C = zero_z3403309356797280102nteger )
% 0.29/0.54 | ( B = one_one_Code_integer ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % mult_cancel_left1
% 0.29/0.54 thf(fact_1558_mult__cancel__left1,axiom,
% 0.29/0.54 ! [C: rat,B: rat] :
% 0.29/0.54 ( ( C
% 0.29/0.54 = ( times_times_rat @ C @ B ) )
% 0.29/0.54 = ( ( C = zero_zero_rat )
% 0.29/0.54 | ( B = one_one_rat ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % mult_cancel_left1
% 0.29/0.54 thf(fact_1559_mult__cancel__left1,axiom,
% 0.29/0.54 ! [C: int,B: int] :
% 0.29/0.54 ( ( C
% 0.29/0.54 = ( times_times_int @ C @ B ) )
% 0.29/0.54 = ( ( C = zero_zero_int )
% 0.29/0.54 | ( B = one_one_int ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % mult_cancel_left1
% 0.29/0.54 thf(fact_1560_mult__cancel__left2,axiom,
% 0.29/0.54 ! [C: code_integer,A: code_integer] :
% 0.29/0.54 ( ( ( times_3573771949741848930nteger @ C @ A )
% 0.29/0.54 = C )
% 0.29/0.54 = ( ( C = zero_z3403309356797280102nteger )
% 0.29/0.54 | ( A = one_one_Code_integer ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % mult_cancel_left2
% 0.29/0.54 thf(fact_1561_mult__cancel__left2,axiom,
% 0.29/0.54 ! [C: rat,A: rat] :
% 0.29/0.54 ( ( ( times_times_rat @ C @ A )
% 0.29/0.54 = C )
% 0.29/0.54 = ( ( C = zero_zero_rat )
% 0.29/0.54 | ( A = one_one_rat ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % mult_cancel_left2
% 0.29/0.54 thf(fact_1562_mult__cancel__left2,axiom,
% 0.29/0.54 ! [C: int,A: int] :
% 0.29/0.54 ( ( ( times_times_int @ C @ A )
% 0.29/0.54 = C )
% 0.29/0.54 = ( ( C = zero_zero_int )
% 0.29/0.54 | ( A = one_one_int ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % mult_cancel_left2
% 0.29/0.54 thf(fact_1563_mult__cancel__right1,axiom,
% 0.29/0.54 ! [C: code_integer,B: code_integer] :
% 0.29/0.54 ( ( C
% 0.29/0.54 = ( times_3573771949741848930nteger @ B @ C ) )
% 0.29/0.54 = ( ( C = zero_z3403309356797280102nteger )
% 0.29/0.54 | ( B = one_one_Code_integer ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % mult_cancel_right1
% 0.29/0.54 thf(fact_1564_mult__cancel__right1,axiom,
% 0.29/0.54 ! [C: rat,B: rat] :
% 0.29/0.54 ( ( C
% 0.29/0.54 = ( times_times_rat @ B @ C ) )
% 0.29/0.54 = ( ( C = zero_zero_rat )
% 0.29/0.54 | ( B = one_one_rat ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % mult_cancel_right1
% 0.29/0.54 thf(fact_1565_mult__cancel__right1,axiom,
% 0.29/0.54 ! [C: int,B: int] :
% 0.29/0.54 ( ( C
% 0.29/0.54 = ( times_times_int @ B @ C ) )
% 0.29/0.54 = ( ( C = zero_zero_int )
% 0.29/0.54 | ( B = one_one_int ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % mult_cancel_right1
% 0.29/0.54 thf(fact_1566_mult__cancel__right2,axiom,
% 0.29/0.54 ! [A: code_integer,C: code_integer] :
% 0.29/0.54 ( ( ( times_3573771949741848930nteger @ A @ C )
% 0.29/0.54 = C )
% 0.29/0.54 = ( ( C = zero_z3403309356797280102nteger )
% 0.29/0.54 | ( A = one_one_Code_integer ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % mult_cancel_right2
% 0.29/0.54 thf(fact_1567_mult__cancel__right2,axiom,
% 0.29/0.54 ! [A: rat,C: rat] :
% 0.29/0.54 ( ( ( times_times_rat @ A @ C )
% 0.29/0.54 = C )
% 0.29/0.54 = ( ( C = zero_zero_rat )
% 0.29/0.54 | ( A = one_one_rat ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % mult_cancel_right2
% 0.29/0.54 thf(fact_1568_mult__cancel__right2,axiom,
% 0.29/0.54 ! [A: int,C: int] :
% 0.29/0.54 ( ( ( times_times_int @ A @ C )
% 0.29/0.54 = C )
% 0.29/0.54 = ( ( C = zero_zero_int )
% 0.29/0.54 | ( A = one_one_int ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % mult_cancel_right2
% 0.29/0.54 thf(fact_1569_diff__add__zero,axiom,
% 0.29/0.54 ! [A: multis2468970476368604999at_nat,B: multis2468970476368604999at_nat] :
% 0.29/0.54 ( ( minus_4286766774447292334at_nat @ A @ ( plus_p7104986032573967614at_nat @ A @ B ) )
% 0.29/0.54 = zero_z1048942125864253310at_nat ) ).
% 0.29/0.54
% 0.29/0.54 % diff_add_zero
% 0.29/0.54 thf(fact_1570_diff__add__zero,axiom,
% 0.29/0.54 ! [A: nat,B: nat] :
% 0.29/0.54 ( ( minus_minus_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 0.29/0.54 = zero_zero_nat ) ).
% 0.29/0.54
% 0.29/0.54 % diff_add_zero
% 0.29/0.54 thf(fact_1571_diff__numeral__special_I9_J,axiom,
% 0.29/0.54 ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ one_one_Code_integer )
% 0.29/0.54 = zero_z3403309356797280102nteger ) ).
% 0.29/0.54
% 0.29/0.54 % diff_numeral_special(9)
% 0.29/0.54 thf(fact_1572_diff__numeral__special_I9_J,axiom,
% 0.29/0.54 ( ( minus_minus_rat @ one_one_rat @ one_one_rat )
% 0.29/0.54 = zero_zero_rat ) ).
% 0.29/0.54
% 0.29/0.54 % diff_numeral_special(9)
% 0.29/0.54 thf(fact_1573_diff__numeral__special_I9_J,axiom,
% 0.29/0.54 ( ( minus_minus_int @ one_one_int @ one_one_int )
% 0.29/0.54 = zero_zero_int ) ).
% 0.29/0.54
% 0.29/0.54 % diff_numeral_special(9)
% 0.29/0.54 thf(fact_1574_diff__0,axiom,
% 0.29/0.54 ! [A: int] :
% 0.29/0.54 ( ( minus_minus_int @ zero_zero_int @ A )
% 0.29/0.54 = ( uminus_uminus_int @ A ) ) ).
% 0.29/0.54
% 0.29/0.54 % diff_0
% 0.29/0.54 thf(fact_1575_diff__0,axiom,
% 0.29/0.54 ! [A: code_integer] :
% 0.29/0.54 ( ( minus_8373710615458151222nteger @ zero_z3403309356797280102nteger @ A )
% 0.29/0.54 = ( uminus1351360451143612070nteger @ A ) ) ).
% 0.29/0.54
% 0.29/0.54 % diff_0
% 0.29/0.54 thf(fact_1576_diff__0,axiom,
% 0.29/0.54 ! [A: rat] :
% 0.29/0.54 ( ( minus_minus_rat @ zero_zero_rat @ A )
% 0.29/0.54 = ( uminus_uminus_rat @ A ) ) ).
% 0.29/0.54
% 0.29/0.54 % diff_0
% 0.29/0.54 thf(fact_1577_mult__minus1,axiom,
% 0.29/0.54 ! [Z: int] :
% 0.29/0.54 ( ( times_times_int @ ( uminus_uminus_int @ one_one_int ) @ Z )
% 0.29/0.54 = ( uminus_uminus_int @ Z ) ) ).
% 0.29/0.54
% 0.29/0.54 % mult_minus1
% 0.29/0.54 thf(fact_1578_mult__minus1,axiom,
% 0.29/0.54 ! [Z: code_integer] :
% 0.29/0.54 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ Z )
% 0.29/0.54 = ( uminus1351360451143612070nteger @ Z ) ) ).
% 0.29/0.54
% 0.29/0.54 % mult_minus1
% 0.29/0.54 thf(fact_1579_mult__minus1,axiom,
% 0.29/0.54 ! [Z: rat] :
% 0.29/0.54 ( ( times_times_rat @ ( uminus_uminus_rat @ one_one_rat ) @ Z )
% 0.29/0.54 = ( uminus_uminus_rat @ Z ) ) ).
% 0.29/0.54
% 0.29/0.54 % mult_minus1
% 0.29/0.54 thf(fact_1580_mult__minus1__right,axiom,
% 0.29/0.54 ! [Z: int] :
% 0.29/0.54 ( ( times_times_int @ Z @ ( uminus_uminus_int @ one_one_int ) )
% 0.29/0.54 = ( uminus_uminus_int @ Z ) ) ).
% 0.29/0.54
% 0.29/0.54 % mult_minus1_right
% 0.29/0.54 thf(fact_1581_mult__minus1__right,axiom,
% 0.29/0.54 ! [Z: code_integer] :
% 0.29/0.54 ( ( times_3573771949741848930nteger @ Z @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.29/0.54 = ( uminus1351360451143612070nteger @ Z ) ) ).
% 0.29/0.54
% 0.29/0.54 % mult_minus1_right
% 0.29/0.54 thf(fact_1582_mult__minus1__right,axiom,
% 0.29/0.54 ! [Z: rat] :
% 0.29/0.54 ( ( times_times_rat @ Z @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.29/0.54 = ( uminus_uminus_rat @ Z ) ) ).
% 0.29/0.54
% 0.29/0.54 % mult_minus1_right
% 0.29/0.54 thf(fact_1583_uminus__add__conv__diff,axiom,
% 0.29/0.54 ! [A: int,B: int] :
% 0.29/0.54 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B )
% 0.29/0.54 = ( minus_minus_int @ B @ A ) ) ).
% 0.29/0.54
% 0.29/0.54 % uminus_add_conv_diff
% 0.29/0.54 thf(fact_1584_uminus__add__conv__diff,axiom,
% 0.29/0.54 ! [A: code_integer,B: code_integer] :
% 0.29/0.54 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 0.29/0.54 = ( minus_8373710615458151222nteger @ B @ A ) ) ).
% 0.29/0.54
% 0.29/0.54 % uminus_add_conv_diff
% 0.29/0.54 thf(fact_1585_uminus__add__conv__diff,axiom,
% 0.29/0.54 ! [A: rat,B: rat] :
% 0.29/0.54 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ B )
% 0.29/0.54 = ( minus_minus_rat @ B @ A ) ) ).
% 0.29/0.54
% 0.29/0.54 % uminus_add_conv_diff
% 0.29/0.54 thf(fact_1586_diff__minus__eq__add,axiom,
% 0.29/0.54 ! [A: int,B: int] :
% 0.29/0.54 ( ( minus_minus_int @ A @ ( uminus_uminus_int @ B ) )
% 0.29/0.54 = ( plus_plus_int @ A @ B ) ) ).
% 0.29/0.54
% 0.29/0.54 % diff_minus_eq_add
% 0.29/0.54 thf(fact_1587_diff__minus__eq__add,axiom,
% 0.29/0.54 ! [A: code_integer,B: code_integer] :
% 0.29/0.54 ( ( minus_8373710615458151222nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 0.29/0.54 = ( plus_p5714425477246183910nteger @ A @ B ) ) ).
% 0.29/0.54
% 0.29/0.54 % diff_minus_eq_add
% 0.29/0.54 thf(fact_1588_diff__minus__eq__add,axiom,
% 0.29/0.54 ! [A: rat,B: rat] :
% 0.29/0.54 ( ( minus_minus_rat @ A @ ( uminus_uminus_rat @ B ) )
% 0.29/0.54 = ( plus_plus_rat @ A @ B ) ) ).
% 0.29/0.54
% 0.29/0.54 % diff_minus_eq_add
% 0.29/0.54 thf(fact_1589_diff__numeral__special_I12_J,axiom,
% 0.29/0.54 ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ one_one_int ) )
% 0.29/0.54 = zero_zero_int ) ).
% 0.29/0.54
% 0.29/0.54 % diff_numeral_special(12)
% 0.29/0.54 thf(fact_1590_diff__numeral__special_I12_J,axiom,
% 0.29/0.54 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.29/0.54 = zero_z3403309356797280102nteger ) ).
% 0.29/0.54
% 0.29/0.54 % diff_numeral_special(12)
% 0.29/0.54 thf(fact_1591_diff__numeral__special_I12_J,axiom,
% 0.29/0.54 ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.29/0.54 = zero_zero_rat ) ).
% 0.29/0.54
% 0.29/0.54 % diff_numeral_special(12)
% 0.29/0.54 thf(fact_1592_le__imp__0__less,axiom,
% 0.29/0.54 ! [Z: int] :
% 0.29/0.54 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 0.29/0.54 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ Z ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % le_imp_0_less
% 0.29/0.54 thf(fact_1593_q__pos__lemma,axiom,
% 0.29/0.54 ! [B3: int,Q4: int,R6: int] :
% 0.29/0.54 ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B3 @ Q4 ) @ R6 ) )
% 0.29/0.54 => ( ( ord_less_int @ R6 @ B3 )
% 0.29/0.54 => ( ( ord_less_int @ zero_zero_int @ B3 )
% 0.29/0.54 => ( ord_less_eq_int @ zero_zero_int @ Q4 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % q_pos_lemma
% 0.29/0.54 thf(fact_1594_zdiv__mono2__lemma,axiom,
% 0.29/0.54 ! [B: int,Q3: int,R2: int,B3: int,Q4: int,R6: int] :
% 0.29/0.54 ( ( ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R2 )
% 0.29/0.54 = ( plus_plus_int @ ( times_times_int @ B3 @ Q4 ) @ R6 ) )
% 0.29/0.54 => ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B3 @ Q4 ) @ R6 ) )
% 0.29/0.54 => ( ( ord_less_int @ R6 @ B3 )
% 0.29/0.54 => ( ( ord_less_eq_int @ zero_zero_int @ R2 )
% 0.29/0.54 => ( ( ord_less_int @ zero_zero_int @ B3 )
% 0.29/0.54 => ( ( ord_less_eq_int @ B3 @ B )
% 0.29/0.54 => ( ord_less_eq_int @ Q3 @ Q4 ) ) ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % zdiv_mono2_lemma
% 0.29/0.54 thf(fact_1595_zdiv__mono2__neg__lemma,axiom,
% 0.29/0.54 ! [B: int,Q3: int,R2: int,B3: int,Q4: int,R6: int] :
% 0.29/0.54 ( ( ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R2 )
% 0.29/0.54 = ( plus_plus_int @ ( times_times_int @ B3 @ Q4 ) @ R6 ) )
% 0.29/0.54 => ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ B3 @ Q4 ) @ R6 ) @ zero_zero_int )
% 0.29/0.54 => ( ( ord_less_int @ R2 @ B )
% 0.29/0.54 => ( ( ord_less_eq_int @ zero_zero_int @ R6 )
% 0.29/0.54 => ( ( ord_less_int @ zero_zero_int @ B3 )
% 0.29/0.54 => ( ( ord_less_eq_int @ B3 @ B )
% 0.29/0.54 => ( ord_less_eq_int @ Q4 @ Q3 ) ) ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % zdiv_mono2_neg_lemma
% 0.29/0.54 thf(fact_1596_unique__quotient__lemma,axiom,
% 0.29/0.54 ! [B: int,Q4: int,R6: int,Q3: int,R2: int] :
% 0.29/0.54 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ Q4 ) @ R6 ) @ ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R2 ) )
% 0.29/0.54 => ( ( ord_less_eq_int @ zero_zero_int @ R6 )
% 0.29/0.54 => ( ( ord_less_int @ R6 @ B )
% 0.29/0.54 => ( ( ord_less_int @ R2 @ B )
% 0.29/0.54 => ( ord_less_eq_int @ Q4 @ Q3 ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % unique_quotient_lemma
% 0.29/0.54 thf(fact_1597_unique__quotient__lemma__neg,axiom,
% 0.29/0.54 ! [B: int,Q4: int,R6: int,Q3: int,R2: int] :
% 0.29/0.54 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ Q4 ) @ R6 ) @ ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R2 ) )
% 0.29/0.54 => ( ( ord_less_eq_int @ R2 @ zero_zero_int )
% 0.29/0.54 => ( ( ord_less_int @ B @ R2 )
% 0.29/0.54 => ( ( ord_less_int @ B @ R6 )
% 0.29/0.54 => ( ord_less_eq_int @ Q3 @ Q4 ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % unique_quotient_lemma_neg
% 0.29/0.54 thf(fact_1598_int__ge__induct,axiom,
% 0.29/0.54 ! [K: int,I: int,P: int > $o] :
% 0.29/0.54 ( ( ord_less_eq_int @ K @ I )
% 0.29/0.54 => ( ( P @ K )
% 0.29/0.54 => ( ! [I2: int] :
% 0.29/0.54 ( ( ord_less_eq_int @ K @ I2 )
% 0.29/0.54 => ( ( P @ I2 )
% 0.29/0.54 => ( P @ ( plus_plus_int @ I2 @ one_one_int ) ) ) )
% 0.29/0.54 => ( P @ I ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % int_ge_induct
% 0.29/0.54 thf(fact_1599_int__induct,axiom,
% 0.29/0.54 ! [P: int > $o,K: int,I: int] :
% 0.29/0.54 ( ( P @ K )
% 0.29/0.54 => ( ! [I2: int] :
% 0.29/0.54 ( ( ord_less_eq_int @ K @ I2 )
% 0.29/0.54 => ( ( P @ I2 )
% 0.29/0.54 => ( P @ ( plus_plus_int @ I2 @ one_one_int ) ) ) )
% 0.29/0.54 => ( ! [I2: int] :
% 0.29/0.54 ( ( ord_less_eq_int @ I2 @ K )
% 0.29/0.54 => ( ( P @ I2 )
% 0.29/0.54 => ( P @ ( minus_minus_int @ I2 @ one_one_int ) ) ) )
% 0.29/0.54 => ( P @ I ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % int_induct
% 0.29/0.54 thf(fact_1600_zless__imp__add1__zle,axiom,
% 0.29/0.54 ! [W: int,Z: int] :
% 0.29/0.54 ( ( ord_less_int @ W @ Z )
% 0.29/0.54 => ( ord_less_eq_int @ ( plus_plus_int @ W @ one_one_int ) @ Z ) ) ).
% 0.29/0.54
% 0.29/0.54 % zless_imp_add1_zle
% 0.29/0.54 thf(fact_1601_add1__zle__eq,axiom,
% 0.29/0.54 ! [W: int,Z: int] :
% 0.29/0.54 ( ( ord_less_eq_int @ ( plus_plus_int @ W @ one_one_int ) @ Z )
% 0.29/0.54 = ( ord_less_int @ W @ Z ) ) ).
% 0.29/0.54
% 0.29/0.54 % add1_zle_eq
% 0.29/0.54 thf(fact_1602_nat__eq__add__iff1,axiom,
% 0.29/0.54 ! [J: nat,I: nat,U: nat,M2: nat,N2: nat] :
% 0.29/0.54 ( ( ord_less_eq_nat @ J @ I )
% 0.29/0.54 => ( ( ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M2 )
% 0.29/0.54 = ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 0.29/0.54 = ( ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M2 )
% 0.29/0.54 = N2 ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % nat_eq_add_iff1
% 0.29/0.54 thf(fact_1603_nat__eq__add__iff2,axiom,
% 0.29/0.54 ! [I: nat,J: nat,U: nat,M2: nat,N2: nat] :
% 0.29/0.54 ( ( ord_less_eq_nat @ I @ J )
% 0.29/0.54 => ( ( ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M2 )
% 0.29/0.54 = ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 0.29/0.54 = ( M2
% 0.29/0.54 = ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N2 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % nat_eq_add_iff2
% 0.29/0.54 thf(fact_1604_nat__le__add__iff1,axiom,
% 0.29/0.54 ! [J: nat,I: nat,U: nat,M2: nat,N2: nat] :
% 0.29/0.54 ( ( ord_less_eq_nat @ J @ I )
% 0.29/0.54 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M2 ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 0.29/0.54 = ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M2 ) @ N2 ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % nat_le_add_iff1
% 0.29/0.54 thf(fact_1605_nat__le__add__iff2,axiom,
% 0.29/0.54 ! [I: nat,J: nat,U: nat,M2: nat,N2: nat] :
% 0.29/0.54 ( ( ord_less_eq_nat @ I @ J )
% 0.29/0.54 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M2 ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 0.29/0.54 = ( ord_less_eq_nat @ M2 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N2 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % nat_le_add_iff2
% 0.29/0.54 thf(fact_1606_nat__diff__add__eq1,axiom,
% 0.29/0.54 ! [J: nat,I: nat,U: nat,M2: nat,N2: nat] :
% 0.29/0.54 ( ( ord_less_eq_nat @ J @ I )
% 0.29/0.54 => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M2 ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 0.29/0.54 = ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M2 ) @ N2 ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % nat_diff_add_eq1
% 0.29/0.54 thf(fact_1607_nat__diff__add__eq2,axiom,
% 0.29/0.54 ! [I: nat,J: nat,U: nat,M2: nat,N2: nat] :
% 0.29/0.54 ( ( ord_less_eq_nat @ I @ J )
% 0.29/0.54 => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M2 ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 0.29/0.54 = ( minus_minus_nat @ M2 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N2 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % nat_diff_add_eq2
% 0.29/0.54 thf(fact_1608_bounded__Max__nat,axiom,
% 0.29/0.54 ! [P: nat > $o,X: nat,M3: nat] :
% 0.29/0.54 ( ( P @ X )
% 0.29/0.54 => ( ! [X4: nat] :
% 0.29/0.54 ( ( P @ X4 )
% 0.29/0.54 => ( ord_less_eq_nat @ X4 @ M3 ) )
% 0.29/0.54 => ~ ! [M5: nat] :
% 0.29/0.54 ( ( P @ M5 )
% 0.29/0.54 => ~ ! [X8: nat] :
% 0.29/0.54 ( ( P @ X8 )
% 0.29/0.54 => ( ord_less_eq_nat @ X8 @ M5 ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % bounded_Max_nat
% 0.29/0.54 thf(fact_1609_subset__Collect__conv,axiom,
% 0.29/0.54 ! [S2: set_list_nat,P: list_nat > $o] :
% 0.29/0.54 ( ( ord_le6045566169113846134st_nat @ S2 @ ( collect_list_nat @ P ) )
% 0.29/0.54 = ( ! [X3: list_nat] :
% 0.29/0.54 ( ( member_list_nat @ X3 @ S2 )
% 0.29/0.54 => ( P @ X3 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % subset_Collect_conv
% 0.29/0.54 thf(fact_1610_subset__Collect__conv,axiom,
% 0.29/0.54 ! [S2: set_nat,P: nat > $o] :
% 0.29/0.54 ( ( ord_less_eq_set_nat @ S2 @ ( collect_nat @ P ) )
% 0.29/0.54 = ( ! [X3: nat] :
% 0.29/0.54 ( ( member_nat @ X3 @ S2 )
% 0.29/0.54 => ( P @ X3 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % subset_Collect_conv
% 0.29/0.54 thf(fact_1611_cancel__ab__semigroup__add__class_Odiff__right__commute,axiom,
% 0.29/0.54 ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.29/0.54 ( ( minus_8373710615458151222nteger @ ( minus_8373710615458151222nteger @ A @ C ) @ B )
% 0.29/0.54 = ( minus_8373710615458151222nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C ) ) ).
% 0.29/0.54
% 0.29/0.54 % cancel_ab_semigroup_add_class.diff_right_commute
% 0.29/0.54 thf(fact_1612_cancel__ab__semigroup__add__class_Odiff__right__commute,axiom,
% 0.29/0.54 ! [A: rat,C: rat,B: rat] :
% 0.29/0.54 ( ( minus_minus_rat @ ( minus_minus_rat @ A @ C ) @ B )
% 0.29/0.54 = ( minus_minus_rat @ ( minus_minus_rat @ A @ B ) @ C ) ) ).
% 0.29/0.54
% 0.29/0.54 % cancel_ab_semigroup_add_class.diff_right_commute
% 0.29/0.54 thf(fact_1613_cancel__ab__semigroup__add__class_Odiff__right__commute,axiom,
% 0.29/0.54 ! [A: nat,C: nat,B: nat] :
% 0.29/0.54 ( ( minus_minus_nat @ ( minus_minus_nat @ A @ C ) @ B )
% 0.29/0.54 = ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C ) ) ).
% 0.29/0.54
% 0.29/0.54 % cancel_ab_semigroup_add_class.diff_right_commute
% 0.29/0.54 thf(fact_1614_cancel__ab__semigroup__add__class_Odiff__right__commute,axiom,
% 0.29/0.54 ! [A: int,C: int,B: int] :
% 0.29/0.54 ( ( minus_minus_int @ ( minus_minus_int @ A @ C ) @ B )
% 0.29/0.54 = ( minus_minus_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 0.29/0.54
% 0.29/0.54 % cancel_ab_semigroup_add_class.diff_right_commute
% 0.29/0.54 thf(fact_1615_ab__semigroup__mult__class_Omult_Oleft__commute,axiom,
% 0.29/0.54 ! [B: assn,A: assn,C: assn] :
% 0.29/0.54 ( ( times_times_assn @ B @ ( times_times_assn @ A @ C ) )
% 0.29/0.54 = ( times_times_assn @ A @ ( times_times_assn @ B @ C ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % ab_semigroup_mult_class.mult.left_commute
% 0.29/0.54 thf(fact_1616_ab__semigroup__mult__class_Omult_Oleft__commute,axiom,
% 0.29/0.54 ! [B: rat,A: rat,C: rat] :
% 0.29/0.54 ( ( times_times_rat @ B @ ( times_times_rat @ A @ C ) )
% 0.29/0.54 = ( times_times_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % ab_semigroup_mult_class.mult.left_commute
% 0.29/0.54 thf(fact_1617_ab__semigroup__mult__class_Omult_Oleft__commute,axiom,
% 0.29/0.54 ! [B: nat,A: nat,C: nat] :
% 0.29/0.54 ( ( times_times_nat @ B @ ( times_times_nat @ A @ C ) )
% 0.29/0.54 = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % ab_semigroup_mult_class.mult.left_commute
% 0.29/0.54 thf(fact_1618_ab__semigroup__mult__class_Omult_Oleft__commute,axiom,
% 0.29/0.54 ! [B: int,A: int,C: int] :
% 0.29/0.54 ( ( times_times_int @ B @ ( times_times_int @ A @ C ) )
% 0.29/0.54 = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % ab_semigroup_mult_class.mult.left_commute
% 0.29/0.54 thf(fact_1619_ab__semigroup__mult__class_Omult_Ocommute,axiom,
% 0.29/0.54 ( times_times_assn
% 0.29/0.54 = ( ^ [A5: assn,B4: assn] : ( times_times_assn @ B4 @ A5 ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % ab_semigroup_mult_class.mult.commute
% 0.29/0.54 thf(fact_1620_ab__semigroup__mult__class_Omult_Ocommute,axiom,
% 0.29/0.54 ( times_times_rat
% 0.29/0.54 = ( ^ [A5: rat,B4: rat] : ( times_times_rat @ B4 @ A5 ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % ab_semigroup_mult_class.mult.commute
% 0.29/0.54 thf(fact_1621_ab__semigroup__mult__class_Omult_Ocommute,axiom,
% 0.29/0.54 ( times_times_nat
% 0.29/0.54 = ( ^ [A5: nat,B4: nat] : ( times_times_nat @ B4 @ A5 ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % ab_semigroup_mult_class.mult.commute
% 0.29/0.54 thf(fact_1622_ab__semigroup__mult__class_Omult_Ocommute,axiom,
% 0.29/0.54 ( times_times_int
% 0.29/0.54 = ( ^ [A5: int,B4: int] : ( times_times_int @ B4 @ A5 ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % ab_semigroup_mult_class.mult.commute
% 0.29/0.54 thf(fact_1623_mult_Oassoc,axiom,
% 0.29/0.54 ! [A: assn,B: assn,C: assn] :
% 0.29/0.54 ( ( times_times_assn @ ( times_times_assn @ A @ B ) @ C )
% 0.29/0.54 = ( times_times_assn @ A @ ( times_times_assn @ B @ C ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % mult.assoc
% 0.29/0.54 thf(fact_1624_mult_Oassoc,axiom,
% 0.29/0.54 ! [A: rat,B: rat,C: rat] :
% 0.29/0.54 ( ( times_times_rat @ ( times_times_rat @ A @ B ) @ C )
% 0.29/0.54 = ( times_times_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % mult.assoc
% 0.29/0.54 thf(fact_1625_mult_Oassoc,axiom,
% 0.29/0.54 ! [A: nat,B: nat,C: nat] :
% 0.29/0.54 ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
% 0.29/0.54 = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % mult.assoc
% 0.29/0.54 thf(fact_1626_mult_Oassoc,axiom,
% 0.29/0.54 ! [A: int,B: int,C: int] :
% 0.29/0.54 ( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
% 0.29/0.54 = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % mult.assoc
% 0.29/0.54 thf(fact_1627_diff__eq__diff__eq,axiom,
% 0.29/0.54 ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 0.29/0.54 ( ( ( minus_8373710615458151222nteger @ A @ B )
% 0.29/0.54 = ( minus_8373710615458151222nteger @ C @ D2 ) )
% 0.29/0.54 => ( ( A = B )
% 0.29/0.54 = ( C = D2 ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % diff_eq_diff_eq
% 0.29/0.54 thf(fact_1628_diff__eq__diff__eq,axiom,
% 0.29/0.54 ! [A: rat,B: rat,C: rat,D2: rat] :
% 0.29/0.54 ( ( ( minus_minus_rat @ A @ B )
% 0.29/0.54 = ( minus_minus_rat @ C @ D2 ) )
% 0.29/0.54 => ( ( A = B )
% 0.29/0.54 = ( C = D2 ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % diff_eq_diff_eq
% 0.29/0.54 thf(fact_1629_diff__eq__diff__eq,axiom,
% 0.29/0.54 ! [A: int,B: int,C: int,D2: int] :
% 0.29/0.54 ( ( ( minus_minus_int @ A @ B )
% 0.29/0.54 = ( minus_minus_int @ C @ D2 ) )
% 0.29/0.54 => ( ( A = B )
% 0.29/0.54 = ( C = D2 ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % diff_eq_diff_eq
% 0.29/0.54 thf(fact_1630_one__integer_Orsp,axiom,
% 0.29/0.54 one_one_int = one_one_int ).
% 0.29/0.54
% 0.29/0.54 % one_integer.rsp
% 0.29/0.54 thf(fact_1631_int__gr__induct,axiom,
% 0.29/0.54 ! [K: int,I: int,P: int > $o] :
% 0.29/0.54 ( ( ord_less_int @ K @ I )
% 0.29/0.54 => ( ( P @ ( plus_plus_int @ K @ one_one_int ) )
% 0.29/0.54 => ( ! [I2: int] :
% 0.29/0.54 ( ( ord_less_int @ K @ I2 )
% 0.29/0.54 => ( ( P @ I2 )
% 0.29/0.54 => ( P @ ( plus_plus_int @ I2 @ one_one_int ) ) ) )
% 0.29/0.54 => ( P @ I ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % int_gr_induct
% 0.29/0.54 thf(fact_1632_zless__add1__eq,axiom,
% 0.29/0.54 ! [W: int,Z: int] :
% 0.29/0.54 ( ( ord_less_int @ W @ ( plus_plus_int @ Z @ one_one_int ) )
% 0.29/0.54 = ( ( ord_less_int @ W @ Z )
% 0.29/0.54 | ( W = Z ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % zless_add1_eq
% 0.29/0.54 thf(fact_1633_odd__nonzero,axiom,
% 0.29/0.54 ! [Z: int] :
% 0.29/0.54 ( ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z ) @ Z )
% 0.29/0.54 != zero_zero_int ) ).
% 0.29/0.54
% 0.29/0.54 % odd_nonzero
% 0.29/0.54 thf(fact_1634_odd__less__0__iff,axiom,
% 0.29/0.54 ! [Z: int] :
% 0.29/0.54 ( ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z ) @ Z ) @ zero_zero_int )
% 0.29/0.54 = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 0.29/0.54
% 0.29/0.54 % odd_less_0_iff
% 0.29/0.54 thf(fact_1635_eq__add__iff1,axiom,
% 0.29/0.54 ! [A: code_integer,E: code_integer,C: code_integer,B: code_integer,D2: code_integer] :
% 0.29/0.54 ( ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ E ) @ C )
% 0.29/0.54 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ E ) @ D2 ) )
% 0.29/0.54 = ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ E ) @ C )
% 0.29/0.54 = D2 ) ) ).
% 0.29/0.54
% 0.29/0.54 % eq_add_iff1
% 0.29/0.54 thf(fact_1636_eq__add__iff1,axiom,
% 0.29/0.54 ! [A: rat,E: rat,C: rat,B: rat,D2: rat] :
% 0.29/0.54 ( ( ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C )
% 0.29/0.54 = ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D2 ) )
% 0.29/0.54 = ( ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E ) @ C )
% 0.29/0.54 = D2 ) ) ).
% 0.29/0.54
% 0.29/0.54 % eq_add_iff1
% 0.29/0.54 thf(fact_1637_eq__add__iff1,axiom,
% 0.29/0.54 ! [A: int,E: int,C: int,B: int,D2: int] :
% 0.29/0.54 ( ( ( plus_plus_int @ ( times_times_int @ A @ E ) @ C )
% 0.29/0.54 = ( plus_plus_int @ ( times_times_int @ B @ E ) @ D2 ) )
% 0.29/0.54 = ( ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E ) @ C )
% 0.29/0.54 = D2 ) ) ).
% 0.29/0.54
% 0.29/0.54 % eq_add_iff1
% 0.29/0.54 thf(fact_1638_eq__add__iff2,axiom,
% 0.29/0.54 ! [A: code_integer,E: code_integer,C: code_integer,B: code_integer,D2: code_integer] :
% 0.29/0.54 ( ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ E ) @ C )
% 0.29/0.54 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ E ) @ D2 ) )
% 0.29/0.54 = ( C
% 0.29/0.54 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ B @ A ) @ E ) @ D2 ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % eq_add_iff2
% 0.29/0.54 thf(fact_1639_eq__add__iff2,axiom,
% 0.29/0.54 ! [A: rat,E: rat,C: rat,B: rat,D2: rat] :
% 0.29/0.54 ( ( ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C )
% 0.29/0.54 = ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D2 ) )
% 0.29/0.54 = ( C
% 0.29/0.54 = ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E ) @ D2 ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % eq_add_iff2
% 0.29/0.54 thf(fact_1640_eq__add__iff2,axiom,
% 0.29/0.54 ! [A: int,E: int,C: int,B: int,D2: int] :
% 0.29/0.54 ( ( ( plus_plus_int @ ( times_times_int @ A @ E ) @ C )
% 0.29/0.54 = ( plus_plus_int @ ( times_times_int @ B @ E ) @ D2 ) )
% 0.29/0.54 = ( C
% 0.29/0.54 = ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E ) @ D2 ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % eq_add_iff2
% 0.29/0.54 thf(fact_1641_square__diff__square__factored,axiom,
% 0.29/0.54 ! [X: code_integer,Y: code_integer] :
% 0.29/0.54 ( ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ X @ X ) @ ( times_3573771949741848930nteger @ Y @ Y ) )
% 0.29/0.54 = ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ X @ Y ) @ ( minus_8373710615458151222nteger @ X @ Y ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % square_diff_square_factored
% 0.29/0.54 thf(fact_1642_square__diff__square__factored,axiom,
% 0.29/0.54 ! [X: rat,Y: rat] :
% 0.29/0.54 ( ( minus_minus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) )
% 0.29/0.54 = ( times_times_rat @ ( plus_plus_rat @ X @ Y ) @ ( minus_minus_rat @ X @ Y ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % square_diff_square_factored
% 0.29/0.54 thf(fact_1643_square__diff__square__factored,axiom,
% 0.29/0.54 ! [X: int,Y: int] :
% 0.29/0.54 ( ( minus_minus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) )
% 0.29/0.54 = ( times_times_int @ ( plus_plus_int @ X @ Y ) @ ( minus_minus_int @ X @ Y ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % square_diff_square_factored
% 0.29/0.54 thf(fact_1644_left__add__mult__distrib,axiom,
% 0.29/0.54 ! [I: nat,U: nat,J: nat,K: nat] :
% 0.29/0.54 ( ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ K ) )
% 0.29/0.54 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ I @ J ) @ U ) @ K ) ) ).
% 0.29/0.54
% 0.29/0.54 % left_add_mult_distrib
% 0.29/0.54 thf(fact_1645_nat__less__add__iff1,axiom,
% 0.29/0.54 ! [J: nat,I: nat,U: nat,M2: nat,N2: nat] :
% 0.29/0.54 ( ( ord_less_eq_nat @ J @ I )
% 0.29/0.54 => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M2 ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 0.29/0.54 = ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M2 ) @ N2 ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % nat_less_add_iff1
% 0.29/0.54 thf(fact_1646_nat__less__add__iff2,axiom,
% 0.29/0.54 ! [I: nat,J: nat,U: nat,M2: nat,N2: nat] :
% 0.29/0.54 ( ( ord_less_eq_nat @ I @ J )
% 0.29/0.54 => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M2 ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 0.29/0.54 = ( ord_less_nat @ M2 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N2 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % nat_less_add_iff2
% 0.29/0.54 thf(fact_1647_le__add__iff1,axiom,
% 0.29/0.54 ! [A: code_integer,E: code_integer,C: code_integer,B: code_integer,D2: code_integer] :
% 0.29/0.54 ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ E ) @ C ) @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ E ) @ D2 ) )
% 0.29/0.54 = ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ E ) @ C ) @ D2 ) ) ).
% 0.29/0.54
% 0.29/0.54 % le_add_iff1
% 0.29/0.54 thf(fact_1648_le__add__iff1,axiom,
% 0.29/0.54 ! [A: rat,E: rat,C: rat,B: rat,D2: rat] :
% 0.29/0.54 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D2 ) )
% 0.29/0.54 = ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E ) @ C ) @ D2 ) ) ).
% 0.29/0.54
% 0.29/0.54 % le_add_iff1
% 0.29/0.54 thf(fact_1649_le__add__iff1,axiom,
% 0.29/0.54 ! [A: int,E: int,C: int,B: int,D2: int] :
% 0.29/0.54 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D2 ) )
% 0.29/0.54 = ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E ) @ C ) @ D2 ) ) ).
% 0.29/0.54
% 0.29/0.54 % le_add_iff1
% 0.29/0.54 thf(fact_1650_le__add__iff2,axiom,
% 0.29/0.54 ! [A: code_integer,E: code_integer,C: code_integer,B: code_integer,D2: code_integer] :
% 0.29/0.54 ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ E ) @ C ) @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ E ) @ D2 ) )
% 0.29/0.54 = ( ord_le3102999989581377725nteger @ C @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ B @ A ) @ E ) @ D2 ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % le_add_iff2
% 0.29/0.54 thf(fact_1651_le__add__iff2,axiom,
% 0.29/0.54 ! [A: rat,E: rat,C: rat,B: rat,D2: rat] :
% 0.29/0.54 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D2 ) )
% 0.29/0.54 = ( ord_less_eq_rat @ C @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E ) @ D2 ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % le_add_iff2
% 0.29/0.54 thf(fact_1652_le__add__iff2,axiom,
% 0.29/0.54 ! [A: int,E: int,C: int,B: int,D2: int] :
% 0.29/0.54 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D2 ) )
% 0.29/0.54 = ( ord_less_eq_int @ C @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E ) @ D2 ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % le_add_iff2
% 0.29/0.54 thf(fact_1653_less__add__iff1,axiom,
% 0.29/0.54 ! [A: code_integer,E: code_integer,C: code_integer,B: code_integer,D2: code_integer] :
% 0.29/0.54 ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ E ) @ C ) @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ E ) @ D2 ) )
% 0.29/0.54 = ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ E ) @ C ) @ D2 ) ) ).
% 0.29/0.54
% 0.29/0.54 % less_add_iff1
% 0.29/0.54 thf(fact_1654_less__add__iff1,axiom,
% 0.29/0.54 ! [A: rat,E: rat,C: rat,B: rat,D2: rat] :
% 0.29/0.54 ( ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D2 ) )
% 0.29/0.54 = ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E ) @ C ) @ D2 ) ) ).
% 0.29/0.54
% 0.29/0.54 % less_add_iff1
% 0.29/0.54 thf(fact_1655_less__add__iff1,axiom,
% 0.29/0.54 ! [A: int,E: int,C: int,B: int,D2: int] :
% 0.29/0.54 ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D2 ) )
% 0.29/0.54 = ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E ) @ C ) @ D2 ) ) ).
% 0.29/0.54
% 0.29/0.54 % less_add_iff1
% 0.29/0.54 thf(fact_1656_less__add__iff2,axiom,
% 0.29/0.54 ! [A: code_integer,E: code_integer,C: code_integer,B: code_integer,D2: code_integer] :
% 0.29/0.54 ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ E ) @ C ) @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ E ) @ D2 ) )
% 0.29/0.54 = ( ord_le6747313008572928689nteger @ C @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ B @ A ) @ E ) @ D2 ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % less_add_iff2
% 0.29/0.54 thf(fact_1657_less__add__iff2,axiom,
% 0.29/0.54 ! [A: rat,E: rat,C: rat,B: rat,D2: rat] :
% 0.29/0.54 ( ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D2 ) )
% 0.29/0.54 = ( ord_less_rat @ C @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E ) @ D2 ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % less_add_iff2
% 0.29/0.54 thf(fact_1658_less__add__iff2,axiom,
% 0.29/0.54 ! [A: int,E: int,C: int,B: int,D2: int] :
% 0.29/0.54 ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D2 ) )
% 0.29/0.54 = ( ord_less_int @ C @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E ) @ D2 ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % less_add_iff2
% 0.29/0.54 thf(fact_1659_square__diff__one__factored,axiom,
% 0.29/0.54 ! [X: code_integer] :
% 0.29/0.54 ( ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ X @ X ) @ one_one_Code_integer )
% 0.29/0.54 = ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ X @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ X @ one_one_Code_integer ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % square_diff_one_factored
% 0.29/0.54 thf(fact_1660_square__diff__one__factored,axiom,
% 0.29/0.54 ! [X: rat] :
% 0.29/0.54 ( ( minus_minus_rat @ ( times_times_rat @ X @ X ) @ one_one_rat )
% 0.29/0.54 = ( times_times_rat @ ( plus_plus_rat @ X @ one_one_rat ) @ ( minus_minus_rat @ X @ one_one_rat ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % square_diff_one_factored
% 0.29/0.54 thf(fact_1661_square__diff__one__factored,axiom,
% 0.29/0.54 ! [X: int] :
% 0.29/0.54 ( ( minus_minus_int @ ( times_times_int @ X @ X ) @ one_one_int )
% 0.29/0.54 = ( times_times_int @ ( plus_plus_int @ X @ one_one_int ) @ ( minus_minus_int @ X @ one_one_int ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % square_diff_one_factored
% 0.29/0.54 thf(fact_1662_diff__eq__diff__less__eq,axiom,
% 0.29/0.54 ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 0.29/0.54 ( ( ( minus_8373710615458151222nteger @ A @ B )
% 0.29/0.54 = ( minus_8373710615458151222nteger @ C @ D2 ) )
% 0.29/0.54 => ( ( ord_le3102999989581377725nteger @ A @ B )
% 0.29/0.54 = ( ord_le3102999989581377725nteger @ C @ D2 ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % diff_eq_diff_less_eq
% 0.29/0.54 thf(fact_1663_diff__eq__diff__less__eq,axiom,
% 0.29/0.54 ! [A: rat,B: rat,C: rat,D2: rat] :
% 0.29/0.54 ( ( ( minus_minus_rat @ A @ B )
% 0.29/0.54 = ( minus_minus_rat @ C @ D2 ) )
% 0.29/0.54 => ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.54 = ( ord_less_eq_rat @ C @ D2 ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % diff_eq_diff_less_eq
% 0.29/0.54 thf(fact_1664_diff__eq__diff__less__eq,axiom,
% 0.29/0.54 ! [A: int,B: int,C: int,D2: int] :
% 0.29/0.54 ( ( ( minus_minus_int @ A @ B )
% 0.29/0.54 = ( minus_minus_int @ C @ D2 ) )
% 0.29/0.54 => ( ( ord_less_eq_int @ A @ B )
% 0.29/0.54 = ( ord_less_eq_int @ C @ D2 ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % diff_eq_diff_less_eq
% 0.29/0.54 thf(fact_1665_diff__right__mono,axiom,
% 0.29/0.54 ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.29/0.54 ( ( ord_le3102999989581377725nteger @ A @ B )
% 0.29/0.54 => ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ A @ C ) @ ( minus_8373710615458151222nteger @ B @ C ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % diff_right_mono
% 0.29/0.54 thf(fact_1666_diff__right__mono,axiom,
% 0.29/0.54 ! [A: rat,B: rat,C: rat] :
% 0.29/0.54 ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.54 => ( ord_less_eq_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ C ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % diff_right_mono
% 0.29/0.54 thf(fact_1667_diff__right__mono,axiom,
% 0.29/0.54 ! [A: int,B: int,C: int] :
% 0.29/0.54 ( ( ord_less_eq_int @ A @ B )
% 0.29/0.54 => ( ord_less_eq_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ C ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % diff_right_mono
% 0.29/0.54 thf(fact_1668_diff__left__mono,axiom,
% 0.29/0.54 ! [B: code_integer,A: code_integer,C: code_integer] :
% 0.29/0.54 ( ( ord_le3102999989581377725nteger @ B @ A )
% 0.29/0.54 => ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ C @ A ) @ ( minus_8373710615458151222nteger @ C @ B ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % diff_left_mono
% 0.29/0.54 thf(fact_1669_diff__left__mono,axiom,
% 0.29/0.54 ! [B: rat,A: rat,C: rat] :
% 0.29/0.54 ( ( ord_less_eq_rat @ B @ A )
% 0.29/0.54 => ( ord_less_eq_rat @ ( minus_minus_rat @ C @ A ) @ ( minus_minus_rat @ C @ B ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % diff_left_mono
% 0.29/0.54 thf(fact_1670_diff__left__mono,axiom,
% 0.29/0.54 ! [B: int,A: int,C: int] :
% 0.29/0.54 ( ( ord_less_eq_int @ B @ A )
% 0.29/0.54 => ( ord_less_eq_int @ ( minus_minus_int @ C @ A ) @ ( minus_minus_int @ C @ B ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % diff_left_mono
% 0.29/0.54 thf(fact_1671_diff__mono,axiom,
% 0.29/0.54 ! [A: code_integer,B: code_integer,D2: code_integer,C: code_integer] :
% 0.29/0.54 ( ( ord_le3102999989581377725nteger @ A @ B )
% 0.29/0.54 => ( ( ord_le3102999989581377725nteger @ D2 @ C )
% 0.29/0.54 => ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ A @ C ) @ ( minus_8373710615458151222nteger @ B @ D2 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % diff_mono
% 0.29/0.54 thf(fact_1672_diff__mono,axiom,
% 0.29/0.54 ! [A: rat,B: rat,D2: rat,C: rat] :
% 0.29/0.54 ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.54 => ( ( ord_less_eq_rat @ D2 @ C )
% 0.29/0.54 => ( ord_less_eq_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ D2 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % diff_mono
% 0.29/0.54 thf(fact_1673_diff__mono,axiom,
% 0.29/0.54 ! [A: int,B: int,D2: int,C: int] :
% 0.29/0.54 ( ( ord_less_eq_int @ A @ B )
% 0.29/0.54 => ( ( ord_less_eq_int @ D2 @ C )
% 0.29/0.54 => ( ord_less_eq_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ D2 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % diff_mono
% 0.29/0.54 thf(fact_1674_eq__iff__diff__eq__0,axiom,
% 0.29/0.54 ( ( ^ [Y4: code_integer,Z2: code_integer] : ( Y4 = Z2 ) )
% 0.29/0.54 = ( ^ [A5: code_integer,B4: code_integer] :
% 0.29/0.54 ( ( minus_8373710615458151222nteger @ A5 @ B4 )
% 0.29/0.54 = zero_z3403309356797280102nteger ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % eq_iff_diff_eq_0
% 0.29/0.54 thf(fact_1675_eq__iff__diff__eq__0,axiom,
% 0.29/0.54 ( ( ^ [Y4: rat,Z2: rat] : ( Y4 = Z2 ) )
% 0.29/0.54 = ( ^ [A5: rat,B4: rat] :
% 0.29/0.54 ( ( minus_minus_rat @ A5 @ B4 )
% 0.29/0.54 = zero_zero_rat ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % eq_iff_diff_eq_0
% 0.29/0.54 thf(fact_1676_eq__iff__diff__eq__0,axiom,
% 0.29/0.54 ( ( ^ [Y4: int,Z2: int] : ( Y4 = Z2 ) )
% 0.29/0.54 = ( ^ [A5: int,B4: int] :
% 0.29/0.54 ( ( minus_minus_int @ A5 @ B4 )
% 0.29/0.54 = zero_zero_int ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % eq_iff_diff_eq_0
% 0.29/0.54 thf(fact_1677_diff__strict__right__mono,axiom,
% 0.29/0.54 ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.29/0.54 ( ( ord_le6747313008572928689nteger @ A @ B )
% 0.29/0.54 => ( ord_le6747313008572928689nteger @ ( minus_8373710615458151222nteger @ A @ C ) @ ( minus_8373710615458151222nteger @ B @ C ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % diff_strict_right_mono
% 0.29/0.54 thf(fact_1678_diff__strict__right__mono,axiom,
% 0.29/0.54 ! [A: rat,B: rat,C: rat] :
% 0.29/0.54 ( ( ord_less_rat @ A @ B )
% 0.29/0.54 => ( ord_less_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ C ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % diff_strict_right_mono
% 0.29/0.54 thf(fact_1679_diff__strict__right__mono,axiom,
% 0.29/0.54 ! [A: int,B: int,C: int] :
% 0.29/0.54 ( ( ord_less_int @ A @ B )
% 0.29/0.54 => ( ord_less_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ C ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % diff_strict_right_mono
% 0.29/0.54 thf(fact_1680_diff__strict__left__mono,axiom,
% 0.29/0.54 ! [B: code_integer,A: code_integer,C: code_integer] :
% 0.29/0.54 ( ( ord_le6747313008572928689nteger @ B @ A )
% 0.29/0.54 => ( ord_le6747313008572928689nteger @ ( minus_8373710615458151222nteger @ C @ A ) @ ( minus_8373710615458151222nteger @ C @ B ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % diff_strict_left_mono
% 0.29/0.54 thf(fact_1681_diff__strict__left__mono,axiom,
% 0.29/0.54 ! [B: rat,A: rat,C: rat] :
% 0.29/0.54 ( ( ord_less_rat @ B @ A )
% 0.29/0.54 => ( ord_less_rat @ ( minus_minus_rat @ C @ A ) @ ( minus_minus_rat @ C @ B ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % diff_strict_left_mono
% 0.29/0.54 thf(fact_1682_diff__strict__left__mono,axiom,
% 0.29/0.54 ! [B: int,A: int,C: int] :
% 0.29/0.54 ( ( ord_less_int @ B @ A )
% 0.29/0.54 => ( ord_less_int @ ( minus_minus_int @ C @ A ) @ ( minus_minus_int @ C @ B ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % diff_strict_left_mono
% 0.29/0.54 thf(fact_1683_diff__eq__diff__less,axiom,
% 0.29/0.54 ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 0.29/0.54 ( ( ( minus_8373710615458151222nteger @ A @ B )
% 0.29/0.54 = ( minus_8373710615458151222nteger @ C @ D2 ) )
% 0.29/0.54 => ( ( ord_le6747313008572928689nteger @ A @ B )
% 0.29/0.54 = ( ord_le6747313008572928689nteger @ C @ D2 ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % diff_eq_diff_less
% 0.29/0.54 thf(fact_1684_diff__eq__diff__less,axiom,
% 0.29/0.54 ! [A: rat,B: rat,C: rat,D2: rat] :
% 0.29/0.54 ( ( ( minus_minus_rat @ A @ B )
% 0.29/0.54 = ( minus_minus_rat @ C @ D2 ) )
% 0.29/0.54 => ( ( ord_less_rat @ A @ B )
% 0.29/0.54 = ( ord_less_rat @ C @ D2 ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % diff_eq_diff_less
% 0.29/0.54 thf(fact_1685_diff__eq__diff__less,axiom,
% 0.29/0.54 ! [A: int,B: int,C: int,D2: int] :
% 0.29/0.54 ( ( ( minus_minus_int @ A @ B )
% 0.29/0.54 = ( minus_minus_int @ C @ D2 ) )
% 0.29/0.54 => ( ( ord_less_int @ A @ B )
% 0.29/0.54 = ( ord_less_int @ C @ D2 ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % diff_eq_diff_less
% 0.29/0.54 thf(fact_1686_diff__strict__mono,axiom,
% 0.29/0.54 ! [A: code_integer,B: code_integer,D2: code_integer,C: code_integer] :
% 0.29/0.54 ( ( ord_le6747313008572928689nteger @ A @ B )
% 0.29/0.54 => ( ( ord_le6747313008572928689nteger @ D2 @ C )
% 0.29/0.54 => ( ord_le6747313008572928689nteger @ ( minus_8373710615458151222nteger @ A @ C ) @ ( minus_8373710615458151222nteger @ B @ D2 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % diff_strict_mono
% 0.29/0.54 thf(fact_1687_diff__strict__mono,axiom,
% 0.29/0.54 ! [A: rat,B: rat,D2: rat,C: rat] :
% 0.29/0.54 ( ( ord_less_rat @ A @ B )
% 0.29/0.54 => ( ( ord_less_rat @ D2 @ C )
% 0.29/0.54 => ( ord_less_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ D2 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % diff_strict_mono
% 0.29/0.54 thf(fact_1688_diff__strict__mono,axiom,
% 0.29/0.54 ! [A: int,B: int,D2: int,C: int] :
% 0.29/0.54 ( ( ord_less_int @ A @ B )
% 0.29/0.54 => ( ( ord_less_int @ D2 @ C )
% 0.29/0.54 => ( ord_less_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ D2 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % diff_strict_mono
% 0.29/0.54 thf(fact_1689_diff__diff__eq,axiom,
% 0.29/0.54 ! [A: multis2468970476368604999at_nat,B: multis2468970476368604999at_nat,C: multis2468970476368604999at_nat] :
% 0.29/0.54 ( ( minus_4286766774447292334at_nat @ ( minus_4286766774447292334at_nat @ A @ B ) @ C )
% 0.29/0.54 = ( minus_4286766774447292334at_nat @ A @ ( plus_p7104986032573967614at_nat @ B @ C ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % diff_diff_eq
% 0.29/0.54 thf(fact_1690_diff__diff__eq,axiom,
% 0.29/0.54 ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.29/0.54 ( ( minus_8373710615458151222nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C )
% 0.29/0.54 = ( minus_8373710615458151222nteger @ A @ ( plus_p5714425477246183910nteger @ B @ C ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % diff_diff_eq
% 0.29/0.54 thf(fact_1691_diff__diff__eq,axiom,
% 0.29/0.54 ! [A: rat,B: rat,C: rat] :
% 0.29/0.54 ( ( minus_minus_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 0.29/0.54 = ( minus_minus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % diff_diff_eq
% 0.29/0.54 thf(fact_1692_diff__diff__eq,axiom,
% 0.29/0.54 ! [A: nat,B: nat,C: nat] :
% 0.29/0.54 ( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C )
% 0.29/0.54 = ( minus_minus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % diff_diff_eq
% 0.29/0.54 thf(fact_1693_diff__diff__eq,axiom,
% 0.29/0.54 ! [A: int,B: int,C: int] :
% 0.29/0.54 ( ( minus_minus_int @ ( minus_minus_int @ A @ B ) @ C )
% 0.29/0.54 = ( minus_minus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % diff_diff_eq
% 0.29/0.54 thf(fact_1694_add__implies__diff,axiom,
% 0.29/0.54 ! [C: multis2468970476368604999at_nat,B: multis2468970476368604999at_nat,A: multis2468970476368604999at_nat] :
% 0.29/0.54 ( ( ( plus_p7104986032573967614at_nat @ C @ B )
% 0.29/0.54 = A )
% 0.29/0.54 => ( C
% 0.29/0.54 = ( minus_4286766774447292334at_nat @ A @ B ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_implies_diff
% 0.29/0.54 thf(fact_1695_add__implies__diff,axiom,
% 0.29/0.54 ! [C: code_integer,B: code_integer,A: code_integer] :
% 0.29/0.54 ( ( ( plus_p5714425477246183910nteger @ C @ B )
% 0.29/0.54 = A )
% 0.29/0.54 => ( C
% 0.29/0.54 = ( minus_8373710615458151222nteger @ A @ B ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_implies_diff
% 0.29/0.54 thf(fact_1696_add__implies__diff,axiom,
% 0.29/0.54 ! [C: rat,B: rat,A: rat] :
% 0.29/0.54 ( ( ( plus_plus_rat @ C @ B )
% 0.29/0.54 = A )
% 0.29/0.54 => ( C
% 0.29/0.54 = ( minus_minus_rat @ A @ B ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_implies_diff
% 0.29/0.54 thf(fact_1697_add__implies__diff,axiom,
% 0.29/0.54 ! [C: nat,B: nat,A: nat] :
% 0.29/0.54 ( ( ( plus_plus_nat @ C @ B )
% 0.29/0.54 = A )
% 0.29/0.54 => ( C
% 0.29/0.54 = ( minus_minus_nat @ A @ B ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_implies_diff
% 0.29/0.54 thf(fact_1698_add__implies__diff,axiom,
% 0.29/0.54 ! [C: int,B: int,A: int] :
% 0.29/0.54 ( ( ( plus_plus_int @ C @ B )
% 0.29/0.54 = A )
% 0.29/0.54 => ( C
% 0.29/0.54 = ( minus_minus_int @ A @ B ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_implies_diff
% 0.29/0.54 thf(fact_1699_diff__add__eq__diff__diff__swap,axiom,
% 0.29/0.54 ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.29/0.54 ( ( minus_8373710615458151222nteger @ A @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 0.29/0.54 = ( minus_8373710615458151222nteger @ ( minus_8373710615458151222nteger @ A @ C ) @ B ) ) ).
% 0.29/0.54
% 0.29/0.54 % diff_add_eq_diff_diff_swap
% 0.29/0.54 thf(fact_1700_diff__add__eq__diff__diff__swap,axiom,
% 0.29/0.54 ! [A: rat,B: rat,C: rat] :
% 0.29/0.54 ( ( minus_minus_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 0.29/0.54 = ( minus_minus_rat @ ( minus_minus_rat @ A @ C ) @ B ) ) ).
% 0.29/0.54
% 0.29/0.54 % diff_add_eq_diff_diff_swap
% 0.29/0.54 thf(fact_1701_diff__add__eq__diff__diff__swap,axiom,
% 0.29/0.54 ! [A: int,B: int,C: int] :
% 0.29/0.54 ( ( minus_minus_int @ A @ ( plus_plus_int @ B @ C ) )
% 0.29/0.54 = ( minus_minus_int @ ( minus_minus_int @ A @ C ) @ B ) ) ).
% 0.29/0.54
% 0.29/0.54 % diff_add_eq_diff_diff_swap
% 0.29/0.54 thf(fact_1702_diff__add__eq,axiom,
% 0.29/0.54 ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.29/0.54 ( ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C )
% 0.29/0.54 = ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A @ C ) @ B ) ) ).
% 0.29/0.54
% 0.29/0.54 % diff_add_eq
% 0.29/0.54 thf(fact_1703_diff__add__eq,axiom,
% 0.29/0.54 ! [A: rat,B: rat,C: rat] :
% 0.29/0.54 ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 0.29/0.54 = ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ).
% 0.29/0.54
% 0.29/0.54 % diff_add_eq
% 0.29/0.54 thf(fact_1704_diff__add__eq,axiom,
% 0.29/0.54 ! [A: int,B: int,C: int] :
% 0.29/0.54 ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ C )
% 0.29/0.54 = ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ B ) ) ).
% 0.29/0.54
% 0.29/0.54 % diff_add_eq
% 0.29/0.54 thf(fact_1705_diff__diff__eq2,axiom,
% 0.29/0.54 ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.29/0.54 ( ( minus_8373710615458151222nteger @ A @ ( minus_8373710615458151222nteger @ B @ C ) )
% 0.29/0.54 = ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A @ C ) @ B ) ) ).
% 0.29/0.54
% 0.29/0.54 % diff_diff_eq2
% 0.29/0.54 thf(fact_1706_diff__diff__eq2,axiom,
% 0.29/0.54 ! [A: rat,B: rat,C: rat] :
% 0.29/0.54 ( ( minus_minus_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 0.29/0.54 = ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ).
% 0.29/0.54
% 0.29/0.54 % diff_diff_eq2
% 0.29/0.54 thf(fact_1707_diff__diff__eq2,axiom,
% 0.29/0.54 ! [A: int,B: int,C: int] :
% 0.29/0.54 ( ( minus_minus_int @ A @ ( minus_minus_int @ B @ C ) )
% 0.29/0.54 = ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ B ) ) ).
% 0.29/0.54
% 0.29/0.54 % diff_diff_eq2
% 0.29/0.54 thf(fact_1708_add__diff__eq,axiom,
% 0.29/0.54 ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.29/0.54 ( ( plus_p5714425477246183910nteger @ A @ ( minus_8373710615458151222nteger @ B @ C ) )
% 0.29/0.54 = ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_diff_eq
% 0.29/0.54 thf(fact_1709_add__diff__eq,axiom,
% 0.29/0.54 ! [A: rat,B: rat,C: rat] :
% 0.29/0.54 ( ( plus_plus_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 0.29/0.54 = ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_diff_eq
% 0.29/0.54 thf(fact_1710_add__diff__eq,axiom,
% 0.29/0.54 ! [A: int,B: int,C: int] :
% 0.29/0.54 ( ( plus_plus_int @ A @ ( minus_minus_int @ B @ C ) )
% 0.29/0.54 = ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 0.29/0.54
% 0.29/0.54 % add_diff_eq
% 0.29/0.54 thf(fact_1711_eq__diff__eq,axiom,
% 0.29/0.54 ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.29/0.54 ( ( A
% 0.29/0.54 = ( minus_8373710615458151222nteger @ C @ B ) )
% 0.29/0.54 = ( ( plus_p5714425477246183910nteger @ A @ B )
% 0.29/0.54 = C ) ) ).
% 0.29/0.54
% 0.29/0.54 % eq_diff_eq
% 0.29/0.54 thf(fact_1712_eq__diff__eq,axiom,
% 0.29/0.54 ! [A: rat,C: rat,B: rat] :
% 0.29/0.54 ( ( A
% 0.29/0.54 = ( minus_minus_rat @ C @ B ) )
% 0.29/0.54 = ( ( plus_plus_rat @ A @ B )
% 0.29/0.54 = C ) ) ).
% 0.29/0.54
% 0.29/0.54 % eq_diff_eq
% 0.29/0.54 thf(fact_1713_eq__diff__eq,axiom,
% 0.29/0.54 ! [A: int,C: int,B: int] :
% 0.29/0.54 ( ( A
% 0.29/0.54 = ( minus_minus_int @ C @ B ) )
% 0.29/0.54 = ( ( plus_plus_int @ A @ B )
% 0.29/0.54 = C ) ) ).
% 0.29/0.54
% 0.29/0.54 % eq_diff_eq
% 0.29/0.54 thf(fact_1714_diff__eq__eq,axiom,
% 0.29/0.54 ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.29/0.54 ( ( ( minus_8373710615458151222nteger @ A @ B )
% 0.29/0.54 = C )
% 0.29/0.54 = ( A
% 0.29/0.54 = ( plus_p5714425477246183910nteger @ C @ B ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % diff_eq_eq
% 0.29/0.54 thf(fact_1715_diff__eq__eq,axiom,
% 0.29/0.54 ! [A: rat,B: rat,C: rat] :
% 0.29/0.54 ( ( ( minus_minus_rat @ A @ B )
% 0.29/0.54 = C )
% 0.29/0.54 = ( A
% 0.29/0.54 = ( plus_plus_rat @ C @ B ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % diff_eq_eq
% 0.29/0.54 thf(fact_1716_diff__eq__eq,axiom,
% 0.29/0.54 ! [A: int,B: int,C: int] :
% 0.29/0.54 ( ( ( minus_minus_int @ A @ B )
% 0.29/0.54 = C )
% 0.29/0.54 = ( A
% 0.29/0.54 = ( plus_plus_int @ C @ B ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % diff_eq_eq
% 0.29/0.54 thf(fact_1717_group__cancel_Osub1,axiom,
% 0.29/0.54 ! [A2: code_integer,K: code_integer,A: code_integer,B: code_integer] :
% 0.29/0.54 ( ( A2
% 0.29/0.54 = ( plus_p5714425477246183910nteger @ K @ A ) )
% 0.29/0.54 => ( ( minus_8373710615458151222nteger @ A2 @ B )
% 0.29/0.54 = ( plus_p5714425477246183910nteger @ K @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % group_cancel.sub1
% 0.29/0.54 thf(fact_1718_group__cancel_Osub1,axiom,
% 0.29/0.54 ! [A2: rat,K: rat,A: rat,B: rat] :
% 0.29/0.54 ( ( A2
% 0.29/0.54 = ( plus_plus_rat @ K @ A ) )
% 0.29/0.54 => ( ( minus_minus_rat @ A2 @ B )
% 0.29/0.54 = ( plus_plus_rat @ K @ ( minus_minus_rat @ A @ B ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % group_cancel.sub1
% 0.29/0.54 thf(fact_1719_group__cancel_Osub1,axiom,
% 0.29/0.54 ! [A2: int,K: int,A: int,B: int] :
% 0.29/0.54 ( ( A2
% 0.29/0.54 = ( plus_plus_int @ K @ A ) )
% 0.29/0.54 => ( ( minus_minus_int @ A2 @ B )
% 0.29/0.54 = ( plus_plus_int @ K @ ( minus_minus_int @ A @ B ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % group_cancel.sub1
% 0.29/0.54 thf(fact_1720_minus__diff__commute,axiom,
% 0.29/0.54 ! [B: int,A: int] :
% 0.29/0.54 ( ( minus_minus_int @ ( uminus_uminus_int @ B ) @ A )
% 0.29/0.54 = ( minus_minus_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 0.29/0.54
% 0.29/0.54 % minus_diff_commute
% 0.29/0.54 thf(fact_1721_minus__diff__commute,axiom,
% 0.29/0.54 ! [B: code_integer,A: code_integer] :
% 0.29/0.54 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ B ) @ A )
% 0.29/0.54 = ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 0.29/0.54
% 0.29/0.54 % minus_diff_commute
% 0.29/0.54 thf(fact_1722_minus__diff__commute,axiom,
% 0.29/0.54 ! [B: rat,A: rat] :
% 0.29/0.54 ( ( minus_minus_rat @ ( uminus_uminus_rat @ B ) @ A )
% 0.29/0.54 = ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 0.29/0.54
% 0.29/0.54 % minus_diff_commute
% 0.29/0.54 thf(fact_1723_ring__class_Oring__distribs_I2_J,axiom,
% 0.29/0.54 ! [A: rat,B: rat,C: rat] :
% 0.29/0.54 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 0.29/0.54 = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % ring_class.ring_distribs(2)
% 0.29/0.54 thf(fact_1724_ring__class_Oring__distribs_I2_J,axiom,
% 0.29/0.54 ! [A: int,B: int,C: int] :
% 0.29/0.54 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 0.29/0.54 = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % ring_class.ring_distribs(2)
% 0.29/0.54 thf(fact_1725_ring__class_Oring__distribs_I1_J,axiom,
% 0.29/0.54 ! [A: rat,B: rat,C: rat] :
% 0.29/0.54 ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 0.29/0.54 = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % ring_class.ring_distribs(1)
% 0.29/0.54 thf(fact_1726_ring__class_Oring__distribs_I1_J,axiom,
% 0.29/0.54 ! [A: int,B: int,C: int] :
% 0.29/0.54 ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 0.29/0.54 = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % ring_class.ring_distribs(1)
% 0.33/0.54 thf(fact_1727_comm__semiring__class_Odistrib,axiom,
% 0.33/0.54 ! [A: rat,B: rat,C: rat] :
% 0.33/0.54 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 0.33/0.54 = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 0.33/0.54
% 0.33/0.54 % comm_semiring_class.distrib
% 0.33/0.54 thf(fact_1728_comm__semiring__class_Odistrib,axiom,
% 0.33/0.54 ! [A: nat,B: nat,C: nat] :
% 0.33/0.54 ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 0.33/0.54 = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ).
% 0.33/0.54
% 0.33/0.54 % comm_semiring_class.distrib
% 0.33/0.54 thf(fact_1729_comm__semiring__class_Odistrib,axiom,
% 0.33/0.54 ! [A: int,B: int,C: int] :
% 0.33/0.54 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 0.33/0.54 = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 0.33/0.54
% 0.33/0.54 % comm_semiring_class.distrib
% 0.33/0.54 thf(fact_1730_distrib__left,axiom,
% 0.33/0.54 ! [A: rat,B: rat,C: rat] :
% 0.33/0.54 ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 0.33/0.54 = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 0.33/0.54
% 0.33/0.54 % distrib_left
% 0.33/0.54 thf(fact_1731_distrib__left,axiom,
% 0.33/0.54 ! [A: nat,B: nat,C: nat] :
% 0.33/0.54 ( ( times_times_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 0.33/0.54 = ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ).
% 0.33/0.54
% 0.33/0.54 % distrib_left
% 0.33/0.54 thf(fact_1732_distrib__left,axiom,
% 0.33/0.54 ! [A: int,B: int,C: int] :
% 0.33/0.54 ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 0.33/0.54 = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 0.33/0.54
% 0.33/0.54 % distrib_left
% 0.33/0.54 thf(fact_1733_distrib__right,axiom,
% 0.33/0.54 ! [A: rat,B: rat,C: rat] :
% 0.33/0.54 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 0.33/0.54 = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 0.33/0.54
% 0.33/0.54 % distrib_right
% 0.33/0.54 thf(fact_1734_distrib__right,axiom,
% 0.33/0.54 ! [A: nat,B: nat,C: nat] :
% 0.33/0.54 ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 0.33/0.54 = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ).
% 0.33/0.54
% 0.33/0.54 % distrib_right
% 0.33/0.54 thf(fact_1735_distrib__right,axiom,
% 0.33/0.54 ! [A: int,B: int,C: int] :
% 0.33/0.54 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 0.33/0.54 = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 0.33/0.54
% 0.33/0.54 % distrib_right
% 0.33/0.54 thf(fact_1736_combine__common__factor,axiom,
% 0.33/0.54 ! [A: rat,E: rat,B: rat,C: rat] :
% 0.33/0.54 ( ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ C ) )
% 0.33/0.54 = ( plus_plus_rat @ ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ E ) @ C ) ) ).
% 0.33/0.54
% 0.33/0.54 % combine_common_factor
% 0.33/0.54 thf(fact_1737_combine__common__factor,axiom,
% 0.33/0.54 ! [A: nat,E: nat,B: nat,C: nat] :
% 0.33/0.54 ( ( plus_plus_nat @ ( times_times_nat @ A @ E ) @ ( plus_plus_nat @ ( times_times_nat @ B @ E ) @ C ) )
% 0.33/0.54 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ E ) @ C ) ) ).
% 0.33/0.54
% 0.33/0.54 % combine_common_factor
% 0.33/0.54 thf(fact_1738_combine__common__factor,axiom,
% 0.33/0.54 ! [A: int,E: int,B: int,C: int] :
% 0.33/0.54 ( ( plus_plus_int @ ( times_times_int @ A @ E ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ C ) )
% 0.33/0.54 = ( plus_plus_int @ ( times_times_int @ ( plus_plus_int @ A @ B ) @ E ) @ C ) ) ).
% 0.33/0.54
% 0.33/0.54 % combine_common_factor
% 0.33/0.54 thf(fact_1739_crossproduct__eq,axiom,
% 0.33/0.54 ! [W: rat,Y: rat,X: rat,Z: rat] :
% 0.33/0.54 ( ( ( plus_plus_rat @ ( times_times_rat @ W @ Y ) @ ( times_times_rat @ X @ Z ) )
% 0.33/0.54 = ( plus_plus_rat @ ( times_times_rat @ W @ Z ) @ ( times_times_rat @ X @ Y ) ) )
% 0.33/0.54 = ( ( W = X )
% 0.33/0.54 | ( Y = Z ) ) ) ).
% 0.33/0.54
% 0.33/0.54 % crossproduct_eq
% 0.33/0.54 thf(fact_1740_crossproduct__eq,axiom,
% 0.33/0.54 ! [W: nat,Y: nat,X: nat,Z: nat] :
% 0.33/0.54 ( ( ( plus_plus_nat @ ( times_times_nat @ W @ Y ) @ ( times_times_nat @ X @ Z ) )
% 0.33/0.54 = ( plus_plus_nat @ ( times_times_nat @ W @ Z ) @ ( times_times_nat @ X @ Y ) ) )
% 0.33/0.54 = ( ( W = X )
% 0.33/0.54 | ( Y = Z ) ) ) ).
% 0.33/0.54
% 0.33/0.54 % crossproduct_eq
% 0.33/0.54 thf(fact_1741_crossproduct__eq,axiom,
% 0.33/0.54 ! [W: int,Y: int,X: int,Z: int] :
% 0.33/0.54 ( ( ( plus_plus_int @ ( times_times_int @ W @ Y ) @ ( times_times_int @ X @ Z ) )
% 0.33/0.54 = ( plus_plus_int @ ( times_times_int @ W @ Z ) @ ( times_times_int @ X @ Y ) ) )
% 0.33/0.54 = ( ( W = X )
% 0.33/0.54 | ( Y = Z ) ) ) ).
% 0.33/0.54
% 0.33/0.54 % crossproduct_eq
% 0.33/0.55 thf(fact_1742_crossproduct__noteq,axiom,
% 0.33/0.55 ! [A: rat,B: rat,C: rat,D2: rat] :
% 0.33/0.55 ( ( ( A != B )
% 0.33/0.55 & ( C != D2 ) )
% 0.33/0.55 = ( ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D2 ) )
% 0.33/0.55 != ( plus_plus_rat @ ( times_times_rat @ A @ D2 ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % crossproduct_noteq
% 0.33/0.55 thf(fact_1743_crossproduct__noteq,axiom,
% 0.33/0.55 ! [A: nat,B: nat,C: nat,D2: nat] :
% 0.33/0.55 ( ( ( A != B )
% 0.33/0.55 & ( C != D2 ) )
% 0.33/0.55 = ( ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D2 ) )
% 0.33/0.55 != ( plus_plus_nat @ ( times_times_nat @ A @ D2 ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % crossproduct_noteq
% 0.33/0.55 thf(fact_1744_crossproduct__noteq,axiom,
% 0.33/0.55 ! [A: int,B: int,C: int,D2: int] :
% 0.33/0.55 ( ( ( A != B )
% 0.33/0.55 & ( C != D2 ) )
% 0.33/0.55 = ( ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D2 ) )
% 0.33/0.55 != ( plus_plus_int @ ( times_times_int @ A @ D2 ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % crossproduct_noteq
% 0.33/0.55 thf(fact_1745_comm__monoid__mult__class_Omult__1,axiom,
% 0.33/0.55 ! [A: code_integer] :
% 0.33/0.55 ( ( times_3573771949741848930nteger @ one_one_Code_integer @ A )
% 0.33/0.55 = A ) ).
% 0.33/0.55
% 0.33/0.55 % comm_monoid_mult_class.mult_1
% 0.33/0.55 thf(fact_1746_comm__monoid__mult__class_Omult__1,axiom,
% 0.33/0.55 ! [A: assn] :
% 0.33/0.55 ( ( times_times_assn @ one_one_assn @ A )
% 0.33/0.55 = A ) ).
% 0.33/0.55
% 0.33/0.55 % comm_monoid_mult_class.mult_1
% 0.33/0.55 thf(fact_1747_comm__monoid__mult__class_Omult__1,axiom,
% 0.33/0.55 ! [A: rat] :
% 0.33/0.55 ( ( times_times_rat @ one_one_rat @ A )
% 0.33/0.55 = A ) ).
% 0.33/0.55
% 0.33/0.55 % comm_monoid_mult_class.mult_1
% 0.33/0.55 thf(fact_1748_comm__monoid__mult__class_Omult__1,axiom,
% 0.33/0.55 ! [A: nat] :
% 0.33/0.55 ( ( times_times_nat @ one_one_nat @ A )
% 0.33/0.55 = A ) ).
% 0.33/0.55
% 0.33/0.55 % comm_monoid_mult_class.mult_1
% 0.33/0.55 thf(fact_1749_comm__monoid__mult__class_Omult__1,axiom,
% 0.33/0.55 ! [A: int] :
% 0.33/0.55 ( ( times_times_int @ one_one_int @ A )
% 0.33/0.55 = A ) ).
% 0.33/0.55
% 0.33/0.55 % comm_monoid_mult_class.mult_1
% 0.33/0.55 thf(fact_1750_mult_Ocomm__neutral,axiom,
% 0.33/0.55 ! [A: code_integer] :
% 0.33/0.55 ( ( times_3573771949741848930nteger @ A @ one_one_Code_integer )
% 0.33/0.55 = A ) ).
% 0.33/0.55
% 0.33/0.55 % mult.comm_neutral
% 0.33/0.55 thf(fact_1751_mult_Ocomm__neutral,axiom,
% 0.33/0.55 ! [A: assn] :
% 0.33/0.55 ( ( times_times_assn @ A @ one_one_assn )
% 0.33/0.55 = A ) ).
% 0.33/0.55
% 0.33/0.55 % mult.comm_neutral
% 0.33/0.55 thf(fact_1752_mult_Ocomm__neutral,axiom,
% 0.33/0.55 ! [A: rat] :
% 0.33/0.55 ( ( times_times_rat @ A @ one_one_rat )
% 0.33/0.55 = A ) ).
% 0.33/0.55
% 0.33/0.55 % mult.comm_neutral
% 0.33/0.55 thf(fact_1753_mult_Ocomm__neutral,axiom,
% 0.33/0.55 ! [A: nat] :
% 0.33/0.55 ( ( times_times_nat @ A @ one_one_nat )
% 0.33/0.55 = A ) ).
% 0.33/0.55
% 0.33/0.55 % mult.comm_neutral
% 0.33/0.55 thf(fact_1754_mult_Ocomm__neutral,axiom,
% 0.33/0.55 ! [A: int] :
% 0.33/0.55 ( ( times_times_int @ A @ one_one_int )
% 0.33/0.55 = A ) ).
% 0.33/0.55
% 0.33/0.55 % mult.comm_neutral
% 0.33/0.55 thf(fact_1755_abs__minus__commute,axiom,
% 0.33/0.55 ! [A: code_integer,B: code_integer] :
% 0.33/0.55 ( ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ B ) )
% 0.33/0.55 = ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ B @ A ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % abs_minus_commute
% 0.33/0.55 thf(fact_1756_abs__minus__commute,axiom,
% 0.33/0.55 ! [A: rat,B: rat] :
% 0.33/0.55 ( ( abs_abs_rat @ ( minus_minus_rat @ A @ B ) )
% 0.33/0.55 = ( abs_abs_rat @ ( minus_minus_rat @ B @ A ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % abs_minus_commute
% 0.33/0.55 thf(fact_1757_abs__minus__commute,axiom,
% 0.33/0.55 ! [A: int,B: int] :
% 0.33/0.55 ( ( abs_abs_int @ ( minus_minus_int @ A @ B ) )
% 0.33/0.55 = ( abs_abs_int @ ( minus_minus_int @ B @ A ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % abs_minus_commute
% 0.33/0.55 thf(fact_1758_Nat_Odiff__cancel,axiom,
% 0.33/0.55 ! [K: nat,M2: nat,N2: nat] :
% 0.33/0.55 ( ( minus_minus_nat @ ( plus_plus_nat @ K @ M2 ) @ ( plus_plus_nat @ K @ N2 ) )
% 0.33/0.55 = ( minus_minus_nat @ M2 @ N2 ) ) ).
% 0.33/0.55
% 0.33/0.55 % Nat.diff_cancel
% 0.33/0.55 thf(fact_1759_diff__cancel2,axiom,
% 0.33/0.55 ! [M2: nat,K: nat,N2: nat] :
% 0.33/0.55 ( ( minus_minus_nat @ ( plus_plus_nat @ M2 @ K ) @ ( plus_plus_nat @ N2 @ K ) )
% 0.33/0.55 = ( minus_minus_nat @ M2 @ N2 ) ) ).
% 0.33/0.55
% 0.33/0.55 % diff_cancel2
% 0.33/0.55 thf(fact_1760_diff__add__inverse,axiom,
% 0.33/0.55 ! [N2: nat,M2: nat] :
% 0.33/0.55 ( ( minus_minus_nat @ ( plus_plus_nat @ N2 @ M2 ) @ N2 )
% 0.33/0.55 = M2 ) ).
% 0.33/0.55
% 0.33/0.55 % diff_add_inverse
% 0.33/0.55 thf(fact_1761_diff__add__inverse2,axiom,
% 0.33/0.55 ! [M2: nat,N2: nat] :
% 0.33/0.55 ( ( minus_minus_nat @ ( plus_plus_nat @ M2 @ N2 ) @ N2 )
% 0.33/0.55 = M2 ) ).
% 0.33/0.55
% 0.33/0.55 % diff_add_inverse2
% 0.33/0.55 thf(fact_1762_le__diff__conv,axiom,
% 0.33/0.55 ! [J: nat,K: nat,I: nat] :
% 0.33/0.55 ( ( ord_less_eq_nat @ ( minus_minus_nat @ J @ K ) @ I )
% 0.33/0.55 = ( ord_less_eq_nat @ J @ ( plus_plus_nat @ I @ K ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % le_diff_conv
% 0.33/0.55 thf(fact_1763_Nat_Ole__diff__conv2,axiom,
% 0.33/0.55 ! [K: nat,J: nat,I: nat] :
% 0.33/0.55 ( ( ord_less_eq_nat @ K @ J )
% 0.33/0.55 => ( ( ord_less_eq_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 0.33/0.55 = ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ J ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % Nat.le_diff_conv2
% 0.33/0.55 thf(fact_1764_Nat_Odiff__add__assoc,axiom,
% 0.33/0.55 ! [K: nat,J: nat,I: nat] :
% 0.33/0.55 ( ( ord_less_eq_nat @ K @ J )
% 0.33/0.55 => ( ( minus_minus_nat @ ( plus_plus_nat @ I @ J ) @ K )
% 0.33/0.55 = ( plus_plus_nat @ I @ ( minus_minus_nat @ J @ K ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % Nat.diff_add_assoc
% 0.33/0.55 thf(fact_1765_Nat_Odiff__add__assoc2,axiom,
% 0.33/0.55 ! [K: nat,J: nat,I: nat] :
% 0.33/0.55 ( ( ord_less_eq_nat @ K @ J )
% 0.33/0.55 => ( ( minus_minus_nat @ ( plus_plus_nat @ J @ I ) @ K )
% 0.33/0.55 = ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % Nat.diff_add_assoc2
% 0.33/0.55 thf(fact_1766_Nat_Ole__imp__diff__is__add,axiom,
% 0.33/0.55 ! [I: nat,J: nat,K: nat] :
% 0.33/0.55 ( ( ord_less_eq_nat @ I @ J )
% 0.33/0.55 => ( ( ( minus_minus_nat @ J @ I )
% 0.33/0.55 = K )
% 0.33/0.55 = ( J
% 0.33/0.55 = ( plus_plus_nat @ K @ I ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % Nat.le_imp_diff_is_add
% 0.33/0.55 thf(fact_1767_add__mult__distrib,axiom,
% 0.33/0.55 ! [M2: nat,N2: nat,K: nat] :
% 0.33/0.55 ( ( times_times_nat @ ( plus_plus_nat @ M2 @ N2 ) @ K )
% 0.33/0.55 = ( plus_plus_nat @ ( times_times_nat @ M2 @ K ) @ ( times_times_nat @ N2 @ K ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % add_mult_distrib
% 0.33/0.55 thf(fact_1768_add__mult__distrib2,axiom,
% 0.33/0.55 ! [K: nat,M2: nat,N2: nat] :
% 0.33/0.55 ( ( times_times_nat @ K @ ( plus_plus_nat @ M2 @ N2 ) )
% 0.33/0.55 = ( plus_plus_nat @ ( times_times_nat @ K @ M2 ) @ ( times_times_nat @ K @ N2 ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % add_mult_distrib2
% 0.33/0.55 thf(fact_1769_mlex__leI,axiom,
% 0.33/0.55 ! [A: nat,A4: nat,B: nat,B3: nat,N6: nat] :
% 0.33/0.55 ( ( ord_less_eq_nat @ A @ A4 )
% 0.33/0.55 => ( ( ord_less_eq_nat @ B @ B3 )
% 0.33/0.55 => ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ A @ N6 ) @ B ) @ ( plus_plus_nat @ ( times_times_nat @ A4 @ N6 ) @ B3 ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % mlex_leI
% 0.33/0.55 thf(fact_1770_nat__mult__1,axiom,
% 0.33/0.55 ! [N2: nat] :
% 0.33/0.55 ( ( times_times_nat @ one_one_nat @ N2 )
% 0.33/0.55 = N2 ) ).
% 0.33/0.55
% 0.33/0.55 % nat_mult_1
% 0.33/0.55 thf(fact_1771_nat__mult__1__right,axiom,
% 0.33/0.55 ! [N2: nat] :
% 0.33/0.55 ( ( times_times_nat @ N2 @ one_one_nat )
% 0.33/0.55 = N2 ) ).
% 0.33/0.55
% 0.33/0.55 % nat_mult_1_right
% 0.33/0.55 thf(fact_1772_mult__eq__if,axiom,
% 0.33/0.55 ( times_times_nat
% 0.33/0.55 = ( ^ [M: nat,N4: nat] : ( if_nat @ ( M = zero_zero_nat ) @ zero_zero_nat @ ( plus_plus_nat @ N4 @ ( times_times_nat @ ( minus_minus_nat @ M @ one_one_nat ) @ N4 ) ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % mult_eq_if
% 0.33/0.55 thf(fact_1773_lambda__one,axiom,
% 0.33/0.55 ( ( ^ [X3: code_integer] : X3 )
% 0.33/0.55 = ( times_3573771949741848930nteger @ one_one_Code_integer ) ) ).
% 0.33/0.55
% 0.33/0.55 % lambda_one
% 0.33/0.55 thf(fact_1774_lambda__one,axiom,
% 0.33/0.55 ( ( ^ [X3: assn] : X3 )
% 0.33/0.55 = ( times_times_assn @ one_one_assn ) ) ).
% 0.33/0.55
% 0.33/0.55 % lambda_one
% 0.33/0.55 thf(fact_1775_lambda__one,axiom,
% 0.33/0.55 ( ( ^ [X3: rat] : X3 )
% 0.33/0.55 = ( times_times_rat @ one_one_rat ) ) ).
% 0.33/0.55
% 0.33/0.55 % lambda_one
% 0.33/0.55 thf(fact_1776_lambda__one,axiom,
% 0.33/0.55 ( ( ^ [X3: nat] : X3 )
% 0.33/0.55 = ( times_times_nat @ one_one_nat ) ) ).
% 0.33/0.55
% 0.33/0.55 % lambda_one
% 0.33/0.55 thf(fact_1777_lambda__one,axiom,
% 0.33/0.55 ( ( ^ [X3: int] : X3 )
% 0.33/0.55 = ( times_times_int @ one_one_int ) ) ).
% 0.33/0.55
% 0.33/0.55 % lambda_one
% 0.33/0.55 thf(fact_1778_is__num__normalize_I6_J,axiom,
% 0.33/0.55 ! [X: rat,Y: rat] :
% 0.33/0.55 ( ( neg_nu6808929389511037909um_rat @ X )
% 0.33/0.55 => ( ( neg_nu6808929389511037909um_rat @ Y )
% 0.33/0.55 => ( neg_nu6808929389511037909um_rat @ ( plus_plus_rat @ X @ Y ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % is_num_normalize(6)
% 0.33/0.55 thf(fact_1779_is__num__normalize_I6_J,axiom,
% 0.33/0.55 ! [X: int,Y: int] :
% 0.33/0.55 ( ( neg_nu7441568979088483369um_int @ X )
% 0.33/0.55 => ( ( neg_nu7441568979088483369um_int @ Y )
% 0.33/0.55 => ( neg_nu7441568979088483369um_int @ ( plus_plus_int @ X @ Y ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % is_num_normalize(6)
% 0.33/0.55 thf(fact_1780_is__num__add__commute,axiom,
% 0.33/0.55 ! [X: rat,Y: rat] :
% 0.33/0.55 ( ( neg_nu6808929389511037909um_rat @ X )
% 0.33/0.55 => ( ( neg_nu6808929389511037909um_rat @ Y )
% 0.33/0.55 => ( ( plus_plus_rat @ X @ Y )
% 0.33/0.55 = ( plus_plus_rat @ Y @ X ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % is_num_add_commute
% 0.33/0.55 thf(fact_1781_is__num__add__commute,axiom,
% 0.33/0.55 ! [X: int,Y: int] :
% 0.33/0.55 ( ( neg_nu7441568979088483369um_int @ X )
% 0.33/0.55 => ( ( neg_nu7441568979088483369um_int @ Y )
% 0.33/0.55 => ( ( plus_plus_int @ X @ Y )
% 0.33/0.55 = ( plus_plus_int @ Y @ X ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % is_num_add_commute
% 0.33/0.55 thf(fact_1782_is__num__add__left__commute,axiom,
% 0.33/0.55 ! [X: rat,Y: rat,Z: rat] :
% 0.33/0.55 ( ( neg_nu6808929389511037909um_rat @ X )
% 0.33/0.55 => ( ( neg_nu6808929389511037909um_rat @ Y )
% 0.33/0.55 => ( ( plus_plus_rat @ X @ ( plus_plus_rat @ Y @ Z ) )
% 0.33/0.55 = ( plus_plus_rat @ Y @ ( plus_plus_rat @ X @ Z ) ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % is_num_add_left_commute
% 0.33/0.55 thf(fact_1783_is__num__add__left__commute,axiom,
% 0.33/0.55 ! [X: int,Y: int,Z: int] :
% 0.33/0.55 ( ( neg_nu7441568979088483369um_int @ X )
% 0.33/0.55 => ( ( neg_nu7441568979088483369um_int @ Y )
% 0.33/0.55 => ( ( plus_plus_int @ X @ ( plus_plus_int @ Y @ Z ) )
% 0.33/0.55 = ( plus_plus_int @ Y @ ( plus_plus_int @ X @ Z ) ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % is_num_add_left_commute
% 0.33/0.55 thf(fact_1784_is__num__normalize_I4_J,axiom,
% 0.33/0.55 neg_nu2435721316971906650nteger @ one_one_Code_integer ).
% 0.33/0.55
% 0.33/0.55 % is_num_normalize(4)
% 0.33/0.55 thf(fact_1785_is__num__normalize_I4_J,axiom,
% 0.33/0.55 neg_nu6808929389511037909um_rat @ one_one_rat ).
% 0.33/0.55
% 0.33/0.55 % is_num_normalize(4)
% 0.33/0.55 thf(fact_1786_is__num__normalize_I4_J,axiom,
% 0.33/0.55 neg_nu7441568979088483369um_int @ one_one_int ).
% 0.33/0.55
% 0.33/0.55 % is_num_normalize(4)
% 0.33/0.55 thf(fact_1787_le__iff__diff__le__0,axiom,
% 0.33/0.55 ( ord_le3102999989581377725nteger
% 0.33/0.55 = ( ^ [A5: code_integer,B4: code_integer] : ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ A5 @ B4 ) @ zero_z3403309356797280102nteger ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % le_iff_diff_le_0
% 0.33/0.55 thf(fact_1788_le__iff__diff__le__0,axiom,
% 0.33/0.55 ( ord_less_eq_rat
% 0.33/0.55 = ( ^ [A5: rat,B4: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ A5 @ B4 ) @ zero_zero_rat ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % le_iff_diff_le_0
% 0.33/0.55 thf(fact_1789_le__iff__diff__le__0,axiom,
% 0.33/0.55 ( ord_less_eq_int
% 0.33/0.55 = ( ^ [A5: int,B4: int] : ( ord_less_eq_int @ ( minus_minus_int @ A5 @ B4 ) @ zero_zero_int ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % le_iff_diff_le_0
% 0.33/0.55 thf(fact_1790_less__iff__diff__less__0,axiom,
% 0.33/0.55 ( ord_le6747313008572928689nteger
% 0.33/0.55 = ( ^ [A5: code_integer,B4: code_integer] : ( ord_le6747313008572928689nteger @ ( minus_8373710615458151222nteger @ A5 @ B4 ) @ zero_z3403309356797280102nteger ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % less_iff_diff_less_0
% 0.33/0.55 thf(fact_1791_less__iff__diff__less__0,axiom,
% 0.33/0.55 ( ord_less_rat
% 0.33/0.55 = ( ^ [A5: rat,B4: rat] : ( ord_less_rat @ ( minus_minus_rat @ A5 @ B4 ) @ zero_zero_rat ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % less_iff_diff_less_0
% 0.33/0.55 thf(fact_1792_less__iff__diff__less__0,axiom,
% 0.33/0.55 ( ord_less_int
% 0.33/0.55 = ( ^ [A5: int,B4: int] : ( ord_less_int @ ( minus_minus_int @ A5 @ B4 ) @ zero_zero_int ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % less_iff_diff_less_0
% 0.33/0.55 thf(fact_1793_ordered__cancel__comm__monoid__diff__class_Ole__imp__diff__is__add,axiom,
% 0.33/0.55 ! [A: nat,B: nat,C: nat] :
% 0.33/0.55 ( ( ord_less_eq_nat @ A @ B )
% 0.33/0.55 => ( ( ord_less_eq_nat @ A @ B )
% 0.33/0.55 => ( ( ( minus_minus_nat @ B @ A )
% 0.33/0.55 = C )
% 0.33/0.55 = ( B
% 0.33/0.55 = ( plus_plus_nat @ C @ A ) ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % ordered_cancel_comm_monoid_diff_class.le_imp_diff_is_add
% 0.33/0.55 thf(fact_1794_ordered__cancel__comm__monoid__diff__class_Oadd__diff__inverse,axiom,
% 0.33/0.55 ! [A: nat,B: nat] :
% 0.33/0.55 ( ( ord_less_eq_nat @ A @ B )
% 0.33/0.55 => ( ( plus_plus_nat @ A @ ( minus_minus_nat @ B @ A ) )
% 0.33/0.55 = B ) ) ).
% 0.33/0.55
% 0.33/0.55 % ordered_cancel_comm_monoid_diff_class.add_diff_inverse
% 0.33/0.55 thf(fact_1795_ordered__cancel__comm__monoid__diff__class_Odiff__diff__right,axiom,
% 0.33/0.55 ! [A: nat,B: nat,C: nat] :
% 0.33/0.55 ( ( ord_less_eq_nat @ A @ B )
% 0.33/0.55 => ( ( minus_minus_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 0.33/0.55 = ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % ordered_cancel_comm_monoid_diff_class.diff_diff_right
% 0.33/0.55 thf(fact_1796_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc2,axiom,
% 0.33/0.55 ! [A: nat,B: nat,C: nat] :
% 0.33/0.55 ( ( ord_less_eq_nat @ A @ B )
% 0.33/0.55 => ( ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A )
% 0.33/0.55 = ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % ordered_cancel_comm_monoid_diff_class.diff_add_assoc2
% 0.33/0.55 thf(fact_1797_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc2,axiom,
% 0.33/0.55 ! [A: nat,B: nat,C: nat] :
% 0.33/0.55 ( ( ord_less_eq_nat @ A @ B )
% 0.33/0.55 => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C )
% 0.33/0.55 = ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % ordered_cancel_comm_monoid_diff_class.add_diff_assoc2
% 0.33/0.55 thf(fact_1798_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc,axiom,
% 0.33/0.55 ! [A: nat,B: nat,C: nat] :
% 0.33/0.55 ( ( ord_less_eq_nat @ A @ B )
% 0.33/0.55 => ( ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A )
% 0.33/0.55 = ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % ordered_cancel_comm_monoid_diff_class.diff_add_assoc
% 0.33/0.55 thf(fact_1799_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc,axiom,
% 0.33/0.55 ! [A: nat,B: nat,C: nat] :
% 0.33/0.55 ( ( ord_less_eq_nat @ A @ B )
% 0.33/0.55 => ( ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 0.33/0.55 = ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % ordered_cancel_comm_monoid_diff_class.add_diff_assoc
% 0.33/0.55 thf(fact_1800_ordered__cancel__comm__monoid__diff__class_Ole__diff__conv2,axiom,
% 0.33/0.55 ! [A: nat,B: nat,C: nat] :
% 0.33/0.55 ( ( ord_less_eq_nat @ A @ B )
% 0.33/0.55 => ( ( ord_less_eq_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 0.33/0.55 = ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % ordered_cancel_comm_monoid_diff_class.le_diff_conv2
% 0.33/0.55 thf(fact_1801_le__add__diff,axiom,
% 0.33/0.55 ! [A: nat,B: nat,C: nat] :
% 0.33/0.55 ( ( ord_less_eq_nat @ A @ B )
% 0.33/0.55 => ( ord_less_eq_nat @ C @ ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % le_add_diff
% 0.33/0.55 thf(fact_1802_ordered__cancel__comm__monoid__diff__class_Odiff__add,axiom,
% 0.33/0.55 ! [A: nat,B: nat] :
% 0.33/0.55 ( ( ord_less_eq_nat @ A @ B )
% 0.33/0.55 => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ A )
% 0.33/0.55 = B ) ) ).
% 0.33/0.55
% 0.33/0.55 % ordered_cancel_comm_monoid_diff_class.diff_add
% 0.33/0.55 thf(fact_1803_le__diff__eq,axiom,
% 0.33/0.55 ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.33/0.55 ( ( ord_le3102999989581377725nteger @ A @ ( minus_8373710615458151222nteger @ C @ B ) )
% 0.33/0.55 = ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C ) ) ).
% 0.33/0.55
% 0.33/0.55 % le_diff_eq
% 0.33/0.55 thf(fact_1804_le__diff__eq,axiom,
% 0.33/0.55 ! [A: rat,C: rat,B: rat] :
% 0.33/0.55 ( ( ord_less_eq_rat @ A @ ( minus_minus_rat @ C @ B ) )
% 0.33/0.55 = ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 0.33/0.55
% 0.33/0.55 % le_diff_eq
% 0.33/0.55 thf(fact_1805_le__diff__eq,axiom,
% 0.33/0.55 ! [A: int,C: int,B: int] :
% 0.33/0.55 ( ( ord_less_eq_int @ A @ ( minus_minus_int @ C @ B ) )
% 0.33/0.55 = ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 0.33/0.55
% 0.33/0.55 % le_diff_eq
% 0.33/0.55 thf(fact_1806_diff__le__eq,axiom,
% 0.33/0.55 ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.33/0.55 ( ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C )
% 0.33/0.55 = ( ord_le3102999989581377725nteger @ A @ ( plus_p5714425477246183910nteger @ C @ B ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % diff_le_eq
% 0.33/0.55 thf(fact_1807_diff__le__eq,axiom,
% 0.33/0.55 ! [A: rat,B: rat,C: rat] :
% 0.33/0.55 ( ( ord_less_eq_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 0.33/0.55 = ( ord_less_eq_rat @ A @ ( plus_plus_rat @ C @ B ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % diff_le_eq
% 0.33/0.55 thf(fact_1808_diff__le__eq,axiom,
% 0.33/0.55 ! [A: int,B: int,C: int] :
% 0.33/0.55 ( ( ord_less_eq_int @ ( minus_minus_int @ A @ B ) @ C )
% 0.33/0.55 = ( ord_less_eq_int @ A @ ( plus_plus_int @ C @ B ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % diff_le_eq
% 0.33/0.55 thf(fact_1809_add__le__imp__le__diff,axiom,
% 0.33/0.55 ! [I: code_integer,K: code_integer,N2: code_integer] :
% 0.33/0.55 ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ I @ K ) @ N2 )
% 0.33/0.55 => ( ord_le3102999989581377725nteger @ I @ ( minus_8373710615458151222nteger @ N2 @ K ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % add_le_imp_le_diff
% 0.33/0.55 thf(fact_1810_add__le__imp__le__diff,axiom,
% 0.33/0.55 ! [I: rat,K: rat,N2: rat] :
% 0.33/0.55 ( ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ N2 )
% 0.33/0.55 => ( ord_less_eq_rat @ I @ ( minus_minus_rat @ N2 @ K ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % add_le_imp_le_diff
% 0.33/0.55 thf(fact_1811_add__le__imp__le__diff,axiom,
% 0.33/0.55 ! [I: nat,K: nat,N2: nat] :
% 0.33/0.55 ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N2 )
% 0.33/0.55 => ( ord_less_eq_nat @ I @ ( minus_minus_nat @ N2 @ K ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % add_le_imp_le_diff
% 0.33/0.55 thf(fact_1812_add__le__imp__le__diff,axiom,
% 0.33/0.55 ! [I: int,K: int,N2: int] :
% 0.33/0.55 ( ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ N2 )
% 0.33/0.55 => ( ord_less_eq_int @ I @ ( minus_minus_int @ N2 @ K ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % add_le_imp_le_diff
% 0.33/0.55 thf(fact_1813_add__le__add__imp__diff__le,axiom,
% 0.33/0.55 ! [I: code_integer,K: code_integer,N2: code_integer,J: code_integer] :
% 0.33/0.55 ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ I @ K ) @ N2 )
% 0.33/0.55 => ( ( ord_le3102999989581377725nteger @ N2 @ ( plus_p5714425477246183910nteger @ J @ K ) )
% 0.33/0.55 => ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ I @ K ) @ N2 )
% 0.33/0.55 => ( ( ord_le3102999989581377725nteger @ N2 @ ( plus_p5714425477246183910nteger @ J @ K ) )
% 0.33/0.55 => ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ N2 @ K ) @ J ) ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % add_le_add_imp_diff_le
% 0.33/0.55 thf(fact_1814_add__le__add__imp__diff__le,axiom,
% 0.33/0.55 ! [I: rat,K: rat,N2: rat,J: rat] :
% 0.33/0.55 ( ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ N2 )
% 0.33/0.55 => ( ( ord_less_eq_rat @ N2 @ ( plus_plus_rat @ J @ K ) )
% 0.33/0.55 => ( ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ N2 )
% 0.33/0.55 => ( ( ord_less_eq_rat @ N2 @ ( plus_plus_rat @ J @ K ) )
% 0.33/0.55 => ( ord_less_eq_rat @ ( minus_minus_rat @ N2 @ K ) @ J ) ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % add_le_add_imp_diff_le
% 0.33/0.55 thf(fact_1815_add__le__add__imp__diff__le,axiom,
% 0.33/0.55 ! [I: nat,K: nat,N2: nat,J: nat] :
% 0.33/0.55 ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N2 )
% 0.33/0.55 => ( ( ord_less_eq_nat @ N2 @ ( plus_plus_nat @ J @ K ) )
% 0.33/0.55 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N2 )
% 0.33/0.55 => ( ( ord_less_eq_nat @ N2 @ ( plus_plus_nat @ J @ K ) )
% 0.33/0.55 => ( ord_less_eq_nat @ ( minus_minus_nat @ N2 @ K ) @ J ) ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % add_le_add_imp_diff_le
% 0.33/0.55 thf(fact_1816_add__le__add__imp__diff__le,axiom,
% 0.33/0.55 ! [I: int,K: int,N2: int,J: int] :
% 0.33/0.55 ( ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ N2 )
% 0.33/0.55 => ( ( ord_less_eq_int @ N2 @ ( plus_plus_int @ J @ K ) )
% 0.33/0.55 => ( ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ N2 )
% 0.33/0.55 => ( ( ord_less_eq_int @ N2 @ ( plus_plus_int @ J @ K ) )
% 0.33/0.55 => ( ord_less_eq_int @ ( minus_minus_int @ N2 @ K ) @ J ) ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % add_le_add_imp_diff_le
% 0.33/0.55 thf(fact_1817_less__diff__eq,axiom,
% 0.33/0.55 ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.33/0.55 ( ( ord_le6747313008572928689nteger @ A @ ( minus_8373710615458151222nteger @ C @ B ) )
% 0.33/0.55 = ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C ) ) ).
% 0.33/0.55
% 0.33/0.55 % less_diff_eq
% 0.33/0.55 thf(fact_1818_less__diff__eq,axiom,
% 0.33/0.55 ! [A: rat,C: rat,B: rat] :
% 0.33/0.55 ( ( ord_less_rat @ A @ ( minus_minus_rat @ C @ B ) )
% 0.33/0.55 = ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 0.33/0.55
% 0.33/0.55 % less_diff_eq
% 0.33/0.55 thf(fact_1819_less__diff__eq,axiom,
% 0.33/0.55 ! [A: int,C: int,B: int] :
% 0.33/0.55 ( ( ord_less_int @ A @ ( minus_minus_int @ C @ B ) )
% 0.33/0.55 = ( ord_less_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 0.33/0.55
% 0.33/0.55 % less_diff_eq
% 0.33/0.55 thf(fact_1820_diff__less__eq,axiom,
% 0.33/0.55 ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.33/0.55 ( ( ord_le6747313008572928689nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C )
% 0.33/0.55 = ( ord_le6747313008572928689nteger @ A @ ( plus_p5714425477246183910nteger @ C @ B ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % diff_less_eq
% 0.33/0.55 thf(fact_1821_diff__less__eq,axiom,
% 0.33/0.55 ! [A: rat,B: rat,C: rat] :
% 0.33/0.55 ( ( ord_less_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 0.33/0.55 = ( ord_less_rat @ A @ ( plus_plus_rat @ C @ B ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % diff_less_eq
% 0.33/0.55 thf(fact_1822_diff__less__eq,axiom,
% 0.33/0.55 ! [A: int,B: int,C: int] :
% 0.33/0.55 ( ( ord_less_int @ ( minus_minus_int @ A @ B ) @ C )
% 0.33/0.55 = ( ord_less_int @ A @ ( plus_plus_int @ C @ B ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % diff_less_eq
% 0.33/0.55 thf(fact_1823_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 0.33/0.55 ! [A: code_integer,B: code_integer] :
% 0.33/0.55 ( ~ ( ord_le6747313008572928689nteger @ A @ B )
% 0.33/0.55 => ( ( plus_p5714425477246183910nteger @ B @ ( minus_8373710615458151222nteger @ A @ B ) )
% 0.33/0.55 = A ) ) ).
% 0.33/0.55
% 0.33/0.55 % linordered_semidom_class.add_diff_inverse
% 0.33/0.55 thf(fact_1824_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 0.33/0.55 ! [A: rat,B: rat] :
% 0.33/0.55 ( ~ ( ord_less_rat @ A @ B )
% 0.33/0.55 => ( ( plus_plus_rat @ B @ ( minus_minus_rat @ A @ B ) )
% 0.33/0.55 = A ) ) ).
% 0.33/0.55
% 0.33/0.55 % linordered_semidom_class.add_diff_inverse
% 0.33/0.55 thf(fact_1825_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 0.33/0.55 ! [A: nat,B: nat] :
% 0.33/0.55 ( ~ ( ord_less_nat @ A @ B )
% 0.33/0.55 => ( ( plus_plus_nat @ B @ ( minus_minus_nat @ A @ B ) )
% 0.33/0.55 = A ) ) ).
% 0.33/0.55
% 0.33/0.55 % linordered_semidom_class.add_diff_inverse
% 0.33/0.55 thf(fact_1826_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 0.33/0.55 ! [A: int,B: int] :
% 0.33/0.55 ( ~ ( ord_less_int @ A @ B )
% 0.33/0.55 => ( ( plus_plus_int @ B @ ( minus_minus_int @ A @ B ) )
% 0.33/0.55 = A ) ) ).
% 0.33/0.55
% 0.33/0.55 % linordered_semidom_class.add_diff_inverse
% 0.33/0.55 thf(fact_1827_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 0.33/0.55 ( minus_minus_int
% 0.33/0.55 = ( ^ [A5: int,B4: int] : ( plus_plus_int @ A5 @ ( uminus_uminus_int @ B4 ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % ab_group_add_class.ab_diff_conv_add_uminus
% 0.33/0.55 thf(fact_1828_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 0.33/0.55 ( minus_8373710615458151222nteger
% 0.33/0.55 = ( ^ [A5: code_integer,B4: code_integer] : ( plus_p5714425477246183910nteger @ A5 @ ( uminus1351360451143612070nteger @ B4 ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % ab_group_add_class.ab_diff_conv_add_uminus
% 0.33/0.55 thf(fact_1829_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 0.33/0.55 ( minus_minus_rat
% 0.33/0.55 = ( ^ [A5: rat,B4: rat] : ( plus_plus_rat @ A5 @ ( uminus_uminus_rat @ B4 ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % ab_group_add_class.ab_diff_conv_add_uminus
% 0.33/0.55 thf(fact_1830_diff__conv__add__uminus,axiom,
% 0.33/0.55 ( minus_minus_int
% 0.33/0.55 = ( ^ [A5: int,B4: int] : ( plus_plus_int @ A5 @ ( uminus_uminus_int @ B4 ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % diff_conv_add_uminus
% 0.33/0.55 thf(fact_1831_diff__conv__add__uminus,axiom,
% 0.33/0.55 ( minus_8373710615458151222nteger
% 0.33/0.55 = ( ^ [A5: code_integer,B4: code_integer] : ( plus_p5714425477246183910nteger @ A5 @ ( uminus1351360451143612070nteger @ B4 ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % diff_conv_add_uminus
% 0.33/0.55 thf(fact_1832_diff__conv__add__uminus,axiom,
% 0.33/0.55 ( minus_minus_rat
% 0.33/0.55 = ( ^ [A5: rat,B4: rat] : ( plus_plus_rat @ A5 @ ( uminus_uminus_rat @ B4 ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % diff_conv_add_uminus
% 0.33/0.55 thf(fact_1833_group__cancel_Osub2,axiom,
% 0.33/0.55 ! [B5: int,K: int,B: int,A: int] :
% 0.33/0.55 ( ( B5
% 0.33/0.55 = ( plus_plus_int @ K @ B ) )
% 0.33/0.55 => ( ( minus_minus_int @ A @ B5 )
% 0.33/0.55 = ( plus_plus_int @ ( uminus_uminus_int @ K ) @ ( minus_minus_int @ A @ B ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % group_cancel.sub2
% 0.33/0.55 thf(fact_1834_group__cancel_Osub2,axiom,
% 0.33/0.55 ! [B5: code_integer,K: code_integer,B: code_integer,A: code_integer] :
% 0.33/0.55 ( ( B5
% 0.33/0.55 = ( plus_p5714425477246183910nteger @ K @ B ) )
% 0.33/0.55 => ( ( minus_8373710615458151222nteger @ A @ B5 )
% 0.33/0.55 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ K ) @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % group_cancel.sub2
% 0.33/0.55 thf(fact_1835_group__cancel_Osub2,axiom,
% 0.33/0.55 ! [B5: rat,K: rat,B: rat,A: rat] :
% 0.33/0.55 ( ( B5
% 0.33/0.55 = ( plus_plus_rat @ K @ B ) )
% 0.33/0.55 => ( ( minus_minus_rat @ A @ B5 )
% 0.33/0.55 = ( plus_plus_rat @ ( uminus_uminus_rat @ K ) @ ( minus_minus_rat @ A @ B ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % group_cancel.sub2
% 0.33/0.55 thf(fact_1836_abs__triangle__ineq2__sym,axiom,
% 0.33/0.55 ! [A: code_integer,B: code_integer] : ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ B @ A ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % abs_triangle_ineq2_sym
% 0.33/0.55 thf(fact_1837_abs__triangle__ineq2__sym,axiom,
% 0.33/0.55 ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ B @ A ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % abs_triangle_ineq2_sym
% 0.33/0.55 thf(fact_1838_abs__triangle__ineq2__sym,axiom,
% 0.33/0.55 ! [A: int,B: int] : ( ord_less_eq_int @ ( minus_minus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) @ ( abs_abs_int @ ( minus_minus_int @ B @ A ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % abs_triangle_ineq2_sym
% 0.33/0.55 thf(fact_1839_abs__triangle__ineq3,axiom,
% 0.33/0.55 ! [A: code_integer,B: code_integer] : ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % abs_triangle_ineq3
% 0.33/0.55 thf(fact_1840_abs__triangle__ineq3,axiom,
% 0.33/0.55 ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ A @ B ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % abs_triangle_ineq3
% 0.33/0.55 thf(fact_1841_abs__triangle__ineq3,axiom,
% 0.33/0.55 ! [A: int,B: int] : ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) @ ( abs_abs_int @ ( minus_minus_int @ A @ B ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % abs_triangle_ineq3
% 0.33/0.55 thf(fact_1842_abs__triangle__ineq2,axiom,
% 0.33/0.55 ! [A: code_integer,B: code_integer] : ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % abs_triangle_ineq2
% 0.33/0.55 thf(fact_1843_abs__triangle__ineq2,axiom,
% 0.33/0.55 ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ A @ B ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % abs_triangle_ineq2
% 0.33/0.55 thf(fact_1844_abs__triangle__ineq2,axiom,
% 0.33/0.55 ! [A: int,B: int] : ( ord_less_eq_int @ ( minus_minus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) @ ( abs_abs_int @ ( minus_minus_int @ A @ B ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % abs_triangle_ineq2
% 0.33/0.55 thf(fact_1845_add__scale__eq__noteq,axiom,
% 0.33/0.55 ! [R2: code_integer,A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 0.33/0.55 ( ( R2 != zero_z3403309356797280102nteger )
% 0.33/0.55 => ( ( ( A = B )
% 0.33/0.55 & ( C != D2 ) )
% 0.33/0.55 => ( ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ R2 @ C ) )
% 0.33/0.55 != ( plus_p5714425477246183910nteger @ B @ ( times_3573771949741848930nteger @ R2 @ D2 ) ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % add_scale_eq_noteq
% 0.33/0.55 thf(fact_1846_add__scale__eq__noteq,axiom,
% 0.33/0.55 ! [R2: rat,A: rat,B: rat,C: rat,D2: rat] :
% 0.33/0.55 ( ( R2 != zero_zero_rat )
% 0.33/0.55 => ( ( ( A = B )
% 0.33/0.55 & ( C != D2 ) )
% 0.33/0.55 => ( ( plus_plus_rat @ A @ ( times_times_rat @ R2 @ C ) )
% 0.33/0.55 != ( plus_plus_rat @ B @ ( times_times_rat @ R2 @ D2 ) ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % add_scale_eq_noteq
% 0.33/0.55 thf(fact_1847_add__scale__eq__noteq,axiom,
% 0.33/0.55 ! [R2: nat,A: nat,B: nat,C: nat,D2: nat] :
% 0.33/0.55 ( ( R2 != zero_zero_nat )
% 0.33/0.55 => ( ( ( A = B )
% 0.33/0.55 & ( C != D2 ) )
% 0.33/0.55 => ( ( plus_plus_nat @ A @ ( times_times_nat @ R2 @ C ) )
% 0.33/0.55 != ( plus_plus_nat @ B @ ( times_times_nat @ R2 @ D2 ) ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % add_scale_eq_noteq
% 0.33/0.55 thf(fact_1848_add__scale__eq__noteq,axiom,
% 0.33/0.55 ! [R2: int,A: int,B: int,C: int,D2: int] :
% 0.33/0.55 ( ( R2 != zero_zero_int )
% 0.33/0.55 => ( ( ( A = B )
% 0.33/0.55 & ( C != D2 ) )
% 0.33/0.55 => ( ( plus_plus_int @ A @ ( times_times_int @ R2 @ C ) )
% 0.33/0.55 != ( plus_plus_int @ B @ ( times_times_int @ R2 @ D2 ) ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % add_scale_eq_noteq
% 0.33/0.55 thf(fact_1849_less__1__mult,axiom,
% 0.33/0.55 ! [M2: code_integer,N2: code_integer] :
% 0.33/0.55 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ M2 )
% 0.33/0.55 => ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ N2 )
% 0.33/0.55 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ M2 @ N2 ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % less_1_mult
% 0.33/0.55 thf(fact_1850_less__1__mult,axiom,
% 0.33/0.55 ! [M2: rat,N2: rat] :
% 0.33/0.55 ( ( ord_less_rat @ one_one_rat @ M2 )
% 0.33/0.55 => ( ( ord_less_rat @ one_one_rat @ N2 )
% 0.33/0.55 => ( ord_less_rat @ one_one_rat @ ( times_times_rat @ M2 @ N2 ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % less_1_mult
% 0.33/0.55 thf(fact_1851_less__1__mult,axiom,
% 0.33/0.55 ! [M2: nat,N2: nat] :
% 0.33/0.55 ( ( ord_less_nat @ one_one_nat @ M2 )
% 0.33/0.55 => ( ( ord_less_nat @ one_one_nat @ N2 )
% 0.33/0.55 => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ M2 @ N2 ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % less_1_mult
% 0.33/0.55 thf(fact_1852_less__1__mult,axiom,
% 0.33/0.55 ! [M2: int,N2: int] :
% 0.33/0.55 ( ( ord_less_int @ one_one_int @ M2 )
% 0.33/0.55 => ( ( ord_less_int @ one_one_int @ N2 )
% 0.33/0.55 => ( ord_less_int @ one_one_int @ ( times_times_int @ M2 @ N2 ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % less_1_mult
% 0.33/0.55 thf(fact_1853_square__eq__1__iff,axiom,
% 0.33/0.55 ! [X: int] :
% 0.33/0.55 ( ( ( times_times_int @ X @ X )
% 0.33/0.55 = one_one_int )
% 0.33/0.55 = ( ( X = one_one_int )
% 0.33/0.55 | ( X
% 0.33/0.55 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % square_eq_1_iff
% 0.33/0.55 thf(fact_1854_square__eq__1__iff,axiom,
% 0.33/0.55 ! [X: code_integer] :
% 0.33/0.55 ( ( ( times_3573771949741848930nteger @ X @ X )
% 0.33/0.55 = one_one_Code_integer )
% 0.33/0.55 = ( ( X = one_one_Code_integer )
% 0.33/0.55 | ( X
% 0.33/0.55 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % square_eq_1_iff
% 0.33/0.55 thf(fact_1855_square__eq__1__iff,axiom,
% 0.33/0.55 ! [X: rat] :
% 0.33/0.55 ( ( ( times_times_rat @ X @ X )
% 0.33/0.55 = one_one_rat )
% 0.33/0.55 = ( ( X = one_one_rat )
% 0.33/0.55 | ( X
% 0.33/0.55 = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % square_eq_1_iff
% 0.33/0.55 thf(fact_1856_diff__add__0,axiom,
% 0.33/0.55 ! [N2: nat,M2: nat] :
% 0.33/0.55 ( ( minus_minus_nat @ N2 @ ( plus_plus_nat @ N2 @ M2 ) )
% 0.33/0.55 = zero_zero_nat ) ).
% 0.33/0.55
% 0.33/0.55 % diff_add_0
% 0.33/0.55 thf(fact_1857_less__diff__conv,axiom,
% 0.33/0.55 ! [I: nat,J: nat,K: nat] :
% 0.33/0.55 ( ( ord_less_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 0.33/0.55 = ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ J ) ) ).
% 0.33/0.55
% 0.33/0.55 % less_diff_conv
% 0.33/0.55 thf(fact_1858_add__diff__inverse__nat,axiom,
% 0.33/0.55 ! [M2: nat,N2: nat] :
% 0.33/0.55 ( ~ ( ord_less_nat @ M2 @ N2 )
% 0.33/0.55 => ( ( plus_plus_nat @ N2 @ ( minus_minus_nat @ M2 @ N2 ) )
% 0.33/0.55 = M2 ) ) ).
% 0.33/0.55
% 0.33/0.55 % add_diff_inverse_nat
% 0.33/0.55 thf(fact_1859_less__diff__conv2,axiom,
% 0.33/0.55 ! [K: nat,J: nat,I: nat] :
% 0.33/0.55 ( ( ord_less_eq_nat @ K @ J )
% 0.33/0.55 => ( ( ord_less_nat @ ( minus_minus_nat @ J @ K ) @ I )
% 0.33/0.55 = ( ord_less_nat @ J @ ( plus_plus_nat @ I @ K ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % less_diff_conv2
% 0.33/0.55 thf(fact_1860_mlex__snd__decrI,axiom,
% 0.33/0.55 ! [A: nat,A4: nat,B: nat,B3: nat,N6: nat] :
% 0.33/0.55 ( ( A = A4 )
% 0.33/0.55 => ( ( ord_less_nat @ B @ B3 )
% 0.33/0.55 => ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ A @ N6 ) @ B ) @ ( plus_plus_nat @ ( times_times_nat @ A4 @ N6 ) @ B3 ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % mlex_snd_decrI
% 0.33/0.55 thf(fact_1861_mlex__fst__decrI,axiom,
% 0.33/0.55 ! [A: nat,A4: nat,B: nat,N6: nat,B3: nat] :
% 0.33/0.55 ( ( ord_less_nat @ A @ A4 )
% 0.33/0.55 => ( ( ord_less_nat @ B @ N6 )
% 0.33/0.55 => ( ( ord_less_nat @ B3 @ N6 )
% 0.33/0.55 => ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ A @ N6 ) @ B ) @ ( plus_plus_nat @ ( times_times_nat @ A4 @ N6 ) @ B3 ) ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % mlex_fst_decrI
% 0.33/0.55 thf(fact_1862_mlex__bound,axiom,
% 0.33/0.55 ! [A: nat,A2: nat,B: nat,N6: nat] :
% 0.33/0.55 ( ( ord_less_nat @ A @ A2 )
% 0.33/0.55 => ( ( ord_less_nat @ B @ N6 )
% 0.33/0.55 => ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ A @ N6 ) @ B ) @ ( times_times_nat @ A2 @ N6 ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % mlex_bound
% 0.33/0.55 thf(fact_1863_mult__eq__self__implies__10,axiom,
% 0.33/0.55 ! [M2: nat,N2: nat] :
% 0.33/0.55 ( ( M2
% 0.33/0.55 = ( times_times_nat @ M2 @ N2 ) )
% 0.33/0.55 => ( ( N2 = one_one_nat )
% 0.33/0.55 | ( M2 = zero_zero_nat ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % mult_eq_self_implies_10
% 0.33/0.55 thf(fact_1864_field__le__mult__one__interval,axiom,
% 0.33/0.55 ! [X: rat,Y: rat] :
% 0.33/0.55 ( ! [Z3: rat] :
% 0.33/0.55 ( ( ord_less_rat @ zero_zero_rat @ Z3 )
% 0.33/0.55 => ( ( ord_less_rat @ Z3 @ one_one_rat )
% 0.33/0.55 => ( ord_less_eq_rat @ ( times_times_rat @ Z3 @ X ) @ Y ) ) )
% 0.33/0.55 => ( ord_less_eq_rat @ X @ Y ) ) ).
% 0.33/0.55
% 0.33/0.55 % field_le_mult_one_interval
% 0.33/0.55 thf(fact_1865_abs__diff__le__iff,axiom,
% 0.33/0.55 ! [X: code_integer,A: code_integer,R2: code_integer] :
% 0.33/0.55 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ X @ A ) ) @ R2 )
% 0.33/0.55 = ( ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ A @ R2 ) @ X )
% 0.33/0.55 & ( ord_le3102999989581377725nteger @ X @ ( plus_p5714425477246183910nteger @ A @ R2 ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % abs_diff_le_iff
% 0.33/0.55 thf(fact_1866_abs__diff__le__iff,axiom,
% 0.33/0.55 ! [X: rat,A: rat,R2: rat] :
% 0.33/0.55 ( ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X @ A ) ) @ R2 )
% 0.33/0.55 = ( ( ord_less_eq_rat @ ( minus_minus_rat @ A @ R2 ) @ X )
% 0.33/0.55 & ( ord_less_eq_rat @ X @ ( plus_plus_rat @ A @ R2 ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % abs_diff_le_iff
% 0.33/0.55 thf(fact_1867_abs__diff__le__iff,axiom,
% 0.33/0.55 ! [X: int,A: int,R2: int] :
% 0.33/0.55 ( ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ X @ A ) ) @ R2 )
% 0.33/0.55 = ( ( ord_less_eq_int @ ( minus_minus_int @ A @ R2 ) @ X )
% 0.33/0.55 & ( ord_less_eq_int @ X @ ( plus_plus_int @ A @ R2 ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % abs_diff_le_iff
% 0.33/0.55 thf(fact_1868_abs__diff__triangle__ineq,axiom,
% 0.33/0.55 ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] : ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ ( plus_p5714425477246183910nteger @ C @ D2 ) ) ) @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ C ) ) @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ B @ D2 ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % abs_diff_triangle_ineq
% 0.33/0.55 thf(fact_1869_abs__diff__triangle__ineq,axiom,
% 0.33/0.55 ! [A: rat,B: rat,C: rat,D2: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ C @ D2 ) ) ) @ ( plus_plus_rat @ ( abs_abs_rat @ ( minus_minus_rat @ A @ C ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ B @ D2 ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % abs_diff_triangle_ineq
% 0.33/0.55 thf(fact_1870_abs__diff__triangle__ineq,axiom,
% 0.33/0.55 ! [A: int,B: int,C: int,D2: int] : ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ ( plus_plus_int @ C @ D2 ) ) ) @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ A @ C ) ) @ ( abs_abs_int @ ( minus_minus_int @ B @ D2 ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % abs_diff_triangle_ineq
% 0.33/0.55 thf(fact_1871_abs__triangle__ineq4,axiom,
% 0.33/0.55 ! [A: code_integer,B: code_integer] : ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ B ) ) @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % abs_triangle_ineq4
% 0.33/0.55 thf(fact_1872_abs__triangle__ineq4,axiom,
% 0.33/0.55 ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ A @ B ) ) @ ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % abs_triangle_ineq4
% 0.33/0.55 thf(fact_1873_abs__triangle__ineq4,axiom,
% 0.33/0.55 ! [A: int,B: int] : ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ A @ B ) ) @ ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % abs_triangle_ineq4
% 0.33/0.55 thf(fact_1874_abs__diff__less__iff,axiom,
% 0.33/0.55 ! [X: code_integer,A: code_integer,R2: code_integer] :
% 0.33/0.55 ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ X @ A ) ) @ R2 )
% 0.33/0.55 = ( ( ord_le6747313008572928689nteger @ ( minus_8373710615458151222nteger @ A @ R2 ) @ X )
% 0.33/0.55 & ( ord_le6747313008572928689nteger @ X @ ( plus_p5714425477246183910nteger @ A @ R2 ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % abs_diff_less_iff
% 0.33/0.55 thf(fact_1875_abs__diff__less__iff,axiom,
% 0.33/0.55 ! [X: rat,A: rat,R2: rat] :
% 0.33/0.55 ( ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X @ A ) ) @ R2 )
% 0.33/0.55 = ( ( ord_less_rat @ ( minus_minus_rat @ A @ R2 ) @ X )
% 0.33/0.55 & ( ord_less_rat @ X @ ( plus_plus_rat @ A @ R2 ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % abs_diff_less_iff
% 0.33/0.55 thf(fact_1876_abs__diff__less__iff,axiom,
% 0.33/0.55 ! [X: int,A: int,R2: int] :
% 0.33/0.55 ( ( ord_less_int @ ( abs_abs_int @ ( minus_minus_int @ X @ A ) ) @ R2 )
% 0.33/0.55 = ( ( ord_less_int @ ( minus_minus_int @ A @ R2 ) @ X )
% 0.33/0.55 & ( ord_less_int @ X @ ( plus_plus_int @ A @ R2 ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % abs_diff_less_iff
% 0.33/0.55 thf(fact_1877_sum__squares__ge__zero,axiom,
% 0.33/0.55 ! [X: code_integer,Y: code_integer] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ X @ X ) @ ( times_3573771949741848930nteger @ Y @ Y ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % sum_squares_ge_zero
% 0.33/0.55 thf(fact_1878_sum__squares__ge__zero,axiom,
% 0.33/0.55 ! [X: rat,Y: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % sum_squares_ge_zero
% 0.33/0.55 thf(fact_1879_sum__squares__ge__zero,axiom,
% 0.33/0.55 ! [X: int,Y: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % sum_squares_ge_zero
% 0.33/0.55 thf(fact_1880_mult__left__le,axiom,
% 0.33/0.55 ! [C: code_integer,A: code_integer] :
% 0.33/0.55 ( ( ord_le3102999989581377725nteger @ C @ one_one_Code_integer )
% 0.33/0.55 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.33/0.55 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ C ) @ A ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % mult_left_le
% 0.33/0.55 thf(fact_1881_mult__left__le,axiom,
% 0.33/0.55 ! [C: rat,A: rat] :
% 0.33/0.55 ( ( ord_less_eq_rat @ C @ one_one_rat )
% 0.33/0.55 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.33/0.55 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ A ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % mult_left_le
% 0.33/0.55 thf(fact_1882_mult__left__le,axiom,
% 0.33/0.55 ! [C: nat,A: nat] :
% 0.33/0.55 ( ( ord_less_eq_nat @ C @ one_one_nat )
% 0.33/0.55 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.33/0.55 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ A ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % mult_left_le
% 0.33/0.55 thf(fact_1883_mult__left__le,axiom,
% 0.33/0.55 ! [C: int,A: int] :
% 0.33/0.55 ( ( ord_less_eq_int @ C @ one_one_int )
% 0.33/0.55 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.33/0.55 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ A ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % mult_left_le
% 0.33/0.55 thf(fact_1884_mult__le__one,axiom,
% 0.33/0.55 ! [A: code_integer,B: code_integer] :
% 0.33/0.55 ( ( ord_le3102999989581377725nteger @ A @ one_one_Code_integer )
% 0.33/0.55 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 0.33/0.55 => ( ( ord_le3102999989581377725nteger @ B @ one_one_Code_integer )
% 0.33/0.55 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ B ) @ one_one_Code_integer ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % mult_le_one
% 0.33/0.55 thf(fact_1885_mult__le__one,axiom,
% 0.33/0.55 ! [A: rat,B: rat] :
% 0.33/0.55 ( ( ord_less_eq_rat @ A @ one_one_rat )
% 0.33/0.55 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.33/0.55 => ( ( ord_less_eq_rat @ B @ one_one_rat )
% 0.33/0.55 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ one_one_rat ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % mult_le_one
% 0.33/0.55 thf(fact_1886_mult__le__one,axiom,
% 0.33/0.55 ! [A: nat,B: nat] :
% 0.33/0.55 ( ( ord_less_eq_nat @ A @ one_one_nat )
% 0.33/0.55 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.33/0.55 => ( ( ord_less_eq_nat @ B @ one_one_nat )
% 0.33/0.55 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ one_one_nat ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % mult_le_one
% 0.33/0.55 thf(fact_1887_mult__le__one,axiom,
% 0.33/0.55 ! [A: int,B: int] :
% 0.33/0.55 ( ( ord_less_eq_int @ A @ one_one_int )
% 0.33/0.55 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.33/0.55 => ( ( ord_less_eq_int @ B @ one_one_int )
% 0.33/0.55 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ one_one_int ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % mult_le_one
% 0.33/0.55 thf(fact_1888_mult__right__le__one__le,axiom,
% 0.33/0.55 ! [X: code_integer,Y: code_integer] :
% 0.33/0.55 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X )
% 0.33/0.55 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y )
% 0.33/0.55 => ( ( ord_le3102999989581377725nteger @ Y @ one_one_Code_integer )
% 0.33/0.55 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ X @ Y ) @ X ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % mult_right_le_one_le
% 0.33/0.55 thf(fact_1889_mult__right__le__one__le,axiom,
% 0.33/0.55 ! [X: rat,Y: rat] :
% 0.33/0.55 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 0.33/0.55 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 0.33/0.55 => ( ( ord_less_eq_rat @ Y @ one_one_rat )
% 0.33/0.55 => ( ord_less_eq_rat @ ( times_times_rat @ X @ Y ) @ X ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % mult_right_le_one_le
% 0.33/0.55 thf(fact_1890_mult__right__le__one__le,axiom,
% 0.33/0.55 ! [X: int,Y: int] :
% 0.33/0.55 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.33/0.55 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.33/0.55 => ( ( ord_less_eq_int @ Y @ one_one_int )
% 0.33/0.55 => ( ord_less_eq_int @ ( times_times_int @ X @ Y ) @ X ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % mult_right_le_one_le
% 0.33/0.55 thf(fact_1891_mult__left__le__one__le,axiom,
% 0.33/0.55 ! [X: code_integer,Y: code_integer] :
% 0.33/0.55 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X )
% 0.33/0.55 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y )
% 0.33/0.55 => ( ( ord_le3102999989581377725nteger @ Y @ one_one_Code_integer )
% 0.33/0.55 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ Y @ X ) @ X ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % mult_left_le_one_le
% 0.33/0.55 thf(fact_1892_mult__left__le__one__le,axiom,
% 0.33/0.55 ! [X: rat,Y: rat] :
% 0.33/0.55 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 0.33/0.55 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 0.33/0.55 => ( ( ord_less_eq_rat @ Y @ one_one_rat )
% 0.33/0.55 => ( ord_less_eq_rat @ ( times_times_rat @ Y @ X ) @ X ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % mult_left_le_one_le
% 0.33/0.55 thf(fact_1893_mult__left__le__one__le,axiom,
% 0.33/0.55 ! [X: int,Y: int] :
% 0.33/0.55 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.33/0.55 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.33/0.55 => ( ( ord_less_eq_int @ Y @ one_one_int )
% 0.33/0.55 => ( ord_less_eq_int @ ( times_times_int @ Y @ X ) @ X ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % mult_left_le_one_le
% 0.33/0.55 thf(fact_1894_not__sum__squares__lt__zero,axiom,
% 0.33/0.55 ! [X: code_integer,Y: code_integer] :
% 0.33/0.55 ~ ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ X @ X ) @ ( times_3573771949741848930nteger @ Y @ Y ) ) @ zero_z3403309356797280102nteger ) ).
% 0.33/0.55
% 0.33/0.55 % not_sum_squares_lt_zero
% 0.33/0.55 thf(fact_1895_not__sum__squares__lt__zero,axiom,
% 0.33/0.55 ! [X: rat,Y: rat] :
% 0.33/0.55 ~ ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) ) @ zero_zero_rat ) ).
% 0.33/0.55
% 0.33/0.55 % not_sum_squares_lt_zero
% 0.33/0.55 thf(fact_1896_not__sum__squares__lt__zero,axiom,
% 0.33/0.55 ! [X: int,Y: int] :
% 0.33/0.55 ~ ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) @ zero_zero_int ) ).
% 0.33/0.55
% 0.33/0.55 % not_sum_squares_lt_zero
% 0.33/0.55 thf(fact_1897_nat__diff__split,axiom,
% 0.33/0.55 ! [P: nat > $o,A: nat,B: nat] :
% 0.33/0.55 ( ( P @ ( minus_minus_nat @ A @ B ) )
% 0.33/0.55 = ( ( ( ord_less_nat @ A @ B )
% 0.33/0.55 => ( P @ zero_zero_nat ) )
% 0.33/0.55 & ! [D4: nat] :
% 0.33/0.55 ( ( A
% 0.33/0.55 = ( plus_plus_nat @ B @ D4 ) )
% 0.33/0.55 => ( P @ D4 ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % nat_diff_split
% 0.33/0.55 thf(fact_1898_nat__diff__split__asm,axiom,
% 0.33/0.55 ! [P: nat > $o,A: nat,B: nat] :
% 0.33/0.55 ( ( P @ ( minus_minus_nat @ A @ B ) )
% 0.33/0.55 = ( ~ ( ( ( ord_less_nat @ A @ B )
% 0.33/0.55 & ~ ( P @ zero_zero_nat ) )
% 0.33/0.55 | ? [D4: nat] :
% 0.33/0.55 ( ( A
% 0.33/0.55 = ( plus_plus_nat @ B @ D4 ) )
% 0.33/0.55 & ~ ( P @ D4 ) ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % nat_diff_split_asm
% 0.33/0.55 thf(fact_1899_dbl__dec__def,axiom,
% 0.33/0.55 ( neg_nu7757733837767384882nteger
% 0.33/0.55 = ( ^ [X3: code_integer] : ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ X3 @ X3 ) @ one_one_Code_integer ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % dbl_dec_def
% 0.33/0.55 thf(fact_1900_dbl__dec__def,axiom,
% 0.33/0.55 ( neg_nu3179335615603231917ec_rat
% 0.33/0.55 = ( ^ [X3: rat] : ( minus_minus_rat @ ( plus_plus_rat @ X3 @ X3 ) @ one_one_rat ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % dbl_dec_def
% 0.33/0.55 thf(fact_1901_dbl__dec__def,axiom,
% 0.33/0.55 ( neg_nu3811975205180677377ec_int
% 0.33/0.55 = ( ^ [X3: int] : ( minus_minus_int @ ( plus_plus_int @ X3 @ X3 ) @ one_one_int ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % dbl_dec_def
% 0.33/0.55 thf(fact_1902_mult__le__cancel__left1,axiom,
% 0.33/0.55 ! [C: code_integer,B: code_integer] :
% 0.33/0.55 ( ( ord_le3102999989581377725nteger @ C @ ( times_3573771949741848930nteger @ C @ B ) )
% 0.33/0.55 = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 0.33/0.55 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ B ) )
% 0.33/0.55 & ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 0.33/0.55 => ( ord_le3102999989581377725nteger @ B @ one_one_Code_integer ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % mult_le_cancel_left1
% 0.33/0.55 thf(fact_1903_mult__le__cancel__left1,axiom,
% 0.33/0.55 ! [C: rat,B: rat] :
% 0.33/0.55 ( ( ord_less_eq_rat @ C @ ( times_times_rat @ C @ B ) )
% 0.33/0.55 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.33/0.55 => ( ord_less_eq_rat @ one_one_rat @ B ) )
% 0.33/0.55 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.33/0.55 => ( ord_less_eq_rat @ B @ one_one_rat ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % mult_le_cancel_left1
% 0.33/0.55 thf(fact_1904_mult__le__cancel__left1,axiom,
% 0.33/0.55 ! [C: int,B: int] :
% 0.33/0.55 ( ( ord_less_eq_int @ C @ ( times_times_int @ C @ B ) )
% 0.33/0.55 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 0.33/0.55 => ( ord_less_eq_int @ one_one_int @ B ) )
% 0.33/0.55 & ( ( ord_less_int @ C @ zero_zero_int )
% 0.33/0.55 => ( ord_less_eq_int @ B @ one_one_int ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % mult_le_cancel_left1
% 0.33/0.55 thf(fact_1905_mult__le__cancel__left2,axiom,
% 0.33/0.55 ! [C: code_integer,A: code_integer] :
% 0.33/0.55 ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ C @ A ) @ C )
% 0.33/0.55 = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 0.33/0.55 => ( ord_le3102999989581377725nteger @ A @ one_one_Code_integer ) )
% 0.33/0.55 & ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 0.33/0.55 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ A ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % mult_le_cancel_left2
% 0.33/0.55 thf(fact_1906_mult__le__cancel__left2,axiom,
% 0.33/0.55 ! [C: rat,A: rat] :
% 0.33/0.55 ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ C )
% 0.33/0.55 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.33/0.55 => ( ord_less_eq_rat @ A @ one_one_rat ) )
% 0.33/0.55 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.33/0.55 => ( ord_less_eq_rat @ one_one_rat @ A ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % mult_le_cancel_left2
% 0.33/0.55 thf(fact_1907_mult__le__cancel__left2,axiom,
% 0.33/0.55 ! [C: int,A: int] :
% 0.33/0.55 ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ C )
% 0.33/0.55 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 0.33/0.55 => ( ord_less_eq_int @ A @ one_one_int ) )
% 0.33/0.55 & ( ( ord_less_int @ C @ zero_zero_int )
% 0.33/0.55 => ( ord_less_eq_int @ one_one_int @ A ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % mult_le_cancel_left2
% 0.33/0.55 thf(fact_1908_mult__le__cancel__right1,axiom,
% 0.33/0.55 ! [C: code_integer,B: code_integer] :
% 0.33/0.55 ( ( ord_le3102999989581377725nteger @ C @ ( times_3573771949741848930nteger @ B @ C ) )
% 0.33/0.55 = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 0.33/0.55 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ B ) )
% 0.33/0.55 & ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 0.33/0.55 => ( ord_le3102999989581377725nteger @ B @ one_one_Code_integer ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % mult_le_cancel_right1
% 0.33/0.55 thf(fact_1909_mult__le__cancel__right1,axiom,
% 0.33/0.55 ! [C: rat,B: rat] :
% 0.33/0.55 ( ( ord_less_eq_rat @ C @ ( times_times_rat @ B @ C ) )
% 0.33/0.55 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.33/0.55 => ( ord_less_eq_rat @ one_one_rat @ B ) )
% 0.33/0.55 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.33/0.55 => ( ord_less_eq_rat @ B @ one_one_rat ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % mult_le_cancel_right1
% 0.33/0.55 thf(fact_1910_mult__le__cancel__right1,axiom,
% 0.33/0.55 ! [C: int,B: int] :
% 0.33/0.55 ( ( ord_less_eq_int @ C @ ( times_times_int @ B @ C ) )
% 0.33/0.55 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 0.33/0.55 => ( ord_less_eq_int @ one_one_int @ B ) )
% 0.33/0.55 & ( ( ord_less_int @ C @ zero_zero_int )
% 0.33/0.55 => ( ord_less_eq_int @ B @ one_one_int ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % mult_le_cancel_right1
% 0.33/0.55 thf(fact_1911_mult__le__cancel__right2,axiom,
% 0.33/0.55 ! [A: code_integer,C: code_integer] :
% 0.33/0.55 ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ C ) @ C )
% 0.33/0.55 = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 0.33/0.55 => ( ord_le3102999989581377725nteger @ A @ one_one_Code_integer ) )
% 0.33/0.55 & ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 0.33/0.55 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ A ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % mult_le_cancel_right2
% 0.33/0.55 thf(fact_1912_mult__le__cancel__right2,axiom,
% 0.33/0.55 ! [A: rat,C: rat] :
% 0.33/0.55 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ C )
% 0.33/0.55 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.33/0.55 => ( ord_less_eq_rat @ A @ one_one_rat ) )
% 0.33/0.55 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.33/0.55 => ( ord_less_eq_rat @ one_one_rat @ A ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % mult_le_cancel_right2
% 0.33/0.55 thf(fact_1913_mult__le__cancel__right2,axiom,
% 0.33/0.55 ! [A: int,C: int] :
% 0.33/0.55 ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ C )
% 0.33/0.55 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 0.33/0.55 => ( ord_less_eq_int @ A @ one_one_int ) )
% 0.33/0.55 & ( ( ord_less_int @ C @ zero_zero_int )
% 0.33/0.55 => ( ord_less_eq_int @ one_one_int @ A ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % mult_le_cancel_right2
% 0.33/0.55 thf(fact_1914_mult__less__cancel__left1,axiom,
% 0.33/0.55 ! [C: code_integer,B: code_integer] :
% 0.33/0.55 ( ( ord_le6747313008572928689nteger @ C @ ( times_3573771949741848930nteger @ C @ B ) )
% 0.33/0.55 = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 0.33/0.55 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ B ) )
% 0.33/0.55 & ( ( ord_le3102999989581377725nteger @ C @ zero_z3403309356797280102nteger )
% 0.33/0.55 => ( ord_le6747313008572928689nteger @ B @ one_one_Code_integer ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % mult_less_cancel_left1
% 0.33/0.55 thf(fact_1915_mult__less__cancel__left1,axiom,
% 0.33/0.55 ! [C: rat,B: rat] :
% 0.33/0.55 ( ( ord_less_rat @ C @ ( times_times_rat @ C @ B ) )
% 0.33/0.55 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.33/0.55 => ( ord_less_rat @ one_one_rat @ B ) )
% 0.33/0.55 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 0.33/0.55 => ( ord_less_rat @ B @ one_one_rat ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % mult_less_cancel_left1
% 0.33/0.55 thf(fact_1916_mult__less__cancel__left1,axiom,
% 0.33/0.55 ! [C: int,B: int] :
% 0.33/0.55 ( ( ord_less_int @ C @ ( times_times_int @ C @ B ) )
% 0.33/0.55 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.33/0.55 => ( ord_less_int @ one_one_int @ B ) )
% 0.33/0.55 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 0.33/0.55 => ( ord_less_int @ B @ one_one_int ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % mult_less_cancel_left1
% 0.33/0.55 thf(fact_1917_mult__less__cancel__left2,axiom,
% 0.33/0.55 ! [C: code_integer,A: code_integer] :
% 0.33/0.55 ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C @ A ) @ C )
% 0.33/0.55 = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 0.33/0.55 => ( ord_le6747313008572928689nteger @ A @ one_one_Code_integer ) )
% 0.33/0.55 & ( ( ord_le3102999989581377725nteger @ C @ zero_z3403309356797280102nteger )
% 0.33/0.55 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % mult_less_cancel_left2
% 0.33/0.55 thf(fact_1918_mult__less__cancel__left2,axiom,
% 0.33/0.55 ! [C: rat,A: rat] :
% 0.33/0.55 ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ C )
% 0.33/0.55 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.33/0.55 => ( ord_less_rat @ A @ one_one_rat ) )
% 0.33/0.55 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 0.33/0.55 => ( ord_less_rat @ one_one_rat @ A ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % mult_less_cancel_left2
% 0.33/0.55 thf(fact_1919_mult__less__cancel__left2,axiom,
% 0.33/0.55 ! [C: int,A: int] :
% 0.33/0.55 ( ( ord_less_int @ ( times_times_int @ C @ A ) @ C )
% 0.33/0.55 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.33/0.55 => ( ord_less_int @ A @ one_one_int ) )
% 0.33/0.55 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 0.33/0.55 => ( ord_less_int @ one_one_int @ A ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % mult_less_cancel_left2
% 0.33/0.55 thf(fact_1920_mult__less__cancel__right1,axiom,
% 0.33/0.55 ! [C: code_integer,B: code_integer] :
% 0.33/0.55 ( ( ord_le6747313008572928689nteger @ C @ ( times_3573771949741848930nteger @ B @ C ) )
% 0.33/0.55 = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 0.33/0.55 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ B ) )
% 0.33/0.55 & ( ( ord_le3102999989581377725nteger @ C @ zero_z3403309356797280102nteger )
% 0.33/0.55 => ( ord_le6747313008572928689nteger @ B @ one_one_Code_integer ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % mult_less_cancel_right1
% 0.33/0.55 thf(fact_1921_mult__less__cancel__right1,axiom,
% 0.33/0.55 ! [C: rat,B: rat] :
% 0.33/0.55 ( ( ord_less_rat @ C @ ( times_times_rat @ B @ C ) )
% 0.33/0.55 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.33/0.55 => ( ord_less_rat @ one_one_rat @ B ) )
% 0.33/0.55 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 0.33/0.55 => ( ord_less_rat @ B @ one_one_rat ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % mult_less_cancel_right1
% 0.33/0.55 thf(fact_1922_mult__less__cancel__right1,axiom,
% 0.33/0.55 ! [C: int,B: int] :
% 0.33/0.55 ( ( ord_less_int @ C @ ( times_times_int @ B @ C ) )
% 0.33/0.55 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.33/0.55 => ( ord_less_int @ one_one_int @ B ) )
% 0.33/0.55 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 0.33/0.55 => ( ord_less_int @ B @ one_one_int ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % mult_less_cancel_right1
% 0.33/0.55 thf(fact_1923_mult__less__cancel__right2,axiom,
% 0.33/0.55 ! [A: code_integer,C: code_integer] :
% 0.33/0.55 ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ C ) @ C )
% 0.33/0.55 = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 0.33/0.55 => ( ord_le6747313008572928689nteger @ A @ one_one_Code_integer ) )
% 0.33/0.55 & ( ( ord_le3102999989581377725nteger @ C @ zero_z3403309356797280102nteger )
% 0.33/0.55 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % mult_less_cancel_right2
% 0.33/0.55 thf(fact_1924_mult__less__cancel__right2,axiom,
% 0.33/0.55 ! [A: rat,C: rat] :
% 0.33/0.55 ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ C )
% 0.33/0.55 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.33/0.55 => ( ord_less_rat @ A @ one_one_rat ) )
% 0.33/0.55 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 0.33/0.55 => ( ord_less_rat @ one_one_rat @ A ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % mult_less_cancel_right2
% 0.33/0.55 thf(fact_1925_mult__less__cancel__right2,axiom,
% 0.33/0.55 ! [A: int,C: int] :
% 0.33/0.55 ( ( ord_less_int @ ( times_times_int @ A @ C ) @ C )
% 0.33/0.55 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.33/0.55 => ( ord_less_int @ A @ one_one_int ) )
% 0.33/0.55 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 0.33/0.55 => ( ord_less_int @ one_one_int @ A ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % mult_less_cancel_right2
% 0.33/0.55 thf(fact_1926_convex__bound__le,axiom,
% 0.33/0.55 ! [X: code_integer,A: code_integer,Y: code_integer,U: code_integer,V: code_integer] :
% 0.33/0.55 ( ( ord_le3102999989581377725nteger @ X @ A )
% 0.33/0.55 => ( ( ord_le3102999989581377725nteger @ Y @ A )
% 0.33/0.55 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ U )
% 0.33/0.55 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ V )
% 0.33/0.55 => ( ( ( plus_p5714425477246183910nteger @ U @ V )
% 0.33/0.55 = one_one_Code_integer )
% 0.33/0.55 => ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ U @ X ) @ ( times_3573771949741848930nteger @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % convex_bound_le
% 0.33/0.55 thf(fact_1927_convex__bound__le,axiom,
% 0.33/0.55 ! [X: rat,A: rat,Y: rat,U: rat,V: rat] :
% 0.33/0.55 ( ( ord_less_eq_rat @ X @ A )
% 0.33/0.55 => ( ( ord_less_eq_rat @ Y @ A )
% 0.33/0.55 => ( ( ord_less_eq_rat @ zero_zero_rat @ U )
% 0.33/0.55 => ( ( ord_less_eq_rat @ zero_zero_rat @ V )
% 0.33/0.55 => ( ( ( plus_plus_rat @ U @ V )
% 0.33/0.55 = one_one_rat )
% 0.33/0.55 => ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ U @ X ) @ ( times_times_rat @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % convex_bound_le
% 0.33/0.55 thf(fact_1928_convex__bound__le,axiom,
% 0.33/0.55 ! [X: int,A: int,Y: int,U: int,V: int] :
% 0.33/0.55 ( ( ord_less_eq_int @ X @ A )
% 0.33/0.55 => ( ( ord_less_eq_int @ Y @ A )
% 0.33/0.55 => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 0.33/0.55 => ( ( ord_less_eq_int @ zero_zero_int @ V )
% 0.33/0.55 => ( ( ( plus_plus_int @ U @ V )
% 0.33/0.55 = one_one_int )
% 0.33/0.55 => ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ U @ X ) @ ( times_times_int @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % convex_bound_le
% 0.33/0.55 thf(fact_1929_is__num_Ocases,axiom,
% 0.33/0.55 ! [A: int] :
% 0.33/0.55 ( ( neg_nu7441568979088483369um_int @ A )
% 0.33/0.55 => ( ( A != one_one_int )
% 0.33/0.55 => ( ! [X4: int] :
% 0.33/0.55 ( ( A
% 0.33/0.55 = ( uminus_uminus_int @ X4 ) )
% 0.33/0.55 => ~ ( neg_nu7441568979088483369um_int @ X4 ) )
% 0.33/0.55 => ~ ! [X4: int,Y5: int] :
% 0.33/0.55 ( ( A
% 0.33/0.55 = ( plus_plus_int @ X4 @ Y5 ) )
% 0.33/0.55 => ( ( neg_nu7441568979088483369um_int @ X4 )
% 0.33/0.55 => ~ ( neg_nu7441568979088483369um_int @ Y5 ) ) ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % is_num.cases
% 0.33/0.55 thf(fact_1930_is__num_Ocases,axiom,
% 0.33/0.55 ! [A: code_integer] :
% 0.33/0.55 ( ( neg_nu2435721316971906650nteger @ A )
% 0.33/0.55 => ( ( A != one_one_Code_integer )
% 0.33/0.55 => ( ! [X4: code_integer] :
% 0.33/0.55 ( ( A
% 0.33/0.55 = ( uminus1351360451143612070nteger @ X4 ) )
% 0.33/0.55 => ~ ( neg_nu2435721316971906650nteger @ X4 ) )
% 0.33/0.55 => ~ ! [X4: code_integer,Y5: code_integer] :
% 0.33/0.55 ( ( A
% 0.33/0.55 = ( plus_p5714425477246183910nteger @ X4 @ Y5 ) )
% 0.33/0.55 => ( ( neg_nu2435721316971906650nteger @ X4 )
% 0.33/0.55 => ~ ( neg_nu2435721316971906650nteger @ Y5 ) ) ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % is_num.cases
% 0.33/0.55 thf(fact_1931_is__num_Ocases,axiom,
% 0.33/0.55 ! [A: rat] :
% 0.33/0.55 ( ( neg_nu6808929389511037909um_rat @ A )
% 0.33/0.55 => ( ( A != one_one_rat )
% 0.33/0.55 => ( ! [X4: rat] :
% 0.33/0.55 ( ( A
% 0.33/0.55 = ( uminus_uminus_rat @ X4 ) )
% 0.33/0.55 => ~ ( neg_nu6808929389511037909um_rat @ X4 ) )
% 0.33/0.55 => ~ ! [X4: rat,Y5: rat] :
% 0.33/0.55 ( ( A
% 0.33/0.55 = ( plus_plus_rat @ X4 @ Y5 ) )
% 0.33/0.55 => ( ( neg_nu6808929389511037909um_rat @ X4 )
% 0.33/0.55 => ~ ( neg_nu6808929389511037909um_rat @ Y5 ) ) ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % is_num.cases
% 0.33/0.55 thf(fact_1932_is__num_Osimps,axiom,
% 0.33/0.55 ( neg_nu7441568979088483369um_int
% 0.33/0.55 = ( ^ [A5: int] :
% 0.33/0.55 ( ( A5 = one_one_int )
% 0.33/0.55 | ? [X3: int] :
% 0.33/0.55 ( ( A5
% 0.33/0.55 = ( uminus_uminus_int @ X3 ) )
% 0.33/0.55 & ( neg_nu7441568979088483369um_int @ X3 ) )
% 0.33/0.55 | ? [X3: int,Y3: int] :
% 0.33/0.55 ( ( A5
% 0.33/0.55 = ( plus_plus_int @ X3 @ Y3 ) )
% 0.33/0.55 & ( neg_nu7441568979088483369um_int @ X3 )
% 0.33/0.55 & ( neg_nu7441568979088483369um_int @ Y3 ) ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % is_num.simps
% 0.33/0.55 thf(fact_1933_is__num_Osimps,axiom,
% 0.33/0.55 ( neg_nu2435721316971906650nteger
% 0.33/0.55 = ( ^ [A5: code_integer] :
% 0.33/0.55 ( ( A5 = one_one_Code_integer )
% 0.33/0.55 | ? [X3: code_integer] :
% 0.33/0.55 ( ( A5
% 0.33/0.55 = ( uminus1351360451143612070nteger @ X3 ) )
% 0.33/0.55 & ( neg_nu2435721316971906650nteger @ X3 ) )
% 0.33/0.55 | ? [X3: code_integer,Y3: code_integer] :
% 0.33/0.55 ( ( A5
% 0.33/0.55 = ( plus_p5714425477246183910nteger @ X3 @ Y3 ) )
% 0.33/0.55 & ( neg_nu2435721316971906650nteger @ X3 )
% 0.33/0.55 & ( neg_nu2435721316971906650nteger @ Y3 ) ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % is_num.simps
% 0.33/0.55 thf(fact_1934_is__num_Osimps,axiom,
% 0.33/0.55 ( neg_nu6808929389511037909um_rat
% 0.33/0.55 = ( ^ [A5: rat] :
% 0.33/0.55 ( ( A5 = one_one_rat )
% 0.33/0.55 | ? [X3: rat] :
% 0.33/0.55 ( ( A5
% 0.33/0.55 = ( uminus_uminus_rat @ X3 ) )
% 0.33/0.55 & ( neg_nu6808929389511037909um_rat @ X3 ) )
% 0.33/0.55 | ? [X3: rat,Y3: rat] :
% 0.33/0.55 ( ( A5
% 0.33/0.55 = ( plus_plus_rat @ X3 @ Y3 ) )
% 0.33/0.55 & ( neg_nu6808929389511037909um_rat @ X3 )
% 0.33/0.55 & ( neg_nu6808929389511037909um_rat @ Y3 ) ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % is_num.simps
% 0.33/0.55 thf(fact_1935_sum__squares__gt__zero__iff,axiom,
% 0.33/0.55 ! [X: code_integer,Y: code_integer] :
% 0.33/0.55 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ X @ X ) @ ( times_3573771949741848930nteger @ Y @ Y ) ) )
% 0.33/0.55 = ( ( X != zero_z3403309356797280102nteger )
% 0.33/0.55 | ( Y != zero_z3403309356797280102nteger ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % sum_squares_gt_zero_iff
% 0.33/0.55 thf(fact_1936_sum__squares__gt__zero__iff,axiom,
% 0.33/0.55 ! [X: rat,Y: rat] :
% 0.33/0.55 ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) ) )
% 0.33/0.55 = ( ( X != zero_zero_rat )
% 0.33/0.55 | ( Y != zero_zero_rat ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % sum_squares_gt_zero_iff
% 0.33/0.55 thf(fact_1937_sum__squares__gt__zero__iff,axiom,
% 0.33/0.55 ! [X: int,Y: int] :
% 0.33/0.55 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) )
% 0.33/0.55 = ( ( X != zero_zero_int )
% 0.33/0.55 | ( Y != zero_zero_int ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % sum_squares_gt_zero_iff
% 0.33/0.55 thf(fact_1938_sum__squares__le__zero__iff,axiom,
% 0.33/0.55 ! [X: code_integer,Y: code_integer] :
% 0.33/0.55 ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ X @ X ) @ ( times_3573771949741848930nteger @ Y @ Y ) ) @ zero_z3403309356797280102nteger )
% 0.33/0.55 = ( ( X = zero_z3403309356797280102nteger )
% 0.33/0.55 & ( Y = zero_z3403309356797280102nteger ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % sum_squares_le_zero_iff
% 0.33/0.55 thf(fact_1939_sum__squares__le__zero__iff,axiom,
% 0.33/0.55 ! [X: rat,Y: rat] :
% 0.33/0.55 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) ) @ zero_zero_rat )
% 0.33/0.55 = ( ( X = zero_zero_rat )
% 0.33/0.55 & ( Y = zero_zero_rat ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % sum_squares_le_zero_iff
% 0.33/0.55 thf(fact_1940_sum__squares__le__zero__iff,axiom,
% 0.33/0.55 ! [X: int,Y: int] :
% 0.33/0.55 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) @ zero_zero_int )
% 0.33/0.55 = ( ( X = zero_zero_int )
% 0.33/0.55 & ( Y = zero_zero_int ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % sum_squares_le_zero_iff
% 0.33/0.55 thf(fact_1941_incr__lemma,axiom,
% 0.33/0.55 ! [D2: int,Z: int,X: int] :
% 0.33/0.55 ( ( ord_less_int @ zero_zero_int @ D2 )
% 0.33/0.55 => ( 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 ) @ D2 ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % incr_lemma
% 0.33/0.55 thf(fact_1942_decr__lemma,axiom,
% 0.33/0.55 ! [D2: int,X: int,Z: int] :
% 0.33/0.55 ( ( ord_less_int @ zero_zero_int @ D2 )
% 0.33/0.55 => ( ord_less_int @ ( minus_minus_int @ X @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ X @ Z ) ) @ one_one_int ) @ D2 ) ) @ Z ) ) ).
% 0.33/0.55
% 0.33/0.55 % decr_lemma
% 0.33/0.55 thf(fact_1943_sum__squares__eq__zero__iff,axiom,
% 0.33/0.55 ! [X: code_integer,Y: code_integer] :
% 0.33/0.55 ( ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ X @ X ) @ ( times_3573771949741848930nteger @ Y @ Y ) )
% 0.33/0.55 = zero_z3403309356797280102nteger )
% 0.33/0.55 = ( ( X = zero_z3403309356797280102nteger )
% 0.33/0.55 & ( Y = zero_z3403309356797280102nteger ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % sum_squares_eq_zero_iff
% 0.33/0.55 thf(fact_1944_sum__squares__eq__zero__iff,axiom,
% 0.33/0.55 ! [X: rat,Y: rat] :
% 0.33/0.55 ( ( ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) )
% 0.33/0.55 = zero_zero_rat )
% 0.33/0.55 = ( ( X = zero_zero_rat )
% 0.33/0.55 & ( Y = zero_zero_rat ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % sum_squares_eq_zero_iff
% 0.33/0.55 thf(fact_1945_sum__squares__eq__zero__iff,axiom,
% 0.33/0.55 ! [X: int,Y: int] :
% 0.33/0.55 ( ( ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) )
% 0.33/0.55 = zero_zero_int )
% 0.33/0.55 = ( ( X = zero_zero_int )
% 0.33/0.55 & ( Y = zero_zero_int ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % sum_squares_eq_zero_iff
% 0.33/0.55 thf(fact_1946_frac__unique__iff,axiom,
% 0.33/0.55 ! [X: rat,A: rat] :
% 0.33/0.55 ( ( ( archimedean_frac_rat @ X )
% 0.33/0.55 = A )
% 0.33/0.55 = ( ( member_rat @ ( minus_minus_rat @ X @ A ) @ ring_1_Ints_rat )
% 0.33/0.55 & ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.33/0.55 & ( ord_less_rat @ A @ one_one_rat ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % frac_unique_iff
% 0.33/0.55 thf(fact_1947_scaling__mono,axiom,
% 0.33/0.55 ! [U: rat,V: rat,R2: rat,S: rat] :
% 0.33/0.55 ( ( ord_less_eq_rat @ U @ V )
% 0.33/0.55 => ( ( ord_less_eq_rat @ zero_zero_rat @ R2 )
% 0.33/0.55 => ( ( ord_less_eq_rat @ R2 @ S )
% 0.33/0.55 => ( ord_less_eq_rat @ ( plus_plus_rat @ U @ ( divide_divide_rat @ ( times_times_rat @ R2 @ ( minus_minus_rat @ V @ U ) ) @ S ) ) @ V ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % scaling_mono
% 0.33/0.55 thf(fact_1948_divide__le__eq__1__neg,axiom,
% 0.33/0.55 ! [A: rat,B: rat] :
% 0.33/0.55 ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.33/0.55 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 0.33/0.55 = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % divide_le_eq_1_neg
% 0.33/0.55 thf(fact_1949_divide__le__eq__1__pos,axiom,
% 0.33/0.55 ! [A: rat,B: rat] :
% 0.33/0.55 ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.33/0.55 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 0.33/0.55 = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % divide_le_eq_1_pos
% 0.33/0.55 thf(fact_1950_div__by__1,axiom,
% 0.33/0.55 ! [A: int] :
% 0.33/0.55 ( ( divide_divide_int @ A @ one_one_int )
% 0.33/0.55 = A ) ).
% 0.33/0.55
% 0.33/0.55 % div_by_1
% 0.33/0.55 thf(fact_1951_div__by__1,axiom,
% 0.33/0.55 ! [A: nat] :
% 0.33/0.55 ( ( divide_divide_nat @ A @ one_one_nat )
% 0.33/0.55 = A ) ).
% 0.33/0.55
% 0.33/0.55 % div_by_1
% 0.33/0.55 thf(fact_1952_div__by__1,axiom,
% 0.33/0.55 ! [A: code_integer] :
% 0.33/0.55 ( ( divide6298287555418463151nteger @ A @ one_one_Code_integer )
% 0.33/0.55 = A ) ).
% 0.33/0.55
% 0.33/0.55 % div_by_1
% 0.33/0.55 thf(fact_1953_div__by__1,axiom,
% 0.33/0.55 ! [A: rat] :
% 0.33/0.55 ( ( divide_divide_rat @ A @ one_one_rat )
% 0.33/0.55 = A ) ).
% 0.33/0.55
% 0.33/0.55 % div_by_1
% 0.33/0.55 thf(fact_1954_div__by__1,axiom,
% 0.33/0.55 ! [A: code_natural] :
% 0.33/0.55 ( ( divide5121882707175180666atural @ A @ one_one_Code_natural )
% 0.33/0.55 = A ) ).
% 0.33/0.55
% 0.33/0.55 % div_by_1
% 0.33/0.55 thf(fact_1955_div__self,axiom,
% 0.33/0.55 ! [A: int] :
% 0.33/0.55 ( ( A != zero_zero_int )
% 0.33/0.55 => ( ( divide_divide_int @ A @ A )
% 0.33/0.55 = one_one_int ) ) ).
% 0.33/0.55
% 0.33/0.55 % div_self
% 0.33/0.55 thf(fact_1956_div__self,axiom,
% 0.33/0.55 ! [A: nat] :
% 0.33/0.55 ( ( A != zero_zero_nat )
% 0.33/0.55 => ( ( divide_divide_nat @ A @ A )
% 0.33/0.55 = one_one_nat ) ) ).
% 0.33/0.55
% 0.33/0.55 % div_self
% 0.33/0.55 thf(fact_1957_div__self,axiom,
% 0.33/0.55 ! [A: code_integer] :
% 0.33/0.55 ( ( A != zero_z3403309356797280102nteger )
% 0.33/0.55 => ( ( divide6298287555418463151nteger @ A @ A )
% 0.33/0.55 = one_one_Code_integer ) ) ).
% 0.33/0.55
% 0.33/0.55 % div_self
% 0.33/0.55 thf(fact_1958_div__self,axiom,
% 0.33/0.55 ! [A: rat] :
% 0.33/0.55 ( ( A != zero_zero_rat )
% 0.33/0.55 => ( ( divide_divide_rat @ A @ A )
% 0.33/0.55 = one_one_rat ) ) ).
% 0.33/0.55
% 0.33/0.55 % div_self
% 0.33/0.55 thf(fact_1959_div__self,axiom,
% 0.33/0.55 ! [A: code_natural] :
% 0.33/0.55 ( ( A != zero_z2226904508553997617atural )
% 0.33/0.55 => ( ( divide5121882707175180666atural @ A @ A )
% 0.33/0.55 = one_one_Code_natural ) ) ).
% 0.33/0.55
% 0.33/0.55 % div_self
% 0.33/0.55 thf(fact_1960_zero__eq__1__divide__iff,axiom,
% 0.33/0.55 ! [A: rat] :
% 0.33/0.55 ( ( zero_zero_rat
% 0.33/0.55 = ( divide_divide_rat @ one_one_rat @ A ) )
% 0.33/0.55 = ( A = zero_zero_rat ) ) ).
% 0.33/0.55
% 0.33/0.55 % zero_eq_1_divide_iff
% 0.33/0.55 thf(fact_1961_one__divide__eq__0__iff,axiom,
% 0.33/0.55 ! [A: rat] :
% 0.33/0.55 ( ( ( divide_divide_rat @ one_one_rat @ A )
% 0.33/0.55 = zero_zero_rat )
% 0.33/0.55 = ( A = zero_zero_rat ) ) ).
% 0.33/0.55
% 0.33/0.55 % one_divide_eq_0_iff
% 0.33/0.55 thf(fact_1962_eq__divide__eq__1,axiom,
% 0.33/0.55 ! [B: rat,A: rat] :
% 0.33/0.55 ( ( one_one_rat
% 0.33/0.55 = ( divide_divide_rat @ B @ A ) )
% 0.33/0.55 = ( ( A != zero_zero_rat )
% 0.33/0.55 & ( A = B ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % eq_divide_eq_1
% 0.33/0.55 thf(fact_1963_divide__eq__eq__1,axiom,
% 0.33/0.55 ! [B: rat,A: rat] :
% 0.33/0.55 ( ( ( divide_divide_rat @ B @ A )
% 0.33/0.55 = one_one_rat )
% 0.33/0.55 = ( ( A != zero_zero_rat )
% 0.33/0.55 & ( A = B ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % divide_eq_eq_1
% 0.33/0.55 thf(fact_1964_divide__self__if,axiom,
% 0.33/0.55 ! [A: rat] :
% 0.33/0.55 ( ( ( A = zero_zero_rat )
% 0.33/0.55 => ( ( divide_divide_rat @ A @ A )
% 0.33/0.55 = zero_zero_rat ) )
% 0.33/0.55 & ( ( A != zero_zero_rat )
% 0.33/0.55 => ( ( divide_divide_rat @ A @ A )
% 0.33/0.55 = one_one_rat ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % divide_self_if
% 0.33/0.55 thf(fact_1965_divide__self,axiom,
% 0.33/0.55 ! [A: rat] :
% 0.33/0.55 ( ( A != zero_zero_rat )
% 0.33/0.55 => ( ( divide_divide_rat @ A @ A )
% 0.33/0.55 = one_one_rat ) ) ).
% 0.33/0.55
% 0.33/0.55 % divide_self
% 0.33/0.55 thf(fact_1966_one__eq__divide__iff,axiom,
% 0.33/0.55 ! [A: rat,B: rat] :
% 0.33/0.55 ( ( one_one_rat
% 0.33/0.55 = ( divide_divide_rat @ A @ B ) )
% 0.33/0.55 = ( ( B != zero_zero_rat )
% 0.33/0.55 & ( A = B ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % one_eq_divide_iff
% 0.33/0.55 thf(fact_1967_divide__eq__1__iff,axiom,
% 0.33/0.55 ! [A: rat,B: rat] :
% 0.33/0.55 ( ( ( divide_divide_rat @ A @ B )
% 0.33/0.55 = one_one_rat )
% 0.33/0.55 = ( ( B != zero_zero_rat )
% 0.33/0.55 & ( A = B ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % divide_eq_1_iff
% 0.33/0.55 thf(fact_1968_divide__minus1,axiom,
% 0.33/0.55 ! [X: rat] :
% 0.33/0.55 ( ( divide_divide_rat @ X @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.33/0.55 = ( uminus_uminus_rat @ X ) ) ).
% 0.33/0.55
% 0.33/0.55 % divide_minus1
% 0.33/0.55 thf(fact_1969_zero__le__divide__1__iff,axiom,
% 0.33/0.55 ! [A: rat] :
% 0.33/0.55 ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ one_one_rat @ A ) )
% 0.33/0.55 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 0.33/0.55
% 0.33/0.55 % zero_le_divide_1_iff
% 0.33/0.55 thf(fact_1970_divide__le__0__1__iff,axiom,
% 0.33/0.55 ! [A: rat] :
% 0.33/0.55 ( ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ zero_zero_rat )
% 0.33/0.55 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 0.33/0.55
% 0.33/0.55 % divide_le_0_1_iff
% 0.33/0.55 thf(fact_1971_zero__less__divide__1__iff,axiom,
% 0.33/0.55 ! [A: rat] :
% 0.33/0.55 ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ one_one_rat @ A ) )
% 0.33/0.55 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 0.33/0.55
% 0.33/0.55 % zero_less_divide_1_iff
% 0.33/0.55 thf(fact_1972_less__divide__eq__1__pos,axiom,
% 0.33/0.55 ! [A: rat,B: rat] :
% 0.33/0.55 ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.33/0.55 => ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 0.33/0.55 = ( ord_less_rat @ A @ B ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % less_divide_eq_1_pos
% 0.33/0.55 thf(fact_1973_less__divide__eq__1__neg,axiom,
% 0.33/0.55 ! [A: rat,B: rat] :
% 0.33/0.55 ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.33/0.55 => ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 0.33/0.55 = ( ord_less_rat @ B @ A ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % less_divide_eq_1_neg
% 0.33/0.55 thf(fact_1974_divide__less__eq__1__pos,axiom,
% 0.33/0.55 ! [A: rat,B: rat] :
% 0.33/0.55 ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.33/0.55 => ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 0.33/0.55 = ( ord_less_rat @ B @ A ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % divide_less_eq_1_pos
% 0.33/0.55 thf(fact_1975_divide__less__eq__1__neg,axiom,
% 0.33/0.55 ! [A: rat,B: rat] :
% 0.33/0.55 ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.33/0.55 => ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 0.33/0.55 = ( ord_less_rat @ A @ B ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % divide_less_eq_1_neg
% 0.33/0.55 thf(fact_1976_divide__less__0__1__iff,axiom,
% 0.33/0.55 ! [A: rat] :
% 0.33/0.55 ( ( ord_less_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ zero_zero_rat )
% 0.33/0.55 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 0.33/0.55
% 0.33/0.55 % divide_less_0_1_iff
% 0.33/0.55 thf(fact_1977_nonzero__divide__mult__cancel__right,axiom,
% 0.33/0.55 ! [B: rat,A: rat] :
% 0.33/0.55 ( ( B != zero_zero_rat )
% 0.33/0.55 => ( ( divide_divide_rat @ B @ ( times_times_rat @ A @ B ) )
% 0.33/0.55 = ( divide_divide_rat @ one_one_rat @ A ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % nonzero_divide_mult_cancel_right
% 0.33/0.55 thf(fact_1978_nonzero__divide__mult__cancel__left,axiom,
% 0.33/0.55 ! [A: rat,B: rat] :
% 0.33/0.55 ( ( A != zero_zero_rat )
% 0.33/0.55 => ( ( divide_divide_rat @ A @ ( times_times_rat @ A @ B ) )
% 0.33/0.55 = ( divide_divide_rat @ one_one_rat @ B ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % nonzero_divide_mult_cancel_left
% 0.33/0.55 thf(fact_1979_le__divide__eq__1__pos,axiom,
% 0.33/0.55 ! [A: rat,B: rat] :
% 0.33/0.55 ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.33/0.55 => ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 0.33/0.55 = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % le_divide_eq_1_pos
% 0.33/0.55 thf(fact_1980_le__divide__eq__1__neg,axiom,
% 0.33/0.55 ! [A: rat,B: rat] :
% 0.33/0.55 ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.33/0.55 => ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 0.33/0.55 = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % le_divide_eq_1_neg
% 0.33/0.55 thf(fact_1981_int__distrib_I2_J,axiom,
% 0.33/0.55 ! [W: int,Z1: int,Z22: int] :
% 0.33/0.55 ( ( times_times_int @ W @ ( plus_plus_int @ Z1 @ Z22 ) )
% 0.33/0.55 = ( plus_plus_int @ ( times_times_int @ W @ Z1 ) @ ( times_times_int @ W @ Z22 ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % int_distrib(2)
% 0.33/0.55 thf(fact_1982_int__distrib_I1_J,axiom,
% 0.33/0.55 ! [Z1: int,Z22: int,W: int] :
% 0.33/0.55 ( ( times_times_int @ ( plus_plus_int @ Z1 @ Z22 ) @ W )
% 0.33/0.55 = ( plus_plus_int @ ( times_times_int @ Z1 @ W ) @ ( times_times_int @ Z22 @ W ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % int_distrib(1)
% 0.33/0.55 thf(fact_1983_plus__int__code_I2_J,axiom,
% 0.33/0.55 ! [L: int] :
% 0.33/0.55 ( ( plus_plus_int @ zero_zero_int @ L )
% 0.33/0.55 = L ) ).
% 0.33/0.55
% 0.33/0.55 % plus_int_code(2)
% 0.33/0.55 thf(fact_1984_plus__int__code_I1_J,axiom,
% 0.33/0.55 ! [K: int] :
% 0.33/0.55 ( ( plus_plus_int @ K @ zero_zero_int )
% 0.33/0.55 = K ) ).
% 0.33/0.55
% 0.33/0.55 % plus_int_code(1)
% 0.33/0.55 thf(fact_1985_zero__integer_Orsp,axiom,
% 0.33/0.55 zero_zero_int = zero_zero_int ).
% 0.33/0.55
% 0.33/0.55 % zero_integer.rsp
% 0.33/0.55 thf(fact_1986_add__divide__distrib,axiom,
% 0.33/0.55 ! [A: rat,B: rat,C: rat] :
% 0.33/0.55 ( ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 0.33/0.55 = ( plus_plus_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % add_divide_distrib
% 0.33/0.55 thf(fact_1987_int__div__pos__eq,axiom,
% 0.33/0.55 ! [A: int,B: int,Q3: int,R2: int] :
% 0.33/0.55 ( ( A
% 0.33/0.55 = ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R2 ) )
% 0.33/0.55 => ( ( ord_less_eq_int @ zero_zero_int @ R2 )
% 0.33/0.55 => ( ( ord_less_int @ R2 @ B )
% 0.33/0.55 => ( ( divide_divide_int @ A @ B )
% 0.33/0.55 = Q3 ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % int_div_pos_eq
% 0.33/0.55 thf(fact_1988_int__div__neg__eq,axiom,
% 0.33/0.55 ! [A: int,B: int,Q3: int,R2: int] :
% 0.33/0.55 ( ( A
% 0.33/0.55 = ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R2 ) )
% 0.33/0.55 => ( ( ord_less_eq_int @ R2 @ zero_zero_int )
% 0.33/0.55 => ( ( ord_less_int @ B @ R2 )
% 0.33/0.55 => ( ( divide_divide_int @ A @ B )
% 0.33/0.55 = Q3 ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % int_div_neg_eq
% 0.33/0.55 thf(fact_1989_split__zdiv,axiom,
% 0.33/0.55 ! [P: int > $o,N2: int,K: int] :
% 0.33/0.55 ( ( P @ ( divide_divide_int @ N2 @ K ) )
% 0.33/0.55 = ( ( ( K = zero_zero_int )
% 0.33/0.55 => ( P @ zero_zero_int ) )
% 0.33/0.55 & ( ( ord_less_int @ zero_zero_int @ K )
% 0.33/0.55 => ! [I3: int,J2: int] :
% 0.33/0.55 ( ( ( ord_less_eq_int @ zero_zero_int @ J2 )
% 0.33/0.55 & ( ord_less_int @ J2 @ K )
% 0.33/0.55 & ( N2
% 0.33/0.55 = ( plus_plus_int @ ( times_times_int @ K @ I3 ) @ J2 ) ) )
% 0.33/0.55 => ( P @ I3 ) ) )
% 0.33/0.55 & ( ( ord_less_int @ K @ zero_zero_int )
% 0.33/0.55 => ! [I3: int,J2: int] :
% 0.33/0.55 ( ( ( ord_less_int @ K @ J2 )
% 0.33/0.55 & ( ord_less_eq_int @ J2 @ zero_zero_int )
% 0.33/0.55 & ( N2
% 0.33/0.55 = ( plus_plus_int @ ( times_times_int @ K @ I3 ) @ J2 ) ) )
% 0.33/0.55 => ( P @ I3 ) ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % split_zdiv
% 0.33/0.55 thf(fact_1990_frac__lt__1,axiom,
% 0.33/0.55 ! [X: rat] : ( ord_less_rat @ ( archimedean_frac_rat @ X ) @ one_one_rat ) ).
% 0.33/0.55
% 0.33/0.55 % frac_lt_1
% 0.33/0.55 thf(fact_1991_frac__1__eq,axiom,
% 0.33/0.55 ! [X: rat] :
% 0.33/0.55 ( ( archimedean_frac_rat @ ( plus_plus_rat @ X @ one_one_rat ) )
% 0.33/0.55 = ( archimedean_frac_rat @ X ) ) ).
% 0.33/0.55
% 0.33/0.55 % frac_1_eq
% 0.33/0.55 thf(fact_1992_right__inverse__eq,axiom,
% 0.33/0.55 ! [B: rat,A: rat] :
% 0.33/0.55 ( ( B != zero_zero_rat )
% 0.33/0.55 => ( ( ( divide_divide_rat @ A @ B )
% 0.33/0.55 = one_one_rat )
% 0.33/0.55 = ( A = B ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % right_inverse_eq
% 0.33/0.55 thf(fact_1993_less__divide__eq__1,axiom,
% 0.33/0.55 ! [B: rat,A: rat] :
% 0.33/0.55 ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 0.33/0.55 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.33/0.55 & ( ord_less_rat @ A @ B ) )
% 0.33/0.55 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.33/0.55 & ( ord_less_rat @ B @ A ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % less_divide_eq_1
% 0.33/0.55 thf(fact_1994_divide__less__eq__1,axiom,
% 0.33/0.55 ! [B: rat,A: rat] :
% 0.33/0.55 ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 0.33/0.55 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.33/0.55 & ( ord_less_rat @ B @ A ) )
% 0.33/0.55 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.33/0.55 & ( ord_less_rat @ A @ B ) )
% 0.33/0.55 | ( A = zero_zero_rat ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % divide_less_eq_1
% 0.33/0.55 thf(fact_1995_divide__add__eq__iff,axiom,
% 0.33/0.55 ! [Z: rat,X: rat,Y: rat] :
% 0.33/0.55 ( ( Z != zero_zero_rat )
% 0.33/0.55 => ( ( plus_plus_rat @ ( divide_divide_rat @ X @ Z ) @ Y )
% 0.33/0.55 = ( divide_divide_rat @ ( plus_plus_rat @ X @ ( times_times_rat @ Y @ Z ) ) @ Z ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % divide_add_eq_iff
% 0.33/0.55 thf(fact_1996_add__divide__eq__iff,axiom,
% 0.33/0.55 ! [Z: rat,X: rat,Y: rat] :
% 0.33/0.55 ( ( Z != zero_zero_rat )
% 0.33/0.55 => ( ( plus_plus_rat @ X @ ( divide_divide_rat @ Y @ Z ) )
% 0.33/0.55 = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ Z ) @ Y ) @ Z ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % add_divide_eq_iff
% 0.33/0.55 thf(fact_1997_add__num__frac,axiom,
% 0.33/0.55 ! [Y: rat,Z: rat,X: rat] :
% 0.33/0.55 ( ( Y != zero_zero_rat )
% 0.33/0.55 => ( ( plus_plus_rat @ Z @ ( divide_divide_rat @ X @ Y ) )
% 0.33/0.55 = ( divide_divide_rat @ ( plus_plus_rat @ X @ ( times_times_rat @ Z @ Y ) ) @ Y ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % add_num_frac
% 0.33/0.55 thf(fact_1998_add__frac__num,axiom,
% 0.33/0.55 ! [Y: rat,X: rat,Z: rat] :
% 0.33/0.55 ( ( Y != zero_zero_rat )
% 0.33/0.55 => ( ( plus_plus_rat @ ( divide_divide_rat @ X @ Y ) @ Z )
% 0.33/0.55 = ( divide_divide_rat @ ( plus_plus_rat @ X @ ( times_times_rat @ Z @ Y ) ) @ Y ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % add_frac_num
% 0.33/0.55 thf(fact_1999_add__frac__eq,axiom,
% 0.33/0.55 ! [Y: rat,Z: rat,X: rat,W: rat] :
% 0.33/0.55 ( ( Y != zero_zero_rat )
% 0.33/0.55 => ( ( Z != zero_zero_rat )
% 0.33/0.55 => ( ( plus_plus_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ W @ Z ) )
% 0.33/0.55 = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ W @ Y ) ) @ ( times_times_rat @ Y @ Z ) ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % add_frac_eq
% 0.33/0.55 thf(fact_2000_add__divide__eq__if__simps_I1_J,axiom,
% 0.33/0.55 ! [Z: rat,A: rat,B: rat] :
% 0.33/0.55 ( ( ( Z = zero_zero_rat )
% 0.33/0.55 => ( ( plus_plus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 0.33/0.55 = A ) )
% 0.33/0.55 & ( ( Z != zero_zero_rat )
% 0.33/0.55 => ( ( plus_plus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 0.33/0.55 = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % add_divide_eq_if_simps(1)
% 0.33/0.55 thf(fact_2001_add__divide__eq__if__simps_I2_J,axiom,
% 0.33/0.55 ! [Z: rat,A: rat,B: rat] :
% 0.33/0.55 ( ( ( Z = zero_zero_rat )
% 0.33/0.55 => ( ( plus_plus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 0.33/0.55 = B ) )
% 0.33/0.55 & ( ( Z != zero_zero_rat )
% 0.33/0.55 => ( ( plus_plus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 0.33/0.55 = ( divide_divide_rat @ ( plus_plus_rat @ A @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % add_divide_eq_if_simps(2)
% 0.33/0.55 thf(fact_2002_less__half__sum,axiom,
% 0.33/0.55 ! [A: rat,B: rat] :
% 0.33/0.55 ( ( ord_less_rat @ A @ B )
% 0.33/0.55 => ( ord_less_rat @ A @ ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % less_half_sum
% 0.33/0.55 thf(fact_2003_gt__half__sum,axiom,
% 0.33/0.55 ! [A: rat,B: rat] :
% 0.33/0.55 ( ( ord_less_rat @ A @ B )
% 0.33/0.55 => ( ord_less_rat @ ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ) @ B ) ) ).
% 0.33/0.55
% 0.33/0.55 % gt_half_sum
% 0.33/0.55 thf(fact_2004_divide__eq__minus__1__iff,axiom,
% 0.33/0.55 ! [A: rat,B: rat] :
% 0.33/0.55 ( ( ( divide_divide_rat @ A @ B )
% 0.33/0.55 = ( uminus_uminus_rat @ one_one_rat ) )
% 0.33/0.55 = ( ( B != zero_zero_rat )
% 0.33/0.55 & ( A
% 0.33/0.55 = ( uminus_uminus_rat @ B ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % divide_eq_minus_1_iff
% 0.33/0.55 thf(fact_2005_div__pos__geq,axiom,
% 0.33/0.55 ! [L: int,K: int] :
% 0.33/0.55 ( ( ord_less_int @ zero_zero_int @ L )
% 0.33/0.55 => ( ( ord_less_eq_int @ L @ K )
% 0.33/0.55 => ( ( divide_divide_int @ K @ L )
% 0.33/0.55 = ( plus_plus_int @ ( divide_divide_int @ ( minus_minus_int @ K @ L ) @ L ) @ one_one_int ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % div_pos_geq
% 0.33/0.55 thf(fact_2006_frac__eq,axiom,
% 0.33/0.55 ! [X: rat] :
% 0.33/0.55 ( ( ( archimedean_frac_rat @ X )
% 0.33/0.55 = X )
% 0.33/0.55 = ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 0.33/0.55 & ( ord_less_rat @ X @ one_one_rat ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % frac_eq
% 0.33/0.55 thf(fact_2007_frac__add,axiom,
% 0.33/0.55 ! [X: rat,Y: rat] :
% 0.33/0.55 ( ( ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X ) @ ( archimedean_frac_rat @ Y ) ) @ one_one_rat )
% 0.33/0.55 => ( ( archimedean_frac_rat @ ( plus_plus_rat @ X @ Y ) )
% 0.33/0.55 = ( plus_plus_rat @ ( archimedean_frac_rat @ X ) @ ( archimedean_frac_rat @ Y ) ) ) )
% 0.33/0.55 & ( ~ ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X ) @ ( archimedean_frac_rat @ Y ) ) @ one_one_rat )
% 0.33/0.55 => ( ( archimedean_frac_rat @ ( plus_plus_rat @ X @ Y ) )
% 0.33/0.55 = ( minus_minus_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X ) @ ( archimedean_frac_rat @ Y ) ) @ one_one_rat ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % frac_add
% 0.33/0.55 thf(fact_2008_incr__mult__lemma,axiom,
% 0.33/0.55 ! [D2: int,P: int > $o,K: int] :
% 0.33/0.55 ( ( ord_less_int @ zero_zero_int @ D2 )
% 0.33/0.55 => ( ! [X4: int] :
% 0.33/0.55 ( ( P @ X4 )
% 0.33/0.55 => ( P @ ( plus_plus_int @ X4 @ D2 ) ) )
% 0.33/0.55 => ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.33/0.55 => ! [X8: int] :
% 0.33/0.55 ( ( P @ X8 )
% 0.33/0.55 => ( P @ ( plus_plus_int @ X8 @ ( times_times_int @ K @ D2 ) ) ) ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % incr_mult_lemma
% 0.33/0.55 thf(fact_2009_divide__le__eq__1,axiom,
% 0.33/0.55 ! [B: rat,A: rat] :
% 0.33/0.55 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 0.33/0.55 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.33/0.55 & ( ord_less_eq_rat @ B @ A ) )
% 0.33/0.55 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.33/0.55 & ( ord_less_eq_rat @ A @ B ) )
% 0.33/0.55 | ( A = zero_zero_rat ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % divide_le_eq_1
% 0.33/0.55 thf(fact_2010_le__divide__eq__1,axiom,
% 0.33/0.55 ! [B: rat,A: rat] :
% 0.33/0.55 ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 0.33/0.55 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.33/0.55 & ( ord_less_eq_rat @ A @ B ) )
% 0.33/0.55 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.33/0.55 & ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % le_divide_eq_1
% 0.33/0.55 thf(fact_2011_minus__divide__add__eq__iff,axiom,
% 0.33/0.55 ! [Z: rat,X: rat,Y: rat] :
% 0.33/0.55 ( ( Z != zero_zero_rat )
% 0.33/0.55 => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ X @ Z ) ) @ Y )
% 0.33/0.55 = ( divide_divide_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ X ) @ ( times_times_rat @ Y @ Z ) ) @ Z ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % minus_divide_add_eq_iff
% 0.33/0.55 thf(fact_2012_add__divide__eq__if__simps_I3_J,axiom,
% 0.33/0.55 ! [Z: rat,A: rat,B: rat] :
% 0.33/0.55 ( ( ( Z = zero_zero_rat )
% 0.33/0.55 => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 0.33/0.55 = B ) )
% 0.33/0.55 & ( ( Z != zero_zero_rat )
% 0.33/0.55 => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 0.33/0.55 = ( divide_divide_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % add_divide_eq_if_simps(3)
% 0.33/0.55 thf(fact_2013_frac__neg,axiom,
% 0.33/0.55 ! [X: rat] :
% 0.33/0.55 ( ( ( member_rat @ X @ ring_1_Ints_rat )
% 0.33/0.55 => ( ( archimedean_frac_rat @ ( uminus_uminus_rat @ X ) )
% 0.33/0.55 = zero_zero_rat ) )
% 0.33/0.55 & ( ~ ( member_rat @ X @ ring_1_Ints_rat )
% 0.33/0.55 => ( ( archimedean_frac_rat @ ( uminus_uminus_rat @ X ) )
% 0.33/0.55 = ( minus_minus_rat @ one_one_rat @ ( archimedean_frac_rat @ X ) ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % frac_neg
% 0.33/0.55 thf(fact_2014_div__mult__self4,axiom,
% 0.33/0.55 ! [B: int,C: int,A: int] :
% 0.33/0.55 ( ( B != zero_zero_int )
% 0.33/0.55 => ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ B @ C ) @ A ) @ B )
% 0.33/0.55 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % div_mult_self4
% 0.33/0.55 thf(fact_2015_div__mult__self4,axiom,
% 0.33/0.55 ! [B: nat,C: nat,A: nat] :
% 0.33/0.55 ( ( B != zero_zero_nat )
% 0.33/0.55 => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ A ) @ B )
% 0.33/0.55 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % div_mult_self4
% 0.33/0.55 thf(fact_2016_div__mult__self4,axiom,
% 0.33/0.55 ! [B: code_integer,C: code_integer,A: code_integer] :
% 0.33/0.55 ( ( B != zero_z3403309356797280102nteger )
% 0.33/0.55 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ C ) @ A ) @ B )
% 0.33/0.55 = ( plus_p5714425477246183910nteger @ C @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % div_mult_self4
% 0.33/0.55 thf(fact_2017_div__mult__self4,axiom,
% 0.33/0.55 ! [B: code_natural,C: code_natural,A: code_natural] :
% 0.33/0.55 ( ( B != zero_z2226904508553997617atural )
% 0.33/0.55 => ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ B @ C ) @ A ) @ B )
% 0.33/0.55 = ( plus_p4538020629002901425atural @ C @ ( divide5121882707175180666atural @ A @ B ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % div_mult_self4
% 0.33/0.55 thf(fact_2018_div__mult__self3,axiom,
% 0.33/0.55 ! [B: int,C: int,A: int] :
% 0.33/0.55 ( ( B != zero_zero_int )
% 0.33/0.55 => ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ C @ B ) @ A ) @ B )
% 0.33/0.55 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % div_mult_self3
% 0.33/0.55 thf(fact_2019_div__mult__self3,axiom,
% 0.33/0.55 ! [B: nat,C: nat,A: nat] :
% 0.33/0.55 ( ( B != zero_zero_nat )
% 0.33/0.55 => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ A ) @ B )
% 0.33/0.55 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % div_mult_self3
% 0.33/0.55 thf(fact_2020_div__mult__self3,axiom,
% 0.33/0.55 ! [B: code_integer,C: code_integer,A: code_integer] :
% 0.33/0.55 ( ( B != zero_z3403309356797280102nteger )
% 0.33/0.55 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ C @ B ) @ A ) @ B )
% 0.33/0.55 = ( plus_p5714425477246183910nteger @ C @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % div_mult_self3
% 0.33/0.55 thf(fact_2021_div__mult__self3,axiom,
% 0.33/0.55 ! [B: code_natural,C: code_natural,A: code_natural] :
% 0.33/0.55 ( ( B != zero_z2226904508553997617atural )
% 0.33/0.55 => ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ C @ B ) @ A ) @ B )
% 0.33/0.55 = ( plus_p4538020629002901425atural @ C @ ( divide5121882707175180666atural @ A @ B ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % div_mult_self3
% 0.33/0.55 thf(fact_2022_div__mult__self2,axiom,
% 0.33/0.55 ! [B: int,A: int,C: int] :
% 0.33/0.55 ( ( B != zero_zero_int )
% 0.33/0.55 => ( ( divide_divide_int @ ( plus_plus_int @ A @ ( times_times_int @ B @ C ) ) @ B )
% 0.33/0.55 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % div_mult_self2
% 0.33/0.55 thf(fact_2023_div__mult__self2,axiom,
% 0.33/0.55 ! [B: nat,A: nat,C: nat] :
% 0.33/0.55 ( ( B != zero_zero_nat )
% 0.33/0.55 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ B @ C ) ) @ B )
% 0.33/0.55 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % div_mult_self2
% 0.33/0.55 thf(fact_2024_div__mult__self2,axiom,
% 0.33/0.55 ! [B: code_integer,A: code_integer,C: code_integer] :
% 0.33/0.55 ( ( B != zero_z3403309356797280102nteger )
% 0.33/0.55 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) ) @ B )
% 0.33/0.55 = ( plus_p5714425477246183910nteger @ C @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % div_mult_self2
% 0.33/0.55 thf(fact_2025_div__mult__self2,axiom,
% 0.33/0.55 ! [B: code_natural,A: code_natural,C: code_natural] :
% 0.33/0.55 ( ( B != zero_z2226904508553997617atural )
% 0.33/0.55 => ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ A @ ( times_2397367101498566445atural @ B @ C ) ) @ B )
% 0.33/0.55 = ( plus_p4538020629002901425atural @ C @ ( divide5121882707175180666atural @ A @ B ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % div_mult_self2
% 0.33/0.55 thf(fact_2026_div__mult__self1,axiom,
% 0.33/0.55 ! [B: int,A: int,C: int] :
% 0.33/0.55 ( ( B != zero_zero_int )
% 0.33/0.55 => ( ( divide_divide_int @ ( plus_plus_int @ A @ ( times_times_int @ C @ B ) ) @ B )
% 0.33/0.55 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % div_mult_self1
% 0.33/0.55 thf(fact_2027_div__mult__self1,axiom,
% 0.33/0.55 ! [B: nat,A: nat,C: nat] :
% 0.33/0.55 ( ( B != zero_zero_nat )
% 0.33/0.55 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ C @ B ) ) @ B )
% 0.33/0.55 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % div_mult_self1
% 0.33/0.55 thf(fact_2028_div__mult__self1,axiom,
% 0.33/0.55 ! [B: code_integer,A: code_integer,C: code_integer] :
% 0.33/0.55 ( ( B != zero_z3403309356797280102nteger )
% 0.33/0.55 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ C @ B ) ) @ B )
% 0.33/0.55 = ( plus_p5714425477246183910nteger @ C @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % div_mult_self1
% 0.33/0.55 thf(fact_2029_div__mult__self1,axiom,
% 0.33/0.55 ! [B: code_natural,A: code_natural,C: code_natural] :
% 0.33/0.55 ( ( B != zero_z2226904508553997617atural )
% 0.33/0.55 => ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ A @ ( times_2397367101498566445atural @ C @ B ) ) @ B )
% 0.33/0.55 = ( plus_p4538020629002901425atural @ C @ ( divide5121882707175180666atural @ A @ B ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % div_mult_self1
% 0.33/0.55 thf(fact_2030_div__minus1__right,axiom,
% 0.33/0.55 ! [A: int] :
% 0.33/0.55 ( ( divide_divide_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 0.33/0.55 = ( uminus_uminus_int @ A ) ) ).
% 0.33/0.55
% 0.33/0.55 % div_minus1_right
% 0.33/0.55 thf(fact_2031_div__minus1__right,axiom,
% 0.33/0.55 ! [A: code_integer] :
% 0.33/0.55 ( ( divide6298287555418463151nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.33/0.55 = ( uminus1351360451143612070nteger @ A ) ) ).
% 0.33/0.55
% 0.33/0.55 % div_minus1_right
% 0.33/0.55 thf(fact_2032_div__pos__neg__trivial,axiom,
% 0.33/0.55 ! [K: int,L: int] :
% 0.33/0.55 ( ( ord_less_int @ zero_zero_int @ K )
% 0.33/0.55 => ( ( ord_less_eq_int @ ( plus_plus_int @ K @ L ) @ zero_zero_int )
% 0.33/0.55 => ( ( divide_divide_int @ K @ L )
% 0.33/0.55 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % div_pos_neg_trivial
% 0.33/0.55 thf(fact_2033_bits__div__by__1,axiom,
% 0.33/0.55 ! [A: int] :
% 0.33/0.55 ( ( divide_divide_int @ A @ one_one_int )
% 0.33/0.55 = A ) ).
% 0.33/0.55
% 0.33/0.55 % bits_div_by_1
% 0.33/0.55 thf(fact_2034_bits__div__by__1,axiom,
% 0.33/0.55 ! [A: nat] :
% 0.33/0.55 ( ( divide_divide_nat @ A @ one_one_nat )
% 0.33/0.55 = A ) ).
% 0.33/0.55
% 0.33/0.55 % bits_div_by_1
% 0.33/0.55 thf(fact_2035_bits__div__by__1,axiom,
% 0.33/0.55 ! [A: code_integer] :
% 0.33/0.55 ( ( divide6298287555418463151nteger @ A @ one_one_Code_integer )
% 0.33/0.55 = A ) ).
% 0.33/0.55
% 0.33/0.55 % bits_div_by_1
% 0.33/0.55 thf(fact_2036_bits__div__by__1,axiom,
% 0.33/0.55 ! [A: code_natural] :
% 0.33/0.55 ( ( divide5121882707175180666atural @ A @ one_one_Code_natural )
% 0.33/0.55 = A ) ).
% 0.33/0.55
% 0.33/0.55 % bits_div_by_1
% 0.33/0.55 thf(fact_2037_dividend__less__times__div,axiom,
% 0.33/0.55 ! [N2: nat,M2: nat] :
% 0.33/0.55 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.33/0.55 => ( ord_less_nat @ M2 @ ( plus_plus_nat @ N2 @ ( times_times_nat @ N2 @ ( divide_divide_nat @ M2 @ N2 ) ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % dividend_less_times_div
% 0.33/0.55 thf(fact_2038_dividend__less__div__times,axiom,
% 0.33/0.55 ! [N2: nat,M2: nat] :
% 0.33/0.55 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.33/0.55 => ( ord_less_nat @ M2 @ ( plus_plus_nat @ N2 @ ( times_times_nat @ ( divide_divide_nat @ M2 @ N2 ) @ N2 ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % dividend_less_div_times
% 0.33/0.55 thf(fact_2039_split__div,axiom,
% 0.33/0.55 ! [P: nat > $o,M2: nat,N2: nat] :
% 0.33/0.55 ( ( P @ ( divide_divide_nat @ M2 @ N2 ) )
% 0.33/0.55 = ( ( ( N2 = zero_zero_nat )
% 0.33/0.55 => ( P @ zero_zero_nat ) )
% 0.33/0.55 & ( ( N2 != zero_zero_nat )
% 0.33/0.55 => ! [I3: nat,J2: nat] :
% 0.33/0.55 ( ( ord_less_nat @ J2 @ N2 )
% 0.33/0.55 => ( ( M2
% 0.33/0.55 = ( plus_plus_nat @ ( times_times_nat @ N2 @ I3 ) @ J2 ) )
% 0.33/0.55 => ( P @ I3 ) ) ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % split_div
% 0.33/0.55 thf(fact_2040_div__less__dividend,axiom,
% 0.33/0.55 ! [N2: nat,M2: nat] :
% 0.33/0.55 ( ( ord_less_nat @ one_one_nat @ N2 )
% 0.33/0.55 => ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 0.33/0.55 => ( ord_less_nat @ ( divide_divide_nat @ M2 @ N2 ) @ M2 ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % div_less_dividend
% 0.33/0.55 thf(fact_2041_div__eq__dividend__iff,axiom,
% 0.33/0.55 ! [M2: nat,N2: nat] :
% 0.33/0.55 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 0.33/0.55 => ( ( ( divide_divide_nat @ M2 @ N2 )
% 0.33/0.55 = M2 )
% 0.33/0.55 = ( N2 = one_one_nat ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % div_eq_dividend_iff
% 0.33/0.55 thf(fact_2042_div__add__self1,axiom,
% 0.33/0.55 ! [B: int,A: int] :
% 0.33/0.55 ( ( B != zero_zero_int )
% 0.33/0.55 => ( ( divide_divide_int @ ( plus_plus_int @ B @ A ) @ B )
% 0.33/0.55 = ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % div_add_self1
% 0.33/0.55 thf(fact_2043_div__add__self1,axiom,
% 0.33/0.55 ! [B: nat,A: nat] :
% 0.33/0.55 ( ( B != zero_zero_nat )
% 0.33/0.55 => ( ( divide_divide_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 0.33/0.55 = ( plus_plus_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % div_add_self1
% 0.33/0.55 thf(fact_2044_div__add__self1,axiom,
% 0.33/0.55 ! [B: code_integer,A: code_integer] :
% 0.33/0.55 ( ( B != zero_z3403309356797280102nteger )
% 0.33/0.55 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ B @ A ) @ B )
% 0.33/0.55 = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ B ) @ one_one_Code_integer ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % div_add_self1
% 0.33/0.55 thf(fact_2045_div__add__self1,axiom,
% 0.33/0.55 ! [B: code_natural,A: code_natural] :
% 0.33/0.55 ( ( B != zero_z2226904508553997617atural )
% 0.33/0.55 => ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ B @ A ) @ B )
% 0.33/0.55 = ( plus_p4538020629002901425atural @ ( divide5121882707175180666atural @ A @ B ) @ one_one_Code_natural ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % div_add_self1
% 0.33/0.55 thf(fact_2046_div__add__self2,axiom,
% 0.33/0.55 ! [B: int,A: int] :
% 0.33/0.55 ( ( B != zero_zero_int )
% 0.33/0.55 => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ B )
% 0.33/0.55 = ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % div_add_self2
% 0.33/0.55 thf(fact_2047_div__add__self2,axiom,
% 0.33/0.55 ! [B: nat,A: nat] :
% 0.33/0.55 ( ( B != zero_zero_nat )
% 0.33/0.55 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 0.33/0.55 = ( plus_plus_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % div_add_self2
% 0.33/0.55 thf(fact_2048_div__add__self2,axiom,
% 0.33/0.55 ! [B: code_integer,A: code_integer] :
% 0.33/0.55 ( ( B != zero_z3403309356797280102nteger )
% 0.33/0.55 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ B )
% 0.33/0.55 = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ B ) @ one_one_Code_integer ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % div_add_self2
% 0.33/0.55 thf(fact_2049_div__add__self2,axiom,
% 0.33/0.55 ! [B: code_natural,A: code_natural] :
% 0.33/0.55 ( ( B != zero_z2226904508553997617atural )
% 0.33/0.55 => ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ A @ B ) @ B )
% 0.33/0.55 = ( plus_p4538020629002901425atural @ ( divide5121882707175180666atural @ A @ B ) @ one_one_Code_natural ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % div_add_self2
% 0.33/0.55 thf(fact_2050_upto_Opinduct,axiom,
% 0.33/0.55 ! [A0: int,A1: int,P: int > int > $o] :
% 0.33/0.55 ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ A0 @ A1 ) )
% 0.33/0.55 => ( ! [I2: int,J3: int] :
% 0.33/0.55 ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ I2 @ J3 ) )
% 0.33/0.55 => ( ( ( ord_less_eq_int @ I2 @ J3 )
% 0.33/0.55 => ( P @ ( plus_plus_int @ I2 @ one_one_int ) @ J3 ) )
% 0.33/0.55 => ( P @ I2 @ J3 ) ) )
% 0.33/0.55 => ( P @ A0 @ A1 ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % upto.pinduct
% 0.33/0.55 thf(fact_2051_eucl__rel__int_Osimps,axiom,
% 0.33/0.55 ( eucl_rel_int
% 0.33/0.55 = ( ^ [A12: int,A22: int,A32: product_prod_int_int] :
% 0.33/0.55 ( ? [K4: int] :
% 0.33/0.55 ( ( A12 = K4 )
% 0.33/0.55 & ( A22 = zero_zero_int )
% 0.33/0.55 & ( A32
% 0.33/0.55 = ( product_Pair_int_int @ zero_zero_int @ K4 ) ) )
% 0.33/0.55 | ? [L3: int,K4: int,Q5: int] :
% 0.33/0.55 ( ( A12 = K4 )
% 0.33/0.55 & ( A22 = L3 )
% 0.33/0.55 & ( A32
% 0.33/0.55 = ( product_Pair_int_int @ Q5 @ zero_zero_int ) )
% 0.33/0.55 & ( L3 != zero_zero_int )
% 0.33/0.55 & ( K4
% 0.33/0.55 = ( times_times_int @ Q5 @ L3 ) ) )
% 0.33/0.55 | ? [R3: int,L3: int,K4: int,Q5: int] :
% 0.33/0.55 ( ( A12 = K4 )
% 0.33/0.55 & ( A22 = L3 )
% 0.33/0.55 & ( A32
% 0.33/0.55 = ( product_Pair_int_int @ Q5 @ R3 ) )
% 0.33/0.55 & ( ( sgn_sgn_int @ R3 )
% 0.33/0.55 = ( sgn_sgn_int @ L3 ) )
% 0.33/0.55 & ( ord_less_int @ ( abs_abs_int @ R3 ) @ ( abs_abs_int @ L3 ) )
% 0.33/0.55 & ( K4
% 0.33/0.55 = ( plus_plus_int @ ( times_times_int @ Q5 @ L3 ) @ R3 ) ) ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % eucl_rel_int.simps
% 0.33/0.55 thf(fact_2052_eucl__rel__int_Ocases,axiom,
% 0.33/0.55 ! [A1: int,A23: int,A33: product_prod_int_int] :
% 0.33/0.55 ( ( eucl_rel_int @ A1 @ A23 @ A33 )
% 0.33/0.55 => ( ( ( A23 = zero_zero_int )
% 0.33/0.55 => ( A33
% 0.33/0.55 != ( product_Pair_int_int @ zero_zero_int @ A1 ) ) )
% 0.33/0.55 => ( ! [Q2: int] :
% 0.33/0.55 ( ( A33
% 0.33/0.55 = ( product_Pair_int_int @ Q2 @ zero_zero_int ) )
% 0.33/0.55 => ( ( A23 != zero_zero_int )
% 0.33/0.55 => ( A1
% 0.33/0.55 != ( times_times_int @ Q2 @ A23 ) ) ) )
% 0.33/0.55 => ~ ! [R: int,Q2: int] :
% 0.33/0.55 ( ( A33
% 0.33/0.55 = ( product_Pair_int_int @ Q2 @ R ) )
% 0.33/0.55 => ( ( ( sgn_sgn_int @ R )
% 0.33/0.55 = ( sgn_sgn_int @ A23 ) )
% 0.33/0.55 => ( ( ord_less_int @ ( abs_abs_int @ R ) @ ( abs_abs_int @ A23 ) )
% 0.33/0.55 => ( A1
% 0.33/0.55 != ( plus_plus_int @ ( times_times_int @ Q2 @ A23 ) @ R ) ) ) ) ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % eucl_rel_int.cases
% 0.33/0.55 thf(fact_2053_eucl__rel__int__iff,axiom,
% 0.33/0.55 ! [K: int,L: int,Q3: int,R2: int] :
% 0.33/0.55 ( ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q3 @ R2 ) )
% 0.33/0.55 = ( ( K
% 0.33/0.55 = ( plus_plus_int @ ( times_times_int @ L @ Q3 ) @ R2 ) )
% 0.33/0.55 & ( ( ord_less_int @ zero_zero_int @ L )
% 0.33/0.55 => ( ( ord_less_eq_int @ zero_zero_int @ R2 )
% 0.33/0.55 & ( ord_less_int @ R2 @ L ) ) )
% 0.33/0.55 & ( ~ ( ord_less_int @ zero_zero_int @ L )
% 0.33/0.55 => ( ( ( ord_less_int @ L @ zero_zero_int )
% 0.33/0.55 => ( ( ord_less_int @ L @ R2 )
% 0.33/0.55 & ( ord_less_eq_int @ R2 @ zero_zero_int ) ) )
% 0.33/0.55 & ( ~ ( ord_less_int @ L @ zero_zero_int )
% 0.33/0.55 => ( Q3 = zero_zero_int ) ) ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % eucl_rel_int_iff
% 0.33/0.55 thf(fact_2054_split__neg__lemma,axiom,
% 0.33/0.55 ! [K: int,P: int > int > $o,N2: int] :
% 0.33/0.55 ( ( ord_less_int @ K @ zero_zero_int )
% 0.33/0.55 => ( ( P @ ( divide_divide_int @ N2 @ K ) @ ( modulo_modulo_int @ N2 @ K ) )
% 0.33/0.55 = ( ! [I3: int,J2: int] :
% 0.33/0.55 ( ( ( ord_less_int @ K @ J2 )
% 0.33/0.55 & ( ord_less_eq_int @ J2 @ zero_zero_int )
% 0.33/0.55 & ( N2
% 0.33/0.55 = ( plus_plus_int @ ( times_times_int @ K @ I3 ) @ J2 ) ) )
% 0.33/0.55 => ( P @ I3 @ J2 ) ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % split_neg_lemma
% 0.33/0.55 thf(fact_2055_split__pos__lemma,axiom,
% 0.33/0.55 ! [K: int,P: int > int > $o,N2: int] :
% 0.33/0.55 ( ( ord_less_int @ zero_zero_int @ K )
% 0.33/0.55 => ( ( P @ ( divide_divide_int @ N2 @ K ) @ ( modulo_modulo_int @ N2 @ K ) )
% 0.33/0.55 = ( ! [I3: int,J2: int] :
% 0.33/0.55 ( ( ( ord_less_eq_int @ zero_zero_int @ J2 )
% 0.33/0.55 & ( ord_less_int @ J2 @ K )
% 0.33/0.55 & ( N2
% 0.33/0.55 = ( plus_plus_int @ ( times_times_int @ K @ I3 ) @ J2 ) ) )
% 0.33/0.55 => ( P @ I3 @ J2 ) ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % split_pos_lemma
% 0.33/0.55 thf(fact_2056_mod__add__self2,axiom,
% 0.33/0.55 ! [A: int,B: int] :
% 0.33/0.55 ( ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ B )
% 0.33/0.55 = ( modulo_modulo_int @ A @ B ) ) ).
% 0.33/0.55
% 0.33/0.55 % mod_add_self2
% 0.33/0.55 thf(fact_2057_mod__add__self2,axiom,
% 0.33/0.55 ! [A: nat,B: nat] :
% 0.33/0.55 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 0.33/0.55 = ( modulo_modulo_nat @ A @ B ) ) ).
% 0.33/0.55
% 0.33/0.55 % mod_add_self2
% 0.33/0.55 thf(fact_2058_mod__add__self2,axiom,
% 0.33/0.55 ! [A: code_integer,B: code_integer] :
% 0.33/0.55 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ B )
% 0.33/0.55 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 0.33/0.55
% 0.33/0.55 % mod_add_self2
% 0.33/0.55 thf(fact_2059_mod__add__self2,axiom,
% 0.33/0.55 ! [A: code_natural,B: code_natural] :
% 0.33/0.55 ( ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ A @ B ) @ B )
% 0.33/0.55 = ( modulo8411746178871703098atural @ A @ B ) ) ).
% 0.33/0.55
% 0.33/0.55 % mod_add_self2
% 0.33/0.55 thf(fact_2060_mod__add__self1,axiom,
% 0.33/0.55 ! [B: int,A: int] :
% 0.33/0.55 ( ( modulo_modulo_int @ ( plus_plus_int @ B @ A ) @ B )
% 0.33/0.55 = ( modulo_modulo_int @ A @ B ) ) ).
% 0.33/0.55
% 0.33/0.55 % mod_add_self1
% 0.33/0.55 thf(fact_2061_mod__add__self1,axiom,
% 0.33/0.55 ! [B: nat,A: nat] :
% 0.33/0.55 ( ( modulo_modulo_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 0.33/0.55 = ( modulo_modulo_nat @ A @ B ) ) ).
% 0.33/0.55
% 0.33/0.55 % mod_add_self1
% 0.33/0.55 thf(fact_2062_mod__add__self1,axiom,
% 0.33/0.55 ! [B: code_integer,A: code_integer] :
% 0.33/0.55 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ B @ A ) @ B )
% 0.33/0.55 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 0.33/0.55
% 0.33/0.55 % mod_add_self1
% 0.33/0.55 thf(fact_2063_mod__add__self1,axiom,
% 0.33/0.55 ! [B: code_natural,A: code_natural] :
% 0.33/0.55 ( ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ B @ A ) @ B )
% 0.33/0.55 = ( modulo8411746178871703098atural @ A @ B ) ) ).
% 0.33/0.55
% 0.33/0.55 % mod_add_self1
% 0.33/0.55 thf(fact_2064_mod__by__1,axiom,
% 0.33/0.55 ! [A: int] :
% 0.33/0.55 ( ( modulo_modulo_int @ A @ one_one_int )
% 0.33/0.55 = zero_zero_int ) ).
% 0.33/0.55
% 0.33/0.55 % mod_by_1
% 0.33/0.55 thf(fact_2065_mod__by__1,axiom,
% 0.33/0.55 ! [A: nat] :
% 0.33/0.55 ( ( modulo_modulo_nat @ A @ one_one_nat )
% 0.33/0.55 = zero_zero_nat ) ).
% 0.33/0.55
% 0.33/0.55 % mod_by_1
% 0.33/0.55 thf(fact_2066_mod__by__1,axiom,
% 0.33/0.55 ! [A: code_integer] :
% 0.33/0.55 ( ( modulo364778990260209775nteger @ A @ one_one_Code_integer )
% 0.33/0.55 = zero_z3403309356797280102nteger ) ).
% 0.33/0.55
% 0.33/0.55 % mod_by_1
% 0.33/0.55 thf(fact_2067_mod__by__1,axiom,
% 0.33/0.55 ! [A: code_natural] :
% 0.33/0.55 ( ( modulo8411746178871703098atural @ A @ one_one_Code_natural )
% 0.33/0.55 = zero_z2226904508553997617atural ) ).
% 0.33/0.55
% 0.33/0.55 % mod_by_1
% 0.33/0.55 thf(fact_2068_bits__mod__by__1,axiom,
% 0.33/0.55 ! [A: int] :
% 0.33/0.55 ( ( modulo_modulo_int @ A @ one_one_int )
% 0.33/0.55 = zero_zero_int ) ).
% 0.33/0.55
% 0.33/0.55 % bits_mod_by_1
% 0.33/0.55 thf(fact_2069_bits__mod__by__1,axiom,
% 0.33/0.55 ! [A: nat] :
% 0.33/0.55 ( ( modulo_modulo_nat @ A @ one_one_nat )
% 0.33/0.55 = zero_zero_nat ) ).
% 0.33/0.55
% 0.33/0.55 % bits_mod_by_1
% 0.33/0.55 thf(fact_2070_bits__mod__by__1,axiom,
% 0.33/0.55 ! [A: code_integer] :
% 0.33/0.55 ( ( modulo364778990260209775nteger @ A @ one_one_Code_integer )
% 0.33/0.55 = zero_z3403309356797280102nteger ) ).
% 0.33/0.55
% 0.33/0.55 % bits_mod_by_1
% 0.33/0.55 thf(fact_2071_bits__mod__by__1,axiom,
% 0.33/0.55 ! [A: code_natural] :
% 0.33/0.55 ( ( modulo8411746178871703098atural @ A @ one_one_Code_natural )
% 0.33/0.55 = zero_z2226904508553997617atural ) ).
% 0.33/0.55
% 0.33/0.55 % bits_mod_by_1
% 0.33/0.55 thf(fact_2072_mod__mult__self1,axiom,
% 0.33/0.55 ! [A: int,C: int,B: int] :
% 0.33/0.55 ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( times_times_int @ C @ B ) ) @ B )
% 0.33/0.55 = ( modulo_modulo_int @ A @ B ) ) ).
% 0.33/0.55
% 0.33/0.55 % mod_mult_self1
% 0.33/0.55 thf(fact_2073_mod__mult__self1,axiom,
% 0.33/0.55 ! [A: nat,C: nat,B: nat] :
% 0.33/0.55 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ C @ B ) ) @ B )
% 0.33/0.55 = ( modulo_modulo_nat @ A @ B ) ) ).
% 0.33/0.55
% 0.33/0.55 % mod_mult_self1
% 0.33/0.55 thf(fact_2074_mod__mult__self1,axiom,
% 0.33/0.55 ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.33/0.55 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ C @ B ) ) @ B )
% 0.33/0.55 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 0.33/0.55
% 0.33/0.55 % mod_mult_self1
% 0.33/0.55 thf(fact_2075_mod__mult__self1,axiom,
% 0.33/0.55 ! [A: code_natural,C: code_natural,B: code_natural] :
% 0.33/0.55 ( ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ A @ ( times_2397367101498566445atural @ C @ B ) ) @ B )
% 0.33/0.55 = ( modulo8411746178871703098atural @ A @ B ) ) ).
% 0.33/0.55
% 0.33/0.55 % mod_mult_self1
% 0.33/0.55 thf(fact_2076_mod__mult__self2,axiom,
% 0.33/0.55 ! [A: int,B: int,C: int] :
% 0.33/0.55 ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( times_times_int @ B @ C ) ) @ B )
% 0.33/0.55 = ( modulo_modulo_int @ A @ B ) ) ).
% 0.33/0.55
% 0.33/0.55 % mod_mult_self2
% 0.33/0.55 thf(fact_2077_mod__mult__self2,axiom,
% 0.33/0.55 ! [A: nat,B: nat,C: nat] :
% 0.33/0.55 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ B @ C ) ) @ B )
% 0.33/0.55 = ( modulo_modulo_nat @ A @ B ) ) ).
% 0.33/0.55
% 0.33/0.55 % mod_mult_self2
% 0.33/0.55 thf(fact_2078_mod__mult__self2,axiom,
% 0.33/0.55 ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.33/0.55 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) ) @ B )
% 0.33/0.55 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 0.33/0.55
% 0.33/0.55 % mod_mult_self2
% 0.33/0.55 thf(fact_2079_mod__mult__self2,axiom,
% 0.33/0.55 ! [A: code_natural,B: code_natural,C: code_natural] :
% 0.33/0.55 ( ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ A @ ( times_2397367101498566445atural @ B @ C ) ) @ B )
% 0.33/0.55 = ( modulo8411746178871703098atural @ A @ B ) ) ).
% 0.33/0.55
% 0.33/0.55 % mod_mult_self2
% 0.33/0.55 thf(fact_2080_mod__mult__self3,axiom,
% 0.33/0.55 ! [C: int,B: int,A: int] :
% 0.33/0.55 ( ( modulo_modulo_int @ ( plus_plus_int @ ( times_times_int @ C @ B ) @ A ) @ B )
% 0.33/0.55 = ( modulo_modulo_int @ A @ B ) ) ).
% 0.33/0.55
% 0.33/0.55 % mod_mult_self3
% 0.33/0.55 thf(fact_2081_mod__mult__self3,axiom,
% 0.33/0.55 ! [C: nat,B: nat,A: nat] :
% 0.33/0.55 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ A ) @ B )
% 0.33/0.55 = ( modulo_modulo_nat @ A @ B ) ) ).
% 0.33/0.55
% 0.33/0.55 % mod_mult_self3
% 0.33/0.55 thf(fact_2082_mod__mult__self3,axiom,
% 0.33/0.55 ! [C: code_integer,B: code_integer,A: code_integer] :
% 0.33/0.55 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ C @ B ) @ A ) @ B )
% 0.33/0.55 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 0.33/0.55
% 0.33/0.55 % mod_mult_self3
% 0.33/0.55 thf(fact_2083_mod__mult__self3,axiom,
% 0.33/0.55 ! [C: code_natural,B: code_natural,A: code_natural] :
% 0.33/0.55 ( ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ C @ B ) @ A ) @ B )
% 0.33/0.55 = ( modulo8411746178871703098atural @ A @ B ) ) ).
% 0.33/0.55
% 0.33/0.55 % mod_mult_self3
% 0.33/0.55 thf(fact_2084_mod__mult__self4,axiom,
% 0.33/0.55 ! [B: int,C: int,A: int] :
% 0.33/0.55 ( ( modulo_modulo_int @ ( plus_plus_int @ ( times_times_int @ B @ C ) @ A ) @ B )
% 0.33/0.55 = ( modulo_modulo_int @ A @ B ) ) ).
% 0.33/0.55
% 0.33/0.55 % mod_mult_self4
% 0.33/0.55 thf(fact_2085_mod__mult__self4,axiom,
% 0.33/0.55 ! [B: nat,C: nat,A: nat] :
% 0.33/0.55 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ A ) @ B )
% 0.33/0.55 = ( modulo_modulo_nat @ A @ B ) ) ).
% 0.33/0.55
% 0.33/0.55 % mod_mult_self4
% 0.33/0.55 thf(fact_2086_mod__mult__self4,axiom,
% 0.33/0.55 ! [B: code_integer,C: code_integer,A: code_integer] :
% 0.33/0.55 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ C ) @ A ) @ B )
% 0.33/0.55 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 0.33/0.55
% 0.33/0.55 % mod_mult_self4
% 0.33/0.55 thf(fact_2087_mod__mult__self4,axiom,
% 0.33/0.55 ! [B: code_natural,C: code_natural,A: code_natural] :
% 0.33/0.55 ( ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ B @ C ) @ A ) @ B )
% 0.33/0.55 = ( modulo8411746178871703098atural @ A @ B ) ) ).
% 0.33/0.55
% 0.33/0.55 % mod_mult_self4
% 0.33/0.55 thf(fact_2088_mod__minus1__right,axiom,
% 0.33/0.55 ! [A: int] :
% 0.33/0.55 ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 0.33/0.55 = zero_zero_int ) ).
% 0.33/0.55
% 0.33/0.55 % mod_minus1_right
% 0.33/0.55 thf(fact_2089_mod__minus1__right,axiom,
% 0.33/0.55 ! [A: code_integer] :
% 0.33/0.55 ( ( modulo364778990260209775nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.33/0.55 = zero_z3403309356797280102nteger ) ).
% 0.33/0.55
% 0.33/0.55 % mod_minus1_right
% 0.33/0.55 thf(fact_2090_mod__int__unique,axiom,
% 0.33/0.55 ! [K: int,L: int,Q3: int,R2: int] :
% 0.33/0.55 ( ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q3 @ R2 ) )
% 0.33/0.55 => ( ( modulo_modulo_int @ K @ L )
% 0.33/0.55 = R2 ) ) ).
% 0.33/0.55
% 0.33/0.55 % mod_int_unique
% 0.33/0.55 thf(fact_2091_unique__quotient,axiom,
% 0.33/0.55 ! [A: int,B: int,Q3: int,R2: int,Q4: int,R6: int] :
% 0.33/0.55 ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q3 @ R2 ) )
% 0.33/0.55 => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q4 @ R6 ) )
% 0.33/0.55 => ( Q3 = Q4 ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % unique_quotient
% 0.33/0.55 thf(fact_2092_unique__remainder,axiom,
% 0.33/0.55 ! [A: int,B: int,Q3: int,R2: int,Q4: int,R6: int] :
% 0.33/0.55 ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q3 @ R2 ) )
% 0.33/0.55 => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q4 @ R6 ) )
% 0.33/0.55 => ( R2 = R6 ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % unique_remainder
% 0.33/0.55 thf(fact_2093_full__exhaustive__int_H_Ocases,axiom,
% 0.33/0.55 ! [X: produc2285326912895808259nt_int] :
% 0.33/0.55 ~ ! [F3: produc8551481072490612790e_term > option6357759511663192854e_term,D: int,I2: int] :
% 0.33/0.55 ( X
% 0.33/0.55 != ( produc5700946648718959541nt_int @ F3 @ ( product_Pair_int_int @ D @ I2 ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % full_exhaustive_int'.cases
% 0.33/0.55 thf(fact_2094_exhaustive__int_H_Ocases,axiom,
% 0.33/0.55 ! [X: produc7773217078559923341nt_int] :
% 0.33/0.55 ~ ! [F3: int > option6357759511663192854e_term,D: int,I2: int] :
% 0.33/0.55 ( X
% 0.33/0.55 != ( produc4305682042979456191nt_int @ F3 @ ( product_Pair_int_int @ D @ I2 ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % exhaustive_int'.cases
% 0.33/0.55 thf(fact_2095_small__lazy_H_Ocases,axiom,
% 0.33/0.55 ! [X: product_prod_int_int] :
% 0.33/0.55 ~ ! [D: int,I2: int] :
% 0.33/0.55 ( X
% 0.33/0.55 != ( product_Pair_int_int @ D @ I2 ) ) ).
% 0.33/0.55
% 0.33/0.55 % small_lazy'.cases
% 0.33/0.55 thf(fact_2096_eucl__rel__int,axiom,
% 0.33/0.55 ! [K: int,L: int] : ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ ( divide_divide_int @ K @ L ) @ ( modulo_modulo_int @ K @ L ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % eucl_rel_int
% 0.33/0.55 thf(fact_2097_mod__add__right__eq,axiom,
% 0.33/0.55 ! [A: int,B: int,C: int] :
% 0.33/0.55 ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 0.33/0.55 = ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 0.33/0.55
% 0.33/0.55 % mod_add_right_eq
% 0.33/0.55 thf(fact_2098_mod__add__right__eq,axiom,
% 0.33/0.55 ! [A: nat,B: nat,C: nat] :
% 0.33/0.55 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 0.33/0.55 = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) ).
% 0.33/0.55
% 0.33/0.55 % mod_add_right_eq
% 0.33/0.55 thf(fact_2099_mod__add__right__eq,axiom,
% 0.33/0.55 ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.33/0.55 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 0.33/0.55 = ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C ) ) ).
% 0.33/0.55
% 0.33/0.55 % mod_add_right_eq
% 0.33/0.55 thf(fact_2100_mod__add__right__eq,axiom,
% 0.33/0.55 ! [A: code_natural,B: code_natural,C: code_natural] :
% 0.33/0.55 ( ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ A @ ( modulo8411746178871703098atural @ B @ C ) ) @ C )
% 0.33/0.55 = ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ A @ B ) @ C ) ) ).
% 0.33/0.55
% 0.33/0.55 % mod_add_right_eq
% 0.33/0.55 thf(fact_2101_mod__add__left__eq,axiom,
% 0.33/0.55 ! [A: int,C: int,B: int] :
% 0.33/0.55 ( ( modulo_modulo_int @ ( plus_plus_int @ ( modulo_modulo_int @ A @ C ) @ B ) @ C )
% 0.33/0.55 = ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 0.33/0.55
% 0.33/0.55 % mod_add_left_eq
% 0.33/0.55 thf(fact_2102_mod__add__left__eq,axiom,
% 0.33/0.55 ! [A: nat,C: nat,B: nat] :
% 0.33/0.55 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ A @ C ) @ B ) @ C )
% 0.33/0.55 = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) ).
% 0.33/0.55
% 0.33/0.55 % mod_add_left_eq
% 0.33/0.55 thf(fact_2103_mod__add__left__eq,axiom,
% 0.33/0.55 ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.33/0.55 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ C ) @ B ) @ C )
% 0.33/0.55 = ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C ) ) ).
% 0.33/0.55
% 0.33/0.55 % mod_add_left_eq
% 0.33/0.55 thf(fact_2104_mod__add__left__eq,axiom,
% 0.33/0.55 ! [A: code_natural,C: code_natural,B: code_natural] :
% 0.33/0.55 ( ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ ( modulo8411746178871703098atural @ A @ C ) @ B ) @ C )
% 0.33/0.55 = ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ A @ B ) @ C ) ) ).
% 0.33/0.55
% 0.33/0.55 % mod_add_left_eq
% 0.33/0.55 thf(fact_2105_mod__add__cong,axiom,
% 0.33/0.55 ! [A: int,C: int,A4: int,B: int,B3: int] :
% 0.33/0.55 ( ( ( modulo_modulo_int @ A @ C )
% 0.33/0.55 = ( modulo_modulo_int @ A4 @ C ) )
% 0.33/0.55 => ( ( ( modulo_modulo_int @ B @ C )
% 0.33/0.55 = ( modulo_modulo_int @ B3 @ C ) )
% 0.33/0.55 => ( ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C )
% 0.33/0.55 = ( modulo_modulo_int @ ( plus_plus_int @ A4 @ B3 ) @ C ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % mod_add_cong
% 0.33/0.55 thf(fact_2106_mod__add__cong,axiom,
% 0.33/0.55 ! [A: nat,C: nat,A4: nat,B: nat,B3: nat] :
% 0.33/0.55 ( ( ( modulo_modulo_nat @ A @ C )
% 0.33/0.55 = ( modulo_modulo_nat @ A4 @ C ) )
% 0.33/0.55 => ( ( ( modulo_modulo_nat @ B @ C )
% 0.33/0.55 = ( modulo_modulo_nat @ B3 @ C ) )
% 0.33/0.55 => ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 0.33/0.55 = ( modulo_modulo_nat @ ( plus_plus_nat @ A4 @ B3 ) @ C ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % mod_add_cong
% 0.33/0.55 thf(fact_2107_mod__add__cong,axiom,
% 0.33/0.55 ! [A: code_integer,C: code_integer,A4: code_integer,B: code_integer,B3: code_integer] :
% 0.33/0.55 ( ( ( modulo364778990260209775nteger @ A @ C )
% 0.33/0.55 = ( modulo364778990260209775nteger @ A4 @ C ) )
% 0.33/0.55 => ( ( ( modulo364778990260209775nteger @ B @ C )
% 0.33/0.55 = ( modulo364778990260209775nteger @ B3 @ C ) )
% 0.33/0.55 => ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 0.33/0.55 = ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A4 @ B3 ) @ C ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % mod_add_cong
% 0.33/0.55 thf(fact_2108_mod__add__cong,axiom,
% 0.33/0.55 ! [A: code_natural,C: code_natural,A4: code_natural,B: code_natural,B3: code_natural] :
% 0.33/0.55 ( ( ( modulo8411746178871703098atural @ A @ C )
% 0.33/0.55 = ( modulo8411746178871703098atural @ A4 @ C ) )
% 0.33/0.55 => ( ( ( modulo8411746178871703098atural @ B @ C )
% 0.33/0.55 = ( modulo8411746178871703098atural @ B3 @ C ) )
% 0.33/0.55 => ( ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ A @ B ) @ C )
% 0.33/0.55 = ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ A4 @ B3 ) @ C ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % mod_add_cong
% 0.33/0.55 thf(fact_2109_mod__add__eq,axiom,
% 0.33/0.55 ! [A: int,C: int,B: int] :
% 0.33/0.55 ( ( modulo_modulo_int @ ( plus_plus_int @ ( modulo_modulo_int @ A @ C ) @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 0.33/0.55 = ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 0.33/0.55
% 0.33/0.55 % mod_add_eq
% 0.33/0.55 thf(fact_2110_mod__add__eq,axiom,
% 0.33/0.55 ! [A: nat,C: nat,B: nat] :
% 0.33/0.55 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ A @ C ) @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 0.33/0.55 = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) ).
% 0.33/0.55
% 0.33/0.55 % mod_add_eq
% 0.33/0.55 thf(fact_2111_mod__add__eq,axiom,
% 0.33/0.55 ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.33/0.55 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ C ) @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 0.33/0.55 = ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C ) ) ).
% 0.33/0.55
% 0.33/0.55 % mod_add_eq
% 0.33/0.55 thf(fact_2112_mod__add__eq,axiom,
% 0.33/0.55 ! [A: code_natural,C: code_natural,B: code_natural] :
% 0.33/0.55 ( ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ ( modulo8411746178871703098atural @ A @ C ) @ ( modulo8411746178871703098atural @ B @ C ) ) @ C )
% 0.33/0.55 = ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ A @ B ) @ C ) ) ).
% 0.33/0.55
% 0.33/0.55 % mod_add_eq
% 0.33/0.55 thf(fact_2113_eucl__rel__int__by0,axiom,
% 0.33/0.55 ! [K: int] : ( eucl_rel_int @ K @ zero_zero_int @ ( product_Pair_int_int @ zero_zero_int @ K ) ) ).
% 0.33/0.55
% 0.33/0.55 % eucl_rel_int_by0
% 0.33/0.55 thf(fact_2114_div__int__unique,axiom,
% 0.33/0.55 ! [K: int,L: int,Q3: int,R2: int] :
% 0.33/0.55 ( ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q3 @ R2 ) )
% 0.33/0.55 => ( ( divide_divide_int @ K @ L )
% 0.33/0.55 = Q3 ) ) ).
% 0.33/0.55
% 0.33/0.55 % div_int_unique
% 0.33/0.55 thf(fact_2115_mod__eqE,axiom,
% 0.33/0.55 ! [A: int,C: int,B: int] :
% 0.33/0.55 ( ( ( modulo_modulo_int @ A @ C )
% 0.33/0.55 = ( modulo_modulo_int @ B @ C ) )
% 0.33/0.55 => ~ ! [D: int] :
% 0.33/0.55 ( B
% 0.33/0.55 != ( plus_plus_int @ A @ ( times_times_int @ C @ D ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % mod_eqE
% 0.33/0.55 thf(fact_2116_mod__eqE,axiom,
% 0.33/0.55 ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.33/0.55 ( ( ( modulo364778990260209775nteger @ A @ C )
% 0.33/0.55 = ( modulo364778990260209775nteger @ B @ C ) )
% 0.33/0.55 => ~ ! [D: code_integer] :
% 0.33/0.55 ( B
% 0.33/0.55 != ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ C @ D ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % mod_eqE
% 0.33/0.55 thf(fact_2117_div__add1__eq,axiom,
% 0.33/0.55 ! [A: int,B: int,C: int] :
% 0.33/0.55 ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 0.33/0.55 = ( plus_plus_int @ ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) @ ( divide_divide_int @ ( plus_plus_int @ ( modulo_modulo_int @ A @ C ) @ ( modulo_modulo_int @ B @ C ) ) @ C ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % div_add1_eq
% 0.33/0.55 thf(fact_2118_div__add1__eq,axiom,
% 0.33/0.55 ! [A: nat,B: nat,C: nat] :
% 0.33/0.55 ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 0.33/0.55 = ( plus_plus_nat @ ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) @ ( divide_divide_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ A @ C ) @ ( modulo_modulo_nat @ B @ C ) ) @ C ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % div_add1_eq
% 0.33/0.55 thf(fact_2119_div__add1__eq,axiom,
% 0.33/0.55 ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.33/0.55 ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 0.33/0.55 = ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) @ ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ C ) @ ( modulo364778990260209775nteger @ B @ C ) ) @ C ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % div_add1_eq
% 0.33/0.55 thf(fact_2120_div__add1__eq,axiom,
% 0.33/0.55 ! [A: code_natural,B: code_natural,C: code_natural] :
% 0.33/0.55 ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ A @ B ) @ C )
% 0.33/0.55 = ( plus_p4538020629002901425atural @ ( plus_p4538020629002901425atural @ ( divide5121882707175180666atural @ A @ C ) @ ( divide5121882707175180666atural @ B @ C ) ) @ ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ ( modulo8411746178871703098atural @ A @ C ) @ ( modulo8411746178871703098atural @ B @ C ) ) @ C ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % div_add1_eq
% 0.33/0.55 thf(fact_2121_mult__div__mod__eq,axiom,
% 0.33/0.55 ! [B: int,A: int] :
% 0.33/0.55 ( ( plus_plus_int @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) @ ( modulo_modulo_int @ A @ B ) )
% 0.33/0.55 = A ) ).
% 0.33/0.55
% 0.33/0.55 % mult_div_mod_eq
% 0.33/0.55 thf(fact_2122_mult__div__mod__eq,axiom,
% 0.33/0.55 ! [B: nat,A: nat] :
% 0.33/0.55 ( ( plus_plus_nat @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) @ ( modulo_modulo_nat @ A @ B ) )
% 0.33/0.55 = A ) ).
% 0.33/0.55
% 0.33/0.55 % mult_div_mod_eq
% 0.33/0.55 thf(fact_2123_mult__div__mod__eq,axiom,
% 0.33/0.55 ! [B: code_integer,A: code_integer] :
% 0.33/0.55 ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) @ ( modulo364778990260209775nteger @ A @ B ) )
% 0.33/0.55 = A ) ).
% 0.33/0.55
% 0.33/0.55 % mult_div_mod_eq
% 0.33/0.55 thf(fact_2124_mult__div__mod__eq,axiom,
% 0.33/0.55 ! [B: code_natural,A: code_natural] :
% 0.33/0.55 ( ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ B @ ( divide5121882707175180666atural @ A @ B ) ) @ ( modulo8411746178871703098atural @ A @ B ) )
% 0.33/0.55 = A ) ).
% 0.33/0.55
% 0.33/0.55 % mult_div_mod_eq
% 0.33/0.55 thf(fact_2125_mod__mult__div__eq,axiom,
% 0.33/0.55 ! [A: int,B: int] :
% 0.33/0.55 ( ( plus_plus_int @ ( modulo_modulo_int @ A @ B ) @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) )
% 0.33/0.55 = A ) ).
% 0.33/0.55
% 0.33/0.55 % mod_mult_div_eq
% 0.33/0.55 thf(fact_2126_mod__mult__div__eq,axiom,
% 0.33/0.55 ! [A: nat,B: nat] :
% 0.33/0.55 ( ( plus_plus_nat @ ( modulo_modulo_nat @ A @ B ) @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) )
% 0.33/0.55 = A ) ).
% 0.33/0.55
% 0.33/0.55 % mod_mult_div_eq
% 0.33/0.55 thf(fact_2127_mod__mult__div__eq,axiom,
% 0.33/0.55 ! [A: code_integer,B: code_integer] :
% 0.33/0.55 ( ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ B ) @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) )
% 0.33/0.55 = A ) ).
% 0.33/0.55
% 0.33/0.55 % mod_mult_div_eq
% 0.33/0.55 thf(fact_2128_mod__mult__div__eq,axiom,
% 0.33/0.55 ! [A: code_natural,B: code_natural] :
% 0.33/0.55 ( ( plus_p4538020629002901425atural @ ( modulo8411746178871703098atural @ A @ B ) @ ( times_2397367101498566445atural @ B @ ( divide5121882707175180666atural @ A @ B ) ) )
% 0.33/0.55 = A ) ).
% 0.33/0.55
% 0.33/0.55 % mod_mult_div_eq
% 0.33/0.55 thf(fact_2129_mod__div__mult__eq,axiom,
% 0.33/0.55 ! [A: int,B: int] :
% 0.33/0.55 ( ( plus_plus_int @ ( modulo_modulo_int @ A @ B ) @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) )
% 0.33/0.55 = A ) ).
% 0.33/0.55
% 0.33/0.55 % mod_div_mult_eq
% 0.33/0.55 thf(fact_2130_mod__div__mult__eq,axiom,
% 0.33/0.55 ! [A: nat,B: nat] :
% 0.33/0.55 ( ( plus_plus_nat @ ( modulo_modulo_nat @ A @ B ) @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) )
% 0.33/0.55 = A ) ).
% 0.33/0.55
% 0.33/0.55 % mod_div_mult_eq
% 0.33/0.55 thf(fact_2131_mod__div__mult__eq,axiom,
% 0.33/0.55 ! [A: code_integer,B: code_integer] :
% 0.33/0.55 ( ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ B ) @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) )
% 0.33/0.55 = A ) ).
% 0.33/0.55
% 0.33/0.55 % mod_div_mult_eq
% 0.33/0.55 thf(fact_2132_mod__div__mult__eq,axiom,
% 0.33/0.55 ! [A: code_natural,B: code_natural] :
% 0.33/0.55 ( ( plus_p4538020629002901425atural @ ( modulo8411746178871703098atural @ A @ B ) @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ A @ B ) @ B ) )
% 0.33/0.55 = A ) ).
% 0.33/0.55
% 0.33/0.55 % mod_div_mult_eq
% 0.33/0.55 thf(fact_2133_div__mult__mod__eq,axiom,
% 0.33/0.55 ! [A: int,B: int] :
% 0.33/0.55 ( ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) )
% 0.33/0.55 = A ) ).
% 0.33/0.55
% 0.33/0.55 % div_mult_mod_eq
% 0.33/0.55 thf(fact_2134_div__mult__mod__eq,axiom,
% 0.33/0.55 ! [A: nat,B: nat] :
% 0.33/0.55 ( ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) )
% 0.33/0.55 = A ) ).
% 0.33/0.55
% 0.33/0.55 % div_mult_mod_eq
% 0.33/0.55 thf(fact_2135_div__mult__mod__eq,axiom,
% 0.33/0.55 ! [A: code_integer,B: code_integer] :
% 0.33/0.55 ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) @ ( modulo364778990260209775nteger @ A @ B ) )
% 0.33/0.55 = A ) ).
% 0.33/0.55
% 0.33/0.55 % div_mult_mod_eq
% 0.33/0.55 thf(fact_2136_div__mult__mod__eq,axiom,
% 0.33/0.55 ! [A: code_natural,B: code_natural] :
% 0.33/0.55 ( ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ A @ B ) @ B ) @ ( modulo8411746178871703098atural @ A @ B ) )
% 0.33/0.55 = A ) ).
% 0.33/0.55
% 0.33/0.55 % div_mult_mod_eq
% 0.33/0.55 thf(fact_2137_mod__div__decomp,axiom,
% 0.33/0.55 ! [A: int,B: int] :
% 0.33/0.55 ( A
% 0.33/0.55 = ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % mod_div_decomp
% 0.33/0.55 thf(fact_2138_mod__div__decomp,axiom,
% 0.33/0.55 ! [A: nat,B: nat] :
% 0.33/0.55 ( A
% 0.33/0.55 = ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % mod_div_decomp
% 0.33/0.55 thf(fact_2139_mod__div__decomp,axiom,
% 0.33/0.55 ! [A: code_integer,B: code_integer] :
% 0.33/0.55 ( A
% 0.33/0.55 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) @ ( modulo364778990260209775nteger @ A @ B ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % mod_div_decomp
% 0.33/0.55 thf(fact_2140_mod__div__decomp,axiom,
% 0.33/0.55 ! [A: code_natural,B: code_natural] :
% 0.33/0.55 ( A
% 0.33/0.55 = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ A @ B ) @ B ) @ ( modulo8411746178871703098atural @ A @ B ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % mod_div_decomp
% 0.33/0.55 thf(fact_2141_cancel__div__mod__rules_I1_J,axiom,
% 0.33/0.55 ! [A: int,B: int,C: int] :
% 0.33/0.55 ( ( plus_plus_int @ ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) ) @ C )
% 0.33/0.55 = ( plus_plus_int @ A @ C ) ) ).
% 0.33/0.55
% 0.33/0.55 % cancel_div_mod_rules(1)
% 0.33/0.55 thf(fact_2142_cancel__div__mod__rules_I1_J,axiom,
% 0.33/0.55 ! [A: nat,B: nat,C: nat] :
% 0.33/0.55 ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) ) @ C )
% 0.33/0.55 = ( plus_plus_nat @ A @ C ) ) ).
% 0.33/0.55
% 0.33/0.55 % cancel_div_mod_rules(1)
% 0.33/0.55 thf(fact_2143_cancel__div__mod__rules_I1_J,axiom,
% 0.33/0.55 ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.33/0.55 ( ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) @ ( modulo364778990260209775nteger @ A @ B ) ) @ C )
% 0.33/0.55 = ( plus_p5714425477246183910nteger @ A @ C ) ) ).
% 0.33/0.55
% 0.33/0.55 % cancel_div_mod_rules(1)
% 0.33/0.55 thf(fact_2144_cancel__div__mod__rules_I1_J,axiom,
% 0.33/0.55 ! [A: code_natural,B: code_natural,C: code_natural] :
% 0.33/0.55 ( ( plus_p4538020629002901425atural @ ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ A @ B ) @ B ) @ ( modulo8411746178871703098atural @ A @ B ) ) @ C )
% 0.33/0.55 = ( plus_p4538020629002901425atural @ A @ C ) ) ).
% 0.33/0.55
% 0.33/0.55 % cancel_div_mod_rules(1)
% 0.33/0.55 thf(fact_2145_cancel__div__mod__rules_I2_J,axiom,
% 0.33/0.55 ! [B: int,A: int,C: int] :
% 0.33/0.55 ( ( plus_plus_int @ ( plus_plus_int @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) @ ( modulo_modulo_int @ A @ B ) ) @ C )
% 0.33/0.55 = ( plus_plus_int @ A @ C ) ) ).
% 0.33/0.55
% 0.33/0.55 % cancel_div_mod_rules(2)
% 0.33/0.55 thf(fact_2146_cancel__div__mod__rules_I2_J,axiom,
% 0.33/0.55 ! [B: nat,A: nat,C: nat] :
% 0.33/0.55 ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) @ ( modulo_modulo_nat @ A @ B ) ) @ C )
% 0.33/0.55 = ( plus_plus_nat @ A @ C ) ) ).
% 0.33/0.55
% 0.33/0.55 % cancel_div_mod_rules(2)
% 0.33/0.55 thf(fact_2147_cancel__div__mod__rules_I2_J,axiom,
% 0.33/0.55 ! [B: code_integer,A: code_integer,C: code_integer] :
% 0.33/0.55 ( ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) @ ( modulo364778990260209775nteger @ A @ B ) ) @ C )
% 0.33/0.55 = ( plus_p5714425477246183910nteger @ A @ C ) ) ).
% 0.33/0.55
% 0.33/0.55 % cancel_div_mod_rules(2)
% 0.33/0.55 thf(fact_2148_cancel__div__mod__rules_I2_J,axiom,
% 0.33/0.55 ! [B: code_natural,A: code_natural,C: code_natural] :
% 0.33/0.55 ( ( plus_p4538020629002901425atural @ ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ B @ ( divide5121882707175180666atural @ A @ B ) ) @ ( modulo8411746178871703098atural @ A @ B ) ) @ C )
% 0.33/0.55 = ( plus_p4538020629002901425atural @ A @ C ) ) ).
% 0.33/0.55
% 0.33/0.55 % cancel_div_mod_rules(2)
% 0.33/0.55 thf(fact_2149_div__mult1__eq,axiom,
% 0.33/0.55 ! [A: int,B: int,C: int] :
% 0.33/0.55 ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ C )
% 0.33/0.55 = ( plus_plus_int @ ( times_times_int @ A @ ( divide_divide_int @ B @ C ) ) @ ( divide_divide_int @ ( times_times_int @ A @ ( modulo_modulo_int @ B @ C ) ) @ C ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % div_mult1_eq
% 0.33/0.55 thf(fact_2150_div__mult1__eq,axiom,
% 0.33/0.55 ! [A: nat,B: nat,C: nat] :
% 0.33/0.55 ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C )
% 0.33/0.55 = ( plus_plus_nat @ ( times_times_nat @ A @ ( divide_divide_nat @ B @ C ) ) @ ( divide_divide_nat @ ( times_times_nat @ A @ ( modulo_modulo_nat @ B @ C ) ) @ C ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % div_mult1_eq
% 0.33/0.55 thf(fact_2151_div__mult1__eq,axiom,
% 0.33/0.55 ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.33/0.55 ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 0.33/0.55 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) ) @ ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ ( modulo364778990260209775nteger @ B @ C ) ) @ C ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % div_mult1_eq
% 0.33/0.55 thf(fact_2152_div__mult1__eq,axiom,
% 0.33/0.55 ! [A: code_natural,B: code_natural,C: code_natural] :
% 0.33/0.55 ( ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ A @ B ) @ C )
% 0.33/0.55 = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ A @ ( divide5121882707175180666atural @ B @ C ) ) @ ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ A @ ( modulo8411746178871703098atural @ B @ C ) ) @ C ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % div_mult1_eq
% 0.33/0.55 thf(fact_2153_eucl__rel__int__dividesI,axiom,
% 0.33/0.55 ! [L: int,K: int,Q3: int] :
% 0.33/0.55 ( ( L != zero_zero_int )
% 0.33/0.55 => ( ( K
% 0.33/0.55 = ( times_times_int @ Q3 @ L ) )
% 0.33/0.55 => ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q3 @ zero_zero_int ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % eucl_rel_int_dividesI
% 0.33/0.55 thf(fact_2154_div__mod__decomp__int,axiom,
% 0.33/0.55 ! [A2: int,N2: int] :
% 0.33/0.55 ( A2
% 0.33/0.55 = ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A2 @ N2 ) @ N2 ) @ ( modulo_modulo_int @ A2 @ N2 ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % div_mod_decomp_int
% 0.33/0.55 thf(fact_2155_mod__pos__neg__trivial,axiom,
% 0.33/0.55 ! [K: int,L: int] :
% 0.33/0.55 ( ( ord_less_int @ zero_zero_int @ K )
% 0.33/0.55 => ( ( ord_less_eq_int @ ( plus_plus_int @ K @ L ) @ zero_zero_int )
% 0.33/0.55 => ( ( modulo_modulo_int @ K @ L )
% 0.33/0.55 = ( plus_plus_int @ K @ L ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % mod_pos_neg_trivial
% 0.33/0.55 thf(fact_2156_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 0.33/0.55 ! [C: code_integer,A: code_integer,B: code_integer] :
% 0.33/0.55 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 0.33/0.55 => ( ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 0.33/0.55 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ ( modulo364778990260209775nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) @ ( modulo364778990260209775nteger @ A @ B ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 0.33/0.55 thf(fact_2157_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 0.33/0.55 ! [C: nat,A: nat,B: nat] :
% 0.33/0.55 ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 0.33/0.55 => ( ( modulo_modulo_nat @ A @ ( times_times_nat @ B @ C ) )
% 0.33/0.55 = ( plus_plus_nat @ ( times_times_nat @ B @ ( modulo_modulo_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) @ ( modulo_modulo_nat @ A @ B ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 0.33/0.55 thf(fact_2158_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 0.33/0.55 ! [C: int,A: int,B: int] :
% 0.33/0.55 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.33/0.55 => ( ( modulo_modulo_int @ A @ ( times_times_int @ B @ C ) )
% 0.33/0.55 = ( plus_plus_int @ ( times_times_int @ B @ ( modulo_modulo_int @ ( divide_divide_int @ A @ B ) @ C ) ) @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 0.33/0.55 thf(fact_2159_int__mod__pos__eq,axiom,
% 0.33/0.55 ! [A: int,B: int,Q3: int,R2: int] :
% 0.33/0.55 ( ( A
% 0.33/0.55 = ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R2 ) )
% 0.33/0.55 => ( ( ord_less_eq_int @ zero_zero_int @ R2 )
% 0.33/0.55 => ( ( ord_less_int @ R2 @ B )
% 0.33/0.55 => ( ( modulo_modulo_int @ A @ B )
% 0.33/0.55 = R2 ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % int_mod_pos_eq
% 0.33/0.55 thf(fact_2160_int__mod__neg__eq,axiom,
% 0.33/0.55 ! [A: int,B: int,Q3: int,R2: int] :
% 0.33/0.55 ( ( A
% 0.33/0.55 = ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R2 ) )
% 0.33/0.55 => ( ( ord_less_eq_int @ R2 @ zero_zero_int )
% 0.33/0.55 => ( ( ord_less_int @ B @ R2 )
% 0.33/0.55 => ( ( modulo_modulo_int @ A @ B )
% 0.33/0.55 = R2 ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % int_mod_neg_eq
% 0.33/0.55 thf(fact_2161_split__zmod,axiom,
% 0.33/0.55 ! [P: int > $o,N2: int,K: int] :
% 0.33/0.55 ( ( P @ ( modulo_modulo_int @ N2 @ K ) )
% 0.33/0.55 = ( ( ( K = zero_zero_int )
% 0.33/0.55 => ( P @ N2 ) )
% 0.33/0.55 & ( ( ord_less_int @ zero_zero_int @ K )
% 0.33/0.55 => ! [I3: int,J2: int] :
% 0.33/0.55 ( ( ( ord_less_eq_int @ zero_zero_int @ J2 )
% 0.33/0.55 & ( ord_less_int @ J2 @ K )
% 0.33/0.55 & ( N2
% 0.33/0.55 = ( plus_plus_int @ ( times_times_int @ K @ I3 ) @ J2 ) ) )
% 0.33/0.55 => ( P @ J2 ) ) )
% 0.33/0.55 & ( ( ord_less_int @ K @ zero_zero_int )
% 0.33/0.55 => ! [I3: int,J2: int] :
% 0.33/0.55 ( ( ( ord_less_int @ K @ J2 )
% 0.33/0.55 & ( ord_less_eq_int @ J2 @ zero_zero_int )
% 0.33/0.55 & ( N2
% 0.33/0.55 = ( plus_plus_int @ ( times_times_int @ K @ I3 ) @ J2 ) ) )
% 0.33/0.55 => ( P @ J2 ) ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % split_zmod
% 0.33/0.55 thf(fact_2162_zmod__zmult2__eq,axiom,
% 0.33/0.55 ! [C: int,A: int,B: int] :
% 0.33/0.55 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.33/0.55 => ( ( modulo_modulo_int @ A @ ( times_times_int @ B @ C ) )
% 0.33/0.55 = ( plus_plus_int @ ( times_times_int @ B @ ( modulo_modulo_int @ ( divide_divide_int @ A @ B ) @ C ) ) @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % zmod_zmult2_eq
% 0.33/0.55 thf(fact_2163_zminus1__lemma,axiom,
% 0.33/0.55 ! [A: int,B: int,Q3: int,R2: int] :
% 0.33/0.55 ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q3 @ R2 ) )
% 0.33/0.55 => ( ( B != zero_zero_int )
% 0.33/0.55 => ( eucl_rel_int @ ( uminus_uminus_int @ A ) @ B @ ( product_Pair_int_int @ ( if_int @ ( R2 = zero_zero_int ) @ ( uminus_uminus_int @ Q3 ) @ ( minus_minus_int @ ( uminus_uminus_int @ Q3 ) @ one_one_int ) ) @ ( if_int @ ( R2 = zero_zero_int ) @ zero_zero_int @ ( minus_minus_int @ B @ R2 ) ) ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % zminus1_lemma
% 0.33/0.55 thf(fact_2164_eucl__rel__int__remainderI,axiom,
% 0.33/0.55 ! [R2: int,L: int,K: int,Q3: int] :
% 0.33/0.55 ( ( ( sgn_sgn_int @ R2 )
% 0.33/0.55 = ( sgn_sgn_int @ L ) )
% 0.33/0.55 => ( ( ord_less_int @ ( abs_abs_int @ R2 ) @ ( abs_abs_int @ L ) )
% 0.33/0.55 => ( ( K
% 0.33/0.55 = ( plus_plus_int @ ( times_times_int @ Q3 @ L ) @ R2 ) )
% 0.33/0.55 => ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q3 @ R2 ) ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % eucl_rel_int_remainderI
% 0.33/0.55 thf(fact_2165_verit__le__mono__div__int,axiom,
% 0.33/0.55 ! [A2: int,B5: int,N2: int] :
% 0.33/0.55 ( ( ord_less_int @ A2 @ B5 )
% 0.33/0.55 => ( ( ord_less_int @ zero_zero_int @ N2 )
% 0.33/0.55 => ( ord_less_eq_int
% 0.33/0.55 @ ( plus_plus_int @ ( divide_divide_int @ A2 @ N2 )
% 0.33/0.55 @ ( if_int
% 0.33/0.55 @ ( ( modulo_modulo_int @ B5 @ N2 )
% 0.33/0.55 = zero_zero_int )
% 0.33/0.55 @ one_one_int
% 0.33/0.55 @ zero_zero_int ) )
% 0.33/0.55 @ ( divide_divide_int @ B5 @ N2 ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % verit_le_mono_div_int
% 0.33/0.55 thf(fact_2166_bezw__0,axiom,
% 0.33/0.55 ! [X: nat] :
% 0.33/0.55 ( ( bezw @ X @ zero_zero_nat )
% 0.33/0.55 = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) ).
% 0.33/0.55
% 0.33/0.55 % bezw_0
% 0.33/0.55 thf(fact_2167_verit__le__mono__div,axiom,
% 0.33/0.55 ! [A2: nat,B5: nat,N2: nat] :
% 0.33/0.55 ( ( ord_less_nat @ A2 @ B5 )
% 0.33/0.55 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.33/0.55 => ( ord_less_eq_nat
% 0.33/0.55 @ ( plus_plus_nat @ ( divide_divide_nat @ A2 @ N2 )
% 0.33/0.55 @ ( if_nat
% 0.33/0.55 @ ( ( modulo_modulo_nat @ B5 @ N2 )
% 0.33/0.55 = zero_zero_nat )
% 0.33/0.55 @ one_one_nat
% 0.33/0.55 @ zero_zero_nat ) )
% 0.33/0.55 @ ( divide_divide_nat @ B5 @ N2 ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % verit_le_mono_div
% 0.33/0.55 thf(fact_2168_zero__le__ceiling,axiom,
% 0.33/0.55 ! [X: rat] :
% 0.33/0.55 ( ( ord_less_eq_int @ zero_zero_int @ ( archim2889992004027027881ng_rat @ X ) )
% 0.33/0.55 = ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ X ) ) ).
% 0.33/0.55
% 0.33/0.55 % zero_le_ceiling
% 0.33/0.55 thf(fact_2169_ceiling__less__zero,axiom,
% 0.33/0.55 ! [X: rat] :
% 0.33/0.55 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X ) @ zero_zero_int )
% 0.33/0.55 = ( ord_less_eq_rat @ X @ ( uminus_uminus_rat @ one_one_rat ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % ceiling_less_zero
% 0.33/0.55 thf(fact_2170_floor__add,axiom,
% 0.33/0.55 ! [X: rat,Y: rat] :
% 0.33/0.55 ( ( ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X ) @ ( archimedean_frac_rat @ Y ) ) @ one_one_rat )
% 0.33/0.55 => ( ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X @ Y ) )
% 0.33/0.55 = ( plus_plus_int @ ( archim3151403230148437115or_rat @ X ) @ ( archim3151403230148437115or_rat @ Y ) ) ) )
% 0.33/0.55 & ( ~ ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X ) @ ( archimedean_frac_rat @ Y ) ) @ one_one_rat )
% 0.33/0.55 => ( ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X @ Y ) )
% 0.33/0.55 = ( plus_plus_int @ ( plus_plus_int @ ( archim3151403230148437115or_rat @ X ) @ ( archim3151403230148437115or_rat @ Y ) ) @ one_one_int ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % floor_add
% 0.33/0.55 thf(fact_2171_cpmi,axiom,
% 0.33/0.55 ! [D3: int,P: int > $o,P5: int > $o,B5: set_int] :
% 0.33/0.55 ( ( ord_less_int @ zero_zero_int @ D3 )
% 0.33/0.55 => ( ? [Z5: int] :
% 0.33/0.55 ! [X4: int] :
% 0.33/0.55 ( ( ord_less_int @ X4 @ Z5 )
% 0.33/0.55 => ( ( P @ X4 )
% 0.33/0.55 = ( P5 @ X4 ) ) )
% 0.33/0.55 => ( ! [X4: int] :
% 0.33/0.55 ( ! [Xa2: int] :
% 0.33/0.55 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.33/0.55 => ! [Xb2: int] :
% 0.33/0.55 ( ( member_int @ Xb2 @ B5 )
% 0.33/0.55 => ( X4
% 0.33/0.55 != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 0.33/0.55 => ( ( P @ X4 )
% 0.33/0.55 => ( P @ ( minus_minus_int @ X4 @ D3 ) ) ) )
% 0.33/0.55 => ( ! [X4: int,K5: int] :
% 0.33/0.55 ( ( P5 @ X4 )
% 0.33/0.55 = ( P5 @ ( minus_minus_int @ X4 @ ( times_times_int @ K5 @ D3 ) ) ) )
% 0.33/0.55 => ( ( ? [X9: int] : ( P @ X9 ) )
% 0.33/0.55 = ( ? [X3: int] :
% 0.33/0.55 ( ( member_int @ X3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.33/0.55 & ( P5 @ X3 ) )
% 0.33/0.55 | ? [X3: int] :
% 0.33/0.55 ( ( member_int @ X3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.33/0.55 & ? [Y3: int] :
% 0.33/0.55 ( ( member_int @ Y3 @ B5 )
% 0.33/0.55 & ( P @ ( plus_plus_int @ Y3 @ X3 ) ) ) ) ) ) ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % cpmi
% 0.33/0.55 thf(fact_2172_cppi,axiom,
% 0.33/0.55 ! [D3: int,P: int > $o,P5: int > $o,A2: set_int] :
% 0.33/0.55 ( ( ord_less_int @ zero_zero_int @ D3 )
% 0.33/0.55 => ( ? [Z5: int] :
% 0.33/0.55 ! [X4: int] :
% 0.33/0.55 ( ( ord_less_int @ Z5 @ X4 )
% 0.33/0.55 => ( ( P @ X4 )
% 0.33/0.55 = ( P5 @ X4 ) ) )
% 0.33/0.55 => ( ! [X4: int] :
% 0.33/0.55 ( ! [Xa2: int] :
% 0.33/0.55 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.33/0.55 => ! [Xb2: int] :
% 0.33/0.55 ( ( member_int @ Xb2 @ A2 )
% 0.33/0.55 => ( X4
% 0.33/0.55 != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 0.33/0.55 => ( ( P @ X4 )
% 0.33/0.55 => ( P @ ( plus_plus_int @ X4 @ D3 ) ) ) )
% 0.33/0.55 => ( ! [X4: int,K5: int] :
% 0.33/0.55 ( ( P5 @ X4 )
% 0.33/0.55 = ( P5 @ ( minus_minus_int @ X4 @ ( times_times_int @ K5 @ D3 ) ) ) )
% 0.33/0.55 => ( ( ? [X9: int] : ( P @ X9 ) )
% 0.33/0.55 = ( ? [X3: int] :
% 0.33/0.55 ( ( member_int @ X3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.33/0.55 & ( P5 @ X3 ) )
% 0.33/0.55 | ? [X3: int] :
% 0.33/0.55 ( ( member_int @ X3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.33/0.55 & ? [Y3: int] :
% 0.33/0.55 ( ( member_int @ Y3 @ A2 )
% 0.33/0.55 & ( P @ ( minus_minus_int @ Y3 @ X3 ) ) ) ) ) ) ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % cppi
% 0.33/0.55 thf(fact_2173_bset_I6_J,axiom,
% 0.33/0.55 ! [D3: int,B5: set_int,T: int] :
% 0.33/0.55 ( ( ord_less_int @ zero_zero_int @ D3 )
% 0.33/0.55 => ! [X8: int] :
% 0.33/0.55 ( ! [Xa3: int] :
% 0.33/0.55 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.33/0.55 => ! [Xb3: int] :
% 0.33/0.55 ( ( member_int @ Xb3 @ B5 )
% 0.33/0.55 => ( X8
% 0.33/0.55 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 0.33/0.55 => ( ( ord_less_eq_int @ X8 @ T )
% 0.33/0.55 => ( ord_less_eq_int @ ( minus_minus_int @ X8 @ D3 ) @ T ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % bset(6)
% 0.33/0.55 thf(fact_2174_bset_I8_J,axiom,
% 0.33/0.55 ! [D3: int,T: int,B5: set_int] :
% 0.33/0.55 ( ( ord_less_int @ zero_zero_int @ D3 )
% 0.33/0.55 => ( ( member_int @ ( minus_minus_int @ T @ one_one_int ) @ B5 )
% 0.33/0.55 => ! [X8: int] :
% 0.33/0.55 ( ! [Xa3: int] :
% 0.33/0.55 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.33/0.55 => ! [Xb3: int] :
% 0.33/0.55 ( ( member_int @ Xb3 @ B5 )
% 0.33/0.55 => ( X8
% 0.33/0.55 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 0.33/0.55 => ( ( ord_less_eq_int @ T @ X8 )
% 0.33/0.55 => ( ord_less_eq_int @ T @ ( minus_minus_int @ X8 @ D3 ) ) ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % bset(8)
% 0.33/0.55 thf(fact_2175_aset_I6_J,axiom,
% 0.33/0.55 ! [D3: int,T: int,A2: set_int] :
% 0.33/0.55 ( ( ord_less_int @ zero_zero_int @ D3 )
% 0.33/0.55 => ( ( member_int @ ( plus_plus_int @ T @ one_one_int ) @ A2 )
% 0.33/0.55 => ! [X8: int] :
% 0.33/0.55 ( ! [Xa3: int] :
% 0.33/0.55 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.33/0.55 => ! [Xb3: int] :
% 0.33/0.55 ( ( member_int @ Xb3 @ A2 )
% 0.33/0.55 => ( X8
% 0.33/0.55 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 0.33/0.55 => ( ( ord_less_eq_int @ X8 @ T )
% 0.33/0.55 => ( ord_less_eq_int @ ( plus_plus_int @ X8 @ D3 ) @ T ) ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % aset(6)
% 0.33/0.55 thf(fact_2176_atLeastAtMost__iff,axiom,
% 0.33/0.55 ! [I: $o,L: $o,U: $o] :
% 0.33/0.55 ( ( member_o @ I @ ( set_or8904488021354931149Most_o @ L @ U ) )
% 0.33/0.55 = ( ( ord_less_eq_o @ L @ I )
% 0.33/0.55 & ( ord_less_eq_o @ I @ U ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % atLeastAtMost_iff
% 0.33/0.55 thf(fact_2177_atLeastAtMost__iff,axiom,
% 0.33/0.55 ! [I: set_nat,L: set_nat,U: set_nat] :
% 0.33/0.55 ( ( member_set_nat @ I @ ( set_or4548717258645045905et_nat @ L @ U ) )
% 0.33/0.55 = ( ( ord_less_eq_set_nat @ L @ I )
% 0.33/0.55 & ( ord_less_eq_set_nat @ I @ U ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % atLeastAtMost_iff
% 0.33/0.55 thf(fact_2178_atLeastAtMost__iff,axiom,
% 0.33/0.55 ! [I: rat,L: rat,U: rat] :
% 0.33/0.55 ( ( member_rat @ I @ ( set_or633870826150836451st_rat @ L @ U ) )
% 0.33/0.55 = ( ( ord_less_eq_rat @ L @ I )
% 0.33/0.55 & ( ord_less_eq_rat @ I @ U ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % atLeastAtMost_iff
% 0.33/0.55 thf(fact_2179_atLeastAtMost__iff,axiom,
% 0.33/0.55 ! [I: num,L: num,U: num] :
% 0.33/0.55 ( ( member_num @ I @ ( set_or7049704709247886629st_num @ L @ U ) )
% 0.33/0.55 = ( ( ord_less_eq_num @ L @ I )
% 0.33/0.55 & ( ord_less_eq_num @ I @ U ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % atLeastAtMost_iff
% 0.33/0.55 thf(fact_2180_atLeastAtMost__iff,axiom,
% 0.33/0.55 ! [I: int,L: int,U: int] :
% 0.33/0.55 ( ( member_int @ I @ ( set_or1266510415728281911st_int @ L @ U ) )
% 0.33/0.55 = ( ( ord_less_eq_int @ L @ I )
% 0.33/0.55 & ( ord_less_eq_int @ I @ U ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % atLeastAtMost_iff
% 0.33/0.55 thf(fact_2181_atLeastAtMost__iff,axiom,
% 0.33/0.55 ! [I: nat,L: nat,U: nat] :
% 0.33/0.55 ( ( member_nat @ I @ ( set_or1269000886237332187st_nat @ L @ U ) )
% 0.33/0.55 = ( ( ord_less_eq_nat @ L @ I )
% 0.33/0.55 & ( ord_less_eq_nat @ I @ U ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % atLeastAtMost_iff
% 0.33/0.55 thf(fact_2182_atLeastAtMost__iff,axiom,
% 0.33/0.55 ! [I: code_integer,L: code_integer,U: code_integer] :
% 0.33/0.55 ( ( member_Code_integer @ I @ ( set_or189985376899183464nteger @ L @ U ) )
% 0.33/0.55 = ( ( ord_le3102999989581377725nteger @ L @ I )
% 0.33/0.55 & ( ord_le3102999989581377725nteger @ I @ U ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % atLeastAtMost_iff
% 0.33/0.55 thf(fact_2183_Icc__eq__Icc,axiom,
% 0.33/0.55 ! [L: set_nat,H3: set_nat,L4: set_nat,H5: set_nat] :
% 0.33/0.55 ( ( ( set_or4548717258645045905et_nat @ L @ H3 )
% 0.33/0.55 = ( set_or4548717258645045905et_nat @ L4 @ H5 ) )
% 0.33/0.55 = ( ( ( L = L4 )
% 0.33/0.55 & ( H3 = H5 ) )
% 0.33/0.55 | ( ~ ( ord_less_eq_set_nat @ L @ H3 )
% 0.33/0.55 & ~ ( ord_less_eq_set_nat @ L4 @ H5 ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % Icc_eq_Icc
% 0.33/0.55 thf(fact_2184_Icc__eq__Icc,axiom,
% 0.33/0.55 ! [L: rat,H3: rat,L4: rat,H5: rat] :
% 0.33/0.55 ( ( ( set_or633870826150836451st_rat @ L @ H3 )
% 0.33/0.55 = ( set_or633870826150836451st_rat @ L4 @ H5 ) )
% 0.33/0.55 = ( ( ( L = L4 )
% 0.33/0.55 & ( H3 = H5 ) )
% 0.33/0.55 | ( ~ ( ord_less_eq_rat @ L @ H3 )
% 0.33/0.55 & ~ ( ord_less_eq_rat @ L4 @ H5 ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % Icc_eq_Icc
% 0.33/0.55 thf(fact_2185_Icc__eq__Icc,axiom,
% 0.33/0.55 ! [L: num,H3: num,L4: num,H5: num] :
% 0.33/0.55 ( ( ( set_or7049704709247886629st_num @ L @ H3 )
% 0.33/0.55 = ( set_or7049704709247886629st_num @ L4 @ H5 ) )
% 0.33/0.55 = ( ( ( L = L4 )
% 0.33/0.55 & ( H3 = H5 ) )
% 0.33/0.55 | ( ~ ( ord_less_eq_num @ L @ H3 )
% 0.33/0.55 & ~ ( ord_less_eq_num @ L4 @ H5 ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % Icc_eq_Icc
% 0.33/0.55 thf(fact_2186_Icc__eq__Icc,axiom,
% 0.33/0.55 ! [L: int,H3: int,L4: int,H5: int] :
% 0.33/0.55 ( ( ( set_or1266510415728281911st_int @ L @ H3 )
% 0.33/0.55 = ( set_or1266510415728281911st_int @ L4 @ H5 ) )
% 0.33/0.55 = ( ( ( L = L4 )
% 0.33/0.55 & ( H3 = H5 ) )
% 0.33/0.55 | ( ~ ( ord_less_eq_int @ L @ H3 )
% 0.33/0.55 & ~ ( ord_less_eq_int @ L4 @ H5 ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % Icc_eq_Icc
% 0.33/0.55 thf(fact_2187_Icc__eq__Icc,axiom,
% 0.33/0.55 ! [L: nat,H3: nat,L4: nat,H5: nat] :
% 0.33/0.55 ( ( ( set_or1269000886237332187st_nat @ L @ H3 )
% 0.33/0.55 = ( set_or1269000886237332187st_nat @ L4 @ H5 ) )
% 0.33/0.55 = ( ( ( L = L4 )
% 0.33/0.55 & ( H3 = H5 ) )
% 0.33/0.55 | ( ~ ( ord_less_eq_nat @ L @ H3 )
% 0.33/0.55 & ~ ( ord_less_eq_nat @ L4 @ H5 ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % Icc_eq_Icc
% 0.33/0.55 thf(fact_2188_Icc__eq__Icc,axiom,
% 0.33/0.55 ! [L: code_integer,H3: code_integer,L4: code_integer,H5: code_integer] :
% 0.33/0.55 ( ( ( set_or189985376899183464nteger @ L @ H3 )
% 0.33/0.55 = ( set_or189985376899183464nteger @ L4 @ H5 ) )
% 0.33/0.55 = ( ( ( L = L4 )
% 0.33/0.55 & ( H3 = H5 ) )
% 0.33/0.55 | ( ~ ( ord_le3102999989581377725nteger @ L @ H3 )
% 0.33/0.55 & ~ ( ord_le3102999989581377725nteger @ L4 @ H5 ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % Icc_eq_Icc
% 0.33/0.55 thf(fact_2189_atLeastatMost__subset__iff,axiom,
% 0.33/0.55 ! [A: set_nat,B: set_nat,C: set_nat,D2: set_nat] :
% 0.33/0.55 ( ( ord_le6893508408891458716et_nat @ ( set_or4548717258645045905et_nat @ A @ B ) @ ( set_or4548717258645045905et_nat @ C @ D2 ) )
% 0.33/0.55 = ( ~ ( ord_less_eq_set_nat @ A @ B )
% 0.33/0.55 | ( ( ord_less_eq_set_nat @ C @ A )
% 0.33/0.55 & ( ord_less_eq_set_nat @ B @ D2 ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % atLeastatMost_subset_iff
% 0.33/0.55 thf(fact_2190_atLeastatMost__subset__iff,axiom,
% 0.33/0.55 ! [A: rat,B: rat,C: rat,D2: rat] :
% 0.33/0.55 ( ( ord_less_eq_set_rat @ ( set_or633870826150836451st_rat @ A @ B ) @ ( set_or633870826150836451st_rat @ C @ D2 ) )
% 0.33/0.55 = ( ~ ( ord_less_eq_rat @ A @ B )
% 0.33/0.55 | ( ( ord_less_eq_rat @ C @ A )
% 0.33/0.55 & ( ord_less_eq_rat @ B @ D2 ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % atLeastatMost_subset_iff
% 0.33/0.55 thf(fact_2191_atLeastatMost__subset__iff,axiom,
% 0.33/0.55 ! [A: num,B: num,C: num,D2: num] :
% 0.33/0.55 ( ( ord_less_eq_set_num @ ( set_or7049704709247886629st_num @ A @ B ) @ ( set_or7049704709247886629st_num @ C @ D2 ) )
% 0.33/0.55 = ( ~ ( ord_less_eq_num @ A @ B )
% 0.33/0.55 | ( ( ord_less_eq_num @ C @ A )
% 0.33/0.55 & ( ord_less_eq_num @ B @ D2 ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % atLeastatMost_subset_iff
% 0.33/0.55 thf(fact_2192_atLeastatMost__subset__iff,axiom,
% 0.33/0.55 ! [A: int,B: int,C: int,D2: int] :
% 0.33/0.55 ( ( ord_less_eq_set_int @ ( set_or1266510415728281911st_int @ A @ B ) @ ( set_or1266510415728281911st_int @ C @ D2 ) )
% 0.33/0.55 = ( ~ ( ord_less_eq_int @ A @ B )
% 0.33/0.55 | ( ( ord_less_eq_int @ C @ A )
% 0.33/0.55 & ( ord_less_eq_int @ B @ D2 ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % atLeastatMost_subset_iff
% 0.33/0.55 thf(fact_2193_atLeastatMost__subset__iff,axiom,
% 0.33/0.55 ! [A: nat,B: nat,C: nat,D2: nat] :
% 0.33/0.55 ( ( ord_less_eq_set_nat @ ( set_or1269000886237332187st_nat @ A @ B ) @ ( set_or1269000886237332187st_nat @ C @ D2 ) )
% 0.33/0.55 = ( ~ ( ord_less_eq_nat @ A @ B )
% 0.33/0.55 | ( ( ord_less_eq_nat @ C @ A )
% 0.33/0.55 & ( ord_less_eq_nat @ B @ D2 ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % atLeastatMost_subset_iff
% 0.33/0.55 thf(fact_2194_atLeastatMost__subset__iff,axiom,
% 0.33/0.55 ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 0.33/0.55 ( ( ord_le7084787975880047091nteger @ ( set_or189985376899183464nteger @ A @ B ) @ ( set_or189985376899183464nteger @ C @ D2 ) )
% 0.33/0.55 = ( ~ ( ord_le3102999989581377725nteger @ A @ B )
% 0.33/0.55 | ( ( ord_le3102999989581377725nteger @ C @ A )
% 0.33/0.55 & ( ord_le3102999989581377725nteger @ B @ D2 ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % atLeastatMost_subset_iff
% 0.33/0.55 thf(fact_2195_floor__one,axiom,
% 0.33/0.55 ( ( archim3151403230148437115or_rat @ one_one_rat )
% 0.33/0.55 = one_one_int ) ).
% 0.33/0.55
% 0.33/0.55 % floor_one
% 0.33/0.55 thf(fact_2196_ceiling__one,axiom,
% 0.33/0.55 ( ( archim2889992004027027881ng_rat @ one_one_rat )
% 0.33/0.55 = one_one_int ) ).
% 0.33/0.55
% 0.33/0.55 % ceiling_one
% 0.33/0.55 thf(fact_2197_floor__add2,axiom,
% 0.33/0.55 ! [X: rat,Y: rat] :
% 0.33/0.55 ( ( ( member_rat @ X @ ring_1_Ints_rat )
% 0.33/0.55 | ( member_rat @ Y @ ring_1_Ints_rat ) )
% 0.33/0.55 => ( ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X @ Y ) )
% 0.33/0.55 = ( plus_plus_int @ ( archim3151403230148437115or_rat @ X ) @ ( archim3151403230148437115or_rat @ Y ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % floor_add2
% 0.33/0.55 thf(fact_2198_zero__less__floor,axiom,
% 0.33/0.55 ! [X: rat] :
% 0.33/0.55 ( ( ord_less_int @ zero_zero_int @ ( archim3151403230148437115or_rat @ X ) )
% 0.33/0.55 = ( ord_less_eq_rat @ one_one_rat @ X ) ) ).
% 0.33/0.55
% 0.33/0.55 % zero_less_floor
% 0.33/0.55 thf(fact_2199_floor__le__zero,axiom,
% 0.33/0.55 ! [X: rat] :
% 0.33/0.55 ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X ) @ zero_zero_int )
% 0.33/0.55 = ( ord_less_rat @ X @ one_one_rat ) ) ).
% 0.33/0.55
% 0.33/0.55 % floor_le_zero
% 0.33/0.55 thf(fact_2200_one__le__floor,axiom,
% 0.33/0.55 ! [X: rat] :
% 0.33/0.55 ( ( ord_less_eq_int @ one_one_int @ ( archim3151403230148437115or_rat @ X ) )
% 0.33/0.55 = ( ord_less_eq_rat @ one_one_rat @ X ) ) ).
% 0.33/0.55
% 0.33/0.55 % one_le_floor
% 0.33/0.55 thf(fact_2201_floor__less__one,axiom,
% 0.33/0.55 ! [X: rat] :
% 0.33/0.55 ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X ) @ one_one_int )
% 0.33/0.55 = ( ord_less_rat @ X @ one_one_rat ) ) ).
% 0.33/0.55
% 0.33/0.55 % floor_less_one
% 0.33/0.55 thf(fact_2202_ceiling__le__one,axiom,
% 0.33/0.55 ! [X: rat] :
% 0.33/0.55 ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X ) @ one_one_int )
% 0.33/0.55 = ( ord_less_eq_rat @ X @ one_one_rat ) ) ).
% 0.33/0.55
% 0.33/0.55 % ceiling_le_one
% 0.33/0.55 thf(fact_2203_one__less__ceiling,axiom,
% 0.33/0.55 ! [X: rat] :
% 0.33/0.55 ( ( ord_less_int @ one_one_int @ ( archim2889992004027027881ng_rat @ X ) )
% 0.33/0.55 = ( ord_less_rat @ one_one_rat @ X ) ) ).
% 0.33/0.55
% 0.33/0.55 % one_less_ceiling
% 0.33/0.55 thf(fact_2204_ceiling__add__one,axiom,
% 0.33/0.55 ! [X: rat] :
% 0.33/0.55 ( ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X @ one_one_rat ) )
% 0.33/0.55 = ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X ) @ one_one_int ) ) ).
% 0.33/0.55
% 0.33/0.55 % ceiling_add_one
% 0.33/0.55 thf(fact_2205_floor__diff__one,axiom,
% 0.33/0.55 ! [X: rat] :
% 0.33/0.55 ( ( archim3151403230148437115or_rat @ ( minus_minus_rat @ X @ one_one_rat ) )
% 0.33/0.55 = ( minus_minus_int @ ( archim3151403230148437115or_rat @ X ) @ one_one_int ) ) ).
% 0.33/0.55
% 0.33/0.55 % floor_diff_one
% 0.33/0.55 thf(fact_2206_ceiling__diff__one,axiom,
% 0.33/0.55 ! [X: rat] :
% 0.33/0.55 ( ( archim2889992004027027881ng_rat @ ( minus_minus_rat @ X @ one_one_rat ) )
% 0.33/0.55 = ( minus_minus_int @ ( archim2889992004027027881ng_rat @ X ) @ one_one_int ) ) ).
% 0.33/0.55
% 0.33/0.55 % ceiling_diff_one
% 0.33/0.55 thf(fact_2207_atLeastatMost__psubset__iff,axiom,
% 0.33/0.55 ! [A: set_nat,B: set_nat,C: set_nat,D2: set_nat] :
% 0.33/0.55 ( ( ord_less_set_set_nat @ ( set_or4548717258645045905et_nat @ A @ B ) @ ( set_or4548717258645045905et_nat @ C @ D2 ) )
% 0.33/0.55 = ( ( ~ ( ord_less_eq_set_nat @ A @ B )
% 0.33/0.55 | ( ( ord_less_eq_set_nat @ C @ A )
% 0.33/0.55 & ( ord_less_eq_set_nat @ B @ D2 )
% 0.33/0.55 & ( ( ord_less_set_nat @ C @ A )
% 0.33/0.55 | ( ord_less_set_nat @ B @ D2 ) ) ) )
% 0.33/0.55 & ( ord_less_eq_set_nat @ C @ D2 ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % atLeastatMost_psubset_iff
% 0.33/0.55 thf(fact_2208_atLeastatMost__psubset__iff,axiom,
% 0.33/0.55 ! [A: rat,B: rat,C: rat,D2: rat] :
% 0.33/0.55 ( ( ord_less_set_rat @ ( set_or633870826150836451st_rat @ A @ B ) @ ( set_or633870826150836451st_rat @ C @ D2 ) )
% 0.33/0.55 = ( ( ~ ( ord_less_eq_rat @ A @ B )
% 0.33/0.55 | ( ( ord_less_eq_rat @ C @ A )
% 0.33/0.55 & ( ord_less_eq_rat @ B @ D2 )
% 0.33/0.55 & ( ( ord_less_rat @ C @ A )
% 0.33/0.55 | ( ord_less_rat @ B @ D2 ) ) ) )
% 0.33/0.55 & ( ord_less_eq_rat @ C @ D2 ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % atLeastatMost_psubset_iff
% 0.33/0.55 thf(fact_2209_atLeastatMost__psubset__iff,axiom,
% 0.33/0.55 ! [A: num,B: num,C: num,D2: num] :
% 0.33/0.55 ( ( ord_less_set_num @ ( set_or7049704709247886629st_num @ A @ B ) @ ( set_or7049704709247886629st_num @ C @ D2 ) )
% 0.33/0.55 = ( ( ~ ( ord_less_eq_num @ A @ B )
% 0.33/0.55 | ( ( ord_less_eq_num @ C @ A )
% 0.33/0.55 & ( ord_less_eq_num @ B @ D2 )
% 0.33/0.55 & ( ( ord_less_num @ C @ A )
% 0.33/0.55 | ( ord_less_num @ B @ D2 ) ) ) )
% 0.33/0.55 & ( ord_less_eq_num @ C @ D2 ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % atLeastatMost_psubset_iff
% 0.33/0.55 thf(fact_2210_atLeastatMost__psubset__iff,axiom,
% 0.33/0.55 ! [A: int,B: int,C: int,D2: int] :
% 0.33/0.55 ( ( ord_less_set_int @ ( set_or1266510415728281911st_int @ A @ B ) @ ( set_or1266510415728281911st_int @ C @ D2 ) )
% 0.33/0.55 = ( ( ~ ( ord_less_eq_int @ A @ B )
% 0.33/0.55 | ( ( ord_less_eq_int @ C @ A )
% 0.33/0.55 & ( ord_less_eq_int @ B @ D2 )
% 0.33/0.55 & ( ( ord_less_int @ C @ A )
% 0.33/0.55 | ( ord_less_int @ B @ D2 ) ) ) )
% 0.33/0.55 & ( ord_less_eq_int @ C @ D2 ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % atLeastatMost_psubset_iff
% 0.33/0.55 thf(fact_2211_atLeastatMost__psubset__iff,axiom,
% 0.33/0.55 ! [A: nat,B: nat,C: nat,D2: nat] :
% 0.33/0.55 ( ( ord_less_set_nat @ ( set_or1269000886237332187st_nat @ A @ B ) @ ( set_or1269000886237332187st_nat @ C @ D2 ) )
% 0.33/0.55 = ( ( ~ ( ord_less_eq_nat @ A @ B )
% 0.33/0.55 | ( ( ord_less_eq_nat @ C @ A )
% 0.33/0.55 & ( ord_less_eq_nat @ B @ D2 )
% 0.33/0.55 & ( ( ord_less_nat @ C @ A )
% 0.33/0.55 | ( ord_less_nat @ B @ D2 ) ) ) )
% 0.33/0.55 & ( ord_less_eq_nat @ C @ D2 ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % atLeastatMost_psubset_iff
% 0.33/0.55 thf(fact_2212_atLeastatMost__psubset__iff,axiom,
% 0.33/0.55 ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 0.33/0.55 ( ( ord_le1307284697595431911nteger @ ( set_or189985376899183464nteger @ A @ B ) @ ( set_or189985376899183464nteger @ C @ D2 ) )
% 0.33/0.55 = ( ( ~ ( ord_le3102999989581377725nteger @ A @ B )
% 0.33/0.55 | ( ( ord_le3102999989581377725nteger @ C @ A )
% 0.33/0.55 & ( ord_le3102999989581377725nteger @ B @ D2 )
% 0.33/0.55 & ( ( ord_le6747313008572928689nteger @ C @ A )
% 0.33/0.55 | ( ord_le6747313008572928689nteger @ B @ D2 ) ) ) )
% 0.33/0.55 & ( ord_le3102999989581377725nteger @ C @ D2 ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % atLeastatMost_psubset_iff
% 0.33/0.55 thf(fact_2213_nat__mod__eq__iff,axiom,
% 0.33/0.55 ! [X: nat,N2: nat,Y: nat] :
% 0.33/0.55 ( ( ( modulo_modulo_nat @ X @ N2 )
% 0.33/0.55 = ( modulo_modulo_nat @ Y @ N2 ) )
% 0.33/0.55 = ( ? [Q1: nat,Q22: nat] :
% 0.33/0.55 ( ( plus_plus_nat @ X @ ( times_times_nat @ N2 @ Q1 ) )
% 0.33/0.55 = ( plus_plus_nat @ Y @ ( times_times_nat @ N2 @ Q22 ) ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % nat_mod_eq_iff
% 0.33/0.55 thf(fact_2214_le__floor__add,axiom,
% 0.33/0.55 ! [X: rat,Y: rat] : ( ord_less_eq_int @ ( plus_plus_int @ ( archim3151403230148437115or_rat @ X ) @ ( archim3151403230148437115or_rat @ Y ) ) @ ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X @ Y ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % le_floor_add
% 0.33/0.55 thf(fact_2215_bset_I1_J,axiom,
% 0.33/0.55 ! [D3: int,B5: set_int,P: int > $o,Q: int > $o] :
% 0.33/0.55 ( ! [X4: int] :
% 0.33/0.55 ( ! [Xa2: int] :
% 0.33/0.55 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.33/0.55 => ! [Xb2: int] :
% 0.33/0.55 ( ( member_int @ Xb2 @ B5 )
% 0.33/0.55 => ( X4
% 0.33/0.55 != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 0.33/0.55 => ( ( P @ X4 )
% 0.33/0.55 => ( P @ ( minus_minus_int @ X4 @ D3 ) ) ) )
% 0.33/0.55 => ( ! [X4: int] :
% 0.33/0.55 ( ! [Xa2: int] :
% 0.33/0.55 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.33/0.55 => ! [Xb2: int] :
% 0.33/0.55 ( ( member_int @ Xb2 @ B5 )
% 0.33/0.55 => ( X4
% 0.33/0.55 != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 0.33/0.55 => ( ( Q @ X4 )
% 0.33/0.55 => ( Q @ ( minus_minus_int @ X4 @ D3 ) ) ) )
% 0.33/0.55 => ! [X8: int] :
% 0.33/0.55 ( ! [Xa3: int] :
% 0.33/0.55 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.33/0.55 => ! [Xb3: int] :
% 0.33/0.55 ( ( member_int @ Xb3 @ B5 )
% 0.33/0.55 => ( X8
% 0.33/0.55 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 0.33/0.55 => ( ( ( P @ X8 )
% 0.33/0.55 & ( Q @ X8 ) )
% 0.33/0.55 => ( ( P @ ( minus_minus_int @ X8 @ D3 ) )
% 0.33/0.55 & ( Q @ ( minus_minus_int @ X8 @ D3 ) ) ) ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % bset(1)
% 0.33/0.55 thf(fact_2216_bset_I2_J,axiom,
% 0.33/0.55 ! [D3: int,B5: set_int,P: int > $o,Q: int > $o] :
% 0.33/0.55 ( ! [X4: int] :
% 0.33/0.55 ( ! [Xa2: int] :
% 0.33/0.55 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.33/0.55 => ! [Xb2: int] :
% 0.33/0.55 ( ( member_int @ Xb2 @ B5 )
% 0.33/0.55 => ( X4
% 0.33/0.55 != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 0.33/0.55 => ( ( P @ X4 )
% 0.33/0.55 => ( P @ ( minus_minus_int @ X4 @ D3 ) ) ) )
% 0.33/0.55 => ( ! [X4: int] :
% 0.33/0.55 ( ! [Xa2: int] :
% 0.33/0.55 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.33/0.55 => ! [Xb2: int] :
% 0.33/0.55 ( ( member_int @ Xb2 @ B5 )
% 0.33/0.55 => ( X4
% 0.33/0.55 != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 0.33/0.55 => ( ( Q @ X4 )
% 0.33/0.55 => ( Q @ ( minus_minus_int @ X4 @ D3 ) ) ) )
% 0.33/0.55 => ! [X8: int] :
% 0.33/0.55 ( ! [Xa3: int] :
% 0.33/0.55 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.33/0.55 => ! [Xb3: int] :
% 0.33/0.55 ( ( member_int @ Xb3 @ B5 )
% 0.33/0.55 => ( X8
% 0.33/0.55 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 0.33/0.55 => ( ( ( P @ X8 )
% 0.33/0.55 | ( Q @ X8 ) )
% 0.33/0.55 => ( ( P @ ( minus_minus_int @ X8 @ D3 ) )
% 0.33/0.55 | ( Q @ ( minus_minus_int @ X8 @ D3 ) ) ) ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % bset(2)
% 0.33/0.55 thf(fact_2217_aset_I1_J,axiom,
% 0.33/0.55 ! [D3: int,A2: set_int,P: int > $o,Q: int > $o] :
% 0.33/0.55 ( ! [X4: int] :
% 0.33/0.55 ( ! [Xa2: int] :
% 0.33/0.55 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.33/0.55 => ! [Xb2: int] :
% 0.33/0.55 ( ( member_int @ Xb2 @ A2 )
% 0.33/0.55 => ( X4
% 0.33/0.55 != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 0.33/0.55 => ( ( P @ X4 )
% 0.33/0.55 => ( P @ ( plus_plus_int @ X4 @ D3 ) ) ) )
% 0.33/0.55 => ( ! [X4: int] :
% 0.33/0.55 ( ! [Xa2: int] :
% 0.33/0.55 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.33/0.55 => ! [Xb2: int] :
% 0.33/0.55 ( ( member_int @ Xb2 @ A2 )
% 0.33/0.55 => ( X4
% 0.33/0.55 != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 0.33/0.55 => ( ( Q @ X4 )
% 0.33/0.55 => ( Q @ ( plus_plus_int @ X4 @ D3 ) ) ) )
% 0.33/0.55 => ! [X8: int] :
% 0.33/0.55 ( ! [Xa3: int] :
% 0.33/0.55 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.33/0.55 => ! [Xb3: int] :
% 0.33/0.55 ( ( member_int @ Xb3 @ A2 )
% 0.33/0.55 => ( X8
% 0.33/0.55 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 0.33/0.55 => ( ( ( P @ X8 )
% 0.33/0.55 & ( Q @ X8 ) )
% 0.33/0.55 => ( ( P @ ( plus_plus_int @ X8 @ D3 ) )
% 0.33/0.55 & ( Q @ ( plus_plus_int @ X8 @ D3 ) ) ) ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % aset(1)
% 0.33/0.55 thf(fact_2218_aset_I2_J,axiom,
% 0.33/0.55 ! [D3: int,A2: set_int,P: int > $o,Q: int > $o] :
% 0.33/0.55 ( ! [X4: int] :
% 0.33/0.55 ( ! [Xa2: int] :
% 0.33/0.55 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.33/0.55 => ! [Xb2: int] :
% 0.33/0.55 ( ( member_int @ Xb2 @ A2 )
% 0.33/0.55 => ( X4
% 0.33/0.55 != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 0.33/0.55 => ( ( P @ X4 )
% 0.33/0.55 => ( P @ ( plus_plus_int @ X4 @ D3 ) ) ) )
% 0.33/0.55 => ( ! [X4: int] :
% 0.33/0.55 ( ! [Xa2: int] :
% 0.33/0.55 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.33/0.55 => ! [Xb2: int] :
% 0.33/0.55 ( ( member_int @ Xb2 @ A2 )
% 0.33/0.55 => ( X4
% 0.33/0.55 != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 0.33/0.55 => ( ( Q @ X4 )
% 0.33/0.55 => ( Q @ ( plus_plus_int @ X4 @ D3 ) ) ) )
% 0.33/0.55 => ! [X8: int] :
% 0.33/0.55 ( ! [Xa3: int] :
% 0.33/0.55 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.33/0.55 => ! [Xb3: int] :
% 0.33/0.55 ( ( member_int @ Xb3 @ A2 )
% 0.33/0.55 => ( X8
% 0.33/0.55 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 0.33/0.55 => ( ( ( P @ X8 )
% 0.33/0.55 | ( Q @ X8 ) )
% 0.33/0.55 => ( ( P @ ( plus_plus_int @ X8 @ D3 ) )
% 0.33/0.55 | ( Q @ ( plus_plus_int @ X8 @ D3 ) ) ) ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % aset(2)
% 0.33/0.55 thf(fact_2219_nat__mod__eq__lemma,axiom,
% 0.33/0.55 ! [X: nat,N2: nat,Y: nat] :
% 0.33/0.55 ( ( ( modulo_modulo_nat @ X @ N2 )
% 0.33/0.55 = ( modulo_modulo_nat @ Y @ N2 ) )
% 0.33/0.55 => ( ( ord_less_eq_nat @ Y @ X )
% 0.33/0.55 => ? [Q2: nat] :
% 0.33/0.55 ( X
% 0.33/0.55 = ( plus_plus_nat @ Y @ ( times_times_nat @ N2 @ Q2 ) ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % nat_mod_eq_lemma
% 0.33/0.55 thf(fact_2220_mod__eq__nat2E,axiom,
% 0.33/0.55 ! [M2: nat,Q3: nat,N2: nat] :
% 0.33/0.55 ( ( ( modulo_modulo_nat @ M2 @ Q3 )
% 0.33/0.55 = ( modulo_modulo_nat @ N2 @ Q3 ) )
% 0.33/0.55 => ( ( ord_less_eq_nat @ M2 @ N2 )
% 0.33/0.55 => ~ ! [S6: nat] :
% 0.33/0.55 ( N2
% 0.33/0.55 != ( plus_plus_nat @ M2 @ ( times_times_nat @ Q3 @ S6 ) ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % mod_eq_nat2E
% 0.33/0.55 thf(fact_2221_mod__eq__nat1E,axiom,
% 0.33/0.55 ! [M2: nat,Q3: nat,N2: nat] :
% 0.33/0.55 ( ( ( modulo_modulo_nat @ M2 @ Q3 )
% 0.33/0.55 = ( modulo_modulo_nat @ N2 @ Q3 ) )
% 0.33/0.55 => ( ( ord_less_eq_nat @ N2 @ M2 )
% 0.33/0.55 => ~ ! [S6: nat] :
% 0.33/0.55 ( M2
% 0.33/0.55 != ( plus_plus_nat @ N2 @ ( times_times_nat @ Q3 @ S6 ) ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % mod_eq_nat1E
% 0.33/0.55 thf(fact_2222_ceiling__add__le,axiom,
% 0.33/0.55 ! [X: rat,Y: rat] : ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X @ Y ) ) @ ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X ) @ ( archim2889992004027027881ng_rat @ Y ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % ceiling_add_le
% 0.33/0.55 thf(fact_2223_mod__mult2__eq,axiom,
% 0.33/0.55 ! [M2: nat,N2: nat,Q3: nat] :
% 0.33/0.55 ( ( modulo_modulo_nat @ M2 @ ( times_times_nat @ N2 @ Q3 ) )
% 0.33/0.55 = ( plus_plus_nat @ ( times_times_nat @ N2 @ ( modulo_modulo_nat @ ( divide_divide_nat @ M2 @ N2 ) @ Q3 ) ) @ ( modulo_modulo_nat @ M2 @ N2 ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % mod_mult2_eq
% 0.33/0.55 thf(fact_2224_div__mod__decomp,axiom,
% 0.33/0.55 ! [A2: nat,N2: nat] :
% 0.33/0.55 ( A2
% 0.33/0.55 = ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A2 @ N2 ) @ N2 ) @ ( modulo_modulo_nat @ A2 @ N2 ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % div_mod_decomp
% 0.33/0.55 thf(fact_2225_one__add__floor,axiom,
% 0.33/0.55 ! [X: rat] :
% 0.33/0.55 ( ( plus_plus_int @ ( archim3151403230148437115or_rat @ X ) @ one_one_int )
% 0.33/0.55 = ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X @ one_one_rat ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % one_add_floor
% 0.33/0.55 thf(fact_2226_split__mod,axiom,
% 0.33/0.55 ! [P: nat > $o,M2: nat,N2: nat] :
% 0.33/0.55 ( ( P @ ( modulo_modulo_nat @ M2 @ N2 ) )
% 0.33/0.55 = ( ( ( N2 = zero_zero_nat )
% 0.33/0.55 => ( P @ M2 ) )
% 0.33/0.55 & ( ( N2 != zero_zero_nat )
% 0.33/0.55 => ! [I3: nat,J2: nat] :
% 0.33/0.55 ( ( ord_less_nat @ J2 @ N2 )
% 0.33/0.55 => ( ( M2
% 0.33/0.55 = ( plus_plus_nat @ ( times_times_nat @ N2 @ I3 ) @ J2 ) )
% 0.33/0.55 => ( P @ J2 ) ) ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % split_mod
% 0.33/0.55 thf(fact_2227_bset_I3_J,axiom,
% 0.33/0.55 ! [D3: int,T: int,B5: set_int] :
% 0.33/0.55 ( ( ord_less_int @ zero_zero_int @ D3 )
% 0.33/0.55 => ( ( member_int @ ( minus_minus_int @ T @ one_one_int ) @ B5 )
% 0.33/0.55 => ! [X8: int] :
% 0.33/0.55 ( ! [Xa3: int] :
% 0.33/0.55 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.33/0.55 => ! [Xb3: int] :
% 0.33/0.55 ( ( member_int @ Xb3 @ B5 )
% 0.33/0.55 => ( X8
% 0.33/0.55 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 0.33/0.55 => ( ( X8 = T )
% 0.33/0.55 => ( ( minus_minus_int @ X8 @ D3 )
% 0.33/0.55 = T ) ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % bset(3)
% 0.33/0.55 thf(fact_2228_bset_I4_J,axiom,
% 0.33/0.55 ! [D3: int,T: int,B5: set_int] :
% 0.33/0.55 ( ( ord_less_int @ zero_zero_int @ D3 )
% 0.33/0.55 => ( ( member_int @ T @ B5 )
% 0.33/0.55 => ! [X8: int] :
% 0.33/0.55 ( ! [Xa3: int] :
% 0.33/0.55 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.33/0.55 => ! [Xb3: int] :
% 0.33/0.55 ( ( member_int @ Xb3 @ B5 )
% 0.33/0.55 => ( X8
% 0.33/0.55 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 0.33/0.55 => ( ( X8 != T )
% 0.33/0.55 => ( ( minus_minus_int @ X8 @ D3 )
% 0.33/0.55 != T ) ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % bset(4)
% 0.33/0.55 thf(fact_2229_bset_I5_J,axiom,
% 0.33/0.55 ! [D3: int,B5: set_int,T: int] :
% 0.33/0.55 ( ( ord_less_int @ zero_zero_int @ D3 )
% 0.33/0.55 => ! [X8: int] :
% 0.33/0.55 ( ! [Xa3: int] :
% 0.33/0.55 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.33/0.55 => ! [Xb3: int] :
% 0.33/0.55 ( ( member_int @ Xb3 @ B5 )
% 0.33/0.55 => ( X8
% 0.33/0.55 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 0.33/0.55 => ( ( ord_less_int @ X8 @ T )
% 0.33/0.55 => ( ord_less_int @ ( minus_minus_int @ X8 @ D3 ) @ T ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % bset(5)
% 0.33/0.55 thf(fact_2230_bset_I7_J,axiom,
% 0.33/0.55 ! [D3: int,T: int,B5: set_int] :
% 0.33/0.55 ( ( ord_less_int @ zero_zero_int @ D3 )
% 0.33/0.55 => ( ( member_int @ T @ B5 )
% 0.33/0.55 => ! [X8: int] :
% 0.33/0.55 ( ! [Xa3: int] :
% 0.33/0.55 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.33/0.55 => ! [Xb3: int] :
% 0.33/0.55 ( ( member_int @ Xb3 @ B5 )
% 0.33/0.55 => ( X8
% 0.33/0.55 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 0.33/0.55 => ( ( ord_less_int @ T @ X8 )
% 0.33/0.55 => ( ord_less_int @ T @ ( minus_minus_int @ X8 @ D3 ) ) ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % bset(7)
% 0.33/0.55 thf(fact_2231_aset_I3_J,axiom,
% 0.33/0.55 ! [D3: int,T: int,A2: set_int] :
% 0.33/0.55 ( ( ord_less_int @ zero_zero_int @ D3 )
% 0.33/0.55 => ( ( member_int @ ( plus_plus_int @ T @ one_one_int ) @ A2 )
% 0.33/0.55 => ! [X8: int] :
% 0.33/0.55 ( ! [Xa3: int] :
% 0.33/0.55 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.33/0.55 => ! [Xb3: int] :
% 0.33/0.55 ( ( member_int @ Xb3 @ A2 )
% 0.33/0.55 => ( X8
% 0.33/0.55 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 0.33/0.55 => ( ( X8 = T )
% 0.33/0.55 => ( ( plus_plus_int @ X8 @ D3 )
% 0.33/0.55 = T ) ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % aset(3)
% 0.33/0.55 thf(fact_2232_aset_I4_J,axiom,
% 0.33/0.55 ! [D3: int,T: int,A2: set_int] :
% 0.33/0.55 ( ( ord_less_int @ zero_zero_int @ D3 )
% 0.33/0.55 => ( ( member_int @ T @ A2 )
% 0.33/0.55 => ! [X8: int] :
% 0.33/0.55 ( ! [Xa3: int] :
% 0.33/0.55 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.33/0.55 => ! [Xb3: int] :
% 0.33/0.55 ( ( member_int @ Xb3 @ A2 )
% 0.33/0.55 => ( X8
% 0.33/0.55 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 0.33/0.55 => ( ( X8 != T )
% 0.33/0.55 => ( ( plus_plus_int @ X8 @ D3 )
% 0.33/0.55 != T ) ) ) ) ) ).
% 0.33/0.55
% 0.33/0.55 % aset(4)
% 0.33/0.55 thf(fact_2233_aset_I5_J,axiom,
% 0.33/0.55 ! [D3: int,T: int,A2: set_int] :
% 0.33/0.55 ( ( ord_less_int @ zero_zero_int @ D3 )
% 0.33/0.55 => ( ( member_int @ T @ A2 )
% 0.33/0.56 => ! [X8: int] :
% 0.33/0.56 ( ! [Xa3: int] :
% 0.33/0.56 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.33/0.56 => ! [Xb3: int] :
% 0.33/0.56 ( ( member_int @ Xb3 @ A2 )
% 0.33/0.56 => ( X8
% 0.33/0.56 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 0.33/0.56 => ( ( ord_less_int @ X8 @ T )
% 0.33/0.56 => ( ord_less_int @ ( plus_plus_int @ X8 @ D3 ) @ T ) ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % aset(5)
% 0.33/0.56 thf(fact_2234_aset_I7_J,axiom,
% 0.33/0.56 ! [D3: int,A2: set_int,T: int] :
% 0.33/0.56 ( ( ord_less_int @ zero_zero_int @ D3 )
% 0.33/0.56 => ! [X8: int] :
% 0.33/0.56 ( ! [Xa3: int] :
% 0.33/0.56 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.33/0.56 => ! [Xb3: int] :
% 0.33/0.56 ( ( member_int @ Xb3 @ A2 )
% 0.33/0.56 => ( X8
% 0.33/0.56 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 0.33/0.56 => ( ( ord_less_int @ T @ X8 )
% 0.33/0.56 => ( ord_less_int @ T @ ( plus_plus_int @ X8 @ D3 ) ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % aset(7)
% 0.33/0.56 thf(fact_2235_aset_I8_J,axiom,
% 0.33/0.56 ! [D3: int,A2: set_int,T: int] :
% 0.33/0.56 ( ( ord_less_int @ zero_zero_int @ D3 )
% 0.33/0.56 => ! [X8: int] :
% 0.33/0.56 ( ! [Xa3: int] :
% 0.33/0.56 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.33/0.56 => ! [Xb3: int] :
% 0.33/0.56 ( ( member_int @ Xb3 @ A2 )
% 0.33/0.56 => ( X8
% 0.33/0.56 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 0.33/0.56 => ( ( ord_less_eq_int @ T @ X8 )
% 0.33/0.56 => ( ord_less_eq_int @ T @ ( plus_plus_int @ X8 @ D3 ) ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % aset(8)
% 0.33/0.56 thf(fact_2236_ceiling__divide__lower,axiom,
% 0.33/0.56 ! [Q3: rat,P4: rat] :
% 0.33/0.56 ( ( ord_less_rat @ zero_zero_rat @ Q3 )
% 0.33/0.56 => ( ord_less_rat @ ( times_times_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ ( divide_divide_rat @ P4 @ Q3 ) ) ) @ one_one_rat ) @ Q3 ) @ P4 ) ) ).
% 0.33/0.56
% 0.33/0.56 % ceiling_divide_lower
% 0.33/0.56 thf(fact_2237_floor__divide__upper,axiom,
% 0.33/0.56 ! [Q3: rat,P4: rat] :
% 0.33/0.56 ( ( ord_less_rat @ zero_zero_rat @ Q3 )
% 0.33/0.56 => ( ord_less_rat @ P4 @ ( times_times_rat @ ( plus_plus_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ ( divide_divide_rat @ P4 @ Q3 ) ) ) @ one_one_rat ) @ Q3 ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % floor_divide_upper
% 0.33/0.56 thf(fact_2238_power__decreasing__iff,axiom,
% 0.33/0.56 ! [B: code_integer,M2: nat,N2: nat] :
% 0.33/0.56 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 0.33/0.56 => ( ( ord_le6747313008572928689nteger @ B @ one_one_Code_integer )
% 0.33/0.56 => ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ B @ M2 ) @ ( power_8256067586552552935nteger @ B @ N2 ) )
% 0.33/0.56 = ( ord_less_eq_nat @ N2 @ M2 ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_decreasing_iff
% 0.33/0.56 thf(fact_2239_power__decreasing__iff,axiom,
% 0.33/0.56 ! [B: rat,M2: nat,N2: nat] :
% 0.33/0.56 ( ( ord_less_rat @ zero_zero_rat @ B )
% 0.33/0.56 => ( ( ord_less_rat @ B @ one_one_rat )
% 0.33/0.56 => ( ( ord_less_eq_rat @ ( power_power_rat @ B @ M2 ) @ ( power_power_rat @ B @ N2 ) )
% 0.33/0.56 = ( ord_less_eq_nat @ N2 @ M2 ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_decreasing_iff
% 0.33/0.56 thf(fact_2240_power__decreasing__iff,axiom,
% 0.33/0.56 ! [B: nat,M2: nat,N2: nat] :
% 0.33/0.56 ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.33/0.56 => ( ( ord_less_nat @ B @ one_one_nat )
% 0.33/0.56 => ( ( ord_less_eq_nat @ ( power_power_nat @ B @ M2 ) @ ( power_power_nat @ B @ N2 ) )
% 0.33/0.56 = ( ord_less_eq_nat @ N2 @ M2 ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_decreasing_iff
% 0.33/0.56 thf(fact_2241_power__decreasing__iff,axiom,
% 0.33/0.56 ! [B: int,M2: nat,N2: nat] :
% 0.33/0.56 ( ( ord_less_int @ zero_zero_int @ B )
% 0.33/0.56 => ( ( ord_less_int @ B @ one_one_int )
% 0.33/0.56 => ( ( ord_less_eq_int @ ( power_power_int @ B @ M2 ) @ ( power_power_int @ B @ N2 ) )
% 0.33/0.56 = ( ord_less_eq_nat @ N2 @ M2 ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_decreasing_iff
% 0.33/0.56 thf(fact_2242_divmod__nat__def,axiom,
% 0.33/0.56 ( divmod_nat
% 0.33/0.56 = ( ^ [M: nat,N4: nat] : ( product_Pair_nat_nat @ ( divide_divide_nat @ M @ N4 ) @ ( modulo_modulo_nat @ M @ N4 ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % divmod_nat_def
% 0.33/0.56 thf(fact_2243_distrib__left__NO__MATCH,axiom,
% 0.33/0.56 ! [X: int,Y: int,A: rat,B: rat,C: rat] :
% 0.33/0.56 ( ( nO_MATCH_int_rat @ ( divide_divide_int @ X @ Y ) @ A )
% 0.33/0.56 => ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 0.33/0.56 = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % distrib_left_NO_MATCH
% 0.33/0.56 thf(fact_2244_distrib__left__NO__MATCH,axiom,
% 0.33/0.56 ! [X: int,Y: int,A: nat,B: nat,C: nat] :
% 0.33/0.56 ( ( nO_MATCH_int_nat @ ( divide_divide_int @ X @ Y ) @ A )
% 0.33/0.56 => ( ( times_times_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 0.33/0.56 = ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % distrib_left_NO_MATCH
% 0.33/0.56 thf(fact_2245_distrib__left__NO__MATCH,axiom,
% 0.33/0.56 ! [X: int,Y: int,A: int,B: int,C: int] :
% 0.33/0.56 ( ( nO_MATCH_int_int @ ( divide_divide_int @ X @ Y ) @ A )
% 0.33/0.56 => ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 0.33/0.56 = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % distrib_left_NO_MATCH
% 0.33/0.56 thf(fact_2246_distrib__left__NO__MATCH,axiom,
% 0.33/0.56 ! [X: nat,Y: nat,A: rat,B: rat,C: rat] :
% 0.33/0.56 ( ( nO_MATCH_nat_rat @ ( divide_divide_nat @ X @ Y ) @ A )
% 0.33/0.56 => ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 0.33/0.56 = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % distrib_left_NO_MATCH
% 0.33/0.56 thf(fact_2247_distrib__left__NO__MATCH,axiom,
% 0.33/0.56 ! [X: nat,Y: nat,A: nat,B: nat,C: nat] :
% 0.33/0.56 ( ( nO_MATCH_nat_nat @ ( divide_divide_nat @ X @ Y ) @ A )
% 0.33/0.56 => ( ( times_times_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 0.33/0.56 = ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % distrib_left_NO_MATCH
% 0.33/0.56 thf(fact_2248_distrib__left__NO__MATCH,axiom,
% 0.33/0.56 ! [X: nat,Y: nat,A: int,B: int,C: int] :
% 0.33/0.56 ( ( nO_MATCH_nat_int @ ( divide_divide_nat @ X @ Y ) @ A )
% 0.33/0.56 => ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 0.33/0.56 = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % distrib_left_NO_MATCH
% 0.33/0.56 thf(fact_2249_distrib__left__NO__MATCH,axiom,
% 0.33/0.56 ! [X: code_integer,Y: code_integer,A: rat,B: rat,C: rat] :
% 0.33/0.56 ( ( nO_MAT7795273704451493282er_rat @ ( divide6298287555418463151nteger @ X @ Y ) @ A )
% 0.33/0.56 => ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 0.33/0.56 = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % distrib_left_NO_MATCH
% 0.33/0.56 thf(fact_2250_distrib__left__NO__MATCH,axiom,
% 0.33/0.56 ! [X: code_integer,Y: code_integer,A: nat,B: nat,C: nat] :
% 0.33/0.56 ( ( nO_MAT8430403764537989018er_nat @ ( divide6298287555418463151nteger @ X @ Y ) @ A )
% 0.33/0.56 => ( ( times_times_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 0.33/0.56 = ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % distrib_left_NO_MATCH
% 0.33/0.56 thf(fact_2251_distrib__left__NO__MATCH,axiom,
% 0.33/0.56 ! [X: code_integer,Y: code_integer,A: int,B: int,C: int] :
% 0.33/0.56 ( ( nO_MAT8427913294028938742er_int @ ( divide6298287555418463151nteger @ X @ Y ) @ A )
% 0.33/0.56 => ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 0.33/0.56 = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % distrib_left_NO_MATCH
% 0.33/0.56 thf(fact_2252_distrib__left__NO__MATCH,axiom,
% 0.33/0.56 ! [X: rat,Y: rat,A: rat,B: rat,C: rat] :
% 0.33/0.56 ( ( nO_MATCH_rat_rat @ ( divide_divide_rat @ X @ Y ) @ A )
% 0.33/0.56 => ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 0.33/0.56 = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % distrib_left_NO_MATCH
% 0.33/0.56 thf(fact_2253_distrib__right__NO__MATCH,axiom,
% 0.33/0.56 ! [X: int,Y: int,C: rat,A: rat,B: rat] :
% 0.33/0.56 ( ( nO_MATCH_int_rat @ ( divide_divide_int @ X @ Y ) @ C )
% 0.33/0.56 => ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 0.33/0.56 = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % distrib_right_NO_MATCH
% 0.33/0.56 thf(fact_2254_distrib__right__NO__MATCH,axiom,
% 0.33/0.56 ! [X: int,Y: int,C: nat,A: nat,B: nat] :
% 0.33/0.56 ( ( nO_MATCH_int_nat @ ( divide_divide_int @ X @ Y ) @ C )
% 0.33/0.56 => ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 0.33/0.56 = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % distrib_right_NO_MATCH
% 0.33/0.56 thf(fact_2255_distrib__right__NO__MATCH,axiom,
% 0.33/0.56 ! [X: int,Y: int,C: int,A: int,B: int] :
% 0.33/0.56 ( ( nO_MATCH_int_int @ ( divide_divide_int @ X @ Y ) @ C )
% 0.33/0.56 => ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 0.33/0.56 = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % distrib_right_NO_MATCH
% 0.33/0.56 thf(fact_2256_distrib__right__NO__MATCH,axiom,
% 0.33/0.56 ! [X: nat,Y: nat,C: rat,A: rat,B: rat] :
% 0.33/0.56 ( ( nO_MATCH_nat_rat @ ( divide_divide_nat @ X @ Y ) @ C )
% 0.33/0.56 => ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 0.33/0.56 = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % distrib_right_NO_MATCH
% 0.33/0.56 thf(fact_2257_distrib__right__NO__MATCH,axiom,
% 0.33/0.56 ! [X: nat,Y: nat,C: nat,A: nat,B: nat] :
% 0.33/0.56 ( ( nO_MATCH_nat_nat @ ( divide_divide_nat @ X @ Y ) @ C )
% 0.33/0.56 => ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 0.33/0.56 = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % distrib_right_NO_MATCH
% 0.33/0.56 thf(fact_2258_distrib__right__NO__MATCH,axiom,
% 0.33/0.56 ! [X: nat,Y: nat,C: int,A: int,B: int] :
% 0.33/0.56 ( ( nO_MATCH_nat_int @ ( divide_divide_nat @ X @ Y ) @ C )
% 0.33/0.56 => ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 0.33/0.56 = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % distrib_right_NO_MATCH
% 0.33/0.56 thf(fact_2259_distrib__right__NO__MATCH,axiom,
% 0.33/0.56 ! [X: code_integer,Y: code_integer,C: rat,A: rat,B: rat] :
% 0.33/0.56 ( ( nO_MAT7795273704451493282er_rat @ ( divide6298287555418463151nteger @ X @ Y ) @ C )
% 0.33/0.56 => ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 0.33/0.56 = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % distrib_right_NO_MATCH
% 0.33/0.56 thf(fact_2260_distrib__right__NO__MATCH,axiom,
% 0.33/0.56 ! [X: code_integer,Y: code_integer,C: nat,A: nat,B: nat] :
% 0.33/0.56 ( ( nO_MAT8430403764537989018er_nat @ ( divide6298287555418463151nteger @ X @ Y ) @ C )
% 0.33/0.56 => ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 0.33/0.56 = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % distrib_right_NO_MATCH
% 0.33/0.56 thf(fact_2261_distrib__right__NO__MATCH,axiom,
% 0.33/0.56 ! [X: code_integer,Y: code_integer,C: int,A: int,B: int] :
% 0.33/0.56 ( ( nO_MAT8427913294028938742er_int @ ( divide6298287555418463151nteger @ X @ Y ) @ C )
% 0.33/0.56 => ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 0.33/0.56 = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % distrib_right_NO_MATCH
% 0.33/0.56 thf(fact_2262_distrib__right__NO__MATCH,axiom,
% 0.33/0.56 ! [X: rat,Y: rat,C: rat,A: rat,B: rat] :
% 0.33/0.56 ( ( nO_MATCH_rat_rat @ ( divide_divide_rat @ X @ Y ) @ C )
% 0.33/0.56 => ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 0.33/0.56 = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % distrib_right_NO_MATCH
% 0.33/0.56 thf(fact_2263_Suc__times__mod__eq,axiom,
% 0.33/0.56 ! [M2: nat,N2: nat] :
% 0.33/0.56 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M2 )
% 0.33/0.56 => ( ( modulo_modulo_nat @ ( suc @ ( times_times_nat @ M2 @ N2 ) ) @ M2 )
% 0.33/0.56 = one_one_nat ) ) ).
% 0.33/0.56
% 0.33/0.56 % Suc_times_mod_eq
% 0.33/0.56 thf(fact_2264_power__one,axiom,
% 0.33/0.56 ! [N2: nat] :
% 0.33/0.56 ( ( power_8256067586552552935nteger @ one_one_Code_integer @ N2 )
% 0.33/0.56 = one_one_Code_integer ) ).
% 0.33/0.56
% 0.33/0.56 % power_one
% 0.33/0.56 thf(fact_2265_power__one,axiom,
% 0.33/0.56 ! [N2: nat] :
% 0.33/0.56 ( ( power_power_assn @ one_one_assn @ N2 )
% 0.33/0.56 = one_one_assn ) ).
% 0.33/0.56
% 0.33/0.56 % power_one
% 0.33/0.56 thf(fact_2266_power__one,axiom,
% 0.33/0.56 ! [N2: nat] :
% 0.33/0.56 ( ( power_power_rat @ one_one_rat @ N2 )
% 0.33/0.56 = one_one_rat ) ).
% 0.33/0.56
% 0.33/0.56 % power_one
% 0.33/0.56 thf(fact_2267_power__one,axiom,
% 0.33/0.56 ! [N2: nat] :
% 0.33/0.56 ( ( power_power_nat @ one_one_nat @ N2 )
% 0.33/0.56 = one_one_nat ) ).
% 0.33/0.56
% 0.33/0.56 % power_one
% 0.33/0.56 thf(fact_2268_power__one,axiom,
% 0.33/0.56 ! [N2: nat] :
% 0.33/0.56 ( ( power_power_int @ one_one_int @ N2 )
% 0.33/0.56 = one_one_int ) ).
% 0.33/0.56
% 0.33/0.56 % power_one
% 0.33/0.56 thf(fact_2269_add__Suc__right,axiom,
% 0.33/0.56 ! [M2: nat,N2: nat] :
% 0.33/0.56 ( ( plus_plus_nat @ M2 @ ( suc @ N2 ) )
% 0.33/0.56 = ( suc @ ( plus_plus_nat @ M2 @ N2 ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % add_Suc_right
% 0.33/0.56 thf(fact_2270_power__one__right,axiom,
% 0.33/0.56 ! [A: nat] :
% 0.33/0.56 ( ( power_power_nat @ A @ one_one_nat )
% 0.33/0.56 = A ) ).
% 0.33/0.56
% 0.33/0.56 % power_one_right
% 0.33/0.56 thf(fact_2271_power__one__right,axiom,
% 0.33/0.56 ! [A: int] :
% 0.33/0.56 ( ( power_power_int @ A @ one_one_nat )
% 0.33/0.56 = A ) ).
% 0.33/0.56
% 0.33/0.56 % power_one_right
% 0.33/0.56 thf(fact_2272_power__inject__exp,axiom,
% 0.33/0.56 ! [A: code_integer,M2: nat,N2: nat] :
% 0.33/0.56 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 0.33/0.56 => ( ( ( power_8256067586552552935nteger @ A @ M2 )
% 0.33/0.56 = ( power_8256067586552552935nteger @ A @ N2 ) )
% 0.33/0.56 = ( M2 = N2 ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_inject_exp
% 0.33/0.56 thf(fact_2273_power__inject__exp,axiom,
% 0.33/0.56 ! [A: rat,M2: nat,N2: nat] :
% 0.33/0.56 ( ( ord_less_rat @ one_one_rat @ A )
% 0.33/0.56 => ( ( ( power_power_rat @ A @ M2 )
% 0.33/0.56 = ( power_power_rat @ A @ N2 ) )
% 0.33/0.56 = ( M2 = N2 ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_inject_exp
% 0.33/0.56 thf(fact_2274_power__inject__exp,axiom,
% 0.33/0.56 ! [A: nat,M2: nat,N2: nat] :
% 0.33/0.56 ( ( ord_less_nat @ one_one_nat @ A )
% 0.33/0.56 => ( ( ( power_power_nat @ A @ M2 )
% 0.33/0.56 = ( power_power_nat @ A @ N2 ) )
% 0.33/0.56 = ( M2 = N2 ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_inject_exp
% 0.33/0.56 thf(fact_2275_power__inject__exp,axiom,
% 0.33/0.56 ! [A: int,M2: nat,N2: nat] :
% 0.33/0.56 ( ( ord_less_int @ one_one_int @ A )
% 0.33/0.56 => ( ( ( power_power_int @ A @ M2 )
% 0.33/0.56 = ( power_power_int @ A @ N2 ) )
% 0.33/0.56 = ( M2 = N2 ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_inject_exp
% 0.33/0.56 thf(fact_2276_mult__Suc__right,axiom,
% 0.33/0.56 ! [M2: nat,N2: nat] :
% 0.33/0.56 ( ( times_times_nat @ M2 @ ( suc @ N2 ) )
% 0.33/0.56 = ( plus_plus_nat @ M2 @ ( times_times_nat @ M2 @ N2 ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % mult_Suc_right
% 0.33/0.56 thf(fact_2277_diff__Suc__1,axiom,
% 0.33/0.56 ! [N2: nat] :
% 0.33/0.56 ( ( minus_minus_nat @ ( suc @ N2 ) @ one_one_nat )
% 0.33/0.56 = N2 ) ).
% 0.33/0.56
% 0.33/0.56 % diff_Suc_1
% 0.33/0.56 thf(fact_2278_of__int__eq__1__iff,axiom,
% 0.33/0.56 ! [Z: int] :
% 0.33/0.56 ( ( ( ring_1_of_int_int @ Z )
% 0.33/0.56 = one_one_int )
% 0.33/0.56 = ( Z = one_one_int ) ) ).
% 0.33/0.56
% 0.33/0.56 % of_int_eq_1_iff
% 0.33/0.56 thf(fact_2279_of__int__eq__1__iff,axiom,
% 0.33/0.56 ! [Z: int] :
% 0.33/0.56 ( ( ( ring_18347121197199848620nteger @ Z )
% 0.33/0.56 = one_one_Code_integer )
% 0.33/0.56 = ( Z = one_one_int ) ) ).
% 0.33/0.56
% 0.33/0.56 % of_int_eq_1_iff
% 0.33/0.56 thf(fact_2280_of__int__eq__1__iff,axiom,
% 0.33/0.56 ! [Z: int] :
% 0.33/0.56 ( ( ( ring_1_of_int_rat @ Z )
% 0.33/0.56 = one_one_rat )
% 0.33/0.56 = ( Z = one_one_int ) ) ).
% 0.33/0.56
% 0.33/0.56 % of_int_eq_1_iff
% 0.33/0.56 thf(fact_2281_of__int__1,axiom,
% 0.33/0.56 ( ( ring_1_of_int_int @ one_one_int )
% 0.33/0.56 = one_one_int ) ).
% 0.33/0.56
% 0.33/0.56 % of_int_1
% 0.33/0.56 thf(fact_2282_of__int__1,axiom,
% 0.33/0.56 ( ( ring_18347121197199848620nteger @ one_one_int )
% 0.33/0.56 = one_one_Code_integer ) ).
% 0.33/0.56
% 0.33/0.56 % of_int_1
% 0.33/0.56 thf(fact_2283_of__int__1,axiom,
% 0.33/0.56 ( ( ring_1_of_int_rat @ one_one_int )
% 0.33/0.56 = one_one_rat ) ).
% 0.33/0.56
% 0.33/0.56 % of_int_1
% 0.33/0.56 thf(fact_2284_of__int__add,axiom,
% 0.33/0.56 ! [W: int,Z: int] :
% 0.33/0.56 ( ( ring_1_of_int_int @ ( plus_plus_int @ W @ Z ) )
% 0.33/0.56 = ( plus_plus_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % of_int_add
% 0.33/0.56 thf(fact_2285_of__int__add,axiom,
% 0.33/0.56 ! [W: int,Z: int] :
% 0.33/0.56 ( ( ring_18347121197199848620nteger @ ( plus_plus_int @ W @ Z ) )
% 0.33/0.56 = ( plus_p5714425477246183910nteger @ ( ring_18347121197199848620nteger @ W ) @ ( ring_18347121197199848620nteger @ Z ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % of_int_add
% 0.33/0.56 thf(fact_2286_of__int__add,axiom,
% 0.33/0.56 ! [W: int,Z: int] :
% 0.33/0.56 ( ( ring_1_of_int_rat @ ( plus_plus_int @ W @ Z ) )
% 0.33/0.56 = ( plus_plus_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % of_int_add
% 0.33/0.56 thf(fact_2287_power__strict__increasing__iff,axiom,
% 0.33/0.56 ! [B: code_integer,X: nat,Y: nat] :
% 0.33/0.56 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ B )
% 0.33/0.56 => ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ B @ X ) @ ( power_8256067586552552935nteger @ B @ Y ) )
% 0.33/0.56 = ( ord_less_nat @ X @ Y ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_strict_increasing_iff
% 0.33/0.56 thf(fact_2288_power__strict__increasing__iff,axiom,
% 0.33/0.56 ! [B: rat,X: nat,Y: nat] :
% 0.33/0.56 ( ( ord_less_rat @ one_one_rat @ B )
% 0.33/0.56 => ( ( ord_less_rat @ ( power_power_rat @ B @ X ) @ ( power_power_rat @ B @ Y ) )
% 0.33/0.56 = ( ord_less_nat @ X @ Y ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_strict_increasing_iff
% 0.33/0.56 thf(fact_2289_power__strict__increasing__iff,axiom,
% 0.33/0.56 ! [B: nat,X: nat,Y: nat] :
% 0.33/0.56 ( ( ord_less_nat @ one_one_nat @ B )
% 0.33/0.56 => ( ( ord_less_nat @ ( power_power_nat @ B @ X ) @ ( power_power_nat @ B @ Y ) )
% 0.33/0.56 = ( ord_less_nat @ X @ Y ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_strict_increasing_iff
% 0.33/0.56 thf(fact_2290_power__strict__increasing__iff,axiom,
% 0.33/0.56 ! [B: int,X: nat,Y: nat] :
% 0.33/0.56 ( ( ord_less_int @ one_one_int @ B )
% 0.33/0.56 => ( ( ord_less_int @ ( power_power_int @ B @ X ) @ ( power_power_int @ B @ Y ) )
% 0.33/0.56 = ( ord_less_nat @ X @ Y ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_strict_increasing_iff
% 0.33/0.56 thf(fact_2291_left__minus__one__mult__self,axiom,
% 0.33/0.56 ! [N2: nat,A: int] :
% 0.33/0.56 ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 ) @ ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 ) @ A ) )
% 0.33/0.56 = A ) ).
% 0.33/0.56
% 0.33/0.56 % left_minus_one_mult_self
% 0.33/0.56 thf(fact_2292_left__minus__one__mult__self,axiom,
% 0.33/0.56 ! [N2: nat,A: code_integer] :
% 0.33/0.56 ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 ) @ ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 ) @ A ) )
% 0.33/0.56 = A ) ).
% 0.33/0.56
% 0.33/0.56 % left_minus_one_mult_self
% 0.33/0.56 thf(fact_2293_left__minus__one__mult__self,axiom,
% 0.33/0.56 ! [N2: nat,A: rat] :
% 0.33/0.56 ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 ) @ ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 ) @ A ) )
% 0.33/0.56 = A ) ).
% 0.33/0.56
% 0.33/0.56 % left_minus_one_mult_self
% 0.33/0.56 thf(fact_2294_minus__one__mult__self,axiom,
% 0.33/0.56 ! [N2: nat] :
% 0.33/0.56 ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 ) @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 ) )
% 0.33/0.56 = one_one_int ) ).
% 0.33/0.56
% 0.33/0.56 % minus_one_mult_self
% 0.33/0.56 thf(fact_2295_minus__one__mult__self,axiom,
% 0.33/0.56 ! [N2: nat] :
% 0.33/0.56 ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 ) )
% 0.33/0.56 = one_one_Code_integer ) ).
% 0.33/0.56
% 0.33/0.56 % minus_one_mult_self
% 0.33/0.56 thf(fact_2296_minus__one__mult__self,axiom,
% 0.33/0.56 ! [N2: nat] :
% 0.33/0.56 ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 ) @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 ) )
% 0.33/0.56 = one_one_rat ) ).
% 0.33/0.56
% 0.33/0.56 % minus_one_mult_self
% 0.33/0.56 thf(fact_2297_diff__Suc__diff__eq2,axiom,
% 0.33/0.56 ! [K: nat,J: nat,I: nat] :
% 0.33/0.56 ( ( ord_less_eq_nat @ K @ J )
% 0.33/0.56 => ( ( minus_minus_nat @ ( suc @ ( minus_minus_nat @ J @ K ) ) @ I )
% 0.33/0.56 = ( minus_minus_nat @ ( suc @ J ) @ ( plus_plus_nat @ K @ I ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % diff_Suc_diff_eq2
% 0.33/0.56 thf(fact_2298_diff__Suc__diff__eq1,axiom,
% 0.33/0.56 ! [K: nat,J: nat,I: nat] :
% 0.33/0.56 ( ( ord_less_eq_nat @ K @ J )
% 0.33/0.56 => ( ( minus_minus_nat @ I @ ( suc @ ( minus_minus_nat @ J @ K ) ) )
% 0.33/0.56 = ( minus_minus_nat @ ( plus_plus_nat @ I @ K ) @ ( suc @ J ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % diff_Suc_diff_eq1
% 0.33/0.56 thf(fact_2299_Suc__diff,axiom,
% 0.33/0.56 ! [M2: nat,N2: nat] :
% 0.33/0.56 ( ( ord_less_eq_nat @ M2 @ N2 )
% 0.33/0.56 => ( ( ord_less_eq_nat @ one_one_nat @ M2 )
% 0.33/0.56 => ( ( suc @ ( minus_minus_nat @ N2 @ M2 ) )
% 0.33/0.56 = ( minus_minus_nat @ N2 @ ( minus_minus_nat @ M2 @ one_one_nat ) ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % Suc_diff
% 0.33/0.56 thf(fact_2300_Suc__mod__mult__self4,axiom,
% 0.33/0.56 ! [N2: nat,K: nat,M2: nat] :
% 0.33/0.56 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ ( times_times_nat @ N2 @ K ) @ M2 ) ) @ N2 )
% 0.33/0.56 = ( modulo_modulo_nat @ ( suc @ M2 ) @ N2 ) ) ).
% 0.33/0.56
% 0.33/0.56 % Suc_mod_mult_self4
% 0.33/0.56 thf(fact_2301_Suc__mod__mult__self3,axiom,
% 0.33/0.56 ! [K: nat,N2: nat,M2: nat] :
% 0.33/0.56 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ ( times_times_nat @ K @ N2 ) @ M2 ) ) @ N2 )
% 0.33/0.56 = ( modulo_modulo_nat @ ( suc @ M2 ) @ N2 ) ) ).
% 0.33/0.56
% 0.33/0.56 % Suc_mod_mult_self3
% 0.33/0.56 thf(fact_2302_Suc__mod__mult__self2,axiom,
% 0.33/0.56 ! [M2: nat,N2: nat,K: nat] :
% 0.33/0.56 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ M2 @ ( times_times_nat @ N2 @ K ) ) ) @ N2 )
% 0.33/0.56 = ( modulo_modulo_nat @ ( suc @ M2 ) @ N2 ) ) ).
% 0.33/0.56
% 0.33/0.56 % Suc_mod_mult_self2
% 0.33/0.56 thf(fact_2303_Suc__mod__mult__self1,axiom,
% 0.33/0.56 ! [M2: nat,K: nat,N2: nat] :
% 0.33/0.56 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ M2 @ ( times_times_nat @ K @ N2 ) ) ) @ N2 )
% 0.33/0.56 = ( modulo_modulo_nat @ ( suc @ M2 ) @ N2 ) ) ).
% 0.33/0.56
% 0.33/0.56 % Suc_mod_mult_self1
% 0.33/0.56 thf(fact_2304_ceiling__add__of__int,axiom,
% 0.33/0.56 ! [X: rat,Z: int] :
% 0.33/0.56 ( ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X @ ( ring_1_of_int_rat @ Z ) ) )
% 0.33/0.56 = ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X ) @ Z ) ) ).
% 0.33/0.56
% 0.33/0.56 % ceiling_add_of_int
% 0.33/0.56 thf(fact_2305_power__strict__decreasing__iff,axiom,
% 0.33/0.56 ! [B: code_integer,M2: nat,N2: nat] :
% 0.33/0.56 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 0.33/0.56 => ( ( ord_le6747313008572928689nteger @ B @ one_one_Code_integer )
% 0.33/0.56 => ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ B @ M2 ) @ ( power_8256067586552552935nteger @ B @ N2 ) )
% 0.33/0.56 = ( ord_less_nat @ N2 @ M2 ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_strict_decreasing_iff
% 0.33/0.56 thf(fact_2306_power__strict__decreasing__iff,axiom,
% 0.33/0.56 ! [B: rat,M2: nat,N2: nat] :
% 0.33/0.56 ( ( ord_less_rat @ zero_zero_rat @ B )
% 0.33/0.56 => ( ( ord_less_rat @ B @ one_one_rat )
% 0.33/0.56 => ( ( ord_less_rat @ ( power_power_rat @ B @ M2 ) @ ( power_power_rat @ B @ N2 ) )
% 0.33/0.56 = ( ord_less_nat @ N2 @ M2 ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_strict_decreasing_iff
% 0.33/0.56 thf(fact_2307_power__strict__decreasing__iff,axiom,
% 0.33/0.56 ! [B: nat,M2: nat,N2: nat] :
% 0.33/0.56 ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.33/0.56 => ( ( ord_less_nat @ B @ one_one_nat )
% 0.33/0.56 => ( ( ord_less_nat @ ( power_power_nat @ B @ M2 ) @ ( power_power_nat @ B @ N2 ) )
% 0.33/0.56 = ( ord_less_nat @ N2 @ M2 ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_strict_decreasing_iff
% 0.33/0.56 thf(fact_2308_power__strict__decreasing__iff,axiom,
% 0.33/0.56 ! [B: int,M2: nat,N2: nat] :
% 0.33/0.56 ( ( ord_less_int @ zero_zero_int @ B )
% 0.33/0.56 => ( ( ord_less_int @ B @ one_one_int )
% 0.33/0.56 => ( ( ord_less_int @ ( power_power_int @ B @ M2 ) @ ( power_power_int @ B @ N2 ) )
% 0.33/0.56 = ( ord_less_nat @ N2 @ M2 ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_strict_decreasing_iff
% 0.33/0.56 thf(fact_2309_power__increasing__iff,axiom,
% 0.33/0.56 ! [B: code_integer,X: nat,Y: nat] :
% 0.33/0.56 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ B )
% 0.33/0.56 => ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ B @ X ) @ ( power_8256067586552552935nteger @ B @ Y ) )
% 0.33/0.56 = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_increasing_iff
% 0.33/0.56 thf(fact_2310_power__increasing__iff,axiom,
% 0.33/0.56 ! [B: rat,X: nat,Y: nat] :
% 0.33/0.56 ( ( ord_less_rat @ one_one_rat @ B )
% 0.33/0.56 => ( ( ord_less_eq_rat @ ( power_power_rat @ B @ X ) @ ( power_power_rat @ B @ Y ) )
% 0.33/0.56 = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_increasing_iff
% 0.33/0.56 thf(fact_2311_power__increasing__iff,axiom,
% 0.33/0.56 ! [B: nat,X: nat,Y: nat] :
% 0.33/0.56 ( ( ord_less_nat @ one_one_nat @ B )
% 0.33/0.56 => ( ( ord_less_eq_nat @ ( power_power_nat @ B @ X ) @ ( power_power_nat @ B @ Y ) )
% 0.33/0.56 = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_increasing_iff
% 0.33/0.56 thf(fact_2312_power__increasing__iff,axiom,
% 0.33/0.56 ! [B: int,X: nat,Y: nat] :
% 0.33/0.56 ( ( ord_less_int @ one_one_int @ B )
% 0.33/0.56 => ( ( ord_less_eq_int @ ( power_power_int @ B @ X ) @ ( power_power_int @ B @ Y ) )
% 0.33/0.56 = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_increasing_iff
% 0.33/0.56 thf(fact_2313_Suc__diff__1,axiom,
% 0.33/0.56 ! [N2: nat] :
% 0.33/0.56 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.33/0.56 => ( ( suc @ ( minus_minus_nat @ N2 @ one_one_nat ) )
% 0.33/0.56 = N2 ) ) ).
% 0.33/0.56
% 0.33/0.56 % Suc_diff_1
% 0.33/0.56 thf(fact_2314_of__int__1__le__iff,axiom,
% 0.33/0.56 ! [Z: int] :
% 0.33/0.56 ( ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( ring_18347121197199848620nteger @ Z ) )
% 0.33/0.56 = ( ord_less_eq_int @ one_one_int @ Z ) ) ).
% 0.33/0.56
% 0.33/0.56 % of_int_1_le_iff
% 0.33/0.56 thf(fact_2315_of__int__1__le__iff,axiom,
% 0.33/0.56 ! [Z: int] :
% 0.33/0.56 ( ( ord_less_eq_rat @ one_one_rat @ ( ring_1_of_int_rat @ Z ) )
% 0.33/0.56 = ( ord_less_eq_int @ one_one_int @ Z ) ) ).
% 0.33/0.56
% 0.33/0.56 % of_int_1_le_iff
% 0.33/0.56 thf(fact_2316_of__int__1__le__iff,axiom,
% 0.33/0.56 ! [Z: int] :
% 0.33/0.56 ( ( ord_less_eq_int @ one_one_int @ ( ring_1_of_int_int @ Z ) )
% 0.33/0.56 = ( ord_less_eq_int @ one_one_int @ Z ) ) ).
% 0.33/0.56
% 0.33/0.56 % of_int_1_le_iff
% 0.33/0.56 thf(fact_2317_of__int__le__1__iff,axiom,
% 0.33/0.56 ! [Z: int] :
% 0.33/0.56 ( ( ord_le3102999989581377725nteger @ ( ring_18347121197199848620nteger @ Z ) @ one_one_Code_integer )
% 0.33/0.56 = ( ord_less_eq_int @ Z @ one_one_int ) ) ).
% 0.33/0.56
% 0.33/0.56 % of_int_le_1_iff
% 0.33/0.56 thf(fact_2318_of__int__le__1__iff,axiom,
% 0.33/0.56 ! [Z: int] :
% 0.33/0.56 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat )
% 0.33/0.56 = ( ord_less_eq_int @ Z @ one_one_int ) ) ).
% 0.33/0.56
% 0.33/0.56 % of_int_le_1_iff
% 0.33/0.56 thf(fact_2319_of__int__le__1__iff,axiom,
% 0.33/0.56 ! [Z: int] :
% 0.33/0.56 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z ) @ one_one_int )
% 0.33/0.56 = ( ord_less_eq_int @ Z @ one_one_int ) ) ).
% 0.33/0.56
% 0.33/0.56 % of_int_le_1_iff
% 0.33/0.56 thf(fact_2320_of__int__less__1__iff,axiom,
% 0.33/0.56 ! [Z: int] :
% 0.33/0.56 ( ( ord_le6747313008572928689nteger @ ( ring_18347121197199848620nteger @ Z ) @ one_one_Code_integer )
% 0.33/0.56 = ( ord_less_int @ Z @ one_one_int ) ) ).
% 0.33/0.56
% 0.33/0.56 % of_int_less_1_iff
% 0.33/0.56 thf(fact_2321_of__int__less__1__iff,axiom,
% 0.33/0.56 ! [Z: int] :
% 0.33/0.56 ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat )
% 0.33/0.56 = ( ord_less_int @ Z @ one_one_int ) ) ).
% 0.33/0.56
% 0.33/0.56 % of_int_less_1_iff
% 0.33/0.56 thf(fact_2322_of__int__less__1__iff,axiom,
% 0.33/0.56 ! [Z: int] :
% 0.33/0.56 ( ( ord_less_int @ ( ring_1_of_int_int @ Z ) @ one_one_int )
% 0.33/0.56 = ( ord_less_int @ Z @ one_one_int ) ) ).
% 0.33/0.56
% 0.33/0.56 % of_int_less_1_iff
% 0.33/0.56 thf(fact_2323_of__int__1__less__iff,axiom,
% 0.33/0.56 ! [Z: int] :
% 0.33/0.56 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( ring_18347121197199848620nteger @ Z ) )
% 0.33/0.56 = ( ord_less_int @ one_one_int @ Z ) ) ).
% 0.33/0.56
% 0.33/0.56 % of_int_1_less_iff
% 0.33/0.56 thf(fact_2324_of__int__1__less__iff,axiom,
% 0.33/0.56 ! [Z: int] :
% 0.33/0.56 ( ( ord_less_rat @ one_one_rat @ ( ring_1_of_int_rat @ Z ) )
% 0.33/0.56 = ( ord_less_int @ one_one_int @ Z ) ) ).
% 0.33/0.56
% 0.33/0.56 % of_int_1_less_iff
% 0.33/0.56 thf(fact_2325_of__int__1__less__iff,axiom,
% 0.33/0.56 ! [Z: int] :
% 0.33/0.56 ( ( ord_less_int @ one_one_int @ ( ring_1_of_int_int @ Z ) )
% 0.33/0.56 = ( ord_less_int @ one_one_int @ Z ) ) ).
% 0.33/0.56
% 0.33/0.56 % of_int_1_less_iff
% 0.33/0.56 thf(fact_2326_power__gt1,axiom,
% 0.33/0.56 ! [A: code_integer,N2: nat] :
% 0.33/0.56 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 0.33/0.56 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ A @ ( suc @ N2 ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_gt1
% 0.33/0.56 thf(fact_2327_power__gt1,axiom,
% 0.33/0.56 ! [A: rat,N2: nat] :
% 0.33/0.56 ( ( ord_less_rat @ one_one_rat @ A )
% 0.33/0.56 => ( ord_less_rat @ one_one_rat @ ( power_power_rat @ A @ ( suc @ N2 ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_gt1
% 0.33/0.56 thf(fact_2328_power__gt1,axiom,
% 0.33/0.56 ! [A: nat,N2: nat] :
% 0.33/0.56 ( ( ord_less_nat @ one_one_nat @ A )
% 0.33/0.56 => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A @ ( suc @ N2 ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_gt1
% 0.33/0.56 thf(fact_2329_power__gt1,axiom,
% 0.33/0.56 ! [A: int,N2: nat] :
% 0.33/0.56 ( ( ord_less_int @ one_one_int @ A )
% 0.33/0.56 => ( ord_less_int @ one_one_int @ ( power_power_int @ A @ ( suc @ N2 ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_gt1
% 0.33/0.56 thf(fact_2330_add__Suc__shift,axiom,
% 0.33/0.56 ! [M2: nat,N2: nat] :
% 0.33/0.56 ( ( plus_plus_nat @ ( suc @ M2 ) @ N2 )
% 0.33/0.56 = ( plus_plus_nat @ M2 @ ( suc @ N2 ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % add_Suc_shift
% 0.33/0.56 thf(fact_2331_add__Suc,axiom,
% 0.33/0.56 ! [M2: nat,N2: nat] :
% 0.33/0.56 ( ( plus_plus_nat @ ( suc @ M2 ) @ N2 )
% 0.33/0.56 = ( suc @ ( plus_plus_nat @ M2 @ N2 ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % add_Suc
% 0.33/0.56 thf(fact_2332_nat__arith_Osuc1,axiom,
% 0.33/0.56 ! [A2: nat,K: nat,A: nat] :
% 0.33/0.56 ( ( A2
% 0.33/0.56 = ( plus_plus_nat @ K @ A ) )
% 0.33/0.56 => ( ( suc @ A2 )
% 0.33/0.56 = ( plus_plus_nat @ K @ ( suc @ A ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % nat_arith.suc1
% 0.33/0.56 thf(fact_2333_power__Suc__le__self,axiom,
% 0.33/0.56 ! [A: code_integer,N2: nat] :
% 0.33/0.56 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.33/0.56 => ( ( ord_le3102999989581377725nteger @ A @ one_one_Code_integer )
% 0.33/0.56 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ ( suc @ N2 ) ) @ A ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_Suc_le_self
% 0.33/0.56 thf(fact_2334_power__Suc__le__self,axiom,
% 0.33/0.56 ! [A: rat,N2: nat] :
% 0.33/0.56 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.33/0.56 => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 0.33/0.56 => ( ord_less_eq_rat @ ( power_power_rat @ A @ ( suc @ N2 ) ) @ A ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_Suc_le_self
% 0.33/0.56 thf(fact_2335_power__Suc__le__self,axiom,
% 0.33/0.56 ! [A: nat,N2: nat] :
% 0.33/0.56 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.33/0.56 => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 0.33/0.56 => ( ord_less_eq_nat @ ( power_power_nat @ A @ ( suc @ N2 ) ) @ A ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_Suc_le_self
% 0.33/0.56 thf(fact_2336_power__Suc__le__self,axiom,
% 0.33/0.56 ! [A: int,N2: nat] :
% 0.33/0.56 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.33/0.56 => ( ( ord_less_eq_int @ A @ one_one_int )
% 0.33/0.56 => ( ord_less_eq_int @ ( power_power_int @ A @ ( suc @ N2 ) ) @ A ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_Suc_le_self
% 0.33/0.56 thf(fact_2337_power__Suc__less__one,axiom,
% 0.33/0.56 ! [A: code_integer,N2: nat] :
% 0.33/0.56 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 0.33/0.56 => ( ( ord_le6747313008572928689nteger @ A @ one_one_Code_integer )
% 0.33/0.56 => ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A @ ( suc @ N2 ) ) @ one_one_Code_integer ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_Suc_less_one
% 0.33/0.56 thf(fact_2338_power__Suc__less__one,axiom,
% 0.33/0.56 ! [A: rat,N2: nat] :
% 0.33/0.56 ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.33/0.56 => ( ( ord_less_rat @ A @ one_one_rat )
% 0.33/0.56 => ( ord_less_rat @ ( power_power_rat @ A @ ( suc @ N2 ) ) @ one_one_rat ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_Suc_less_one
% 0.33/0.56 thf(fact_2339_power__Suc__less__one,axiom,
% 0.33/0.56 ! [A: nat,N2: nat] :
% 0.33/0.56 ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.33/0.56 => ( ( ord_less_nat @ A @ one_one_nat )
% 0.33/0.56 => ( ord_less_nat @ ( power_power_nat @ A @ ( suc @ N2 ) ) @ one_one_nat ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_Suc_less_one
% 0.33/0.56 thf(fact_2340_power__Suc__less__one,axiom,
% 0.33/0.56 ! [A: int,N2: nat] :
% 0.33/0.56 ( ( ord_less_int @ zero_zero_int @ A )
% 0.33/0.56 => ( ( ord_less_int @ A @ one_one_int )
% 0.33/0.56 => ( ord_less_int @ ( power_power_int @ A @ ( suc @ N2 ) ) @ one_one_int ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_Suc_less_one
% 0.33/0.56 thf(fact_2341_power__minus_H,axiom,
% 0.33/0.56 ! [X: int,N2: nat] :
% 0.33/0.56 ( ( nO_MATCH_int_int @ one_one_int @ X )
% 0.33/0.56 => ( ( power_power_int @ ( uminus_uminus_int @ X ) @ N2 )
% 0.33/0.56 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 ) @ ( power_power_int @ X @ N2 ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_minus'
% 0.33/0.56 thf(fact_2342_power__minus_H,axiom,
% 0.33/0.56 ! [X: code_integer,N2: nat] :
% 0.33/0.56 ( ( nO_MAT8252062027627875367nteger @ one_one_Code_integer @ X )
% 0.33/0.56 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ X ) @ N2 )
% 0.33/0.56 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 ) @ ( power_8256067586552552935nteger @ X @ N2 ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_minus'
% 0.33/0.56 thf(fact_2343_power__minus_H,axiom,
% 0.33/0.56 ! [X: rat,N2: nat] :
% 0.33/0.56 ( ( nO_MATCH_rat_rat @ one_one_rat @ X )
% 0.33/0.56 => ( ( power_power_rat @ ( uminus_uminus_rat @ X ) @ N2 )
% 0.33/0.56 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 ) @ ( power_power_rat @ X @ N2 ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_minus'
% 0.33/0.56 thf(fact_2344_one__le__power,axiom,
% 0.33/0.56 ! [A: code_integer,N2: nat] :
% 0.33/0.56 ( ( ord_le3102999989581377725nteger @ one_one_Code_integer @ A )
% 0.33/0.56 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ A @ N2 ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % one_le_power
% 0.33/0.56 thf(fact_2345_one__le__power,axiom,
% 0.33/0.56 ! [A: rat,N2: nat] :
% 0.33/0.56 ( ( ord_less_eq_rat @ one_one_rat @ A )
% 0.33/0.56 => ( ord_less_eq_rat @ one_one_rat @ ( power_power_rat @ A @ N2 ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % one_le_power
% 0.33/0.56 thf(fact_2346_one__le__power,axiom,
% 0.33/0.56 ! [A: nat,N2: nat] :
% 0.33/0.56 ( ( ord_less_eq_nat @ one_one_nat @ A )
% 0.33/0.56 => ( ord_less_eq_nat @ one_one_nat @ ( power_power_nat @ A @ N2 ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % one_le_power
% 0.33/0.56 thf(fact_2347_one__le__power,axiom,
% 0.33/0.56 ! [A: int,N2: nat] :
% 0.33/0.56 ( ( ord_less_eq_int @ one_one_int @ A )
% 0.33/0.56 => ( ord_less_eq_int @ one_one_int @ ( power_power_int @ A @ N2 ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % one_le_power
% 0.33/0.56 thf(fact_2348_left__right__inverse__power,axiom,
% 0.33/0.56 ! [X: code_integer,Y: code_integer,N2: nat] :
% 0.33/0.56 ( ( ( times_3573771949741848930nteger @ X @ Y )
% 0.33/0.56 = one_one_Code_integer )
% 0.33/0.56 => ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ X @ N2 ) @ ( power_8256067586552552935nteger @ Y @ N2 ) )
% 0.33/0.56 = one_one_Code_integer ) ) ).
% 0.33/0.56
% 0.33/0.56 % left_right_inverse_power
% 0.33/0.56 thf(fact_2349_left__right__inverse__power,axiom,
% 0.33/0.56 ! [X: assn,Y: assn,N2: nat] :
% 0.33/0.56 ( ( ( times_times_assn @ X @ Y )
% 0.33/0.56 = one_one_assn )
% 0.33/0.56 => ( ( times_times_assn @ ( power_power_assn @ X @ N2 ) @ ( power_power_assn @ Y @ N2 ) )
% 0.33/0.56 = one_one_assn ) ) ).
% 0.33/0.56
% 0.33/0.56 % left_right_inverse_power
% 0.33/0.56 thf(fact_2350_left__right__inverse__power,axiom,
% 0.33/0.56 ! [X: rat,Y: rat,N2: nat] :
% 0.33/0.56 ( ( ( times_times_rat @ X @ Y )
% 0.33/0.56 = one_one_rat )
% 0.33/0.56 => ( ( times_times_rat @ ( power_power_rat @ X @ N2 ) @ ( power_power_rat @ Y @ N2 ) )
% 0.33/0.56 = one_one_rat ) ) ).
% 0.33/0.56
% 0.33/0.56 % left_right_inverse_power
% 0.33/0.56 thf(fact_2351_left__right__inverse__power,axiom,
% 0.33/0.56 ! [X: nat,Y: nat,N2: nat] :
% 0.33/0.56 ( ( ( times_times_nat @ X @ Y )
% 0.33/0.56 = one_one_nat )
% 0.33/0.56 => ( ( times_times_nat @ ( power_power_nat @ X @ N2 ) @ ( power_power_nat @ Y @ N2 ) )
% 0.33/0.56 = one_one_nat ) ) ).
% 0.33/0.56
% 0.33/0.56 % left_right_inverse_power
% 0.33/0.56 thf(fact_2352_left__right__inverse__power,axiom,
% 0.33/0.56 ! [X: int,Y: int,N2: nat] :
% 0.33/0.56 ( ( ( times_times_int @ X @ Y )
% 0.33/0.56 = one_one_int )
% 0.33/0.56 => ( ( times_times_int @ ( power_power_int @ X @ N2 ) @ ( power_power_int @ Y @ N2 ) )
% 0.33/0.56 = one_one_int ) ) ).
% 0.33/0.56
% 0.33/0.56 % left_right_inverse_power
% 0.33/0.56 thf(fact_2353_power__0,axiom,
% 0.33/0.56 ! [A: code_integer] :
% 0.33/0.56 ( ( power_8256067586552552935nteger @ A @ zero_zero_nat )
% 0.33/0.56 = one_one_Code_integer ) ).
% 0.33/0.56
% 0.33/0.56 % power_0
% 0.33/0.56 thf(fact_2354_power__0,axiom,
% 0.33/0.56 ! [A: assn] :
% 0.33/0.56 ( ( power_power_assn @ A @ zero_zero_nat )
% 0.33/0.56 = one_one_assn ) ).
% 0.33/0.56
% 0.33/0.56 % power_0
% 0.33/0.56 thf(fact_2355_power__0,axiom,
% 0.33/0.56 ! [A: rat] :
% 0.33/0.56 ( ( power_power_rat @ A @ zero_zero_nat )
% 0.33/0.56 = one_one_rat ) ).
% 0.33/0.56
% 0.33/0.56 % power_0
% 0.33/0.56 thf(fact_2356_power__0,axiom,
% 0.33/0.56 ! [A: nat] :
% 0.33/0.56 ( ( power_power_nat @ A @ zero_zero_nat )
% 0.33/0.56 = one_one_nat ) ).
% 0.33/0.56
% 0.33/0.56 % power_0
% 0.33/0.56 thf(fact_2357_power__0,axiom,
% 0.33/0.56 ! [A: int] :
% 0.33/0.56 ( ( power_power_int @ A @ zero_zero_nat )
% 0.33/0.56 = one_one_int ) ).
% 0.33/0.56
% 0.33/0.56 % power_0
% 0.33/0.56 thf(fact_2358_power__one__over,axiom,
% 0.33/0.56 ! [A: rat,N2: nat] :
% 0.33/0.56 ( ( power_power_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ N2 )
% 0.33/0.56 = ( divide_divide_rat @ one_one_rat @ ( power_power_rat @ A @ N2 ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_one_over
% 0.33/0.56 thf(fact_2359_power__add,axiom,
% 0.33/0.56 ! [A: assn,M2: nat,N2: nat] :
% 0.33/0.56 ( ( power_power_assn @ A @ ( plus_plus_nat @ M2 @ N2 ) )
% 0.33/0.56 = ( times_times_assn @ ( power_power_assn @ A @ M2 ) @ ( power_power_assn @ A @ N2 ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_add
% 0.33/0.56 thf(fact_2360_power__add,axiom,
% 0.33/0.56 ! [A: rat,M2: nat,N2: nat] :
% 0.33/0.56 ( ( power_power_rat @ A @ ( plus_plus_nat @ M2 @ N2 ) )
% 0.33/0.56 = ( times_times_rat @ ( power_power_rat @ A @ M2 ) @ ( power_power_rat @ A @ N2 ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_add
% 0.33/0.56 thf(fact_2361_power__add,axiom,
% 0.33/0.56 ! [A: nat,M2: nat,N2: nat] :
% 0.33/0.56 ( ( power_power_nat @ A @ ( plus_plus_nat @ M2 @ N2 ) )
% 0.33/0.56 = ( times_times_nat @ ( power_power_nat @ A @ M2 ) @ ( power_power_nat @ A @ N2 ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_add
% 0.33/0.56 thf(fact_2362_power__add,axiom,
% 0.33/0.56 ! [A: int,M2: nat,N2: nat] :
% 0.33/0.56 ( ( power_power_int @ A @ ( plus_plus_nat @ M2 @ N2 ) )
% 0.33/0.56 = ( times_times_int @ ( power_power_int @ A @ M2 ) @ ( power_power_int @ A @ N2 ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_add
% 0.33/0.56 thf(fact_2363_nat__compl__induct_H,axiom,
% 0.33/0.56 ! [P: nat > $o,N2: nat] :
% 0.33/0.56 ( ( P @ zero_zero_nat )
% 0.33/0.56 => ( ! [N: nat] :
% 0.33/0.56 ( ! [Nn: nat] :
% 0.33/0.56 ( ( ord_less_eq_nat @ Nn @ N )
% 0.33/0.56 => ( P @ Nn ) )
% 0.33/0.56 => ( P @ ( suc @ N ) ) )
% 0.33/0.56 => ( P @ N2 ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % nat_compl_induct'
% 0.33/0.56 thf(fact_2364_nat__compl__induct,axiom,
% 0.33/0.56 ! [P: nat > $o,N2: nat] :
% 0.33/0.56 ( ( P @ zero_zero_nat )
% 0.33/0.56 => ( ! [N: nat] :
% 0.33/0.56 ( ! [Nn: nat] :
% 0.33/0.56 ( ( ord_less_eq_nat @ Nn @ N )
% 0.33/0.56 => ( P @ Nn ) )
% 0.33/0.56 => ( P @ ( suc @ N ) ) )
% 0.33/0.56 => ( P @ N2 ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % nat_compl_induct
% 0.33/0.56 thf(fact_2365_one__is__add,axiom,
% 0.33/0.56 ! [M2: nat,N2: nat] :
% 0.33/0.56 ( ( ( suc @ zero_zero_nat )
% 0.33/0.56 = ( plus_plus_nat @ M2 @ N2 ) )
% 0.33/0.56 = ( ( ( M2
% 0.33/0.56 = ( suc @ zero_zero_nat ) )
% 0.33/0.56 & ( N2 = zero_zero_nat ) )
% 0.33/0.56 | ( ( M2 = zero_zero_nat )
% 0.33/0.56 & ( N2
% 0.33/0.56 = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % one_is_add
% 0.33/0.56 thf(fact_2366_add__is__1,axiom,
% 0.33/0.56 ! [M2: nat,N2: nat] :
% 0.33/0.56 ( ( ( plus_plus_nat @ M2 @ N2 )
% 0.33/0.56 = ( suc @ zero_zero_nat ) )
% 0.33/0.56 = ( ( ( M2
% 0.33/0.56 = ( suc @ zero_zero_nat ) )
% 0.33/0.56 & ( N2 = zero_zero_nat ) )
% 0.33/0.56 | ( ( M2 = zero_zero_nat )
% 0.33/0.56 & ( N2
% 0.33/0.56 = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % add_is_1
% 0.33/0.56 thf(fact_2367_nat__in__between__eq_I2_J,axiom,
% 0.33/0.56 ! [A: nat,B: nat] :
% 0.33/0.56 ( ( ( ord_less_eq_nat @ A @ B )
% 0.33/0.56 & ( ord_less_nat @ B @ ( suc @ A ) ) )
% 0.33/0.56 = ( B = A ) ) ).
% 0.33/0.56
% 0.33/0.56 % nat_in_between_eq(2)
% 0.33/0.56 thf(fact_2368_nat__in__between__eq_I1_J,axiom,
% 0.33/0.56 ! [A: nat,B: nat] :
% 0.33/0.56 ( ( ( ord_less_nat @ A @ B )
% 0.33/0.56 & ( ord_less_eq_nat @ B @ ( suc @ A ) ) )
% 0.33/0.56 = ( B
% 0.33/0.56 = ( suc @ A ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % nat_in_between_eq(1)
% 0.33/0.56 thf(fact_2369_less__imp__Suc__add,axiom,
% 0.33/0.56 ! [M2: nat,N2: nat] :
% 0.33/0.56 ( ( ord_less_nat @ M2 @ N2 )
% 0.33/0.56 => ? [K5: nat] :
% 0.33/0.56 ( N2
% 0.33/0.56 = ( suc @ ( plus_plus_nat @ M2 @ K5 ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % less_imp_Suc_add
% 0.33/0.56 thf(fact_2370_less__iff__Suc__add,axiom,
% 0.33/0.56 ( ord_less_nat
% 0.33/0.56 = ( ^ [M: nat,N4: nat] :
% 0.33/0.56 ? [K4: nat] :
% 0.33/0.56 ( N4
% 0.33/0.56 = ( suc @ ( plus_plus_nat @ M @ K4 ) ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % less_iff_Suc_add
% 0.33/0.56 thf(fact_2371_less__add__Suc2,axiom,
% 0.33/0.56 ! [I: nat,M2: nat] : ( ord_less_nat @ I @ ( suc @ ( plus_plus_nat @ M2 @ I ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % less_add_Suc2
% 0.33/0.56 thf(fact_2372_less__add__Suc1,axiom,
% 0.33/0.56 ! [I: nat,M2: nat] : ( ord_less_nat @ I @ ( suc @ ( plus_plus_nat @ I @ M2 ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % less_add_Suc1
% 0.33/0.56 thf(fact_2373_less__natE,axiom,
% 0.33/0.56 ! [M2: nat,N2: nat] :
% 0.33/0.56 ( ( ord_less_nat @ M2 @ N2 )
% 0.33/0.56 => ~ ! [Q2: nat] :
% 0.33/0.56 ( N2
% 0.33/0.56 != ( suc @ ( plus_plus_nat @ M2 @ Q2 ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % less_natE
% 0.33/0.56 thf(fact_2374_Suc__to__right,axiom,
% 0.33/0.56 ! [N2: nat,M2: nat] :
% 0.33/0.56 ( ( ( suc @ N2 )
% 0.33/0.56 = M2 )
% 0.33/0.56 => ( N2
% 0.33/0.56 = ( minus_minus_nat @ M2 @ ( suc @ zero_zero_nat ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % Suc_to_right
% 0.33/0.56 thf(fact_2375_One__nat__def,axiom,
% 0.33/0.56 ( one_one_nat
% 0.33/0.56 = ( suc @ zero_zero_nat ) ) ).
% 0.33/0.56
% 0.33/0.56 % One_nat_def
% 0.33/0.56 thf(fact_2376_mult__Suc,axiom,
% 0.33/0.56 ! [M2: nat,N2: nat] :
% 0.33/0.56 ( ( times_times_nat @ ( suc @ M2 ) @ N2 )
% 0.33/0.56 = ( plus_plus_nat @ N2 @ ( times_times_nat @ M2 @ N2 ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % mult_Suc
% 0.33/0.56 thf(fact_2377_Suc__eq__plus1__left,axiom,
% 0.33/0.56 ( suc
% 0.33/0.56 = ( plus_plus_nat @ one_one_nat ) ) ).
% 0.33/0.56
% 0.33/0.56 % Suc_eq_plus1_left
% 0.33/0.56 thf(fact_2378_plus__1__eq__Suc,axiom,
% 0.33/0.56 ( ( plus_plus_nat @ one_one_nat )
% 0.33/0.56 = suc ) ).
% 0.33/0.56
% 0.33/0.56 % plus_1_eq_Suc
% 0.33/0.56 thf(fact_2379_Suc__eq__plus1,axiom,
% 0.33/0.56 ( suc
% 0.33/0.56 = ( ^ [N4: nat] : ( plus_plus_nat @ N4 @ one_one_nat ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % Suc_eq_plus1
% 0.33/0.56 thf(fact_2380_diff__Suc__eq__diff__pred,axiom,
% 0.33/0.56 ! [M2: nat,N2: nat] :
% 0.33/0.56 ( ( minus_minus_nat @ M2 @ ( suc @ N2 ) )
% 0.33/0.56 = ( minus_minus_nat @ ( minus_minus_nat @ M2 @ one_one_nat ) @ N2 ) ) ).
% 0.33/0.56
% 0.33/0.56 % diff_Suc_eq_diff_pred
% 0.33/0.56 thf(fact_2381_power__le__one,axiom,
% 0.33/0.56 ! [A: code_integer,N2: nat] :
% 0.33/0.56 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.33/0.56 => ( ( ord_le3102999989581377725nteger @ A @ one_one_Code_integer )
% 0.33/0.56 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ N2 ) @ one_one_Code_integer ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_le_one
% 0.33/0.56 thf(fact_2382_power__le__one,axiom,
% 0.33/0.56 ! [A: rat,N2: nat] :
% 0.33/0.56 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.33/0.56 => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 0.33/0.56 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N2 ) @ one_one_rat ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_le_one
% 0.33/0.56 thf(fact_2383_power__le__one,axiom,
% 0.33/0.56 ! [A: nat,N2: nat] :
% 0.33/0.56 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.33/0.56 => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 0.33/0.56 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N2 ) @ one_one_nat ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_le_one
% 0.33/0.56 thf(fact_2384_power__le__one,axiom,
% 0.33/0.56 ! [A: int,N2: nat] :
% 0.33/0.56 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.33/0.56 => ( ( ord_less_eq_int @ A @ one_one_int )
% 0.33/0.56 => ( ord_less_eq_int @ ( power_power_int @ A @ N2 ) @ one_one_int ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_le_one
% 0.33/0.56 thf(fact_2385_power__less__power__Suc,axiom,
% 0.33/0.56 ! [A: code_integer,N2: nat] :
% 0.33/0.56 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 0.33/0.56 => ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A @ N2 ) @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ A @ N2 ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_less_power_Suc
% 0.33/0.56 thf(fact_2386_power__less__power__Suc,axiom,
% 0.33/0.56 ! [A: rat,N2: nat] :
% 0.33/0.56 ( ( ord_less_rat @ one_one_rat @ A )
% 0.33/0.56 => ( ord_less_rat @ ( power_power_rat @ A @ N2 ) @ ( times_times_rat @ A @ ( power_power_rat @ A @ N2 ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_less_power_Suc
% 0.33/0.56 thf(fact_2387_power__less__power__Suc,axiom,
% 0.33/0.56 ! [A: nat,N2: nat] :
% 0.33/0.56 ( ( ord_less_nat @ one_one_nat @ A )
% 0.33/0.56 => ( ord_less_nat @ ( power_power_nat @ A @ N2 ) @ ( times_times_nat @ A @ ( power_power_nat @ A @ N2 ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_less_power_Suc
% 0.33/0.56 thf(fact_2388_power__less__power__Suc,axiom,
% 0.33/0.56 ! [A: int,N2: nat] :
% 0.33/0.56 ( ( ord_less_int @ one_one_int @ A )
% 0.33/0.56 => ( ord_less_int @ ( power_power_int @ A @ N2 ) @ ( times_times_int @ A @ ( power_power_int @ A @ N2 ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_less_power_Suc
% 0.33/0.56 thf(fact_2389_power__gt1__lemma,axiom,
% 0.33/0.56 ! [A: code_integer,N2: nat] :
% 0.33/0.56 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 0.33/0.56 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ A @ N2 ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_gt1_lemma
% 0.33/0.56 thf(fact_2390_power__gt1__lemma,axiom,
% 0.33/0.56 ! [A: rat,N2: nat] :
% 0.33/0.56 ( ( ord_less_rat @ one_one_rat @ A )
% 0.33/0.56 => ( ord_less_rat @ one_one_rat @ ( times_times_rat @ A @ ( power_power_rat @ A @ N2 ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_gt1_lemma
% 0.33/0.56 thf(fact_2391_power__gt1__lemma,axiom,
% 0.33/0.56 ! [A: nat,N2: nat] :
% 0.33/0.56 ( ( ord_less_nat @ one_one_nat @ A )
% 0.33/0.56 => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ A @ ( power_power_nat @ A @ N2 ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_gt1_lemma
% 0.33/0.56 thf(fact_2392_power__gt1__lemma,axiom,
% 0.33/0.56 ! [A: int,N2: nat] :
% 0.33/0.56 ( ( ord_less_int @ one_one_int @ A )
% 0.33/0.56 => ( ord_less_int @ one_one_int @ ( times_times_int @ A @ ( power_power_int @ A @ N2 ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_gt1_lemma
% 0.33/0.56 thf(fact_2393_power__0__left,axiom,
% 0.33/0.56 ! [N2: nat] :
% 0.33/0.56 ( ( ( N2 = zero_zero_nat )
% 0.33/0.56 => ( ( power_8256067586552552935nteger @ zero_z3403309356797280102nteger @ N2 )
% 0.33/0.56 = one_one_Code_integer ) )
% 0.33/0.56 & ( ( N2 != zero_zero_nat )
% 0.33/0.56 => ( ( power_8256067586552552935nteger @ zero_z3403309356797280102nteger @ N2 )
% 0.33/0.56 = zero_z3403309356797280102nteger ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_0_left
% 0.33/0.56 thf(fact_2394_power__0__left,axiom,
% 0.33/0.56 ! [N2: nat] :
% 0.33/0.56 ( ( ( N2 = zero_zero_nat )
% 0.33/0.56 => ( ( power_power_rat @ zero_zero_rat @ N2 )
% 0.33/0.56 = one_one_rat ) )
% 0.33/0.56 & ( ( N2 != zero_zero_nat )
% 0.33/0.56 => ( ( power_power_rat @ zero_zero_rat @ N2 )
% 0.33/0.56 = zero_zero_rat ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_0_left
% 0.33/0.56 thf(fact_2395_power__0__left,axiom,
% 0.33/0.56 ! [N2: nat] :
% 0.33/0.56 ( ( ( N2 = zero_zero_nat )
% 0.33/0.56 => ( ( power_power_nat @ zero_zero_nat @ N2 )
% 0.33/0.56 = one_one_nat ) )
% 0.33/0.56 & ( ( N2 != zero_zero_nat )
% 0.33/0.56 => ( ( power_power_nat @ zero_zero_nat @ N2 )
% 0.33/0.56 = zero_zero_nat ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_0_left
% 0.33/0.56 thf(fact_2396_power__0__left,axiom,
% 0.33/0.56 ! [N2: nat] :
% 0.33/0.56 ( ( ( N2 = zero_zero_nat )
% 0.33/0.56 => ( ( power_power_int @ zero_zero_int @ N2 )
% 0.33/0.56 = one_one_int ) )
% 0.33/0.56 & ( ( N2 != zero_zero_nat )
% 0.33/0.56 => ( ( power_power_int @ zero_zero_int @ N2 )
% 0.33/0.56 = zero_zero_int ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_0_left
% 0.33/0.56 thf(fact_2397_power__strict__increasing,axiom,
% 0.33/0.56 ! [N2: nat,N6: nat,A: code_integer] :
% 0.33/0.56 ( ( ord_less_nat @ N2 @ N6 )
% 0.33/0.56 => ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 0.33/0.56 => ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A @ N2 ) @ ( power_8256067586552552935nteger @ A @ N6 ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_strict_increasing
% 0.33/0.56 thf(fact_2398_power__strict__increasing,axiom,
% 0.33/0.56 ! [N2: nat,N6: nat,A: rat] :
% 0.33/0.56 ( ( ord_less_nat @ N2 @ N6 )
% 0.33/0.56 => ( ( ord_less_rat @ one_one_rat @ A )
% 0.33/0.56 => ( ord_less_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ A @ N6 ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_strict_increasing
% 0.33/0.56 thf(fact_2399_power__strict__increasing,axiom,
% 0.33/0.56 ! [N2: nat,N6: nat,A: nat] :
% 0.33/0.56 ( ( ord_less_nat @ N2 @ N6 )
% 0.33/0.56 => ( ( ord_less_nat @ one_one_nat @ A )
% 0.33/0.56 => ( ord_less_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ A @ N6 ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_strict_increasing
% 0.33/0.56 thf(fact_2400_power__strict__increasing,axiom,
% 0.33/0.56 ! [N2: nat,N6: nat,A: int] :
% 0.33/0.56 ( ( ord_less_nat @ N2 @ N6 )
% 0.33/0.56 => ( ( ord_less_int @ one_one_int @ A )
% 0.33/0.56 => ( ord_less_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ A @ N6 ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_strict_increasing
% 0.33/0.56 thf(fact_2401_power__less__imp__less__exp,axiom,
% 0.33/0.56 ! [A: code_integer,M2: nat,N2: nat] :
% 0.33/0.56 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 0.33/0.56 => ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A @ M2 ) @ ( power_8256067586552552935nteger @ A @ N2 ) )
% 0.33/0.56 => ( ord_less_nat @ M2 @ N2 ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_less_imp_less_exp
% 0.33/0.56 thf(fact_2402_power__less__imp__less__exp,axiom,
% 0.33/0.56 ! [A: rat,M2: nat,N2: nat] :
% 0.33/0.56 ( ( ord_less_rat @ one_one_rat @ A )
% 0.33/0.56 => ( ( ord_less_rat @ ( power_power_rat @ A @ M2 ) @ ( power_power_rat @ A @ N2 ) )
% 0.33/0.56 => ( ord_less_nat @ M2 @ N2 ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_less_imp_less_exp
% 0.33/0.56 thf(fact_2403_power__less__imp__less__exp,axiom,
% 0.33/0.56 ! [A: nat,M2: nat,N2: nat] :
% 0.33/0.56 ( ( ord_less_nat @ one_one_nat @ A )
% 0.33/0.56 => ( ( ord_less_nat @ ( power_power_nat @ A @ M2 ) @ ( power_power_nat @ A @ N2 ) )
% 0.33/0.56 => ( ord_less_nat @ M2 @ N2 ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_less_imp_less_exp
% 0.33/0.56 thf(fact_2404_power__less__imp__less__exp,axiom,
% 0.33/0.56 ! [A: int,M2: nat,N2: nat] :
% 0.33/0.56 ( ( ord_less_int @ one_one_int @ A )
% 0.33/0.56 => ( ( ord_less_int @ ( power_power_int @ A @ M2 ) @ ( power_power_int @ A @ N2 ) )
% 0.33/0.56 => ( ord_less_nat @ M2 @ N2 ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_less_imp_less_exp
% 0.33/0.56 thf(fact_2405_power__minus,axiom,
% 0.33/0.56 ! [A: int,N2: nat] :
% 0.33/0.56 ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N2 )
% 0.33/0.56 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 ) @ ( power_power_int @ A @ N2 ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_minus
% 0.33/0.56 thf(fact_2406_power__minus,axiom,
% 0.33/0.56 ! [A: code_integer,N2: nat] :
% 0.33/0.56 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N2 )
% 0.33/0.56 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 ) @ ( power_8256067586552552935nteger @ A @ N2 ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_minus
% 0.33/0.56 thf(fact_2407_power__minus,axiom,
% 0.33/0.56 ! [A: rat,N2: nat] :
% 0.33/0.56 ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N2 )
% 0.33/0.56 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 ) @ ( power_power_rat @ A @ N2 ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_minus
% 0.33/0.56 thf(fact_2408_power__increasing,axiom,
% 0.33/0.56 ! [N2: nat,N6: nat,A: code_integer] :
% 0.33/0.56 ( ( ord_less_eq_nat @ N2 @ N6 )
% 0.33/0.56 => ( ( ord_le3102999989581377725nteger @ one_one_Code_integer @ A )
% 0.33/0.56 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ N2 ) @ ( power_8256067586552552935nteger @ A @ N6 ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_increasing
% 0.33/0.56 thf(fact_2409_power__increasing,axiom,
% 0.33/0.56 ! [N2: nat,N6: nat,A: rat] :
% 0.33/0.56 ( ( ord_less_eq_nat @ N2 @ N6 )
% 0.33/0.56 => ( ( ord_less_eq_rat @ one_one_rat @ A )
% 0.33/0.56 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ A @ N6 ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_increasing
% 0.33/0.56 thf(fact_2410_power__increasing,axiom,
% 0.33/0.56 ! [N2: nat,N6: nat,A: nat] :
% 0.33/0.56 ( ( ord_less_eq_nat @ N2 @ N6 )
% 0.33/0.56 => ( ( ord_less_eq_nat @ one_one_nat @ A )
% 0.33/0.56 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ A @ N6 ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_increasing
% 0.33/0.56 thf(fact_2411_power__increasing,axiom,
% 0.33/0.56 ! [N2: nat,N6: nat,A: int] :
% 0.33/0.56 ( ( ord_less_eq_nat @ N2 @ N6 )
% 0.33/0.56 => ( ( ord_less_eq_int @ one_one_int @ A )
% 0.33/0.56 => ( ord_less_eq_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ A @ N6 ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_increasing
% 0.33/0.56 thf(fact_2412_floor__add__int,axiom,
% 0.33/0.56 ! [X: rat,Z: int] :
% 0.33/0.56 ( ( plus_plus_int @ ( archim3151403230148437115or_rat @ X ) @ Z )
% 0.33/0.56 = ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X @ ( ring_1_of_int_rat @ Z ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % floor_add_int
% 0.33/0.56 thf(fact_2413_int__add__floor,axiom,
% 0.33/0.56 ! [Z: int,X: rat] :
% 0.33/0.56 ( ( plus_plus_int @ Z @ ( archim3151403230148437115or_rat @ X ) )
% 0.33/0.56 = ( archim3151403230148437115or_rat @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z ) @ X ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % int_add_floor
% 0.33/0.56 thf(fact_2414_nat__induct__non__zero,axiom,
% 0.33/0.56 ! [N2: nat,P: nat > $o] :
% 0.33/0.56 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.33/0.56 => ( ( P @ one_one_nat )
% 0.33/0.56 => ( ! [N: nat] :
% 0.33/0.56 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.33/0.56 => ( ( P @ N )
% 0.33/0.56 => ( P @ ( suc @ N ) ) ) )
% 0.33/0.56 => ( P @ N2 ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % nat_induct_non_zero
% 0.33/0.56 thf(fact_2415_of__int__leD,axiom,
% 0.33/0.56 ! [N2: int,X: code_integer] :
% 0.33/0.56 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( ring_18347121197199848620nteger @ N2 ) ) @ X )
% 0.33/0.56 => ( ( N2 = zero_zero_int )
% 0.33/0.56 | ( ord_le3102999989581377725nteger @ one_one_Code_integer @ X ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % of_int_leD
% 0.33/0.56 thf(fact_2416_of__int__leD,axiom,
% 0.33/0.56 ! [N2: int,X: rat] :
% 0.33/0.56 ( ( ord_less_eq_rat @ ( abs_abs_rat @ ( ring_1_of_int_rat @ N2 ) ) @ X )
% 0.33/0.56 => ( ( N2 = zero_zero_int )
% 0.33/0.56 | ( ord_less_eq_rat @ one_one_rat @ X ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % of_int_leD
% 0.33/0.56 thf(fact_2417_of__int__leD,axiom,
% 0.33/0.56 ! [N2: int,X: int] :
% 0.33/0.56 ( ( ord_less_eq_int @ ( abs_abs_int @ ( ring_1_of_int_int @ N2 ) ) @ X )
% 0.33/0.56 => ( ( N2 = zero_zero_int )
% 0.33/0.56 | ( ord_less_eq_int @ one_one_int @ X ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % of_int_leD
% 0.33/0.56 thf(fact_2418_of__int__lessD,axiom,
% 0.33/0.56 ! [N2: int,X: code_integer] :
% 0.33/0.56 ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ ( ring_18347121197199848620nteger @ N2 ) ) @ X )
% 0.33/0.56 => ( ( N2 = zero_zero_int )
% 0.33/0.56 | ( ord_le6747313008572928689nteger @ one_one_Code_integer @ X ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % of_int_lessD
% 0.33/0.56 thf(fact_2419_of__int__lessD,axiom,
% 0.33/0.56 ! [N2: int,X: rat] :
% 0.33/0.56 ( ( ord_less_rat @ ( abs_abs_rat @ ( ring_1_of_int_rat @ N2 ) ) @ X )
% 0.33/0.56 => ( ( N2 = zero_zero_int )
% 0.33/0.56 | ( ord_less_rat @ one_one_rat @ X ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % of_int_lessD
% 0.33/0.56 thf(fact_2420_of__int__lessD,axiom,
% 0.33/0.56 ! [N2: int,X: int] :
% 0.33/0.56 ( ( ord_less_int @ ( abs_abs_int @ ( ring_1_of_int_int @ N2 ) ) @ X )
% 0.33/0.56 => ( ( N2 = zero_zero_int )
% 0.33/0.56 | ( ord_less_int @ one_one_int @ X ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % of_int_lessD
% 0.33/0.56 thf(fact_2421_floor__exists,axiom,
% 0.33/0.56 ! [X: rat] :
% 0.33/0.56 ? [Z3: int] :
% 0.33/0.56 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z3 ) @ X )
% 0.33/0.56 & ( ord_less_rat @ X @ ( ring_1_of_int_rat @ ( plus_plus_int @ Z3 @ one_one_int ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % floor_exists
% 0.33/0.56 thf(fact_2422_floor__exists1,axiom,
% 0.33/0.56 ! [X: rat] :
% 0.33/0.56 ? [X4: int] :
% 0.33/0.56 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ X4 ) @ X )
% 0.33/0.56 & ( ord_less_rat @ X @ ( ring_1_of_int_rat @ ( plus_plus_int @ X4 @ one_one_int ) ) )
% 0.33/0.56 & ! [Y6: int] :
% 0.33/0.56 ( ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Y6 ) @ X )
% 0.33/0.56 & ( ord_less_rat @ X @ ( ring_1_of_int_rat @ ( plus_plus_int @ Y6 @ one_one_int ) ) ) )
% 0.33/0.56 => ( Y6 = X4 ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % floor_exists1
% 0.33/0.56 thf(fact_2423_power__Suc__less,axiom,
% 0.33/0.56 ! [A: code_integer,N2: nat] :
% 0.33/0.56 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 0.33/0.56 => ( ( ord_le6747313008572928689nteger @ A @ one_one_Code_integer )
% 0.33/0.56 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ A @ N2 ) ) @ ( power_8256067586552552935nteger @ A @ N2 ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_Suc_less
% 0.33/0.56 thf(fact_2424_power__Suc__less,axiom,
% 0.33/0.56 ! [A: rat,N2: nat] :
% 0.33/0.56 ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.33/0.56 => ( ( ord_less_rat @ A @ one_one_rat )
% 0.33/0.56 => ( ord_less_rat @ ( times_times_rat @ A @ ( power_power_rat @ A @ N2 ) ) @ ( power_power_rat @ A @ N2 ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_Suc_less
% 0.33/0.56 thf(fact_2425_power__Suc__less,axiom,
% 0.33/0.56 ! [A: nat,N2: nat] :
% 0.33/0.56 ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.33/0.56 => ( ( ord_less_nat @ A @ one_one_nat )
% 0.33/0.56 => ( ord_less_nat @ ( times_times_nat @ A @ ( power_power_nat @ A @ N2 ) ) @ ( power_power_nat @ A @ N2 ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_Suc_less
% 0.33/0.56 thf(fact_2426_power__Suc__less,axiom,
% 0.33/0.56 ! [A: int,N2: nat] :
% 0.33/0.56 ( ( ord_less_int @ zero_zero_int @ A )
% 0.33/0.56 => ( ( ord_less_int @ A @ one_one_int )
% 0.33/0.56 => ( ord_less_int @ ( times_times_int @ A @ ( power_power_int @ A @ N2 ) ) @ ( power_power_int @ A @ N2 ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_Suc_less
% 0.33/0.56 thf(fact_2427_power__strict__decreasing,axiom,
% 0.33/0.56 ! [N2: nat,N6: nat,A: code_integer] :
% 0.33/0.56 ( ( ord_less_nat @ N2 @ N6 )
% 0.33/0.56 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 0.33/0.56 => ( ( ord_le6747313008572928689nteger @ A @ one_one_Code_integer )
% 0.33/0.56 => ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A @ N6 ) @ ( power_8256067586552552935nteger @ A @ N2 ) ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_strict_decreasing
% 0.33/0.56 thf(fact_2428_power__strict__decreasing,axiom,
% 0.33/0.56 ! [N2: nat,N6: nat,A: rat] :
% 0.33/0.56 ( ( ord_less_nat @ N2 @ N6 )
% 0.33/0.56 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.33/0.56 => ( ( ord_less_rat @ A @ one_one_rat )
% 0.33/0.56 => ( ord_less_rat @ ( power_power_rat @ A @ N6 ) @ ( power_power_rat @ A @ N2 ) ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_strict_decreasing
% 0.33/0.56 thf(fact_2429_power__strict__decreasing,axiom,
% 0.33/0.56 ! [N2: nat,N6: nat,A: nat] :
% 0.33/0.56 ( ( ord_less_nat @ N2 @ N6 )
% 0.33/0.56 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.33/0.56 => ( ( ord_less_nat @ A @ one_one_nat )
% 0.33/0.56 => ( ord_less_nat @ ( power_power_nat @ A @ N6 ) @ ( power_power_nat @ A @ N2 ) ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_strict_decreasing
% 0.33/0.56 thf(fact_2430_power__strict__decreasing,axiom,
% 0.33/0.56 ! [N2: nat,N6: nat,A: int] :
% 0.33/0.56 ( ( ord_less_nat @ N2 @ N6 )
% 0.33/0.56 => ( ( ord_less_int @ zero_zero_int @ A )
% 0.33/0.56 => ( ( ord_less_int @ A @ one_one_int )
% 0.33/0.56 => ( ord_less_int @ ( power_power_int @ A @ N6 ) @ ( power_power_int @ A @ N2 ) ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_strict_decreasing
% 0.33/0.56 thf(fact_2431_power__decreasing,axiom,
% 0.33/0.56 ! [N2: nat,N6: nat,A: code_integer] :
% 0.33/0.56 ( ( ord_less_eq_nat @ N2 @ N6 )
% 0.33/0.56 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.33/0.56 => ( ( ord_le3102999989581377725nteger @ A @ one_one_Code_integer )
% 0.33/0.56 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ N6 ) @ ( power_8256067586552552935nteger @ A @ N2 ) ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_decreasing
% 0.33/0.56 thf(fact_2432_power__decreasing,axiom,
% 0.33/0.56 ! [N2: nat,N6: nat,A: rat] :
% 0.33/0.56 ( ( ord_less_eq_nat @ N2 @ N6 )
% 0.33/0.56 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.33/0.56 => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 0.33/0.56 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N6 ) @ ( power_power_rat @ A @ N2 ) ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_decreasing
% 0.33/0.56 thf(fact_2433_power__decreasing,axiom,
% 0.33/0.56 ! [N2: nat,N6: nat,A: nat] :
% 0.33/0.56 ( ( ord_less_eq_nat @ N2 @ N6 )
% 0.33/0.56 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.33/0.56 => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 0.33/0.56 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N6 ) @ ( power_power_nat @ A @ N2 ) ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_decreasing
% 0.33/0.56 thf(fact_2434_power__decreasing,axiom,
% 0.33/0.56 ! [N2: nat,N6: nat,A: int] :
% 0.33/0.56 ( ( ord_less_eq_nat @ N2 @ N6 )
% 0.33/0.56 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.33/0.56 => ( ( ord_less_eq_int @ A @ one_one_int )
% 0.33/0.56 => ( ord_less_eq_int @ ( power_power_int @ A @ N6 ) @ ( power_power_int @ A @ N2 ) ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_decreasing
% 0.33/0.56 thf(fact_2435_power__le__imp__le__exp,axiom,
% 0.33/0.56 ! [A: code_integer,M2: nat,N2: nat] :
% 0.33/0.56 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 0.33/0.56 => ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ M2 ) @ ( power_8256067586552552935nteger @ A @ N2 ) )
% 0.33/0.56 => ( ord_less_eq_nat @ M2 @ N2 ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_le_imp_le_exp
% 0.33/0.56 thf(fact_2436_power__le__imp__le__exp,axiom,
% 0.33/0.56 ! [A: rat,M2: nat,N2: nat] :
% 0.33/0.56 ( ( ord_less_rat @ one_one_rat @ A )
% 0.33/0.56 => ( ( ord_less_eq_rat @ ( power_power_rat @ A @ M2 ) @ ( power_power_rat @ A @ N2 ) )
% 0.33/0.56 => ( ord_less_eq_nat @ M2 @ N2 ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_le_imp_le_exp
% 0.33/0.56 thf(fact_2437_power__le__imp__le__exp,axiom,
% 0.33/0.56 ! [A: nat,M2: nat,N2: nat] :
% 0.33/0.56 ( ( ord_less_nat @ one_one_nat @ A )
% 0.33/0.56 => ( ( ord_less_eq_nat @ ( power_power_nat @ A @ M2 ) @ ( power_power_nat @ A @ N2 ) )
% 0.33/0.56 => ( ord_less_eq_nat @ M2 @ N2 ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_le_imp_le_exp
% 0.33/0.56 thf(fact_2438_power__le__imp__le__exp,axiom,
% 0.33/0.56 ! [A: int,M2: nat,N2: nat] :
% 0.33/0.56 ( ( ord_less_int @ one_one_int @ A )
% 0.33/0.56 => ( ( ord_less_eq_int @ ( power_power_int @ A @ M2 ) @ ( power_power_int @ A @ N2 ) )
% 0.33/0.56 => ( ord_less_eq_nat @ M2 @ N2 ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_le_imp_le_exp
% 0.33/0.56 thf(fact_2439_self__le__power,axiom,
% 0.33/0.56 ! [A: code_integer,N2: nat] :
% 0.33/0.56 ( ( ord_le3102999989581377725nteger @ one_one_Code_integer @ A )
% 0.33/0.56 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.33/0.56 => ( ord_le3102999989581377725nteger @ A @ ( power_8256067586552552935nteger @ A @ N2 ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % self_le_power
% 0.33/0.56 thf(fact_2440_self__le__power,axiom,
% 0.33/0.56 ! [A: rat,N2: nat] :
% 0.33/0.56 ( ( ord_less_eq_rat @ one_one_rat @ A )
% 0.33/0.56 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.33/0.56 => ( ord_less_eq_rat @ A @ ( power_power_rat @ A @ N2 ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % self_le_power
% 0.33/0.56 thf(fact_2441_self__le__power,axiom,
% 0.33/0.56 ! [A: nat,N2: nat] :
% 0.33/0.56 ( ( ord_less_eq_nat @ one_one_nat @ A )
% 0.33/0.56 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.33/0.56 => ( ord_less_eq_nat @ A @ ( power_power_nat @ A @ N2 ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % self_le_power
% 0.33/0.56 thf(fact_2442_self__le__power,axiom,
% 0.33/0.56 ! [A: int,N2: nat] :
% 0.33/0.56 ( ( ord_less_eq_int @ one_one_int @ A )
% 0.33/0.56 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.33/0.56 => ( ord_less_eq_int @ A @ ( power_power_int @ A @ N2 ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % self_le_power
% 0.33/0.56 thf(fact_2443_one__less__power,axiom,
% 0.33/0.56 ! [A: code_integer,N2: nat] :
% 0.33/0.56 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 0.33/0.56 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.33/0.56 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ A @ N2 ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % one_less_power
% 0.33/0.56 thf(fact_2444_one__less__power,axiom,
% 0.33/0.56 ! [A: rat,N2: nat] :
% 0.33/0.56 ( ( ord_less_rat @ one_one_rat @ A )
% 0.33/0.56 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.33/0.56 => ( ord_less_rat @ one_one_rat @ ( power_power_rat @ A @ N2 ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % one_less_power
% 0.33/0.56 thf(fact_2445_one__less__power,axiom,
% 0.33/0.56 ! [A: nat,N2: nat] :
% 0.33/0.56 ( ( ord_less_nat @ one_one_nat @ A )
% 0.33/0.56 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.33/0.56 => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A @ N2 ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % one_less_power
% 0.33/0.56 thf(fact_2446_one__less__power,axiom,
% 0.33/0.56 ! [A: int,N2: nat] :
% 0.33/0.56 ( ( ord_less_int @ one_one_int @ A )
% 0.33/0.56 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.33/0.56 => ( ord_less_int @ one_one_int @ ( power_power_int @ A @ N2 ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % one_less_power
% 0.33/0.56 thf(fact_2447_nz__le__conv__less,axiom,
% 0.33/0.56 ! [K: nat,M2: nat] :
% 0.33/0.56 ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.33/0.56 => ( ( ord_less_eq_nat @ K @ M2 )
% 0.33/0.56 => ( ord_less_nat @ ( minus_minus_nat @ K @ ( suc @ zero_zero_nat ) ) @ M2 ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % nz_le_conv_less
% 0.33/0.56 thf(fact_2448_ceiling__altdef,axiom,
% 0.33/0.56 ( archim2889992004027027881ng_rat
% 0.33/0.56 = ( ^ [X3: rat] :
% 0.33/0.56 ( if_int
% 0.33/0.56 @ ( X3
% 0.33/0.56 = ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X3 ) ) )
% 0.33/0.56 @ ( archim3151403230148437115or_rat @ X3 )
% 0.33/0.56 @ ( plus_plus_int @ ( archim3151403230148437115or_rat @ X3 ) @ one_one_int ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % ceiling_altdef
% 0.33/0.56 thf(fact_2449_Suc__diff__eq__diff__pred,axiom,
% 0.33/0.56 ! [N2: nat,M2: nat] :
% 0.33/0.56 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.33/0.56 => ( ( minus_minus_nat @ ( suc @ M2 ) @ N2 )
% 0.33/0.56 = ( minus_minus_nat @ M2 @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % Suc_diff_eq_diff_pred
% 0.33/0.56 thf(fact_2450_Suc__pred_H,axiom,
% 0.33/0.56 ! [N2: nat] :
% 0.33/0.56 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.33/0.56 => ( N2
% 0.33/0.56 = ( suc @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % Suc_pred'
% 0.33/0.56 thf(fact_2451_add__eq__if,axiom,
% 0.33/0.56 ( plus_plus_nat
% 0.33/0.56 = ( ^ [M: nat,N4: nat] : ( if_nat @ ( M = zero_zero_nat ) @ N4 @ ( suc @ ( plus_plus_nat @ ( minus_minus_nat @ M @ one_one_nat ) @ N4 ) ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % add_eq_if
% 0.33/0.56 thf(fact_2452_Suc__n__minus__m__eq,axiom,
% 0.33/0.56 ! [M2: nat,N2: nat] :
% 0.33/0.56 ( ( ord_less_eq_nat @ M2 @ N2 )
% 0.33/0.56 => ( ( ord_less_nat @ one_one_nat @ M2 )
% 0.33/0.56 => ( ( suc @ ( minus_minus_nat @ N2 @ M2 ) )
% 0.33/0.56 = ( minus_minus_nat @ N2 @ ( minus_minus_nat @ M2 @ one_one_nat ) ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % Suc_n_minus_m_eq
% 0.33/0.56 thf(fact_2453_floor__unique,axiom,
% 0.33/0.56 ! [Z: int,X: rat] :
% 0.33/0.56 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ X )
% 0.33/0.56 => ( ( ord_less_rat @ X @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) )
% 0.33/0.56 => ( ( archim3151403230148437115or_rat @ X )
% 0.33/0.56 = Z ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % floor_unique
% 0.33/0.56 thf(fact_2454_floor__eq__iff,axiom,
% 0.33/0.56 ! [X: rat,A: int] :
% 0.33/0.56 ( ( ( archim3151403230148437115or_rat @ X )
% 0.33/0.56 = A )
% 0.33/0.56 = ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ A ) @ X )
% 0.33/0.56 & ( ord_less_rat @ X @ ( plus_plus_rat @ ( ring_1_of_int_rat @ A ) @ one_one_rat ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % floor_eq_iff
% 0.33/0.56 thf(fact_2455_floor__split,axiom,
% 0.33/0.56 ! [P: int > $o,T: rat] :
% 0.33/0.56 ( ( P @ ( archim3151403230148437115or_rat @ T ) )
% 0.33/0.56 = ( ! [I3: int] :
% 0.33/0.56 ( ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ I3 ) @ T )
% 0.33/0.56 & ( ord_less_rat @ T @ ( plus_plus_rat @ ( ring_1_of_int_rat @ I3 ) @ one_one_rat ) ) )
% 0.33/0.56 => ( P @ I3 ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % floor_split
% 0.33/0.56 thf(fact_2456_ceiling__correct,axiom,
% 0.33/0.56 ! [X: rat] :
% 0.33/0.56 ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ X ) ) @ one_one_rat ) @ X )
% 0.33/0.56 & ( ord_less_eq_rat @ X @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ X ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % ceiling_correct
% 0.33/0.56 thf(fact_2457_ceiling__unique,axiom,
% 0.33/0.56 ! [Z: int,X: rat] :
% 0.33/0.56 ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) @ X )
% 0.33/0.56 => ( ( ord_less_eq_rat @ X @ ( ring_1_of_int_rat @ Z ) )
% 0.33/0.56 => ( ( archim2889992004027027881ng_rat @ X )
% 0.33/0.56 = Z ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % ceiling_unique
% 0.33/0.56 thf(fact_2458_ceiling__eq__iff,axiom,
% 0.33/0.56 ! [X: rat,A: int] :
% 0.33/0.56 ( ( ( archim2889992004027027881ng_rat @ X )
% 0.33/0.56 = A )
% 0.33/0.56 = ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ A ) @ one_one_rat ) @ X )
% 0.33/0.56 & ( ord_less_eq_rat @ X @ ( ring_1_of_int_rat @ A ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % ceiling_eq_iff
% 0.33/0.56 thf(fact_2459_ceiling__split,axiom,
% 0.33/0.56 ! [P: int > $o,T: rat] :
% 0.33/0.56 ( ( P @ ( archim2889992004027027881ng_rat @ T ) )
% 0.33/0.56 = ( ! [I3: int] :
% 0.33/0.56 ( ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ I3 ) @ one_one_rat ) @ T )
% 0.33/0.56 & ( ord_less_eq_rat @ T @ ( ring_1_of_int_rat @ I3 ) ) )
% 0.33/0.56 => ( P @ I3 ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % ceiling_split
% 0.33/0.56 thf(fact_2460_less__floor__iff,axiom,
% 0.33/0.56 ! [Z: int,X: rat] :
% 0.33/0.56 ( ( ord_less_int @ Z @ ( archim3151403230148437115or_rat @ X ) )
% 0.33/0.56 = ( ord_less_eq_rat @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) @ X ) ) ).
% 0.33/0.56
% 0.33/0.56 % less_floor_iff
% 0.33/0.56 thf(fact_2461_floor__le__iff,axiom,
% 0.33/0.56 ! [X: rat,Z: int] :
% 0.33/0.56 ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X ) @ Z )
% 0.33/0.56 = ( ord_less_rat @ X @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % floor_le_iff
% 0.33/0.56 thf(fact_2462_ceiling__less__iff,axiom,
% 0.33/0.56 ! [X: rat,Z: int] :
% 0.33/0.56 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X ) @ Z )
% 0.33/0.56 = ( ord_less_eq_rat @ X @ ( minus_minus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % ceiling_less_iff
% 0.33/0.56 thf(fact_2463_le__ceiling__iff,axiom,
% 0.33/0.56 ! [Z: int,X: rat] :
% 0.33/0.56 ( ( ord_less_eq_int @ Z @ ( archim2889992004027027881ng_rat @ X ) )
% 0.33/0.56 = ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) @ X ) ) ).
% 0.33/0.56
% 0.33/0.56 % le_ceiling_iff
% 0.33/0.56 thf(fact_2464_floor__correct,axiom,
% 0.33/0.56 ! [X: rat] :
% 0.33/0.56 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X ) ) @ X )
% 0.33/0.56 & ( ord_less_rat @ X @ ( ring_1_of_int_rat @ ( plus_plus_int @ ( archim3151403230148437115or_rat @ X ) @ one_one_int ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % floor_correct
% 0.33/0.56 thf(fact_2465_power__diff__power__eq,axiom,
% 0.33/0.56 ! [A: int,N2: nat,M2: nat] :
% 0.33/0.56 ( ( A != zero_zero_int )
% 0.33/0.56 => ( ( ( ord_less_eq_nat @ N2 @ M2 )
% 0.33/0.56 => ( ( divide_divide_int @ ( power_power_int @ A @ M2 ) @ ( power_power_int @ A @ N2 ) )
% 0.33/0.56 = ( power_power_int @ A @ ( minus_minus_nat @ M2 @ N2 ) ) ) )
% 0.33/0.56 & ( ~ ( ord_less_eq_nat @ N2 @ M2 )
% 0.33/0.56 => ( ( divide_divide_int @ ( power_power_int @ A @ M2 ) @ ( power_power_int @ A @ N2 ) )
% 0.33/0.56 = ( divide_divide_int @ one_one_int @ ( power_power_int @ A @ ( minus_minus_nat @ N2 @ M2 ) ) ) ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_diff_power_eq
% 0.33/0.56 thf(fact_2466_power__diff__power__eq,axiom,
% 0.33/0.56 ! [A: nat,N2: nat,M2: nat] :
% 0.33/0.56 ( ( A != zero_zero_nat )
% 0.33/0.56 => ( ( ( ord_less_eq_nat @ N2 @ M2 )
% 0.33/0.56 => ( ( divide_divide_nat @ ( power_power_nat @ A @ M2 ) @ ( power_power_nat @ A @ N2 ) )
% 0.33/0.56 = ( power_power_nat @ A @ ( minus_minus_nat @ M2 @ N2 ) ) ) )
% 0.33/0.56 & ( ~ ( ord_less_eq_nat @ N2 @ M2 )
% 0.33/0.56 => ( ( divide_divide_nat @ ( power_power_nat @ A @ M2 ) @ ( power_power_nat @ A @ N2 ) )
% 0.33/0.56 = ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ A @ ( minus_minus_nat @ N2 @ M2 ) ) ) ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_diff_power_eq
% 0.33/0.56 thf(fact_2467_power__diff__power__eq,axiom,
% 0.33/0.56 ! [A: code_integer,N2: nat,M2: nat] :
% 0.33/0.56 ( ( A != zero_z3403309356797280102nteger )
% 0.33/0.56 => ( ( ( ord_less_eq_nat @ N2 @ M2 )
% 0.33/0.56 => ( ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ A @ M2 ) @ ( power_8256067586552552935nteger @ A @ N2 ) )
% 0.33/0.56 = ( power_8256067586552552935nteger @ A @ ( minus_minus_nat @ M2 @ N2 ) ) ) )
% 0.33/0.56 & ( ~ ( ord_less_eq_nat @ N2 @ M2 )
% 0.33/0.56 => ( ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ A @ M2 ) @ ( power_8256067586552552935nteger @ A @ N2 ) )
% 0.33/0.56 = ( divide6298287555418463151nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ A @ ( minus_minus_nat @ N2 @ M2 ) ) ) ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_diff_power_eq
% 0.33/0.56 thf(fact_2468_power__diff__power__eq,axiom,
% 0.33/0.56 ! [A: code_natural,N2: nat,M2: nat] :
% 0.33/0.56 ( ( A != zero_z2226904508553997617atural )
% 0.33/0.56 => ( ( ( ord_less_eq_nat @ N2 @ M2 )
% 0.33/0.56 => ( ( divide5121882707175180666atural @ ( power_7079662738309270450atural @ A @ M2 ) @ ( power_7079662738309270450atural @ A @ N2 ) )
% 0.33/0.56 = ( power_7079662738309270450atural @ A @ ( minus_minus_nat @ M2 @ N2 ) ) ) )
% 0.33/0.56 & ( ~ ( ord_less_eq_nat @ N2 @ M2 )
% 0.33/0.56 => ( ( divide5121882707175180666atural @ ( power_7079662738309270450atural @ A @ M2 ) @ ( power_7079662738309270450atural @ A @ N2 ) )
% 0.33/0.56 = ( divide5121882707175180666atural @ one_one_Code_natural @ ( power_7079662738309270450atural @ A @ ( minus_minus_nat @ N2 @ M2 ) ) ) ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_diff_power_eq
% 0.33/0.56 thf(fact_2469_power__eq__if,axiom,
% 0.33/0.56 ( power_8256067586552552935nteger
% 0.33/0.56 = ( ^ [P6: code_integer,M: nat] : ( if_Code_integer @ ( M = zero_zero_nat ) @ one_one_Code_integer @ ( times_3573771949741848930nteger @ P6 @ ( power_8256067586552552935nteger @ P6 @ ( minus_minus_nat @ M @ one_one_nat ) ) ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_eq_if
% 0.33/0.56 thf(fact_2470_power__eq__if,axiom,
% 0.33/0.56 ( power_power_assn
% 0.33/0.56 = ( ^ [P6: assn,M: nat] : ( if_assn @ ( M = zero_zero_nat ) @ one_one_assn @ ( times_times_assn @ P6 @ ( power_power_assn @ P6 @ ( minus_minus_nat @ M @ one_one_nat ) ) ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_eq_if
% 0.33/0.56 thf(fact_2471_power__eq__if,axiom,
% 0.33/0.56 ( power_power_rat
% 0.33/0.56 = ( ^ [P6: rat,M: nat] : ( if_rat @ ( M = zero_zero_nat ) @ one_one_rat @ ( times_times_rat @ P6 @ ( power_power_rat @ P6 @ ( minus_minus_nat @ M @ one_one_nat ) ) ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_eq_if
% 0.33/0.56 thf(fact_2472_power__eq__if,axiom,
% 0.33/0.56 ( power_power_nat
% 0.33/0.56 = ( ^ [P6: nat,M: nat] : ( if_nat @ ( M = zero_zero_nat ) @ one_one_nat @ ( times_times_nat @ P6 @ ( power_power_nat @ P6 @ ( minus_minus_nat @ M @ one_one_nat ) ) ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_eq_if
% 0.33/0.56 thf(fact_2473_power__eq__if,axiom,
% 0.33/0.56 ( power_power_int
% 0.33/0.56 = ( ^ [P6: int,M: nat] : ( if_int @ ( M = zero_zero_nat ) @ one_one_int @ ( times_times_int @ P6 @ ( power_power_int @ P6 @ ( minus_minus_nat @ M @ one_one_nat ) ) ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_eq_if
% 0.33/0.56 thf(fact_2474_power__minus__mult,axiom,
% 0.33/0.56 ! [N2: nat,A: assn] :
% 0.33/0.56 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.33/0.56 => ( ( times_times_assn @ ( power_power_assn @ A @ ( minus_minus_nat @ N2 @ one_one_nat ) ) @ A )
% 0.33/0.56 = ( power_power_assn @ A @ N2 ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_minus_mult
% 0.33/0.56 thf(fact_2475_power__minus__mult,axiom,
% 0.33/0.56 ! [N2: nat,A: rat] :
% 0.33/0.56 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.33/0.56 => ( ( times_times_rat @ ( power_power_rat @ A @ ( minus_minus_nat @ N2 @ one_one_nat ) ) @ A )
% 0.33/0.56 = ( power_power_rat @ A @ N2 ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_minus_mult
% 0.33/0.56 thf(fact_2476_power__minus__mult,axiom,
% 0.33/0.56 ! [N2: nat,A: nat] :
% 0.33/0.56 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.33/0.56 => ( ( times_times_nat @ ( power_power_nat @ A @ ( minus_minus_nat @ N2 @ one_one_nat ) ) @ A )
% 0.33/0.56 = ( power_power_nat @ A @ N2 ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_minus_mult
% 0.33/0.56 thf(fact_2477_power__minus__mult,axiom,
% 0.33/0.56 ! [N2: nat,A: int] :
% 0.33/0.56 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.33/0.56 => ( ( times_times_int @ ( power_power_int @ A @ ( minus_minus_nat @ N2 @ one_one_nat ) ) @ A )
% 0.33/0.56 = ( power_power_int @ A @ N2 ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_minus_mult
% 0.33/0.56 thf(fact_2478_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 0.33/0.56 ! [K: nat,N2: nat] :
% 0.33/0.56 ( ( ord_less_eq_nat @ K @ N2 )
% 0.33/0.56 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( plus_plus_nat @ N2 @ K ) )
% 0.33/0.56 = ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( minus_minus_nat @ N2 @ K ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % neg_one_power_add_eq_neg_one_power_diff
% 0.33/0.56 thf(fact_2479_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 0.33/0.56 ! [K: nat,N2: nat] :
% 0.33/0.56 ( ( ord_less_eq_nat @ K @ N2 )
% 0.33/0.56 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( plus_plus_nat @ N2 @ K ) )
% 0.33/0.56 = ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( minus_minus_nat @ N2 @ K ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % neg_one_power_add_eq_neg_one_power_diff
% 0.33/0.56 thf(fact_2480_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 0.33/0.56 ! [K: nat,N2: nat] :
% 0.33/0.56 ( ( ord_less_eq_nat @ K @ N2 )
% 0.33/0.56 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( plus_plus_nat @ N2 @ K ) )
% 0.33/0.56 = ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( minus_minus_nat @ N2 @ K ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % neg_one_power_add_eq_neg_one_power_diff
% 0.33/0.56 thf(fact_2481_option_Osize__gen_I2_J,axiom,
% 0.33/0.56 ! [X: num > nat,X2: num] :
% 0.33/0.56 ( ( size_option_num @ X @ ( some_num @ X2 ) )
% 0.33/0.56 = ( plus_plus_nat @ ( X @ X2 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % option.size_gen(2)
% 0.33/0.56 thf(fact_2482_option_Osize__gen_I2_J,axiom,
% 0.33/0.56 ! [X: produc8664842809031399944it_nat > nat,X2: produc8664842809031399944it_nat] :
% 0.33/0.56 ( ( size_o29782932136985253it_nat @ X @ ( some_P1914260805536162275it_nat @ X2 ) )
% 0.33/0.56 = ( plus_plus_nat @ ( X @ X2 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % option.size_gen(2)
% 0.33/0.56 thf(fact_2483_Heap_Osize__gen,axiom,
% 0.33/0.56 ! [Xa: product_unit > nat,X: heap_e7401611519738050253t_unit > option8956607266484857688it_nat] :
% 0.33/0.56 ( ( heap_T4142866422068808505t_unit @ Xa @ ( heap_T6183433275982383450t_unit @ X ) )
% 0.33/0.56 = ( suc @ zero_zero_nat ) ) ).
% 0.33/0.56
% 0.33/0.56 % Heap.size_gen
% 0.33/0.56 thf(fact_2484_num_Osize__gen_I2_J,axiom,
% 0.33/0.56 ! [X2: num] :
% 0.33/0.56 ( ( size_num @ ( bit0 @ X2 ) )
% 0.33/0.56 = ( plus_plus_nat @ ( size_num @ X2 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % num.size_gen(2)
% 0.33/0.56 thf(fact_2485_normalize__negative,axiom,
% 0.33/0.56 ! [Q3: int,P4: int] :
% 0.33/0.56 ( ( ord_less_int @ Q3 @ zero_zero_int )
% 0.33/0.56 => ( ( normalize @ ( product_Pair_int_int @ P4 @ Q3 ) )
% 0.33/0.56 = ( normalize @ ( product_Pair_int_int @ ( uminus_uminus_int @ P4 ) @ ( uminus_uminus_int @ Q3 ) ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % normalize_negative
% 0.33/0.56 thf(fact_2486_option_Osize__gen_I1_J,axiom,
% 0.33/0.56 ! [X: produc6714399278180371524it_nat > nat] :
% 0.33/0.56 ( ( size_o5312321843473198183it_nat @ X @ none_P2587165478634041381it_nat )
% 0.33/0.56 = ( suc @ zero_zero_nat ) ) ).
% 0.33/0.56
% 0.33/0.56 % option.size_gen(1)
% 0.33/0.56 thf(fact_2487_option_Osize__gen_I1_J,axiom,
% 0.33/0.56 ! [X: num > nat] :
% 0.33/0.56 ( ( size_option_num @ X @ none_num )
% 0.33/0.56 = ( suc @ zero_zero_nat ) ) ).
% 0.33/0.56
% 0.33/0.56 % option.size_gen(1)
% 0.33/0.56 thf(fact_2488_option_Osize__gen_I1_J,axiom,
% 0.33/0.56 ! [X: produc8664842809031399944it_nat > nat] :
% 0.33/0.56 ( ( size_o29782932136985253it_nat @ X @ none_P9117596204409417319it_nat )
% 0.33/0.56 = ( suc @ zero_zero_nat ) ) ).
% 0.33/0.56
% 0.33/0.56 % option.size_gen(1)
% 0.33/0.56 thf(fact_2489_Heap_Osize_I2_J,axiom,
% 0.33/0.56 ! [X: heap_e7401611519738050253t_unit > option8956607266484857688it_nat] :
% 0.33/0.56 ( ( size_s1564113455978345259t_unit @ ( heap_T6183433275982383450t_unit @ X ) )
% 0.33/0.56 = ( suc @ zero_zero_nat ) ) ).
% 0.33/0.56
% 0.33/0.56 % Heap.size(2)
% 0.33/0.56 thf(fact_2490_num_Osize_I5_J,axiom,
% 0.33/0.56 ! [X2: num] :
% 0.33/0.56 ( ( size_size_num @ ( bit0 @ X2 ) )
% 0.33/0.56 = ( plus_plus_nat @ ( size_size_num @ X2 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % num.size(5)
% 0.33/0.56 thf(fact_2491_option_Osize_I3_J,axiom,
% 0.33/0.56 ( ( size_s6797157356856800118it_nat @ none_P2587165478634041381it_nat )
% 0.33/0.56 = ( suc @ zero_zero_nat ) ) ).
% 0.33/0.56
% 0.33/0.56 % option.size(3)
% 0.33/0.56 thf(fact_2492_option_Osize_I3_J,axiom,
% 0.33/0.56 ( ( size_size_option_num @ none_num )
% 0.33/0.56 = ( suc @ zero_zero_nat ) ) ).
% 0.33/0.56
% 0.33/0.56 % option.size(3)
% 0.33/0.56 thf(fact_2493_option_Osize_I3_J,axiom,
% 0.33/0.56 ( ( size_s8766407808098229740it_nat @ none_P9117596204409417319it_nat )
% 0.33/0.56 = ( suc @ zero_zero_nat ) ) ).
% 0.33/0.56
% 0.33/0.56 % option.size(3)
% 0.33/0.56 thf(fact_2494_normalize__denom__zero,axiom,
% 0.33/0.56 ! [P4: int] :
% 0.33/0.56 ( ( normalize @ ( product_Pair_int_int @ P4 @ zero_zero_int ) )
% 0.33/0.56 = ( product_Pair_int_int @ zero_zero_int @ one_one_int ) ) ).
% 0.33/0.56
% 0.33/0.56 % normalize_denom_zero
% 0.33/0.56 thf(fact_2495_option_Osize__gen__o__map,axiom,
% 0.33/0.56 ! [F: num > nat,G: num > num] :
% 0.33/0.56 ( ( comp_o6878144249584144265on_num @ ( size_option_num @ F ) @ ( map_option_num_num @ G ) )
% 0.33/0.56 = ( size_option_num @ ( comp_num_nat_num @ F @ G ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % option.size_gen_o_map
% 0.33/0.56 thf(fact_2496_normalize__denom__pos,axiom,
% 0.33/0.56 ! [R2: product_prod_int_int,P4: int,Q3: int] :
% 0.33/0.56 ( ( ( normalize @ R2 )
% 0.33/0.56 = ( product_Pair_int_int @ P4 @ Q3 ) )
% 0.33/0.56 => ( ord_less_int @ zero_zero_int @ Q3 ) ) ).
% 0.33/0.56
% 0.33/0.56 % normalize_denom_pos
% 0.33/0.56 thf(fact_2497_normalize__crossproduct,axiom,
% 0.33/0.56 ! [Q3: int,S: int,P4: int,R2: int] :
% 0.33/0.56 ( ( Q3 != zero_zero_int )
% 0.33/0.56 => ( ( S != zero_zero_int )
% 0.33/0.56 => ( ( ( normalize @ ( product_Pair_int_int @ P4 @ Q3 ) )
% 0.33/0.56 = ( normalize @ ( product_Pair_int_int @ R2 @ S ) ) )
% 0.33/0.56 => ( ( times_times_int @ P4 @ S )
% 0.33/0.56 = ( times_times_int @ R2 @ Q3 ) ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % normalize_crossproduct
% 0.33/0.56 thf(fact_2498_option_Osize_I4_J,axiom,
% 0.33/0.56 ! [X2: num] :
% 0.33/0.56 ( ( size_size_option_num @ ( some_num @ X2 ) )
% 0.33/0.56 = ( suc @ zero_zero_nat ) ) ).
% 0.33/0.56
% 0.33/0.56 % option.size(4)
% 0.33/0.56 thf(fact_2499_option_Osize_I4_J,axiom,
% 0.33/0.56 ! [X2: produc8664842809031399944it_nat] :
% 0.33/0.56 ( ( size_s8766407808098229740it_nat @ ( some_P1914260805536162275it_nat @ X2 ) )
% 0.33/0.56 = ( suc @ zero_zero_nat ) ) ).
% 0.33/0.56
% 0.33/0.56 % option.size(4)
% 0.33/0.56 thf(fact_2500_divmod__nat__if,axiom,
% 0.33/0.56 ( divmod_nat
% 0.33/0.56 = ( ^ [M: nat,N4: nat] :
% 0.33/0.56 ( if_Pro6206227464963214023at_nat
% 0.33/0.56 @ ( ( N4 = zero_zero_nat )
% 0.33/0.56 | ( ord_less_nat @ M @ N4 ) )
% 0.33/0.56 @ ( product_Pair_nat_nat @ zero_zero_nat @ M )
% 0.33/0.56 @ ( produc2626176000494625587at_nat
% 0.33/0.56 @ ^ [Q5: nat] : ( product_Pair_nat_nat @ ( suc @ Q5 ) )
% 0.33/0.56 @ ( divmod_nat @ ( minus_minus_nat @ M @ N4 ) @ N4 ) ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % divmod_nat_if
% 0.33/0.56 thf(fact_2501_sum__gp__multiplied,axiom,
% 0.33/0.56 ! [M2: nat,N2: nat,X: code_integer] :
% 0.33/0.56 ( ( ord_less_eq_nat @ M2 @ N2 )
% 0.33/0.56 => ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ one_one_Code_integer @ X ) @ ( groups7501900531339628137nteger @ ( power_8256067586552552935nteger @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) )
% 0.33/0.56 = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ X @ M2 ) @ ( power_8256067586552552935nteger @ X @ ( suc @ N2 ) ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % sum_gp_multiplied
% 0.33/0.56 thf(fact_2502_sum__gp__multiplied,axiom,
% 0.33/0.56 ! [M2: nat,N2: nat,X: rat] :
% 0.33/0.56 ( ( ord_less_eq_nat @ M2 @ N2 )
% 0.33/0.56 => ( ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) )
% 0.33/0.56 = ( minus_minus_rat @ ( power_power_rat @ X @ M2 ) @ ( power_power_rat @ X @ ( suc @ N2 ) ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % sum_gp_multiplied
% 0.33/0.56 thf(fact_2503_sum__gp__multiplied,axiom,
% 0.33/0.56 ! [M2: nat,N2: nat,X: int] :
% 0.33/0.56 ( ( ord_less_eq_nat @ M2 @ N2 )
% 0.33/0.56 => ( ( times_times_int @ ( minus_minus_int @ one_one_int @ X ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) )
% 0.33/0.56 = ( minus_minus_int @ ( power_power_int @ X @ M2 ) @ ( power_power_int @ X @ ( suc @ N2 ) ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % sum_gp_multiplied
% 0.33/0.56 thf(fact_2504_pair__lessI2,axiom,
% 0.33/0.56 ! [A: nat,B: nat,S: nat,T: nat] :
% 0.33/0.56 ( ( ord_less_eq_nat @ A @ B )
% 0.33/0.56 => ( ( ord_less_nat @ S @ T )
% 0.33/0.56 => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A @ S ) @ ( product_Pair_nat_nat @ B @ T ) ) @ fun_pair_less ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % pair_lessI2
% 0.33/0.56 thf(fact_2505_pair__less__iff1,axiom,
% 0.33/0.56 ! [X: nat,Y: nat,Z: nat] :
% 0.33/0.56 ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( product_Pair_nat_nat @ X @ Z ) ) @ fun_pair_less )
% 0.33/0.56 = ( ord_less_nat @ Y @ Z ) ) ).
% 0.33/0.56
% 0.33/0.56 % pair_less_iff1
% 0.33/0.56 thf(fact_2506_Suc__times__numeral__mod__eq,axiom,
% 0.33/0.56 ! [K: num,N2: nat] :
% 0.33/0.56 ( ( ( numeral_numeral_nat @ K )
% 0.33/0.56 != one_one_nat )
% 0.33/0.56 => ( ( modulo_modulo_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ K ) @ N2 ) ) @ ( numeral_numeral_nat @ K ) )
% 0.33/0.56 = one_one_nat ) ) ).
% 0.33/0.56
% 0.33/0.56 % Suc_times_numeral_mod_eq
% 0.33/0.56 thf(fact_2507_one__int_Otransfer,axiom,
% 0.33/0.56 pcr_int @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) @ one_one_int ).
% 0.33/0.56
% 0.33/0.56 % one_int.transfer
% 0.33/0.56 thf(fact_2508_less__than__iff,axiom,
% 0.33/0.56 ! [X: nat,Y: nat] :
% 0.33/0.56 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ less_than )
% 0.33/0.56 = ( ord_less_nat @ X @ Y ) ) ).
% 0.33/0.56
% 0.33/0.56 % less_than_iff
% 0.33/0.56 thf(fact_2509_one__int__def,axiom,
% 0.33/0.56 ( one_one_int
% 0.33/0.56 = ( abs_Integ @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % one_int_def
% 0.33/0.56 thf(fact_2510_sum__telescope_H_H,axiom,
% 0.33/0.56 ! [M2: nat,N2: nat,F: nat > code_integer] :
% 0.33/0.56 ( ( ord_less_eq_nat @ M2 @ N2 )
% 0.33/0.56 => ( ( groups7501900531339628137nteger
% 0.33/0.56 @ ^ [K4: nat] : ( minus_8373710615458151222nteger @ ( F @ K4 ) @ ( F @ ( minus_minus_nat @ K4 @ one_one_nat ) ) )
% 0.33/0.56 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N2 ) )
% 0.33/0.56 = ( minus_8373710615458151222nteger @ ( F @ N2 ) @ ( F @ M2 ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % sum_telescope''
% 0.33/0.56 thf(fact_2511_sum__telescope_H_H,axiom,
% 0.33/0.56 ! [M2: nat,N2: nat,F: nat > rat] :
% 0.33/0.56 ( ( ord_less_eq_nat @ M2 @ N2 )
% 0.33/0.56 => ( ( groups2906978787729119204at_rat
% 0.33/0.56 @ ^ [K4: nat] : ( minus_minus_rat @ ( F @ K4 ) @ ( F @ ( minus_minus_nat @ K4 @ one_one_nat ) ) )
% 0.33/0.56 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N2 ) )
% 0.33/0.56 = ( minus_minus_rat @ ( F @ N2 ) @ ( F @ M2 ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % sum_telescope''
% 0.33/0.56 thf(fact_2512_sum__telescope_H_H,axiom,
% 0.33/0.56 ! [M2: nat,N2: nat,F: nat > int] :
% 0.33/0.56 ( ( ord_less_eq_nat @ M2 @ N2 )
% 0.33/0.56 => ( ( groups3539618377306564664at_int
% 0.33/0.56 @ ^ [K4: nat] : ( minus_minus_int @ ( F @ K4 ) @ ( F @ ( minus_minus_nat @ K4 @ one_one_nat ) ) )
% 0.33/0.56 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N2 ) )
% 0.33/0.56 = ( minus_minus_int @ ( F @ N2 ) @ ( F @ M2 ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % sum_telescope''
% 0.33/0.56 thf(fact_2513_case__prod__conv,axiom,
% 0.33/0.56 ! [F: nat > nat > nat,A: nat,B: nat] :
% 0.33/0.56 ( ( produc6842872674320459806at_nat @ F @ ( product_Pair_nat_nat @ A @ B ) )
% 0.33/0.56 = ( F @ A @ B ) ) ).
% 0.33/0.56
% 0.33/0.56 % case_prod_conv
% 0.33/0.56 thf(fact_2514_case__prod__conv,axiom,
% 0.33/0.56 ! [F: nat > nat > product_prod_nat_nat > product_prod_nat_nat,A: nat,B: nat] :
% 0.33/0.56 ( ( produc27273713700761075at_nat @ F @ ( product_Pair_nat_nat @ A @ B ) )
% 0.33/0.56 = ( F @ A @ B ) ) ).
% 0.33/0.56
% 0.33/0.56 % case_prod_conv
% 0.33/0.56 thf(fact_2515_case__prod__conv,axiom,
% 0.33/0.56 ! [F: nat > nat > product_prod_nat_nat > $o,A: nat,B: nat] :
% 0.33/0.56 ( ( produc8739625826339149834_nat_o @ F @ ( product_Pair_nat_nat @ A @ B ) )
% 0.33/0.56 = ( F @ A @ B ) ) ).
% 0.33/0.56
% 0.33/0.56 % case_prod_conv
% 0.33/0.56 thf(fact_2516_case__prod__conv,axiom,
% 0.33/0.56 ! [F: int > int > product_prod_int_int,A: int,B: int] :
% 0.33/0.56 ( ( produc4245557441103728435nt_int @ F @ ( product_Pair_int_int @ A @ B ) )
% 0.33/0.56 = ( F @ A @ B ) ) ).
% 0.33/0.56
% 0.33/0.56 % case_prod_conv
% 0.33/0.56 thf(fact_2517_case__prod__conv,axiom,
% 0.33/0.56 ! [F: int > int > int,A: int,B: int] :
% 0.33/0.56 ( ( produc8211389475949308722nt_int @ F @ ( product_Pair_int_int @ A @ B ) )
% 0.33/0.56 = ( F @ A @ B ) ) ).
% 0.33/0.56
% 0.33/0.56 % case_prod_conv
% 0.33/0.56 thf(fact_2518_case__prod__curry,axiom,
% 0.33/0.56 ! [F: product_prod_nat_nat > nat] :
% 0.33/0.56 ( ( produc6842872674320459806at_nat @ ( produc8871627978511607229at_nat @ F ) )
% 0.33/0.56 = F ) ).
% 0.33/0.56
% 0.33/0.56 % case_prod_curry
% 0.33/0.56 thf(fact_2519_case__prod__curry,axiom,
% 0.33/0.56 ! [F: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat] :
% 0.33/0.56 ( ( produc27273713700761075at_nat @ ( produc3610074571335452306at_nat @ F ) )
% 0.33/0.56 = F ) ).
% 0.33/0.56
% 0.33/0.56 % case_prod_curry
% 0.33/0.56 thf(fact_2520_case__prod__curry,axiom,
% 0.33/0.56 ! [F: product_prod_nat_nat > product_prod_nat_nat > $o] :
% 0.33/0.56 ( ( produc8739625826339149834_nat_o @ ( produc3704529784387675049_nat_o @ F ) )
% 0.33/0.56 = F ) ).
% 0.33/0.56
% 0.33/0.56 % case_prod_curry
% 0.33/0.56 thf(fact_2521_case__prod__curry,axiom,
% 0.33/0.56 ! [F: product_prod_int_int > product_prod_int_int] :
% 0.33/0.56 ( ( produc4245557441103728435nt_int @ ( produc8249235968001453780nt_int @ F ) )
% 0.33/0.56 = F ) ).
% 0.33/0.56
% 0.33/0.56 % case_prod_curry
% 0.33/0.56 thf(fact_2522_case__prod__curry,axiom,
% 0.33/0.56 ! [F: product_prod_int_int > int] :
% 0.33/0.56 ( ( produc8211389475949308722nt_int @ ( produc1016772743285680337nt_int @ F ) )
% 0.33/0.56 = F ) ).
% 0.33/0.56
% 0.33/0.56 % case_prod_curry
% 0.33/0.56 thf(fact_2523_curry__case__prod,axiom,
% 0.33/0.56 ! [F: nat > nat > nat] :
% 0.33/0.56 ( ( produc8871627978511607229at_nat @ ( produc6842872674320459806at_nat @ F ) )
% 0.33/0.56 = F ) ).
% 0.33/0.56
% 0.33/0.56 % curry_case_prod
% 0.33/0.56 thf(fact_2524_curry__case__prod,axiom,
% 0.33/0.56 ! [F: nat > nat > product_prod_nat_nat > product_prod_nat_nat] :
% 0.33/0.56 ( ( produc3610074571335452306at_nat @ ( produc27273713700761075at_nat @ F ) )
% 0.33/0.56 = F ) ).
% 0.33/0.56
% 0.33/0.56 % curry_case_prod
% 0.33/0.56 thf(fact_2525_curry__case__prod,axiom,
% 0.33/0.56 ! [F: nat > nat > product_prod_nat_nat > $o] :
% 0.33/0.56 ( ( produc3704529784387675049_nat_o @ ( produc8739625826339149834_nat_o @ F ) )
% 0.33/0.56 = F ) ).
% 0.33/0.56
% 0.33/0.56 % curry_case_prod
% 0.33/0.56 thf(fact_2526_curry__case__prod,axiom,
% 0.33/0.56 ! [F: int > int > product_prod_int_int] :
% 0.33/0.56 ( ( produc8249235968001453780nt_int @ ( produc4245557441103728435nt_int @ F ) )
% 0.33/0.56 = F ) ).
% 0.33/0.56
% 0.33/0.56 % curry_case_prod
% 0.33/0.56 thf(fact_2527_curry__case__prod,axiom,
% 0.33/0.56 ! [F: int > int > int] :
% 0.33/0.56 ( ( produc1016772743285680337nt_int @ ( produc8211389475949308722nt_int @ F ) )
% 0.33/0.56 = F ) ).
% 0.33/0.56
% 0.33/0.56 % curry_case_prod
% 0.33/0.56 thf(fact_2528_distrib__right__numeral,axiom,
% 0.33/0.56 ! [A: nat,B: nat,V: num] :
% 0.33/0.56 ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ ( numeral_numeral_nat @ V ) )
% 0.33/0.56 = ( plus_plus_nat @ ( times_times_nat @ A @ ( numeral_numeral_nat @ V ) ) @ ( times_times_nat @ B @ ( numeral_numeral_nat @ V ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % distrib_right_numeral
% 0.33/0.56 thf(fact_2529_distrib__right__numeral,axiom,
% 0.33/0.56 ! [A: int,B: int,V: num] :
% 0.33/0.56 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ ( numeral_numeral_int @ V ) )
% 0.33/0.56 = ( plus_plus_int @ ( times_times_int @ A @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ B @ ( numeral_numeral_int @ V ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % distrib_right_numeral
% 0.33/0.56 thf(fact_2530_distrib__right__numeral,axiom,
% 0.33/0.56 ! [A: code_integer,B: code_integer,V: num] :
% 0.33/0.56 ( ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ ( numera6620942414471956472nteger @ V ) )
% 0.33/0.56 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ ( numera6620942414471956472nteger @ V ) ) @ ( times_3573771949741848930nteger @ B @ ( numera6620942414471956472nteger @ V ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % distrib_right_numeral
% 0.33/0.56 thf(fact_2531_distrib__right__numeral,axiom,
% 0.33/0.56 ! [A: rat,B: rat,V: num] :
% 0.33/0.56 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ ( numeral_numeral_rat @ V ) )
% 0.33/0.56 = ( plus_plus_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ B @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % distrib_right_numeral
% 0.33/0.56 thf(fact_2532_distrib__right__numeral,axiom,
% 0.33/0.56 ! [A: code_natural,B: code_natural,V: num] :
% 0.33/0.56 ( ( times_2397367101498566445atural @ ( plus_p4538020629002901425atural @ A @ B ) @ ( numera5444537566228673987atural @ V ) )
% 0.33/0.56 = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ A @ ( numera5444537566228673987atural @ V ) ) @ ( times_2397367101498566445atural @ B @ ( numera5444537566228673987atural @ V ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % distrib_right_numeral
% 0.33/0.56 thf(fact_2533_distrib__left__numeral,axiom,
% 0.33/0.56 ! [V: num,B: nat,C: nat] :
% 0.33/0.56 ( ( times_times_nat @ ( numeral_numeral_nat @ V ) @ ( plus_plus_nat @ B @ C ) )
% 0.33/0.56 = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ V ) @ B ) @ ( times_times_nat @ ( numeral_numeral_nat @ V ) @ C ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % distrib_left_numeral
% 0.33/0.56 thf(fact_2534_distrib__left__numeral,axiom,
% 0.33/0.56 ! [V: num,B: int,C: int] :
% 0.33/0.56 ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( plus_plus_int @ B @ C ) )
% 0.33/0.56 = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ V ) @ B ) @ ( times_times_int @ ( numeral_numeral_int @ V ) @ C ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % distrib_left_numeral
% 0.33/0.56 thf(fact_2535_distrib__left__numeral,axiom,
% 0.33/0.56 ! [V: num,B: code_integer,C: code_integer] :
% 0.33/0.56 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 0.33/0.56 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ B ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ C ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % distrib_left_numeral
% 0.33/0.56 thf(fact_2536_distrib__left__numeral,axiom,
% 0.33/0.56 ! [V: num,B: rat,C: rat] :
% 0.33/0.56 ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( plus_plus_rat @ B @ C ) )
% 0.33/0.56 = ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ B ) @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ C ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % distrib_left_numeral
% 0.33/0.56 thf(fact_2537_distrib__left__numeral,axiom,
% 0.33/0.56 ! [V: num,B: code_natural,C: code_natural] :
% 0.33/0.56 ( ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ V ) @ ( plus_p4538020629002901425atural @ B @ C ) )
% 0.33/0.56 = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ V ) @ B ) @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ V ) @ C ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % distrib_left_numeral
% 0.33/0.56 thf(fact_2538_add__neg__numeral__simps_I3_J,axiom,
% 0.33/0.56 ! [M2: num,N2: num] :
% 0.33/0.56 ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 0.33/0.56 = ( uminus_uminus_int @ ( plus_plus_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N2 ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % add_neg_numeral_simps(3)
% 0.33/0.56 thf(fact_2539_add__neg__numeral__simps_I3_J,axiom,
% 0.33/0.56 ! [M2: num,N2: num] :
% 0.33/0.56 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 0.33/0.56 = ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ M2 ) @ ( numera6620942414471956472nteger @ N2 ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % add_neg_numeral_simps(3)
% 0.33/0.56 thf(fact_2540_add__neg__numeral__simps_I3_J,axiom,
% 0.33/0.56 ! [M2: num,N2: num] :
% 0.33/0.56 ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 0.33/0.56 = ( uminus_uminus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ M2 ) @ ( numeral_numeral_rat @ N2 ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % add_neg_numeral_simps(3)
% 0.33/0.56 thf(fact_2541_add__numeral__left,axiom,
% 0.33/0.56 ! [V: num,W: num,Z: nat] :
% 0.33/0.56 ( ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ W ) @ Z ) )
% 0.33/0.56 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 0.33/0.56
% 0.33/0.56 % add_numeral_left
% 0.33/0.56 thf(fact_2542_add__numeral__left,axiom,
% 0.33/0.56 ! [V: num,W: num,Z: int] :
% 0.33/0.56 ( ( plus_plus_int @ ( numeral_numeral_int @ V ) @ ( plus_plus_int @ ( numeral_numeral_int @ W ) @ Z ) )
% 0.33/0.56 = ( plus_plus_int @ ( numeral_numeral_int @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 0.33/0.56
% 0.33/0.56 % add_numeral_left
% 0.33/0.56 thf(fact_2543_add__numeral__left,axiom,
% 0.33/0.56 ! [V: num,W: num,Z: code_integer] :
% 0.33/0.56 ( ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ V ) @ ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ W ) @ Z ) )
% 0.33/0.56 = ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 0.33/0.56
% 0.33/0.56 % add_numeral_left
% 0.33/0.56 thf(fact_2544_add__numeral__left,axiom,
% 0.33/0.56 ! [V: num,W: num,Z: rat] :
% 0.33/0.56 ( ( plus_plus_rat @ ( numeral_numeral_rat @ V ) @ ( plus_plus_rat @ ( numeral_numeral_rat @ W ) @ Z ) )
% 0.33/0.56 = ( plus_plus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 0.33/0.56
% 0.33/0.56 % add_numeral_left
% 0.33/0.56 thf(fact_2545_add__numeral__left,axiom,
% 0.33/0.56 ! [V: num,W: num,Z: code_natural] :
% 0.33/0.56 ( ( plus_p4538020629002901425atural @ ( numera5444537566228673987atural @ V ) @ ( plus_p4538020629002901425atural @ ( numera5444537566228673987atural @ W ) @ Z ) )
% 0.33/0.56 = ( plus_p4538020629002901425atural @ ( numera5444537566228673987atural @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 0.33/0.56
% 0.33/0.56 % add_numeral_left
% 0.33/0.56 thf(fact_2546_numeral__plus__numeral,axiom,
% 0.33/0.56 ! [M2: num,N2: num] :
% 0.33/0.56 ( ( plus_plus_nat @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ N2 ) )
% 0.33/0.56 = ( numeral_numeral_nat @ ( plus_plus_num @ M2 @ N2 ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % numeral_plus_numeral
% 0.33/0.56 thf(fact_2547_numeral__plus__numeral,axiom,
% 0.33/0.56 ! [M2: num,N2: num] :
% 0.33/0.56 ( ( plus_plus_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N2 ) )
% 0.33/0.56 = ( numeral_numeral_int @ ( plus_plus_num @ M2 @ N2 ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % numeral_plus_numeral
% 0.33/0.56 thf(fact_2548_numeral__plus__numeral,axiom,
% 0.33/0.56 ! [M2: num,N2: num] :
% 0.33/0.56 ( ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ M2 ) @ ( numera6620942414471956472nteger @ N2 ) )
% 0.33/0.56 = ( numera6620942414471956472nteger @ ( plus_plus_num @ M2 @ N2 ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % numeral_plus_numeral
% 0.33/0.56 thf(fact_2549_numeral__plus__numeral,axiom,
% 0.33/0.56 ! [M2: num,N2: num] :
% 0.33/0.56 ( ( plus_plus_rat @ ( numeral_numeral_rat @ M2 ) @ ( numeral_numeral_rat @ N2 ) )
% 0.33/0.56 = ( numeral_numeral_rat @ ( plus_plus_num @ M2 @ N2 ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % numeral_plus_numeral
% 0.33/0.56 thf(fact_2550_numeral__plus__numeral,axiom,
% 0.33/0.56 ! [M2: num,N2: num] :
% 0.33/0.56 ( ( plus_p4538020629002901425atural @ ( numera5444537566228673987atural @ M2 ) @ ( numera5444537566228673987atural @ N2 ) )
% 0.33/0.56 = ( numera5444537566228673987atural @ ( plus_plus_num @ M2 @ N2 ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % numeral_plus_numeral
% 0.33/0.56 thf(fact_2551_semiring__norm_I168_J,axiom,
% 0.33/0.56 ! [V: num,W: num,Y: int] :
% 0.33/0.56 ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ Y ) )
% 0.33/0.56 = ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ V @ W ) ) ) @ Y ) ) ).
% 0.33/0.56
% 0.33/0.56 % semiring_norm(168)
% 0.33/0.56 thf(fact_2552_semiring__norm_I168_J,axiom,
% 0.33/0.56 ! [V: num,W: num,Y: code_integer] :
% 0.33/0.56 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) @ Y ) )
% 0.33/0.56 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ V @ W ) ) ) @ Y ) ) ).
% 0.33/0.56
% 0.33/0.56 % semiring_norm(168)
% 0.33/0.56 thf(fact_2553_semiring__norm_I168_J,axiom,
% 0.33/0.56 ! [V: num,W: num,Y: rat] :
% 0.33/0.56 ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ Y ) )
% 0.33/0.56 = ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ V @ W ) ) ) @ Y ) ) ).
% 0.33/0.56
% 0.33/0.56 % semiring_norm(168)
% 0.33/0.56 thf(fact_2554_diff__numeral__simps_I3_J,axiom,
% 0.33/0.56 ! [M2: num,N2: num] :
% 0.33/0.56 ( ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( numeral_numeral_int @ N2 ) )
% 0.33/0.56 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ M2 @ N2 ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % diff_numeral_simps(3)
% 0.33/0.56 thf(fact_2555_diff__numeral__simps_I3_J,axiom,
% 0.33/0.56 ! [M2: num,N2: num] :
% 0.33/0.56 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ ( numera6620942414471956472nteger @ N2 ) )
% 0.33/0.56 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ M2 @ N2 ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % diff_numeral_simps(3)
% 0.33/0.56 thf(fact_2556_diff__numeral__simps_I3_J,axiom,
% 0.33/0.56 ! [M2: num,N2: num] :
% 0.33/0.56 ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ ( numeral_numeral_rat @ N2 ) )
% 0.33/0.56 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ M2 @ N2 ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % diff_numeral_simps(3)
% 0.33/0.56 thf(fact_2557_diff__numeral__simps_I2_J,axiom,
% 0.33/0.56 ! [M2: num,N2: num] :
% 0.33/0.56 ( ( minus_minus_int @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 0.33/0.56 = ( numeral_numeral_int @ ( plus_plus_num @ M2 @ N2 ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % diff_numeral_simps(2)
% 0.33/0.56 thf(fact_2558_diff__numeral__simps_I2_J,axiom,
% 0.33/0.56 ! [M2: num,N2: num] :
% 0.33/0.56 ( ( minus_8373710615458151222nteger @ ( numera6620942414471956472nteger @ M2 ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 0.33/0.56 = ( numera6620942414471956472nteger @ ( plus_plus_num @ M2 @ N2 ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % diff_numeral_simps(2)
% 0.33/0.56 thf(fact_2559_diff__numeral__simps_I2_J,axiom,
% 0.33/0.56 ! [M2: num,N2: num] :
% 0.33/0.56 ( ( minus_minus_rat @ ( numeral_numeral_rat @ M2 ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 0.33/0.56 = ( numeral_numeral_rat @ ( plus_plus_num @ M2 @ N2 ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % diff_numeral_simps(2)
% 0.33/0.56 thf(fact_2560_ceiling__add__numeral,axiom,
% 0.33/0.56 ! [X: rat,V: num] :
% 0.33/0.56 ( ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X @ ( numeral_numeral_rat @ V ) ) )
% 0.33/0.56 = ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X ) @ ( numeral_numeral_int @ V ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % ceiling_add_numeral
% 0.33/0.56 thf(fact_2561_power__add__numeral,axiom,
% 0.33/0.56 ! [A: assn,M2: num,N2: num] :
% 0.33/0.56 ( ( times_times_assn @ ( power_power_assn @ A @ ( numeral_numeral_nat @ M2 ) ) @ ( power_power_assn @ A @ ( numeral_numeral_nat @ N2 ) ) )
% 0.33/0.56 = ( power_power_assn @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M2 @ N2 ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_add_numeral
% 0.33/0.56 thf(fact_2562_power__add__numeral,axiom,
% 0.33/0.56 ! [A: rat,M2: num,N2: num] :
% 0.33/0.56 ( ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ M2 ) ) @ ( power_power_rat @ A @ ( numeral_numeral_nat @ N2 ) ) )
% 0.33/0.56 = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M2 @ N2 ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_add_numeral
% 0.33/0.56 thf(fact_2563_power__add__numeral,axiom,
% 0.33/0.56 ! [A: nat,M2: num,N2: num] :
% 0.33/0.56 ( ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M2 ) ) @ ( power_power_nat @ A @ ( numeral_numeral_nat @ N2 ) ) )
% 0.33/0.56 = ( power_power_nat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M2 @ N2 ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_add_numeral
% 0.33/0.56 thf(fact_2564_power__add__numeral,axiom,
% 0.33/0.56 ! [A: int,M2: num,N2: num] :
% 0.33/0.56 ( ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M2 ) ) @ ( power_power_int @ A @ ( numeral_numeral_nat @ N2 ) ) )
% 0.33/0.56 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M2 @ N2 ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_add_numeral
% 0.33/0.56 thf(fact_2565_power__add__numeral2,axiom,
% 0.33/0.56 ! [A: assn,M2: num,N2: num,B: assn] :
% 0.33/0.56 ( ( times_times_assn @ ( power_power_assn @ A @ ( numeral_numeral_nat @ M2 ) ) @ ( times_times_assn @ ( power_power_assn @ A @ ( numeral_numeral_nat @ N2 ) ) @ B ) )
% 0.33/0.56 = ( times_times_assn @ ( power_power_assn @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M2 @ N2 ) ) ) @ B ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_add_numeral2
% 0.33/0.56 thf(fact_2566_power__add__numeral2,axiom,
% 0.33/0.56 ! [A: rat,M2: num,N2: num,B: rat] :
% 0.33/0.56 ( ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ M2 ) ) @ ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ N2 ) ) @ B ) )
% 0.33/0.56 = ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M2 @ N2 ) ) ) @ B ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_add_numeral2
% 0.33/0.56 thf(fact_2567_power__add__numeral2,axiom,
% 0.33/0.56 ! [A: nat,M2: num,N2: num,B: nat] :
% 0.33/0.56 ( ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M2 ) ) @ ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ N2 ) ) @ B ) )
% 0.33/0.56 = ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M2 @ N2 ) ) ) @ B ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_add_numeral2
% 0.33/0.56 thf(fact_2568_power__add__numeral2,axiom,
% 0.33/0.56 ! [A: int,M2: num,N2: num,B: int] :
% 0.33/0.56 ( ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M2 ) ) @ ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ N2 ) ) @ B ) )
% 0.33/0.56 = ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M2 @ N2 ) ) ) @ B ) ) ).
% 0.33/0.56
% 0.33/0.56 % power_add_numeral2
% 0.33/0.56 thf(fact_2569_numeral__less__floor,axiom,
% 0.33/0.56 ! [V: num,X: rat] :
% 0.33/0.56 ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim3151403230148437115or_rat @ X ) )
% 0.33/0.56 = ( ord_less_eq_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) @ X ) ) ).
% 0.33/0.56
% 0.33/0.56 % numeral_less_floor
% 0.33/0.56 thf(fact_2570_floor__le__numeral,axiom,
% 0.33/0.56 ! [X: rat,V: num] :
% 0.33/0.56 ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X ) @ ( numeral_numeral_int @ V ) )
% 0.33/0.56 = ( ord_less_rat @ X @ ( plus_plus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % floor_le_numeral
% 0.33/0.56 thf(fact_2571_sum_Ocl__ivl__Suc,axiom,
% 0.33/0.56 ! [N2: nat,M2: nat,G: nat > code_integer] :
% 0.33/0.56 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M2 )
% 0.33/0.56 => ( ( groups7501900531339628137nteger @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N2 ) ) )
% 0.33/0.56 = zero_z3403309356797280102nteger ) )
% 0.33/0.56 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M2 )
% 0.33/0.56 => ( ( groups7501900531339628137nteger @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N2 ) ) )
% 0.33/0.56 = ( plus_p5714425477246183910nteger @ ( groups7501900531339628137nteger @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % sum.cl_ivl_Suc
% 0.33/0.56 thf(fact_2572_sum_Ocl__ivl__Suc,axiom,
% 0.33/0.56 ! [N2: nat,M2: nat,G: nat > multis2468970476368604999at_nat] :
% 0.33/0.56 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M2 )
% 0.33/0.56 => ( ( groups6857163185585827899at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N2 ) ) )
% 0.33/0.56 = zero_z1048942125864253310at_nat ) )
% 0.33/0.56 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M2 )
% 0.33/0.56 => ( ( groups6857163185585827899at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N2 ) ) )
% 0.33/0.56 = ( plus_p7104986032573967614at_nat @ ( groups6857163185585827899at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % sum.cl_ivl_Suc
% 0.33/0.56 thf(fact_2573_sum_Ocl__ivl__Suc,axiom,
% 0.33/0.56 ! [N2: nat,M2: nat,G: nat > rat] :
% 0.33/0.56 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M2 )
% 0.33/0.56 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N2 ) ) )
% 0.33/0.56 = zero_zero_rat ) )
% 0.33/0.56 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M2 )
% 0.33/0.56 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N2 ) ) )
% 0.33/0.56 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % sum.cl_ivl_Suc
% 0.33/0.56 thf(fact_2574_sum_Ocl__ivl__Suc,axiom,
% 0.33/0.56 ! [N2: nat,M2: nat,G: nat > int] :
% 0.33/0.56 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M2 )
% 0.33/0.56 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N2 ) ) )
% 0.33/0.56 = zero_zero_int ) )
% 0.33/0.56 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M2 )
% 0.33/0.56 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N2 ) ) )
% 0.33/0.56 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % sum.cl_ivl_Suc
% 0.33/0.56 thf(fact_2575_sum_Ocl__ivl__Suc,axiom,
% 0.33/0.56 ! [N2: nat,M2: nat,G: nat > nat] :
% 0.33/0.56 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M2 )
% 0.33/0.56 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N2 ) ) )
% 0.33/0.56 = zero_zero_nat ) )
% 0.33/0.56 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M2 )
% 0.33/0.56 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N2 ) ) )
% 0.33/0.56 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % sum.cl_ivl_Suc
% 0.33/0.56 thf(fact_2576_ceiling__less__numeral,axiom,
% 0.33/0.56 ! [X: rat,V: num] :
% 0.33/0.56 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X ) @ ( numeral_numeral_int @ V ) )
% 0.33/0.56 = ( ord_less_eq_rat @ X @ ( minus_minus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % ceiling_less_numeral
% 0.33/0.56 thf(fact_2577_numeral__le__ceiling,axiom,
% 0.33/0.56 ! [V: num,X: rat] :
% 0.33/0.56 ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim2889992004027027881ng_rat @ X ) )
% 0.33/0.56 = ( ord_less_rat @ ( minus_minus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) @ X ) ) ).
% 0.33/0.56
% 0.33/0.56 % numeral_le_ceiling
% 0.33/0.56 thf(fact_2578_neg__numeral__less__floor,axiom,
% 0.33/0.56 ! [V: num,X: rat] :
% 0.33/0.56 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim3151403230148437115or_rat @ X ) )
% 0.33/0.56 = ( ord_less_eq_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) @ X ) ) ).
% 0.33/0.56
% 0.33/0.56 % neg_numeral_less_floor
% 0.33/0.56 thf(fact_2579_floor__le__neg__numeral,axiom,
% 0.33/0.56 ! [X: rat,V: num] :
% 0.33/0.56 ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 0.33/0.56 = ( ord_less_rat @ X @ ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % floor_le_neg_numeral
% 0.33/0.56 thf(fact_2580_ceiling__less__neg__numeral,axiom,
% 0.33/0.56 ! [X: rat,V: num] :
% 0.33/0.56 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 0.33/0.56 = ( ord_less_eq_rat @ X @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % ceiling_less_neg_numeral
% 0.33/0.56 thf(fact_2581_neg__numeral__le__ceiling,axiom,
% 0.33/0.56 ! [V: num,X: rat] :
% 0.33/0.56 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim2889992004027027881ng_rat @ X ) )
% 0.33/0.56 = ( ord_less_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) @ X ) ) ).
% 0.33/0.56
% 0.33/0.56 % neg_numeral_le_ceiling
% 0.33/0.56 thf(fact_2582_nested__case__prod__simp,axiom,
% 0.33/0.56 ( produc27273713700761075at_nat
% 0.33/0.56 = ( ^ [F2: nat > nat > product_prod_nat_nat > product_prod_nat_nat,X3: product_prod_nat_nat,Y3: product_prod_nat_nat] :
% 0.33/0.56 ( produc2626176000494625587at_nat
% 0.33/0.56 @ ^ [A5: nat,B4: nat] : ( F2 @ A5 @ B4 @ Y3 )
% 0.33/0.56 @ X3 ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % nested_case_prod_simp
% 0.33/0.56 thf(fact_2583_nested__case__prod__simp,axiom,
% 0.33/0.56 ( produc8739625826339149834_nat_o
% 0.33/0.56 = ( ^ [F2: nat > nat > product_prod_nat_nat > $o,X3: product_prod_nat_nat,Y3: product_prod_nat_nat] :
% 0.33/0.56 ( produc6081775807080527818_nat_o
% 0.33/0.56 @ ^ [A5: nat,B4: nat] : ( F2 @ A5 @ B4 @ Y3 )
% 0.33/0.56 @ X3 ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % nested_case_prod_simp
% 0.33/0.56 thf(fact_2584_prod_Ocase__distrib,axiom,
% 0.33/0.56 ! [H3: nat > nat,F: nat > nat > nat,Prod: product_prod_nat_nat] :
% 0.33/0.56 ( ( H3 @ ( produc6842872674320459806at_nat @ F @ Prod ) )
% 0.33/0.56 = ( produc6842872674320459806at_nat
% 0.33/0.56 @ ^ [X12: nat,X23: nat] : ( H3 @ ( F @ X12 @ X23 ) )
% 0.33/0.56 @ Prod ) ) ).
% 0.33/0.56
% 0.33/0.56 % prod.case_distrib
% 0.33/0.56 thf(fact_2585_prod_Ocase__distrib,axiom,
% 0.33/0.56 ! [H3: int > int,F: int > int > int,Prod: product_prod_int_int] :
% 0.33/0.56 ( ( H3 @ ( produc8211389475949308722nt_int @ F @ Prod ) )
% 0.33/0.56 = ( produc8211389475949308722nt_int
% 0.33/0.56 @ ^ [X12: int,X23: int] : ( H3 @ ( F @ X12 @ X23 ) )
% 0.33/0.56 @ Prod ) ) ).
% 0.33/0.56
% 0.33/0.56 % prod.case_distrib
% 0.33/0.56 thf(fact_2586_prod_Ocase__distrib,axiom,
% 0.33/0.56 ! [H3: product_prod_int_int > int,F: int > int > product_prod_int_int,Prod: product_prod_int_int] :
% 0.33/0.56 ( ( H3 @ ( produc4245557441103728435nt_int @ F @ Prod ) )
% 0.33/0.56 = ( produc8211389475949308722nt_int
% 0.33/0.56 @ ^ [X12: int,X23: int] : ( H3 @ ( F @ X12 @ X23 ) )
% 0.33/0.56 @ Prod ) ) ).
% 0.33/0.56
% 0.33/0.56 % prod.case_distrib
% 0.33/0.56 thf(fact_2587_prod_Ocase__distrib,axiom,
% 0.33/0.56 ! [H3: int > product_prod_int_int,F: int > int > int,Prod: product_prod_int_int] :
% 0.33/0.56 ( ( H3 @ ( produc8211389475949308722nt_int @ F @ Prod ) )
% 0.33/0.56 = ( produc4245557441103728435nt_int
% 0.33/0.56 @ ^ [X12: int,X23: int] : ( H3 @ ( F @ X12 @ X23 ) )
% 0.33/0.56 @ Prod ) ) ).
% 0.33/0.56
% 0.33/0.56 % prod.case_distrib
% 0.33/0.56 thf(fact_2588_prod_Ocase__distrib,axiom,
% 0.33/0.56 ! [H3: nat > product_prod_nat_nat > $o,F: nat > nat > nat,Prod: product_prod_nat_nat] :
% 0.33/0.56 ( ( H3 @ ( produc6842872674320459806at_nat @ F @ Prod ) )
% 0.33/0.56 = ( produc8739625826339149834_nat_o
% 0.33/0.56 @ ^ [X12: nat,X23: nat] : ( H3 @ ( F @ X12 @ X23 ) )
% 0.33/0.56 @ Prod ) ) ).
% 0.33/0.56
% 0.33/0.56 % prod.case_distrib
% 0.33/0.56 thf(fact_2589_prod_Ocase__distrib,axiom,
% 0.33/0.56 ! [H3: ( product_prod_nat_nat > $o ) > nat,F: nat > nat > product_prod_nat_nat > $o,Prod: product_prod_nat_nat] :
% 0.33/0.56 ( ( H3 @ ( produc8739625826339149834_nat_o @ F @ Prod ) )
% 0.33/0.56 = ( produc6842872674320459806at_nat
% 0.33/0.56 @ ^ [X12: nat,X23: nat] : ( H3 @ ( F @ X12 @ X23 ) )
% 0.33/0.56 @ Prod ) ) ).
% 0.33/0.56
% 0.33/0.56 % prod.case_distrib
% 0.33/0.56 thf(fact_2590_prod_Ocase__distrib,axiom,
% 0.33/0.56 ! [H3: product_prod_int_int > product_prod_int_int,F: int > int > product_prod_int_int,Prod: product_prod_int_int] :
% 0.33/0.56 ( ( H3 @ ( produc4245557441103728435nt_int @ F @ Prod ) )
% 0.33/0.56 = ( produc4245557441103728435nt_int
% 0.33/0.56 @ ^ [X12: int,X23: int] : ( H3 @ ( F @ X12 @ X23 ) )
% 0.33/0.56 @ Prod ) ) ).
% 0.33/0.56
% 0.33/0.56 % prod.case_distrib
% 0.33/0.56 thf(fact_2591_prod_Ocase__distrib,axiom,
% 0.33/0.56 ! [H3: nat > product_prod_nat_nat > product_prod_nat_nat,F: nat > nat > nat,Prod: product_prod_nat_nat] :
% 0.33/0.56 ( ( H3 @ ( produc6842872674320459806at_nat @ F @ Prod ) )
% 0.33/0.56 = ( produc27273713700761075at_nat
% 0.33/0.56 @ ^ [X12: nat,X23: nat] : ( H3 @ ( F @ X12 @ X23 ) )
% 0.33/0.56 @ Prod ) ) ).
% 0.33/0.56
% 0.33/0.56 % prod.case_distrib
% 0.33/0.56 thf(fact_2592_prod_Ocase__distrib,axiom,
% 0.33/0.56 ! [H3: ( product_prod_nat_nat > product_prod_nat_nat ) > nat,F: nat > nat > product_prod_nat_nat > product_prod_nat_nat,Prod: product_prod_nat_nat] :
% 0.33/0.56 ( ( H3 @ ( produc27273713700761075at_nat @ F @ Prod ) )
% 0.33/0.56 = ( produc6842872674320459806at_nat
% 0.33/0.56 @ ^ [X12: nat,X23: nat] : ( H3 @ ( F @ X12 @ X23 ) )
% 0.33/0.56 @ Prod ) ) ).
% 0.33/0.56
% 0.33/0.56 % prod.case_distrib
% 0.33/0.56 thf(fact_2593_prod_Ocase__distrib,axiom,
% 0.33/0.56 ! [H3: ( product_prod_nat_nat > $o ) > product_prod_nat_nat > $o,F: nat > nat > product_prod_nat_nat > $o,Prod: product_prod_nat_nat] :
% 0.33/0.56 ( ( H3 @ ( produc8739625826339149834_nat_o @ F @ Prod ) )
% 0.33/0.56 = ( produc8739625826339149834_nat_o
% 0.33/0.56 @ ^ [X12: nat,X23: nat] : ( H3 @ ( F @ X12 @ X23 ) )
% 0.33/0.56 @ Prod ) ) ).
% 0.33/0.56
% 0.33/0.56 % prod.case_distrib
% 0.33/0.56 thf(fact_2594_sum_OatLeast__Suc__atMost__Suc__shift,axiom,
% 0.33/0.56 ! [G: nat > nat,M2: nat,N2: nat] :
% 0.33/0.56 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ ( suc @ N2 ) ) )
% 0.33/0.56 = ( groups3542108847815614940at_nat @ ( comp_nat_nat_nat @ G @ suc ) @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % sum.atLeast_Suc_atMost_Suc_shift
% 0.33/0.56 thf(fact_2595_sum_OatLeastAtMost__shift__bounds,axiom,
% 0.33/0.56 ! [G: nat > nat,M2: nat,K: nat,N2: nat] :
% 0.33/0.56 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M2 @ K ) @ ( plus_plus_nat @ N2 @ K ) ) )
% 0.33/0.56 = ( groups3542108847815614940at_nat @ ( comp_nat_nat_nat @ G @ ( plus_plus_nat @ K ) ) @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % sum.atLeastAtMost_shift_bounds
% 0.33/0.56 thf(fact_2596_split__cong,axiom,
% 0.33/0.56 ! [Q3: product_prod_nat_nat,F: nat > nat > nat,G: nat > nat > nat,P4: product_prod_nat_nat] :
% 0.33/0.56 ( ! [X4: nat,Y5: nat] :
% 0.33/0.56 ( ( ( product_Pair_nat_nat @ X4 @ Y5 )
% 0.33/0.56 = Q3 )
% 0.33/0.56 => ( ( F @ X4 @ Y5 )
% 0.33/0.56 = ( G @ X4 @ Y5 ) ) )
% 0.33/0.56 => ( ( P4 = Q3 )
% 0.33/0.56 => ( ( produc6842872674320459806at_nat @ F @ P4 )
% 0.33/0.56 = ( produc6842872674320459806at_nat @ G @ Q3 ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % split_cong
% 0.33/0.56 thf(fact_2597_split__cong,axiom,
% 0.33/0.56 ! [Q3: product_prod_nat_nat,F: nat > nat > product_prod_nat_nat > product_prod_nat_nat,G: nat > nat > product_prod_nat_nat > product_prod_nat_nat,P4: product_prod_nat_nat] :
% 0.33/0.56 ( ! [X4: nat,Y5: nat] :
% 0.33/0.56 ( ( ( product_Pair_nat_nat @ X4 @ Y5 )
% 0.33/0.56 = Q3 )
% 0.33/0.56 => ( ( F @ X4 @ Y5 )
% 0.33/0.56 = ( G @ X4 @ Y5 ) ) )
% 0.33/0.56 => ( ( P4 = Q3 )
% 0.33/0.56 => ( ( produc27273713700761075at_nat @ F @ P4 )
% 0.33/0.56 = ( produc27273713700761075at_nat @ G @ Q3 ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % split_cong
% 0.33/0.56 thf(fact_2598_split__cong,axiom,
% 0.33/0.56 ! [Q3: product_prod_nat_nat,F: nat > nat > product_prod_nat_nat > $o,G: nat > nat > product_prod_nat_nat > $o,P4: product_prod_nat_nat] :
% 0.33/0.56 ( ! [X4: nat,Y5: nat] :
% 0.33/0.56 ( ( ( product_Pair_nat_nat @ X4 @ Y5 )
% 0.33/0.56 = Q3 )
% 0.33/0.56 => ( ( F @ X4 @ Y5 )
% 0.33/0.56 = ( G @ X4 @ Y5 ) ) )
% 0.33/0.56 => ( ( P4 = Q3 )
% 0.33/0.56 => ( ( produc8739625826339149834_nat_o @ F @ P4 )
% 0.33/0.56 = ( produc8739625826339149834_nat_o @ G @ Q3 ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % split_cong
% 0.33/0.56 thf(fact_2599_split__cong,axiom,
% 0.33/0.56 ! [Q3: product_prod_int_int,F: int > int > product_prod_int_int,G: int > int > product_prod_int_int,P4: product_prod_int_int] :
% 0.33/0.56 ( ! [X4: int,Y5: int] :
% 0.33/0.56 ( ( ( product_Pair_int_int @ X4 @ Y5 )
% 0.33/0.56 = Q3 )
% 0.33/0.56 => ( ( F @ X4 @ Y5 )
% 0.33/0.56 = ( G @ X4 @ Y5 ) ) )
% 0.33/0.56 => ( ( P4 = Q3 )
% 0.33/0.56 => ( ( produc4245557441103728435nt_int @ F @ P4 )
% 0.33/0.56 = ( produc4245557441103728435nt_int @ G @ Q3 ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % split_cong
% 0.33/0.56 thf(fact_2600_split__cong,axiom,
% 0.33/0.56 ! [Q3: product_prod_int_int,F: int > int > int,G: int > int > int,P4: product_prod_int_int] :
% 0.33/0.56 ( ! [X4: int,Y5: int] :
% 0.33/0.56 ( ( ( product_Pair_int_int @ X4 @ Y5 )
% 0.33/0.56 = Q3 )
% 0.33/0.56 => ( ( F @ X4 @ Y5 )
% 0.33/0.56 = ( G @ X4 @ Y5 ) ) )
% 0.33/0.56 => ( ( P4 = Q3 )
% 0.33/0.56 => ( ( produc8211389475949308722nt_int @ F @ P4 )
% 0.33/0.56 = ( produc8211389475949308722nt_int @ G @ Q3 ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % split_cong
% 0.33/0.56 thf(fact_2601_old_Oprod_Ocase,axiom,
% 0.33/0.56 ! [F: nat > nat > nat,X1: nat,X2: nat] :
% 0.33/0.56 ( ( produc6842872674320459806at_nat @ F @ ( product_Pair_nat_nat @ X1 @ X2 ) )
% 0.33/0.56 = ( F @ X1 @ X2 ) ) ).
% 0.33/0.56
% 0.33/0.56 % old.prod.case
% 0.33/0.56 thf(fact_2602_old_Oprod_Ocase,axiom,
% 0.33/0.56 ! [F: nat > nat > product_prod_nat_nat > product_prod_nat_nat,X1: nat,X2: nat] :
% 0.33/0.56 ( ( produc27273713700761075at_nat @ F @ ( product_Pair_nat_nat @ X1 @ X2 ) )
% 0.33/0.56 = ( F @ X1 @ X2 ) ) ).
% 0.33/0.56
% 0.33/0.56 % old.prod.case
% 0.33/0.56 thf(fact_2603_old_Oprod_Ocase,axiom,
% 0.33/0.56 ! [F: nat > nat > product_prod_nat_nat > $o,X1: nat,X2: nat] :
% 0.33/0.56 ( ( produc8739625826339149834_nat_o @ F @ ( product_Pair_nat_nat @ X1 @ X2 ) )
% 0.33/0.56 = ( F @ X1 @ X2 ) ) ).
% 0.33/0.56
% 0.33/0.56 % old.prod.case
% 0.33/0.56 thf(fact_2604_old_Oprod_Ocase,axiom,
% 0.33/0.56 ! [F: int > int > product_prod_int_int,X1: int,X2: int] :
% 0.33/0.56 ( ( produc4245557441103728435nt_int @ F @ ( product_Pair_int_int @ X1 @ X2 ) )
% 0.33/0.56 = ( F @ X1 @ X2 ) ) ).
% 0.33/0.56
% 0.33/0.56 % old.prod.case
% 0.33/0.56 thf(fact_2605_old_Oprod_Ocase,axiom,
% 0.33/0.56 ! [F: int > int > int,X1: int,X2: int] :
% 0.33/0.56 ( ( produc8211389475949308722nt_int @ F @ ( product_Pair_int_int @ X1 @ X2 ) )
% 0.33/0.56 = ( F @ X1 @ X2 ) ) ).
% 0.33/0.56
% 0.33/0.56 % old.prod.case
% 0.33/0.56 thf(fact_2606_uminus__int_Oabs__eq,axiom,
% 0.33/0.56 ! [X: product_prod_nat_nat] :
% 0.33/0.56 ( ( uminus_uminus_int @ ( abs_Integ @ X ) )
% 0.33/0.56 = ( abs_Integ
% 0.33/0.56 @ ( produc2626176000494625587at_nat
% 0.33/0.56 @ ^ [X3: nat,Y3: nat] : ( product_Pair_nat_nat @ Y3 @ X3 )
% 0.33/0.56 @ X ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % uminus_int.abs_eq
% 0.33/0.56 thf(fact_2607_case__prod__Pair__iden,axiom,
% 0.33/0.56 ! [P4: produc1908205239877642774nteger] :
% 0.33/0.56 ( ( produc6512950862096126219nteger @ produc8603105652947943368nteger @ P4 )
% 0.33/0.56 = P4 ) ).
% 0.33/0.56
% 0.33/0.56 % case_prod_Pair_iden
% 0.33/0.56 thf(fact_2608_case__prod__Pair__iden,axiom,
% 0.33/0.56 ! [P4: produc3925858234332021118et_nat] :
% 0.33/0.56 ( ( produc4058941399401191971et_nat @ produc5001842942810119800et_nat @ P4 )
% 0.33/0.56 = P4 ) ).
% 0.33/0.56
% 0.33/0.56 % case_prod_Pair_iden
% 0.33/0.56 thf(fact_2609_case__prod__Pair__iden,axiom,
% 0.33/0.56 ! [P4: produc2732055786443039994et_nat] :
% 0.33/0.56 ( ( produc2377985495875741467et_nat @ produc2245416461498447860et_nat @ P4 )
% 0.33/0.56 = P4 ) ).
% 0.33/0.56
% 0.33/0.56 % case_prod_Pair_iden
% 0.33/0.56 thf(fact_2610_case__prod__Pair__iden,axiom,
% 0.33/0.56 ! [P4: produc2285326912895808259nt_int] :
% 0.33/0.56 ( ( produc8492565224438309093nt_int @ produc5700946648718959541nt_int @ P4 )
% 0.33/0.56 = P4 ) ).
% 0.33/0.56
% 0.33/0.56 % case_prod_Pair_iden
% 0.33/0.56 thf(fact_2611_case__prod__Pair__iden,axiom,
% 0.33/0.56 ! [P4: produc7773217078559923341nt_int] :
% 0.33/0.56 ( ( produc5122537100556696953nt_int @ produc4305682042979456191nt_int @ P4 )
% 0.33/0.56 = P4 ) ).
% 0.33/0.56
% 0.33/0.56 % case_prod_Pair_iden
% 0.33/0.56 thf(fact_2612_case__prod__Pair__iden,axiom,
% 0.33/0.56 ! [P4: product_prod_int_int] :
% 0.33/0.56 ( ( produc4245557441103728435nt_int @ product_Pair_int_int @ P4 )
% 0.33/0.56 = P4 ) ).
% 0.33/0.56
% 0.33/0.56 % case_prod_Pair_iden
% 0.33/0.56 thf(fact_2613_sum_Oshift__bounds__cl__Suc__ivl,axiom,
% 0.33/0.56 ! [G: nat > nat,M2: nat,N2: nat] :
% 0.33/0.56 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ ( suc @ N2 ) ) )
% 0.33/0.56 = ( groups3542108847815614940at_nat
% 0.33/0.56 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 0.33/0.56 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % sum.shift_bounds_cl_Suc_ivl
% 0.33/0.56 thf(fact_2614_sum_Oshift__bounds__cl__nat__ivl,axiom,
% 0.33/0.56 ! [G: nat > nat,M2: nat,K: nat,N2: nat] :
% 0.33/0.56 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M2 @ K ) @ ( plus_plus_nat @ N2 @ K ) ) )
% 0.33/0.56 = ( groups3542108847815614940at_nat
% 0.33/0.56 @ ^ [I3: nat] : ( G @ ( plus_plus_nat @ I3 @ K ) )
% 0.33/0.56 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % sum.shift_bounds_cl_nat_ivl
% 0.33/0.56 thf(fact_2615_cond__case__prod__eta,axiom,
% 0.33/0.56 ! [F: nat > nat > nat,G: product_prod_nat_nat > nat] :
% 0.33/0.56 ( ! [X4: nat,Y5: nat] :
% 0.33/0.56 ( ( F @ X4 @ Y5 )
% 0.33/0.56 = ( G @ ( product_Pair_nat_nat @ X4 @ Y5 ) ) )
% 0.33/0.56 => ( ( produc6842872674320459806at_nat @ F )
% 0.33/0.56 = G ) ) ).
% 0.33/0.56
% 0.33/0.56 % cond_case_prod_eta
% 0.33/0.56 thf(fact_2616_cond__case__prod__eta,axiom,
% 0.33/0.56 ! [F: nat > nat > product_prod_nat_nat > product_prod_nat_nat,G: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat] :
% 0.33/0.56 ( ! [X4: nat,Y5: nat] :
% 0.33/0.56 ( ( F @ X4 @ Y5 )
% 0.33/0.56 = ( G @ ( product_Pair_nat_nat @ X4 @ Y5 ) ) )
% 0.33/0.56 => ( ( produc27273713700761075at_nat @ F )
% 0.33/0.56 = G ) ) ).
% 0.33/0.56
% 0.33/0.56 % cond_case_prod_eta
% 0.33/0.56 thf(fact_2617_cond__case__prod__eta,axiom,
% 0.33/0.56 ! [F: nat > nat > product_prod_nat_nat > $o,G: product_prod_nat_nat > product_prod_nat_nat > $o] :
% 0.33/0.56 ( ! [X4: nat,Y5: nat] :
% 0.33/0.56 ( ( F @ X4 @ Y5 )
% 0.33/0.56 = ( G @ ( product_Pair_nat_nat @ X4 @ Y5 ) ) )
% 0.33/0.56 => ( ( produc8739625826339149834_nat_o @ F )
% 0.33/0.56 = G ) ) ).
% 0.33/0.56
% 0.33/0.56 % cond_case_prod_eta
% 0.33/0.56 thf(fact_2618_cond__case__prod__eta,axiom,
% 0.33/0.56 ! [F: int > int > product_prod_int_int,G: product_prod_int_int > product_prod_int_int] :
% 0.33/0.56 ( ! [X4: int,Y5: int] :
% 0.33/0.56 ( ( F @ X4 @ Y5 )
% 0.33/0.56 = ( G @ ( product_Pair_int_int @ X4 @ Y5 ) ) )
% 0.33/0.56 => ( ( produc4245557441103728435nt_int @ F )
% 0.33/0.56 = G ) ) ).
% 0.33/0.56
% 0.33/0.56 % cond_case_prod_eta
% 0.33/0.56 thf(fact_2619_cond__case__prod__eta,axiom,
% 0.33/0.56 ! [F: int > int > int,G: product_prod_int_int > int] :
% 0.33/0.56 ( ! [X4: int,Y5: int] :
% 0.33/0.56 ( ( F @ X4 @ Y5 )
% 0.33/0.56 = ( G @ ( product_Pair_int_int @ X4 @ Y5 ) ) )
% 0.33/0.56 => ( ( produc8211389475949308722nt_int @ F )
% 0.33/0.56 = G ) ) ).
% 0.33/0.56
% 0.33/0.56 % cond_case_prod_eta
% 0.33/0.56 thf(fact_2620_case__prod__eta,axiom,
% 0.33/0.56 ! [F: product_prod_nat_nat > nat] :
% 0.33/0.56 ( ( produc6842872674320459806at_nat
% 0.33/0.56 @ ^ [X3: nat,Y3: nat] : ( F @ ( product_Pair_nat_nat @ X3 @ Y3 ) ) )
% 0.33/0.56 = F ) ).
% 0.33/0.56
% 0.33/0.56 % case_prod_eta
% 0.33/0.56 thf(fact_2621_case__prod__eta,axiom,
% 0.33/0.56 ! [F: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat] :
% 0.33/0.56 ( ( produc27273713700761075at_nat
% 0.33/0.56 @ ^ [X3: nat,Y3: nat] : ( F @ ( product_Pair_nat_nat @ X3 @ Y3 ) ) )
% 0.33/0.56 = F ) ).
% 0.33/0.56
% 0.33/0.56 % case_prod_eta
% 0.33/0.56 thf(fact_2622_case__prod__eta,axiom,
% 0.33/0.56 ! [F: product_prod_nat_nat > product_prod_nat_nat > $o] :
% 0.33/0.56 ( ( produc8739625826339149834_nat_o
% 0.33/0.56 @ ^ [X3: nat,Y3: nat] : ( F @ ( product_Pair_nat_nat @ X3 @ Y3 ) ) )
% 0.33/0.56 = F ) ).
% 0.33/0.56
% 0.33/0.56 % case_prod_eta
% 0.33/0.56 thf(fact_2623_case__prod__eta,axiom,
% 0.33/0.56 ! [F: product_prod_int_int > product_prod_int_int] :
% 0.33/0.56 ( ( produc4245557441103728435nt_int
% 0.33/0.56 @ ^ [X3: int,Y3: int] : ( F @ ( product_Pair_int_int @ X3 @ Y3 ) ) )
% 0.33/0.56 = F ) ).
% 0.33/0.56
% 0.33/0.56 % case_prod_eta
% 0.33/0.56 thf(fact_2624_case__prod__eta,axiom,
% 0.33/0.56 ! [F: product_prod_int_int > int] :
% 0.33/0.56 ( ( produc8211389475949308722nt_int
% 0.33/0.56 @ ^ [X3: int,Y3: int] : ( F @ ( product_Pair_int_int @ X3 @ Y3 ) ) )
% 0.33/0.56 = F ) ).
% 0.33/0.56
% 0.33/0.56 % case_prod_eta
% 0.33/0.56 thf(fact_2625_case__prodE2,axiom,
% 0.33/0.56 ! [Q: nat > $o,P: nat > nat > nat,Z: product_prod_nat_nat] :
% 0.33/0.56 ( ( Q @ ( produc6842872674320459806at_nat @ P @ Z ) )
% 0.33/0.56 => ~ ! [X4: nat,Y5: nat] :
% 0.33/0.56 ( ( Z
% 0.33/0.56 = ( product_Pair_nat_nat @ X4 @ Y5 ) )
% 0.33/0.56 => ~ ( Q @ ( P @ X4 @ Y5 ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % case_prodE2
% 0.33/0.56 thf(fact_2626_case__prodE2,axiom,
% 0.33/0.56 ! [Q: ( product_prod_nat_nat > product_prod_nat_nat ) > $o,P: nat > nat > product_prod_nat_nat > product_prod_nat_nat,Z: product_prod_nat_nat] :
% 0.33/0.56 ( ( Q @ ( produc27273713700761075at_nat @ P @ Z ) )
% 0.33/0.56 => ~ ! [X4: nat,Y5: nat] :
% 0.33/0.56 ( ( Z
% 0.33/0.56 = ( product_Pair_nat_nat @ X4 @ Y5 ) )
% 0.33/0.56 => ~ ( Q @ ( P @ X4 @ Y5 ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % case_prodE2
% 0.33/0.56 thf(fact_2627_case__prodE2,axiom,
% 0.33/0.56 ! [Q: ( product_prod_nat_nat > $o ) > $o,P: nat > nat > product_prod_nat_nat > $o,Z: product_prod_nat_nat] :
% 0.33/0.56 ( ( Q @ ( produc8739625826339149834_nat_o @ P @ Z ) )
% 0.33/0.56 => ~ ! [X4: nat,Y5: nat] :
% 0.33/0.56 ( ( Z
% 0.33/0.56 = ( product_Pair_nat_nat @ X4 @ Y5 ) )
% 0.33/0.56 => ~ ( Q @ ( P @ X4 @ Y5 ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % case_prodE2
% 0.33/0.56 thf(fact_2628_case__prodE2,axiom,
% 0.33/0.56 ! [Q: product_prod_int_int > $o,P: int > int > product_prod_int_int,Z: product_prod_int_int] :
% 0.33/0.56 ( ( Q @ ( produc4245557441103728435nt_int @ P @ Z ) )
% 0.33/0.56 => ~ ! [X4: int,Y5: int] :
% 0.33/0.56 ( ( Z
% 0.33/0.56 = ( product_Pair_int_int @ X4 @ Y5 ) )
% 0.33/0.56 => ~ ( Q @ ( P @ X4 @ Y5 ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % case_prodE2
% 0.33/0.56 thf(fact_2629_case__prodE2,axiom,
% 0.33/0.56 ! [Q: int > $o,P: int > int > int,Z: product_prod_int_int] :
% 0.33/0.56 ( ( Q @ ( produc8211389475949308722nt_int @ P @ Z ) )
% 0.33/0.56 => ~ ! [X4: int,Y5: int] :
% 0.33/0.56 ( ( Z
% 0.33/0.56 = ( product_Pair_int_int @ X4 @ Y5 ) )
% 0.33/0.56 => ~ ( Q @ ( P @ X4 @ Y5 ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % case_prodE2
% 0.33/0.56 thf(fact_2630_eq__Abs__Integ,axiom,
% 0.33/0.56 ! [Z: int] :
% 0.33/0.56 ~ ! [X4: nat,Y5: nat] :
% 0.33/0.56 ( Z
% 0.33/0.56 != ( abs_Integ @ ( product_Pair_nat_nat @ X4 @ Y5 ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % eq_Abs_Integ
% 0.33/0.56 thf(fact_2631_one__le__numeral,axiom,
% 0.33/0.56 ! [N2: num] : ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ N2 ) ) ).
% 0.33/0.56
% 0.33/0.56 % one_le_numeral
% 0.33/0.56 thf(fact_2632_one__le__numeral,axiom,
% 0.33/0.56 ! [N2: num] : ( ord_le1926595141338095240atural @ one_one_Code_natural @ ( numera5444537566228673987atural @ N2 ) ) ).
% 0.33/0.56
% 0.33/0.56 % one_le_numeral
% 0.33/0.56 thf(fact_2633_one__le__numeral,axiom,
% 0.33/0.56 ! [N2: num] : ( ord_less_eq_rat @ one_one_rat @ ( numeral_numeral_rat @ N2 ) ) ).
% 0.33/0.56
% 0.33/0.56 % one_le_numeral
% 0.33/0.56 thf(fact_2634_one__le__numeral,axiom,
% 0.33/0.56 ! [N2: num] : ( ord_less_eq_nat @ one_one_nat @ ( numeral_numeral_nat @ N2 ) ) ).
% 0.33/0.56
% 0.33/0.56 % one_le_numeral
% 0.33/0.56 thf(fact_2635_one__le__numeral,axiom,
% 0.33/0.56 ! [N2: num] : ( ord_less_eq_int @ one_one_int @ ( numeral_numeral_int @ N2 ) ) ).
% 0.33/0.56
% 0.33/0.56 % one_le_numeral
% 0.33/0.56 thf(fact_2636_not__numeral__less__one,axiom,
% 0.33/0.56 ! [N2: num] :
% 0.33/0.56 ~ ( ord_less_nat @ ( numeral_numeral_nat @ N2 ) @ one_one_nat ) ).
% 0.33/0.56
% 0.33/0.56 % not_numeral_less_one
% 0.33/0.56 thf(fact_2637_not__numeral__less__one,axiom,
% 0.33/0.56 ! [N2: num] :
% 0.33/0.56 ~ ( ord_less_int @ ( numeral_numeral_int @ N2 ) @ one_one_int ) ).
% 0.33/0.56
% 0.33/0.56 % not_numeral_less_one
% 0.33/0.56 thf(fact_2638_not__numeral__less__one,axiom,
% 0.33/0.56 ! [N2: num] :
% 0.33/0.56 ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ N2 ) @ one_one_Code_integer ) ).
% 0.33/0.56
% 0.33/0.56 % not_numeral_less_one
% 0.33/0.56 thf(fact_2639_not__numeral__less__one,axiom,
% 0.33/0.56 ! [N2: num] :
% 0.33/0.56 ~ ( ord_less_rat @ ( numeral_numeral_rat @ N2 ) @ one_one_rat ) ).
% 0.33/0.56
% 0.33/0.56 % not_numeral_less_one
% 0.33/0.56 thf(fact_2640_not__numeral__less__one,axiom,
% 0.33/0.56 ! [N2: num] :
% 0.33/0.56 ~ ( ord_le5570908160329646204atural @ ( numera5444537566228673987atural @ N2 ) @ one_one_Code_natural ) ).
% 0.33/0.56
% 0.33/0.56 % not_numeral_less_one
% 0.33/0.56 thf(fact_2641_one__plus__numeral__commute,axiom,
% 0.33/0.56 ! [X: num] :
% 0.33/0.56 ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ X ) )
% 0.33/0.56 = ( plus_plus_nat @ ( numeral_numeral_nat @ X ) @ one_one_nat ) ) ).
% 0.33/0.56
% 0.33/0.56 % one_plus_numeral_commute
% 0.33/0.56 thf(fact_2642_one__plus__numeral__commute,axiom,
% 0.33/0.56 ! [X: num] :
% 0.33/0.56 ( ( plus_plus_int @ one_one_int @ ( numeral_numeral_int @ X ) )
% 0.33/0.56 = ( plus_plus_int @ ( numeral_numeral_int @ X ) @ one_one_int ) ) ).
% 0.33/0.56
% 0.33/0.56 % one_plus_numeral_commute
% 0.33/0.56 thf(fact_2643_one__plus__numeral__commute,axiom,
% 0.33/0.56 ! [X: num] :
% 0.33/0.56 ( ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ X ) )
% 0.33/0.56 = ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ X ) @ one_one_Code_integer ) ) ).
% 0.33/0.56
% 0.33/0.56 % one_plus_numeral_commute
% 0.33/0.56 thf(fact_2644_one__plus__numeral__commute,axiom,
% 0.33/0.56 ! [X: num] :
% 0.33/0.56 ( ( plus_plus_rat @ one_one_rat @ ( numeral_numeral_rat @ X ) )
% 0.33/0.56 = ( plus_plus_rat @ ( numeral_numeral_rat @ X ) @ one_one_rat ) ) ).
% 0.33/0.56
% 0.33/0.56 % one_plus_numeral_commute
% 0.33/0.56 thf(fact_2645_one__plus__numeral__commute,axiom,
% 0.33/0.56 ! [X: num] :
% 0.33/0.56 ( ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( numera5444537566228673987atural @ X ) )
% 0.33/0.56 = ( plus_p4538020629002901425atural @ ( numera5444537566228673987atural @ X ) @ one_one_Code_natural ) ) ).
% 0.33/0.56
% 0.33/0.56 % one_plus_numeral_commute
% 0.33/0.56 thf(fact_2646_numeral__Bit0,axiom,
% 0.33/0.56 ! [N2: num] :
% 0.33/0.56 ( ( numeral_numeral_nat @ ( bit0 @ N2 ) )
% 0.33/0.56 = ( plus_plus_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ N2 ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % numeral_Bit0
% 0.33/0.56 thf(fact_2647_numeral__Bit0,axiom,
% 0.33/0.56 ! [N2: num] :
% 0.33/0.56 ( ( numeral_numeral_int @ ( bit0 @ N2 ) )
% 0.33/0.56 = ( plus_plus_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ N2 ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % numeral_Bit0
% 0.33/0.56 thf(fact_2648_numeral__Bit0,axiom,
% 0.33/0.56 ! [N2: num] :
% 0.33/0.56 ( ( numera6620942414471956472nteger @ ( bit0 @ N2 ) )
% 0.33/0.56 = ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ N2 ) @ ( numera6620942414471956472nteger @ N2 ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % numeral_Bit0
% 0.33/0.56 thf(fact_2649_numeral__Bit0,axiom,
% 0.33/0.56 ! [N2: num] :
% 0.33/0.56 ( ( numeral_numeral_rat @ ( bit0 @ N2 ) )
% 0.33/0.56 = ( plus_plus_rat @ ( numeral_numeral_rat @ N2 ) @ ( numeral_numeral_rat @ N2 ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % numeral_Bit0
% 0.33/0.56 thf(fact_2650_numeral__Bit0,axiom,
% 0.33/0.56 ! [N2: num] :
% 0.33/0.56 ( ( numera5444537566228673987atural @ ( bit0 @ N2 ) )
% 0.33/0.56 = ( plus_p4538020629002901425atural @ ( numera5444537566228673987atural @ N2 ) @ ( numera5444537566228673987atural @ N2 ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % numeral_Bit0
% 0.33/0.56 thf(fact_2651_one__neq__neg__numeral,axiom,
% 0.33/0.56 ! [N2: num] :
% 0.33/0.56 ( one_one_int
% 0.33/0.56 != ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % one_neq_neg_numeral
% 0.33/0.56 thf(fact_2652_one__neq__neg__numeral,axiom,
% 0.33/0.56 ! [N2: num] :
% 0.33/0.56 ( one_one_Code_integer
% 0.33/0.56 != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % one_neq_neg_numeral
% 0.33/0.56 thf(fact_2653_one__neq__neg__numeral,axiom,
% 0.33/0.56 ! [N2: num] :
% 0.33/0.56 ( one_one_rat
% 0.33/0.56 != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % one_neq_neg_numeral
% 0.33/0.56 thf(fact_2654_numeral__neq__neg__one,axiom,
% 0.33/0.56 ! [N2: num] :
% 0.33/0.56 ( ( numeral_numeral_int @ N2 )
% 0.33/0.56 != ( uminus_uminus_int @ one_one_int ) ) ).
% 0.33/0.56
% 0.33/0.56 % numeral_neq_neg_one
% 0.33/0.56 thf(fact_2655_numeral__neq__neg__one,axiom,
% 0.33/0.56 ! [N2: num] :
% 0.33/0.56 ( ( numera6620942414471956472nteger @ N2 )
% 0.33/0.56 != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.33/0.56
% 0.33/0.56 % numeral_neq_neg_one
% 0.33/0.56 thf(fact_2656_numeral__neq__neg__one,axiom,
% 0.33/0.56 ! [N2: num] :
% 0.33/0.56 ( ( numeral_numeral_rat @ N2 )
% 0.33/0.56 != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.33/0.56
% 0.33/0.56 % numeral_neq_neg_one
% 0.33/0.56 thf(fact_2657_uncurry__def,axiom,
% 0.33/0.56 uncurry_nat_nat_nat = produc6842872674320459806at_nat ).
% 0.33/0.56
% 0.33/0.56 % uncurry_def
% 0.33/0.56 thf(fact_2658_uncurry__def,axiom,
% 0.33/0.56 uncurr8011562610307062878at_nat = produc27273713700761075at_nat ).
% 0.33/0.56
% 0.33/0.56 % uncurry_def
% 0.33/0.56 thf(fact_2659_uncurry__def,axiom,
% 0.33/0.56 uncurr7511940902602773877_nat_o = produc8739625826339149834_nat_o ).
% 0.33/0.56
% 0.33/0.56 % uncurry_def
% 0.33/0.56 thf(fact_2660_uncurry__def,axiom,
% 0.33/0.56 uncurr7650761721940715016nt_int = produc4245557441103728435nt_int ).
% 0.33/0.56
% 0.33/0.56 % uncurry_def
% 0.33/0.56 thf(fact_2661_uncurry__def,axiom,
% 0.33/0.56 uncurry_int_int_int = produc8211389475949308722nt_int ).
% 0.33/0.56
% 0.33/0.56 % uncurry_def
% 0.33/0.56 thf(fact_2662_internal__case__prod__def,axiom,
% 0.33/0.56 produc6557683772455589876at_nat = produc6842872674320459806at_nat ).
% 0.33/0.56
% 0.33/0.56 % internal_case_prod_def
% 0.33/0.56 thf(fact_2663_internal__case__prod__def,axiom,
% 0.33/0.56 produc1854806715440696265at_nat = produc27273713700761075at_nat ).
% 0.33/0.56
% 0.33/0.56 % internal_case_prod_def
% 0.33/0.56 thf(fact_2664_internal__case__prod__def,axiom,
% 0.33/0.56 produc4780622933104268256_nat_o = produc8739625826339149834_nat_o ).
% 0.33/0.56
% 0.33/0.56 % internal_case_prod_def
% 0.33/0.56 thf(fact_2665_internal__case__prod__def,axiom,
% 0.33/0.56 produc297006045350968285nt_int = produc4245557441103728435nt_int ).
% 0.33/0.56
% 0.33/0.56 % internal_case_prod_def
% 0.33/0.56 thf(fact_2666_internal__case__prod__def,axiom,
% 0.33/0.56 produc7926200574084438792nt_int = produc8211389475949308722nt_int ).
% 0.33/0.56
% 0.33/0.56 % internal_case_prod_def
% 0.33/0.56 thf(fact_2667_sum_OatLeastAtMost__rev,axiom,
% 0.33/0.56 ! [G: nat > nat,N2: nat,M2: nat] :
% 0.33/0.56 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ N2 @ M2 ) )
% 0.33/0.56 = ( groups3542108847815614940at_nat
% 0.33/0.56 @ ^ [I3: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M2 @ N2 ) @ I3 ) )
% 0.33/0.56 @ ( set_or1269000886237332187st_nat @ N2 @ M2 ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % sum.atLeastAtMost_rev
% 0.33/0.56 thf(fact_2668_numeral__code_I2_J,axiom,
% 0.33/0.56 ! [N2: num] :
% 0.33/0.56 ( ( numeral_numeral_nat @ ( bit0 @ N2 ) )
% 0.33/0.56 = ( plus_plus_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ N2 ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % numeral_code(2)
% 0.33/0.56 thf(fact_2669_numeral__code_I2_J,axiom,
% 0.33/0.56 ! [N2: num] :
% 0.33/0.56 ( ( numeral_numeral_int @ ( bit0 @ N2 ) )
% 0.33/0.56 = ( plus_plus_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ N2 ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % numeral_code(2)
% 0.33/0.56 thf(fact_2670_numeral__code_I2_J,axiom,
% 0.33/0.56 ! [N2: num] :
% 0.33/0.56 ( ( numera6620942414471956472nteger @ ( bit0 @ N2 ) )
% 0.33/0.56 = ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ N2 ) @ ( numera6620942414471956472nteger @ N2 ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % numeral_code(2)
% 0.33/0.56 thf(fact_2671_numeral__code_I2_J,axiom,
% 0.33/0.56 ! [N2: num] :
% 0.33/0.56 ( ( numeral_numeral_rat @ ( bit0 @ N2 ) )
% 0.33/0.56 = ( plus_plus_rat @ ( numeral_numeral_rat @ N2 ) @ ( numeral_numeral_rat @ N2 ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % numeral_code(2)
% 0.33/0.56 thf(fact_2672_numeral__code_I2_J,axiom,
% 0.33/0.56 ! [N2: num] :
% 0.33/0.56 ( ( numera5444537566228673987atural @ ( bit0 @ N2 ) )
% 0.33/0.56 = ( plus_p4538020629002901425atural @ ( numera5444537566228673987atural @ N2 ) @ ( numera5444537566228673987atural @ N2 ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % numeral_code(2)
% 0.33/0.56 thf(fact_2673_sum__shift__lb__Suc0__0,axiom,
% 0.33/0.56 ! [F: nat > code_integer,K: nat] :
% 0.33/0.56 ( ( ( F @ zero_zero_nat )
% 0.33/0.56 = zero_z3403309356797280102nteger )
% 0.33/0.56 => ( ( groups7501900531339628137nteger @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 0.33/0.56 = ( groups7501900531339628137nteger @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % sum_shift_lb_Suc0_0
% 0.33/0.56 thf(fact_2674_sum__shift__lb__Suc0__0,axiom,
% 0.33/0.56 ! [F: nat > multis2468970476368604999at_nat,K: nat] :
% 0.33/0.56 ( ( ( F @ zero_zero_nat )
% 0.33/0.56 = zero_z1048942125864253310at_nat )
% 0.33/0.56 => ( ( groups6857163185585827899at_nat @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 0.33/0.56 = ( groups6857163185585827899at_nat @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % sum_shift_lb_Suc0_0
% 0.33/0.56 thf(fact_2675_sum__shift__lb__Suc0__0,axiom,
% 0.33/0.56 ! [F: nat > rat,K: nat] :
% 0.33/0.56 ( ( ( F @ zero_zero_nat )
% 0.33/0.56 = zero_zero_rat )
% 0.33/0.56 => ( ( groups2906978787729119204at_rat @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 0.33/0.56 = ( groups2906978787729119204at_rat @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % sum_shift_lb_Suc0_0
% 0.33/0.56 thf(fact_2676_sum__shift__lb__Suc0__0,axiom,
% 0.33/0.56 ! [F: nat > int,K: nat] :
% 0.33/0.56 ( ( ( F @ zero_zero_nat )
% 0.33/0.56 = zero_zero_int )
% 0.33/0.56 => ( ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 0.33/0.56 = ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % sum_shift_lb_Suc0_0
% 0.33/0.56 thf(fact_2677_sum__shift__lb__Suc0__0,axiom,
% 0.33/0.56 ! [F: nat > nat,K: nat] :
% 0.33/0.56 ( ( ( F @ zero_zero_nat )
% 0.33/0.56 = zero_zero_nat )
% 0.33/0.56 => ( ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 0.33/0.56 = ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % sum_shift_lb_Suc0_0
% 0.33/0.56 thf(fact_2678_sum_OatLeast0__atMost__Suc,axiom,
% 0.33/0.56 ! [G: nat > multis2468970476368604999at_nat,N2: nat] :
% 0.33/0.56 ( ( groups6857163185585827899at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 0.33/0.56 = ( plus_p7104986032573967614at_nat @ ( groups6857163185585827899at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % sum.atLeast0_atMost_Suc
% 0.33/0.56 thf(fact_2679_sum_OatLeast0__atMost__Suc,axiom,
% 0.33/0.56 ! [G: nat > rat,N2: nat] :
% 0.33/0.56 ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 0.33/0.56 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % sum.atLeast0_atMost_Suc
% 0.33/0.56 thf(fact_2680_sum_OatLeast0__atMost__Suc,axiom,
% 0.33/0.56 ! [G: nat > int,N2: nat] :
% 0.33/0.56 ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 0.33/0.56 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % sum.atLeast0_atMost_Suc
% 0.33/0.56 thf(fact_2681_sum_OatLeast0__atMost__Suc,axiom,
% 0.33/0.56 ! [G: nat > nat,N2: nat] :
% 0.33/0.56 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 0.33/0.56 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % sum.atLeast0_atMost_Suc
% 0.33/0.56 thf(fact_2682_sum_OatLeast0__atMost__Suc__shift,axiom,
% 0.33/0.56 ! [G: nat > multis2468970476368604999at_nat,N2: nat] :
% 0.33/0.56 ( ( groups6857163185585827899at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 0.33/0.56 = ( plus_p7104986032573967614at_nat @ ( G @ zero_zero_nat ) @ ( groups6857163185585827899at_nat @ ( comp_n8698576032424989604at_nat @ G @ suc ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % sum.atLeast0_atMost_Suc_shift
% 0.33/0.56 thf(fact_2683_sum_OatLeast0__atMost__Suc__shift,axiom,
% 0.33/0.56 ! [G: nat > rat,N2: nat] :
% 0.33/0.56 ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 0.33/0.56 = ( plus_plus_rat @ ( G @ zero_zero_nat ) @ ( groups2906978787729119204at_rat @ ( comp_nat_rat_nat @ G @ suc ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % sum.atLeast0_atMost_Suc_shift
% 0.33/0.56 thf(fact_2684_sum_OatLeast0__atMost__Suc__shift,axiom,
% 0.33/0.56 ! [G: nat > int,N2: nat] :
% 0.33/0.56 ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 0.33/0.56 = ( plus_plus_int @ ( G @ zero_zero_nat ) @ ( groups3539618377306564664at_int @ ( comp_nat_int_nat @ G @ suc ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % sum.atLeast0_atMost_Suc_shift
% 0.33/0.56 thf(fact_2685_sum_OatLeast0__atMost__Suc__shift,axiom,
% 0.33/0.56 ! [G: nat > nat,N2: nat] :
% 0.33/0.56 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 0.33/0.56 = ( plus_plus_nat @ ( G @ zero_zero_nat ) @ ( groups3542108847815614940at_nat @ ( comp_nat_nat_nat @ G @ suc ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % sum.atLeast0_atMost_Suc_shift
% 0.33/0.56 thf(fact_2686_sum_OatLeast__Suc__atMost,axiom,
% 0.33/0.56 ! [M2: nat,N2: nat,G: nat > multis2468970476368604999at_nat] :
% 0.33/0.56 ( ( ord_less_eq_nat @ M2 @ N2 )
% 0.33/0.56 => ( ( groups6857163185585827899at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 0.33/0.56 = ( plus_p7104986032573967614at_nat @ ( G @ M2 ) @ ( groups6857163185585827899at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N2 ) ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % sum.atLeast_Suc_atMost
% 0.33/0.56 thf(fact_2687_sum_OatLeast__Suc__atMost,axiom,
% 0.33/0.56 ! [M2: nat,N2: nat,G: nat > rat] :
% 0.33/0.56 ( ( ord_less_eq_nat @ M2 @ N2 )
% 0.33/0.56 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 0.33/0.56 = ( plus_plus_rat @ ( G @ M2 ) @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N2 ) ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % sum.atLeast_Suc_atMost
% 0.33/0.56 thf(fact_2688_sum_OatLeast__Suc__atMost,axiom,
% 0.33/0.56 ! [M2: nat,N2: nat,G: nat > int] :
% 0.33/0.56 ( ( ord_less_eq_nat @ M2 @ N2 )
% 0.33/0.56 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 0.33/0.56 = ( plus_plus_int @ ( G @ M2 ) @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N2 ) ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % sum.atLeast_Suc_atMost
% 0.33/0.56 thf(fact_2689_sum_OatLeast__Suc__atMost,axiom,
% 0.33/0.56 ! [M2: nat,N2: nat,G: nat > nat] :
% 0.33/0.56 ( ( ord_less_eq_nat @ M2 @ N2 )
% 0.33/0.56 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 0.33/0.56 = ( plus_plus_nat @ ( G @ M2 ) @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N2 ) ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % sum.atLeast_Suc_atMost
% 0.33/0.56 thf(fact_2690_sum_Onat__ivl__Suc_H,axiom,
% 0.33/0.56 ! [M2: nat,N2: nat,G: nat > multis2468970476368604999at_nat] :
% 0.33/0.56 ( ( ord_less_eq_nat @ M2 @ ( suc @ N2 ) )
% 0.33/0.56 => ( ( groups6857163185585827899at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N2 ) ) )
% 0.33/0.56 = ( plus_p7104986032573967614at_nat @ ( G @ ( suc @ N2 ) ) @ ( groups6857163185585827899at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % sum.nat_ivl_Suc'
% 0.33/0.56 thf(fact_2691_sum_Onat__ivl__Suc_H,axiom,
% 0.33/0.56 ! [M2: nat,N2: nat,G: nat > rat] :
% 0.33/0.56 ( ( ord_less_eq_nat @ M2 @ ( suc @ N2 ) )
% 0.33/0.56 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N2 ) ) )
% 0.33/0.56 = ( plus_plus_rat @ ( G @ ( suc @ N2 ) ) @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % sum.nat_ivl_Suc'
% 0.33/0.56 thf(fact_2692_sum_Onat__ivl__Suc_H,axiom,
% 0.33/0.56 ! [M2: nat,N2: nat,G: nat > int] :
% 0.33/0.56 ( ( ord_less_eq_nat @ M2 @ ( suc @ N2 ) )
% 0.33/0.56 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N2 ) ) )
% 0.33/0.56 = ( plus_plus_int @ ( G @ ( suc @ N2 ) ) @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % sum.nat_ivl_Suc'
% 0.33/0.56 thf(fact_2693_sum_Onat__ivl__Suc_H,axiom,
% 0.33/0.56 ! [M2: nat,N2: nat,G: nat > nat] :
% 0.33/0.56 ( ( ord_less_eq_nat @ M2 @ ( suc @ N2 ) )
% 0.33/0.56 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N2 ) ) )
% 0.33/0.56 = ( plus_plus_nat @ ( G @ ( suc @ N2 ) ) @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % sum.nat_ivl_Suc'
% 0.33/0.56 thf(fact_2694_neg__numeral__le__one,axiom,
% 0.33/0.56 ! [M2: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ one_one_Code_integer ) ).
% 0.33/0.56
% 0.33/0.56 % neg_numeral_le_one
% 0.33/0.56 thf(fact_2695_neg__numeral__le__one,axiom,
% 0.33/0.56 ! [M2: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ one_one_rat ) ).
% 0.33/0.56
% 0.33/0.56 % neg_numeral_le_one
% 0.33/0.56 thf(fact_2696_neg__numeral__le__one,axiom,
% 0.33/0.56 ! [M2: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ one_one_int ) ).
% 0.33/0.56
% 0.33/0.56 % neg_numeral_le_one
% 0.33/0.56 thf(fact_2697_neg__one__le__numeral,axiom,
% 0.33/0.56 ! [M2: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ M2 ) ) ).
% 0.33/0.56
% 0.33/0.56 % neg_one_le_numeral
% 0.33/0.56 thf(fact_2698_neg__one__le__numeral,axiom,
% 0.33/0.56 ! [M2: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ M2 ) ) ).
% 0.33/0.56
% 0.33/0.56 % neg_one_le_numeral
% 0.33/0.56 thf(fact_2699_neg__one__le__numeral,axiom,
% 0.33/0.56 ! [M2: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ M2 ) ) ).
% 0.33/0.56
% 0.33/0.56 % neg_one_le_numeral
% 0.33/0.56 thf(fact_2700_neg__numeral__le__neg__one,axiom,
% 0.33/0.56 ! [M2: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.33/0.56
% 0.33/0.56 % neg_numeral_le_neg_one
% 0.33/0.56 thf(fact_2701_neg__numeral__le__neg__one,axiom,
% 0.33/0.56 ! [M2: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.33/0.56
% 0.33/0.56 % neg_numeral_le_neg_one
% 0.33/0.56 thf(fact_2702_neg__numeral__le__neg__one,axiom,
% 0.33/0.56 ! [M2: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 0.33/0.56
% 0.33/0.56 % neg_numeral_le_neg_one
% 0.33/0.56 thf(fact_2703_not__numeral__le__neg__one,axiom,
% 0.33/0.56 ! [M2: num] :
% 0.33/0.56 ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ M2 ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.33/0.56
% 0.33/0.56 % not_numeral_le_neg_one
% 0.33/0.56 thf(fact_2704_not__numeral__le__neg__one,axiom,
% 0.33/0.56 ! [M2: num] :
% 0.33/0.56 ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ M2 ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.33/0.56
% 0.33/0.56 % not_numeral_le_neg_one
% 0.33/0.56 thf(fact_2705_not__numeral__le__neg__one,axiom,
% 0.33/0.56 ! [M2: num] :
% 0.33/0.56 ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 0.33/0.56
% 0.33/0.56 % not_numeral_le_neg_one
% 0.33/0.56 thf(fact_2706_not__one__le__neg__numeral,axiom,
% 0.33/0.56 ! [M2: num] :
% 0.33/0.56 ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % not_one_le_neg_numeral
% 0.33/0.56 thf(fact_2707_not__one__le__neg__numeral,axiom,
% 0.33/0.56 ! [M2: num] :
% 0.33/0.56 ~ ( ord_less_eq_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % not_one_le_neg_numeral
% 0.33/0.56 thf(fact_2708_not__one__le__neg__numeral,axiom,
% 0.33/0.56 ! [M2: num] :
% 0.33/0.56 ~ ( ord_less_eq_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % not_one_le_neg_numeral
% 0.33/0.56 thf(fact_2709_not__neg__one__less__neg__numeral,axiom,
% 0.33/0.56 ! [M2: num] :
% 0.33/0.56 ~ ( ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % not_neg_one_less_neg_numeral
% 0.33/0.56 thf(fact_2710_not__neg__one__less__neg__numeral,axiom,
% 0.33/0.56 ! [M2: num] :
% 0.33/0.56 ~ ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % not_neg_one_less_neg_numeral
% 0.33/0.56 thf(fact_2711_not__neg__one__less__neg__numeral,axiom,
% 0.33/0.56 ! [M2: num] :
% 0.33/0.56 ~ ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % not_neg_one_less_neg_numeral
% 0.33/0.56 thf(fact_2712_not__one__less__neg__numeral,axiom,
% 0.33/0.56 ! [M2: num] :
% 0.33/0.56 ~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % not_one_less_neg_numeral
% 0.33/0.56 thf(fact_2713_not__one__less__neg__numeral,axiom,
% 0.33/0.56 ! [M2: num] :
% 0.33/0.56 ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % not_one_less_neg_numeral
% 0.33/0.56 thf(fact_2714_not__one__less__neg__numeral,axiom,
% 0.33/0.56 ! [M2: num] :
% 0.33/0.56 ~ ( ord_less_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % not_one_less_neg_numeral
% 0.33/0.56 thf(fact_2715_not__numeral__less__neg__one,axiom,
% 0.33/0.56 ! [M2: num] :
% 0.33/0.56 ~ ( ord_less_int @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 0.33/0.56
% 0.33/0.56 % not_numeral_less_neg_one
% 0.33/0.56 thf(fact_2716_not__numeral__less__neg__one,axiom,
% 0.33/0.56 ! [M2: num] :
% 0.33/0.56 ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ M2 ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.33/0.56
% 0.33/0.56 % not_numeral_less_neg_one
% 0.33/0.56 thf(fact_2717_not__numeral__less__neg__one,axiom,
% 0.33/0.56 ! [M2: num] :
% 0.33/0.56 ~ ( ord_less_rat @ ( numeral_numeral_rat @ M2 ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.33/0.56
% 0.33/0.56 % not_numeral_less_neg_one
% 0.33/0.56 thf(fact_2718_neg__one__less__numeral,axiom,
% 0.33/0.56 ! [M2: num] : ( ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ M2 ) ) ).
% 0.33/0.56
% 0.33/0.56 % neg_one_less_numeral
% 0.33/0.56 thf(fact_2719_neg__one__less__numeral,axiom,
% 0.33/0.56 ! [M2: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ M2 ) ) ).
% 0.33/0.56
% 0.33/0.56 % neg_one_less_numeral
% 0.33/0.56 thf(fact_2720_neg__one__less__numeral,axiom,
% 0.33/0.56 ! [M2: num] : ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ M2 ) ) ).
% 0.33/0.56
% 0.33/0.56 % neg_one_less_numeral
% 0.33/0.56 thf(fact_2721_neg__numeral__less__one,axiom,
% 0.33/0.56 ! [M2: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ one_one_int ) ).
% 0.33/0.56
% 0.33/0.56 % neg_numeral_less_one
% 0.33/0.56 thf(fact_2722_neg__numeral__less__one,axiom,
% 0.33/0.56 ! [M2: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ one_one_Code_integer ) ).
% 0.33/0.56
% 0.33/0.56 % neg_numeral_less_one
% 0.33/0.56 thf(fact_2723_neg__numeral__less__one,axiom,
% 0.33/0.56 ! [M2: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ one_one_rat ) ).
% 0.33/0.56
% 0.33/0.56 % neg_numeral_less_one
% 0.33/0.56 thf(fact_2724_sum_OSuc__reindex__ivl,axiom,
% 0.33/0.56 ! [M2: nat,N2: nat,G: nat > multis2468970476368604999at_nat] :
% 0.33/0.56 ( ( ord_less_eq_nat @ M2 @ N2 )
% 0.33/0.56 => ( ( plus_p7104986032573967614at_nat @ ( groups6857163185585827899at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 0.33/0.56 = ( plus_p7104986032573967614at_nat @ ( G @ M2 )
% 0.33/0.56 @ ( groups6857163185585827899at_nat
% 0.33/0.56 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 0.33/0.56 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % sum.Suc_reindex_ivl
% 0.33/0.56 thf(fact_2725_sum_OSuc__reindex__ivl,axiom,
% 0.33/0.56 ! [M2: nat,N2: nat,G: nat > rat] :
% 0.33/0.56 ( ( ord_less_eq_nat @ M2 @ N2 )
% 0.33/0.56 => ( ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 0.33/0.56 = ( plus_plus_rat @ ( G @ M2 )
% 0.33/0.56 @ ( groups2906978787729119204at_rat
% 0.33/0.56 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 0.33/0.56 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % sum.Suc_reindex_ivl
% 0.33/0.56 thf(fact_2726_sum_OSuc__reindex__ivl,axiom,
% 0.33/0.56 ! [M2: nat,N2: nat,G: nat > int] :
% 0.33/0.56 ( ( ord_less_eq_nat @ M2 @ N2 )
% 0.33/0.56 => ( ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 0.33/0.56 = ( plus_plus_int @ ( G @ M2 )
% 0.33/0.56 @ ( groups3539618377306564664at_int
% 0.33/0.56 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 0.33/0.56 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % sum.Suc_reindex_ivl
% 0.33/0.56 thf(fact_2727_sum_OSuc__reindex__ivl,axiom,
% 0.33/0.56 ! [M2: nat,N2: nat,G: nat > nat] :
% 0.33/0.56 ( ( ord_less_eq_nat @ M2 @ N2 )
% 0.33/0.56 => ( ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 0.33/0.56 = ( plus_plus_nat @ ( G @ M2 )
% 0.33/0.56 @ ( groups3542108847815614940at_nat
% 0.33/0.56 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 0.33/0.56 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % sum.Suc_reindex_ivl
% 0.33/0.56 thf(fact_2728_sum__Suc__diff,axiom,
% 0.33/0.56 ! [M2: nat,N2: nat,F: nat > code_integer] :
% 0.33/0.56 ( ( ord_less_eq_nat @ M2 @ ( suc @ N2 ) )
% 0.33/0.56 => ( ( groups7501900531339628137nteger
% 0.33/0.56 @ ^ [I3: nat] : ( minus_8373710615458151222nteger @ ( F @ ( suc @ I3 ) ) @ ( F @ I3 ) )
% 0.33/0.56 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 0.33/0.56 = ( minus_8373710615458151222nteger @ ( F @ ( suc @ N2 ) ) @ ( F @ M2 ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % sum_Suc_diff
% 0.33/0.56 thf(fact_2729_sum__Suc__diff,axiom,
% 0.33/0.56 ! [M2: nat,N2: nat,F: nat > rat] :
% 0.33/0.56 ( ( ord_less_eq_nat @ M2 @ ( suc @ N2 ) )
% 0.33/0.56 => ( ( groups2906978787729119204at_rat
% 0.33/0.56 @ ^ [I3: nat] : ( minus_minus_rat @ ( F @ ( suc @ I3 ) ) @ ( F @ I3 ) )
% 0.33/0.56 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 0.33/0.56 = ( minus_minus_rat @ ( F @ ( suc @ N2 ) ) @ ( F @ M2 ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % sum_Suc_diff
% 0.33/0.56 thf(fact_2730_sum__Suc__diff,axiom,
% 0.33/0.56 ! [M2: nat,N2: nat,F: nat > int] :
% 0.33/0.56 ( ( ord_less_eq_nat @ M2 @ ( suc @ N2 ) )
% 0.33/0.56 => ( ( groups3539618377306564664at_int
% 0.33/0.56 @ ^ [I3: nat] : ( minus_minus_int @ ( F @ ( suc @ I3 ) ) @ ( F @ I3 ) )
% 0.33/0.56 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 0.33/0.56 = ( minus_minus_int @ ( F @ ( suc @ N2 ) ) @ ( F @ M2 ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % sum_Suc_diff
% 0.33/0.56 thf(fact_2731_sum__power__add,axiom,
% 0.33/0.56 ! [X: rat,M2: nat,I4: set_nat] :
% 0.33/0.56 ( ( groups2906978787729119204at_rat
% 0.33/0.56 @ ^ [I3: nat] : ( power_power_rat @ X @ ( plus_plus_nat @ M2 @ I3 ) )
% 0.33/0.56 @ I4 )
% 0.33/0.56 = ( times_times_rat @ ( power_power_rat @ X @ M2 ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ I4 ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % sum_power_add
% 0.33/0.56 thf(fact_2732_sum__power__add,axiom,
% 0.33/0.56 ! [X: int,M2: nat,I4: set_nat] :
% 0.33/0.56 ( ( groups3539618377306564664at_int
% 0.33/0.56 @ ^ [I3: nat] : ( power_power_int @ X @ ( plus_plus_nat @ M2 @ I3 ) )
% 0.33/0.56 @ I4 )
% 0.33/0.56 = ( times_times_int @ ( power_power_int @ X @ M2 ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ I4 ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % sum_power_add
% 0.33/0.56 thf(fact_2733_sum_OatLeast__atMost__pred__shift,axiom,
% 0.33/0.56 ! [G: nat > nat,M2: nat,N2: nat] :
% 0.33/0.56 ( ( groups3542108847815614940at_nat
% 0.33/0.56 @ ( comp_nat_nat_nat @ G
% 0.33/0.56 @ ^ [N4: nat] : ( minus_minus_nat @ N4 @ ( suc @ zero_zero_nat ) ) )
% 0.33/0.56 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ ( suc @ N2 ) ) )
% 0.33/0.56 = ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % sum.atLeast_atMost_pred_shift
% 0.33/0.56 thf(fact_2734_sum__atLeastAtMost__code,axiom,
% 0.33/0.56 ! [F: nat > code_integer,A: nat,B: nat] :
% 0.33/0.56 ( ( groups7501900531339628137nteger @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 0.33/0.56 = ( set_fo1084959871951514735nteger
% 0.33/0.56 @ ^ [A5: nat] : ( plus_p5714425477246183910nteger @ ( F @ A5 ) )
% 0.33/0.56 @ A
% 0.33/0.56 @ B
% 0.33/0.56 @ zero_z3403309356797280102nteger ) ) ).
% 0.33/0.56
% 0.33/0.56 % sum_atLeastAtMost_code
% 0.33/0.56 thf(fact_2735_sum__atLeastAtMost__code,axiom,
% 0.33/0.56 ! [F: nat > multis2468970476368604999at_nat,A: nat,B: nat] :
% 0.33/0.56 ( ( groups6857163185585827899at_nat @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 0.33/0.56 = ( set_fo4497565046347964853at_nat
% 0.33/0.56 @ ^ [A5: nat] : ( plus_p7104986032573967614at_nat @ ( F @ A5 ) )
% 0.33/0.56 @ A
% 0.33/0.56 @ B
% 0.33/0.56 @ zero_z1048942125864253310at_nat ) ) ).
% 0.33/0.56
% 0.33/0.56 % sum_atLeastAtMost_code
% 0.33/0.56 thf(fact_2736_sum__atLeastAtMost__code,axiom,
% 0.33/0.56 ! [F: nat > rat,A: nat,B: nat] :
% 0.33/0.56 ( ( groups2906978787729119204at_rat @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 0.33/0.56 = ( set_fo1949268297981939178at_rat
% 0.33/0.56 @ ^ [A5: nat] : ( plus_plus_rat @ ( F @ A5 ) )
% 0.33/0.56 @ A
% 0.33/0.56 @ B
% 0.33/0.56 @ zero_zero_rat ) ) ).
% 0.33/0.56
% 0.33/0.56 % sum_atLeastAtMost_code
% 0.33/0.56 thf(fact_2737_sum__atLeastAtMost__code,axiom,
% 0.33/0.56 ! [F: nat > int,A: nat,B: nat] :
% 0.33/0.56 ( ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 0.33/0.56 = ( set_fo2581907887559384638at_int
% 0.33/0.56 @ ^ [A5: nat] : ( plus_plus_int @ ( F @ A5 ) )
% 0.33/0.56 @ A
% 0.33/0.56 @ B
% 0.33/0.56 @ zero_zero_int ) ) ).
% 0.33/0.56
% 0.33/0.56 % sum_atLeastAtMost_code
% 0.33/0.56 thf(fact_2738_sum__atLeastAtMost__code,axiom,
% 0.33/0.56 ! [F: nat > nat,A: nat,B: nat] :
% 0.33/0.56 ( ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 0.33/0.56 = ( set_fo2584398358068434914at_nat
% 0.33/0.56 @ ^ [A5: nat] : ( plus_plus_nat @ ( F @ A5 ) )
% 0.33/0.56 @ A
% 0.33/0.56 @ B
% 0.33/0.56 @ zero_zero_nat ) ) ).
% 0.33/0.56
% 0.33/0.56 % sum_atLeastAtMost_code
% 0.33/0.56 thf(fact_2739_sum_Oub__add__nat,axiom,
% 0.33/0.56 ! [M2: nat,N2: nat,G: nat > multis2468970476368604999at_nat,P4: nat] :
% 0.33/0.56 ( ( ord_less_eq_nat @ M2 @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 0.33/0.56 => ( ( groups6857163185585827899at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ N2 @ P4 ) ) )
% 0.33/0.56 = ( plus_p7104986032573967614at_nat @ ( groups6857163185585827899at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) @ ( groups6857163185585827899at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ ( plus_plus_nat @ N2 @ P4 ) ) ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % sum.ub_add_nat
% 0.33/0.56 thf(fact_2740_sum_Oub__add__nat,axiom,
% 0.33/0.56 ! [M2: nat,N2: nat,G: nat > rat,P4: nat] :
% 0.33/0.56 ( ( ord_less_eq_nat @ M2 @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 0.33/0.56 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ N2 @ P4 ) ) )
% 0.33/0.56 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ ( plus_plus_nat @ N2 @ P4 ) ) ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % sum.ub_add_nat
% 0.33/0.56 thf(fact_2741_sum_Oub__add__nat,axiom,
% 0.33/0.56 ! [M2: nat,N2: nat,G: nat > int,P4: nat] :
% 0.33/0.56 ( ( ord_less_eq_nat @ M2 @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 0.33/0.56 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ N2 @ P4 ) ) )
% 0.33/0.56 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ ( plus_plus_nat @ N2 @ P4 ) ) ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % sum.ub_add_nat
% 0.33/0.56 thf(fact_2742_sum_Oub__add__nat,axiom,
% 0.33/0.56 ! [M2: nat,N2: nat,G: nat > nat,P4: nat] :
% 0.33/0.56 ( ( ord_less_eq_nat @ M2 @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 0.33/0.56 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ N2 @ P4 ) ) )
% 0.33/0.56 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ ( plus_plus_nat @ N2 @ P4 ) ) ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % sum.ub_add_nat
% 0.33/0.56 thf(fact_2743_sum_OatLeastAtMost__shift__0,axiom,
% 0.33/0.56 ! [M2: nat,N2: nat,G: nat > nat] :
% 0.33/0.56 ( ( ord_less_eq_nat @ M2 @ N2 )
% 0.33/0.56 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 0.33/0.56 = ( groups3542108847815614940at_nat @ ( comp_nat_nat_nat @ G @ ( plus_plus_nat @ M2 ) ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( minus_minus_nat @ N2 @ M2 ) ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % sum.atLeastAtMost_shift_0
% 0.33/0.56 thf(fact_2744_zero__int__def,axiom,
% 0.33/0.56 ( zero_zero_int
% 0.33/0.56 = ( abs_Integ @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % zero_int_def
% 0.33/0.56 thf(fact_2745_pair__lessI1,axiom,
% 0.33/0.56 ! [A: nat,B: nat,S: nat,T: nat] :
% 0.33/0.56 ( ( ord_less_nat @ A @ B )
% 0.33/0.56 => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A @ S ) @ ( product_Pair_nat_nat @ B @ T ) ) @ fun_pair_less ) ) ).
% 0.33/0.56
% 0.33/0.56 % pair_lessI1
% 0.33/0.56 thf(fact_2746_zero__int_Otransfer,axiom,
% 0.33/0.56 pcr_int @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) @ zero_zero_int ).
% 0.33/0.56
% 0.33/0.56 % zero_int.transfer
% 0.33/0.56 thf(fact_2747_sum__natinterval__diff,axiom,
% 0.33/0.56 ! [M2: nat,N2: nat,F: nat > code_integer] :
% 0.33/0.56 ( ( ( ord_less_eq_nat @ M2 @ N2 )
% 0.33/0.56 => ( ( groups7501900531339628137nteger
% 0.33/0.56 @ ^ [K4: nat] : ( minus_8373710615458151222nteger @ ( F @ K4 ) @ ( F @ ( plus_plus_nat @ K4 @ one_one_nat ) ) )
% 0.33/0.56 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 0.33/0.56 = ( minus_8373710615458151222nteger @ ( F @ M2 ) @ ( F @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) )
% 0.33/0.56 & ( ~ ( ord_less_eq_nat @ M2 @ N2 )
% 0.33/0.56 => ( ( groups7501900531339628137nteger
% 0.33/0.56 @ ^ [K4: nat] : ( minus_8373710615458151222nteger @ ( F @ K4 ) @ ( F @ ( plus_plus_nat @ K4 @ one_one_nat ) ) )
% 0.33/0.56 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 0.33/0.56 = zero_z3403309356797280102nteger ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % sum_natinterval_diff
% 0.33/0.56 thf(fact_2748_sum__natinterval__diff,axiom,
% 0.33/0.56 ! [M2: nat,N2: nat,F: nat > rat] :
% 0.33/0.56 ( ( ( ord_less_eq_nat @ M2 @ N2 )
% 0.33/0.56 => ( ( groups2906978787729119204at_rat
% 0.33/0.56 @ ^ [K4: nat] : ( minus_minus_rat @ ( F @ K4 ) @ ( F @ ( plus_plus_nat @ K4 @ one_one_nat ) ) )
% 0.33/0.56 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 0.33/0.56 = ( minus_minus_rat @ ( F @ M2 ) @ ( F @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) )
% 0.33/0.56 & ( ~ ( ord_less_eq_nat @ M2 @ N2 )
% 0.33/0.56 => ( ( groups2906978787729119204at_rat
% 0.33/0.56 @ ^ [K4: nat] : ( minus_minus_rat @ ( F @ K4 ) @ ( F @ ( plus_plus_nat @ K4 @ one_one_nat ) ) )
% 0.33/0.56 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 0.33/0.56 = zero_zero_rat ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % sum_natinterval_diff
% 0.33/0.56 thf(fact_2749_sum__natinterval__diff,axiom,
% 0.33/0.56 ! [M2: nat,N2: nat,F: nat > int] :
% 0.33/0.56 ( ( ( ord_less_eq_nat @ M2 @ N2 )
% 0.33/0.56 => ( ( groups3539618377306564664at_int
% 0.33/0.56 @ ^ [K4: nat] : ( minus_minus_int @ ( F @ K4 ) @ ( F @ ( plus_plus_nat @ K4 @ one_one_nat ) ) )
% 0.33/0.56 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 0.33/0.56 = ( minus_minus_int @ ( F @ M2 ) @ ( F @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) )
% 0.33/0.56 & ( ~ ( ord_less_eq_nat @ M2 @ N2 )
% 0.33/0.56 => ( ( groups3539618377306564664at_int
% 0.33/0.56 @ ^ [K4: nat] : ( minus_minus_int @ ( F @ K4 ) @ ( F @ ( plus_plus_nat @ K4 @ one_one_nat ) ) )
% 0.33/0.56 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 0.33/0.56 = zero_zero_int ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % sum_natinterval_diff
% 0.33/0.56 thf(fact_2750_convex__sum__bound__le,axiom,
% 0.33/0.56 ! [I4: set_o,X: $o > code_integer,A: $o > code_integer,B: code_integer,Delta: code_integer] :
% 0.33/0.56 ( ! [I2: $o] :
% 0.33/0.56 ( ( member_o @ I2 @ I4 )
% 0.33/0.56 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X @ I2 ) ) )
% 0.33/0.56 => ( ( ( groups4406642042086082107nteger @ X @ I4 )
% 0.33/0.56 = one_one_Code_integer )
% 0.33/0.56 => ( ! [I2: $o] :
% 0.33/0.56 ( ( member_o @ I2 @ I4 )
% 0.33/0.56 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I2 ) @ B ) ) @ Delta ) )
% 0.33/0.56 => ( ord_le3102999989581377725nteger
% 0.33/0.56 @ ( abs_abs_Code_integer
% 0.33/0.56 @ ( minus_8373710615458151222nteger
% 0.33/0.56 @ ( groups4406642042086082107nteger
% 0.33/0.56 @ ^ [I3: $o] : ( times_3573771949741848930nteger @ ( A @ I3 ) @ ( X @ I3 ) )
% 0.33/0.56 @ I4 )
% 0.33/0.56 @ B ) )
% 0.33/0.56 @ Delta ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % convex_sum_bound_le
% 0.33/0.56 thf(fact_2751_convex__sum__bound__le,axiom,
% 0.33/0.56 ! [I4: set_nat,X: nat > code_integer,A: nat > code_integer,B: code_integer,Delta: code_integer] :
% 0.33/0.56 ( ! [I2: nat] :
% 0.33/0.56 ( ( member_nat @ I2 @ I4 )
% 0.33/0.56 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X @ I2 ) ) )
% 0.33/0.56 => ( ( ( groups7501900531339628137nteger @ X @ I4 )
% 0.33/0.56 = one_one_Code_integer )
% 0.33/0.56 => ( ! [I2: nat] :
% 0.33/0.56 ( ( member_nat @ I2 @ I4 )
% 0.33/0.56 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I2 ) @ B ) ) @ Delta ) )
% 0.33/0.56 => ( ord_le3102999989581377725nteger
% 0.33/0.56 @ ( abs_abs_Code_integer
% 0.33/0.56 @ ( minus_8373710615458151222nteger
% 0.33/0.56 @ ( groups7501900531339628137nteger
% 0.33/0.56 @ ^ [I3: nat] : ( times_3573771949741848930nteger @ ( A @ I3 ) @ ( X @ I3 ) )
% 0.33/0.56 @ I4 )
% 0.33/0.56 @ B ) )
% 0.33/0.56 @ Delta ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % convex_sum_bound_le
% 0.33/0.56 thf(fact_2752_convex__sum__bound__le,axiom,
% 0.33/0.56 ! [I4: set_int,X: int > code_integer,A: int > code_integer,B: code_integer,Delta: code_integer] :
% 0.33/0.56 ( ! [I2: int] :
% 0.33/0.56 ( ( member_int @ I2 @ I4 )
% 0.33/0.56 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X @ I2 ) ) )
% 0.33/0.56 => ( ( ( groups7873554091576472773nteger @ X @ I4 )
% 0.33/0.56 = one_one_Code_integer )
% 0.33/0.56 => ( ! [I2: int] :
% 0.33/0.56 ( ( member_int @ I2 @ I4 )
% 0.33/0.56 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I2 ) @ B ) ) @ Delta ) )
% 0.33/0.56 => ( ord_le3102999989581377725nteger
% 0.33/0.56 @ ( abs_abs_Code_integer
% 0.33/0.56 @ ( minus_8373710615458151222nteger
% 0.33/0.56 @ ( groups7873554091576472773nteger
% 0.33/0.56 @ ^ [I3: int] : ( times_3573771949741848930nteger @ ( A @ I3 ) @ ( X @ I3 ) )
% 0.33/0.56 @ I4 )
% 0.33/0.56 @ B ) )
% 0.33/0.56 @ Delta ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % convex_sum_bound_le
% 0.33/0.56 thf(fact_2753_convex__sum__bound__le,axiom,
% 0.33/0.56 ! [I4: set_o,X: $o > rat,A: $o > rat,B: rat,Delta: rat] :
% 0.33/0.56 ( ! [I2: $o] :
% 0.33/0.56 ( ( member_o @ I2 @ I4 )
% 0.33/0.56 => ( ord_less_eq_rat @ zero_zero_rat @ ( X @ I2 ) ) )
% 0.33/0.56 => ( ( ( groups7872700643590313910_o_rat @ X @ I4 )
% 0.33/0.56 = one_one_rat )
% 0.33/0.56 => ( ! [I2: $o] :
% 0.33/0.56 ( ( member_o @ I2 @ I4 )
% 0.33/0.56 => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I2 ) @ B ) ) @ Delta ) )
% 0.33/0.56 => ( ord_less_eq_rat
% 0.33/0.56 @ ( abs_abs_rat
% 0.33/0.56 @ ( minus_minus_rat
% 0.33/0.56 @ ( groups7872700643590313910_o_rat
% 0.33/0.56 @ ^ [I3: $o] : ( times_times_rat @ ( A @ I3 ) @ ( X @ I3 ) )
% 0.33/0.56 @ I4 )
% 0.33/0.56 @ B ) )
% 0.33/0.56 @ Delta ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % convex_sum_bound_le
% 0.33/0.56 thf(fact_2754_convex__sum__bound__le,axiom,
% 0.33/0.56 ! [I4: set_nat,X: nat > rat,A: nat > rat,B: rat,Delta: rat] :
% 0.33/0.56 ( ! [I2: nat] :
% 0.33/0.56 ( ( member_nat @ I2 @ I4 )
% 0.33/0.56 => ( ord_less_eq_rat @ zero_zero_rat @ ( X @ I2 ) ) )
% 0.33/0.56 => ( ( ( groups2906978787729119204at_rat @ X @ I4 )
% 0.33/0.56 = one_one_rat )
% 0.33/0.56 => ( ! [I2: nat] :
% 0.33/0.56 ( ( member_nat @ I2 @ I4 )
% 0.33/0.56 => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I2 ) @ B ) ) @ Delta ) )
% 0.33/0.56 => ( ord_less_eq_rat
% 0.33/0.56 @ ( abs_abs_rat
% 0.33/0.56 @ ( minus_minus_rat
% 0.33/0.56 @ ( groups2906978787729119204at_rat
% 0.33/0.56 @ ^ [I3: nat] : ( times_times_rat @ ( A @ I3 ) @ ( X @ I3 ) )
% 0.33/0.56 @ I4 )
% 0.33/0.56 @ B ) )
% 0.33/0.56 @ Delta ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % convex_sum_bound_le
% 0.33/0.56 thf(fact_2755_convex__sum__bound__le,axiom,
% 0.33/0.56 ! [I4: set_int,X: int > rat,A: int > rat,B: rat,Delta: rat] :
% 0.33/0.56 ( ! [I2: int] :
% 0.33/0.56 ( ( member_int @ I2 @ I4 )
% 0.33/0.56 => ( ord_less_eq_rat @ zero_zero_rat @ ( X @ I2 ) ) )
% 0.33/0.56 => ( ( ( groups3906332499630173760nt_rat @ X @ I4 )
% 0.33/0.56 = one_one_rat )
% 0.33/0.56 => ( ! [I2: int] :
% 0.33/0.56 ( ( member_int @ I2 @ I4 )
% 0.33/0.56 => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I2 ) @ B ) ) @ Delta ) )
% 0.33/0.56 => ( ord_less_eq_rat
% 0.33/0.56 @ ( abs_abs_rat
% 0.33/0.56 @ ( minus_minus_rat
% 0.33/0.56 @ ( groups3906332499630173760nt_rat
% 0.33/0.56 @ ^ [I3: int] : ( times_times_rat @ ( A @ I3 ) @ ( X @ I3 ) )
% 0.33/0.56 @ I4 )
% 0.33/0.56 @ B ) )
% 0.33/0.56 @ Delta ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % convex_sum_bound_le
% 0.33/0.56 thf(fact_2756_convex__sum__bound__le,axiom,
% 0.33/0.56 ! [I4: set_o,X: $o > int,A: $o > int,B: int,Delta: int] :
% 0.33/0.56 ( ! [I2: $o] :
% 0.33/0.56 ( ( member_o @ I2 @ I4 )
% 0.33/0.56 => ( ord_less_eq_int @ zero_zero_int @ ( X @ I2 ) ) )
% 0.33/0.56 => ( ( ( groups8505340233167759370_o_int @ X @ I4 )
% 0.33/0.56 = one_one_int )
% 0.33/0.56 => ( ! [I2: $o] :
% 0.33/0.56 ( ( member_o @ I2 @ I4 )
% 0.33/0.56 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( A @ I2 ) @ B ) ) @ Delta ) )
% 0.33/0.56 => ( ord_less_eq_int
% 0.33/0.56 @ ( abs_abs_int
% 0.33/0.56 @ ( minus_minus_int
% 0.33/0.56 @ ( groups8505340233167759370_o_int
% 0.33/0.56 @ ^ [I3: $o] : ( times_times_int @ ( A @ I3 ) @ ( X @ I3 ) )
% 0.33/0.56 @ I4 )
% 0.33/0.56 @ B ) )
% 0.33/0.56 @ Delta ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % convex_sum_bound_le
% 0.33/0.56 thf(fact_2757_convex__sum__bound__le,axiom,
% 0.33/0.56 ! [I4: set_nat,X: nat > int,A: nat > int,B: int,Delta: int] :
% 0.33/0.56 ( ! [I2: nat] :
% 0.33/0.56 ( ( member_nat @ I2 @ I4 )
% 0.33/0.56 => ( ord_less_eq_int @ zero_zero_int @ ( X @ I2 ) ) )
% 0.33/0.56 => ( ( ( groups3539618377306564664at_int @ X @ I4 )
% 0.33/0.56 = one_one_int )
% 0.33/0.56 => ( ! [I2: nat] :
% 0.33/0.56 ( ( member_nat @ I2 @ I4 )
% 0.33/0.56 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( A @ I2 ) @ B ) ) @ Delta ) )
% 0.33/0.56 => ( ord_less_eq_int
% 0.33/0.56 @ ( abs_abs_int
% 0.33/0.56 @ ( minus_minus_int
% 0.33/0.56 @ ( groups3539618377306564664at_int
% 0.33/0.56 @ ^ [I3: nat] : ( times_times_int @ ( A @ I3 ) @ ( X @ I3 ) )
% 0.33/0.56 @ I4 )
% 0.33/0.56 @ B ) )
% 0.33/0.56 @ Delta ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % convex_sum_bound_le
% 0.33/0.56 thf(fact_2758_convex__sum__bound__le,axiom,
% 0.33/0.56 ! [I4: set_int,X: int > int,A: int > int,B: int,Delta: int] :
% 0.33/0.56 ( ! [I2: int] :
% 0.33/0.56 ( ( member_int @ I2 @ I4 )
% 0.33/0.56 => ( ord_less_eq_int @ zero_zero_int @ ( X @ I2 ) ) )
% 0.33/0.56 => ( ( ( groups4538972089207619220nt_int @ X @ I4 )
% 0.33/0.56 = one_one_int )
% 0.33/0.56 => ( ! [I2: int] :
% 0.33/0.56 ( ( member_int @ I2 @ I4 )
% 0.33/0.56 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( A @ I2 ) @ B ) ) @ Delta ) )
% 0.33/0.56 => ( ord_less_eq_int
% 0.33/0.56 @ ( abs_abs_int
% 0.33/0.56 @ ( minus_minus_int
% 0.33/0.56 @ ( groups4538972089207619220nt_int
% 0.33/0.56 @ ^ [I3: int] : ( times_times_int @ ( A @ I3 ) @ ( X @ I3 ) )
% 0.33/0.56 @ I4 )
% 0.33/0.56 @ B ) )
% 0.33/0.56 @ Delta ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % convex_sum_bound_le
% 0.33/0.56 thf(fact_2759_convex__sum__bound__le,axiom,
% 0.33/0.56 ! [I4: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat > code_integer,A: product_prod_nat_nat > code_integer,B: code_integer,Delta: code_integer] :
% 0.33/0.56 ( ! [I2: product_prod_nat_nat] :
% 0.33/0.56 ( ( member8440522571783428010at_nat @ I2 @ I4 )
% 0.33/0.56 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X @ I2 ) ) )
% 0.33/0.56 => ( ( ( groups196832835297161892nteger @ X @ I4 )
% 0.33/0.56 = one_one_Code_integer )
% 0.33/0.56 => ( ! [I2: product_prod_nat_nat] :
% 0.33/0.56 ( ( member8440522571783428010at_nat @ I2 @ I4 )
% 0.33/0.56 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I2 ) @ B ) ) @ Delta ) )
% 0.33/0.56 => ( ord_le3102999989581377725nteger
% 0.33/0.56 @ ( abs_abs_Code_integer
% 0.33/0.56 @ ( minus_8373710615458151222nteger
% 0.33/0.56 @ ( groups196832835297161892nteger
% 0.33/0.56 @ ^ [I3: product_prod_nat_nat] : ( times_3573771949741848930nteger @ ( A @ I3 ) @ ( X @ I3 ) )
% 0.33/0.56 @ I4 )
% 0.33/0.56 @ B ) )
% 0.33/0.56 @ Delta ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % convex_sum_bound_le
% 0.33/0.56 thf(fact_2760_sum__comp__morphism,axiom,
% 0.33/0.56 ! [H3: code_integer > code_integer,G: num > code_integer,A2: set_num] :
% 0.33/0.56 ( ( ( H3 @ zero_z3403309356797280102nteger )
% 0.33/0.56 = zero_z3403309356797280102nteger )
% 0.33/0.56 => ( ! [X4: code_integer,Y5: code_integer] :
% 0.33/0.56 ( ( H3 @ ( plus_p5714425477246183910nteger @ X4 @ Y5 ) )
% 0.33/0.56 = ( plus_p5714425477246183910nteger @ ( H3 @ X4 ) @ ( H3 @ Y5 ) ) )
% 0.33/0.56 => ( ( groups5442708359310287027nteger @ ( comp_C3531382070062128313er_num @ H3 @ G ) @ A2 )
% 0.33/0.56 = ( H3 @ ( groups5442708359310287027nteger @ G @ A2 ) ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % sum_comp_morphism
% 0.33/0.56 thf(fact_2761_sum__comp__morphism,axiom,
% 0.33/0.56 ! [H3: nat > code_integer,G: nat > nat,A2: set_nat] :
% 0.33/0.56 ( ( ( H3 @ zero_zero_nat )
% 0.33/0.56 = zero_z3403309356797280102nteger )
% 0.33/0.56 => ( ! [X4: nat,Y5: nat] :
% 0.33/0.56 ( ( H3 @ ( plus_plus_nat @ X4 @ Y5 ) )
% 0.33/0.56 = ( plus_p5714425477246183910nteger @ ( H3 @ X4 ) @ ( H3 @ Y5 ) ) )
% 0.33/0.56 => ( ( groups7501900531339628137nteger @ ( comp_n3898172953802868194er_nat @ H3 @ G ) @ A2 )
% 0.33/0.56 = ( H3 @ ( groups3542108847815614940at_nat @ G @ A2 ) ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % sum_comp_morphism
% 0.33/0.56 thf(fact_2762_sum__comp__morphism,axiom,
% 0.33/0.56 ! [H3: nat > rat,G: nat > nat,A2: set_nat] :
% 0.33/0.56 ( ( ( H3 @ zero_zero_nat )
% 0.33/0.56 = zero_zero_rat )
% 0.33/0.56 => ( ! [X4: nat,Y5: nat] :
% 0.33/0.56 ( ( H3 @ ( plus_plus_nat @ X4 @ Y5 ) )
% 0.33/0.56 = ( plus_plus_rat @ ( H3 @ X4 ) @ ( H3 @ Y5 ) ) )
% 0.33/0.56 => ( ( groups2906978787729119204at_rat @ ( comp_nat_rat_nat @ H3 @ G ) @ A2 )
% 0.33/0.56 = ( H3 @ ( groups3542108847815614940at_nat @ G @ A2 ) ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % sum_comp_morphism
% 0.33/0.56 thf(fact_2763_sum__comp__morphism,axiom,
% 0.33/0.56 ! [H3: nat > int,G: nat > nat,A2: set_nat] :
% 0.33/0.56 ( ( ( H3 @ zero_zero_nat )
% 0.33/0.56 = zero_zero_int )
% 0.33/0.56 => ( ! [X4: nat,Y5: nat] :
% 0.33/0.56 ( ( H3 @ ( plus_plus_nat @ X4 @ Y5 ) )
% 0.33/0.56 = ( plus_plus_int @ ( H3 @ X4 ) @ ( H3 @ Y5 ) ) )
% 0.33/0.56 => ( ( groups3539618377306564664at_int @ ( comp_nat_int_nat @ H3 @ G ) @ A2 )
% 0.33/0.56 = ( H3 @ ( groups3542108847815614940at_nat @ G @ A2 ) ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % sum_comp_morphism
% 0.33/0.56 thf(fact_2764_sum__comp__morphism,axiom,
% 0.33/0.56 ! [H3: int > code_integer,G: int > int,A2: set_int] :
% 0.33/0.56 ( ( ( H3 @ zero_zero_int )
% 0.33/0.56 = zero_z3403309356797280102nteger )
% 0.33/0.56 => ( ! [X4: int,Y5: int] :
% 0.33/0.56 ( ( H3 @ ( plus_plus_int @ X4 @ Y5 ) )
% 0.33/0.56 = ( plus_p5714425477246183910nteger @ ( H3 @ X4 ) @ ( H3 @ Y5 ) ) )
% 0.33/0.56 => ( ( groups7873554091576472773nteger @ ( comp_i1585864551200866970er_int @ H3 @ G ) @ A2 )
% 0.33/0.56 = ( H3 @ ( groups4538972089207619220nt_int @ G @ A2 ) ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % sum_comp_morphism
% 0.33/0.56 thf(fact_2765_sum__comp__morphism,axiom,
% 0.33/0.56 ! [H3: int > rat,G: int > int,A2: set_int] :
% 0.33/0.56 ( ( ( H3 @ zero_zero_int )
% 0.33/0.56 = zero_zero_rat )
% 0.33/0.56 => ( ! [X4: int,Y5: int] :
% 0.33/0.56 ( ( H3 @ ( plus_plus_int @ X4 @ Y5 ) )
% 0.33/0.56 = ( plus_plus_rat @ ( H3 @ X4 ) @ ( H3 @ Y5 ) ) )
% 0.33/0.56 => ( ( groups3906332499630173760nt_rat @ ( comp_int_rat_int @ H3 @ G ) @ A2 )
% 0.33/0.56 = ( H3 @ ( groups4538972089207619220nt_int @ G @ A2 ) ) ) ) ) ).
% 0.33/0.56
% 0.33/0.56 % sum_comp_morphism
% 0.33/0.56 thf(fact_2766_sum__comp__morphism,axiom,
% 0.33/0.56 ! [H3: int > nat,G: int > int,A2: set_int] :
% 0.33/0.56 ( ( ( H3 @ zero_zero_int )
% 0.33/0.56 = zero_zero_nat )
% 0.33/0.56 => ( ! [X4: int,Y5: int] :
% 0.33/0.56 ( ( H3 @ ( plus_plus_int @ X4 @ Y5 ) )
% 0.33/0.57 = ( plus_plus_nat @ ( H3 @ X4 ) @ ( H3 @ Y5 ) ) )
% 0.33/0.57 => ( ( groups4541462559716669496nt_nat @ ( comp_int_nat_int @ H3 @ G ) @ A2 )
% 0.33/0.57 = ( H3 @ ( groups4538972089207619220nt_int @ G @ A2 ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % sum_comp_morphism
% 0.33/0.57 thf(fact_2767_sum__comp__morphism,axiom,
% 0.33/0.57 ! [H3: code_integer > nat,G: nat > code_integer,A2: set_nat] :
% 0.33/0.57 ( ( ( H3 @ zero_z3403309356797280102nteger )
% 0.33/0.57 = zero_zero_nat )
% 0.33/0.57 => ( ! [X4: code_integer,Y5: code_integer] :
% 0.33/0.57 ( ( H3 @ ( plus_p5714425477246183910nteger @ X4 @ Y5 ) )
% 0.33/0.57 = ( plus_plus_nat @ ( H3 @ X4 ) @ ( H3 @ Y5 ) ) )
% 0.33/0.57 => ( ( groups3542108847815614940at_nat @ ( comp_C4049556595663050210at_nat @ H3 @ G ) @ A2 )
% 0.33/0.57 = ( H3 @ ( groups7501900531339628137nteger @ G @ A2 ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % sum_comp_morphism
% 0.33/0.57 thf(fact_2768_sum__comp__morphism,axiom,
% 0.33/0.57 ! [H3: rat > nat,G: nat > rat,A2: set_nat] :
% 0.33/0.57 ( ( ( H3 @ zero_zero_rat )
% 0.33/0.57 = zero_zero_nat )
% 0.33/0.57 => ( ! [X4: rat,Y5: rat] :
% 0.33/0.57 ( ( H3 @ ( plus_plus_rat @ X4 @ Y5 ) )
% 0.33/0.57 = ( plus_plus_nat @ ( H3 @ X4 ) @ ( H3 @ Y5 ) ) )
% 0.33/0.57 => ( ( groups3542108847815614940at_nat @ ( comp_rat_nat_nat @ H3 @ G ) @ A2 )
% 0.33/0.57 = ( H3 @ ( groups2906978787729119204at_rat @ G @ A2 ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % sum_comp_morphism
% 0.33/0.57 thf(fact_2769_sum__comp__morphism,axiom,
% 0.33/0.57 ! [H3: int > nat,G: nat > int,A2: set_nat] :
% 0.33/0.57 ( ( ( H3 @ zero_zero_int )
% 0.33/0.57 = zero_zero_nat )
% 0.33/0.57 => ( ! [X4: int,Y5: int] :
% 0.33/0.57 ( ( H3 @ ( plus_plus_int @ X4 @ Y5 ) )
% 0.33/0.57 = ( plus_plus_nat @ ( H3 @ X4 ) @ ( H3 @ Y5 ) ) )
% 0.33/0.57 => ( ( groups3542108847815614940at_nat @ ( comp_int_nat_nat @ H3 @ G ) @ A2 )
% 0.33/0.57 = ( H3 @ ( groups3539618377306564664at_int @ G @ A2 ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % sum_comp_morphism
% 0.33/0.57 thf(fact_2770_sum__gp,axiom,
% 0.33/0.57 ! [N2: nat,M2: nat,X: rat] :
% 0.33/0.57 ( ( ( ord_less_nat @ N2 @ M2 )
% 0.33/0.57 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 0.33/0.57 = zero_zero_rat ) )
% 0.33/0.57 & ( ~ ( ord_less_nat @ N2 @ M2 )
% 0.33/0.57 => ( ( ( X = one_one_rat )
% 0.33/0.57 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 0.33/0.57 = ( semiri681578069525770553at_rat @ ( minus_minus_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ M2 ) ) ) )
% 0.33/0.57 & ( ( X != one_one_rat )
% 0.33/0.57 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 0.33/0.57 = ( divide_divide_rat @ ( minus_minus_rat @ ( power_power_rat @ X @ M2 ) @ ( power_power_rat @ X @ ( suc @ N2 ) ) ) @ ( minus_minus_rat @ one_one_rat @ X ) ) ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % sum_gp
% 0.33/0.57 thf(fact_2771_divmod__digit__1_I1_J,axiom,
% 0.33/0.57 ! [A: code_integer,B: code_integer] :
% 0.33/0.57 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.33/0.57 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 0.33/0.57 => ( ( ord_le3102999989581377725nteger @ B @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) )
% 0.33/0.57 => ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) @ one_one_Code_integer )
% 0.33/0.57 = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % divmod_digit_1(1)
% 0.33/0.57 thf(fact_2772_divmod__digit__1_I1_J,axiom,
% 0.33/0.57 ! [A: nat,B: nat] :
% 0.33/0.57 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.33/0.57 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.33/0.57 => ( ( ord_less_eq_nat @ B @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 0.33/0.57 => ( ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) @ one_one_nat )
% 0.33/0.57 = ( divide_divide_nat @ A @ B ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % divmod_digit_1(1)
% 0.33/0.57 thf(fact_2773_divmod__digit__1_I1_J,axiom,
% 0.33/0.57 ! [A: int,B: int] :
% 0.33/0.57 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.33/0.57 => ( ( ord_less_int @ zero_zero_int @ B )
% 0.33/0.57 => ( ( ord_less_eq_int @ B @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 0.33/0.57 => ( ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) @ one_one_int )
% 0.33/0.57 = ( divide_divide_int @ A @ B ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % divmod_digit_1(1)
% 0.33/0.57 thf(fact_2774_sum__gp__offset,axiom,
% 0.33/0.57 ! [X: rat,M2: nat,N2: nat] :
% 0.33/0.57 ( ( ( X = one_one_rat )
% 0.33/0.57 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ M2 @ N2 ) ) )
% 0.33/0.57 = ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N2 ) @ one_one_rat ) ) )
% 0.33/0.57 & ( ( X != one_one_rat )
% 0.33/0.57 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ M2 @ N2 ) ) )
% 0.33/0.57 = ( divide_divide_rat @ ( times_times_rat @ ( power_power_rat @ X @ M2 ) @ ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ ( suc @ N2 ) ) ) ) @ ( minus_minus_rat @ one_one_rat @ X ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % sum_gp_offset
% 0.33/0.57 thf(fact_2775_Sum__Icc__nat,axiom,
% 0.33/0.57 ! [M2: nat,N2: nat] :
% 0.33/0.57 ( ( groups3542108847815614940at_nat
% 0.33/0.57 @ ^ [X3: nat] : X3
% 0.33/0.57 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 0.33/0.57 = ( divide_divide_nat @ ( minus_minus_nat @ ( times_times_nat @ N2 @ ( plus_plus_nat @ N2 @ one_one_nat ) ) @ ( times_times_nat @ M2 @ ( minus_minus_nat @ M2 @ one_one_nat ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % Sum_Icc_nat
% 0.33/0.57 thf(fact_2776_arith__series__nat,axiom,
% 0.33/0.57 ! [A: nat,D2: nat,N2: nat] :
% 0.33/0.57 ( ( groups3542108847815614940at_nat
% 0.33/0.57 @ ^ [I3: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ I3 @ D2 ) )
% 0.33/0.57 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 0.33/0.57 = ( divide_divide_nat @ ( times_times_nat @ ( suc @ N2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( times_times_nat @ N2 @ D2 ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % arith_series_nat
% 0.33/0.57 thf(fact_2777_mod__double__modulus,axiom,
% 0.33/0.57 ! [M2: code_integer,X: code_integer] :
% 0.33/0.57 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ M2 )
% 0.33/0.57 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X )
% 0.33/0.57 => ( ( ( modulo364778990260209775nteger @ X @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M2 ) )
% 0.33/0.57 = ( modulo364778990260209775nteger @ X @ M2 ) )
% 0.33/0.57 | ( ( modulo364778990260209775nteger @ X @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M2 ) )
% 0.33/0.57 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ X @ M2 ) @ M2 ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % mod_double_modulus
% 0.33/0.57 thf(fact_2778_mod__double__modulus,axiom,
% 0.33/0.57 ! [M2: nat,X: nat] :
% 0.33/0.57 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 0.33/0.57 => ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 0.33/0.57 => ( ( ( modulo_modulo_nat @ X @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 0.33/0.57 = ( modulo_modulo_nat @ X @ M2 ) )
% 0.33/0.57 | ( ( modulo_modulo_nat @ X @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 0.33/0.57 = ( plus_plus_nat @ ( modulo_modulo_nat @ X @ M2 ) @ M2 ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % mod_double_modulus
% 0.33/0.57 thf(fact_2779_mod__double__modulus,axiom,
% 0.33/0.57 ! [M2: int,X: int] :
% 0.33/0.57 ( ( ord_less_int @ zero_zero_int @ M2 )
% 0.33/0.57 => ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.33/0.57 => ( ( ( modulo_modulo_int @ X @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 ) )
% 0.33/0.57 = ( modulo_modulo_int @ X @ M2 ) )
% 0.33/0.57 | ( ( modulo_modulo_int @ X @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 ) )
% 0.33/0.57 = ( plus_plus_int @ ( modulo_modulo_int @ X @ M2 ) @ M2 ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % mod_double_modulus
% 0.33/0.57 thf(fact_2780_sum_Odistrib,axiom,
% 0.33/0.57 ! [G: nat > nat,H3: nat > nat,A2: set_nat] :
% 0.33/0.57 ( ( groups3542108847815614940at_nat
% 0.33/0.57 @ ^ [X3: nat] : ( plus_plus_nat @ ( G @ X3 ) @ ( H3 @ X3 ) )
% 0.33/0.57 @ A2 )
% 0.33/0.57 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ A2 ) @ ( groups3542108847815614940at_nat @ H3 @ A2 ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % sum.distrib
% 0.33/0.57 thf(fact_2781_sum_Odistrib,axiom,
% 0.33/0.57 ! [G: int > int,H3: int > int,A2: set_int] :
% 0.33/0.57 ( ( groups4538972089207619220nt_int
% 0.33/0.57 @ ^ [X3: int] : ( plus_plus_int @ ( G @ X3 ) @ ( H3 @ X3 ) )
% 0.33/0.57 @ A2 )
% 0.33/0.57 = ( plus_plus_int @ ( groups4538972089207619220nt_int @ G @ A2 ) @ ( groups4538972089207619220nt_int @ H3 @ A2 ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % sum.distrib
% 0.33/0.57 thf(fact_2782_case__prodI,axiom,
% 0.33/0.57 ! [F: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o,A: produc6241069584506657477e_term > option6357759511663192854e_term,B: produc8923325533196201883nteger] :
% 0.33/0.57 ( ( F @ A @ B )
% 0.33/0.57 => ( produc6253627499356882019eger_o @ F @ ( produc8603105652947943368nteger @ A @ B ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % case_prodI
% 0.33/0.57 thf(fact_2783_case__prodI,axiom,
% 0.33/0.57 ! [F: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o,A: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat] :
% 0.33/0.57 ( ( F @ A @ B )
% 0.33/0.57 => ( produc1437786849005270451_nat_o @ F @ ( produc5001842942810119800et_nat @ A @ B ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % case_prodI
% 0.33/0.57 thf(fact_2784_case__prodI,axiom,
% 0.33/0.57 ! [F: ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o,A: produc3658429121746597890et_nat > $o,B: produc3925858234332021118et_nat] :
% 0.33/0.57 ( ( F @ A @ B )
% 0.33/0.57 => ( produc838355143741117751_nat_o @ F @ ( produc2245416461498447860et_nat @ A @ B ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % case_prodI
% 0.33/0.57 thf(fact_2785_case__prodI,axiom,
% 0.33/0.57 ! [F: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o,A: produc8551481072490612790e_term > option6357759511663192854e_term,B: product_prod_int_int] :
% 0.33/0.57 ( ( F @ A @ B )
% 0.33/0.57 => ( produc1573362020775583542_int_o @ F @ ( produc5700946648718959541nt_int @ A @ B ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % case_prodI
% 0.33/0.57 thf(fact_2786_case__prodI,axiom,
% 0.33/0.57 ! [F: ( int > option6357759511663192854e_term ) > product_prod_int_int > $o,A: int > option6357759511663192854e_term,B: product_prod_int_int] :
% 0.33/0.57 ( ( F @ A @ B )
% 0.33/0.57 => ( produc2558449545302689196_int_o @ F @ ( produc4305682042979456191nt_int @ A @ B ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % case_prodI
% 0.33/0.57 thf(fact_2787_case__prodI2,axiom,
% 0.33/0.57 ! [P4: produc1908205239877642774nteger,C: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o] :
% 0.33/0.57 ( ! [A3: produc6241069584506657477e_term > option6357759511663192854e_term,B2: produc8923325533196201883nteger] :
% 0.33/0.57 ( ( P4
% 0.33/0.57 = ( produc8603105652947943368nteger @ A3 @ B2 ) )
% 0.33/0.57 => ( C @ A3 @ B2 ) )
% 0.33/0.57 => ( produc6253627499356882019eger_o @ C @ P4 ) ) ).
% 0.33/0.57
% 0.33/0.57 % case_prodI2
% 0.33/0.57 thf(fact_2788_case__prodI2,axiom,
% 0.33/0.57 ! [P4: produc3925858234332021118et_nat,C: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o] :
% 0.33/0.57 ( ! [A3: produc3658429121746597890et_nat > $o,B2: produc3658429121746597890et_nat] :
% 0.33/0.57 ( ( P4
% 0.33/0.57 = ( produc5001842942810119800et_nat @ A3 @ B2 ) )
% 0.33/0.57 => ( C @ A3 @ B2 ) )
% 0.33/0.57 => ( produc1437786849005270451_nat_o @ C @ P4 ) ) ).
% 0.33/0.57
% 0.33/0.57 % case_prodI2
% 0.33/0.57 thf(fact_2789_case__prodI2,axiom,
% 0.33/0.57 ! [P4: produc2732055786443039994et_nat,C: ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o] :
% 0.33/0.57 ( ! [A3: produc3658429121746597890et_nat > $o,B2: produc3925858234332021118et_nat] :
% 0.33/0.57 ( ( P4
% 0.33/0.57 = ( produc2245416461498447860et_nat @ A3 @ B2 ) )
% 0.33/0.57 => ( C @ A3 @ B2 ) )
% 0.33/0.57 => ( produc838355143741117751_nat_o @ C @ P4 ) ) ).
% 0.33/0.57
% 0.33/0.57 % case_prodI2
% 0.33/0.57 thf(fact_2790_case__prodI2,axiom,
% 0.33/0.57 ! [P4: produc2285326912895808259nt_int,C: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o] :
% 0.33/0.57 ( ! [A3: produc8551481072490612790e_term > option6357759511663192854e_term,B2: product_prod_int_int] :
% 0.33/0.57 ( ( P4
% 0.33/0.57 = ( produc5700946648718959541nt_int @ A3 @ B2 ) )
% 0.33/0.57 => ( C @ A3 @ B2 ) )
% 0.33/0.57 => ( produc1573362020775583542_int_o @ C @ P4 ) ) ).
% 0.33/0.57
% 0.33/0.57 % case_prodI2
% 0.33/0.57 thf(fact_2791_case__prodI2,axiom,
% 0.33/0.57 ! [P4: produc7773217078559923341nt_int,C: ( int > option6357759511663192854e_term ) > product_prod_int_int > $o] :
% 0.33/0.57 ( ! [A3: int > option6357759511663192854e_term,B2: product_prod_int_int] :
% 0.33/0.57 ( ( P4
% 0.33/0.57 = ( produc4305682042979456191nt_int @ A3 @ B2 ) )
% 0.33/0.57 => ( C @ A3 @ B2 ) )
% 0.33/0.57 => ( produc2558449545302689196_int_o @ C @ P4 ) ) ).
% 0.33/0.57
% 0.33/0.57 % case_prodI2
% 0.33/0.57 thf(fact_2792_mem__case__prodI,axiom,
% 0.33/0.57 ! [Z: $o,C: ( int > option6357759511663192854e_term ) > product_prod_int_int > set_o,A: int > option6357759511663192854e_term,B: product_prod_int_int] :
% 0.33/0.57 ( ( member_o @ Z @ ( C @ A @ B ) )
% 0.33/0.57 => ( member_o @ Z @ ( produc8646739037753556108_set_o @ C @ ( produc4305682042979456191nt_int @ A @ B ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % mem_case_prodI
% 0.33/0.57 thf(fact_2793_mem__case__prodI,axiom,
% 0.33/0.57 ! [Z: nat,C: ( int > option6357759511663192854e_term ) > product_prod_int_int > set_nat,A: int > option6357759511663192854e_term,B: product_prod_int_int] :
% 0.33/0.57 ( ( member_nat @ Z @ ( C @ A @ B ) )
% 0.33/0.57 => ( member_nat @ Z @ ( produc8289552606927098482et_nat @ C @ ( produc4305682042979456191nt_int @ A @ B ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % mem_case_prodI
% 0.33/0.57 thf(fact_2794_mem__case__prodI,axiom,
% 0.33/0.57 ! [Z: int,C: ( int > option6357759511663192854e_term ) > product_prod_int_int > set_int,A: int > option6357759511663192854e_term,B: product_prod_int_int] :
% 0.33/0.57 ( ( member_int @ Z @ ( C @ A @ B ) )
% 0.33/0.57 => ( member_int @ Z @ ( produc4111701587417901774et_int @ C @ ( produc4305682042979456191nt_int @ A @ B ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % mem_case_prodI
% 0.33/0.57 thf(fact_2795_mem__case__prodI,axiom,
% 0.33/0.57 ! [Z: $o,C: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > set_o,A: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat] :
% 0.33/0.57 ( ( member_o @ Z @ ( C @ A @ B ) )
% 0.33/0.57 => ( member_o @ Z @ ( produc7715693535893868691_set_o @ C @ ( produc5001842942810119800et_nat @ A @ B ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % mem_case_prodI
% 0.33/0.57 thf(fact_2796_mem__case__prodI,axiom,
% 0.33/0.57 ! [Z: nat,C: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > set_nat,A: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat] :
% 0.33/0.57 ( ( member_nat @ Z @ ( C @ A @ B ) )
% 0.33/0.57 => ( member_nat @ Z @ ( produc8805491454895738411et_nat @ C @ ( produc5001842942810119800et_nat @ A @ B ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % mem_case_prodI
% 0.33/0.57 thf(fact_2797_mem__case__prodI,axiom,
% 0.33/0.57 ! [Z: int,C: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > set_int,A: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat] :
% 0.33/0.57 ( ( member_int @ Z @ ( C @ A @ B ) )
% 0.33/0.57 => ( member_int @ Z @ ( produc4627640435386541703et_int @ C @ ( produc5001842942810119800et_nat @ A @ B ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % mem_case_prodI
% 0.33/0.57 thf(fact_2798_mem__case__prodI,axiom,
% 0.33/0.57 ! [Z: product_prod_nat_nat,C: ( int > option6357759511663192854e_term ) > product_prod_int_int > set_Pr1261947904930325089at_nat,A: int > option6357759511663192854e_term,B: product_prod_int_int] :
% 0.33/0.57 ( ( member8440522571783428010at_nat @ Z @ ( C @ A @ B ) )
% 0.33/0.57 => ( member8440522571783428010at_nat @ Z @ ( produc5154663461364529269at_nat @ C @ ( produc4305682042979456191nt_int @ A @ B ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % mem_case_prodI
% 0.33/0.57 thf(fact_2799_mem__case__prodI,axiom,
% 0.33/0.57 ! [Z: $o,C: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_o,A: produc6241069584506657477e_term > option6357759511663192854e_term,B: produc8923325533196201883nteger] :
% 0.33/0.57 ( ( member_o @ Z @ ( C @ A @ B ) )
% 0.33/0.57 => ( member_o @ Z @ ( produc2373554395599118147_set_o @ C @ ( produc8603105652947943368nteger @ A @ B ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % mem_case_prodI
% 0.33/0.57 thf(fact_2800_mem__case__prodI,axiom,
% 0.33/0.57 ! [Z: nat,C: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_nat,A: produc6241069584506657477e_term > option6357759511663192854e_term,B: produc8923325533196201883nteger] :
% 0.33/0.57 ( ( member_nat @ Z @ ( C @ A @ B ) )
% 0.33/0.57 => ( member_nat @ Z @ ( produc654622801845291899et_nat @ C @ ( produc8603105652947943368nteger @ A @ B ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % mem_case_prodI
% 0.33/0.57 thf(fact_2801_mem__case__prodI,axiom,
% 0.33/0.57 ! [Z: int,C: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_int,A: produc6241069584506657477e_term > option6357759511663192854e_term,B: produc8923325533196201883nteger] :
% 0.33/0.57 ( ( member_int @ Z @ ( C @ A @ B ) )
% 0.33/0.57 => ( member_int @ Z @ ( produc5700143819190870999et_int @ C @ ( produc8603105652947943368nteger @ A @ B ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % mem_case_prodI
% 0.33/0.57 thf(fact_2802_mem__case__prodI2,axiom,
% 0.33/0.57 ! [P4: produc7773217078559923341nt_int,Z: $o,C: ( int > option6357759511663192854e_term ) > product_prod_int_int > set_o] :
% 0.33/0.57 ( ! [A3: int > option6357759511663192854e_term,B2: product_prod_int_int] :
% 0.33/0.57 ( ( P4
% 0.33/0.57 = ( produc4305682042979456191nt_int @ A3 @ B2 ) )
% 0.33/0.57 => ( member_o @ Z @ ( C @ A3 @ B2 ) ) )
% 0.33/0.57 => ( member_o @ Z @ ( produc8646739037753556108_set_o @ C @ P4 ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % mem_case_prodI2
% 0.33/0.57 thf(fact_2803_mem__case__prodI2,axiom,
% 0.33/0.57 ! [P4: produc7773217078559923341nt_int,Z: nat,C: ( int > option6357759511663192854e_term ) > product_prod_int_int > set_nat] :
% 0.33/0.57 ( ! [A3: int > option6357759511663192854e_term,B2: product_prod_int_int] :
% 0.33/0.57 ( ( P4
% 0.33/0.57 = ( produc4305682042979456191nt_int @ A3 @ B2 ) )
% 0.33/0.57 => ( member_nat @ Z @ ( C @ A3 @ B2 ) ) )
% 0.33/0.57 => ( member_nat @ Z @ ( produc8289552606927098482et_nat @ C @ P4 ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % mem_case_prodI2
% 0.33/0.57 thf(fact_2804_mem__case__prodI2,axiom,
% 0.33/0.57 ! [P4: produc7773217078559923341nt_int,Z: int,C: ( int > option6357759511663192854e_term ) > product_prod_int_int > set_int] :
% 0.33/0.57 ( ! [A3: int > option6357759511663192854e_term,B2: product_prod_int_int] :
% 0.33/0.57 ( ( P4
% 0.33/0.57 = ( produc4305682042979456191nt_int @ A3 @ B2 ) )
% 0.33/0.57 => ( member_int @ Z @ ( C @ A3 @ B2 ) ) )
% 0.33/0.57 => ( member_int @ Z @ ( produc4111701587417901774et_int @ C @ P4 ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % mem_case_prodI2
% 0.33/0.57 thf(fact_2805_mem__case__prodI2,axiom,
% 0.33/0.57 ! [P4: produc3925858234332021118et_nat,Z: $o,C: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > set_o] :
% 0.33/0.57 ( ! [A3: produc3658429121746597890et_nat > $o,B2: produc3658429121746597890et_nat] :
% 0.33/0.57 ( ( P4
% 0.33/0.57 = ( produc5001842942810119800et_nat @ A3 @ B2 ) )
% 0.33/0.57 => ( member_o @ Z @ ( C @ A3 @ B2 ) ) )
% 0.33/0.57 => ( member_o @ Z @ ( produc7715693535893868691_set_o @ C @ P4 ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % mem_case_prodI2
% 0.33/0.57 thf(fact_2806_mem__case__prodI2,axiom,
% 0.33/0.57 ! [P4: produc3925858234332021118et_nat,Z: nat,C: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > set_nat] :
% 0.33/0.57 ( ! [A3: produc3658429121746597890et_nat > $o,B2: produc3658429121746597890et_nat] :
% 0.33/0.57 ( ( P4
% 0.33/0.57 = ( produc5001842942810119800et_nat @ A3 @ B2 ) )
% 0.33/0.57 => ( member_nat @ Z @ ( C @ A3 @ B2 ) ) )
% 0.33/0.57 => ( member_nat @ Z @ ( produc8805491454895738411et_nat @ C @ P4 ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % mem_case_prodI2
% 0.33/0.57 thf(fact_2807_mem__case__prodI2,axiom,
% 0.33/0.57 ! [P4: produc3925858234332021118et_nat,Z: int,C: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > set_int] :
% 0.33/0.57 ( ! [A3: produc3658429121746597890et_nat > $o,B2: produc3658429121746597890et_nat] :
% 0.33/0.57 ( ( P4
% 0.33/0.57 = ( produc5001842942810119800et_nat @ A3 @ B2 ) )
% 0.33/0.57 => ( member_int @ Z @ ( C @ A3 @ B2 ) ) )
% 0.33/0.57 => ( member_int @ Z @ ( produc4627640435386541703et_int @ C @ P4 ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % mem_case_prodI2
% 0.33/0.57 thf(fact_2808_mem__case__prodI2,axiom,
% 0.33/0.57 ! [P4: produc7773217078559923341nt_int,Z: product_prod_nat_nat,C: ( int > option6357759511663192854e_term ) > product_prod_int_int > set_Pr1261947904930325089at_nat] :
% 0.33/0.57 ( ! [A3: int > option6357759511663192854e_term,B2: product_prod_int_int] :
% 0.33/0.57 ( ( P4
% 0.33/0.57 = ( produc4305682042979456191nt_int @ A3 @ B2 ) )
% 0.33/0.57 => ( member8440522571783428010at_nat @ Z @ ( C @ A3 @ B2 ) ) )
% 0.33/0.57 => ( member8440522571783428010at_nat @ Z @ ( produc5154663461364529269at_nat @ C @ P4 ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % mem_case_prodI2
% 0.33/0.57 thf(fact_2809_mem__case__prodI2,axiom,
% 0.33/0.57 ! [P4: produc1908205239877642774nteger,Z: $o,C: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_o] :
% 0.33/0.57 ( ! [A3: produc6241069584506657477e_term > option6357759511663192854e_term,B2: produc8923325533196201883nteger] :
% 0.33/0.57 ( ( P4
% 0.33/0.57 = ( produc8603105652947943368nteger @ A3 @ B2 ) )
% 0.33/0.57 => ( member_o @ Z @ ( C @ A3 @ B2 ) ) )
% 0.33/0.57 => ( member_o @ Z @ ( produc2373554395599118147_set_o @ C @ P4 ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % mem_case_prodI2
% 0.33/0.57 thf(fact_2810_mem__case__prodI2,axiom,
% 0.33/0.57 ! [P4: produc1908205239877642774nteger,Z: nat,C: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_nat] :
% 0.33/0.57 ( ! [A3: produc6241069584506657477e_term > option6357759511663192854e_term,B2: produc8923325533196201883nteger] :
% 0.33/0.57 ( ( P4
% 0.33/0.57 = ( produc8603105652947943368nteger @ A3 @ B2 ) )
% 0.33/0.57 => ( member_nat @ Z @ ( C @ A3 @ B2 ) ) )
% 0.33/0.57 => ( member_nat @ Z @ ( produc654622801845291899et_nat @ C @ P4 ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % mem_case_prodI2
% 0.33/0.57 thf(fact_2811_mem__case__prodI2,axiom,
% 0.33/0.57 ! [P4: produc1908205239877642774nteger,Z: int,C: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_int] :
% 0.33/0.57 ( ! [A3: produc6241069584506657477e_term > option6357759511663192854e_term,B2: produc8923325533196201883nteger] :
% 0.33/0.57 ( ( P4
% 0.33/0.57 = ( produc8603105652947943368nteger @ A3 @ B2 ) )
% 0.33/0.57 => ( member_int @ Z @ ( C @ A3 @ B2 ) ) )
% 0.33/0.57 => ( member_int @ Z @ ( produc5700143819190870999et_int @ C @ P4 ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % mem_case_prodI2
% 0.33/0.57 thf(fact_2812_case__prodI2_H,axiom,
% 0.33/0.57 ! [P4: product_prod_nat_nat,C: nat > nat > product_prod_nat_nat > $o,X: product_prod_nat_nat] :
% 0.33/0.57 ( ! [A3: nat,B2: nat] :
% 0.33/0.57 ( ( ( product_Pair_nat_nat @ A3 @ B2 )
% 0.33/0.57 = P4 )
% 0.33/0.57 => ( C @ A3 @ B2 @ X ) )
% 0.33/0.57 => ( produc8739625826339149834_nat_o @ C @ P4 @ X ) ) ).
% 0.33/0.57
% 0.33/0.57 % case_prodI2'
% 0.33/0.57 thf(fact_2813_one__eq__numeral__iff,axiom,
% 0.33/0.57 ! [N2: num] :
% 0.33/0.57 ( ( one_one_nat
% 0.33/0.57 = ( numeral_numeral_nat @ N2 ) )
% 0.33/0.57 = ( one = N2 ) ) ).
% 0.33/0.57
% 0.33/0.57 % one_eq_numeral_iff
% 0.33/0.57 thf(fact_2814_one__eq__numeral__iff,axiom,
% 0.33/0.57 ! [N2: num] :
% 0.33/0.57 ( ( one_one_int
% 0.33/0.57 = ( numeral_numeral_int @ N2 ) )
% 0.33/0.57 = ( one = N2 ) ) ).
% 0.33/0.57
% 0.33/0.57 % one_eq_numeral_iff
% 0.33/0.57 thf(fact_2815_one__eq__numeral__iff,axiom,
% 0.33/0.57 ! [N2: num] :
% 0.33/0.57 ( ( one_one_Code_integer
% 0.33/0.57 = ( numera6620942414471956472nteger @ N2 ) )
% 0.33/0.57 = ( one = N2 ) ) ).
% 0.33/0.57
% 0.33/0.57 % one_eq_numeral_iff
% 0.33/0.57 thf(fact_2816_one__eq__numeral__iff,axiom,
% 0.33/0.57 ! [N2: num] :
% 0.33/0.57 ( ( one_one_rat
% 0.33/0.57 = ( numeral_numeral_rat @ N2 ) )
% 0.33/0.57 = ( one = N2 ) ) ).
% 0.33/0.57
% 0.33/0.57 % one_eq_numeral_iff
% 0.33/0.57 thf(fact_2817_one__eq__numeral__iff,axiom,
% 0.33/0.57 ! [N2: num] :
% 0.33/0.57 ( ( one_one_Code_natural
% 0.33/0.57 = ( numera5444537566228673987atural @ N2 ) )
% 0.33/0.57 = ( one = N2 ) ) ).
% 0.33/0.57
% 0.33/0.57 % one_eq_numeral_iff
% 0.33/0.57 thf(fact_2818_numeral__eq__one__iff,axiom,
% 0.33/0.57 ! [N2: num] :
% 0.33/0.57 ( ( ( numeral_numeral_nat @ N2 )
% 0.33/0.57 = one_one_nat )
% 0.33/0.57 = ( N2 = one ) ) ).
% 0.33/0.57
% 0.33/0.57 % numeral_eq_one_iff
% 0.33/0.57 thf(fact_2819_numeral__eq__one__iff,axiom,
% 0.33/0.57 ! [N2: num] :
% 0.33/0.57 ( ( ( numeral_numeral_int @ N2 )
% 0.33/0.57 = one_one_int )
% 0.33/0.57 = ( N2 = one ) ) ).
% 0.33/0.57
% 0.33/0.57 % numeral_eq_one_iff
% 0.33/0.57 thf(fact_2820_numeral__eq__one__iff,axiom,
% 0.33/0.57 ! [N2: num] :
% 0.33/0.57 ( ( ( numera6620942414471956472nteger @ N2 )
% 0.33/0.57 = one_one_Code_integer )
% 0.33/0.57 = ( N2 = one ) ) ).
% 0.33/0.57
% 0.33/0.57 % numeral_eq_one_iff
% 0.33/0.57 thf(fact_2821_numeral__eq__one__iff,axiom,
% 0.33/0.57 ! [N2: num] :
% 0.33/0.57 ( ( ( numeral_numeral_rat @ N2 )
% 0.33/0.57 = one_one_rat )
% 0.33/0.57 = ( N2 = one ) ) ).
% 0.33/0.57
% 0.33/0.57 % numeral_eq_one_iff
% 0.33/0.57 thf(fact_2822_numeral__eq__one__iff,axiom,
% 0.33/0.57 ! [N2: num] :
% 0.33/0.57 ( ( ( numera5444537566228673987atural @ N2 )
% 0.33/0.57 = one_one_Code_natural )
% 0.33/0.57 = ( N2 = one ) ) ).
% 0.33/0.57
% 0.33/0.57 % numeral_eq_one_iff
% 0.33/0.57 thf(fact_2823_of__nat__add,axiom,
% 0.33/0.57 ! [M2: nat,N2: nat] :
% 0.33/0.57 ( ( semiri681578069525770553at_rat @ ( plus_plus_nat @ M2 @ N2 ) )
% 0.33/0.57 = ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M2 ) @ ( semiri681578069525770553at_rat @ N2 ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % of_nat_add
% 0.33/0.57 thf(fact_2824_of__nat__add,axiom,
% 0.33/0.57 ! [M2: nat,N2: nat] :
% 0.33/0.57 ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ M2 @ N2 ) )
% 0.33/0.57 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % of_nat_add
% 0.33/0.57 thf(fact_2825_of__nat__add,axiom,
% 0.33/0.57 ! [M2: nat,N2: nat] :
% 0.33/0.57 ( ( semiri1316708129612266289at_nat @ ( plus_plus_nat @ M2 @ N2 ) )
% 0.33/0.57 = ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ M2 ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % of_nat_add
% 0.33/0.57 thf(fact_2826_of__nat__add,axiom,
% 0.33/0.57 ! [M2: nat,N2: nat] :
% 0.33/0.57 ( ( semiri4939895301339042750nteger @ ( plus_plus_nat @ M2 @ N2 ) )
% 0.33/0.57 = ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ M2 ) @ ( semiri4939895301339042750nteger @ N2 ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % of_nat_add
% 0.33/0.57 thf(fact_2827_of__nat__add,axiom,
% 0.33/0.57 ! [M2: nat,N2: nat] :
% 0.33/0.57 ( ( semiri3763490453095760265atural @ ( plus_plus_nat @ M2 @ N2 ) )
% 0.33/0.57 = ( plus_p4538020629002901425atural @ ( semiri3763490453095760265atural @ M2 ) @ ( semiri3763490453095760265atural @ N2 ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % of_nat_add
% 0.33/0.57 thf(fact_2828_of__nat__1,axiom,
% 0.33/0.57 ( ( semiri681578069525770553at_rat @ one_one_nat )
% 0.33/0.57 = one_one_rat ) ).
% 0.33/0.57
% 0.33/0.57 % of_nat_1
% 0.33/0.57 thf(fact_2829_of__nat__1,axiom,
% 0.33/0.57 ( ( semiri1314217659103216013at_int @ one_one_nat )
% 0.33/0.57 = one_one_int ) ).
% 0.33/0.57
% 0.33/0.57 % of_nat_1
% 0.33/0.57 thf(fact_2830_of__nat__1,axiom,
% 0.33/0.57 ( ( semiri1316708129612266289at_nat @ one_one_nat )
% 0.33/0.57 = one_one_nat ) ).
% 0.33/0.57
% 0.33/0.57 % of_nat_1
% 0.33/0.57 thf(fact_2831_of__nat__1,axiom,
% 0.33/0.57 ( ( semiri4939895301339042750nteger @ one_one_nat )
% 0.33/0.57 = one_one_Code_integer ) ).
% 0.33/0.57
% 0.33/0.57 % of_nat_1
% 0.33/0.57 thf(fact_2832_of__nat__1,axiom,
% 0.33/0.57 ( ( semiri3763490453095760265atural @ one_one_nat )
% 0.33/0.57 = one_one_Code_natural ) ).
% 0.33/0.57
% 0.33/0.57 % of_nat_1
% 0.33/0.57 thf(fact_2833_of__nat__1__eq__iff,axiom,
% 0.33/0.57 ! [N2: nat] :
% 0.33/0.57 ( ( one_one_rat
% 0.33/0.57 = ( semiri681578069525770553at_rat @ N2 ) )
% 0.33/0.57 = ( N2 = one_one_nat ) ) ).
% 0.33/0.57
% 0.33/0.57 % of_nat_1_eq_iff
% 0.33/0.57 thf(fact_2834_of__nat__1__eq__iff,axiom,
% 0.33/0.57 ! [N2: nat] :
% 0.33/0.57 ( ( one_one_int
% 0.33/0.57 = ( semiri1314217659103216013at_int @ N2 ) )
% 0.33/0.57 = ( N2 = one_one_nat ) ) ).
% 0.33/0.57
% 0.33/0.57 % of_nat_1_eq_iff
% 0.33/0.57 thf(fact_2835_of__nat__1__eq__iff,axiom,
% 0.33/0.57 ! [N2: nat] :
% 0.33/0.57 ( ( one_one_nat
% 0.33/0.57 = ( semiri1316708129612266289at_nat @ N2 ) )
% 0.33/0.57 = ( N2 = one_one_nat ) ) ).
% 0.33/0.57
% 0.33/0.57 % of_nat_1_eq_iff
% 0.33/0.57 thf(fact_2836_of__nat__1__eq__iff,axiom,
% 0.33/0.57 ! [N2: nat] :
% 0.33/0.57 ( ( one_one_Code_integer
% 0.33/0.57 = ( semiri4939895301339042750nteger @ N2 ) )
% 0.33/0.57 = ( N2 = one_one_nat ) ) ).
% 0.33/0.57
% 0.33/0.57 % of_nat_1_eq_iff
% 0.33/0.57 thf(fact_2837_of__nat__1__eq__iff,axiom,
% 0.33/0.57 ! [N2: nat] :
% 0.33/0.57 ( ( one_one_Code_natural
% 0.33/0.57 = ( semiri3763490453095760265atural @ N2 ) )
% 0.33/0.57 = ( N2 = one_one_nat ) ) ).
% 0.33/0.57
% 0.33/0.57 % of_nat_1_eq_iff
% 0.33/0.57 thf(fact_2838_of__nat__eq__1__iff,axiom,
% 0.33/0.57 ! [N2: nat] :
% 0.33/0.57 ( ( ( semiri681578069525770553at_rat @ N2 )
% 0.33/0.57 = one_one_rat )
% 0.33/0.57 = ( N2 = one_one_nat ) ) ).
% 0.33/0.57
% 0.33/0.57 % of_nat_eq_1_iff
% 0.33/0.57 thf(fact_2839_of__nat__eq__1__iff,axiom,
% 0.33/0.57 ! [N2: nat] :
% 0.33/0.57 ( ( ( semiri1314217659103216013at_int @ N2 )
% 0.33/0.57 = one_one_int )
% 0.33/0.57 = ( N2 = one_one_nat ) ) ).
% 0.33/0.57
% 0.33/0.57 % of_nat_eq_1_iff
% 0.33/0.57 thf(fact_2840_of__nat__eq__1__iff,axiom,
% 0.33/0.57 ! [N2: nat] :
% 0.33/0.57 ( ( ( semiri1316708129612266289at_nat @ N2 )
% 0.33/0.57 = one_one_nat )
% 0.33/0.57 = ( N2 = one_one_nat ) ) ).
% 0.33/0.57
% 0.33/0.57 % of_nat_eq_1_iff
% 0.33/0.57 thf(fact_2841_of__nat__eq__1__iff,axiom,
% 0.33/0.57 ! [N2: nat] :
% 0.33/0.57 ( ( ( semiri4939895301339042750nteger @ N2 )
% 0.33/0.57 = one_one_Code_integer )
% 0.33/0.57 = ( N2 = one_one_nat ) ) ).
% 0.33/0.57
% 0.33/0.57 % of_nat_eq_1_iff
% 0.33/0.57 thf(fact_2842_of__nat__eq__1__iff,axiom,
% 0.33/0.57 ! [N2: nat] :
% 0.33/0.57 ( ( ( semiri3763490453095760265atural @ N2 )
% 0.33/0.57 = one_one_Code_natural )
% 0.33/0.57 = ( N2 = one_one_nat ) ) ).
% 0.33/0.57
% 0.33/0.57 % of_nat_eq_1_iff
% 0.33/0.57 thf(fact_2843_semiring__norm_I2_J,axiom,
% 0.33/0.57 ( ( plus_plus_num @ one @ one )
% 0.33/0.57 = ( bit0 @ one ) ) ).
% 0.33/0.57
% 0.33/0.57 % semiring_norm(2)
% 0.33/0.57 thf(fact_2844_numeral__le__one__iff,axiom,
% 0.33/0.57 ! [N2: num] :
% 0.33/0.57 ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ N2 ) @ one_one_Code_integer )
% 0.33/0.57 = ( ord_less_eq_num @ N2 @ one ) ) ).
% 0.33/0.57
% 0.33/0.57 % numeral_le_one_iff
% 0.33/0.57 thf(fact_2845_numeral__le__one__iff,axiom,
% 0.33/0.57 ! [N2: num] :
% 0.33/0.57 ( ( ord_le1926595141338095240atural @ ( numera5444537566228673987atural @ N2 ) @ one_one_Code_natural )
% 0.33/0.57 = ( ord_less_eq_num @ N2 @ one ) ) ).
% 0.33/0.57
% 0.33/0.57 % numeral_le_one_iff
% 0.33/0.57 thf(fact_2846_numeral__le__one__iff,axiom,
% 0.33/0.57 ! [N2: num] :
% 0.33/0.57 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ N2 ) @ one_one_rat )
% 0.33/0.57 = ( ord_less_eq_num @ N2 @ one ) ) ).
% 0.33/0.57
% 0.33/0.57 % numeral_le_one_iff
% 0.33/0.57 thf(fact_2847_numeral__le__one__iff,axiom,
% 0.33/0.57 ! [N2: num] :
% 0.33/0.57 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ N2 ) @ one_one_nat )
% 0.33/0.57 = ( ord_less_eq_num @ N2 @ one ) ) ).
% 0.33/0.57
% 0.33/0.57 % numeral_le_one_iff
% 0.33/0.57 thf(fact_2848_numeral__le__one__iff,axiom,
% 0.33/0.57 ! [N2: num] :
% 0.33/0.57 ( ( ord_less_eq_int @ ( numeral_numeral_int @ N2 ) @ one_one_int )
% 0.33/0.57 = ( ord_less_eq_num @ N2 @ one ) ) ).
% 0.33/0.57
% 0.33/0.57 % numeral_le_one_iff
% 0.33/0.57 thf(fact_2849_one__less__numeral__iff,axiom,
% 0.33/0.57 ! [N2: num] :
% 0.33/0.57 ( ( ord_less_nat @ one_one_nat @ ( numeral_numeral_nat @ N2 ) )
% 0.33/0.57 = ( ord_less_num @ one @ N2 ) ) ).
% 0.33/0.57
% 0.33/0.57 % one_less_numeral_iff
% 0.33/0.57 thf(fact_2850_one__less__numeral__iff,axiom,
% 0.33/0.57 ! [N2: num] :
% 0.33/0.57 ( ( ord_less_int @ one_one_int @ ( numeral_numeral_int @ N2 ) )
% 0.33/0.57 = ( ord_less_num @ one @ N2 ) ) ).
% 0.33/0.57
% 0.33/0.57 % one_less_numeral_iff
% 0.33/0.57 thf(fact_2851_one__less__numeral__iff,axiom,
% 0.33/0.57 ! [N2: num] :
% 0.33/0.57 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ N2 ) )
% 0.33/0.57 = ( ord_less_num @ one @ N2 ) ) ).
% 0.33/0.57
% 0.33/0.57 % one_less_numeral_iff
% 0.33/0.57 thf(fact_2852_one__less__numeral__iff,axiom,
% 0.33/0.57 ! [N2: num] :
% 0.33/0.57 ( ( ord_less_rat @ one_one_rat @ ( numeral_numeral_rat @ N2 ) )
% 0.33/0.57 = ( ord_less_num @ one @ N2 ) ) ).
% 0.33/0.57
% 0.33/0.57 % one_less_numeral_iff
% 0.33/0.57 thf(fact_2853_one__less__numeral__iff,axiom,
% 0.33/0.57 ! [N2: num] :
% 0.33/0.57 ( ( ord_le5570908160329646204atural @ one_one_Code_natural @ ( numera5444537566228673987atural @ N2 ) )
% 0.33/0.57 = ( ord_less_num @ one @ N2 ) ) ).
% 0.33/0.57
% 0.33/0.57 % one_less_numeral_iff
% 0.33/0.57 thf(fact_2854_numeral__eq__neg__one__iff,axiom,
% 0.33/0.57 ! [N2: num] :
% 0.33/0.57 ( ( ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) )
% 0.33/0.57 = ( uminus_uminus_int @ one_one_int ) )
% 0.33/0.57 = ( N2 = one ) ) ).
% 0.33/0.57
% 0.33/0.57 % numeral_eq_neg_one_iff
% 0.33/0.57 thf(fact_2855_numeral__eq__neg__one__iff,axiom,
% 0.33/0.57 ! [N2: num] :
% 0.33/0.57 ( ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) )
% 0.33/0.57 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.33/0.57 = ( N2 = one ) ) ).
% 0.33/0.57
% 0.33/0.57 % numeral_eq_neg_one_iff
% 0.33/0.57 thf(fact_2856_numeral__eq__neg__one__iff,axiom,
% 0.33/0.57 ! [N2: num] :
% 0.33/0.57 ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) )
% 0.33/0.57 = ( uminus_uminus_rat @ one_one_rat ) )
% 0.33/0.57 = ( N2 = one ) ) ).
% 0.33/0.57
% 0.33/0.57 % numeral_eq_neg_one_iff
% 0.33/0.57 thf(fact_2857_neg__one__eq__numeral__iff,axiom,
% 0.33/0.57 ! [N2: num] :
% 0.33/0.57 ( ( ( uminus_uminus_int @ one_one_int )
% 0.33/0.57 = ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 0.33/0.57 = ( N2 = one ) ) ).
% 0.33/0.57
% 0.33/0.57 % neg_one_eq_numeral_iff
% 0.33/0.57 thf(fact_2858_neg__one__eq__numeral__iff,axiom,
% 0.33/0.57 ! [N2: num] :
% 0.33/0.57 ( ( ( uminus1351360451143612070nteger @ one_one_Code_integer )
% 0.33/0.57 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 0.33/0.57 = ( N2 = one ) ) ).
% 0.33/0.57
% 0.33/0.57 % neg_one_eq_numeral_iff
% 0.33/0.57 thf(fact_2859_neg__one__eq__numeral__iff,axiom,
% 0.33/0.57 ! [N2: num] :
% 0.33/0.57 ( ( ( uminus_uminus_rat @ one_one_rat )
% 0.33/0.57 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 0.33/0.57 = ( N2 = one ) ) ).
% 0.33/0.57
% 0.33/0.57 % neg_one_eq_numeral_iff
% 0.33/0.57 thf(fact_2860_of__nat__Suc,axiom,
% 0.33/0.57 ! [M2: nat] :
% 0.33/0.57 ( ( semiri681578069525770553at_rat @ ( suc @ M2 ) )
% 0.33/0.57 = ( plus_plus_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ M2 ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % of_nat_Suc
% 0.33/0.57 thf(fact_2861_of__nat__Suc,axiom,
% 0.33/0.57 ! [M2: nat] :
% 0.33/0.57 ( ( semiri1314217659103216013at_int @ ( suc @ M2 ) )
% 0.33/0.57 = ( plus_plus_int @ one_one_int @ ( semiri1314217659103216013at_int @ M2 ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % of_nat_Suc
% 0.33/0.57 thf(fact_2862_of__nat__Suc,axiom,
% 0.33/0.57 ! [M2: nat] :
% 0.33/0.57 ( ( semiri1316708129612266289at_nat @ ( suc @ M2 ) )
% 0.33/0.57 = ( plus_plus_nat @ one_one_nat @ ( semiri1316708129612266289at_nat @ M2 ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % of_nat_Suc
% 0.33/0.57 thf(fact_2863_of__nat__Suc,axiom,
% 0.33/0.57 ! [M2: nat] :
% 0.33/0.57 ( ( semiri4939895301339042750nteger @ ( suc @ M2 ) )
% 0.33/0.57 = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( semiri4939895301339042750nteger @ M2 ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % of_nat_Suc
% 0.33/0.57 thf(fact_2864_of__nat__Suc,axiom,
% 0.33/0.57 ! [M2: nat] :
% 0.33/0.57 ( ( semiri3763490453095760265atural @ ( suc @ M2 ) )
% 0.33/0.57 = ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( semiri3763490453095760265atural @ M2 ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % of_nat_Suc
% 0.33/0.57 thf(fact_2865_Suc__numeral,axiom,
% 0.33/0.57 ! [N2: num] :
% 0.33/0.57 ( ( suc @ ( numeral_numeral_nat @ N2 ) )
% 0.33/0.57 = ( numeral_numeral_nat @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % Suc_numeral
% 0.33/0.57 thf(fact_2866_not__neg__one__le__neg__numeral__iff,axiom,
% 0.33/0.57 ! [M2: num] :
% 0.33/0.57 ( ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) ) )
% 0.33/0.57 = ( M2 != one ) ) ).
% 0.33/0.57
% 0.33/0.57 % not_neg_one_le_neg_numeral_iff
% 0.33/0.57 thf(fact_2867_not__neg__one__le__neg__numeral__iff,axiom,
% 0.33/0.57 ! [M2: num] :
% 0.33/0.57 ( ( ~ ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) ) )
% 0.33/0.57 = ( M2 != one ) ) ).
% 0.33/0.57
% 0.33/0.57 % not_neg_one_le_neg_numeral_iff
% 0.33/0.57 thf(fact_2868_not__neg__one__le__neg__numeral__iff,axiom,
% 0.33/0.57 ! [M2: num] :
% 0.33/0.57 ( ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) ) )
% 0.33/0.57 = ( M2 != one ) ) ).
% 0.33/0.57
% 0.33/0.57 % not_neg_one_le_neg_numeral_iff
% 0.33/0.57 thf(fact_2869_one__add__one,axiom,
% 0.33/0.57 ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 0.33/0.57 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % one_add_one
% 0.33/0.57 thf(fact_2870_one__add__one,axiom,
% 0.33/0.57 ( ( plus_plus_int @ one_one_int @ one_one_int )
% 0.33/0.57 = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % one_add_one
% 0.33/0.57 thf(fact_2871_one__add__one,axiom,
% 0.33/0.57 ( ( plus_p5714425477246183910nteger @ one_one_Code_integer @ one_one_Code_integer )
% 0.33/0.57 = ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % one_add_one
% 0.33/0.57 thf(fact_2872_one__add__one,axiom,
% 0.33/0.57 ( ( plus_plus_rat @ one_one_rat @ one_one_rat )
% 0.33/0.57 = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % one_add_one
% 0.33/0.57 thf(fact_2873_one__add__one,axiom,
% 0.33/0.57 ( ( plus_p4538020629002901425atural @ one_one_Code_natural @ one_one_Code_natural )
% 0.33/0.57 = ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % one_add_one
% 0.33/0.57 thf(fact_2874_neg__numeral__less__neg__one__iff,axiom,
% 0.33/0.57 ! [M2: num] :
% 0.33/0.57 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( uminus_uminus_int @ one_one_int ) )
% 0.33/0.57 = ( M2 != one ) ) ).
% 0.33/0.57
% 0.33/0.57 % neg_numeral_less_neg_one_iff
% 0.33/0.57 thf(fact_2875_neg__numeral__less__neg__one__iff,axiom,
% 0.33/0.57 ! [M2: num] :
% 0.33/0.57 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.33/0.57 = ( M2 != one ) ) ).
% 0.33/0.57
% 0.33/0.57 % neg_numeral_less_neg_one_iff
% 0.33/0.57 thf(fact_2876_neg__numeral__less__neg__one__iff,axiom,
% 0.33/0.57 ! [M2: num] :
% 0.33/0.57 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.33/0.57 = ( M2 != one ) ) ).
% 0.33/0.57
% 0.33/0.57 % neg_numeral_less_neg_one_iff
% 0.33/0.57 thf(fact_2877_bits__one__mod__two__eq__one,axiom,
% 0.33/0.57 ( ( modulo_modulo_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.33/0.57 = one_one_int ) ).
% 0.33/0.57
% 0.33/0.57 % bits_one_mod_two_eq_one
% 0.33/0.57 thf(fact_2878_bits__one__mod__two__eq__one,axiom,
% 0.33/0.57 ( ( modulo_modulo_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.33/0.57 = one_one_nat ) ).
% 0.33/0.57
% 0.33/0.57 % bits_one_mod_two_eq_one
% 0.33/0.57 thf(fact_2879_bits__one__mod__two__eq__one,axiom,
% 0.33/0.57 ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.33/0.57 = one_one_Code_integer ) ).
% 0.33/0.57
% 0.33/0.57 % bits_one_mod_two_eq_one
% 0.33/0.57 thf(fact_2880_bits__one__mod__two__eq__one,axiom,
% 0.33/0.57 ( ( modulo8411746178871703098atural @ one_one_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 0.33/0.57 = one_one_Code_natural ) ).
% 0.33/0.57
% 0.33/0.57 % bits_one_mod_two_eq_one
% 0.33/0.57 thf(fact_2881_one__mod__two__eq__one,axiom,
% 0.33/0.57 ( ( modulo_modulo_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.33/0.57 = one_one_int ) ).
% 0.33/0.57
% 0.33/0.57 % one_mod_two_eq_one
% 0.33/0.57 thf(fact_2882_one__mod__two__eq__one,axiom,
% 0.33/0.57 ( ( modulo_modulo_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.33/0.57 = one_one_nat ) ).
% 0.33/0.57
% 0.33/0.57 % one_mod_two_eq_one
% 0.33/0.57 thf(fact_2883_one__mod__two__eq__one,axiom,
% 0.33/0.57 ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.33/0.57 = one_one_Code_integer ) ).
% 0.33/0.57
% 0.33/0.57 % one_mod_two_eq_one
% 0.33/0.57 thf(fact_2884_one__mod__two__eq__one,axiom,
% 0.33/0.57 ( ( modulo8411746178871703098atural @ one_one_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 0.33/0.57 = one_one_Code_natural ) ).
% 0.33/0.57
% 0.33/0.57 % one_mod_two_eq_one
% 0.33/0.57 thf(fact_2885_add__2__eq__Suc,axiom,
% 0.33/0.57 ! [N2: nat] :
% 0.33/0.57 ( ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.33/0.57 = ( suc @ ( suc @ N2 ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % add_2_eq_Suc
% 0.33/0.57 thf(fact_2886_add__2__eq__Suc_H,axiom,
% 0.33/0.57 ! [N2: nat] :
% 0.33/0.57 ( ( plus_plus_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.33/0.57 = ( suc @ ( suc @ N2 ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % add_2_eq_Suc'
% 0.33/0.57 thf(fact_2887_Suc__1,axiom,
% 0.33/0.57 ( ( suc @ one_one_nat )
% 0.33/0.57 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % Suc_1
% 0.33/0.57 thf(fact_2888_numeral__plus__one,axiom,
% 0.33/0.57 ! [N2: num] :
% 0.33/0.57 ( ( plus_plus_nat @ ( numeral_numeral_nat @ N2 ) @ one_one_nat )
% 0.33/0.57 = ( numeral_numeral_nat @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % numeral_plus_one
% 0.33/0.57 thf(fact_2889_numeral__plus__one,axiom,
% 0.33/0.57 ! [N2: num] :
% 0.33/0.57 ( ( plus_plus_int @ ( numeral_numeral_int @ N2 ) @ one_one_int )
% 0.33/0.57 = ( numeral_numeral_int @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % numeral_plus_one
% 0.33/0.57 thf(fact_2890_numeral__plus__one,axiom,
% 0.33/0.57 ! [N2: num] :
% 0.33/0.57 ( ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ N2 ) @ one_one_Code_integer )
% 0.33/0.57 = ( numera6620942414471956472nteger @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % numeral_plus_one
% 0.33/0.57 thf(fact_2891_numeral__plus__one,axiom,
% 0.33/0.57 ! [N2: num] :
% 0.33/0.57 ( ( plus_plus_rat @ ( numeral_numeral_rat @ N2 ) @ one_one_rat )
% 0.33/0.57 = ( numeral_numeral_rat @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % numeral_plus_one
% 0.33/0.57 thf(fact_2892_numeral__plus__one,axiom,
% 0.33/0.57 ! [N2: num] :
% 0.33/0.57 ( ( plus_p4538020629002901425atural @ ( numera5444537566228673987atural @ N2 ) @ one_one_Code_natural )
% 0.33/0.57 = ( numera5444537566228673987atural @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % numeral_plus_one
% 0.33/0.57 thf(fact_2893_one__plus__numeral,axiom,
% 0.33/0.57 ! [N2: num] :
% 0.33/0.57 ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ N2 ) )
% 0.33/0.57 = ( numeral_numeral_nat @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % one_plus_numeral
% 0.33/0.57 thf(fact_2894_one__plus__numeral,axiom,
% 0.33/0.57 ! [N2: num] :
% 0.33/0.57 ( ( plus_plus_int @ one_one_int @ ( numeral_numeral_int @ N2 ) )
% 0.33/0.57 = ( numeral_numeral_int @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % one_plus_numeral
% 0.33/0.57 thf(fact_2895_one__plus__numeral,axiom,
% 0.33/0.57 ! [N2: num] :
% 0.33/0.57 ( ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ N2 ) )
% 0.33/0.57 = ( numera6620942414471956472nteger @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % one_plus_numeral
% 0.33/0.57 thf(fact_2896_one__plus__numeral,axiom,
% 0.33/0.57 ! [N2: num] :
% 0.33/0.57 ( ( plus_plus_rat @ one_one_rat @ ( numeral_numeral_rat @ N2 ) )
% 0.33/0.57 = ( numeral_numeral_rat @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % one_plus_numeral
% 0.33/0.57 thf(fact_2897_one__plus__numeral,axiom,
% 0.33/0.57 ! [N2: num] :
% 0.33/0.57 ( ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( numera5444537566228673987atural @ N2 ) )
% 0.33/0.57 = ( numera5444537566228673987atural @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % one_plus_numeral
% 0.33/0.57 thf(fact_2898_add__self__div__2,axiom,
% 0.33/0.57 ! [M2: nat] :
% 0.33/0.57 ( ( divide_divide_nat @ ( plus_plus_nat @ M2 @ M2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.33/0.57 = M2 ) ).
% 0.33/0.57
% 0.33/0.57 % add_self_div_2
% 0.33/0.57 thf(fact_2899_bits__1__div__2,axiom,
% 0.33/0.57 ( ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.33/0.57 = zero_zero_int ) ).
% 0.33/0.57
% 0.33/0.57 % bits_1_div_2
% 0.33/0.57 thf(fact_2900_bits__1__div__2,axiom,
% 0.33/0.57 ( ( divide_divide_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.33/0.57 = zero_zero_nat ) ).
% 0.33/0.57
% 0.33/0.57 % bits_1_div_2
% 0.33/0.57 thf(fact_2901_bits__1__div__2,axiom,
% 0.33/0.57 ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.33/0.57 = zero_z3403309356797280102nteger ) ).
% 0.33/0.57
% 0.33/0.57 % bits_1_div_2
% 0.33/0.57 thf(fact_2902_bits__1__div__2,axiom,
% 0.33/0.57 ( ( divide5121882707175180666atural @ one_one_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 0.33/0.57 = zero_z2226904508553997617atural ) ).
% 0.33/0.57
% 0.33/0.57 % bits_1_div_2
% 0.33/0.57 thf(fact_2903_one__div__two__eq__zero,axiom,
% 0.33/0.57 ( ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.33/0.57 = zero_zero_int ) ).
% 0.33/0.57
% 0.33/0.57 % one_div_two_eq_zero
% 0.33/0.57 thf(fact_2904_one__div__two__eq__zero,axiom,
% 0.33/0.57 ( ( divide_divide_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.33/0.57 = zero_zero_nat ) ).
% 0.33/0.57
% 0.33/0.57 % one_div_two_eq_zero
% 0.33/0.57 thf(fact_2905_one__div__two__eq__zero,axiom,
% 0.33/0.57 ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.33/0.57 = zero_z3403309356797280102nteger ) ).
% 0.33/0.57
% 0.33/0.57 % one_div_two_eq_zero
% 0.33/0.57 thf(fact_2906_one__div__two__eq__zero,axiom,
% 0.33/0.57 ( ( divide5121882707175180666atural @ one_one_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 0.33/0.57 = zero_z2226904508553997617atural ) ).
% 0.33/0.57
% 0.33/0.57 % one_div_two_eq_zero
% 0.33/0.57 thf(fact_2907_add__neg__numeral__special_I9_J,axiom,
% 0.33/0.57 ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ one_one_int ) )
% 0.33/0.57 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % add_neg_numeral_special(9)
% 0.33/0.57 thf(fact_2908_add__neg__numeral__special_I9_J,axiom,
% 0.33/0.57 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.33/0.57 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % add_neg_numeral_special(9)
% 0.33/0.57 thf(fact_2909_add__neg__numeral__special_I9_J,axiom,
% 0.33/0.57 ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.33/0.57 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % add_neg_numeral_special(9)
% 0.33/0.57 thf(fact_2910_diff__numeral__special_I11_J,axiom,
% 0.33/0.57 ( ( minus_minus_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) )
% 0.33/0.57 = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % diff_numeral_special(11)
% 0.33/0.57 thf(fact_2911_diff__numeral__special_I11_J,axiom,
% 0.33/0.57 ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.33/0.57 = ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % diff_numeral_special(11)
% 0.33/0.57 thf(fact_2912_diff__numeral__special_I11_J,axiom,
% 0.33/0.57 ( ( minus_minus_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.33/0.57 = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % diff_numeral_special(11)
% 0.33/0.57 thf(fact_2913_diff__numeral__special_I10_J,axiom,
% 0.33/0.57 ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 0.33/0.57 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % diff_numeral_special(10)
% 0.33/0.57 thf(fact_2914_diff__numeral__special_I10_J,axiom,
% 0.33/0.57 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer )
% 0.33/0.57 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % diff_numeral_special(10)
% 0.33/0.57 thf(fact_2915_diff__numeral__special_I10_J,axiom,
% 0.33/0.57 ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat )
% 0.33/0.57 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % diff_numeral_special(10)
% 0.33/0.57 thf(fact_2916_not__mod__2__eq__0__eq__1,axiom,
% 0.33/0.57 ! [A: int] :
% 0.33/0.57 ( ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.33/0.57 != zero_zero_int )
% 0.33/0.57 = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.33/0.57 = one_one_int ) ) ).
% 0.33/0.57
% 0.33/0.57 % not_mod_2_eq_0_eq_1
% 0.33/0.57 thf(fact_2917_not__mod__2__eq__0__eq__1,axiom,
% 0.33/0.57 ! [A: nat] :
% 0.33/0.57 ( ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.33/0.57 != zero_zero_nat )
% 0.33/0.57 = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.33/0.57 = one_one_nat ) ) ).
% 0.33/0.57
% 0.33/0.57 % not_mod_2_eq_0_eq_1
% 0.33/0.57 thf(fact_2918_not__mod__2__eq__0__eq__1,axiom,
% 0.33/0.57 ! [A: code_integer] :
% 0.33/0.57 ( ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.33/0.57 != zero_z3403309356797280102nteger )
% 0.33/0.57 = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.33/0.57 = one_one_Code_integer ) ) ).
% 0.33/0.57
% 0.33/0.57 % not_mod_2_eq_0_eq_1
% 0.33/0.57 thf(fact_2919_not__mod__2__eq__0__eq__1,axiom,
% 0.33/0.57 ! [A: code_natural] :
% 0.33/0.57 ( ( ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 0.33/0.57 != zero_z2226904508553997617atural )
% 0.33/0.57 = ( ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 0.33/0.57 = one_one_Code_natural ) ) ).
% 0.33/0.57
% 0.33/0.57 % not_mod_2_eq_0_eq_1
% 0.33/0.57 thf(fact_2920_not__mod__2__eq__1__eq__0,axiom,
% 0.33/0.57 ! [A: int] :
% 0.33/0.57 ( ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.33/0.57 != one_one_int )
% 0.33/0.57 = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.33/0.57 = zero_zero_int ) ) ).
% 0.33/0.57
% 0.33/0.57 % not_mod_2_eq_1_eq_0
% 0.33/0.57 thf(fact_2921_not__mod__2__eq__1__eq__0,axiom,
% 0.33/0.57 ! [A: nat] :
% 0.33/0.57 ( ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.33/0.57 != one_one_nat )
% 0.33/0.57 = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.33/0.57 = zero_zero_nat ) ) ).
% 0.33/0.57
% 0.33/0.57 % not_mod_2_eq_1_eq_0
% 0.33/0.57 thf(fact_2922_not__mod__2__eq__1__eq__0,axiom,
% 0.33/0.57 ! [A: code_integer] :
% 0.33/0.57 ( ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.33/0.57 != one_one_Code_integer )
% 0.33/0.57 = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.33/0.57 = zero_z3403309356797280102nteger ) ) ).
% 0.33/0.57
% 0.33/0.57 % not_mod_2_eq_1_eq_0
% 0.33/0.57 thf(fact_2923_not__mod__2__eq__1__eq__0,axiom,
% 0.33/0.57 ! [A: code_natural] :
% 0.33/0.57 ( ( ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 0.33/0.57 != one_one_Code_natural )
% 0.33/0.57 = ( ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 0.33/0.57 = zero_z2226904508553997617atural ) ) ).
% 0.33/0.57
% 0.33/0.57 % not_mod_2_eq_1_eq_0
% 0.33/0.57 thf(fact_2924_minus__1__div__2__eq,axiom,
% 0.33/0.57 ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.33/0.57 = ( uminus_uminus_int @ one_one_int ) ) ).
% 0.33/0.57
% 0.33/0.57 % minus_1_div_2_eq
% 0.33/0.57 thf(fact_2925_minus__1__div__2__eq,axiom,
% 0.33/0.57 ( ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.33/0.57 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.33/0.57
% 0.33/0.57 % minus_1_div_2_eq
% 0.33/0.57 thf(fact_2926_bits__minus__1__mod__2__eq,axiom,
% 0.33/0.57 ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.33/0.57 = one_one_int ) ).
% 0.33/0.57
% 0.33/0.57 % bits_minus_1_mod_2_eq
% 0.33/0.57 thf(fact_2927_bits__minus__1__mod__2__eq,axiom,
% 0.33/0.57 ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.33/0.57 = one_one_Code_integer ) ).
% 0.33/0.57
% 0.33/0.57 % bits_minus_1_mod_2_eq
% 0.33/0.57 thf(fact_2928_minus__1__mod__2__eq,axiom,
% 0.33/0.57 ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.33/0.57 = one_one_int ) ).
% 0.33/0.57
% 0.33/0.57 % minus_1_mod_2_eq
% 0.33/0.57 thf(fact_2929_minus__1__mod__2__eq,axiom,
% 0.33/0.57 ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.33/0.57 = one_one_Code_integer ) ).
% 0.33/0.57
% 0.33/0.57 % minus_1_mod_2_eq
% 0.33/0.57 thf(fact_2930_diff__numeral__special_I3_J,axiom,
% 0.33/0.57 ! [N2: num] :
% 0.33/0.57 ( ( minus_minus_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 0.33/0.57 = ( numeral_numeral_int @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % diff_numeral_special(3)
% 0.33/0.57 thf(fact_2931_diff__numeral__special_I3_J,axiom,
% 0.33/0.57 ! [N2: num] :
% 0.33/0.57 ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 0.33/0.57 = ( numera6620942414471956472nteger @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % diff_numeral_special(3)
% 0.33/0.57 thf(fact_2932_diff__numeral__special_I3_J,axiom,
% 0.33/0.57 ! [N2: num] :
% 0.33/0.57 ( ( minus_minus_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 0.33/0.57 = ( numeral_numeral_rat @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % diff_numeral_special(3)
% 0.33/0.57 thf(fact_2933_diff__numeral__special_I4_J,axiom,
% 0.33/0.57 ! [M2: num] :
% 0.33/0.57 ( ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ one_one_int )
% 0.33/0.57 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ M2 @ one ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % diff_numeral_special(4)
% 0.33/0.57 thf(fact_2934_diff__numeral__special_I4_J,axiom,
% 0.33/0.57 ! [M2: num] :
% 0.33/0.57 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ one_one_Code_integer )
% 0.33/0.57 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ M2 @ one ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % diff_numeral_special(4)
% 0.33/0.57 thf(fact_2935_diff__numeral__special_I4_J,axiom,
% 0.33/0.57 ! [M2: num] :
% 0.33/0.57 ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ one_one_rat )
% 0.33/0.57 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ M2 @ one ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % diff_numeral_special(4)
% 0.33/0.57 thf(fact_2936_add__self__mod__2,axiom,
% 0.33/0.57 ! [M2: nat] :
% 0.33/0.57 ( ( modulo_modulo_nat @ ( plus_plus_nat @ M2 @ M2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.33/0.57 = zero_zero_nat ) ).
% 0.33/0.57
% 0.33/0.57 % add_self_mod_2
% 0.33/0.57 thf(fact_2937_power__minus1__even,axiom,
% 0.33/0.57 ! [N2: nat] :
% 0.33/0.57 ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 0.33/0.57 = one_one_int ) ).
% 0.33/0.57
% 0.33/0.57 % power_minus1_even
% 0.33/0.57 thf(fact_2938_power__minus1__even,axiom,
% 0.33/0.57 ! [N2: nat] :
% 0.33/0.57 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 0.33/0.57 = one_one_Code_integer ) ).
% 0.33/0.57
% 0.33/0.57 % power_minus1_even
% 0.33/0.57 thf(fact_2939_power__minus1__even,axiom,
% 0.33/0.57 ! [N2: nat] :
% 0.33/0.57 ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 0.33/0.57 = one_one_rat ) ).
% 0.33/0.57
% 0.33/0.57 % power_minus1_even
% 0.33/0.57 thf(fact_2940_mod2__gr__0,axiom,
% 0.33/0.57 ! [M2: nat] :
% 0.33/0.57 ( ( ord_less_nat @ zero_zero_nat @ ( modulo_modulo_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.33/0.57 = ( ( modulo_modulo_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.33/0.57 = one_one_nat ) ) ).
% 0.33/0.57
% 0.33/0.57 % mod2_gr_0
% 0.33/0.57 thf(fact_2941_lex__prod__def,axiom,
% 0.33/0.57 ( lex_pr8000699672184251119at_nat
% 0.33/0.57 = ( ^ [Ra: set_Pr4329608150637261639at_nat,Rb: set_Pr4329608150637261639at_nat] :
% 0.33/0.57 ( collec223960383693904210at_nat
% 0.33/0.57 @ ( produc1561160019221259564_nat_o
% 0.33/0.57 @ ( produc1971064617671185730_nat_o
% 0.33/0.57 @ ^ [A5: set_Pr1261947904930325089at_nat,B4: set_Pr1261947904930325089at_nat] :
% 0.33/0.57 ( produc410239310623530412_nat_o
% 0.33/0.57 @ ^ [A6: set_Pr1261947904930325089at_nat,B6: set_Pr1261947904930325089at_nat] :
% 0.33/0.57 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A5 @ A6 ) @ Ra )
% 0.33/0.57 | ( ( A5 = A6 )
% 0.33/0.57 & ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ B4 @ B6 ) @ Rb ) ) ) ) ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % lex_prod_def
% 0.33/0.57 thf(fact_2942_lex__prod__def,axiom,
% 0.33/0.57 ( lex_pr1951919194703979714at_nat
% 0.33/0.57 = ( ^ [Ra: set_Pr4329608150637261639at_nat,Rb: set_Pr1261947904930325089at_nat] :
% 0.33/0.57 ( collec1461227866750739596at_nat
% 0.33/0.57 @ ( produc8701595406162815018_nat_o
% 0.33/0.57 @ ( produc7110675705651593384_nat_o
% 0.33/0.57 @ ^ [A5: set_Pr1261947904930325089at_nat,B4: nat] :
% 0.33/0.57 ( produc3595121349294487249_nat_o
% 0.33/0.57 @ ^ [A6: set_Pr1261947904930325089at_nat,B6: nat] :
% 0.33/0.57 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A5 @ A6 ) @ Ra )
% 0.33/0.57 | ( ( A5 = A6 )
% 0.33/0.57 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ B4 @ B6 ) @ Rb ) ) ) ) ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % lex_prod_def
% 0.33/0.57 thf(fact_2943_lex__prod__def,axiom,
% 0.33/0.57 ( lex_pr4265550801952275104at_nat
% 0.33/0.57 = ( ^ [Ra: set_Pr1261947904930325089at_nat,Rb: set_Pr4329608150637261639at_nat] :
% 0.33/0.57 ( collec2088441199205367000at_nat
% 0.33/0.57 @ ( produc7830147906768200158_nat_o
% 0.33/0.57 @ ( produc1908958340173245860_nat_o
% 0.33/0.57 @ ^ [A5: nat,B4: set_Pr1261947904930325089at_nat] :
% 0.33/0.57 ( produc7997411485876045171_nat_o
% 0.33/0.57 @ ^ [A6: nat,B6: set_Pr1261947904930325089at_nat] :
% 0.33/0.57 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A5 @ A6 ) @ Ra )
% 0.33/0.57 | ( ( A5 = A6 )
% 0.33/0.57 & ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ B4 @ B6 ) @ Rb ) ) ) ) ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % lex_prod_def
% 0.33/0.57 thf(fact_2944_lex__prod__def,axiom,
% 0.33/0.57 ( lex_prod_nat_nat
% 0.33/0.57 = ( ^ [Ra: set_Pr1261947904930325089at_nat,Rb: set_Pr1261947904930325089at_nat] :
% 0.33/0.57 ( collec7088162979684241874at_nat
% 0.33/0.57 @ ( produc6590410687421337004_nat_o
% 0.33/0.57 @ ( produc8739625826339149834_nat_o
% 0.33/0.57 @ ^ [A5: nat,B4: nat] :
% 0.33/0.57 ( produc6081775807080527818_nat_o
% 0.33/0.57 @ ^ [A6: nat,B6: nat] :
% 0.33/0.57 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A5 @ A6 ) @ Ra )
% 0.33/0.57 | ( ( A5 = A6 )
% 0.33/0.57 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ B4 @ B6 ) @ Rb ) ) ) ) ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % lex_prod_def
% 0.33/0.57 thf(fact_2945_same__fst__def,axiom,
% 0.33/0.57 ( same_fst_nat_nat
% 0.33/0.57 = ( ^ [P3: nat > $o,R5: nat > set_Pr1261947904930325089at_nat] :
% 0.33/0.57 ( collec7088162979684241874at_nat
% 0.33/0.57 @ ( produc6590410687421337004_nat_o
% 0.33/0.57 @ ( produc8739625826339149834_nat_o
% 0.33/0.57 @ ^ [X10: nat,Y8: nat] :
% 0.33/0.57 ( produc6081775807080527818_nat_o
% 0.33/0.57 @ ^ [X3: nat,Y3: nat] :
% 0.33/0.57 ( ( X10 = X3 )
% 0.33/0.57 & ( P3 @ X3 )
% 0.33/0.57 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y8 @ Y3 ) @ ( R5 @ X3 ) ) ) ) ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % same_fst_def
% 0.33/0.57 thf(fact_2946_mem__case__prodE,axiom,
% 0.33/0.57 ! [Z: $o,C: ( int > option6357759511663192854e_term ) > product_prod_int_int > set_o,P4: produc7773217078559923341nt_int] :
% 0.33/0.57 ( ( member_o @ Z @ ( produc8646739037753556108_set_o @ C @ P4 ) )
% 0.33/0.57 => ~ ! [X4: int > option6357759511663192854e_term,Y5: product_prod_int_int] :
% 0.33/0.57 ( ( P4
% 0.33/0.57 = ( produc4305682042979456191nt_int @ X4 @ Y5 ) )
% 0.33/0.57 => ~ ( member_o @ Z @ ( C @ X4 @ Y5 ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % mem_case_prodE
% 0.33/0.57 thf(fact_2947_mem__case__prodE,axiom,
% 0.33/0.57 ! [Z: nat,C: ( int > option6357759511663192854e_term ) > product_prod_int_int > set_nat,P4: produc7773217078559923341nt_int] :
% 0.33/0.57 ( ( member_nat @ Z @ ( produc8289552606927098482et_nat @ C @ P4 ) )
% 0.33/0.57 => ~ ! [X4: int > option6357759511663192854e_term,Y5: product_prod_int_int] :
% 0.33/0.57 ( ( P4
% 0.33/0.57 = ( produc4305682042979456191nt_int @ X4 @ Y5 ) )
% 0.33/0.57 => ~ ( member_nat @ Z @ ( C @ X4 @ Y5 ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % mem_case_prodE
% 0.33/0.57 thf(fact_2948_mem__case__prodE,axiom,
% 0.33/0.57 ! [Z: int,C: ( int > option6357759511663192854e_term ) > product_prod_int_int > set_int,P4: produc7773217078559923341nt_int] :
% 0.33/0.57 ( ( member_int @ Z @ ( produc4111701587417901774et_int @ C @ P4 ) )
% 0.33/0.57 => ~ ! [X4: int > option6357759511663192854e_term,Y5: product_prod_int_int] :
% 0.33/0.57 ( ( P4
% 0.33/0.57 = ( produc4305682042979456191nt_int @ X4 @ Y5 ) )
% 0.33/0.57 => ~ ( member_int @ Z @ ( C @ X4 @ Y5 ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % mem_case_prodE
% 0.33/0.57 thf(fact_2949_mem__case__prodE,axiom,
% 0.33/0.57 ! [Z: $o,C: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > set_o,P4: produc3925858234332021118et_nat] :
% 0.33/0.57 ( ( member_o @ Z @ ( produc7715693535893868691_set_o @ C @ P4 ) )
% 0.33/0.57 => ~ ! [X4: produc3658429121746597890et_nat > $o,Y5: produc3658429121746597890et_nat] :
% 0.33/0.57 ( ( P4
% 0.33/0.57 = ( produc5001842942810119800et_nat @ X4 @ Y5 ) )
% 0.33/0.57 => ~ ( member_o @ Z @ ( C @ X4 @ Y5 ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % mem_case_prodE
% 0.33/0.57 thf(fact_2950_mem__case__prodE,axiom,
% 0.33/0.57 ! [Z: nat,C: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > set_nat,P4: produc3925858234332021118et_nat] :
% 0.33/0.57 ( ( member_nat @ Z @ ( produc8805491454895738411et_nat @ C @ P4 ) )
% 0.33/0.57 => ~ ! [X4: produc3658429121746597890et_nat > $o,Y5: produc3658429121746597890et_nat] :
% 0.33/0.57 ( ( P4
% 0.33/0.57 = ( produc5001842942810119800et_nat @ X4 @ Y5 ) )
% 0.33/0.57 => ~ ( member_nat @ Z @ ( C @ X4 @ Y5 ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % mem_case_prodE
% 0.33/0.57 thf(fact_2951_mem__case__prodE,axiom,
% 0.33/0.57 ! [Z: int,C: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > set_int,P4: produc3925858234332021118et_nat] :
% 0.33/0.57 ( ( member_int @ Z @ ( produc4627640435386541703et_int @ C @ P4 ) )
% 0.33/0.57 => ~ ! [X4: produc3658429121746597890et_nat > $o,Y5: produc3658429121746597890et_nat] :
% 0.33/0.57 ( ( P4
% 0.33/0.57 = ( produc5001842942810119800et_nat @ X4 @ Y5 ) )
% 0.33/0.57 => ~ ( member_int @ Z @ ( C @ X4 @ Y5 ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % mem_case_prodE
% 0.33/0.57 thf(fact_2952_mem__case__prodE,axiom,
% 0.33/0.57 ! [Z: product_prod_nat_nat,C: ( int > option6357759511663192854e_term ) > product_prod_int_int > set_Pr1261947904930325089at_nat,P4: produc7773217078559923341nt_int] :
% 0.33/0.57 ( ( member8440522571783428010at_nat @ Z @ ( produc5154663461364529269at_nat @ C @ P4 ) )
% 0.33/0.57 => ~ ! [X4: int > option6357759511663192854e_term,Y5: product_prod_int_int] :
% 0.33/0.57 ( ( P4
% 0.33/0.57 = ( produc4305682042979456191nt_int @ X4 @ Y5 ) )
% 0.33/0.57 => ~ ( member8440522571783428010at_nat @ Z @ ( C @ X4 @ Y5 ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % mem_case_prodE
% 0.33/0.57 thf(fact_2953_mem__case__prodE,axiom,
% 0.33/0.57 ! [Z: $o,C: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_o,P4: produc1908205239877642774nteger] :
% 0.33/0.57 ( ( member_o @ Z @ ( produc2373554395599118147_set_o @ C @ P4 ) )
% 0.33/0.57 => ~ ! [X4: produc6241069584506657477e_term > option6357759511663192854e_term,Y5: produc8923325533196201883nteger] :
% 0.33/0.57 ( ( P4
% 0.33/0.57 = ( produc8603105652947943368nteger @ X4 @ Y5 ) )
% 0.33/0.57 => ~ ( member_o @ Z @ ( C @ X4 @ Y5 ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % mem_case_prodE
% 0.33/0.57 thf(fact_2954_mem__case__prodE,axiom,
% 0.33/0.57 ! [Z: nat,C: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_nat,P4: produc1908205239877642774nteger] :
% 0.33/0.57 ( ( member_nat @ Z @ ( produc654622801845291899et_nat @ C @ P4 ) )
% 0.33/0.57 => ~ ! [X4: produc6241069584506657477e_term > option6357759511663192854e_term,Y5: produc8923325533196201883nteger] :
% 0.33/0.57 ( ( P4
% 0.33/0.57 = ( produc8603105652947943368nteger @ X4 @ Y5 ) )
% 0.33/0.57 => ~ ( member_nat @ Z @ ( C @ X4 @ Y5 ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % mem_case_prodE
% 0.33/0.57 thf(fact_2955_mem__case__prodE,axiom,
% 0.33/0.57 ! [Z: int,C: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_int,P4: produc1908205239877642774nteger] :
% 0.33/0.57 ( ( member_int @ Z @ ( produc5700143819190870999et_int @ C @ P4 ) )
% 0.33/0.57 => ~ ! [X4: produc6241069584506657477e_term > option6357759511663192854e_term,Y5: produc8923325533196201883nteger] :
% 0.33/0.57 ( ( P4
% 0.33/0.57 = ( produc8603105652947943368nteger @ X4 @ Y5 ) )
% 0.33/0.57 => ~ ( member_int @ Z @ ( C @ X4 @ Y5 ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % mem_case_prodE
% 0.33/0.57 thf(fact_2956_case__prodD,axiom,
% 0.33/0.57 ! [F: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o,A: produc6241069584506657477e_term > option6357759511663192854e_term,B: produc8923325533196201883nteger] :
% 0.33/0.57 ( ( produc6253627499356882019eger_o @ F @ ( produc8603105652947943368nteger @ A @ B ) )
% 0.33/0.57 => ( F @ A @ B ) ) ).
% 0.33/0.57
% 0.33/0.57 % case_prodD
% 0.33/0.57 thf(fact_2957_case__prodD,axiom,
% 0.33/0.57 ! [F: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o,A: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat] :
% 0.33/0.57 ( ( produc1437786849005270451_nat_o @ F @ ( produc5001842942810119800et_nat @ A @ B ) )
% 0.33/0.57 => ( F @ A @ B ) ) ).
% 0.33/0.57
% 0.33/0.57 % case_prodD
% 0.33/0.57 thf(fact_2958_case__prodD,axiom,
% 0.33/0.57 ! [F: ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o,A: produc3658429121746597890et_nat > $o,B: produc3925858234332021118et_nat] :
% 0.33/0.57 ( ( produc838355143741117751_nat_o @ F @ ( produc2245416461498447860et_nat @ A @ B ) )
% 0.33/0.57 => ( F @ A @ B ) ) ).
% 0.33/0.57
% 0.33/0.57 % case_prodD
% 0.33/0.57 thf(fact_2959_case__prodD,axiom,
% 0.33/0.57 ! [F: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o,A: produc8551481072490612790e_term > option6357759511663192854e_term,B: product_prod_int_int] :
% 0.33/0.57 ( ( produc1573362020775583542_int_o @ F @ ( produc5700946648718959541nt_int @ A @ B ) )
% 0.33/0.57 => ( F @ A @ B ) ) ).
% 0.33/0.57
% 0.33/0.57 % case_prodD
% 0.33/0.57 thf(fact_2960_case__prodD,axiom,
% 0.33/0.57 ! [F: ( int > option6357759511663192854e_term ) > product_prod_int_int > $o,A: int > option6357759511663192854e_term,B: product_prod_int_int] :
% 0.33/0.57 ( ( produc2558449545302689196_int_o @ F @ ( produc4305682042979456191nt_int @ A @ B ) )
% 0.33/0.57 => ( F @ A @ B ) ) ).
% 0.33/0.57
% 0.33/0.57 % case_prodD
% 0.33/0.57 thf(fact_2961_case__prodE,axiom,
% 0.33/0.57 ! [C: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o,P4: produc1908205239877642774nteger] :
% 0.33/0.57 ( ( produc6253627499356882019eger_o @ C @ P4 )
% 0.33/0.57 => ~ ! [X4: produc6241069584506657477e_term > option6357759511663192854e_term,Y5: produc8923325533196201883nteger] :
% 0.33/0.57 ( ( P4
% 0.33/0.57 = ( produc8603105652947943368nteger @ X4 @ Y5 ) )
% 0.33/0.57 => ~ ( C @ X4 @ Y5 ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % case_prodE
% 0.33/0.57 thf(fact_2962_case__prodE,axiom,
% 0.33/0.57 ! [C: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o,P4: produc3925858234332021118et_nat] :
% 0.33/0.57 ( ( produc1437786849005270451_nat_o @ C @ P4 )
% 0.33/0.57 => ~ ! [X4: produc3658429121746597890et_nat > $o,Y5: produc3658429121746597890et_nat] :
% 0.33/0.57 ( ( P4
% 0.33/0.57 = ( produc5001842942810119800et_nat @ X4 @ Y5 ) )
% 0.33/0.57 => ~ ( C @ X4 @ Y5 ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % case_prodE
% 0.33/0.57 thf(fact_2963_case__prodE,axiom,
% 0.33/0.57 ! [C: ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o,P4: produc2732055786443039994et_nat] :
% 0.33/0.57 ( ( produc838355143741117751_nat_o @ C @ P4 )
% 0.33/0.57 => ~ ! [X4: produc3658429121746597890et_nat > $o,Y5: produc3925858234332021118et_nat] :
% 0.33/0.57 ( ( P4
% 0.33/0.57 = ( produc2245416461498447860et_nat @ X4 @ Y5 ) )
% 0.33/0.57 => ~ ( C @ X4 @ Y5 ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % case_prodE
% 0.33/0.57 thf(fact_2964_case__prodE,axiom,
% 0.33/0.57 ! [C: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o,P4: produc2285326912895808259nt_int] :
% 0.33/0.57 ( ( produc1573362020775583542_int_o @ C @ P4 )
% 0.33/0.57 => ~ ! [X4: produc8551481072490612790e_term > option6357759511663192854e_term,Y5: product_prod_int_int] :
% 0.33/0.57 ( ( P4
% 0.33/0.57 = ( produc5700946648718959541nt_int @ X4 @ Y5 ) )
% 0.33/0.57 => ~ ( C @ X4 @ Y5 ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % case_prodE
% 0.33/0.57 thf(fact_2965_case__prodE,axiom,
% 0.33/0.57 ! [C: ( int > option6357759511663192854e_term ) > product_prod_int_int > $o,P4: produc7773217078559923341nt_int] :
% 0.33/0.57 ( ( produc2558449545302689196_int_o @ C @ P4 )
% 0.33/0.57 => ~ ! [X4: int > option6357759511663192854e_term,Y5: product_prod_int_int] :
% 0.33/0.57 ( ( P4
% 0.33/0.57 = ( produc4305682042979456191nt_int @ X4 @ Y5 ) )
% 0.33/0.57 => ~ ( C @ X4 @ Y5 ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % case_prodE
% 0.33/0.57 thf(fact_2966_add__One__commute,axiom,
% 0.33/0.57 ! [N2: num] :
% 0.33/0.57 ( ( plus_plus_num @ one @ N2 )
% 0.33/0.57 = ( plus_plus_num @ N2 @ one ) ) ).
% 0.33/0.57
% 0.33/0.57 % add_One_commute
% 0.33/0.57 thf(fact_2967_case__prodD_H,axiom,
% 0.33/0.57 ! [R4: nat > nat > product_prod_nat_nat > $o,A: nat,B: nat,C: product_prod_nat_nat] :
% 0.33/0.57 ( ( produc8739625826339149834_nat_o @ R4 @ ( product_Pair_nat_nat @ A @ B ) @ C )
% 0.33/0.57 => ( R4 @ A @ B @ C ) ) ).
% 0.33/0.57
% 0.33/0.57 % case_prodD'
% 0.33/0.57 thf(fact_2968_case__prodE_H,axiom,
% 0.33/0.57 ! [C: nat > nat > product_prod_nat_nat > $o,P4: product_prod_nat_nat,Z: product_prod_nat_nat] :
% 0.33/0.57 ( ( produc8739625826339149834_nat_o @ C @ P4 @ Z )
% 0.33/0.57 => ~ ! [X4: nat,Y5: nat] :
% 0.33/0.57 ( ( P4
% 0.33/0.57 = ( product_Pair_nat_nat @ X4 @ Y5 ) )
% 0.33/0.57 => ~ ( C @ X4 @ Y5 @ Z ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % case_prodE'
% 0.33/0.57 thf(fact_2969_sum_OatLeast__int__atMost__int__shift,axiom,
% 0.33/0.57 ! [G: int > nat,M2: nat,N2: nat] :
% 0.33/0.57 ( ( groups4541462559716669496nt_nat @ G @ ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 0.33/0.57 = ( groups3542108847815614940at_nat @ ( comp_int_nat_nat @ G @ semiri1314217659103216013at_int ) @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % sum.atLeast_int_atMost_int_shift
% 0.33/0.57 thf(fact_2970_sum_OatLeast__int__atMost__int__shift,axiom,
% 0.33/0.57 ! [G: int > int,M2: nat,N2: nat] :
% 0.33/0.57 ( ( groups4538972089207619220nt_int @ G @ ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 0.33/0.57 = ( groups3539618377306564664at_int @ ( comp_int_int_nat @ G @ semiri1314217659103216013at_int ) @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % sum.atLeast_int_atMost_int_shift
% 0.33/0.57 thf(fact_2971_less__int_Oabs__eq,axiom,
% 0.33/0.57 ! [Xa: product_prod_nat_nat,X: product_prod_nat_nat] :
% 0.33/0.57 ( ( ord_less_int @ ( abs_Integ @ Xa ) @ ( abs_Integ @ X ) )
% 0.33/0.57 = ( produc8739625826339149834_nat_o
% 0.33/0.57 @ ^ [X3: nat,Y3: nat] :
% 0.33/0.57 ( produc6081775807080527818_nat_o
% 0.33/0.57 @ ^ [U2: nat,V2: nat] : ( ord_less_nat @ ( plus_plus_nat @ X3 @ V2 ) @ ( plus_plus_nat @ U2 @ Y3 ) ) )
% 0.33/0.57 @ Xa
% 0.33/0.57 @ X ) ) ).
% 0.33/0.57
% 0.33/0.57 % less_int.abs_eq
% 0.33/0.57 thf(fact_2972_less__eq__int_Oabs__eq,axiom,
% 0.33/0.57 ! [Xa: product_prod_nat_nat,X: product_prod_nat_nat] :
% 0.33/0.57 ( ( ord_less_eq_int @ ( abs_Integ @ Xa ) @ ( abs_Integ @ X ) )
% 0.33/0.57 = ( produc8739625826339149834_nat_o
% 0.33/0.57 @ ^ [X3: nat,Y3: nat] :
% 0.33/0.57 ( produc6081775807080527818_nat_o
% 0.33/0.57 @ ^ [U2: nat,V2: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X3 @ V2 ) @ ( plus_plus_nat @ U2 @ Y3 ) ) )
% 0.33/0.57 @ Xa
% 0.33/0.57 @ X ) ) ).
% 0.33/0.57
% 0.33/0.57 % less_eq_int.abs_eq
% 0.33/0.57 thf(fact_2973_zadd__int__left,axiom,
% 0.33/0.57 ! [M2: nat,N2: nat,Z: int] :
% 0.33/0.57 ( ( plus_plus_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ Z ) )
% 0.33/0.57 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ ( plus_plus_nat @ M2 @ N2 ) ) @ Z ) ) ).
% 0.33/0.57
% 0.33/0.57 % zadd_int_left
% 0.33/0.57 thf(fact_2974_int__plus,axiom,
% 0.33/0.57 ! [N2: nat,M2: nat] :
% 0.33/0.57 ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ N2 @ M2 ) )
% 0.33/0.57 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( semiri1314217659103216013at_int @ M2 ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % int_plus
% 0.33/0.57 thf(fact_2975_int__ops_I5_J,axiom,
% 0.33/0.57 ! [A: nat,B: nat] :
% 0.33/0.57 ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ A @ B ) )
% 0.33/0.57 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % int_ops(5)
% 0.33/0.57 thf(fact_2976_int__ops_I2_J,axiom,
% 0.33/0.57 ( ( semiri1314217659103216013at_int @ one_one_nat )
% 0.33/0.57 = one_one_int ) ).
% 0.33/0.57
% 0.33/0.57 % int_ops(2)
% 0.33/0.57 thf(fact_2977_zle__iff__zadd,axiom,
% 0.33/0.57 ( ord_less_eq_int
% 0.33/0.57 = ( ^ [W2: int,Z4: int] :
% 0.33/0.57 ? [N4: nat] :
% 0.33/0.57 ( Z4
% 0.33/0.57 = ( plus_plus_int @ W2 @ ( semiri1314217659103216013at_int @ N4 ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % zle_iff_zadd
% 0.33/0.57 thf(fact_2978_numeral__One,axiom,
% 0.33/0.57 ( ( numeral_numeral_nat @ one )
% 0.33/0.57 = one_one_nat ) ).
% 0.33/0.57
% 0.33/0.57 % numeral_One
% 0.33/0.57 thf(fact_2979_numeral__One,axiom,
% 0.33/0.57 ( ( numeral_numeral_int @ one )
% 0.33/0.57 = one_one_int ) ).
% 0.33/0.57
% 0.33/0.57 % numeral_One
% 0.33/0.57 thf(fact_2980_numeral__One,axiom,
% 0.33/0.57 ( ( numera6620942414471956472nteger @ one )
% 0.33/0.57 = one_one_Code_integer ) ).
% 0.33/0.57
% 0.33/0.57 % numeral_One
% 0.33/0.57 thf(fact_2981_numeral__One,axiom,
% 0.33/0.57 ( ( numeral_numeral_rat @ one )
% 0.33/0.57 = one_one_rat ) ).
% 0.33/0.57
% 0.33/0.57 % numeral_One
% 0.33/0.57 thf(fact_2982_numeral__One,axiom,
% 0.33/0.57 ( ( numera5444537566228673987atural @ one )
% 0.33/0.57 = one_one_Code_natural ) ).
% 0.33/0.57
% 0.33/0.57 % numeral_One
% 0.33/0.57 thf(fact_2983_numerals_I1_J,axiom,
% 0.33/0.57 ( ( numeral_numeral_nat @ one )
% 0.33/0.57 = one_one_nat ) ).
% 0.33/0.57
% 0.33/0.57 % numerals(1)
% 0.33/0.57 thf(fact_2984_execute__bind__case,axiom,
% 0.33/0.57 ! [F: heap_T6362127782908069795rray_a,G: array_a > heap_T6362127782908069795rray_a,H3: heap_e7401611519738050253t_unit] :
% 0.33/0.57 ( ( heap_T5591663578999710211rray_a @ ( heap_T2407400398799471159rray_a @ F @ G ) @ H3 )
% 0.33/0.57 = ( case_o8555119740594961093it_nat @ none_P2587165478634041381it_nat
% 0.33/0.57 @ ( produc8915672860170107321it_nat
% 0.33/0.57 @ ^ [X3: array_a] :
% 0.33/0.57 ( produc921929042997482327it_nat
% 0.33/0.57 @ ^ [H6: heap_e7401611519738050253t_unit,N4: nat] : ( heap_T531568236820715630rray_a @ N4 @ ( heap_T5591663578999710211rray_a @ ( G @ X3 ) @ H6 ) ) ) )
% 0.33/0.57 @ ( heap_T5591663578999710211rray_a @ F @ H3 ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % execute_bind_case
% 0.33/0.57 thf(fact_2985_execute__bind__case,axiom,
% 0.33/0.57 ! [F: heap_T5738788834812785303t_unit,G: product_unit > heap_T6362127782908069795rray_a,H3: heap_e7401611519738050253t_unit] :
% 0.33/0.57 ( ( heap_T5591663578999710211rray_a @ ( heap_T7158140910958840029rray_a @ F @ G ) @ H3 )
% 0.33/0.57 = ( case_o5699750240967658439it_nat @ none_P2587165478634041381it_nat
% 0.33/0.57 @ ( produc875294279294635931it_nat
% 0.33/0.57 @ ^ [X3: product_unit] :
% 0.33/0.57 ( produc921929042997482327it_nat
% 0.33/0.57 @ ^ [H6: heap_e7401611519738050253t_unit,N4: nat] : ( heap_T531568236820715630rray_a @ N4 @ ( heap_T5591663578999710211rray_a @ ( G @ X3 ) @ H6 ) ) ) )
% 0.33/0.57 @ ( heap_T875086893843062177t_unit @ F @ H3 ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % execute_bind_case
% 0.33/0.57 thf(fact_2986_execute__bind__case,axiom,
% 0.33/0.57 ! [F: heap_T6362127782908069795rray_a,G: array_a > heap_T5738788834812785303t_unit,H3: heap_e7401611519738050253t_unit] :
% 0.33/0.57 ( ( heap_T875086893843062177t_unit @ ( heap_T7324619625323989613t_unit @ F @ G ) @ H3 )
% 0.33/0.57 = ( case_o3886096569520666655it_nat @ none_P9117596204409417319it_nat
% 0.33/0.57 @ ( produc3495058329975564393it_nat
% 0.33/0.57 @ ^ [X3: array_a] :
% 0.33/0.57 ( produc7488178964372371019it_nat
% 0.33/0.57 @ ^ [H6: heap_e7401611519738050253t_unit,N4: nat] : ( heap_T3616969660504097270t_unit @ N4 @ ( heap_T875086893843062177t_unit @ ( G @ X3 ) @ H6 ) ) ) )
% 0.33/0.57 @ ( heap_T5591663578999710211rray_a @ F @ H3 ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % execute_bind_case
% 0.33/0.57 thf(fact_2987_execute__bind__case,axiom,
% 0.33/0.57 ! [F: heap_T5738788834812785303t_unit,G: product_unit > heap_T5738788834812785303t_unit,H3: heap_e7401611519738050253t_unit] :
% 0.33/0.57 ( ( heap_T875086893843062177t_unit @ ( heap_T2633723481742716231t_unit @ F @ G ) @ H3 )
% 0.33/0.57 = ( case_o2963978774867076333it_nat @ none_P9117596204409417319it_nat
% 0.33/0.57 @ ( produc1230459020282432263it_nat
% 0.33/0.57 @ ^ [X3: product_unit] :
% 0.33/0.57 ( produc7488178964372371019it_nat
% 0.33/0.57 @ ^ [H6: heap_e7401611519738050253t_unit,N4: nat] : ( heap_T3616969660504097270t_unit @ N4 @ ( heap_T875086893843062177t_unit @ ( G @ X3 ) @ H6 ) ) ) )
% 0.33/0.57 @ ( heap_T875086893843062177t_unit @ F @ H3 ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % execute_bind_case
% 0.33/0.57 thf(fact_2988_Sum__Icc__int,axiom,
% 0.33/0.57 ! [M2: int,N2: int] :
% 0.33/0.57 ( ( ord_less_eq_int @ M2 @ N2 )
% 0.33/0.57 => ( ( groups4538972089207619220nt_int
% 0.33/0.57 @ ^ [X3: int] : X3
% 0.33/0.57 @ ( set_or1266510415728281911st_int @ M2 @ N2 ) )
% 0.33/0.57 = ( divide_divide_int @ ( minus_minus_int @ ( times_times_int @ N2 @ ( plus_plus_int @ N2 @ one_one_int ) ) @ ( times_times_int @ M2 @ ( minus_minus_int @ M2 @ one_one_int ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % Sum_Icc_int
% 0.33/0.57 thf(fact_2989_Heap__Time__Monad_Obind__def,axiom,
% 0.33/0.57 ( heap_T2407400398799471159rray_a
% 0.33/0.57 = ( ^ [F2: heap_T6362127782908069795rray_a,G2: array_a > heap_T6362127782908069795rray_a] :
% 0.33/0.57 ( heap_T1488828001306802186rray_a
% 0.33/0.57 @ ^ [H: heap_e7401611519738050253t_unit] :
% 0.33/0.57 ( case_o8555119740594961093it_nat @ none_P2587165478634041381it_nat
% 0.33/0.57 @ ( produc8915672860170107321it_nat
% 0.33/0.57 @ ^ [R3: array_a] :
% 0.33/0.57 ( produc921929042997482327it_nat
% 0.33/0.57 @ ^ [H6: heap_e7401611519738050253t_unit,N4: nat] : ( heap_T531568236820715630rray_a @ N4 @ ( heap_T5591663578999710211rray_a @ ( G2 @ R3 ) @ H6 ) ) ) )
% 0.33/0.57 @ ( heap_T5591663578999710211rray_a @ F2 @ H ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % Heap_Time_Monad.bind_def
% 0.33/0.57 thf(fact_2990_Heap__Time__Monad_Obind__def,axiom,
% 0.33/0.57 ( heap_T7158140910958840029rray_a
% 0.33/0.57 = ( ^ [F2: heap_T5738788834812785303t_unit,G2: product_unit > heap_T6362127782908069795rray_a] :
% 0.33/0.57 ( heap_T1488828001306802186rray_a
% 0.33/0.57 @ ^ [H: heap_e7401611519738050253t_unit] :
% 0.33/0.57 ( case_o5699750240967658439it_nat @ none_P2587165478634041381it_nat
% 0.33/0.57 @ ( produc875294279294635931it_nat
% 0.33/0.57 @ ^ [R3: product_unit] :
% 0.33/0.57 ( produc921929042997482327it_nat
% 0.33/0.57 @ ^ [H6: heap_e7401611519738050253t_unit,N4: nat] : ( heap_T531568236820715630rray_a @ N4 @ ( heap_T5591663578999710211rray_a @ ( G2 @ R3 ) @ H6 ) ) ) )
% 0.33/0.57 @ ( heap_T875086893843062177t_unit @ F2 @ H ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % Heap_Time_Monad.bind_def
% 0.33/0.57 thf(fact_2991_Heap__Time__Monad_Obind__def,axiom,
% 0.33/0.57 ( heap_T7324619625323989613t_unit
% 0.33/0.57 = ( ^ [F2: heap_T6362127782908069795rray_a,G2: array_a > heap_T5738788834812785303t_unit] :
% 0.33/0.57 ( heap_T6183433275982383450t_unit
% 0.33/0.57 @ ^ [H: heap_e7401611519738050253t_unit] :
% 0.33/0.57 ( case_o3886096569520666655it_nat @ none_P9117596204409417319it_nat
% 0.33/0.57 @ ( produc3495058329975564393it_nat
% 0.33/0.57 @ ^ [R3: array_a] :
% 0.33/0.57 ( produc7488178964372371019it_nat
% 0.33/0.57 @ ^ [H6: heap_e7401611519738050253t_unit,N4: nat] : ( heap_T3616969660504097270t_unit @ N4 @ ( heap_T875086893843062177t_unit @ ( G2 @ R3 ) @ H6 ) ) ) )
% 0.33/0.57 @ ( heap_T5591663578999710211rray_a @ F2 @ H ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % Heap_Time_Monad.bind_def
% 0.33/0.57 thf(fact_2992_Heap__Time__Monad_Obind__def,axiom,
% 0.33/0.57 ( heap_T2633723481742716231t_unit
% 0.33/0.57 = ( ^ [F2: heap_T5738788834812785303t_unit,G2: product_unit > heap_T5738788834812785303t_unit] :
% 0.33/0.57 ( heap_T6183433275982383450t_unit
% 0.33/0.57 @ ^ [H: heap_e7401611519738050253t_unit] :
% 0.33/0.57 ( case_o2963978774867076333it_nat @ none_P9117596204409417319it_nat
% 0.33/0.57 @ ( produc1230459020282432263it_nat
% 0.33/0.57 @ ^ [R3: product_unit] :
% 0.33/0.57 ( produc7488178964372371019it_nat
% 0.33/0.57 @ ^ [H6: heap_e7401611519738050253t_unit,N4: nat] : ( heap_T3616969660504097270t_unit @ N4 @ ( heap_T875086893843062177t_unit @ ( G2 @ R3 ) @ H6 ) ) ) )
% 0.33/0.57 @ ( heap_T875086893843062177t_unit @ F2 @ H ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % Heap_Time_Monad.bind_def
% 0.33/0.57 thf(fact_2993_zless__iff__Suc__zadd,axiom,
% 0.33/0.57 ( ord_less_int
% 0.33/0.57 = ( ^ [W2: int,Z4: int] :
% 0.33/0.57 ? [N4: nat] :
% 0.33/0.57 ( Z4
% 0.33/0.57 = ( plus_plus_int @ W2 @ ( semiri1314217659103216013at_int @ ( suc @ N4 ) ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % zless_iff_Suc_zadd
% 0.33/0.57 thf(fact_2994_int__ops_I4_J,axiom,
% 0.33/0.57 ! [A: nat] :
% 0.33/0.57 ( ( semiri1314217659103216013at_int @ ( suc @ A ) )
% 0.33/0.57 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ one_one_int ) ) ).
% 0.33/0.57
% 0.33/0.57 % int_ops(4)
% 0.33/0.57 thf(fact_2995_int__Suc,axiom,
% 0.33/0.57 ! [N2: nat] :
% 0.33/0.57 ( ( semiri1314217659103216013at_int @ ( suc @ N2 ) )
% 0.33/0.57 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) ) ).
% 0.33/0.57
% 0.33/0.57 % int_Suc
% 0.33/0.57 thf(fact_2996_int__bit__induct,axiom,
% 0.33/0.57 ! [P: int > $o,K: int] :
% 0.33/0.57 ( ( P @ zero_zero_int )
% 0.33/0.57 => ( ( P @ ( uminus_uminus_int @ one_one_int ) )
% 0.33/0.57 => ( ! [K5: int] :
% 0.33/0.57 ( ( P @ K5 )
% 0.33/0.57 => ( ( K5 != zero_zero_int )
% 0.33/0.57 => ( P @ ( times_times_int @ K5 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) )
% 0.33/0.57 => ( ! [K5: int] :
% 0.33/0.57 ( ( P @ K5 )
% 0.33/0.57 => ( ( K5
% 0.33/0.57 != ( uminus_uminus_int @ one_one_int ) )
% 0.33/0.57 => ( P @ ( plus_plus_int @ one_one_int @ ( times_times_int @ K5 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) )
% 0.33/0.57 => ( P @ K ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % int_bit_induct
% 0.33/0.57 thf(fact_2997_uminus__numeral__One,axiom,
% 0.33/0.57 ( ( uminus_uminus_int @ ( numeral_numeral_int @ one ) )
% 0.33/0.57 = ( uminus_uminus_int @ one_one_int ) ) ).
% 0.33/0.57
% 0.33/0.57 % uminus_numeral_One
% 0.33/0.57 thf(fact_2998_uminus__numeral__One,axiom,
% 0.33/0.57 ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) )
% 0.33/0.57 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.33/0.57
% 0.33/0.57 % uminus_numeral_One
% 0.33/0.57 thf(fact_2999_uminus__numeral__One,axiom,
% 0.33/0.57 ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) )
% 0.33/0.57 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.33/0.57
% 0.33/0.57 % uminus_numeral_One
% 0.33/0.57 thf(fact_3000_int__def,axiom,
% 0.33/0.57 ( semiri1314217659103216013at_int
% 0.33/0.57 = ( ^ [N4: nat] : ( abs_Integ @ ( product_Pair_nat_nat @ N4 @ zero_zero_nat ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % int_def
% 0.33/0.57 thf(fact_3001_num__of__nat__One,axiom,
% 0.33/0.57 ! [N2: nat] :
% 0.33/0.57 ( ( ord_less_eq_nat @ N2 @ one_one_nat )
% 0.33/0.57 => ( ( num_of_nat @ N2 )
% 0.33/0.57 = one ) ) ).
% 0.33/0.57
% 0.33/0.57 % num_of_nat_One
% 0.33/0.57 thf(fact_3002_neg__zdiv__mult__2,axiom,
% 0.33/0.57 ! [A: int,B: int] :
% 0.33/0.57 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.33/0.57 => ( ( 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 ) )
% 0.33/0.57 = ( divide_divide_int @ ( plus_plus_int @ B @ one_one_int ) @ A ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % neg_zdiv_mult_2
% 0.33/0.57 thf(fact_3003_pos__zdiv__mult__2,axiom,
% 0.33/0.57 ! [A: int,B: int] :
% 0.33/0.57 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.33/0.57 => ( ( 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 ) )
% 0.33/0.57 = ( divide_divide_int @ B @ A ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % pos_zdiv_mult_2
% 0.33/0.57 thf(fact_3004_pos__zmod__mult__2,axiom,
% 0.33/0.57 ! [A: int,B: int] :
% 0.33/0.57 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.33/0.57 => ( ( 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 ) )
% 0.33/0.57 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ B @ A ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % pos_zmod_mult_2
% 0.33/0.57 thf(fact_3005_mod__mult2__eq_H,axiom,
% 0.33/0.57 ! [A: int,M2: nat,N2: nat] :
% 0.33/0.57 ( ( modulo_modulo_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 0.33/0.57 = ( plus_plus_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( modulo_modulo_int @ ( divide_divide_int @ A @ ( semiri1314217659103216013at_int @ M2 ) ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) @ ( modulo_modulo_int @ A @ ( semiri1314217659103216013at_int @ M2 ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % mod_mult2_eq'
% 0.33/0.57 thf(fact_3006_mod__mult2__eq_H,axiom,
% 0.33/0.57 ! [A: nat,M2: nat,N2: nat] :
% 0.33/0.57 ( ( modulo_modulo_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M2 ) @ ( semiri1316708129612266289at_nat @ N2 ) ) )
% 0.33/0.57 = ( plus_plus_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M2 ) @ ( modulo_modulo_nat @ ( divide_divide_nat @ A @ ( semiri1316708129612266289at_nat @ M2 ) ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) @ ( modulo_modulo_nat @ A @ ( semiri1316708129612266289at_nat @ M2 ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % mod_mult2_eq'
% 0.33/0.57 thf(fact_3007_mod__mult2__eq_H,axiom,
% 0.33/0.57 ! [A: code_integer,M2: nat,N2: nat] :
% 0.33/0.57 ( ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M2 ) @ ( semiri4939895301339042750nteger @ N2 ) ) )
% 0.33/0.57 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M2 ) @ ( modulo364778990260209775nteger @ ( divide6298287555418463151nteger @ A @ ( semiri4939895301339042750nteger @ M2 ) ) @ ( semiri4939895301339042750nteger @ N2 ) ) ) @ ( modulo364778990260209775nteger @ A @ ( semiri4939895301339042750nteger @ M2 ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % mod_mult2_eq'
% 0.33/0.57 thf(fact_3008_mod__mult2__eq_H,axiom,
% 0.33/0.57 ! [A: code_natural,M2: nat,N2: nat] :
% 0.33/0.57 ( ( modulo8411746178871703098atural @ A @ ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ M2 ) @ ( semiri3763490453095760265atural @ N2 ) ) )
% 0.33/0.57 = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ M2 ) @ ( modulo8411746178871703098atural @ ( divide5121882707175180666atural @ A @ ( semiri3763490453095760265atural @ M2 ) ) @ ( semiri3763490453095760265atural @ N2 ) ) ) @ ( modulo8411746178871703098atural @ A @ ( semiri3763490453095760265atural @ M2 ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % mod_mult2_eq'
% 0.33/0.57 thf(fact_3009_numeral__num__of__nat__unfold,axiom,
% 0.33/0.57 ! [N2: nat] :
% 0.33/0.57 ( ( ( N2 = zero_zero_nat )
% 0.33/0.57 => ( ( numeral_numeral_rat @ ( num_of_nat @ N2 ) )
% 0.33/0.57 = one_one_rat ) )
% 0.33/0.57 & ( ( N2 != zero_zero_nat )
% 0.33/0.57 => ( ( numeral_numeral_rat @ ( num_of_nat @ N2 ) )
% 0.33/0.57 = ( semiri681578069525770553at_rat @ N2 ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % numeral_num_of_nat_unfold
% 0.33/0.57 thf(fact_3010_numeral__num__of__nat__unfold,axiom,
% 0.33/0.57 ! [N2: nat] :
% 0.33/0.57 ( ( ( N2 = zero_zero_nat )
% 0.33/0.57 => ( ( numeral_numeral_int @ ( num_of_nat @ N2 ) )
% 0.33/0.57 = one_one_int ) )
% 0.33/0.57 & ( ( N2 != zero_zero_nat )
% 0.33/0.57 => ( ( numeral_numeral_int @ ( num_of_nat @ N2 ) )
% 0.33/0.57 = ( semiri1314217659103216013at_int @ N2 ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % numeral_num_of_nat_unfold
% 0.33/0.57 thf(fact_3011_numeral__num__of__nat__unfold,axiom,
% 0.33/0.57 ! [N2: nat] :
% 0.33/0.57 ( ( ( N2 = zero_zero_nat )
% 0.33/0.57 => ( ( numeral_numeral_nat @ ( num_of_nat @ N2 ) )
% 0.33/0.57 = one_one_nat ) )
% 0.33/0.57 & ( ( N2 != zero_zero_nat )
% 0.33/0.57 => ( ( numeral_numeral_nat @ ( num_of_nat @ N2 ) )
% 0.33/0.57 = ( semiri1316708129612266289at_nat @ N2 ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % numeral_num_of_nat_unfold
% 0.33/0.57 thf(fact_3012_numeral__num__of__nat__unfold,axiom,
% 0.33/0.57 ! [N2: nat] :
% 0.33/0.57 ( ( ( N2 = zero_zero_nat )
% 0.33/0.57 => ( ( numera6620942414471956472nteger @ ( num_of_nat @ N2 ) )
% 0.33/0.57 = one_one_Code_integer ) )
% 0.33/0.57 & ( ( N2 != zero_zero_nat )
% 0.33/0.57 => ( ( numera6620942414471956472nteger @ ( num_of_nat @ N2 ) )
% 0.33/0.57 = ( semiri4939895301339042750nteger @ N2 ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % numeral_num_of_nat_unfold
% 0.33/0.57 thf(fact_3013_numeral__num__of__nat__unfold,axiom,
% 0.33/0.57 ! [N2: nat] :
% 0.33/0.57 ( ( ( N2 = zero_zero_nat )
% 0.33/0.57 => ( ( numera5444537566228673987atural @ ( num_of_nat @ N2 ) )
% 0.33/0.57 = one_one_Code_natural ) )
% 0.33/0.57 & ( ( N2 != zero_zero_nat )
% 0.33/0.57 => ( ( numera5444537566228673987atural @ ( num_of_nat @ N2 ) )
% 0.33/0.57 = ( semiri3763490453095760265atural @ N2 ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % numeral_num_of_nat_unfold
% 0.33/0.57 thf(fact_3014_double__arith__series,axiom,
% 0.33/0.57 ! [A: rat,D2: rat,N2: nat] :
% 0.33/0.57 ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) )
% 0.33/0.57 @ ( groups2906978787729119204at_rat
% 0.33/0.57 @ ^ [I3: nat] : ( plus_plus_rat @ A @ ( times_times_rat @ ( semiri681578069525770553at_rat @ I3 ) @ D2 ) )
% 0.33/0.57 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 0.33/0.57 = ( times_times_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N2 ) @ one_one_rat ) @ ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ A ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N2 ) @ D2 ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % double_arith_series
% 0.33/0.57 thf(fact_3015_double__arith__series,axiom,
% 0.33/0.57 ! [A: int,D2: int,N2: nat] :
% 0.33/0.57 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) )
% 0.33/0.57 @ ( groups3539618377306564664at_int
% 0.33/0.57 @ ^ [I3: nat] : ( plus_plus_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ I3 ) @ D2 ) )
% 0.33/0.57 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 0.33/0.57 = ( times_times_int @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ D2 ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % double_arith_series
% 0.33/0.57 thf(fact_3016_double__arith__series,axiom,
% 0.33/0.57 ! [A: code_integer,D2: code_integer,N2: nat] :
% 0.33/0.57 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) )
% 0.33/0.57 @ ( groups7501900531339628137nteger
% 0.33/0.57 @ ^ [I3: nat] : ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ I3 ) @ D2 ) )
% 0.33/0.57 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 0.33/0.57 = ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N2 ) @ one_one_Code_integer ) @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N2 ) @ D2 ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % double_arith_series
% 0.33/0.57 thf(fact_3017_double__arith__series,axiom,
% 0.33/0.57 ! [A: code_natural,D2: code_natural,N2: nat] :
% 0.33/0.57 ( ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) )
% 0.33/0.57 @ ( groups6325495683096345652atural
% 0.33/0.57 @ ^ [I3: nat] : ( plus_p4538020629002901425atural @ A @ ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ I3 ) @ D2 ) )
% 0.33/0.57 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 0.33/0.57 = ( times_2397367101498566445atural @ ( plus_p4538020629002901425atural @ ( semiri3763490453095760265atural @ N2 ) @ one_one_Code_natural ) @ ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A ) @ ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ N2 ) @ D2 ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % double_arith_series
% 0.33/0.57 thf(fact_3018_double__arith__series,axiom,
% 0.33/0.57 ! [A: nat,D2: nat,N2: nat] :
% 0.33/0.57 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 0.33/0.57 @ ( groups3542108847815614940at_nat
% 0.33/0.57 @ ^ [I3: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ I3 ) @ D2 ) )
% 0.33/0.57 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 0.33/0.57 = ( times_times_nat @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ one_one_nat ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ D2 ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % double_arith_series
% 0.33/0.57 thf(fact_3019_double__gauss__sum,axiom,
% 0.33/0.57 ! [N2: nat] :
% 0.33/0.57 ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( groups2906978787729119204at_rat @ semiri681578069525770553at_rat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 0.33/0.57 = ( times_times_rat @ ( semiri681578069525770553at_rat @ N2 ) @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N2 ) @ one_one_rat ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % double_gauss_sum
% 0.33/0.57 thf(fact_3020_double__gauss__sum,axiom,
% 0.33/0.57 ! [N2: nat] :
% 0.33/0.57 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 0.33/0.57 = ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % double_gauss_sum
% 0.33/0.57 thf(fact_3021_double__gauss__sum,axiom,
% 0.33/0.57 ! [N2: nat] :
% 0.33/0.57 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( groups7501900531339628137nteger @ semiri4939895301339042750nteger @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 0.33/0.57 = ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N2 ) @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N2 ) @ one_one_Code_integer ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % double_gauss_sum
% 0.33/0.57 thf(fact_3022_double__gauss__sum,axiom,
% 0.33/0.57 ! [N2: nat] :
% 0.33/0.57 ( ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( groups6325495683096345652atural @ semiri3763490453095760265atural @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 0.33/0.57 = ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ N2 ) @ ( plus_p4538020629002901425atural @ ( semiri3763490453095760265atural @ N2 ) @ one_one_Code_natural ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % double_gauss_sum
% 0.33/0.57 thf(fact_3023_double__gauss__sum,axiom,
% 0.33/0.57 ! [N2: nat] :
% 0.33/0.57 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 0.33/0.57 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ one_one_nat ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % double_gauss_sum
% 0.33/0.57 thf(fact_3024_neg__zmod__mult__2,axiom,
% 0.33/0.57 ! [A: int,B: int] :
% 0.33/0.57 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.33/0.57 => ( ( 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 ) )
% 0.33/0.57 = ( 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 ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % neg_zmod_mult_2
% 0.33/0.57 thf(fact_3025_mult__2,axiom,
% 0.33/0.57 ! [Z: nat] :
% 0.33/0.57 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Z )
% 0.33/0.57 = ( plus_plus_nat @ Z @ Z ) ) ).
% 0.33/0.57
% 0.33/0.57 % mult_2
% 0.33/0.57 thf(fact_3026_mult__2,axiom,
% 0.33/0.57 ! [Z: int] :
% 0.33/0.57 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Z )
% 0.33/0.57 = ( plus_plus_int @ Z @ Z ) ) ).
% 0.33/0.57
% 0.33/0.57 % mult_2
% 0.33/0.57 thf(fact_3027_mult__2,axiom,
% 0.33/0.57 ! [Z: code_integer] :
% 0.33/0.57 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Z )
% 0.33/0.57 = ( plus_p5714425477246183910nteger @ Z @ Z ) ) ).
% 0.33/0.57
% 0.33/0.57 % mult_2
% 0.33/0.57 thf(fact_3028_mult__2,axiom,
% 0.33/0.57 ! [Z: rat] :
% 0.33/0.57 ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ Z )
% 0.33/0.57 = ( plus_plus_rat @ Z @ Z ) ) ).
% 0.33/0.57
% 0.33/0.57 % mult_2
% 0.33/0.57 thf(fact_3029_mult__2,axiom,
% 0.33/0.57 ! [Z: code_natural] :
% 0.33/0.57 ( ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ Z )
% 0.33/0.57 = ( plus_p4538020629002901425atural @ Z @ Z ) ) ).
% 0.33/0.57
% 0.33/0.57 % mult_2
% 0.33/0.57 thf(fact_3030_mult__2__right,axiom,
% 0.33/0.57 ! [Z: nat] :
% 0.33/0.57 ( ( times_times_nat @ Z @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.33/0.57 = ( plus_plus_nat @ Z @ Z ) ) ).
% 0.33/0.57
% 0.33/0.57 % mult_2_right
% 0.33/0.57 thf(fact_3031_mult__2__right,axiom,
% 0.33/0.57 ! [Z: int] :
% 0.33/0.57 ( ( times_times_int @ Z @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.33/0.57 = ( plus_plus_int @ Z @ Z ) ) ).
% 0.33/0.57
% 0.33/0.57 % mult_2_right
% 0.33/0.57 thf(fact_3032_mult__2__right,axiom,
% 0.33/0.57 ! [Z: code_integer] :
% 0.33/0.57 ( ( times_3573771949741848930nteger @ Z @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.33/0.57 = ( plus_p5714425477246183910nteger @ Z @ Z ) ) ).
% 0.33/0.57
% 0.33/0.57 % mult_2_right
% 0.33/0.57 thf(fact_3033_mult__2__right,axiom,
% 0.33/0.57 ! [Z: rat] :
% 0.33/0.57 ( ( times_times_rat @ Z @ ( numeral_numeral_rat @ ( bit0 @ one ) ) )
% 0.33/0.57 = ( plus_plus_rat @ Z @ Z ) ) ).
% 0.33/0.57
% 0.33/0.57 % mult_2_right
% 0.33/0.57 thf(fact_3034_mult__2__right,axiom,
% 0.33/0.57 ! [Z: code_natural] :
% 0.33/0.57 ( ( times_2397367101498566445atural @ Z @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 0.33/0.57 = ( plus_p4538020629002901425atural @ Z @ Z ) ) ).
% 0.33/0.57
% 0.33/0.57 % mult_2_right
% 0.33/0.57 thf(fact_3035_left__add__twice,axiom,
% 0.33/0.57 ! [A: nat,B: nat] :
% 0.33/0.57 ( ( plus_plus_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 0.33/0.57 = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 0.33/0.57
% 0.33/0.57 % left_add_twice
% 0.33/0.57 thf(fact_3036_left__add__twice,axiom,
% 0.33/0.57 ! [A: int,B: int] :
% 0.33/0.57 ( ( plus_plus_int @ A @ ( plus_plus_int @ A @ B ) )
% 0.33/0.57 = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 0.33/0.57
% 0.33/0.57 % left_add_twice
% 0.33/0.57 thf(fact_3037_left__add__twice,axiom,
% 0.33/0.57 ! [A: code_integer,B: code_integer] :
% 0.33/0.57 ( ( plus_p5714425477246183910nteger @ A @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 0.33/0.57 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 0.33/0.57
% 0.33/0.57 % left_add_twice
% 0.33/0.57 thf(fact_3038_left__add__twice,axiom,
% 0.33/0.57 ! [A: rat,B: rat] :
% 0.33/0.57 ( ( plus_plus_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 0.33/0.57 = ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 0.33/0.57
% 0.33/0.57 % left_add_twice
% 0.33/0.57 thf(fact_3039_left__add__twice,axiom,
% 0.33/0.57 ! [A: code_natural,B: code_natural] :
% 0.33/0.57 ( ( plus_p4538020629002901425atural @ A @ ( plus_p4538020629002901425atural @ A @ B ) )
% 0.33/0.57 = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 0.33/0.57
% 0.33/0.57 % left_add_twice
% 0.33/0.57 thf(fact_3040_pos__eucl__rel__int__mult__2,axiom,
% 0.33/0.57 ! [B: int,A: int,Q3: int,R2: int] :
% 0.33/0.57 ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.33/0.57 => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q3 @ R2 ) )
% 0.33/0.57 => ( 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 ) ) @ R2 ) ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % pos_eucl_rel_int_mult_2
% 0.33/0.57 thf(fact_3041_one__power2,axiom,
% 0.33/0.57 ( ( power_8256067586552552935nteger @ one_one_Code_integer @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.33/0.57 = one_one_Code_integer ) ).
% 0.33/0.57
% 0.33/0.57 % one_power2
% 0.33/0.57 thf(fact_3042_one__power2,axiom,
% 0.33/0.57 ( ( power_power_rat @ one_one_rat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.33/0.57 = one_one_rat ) ).
% 0.33/0.57
% 0.33/0.57 % one_power2
% 0.33/0.57 thf(fact_3043_one__power2,axiom,
% 0.33/0.57 ( ( power_power_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.33/0.57 = one_one_nat ) ).
% 0.33/0.57
% 0.33/0.57 % one_power2
% 0.33/0.57 thf(fact_3044_one__power2,axiom,
% 0.33/0.57 ( ( power_power_int @ one_one_int @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.33/0.57 = one_one_int ) ).
% 0.33/0.57
% 0.33/0.57 % one_power2
% 0.33/0.57 thf(fact_3045_nat__1__add__1,axiom,
% 0.33/0.57 ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 0.33/0.57 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % nat_1_add_1
% 0.33/0.57 thf(fact_3046_Suc__nat__number__of__add,axiom,
% 0.33/0.57 ! [V: num,N2: nat] :
% 0.33/0.57 ( ( suc @ ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ N2 ) )
% 0.33/0.57 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ V @ one ) ) @ N2 ) ) ).
% 0.33/0.57
% 0.33/0.57 % Suc_nat_number_of_add
% 0.33/0.57 thf(fact_3047_double__gauss__sum__from__Suc__0,axiom,
% 0.33/0.57 ! [N2: nat] :
% 0.33/0.57 ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( groups2906978787729119204at_rat @ semiri681578069525770553at_rat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) )
% 0.33/0.57 = ( times_times_rat @ ( semiri681578069525770553at_rat @ N2 ) @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N2 ) @ one_one_rat ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % double_gauss_sum_from_Suc_0
% 0.33/0.57 thf(fact_3048_double__gauss__sum__from__Suc__0,axiom,
% 0.33/0.57 ! [N2: nat] :
% 0.33/0.57 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) )
% 0.33/0.57 = ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % double_gauss_sum_from_Suc_0
% 0.33/0.57 thf(fact_3049_double__gauss__sum__from__Suc__0,axiom,
% 0.33/0.57 ! [N2: nat] :
% 0.33/0.57 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( groups7501900531339628137nteger @ semiri4939895301339042750nteger @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) )
% 0.33/0.57 = ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N2 ) @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N2 ) @ one_one_Code_integer ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % double_gauss_sum_from_Suc_0
% 0.33/0.57 thf(fact_3050_double__gauss__sum__from__Suc__0,axiom,
% 0.33/0.57 ! [N2: nat] :
% 0.33/0.57 ( ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( groups6325495683096345652atural @ semiri3763490453095760265atural @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) )
% 0.33/0.57 = ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ N2 ) @ ( plus_p4538020629002901425atural @ ( semiri3763490453095760265atural @ N2 ) @ one_one_Code_natural ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % double_gauss_sum_from_Suc_0
% 0.33/0.57 thf(fact_3051_double__gauss__sum__from__Suc__0,axiom,
% 0.33/0.57 ! [N2: nat] :
% 0.33/0.57 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) )
% 0.33/0.57 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ one_one_nat ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % double_gauss_sum_from_Suc_0
% 0.33/0.57 thf(fact_3052_arith__series,axiom,
% 0.33/0.57 ! [A: int,D2: int,N2: nat] :
% 0.33/0.57 ( ( groups3539618377306564664at_int
% 0.33/0.57 @ ^ [I3: nat] : ( plus_plus_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ I3 ) @ D2 ) )
% 0.33/0.57 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 0.33/0.57 = ( divide_divide_int @ ( times_times_int @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ D2 ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % arith_series
% 0.33/0.57 thf(fact_3053_arith__series,axiom,
% 0.33/0.57 ! [A: code_integer,D2: code_integer,N2: nat] :
% 0.33/0.57 ( ( groups7501900531339628137nteger
% 0.33/0.57 @ ^ [I3: nat] : ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ I3 ) @ D2 ) )
% 0.33/0.57 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 0.33/0.57 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N2 ) @ one_one_Code_integer ) @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N2 ) @ D2 ) ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % arith_series
% 0.33/0.57 thf(fact_3054_arith__series,axiom,
% 0.33/0.57 ! [A: code_natural,D2: code_natural,N2: nat] :
% 0.33/0.57 ( ( groups6325495683096345652atural
% 0.33/0.57 @ ^ [I3: nat] : ( plus_p4538020629002901425atural @ A @ ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ I3 ) @ D2 ) )
% 0.33/0.57 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 0.33/0.57 = ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ ( plus_p4538020629002901425atural @ ( semiri3763490453095760265atural @ N2 ) @ one_one_Code_natural ) @ ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A ) @ ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ N2 ) @ D2 ) ) ) @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % arith_series
% 0.33/0.57 thf(fact_3055_arith__series,axiom,
% 0.33/0.57 ! [A: nat,D2: nat,N2: nat] :
% 0.33/0.57 ( ( groups3542108847815614940at_nat
% 0.33/0.57 @ ^ [I3: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ I3 ) @ D2 ) )
% 0.33/0.57 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 0.33/0.57 = ( divide_divide_nat @ ( times_times_nat @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ one_one_nat ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ D2 ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % arith_series
% 0.33/0.57 thf(fact_3056_gauss__sum,axiom,
% 0.33/0.57 ! [N2: nat] :
% 0.33/0.57 ( ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 0.33/0.57 = ( divide_divide_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % gauss_sum
% 0.33/0.57 thf(fact_3057_gauss__sum,axiom,
% 0.33/0.57 ! [N2: nat] :
% 0.33/0.57 ( ( groups7501900531339628137nteger @ semiri4939895301339042750nteger @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 0.33/0.57 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N2 ) @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N2 ) @ one_one_Code_integer ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % gauss_sum
% 0.33/0.57 thf(fact_3058_gauss__sum,axiom,
% 0.33/0.57 ! [N2: nat] :
% 0.33/0.57 ( ( groups6325495683096345652atural @ semiri3763490453095760265atural @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 0.33/0.57 = ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ N2 ) @ ( plus_p4538020629002901425atural @ ( semiri3763490453095760265atural @ N2 ) @ one_one_Code_natural ) ) @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % gauss_sum
% 0.33/0.57 thf(fact_3059_gauss__sum,axiom,
% 0.33/0.57 ! [N2: nat] :
% 0.33/0.57 ( ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 0.33/0.57 = ( divide_divide_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % gauss_sum
% 0.33/0.57 thf(fact_3060_nat__approx__posE,axiom,
% 0.33/0.57 ! [E: rat] :
% 0.33/0.57 ( ( ord_less_rat @ zero_zero_rat @ E )
% 0.33/0.57 => ~ ! [N: nat] :
% 0.33/0.57 ~ ( ord_less_rat @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ ( suc @ N ) ) ) @ E ) ) ).
% 0.33/0.57
% 0.33/0.57 % nat_approx_posE
% 0.33/0.57 thf(fact_3061_neg__eucl__rel__int__mult__2,axiom,
% 0.33/0.57 ! [B: int,A: int,Q3: int,R2: int] :
% 0.33/0.57 ( ( ord_less_eq_int @ B @ zero_zero_int )
% 0.33/0.57 => ( ( eucl_rel_int @ ( plus_plus_int @ A @ one_one_int ) @ B @ ( product_Pair_int_int @ Q3 @ R2 ) )
% 0.33/0.57 => ( 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 ) ) @ R2 ) @ one_one_int ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % neg_eucl_rel_int_mult_2
% 0.33/0.57 thf(fact_3062_gauss__sum__from__Suc__0,axiom,
% 0.33/0.57 ! [N2: nat] :
% 0.33/0.57 ( ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 0.33/0.57 = ( divide_divide_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % gauss_sum_from_Suc_0
% 0.33/0.57 thf(fact_3063_gauss__sum__from__Suc__0,axiom,
% 0.33/0.57 ! [N2: nat] :
% 0.33/0.57 ( ( groups7501900531339628137nteger @ semiri4939895301339042750nteger @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 0.33/0.57 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N2 ) @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N2 ) @ one_one_Code_integer ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % gauss_sum_from_Suc_0
% 0.33/0.57 thf(fact_3064_gauss__sum__from__Suc__0,axiom,
% 0.33/0.57 ! [N2: nat] :
% 0.33/0.57 ( ( groups6325495683096345652atural @ semiri3763490453095760265atural @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 0.33/0.57 = ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ N2 ) @ ( plus_p4538020629002901425atural @ ( semiri3763490453095760265atural @ N2 ) @ one_one_Code_natural ) ) @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % gauss_sum_from_Suc_0
% 0.33/0.57 thf(fact_3065_gauss__sum__from__Suc__0,axiom,
% 0.33/0.57 ! [N2: nat] :
% 0.33/0.57 ( ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 0.33/0.57 = ( divide_divide_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % gauss_sum_from_Suc_0
% 0.33/0.57 thf(fact_3066_exp__add__not__zero__imp__right,axiom,
% 0.33/0.57 ! [M2: nat,N2: nat] :
% 0.33/0.57 ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M2 @ N2 ) )
% 0.33/0.57 != zero_zero_nat )
% 0.33/0.57 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.33/0.57 != zero_zero_nat ) ) ).
% 0.33/0.57
% 0.33/0.57 % exp_add_not_zero_imp_right
% 0.33/0.57 thf(fact_3067_exp__add__not__zero__imp__right,axiom,
% 0.33/0.57 ! [M2: nat,N2: nat] :
% 0.33/0.57 ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M2 @ N2 ) )
% 0.33/0.57 != zero_zero_int )
% 0.33/0.57 => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 )
% 0.33/0.57 != zero_zero_int ) ) ).
% 0.33/0.57
% 0.33/0.57 % exp_add_not_zero_imp_right
% 0.33/0.57 thf(fact_3068_exp__add__not__zero__imp__right,axiom,
% 0.33/0.57 ! [M2: nat,N2: nat] :
% 0.33/0.57 ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M2 @ N2 ) )
% 0.33/0.57 != zero_z3403309356797280102nteger )
% 0.33/0.57 => ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 )
% 0.33/0.57 != zero_z3403309356797280102nteger ) ) ).
% 0.33/0.57
% 0.33/0.57 % exp_add_not_zero_imp_right
% 0.33/0.57 thf(fact_3069_exp__add__not__zero__imp__right,axiom,
% 0.33/0.57 ! [M2: nat,N2: nat] :
% 0.33/0.57 ( ( ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M2 @ N2 ) )
% 0.33/0.57 != zero_z2226904508553997617atural )
% 0.33/0.57 => ( ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N2 )
% 0.33/0.57 != zero_z2226904508553997617atural ) ) ).
% 0.33/0.57
% 0.33/0.57 % exp_add_not_zero_imp_right
% 0.33/0.57 thf(fact_3070_exp__add__not__zero__imp__left,axiom,
% 0.33/0.57 ! [M2: nat,N2: nat] :
% 0.33/0.57 ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M2 @ N2 ) )
% 0.33/0.57 != zero_zero_nat )
% 0.33/0.57 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 )
% 0.33/0.57 != zero_zero_nat ) ) ).
% 0.33/0.57
% 0.33/0.57 % exp_add_not_zero_imp_left
% 0.33/0.57 thf(fact_3071_exp__add__not__zero__imp__left,axiom,
% 0.33/0.57 ! [M2: nat,N2: nat] :
% 0.33/0.57 ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M2 @ N2 ) )
% 0.33/0.57 != zero_zero_int )
% 0.33/0.57 => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 )
% 0.33/0.57 != zero_zero_int ) ) ).
% 0.33/0.57
% 0.33/0.57 % exp_add_not_zero_imp_left
% 0.33/0.57 thf(fact_3072_exp__add__not__zero__imp__left,axiom,
% 0.33/0.57 ! [M2: nat,N2: nat] :
% 0.33/0.57 ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M2 @ N2 ) )
% 0.33/0.57 != zero_z3403309356797280102nteger )
% 0.33/0.57 => ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M2 )
% 0.33/0.57 != zero_z3403309356797280102nteger ) ) ).
% 0.33/0.57
% 0.33/0.57 % exp_add_not_zero_imp_left
% 0.33/0.57 thf(fact_3073_exp__add__not__zero__imp__left,axiom,
% 0.33/0.57 ! [M2: nat,N2: nat] :
% 0.33/0.57 ( ( ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M2 @ N2 ) )
% 0.33/0.57 != zero_z2226904508553997617atural )
% 0.33/0.57 => ( ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ M2 )
% 0.33/0.57 != zero_z2226904508553997617atural ) ) ).
% 0.33/0.57
% 0.33/0.57 % exp_add_not_zero_imp_left
% 0.33/0.57 thf(fact_3074_sum__power2__eq__zero__iff,axiom,
% 0.33/0.57 ! [X: code_integer,Y: code_integer] :
% 0.33/0.57 ( ( ( plus_p5714425477246183910nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.33/0.57 = zero_z3403309356797280102nteger )
% 0.33/0.57 = ( ( X = zero_z3403309356797280102nteger )
% 0.33/0.57 & ( Y = zero_z3403309356797280102nteger ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % sum_power2_eq_zero_iff
% 0.33/0.57 thf(fact_3075_sum__power2__eq__zero__iff,axiom,
% 0.33/0.57 ! [X: rat,Y: rat] :
% 0.33/0.57 ( ( ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.33/0.57 = zero_zero_rat )
% 0.33/0.57 = ( ( X = zero_zero_rat )
% 0.33/0.57 & ( Y = zero_zero_rat ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % sum_power2_eq_zero_iff
% 0.33/0.57 thf(fact_3076_sum__power2__eq__zero__iff,axiom,
% 0.33/0.57 ! [X: int,Y: int] :
% 0.33/0.57 ( ( ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.33/0.57 = zero_zero_int )
% 0.33/0.57 = ( ( X = zero_zero_int )
% 0.33/0.57 & ( Y = zero_zero_int ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % sum_power2_eq_zero_iff
% 0.33/0.57 thf(fact_3077_div__exp__eq,axiom,
% 0.33/0.57 ! [A: int,M2: nat,N2: nat] :
% 0.33/0.57 ( ( divide_divide_int @ ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 0.33/0.57 = ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M2 @ N2 ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % div_exp_eq
% 0.33/0.57 thf(fact_3078_div__exp__eq,axiom,
% 0.33/0.57 ! [A: nat,M2: nat,N2: nat] :
% 0.33/0.57 ( ( divide_divide_nat @ ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 0.33/0.57 = ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M2 @ N2 ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % div_exp_eq
% 0.33/0.57 thf(fact_3079_div__exp__eq,axiom,
% 0.33/0.57 ! [A: code_integer,M2: nat,N2: nat] :
% 0.33/0.57 ( ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M2 ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 0.33/0.57 = ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M2 @ N2 ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % div_exp_eq
% 0.33/0.57 thf(fact_3080_div__exp__eq,axiom,
% 0.33/0.57 ! [A: code_natural,M2: nat,N2: nat] :
% 0.33/0.57 ( ( divide5121882707175180666atural @ ( divide5121882707175180666atural @ A @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ M2 ) ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N2 ) )
% 0.33/0.57 = ( divide5121882707175180666atural @ A @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M2 @ N2 ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % div_exp_eq
% 0.33/0.57 thf(fact_3081_power2__eq__1__iff,axiom,
% 0.33/0.57 ! [A: int] :
% 0.33/0.57 ( ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.33/0.57 = one_one_int )
% 0.33/0.57 = ( ( A = one_one_int )
% 0.33/0.57 | ( A
% 0.33/0.57 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % power2_eq_1_iff
% 0.33/0.57 thf(fact_3082_power2__eq__1__iff,axiom,
% 0.33/0.57 ! [A: code_integer] :
% 0.33/0.57 ( ( ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.33/0.57 = one_one_Code_integer )
% 0.33/0.57 = ( ( A = one_one_Code_integer )
% 0.33/0.57 | ( A
% 0.33/0.57 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % power2_eq_1_iff
% 0.33/0.57 thf(fact_3083_power2__eq__1__iff,axiom,
% 0.33/0.57 ! [A: rat] :
% 0.33/0.57 ( ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.33/0.57 = one_one_rat )
% 0.33/0.57 = ( ( A = one_one_rat )
% 0.33/0.57 | ( A
% 0.33/0.57 = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % power2_eq_1_iff
% 0.33/0.57 thf(fact_3084_plus__int_Oabs__eq,axiom,
% 0.33/0.57 ! [Xa: product_prod_nat_nat,X: product_prod_nat_nat] :
% 0.33/0.57 ( ( plus_plus_int @ ( abs_Integ @ Xa ) @ ( abs_Integ @ X ) )
% 0.33/0.57 = ( abs_Integ
% 0.33/0.57 @ ( produc27273713700761075at_nat
% 0.33/0.57 @ ^ [X3: nat,Y3: nat] :
% 0.33/0.57 ( produc2626176000494625587at_nat
% 0.33/0.57 @ ^ [U2: nat,V2: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X3 @ U2 ) @ ( plus_plus_nat @ Y3 @ V2 ) ) )
% 0.33/0.57 @ Xa
% 0.33/0.57 @ X ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % plus_int.abs_eq
% 0.33/0.57 thf(fact_3085_abs__square__eq__1,axiom,
% 0.33/0.57 ! [X: code_integer] :
% 0.33/0.57 ( ( ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.33/0.57 = one_one_Code_integer )
% 0.33/0.57 = ( ( abs_abs_Code_integer @ X )
% 0.33/0.57 = one_one_Code_integer ) ) ).
% 0.33/0.57
% 0.33/0.57 % abs_square_eq_1
% 0.33/0.57 thf(fact_3086_abs__square__eq__1,axiom,
% 0.33/0.57 ! [X: rat] :
% 0.33/0.57 ( ( ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.33/0.57 = one_one_rat )
% 0.33/0.57 = ( ( abs_abs_rat @ X )
% 0.33/0.57 = one_one_rat ) ) ).
% 0.33/0.57
% 0.33/0.57 % abs_square_eq_1
% 0.33/0.57 thf(fact_3087_abs__square__eq__1,axiom,
% 0.33/0.57 ! [X: int] :
% 0.33/0.57 ( ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.33/0.57 = one_one_int )
% 0.33/0.57 = ( ( abs_abs_int @ X )
% 0.33/0.57 = one_one_int ) ) ).
% 0.33/0.57
% 0.33/0.57 % abs_square_eq_1
% 0.33/0.57 thf(fact_3088_minus__int_Oabs__eq,axiom,
% 0.33/0.57 ! [Xa: product_prod_nat_nat,X: product_prod_nat_nat] :
% 0.33/0.57 ( ( minus_minus_int @ ( abs_Integ @ Xa ) @ ( abs_Integ @ X ) )
% 0.33/0.57 = ( abs_Integ
% 0.33/0.57 @ ( produc27273713700761075at_nat
% 0.33/0.57 @ ^ [X3: nat,Y3: nat] :
% 0.33/0.57 ( produc2626176000494625587at_nat
% 0.33/0.57 @ ^ [U2: nat,V2: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X3 @ V2 ) @ ( plus_plus_nat @ Y3 @ U2 ) ) )
% 0.33/0.57 @ Xa
% 0.33/0.57 @ X ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % minus_int.abs_eq
% 0.33/0.57 thf(fact_3089_nat__induct2,axiom,
% 0.33/0.57 ! [P: nat > $o,N2: nat] :
% 0.33/0.57 ( ( P @ zero_zero_nat )
% 0.33/0.57 => ( ( P @ one_one_nat )
% 0.33/0.57 => ( ! [N: nat] :
% 0.33/0.57 ( ( P @ N )
% 0.33/0.57 => ( P @ ( plus_plus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.33/0.57 => ( P @ N2 ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % nat_induct2
% 0.33/0.57 thf(fact_3090_times__int_Oabs__eq,axiom,
% 0.33/0.57 ! [Xa: product_prod_nat_nat,X: product_prod_nat_nat] :
% 0.33/0.57 ( ( times_times_int @ ( abs_Integ @ Xa ) @ ( abs_Integ @ X ) )
% 0.33/0.57 = ( abs_Integ
% 0.33/0.57 @ ( produc27273713700761075at_nat
% 0.33/0.57 @ ^ [X3: nat,Y3: nat] :
% 0.33/0.57 ( produc2626176000494625587at_nat
% 0.33/0.57 @ ^ [U2: nat,V2: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X3 @ U2 ) @ ( times_times_nat @ Y3 @ V2 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X3 @ V2 ) @ ( times_times_nat @ Y3 @ U2 ) ) ) )
% 0.33/0.57 @ Xa
% 0.33/0.57 @ X ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % times_int.abs_eq
% 0.33/0.57 thf(fact_3091_sum__power2__le__zero__iff,axiom,
% 0.33/0.57 ! [X: code_integer,Y: code_integer] :
% 0.33/0.57 ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_z3403309356797280102nteger )
% 0.33/0.57 = ( ( X = zero_z3403309356797280102nteger )
% 0.33/0.57 & ( Y = zero_z3403309356797280102nteger ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % sum_power2_le_zero_iff
% 0.33/0.57 thf(fact_3092_sum__power2__le__zero__iff,axiom,
% 0.33/0.57 ! [X: rat,Y: rat] :
% 0.33/0.57 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_rat )
% 0.33/0.57 = ( ( X = zero_zero_rat )
% 0.33/0.57 & ( Y = zero_zero_rat ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % sum_power2_le_zero_iff
% 0.33/0.57 thf(fact_3093_sum__power2__le__zero__iff,axiom,
% 0.33/0.57 ! [X: int,Y: int] :
% 0.33/0.57 ( ( ord_less_eq_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_int )
% 0.33/0.57 = ( ( X = zero_zero_int )
% 0.33/0.57 & ( Y = zero_zero_int ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % sum_power2_le_zero_iff
% 0.33/0.57 thf(fact_3094_sum__power2__ge__zero,axiom,
% 0.33/0.57 ! [X: code_integer,Y: code_integer] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % sum_power2_ge_zero
% 0.33/0.57 thf(fact_3095_sum__power2__ge__zero,axiom,
% 0.33/0.57 ! [X: rat,Y: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % sum_power2_ge_zero
% 0.33/0.57 thf(fact_3096_sum__power2__ge__zero,axiom,
% 0.33/0.57 ! [X: int,Y: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % sum_power2_ge_zero
% 0.33/0.57 thf(fact_3097_bits__stable__imp__add__self,axiom,
% 0.33/0.57 ! [A: int] :
% 0.33/0.57 ( ( ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.33/0.57 = A )
% 0.33/0.57 => ( ( plus_plus_int @ A @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 0.33/0.57 = zero_zero_int ) ) ).
% 0.33/0.57
% 0.33/0.57 % bits_stable_imp_add_self
% 0.33/0.57 thf(fact_3098_bits__stable__imp__add__self,axiom,
% 0.33/0.57 ! [A: nat] :
% 0.33/0.57 ( ( ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.33/0.57 = A )
% 0.33/0.57 => ( ( plus_plus_nat @ A @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.33/0.57 = zero_zero_nat ) ) ).
% 0.33/0.57
% 0.33/0.57 % bits_stable_imp_add_self
% 0.33/0.57 thf(fact_3099_bits__stable__imp__add__self,axiom,
% 0.33/0.57 ! [A: code_integer] :
% 0.33/0.57 ( ( ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.33/0.57 = A )
% 0.33/0.57 => ( ( plus_p5714425477246183910nteger @ A @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) )
% 0.33/0.57 = zero_z3403309356797280102nteger ) ) ).
% 0.33/0.57
% 0.33/0.57 % bits_stable_imp_add_self
% 0.33/0.57 thf(fact_3100_bits__stable__imp__add__self,axiom,
% 0.33/0.57 ! [A: code_natural] :
% 0.33/0.57 ( ( ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 0.33/0.57 = A )
% 0.33/0.57 => ( ( plus_p4538020629002901425atural @ A @ ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) )
% 0.33/0.57 = zero_z2226904508553997617atural ) ) ).
% 0.33/0.57
% 0.33/0.57 % bits_stable_imp_add_self
% 0.33/0.57 thf(fact_3101_not__sum__power2__lt__zero,axiom,
% 0.33/0.57 ! [X: code_integer,Y: code_integer] :
% 0.33/0.57 ~ ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_z3403309356797280102nteger ) ).
% 0.33/0.57
% 0.33/0.57 % not_sum_power2_lt_zero
% 0.33/0.57 thf(fact_3102_not__sum__power2__lt__zero,axiom,
% 0.33/0.57 ! [X: rat,Y: rat] :
% 0.33/0.57 ~ ( ord_less_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_rat ) ).
% 0.33/0.57
% 0.33/0.57 % not_sum_power2_lt_zero
% 0.33/0.57 thf(fact_3103_not__sum__power2__lt__zero,axiom,
% 0.33/0.57 ! [X: int,Y: int] :
% 0.33/0.57 ~ ( ord_less_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_int ) ).
% 0.33/0.57
% 0.33/0.57 % not_sum_power2_lt_zero
% 0.33/0.57 thf(fact_3104_sum__power2__gt__zero__iff,axiom,
% 0.33/0.57 ! [X: code_integer,Y: code_integer] :
% 0.33/0.57 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.33/0.57 = ( ( X != zero_z3403309356797280102nteger )
% 0.33/0.57 | ( Y != zero_z3403309356797280102nteger ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % sum_power2_gt_zero_iff
% 0.33/0.57 thf(fact_3105_sum__power2__gt__zero__iff,axiom,
% 0.33/0.57 ! [X: rat,Y: rat] :
% 0.33/0.57 ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.33/0.57 = ( ( X != zero_zero_rat )
% 0.33/0.57 | ( Y != zero_zero_rat ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % sum_power2_gt_zero_iff
% 0.33/0.57 thf(fact_3106_sum__power2__gt__zero__iff,axiom,
% 0.33/0.57 ! [X: int,Y: int] :
% 0.33/0.57 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.33/0.57 = ( ( X != zero_zero_int )
% 0.33/0.57 | ( Y != zero_zero_int ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % sum_power2_gt_zero_iff
% 0.33/0.57 thf(fact_3107_power2__sum,axiom,
% 0.33/0.57 ! [X: nat,Y: nat] :
% 0.33/0.57 ( ( power_power_nat @ ( plus_plus_nat @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.33/0.57 = ( plus_plus_nat @ ( plus_plus_nat @ ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % power2_sum
% 0.33/0.57 thf(fact_3108_power2__sum,axiom,
% 0.33/0.57 ! [X: int,Y: int] :
% 0.33/0.57 ( ( power_power_int @ ( plus_plus_int @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.33/0.57 = ( plus_plus_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % power2_sum
% 0.33/0.57 thf(fact_3109_power2__sum,axiom,
% 0.33/0.57 ! [X: code_integer,Y: code_integer] :
% 0.33/0.57 ( ( power_8256067586552552935nteger @ ( plus_p5714425477246183910nteger @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.33/0.57 = ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % power2_sum
% 0.33/0.57 thf(fact_3110_power2__sum,axiom,
% 0.33/0.57 ! [X: rat,Y: rat] :
% 0.33/0.57 ( ( power_power_rat @ ( plus_plus_rat @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.33/0.57 = ( plus_plus_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % power2_sum
% 0.33/0.57 thf(fact_3111_power2__sum,axiom,
% 0.33/0.57 ! [X: code_natural,Y: code_natural] :
% 0.33/0.57 ( ( power_7079662738309270450atural @ ( plus_p4538020629002901425atural @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.33/0.57 = ( plus_p4538020629002901425atural @ ( plus_p4538020629002901425atural @ ( power_7079662738309270450atural @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_7079662738309270450atural @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_2397367101498566445atural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % power2_sum
% 0.33/0.57 thf(fact_3112_square__le__1,axiom,
% 0.33/0.57 ! [X: code_integer] :
% 0.33/0.57 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ X )
% 0.33/0.57 => ( ( ord_le3102999989581377725nteger @ X @ one_one_Code_integer )
% 0.33/0.57 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % square_le_1
% 0.33/0.57 thf(fact_3113_square__le__1,axiom,
% 0.33/0.57 ! [X: rat] :
% 0.33/0.57 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ X )
% 0.33/0.57 => ( ( ord_less_eq_rat @ X @ one_one_rat )
% 0.33/0.57 => ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % square_le_1
% 0.33/0.57 thf(fact_3114_square__le__1,axiom,
% 0.33/0.57 ! [X: int] :
% 0.33/0.57 ( ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ X )
% 0.33/0.57 => ( ( ord_less_eq_int @ X @ one_one_int )
% 0.33/0.57 => ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % square_le_1
% 0.33/0.57 thf(fact_3115_abs__square__le__1,axiom,
% 0.33/0.57 ! [X: code_integer] :
% 0.33/0.57 ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer )
% 0.33/0.57 = ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X ) @ one_one_Code_integer ) ) ).
% 0.33/0.57
% 0.33/0.57 % abs_square_le_1
% 0.33/0.57 thf(fact_3116_abs__square__le__1,axiom,
% 0.33/0.57 ! [X: rat] :
% 0.33/0.57 ( ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat )
% 0.33/0.57 = ( ord_less_eq_rat @ ( abs_abs_rat @ X ) @ one_one_rat ) ) ).
% 0.33/0.57
% 0.33/0.57 % abs_square_le_1
% 0.33/0.57 thf(fact_3117_abs__square__le__1,axiom,
% 0.33/0.57 ! [X: int] :
% 0.33/0.57 ( ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int )
% 0.33/0.57 = ( ord_less_eq_int @ ( abs_abs_int @ X ) @ one_one_int ) ) ).
% 0.33/0.57
% 0.33/0.57 % abs_square_le_1
% 0.33/0.57 thf(fact_3118_abs__square__less__1,axiom,
% 0.33/0.57 ! [X: code_integer] :
% 0.33/0.57 ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer )
% 0.33/0.57 = ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ X ) @ one_one_Code_integer ) ) ).
% 0.33/0.57
% 0.33/0.57 % abs_square_less_1
% 0.33/0.57 thf(fact_3119_abs__square__less__1,axiom,
% 0.33/0.57 ! [X: rat] :
% 0.33/0.57 ( ( ord_less_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat )
% 0.33/0.57 = ( ord_less_rat @ ( abs_abs_rat @ X ) @ one_one_rat ) ) ).
% 0.33/0.57
% 0.33/0.57 % abs_square_less_1
% 0.33/0.57 thf(fact_3120_abs__square__less__1,axiom,
% 0.33/0.57 ! [X: int] :
% 0.33/0.57 ( ( ord_less_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int )
% 0.33/0.57 = ( ord_less_int @ ( abs_abs_int @ X ) @ one_one_int ) ) ).
% 0.33/0.57
% 0.33/0.57 % abs_square_less_1
% 0.33/0.57 thf(fact_3121_div__exp__mod__exp__eq,axiom,
% 0.33/0.57 ! [A: int,N2: nat,M2: nat] :
% 0.33/0.57 ( ( modulo_modulo_int @ ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 ) )
% 0.33/0.57 = ( divide_divide_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N2 @ M2 ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % div_exp_mod_exp_eq
% 0.33/0.57 thf(fact_3122_div__exp__mod__exp__eq,axiom,
% 0.33/0.57 ! [A: nat,N2: nat,M2: nat] :
% 0.33/0.57 ( ( modulo_modulo_nat @ ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 0.33/0.57 = ( divide_divide_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N2 @ M2 ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % div_exp_mod_exp_eq
% 0.33/0.57 thf(fact_3123_div__exp__mod__exp__eq,axiom,
% 0.33/0.57 ! [A: code_integer,N2: nat,M2: nat] :
% 0.33/0.57 ( ( modulo364778990260209775nteger @ ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M2 ) )
% 0.33/0.57 = ( divide6298287555418463151nteger @ ( modulo364778990260209775nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N2 @ M2 ) ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % div_exp_mod_exp_eq
% 0.33/0.57 thf(fact_3124_div__exp__mod__exp__eq,axiom,
% 0.33/0.57 ! [A: code_natural,N2: nat,M2: nat] :
% 0.33/0.57 ( ( modulo8411746178871703098atural @ ( divide5121882707175180666atural @ A @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N2 ) ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ M2 ) )
% 0.33/0.57 = ( divide5121882707175180666atural @ ( modulo8411746178871703098atural @ A @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N2 @ M2 ) ) ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % div_exp_mod_exp_eq
% 0.33/0.57 thf(fact_3125_ex__power__ivl2,axiom,
% 0.33/0.57 ! [B: nat,K: nat] :
% 0.33/0.57 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 0.33/0.57 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 0.33/0.57 => ? [N: nat] :
% 0.33/0.57 ( ( ord_less_nat @ ( power_power_nat @ B @ N ) @ K )
% 0.33/0.57 & ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % ex_power_ivl2
% 0.33/0.57 thf(fact_3126_ex__power__ivl1,axiom,
% 0.33/0.57 ! [B: nat,K: nat] :
% 0.33/0.57 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 0.33/0.57 => ( ( ord_less_eq_nat @ one_one_nat @ K )
% 0.33/0.57 => ? [N: nat] :
% 0.33/0.57 ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N ) @ K )
% 0.33/0.57 & ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % ex_power_ivl1
% 0.33/0.57 thf(fact_3127_power2__diff,axiom,
% 0.33/0.57 ! [X: int,Y: int] :
% 0.33/0.57 ( ( power_power_int @ ( minus_minus_int @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.33/0.57 = ( minus_minus_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % power2_diff
% 0.33/0.57 thf(fact_3128_power2__diff,axiom,
% 0.33/0.57 ! [X: code_integer,Y: code_integer] :
% 0.33/0.57 ( ( power_8256067586552552935nteger @ ( minus_8373710615458151222nteger @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.33/0.57 = ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % power2_diff
% 0.33/0.57 thf(fact_3129_power2__diff,axiom,
% 0.33/0.57 ! [X: rat,Y: rat] :
% 0.33/0.57 ( ( power_power_rat @ ( minus_minus_rat @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.33/0.57 = ( minus_minus_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % power2_diff
% 0.33/0.57 thf(fact_3130_power__minus1__odd,axiom,
% 0.33/0.57 ! [N2: nat] :
% 0.33/0.57 ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 0.33/0.57 = ( uminus_uminus_int @ one_one_int ) ) ).
% 0.33/0.57
% 0.33/0.57 % power_minus1_odd
% 0.33/0.57 thf(fact_3131_power__minus1__odd,axiom,
% 0.33/0.57 ! [N2: nat] :
% 0.33/0.57 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 0.33/0.57 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.33/0.57
% 0.33/0.57 % power_minus1_odd
% 0.33/0.57 thf(fact_3132_power__minus1__odd,axiom,
% 0.33/0.57 ! [N2: nat] :
% 0.33/0.57 ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 0.33/0.57 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.33/0.57
% 0.33/0.57 % power_minus1_odd
% 0.33/0.57 thf(fact_3133_mask__eq__sum__exp,axiom,
% 0.33/0.57 ! [N2: nat] :
% 0.33/0.57 ( ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ one_one_int )
% 0.33/0.57 = ( groups3539618377306564664at_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.33/0.57 @ ( collect_nat
% 0.33/0.57 @ ^ [Q5: nat] : ( ord_less_nat @ Q5 @ N2 ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % mask_eq_sum_exp
% 0.33/0.57 thf(fact_3134_mask__eq__sum__exp,axiom,
% 0.33/0.57 ! [N2: nat] :
% 0.33/0.57 ( ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) @ one_one_Code_integer )
% 0.33/0.57 = ( groups7501900531339628137nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.33/0.57 @ ( collect_nat
% 0.33/0.57 @ ^ [Q5: nat] : ( ord_less_nat @ Q5 @ N2 ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % mask_eq_sum_exp
% 0.33/0.57 thf(fact_3135_mask__eq__sum__exp,axiom,
% 0.33/0.57 ! [N2: nat] :
% 0.33/0.57 ( ( minus_7197305767214868737atural @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N2 ) @ one_one_Code_natural )
% 0.33/0.57 = ( groups6325495683096345652atural @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 0.33/0.57 @ ( collect_nat
% 0.33/0.57 @ ^ [Q5: nat] : ( ord_less_nat @ Q5 @ N2 ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % mask_eq_sum_exp
% 0.33/0.57 thf(fact_3136_mask__eq__sum__exp,axiom,
% 0.33/0.57 ! [N2: nat] :
% 0.33/0.57 ( ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat )
% 0.33/0.57 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.33/0.57 @ ( collect_nat
% 0.33/0.57 @ ^ [Q5: nat] : ( ord_less_nat @ Q5 @ N2 ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % mask_eq_sum_exp
% 0.33/0.57 thf(fact_3137_sum_Oin__pairs,axiom,
% 0.33/0.57 ! [G: nat > multis2468970476368604999at_nat,M2: nat,N2: nat] :
% 0.33/0.57 ( ( groups6857163185585827899at_nat @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 0.33/0.57 = ( groups6857163185585827899at_nat
% 0.33/0.57 @ ^ [I3: nat] : ( plus_p7104986032573967614at_nat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 0.33/0.57 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % sum.in_pairs
% 0.33/0.57 thf(fact_3138_sum_Oin__pairs,axiom,
% 0.33/0.57 ! [G: nat > rat,M2: nat,N2: nat] :
% 0.33/0.57 ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 0.33/0.57 = ( groups2906978787729119204at_rat
% 0.33/0.57 @ ^ [I3: nat] : ( plus_plus_rat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 0.33/0.57 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % sum.in_pairs
% 0.33/0.57 thf(fact_3139_sum_Oin__pairs,axiom,
% 0.33/0.57 ! [G: nat > int,M2: nat,N2: nat] :
% 0.33/0.57 ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 0.33/0.57 = ( groups3539618377306564664at_int
% 0.33/0.57 @ ^ [I3: nat] : ( plus_plus_int @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 0.33/0.57 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % sum.in_pairs
% 0.33/0.57 thf(fact_3140_sum_Oin__pairs,axiom,
% 0.33/0.57 ! [G: nat > nat,M2: nat,N2: nat] :
% 0.33/0.57 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 0.33/0.57 = ( groups3542108847815614940at_nat
% 0.33/0.57 @ ^ [I3: nat] : ( plus_plus_nat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 0.33/0.57 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % sum.in_pairs
% 0.33/0.57 thf(fact_3141_gauss__sum__nat,axiom,
% 0.33/0.57 ! [N2: nat] :
% 0.33/0.57 ( ( groups3542108847815614940at_nat
% 0.33/0.57 @ ^ [X3: nat] : X3
% 0.33/0.57 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 0.33/0.57 = ( divide_divide_nat @ ( times_times_nat @ N2 @ ( suc @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % gauss_sum_nat
% 0.33/0.57 thf(fact_3142_divmod__step__eq,axiom,
% 0.33/0.57 ! [L: num,R2: nat,Q3: nat] :
% 0.33/0.57 ( ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ L ) @ R2 )
% 0.33/0.57 => ( ( unique5026877609467782581ep_nat @ L @ ( product_Pair_nat_nat @ Q3 @ R2 ) )
% 0.33/0.57 = ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q3 ) @ one_one_nat ) @ ( minus_minus_nat @ R2 @ ( numeral_numeral_nat @ L ) ) ) ) )
% 0.33/0.57 & ( ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L ) @ R2 )
% 0.33/0.57 => ( ( unique5026877609467782581ep_nat @ L @ ( product_Pair_nat_nat @ Q3 @ R2 ) )
% 0.33/0.57 = ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q3 ) @ R2 ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % divmod_step_eq
% 0.33/0.57 thf(fact_3143_divmod__step__eq,axiom,
% 0.33/0.57 ! [L: num,R2: int,Q3: int] :
% 0.33/0.57 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ L ) @ R2 )
% 0.33/0.57 => ( ( unique5024387138958732305ep_int @ L @ ( product_Pair_int_int @ Q3 @ R2 ) )
% 0.33/0.57 = ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q3 ) @ one_one_int ) @ ( minus_minus_int @ R2 @ ( numeral_numeral_int @ L ) ) ) ) )
% 0.33/0.57 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ L ) @ R2 )
% 0.33/0.57 => ( ( unique5024387138958732305ep_int @ L @ ( product_Pair_int_int @ Q3 @ R2 ) )
% 0.33/0.57 = ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q3 ) @ R2 ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % divmod_step_eq
% 0.33/0.57 thf(fact_3144_divmod__step__eq,axiom,
% 0.33/0.57 ! [L: num,R2: code_integer,Q3: code_integer] :
% 0.33/0.57 ( ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L ) @ R2 )
% 0.33/0.57 => ( ( unique4921790084139445826nteger @ L @ ( produc1086072967326762835nteger @ Q3 @ R2 ) )
% 0.33/0.57 = ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q3 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R2 @ ( numera6620942414471956472nteger @ L ) ) ) ) )
% 0.33/0.57 & ( ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L ) @ R2 )
% 0.33/0.57 => ( ( unique4921790084139445826nteger @ L @ ( produc1086072967326762835nteger @ Q3 @ R2 ) )
% 0.33/0.57 = ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q3 ) @ R2 ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % divmod_step_eq
% 0.33/0.57 thf(fact_3145_divmod__step__def,axiom,
% 0.33/0.57 ( unique5026877609467782581ep_nat
% 0.33/0.57 = ( ^ [L3: num] :
% 0.33/0.57 ( produc2626176000494625587at_nat
% 0.33/0.57 @ ^ [Q5: nat,R3: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L3 ) @ R3 ) @ ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q5 ) @ one_one_nat ) @ ( minus_minus_nat @ R3 @ ( numeral_numeral_nat @ L3 ) ) ) @ ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q5 ) @ R3 ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % divmod_step_def
% 0.33/0.57 thf(fact_3146_divmod__step__def,axiom,
% 0.33/0.57 ( unique5024387138958732305ep_int
% 0.33/0.57 = ( ^ [L3: num] :
% 0.33/0.57 ( produc4245557441103728435nt_int
% 0.33/0.57 @ ^ [Q5: int,R3: int] : ( if_Pro3027730157355071871nt_int @ ( ord_less_eq_int @ ( numeral_numeral_int @ L3 ) @ R3 ) @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q5 ) @ one_one_int ) @ ( minus_minus_int @ R3 @ ( numeral_numeral_int @ L3 ) ) ) @ ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q5 ) @ R3 ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % divmod_step_def
% 0.33/0.57 thf(fact_3147_divmod__step__def,axiom,
% 0.33/0.57 ( unique4921790084139445826nteger
% 0.33/0.57 = ( ^ [L3: num] :
% 0.33/0.57 ( produc6916734918728496179nteger
% 0.33/0.57 @ ^ [Q5: code_integer,R3: code_integer] : ( if_Pro6119634080678213985nteger @ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L3 ) @ R3 ) @ ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R3 @ ( numera6620942414471956472nteger @ L3 ) ) ) @ ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q5 ) @ R3 ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % divmod_step_def
% 0.33/0.57 thf(fact_3148_divmod__step__nat__def,axiom,
% 0.33/0.57 ( unique5026877609467782581ep_nat
% 0.33/0.57 = ( ^ [L3: num] :
% 0.33/0.57 ( produc2626176000494625587at_nat
% 0.33/0.57 @ ^ [Q5: nat,R3: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L3 ) @ R3 ) @ ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q5 ) @ one_one_nat ) @ ( minus_minus_nat @ R3 @ ( numeral_numeral_nat @ L3 ) ) ) @ ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q5 ) @ R3 ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % divmod_step_nat_def
% 0.33/0.57 thf(fact_3149_divmod__step__int__def,axiom,
% 0.33/0.57 ( unique5024387138958732305ep_int
% 0.33/0.57 = ( ^ [L3: num] :
% 0.33/0.57 ( produc4245557441103728435nt_int
% 0.33/0.57 @ ^ [Q5: int,R3: int] : ( if_Pro3027730157355071871nt_int @ ( ord_less_eq_int @ ( numeral_numeral_int @ L3 ) @ R3 ) @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q5 ) @ one_one_int ) @ ( minus_minus_int @ R3 @ ( numeral_numeral_int @ L3 ) ) ) @ ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q5 ) @ R3 ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % divmod_step_int_def
% 0.33/0.57 thf(fact_3150_set__bit__0,axiom,
% 0.33/0.57 ! [A: code_integer] :
% 0.33/0.57 ( ( bit_se2793503036327961859nteger @ zero_zero_nat @ A )
% 0.33/0.57 = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % set_bit_0
% 0.33/0.57 thf(fact_3151_set__bit__0,axiom,
% 0.33/0.57 ! [A: int] :
% 0.33/0.57 ( ( bit_se7879613467334960850it_int @ zero_zero_nat @ A )
% 0.33/0.57 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % set_bit_0
% 0.33/0.57 thf(fact_3152_set__bit__0,axiom,
% 0.33/0.57 ! [A: nat] :
% 0.33/0.57 ( ( bit_se7882103937844011126it_nat @ zero_zero_nat @ A )
% 0.33/0.57 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % set_bit_0
% 0.33/0.57 thf(fact_3153_set__bit__0,axiom,
% 0.33/0.57 ! [A: code_natural] :
% 0.33/0.57 ( ( bit_se1617098188084679374atural @ zero_zero_nat @ A )
% 0.33/0.57 = ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % set_bit_0
% 0.33/0.57 thf(fact_3154_mlex__eq,axiom,
% 0.33/0.57 ( mlex_p3502713205431853936at_nat
% 0.33/0.57 = ( ^ [F2: set_Pr1261947904930325089at_nat > nat,R5: set_Pr4329608150637261639at_nat] :
% 0.33/0.57 ( collec6321179662152712658at_nat
% 0.33/0.57 @ ( produc410239310623530412_nat_o
% 0.33/0.57 @ ^ [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] :
% 0.33/0.57 ( ( ord_less_nat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) )
% 0.33/0.57 | ( ( ord_less_eq_nat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) )
% 0.33/0.57 & ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ Y3 ) @ R5 ) ) ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % mlex_eq
% 0.33/0.57 thf(fact_3155_mlex__eq,axiom,
% 0.33/0.57 ( mlex_prod_nat
% 0.33/0.57 = ( ^ [F2: nat > nat,R5: set_Pr1261947904930325089at_nat] :
% 0.33/0.57 ( collec3392354462482085612at_nat
% 0.33/0.57 @ ( produc6081775807080527818_nat_o
% 0.33/0.57 @ ^ [X3: nat,Y3: nat] :
% 0.33/0.57 ( ( ord_less_nat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) )
% 0.33/0.57 | ( ( ord_less_eq_nat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) )
% 0.33/0.57 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y3 ) @ R5 ) ) ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % mlex_eq
% 0.33/0.57 thf(fact_3156_unset__bit__Suc,axiom,
% 0.33/0.57 ! [N2: nat,A: code_integer] :
% 0.33/0.57 ( ( bit_se8260200283734997820nteger @ ( suc @ N2 ) @ A )
% 0.33/0.57 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se8260200283734997820nteger @ N2 @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % unset_bit_Suc
% 0.33/0.57 thf(fact_3157_unset__bit__Suc,axiom,
% 0.33/0.57 ! [N2: nat,A: int] :
% 0.33/0.57 ( ( bit_se4203085406695923979it_int @ ( suc @ N2 ) @ A )
% 0.33/0.57 = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se4203085406695923979it_int @ N2 @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % unset_bit_Suc
% 0.33/0.57 thf(fact_3158_unset__bit__Suc,axiom,
% 0.33/0.57 ! [N2: nat,A: nat] :
% 0.33/0.57 ( ( bit_se4205575877204974255it_nat @ ( suc @ N2 ) @ A )
% 0.33/0.57 = ( plus_plus_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se4205575877204974255it_nat @ N2 @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % unset_bit_Suc
% 0.33/0.57 thf(fact_3159_unset__bit__Suc,axiom,
% 0.33/0.57 ! [N2: nat,A: code_natural] :
% 0.33/0.57 ( ( bit_se7083795435491715335atural @ ( suc @ N2 ) @ A )
% 0.33/0.57 = ( plus_p4538020629002901425atural @ ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se7083795435491715335atural @ N2 @ ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % unset_bit_Suc
% 0.33/0.57 thf(fact_3160_flip__bit__Suc,axiom,
% 0.33/0.57 ! [N2: nat,A: code_integer] :
% 0.33/0.57 ( ( bit_se1345352211410354436nteger @ ( suc @ N2 ) @ A )
% 0.33/0.57 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1345352211410354436nteger @ N2 @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % flip_bit_Suc
% 0.33/0.57 thf(fact_3161_flip__bit__Suc,axiom,
% 0.33/0.57 ! [N2: nat,A: int] :
% 0.33/0.57 ( ( bit_se2159334234014336723it_int @ ( suc @ N2 ) @ A )
% 0.33/0.57 = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2159334234014336723it_int @ N2 @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % flip_bit_Suc
% 0.33/0.57 thf(fact_3162_flip__bit__Suc,axiom,
% 0.33/0.57 ! [N2: nat,A: nat] :
% 0.33/0.57 ( ( bit_se2161824704523386999it_nat @ ( suc @ N2 ) @ A )
% 0.33/0.57 = ( plus_plus_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2161824704523386999it_nat @ N2 @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % flip_bit_Suc
% 0.33/0.57 thf(fact_3163_flip__bit__Suc,axiom,
% 0.33/0.57 ! [N2: nat,A: code_natural] :
% 0.33/0.57 ( ( bit_se168947363167071951atural @ ( suc @ N2 ) @ A )
% 0.33/0.57 = ( plus_p4538020629002901425atural @ ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se168947363167071951atural @ N2 @ ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % flip_bit_Suc
% 0.33/0.57 thf(fact_3164_set__bit__Suc,axiom,
% 0.33/0.57 ! [N2: nat,A: code_integer] :
% 0.33/0.57 ( ( bit_se2793503036327961859nteger @ ( suc @ N2 ) @ A )
% 0.33/0.57 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se2793503036327961859nteger @ N2 @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % set_bit_Suc
% 0.33/0.57 thf(fact_3165_set__bit__Suc,axiom,
% 0.33/0.57 ! [N2: nat,A: int] :
% 0.33/0.57 ( ( bit_se7879613467334960850it_int @ ( suc @ N2 ) @ A )
% 0.33/0.57 = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se7879613467334960850it_int @ N2 @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % set_bit_Suc
% 0.33/0.57 thf(fact_3166_set__bit__Suc,axiom,
% 0.33/0.57 ! [N2: nat,A: nat] :
% 0.33/0.57 ( ( bit_se7882103937844011126it_nat @ ( suc @ N2 ) @ A )
% 0.33/0.57 = ( plus_plus_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se7882103937844011126it_nat @ N2 @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % set_bit_Suc
% 0.33/0.57 thf(fact_3167_set__bit__Suc,axiom,
% 0.33/0.57 ! [N2: nat,A: code_natural] :
% 0.33/0.57 ( ( bit_se1617098188084679374atural @ ( suc @ N2 ) @ A )
% 0.33/0.57 = ( plus_p4538020629002901425atural @ ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se1617098188084679374atural @ N2 @ ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % set_bit_Suc
% 0.33/0.57 thf(fact_3168_divmod__step__integer__def,axiom,
% 0.33/0.57 ( unique4921790084139445826nteger
% 0.33/0.57 = ( ^ [L3: num] :
% 0.33/0.57 ( produc6916734918728496179nteger
% 0.33/0.57 @ ^ [Q5: code_integer,R3: code_integer] : ( if_Pro6119634080678213985nteger @ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L3 ) @ R3 ) @ ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R3 @ ( numera6620942414471956472nteger @ L3 ) ) ) @ ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q5 ) @ R3 ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % divmod_step_integer_def
% 0.33/0.57 thf(fact_3169_signed__take__bit__rec,axiom,
% 0.33/0.57 ( bit_ri6519982836138164636nteger
% 0.33/0.57 = ( ^ [N4: nat,A5: code_integer] : ( if_Code_integer @ ( N4 = zero_zero_nat ) @ ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A5 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A5 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_ri6519982836138164636nteger @ ( minus_minus_nat @ N4 @ one_one_nat ) @ ( divide6298287555418463151nteger @ A5 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % signed_take_bit_rec
% 0.33/0.57 thf(fact_3170_signed__take__bit__rec,axiom,
% 0.33/0.57 ( bit_ri631733984087533419it_int
% 0.33/0.57 = ( ^ [N4: nat,A5: int] : ( if_int @ ( N4 = zero_zero_nat ) @ ( uminus_uminus_int @ ( modulo_modulo_int @ A5 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( plus_plus_int @ ( modulo_modulo_int @ A5 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri631733984087533419it_int @ ( minus_minus_nat @ N4 @ one_one_nat ) @ ( divide_divide_int @ A5 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % signed_take_bit_rec
% 0.33/0.57 thf(fact_3171_round__unique,axiom,
% 0.33/0.57 ! [X: rat,Y: int] :
% 0.33/0.57 ( ( ord_less_rat @ ( minus_minus_rat @ X @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_rat @ Y ) )
% 0.33/0.57 => ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Y ) @ ( plus_plus_rat @ X @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) )
% 0.33/0.57 => ( ( archim7778729529865785530nd_rat @ X )
% 0.33/0.57 = Y ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % round_unique
% 0.33/0.57 thf(fact_3172_rel__of__def,axiom,
% 0.33/0.57 ( rel_of7835217753297429671nteger
% 0.33/0.57 = ( ^ [M: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > option2651255830984564193nteger,P3: produc1908205239877642774nteger > $o] :
% 0.33/0.57 ( collec6950949345391930603nteger
% 0.33/0.57 @ ( produc6253627499356882019eger_o
% 0.33/0.57 @ ^ [K4: produc6241069584506657477e_term > option6357759511663192854e_term,V2: produc8923325533196201883nteger] :
% 0.33/0.57 ( ( ( M @ K4 )
% 0.33/0.57 = ( some_P6772290148444788224nteger @ V2 ) )
% 0.33/0.57 & ( P3 @ ( produc8603105652947943368nteger @ K4 @ V2 ) ) ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % rel_of_def
% 0.33/0.57 thf(fact_3173_rel__of__def,axiom,
% 0.33/0.57 ( rel_of4838799251197538391et_nat
% 0.33/0.57 = ( ^ [M: ( produc3658429121746597890et_nat > $o ) > option936205604648967762et_nat,P3: produc3925858234332021118et_nat > $o] :
% 0.33/0.57 ( collec1402215087704437587et_nat
% 0.33/0.57 @ ( produc1437786849005270451_nat_o
% 0.33/0.57 @ ^ [K4: produc3658429121746597890et_nat > $o,V2: produc3658429121746597890et_nat] :
% 0.33/0.57 ( ( ( M @ K4 )
% 0.33/0.57 = ( some_P624177172695371229et_nat @ V2 ) )
% 0.33/0.57 & ( P3 @ ( produc5001842942810119800et_nat @ K4 @ V2 ) ) ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % rel_of_def
% 0.33/0.57 thf(fact_3174_rel__of__def,axiom,
% 0.33/0.57 ( rel_of7774016450764239315et_nat
% 0.33/0.57 = ( ^ [M: ( produc3658429121746597890et_nat > $o ) > option5190343406534369742et_nat,P3: produc2732055786443039994et_nat > $o] :
% 0.33/0.57 ( collec5543584681430388431et_nat
% 0.33/0.57 @ ( produc838355143741117751_nat_o
% 0.33/0.57 @ ^ [K4: produc3658429121746597890et_nat > $o,V2: produc3925858234332021118et_nat] :
% 0.33/0.57 ( ( ( M @ K4 )
% 0.33/0.57 = ( some_P750831030444334937et_nat @ V2 ) )
% 0.33/0.57 & ( P3 @ ( produc2245416461498447860et_nat @ K4 @ V2 ) ) ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % rel_of_def
% 0.33/0.57 thf(fact_3175_rel__of__def,axiom,
% 0.33/0.57 ( rel_of8306664904814525588nt_int
% 0.33/0.57 = ( ^ [M: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > option4624381673175914239nt_int,P3: produc2285326912895808259nt_int > $o] :
% 0.33/0.57 ( collec1790188477890212312nt_int
% 0.33/0.57 @ ( produc1573362020775583542_int_o
% 0.33/0.57 @ ^ [K4: produc8551481072490612790e_term > option6357759511663192854e_term,V2: product_prod_int_int] :
% 0.33/0.57 ( ( ( M @ K4 )
% 0.33/0.57 = ( some_P4184893108420464158nt_int @ V2 ) )
% 0.33/0.57 & ( P3 @ ( produc5700946648718959541nt_int @ K4 @ V2 ) ) ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % rel_of_def
% 0.33/0.57 thf(fact_3176_rel__of__def,axiom,
% 0.33/0.57 ( rel_of5543720577181062686nt_int
% 0.33/0.57 = ( ^ [M: ( int > option6357759511663192854e_term ) > option4624381673175914239nt_int,P3: produc7773217078559923341nt_int > $o] :
% 0.33/0.57 ( collec506566255779805410nt_int
% 0.33/0.57 @ ( produc2558449545302689196_int_o
% 0.33/0.57 @ ^ [K4: int > option6357759511663192854e_term,V2: product_prod_int_int] :
% 0.33/0.57 ( ( ( M @ K4 )
% 0.33/0.57 = ( some_P4184893108420464158nt_int @ V2 ) )
% 0.33/0.57 & ( P3 @ ( produc4305682042979456191nt_int @ K4 @ V2 ) ) ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % rel_of_def
% 0.33/0.57 thf(fact_3177_dbl__simps_I4_J,axiom,
% 0.33/0.57 ( ( neg_numeral_dbl_int @ ( uminus_uminus_int @ one_one_int ) )
% 0.33/0.57 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % dbl_simps(4)
% 0.33/0.57 thf(fact_3178_dbl__simps_I4_J,axiom,
% 0.33/0.57 ( ( neg_nu8804712462038260780nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.33/0.57 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % dbl_simps(4)
% 0.33/0.57 thf(fact_3179_dbl__simps_I4_J,axiom,
% 0.33/0.57 ( ( neg_numeral_dbl_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.33/0.57 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % dbl_simps(4)
% 0.33/0.57 thf(fact_3180_round__altdef,axiom,
% 0.33/0.57 ( archim7778729529865785530nd_rat
% 0.33/0.57 = ( ^ [X3: rat] : ( if_int @ ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( archimedean_frac_rat @ X3 ) ) @ ( archim2889992004027027881ng_rat @ X3 ) @ ( archim3151403230148437115or_rat @ X3 ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % round_altdef
% 0.33/0.57 thf(fact_3181_round__unique_H,axiom,
% 0.33/0.57 ! [X: rat,N2: int] :
% 0.33/0.57 ( ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X @ ( ring_1_of_int_rat @ N2 ) ) ) @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 0.33/0.57 => ( ( archim7778729529865785530nd_rat @ X )
% 0.33/0.57 = N2 ) ) ).
% 0.33/0.57
% 0.33/0.57 % round_unique'
% 0.33/0.57 thf(fact_3182_of__int__round__abs__le,axiom,
% 0.33/0.57 ! [X: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X ) ) @ X ) ) @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % of_int_round_abs_le
% 0.33/0.57 thf(fact_3183_divmod__algorithm__code_I5_J,axiom,
% 0.33/0.57 ! [M2: num,N2: num] :
% 0.33/0.57 ( ( unique3479559517661332726nteger @ ( bit0 @ M2 ) @ ( bit0 @ N2 ) )
% 0.33/0.57 = ( produc6916734918728496179nteger
% 0.33/0.57 @ ^ [Q5: code_integer,R3: code_integer] : ( produc1086072967326762835nteger @ Q5 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ R3 ) )
% 0.33/0.57 @ ( unique3479559517661332726nteger @ M2 @ N2 ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % divmod_algorithm_code(5)
% 0.33/0.57 thf(fact_3184_divmod__algorithm__code_I5_J,axiom,
% 0.33/0.57 ! [M2: num,N2: num] :
% 0.33/0.57 ( ( unique5052692396658037445od_int @ ( bit0 @ M2 ) @ ( bit0 @ N2 ) )
% 0.33/0.57 = ( produc4245557441103728435nt_int
% 0.33/0.57 @ ^ [Q5: int,R3: int] : ( product_Pair_int_int @ Q5 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R3 ) )
% 0.33/0.57 @ ( unique5052692396658037445od_int @ M2 @ N2 ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % divmod_algorithm_code(5)
% 0.33/0.57 thf(fact_3185_divmod__algorithm__code_I5_J,axiom,
% 0.33/0.57 ! [M2: num,N2: num] :
% 0.33/0.57 ( ( unique5055182867167087721od_nat @ ( bit0 @ M2 ) @ ( bit0 @ N2 ) )
% 0.33/0.57 = ( produc2626176000494625587at_nat
% 0.33/0.57 @ ^ [Q5: nat,R3: nat] : ( product_Pair_nat_nat @ Q5 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ R3 ) )
% 0.33/0.57 @ ( unique5055182867167087721od_nat @ M2 @ N2 ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % divmod_algorithm_code(5)
% 0.33/0.57 thf(fact_3186_signed__take__bit__of__minus__1,axiom,
% 0.33/0.57 ! [N2: nat] :
% 0.33/0.57 ( ( bit_ri6519982836138164636nteger @ N2 @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.33/0.57 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.33/0.57
% 0.33/0.57 % signed_take_bit_of_minus_1
% 0.33/0.57 thf(fact_3187_signed__take__bit__of__minus__1,axiom,
% 0.33/0.57 ! [N2: nat] :
% 0.33/0.57 ( ( bit_ri631733984087533419it_int @ N2 @ ( uminus_uminus_int @ one_one_int ) )
% 0.33/0.57 = ( uminus_uminus_int @ one_one_int ) ) ).
% 0.33/0.57
% 0.33/0.57 % signed_take_bit_of_minus_1
% 0.33/0.57 thf(fact_3188_signed__take__bit__Suc__1,axiom,
% 0.33/0.57 ! [N2: nat] :
% 0.33/0.57 ( ( bit_ri6519982836138164636nteger @ ( suc @ N2 ) @ one_one_Code_integer )
% 0.33/0.57 = one_one_Code_integer ) ).
% 0.33/0.57
% 0.33/0.57 % signed_take_bit_Suc_1
% 0.33/0.57 thf(fact_3189_signed__take__bit__Suc__1,axiom,
% 0.33/0.57 ! [N2: nat] :
% 0.33/0.57 ( ( bit_ri631733984087533419it_int @ ( suc @ N2 ) @ one_one_int )
% 0.33/0.57 = one_one_int ) ).
% 0.33/0.57
% 0.33/0.57 % signed_take_bit_Suc_1
% 0.33/0.57 thf(fact_3190_signed__take__bit__numeral__of__1,axiom,
% 0.33/0.57 ! [K: num] :
% 0.33/0.57 ( ( bit_ri6519982836138164636nteger @ ( numeral_numeral_nat @ K ) @ one_one_Code_integer )
% 0.33/0.57 = one_one_Code_integer ) ).
% 0.33/0.57
% 0.33/0.57 % signed_take_bit_numeral_of_1
% 0.33/0.57 thf(fact_3191_signed__take__bit__numeral__of__1,axiom,
% 0.33/0.57 ! [K: num] :
% 0.33/0.57 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ K ) @ one_one_int )
% 0.33/0.57 = one_one_int ) ).
% 0.33/0.57
% 0.33/0.57 % signed_take_bit_numeral_of_1
% 0.33/0.57 thf(fact_3192_round__1,axiom,
% 0.33/0.57 ( ( archim7778729529865785530nd_rat @ one_one_rat )
% 0.33/0.57 = one_one_int ) ).
% 0.33/0.57
% 0.33/0.57 % round_1
% 0.33/0.57 thf(fact_3193_divmod__algorithm__code_I2_J,axiom,
% 0.33/0.57 ! [M2: num] :
% 0.33/0.57 ( ( unique3479559517661332726nteger @ M2 @ one )
% 0.33/0.57 = ( produc1086072967326762835nteger @ ( numera6620942414471956472nteger @ M2 ) @ zero_z3403309356797280102nteger ) ) ).
% 0.33/0.57
% 0.33/0.57 % divmod_algorithm_code(2)
% 0.33/0.57 thf(fact_3194_divmod__algorithm__code_I2_J,axiom,
% 0.33/0.57 ! [M2: num] :
% 0.33/0.57 ( ( unique5052692396658037445od_int @ M2 @ one )
% 0.33/0.57 = ( product_Pair_int_int @ ( numeral_numeral_int @ M2 ) @ zero_zero_int ) ) ).
% 0.33/0.57
% 0.33/0.57 % divmod_algorithm_code(2)
% 0.33/0.57 thf(fact_3195_divmod__algorithm__code_I2_J,axiom,
% 0.33/0.57 ! [M2: num] :
% 0.33/0.57 ( ( unique5055182867167087721od_nat @ M2 @ one )
% 0.33/0.57 = ( product_Pair_nat_nat @ ( numeral_numeral_nat @ M2 ) @ zero_zero_nat ) ) ).
% 0.33/0.57
% 0.33/0.57 % divmod_algorithm_code(2)
% 0.33/0.57 thf(fact_3196_dbl__simps_I3_J,axiom,
% 0.33/0.57 ( ( neg_numeral_dbl_int @ one_one_int )
% 0.33/0.57 = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % dbl_simps(3)
% 0.33/0.57 thf(fact_3197_dbl__simps_I3_J,axiom,
% 0.33/0.57 ( ( neg_nu8804712462038260780nteger @ one_one_Code_integer )
% 0.33/0.57 = ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % dbl_simps(3)
% 0.33/0.57 thf(fact_3198_dbl__simps_I3_J,axiom,
% 0.33/0.57 ( ( neg_numeral_dbl_rat @ one_one_rat )
% 0.33/0.57 = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % dbl_simps(3)
% 0.33/0.57 thf(fact_3199_divmod__algorithm__code_I3_J,axiom,
% 0.33/0.57 ! [N2: num] :
% 0.33/0.57 ( ( unique3479559517661332726nteger @ one @ ( bit0 @ N2 ) )
% 0.33/0.57 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ one ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % divmod_algorithm_code(3)
% 0.33/0.57 thf(fact_3200_divmod__algorithm__code_I3_J,axiom,
% 0.33/0.57 ! [N2: num] :
% 0.33/0.57 ( ( unique5052692396658037445od_int @ one @ ( bit0 @ N2 ) )
% 0.33/0.57 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ one ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % divmod_algorithm_code(3)
% 0.33/0.57 thf(fact_3201_divmod__algorithm__code_I3_J,axiom,
% 0.33/0.57 ! [N2: num] :
% 0.33/0.57 ( ( unique5055182867167087721od_nat @ one @ ( bit0 @ N2 ) )
% 0.33/0.57 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ one ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % divmod_algorithm_code(3)
% 0.33/0.57 thf(fact_3202_less__eq__integer__code_I1_J,axiom,
% 0.33/0.57 ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger ).
% 0.33/0.57
% 0.33/0.57 % less_eq_integer_code(1)
% 0.33/0.57 thf(fact_3203_sgn__integer__code,axiom,
% 0.33/0.57 ( sgn_sgn_Code_integer
% 0.33/0.57 = ( ^ [K4: code_integer] : ( if_Code_integer @ ( K4 = zero_z3403309356797280102nteger ) @ zero_z3403309356797280102nteger @ ( if_Code_integer @ ( ord_le6747313008572928689nteger @ K4 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % sgn_integer_code
% 0.33/0.57 thf(fact_3204_exhaustive__integer_H_Ocases,axiom,
% 0.33/0.57 ! [X: produc8763457246119570046nteger] :
% 0.33/0.57 ~ ! [F3: code_integer > option6357759511663192854e_term,D: code_integer,I2: code_integer] :
% 0.33/0.57 ( X
% 0.33/0.57 != ( produc6137756002093451184nteger @ F3 @ ( produc1086072967326762835nteger @ D @ I2 ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % exhaustive_integer'.cases
% 0.33/0.57 thf(fact_3205_full__exhaustive__integer_H_Ocases,axiom,
% 0.33/0.57 ! [X: produc1908205239877642774nteger] :
% 0.33/0.57 ~ ! [F3: produc6241069584506657477e_term > option6357759511663192854e_term,D: code_integer,I2: code_integer] :
% 0.33/0.57 ( X
% 0.33/0.57 != ( produc8603105652947943368nteger @ F3 @ ( produc1086072967326762835nteger @ D @ I2 ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % full_exhaustive_integer'.cases
% 0.33/0.57 thf(fact_3206_times__integer__code_I1_J,axiom,
% 0.33/0.57 ! [K: code_integer] :
% 0.33/0.57 ( ( times_3573771949741848930nteger @ K @ zero_z3403309356797280102nteger )
% 0.33/0.57 = zero_z3403309356797280102nteger ) ).
% 0.33/0.57
% 0.33/0.57 % times_integer_code(1)
% 0.33/0.57 thf(fact_3207_times__integer__code_I2_J,axiom,
% 0.33/0.57 ! [L: code_integer] :
% 0.33/0.57 ( ( times_3573771949741848930nteger @ zero_z3403309356797280102nteger @ L )
% 0.33/0.57 = zero_z3403309356797280102nteger ) ).
% 0.33/0.57
% 0.33/0.57 % times_integer_code(2)
% 0.33/0.57 thf(fact_3208_minus__integer__code_I1_J,axiom,
% 0.33/0.57 ! [K: code_integer] :
% 0.33/0.57 ( ( minus_8373710615458151222nteger @ K @ zero_z3403309356797280102nteger )
% 0.33/0.57 = K ) ).
% 0.33/0.57
% 0.33/0.57 % minus_integer_code(1)
% 0.33/0.57 thf(fact_3209_plus__integer__code_I2_J,axiom,
% 0.33/0.57 ! [L: code_integer] :
% 0.33/0.57 ( ( plus_p5714425477246183910nteger @ zero_z3403309356797280102nteger @ L )
% 0.33/0.57 = L ) ).
% 0.33/0.57
% 0.33/0.57 % plus_integer_code(2)
% 0.33/0.57 thf(fact_3210_plus__integer__code_I1_J,axiom,
% 0.33/0.57 ! [K: code_integer] :
% 0.33/0.57 ( ( plus_p5714425477246183910nteger @ K @ zero_z3403309356797280102nteger )
% 0.33/0.57 = K ) ).
% 0.33/0.57
% 0.33/0.57 % plus_integer_code(1)
% 0.33/0.57 thf(fact_3211_minus__integer__code_I2_J,axiom,
% 0.33/0.57 ! [L: code_integer] :
% 0.33/0.57 ( ( minus_8373710615458151222nteger @ zero_z3403309356797280102nteger @ L )
% 0.33/0.57 = ( uminus1351360451143612070nteger @ L ) ) ).
% 0.33/0.57
% 0.33/0.57 % minus_integer_code(2)
% 0.33/0.57 thf(fact_3212_divmod__integer_H__def,axiom,
% 0.33/0.57 ( unique3479559517661332726nteger
% 0.33/0.57 = ( ^ [M: num,N4: num] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ N4 ) ) @ ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ N4 ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % divmod_integer'_def
% 0.33/0.57 thf(fact_3213_signed__take__bit__add,axiom,
% 0.33/0.57 ! [N2: nat,K: int,L: int] :
% 0.33/0.57 ( ( bit_ri631733984087533419it_int @ N2 @ ( plus_plus_int @ ( bit_ri631733984087533419it_int @ N2 @ K ) @ ( bit_ri631733984087533419it_int @ N2 @ L ) ) )
% 0.33/0.57 = ( bit_ri631733984087533419it_int @ N2 @ ( plus_plus_int @ K @ L ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % signed_take_bit_add
% 0.33/0.57 thf(fact_3214_dbl__def,axiom,
% 0.33/0.57 ( neg_numeral_dbl_rat
% 0.33/0.57 = ( ^ [X3: rat] : ( plus_plus_rat @ X3 @ X3 ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % dbl_def
% 0.33/0.57 thf(fact_3215_dbl__def,axiom,
% 0.33/0.57 ( neg_numeral_dbl_int
% 0.33/0.57 = ( ^ [X3: int] : ( plus_plus_int @ X3 @ X3 ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % dbl_def
% 0.33/0.57 thf(fact_3216_divmod__int__def,axiom,
% 0.33/0.57 ( unique5052692396658037445od_int
% 0.33/0.57 = ( ^ [M: num,N4: num] : ( product_Pair_int_int @ ( divide_divide_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N4 ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N4 ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % divmod_int_def
% 0.33/0.57 thf(fact_3217_divmod__def,axiom,
% 0.33/0.57 ( unique3479559517661332726nteger
% 0.33/0.57 = ( ^ [M: num,N4: num] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ N4 ) ) @ ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ N4 ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % divmod_def
% 0.33/0.57 thf(fact_3218_divmod__def,axiom,
% 0.33/0.57 ( unique5052692396658037445od_int
% 0.33/0.57 = ( ^ [M: num,N4: num] : ( product_Pair_int_int @ ( divide_divide_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N4 ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N4 ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % divmod_def
% 0.33/0.57 thf(fact_3219_divmod__def,axiom,
% 0.33/0.57 ( unique5055182867167087721od_nat
% 0.33/0.57 = ( ^ [M: num,N4: num] : ( product_Pair_nat_nat @ ( divide_divide_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N4 ) ) @ ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N4 ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % divmod_def
% 0.33/0.57 thf(fact_3220_divmod_H__nat__def,axiom,
% 0.33/0.57 ( unique5055182867167087721od_nat
% 0.33/0.57 = ( ^ [M: num,N4: num] : ( product_Pair_nat_nat @ ( divide_divide_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N4 ) ) @ ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N4 ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % divmod'_nat_def
% 0.33/0.57 thf(fact_3221_signed__take__bit__int__greater__eq,axiom,
% 0.33/0.57 ! [K: int,N2: nat] :
% 0.33/0.57 ( ( ord_less_int @ K @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) )
% 0.33/0.57 => ( ord_less_eq_int @ ( plus_plus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) ) @ ( bit_ri631733984087533419it_int @ N2 @ K ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % signed_take_bit_int_greater_eq
% 0.33/0.57 thf(fact_3222_divmod__divmod__step,axiom,
% 0.33/0.57 ( unique5055182867167087721od_nat
% 0.33/0.57 = ( ^ [M: num,N4: num] : ( if_Pro6206227464963214023at_nat @ ( ord_less_num @ M @ N4 ) @ ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ M ) ) @ ( unique5026877609467782581ep_nat @ N4 @ ( unique5055182867167087721od_nat @ M @ ( bit0 @ N4 ) ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % divmod_divmod_step
% 0.33/0.57 thf(fact_3223_divmod__divmod__step,axiom,
% 0.33/0.57 ( unique5052692396658037445od_int
% 0.33/0.57 = ( ^ [M: num,N4: num] : ( if_Pro3027730157355071871nt_int @ ( ord_less_num @ M @ N4 ) @ ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ M ) ) @ ( unique5024387138958732305ep_int @ N4 @ ( unique5052692396658037445od_int @ M @ ( bit0 @ N4 ) ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % divmod_divmod_step
% 0.33/0.57 thf(fact_3224_divmod__divmod__step,axiom,
% 0.33/0.57 ( unique3479559517661332726nteger
% 0.33/0.57 = ( ^ [M: num,N4: num] : ( if_Pro6119634080678213985nteger @ ( ord_less_num @ M @ N4 ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( unique4921790084139445826nteger @ N4 @ ( unique3479559517661332726nteger @ M @ ( bit0 @ N4 ) ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % divmod_divmod_step
% 0.33/0.57 thf(fact_3225_round__def,axiom,
% 0.33/0.57 ( archim7778729529865785530nd_rat
% 0.33/0.57 = ( ^ [X3: rat] : ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X3 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % round_def
% 0.33/0.57 thf(fact_3226_signed__take__bit__Suc,axiom,
% 0.33/0.57 ! [N2: nat,A: code_integer] :
% 0.33/0.57 ( ( bit_ri6519982836138164636nteger @ ( suc @ N2 ) @ A )
% 0.33/0.57 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_ri6519982836138164636nteger @ N2 @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % signed_take_bit_Suc
% 0.33/0.57 thf(fact_3227_signed__take__bit__Suc,axiom,
% 0.33/0.57 ! [N2: nat,A: int] :
% 0.33/0.57 ( ( bit_ri631733984087533419it_int @ ( suc @ N2 ) @ A )
% 0.33/0.57 = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri631733984087533419it_int @ N2 @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % signed_take_bit_Suc
% 0.33/0.57 thf(fact_3228_of__int__round__le,axiom,
% 0.33/0.57 ! [X: rat] : ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X ) ) @ ( plus_plus_rat @ X @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % of_int_round_le
% 0.33/0.57 thf(fact_3229_of__int__round__ge,axiom,
% 0.33/0.57 ! [X: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ X @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % of_int_round_ge
% 0.33/0.57 thf(fact_3230_of__int__round__gt,axiom,
% 0.33/0.57 ! [X: rat] : ( ord_less_rat @ ( minus_minus_rat @ X @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % of_int_round_gt
% 0.33/0.57 thf(fact_3231_integer__of__int__code,axiom,
% 0.33/0.57 ( code_integer_of_int
% 0.33/0.57 = ( ^ [K4: int] :
% 0.33/0.57 ( if_Code_integer @ ( ord_less_int @ K4 @ zero_zero_int ) @ ( uminus1351360451143612070nteger @ ( code_integer_of_int @ ( uminus_uminus_int @ K4 ) ) )
% 0.33/0.57 @ ( if_Code_integer @ ( K4 = zero_zero_int ) @ zero_z3403309356797280102nteger
% 0.33/0.57 @ ( if_Code_integer
% 0.33/0.57 @ ( ( modulo_modulo_int @ K4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.33/0.57 = zero_zero_int )
% 0.33/0.57 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( code_integer_of_int @ ( divide_divide_int @ K4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 0.33/0.57 @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( code_integer_of_int @ ( divide_divide_int @ K4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_Code_integer ) ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % integer_of_int_code
% 0.33/0.57 thf(fact_3232_divmod__algorithm__code_I6_J,axiom,
% 0.33/0.57 ! [M2: num,N2: num] :
% 0.33/0.57 ( ( unique3479559517661332726nteger @ ( bit1 @ M2 ) @ ( bit0 @ N2 ) )
% 0.33/0.57 = ( produc6916734918728496179nteger
% 0.33/0.57 @ ^ [Q5: code_integer,R3: code_integer] : ( produc1086072967326762835nteger @ Q5 @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ R3 ) @ one_one_Code_integer ) )
% 0.33/0.57 @ ( unique3479559517661332726nteger @ M2 @ N2 ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % divmod_algorithm_code(6)
% 0.33/0.57 thf(fact_3233_divmod__algorithm__code_I6_J,axiom,
% 0.33/0.57 ! [M2: num,N2: num] :
% 0.33/0.57 ( ( unique5052692396658037445od_int @ ( bit1 @ M2 ) @ ( bit0 @ N2 ) )
% 0.33/0.57 = ( produc4245557441103728435nt_int
% 0.33/0.57 @ ^ [Q5: int,R3: int] : ( product_Pair_int_int @ Q5 @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R3 ) @ one_one_int ) )
% 0.33/0.57 @ ( unique5052692396658037445od_int @ M2 @ N2 ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % divmod_algorithm_code(6)
% 0.33/0.57 thf(fact_3234_divmod__algorithm__code_I6_J,axiom,
% 0.33/0.57 ! [M2: num,N2: num] :
% 0.33/0.57 ( ( unique5055182867167087721od_nat @ ( bit1 @ M2 ) @ ( bit0 @ N2 ) )
% 0.33/0.57 = ( produc2626176000494625587at_nat
% 0.33/0.57 @ ^ [Q5: nat,R3: nat] : ( product_Pair_nat_nat @ Q5 @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ R3 ) @ one_one_nat ) )
% 0.33/0.57 @ ( unique5055182867167087721od_nat @ M2 @ N2 ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % divmod_algorithm_code(6)
% 0.33/0.57 thf(fact_3235_of__nat__code,axiom,
% 0.33/0.57 ( semiri681578069525770553at_rat
% 0.33/0.57 = ( ^ [N4: nat] :
% 0.33/0.57 ( semiri7787848453975740701ux_rat
% 0.33/0.57 @ ^ [I3: rat] : ( plus_plus_rat @ I3 @ one_one_rat )
% 0.33/0.57 @ N4
% 0.33/0.57 @ zero_zero_rat ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % of_nat_code
% 0.33/0.57 thf(fact_3236_of__nat__code,axiom,
% 0.33/0.57 ( semiri1314217659103216013at_int
% 0.33/0.57 = ( ^ [N4: nat] :
% 0.33/0.57 ( semiri8420488043553186161ux_int
% 0.33/0.57 @ ^ [I3: int] : ( plus_plus_int @ I3 @ one_one_int )
% 0.33/0.57 @ N4
% 0.33/0.57 @ zero_zero_int ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % of_nat_code
% 0.33/0.57 thf(fact_3237_of__nat__code,axiom,
% 0.33/0.57 ( semiri1316708129612266289at_nat
% 0.33/0.57 = ( ^ [N4: nat] :
% 0.33/0.57 ( semiri8422978514062236437ux_nat
% 0.33/0.57 @ ^ [I3: nat] : ( plus_plus_nat @ I3 @ one_one_nat )
% 0.33/0.57 @ N4
% 0.33/0.57 @ zero_zero_nat ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % of_nat_code
% 0.33/0.57 thf(fact_3238_of__nat__code,axiom,
% 0.33/0.57 ( semiri4939895301339042750nteger
% 0.33/0.57 = ( ^ [N4: nat] :
% 0.33/0.57 ( semiri4055485073559036834nteger
% 0.33/0.57 @ ^ [I3: code_integer] : ( plus_p5714425477246183910nteger @ I3 @ one_one_Code_integer )
% 0.33/0.57 @ N4
% 0.33/0.57 @ zero_z3403309356797280102nteger ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % of_nat_code
% 0.33/0.57 thf(fact_3239_of__nat__code,axiom,
% 0.33/0.57 ( semiri3763490453095760265atural
% 0.33/0.57 = ( ^ [N4: nat] :
% 0.33/0.57 ( semiri2879080225315754349atural
% 0.33/0.57 @ ^ [I3: code_natural] : ( plus_p4538020629002901425atural @ I3 @ one_one_Code_natural )
% 0.33/0.57 @ N4
% 0.33/0.57 @ zero_z2226904508553997617atural ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % of_nat_code
% 0.33/0.57 thf(fact_3240_signed__take__bit__Suc__minus__bit1,axiom,
% 0.33/0.57 ! [N2: nat,K: num] :
% 0.33/0.57 ( ( bit_ri631733984087533419it_int @ ( suc @ N2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 0.33/0.57 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N2 @ ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 0.33/0.57
% 0.33/0.57 % signed_take_bit_Suc_minus_bit1
% 0.33/0.57 thf(fact_3241_concat__bit__Suc,axiom,
% 0.33/0.57 ! [N2: nat,K: int,L: int] :
% 0.33/0.57 ( ( bit_concat_bit @ ( suc @ N2 ) @ K @ L )
% 0.33/0.57 = ( plus_plus_int @ ( modulo_modulo_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_concat_bit @ N2 @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ L ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % concat_bit_Suc
% 0.33/0.57 thf(fact_3242_even__succ__mod__exp,axiom,
% 0.33/0.57 ! [A: int,N2: nat] :
% 0.33/0.57 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.33/0.57 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.33/0.57 => ( ( modulo_modulo_int @ ( plus_plus_int @ one_one_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 0.33/0.57 = ( plus_plus_int @ one_one_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % even_succ_mod_exp
% 0.33/0.57 thf(fact_3243_even__succ__mod__exp,axiom,
% 0.33/0.57 ! [A: nat,N2: nat] :
% 0.33/0.57 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.33/0.57 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.33/0.57 => ( ( modulo_modulo_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 0.33/0.57 = ( plus_plus_nat @ one_one_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % even_succ_mod_exp
% 0.33/0.57 thf(fact_3244_even__succ__mod__exp,axiom,
% 0.33/0.57 ! [A: code_integer,N2: nat] :
% 0.33/0.57 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.33/0.57 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.33/0.57 => ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 0.33/0.57 = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( modulo364778990260209775nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % even_succ_mod_exp
% 0.33/0.57 thf(fact_3245_even__succ__mod__exp,axiom,
% 0.33/0.57 ! [A: code_natural,N2: nat] :
% 0.33/0.57 ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 0.33/0.57 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.33/0.57 => ( ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ one_one_Code_natural @ A ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N2 ) )
% 0.33/0.57 = ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( modulo8411746178871703098atural @ A @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % even_succ_mod_exp
% 0.33/0.57 thf(fact_3246_even__succ__div__exp,axiom,
% 0.33/0.57 ! [A: int,N2: nat] :
% 0.33/0.57 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.33/0.57 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.33/0.57 => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 0.33/0.57 = ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % even_succ_div_exp
% 0.33/0.57 thf(fact_3247_even__succ__div__exp,axiom,
% 0.33/0.57 ! [A: nat,N2: nat] :
% 0.33/0.57 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.33/0.57 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.33/0.57 => ( ( divide_divide_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 0.33/0.57 = ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % even_succ_div_exp
% 0.33/0.57 thf(fact_3248_even__succ__div__exp,axiom,
% 0.33/0.57 ! [A: code_integer,N2: nat] :
% 0.33/0.57 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.33/0.57 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.33/0.57 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 0.33/0.57 = ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % even_succ_div_exp
% 0.33/0.57 thf(fact_3249_even__succ__div__exp,axiom,
% 0.33/0.57 ! [A: code_natural,N2: nat] :
% 0.33/0.57 ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 0.33/0.57 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.33/0.57 => ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ one_one_Code_natural @ A ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N2 ) )
% 0.33/0.57 = ( divide5121882707175180666atural @ A @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % even_succ_div_exp
% 0.33/0.57 thf(fact_3250_take__bit__rec,axiom,
% 0.33/0.57 ( bit_se1745604003318907178nteger
% 0.33/0.57 = ( ^ [N4: nat,A5: code_integer] : ( if_Code_integer @ ( N4 = zero_zero_nat ) @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( bit_se1745604003318907178nteger @ ( minus_minus_nat @ N4 @ one_one_nat ) @ ( divide6298287555418463151nteger @ A5 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( modulo364778990260209775nteger @ A5 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % take_bit_rec
% 0.33/0.57 thf(fact_3251_take__bit__rec,axiom,
% 0.33/0.57 ( bit_se2923211474154528505it_int
% 0.33/0.57 = ( ^ [N4: nat,A5: int] : ( if_int @ ( N4 = zero_zero_nat ) @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ ( minus_minus_nat @ N4 @ one_one_nat ) @ ( divide_divide_int @ A5 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ A5 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % take_bit_rec
% 0.33/0.57 thf(fact_3252_take__bit__rec,axiom,
% 0.33/0.57 ( bit_se2925701944663578781it_nat
% 0.33/0.57 = ( ^ [N4: nat,A5: nat] : ( if_nat @ ( N4 = zero_zero_nat ) @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ ( minus_minus_nat @ N4 @ one_one_nat ) @ ( divide_divide_nat @ A5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ A5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % take_bit_rec
% 0.33/0.57 thf(fact_3253_take__bit__rec,axiom,
% 0.33/0.57 ( bit_se569199155075624693atural
% 0.33/0.57 = ( ^ [N4: nat,A5: code_natural] : ( if_Code_natural @ ( N4 = zero_zero_nat ) @ zero_z2226904508553997617atural @ ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( bit_se569199155075624693atural @ ( minus_minus_nat @ N4 @ one_one_nat ) @ ( divide5121882707175180666atural @ A5 @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) @ ( modulo8411746178871703098atural @ A5 @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % take_bit_rec
% 0.33/0.57 thf(fact_3254_nat__dvd__1__iff__1,axiom,
% 0.33/0.57 ! [M2: nat] :
% 0.33/0.57 ( ( dvd_dvd_nat @ M2 @ one_one_nat )
% 0.33/0.57 = ( M2 = one_one_nat ) ) ).
% 0.33/0.57
% 0.33/0.57 % nat_dvd_1_iff_1
% 0.33/0.57 thf(fact_3255_integer__of__int__eq__of__int,axiom,
% 0.33/0.57 code_integer_of_int = ring_18347121197199848620nteger ).
% 0.33/0.57
% 0.33/0.57 % integer_of_int_eq_of_int
% 0.33/0.57 thf(fact_3256_dvd__add__triv__right__iff,axiom,
% 0.33/0.57 ! [A: code_integer,B: code_integer] :
% 0.33/0.57 ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ A ) )
% 0.33/0.57 = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 0.33/0.57
% 0.33/0.57 % dvd_add_triv_right_iff
% 0.33/0.57 thf(fact_3257_dvd__add__triv__right__iff,axiom,
% 0.33/0.57 ! [A: rat,B: rat] :
% 0.33/0.57 ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 0.33/0.57 = ( dvd_dvd_rat @ A @ B ) ) ).
% 0.33/0.57
% 0.33/0.57 % dvd_add_triv_right_iff
% 0.33/0.57 thf(fact_3258_dvd__add__triv__right__iff,axiom,
% 0.33/0.57 ! [A: nat,B: nat] :
% 0.33/0.57 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 0.33/0.57 = ( dvd_dvd_nat @ A @ B ) ) ).
% 0.33/0.57
% 0.33/0.57 % dvd_add_triv_right_iff
% 0.33/0.57 thf(fact_3259_dvd__add__triv__right__iff,axiom,
% 0.33/0.57 ! [A: int,B: int] :
% 0.33/0.57 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ A ) )
% 0.33/0.57 = ( dvd_dvd_int @ A @ B ) ) ).
% 0.33/0.57
% 0.33/0.57 % dvd_add_triv_right_iff
% 0.33/0.57 thf(fact_3260_dvd__add__triv__left__iff,axiom,
% 0.33/0.57 ! [A: code_integer,B: code_integer] :
% 0.33/0.57 ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 0.33/0.57 = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 0.33/0.57
% 0.33/0.57 % dvd_add_triv_left_iff
% 0.33/0.57 thf(fact_3261_dvd__add__triv__left__iff,axiom,
% 0.33/0.57 ! [A: rat,B: rat] :
% 0.33/0.57 ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 0.33/0.57 = ( dvd_dvd_rat @ A @ B ) ) ).
% 0.33/0.57
% 0.33/0.57 % dvd_add_triv_left_iff
% 0.33/0.57 thf(fact_3262_dvd__add__triv__left__iff,axiom,
% 0.33/0.57 ! [A: nat,B: nat] :
% 0.33/0.57 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 0.33/0.57 = ( dvd_dvd_nat @ A @ B ) ) ).
% 0.33/0.57
% 0.33/0.57 % dvd_add_triv_left_iff
% 0.33/0.57 thf(fact_3263_dvd__add__triv__left__iff,axiom,
% 0.33/0.57 ! [A: int,B: int] :
% 0.33/0.57 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ A @ B ) )
% 0.33/0.57 = ( dvd_dvd_int @ A @ B ) ) ).
% 0.33/0.57
% 0.33/0.57 % dvd_add_triv_left_iff
% 0.33/0.57 thf(fact_3264_dvd__add__times__triv__right__iff,axiom,
% 0.33/0.57 ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.33/0.57 ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ ( times_3573771949741848930nteger @ C @ A ) ) )
% 0.33/0.57 = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 0.33/0.57
% 0.33/0.57 % dvd_add_times_triv_right_iff
% 0.33/0.57 thf(fact_3265_dvd__add__times__triv__right__iff,axiom,
% 0.33/0.57 ! [A: rat,B: rat,C: rat] :
% 0.33/0.57 ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ ( times_times_rat @ C @ A ) ) )
% 0.33/0.57 = ( dvd_dvd_rat @ A @ B ) ) ).
% 0.33/0.57
% 0.33/0.57 % dvd_add_times_triv_right_iff
% 0.33/0.57 thf(fact_3266_dvd__add__times__triv__right__iff,axiom,
% 0.33/0.57 ! [A: nat,B: nat,C: nat] :
% 0.33/0.57 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ ( times_times_nat @ C @ A ) ) )
% 0.33/0.57 = ( dvd_dvd_nat @ A @ B ) ) ).
% 0.33/0.57
% 0.33/0.57 % dvd_add_times_triv_right_iff
% 0.33/0.57 thf(fact_3267_dvd__add__times__triv__right__iff,axiom,
% 0.33/0.57 ! [A: int,B: int,C: int] :
% 0.33/0.57 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ ( times_times_int @ C @ A ) ) )
% 0.33/0.57 = ( dvd_dvd_int @ A @ B ) ) ).
% 0.33/0.57
% 0.33/0.57 % dvd_add_times_triv_right_iff
% 0.33/0.57 thf(fact_3268_dvd__add__times__triv__left__iff,axiom,
% 0.33/0.57 ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.33/0.57 ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ C @ A ) @ B ) )
% 0.33/0.57 = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 0.33/0.57
% 0.33/0.57 % dvd_add_times_triv_left_iff
% 0.33/0.57 thf(fact_3269_dvd__add__times__triv__left__iff,axiom,
% 0.33/0.57 ! [A: rat,C: rat,B: rat] :
% 0.33/0.57 ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ ( times_times_rat @ C @ A ) @ B ) )
% 0.33/0.57 = ( dvd_dvd_rat @ A @ B ) ) ).
% 0.33/0.57
% 0.33/0.57 % dvd_add_times_triv_left_iff
% 0.33/0.57 thf(fact_3270_dvd__add__times__triv__left__iff,axiom,
% 0.33/0.57 ! [A: nat,C: nat,B: nat] :
% 0.33/0.57 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ ( times_times_nat @ C @ A ) @ B ) )
% 0.33/0.57 = ( dvd_dvd_nat @ A @ B ) ) ).
% 0.33/0.57
% 0.33/0.57 % dvd_add_times_triv_left_iff
% 0.33/0.57 thf(fact_3271_dvd__add__times__triv__left__iff,axiom,
% 0.33/0.57 ! [A: int,C: int,B: int] :
% 0.33/0.57 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ ( times_times_int @ C @ A ) @ B ) )
% 0.33/0.57 = ( dvd_dvd_int @ A @ B ) ) ).
% 0.33/0.57
% 0.33/0.57 % dvd_add_times_triv_left_iff
% 0.33/0.57 thf(fact_3272_unit__prod,axiom,
% 0.33/0.57 ! [A: code_integer,B: code_integer] :
% 0.33/0.57 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 0.33/0.57 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.33/0.57 => ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ one_one_Code_integer ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % unit_prod
% 0.33/0.57 thf(fact_3273_unit__prod,axiom,
% 0.33/0.57 ! [A: nat,B: nat] :
% 0.33/0.57 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.33/0.57 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.33/0.57 => ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % unit_prod
% 0.33/0.57 thf(fact_3274_unit__prod,axiom,
% 0.33/0.57 ! [A: int,B: int] :
% 0.33/0.57 ( ( dvd_dvd_int @ A @ one_one_int )
% 0.33/0.57 => ( ( dvd_dvd_int @ B @ one_one_int )
% 0.33/0.57 => ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ one_one_int ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % unit_prod
% 0.33/0.57 thf(fact_3275_div__add,axiom,
% 0.33/0.57 ! [C: int,A: int,B: int] :
% 0.33/0.57 ( ( dvd_dvd_int @ C @ A )
% 0.33/0.57 => ( ( dvd_dvd_int @ C @ B )
% 0.33/0.57 => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 0.33/0.57 = ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % div_add
% 0.33/0.57 thf(fact_3276_div__add,axiom,
% 0.33/0.57 ! [C: nat,A: nat,B: nat] :
% 0.33/0.57 ( ( dvd_dvd_nat @ C @ A )
% 0.33/0.57 => ( ( dvd_dvd_nat @ C @ B )
% 0.33/0.57 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 0.33/0.57 = ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % div_add
% 0.33/0.57 thf(fact_3277_div__add,axiom,
% 0.33/0.57 ! [C: code_integer,A: code_integer,B: code_integer] :
% 0.33/0.57 ( ( dvd_dvd_Code_integer @ C @ A )
% 0.33/0.57 => ( ( dvd_dvd_Code_integer @ C @ B )
% 0.33/0.57 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 0.33/0.57 = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % div_add
% 0.33/0.57 thf(fact_3278_div__add,axiom,
% 0.33/0.57 ! [C: code_natural,A: code_natural,B: code_natural] :
% 0.33/0.57 ( ( dvd_dvd_Code_natural @ C @ A )
% 0.33/0.57 => ( ( dvd_dvd_Code_natural @ C @ B )
% 0.33/0.57 => ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ A @ B ) @ C )
% 0.33/0.57 = ( plus_p4538020629002901425atural @ ( divide5121882707175180666atural @ A @ C ) @ ( divide5121882707175180666atural @ B @ C ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % div_add
% 0.33/0.57 thf(fact_3279_unit__div__1__div__1,axiom,
% 0.33/0.57 ! [A: int] :
% 0.33/0.57 ( ( dvd_dvd_int @ A @ one_one_int )
% 0.33/0.57 => ( ( divide_divide_int @ one_one_int @ ( divide_divide_int @ one_one_int @ A ) )
% 0.33/0.57 = A ) ) ).
% 0.33/0.57
% 0.33/0.57 % unit_div_1_div_1
% 0.33/0.57 thf(fact_3280_unit__div__1__div__1,axiom,
% 0.33/0.57 ! [A: nat] :
% 0.33/0.57 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.33/0.57 => ( ( divide_divide_nat @ one_one_nat @ ( divide_divide_nat @ one_one_nat @ A ) )
% 0.33/0.57 = A ) ) ).
% 0.33/0.57
% 0.33/0.57 % unit_div_1_div_1
% 0.33/0.57 thf(fact_3281_unit__div__1__div__1,axiom,
% 0.33/0.57 ! [A: code_integer] :
% 0.33/0.57 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 0.33/0.57 => ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( divide6298287555418463151nteger @ one_one_Code_integer @ A ) )
% 0.33/0.57 = A ) ) ).
% 0.33/0.57
% 0.33/0.57 % unit_div_1_div_1
% 0.33/0.57 thf(fact_3282_unit__div__1__div__1,axiom,
% 0.33/0.57 ! [A: code_natural] :
% 0.33/0.57 ( ( dvd_dvd_Code_natural @ A @ one_one_Code_natural )
% 0.33/0.57 => ( ( divide5121882707175180666atural @ one_one_Code_natural @ ( divide5121882707175180666atural @ one_one_Code_natural @ A ) )
% 0.33/0.57 = A ) ) ).
% 0.33/0.57
% 0.33/0.57 % unit_div_1_div_1
% 0.33/0.57 thf(fact_3283_unit__div__1__unit,axiom,
% 0.33/0.57 ! [A: int] :
% 0.33/0.57 ( ( dvd_dvd_int @ A @ one_one_int )
% 0.33/0.57 => ( dvd_dvd_int @ ( divide_divide_int @ one_one_int @ A ) @ one_one_int ) ) ).
% 0.33/0.57
% 0.33/0.57 % unit_div_1_unit
% 0.33/0.57 thf(fact_3284_unit__div__1__unit,axiom,
% 0.33/0.57 ! [A: nat] :
% 0.33/0.57 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.33/0.57 => ( dvd_dvd_nat @ ( divide_divide_nat @ one_one_nat @ A ) @ one_one_nat ) ) ).
% 0.33/0.57
% 0.33/0.57 % unit_div_1_unit
% 0.33/0.57 thf(fact_3285_unit__div__1__unit,axiom,
% 0.33/0.57 ! [A: code_integer] :
% 0.33/0.57 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 0.33/0.57 => ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ one_one_Code_integer @ A ) @ one_one_Code_integer ) ) ).
% 0.33/0.57
% 0.33/0.57 % unit_div_1_unit
% 0.33/0.57 thf(fact_3286_unit__div__1__unit,axiom,
% 0.33/0.57 ! [A: code_natural] :
% 0.33/0.57 ( ( dvd_dvd_Code_natural @ A @ one_one_Code_natural )
% 0.33/0.57 => ( dvd_dvd_Code_natural @ ( divide5121882707175180666atural @ one_one_Code_natural @ A ) @ one_one_Code_natural ) ) ).
% 0.33/0.57
% 0.33/0.57 % unit_div_1_unit
% 0.33/0.57 thf(fact_3287_unit__div,axiom,
% 0.33/0.57 ! [A: int,B: int] :
% 0.33/0.57 ( ( dvd_dvd_int @ A @ one_one_int )
% 0.33/0.57 => ( ( dvd_dvd_int @ B @ one_one_int )
% 0.33/0.57 => ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % unit_div
% 0.33/0.57 thf(fact_3288_unit__div,axiom,
% 0.33/0.57 ! [A: nat,B: nat] :
% 0.33/0.57 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.33/0.57 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.33/0.57 => ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % unit_div
% 0.33/0.57 thf(fact_3289_unit__div,axiom,
% 0.33/0.57 ! [A: code_integer,B: code_integer] :
% 0.33/0.57 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 0.33/0.57 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.33/0.57 => ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ A @ B ) @ one_one_Code_integer ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % unit_div
% 0.33/0.57 thf(fact_3290_unit__div,axiom,
% 0.33/0.57 ! [A: code_natural,B: code_natural] :
% 0.33/0.57 ( ( dvd_dvd_Code_natural @ A @ one_one_Code_natural )
% 0.33/0.57 => ( ( dvd_dvd_Code_natural @ B @ one_one_Code_natural )
% 0.33/0.57 => ( dvd_dvd_Code_natural @ ( divide5121882707175180666atural @ A @ B ) @ one_one_Code_natural ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % unit_div
% 0.33/0.57 thf(fact_3291_take__bit__Suc__1,axiom,
% 0.33/0.57 ! [N2: nat] :
% 0.33/0.57 ( ( bit_se1745604003318907178nteger @ ( suc @ N2 ) @ one_one_Code_integer )
% 0.33/0.57 = one_one_Code_integer ) ).
% 0.33/0.57
% 0.33/0.57 % take_bit_Suc_1
% 0.33/0.57 thf(fact_3292_take__bit__Suc__1,axiom,
% 0.33/0.57 ! [N2: nat] :
% 0.33/0.57 ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ one_one_int )
% 0.33/0.57 = one_one_int ) ).
% 0.33/0.57
% 0.33/0.57 % take_bit_Suc_1
% 0.33/0.57 thf(fact_3293_take__bit__Suc__1,axiom,
% 0.33/0.57 ! [N2: nat] :
% 0.33/0.57 ( ( bit_se2925701944663578781it_nat @ ( suc @ N2 ) @ one_one_nat )
% 0.33/0.57 = one_one_nat ) ).
% 0.33/0.57
% 0.33/0.57 % take_bit_Suc_1
% 0.33/0.57 thf(fact_3294_take__bit__Suc__1,axiom,
% 0.33/0.57 ! [N2: nat] :
% 0.33/0.57 ( ( bit_se569199155075624693atural @ ( suc @ N2 ) @ one_one_Code_natural )
% 0.33/0.57 = one_one_Code_natural ) ).
% 0.33/0.57
% 0.33/0.57 % take_bit_Suc_1
% 0.33/0.57 thf(fact_3295_take__bit__numeral__1,axiom,
% 0.33/0.57 ! [L: num] :
% 0.33/0.57 ( ( bit_se1745604003318907178nteger @ ( numeral_numeral_nat @ L ) @ one_one_Code_integer )
% 0.33/0.57 = one_one_Code_integer ) ).
% 0.33/0.57
% 0.33/0.57 % take_bit_numeral_1
% 0.33/0.57 thf(fact_3296_take__bit__numeral__1,axiom,
% 0.33/0.57 ! [L: num] :
% 0.33/0.57 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ one_one_int )
% 0.33/0.57 = one_one_int ) ).
% 0.33/0.57
% 0.33/0.57 % take_bit_numeral_1
% 0.33/0.57 thf(fact_3297_take__bit__numeral__1,axiom,
% 0.33/0.57 ! [L: num] :
% 0.33/0.57 ( ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ L ) @ one_one_nat )
% 0.33/0.57 = one_one_nat ) ).
% 0.33/0.57
% 0.33/0.57 % take_bit_numeral_1
% 0.33/0.57 thf(fact_3298_take__bit__numeral__1,axiom,
% 0.33/0.57 ! [L: num] :
% 0.33/0.57 ( ( bit_se569199155075624693atural @ ( numeral_numeral_nat @ L ) @ one_one_Code_natural )
% 0.33/0.57 = one_one_Code_natural ) ).
% 0.33/0.57
% 0.33/0.57 % take_bit_numeral_1
% 0.33/0.57 thf(fact_3299_semiring__norm_I9_J,axiom,
% 0.33/0.57 ! [M2: num,N2: num] :
% 0.33/0.57 ( ( plus_plus_num @ ( bit1 @ M2 ) @ ( bit0 @ N2 ) )
% 0.33/0.57 = ( bit1 @ ( plus_plus_num @ M2 @ N2 ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % semiring_norm(9)
% 0.33/0.57 thf(fact_3300_semiring__norm_I7_J,axiom,
% 0.33/0.57 ! [M2: num,N2: num] :
% 0.33/0.57 ( ( plus_plus_num @ ( bit0 @ M2 ) @ ( bit1 @ N2 ) )
% 0.33/0.57 = ( bit1 @ ( plus_plus_num @ M2 @ N2 ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % semiring_norm(7)
% 0.33/0.57 thf(fact_3301_semiring__norm_I16_J,axiom,
% 0.33/0.57 ! [M2: num,N2: num] :
% 0.33/0.57 ( ( times_times_num @ ( bit1 @ M2 ) @ ( bit1 @ N2 ) )
% 0.33/0.57 = ( bit1 @ ( plus_plus_num @ ( plus_plus_num @ M2 @ N2 ) @ ( bit0 @ ( times_times_num @ M2 @ N2 ) ) ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % semiring_norm(16)
% 0.33/0.57 thf(fact_3302_unit__mult__div__div,axiom,
% 0.33/0.57 ! [A: int,B: int] :
% 0.33/0.57 ( ( dvd_dvd_int @ A @ one_one_int )
% 0.33/0.57 => ( ( times_times_int @ B @ ( divide_divide_int @ one_one_int @ A ) )
% 0.33/0.57 = ( divide_divide_int @ B @ A ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % unit_mult_div_div
% 0.33/0.57 thf(fact_3303_unit__mult__div__div,axiom,
% 0.33/0.57 ! [A: nat,B: nat] :
% 0.33/0.57 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.33/0.57 => ( ( times_times_nat @ B @ ( divide_divide_nat @ one_one_nat @ A ) )
% 0.33/0.57 = ( divide_divide_nat @ B @ A ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % unit_mult_div_div
% 0.33/0.57 thf(fact_3304_unit__mult__div__div,axiom,
% 0.33/0.57 ! [A: code_integer,B: code_integer] :
% 0.33/0.57 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 0.33/0.57 => ( ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ one_one_Code_integer @ A ) )
% 0.33/0.57 = ( divide6298287555418463151nteger @ B @ A ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % unit_mult_div_div
% 0.33/0.57 thf(fact_3305_unit__mult__div__div,axiom,
% 0.33/0.57 ! [A: code_natural,B: code_natural] :
% 0.33/0.57 ( ( dvd_dvd_Code_natural @ A @ one_one_Code_natural )
% 0.33/0.57 => ( ( times_2397367101498566445atural @ B @ ( divide5121882707175180666atural @ one_one_Code_natural @ A ) )
% 0.33/0.57 = ( divide5121882707175180666atural @ B @ A ) ) ) ).
% 0.33/0.57
% 0.33/0.57 % unit_mult_div_div
% 0.33/0.57 thf(fact_3306_unit__div__mult__self,axiom,
% 0.33/0.57 ! [A: int,B: int] :
% 0.33/0.57 ( ( dvd_dvd_int @ A @ one_one_int )
% 0.33/0.57 => ( ( times_times_int @ ( divide_divide_int @ B @ A ) @ A )
% 0.33/0.57 = B ) ) ).
% 0.33/0.57
% 0.33/0.57 % unit_div_mult_self
% 0.33/0.57 thf(fact_3307_unit__div__mult__self,axiom,
% 0.33/0.57 ! [A: nat,B: nat] :
% 0.33/0.58 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.33/0.58 => ( ( times_times_nat @ ( divide_divide_nat @ B @ A ) @ A )
% 0.33/0.58 = B ) ) ).
% 0.33/0.58
% 0.33/0.58 % unit_div_mult_self
% 0.33/0.58 thf(fact_3308_unit__div__mult__self,axiom,
% 0.33/0.58 ! [A: code_integer,B: code_integer] :
% 0.33/0.58 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 0.33/0.58 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ B @ A ) @ A )
% 0.33/0.58 = B ) ) ).
% 0.33/0.58
% 0.33/0.58 % unit_div_mult_self
% 0.33/0.58 thf(fact_3309_unit__div__mult__self,axiom,
% 0.33/0.58 ! [A: code_natural,B: code_natural] :
% 0.33/0.58 ( ( dvd_dvd_Code_natural @ A @ one_one_Code_natural )
% 0.33/0.58 => ( ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ B @ A ) @ A )
% 0.33/0.58 = B ) ) ).
% 0.33/0.58
% 0.33/0.58 % unit_div_mult_self
% 0.33/0.58 thf(fact_3310_take__bit__of__1__eq__0__iff,axiom,
% 0.33/0.58 ! [N2: nat] :
% 0.33/0.58 ( ( ( bit_se1745604003318907178nteger @ N2 @ one_one_Code_integer )
% 0.33/0.58 = zero_z3403309356797280102nteger )
% 0.33/0.58 = ( N2 = zero_zero_nat ) ) ).
% 0.33/0.58
% 0.33/0.58 % take_bit_of_1_eq_0_iff
% 0.33/0.58 thf(fact_3311_take__bit__of__1__eq__0__iff,axiom,
% 0.33/0.58 ! [N2: nat] :
% 0.33/0.58 ( ( ( bit_se2923211474154528505it_int @ N2 @ one_one_int )
% 0.33/0.58 = zero_zero_int )
% 0.33/0.58 = ( N2 = zero_zero_nat ) ) ).
% 0.33/0.58
% 0.33/0.58 % take_bit_of_1_eq_0_iff
% 0.33/0.58 thf(fact_3312_take__bit__of__1__eq__0__iff,axiom,
% 0.33/0.58 ! [N2: nat] :
% 0.33/0.58 ( ( ( bit_se2925701944663578781it_nat @ N2 @ one_one_nat )
% 0.33/0.58 = zero_zero_nat )
% 0.33/0.58 = ( N2 = zero_zero_nat ) ) ).
% 0.33/0.58
% 0.33/0.58 % take_bit_of_1_eq_0_iff
% 0.33/0.58 thf(fact_3313_take__bit__of__1__eq__0__iff,axiom,
% 0.33/0.58 ! [N2: nat] :
% 0.33/0.58 ( ( ( bit_se569199155075624693atural @ N2 @ one_one_Code_natural )
% 0.33/0.58 = zero_z2226904508553997617atural )
% 0.33/0.58 = ( N2 = zero_zero_nat ) ) ).
% 0.33/0.58
% 0.33/0.58 % take_bit_of_1_eq_0_iff
% 0.33/0.58 thf(fact_3314_semiring__norm_I10_J,axiom,
% 0.33/0.58 ! [M2: num,N2: num] :
% 0.33/0.58 ( ( plus_plus_num @ ( bit1 @ M2 ) @ ( bit1 @ N2 ) )
% 0.33/0.58 = ( bit0 @ ( plus_plus_num @ ( plus_plus_num @ M2 @ N2 ) @ one ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % semiring_norm(10)
% 0.33/0.58 thf(fact_3315_semiring__norm_I8_J,axiom,
% 0.33/0.58 ! [M2: num] :
% 0.33/0.58 ( ( plus_plus_num @ ( bit1 @ M2 ) @ one )
% 0.33/0.58 = ( bit0 @ ( plus_plus_num @ M2 @ one ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % semiring_norm(8)
% 0.33/0.58 thf(fact_3316_semiring__norm_I5_J,axiom,
% 0.33/0.58 ! [M2: num] :
% 0.33/0.58 ( ( plus_plus_num @ ( bit0 @ M2 ) @ one )
% 0.33/0.58 = ( bit1 @ M2 ) ) ).
% 0.33/0.58
% 0.33/0.58 % semiring_norm(5)
% 0.33/0.58 thf(fact_3317_semiring__norm_I4_J,axiom,
% 0.33/0.58 ! [N2: num] :
% 0.33/0.58 ( ( plus_plus_num @ one @ ( bit1 @ N2 ) )
% 0.33/0.58 = ( bit0 @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % semiring_norm(4)
% 0.33/0.58 thf(fact_3318_semiring__norm_I3_J,axiom,
% 0.33/0.58 ! [N2: num] :
% 0.33/0.58 ( ( plus_plus_num @ one @ ( bit0 @ N2 ) )
% 0.33/0.58 = ( bit1 @ N2 ) ) ).
% 0.33/0.58
% 0.33/0.58 % semiring_norm(3)
% 0.33/0.58 thf(fact_3319_odd__add,axiom,
% 0.33/0.58 ! [A: nat,B: nat] :
% 0.33/0.58 ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) ) )
% 0.33/0.58 = ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 0.33/0.58 != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % odd_add
% 0.33/0.58 thf(fact_3320_odd__add,axiom,
% 0.33/0.58 ! [A: int,B: int] :
% 0.33/0.58 ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) ) )
% 0.33/0.58 = ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 0.33/0.58 != ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % odd_add
% 0.33/0.58 thf(fact_3321_odd__add,axiom,
% 0.33/0.58 ! [A: code_integer,B: code_integer] :
% 0.33/0.58 ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) ) )
% 0.33/0.58 = ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 0.33/0.58 != ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % odd_add
% 0.33/0.58 thf(fact_3322_odd__add,axiom,
% 0.33/0.58 ! [A: code_natural,B: code_natural] :
% 0.33/0.58 ( ( ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( plus_p4538020629002901425atural @ A @ B ) ) )
% 0.33/0.58 = ( ( ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A ) )
% 0.33/0.58 != ( ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % odd_add
% 0.33/0.58 thf(fact_3323_even__add,axiom,
% 0.33/0.58 ! [A: nat,B: nat] :
% 0.33/0.58 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) )
% 0.33/0.58 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.33/0.58 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % even_add
% 0.33/0.58 thf(fact_3324_even__add,axiom,
% 0.33/0.58 ! [A: int,B: int] :
% 0.33/0.58 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) )
% 0.33/0.58 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.33/0.58 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % even_add
% 0.33/0.58 thf(fact_3325_even__add,axiom,
% 0.33/0.58 ! [A: code_integer,B: code_integer] :
% 0.33/0.58 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 0.33/0.58 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.33/0.58 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % even_add
% 0.33/0.58 thf(fact_3326_even__add,axiom,
% 0.33/0.58 ! [A: code_natural,B: code_natural] :
% 0.33/0.58 ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( plus_p4538020629002901425atural @ A @ B ) )
% 0.33/0.58 = ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 0.33/0.58 = ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ B ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % even_add
% 0.33/0.58 thf(fact_3327_dbl__inc__simps_I3_J,axiom,
% 0.33/0.58 ( ( neg_nu5851722552734809277nc_int @ one_one_int )
% 0.33/0.58 = ( numeral_numeral_int @ ( bit1 @ one ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % dbl_inc_simps(3)
% 0.33/0.58 thf(fact_3328_dbl__inc__simps_I3_J,axiom,
% 0.33/0.58 ( ( neg_nu5831290666863070958nteger @ one_one_Code_integer )
% 0.33/0.58 = ( numera6620942414471956472nteger @ ( bit1 @ one ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % dbl_inc_simps(3)
% 0.33/0.58 thf(fact_3329_dbl__inc__simps_I3_J,axiom,
% 0.33/0.58 ( ( neg_nu5219082963157363817nc_rat @ one_one_rat )
% 0.33/0.58 = ( numeral_numeral_rat @ ( bit1 @ one ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % dbl_inc_simps(3)
% 0.33/0.58 thf(fact_3330_even__plus__one__iff,axiom,
% 0.33/0.58 ! [A: nat] :
% 0.33/0.58 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ one_one_nat ) )
% 0.33/0.58 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % even_plus_one_iff
% 0.33/0.58 thf(fact_3331_even__plus__one__iff,axiom,
% 0.33/0.58 ! [A: int] :
% 0.33/0.58 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ one_one_int ) )
% 0.33/0.58 = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % even_plus_one_iff
% 0.33/0.58 thf(fact_3332_even__plus__one__iff,axiom,
% 0.33/0.58 ! [A: code_integer] :
% 0.33/0.58 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) )
% 0.33/0.58 = ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % even_plus_one_iff
% 0.33/0.58 thf(fact_3333_even__plus__one__iff,axiom,
% 0.33/0.58 ! [A: code_natural] :
% 0.33/0.58 ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( plus_p4538020629002901425atural @ A @ one_one_Code_natural ) )
% 0.33/0.58 = ( ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % even_plus_one_iff
% 0.33/0.58 thf(fact_3334_even__diff,axiom,
% 0.33/0.58 ! [A: int,B: int] :
% 0.33/0.58 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ A @ B ) )
% 0.33/0.58 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % even_diff
% 0.33/0.58 thf(fact_3335_even__diff,axiom,
% 0.33/0.58 ! [A: code_integer,B: code_integer] :
% 0.33/0.58 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_8373710615458151222nteger @ A @ B ) )
% 0.33/0.58 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % even_diff
% 0.33/0.58 thf(fact_3336_neg__one__even__power,axiom,
% 0.33/0.58 ! [N2: nat] :
% 0.33/0.58 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.33/0.58 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 )
% 0.33/0.58 = one_one_int ) ) ).
% 0.33/0.58
% 0.33/0.58 % neg_one_even_power
% 0.33/0.58 thf(fact_3337_neg__one__even__power,axiom,
% 0.33/0.58 ! [N2: nat] :
% 0.33/0.58 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.33/0.58 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 )
% 0.33/0.58 = one_one_Code_integer ) ) ).
% 0.33/0.58
% 0.33/0.58 % neg_one_even_power
% 0.33/0.58 thf(fact_3338_neg__one__even__power,axiom,
% 0.33/0.58 ! [N2: nat] :
% 0.33/0.58 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.33/0.58 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 )
% 0.33/0.58 = one_one_rat ) ) ).
% 0.33/0.58
% 0.33/0.58 % neg_one_even_power
% 0.33/0.58 thf(fact_3339_neg__one__odd__power,axiom,
% 0.33/0.58 ! [N2: nat] :
% 0.33/0.58 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.33/0.58 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 )
% 0.33/0.58 = ( uminus_uminus_int @ one_one_int ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % neg_one_odd_power
% 0.33/0.58 thf(fact_3340_neg__one__odd__power,axiom,
% 0.33/0.58 ! [N2: nat] :
% 0.33/0.58 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.33/0.58 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 )
% 0.33/0.58 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % neg_one_odd_power
% 0.33/0.58 thf(fact_3341_neg__one__odd__power,axiom,
% 0.33/0.58 ! [N2: nat] :
% 0.33/0.58 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.33/0.58 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 )
% 0.33/0.58 = ( uminus_uminus_rat @ one_one_rat ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % neg_one_odd_power
% 0.33/0.58 thf(fact_3342_even__diff__nat,axiom,
% 0.33/0.58 ! [M2: nat,N2: nat] :
% 0.33/0.58 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M2 @ N2 ) )
% 0.33/0.58 = ( ( ord_less_nat @ M2 @ N2 )
% 0.33/0.58 | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M2 @ N2 ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % even_diff_nat
% 0.33/0.58 thf(fact_3343_divmod__algorithm__code_I4_J,axiom,
% 0.33/0.58 ! [N2: num] :
% 0.33/0.58 ( ( unique3479559517661332726nteger @ one @ ( bit1 @ N2 ) )
% 0.33/0.58 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ one ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % divmod_algorithm_code(4)
% 0.33/0.58 thf(fact_3344_divmod__algorithm__code_I4_J,axiom,
% 0.33/0.58 ! [N2: num] :
% 0.33/0.58 ( ( unique5052692396658037445od_int @ one @ ( bit1 @ N2 ) )
% 0.33/0.58 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ one ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % divmod_algorithm_code(4)
% 0.33/0.58 thf(fact_3345_divmod__algorithm__code_I4_J,axiom,
% 0.33/0.58 ! [N2: num] :
% 0.33/0.58 ( ( unique5055182867167087721od_nat @ one @ ( bit1 @ N2 ) )
% 0.33/0.58 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ one ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % divmod_algorithm_code(4)
% 0.33/0.58 thf(fact_3346_mod__Suc__eq__mod__add3,axiom,
% 0.33/0.58 ! [M2: nat,N2: nat] :
% 0.33/0.58 ( ( modulo_modulo_nat @ M2 @ ( suc @ ( suc @ ( suc @ N2 ) ) ) )
% 0.33/0.58 = ( modulo_modulo_nat @ M2 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N2 ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % mod_Suc_eq_mod_add3
% 0.33/0.58 thf(fact_3347_Suc__mod__eq__add3__mod__numeral,axiom,
% 0.33/0.58 ! [M2: nat,V: num] :
% 0.33/0.58 ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( suc @ M2 ) ) ) @ ( numeral_numeral_nat @ V ) )
% 0.33/0.58 = ( modulo_modulo_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M2 ) @ ( numeral_numeral_nat @ V ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % Suc_mod_eq_add3_mod_numeral
% 0.33/0.58 thf(fact_3348_div__Suc__eq__div__add3,axiom,
% 0.33/0.58 ! [M2: nat,N2: nat] :
% 0.33/0.58 ( ( divide_divide_nat @ M2 @ ( suc @ ( suc @ ( suc @ N2 ) ) ) )
% 0.33/0.58 = ( divide_divide_nat @ M2 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N2 ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % div_Suc_eq_div_add3
% 0.33/0.58 thf(fact_3349_Suc__div__eq__add3__div__numeral,axiom,
% 0.33/0.58 ! [M2: nat,V: num] :
% 0.33/0.58 ( ( divide_divide_nat @ ( suc @ ( suc @ ( suc @ M2 ) ) ) @ ( numeral_numeral_nat @ V ) )
% 0.33/0.58 = ( divide_divide_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M2 ) @ ( numeral_numeral_nat @ V ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % Suc_div_eq_add3_div_numeral
% 0.33/0.58 thf(fact_3350_dbl__dec__simps_I4_J,axiom,
% 0.33/0.58 ( ( neg_nu3811975205180677377ec_int @ ( uminus_uminus_int @ one_one_int ) )
% 0.33/0.58 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ one ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % dbl_dec_simps(4)
% 0.33/0.58 thf(fact_3351_dbl__dec__simps_I4_J,axiom,
% 0.33/0.58 ( ( neg_nu7757733837767384882nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.33/0.58 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit1 @ one ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % dbl_dec_simps(4)
% 0.33/0.58 thf(fact_3352_dbl__dec__simps_I4_J,axiom,
% 0.33/0.58 ( ( neg_nu3179335615603231917ec_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.33/0.58 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit1 @ one ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % dbl_dec_simps(4)
% 0.33/0.58 thf(fact_3353_even__succ__div__2,axiom,
% 0.33/0.58 ! [A: int] :
% 0.33/0.58 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.33/0.58 => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ A ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.33/0.58 = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % even_succ_div_2
% 0.33/0.58 thf(fact_3354_even__succ__div__2,axiom,
% 0.33/0.58 ! [A: nat] :
% 0.33/0.58 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.33/0.58 => ( ( divide_divide_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.33/0.58 = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % even_succ_div_2
% 0.33/0.58 thf(fact_3355_even__succ__div__2,axiom,
% 0.33/0.58 ! [A: code_integer] :
% 0.33/0.58 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.33/0.58 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.33/0.58 = ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % even_succ_div_2
% 0.33/0.58 thf(fact_3356_even__succ__div__2,axiom,
% 0.33/0.58 ! [A: code_natural] :
% 0.33/0.58 ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 0.33/0.58 => ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ one_one_Code_natural @ A ) @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 0.33/0.58 = ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % even_succ_div_2
% 0.33/0.58 thf(fact_3357_odd__succ__div__two,axiom,
% 0.33/0.58 ! [A: int] :
% 0.33/0.58 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.33/0.58 => ( ( divide_divide_int @ ( plus_plus_int @ A @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.33/0.58 = ( plus_plus_int @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % odd_succ_div_two
% 0.33/0.58 thf(fact_3358_odd__succ__div__two,axiom,
% 0.33/0.58 ! [A: nat] :
% 0.33/0.58 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.33/0.58 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.33/0.58 = ( plus_plus_nat @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % odd_succ_div_two
% 0.33/0.58 thf(fact_3359_odd__succ__div__two,axiom,
% 0.33/0.58 ! [A: code_integer] :
% 0.33/0.58 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.33/0.58 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.33/0.58 = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ one_one_Code_integer ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % odd_succ_div_two
% 0.33/0.58 thf(fact_3360_odd__succ__div__two,axiom,
% 0.33/0.58 ! [A: code_natural] :
% 0.33/0.58 ( ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 0.33/0.58 => ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ A @ one_one_Code_natural ) @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 0.33/0.58 = ( plus_p4538020629002901425atural @ ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) @ one_one_Code_natural ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % odd_succ_div_two
% 0.33/0.58 thf(fact_3361_even__succ__div__two,axiom,
% 0.33/0.58 ! [A: int] :
% 0.33/0.58 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.33/0.58 => ( ( divide_divide_int @ ( plus_plus_int @ A @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.33/0.58 = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % even_succ_div_two
% 0.33/0.58 thf(fact_3362_even__succ__div__two,axiom,
% 0.33/0.58 ! [A: nat] :
% 0.33/0.58 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.33/0.58 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.33/0.58 = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % even_succ_div_two
% 0.33/0.58 thf(fact_3363_even__succ__div__two,axiom,
% 0.33/0.58 ! [A: code_integer] :
% 0.33/0.58 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.33/0.58 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.33/0.58 = ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % even_succ_div_two
% 0.33/0.58 thf(fact_3364_even__succ__div__two,axiom,
% 0.33/0.58 ! [A: code_natural] :
% 0.33/0.58 ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 0.33/0.58 => ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ A @ one_one_Code_natural ) @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 0.33/0.58 = ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % even_succ_div_two
% 0.33/0.58 thf(fact_3365_odd__two__times__div__two__nat,axiom,
% 0.33/0.58 ! [N2: nat] :
% 0.33/0.58 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.33/0.58 => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.33/0.58 = ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % odd_two_times_div_two_nat
% 0.33/0.58 thf(fact_3366_odd__two__times__div__two__succ,axiom,
% 0.33/0.58 ! [A: int] :
% 0.33/0.58 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.33/0.58 => ( ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ one_one_int )
% 0.33/0.58 = A ) ) ).
% 0.33/0.58
% 0.33/0.58 % odd_two_times_div_two_succ
% 0.33/0.58 thf(fact_3367_odd__two__times__div__two__succ,axiom,
% 0.33/0.58 ! [A: nat] :
% 0.33/0.58 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.33/0.58 => ( ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_nat )
% 0.33/0.58 = A ) ) ).
% 0.33/0.58
% 0.33/0.58 % odd_two_times_div_two_succ
% 0.33/0.58 thf(fact_3368_odd__two__times__div__two__succ,axiom,
% 0.33/0.58 ! [A: code_integer] :
% 0.33/0.58 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.33/0.58 => ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ one_one_Code_integer )
% 0.33/0.58 = A ) ) ).
% 0.33/0.58
% 0.33/0.58 % odd_two_times_div_two_succ
% 0.33/0.58 thf(fact_3369_odd__two__times__div__two__succ,axiom,
% 0.33/0.58 ! [A: code_natural] :
% 0.33/0.58 ( ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 0.33/0.58 => ( ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) @ one_one_Code_natural )
% 0.33/0.58 = A ) ) ).
% 0.33/0.58
% 0.33/0.58 % odd_two_times_div_two_succ
% 0.33/0.58 thf(fact_3370_semiring__parity__class_Oeven__mask__iff,axiom,
% 0.33/0.58 ! [N2: nat] :
% 0.33/0.58 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) )
% 0.33/0.58 = ( N2 = zero_zero_nat ) ) ).
% 0.33/0.58
% 0.33/0.58 % semiring_parity_class.even_mask_iff
% 0.33/0.58 thf(fact_3371_semiring__parity__class_Oeven__mask__iff,axiom,
% 0.33/0.58 ! [N2: nat] :
% 0.33/0.58 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ one_one_int ) )
% 0.33/0.58 = ( N2 = zero_zero_nat ) ) ).
% 0.33/0.58
% 0.33/0.58 % semiring_parity_class.even_mask_iff
% 0.33/0.58 thf(fact_3372_semiring__parity__class_Oeven__mask__iff,axiom,
% 0.33/0.58 ! [N2: nat] :
% 0.33/0.58 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) @ one_one_Code_integer ) )
% 0.33/0.58 = ( N2 = zero_zero_nat ) ) ).
% 0.33/0.58
% 0.33/0.58 % semiring_parity_class.even_mask_iff
% 0.33/0.58 thf(fact_3373_semiring__parity__class_Oeven__mask__iff,axiom,
% 0.33/0.58 ! [N2: nat] :
% 0.33/0.58 ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( minus_7197305767214868737atural @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N2 ) @ one_one_Code_natural ) )
% 0.33/0.58 = ( N2 = zero_zero_nat ) ) ).
% 0.33/0.58
% 0.33/0.58 % semiring_parity_class.even_mask_iff
% 0.33/0.58 thf(fact_3374_zmod__numeral__Bit1,axiom,
% 0.33/0.58 ! [V: num,W: num] :
% 0.33/0.58 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 0.33/0.58 = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) @ one_one_int ) ) ).
% 0.33/0.58
% 0.33/0.58 % zmod_numeral_Bit1
% 0.33/0.58 thf(fact_3375_divmod__algorithm__code_I8_J,axiom,
% 0.33/0.58 ! [M2: num,N2: num] :
% 0.33/0.58 ( ( ( ord_less_num @ M2 @ N2 )
% 0.33/0.58 => ( ( unique5055182867167087721od_nat @ ( bit1 @ M2 ) @ ( bit1 @ N2 ) )
% 0.33/0.58 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit1 @ M2 ) ) ) ) )
% 0.33/0.58 & ( ~ ( ord_less_num @ M2 @ N2 )
% 0.33/0.58 => ( ( unique5055182867167087721od_nat @ ( bit1 @ M2 ) @ ( bit1 @ N2 ) )
% 0.33/0.58 = ( unique5026877609467782581ep_nat @ ( bit1 @ N2 ) @ ( unique5055182867167087721od_nat @ ( bit1 @ M2 ) @ ( bit0 @ ( bit1 @ N2 ) ) ) ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % divmod_algorithm_code(8)
% 0.33/0.58 thf(fact_3376_divmod__algorithm__code_I8_J,axiom,
% 0.33/0.58 ! [M2: num,N2: num] :
% 0.33/0.58 ( ( ( ord_less_num @ M2 @ N2 )
% 0.33/0.58 => ( ( unique5052692396658037445od_int @ ( bit1 @ M2 ) @ ( bit1 @ N2 ) )
% 0.33/0.58 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ ( bit1 @ M2 ) ) ) ) )
% 0.33/0.58 & ( ~ ( ord_less_num @ M2 @ N2 )
% 0.33/0.58 => ( ( unique5052692396658037445od_int @ ( bit1 @ M2 ) @ ( bit1 @ N2 ) )
% 0.33/0.58 = ( unique5024387138958732305ep_int @ ( bit1 @ N2 ) @ ( unique5052692396658037445od_int @ ( bit1 @ M2 ) @ ( bit0 @ ( bit1 @ N2 ) ) ) ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % divmod_algorithm_code(8)
% 0.33/0.58 thf(fact_3377_divmod__algorithm__code_I8_J,axiom,
% 0.33/0.58 ! [M2: num,N2: num] :
% 0.33/0.58 ( ( ( ord_less_num @ M2 @ N2 )
% 0.33/0.58 => ( ( unique3479559517661332726nteger @ ( bit1 @ M2 ) @ ( bit1 @ N2 ) )
% 0.33/0.58 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M2 ) ) ) ) )
% 0.33/0.58 & ( ~ ( ord_less_num @ M2 @ N2 )
% 0.33/0.58 => ( ( unique3479559517661332726nteger @ ( bit1 @ M2 ) @ ( bit1 @ N2 ) )
% 0.33/0.58 = ( unique4921790084139445826nteger @ ( bit1 @ N2 ) @ ( unique3479559517661332726nteger @ ( bit1 @ M2 ) @ ( bit0 @ ( bit1 @ N2 ) ) ) ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % divmod_algorithm_code(8)
% 0.33/0.58 thf(fact_3378_divmod__algorithm__code_I7_J,axiom,
% 0.33/0.58 ! [M2: num,N2: num] :
% 0.33/0.58 ( ( ( ord_less_eq_num @ M2 @ N2 )
% 0.33/0.58 => ( ( unique5055182867167087721od_nat @ ( bit0 @ M2 ) @ ( bit1 @ N2 ) )
% 0.33/0.58 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ M2 ) ) ) ) )
% 0.33/0.58 & ( ~ ( ord_less_eq_num @ M2 @ N2 )
% 0.33/0.58 => ( ( unique5055182867167087721od_nat @ ( bit0 @ M2 ) @ ( bit1 @ N2 ) )
% 0.33/0.58 = ( unique5026877609467782581ep_nat @ ( bit1 @ N2 ) @ ( unique5055182867167087721od_nat @ ( bit0 @ M2 ) @ ( bit0 @ ( bit1 @ N2 ) ) ) ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % divmod_algorithm_code(7)
% 0.33/0.58 thf(fact_3379_divmod__algorithm__code_I7_J,axiom,
% 0.33/0.58 ! [M2: num,N2: num] :
% 0.33/0.58 ( ( ( ord_less_eq_num @ M2 @ N2 )
% 0.33/0.58 => ( ( unique5052692396658037445od_int @ ( bit0 @ M2 ) @ ( bit1 @ N2 ) )
% 0.33/0.58 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ ( bit0 @ M2 ) ) ) ) )
% 0.33/0.58 & ( ~ ( ord_less_eq_num @ M2 @ N2 )
% 0.33/0.58 => ( ( unique5052692396658037445od_int @ ( bit0 @ M2 ) @ ( bit1 @ N2 ) )
% 0.33/0.58 = ( unique5024387138958732305ep_int @ ( bit1 @ N2 ) @ ( unique5052692396658037445od_int @ ( bit0 @ M2 ) @ ( bit0 @ ( bit1 @ N2 ) ) ) ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % divmod_algorithm_code(7)
% 0.33/0.58 thf(fact_3380_divmod__algorithm__code_I7_J,axiom,
% 0.33/0.58 ! [M2: num,N2: num] :
% 0.33/0.58 ( ( ( ord_less_eq_num @ M2 @ N2 )
% 0.33/0.58 => ( ( unique3479559517661332726nteger @ ( bit0 @ M2 ) @ ( bit1 @ N2 ) )
% 0.33/0.58 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M2 ) ) ) ) )
% 0.33/0.58 & ( ~ ( ord_less_eq_num @ M2 @ N2 )
% 0.33/0.58 => ( ( unique3479559517661332726nteger @ ( bit0 @ M2 ) @ ( bit1 @ N2 ) )
% 0.33/0.58 = ( unique4921790084139445826nteger @ ( bit1 @ N2 ) @ ( unique3479559517661332726nteger @ ( bit0 @ M2 ) @ ( bit0 @ ( bit1 @ N2 ) ) ) ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % divmod_algorithm_code(7)
% 0.33/0.58 thf(fact_3381_signed__take__bit__Suc__bit1,axiom,
% 0.33/0.58 ! [N2: nat,K: num] :
% 0.33/0.58 ( ( bit_ri631733984087533419it_int @ ( suc @ N2 ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 0.33/0.58 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N2 @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 0.33/0.58
% 0.33/0.58 % signed_take_bit_Suc_bit1
% 0.33/0.58 thf(fact_3382_uminus__integer__code_I1_J,axiom,
% 0.33/0.58 ( ( uminus1351360451143612070nteger @ zero_z3403309356797280102nteger )
% 0.33/0.58 = zero_z3403309356797280102nteger ) ).
% 0.33/0.58
% 0.33/0.58 % uminus_integer_code(1)
% 0.33/0.58 thf(fact_3383_take__bit__integer_Oabs__eq,axiom,
% 0.33/0.58 ! [Xa: nat,X: int] :
% 0.33/0.58 ( ( bit_se1745604003318907178nteger @ Xa @ ( code_integer_of_int @ X ) )
% 0.33/0.58 = ( code_integer_of_int @ ( bit_se2923211474154528505it_int @ Xa @ X ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % take_bit_integer.abs_eq
% 0.33/0.58 thf(fact_3384_abs__integer__code,axiom,
% 0.33/0.58 ( abs_abs_Code_integer
% 0.33/0.58 = ( ^ [K4: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ K4 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ K4 ) @ K4 ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % abs_integer_code
% 0.33/0.58 thf(fact_3385_less__integer__code_I1_J,axiom,
% 0.33/0.58 ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger ) ).
% 0.33/0.58
% 0.33/0.58 % less_integer_code(1)
% 0.33/0.58 thf(fact_3386_unset__bit__integer_Oabs__eq,axiom,
% 0.33/0.58 ! [Xa: nat,X: int] :
% 0.33/0.58 ( ( bit_se8260200283734997820nteger @ Xa @ ( code_integer_of_int @ X ) )
% 0.33/0.58 = ( code_integer_of_int @ ( bit_se4203085406695923979it_int @ Xa @ X ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % unset_bit_integer.abs_eq
% 0.33/0.58 thf(fact_3387_flip__bit__integer_Oabs__eq,axiom,
% 0.33/0.58 ! [Xa: nat,X: int] :
% 0.33/0.58 ( ( bit_se1345352211410354436nteger @ Xa @ ( code_integer_of_int @ X ) )
% 0.33/0.58 = ( code_integer_of_int @ ( bit_se2159334234014336723it_int @ Xa @ X ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % flip_bit_integer.abs_eq
% 0.33/0.58 thf(fact_3388_set__bit__integer_Oabs__eq,axiom,
% 0.33/0.58 ! [Xa: nat,X: int] :
% 0.33/0.58 ( ( bit_se2793503036327961859nteger @ Xa @ ( code_integer_of_int @ X ) )
% 0.33/0.58 = ( code_integer_of_int @ ( bit_se7879613467334960850it_int @ Xa @ X ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % set_bit_integer.abs_eq
% 0.33/0.58 thf(fact_3389_take__bit__add,axiom,
% 0.33/0.58 ! [N2: nat,A: code_integer,B: code_integer] :
% 0.33/0.58 ( ( bit_se1745604003318907178nteger @ N2 @ ( plus_p5714425477246183910nteger @ ( bit_se1745604003318907178nteger @ N2 @ A ) @ ( bit_se1745604003318907178nteger @ N2 @ B ) ) )
% 0.33/0.58 = ( bit_se1745604003318907178nteger @ N2 @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % take_bit_add
% 0.33/0.58 thf(fact_3390_take__bit__add,axiom,
% 0.33/0.58 ! [N2: nat,A: int,B: int] :
% 0.33/0.58 ( ( bit_se2923211474154528505it_int @ N2 @ ( plus_plus_int @ ( bit_se2923211474154528505it_int @ N2 @ A ) @ ( bit_se2923211474154528505it_int @ N2 @ B ) ) )
% 0.33/0.58 = ( bit_se2923211474154528505it_int @ N2 @ ( plus_plus_int @ A @ B ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % take_bit_add
% 0.33/0.58 thf(fact_3391_take__bit__add,axiom,
% 0.33/0.58 ! [N2: nat,A: nat,B: nat] :
% 0.33/0.58 ( ( bit_se2925701944663578781it_nat @ N2 @ ( plus_plus_nat @ ( bit_se2925701944663578781it_nat @ N2 @ A ) @ ( bit_se2925701944663578781it_nat @ N2 @ B ) ) )
% 0.33/0.58 = ( bit_se2925701944663578781it_nat @ N2 @ ( plus_plus_nat @ A @ B ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % take_bit_add
% 0.33/0.58 thf(fact_3392_take__bit__add,axiom,
% 0.33/0.58 ! [N2: nat,A: code_natural,B: code_natural] :
% 0.33/0.58 ( ( bit_se569199155075624693atural @ N2 @ ( plus_p4538020629002901425atural @ ( bit_se569199155075624693atural @ N2 @ A ) @ ( bit_se569199155075624693atural @ N2 @ B ) ) )
% 0.33/0.58 = ( bit_se569199155075624693atural @ N2 @ ( plus_p4538020629002901425atural @ A @ B ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % take_bit_add
% 0.33/0.58 thf(fact_3393_zero__integer__def,axiom,
% 0.33/0.58 ( zero_z3403309356797280102nteger
% 0.33/0.58 = ( code_integer_of_int @ zero_zero_int ) ) ).
% 0.33/0.58
% 0.33/0.58 % zero_integer_def
% 0.33/0.58 thf(fact_3394_less__integer_Oabs__eq,axiom,
% 0.33/0.58 ! [Xa: int,X: int] :
% 0.33/0.58 ( ( ord_le6747313008572928689nteger @ ( code_integer_of_int @ Xa ) @ ( code_integer_of_int @ X ) )
% 0.33/0.58 = ( ord_less_int @ Xa @ X ) ) ).
% 0.33/0.58
% 0.33/0.58 % less_integer.abs_eq
% 0.33/0.58 thf(fact_3395_uminus__integer_Oabs__eq,axiom,
% 0.33/0.58 ! [X: int] :
% 0.33/0.58 ( ( uminus1351360451143612070nteger @ ( code_integer_of_int @ X ) )
% 0.33/0.58 = ( code_integer_of_int @ ( uminus_uminus_int @ X ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % uminus_integer.abs_eq
% 0.33/0.58 thf(fact_3396_abs__integer_Oabs__eq,axiom,
% 0.33/0.58 ! [X: int] :
% 0.33/0.58 ( ( abs_abs_Code_integer @ ( code_integer_of_int @ X ) )
% 0.33/0.58 = ( code_integer_of_int @ ( abs_abs_int @ X ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % abs_integer.abs_eq
% 0.33/0.58 thf(fact_3397_dvd__add__right__iff,axiom,
% 0.33/0.58 ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.33/0.58 ( ( dvd_dvd_Code_integer @ A @ B )
% 0.33/0.58 => ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 0.33/0.58 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % dvd_add_right_iff
% 0.33/0.58 thf(fact_3398_dvd__add__right__iff,axiom,
% 0.33/0.58 ! [A: rat,B: rat,C: rat] :
% 0.33/0.58 ( ( dvd_dvd_rat @ A @ B )
% 0.33/0.58 => ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 0.33/0.58 = ( dvd_dvd_rat @ A @ C ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % dvd_add_right_iff
% 0.33/0.58 thf(fact_3399_dvd__add__right__iff,axiom,
% 0.33/0.58 ! [A: nat,B: nat,C: nat] :
% 0.33/0.58 ( ( dvd_dvd_nat @ A @ B )
% 0.33/0.58 => ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 0.33/0.58 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % dvd_add_right_iff
% 0.33/0.58 thf(fact_3400_dvd__add__right__iff,axiom,
% 0.33/0.58 ! [A: int,B: int,C: int] :
% 0.33/0.58 ( ( dvd_dvd_int @ A @ B )
% 0.33/0.58 => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ C ) )
% 0.33/0.58 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % dvd_add_right_iff
% 0.33/0.58 thf(fact_3401_dvd__add__left__iff,axiom,
% 0.33/0.58 ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.33/0.58 ( ( dvd_dvd_Code_integer @ A @ C )
% 0.33/0.58 => ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 0.33/0.58 = ( dvd_dvd_Code_integer @ A @ B ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % dvd_add_left_iff
% 0.33/0.58 thf(fact_3402_dvd__add__left__iff,axiom,
% 0.33/0.58 ! [A: rat,C: rat,B: rat] :
% 0.33/0.58 ( ( dvd_dvd_rat @ A @ C )
% 0.33/0.58 => ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 0.33/0.58 = ( dvd_dvd_rat @ A @ B ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % dvd_add_left_iff
% 0.33/0.58 thf(fact_3403_dvd__add__left__iff,axiom,
% 0.33/0.58 ! [A: nat,C: nat,B: nat] :
% 0.33/0.58 ( ( dvd_dvd_nat @ A @ C )
% 0.33/0.58 => ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 0.33/0.58 = ( dvd_dvd_nat @ A @ B ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % dvd_add_left_iff
% 0.33/0.58 thf(fact_3404_dvd__add__left__iff,axiom,
% 0.33/0.58 ! [A: int,C: int,B: int] :
% 0.33/0.58 ( ( dvd_dvd_int @ A @ C )
% 0.33/0.58 => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ C ) )
% 0.33/0.58 = ( dvd_dvd_int @ A @ B ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % dvd_add_left_iff
% 0.33/0.58 thf(fact_3405_dvd__add,axiom,
% 0.33/0.58 ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.33/0.58 ( ( dvd_dvd_Code_integer @ A @ B )
% 0.33/0.58 => ( ( dvd_dvd_Code_integer @ A @ C )
% 0.33/0.58 => ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ C ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % dvd_add
% 0.33/0.58 thf(fact_3406_dvd__add,axiom,
% 0.33/0.58 ! [A: rat,B: rat,C: rat] :
% 0.33/0.58 ( ( dvd_dvd_rat @ A @ B )
% 0.33/0.58 => ( ( dvd_dvd_rat @ A @ C )
% 0.33/0.58 => ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % dvd_add
% 0.33/0.58 thf(fact_3407_dvd__add,axiom,
% 0.33/0.58 ! [A: nat,B: nat,C: nat] :
% 0.33/0.58 ( ( dvd_dvd_nat @ A @ B )
% 0.33/0.58 => ( ( dvd_dvd_nat @ A @ C )
% 0.33/0.58 => ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % dvd_add
% 0.33/0.58 thf(fact_3408_dvd__add,axiom,
% 0.33/0.58 ! [A: int,B: int,C: int] :
% 0.33/0.58 ( ( dvd_dvd_int @ A @ B )
% 0.33/0.58 => ( ( dvd_dvd_int @ A @ C )
% 0.33/0.58 => ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ C ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % dvd_add
% 0.33/0.58 thf(fact_3409_divide__integer_Oabs__eq,axiom,
% 0.33/0.58 ! [Xa: int,X: int] :
% 0.33/0.58 ( ( divide6298287555418463151nteger @ ( code_integer_of_int @ Xa ) @ ( code_integer_of_int @ X ) )
% 0.33/0.58 = ( code_integer_of_int @ ( divide_divide_int @ Xa @ X ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % divide_integer.abs_eq
% 0.33/0.58 thf(fact_3410_dvd__unit__imp__unit,axiom,
% 0.33/0.58 ! [A: code_integer,B: code_integer] :
% 0.33/0.58 ( ( dvd_dvd_Code_integer @ A @ B )
% 0.33/0.58 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.33/0.58 => ( dvd_dvd_Code_integer @ A @ one_one_Code_integer ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % dvd_unit_imp_unit
% 0.33/0.58 thf(fact_3411_dvd__unit__imp__unit,axiom,
% 0.33/0.58 ! [A: nat,B: nat] :
% 0.33/0.58 ( ( dvd_dvd_nat @ A @ B )
% 0.33/0.58 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.33/0.58 => ( dvd_dvd_nat @ A @ one_one_nat ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % dvd_unit_imp_unit
% 0.33/0.58 thf(fact_3412_dvd__unit__imp__unit,axiom,
% 0.33/0.58 ! [A: int,B: int] :
% 0.33/0.58 ( ( dvd_dvd_int @ A @ B )
% 0.33/0.58 => ( ( dvd_dvd_int @ B @ one_one_int )
% 0.33/0.58 => ( dvd_dvd_int @ A @ one_one_int ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % dvd_unit_imp_unit
% 0.33/0.58 thf(fact_3413_unit__imp__dvd,axiom,
% 0.33/0.58 ! [B: code_integer,A: code_integer] :
% 0.33/0.58 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.33/0.58 => ( dvd_dvd_Code_integer @ B @ A ) ) ).
% 0.33/0.58
% 0.33/0.58 % unit_imp_dvd
% 0.33/0.58 thf(fact_3414_unit__imp__dvd,axiom,
% 0.33/0.58 ! [B: nat,A: nat] :
% 0.33/0.58 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.33/0.58 => ( dvd_dvd_nat @ B @ A ) ) ).
% 0.33/0.58
% 0.33/0.58 % unit_imp_dvd
% 0.33/0.58 thf(fact_3415_unit__imp__dvd,axiom,
% 0.33/0.58 ! [B: int,A: int] :
% 0.33/0.58 ( ( dvd_dvd_int @ B @ one_one_int )
% 0.33/0.58 => ( dvd_dvd_int @ B @ A ) ) ).
% 0.33/0.58
% 0.33/0.58 % unit_imp_dvd
% 0.33/0.58 thf(fact_3416_one__dvd,axiom,
% 0.33/0.58 ! [A: code_integer] : ( dvd_dvd_Code_integer @ one_one_Code_integer @ A ) ).
% 0.33/0.58
% 0.33/0.58 % one_dvd
% 0.33/0.58 thf(fact_3417_one__dvd,axiom,
% 0.33/0.58 ! [A: assn] : ( dvd_dvd_assn @ one_one_assn @ A ) ).
% 0.33/0.58
% 0.33/0.58 % one_dvd
% 0.33/0.58 thf(fact_3418_one__dvd,axiom,
% 0.33/0.58 ! [A: rat] : ( dvd_dvd_rat @ one_one_rat @ A ) ).
% 0.33/0.58
% 0.33/0.58 % one_dvd
% 0.33/0.58 thf(fact_3419_one__dvd,axiom,
% 0.33/0.58 ! [A: nat] : ( dvd_dvd_nat @ one_one_nat @ A ) ).
% 0.33/0.58
% 0.33/0.58 % one_dvd
% 0.33/0.58 thf(fact_3420_one__dvd,axiom,
% 0.33/0.58 ! [A: int] : ( dvd_dvd_int @ one_one_int @ A ) ).
% 0.33/0.58
% 0.33/0.58 % one_dvd
% 0.33/0.58 thf(fact_3421_modulo__integer_Oabs__eq,axiom,
% 0.33/0.58 ! [Xa: int,X: int] :
% 0.33/0.58 ( ( modulo364778990260209775nteger @ ( code_integer_of_int @ Xa ) @ ( code_integer_of_int @ X ) )
% 0.33/0.58 = ( code_integer_of_int @ ( modulo_modulo_int @ Xa @ X ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % modulo_integer.abs_eq
% 0.33/0.58 thf(fact_3422_sgn__integer_Oabs__eq,axiom,
% 0.33/0.58 ! [X: int] :
% 0.33/0.58 ( ( sgn_sgn_Code_integer @ ( code_integer_of_int @ X ) )
% 0.33/0.58 = ( code_integer_of_int @ ( sgn_sgn_int @ X ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % sgn_integer.abs_eq
% 0.33/0.58 thf(fact_3423_concat__bit__assoc,axiom,
% 0.33/0.58 ! [N2: nat,K: int,M2: nat,L: int,R2: int] :
% 0.33/0.58 ( ( bit_concat_bit @ N2 @ K @ ( bit_concat_bit @ M2 @ L @ R2 ) )
% 0.33/0.58 = ( bit_concat_bit @ ( plus_plus_nat @ M2 @ N2 ) @ ( bit_concat_bit @ N2 @ K @ L ) @ R2 ) ) ).
% 0.33/0.58
% 0.33/0.58 % concat_bit_assoc
% 0.33/0.58 thf(fact_3424_not__is__unit__0,axiom,
% 0.33/0.58 ~ ( dvd_dvd_Code_integer @ zero_z3403309356797280102nteger @ one_one_Code_integer ) ).
% 0.33/0.58
% 0.33/0.58 % not_is_unit_0
% 0.33/0.58 thf(fact_3425_not__is__unit__0,axiom,
% 0.33/0.58 ~ ( dvd_dvd_nat @ zero_zero_nat @ one_one_nat ) ).
% 0.33/0.58
% 0.33/0.58 % not_is_unit_0
% 0.33/0.58 thf(fact_3426_not__is__unit__0,axiom,
% 0.33/0.58 ~ ( dvd_dvd_int @ zero_zero_int @ one_one_int ) ).
% 0.33/0.58
% 0.33/0.58 % not_is_unit_0
% 0.33/0.58 thf(fact_3427_pinf_I9_J,axiom,
% 0.33/0.58 ! [D2: code_integer,S: code_integer] :
% 0.33/0.58 ? [Z3: code_integer] :
% 0.33/0.58 ! [X8: code_integer] :
% 0.33/0.58 ( ( ord_le6747313008572928689nteger @ Z3 @ X8 )
% 0.33/0.58 => ( ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ X8 @ S ) )
% 0.33/0.58 = ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ X8 @ S ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % pinf(9)
% 0.33/0.58 thf(fact_3428_pinf_I9_J,axiom,
% 0.33/0.58 ! [D2: rat,S: rat] :
% 0.33/0.58 ? [Z3: rat] :
% 0.33/0.58 ! [X8: rat] :
% 0.33/0.58 ( ( ord_less_rat @ Z3 @ X8 )
% 0.33/0.58 => ( ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X8 @ S ) )
% 0.33/0.58 = ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X8 @ S ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % pinf(9)
% 0.33/0.58 thf(fact_3429_pinf_I9_J,axiom,
% 0.33/0.58 ! [D2: nat,S: nat] :
% 0.33/0.58 ? [Z3: nat] :
% 0.33/0.58 ! [X8: nat] :
% 0.33/0.58 ( ( ord_less_nat @ Z3 @ X8 )
% 0.33/0.58 => ( ( dvd_dvd_nat @ D2 @ ( plus_plus_nat @ X8 @ S ) )
% 0.33/0.58 = ( dvd_dvd_nat @ D2 @ ( plus_plus_nat @ X8 @ S ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % pinf(9)
% 0.33/0.58 thf(fact_3430_pinf_I9_J,axiom,
% 0.33/0.58 ! [D2: int,S: int] :
% 0.33/0.58 ? [Z3: int] :
% 0.33/0.58 ! [X8: int] :
% 0.33/0.58 ( ( ord_less_int @ Z3 @ X8 )
% 0.33/0.58 => ( ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X8 @ S ) )
% 0.33/0.58 = ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X8 @ S ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % pinf(9)
% 0.33/0.58 thf(fact_3431_pinf_I10_J,axiom,
% 0.33/0.58 ! [D2: code_integer,S: code_integer] :
% 0.33/0.58 ? [Z3: code_integer] :
% 0.33/0.58 ! [X8: code_integer] :
% 0.33/0.58 ( ( ord_le6747313008572928689nteger @ Z3 @ X8 )
% 0.33/0.58 => ( ( ~ ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ X8 @ S ) ) )
% 0.33/0.58 = ( ~ ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ X8 @ S ) ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % pinf(10)
% 0.33/0.58 thf(fact_3432_pinf_I10_J,axiom,
% 0.33/0.58 ! [D2: rat,S: rat] :
% 0.33/0.58 ? [Z3: rat] :
% 0.33/0.58 ! [X8: rat] :
% 0.33/0.58 ( ( ord_less_rat @ Z3 @ X8 )
% 0.33/0.58 => ( ( ~ ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X8 @ S ) ) )
% 0.33/0.58 = ( ~ ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X8 @ S ) ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % pinf(10)
% 0.33/0.58 thf(fact_3433_pinf_I10_J,axiom,
% 0.33/0.58 ! [D2: nat,S: nat] :
% 0.33/0.58 ? [Z3: nat] :
% 0.33/0.58 ! [X8: nat] :
% 0.33/0.58 ( ( ord_less_nat @ Z3 @ X8 )
% 0.33/0.58 => ( ( ~ ( dvd_dvd_nat @ D2 @ ( plus_plus_nat @ X8 @ S ) ) )
% 0.33/0.58 = ( ~ ( dvd_dvd_nat @ D2 @ ( plus_plus_nat @ X8 @ S ) ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % pinf(10)
% 0.33/0.58 thf(fact_3434_pinf_I10_J,axiom,
% 0.33/0.58 ! [D2: int,S: int] :
% 0.33/0.58 ? [Z3: int] :
% 0.33/0.58 ! [X8: int] :
% 0.33/0.58 ( ( ord_less_int @ Z3 @ X8 )
% 0.33/0.58 => ( ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X8 @ S ) ) )
% 0.33/0.58 = ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X8 @ S ) ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % pinf(10)
% 0.33/0.58 thf(fact_3435_minf_I9_J,axiom,
% 0.33/0.58 ! [D2: code_integer,S: code_integer] :
% 0.33/0.58 ? [Z3: code_integer] :
% 0.33/0.58 ! [X8: code_integer] :
% 0.33/0.58 ( ( ord_le6747313008572928689nteger @ X8 @ Z3 )
% 0.33/0.58 => ( ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ X8 @ S ) )
% 0.33/0.58 = ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ X8 @ S ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % minf(9)
% 0.33/0.58 thf(fact_3436_minf_I9_J,axiom,
% 0.33/0.58 ! [D2: rat,S: rat] :
% 0.33/0.58 ? [Z3: rat] :
% 0.33/0.58 ! [X8: rat] :
% 0.33/0.58 ( ( ord_less_rat @ X8 @ Z3 )
% 0.33/0.58 => ( ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X8 @ S ) )
% 0.33/0.58 = ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X8 @ S ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % minf(9)
% 0.33/0.58 thf(fact_3437_minf_I9_J,axiom,
% 0.33/0.58 ! [D2: nat,S: nat] :
% 0.33/0.58 ? [Z3: nat] :
% 0.33/0.58 ! [X8: nat] :
% 0.33/0.58 ( ( ord_less_nat @ X8 @ Z3 )
% 0.33/0.58 => ( ( dvd_dvd_nat @ D2 @ ( plus_plus_nat @ X8 @ S ) )
% 0.33/0.58 = ( dvd_dvd_nat @ D2 @ ( plus_plus_nat @ X8 @ S ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % minf(9)
% 0.33/0.58 thf(fact_3438_minf_I9_J,axiom,
% 0.33/0.58 ! [D2: int,S: int] :
% 0.33/0.58 ? [Z3: int] :
% 0.33/0.58 ! [X8: int] :
% 0.33/0.58 ( ( ord_less_int @ X8 @ Z3 )
% 0.33/0.58 => ( ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X8 @ S ) )
% 0.33/0.58 = ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X8 @ S ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % minf(9)
% 0.33/0.58 thf(fact_3439_minf_I10_J,axiom,
% 0.33/0.58 ! [D2: code_integer,S: code_integer] :
% 0.33/0.58 ? [Z3: code_integer] :
% 0.33/0.58 ! [X8: code_integer] :
% 0.33/0.58 ( ( ord_le6747313008572928689nteger @ X8 @ Z3 )
% 0.33/0.58 => ( ( ~ ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ X8 @ S ) ) )
% 0.33/0.58 = ( ~ ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ X8 @ S ) ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % minf(10)
% 0.33/0.58 thf(fact_3440_minf_I10_J,axiom,
% 0.33/0.58 ! [D2: rat,S: rat] :
% 0.33/0.58 ? [Z3: rat] :
% 0.33/0.58 ! [X8: rat] :
% 0.33/0.58 ( ( ord_less_rat @ X8 @ Z3 )
% 0.33/0.58 => ( ( ~ ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X8 @ S ) ) )
% 0.33/0.58 = ( ~ ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X8 @ S ) ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % minf(10)
% 0.33/0.58 thf(fact_3441_minf_I10_J,axiom,
% 0.33/0.58 ! [D2: nat,S: nat] :
% 0.33/0.58 ? [Z3: nat] :
% 0.33/0.58 ! [X8: nat] :
% 0.33/0.58 ( ( ord_less_nat @ X8 @ Z3 )
% 0.33/0.58 => ( ( ~ ( dvd_dvd_nat @ D2 @ ( plus_plus_nat @ X8 @ S ) ) )
% 0.33/0.58 = ( ~ ( dvd_dvd_nat @ D2 @ ( plus_plus_nat @ X8 @ S ) ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % minf(10)
% 0.33/0.58 thf(fact_3442_minf_I10_J,axiom,
% 0.33/0.58 ! [D2: int,S: int] :
% 0.33/0.58 ? [Z3: int] :
% 0.33/0.58 ! [X8: int] :
% 0.33/0.58 ( ( ord_less_int @ X8 @ Z3 )
% 0.33/0.58 => ( ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X8 @ S ) ) )
% 0.33/0.58 = ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X8 @ S ) ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % minf(10)
% 0.33/0.58 thf(fact_3443_unit__mult__right__cancel,axiom,
% 0.33/0.58 ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.33/0.58 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 0.33/0.58 => ( ( ( times_3573771949741848930nteger @ B @ A )
% 0.33/0.58 = ( times_3573771949741848930nteger @ C @ A ) )
% 0.33/0.58 = ( B = C ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % unit_mult_right_cancel
% 0.33/0.58 thf(fact_3444_unit__mult__right__cancel,axiom,
% 0.33/0.58 ! [A: nat,B: nat,C: nat] :
% 0.33/0.58 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.33/0.58 => ( ( ( times_times_nat @ B @ A )
% 0.33/0.58 = ( times_times_nat @ C @ A ) )
% 0.33/0.58 = ( B = C ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % unit_mult_right_cancel
% 0.33/0.58 thf(fact_3445_unit__mult__right__cancel,axiom,
% 0.33/0.58 ! [A: int,B: int,C: int] :
% 0.33/0.58 ( ( dvd_dvd_int @ A @ one_one_int )
% 0.33/0.58 => ( ( ( times_times_int @ B @ A )
% 0.33/0.58 = ( times_times_int @ C @ A ) )
% 0.33/0.58 = ( B = C ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % unit_mult_right_cancel
% 0.33/0.58 thf(fact_3446_unit__mult__left__cancel,axiom,
% 0.33/0.58 ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.33/0.58 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 0.33/0.58 => ( ( ( times_3573771949741848930nteger @ A @ B )
% 0.33/0.58 = ( times_3573771949741848930nteger @ A @ C ) )
% 0.33/0.58 = ( B = C ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % unit_mult_left_cancel
% 0.33/0.58 thf(fact_3447_unit__mult__left__cancel,axiom,
% 0.33/0.58 ! [A: nat,B: nat,C: nat] :
% 0.33/0.58 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.33/0.58 => ( ( ( times_times_nat @ A @ B )
% 0.33/0.58 = ( times_times_nat @ A @ C ) )
% 0.33/0.58 = ( B = C ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % unit_mult_left_cancel
% 0.33/0.58 thf(fact_3448_unit__mult__left__cancel,axiom,
% 0.33/0.58 ! [A: int,B: int,C: int] :
% 0.33/0.58 ( ( dvd_dvd_int @ A @ one_one_int )
% 0.33/0.58 => ( ( ( times_times_int @ A @ B )
% 0.33/0.58 = ( times_times_int @ A @ C ) )
% 0.33/0.58 = ( B = C ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % unit_mult_left_cancel
% 0.33/0.58 thf(fact_3449_mult__unit__dvd__iff_H,axiom,
% 0.33/0.58 ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.33/0.58 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 0.33/0.58 => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 0.33/0.58 = ( dvd_dvd_Code_integer @ B @ C ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % mult_unit_dvd_iff'
% 0.33/0.58 thf(fact_3450_mult__unit__dvd__iff_H,axiom,
% 0.33/0.58 ! [A: nat,B: nat,C: nat] :
% 0.33/0.58 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.33/0.58 => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 0.33/0.58 = ( dvd_dvd_nat @ B @ C ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % mult_unit_dvd_iff'
% 0.33/0.58 thf(fact_3451_mult__unit__dvd__iff_H,axiom,
% 0.33/0.58 ! [A: int,B: int,C: int] :
% 0.33/0.58 ( ( dvd_dvd_int @ A @ one_one_int )
% 0.33/0.58 => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 0.33/0.58 = ( dvd_dvd_int @ B @ C ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % mult_unit_dvd_iff'
% 0.33/0.58 thf(fact_3452_dvd__mult__unit__iff_H,axiom,
% 0.33/0.58 ! [B: code_integer,A: code_integer,C: code_integer] :
% 0.33/0.58 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.33/0.58 => ( ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 0.33/0.58 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % dvd_mult_unit_iff'
% 0.33/0.58 thf(fact_3453_dvd__mult__unit__iff_H,axiom,
% 0.33/0.58 ! [B: nat,A: nat,C: nat] :
% 0.33/0.58 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.33/0.58 => ( ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) )
% 0.33/0.58 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % dvd_mult_unit_iff'
% 0.33/0.58 thf(fact_3454_dvd__mult__unit__iff_H,axiom,
% 0.33/0.58 ! [B: int,A: int,C: int] :
% 0.33/0.58 ( ( dvd_dvd_int @ B @ one_one_int )
% 0.33/0.58 => ( ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) )
% 0.33/0.58 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % dvd_mult_unit_iff'
% 0.33/0.58 thf(fact_3455_mult__unit__dvd__iff,axiom,
% 0.33/0.58 ! [B: code_integer,A: code_integer,C: code_integer] :
% 0.33/0.58 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.33/0.58 => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 0.33/0.58 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % mult_unit_dvd_iff
% 0.33/0.58 thf(fact_3456_mult__unit__dvd__iff,axiom,
% 0.33/0.58 ! [B: nat,A: nat,C: nat] :
% 0.33/0.58 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.33/0.58 => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 0.33/0.58 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % mult_unit_dvd_iff
% 0.33/0.58 thf(fact_3457_mult__unit__dvd__iff,axiom,
% 0.33/0.58 ! [B: int,A: int,C: int] :
% 0.33/0.58 ( ( dvd_dvd_int @ B @ one_one_int )
% 0.33/0.58 => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 0.33/0.58 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % mult_unit_dvd_iff
% 0.33/0.58 thf(fact_3458_dvd__mult__unit__iff,axiom,
% 0.33/0.58 ! [B: code_integer,A: code_integer,C: code_integer] :
% 0.33/0.58 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.33/0.58 => ( ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ C @ B ) )
% 0.33/0.58 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % dvd_mult_unit_iff
% 0.33/0.58 thf(fact_3459_dvd__mult__unit__iff,axiom,
% 0.33/0.58 ! [B: nat,A: nat,C: nat] :
% 0.33/0.58 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.33/0.58 => ( ( dvd_dvd_nat @ A @ ( times_times_nat @ C @ B ) )
% 0.33/0.58 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % dvd_mult_unit_iff
% 0.33/0.58 thf(fact_3460_dvd__mult__unit__iff,axiom,
% 0.33/0.58 ! [B: int,A: int,C: int] :
% 0.33/0.58 ( ( dvd_dvd_int @ B @ one_one_int )
% 0.33/0.58 => ( ( dvd_dvd_int @ A @ ( times_times_int @ C @ B ) )
% 0.33/0.58 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % dvd_mult_unit_iff
% 0.33/0.58 thf(fact_3461_is__unit__mult__iff,axiom,
% 0.33/0.58 ! [A: code_integer,B: code_integer] :
% 0.33/0.58 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ one_one_Code_integer )
% 0.33/0.58 = ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 0.33/0.58 & ( dvd_dvd_Code_integer @ B @ one_one_Code_integer ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % is_unit_mult_iff
% 0.33/0.58 thf(fact_3462_is__unit__mult__iff,axiom,
% 0.33/0.58 ! [A: nat,B: nat] :
% 0.33/0.58 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ one_one_nat )
% 0.33/0.58 = ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.33/0.58 & ( dvd_dvd_nat @ B @ one_one_nat ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % is_unit_mult_iff
% 0.33/0.58 thf(fact_3463_is__unit__mult__iff,axiom,
% 0.33/0.58 ! [A: int,B: int] :
% 0.33/0.58 ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ one_one_int )
% 0.33/0.58 = ( ( dvd_dvd_int @ A @ one_one_int )
% 0.33/0.58 & ( dvd_dvd_int @ B @ one_one_int ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % is_unit_mult_iff
% 0.33/0.58 thf(fact_3464_div__plus__div__distrib__dvd__left,axiom,
% 0.33/0.58 ! [C: int,A: int,B: int] :
% 0.33/0.58 ( ( dvd_dvd_int @ C @ A )
% 0.33/0.58 => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 0.33/0.58 = ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % div_plus_div_distrib_dvd_left
% 0.33/0.58 thf(fact_3465_div__plus__div__distrib__dvd__left,axiom,
% 0.33/0.58 ! [C: nat,A: nat,B: nat] :
% 0.33/0.58 ( ( dvd_dvd_nat @ C @ A )
% 0.33/0.58 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 0.33/0.58 = ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % div_plus_div_distrib_dvd_left
% 0.33/0.58 thf(fact_3466_div__plus__div__distrib__dvd__left,axiom,
% 0.33/0.58 ! [C: code_integer,A: code_integer,B: code_integer] :
% 0.33/0.58 ( ( dvd_dvd_Code_integer @ C @ A )
% 0.33/0.58 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 0.33/0.58 = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % div_plus_div_distrib_dvd_left
% 0.33/0.58 thf(fact_3467_div__plus__div__distrib__dvd__left,axiom,
% 0.33/0.58 ! [C: code_natural,A: code_natural,B: code_natural] :
% 0.33/0.58 ( ( dvd_dvd_Code_natural @ C @ A )
% 0.33/0.58 => ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ A @ B ) @ C )
% 0.33/0.58 = ( plus_p4538020629002901425atural @ ( divide5121882707175180666atural @ A @ C ) @ ( divide5121882707175180666atural @ B @ C ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % div_plus_div_distrib_dvd_left
% 0.33/0.58 thf(fact_3468_div__plus__div__distrib__dvd__right,axiom,
% 0.33/0.58 ! [C: int,B: int,A: int] :
% 0.33/0.58 ( ( dvd_dvd_int @ C @ B )
% 0.33/0.58 => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 0.33/0.58 = ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % div_plus_div_distrib_dvd_right
% 0.33/0.58 thf(fact_3469_div__plus__div__distrib__dvd__right,axiom,
% 0.33/0.58 ! [C: nat,B: nat,A: nat] :
% 0.33/0.58 ( ( dvd_dvd_nat @ C @ B )
% 0.33/0.58 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 0.33/0.58 = ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % div_plus_div_distrib_dvd_right
% 0.33/0.58 thf(fact_3470_div__plus__div__distrib__dvd__right,axiom,
% 0.33/0.58 ! [C: code_integer,B: code_integer,A: code_integer] :
% 0.33/0.58 ( ( dvd_dvd_Code_integer @ C @ B )
% 0.33/0.58 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 0.33/0.58 = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % div_plus_div_distrib_dvd_right
% 0.33/0.58 thf(fact_3471_div__plus__div__distrib__dvd__right,axiom,
% 0.33/0.58 ! [C: code_natural,B: code_natural,A: code_natural] :
% 0.33/0.58 ( ( dvd_dvd_Code_natural @ C @ B )
% 0.33/0.58 => ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ A @ B ) @ C )
% 0.33/0.58 = ( plus_p4538020629002901425atural @ ( divide5121882707175180666atural @ A @ C ) @ ( divide5121882707175180666atural @ B @ C ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % div_plus_div_distrib_dvd_right
% 0.33/0.58 thf(fact_3472_unit__div__cancel,axiom,
% 0.33/0.58 ! [A: int,B: int,C: int] :
% 0.33/0.58 ( ( dvd_dvd_int @ A @ one_one_int )
% 0.33/0.58 => ( ( ( divide_divide_int @ B @ A )
% 0.33/0.58 = ( divide_divide_int @ C @ A ) )
% 0.33/0.58 = ( B = C ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % unit_div_cancel
% 0.33/0.58 thf(fact_3473_unit__div__cancel,axiom,
% 0.33/0.58 ! [A: nat,B: nat,C: nat] :
% 0.33/0.58 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.33/0.58 => ( ( ( divide_divide_nat @ B @ A )
% 0.33/0.58 = ( divide_divide_nat @ C @ A ) )
% 0.33/0.58 = ( B = C ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % unit_div_cancel
% 0.33/0.58 thf(fact_3474_unit__div__cancel,axiom,
% 0.33/0.58 ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.33/0.58 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 0.33/0.58 => ( ( ( divide6298287555418463151nteger @ B @ A )
% 0.33/0.58 = ( divide6298287555418463151nteger @ C @ A ) )
% 0.33/0.58 = ( B = C ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % unit_div_cancel
% 0.33/0.58 thf(fact_3475_unit__div__cancel,axiom,
% 0.33/0.58 ! [A: code_natural,B: code_natural,C: code_natural] :
% 0.33/0.58 ( ( dvd_dvd_Code_natural @ A @ one_one_Code_natural )
% 0.33/0.58 => ( ( ( divide5121882707175180666atural @ B @ A )
% 0.33/0.58 = ( divide5121882707175180666atural @ C @ A ) )
% 0.33/0.58 = ( B = C ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % unit_div_cancel
% 0.33/0.58 thf(fact_3476_div__unit__dvd__iff,axiom,
% 0.33/0.58 ! [B: int,A: int,C: int] :
% 0.33/0.58 ( ( dvd_dvd_int @ B @ one_one_int )
% 0.33/0.58 => ( ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ C )
% 0.33/0.58 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % div_unit_dvd_iff
% 0.33/0.58 thf(fact_3477_div__unit__dvd__iff,axiom,
% 0.33/0.58 ! [B: nat,A: nat,C: nat] :
% 0.33/0.58 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.33/0.58 => ( ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ C )
% 0.33/0.58 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % div_unit_dvd_iff
% 0.33/0.58 thf(fact_3478_div__unit__dvd__iff,axiom,
% 0.33/0.58 ! [B: code_integer,A: code_integer,C: code_integer] :
% 0.33/0.58 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.33/0.58 => ( ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ A @ B ) @ C )
% 0.33/0.58 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % div_unit_dvd_iff
% 0.33/0.58 thf(fact_3479_div__unit__dvd__iff,axiom,
% 0.33/0.58 ! [B: code_natural,A: code_natural,C: code_natural] :
% 0.33/0.58 ( ( dvd_dvd_Code_natural @ B @ one_one_Code_natural )
% 0.33/0.58 => ( ( dvd_dvd_Code_natural @ ( divide5121882707175180666atural @ A @ B ) @ C )
% 0.33/0.58 = ( dvd_dvd_Code_natural @ A @ C ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % div_unit_dvd_iff
% 0.33/0.58 thf(fact_3480_dvd__div__unit__iff,axiom,
% 0.33/0.58 ! [B: int,A: int,C: int] :
% 0.33/0.58 ( ( dvd_dvd_int @ B @ one_one_int )
% 0.33/0.58 => ( ( dvd_dvd_int @ A @ ( divide_divide_int @ C @ B ) )
% 0.33/0.58 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % dvd_div_unit_iff
% 0.33/0.58 thf(fact_3481_dvd__div__unit__iff,axiom,
% 0.33/0.58 ! [B: nat,A: nat,C: nat] :
% 0.33/0.58 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.33/0.58 => ( ( dvd_dvd_nat @ A @ ( divide_divide_nat @ C @ B ) )
% 0.33/0.58 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % dvd_div_unit_iff
% 0.33/0.58 thf(fact_3482_dvd__div__unit__iff,axiom,
% 0.33/0.58 ! [B: code_integer,A: code_integer,C: code_integer] :
% 0.33/0.58 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.33/0.58 => ( ( dvd_dvd_Code_integer @ A @ ( divide6298287555418463151nteger @ C @ B ) )
% 0.33/0.58 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % dvd_div_unit_iff
% 0.33/0.58 thf(fact_3483_dvd__div__unit__iff,axiom,
% 0.33/0.58 ! [B: code_natural,A: code_natural,C: code_natural] :
% 0.33/0.58 ( ( dvd_dvd_Code_natural @ B @ one_one_Code_natural )
% 0.33/0.58 => ( ( dvd_dvd_Code_natural @ A @ ( divide5121882707175180666atural @ C @ B ) )
% 0.33/0.58 = ( dvd_dvd_Code_natural @ A @ C ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % dvd_div_unit_iff
% 0.33/0.58 thf(fact_3484_xor__num_Ocases,axiom,
% 0.33/0.58 ! [X: product_prod_num_num] :
% 0.33/0.58 ( ( X
% 0.33/0.58 != ( product_Pair_num_num @ one @ one ) )
% 0.33/0.58 => ( ! [N: num] :
% 0.33/0.58 ( X
% 0.33/0.58 != ( product_Pair_num_num @ one @ ( bit0 @ N ) ) )
% 0.33/0.58 => ( ! [N: num] :
% 0.33/0.58 ( X
% 0.33/0.58 != ( product_Pair_num_num @ one @ ( bit1 @ N ) ) )
% 0.33/0.58 => ( ! [M5: num] :
% 0.33/0.58 ( X
% 0.33/0.58 != ( product_Pair_num_num @ ( bit0 @ M5 ) @ one ) )
% 0.33/0.58 => ( ! [M5: num,N: num] :
% 0.33/0.58 ( X
% 0.33/0.58 != ( product_Pair_num_num @ ( bit0 @ M5 ) @ ( bit0 @ N ) ) )
% 0.33/0.58 => ( ! [M5: num,N: num] :
% 0.33/0.58 ( X
% 0.33/0.58 != ( product_Pair_num_num @ ( bit0 @ M5 ) @ ( bit1 @ N ) ) )
% 0.33/0.58 => ( ! [M5: num] :
% 0.33/0.58 ( X
% 0.33/0.58 != ( product_Pair_num_num @ ( bit1 @ M5 ) @ one ) )
% 0.33/0.58 => ( ! [M5: num,N: num] :
% 0.33/0.58 ( X
% 0.33/0.58 != ( product_Pair_num_num @ ( bit1 @ M5 ) @ ( bit0 @ N ) ) )
% 0.33/0.58 => ~ ! [M5: num,N: num] :
% 0.33/0.58 ( X
% 0.33/0.58 != ( product_Pair_num_num @ ( bit1 @ M5 ) @ ( bit1 @ N ) ) ) ) ) ) ) ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % xor_num.cases
% 0.33/0.58 thf(fact_3485_plus__integer_Oabs__eq,axiom,
% 0.33/0.58 ! [Xa: int,X: int] :
% 0.33/0.58 ( ( plus_p5714425477246183910nteger @ ( code_integer_of_int @ Xa ) @ ( code_integer_of_int @ X ) )
% 0.33/0.58 = ( code_integer_of_int @ ( plus_plus_int @ Xa @ X ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % plus_integer.abs_eq
% 0.33/0.58 thf(fact_3486_bezout__lemma__nat,axiom,
% 0.33/0.58 ! [D2: nat,A: nat,B: nat,X: nat,Y: nat] :
% 0.33/0.58 ( ( dvd_dvd_nat @ D2 @ A )
% 0.33/0.58 => ( ( dvd_dvd_nat @ D2 @ B )
% 0.33/0.58 => ( ( ( ( times_times_nat @ A @ X )
% 0.33/0.58 = ( plus_plus_nat @ ( times_times_nat @ B @ Y ) @ D2 ) )
% 0.33/0.58 | ( ( times_times_nat @ B @ X )
% 0.33/0.58 = ( plus_plus_nat @ ( times_times_nat @ A @ Y ) @ D2 ) ) )
% 0.33/0.58 => ? [X4: nat,Y5: nat] :
% 0.33/0.58 ( ( dvd_dvd_nat @ D2 @ A )
% 0.33/0.58 & ( dvd_dvd_nat @ D2 @ ( plus_plus_nat @ A @ B ) )
% 0.33/0.58 & ( ( ( times_times_nat @ A @ X4 )
% 0.33/0.58 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ Y5 ) @ D2 ) )
% 0.33/0.58 | ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ X4 )
% 0.33/0.58 = ( plus_plus_nat @ ( times_times_nat @ A @ Y5 ) @ D2 ) ) ) ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % bezout_lemma_nat
% 0.33/0.58 thf(fact_3487_bezout__add__nat,axiom,
% 0.33/0.58 ! [A: nat,B: nat] :
% 0.33/0.58 ? [D: nat,X4: nat,Y5: nat] :
% 0.33/0.58 ( ( dvd_dvd_nat @ D @ A )
% 0.33/0.58 & ( dvd_dvd_nat @ D @ B )
% 0.33/0.58 & ( ( ( times_times_nat @ A @ X4 )
% 0.33/0.58 = ( plus_plus_nat @ ( times_times_nat @ B @ Y5 ) @ D ) )
% 0.33/0.58 | ( ( times_times_nat @ B @ X4 )
% 0.33/0.58 = ( plus_plus_nat @ ( times_times_nat @ A @ Y5 ) @ D ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % bezout_add_nat
% 0.33/0.58 thf(fact_3488_one__integer__def,axiom,
% 0.33/0.58 ( one_one_Code_integer
% 0.33/0.58 = ( code_integer_of_int @ one_one_int ) ) ).
% 0.33/0.58
% 0.33/0.58 % one_integer_def
% 0.33/0.58 thf(fact_3489_less__eq__integer_Oabs__eq,axiom,
% 0.33/0.58 ! [Xa: int,X: int] :
% 0.33/0.58 ( ( ord_le3102999989581377725nteger @ ( code_integer_of_int @ Xa ) @ ( code_integer_of_int @ X ) )
% 0.33/0.58 = ( ord_less_eq_int @ Xa @ X ) ) ).
% 0.33/0.58
% 0.33/0.58 % less_eq_integer.abs_eq
% 0.33/0.58 thf(fact_3490_times__integer_Oabs__eq,axiom,
% 0.33/0.58 ! [Xa: int,X: int] :
% 0.33/0.58 ( ( times_3573771949741848930nteger @ ( code_integer_of_int @ Xa ) @ ( code_integer_of_int @ X ) )
% 0.33/0.58 = ( code_integer_of_int @ ( times_times_int @ Xa @ X ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % times_integer.abs_eq
% 0.33/0.58 thf(fact_3491_zdvd__period,axiom,
% 0.33/0.58 ! [A: int,D2: int,X: int,T: int,C: int] :
% 0.33/0.58 ( ( dvd_dvd_int @ A @ D2 )
% 0.33/0.58 => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ X @ T ) )
% 0.33/0.58 = ( dvd_dvd_int @ A @ ( plus_plus_int @ ( plus_plus_int @ X @ ( times_times_int @ C @ D2 ) ) @ T ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % zdvd_period
% 0.33/0.58 thf(fact_3492_zdvd__reduce,axiom,
% 0.33/0.58 ! [K: int,N2: int,M2: int] :
% 0.33/0.58 ( ( dvd_dvd_int @ K @ ( plus_plus_int @ N2 @ ( times_times_int @ K @ M2 ) ) )
% 0.33/0.58 = ( dvd_dvd_int @ K @ N2 ) ) ).
% 0.33/0.58
% 0.33/0.58 % zdvd_reduce
% 0.33/0.58 thf(fact_3493_minus__integer_Oabs__eq,axiom,
% 0.33/0.58 ! [Xa: int,X: int] :
% 0.33/0.58 ( ( minus_8373710615458151222nteger @ ( code_integer_of_int @ Xa ) @ ( code_integer_of_int @ X ) )
% 0.33/0.58 = ( code_integer_of_int @ ( minus_minus_int @ Xa @ X ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % minus_integer.abs_eq
% 0.33/0.58 thf(fact_3494_unity__coeff__ex,axiom,
% 0.33/0.58 ! [P: code_integer > $o,L: code_integer] :
% 0.33/0.58 ( ( ? [X3: code_integer] : ( P @ ( times_3573771949741848930nteger @ L @ X3 ) ) )
% 0.33/0.58 = ( ? [X3: code_integer] :
% 0.33/0.58 ( ( dvd_dvd_Code_integer @ L @ ( plus_p5714425477246183910nteger @ X3 @ zero_z3403309356797280102nteger ) )
% 0.33/0.58 & ( P @ X3 ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % unity_coeff_ex
% 0.33/0.58 thf(fact_3495_unity__coeff__ex,axiom,
% 0.33/0.58 ! [P: rat > $o,L: rat] :
% 0.33/0.58 ( ( ? [X3: rat] : ( P @ ( times_times_rat @ L @ X3 ) ) )
% 0.33/0.58 = ( ? [X3: rat] :
% 0.33/0.58 ( ( dvd_dvd_rat @ L @ ( plus_plus_rat @ X3 @ zero_zero_rat ) )
% 0.33/0.58 & ( P @ X3 ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % unity_coeff_ex
% 0.33/0.58 thf(fact_3496_unity__coeff__ex,axiom,
% 0.33/0.58 ! [P: nat > $o,L: nat] :
% 0.33/0.58 ( ( ? [X3: nat] : ( P @ ( times_times_nat @ L @ X3 ) ) )
% 0.33/0.58 = ( ? [X3: nat] :
% 0.33/0.58 ( ( dvd_dvd_nat @ L @ ( plus_plus_nat @ X3 @ zero_zero_nat ) )
% 0.33/0.58 & ( P @ X3 ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % unity_coeff_ex
% 0.33/0.58 thf(fact_3497_unity__coeff__ex,axiom,
% 0.33/0.58 ! [P: int > $o,L: int] :
% 0.33/0.58 ( ( ? [X3: int] : ( P @ ( times_times_int @ L @ X3 ) ) )
% 0.33/0.58 = ( ? [X3: int] :
% 0.33/0.58 ( ( dvd_dvd_int @ L @ ( plus_plus_int @ X3 @ zero_zero_int ) )
% 0.33/0.58 & ( P @ X3 ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % unity_coeff_ex
% 0.33/0.58 thf(fact_3498_unit__dvdE,axiom,
% 0.33/0.58 ! [A: code_integer,B: code_integer] :
% 0.33/0.58 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 0.33/0.58 => ~ ( ( A != zero_z3403309356797280102nteger )
% 0.33/0.58 => ! [C3: code_integer] :
% 0.33/0.58 ( B
% 0.33/0.58 != ( times_3573771949741848930nteger @ A @ C3 ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % unit_dvdE
% 0.33/0.58 thf(fact_3499_unit__dvdE,axiom,
% 0.33/0.58 ! [A: nat,B: nat] :
% 0.33/0.58 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.33/0.58 => ~ ( ( A != zero_zero_nat )
% 0.33/0.58 => ! [C3: nat] :
% 0.33/0.58 ( B
% 0.33/0.58 != ( times_times_nat @ A @ C3 ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % unit_dvdE
% 0.33/0.58 thf(fact_3500_unit__dvdE,axiom,
% 0.33/0.58 ! [A: int,B: int] :
% 0.33/0.58 ( ( dvd_dvd_int @ A @ one_one_int )
% 0.33/0.58 => ~ ( ( A != zero_zero_int )
% 0.33/0.58 => ! [C3: int] :
% 0.33/0.58 ( B
% 0.33/0.58 != ( times_times_int @ A @ C3 ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % unit_dvdE
% 0.33/0.58 thf(fact_3501_inf__period_I4_J,axiom,
% 0.33/0.58 ! [D2: code_integer,D3: code_integer,T: code_integer] :
% 0.33/0.58 ( ( dvd_dvd_Code_integer @ D2 @ D3 )
% 0.33/0.58 => ! [X8: code_integer,K6: code_integer] :
% 0.33/0.58 ( ( ~ ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ X8 @ T ) ) )
% 0.33/0.58 = ( ~ ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ X8 @ ( times_3573771949741848930nteger @ K6 @ D3 ) ) @ T ) ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % inf_period(4)
% 0.33/0.58 thf(fact_3502_inf__period_I4_J,axiom,
% 0.33/0.58 ! [D2: rat,D3: rat,T: rat] :
% 0.33/0.58 ( ( dvd_dvd_rat @ D2 @ D3 )
% 0.33/0.58 => ! [X8: rat,K6: rat] :
% 0.33/0.58 ( ( ~ ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X8 @ T ) ) )
% 0.33/0.58 = ( ~ ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ ( minus_minus_rat @ X8 @ ( times_times_rat @ K6 @ D3 ) ) @ T ) ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % inf_period(4)
% 0.33/0.58 thf(fact_3503_inf__period_I4_J,axiom,
% 0.33/0.58 ! [D2: int,D3: int,T: int] :
% 0.33/0.58 ( ( dvd_dvd_int @ D2 @ D3 )
% 0.33/0.58 => ! [X8: int,K6: int] :
% 0.33/0.58 ( ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X8 @ T ) ) )
% 0.33/0.58 = ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ ( minus_minus_int @ X8 @ ( times_times_int @ K6 @ D3 ) ) @ T ) ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % inf_period(4)
% 0.33/0.58 thf(fact_3504_inf__period_I3_J,axiom,
% 0.33/0.58 ! [D2: code_integer,D3: code_integer,T: code_integer] :
% 0.33/0.58 ( ( dvd_dvd_Code_integer @ D2 @ D3 )
% 0.33/0.58 => ! [X8: code_integer,K6: code_integer] :
% 0.33/0.58 ( ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ X8 @ T ) )
% 0.33/0.58 = ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ X8 @ ( times_3573771949741848930nteger @ K6 @ D3 ) ) @ T ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % inf_period(3)
% 0.33/0.58 thf(fact_3505_inf__period_I3_J,axiom,
% 0.33/0.58 ! [D2: rat,D3: rat,T: rat] :
% 0.33/0.58 ( ( dvd_dvd_rat @ D2 @ D3 )
% 0.33/0.58 => ! [X8: rat,K6: rat] :
% 0.33/0.58 ( ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X8 @ T ) )
% 0.33/0.58 = ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ ( minus_minus_rat @ X8 @ ( times_times_rat @ K6 @ D3 ) ) @ T ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % inf_period(3)
% 0.33/0.58 thf(fact_3506_inf__period_I3_J,axiom,
% 0.33/0.58 ! [D2: int,D3: int,T: int] :
% 0.33/0.58 ( ( dvd_dvd_int @ D2 @ D3 )
% 0.33/0.58 => ! [X8: int,K6: int] :
% 0.33/0.58 ( ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X8 @ T ) )
% 0.33/0.58 = ( dvd_dvd_int @ D2 @ ( plus_plus_int @ ( minus_minus_int @ X8 @ ( times_times_int @ K6 @ D3 ) ) @ T ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % inf_period(3)
% 0.33/0.58 thf(fact_3507_unit__div__eq__0__iff,axiom,
% 0.33/0.58 ! [B: int,A: int] :
% 0.33/0.58 ( ( dvd_dvd_int @ B @ one_one_int )
% 0.33/0.58 => ( ( ( divide_divide_int @ A @ B )
% 0.33/0.58 = zero_zero_int )
% 0.33/0.58 = ( A = zero_zero_int ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % unit_div_eq_0_iff
% 0.33/0.58 thf(fact_3508_unit__div__eq__0__iff,axiom,
% 0.33/0.58 ! [B: nat,A: nat] :
% 0.33/0.58 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.33/0.58 => ( ( ( divide_divide_nat @ A @ B )
% 0.33/0.58 = zero_zero_nat )
% 0.33/0.58 = ( A = zero_zero_nat ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % unit_div_eq_0_iff
% 0.33/0.58 thf(fact_3509_unit__div__eq__0__iff,axiom,
% 0.33/0.58 ! [B: code_integer,A: code_integer] :
% 0.33/0.58 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.33/0.58 => ( ( ( divide6298287555418463151nteger @ A @ B )
% 0.33/0.58 = zero_z3403309356797280102nteger )
% 0.33/0.58 = ( A = zero_z3403309356797280102nteger ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % unit_div_eq_0_iff
% 0.33/0.58 thf(fact_3510_unit__div__eq__0__iff,axiom,
% 0.33/0.58 ! [B: code_natural,A: code_natural] :
% 0.33/0.58 ( ( dvd_dvd_Code_natural @ B @ one_one_Code_natural )
% 0.33/0.58 => ( ( ( divide5121882707175180666atural @ A @ B )
% 0.33/0.58 = zero_z2226904508553997617atural )
% 0.33/0.58 = ( A = zero_z2226904508553997617atural ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % unit_div_eq_0_iff
% 0.33/0.58 thf(fact_3511_numeral__Bit1,axiom,
% 0.33/0.58 ! [N2: num] :
% 0.33/0.58 ( ( numeral_numeral_nat @ ( bit1 @ N2 ) )
% 0.33/0.58 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ N2 ) ) @ one_one_nat ) ) ).
% 0.33/0.58
% 0.33/0.58 % numeral_Bit1
% 0.33/0.58 thf(fact_3512_numeral__Bit1,axiom,
% 0.33/0.58 ! [N2: num] :
% 0.33/0.58 ( ( numeral_numeral_int @ ( bit1 @ N2 ) )
% 0.33/0.58 = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ N2 ) ) @ one_one_int ) ) ).
% 0.33/0.58
% 0.33/0.58 % numeral_Bit1
% 0.33/0.58 thf(fact_3513_numeral__Bit1,axiom,
% 0.33/0.58 ! [N2: num] :
% 0.33/0.58 ( ( numera6620942414471956472nteger @ ( bit1 @ N2 ) )
% 0.33/0.58 = ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ N2 ) @ ( numera6620942414471956472nteger @ N2 ) ) @ one_one_Code_integer ) ) ).
% 0.33/0.58
% 0.33/0.58 % numeral_Bit1
% 0.33/0.58 thf(fact_3514_numeral__Bit1,axiom,
% 0.33/0.58 ! [N2: num] :
% 0.33/0.58 ( ( numeral_numeral_rat @ ( bit1 @ N2 ) )
% 0.33/0.58 = ( plus_plus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ N2 ) @ ( numeral_numeral_rat @ N2 ) ) @ one_one_rat ) ) ).
% 0.33/0.58
% 0.33/0.58 % numeral_Bit1
% 0.33/0.58 thf(fact_3515_numeral__Bit1,axiom,
% 0.33/0.58 ! [N2: num] :
% 0.33/0.58 ( ( numera5444537566228673987atural @ ( bit1 @ N2 ) )
% 0.33/0.58 = ( plus_p4538020629002901425atural @ ( plus_p4538020629002901425atural @ ( numera5444537566228673987atural @ N2 ) @ ( numera5444537566228673987atural @ N2 ) ) @ one_one_Code_natural ) ) ).
% 0.33/0.58
% 0.33/0.58 % numeral_Bit1
% 0.33/0.58 thf(fact_3516_unit__eq__div1,axiom,
% 0.33/0.58 ! [B: int,A: int,C: int] :
% 0.33/0.58 ( ( dvd_dvd_int @ B @ one_one_int )
% 0.33/0.58 => ( ( ( divide_divide_int @ A @ B )
% 0.33/0.58 = C )
% 0.33/0.58 = ( A
% 0.33/0.58 = ( times_times_int @ C @ B ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % unit_eq_div1
% 0.33/0.58 thf(fact_3517_unit__eq__div1,axiom,
% 0.33/0.58 ! [B: nat,A: nat,C: nat] :
% 0.33/0.58 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.33/0.58 => ( ( ( divide_divide_nat @ A @ B )
% 0.33/0.58 = C )
% 0.33/0.58 = ( A
% 0.33/0.58 = ( times_times_nat @ C @ B ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % unit_eq_div1
% 0.33/0.58 thf(fact_3518_unit__eq__div1,axiom,
% 0.33/0.58 ! [B: code_integer,A: code_integer,C: code_integer] :
% 0.33/0.58 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.33/0.58 => ( ( ( divide6298287555418463151nteger @ A @ B )
% 0.33/0.58 = C )
% 0.33/0.58 = ( A
% 0.33/0.58 = ( times_3573771949741848930nteger @ C @ B ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % unit_eq_div1
% 0.33/0.58 thf(fact_3519_unit__eq__div1,axiom,
% 0.33/0.58 ! [B: code_natural,A: code_natural,C: code_natural] :
% 0.33/0.58 ( ( dvd_dvd_Code_natural @ B @ one_one_Code_natural )
% 0.33/0.58 => ( ( ( divide5121882707175180666atural @ A @ B )
% 0.33/0.58 = C )
% 0.33/0.58 = ( A
% 0.33/0.58 = ( times_2397367101498566445atural @ C @ B ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % unit_eq_div1
% 0.33/0.58 thf(fact_3520_unit__eq__div2,axiom,
% 0.33/0.58 ! [B: int,A: int,C: int] :
% 0.33/0.58 ( ( dvd_dvd_int @ B @ one_one_int )
% 0.33/0.58 => ( ( A
% 0.33/0.58 = ( divide_divide_int @ C @ B ) )
% 0.33/0.58 = ( ( times_times_int @ A @ B )
% 0.33/0.58 = C ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % unit_eq_div2
% 0.33/0.58 thf(fact_3521_unit__eq__div2,axiom,
% 0.33/0.58 ! [B: nat,A: nat,C: nat] :
% 0.33/0.58 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.33/0.58 => ( ( A
% 0.33/0.58 = ( divide_divide_nat @ C @ B ) )
% 0.33/0.58 = ( ( times_times_nat @ A @ B )
% 0.33/0.58 = C ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % unit_eq_div2
% 0.33/0.58 thf(fact_3522_unit__eq__div2,axiom,
% 0.33/0.58 ! [B: code_integer,A: code_integer,C: code_integer] :
% 0.33/0.58 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.33/0.58 => ( ( A
% 0.33/0.58 = ( divide6298287555418463151nteger @ C @ B ) )
% 0.33/0.58 = ( ( times_3573771949741848930nteger @ A @ B )
% 0.33/0.58 = C ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % unit_eq_div2
% 0.33/0.58 thf(fact_3523_unit__eq__div2,axiom,
% 0.33/0.58 ! [B: code_natural,A: code_natural,C: code_natural] :
% 0.33/0.58 ( ( dvd_dvd_Code_natural @ B @ one_one_Code_natural )
% 0.33/0.58 => ( ( A
% 0.33/0.58 = ( divide5121882707175180666atural @ C @ B ) )
% 0.33/0.58 = ( ( times_2397367101498566445atural @ A @ B )
% 0.33/0.58 = C ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % unit_eq_div2
% 0.33/0.58 thf(fact_3524_div__mult__unit2,axiom,
% 0.33/0.58 ! [C: int,B: int,A: int] :
% 0.33/0.58 ( ( dvd_dvd_int @ C @ one_one_int )
% 0.33/0.58 => ( ( dvd_dvd_int @ B @ A )
% 0.33/0.58 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 0.33/0.58 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % div_mult_unit2
% 0.33/0.58 thf(fact_3525_div__mult__unit2,axiom,
% 0.33/0.58 ! [C: nat,B: nat,A: nat] :
% 0.33/0.58 ( ( dvd_dvd_nat @ C @ one_one_nat )
% 0.33/0.58 => ( ( dvd_dvd_nat @ B @ A )
% 0.33/0.58 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 0.33/0.58 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % div_mult_unit2
% 0.33/0.58 thf(fact_3526_div__mult__unit2,axiom,
% 0.33/0.58 ! [C: code_integer,B: code_integer,A: code_integer] :
% 0.33/0.58 ( ( dvd_dvd_Code_integer @ C @ one_one_Code_integer )
% 0.33/0.58 => ( ( dvd_dvd_Code_integer @ B @ A )
% 0.33/0.58 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 0.33/0.58 = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % div_mult_unit2
% 0.33/0.58 thf(fact_3527_div__mult__unit2,axiom,
% 0.33/0.58 ! [C: code_natural,B: code_natural,A: code_natural] :
% 0.33/0.58 ( ( dvd_dvd_Code_natural @ C @ one_one_Code_natural )
% 0.33/0.58 => ( ( dvd_dvd_Code_natural @ B @ A )
% 0.33/0.58 => ( ( divide5121882707175180666atural @ A @ ( times_2397367101498566445atural @ B @ C ) )
% 0.33/0.58 = ( divide5121882707175180666atural @ ( divide5121882707175180666atural @ A @ B ) @ C ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % div_mult_unit2
% 0.33/0.58 thf(fact_3528_unit__div__commute,axiom,
% 0.33/0.58 ! [B: int,A: int,C: int] :
% 0.33/0.58 ( ( dvd_dvd_int @ B @ one_one_int )
% 0.33/0.58 => ( ( times_times_int @ ( divide_divide_int @ A @ B ) @ C )
% 0.33/0.58 = ( divide_divide_int @ ( times_times_int @ A @ C ) @ B ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % unit_div_commute
% 0.33/0.58 thf(fact_3529_unit__div__commute,axiom,
% 0.33/0.58 ! [B: nat,A: nat,C: nat] :
% 0.33/0.58 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.33/0.58 => ( ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ C )
% 0.33/0.58 = ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ B ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % unit_div_commute
% 0.33/0.58 thf(fact_3530_unit__div__commute,axiom,
% 0.33/0.58 ! [B: code_integer,A: code_integer,C: code_integer] :
% 0.33/0.58 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.33/0.58 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C )
% 0.33/0.58 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ C ) @ B ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % unit_div_commute
% 0.33/0.58 thf(fact_3531_unit__div__commute,axiom,
% 0.33/0.58 ! [B: code_natural,A: code_natural,C: code_natural] :
% 0.33/0.58 ( ( dvd_dvd_Code_natural @ B @ one_one_Code_natural )
% 0.33/0.58 => ( ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ A @ B ) @ C )
% 0.33/0.58 = ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ A @ C ) @ B ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % unit_div_commute
% 0.33/0.58 thf(fact_3532_unit__div__mult__swap,axiom,
% 0.33/0.58 ! [C: int,A: int,B: int] :
% 0.33/0.58 ( ( dvd_dvd_int @ C @ one_one_int )
% 0.33/0.58 => ( ( times_times_int @ A @ ( divide_divide_int @ B @ C ) )
% 0.33/0.58 = ( divide_divide_int @ ( times_times_int @ A @ B ) @ C ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % unit_div_mult_swap
% 0.33/0.58 thf(fact_3533_unit__div__mult__swap,axiom,
% 0.33/0.58 ! [C: nat,A: nat,B: nat] :
% 0.33/0.58 ( ( dvd_dvd_nat @ C @ one_one_nat )
% 0.33/0.58 => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 0.33/0.58 = ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % unit_div_mult_swap
% 0.33/0.58 thf(fact_3534_unit__div__mult__swap,axiom,
% 0.33/0.58 ! [C: code_integer,A: code_integer,B: code_integer] :
% 0.33/0.58 ( ( dvd_dvd_Code_integer @ C @ one_one_Code_integer )
% 0.33/0.58 => ( ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 0.33/0.58 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % unit_div_mult_swap
% 0.33/0.58 thf(fact_3535_unit__div__mult__swap,axiom,
% 0.33/0.58 ! [C: code_natural,A: code_natural,B: code_natural] :
% 0.33/0.58 ( ( dvd_dvd_Code_natural @ C @ one_one_Code_natural )
% 0.33/0.58 => ( ( times_2397367101498566445atural @ A @ ( divide5121882707175180666atural @ B @ C ) )
% 0.33/0.58 = ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ A @ B ) @ C ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % unit_div_mult_swap
% 0.33/0.58 thf(fact_3536_is__unit__div__mult2__eq,axiom,
% 0.33/0.58 ! [B: int,C: int,A: int] :
% 0.33/0.58 ( ( dvd_dvd_int @ B @ one_one_int )
% 0.33/0.58 => ( ( dvd_dvd_int @ C @ one_one_int )
% 0.33/0.58 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 0.33/0.58 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % is_unit_div_mult2_eq
% 0.33/0.58 thf(fact_3537_is__unit__div__mult2__eq,axiom,
% 0.33/0.58 ! [B: nat,C: nat,A: nat] :
% 0.33/0.58 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.33/0.58 => ( ( dvd_dvd_nat @ C @ one_one_nat )
% 0.33/0.58 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 0.33/0.58 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % is_unit_div_mult2_eq
% 0.33/0.58 thf(fact_3538_is__unit__div__mult2__eq,axiom,
% 0.33/0.58 ! [B: code_integer,C: code_integer,A: code_integer] :
% 0.33/0.58 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.33/0.58 => ( ( dvd_dvd_Code_integer @ C @ one_one_Code_integer )
% 0.33/0.58 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 0.33/0.58 = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % is_unit_div_mult2_eq
% 0.33/0.58 thf(fact_3539_is__unit__div__mult2__eq,axiom,
% 0.33/0.58 ! [B: code_natural,C: code_natural,A: code_natural] :
% 0.33/0.58 ( ( dvd_dvd_Code_natural @ B @ one_one_Code_natural )
% 0.33/0.58 => ( ( dvd_dvd_Code_natural @ C @ one_one_Code_natural )
% 0.33/0.58 => ( ( divide5121882707175180666atural @ A @ ( times_2397367101498566445atural @ B @ C ) )
% 0.33/0.58 = ( divide5121882707175180666atural @ ( divide5121882707175180666atural @ A @ B ) @ C ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % is_unit_div_mult2_eq
% 0.33/0.58 thf(fact_3540_unit__imp__mod__eq__0,axiom,
% 0.33/0.58 ! [B: int,A: int] :
% 0.33/0.58 ( ( dvd_dvd_int @ B @ one_one_int )
% 0.33/0.58 => ( ( modulo_modulo_int @ A @ B )
% 0.33/0.58 = zero_zero_int ) ) ).
% 0.33/0.58
% 0.33/0.58 % unit_imp_mod_eq_0
% 0.33/0.58 thf(fact_3541_unit__imp__mod__eq__0,axiom,
% 0.33/0.58 ! [B: nat,A: nat] :
% 0.33/0.58 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.33/0.58 => ( ( modulo_modulo_nat @ A @ B )
% 0.33/0.58 = zero_zero_nat ) ) ).
% 0.33/0.58
% 0.33/0.58 % unit_imp_mod_eq_0
% 0.33/0.58 thf(fact_3542_unit__imp__mod__eq__0,axiom,
% 0.33/0.58 ! [B: code_integer,A: code_integer] :
% 0.33/0.58 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.33/0.58 => ( ( modulo364778990260209775nteger @ A @ B )
% 0.33/0.58 = zero_z3403309356797280102nteger ) ) ).
% 0.33/0.58
% 0.33/0.58 % unit_imp_mod_eq_0
% 0.33/0.58 thf(fact_3543_unit__imp__mod__eq__0,axiom,
% 0.33/0.58 ! [B: code_natural,A: code_natural] :
% 0.33/0.58 ( ( dvd_dvd_Code_natural @ B @ one_one_Code_natural )
% 0.33/0.58 => ( ( modulo8411746178871703098atural @ A @ B )
% 0.33/0.58 = zero_z2226904508553997617atural ) ) ).
% 0.33/0.58
% 0.33/0.58 % unit_imp_mod_eq_0
% 0.33/0.58 thf(fact_3544_is__unit__power__iff,axiom,
% 0.33/0.58 ! [A: code_integer,N2: nat] :
% 0.33/0.58 ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ N2 ) @ one_one_Code_integer )
% 0.33/0.58 = ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 0.33/0.58 | ( N2 = zero_zero_nat ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % is_unit_power_iff
% 0.33/0.58 thf(fact_3545_is__unit__power__iff,axiom,
% 0.33/0.58 ! [A: nat,N2: nat] :
% 0.33/0.58 ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N2 ) @ one_one_nat )
% 0.33/0.58 = ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.33/0.58 | ( N2 = zero_zero_nat ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % is_unit_power_iff
% 0.33/0.58 thf(fact_3546_is__unit__power__iff,axiom,
% 0.33/0.58 ! [A: int,N2: nat] :
% 0.33/0.58 ( ( dvd_dvd_int @ ( power_power_int @ A @ N2 ) @ one_one_int )
% 0.33/0.58 = ( ( dvd_dvd_int @ A @ one_one_int )
% 0.33/0.58 | ( N2 = zero_zero_nat ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % is_unit_power_iff
% 0.33/0.58 thf(fact_3547_bezout__add__strong__nat,axiom,
% 0.33/0.58 ! [A: nat,B: nat] :
% 0.33/0.58 ( ( A != zero_zero_nat )
% 0.33/0.58 => ? [D: nat,X4: nat,Y5: nat] :
% 0.33/0.58 ( ( dvd_dvd_nat @ D @ A )
% 0.33/0.58 & ( dvd_dvd_nat @ D @ B )
% 0.33/0.58 & ( ( times_times_nat @ A @ X4 )
% 0.33/0.58 = ( plus_plus_nat @ ( times_times_nat @ B @ Y5 ) @ D ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % bezout_add_strong_nat
% 0.33/0.58 thf(fact_3548_take__bit__Suc__bit1,axiom,
% 0.33/0.58 ! [N2: nat,K: num] :
% 0.33/0.58 ( ( bit_se1745604003318907178nteger @ ( suc @ N2 ) @ ( numera6620942414471956472nteger @ ( bit1 @ K ) ) )
% 0.33/0.58 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( bit_se1745604003318907178nteger @ N2 @ ( numera6620942414471956472nteger @ K ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ one_one_Code_integer ) ) ).
% 0.33/0.58
% 0.33/0.58 % take_bit_Suc_bit1
% 0.33/0.58 thf(fact_3549_take__bit__Suc__bit1,axiom,
% 0.33/0.58 ! [N2: nat,K: num] :
% 0.33/0.58 ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 0.33/0.58 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N2 @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 0.33/0.58
% 0.33/0.58 % take_bit_Suc_bit1
% 0.33/0.58 thf(fact_3550_take__bit__Suc__bit1,axiom,
% 0.33/0.58 ! [N2: nat,K: num] :
% 0.33/0.58 ( ( bit_se2925701944663578781it_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 0.33/0.58 = ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ N2 @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ).
% 0.33/0.58
% 0.33/0.58 % take_bit_Suc_bit1
% 0.33/0.58 thf(fact_3551_take__bit__Suc__bit1,axiom,
% 0.33/0.58 ! [N2: nat,K: num] :
% 0.33/0.58 ( ( bit_se569199155075624693atural @ ( suc @ N2 ) @ ( numera5444537566228673987atural @ ( bit1 @ K ) ) )
% 0.33/0.58 = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( bit_se569199155075624693atural @ N2 @ ( numera5444537566228673987atural @ K ) ) @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) @ one_one_Code_natural ) ) ).
% 0.33/0.58
% 0.33/0.58 % take_bit_Suc_bit1
% 0.33/0.58 thf(fact_3552_numeral__code_I3_J,axiom,
% 0.33/0.58 ! [N2: num] :
% 0.33/0.58 ( ( numeral_numeral_nat @ ( bit1 @ N2 ) )
% 0.33/0.58 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ N2 ) ) @ one_one_nat ) ) ).
% 0.33/0.58
% 0.33/0.58 % numeral_code(3)
% 0.33/0.58 thf(fact_3553_numeral__code_I3_J,axiom,
% 0.33/0.58 ! [N2: num] :
% 0.33/0.58 ( ( numeral_numeral_int @ ( bit1 @ N2 ) )
% 0.33/0.58 = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ N2 ) ) @ one_one_int ) ) ).
% 0.33/0.58
% 0.33/0.58 % numeral_code(3)
% 0.33/0.58 thf(fact_3554_numeral__code_I3_J,axiom,
% 0.33/0.58 ! [N2: num] :
% 0.33/0.58 ( ( numera6620942414471956472nteger @ ( bit1 @ N2 ) )
% 0.33/0.58 = ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ N2 ) @ ( numera6620942414471956472nteger @ N2 ) ) @ one_one_Code_integer ) ) ).
% 0.33/0.58
% 0.33/0.58 % numeral_code(3)
% 0.33/0.58 thf(fact_3555_numeral__code_I3_J,axiom,
% 0.33/0.58 ! [N2: num] :
% 0.33/0.58 ( ( numeral_numeral_rat @ ( bit1 @ N2 ) )
% 0.33/0.58 = ( plus_plus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ N2 ) @ ( numeral_numeral_rat @ N2 ) ) @ one_one_rat ) ) ).
% 0.33/0.58
% 0.33/0.58 % numeral_code(3)
% 0.33/0.58 thf(fact_3556_numeral__code_I3_J,axiom,
% 0.33/0.58 ! [N2: num] :
% 0.33/0.58 ( ( numera5444537566228673987atural @ ( bit1 @ N2 ) )
% 0.33/0.58 = ( plus_p4538020629002901425atural @ ( plus_p4538020629002901425atural @ ( numera5444537566228673987atural @ N2 ) @ ( numera5444537566228673987atural @ N2 ) ) @ one_one_Code_natural ) ) ).
% 0.33/0.58
% 0.33/0.58 % numeral_code(3)
% 0.33/0.58 thf(fact_3557_stable__imp__take__bit__eq,axiom,
% 0.33/0.58 ! [A: code_integer,N2: nat] :
% 0.33/0.58 ( ( ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.33/0.58 = A )
% 0.33/0.58 => ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.33/0.58 => ( ( bit_se1745604003318907178nteger @ N2 @ A )
% 0.33/0.58 = zero_z3403309356797280102nteger ) )
% 0.33/0.58 & ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.33/0.58 => ( ( bit_se1745604003318907178nteger @ N2 @ A )
% 0.33/0.58 = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) @ one_one_Code_integer ) ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % stable_imp_take_bit_eq
% 0.33/0.58 thf(fact_3558_stable__imp__take__bit__eq,axiom,
% 0.33/0.58 ! [A: int,N2: nat] :
% 0.33/0.58 ( ( ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.33/0.58 = A )
% 0.33/0.58 => ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.33/0.58 => ( ( bit_se2923211474154528505it_int @ N2 @ A )
% 0.33/0.58 = zero_zero_int ) )
% 0.33/0.58 & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.33/0.58 => ( ( bit_se2923211474154528505it_int @ N2 @ A )
% 0.33/0.58 = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ one_one_int ) ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % stable_imp_take_bit_eq
% 0.33/0.58 thf(fact_3559_stable__imp__take__bit__eq,axiom,
% 0.33/0.58 ! [A: nat,N2: nat] :
% 0.33/0.58 ( ( ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.33/0.58 = A )
% 0.33/0.58 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.33/0.58 => ( ( bit_se2925701944663578781it_nat @ N2 @ A )
% 0.33/0.58 = zero_zero_nat ) )
% 0.33/0.58 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.33/0.58 => ( ( bit_se2925701944663578781it_nat @ N2 @ A )
% 0.33/0.58 = ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % stable_imp_take_bit_eq
% 0.33/0.58 thf(fact_3560_stable__imp__take__bit__eq,axiom,
% 0.33/0.58 ! [A: code_natural,N2: nat] :
% 0.33/0.58 ( ( ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 0.33/0.58 = A )
% 0.33/0.58 => ( ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 0.33/0.58 => ( ( bit_se569199155075624693atural @ N2 @ A )
% 0.33/0.58 = zero_z2226904508553997617atural ) )
% 0.33/0.58 & ( ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 0.33/0.58 => ( ( bit_se569199155075624693atural @ N2 @ A )
% 0.33/0.58 = ( minus_7197305767214868737atural @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N2 ) @ one_one_Code_natural ) ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % stable_imp_take_bit_eq
% 0.33/0.58 thf(fact_3561_is__unitE,axiom,
% 0.33/0.58 ! [A: int,C: int] :
% 0.33/0.58 ( ( dvd_dvd_int @ A @ one_one_int )
% 0.33/0.58 => ~ ( ( A != zero_zero_int )
% 0.33/0.58 => ! [B2: int] :
% 0.33/0.58 ( ( B2 != zero_zero_int )
% 0.33/0.58 => ( ( dvd_dvd_int @ B2 @ one_one_int )
% 0.33/0.58 => ( ( ( divide_divide_int @ one_one_int @ A )
% 0.33/0.58 = B2 )
% 0.33/0.58 => ( ( ( divide_divide_int @ one_one_int @ B2 )
% 0.33/0.58 = A )
% 0.33/0.58 => ( ( ( times_times_int @ A @ B2 )
% 0.33/0.58 = one_one_int )
% 0.33/0.58 => ( ( divide_divide_int @ C @ A )
% 0.33/0.58 != ( times_times_int @ C @ B2 ) ) ) ) ) ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % is_unitE
% 0.33/0.58 thf(fact_3562_is__unitE,axiom,
% 0.33/0.58 ! [A: nat,C: nat] :
% 0.33/0.58 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.33/0.58 => ~ ( ( A != zero_zero_nat )
% 0.33/0.58 => ! [B2: nat] :
% 0.33/0.58 ( ( B2 != zero_zero_nat )
% 0.33/0.58 => ( ( dvd_dvd_nat @ B2 @ one_one_nat )
% 0.33/0.58 => ( ( ( divide_divide_nat @ one_one_nat @ A )
% 0.33/0.58 = B2 )
% 0.33/0.58 => ( ( ( divide_divide_nat @ one_one_nat @ B2 )
% 0.33/0.58 = A )
% 0.33/0.58 => ( ( ( times_times_nat @ A @ B2 )
% 0.33/0.58 = one_one_nat )
% 0.33/0.58 => ( ( divide_divide_nat @ C @ A )
% 0.33/0.58 != ( times_times_nat @ C @ B2 ) ) ) ) ) ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % is_unitE
% 0.33/0.58 thf(fact_3563_is__unitE,axiom,
% 0.33/0.58 ! [A: code_integer,C: code_integer] :
% 0.33/0.58 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 0.33/0.58 => ~ ( ( A != zero_z3403309356797280102nteger )
% 0.33/0.58 => ! [B2: code_integer] :
% 0.33/0.58 ( ( B2 != zero_z3403309356797280102nteger )
% 0.33/0.58 => ( ( dvd_dvd_Code_integer @ B2 @ one_one_Code_integer )
% 0.33/0.58 => ( ( ( divide6298287555418463151nteger @ one_one_Code_integer @ A )
% 0.33/0.58 = B2 )
% 0.33/0.58 => ( ( ( divide6298287555418463151nteger @ one_one_Code_integer @ B2 )
% 0.33/0.58 = A )
% 0.33/0.58 => ( ( ( times_3573771949741848930nteger @ A @ B2 )
% 0.33/0.58 = one_one_Code_integer )
% 0.33/0.58 => ( ( divide6298287555418463151nteger @ C @ A )
% 0.33/0.58 != ( times_3573771949741848930nteger @ C @ B2 ) ) ) ) ) ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % is_unitE
% 0.33/0.58 thf(fact_3564_is__unitE,axiom,
% 0.33/0.58 ! [A: code_natural,C: code_natural] :
% 0.33/0.58 ( ( dvd_dvd_Code_natural @ A @ one_one_Code_natural )
% 0.33/0.58 => ~ ( ( A != zero_z2226904508553997617atural )
% 0.33/0.58 => ! [B2: code_natural] :
% 0.33/0.58 ( ( B2 != zero_z2226904508553997617atural )
% 0.33/0.58 => ( ( dvd_dvd_Code_natural @ B2 @ one_one_Code_natural )
% 0.33/0.58 => ( ( ( divide5121882707175180666atural @ one_one_Code_natural @ A )
% 0.33/0.58 = B2 )
% 0.33/0.58 => ( ( ( divide5121882707175180666atural @ one_one_Code_natural @ B2 )
% 0.33/0.58 = A )
% 0.33/0.58 => ( ( ( times_2397367101498566445atural @ A @ B2 )
% 0.33/0.58 = one_one_Code_natural )
% 0.33/0.58 => ( ( divide5121882707175180666atural @ C @ A )
% 0.33/0.58 != ( times_2397367101498566445atural @ C @ B2 ) ) ) ) ) ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % is_unitE
% 0.33/0.58 thf(fact_3565_is__unit__div__mult__cancel__left,axiom,
% 0.33/0.58 ! [A: int,B: int] :
% 0.33/0.58 ( ( A != zero_zero_int )
% 0.33/0.58 => ( ( dvd_dvd_int @ B @ one_one_int )
% 0.33/0.58 => ( ( divide_divide_int @ A @ ( times_times_int @ A @ B ) )
% 0.33/0.58 = ( divide_divide_int @ one_one_int @ B ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % is_unit_div_mult_cancel_left
% 0.33/0.58 thf(fact_3566_is__unit__div__mult__cancel__left,axiom,
% 0.33/0.58 ! [A: nat,B: nat] :
% 0.33/0.58 ( ( A != zero_zero_nat )
% 0.33/0.58 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.33/0.58 => ( ( divide_divide_nat @ A @ ( times_times_nat @ A @ B ) )
% 0.33/0.58 = ( divide_divide_nat @ one_one_nat @ B ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % is_unit_div_mult_cancel_left
% 0.33/0.58 thf(fact_3567_is__unit__div__mult__cancel__left,axiom,
% 0.33/0.58 ! [A: code_integer,B: code_integer] :
% 0.33/0.58 ( ( A != zero_z3403309356797280102nteger )
% 0.33/0.58 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.33/0.58 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ A @ B ) )
% 0.33/0.58 = ( divide6298287555418463151nteger @ one_one_Code_integer @ B ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % is_unit_div_mult_cancel_left
% 0.33/0.58 thf(fact_3568_is__unit__div__mult__cancel__left,axiom,
% 0.33/0.58 ! [A: code_natural,B: code_natural] :
% 0.33/0.58 ( ( A != zero_z2226904508553997617atural )
% 0.33/0.58 => ( ( dvd_dvd_Code_natural @ B @ one_one_Code_natural )
% 0.33/0.58 => ( ( divide5121882707175180666atural @ A @ ( times_2397367101498566445atural @ A @ B ) )
% 0.33/0.58 = ( divide5121882707175180666atural @ one_one_Code_natural @ B ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % is_unit_div_mult_cancel_left
% 0.33/0.58 thf(fact_3569_is__unit__div__mult__cancel__right,axiom,
% 0.33/0.58 ! [A: int,B: int] :
% 0.33/0.58 ( ( A != zero_zero_int )
% 0.33/0.58 => ( ( dvd_dvd_int @ B @ one_one_int )
% 0.33/0.58 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ A ) )
% 0.33/0.58 = ( divide_divide_int @ one_one_int @ B ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % is_unit_div_mult_cancel_right
% 0.33/0.58 thf(fact_3570_is__unit__div__mult__cancel__right,axiom,
% 0.33/0.58 ! [A: nat,B: nat] :
% 0.33/0.58 ( ( A != zero_zero_nat )
% 0.33/0.58 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.33/0.58 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ A ) )
% 0.33/0.58 = ( divide_divide_nat @ one_one_nat @ B ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % is_unit_div_mult_cancel_right
% 0.33/0.58 thf(fact_3571_is__unit__div__mult__cancel__right,axiom,
% 0.33/0.58 ! [A: code_integer,B: code_integer] :
% 0.33/0.58 ( ( A != zero_z3403309356797280102nteger )
% 0.33/0.58 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.33/0.58 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ A ) )
% 0.33/0.58 = ( divide6298287555418463151nteger @ one_one_Code_integer @ B ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % is_unit_div_mult_cancel_right
% 0.33/0.58 thf(fact_3572_is__unit__div__mult__cancel__right,axiom,
% 0.33/0.58 ! [A: code_natural,B: code_natural] :
% 0.33/0.58 ( ( A != zero_z2226904508553997617atural )
% 0.33/0.58 => ( ( dvd_dvd_Code_natural @ B @ one_one_Code_natural )
% 0.33/0.58 => ( ( divide5121882707175180666atural @ A @ ( times_2397367101498566445atural @ B @ A ) )
% 0.33/0.58 = ( divide5121882707175180666atural @ one_one_Code_natural @ B ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % is_unit_div_mult_cancel_right
% 0.33/0.58 thf(fact_3573_odd__even__add,axiom,
% 0.33/0.58 ! [A: nat,B: nat] :
% 0.33/0.58 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.33/0.58 => ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 0.33/0.58 => ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % odd_even_add
% 0.33/0.58 thf(fact_3574_odd__even__add,axiom,
% 0.33/0.58 ! [A: int,B: int] :
% 0.33/0.58 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.33/0.58 => ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B )
% 0.33/0.58 => ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % odd_even_add
% 0.33/0.58 thf(fact_3575_odd__even__add,axiom,
% 0.33/0.58 ! [A: code_integer,B: code_integer] :
% 0.33/0.58 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.33/0.58 => ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B )
% 0.33/0.58 => ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % odd_even_add
% 0.33/0.58 thf(fact_3576_odd__even__add,axiom,
% 0.33/0.58 ! [A: code_natural,B: code_natural] :
% 0.33/0.58 ( ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 0.33/0.58 => ( ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ B )
% 0.33/0.58 => ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( plus_p4538020629002901425atural @ A @ B ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % odd_even_add
% 0.33/0.58 thf(fact_3577_odd__one,axiom,
% 0.33/0.58 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ one_one_nat ) ).
% 0.33/0.58
% 0.33/0.58 % odd_one
% 0.33/0.58 thf(fact_3578_odd__one,axiom,
% 0.33/0.58 ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ one_one_int ) ).
% 0.33/0.58
% 0.33/0.58 % odd_one
% 0.33/0.58 thf(fact_3579_odd__one,axiom,
% 0.33/0.58 ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ one_one_Code_integer ) ).
% 0.33/0.58
% 0.33/0.58 % odd_one
% 0.33/0.58 thf(fact_3580_odd__one,axiom,
% 0.33/0.58 ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ one_one_Code_natural ) ).
% 0.33/0.58
% 0.33/0.58 % odd_one
% 0.33/0.58 thf(fact_3581_dvd__power__iff,axiom,
% 0.33/0.58 ! [X: code_integer,M2: nat,N2: nat] :
% 0.33/0.58 ( ( X != zero_z3403309356797280102nteger )
% 0.33/0.58 => ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ X @ M2 ) @ ( power_8256067586552552935nteger @ X @ N2 ) )
% 0.33/0.58 = ( ( dvd_dvd_Code_integer @ X @ one_one_Code_integer )
% 0.33/0.58 | ( ord_less_eq_nat @ M2 @ N2 ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % dvd_power_iff
% 0.33/0.58 thf(fact_3582_dvd__power__iff,axiom,
% 0.33/0.58 ! [X: nat,M2: nat,N2: nat] :
% 0.33/0.58 ( ( X != zero_zero_nat )
% 0.33/0.58 => ( ( dvd_dvd_nat @ ( power_power_nat @ X @ M2 ) @ ( power_power_nat @ X @ N2 ) )
% 0.33/0.58 = ( ( dvd_dvd_nat @ X @ one_one_nat )
% 0.33/0.58 | ( ord_less_eq_nat @ M2 @ N2 ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % dvd_power_iff
% 0.33/0.58 thf(fact_3583_dvd__power__iff,axiom,
% 0.33/0.58 ! [X: int,M2: nat,N2: nat] :
% 0.33/0.58 ( ( X != zero_zero_int )
% 0.33/0.58 => ( ( dvd_dvd_int @ ( power_power_int @ X @ M2 ) @ ( power_power_int @ X @ N2 ) )
% 0.33/0.58 = ( ( dvd_dvd_int @ X @ one_one_int )
% 0.33/0.58 | ( ord_less_eq_nat @ M2 @ N2 ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % dvd_power_iff
% 0.33/0.58 thf(fact_3584_dvd__power,axiom,
% 0.33/0.58 ! [N2: nat,X: code_integer] :
% 0.33/0.58 ( ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.33/0.58 | ( X = one_one_Code_integer ) )
% 0.33/0.58 => ( dvd_dvd_Code_integer @ X @ ( power_8256067586552552935nteger @ X @ N2 ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % dvd_power
% 0.33/0.58 thf(fact_3585_dvd__power,axiom,
% 0.33/0.58 ! [N2: nat,X: rat] :
% 0.33/0.58 ( ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.33/0.58 | ( X = one_one_rat ) )
% 0.33/0.58 => ( dvd_dvd_rat @ X @ ( power_power_rat @ X @ N2 ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % dvd_power
% 0.33/0.58 thf(fact_3586_dvd__power,axiom,
% 0.33/0.58 ! [N2: nat,X: nat] :
% 0.33/0.58 ( ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.33/0.58 | ( X = one_one_nat ) )
% 0.33/0.58 => ( dvd_dvd_nat @ X @ ( power_power_nat @ X @ N2 ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % dvd_power
% 0.33/0.58 thf(fact_3587_dvd__power,axiom,
% 0.33/0.58 ! [N2: nat,X: int] :
% 0.33/0.58 ( ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.33/0.58 | ( X = one_one_int ) )
% 0.33/0.58 => ( dvd_dvd_int @ X @ ( power_power_int @ X @ N2 ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % dvd_power
% 0.33/0.58 thf(fact_3588_Suc3__eq__add__3,axiom,
% 0.33/0.58 ! [N2: nat] :
% 0.33/0.58 ( ( suc @ ( suc @ ( suc @ N2 ) ) )
% 0.33/0.58 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N2 ) ) ).
% 0.33/0.58
% 0.33/0.58 % Suc3_eq_add_3
% 0.33/0.58 thf(fact_3589_dvd__mult__cancel2,axiom,
% 0.33/0.58 ! [M2: nat,N2: nat] :
% 0.33/0.58 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 0.33/0.58 => ( ( dvd_dvd_nat @ ( times_times_nat @ N2 @ M2 ) @ M2 )
% 0.33/0.58 = ( N2 = one_one_nat ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % dvd_mult_cancel2
% 0.33/0.58 thf(fact_3590_dvd__mult__cancel1,axiom,
% 0.33/0.58 ! [M2: nat,N2: nat] :
% 0.33/0.58 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 0.33/0.58 => ( ( dvd_dvd_nat @ ( times_times_nat @ M2 @ N2 ) @ M2 )
% 0.33/0.58 = ( N2 = one_one_nat ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % dvd_mult_cancel1
% 0.33/0.58 thf(fact_3591_dvd__minus__add,axiom,
% 0.33/0.58 ! [Q3: nat,N2: nat,R2: nat,M2: nat] :
% 0.33/0.58 ( ( ord_less_eq_nat @ Q3 @ N2 )
% 0.33/0.58 => ( ( ord_less_eq_nat @ Q3 @ ( times_times_nat @ R2 @ M2 ) )
% 0.33/0.58 => ( ( dvd_dvd_nat @ M2 @ ( minus_minus_nat @ N2 @ Q3 ) )
% 0.33/0.58 = ( dvd_dvd_nat @ M2 @ ( plus_plus_nat @ N2 @ ( minus_minus_nat @ ( times_times_nat @ R2 @ M2 ) @ Q3 ) ) ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % dvd_minus_add
% 0.33/0.58 thf(fact_3592_power__dvd__imp__le,axiom,
% 0.33/0.58 ! [I: nat,M2: nat,N2: nat] :
% 0.33/0.58 ( ( dvd_dvd_nat @ ( power_power_nat @ I @ M2 ) @ ( power_power_nat @ I @ N2 ) )
% 0.33/0.58 => ( ( ord_less_nat @ one_one_nat @ I )
% 0.33/0.58 => ( ord_less_eq_nat @ M2 @ N2 ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % power_dvd_imp_le
% 0.33/0.58 thf(fact_3593_aset_I10_J,axiom,
% 0.33/0.58 ! [D2: int,D3: int,A2: set_int,T: int] :
% 0.33/0.58 ( ( dvd_dvd_int @ D2 @ D3 )
% 0.33/0.58 => ! [X8: int] :
% 0.33/0.58 ( ! [Xa3: int] :
% 0.33/0.58 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.33/0.58 => ! [Xb3: int] :
% 0.33/0.58 ( ( member_int @ Xb3 @ A2 )
% 0.33/0.58 => ( X8
% 0.33/0.58 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 0.33/0.58 => ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X8 @ T ) )
% 0.33/0.58 => ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ ( plus_plus_int @ X8 @ D3 ) @ T ) ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % aset(10)
% 0.33/0.58 thf(fact_3594_aset_I9_J,axiom,
% 0.33/0.58 ! [D2: int,D3: int,A2: set_int,T: int] :
% 0.33/0.58 ( ( dvd_dvd_int @ D2 @ D3 )
% 0.33/0.58 => ! [X8: int] :
% 0.33/0.58 ( ! [Xa3: int] :
% 0.33/0.58 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.33/0.58 => ! [Xb3: int] :
% 0.33/0.58 ( ( member_int @ Xb3 @ A2 )
% 0.33/0.58 => ( X8
% 0.33/0.58 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 0.33/0.58 => ( ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X8 @ T ) )
% 0.33/0.58 => ( dvd_dvd_int @ D2 @ ( plus_plus_int @ ( plus_plus_int @ X8 @ D3 ) @ T ) ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % aset(9)
% 0.33/0.58 thf(fact_3595_bset_I10_J,axiom,
% 0.33/0.58 ! [D2: int,D3: int,B5: set_int,T: int] :
% 0.33/0.58 ( ( dvd_dvd_int @ D2 @ D3 )
% 0.33/0.58 => ! [X8: int] :
% 0.33/0.58 ( ! [Xa3: int] :
% 0.33/0.58 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.33/0.58 => ! [Xb3: int] :
% 0.33/0.58 ( ( member_int @ Xb3 @ B5 )
% 0.33/0.58 => ( X8
% 0.33/0.58 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 0.33/0.58 => ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X8 @ T ) )
% 0.33/0.58 => ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ ( minus_minus_int @ X8 @ D3 ) @ T ) ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % bset(10)
% 0.33/0.58 thf(fact_3596_bset_I9_J,axiom,
% 0.33/0.58 ! [D2: int,D3: int,B5: set_int,T: int] :
% 0.33/0.58 ( ( dvd_dvd_int @ D2 @ D3 )
% 0.33/0.58 => ! [X8: int] :
% 0.33/0.58 ( ! [Xa3: int] :
% 0.33/0.58 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.33/0.58 => ! [Xb3: int] :
% 0.33/0.58 ( ( member_int @ Xb3 @ B5 )
% 0.33/0.58 => ( X8
% 0.33/0.58 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 0.33/0.58 => ( ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X8 @ T ) )
% 0.33/0.58 => ( dvd_dvd_int @ D2 @ ( plus_plus_int @ ( minus_minus_int @ X8 @ D3 ) @ T ) ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % bset(9)
% 0.33/0.58 thf(fact_3597_num_Osize__gen_I3_J,axiom,
% 0.33/0.58 ! [X32: num] :
% 0.33/0.58 ( ( size_num @ ( bit1 @ X32 ) )
% 0.33/0.58 = ( plus_plus_nat @ ( size_num @ X32 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % num.size_gen(3)
% 0.33/0.58 thf(fact_3598_num_Osize_I6_J,axiom,
% 0.33/0.58 ! [X32: num] :
% 0.33/0.58 ( ( size_size_num @ ( bit1 @ X32 ) )
% 0.33/0.58 = ( plus_plus_nat @ ( size_size_num @ X32 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % num.size(6)
% 0.33/0.58 thf(fact_3599_odd__iff__mod__2__eq__one,axiom,
% 0.33/0.58 ! [A: int] :
% 0.33/0.58 ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 0.33/0.58 = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.33/0.58 = one_one_int ) ) ).
% 0.33/0.58
% 0.33/0.58 % odd_iff_mod_2_eq_one
% 0.33/0.58 thf(fact_3600_odd__iff__mod__2__eq__one,axiom,
% 0.33/0.58 ! [A: nat] :
% 0.33/0.58 ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 0.33/0.58 = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.33/0.58 = one_one_nat ) ) ).
% 0.33/0.58
% 0.33/0.58 % odd_iff_mod_2_eq_one
% 0.33/0.58 thf(fact_3601_odd__iff__mod__2__eq__one,axiom,
% 0.33/0.58 ! [A: code_integer] :
% 0.33/0.58 ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 0.33/0.58 = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.33/0.58 = one_one_Code_integer ) ) ).
% 0.33/0.58
% 0.33/0.58 % odd_iff_mod_2_eq_one
% 0.33/0.58 thf(fact_3602_odd__iff__mod__2__eq__one,axiom,
% 0.33/0.58 ! [A: code_natural] :
% 0.33/0.58 ( ( ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A ) )
% 0.33/0.58 = ( ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 0.33/0.58 = one_one_Code_natural ) ) ).
% 0.33/0.58
% 0.33/0.58 % odd_iff_mod_2_eq_one
% 0.33/0.58 thf(fact_3603_Suc__mod__eq__add3__mod,axiom,
% 0.33/0.58 ! [M2: nat,N2: nat] :
% 0.33/0.58 ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( suc @ M2 ) ) ) @ N2 )
% 0.33/0.58 = ( modulo_modulo_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M2 ) @ N2 ) ) ).
% 0.33/0.58
% 0.33/0.58 % Suc_mod_eq_add3_mod
% 0.33/0.58 thf(fact_3604_Suc__div__eq__add3__div,axiom,
% 0.33/0.58 ! [M2: nat,N2: nat] :
% 0.33/0.58 ( ( divide_divide_nat @ ( suc @ ( suc @ ( suc @ M2 ) ) ) @ N2 )
% 0.33/0.58 = ( divide_divide_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M2 ) @ N2 ) ) ).
% 0.33/0.58
% 0.33/0.58 % Suc_div_eq_add3_div
% 0.33/0.58 thf(fact_3605_even__diff__iff,axiom,
% 0.33/0.58 ! [K: int,L: int] :
% 0.33/0.58 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ K @ L ) )
% 0.33/0.58 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ L ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % even_diff_iff
% 0.33/0.58 thf(fact_3606_even__abs__add__iff,axiom,
% 0.33/0.58 ! [K: int,L: int] :
% 0.33/0.58 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ ( abs_abs_int @ K ) @ L ) )
% 0.33/0.58 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ L ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % even_abs_add_iff
% 0.33/0.58 thf(fact_3607_even__add__abs__iff,axiom,
% 0.33/0.58 ! [K: int,L: int] :
% 0.33/0.58 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ ( abs_abs_int @ L ) ) )
% 0.33/0.58 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ L ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % even_add_abs_iff
% 0.33/0.58 thf(fact_3608_signed__take__bit__eq__take__bit__shift,axiom,
% 0.33/0.58 ( bit_ri631733984087533419it_int
% 0.33/0.58 = ( ^ [N4: nat,K4: int] : ( minus_minus_int @ ( bit_se2923211474154528505it_int @ ( suc @ N4 ) @ ( plus_plus_int @ K4 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N4 ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N4 ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % signed_take_bit_eq_take_bit_shift
% 0.33/0.58 thf(fact_3609_take__bit__incr__eq,axiom,
% 0.33/0.58 ! [N2: nat,K: int] :
% 0.33/0.58 ( ( ( bit_se2923211474154528505it_int @ N2 @ K )
% 0.33/0.58 != ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ one_one_int ) )
% 0.33/0.58 => ( ( bit_se2923211474154528505it_int @ N2 @ ( plus_plus_int @ K @ one_one_int ) )
% 0.33/0.58 = ( plus_plus_int @ one_one_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % take_bit_incr_eq
% 0.33/0.58 thf(fact_3610_oddE,axiom,
% 0.33/0.58 ! [A: nat] :
% 0.33/0.58 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.33/0.58 => ~ ! [B2: nat] :
% 0.33/0.58 ( A
% 0.33/0.58 != ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 ) @ one_one_nat ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % oddE
% 0.33/0.58 thf(fact_3611_oddE,axiom,
% 0.33/0.58 ! [A: int] :
% 0.33/0.58 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.33/0.58 => ~ ! [B2: int] :
% 0.33/0.58 ( A
% 0.33/0.58 != ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B2 ) @ one_one_int ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % oddE
% 0.33/0.58 thf(fact_3612_oddE,axiom,
% 0.33/0.58 ! [A: code_integer] :
% 0.33/0.58 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.33/0.58 => ~ ! [B2: code_integer] :
% 0.33/0.58 ( A
% 0.33/0.58 != ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B2 ) @ one_one_Code_integer ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % oddE
% 0.33/0.58 thf(fact_3613_oddE,axiom,
% 0.33/0.58 ! [A: code_natural] :
% 0.33/0.58 ( ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 0.33/0.58 => ~ ! [B2: code_natural] :
% 0.33/0.58 ( A
% 0.33/0.58 != ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ B2 ) @ one_one_Code_natural ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % oddE
% 0.33/0.58 thf(fact_3614_parity__cases,axiom,
% 0.33/0.58 ! [A: int] :
% 0.33/0.58 ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.33/0.58 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.33/0.58 != zero_zero_int ) )
% 0.33/0.58 => ~ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.33/0.58 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.33/0.58 != one_one_int ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % parity_cases
% 0.33/0.58 thf(fact_3615_parity__cases,axiom,
% 0.33/0.58 ! [A: nat] :
% 0.33/0.58 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.33/0.58 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.33/0.58 != zero_zero_nat ) )
% 0.33/0.58 => ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.33/0.58 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.33/0.58 != one_one_nat ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % parity_cases
% 0.33/0.58 thf(fact_3616_parity__cases,axiom,
% 0.33/0.58 ! [A: code_integer] :
% 0.33/0.58 ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.33/0.58 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.33/0.58 != zero_z3403309356797280102nteger ) )
% 0.33/0.58 => ~ ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.33/0.58 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.33/0.58 != one_one_Code_integer ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % parity_cases
% 0.33/0.58 thf(fact_3617_parity__cases,axiom,
% 0.33/0.58 ! [A: code_natural] :
% 0.33/0.58 ( ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 0.33/0.58 => ( ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 0.33/0.58 != zero_z2226904508553997617atural ) )
% 0.33/0.58 => ~ ( ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 0.33/0.58 => ( ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 0.33/0.58 != one_one_Code_natural ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % parity_cases
% 0.33/0.58 thf(fact_3618_mod2__eq__if,axiom,
% 0.33/0.58 ! [A: int] :
% 0.33/0.58 ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.33/0.58 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.33/0.58 = zero_zero_int ) )
% 0.33/0.58 & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.33/0.58 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.33/0.58 = one_one_int ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % mod2_eq_if
% 0.33/0.58 thf(fact_3619_mod2__eq__if,axiom,
% 0.33/0.58 ! [A: nat] :
% 0.33/0.58 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.33/0.58 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.33/0.58 = zero_zero_nat ) )
% 0.33/0.58 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.33/0.58 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.33/0.58 = one_one_nat ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % mod2_eq_if
% 0.33/0.58 thf(fact_3620_mod2__eq__if,axiom,
% 0.33/0.58 ! [A: code_integer] :
% 0.33/0.58 ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.33/0.58 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.33/0.58 = zero_z3403309356797280102nteger ) )
% 0.33/0.58 & ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.33/0.58 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.33/0.58 = one_one_Code_integer ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % mod2_eq_if
% 0.33/0.58 thf(fact_3621_mod2__eq__if,axiom,
% 0.33/0.58 ! [A: code_natural] :
% 0.33/0.58 ( ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 0.33/0.58 => ( ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 0.33/0.58 = zero_z2226904508553997617atural ) )
% 0.33/0.58 & ( ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 0.33/0.58 => ( ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 0.33/0.58 = one_one_Code_natural ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % mod2_eq_if
% 0.33/0.58 thf(fact_3622_minus__one__power__iff,axiom,
% 0.33/0.58 ! [N2: nat] :
% 0.33/0.58 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.33/0.58 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 )
% 0.33/0.58 = one_one_int ) )
% 0.33/0.58 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.33/0.58 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 )
% 0.33/0.58 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % minus_one_power_iff
% 0.33/0.58 thf(fact_3623_minus__one__power__iff,axiom,
% 0.33/0.58 ! [N2: nat] :
% 0.33/0.58 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.33/0.58 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 )
% 0.33/0.58 = one_one_Code_integer ) )
% 0.33/0.58 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.33/0.58 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 )
% 0.33/0.58 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % minus_one_power_iff
% 0.33/0.58 thf(fact_3624_minus__one__power__iff,axiom,
% 0.33/0.58 ! [N2: nat] :
% 0.33/0.58 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.33/0.58 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 )
% 0.33/0.58 = one_one_rat ) )
% 0.33/0.58 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.33/0.58 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 )
% 0.33/0.58 = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % minus_one_power_iff
% 0.33/0.58 thf(fact_3625_take__bit__int__greater__eq,axiom,
% 0.33/0.58 ! [K: int,N2: nat] :
% 0.33/0.58 ( ( ord_less_int @ K @ zero_zero_int )
% 0.33/0.58 => ( ord_less_eq_int @ ( plus_plus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) @ ( bit_se2923211474154528505it_int @ N2 @ K ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % take_bit_int_greater_eq
% 0.33/0.58 thf(fact_3626_take__bit__Suc__minus__1__eq,axiom,
% 0.33/0.58 ! [N2: nat] :
% 0.33/0.58 ( ( bit_se1745604003318907178nteger @ ( suc @ N2 ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.33/0.58 = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) @ one_one_Code_integer ) ) ).
% 0.33/0.58
% 0.33/0.58 % take_bit_Suc_minus_1_eq
% 0.33/0.58 thf(fact_3627_take__bit__Suc__minus__1__eq,axiom,
% 0.33/0.58 ! [N2: nat] :
% 0.33/0.58 ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ ( uminus_uminus_int @ one_one_int ) )
% 0.33/0.58 = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) @ one_one_int ) ) ).
% 0.33/0.58
% 0.33/0.58 % take_bit_Suc_minus_1_eq
% 0.33/0.58 thf(fact_3628_take__bit__Suc,axiom,
% 0.33/0.58 ! [N2: nat,A: code_integer] :
% 0.33/0.58 ( ( bit_se1745604003318907178nteger @ ( suc @ N2 ) @ A )
% 0.33/0.58 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( bit_se1745604003318907178nteger @ N2 @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % take_bit_Suc
% 0.33/0.58 thf(fact_3629_take__bit__Suc,axiom,
% 0.33/0.58 ! [N2: nat,A: int] :
% 0.33/0.58 ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ A )
% 0.33/0.58 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N2 @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % take_bit_Suc
% 0.33/0.58 thf(fact_3630_take__bit__Suc,axiom,
% 0.33/0.58 ! [N2: nat,A: nat] :
% 0.33/0.58 ( ( bit_se2925701944663578781it_nat @ ( suc @ N2 ) @ A )
% 0.33/0.58 = ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ N2 @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % take_bit_Suc
% 0.33/0.58 thf(fact_3631_take__bit__Suc,axiom,
% 0.33/0.58 ! [N2: nat,A: code_natural] :
% 0.33/0.58 ( ( bit_se569199155075624693atural @ ( suc @ N2 ) @ A )
% 0.33/0.58 = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( bit_se569199155075624693atural @ N2 @ ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) @ ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % take_bit_Suc
% 0.33/0.58 thf(fact_3632_take__bit__numeral__minus__1__eq,axiom,
% 0.33/0.58 ! [K: num] :
% 0.33/0.58 ( ( bit_se1745604003318907178nteger @ ( numeral_numeral_nat @ K ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.33/0.58 = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ K ) ) @ one_one_Code_integer ) ) ).
% 0.33/0.58
% 0.33/0.58 % take_bit_numeral_minus_1_eq
% 0.33/0.58 thf(fact_3633_take__bit__numeral__minus__1__eq,axiom,
% 0.33/0.58 ! [K: num] :
% 0.33/0.58 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ K ) @ ( uminus_uminus_int @ one_one_int ) )
% 0.33/0.58 = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ K ) ) @ one_one_int ) ) ).
% 0.33/0.58
% 0.33/0.58 % take_bit_numeral_minus_1_eq
% 0.33/0.58 thf(fact_3634_even__mask__div__iff_H,axiom,
% 0.33/0.58 ! [M2: nat,N2: nat] :
% 0.33/0.58 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 ) @ one_one_int ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) )
% 0.33/0.58 = ( ord_less_eq_nat @ M2 @ N2 ) ) ).
% 0.33/0.58
% 0.33/0.58 % even_mask_div_iff'
% 0.33/0.58 thf(fact_3635_even__mask__div__iff_H,axiom,
% 0.33/0.58 ! [M2: nat,N2: nat] :
% 0.33/0.58 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ one_one_nat ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 0.33/0.58 = ( ord_less_eq_nat @ M2 @ N2 ) ) ).
% 0.33/0.58
% 0.33/0.58 % even_mask_div_iff'
% 0.33/0.58 thf(fact_3636_even__mask__div__iff_H,axiom,
% 0.33/0.58 ! [M2: nat,N2: nat] :
% 0.33/0.58 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M2 ) @ one_one_Code_integer ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) )
% 0.33/0.58 = ( ord_less_eq_nat @ M2 @ N2 ) ) ).
% 0.33/0.58
% 0.33/0.58 % even_mask_div_iff'
% 0.33/0.58 thf(fact_3637_even__mask__div__iff_H,axiom,
% 0.33/0.58 ! [M2: nat,N2: nat] :
% 0.33/0.58 ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( divide5121882707175180666atural @ ( minus_7197305767214868737atural @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ M2 ) @ one_one_Code_natural ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N2 ) ) )
% 0.33/0.58 = ( ord_less_eq_nat @ M2 @ N2 ) ) ).
% 0.33/0.58
% 0.33/0.58 % even_mask_div_iff'
% 0.33/0.58 thf(fact_3638_even__mask__div__iff,axiom,
% 0.33/0.58 ! [M2: nat,N2: nat] :
% 0.33/0.58 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 ) @ one_one_int ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) )
% 0.33/0.58 = ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 )
% 0.33/0.58 = zero_zero_int )
% 0.33/0.58 | ( ord_less_eq_nat @ M2 @ N2 ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % even_mask_div_iff
% 0.33/0.58 thf(fact_3639_even__mask__div__iff,axiom,
% 0.33/0.58 ! [M2: nat,N2: nat] :
% 0.33/0.58 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ one_one_nat ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 0.33/0.58 = ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.33/0.58 = zero_zero_nat )
% 0.33/0.58 | ( ord_less_eq_nat @ M2 @ N2 ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % even_mask_div_iff
% 0.33/0.58 thf(fact_3640_even__mask__div__iff,axiom,
% 0.33/0.58 ! [M2: nat,N2: nat] :
% 0.33/0.58 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M2 ) @ one_one_Code_integer ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) )
% 0.33/0.58 = ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 )
% 0.33/0.58 = zero_z3403309356797280102nteger )
% 0.33/0.58 | ( ord_less_eq_nat @ M2 @ N2 ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % even_mask_div_iff
% 0.33/0.58 thf(fact_3641_even__mask__div__iff,axiom,
% 0.33/0.58 ! [M2: nat,N2: nat] :
% 0.33/0.58 ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( divide5121882707175180666atural @ ( minus_7197305767214868737atural @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ M2 ) @ one_one_Code_natural ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N2 ) ) )
% 0.33/0.58 = ( ( ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N2 )
% 0.33/0.58 = zero_z2226904508553997617atural )
% 0.33/0.58 | ( ord_less_eq_nat @ M2 @ N2 ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % even_mask_div_iff
% 0.33/0.58 thf(fact_3642_Code__Numeral_Onegative__def,axiom,
% 0.33/0.58 ( code_negative
% 0.33/0.58 = ( comp_C3531382070062128313er_num @ uminus1351360451143612070nteger @ numera6620942414471956472nteger ) ) ).
% 0.33/0.58
% 0.33/0.58 % Code_Numeral.negative_def
% 0.33/0.58 thf(fact_3643_take__bit__numeral__minus__numeral__int,axiom,
% 0.33/0.58 ! [M2: num,N2: num] :
% 0.33/0.58 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ M2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 0.33/0.58 = ( case_option_int_num @ zero_zero_int
% 0.33/0.58 @ ^ [Q5: num] : ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ M2 ) @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ M2 ) ) @ ( numeral_numeral_int @ Q5 ) ) )
% 0.33/0.58 @ ( bit_take_bit_num @ ( numeral_numeral_nat @ M2 ) @ N2 ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % take_bit_numeral_minus_numeral_int
% 0.33/0.58 thf(fact_3644_signed__take__bit__numeral__minus__bit1,axiom,
% 0.33/0.58 ! [L: num,K: num] :
% 0.33/0.58 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 0.33/0.58 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L ) @ ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 0.33/0.58
% 0.33/0.58 % signed_take_bit_numeral_minus_bit1
% 0.33/0.58 thf(fact_3645_execute__change,axiom,
% 0.33/0.58 ! [F: array_a > array_a,R2: ref_array_a,H3: heap_e7401611519738050253t_unit] :
% 0.33/0.58 ( ( heap_T5591663578999710211rray_a @ ( ref_change_array_a @ F @ R2 ) @ H3 )
% 0.33/0.58 = ( some_P6105628898608307625it_nat @ ( produc1733996804261680252it_nat @ ( F @ ( ref_get_array_a @ H3 @ R2 ) ) @ ( produc584006145561248582it_nat @ ( ref_set_array_a @ R2 @ ( F @ ( ref_get_array_a @ H3 @ R2 ) ) @ H3 ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % execute_change
% 0.33/0.58 thf(fact_3646_execute__change,axiom,
% 0.33/0.58 ! [F: product_unit > product_unit,R2: ref_Product_unit,H3: heap_e7401611519738050253t_unit] :
% 0.33/0.58 ( ( heap_T875086893843062177t_unit @ ( ref_ch7259622376331601608t_unit @ F @ R2 ) @ H3 )
% 0.33/0.58 = ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ ( F @ ( ref_get_Product_unit @ H3 @ R2 ) ) @ ( produc584006145561248582it_nat @ ( ref_set_Product_unit @ R2 @ ( F @ ( ref_get_Product_unit @ H3 @ R2 ) ) @ H3 ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % execute_change
% 0.33/0.58 thf(fact_3647_signed__take__bit__numeral__bit1,axiom,
% 0.33/0.58 ! [L: num,K: num] :
% 0.33/0.58 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 0.33/0.58 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 0.33/0.58
% 0.33/0.58 % signed_take_bit_numeral_bit1
% 0.33/0.58 thf(fact_3648_take__bit__Suc__minus__bit1,axiom,
% 0.33/0.58 ! [N2: nat,K: num] :
% 0.33/0.58 ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 0.33/0.58 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 0.33/0.58
% 0.33/0.58 % take_bit_Suc_minus_bit1
% 0.33/0.58 thf(fact_3649_divmod__BitM__2__eq,axiom,
% 0.33/0.58 ! [M2: num] :
% 0.33/0.58 ( ( unique5052692396658037445od_int @ ( bitM @ M2 ) @ ( bit0 @ one ) )
% 0.33/0.58 = ( product_Pair_int_int @ ( minus_minus_int @ ( numeral_numeral_int @ M2 ) @ one_one_int ) @ one_one_int ) ) ).
% 0.33/0.58
% 0.33/0.58 % divmod_BitM_2_eq
% 0.33/0.58 thf(fact_3650_flip__bit__0,axiom,
% 0.33/0.58 ! [A: code_integer] :
% 0.33/0.58 ( ( bit_se1345352211410354436nteger @ zero_zero_nat @ A )
% 0.33/0.58 = ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % flip_bit_0
% 0.33/0.58 thf(fact_3651_flip__bit__0,axiom,
% 0.33/0.58 ! [A: int] :
% 0.33/0.58 ( ( bit_se2159334234014336723it_int @ zero_zero_nat @ A )
% 0.33/0.58 = ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % flip_bit_0
% 0.33/0.58 thf(fact_3652_flip__bit__0,axiom,
% 0.33/0.58 ! [A: nat] :
% 0.33/0.58 ( ( bit_se2161824704523386999it_nat @ zero_zero_nat @ A )
% 0.33/0.58 = ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % flip_bit_0
% 0.33/0.58 thf(fact_3653_flip__bit__0,axiom,
% 0.33/0.58 ! [A: code_natural] :
% 0.33/0.58 ( ( bit_se168947363167071951atural @ zero_zero_nat @ A )
% 0.33/0.58 = ( plus_p4538020629002901425atural @ ( zero_n8403883297036319079atural @ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A ) ) @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % flip_bit_0
% 0.33/0.58 thf(fact_3654_of__bool__eq_I2_J,axiom,
% 0.33/0.58 ( ( zero_n2052037380579107095ol_rat @ $true )
% 0.33/0.58 = one_one_rat ) ).
% 0.33/0.58
% 0.33/0.58 % of_bool_eq(2)
% 0.33/0.58 thf(fact_3655_of__bool__eq_I2_J,axiom,
% 0.33/0.58 ( ( zero_n2687167440665602831ol_nat @ $true )
% 0.33/0.58 = one_one_nat ) ).
% 0.33/0.58
% 0.33/0.58 % of_bool_eq(2)
% 0.33/0.58 thf(fact_3656_of__bool__eq_I2_J,axiom,
% 0.33/0.58 ( ( zero_n2684676970156552555ol_int @ $true )
% 0.33/0.58 = one_one_int ) ).
% 0.33/0.58
% 0.33/0.58 % of_bool_eq(2)
% 0.33/0.58 thf(fact_3657_of__bool__eq_I2_J,axiom,
% 0.33/0.58 ( ( zero_n356916108424825756nteger @ $true )
% 0.33/0.58 = one_one_Code_integer ) ).
% 0.33/0.58
% 0.33/0.58 % of_bool_eq(2)
% 0.33/0.58 thf(fact_3658_of__bool__eq__1__iff,axiom,
% 0.33/0.58 ! [P: $o] :
% 0.33/0.58 ( ( ( zero_n2052037380579107095ol_rat @ P )
% 0.33/0.58 = one_one_rat )
% 0.33/0.58 = P ) ).
% 0.33/0.58
% 0.33/0.58 % of_bool_eq_1_iff
% 0.33/0.58 thf(fact_3659_of__bool__eq__1__iff,axiom,
% 0.33/0.58 ! [P: $o] :
% 0.33/0.58 ( ( ( zero_n2687167440665602831ol_nat @ P )
% 0.33/0.58 = one_one_nat )
% 0.33/0.58 = P ) ).
% 0.33/0.58
% 0.33/0.58 % of_bool_eq_1_iff
% 0.33/0.58 thf(fact_3660_of__bool__eq__1__iff,axiom,
% 0.33/0.58 ! [P: $o] :
% 0.33/0.58 ( ( ( zero_n2684676970156552555ol_int @ P )
% 0.33/0.58 = one_one_int )
% 0.33/0.58 = P ) ).
% 0.33/0.58
% 0.33/0.58 % of_bool_eq_1_iff
% 0.33/0.58 thf(fact_3661_of__bool__eq__1__iff,axiom,
% 0.33/0.58 ! [P: $o] :
% 0.33/0.58 ( ( ( zero_n356916108424825756nteger @ P )
% 0.33/0.58 = one_one_Code_integer )
% 0.33/0.58 = P ) ).
% 0.33/0.58
% 0.33/0.58 % of_bool_eq_1_iff
% 0.33/0.58 thf(fact_3662_of__bool__less__one__iff,axiom,
% 0.33/0.58 ! [P: $o] :
% 0.33/0.58 ( ( ord_less_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ one_one_rat )
% 0.33/0.58 = ( ~ P ) ) ).
% 0.33/0.58
% 0.33/0.58 % of_bool_less_one_iff
% 0.33/0.58 thf(fact_3663_of__bool__less__one__iff,axiom,
% 0.33/0.58 ! [P: $o] :
% 0.33/0.58 ( ( ord_less_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ one_one_nat )
% 0.33/0.58 = ( ~ P ) ) ).
% 0.33/0.58
% 0.33/0.58 % of_bool_less_one_iff
% 0.33/0.58 thf(fact_3664_of__bool__less__one__iff,axiom,
% 0.33/0.58 ! [P: $o] :
% 0.33/0.58 ( ( ord_less_int @ ( zero_n2684676970156552555ol_int @ P ) @ one_one_int )
% 0.33/0.58 = ( ~ P ) ) ).
% 0.33/0.58
% 0.33/0.58 % of_bool_less_one_iff
% 0.33/0.58 thf(fact_3665_of__bool__less__one__iff,axiom,
% 0.33/0.58 ! [P: $o] :
% 0.33/0.58 ( ( ord_le6747313008572928689nteger @ ( zero_n356916108424825756nteger @ P ) @ one_one_Code_integer )
% 0.33/0.58 = ( ~ P ) ) ).
% 0.33/0.58
% 0.33/0.58 % of_bool_less_one_iff
% 0.33/0.58 thf(fact_3666_of__bool__not__iff,axiom,
% 0.33/0.58 ! [P: $o] :
% 0.33/0.58 ( ( zero_n2052037380579107095ol_rat @ ~ P )
% 0.33/0.58 = ( minus_minus_rat @ one_one_rat @ ( zero_n2052037380579107095ol_rat @ P ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % of_bool_not_iff
% 0.33/0.58 thf(fact_3667_of__bool__not__iff,axiom,
% 0.33/0.58 ! [P: $o] :
% 0.33/0.58 ( ( zero_n2684676970156552555ol_int @ ~ P )
% 0.33/0.58 = ( minus_minus_int @ one_one_int @ ( zero_n2684676970156552555ol_int @ P ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % of_bool_not_iff
% 0.33/0.58 thf(fact_3668_of__bool__not__iff,axiom,
% 0.33/0.58 ! [P: $o] :
% 0.33/0.58 ( ( zero_n356916108424825756nteger @ ~ P )
% 0.33/0.58 = ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( zero_n356916108424825756nteger @ P ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % of_bool_not_iff
% 0.33/0.58 thf(fact_3669_take__bit__num__simps_I3_J,axiom,
% 0.33/0.58 ! [N2: nat,M2: num] :
% 0.33/0.58 ( ( bit_take_bit_num @ ( suc @ N2 ) @ ( bit0 @ M2 ) )
% 0.33/0.58 = ( case_o6005452278849405969um_num @ none_num
% 0.33/0.58 @ ^ [Q5: num] : ( some_num @ ( bit0 @ Q5 ) )
% 0.33/0.58 @ ( bit_take_bit_num @ N2 @ M2 ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % take_bit_num_simps(3)
% 0.33/0.58 thf(fact_3670_take__bit__num__simps_I4_J,axiom,
% 0.33/0.58 ! [N2: nat,M2: num] :
% 0.33/0.58 ( ( bit_take_bit_num @ ( suc @ N2 ) @ ( bit1 @ M2 ) )
% 0.33/0.58 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ N2 @ M2 ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % take_bit_num_simps(4)
% 0.33/0.58 thf(fact_3671_take__bit__num__simps_I6_J,axiom,
% 0.33/0.58 ! [R2: num,M2: num] :
% 0.33/0.58 ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R2 ) @ ( bit0 @ M2 ) )
% 0.33/0.58 = ( case_o6005452278849405969um_num @ none_num
% 0.33/0.58 @ ^ [Q5: num] : ( some_num @ ( bit0 @ Q5 ) )
% 0.33/0.58 @ ( bit_take_bit_num @ ( pred_numeral @ R2 ) @ M2 ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % take_bit_num_simps(6)
% 0.33/0.58 thf(fact_3672_take__bit__of__1,axiom,
% 0.33/0.58 ! [N2: nat] :
% 0.33/0.58 ( ( bit_se1745604003318907178nteger @ N2 @ one_one_Code_integer )
% 0.33/0.58 = ( zero_n356916108424825756nteger @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % take_bit_of_1
% 0.33/0.58 thf(fact_3673_take__bit__of__1,axiom,
% 0.33/0.58 ! [N2: nat] :
% 0.33/0.58 ( ( bit_se2923211474154528505it_int @ N2 @ one_one_int )
% 0.33/0.58 = ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % take_bit_of_1
% 0.33/0.58 thf(fact_3674_take__bit__of__1,axiom,
% 0.33/0.58 ! [N2: nat] :
% 0.33/0.58 ( ( bit_se2925701944663578781it_nat @ N2 @ one_one_nat )
% 0.33/0.58 = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % take_bit_of_1
% 0.33/0.58 thf(fact_3675_take__bit__of__1,axiom,
% 0.33/0.58 ! [N2: nat] :
% 0.33/0.58 ( ( bit_se569199155075624693atural @ N2 @ one_one_Code_natural )
% 0.33/0.58 = ( zero_n8403883297036319079atural @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % take_bit_of_1
% 0.33/0.58 thf(fact_3676_add__neg__numeral__special_I6_J,axiom,
% 0.33/0.58 ! [M2: num] :
% 0.33/0.58 ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( uminus_uminus_int @ one_one_int ) )
% 0.33/0.58 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ M2 ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % add_neg_numeral_special(6)
% 0.33/0.58 thf(fact_3677_add__neg__numeral__special_I6_J,axiom,
% 0.33/0.58 ! [M2: num] :
% 0.33/0.58 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.33/0.58 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ M2 ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % add_neg_numeral_special(6)
% 0.33/0.58 thf(fact_3678_add__neg__numeral__special_I6_J,axiom,
% 0.33/0.58 ! [M2: num] :
% 0.33/0.58 ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.33/0.58 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( inc @ M2 ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % add_neg_numeral_special(6)
% 0.33/0.58 thf(fact_3679_add__neg__numeral__special_I5_J,axiom,
% 0.33/0.58 ! [N2: num] :
% 0.33/0.58 ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 0.33/0.58 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ N2 ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % add_neg_numeral_special(5)
% 0.33/0.58 thf(fact_3680_add__neg__numeral__special_I5_J,axiom,
% 0.33/0.58 ! [N2: num] :
% 0.33/0.58 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 0.33/0.58 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ N2 ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % add_neg_numeral_special(5)
% 0.33/0.58 thf(fact_3681_add__neg__numeral__special_I5_J,axiom,
% 0.33/0.58 ! [N2: num] :
% 0.33/0.58 ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 0.33/0.58 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( inc @ N2 ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % add_neg_numeral_special(5)
% 0.33/0.58 thf(fact_3682_diff__numeral__special_I5_J,axiom,
% 0.33/0.58 ! [N2: num] :
% 0.33/0.58 ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N2 ) )
% 0.33/0.58 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ N2 ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % diff_numeral_special(5)
% 0.33/0.58 thf(fact_3683_diff__numeral__special_I5_J,axiom,
% 0.33/0.58 ! [N2: num] :
% 0.33/0.58 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ N2 ) )
% 0.33/0.58 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ N2 ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % diff_numeral_special(5)
% 0.33/0.58 thf(fact_3684_diff__numeral__special_I5_J,axiom,
% 0.33/0.58 ! [N2: num] :
% 0.33/0.58 ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ N2 ) )
% 0.33/0.58 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( inc @ N2 ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % diff_numeral_special(5)
% 0.33/0.58 thf(fact_3685_diff__numeral__special_I6_J,axiom,
% 0.33/0.58 ! [M2: num] :
% 0.33/0.58 ( ( minus_minus_int @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ one_one_int ) )
% 0.33/0.58 = ( numeral_numeral_int @ ( inc @ M2 ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % diff_numeral_special(6)
% 0.33/0.58 thf(fact_3686_diff__numeral__special_I6_J,axiom,
% 0.33/0.58 ! [M2: num] :
% 0.33/0.58 ( ( minus_8373710615458151222nteger @ ( numera6620942414471956472nteger @ M2 ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.33/0.58 = ( numera6620942414471956472nteger @ ( inc @ M2 ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % diff_numeral_special(6)
% 0.33/0.58 thf(fact_3687_diff__numeral__special_I6_J,axiom,
% 0.33/0.58 ! [M2: num] :
% 0.33/0.58 ( ( minus_minus_rat @ ( numeral_numeral_rat @ M2 ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.33/0.58 = ( numeral_numeral_rat @ ( inc @ M2 ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % diff_numeral_special(6)
% 0.33/0.58 thf(fact_3688_take__bit__num__simps_I7_J,axiom,
% 0.33/0.58 ! [R2: num,M2: num] :
% 0.33/0.58 ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R2 ) @ ( bit1 @ M2 ) )
% 0.33/0.58 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ ( pred_numeral @ R2 ) @ M2 ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % take_bit_num_simps(7)
% 0.33/0.58 thf(fact_3689_take__bit__numeral__numeral,axiom,
% 0.33/0.58 ! [M2: num,N2: num] :
% 0.33/0.58 ( ( bit_se1745604003318907178nteger @ ( numeral_numeral_nat @ M2 ) @ ( numera6620942414471956472nteger @ N2 ) )
% 0.33/0.58 = ( case_o356765784539232260er_num @ zero_z3403309356797280102nteger @ numera6620942414471956472nteger @ ( bit_take_bit_num @ ( numeral_numeral_nat @ M2 ) @ N2 ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % take_bit_numeral_numeral
% 0.33/0.58 thf(fact_3690_take__bit__numeral__numeral,axiom,
% 0.33/0.58 ! [M2: num,N2: num] :
% 0.33/0.58 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_int @ N2 ) )
% 0.33/0.58 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_take_bit_num @ ( numeral_numeral_nat @ M2 ) @ N2 ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % take_bit_numeral_numeral
% 0.33/0.58 thf(fact_3691_take__bit__numeral__numeral,axiom,
% 0.33/0.58 ! [M2: num,N2: num] :
% 0.33/0.58 ( ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ N2 ) )
% 0.33/0.58 = ( case_option_nat_num @ zero_zero_nat @ numeral_numeral_nat @ ( bit_take_bit_num @ ( numeral_numeral_nat @ M2 ) @ N2 ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % take_bit_numeral_numeral
% 0.33/0.58 thf(fact_3692_take__bit__numeral__numeral,axiom,
% 0.33/0.58 ! [M2: num,N2: num] :
% 0.33/0.58 ( ( bit_se569199155075624693atural @ ( numeral_numeral_nat @ M2 ) @ ( numera5444537566228673987atural @ N2 ) )
% 0.33/0.58 = ( case_o5621594795226839503al_num @ zero_z2226904508553997617atural @ numera5444537566228673987atural @ ( bit_take_bit_num @ ( numeral_numeral_nat @ M2 ) @ N2 ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % take_bit_numeral_numeral
% 0.33/0.58 thf(fact_3693_bits__1__div__exp,axiom,
% 0.33/0.58 ! [N2: nat] :
% 0.33/0.58 ( ( divide5121882707175180666atural @ one_one_Code_natural @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N2 ) )
% 0.33/0.58 = ( zero_n8403883297036319079atural @ ( N2 = zero_zero_nat ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % bits_1_div_exp
% 0.33/0.58 thf(fact_3694_bits__1__div__exp,axiom,
% 0.33/0.58 ! [N2: nat] :
% 0.33/0.58 ( ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 0.33/0.58 = ( zero_n2687167440665602831ol_nat @ ( N2 = zero_zero_nat ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % bits_1_div_exp
% 0.33/0.58 thf(fact_3695_bits__1__div__exp,axiom,
% 0.33/0.58 ! [N2: nat] :
% 0.33/0.58 ( ( divide_divide_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 0.33/0.58 = ( zero_n2684676970156552555ol_int @ ( N2 = zero_zero_nat ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % bits_1_div_exp
% 0.33/0.58 thf(fact_3696_bits__1__div__exp,axiom,
% 0.33/0.58 ! [N2: nat] :
% 0.33/0.58 ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 0.33/0.58 = ( zero_n356916108424825756nteger @ ( N2 = zero_zero_nat ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % bits_1_div_exp
% 0.33/0.58 thf(fact_3697_one__div__2__pow__eq,axiom,
% 0.33/0.58 ! [N2: nat] :
% 0.33/0.58 ( ( divide5121882707175180666atural @ one_one_Code_natural @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N2 ) )
% 0.33/0.58 = ( zero_n8403883297036319079atural @ ( N2 = zero_zero_nat ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % one_div_2_pow_eq
% 0.33/0.58 thf(fact_3698_one__div__2__pow__eq,axiom,
% 0.33/0.58 ! [N2: nat] :
% 0.33/0.58 ( ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 0.33/0.58 = ( zero_n2687167440665602831ol_nat @ ( N2 = zero_zero_nat ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % one_div_2_pow_eq
% 0.33/0.58 thf(fact_3699_one__div__2__pow__eq,axiom,
% 0.33/0.58 ! [N2: nat] :
% 0.33/0.58 ( ( divide_divide_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 0.33/0.58 = ( zero_n2684676970156552555ol_int @ ( N2 = zero_zero_nat ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % one_div_2_pow_eq
% 0.33/0.58 thf(fact_3700_one__div__2__pow__eq,axiom,
% 0.33/0.58 ! [N2: nat] :
% 0.33/0.58 ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 0.33/0.58 = ( zero_n356916108424825756nteger @ ( N2 = zero_zero_nat ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % one_div_2_pow_eq
% 0.33/0.58 thf(fact_3701_one__mod__2__pow__eq,axiom,
% 0.33/0.58 ! [N2: nat] :
% 0.33/0.58 ( ( modulo8411746178871703098atural @ one_one_Code_natural @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N2 ) )
% 0.33/0.58 = ( zero_n8403883297036319079atural @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % one_mod_2_pow_eq
% 0.33/0.58 thf(fact_3702_one__mod__2__pow__eq,axiom,
% 0.33/0.58 ! [N2: nat] :
% 0.33/0.58 ( ( modulo_modulo_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 0.33/0.58 = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % one_mod_2_pow_eq
% 0.33/0.58 thf(fact_3703_one__mod__2__pow__eq,axiom,
% 0.33/0.58 ! [N2: nat] :
% 0.33/0.58 ( ( modulo_modulo_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 0.33/0.58 = ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % one_mod_2_pow_eq
% 0.33/0.58 thf(fact_3704_one__mod__2__pow__eq,axiom,
% 0.33/0.58 ! [N2: nat] :
% 0.33/0.58 ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 0.33/0.58 = ( zero_n356916108424825756nteger @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % one_mod_2_pow_eq
% 0.33/0.58 thf(fact_3705_mult__inc,axiom,
% 0.33/0.58 ! [X: num,Y: num] :
% 0.33/0.58 ( ( times_times_num @ X @ ( inc @ Y ) )
% 0.33/0.58 = ( plus_plus_num @ ( times_times_num @ X @ Y ) @ X ) ) ).
% 0.33/0.58
% 0.33/0.58 % mult_inc
% 0.33/0.58 thf(fact_3706_add__inc,axiom,
% 0.33/0.58 ! [X: num,Y: num] :
% 0.33/0.58 ( ( plus_plus_num @ X @ ( inc @ Y ) )
% 0.33/0.58 = ( inc @ ( plus_plus_num @ X @ Y ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % add_inc
% 0.33/0.58 thf(fact_3707_of__bool__less__eq__one,axiom,
% 0.33/0.58 ! [P: $o] : ( ord_less_eq_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ one_one_rat ) ).
% 0.33/0.58
% 0.33/0.58 % of_bool_less_eq_one
% 0.33/0.58 thf(fact_3708_of__bool__less__eq__one,axiom,
% 0.33/0.58 ! [P: $o] : ( ord_less_eq_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ one_one_nat ) ).
% 0.33/0.58
% 0.33/0.58 % of_bool_less_eq_one
% 0.33/0.58 thf(fact_3709_of__bool__less__eq__one,axiom,
% 0.33/0.58 ! [P: $o] : ( ord_less_eq_int @ ( zero_n2684676970156552555ol_int @ P ) @ one_one_int ) ).
% 0.33/0.58
% 0.33/0.58 % of_bool_less_eq_one
% 0.33/0.58 thf(fact_3710_of__bool__less__eq__one,axiom,
% 0.33/0.58 ! [P: $o] : ( ord_le3102999989581377725nteger @ ( zero_n356916108424825756nteger @ P ) @ one_one_Code_integer ) ).
% 0.33/0.58
% 0.33/0.58 % of_bool_less_eq_one
% 0.33/0.58 thf(fact_3711_of__bool__def,axiom,
% 0.33/0.58 ( zero_n2052037380579107095ol_rat
% 0.33/0.58 = ( ^ [P6: $o] : ( if_rat @ P6 @ one_one_rat @ zero_zero_rat ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % of_bool_def
% 0.33/0.58 thf(fact_3712_of__bool__def,axiom,
% 0.33/0.58 ( zero_n2687167440665602831ol_nat
% 0.33/0.58 = ( ^ [P6: $o] : ( if_nat @ P6 @ one_one_nat @ zero_zero_nat ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % of_bool_def
% 0.33/0.58 thf(fact_3713_of__bool__def,axiom,
% 0.33/0.58 ( zero_n2684676970156552555ol_int
% 0.33/0.58 = ( ^ [P6: $o] : ( if_int @ P6 @ one_one_int @ zero_zero_int ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % of_bool_def
% 0.33/0.58 thf(fact_3714_of__bool__def,axiom,
% 0.33/0.58 ( zero_n356916108424825756nteger
% 0.33/0.58 = ( ^ [P6: $o] : ( if_Code_integer @ P6 @ one_one_Code_integer @ zero_z3403309356797280102nteger ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % of_bool_def
% 0.33/0.58 thf(fact_3715_split__of__bool,axiom,
% 0.33/0.58 ! [P: rat > $o,P4: $o] :
% 0.33/0.58 ( ( P @ ( zero_n2052037380579107095ol_rat @ P4 ) )
% 0.33/0.58 = ( ( P4
% 0.33/0.58 => ( P @ one_one_rat ) )
% 0.33/0.58 & ( ~ P4
% 0.33/0.58 => ( P @ zero_zero_rat ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % split_of_bool
% 0.33/0.58 thf(fact_3716_split__of__bool,axiom,
% 0.33/0.58 ! [P: nat > $o,P4: $o] :
% 0.33/0.58 ( ( P @ ( zero_n2687167440665602831ol_nat @ P4 ) )
% 0.33/0.58 = ( ( P4
% 0.33/0.58 => ( P @ one_one_nat ) )
% 0.33/0.58 & ( ~ P4
% 0.33/0.58 => ( P @ zero_zero_nat ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % split_of_bool
% 0.33/0.58 thf(fact_3717_split__of__bool,axiom,
% 0.33/0.58 ! [P: int > $o,P4: $o] :
% 0.33/0.58 ( ( P @ ( zero_n2684676970156552555ol_int @ P4 ) )
% 0.33/0.58 = ( ( P4
% 0.33/0.58 => ( P @ one_one_int ) )
% 0.33/0.58 & ( ~ P4
% 0.33/0.58 => ( P @ zero_zero_int ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % split_of_bool
% 0.33/0.58 thf(fact_3718_split__of__bool,axiom,
% 0.33/0.58 ! [P: code_integer > $o,P4: $o] :
% 0.33/0.58 ( ( P @ ( zero_n356916108424825756nteger @ P4 ) )
% 0.33/0.58 = ( ( P4
% 0.33/0.58 => ( P @ one_one_Code_integer ) )
% 0.33/0.58 & ( ~ P4
% 0.33/0.58 => ( P @ zero_z3403309356797280102nteger ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % split_of_bool
% 0.33/0.58 thf(fact_3719_split__of__bool__asm,axiom,
% 0.33/0.58 ! [P: rat > $o,P4: $o] :
% 0.33/0.58 ( ( P @ ( zero_n2052037380579107095ol_rat @ P4 ) )
% 0.33/0.58 = ( ~ ( ( P4
% 0.33/0.58 & ~ ( P @ one_one_rat ) )
% 0.33/0.58 | ( ~ P4
% 0.33/0.58 & ~ ( P @ zero_zero_rat ) ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % split_of_bool_asm
% 0.33/0.58 thf(fact_3720_split__of__bool__asm,axiom,
% 0.33/0.58 ! [P: nat > $o,P4: $o] :
% 0.33/0.58 ( ( P @ ( zero_n2687167440665602831ol_nat @ P4 ) )
% 0.33/0.58 = ( ~ ( ( P4
% 0.33/0.58 & ~ ( P @ one_one_nat ) )
% 0.33/0.58 | ( ~ P4
% 0.33/0.58 & ~ ( P @ zero_zero_nat ) ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % split_of_bool_asm
% 0.33/0.58 thf(fact_3721_split__of__bool__asm,axiom,
% 0.33/0.58 ! [P: int > $o,P4: $o] :
% 0.33/0.58 ( ( P @ ( zero_n2684676970156552555ol_int @ P4 ) )
% 0.33/0.58 = ( ~ ( ( P4
% 0.33/0.58 & ~ ( P @ one_one_int ) )
% 0.33/0.58 | ( ~ P4
% 0.33/0.58 & ~ ( P @ zero_zero_int ) ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % split_of_bool_asm
% 0.33/0.58 thf(fact_3722_split__of__bool__asm,axiom,
% 0.33/0.58 ! [P: code_integer > $o,P4: $o] :
% 0.33/0.58 ( ( P @ ( zero_n356916108424825756nteger @ P4 ) )
% 0.33/0.58 = ( ~ ( ( P4
% 0.33/0.58 & ~ ( P @ one_one_Code_integer ) )
% 0.33/0.58 | ( ~ P4
% 0.33/0.58 & ~ ( P @ zero_z3403309356797280102nteger ) ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % split_of_bool_asm
% 0.33/0.58 thf(fact_3723_add__One,axiom,
% 0.33/0.58 ! [X: num] :
% 0.33/0.58 ( ( plus_plus_num @ X @ one )
% 0.33/0.58 = ( inc @ X ) ) ).
% 0.33/0.58
% 0.33/0.58 % add_One
% 0.33/0.58 thf(fact_3724_pred__numeral__def,axiom,
% 0.33/0.58 ( pred_numeral
% 0.33/0.58 = ( ^ [K4: num] : ( minus_minus_nat @ ( numeral_numeral_nat @ K4 ) @ one_one_nat ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % pred_numeral_def
% 0.33/0.58 thf(fact_3725_BitM__plus__one,axiom,
% 0.33/0.58 ! [N2: num] :
% 0.33/0.58 ( ( plus_plus_num @ ( bitM @ N2 ) @ one )
% 0.33/0.58 = ( bit0 @ N2 ) ) ).
% 0.33/0.58
% 0.33/0.58 % BitM_plus_one
% 0.33/0.58 thf(fact_3726_one__plus__BitM,axiom,
% 0.33/0.58 ! [N2: num] :
% 0.33/0.58 ( ( plus_plus_num @ one @ ( bitM @ N2 ) )
% 0.33/0.58 = ( bit0 @ N2 ) ) ).
% 0.33/0.58
% 0.33/0.58 % one_plus_BitM
% 0.33/0.58 thf(fact_3727_numeral__inc,axiom,
% 0.33/0.58 ! [X: num] :
% 0.33/0.58 ( ( numeral_numeral_nat @ ( inc @ X ) )
% 0.33/0.58 = ( plus_plus_nat @ ( numeral_numeral_nat @ X ) @ one_one_nat ) ) ).
% 0.33/0.58
% 0.33/0.58 % numeral_inc
% 0.33/0.58 thf(fact_3728_numeral__inc,axiom,
% 0.33/0.58 ! [X: num] :
% 0.33/0.58 ( ( numeral_numeral_int @ ( inc @ X ) )
% 0.33/0.58 = ( plus_plus_int @ ( numeral_numeral_int @ X ) @ one_one_int ) ) ).
% 0.33/0.58
% 0.33/0.58 % numeral_inc
% 0.33/0.58 thf(fact_3729_numeral__inc,axiom,
% 0.33/0.58 ! [X: num] :
% 0.33/0.58 ( ( numera6620942414471956472nteger @ ( inc @ X ) )
% 0.33/0.58 = ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ X ) @ one_one_Code_integer ) ) ).
% 0.33/0.58
% 0.33/0.58 % numeral_inc
% 0.33/0.58 thf(fact_3730_numeral__inc,axiom,
% 0.33/0.58 ! [X: num] :
% 0.33/0.58 ( ( numeral_numeral_rat @ ( inc @ X ) )
% 0.33/0.58 = ( plus_plus_rat @ ( numeral_numeral_rat @ X ) @ one_one_rat ) ) ).
% 0.33/0.58
% 0.33/0.58 % numeral_inc
% 0.33/0.58 thf(fact_3731_numeral__inc,axiom,
% 0.33/0.58 ! [X: num] :
% 0.33/0.58 ( ( numera5444537566228673987atural @ ( inc @ X ) )
% 0.33/0.58 = ( plus_p4538020629002901425atural @ ( numera5444537566228673987atural @ X ) @ one_one_Code_natural ) ) ).
% 0.33/0.58
% 0.33/0.58 % numeral_inc
% 0.33/0.58 thf(fact_3732_numeral__BitM,axiom,
% 0.33/0.58 ! [N2: num] :
% 0.33/0.58 ( ( numeral_numeral_int @ ( bitM @ N2 ) )
% 0.33/0.58 = ( minus_minus_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) @ one_one_int ) ) ).
% 0.33/0.58
% 0.33/0.58 % numeral_BitM
% 0.33/0.58 thf(fact_3733_numeral__BitM,axiom,
% 0.33/0.58 ! [N2: num] :
% 0.33/0.58 ( ( numera6620942414471956472nteger @ ( bitM @ N2 ) )
% 0.33/0.58 = ( minus_8373710615458151222nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N2 ) ) @ one_one_Code_integer ) ) ).
% 0.33/0.58
% 0.33/0.58 % numeral_BitM
% 0.33/0.58 thf(fact_3734_numeral__BitM,axiom,
% 0.33/0.58 ! [N2: num] :
% 0.33/0.58 ( ( numeral_numeral_rat @ ( bitM @ N2 ) )
% 0.33/0.58 = ( minus_minus_rat @ ( numeral_numeral_rat @ ( bit0 @ N2 ) ) @ one_one_rat ) ) ).
% 0.33/0.58
% 0.33/0.58 % numeral_BitM
% 0.33/0.58 thf(fact_3735_take__bit__numeral__minus__bit1,axiom,
% 0.33/0.58 ! [L: num,K: num] :
% 0.33/0.58 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 0.33/0.58 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 0.33/0.58
% 0.33/0.58 % take_bit_numeral_minus_bit1
% 0.33/0.58 thf(fact_3736_bits__induct,axiom,
% 0.33/0.58 ! [P: code_natural > $o,A: code_natural] :
% 0.33/0.58 ( ! [A3: code_natural] :
% 0.33/0.58 ( ( ( divide5121882707175180666atural @ A3 @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 0.33/0.58 = A3 )
% 0.33/0.58 => ( P @ A3 ) )
% 0.33/0.58 => ( ! [A3: code_natural,B2: $o] :
% 0.33/0.58 ( ( P @ A3 )
% 0.33/0.58 => ( ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ ( zero_n8403883297036319079atural @ B2 ) @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A3 ) ) @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 0.33/0.58 = A3 )
% 0.33/0.58 => ( P @ ( plus_p4538020629002901425atural @ ( zero_n8403883297036319079atural @ B2 ) @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A3 ) ) ) ) )
% 0.33/0.58 => ( P @ A ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % bits_induct
% 0.33/0.58 thf(fact_3737_bits__induct,axiom,
% 0.33/0.58 ! [P: nat > $o,A: nat] :
% 0.33/0.58 ( ! [A3: nat] :
% 0.33/0.58 ( ( ( divide_divide_nat @ A3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.33/0.58 = A3 )
% 0.33/0.58 => ( P @ A3 ) )
% 0.33/0.58 => ( ! [A3: nat,B2: $o] :
% 0.33/0.58 ( ( P @ A3 )
% 0.33/0.58 => ( ( ( divide_divide_nat @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ B2 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.33/0.58 = A3 )
% 0.33/0.58 => ( P @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ B2 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A3 ) ) ) ) )
% 0.33/0.58 => ( P @ A ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % bits_induct
% 0.33/0.58 thf(fact_3738_bits__induct,axiom,
% 0.33/0.58 ! [P: int > $o,A: int] :
% 0.33/0.58 ( ! [A3: int] :
% 0.33/0.58 ( ( ( divide_divide_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.33/0.58 = A3 )
% 0.33/0.58 => ( P @ A3 ) )
% 0.33/0.58 => ( ! [A3: int,B2: $o] :
% 0.33/0.58 ( ( P @ A3 )
% 0.33/0.58 => ( ( ( divide_divide_int @ ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ B2 ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A3 ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.33/0.58 = A3 )
% 0.33/0.58 => ( P @ ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ B2 ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A3 ) ) ) ) )
% 0.33/0.58 => ( P @ A ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % bits_induct
% 0.33/0.58 thf(fact_3739_bits__induct,axiom,
% 0.33/0.58 ! [P: code_integer > $o,A: code_integer] :
% 0.33/0.58 ( ! [A3: code_integer] :
% 0.33/0.58 ( ( ( divide6298287555418463151nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.33/0.58 = A3 )
% 0.33/0.58 => ( P @ A3 ) )
% 0.33/0.58 => ( ! [A3: code_integer,B2: $o] :
% 0.33/0.58 ( ( P @ A3 )
% 0.33/0.58 => ( ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ B2 ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A3 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.33/0.58 = A3 )
% 0.33/0.58 => ( P @ ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ B2 ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A3 ) ) ) ) )
% 0.33/0.58 => ( P @ A ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % bits_induct
% 0.33/0.58 thf(fact_3740_divide__int__unfold,axiom,
% 0.33/0.58 ! [L: int,K: int,N2: nat,M2: nat] :
% 0.33/0.58 ( ( ( ( ( sgn_sgn_int @ L )
% 0.33/0.58 = zero_zero_int )
% 0.33/0.58 | ( ( sgn_sgn_int @ K )
% 0.33/0.58 = zero_zero_int )
% 0.33/0.58 | ( N2 = zero_zero_nat ) )
% 0.33/0.58 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M2 ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 0.33/0.58 = zero_zero_int ) )
% 0.33/0.58 & ( ~ ( ( ( sgn_sgn_int @ L )
% 0.33/0.58 = zero_zero_int )
% 0.33/0.58 | ( ( sgn_sgn_int @ K )
% 0.33/0.58 = zero_zero_int )
% 0.33/0.58 | ( N2 = zero_zero_nat ) )
% 0.33/0.58 => ( ( ( ( sgn_sgn_int @ K )
% 0.33/0.58 = ( sgn_sgn_int @ L ) )
% 0.33/0.58 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M2 ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 0.33/0.58 = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M2 @ N2 ) ) ) )
% 0.33/0.58 & ( ( ( sgn_sgn_int @ K )
% 0.33/0.58 != ( sgn_sgn_int @ L ) )
% 0.33/0.58 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M2 ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 0.33/0.58 = ( uminus_uminus_int
% 0.33/0.58 @ ( semiri1314217659103216013at_int
% 0.33/0.58 @ ( plus_plus_nat @ ( divide_divide_nat @ M2 @ N2 )
% 0.33/0.58 @ ( zero_n2687167440665602831ol_nat
% 0.33/0.58 @ ~ ( dvd_dvd_nat @ N2 @ M2 ) ) ) ) ) ) ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % divide_int_unfold
% 0.33/0.58 thf(fact_3741_take__bit__numeral__bit1,axiom,
% 0.33/0.58 ! [L: num,K: num] :
% 0.33/0.58 ( ( bit_se1745604003318907178nteger @ ( numeral_numeral_nat @ L ) @ ( numera6620942414471956472nteger @ ( bit1 @ K ) ) )
% 0.33/0.58 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( bit_se1745604003318907178nteger @ ( pred_numeral @ L ) @ ( numera6620942414471956472nteger @ K ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ one_one_Code_integer ) ) ).
% 0.33/0.58
% 0.33/0.58 % take_bit_numeral_bit1
% 0.33/0.58 thf(fact_3742_take__bit__numeral__bit1,axiom,
% 0.33/0.58 ! [L: num,K: num] :
% 0.33/0.58 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 0.33/0.58 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 0.33/0.58
% 0.33/0.58 % take_bit_numeral_bit1
% 0.33/0.58 thf(fact_3743_take__bit__numeral__bit1,axiom,
% 0.33/0.58 ! [L: num,K: num] :
% 0.33/0.58 ( ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 0.33/0.58 = ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ ( pred_numeral @ L ) @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ).
% 0.33/0.58
% 0.33/0.58 % take_bit_numeral_bit1
% 0.33/0.58 thf(fact_3744_take__bit__numeral__bit1,axiom,
% 0.33/0.58 ! [L: num,K: num] :
% 0.33/0.58 ( ( bit_se569199155075624693atural @ ( numeral_numeral_nat @ L ) @ ( numera5444537566228673987atural @ ( bit1 @ K ) ) )
% 0.33/0.58 = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( bit_se569199155075624693atural @ ( pred_numeral @ L ) @ ( numera5444537566228673987atural @ K ) ) @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) @ one_one_Code_natural ) ) ).
% 0.33/0.58
% 0.33/0.58 % take_bit_numeral_bit1
% 0.33/0.58 thf(fact_3745_Divides_Oadjust__div__eq,axiom,
% 0.33/0.58 ! [Q3: int,R2: int] :
% 0.33/0.58 ( ( adjust_div @ ( product_Pair_int_int @ Q3 @ R2 ) )
% 0.33/0.58 = ( plus_plus_int @ Q3 @ ( zero_n2684676970156552555ol_int @ ( R2 != zero_zero_int ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % Divides.adjust_div_eq
% 0.33/0.58 thf(fact_3746_mask__numeral,axiom,
% 0.33/0.58 ! [N2: num] :
% 0.33/0.58 ( ( bit_se2000444600071755411sk_int @ ( numeral_numeral_nat @ N2 ) )
% 0.33/0.58 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2000444600071755411sk_int @ ( pred_numeral @ N2 ) ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % mask_numeral
% 0.33/0.58 thf(fact_3747_mask__numeral,axiom,
% 0.33/0.58 ! [N2: num] :
% 0.33/0.58 ( ( bit_se2119862282449309892nteger @ ( numeral_numeral_nat @ N2 ) )
% 0.33/0.58 = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se2119862282449309892nteger @ ( pred_numeral @ N2 ) ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % mask_numeral
% 0.33/0.58 thf(fact_3748_mask__numeral,axiom,
% 0.33/0.58 ! [N2: num] :
% 0.33/0.58 ( ( bit_se2002935070580805687sk_nat @ ( numeral_numeral_nat @ N2 ) )
% 0.33/0.58 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2002935070580805687sk_nat @ ( pred_numeral @ N2 ) ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % mask_numeral
% 0.33/0.58 thf(fact_3749_mask__numeral,axiom,
% 0.33/0.58 ! [N2: num] :
% 0.33/0.58 ( ( bit_se943457434206027407atural @ ( numeral_numeral_nat @ N2 ) )
% 0.33/0.58 = ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se943457434206027407atural @ ( pred_numeral @ N2 ) ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % mask_numeral
% 0.33/0.58 thf(fact_3750_and__int__unfold,axiom,
% 0.33/0.58 ( bit_se725231765392027082nd_int
% 0.33/0.58 = ( ^ [K4: int,L3: int] :
% 0.33/0.58 ( if_int
% 0.33/0.58 @ ( ( K4 = zero_zero_int )
% 0.33/0.58 | ( L3 = zero_zero_int ) )
% 0.33/0.58 @ zero_zero_int
% 0.33/0.58 @ ( if_int
% 0.33/0.58 @ ( K4
% 0.33/0.58 = ( uminus_uminus_int @ one_one_int ) )
% 0.33/0.58 @ L3
% 0.33/0.58 @ ( if_int
% 0.33/0.58 @ ( L3
% 0.33/0.58 = ( uminus_uminus_int @ one_one_int ) )
% 0.33/0.58 @ K4
% 0.33/0.58 @ ( plus_plus_int @ ( times_times_int @ ( modulo_modulo_int @ K4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ L3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % and_int_unfold
% 0.33/0.58 thf(fact_3751_the__res__def,axiom,
% 0.33/0.58 ( time_the_res_array_a
% 0.33/0.58 = ( ^ [M: heap_T6362127782908069795rray_a,H: heap_e7401611519738050253t_unit] :
% 0.33/0.58 ( case_o8314599424437789472it_nat @ undefined_array_a
% 0.33/0.58 @ ( produc8767961711439910440rray_a
% 0.33/0.58 @ ^ [R3: array_a] :
% 0.33/0.58 ( produc2025300630104146186rray_a
% 0.33/0.58 @ ^ [X3: heap_e7401611519738050253t_unit,Xa4: nat] : R3 ) )
% 0.33/0.58 @ ( heap_T5591663578999710211rray_a @ M @ H ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % the_res_def
% 0.33/0.58 thf(fact_3752_the__res__def,axiom,
% 0.33/0.58 ( time_t2745601220510131320t_unit
% 0.33/0.58 = ( ^ [M: heap_T5738788834812785303t_unit,H: heap_e7401611519738050253t_unit] :
% 0.33/0.58 ( case_o9196786658626276042it_nat @ undefi2974082611360736373t_unit
% 0.33/0.58 @ ( produc5075907435489727646t_unit
% 0.33/0.58 @ ^ [R3: product_unit] :
% 0.33/0.58 ( produc1863717115126956122t_unit
% 0.33/0.58 @ ^ [X3: heap_e7401611519738050253t_unit,Xa4: nat] : R3 ) )
% 0.33/0.58 @ ( heap_T875086893843062177t_unit @ M @ H ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % the_res_def
% 0.33/0.58 thf(fact_3753_take__bit__eq__mask__iff__exp__dvd,axiom,
% 0.33/0.58 ! [N2: nat,K: int] :
% 0.33/0.58 ( ( ( bit_se2923211474154528505it_int @ N2 @ K )
% 0.33/0.58 = ( bit_se2000444600071755411sk_int @ N2 ) )
% 0.33/0.58 = ( dvd_dvd_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ ( plus_plus_int @ K @ one_one_int ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % take_bit_eq_mask_iff_exp_dvd
% 0.33/0.58 thf(fact_3754_Code__Numeral_Opositive__def,axiom,
% 0.33/0.58 code_positive = numera6620942414471956472nteger ).
% 0.33/0.58
% 0.33/0.58 % Code_Numeral.positive_def
% 0.33/0.58 thf(fact_3755_divide__int__def,axiom,
% 0.33/0.58 ( divide_divide_int
% 0.33/0.58 = ( ^ [K4: int,L3: int] :
% 0.33/0.58 ( if_int @ ( L3 = zero_zero_int ) @ zero_zero_int
% 0.33/0.58 @ ( if_int
% 0.33/0.58 @ ( ( sgn_sgn_int @ K4 )
% 0.33/0.58 = ( sgn_sgn_int @ L3 ) )
% 0.33/0.58 @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K4 ) ) @ ( nat2 @ ( abs_abs_int @ L3 ) ) ) )
% 0.33/0.58 @ ( uminus_uminus_int
% 0.33/0.58 @ ( semiri1314217659103216013at_int
% 0.33/0.58 @ ( plus_plus_nat @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K4 ) ) @ ( nat2 @ ( abs_abs_int @ L3 ) ) )
% 0.33/0.58 @ ( zero_n2687167440665602831ol_nat
% 0.33/0.58 @ ~ ( dvd_dvd_int @ L3 @ K4 ) ) ) ) ) ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % divide_int_def
% 0.33/0.58 thf(fact_3756_sum__gp0,axiom,
% 0.33/0.58 ! [X: rat,N2: nat] :
% 0.33/0.58 ( ( ( X = one_one_rat )
% 0.33/0.58 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_atMost_nat @ N2 ) )
% 0.33/0.58 = ( semiri681578069525770553at_rat @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) )
% 0.33/0.58 & ( ( X != one_one_rat )
% 0.33/0.58 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_atMost_nat @ N2 ) )
% 0.33/0.58 = ( divide_divide_rat @ ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ ( suc @ N2 ) ) ) @ ( minus_minus_rat @ one_one_rat @ X ) ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % sum_gp0
% 0.33/0.58 thf(fact_3757_atMost__eq__iff,axiom,
% 0.33/0.58 ! [X: nat,Y: nat] :
% 0.33/0.58 ( ( ( set_ord_atMost_nat @ X )
% 0.33/0.58 = ( set_ord_atMost_nat @ Y ) )
% 0.33/0.58 = ( X = Y ) ) ).
% 0.33/0.58
% 0.33/0.58 % atMost_eq_iff
% 0.33/0.58 thf(fact_3758_atMost__iff,axiom,
% 0.33/0.58 ! [I: $o,K: $o] :
% 0.33/0.58 ( ( member_o @ I @ ( set_ord_atMost_o @ K ) )
% 0.33/0.58 = ( ord_less_eq_o @ I @ K ) ) ).
% 0.33/0.58
% 0.33/0.58 % atMost_iff
% 0.33/0.58 thf(fact_3759_atMost__iff,axiom,
% 0.33/0.58 ! [I: set_nat,K: set_nat] :
% 0.33/0.58 ( ( member_set_nat @ I @ ( set_or4236626031148496127et_nat @ K ) )
% 0.33/0.58 = ( ord_less_eq_set_nat @ I @ K ) ) ).
% 0.33/0.58
% 0.33/0.58 % atMost_iff
% 0.33/0.58 thf(fact_3760_atMost__iff,axiom,
% 0.33/0.58 ! [I: rat,K: rat] :
% 0.33/0.58 ( ( member_rat @ I @ ( set_ord_atMost_rat @ K ) )
% 0.33/0.58 = ( ord_less_eq_rat @ I @ K ) ) ).
% 0.33/0.58
% 0.33/0.58 % atMost_iff
% 0.33/0.58 thf(fact_3761_atMost__iff,axiom,
% 0.33/0.58 ! [I: num,K: num] :
% 0.33/0.58 ( ( member_num @ I @ ( set_ord_atMost_num @ K ) )
% 0.33/0.58 = ( ord_less_eq_num @ I @ K ) ) ).
% 0.33/0.58
% 0.33/0.58 % atMost_iff
% 0.33/0.58 thf(fact_3762_atMost__iff,axiom,
% 0.33/0.58 ! [I: int,K: int] :
% 0.33/0.58 ( ( member_int @ I @ ( set_ord_atMost_int @ K ) )
% 0.33/0.58 = ( ord_less_eq_int @ I @ K ) ) ).
% 0.33/0.58
% 0.33/0.58 % atMost_iff
% 0.33/0.58 thf(fact_3763_atMost__iff,axiom,
% 0.33/0.58 ! [I: nat,K: nat] :
% 0.33/0.58 ( ( member_nat @ I @ ( set_ord_atMost_nat @ K ) )
% 0.33/0.58 = ( ord_less_eq_nat @ I @ K ) ) ).
% 0.33/0.58
% 0.33/0.58 % atMost_iff
% 0.33/0.58 thf(fact_3764_atMost__subset__iff,axiom,
% 0.33/0.58 ! [X: set_nat,Y: set_nat] :
% 0.33/0.58 ( ( ord_le6893508408891458716et_nat @ ( set_or4236626031148496127et_nat @ X ) @ ( set_or4236626031148496127et_nat @ Y ) )
% 0.33/0.58 = ( ord_less_eq_set_nat @ X @ Y ) ) ).
% 0.33/0.58
% 0.33/0.58 % atMost_subset_iff
% 0.33/0.58 thf(fact_3765_atMost__subset__iff,axiom,
% 0.33/0.58 ! [X: rat,Y: rat] :
% 0.33/0.58 ( ( ord_less_eq_set_rat @ ( set_ord_atMost_rat @ X ) @ ( set_ord_atMost_rat @ Y ) )
% 0.33/0.58 = ( ord_less_eq_rat @ X @ Y ) ) ).
% 0.33/0.58
% 0.33/0.58 % atMost_subset_iff
% 0.33/0.58 thf(fact_3766_atMost__subset__iff,axiom,
% 0.33/0.58 ! [X: num,Y: num] :
% 0.33/0.58 ( ( ord_less_eq_set_num @ ( set_ord_atMost_num @ X ) @ ( set_ord_atMost_num @ Y ) )
% 0.33/0.58 = ( ord_less_eq_num @ X @ Y ) ) ).
% 0.33/0.58
% 0.33/0.58 % atMost_subset_iff
% 0.33/0.58 thf(fact_3767_atMost__subset__iff,axiom,
% 0.33/0.58 ! [X: int,Y: int] :
% 0.33/0.58 ( ( ord_less_eq_set_int @ ( set_ord_atMost_int @ X ) @ ( set_ord_atMost_int @ Y ) )
% 0.33/0.58 = ( ord_less_eq_int @ X @ Y ) ) ).
% 0.33/0.58
% 0.33/0.58 % atMost_subset_iff
% 0.33/0.58 thf(fact_3768_atMost__subset__iff,axiom,
% 0.33/0.58 ! [X: nat,Y: nat] :
% 0.33/0.58 ( ( ord_less_eq_set_nat @ ( set_ord_atMost_nat @ X ) @ ( set_ord_atMost_nat @ Y ) )
% 0.33/0.58 = ( ord_less_eq_nat @ X @ Y ) ) ).
% 0.33/0.58
% 0.33/0.58 % atMost_subset_iff
% 0.33/0.58 thf(fact_3769_bit_Oconj__one__right,axiom,
% 0.33/0.58 ! [X: int] :
% 0.33/0.58 ( ( bit_se725231765392027082nd_int @ X @ ( uminus_uminus_int @ one_one_int ) )
% 0.33/0.58 = X ) ).
% 0.33/0.58
% 0.33/0.58 % bit.conj_one_right
% 0.33/0.58 thf(fact_3770_bit_Oconj__one__right,axiom,
% 0.33/0.58 ! [X: code_integer] :
% 0.33/0.58 ( ( bit_se3949692690581998587nteger @ X @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.33/0.58 = X ) ).
% 0.33/0.58
% 0.33/0.58 % bit.conj_one_right
% 0.33/0.58 thf(fact_3771_and_Oright__neutral,axiom,
% 0.33/0.58 ! [A: int] :
% 0.33/0.58 ( ( bit_se725231765392027082nd_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 0.33/0.58 = A ) ).
% 0.33/0.58
% 0.33/0.58 % and.right_neutral
% 0.33/0.58 thf(fact_3772_and_Oright__neutral,axiom,
% 0.33/0.58 ! [A: code_integer] :
% 0.33/0.58 ( ( bit_se3949692690581998587nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.33/0.58 = A ) ).
% 0.33/0.58
% 0.33/0.58 % and.right_neutral
% 0.33/0.58 thf(fact_3773_and_Oleft__neutral,axiom,
% 0.33/0.58 ! [A: int] :
% 0.33/0.58 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ one_one_int ) @ A )
% 0.33/0.58 = A ) ).
% 0.33/0.58
% 0.33/0.58 % and.left_neutral
% 0.33/0.58 thf(fact_3774_and_Oleft__neutral,axiom,
% 0.33/0.58 ! [A: code_integer] :
% 0.33/0.58 ( ( bit_se3949692690581998587nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ A )
% 0.33/0.58 = A ) ).
% 0.33/0.58
% 0.33/0.58 % and.left_neutral
% 0.33/0.58 thf(fact_3775_and__numerals_I2_J,axiom,
% 0.33/0.58 ! [Y: num] :
% 0.33/0.58 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 0.33/0.58 = one_one_int ) ).
% 0.33/0.58
% 0.33/0.58 % and_numerals(2)
% 0.33/0.58 thf(fact_3776_and__numerals_I2_J,axiom,
% 0.33/0.58 ! [Y: num] :
% 0.33/0.58 ( ( bit_se727722235901077358nd_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 0.33/0.58 = one_one_nat ) ).
% 0.33/0.58
% 0.33/0.58 % and_numerals(2)
% 0.33/0.58 thf(fact_3777_and__numerals_I2_J,axiom,
% 0.33/0.58 ! [Y: num] :
% 0.33/0.58 ( ( bit_se3949692690581998587nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit1 @ Y ) ) )
% 0.33/0.58 = one_one_Code_integer ) ).
% 0.33/0.58
% 0.33/0.58 % and_numerals(2)
% 0.33/0.58 thf(fact_3778_and__numerals_I2_J,axiom,
% 0.33/0.58 ! [Y: num] :
% 0.33/0.58 ( ( bit_se2773287842338716102atural @ one_one_Code_natural @ ( numera5444537566228673987atural @ ( bit1 @ Y ) ) )
% 0.33/0.58 = one_one_Code_natural ) ).
% 0.33/0.58
% 0.33/0.58 % and_numerals(2)
% 0.33/0.58 thf(fact_3779_and__numerals_I8_J,axiom,
% 0.33/0.58 ! [X: num] :
% 0.33/0.58 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ one_one_int )
% 0.33/0.58 = one_one_int ) ).
% 0.33/0.58
% 0.33/0.58 % and_numerals(8)
% 0.33/0.58 thf(fact_3780_and__numerals_I8_J,axiom,
% 0.33/0.58 ! [X: num] :
% 0.33/0.58 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ one_one_nat )
% 0.33/0.58 = one_one_nat ) ).
% 0.33/0.58
% 0.33/0.58 % and_numerals(8)
% 0.33/0.58 thf(fact_3781_and__numerals_I8_J,axiom,
% 0.33/0.58 ! [X: num] :
% 0.33/0.58 ( ( bit_se3949692690581998587nteger @ ( numera6620942414471956472nteger @ ( bit1 @ X ) ) @ one_one_Code_integer )
% 0.33/0.58 = one_one_Code_integer ) ).
% 0.33/0.58
% 0.33/0.58 % and_numerals(8)
% 0.33/0.58 thf(fact_3782_and__numerals_I8_J,axiom,
% 0.33/0.58 ! [X: num] :
% 0.33/0.58 ( ( bit_se2773287842338716102atural @ ( numera5444537566228673987atural @ ( bit1 @ X ) ) @ one_one_Code_natural )
% 0.33/0.58 = one_one_Code_natural ) ).
% 0.33/0.58
% 0.33/0.58 % and_numerals(8)
% 0.33/0.58 thf(fact_3783_Icc__subset__Iic__iff,axiom,
% 0.33/0.58 ! [L: set_nat,H3: set_nat,H5: set_nat] :
% 0.33/0.58 ( ( ord_le6893508408891458716et_nat @ ( set_or4548717258645045905et_nat @ L @ H3 ) @ ( set_or4236626031148496127et_nat @ H5 ) )
% 0.33/0.58 = ( ~ ( ord_less_eq_set_nat @ L @ H3 )
% 0.33/0.58 | ( ord_less_eq_set_nat @ H3 @ H5 ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % Icc_subset_Iic_iff
% 0.33/0.58 thf(fact_3784_Icc__subset__Iic__iff,axiom,
% 0.33/0.58 ! [L: rat,H3: rat,H5: rat] :
% 0.33/0.58 ( ( ord_less_eq_set_rat @ ( set_or633870826150836451st_rat @ L @ H3 ) @ ( set_ord_atMost_rat @ H5 ) )
% 0.33/0.58 = ( ~ ( ord_less_eq_rat @ L @ H3 )
% 0.33/0.58 | ( ord_less_eq_rat @ H3 @ H5 ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % Icc_subset_Iic_iff
% 0.33/0.58 thf(fact_3785_Icc__subset__Iic__iff,axiom,
% 0.33/0.58 ! [L: num,H3: num,H5: num] :
% 0.33/0.58 ( ( ord_less_eq_set_num @ ( set_or7049704709247886629st_num @ L @ H3 ) @ ( set_ord_atMost_num @ H5 ) )
% 0.33/0.58 = ( ~ ( ord_less_eq_num @ L @ H3 )
% 0.33/0.58 | ( ord_less_eq_num @ H3 @ H5 ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % Icc_subset_Iic_iff
% 0.33/0.58 thf(fact_3786_Icc__subset__Iic__iff,axiom,
% 0.33/0.58 ! [L: int,H3: int,H5: int] :
% 0.33/0.58 ( ( ord_less_eq_set_int @ ( set_or1266510415728281911st_int @ L @ H3 ) @ ( set_ord_atMost_int @ H5 ) )
% 0.33/0.58 = ( ~ ( ord_less_eq_int @ L @ H3 )
% 0.33/0.58 | ( ord_less_eq_int @ H3 @ H5 ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % Icc_subset_Iic_iff
% 0.33/0.58 thf(fact_3787_Icc__subset__Iic__iff,axiom,
% 0.33/0.58 ! [L: nat,H3: nat,H5: nat] :
% 0.33/0.58 ( ( ord_less_eq_set_nat @ ( set_or1269000886237332187st_nat @ L @ H3 ) @ ( set_ord_atMost_nat @ H5 ) )
% 0.33/0.58 = ( ~ ( ord_less_eq_nat @ L @ H3 )
% 0.33/0.58 | ( ord_less_eq_nat @ H3 @ H5 ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % Icc_subset_Iic_iff
% 0.33/0.58 thf(fact_3788_Icc__subset__Iic__iff,axiom,
% 0.33/0.58 ! [L: code_integer,H3: code_integer,H5: code_integer] :
% 0.33/0.58 ( ( ord_le7084787975880047091nteger @ ( set_or189985376899183464nteger @ L @ H3 ) @ ( set_or9101266186257409494nteger @ H5 ) )
% 0.33/0.58 = ( ~ ( ord_le3102999989581377725nteger @ L @ H3 )
% 0.33/0.58 | ( ord_le3102999989581377725nteger @ H3 @ H5 ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % Icc_subset_Iic_iff
% 0.33/0.58 thf(fact_3789_mask__Suc__0,axiom,
% 0.33/0.58 ( ( bit_se2000444600071755411sk_int @ ( suc @ zero_zero_nat ) )
% 0.33/0.58 = one_one_int ) ).
% 0.33/0.58
% 0.33/0.58 % mask_Suc_0
% 0.33/0.58 thf(fact_3790_mask__Suc__0,axiom,
% 0.33/0.58 ( ( bit_se2119862282449309892nteger @ ( suc @ zero_zero_nat ) )
% 0.33/0.58 = one_one_Code_integer ) ).
% 0.33/0.58
% 0.33/0.58 % mask_Suc_0
% 0.33/0.58 thf(fact_3791_mask__Suc__0,axiom,
% 0.33/0.58 ( ( bit_se2002935070580805687sk_nat @ ( suc @ zero_zero_nat ) )
% 0.33/0.58 = one_one_nat ) ).
% 0.33/0.58
% 0.33/0.58 % mask_Suc_0
% 0.33/0.58 thf(fact_3792_mask__Suc__0,axiom,
% 0.33/0.58 ( ( bit_se943457434206027407atural @ ( suc @ zero_zero_nat ) )
% 0.33/0.58 = one_one_Code_natural ) ).
% 0.33/0.58
% 0.33/0.58 % mask_Suc_0
% 0.33/0.58 thf(fact_3793_sum_OatMost__Suc,axiom,
% 0.33/0.58 ! [G: nat > multis2468970476368604999at_nat,N2: nat] :
% 0.33/0.58 ( ( groups6857163185585827899at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 0.33/0.58 = ( plus_p7104986032573967614at_nat @ ( groups6857163185585827899at_nat @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % sum.atMost_Suc
% 0.33/0.58 thf(fact_3794_sum_OatMost__Suc,axiom,
% 0.33/0.58 ! [G: nat > rat,N2: nat] :
% 0.33/0.58 ( ( groups2906978787729119204at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 0.33/0.58 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % sum.atMost_Suc
% 0.33/0.58 thf(fact_3795_sum_OatMost__Suc,axiom,
% 0.33/0.58 ! [G: nat > int,N2: nat] :
% 0.33/0.58 ( ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 0.33/0.58 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % sum.atMost_Suc
% 0.33/0.58 thf(fact_3796_sum_OatMost__Suc,axiom,
% 0.33/0.58 ! [G: nat > nat,N2: nat] :
% 0.33/0.58 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 0.33/0.58 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % sum.atMost_Suc
% 0.33/0.58 thf(fact_3797_take__bit__minus__one__eq__mask,axiom,
% 0.33/0.58 ! [N2: nat] :
% 0.33/0.58 ( ( bit_se1745604003318907178nteger @ N2 @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.33/0.58 = ( bit_se2119862282449309892nteger @ N2 ) ) ).
% 0.33/0.58
% 0.33/0.58 % take_bit_minus_one_eq_mask
% 0.33/0.58 thf(fact_3798_take__bit__minus__one__eq__mask,axiom,
% 0.33/0.58 ! [N2: nat] :
% 0.33/0.58 ( ( bit_se2923211474154528505it_int @ N2 @ ( uminus_uminus_int @ one_one_int ) )
% 0.33/0.58 = ( bit_se2000444600071755411sk_int @ N2 ) ) ).
% 0.33/0.58
% 0.33/0.58 % take_bit_minus_one_eq_mask
% 0.33/0.58 thf(fact_3799_and__numerals_I1_J,axiom,
% 0.33/0.58 ! [Y: num] :
% 0.33/0.58 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 0.33/0.58 = zero_zero_int ) ).
% 0.33/0.58
% 0.33/0.58 % and_numerals(1)
% 0.33/0.58 thf(fact_3800_and__numerals_I1_J,axiom,
% 0.33/0.58 ! [Y: num] :
% 0.33/0.58 ( ( bit_se727722235901077358nd_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 0.33/0.58 = zero_zero_nat ) ).
% 0.33/0.58
% 0.33/0.58 % and_numerals(1)
% 0.33/0.58 thf(fact_3801_and__numerals_I1_J,axiom,
% 0.33/0.58 ! [Y: num] :
% 0.33/0.58 ( ( bit_se3949692690581998587nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ Y ) ) )
% 0.33/0.58 = zero_z3403309356797280102nteger ) ).
% 0.33/0.58
% 0.33/0.58 % and_numerals(1)
% 0.33/0.58 thf(fact_3802_and__numerals_I1_J,axiom,
% 0.33/0.58 ! [Y: num] :
% 0.33/0.58 ( ( bit_se2773287842338716102atural @ one_one_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ Y ) ) )
% 0.33/0.58 = zero_z2226904508553997617atural ) ).
% 0.33/0.58
% 0.33/0.58 % and_numerals(1)
% 0.33/0.58 thf(fact_3803_and__numerals_I5_J,axiom,
% 0.33/0.58 ! [X: num] :
% 0.33/0.58 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ one_one_int )
% 0.33/0.58 = zero_zero_int ) ).
% 0.33/0.58
% 0.33/0.58 % and_numerals(5)
% 0.33/0.58 thf(fact_3804_and__numerals_I5_J,axiom,
% 0.33/0.58 ! [X: num] :
% 0.33/0.58 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ one_one_nat )
% 0.33/0.58 = zero_zero_nat ) ).
% 0.33/0.58
% 0.33/0.58 % and_numerals(5)
% 0.33/0.58 thf(fact_3805_and__numerals_I5_J,axiom,
% 0.33/0.58 ! [X: num] :
% 0.33/0.58 ( ( bit_se3949692690581998587nteger @ ( numera6620942414471956472nteger @ ( bit0 @ X ) ) @ one_one_Code_integer )
% 0.33/0.58 = zero_z3403309356797280102nteger ) ).
% 0.33/0.58
% 0.33/0.58 % and_numerals(5)
% 0.33/0.58 thf(fact_3806_and__numerals_I5_J,axiom,
% 0.33/0.58 ! [X: num] :
% 0.33/0.58 ( ( bit_se2773287842338716102atural @ ( numera5444537566228673987atural @ ( bit0 @ X ) ) @ one_one_Code_natural )
% 0.33/0.58 = zero_z2226904508553997617atural ) ).
% 0.33/0.58
% 0.33/0.58 % and_numerals(5)
% 0.33/0.58 thf(fact_3807_nat__numeral__diff__1,axiom,
% 0.33/0.58 ! [V: num] :
% 0.33/0.58 ( ( minus_minus_nat @ ( numeral_numeral_nat @ V ) @ one_one_nat )
% 0.33/0.58 = ( nat2 @ ( minus_minus_int @ ( numeral_numeral_int @ V ) @ one_one_int ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % nat_numeral_diff_1
% 0.33/0.58 thf(fact_3808_and__numerals_I7_J,axiom,
% 0.33/0.58 ! [X: num,Y: num] :
% 0.33/0.58 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 0.33/0.58 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % and_numerals(7)
% 0.33/0.58 thf(fact_3809_and__numerals_I7_J,axiom,
% 0.33/0.58 ! [X: num,Y: num] :
% 0.33/0.58 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 0.33/0.58 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % and_numerals(7)
% 0.33/0.58 thf(fact_3810_and__numerals_I7_J,axiom,
% 0.33/0.58 ! [X: num,Y: num] :
% 0.33/0.58 ( ( bit_se3949692690581998587nteger @ ( numera6620942414471956472nteger @ ( bit1 @ X ) ) @ ( numera6620942414471956472nteger @ ( bit1 @ Y ) ) )
% 0.33/0.58 = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se3949692690581998587nteger @ ( numera6620942414471956472nteger @ X ) @ ( numera6620942414471956472nteger @ Y ) ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % and_numerals(7)
% 0.33/0.58 thf(fact_3811_and__numerals_I7_J,axiom,
% 0.33/0.58 ! [X: num,Y: num] :
% 0.33/0.58 ( ( bit_se2773287842338716102atural @ ( numera5444537566228673987atural @ ( bit1 @ X ) ) @ ( numera5444537566228673987atural @ ( bit1 @ Y ) ) )
% 0.33/0.58 = ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se2773287842338716102atural @ ( numera5444537566228673987atural @ X ) @ ( numera5444537566228673987atural @ Y ) ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % and_numerals(7)
% 0.33/0.58 thf(fact_3812_mask__integer_Oabs__eq,axiom,
% 0.33/0.58 ( bit_se2119862282449309892nteger
% 0.33/0.58 = ( ^ [X3: nat] : ( code_integer_of_int @ ( bit_se2000444600071755411sk_int @ X3 ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % mask_integer.abs_eq
% 0.33/0.58 thf(fact_3813_not__Iic__eq__Icc,axiom,
% 0.33/0.58 ! [H5: int,L: int,H3: int] :
% 0.33/0.58 ( ( set_ord_atMost_int @ H5 )
% 0.33/0.58 != ( set_or1266510415728281911st_int @ L @ H3 ) ) ).
% 0.33/0.58
% 0.33/0.58 % not_Iic_eq_Icc
% 0.33/0.58 thf(fact_3814_atMost__def,axiom,
% 0.33/0.58 ( set_or4236626031148496127et_nat
% 0.33/0.58 = ( ^ [U2: set_nat] :
% 0.33/0.58 ( collect_set_nat
% 0.33/0.58 @ ^ [X3: set_nat] : ( ord_less_eq_set_nat @ X3 @ U2 ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % atMost_def
% 0.33/0.58 thf(fact_3815_atMost__def,axiom,
% 0.33/0.58 ( set_ord_atMost_rat
% 0.33/0.58 = ( ^ [U2: rat] :
% 0.33/0.58 ( collect_rat
% 0.33/0.58 @ ^ [X3: rat] : ( ord_less_eq_rat @ X3 @ U2 ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % atMost_def
% 0.33/0.58 thf(fact_3816_atMost__def,axiom,
% 0.33/0.58 ( set_ord_atMost_num
% 0.33/0.58 = ( ^ [U2: num] :
% 0.33/0.58 ( collect_num
% 0.33/0.58 @ ^ [X3: num] : ( ord_less_eq_num @ X3 @ U2 ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % atMost_def
% 0.33/0.58 thf(fact_3817_atMost__def,axiom,
% 0.33/0.58 ( set_ord_atMost_int
% 0.33/0.58 = ( ^ [U2: int] :
% 0.33/0.58 ( collect_int
% 0.33/0.58 @ ^ [X3: int] : ( ord_less_eq_int @ X3 @ U2 ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % atMost_def
% 0.33/0.58 thf(fact_3818_atMost__def,axiom,
% 0.33/0.58 ( set_ord_atMost_nat
% 0.33/0.58 = ( ^ [U2: nat] :
% 0.33/0.58 ( collect_nat
% 0.33/0.58 @ ^ [X3: nat] : ( ord_less_eq_nat @ X3 @ U2 ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % atMost_def
% 0.33/0.58 thf(fact_3819_and__eq__minus__1__iff,axiom,
% 0.33/0.58 ! [A: int,B: int] :
% 0.33/0.58 ( ( ( bit_se725231765392027082nd_int @ A @ B )
% 0.33/0.58 = ( uminus_uminus_int @ one_one_int ) )
% 0.33/0.58 = ( ( A
% 0.33/0.58 = ( uminus_uminus_int @ one_one_int ) )
% 0.33/0.58 & ( B
% 0.33/0.58 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % and_eq_minus_1_iff
% 0.33/0.58 thf(fact_3820_and__eq__minus__1__iff,axiom,
% 0.33/0.58 ! [A: code_integer,B: code_integer] :
% 0.33/0.58 ( ( ( bit_se3949692690581998587nteger @ A @ B )
% 0.33/0.58 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.33/0.58 = ( ( A
% 0.33/0.58 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.33/0.58 & ( B
% 0.33/0.58 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % and_eq_minus_1_iff
% 0.33/0.58 thf(fact_3821_atMost__atLeast0,axiom,
% 0.33/0.58 ( set_ord_atMost_nat
% 0.33/0.58 = ( set_or1269000886237332187st_nat @ zero_zero_nat ) ) ).
% 0.33/0.58
% 0.33/0.58 % atMost_atLeast0
% 0.33/0.58 thf(fact_3822_nat__one__as__int,axiom,
% 0.33/0.58 ( one_one_nat
% 0.33/0.58 = ( nat2 @ one_one_int ) ) ).
% 0.33/0.58
% 0.33/0.58 % nat_one_as_int
% 0.33/0.58 thf(fact_3823_not__Iic__le__Icc,axiom,
% 0.33/0.58 ! [H3: int,L4: int,H5: int] :
% 0.33/0.58 ~ ( ord_less_eq_set_int @ ( set_ord_atMost_int @ H3 ) @ ( set_or1266510415728281911st_int @ L4 @ H5 ) ) ).
% 0.33/0.58
% 0.33/0.58 % not_Iic_le_Icc
% 0.33/0.58 thf(fact_3824_nat__int__add,axiom,
% 0.33/0.58 ! [A: nat,B: nat] :
% 0.33/0.58 ( ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) )
% 0.33/0.58 = ( plus_plus_nat @ A @ B ) ) ).
% 0.33/0.58
% 0.33/0.58 % nat_int_add
% 0.33/0.58 thf(fact_3825_option_Othe__def,axiom,
% 0.33/0.58 ( the_num
% 0.33/0.58 = ( case_option_num_num @ undefined_num
% 0.33/0.58 @ ^ [X23: num] : X23 ) ) ).
% 0.33/0.58
% 0.33/0.58 % option.the_def
% 0.33/0.58 thf(fact_3826_nat__plus__as__int,axiom,
% 0.33/0.58 ( plus_plus_nat
% 0.33/0.58 = ( ^ [A5: nat,B4: nat] : ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A5 ) @ ( semiri1314217659103216013at_int @ B4 ) ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % nat_plus_as_int
% 0.33/0.58 thf(fact_3827_nat__add__distrib,axiom,
% 0.33/0.58 ! [Z: int,Z6: int] :
% 0.33/0.58 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 0.33/0.58 => ( ( ord_less_eq_int @ zero_zero_int @ Z6 )
% 0.33/0.58 => ( ( nat2 @ ( plus_plus_int @ Z @ Z6 ) )
% 0.33/0.58 = ( plus_plus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z6 ) ) ) ) ) ).
% 0.33/0.58
% 0.33/0.58 % nat_add_distrib
% 0.33/0.58 thf(fact_3828_Suc__as__int,axiom,
% 0.33/0.58 ( suc
% 0.33/0.58 = ( ^ [A5: nat] : ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A5 ) @ one_one_int ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % Suc_as_int
% 0.33/0.59 thf(fact_3829_nat__abs__triangle__ineq,axiom,
% 0.33/0.59 ! [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 ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % nat_abs_triangle_ineq
% 0.33/0.59 thf(fact_3830_sum_OatMost__Suc__shift,axiom,
% 0.33/0.59 ! [G: nat > multis2468970476368604999at_nat,N2: nat] :
% 0.33/0.59 ( ( groups6857163185585827899at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 0.33/0.59 = ( plus_p7104986032573967614at_nat @ ( G @ zero_zero_nat )
% 0.33/0.59 @ ( groups6857163185585827899at_nat
% 0.33/0.59 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 0.33/0.59 @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum.atMost_Suc_shift
% 0.33/0.59 thf(fact_3831_sum_OatMost__Suc__shift,axiom,
% 0.33/0.59 ! [G: nat > rat,N2: nat] :
% 0.33/0.59 ( ( groups2906978787729119204at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 0.33/0.59 = ( plus_plus_rat @ ( G @ zero_zero_nat )
% 0.33/0.59 @ ( groups2906978787729119204at_rat
% 0.33/0.59 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 0.33/0.59 @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum.atMost_Suc_shift
% 0.33/0.59 thf(fact_3832_sum_OatMost__Suc__shift,axiom,
% 0.33/0.59 ! [G: nat > int,N2: nat] :
% 0.33/0.59 ( ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 0.33/0.59 = ( plus_plus_int @ ( G @ zero_zero_nat )
% 0.33/0.59 @ ( groups3539618377306564664at_int
% 0.33/0.59 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 0.33/0.59 @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum.atMost_Suc_shift
% 0.33/0.59 thf(fact_3833_sum_OatMost__Suc__shift,axiom,
% 0.33/0.59 ! [G: nat > nat,N2: nat] :
% 0.33/0.59 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 0.33/0.59 = ( plus_plus_nat @ ( G @ zero_zero_nat )
% 0.33/0.59 @ ( groups3542108847815614940at_nat
% 0.33/0.59 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 0.33/0.59 @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum.atMost_Suc_shift
% 0.33/0.59 thf(fact_3834_sum__telescope,axiom,
% 0.33/0.59 ! [F: nat > code_integer,I: nat] :
% 0.33/0.59 ( ( groups7501900531339628137nteger
% 0.33/0.59 @ ^ [I3: nat] : ( minus_8373710615458151222nteger @ ( F @ I3 ) @ ( F @ ( suc @ I3 ) ) )
% 0.33/0.59 @ ( set_ord_atMost_nat @ I ) )
% 0.33/0.59 = ( minus_8373710615458151222nteger @ ( F @ zero_zero_nat ) @ ( F @ ( suc @ I ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum_telescope
% 0.33/0.59 thf(fact_3835_sum__telescope,axiom,
% 0.33/0.59 ! [F: nat > rat,I: nat] :
% 0.33/0.59 ( ( groups2906978787729119204at_rat
% 0.33/0.59 @ ^ [I3: nat] : ( minus_minus_rat @ ( F @ I3 ) @ ( F @ ( suc @ I3 ) ) )
% 0.33/0.59 @ ( set_ord_atMost_nat @ I ) )
% 0.33/0.59 = ( minus_minus_rat @ ( F @ zero_zero_nat ) @ ( F @ ( suc @ I ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum_telescope
% 0.33/0.59 thf(fact_3836_sum__telescope,axiom,
% 0.33/0.59 ! [F: nat > int,I: nat] :
% 0.33/0.59 ( ( groups3539618377306564664at_int
% 0.33/0.59 @ ^ [I3: nat] : ( minus_minus_int @ ( F @ I3 ) @ ( F @ ( suc @ I3 ) ) )
% 0.33/0.59 @ ( set_ord_atMost_nat @ I ) )
% 0.33/0.59 = ( minus_minus_int @ ( F @ zero_zero_nat ) @ ( F @ ( suc @ I ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum_telescope
% 0.33/0.59 thf(fact_3837_the__heap__def,axiom,
% 0.33/0.59 ( time_t490086488869527696rray_a
% 0.33/0.59 = ( ^ [M: heap_T6362127782908069795rray_a,H: heap_e7401611519738050253t_unit] :
% 0.33/0.59 ( case_o8180226181140434498it_nat @ undefi8805113437130903861t_unit
% 0.33/0.59 @ ( produc7016084256669755260t_unit
% 0.33/0.59 @ ^ [X3: array_a] :
% 0.33/0.59 ( produc9092781844693468442t_unit
% 0.33/0.59 @ ^ [H6: heap_e7401611519738050253t_unit,Xa4: nat] : H6 ) )
% 0.33/0.59 @ ( heap_T5591663578999710211rray_a @ M @ H ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % the_heap_def
% 0.33/0.59 thf(fact_3838_the__heap__def,axiom,
% 0.33/0.59 ( time_t3350536682685678164t_unit
% 0.33/0.59 = ( ^ [M: heap_T5738788834812785303t_unit,H: heap_e7401611519738050253t_unit] :
% 0.33/0.59 ( case_o2566993838309857162it_nat @ undefi8805113437130903861t_unit
% 0.33/0.59 @ ( produc6568152436032731486t_unit
% 0.33/0.59 @ ^ [X3: product_unit] :
% 0.33/0.59 ( produc9092781844693468442t_unit
% 0.33/0.59 @ ^ [H6: heap_e7401611519738050253t_unit,Xa4: nat] : H6 ) )
% 0.33/0.59 @ ( heap_T875086893843062177t_unit @ M @ H ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % the_heap_def
% 0.33/0.59 thf(fact_3839_and__one__eq,axiom,
% 0.33/0.59 ! [A: int] :
% 0.33/0.59 ( ( bit_se725231765392027082nd_int @ A @ one_one_int )
% 0.33/0.59 = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % and_one_eq
% 0.33/0.59 thf(fact_3840_and__one__eq,axiom,
% 0.33/0.59 ! [A: nat] :
% 0.33/0.59 ( ( bit_se727722235901077358nd_nat @ A @ one_one_nat )
% 0.33/0.59 = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % and_one_eq
% 0.33/0.59 thf(fact_3841_and__one__eq,axiom,
% 0.33/0.59 ! [A: code_integer] :
% 0.33/0.59 ( ( bit_se3949692690581998587nteger @ A @ one_one_Code_integer )
% 0.33/0.59 = ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % and_one_eq
% 0.33/0.59 thf(fact_3842_and__one__eq,axiom,
% 0.33/0.59 ! [A: code_natural] :
% 0.33/0.59 ( ( bit_se2773287842338716102atural @ A @ one_one_Code_natural )
% 0.33/0.59 = ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % and_one_eq
% 0.33/0.59 thf(fact_3843_one__and__eq,axiom,
% 0.33/0.59 ! [A: int] :
% 0.33/0.59 ( ( bit_se725231765392027082nd_int @ one_one_int @ A )
% 0.33/0.59 = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % one_and_eq
% 0.33/0.59 thf(fact_3844_one__and__eq,axiom,
% 0.33/0.59 ! [A: nat] :
% 0.33/0.59 ( ( bit_se727722235901077358nd_nat @ one_one_nat @ A )
% 0.33/0.59 = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % one_and_eq
% 0.33/0.59 thf(fact_3845_one__and__eq,axiom,
% 0.33/0.59 ! [A: code_integer] :
% 0.33/0.59 ( ( bit_se3949692690581998587nteger @ one_one_Code_integer @ A )
% 0.33/0.59 = ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % one_and_eq
% 0.33/0.59 thf(fact_3846_one__and__eq,axiom,
% 0.33/0.59 ! [A: code_natural] :
% 0.33/0.59 ( ( bit_se2773287842338716102atural @ one_one_Code_natural @ A )
% 0.33/0.59 = ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % one_and_eq
% 0.33/0.59 thf(fact_3847_take__bit__eq__mask__iff,axiom,
% 0.33/0.59 ! [N2: nat,K: int] :
% 0.33/0.59 ( ( ( bit_se2923211474154528505it_int @ N2 @ K )
% 0.33/0.59 = ( bit_se2000444600071755411sk_int @ N2 ) )
% 0.33/0.59 = ( ( bit_se2923211474154528505it_int @ N2 @ ( plus_plus_int @ K @ one_one_int ) )
% 0.33/0.59 = zero_zero_int ) ) ).
% 0.33/0.59
% 0.33/0.59 % take_bit_eq_mask_iff
% 0.33/0.59 thf(fact_3848_Suc__nat__eq__nat__zadd1,axiom,
% 0.33/0.59 ! [Z: int] :
% 0.33/0.59 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 0.33/0.59 => ( ( suc @ ( nat2 @ Z ) )
% 0.33/0.59 = ( nat2 @ ( plus_plus_int @ one_one_int @ Z ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % Suc_nat_eq_nat_zadd1
% 0.33/0.59 thf(fact_3849_Divides_Oadjust__div__def,axiom,
% 0.33/0.59 ( adjust_div
% 0.33/0.59 = ( produc8211389475949308722nt_int
% 0.33/0.59 @ ^ [Q5: int,R3: int] : ( plus_plus_int @ Q5 @ ( zero_n2684676970156552555ol_int @ ( R3 != zero_zero_int ) ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % Divides.adjust_div_def
% 0.33/0.59 thf(fact_3850_sum__gp__basic,axiom,
% 0.33/0.59 ! [X: code_integer,N2: nat] :
% 0.33/0.59 ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ one_one_Code_integer @ X ) @ ( groups7501900531339628137nteger @ ( power_8256067586552552935nteger @ X ) @ ( set_ord_atMost_nat @ N2 ) ) )
% 0.33/0.59 = ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ X @ ( suc @ N2 ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum_gp_basic
% 0.33/0.59 thf(fact_3851_sum__gp__basic,axiom,
% 0.33/0.59 ! [X: rat,N2: nat] :
% 0.33/0.59 ( ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_atMost_nat @ N2 ) ) )
% 0.33/0.59 = ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ ( suc @ N2 ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum_gp_basic
% 0.33/0.59 thf(fact_3852_sum__gp__basic,axiom,
% 0.33/0.59 ! [X: int,N2: nat] :
% 0.33/0.59 ( ( times_times_int @ ( minus_minus_int @ one_one_int @ X ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_ord_atMost_nat @ N2 ) ) )
% 0.33/0.59 = ( minus_minus_int @ one_one_int @ ( power_power_int @ X @ ( suc @ N2 ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum_gp_basic
% 0.33/0.59 thf(fact_3853_sum__power__shift,axiom,
% 0.33/0.59 ! [M2: nat,N2: nat,X: rat] :
% 0.33/0.59 ( ( ord_less_eq_nat @ M2 @ N2 )
% 0.33/0.59 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 0.33/0.59 = ( times_times_rat @ ( power_power_rat @ X @ M2 ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_atMost_nat @ ( minus_minus_nat @ N2 @ M2 ) ) ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum_power_shift
% 0.33/0.59 thf(fact_3854_sum__power__shift,axiom,
% 0.33/0.59 ! [M2: nat,N2: nat,X: int] :
% 0.33/0.59 ( ( ord_less_eq_nat @ M2 @ N2 )
% 0.33/0.59 => ( ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 0.33/0.59 = ( times_times_int @ ( power_power_int @ X @ M2 ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_ord_atMost_nat @ ( minus_minus_nat @ N2 @ M2 ) ) ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum_power_shift
% 0.33/0.59 thf(fact_3855_sum_Otriangle__reindex__eq,axiom,
% 0.33/0.59 ! [G: nat > nat > nat,N2: nat] :
% 0.33/0.59 ( ( groups977919841031483927at_nat @ ( produc6842872674320459806at_nat @ G )
% 0.33/0.59 @ ( collec3392354462482085612at_nat
% 0.33/0.59 @ ( produc6081775807080527818_nat_o
% 0.33/0.59 @ ^ [I3: nat,J2: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ I3 @ J2 ) @ N2 ) ) ) )
% 0.33/0.59 = ( groups3542108847815614940at_nat
% 0.33/0.59 @ ^ [K4: nat] :
% 0.33/0.59 ( groups3542108847815614940at_nat
% 0.33/0.59 @ ^ [I3: nat] : ( G @ I3 @ ( minus_minus_nat @ K4 @ I3 ) )
% 0.33/0.59 @ ( set_ord_atMost_nat @ K4 ) )
% 0.33/0.59 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum.triangle_reindex_eq
% 0.33/0.59 thf(fact_3856_and__int__rec,axiom,
% 0.33/0.59 ( bit_se725231765392027082nd_int
% 0.33/0.59 = ( ^ [K4: int,L3: int] :
% 0.33/0.59 ( plus_plus_int
% 0.33/0.59 @ ( zero_n2684676970156552555ol_int
% 0.33/0.59 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K4 )
% 0.33/0.59 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L3 ) ) )
% 0.33/0.59 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % and_int_rec
% 0.33/0.59 thf(fact_3857_mask__half__int,axiom,
% 0.33/0.59 ! [N2: nat] :
% 0.33/0.59 ( ( divide_divide_int @ ( bit_se2000444600071755411sk_int @ N2 ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.33/0.59 = ( bit_se2000444600071755411sk_int @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % mask_half_int
% 0.33/0.59 thf(fact_3858_sum_Oin__pairs__0,axiom,
% 0.33/0.59 ! [G: nat > multis2468970476368604999at_nat,N2: nat] :
% 0.33/0.59 ( ( groups6857163185585827899at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 0.33/0.59 = ( groups6857163185585827899at_nat
% 0.33/0.59 @ ^ [I3: nat] : ( plus_p7104986032573967614at_nat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 0.33/0.59 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum.in_pairs_0
% 0.33/0.59 thf(fact_3859_sum_Oin__pairs__0,axiom,
% 0.33/0.59 ! [G: nat > rat,N2: nat] :
% 0.33/0.59 ( ( groups2906978787729119204at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 0.33/0.59 = ( groups2906978787729119204at_rat
% 0.33/0.59 @ ^ [I3: nat] : ( plus_plus_rat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 0.33/0.59 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum.in_pairs_0
% 0.33/0.59 thf(fact_3860_sum_Oin__pairs__0,axiom,
% 0.33/0.59 ! [G: nat > int,N2: nat] :
% 0.33/0.59 ( ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 0.33/0.59 = ( groups3539618377306564664at_int
% 0.33/0.59 @ ^ [I3: nat] : ( plus_plus_int @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 0.33/0.59 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum.in_pairs_0
% 0.33/0.59 thf(fact_3861_sum_Oin__pairs__0,axiom,
% 0.33/0.59 ! [G: nat > nat,N2: nat] :
% 0.33/0.59 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 0.33/0.59 = ( groups3542108847815614940at_nat
% 0.33/0.59 @ ^ [I3: nat] : ( plus_plus_nat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 0.33/0.59 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum.in_pairs_0
% 0.33/0.59 thf(fact_3862_mask__nat__def,axiom,
% 0.33/0.59 ( bit_se2002935070580805687sk_nat
% 0.33/0.59 = ( ^ [N4: nat] : ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) @ one_one_nat ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % mask_nat_def
% 0.33/0.59 thf(fact_3863_mask__eq__exp__minus__1,axiom,
% 0.33/0.59 ( bit_se2000444600071755411sk_int
% 0.33/0.59 = ( ^ [N4: nat] : ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N4 ) @ one_one_int ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % mask_eq_exp_minus_1
% 0.33/0.59 thf(fact_3864_mask__eq__exp__minus__1,axiom,
% 0.33/0.59 ( bit_se2119862282449309892nteger
% 0.33/0.59 = ( ^ [N4: nat] : ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N4 ) @ one_one_Code_integer ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % mask_eq_exp_minus_1
% 0.33/0.59 thf(fact_3865_mask__eq__exp__minus__1,axiom,
% 0.33/0.59 ( bit_se2002935070580805687sk_nat
% 0.33/0.59 = ( ^ [N4: nat] : ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) @ one_one_nat ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % mask_eq_exp_minus_1
% 0.33/0.59 thf(fact_3866_mask__eq__exp__minus__1,axiom,
% 0.33/0.59 ( bit_se943457434206027407atural
% 0.33/0.59 = ( ^ [N4: nat] : ( minus_7197305767214868737atural @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N4 ) @ one_one_Code_natural ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % mask_eq_exp_minus_1
% 0.33/0.59 thf(fact_3867_sum_Ozero__middle,axiom,
% 0.33/0.59 ! [P4: nat,K: nat,G: nat > code_integer,H3: nat > code_integer] :
% 0.33/0.59 ( ( ord_less_eq_nat @ one_one_nat @ P4 )
% 0.33/0.59 => ( ( ord_less_eq_nat @ K @ P4 )
% 0.33/0.59 => ( ( groups7501900531339628137nteger
% 0.33/0.59 @ ^ [J2: nat] : ( if_Code_integer @ ( ord_less_nat @ J2 @ K ) @ ( G @ J2 ) @ ( if_Code_integer @ ( J2 = K ) @ zero_z3403309356797280102nteger @ ( H3 @ ( minus_minus_nat @ J2 @ ( suc @ zero_zero_nat ) ) ) ) )
% 0.33/0.59 @ ( set_ord_atMost_nat @ P4 ) )
% 0.33/0.59 = ( groups7501900531339628137nteger
% 0.33/0.59 @ ^ [J2: nat] : ( if_Code_integer @ ( ord_less_nat @ J2 @ K ) @ ( G @ J2 ) @ ( H3 @ J2 ) )
% 0.33/0.59 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P4 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum.zero_middle
% 0.33/0.59 thf(fact_3868_sum_Ozero__middle,axiom,
% 0.33/0.59 ! [P4: nat,K: nat,G: nat > multis2468970476368604999at_nat,H3: nat > multis2468970476368604999at_nat] :
% 0.33/0.59 ( ( ord_less_eq_nat @ one_one_nat @ P4 )
% 0.33/0.59 => ( ( ord_less_eq_nat @ K @ P4 )
% 0.33/0.59 => ( ( groups6857163185585827899at_nat
% 0.33/0.59 @ ^ [J2: nat] : ( if_mul8430962117462786573at_nat @ ( ord_less_nat @ J2 @ K ) @ ( G @ J2 ) @ ( if_mul8430962117462786573at_nat @ ( J2 = K ) @ zero_z1048942125864253310at_nat @ ( H3 @ ( minus_minus_nat @ J2 @ ( suc @ zero_zero_nat ) ) ) ) )
% 0.33/0.59 @ ( set_ord_atMost_nat @ P4 ) )
% 0.33/0.59 = ( groups6857163185585827899at_nat
% 0.33/0.59 @ ^ [J2: nat] : ( if_mul8430962117462786573at_nat @ ( ord_less_nat @ J2 @ K ) @ ( G @ J2 ) @ ( H3 @ J2 ) )
% 0.33/0.59 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P4 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum.zero_middle
% 0.33/0.59 thf(fact_3869_sum_Ozero__middle,axiom,
% 0.33/0.59 ! [P4: nat,K: nat,G: nat > rat,H3: nat > rat] :
% 0.33/0.59 ( ( ord_less_eq_nat @ one_one_nat @ P4 )
% 0.33/0.59 => ( ( ord_less_eq_nat @ K @ P4 )
% 0.33/0.59 => ( ( groups2906978787729119204at_rat
% 0.33/0.59 @ ^ [J2: nat] : ( if_rat @ ( ord_less_nat @ J2 @ K ) @ ( G @ J2 ) @ ( if_rat @ ( J2 = K ) @ zero_zero_rat @ ( H3 @ ( minus_minus_nat @ J2 @ ( suc @ zero_zero_nat ) ) ) ) )
% 0.33/0.59 @ ( set_ord_atMost_nat @ P4 ) )
% 0.33/0.59 = ( groups2906978787729119204at_rat
% 0.33/0.59 @ ^ [J2: nat] : ( if_rat @ ( ord_less_nat @ J2 @ K ) @ ( G @ J2 ) @ ( H3 @ J2 ) )
% 0.33/0.59 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P4 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum.zero_middle
% 0.33/0.59 thf(fact_3870_sum_Ozero__middle,axiom,
% 0.33/0.59 ! [P4: nat,K: nat,G: nat > int,H3: nat > int] :
% 0.33/0.59 ( ( ord_less_eq_nat @ one_one_nat @ P4 )
% 0.33/0.59 => ( ( ord_less_eq_nat @ K @ P4 )
% 0.33/0.59 => ( ( groups3539618377306564664at_int
% 0.33/0.59 @ ^ [J2: nat] : ( if_int @ ( ord_less_nat @ J2 @ K ) @ ( G @ J2 ) @ ( if_int @ ( J2 = K ) @ zero_zero_int @ ( H3 @ ( minus_minus_nat @ J2 @ ( suc @ zero_zero_nat ) ) ) ) )
% 0.33/0.59 @ ( set_ord_atMost_nat @ P4 ) )
% 0.33/0.59 = ( groups3539618377306564664at_int
% 0.33/0.59 @ ^ [J2: nat] : ( if_int @ ( ord_less_nat @ J2 @ K ) @ ( G @ J2 ) @ ( H3 @ J2 ) )
% 0.33/0.59 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P4 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum.zero_middle
% 0.33/0.59 thf(fact_3871_sum_Ozero__middle,axiom,
% 0.33/0.59 ! [P4: nat,K: nat,G: nat > nat,H3: nat > nat] :
% 0.33/0.59 ( ( ord_less_eq_nat @ one_one_nat @ P4 )
% 0.33/0.59 => ( ( ord_less_eq_nat @ K @ P4 )
% 0.33/0.59 => ( ( groups3542108847815614940at_nat
% 0.33/0.59 @ ^ [J2: nat] : ( if_nat @ ( ord_less_nat @ J2 @ K ) @ ( G @ J2 ) @ ( if_nat @ ( J2 = K ) @ zero_zero_nat @ ( H3 @ ( minus_minus_nat @ J2 @ ( suc @ zero_zero_nat ) ) ) ) )
% 0.33/0.59 @ ( set_ord_atMost_nat @ P4 ) )
% 0.33/0.59 = ( groups3542108847815614940at_nat
% 0.33/0.59 @ ^ [J2: nat] : ( if_nat @ ( ord_less_nat @ J2 @ K ) @ ( G @ J2 ) @ ( H3 @ J2 ) )
% 0.33/0.59 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P4 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum.zero_middle
% 0.33/0.59 thf(fact_3872_and__minus__numerals_I3_J,axiom,
% 0.33/0.59 ! [M2: num,N2: num] :
% 0.33/0.59 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) )
% 0.33/0.59 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M2 @ ( bitM @ N2 ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % and_minus_numerals(3)
% 0.33/0.59 thf(fact_3873_and__minus__numerals_I7_J,axiom,
% 0.33/0.59 ! [N2: num,M2: num] :
% 0.33/0.59 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) @ ( numeral_numeral_int @ M2 ) )
% 0.33/0.59 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M2 @ ( bitM @ N2 ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % and_minus_numerals(7)
% 0.33/0.59 thf(fact_3874_and__minus__numerals_I4_J,axiom,
% 0.33/0.59 ! [M2: num,N2: num] :
% 0.33/0.59 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) )
% 0.33/0.59 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M2 @ ( bit0 @ N2 ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % and_minus_numerals(4)
% 0.33/0.59 thf(fact_3875_and__minus__numerals_I8_J,axiom,
% 0.33/0.59 ! [N2: num,M2: num] :
% 0.33/0.59 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) @ ( numeral_numeral_int @ M2 ) )
% 0.33/0.59 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M2 @ ( bit0 @ N2 ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % and_minus_numerals(8)
% 0.33/0.59 thf(fact_3876_gbinomial__partial__row__sum,axiom,
% 0.33/0.59 ! [A: rat,M2: nat] :
% 0.33/0.59 ( ( groups2906978787729119204at_rat
% 0.33/0.59 @ ^ [K4: nat] : ( times_times_rat @ ( gbinomial_rat @ A @ K4 ) @ ( minus_minus_rat @ ( divide_divide_rat @ A @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( semiri681578069525770553at_rat @ K4 ) ) )
% 0.33/0.59 @ ( set_ord_atMost_nat @ M2 ) )
% 0.33/0.59 = ( times_times_rat @ ( divide_divide_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M2 ) @ one_one_rat ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( gbinomial_rat @ A @ ( plus_plus_nat @ M2 @ one_one_nat ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % gbinomial_partial_row_sum
% 0.33/0.59 thf(fact_3877_gbinomial__r__part__sum,axiom,
% 0.33/0.59 ! [M2: nat] :
% 0.33/0.59 ( ( groups2906978787729119204at_rat @ ( gbinomial_rat @ ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( semiri681578069525770553at_rat @ M2 ) ) @ one_one_rat ) ) @ ( set_ord_atMost_nat @ M2 ) )
% 0.33/0.59 = ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % gbinomial_r_part_sum
% 0.33/0.59 thf(fact_3878_and__num_Oelims,axiom,
% 0.33/0.59 ! [X: num,Xa: num,Y: option_num] :
% 0.33/0.59 ( ( ( bit_un7362597486090784418nd_num @ X @ Xa )
% 0.33/0.59 = Y )
% 0.33/0.59 => ( ( ( X = one )
% 0.33/0.59 => ( ( Xa = one )
% 0.33/0.59 => ( Y
% 0.33/0.59 != ( some_num @ one ) ) ) )
% 0.33/0.59 => ( ( ( X = one )
% 0.33/0.59 => ( ? [N: num] :
% 0.33/0.59 ( Xa
% 0.33/0.59 = ( bit0 @ N ) )
% 0.33/0.59 => ( Y != none_num ) ) )
% 0.33/0.59 => ( ( ( X = one )
% 0.33/0.59 => ( ? [N: num] :
% 0.33/0.59 ( Xa
% 0.33/0.59 = ( bit1 @ N ) )
% 0.33/0.59 => ( Y
% 0.33/0.59 != ( some_num @ one ) ) ) )
% 0.33/0.59 => ( ( ? [M5: num] :
% 0.33/0.59 ( X
% 0.33/0.59 = ( bit0 @ M5 ) )
% 0.33/0.59 => ( ( Xa = one )
% 0.33/0.59 => ( Y != none_num ) ) )
% 0.33/0.59 => ( ! [M5: num] :
% 0.33/0.59 ( ( X
% 0.33/0.59 = ( bit0 @ M5 ) )
% 0.33/0.59 => ! [N: num] :
% 0.33/0.59 ( ( Xa
% 0.33/0.59 = ( bit0 @ N ) )
% 0.33/0.59 => ( Y
% 0.33/0.59 != ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M5 @ N ) ) ) ) )
% 0.33/0.59 => ( ! [M5: num] :
% 0.33/0.59 ( ( X
% 0.33/0.59 = ( bit0 @ M5 ) )
% 0.33/0.59 => ! [N: num] :
% 0.33/0.59 ( ( Xa
% 0.33/0.59 = ( bit1 @ N ) )
% 0.33/0.59 => ( Y
% 0.33/0.59 != ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M5 @ N ) ) ) ) )
% 0.33/0.59 => ( ( ? [M5: num] :
% 0.33/0.59 ( X
% 0.33/0.59 = ( bit1 @ M5 ) )
% 0.33/0.59 => ( ( Xa = one )
% 0.33/0.59 => ( Y
% 0.33/0.59 != ( some_num @ one ) ) ) )
% 0.33/0.59 => ( ! [M5: num] :
% 0.33/0.59 ( ( X
% 0.33/0.59 = ( bit1 @ M5 ) )
% 0.33/0.59 => ! [N: num] :
% 0.33/0.59 ( ( Xa
% 0.33/0.59 = ( bit0 @ N ) )
% 0.33/0.59 => ( Y
% 0.33/0.59 != ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M5 @ N ) ) ) ) )
% 0.33/0.59 => ~ ! [M5: num] :
% 0.33/0.59 ( ( X
% 0.33/0.59 = ( bit1 @ M5 ) )
% 0.33/0.59 => ! [N: num] :
% 0.33/0.59 ( ( Xa
% 0.33/0.59 = ( bit1 @ N ) )
% 0.33/0.59 => ( Y
% 0.33/0.59 != ( case_o6005452278849405969um_num @ ( some_num @ one )
% 0.33/0.59 @ ^ [N8: num] : ( some_num @ ( bit1 @ N8 ) )
% 0.33/0.59 @ ( bit_un7362597486090784418nd_num @ M5 @ N ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % and_num.elims
% 0.33/0.59 thf(fact_3879_take__bit__Suc__from__most,axiom,
% 0.33/0.59 ! [N2: nat,K: int] :
% 0.33/0.59 ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ K )
% 0.33/0.59 = ( plus_plus_int @ ( times_times_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K @ N2 ) ) ) @ ( bit_se2923211474154528505it_int @ N2 @ K ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % take_bit_Suc_from_most
% 0.33/0.59 thf(fact_3880_gbinomial__0_I1_J,axiom,
% 0.33/0.59 ! [A: code_integer] :
% 0.33/0.59 ( ( gbinom8545251970709558553nteger @ A @ zero_zero_nat )
% 0.33/0.59 = one_one_Code_integer ) ).
% 0.33/0.59
% 0.33/0.59 % gbinomial_0(1)
% 0.33/0.59 thf(fact_3881_gbinomial__0_I1_J,axiom,
% 0.33/0.59 ! [A: rat] :
% 0.33/0.59 ( ( gbinomial_rat @ A @ zero_zero_nat )
% 0.33/0.59 = one_one_rat ) ).
% 0.33/0.59
% 0.33/0.59 % gbinomial_0(1)
% 0.33/0.59 thf(fact_3882_gbinomial__0_I1_J,axiom,
% 0.33/0.59 ! [A: nat] :
% 0.33/0.59 ( ( gbinomial_nat @ A @ zero_zero_nat )
% 0.33/0.59 = one_one_nat ) ).
% 0.33/0.59
% 0.33/0.59 % gbinomial_0(1)
% 0.33/0.59 thf(fact_3883_gbinomial__0_I1_J,axiom,
% 0.33/0.59 ! [A: int] :
% 0.33/0.59 ( ( gbinomial_int @ A @ zero_zero_nat )
% 0.33/0.59 = one_one_int ) ).
% 0.33/0.59
% 0.33/0.59 % gbinomial_0(1)
% 0.33/0.59 thf(fact_3884_and__nat__numerals_I2_J,axiom,
% 0.33/0.59 ! [Y: num] :
% 0.33/0.59 ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 0.33/0.59 = one_one_nat ) ).
% 0.33/0.59
% 0.33/0.59 % and_nat_numerals(2)
% 0.33/0.59 thf(fact_3885_and__nat__numerals_I4_J,axiom,
% 0.33/0.59 ! [X: num] :
% 0.33/0.59 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 0.33/0.59 = one_one_nat ) ).
% 0.33/0.59
% 0.33/0.59 % and_nat_numerals(4)
% 0.33/0.59 thf(fact_3886_bit__disjunctive__add__iff,axiom,
% 0.33/0.59 ! [A: int,B: int,N2: nat] :
% 0.33/0.59 ( ! [N: nat] :
% 0.33/0.59 ( ~ ( bit_se1146084159140164899it_int @ A @ N )
% 0.33/0.59 | ~ ( bit_se1146084159140164899it_int @ B @ N ) )
% 0.33/0.59 => ( ( bit_se1146084159140164899it_int @ ( plus_plus_int @ A @ B ) @ N2 )
% 0.33/0.59 = ( ( bit_se1146084159140164899it_int @ A @ N2 )
% 0.33/0.59 | ( bit_se1146084159140164899it_int @ B @ N2 ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % bit_disjunctive_add_iff
% 0.33/0.59 thf(fact_3887_bit__disjunctive__add__iff,axiom,
% 0.33/0.59 ! [A: code_integer,B: code_integer,N2: nat] :
% 0.33/0.59 ( ! [N: nat] :
% 0.33/0.59 ( ~ ( bit_se9216721137139052372nteger @ A @ N )
% 0.33/0.59 | ~ ( bit_se9216721137139052372nteger @ B @ N ) )
% 0.33/0.59 => ( ( bit_se9216721137139052372nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ N2 )
% 0.33/0.59 = ( ( bit_se9216721137139052372nteger @ A @ N2 )
% 0.33/0.59 | ( bit_se9216721137139052372nteger @ B @ N2 ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % bit_disjunctive_add_iff
% 0.33/0.59 thf(fact_3888_bit__disjunctive__add__iff,axiom,
% 0.33/0.59 ! [A: nat,B: nat,N2: nat] :
% 0.33/0.59 ( ! [N: nat] :
% 0.33/0.59 ( ~ ( bit_se1148574629649215175it_nat @ A @ N )
% 0.33/0.59 | ~ ( bit_se1148574629649215175it_nat @ B @ N ) )
% 0.33/0.59 => ( ( bit_se1148574629649215175it_nat @ ( plus_plus_nat @ A @ B ) @ N2 )
% 0.33/0.59 = ( ( bit_se1148574629649215175it_nat @ A @ N2 )
% 0.33/0.59 | ( bit_se1148574629649215175it_nat @ B @ N2 ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % bit_disjunctive_add_iff
% 0.33/0.59 thf(fact_3889_bit__disjunctive__add__iff,axiom,
% 0.33/0.59 ! [A: code_natural,B: code_natural,N2: nat] :
% 0.33/0.59 ( ! [N: nat] :
% 0.33/0.59 ( ~ ( bit_se8040316288895769887atural @ A @ N )
% 0.33/0.59 | ~ ( bit_se8040316288895769887atural @ B @ N ) )
% 0.33/0.59 => ( ( bit_se8040316288895769887atural @ ( plus_p4538020629002901425atural @ A @ B ) @ N2 )
% 0.33/0.59 = ( ( bit_se8040316288895769887atural @ A @ N2 )
% 0.33/0.59 | ( bit_se8040316288895769887atural @ B @ N2 ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % bit_disjunctive_add_iff
% 0.33/0.59 thf(fact_3890_bit__1__iff,axiom,
% 0.33/0.59 ! [N2: nat] :
% 0.33/0.59 ( ( bit_se1146084159140164899it_int @ one_one_int @ N2 )
% 0.33/0.59 = ( N2 = zero_zero_nat ) ) ).
% 0.33/0.59
% 0.33/0.59 % bit_1_iff
% 0.33/0.59 thf(fact_3891_bit__1__iff,axiom,
% 0.33/0.59 ! [N2: nat] :
% 0.33/0.59 ( ( bit_se9216721137139052372nteger @ one_one_Code_integer @ N2 )
% 0.33/0.59 = ( N2 = zero_zero_nat ) ) ).
% 0.33/0.59
% 0.33/0.59 % bit_1_iff
% 0.33/0.59 thf(fact_3892_bit__1__iff,axiom,
% 0.33/0.59 ! [N2: nat] :
% 0.33/0.59 ( ( bit_se1148574629649215175it_nat @ one_one_nat @ N2 )
% 0.33/0.59 = ( N2 = zero_zero_nat ) ) ).
% 0.33/0.59
% 0.33/0.59 % bit_1_iff
% 0.33/0.59 thf(fact_3893_bit__1__iff,axiom,
% 0.33/0.59 ! [N2: nat] :
% 0.33/0.59 ( ( bit_se8040316288895769887atural @ one_one_Code_natural @ N2 )
% 0.33/0.59 = ( N2 = zero_zero_nat ) ) ).
% 0.33/0.59
% 0.33/0.59 % bit_1_iff
% 0.33/0.59 thf(fact_3894_not__bit__1__Suc,axiom,
% 0.33/0.59 ! [N2: nat] :
% 0.33/0.59 ~ ( bit_se1146084159140164899it_int @ one_one_int @ ( suc @ N2 ) ) ).
% 0.33/0.59
% 0.33/0.59 % not_bit_1_Suc
% 0.33/0.59 thf(fact_3895_not__bit__1__Suc,axiom,
% 0.33/0.59 ! [N2: nat] :
% 0.33/0.59 ~ ( bit_se9216721137139052372nteger @ one_one_Code_integer @ ( suc @ N2 ) ) ).
% 0.33/0.59
% 0.33/0.59 % not_bit_1_Suc
% 0.33/0.59 thf(fact_3896_not__bit__1__Suc,axiom,
% 0.33/0.59 ! [N2: nat] :
% 0.33/0.59 ~ ( bit_se1148574629649215175it_nat @ one_one_nat @ ( suc @ N2 ) ) ).
% 0.33/0.59
% 0.33/0.59 % not_bit_1_Suc
% 0.33/0.59 thf(fact_3897_not__bit__1__Suc,axiom,
% 0.33/0.59 ! [N2: nat] :
% 0.33/0.59 ~ ( bit_se8040316288895769887atural @ one_one_Code_natural @ ( suc @ N2 ) ) ).
% 0.33/0.59
% 0.33/0.59 % not_bit_1_Suc
% 0.33/0.59 thf(fact_3898_bit__numeral__simps_I1_J,axiom,
% 0.33/0.59 ! [N2: num] :
% 0.33/0.59 ~ ( bit_se1146084159140164899it_int @ one_one_int @ ( numeral_numeral_nat @ N2 ) ) ).
% 0.33/0.59
% 0.33/0.59 % bit_numeral_simps(1)
% 0.33/0.59 thf(fact_3899_bit__numeral__simps_I1_J,axiom,
% 0.33/0.59 ! [N2: num] :
% 0.33/0.59 ~ ( bit_se9216721137139052372nteger @ one_one_Code_integer @ ( numeral_numeral_nat @ N2 ) ) ).
% 0.33/0.59
% 0.33/0.59 % bit_numeral_simps(1)
% 0.33/0.59 thf(fact_3900_bit__numeral__simps_I1_J,axiom,
% 0.33/0.59 ! [N2: num] :
% 0.33/0.59 ~ ( bit_se1148574629649215175it_nat @ one_one_nat @ ( numeral_numeral_nat @ N2 ) ) ).
% 0.33/0.59
% 0.33/0.59 % bit_numeral_simps(1)
% 0.33/0.59 thf(fact_3901_bit__numeral__simps_I1_J,axiom,
% 0.33/0.59 ! [N2: num] :
% 0.33/0.59 ~ ( bit_se8040316288895769887atural @ one_one_Code_natural @ ( numeral_numeral_nat @ N2 ) ) ).
% 0.33/0.59
% 0.33/0.59 % bit_numeral_simps(1)
% 0.33/0.59 thf(fact_3902_gbinomial__Suc__Suc,axiom,
% 0.33/0.59 ! [A: rat,K: nat] :
% 0.33/0.59 ( ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) )
% 0.33/0.59 = ( plus_plus_rat @ ( gbinomial_rat @ A @ K ) @ ( gbinomial_rat @ A @ ( suc @ K ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % gbinomial_Suc_Suc
% 0.33/0.59 thf(fact_3903_and__integer_Oabs__eq,axiom,
% 0.33/0.59 ! [Xa: int,X: int] :
% 0.33/0.59 ( ( bit_se3949692690581998587nteger @ ( code_integer_of_int @ Xa ) @ ( code_integer_of_int @ X ) )
% 0.33/0.59 = ( code_integer_of_int @ ( bit_se725231765392027082nd_int @ Xa @ X ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % and_integer.abs_eq
% 0.33/0.59 thf(fact_3904_gbinomial__addition__formula,axiom,
% 0.33/0.59 ! [A: rat,K: nat] :
% 0.33/0.59 ( ( gbinomial_rat @ A @ ( suc @ K ) )
% 0.33/0.59 = ( plus_plus_rat @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ ( suc @ K ) ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % gbinomial_addition_formula
% 0.33/0.59 thf(fact_3905_gbinomial__absorb__comp,axiom,
% 0.33/0.59 ! [A: rat,K: nat] :
% 0.33/0.59 ( ( times_times_rat @ ( minus_minus_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ ( gbinomial_rat @ A @ K ) )
% 0.33/0.59 = ( times_times_rat @ A @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % gbinomial_absorb_comp
% 0.33/0.59 thf(fact_3906_gbinomial__mult__1_H,axiom,
% 0.33/0.59 ! [A: rat,K: nat] :
% 0.33/0.59 ( ( times_times_rat @ ( gbinomial_rat @ A @ K ) @ A )
% 0.33/0.59 = ( plus_plus_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ K ) @ ( gbinomial_rat @ A @ K ) ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) @ ( gbinomial_rat @ A @ ( suc @ K ) ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % gbinomial_mult_1'
% 0.33/0.59 thf(fact_3907_gbinomial__mult__1,axiom,
% 0.33/0.59 ! [A: rat,K: nat] :
% 0.33/0.59 ( ( times_times_rat @ A @ ( gbinomial_rat @ A @ K ) )
% 0.33/0.59 = ( plus_plus_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ K ) @ ( gbinomial_rat @ A @ K ) ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) @ ( gbinomial_rat @ A @ ( suc @ K ) ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % gbinomial_mult_1
% 0.33/0.59 thf(fact_3908_Suc__times__gbinomial,axiom,
% 0.33/0.59 ! [K: nat,A: rat] :
% 0.33/0.59 ( ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) @ ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) ) )
% 0.33/0.59 = ( times_times_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( gbinomial_rat @ A @ K ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % Suc_times_gbinomial
% 0.33/0.59 thf(fact_3909_gbinomial__absorption,axiom,
% 0.33/0.59 ! [K: nat,A: rat] :
% 0.33/0.59 ( ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) @ ( gbinomial_rat @ A @ ( suc @ K ) ) )
% 0.33/0.59 = ( times_times_rat @ A @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % gbinomial_absorption
% 0.33/0.59 thf(fact_3910_gbinomial__parallel__sum,axiom,
% 0.33/0.59 ! [A: rat,N2: nat] :
% 0.33/0.59 ( ( groups2906978787729119204at_rat
% 0.33/0.59 @ ^ [K4: nat] : ( gbinomial_rat @ ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ K4 ) ) @ K4 )
% 0.33/0.59 @ ( set_ord_atMost_nat @ N2 ) )
% 0.33/0.59 = ( gbinomial_rat @ ( plus_plus_rat @ ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ N2 ) ) @ one_one_rat ) @ N2 ) ) ).
% 0.33/0.59
% 0.33/0.59 % gbinomial_parallel_sum
% 0.33/0.59 thf(fact_3911_gbinomial__rec,axiom,
% 0.33/0.59 ! [A: rat,K: nat] :
% 0.33/0.59 ( ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) )
% 0.33/0.59 = ( times_times_rat @ ( gbinomial_rat @ A @ K ) @ ( divide_divide_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % gbinomial_rec
% 0.33/0.59 thf(fact_3912_gbinomial__factors,axiom,
% 0.33/0.59 ! [A: rat,K: nat] :
% 0.33/0.59 ( ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) )
% 0.33/0.59 = ( times_times_rat @ ( divide_divide_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) ) @ ( gbinomial_rat @ A @ K ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % gbinomial_factors
% 0.33/0.59 thf(fact_3913_gbinomial__negated__upper,axiom,
% 0.33/0.59 ( gbinomial_rat
% 0.33/0.59 = ( ^ [A5: rat,K4: nat] : ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K4 ) @ ( gbinomial_rat @ ( minus_minus_rat @ ( minus_minus_rat @ ( semiri681578069525770553at_rat @ K4 ) @ A5 ) @ one_one_rat ) @ K4 ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % gbinomial_negated_upper
% 0.33/0.59 thf(fact_3914_gbinomial__index__swap,axiom,
% 0.33/0.59 ! [K: nat,N2: nat] :
% 0.33/0.59 ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K ) @ ( gbinomial_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N2 ) ) @ one_one_rat ) @ K ) )
% 0.33/0.59 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 ) @ ( gbinomial_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ K ) ) @ one_one_rat ) @ N2 ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % gbinomial_index_swap
% 0.33/0.59 thf(fact_3915_int__bit__bound,axiom,
% 0.33/0.59 ! [K: int] :
% 0.33/0.59 ~ ! [N: nat] :
% 0.33/0.59 ( ! [M6: nat] :
% 0.33/0.59 ( ( ord_less_eq_nat @ N @ M6 )
% 0.33/0.59 => ( ( bit_se1146084159140164899it_int @ K @ M6 )
% 0.33/0.59 = ( bit_se1146084159140164899it_int @ K @ N ) ) )
% 0.33/0.59 => ~ ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.33/0.59 => ( ( bit_se1146084159140164899it_int @ K @ ( minus_minus_nat @ N @ one_one_nat ) )
% 0.33/0.59 = ( ~ ( bit_se1146084159140164899it_int @ K @ N ) ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % int_bit_bound
% 0.33/0.59 thf(fact_3916_gbinomial__minus,axiom,
% 0.33/0.59 ! [A: rat,K: nat] :
% 0.33/0.59 ( ( gbinomial_rat @ ( uminus_uminus_rat @ A ) @ K )
% 0.33/0.59 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K ) @ ( gbinomial_rat @ ( minus_minus_rat @ ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ one_one_rat ) @ K ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % gbinomial_minus
% 0.33/0.59 thf(fact_3917_gbinomial__reduce__nat,axiom,
% 0.33/0.59 ! [K: nat,A: rat] :
% 0.33/0.59 ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.33/0.59 => ( ( gbinomial_rat @ A @ K )
% 0.33/0.59 = ( plus_plus_rat @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % gbinomial_reduce_nat
% 0.33/0.59 thf(fact_3918_gbinomial__sum__lower__neg,axiom,
% 0.33/0.59 ! [A: rat,M2: nat] :
% 0.33/0.59 ( ( groups2906978787729119204at_rat
% 0.33/0.59 @ ^ [K4: nat] : ( times_times_rat @ ( gbinomial_rat @ A @ K4 ) @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K4 ) )
% 0.33/0.59 @ ( set_ord_atMost_nat @ M2 ) )
% 0.33/0.59 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ M2 ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ M2 ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % gbinomial_sum_lower_neg
% 0.33/0.59 thf(fact_3919_numeral__and__num,axiom,
% 0.33/0.59 ! [M2: num,N2: num] :
% 0.33/0.59 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N2 ) )
% 0.33/0.59 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_un7362597486090784418nd_num @ M2 @ N2 ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % numeral_and_num
% 0.33/0.59 thf(fact_3920_numeral__and__num,axiom,
% 0.33/0.59 ! [M2: num,N2: num] :
% 0.33/0.59 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ N2 ) )
% 0.33/0.59 = ( case_option_nat_num @ zero_zero_nat @ numeral_numeral_nat @ ( bit_un7362597486090784418nd_num @ M2 @ N2 ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % numeral_and_num
% 0.33/0.59 thf(fact_3921_numeral__and__num,axiom,
% 0.33/0.59 ! [M2: num,N2: num] :
% 0.33/0.59 ( ( bit_se3949692690581998587nteger @ ( numera6620942414471956472nteger @ M2 ) @ ( numera6620942414471956472nteger @ N2 ) )
% 0.33/0.59 = ( case_o356765784539232260er_num @ zero_z3403309356797280102nteger @ numera6620942414471956472nteger @ ( bit_un7362597486090784418nd_num @ M2 @ N2 ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % numeral_and_num
% 0.33/0.59 thf(fact_3922_numeral__and__num,axiom,
% 0.33/0.59 ! [M2: num,N2: num] :
% 0.33/0.59 ( ( bit_se2773287842338716102atural @ ( numera5444537566228673987atural @ M2 ) @ ( numera5444537566228673987atural @ N2 ) )
% 0.33/0.59 = ( case_o5621594795226839503al_num @ zero_z2226904508553997617atural @ numera5444537566228673987atural @ ( bit_un7362597486090784418nd_num @ M2 @ N2 ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % numeral_and_num
% 0.33/0.59 thf(fact_3923_gbinomial__sum__up__index,axiom,
% 0.33/0.59 ! [K: nat,N2: nat] :
% 0.33/0.59 ( ( groups2906978787729119204at_rat
% 0.33/0.59 @ ^ [J2: nat] : ( gbinomial_rat @ ( semiri681578069525770553at_rat @ J2 ) @ K )
% 0.33/0.59 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 0.33/0.59 = ( gbinomial_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N2 ) @ one_one_rat ) @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % gbinomial_sum_up_index
% 0.33/0.59 thf(fact_3924_gbinomial__partial__sum__poly,axiom,
% 0.33/0.59 ! [M2: nat,A: rat,X: rat,Y: rat] :
% 0.33/0.59 ( ( groups2906978787729119204at_rat
% 0.33/0.59 @ ^ [K4: nat] : ( times_times_rat @ ( times_times_rat @ ( gbinomial_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M2 ) @ A ) @ K4 ) @ ( power_power_rat @ X @ K4 ) ) @ ( power_power_rat @ Y @ ( minus_minus_nat @ M2 @ K4 ) ) )
% 0.33/0.59 @ ( set_ord_atMost_nat @ M2 ) )
% 0.33/0.59 = ( groups2906978787729119204at_rat
% 0.33/0.59 @ ^ [K4: nat] : ( times_times_rat @ ( times_times_rat @ ( gbinomial_rat @ ( uminus_uminus_rat @ A ) @ K4 ) @ ( power_power_rat @ ( uminus_uminus_rat @ X ) @ K4 ) ) @ ( power_power_rat @ ( plus_plus_rat @ X @ Y ) @ ( minus_minus_nat @ M2 @ K4 ) ) )
% 0.33/0.59 @ ( set_ord_atMost_nat @ M2 ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % gbinomial_partial_sum_poly
% 0.33/0.59 thf(fact_3925_even__bit__succ__iff,axiom,
% 0.33/0.59 ! [A: int,N2: nat] :
% 0.33/0.59 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.33/0.59 => ( ( bit_se1146084159140164899it_int @ ( plus_plus_int @ one_one_int @ A ) @ N2 )
% 0.33/0.59 = ( ( bit_se1146084159140164899it_int @ A @ N2 )
% 0.33/0.59 | ( N2 = zero_zero_nat ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % even_bit_succ_iff
% 0.33/0.59 thf(fact_3926_even__bit__succ__iff,axiom,
% 0.33/0.59 ! [A: code_integer,N2: nat] :
% 0.33/0.59 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.33/0.59 => ( ( bit_se9216721137139052372nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ N2 )
% 0.33/0.59 = ( ( bit_se9216721137139052372nteger @ A @ N2 )
% 0.33/0.59 | ( N2 = zero_zero_nat ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % even_bit_succ_iff
% 0.33/0.59 thf(fact_3927_even__bit__succ__iff,axiom,
% 0.33/0.59 ! [A: nat,N2: nat] :
% 0.33/0.59 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.33/0.59 => ( ( bit_se1148574629649215175it_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ N2 )
% 0.33/0.59 = ( ( bit_se1148574629649215175it_nat @ A @ N2 )
% 0.33/0.59 | ( N2 = zero_zero_nat ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % even_bit_succ_iff
% 0.33/0.59 thf(fact_3928_even__bit__succ__iff,axiom,
% 0.33/0.59 ! [A: code_natural,N2: nat] :
% 0.33/0.59 ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 0.33/0.59 => ( ( bit_se8040316288895769887atural @ ( plus_p4538020629002901425atural @ one_one_Code_natural @ A ) @ N2 )
% 0.33/0.59 = ( ( bit_se8040316288895769887atural @ A @ N2 )
% 0.33/0.59 | ( N2 = zero_zero_nat ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % even_bit_succ_iff
% 0.33/0.59 thf(fact_3929_odd__bit__iff__bit__pred,axiom,
% 0.33/0.59 ! [A: int,N2: nat] :
% 0.33/0.59 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.33/0.59 => ( ( bit_se1146084159140164899it_int @ A @ N2 )
% 0.33/0.59 = ( ( bit_se1146084159140164899it_int @ ( minus_minus_int @ A @ one_one_int ) @ N2 )
% 0.33/0.59 | ( N2 = zero_zero_nat ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % odd_bit_iff_bit_pred
% 0.33/0.59 thf(fact_3930_odd__bit__iff__bit__pred,axiom,
% 0.33/0.59 ! [A: code_integer,N2: nat] :
% 0.33/0.59 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.33/0.59 => ( ( bit_se9216721137139052372nteger @ A @ N2 )
% 0.33/0.59 = ( ( bit_se9216721137139052372nteger @ ( minus_8373710615458151222nteger @ A @ one_one_Code_integer ) @ N2 )
% 0.33/0.59 | ( N2 = zero_zero_nat ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % odd_bit_iff_bit_pred
% 0.33/0.59 thf(fact_3931_odd__bit__iff__bit__pred,axiom,
% 0.33/0.59 ! [A: nat,N2: nat] :
% 0.33/0.59 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.33/0.59 => ( ( bit_se1148574629649215175it_nat @ A @ N2 )
% 0.33/0.59 = ( ( bit_se1148574629649215175it_nat @ ( minus_minus_nat @ A @ one_one_nat ) @ N2 )
% 0.33/0.59 | ( N2 = zero_zero_nat ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % odd_bit_iff_bit_pred
% 0.33/0.59 thf(fact_3932_odd__bit__iff__bit__pred,axiom,
% 0.33/0.59 ! [A: code_natural,N2: nat] :
% 0.33/0.59 ( ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 0.33/0.59 => ( ( bit_se8040316288895769887atural @ A @ N2 )
% 0.33/0.59 = ( ( bit_se8040316288895769887atural @ ( minus_7197305767214868737atural @ A @ one_one_Code_natural ) @ N2 )
% 0.33/0.59 | ( N2 = zero_zero_nat ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % odd_bit_iff_bit_pred
% 0.33/0.59 thf(fact_3933_and__num_Osimps_I9_J,axiom,
% 0.33/0.59 ! [M2: num,N2: num] :
% 0.33/0.59 ( ( bit_un7362597486090784418nd_num @ ( bit1 @ M2 ) @ ( bit1 @ N2 ) )
% 0.33/0.59 = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 0.33/0.59 @ ^ [N8: num] : ( some_num @ ( bit1 @ N8 ) )
% 0.33/0.59 @ ( bit_un7362597486090784418nd_num @ M2 @ N2 ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % and_num.simps(9)
% 0.33/0.59 thf(fact_3934_gbinomial__absorption_H,axiom,
% 0.33/0.59 ! [K: nat,A: rat] :
% 0.33/0.59 ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.33/0.59 => ( ( gbinomial_rat @ A @ K )
% 0.33/0.59 = ( times_times_rat @ ( divide_divide_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % gbinomial_absorption'
% 0.33/0.59 thf(fact_3935_gbinomial__partial__sum__poly__xpos,axiom,
% 0.33/0.59 ! [M2: nat,A: rat,X: rat,Y: rat] :
% 0.33/0.59 ( ( groups2906978787729119204at_rat
% 0.33/0.59 @ ^ [K4: nat] : ( times_times_rat @ ( times_times_rat @ ( gbinomial_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M2 ) @ A ) @ K4 ) @ ( power_power_rat @ X @ K4 ) ) @ ( power_power_rat @ Y @ ( minus_minus_nat @ M2 @ K4 ) ) )
% 0.33/0.59 @ ( set_ord_atMost_nat @ M2 ) )
% 0.33/0.59 = ( groups2906978787729119204at_rat
% 0.33/0.59 @ ^ [K4: nat] : ( times_times_rat @ ( times_times_rat @ ( gbinomial_rat @ ( minus_minus_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ K4 ) @ A ) @ one_one_rat ) @ K4 ) @ ( power_power_rat @ X @ K4 ) ) @ ( power_power_rat @ ( plus_plus_rat @ X @ Y ) @ ( minus_minus_nat @ M2 @ K4 ) ) )
% 0.33/0.59 @ ( set_ord_atMost_nat @ M2 ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % gbinomial_partial_sum_poly_xpos
% 0.33/0.59 thf(fact_3936_gbinomial__sum__nat__pow2,axiom,
% 0.33/0.59 ! [M2: nat] :
% 0.33/0.59 ( ( groups2906978787729119204at_rat
% 0.33/0.59 @ ^ [K4: nat] : ( divide_divide_rat @ ( gbinomial_rat @ ( semiri681578069525770553at_rat @ ( plus_plus_nat @ M2 @ K4 ) ) @ K4 ) @ ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ K4 ) )
% 0.33/0.59 @ ( set_ord_atMost_nat @ M2 ) )
% 0.33/0.59 = ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ M2 ) ) ).
% 0.33/0.59
% 0.33/0.59 % gbinomial_sum_nat_pow2
% 0.33/0.59 thf(fact_3937_bit__sum__mult__2__cases,axiom,
% 0.33/0.59 ! [A: int,B: int,N2: nat] :
% 0.33/0.59 ( ! [J3: nat] :
% 0.33/0.59 ~ ( bit_se1146084159140164899it_int @ A @ ( suc @ J3 ) )
% 0.33/0.59 => ( ( bit_se1146084159140164899it_int @ ( plus_plus_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ N2 )
% 0.33/0.59 = ( ( ( N2 = zero_zero_nat )
% 0.33/0.59 => ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 0.33/0.59 & ( ( N2 != zero_zero_nat )
% 0.33/0.59 => ( bit_se1146084159140164899it_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) @ N2 ) ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % bit_sum_mult_2_cases
% 0.33/0.59 thf(fact_3938_bit__sum__mult__2__cases,axiom,
% 0.33/0.59 ! [A: code_integer,B: code_integer,N2: nat] :
% 0.33/0.59 ( ! [J3: nat] :
% 0.33/0.59 ~ ( bit_se9216721137139052372nteger @ A @ ( suc @ J3 ) )
% 0.33/0.59 => ( ( bit_se9216721137139052372nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ N2 )
% 0.33/0.59 = ( ( ( N2 = zero_zero_nat )
% 0.33/0.59 => ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 0.33/0.59 & ( ( N2 != zero_zero_nat )
% 0.33/0.59 => ( bit_se9216721137139052372nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) @ N2 ) ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % bit_sum_mult_2_cases
% 0.33/0.59 thf(fact_3939_bit__sum__mult__2__cases,axiom,
% 0.33/0.59 ! [A: nat,B: nat,N2: nat] :
% 0.33/0.59 ( ! [J3: nat] :
% 0.33/0.59 ~ ( bit_se1148574629649215175it_nat @ A @ ( suc @ J3 ) )
% 0.33/0.59 => ( ( bit_se1148574629649215175it_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ N2 )
% 0.33/0.59 = ( ( ( N2 = zero_zero_nat )
% 0.33/0.59 => ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 0.33/0.59 & ( ( N2 != zero_zero_nat )
% 0.33/0.59 => ( bit_se1148574629649215175it_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) @ N2 ) ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % bit_sum_mult_2_cases
% 0.33/0.59 thf(fact_3940_bit__sum__mult__2__cases,axiom,
% 0.33/0.59 ! [A: code_natural,B: code_natural,N2: nat] :
% 0.33/0.59 ( ! [J3: nat] :
% 0.33/0.59 ~ ( bit_se8040316288895769887atural @ A @ ( suc @ J3 ) )
% 0.33/0.59 => ( ( bit_se8040316288895769887atural @ ( plus_p4538020629002901425atural @ A @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ B ) ) @ N2 )
% 0.33/0.59 = ( ( ( N2 = zero_zero_nat )
% 0.33/0.59 => ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A ) )
% 0.33/0.59 & ( ( N2 != zero_zero_nat )
% 0.33/0.59 => ( bit_se8040316288895769887atural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ B ) @ N2 ) ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % bit_sum_mult_2_cases
% 0.33/0.59 thf(fact_3941_and__not__num_Osimps_I8_J,axiom,
% 0.33/0.59 ! [M2: num,N2: num] :
% 0.33/0.59 ( ( bit_and_not_num @ ( bit1 @ M2 ) @ ( bit0 @ N2 ) )
% 0.33/0.59 = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 0.33/0.59 @ ^ [N8: num] : ( some_num @ ( bit1 @ N8 ) )
% 0.33/0.59 @ ( bit_and_not_num @ M2 @ N2 ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % and_not_num.simps(8)
% 0.33/0.59 thf(fact_3942_bit__rec,axiom,
% 0.33/0.59 ( bit_se1146084159140164899it_int
% 0.33/0.59 = ( ^ [A5: int,N4: nat] :
% 0.33/0.59 ( ( ( N4 = zero_zero_nat )
% 0.33/0.59 => ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A5 ) )
% 0.33/0.59 & ( ( N4 != zero_zero_nat )
% 0.33/0.59 => ( bit_se1146084159140164899it_int @ ( divide_divide_int @ A5 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( minus_minus_nat @ N4 @ one_one_nat ) ) ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % bit_rec
% 0.33/0.59 thf(fact_3943_bit__rec,axiom,
% 0.33/0.59 ( bit_se9216721137139052372nteger
% 0.33/0.59 = ( ^ [A5: code_integer,N4: nat] :
% 0.33/0.59 ( ( ( N4 = zero_zero_nat )
% 0.33/0.59 => ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A5 ) )
% 0.33/0.59 & ( ( N4 != zero_zero_nat )
% 0.33/0.59 => ( bit_se9216721137139052372nteger @ ( divide6298287555418463151nteger @ A5 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( minus_minus_nat @ N4 @ one_one_nat ) ) ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % bit_rec
% 0.33/0.59 thf(fact_3944_bit__rec,axiom,
% 0.33/0.59 ( bit_se1148574629649215175it_nat
% 0.33/0.59 = ( ^ [A5: nat,N4: nat] :
% 0.33/0.59 ( ( ( N4 = zero_zero_nat )
% 0.33/0.59 => ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A5 ) )
% 0.33/0.59 & ( ( N4 != zero_zero_nat )
% 0.33/0.59 => ( bit_se1148574629649215175it_nat @ ( divide_divide_nat @ A5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( minus_minus_nat @ N4 @ one_one_nat ) ) ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % bit_rec
% 0.33/0.59 thf(fact_3945_bit__rec,axiom,
% 0.33/0.59 ( bit_se8040316288895769887atural
% 0.33/0.59 = ( ^ [A5: code_natural,N4: nat] :
% 0.33/0.59 ( ( ( N4 = zero_zero_nat )
% 0.33/0.59 => ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A5 ) )
% 0.33/0.59 & ( ( N4 != zero_zero_nat )
% 0.33/0.59 => ( bit_se8040316288895769887atural @ ( divide5121882707175180666atural @ A5 @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) @ ( minus_minus_nat @ N4 @ one_one_nat ) ) ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % bit_rec
% 0.33/0.59 thf(fact_3946_and__nat__unfold,axiom,
% 0.33/0.59 ( bit_se727722235901077358nd_nat
% 0.33/0.59 = ( ^ [M: nat,N4: nat] :
% 0.33/0.59 ( if_nat
% 0.33/0.59 @ ( ( M = zero_zero_nat )
% 0.33/0.59 | ( N4 = zero_zero_nat ) )
% 0.33/0.59 @ zero_zero_nat
% 0.33/0.59 @ ( plus_plus_nat @ ( times_times_nat @ ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( divide_divide_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % and_nat_unfold
% 0.33/0.59 thf(fact_3947_and__nat__rec,axiom,
% 0.33/0.59 ( bit_se727722235901077358nd_nat
% 0.33/0.59 = ( ^ [M: nat,N4: nat] :
% 0.33/0.59 ( plus_plus_nat
% 0.33/0.59 @ ( zero_n2687167440665602831ol_nat
% 0.33/0.59 @ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
% 0.33/0.59 & ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) )
% 0.33/0.59 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( divide_divide_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % and_nat_rec
% 0.33/0.59 thf(fact_3948_set__bit__eq,axiom,
% 0.33/0.59 ( bit_se7879613467334960850it_int
% 0.33/0.59 = ( ^ [N4: nat,K4: int] :
% 0.33/0.59 ( plus_plus_int @ K4
% 0.33/0.59 @ ( times_times_int
% 0.33/0.59 @ ( zero_n2684676970156552555ol_int
% 0.33/0.59 @ ~ ( bit_se1146084159140164899it_int @ K4 @ N4 ) )
% 0.33/0.59 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N4 ) ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % set_bit_eq
% 0.33/0.59 thf(fact_3949_and__not__num_Oelims,axiom,
% 0.33/0.59 ! [X: num,Xa: num,Y: option_num] :
% 0.33/0.59 ( ( ( bit_and_not_num @ X @ Xa )
% 0.33/0.59 = Y )
% 0.33/0.59 => ( ( ( X = one )
% 0.33/0.59 => ( ( Xa = one )
% 0.33/0.59 => ( Y != none_num ) ) )
% 0.33/0.59 => ( ( ( X = one )
% 0.33/0.59 => ( ? [N: num] :
% 0.33/0.59 ( Xa
% 0.33/0.59 = ( bit0 @ N ) )
% 0.33/0.59 => ( Y
% 0.33/0.59 != ( some_num @ one ) ) ) )
% 0.33/0.59 => ( ( ( X = one )
% 0.33/0.59 => ( ? [N: num] :
% 0.33/0.59 ( Xa
% 0.33/0.59 = ( bit1 @ N ) )
% 0.33/0.59 => ( Y != none_num ) ) )
% 0.33/0.59 => ( ! [M5: num] :
% 0.33/0.59 ( ( X
% 0.33/0.59 = ( bit0 @ M5 ) )
% 0.33/0.59 => ( ( Xa = one )
% 0.33/0.59 => ( Y
% 0.33/0.59 != ( some_num @ ( bit0 @ M5 ) ) ) ) )
% 0.33/0.59 => ( ! [M5: num] :
% 0.33/0.59 ( ( X
% 0.33/0.59 = ( bit0 @ M5 ) )
% 0.33/0.59 => ! [N: num] :
% 0.33/0.59 ( ( Xa
% 0.33/0.59 = ( bit0 @ N ) )
% 0.33/0.59 => ( Y
% 0.33/0.59 != ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M5 @ N ) ) ) ) )
% 0.33/0.59 => ( ! [M5: num] :
% 0.33/0.59 ( ( X
% 0.33/0.59 = ( bit0 @ M5 ) )
% 0.33/0.59 => ! [N: num] :
% 0.33/0.59 ( ( Xa
% 0.33/0.59 = ( bit1 @ N ) )
% 0.33/0.59 => ( Y
% 0.33/0.59 != ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M5 @ N ) ) ) ) )
% 0.33/0.59 => ( ! [M5: num] :
% 0.33/0.59 ( ( X
% 0.33/0.59 = ( bit1 @ M5 ) )
% 0.33/0.59 => ( ( Xa = one )
% 0.33/0.59 => ( Y
% 0.33/0.59 != ( some_num @ ( bit0 @ M5 ) ) ) ) )
% 0.33/0.59 => ( ! [M5: num] :
% 0.33/0.59 ( ( X
% 0.33/0.59 = ( bit1 @ M5 ) )
% 0.33/0.59 => ! [N: num] :
% 0.33/0.59 ( ( Xa
% 0.33/0.59 = ( bit0 @ N ) )
% 0.33/0.59 => ( Y
% 0.33/0.59 != ( case_o6005452278849405969um_num @ ( some_num @ one )
% 0.33/0.59 @ ^ [N8: num] : ( some_num @ ( bit1 @ N8 ) )
% 0.33/0.59 @ ( bit_and_not_num @ M5 @ N ) ) ) ) )
% 0.33/0.59 => ~ ! [M5: num] :
% 0.33/0.59 ( ( X
% 0.33/0.59 = ( bit1 @ M5 ) )
% 0.33/0.59 => ! [N: num] :
% 0.33/0.59 ( ( Xa
% 0.33/0.59 = ( bit1 @ N ) )
% 0.33/0.59 => ( Y
% 0.33/0.59 != ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M5 @ N ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % and_not_num.elims
% 0.33/0.59 thf(fact_3950_and__not__num_Opelims,axiom,
% 0.33/0.59 ! [X: num,Xa: num,Y: option_num] :
% 0.33/0.59 ( ( ( bit_and_not_num @ X @ Xa )
% 0.33/0.59 = Y )
% 0.33/0.59 => ( ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ X @ Xa ) )
% 0.33/0.59 => ( ( ( X = one )
% 0.33/0.59 => ( ( Xa = one )
% 0.33/0.59 => ( ( Y = none_num )
% 0.33/0.59 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 0.33/0.59 => ( ( ( X = one )
% 0.33/0.59 => ! [N: num] :
% 0.33/0.59 ( ( Xa
% 0.33/0.59 = ( bit0 @ N ) )
% 0.33/0.59 => ( ( Y
% 0.33/0.59 = ( some_num @ one ) )
% 0.33/0.59 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ one @ ( bit0 @ N ) ) ) ) ) )
% 0.33/0.59 => ( ( ( X = one )
% 0.33/0.59 => ! [N: num] :
% 0.33/0.59 ( ( Xa
% 0.33/0.59 = ( bit1 @ N ) )
% 0.33/0.59 => ( ( Y = none_num )
% 0.33/0.59 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ one @ ( bit1 @ N ) ) ) ) ) )
% 0.33/0.59 => ( ! [M5: num] :
% 0.33/0.59 ( ( X
% 0.33/0.59 = ( bit0 @ M5 ) )
% 0.33/0.59 => ( ( Xa = one )
% 0.33/0.59 => ( ( Y
% 0.33/0.59 = ( some_num @ ( bit0 @ M5 ) ) )
% 0.33/0.59 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ one ) ) ) ) )
% 0.33/0.59 => ( ! [M5: num] :
% 0.33/0.59 ( ( X
% 0.33/0.59 = ( bit0 @ M5 ) )
% 0.33/0.59 => ! [N: num] :
% 0.33/0.59 ( ( Xa
% 0.33/0.59 = ( bit0 @ N ) )
% 0.33/0.59 => ( ( Y
% 0.33/0.59 = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M5 @ N ) ) )
% 0.33/0.59 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ ( bit0 @ N ) ) ) ) ) )
% 0.33/0.59 => ( ! [M5: num] :
% 0.33/0.59 ( ( X
% 0.33/0.59 = ( bit0 @ M5 ) )
% 0.33/0.59 => ! [N: num] :
% 0.33/0.59 ( ( Xa
% 0.33/0.59 = ( bit1 @ N ) )
% 0.33/0.59 => ( ( Y
% 0.33/0.59 = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M5 @ N ) ) )
% 0.33/0.59 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ ( bit1 @ N ) ) ) ) ) )
% 0.33/0.59 => ( ! [M5: num] :
% 0.33/0.59 ( ( X
% 0.33/0.59 = ( bit1 @ M5 ) )
% 0.33/0.59 => ( ( Xa = one )
% 0.33/0.59 => ( ( Y
% 0.33/0.59 = ( some_num @ ( bit0 @ M5 ) ) )
% 0.33/0.59 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ one ) ) ) ) )
% 0.33/0.59 => ( ! [M5: num] :
% 0.33/0.59 ( ( X
% 0.33/0.59 = ( bit1 @ M5 ) )
% 0.33/0.59 => ! [N: num] :
% 0.33/0.59 ( ( Xa
% 0.33/0.59 = ( bit0 @ N ) )
% 0.33/0.59 => ( ( Y
% 0.33/0.59 = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 0.33/0.59 @ ^ [N8: num] : ( some_num @ ( bit1 @ N8 ) )
% 0.33/0.59 @ ( bit_and_not_num @ M5 @ N ) ) )
% 0.33/0.59 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ ( bit0 @ N ) ) ) ) ) )
% 0.33/0.59 => ~ ! [M5: num] :
% 0.33/0.59 ( ( X
% 0.33/0.59 = ( bit1 @ M5 ) )
% 0.33/0.59 => ! [N: num] :
% 0.33/0.59 ( ( Xa
% 0.33/0.59 = ( bit1 @ N ) )
% 0.33/0.59 => ( ( Y
% 0.33/0.59 = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M5 @ N ) ) )
% 0.33/0.59 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ ( bit1 @ N ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % and_not_num.pelims
% 0.33/0.59 thf(fact_3951_and__num_Opelims,axiom,
% 0.33/0.59 ! [X: num,Xa: num,Y: option_num] :
% 0.33/0.59 ( ( ( bit_un7362597486090784418nd_num @ X @ Xa )
% 0.33/0.59 = Y )
% 0.33/0.59 => ( ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ X @ Xa ) )
% 0.33/0.59 => ( ( ( X = one )
% 0.33/0.59 => ( ( Xa = one )
% 0.33/0.59 => ( ( Y
% 0.33/0.59 = ( some_num @ one ) )
% 0.33/0.59 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 0.33/0.59 => ( ( ( X = one )
% 0.33/0.59 => ! [N: num] :
% 0.33/0.59 ( ( Xa
% 0.33/0.59 = ( bit0 @ N ) )
% 0.33/0.59 => ( ( Y = none_num )
% 0.33/0.59 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ one @ ( bit0 @ N ) ) ) ) ) )
% 0.33/0.59 => ( ( ( X = one )
% 0.33/0.59 => ! [N: num] :
% 0.33/0.59 ( ( Xa
% 0.33/0.59 = ( bit1 @ N ) )
% 0.33/0.59 => ( ( Y
% 0.33/0.59 = ( some_num @ one ) )
% 0.33/0.59 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ one @ ( bit1 @ N ) ) ) ) ) )
% 0.33/0.59 => ( ! [M5: num] :
% 0.33/0.59 ( ( X
% 0.33/0.59 = ( bit0 @ M5 ) )
% 0.33/0.59 => ( ( Xa = one )
% 0.33/0.59 => ( ( Y = none_num )
% 0.33/0.59 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ one ) ) ) ) )
% 0.33/0.59 => ( ! [M5: num] :
% 0.33/0.59 ( ( X
% 0.33/0.59 = ( bit0 @ M5 ) )
% 0.33/0.59 => ! [N: num] :
% 0.33/0.59 ( ( Xa
% 0.33/0.59 = ( bit0 @ N ) )
% 0.33/0.59 => ( ( Y
% 0.33/0.59 = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M5 @ N ) ) )
% 0.33/0.59 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ ( bit0 @ N ) ) ) ) ) )
% 0.33/0.59 => ( ! [M5: num] :
% 0.33/0.59 ( ( X
% 0.33/0.59 = ( bit0 @ M5 ) )
% 0.33/0.59 => ! [N: num] :
% 0.33/0.59 ( ( Xa
% 0.33/0.59 = ( bit1 @ N ) )
% 0.33/0.59 => ( ( Y
% 0.33/0.59 = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M5 @ N ) ) )
% 0.33/0.59 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ ( bit1 @ N ) ) ) ) ) )
% 0.33/0.59 => ( ! [M5: num] :
% 0.33/0.59 ( ( X
% 0.33/0.59 = ( bit1 @ M5 ) )
% 0.33/0.59 => ( ( Xa = one )
% 0.33/0.59 => ( ( Y
% 0.33/0.59 = ( some_num @ one ) )
% 0.33/0.59 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ one ) ) ) ) )
% 0.33/0.59 => ( ! [M5: num] :
% 0.33/0.59 ( ( X
% 0.33/0.59 = ( bit1 @ M5 ) )
% 0.33/0.59 => ! [N: num] :
% 0.33/0.59 ( ( Xa
% 0.33/0.59 = ( bit0 @ N ) )
% 0.33/0.59 => ( ( Y
% 0.33/0.59 = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M5 @ N ) ) )
% 0.33/0.59 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ ( bit0 @ N ) ) ) ) ) )
% 0.33/0.59 => ~ ! [M5: num] :
% 0.33/0.59 ( ( X
% 0.33/0.59 = ( bit1 @ M5 ) )
% 0.33/0.59 => ! [N: num] :
% 0.33/0.59 ( ( Xa
% 0.33/0.59 = ( bit1 @ N ) )
% 0.33/0.59 => ( ( Y
% 0.33/0.59 = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 0.33/0.59 @ ^ [N8: num] : ( some_num @ ( bit1 @ N8 ) )
% 0.33/0.59 @ ( bit_un7362597486090784418nd_num @ M5 @ N ) ) )
% 0.33/0.59 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ ( bit1 @ N ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % and_num.pelims
% 0.33/0.59 thf(fact_3952_gbinomial__code,axiom,
% 0.33/0.59 ( gbinomial_rat
% 0.33/0.59 = ( ^ [A5: rat,K4: nat] :
% 0.33/0.59 ( if_rat @ ( K4 = zero_zero_nat ) @ one_one_rat
% 0.33/0.59 @ ( divide_divide_rat
% 0.33/0.59 @ ( set_fo1949268297981939178at_rat
% 0.33/0.59 @ ^ [L3: nat] : ( times_times_rat @ ( minus_minus_rat @ A5 @ ( semiri681578069525770553at_rat @ L3 ) ) )
% 0.33/0.59 @ zero_zero_nat
% 0.33/0.59 @ ( minus_minus_nat @ K4 @ one_one_nat )
% 0.33/0.59 @ one_one_rat )
% 0.33/0.59 @ ( semiri773545260158071498ct_rat @ K4 ) ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % gbinomial_code
% 0.33/0.59 thf(fact_3953_xor__num_Oelims,axiom,
% 0.33/0.59 ! [X: num,Xa: num,Y: option_num] :
% 0.33/0.59 ( ( ( bit_un2480387367778600638or_num @ X @ Xa )
% 0.33/0.59 = Y )
% 0.33/0.59 => ( ( ( X = one )
% 0.33/0.59 => ( ( Xa = one )
% 0.33/0.59 => ( Y != none_num ) ) )
% 0.33/0.59 => ( ( ( X = one )
% 0.33/0.59 => ! [N: num] :
% 0.33/0.59 ( ( Xa
% 0.33/0.59 = ( bit0 @ N ) )
% 0.33/0.59 => ( Y
% 0.33/0.59 != ( some_num @ ( bit1 @ N ) ) ) ) )
% 0.33/0.59 => ( ( ( X = one )
% 0.33/0.59 => ! [N: num] :
% 0.33/0.59 ( ( Xa
% 0.33/0.59 = ( bit1 @ N ) )
% 0.33/0.59 => ( Y
% 0.33/0.59 != ( some_num @ ( bit0 @ N ) ) ) ) )
% 0.33/0.59 => ( ! [M5: num] :
% 0.33/0.59 ( ( X
% 0.33/0.59 = ( bit0 @ M5 ) )
% 0.33/0.59 => ( ( Xa = one )
% 0.33/0.59 => ( Y
% 0.33/0.59 != ( some_num @ ( bit1 @ M5 ) ) ) ) )
% 0.33/0.59 => ( ! [M5: num] :
% 0.33/0.59 ( ( X
% 0.33/0.59 = ( bit0 @ M5 ) )
% 0.33/0.59 => ! [N: num] :
% 0.33/0.59 ( ( Xa
% 0.33/0.59 = ( bit0 @ N ) )
% 0.33/0.59 => ( Y
% 0.33/0.59 != ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M5 @ N ) ) ) ) )
% 0.33/0.59 => ( ! [M5: num] :
% 0.33/0.59 ( ( X
% 0.33/0.59 = ( bit0 @ M5 ) )
% 0.33/0.59 => ! [N: num] :
% 0.33/0.59 ( ( Xa
% 0.33/0.59 = ( bit1 @ N ) )
% 0.33/0.59 => ( Y
% 0.33/0.59 != ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M5 @ N ) ) ) ) ) )
% 0.33/0.59 => ( ! [M5: num] :
% 0.33/0.59 ( ( X
% 0.33/0.59 = ( bit1 @ M5 ) )
% 0.33/0.59 => ( ( Xa = one )
% 0.33/0.59 => ( Y
% 0.33/0.59 != ( some_num @ ( bit0 @ M5 ) ) ) ) )
% 0.33/0.59 => ( ! [M5: num] :
% 0.33/0.59 ( ( X
% 0.33/0.59 = ( bit1 @ M5 ) )
% 0.33/0.59 => ! [N: num] :
% 0.33/0.59 ( ( Xa
% 0.33/0.59 = ( bit0 @ N ) )
% 0.33/0.59 => ( Y
% 0.33/0.59 != ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M5 @ N ) ) ) ) ) )
% 0.33/0.59 => ~ ! [M5: num] :
% 0.33/0.59 ( ( X
% 0.33/0.59 = ( bit1 @ M5 ) )
% 0.33/0.59 => ! [N: num] :
% 0.33/0.59 ( ( Xa
% 0.33/0.59 = ( bit1 @ N ) )
% 0.33/0.59 => ( Y
% 0.33/0.59 != ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M5 @ N ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % xor_num.elims
% 0.33/0.59 thf(fact_3954_choose__alternating__sum,axiom,
% 0.33/0.59 ! [N2: nat] :
% 0.33/0.59 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.33/0.59 => ( ( groups2906978787729119204at_rat
% 0.33/0.59 @ ^ [I3: nat] : ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ I3 ) @ ( semiri681578069525770553at_rat @ ( binomial @ N2 @ I3 ) ) )
% 0.33/0.59 @ ( set_ord_atMost_nat @ N2 ) )
% 0.33/0.59 = zero_zero_rat ) ) ).
% 0.33/0.59
% 0.33/0.59 % choose_alternating_sum
% 0.33/0.59 thf(fact_3955_choose__alternating__sum,axiom,
% 0.33/0.59 ! [N2: nat] :
% 0.33/0.59 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.33/0.59 => ( ( groups3539618377306564664at_int
% 0.33/0.59 @ ^ [I3: nat] : ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ I3 ) @ ( semiri1314217659103216013at_int @ ( binomial @ N2 @ I3 ) ) )
% 0.33/0.59 @ ( set_ord_atMost_nat @ N2 ) )
% 0.33/0.59 = zero_zero_int ) ) ).
% 0.33/0.59
% 0.33/0.59 % choose_alternating_sum
% 0.33/0.59 thf(fact_3956_choose__alternating__sum,axiom,
% 0.33/0.59 ! [N2: nat] :
% 0.33/0.59 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.33/0.59 => ( ( groups7501900531339628137nteger
% 0.33/0.59 @ ^ [I3: nat] : ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ I3 ) @ ( semiri4939895301339042750nteger @ ( binomial @ N2 @ I3 ) ) )
% 0.33/0.59 @ ( set_ord_atMost_nat @ N2 ) )
% 0.33/0.59 = zero_z3403309356797280102nteger ) ) ).
% 0.33/0.59
% 0.33/0.59 % choose_alternating_sum
% 0.33/0.59 thf(fact_3957_choose__linear__sum,axiom,
% 0.33/0.59 ! [N2: nat] :
% 0.33/0.59 ( ( groups3542108847815614940at_nat
% 0.33/0.59 @ ^ [I3: nat] : ( times_times_nat @ I3 @ ( binomial @ N2 @ I3 ) )
% 0.33/0.59 @ ( set_ord_atMost_nat @ N2 ) )
% 0.33/0.59 = ( times_times_nat @ N2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % choose_linear_sum
% 0.33/0.59 thf(fact_3958_binomial__r__part__sum,axiom,
% 0.33/0.59 ! [M2: nat] :
% 0.33/0.59 ( ( groups3542108847815614940at_nat @ ( binomial @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ one_one_nat ) ) @ ( set_ord_atMost_nat @ M2 ) )
% 0.33/0.59 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % binomial_r_part_sum
% 0.33/0.59 thf(fact_3959_sum_Otriangle__reindex,axiom,
% 0.33/0.59 ! [G: nat > nat > nat,N2: nat] :
% 0.33/0.59 ( ( groups977919841031483927at_nat @ ( produc6842872674320459806at_nat @ G )
% 0.33/0.59 @ ( collec3392354462482085612at_nat
% 0.33/0.59 @ ( produc6081775807080527818_nat_o
% 0.33/0.59 @ ^ [I3: nat,J2: nat] : ( ord_less_nat @ ( plus_plus_nat @ I3 @ J2 ) @ N2 ) ) ) )
% 0.33/0.59 = ( groups3542108847815614940at_nat
% 0.33/0.59 @ ^ [K4: nat] :
% 0.33/0.59 ( groups3542108847815614940at_nat
% 0.33/0.59 @ ^ [I3: nat] : ( G @ I3 @ ( minus_minus_nat @ K4 @ I3 ) )
% 0.33/0.59 @ ( set_ord_atMost_nat @ K4 ) )
% 0.33/0.59 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum.triangle_reindex
% 0.33/0.59 thf(fact_3960_lessThan__eq__iff,axiom,
% 0.33/0.59 ! [X: nat,Y: nat] :
% 0.33/0.59 ( ( ( set_ord_lessThan_nat @ X )
% 0.33/0.59 = ( set_ord_lessThan_nat @ Y ) )
% 0.33/0.59 = ( X = Y ) ) ).
% 0.33/0.59
% 0.33/0.59 % lessThan_eq_iff
% 0.33/0.59 thf(fact_3961_lessThan__iff,axiom,
% 0.33/0.59 ! [I: $o,K: $o] :
% 0.33/0.59 ( ( member_o @ I @ ( set_ord_lessThan_o @ K ) )
% 0.33/0.59 = ( ord_less_o @ I @ K ) ) ).
% 0.33/0.59
% 0.33/0.59 % lessThan_iff
% 0.33/0.59 thf(fact_3962_lessThan__iff,axiom,
% 0.33/0.59 ! [I: code_integer,K: code_integer] :
% 0.33/0.59 ( ( member_Code_integer @ I @ ( set_or5754767410780653050nteger @ K ) )
% 0.33/0.59 = ( ord_le6747313008572928689nteger @ I @ K ) ) ).
% 0.33/0.59
% 0.33/0.59 % lessThan_iff
% 0.33/0.59 thf(fact_3963_lessThan__iff,axiom,
% 0.33/0.59 ! [I: rat,K: rat] :
% 0.33/0.59 ( ( member_rat @ I @ ( set_ord_lessThan_rat @ K ) )
% 0.33/0.59 = ( ord_less_rat @ I @ K ) ) ).
% 0.33/0.59
% 0.33/0.59 % lessThan_iff
% 0.33/0.59 thf(fact_3964_lessThan__iff,axiom,
% 0.33/0.59 ! [I: num,K: num] :
% 0.33/0.59 ( ( member_num @ I @ ( set_ord_lessThan_num @ K ) )
% 0.33/0.59 = ( ord_less_num @ I @ K ) ) ).
% 0.33/0.59
% 0.33/0.59 % lessThan_iff
% 0.33/0.59 thf(fact_3965_lessThan__iff,axiom,
% 0.33/0.59 ! [I: int,K: int] :
% 0.33/0.59 ( ( member_int @ I @ ( set_ord_lessThan_int @ K ) )
% 0.33/0.59 = ( ord_less_int @ I @ K ) ) ).
% 0.33/0.59
% 0.33/0.59 % lessThan_iff
% 0.33/0.59 thf(fact_3966_lessThan__iff,axiom,
% 0.33/0.59 ! [I: nat,K: nat] :
% 0.33/0.59 ( ( member_nat @ I @ ( set_ord_lessThan_nat @ K ) )
% 0.33/0.59 = ( ord_less_nat @ I @ K ) ) ).
% 0.33/0.59
% 0.33/0.59 % lessThan_iff
% 0.33/0.59 thf(fact_3967_binomial__n__n,axiom,
% 0.33/0.59 ! [N2: nat] :
% 0.33/0.59 ( ( binomial @ N2 @ N2 )
% 0.33/0.59 = one_one_nat ) ).
% 0.33/0.59
% 0.33/0.59 % binomial_n_n
% 0.33/0.59 thf(fact_3968_lessThan__subset__iff,axiom,
% 0.33/0.59 ! [X: rat,Y: rat] :
% 0.33/0.59 ( ( ord_less_eq_set_rat @ ( set_ord_lessThan_rat @ X ) @ ( set_ord_lessThan_rat @ Y ) )
% 0.33/0.59 = ( ord_less_eq_rat @ X @ Y ) ) ).
% 0.33/0.59
% 0.33/0.59 % lessThan_subset_iff
% 0.33/0.59 thf(fact_3969_lessThan__subset__iff,axiom,
% 0.33/0.59 ! [X: num,Y: num] :
% 0.33/0.59 ( ( ord_less_eq_set_num @ ( set_ord_lessThan_num @ X ) @ ( set_ord_lessThan_num @ Y ) )
% 0.33/0.59 = ( ord_less_eq_num @ X @ Y ) ) ).
% 0.33/0.59
% 0.33/0.59 % lessThan_subset_iff
% 0.33/0.59 thf(fact_3970_lessThan__subset__iff,axiom,
% 0.33/0.59 ! [X: int,Y: int] :
% 0.33/0.59 ( ( ord_less_eq_set_int @ ( set_ord_lessThan_int @ X ) @ ( set_ord_lessThan_int @ Y ) )
% 0.33/0.59 = ( ord_less_eq_int @ X @ Y ) ) ).
% 0.33/0.59
% 0.33/0.59 % lessThan_subset_iff
% 0.33/0.59 thf(fact_3971_lessThan__subset__iff,axiom,
% 0.33/0.59 ! [X: nat,Y: nat] :
% 0.33/0.59 ( ( ord_less_eq_set_nat @ ( set_ord_lessThan_nat @ X ) @ ( set_ord_lessThan_nat @ Y ) )
% 0.33/0.59 = ( ord_less_eq_nat @ X @ Y ) ) ).
% 0.33/0.59
% 0.33/0.59 % lessThan_subset_iff
% 0.33/0.59 thf(fact_3972_binomial__Suc__Suc,axiom,
% 0.33/0.59 ! [N2: nat,K: nat] :
% 0.33/0.59 ( ( binomial @ ( suc @ N2 ) @ ( suc @ K ) )
% 0.33/0.59 = ( plus_plus_nat @ ( binomial @ N2 @ K ) @ ( binomial @ N2 @ ( suc @ K ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % binomial_Suc_Suc
% 0.33/0.59 thf(fact_3973_binomial__n__0,axiom,
% 0.33/0.59 ! [N2: nat] :
% 0.33/0.59 ( ( binomial @ N2 @ zero_zero_nat )
% 0.33/0.59 = one_one_nat ) ).
% 0.33/0.59
% 0.33/0.59 % binomial_n_0
% 0.33/0.59 thf(fact_3974_sum_OlessThan__Suc,axiom,
% 0.33/0.59 ! [G: nat > multis2468970476368604999at_nat,N2: nat] :
% 0.33/0.59 ( ( groups6857163185585827899at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 0.33/0.59 = ( plus_p7104986032573967614at_nat @ ( groups6857163185585827899at_nat @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum.lessThan_Suc
% 0.33/0.59 thf(fact_3975_sum_OlessThan__Suc,axiom,
% 0.33/0.59 ! [G: nat > rat,N2: nat] :
% 0.33/0.59 ( ( groups2906978787729119204at_rat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 0.33/0.59 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum.lessThan_Suc
% 0.33/0.59 thf(fact_3976_sum_OlessThan__Suc,axiom,
% 0.33/0.59 ! [G: nat > int,N2: nat] :
% 0.33/0.59 ( ( groups3539618377306564664at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 0.33/0.59 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum.lessThan_Suc
% 0.33/0.59 thf(fact_3977_sum_OlessThan__Suc,axiom,
% 0.33/0.59 ! [G: nat > nat,N2: nat] :
% 0.33/0.59 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 0.33/0.59 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum.lessThan_Suc
% 0.33/0.59 thf(fact_3978_choose__one,axiom,
% 0.33/0.59 ! [N2: nat] :
% 0.33/0.59 ( ( binomial @ N2 @ one_one_nat )
% 0.33/0.59 = N2 ) ).
% 0.33/0.59
% 0.33/0.59 % choose_one
% 0.33/0.59 thf(fact_3979_lessThan__def,axiom,
% 0.33/0.59 ( set_or5754767410780653050nteger
% 0.33/0.59 = ( ^ [U2: code_integer] :
% 0.33/0.59 ( collect_Code_integer
% 0.33/0.59 @ ^ [X3: code_integer] : ( ord_le6747313008572928689nteger @ X3 @ U2 ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % lessThan_def
% 0.33/0.59 thf(fact_3980_lessThan__def,axiom,
% 0.33/0.59 ( set_ord_lessThan_rat
% 0.33/0.59 = ( ^ [U2: rat] :
% 0.33/0.59 ( collect_rat
% 0.33/0.59 @ ^ [X3: rat] : ( ord_less_rat @ X3 @ U2 ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % lessThan_def
% 0.33/0.59 thf(fact_3981_lessThan__def,axiom,
% 0.33/0.59 ( set_ord_lessThan_num
% 0.33/0.59 = ( ^ [U2: num] :
% 0.33/0.59 ( collect_num
% 0.33/0.59 @ ^ [X3: num] : ( ord_less_num @ X3 @ U2 ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % lessThan_def
% 0.33/0.59 thf(fact_3982_lessThan__def,axiom,
% 0.33/0.59 ( set_ord_lessThan_int
% 0.33/0.59 = ( ^ [U2: int] :
% 0.33/0.59 ( collect_int
% 0.33/0.59 @ ^ [X3: int] : ( ord_less_int @ X3 @ U2 ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % lessThan_def
% 0.33/0.59 thf(fact_3983_lessThan__def,axiom,
% 0.33/0.59 ( set_ord_lessThan_nat
% 0.33/0.59 = ( ^ [U2: nat] :
% 0.33/0.59 ( collect_nat
% 0.33/0.59 @ ^ [X3: nat] : ( ord_less_nat @ X3 @ U2 ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % lessThan_def
% 0.33/0.59 thf(fact_3984_choose__mult__lemma,axiom,
% 0.33/0.59 ! [M2: nat,R2: nat,K: nat] :
% 0.33/0.59 ( ( times_times_nat @ ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ M2 @ R2 ) @ K ) @ ( plus_plus_nat @ M2 @ K ) ) @ ( binomial @ ( plus_plus_nat @ M2 @ K ) @ K ) )
% 0.33/0.59 = ( times_times_nat @ ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ M2 @ R2 ) @ K ) @ K ) @ ( binomial @ ( plus_plus_nat @ M2 @ R2 ) @ M2 ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % choose_mult_lemma
% 0.33/0.59 thf(fact_3985_lessThan__Suc__atMost,axiom,
% 0.33/0.59 ! [K: nat] :
% 0.33/0.59 ( ( set_ord_lessThan_nat @ ( suc @ K ) )
% 0.33/0.59 = ( set_ord_atMost_nat @ K ) ) ).
% 0.33/0.59
% 0.33/0.59 % lessThan_Suc_atMost
% 0.33/0.59 thf(fact_3986_bit__integer_Oabs__eq,axiom,
% 0.33/0.59 ! [X: int] :
% 0.33/0.59 ( ( bit_se9216721137139052372nteger @ ( code_integer_of_int @ X ) )
% 0.33/0.59 = ( bit_se1146084159140164899it_int @ X ) ) ).
% 0.33/0.59
% 0.33/0.59 % bit_integer.abs_eq
% 0.33/0.59 thf(fact_3987_lessThan__strict__subset__iff,axiom,
% 0.33/0.59 ! [M2: code_integer,N2: code_integer] :
% 0.33/0.59 ( ( ord_le1307284697595431911nteger @ ( set_or5754767410780653050nteger @ M2 ) @ ( set_or5754767410780653050nteger @ N2 ) )
% 0.33/0.59 = ( ord_le6747313008572928689nteger @ M2 @ N2 ) ) ).
% 0.33/0.59
% 0.33/0.59 % lessThan_strict_subset_iff
% 0.33/0.59 thf(fact_3988_lessThan__strict__subset__iff,axiom,
% 0.33/0.59 ! [M2: rat,N2: rat] :
% 0.33/0.59 ( ( ord_less_set_rat @ ( set_ord_lessThan_rat @ M2 ) @ ( set_ord_lessThan_rat @ N2 ) )
% 0.33/0.59 = ( ord_less_rat @ M2 @ N2 ) ) ).
% 0.33/0.59
% 0.33/0.59 % lessThan_strict_subset_iff
% 0.33/0.59 thf(fact_3989_lessThan__strict__subset__iff,axiom,
% 0.33/0.59 ! [M2: num,N2: num] :
% 0.33/0.59 ( ( ord_less_set_num @ ( set_ord_lessThan_num @ M2 ) @ ( set_ord_lessThan_num @ N2 ) )
% 0.33/0.59 = ( ord_less_num @ M2 @ N2 ) ) ).
% 0.33/0.59
% 0.33/0.59 % lessThan_strict_subset_iff
% 0.33/0.59 thf(fact_3990_lessThan__strict__subset__iff,axiom,
% 0.33/0.59 ! [M2: int,N2: int] :
% 0.33/0.59 ( ( ord_less_set_int @ ( set_ord_lessThan_int @ M2 ) @ ( set_ord_lessThan_int @ N2 ) )
% 0.33/0.59 = ( ord_less_int @ M2 @ N2 ) ) ).
% 0.33/0.59
% 0.33/0.59 % lessThan_strict_subset_iff
% 0.33/0.59 thf(fact_3991_lessThan__strict__subset__iff,axiom,
% 0.33/0.59 ! [M2: nat,N2: nat] :
% 0.33/0.59 ( ( ord_less_set_nat @ ( set_ord_lessThan_nat @ M2 ) @ ( set_ord_lessThan_nat @ N2 ) )
% 0.33/0.59 = ( ord_less_nat @ M2 @ N2 ) ) ).
% 0.33/0.59
% 0.33/0.59 % lessThan_strict_subset_iff
% 0.33/0.59 thf(fact_3992_Suc__times__binomial__add,axiom,
% 0.33/0.59 ! [A: nat,B: nat] :
% 0.33/0.59 ( ( times_times_nat @ ( suc @ A ) @ ( binomial @ ( suc @ ( plus_plus_nat @ A @ B ) ) @ ( suc @ A ) ) )
% 0.33/0.59 = ( times_times_nat @ ( suc @ B ) @ ( binomial @ ( suc @ ( plus_plus_nat @ A @ B ) ) @ A ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % Suc_times_binomial_add
% 0.33/0.59 thf(fact_3993_binomial__absorb__comp,axiom,
% 0.33/0.59 ! [N2: nat,K: nat] :
% 0.33/0.59 ( ( times_times_nat @ ( minus_minus_nat @ N2 @ K ) @ ( binomial @ N2 @ K ) )
% 0.33/0.59 = ( times_times_nat @ N2 @ ( binomial @ ( minus_minus_nat @ N2 @ one_one_nat ) @ K ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % binomial_absorb_comp
% 0.33/0.59 thf(fact_3994_fact__fact__dvd__fact,axiom,
% 0.33/0.59 ! [K: nat,N2: nat] : ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ ( semiri3624122377584611663nteger @ K ) @ ( semiri3624122377584611663nteger @ N2 ) ) @ ( semiri3624122377584611663nteger @ ( plus_plus_nat @ K @ N2 ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % fact_fact_dvd_fact
% 0.33/0.59 thf(fact_3995_fact__fact__dvd__fact,axiom,
% 0.33/0.59 ! [K: nat,N2: nat] : ( dvd_dvd_rat @ ( times_times_rat @ ( semiri773545260158071498ct_rat @ K ) @ ( semiri773545260158071498ct_rat @ N2 ) ) @ ( semiri773545260158071498ct_rat @ ( plus_plus_nat @ K @ N2 ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % fact_fact_dvd_fact
% 0.33/0.59 thf(fact_3996_fact__fact__dvd__fact,axiom,
% 0.33/0.59 ! [K: nat,N2: nat] : ( dvd_dvd_int @ ( times_times_int @ ( semiri1406184849735516958ct_int @ K ) @ ( semiri1406184849735516958ct_int @ N2 ) ) @ ( semiri1406184849735516958ct_int @ ( plus_plus_nat @ K @ N2 ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % fact_fact_dvd_fact
% 0.33/0.59 thf(fact_3997_fact__fact__dvd__fact,axiom,
% 0.33/0.59 ! [K: nat,N2: nat] : ( dvd_dvd_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ N2 ) ) @ ( semiri1408675320244567234ct_nat @ ( plus_plus_nat @ K @ N2 ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % fact_fact_dvd_fact
% 0.33/0.59 thf(fact_3998_sum_Onat__diff__reindex,axiom,
% 0.33/0.59 ! [G: nat > nat,N2: nat] :
% 0.33/0.59 ( ( groups3542108847815614940at_nat
% 0.33/0.59 @ ^ [I3: nat] : ( G @ ( minus_minus_nat @ N2 @ ( suc @ I3 ) ) )
% 0.33/0.59 @ ( set_ord_lessThan_nat @ N2 ) )
% 0.33/0.59 = ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum.nat_diff_reindex
% 0.33/0.59 thf(fact_3999_Iic__subset__Iio__iff,axiom,
% 0.33/0.59 ! [A: code_integer,B: code_integer] :
% 0.33/0.59 ( ( ord_le7084787975880047091nteger @ ( set_or9101266186257409494nteger @ A ) @ ( set_or5754767410780653050nteger @ B ) )
% 0.33/0.59 = ( ord_le6747313008572928689nteger @ A @ B ) ) ).
% 0.33/0.59
% 0.33/0.59 % Iic_subset_Iio_iff
% 0.33/0.59 thf(fact_4000_Iic__subset__Iio__iff,axiom,
% 0.33/0.59 ! [A: rat,B: rat] :
% 0.33/0.59 ( ( ord_less_eq_set_rat @ ( set_ord_atMost_rat @ A ) @ ( set_ord_lessThan_rat @ B ) )
% 0.33/0.59 = ( ord_less_rat @ A @ B ) ) ).
% 0.33/0.59
% 0.33/0.59 % Iic_subset_Iio_iff
% 0.33/0.59 thf(fact_4001_Iic__subset__Iio__iff,axiom,
% 0.33/0.59 ! [A: num,B: num] :
% 0.33/0.59 ( ( ord_less_eq_set_num @ ( set_ord_atMost_num @ A ) @ ( set_ord_lessThan_num @ B ) )
% 0.33/0.59 = ( ord_less_num @ A @ B ) ) ).
% 0.33/0.59
% 0.33/0.59 % Iic_subset_Iio_iff
% 0.33/0.59 thf(fact_4002_Iic__subset__Iio__iff,axiom,
% 0.33/0.59 ! [A: int,B: int] :
% 0.33/0.59 ( ( ord_less_eq_set_int @ ( set_ord_atMost_int @ A ) @ ( set_ord_lessThan_int @ B ) )
% 0.33/0.59 = ( ord_less_int @ A @ B ) ) ).
% 0.33/0.59
% 0.33/0.59 % Iic_subset_Iio_iff
% 0.33/0.59 thf(fact_4003_Iic__subset__Iio__iff,axiom,
% 0.33/0.59 ! [A: nat,B: nat] :
% 0.33/0.59 ( ( ord_less_eq_set_nat @ ( set_ord_atMost_nat @ A ) @ ( set_ord_lessThan_nat @ B ) )
% 0.33/0.59 = ( ord_less_nat @ A @ B ) ) ).
% 0.33/0.59
% 0.33/0.59 % Iic_subset_Iio_iff
% 0.33/0.59 thf(fact_4004_binomial__absorption,axiom,
% 0.33/0.59 ! [K: nat,N2: nat] :
% 0.33/0.59 ( ( times_times_nat @ ( suc @ K ) @ ( binomial @ N2 @ ( suc @ K ) ) )
% 0.33/0.59 = ( times_times_nat @ N2 @ ( binomial @ ( minus_minus_nat @ N2 @ one_one_nat ) @ K ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % binomial_absorption
% 0.33/0.59 thf(fact_4005_sum__diff__distrib,axiom,
% 0.33/0.59 ! [Q: nat > nat,P: nat > nat,N2: nat] :
% 0.33/0.59 ( ! [X4: nat] : ( ord_less_eq_nat @ ( Q @ X4 ) @ ( P @ X4 ) )
% 0.33/0.59 => ( ( minus_minus_nat @ ( groups3542108847815614940at_nat @ P @ ( set_ord_lessThan_nat @ N2 ) ) @ ( groups3542108847815614940at_nat @ Q @ ( set_ord_lessThan_nat @ N2 ) ) )
% 0.33/0.59 = ( groups3542108847815614940at_nat
% 0.33/0.59 @ ^ [X3: nat] : ( minus_minus_nat @ ( P @ X3 ) @ ( Q @ X3 ) )
% 0.33/0.59 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum_diff_distrib
% 0.33/0.59 thf(fact_4006_sum_OlessThan__Suc__shift,axiom,
% 0.33/0.59 ! [G: nat > multis2468970476368604999at_nat,N2: nat] :
% 0.33/0.59 ( ( groups6857163185585827899at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 0.33/0.59 = ( plus_p7104986032573967614at_nat @ ( G @ zero_zero_nat )
% 0.33/0.59 @ ( groups6857163185585827899at_nat
% 0.33/0.59 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 0.33/0.59 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum.lessThan_Suc_shift
% 0.33/0.59 thf(fact_4007_sum_OlessThan__Suc__shift,axiom,
% 0.33/0.59 ! [G: nat > rat,N2: nat] :
% 0.33/0.59 ( ( groups2906978787729119204at_rat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 0.33/0.59 = ( plus_plus_rat @ ( G @ zero_zero_nat )
% 0.33/0.59 @ ( groups2906978787729119204at_rat
% 0.33/0.59 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 0.33/0.59 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum.lessThan_Suc_shift
% 0.33/0.59 thf(fact_4008_sum_OlessThan__Suc__shift,axiom,
% 0.33/0.59 ! [G: nat > int,N2: nat] :
% 0.33/0.59 ( ( groups3539618377306564664at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 0.33/0.59 = ( plus_plus_int @ ( G @ zero_zero_nat )
% 0.33/0.59 @ ( groups3539618377306564664at_int
% 0.33/0.59 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 0.33/0.59 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum.lessThan_Suc_shift
% 0.33/0.59 thf(fact_4009_sum_OlessThan__Suc__shift,axiom,
% 0.33/0.59 ! [G: nat > nat,N2: nat] :
% 0.33/0.59 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 0.33/0.59 = ( plus_plus_nat @ ( G @ zero_zero_nat )
% 0.33/0.59 @ ( groups3542108847815614940at_nat
% 0.33/0.59 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 0.33/0.59 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum.lessThan_Suc_shift
% 0.33/0.59 thf(fact_4010_sum__lessThan__telescope,axiom,
% 0.33/0.59 ! [F: nat > code_integer,M2: nat] :
% 0.33/0.59 ( ( groups7501900531339628137nteger
% 0.33/0.59 @ ^ [N4: nat] : ( minus_8373710615458151222nteger @ ( F @ ( suc @ N4 ) ) @ ( F @ N4 ) )
% 0.33/0.59 @ ( set_ord_lessThan_nat @ M2 ) )
% 0.33/0.59 = ( minus_8373710615458151222nteger @ ( F @ M2 ) @ ( F @ zero_zero_nat ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum_lessThan_telescope
% 0.33/0.59 thf(fact_4011_sum__lessThan__telescope,axiom,
% 0.33/0.59 ! [F: nat > rat,M2: nat] :
% 0.33/0.59 ( ( groups2906978787729119204at_rat
% 0.33/0.59 @ ^ [N4: nat] : ( minus_minus_rat @ ( F @ ( suc @ N4 ) ) @ ( F @ N4 ) )
% 0.33/0.59 @ ( set_ord_lessThan_nat @ M2 ) )
% 0.33/0.59 = ( minus_minus_rat @ ( F @ M2 ) @ ( F @ zero_zero_nat ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum_lessThan_telescope
% 0.33/0.59 thf(fact_4012_sum__lessThan__telescope,axiom,
% 0.33/0.59 ! [F: nat > int,M2: nat] :
% 0.33/0.59 ( ( groups3539618377306564664at_int
% 0.33/0.59 @ ^ [N4: nat] : ( minus_minus_int @ ( F @ ( suc @ N4 ) ) @ ( F @ N4 ) )
% 0.33/0.59 @ ( set_ord_lessThan_nat @ M2 ) )
% 0.33/0.59 = ( minus_minus_int @ ( F @ M2 ) @ ( F @ zero_zero_nat ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum_lessThan_telescope
% 0.33/0.59 thf(fact_4013_sum__lessThan__telescope_H,axiom,
% 0.33/0.59 ! [F: nat > code_integer,M2: nat] :
% 0.33/0.59 ( ( groups7501900531339628137nteger
% 0.33/0.59 @ ^ [N4: nat] : ( minus_8373710615458151222nteger @ ( F @ N4 ) @ ( F @ ( suc @ N4 ) ) )
% 0.33/0.59 @ ( set_ord_lessThan_nat @ M2 ) )
% 0.33/0.59 = ( minus_8373710615458151222nteger @ ( F @ zero_zero_nat ) @ ( F @ M2 ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum_lessThan_telescope'
% 0.33/0.59 thf(fact_4014_sum__lessThan__telescope_H,axiom,
% 0.33/0.59 ! [F: nat > rat,M2: nat] :
% 0.33/0.59 ( ( groups2906978787729119204at_rat
% 0.33/0.59 @ ^ [N4: nat] : ( minus_minus_rat @ ( F @ N4 ) @ ( F @ ( suc @ N4 ) ) )
% 0.33/0.59 @ ( set_ord_lessThan_nat @ M2 ) )
% 0.33/0.59 = ( minus_minus_rat @ ( F @ zero_zero_nat ) @ ( F @ M2 ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum_lessThan_telescope'
% 0.33/0.59 thf(fact_4015_sum__lessThan__telescope_H,axiom,
% 0.33/0.59 ! [F: nat > int,M2: nat] :
% 0.33/0.59 ( ( groups3539618377306564664at_int
% 0.33/0.59 @ ^ [N4: nat] : ( minus_minus_int @ ( F @ N4 ) @ ( F @ ( suc @ N4 ) ) )
% 0.33/0.59 @ ( set_ord_lessThan_nat @ M2 ) )
% 0.33/0.59 = ( minus_minus_int @ ( F @ zero_zero_nat ) @ ( F @ M2 ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum_lessThan_telescope'
% 0.33/0.59 thf(fact_4016_sum_OatLeast1__atMost__eq,axiom,
% 0.33/0.59 ! [G: nat > nat,N2: nat] :
% 0.33/0.59 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 0.33/0.59 = ( groups3542108847815614940at_nat
% 0.33/0.59 @ ^ [K4: nat] : ( G @ ( suc @ K4 ) )
% 0.33/0.59 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum.atLeast1_atMost_eq
% 0.33/0.59 thf(fact_4017_sum__bounds__lt__plus1,axiom,
% 0.33/0.59 ! [F: nat > nat,Mm: nat] :
% 0.33/0.59 ( ( groups3542108847815614940at_nat
% 0.33/0.59 @ ^ [K4: nat] : ( F @ ( suc @ K4 ) )
% 0.33/0.59 @ ( set_ord_lessThan_nat @ Mm ) )
% 0.33/0.59 = ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ one_one_nat @ Mm ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum_bounds_lt_plus1
% 0.33/0.59 thf(fact_4018_sum_Onested__swap_H,axiom,
% 0.33/0.59 ! [A: nat > nat > nat,N2: nat] :
% 0.33/0.59 ( ( groups3542108847815614940at_nat
% 0.33/0.59 @ ^ [I3: nat] : ( groups3542108847815614940at_nat @ ( A @ I3 ) @ ( set_ord_lessThan_nat @ I3 ) )
% 0.33/0.59 @ ( set_ord_atMost_nat @ N2 ) )
% 0.33/0.59 = ( groups3542108847815614940at_nat
% 0.33/0.59 @ ^ [J2: nat] :
% 0.33/0.59 ( groups3542108847815614940at_nat
% 0.33/0.59 @ ^ [I3: nat] : ( A @ I3 @ J2 )
% 0.33/0.59 @ ( set_or1269000886237332187st_nat @ ( suc @ J2 ) @ N2 ) )
% 0.33/0.59 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum.nested_swap'
% 0.33/0.59 thf(fact_4019_sum__choose__lower,axiom,
% 0.33/0.59 ! [R2: nat,N2: nat] :
% 0.33/0.59 ( ( groups3542108847815614940at_nat
% 0.33/0.59 @ ^ [K4: nat] : ( binomial @ ( plus_plus_nat @ R2 @ K4 ) @ K4 )
% 0.33/0.59 @ ( set_ord_atMost_nat @ N2 ) )
% 0.33/0.59 = ( binomial @ ( suc @ ( plus_plus_nat @ R2 @ N2 ) ) @ N2 ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum_choose_lower
% 0.33/0.59 thf(fact_4020_choose__rising__sum_I2_J,axiom,
% 0.33/0.59 ! [N2: nat,M2: nat] :
% 0.33/0.59 ( ( groups3542108847815614940at_nat
% 0.33/0.59 @ ^ [J2: nat] : ( binomial @ ( plus_plus_nat @ N2 @ J2 ) @ N2 )
% 0.33/0.59 @ ( set_ord_atMost_nat @ M2 ) )
% 0.33/0.59 = ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ N2 @ M2 ) @ one_one_nat ) @ M2 ) ) ).
% 0.33/0.59
% 0.33/0.59 % choose_rising_sum(2)
% 0.33/0.59 thf(fact_4021_choose__rising__sum_I1_J,axiom,
% 0.33/0.59 ! [N2: nat,M2: nat] :
% 0.33/0.59 ( ( groups3542108847815614940at_nat
% 0.33/0.59 @ ^ [J2: nat] : ( binomial @ ( plus_plus_nat @ N2 @ J2 ) @ N2 )
% 0.33/0.59 @ ( set_ord_atMost_nat @ M2 ) )
% 0.33/0.59 = ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ N2 @ M2 ) @ one_one_nat ) @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % choose_rising_sum(1)
% 0.33/0.59 thf(fact_4022_binomial__code,axiom,
% 0.33/0.59 ( binomial
% 0.33/0.59 = ( ^ [N4: nat,K4: nat] : ( if_nat @ ( ord_less_nat @ N4 @ K4 ) @ zero_zero_nat @ ( if_nat @ ( ord_less_nat @ N4 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K4 ) ) @ ( binomial @ N4 @ ( minus_minus_nat @ N4 @ K4 ) ) @ ( divide_divide_nat @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( plus_plus_nat @ ( minus_minus_nat @ N4 @ K4 ) @ one_one_nat ) @ N4 @ one_one_nat ) @ ( semiri1408675320244567234ct_nat @ K4 ) ) ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % binomial_code
% 0.33/0.59 thf(fact_4023_choose__reduce__nat,axiom,
% 0.33/0.59 ! [N2: nat,K: nat] :
% 0.33/0.59 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.33/0.59 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.33/0.59 => ( ( binomial @ N2 @ K )
% 0.33/0.59 = ( plus_plus_nat @ ( binomial @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) @ ( binomial @ ( minus_minus_nat @ N2 @ one_one_nat ) @ K ) ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % choose_reduce_nat
% 0.33/0.59 thf(fact_4024_times__binomial__minus1__eq,axiom,
% 0.33/0.59 ! [K: nat,N2: nat] :
% 0.33/0.59 ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.33/0.59 => ( ( times_times_nat @ K @ ( binomial @ N2 @ K ) )
% 0.33/0.59 = ( times_times_nat @ N2 @ ( binomial @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % times_binomial_minus1_eq
% 0.33/0.59 thf(fact_4025_one__diff__power__eq,axiom,
% 0.33/0.59 ! [X: code_integer,N2: nat] :
% 0.33/0.59 ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ X @ N2 ) )
% 0.33/0.59 = ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ one_one_Code_integer @ X ) @ ( groups7501900531339628137nteger @ ( power_8256067586552552935nteger @ X ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % one_diff_power_eq
% 0.33/0.59 thf(fact_4026_one__diff__power__eq,axiom,
% 0.33/0.59 ! [X: rat,N2: nat] :
% 0.33/0.59 ( ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ N2 ) )
% 0.33/0.59 = ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % one_diff_power_eq
% 0.33/0.59 thf(fact_4027_one__diff__power__eq,axiom,
% 0.33/0.59 ! [X: int,N2: nat] :
% 0.33/0.59 ( ( minus_minus_int @ one_one_int @ ( power_power_int @ X @ N2 ) )
% 0.33/0.59 = ( times_times_int @ ( minus_minus_int @ one_one_int @ X ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % one_diff_power_eq
% 0.33/0.59 thf(fact_4028_power__diff__1__eq,axiom,
% 0.33/0.59 ! [X: code_integer,N2: nat] :
% 0.33/0.59 ( ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ X @ N2 ) @ one_one_Code_integer )
% 0.33/0.59 = ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ X @ one_one_Code_integer ) @ ( groups7501900531339628137nteger @ ( power_8256067586552552935nteger @ X ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % power_diff_1_eq
% 0.33/0.59 thf(fact_4029_power__diff__1__eq,axiom,
% 0.33/0.59 ! [X: rat,N2: nat] :
% 0.33/0.59 ( ( minus_minus_rat @ ( power_power_rat @ X @ N2 ) @ one_one_rat )
% 0.33/0.59 = ( times_times_rat @ ( minus_minus_rat @ X @ one_one_rat ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % power_diff_1_eq
% 0.33/0.59 thf(fact_4030_power__diff__1__eq,axiom,
% 0.33/0.59 ! [X: int,N2: nat] :
% 0.33/0.59 ( ( minus_minus_int @ ( power_power_int @ X @ N2 ) @ one_one_int )
% 0.33/0.59 = ( times_times_int @ ( minus_minus_int @ X @ one_one_int ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % power_diff_1_eq
% 0.33/0.59 thf(fact_4031_geometric__sum,axiom,
% 0.33/0.59 ! [X: rat,N2: nat] :
% 0.33/0.59 ( ( X != one_one_rat )
% 0.33/0.59 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_lessThan_nat @ N2 ) )
% 0.33/0.59 = ( divide_divide_rat @ ( minus_minus_rat @ ( power_power_rat @ X @ N2 ) @ one_one_rat ) @ ( minus_minus_rat @ X @ one_one_rat ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % geometric_sum
% 0.33/0.59 thf(fact_4032_sum_OatMost__shift,axiom,
% 0.33/0.59 ! [G: nat > multis2468970476368604999at_nat,N2: nat] :
% 0.33/0.59 ( ( groups6857163185585827899at_nat @ G @ ( set_ord_atMost_nat @ N2 ) )
% 0.33/0.59 = ( plus_p7104986032573967614at_nat @ ( G @ zero_zero_nat )
% 0.33/0.59 @ ( groups6857163185585827899at_nat
% 0.33/0.59 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 0.33/0.59 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum.atMost_shift
% 0.33/0.59 thf(fact_4033_sum_OatMost__shift,axiom,
% 0.33/0.59 ! [G: nat > rat,N2: nat] :
% 0.33/0.59 ( ( groups2906978787729119204at_rat @ G @ ( set_ord_atMost_nat @ N2 ) )
% 0.33/0.59 = ( plus_plus_rat @ ( G @ zero_zero_nat )
% 0.33/0.59 @ ( groups2906978787729119204at_rat
% 0.33/0.59 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 0.33/0.59 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum.atMost_shift
% 0.33/0.59 thf(fact_4034_sum_OatMost__shift,axiom,
% 0.33/0.59 ! [G: nat > int,N2: nat] :
% 0.33/0.59 ( ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ N2 ) )
% 0.33/0.59 = ( plus_plus_int @ ( G @ zero_zero_nat )
% 0.33/0.59 @ ( groups3539618377306564664at_int
% 0.33/0.59 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 0.33/0.59 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum.atMost_shift
% 0.33/0.59 thf(fact_4035_sum_OatMost__shift,axiom,
% 0.33/0.59 ! [G: nat > nat,N2: nat] :
% 0.33/0.59 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ N2 ) )
% 0.33/0.59 = ( plus_plus_nat @ ( G @ zero_zero_nat )
% 0.33/0.59 @ ( groups3542108847815614940at_nat
% 0.33/0.59 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 0.33/0.59 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum.atMost_shift
% 0.33/0.59 thf(fact_4036_vandermonde,axiom,
% 0.33/0.59 ! [M2: nat,N2: nat,R2: nat] :
% 0.33/0.59 ( ( groups3542108847815614940at_nat
% 0.33/0.59 @ ^ [K4: nat] : ( times_times_nat @ ( binomial @ M2 @ K4 ) @ ( binomial @ N2 @ ( minus_minus_nat @ R2 @ K4 ) ) )
% 0.33/0.59 @ ( set_ord_atMost_nat @ R2 ) )
% 0.33/0.59 = ( binomial @ ( plus_plus_nat @ M2 @ N2 ) @ R2 ) ) ).
% 0.33/0.59
% 0.33/0.59 % vandermonde
% 0.33/0.59 thf(fact_4037_binomial__addition__formula,axiom,
% 0.33/0.59 ! [N2: nat,K: nat] :
% 0.33/0.59 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.33/0.59 => ( ( binomial @ N2 @ ( suc @ K ) )
% 0.33/0.59 = ( plus_plus_nat @ ( binomial @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( suc @ K ) ) @ ( binomial @ ( minus_minus_nat @ N2 @ one_one_nat ) @ K ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % binomial_addition_formula
% 0.33/0.59 thf(fact_4038_power__diff__sumr2,axiom,
% 0.33/0.59 ! [X: code_integer,N2: nat,Y: code_integer] :
% 0.33/0.59 ( ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ X @ N2 ) @ ( power_8256067586552552935nteger @ Y @ N2 ) )
% 0.33/0.59 = ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ X @ Y )
% 0.33/0.59 @ ( groups7501900531339628137nteger
% 0.33/0.59 @ ^ [I3: nat] : ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ Y @ ( minus_minus_nat @ N2 @ ( suc @ I3 ) ) ) @ ( power_8256067586552552935nteger @ X @ I3 ) )
% 0.33/0.59 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % power_diff_sumr2
% 0.33/0.59 thf(fact_4039_power__diff__sumr2,axiom,
% 0.33/0.59 ! [X: rat,N2: nat,Y: rat] :
% 0.33/0.59 ( ( minus_minus_rat @ ( power_power_rat @ X @ N2 ) @ ( power_power_rat @ Y @ N2 ) )
% 0.33/0.59 = ( times_times_rat @ ( minus_minus_rat @ X @ Y )
% 0.33/0.59 @ ( groups2906978787729119204at_rat
% 0.33/0.59 @ ^ [I3: nat] : ( times_times_rat @ ( power_power_rat @ Y @ ( minus_minus_nat @ N2 @ ( suc @ I3 ) ) ) @ ( power_power_rat @ X @ I3 ) )
% 0.33/0.59 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % power_diff_sumr2
% 0.33/0.59 thf(fact_4040_power__diff__sumr2,axiom,
% 0.33/0.59 ! [X: int,N2: nat,Y: int] :
% 0.33/0.59 ( ( minus_minus_int @ ( power_power_int @ X @ N2 ) @ ( power_power_int @ Y @ N2 ) )
% 0.33/0.59 = ( times_times_int @ ( minus_minus_int @ X @ Y )
% 0.33/0.59 @ ( groups3539618377306564664at_int
% 0.33/0.59 @ ^ [I3: nat] : ( times_times_int @ ( power_power_int @ Y @ ( minus_minus_nat @ N2 @ ( suc @ I3 ) ) ) @ ( power_power_int @ X @ I3 ) )
% 0.33/0.59 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % power_diff_sumr2
% 0.33/0.59 thf(fact_4041_diff__power__eq__sum,axiom,
% 0.33/0.59 ! [X: code_integer,N2: nat,Y: code_integer] :
% 0.33/0.59 ( ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ X @ ( suc @ N2 ) ) @ ( power_8256067586552552935nteger @ Y @ ( suc @ N2 ) ) )
% 0.33/0.59 = ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ X @ Y )
% 0.33/0.59 @ ( groups7501900531339628137nteger
% 0.33/0.59 @ ^ [P6: nat] : ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ X @ P6 ) @ ( power_8256067586552552935nteger @ Y @ ( minus_minus_nat @ N2 @ P6 ) ) )
% 0.33/0.59 @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % diff_power_eq_sum
% 0.33/0.59 thf(fact_4042_diff__power__eq__sum,axiom,
% 0.33/0.59 ! [X: rat,N2: nat,Y: rat] :
% 0.33/0.59 ( ( minus_minus_rat @ ( power_power_rat @ X @ ( suc @ N2 ) ) @ ( power_power_rat @ Y @ ( suc @ N2 ) ) )
% 0.33/0.59 = ( times_times_rat @ ( minus_minus_rat @ X @ Y )
% 0.33/0.59 @ ( groups2906978787729119204at_rat
% 0.33/0.59 @ ^ [P6: nat] : ( times_times_rat @ ( power_power_rat @ X @ P6 ) @ ( power_power_rat @ Y @ ( minus_minus_nat @ N2 @ P6 ) ) )
% 0.33/0.59 @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % diff_power_eq_sum
% 0.33/0.59 thf(fact_4043_diff__power__eq__sum,axiom,
% 0.33/0.59 ! [X: int,N2: nat,Y: int] :
% 0.33/0.59 ( ( minus_minus_int @ ( power_power_int @ X @ ( suc @ N2 ) ) @ ( power_power_int @ Y @ ( suc @ N2 ) ) )
% 0.33/0.59 = ( times_times_int @ ( minus_minus_int @ X @ Y )
% 0.33/0.59 @ ( groups3539618377306564664at_int
% 0.33/0.59 @ ^ [P6: nat] : ( times_times_int @ ( power_power_int @ X @ P6 ) @ ( power_power_int @ Y @ ( minus_minus_nat @ N2 @ P6 ) ) )
% 0.33/0.59 @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % diff_power_eq_sum
% 0.33/0.59 thf(fact_4044_sum__gp__strict,axiom,
% 0.33/0.59 ! [X: rat,N2: nat] :
% 0.33/0.59 ( ( ( X = one_one_rat )
% 0.33/0.59 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_lessThan_nat @ N2 ) )
% 0.33/0.59 = ( semiri681578069525770553at_rat @ N2 ) ) )
% 0.33/0.59 & ( ( X != one_one_rat )
% 0.33/0.59 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_lessThan_nat @ N2 ) )
% 0.33/0.59 = ( divide_divide_rat @ ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ N2 ) ) @ ( minus_minus_rat @ one_one_rat @ X ) ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum_gp_strict
% 0.33/0.59 thf(fact_4045_binomial,axiom,
% 0.33/0.59 ! [A: nat,B: nat,N2: nat] :
% 0.33/0.59 ( ( power_power_nat @ ( plus_plus_nat @ A @ B ) @ N2 )
% 0.33/0.59 = ( groups3542108847815614940at_nat
% 0.33/0.59 @ ^ [K4: nat] : ( times_times_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( binomial @ N2 @ K4 ) ) @ ( power_power_nat @ A @ K4 ) ) @ ( power_power_nat @ B @ ( minus_minus_nat @ N2 @ K4 ) ) )
% 0.33/0.59 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % binomial
% 0.33/0.59 thf(fact_4046_choose__two,axiom,
% 0.33/0.59 ! [N2: nat] :
% 0.33/0.59 ( ( binomial @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.33/0.59 = ( divide_divide_nat @ ( times_times_nat @ N2 @ ( minus_minus_nat @ N2 @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % choose_two
% 0.33/0.59 thf(fact_4047_one__diff__power__eq_H,axiom,
% 0.33/0.59 ! [X: code_integer,N2: nat] :
% 0.33/0.59 ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ X @ N2 ) )
% 0.33/0.59 = ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ one_one_Code_integer @ X )
% 0.33/0.59 @ ( groups7501900531339628137nteger
% 0.33/0.59 @ ^ [I3: nat] : ( power_8256067586552552935nteger @ X @ ( minus_minus_nat @ N2 @ ( suc @ I3 ) ) )
% 0.33/0.59 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % one_diff_power_eq'
% 0.33/0.59 thf(fact_4048_one__diff__power__eq_H,axiom,
% 0.33/0.59 ! [X: rat,N2: nat] :
% 0.33/0.59 ( ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ N2 ) )
% 0.33/0.59 = ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X )
% 0.33/0.59 @ ( groups2906978787729119204at_rat
% 0.33/0.59 @ ^ [I3: nat] : ( power_power_rat @ X @ ( minus_minus_nat @ N2 @ ( suc @ I3 ) ) )
% 0.33/0.59 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % one_diff_power_eq'
% 0.33/0.59 thf(fact_4049_one__diff__power__eq_H,axiom,
% 0.33/0.59 ! [X: int,N2: nat] :
% 0.33/0.59 ( ( minus_minus_int @ one_one_int @ ( power_power_int @ X @ N2 ) )
% 0.33/0.59 = ( times_times_int @ ( minus_minus_int @ one_one_int @ X )
% 0.33/0.59 @ ( groups3539618377306564664at_int
% 0.33/0.59 @ ^ [I3: nat] : ( power_power_int @ X @ ( minus_minus_nat @ N2 @ ( suc @ I3 ) ) )
% 0.33/0.59 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % one_diff_power_eq'
% 0.33/0.59 thf(fact_4050_binomial__ring,axiom,
% 0.33/0.59 ! [A: rat,B: rat,N2: nat] :
% 0.33/0.59 ( ( power_power_rat @ ( plus_plus_rat @ A @ B ) @ N2 )
% 0.33/0.59 = ( groups2906978787729119204at_rat
% 0.33/0.59 @ ^ [K4: nat] : ( times_times_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( binomial @ N2 @ K4 ) ) @ ( power_power_rat @ A @ K4 ) ) @ ( power_power_rat @ B @ ( minus_minus_nat @ N2 @ K4 ) ) )
% 0.33/0.59 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % binomial_ring
% 0.33/0.59 thf(fact_4051_binomial__ring,axiom,
% 0.33/0.59 ! [A: int,B: int,N2: nat] :
% 0.33/0.59 ( ( power_power_int @ ( plus_plus_int @ A @ B ) @ N2 )
% 0.33/0.59 = ( groups3539618377306564664at_int
% 0.33/0.59 @ ^ [K4: nat] : ( times_times_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ ( binomial @ N2 @ K4 ) ) @ ( power_power_int @ A @ K4 ) ) @ ( power_power_int @ B @ ( minus_minus_nat @ N2 @ K4 ) ) )
% 0.33/0.59 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % binomial_ring
% 0.33/0.59 thf(fact_4052_binomial__ring,axiom,
% 0.33/0.59 ! [A: code_integer,B: code_integer,N2: nat] :
% 0.33/0.59 ( ( power_8256067586552552935nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ N2 )
% 0.33/0.59 = ( groups7501900531339628137nteger
% 0.33/0.59 @ ^ [K4: nat] : ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ ( binomial @ N2 @ K4 ) ) @ ( power_8256067586552552935nteger @ A @ K4 ) ) @ ( power_8256067586552552935nteger @ B @ ( minus_minus_nat @ N2 @ K4 ) ) )
% 0.33/0.59 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % binomial_ring
% 0.33/0.59 thf(fact_4053_binomial__ring,axiom,
% 0.33/0.59 ! [A: code_natural,B: code_natural,N2: nat] :
% 0.33/0.59 ( ( power_7079662738309270450atural @ ( plus_p4538020629002901425atural @ A @ B ) @ N2 )
% 0.33/0.59 = ( groups6325495683096345652atural
% 0.33/0.59 @ ^ [K4: nat] : ( times_2397367101498566445atural @ ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ ( binomial @ N2 @ K4 ) ) @ ( power_7079662738309270450atural @ A @ K4 ) ) @ ( power_7079662738309270450atural @ B @ ( minus_minus_nat @ N2 @ K4 ) ) )
% 0.33/0.59 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % binomial_ring
% 0.33/0.59 thf(fact_4054_binomial__ring,axiom,
% 0.33/0.59 ! [A: nat,B: nat,N2: nat] :
% 0.33/0.59 ( ( power_power_nat @ ( plus_plus_nat @ A @ B ) @ N2 )
% 0.33/0.59 = ( groups3542108847815614940at_nat
% 0.33/0.59 @ ^ [K4: nat] : ( times_times_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( binomial @ N2 @ K4 ) ) @ ( power_power_nat @ A @ K4 ) ) @ ( power_power_nat @ B @ ( minus_minus_nat @ N2 @ K4 ) ) )
% 0.33/0.59 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % binomial_ring
% 0.33/0.59 thf(fact_4055_xor__num_Osimps_I6_J,axiom,
% 0.33/0.59 ! [M2: num,N2: num] :
% 0.33/0.59 ( ( bit_un2480387367778600638or_num @ ( bit0 @ M2 ) @ ( bit1 @ N2 ) )
% 0.33/0.59 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M2 @ N2 ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % xor_num.simps(6)
% 0.33/0.59 thf(fact_4056_xor__num_Osimps_I8_J,axiom,
% 0.33/0.59 ! [M2: num,N2: num] :
% 0.33/0.59 ( ( bit_un2480387367778600638or_num @ ( bit1 @ M2 ) @ ( bit0 @ N2 ) )
% 0.33/0.59 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M2 @ N2 ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % xor_num.simps(8)
% 0.33/0.59 thf(fact_4057_choose__alternating__linear__sum,axiom,
% 0.33/0.59 ! [N2: nat] :
% 0.33/0.59 ( ( N2 != one_one_nat )
% 0.33/0.59 => ( ( groups2906978787729119204at_rat
% 0.33/0.59 @ ^ [I3: nat] : ( times_times_rat @ ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ I3 ) @ ( semiri681578069525770553at_rat @ I3 ) ) @ ( semiri681578069525770553at_rat @ ( binomial @ N2 @ I3 ) ) )
% 0.33/0.59 @ ( set_ord_atMost_nat @ N2 ) )
% 0.33/0.59 = zero_zero_rat ) ) ).
% 0.33/0.59
% 0.33/0.59 % choose_alternating_linear_sum
% 0.33/0.59 thf(fact_4058_choose__alternating__linear__sum,axiom,
% 0.33/0.59 ! [N2: nat] :
% 0.33/0.59 ( ( N2 != one_one_nat )
% 0.33/0.59 => ( ( groups3539618377306564664at_int
% 0.33/0.59 @ ^ [I3: nat] : ( times_times_int @ ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ I3 ) @ ( semiri1314217659103216013at_int @ I3 ) ) @ ( semiri1314217659103216013at_int @ ( binomial @ N2 @ I3 ) ) )
% 0.33/0.59 @ ( set_ord_atMost_nat @ N2 ) )
% 0.33/0.59 = zero_zero_int ) ) ).
% 0.33/0.59
% 0.33/0.59 % choose_alternating_linear_sum
% 0.33/0.59 thf(fact_4059_choose__alternating__linear__sum,axiom,
% 0.33/0.59 ! [N2: nat] :
% 0.33/0.59 ( ( N2 != one_one_nat )
% 0.33/0.59 => ( ( groups7501900531339628137nteger
% 0.33/0.59 @ ^ [I3: nat] : ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ I3 ) @ ( semiri4939895301339042750nteger @ I3 ) ) @ ( semiri4939895301339042750nteger @ ( binomial @ N2 @ I3 ) ) )
% 0.33/0.59 @ ( set_ord_atMost_nat @ N2 ) )
% 0.33/0.59 = zero_z3403309356797280102nteger ) ) ).
% 0.33/0.59
% 0.33/0.59 % choose_alternating_linear_sum
% 0.33/0.59 thf(fact_4060_fact__Suc__0,axiom,
% 0.33/0.59 ( ( semiri3624122377584611663nteger @ ( suc @ zero_zero_nat ) )
% 0.33/0.59 = one_one_Code_integer ) ).
% 0.33/0.59
% 0.33/0.59 % fact_Suc_0
% 0.33/0.59 thf(fact_4061_fact__Suc__0,axiom,
% 0.33/0.59 ( ( semiri773545260158071498ct_rat @ ( suc @ zero_zero_nat ) )
% 0.33/0.59 = one_one_rat ) ).
% 0.33/0.59
% 0.33/0.59 % fact_Suc_0
% 0.33/0.59 thf(fact_4062_fact__Suc__0,axiom,
% 0.33/0.59 ( ( semiri1406184849735516958ct_int @ ( suc @ zero_zero_nat ) )
% 0.33/0.59 = one_one_int ) ).
% 0.33/0.59
% 0.33/0.59 % fact_Suc_0
% 0.33/0.59 thf(fact_4063_fact__Suc__0,axiom,
% 0.33/0.59 ( ( semiri1408675320244567234ct_nat @ ( suc @ zero_zero_nat ) )
% 0.33/0.59 = one_one_nat ) ).
% 0.33/0.59
% 0.33/0.59 % fact_Suc_0
% 0.33/0.59 thf(fact_4064_fact__1,axiom,
% 0.33/0.59 ( ( semiri3624122377584611663nteger @ one_one_nat )
% 0.33/0.59 = one_one_Code_integer ) ).
% 0.33/0.59
% 0.33/0.59 % fact_1
% 0.33/0.59 thf(fact_4065_fact__1,axiom,
% 0.33/0.59 ( ( semiri773545260158071498ct_rat @ one_one_nat )
% 0.33/0.59 = one_one_rat ) ).
% 0.33/0.59
% 0.33/0.59 % fact_1
% 0.33/0.59 thf(fact_4066_fact__1,axiom,
% 0.33/0.59 ( ( semiri1406184849735516958ct_int @ one_one_nat )
% 0.33/0.59 = one_one_int ) ).
% 0.33/0.59
% 0.33/0.59 % fact_1
% 0.33/0.59 thf(fact_4067_fact__1,axiom,
% 0.33/0.59 ( ( semiri1408675320244567234ct_nat @ one_one_nat )
% 0.33/0.59 = one_one_nat ) ).
% 0.33/0.59
% 0.33/0.59 % fact_1
% 0.33/0.59 thf(fact_4068_fact__0,axiom,
% 0.33/0.59 ( ( semiri3624122377584611663nteger @ zero_zero_nat )
% 0.33/0.59 = one_one_Code_integer ) ).
% 0.33/0.59
% 0.33/0.59 % fact_0
% 0.33/0.59 thf(fact_4069_fact__0,axiom,
% 0.33/0.59 ( ( semiri773545260158071498ct_rat @ zero_zero_nat )
% 0.33/0.59 = one_one_rat ) ).
% 0.33/0.59
% 0.33/0.59 % fact_0
% 0.33/0.59 thf(fact_4070_fact__0,axiom,
% 0.33/0.59 ( ( semiri1406184849735516958ct_int @ zero_zero_nat )
% 0.33/0.59 = one_one_int ) ).
% 0.33/0.59
% 0.33/0.59 % fact_0
% 0.33/0.59 thf(fact_4071_fact__0,axiom,
% 0.33/0.59 ( ( semiri1408675320244567234ct_nat @ zero_zero_nat )
% 0.33/0.59 = one_one_nat ) ).
% 0.33/0.59
% 0.33/0.59 % fact_0
% 0.33/0.59 thf(fact_4072_fact__code,axiom,
% 0.33/0.59 ( semiri1406184849735516958ct_int
% 0.33/0.59 = ( ^ [N4: nat] : ( semiri1314217659103216013at_int @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 @ one_one_nat ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % fact_code
% 0.33/0.59 thf(fact_4073_fact__code,axiom,
% 0.33/0.59 ( semiri3624122377584611663nteger
% 0.33/0.59 = ( ^ [N4: nat] : ( semiri4939895301339042750nteger @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 @ one_one_nat ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % fact_code
% 0.33/0.59 thf(fact_4074_fact__code,axiom,
% 0.33/0.59 ( semiri2447717529341329178atural
% 0.33/0.59 = ( ^ [N4: nat] : ( semiri3763490453095760265atural @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 @ one_one_nat ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % fact_code
% 0.33/0.59 thf(fact_4075_fact__code,axiom,
% 0.33/0.59 ( semiri1408675320244567234ct_nat
% 0.33/0.59 = ( ^ [N4: nat] : ( semiri1316708129612266289at_nat @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 @ one_one_nat ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % fact_code
% 0.33/0.59 thf(fact_4076_fact__reduce,axiom,
% 0.33/0.59 ! [N2: nat] :
% 0.33/0.59 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.33/0.59 => ( ( semiri773545260158071498ct_rat @ N2 )
% 0.33/0.59 = ( times_times_rat @ ( semiri681578069525770553at_rat @ N2 ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % fact_reduce
% 0.33/0.59 thf(fact_4077_fact__reduce,axiom,
% 0.33/0.59 ! [N2: nat] :
% 0.33/0.59 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.33/0.59 => ( ( semiri1406184849735516958ct_int @ N2 )
% 0.33/0.59 = ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( semiri1406184849735516958ct_int @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % fact_reduce
% 0.33/0.59 thf(fact_4078_fact__reduce,axiom,
% 0.33/0.59 ! [N2: nat] :
% 0.33/0.59 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.33/0.59 => ( ( semiri3624122377584611663nteger @ N2 )
% 0.33/0.59 = ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N2 ) @ ( semiri3624122377584611663nteger @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % fact_reduce
% 0.33/0.59 thf(fact_4079_fact__reduce,axiom,
% 0.33/0.59 ! [N2: nat] :
% 0.33/0.59 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.33/0.59 => ( ( semiri2447717529341329178atural @ N2 )
% 0.33/0.59 = ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ N2 ) @ ( semiri2447717529341329178atural @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % fact_reduce
% 0.33/0.59 thf(fact_4080_fact__reduce,axiom,
% 0.33/0.59 ! [N2: nat] :
% 0.33/0.59 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.33/0.59 => ( ( semiri1408675320244567234ct_nat @ N2 )
% 0.33/0.59 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % fact_reduce
% 0.33/0.59 thf(fact_4081_fact__num__eq__if,axiom,
% 0.33/0.59 ( semiri773545260158071498ct_rat
% 0.33/0.59 = ( ^ [M: nat] : ( if_rat @ ( M = zero_zero_nat ) @ one_one_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ M @ one_one_nat ) ) ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % fact_num_eq_if
% 0.33/0.59 thf(fact_4082_fact__num__eq__if,axiom,
% 0.33/0.59 ( semiri1406184849735516958ct_int
% 0.33/0.59 = ( ^ [M: nat] : ( if_int @ ( M = zero_zero_nat ) @ one_one_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1406184849735516958ct_int @ ( minus_minus_nat @ M @ one_one_nat ) ) ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % fact_num_eq_if
% 0.33/0.59 thf(fact_4083_fact__num__eq__if,axiom,
% 0.33/0.59 ( semiri3624122377584611663nteger
% 0.33/0.59 = ( ^ [M: nat] : ( if_Code_integer @ ( M = zero_zero_nat ) @ one_one_Code_integer @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri3624122377584611663nteger @ ( minus_minus_nat @ M @ one_one_nat ) ) ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % fact_num_eq_if
% 0.33/0.59 thf(fact_4084_fact__num__eq__if,axiom,
% 0.33/0.59 ( semiri2447717529341329178atural
% 0.33/0.59 = ( ^ [M: nat] : ( if_Code_natural @ ( M = zero_zero_nat ) @ one_one_Code_natural @ ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ M ) @ ( semiri2447717529341329178atural @ ( minus_minus_nat @ M @ one_one_nat ) ) ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % fact_num_eq_if
% 0.33/0.59 thf(fact_4085_fact__num__eq__if,axiom,
% 0.33/0.59 ( semiri1408675320244567234ct_nat
% 0.33/0.59 = ( ^ [M: nat] : ( if_nat @ ( M = zero_zero_nat ) @ one_one_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ M @ one_one_nat ) ) ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % fact_num_eq_if
% 0.33/0.59 thf(fact_4086_xor__num_Opelims,axiom,
% 0.33/0.59 ! [X: num,Xa: num,Y: option_num] :
% 0.33/0.59 ( ( ( bit_un2480387367778600638or_num @ X @ Xa )
% 0.33/0.59 = Y )
% 0.33/0.59 => ( ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ X @ Xa ) )
% 0.33/0.59 => ( ( ( X = one )
% 0.33/0.59 => ( ( Xa = one )
% 0.33/0.59 => ( ( Y = none_num )
% 0.33/0.59 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 0.33/0.59 => ( ( ( X = one )
% 0.33/0.59 => ! [N: num] :
% 0.33/0.59 ( ( Xa
% 0.33/0.59 = ( bit0 @ N ) )
% 0.33/0.59 => ( ( Y
% 0.33/0.59 = ( some_num @ ( bit1 @ N ) ) )
% 0.33/0.59 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ one @ ( bit0 @ N ) ) ) ) ) )
% 0.33/0.59 => ( ( ( X = one )
% 0.33/0.59 => ! [N: num] :
% 0.33/0.59 ( ( Xa
% 0.33/0.59 = ( bit1 @ N ) )
% 0.33/0.59 => ( ( Y
% 0.33/0.59 = ( some_num @ ( bit0 @ N ) ) )
% 0.33/0.59 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ one @ ( bit1 @ N ) ) ) ) ) )
% 0.33/0.59 => ( ! [M5: num] :
% 0.33/0.59 ( ( X
% 0.33/0.59 = ( bit0 @ M5 ) )
% 0.33/0.59 => ( ( Xa = one )
% 0.33/0.59 => ( ( Y
% 0.33/0.59 = ( some_num @ ( bit1 @ M5 ) ) )
% 0.33/0.59 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ one ) ) ) ) )
% 0.33/0.59 => ( ! [M5: num] :
% 0.33/0.59 ( ( X
% 0.33/0.59 = ( bit0 @ M5 ) )
% 0.33/0.59 => ! [N: num] :
% 0.33/0.59 ( ( Xa
% 0.33/0.59 = ( bit0 @ N ) )
% 0.33/0.59 => ( ( Y
% 0.33/0.59 = ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M5 @ N ) ) )
% 0.33/0.59 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ ( bit0 @ N ) ) ) ) ) )
% 0.33/0.59 => ( ! [M5: num] :
% 0.33/0.59 ( ( X
% 0.33/0.59 = ( bit0 @ M5 ) )
% 0.33/0.59 => ! [N: num] :
% 0.33/0.59 ( ( Xa
% 0.33/0.59 = ( bit1 @ N ) )
% 0.33/0.59 => ( ( Y
% 0.33/0.59 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M5 @ N ) ) ) )
% 0.33/0.59 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ ( bit1 @ N ) ) ) ) ) )
% 0.33/0.59 => ( ! [M5: num] :
% 0.33/0.59 ( ( X
% 0.33/0.59 = ( bit1 @ M5 ) )
% 0.33/0.59 => ( ( Xa = one )
% 0.33/0.59 => ( ( Y
% 0.33/0.59 = ( some_num @ ( bit0 @ M5 ) ) )
% 0.33/0.59 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ one ) ) ) ) )
% 0.33/0.59 => ( ! [M5: num] :
% 0.33/0.59 ( ( X
% 0.33/0.59 = ( bit1 @ M5 ) )
% 0.33/0.59 => ! [N: num] :
% 0.33/0.59 ( ( Xa
% 0.33/0.59 = ( bit0 @ N ) )
% 0.33/0.59 => ( ( Y
% 0.33/0.59 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M5 @ N ) ) ) )
% 0.33/0.59 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ ( bit0 @ N ) ) ) ) ) )
% 0.33/0.59 => ~ ! [M5: num] :
% 0.33/0.59 ( ( X
% 0.33/0.59 = ( bit1 @ M5 ) )
% 0.33/0.59 => ! [N: num] :
% 0.33/0.59 ( ( Xa
% 0.33/0.59 = ( bit1 @ N ) )
% 0.33/0.59 => ( ( Y
% 0.33/0.59 = ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M5 @ N ) ) )
% 0.33/0.59 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ ( bit1 @ N ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % xor_num.pelims
% 0.33/0.59 thf(fact_4087_dvd__fact,axiom,
% 0.33/0.59 ! [M2: nat,N2: nat] :
% 0.33/0.59 ( ( ord_less_eq_nat @ one_one_nat @ M2 )
% 0.33/0.59 => ( ( ord_less_eq_nat @ M2 @ N2 )
% 0.33/0.59 => ( dvd_dvd_nat @ M2 @ ( semiri1408675320244567234ct_nat @ N2 ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % dvd_fact
% 0.33/0.59 thf(fact_4088_fact__ge__1,axiom,
% 0.33/0.59 ! [N2: nat] : ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( semiri3624122377584611663nteger @ N2 ) ) ).
% 0.33/0.59
% 0.33/0.59 % fact_ge_1
% 0.33/0.59 thf(fact_4089_fact__ge__1,axiom,
% 0.33/0.59 ! [N2: nat] : ( ord_less_eq_rat @ one_one_rat @ ( semiri773545260158071498ct_rat @ N2 ) ) ).
% 0.33/0.59
% 0.33/0.59 % fact_ge_1
% 0.33/0.59 thf(fact_4090_fact__ge__1,axiom,
% 0.33/0.59 ! [N2: nat] : ( ord_less_eq_int @ one_one_int @ ( semiri1406184849735516958ct_int @ N2 ) ) ).
% 0.33/0.59
% 0.33/0.59 % fact_ge_1
% 0.33/0.59 thf(fact_4091_fact__ge__1,axiom,
% 0.33/0.59 ! [N2: nat] : ( ord_less_eq_nat @ one_one_nat @ ( semiri1408675320244567234ct_nat @ N2 ) ) ).
% 0.33/0.59
% 0.33/0.59 % fact_ge_1
% 0.33/0.59 thf(fact_4092_pochhammer__double,axiom,
% 0.33/0.59 ! [Z: rat,N2: nat] :
% 0.33/0.59 ( ( comm_s4028243227959126397er_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ Z ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 0.33/0.59 = ( times_times_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) @ ( comm_s4028243227959126397er_rat @ Z @ N2 ) ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ N2 ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % pochhammer_double
% 0.33/0.59 thf(fact_4093_fact__double,axiom,
% 0.33/0.59 ! [N2: nat] :
% 0.33/0.59 ( ( semiri773545260158071498ct_rat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 0.33/0.59 = ( times_times_rat @ ( times_times_rat @ ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) @ ( comm_s4028243227959126397er_rat @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ N2 ) ) @ ( semiri773545260158071498ct_rat @ N2 ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % fact_double
% 0.33/0.59 thf(fact_4094_pochhammer__code,axiom,
% 0.33/0.59 ( comm_s4028243227959126397er_rat
% 0.33/0.59 = ( ^ [A5: rat,N4: nat] :
% 0.33/0.59 ( if_rat @ ( N4 = zero_zero_nat ) @ one_one_rat
% 0.33/0.59 @ ( set_fo1949268297981939178at_rat
% 0.33/0.59 @ ^ [O: nat] : ( times_times_rat @ ( plus_plus_rat @ A5 @ ( semiri681578069525770553at_rat @ O ) ) )
% 0.33/0.59 @ zero_zero_nat
% 0.33/0.59 @ ( minus_minus_nat @ N4 @ one_one_nat )
% 0.33/0.59 @ one_one_rat ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % pochhammer_code
% 0.33/0.59 thf(fact_4095_pochhammer__code,axiom,
% 0.33/0.59 ( comm_s4660882817536571857er_int
% 0.33/0.59 = ( ^ [A5: int,N4: nat] :
% 0.33/0.59 ( if_int @ ( N4 = zero_zero_nat ) @ one_one_int
% 0.33/0.59 @ ( set_fo2581907887559384638at_int
% 0.33/0.59 @ ^ [O: nat] : ( times_times_int @ ( plus_plus_int @ A5 @ ( semiri1314217659103216013at_int @ O ) ) )
% 0.33/0.59 @ zero_zero_nat
% 0.33/0.59 @ ( minus_minus_nat @ N4 @ one_one_nat )
% 0.33/0.59 @ one_one_int ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % pochhammer_code
% 0.33/0.59 thf(fact_4096_pochhammer__code,axiom,
% 0.33/0.59 ( comm_s8582702949713902594nteger
% 0.33/0.59 = ( ^ [A5: code_integer,N4: nat] :
% 0.33/0.59 ( if_Code_integer @ ( N4 = zero_zero_nat ) @ one_one_Code_integer
% 0.33/0.59 @ ( set_fo1084959871951514735nteger
% 0.33/0.59 @ ^ [O: nat] : ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ A5 @ ( semiri4939895301339042750nteger @ O ) ) )
% 0.33/0.59 @ zero_zero_nat
% 0.33/0.59 @ ( minus_minus_nat @ N4 @ one_one_nat )
% 0.33/0.59 @ one_one_Code_integer ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % pochhammer_code
% 0.33/0.59 thf(fact_4097_pochhammer__code,axiom,
% 0.33/0.59 ( comm_s7406298101470620109atural
% 0.33/0.59 = ( ^ [A5: code_natural,N4: nat] :
% 0.33/0.59 ( if_Code_natural @ ( N4 = zero_zero_nat ) @ one_one_Code_natural
% 0.33/0.59 @ ( set_fo9131927060563008058atural
% 0.33/0.59 @ ^ [O: nat] : ( times_2397367101498566445atural @ ( plus_p4538020629002901425atural @ A5 @ ( semiri3763490453095760265atural @ O ) ) )
% 0.33/0.59 @ zero_zero_nat
% 0.33/0.59 @ ( minus_minus_nat @ N4 @ one_one_nat )
% 0.33/0.59 @ one_one_Code_natural ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % pochhammer_code
% 0.33/0.59 thf(fact_4098_pochhammer__code,axiom,
% 0.33/0.59 ( comm_s4663373288045622133er_nat
% 0.33/0.59 = ( ^ [A5: nat,N4: nat] :
% 0.33/0.59 ( if_nat @ ( N4 = zero_zero_nat ) @ one_one_nat
% 0.33/0.59 @ ( set_fo2584398358068434914at_nat
% 0.33/0.59 @ ^ [O: nat] : ( times_times_nat @ ( plus_plus_nat @ A5 @ ( semiri1316708129612266289at_nat @ O ) ) )
% 0.33/0.59 @ zero_zero_nat
% 0.33/0.59 @ ( minus_minus_nat @ N4 @ one_one_nat )
% 0.33/0.59 @ one_one_nat ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % pochhammer_code
% 0.33/0.59 thf(fact_4099_xor__Suc__0__eq,axiom,
% 0.33/0.59 ! [N2: nat] :
% 0.33/0.59 ( ( bit_se6528837805403552850or_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 0.33/0.59 = ( minus_minus_nat @ ( plus_plus_nat @ N2 @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 0.33/0.59 @ ( zero_n2687167440665602831ol_nat
% 0.33/0.59 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % xor_Suc_0_eq
% 0.33/0.59 thf(fact_4100_Suc__0__xor__eq,axiom,
% 0.33/0.59 ! [N2: nat] :
% 0.33/0.59 ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 0.33/0.59 = ( minus_minus_nat @ ( plus_plus_nat @ N2 @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 0.33/0.59 @ ( zero_n2687167440665602831ol_nat
% 0.33/0.59 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % Suc_0_xor_eq
% 0.33/0.59 thf(fact_4101_push__bit__numeral__minus__1,axiom,
% 0.33/0.59 ! [N2: num] :
% 0.33/0.59 ( ( bit_se7788150548672797655nteger @ ( numeral_numeral_nat @ N2 ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.33/0.59 = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ N2 ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % push_bit_numeral_minus_1
% 0.33/0.59 thf(fact_4102_push__bit__numeral__minus__1,axiom,
% 0.33/0.59 ! [N2: num] :
% 0.33/0.59 ( ( bit_se545348938243370406it_int @ ( numeral_numeral_nat @ N2 ) @ ( uminus_uminus_int @ one_one_int ) )
% 0.33/0.59 = ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ N2 ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % push_bit_numeral_minus_1
% 0.33/0.59 thf(fact_4103_num__of__integer__code,axiom,
% 0.33/0.59 ( code_num_of_integer
% 0.33/0.59 = ( ^ [K4: code_integer] :
% 0.33/0.59 ( if_num @ ( ord_le3102999989581377725nteger @ K4 @ one_one_Code_integer ) @ one
% 0.33/0.59 @ ( produc7336495610019696514er_num
% 0.33/0.59 @ ^ [L3: code_integer,J2: code_integer] : ( if_num @ ( J2 = zero_z3403309356797280102nteger ) @ ( plus_plus_num @ ( code_num_of_integer @ L3 ) @ ( code_num_of_integer @ L3 ) ) @ ( plus_plus_num @ ( plus_plus_num @ ( code_num_of_integer @ L3 ) @ ( code_num_of_integer @ L3 ) ) @ one ) )
% 0.33/0.59 @ ( code_divmod_integer @ K4 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % num_of_integer_code
% 0.33/0.59 thf(fact_4104_Sum__Ico__nat,axiom,
% 0.33/0.59 ! [M2: nat,N2: nat] :
% 0.33/0.59 ( ( groups3542108847815614940at_nat
% 0.33/0.59 @ ^ [X3: nat] : X3
% 0.33/0.59 @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) )
% 0.33/0.59 = ( divide_divide_nat @ ( minus_minus_nat @ ( times_times_nat @ N2 @ ( minus_minus_nat @ N2 @ one_one_nat ) ) @ ( times_times_nat @ M2 @ ( minus_minus_nat @ M2 @ one_one_nat ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % Sum_Ico_nat
% 0.33/0.59 thf(fact_4105_ivl__diff,axiom,
% 0.33/0.59 ! [I: rat,N2: rat,M2: rat] :
% 0.33/0.59 ( ( ord_less_eq_rat @ I @ N2 )
% 0.33/0.59 => ( ( minus_minus_set_rat @ ( set_or4029947393144176647an_rat @ I @ M2 ) @ ( set_or4029947393144176647an_rat @ I @ N2 ) )
% 0.33/0.59 = ( set_or4029947393144176647an_rat @ N2 @ M2 ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % ivl_diff
% 0.33/0.59 thf(fact_4106_ivl__diff,axiom,
% 0.33/0.59 ! [I: num,N2: num,M2: num] :
% 0.33/0.59 ( ( ord_less_eq_num @ I @ N2 )
% 0.33/0.59 => ( ( minus_minus_set_num @ ( set_or1222409239386451017an_num @ I @ M2 ) @ ( set_or1222409239386451017an_num @ I @ N2 ) )
% 0.33/0.59 = ( set_or1222409239386451017an_num @ N2 @ M2 ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % ivl_diff
% 0.33/0.59 thf(fact_4107_ivl__diff,axiom,
% 0.33/0.59 ! [I: nat,N2: nat,M2: nat] :
% 0.33/0.59 ( ( ord_less_eq_nat @ I @ N2 )
% 0.33/0.59 => ( ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ I @ M2 ) @ ( set_or4665077453230672383an_nat @ I @ N2 ) )
% 0.33/0.59 = ( set_or4665077453230672383an_nat @ N2 @ M2 ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % ivl_diff
% 0.33/0.59 thf(fact_4108_ivl__diff,axiom,
% 0.33/0.59 ! [I: code_integer,N2: code_integer,M2: code_integer] :
% 0.33/0.59 ( ( ord_le3102999989581377725nteger @ I @ N2 )
% 0.33/0.59 => ( ( minus_2355218937544613996nteger @ ( set_or8404916559141939852nteger @ I @ M2 ) @ ( set_or8404916559141939852nteger @ I @ N2 ) )
% 0.33/0.59 = ( set_or8404916559141939852nteger @ N2 @ M2 ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % ivl_diff
% 0.33/0.59 thf(fact_4109_ivl__diff,axiom,
% 0.33/0.59 ! [I: int,N2: int,M2: int] :
% 0.33/0.59 ( ( ord_less_eq_int @ I @ N2 )
% 0.33/0.59 => ( ( minus_minus_set_int @ ( set_or4662586982721622107an_int @ I @ M2 ) @ ( set_or4662586982721622107an_int @ I @ N2 ) )
% 0.33/0.59 = ( set_or4662586982721622107an_int @ N2 @ M2 ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % ivl_diff
% 0.33/0.59 thf(fact_4110_push__bit__push__bit,axiom,
% 0.33/0.59 ! [M2: nat,N2: nat,A: nat] :
% 0.33/0.59 ( ( bit_se547839408752420682it_nat @ M2 @ ( bit_se547839408752420682it_nat @ N2 @ A ) )
% 0.33/0.59 = ( bit_se547839408752420682it_nat @ ( plus_plus_nat @ M2 @ N2 ) @ A ) ) ).
% 0.33/0.59
% 0.33/0.59 % push_bit_push_bit
% 0.33/0.59 thf(fact_4111_push__bit__push__bit,axiom,
% 0.33/0.59 ! [M2: nat,N2: nat,A: code_integer] :
% 0.33/0.59 ( ( bit_se7788150548672797655nteger @ M2 @ ( bit_se7788150548672797655nteger @ N2 @ A ) )
% 0.33/0.59 = ( bit_se7788150548672797655nteger @ ( plus_plus_nat @ M2 @ N2 ) @ A ) ) ).
% 0.33/0.59
% 0.33/0.59 % push_bit_push_bit
% 0.33/0.59 thf(fact_4112_push__bit__push__bit,axiom,
% 0.33/0.59 ! [M2: nat,N2: nat,A: int] :
% 0.33/0.59 ( ( bit_se545348938243370406it_int @ M2 @ ( bit_se545348938243370406it_int @ N2 @ A ) )
% 0.33/0.59 = ( bit_se545348938243370406it_int @ ( plus_plus_nat @ M2 @ N2 ) @ A ) ) ).
% 0.33/0.59
% 0.33/0.59 % push_bit_push_bit
% 0.33/0.59 thf(fact_4113_push__bit__push__bit,axiom,
% 0.33/0.59 ! [M2: nat,N2: nat,A: code_natural] :
% 0.33/0.59 ( ( bit_se6611745700429515170atural @ M2 @ ( bit_se6611745700429515170atural @ N2 @ A ) )
% 0.33/0.59 = ( bit_se6611745700429515170atural @ ( plus_plus_nat @ M2 @ N2 ) @ A ) ) ).
% 0.33/0.59
% 0.33/0.59 % push_bit_push_bit
% 0.33/0.59 thf(fact_4114_lessThan__minus__lessThan,axiom,
% 0.33/0.59 ! [N2: nat,M2: nat] :
% 0.33/0.59 ( ( minus_minus_set_nat @ ( set_ord_lessThan_nat @ N2 ) @ ( set_ord_lessThan_nat @ M2 ) )
% 0.33/0.59 = ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) ).
% 0.33/0.59
% 0.33/0.59 % lessThan_minus_lessThan
% 0.33/0.59 thf(fact_4115_lessThan__minus__lessThan,axiom,
% 0.33/0.59 ! [N2: code_integer,M2: code_integer] :
% 0.33/0.59 ( ( minus_2355218937544613996nteger @ ( set_or5754767410780653050nteger @ N2 ) @ ( set_or5754767410780653050nteger @ M2 ) )
% 0.33/0.59 = ( set_or8404916559141939852nteger @ M2 @ N2 ) ) ).
% 0.33/0.59
% 0.33/0.59 % lessThan_minus_lessThan
% 0.33/0.59 thf(fact_4116_lessThan__minus__lessThan,axiom,
% 0.33/0.59 ! [N2: int,M2: int] :
% 0.33/0.59 ( ( minus_minus_set_int @ ( set_ord_lessThan_int @ N2 ) @ ( set_ord_lessThan_int @ M2 ) )
% 0.33/0.59 = ( set_or4662586982721622107an_int @ M2 @ N2 ) ) ).
% 0.33/0.59
% 0.33/0.59 % lessThan_minus_lessThan
% 0.33/0.59 thf(fact_4117_atLeastLessThan__iff,axiom,
% 0.33/0.59 ! [I: $o,L: $o,U: $o] :
% 0.33/0.59 ( ( member_o @ I @ ( set_or7139685690850216873Than_o @ L @ U ) )
% 0.33/0.59 = ( ( ord_less_eq_o @ L @ I )
% 0.33/0.59 & ( ord_less_o @ I @ U ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % atLeastLessThan_iff
% 0.33/0.59 thf(fact_4118_atLeastLessThan__iff,axiom,
% 0.33/0.59 ! [I: set_nat,L: set_nat,U: set_nat] :
% 0.33/0.59 ( ( member_set_nat @ I @ ( set_or3540276404033026485et_nat @ L @ U ) )
% 0.33/0.59 = ( ( ord_less_eq_set_nat @ L @ I )
% 0.33/0.59 & ( ord_less_set_nat @ I @ U ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % atLeastLessThan_iff
% 0.33/0.59 thf(fact_4119_atLeastLessThan__iff,axiom,
% 0.33/0.59 ! [I: rat,L: rat,U: rat] :
% 0.33/0.59 ( ( member_rat @ I @ ( set_or4029947393144176647an_rat @ L @ U ) )
% 0.33/0.59 = ( ( ord_less_eq_rat @ L @ I )
% 0.33/0.59 & ( ord_less_rat @ I @ U ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % atLeastLessThan_iff
% 0.33/0.59 thf(fact_4120_atLeastLessThan__iff,axiom,
% 0.33/0.59 ! [I: num,L: num,U: num] :
% 0.33/0.59 ( ( member_num @ I @ ( set_or1222409239386451017an_num @ L @ U ) )
% 0.33/0.59 = ( ( ord_less_eq_num @ L @ I )
% 0.33/0.59 & ( ord_less_num @ I @ U ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % atLeastLessThan_iff
% 0.33/0.59 thf(fact_4121_atLeastLessThan__iff,axiom,
% 0.33/0.59 ! [I: nat,L: nat,U: nat] :
% 0.33/0.59 ( ( member_nat @ I @ ( set_or4665077453230672383an_nat @ L @ U ) )
% 0.33/0.59 = ( ( ord_less_eq_nat @ L @ I )
% 0.33/0.59 & ( ord_less_nat @ I @ U ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % atLeastLessThan_iff
% 0.33/0.59 thf(fact_4122_atLeastLessThan__iff,axiom,
% 0.33/0.59 ! [I: code_integer,L: code_integer,U: code_integer] :
% 0.33/0.59 ( ( member_Code_integer @ I @ ( set_or8404916559141939852nteger @ L @ U ) )
% 0.33/0.59 = ( ( ord_le3102999989581377725nteger @ L @ I )
% 0.33/0.59 & ( ord_le6747313008572928689nteger @ I @ U ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % atLeastLessThan_iff
% 0.33/0.59 thf(fact_4123_atLeastLessThan__iff,axiom,
% 0.33/0.59 ! [I: int,L: int,U: int] :
% 0.33/0.59 ( ( member_int @ I @ ( set_or4662586982721622107an_int @ L @ U ) )
% 0.33/0.59 = ( ( ord_less_eq_int @ L @ I )
% 0.33/0.59 & ( ord_less_int @ I @ U ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % atLeastLessThan_iff
% 0.33/0.59 thf(fact_4124_ivl__subset,axiom,
% 0.33/0.59 ! [I: rat,J: rat,M2: rat,N2: rat] :
% 0.33/0.59 ( ( ord_less_eq_set_rat @ ( set_or4029947393144176647an_rat @ I @ J ) @ ( set_or4029947393144176647an_rat @ M2 @ N2 ) )
% 0.33/0.59 = ( ( ord_less_eq_rat @ J @ I )
% 0.33/0.59 | ( ( ord_less_eq_rat @ M2 @ I )
% 0.33/0.59 & ( ord_less_eq_rat @ J @ N2 ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % ivl_subset
% 0.33/0.59 thf(fact_4125_ivl__subset,axiom,
% 0.33/0.59 ! [I: num,J: num,M2: num,N2: num] :
% 0.33/0.59 ( ( ord_less_eq_set_num @ ( set_or1222409239386451017an_num @ I @ J ) @ ( set_or1222409239386451017an_num @ M2 @ N2 ) )
% 0.33/0.59 = ( ( ord_less_eq_num @ J @ I )
% 0.33/0.59 | ( ( ord_less_eq_num @ M2 @ I )
% 0.33/0.59 & ( ord_less_eq_num @ J @ N2 ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % ivl_subset
% 0.33/0.59 thf(fact_4126_ivl__subset,axiom,
% 0.33/0.59 ! [I: nat,J: nat,M2: nat,N2: nat] :
% 0.33/0.59 ( ( ord_less_eq_set_nat @ ( set_or4665077453230672383an_nat @ I @ J ) @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) )
% 0.33/0.59 = ( ( ord_less_eq_nat @ J @ I )
% 0.33/0.59 | ( ( ord_less_eq_nat @ M2 @ I )
% 0.33/0.59 & ( ord_less_eq_nat @ J @ N2 ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % ivl_subset
% 0.33/0.59 thf(fact_4127_ivl__subset,axiom,
% 0.33/0.59 ! [I: code_integer,J: code_integer,M2: code_integer,N2: code_integer] :
% 0.33/0.59 ( ( ord_le7084787975880047091nteger @ ( set_or8404916559141939852nteger @ I @ J ) @ ( set_or8404916559141939852nteger @ M2 @ N2 ) )
% 0.33/0.59 = ( ( ord_le3102999989581377725nteger @ J @ I )
% 0.33/0.59 | ( ( ord_le3102999989581377725nteger @ M2 @ I )
% 0.33/0.59 & ( ord_le3102999989581377725nteger @ J @ N2 ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % ivl_subset
% 0.33/0.59 thf(fact_4128_ivl__subset,axiom,
% 0.33/0.59 ! [I: int,J: int,M2: int,N2: int] :
% 0.33/0.59 ( ( ord_less_eq_set_int @ ( set_or4662586982721622107an_int @ I @ J ) @ ( set_or4662586982721622107an_int @ M2 @ N2 ) )
% 0.33/0.59 = ( ( ord_less_eq_int @ J @ I )
% 0.33/0.59 | ( ( ord_less_eq_int @ M2 @ I )
% 0.33/0.59 & ( ord_less_eq_int @ J @ N2 ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % ivl_subset
% 0.33/0.59 thf(fact_4129_pochhammer__0,axiom,
% 0.33/0.59 ! [A: code_integer] :
% 0.33/0.59 ( ( comm_s8582702949713902594nteger @ A @ zero_zero_nat )
% 0.33/0.59 = one_one_Code_integer ) ).
% 0.33/0.59
% 0.33/0.59 % pochhammer_0
% 0.33/0.59 thf(fact_4130_pochhammer__0,axiom,
% 0.33/0.59 ! [A: rat] :
% 0.33/0.59 ( ( comm_s4028243227959126397er_rat @ A @ zero_zero_nat )
% 0.33/0.59 = one_one_rat ) ).
% 0.33/0.59
% 0.33/0.59 % pochhammer_0
% 0.33/0.59 thf(fact_4131_pochhammer__0,axiom,
% 0.33/0.59 ! [A: nat] :
% 0.33/0.59 ( ( comm_s4663373288045622133er_nat @ A @ zero_zero_nat )
% 0.33/0.59 = one_one_nat ) ).
% 0.33/0.59
% 0.33/0.59 % pochhammer_0
% 0.33/0.59 thf(fact_4132_pochhammer__0,axiom,
% 0.33/0.59 ! [A: int] :
% 0.33/0.59 ( ( comm_s4660882817536571857er_int @ A @ zero_zero_nat )
% 0.33/0.59 = one_one_int ) ).
% 0.33/0.59
% 0.33/0.59 % pochhammer_0
% 0.33/0.59 thf(fact_4133_xor__numerals_I1_J,axiom,
% 0.33/0.59 ! [Y: num] :
% 0.33/0.59 ( ( bit_se6528837805403552850or_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 0.33/0.59 = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % xor_numerals(1)
% 0.33/0.59 thf(fact_4134_xor__numerals_I1_J,axiom,
% 0.33/0.59 ! [Y: num] :
% 0.33/0.59 ( ( bit_se3222712562003087583nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ Y ) ) )
% 0.33/0.59 = ( numera6620942414471956472nteger @ ( bit1 @ Y ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % xor_numerals(1)
% 0.33/0.59 thf(fact_4135_xor__numerals_I1_J,axiom,
% 0.33/0.59 ! [Y: num] :
% 0.33/0.59 ( ( bit_se6526347334894502574or_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 0.33/0.59 = ( numeral_numeral_int @ ( bit1 @ Y ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % xor_numerals(1)
% 0.33/0.59 thf(fact_4136_xor__numerals_I1_J,axiom,
% 0.33/0.59 ! [Y: num] :
% 0.33/0.59 ( ( bit_se2046307713759805098atural @ one_one_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ Y ) ) )
% 0.33/0.59 = ( numera5444537566228673987atural @ ( bit1 @ Y ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % xor_numerals(1)
% 0.33/0.59 thf(fact_4137_xor__numerals_I2_J,axiom,
% 0.33/0.59 ! [Y: num] :
% 0.33/0.59 ( ( bit_se6528837805403552850or_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 0.33/0.59 = ( numeral_numeral_nat @ ( bit0 @ Y ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % xor_numerals(2)
% 0.33/0.59 thf(fact_4138_xor__numerals_I2_J,axiom,
% 0.33/0.59 ! [Y: num] :
% 0.33/0.59 ( ( bit_se3222712562003087583nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit1 @ Y ) ) )
% 0.33/0.59 = ( numera6620942414471956472nteger @ ( bit0 @ Y ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % xor_numerals(2)
% 0.33/0.59 thf(fact_4139_xor__numerals_I2_J,axiom,
% 0.33/0.59 ! [Y: num] :
% 0.33/0.59 ( ( bit_se6526347334894502574or_int @ one_one_int @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 0.33/0.59 = ( numeral_numeral_int @ ( bit0 @ Y ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % xor_numerals(2)
% 0.33/0.59 thf(fact_4140_xor__numerals_I2_J,axiom,
% 0.33/0.59 ! [Y: num] :
% 0.33/0.59 ( ( bit_se2046307713759805098atural @ one_one_Code_natural @ ( numera5444537566228673987atural @ ( bit1 @ Y ) ) )
% 0.33/0.59 = ( numera5444537566228673987atural @ ( bit0 @ Y ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % xor_numerals(2)
% 0.33/0.59 thf(fact_4141_xor__numerals_I5_J,axiom,
% 0.33/0.59 ! [X: num] :
% 0.33/0.59 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ one_one_nat )
% 0.33/0.59 = ( numeral_numeral_nat @ ( bit1 @ X ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % xor_numerals(5)
% 0.33/0.59 thf(fact_4142_xor__numerals_I5_J,axiom,
% 0.33/0.59 ! [X: num] :
% 0.33/0.59 ( ( bit_se3222712562003087583nteger @ ( numera6620942414471956472nteger @ ( bit0 @ X ) ) @ one_one_Code_integer )
% 0.33/0.59 = ( numera6620942414471956472nteger @ ( bit1 @ X ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % xor_numerals(5)
% 0.33/0.59 thf(fact_4143_xor__numerals_I5_J,axiom,
% 0.33/0.59 ! [X: num] :
% 0.33/0.59 ( ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ one_one_int )
% 0.33/0.59 = ( numeral_numeral_int @ ( bit1 @ X ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % xor_numerals(5)
% 0.33/0.59 thf(fact_4144_xor__numerals_I5_J,axiom,
% 0.33/0.59 ! [X: num] :
% 0.33/0.59 ( ( bit_se2046307713759805098atural @ ( numera5444537566228673987atural @ ( bit0 @ X ) ) @ one_one_Code_natural )
% 0.33/0.59 = ( numera5444537566228673987atural @ ( bit1 @ X ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % xor_numerals(5)
% 0.33/0.59 thf(fact_4145_xor__numerals_I8_J,axiom,
% 0.33/0.59 ! [X: num] :
% 0.33/0.59 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ one_one_nat )
% 0.33/0.59 = ( numeral_numeral_nat @ ( bit0 @ X ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % xor_numerals(8)
% 0.33/0.59 thf(fact_4146_xor__numerals_I8_J,axiom,
% 0.33/0.59 ! [X: num] :
% 0.33/0.59 ( ( bit_se3222712562003087583nteger @ ( numera6620942414471956472nteger @ ( bit1 @ X ) ) @ one_one_Code_integer )
% 0.33/0.59 = ( numera6620942414471956472nteger @ ( bit0 @ X ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % xor_numerals(8)
% 0.33/0.59 thf(fact_4147_xor__numerals_I8_J,axiom,
% 0.33/0.59 ! [X: num] :
% 0.33/0.59 ( ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ one_one_int )
% 0.33/0.59 = ( numeral_numeral_int @ ( bit0 @ X ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % xor_numerals(8)
% 0.33/0.59 thf(fact_4148_xor__numerals_I8_J,axiom,
% 0.33/0.59 ! [X: num] :
% 0.33/0.59 ( ( bit_se2046307713759805098atural @ ( numera5444537566228673987atural @ ( bit1 @ X ) ) @ one_one_Code_natural )
% 0.33/0.59 = ( numera5444537566228673987atural @ ( bit0 @ X ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % xor_numerals(8)
% 0.33/0.59 thf(fact_4149_push__bit__of__1,axiom,
% 0.33/0.59 ! [N2: nat] :
% 0.33/0.59 ( ( bit_se547839408752420682it_nat @ N2 @ one_one_nat )
% 0.33/0.59 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 0.33/0.59
% 0.33/0.59 % push_bit_of_1
% 0.33/0.59 thf(fact_4150_push__bit__of__1,axiom,
% 0.33/0.59 ! [N2: nat] :
% 0.33/0.59 ( ( bit_se7788150548672797655nteger @ N2 @ one_one_Code_integer )
% 0.33/0.59 = ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) ).
% 0.33/0.59
% 0.33/0.59 % push_bit_of_1
% 0.33/0.59 thf(fact_4151_push__bit__of__1,axiom,
% 0.33/0.59 ! [N2: nat] :
% 0.33/0.59 ( ( bit_se545348938243370406it_int @ N2 @ one_one_int )
% 0.33/0.59 = ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ).
% 0.33/0.59
% 0.33/0.59 % push_bit_of_1
% 0.33/0.59 thf(fact_4152_push__bit__of__1,axiom,
% 0.33/0.59 ! [N2: nat] :
% 0.33/0.59 ( ( bit_se6611745700429515170atural @ N2 @ one_one_Code_natural )
% 0.33/0.59 = ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N2 ) ) ).
% 0.33/0.59
% 0.33/0.59 % push_bit_of_1
% 0.33/0.59 thf(fact_4153_sum_Oop__ivl__Suc,axiom,
% 0.33/0.59 ! [N2: nat,M2: nat,G: nat > code_integer] :
% 0.33/0.59 ( ( ( ord_less_nat @ N2 @ M2 )
% 0.33/0.59 => ( ( groups7501900531339628137nteger @ G @ ( set_or4665077453230672383an_nat @ M2 @ ( suc @ N2 ) ) )
% 0.33/0.59 = zero_z3403309356797280102nteger ) )
% 0.33/0.59 & ( ~ ( ord_less_nat @ N2 @ M2 )
% 0.33/0.59 => ( ( groups7501900531339628137nteger @ G @ ( set_or4665077453230672383an_nat @ M2 @ ( suc @ N2 ) ) )
% 0.33/0.59 = ( plus_p5714425477246183910nteger @ ( groups7501900531339628137nteger @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) @ ( G @ N2 ) ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum.op_ivl_Suc
% 0.33/0.59 thf(fact_4154_sum_Oop__ivl__Suc,axiom,
% 0.33/0.59 ! [N2: nat,M2: nat,G: nat > multis2468970476368604999at_nat] :
% 0.33/0.59 ( ( ( ord_less_nat @ N2 @ M2 )
% 0.33/0.59 => ( ( groups6857163185585827899at_nat @ G @ ( set_or4665077453230672383an_nat @ M2 @ ( suc @ N2 ) ) )
% 0.33/0.59 = zero_z1048942125864253310at_nat ) )
% 0.33/0.59 & ( ~ ( ord_less_nat @ N2 @ M2 )
% 0.33/0.59 => ( ( groups6857163185585827899at_nat @ G @ ( set_or4665077453230672383an_nat @ M2 @ ( suc @ N2 ) ) )
% 0.33/0.59 = ( plus_p7104986032573967614at_nat @ ( groups6857163185585827899at_nat @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) @ ( G @ N2 ) ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum.op_ivl_Suc
% 0.33/0.59 thf(fact_4155_sum_Oop__ivl__Suc,axiom,
% 0.33/0.59 ! [N2: nat,M2: nat,G: nat > rat] :
% 0.33/0.59 ( ( ( ord_less_nat @ N2 @ M2 )
% 0.33/0.59 => ( ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ M2 @ ( suc @ N2 ) ) )
% 0.33/0.59 = zero_zero_rat ) )
% 0.33/0.59 & ( ~ ( ord_less_nat @ N2 @ M2 )
% 0.33/0.59 => ( ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ M2 @ ( suc @ N2 ) ) )
% 0.33/0.59 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) @ ( G @ N2 ) ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum.op_ivl_Suc
% 0.33/0.59 thf(fact_4156_sum_Oop__ivl__Suc,axiom,
% 0.33/0.59 ! [N2: nat,M2: nat,G: nat > int] :
% 0.33/0.59 ( ( ( ord_less_nat @ N2 @ M2 )
% 0.33/0.59 => ( ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ M2 @ ( suc @ N2 ) ) )
% 0.33/0.59 = zero_zero_int ) )
% 0.33/0.59 & ( ~ ( ord_less_nat @ N2 @ M2 )
% 0.33/0.59 => ( ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ M2 @ ( suc @ N2 ) ) )
% 0.33/0.59 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) @ ( G @ N2 ) ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum.op_ivl_Suc
% 0.33/0.59 thf(fact_4157_sum_Oop__ivl__Suc,axiom,
% 0.33/0.59 ! [N2: nat,M2: nat,G: nat > nat] :
% 0.33/0.59 ( ( ( ord_less_nat @ N2 @ M2 )
% 0.33/0.59 => ( ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ M2 @ ( suc @ N2 ) ) )
% 0.33/0.59 = zero_zero_nat ) )
% 0.33/0.59 & ( ~ ( ord_less_nat @ N2 @ M2 )
% 0.33/0.59 => ( ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ M2 @ ( suc @ N2 ) ) )
% 0.33/0.59 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) @ ( G @ N2 ) ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum.op_ivl_Suc
% 0.33/0.59 thf(fact_4158_xor__numerals_I4_J,axiom,
% 0.33/0.59 ! [X: num,Y: num] :
% 0.33/0.59 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 0.33/0.59 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % xor_numerals(4)
% 0.33/0.59 thf(fact_4159_xor__numerals_I4_J,axiom,
% 0.33/0.59 ! [X: num,Y: num] :
% 0.33/0.59 ( ( bit_se3222712562003087583nteger @ ( numera6620942414471956472nteger @ ( bit0 @ X ) ) @ ( numera6620942414471956472nteger @ ( bit1 @ Y ) ) )
% 0.33/0.59 = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se3222712562003087583nteger @ ( numera6620942414471956472nteger @ X ) @ ( numera6620942414471956472nteger @ Y ) ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % xor_numerals(4)
% 0.33/0.59 thf(fact_4160_xor__numerals_I4_J,axiom,
% 0.33/0.59 ! [X: num,Y: num] :
% 0.33/0.59 ( ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 0.33/0.59 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % xor_numerals(4)
% 0.33/0.59 thf(fact_4161_xor__numerals_I4_J,axiom,
% 0.33/0.59 ! [X: num,Y: num] :
% 0.33/0.59 ( ( bit_se2046307713759805098atural @ ( numera5444537566228673987atural @ ( bit0 @ X ) ) @ ( numera5444537566228673987atural @ ( bit1 @ Y ) ) )
% 0.33/0.59 = ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se2046307713759805098atural @ ( numera5444537566228673987atural @ X ) @ ( numera5444537566228673987atural @ Y ) ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % xor_numerals(4)
% 0.33/0.59 thf(fact_4162_xor__numerals_I6_J,axiom,
% 0.33/0.59 ! [X: num,Y: num] :
% 0.33/0.59 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 0.33/0.59 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % xor_numerals(6)
% 0.33/0.59 thf(fact_4163_xor__numerals_I6_J,axiom,
% 0.33/0.59 ! [X: num,Y: num] :
% 0.33/0.59 ( ( bit_se3222712562003087583nteger @ ( numera6620942414471956472nteger @ ( bit1 @ X ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Y ) ) )
% 0.33/0.59 = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se3222712562003087583nteger @ ( numera6620942414471956472nteger @ X ) @ ( numera6620942414471956472nteger @ Y ) ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % xor_numerals(6)
% 0.33/0.59 thf(fact_4164_xor__numerals_I6_J,axiom,
% 0.33/0.59 ! [X: num,Y: num] :
% 0.33/0.59 ( ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 0.33/0.59 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % xor_numerals(6)
% 0.33/0.59 thf(fact_4165_xor__numerals_I6_J,axiom,
% 0.33/0.59 ! [X: num,Y: num] :
% 0.33/0.59 ( ( bit_se2046307713759805098atural @ ( numera5444537566228673987atural @ ( bit1 @ X ) ) @ ( numera5444537566228673987atural @ ( bit0 @ Y ) ) )
% 0.33/0.59 = ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se2046307713759805098atural @ ( numera5444537566228673987atural @ X ) @ ( numera5444537566228673987atural @ Y ) ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % xor_numerals(6)
% 0.33/0.59 thf(fact_4166_flip__bit__nat__def,axiom,
% 0.33/0.59 ( bit_se2161824704523386999it_nat
% 0.33/0.59 = ( ^ [M: nat,N4: nat] : ( bit_se6528837805403552850or_nat @ N4 @ ( bit_se547839408752420682it_nat @ M @ one_one_nat ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % flip_bit_nat_def
% 0.33/0.59 thf(fact_4167_push__bit__integer_Oabs__eq,axiom,
% 0.33/0.59 ! [Xa: nat,X: int] :
% 0.33/0.59 ( ( bit_se7788150548672797655nteger @ Xa @ ( code_integer_of_int @ X ) )
% 0.33/0.59 = ( code_integer_of_int @ ( bit_se545348938243370406it_int @ Xa @ X ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % push_bit_integer.abs_eq
% 0.33/0.59 thf(fact_4168_atLeastLessThan__inj_I2_J,axiom,
% 0.33/0.59 ! [A: rat,B: rat,C: rat,D2: rat] :
% 0.33/0.59 ( ( ( set_or4029947393144176647an_rat @ A @ B )
% 0.33/0.59 = ( set_or4029947393144176647an_rat @ C @ D2 ) )
% 0.33/0.59 => ( ( ord_less_rat @ A @ B )
% 0.33/0.59 => ( ( ord_less_rat @ C @ D2 )
% 0.33/0.59 => ( B = D2 ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % atLeastLessThan_inj(2)
% 0.33/0.59 thf(fact_4169_atLeastLessThan__inj_I2_J,axiom,
% 0.33/0.59 ! [A: num,B: num,C: num,D2: num] :
% 0.33/0.59 ( ( ( set_or1222409239386451017an_num @ A @ B )
% 0.33/0.59 = ( set_or1222409239386451017an_num @ C @ D2 ) )
% 0.33/0.59 => ( ( ord_less_num @ A @ B )
% 0.33/0.59 => ( ( ord_less_num @ C @ D2 )
% 0.33/0.59 => ( B = D2 ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % atLeastLessThan_inj(2)
% 0.33/0.59 thf(fact_4170_atLeastLessThan__inj_I2_J,axiom,
% 0.33/0.59 ! [A: nat,B: nat,C: nat,D2: nat] :
% 0.33/0.59 ( ( ( set_or4665077453230672383an_nat @ A @ B )
% 0.33/0.59 = ( set_or4665077453230672383an_nat @ C @ D2 ) )
% 0.33/0.59 => ( ( ord_less_nat @ A @ B )
% 0.33/0.59 => ( ( ord_less_nat @ C @ D2 )
% 0.33/0.59 => ( B = D2 ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % atLeastLessThan_inj(2)
% 0.33/0.59 thf(fact_4171_atLeastLessThan__inj_I2_J,axiom,
% 0.33/0.59 ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 0.33/0.59 ( ( ( set_or8404916559141939852nteger @ A @ B )
% 0.33/0.59 = ( set_or8404916559141939852nteger @ C @ D2 ) )
% 0.33/0.59 => ( ( ord_le6747313008572928689nteger @ A @ B )
% 0.33/0.59 => ( ( ord_le6747313008572928689nteger @ C @ D2 )
% 0.33/0.59 => ( B = D2 ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % atLeastLessThan_inj(2)
% 0.33/0.59 thf(fact_4172_atLeastLessThan__inj_I2_J,axiom,
% 0.33/0.59 ! [A: int,B: int,C: int,D2: int] :
% 0.33/0.59 ( ( ( set_or4662586982721622107an_int @ A @ B )
% 0.33/0.59 = ( set_or4662586982721622107an_int @ C @ D2 ) )
% 0.33/0.59 => ( ( ord_less_int @ A @ B )
% 0.33/0.59 => ( ( ord_less_int @ C @ D2 )
% 0.33/0.59 => ( B = D2 ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % atLeastLessThan_inj(2)
% 0.33/0.59 thf(fact_4173_atLeastLessThan__inj_I1_J,axiom,
% 0.33/0.59 ! [A: rat,B: rat,C: rat,D2: rat] :
% 0.33/0.59 ( ( ( set_or4029947393144176647an_rat @ A @ B )
% 0.33/0.59 = ( set_or4029947393144176647an_rat @ C @ D2 ) )
% 0.33/0.59 => ( ( ord_less_rat @ A @ B )
% 0.33/0.59 => ( ( ord_less_rat @ C @ D2 )
% 0.33/0.59 => ( A = C ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % atLeastLessThan_inj(1)
% 0.33/0.59 thf(fact_4174_atLeastLessThan__inj_I1_J,axiom,
% 0.33/0.59 ! [A: num,B: num,C: num,D2: num] :
% 0.33/0.59 ( ( ( set_or1222409239386451017an_num @ A @ B )
% 0.33/0.59 = ( set_or1222409239386451017an_num @ C @ D2 ) )
% 0.33/0.59 => ( ( ord_less_num @ A @ B )
% 0.33/0.59 => ( ( ord_less_num @ C @ D2 )
% 0.33/0.59 => ( A = C ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % atLeastLessThan_inj(1)
% 0.33/0.59 thf(fact_4175_atLeastLessThan__inj_I1_J,axiom,
% 0.33/0.59 ! [A: nat,B: nat,C: nat,D2: nat] :
% 0.33/0.59 ( ( ( set_or4665077453230672383an_nat @ A @ B )
% 0.33/0.59 = ( set_or4665077453230672383an_nat @ C @ D2 ) )
% 0.33/0.59 => ( ( ord_less_nat @ A @ B )
% 0.33/0.59 => ( ( ord_less_nat @ C @ D2 )
% 0.33/0.59 => ( A = C ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % atLeastLessThan_inj(1)
% 0.33/0.59 thf(fact_4176_atLeastLessThan__inj_I1_J,axiom,
% 0.33/0.59 ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 0.33/0.59 ( ( ( set_or8404916559141939852nteger @ A @ B )
% 0.33/0.59 = ( set_or8404916559141939852nteger @ C @ D2 ) )
% 0.33/0.59 => ( ( ord_le6747313008572928689nteger @ A @ B )
% 0.33/0.59 => ( ( ord_le6747313008572928689nteger @ C @ D2 )
% 0.33/0.59 => ( A = C ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % atLeastLessThan_inj(1)
% 0.33/0.59 thf(fact_4177_atLeastLessThan__inj_I1_J,axiom,
% 0.33/0.59 ! [A: int,B: int,C: int,D2: int] :
% 0.33/0.59 ( ( ( set_or4662586982721622107an_int @ A @ B )
% 0.33/0.59 = ( set_or4662586982721622107an_int @ C @ D2 ) )
% 0.33/0.59 => ( ( ord_less_int @ A @ B )
% 0.33/0.59 => ( ( ord_less_int @ C @ D2 )
% 0.33/0.59 => ( A = C ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % atLeastLessThan_inj(1)
% 0.33/0.59 thf(fact_4178_atLeastLessThan__eq__iff,axiom,
% 0.33/0.59 ! [A: rat,B: rat,C: rat,D2: rat] :
% 0.33/0.59 ( ( ord_less_rat @ A @ B )
% 0.33/0.59 => ( ( ord_less_rat @ C @ D2 )
% 0.33/0.59 => ( ( ( set_or4029947393144176647an_rat @ A @ B )
% 0.33/0.59 = ( set_or4029947393144176647an_rat @ C @ D2 ) )
% 0.33/0.59 = ( ( A = C )
% 0.33/0.59 & ( B = D2 ) ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % atLeastLessThan_eq_iff
% 0.33/0.59 thf(fact_4179_atLeastLessThan__eq__iff,axiom,
% 0.33/0.59 ! [A: num,B: num,C: num,D2: num] :
% 0.33/0.59 ( ( ord_less_num @ A @ B )
% 0.33/0.59 => ( ( ord_less_num @ C @ D2 )
% 0.33/0.59 => ( ( ( set_or1222409239386451017an_num @ A @ B )
% 0.33/0.59 = ( set_or1222409239386451017an_num @ C @ D2 ) )
% 0.33/0.59 = ( ( A = C )
% 0.33/0.59 & ( B = D2 ) ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % atLeastLessThan_eq_iff
% 0.33/0.59 thf(fact_4180_atLeastLessThan__eq__iff,axiom,
% 0.33/0.59 ! [A: nat,B: nat,C: nat,D2: nat] :
% 0.33/0.59 ( ( ord_less_nat @ A @ B )
% 0.33/0.59 => ( ( ord_less_nat @ C @ D2 )
% 0.33/0.59 => ( ( ( set_or4665077453230672383an_nat @ A @ B )
% 0.33/0.59 = ( set_or4665077453230672383an_nat @ C @ D2 ) )
% 0.33/0.59 = ( ( A = C )
% 0.33/0.59 & ( B = D2 ) ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % atLeastLessThan_eq_iff
% 0.33/0.59 thf(fact_4181_atLeastLessThan__eq__iff,axiom,
% 0.33/0.59 ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 0.33/0.59 ( ( ord_le6747313008572928689nteger @ A @ B )
% 0.33/0.59 => ( ( ord_le6747313008572928689nteger @ C @ D2 )
% 0.33/0.59 => ( ( ( set_or8404916559141939852nteger @ A @ B )
% 0.33/0.59 = ( set_or8404916559141939852nteger @ C @ D2 ) )
% 0.33/0.59 = ( ( A = C )
% 0.33/0.59 & ( B = D2 ) ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % atLeastLessThan_eq_iff
% 0.33/0.59 thf(fact_4182_atLeastLessThan__eq__iff,axiom,
% 0.33/0.59 ! [A: int,B: int,C: int,D2: int] :
% 0.33/0.59 ( ( ord_less_int @ A @ B )
% 0.33/0.59 => ( ( ord_less_int @ C @ D2 )
% 0.33/0.59 => ( ( ( set_or4662586982721622107an_int @ A @ B )
% 0.33/0.59 = ( set_or4662586982721622107an_int @ C @ D2 ) )
% 0.33/0.59 = ( ( A = C )
% 0.33/0.59 & ( B = D2 ) ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % atLeastLessThan_eq_iff
% 0.33/0.59 thf(fact_4183_flip__bit__eq__xor,axiom,
% 0.33/0.59 ( bit_se2161824704523386999it_nat
% 0.33/0.59 = ( ^ [N4: nat,A5: nat] : ( bit_se6528837805403552850or_nat @ A5 @ ( bit_se547839408752420682it_nat @ N4 @ one_one_nat ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % flip_bit_eq_xor
% 0.33/0.59 thf(fact_4184_flip__bit__eq__xor,axiom,
% 0.33/0.59 ( bit_se1345352211410354436nteger
% 0.33/0.59 = ( ^ [N4: nat,A5: code_integer] : ( bit_se3222712562003087583nteger @ A5 @ ( bit_se7788150548672797655nteger @ N4 @ one_one_Code_integer ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % flip_bit_eq_xor
% 0.33/0.59 thf(fact_4185_flip__bit__eq__xor,axiom,
% 0.33/0.59 ( bit_se2159334234014336723it_int
% 0.33/0.59 = ( ^ [N4: nat,A5: int] : ( bit_se6526347334894502574or_int @ A5 @ ( bit_se545348938243370406it_int @ N4 @ one_one_int ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % flip_bit_eq_xor
% 0.33/0.59 thf(fact_4186_flip__bit__eq__xor,axiom,
% 0.33/0.59 ( bit_se168947363167071951atural
% 0.33/0.59 = ( ^ [N4: nat,A5: code_natural] : ( bit_se2046307713759805098atural @ A5 @ ( bit_se6611745700429515170atural @ N4 @ one_one_Code_natural ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % flip_bit_eq_xor
% 0.33/0.59 thf(fact_4187_push__bit__add,axiom,
% 0.33/0.59 ! [N2: nat,A: nat,B: nat] :
% 0.33/0.59 ( ( bit_se547839408752420682it_nat @ N2 @ ( plus_plus_nat @ A @ B ) )
% 0.33/0.59 = ( plus_plus_nat @ ( bit_se547839408752420682it_nat @ N2 @ A ) @ ( bit_se547839408752420682it_nat @ N2 @ B ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % push_bit_add
% 0.33/0.59 thf(fact_4188_push__bit__add,axiom,
% 0.33/0.59 ! [N2: nat,A: code_integer,B: code_integer] :
% 0.33/0.59 ( ( bit_se7788150548672797655nteger @ N2 @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 0.33/0.59 = ( plus_p5714425477246183910nteger @ ( bit_se7788150548672797655nteger @ N2 @ A ) @ ( bit_se7788150548672797655nteger @ N2 @ B ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % push_bit_add
% 0.33/0.59 thf(fact_4189_push__bit__add,axiom,
% 0.33/0.59 ! [N2: nat,A: int,B: int] :
% 0.33/0.59 ( ( bit_se545348938243370406it_int @ N2 @ ( plus_plus_int @ A @ B ) )
% 0.33/0.59 = ( plus_plus_int @ ( bit_se545348938243370406it_int @ N2 @ A ) @ ( bit_se545348938243370406it_int @ N2 @ B ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % push_bit_add
% 0.33/0.59 thf(fact_4190_push__bit__add,axiom,
% 0.33/0.59 ! [N2: nat,A: code_natural,B: code_natural] :
% 0.33/0.59 ( ( bit_se6611745700429515170atural @ N2 @ ( plus_p4538020629002901425atural @ A @ B ) )
% 0.33/0.59 = ( plus_p4538020629002901425atural @ ( bit_se6611745700429515170atural @ N2 @ A ) @ ( bit_se6611745700429515170atural @ N2 @ B ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % push_bit_add
% 0.33/0.59 thf(fact_4191_atLeastLessThan__subset__iff,axiom,
% 0.33/0.59 ! [A: rat,B: rat,C: rat,D2: rat] :
% 0.33/0.59 ( ( ord_less_eq_set_rat @ ( set_or4029947393144176647an_rat @ A @ B ) @ ( set_or4029947393144176647an_rat @ C @ D2 ) )
% 0.33/0.59 => ( ( ord_less_eq_rat @ B @ A )
% 0.33/0.59 | ( ( ord_less_eq_rat @ C @ A )
% 0.33/0.59 & ( ord_less_eq_rat @ B @ D2 ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % atLeastLessThan_subset_iff
% 0.33/0.59 thf(fact_4192_atLeastLessThan__subset__iff,axiom,
% 0.33/0.59 ! [A: num,B: num,C: num,D2: num] :
% 0.33/0.59 ( ( ord_less_eq_set_num @ ( set_or1222409239386451017an_num @ A @ B ) @ ( set_or1222409239386451017an_num @ C @ D2 ) )
% 0.33/0.59 => ( ( ord_less_eq_num @ B @ A )
% 0.33/0.59 | ( ( ord_less_eq_num @ C @ A )
% 0.33/0.59 & ( ord_less_eq_num @ B @ D2 ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % atLeastLessThan_subset_iff
% 0.33/0.59 thf(fact_4193_atLeastLessThan__subset__iff,axiom,
% 0.33/0.59 ! [A: nat,B: nat,C: nat,D2: nat] :
% 0.33/0.59 ( ( ord_less_eq_set_nat @ ( set_or4665077453230672383an_nat @ A @ B ) @ ( set_or4665077453230672383an_nat @ C @ D2 ) )
% 0.33/0.59 => ( ( ord_less_eq_nat @ B @ A )
% 0.33/0.59 | ( ( ord_less_eq_nat @ C @ A )
% 0.33/0.59 & ( ord_less_eq_nat @ B @ D2 ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % atLeastLessThan_subset_iff
% 0.33/0.59 thf(fact_4194_atLeastLessThan__subset__iff,axiom,
% 0.33/0.59 ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 0.33/0.59 ( ( ord_le7084787975880047091nteger @ ( set_or8404916559141939852nteger @ A @ B ) @ ( set_or8404916559141939852nteger @ C @ D2 ) )
% 0.33/0.59 => ( ( ord_le3102999989581377725nteger @ B @ A )
% 0.33/0.59 | ( ( ord_le3102999989581377725nteger @ C @ A )
% 0.33/0.59 & ( ord_le3102999989581377725nteger @ B @ D2 ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % atLeastLessThan_subset_iff
% 0.33/0.59 thf(fact_4195_atLeastLessThan__subset__iff,axiom,
% 0.33/0.59 ! [A: int,B: int,C: int,D2: int] :
% 0.33/0.59 ( ( ord_less_eq_set_int @ ( set_or4662586982721622107an_int @ A @ B ) @ ( set_or4662586982721622107an_int @ C @ D2 ) )
% 0.33/0.59 => ( ( ord_less_eq_int @ B @ A )
% 0.33/0.59 | ( ( ord_less_eq_int @ C @ A )
% 0.33/0.59 & ( ord_less_eq_int @ B @ D2 ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % atLeastLessThan_subset_iff
% 0.33/0.59 thf(fact_4196_atLeastLessThanSuc__atLeastAtMost,axiom,
% 0.33/0.59 ! [L: nat,U: nat] :
% 0.33/0.59 ( ( set_or4665077453230672383an_nat @ L @ ( suc @ U ) )
% 0.33/0.59 = ( set_or1269000886237332187st_nat @ L @ U ) ) ).
% 0.33/0.59
% 0.33/0.59 % atLeastLessThanSuc_atLeastAtMost
% 0.33/0.59 thf(fact_4197_lessThan__atLeast0,axiom,
% 0.33/0.59 ( set_ord_lessThan_nat
% 0.33/0.59 = ( set_or4665077453230672383an_nat @ zero_zero_nat ) ) ).
% 0.33/0.59
% 0.33/0.59 % lessThan_atLeast0
% 0.33/0.59 thf(fact_4198_push__bit__take__bit,axiom,
% 0.33/0.59 ! [M2: nat,N2: nat,A: code_integer] :
% 0.33/0.59 ( ( bit_se7788150548672797655nteger @ M2 @ ( bit_se1745604003318907178nteger @ N2 @ A ) )
% 0.33/0.59 = ( bit_se1745604003318907178nteger @ ( plus_plus_nat @ M2 @ N2 ) @ ( bit_se7788150548672797655nteger @ M2 @ A ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % push_bit_take_bit
% 0.33/0.59 thf(fact_4199_push__bit__take__bit,axiom,
% 0.33/0.59 ! [M2: nat,N2: nat,A: int] :
% 0.33/0.59 ( ( bit_se545348938243370406it_int @ M2 @ ( bit_se2923211474154528505it_int @ N2 @ A ) )
% 0.33/0.59 = ( bit_se2923211474154528505it_int @ ( plus_plus_nat @ M2 @ N2 ) @ ( bit_se545348938243370406it_int @ M2 @ A ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % push_bit_take_bit
% 0.33/0.59 thf(fact_4200_push__bit__take__bit,axiom,
% 0.33/0.59 ! [M2: nat,N2: nat,A: nat] :
% 0.33/0.59 ( ( bit_se547839408752420682it_nat @ M2 @ ( bit_se2925701944663578781it_nat @ N2 @ A ) )
% 0.33/0.59 = ( bit_se2925701944663578781it_nat @ ( plus_plus_nat @ M2 @ N2 ) @ ( bit_se547839408752420682it_nat @ M2 @ A ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % push_bit_take_bit
% 0.33/0.59 thf(fact_4201_push__bit__take__bit,axiom,
% 0.33/0.59 ! [M2: nat,N2: nat,A: code_natural] :
% 0.33/0.59 ( ( bit_se6611745700429515170atural @ M2 @ ( bit_se569199155075624693atural @ N2 @ A ) )
% 0.33/0.59 = ( bit_se569199155075624693atural @ ( plus_plus_nat @ M2 @ N2 ) @ ( bit_se6611745700429515170atural @ M2 @ A ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % push_bit_take_bit
% 0.33/0.59 thf(fact_4202_pochhammer__fact,axiom,
% 0.33/0.59 ( semiri3624122377584611663nteger
% 0.33/0.59 = ( comm_s8582702949713902594nteger @ one_one_Code_integer ) ) ).
% 0.33/0.59
% 0.33/0.59 % pochhammer_fact
% 0.33/0.59 thf(fact_4203_pochhammer__fact,axiom,
% 0.33/0.59 ( semiri773545260158071498ct_rat
% 0.33/0.59 = ( comm_s4028243227959126397er_rat @ one_one_rat ) ) ).
% 0.33/0.59
% 0.33/0.59 % pochhammer_fact
% 0.33/0.59 thf(fact_4204_pochhammer__fact,axiom,
% 0.33/0.59 ( semiri1406184849735516958ct_int
% 0.33/0.59 = ( comm_s4660882817536571857er_int @ one_one_int ) ) ).
% 0.33/0.59
% 0.33/0.59 % pochhammer_fact
% 0.33/0.59 thf(fact_4205_pochhammer__fact,axiom,
% 0.33/0.59 ( semiri1408675320244567234ct_nat
% 0.33/0.59 = ( comm_s4663373288045622133er_nat @ one_one_nat ) ) ).
% 0.33/0.59
% 0.33/0.59 % pochhammer_fact
% 0.33/0.59 thf(fact_4206_sum_Oshift__bounds__Suc__ivl,axiom,
% 0.33/0.59 ! [G: nat > nat,M2: nat,N2: nat] :
% 0.33/0.59 ( ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ ( suc @ M2 ) @ ( suc @ N2 ) ) )
% 0.33/0.59 = ( groups3542108847815614940at_nat
% 0.33/0.59 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 0.33/0.59 @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum.shift_bounds_Suc_ivl
% 0.33/0.59 thf(fact_4207_sum_Oshift__bounds__nat__ivl,axiom,
% 0.33/0.59 ! [G: nat > nat,M2: nat,K: nat,N2: nat] :
% 0.33/0.59 ( ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ ( plus_plus_nat @ M2 @ K ) @ ( plus_plus_nat @ N2 @ K ) ) )
% 0.33/0.59 = ( groups3542108847815614940at_nat
% 0.33/0.59 @ ^ [I3: nat] : ( G @ ( plus_plus_nat @ I3 @ K ) )
% 0.33/0.59 @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum.shift_bounds_nat_ivl
% 0.33/0.59 thf(fact_4208_sum_Oivl__cong,axiom,
% 0.33/0.59 ! [A: nat,C: nat,B: nat,D2: nat,G: nat > nat,H3: nat > nat] :
% 0.33/0.59 ( ( A = C )
% 0.33/0.59 => ( ( B = D2 )
% 0.33/0.59 => ( ! [X4: nat] :
% 0.33/0.59 ( ( ord_less_eq_nat @ C @ X4 )
% 0.33/0.59 => ( ( ord_less_nat @ X4 @ D2 )
% 0.33/0.59 => ( ( G @ X4 )
% 0.33/0.59 = ( H3 @ X4 ) ) ) )
% 0.33/0.59 => ( ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ A @ B ) )
% 0.33/0.59 = ( groups3542108847815614940at_nat @ H3 @ ( set_or4665077453230672383an_nat @ C @ D2 ) ) ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum.ivl_cong
% 0.33/0.59 thf(fact_4209_sum_Oivl__cong,axiom,
% 0.33/0.59 ! [A: int,C: int,B: int,D2: int,G: int > int,H3: int > int] :
% 0.33/0.59 ( ( A = C )
% 0.33/0.59 => ( ( B = D2 )
% 0.33/0.59 => ( ! [X4: int] :
% 0.33/0.59 ( ( ord_less_eq_int @ C @ X4 )
% 0.33/0.59 => ( ( ord_less_int @ X4 @ D2 )
% 0.33/0.59 => ( ( G @ X4 )
% 0.33/0.59 = ( H3 @ X4 ) ) ) )
% 0.33/0.59 => ( ( groups4538972089207619220nt_int @ G @ ( set_or4662586982721622107an_int @ A @ B ) )
% 0.33/0.59 = ( groups4538972089207619220nt_int @ H3 @ ( set_or4662586982721622107an_int @ C @ D2 ) ) ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum.ivl_cong
% 0.33/0.59 thf(fact_4210_sum_OatLeastLessThan__concat,axiom,
% 0.33/0.59 ! [M2: nat,N2: nat,P4: nat,G: nat > multis2468970476368604999at_nat] :
% 0.33/0.59 ( ( ord_less_eq_nat @ M2 @ N2 )
% 0.33/0.59 => ( ( ord_less_eq_nat @ N2 @ P4 )
% 0.33/0.59 => ( ( plus_p7104986032573967614at_nat @ ( groups6857163185585827899at_nat @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) @ ( groups6857163185585827899at_nat @ G @ ( set_or4665077453230672383an_nat @ N2 @ P4 ) ) )
% 0.33/0.59 = ( groups6857163185585827899at_nat @ G @ ( set_or4665077453230672383an_nat @ M2 @ P4 ) ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum.atLeastLessThan_concat
% 0.33/0.59 thf(fact_4211_sum_OatLeastLessThan__concat,axiom,
% 0.33/0.59 ! [M2: nat,N2: nat,P4: nat,G: nat > rat] :
% 0.33/0.59 ( ( ord_less_eq_nat @ M2 @ N2 )
% 0.33/0.59 => ( ( ord_less_eq_nat @ N2 @ P4 )
% 0.33/0.59 => ( ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) @ ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ N2 @ P4 ) ) )
% 0.33/0.59 = ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ M2 @ P4 ) ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum.atLeastLessThan_concat
% 0.33/0.59 thf(fact_4212_sum_OatLeastLessThan__concat,axiom,
% 0.33/0.59 ! [M2: nat,N2: nat,P4: nat,G: nat > int] :
% 0.33/0.59 ( ( ord_less_eq_nat @ M2 @ N2 )
% 0.33/0.59 => ( ( ord_less_eq_nat @ N2 @ P4 )
% 0.33/0.59 => ( ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) @ ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ N2 @ P4 ) ) )
% 0.33/0.59 = ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ M2 @ P4 ) ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum.atLeastLessThan_concat
% 0.33/0.59 thf(fact_4213_sum_OatLeastLessThan__concat,axiom,
% 0.33/0.59 ! [M2: nat,N2: nat,P4: nat,G: nat > nat] :
% 0.33/0.59 ( ( ord_less_eq_nat @ M2 @ N2 )
% 0.33/0.59 => ( ( ord_less_eq_nat @ N2 @ P4 )
% 0.33/0.59 => ( ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) @ ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ N2 @ P4 ) ) )
% 0.33/0.59 = ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ M2 @ P4 ) ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum.atLeastLessThan_concat
% 0.33/0.59 thf(fact_4214_sum__diff__nat__ivl,axiom,
% 0.33/0.59 ! [M2: nat,N2: nat,P4: nat,F: nat > code_integer] :
% 0.33/0.59 ( ( ord_less_eq_nat @ M2 @ N2 )
% 0.33/0.59 => ( ( ord_less_eq_nat @ N2 @ P4 )
% 0.33/0.59 => ( ( minus_8373710615458151222nteger @ ( groups7501900531339628137nteger @ F @ ( set_or4665077453230672383an_nat @ M2 @ P4 ) ) @ ( groups7501900531339628137nteger @ F @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) )
% 0.33/0.59 = ( groups7501900531339628137nteger @ F @ ( set_or4665077453230672383an_nat @ N2 @ P4 ) ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum_diff_nat_ivl
% 0.33/0.59 thf(fact_4215_sum__diff__nat__ivl,axiom,
% 0.33/0.59 ! [M2: nat,N2: nat,P4: nat,F: nat > rat] :
% 0.33/0.59 ( ( ord_less_eq_nat @ M2 @ N2 )
% 0.33/0.59 => ( ( ord_less_eq_nat @ N2 @ P4 )
% 0.33/0.59 => ( ( minus_minus_rat @ ( groups2906978787729119204at_rat @ F @ ( set_or4665077453230672383an_nat @ M2 @ P4 ) ) @ ( groups2906978787729119204at_rat @ F @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) )
% 0.33/0.59 = ( groups2906978787729119204at_rat @ F @ ( set_or4665077453230672383an_nat @ N2 @ P4 ) ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum_diff_nat_ivl
% 0.33/0.59 thf(fact_4216_sum__diff__nat__ivl,axiom,
% 0.33/0.59 ! [M2: nat,N2: nat,P4: nat,F: nat > int] :
% 0.33/0.59 ( ( ord_less_eq_nat @ M2 @ N2 )
% 0.33/0.59 => ( ( ord_less_eq_nat @ N2 @ P4 )
% 0.33/0.59 => ( ( minus_minus_int @ ( groups3539618377306564664at_int @ F @ ( set_or4665077453230672383an_nat @ M2 @ P4 ) ) @ ( groups3539618377306564664at_int @ F @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) )
% 0.33/0.59 = ( groups3539618377306564664at_int @ F @ ( set_or4665077453230672383an_nat @ N2 @ P4 ) ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum_diff_nat_ivl
% 0.33/0.59 thf(fact_4217_pochhammer__0__left,axiom,
% 0.33/0.59 ! [N2: nat] :
% 0.33/0.59 ( ( ( N2 = zero_zero_nat )
% 0.33/0.59 => ( ( comm_s8582702949713902594nteger @ zero_z3403309356797280102nteger @ N2 )
% 0.33/0.59 = one_one_Code_integer ) )
% 0.33/0.59 & ( ( N2 != zero_zero_nat )
% 0.33/0.59 => ( ( comm_s8582702949713902594nteger @ zero_z3403309356797280102nteger @ N2 )
% 0.33/0.59 = zero_z3403309356797280102nteger ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % pochhammer_0_left
% 0.33/0.59 thf(fact_4218_pochhammer__0__left,axiom,
% 0.33/0.59 ! [N2: nat] :
% 0.33/0.59 ( ( ( N2 = zero_zero_nat )
% 0.33/0.59 => ( ( comm_s4028243227959126397er_rat @ zero_zero_rat @ N2 )
% 0.33/0.59 = one_one_rat ) )
% 0.33/0.59 & ( ( N2 != zero_zero_nat )
% 0.33/0.59 => ( ( comm_s4028243227959126397er_rat @ zero_zero_rat @ N2 )
% 0.33/0.59 = zero_zero_rat ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % pochhammer_0_left
% 0.33/0.59 thf(fact_4219_pochhammer__0__left,axiom,
% 0.33/0.59 ! [N2: nat] :
% 0.33/0.59 ( ( ( N2 = zero_zero_nat )
% 0.33/0.59 => ( ( comm_s4663373288045622133er_nat @ zero_zero_nat @ N2 )
% 0.33/0.59 = one_one_nat ) )
% 0.33/0.59 & ( ( N2 != zero_zero_nat )
% 0.33/0.59 => ( ( comm_s4663373288045622133er_nat @ zero_zero_nat @ N2 )
% 0.33/0.59 = zero_zero_nat ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % pochhammer_0_left
% 0.33/0.59 thf(fact_4220_pochhammer__0__left,axiom,
% 0.33/0.59 ! [N2: nat] :
% 0.33/0.59 ( ( ( N2 = zero_zero_nat )
% 0.33/0.59 => ( ( comm_s4660882817536571857er_int @ zero_zero_int @ N2 )
% 0.33/0.59 = one_one_int ) )
% 0.33/0.59 & ( ( N2 != zero_zero_nat )
% 0.33/0.59 => ( ( comm_s4660882817536571857er_int @ zero_zero_int @ N2 )
% 0.33/0.59 = zero_zero_int ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % pochhammer_0_left
% 0.33/0.59 thf(fact_4221_sum_OatLeast__Suc__lessThan__Suc__shift,axiom,
% 0.33/0.59 ! [G: nat > nat,M2: nat,N2: nat] :
% 0.33/0.59 ( ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ ( suc @ M2 ) @ ( suc @ N2 ) ) )
% 0.33/0.59 = ( groups3542108847815614940at_nat @ ( comp_nat_nat_nat @ G @ suc ) @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum.atLeast_Suc_lessThan_Suc_shift
% 0.33/0.59 thf(fact_4222_sum_OatLeastLessThan__shift__bounds,axiom,
% 0.33/0.59 ! [G: nat > nat,M2: nat,K: nat,N2: nat] :
% 0.33/0.59 ( ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ ( plus_plus_nat @ M2 @ K ) @ ( plus_plus_nat @ N2 @ K ) ) )
% 0.33/0.59 = ( groups3542108847815614940at_nat @ ( comp_nat_nat_nat @ G @ ( plus_plus_nat @ K ) ) @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum.atLeastLessThan_shift_bounds
% 0.33/0.59 thf(fact_4223_concat__bit__eq,axiom,
% 0.33/0.59 ( bit_concat_bit
% 0.33/0.59 = ( ^ [N4: nat,K4: int,L3: int] : ( plus_plus_int @ ( bit_se2923211474154528505it_int @ N4 @ K4 ) @ ( bit_se545348938243370406it_int @ N4 @ L3 ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % concat_bit_eq
% 0.33/0.59 thf(fact_4224_atLeastAtMost__subseteq__atLeastLessThan__iff,axiom,
% 0.33/0.59 ! [A: set_nat,B: set_nat,C: set_nat,D2: set_nat] :
% 0.33/0.59 ( ( ord_le6893508408891458716et_nat @ ( set_or4548717258645045905et_nat @ A @ B ) @ ( set_or3540276404033026485et_nat @ C @ D2 ) )
% 0.33/0.59 = ( ( ord_less_eq_set_nat @ A @ B )
% 0.33/0.59 => ( ( ord_less_eq_set_nat @ C @ A )
% 0.33/0.59 & ( ord_less_set_nat @ B @ D2 ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % atLeastAtMost_subseteq_atLeastLessThan_iff
% 0.33/0.59 thf(fact_4225_atLeastAtMost__subseteq__atLeastLessThan__iff,axiom,
% 0.33/0.59 ! [A: rat,B: rat,C: rat,D2: rat] :
% 0.33/0.59 ( ( ord_less_eq_set_rat @ ( set_or633870826150836451st_rat @ A @ B ) @ ( set_or4029947393144176647an_rat @ C @ D2 ) )
% 0.33/0.59 = ( ( ord_less_eq_rat @ A @ B )
% 0.33/0.59 => ( ( ord_less_eq_rat @ C @ A )
% 0.33/0.59 & ( ord_less_rat @ B @ D2 ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % atLeastAtMost_subseteq_atLeastLessThan_iff
% 0.33/0.59 thf(fact_4226_atLeastAtMost__subseteq__atLeastLessThan__iff,axiom,
% 0.33/0.59 ! [A: num,B: num,C: num,D2: num] :
% 0.33/0.59 ( ( ord_less_eq_set_num @ ( set_or7049704709247886629st_num @ A @ B ) @ ( set_or1222409239386451017an_num @ C @ D2 ) )
% 0.33/0.59 = ( ( ord_less_eq_num @ A @ B )
% 0.33/0.59 => ( ( ord_less_eq_num @ C @ A )
% 0.33/0.59 & ( ord_less_num @ B @ D2 ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % atLeastAtMost_subseteq_atLeastLessThan_iff
% 0.33/0.59 thf(fact_4227_atLeastAtMost__subseteq__atLeastLessThan__iff,axiom,
% 0.33/0.59 ! [A: nat,B: nat,C: nat,D2: nat] :
% 0.33/0.59 ( ( ord_less_eq_set_nat @ ( set_or1269000886237332187st_nat @ A @ B ) @ ( set_or4665077453230672383an_nat @ C @ D2 ) )
% 0.33/0.59 = ( ( ord_less_eq_nat @ A @ B )
% 0.33/0.59 => ( ( ord_less_eq_nat @ C @ A )
% 0.33/0.59 & ( ord_less_nat @ B @ D2 ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % atLeastAtMost_subseteq_atLeastLessThan_iff
% 0.33/0.59 thf(fact_4228_atLeastAtMost__subseteq__atLeastLessThan__iff,axiom,
% 0.33/0.59 ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 0.33/0.59 ( ( ord_le7084787975880047091nteger @ ( set_or189985376899183464nteger @ A @ B ) @ ( set_or8404916559141939852nteger @ C @ D2 ) )
% 0.33/0.59 = ( ( ord_le3102999989581377725nteger @ A @ B )
% 0.33/0.59 => ( ( ord_le3102999989581377725nteger @ C @ A )
% 0.33/0.59 & ( ord_le6747313008572928689nteger @ B @ D2 ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % atLeastAtMost_subseteq_atLeastLessThan_iff
% 0.33/0.59 thf(fact_4229_atLeastAtMost__subseteq__atLeastLessThan__iff,axiom,
% 0.33/0.59 ! [A: int,B: int,C: int,D2: int] :
% 0.33/0.59 ( ( ord_less_eq_set_int @ ( set_or1266510415728281911st_int @ A @ B ) @ ( set_or4662586982721622107an_int @ C @ D2 ) )
% 0.33/0.59 = ( ( ord_less_eq_int @ A @ B )
% 0.33/0.59 => ( ( ord_less_eq_int @ C @ A )
% 0.33/0.59 & ( ord_less_int @ B @ D2 ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % atLeastAtMost_subseteq_atLeastLessThan_iff
% 0.33/0.59 thf(fact_4230_atLeastLessThan__subseteq__atLeastAtMost__iff,axiom,
% 0.33/0.59 ! [A: rat,B: rat,C: rat,D2: rat] :
% 0.33/0.59 ( ( ord_less_eq_set_rat @ ( set_or4029947393144176647an_rat @ A @ B ) @ ( set_or633870826150836451st_rat @ C @ D2 ) )
% 0.33/0.59 = ( ( ord_less_rat @ A @ B )
% 0.33/0.59 => ( ( ord_less_eq_rat @ C @ A )
% 0.33/0.59 & ( ord_less_eq_rat @ B @ D2 ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % atLeastLessThan_subseteq_atLeastAtMost_iff
% 0.33/0.59 thf(fact_4231_sum__shift__lb__Suc0__0__upt,axiom,
% 0.33/0.59 ! [F: nat > code_integer,K: nat] :
% 0.33/0.59 ( ( ( F @ zero_zero_nat )
% 0.33/0.59 = zero_z3403309356797280102nteger )
% 0.33/0.59 => ( ( groups7501900531339628137nteger @ F @ ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 0.33/0.59 = ( groups7501900531339628137nteger @ F @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum_shift_lb_Suc0_0_upt
% 0.33/0.59 thf(fact_4232_sum__shift__lb__Suc0__0__upt,axiom,
% 0.33/0.59 ! [F: nat > multis2468970476368604999at_nat,K: nat] :
% 0.33/0.59 ( ( ( F @ zero_zero_nat )
% 0.33/0.59 = zero_z1048942125864253310at_nat )
% 0.33/0.59 => ( ( groups6857163185585827899at_nat @ F @ ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 0.33/0.59 = ( groups6857163185585827899at_nat @ F @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum_shift_lb_Suc0_0_upt
% 0.33/0.59 thf(fact_4233_sum__shift__lb__Suc0__0__upt,axiom,
% 0.33/0.59 ! [F: nat > rat,K: nat] :
% 0.33/0.59 ( ( ( F @ zero_zero_nat )
% 0.33/0.59 = zero_zero_rat )
% 0.33/0.59 => ( ( groups2906978787729119204at_rat @ F @ ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 0.33/0.59 = ( groups2906978787729119204at_rat @ F @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum_shift_lb_Suc0_0_upt
% 0.33/0.59 thf(fact_4234_sum__shift__lb__Suc0__0__upt,axiom,
% 0.33/0.59 ! [F: nat > int,K: nat] :
% 0.33/0.59 ( ( ( F @ zero_zero_nat )
% 0.33/0.59 = zero_zero_int )
% 0.33/0.59 => ( ( groups3539618377306564664at_int @ F @ ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 0.33/0.59 = ( groups3539618377306564664at_int @ F @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum_shift_lb_Suc0_0_upt
% 0.33/0.59 thf(fact_4235_sum__shift__lb__Suc0__0__upt,axiom,
% 0.33/0.59 ! [F: nat > nat,K: nat] :
% 0.33/0.59 ( ( ( F @ zero_zero_nat )
% 0.33/0.59 = zero_zero_nat )
% 0.33/0.59 => ( ( groups3542108847815614940at_nat @ F @ ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 0.33/0.59 = ( groups3542108847815614940at_nat @ F @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum_shift_lb_Suc0_0_upt
% 0.33/0.59 thf(fact_4236_sum_OatLeast0__lessThan__Suc,axiom,
% 0.33/0.59 ! [G: nat > multis2468970476368604999at_nat,N2: nat] :
% 0.33/0.59 ( ( groups6857163185585827899at_nat @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 0.33/0.59 = ( plus_p7104986032573967614at_nat @ ( groups6857163185585827899at_nat @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum.atLeast0_lessThan_Suc
% 0.33/0.59 thf(fact_4237_sum_OatLeast0__lessThan__Suc,axiom,
% 0.33/0.59 ! [G: nat > rat,N2: nat] :
% 0.33/0.59 ( ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 0.33/0.59 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum.atLeast0_lessThan_Suc
% 0.33/0.59 thf(fact_4238_sum_OatLeast0__lessThan__Suc,axiom,
% 0.33/0.59 ! [G: nat > int,N2: nat] :
% 0.33/0.59 ( ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 0.33/0.59 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum.atLeast0_lessThan_Suc
% 0.33/0.59 thf(fact_4239_sum_OatLeast0__lessThan__Suc,axiom,
% 0.33/0.59 ! [G: nat > nat,N2: nat] :
% 0.33/0.59 ( ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 0.33/0.59 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum.atLeast0_lessThan_Suc
% 0.33/0.59 thf(fact_4240_sum_OatLeast__Suc__lessThan,axiom,
% 0.33/0.59 ! [M2: nat,N2: nat,G: nat > multis2468970476368604999at_nat] :
% 0.33/0.59 ( ( ord_less_nat @ M2 @ N2 )
% 0.33/0.59 => ( ( groups6857163185585827899at_nat @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) )
% 0.33/0.59 = ( plus_p7104986032573967614at_nat @ ( G @ M2 ) @ ( groups6857163185585827899at_nat @ G @ ( set_or4665077453230672383an_nat @ ( suc @ M2 ) @ N2 ) ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum.atLeast_Suc_lessThan
% 0.33/0.59 thf(fact_4241_sum_OatLeast__Suc__lessThan,axiom,
% 0.33/0.59 ! [M2: nat,N2: nat,G: nat > rat] :
% 0.33/0.59 ( ( ord_less_nat @ M2 @ N2 )
% 0.33/0.59 => ( ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) )
% 0.33/0.59 = ( plus_plus_rat @ ( G @ M2 ) @ ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ ( suc @ M2 ) @ N2 ) ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum.atLeast_Suc_lessThan
% 0.33/0.59 thf(fact_4242_sum_OatLeast__Suc__lessThan,axiom,
% 0.33/0.59 ! [M2: nat,N2: nat,G: nat > int] :
% 0.33/0.59 ( ( ord_less_nat @ M2 @ N2 )
% 0.33/0.59 => ( ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) )
% 0.33/0.59 = ( plus_plus_int @ ( G @ M2 ) @ ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ ( suc @ M2 ) @ N2 ) ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum.atLeast_Suc_lessThan
% 0.33/0.59 thf(fact_4243_sum_OatLeast__Suc__lessThan,axiom,
% 0.33/0.59 ! [M2: nat,N2: nat,G: nat > nat] :
% 0.33/0.59 ( ( ord_less_nat @ M2 @ N2 )
% 0.33/0.59 => ( ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) )
% 0.33/0.59 = ( plus_plus_nat @ ( G @ M2 ) @ ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ ( suc @ M2 ) @ N2 ) ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum.atLeast_Suc_lessThan
% 0.33/0.59 thf(fact_4244_sum_OatLeastLessThan__Suc,axiom,
% 0.33/0.59 ! [A: nat,B: nat,G: nat > multis2468970476368604999at_nat] :
% 0.33/0.59 ( ( ord_less_eq_nat @ A @ B )
% 0.33/0.59 => ( ( groups6857163185585827899at_nat @ G @ ( set_or4665077453230672383an_nat @ A @ ( suc @ B ) ) )
% 0.33/0.59 = ( plus_p7104986032573967614at_nat @ ( groups6857163185585827899at_nat @ G @ ( set_or4665077453230672383an_nat @ A @ B ) ) @ ( G @ B ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum.atLeastLessThan_Suc
% 0.33/0.59 thf(fact_4245_sum_OatLeastLessThan__Suc,axiom,
% 0.33/0.59 ! [A: nat,B: nat,G: nat > rat] :
% 0.33/0.59 ( ( ord_less_eq_nat @ A @ B )
% 0.33/0.59 => ( ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ A @ ( suc @ B ) ) )
% 0.33/0.59 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ A @ B ) ) @ ( G @ B ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum.atLeastLessThan_Suc
% 0.33/0.59 thf(fact_4246_sum_OatLeastLessThan__Suc,axiom,
% 0.33/0.59 ! [A: nat,B: nat,G: nat > int] :
% 0.33/0.59 ( ( ord_less_eq_nat @ A @ B )
% 0.33/0.59 => ( ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ A @ ( suc @ B ) ) )
% 0.33/0.59 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ A @ B ) ) @ ( G @ B ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum.atLeastLessThan_Suc
% 0.33/0.59 thf(fact_4247_sum_OatLeastLessThan__Suc,axiom,
% 0.33/0.59 ! [A: nat,B: nat,G: nat > nat] :
% 0.33/0.59 ( ( ord_less_eq_nat @ A @ B )
% 0.33/0.59 => ( ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ A @ ( suc @ B ) ) )
% 0.33/0.59 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ A @ B ) ) @ ( G @ B ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum.atLeastLessThan_Suc
% 0.33/0.59 thf(fact_4248_sum_Olast__plus,axiom,
% 0.33/0.59 ! [M2: nat,N2: nat,G: nat > multis2468970476368604999at_nat] :
% 0.33/0.59 ( ( ord_less_eq_nat @ M2 @ N2 )
% 0.33/0.59 => ( ( groups6857163185585827899at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 0.33/0.59 = ( plus_p7104986032573967614at_nat @ ( G @ N2 ) @ ( groups6857163185585827899at_nat @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum.last_plus
% 0.33/0.59 thf(fact_4249_sum_Olast__plus,axiom,
% 0.33/0.59 ! [M2: nat,N2: nat,G: nat > rat] :
% 0.33/0.59 ( ( ord_less_eq_nat @ M2 @ N2 )
% 0.33/0.59 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 0.33/0.59 = ( plus_plus_rat @ ( G @ N2 ) @ ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum.last_plus
% 0.33/0.59 thf(fact_4250_sum_Olast__plus,axiom,
% 0.33/0.59 ! [M2: nat,N2: nat,G: nat > int] :
% 0.33/0.59 ( ( ord_less_eq_nat @ M2 @ N2 )
% 0.33/0.59 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 0.33/0.59 = ( plus_plus_int @ ( G @ N2 ) @ ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum.last_plus
% 0.33/0.59 thf(fact_4251_sum_Olast__plus,axiom,
% 0.33/0.59 ! [M2: nat,N2: nat,G: nat > nat] :
% 0.33/0.59 ( ( ord_less_eq_nat @ M2 @ N2 )
% 0.33/0.59 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 0.33/0.59 = ( plus_plus_nat @ ( G @ N2 ) @ ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum.last_plus
% 0.33/0.59 thf(fact_4252_pochhammer__rec,axiom,
% 0.33/0.59 ! [A: code_integer,N2: nat] :
% 0.33/0.59 ( ( comm_s8582702949713902594nteger @ A @ ( suc @ N2 ) )
% 0.33/0.59 = ( times_3573771949741848930nteger @ A @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) @ N2 ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % pochhammer_rec
% 0.33/0.59 thf(fact_4253_pochhammer__rec,axiom,
% 0.33/0.59 ! [A: rat,N2: nat] :
% 0.33/0.59 ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N2 ) )
% 0.33/0.59 = ( times_times_rat @ A @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ N2 ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % pochhammer_rec
% 0.33/0.59 thf(fact_4254_pochhammer__rec,axiom,
% 0.33/0.59 ! [A: nat,N2: nat] :
% 0.33/0.59 ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N2 ) )
% 0.33/0.59 = ( times_times_nat @ A @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ N2 ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % pochhammer_rec
% 0.33/0.59 thf(fact_4255_pochhammer__rec,axiom,
% 0.33/0.59 ! [A: int,N2: nat] :
% 0.33/0.59 ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N2 ) )
% 0.33/0.59 = ( times_times_int @ A @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ A @ one_one_int ) @ N2 ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % pochhammer_rec
% 0.33/0.59 thf(fact_4256_pochhammer__Suc,axiom,
% 0.33/0.59 ! [A: rat,N2: nat] :
% 0.33/0.59 ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N2 ) )
% 0.33/0.59 = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ A @ N2 ) @ ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ N2 ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % pochhammer_Suc
% 0.33/0.59 thf(fact_4257_pochhammer__Suc,axiom,
% 0.33/0.59 ! [A: int,N2: nat] :
% 0.33/0.59 ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N2 ) )
% 0.33/0.59 = ( times_times_int @ ( comm_s4660882817536571857er_int @ A @ N2 ) @ ( plus_plus_int @ A @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % pochhammer_Suc
% 0.33/0.59 thf(fact_4258_pochhammer__Suc,axiom,
% 0.33/0.59 ! [A: nat,N2: nat] :
% 0.33/0.59 ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N2 ) )
% 0.33/0.59 = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ A @ N2 ) @ ( plus_plus_nat @ A @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % pochhammer_Suc
% 0.33/0.59 thf(fact_4259_pochhammer__Suc,axiom,
% 0.33/0.59 ! [A: code_integer,N2: nat] :
% 0.33/0.59 ( ( comm_s8582702949713902594nteger @ A @ ( suc @ N2 ) )
% 0.33/0.59 = ( times_3573771949741848930nteger @ ( comm_s8582702949713902594nteger @ A @ N2 ) @ ( plus_p5714425477246183910nteger @ A @ ( semiri4939895301339042750nteger @ N2 ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % pochhammer_Suc
% 0.33/0.59 thf(fact_4260_pochhammer__Suc,axiom,
% 0.33/0.59 ! [A: code_natural,N2: nat] :
% 0.33/0.59 ( ( comm_s7406298101470620109atural @ A @ ( suc @ N2 ) )
% 0.33/0.59 = ( times_2397367101498566445atural @ ( comm_s7406298101470620109atural @ A @ N2 ) @ ( plus_p4538020629002901425atural @ A @ ( semiri3763490453095760265atural @ N2 ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % pochhammer_Suc
% 0.33/0.59 thf(fact_4261_pochhammer__rec_H,axiom,
% 0.33/0.59 ! [Z: rat,N2: nat] :
% 0.33/0.59 ( ( comm_s4028243227959126397er_rat @ Z @ ( suc @ N2 ) )
% 0.33/0.59 = ( times_times_rat @ ( plus_plus_rat @ Z @ ( semiri681578069525770553at_rat @ N2 ) ) @ ( comm_s4028243227959126397er_rat @ Z @ N2 ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % pochhammer_rec'
% 0.33/0.59 thf(fact_4262_pochhammer__rec_H,axiom,
% 0.33/0.59 ! [Z: int,N2: nat] :
% 0.33/0.59 ( ( comm_s4660882817536571857er_int @ Z @ ( suc @ N2 ) )
% 0.33/0.59 = ( times_times_int @ ( plus_plus_int @ Z @ ( semiri1314217659103216013at_int @ N2 ) ) @ ( comm_s4660882817536571857er_int @ Z @ N2 ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % pochhammer_rec'
% 0.33/0.59 thf(fact_4263_pochhammer__rec_H,axiom,
% 0.33/0.59 ! [Z: nat,N2: nat] :
% 0.33/0.59 ( ( comm_s4663373288045622133er_nat @ Z @ ( suc @ N2 ) )
% 0.33/0.59 = ( times_times_nat @ ( plus_plus_nat @ Z @ ( semiri1316708129612266289at_nat @ N2 ) ) @ ( comm_s4663373288045622133er_nat @ Z @ N2 ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % pochhammer_rec'
% 0.33/0.59 thf(fact_4264_pochhammer__rec_H,axiom,
% 0.33/0.59 ! [Z: code_integer,N2: nat] :
% 0.33/0.59 ( ( comm_s8582702949713902594nteger @ Z @ ( suc @ N2 ) )
% 0.33/0.59 = ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ Z @ ( semiri4939895301339042750nteger @ N2 ) ) @ ( comm_s8582702949713902594nteger @ Z @ N2 ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % pochhammer_rec'
% 0.33/0.59 thf(fact_4265_pochhammer__rec_H,axiom,
% 0.33/0.59 ! [Z: code_natural,N2: nat] :
% 0.33/0.59 ( ( comm_s7406298101470620109atural @ Z @ ( suc @ N2 ) )
% 0.33/0.59 = ( times_2397367101498566445atural @ ( plus_p4538020629002901425atural @ Z @ ( semiri3763490453095760265atural @ N2 ) ) @ ( comm_s7406298101470620109atural @ Z @ N2 ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % pochhammer_rec'
% 0.33/0.59 thf(fact_4266_pochhammer__product_H,axiom,
% 0.33/0.59 ! [Z: rat,N2: nat,M2: nat] :
% 0.33/0.59 ( ( comm_s4028243227959126397er_rat @ Z @ ( plus_plus_nat @ N2 @ M2 ) )
% 0.33/0.59 = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z @ N2 ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( semiri681578069525770553at_rat @ N2 ) ) @ M2 ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % pochhammer_product'
% 0.33/0.59 thf(fact_4267_pochhammer__product_H,axiom,
% 0.33/0.59 ! [Z: int,N2: nat,M2: nat] :
% 0.33/0.59 ( ( comm_s4660882817536571857er_int @ Z @ ( plus_plus_nat @ N2 @ M2 ) )
% 0.33/0.59 = ( times_times_int @ ( comm_s4660882817536571857er_int @ Z @ N2 ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ Z @ ( semiri1314217659103216013at_int @ N2 ) ) @ M2 ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % pochhammer_product'
% 0.33/0.59 thf(fact_4268_pochhammer__product_H,axiom,
% 0.33/0.59 ! [Z: nat,N2: nat,M2: nat] :
% 0.33/0.59 ( ( comm_s4663373288045622133er_nat @ Z @ ( plus_plus_nat @ N2 @ M2 ) )
% 0.33/0.59 = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ Z @ N2 ) @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ Z @ ( semiri1316708129612266289at_nat @ N2 ) ) @ M2 ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % pochhammer_product'
% 0.33/0.59 thf(fact_4269_pochhammer__product_H,axiom,
% 0.33/0.59 ! [Z: code_integer,N2: nat,M2: nat] :
% 0.33/0.59 ( ( comm_s8582702949713902594nteger @ Z @ ( plus_plus_nat @ N2 @ M2 ) )
% 0.33/0.59 = ( times_3573771949741848930nteger @ ( comm_s8582702949713902594nteger @ Z @ N2 ) @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ Z @ ( semiri4939895301339042750nteger @ N2 ) ) @ M2 ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % pochhammer_product'
% 0.33/0.59 thf(fact_4270_pochhammer__product_H,axiom,
% 0.33/0.59 ! [Z: code_natural,N2: nat,M2: nat] :
% 0.33/0.59 ( ( comm_s7406298101470620109atural @ Z @ ( plus_plus_nat @ N2 @ M2 ) )
% 0.33/0.59 = ( times_2397367101498566445atural @ ( comm_s7406298101470620109atural @ Z @ N2 ) @ ( comm_s7406298101470620109atural @ ( plus_p4538020629002901425atural @ Z @ ( semiri3763490453095760265atural @ N2 ) ) @ M2 ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % pochhammer_product'
% 0.33/0.59 thf(fact_4271_bit__iff__and__push__bit__not__eq__0,axiom,
% 0.33/0.59 ( bit_se1148574629649215175it_nat
% 0.33/0.59 = ( ^ [A5: nat,N4: nat] :
% 0.33/0.59 ( ( bit_se727722235901077358nd_nat @ A5 @ ( bit_se547839408752420682it_nat @ N4 @ one_one_nat ) )
% 0.33/0.59 != zero_zero_nat ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % bit_iff_and_push_bit_not_eq_0
% 0.33/0.59 thf(fact_4272_bit__iff__and__push__bit__not__eq__0,axiom,
% 0.33/0.59 ( bit_se9216721137139052372nteger
% 0.33/0.59 = ( ^ [A5: code_integer,N4: nat] :
% 0.33/0.59 ( ( bit_se3949692690581998587nteger @ A5 @ ( bit_se7788150548672797655nteger @ N4 @ one_one_Code_integer ) )
% 0.33/0.59 != zero_z3403309356797280102nteger ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % bit_iff_and_push_bit_not_eq_0
% 0.33/0.59 thf(fact_4273_bit__iff__and__push__bit__not__eq__0,axiom,
% 0.33/0.59 ( bit_se1146084159140164899it_int
% 0.33/0.59 = ( ^ [A5: int,N4: nat] :
% 0.33/0.59 ( ( bit_se725231765392027082nd_int @ A5 @ ( bit_se545348938243370406it_int @ N4 @ one_one_int ) )
% 0.33/0.59 != zero_zero_int ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % bit_iff_and_push_bit_not_eq_0
% 0.33/0.59 thf(fact_4274_bit__iff__and__push__bit__not__eq__0,axiom,
% 0.33/0.59 ( bit_se8040316288895769887atural
% 0.33/0.59 = ( ^ [A5: code_natural,N4: nat] :
% 0.33/0.59 ( ( bit_se2773287842338716102atural @ A5 @ ( bit_se6611745700429515170atural @ N4 @ one_one_Code_natural ) )
% 0.33/0.59 != zero_z2226904508553997617atural ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % bit_iff_and_push_bit_not_eq_0
% 0.33/0.59 thf(fact_4275_sum__Suc__diff_H,axiom,
% 0.33/0.59 ! [M2: nat,N2: nat,F: nat > code_integer] :
% 0.33/0.59 ( ( ord_less_eq_nat @ M2 @ N2 )
% 0.33/0.59 => ( ( groups7501900531339628137nteger
% 0.33/0.59 @ ^ [I3: nat] : ( minus_8373710615458151222nteger @ ( F @ ( suc @ I3 ) ) @ ( F @ I3 ) )
% 0.33/0.59 @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) )
% 0.33/0.59 = ( minus_8373710615458151222nteger @ ( F @ N2 ) @ ( F @ M2 ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum_Suc_diff'
% 0.33/0.59 thf(fact_4276_sum__Suc__diff_H,axiom,
% 0.33/0.59 ! [M2: nat,N2: nat,F: nat > rat] :
% 0.33/0.59 ( ( ord_less_eq_nat @ M2 @ N2 )
% 0.33/0.59 => ( ( groups2906978787729119204at_rat
% 0.33/0.59 @ ^ [I3: nat] : ( minus_minus_rat @ ( F @ ( suc @ I3 ) ) @ ( F @ I3 ) )
% 0.33/0.59 @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) )
% 0.33/0.59 = ( minus_minus_rat @ ( F @ N2 ) @ ( F @ M2 ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum_Suc_diff'
% 0.33/0.59 thf(fact_4277_sum__Suc__diff_H,axiom,
% 0.33/0.59 ! [M2: nat,N2: nat,F: nat > int] :
% 0.33/0.59 ( ( ord_less_eq_nat @ M2 @ N2 )
% 0.33/0.59 => ( ( groups3539618377306564664at_int
% 0.33/0.59 @ ^ [I3: nat] : ( minus_minus_int @ ( F @ ( suc @ I3 ) ) @ ( F @ I3 ) )
% 0.33/0.59 @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) )
% 0.33/0.59 = ( minus_minus_int @ ( F @ N2 ) @ ( F @ M2 ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum_Suc_diff'
% 0.33/0.59 thf(fact_4278_sum_OatLeastLessThan__rev,axiom,
% 0.33/0.59 ! [G: nat > nat,N2: nat,M2: nat] :
% 0.33/0.59 ( ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ N2 @ M2 ) )
% 0.33/0.59 = ( groups3542108847815614940at_nat
% 0.33/0.59 @ ^ [I3: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M2 @ N2 ) @ ( suc @ I3 ) ) )
% 0.33/0.59 @ ( set_or4665077453230672383an_nat @ N2 @ M2 ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum.atLeastLessThan_rev
% 0.33/0.59 thf(fact_4279_sum_Onested__swap,axiom,
% 0.33/0.59 ! [A: nat > nat > nat,N2: nat] :
% 0.33/0.59 ( ( groups3542108847815614940at_nat
% 0.33/0.59 @ ^ [I3: nat] : ( groups3542108847815614940at_nat @ ( A @ I3 ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ I3 ) )
% 0.33/0.59 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 0.33/0.59 = ( groups3542108847815614940at_nat
% 0.33/0.59 @ ^ [J2: nat] :
% 0.33/0.59 ( groups3542108847815614940at_nat
% 0.33/0.59 @ ^ [I3: nat] : ( A @ I3 @ J2 )
% 0.33/0.59 @ ( set_or1269000886237332187st_nat @ ( suc @ J2 ) @ N2 ) )
% 0.33/0.59 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum.nested_swap
% 0.33/0.59 thf(fact_4280_sum_Onat__group,axiom,
% 0.33/0.59 ! [G: nat > nat,K: nat,N2: nat] :
% 0.33/0.59 ( ( groups3542108847815614940at_nat
% 0.33/0.59 @ ^ [M: nat] : ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ ( times_times_nat @ M @ K ) @ ( plus_plus_nat @ ( times_times_nat @ M @ K ) @ K ) ) )
% 0.33/0.59 @ ( set_ord_lessThan_nat @ N2 ) )
% 0.33/0.59 = ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ ( times_times_nat @ N2 @ K ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum.nat_group
% 0.33/0.59 thf(fact_4281_numeral__xor__num,axiom,
% 0.33/0.59 ! [M2: num,N2: num] :
% 0.33/0.59 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ N2 ) )
% 0.33/0.59 = ( case_option_nat_num @ zero_zero_nat @ numeral_numeral_nat @ ( bit_un2480387367778600638or_num @ M2 @ N2 ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % numeral_xor_num
% 0.33/0.59 thf(fact_4282_numeral__xor__num,axiom,
% 0.33/0.59 ! [M2: num,N2: num] :
% 0.33/0.59 ( ( bit_se3222712562003087583nteger @ ( numera6620942414471956472nteger @ M2 ) @ ( numera6620942414471956472nteger @ N2 ) )
% 0.33/0.59 = ( case_o356765784539232260er_num @ zero_z3403309356797280102nteger @ numera6620942414471956472nteger @ ( bit_un2480387367778600638or_num @ M2 @ N2 ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % numeral_xor_num
% 0.33/0.59 thf(fact_4283_numeral__xor__num,axiom,
% 0.33/0.59 ! [M2: num,N2: num] :
% 0.33/0.59 ( ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N2 ) )
% 0.33/0.59 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_un2480387367778600638or_num @ M2 @ N2 ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % numeral_xor_num
% 0.33/0.59 thf(fact_4284_numeral__xor__num,axiom,
% 0.33/0.59 ! [M2: num,N2: num] :
% 0.33/0.59 ( ( bit_se2046307713759805098atural @ ( numera5444537566228673987atural @ M2 ) @ ( numera5444537566228673987atural @ N2 ) )
% 0.33/0.59 = ( case_o5621594795226839503al_num @ zero_z2226904508553997617atural @ numera5444537566228673987atural @ ( bit_un2480387367778600638or_num @ M2 @ N2 ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % numeral_xor_num
% 0.33/0.59 thf(fact_4285_sum_Ohead__if,axiom,
% 0.33/0.59 ! [N2: nat,M2: nat,G: nat > code_integer] :
% 0.33/0.59 ( ( ( ord_less_nat @ N2 @ M2 )
% 0.33/0.59 => ( ( groups7501900531339628137nteger @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 0.33/0.59 = zero_z3403309356797280102nteger ) )
% 0.33/0.59 & ( ~ ( ord_less_nat @ N2 @ M2 )
% 0.33/0.59 => ( ( groups7501900531339628137nteger @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 0.33/0.59 = ( plus_p5714425477246183910nteger @ ( groups7501900531339628137nteger @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) @ ( G @ N2 ) ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum.head_if
% 0.33/0.59 thf(fact_4286_sum_Ohead__if,axiom,
% 0.33/0.59 ! [N2: nat,M2: nat,G: nat > multis2468970476368604999at_nat] :
% 0.33/0.59 ( ( ( ord_less_nat @ N2 @ M2 )
% 0.33/0.59 => ( ( groups6857163185585827899at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 0.33/0.59 = zero_z1048942125864253310at_nat ) )
% 0.33/0.59 & ( ~ ( ord_less_nat @ N2 @ M2 )
% 0.33/0.59 => ( ( groups6857163185585827899at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 0.33/0.59 = ( plus_p7104986032573967614at_nat @ ( groups6857163185585827899at_nat @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) @ ( G @ N2 ) ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum.head_if
% 0.33/0.59 thf(fact_4287_sum_Ohead__if,axiom,
% 0.33/0.59 ! [N2: nat,M2: nat,G: nat > rat] :
% 0.33/0.59 ( ( ( ord_less_nat @ N2 @ M2 )
% 0.33/0.59 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 0.33/0.59 = zero_zero_rat ) )
% 0.33/0.59 & ( ~ ( ord_less_nat @ N2 @ M2 )
% 0.33/0.59 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 0.33/0.59 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) @ ( G @ N2 ) ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum.head_if
% 0.33/0.59 thf(fact_4288_sum_Ohead__if,axiom,
% 0.33/0.59 ! [N2: nat,M2: nat,G: nat > int] :
% 0.33/0.59 ( ( ( ord_less_nat @ N2 @ M2 )
% 0.33/0.59 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 0.33/0.59 = zero_zero_int ) )
% 0.33/0.59 & ( ~ ( ord_less_nat @ N2 @ M2 )
% 0.33/0.59 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 0.33/0.59 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) @ ( G @ N2 ) ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum.head_if
% 0.33/0.59 thf(fact_4289_sum_Ohead__if,axiom,
% 0.33/0.59 ! [N2: nat,M2: nat,G: nat > nat] :
% 0.33/0.59 ( ( ( ord_less_nat @ N2 @ M2 )
% 0.33/0.59 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 0.33/0.59 = zero_zero_nat ) )
% 0.33/0.59 & ( ~ ( ord_less_nat @ N2 @ M2 )
% 0.33/0.59 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 0.33/0.59 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) @ ( G @ N2 ) ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum.head_if
% 0.33/0.59 thf(fact_4290_sum_OatLeast0__lessThan__Suc__shift,axiom,
% 0.33/0.59 ! [G: nat > multis2468970476368604999at_nat,N2: nat] :
% 0.33/0.59 ( ( groups6857163185585827899at_nat @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 0.33/0.59 = ( plus_p7104986032573967614at_nat @ ( G @ zero_zero_nat ) @ ( groups6857163185585827899at_nat @ ( comp_n8698576032424989604at_nat @ G @ suc ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum.atLeast0_lessThan_Suc_shift
% 0.33/0.59 thf(fact_4291_sum_OatLeast0__lessThan__Suc__shift,axiom,
% 0.33/0.59 ! [G: nat > rat,N2: nat] :
% 0.33/0.59 ( ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 0.33/0.59 = ( plus_plus_rat @ ( G @ zero_zero_nat ) @ ( groups2906978787729119204at_rat @ ( comp_nat_rat_nat @ G @ suc ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ) ).
% 0.33/0.59
% 0.33/0.59 % sum.atLeast0_lessThan_Suc_shift
% 0.33/0.59 thf(fact_4292_sum_OatLeast0__lessThan__Suc__shift,axiom,
% 0.33/0.59 ! [G: nat > int,N2: nat] :
% 0.33/0.59 ( ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 0.33/0.59 = ( plus_plus_int @ ( G @ zero_zero_nat ) @ ( groups3539618377306564664at_int @ ( comp_nat_int_nat @ G @ suc ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % sum.atLeast0_lessThan_Suc_shift
% 0.33/0.60 thf(fact_4293_sum_OatLeast0__lessThan__Suc__shift,axiom,
% 0.33/0.60 ! [G: nat > nat,N2: nat] :
% 0.33/0.60 ( ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 0.33/0.60 = ( plus_plus_nat @ ( G @ zero_zero_nat ) @ ( groups3542108847815614940at_nat @ ( comp_nat_nat_nat @ G @ suc ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % sum.atLeast0_lessThan_Suc_shift
% 0.33/0.60 thf(fact_4294_sum_OatLeastLessThan__shift__0,axiom,
% 0.33/0.60 ! [G: nat > nat,M2: nat,N2: nat] :
% 0.33/0.60 ( ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) )
% 0.33/0.60 = ( groups3542108847815614940at_nat @ ( comp_nat_nat_nat @ G @ ( plus_plus_nat @ M2 ) ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( minus_minus_nat @ N2 @ M2 ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % sum.atLeastLessThan_shift_0
% 0.33/0.60 thf(fact_4295_pochhammer__product,axiom,
% 0.33/0.60 ! [M2: nat,N2: nat,Z: rat] :
% 0.33/0.60 ( ( ord_less_eq_nat @ M2 @ N2 )
% 0.33/0.60 => ( ( comm_s4028243227959126397er_rat @ Z @ N2 )
% 0.33/0.60 = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z @ M2 ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( semiri681578069525770553at_rat @ M2 ) ) @ ( minus_minus_nat @ N2 @ M2 ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % pochhammer_product
% 0.33/0.60 thf(fact_4296_pochhammer__product,axiom,
% 0.33/0.60 ! [M2: nat,N2: nat,Z: int] :
% 0.33/0.60 ( ( ord_less_eq_nat @ M2 @ N2 )
% 0.33/0.60 => ( ( comm_s4660882817536571857er_int @ Z @ N2 )
% 0.33/0.60 = ( times_times_int @ ( comm_s4660882817536571857er_int @ Z @ M2 ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ Z @ ( semiri1314217659103216013at_int @ M2 ) ) @ ( minus_minus_nat @ N2 @ M2 ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % pochhammer_product
% 0.33/0.60 thf(fact_4297_pochhammer__product,axiom,
% 0.33/0.60 ! [M2: nat,N2: nat,Z: nat] :
% 0.33/0.60 ( ( ord_less_eq_nat @ M2 @ N2 )
% 0.33/0.60 => ( ( comm_s4663373288045622133er_nat @ Z @ N2 )
% 0.33/0.60 = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ Z @ M2 ) @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ Z @ ( semiri1316708129612266289at_nat @ M2 ) ) @ ( minus_minus_nat @ N2 @ M2 ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % pochhammer_product
% 0.33/0.60 thf(fact_4298_pochhammer__product,axiom,
% 0.33/0.60 ! [M2: nat,N2: nat,Z: code_integer] :
% 0.33/0.60 ( ( ord_less_eq_nat @ M2 @ N2 )
% 0.33/0.60 => ( ( comm_s8582702949713902594nteger @ Z @ N2 )
% 0.33/0.60 = ( times_3573771949741848930nteger @ ( comm_s8582702949713902594nteger @ Z @ M2 ) @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ Z @ ( semiri4939895301339042750nteger @ M2 ) ) @ ( minus_minus_nat @ N2 @ M2 ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % pochhammer_product
% 0.33/0.60 thf(fact_4299_pochhammer__product,axiom,
% 0.33/0.60 ! [M2: nat,N2: nat,Z: code_natural] :
% 0.33/0.60 ( ( ord_less_eq_nat @ M2 @ N2 )
% 0.33/0.60 => ( ( comm_s7406298101470620109atural @ Z @ N2 )
% 0.33/0.60 = ( times_2397367101498566445atural @ ( comm_s7406298101470620109atural @ Z @ M2 ) @ ( comm_s7406298101470620109atural @ ( plus_p4538020629002901425atural @ Z @ ( semiri3763490453095760265atural @ M2 ) ) @ ( minus_minus_nat @ N2 @ M2 ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % pochhammer_product
% 0.33/0.60 thf(fact_4300_sum_OatLeastLessThan__rev__at__least__Suc__atMost,axiom,
% 0.33/0.60 ! [G: nat > nat,N2: nat,M2: nat] :
% 0.33/0.60 ( ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ N2 @ M2 ) )
% 0.33/0.60 = ( groups3542108847815614940at_nat
% 0.33/0.60 @ ^ [I3: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M2 @ N2 ) @ I3 ) )
% 0.33/0.60 @ ( set_or1269000886237332187st_nat @ ( suc @ N2 ) @ M2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % sum.atLeastLessThan_rev_at_least_Suc_atMost
% 0.33/0.60 thf(fact_4301_sum_OatLeast__lessThan__pred__shift,axiom,
% 0.33/0.60 ! [G: nat > nat,M2: nat,N2: nat] :
% 0.33/0.60 ( ( groups3542108847815614940at_nat
% 0.33/0.60 @ ( comp_nat_nat_nat @ G
% 0.33/0.60 @ ^ [N4: nat] : ( minus_minus_nat @ N4 @ ( suc @ zero_zero_nat ) ) )
% 0.33/0.60 @ ( set_or4665077453230672383an_nat @ ( suc @ M2 ) @ ( suc @ N2 ) ) )
% 0.33/0.60 = ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % sum.atLeast_lessThan_pred_shift
% 0.33/0.60 thf(fact_4302_pochhammer__absorb__comp,axiom,
% 0.33/0.60 ! [R2: rat,K: nat] :
% 0.33/0.60 ( ( times_times_rat @ ( minus_minus_rat @ R2 @ ( semiri681578069525770553at_rat @ K ) ) @ ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ R2 ) @ K ) )
% 0.33/0.60 = ( times_times_rat @ R2 @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ R2 ) @ one_one_rat ) @ K ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % pochhammer_absorb_comp
% 0.33/0.60 thf(fact_4303_pochhammer__absorb__comp,axiom,
% 0.33/0.60 ! [R2: int,K: nat] :
% 0.33/0.60 ( ( times_times_int @ ( minus_minus_int @ R2 @ ( semiri1314217659103216013at_int @ K ) ) @ ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ R2 ) @ K ) )
% 0.33/0.60 = ( times_times_int @ R2 @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( uminus_uminus_int @ R2 ) @ one_one_int ) @ K ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % pochhammer_absorb_comp
% 0.33/0.60 thf(fact_4304_pochhammer__absorb__comp,axiom,
% 0.33/0.60 ! [R2: code_integer,K: nat] :
% 0.33/0.60 ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ R2 @ ( semiri4939895301339042750nteger @ K ) ) @ ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ R2 ) @ K ) )
% 0.33/0.60 = ( times_3573771949741848930nteger @ R2 @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ R2 ) @ one_one_Code_integer ) @ K ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % pochhammer_absorb_comp
% 0.33/0.60 thf(fact_4305_pochhammer__same,axiom,
% 0.33/0.60 ! [N2: nat] :
% 0.33/0.60 ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N2 ) ) @ N2 )
% 0.33/0.60 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 ) @ ( semiri773545260158071498ct_rat @ N2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % pochhammer_same
% 0.33/0.60 thf(fact_4306_pochhammer__same,axiom,
% 0.33/0.60 ! [N2: nat] :
% 0.33/0.60 ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) @ N2 )
% 0.33/0.60 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 ) @ ( semiri1406184849735516958ct_int @ N2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % pochhammer_same
% 0.33/0.60 thf(fact_4307_pochhammer__same,axiom,
% 0.33/0.60 ! [N2: nat] :
% 0.33/0.60 ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N2 ) ) @ N2 )
% 0.33/0.60 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 ) @ ( semiri3624122377584611663nteger @ N2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % pochhammer_same
% 0.33/0.60 thf(fact_4308_pochhammer__minus,axiom,
% 0.33/0.60 ! [B: rat,K: nat] :
% 0.33/0.60 ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ B ) @ K )
% 0.33/0.60 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( minus_minus_rat @ B @ ( semiri681578069525770553at_rat @ K ) ) @ one_one_rat ) @ K ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % pochhammer_minus
% 0.33/0.60 thf(fact_4309_pochhammer__minus,axiom,
% 0.33/0.60 ! [B: int,K: nat] :
% 0.33/0.60 ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ B ) @ K )
% 0.33/0.60 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ K ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( minus_minus_int @ B @ ( semiri1314217659103216013at_int @ K ) ) @ one_one_int ) @ K ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % pochhammer_minus
% 0.33/0.60 thf(fact_4310_pochhammer__minus,axiom,
% 0.33/0.60 ! [B: code_integer,K: nat] :
% 0.33/0.60 ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ B ) @ K )
% 0.33/0.60 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ K ) @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ B @ ( semiri4939895301339042750nteger @ K ) ) @ one_one_Code_integer ) @ K ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % pochhammer_minus
% 0.33/0.60 thf(fact_4311_pochhammer__minus_H,axiom,
% 0.33/0.60 ! [B: rat,K: nat] :
% 0.33/0.60 ( ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( minus_minus_rat @ B @ ( semiri681578069525770553at_rat @ K ) ) @ one_one_rat ) @ K )
% 0.33/0.60 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K ) @ ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ B ) @ K ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % pochhammer_minus'
% 0.33/0.60 thf(fact_4312_pochhammer__minus_H,axiom,
% 0.33/0.60 ! [B: int,K: nat] :
% 0.33/0.60 ( ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( minus_minus_int @ B @ ( semiri1314217659103216013at_int @ K ) ) @ one_one_int ) @ K )
% 0.33/0.60 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ K ) @ ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ B ) @ K ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % pochhammer_minus'
% 0.33/0.60 thf(fact_4313_pochhammer__minus_H,axiom,
% 0.33/0.60 ! [B: code_integer,K: nat] :
% 0.33/0.60 ( ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ B @ ( semiri4939895301339042750nteger @ K ) ) @ one_one_Code_integer ) @ K )
% 0.33/0.60 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ K ) @ ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ B ) @ K ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % pochhammer_minus'
% 0.33/0.60 thf(fact_4314_gbinomial__pochhammer_H,axiom,
% 0.33/0.60 ( gbinomial_rat
% 0.33/0.60 = ( ^ [A5: rat,K4: nat] : ( divide_divide_rat @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( minus_minus_rat @ A5 @ ( semiri681578069525770553at_rat @ K4 ) ) @ one_one_rat ) @ K4 ) @ ( semiri773545260158071498ct_rat @ K4 ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % gbinomial_pochhammer'
% 0.33/0.60 thf(fact_4315_gbinomial__pochhammer,axiom,
% 0.33/0.60 ( gbinomial_rat
% 0.33/0.60 = ( ^ [A5: rat,K4: nat] : ( divide_divide_rat @ ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K4 ) @ ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ A5 ) @ K4 ) ) @ ( semiri773545260158071498ct_rat @ K4 ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % gbinomial_pochhammer
% 0.33/0.60 thf(fact_4316_xor__nat__unfold,axiom,
% 0.33/0.60 ( bit_se6528837805403552850or_nat
% 0.33/0.60 = ( ^ [M: nat,N4: nat] : ( if_nat @ ( M = zero_zero_nat ) @ N4 @ ( if_nat @ ( N4 = zero_zero_nat ) @ M @ ( plus_plus_nat @ ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( divide_divide_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % xor_nat_unfold
% 0.33/0.60 thf(fact_4317_num__of__integer_Oabs__eq,axiom,
% 0.33/0.60 ! [X: int] :
% 0.33/0.60 ( ( code_num_of_integer @ ( code_integer_of_int @ X ) )
% 0.33/0.60 = ( num_of_nat @ ( nat2 @ X ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % num_of_integer.abs_eq
% 0.33/0.60 thf(fact_4318_signed__take__bit__code,axiom,
% 0.33/0.60 ( bit_ri6519982836138164636nteger
% 0.33/0.60 = ( ^ [N4: nat,A5: code_integer] : ( if_Code_integer @ ( bit_se9216721137139052372nteger @ ( bit_se1745604003318907178nteger @ ( suc @ N4 ) @ A5 ) @ N4 ) @ ( plus_p5714425477246183910nteger @ ( bit_se1745604003318907178nteger @ ( suc @ N4 ) @ A5 ) @ ( bit_se7788150548672797655nteger @ ( suc @ N4 ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) @ ( bit_se1745604003318907178nteger @ ( suc @ N4 ) @ A5 ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % signed_take_bit_code
% 0.33/0.60 thf(fact_4319_signed__take__bit__code,axiom,
% 0.33/0.60 ( bit_ri631733984087533419it_int
% 0.33/0.60 = ( ^ [N4: nat,A5: int] : ( if_int @ ( bit_se1146084159140164899it_int @ ( bit_se2923211474154528505it_int @ ( suc @ N4 ) @ A5 ) @ N4 ) @ ( plus_plus_int @ ( bit_se2923211474154528505it_int @ ( suc @ N4 ) @ A5 ) @ ( bit_se545348938243370406it_int @ ( suc @ N4 ) @ ( uminus_uminus_int @ one_one_int ) ) ) @ ( bit_se2923211474154528505it_int @ ( suc @ N4 ) @ A5 ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % signed_take_bit_code
% 0.33/0.60 thf(fact_4320_xor__nat__rec,axiom,
% 0.33/0.60 ( bit_se6528837805403552850or_nat
% 0.33/0.60 = ( ^ [M: nat,N4: nat] :
% 0.33/0.60 ( plus_plus_nat
% 0.33/0.60 @ ( zero_n2687167440665602831ol_nat
% 0.33/0.60 @ ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 0.33/0.60 != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) ) )
% 0.33/0.60 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( divide_divide_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % xor_nat_rec
% 0.33/0.60 thf(fact_4321_xor__one__eq,axiom,
% 0.33/0.60 ! [A: nat] :
% 0.33/0.60 ( ( bit_se6528837805403552850or_nat @ A @ one_one_nat )
% 0.33/0.60 = ( minus_minus_nat @ ( plus_plus_nat @ A @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) )
% 0.33/0.60 @ ( zero_n2687167440665602831ol_nat
% 0.33/0.60 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % xor_one_eq
% 0.33/0.60 thf(fact_4322_xor__one__eq,axiom,
% 0.33/0.60 ! [A: code_integer] :
% 0.33/0.60 ( ( bit_se3222712562003087583nteger @ A @ one_one_Code_integer )
% 0.33/0.60 = ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A @ ( zero_n356916108424825756nteger @ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) )
% 0.33/0.60 @ ( zero_n356916108424825756nteger
% 0.33/0.60 @ ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % xor_one_eq
% 0.33/0.60 thf(fact_4323_xor__one__eq,axiom,
% 0.33/0.60 ! [A: int] :
% 0.33/0.60 ( ( bit_se6526347334894502574or_int @ A @ one_one_int )
% 0.33/0.60 = ( minus_minus_int @ ( plus_plus_int @ A @ ( zero_n2684676970156552555ol_int @ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) )
% 0.33/0.60 @ ( zero_n2684676970156552555ol_int
% 0.33/0.60 @ ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % xor_one_eq
% 0.33/0.60 thf(fact_4324_xor__one__eq,axiom,
% 0.33/0.60 ! [A: code_natural] :
% 0.33/0.60 ( ( bit_se2046307713759805098atural @ A @ one_one_Code_natural )
% 0.33/0.60 = ( minus_7197305767214868737atural @ ( plus_p4538020629002901425atural @ A @ ( zero_n8403883297036319079atural @ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A ) ) )
% 0.33/0.60 @ ( zero_n8403883297036319079atural
% 0.33/0.60 @ ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % xor_one_eq
% 0.33/0.60 thf(fact_4325_one__xor__eq,axiom,
% 0.33/0.60 ! [A: nat] :
% 0.33/0.60 ( ( bit_se6528837805403552850or_nat @ one_one_nat @ A )
% 0.33/0.60 = ( minus_minus_nat @ ( plus_plus_nat @ A @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) )
% 0.33/0.60 @ ( zero_n2687167440665602831ol_nat
% 0.33/0.60 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % one_xor_eq
% 0.33/0.60 thf(fact_4326_one__xor__eq,axiom,
% 0.33/0.60 ! [A: code_integer] :
% 0.33/0.60 ( ( bit_se3222712562003087583nteger @ one_one_Code_integer @ A )
% 0.33/0.60 = ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A @ ( zero_n356916108424825756nteger @ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) )
% 0.33/0.60 @ ( zero_n356916108424825756nteger
% 0.33/0.60 @ ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % one_xor_eq
% 0.33/0.60 thf(fact_4327_one__xor__eq,axiom,
% 0.33/0.60 ! [A: int] :
% 0.33/0.60 ( ( bit_se6526347334894502574or_int @ one_one_int @ A )
% 0.33/0.60 = ( minus_minus_int @ ( plus_plus_int @ A @ ( zero_n2684676970156552555ol_int @ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) )
% 0.33/0.60 @ ( zero_n2684676970156552555ol_int
% 0.33/0.60 @ ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % one_xor_eq
% 0.33/0.60 thf(fact_4328_one__xor__eq,axiom,
% 0.33/0.60 ! [A: code_natural] :
% 0.33/0.60 ( ( bit_se2046307713759805098atural @ one_one_Code_natural @ A )
% 0.33/0.60 = ( minus_7197305767214868737atural @ ( plus_p4538020629002901425atural @ A @ ( zero_n8403883297036319079atural @ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A ) ) )
% 0.33/0.60 @ ( zero_n8403883297036319079atural
% 0.33/0.60 @ ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % one_xor_eq
% 0.33/0.60 thf(fact_4329_pochhammer__binomial__sum,axiom,
% 0.33/0.60 ! [A: rat,B: rat,N2: nat] :
% 0.33/0.60 ( ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ A @ B ) @ N2 )
% 0.33/0.60 = ( groups2906978787729119204at_rat
% 0.33/0.60 @ ^ [K4: nat] : ( times_times_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( binomial @ N2 @ K4 ) ) @ ( comm_s4028243227959126397er_rat @ A @ K4 ) ) @ ( comm_s4028243227959126397er_rat @ B @ ( minus_minus_nat @ N2 @ K4 ) ) )
% 0.33/0.60 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % pochhammer_binomial_sum
% 0.33/0.60 thf(fact_4330_pochhammer__binomial__sum,axiom,
% 0.33/0.60 ! [A: int,B: int,N2: nat] :
% 0.33/0.60 ( ( comm_s4660882817536571857er_int @ ( plus_plus_int @ A @ B ) @ N2 )
% 0.33/0.60 = ( groups3539618377306564664at_int
% 0.33/0.60 @ ^ [K4: nat] : ( times_times_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ ( binomial @ N2 @ K4 ) ) @ ( comm_s4660882817536571857er_int @ A @ K4 ) ) @ ( comm_s4660882817536571857er_int @ B @ ( minus_minus_nat @ N2 @ K4 ) ) )
% 0.33/0.60 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % pochhammer_binomial_sum
% 0.33/0.60 thf(fact_4331_pochhammer__binomial__sum,axiom,
% 0.33/0.60 ! [A: code_integer,B: code_integer,N2: nat] :
% 0.33/0.60 ( ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ N2 )
% 0.33/0.60 = ( groups7501900531339628137nteger
% 0.33/0.60 @ ^ [K4: nat] : ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ ( binomial @ N2 @ K4 ) ) @ ( comm_s8582702949713902594nteger @ A @ K4 ) ) @ ( comm_s8582702949713902594nteger @ B @ ( minus_minus_nat @ N2 @ K4 ) ) )
% 0.33/0.60 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % pochhammer_binomial_sum
% 0.33/0.60 thf(fact_4332_divmod__integer__def,axiom,
% 0.33/0.60 ( code_divmod_integer
% 0.33/0.60 = ( ^ [K4: code_integer,L3: code_integer] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ K4 @ L3 ) @ ( modulo364778990260209775nteger @ K4 @ L3 ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % divmod_integer_def
% 0.33/0.60 thf(fact_4333_sum__power2,axiom,
% 0.33/0.60 ! [K: nat] :
% 0.33/0.60 ( ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K ) )
% 0.33/0.60 = ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K ) @ one_one_nat ) ) ).
% 0.33/0.60
% 0.33/0.60 % sum_power2
% 0.33/0.60 thf(fact_4334_nat__of__integer__code,axiom,
% 0.33/0.60 ( code_nat_of_integer
% 0.33/0.60 = ( ^ [K4: code_integer] :
% 0.33/0.60 ( if_nat @ ( ord_le3102999989581377725nteger @ K4 @ zero_z3403309356797280102nteger ) @ zero_zero_nat
% 0.33/0.60 @ ( produc1555791787009142072er_nat
% 0.33/0.60 @ ^ [L3: code_integer,J2: code_integer] : ( if_nat @ ( J2 = zero_z3403309356797280102nteger ) @ ( plus_plus_nat @ ( code_nat_of_integer @ L3 ) @ ( code_nat_of_integer @ L3 ) ) @ ( plus_plus_nat @ ( plus_plus_nat @ ( code_nat_of_integer @ L3 ) @ ( code_nat_of_integer @ L3 ) ) @ one_one_nat ) )
% 0.33/0.60 @ ( code_divmod_integer @ K4 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % nat_of_integer_code
% 0.33/0.60 thf(fact_4335_pochhammer__times__pochhammer__half,axiom,
% 0.33/0.60 ! [Z: rat,N2: nat] :
% 0.33/0.60 ( ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z @ ( suc @ N2 ) ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( suc @ N2 ) ) )
% 0.33/0.60 = ( groups73079841787564623at_rat
% 0.33/0.60 @ ^ [K4: nat] : ( plus_plus_rat @ Z @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ K4 ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 0.33/0.60 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % pochhammer_times_pochhammer_half
% 0.33/0.60 thf(fact_4336_int__of__integer__code,axiom,
% 0.33/0.60 ( code_int_of_integer
% 0.33/0.60 = ( ^ [K4: code_integer] :
% 0.33/0.60 ( if_int @ ( ord_le6747313008572928689nteger @ K4 @ zero_z3403309356797280102nteger ) @ ( uminus_uminus_int @ ( code_int_of_integer @ ( uminus1351360451143612070nteger @ K4 ) ) )
% 0.33/0.60 @ ( if_int @ ( K4 = zero_z3403309356797280102nteger ) @ zero_zero_int
% 0.33/0.60 @ ( produc1553301316500091796er_int
% 0.33/0.60 @ ^ [L3: code_integer,J2: code_integer] : ( if_int @ ( J2 = zero_z3403309356797280102nteger ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( code_int_of_integer @ L3 ) ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( code_int_of_integer @ L3 ) ) @ one_one_int ) )
% 0.33/0.60 @ ( code_divmod_integer @ K4 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % int_of_integer_code
% 0.33/0.60 thf(fact_4337_divmod__integer__eq__cases,axiom,
% 0.33/0.60 ( code_divmod_integer
% 0.33/0.60 = ( ^ [K4: code_integer,L3: code_integer] :
% 0.33/0.60 ( if_Pro6119634080678213985nteger @ ( K4 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 0.33/0.60 @ ( if_Pro6119634080678213985nteger @ ( L3 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ K4 )
% 0.33/0.60 @ ( comp_C1593894019821074884nteger @ ( comp_C8797469213163452608nteger @ produc6499014454317279255nteger @ times_3573771949741848930nteger ) @ sgn_sgn_Code_integer @ L3
% 0.33/0.60 @ ( if_Pro6119634080678213985nteger
% 0.33/0.60 @ ( ( sgn_sgn_Code_integer @ K4 )
% 0.33/0.60 = ( sgn_sgn_Code_integer @ L3 ) )
% 0.33/0.60 @ ( code_divmod_abs @ K4 @ L3 )
% 0.33/0.60 @ ( produc6916734918728496179nteger
% 0.33/0.60 @ ^ [R3: code_integer,S4: code_integer] : ( if_Pro6119634080678213985nteger @ ( S4 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R3 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R3 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ ( abs_abs_Code_integer @ L3 ) @ S4 ) ) )
% 0.33/0.60 @ ( code_divmod_abs @ K4 @ L3 ) ) ) ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % divmod_integer_eq_cases
% 0.33/0.60 thf(fact_4338_time__def,axiom,
% 0.33/0.60 ( time_time_array_a
% 0.33/0.60 = ( ^ [C2: heap_T6362127782908069795rray_a,H: heap_e7401611519738050253t_unit] :
% 0.33/0.60 ( case_o1134687144775446439it_nat @ zero_zero_nat
% 0.33/0.60 @ ( produc6028340861379781217at_nat
% 0.33/0.60 @ ^ [X3: array_a] :
% 0.33/0.60 ( produc4278983685114131267at_nat
% 0.33/0.60 @ ^ [Xa4: heap_e7401611519738050253t_unit,T2: nat] : T2 ) )
% 0.33/0.60 @ ( heap_T5591663578999710211rray_a @ C2 @ H ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % time_def
% 0.33/0.60 thf(fact_4339_time__def,axiom,
% 0.33/0.60 ( time_t4224138285095624986t_unit
% 0.33/0.60 = ( ^ [C2: heap_T5738788834812785303t_unit,H: heap_e7401611519738050253t_unit] :
% 0.33/0.60 ( case_o5424514124273913701it_nat @ zero_zero_nat
% 0.33/0.60 @ ( produc5629734405777326591at_nat
% 0.33/0.60 @ ^ [X3: product_unit] :
% 0.33/0.60 ( produc4278983685114131267at_nat
% 0.33/0.60 @ ^ [Xa4: heap_e7401611519738050253t_unit,T2: nat] : T2 ) )
% 0.33/0.60 @ ( heap_T875086893843062177t_unit @ C2 @ H ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % time_def
% 0.33/0.60 thf(fact_4340_bit__cut__integer__def,axiom,
% 0.33/0.60 ( code_bit_cut_integer
% 0.33/0.60 = ( ^ [K4: code_integer] :
% 0.33/0.60 ( produc6677183202524767010eger_o @ ( divide6298287555418463151nteger @ K4 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.33/0.60 @ ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ K4 ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % bit_cut_integer_def
% 0.33/0.60 thf(fact_4341_integer__of__num_I3_J,axiom,
% 0.33/0.60 ! [N2: num] :
% 0.33/0.60 ( ( code_integer_of_num @ ( bit1 @ N2 ) )
% 0.33/0.60 = ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( code_integer_of_num @ N2 ) @ ( code_integer_of_num @ N2 ) ) @ one_one_Code_integer ) ) ).
% 0.33/0.60
% 0.33/0.60 % integer_of_num(3)
% 0.33/0.60 thf(fact_4342_less__eq__int_Orep__eq,axiom,
% 0.33/0.60 ( ord_less_eq_int
% 0.33/0.60 = ( ^ [X3: int,Xa4: int] :
% 0.33/0.60 ( produc8739625826339149834_nat_o
% 0.33/0.60 @ ^ [Y3: nat,Z4: nat] :
% 0.33/0.60 ( produc6081775807080527818_nat_o
% 0.33/0.60 @ ^ [U2: nat,V2: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ Y3 @ V2 ) @ ( plus_plus_nat @ U2 @ Z4 ) ) )
% 0.33/0.60 @ ( rep_Integ @ X3 )
% 0.33/0.60 @ ( rep_Integ @ Xa4 ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % less_eq_int.rep_eq
% 0.33/0.60 thf(fact_4343_nat__of__integer__of__nat,axiom,
% 0.33/0.60 ! [N2: nat] :
% 0.33/0.60 ( ( code_nat_of_integer @ ( semiri4939895301339042750nteger @ N2 ) )
% 0.33/0.60 = N2 ) ).
% 0.33/0.60
% 0.33/0.60 % nat_of_integer_of_nat
% 0.33/0.60 thf(fact_4344_int__of__integer__of__nat,axiom,
% 0.33/0.60 ! [N2: nat] :
% 0.33/0.60 ( ( code_int_of_integer @ ( semiri4939895301339042750nteger @ N2 ) )
% 0.33/0.60 = ( semiri1314217659103216013at_int @ N2 ) ) ).
% 0.33/0.60
% 0.33/0.60 % int_of_integer_of_nat
% 0.33/0.60 thf(fact_4345_integer__of__int__int__of__integer,axiom,
% 0.33/0.60 ! [K: code_integer] :
% 0.33/0.60 ( ( code_integer_of_int @ ( code_int_of_integer @ K ) )
% 0.33/0.60 = K ) ).
% 0.33/0.60
% 0.33/0.60 % integer_of_int_int_of_integer
% 0.33/0.60 thf(fact_4346_int__of__integer__integer__of__int,axiom,
% 0.33/0.60 ! [K: int] :
% 0.33/0.60 ( ( code_int_of_integer @ ( code_integer_of_int @ K ) )
% 0.33/0.60 = K ) ).
% 0.33/0.60
% 0.33/0.60 % int_of_integer_integer_of_int
% 0.33/0.60 thf(fact_4347_int__of__integer__inverse,axiom,
% 0.33/0.60 ! [X: code_integer] :
% 0.33/0.60 ( ( code_integer_of_int @ ( code_int_of_integer @ X ) )
% 0.33/0.60 = X ) ).
% 0.33/0.60
% 0.33/0.60 % int_of_integer_inverse
% 0.33/0.60 thf(fact_4348_apsnd__conv,axiom,
% 0.33/0.60 ! [F: produc8923325533196201883nteger > produc8923325533196201883nteger,X: produc6241069584506657477e_term > option6357759511663192854e_term,Y: produc8923325533196201883nteger] :
% 0.33/0.60 ( ( produc717174245515237944e_term @ F @ ( produc8603105652947943368nteger @ X @ Y ) )
% 0.33/0.60 = ( produc8603105652947943368nteger @ X @ ( F @ Y ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % apsnd_conv
% 0.33/0.60 thf(fact_4349_apsnd__conv,axiom,
% 0.33/0.60 ! [F: produc3658429121746597890et_nat > produc3658429121746597890et_nat,X: produc3658429121746597890et_nat > $o,Y: produc3658429121746597890et_nat] :
% 0.33/0.60 ( ( produc8750854537940449737_nat_o @ F @ ( produc5001842942810119800et_nat @ X @ Y ) )
% 0.33/0.60 = ( produc5001842942810119800et_nat @ X @ ( F @ Y ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % apsnd_conv
% 0.33/0.60 thf(fact_4350_apsnd__conv,axiom,
% 0.33/0.60 ! [F: produc3658429121746597890et_nat > produc3925858234332021118et_nat,X: produc3658429121746597890et_nat > $o,Y: produc3658429121746597890et_nat] :
% 0.33/0.60 ( ( produc7714581247149323085_nat_o @ F @ ( produc5001842942810119800et_nat @ X @ Y ) )
% 0.33/0.60 = ( produc2245416461498447860et_nat @ X @ ( F @ Y ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % apsnd_conv
% 0.33/0.60 thf(fact_4351_apsnd__conv,axiom,
% 0.33/0.60 ! [F: produc3925858234332021118et_nat > produc3658429121746597890et_nat,X: produc3658429121746597890et_nat > $o,Y: produc3925858234332021118et_nat] :
% 0.33/0.60 ( ( produc1515462096303866701_nat_o @ F @ ( produc2245416461498447860et_nat @ X @ Y ) )
% 0.33/0.60 = ( produc5001842942810119800et_nat @ X @ ( F @ Y ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % apsnd_conv
% 0.33/0.60 thf(fact_4352_apsnd__conv,axiom,
% 0.33/0.60 ! [F: produc3925858234332021118et_nat > produc3925858234332021118et_nat,X: produc3658429121746597890et_nat > $o,Y: produc3925858234332021118et_nat] :
% 0.33/0.60 ( ( produc969530845752564945_nat_o @ F @ ( produc2245416461498447860et_nat @ X @ Y ) )
% 0.33/0.60 = ( produc2245416461498447860et_nat @ X @ ( F @ Y ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % apsnd_conv
% 0.33/0.60 thf(fact_4353_apsnd__conv,axiom,
% 0.33/0.60 ! [F: product_prod_int_int > product_prod_int_int,X: produc8551481072490612790e_term > option6357759511663192854e_term,Y: product_prod_int_int] :
% 0.33/0.60 ( ( produc4973430039190721449e_term @ F @ ( produc5700946648718959541nt_int @ X @ Y ) )
% 0.33/0.60 = ( produc5700946648718959541nt_int @ X @ ( F @ Y ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % apsnd_conv
% 0.33/0.60 thf(fact_4354_apsnd__conv,axiom,
% 0.33/0.60 ! [F: product_prod_int_int > product_prod_int_int,X: int > option6357759511663192854e_term,Y: product_prod_int_int] :
% 0.33/0.60 ( ( produc7011684061226097695e_term @ F @ ( produc4305682042979456191nt_int @ X @ Y ) )
% 0.33/0.60 = ( produc4305682042979456191nt_int @ X @ ( F @ Y ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % apsnd_conv
% 0.33/0.60 thf(fact_4355_apsnd__conv,axiom,
% 0.33/0.60 ! [F: code_integer > code_integer,X: code_integer,Y: code_integer] :
% 0.33/0.60 ( ( produc6499014454317279255nteger @ F @ ( produc1086072967326762835nteger @ X @ Y ) )
% 0.33/0.60 = ( produc1086072967326762835nteger @ X @ ( F @ Y ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % apsnd_conv
% 0.33/0.60 thf(fact_4356_prod_Oneutral__const,axiom,
% 0.33/0.60 ! [A2: set_nat] :
% 0.33/0.60 ( ( groups708209901874060359at_nat
% 0.33/0.60 @ ^ [Uu: nat] : one_one_nat
% 0.33/0.60 @ A2 )
% 0.33/0.60 = one_one_nat ) ).
% 0.33/0.60
% 0.33/0.60 % prod.neutral_const
% 0.33/0.60 thf(fact_4357_prod_Oneutral__const,axiom,
% 0.33/0.60 ! [A2: set_nat] :
% 0.33/0.60 ( ( groups705719431365010083at_int
% 0.33/0.60 @ ^ [Uu: nat] : one_one_int
% 0.33/0.60 @ A2 )
% 0.33/0.60 = one_one_int ) ).
% 0.33/0.60
% 0.33/0.60 % prod.neutral_const
% 0.33/0.60 thf(fact_4358_prod_Oneutral__const,axiom,
% 0.33/0.60 ! [A2: set_int] :
% 0.33/0.60 ( ( groups1705073143266064639nt_int
% 0.33/0.60 @ ^ [Uu: int] : one_one_int
% 0.33/0.60 @ A2 )
% 0.33/0.60 = one_one_int ) ).
% 0.33/0.60
% 0.33/0.60 % prod.neutral_const
% 0.33/0.60 thf(fact_4359_of__int__integer__of,axiom,
% 0.33/0.60 ! [K: code_integer] :
% 0.33/0.60 ( ( ring_18347121197199848620nteger @ ( code_int_of_integer @ K ) )
% 0.33/0.60 = K ) ).
% 0.33/0.60
% 0.33/0.60 % of_int_integer_of
% 0.33/0.60 thf(fact_4360_int__of__integer__of__int,axiom,
% 0.33/0.60 ! [K: int] :
% 0.33/0.60 ( ( code_int_of_integer @ ( ring_18347121197199848620nteger @ K ) )
% 0.33/0.60 = K ) ).
% 0.33/0.60
% 0.33/0.60 % int_of_integer_of_int
% 0.33/0.60 thf(fact_4361_zero__integer_Orep__eq,axiom,
% 0.33/0.60 ( ( code_int_of_integer @ zero_z3403309356797280102nteger )
% 0.33/0.60 = zero_zero_int ) ).
% 0.33/0.60
% 0.33/0.60 % zero_integer.rep_eq
% 0.33/0.60 thf(fact_4362_int__of__integer__numeral,axiom,
% 0.33/0.60 ! [K: num] :
% 0.33/0.60 ( ( code_int_of_integer @ ( numera6620942414471956472nteger @ K ) )
% 0.33/0.60 = ( numeral_numeral_int @ K ) ) ).
% 0.33/0.60
% 0.33/0.60 % int_of_integer_numeral
% 0.33/0.60 thf(fact_4363_plus__integer_Orep__eq,axiom,
% 0.33/0.60 ! [X: code_integer,Xa: code_integer] :
% 0.33/0.60 ( ( code_int_of_integer @ ( plus_p5714425477246183910nteger @ X @ Xa ) )
% 0.33/0.60 = ( plus_plus_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Xa ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % plus_integer.rep_eq
% 0.33/0.60 thf(fact_4364_one__integer_Orep__eq,axiom,
% 0.33/0.60 ( ( code_int_of_integer @ one_one_Code_integer )
% 0.33/0.60 = one_one_int ) ).
% 0.33/0.60
% 0.33/0.60 % one_integer.rep_eq
% 0.33/0.60 thf(fact_4365_uminus__integer_Orep__eq,axiom,
% 0.33/0.60 ! [X: code_integer] :
% 0.33/0.60 ( ( code_int_of_integer @ ( uminus1351360451143612070nteger @ X ) )
% 0.33/0.60 = ( uminus_uminus_int @ ( code_int_of_integer @ X ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % uminus_integer.rep_eq
% 0.33/0.60 thf(fact_4366_times__integer_Orep__eq,axiom,
% 0.33/0.60 ! [X: code_integer,Xa: code_integer] :
% 0.33/0.60 ( ( code_int_of_integer @ ( times_3573771949741848930nteger @ X @ Xa ) )
% 0.33/0.60 = ( times_times_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Xa ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % times_integer.rep_eq
% 0.33/0.60 thf(fact_4367_minus__integer_Orep__eq,axiom,
% 0.33/0.60 ! [X: code_integer,Xa: code_integer] :
% 0.33/0.60 ( ( code_int_of_integer @ ( minus_8373710615458151222nteger @ X @ Xa ) )
% 0.33/0.60 = ( minus_minus_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Xa ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % minus_integer.rep_eq
% 0.33/0.60 thf(fact_4368_abs__integer_Orep__eq,axiom,
% 0.33/0.60 ! [X: code_integer] :
% 0.33/0.60 ( ( code_int_of_integer @ ( abs_abs_Code_integer @ X ) )
% 0.33/0.60 = ( abs_abs_int @ ( code_int_of_integer @ X ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % abs_integer.rep_eq
% 0.33/0.60 thf(fact_4369_divide__integer_Orep__eq,axiom,
% 0.33/0.60 ! [X: code_integer,Xa: code_integer] :
% 0.33/0.60 ( ( code_int_of_integer @ ( divide6298287555418463151nteger @ X @ Xa ) )
% 0.33/0.60 = ( divide_divide_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Xa ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % divide_integer.rep_eq
% 0.33/0.60 thf(fact_4370_modulo__integer_Orep__eq,axiom,
% 0.33/0.60 ! [X: code_integer,Xa: code_integer] :
% 0.33/0.60 ( ( code_int_of_integer @ ( modulo364778990260209775nteger @ X @ Xa ) )
% 0.33/0.60 = ( modulo_modulo_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Xa ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % modulo_integer.rep_eq
% 0.33/0.60 thf(fact_4371_sgn__integer_Orep__eq,axiom,
% 0.33/0.60 ! [X: code_integer] :
% 0.33/0.60 ( ( code_int_of_integer @ ( sgn_sgn_Code_integer @ X ) )
% 0.33/0.60 = ( sgn_sgn_int @ ( code_int_of_integer @ X ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % sgn_integer.rep_eq
% 0.33/0.60 thf(fact_4372_prod_OatMost__Suc,axiom,
% 0.33/0.60 ! [G: nat > assn,N2: nat] :
% 0.33/0.60 ( ( groups6906906614972039071t_assn @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 0.33/0.60 = ( times_times_assn @ ( groups6906906614972039071t_assn @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.atMost_Suc
% 0.33/0.60 thf(fact_4373_prod_OatMost__Suc,axiom,
% 0.33/0.60 ! [G: nat > rat,N2: nat] :
% 0.33/0.60 ( ( groups73079841787564623at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 0.33/0.60 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.atMost_Suc
% 0.33/0.60 thf(fact_4374_prod_OatMost__Suc,axiom,
% 0.33/0.60 ! [G: nat > nat,N2: nat] :
% 0.33/0.60 ( ( groups708209901874060359at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 0.33/0.60 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.atMost_Suc
% 0.33/0.60 thf(fact_4375_prod_OatMost__Suc,axiom,
% 0.33/0.60 ! [G: nat > int,N2: nat] :
% 0.33/0.60 ( ( groups705719431365010083at_int @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 0.33/0.60 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.atMost_Suc
% 0.33/0.60 thf(fact_4376_prod_OlessThan__Suc,axiom,
% 0.33/0.60 ! [G: nat > assn,N2: nat] :
% 0.33/0.60 ( ( groups6906906614972039071t_assn @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 0.33/0.60 = ( times_times_assn @ ( groups6906906614972039071t_assn @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.lessThan_Suc
% 0.33/0.60 thf(fact_4377_prod_OlessThan__Suc,axiom,
% 0.33/0.60 ! [G: nat > rat,N2: nat] :
% 0.33/0.60 ( ( groups73079841787564623at_rat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 0.33/0.60 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.lessThan_Suc
% 0.33/0.60 thf(fact_4378_prod_OlessThan__Suc,axiom,
% 0.33/0.60 ! [G: nat > nat,N2: nat] :
% 0.33/0.60 ( ( groups708209901874060359at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 0.33/0.60 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.lessThan_Suc
% 0.33/0.60 thf(fact_4379_prod_OlessThan__Suc,axiom,
% 0.33/0.60 ! [G: nat > int,N2: nat] :
% 0.33/0.60 ( ( groups705719431365010083at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 0.33/0.60 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.lessThan_Suc
% 0.33/0.60 thf(fact_4380_nat__of__integer__non__positive,axiom,
% 0.33/0.60 ! [K: code_integer] :
% 0.33/0.60 ( ( ord_le3102999989581377725nteger @ K @ zero_z3403309356797280102nteger )
% 0.33/0.60 => ( ( code_nat_of_integer @ K )
% 0.33/0.60 = zero_zero_nat ) ) ).
% 0.33/0.60
% 0.33/0.60 % nat_of_integer_non_positive
% 0.33/0.60 thf(fact_4381_prod_Ocl__ivl__Suc,axiom,
% 0.33/0.60 ! [N2: nat,M2: nat,G: nat > code_integer] :
% 0.33/0.60 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M2 )
% 0.33/0.60 => ( ( groups3455450783089532116nteger @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N2 ) ) )
% 0.33/0.60 = one_one_Code_integer ) )
% 0.33/0.60 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M2 )
% 0.33/0.60 => ( ( groups3455450783089532116nteger @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N2 ) ) )
% 0.33/0.60 = ( times_3573771949741848930nteger @ ( groups3455450783089532116nteger @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.cl_ivl_Suc
% 0.33/0.60 thf(fact_4382_prod_Ocl__ivl__Suc,axiom,
% 0.33/0.60 ! [N2: nat,M2: nat,G: nat > assn] :
% 0.33/0.60 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M2 )
% 0.33/0.60 => ( ( groups6906906614972039071t_assn @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N2 ) ) )
% 0.33/0.60 = one_one_assn ) )
% 0.33/0.60 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M2 )
% 0.33/0.60 => ( ( groups6906906614972039071t_assn @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N2 ) ) )
% 0.33/0.60 = ( times_times_assn @ ( groups6906906614972039071t_assn @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.cl_ivl_Suc
% 0.33/0.60 thf(fact_4383_prod_Ocl__ivl__Suc,axiom,
% 0.33/0.60 ! [N2: nat,M2: nat,G: nat > rat] :
% 0.33/0.60 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M2 )
% 0.33/0.60 => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N2 ) ) )
% 0.33/0.60 = one_one_rat ) )
% 0.33/0.60 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M2 )
% 0.33/0.60 => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N2 ) ) )
% 0.33/0.60 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.cl_ivl_Suc
% 0.33/0.60 thf(fact_4384_prod_Ocl__ivl__Suc,axiom,
% 0.33/0.60 ! [N2: nat,M2: nat,G: nat > nat] :
% 0.33/0.60 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M2 )
% 0.33/0.60 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N2 ) ) )
% 0.33/0.60 = one_one_nat ) )
% 0.33/0.60 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M2 )
% 0.33/0.60 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N2 ) ) )
% 0.33/0.60 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.cl_ivl_Suc
% 0.33/0.60 thf(fact_4385_prod_Ocl__ivl__Suc,axiom,
% 0.33/0.60 ! [N2: nat,M2: nat,G: nat > int] :
% 0.33/0.60 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M2 )
% 0.33/0.60 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N2 ) ) )
% 0.33/0.60 = one_one_int ) )
% 0.33/0.60 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M2 )
% 0.33/0.60 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N2 ) ) )
% 0.33/0.60 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.cl_ivl_Suc
% 0.33/0.60 thf(fact_4386_prod_Oop__ivl__Suc,axiom,
% 0.33/0.60 ! [N2: nat,M2: nat,G: nat > code_integer] :
% 0.33/0.60 ( ( ( ord_less_nat @ N2 @ M2 )
% 0.33/0.60 => ( ( groups3455450783089532116nteger @ G @ ( set_or4665077453230672383an_nat @ M2 @ ( suc @ N2 ) ) )
% 0.33/0.60 = one_one_Code_integer ) )
% 0.33/0.60 & ( ~ ( ord_less_nat @ N2 @ M2 )
% 0.33/0.60 => ( ( groups3455450783089532116nteger @ G @ ( set_or4665077453230672383an_nat @ M2 @ ( suc @ N2 ) ) )
% 0.33/0.60 = ( times_3573771949741848930nteger @ ( groups3455450783089532116nteger @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) @ ( G @ N2 ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.op_ivl_Suc
% 0.33/0.60 thf(fact_4387_prod_Oop__ivl__Suc,axiom,
% 0.33/0.60 ! [N2: nat,M2: nat,G: nat > assn] :
% 0.33/0.60 ( ( ( ord_less_nat @ N2 @ M2 )
% 0.33/0.60 => ( ( groups6906906614972039071t_assn @ G @ ( set_or4665077453230672383an_nat @ M2 @ ( suc @ N2 ) ) )
% 0.33/0.60 = one_one_assn ) )
% 0.33/0.60 & ( ~ ( ord_less_nat @ N2 @ M2 )
% 0.33/0.60 => ( ( groups6906906614972039071t_assn @ G @ ( set_or4665077453230672383an_nat @ M2 @ ( suc @ N2 ) ) )
% 0.33/0.60 = ( times_times_assn @ ( groups6906906614972039071t_assn @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) @ ( G @ N2 ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.op_ivl_Suc
% 0.33/0.60 thf(fact_4388_prod_Oop__ivl__Suc,axiom,
% 0.33/0.60 ! [N2: nat,M2: nat,G: nat > rat] :
% 0.33/0.60 ( ( ( ord_less_nat @ N2 @ M2 )
% 0.33/0.60 => ( ( groups73079841787564623at_rat @ G @ ( set_or4665077453230672383an_nat @ M2 @ ( suc @ N2 ) ) )
% 0.33/0.60 = one_one_rat ) )
% 0.33/0.60 & ( ~ ( ord_less_nat @ N2 @ M2 )
% 0.33/0.60 => ( ( groups73079841787564623at_rat @ G @ ( set_or4665077453230672383an_nat @ M2 @ ( suc @ N2 ) ) )
% 0.33/0.60 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) @ ( G @ N2 ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.op_ivl_Suc
% 0.33/0.60 thf(fact_4389_prod_Oop__ivl__Suc,axiom,
% 0.33/0.60 ! [N2: nat,M2: nat,G: nat > nat] :
% 0.33/0.60 ( ( ( ord_less_nat @ N2 @ M2 )
% 0.33/0.60 => ( ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ M2 @ ( suc @ N2 ) ) )
% 0.33/0.60 = one_one_nat ) )
% 0.33/0.60 & ( ~ ( ord_less_nat @ N2 @ M2 )
% 0.33/0.60 => ( ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ M2 @ ( suc @ N2 ) ) )
% 0.33/0.60 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) @ ( G @ N2 ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.op_ivl_Suc
% 0.33/0.60 thf(fact_4390_prod_Oop__ivl__Suc,axiom,
% 0.33/0.60 ! [N2: nat,M2: nat,G: nat > int] :
% 0.33/0.60 ( ( ( ord_less_nat @ N2 @ M2 )
% 0.33/0.60 => ( ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ M2 @ ( suc @ N2 ) ) )
% 0.33/0.60 = one_one_int ) )
% 0.33/0.60 & ( ~ ( ord_less_nat @ N2 @ M2 )
% 0.33/0.60 => ( ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ M2 @ ( suc @ N2 ) ) )
% 0.33/0.60 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) @ ( G @ N2 ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.op_ivl_Suc
% 0.33/0.60 thf(fact_4391_xor__integer_Orep__eq,axiom,
% 0.33/0.60 ! [X: code_integer,Xa: code_integer] :
% 0.33/0.60 ( ( code_int_of_integer @ ( bit_se3222712562003087583nteger @ X @ Xa ) )
% 0.33/0.60 = ( bit_se6526347334894502574or_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Xa ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % xor_integer.rep_eq
% 0.33/0.60 thf(fact_4392_push__bit__integer_Orep__eq,axiom,
% 0.33/0.60 ! [X: nat,Xa: code_integer] :
% 0.33/0.60 ( ( code_int_of_integer @ ( bit_se7788150548672797655nteger @ X @ Xa ) )
% 0.33/0.60 = ( bit_se545348938243370406it_int @ X @ ( code_int_of_integer @ Xa ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % push_bit_integer.rep_eq
% 0.33/0.60 thf(fact_4393_xor__integer_Oabs__eq,axiom,
% 0.33/0.60 ! [Xa: int,X: int] :
% 0.33/0.60 ( ( bit_se3222712562003087583nteger @ ( code_integer_of_int @ Xa ) @ ( code_integer_of_int @ X ) )
% 0.33/0.60 = ( code_integer_of_int @ ( bit_se6526347334894502574or_int @ Xa @ X ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % xor_integer.abs_eq
% 0.33/0.60 thf(fact_4394_nat__of__integer_Orep__eq,axiom,
% 0.33/0.60 ( code_nat_of_integer
% 0.33/0.60 = ( ^ [X3: code_integer] : ( nat2 @ ( code_int_of_integer @ X3 ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % nat_of_integer.rep_eq
% 0.33/0.60 thf(fact_4395_integer__eq__iff,axiom,
% 0.33/0.60 ( ( ^ [Y4: code_integer,Z2: code_integer] : ( Y4 = Z2 ) )
% 0.33/0.60 = ( ^ [K4: code_integer,L3: code_integer] :
% 0.33/0.60 ( ( code_int_of_integer @ K4 )
% 0.33/0.60 = ( code_int_of_integer @ L3 ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % integer_eq_iff
% 0.33/0.60 thf(fact_4396_integer__eqI,axiom,
% 0.33/0.60 ! [K: code_integer,L: code_integer] :
% 0.33/0.60 ( ( ( code_int_of_integer @ K )
% 0.33/0.60 = ( code_int_of_integer @ L ) )
% 0.33/0.60 => ( K = L ) ) ).
% 0.33/0.60
% 0.33/0.60 % integer_eqI
% 0.33/0.60 thf(fact_4397_int__of__integer__inject,axiom,
% 0.33/0.60 ! [X: code_integer,Y: code_integer] :
% 0.33/0.60 ( ( ( code_int_of_integer @ X )
% 0.33/0.60 = ( code_int_of_integer @ Y ) )
% 0.33/0.60 = ( X = Y ) ) ).
% 0.33/0.60
% 0.33/0.60 % int_of_integer_inject
% 0.33/0.60 thf(fact_4398_prod_Onot__neutral__contains__not__neutral,axiom,
% 0.33/0.60 ! [G: $o > code_integer,A2: set_o] :
% 0.33/0.60 ( ( ( groups7694694392188491536nteger @ G @ A2 )
% 0.33/0.60 != one_one_Code_integer )
% 0.33/0.60 => ~ ! [A3: $o] :
% 0.33/0.60 ( ( member_o @ A3 @ A2 )
% 0.33/0.60 => ( ( G @ A3 )
% 0.33/0.60 = one_one_Code_integer ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.not_neutral_contains_not_neutral
% 0.33/0.60 thf(fact_4399_prod_Onot__neutral__contains__not__neutral,axiom,
% 0.33/0.60 ! [G: nat > code_integer,A2: set_nat] :
% 0.33/0.60 ( ( ( groups3455450783089532116nteger @ G @ A2 )
% 0.33/0.60 != one_one_Code_integer )
% 0.33/0.60 => ~ ! [A3: nat] :
% 0.33/0.60 ( ( member_nat @ A3 @ A2 )
% 0.33/0.60 => ( ( G @ A3 )
% 0.33/0.60 = one_one_Code_integer ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.not_neutral_contains_not_neutral
% 0.33/0.60 thf(fact_4400_prod_Onot__neutral__contains__not__neutral,axiom,
% 0.33/0.60 ! [G: int > code_integer,A2: set_int] :
% 0.33/0.60 ( ( ( groups3827104343326376752nteger @ G @ A2 )
% 0.33/0.60 != one_one_Code_integer )
% 0.33/0.60 => ~ ! [A3: int] :
% 0.33/0.60 ( ( member_int @ A3 @ A2 )
% 0.33/0.60 => ( ( G @ A3 )
% 0.33/0.60 = one_one_Code_integer ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.not_neutral_contains_not_neutral
% 0.33/0.60 thf(fact_4401_prod_Onot__neutral__contains__not__neutral,axiom,
% 0.33/0.60 ! [G: $o > assn,A2: set_o] :
% 0.33/0.60 ( ( ( groups5301882518646026715o_assn @ G @ A2 )
% 0.33/0.60 != one_one_assn )
% 0.33/0.60 => ~ ! [A3: $o] :
% 0.33/0.60 ( ( member_o @ A3 @ A2 )
% 0.33/0.60 => ( ( G @ A3 )
% 0.33/0.60 = one_one_assn ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.not_neutral_contains_not_neutral
% 0.33/0.60 thf(fact_4402_prod_Onot__neutral__contains__not__neutral,axiom,
% 0.33/0.60 ! [G: nat > assn,A2: set_nat] :
% 0.33/0.60 ( ( ( groups6906906614972039071t_assn @ G @ A2 )
% 0.33/0.60 != one_one_assn )
% 0.33/0.60 => ~ ! [A3: nat] :
% 0.33/0.60 ( ( member_nat @ A3 @ A2 )
% 0.33/0.60 => ( ( G @ A3 )
% 0.33/0.60 = one_one_assn ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.not_neutral_contains_not_neutral
% 0.33/0.60 thf(fact_4403_prod_Onot__neutral__contains__not__neutral,axiom,
% 0.33/0.60 ! [G: int > assn,A2: set_int] :
% 0.33/0.60 ( ( ( groups7882442080178216443t_assn @ G @ A2 )
% 0.33/0.60 != one_one_assn )
% 0.33/0.60 => ~ ! [A3: int] :
% 0.33/0.60 ( ( member_int @ A3 @ A2 )
% 0.33/0.60 => ( ( G @ A3 )
% 0.33/0.60 = one_one_assn ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.not_neutral_contains_not_neutral
% 0.33/0.60 thf(fact_4404_prod_Onot__neutral__contains__not__neutral,axiom,
% 0.33/0.60 ! [G: $o > rat,A2: set_o] :
% 0.33/0.60 ( ( ( groups2869687844427037835_o_rat @ G @ A2 )
% 0.33/0.60 != one_one_rat )
% 0.33/0.60 => ~ ! [A3: $o] :
% 0.33/0.60 ( ( member_o @ A3 @ A2 )
% 0.33/0.60 => ( ( G @ A3 )
% 0.33/0.60 = one_one_rat ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.not_neutral_contains_not_neutral
% 0.33/0.60 thf(fact_4405_prod_Onot__neutral__contains__not__neutral,axiom,
% 0.33/0.60 ! [G: nat > rat,A2: set_nat] :
% 0.33/0.60 ( ( ( groups73079841787564623at_rat @ G @ A2 )
% 0.33/0.60 != one_one_rat )
% 0.33/0.60 => ~ ! [A3: nat] :
% 0.33/0.60 ( ( member_nat @ A3 @ A2 )
% 0.33/0.60 => ( ( G @ A3 )
% 0.33/0.60 = one_one_rat ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.not_neutral_contains_not_neutral
% 0.33/0.60 thf(fact_4406_prod_Onot__neutral__contains__not__neutral,axiom,
% 0.33/0.60 ! [G: int > rat,A2: set_int] :
% 0.33/0.60 ( ( ( groups1072433553688619179nt_rat @ G @ A2 )
% 0.33/0.60 != one_one_rat )
% 0.33/0.60 => ~ ! [A3: int] :
% 0.33/0.60 ( ( member_int @ A3 @ A2 )
% 0.33/0.60 => ( ( G @ A3 )
% 0.33/0.60 = one_one_rat ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.not_neutral_contains_not_neutral
% 0.33/0.60 thf(fact_4407_prod_Onot__neutral__contains__not__neutral,axiom,
% 0.33/0.60 ! [G: $o > nat,A2: set_o] :
% 0.33/0.60 ( ( ( groups3504817904513533571_o_nat @ G @ A2 )
% 0.33/0.60 != one_one_nat )
% 0.33/0.60 => ~ ! [A3: $o] :
% 0.33/0.60 ( ( member_o @ A3 @ A2 )
% 0.33/0.60 => ( ( G @ A3 )
% 0.33/0.60 = one_one_nat ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.not_neutral_contains_not_neutral
% 0.33/0.60 thf(fact_4408_prod_Oneutral,axiom,
% 0.33/0.60 ! [A2: set_nat,G: nat > nat] :
% 0.33/0.60 ( ! [X4: nat] :
% 0.33/0.60 ( ( member_nat @ X4 @ A2 )
% 0.33/0.60 => ( ( G @ X4 )
% 0.33/0.60 = one_one_nat ) )
% 0.33/0.60 => ( ( groups708209901874060359at_nat @ G @ A2 )
% 0.33/0.60 = one_one_nat ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.neutral
% 0.33/0.60 thf(fact_4409_prod_Oneutral,axiom,
% 0.33/0.60 ! [A2: set_nat,G: nat > int] :
% 0.33/0.60 ( ! [X4: nat] :
% 0.33/0.60 ( ( member_nat @ X4 @ A2 )
% 0.33/0.60 => ( ( G @ X4 )
% 0.33/0.60 = one_one_int ) )
% 0.33/0.60 => ( ( groups705719431365010083at_int @ G @ A2 )
% 0.33/0.60 = one_one_int ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.neutral
% 0.33/0.60 thf(fact_4410_prod_Oneutral,axiom,
% 0.33/0.60 ! [A2: set_int,G: int > int] :
% 0.33/0.60 ( ! [X4: int] :
% 0.33/0.60 ( ( member_int @ X4 @ A2 )
% 0.33/0.60 => ( ( G @ X4 )
% 0.33/0.60 = one_one_int ) )
% 0.33/0.60 => ( ( groups1705073143266064639nt_int @ G @ A2 )
% 0.33/0.60 = one_one_int ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.neutral
% 0.33/0.60 thf(fact_4411_apsnd__compose,axiom,
% 0.33/0.60 ! [F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer,X: produc8923325533196201883nteger] :
% 0.33/0.60 ( ( produc9020447175693601247nteger @ F @ ( produc6499014454317279255nteger @ G @ X ) )
% 0.33/0.60 = ( produc9020447175693601247nteger @ ( comp_C1593894019821074884nteger @ F @ G ) @ X ) ) ).
% 0.33/0.60
% 0.33/0.60 % apsnd_compose
% 0.33/0.60 thf(fact_4412_apsnd__compose,axiom,
% 0.33/0.60 ! [F: code_integer > code_integer,G: num > code_integer,X: produc7142191362829087448er_num] :
% 0.33/0.60 ( ( produc6499014454317279255nteger @ F @ ( produc7418200839687411156nteger @ G @ X ) )
% 0.33/0.60 = ( produc7418200839687411156nteger @ ( comp_C3531382070062128313er_num @ F @ G ) @ X ) ) ).
% 0.33/0.60
% 0.33/0.60 % apsnd_compose
% 0.33/0.60 thf(fact_4413_apsnd__compose,axiom,
% 0.33/0.60 ! [F: code_integer > code_integer,G: code_integer > code_integer,X: produc8923325533196201883nteger] :
% 0.33/0.60 ( ( produc6499014454317279255nteger @ F @ ( produc6499014454317279255nteger @ G @ X ) )
% 0.33/0.60 = ( produc6499014454317279255nteger @ ( comp_C7449957260575251196nteger @ F @ G ) @ X ) ) ).
% 0.33/0.60
% 0.33/0.60 % apsnd_compose
% 0.33/0.60 thf(fact_4414_prod__ge__1,axiom,
% 0.33/0.60 ! [A2: set_o,F: $o > code_integer] :
% 0.33/0.60 ( ! [X4: $o] :
% 0.33/0.60 ( ( member_o @ X4 @ A2 )
% 0.33/0.60 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F @ X4 ) ) )
% 0.33/0.60 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( groups7694694392188491536nteger @ F @ A2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod_ge_1
% 0.33/0.60 thf(fact_4415_prod__ge__1,axiom,
% 0.33/0.60 ! [A2: set_nat,F: nat > code_integer] :
% 0.33/0.60 ( ! [X4: nat] :
% 0.33/0.60 ( ( member_nat @ X4 @ A2 )
% 0.33/0.60 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F @ X4 ) ) )
% 0.33/0.60 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( groups3455450783089532116nteger @ F @ A2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod_ge_1
% 0.33/0.60 thf(fact_4416_prod__ge__1,axiom,
% 0.33/0.60 ! [A2: set_int,F: int > code_integer] :
% 0.33/0.60 ( ! [X4: int] :
% 0.33/0.60 ( ( member_int @ X4 @ A2 )
% 0.33/0.60 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F @ X4 ) ) )
% 0.33/0.60 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( groups3827104343326376752nteger @ F @ A2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod_ge_1
% 0.33/0.60 thf(fact_4417_prod__ge__1,axiom,
% 0.33/0.60 ! [A2: set_o,F: $o > rat] :
% 0.33/0.60 ( ! [X4: $o] :
% 0.33/0.60 ( ( member_o @ X4 @ A2 )
% 0.33/0.60 => ( ord_less_eq_rat @ one_one_rat @ ( F @ X4 ) ) )
% 0.33/0.60 => ( ord_less_eq_rat @ one_one_rat @ ( groups2869687844427037835_o_rat @ F @ A2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod_ge_1
% 0.33/0.60 thf(fact_4418_prod__ge__1,axiom,
% 0.33/0.60 ! [A2: set_nat,F: nat > rat] :
% 0.33/0.60 ( ! [X4: nat] :
% 0.33/0.60 ( ( member_nat @ X4 @ A2 )
% 0.33/0.60 => ( ord_less_eq_rat @ one_one_rat @ ( F @ X4 ) ) )
% 0.33/0.60 => ( ord_less_eq_rat @ one_one_rat @ ( groups73079841787564623at_rat @ F @ A2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod_ge_1
% 0.33/0.60 thf(fact_4419_prod__ge__1,axiom,
% 0.33/0.60 ! [A2: set_int,F: int > rat] :
% 0.33/0.60 ( ! [X4: int] :
% 0.33/0.60 ( ( member_int @ X4 @ A2 )
% 0.33/0.60 => ( ord_less_eq_rat @ one_one_rat @ ( F @ X4 ) ) )
% 0.33/0.60 => ( ord_less_eq_rat @ one_one_rat @ ( groups1072433553688619179nt_rat @ F @ A2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod_ge_1
% 0.33/0.60 thf(fact_4420_prod__ge__1,axiom,
% 0.33/0.60 ! [A2: set_o,F: $o > nat] :
% 0.33/0.60 ( ! [X4: $o] :
% 0.33/0.60 ( ( member_o @ X4 @ A2 )
% 0.33/0.60 => ( ord_less_eq_nat @ one_one_nat @ ( F @ X4 ) ) )
% 0.33/0.60 => ( ord_less_eq_nat @ one_one_nat @ ( groups3504817904513533571_o_nat @ F @ A2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod_ge_1
% 0.33/0.60 thf(fact_4421_prod__ge__1,axiom,
% 0.33/0.60 ! [A2: set_int,F: int > nat] :
% 0.33/0.60 ( ! [X4: int] :
% 0.33/0.60 ( ( member_int @ X4 @ A2 )
% 0.33/0.60 => ( ord_less_eq_nat @ one_one_nat @ ( F @ X4 ) ) )
% 0.33/0.60 => ( ord_less_eq_nat @ one_one_nat @ ( groups1707563613775114915nt_nat @ F @ A2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod_ge_1
% 0.33/0.60 thf(fact_4422_prod__ge__1,axiom,
% 0.33/0.60 ! [A2: set_o,F: $o > int] :
% 0.33/0.60 ( ! [X4: $o] :
% 0.33/0.60 ( ( member_o @ X4 @ A2 )
% 0.33/0.60 => ( ord_less_eq_int @ one_one_int @ ( F @ X4 ) ) )
% 0.33/0.60 => ( ord_less_eq_int @ one_one_int @ ( groups3502327434004483295_o_int @ F @ A2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod_ge_1
% 0.33/0.60 thf(fact_4423_prod__ge__1,axiom,
% 0.33/0.60 ! [A2: set_nat,F: nat > nat] :
% 0.33/0.60 ( ! [X4: nat] :
% 0.33/0.60 ( ( member_nat @ X4 @ A2 )
% 0.33/0.60 => ( ord_less_eq_nat @ one_one_nat @ ( F @ X4 ) ) )
% 0.33/0.60 => ( ord_less_eq_nat @ one_one_nat @ ( groups708209901874060359at_nat @ F @ A2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod_ge_1
% 0.33/0.60 thf(fact_4424_int__of__integer__less__iff,axiom,
% 0.33/0.60 ! [X: code_integer,Y: code_integer] :
% 0.33/0.60 ( ( ord_less_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Y ) )
% 0.33/0.60 = ( ord_le6747313008572928689nteger @ X @ Y ) ) ).
% 0.33/0.60
% 0.33/0.60 % int_of_integer_less_iff
% 0.33/0.60 thf(fact_4425_integer__less__iff,axiom,
% 0.33/0.60 ( ord_le6747313008572928689nteger
% 0.33/0.60 = ( ^ [K4: code_integer,L3: code_integer] : ( ord_less_int @ ( code_int_of_integer @ K4 ) @ ( code_int_of_integer @ L3 ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % integer_less_iff
% 0.33/0.60 thf(fact_4426_less__integer_Orep__eq,axiom,
% 0.33/0.60 ( ord_le6747313008572928689nteger
% 0.33/0.60 = ( ^ [X3: code_integer,Xa4: code_integer] : ( ord_less_int @ ( code_int_of_integer @ X3 ) @ ( code_int_of_integer @ Xa4 ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % less_integer.rep_eq
% 0.33/0.60 thf(fact_4427_less__eq__integer_Orep__eq,axiom,
% 0.33/0.60 ( ord_le3102999989581377725nteger
% 0.33/0.60 = ( ^ [X3: code_integer,Xa4: code_integer] : ( ord_less_eq_int @ ( code_int_of_integer @ X3 ) @ ( code_int_of_integer @ Xa4 ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % less_eq_integer.rep_eq
% 0.33/0.60 thf(fact_4428_integer__less__eq__iff,axiom,
% 0.33/0.60 ( ord_le3102999989581377725nteger
% 0.33/0.60 = ( ^ [K4: code_integer,L3: code_integer] : ( ord_less_eq_int @ ( code_int_of_integer @ K4 ) @ ( code_int_of_integer @ L3 ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % integer_less_eq_iff
% 0.33/0.60 thf(fact_4429_prod_Oshift__bounds__cl__Suc__ivl,axiom,
% 0.33/0.60 ! [G: nat > nat,M2: nat,N2: nat] :
% 0.33/0.60 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ ( suc @ N2 ) ) )
% 0.33/0.60 = ( groups708209901874060359at_nat
% 0.33/0.60 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 0.33/0.60 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.shift_bounds_cl_Suc_ivl
% 0.33/0.60 thf(fact_4430_prod_Oshift__bounds__cl__Suc__ivl,axiom,
% 0.33/0.60 ! [G: nat > int,M2: nat,N2: nat] :
% 0.33/0.60 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ ( suc @ N2 ) ) )
% 0.33/0.60 = ( groups705719431365010083at_int
% 0.33/0.60 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 0.33/0.60 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.shift_bounds_cl_Suc_ivl
% 0.33/0.60 thf(fact_4431_prod_Oshift__bounds__Suc__ivl,axiom,
% 0.33/0.60 ! [G: nat > nat,M2: nat,N2: nat] :
% 0.33/0.60 ( ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ ( suc @ M2 ) @ ( suc @ N2 ) ) )
% 0.33/0.60 = ( groups708209901874060359at_nat
% 0.33/0.60 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 0.33/0.60 @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.shift_bounds_Suc_ivl
% 0.33/0.60 thf(fact_4432_prod_Oshift__bounds__Suc__ivl,axiom,
% 0.33/0.60 ! [G: nat > int,M2: nat,N2: nat] :
% 0.33/0.60 ( ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ ( suc @ M2 ) @ ( suc @ N2 ) ) )
% 0.33/0.60 = ( groups705719431365010083at_int
% 0.33/0.60 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 0.33/0.60 @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.shift_bounds_Suc_ivl
% 0.33/0.60 thf(fact_4433_prod_Oshift__bounds__cl__nat__ivl,axiom,
% 0.33/0.60 ! [G: nat > nat,M2: nat,K: nat,N2: nat] :
% 0.33/0.60 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M2 @ K ) @ ( plus_plus_nat @ N2 @ K ) ) )
% 0.33/0.60 = ( groups708209901874060359at_nat
% 0.33/0.60 @ ^ [I3: nat] : ( G @ ( plus_plus_nat @ I3 @ K ) )
% 0.33/0.60 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.shift_bounds_cl_nat_ivl
% 0.33/0.60 thf(fact_4434_prod_Oshift__bounds__cl__nat__ivl,axiom,
% 0.33/0.60 ! [G: nat > int,M2: nat,K: nat,N2: nat] :
% 0.33/0.60 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M2 @ K ) @ ( plus_plus_nat @ N2 @ K ) ) )
% 0.33/0.60 = ( groups705719431365010083at_int
% 0.33/0.60 @ ^ [I3: nat] : ( G @ ( plus_plus_nat @ I3 @ K ) )
% 0.33/0.60 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.shift_bounds_cl_nat_ivl
% 0.33/0.60 thf(fact_4435_prod_Oshift__bounds__nat__ivl,axiom,
% 0.33/0.60 ! [G: nat > nat,M2: nat,K: nat,N2: nat] :
% 0.33/0.60 ( ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ ( plus_plus_nat @ M2 @ K ) @ ( plus_plus_nat @ N2 @ K ) ) )
% 0.33/0.60 = ( groups708209901874060359at_nat
% 0.33/0.60 @ ^ [I3: nat] : ( G @ ( plus_plus_nat @ I3 @ K ) )
% 0.33/0.60 @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.shift_bounds_nat_ivl
% 0.33/0.60 thf(fact_4436_prod_Oshift__bounds__nat__ivl,axiom,
% 0.33/0.60 ! [G: nat > int,M2: nat,K: nat,N2: nat] :
% 0.33/0.60 ( ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ ( plus_plus_nat @ M2 @ K ) @ ( plus_plus_nat @ N2 @ K ) ) )
% 0.33/0.60 = ( groups705719431365010083at_int
% 0.33/0.60 @ ^ [I3: nat] : ( G @ ( plus_plus_nat @ I3 @ K ) )
% 0.33/0.60 @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.shift_bounds_nat_ivl
% 0.33/0.60 thf(fact_4437_atLeastLessThanPlusOne__atLeastAtMost__integer,axiom,
% 0.33/0.60 ! [L: code_integer,U: code_integer] :
% 0.33/0.60 ( ( set_or8404916559141939852nteger @ L @ ( plus_p5714425477246183910nteger @ U @ one_one_Code_integer ) )
% 0.33/0.60 = ( set_or189985376899183464nteger @ L @ U ) ) ).
% 0.33/0.60
% 0.33/0.60 % atLeastLessThanPlusOne_atLeastAtMost_integer
% 0.33/0.60 thf(fact_4438_prod__le__1,axiom,
% 0.33/0.60 ! [A2: set_o,F: $o > code_integer] :
% 0.33/0.60 ( ! [X4: $o] :
% 0.33/0.60 ( ( member_o @ X4 @ A2 )
% 0.33/0.60 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ X4 ) )
% 0.33/0.60 & ( ord_le3102999989581377725nteger @ ( F @ X4 ) @ one_one_Code_integer ) ) )
% 0.33/0.60 => ( ord_le3102999989581377725nteger @ ( groups7694694392188491536nteger @ F @ A2 ) @ one_one_Code_integer ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod_le_1
% 0.33/0.60 thf(fact_4439_prod__le__1,axiom,
% 0.33/0.60 ! [A2: set_nat,F: nat > code_integer] :
% 0.33/0.60 ( ! [X4: nat] :
% 0.33/0.60 ( ( member_nat @ X4 @ A2 )
% 0.33/0.60 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ X4 ) )
% 0.33/0.60 & ( ord_le3102999989581377725nteger @ ( F @ X4 ) @ one_one_Code_integer ) ) )
% 0.33/0.60 => ( ord_le3102999989581377725nteger @ ( groups3455450783089532116nteger @ F @ A2 ) @ one_one_Code_integer ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod_le_1
% 0.33/0.60 thf(fact_4440_prod__le__1,axiom,
% 0.33/0.60 ! [A2: set_int,F: int > code_integer] :
% 0.33/0.60 ( ! [X4: int] :
% 0.33/0.60 ( ( member_int @ X4 @ A2 )
% 0.33/0.60 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ X4 ) )
% 0.33/0.60 & ( ord_le3102999989581377725nteger @ ( F @ X4 ) @ one_one_Code_integer ) ) )
% 0.33/0.60 => ( ord_le3102999989581377725nteger @ ( groups3827104343326376752nteger @ F @ A2 ) @ one_one_Code_integer ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod_le_1
% 0.33/0.60 thf(fact_4441_prod__le__1,axiom,
% 0.33/0.60 ! [A2: set_o,F: $o > rat] :
% 0.33/0.60 ( ! [X4: $o] :
% 0.33/0.60 ( ( member_o @ X4 @ A2 )
% 0.33/0.60 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) )
% 0.33/0.60 & ( ord_less_eq_rat @ ( F @ X4 ) @ one_one_rat ) ) )
% 0.33/0.60 => ( ord_less_eq_rat @ ( groups2869687844427037835_o_rat @ F @ A2 ) @ one_one_rat ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod_le_1
% 0.33/0.60 thf(fact_4442_prod__le__1,axiom,
% 0.33/0.60 ! [A2: set_nat,F: nat > rat] :
% 0.33/0.60 ( ! [X4: nat] :
% 0.33/0.60 ( ( member_nat @ X4 @ A2 )
% 0.33/0.60 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) )
% 0.33/0.60 & ( ord_less_eq_rat @ ( F @ X4 ) @ one_one_rat ) ) )
% 0.33/0.60 => ( ord_less_eq_rat @ ( groups73079841787564623at_rat @ F @ A2 ) @ one_one_rat ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod_le_1
% 0.33/0.60 thf(fact_4443_prod__le__1,axiom,
% 0.33/0.60 ! [A2: set_int,F: int > rat] :
% 0.33/0.60 ( ! [X4: int] :
% 0.33/0.60 ( ( member_int @ X4 @ A2 )
% 0.33/0.60 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) )
% 0.33/0.60 & ( ord_less_eq_rat @ ( F @ X4 ) @ one_one_rat ) ) )
% 0.33/0.60 => ( ord_less_eq_rat @ ( groups1072433553688619179nt_rat @ F @ A2 ) @ one_one_rat ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod_le_1
% 0.33/0.60 thf(fact_4444_prod__le__1,axiom,
% 0.33/0.60 ! [A2: set_o,F: $o > nat] :
% 0.33/0.60 ( ! [X4: $o] :
% 0.33/0.60 ( ( member_o @ X4 @ A2 )
% 0.33/0.60 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X4 ) )
% 0.33/0.60 & ( ord_less_eq_nat @ ( F @ X4 ) @ one_one_nat ) ) )
% 0.33/0.60 => ( ord_less_eq_nat @ ( groups3504817904513533571_o_nat @ F @ A2 ) @ one_one_nat ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod_le_1
% 0.33/0.60 thf(fact_4445_prod__le__1,axiom,
% 0.33/0.60 ! [A2: set_int,F: int > nat] :
% 0.33/0.60 ( ! [X4: int] :
% 0.33/0.60 ( ( member_int @ X4 @ A2 )
% 0.33/0.60 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X4 ) )
% 0.33/0.60 & ( ord_less_eq_nat @ ( F @ X4 ) @ one_one_nat ) ) )
% 0.33/0.60 => ( ord_less_eq_nat @ ( groups1707563613775114915nt_nat @ F @ A2 ) @ one_one_nat ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod_le_1
% 0.33/0.60 thf(fact_4446_prod__le__1,axiom,
% 0.33/0.60 ! [A2: set_o,F: $o > int] :
% 0.33/0.60 ( ! [X4: $o] :
% 0.33/0.60 ( ( member_o @ X4 @ A2 )
% 0.33/0.60 => ( ( ord_less_eq_int @ zero_zero_int @ ( F @ X4 ) )
% 0.33/0.60 & ( ord_less_eq_int @ ( F @ X4 ) @ one_one_int ) ) )
% 0.33/0.60 => ( ord_less_eq_int @ ( groups3502327434004483295_o_int @ F @ A2 ) @ one_one_int ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod_le_1
% 0.33/0.60 thf(fact_4447_prod__le__1,axiom,
% 0.33/0.60 ! [A2: set_nat,F: nat > nat] :
% 0.33/0.60 ( ! [X4: nat] :
% 0.33/0.60 ( ( member_nat @ X4 @ A2 )
% 0.33/0.60 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X4 ) )
% 0.33/0.60 & ( ord_less_eq_nat @ ( F @ X4 ) @ one_one_nat ) ) )
% 0.33/0.60 => ( ord_less_eq_nat @ ( groups708209901874060359at_nat @ F @ A2 ) @ one_one_nat ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod_le_1
% 0.33/0.60 thf(fact_4448_prod_Oivl__cong,axiom,
% 0.33/0.60 ! [A: nat,C: nat,B: nat,D2: nat,G: nat > nat,H3: nat > nat] :
% 0.33/0.60 ( ( A = C )
% 0.33/0.60 => ( ( B = D2 )
% 0.33/0.60 => ( ! [X4: nat] :
% 0.33/0.60 ( ( ord_less_eq_nat @ C @ X4 )
% 0.33/0.60 => ( ( ord_less_nat @ X4 @ D2 )
% 0.33/0.60 => ( ( G @ X4 )
% 0.33/0.60 = ( H3 @ X4 ) ) ) )
% 0.33/0.60 => ( ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ A @ B ) )
% 0.33/0.60 = ( groups708209901874060359at_nat @ H3 @ ( set_or4665077453230672383an_nat @ C @ D2 ) ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.ivl_cong
% 0.33/0.60 thf(fact_4449_prod_Oivl__cong,axiom,
% 0.33/0.60 ! [A: nat,C: nat,B: nat,D2: nat,G: nat > int,H3: nat > int] :
% 0.33/0.60 ( ( A = C )
% 0.33/0.60 => ( ( B = D2 )
% 0.33/0.60 => ( ! [X4: nat] :
% 0.33/0.60 ( ( ord_less_eq_nat @ C @ X4 )
% 0.33/0.60 => ( ( ord_less_nat @ X4 @ D2 )
% 0.33/0.60 => ( ( G @ X4 )
% 0.33/0.60 = ( H3 @ X4 ) ) ) )
% 0.33/0.60 => ( ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ A @ B ) )
% 0.33/0.60 = ( groups705719431365010083at_int @ H3 @ ( set_or4665077453230672383an_nat @ C @ D2 ) ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.ivl_cong
% 0.33/0.60 thf(fact_4450_prod_Oivl__cong,axiom,
% 0.33/0.60 ! [A: int,C: int,B: int,D2: int,G: int > int,H3: int > int] :
% 0.33/0.60 ( ( A = C )
% 0.33/0.60 => ( ( B = D2 )
% 0.33/0.60 => ( ! [X4: int] :
% 0.33/0.60 ( ( ord_less_eq_int @ C @ X4 )
% 0.33/0.60 => ( ( ord_less_int @ X4 @ D2 )
% 0.33/0.60 => ( ( G @ X4 )
% 0.33/0.60 = ( H3 @ X4 ) ) ) )
% 0.33/0.60 => ( ( groups1705073143266064639nt_int @ G @ ( set_or4662586982721622107an_int @ A @ B ) )
% 0.33/0.60 = ( groups1705073143266064639nt_int @ H3 @ ( set_or4662586982721622107an_int @ C @ D2 ) ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.ivl_cong
% 0.33/0.60 thf(fact_4451_take__bit__integer_Orep__eq,axiom,
% 0.33/0.60 ! [X: nat,Xa: code_integer] :
% 0.33/0.60 ( ( code_int_of_integer @ ( bit_se1745604003318907178nteger @ X @ Xa ) )
% 0.33/0.60 = ( bit_se2923211474154528505it_int @ X @ ( code_int_of_integer @ Xa ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % take_bit_integer.rep_eq
% 0.33/0.60 thf(fact_4452_and__integer_Orep__eq,axiom,
% 0.33/0.60 ! [X: code_integer,Xa: code_integer] :
% 0.33/0.60 ( ( code_int_of_integer @ ( bit_se3949692690581998587nteger @ X @ Xa ) )
% 0.33/0.60 = ( bit_se725231765392027082nd_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Xa ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % and_integer.rep_eq
% 0.33/0.60 thf(fact_4453_bit__integer_Orep__eq,axiom,
% 0.33/0.60 ( bit_se9216721137139052372nteger
% 0.33/0.60 = ( ^ [X3: code_integer] : ( bit_se1146084159140164899it_int @ ( code_int_of_integer @ X3 ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % bit_integer.rep_eq
% 0.33/0.60 thf(fact_4454_prod_OatLeastLessThan__concat,axiom,
% 0.33/0.60 ! [M2: nat,N2: nat,P4: nat,G: nat > assn] :
% 0.33/0.60 ( ( ord_less_eq_nat @ M2 @ N2 )
% 0.33/0.60 => ( ( ord_less_eq_nat @ N2 @ P4 )
% 0.33/0.60 => ( ( times_times_assn @ ( groups6906906614972039071t_assn @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) @ ( groups6906906614972039071t_assn @ G @ ( set_or4665077453230672383an_nat @ N2 @ P4 ) ) )
% 0.33/0.60 = ( groups6906906614972039071t_assn @ G @ ( set_or4665077453230672383an_nat @ M2 @ P4 ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.atLeastLessThan_concat
% 0.33/0.60 thf(fact_4455_prod_OatLeastLessThan__concat,axiom,
% 0.33/0.60 ! [M2: nat,N2: nat,P4: nat,G: nat > rat] :
% 0.33/0.60 ( ( ord_less_eq_nat @ M2 @ N2 )
% 0.33/0.60 => ( ( ord_less_eq_nat @ N2 @ P4 )
% 0.33/0.60 => ( ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) @ ( groups73079841787564623at_rat @ G @ ( set_or4665077453230672383an_nat @ N2 @ P4 ) ) )
% 0.33/0.60 = ( groups73079841787564623at_rat @ G @ ( set_or4665077453230672383an_nat @ M2 @ P4 ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.atLeastLessThan_concat
% 0.33/0.60 thf(fact_4456_prod_OatLeastLessThan__concat,axiom,
% 0.33/0.60 ! [M2: nat,N2: nat,P4: nat,G: nat > nat] :
% 0.33/0.60 ( ( ord_less_eq_nat @ M2 @ N2 )
% 0.33/0.60 => ( ( ord_less_eq_nat @ N2 @ P4 )
% 0.33/0.60 => ( ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) @ ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ N2 @ P4 ) ) )
% 0.33/0.60 = ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ M2 @ P4 ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.atLeastLessThan_concat
% 0.33/0.60 thf(fact_4457_prod_OatLeastLessThan__concat,axiom,
% 0.33/0.60 ! [M2: nat,N2: nat,P4: nat,G: nat > int] :
% 0.33/0.60 ( ( ord_less_eq_nat @ M2 @ N2 )
% 0.33/0.60 => ( ( ord_less_eq_nat @ N2 @ P4 )
% 0.33/0.60 => ( ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) @ ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ N2 @ P4 ) ) )
% 0.33/0.60 = ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ M2 @ P4 ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.atLeastLessThan_concat
% 0.33/0.60 thf(fact_4458_mask__integer_Orep__eq,axiom,
% 0.33/0.60 ! [X: nat] :
% 0.33/0.60 ( ( code_int_of_integer @ ( bit_se2119862282449309892nteger @ X ) )
% 0.33/0.60 = ( bit_se2000444600071755411sk_int @ X ) ) ).
% 0.33/0.60
% 0.33/0.60 % mask_integer.rep_eq
% 0.33/0.60 thf(fact_4459_integer__of__num__def,axiom,
% 0.33/0.60 code_integer_of_num = numera6620942414471956472nteger ).
% 0.33/0.60
% 0.33/0.60 % integer_of_num_def
% 0.33/0.60 thf(fact_4460_unset__bit__integer_Orep__eq,axiom,
% 0.33/0.60 ! [X: nat,Xa: code_integer] :
% 0.33/0.60 ( ( code_int_of_integer @ ( bit_se8260200283734997820nteger @ X @ Xa ) )
% 0.33/0.60 = ( bit_se4203085406695923979it_int @ X @ ( code_int_of_integer @ Xa ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % unset_bit_integer.rep_eq
% 0.33/0.60 thf(fact_4461_set__bit__integer_Orep__eq,axiom,
% 0.33/0.60 ! [X: nat,Xa: code_integer] :
% 0.33/0.60 ( ( code_int_of_integer @ ( bit_se2793503036327961859nteger @ X @ Xa ) )
% 0.33/0.60 = ( bit_se7879613467334960850it_int @ X @ ( code_int_of_integer @ Xa ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % set_bit_integer.rep_eq
% 0.33/0.60 thf(fact_4462_flip__bit__integer_Orep__eq,axiom,
% 0.33/0.60 ! [X: nat,Xa: code_integer] :
% 0.33/0.60 ( ( code_int_of_integer @ ( bit_se1345352211410354436nteger @ X @ Xa ) )
% 0.33/0.60 = ( bit_se2159334234014336723it_int @ X @ ( code_int_of_integer @ Xa ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % flip_bit_integer.rep_eq
% 0.33/0.60 thf(fact_4463_prod_OatLeast__Suc__atMost__Suc__shift,axiom,
% 0.33/0.60 ! [G: nat > nat,M2: nat,N2: nat] :
% 0.33/0.60 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ ( suc @ N2 ) ) )
% 0.33/0.60 = ( groups708209901874060359at_nat @ ( comp_nat_nat_nat @ G @ suc ) @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.atLeast_Suc_atMost_Suc_shift
% 0.33/0.60 thf(fact_4464_prod_OatLeast__Suc__atMost__Suc__shift,axiom,
% 0.33/0.60 ! [G: nat > int,M2: nat,N2: nat] :
% 0.33/0.60 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ ( suc @ N2 ) ) )
% 0.33/0.60 = ( groups705719431365010083at_int @ ( comp_nat_int_nat @ G @ suc ) @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.atLeast_Suc_atMost_Suc_shift
% 0.33/0.60 thf(fact_4465_prod_OatLeast__Suc__lessThan__Suc__shift,axiom,
% 0.33/0.60 ! [G: nat > nat,M2: nat,N2: nat] :
% 0.33/0.60 ( ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ ( suc @ M2 ) @ ( suc @ N2 ) ) )
% 0.33/0.60 = ( groups708209901874060359at_nat @ ( comp_nat_nat_nat @ G @ suc ) @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.atLeast_Suc_lessThan_Suc_shift
% 0.33/0.60 thf(fact_4466_prod_OatLeast__Suc__lessThan__Suc__shift,axiom,
% 0.33/0.60 ! [G: nat > int,M2: nat,N2: nat] :
% 0.33/0.60 ( ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ ( suc @ M2 ) @ ( suc @ N2 ) ) )
% 0.33/0.60 = ( groups705719431365010083at_int @ ( comp_nat_int_nat @ G @ suc ) @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.atLeast_Suc_lessThan_Suc_shift
% 0.33/0.60 thf(fact_4467_atLeastLessThanPlusOne__atLeastAtMost__int,axiom,
% 0.33/0.60 ! [L: int,U: int] :
% 0.33/0.60 ( ( set_or4662586982721622107an_int @ L @ ( plus_plus_int @ U @ one_one_int ) )
% 0.33/0.60 = ( set_or1266510415728281911st_int @ L @ U ) ) ).
% 0.33/0.60
% 0.33/0.60 % atLeastLessThanPlusOne_atLeastAtMost_int
% 0.33/0.60 thf(fact_4468_prod_OatLeastAtMost__shift__bounds,axiom,
% 0.33/0.60 ! [G: nat > nat,M2: nat,K: nat,N2: nat] :
% 0.33/0.60 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M2 @ K ) @ ( plus_plus_nat @ N2 @ K ) ) )
% 0.33/0.60 = ( groups708209901874060359at_nat @ ( comp_nat_nat_nat @ G @ ( plus_plus_nat @ K ) ) @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.atLeastAtMost_shift_bounds
% 0.33/0.60 thf(fact_4469_prod_OatLeastAtMost__shift__bounds,axiom,
% 0.33/0.60 ! [G: nat > int,M2: nat,K: nat,N2: nat] :
% 0.33/0.60 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M2 @ K ) @ ( plus_plus_nat @ N2 @ K ) ) )
% 0.33/0.60 = ( groups705719431365010083at_int @ ( comp_nat_int_nat @ G @ ( plus_plus_nat @ K ) ) @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.atLeastAtMost_shift_bounds
% 0.33/0.60 thf(fact_4470_prod_OatLeastLessThan__shift__bounds,axiom,
% 0.33/0.60 ! [G: nat > nat,M2: nat,K: nat,N2: nat] :
% 0.33/0.60 ( ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ ( plus_plus_nat @ M2 @ K ) @ ( plus_plus_nat @ N2 @ K ) ) )
% 0.33/0.60 = ( groups708209901874060359at_nat @ ( comp_nat_nat_nat @ G @ ( plus_plus_nat @ K ) ) @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.atLeastLessThan_shift_bounds
% 0.33/0.60 thf(fact_4471_prod_OatLeastLessThan__shift__bounds,axiom,
% 0.33/0.60 ! [G: nat > int,M2: nat,K: nat,N2: nat] :
% 0.33/0.60 ( ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ ( plus_plus_nat @ M2 @ K ) @ ( plus_plus_nat @ N2 @ K ) ) )
% 0.33/0.60 = ( groups705719431365010083at_int @ ( comp_nat_int_nat @ G @ ( plus_plus_nat @ K ) ) @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.atLeastLessThan_shift_bounds
% 0.33/0.60 thf(fact_4472_prod_OatLeastAtMost__rev,axiom,
% 0.33/0.60 ! [G: nat > nat,N2: nat,M2: nat] :
% 0.33/0.60 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ N2 @ M2 ) )
% 0.33/0.60 = ( groups708209901874060359at_nat
% 0.33/0.60 @ ^ [I3: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M2 @ N2 ) @ I3 ) )
% 0.33/0.60 @ ( set_or1269000886237332187st_nat @ N2 @ M2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.atLeastAtMost_rev
% 0.33/0.60 thf(fact_4473_prod_OatLeastAtMost__rev,axiom,
% 0.33/0.60 ! [G: nat > int,N2: nat,M2: nat] :
% 0.33/0.60 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ N2 @ M2 ) )
% 0.33/0.60 = ( groups705719431365010083at_int
% 0.33/0.60 @ ^ [I3: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M2 @ N2 ) @ I3 ) )
% 0.33/0.60 @ ( set_or1269000886237332187st_nat @ N2 @ M2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.atLeastAtMost_rev
% 0.33/0.60 thf(fact_4474_prod_Onat__diff__reindex,axiom,
% 0.33/0.60 ! [G: nat > nat,N2: nat] :
% 0.33/0.60 ( ( groups708209901874060359at_nat
% 0.33/0.60 @ ^ [I3: nat] : ( G @ ( minus_minus_nat @ N2 @ ( suc @ I3 ) ) )
% 0.33/0.60 @ ( set_ord_lessThan_nat @ N2 ) )
% 0.33/0.60 = ( groups708209901874060359at_nat @ G @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.nat_diff_reindex
% 0.33/0.60 thf(fact_4475_prod_Onat__diff__reindex,axiom,
% 0.33/0.60 ! [G: nat > int,N2: nat] :
% 0.33/0.60 ( ( groups705719431365010083at_int
% 0.33/0.60 @ ^ [I3: nat] : ( G @ ( minus_minus_nat @ N2 @ ( suc @ I3 ) ) )
% 0.33/0.60 @ ( set_ord_lessThan_nat @ N2 ) )
% 0.33/0.60 = ( groups705719431365010083at_int @ G @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.nat_diff_reindex
% 0.33/0.60 thf(fact_4476_nat__of__integer_Oabs__eq,axiom,
% 0.33/0.60 ! [X: int] :
% 0.33/0.60 ( ( code_nat_of_integer @ ( code_integer_of_int @ X ) )
% 0.33/0.60 = ( nat2 @ X ) ) ).
% 0.33/0.60
% 0.33/0.60 % nat_of_integer.abs_eq
% 0.33/0.60 thf(fact_4477_num__of__integer_Orep__eq,axiom,
% 0.33/0.60 ( code_num_of_integer
% 0.33/0.60 = ( ^ [X3: code_integer] : ( num_of_nat @ ( nat2 @ ( code_int_of_integer @ X3 ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % num_of_integer.rep_eq
% 0.33/0.60 thf(fact_4478_prod_OatLeast0__atMost__Suc,axiom,
% 0.33/0.60 ! [G: nat > assn,N2: nat] :
% 0.33/0.60 ( ( groups6906906614972039071t_assn @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 0.33/0.60 = ( times_times_assn @ ( groups6906906614972039071t_assn @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.atLeast0_atMost_Suc
% 0.33/0.60 thf(fact_4479_prod_OatLeast0__atMost__Suc,axiom,
% 0.33/0.60 ! [G: nat > rat,N2: nat] :
% 0.33/0.60 ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 0.33/0.60 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.atLeast0_atMost_Suc
% 0.33/0.60 thf(fact_4480_prod_OatLeast0__atMost__Suc,axiom,
% 0.33/0.60 ! [G: nat > nat,N2: nat] :
% 0.33/0.60 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 0.33/0.60 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.atLeast0_atMost_Suc
% 0.33/0.60 thf(fact_4481_prod_OatLeast0__atMost__Suc,axiom,
% 0.33/0.60 ! [G: nat > int,N2: nat] :
% 0.33/0.60 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 0.33/0.60 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.atLeast0_atMost_Suc
% 0.33/0.60 thf(fact_4482_prod_OatLeast0__lessThan__Suc,axiom,
% 0.33/0.60 ! [G: nat > assn,N2: nat] :
% 0.33/0.60 ( ( groups6906906614972039071t_assn @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 0.33/0.60 = ( times_times_assn @ ( groups6906906614972039071t_assn @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.atLeast0_lessThan_Suc
% 0.33/0.60 thf(fact_4483_prod_OatLeast0__lessThan__Suc,axiom,
% 0.33/0.60 ! [G: nat > rat,N2: nat] :
% 0.33/0.60 ( ( groups73079841787564623at_rat @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 0.33/0.60 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.atLeast0_lessThan_Suc
% 0.33/0.60 thf(fact_4484_prod_OatLeast0__lessThan__Suc,axiom,
% 0.33/0.60 ! [G: nat > nat,N2: nat] :
% 0.33/0.60 ( ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 0.33/0.60 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.atLeast0_lessThan_Suc
% 0.33/0.60 thf(fact_4485_prod_OatLeast0__lessThan__Suc,axiom,
% 0.33/0.60 ! [G: nat > int,N2: nat] :
% 0.33/0.60 ( ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 0.33/0.60 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.atLeast0_lessThan_Suc
% 0.33/0.60 thf(fact_4486_prod_OatLeast__Suc__lessThan,axiom,
% 0.33/0.60 ! [M2: nat,N2: nat,G: nat > assn] :
% 0.33/0.60 ( ( ord_less_nat @ M2 @ N2 )
% 0.33/0.60 => ( ( groups6906906614972039071t_assn @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) )
% 0.33/0.60 = ( times_times_assn @ ( G @ M2 ) @ ( groups6906906614972039071t_assn @ G @ ( set_or4665077453230672383an_nat @ ( suc @ M2 ) @ N2 ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.atLeast_Suc_lessThan
% 0.33/0.60 thf(fact_4487_prod_OatLeast__Suc__lessThan,axiom,
% 0.33/0.60 ! [M2: nat,N2: nat,G: nat > rat] :
% 0.33/0.60 ( ( ord_less_nat @ M2 @ N2 )
% 0.33/0.60 => ( ( groups73079841787564623at_rat @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) )
% 0.33/0.60 = ( times_times_rat @ ( G @ M2 ) @ ( groups73079841787564623at_rat @ G @ ( set_or4665077453230672383an_nat @ ( suc @ M2 ) @ N2 ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.atLeast_Suc_lessThan
% 0.33/0.60 thf(fact_4488_prod_OatLeast__Suc__lessThan,axiom,
% 0.33/0.60 ! [M2: nat,N2: nat,G: nat > nat] :
% 0.33/0.60 ( ( ord_less_nat @ M2 @ N2 )
% 0.33/0.60 => ( ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) )
% 0.33/0.60 = ( times_times_nat @ ( G @ M2 ) @ ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ ( suc @ M2 ) @ N2 ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.atLeast_Suc_lessThan
% 0.33/0.60 thf(fact_4489_prod_OatLeast__Suc__lessThan,axiom,
% 0.33/0.60 ! [M2: nat,N2: nat,G: nat > int] :
% 0.33/0.60 ( ( ord_less_nat @ M2 @ N2 )
% 0.33/0.60 => ( ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) )
% 0.33/0.60 = ( times_times_int @ ( G @ M2 ) @ ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ ( suc @ M2 ) @ N2 ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.atLeast_Suc_lessThan
% 0.33/0.60 thf(fact_4490_prod_Onat__ivl__Suc_H,axiom,
% 0.33/0.60 ! [M2: nat,N2: nat,G: nat > assn] :
% 0.33/0.60 ( ( ord_less_eq_nat @ M2 @ ( suc @ N2 ) )
% 0.33/0.60 => ( ( groups6906906614972039071t_assn @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N2 ) ) )
% 0.33/0.60 = ( times_times_assn @ ( G @ ( suc @ N2 ) ) @ ( groups6906906614972039071t_assn @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.nat_ivl_Suc'
% 0.33/0.60 thf(fact_4491_prod_Onat__ivl__Suc_H,axiom,
% 0.33/0.60 ! [M2: nat,N2: nat,G: nat > rat] :
% 0.33/0.60 ( ( ord_less_eq_nat @ M2 @ ( suc @ N2 ) )
% 0.33/0.60 => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N2 ) ) )
% 0.33/0.60 = ( times_times_rat @ ( G @ ( suc @ N2 ) ) @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.nat_ivl_Suc'
% 0.33/0.60 thf(fact_4492_prod_Onat__ivl__Suc_H,axiom,
% 0.33/0.60 ! [M2: nat,N2: nat,G: nat > nat] :
% 0.33/0.60 ( ( ord_less_eq_nat @ M2 @ ( suc @ N2 ) )
% 0.33/0.60 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N2 ) ) )
% 0.33/0.60 = ( times_times_nat @ ( G @ ( suc @ N2 ) ) @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.nat_ivl_Suc'
% 0.33/0.60 thf(fact_4493_prod_Onat__ivl__Suc_H,axiom,
% 0.33/0.60 ! [M2: nat,N2: nat,G: nat > int] :
% 0.33/0.60 ( ( ord_less_eq_nat @ M2 @ ( suc @ N2 ) )
% 0.33/0.60 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N2 ) ) )
% 0.33/0.60 = ( times_times_int @ ( G @ ( suc @ N2 ) ) @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.nat_ivl_Suc'
% 0.33/0.60 thf(fact_4494_prod_OatLeast__Suc__atMost,axiom,
% 0.33/0.60 ! [M2: nat,N2: nat,G: nat > assn] :
% 0.33/0.60 ( ( ord_less_eq_nat @ M2 @ N2 )
% 0.33/0.60 => ( ( groups6906906614972039071t_assn @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 0.33/0.60 = ( times_times_assn @ ( G @ M2 ) @ ( groups6906906614972039071t_assn @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N2 ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.atLeast_Suc_atMost
% 0.33/0.60 thf(fact_4495_prod_OatLeast__Suc__atMost,axiom,
% 0.33/0.60 ! [M2: nat,N2: nat,G: nat > rat] :
% 0.33/0.60 ( ( ord_less_eq_nat @ M2 @ N2 )
% 0.33/0.60 => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 0.33/0.60 = ( times_times_rat @ ( G @ M2 ) @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N2 ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.atLeast_Suc_atMost
% 0.33/0.60 thf(fact_4496_prod_OatLeast__Suc__atMost,axiom,
% 0.33/0.60 ! [M2: nat,N2: nat,G: nat > nat] :
% 0.33/0.60 ( ( ord_less_eq_nat @ M2 @ N2 )
% 0.33/0.60 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 0.33/0.60 = ( times_times_nat @ ( G @ M2 ) @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N2 ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.atLeast_Suc_atMost
% 0.33/0.60 thf(fact_4497_prod_OatLeast__Suc__atMost,axiom,
% 0.33/0.60 ! [M2: nat,N2: nat,G: nat > int] :
% 0.33/0.60 ( ( ord_less_eq_nat @ M2 @ N2 )
% 0.33/0.60 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 0.33/0.60 = ( times_times_int @ ( G @ M2 ) @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N2 ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.atLeast_Suc_atMost
% 0.33/0.60 thf(fact_4498_prod_OatLeastLessThan__Suc,axiom,
% 0.33/0.60 ! [A: nat,B: nat,G: nat > assn] :
% 0.33/0.60 ( ( ord_less_eq_nat @ A @ B )
% 0.33/0.60 => ( ( groups6906906614972039071t_assn @ G @ ( set_or4665077453230672383an_nat @ A @ ( suc @ B ) ) )
% 0.33/0.60 = ( times_times_assn @ ( groups6906906614972039071t_assn @ G @ ( set_or4665077453230672383an_nat @ A @ B ) ) @ ( G @ B ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.atLeastLessThan_Suc
% 0.33/0.60 thf(fact_4499_prod_OatLeastLessThan__Suc,axiom,
% 0.33/0.60 ! [A: nat,B: nat,G: nat > rat] :
% 0.33/0.60 ( ( ord_less_eq_nat @ A @ B )
% 0.33/0.60 => ( ( groups73079841787564623at_rat @ G @ ( set_or4665077453230672383an_nat @ A @ ( suc @ B ) ) )
% 0.33/0.60 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or4665077453230672383an_nat @ A @ B ) ) @ ( G @ B ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.atLeastLessThan_Suc
% 0.33/0.60 thf(fact_4500_prod_OatLeastLessThan__Suc,axiom,
% 0.33/0.60 ! [A: nat,B: nat,G: nat > nat] :
% 0.33/0.60 ( ( ord_less_eq_nat @ A @ B )
% 0.33/0.60 => ( ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ A @ ( suc @ B ) ) )
% 0.33/0.60 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ A @ B ) ) @ ( G @ B ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.atLeastLessThan_Suc
% 0.33/0.60 thf(fact_4501_prod_OatLeastLessThan__Suc,axiom,
% 0.33/0.60 ! [A: nat,B: nat,G: nat > int] :
% 0.33/0.60 ( ( ord_less_eq_nat @ A @ B )
% 0.33/0.60 => ( ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ A @ ( suc @ B ) ) )
% 0.33/0.60 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ A @ B ) ) @ ( G @ B ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.atLeastLessThan_Suc
% 0.33/0.60 thf(fact_4502_divmod__abs__code_I6_J,axiom,
% 0.33/0.60 ! [J: code_integer] :
% 0.33/0.60 ( ( code_divmod_abs @ zero_z3403309356797280102nteger @ J )
% 0.33/0.60 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger ) ) ).
% 0.33/0.60
% 0.33/0.60 % divmod_abs_code(6)
% 0.33/0.60 thf(fact_4503_prod_Olast__plus,axiom,
% 0.33/0.60 ! [M2: nat,N2: nat,G: nat > assn] :
% 0.33/0.60 ( ( ord_less_eq_nat @ M2 @ N2 )
% 0.33/0.60 => ( ( groups6906906614972039071t_assn @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 0.33/0.60 = ( times_times_assn @ ( G @ N2 ) @ ( groups6906906614972039071t_assn @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.last_plus
% 0.33/0.60 thf(fact_4504_prod_Olast__plus,axiom,
% 0.33/0.60 ! [M2: nat,N2: nat,G: nat > rat] :
% 0.33/0.60 ( ( ord_less_eq_nat @ M2 @ N2 )
% 0.33/0.60 => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 0.33/0.60 = ( times_times_rat @ ( G @ N2 ) @ ( groups73079841787564623at_rat @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.last_plus
% 0.33/0.60 thf(fact_4505_prod_Olast__plus,axiom,
% 0.33/0.60 ! [M2: nat,N2: nat,G: nat > nat] :
% 0.33/0.60 ( ( ord_less_eq_nat @ M2 @ N2 )
% 0.33/0.60 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 0.33/0.60 = ( times_times_nat @ ( G @ N2 ) @ ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.last_plus
% 0.33/0.60 thf(fact_4506_prod_Olast__plus,axiom,
% 0.33/0.60 ! [M2: nat,N2: nat,G: nat > int] :
% 0.33/0.60 ( ( ord_less_eq_nat @ M2 @ N2 )
% 0.33/0.60 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 0.33/0.60 = ( times_times_int @ ( G @ N2 ) @ ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.last_plus
% 0.33/0.60 thf(fact_4507_prod_OSuc__reindex__ivl,axiom,
% 0.33/0.60 ! [M2: nat,N2: nat,G: nat > assn] :
% 0.33/0.60 ( ( ord_less_eq_nat @ M2 @ N2 )
% 0.33/0.60 => ( ( times_times_assn @ ( groups6906906614972039071t_assn @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 0.33/0.60 = ( times_times_assn @ ( G @ M2 )
% 0.33/0.60 @ ( groups6906906614972039071t_assn
% 0.33/0.60 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 0.33/0.60 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.Suc_reindex_ivl
% 0.33/0.60 thf(fact_4508_prod_OSuc__reindex__ivl,axiom,
% 0.33/0.60 ! [M2: nat,N2: nat,G: nat > rat] :
% 0.33/0.60 ( ( ord_less_eq_nat @ M2 @ N2 )
% 0.33/0.60 => ( ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 0.33/0.60 = ( times_times_rat @ ( G @ M2 )
% 0.33/0.60 @ ( groups73079841787564623at_rat
% 0.33/0.60 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 0.33/0.60 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.Suc_reindex_ivl
% 0.33/0.60 thf(fact_4509_prod_OSuc__reindex__ivl,axiom,
% 0.33/0.60 ! [M2: nat,N2: nat,G: nat > nat] :
% 0.33/0.60 ( ( ord_less_eq_nat @ M2 @ N2 )
% 0.33/0.60 => ( ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 0.33/0.60 = ( times_times_nat @ ( G @ M2 )
% 0.33/0.60 @ ( groups708209901874060359at_nat
% 0.33/0.60 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 0.33/0.60 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.Suc_reindex_ivl
% 0.33/0.60 thf(fact_4510_prod_OSuc__reindex__ivl,axiom,
% 0.33/0.60 ! [M2: nat,N2: nat,G: nat > int] :
% 0.33/0.60 ( ( ord_less_eq_nat @ M2 @ N2 )
% 0.33/0.60 => ( ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 0.33/0.60 = ( times_times_int @ ( G @ M2 )
% 0.33/0.60 @ ( groups705719431365010083at_int
% 0.33/0.60 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 0.33/0.60 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.Suc_reindex_ivl
% 0.33/0.60 thf(fact_4511_prod_OatMost__Suc__shift,axiom,
% 0.33/0.60 ! [G: nat > assn,N2: nat] :
% 0.33/0.60 ( ( groups6906906614972039071t_assn @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 0.33/0.60 = ( times_times_assn @ ( G @ zero_zero_nat )
% 0.33/0.60 @ ( groups6906906614972039071t_assn
% 0.33/0.60 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 0.33/0.60 @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.atMost_Suc_shift
% 0.33/0.60 thf(fact_4512_prod_OatMost__Suc__shift,axiom,
% 0.33/0.60 ! [G: nat > rat,N2: nat] :
% 0.33/0.60 ( ( groups73079841787564623at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 0.33/0.60 = ( times_times_rat @ ( G @ zero_zero_nat )
% 0.33/0.60 @ ( groups73079841787564623at_rat
% 0.33/0.60 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 0.33/0.60 @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.atMost_Suc_shift
% 0.33/0.60 thf(fact_4513_prod_OatMost__Suc__shift,axiom,
% 0.33/0.60 ! [G: nat > nat,N2: nat] :
% 0.33/0.60 ( ( groups708209901874060359at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 0.33/0.60 = ( times_times_nat @ ( G @ zero_zero_nat )
% 0.33/0.60 @ ( groups708209901874060359at_nat
% 0.33/0.60 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 0.33/0.60 @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.atMost_Suc_shift
% 0.33/0.60 thf(fact_4514_prod_OatMost__Suc__shift,axiom,
% 0.33/0.60 ! [G: nat > int,N2: nat] :
% 0.33/0.60 ( ( groups705719431365010083at_int @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 0.33/0.60 = ( times_times_int @ ( G @ zero_zero_nat )
% 0.33/0.60 @ ( groups705719431365010083at_int
% 0.33/0.60 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 0.33/0.60 @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.atMost_Suc_shift
% 0.33/0.60 thf(fact_4515_prod_OlessThan__Suc__shift,axiom,
% 0.33/0.60 ! [G: nat > assn,N2: nat] :
% 0.33/0.60 ( ( groups6906906614972039071t_assn @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 0.33/0.60 = ( times_times_assn @ ( G @ zero_zero_nat )
% 0.33/0.60 @ ( groups6906906614972039071t_assn
% 0.33/0.60 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 0.33/0.60 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.lessThan_Suc_shift
% 0.33/0.60 thf(fact_4516_prod_OlessThan__Suc__shift,axiom,
% 0.33/0.60 ! [G: nat > rat,N2: nat] :
% 0.33/0.60 ( ( groups73079841787564623at_rat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 0.33/0.60 = ( times_times_rat @ ( G @ zero_zero_nat )
% 0.33/0.60 @ ( groups73079841787564623at_rat
% 0.33/0.60 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 0.33/0.60 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.lessThan_Suc_shift
% 0.33/0.60 thf(fact_4517_prod_OlessThan__Suc__shift,axiom,
% 0.33/0.60 ! [G: nat > nat,N2: nat] :
% 0.33/0.60 ( ( groups708209901874060359at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 0.33/0.60 = ( times_times_nat @ ( G @ zero_zero_nat )
% 0.33/0.60 @ ( groups708209901874060359at_nat
% 0.33/0.60 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 0.33/0.60 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.lessThan_Suc_shift
% 0.33/0.60 thf(fact_4518_prod_OlessThan__Suc__shift,axiom,
% 0.33/0.60 ! [G: nat > int,N2: nat] :
% 0.33/0.60 ( ( groups705719431365010083at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 0.33/0.60 = ( times_times_int @ ( G @ zero_zero_nat )
% 0.33/0.60 @ ( groups705719431365010083at_int
% 0.33/0.60 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 0.33/0.60 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.lessThan_Suc_shift
% 0.33/0.60 thf(fact_4519_prod_OatLeastLessThan__rev,axiom,
% 0.33/0.60 ! [G: nat > nat,N2: nat,M2: nat] :
% 0.33/0.60 ( ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ N2 @ M2 ) )
% 0.33/0.60 = ( groups708209901874060359at_nat
% 0.33/0.60 @ ^ [I3: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M2 @ N2 ) @ ( suc @ I3 ) ) )
% 0.33/0.60 @ ( set_or4665077453230672383an_nat @ N2 @ M2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.atLeastLessThan_rev
% 0.33/0.60 thf(fact_4520_prod_OatLeastLessThan__rev,axiom,
% 0.33/0.60 ! [G: nat > int,N2: nat,M2: nat] :
% 0.33/0.60 ( ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ N2 @ M2 ) )
% 0.33/0.60 = ( groups705719431365010083at_int
% 0.33/0.60 @ ^ [I3: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M2 @ N2 ) @ ( suc @ I3 ) ) )
% 0.33/0.60 @ ( set_or4665077453230672383an_nat @ N2 @ M2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.atLeastLessThan_rev
% 0.33/0.60 thf(fact_4521_prod_Onested__swap,axiom,
% 0.33/0.60 ! [A: nat > nat > nat,N2: nat] :
% 0.33/0.60 ( ( groups708209901874060359at_nat
% 0.33/0.60 @ ^ [I3: nat] : ( groups708209901874060359at_nat @ ( A @ I3 ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ I3 ) )
% 0.33/0.60 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 0.33/0.60 = ( groups708209901874060359at_nat
% 0.33/0.60 @ ^ [J2: nat] :
% 0.33/0.60 ( groups708209901874060359at_nat
% 0.33/0.60 @ ^ [I3: nat] : ( A @ I3 @ J2 )
% 0.33/0.60 @ ( set_or1269000886237332187st_nat @ ( suc @ J2 ) @ N2 ) )
% 0.33/0.60 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.nested_swap
% 0.33/0.60 thf(fact_4522_prod_Onested__swap,axiom,
% 0.33/0.60 ! [A: nat > nat > int,N2: nat] :
% 0.33/0.60 ( ( groups705719431365010083at_int
% 0.33/0.60 @ ^ [I3: nat] : ( groups705719431365010083at_int @ ( A @ I3 ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ I3 ) )
% 0.33/0.60 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 0.33/0.60 = ( groups705719431365010083at_int
% 0.33/0.60 @ ^ [J2: nat] :
% 0.33/0.60 ( groups705719431365010083at_int
% 0.33/0.60 @ ^ [I3: nat] : ( A @ I3 @ J2 )
% 0.33/0.60 @ ( set_or1269000886237332187st_nat @ ( suc @ J2 ) @ N2 ) )
% 0.33/0.60 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.nested_swap
% 0.33/0.60 thf(fact_4523_prod_OatLeast1__atMost__eq,axiom,
% 0.33/0.60 ! [G: nat > nat,N2: nat] :
% 0.33/0.60 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 0.33/0.60 = ( groups708209901874060359at_nat
% 0.33/0.60 @ ^ [K4: nat] : ( G @ ( suc @ K4 ) )
% 0.33/0.60 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.atLeast1_atMost_eq
% 0.33/0.60 thf(fact_4524_prod_OatLeast1__atMost__eq,axiom,
% 0.33/0.60 ! [G: nat > int,N2: nat] :
% 0.33/0.60 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 0.33/0.60 = ( groups705719431365010083at_int
% 0.33/0.60 @ ^ [K4: nat] : ( G @ ( suc @ K4 ) )
% 0.33/0.60 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.atLeast1_atMost_eq
% 0.33/0.60 thf(fact_4525_prod_Onat__group,axiom,
% 0.33/0.60 ! [G: nat > nat,K: nat,N2: nat] :
% 0.33/0.60 ( ( groups708209901874060359at_nat
% 0.33/0.60 @ ^ [M: nat] : ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ ( times_times_nat @ M @ K ) @ ( plus_plus_nat @ ( times_times_nat @ M @ K ) @ K ) ) )
% 0.33/0.60 @ ( set_ord_lessThan_nat @ N2 ) )
% 0.33/0.60 = ( groups708209901874060359at_nat @ G @ ( set_ord_lessThan_nat @ ( times_times_nat @ N2 @ K ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.nat_group
% 0.33/0.60 thf(fact_4526_prod_Onat__group,axiom,
% 0.33/0.60 ! [G: nat > int,K: nat,N2: nat] :
% 0.33/0.60 ( ( groups705719431365010083at_int
% 0.33/0.60 @ ^ [M: nat] : ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ ( times_times_nat @ M @ K ) @ ( plus_plus_nat @ ( times_times_nat @ M @ K ) @ K ) ) )
% 0.33/0.60 @ ( set_ord_lessThan_nat @ N2 ) )
% 0.33/0.60 = ( groups705719431365010083at_int @ G @ ( set_ord_lessThan_nat @ ( times_times_nat @ N2 @ K ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.nat_group
% 0.33/0.60 thf(fact_4527_fact__prod,axiom,
% 0.33/0.60 ( semiri1406184849735516958ct_int
% 0.33/0.60 = ( ^ [N4: nat] :
% 0.33/0.60 ( semiri1314217659103216013at_int
% 0.33/0.60 @ ( groups708209901874060359at_nat
% 0.33/0.60 @ ^ [X3: nat] : X3
% 0.33/0.60 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N4 ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % fact_prod
% 0.33/0.60 thf(fact_4528_fact__prod,axiom,
% 0.33/0.60 ( semiri3624122377584611663nteger
% 0.33/0.60 = ( ^ [N4: nat] :
% 0.33/0.60 ( semiri4939895301339042750nteger
% 0.33/0.60 @ ( groups708209901874060359at_nat
% 0.33/0.60 @ ^ [X3: nat] : X3
% 0.33/0.60 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N4 ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % fact_prod
% 0.33/0.60 thf(fact_4529_fact__prod,axiom,
% 0.33/0.60 ( semiri2447717529341329178atural
% 0.33/0.60 = ( ^ [N4: nat] :
% 0.33/0.60 ( semiri3763490453095760265atural
% 0.33/0.60 @ ( groups708209901874060359at_nat
% 0.33/0.60 @ ^ [X3: nat] : X3
% 0.33/0.60 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N4 ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % fact_prod
% 0.33/0.60 thf(fact_4530_fact__prod,axiom,
% 0.33/0.60 ( semiri1408675320244567234ct_nat
% 0.33/0.60 = ( ^ [N4: nat] :
% 0.33/0.60 ( semiri1316708129612266289at_nat
% 0.33/0.60 @ ( groups708209901874060359at_nat
% 0.33/0.60 @ ^ [X3: nat] : X3
% 0.33/0.60 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N4 ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % fact_prod
% 0.33/0.60 thf(fact_4531_prod_Onested__swap_H,axiom,
% 0.33/0.60 ! [A: nat > nat > nat,N2: nat] :
% 0.33/0.60 ( ( groups708209901874060359at_nat
% 0.33/0.60 @ ^ [I3: nat] : ( groups708209901874060359at_nat @ ( A @ I3 ) @ ( set_ord_lessThan_nat @ I3 ) )
% 0.33/0.60 @ ( set_ord_atMost_nat @ N2 ) )
% 0.33/0.60 = ( groups708209901874060359at_nat
% 0.33/0.60 @ ^ [J2: nat] :
% 0.33/0.60 ( groups708209901874060359at_nat
% 0.33/0.60 @ ^ [I3: nat] : ( A @ I3 @ J2 )
% 0.33/0.60 @ ( set_or1269000886237332187st_nat @ ( suc @ J2 ) @ N2 ) )
% 0.33/0.60 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.nested_swap'
% 0.33/0.60 thf(fact_4532_prod_Onested__swap_H,axiom,
% 0.33/0.60 ! [A: nat > nat > int,N2: nat] :
% 0.33/0.60 ( ( groups705719431365010083at_int
% 0.33/0.60 @ ^ [I3: nat] : ( groups705719431365010083at_int @ ( A @ I3 ) @ ( set_ord_lessThan_nat @ I3 ) )
% 0.33/0.60 @ ( set_ord_atMost_nat @ N2 ) )
% 0.33/0.60 = ( groups705719431365010083at_int
% 0.33/0.60 @ ^ [J2: nat] :
% 0.33/0.60 ( groups705719431365010083at_int
% 0.33/0.60 @ ^ [I3: nat] : ( A @ I3 @ J2 )
% 0.33/0.60 @ ( set_or1269000886237332187st_nat @ ( suc @ J2 ) @ N2 ) )
% 0.33/0.60 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.nested_swap'
% 0.33/0.60 thf(fact_4533_prod__atLeastAtMost__code,axiom,
% 0.33/0.60 ! [F: nat > code_integer,A: nat,B: nat] :
% 0.33/0.60 ( ( groups3455450783089532116nteger @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 0.33/0.60 = ( set_fo1084959871951514735nteger
% 0.33/0.60 @ ^ [A5: nat] : ( times_3573771949741848930nteger @ ( F @ A5 ) )
% 0.33/0.60 @ A
% 0.33/0.60 @ B
% 0.33/0.60 @ one_one_Code_integer ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod_atLeastAtMost_code
% 0.33/0.60 thf(fact_4534_prod__atLeastAtMost__code,axiom,
% 0.33/0.60 ! [F: nat > assn,A: nat,B: nat] :
% 0.33/0.60 ( ( groups6906906614972039071t_assn @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 0.33/0.60 = ( set_fo1959793692361082170t_assn
% 0.33/0.60 @ ^ [A5: nat] : ( times_times_assn @ ( F @ A5 ) )
% 0.33/0.60 @ A
% 0.33/0.60 @ B
% 0.33/0.60 @ one_one_assn ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod_atLeastAtMost_code
% 0.33/0.60 thf(fact_4535_prod__atLeastAtMost__code,axiom,
% 0.33/0.60 ! [F: nat > rat,A: nat,B: nat] :
% 0.33/0.60 ( ( groups73079841787564623at_rat @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 0.33/0.60 = ( set_fo1949268297981939178at_rat
% 0.33/0.60 @ ^ [A5: nat] : ( times_times_rat @ ( F @ A5 ) )
% 0.33/0.60 @ A
% 0.33/0.60 @ B
% 0.33/0.60 @ one_one_rat ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod_atLeastAtMost_code
% 0.33/0.60 thf(fact_4536_prod__atLeastAtMost__code,axiom,
% 0.33/0.60 ! [F: nat > nat,A: nat,B: nat] :
% 0.33/0.60 ( ( groups708209901874060359at_nat @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 0.33/0.60 = ( set_fo2584398358068434914at_nat
% 0.33/0.60 @ ^ [A5: nat] : ( times_times_nat @ ( F @ A5 ) )
% 0.33/0.60 @ A
% 0.33/0.60 @ B
% 0.33/0.60 @ one_one_nat ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod_atLeastAtMost_code
% 0.33/0.60 thf(fact_4537_prod__atLeastAtMost__code,axiom,
% 0.33/0.60 ! [F: nat > int,A: nat,B: nat] :
% 0.33/0.60 ( ( groups705719431365010083at_int @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 0.33/0.60 = ( set_fo2581907887559384638at_int
% 0.33/0.60 @ ^ [A5: nat] : ( times_times_int @ ( F @ A5 ) )
% 0.33/0.60 @ A
% 0.33/0.60 @ B
% 0.33/0.60 @ one_one_int ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod_atLeastAtMost_code
% 0.33/0.60 thf(fact_4538_prod_Ohead__if,axiom,
% 0.33/0.60 ! [N2: nat,M2: nat,G: nat > code_integer] :
% 0.33/0.60 ( ( ( ord_less_nat @ N2 @ M2 )
% 0.33/0.60 => ( ( groups3455450783089532116nteger @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 0.33/0.60 = one_one_Code_integer ) )
% 0.33/0.60 & ( ~ ( ord_less_nat @ N2 @ M2 )
% 0.33/0.60 => ( ( groups3455450783089532116nteger @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 0.33/0.60 = ( times_3573771949741848930nteger @ ( groups3455450783089532116nteger @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) @ ( G @ N2 ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.head_if
% 0.33/0.60 thf(fact_4539_prod_Ohead__if,axiom,
% 0.33/0.60 ! [N2: nat,M2: nat,G: nat > assn] :
% 0.33/0.60 ( ( ( ord_less_nat @ N2 @ M2 )
% 0.33/0.60 => ( ( groups6906906614972039071t_assn @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 0.33/0.60 = one_one_assn ) )
% 0.33/0.60 & ( ~ ( ord_less_nat @ N2 @ M2 )
% 0.33/0.60 => ( ( groups6906906614972039071t_assn @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 0.33/0.60 = ( times_times_assn @ ( groups6906906614972039071t_assn @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) @ ( G @ N2 ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.head_if
% 0.33/0.60 thf(fact_4540_prod_Ohead__if,axiom,
% 0.33/0.60 ! [N2: nat,M2: nat,G: nat > rat] :
% 0.33/0.60 ( ( ( ord_less_nat @ N2 @ M2 )
% 0.33/0.60 => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 0.33/0.60 = one_one_rat ) )
% 0.33/0.60 & ( ~ ( ord_less_nat @ N2 @ M2 )
% 0.33/0.60 => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 0.33/0.60 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) @ ( G @ N2 ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.head_if
% 0.33/0.60 thf(fact_4541_prod_Ohead__if,axiom,
% 0.33/0.60 ! [N2: nat,M2: nat,G: nat > nat] :
% 0.33/0.60 ( ( ( ord_less_nat @ N2 @ M2 )
% 0.33/0.60 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 0.33/0.60 = one_one_nat ) )
% 0.33/0.60 & ( ~ ( ord_less_nat @ N2 @ M2 )
% 0.33/0.60 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 0.33/0.60 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) @ ( G @ N2 ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.head_if
% 0.33/0.60 thf(fact_4542_prod_Ohead__if,axiom,
% 0.33/0.60 ! [N2: nat,M2: nat,G: nat > int] :
% 0.33/0.60 ( ( ( ord_less_nat @ N2 @ M2 )
% 0.33/0.60 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 0.33/0.60 = one_one_int ) )
% 0.33/0.60 & ( ~ ( ord_less_nat @ N2 @ M2 )
% 0.33/0.60 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 0.33/0.60 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) @ ( G @ N2 ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.head_if
% 0.33/0.60 thf(fact_4543_prod_Oub__add__nat,axiom,
% 0.33/0.60 ! [M2: nat,N2: nat,G: nat > assn,P4: nat] :
% 0.33/0.60 ( ( ord_less_eq_nat @ M2 @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 0.33/0.60 => ( ( groups6906906614972039071t_assn @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ N2 @ P4 ) ) )
% 0.33/0.60 = ( times_times_assn @ ( groups6906906614972039071t_assn @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) @ ( groups6906906614972039071t_assn @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ ( plus_plus_nat @ N2 @ P4 ) ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.ub_add_nat
% 0.33/0.60 thf(fact_4544_prod_Oub__add__nat,axiom,
% 0.33/0.60 ! [M2: nat,N2: nat,G: nat > rat,P4: nat] :
% 0.33/0.60 ( ( ord_less_eq_nat @ M2 @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 0.33/0.60 => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ N2 @ P4 ) ) )
% 0.33/0.60 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ ( plus_plus_nat @ N2 @ P4 ) ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.ub_add_nat
% 0.33/0.60 thf(fact_4545_prod_Oub__add__nat,axiom,
% 0.33/0.60 ! [M2: nat,N2: nat,G: nat > nat,P4: nat] :
% 0.33/0.60 ( ( ord_less_eq_nat @ M2 @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 0.33/0.60 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ N2 @ P4 ) ) )
% 0.33/0.60 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ ( plus_plus_nat @ N2 @ P4 ) ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.ub_add_nat
% 0.33/0.60 thf(fact_4546_prod_Oub__add__nat,axiom,
% 0.33/0.60 ! [M2: nat,N2: nat,G: nat > int,P4: nat] :
% 0.33/0.60 ( ( ord_less_eq_nat @ M2 @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 0.33/0.60 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ N2 @ P4 ) ) )
% 0.33/0.60 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ ( plus_plus_nat @ N2 @ P4 ) ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.ub_add_nat
% 0.33/0.60 thf(fact_4547_prod_OatLeast0__atMost__Suc__shift,axiom,
% 0.33/0.60 ! [G: nat > assn,N2: nat] :
% 0.33/0.60 ( ( groups6906906614972039071t_assn @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 0.33/0.60 = ( times_times_assn @ ( G @ zero_zero_nat ) @ ( groups6906906614972039071t_assn @ ( comp_nat_assn_nat @ G @ suc ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.atLeast0_atMost_Suc_shift
% 0.33/0.60 thf(fact_4548_prod_OatLeast0__atMost__Suc__shift,axiom,
% 0.33/0.60 ! [G: nat > rat,N2: nat] :
% 0.33/0.60 ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 0.33/0.60 = ( times_times_rat @ ( G @ zero_zero_nat ) @ ( groups73079841787564623at_rat @ ( comp_nat_rat_nat @ G @ suc ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.atLeast0_atMost_Suc_shift
% 0.33/0.60 thf(fact_4549_prod_OatLeast0__atMost__Suc__shift,axiom,
% 0.33/0.60 ! [G: nat > nat,N2: nat] :
% 0.33/0.60 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 0.33/0.60 = ( times_times_nat @ ( G @ zero_zero_nat ) @ ( groups708209901874060359at_nat @ ( comp_nat_nat_nat @ G @ suc ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.atLeast0_atMost_Suc_shift
% 0.33/0.60 thf(fact_4550_prod_OatLeast0__atMost__Suc__shift,axiom,
% 0.33/0.60 ! [G: nat > int,N2: nat] :
% 0.33/0.60 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 0.33/0.60 = ( times_times_int @ ( G @ zero_zero_nat ) @ ( groups705719431365010083at_int @ ( comp_nat_int_nat @ G @ suc ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.atLeast0_atMost_Suc_shift
% 0.33/0.60 thf(fact_4551_prod_OatLeast0__lessThan__Suc__shift,axiom,
% 0.33/0.60 ! [G: nat > assn,N2: nat] :
% 0.33/0.60 ( ( groups6906906614972039071t_assn @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 0.33/0.60 = ( times_times_assn @ ( G @ zero_zero_nat ) @ ( groups6906906614972039071t_assn @ ( comp_nat_assn_nat @ G @ suc ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.atLeast0_lessThan_Suc_shift
% 0.33/0.60 thf(fact_4552_prod_OatLeast0__lessThan__Suc__shift,axiom,
% 0.33/0.60 ! [G: nat > rat,N2: nat] :
% 0.33/0.60 ( ( groups73079841787564623at_rat @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 0.33/0.60 = ( times_times_rat @ ( G @ zero_zero_nat ) @ ( groups73079841787564623at_rat @ ( comp_nat_rat_nat @ G @ suc ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.atLeast0_lessThan_Suc_shift
% 0.33/0.60 thf(fact_4553_prod_OatLeast0__lessThan__Suc__shift,axiom,
% 0.33/0.60 ! [G: nat > nat,N2: nat] :
% 0.33/0.60 ( ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 0.33/0.60 = ( times_times_nat @ ( G @ zero_zero_nat ) @ ( groups708209901874060359at_nat @ ( comp_nat_nat_nat @ G @ suc ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.atLeast0_lessThan_Suc_shift
% 0.33/0.60 thf(fact_4554_prod_OatLeast0__lessThan__Suc__shift,axiom,
% 0.33/0.60 ! [G: nat > int,N2: nat] :
% 0.33/0.60 ( ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 0.33/0.60 = ( times_times_int @ ( G @ zero_zero_nat ) @ ( groups705719431365010083at_int @ ( comp_nat_int_nat @ G @ suc ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.atLeast0_lessThan_Suc_shift
% 0.33/0.60 thf(fact_4555_prod_OatLeastLessThan__shift__0,axiom,
% 0.33/0.60 ! [G: nat > nat,M2: nat,N2: nat] :
% 0.33/0.60 ( ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) )
% 0.33/0.60 = ( groups708209901874060359at_nat @ ( comp_nat_nat_nat @ G @ ( plus_plus_nat @ M2 ) ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( minus_minus_nat @ N2 @ M2 ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.atLeastLessThan_shift_0
% 0.33/0.60 thf(fact_4556_prod_OatLeastLessThan__shift__0,axiom,
% 0.33/0.60 ! [G: nat > int,M2: nat,N2: nat] :
% 0.33/0.60 ( ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) )
% 0.33/0.60 = ( groups705719431365010083at_int @ ( comp_nat_int_nat @ G @ ( plus_plus_nat @ M2 ) ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( minus_minus_nat @ N2 @ M2 ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.atLeastLessThan_shift_0
% 0.33/0.60 thf(fact_4557_integer__of__num__triv_I1_J,axiom,
% 0.33/0.60 ( ( code_integer_of_num @ one )
% 0.33/0.60 = one_one_Code_integer ) ).
% 0.33/0.60
% 0.33/0.60 % integer_of_num_triv(1)
% 0.33/0.60 thf(fact_4558_prod_OatLeastLessThan__rev__at__least__Suc__atMost,axiom,
% 0.33/0.60 ! [G: nat > nat,N2: nat,M2: nat] :
% 0.33/0.60 ( ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ N2 @ M2 ) )
% 0.33/0.60 = ( groups708209901874060359at_nat
% 0.33/0.60 @ ^ [I3: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M2 @ N2 ) @ I3 ) )
% 0.33/0.60 @ ( set_or1269000886237332187st_nat @ ( suc @ N2 ) @ M2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.atLeastLessThan_rev_at_least_Suc_atMost
% 0.33/0.60 thf(fact_4559_prod_OatLeastLessThan__rev__at__least__Suc__atMost,axiom,
% 0.33/0.60 ! [G: nat > int,N2: nat,M2: nat] :
% 0.33/0.60 ( ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ N2 @ M2 ) )
% 0.33/0.60 = ( groups705719431365010083at_int
% 0.33/0.60 @ ^ [I3: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M2 @ N2 ) @ I3 ) )
% 0.33/0.60 @ ( set_or1269000886237332187st_nat @ ( suc @ N2 ) @ M2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.atLeastLessThan_rev_at_least_Suc_atMost
% 0.33/0.60 thf(fact_4560_prod_OatMost__shift,axiom,
% 0.33/0.60 ! [G: nat > assn,N2: nat] :
% 0.33/0.60 ( ( groups6906906614972039071t_assn @ G @ ( set_ord_atMost_nat @ N2 ) )
% 0.33/0.60 = ( times_times_assn @ ( G @ zero_zero_nat )
% 0.33/0.60 @ ( groups6906906614972039071t_assn
% 0.33/0.60 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 0.33/0.60 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.atMost_shift
% 0.33/0.60 thf(fact_4561_prod_OatMost__shift,axiom,
% 0.33/0.60 ! [G: nat > rat,N2: nat] :
% 0.33/0.60 ( ( groups73079841787564623at_rat @ G @ ( set_ord_atMost_nat @ N2 ) )
% 0.33/0.60 = ( times_times_rat @ ( G @ zero_zero_nat )
% 0.33/0.60 @ ( groups73079841787564623at_rat
% 0.33/0.60 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 0.33/0.60 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.atMost_shift
% 0.33/0.60 thf(fact_4562_prod_OatMost__shift,axiom,
% 0.33/0.60 ! [G: nat > nat,N2: nat] :
% 0.33/0.60 ( ( groups708209901874060359at_nat @ G @ ( set_ord_atMost_nat @ N2 ) )
% 0.33/0.60 = ( times_times_nat @ ( G @ zero_zero_nat )
% 0.33/0.60 @ ( groups708209901874060359at_nat
% 0.33/0.60 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 0.33/0.60 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.atMost_shift
% 0.33/0.60 thf(fact_4563_prod_OatMost__shift,axiom,
% 0.33/0.60 ! [G: nat > int,N2: nat] :
% 0.33/0.60 ( ( groups705719431365010083at_int @ G @ ( set_ord_atMost_nat @ N2 ) )
% 0.33/0.60 = ( times_times_int @ ( G @ zero_zero_nat )
% 0.33/0.60 @ ( groups705719431365010083at_int
% 0.33/0.60 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 0.33/0.60 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.atMost_shift
% 0.33/0.60 thf(fact_4564_pochhammer__prod,axiom,
% 0.33/0.60 ( comm_s4028243227959126397er_rat
% 0.33/0.60 = ( ^ [A5: rat,N4: nat] :
% 0.33/0.60 ( groups73079841787564623at_rat
% 0.33/0.60 @ ^ [I3: nat] : ( plus_plus_rat @ A5 @ ( semiri681578069525770553at_rat @ I3 ) )
% 0.33/0.60 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N4 ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % pochhammer_prod
% 0.33/0.60 thf(fact_4565_pochhammer__prod,axiom,
% 0.33/0.60 ( comm_s8582702949713902594nteger
% 0.33/0.60 = ( ^ [A5: code_integer,N4: nat] :
% 0.33/0.60 ( groups3455450783089532116nteger
% 0.33/0.60 @ ^ [I3: nat] : ( plus_p5714425477246183910nteger @ A5 @ ( semiri4939895301339042750nteger @ I3 ) )
% 0.33/0.60 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N4 ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % pochhammer_prod
% 0.33/0.60 thf(fact_4566_pochhammer__prod,axiom,
% 0.33/0.60 ( comm_s7406298101470620109atural
% 0.33/0.60 = ( ^ [A5: code_natural,N4: nat] :
% 0.33/0.60 ( groups2279045934846249631atural
% 0.33/0.60 @ ^ [I3: nat] : ( plus_p4538020629002901425atural @ A5 @ ( semiri3763490453095760265atural @ I3 ) )
% 0.33/0.60 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N4 ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % pochhammer_prod
% 0.33/0.60 thf(fact_4567_pochhammer__prod,axiom,
% 0.33/0.60 ( comm_s4663373288045622133er_nat
% 0.33/0.60 = ( ^ [A5: nat,N4: nat] :
% 0.33/0.60 ( groups708209901874060359at_nat
% 0.33/0.60 @ ^ [I3: nat] : ( plus_plus_nat @ A5 @ ( semiri1316708129612266289at_nat @ I3 ) )
% 0.33/0.60 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N4 ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % pochhammer_prod
% 0.33/0.60 thf(fact_4568_pochhammer__prod,axiom,
% 0.33/0.60 ( comm_s4660882817536571857er_int
% 0.33/0.60 = ( ^ [A5: int,N4: nat] :
% 0.33/0.60 ( groups705719431365010083at_int
% 0.33/0.60 @ ^ [I3: nat] : ( plus_plus_int @ A5 @ ( semiri1314217659103216013at_int @ I3 ) )
% 0.33/0.60 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N4 ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % pochhammer_prod
% 0.33/0.60 thf(fact_4569_prod_OatLeast__atMost__pred__shift,axiom,
% 0.33/0.60 ! [G: nat > nat,M2: nat,N2: nat] :
% 0.33/0.60 ( ( groups708209901874060359at_nat
% 0.33/0.60 @ ( comp_nat_nat_nat @ G
% 0.33/0.60 @ ^ [N4: nat] : ( minus_minus_nat @ N4 @ ( suc @ zero_zero_nat ) ) )
% 0.33/0.60 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ ( suc @ N2 ) ) )
% 0.33/0.60 = ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.atLeast_atMost_pred_shift
% 0.33/0.60 thf(fact_4570_prod_OatLeast__atMost__pred__shift,axiom,
% 0.33/0.60 ! [G: nat > int,M2: nat,N2: nat] :
% 0.33/0.60 ( ( groups705719431365010083at_int
% 0.33/0.60 @ ( comp_nat_int_nat @ G
% 0.33/0.60 @ ^ [N4: nat] : ( minus_minus_nat @ N4 @ ( suc @ zero_zero_nat ) ) )
% 0.33/0.60 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ ( suc @ N2 ) ) )
% 0.33/0.60 = ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.atLeast_atMost_pred_shift
% 0.33/0.60 thf(fact_4571_prod_OatLeast__lessThan__pred__shift,axiom,
% 0.33/0.60 ! [G: nat > nat,M2: nat,N2: nat] :
% 0.33/0.60 ( ( groups708209901874060359at_nat
% 0.33/0.60 @ ( comp_nat_nat_nat @ G
% 0.33/0.60 @ ^ [N4: nat] : ( minus_minus_nat @ N4 @ ( suc @ zero_zero_nat ) ) )
% 0.33/0.60 @ ( set_or4665077453230672383an_nat @ ( suc @ M2 ) @ ( suc @ N2 ) ) )
% 0.33/0.60 = ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.atLeast_lessThan_pred_shift
% 0.33/0.60 thf(fact_4572_prod_OatLeast__lessThan__pred__shift,axiom,
% 0.33/0.60 ! [G: nat > int,M2: nat,N2: nat] :
% 0.33/0.60 ( ( groups705719431365010083at_int
% 0.33/0.60 @ ( comp_nat_int_nat @ G
% 0.33/0.60 @ ^ [N4: nat] : ( minus_minus_nat @ N4 @ ( suc @ zero_zero_nat ) ) )
% 0.33/0.60 @ ( set_or4665077453230672383an_nat @ ( suc @ M2 ) @ ( suc @ N2 ) ) )
% 0.33/0.60 = ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.atLeast_lessThan_pred_shift
% 0.33/0.60 thf(fact_4573_integer__of__num_I2_J,axiom,
% 0.33/0.60 ! [N2: num] :
% 0.33/0.60 ( ( code_integer_of_num @ ( bit0 @ N2 ) )
% 0.33/0.60 = ( plus_p5714425477246183910nteger @ ( code_integer_of_num @ N2 ) @ ( code_integer_of_num @ N2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % integer_of_num(2)
% 0.33/0.60 thf(fact_4574_divmod__abs__code_I5_J,axiom,
% 0.33/0.60 ! [J: code_integer] :
% 0.33/0.60 ( ( code_divmod_abs @ J @ zero_z3403309356797280102nteger )
% 0.33/0.60 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ J ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % divmod_abs_code(5)
% 0.33/0.60 thf(fact_4575_prod_OatLeastAtMost__shift__0,axiom,
% 0.33/0.60 ! [M2: nat,N2: nat,G: nat > nat] :
% 0.33/0.60 ( ( ord_less_eq_nat @ M2 @ N2 )
% 0.33/0.60 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 0.33/0.60 = ( groups708209901874060359at_nat @ ( comp_nat_nat_nat @ G @ ( plus_plus_nat @ M2 ) ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( minus_minus_nat @ N2 @ M2 ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.atLeastAtMost_shift_0
% 0.33/0.60 thf(fact_4576_prod_OatLeastAtMost__shift__0,axiom,
% 0.33/0.60 ! [M2: nat,N2: nat,G: nat > int] :
% 0.33/0.60 ( ( ord_less_eq_nat @ M2 @ N2 )
% 0.33/0.60 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 0.33/0.60 = ( groups705719431365010083at_int @ ( comp_nat_int_nat @ G @ ( plus_plus_nat @ M2 ) ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( minus_minus_nat @ N2 @ M2 ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.atLeastAtMost_shift_0
% 0.33/0.60 thf(fact_4577_sum_OatLeast__int__lessThan__int__shift,axiom,
% 0.33/0.60 ! [G: int > nat,M2: nat,N2: nat] :
% 0.33/0.60 ( ( groups4541462559716669496nt_nat @ G @ ( set_or4662586982721622107an_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 0.33/0.60 = ( groups3542108847815614940at_nat @ ( comp_int_nat_nat @ G @ semiri1314217659103216013at_int ) @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % sum.atLeast_int_lessThan_int_shift
% 0.33/0.60 thf(fact_4578_sum_OatLeast__int__lessThan__int__shift,axiom,
% 0.33/0.60 ! [G: int > int,M2: nat,N2: nat] :
% 0.33/0.60 ( ( groups4538972089207619220nt_int @ G @ ( set_or4662586982721622107an_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 0.33/0.60 = ( groups3539618377306564664at_int @ ( comp_int_int_nat @ G @ semiri1314217659103216013at_int ) @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % sum.atLeast_int_lessThan_int_shift
% 0.33/0.60 thf(fact_4579_pochhammer__Suc__prod,axiom,
% 0.33/0.60 ! [A: rat,N2: nat] :
% 0.33/0.60 ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N2 ) )
% 0.33/0.60 = ( groups73079841787564623at_rat
% 0.33/0.60 @ ^ [I3: nat] : ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ I3 ) )
% 0.33/0.60 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % pochhammer_Suc_prod
% 0.33/0.60 thf(fact_4580_pochhammer__Suc__prod,axiom,
% 0.33/0.60 ! [A: code_integer,N2: nat] :
% 0.33/0.60 ( ( comm_s8582702949713902594nteger @ A @ ( suc @ N2 ) )
% 0.33/0.60 = ( groups3455450783089532116nteger
% 0.33/0.60 @ ^ [I3: nat] : ( plus_p5714425477246183910nteger @ A @ ( semiri4939895301339042750nteger @ I3 ) )
% 0.33/0.60 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % pochhammer_Suc_prod
% 0.33/0.60 thf(fact_4581_pochhammer__Suc__prod,axiom,
% 0.33/0.60 ! [A: code_natural,N2: nat] :
% 0.33/0.60 ( ( comm_s7406298101470620109atural @ A @ ( suc @ N2 ) )
% 0.33/0.60 = ( groups2279045934846249631atural
% 0.33/0.60 @ ^ [I3: nat] : ( plus_p4538020629002901425atural @ A @ ( semiri3763490453095760265atural @ I3 ) )
% 0.33/0.60 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % pochhammer_Suc_prod
% 0.33/0.60 thf(fact_4582_pochhammer__Suc__prod,axiom,
% 0.33/0.60 ! [A: nat,N2: nat] :
% 0.33/0.60 ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N2 ) )
% 0.33/0.60 = ( groups708209901874060359at_nat
% 0.33/0.60 @ ^ [I3: nat] : ( plus_plus_nat @ A @ ( semiri1316708129612266289at_nat @ I3 ) )
% 0.33/0.60 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % pochhammer_Suc_prod
% 0.33/0.60 thf(fact_4583_pochhammer__Suc__prod,axiom,
% 0.33/0.60 ! [A: int,N2: nat] :
% 0.33/0.60 ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N2 ) )
% 0.33/0.60 = ( groups705719431365010083at_int
% 0.33/0.60 @ ^ [I3: nat] : ( plus_plus_int @ A @ ( semiri1314217659103216013at_int @ I3 ) )
% 0.33/0.60 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % pochhammer_Suc_prod
% 0.33/0.60 thf(fact_4584_pochhammer__prod__rev,axiom,
% 0.33/0.60 ( comm_s4028243227959126397er_rat
% 0.33/0.60 = ( ^ [A5: rat,N4: nat] :
% 0.33/0.60 ( groups73079841787564623at_rat
% 0.33/0.60 @ ^ [I3: nat] : ( plus_plus_rat @ A5 @ ( semiri681578069525770553at_rat @ ( minus_minus_nat @ N4 @ I3 ) ) )
% 0.33/0.60 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N4 ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % pochhammer_prod_rev
% 0.33/0.60 thf(fact_4585_pochhammer__prod__rev,axiom,
% 0.33/0.60 ( comm_s8582702949713902594nteger
% 0.33/0.60 = ( ^ [A5: code_integer,N4: nat] :
% 0.33/0.60 ( groups3455450783089532116nteger
% 0.33/0.60 @ ^ [I3: nat] : ( plus_p5714425477246183910nteger @ A5 @ ( semiri4939895301339042750nteger @ ( minus_minus_nat @ N4 @ I3 ) ) )
% 0.33/0.60 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N4 ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % pochhammer_prod_rev
% 0.33/0.60 thf(fact_4586_pochhammer__prod__rev,axiom,
% 0.33/0.60 ( comm_s7406298101470620109atural
% 0.33/0.60 = ( ^ [A5: code_natural,N4: nat] :
% 0.33/0.60 ( groups2279045934846249631atural
% 0.33/0.60 @ ^ [I3: nat] : ( plus_p4538020629002901425atural @ A5 @ ( semiri3763490453095760265atural @ ( minus_minus_nat @ N4 @ I3 ) ) )
% 0.33/0.60 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N4 ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % pochhammer_prod_rev
% 0.33/0.60 thf(fact_4587_pochhammer__prod__rev,axiom,
% 0.33/0.60 ( comm_s4663373288045622133er_nat
% 0.33/0.60 = ( ^ [A5: nat,N4: nat] :
% 0.33/0.60 ( groups708209901874060359at_nat
% 0.33/0.60 @ ^ [I3: nat] : ( plus_plus_nat @ A5 @ ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ N4 @ I3 ) ) )
% 0.33/0.60 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N4 ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % pochhammer_prod_rev
% 0.33/0.60 thf(fact_4588_pochhammer__prod__rev,axiom,
% 0.33/0.60 ( comm_s4660882817536571857er_int
% 0.33/0.60 = ( ^ [A5: int,N4: nat] :
% 0.33/0.60 ( groups705719431365010083at_int
% 0.33/0.60 @ ^ [I3: nat] : ( plus_plus_int @ A5 @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ N4 @ I3 ) ) )
% 0.33/0.60 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N4 ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % pochhammer_prod_rev
% 0.33/0.60 thf(fact_4589_fact__div__fact,axiom,
% 0.33/0.60 ! [N2: nat,M2: nat] :
% 0.33/0.60 ( ( ord_less_eq_nat @ N2 @ M2 )
% 0.33/0.60 => ( ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ M2 ) @ ( semiri1408675320244567234ct_nat @ N2 ) )
% 0.33/0.60 = ( groups708209901874060359at_nat
% 0.33/0.60 @ ^ [X3: nat] : X3
% 0.33/0.60 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ M2 ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % fact_div_fact
% 0.33/0.60 thf(fact_4590_integer__of__num__triv_I2_J,axiom,
% 0.33/0.60 ( ( code_integer_of_num @ ( bit0 @ one ) )
% 0.33/0.60 = ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % integer_of_num_triv(2)
% 0.33/0.60 thf(fact_4591_prod_Oin__pairs,axiom,
% 0.33/0.60 ! [G: nat > assn,M2: nat,N2: nat] :
% 0.33/0.60 ( ( groups6906906614972039071t_assn @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 0.33/0.60 = ( groups6906906614972039071t_assn
% 0.33/0.60 @ ^ [I3: nat] : ( times_times_assn @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 0.33/0.60 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.in_pairs
% 0.33/0.60 thf(fact_4592_prod_Oin__pairs,axiom,
% 0.33/0.60 ! [G: nat > rat,M2: nat,N2: nat] :
% 0.33/0.60 ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 0.33/0.60 = ( groups73079841787564623at_rat
% 0.33/0.60 @ ^ [I3: nat] : ( times_times_rat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 0.33/0.60 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.in_pairs
% 0.33/0.60 thf(fact_4593_prod_Oin__pairs,axiom,
% 0.33/0.60 ! [G: nat > nat,M2: nat,N2: nat] :
% 0.33/0.60 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 0.33/0.60 = ( groups708209901874060359at_nat
% 0.33/0.60 @ ^ [I3: nat] : ( times_times_nat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 0.33/0.60 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.in_pairs
% 0.33/0.60 thf(fact_4594_prod_Oin__pairs,axiom,
% 0.33/0.60 ! [G: nat > int,M2: nat,N2: nat] :
% 0.33/0.60 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 0.33/0.60 = ( groups705719431365010083at_int
% 0.33/0.60 @ ^ [I3: nat] : ( times_times_int @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 0.33/0.60 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.in_pairs
% 0.33/0.60 thf(fact_4595_prod_Oin__pairs__0,axiom,
% 0.33/0.60 ! [G: nat > assn,N2: nat] :
% 0.33/0.60 ( ( groups6906906614972039071t_assn @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 0.33/0.60 = ( groups6906906614972039071t_assn
% 0.33/0.60 @ ^ [I3: nat] : ( times_times_assn @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 0.33/0.60 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.in_pairs_0
% 0.33/0.60 thf(fact_4596_prod_Oin__pairs__0,axiom,
% 0.33/0.60 ! [G: nat > rat,N2: nat] :
% 0.33/0.60 ( ( groups73079841787564623at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 0.33/0.60 = ( groups73079841787564623at_rat
% 0.33/0.60 @ ^ [I3: nat] : ( times_times_rat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 0.33/0.60 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.in_pairs_0
% 0.33/0.60 thf(fact_4597_prod_Oin__pairs__0,axiom,
% 0.33/0.60 ! [G: nat > nat,N2: nat] :
% 0.33/0.60 ( ( groups708209901874060359at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 0.33/0.60 = ( groups708209901874060359at_nat
% 0.33/0.60 @ ^ [I3: nat] : ( times_times_nat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 0.33/0.60 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.in_pairs_0
% 0.33/0.60 thf(fact_4598_prod_Oin__pairs__0,axiom,
% 0.33/0.60 ! [G: nat > int,N2: nat] :
% 0.33/0.60 ( ( groups705719431365010083at_int @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 0.33/0.60 = ( groups705719431365010083at_int
% 0.33/0.60 @ ^ [I3: nat] : ( times_times_int @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 0.33/0.60 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.in_pairs_0
% 0.33/0.60 thf(fact_4599_nat__of__integer__less__iff,axiom,
% 0.33/0.60 ! [X: code_integer,Y: code_integer] :
% 0.33/0.60 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X )
% 0.33/0.60 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y )
% 0.33/0.60 => ( ( ord_less_nat @ ( code_nat_of_integer @ X ) @ ( code_nat_of_integer @ Y ) )
% 0.33/0.60 = ( ord_le6747313008572928689nteger @ X @ Y ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % nat_of_integer_less_iff
% 0.33/0.60 thf(fact_4600_pochhammer__Suc__prod__rev,axiom,
% 0.33/0.60 ! [A: rat,N2: nat] :
% 0.33/0.60 ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N2 ) )
% 0.33/0.60 = ( groups73079841787564623at_rat
% 0.33/0.60 @ ^ [I3: nat] : ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ ( minus_minus_nat @ N2 @ I3 ) ) )
% 0.33/0.60 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % pochhammer_Suc_prod_rev
% 0.33/0.60 thf(fact_4601_pochhammer__Suc__prod__rev,axiom,
% 0.33/0.60 ! [A: code_integer,N2: nat] :
% 0.33/0.60 ( ( comm_s8582702949713902594nteger @ A @ ( suc @ N2 ) )
% 0.33/0.60 = ( groups3455450783089532116nteger
% 0.33/0.60 @ ^ [I3: nat] : ( plus_p5714425477246183910nteger @ A @ ( semiri4939895301339042750nteger @ ( minus_minus_nat @ N2 @ I3 ) ) )
% 0.33/0.60 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % pochhammer_Suc_prod_rev
% 0.33/0.60 thf(fact_4602_pochhammer__Suc__prod__rev,axiom,
% 0.33/0.60 ! [A: code_natural,N2: nat] :
% 0.33/0.60 ( ( comm_s7406298101470620109atural @ A @ ( suc @ N2 ) )
% 0.33/0.60 = ( groups2279045934846249631atural
% 0.33/0.60 @ ^ [I3: nat] : ( plus_p4538020629002901425atural @ A @ ( semiri3763490453095760265atural @ ( minus_minus_nat @ N2 @ I3 ) ) )
% 0.33/0.60 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % pochhammer_Suc_prod_rev
% 0.33/0.60 thf(fact_4603_pochhammer__Suc__prod__rev,axiom,
% 0.33/0.60 ! [A: nat,N2: nat] :
% 0.33/0.60 ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N2 ) )
% 0.33/0.60 = ( groups708209901874060359at_nat
% 0.33/0.60 @ ^ [I3: nat] : ( plus_plus_nat @ A @ ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ N2 @ I3 ) ) )
% 0.33/0.60 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % pochhammer_Suc_prod_rev
% 0.33/0.60 thf(fact_4604_pochhammer__Suc__prod__rev,axiom,
% 0.33/0.60 ! [A: int,N2: nat] :
% 0.33/0.60 ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N2 ) )
% 0.33/0.60 = ( groups705719431365010083at_int
% 0.33/0.60 @ ^ [I3: nat] : ( plus_plus_int @ A @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ N2 @ I3 ) ) )
% 0.33/0.60 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % pochhammer_Suc_prod_rev
% 0.33/0.60 thf(fact_4605_divmod__integer__code,axiom,
% 0.33/0.60 ( code_divmod_integer
% 0.33/0.60 = ( ^ [K4: code_integer,L3: code_integer] :
% 0.33/0.60 ( if_Pro6119634080678213985nteger @ ( K4 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 0.33/0.60 @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ L3 )
% 0.33/0.60 @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ K4 ) @ ( code_divmod_abs @ K4 @ L3 )
% 0.33/0.60 @ ( produc6916734918728496179nteger
% 0.33/0.60 @ ^ [R3: code_integer,S4: code_integer] : ( if_Pro6119634080678213985nteger @ ( S4 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R3 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R3 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ L3 @ S4 ) ) )
% 0.33/0.60 @ ( code_divmod_abs @ K4 @ L3 ) ) )
% 0.33/0.60 @ ( if_Pro6119634080678213985nteger @ ( L3 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ K4 )
% 0.33/0.60 @ ( produc6499014454317279255nteger @ uminus1351360451143612070nteger
% 0.33/0.60 @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ K4 @ zero_z3403309356797280102nteger ) @ ( code_divmod_abs @ K4 @ L3 )
% 0.33/0.60 @ ( produc6916734918728496179nteger
% 0.33/0.60 @ ^ [R3: code_integer,S4: code_integer] : ( if_Pro6119634080678213985nteger @ ( S4 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R3 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R3 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ L3 ) @ S4 ) ) )
% 0.33/0.60 @ ( code_divmod_abs @ K4 @ L3 ) ) ) ) ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % divmod_integer_code
% 0.33/0.60 thf(fact_4606_bit__cut__integer__code,axiom,
% 0.33/0.60 ( code_bit_cut_integer
% 0.33/0.60 = ( ^ [K4: code_integer] :
% 0.33/0.60 ( if_Pro5737122678794959658eger_o @ ( K4 = zero_z3403309356797280102nteger ) @ ( produc6677183202524767010eger_o @ zero_z3403309356797280102nteger @ $false )
% 0.33/0.60 @ ( produc9125791028180074456eger_o
% 0.33/0.60 @ ^ [R3: code_integer,S4: code_integer] : ( produc6677183202524767010eger_o @ ( if_Code_integer @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ K4 ) @ R3 @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R3 ) @ S4 ) ) @ ( S4 = one_one_Code_integer ) )
% 0.33/0.60 @ ( code_divmod_abs @ K4 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % bit_cut_integer_code
% 0.33/0.60 thf(fact_4607_prod_Ozero__middle,axiom,
% 0.33/0.60 ! [P4: nat,K: nat,G: nat > code_integer,H3: nat > code_integer] :
% 0.33/0.60 ( ( ord_less_eq_nat @ one_one_nat @ P4 )
% 0.33/0.60 => ( ( ord_less_eq_nat @ K @ P4 )
% 0.33/0.60 => ( ( groups3455450783089532116nteger
% 0.33/0.60 @ ^ [J2: nat] : ( if_Code_integer @ ( ord_less_nat @ J2 @ K ) @ ( G @ J2 ) @ ( if_Code_integer @ ( J2 = K ) @ one_one_Code_integer @ ( H3 @ ( minus_minus_nat @ J2 @ ( suc @ zero_zero_nat ) ) ) ) )
% 0.33/0.60 @ ( set_ord_atMost_nat @ P4 ) )
% 0.33/0.60 = ( groups3455450783089532116nteger
% 0.33/0.60 @ ^ [J2: nat] : ( if_Code_integer @ ( ord_less_nat @ J2 @ K ) @ ( G @ J2 ) @ ( H3 @ J2 ) )
% 0.33/0.60 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P4 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.zero_middle
% 0.33/0.60 thf(fact_4608_prod_Ozero__middle,axiom,
% 0.33/0.60 ! [P4: nat,K: nat,G: nat > assn,H3: nat > assn] :
% 0.33/0.60 ( ( ord_less_eq_nat @ one_one_nat @ P4 )
% 0.33/0.60 => ( ( ord_less_eq_nat @ K @ P4 )
% 0.33/0.60 => ( ( groups6906906614972039071t_assn
% 0.33/0.60 @ ^ [J2: nat] : ( if_assn @ ( ord_less_nat @ J2 @ K ) @ ( G @ J2 ) @ ( if_assn @ ( J2 = K ) @ one_one_assn @ ( H3 @ ( minus_minus_nat @ J2 @ ( suc @ zero_zero_nat ) ) ) ) )
% 0.33/0.60 @ ( set_ord_atMost_nat @ P4 ) )
% 0.33/0.60 = ( groups6906906614972039071t_assn
% 0.33/0.60 @ ^ [J2: nat] : ( if_assn @ ( ord_less_nat @ J2 @ K ) @ ( G @ J2 ) @ ( H3 @ J2 ) )
% 0.33/0.60 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P4 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.zero_middle
% 0.33/0.60 thf(fact_4609_prod_Ozero__middle,axiom,
% 0.33/0.60 ! [P4: nat,K: nat,G: nat > rat,H3: nat > rat] :
% 0.33/0.60 ( ( ord_less_eq_nat @ one_one_nat @ P4 )
% 0.33/0.60 => ( ( ord_less_eq_nat @ K @ P4 )
% 0.33/0.60 => ( ( groups73079841787564623at_rat
% 0.33/0.60 @ ^ [J2: nat] : ( if_rat @ ( ord_less_nat @ J2 @ K ) @ ( G @ J2 ) @ ( if_rat @ ( J2 = K ) @ one_one_rat @ ( H3 @ ( minus_minus_nat @ J2 @ ( suc @ zero_zero_nat ) ) ) ) )
% 0.33/0.60 @ ( set_ord_atMost_nat @ P4 ) )
% 0.33/0.60 = ( groups73079841787564623at_rat
% 0.33/0.60 @ ^ [J2: nat] : ( if_rat @ ( ord_less_nat @ J2 @ K ) @ ( G @ J2 ) @ ( H3 @ J2 ) )
% 0.33/0.60 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P4 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.zero_middle
% 0.33/0.60 thf(fact_4610_prod_Ozero__middle,axiom,
% 0.33/0.60 ! [P4: nat,K: nat,G: nat > nat,H3: nat > nat] :
% 0.33/0.60 ( ( ord_less_eq_nat @ one_one_nat @ P4 )
% 0.33/0.60 => ( ( ord_less_eq_nat @ K @ P4 )
% 0.33/0.60 => ( ( groups708209901874060359at_nat
% 0.33/0.60 @ ^ [J2: nat] : ( if_nat @ ( ord_less_nat @ J2 @ K ) @ ( G @ J2 ) @ ( if_nat @ ( J2 = K ) @ one_one_nat @ ( H3 @ ( minus_minus_nat @ J2 @ ( suc @ zero_zero_nat ) ) ) ) )
% 0.33/0.60 @ ( set_ord_atMost_nat @ P4 ) )
% 0.33/0.60 = ( groups708209901874060359at_nat
% 0.33/0.60 @ ^ [J2: nat] : ( if_nat @ ( ord_less_nat @ J2 @ K ) @ ( G @ J2 ) @ ( H3 @ J2 ) )
% 0.33/0.60 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P4 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.zero_middle
% 0.33/0.60 thf(fact_4611_prod_Ozero__middle,axiom,
% 0.33/0.60 ! [P4: nat,K: nat,G: nat > int,H3: nat > int] :
% 0.33/0.60 ( ( ord_less_eq_nat @ one_one_nat @ P4 )
% 0.33/0.60 => ( ( ord_less_eq_nat @ K @ P4 )
% 0.33/0.60 => ( ( groups705719431365010083at_int
% 0.33/0.60 @ ^ [J2: nat] : ( if_int @ ( ord_less_nat @ J2 @ K ) @ ( G @ J2 ) @ ( if_int @ ( J2 = K ) @ one_one_int @ ( H3 @ ( minus_minus_nat @ J2 @ ( suc @ zero_zero_nat ) ) ) ) )
% 0.33/0.60 @ ( set_ord_atMost_nat @ P4 ) )
% 0.33/0.60 = ( groups705719431365010083at_int
% 0.33/0.60 @ ^ [J2: nat] : ( if_int @ ( ord_less_nat @ J2 @ K ) @ ( G @ J2 ) @ ( H3 @ J2 ) )
% 0.33/0.60 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P4 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.zero_middle
% 0.33/0.60 thf(fact_4612_xor__int__rec,axiom,
% 0.33/0.60 ( bit_se6526347334894502574or_int
% 0.33/0.60 = ( ^ [K4: int,L3: int] :
% 0.33/0.60 ( plus_plus_int
% 0.33/0.60 @ ( zero_n2684676970156552555ol_int
% 0.33/0.60 @ ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K4 ) )
% 0.33/0.60 != ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L3 ) ) ) )
% 0.33/0.60 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( divide_divide_int @ K4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % xor_int_rec
% 0.33/0.60 thf(fact_4613_divmod__abs__def,axiom,
% 0.33/0.60 ( code_divmod_abs
% 0.33/0.60 = ( ^ [K4: code_integer,L3: code_integer] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ ( abs_abs_Code_integer @ K4 ) @ ( abs_abs_Code_integer @ L3 ) ) @ ( modulo364778990260209775nteger @ ( abs_abs_Code_integer @ K4 ) @ ( abs_abs_Code_integer @ L3 ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % divmod_abs_def
% 0.33/0.60 thf(fact_4614_less__int_Orep__eq,axiom,
% 0.33/0.60 ( ord_less_int
% 0.33/0.60 = ( ^ [X3: int,Xa4: int] :
% 0.33/0.60 ( produc8739625826339149834_nat_o
% 0.33/0.60 @ ^ [Y3: nat,Z4: nat] :
% 0.33/0.60 ( produc6081775807080527818_nat_o
% 0.33/0.60 @ ^ [U2: nat,V2: nat] : ( ord_less_nat @ ( plus_plus_nat @ Y3 @ V2 ) @ ( plus_plus_nat @ U2 @ Z4 ) ) )
% 0.33/0.60 @ ( rep_Integ @ X3 )
% 0.33/0.60 @ ( rep_Integ @ Xa4 ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % less_int.rep_eq
% 0.33/0.60 thf(fact_4615_xor__int__unfold,axiom,
% 0.33/0.60 ( bit_se6526347334894502574or_int
% 0.33/0.60 = ( ^ [K4: int,L3: int] :
% 0.33/0.60 ( if_int
% 0.33/0.60 @ ( K4
% 0.33/0.60 = ( uminus_uminus_int @ one_one_int ) )
% 0.33/0.60 @ ( bit_ri7919022796975470100ot_int @ L3 )
% 0.33/0.60 @ ( if_int
% 0.33/0.60 @ ( L3
% 0.33/0.60 = ( uminus_uminus_int @ one_one_int ) )
% 0.33/0.60 @ ( bit_ri7919022796975470100ot_int @ K4 )
% 0.33/0.60 @ ( if_int @ ( K4 = zero_zero_int ) @ L3 @ ( if_int @ ( L3 = zero_zero_int ) @ K4 @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ ( modulo_modulo_int @ K4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ L3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( divide_divide_int @ K4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % xor_int_unfold
% 0.33/0.60 thf(fact_4616_take__bit__num__code,axiom,
% 0.33/0.60 ( bit_take_bit_num
% 0.33/0.60 = ( ^ [N4: nat,M: num] :
% 0.33/0.60 ( produc478579273971653890on_num
% 0.33/0.60 @ ^ [A5: nat,X3: num] :
% 0.33/0.60 ( case_nat_option_num @ none_num
% 0.33/0.60 @ ^ [O: nat] :
% 0.33/0.60 ( case_num_option_num @ ( some_num @ one )
% 0.33/0.60 @ ^ [P6: num] :
% 0.33/0.60 ( case_o6005452278849405969um_num @ none_num
% 0.33/0.60 @ ^ [Q5: num] : ( some_num @ ( bit0 @ Q5 ) )
% 0.33/0.60 @ ( bit_take_bit_num @ O @ P6 ) )
% 0.33/0.60 @ ^ [P6: num] : ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ O @ P6 ) ) )
% 0.33/0.60 @ X3 )
% 0.33/0.60 @ A5 )
% 0.33/0.60 @ ( product_Pair_nat_num @ N4 @ M ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % take_bit_num_code
% 0.33/0.60 thf(fact_4617_prod_Otriangle__reindex,axiom,
% 0.33/0.60 ! [G: nat > nat > nat,N2: nat] :
% 0.33/0.60 ( ( groups4077766827762148844at_nat @ ( produc6842872674320459806at_nat @ G )
% 0.33/0.60 @ ( collec3392354462482085612at_nat
% 0.33/0.60 @ ( produc6081775807080527818_nat_o
% 0.33/0.60 @ ^ [I3: nat,J2: nat] : ( ord_less_nat @ ( plus_plus_nat @ I3 @ J2 ) @ N2 ) ) ) )
% 0.33/0.60 = ( groups708209901874060359at_nat
% 0.33/0.60 @ ^ [K4: nat] :
% 0.33/0.60 ( groups708209901874060359at_nat
% 0.33/0.60 @ ^ [I3: nat] : ( G @ I3 @ ( minus_minus_nat @ K4 @ I3 ) )
% 0.33/0.60 @ ( set_ord_atMost_nat @ K4 ) )
% 0.33/0.60 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.triangle_reindex
% 0.33/0.60 thf(fact_4618_prod_Otriangle__reindex,axiom,
% 0.33/0.60 ! [G: nat > nat > int,N2: nat] :
% 0.33/0.60 ( ( groups4075276357253098568at_int @ ( produc6840382203811409530at_int @ G )
% 0.33/0.60 @ ( collec3392354462482085612at_nat
% 0.33/0.60 @ ( produc6081775807080527818_nat_o
% 0.33/0.60 @ ^ [I3: nat,J2: nat] : ( ord_less_nat @ ( plus_plus_nat @ I3 @ J2 ) @ N2 ) ) ) )
% 0.33/0.60 = ( groups705719431365010083at_int
% 0.33/0.60 @ ^ [K4: nat] :
% 0.33/0.60 ( groups705719431365010083at_int
% 0.33/0.60 @ ^ [I3: nat] : ( G @ I3 @ ( minus_minus_nat @ K4 @ I3 ) )
% 0.33/0.60 @ ( set_ord_atMost_nat @ K4 ) )
% 0.33/0.60 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.triangle_reindex
% 0.33/0.60 thf(fact_4619_case__nat__add__eq__if,axiom,
% 0.33/0.60 ! [A: option_num,F: nat > option_num,V: num,N2: nat] :
% 0.33/0.60 ( ( case_nat_option_num @ A @ F @ ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ N2 ) )
% 0.33/0.60 = ( F @ ( plus_plus_nat @ ( pred_numeral @ V ) @ N2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % case_nat_add_eq_if
% 0.33/0.60 thf(fact_4620_bit_Ocompl__zero,axiom,
% 0.33/0.60 ( ( bit_ri7919022796975470100ot_int @ zero_zero_int )
% 0.33/0.60 = ( uminus_uminus_int @ one_one_int ) ) ).
% 0.33/0.60
% 0.33/0.60 % bit.compl_zero
% 0.33/0.60 thf(fact_4621_bit_Ocompl__zero,axiom,
% 0.33/0.60 ( ( bit_ri7632146776885996613nteger @ zero_z3403309356797280102nteger )
% 0.33/0.60 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.33/0.60
% 0.33/0.60 % bit.compl_zero
% 0.33/0.60 thf(fact_4622_bit_Ocompl__one,axiom,
% 0.33/0.60 ( ( bit_ri7919022796975470100ot_int @ ( uminus_uminus_int @ one_one_int ) )
% 0.33/0.60 = zero_zero_int ) ).
% 0.33/0.60
% 0.33/0.60 % bit.compl_one
% 0.33/0.60 thf(fact_4623_bit_Ocompl__one,axiom,
% 0.33/0.60 ( ( bit_ri7632146776885996613nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.33/0.60 = zero_z3403309356797280102nteger ) ).
% 0.33/0.60
% 0.33/0.60 % bit.compl_one
% 0.33/0.60 thf(fact_4624_bit_Oxor__cancel__right,axiom,
% 0.33/0.60 ! [X: code_integer] :
% 0.33/0.60 ( ( bit_se3222712562003087583nteger @ X @ ( bit_ri7632146776885996613nteger @ X ) )
% 0.33/0.60 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.33/0.60
% 0.33/0.60 % bit.xor_cancel_right
% 0.33/0.60 thf(fact_4625_bit_Oxor__cancel__right,axiom,
% 0.33/0.60 ! [X: int] :
% 0.33/0.60 ( ( bit_se6526347334894502574or_int @ X @ ( bit_ri7919022796975470100ot_int @ X ) )
% 0.33/0.60 = ( uminus_uminus_int @ one_one_int ) ) ).
% 0.33/0.60
% 0.33/0.60 % bit.xor_cancel_right
% 0.33/0.60 thf(fact_4626_bit_Oxor__cancel__left,axiom,
% 0.33/0.60 ! [X: code_integer] :
% 0.33/0.60 ( ( bit_se3222712562003087583nteger @ ( bit_ri7632146776885996613nteger @ X ) @ X )
% 0.33/0.60 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.33/0.60
% 0.33/0.60 % bit.xor_cancel_left
% 0.33/0.60 thf(fact_4627_bit_Oxor__cancel__left,axiom,
% 0.33/0.60 ! [X: int] :
% 0.33/0.60 ( ( bit_se6526347334894502574or_int @ ( bit_ri7919022796975470100ot_int @ X ) @ X )
% 0.33/0.60 = ( uminus_uminus_int @ one_one_int ) ) ).
% 0.33/0.60
% 0.33/0.60 % bit.xor_cancel_left
% 0.33/0.60 thf(fact_4628_bit_Oxor__one__right,axiom,
% 0.33/0.60 ! [X: code_integer] :
% 0.33/0.60 ( ( bit_se3222712562003087583nteger @ X @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.33/0.60 = ( bit_ri7632146776885996613nteger @ X ) ) ).
% 0.33/0.60
% 0.33/0.60 % bit.xor_one_right
% 0.33/0.60 thf(fact_4629_bit_Oxor__one__right,axiom,
% 0.33/0.60 ! [X: int] :
% 0.33/0.60 ( ( bit_se6526347334894502574or_int @ X @ ( uminus_uminus_int @ one_one_int ) )
% 0.33/0.60 = ( bit_ri7919022796975470100ot_int @ X ) ) ).
% 0.33/0.60
% 0.33/0.60 % bit.xor_one_right
% 0.33/0.60 thf(fact_4630_bit_Oxor__one__left,axiom,
% 0.33/0.60 ! [X: code_integer] :
% 0.33/0.60 ( ( bit_se3222712562003087583nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ X )
% 0.33/0.60 = ( bit_ri7632146776885996613nteger @ X ) ) ).
% 0.33/0.60
% 0.33/0.60 % bit.xor_one_left
% 0.33/0.60 thf(fact_4631_bit_Oxor__one__left,axiom,
% 0.33/0.60 ! [X: int] :
% 0.33/0.60 ( ( bit_se6526347334894502574or_int @ ( uminus_uminus_int @ one_one_int ) @ X )
% 0.33/0.60 = ( bit_ri7919022796975470100ot_int @ X ) ) ).
% 0.33/0.60
% 0.33/0.60 % bit.xor_one_left
% 0.33/0.60 thf(fact_4632_push__bit__minus__one__eq__not__mask,axiom,
% 0.33/0.60 ! [N2: nat] :
% 0.33/0.60 ( ( bit_se7788150548672797655nteger @ N2 @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.33/0.60 = ( bit_ri7632146776885996613nteger @ ( bit_se2119862282449309892nteger @ N2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % push_bit_minus_one_eq_not_mask
% 0.33/0.60 thf(fact_4633_push__bit__minus__one__eq__not__mask,axiom,
% 0.33/0.60 ! [N2: nat] :
% 0.33/0.60 ( ( bit_se545348938243370406it_int @ N2 @ ( uminus_uminus_int @ one_one_int ) )
% 0.33/0.60 = ( bit_ri7919022796975470100ot_int @ ( bit_se2000444600071755411sk_int @ N2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % push_bit_minus_one_eq_not_mask
% 0.33/0.60 thf(fact_4634_not__one__eq,axiom,
% 0.33/0.60 ( ( bit_ri7919022796975470100ot_int @ one_one_int )
% 0.33/0.60 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % not_one_eq
% 0.33/0.60 thf(fact_4635_not__one__eq,axiom,
% 0.33/0.60 ( ( bit_ri7632146776885996613nteger @ one_one_Code_integer )
% 0.33/0.60 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % not_one_eq
% 0.33/0.60 thf(fact_4636_not__add__distrib,axiom,
% 0.33/0.60 ! [A: int,B: int] :
% 0.33/0.60 ( ( bit_ri7919022796975470100ot_int @ ( plus_plus_int @ A @ B ) )
% 0.33/0.60 = ( minus_minus_int @ ( bit_ri7919022796975470100ot_int @ A ) @ B ) ) ).
% 0.33/0.60
% 0.33/0.60 % not_add_distrib
% 0.33/0.60 thf(fact_4637_not__add__distrib,axiom,
% 0.33/0.60 ! [A: code_integer,B: code_integer] :
% 0.33/0.60 ( ( bit_ri7632146776885996613nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 0.33/0.60 = ( minus_8373710615458151222nteger @ ( bit_ri7632146776885996613nteger @ A ) @ B ) ) ).
% 0.33/0.60
% 0.33/0.60 % not_add_distrib
% 0.33/0.60 thf(fact_4638_not__diff__distrib,axiom,
% 0.33/0.60 ! [A: int,B: int] :
% 0.33/0.60 ( ( bit_ri7919022796975470100ot_int @ ( minus_minus_int @ A @ B ) )
% 0.33/0.60 = ( plus_plus_int @ ( bit_ri7919022796975470100ot_int @ A ) @ B ) ) ).
% 0.33/0.60
% 0.33/0.60 % not_diff_distrib
% 0.33/0.60 thf(fact_4639_not__diff__distrib,axiom,
% 0.33/0.60 ! [A: code_integer,B: code_integer] :
% 0.33/0.60 ( ( bit_ri7632146776885996613nteger @ ( minus_8373710615458151222nteger @ A @ B ) )
% 0.33/0.60 = ( plus_p5714425477246183910nteger @ ( bit_ri7632146776885996613nteger @ A ) @ B ) ) ).
% 0.33/0.60
% 0.33/0.60 % not_diff_distrib
% 0.33/0.60 thf(fact_4640_minus__eq__not__plus__1,axiom,
% 0.33/0.60 ( uminus_uminus_int
% 0.33/0.60 = ( ^ [A5: int] : ( plus_plus_int @ ( bit_ri7919022796975470100ot_int @ A5 ) @ one_one_int ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % minus_eq_not_plus_1
% 0.33/0.60 thf(fact_4641_minus__eq__not__plus__1,axiom,
% 0.33/0.60 ( uminus1351360451143612070nteger
% 0.33/0.60 = ( ^ [A5: code_integer] : ( plus_p5714425477246183910nteger @ ( bit_ri7632146776885996613nteger @ A5 ) @ one_one_Code_integer ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % minus_eq_not_plus_1
% 0.33/0.60 thf(fact_4642_minus__eq__not__minus__1,axiom,
% 0.33/0.60 ( uminus_uminus_int
% 0.33/0.60 = ( ^ [A5: int] : ( bit_ri7919022796975470100ot_int @ ( minus_minus_int @ A5 @ one_one_int ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % minus_eq_not_minus_1
% 0.33/0.60 thf(fact_4643_minus__eq__not__minus__1,axiom,
% 0.33/0.60 ( uminus1351360451143612070nteger
% 0.33/0.60 = ( ^ [A5: code_integer] : ( bit_ri7632146776885996613nteger @ ( minus_8373710615458151222nteger @ A5 @ one_one_Code_integer ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % minus_eq_not_minus_1
% 0.33/0.60 thf(fact_4644_not__eq__complement,axiom,
% 0.33/0.60 ( bit_ri7919022796975470100ot_int
% 0.33/0.60 = ( ^ [A5: int] : ( minus_minus_int @ ( uminus_uminus_int @ A5 ) @ one_one_int ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % not_eq_complement
% 0.33/0.60 thf(fact_4645_not__eq__complement,axiom,
% 0.33/0.60 ( bit_ri7632146776885996613nteger
% 0.33/0.60 = ( ^ [A5: code_integer] : ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ A5 ) @ one_one_Code_integer ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % not_eq_complement
% 0.33/0.60 thf(fact_4646_prod__int__eq,axiom,
% 0.33/0.60 ! [I: nat,J: nat] :
% 0.33/0.60 ( ( groups705719431365010083at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ I @ J ) )
% 0.33/0.60 = ( groups1705073143266064639nt_int
% 0.33/0.60 @ ^ [X3: int] : X3
% 0.33/0.60 @ ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ I ) @ ( semiri1314217659103216013at_int @ J ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod_int_eq
% 0.33/0.60 thf(fact_4647_prod__int__plus__eq,axiom,
% 0.33/0.60 ! [I: nat,J: nat] :
% 0.33/0.60 ( ( groups705719431365010083at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ I @ ( plus_plus_nat @ I @ J ) ) )
% 0.33/0.60 = ( groups1705073143266064639nt_int
% 0.33/0.60 @ ^ [X3: int] : X3
% 0.33/0.60 @ ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ I ) @ ( semiri1314217659103216013at_int @ ( plus_plus_nat @ I @ J ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod_int_plus_eq
% 0.33/0.60 thf(fact_4648_push__bit__mask__eq,axiom,
% 0.33/0.60 ! [M2: nat,N2: nat] :
% 0.33/0.60 ( ( bit_se7788150548672797655nteger @ M2 @ ( bit_se2119862282449309892nteger @ N2 ) )
% 0.33/0.60 = ( bit_se3949692690581998587nteger @ ( bit_se2119862282449309892nteger @ ( plus_plus_nat @ N2 @ M2 ) ) @ ( bit_ri7632146776885996613nteger @ ( bit_se2119862282449309892nteger @ M2 ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % push_bit_mask_eq
% 0.33/0.60 thf(fact_4649_push__bit__mask__eq,axiom,
% 0.33/0.60 ! [M2: nat,N2: nat] :
% 0.33/0.60 ( ( bit_se545348938243370406it_int @ M2 @ ( bit_se2000444600071755411sk_int @ N2 ) )
% 0.33/0.60 = ( bit_se725231765392027082nd_int @ ( bit_se2000444600071755411sk_int @ ( plus_plus_nat @ N2 @ M2 ) ) @ ( bit_ri7919022796975470100ot_int @ ( bit_se2000444600071755411sk_int @ M2 ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % push_bit_mask_eq
% 0.33/0.60 thf(fact_4650_prod_OatLeast__int__lessThan__int__shift,axiom,
% 0.33/0.60 ! [G: int > nat,M2: nat,N2: nat] :
% 0.33/0.60 ( ( groups1707563613775114915nt_nat @ G @ ( set_or4662586982721622107an_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 0.33/0.60 = ( groups708209901874060359at_nat @ ( comp_int_nat_nat @ G @ semiri1314217659103216013at_int ) @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.atLeast_int_lessThan_int_shift
% 0.33/0.60 thf(fact_4651_prod_OatLeast__int__lessThan__int__shift,axiom,
% 0.33/0.60 ! [G: int > int,M2: nat,N2: nat] :
% 0.33/0.60 ( ( groups1705073143266064639nt_int @ G @ ( set_or4662586982721622107an_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 0.33/0.60 = ( groups705719431365010083at_int @ ( comp_int_int_nat @ G @ semiri1314217659103216013at_int ) @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.atLeast_int_lessThan_int_shift
% 0.33/0.60 thf(fact_4652_unset__bit__eq__and__not,axiom,
% 0.33/0.60 ( bit_se8260200283734997820nteger
% 0.33/0.60 = ( ^ [N4: nat,A5: code_integer] : ( bit_se3949692690581998587nteger @ A5 @ ( bit_ri7632146776885996613nteger @ ( bit_se7788150548672797655nteger @ N4 @ one_one_Code_integer ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % unset_bit_eq_and_not
% 0.33/0.60 thf(fact_4653_unset__bit__eq__and__not,axiom,
% 0.33/0.60 ( bit_se4203085406695923979it_int
% 0.33/0.60 = ( ^ [N4: nat,A5: int] : ( bit_se725231765392027082nd_int @ A5 @ ( bit_ri7919022796975470100ot_int @ ( bit_se545348938243370406it_int @ N4 @ one_one_int ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % unset_bit_eq_and_not
% 0.33/0.60 thf(fact_4654_prod_OatLeast__int__atMost__int__shift,axiom,
% 0.33/0.60 ! [G: int > nat,M2: nat,N2: nat] :
% 0.33/0.60 ( ( groups1707563613775114915nt_nat @ G @ ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 0.33/0.60 = ( groups708209901874060359at_nat @ ( comp_int_nat_nat @ G @ semiri1314217659103216013at_int ) @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.atLeast_int_atMost_int_shift
% 0.33/0.60 thf(fact_4655_prod_OatLeast__int__atMost__int__shift,axiom,
% 0.33/0.60 ! [G: int > int,M2: nat,N2: nat] :
% 0.33/0.60 ( ( groups1705073143266064639nt_int @ G @ ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 0.33/0.60 = ( groups705719431365010083at_int @ ( comp_int_int_nat @ G @ semiri1314217659103216013at_int ) @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.atLeast_int_atMost_int_shift
% 0.33/0.60 thf(fact_4656_int__numeral__not__and__num,axiom,
% 0.33/0.60 ! [M2: num,N2: num] :
% 0.33/0.60 ( ( bit_se725231765392027082nd_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ M2 ) ) @ ( numeral_numeral_int @ N2 ) )
% 0.33/0.60 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ N2 @ M2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % int_numeral_not_and_num
% 0.33/0.60 thf(fact_4657_int__numeral__and__not__num,axiom,
% 0.33/0.60 ! [M2: num,N2: num] :
% 0.33/0.60 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M2 ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) )
% 0.33/0.60 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M2 @ N2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % int_numeral_and_not_num
% 0.33/0.60 thf(fact_4658_prod_Otriangle__reindex__eq,axiom,
% 0.33/0.60 ! [G: nat > nat > nat,N2: nat] :
% 0.33/0.60 ( ( groups4077766827762148844at_nat @ ( produc6842872674320459806at_nat @ G )
% 0.33/0.60 @ ( collec3392354462482085612at_nat
% 0.33/0.60 @ ( produc6081775807080527818_nat_o
% 0.33/0.60 @ ^ [I3: nat,J2: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ I3 @ J2 ) @ N2 ) ) ) )
% 0.33/0.60 = ( groups708209901874060359at_nat
% 0.33/0.60 @ ^ [K4: nat] :
% 0.33/0.60 ( groups708209901874060359at_nat
% 0.33/0.60 @ ^ [I3: nat] : ( G @ I3 @ ( minus_minus_nat @ K4 @ I3 ) )
% 0.33/0.60 @ ( set_ord_atMost_nat @ K4 ) )
% 0.33/0.60 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.triangle_reindex_eq
% 0.33/0.60 thf(fact_4659_prod_Otriangle__reindex__eq,axiom,
% 0.33/0.60 ! [G: nat > nat > int,N2: nat] :
% 0.33/0.60 ( ( groups4075276357253098568at_int @ ( produc6840382203811409530at_int @ G )
% 0.33/0.60 @ ( collec3392354462482085612at_nat
% 0.33/0.60 @ ( produc6081775807080527818_nat_o
% 0.33/0.60 @ ^ [I3: nat,J2: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ I3 @ J2 ) @ N2 ) ) ) )
% 0.33/0.60 = ( groups705719431365010083at_int
% 0.33/0.60 @ ^ [K4: nat] :
% 0.33/0.60 ( groups705719431365010083at_int
% 0.33/0.60 @ ^ [I3: nat] : ( G @ I3 @ ( minus_minus_nat @ K4 @ I3 ) )
% 0.33/0.60 @ ( set_ord_atMost_nat @ K4 ) )
% 0.33/0.60 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % prod.triangle_reindex_eq
% 0.33/0.60 thf(fact_4660_and__not__numerals_I8_J,axiom,
% 0.33/0.60 ! [M2: num,N2: num] :
% 0.33/0.60 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M2 ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) )
% 0.33/0.60 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M2 ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % and_not_numerals(8)
% 0.33/0.60 thf(fact_4661_not__int__rec,axiom,
% 0.33/0.60 ( bit_ri7919022796975470100ot_int
% 0.33/0.60 = ( ^ [K4: int] : ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K4 ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri7919022796975470100ot_int @ ( divide_divide_int @ K4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % not_int_rec
% 0.33/0.60 thf(fact_4662_Nitpick_Ocase__nat__unfold,axiom,
% 0.33/0.60 ( case_nat_option_num
% 0.33/0.60 = ( ^ [X3: option_num,F2: nat > option_num,N4: nat] : ( if_option_num @ ( N4 = zero_zero_nat ) @ X3 @ ( F2 @ ( minus_minus_nat @ N4 @ one_one_nat ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % Nitpick.case_nat_unfold
% 0.33/0.60 thf(fact_4663_or__int__rec,axiom,
% 0.33/0.60 ( bit_se1409905431419307370or_int
% 0.33/0.60 = ( ^ [K4: int,L3: int] :
% 0.33/0.60 ( plus_plus_int
% 0.33/0.60 @ ( zero_n2684676970156552555ol_int
% 0.33/0.60 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K4 )
% 0.33/0.60 | ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L3 ) ) )
% 0.33/0.60 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( divide_divide_int @ K4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % or_int_rec
% 0.33/0.60 thf(fact_4664_or__numerals_I4_J,axiom,
% 0.33/0.60 ! [X: num,Y: num] :
% 0.33/0.60 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 0.33/0.60 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % or_numerals(4)
% 0.33/0.60 thf(fact_4665_or__numerals_I4_J,axiom,
% 0.33/0.60 ! [X: num,Y: num] :
% 0.33/0.60 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 0.33/0.60 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % or_numerals(4)
% 0.33/0.60 thf(fact_4666_or__numerals_I4_J,axiom,
% 0.33/0.60 ! [X: num,Y: num] :
% 0.33/0.60 ( ( bit_se1080825931792720795nteger @ ( numera6620942414471956472nteger @ ( bit0 @ X ) ) @ ( numera6620942414471956472nteger @ ( bit1 @ Y ) ) )
% 0.33/0.60 = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1080825931792720795nteger @ ( numera6620942414471956472nteger @ X ) @ ( numera6620942414471956472nteger @ Y ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % or_numerals(4)
% 0.33/0.60 thf(fact_4667_or__numerals_I4_J,axiom,
% 0.33/0.60 ! [X: num,Y: num] :
% 0.33/0.60 ( ( bit_se9127793120404214118atural @ ( numera5444537566228673987atural @ ( bit0 @ X ) ) @ ( numera5444537566228673987atural @ ( bit1 @ Y ) ) )
% 0.33/0.60 = ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se9127793120404214118atural @ ( numera5444537566228673987atural @ X ) @ ( numera5444537566228673987atural @ Y ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % or_numerals(4)
% 0.33/0.60 thf(fact_4668_or__numerals_I6_J,axiom,
% 0.33/0.60 ! [X: num,Y: num] :
% 0.33/0.60 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 0.33/0.60 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % or_numerals(6)
% 0.33/0.60 thf(fact_4669_or__numerals_I6_J,axiom,
% 0.33/0.60 ! [X: num,Y: num] :
% 0.33/0.60 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 0.33/0.60 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % or_numerals(6)
% 0.33/0.60 thf(fact_4670_or__numerals_I6_J,axiom,
% 0.33/0.60 ! [X: num,Y: num] :
% 0.33/0.60 ( ( bit_se1080825931792720795nteger @ ( numera6620942414471956472nteger @ ( bit1 @ X ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Y ) ) )
% 0.33/0.60 = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1080825931792720795nteger @ ( numera6620942414471956472nteger @ X ) @ ( numera6620942414471956472nteger @ Y ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % or_numerals(6)
% 0.33/0.60 thf(fact_4671_or__numerals_I6_J,axiom,
% 0.33/0.60 ! [X: num,Y: num] :
% 0.33/0.60 ( ( bit_se9127793120404214118atural @ ( numera5444537566228673987atural @ ( bit1 @ X ) ) @ ( numera5444537566228673987atural @ ( bit0 @ Y ) ) )
% 0.33/0.60 = ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se9127793120404214118atural @ ( numera5444537566228673987atural @ X ) @ ( numera5444537566228673987atural @ Y ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % or_numerals(6)
% 0.33/0.60 thf(fact_4672_or__numerals_I7_J,axiom,
% 0.33/0.60 ! [X: num,Y: num] :
% 0.33/0.60 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 0.33/0.60 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % or_numerals(7)
% 0.33/0.60 thf(fact_4673_or__numerals_I7_J,axiom,
% 0.33/0.60 ! [X: num,Y: num] :
% 0.33/0.60 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 0.33/0.60 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % or_numerals(7)
% 0.33/0.60 thf(fact_4674_or__numerals_I7_J,axiom,
% 0.33/0.60 ! [X: num,Y: num] :
% 0.33/0.60 ( ( bit_se1080825931792720795nteger @ ( numera6620942414471956472nteger @ ( bit1 @ X ) ) @ ( numera6620942414471956472nteger @ ( bit1 @ Y ) ) )
% 0.33/0.60 = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1080825931792720795nteger @ ( numera6620942414471956472nteger @ X ) @ ( numera6620942414471956472nteger @ Y ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % or_numerals(7)
% 0.33/0.60 thf(fact_4675_or__numerals_I7_J,axiom,
% 0.33/0.60 ! [X: num,Y: num] :
% 0.33/0.60 ( ( bit_se9127793120404214118atural @ ( numera5444537566228673987atural @ ( bit1 @ X ) ) @ ( numera5444537566228673987atural @ ( bit1 @ Y ) ) )
% 0.33/0.60 = ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se9127793120404214118atural @ ( numera5444537566228673987atural @ X ) @ ( numera5444537566228673987atural @ Y ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % or_numerals(7)
% 0.33/0.60 thf(fact_4676_or__nat__rec,axiom,
% 0.33/0.60 ( bit_se1412395901928357646or_nat
% 0.33/0.60 = ( ^ [M: nat,N4: nat] :
% 0.33/0.60 ( plus_plus_nat
% 0.33/0.60 @ ( zero_n2687167440665602831ol_nat
% 0.33/0.60 @ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
% 0.33/0.60 | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) )
% 0.33/0.60 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( divide_divide_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % or_nat_rec
% 0.33/0.60 thf(fact_4677_or__not__numerals_I9_J,axiom,
% 0.33/0.60 ! [M2: num,N2: num] :
% 0.33/0.60 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M2 ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) )
% 0.33/0.60 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M2 ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % or_not_numerals(9)
% 0.33/0.60 thf(fact_4678_bit_Odisj__one__left,axiom,
% 0.33/0.60 ! [X: int] :
% 0.33/0.60 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ one_one_int ) @ X )
% 0.33/0.60 = ( uminus_uminus_int @ one_one_int ) ) ).
% 0.33/0.60
% 0.33/0.60 % bit.disj_one_left
% 0.33/0.60 thf(fact_4679_bit_Odisj__one__left,axiom,
% 0.33/0.60 ! [X: code_integer] :
% 0.33/0.60 ( ( bit_se1080825931792720795nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ X )
% 0.33/0.60 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.33/0.60
% 0.33/0.60 % bit.disj_one_left
% 0.33/0.60 thf(fact_4680_bit_Odisj__one__right,axiom,
% 0.33/0.60 ! [X: int] :
% 0.33/0.60 ( ( bit_se1409905431419307370or_int @ X @ ( uminus_uminus_int @ one_one_int ) )
% 0.33/0.60 = ( uminus_uminus_int @ one_one_int ) ) ).
% 0.33/0.60
% 0.33/0.60 % bit.disj_one_right
% 0.33/0.60 thf(fact_4681_bit_Odisj__one__right,axiom,
% 0.33/0.60 ! [X: code_integer] :
% 0.33/0.60 ( ( bit_se1080825931792720795nteger @ X @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.33/0.60 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.33/0.60
% 0.33/0.60 % bit.disj_one_right
% 0.33/0.60 thf(fact_4682_or__numerals_I8_J,axiom,
% 0.33/0.60 ! [X: num] :
% 0.33/0.60 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ one_one_int )
% 0.33/0.60 = ( numeral_numeral_int @ ( bit1 @ X ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % or_numerals(8)
% 0.33/0.60 thf(fact_4683_or__numerals_I8_J,axiom,
% 0.33/0.60 ! [X: num] :
% 0.33/0.60 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ one_one_nat )
% 0.33/0.60 = ( numeral_numeral_nat @ ( bit1 @ X ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % or_numerals(8)
% 0.33/0.60 thf(fact_4684_or__numerals_I8_J,axiom,
% 0.33/0.60 ! [X: num] :
% 0.33/0.60 ( ( bit_se1080825931792720795nteger @ ( numera6620942414471956472nteger @ ( bit1 @ X ) ) @ one_one_Code_integer )
% 0.33/0.60 = ( numera6620942414471956472nteger @ ( bit1 @ X ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % or_numerals(8)
% 0.33/0.60 thf(fact_4685_or__numerals_I8_J,axiom,
% 0.33/0.60 ! [X: num] :
% 0.33/0.60 ( ( bit_se9127793120404214118atural @ ( numera5444537566228673987atural @ ( bit1 @ X ) ) @ one_one_Code_natural )
% 0.33/0.60 = ( numera5444537566228673987atural @ ( bit1 @ X ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % or_numerals(8)
% 0.33/0.60 thf(fact_4686_or__numerals_I2_J,axiom,
% 0.33/0.60 ! [Y: num] :
% 0.33/0.60 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 0.33/0.60 = ( numeral_numeral_int @ ( bit1 @ Y ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % or_numerals(2)
% 0.33/0.60 thf(fact_4687_or__numerals_I2_J,axiom,
% 0.33/0.60 ! [Y: num] :
% 0.33/0.60 ( ( bit_se1412395901928357646or_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 0.33/0.60 = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % or_numerals(2)
% 0.33/0.60 thf(fact_4688_or__numerals_I2_J,axiom,
% 0.33/0.60 ! [Y: num] :
% 0.33/0.60 ( ( bit_se1080825931792720795nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit1 @ Y ) ) )
% 0.33/0.60 = ( numera6620942414471956472nteger @ ( bit1 @ Y ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % or_numerals(2)
% 0.33/0.60 thf(fact_4689_or__numerals_I2_J,axiom,
% 0.33/0.60 ! [Y: num] :
% 0.33/0.60 ( ( bit_se9127793120404214118atural @ one_one_Code_natural @ ( numera5444537566228673987atural @ ( bit1 @ Y ) ) )
% 0.33/0.60 = ( numera5444537566228673987atural @ ( bit1 @ Y ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % or_numerals(2)
% 0.33/0.60 thf(fact_4690_bit_Odisj__cancel__left,axiom,
% 0.33/0.60 ! [X: int] :
% 0.33/0.60 ( ( bit_se1409905431419307370or_int @ ( bit_ri7919022796975470100ot_int @ X ) @ X )
% 0.33/0.60 = ( uminus_uminus_int @ one_one_int ) ) ).
% 0.33/0.60
% 0.33/0.60 % bit.disj_cancel_left
% 0.33/0.60 thf(fact_4691_bit_Odisj__cancel__left,axiom,
% 0.33/0.60 ! [X: code_integer] :
% 0.33/0.60 ( ( bit_se1080825931792720795nteger @ ( bit_ri7632146776885996613nteger @ X ) @ X )
% 0.33/0.60 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.33/0.60
% 0.33/0.60 % bit.disj_cancel_left
% 0.33/0.60 thf(fact_4692_bit_Odisj__cancel__right,axiom,
% 0.33/0.60 ! [X: int] :
% 0.33/0.60 ( ( bit_se1409905431419307370or_int @ X @ ( bit_ri7919022796975470100ot_int @ X ) )
% 0.33/0.60 = ( uminus_uminus_int @ one_one_int ) ) ).
% 0.33/0.60
% 0.33/0.60 % bit.disj_cancel_right
% 0.33/0.60 thf(fact_4693_bit_Odisj__cancel__right,axiom,
% 0.33/0.60 ! [X: code_integer] :
% 0.33/0.60 ( ( bit_se1080825931792720795nteger @ X @ ( bit_ri7632146776885996613nteger @ X ) )
% 0.33/0.60 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.33/0.60
% 0.33/0.60 % bit.disj_cancel_right
% 0.33/0.60 thf(fact_4694_or__numerals_I5_J,axiom,
% 0.33/0.60 ! [X: num] :
% 0.33/0.60 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ one_one_int )
% 0.33/0.60 = ( numeral_numeral_int @ ( bit1 @ X ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % or_numerals(5)
% 0.33/0.60 thf(fact_4695_or__numerals_I5_J,axiom,
% 0.33/0.60 ! [X: num] :
% 0.33/0.60 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ one_one_nat )
% 0.33/0.60 = ( numeral_numeral_nat @ ( bit1 @ X ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % or_numerals(5)
% 0.33/0.60 thf(fact_4696_or__numerals_I5_J,axiom,
% 0.33/0.60 ! [X: num] :
% 0.33/0.60 ( ( bit_se1080825931792720795nteger @ ( numera6620942414471956472nteger @ ( bit0 @ X ) ) @ one_one_Code_integer )
% 0.33/0.60 = ( numera6620942414471956472nteger @ ( bit1 @ X ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % or_numerals(5)
% 0.33/0.60 thf(fact_4697_or__numerals_I5_J,axiom,
% 0.33/0.60 ! [X: num] :
% 0.33/0.60 ( ( bit_se9127793120404214118atural @ ( numera5444537566228673987atural @ ( bit0 @ X ) ) @ one_one_Code_natural )
% 0.33/0.60 = ( numera5444537566228673987atural @ ( bit1 @ X ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % or_numerals(5)
% 0.33/0.60 thf(fact_4698_or__numerals_I1_J,axiom,
% 0.33/0.60 ! [Y: num] :
% 0.33/0.60 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 0.33/0.60 = ( numeral_numeral_int @ ( bit1 @ Y ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % or_numerals(1)
% 0.33/0.60 thf(fact_4699_or__numerals_I1_J,axiom,
% 0.33/0.60 ! [Y: num] :
% 0.33/0.60 ( ( bit_se1412395901928357646or_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 0.33/0.60 = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % or_numerals(1)
% 0.33/0.60 thf(fact_4700_or__numerals_I1_J,axiom,
% 0.33/0.60 ! [Y: num] :
% 0.33/0.60 ( ( bit_se1080825931792720795nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ Y ) ) )
% 0.33/0.60 = ( numera6620942414471956472nteger @ ( bit1 @ Y ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % or_numerals(1)
% 0.33/0.60 thf(fact_4701_or__numerals_I1_J,axiom,
% 0.33/0.60 ! [Y: num] :
% 0.33/0.60 ( ( bit_se9127793120404214118atural @ one_one_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ Y ) ) )
% 0.33/0.60 = ( numera5444537566228673987atural @ ( bit1 @ Y ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % or_numerals(1)
% 0.33/0.60 thf(fact_4702_or__integer_Oabs__eq,axiom,
% 0.33/0.60 ! [Xa: int,X: int] :
% 0.33/0.60 ( ( bit_se1080825931792720795nteger @ ( code_integer_of_int @ Xa ) @ ( code_integer_of_int @ X ) )
% 0.33/0.60 = ( code_integer_of_int @ ( bit_se1409905431419307370or_int @ Xa @ X ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % or_integer.abs_eq
% 0.33/0.60 thf(fact_4703_or__integer_Orep__eq,axiom,
% 0.33/0.60 ! [X: code_integer,Xa: code_integer] :
% 0.33/0.60 ( ( code_int_of_integer @ ( bit_se1080825931792720795nteger @ X @ Xa ) )
% 0.33/0.60 = ( bit_se1409905431419307370or_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Xa ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % or_integer.rep_eq
% 0.33/0.60 thf(fact_4704_disjunctive__add,axiom,
% 0.33/0.60 ! [A: int,B: int] :
% 0.33/0.60 ( ! [N: nat] :
% 0.33/0.60 ( ~ ( bit_se1146084159140164899it_int @ A @ N )
% 0.33/0.60 | ~ ( bit_se1146084159140164899it_int @ B @ N ) )
% 0.33/0.60 => ( ( plus_plus_int @ A @ B )
% 0.33/0.60 = ( bit_se1409905431419307370or_int @ A @ B ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % disjunctive_add
% 0.33/0.60 thf(fact_4705_disjunctive__add,axiom,
% 0.33/0.60 ! [A: nat,B: nat] :
% 0.33/0.60 ( ! [N: nat] :
% 0.33/0.60 ( ~ ( bit_se1148574629649215175it_nat @ A @ N )
% 0.33/0.60 | ~ ( bit_se1148574629649215175it_nat @ B @ N ) )
% 0.33/0.60 => ( ( plus_plus_nat @ A @ B )
% 0.33/0.60 = ( bit_se1412395901928357646or_nat @ A @ B ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % disjunctive_add
% 0.33/0.60 thf(fact_4706_disjunctive__add,axiom,
% 0.33/0.60 ! [A: code_integer,B: code_integer] :
% 0.33/0.60 ( ! [N: nat] :
% 0.33/0.60 ( ~ ( bit_se9216721137139052372nteger @ A @ N )
% 0.33/0.60 | ~ ( bit_se9216721137139052372nteger @ B @ N ) )
% 0.33/0.60 => ( ( plus_p5714425477246183910nteger @ A @ B )
% 0.33/0.60 = ( bit_se1080825931792720795nteger @ A @ B ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % disjunctive_add
% 0.33/0.60 thf(fact_4707_disjunctive__add,axiom,
% 0.33/0.60 ! [A: code_natural,B: code_natural] :
% 0.33/0.60 ( ! [N: nat] :
% 0.33/0.60 ( ~ ( bit_se8040316288895769887atural @ A @ N )
% 0.33/0.60 | ~ ( bit_se8040316288895769887atural @ B @ N ) )
% 0.33/0.60 => ( ( plus_p4538020629002901425atural @ A @ B )
% 0.33/0.60 = ( bit_se9127793120404214118atural @ A @ B ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % disjunctive_add
% 0.33/0.60 thf(fact_4708_plus__and__or,axiom,
% 0.33/0.60 ! [X: int,Y: int] :
% 0.33/0.60 ( ( plus_plus_int @ ( bit_se725231765392027082nd_int @ X @ Y ) @ ( bit_se1409905431419307370or_int @ X @ Y ) )
% 0.33/0.60 = ( plus_plus_int @ X @ Y ) ) ).
% 0.33/0.60
% 0.33/0.60 % plus_and_or
% 0.33/0.60 thf(fact_4709_not__integer_Orep__eq,axiom,
% 0.33/0.60 ! [X: code_integer] :
% 0.33/0.60 ( ( code_int_of_integer @ ( bit_ri7632146776885996613nteger @ X ) )
% 0.33/0.60 = ( bit_ri7919022796975470100ot_int @ ( code_int_of_integer @ X ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % not_integer.rep_eq
% 0.33/0.60 thf(fact_4710_set__bit__nat__def,axiom,
% 0.33/0.60 ( bit_se7882103937844011126it_nat
% 0.33/0.60 = ( ^ [M: nat,N4: nat] : ( bit_se1412395901928357646or_nat @ N4 @ ( bit_se547839408752420682it_nat @ M @ one_one_nat ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % set_bit_nat_def
% 0.33/0.60 thf(fact_4711_not__integer_Oabs__eq,axiom,
% 0.33/0.60 ! [X: int] :
% 0.33/0.60 ( ( bit_ri7632146776885996613nteger @ ( code_integer_of_int @ X ) )
% 0.33/0.60 = ( code_integer_of_int @ ( bit_ri7919022796975470100ot_int @ X ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % not_integer.abs_eq
% 0.33/0.60 thf(fact_4712_set__bit__eq__or,axiom,
% 0.33/0.60 ( bit_se7882103937844011126it_nat
% 0.33/0.60 = ( ^ [N4: nat,A5: nat] : ( bit_se1412395901928357646or_nat @ A5 @ ( bit_se547839408752420682it_nat @ N4 @ one_one_nat ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % set_bit_eq_or
% 0.33/0.60 thf(fact_4713_set__bit__eq__or,axiom,
% 0.33/0.60 ( bit_se2793503036327961859nteger
% 0.33/0.60 = ( ^ [N4: nat,A5: code_integer] : ( bit_se1080825931792720795nteger @ A5 @ ( bit_se7788150548672797655nteger @ N4 @ one_one_Code_integer ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % set_bit_eq_or
% 0.33/0.60 thf(fact_4714_set__bit__eq__or,axiom,
% 0.33/0.60 ( bit_se7879613467334960850it_int
% 0.33/0.60 = ( ^ [N4: nat,A5: int] : ( bit_se1409905431419307370or_int @ A5 @ ( bit_se545348938243370406it_int @ N4 @ one_one_int ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % set_bit_eq_or
% 0.33/0.60 thf(fact_4715_set__bit__eq__or,axiom,
% 0.33/0.60 ( bit_se1617098188084679374atural
% 0.33/0.60 = ( ^ [N4: nat,A5: code_natural] : ( bit_se9127793120404214118atural @ A5 @ ( bit_se6611745700429515170atural @ N4 @ one_one_Code_natural ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % set_bit_eq_or
% 0.33/0.60 thf(fact_4716_bit_Ocomplement__unique,axiom,
% 0.33/0.60 ! [A: int,X: int,Y: int] :
% 0.33/0.60 ( ( ( bit_se725231765392027082nd_int @ A @ X )
% 0.33/0.60 = zero_zero_int )
% 0.33/0.60 => ( ( ( bit_se1409905431419307370or_int @ A @ X )
% 0.33/0.60 = ( uminus_uminus_int @ one_one_int ) )
% 0.33/0.60 => ( ( ( bit_se725231765392027082nd_int @ A @ Y )
% 0.33/0.60 = zero_zero_int )
% 0.33/0.60 => ( ( ( bit_se1409905431419307370or_int @ A @ Y )
% 0.33/0.60 = ( uminus_uminus_int @ one_one_int ) )
% 0.33/0.60 => ( X = Y ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % bit.complement_unique
% 0.33/0.60 thf(fact_4717_bit_Ocomplement__unique,axiom,
% 0.33/0.60 ! [A: code_integer,X: code_integer,Y: code_integer] :
% 0.33/0.60 ( ( ( bit_se3949692690581998587nteger @ A @ X )
% 0.33/0.60 = zero_z3403309356797280102nteger )
% 0.33/0.60 => ( ( ( bit_se1080825931792720795nteger @ A @ X )
% 0.33/0.60 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.33/0.60 => ( ( ( bit_se3949692690581998587nteger @ A @ Y )
% 0.33/0.60 = zero_z3403309356797280102nteger )
% 0.33/0.60 => ( ( ( bit_se1080825931792720795nteger @ A @ Y )
% 0.33/0.60 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.33/0.60 => ( X = Y ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % bit.complement_unique
% 0.33/0.60 thf(fact_4718_bit_Ocompl__unique,axiom,
% 0.33/0.60 ! [X: int,Y: int] :
% 0.33/0.60 ( ( ( bit_se725231765392027082nd_int @ X @ Y )
% 0.33/0.60 = zero_zero_int )
% 0.33/0.60 => ( ( ( bit_se1409905431419307370or_int @ X @ Y )
% 0.33/0.60 = ( uminus_uminus_int @ one_one_int ) )
% 0.33/0.60 => ( ( bit_ri7919022796975470100ot_int @ X )
% 0.33/0.60 = Y ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % bit.compl_unique
% 0.33/0.60 thf(fact_4719_bit_Ocompl__unique,axiom,
% 0.33/0.60 ! [X: code_integer,Y: code_integer] :
% 0.33/0.60 ( ( ( bit_se3949692690581998587nteger @ X @ Y )
% 0.33/0.60 = zero_z3403309356797280102nteger )
% 0.33/0.60 => ( ( ( bit_se1080825931792720795nteger @ X @ Y )
% 0.33/0.60 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.33/0.60 => ( ( bit_ri7632146776885996613nteger @ X )
% 0.33/0.60 = Y ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % bit.compl_unique
% 0.33/0.60 thf(fact_4720_or__one__eq,axiom,
% 0.33/0.60 ! [A: int] :
% 0.33/0.60 ( ( bit_se1409905431419307370or_int @ A @ one_one_int )
% 0.33/0.60 = ( plus_plus_int @ A @ ( zero_n2684676970156552555ol_int @ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % or_one_eq
% 0.33/0.60 thf(fact_4721_or__one__eq,axiom,
% 0.33/0.60 ! [A: nat] :
% 0.33/0.60 ( ( bit_se1412395901928357646or_nat @ A @ one_one_nat )
% 0.33/0.60 = ( plus_plus_nat @ A @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % or_one_eq
% 0.33/0.60 thf(fact_4722_or__one__eq,axiom,
% 0.33/0.60 ! [A: code_integer] :
% 0.33/0.60 ( ( bit_se1080825931792720795nteger @ A @ one_one_Code_integer )
% 0.33/0.60 = ( plus_p5714425477246183910nteger @ A @ ( zero_n356916108424825756nteger @ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % or_one_eq
% 0.33/0.60 thf(fact_4723_or__one__eq,axiom,
% 0.33/0.60 ! [A: code_natural] :
% 0.33/0.60 ( ( bit_se9127793120404214118atural @ A @ one_one_Code_natural )
% 0.33/0.60 = ( plus_p4538020629002901425atural @ A @ ( zero_n8403883297036319079atural @ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % or_one_eq
% 0.33/0.60 thf(fact_4724_one__or__eq,axiom,
% 0.33/0.60 ! [A: int] :
% 0.33/0.60 ( ( bit_se1409905431419307370or_int @ one_one_int @ A )
% 0.33/0.60 = ( plus_plus_int @ A @ ( zero_n2684676970156552555ol_int @ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % one_or_eq
% 0.33/0.60 thf(fact_4725_one__or__eq,axiom,
% 0.33/0.60 ! [A: nat] :
% 0.33/0.60 ( ( bit_se1412395901928357646or_nat @ one_one_nat @ A )
% 0.33/0.60 = ( plus_plus_nat @ A @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % one_or_eq
% 0.33/0.60 thf(fact_4726_one__or__eq,axiom,
% 0.33/0.60 ! [A: code_integer] :
% 0.33/0.60 ( ( bit_se1080825931792720795nteger @ one_one_Code_integer @ A )
% 0.33/0.60 = ( plus_p5714425477246183910nteger @ A @ ( zero_n356916108424825756nteger @ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % one_or_eq
% 0.33/0.60 thf(fact_4727_one__or__eq,axiom,
% 0.33/0.60 ! [A: code_natural] :
% 0.33/0.60 ( ( bit_se9127793120404214118atural @ one_one_Code_natural @ A )
% 0.33/0.60 = ( plus_p4538020629002901425atural @ A @ ( zero_n8403883297036319079atural @ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % one_or_eq
% 0.33/0.60 thf(fact_4728_mask__Suc__double,axiom,
% 0.33/0.60 ! [N2: nat] :
% 0.33/0.60 ( ( bit_se2000444600071755411sk_int @ ( suc @ N2 ) )
% 0.33/0.60 = ( bit_se1409905431419307370or_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2000444600071755411sk_int @ N2 ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % mask_Suc_double
% 0.33/0.60 thf(fact_4729_mask__Suc__double,axiom,
% 0.33/0.60 ! [N2: nat] :
% 0.33/0.60 ( ( bit_se2119862282449309892nteger @ ( suc @ N2 ) )
% 0.33/0.60 = ( bit_se1080825931792720795nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se2119862282449309892nteger @ N2 ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % mask_Suc_double
% 0.33/0.60 thf(fact_4730_mask__Suc__double,axiom,
% 0.33/0.60 ! [N2: nat] :
% 0.33/0.60 ( ( bit_se2002935070580805687sk_nat @ ( suc @ N2 ) )
% 0.33/0.60 = ( bit_se1412395901928357646or_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2002935070580805687sk_nat @ N2 ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % mask_Suc_double
% 0.33/0.60 thf(fact_4731_mask__Suc__double,axiom,
% 0.33/0.60 ! [N2: nat] :
% 0.33/0.60 ( ( bit_se943457434206027407atural @ ( suc @ N2 ) )
% 0.33/0.60 = ( bit_se9127793120404214118atural @ one_one_Code_natural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se943457434206027407atural @ N2 ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % mask_Suc_double
% 0.33/0.60 thf(fact_4732_or__not__numerals_I5_J,axiom,
% 0.33/0.60 ! [M2: num,N2: num] :
% 0.33/0.60 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M2 ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) )
% 0.33/0.60 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M2 ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % or_not_numerals(5)
% 0.33/0.60 thf(fact_4733_Suc__0__or__eq,axiom,
% 0.33/0.60 ! [N2: nat] :
% 0.33/0.60 ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 0.33/0.60 = ( plus_plus_nat @ N2 @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % Suc_0_or_eq
% 0.33/0.60 thf(fact_4734_or__Suc__0__eq,axiom,
% 0.33/0.60 ! [N2: nat] :
% 0.33/0.60 ( ( bit_se1412395901928357646or_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 0.33/0.60 = ( plus_plus_nat @ N2 @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % or_Suc_0_eq
% 0.33/0.60 thf(fact_4735_or__not__numerals_I8_J,axiom,
% 0.33/0.60 ! [M2: num,N2: num] :
% 0.33/0.60 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M2 ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) )
% 0.33/0.60 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M2 ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % or_not_numerals(8)
% 0.33/0.60 thf(fact_4736_or__int__unfold,axiom,
% 0.33/0.60 ( bit_se1409905431419307370or_int
% 0.33/0.60 = ( ^ [K4: int,L3: int] :
% 0.33/0.60 ( if_int
% 0.33/0.60 @ ( ( K4
% 0.33/0.60 = ( uminus_uminus_int @ one_one_int ) )
% 0.33/0.60 | ( L3
% 0.33/0.60 = ( uminus_uminus_int @ one_one_int ) ) )
% 0.33/0.60 @ ( uminus_uminus_int @ one_one_int )
% 0.33/0.60 @ ( if_int @ ( K4 = zero_zero_int ) @ L3 @ ( if_int @ ( L3 = zero_zero_int ) @ K4 @ ( plus_plus_int @ ( ord_max_int @ ( modulo_modulo_int @ K4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ L3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( divide_divide_int @ K4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % or_int_unfold
% 0.33/0.60 thf(fact_4737_bit_Oabstract__boolean__algebra__sym__diff__axioms,axiom,
% 0.33/0.60 boolea2445317508997433345nteger @ bit_se3949692690581998587nteger @ bit_se1080825931792720795nteger @ bit_ri7632146776885996613nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ bit_se3222712562003087583nteger ).
% 0.33/0.60
% 0.33/0.60 % bit.abstract_boolean_algebra_sym_diff_axioms
% 0.33/0.60 thf(fact_4738_bit_Oabstract__boolean__algebra__sym__diff__axioms,axiom,
% 0.33/0.60 boolea8527374999097803216ff_int @ bit_se725231765392027082nd_int @ bit_se1409905431419307370or_int @ bit_ri7919022796975470100ot_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) @ bit_se6526347334894502574or_int ).
% 0.33/0.60
% 0.33/0.60 % bit.abstract_boolean_algebra_sym_diff_axioms
% 0.33/0.60 thf(fact_4739_or__nat__unfold,axiom,
% 0.33/0.60 ( bit_se1412395901928357646or_nat
% 0.33/0.60 = ( ^ [M: nat,N4: nat] : ( if_nat @ ( M = zero_zero_nat ) @ N4 @ ( if_nat @ ( N4 = zero_zero_nat ) @ M @ ( plus_plus_nat @ ( ord_max_nat @ ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( divide_divide_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % or_nat_unfold
% 0.33/0.60 thf(fact_4740_drop__bit__rec,axiom,
% 0.33/0.60 ( bit_se3928097537394005634nteger
% 0.33/0.60 = ( ^ [N4: nat,A5: code_integer] : ( if_Code_integer @ ( N4 = zero_zero_nat ) @ A5 @ ( bit_se3928097537394005634nteger @ ( minus_minus_nat @ N4 @ one_one_nat ) @ ( divide6298287555418463151nteger @ A5 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % drop_bit_rec
% 0.33/0.60 thf(fact_4741_drop__bit__rec,axiom,
% 0.33/0.60 ( bit_se8568078237143864401it_int
% 0.33/0.60 = ( ^ [N4: nat,A5: int] : ( if_int @ ( N4 = zero_zero_nat ) @ A5 @ ( bit_se8568078237143864401it_int @ ( minus_minus_nat @ N4 @ one_one_nat ) @ ( divide_divide_int @ A5 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % drop_bit_rec
% 0.33/0.60 thf(fact_4742_drop__bit__rec,axiom,
% 0.33/0.60 ( bit_se8570568707652914677it_nat
% 0.33/0.60 = ( ^ [N4: nat,A5: nat] : ( if_nat @ ( N4 = zero_zero_nat ) @ A5 @ ( bit_se8570568707652914677it_nat @ ( minus_minus_nat @ N4 @ one_one_nat ) @ ( divide_divide_nat @ A5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % drop_bit_rec
% 0.33/0.60 thf(fact_4743_drop__bit__rec,axiom,
% 0.33/0.60 ( bit_se2751692689150723149atural
% 0.33/0.60 = ( ^ [N4: nat,A5: code_natural] : ( if_Code_natural @ ( N4 = zero_zero_nat ) @ A5 @ ( bit_se2751692689150723149atural @ ( minus_minus_nat @ N4 @ one_one_nat ) @ ( divide5121882707175180666atural @ A5 @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % drop_bit_rec
% 0.33/0.60 thf(fact_4744_image__atLeastZeroLessThan__integer,axiom,
% 0.33/0.60 ! [U: code_integer] :
% 0.33/0.60 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ U )
% 0.33/0.60 => ( ( set_or8404916559141939852nteger @ zero_z3403309356797280102nteger @ U )
% 0.33/0.60 = ( image_1215581382706833972nteger @ semiri4939895301339042750nteger @ ( set_ord_lessThan_nat @ ( code_nat_of_integer @ U ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % image_atLeastZeroLessThan_integer
% 0.33/0.60 thf(fact_4745_uminus__int__def,axiom,
% 0.33/0.60 ( uminus_uminus_int
% 0.33/0.60 = ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ
% 0.33/0.60 @ ( produc2626176000494625587at_nat
% 0.33/0.60 @ ^ [X3: nat,Y3: nat] : ( product_Pair_nat_nat @ Y3 @ X3 ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % uminus_int_def
% 0.33/0.60 thf(fact_4746_bit_Oabstract__boolean__algebra__axioms,axiom,
% 0.33/0.60 boolea5469654029284665142ra_int @ bit_se725231765392027082nd_int @ bit_se1409905431419307370or_int @ bit_ri7919022796975470100ot_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ).
% 0.33/0.60
% 0.33/0.60 % bit.abstract_boolean_algebra_axioms
% 0.33/0.60 thf(fact_4747_bit_Oabstract__boolean__algebra__axioms,axiom,
% 0.33/0.60 boolea5643492148547655015nteger @ bit_se3949692690581998587nteger @ bit_se1080825931792720795nteger @ bit_ri7632146776885996613nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ).
% 0.33/0.60
% 0.33/0.60 % bit.abstract_boolean_algebra_axioms
% 0.33/0.60 thf(fact_4748_map__fun__apply,axiom,
% 0.33/0.60 ( map_fu4826362097070443709at_o_o
% 0.33/0.60 = ( ^ [F2: int > product_prod_nat_nat,G2: $o > $o,H: product_prod_nat_nat > $o,X3: int] : ( G2 @ ( H @ ( F2 @ X3 ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % map_fun_apply
% 0.33/0.60 thf(fact_4749_map__fun__apply,axiom,
% 0.33/0.60 ( map_fu4960017516451851995nt_int
% 0.33/0.60 = ( ^ [F2: int > product_prod_nat_nat,G2: ( product_prod_nat_nat > product_prod_nat_nat ) > int > int,H: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,X3: int] : ( G2 @ ( H @ ( F2 @ X3 ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % map_fun_apply
% 0.33/0.60 thf(fact_4750_map__fun__apply,axiom,
% 0.33/0.60 ( map_fu434086159418415080_int_o
% 0.33/0.60 = ( ^ [F2: int > product_prod_nat_nat,G2: ( product_prod_nat_nat > $o ) > int > $o,H: product_prod_nat_nat > product_prod_nat_nat > $o,X3: int] : ( G2 @ ( H @ ( F2 @ X3 ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % map_fun_apply
% 0.33/0.60 thf(fact_4751_map__fun__apply,axiom,
% 0.33/0.60 ( map_fu3424225382358772769nt_rat
% 0.33/0.60 = ( ^ [F2: int > int,G2: product_prod_int_int > rat,H: int > product_prod_int_int,X3: int] : ( G2 @ ( H @ ( F2 @ X3 ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % map_fun_apply
% 0.33/0.60 thf(fact_4752_map__fun__apply,axiom,
% 0.33/0.60 ( map_fu7831380289885515383nt_rat
% 0.33/0.60 = ( ^ [F2: int > int,G2: ( int > product_prod_int_int ) > int > rat,H: int > int > product_prod_int_int,X3: int] : ( G2 @ ( H @ ( F2 @ X3 ) ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % map_fun_apply
% 0.33/0.60 thf(fact_4753_drop__bit__drop__bit,axiom,
% 0.33/0.60 ! [M2: nat,N2: nat,A: code_integer] :
% 0.33/0.60 ( ( bit_se3928097537394005634nteger @ M2 @ ( bit_se3928097537394005634nteger @ N2 @ A ) )
% 0.33/0.60 = ( bit_se3928097537394005634nteger @ ( plus_plus_nat @ M2 @ N2 ) @ A ) ) ).
% 0.33/0.60
% 0.33/0.60 % drop_bit_drop_bit
% 0.33/0.60 thf(fact_4754_drop__bit__drop__bit,axiom,
% 0.33/0.60 ! [M2: nat,N2: nat,A: int] :
% 0.33/0.60 ( ( bit_se8568078237143864401it_int @ M2 @ ( bit_se8568078237143864401it_int @ N2 @ A ) )
% 0.33/0.60 = ( bit_se8568078237143864401it_int @ ( plus_plus_nat @ M2 @ N2 ) @ A ) ) ).
% 0.33/0.60
% 0.33/0.60 % drop_bit_drop_bit
% 0.33/0.60 thf(fact_4755_drop__bit__drop__bit,axiom,
% 0.33/0.60 ! [M2: nat,N2: nat,A: nat] :
% 0.33/0.60 ( ( bit_se8570568707652914677it_nat @ M2 @ ( bit_se8570568707652914677it_nat @ N2 @ A ) )
% 0.33/0.60 = ( bit_se8570568707652914677it_nat @ ( plus_plus_nat @ M2 @ N2 ) @ A ) ) ).
% 0.33/0.60
% 0.33/0.60 % drop_bit_drop_bit
% 0.33/0.60 thf(fact_4756_drop__bit__drop__bit,axiom,
% 0.33/0.60 ! [M2: nat,N2: nat,A: code_natural] :
% 0.33/0.60 ( ( bit_se2751692689150723149atural @ M2 @ ( bit_se2751692689150723149atural @ N2 @ A ) )
% 0.33/0.60 = ( bit_se2751692689150723149atural @ ( plus_plus_nat @ M2 @ N2 ) @ A ) ) ).
% 0.33/0.60
% 0.33/0.60 % drop_bit_drop_bit
% 0.33/0.60 thf(fact_4757_image__add__atLeastAtMost,axiom,
% 0.33/0.60 ! [K: rat,I: rat,J: rat] :
% 0.33/0.60 ( ( image_rat_rat @ ( plus_plus_rat @ K ) @ ( set_or633870826150836451st_rat @ I @ J ) )
% 0.33/0.60 = ( set_or633870826150836451st_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ K ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % image_add_atLeastAtMost
% 0.33/0.60 thf(fact_4758_image__add__atLeastAtMost,axiom,
% 0.33/0.60 ! [K: int,I: int,J: int] :
% 0.33/0.60 ( ( image_int_int @ ( plus_plus_int @ K ) @ ( set_or1266510415728281911st_int @ I @ J ) )
% 0.33/0.60 = ( set_or1266510415728281911st_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ K ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % image_add_atLeastAtMost
% 0.33/0.60 thf(fact_4759_image__add__atLeastAtMost,axiom,
% 0.33/0.60 ! [K: nat,I: nat,J: nat] :
% 0.33/0.60 ( ( image_nat_nat @ ( plus_plus_nat @ K ) @ ( set_or1269000886237332187st_nat @ I @ J ) )
% 0.33/0.60 = ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % image_add_atLeastAtMost
% 0.33/0.60 thf(fact_4760_image__add__atLeastAtMost,axiom,
% 0.33/0.60 ! [K: code_integer,I: code_integer,J: code_integer] :
% 0.33/0.60 ( ( image_4470545334726330049nteger @ ( plus_p5714425477246183910nteger @ K ) @ ( set_or189985376899183464nteger @ I @ J ) )
% 0.33/0.60 = ( set_or189985376899183464nteger @ ( plus_p5714425477246183910nteger @ I @ K ) @ ( plus_p5714425477246183910nteger @ J @ K ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % image_add_atLeastAtMost
% 0.33/0.60 thf(fact_4761_image__diff__atLeastAtMost,axiom,
% 0.33/0.60 ! [D2: rat,A: rat,B: rat] :
% 0.33/0.60 ( ( image_rat_rat @ ( minus_minus_rat @ D2 ) @ ( set_or633870826150836451st_rat @ A @ B ) )
% 0.33/0.60 = ( set_or633870826150836451st_rat @ ( minus_minus_rat @ D2 @ B ) @ ( minus_minus_rat @ D2 @ A ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % image_diff_atLeastAtMost
% 0.33/0.60 thf(fact_4762_image__diff__atLeastAtMost,axiom,
% 0.33/0.60 ! [D2: int,A: int,B: int] :
% 0.33/0.60 ( ( image_int_int @ ( minus_minus_int @ D2 ) @ ( set_or1266510415728281911st_int @ A @ B ) )
% 0.33/0.60 = ( set_or1266510415728281911st_int @ ( minus_minus_int @ D2 @ B ) @ ( minus_minus_int @ D2 @ A ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % image_diff_atLeastAtMost
% 0.33/0.60 thf(fact_4763_image__diff__atLeastAtMost,axiom,
% 0.33/0.60 ! [D2: code_integer,A: code_integer,B: code_integer] :
% 0.33/0.60 ( ( image_4470545334726330049nteger @ ( minus_8373710615458151222nteger @ D2 ) @ ( set_or189985376899183464nteger @ A @ B ) )
% 0.33/0.60 = ( set_or189985376899183464nteger @ ( minus_8373710615458151222nteger @ D2 @ B ) @ ( minus_8373710615458151222nteger @ D2 @ A ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % image_diff_atLeastAtMost
% 0.33/0.60 thf(fact_4764_image__add__atLeastLessThan,axiom,
% 0.33/0.60 ! [K: rat,I: rat,J: rat] :
% 0.33/0.60 ( ( image_rat_rat @ ( plus_plus_rat @ K ) @ ( set_or4029947393144176647an_rat @ I @ J ) )
% 0.33/0.60 = ( set_or4029947393144176647an_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ K ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % image_add_atLeastLessThan
% 0.33/0.60 thf(fact_4765_image__add__atLeastLessThan,axiom,
% 0.33/0.60 ! [K: nat,I: nat,J: nat] :
% 0.33/0.60 ( ( image_nat_nat @ ( plus_plus_nat @ K ) @ ( set_or4665077453230672383an_nat @ I @ J ) )
% 0.33/0.60 = ( set_or4665077453230672383an_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % image_add_atLeastLessThan
% 0.33/0.60 thf(fact_4766_image__add__atLeastLessThan,axiom,
% 0.33/0.60 ! [K: code_integer,I: code_integer,J: code_integer] :
% 0.33/0.60 ( ( image_4470545334726330049nteger @ ( plus_p5714425477246183910nteger @ K ) @ ( set_or8404916559141939852nteger @ I @ J ) )
% 0.33/0.60 = ( set_or8404916559141939852nteger @ ( plus_p5714425477246183910nteger @ I @ K ) @ ( plus_p5714425477246183910nteger @ J @ K ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % image_add_atLeastLessThan
% 0.33/0.60 thf(fact_4767_image__add__atLeastLessThan,axiom,
% 0.33/0.60 ! [K: int,I: int,J: int] :
% 0.33/0.60 ( ( image_int_int @ ( plus_plus_int @ K ) @ ( set_or4662586982721622107an_int @ I @ J ) )
% 0.33/0.60 = ( set_or4662586982721622107an_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ K ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % image_add_atLeastLessThan
% 0.33/0.60 thf(fact_4768_max__0__1_I1_J,axiom,
% 0.33/0.60 ( ( ord_max_rat @ zero_zero_rat @ one_one_rat )
% 0.33/0.60 = one_one_rat ) ).
% 0.33/0.60
% 0.33/0.60 % max_0_1(1)
% 0.33/0.60 thf(fact_4769_max__0__1_I1_J,axiom,
% 0.33/0.60 ( ( ord_max_int @ zero_zero_int @ one_one_int )
% 0.33/0.60 = one_one_int ) ).
% 0.33/0.60
% 0.33/0.60 % max_0_1(1)
% 0.33/0.60 thf(fact_4770_max__0__1_I1_J,axiom,
% 0.33/0.60 ( ( ord_max_nat @ zero_zero_nat @ one_one_nat )
% 0.33/0.60 = one_one_nat ) ).
% 0.33/0.60
% 0.33/0.60 % max_0_1(1)
% 0.33/0.60 thf(fact_4771_max__0__1_I1_J,axiom,
% 0.33/0.60 ( ( ord_max_Code_integer @ zero_z3403309356797280102nteger @ one_one_Code_integer )
% 0.33/0.60 = one_one_Code_integer ) ).
% 0.33/0.60
% 0.33/0.60 % max_0_1(1)
% 0.33/0.60 thf(fact_4772_max__0__1_I1_J,axiom,
% 0.33/0.60 ( ( ord_max_Code_natural @ zero_z2226904508553997617atural @ one_one_Code_natural )
% 0.33/0.60 = one_one_Code_natural ) ).
% 0.33/0.60
% 0.33/0.60 % max_0_1(1)
% 0.33/0.60 thf(fact_4773_max__0__1_I2_J,axiom,
% 0.33/0.60 ( ( ord_max_rat @ one_one_rat @ zero_zero_rat )
% 0.33/0.60 = one_one_rat ) ).
% 0.33/0.60
% 0.33/0.60 % max_0_1(2)
% 0.33/0.60 thf(fact_4774_max__0__1_I2_J,axiom,
% 0.33/0.60 ( ( ord_max_int @ one_one_int @ zero_zero_int )
% 0.33/0.60 = one_one_int ) ).
% 0.33/0.60
% 0.33/0.60 % max_0_1(2)
% 0.33/0.60 thf(fact_4775_max__0__1_I2_J,axiom,
% 0.33/0.60 ( ( ord_max_nat @ one_one_nat @ zero_zero_nat )
% 0.33/0.60 = one_one_nat ) ).
% 0.33/0.60
% 0.33/0.60 % max_0_1(2)
% 0.33/0.60 thf(fact_4776_max__0__1_I2_J,axiom,
% 0.33/0.60 ( ( ord_max_Code_integer @ one_one_Code_integer @ zero_z3403309356797280102nteger )
% 0.33/0.60 = one_one_Code_integer ) ).
% 0.33/0.60
% 0.33/0.60 % max_0_1(2)
% 0.33/0.60 thf(fact_4777_max__0__1_I2_J,axiom,
% 0.33/0.60 ( ( ord_max_Code_natural @ one_one_Code_natural @ zero_z2226904508553997617atural )
% 0.33/0.60 = one_one_Code_natural ) ).
% 0.33/0.60
% 0.33/0.60 % max_0_1(2)
% 0.33/0.60 thf(fact_4778_image__uminus__atLeastAtMost,axiom,
% 0.33/0.60 ! [X: rat,Y: rat] :
% 0.33/0.60 ( ( image_rat_rat @ uminus_uminus_rat @ ( set_or633870826150836451st_rat @ X @ Y ) )
% 0.33/0.60 = ( set_or633870826150836451st_rat @ ( uminus_uminus_rat @ Y ) @ ( uminus_uminus_rat @ X ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % image_uminus_atLeastAtMost
% 0.33/0.60 thf(fact_4779_image__uminus__atLeastAtMost,axiom,
% 0.33/0.60 ! [X: int,Y: int] :
% 0.33/0.60 ( ( image_int_int @ uminus_uminus_int @ ( set_or1266510415728281911st_int @ X @ Y ) )
% 0.33/0.60 = ( set_or1266510415728281911st_int @ ( uminus_uminus_int @ Y ) @ ( uminus_uminus_int @ X ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % image_uminus_atLeastAtMost
% 0.33/0.60 thf(fact_4780_image__uminus__atLeastAtMost,axiom,
% 0.33/0.60 ! [X: code_integer,Y: code_integer] :
% 0.33/0.60 ( ( image_4470545334726330049nteger @ uminus1351360451143612070nteger @ ( set_or189985376899183464nteger @ X @ Y ) )
% 0.33/0.60 = ( set_or189985376899183464nteger @ ( uminus1351360451143612070nteger @ Y ) @ ( uminus1351360451143612070nteger @ X ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % image_uminus_atLeastAtMost
% 0.33/0.60 thf(fact_4781_max__0__1_I6_J,axiom,
% 0.33/0.60 ! [X: num] :
% 0.33/0.60 ( ( ord_max_nat @ ( numeral_numeral_nat @ X ) @ one_one_nat )
% 0.33/0.60 = ( numeral_numeral_nat @ X ) ) ).
% 0.33/0.60
% 0.33/0.60 % max_0_1(6)
% 0.33/0.60 thf(fact_4782_max__0__1_I6_J,axiom,
% 0.33/0.60 ! [X: num] :
% 0.33/0.60 ( ( ord_max_int @ ( numeral_numeral_int @ X ) @ one_one_int )
% 0.33/0.60 = ( numeral_numeral_int @ X ) ) ).
% 0.33/0.60
% 0.33/0.60 % max_0_1(6)
% 0.33/0.60 thf(fact_4783_max__0__1_I6_J,axiom,
% 0.33/0.60 ! [X: num] :
% 0.33/0.60 ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ X ) @ one_one_Code_integer )
% 0.33/0.60 = ( numera6620942414471956472nteger @ X ) ) ).
% 0.33/0.60
% 0.33/0.60 % max_0_1(6)
% 0.33/0.60 thf(fact_4784_max__0__1_I6_J,axiom,
% 0.33/0.60 ! [X: num] :
% 0.33/0.60 ( ( ord_max_rat @ ( numeral_numeral_rat @ X ) @ one_one_rat )
% 0.33/0.60 = ( numeral_numeral_rat @ X ) ) ).
% 0.33/0.60
% 0.33/0.60 % max_0_1(6)
% 0.33/0.60 thf(fact_4785_max__0__1_I6_J,axiom,
% 0.33/0.60 ! [X: num] :
% 0.33/0.60 ( ( ord_max_Code_natural @ ( numera5444537566228673987atural @ X ) @ one_one_Code_natural )
% 0.33/0.60 = ( numera5444537566228673987atural @ X ) ) ).
% 0.33/0.60
% 0.33/0.60 % max_0_1(6)
% 0.33/0.60 thf(fact_4786_max__0__1_I5_J,axiom,
% 0.33/0.60 ! [X: num] :
% 0.33/0.60 ( ( ord_max_nat @ one_one_nat @ ( numeral_numeral_nat @ X ) )
% 0.33/0.60 = ( numeral_numeral_nat @ X ) ) ).
% 0.33/0.60
% 0.33/0.60 % max_0_1(5)
% 0.33/0.60 thf(fact_4787_max__0__1_I5_J,axiom,
% 0.33/0.60 ! [X: num] :
% 0.33/0.60 ( ( ord_max_int @ one_one_int @ ( numeral_numeral_int @ X ) )
% 0.33/0.60 = ( numeral_numeral_int @ X ) ) ).
% 0.33/0.60
% 0.33/0.60 % max_0_1(5)
% 0.33/0.60 thf(fact_4788_max__0__1_I5_J,axiom,
% 0.33/0.60 ! [X: num] :
% 0.33/0.60 ( ( ord_max_Code_integer @ one_one_Code_integer @ ( numera6620942414471956472nteger @ X ) )
% 0.33/0.60 = ( numera6620942414471956472nteger @ X ) ) ).
% 0.33/0.60
% 0.33/0.60 % max_0_1(5)
% 0.33/0.60 thf(fact_4789_max__0__1_I5_J,axiom,
% 0.33/0.60 ! [X: num] :
% 0.33/0.60 ( ( ord_max_rat @ one_one_rat @ ( numeral_numeral_rat @ X ) )
% 0.33/0.60 = ( numeral_numeral_rat @ X ) ) ).
% 0.33/0.60
% 0.33/0.60 % max_0_1(5)
% 0.33/0.60 thf(fact_4790_max__0__1_I5_J,axiom,
% 0.33/0.60 ! [X: num] :
% 0.33/0.60 ( ( ord_max_Code_natural @ one_one_Code_natural @ ( numera5444537566228673987atural @ X ) )
% 0.33/0.60 = ( numera5444537566228673987atural @ X ) ) ).
% 0.33/0.60
% 0.33/0.60 % max_0_1(5)
% 0.33/0.60 thf(fact_4791_image__add__atMost,axiom,
% 0.33/0.60 ! [C: rat,A: rat] :
% 0.33/0.60 ( ( image_rat_rat @ ( plus_plus_rat @ C ) @ ( set_ord_atMost_rat @ A ) )
% 0.33/0.60 = ( set_ord_atMost_rat @ ( plus_plus_rat @ C @ A ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % image_add_atMost
% 0.33/0.60 thf(fact_4792_image__add__atMost,axiom,
% 0.33/0.60 ! [C: int,A: int] :
% 0.33/0.60 ( ( image_int_int @ ( plus_plus_int @ C ) @ ( set_ord_atMost_int @ A ) )
% 0.33/0.60 = ( set_ord_atMost_int @ ( plus_plus_int @ C @ A ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % image_add_atMost
% 0.33/0.60 thf(fact_4793_image__add__atLeastAtMost_H,axiom,
% 0.33/0.60 ! [K: rat,I: rat,J: rat] :
% 0.33/0.60 ( ( image_rat_rat
% 0.33/0.60 @ ^ [N4: rat] : ( plus_plus_rat @ N4 @ K )
% 0.33/0.60 @ ( set_or633870826150836451st_rat @ I @ J ) )
% 0.33/0.60 = ( set_or633870826150836451st_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ K ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % image_add_atLeastAtMost'
% 0.33/0.60 thf(fact_4794_image__add__atLeastAtMost_H,axiom,
% 0.33/0.60 ! [K: int,I: int,J: int] :
% 0.33/0.60 ( ( image_int_int
% 0.33/0.60 @ ^ [N4: int] : ( plus_plus_int @ N4 @ K )
% 0.33/0.60 @ ( set_or1266510415728281911st_int @ I @ J ) )
% 0.33/0.60 = ( set_or1266510415728281911st_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ K ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % image_add_atLeastAtMost'
% 0.33/0.60 thf(fact_4795_image__add__atLeastAtMost_H,axiom,
% 0.33/0.60 ! [K: nat,I: nat,J: nat] :
% 0.33/0.60 ( ( image_nat_nat
% 0.33/0.60 @ ^ [N4: nat] : ( plus_plus_nat @ N4 @ K )
% 0.33/0.60 @ ( set_or1269000886237332187st_nat @ I @ J ) )
% 0.33/0.60 = ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % image_add_atLeastAtMost'
% 0.33/0.60 thf(fact_4796_image__add__atLeastAtMost_H,axiom,
% 0.33/0.60 ! [K: code_integer,I: code_integer,J: code_integer] :
% 0.33/0.60 ( ( image_4470545334726330049nteger
% 0.33/0.60 @ ^ [N4: code_integer] : ( plus_p5714425477246183910nteger @ N4 @ K )
% 0.33/0.60 @ ( set_or189985376899183464nteger @ I @ J ) )
% 0.33/0.60 = ( set_or189985376899183464nteger @ ( plus_p5714425477246183910nteger @ I @ K ) @ ( plus_p5714425477246183910nteger @ J @ K ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % image_add_atLeastAtMost'
% 0.33/0.60 thf(fact_4797_image__minus__const__atLeastAtMost_H,axiom,
% 0.33/0.60 ! [D2: rat,A: rat,B: rat] :
% 0.33/0.60 ( ( image_rat_rat
% 0.33/0.60 @ ^ [T2: rat] : ( minus_minus_rat @ T2 @ D2 )
% 0.33/0.60 @ ( set_or633870826150836451st_rat @ A @ B ) )
% 0.33/0.60 = ( set_or633870826150836451st_rat @ ( minus_minus_rat @ A @ D2 ) @ ( minus_minus_rat @ B @ D2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % image_minus_const_atLeastAtMost'
% 0.33/0.60 thf(fact_4798_image__minus__const__atLeastAtMost_H,axiom,
% 0.33/0.60 ! [D2: int,A: int,B: int] :
% 0.33/0.60 ( ( image_int_int
% 0.33/0.60 @ ^ [T2: int] : ( minus_minus_int @ T2 @ D2 )
% 0.33/0.60 @ ( set_or1266510415728281911st_int @ A @ B ) )
% 0.33/0.60 = ( set_or1266510415728281911st_int @ ( minus_minus_int @ A @ D2 ) @ ( minus_minus_int @ B @ D2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % image_minus_const_atLeastAtMost'
% 0.33/0.60 thf(fact_4799_image__minus__const__atLeastAtMost_H,axiom,
% 0.33/0.60 ! [D2: code_integer,A: code_integer,B: code_integer] :
% 0.33/0.60 ( ( image_4470545334726330049nteger
% 0.33/0.60 @ ^ [T2: code_integer] : ( minus_8373710615458151222nteger @ T2 @ D2 )
% 0.33/0.60 @ ( set_or189985376899183464nteger @ A @ B ) )
% 0.33/0.60 = ( set_or189985376899183464nteger @ ( minus_8373710615458151222nteger @ A @ D2 ) @ ( minus_8373710615458151222nteger @ B @ D2 ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % image_minus_const_atLeastAtMost'
% 0.33/0.60 thf(fact_4800_image__add__atLeastLessThan_H,axiom,
% 0.33/0.60 ! [K: rat,I: rat,J: rat] :
% 0.33/0.60 ( ( image_rat_rat
% 0.33/0.60 @ ^ [N4: rat] : ( plus_plus_rat @ N4 @ K )
% 0.33/0.60 @ ( set_or4029947393144176647an_rat @ I @ J ) )
% 0.33/0.60 = ( set_or4029947393144176647an_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ K ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % image_add_atLeastLessThan'
% 0.33/0.60 thf(fact_4801_image__add__atLeastLessThan_H,axiom,
% 0.33/0.60 ! [K: nat,I: nat,J: nat] :
% 0.33/0.60 ( ( image_nat_nat
% 0.33/0.60 @ ^ [N4: nat] : ( plus_plus_nat @ N4 @ K )
% 0.33/0.60 @ ( set_or4665077453230672383an_nat @ I @ J ) )
% 0.33/0.60 = ( set_or4665077453230672383an_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % image_add_atLeastLessThan'
% 0.33/0.60 thf(fact_4802_image__add__atLeastLessThan_H,axiom,
% 0.33/0.60 ! [K: code_integer,I: code_integer,J: code_integer] :
% 0.33/0.60 ( ( image_4470545334726330049nteger
% 0.33/0.60 @ ^ [N4: code_integer] : ( plus_p5714425477246183910nteger @ N4 @ K )
% 0.33/0.60 @ ( set_or8404916559141939852nteger @ I @ J ) )
% 0.33/0.60 = ( set_or8404916559141939852nteger @ ( plus_p5714425477246183910nteger @ I @ K ) @ ( plus_p5714425477246183910nteger @ J @ K ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % image_add_atLeastLessThan'
% 0.33/0.60 thf(fact_4803_image__add__atLeastLessThan_H,axiom,
% 0.33/0.60 ! [K: int,I: int,J: int] :
% 0.33/0.60 ( ( image_int_int
% 0.33/0.60 @ ^ [N4: int] : ( plus_plus_int @ N4 @ K )
% 0.33/0.60 @ ( set_or4662586982721622107an_int @ I @ J ) )
% 0.33/0.60 = ( set_or4662586982721622107an_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ K ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % image_add_atLeastLessThan'
% 0.33/0.60 thf(fact_4804_drop__bit__of__1,axiom,
% 0.33/0.60 ! [N2: nat] :
% 0.33/0.60 ( ( bit_se3928097537394005634nteger @ N2 @ one_one_Code_integer )
% 0.33/0.60 = ( zero_n356916108424825756nteger @ ( N2 = zero_zero_nat ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % drop_bit_of_1
% 0.33/0.60 thf(fact_4805_drop__bit__of__1,axiom,
% 0.33/0.60 ! [N2: nat] :
% 0.33/0.60 ( ( bit_se8568078237143864401it_int @ N2 @ one_one_int )
% 0.33/0.60 = ( zero_n2684676970156552555ol_int @ ( N2 = zero_zero_nat ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % drop_bit_of_1
% 0.33/0.60 thf(fact_4806_drop__bit__of__1,axiom,
% 0.33/0.60 ! [N2: nat] :
% 0.33/0.60 ( ( bit_se8570568707652914677it_nat @ N2 @ one_one_nat )
% 0.33/0.60 = ( zero_n2687167440665602831ol_nat @ ( N2 = zero_zero_nat ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % drop_bit_of_1
% 0.33/0.60 thf(fact_4807_drop__bit__of__1,axiom,
% 0.33/0.60 ! [N2: nat] :
% 0.33/0.60 ( ( bit_se2751692689150723149atural @ N2 @ one_one_Code_natural )
% 0.33/0.60 = ( zero_n8403883297036319079atural @ ( N2 = zero_zero_nat ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % drop_bit_of_1
% 0.33/0.60 thf(fact_4808_image__mult__atLeastAtMost,axiom,
% 0.33/0.60 ! [D2: rat,A: rat,B: rat] :
% 0.33/0.60 ( ( ord_less_rat @ zero_zero_rat @ D2 )
% 0.33/0.60 => ( ( image_rat_rat @ ( times_times_rat @ D2 ) @ ( set_or633870826150836451st_rat @ A @ B ) )
% 0.33/0.60 = ( set_or633870826150836451st_rat @ ( times_times_rat @ D2 @ A ) @ ( times_times_rat @ D2 @ B ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % image_mult_atLeastAtMost
% 0.33/0.60 thf(fact_4809_image__divide__atLeastAtMost,axiom,
% 0.33/0.60 ! [D2: rat,A: rat,B: rat] :
% 0.33/0.60 ( ( ord_less_rat @ zero_zero_rat @ D2 )
% 0.33/0.60 => ( ( image_rat_rat
% 0.33/0.60 @ ^ [C2: rat] : ( divide_divide_rat @ C2 @ D2 )
% 0.33/0.60 @ ( set_or633870826150836451st_rat @ A @ B ) )
% 0.33/0.60 = ( set_or633870826150836451st_rat @ ( divide_divide_rat @ A @ D2 ) @ ( divide_divide_rat @ B @ D2 ) ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % image_divide_atLeastAtMost
% 0.33/0.60 thf(fact_4810_drop__bit__integer_Orep__eq,axiom,
% 0.33/0.60 ! [X: nat,Xa: code_integer] :
% 0.33/0.60 ( ( code_int_of_integer @ ( bit_se3928097537394005634nteger @ X @ Xa ) )
% 0.33/0.60 = ( bit_se8568078237143864401it_int @ X @ ( code_int_of_integer @ Xa ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % drop_bit_integer.rep_eq
% 0.33/0.60 thf(fact_4811_drop__bit__integer_Oabs__eq,axiom,
% 0.33/0.60 ! [Xa: nat,X: int] :
% 0.33/0.60 ( ( bit_se3928097537394005634nteger @ Xa @ ( code_integer_of_int @ X ) )
% 0.33/0.60 = ( code_integer_of_int @ ( bit_se8568078237143864401it_int @ Xa @ X ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % drop_bit_integer.abs_eq
% 0.33/0.60 thf(fact_4812_max__add__distrib__left,axiom,
% 0.33/0.60 ! [X: rat,Y: rat,Z: rat] :
% 0.33/0.60 ( ( plus_plus_rat @ ( ord_max_rat @ X @ Y ) @ Z )
% 0.33/0.60 = ( ord_max_rat @ ( plus_plus_rat @ X @ Z ) @ ( plus_plus_rat @ Y @ Z ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % max_add_distrib_left
% 0.33/0.60 thf(fact_4813_max__add__distrib__left,axiom,
% 0.33/0.60 ! [X: int,Y: int,Z: int] :
% 0.33/0.60 ( ( plus_plus_int @ ( ord_max_int @ X @ Y ) @ Z )
% 0.33/0.60 = ( ord_max_int @ ( plus_plus_int @ X @ Z ) @ ( plus_plus_int @ Y @ Z ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % max_add_distrib_left
% 0.33/0.60 thf(fact_4814_max__add__distrib__left,axiom,
% 0.33/0.60 ! [X: nat,Y: nat,Z: nat] :
% 0.33/0.60 ( ( plus_plus_nat @ ( ord_max_nat @ X @ Y ) @ Z )
% 0.33/0.60 = ( ord_max_nat @ ( plus_plus_nat @ X @ Z ) @ ( plus_plus_nat @ Y @ Z ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % max_add_distrib_left
% 0.33/0.60 thf(fact_4815_max__add__distrib__left,axiom,
% 0.33/0.60 ! [X: code_integer,Y: code_integer,Z: code_integer] :
% 0.33/0.60 ( ( plus_p5714425477246183910nteger @ ( ord_max_Code_integer @ X @ Y ) @ Z )
% 0.33/0.60 = ( ord_max_Code_integer @ ( plus_p5714425477246183910nteger @ X @ Z ) @ ( plus_p5714425477246183910nteger @ Y @ Z ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % max_add_distrib_left
% 0.33/0.60 thf(fact_4816_max__add__distrib__left,axiom,
% 0.33/0.60 ! [X: code_natural,Y: code_natural,Z: code_natural] :
% 0.33/0.60 ( ( plus_p4538020629002901425atural @ ( ord_max_Code_natural @ X @ Y ) @ Z )
% 0.33/0.60 = ( ord_max_Code_natural @ ( plus_p4538020629002901425atural @ X @ Z ) @ ( plus_p4538020629002901425atural @ Y @ Z ) ) ) ).
% 0.33/0.60
% 0.33/0.60 % max_add_distrib_left
% 0.33/0.60 thf(fact_4817_max__add__distrib__right,axiom,
% 0.33/0.60 ! [X: rat,Y: rat,Z: rat] :
% 0.33/0.60 ( ( plus_plus_rat @ X @ ( ord_max_rat @ Y @ Z ) )
% 0.33/0.60 = ( ord_max_rat @ ( plus_plus_rat @ X @ Y ) @ ( plus_plus_rat @ X @ Z ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % max_add_distrib_right
% 0.33/0.61 thf(fact_4818_max__add__distrib__right,axiom,
% 0.33/0.61 ! [X: int,Y: int,Z: int] :
% 0.33/0.61 ( ( plus_plus_int @ X @ ( ord_max_int @ Y @ Z ) )
% 0.33/0.61 = ( ord_max_int @ ( plus_plus_int @ X @ Y ) @ ( plus_plus_int @ X @ Z ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % max_add_distrib_right
% 0.33/0.61 thf(fact_4819_max__add__distrib__right,axiom,
% 0.33/0.61 ! [X: nat,Y: nat,Z: nat] :
% 0.33/0.61 ( ( plus_plus_nat @ X @ ( ord_max_nat @ Y @ Z ) )
% 0.33/0.61 = ( ord_max_nat @ ( plus_plus_nat @ X @ Y ) @ ( plus_plus_nat @ X @ Z ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % max_add_distrib_right
% 0.33/0.61 thf(fact_4820_max__add__distrib__right,axiom,
% 0.33/0.61 ! [X: code_integer,Y: code_integer,Z: code_integer] :
% 0.33/0.61 ( ( plus_p5714425477246183910nteger @ X @ ( ord_max_Code_integer @ Y @ Z ) )
% 0.33/0.61 = ( ord_max_Code_integer @ ( plus_p5714425477246183910nteger @ X @ Y ) @ ( plus_p5714425477246183910nteger @ X @ Z ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % max_add_distrib_right
% 0.33/0.61 thf(fact_4821_max__add__distrib__right,axiom,
% 0.33/0.61 ! [X: code_natural,Y: code_natural,Z: code_natural] :
% 0.33/0.61 ( ( plus_p4538020629002901425atural @ X @ ( ord_max_Code_natural @ Y @ Z ) )
% 0.33/0.61 = ( ord_max_Code_natural @ ( plus_p4538020629002901425atural @ X @ Y ) @ ( plus_p4538020629002901425atural @ X @ Z ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % max_add_distrib_right
% 0.33/0.61 thf(fact_4822_max__diff__distrib__left,axiom,
% 0.33/0.61 ! [X: code_integer,Y: code_integer,Z: code_integer] :
% 0.33/0.61 ( ( minus_8373710615458151222nteger @ ( ord_max_Code_integer @ X @ Y ) @ Z )
% 0.33/0.61 = ( ord_max_Code_integer @ ( minus_8373710615458151222nteger @ X @ Z ) @ ( minus_8373710615458151222nteger @ Y @ Z ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % max_diff_distrib_left
% 0.33/0.61 thf(fact_4823_max__diff__distrib__left,axiom,
% 0.33/0.61 ! [X: rat,Y: rat,Z: rat] :
% 0.33/0.61 ( ( minus_minus_rat @ ( ord_max_rat @ X @ Y ) @ Z )
% 0.33/0.61 = ( ord_max_rat @ ( minus_minus_rat @ X @ Z ) @ ( minus_minus_rat @ Y @ Z ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % max_diff_distrib_left
% 0.33/0.61 thf(fact_4824_max__diff__distrib__left,axiom,
% 0.33/0.61 ! [X: int,Y: int,Z: int] :
% 0.33/0.61 ( ( minus_minus_int @ ( ord_max_int @ X @ Y ) @ Z )
% 0.33/0.61 = ( ord_max_int @ ( minus_minus_int @ X @ Z ) @ ( minus_minus_int @ Y @ Z ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % max_diff_distrib_left
% 0.33/0.61 thf(fact_4825_translation__Compl,axiom,
% 0.33/0.61 ! [A: rat,T: set_rat] :
% 0.33/0.61 ( ( image_rat_rat @ ( plus_plus_rat @ A ) @ ( uminus2201863774496077783et_rat @ T ) )
% 0.33/0.61 = ( uminus2201863774496077783et_rat @ ( image_rat_rat @ ( plus_plus_rat @ A ) @ T ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % translation_Compl
% 0.33/0.61 thf(fact_4826_translation__Compl,axiom,
% 0.33/0.61 ! [A: int,T: set_int] :
% 0.33/0.61 ( ( image_int_int @ ( plus_plus_int @ A ) @ ( uminus1532241313380277803et_int @ T ) )
% 0.33/0.61 = ( uminus1532241313380277803et_int @ ( image_int_int @ ( plus_plus_int @ A ) @ T ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % translation_Compl
% 0.33/0.61 thf(fact_4827_nat__add__max__right,axiom,
% 0.33/0.61 ! [M2: nat,N2: nat,Q3: nat] :
% 0.33/0.61 ( ( plus_plus_nat @ M2 @ ( ord_max_nat @ N2 @ Q3 ) )
% 0.33/0.61 = ( ord_max_nat @ ( plus_plus_nat @ M2 @ N2 ) @ ( plus_plus_nat @ M2 @ Q3 ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % nat_add_max_right
% 0.33/0.61 thf(fact_4828_nat__add__max__left,axiom,
% 0.33/0.61 ! [M2: nat,N2: nat,Q3: nat] :
% 0.33/0.61 ( ( plus_plus_nat @ ( ord_max_nat @ M2 @ N2 ) @ Q3 )
% 0.33/0.61 = ( ord_max_nat @ ( plus_plus_nat @ M2 @ Q3 ) @ ( plus_plus_nat @ N2 @ Q3 ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % nat_add_max_left
% 0.33/0.61 thf(fact_4829_image__eq__imp__comp,axiom,
% 0.33/0.61 ! [F: num > code_integer,A2: set_num,G: num > code_integer,B5: set_num,H3: code_integer > code_integer] :
% 0.33/0.61 ( ( ( image_8379761247532268670nteger @ F @ A2 )
% 0.33/0.61 = ( image_8379761247532268670nteger @ G @ B5 ) )
% 0.33/0.61 => ( ( image_8379761247532268670nteger @ ( comp_C3531382070062128313er_num @ H3 @ F ) @ A2 )
% 0.33/0.61 = ( image_8379761247532268670nteger @ ( comp_C3531382070062128313er_num @ H3 @ G ) @ B5 ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % image_eq_imp_comp
% 0.33/0.61 thf(fact_4830_image__eq__imp__comp,axiom,
% 0.33/0.61 ! [F: int > nat,A2: set_int,G: int > nat,B5: set_int,H3: nat > num] :
% 0.33/0.61 ( ( ( image_int_nat @ F @ A2 )
% 0.33/0.61 = ( image_int_nat @ G @ B5 ) )
% 0.33/0.61 => ( ( image_int_num @ ( comp_nat_num_int @ H3 @ F ) @ A2 )
% 0.33/0.61 = ( image_int_num @ ( comp_nat_num_int @ H3 @ G ) @ B5 ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % image_eq_imp_comp
% 0.33/0.61 thf(fact_4831_image__eq__imp__comp,axiom,
% 0.33/0.61 ! [F: num > code_integer,A2: set_num,G: nat > code_integer,B5: set_nat,H3: code_integer > code_integer] :
% 0.33/0.61 ( ( ( image_8379761247532268670nteger @ F @ A2 )
% 0.33/0.61 = ( image_1215581382706833972nteger @ G @ B5 ) )
% 0.33/0.61 => ( ( image_8379761247532268670nteger @ ( comp_C3531382070062128313er_num @ H3 @ F ) @ A2 )
% 0.33/0.61 = ( image_1215581382706833972nteger @ ( comp_C6974050283906349679er_nat @ H3 @ G ) @ B5 ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % image_eq_imp_comp
% 0.33/0.61 thf(fact_4832_image__eq__imp__comp,axiom,
% 0.33/0.61 ! [F: int > code_integer,A2: set_int,G: nat > code_integer,B5: set_nat,H3: code_integer > int] :
% 0.33/0.61 ( ( ( image_1587234942943678608nteger @ F @ A2 )
% 0.33/0.61 = ( image_1215581382706833972nteger @ G @ B5 ) )
% 0.33/0.61 => ( ( image_int_int @ ( comp_C5046419837055054490nt_int @ H3 @ F ) @ A2 )
% 0.33/0.61 = ( image_nat_int @ ( comp_C5048910307564104766nt_nat @ H3 @ G ) @ B5 ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % image_eq_imp_comp
% 0.33/0.61 thf(fact_4833_image__eq__imp__comp,axiom,
% 0.33/0.61 ! [F: int > nat,A2: set_int,G: nat > nat,B5: set_nat,H3: nat > num] :
% 0.33/0.61 ( ( ( image_int_nat @ F @ A2 )
% 0.33/0.61 = ( image_nat_nat @ G @ B5 ) )
% 0.33/0.61 => ( ( image_int_num @ ( comp_nat_num_int @ H3 @ F ) @ A2 )
% 0.33/0.61 = ( image_nat_num @ ( comp_nat_num_nat @ H3 @ G ) @ B5 ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % image_eq_imp_comp
% 0.33/0.61 thf(fact_4834_image__eq__imp__comp,axiom,
% 0.33/0.61 ! [F: int > nat,A2: set_int,G: nat > nat,B5: set_nat,H3: nat > int] :
% 0.33/0.61 ( ( ( image_int_nat @ F @ A2 )
% 0.33/0.61 = ( image_nat_nat @ G @ B5 ) )
% 0.33/0.61 => ( ( image_int_int @ ( comp_nat_int_int @ H3 @ F ) @ A2 )
% 0.33/0.61 = ( image_nat_int @ ( comp_nat_int_nat @ H3 @ G ) @ B5 ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % image_eq_imp_comp
% 0.33/0.61 thf(fact_4835_image__eq__imp__comp,axiom,
% 0.33/0.61 ! [F: nat > code_integer,A2: set_nat,G: num > code_integer,B5: set_num,H3: code_integer > code_integer] :
% 0.33/0.61 ( ( ( image_1215581382706833972nteger @ F @ A2 )
% 0.33/0.61 = ( image_8379761247532268670nteger @ G @ B5 ) )
% 0.33/0.61 => ( ( image_1215581382706833972nteger @ ( comp_C6974050283906349679er_nat @ H3 @ F ) @ A2 )
% 0.33/0.61 = ( image_8379761247532268670nteger @ ( comp_C3531382070062128313er_num @ H3 @ G ) @ B5 ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % image_eq_imp_comp
% 0.33/0.61 thf(fact_4836_image__eq__imp__comp,axiom,
% 0.33/0.61 ! [F: nat > code_integer,A2: set_nat,G: int > code_integer,B5: set_int,H3: code_integer > int] :
% 0.33/0.61 ( ( ( image_1215581382706833972nteger @ F @ A2 )
% 0.33/0.61 = ( image_1587234942943678608nteger @ G @ B5 ) )
% 0.33/0.61 => ( ( image_nat_int @ ( comp_C5048910307564104766nt_nat @ H3 @ F ) @ A2 )
% 0.33/0.61 = ( image_int_int @ ( comp_C5046419837055054490nt_int @ H3 @ G ) @ B5 ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % image_eq_imp_comp
% 0.33/0.61 thf(fact_4837_image__eq__imp__comp,axiom,
% 0.33/0.61 ! [F: nat > code_integer,A2: set_nat,G: nat > code_integer,B5: set_nat,H3: code_integer > code_integer] :
% 0.33/0.61 ( ( ( image_1215581382706833972nteger @ F @ A2 )
% 0.33/0.61 = ( image_1215581382706833972nteger @ G @ B5 ) )
% 0.33/0.61 => ( ( image_1215581382706833972nteger @ ( comp_C6974050283906349679er_nat @ H3 @ F ) @ A2 )
% 0.33/0.61 = ( image_1215581382706833972nteger @ ( comp_C6974050283906349679er_nat @ H3 @ G ) @ B5 ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % image_eq_imp_comp
% 0.33/0.61 thf(fact_4838_image__eq__imp__comp,axiom,
% 0.33/0.61 ! [F: nat > code_integer,A2: set_nat,G: nat > code_integer,B5: set_nat,H3: code_integer > nat] :
% 0.33/0.61 ( ( ( image_1215581382706833972nteger @ F @ A2 )
% 0.33/0.61 = ( image_1215581382706833972nteger @ G @ B5 ) )
% 0.33/0.61 => ( ( image_nat_nat @ ( comp_C4049556595663050210at_nat @ H3 @ F ) @ A2 )
% 0.33/0.61 = ( image_nat_nat @ ( comp_C4049556595663050210at_nat @ H3 @ G ) @ B5 ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % image_eq_imp_comp
% 0.33/0.61 thf(fact_4839_image__comp,axiom,
% 0.33/0.61 ! [F: code_integer > code_integer,G: num > code_integer,R2: set_num] :
% 0.33/0.61 ( ( image_4470545334726330049nteger @ F @ ( image_8379761247532268670nteger @ G @ R2 ) )
% 0.33/0.61 = ( image_8379761247532268670nteger @ ( comp_C3531382070062128313er_num @ F @ G ) @ R2 ) ) ).
% 0.33/0.61
% 0.33/0.61 % image_comp
% 0.33/0.61 thf(fact_4840_image__comp,axiom,
% 0.33/0.61 ! [F: nat > num,G: int > nat,R2: set_int] :
% 0.33/0.61 ( ( image_nat_num @ F @ ( image_int_nat @ G @ R2 ) )
% 0.33/0.61 = ( image_int_num @ ( comp_nat_num_int @ F @ G ) @ R2 ) ) ).
% 0.33/0.61
% 0.33/0.61 % image_comp
% 0.33/0.61 thf(fact_4841_image__comp,axiom,
% 0.33/0.61 ! [F: code_integer > code_integer,G: nat > code_integer,R2: set_nat] :
% 0.33/0.61 ( ( image_4470545334726330049nteger @ F @ ( image_1215581382706833972nteger @ G @ R2 ) )
% 0.33/0.61 = ( image_1215581382706833972nteger @ ( comp_C6974050283906349679er_nat @ F @ G ) @ R2 ) ) ).
% 0.33/0.61
% 0.33/0.61 % image_comp
% 0.33/0.61 thf(fact_4842_image__comp,axiom,
% 0.33/0.61 ! [F: code_integer > nat,G: nat > code_integer,R2: set_nat] :
% 0.33/0.61 ( ( image_951025933927791156er_nat @ F @ ( image_1215581382706833972nteger @ G @ R2 ) )
% 0.33/0.61 = ( image_nat_nat @ ( comp_C4049556595663050210at_nat @ F @ G ) @ R2 ) ) ).
% 0.33/0.61
% 0.33/0.61 % image_comp
% 0.33/0.61 thf(fact_4843_image__comp,axiom,
% 0.33/0.61 ! [F: code_integer > int,G: nat > code_integer,R2: set_nat] :
% 0.33/0.61 ( ( image_948535463418740880er_int @ F @ ( image_1215581382706833972nteger @ G @ R2 ) )
% 0.33/0.61 = ( image_nat_int @ ( comp_C5048910307564104766nt_nat @ F @ G ) @ R2 ) ) ).
% 0.33/0.61
% 0.33/0.61 % image_comp
% 0.33/0.61 thf(fact_4844_image__comp,axiom,
% 0.33/0.61 ! [F: int > code_integer,G: nat > int,R2: set_nat] :
% 0.33/0.61 ( ( image_1587234942943678608nteger @ F @ ( image_nat_int @ G @ R2 ) )
% 0.33/0.61 = ( image_1215581382706833972nteger @ ( comp_i1588355021709917246er_nat @ F @ G ) @ R2 ) ) ).
% 0.33/0.61
% 0.33/0.61 % image_comp
% 0.33/0.61 thf(fact_4845_image__comp,axiom,
% 0.33/0.61 ! [F: int > nat,G: nat > int,R2: set_nat] :
% 0.33/0.61 ( ( image_int_nat @ F @ ( image_nat_int @ G @ R2 ) )
% 0.33/0.61 = ( image_nat_nat @ ( comp_int_nat_nat @ F @ G ) @ R2 ) ) ).
% 0.33/0.61
% 0.33/0.61 % image_comp
% 0.33/0.61 thf(fact_4846_image__comp,axiom,
% 0.33/0.61 ! [F: nat > code_integer,G: nat > nat,R2: set_nat] :
% 0.33/0.61 ( ( image_1215581382706833972nteger @ F @ ( image_nat_nat @ G @ R2 ) )
% 0.33/0.61 = ( image_1215581382706833972nteger @ ( comp_n3898172953802868194er_nat @ F @ G ) @ R2 ) ) ).
% 0.33/0.61
% 0.33/0.61 % image_comp
% 0.33/0.61 thf(fact_4847_image__comp,axiom,
% 0.33/0.61 ! [F: nat > nat,G: nat > nat,R2: set_nat] :
% 0.33/0.61 ( ( image_nat_nat @ F @ ( image_nat_nat @ G @ R2 ) )
% 0.33/0.61 = ( image_nat_nat @ ( comp_nat_nat_nat @ F @ G ) @ R2 ) ) ).
% 0.33/0.61
% 0.33/0.61 % image_comp
% 0.33/0.61 thf(fact_4848_image__comp,axiom,
% 0.33/0.61 ! [F: nat > int,G: int > nat,R2: set_int] :
% 0.33/0.61 ( ( image_nat_int @ F @ ( image_int_nat @ G @ R2 ) )
% 0.33/0.61 = ( image_int_int @ ( comp_nat_int_int @ F @ G ) @ R2 ) ) ).
% 0.33/0.61
% 0.33/0.61 % image_comp
% 0.33/0.61 thf(fact_4849_map__fun__def,axiom,
% 0.33/0.61 ( map_fu2576242048321985878nteger
% 0.33/0.61 = ( ^ [F2: code_integer > code_integer,G2: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,H: code_integer > code_integer] : ( comp_C1593894019821074884nteger @ ( comp_C1593894019821074884nteger @ G2 @ H ) @ F2 ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % map_fun_def
% 0.33/0.61 thf(fact_4850_map__fun__def,axiom,
% 0.33/0.61 ( map_fu6423247683660063826nteger
% 0.33/0.61 = ( ^ [F2: code_integer > code_integer,G2: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,H: code_integer > code_integer > code_integer] : ( comp_C1593894019821074884nteger @ ( comp_C8797469213163452608nteger @ G2 @ H ) @ F2 ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % map_fun_def
% 0.33/0.61 thf(fact_4851_map__fun__def,axiom,
% 0.33/0.61 ( map_fu4826362097070443709at_o_o
% 0.33/0.61 = ( ^ [F2: int > product_prod_nat_nat,G2: $o > $o,H: product_prod_nat_nat > $o] : ( comp_P1289042343629989734_o_int @ ( comp_o8022916681612831582at_nat @ G2 @ H ) @ F2 ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % map_fun_def
% 0.33/0.61 thf(fact_4852_map__fun__def,axiom,
% 0.33/0.61 ( map_fu4960017516451851995nt_int
% 0.33/0.61 = ( ^ [F2: int > product_prod_nat_nat,G2: ( product_prod_nat_nat > product_prod_nat_nat ) > int > int,H: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat] : ( comp_P1029605119844863363nt_int @ ( comp_P1872448293794610368at_nat @ G2 @ H ) @ F2 ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % map_fun_def
% 0.33/0.61 thf(fact_4853_map__fun__def,axiom,
% 0.33/0.61 ( map_fu434086159418415080_int_o
% 0.33/0.61 = ( ^ [F2: int > product_prod_nat_nat,G2: ( product_prod_nat_nat > $o ) > int > $o,H: product_prod_nat_nat > product_prod_nat_nat > $o] : ( comp_P7507668834397697393_o_int @ ( comp_P9039549498699531069at_nat @ G2 @ H ) @ F2 ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % map_fun_def
% 0.33/0.61 thf(fact_4854_map__fun__def,axiom,
% 0.33/0.61 ( map_fu3424225382358772769nt_rat
% 0.33/0.61 = ( ^ [F2: int > int,G2: product_prod_int_int > rat,H: int > product_prod_int_int] : ( comp_int_rat_int @ ( comp_P5335556815845735580at_int @ G2 @ H ) @ F2 ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % map_fun_def
% 0.33/0.61 thf(fact_4855_map__fun__def,axiom,
% 0.33/0.61 ( map_fu7831380289885515383nt_rat
% 0.33/0.61 = ( ^ [F2: int > int,G2: ( int > product_prod_int_int ) > int > rat,H: int > int > product_prod_int_int] : ( comp_int_int_rat_int @ ( comp_i1302866070986779890at_int @ G2 @ H ) @ F2 ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % map_fun_def
% 0.33/0.61 thf(fact_4856_map__fun_Ocompositionality,axiom,
% 0.33/0.61 ! [F: num > code_integer,G: code_integer > code_integer,H3: code_integer > code_integer,I: num > code_integer,Fun: code_integer > num] :
% 0.33/0.61 ( ( map_fu5269526691104299083nteger @ F @ G @ ( map_fu603974984455542859nteger @ H3 @ I @ Fun ) )
% 0.33/0.61 = ( map_fu8223014087597717000nteger @ ( comp_C3531382070062128313er_num @ H3 @ F ) @ ( comp_C3531382070062128313er_num @ G @ I ) @ Fun ) ) ).
% 0.33/0.61
% 0.33/0.61 % map_fun.compositionality
% 0.33/0.61 thf(fact_4857_map__fun_Ocompositionality,axiom,
% 0.33/0.61 ! [F: num > code_integer,G: nat > num,H3: code_integer > code_integer,I: int > nat,Fun: code_integer > int] :
% 0.33/0.61 ( ( map_fu7479816331989151099at_num @ F @ G @ ( map_fu5423760287386111952nt_nat @ H3 @ I @ Fun ) )
% 0.33/0.61 = ( map_fu8479170043890205655nt_num @ ( comp_C3531382070062128313er_num @ H3 @ F ) @ ( comp_nat_num_int @ G @ I ) @ Fun ) ) ).
% 0.33/0.61
% 0.33/0.61 % map_fun.compositionality
% 0.33/0.61 thf(fact_4858_map__fun_Ocompositionality,axiom,
% 0.33/0.61 ! [F: int > nat,G: code_integer > code_integer,H3: nat > num,I: num > code_integer,Fun: num > num] :
% 0.33/0.61 ( ( map_fu1717202910479192016nteger @ F @ G @ ( map_fu1090464068875036027nteger @ H3 @ I @ Fun ) )
% 0.33/0.61 = ( map_fu229184005524548567nteger @ ( comp_nat_num_int @ H3 @ F ) @ ( comp_C3531382070062128313er_num @ G @ I ) @ Fun ) ) ).
% 0.33/0.61
% 0.33/0.61 % map_fun.compositionality
% 0.33/0.61 thf(fact_4859_map__fun_Ocompositionality,axiom,
% 0.33/0.61 ! [F: int > nat,G: nat > num,H3: nat > num,I: int > nat,Fun: num > int] :
% 0.33/0.61 ( ( map_fu3669222299741785344at_num @ F @ G @ ( map_fu8361869985550671104nt_nat @ H3 @ I @ Fun ) )
% 0.33/0.61 = ( map_fu2609383839613498790nt_num @ ( comp_nat_num_int @ H3 @ F ) @ ( comp_nat_num_int @ G @ I ) @ Fun ) ) ).
% 0.33/0.61
% 0.33/0.61 % map_fun.compositionality
% 0.33/0.61 thf(fact_4860_map__fun_Ocompositionality,axiom,
% 0.33/0.61 ! [F: int > int,G: $o > $o,H3: int > product_prod_nat_nat,I: $o > $o,Fun: product_prod_nat_nat > $o] :
% 0.33/0.61 ( ( map_fun_int_int_o_o @ F @ G @ ( map_fu4826362097070443709at_o_o @ H3 @ I @ Fun ) )
% 0.33/0.61 = ( map_fu4826362097070443709at_o_o @ ( comp_i1108739374719436894at_int @ H3 @ F ) @ ( comp_o_o_o @ G @ I ) @ Fun ) ) ).
% 0.33/0.61
% 0.33/0.61 % map_fun.compositionality
% 0.33/0.61 thf(fact_4861_map__fun_Ocompositionality,axiom,
% 0.33/0.61 ! [F: int > int,G: rat > rat,H3: int > int,I: product_prod_int_int > rat,Fun: int > product_prod_int_int] :
% 0.33/0.61 ( ( map_fu6531859369801489698at_rat @ F @ G @ ( map_fu3424225382358772769nt_rat @ H3 @ I @ Fun ) )
% 0.33/0.61 = ( map_fu3424225382358772769nt_rat @ ( comp_int_int_int @ H3 @ F ) @ ( comp_r4727614531642239972nt_int @ G @ I ) @ Fun ) ) ).
% 0.33/0.61
% 0.33/0.61 % map_fun.compositionality
% 0.33/0.61 thf(fact_4862_map__fun_Ocompositionality,axiom,
% 0.33/0.61 ! [F: int > product_prod_nat_nat,G: $o > $o,H3: product_prod_nat_nat > product_prod_nat_nat,I: $o > $o,Fun: product_prod_nat_nat > $o] :
% 0.33/0.61 ( ( map_fu4826362097070443709at_o_o @ F @ G @ ( map_fu1707080289169145046at_o_o @ H3 @ I @ Fun ) )
% 0.33/0.61 = ( map_fu4826362097070443709at_o_o @ ( comp_P7428279379633703887at_int @ H3 @ F ) @ ( comp_o_o_o @ G @ I ) @ Fun ) ) ).
% 0.33/0.61
% 0.33/0.61 % map_fun.compositionality
% 0.33/0.61 thf(fact_4863_map__fun_Ocompositionality,axiom,
% 0.33/0.61 ! [F: int > int,G: product_prod_int_int > rat,H3: int > int,I: product_prod_int_int > product_prod_int_int,Fun: int > product_prod_int_int] :
% 0.33/0.61 ( ( map_fu3424225382358772769nt_rat @ F @ G @ ( map_fu2180209013632630320nt_int @ H3 @ I @ Fun ) )
% 0.33/0.61 = ( map_fu3424225382358772769nt_rat @ ( comp_int_int_int @ H3 @ F ) @ ( comp_P5648219952011055433nt_int @ G @ I ) @ Fun ) ) ).
% 0.33/0.61
% 0.33/0.61 % map_fun.compositionality
% 0.33/0.61 thf(fact_4864_map__fun_Ocompositionality,axiom,
% 0.33/0.61 ! [F: num > code_integer,G: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,H3: code_integer > code_integer,I: code_integer > code_integer,Fun: code_integer > code_integer] :
% 0.33/0.61 ( ( map_fu1235460277957925907nteger @ F @ G @ ( map_fu5082455417554595470nteger @ H3 @ I @ Fun ) )
% 0.33/0.61 = ( map_fu1235460277957925907nteger @ ( comp_C3531382070062128313er_num @ H3 @ F ) @ ( comp_C1593894019821074884nteger @ G @ I ) @ Fun ) ) ).
% 0.33/0.61
% 0.33/0.61 % map_fun.compositionality
% 0.33/0.61 thf(fact_4865_map__fun_Ocompositionality,axiom,
% 0.33/0.61 ! [F: code_integer > code_integer,G: code_integer > code_integer,H3: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,I: num > code_integer,Fun: ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > num] :
% 0.33/0.61 ( ( map_fu5082455417554595470nteger @ F @ G @ ( map_fu1335501423231535891nteger @ H3 @ I @ Fun ) )
% 0.33/0.61 = ( map_fu1335501423231535891nteger @ ( comp_C1593894019821074884nteger @ H3 @ F ) @ ( comp_C3531382070062128313er_num @ G @ I ) @ Fun ) ) ).
% 0.33/0.61
% 0.33/0.61 % map_fun.compositionality
% 0.33/0.61 thf(fact_4866_map__fun_Ocomp,axiom,
% 0.33/0.61 ! [F: num > code_integer,G: code_integer > code_integer,H3: code_integer > code_integer,I: num > code_integer] :
% 0.33/0.61 ( ( comp_C9104104092898552938er_num @ ( map_fu5269526691104299083nteger @ F @ G ) @ ( map_fu603974984455542859nteger @ H3 @ I ) )
% 0.33/0.61 = ( map_fu8223014087597717000nteger @ ( comp_C3531382070062128313er_num @ H3 @ F ) @ ( comp_C3531382070062128313er_num @ G @ I ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % map_fun.comp
% 0.33/0.61 thf(fact_4867_map__fun_Ocomp,axiom,
% 0.33/0.61 ! [F: num > code_integer,G: nat > num,H3: code_integer > code_integer,I: int > nat] :
% 0.33/0.61 ( ( comp_C8127656796141369388er_int @ ( map_fu7479816331989151099at_num @ F @ G ) @ ( map_fu5423760287386111952nt_nat @ H3 @ I ) )
% 0.33/0.61 = ( map_fu8479170043890205655nt_num @ ( comp_C3531382070062128313er_num @ H3 @ F ) @ ( comp_nat_num_int @ G @ I ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % map_fun.comp
% 0.33/0.61 thf(fact_4868_map__fun_Ocomp,axiom,
% 0.33/0.61 ! [F: int > nat,G: code_integer > code_integer,H3: nat > num,I: num > code_integer] :
% 0.33/0.61 ( ( comp_n3323228797031117228um_num @ ( map_fu1717202910479192016nteger @ F @ G ) @ ( map_fu1090464068875036027nteger @ H3 @ I ) )
% 0.33/0.61 = ( map_fu229184005524548567nteger @ ( comp_nat_num_int @ H3 @ F ) @ ( comp_C3531382070062128313er_num @ G @ I ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % map_fun.comp
% 0.33/0.61 thf(fact_4869_map__fun_Ocomp,axiom,
% 0.33/0.61 ! [F: int > nat,G: nat > num,H3: nat > num,I: int > nat] :
% 0.33/0.61 ( ( comp_n4765151935410462062um_int @ ( map_fu3669222299741785344at_num @ F @ G ) @ ( map_fu8361869985550671104nt_nat @ H3 @ I ) )
% 0.33/0.61 = ( map_fu2609383839613498790nt_num @ ( comp_nat_num_int @ H3 @ F ) @ ( comp_nat_num_int @ G @ I ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % map_fun.comp
% 0.33/0.61 thf(fact_4870_map__fun_Ocomp,axiom,
% 0.33/0.61 ! [F: int > int,G: $o > $o,H3: int > product_prod_nat_nat,I: $o > $o] :
% 0.33/0.61 ( ( comp_i6226780894115828703_nat_o @ ( map_fun_int_int_o_o @ F @ G ) @ ( map_fu4826362097070443709at_o_o @ H3 @ I ) )
% 0.33/0.61 = ( map_fu4826362097070443709at_o_o @ ( comp_i1108739374719436894at_int @ H3 @ F ) @ ( comp_o_o_o @ G @ I ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % map_fun.comp
% 0.33/0.61 thf(fact_4871_map__fun_Ocomp,axiom,
% 0.33/0.61 ! [F: int > int,G: rat > rat,H3: int > int,I: product_prod_int_int > rat] :
% 0.33/0.61 ( ( comp_i5271019637457297241nt_int @ ( map_fu6531859369801489698at_rat @ F @ G ) @ ( map_fu3424225382358772769nt_rat @ H3 @ I ) )
% 0.33/0.61 = ( map_fu3424225382358772769nt_rat @ ( comp_int_int_int @ H3 @ F ) @ ( comp_r4727614531642239972nt_int @ G @ I ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % map_fun.comp
% 0.33/0.61 thf(fact_4872_map__fun_Ocomp,axiom,
% 0.33/0.61 ! [F: int > product_prod_nat_nat,G: $o > $o,H3: product_prod_nat_nat > product_prod_nat_nat,I: $o > $o] :
% 0.33/0.61 ( ( comp_P286844350285437056_nat_o @ ( map_fu4826362097070443709at_o_o @ F @ G ) @ ( map_fu1707080289169145046at_o_o @ H3 @ I ) )
% 0.33/0.61 = ( map_fu4826362097070443709at_o_o @ ( comp_P7428279379633703887at_int @ H3 @ F ) @ ( comp_o_o_o @ G @ I ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % map_fun.comp
% 0.33/0.61 thf(fact_4873_map__fun_Ocomp,axiom,
% 0.33/0.61 ! [F: int > int,G: product_prod_int_int > rat,H3: int > int,I: product_prod_int_int > product_prod_int_int] :
% 0.33/0.61 ( ( comp_i118865614814752126nt_int @ ( map_fu3424225382358772769nt_rat @ F @ G ) @ ( map_fu2180209013632630320nt_int @ H3 @ I ) )
% 0.33/0.61 = ( map_fu3424225382358772769nt_rat @ ( comp_int_int_int @ H3 @ F ) @ ( comp_P5648219952011055433nt_int @ G @ I ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % map_fun.comp
% 0.33/0.61 thf(fact_4874_map__fun_Ocomp,axiom,
% 0.33/0.61 ! [F: num > code_integer,G: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,H3: code_integer > code_integer,I: code_integer > code_integer] :
% 0.33/0.61 ( ( comp_C5301300457492916725nteger @ ( map_fu1235460277957925907nteger @ F @ G ) @ ( map_fu5082455417554595470nteger @ H3 @ I ) )
% 0.33/0.61 = ( map_fu1235460277957925907nteger @ ( comp_C3531382070062128313er_num @ H3 @ F ) @ ( comp_C1593894019821074884nteger @ G @ I ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % map_fun.comp
% 0.33/0.61 thf(fact_4875_map__fun_Ocomp,axiom,
% 0.33/0.61 ! [F: code_integer > code_integer,G: code_integer > code_integer,H3: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,I: num > code_integer] :
% 0.33/0.61 ( ( comp_C3959375555751086581er_num @ ( map_fu5082455417554595470nteger @ F @ G ) @ ( map_fu1335501423231535891nteger @ H3 @ I ) )
% 0.33/0.61 = ( map_fu1335501423231535891nteger @ ( comp_C1593894019821074884nteger @ H3 @ F ) @ ( comp_C3531382070062128313er_num @ G @ I ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % map_fun.comp
% 0.33/0.61 thf(fact_4876_translation__subtract__Compl,axiom,
% 0.33/0.61 ! [A: code_integer,T: set_Code_integer] :
% 0.33/0.61 ( ( image_4470545334726330049nteger
% 0.33/0.61 @ ^ [X3: code_integer] : ( minus_8373710615458151222nteger @ X3 @ A )
% 0.33/0.61 @ ( uminus804700908173204444nteger @ T ) )
% 0.33/0.61 = ( uminus804700908173204444nteger
% 0.33/0.61 @ ( image_4470545334726330049nteger
% 0.33/0.61 @ ^ [X3: code_integer] : ( minus_8373710615458151222nteger @ X3 @ A )
% 0.33/0.61 @ T ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % translation_subtract_Compl
% 0.33/0.61 thf(fact_4877_translation__subtract__Compl,axiom,
% 0.33/0.61 ! [A: rat,T: set_rat] :
% 0.33/0.61 ( ( image_rat_rat
% 0.33/0.61 @ ^ [X3: rat] : ( minus_minus_rat @ X3 @ A )
% 0.33/0.61 @ ( uminus2201863774496077783et_rat @ T ) )
% 0.33/0.61 = ( uminus2201863774496077783et_rat
% 0.33/0.61 @ ( image_rat_rat
% 0.33/0.61 @ ^ [X3: rat] : ( minus_minus_rat @ X3 @ A )
% 0.33/0.61 @ T ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % translation_subtract_Compl
% 0.33/0.61 thf(fact_4878_translation__subtract__Compl,axiom,
% 0.33/0.61 ! [A: int,T: set_int] :
% 0.33/0.61 ( ( image_int_int
% 0.33/0.61 @ ^ [X3: int] : ( minus_minus_int @ X3 @ A )
% 0.33/0.61 @ ( uminus1532241313380277803et_int @ T ) )
% 0.33/0.61 = ( uminus1532241313380277803et_int
% 0.33/0.61 @ ( image_int_int
% 0.33/0.61 @ ^ [X3: int] : ( minus_minus_int @ X3 @ A )
% 0.33/0.61 @ T ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % translation_subtract_Compl
% 0.33/0.61 thf(fact_4879_nat__minus__add__max,axiom,
% 0.33/0.61 ! [N2: nat,M2: nat] :
% 0.33/0.61 ( ( plus_plus_nat @ ( minus_minus_nat @ N2 @ M2 ) @ M2 )
% 0.33/0.61 = ( ord_max_nat @ N2 @ M2 ) ) ).
% 0.33/0.61
% 0.33/0.61 % nat_minus_add_max
% 0.33/0.61 thf(fact_4880_translation__diff,axiom,
% 0.33/0.61 ! [A: rat,S: set_rat,T: set_rat] :
% 0.33/0.61 ( ( image_rat_rat @ ( plus_plus_rat @ A ) @ ( minus_minus_set_rat @ S @ T ) )
% 0.33/0.61 = ( minus_minus_set_rat @ ( image_rat_rat @ ( plus_plus_rat @ A ) @ S ) @ ( image_rat_rat @ ( plus_plus_rat @ A ) @ T ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % translation_diff
% 0.33/0.61 thf(fact_4881_translation__diff,axiom,
% 0.33/0.61 ! [A: int,S: set_int,T: set_int] :
% 0.33/0.61 ( ( image_int_int @ ( plus_plus_int @ A ) @ ( minus_minus_set_int @ S @ T ) )
% 0.33/0.61 = ( minus_minus_set_int @ ( image_int_int @ ( plus_plus_int @ A ) @ S ) @ ( image_int_int @ ( plus_plus_int @ A ) @ T ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % translation_diff
% 0.33/0.61 thf(fact_4882_translation__subtract__diff,axiom,
% 0.33/0.61 ! [A: code_integer,S: set_Code_integer,T: set_Code_integer] :
% 0.33/0.61 ( ( image_4470545334726330049nteger
% 0.33/0.61 @ ^ [X3: code_integer] : ( minus_8373710615458151222nteger @ X3 @ A )
% 0.33/0.61 @ ( minus_2355218937544613996nteger @ S @ T ) )
% 0.33/0.61 = ( minus_2355218937544613996nteger
% 0.33/0.61 @ ( image_4470545334726330049nteger
% 0.33/0.61 @ ^ [X3: code_integer] : ( minus_8373710615458151222nteger @ X3 @ A )
% 0.33/0.61 @ S )
% 0.33/0.61 @ ( image_4470545334726330049nteger
% 0.33/0.61 @ ^ [X3: code_integer] : ( minus_8373710615458151222nteger @ X3 @ A )
% 0.33/0.61 @ T ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % translation_subtract_diff
% 0.33/0.61 thf(fact_4883_translation__subtract__diff,axiom,
% 0.33/0.61 ! [A: rat,S: set_rat,T: set_rat] :
% 0.33/0.61 ( ( image_rat_rat
% 0.33/0.61 @ ^ [X3: rat] : ( minus_minus_rat @ X3 @ A )
% 0.33/0.61 @ ( minus_minus_set_rat @ S @ T ) )
% 0.33/0.61 = ( minus_minus_set_rat
% 0.33/0.61 @ ( image_rat_rat
% 0.33/0.61 @ ^ [X3: rat] : ( minus_minus_rat @ X3 @ A )
% 0.33/0.61 @ S )
% 0.33/0.61 @ ( image_rat_rat
% 0.33/0.61 @ ^ [X3: rat] : ( minus_minus_rat @ X3 @ A )
% 0.33/0.61 @ T ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % translation_subtract_diff
% 0.33/0.61 thf(fact_4884_translation__subtract__diff,axiom,
% 0.33/0.61 ! [A: int,S: set_int,T: set_int] :
% 0.33/0.61 ( ( image_int_int
% 0.33/0.61 @ ^ [X3: int] : ( minus_minus_int @ X3 @ A )
% 0.33/0.61 @ ( minus_minus_set_int @ S @ T ) )
% 0.33/0.61 = ( minus_minus_set_int
% 0.33/0.61 @ ( image_int_int
% 0.33/0.61 @ ^ [X3: int] : ( minus_minus_int @ X3 @ A )
% 0.33/0.61 @ S )
% 0.33/0.61 @ ( image_int_int
% 0.33/0.61 @ ^ [X3: int] : ( minus_minus_int @ X3 @ A )
% 0.33/0.61 @ T ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % translation_subtract_diff
% 0.33/0.61 thf(fact_4885_take__bit__drop__bit,axiom,
% 0.33/0.61 ! [M2: nat,N2: nat,A: code_integer] :
% 0.33/0.61 ( ( bit_se1745604003318907178nteger @ M2 @ ( bit_se3928097537394005634nteger @ N2 @ A ) )
% 0.33/0.61 = ( bit_se3928097537394005634nteger @ N2 @ ( bit_se1745604003318907178nteger @ ( plus_plus_nat @ M2 @ N2 ) @ A ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % take_bit_drop_bit
% 0.33/0.61 thf(fact_4886_take__bit__drop__bit,axiom,
% 0.33/0.61 ! [M2: nat,N2: nat,A: int] :
% 0.33/0.61 ( ( bit_se2923211474154528505it_int @ M2 @ ( bit_se8568078237143864401it_int @ N2 @ A ) )
% 0.33/0.61 = ( bit_se8568078237143864401it_int @ N2 @ ( bit_se2923211474154528505it_int @ ( plus_plus_nat @ M2 @ N2 ) @ A ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % take_bit_drop_bit
% 0.33/0.61 thf(fact_4887_take__bit__drop__bit,axiom,
% 0.33/0.61 ! [M2: nat,N2: nat,A: nat] :
% 0.33/0.61 ( ( bit_se2925701944663578781it_nat @ M2 @ ( bit_se8570568707652914677it_nat @ N2 @ A ) )
% 0.33/0.61 = ( bit_se8570568707652914677it_nat @ N2 @ ( bit_se2925701944663578781it_nat @ ( plus_plus_nat @ M2 @ N2 ) @ A ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % take_bit_drop_bit
% 0.33/0.61 thf(fact_4888_take__bit__drop__bit,axiom,
% 0.33/0.61 ! [M2: nat,N2: nat,A: code_natural] :
% 0.33/0.61 ( ( bit_se569199155075624693atural @ M2 @ ( bit_se2751692689150723149atural @ N2 @ A ) )
% 0.33/0.61 = ( bit_se2751692689150723149atural @ N2 @ ( bit_se569199155075624693atural @ ( plus_plus_nat @ M2 @ N2 ) @ A ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % take_bit_drop_bit
% 0.33/0.61 thf(fact_4889_bit__drop__bit__eq,axiom,
% 0.33/0.61 ! [N2: nat,A: code_integer] :
% 0.33/0.61 ( ( bit_se9216721137139052372nteger @ ( bit_se3928097537394005634nteger @ N2 @ A ) )
% 0.33/0.61 = ( comp_nat_o_nat @ ( bit_se9216721137139052372nteger @ A ) @ ( plus_plus_nat @ N2 ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % bit_drop_bit_eq
% 0.33/0.61 thf(fact_4890_bit__drop__bit__eq,axiom,
% 0.33/0.61 ! [N2: nat,A: int] :
% 0.33/0.61 ( ( bit_se1146084159140164899it_int @ ( bit_se8568078237143864401it_int @ N2 @ A ) )
% 0.33/0.61 = ( comp_nat_o_nat @ ( bit_se1146084159140164899it_int @ A ) @ ( plus_plus_nat @ N2 ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % bit_drop_bit_eq
% 0.33/0.61 thf(fact_4891_bit__drop__bit__eq,axiom,
% 0.33/0.61 ! [N2: nat,A: nat] :
% 0.33/0.61 ( ( bit_se1148574629649215175it_nat @ ( bit_se8570568707652914677it_nat @ N2 @ A ) )
% 0.33/0.61 = ( comp_nat_o_nat @ ( bit_se1148574629649215175it_nat @ A ) @ ( plus_plus_nat @ N2 ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % bit_drop_bit_eq
% 0.33/0.61 thf(fact_4892_bit__drop__bit__eq,axiom,
% 0.33/0.61 ! [N2: nat,A: code_natural] :
% 0.33/0.61 ( ( bit_se8040316288895769887atural @ ( bit_se2751692689150723149atural @ N2 @ A ) )
% 0.33/0.61 = ( comp_nat_o_nat @ ( bit_se8040316288895769887atural @ A ) @ ( plus_plus_nat @ N2 ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % bit_drop_bit_eq
% 0.33/0.61 thf(fact_4893_div__push__bit__of__1__eq__drop__bit,axiom,
% 0.33/0.61 ! [A: nat,N2: nat] :
% 0.33/0.61 ( ( divide_divide_nat @ A @ ( bit_se547839408752420682it_nat @ N2 @ one_one_nat ) )
% 0.33/0.61 = ( bit_se8570568707652914677it_nat @ N2 @ A ) ) ).
% 0.33/0.61
% 0.33/0.61 % div_push_bit_of_1_eq_drop_bit
% 0.33/0.61 thf(fact_4894_div__push__bit__of__1__eq__drop__bit,axiom,
% 0.33/0.61 ! [A: code_integer,N2: nat] :
% 0.33/0.61 ( ( divide6298287555418463151nteger @ A @ ( bit_se7788150548672797655nteger @ N2 @ one_one_Code_integer ) )
% 0.33/0.61 = ( bit_se3928097537394005634nteger @ N2 @ A ) ) ).
% 0.33/0.61
% 0.33/0.61 % div_push_bit_of_1_eq_drop_bit
% 0.33/0.61 thf(fact_4895_div__push__bit__of__1__eq__drop__bit,axiom,
% 0.33/0.61 ! [A: int,N2: nat] :
% 0.33/0.61 ( ( divide_divide_int @ A @ ( bit_se545348938243370406it_int @ N2 @ one_one_int ) )
% 0.33/0.61 = ( bit_se8568078237143864401it_int @ N2 @ A ) ) ).
% 0.33/0.61
% 0.33/0.61 % div_push_bit_of_1_eq_drop_bit
% 0.33/0.61 thf(fact_4896_div__push__bit__of__1__eq__drop__bit,axiom,
% 0.33/0.61 ! [A: code_natural,N2: nat] :
% 0.33/0.61 ( ( divide5121882707175180666atural @ A @ ( bit_se6611745700429515170atural @ N2 @ one_one_Code_natural ) )
% 0.33/0.61 = ( bit_se2751692689150723149atural @ N2 @ A ) ) ).
% 0.33/0.61
% 0.33/0.61 % div_push_bit_of_1_eq_drop_bit
% 0.33/0.61 thf(fact_4897_bit__iff__and__drop__bit__eq__1,axiom,
% 0.33/0.61 ( bit_se9216721137139052372nteger
% 0.33/0.61 = ( ^ [A5: code_integer,N4: nat] :
% 0.33/0.61 ( ( bit_se3949692690581998587nteger @ ( bit_se3928097537394005634nteger @ N4 @ A5 ) @ one_one_Code_integer )
% 0.33/0.61 = one_one_Code_integer ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % bit_iff_and_drop_bit_eq_1
% 0.33/0.61 thf(fact_4898_bit__iff__and__drop__bit__eq__1,axiom,
% 0.33/0.61 ( bit_se1146084159140164899it_int
% 0.33/0.61 = ( ^ [A5: int,N4: nat] :
% 0.33/0.61 ( ( bit_se725231765392027082nd_int @ ( bit_se8568078237143864401it_int @ N4 @ A5 ) @ one_one_int )
% 0.33/0.61 = one_one_int ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % bit_iff_and_drop_bit_eq_1
% 0.33/0.61 thf(fact_4899_bit__iff__and__drop__bit__eq__1,axiom,
% 0.33/0.61 ( bit_se1148574629649215175it_nat
% 0.33/0.61 = ( ^ [A5: nat,N4: nat] :
% 0.33/0.61 ( ( bit_se727722235901077358nd_nat @ ( bit_se8570568707652914677it_nat @ N4 @ A5 ) @ one_one_nat )
% 0.33/0.61 = one_one_nat ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % bit_iff_and_drop_bit_eq_1
% 0.33/0.61 thf(fact_4900_bit__iff__and__drop__bit__eq__1,axiom,
% 0.33/0.61 ( bit_se8040316288895769887atural
% 0.33/0.61 = ( ^ [A5: code_natural,N4: nat] :
% 0.33/0.61 ( ( bit_se2773287842338716102atural @ ( bit_se2751692689150723149atural @ N4 @ A5 ) @ one_one_Code_natural )
% 0.33/0.61 = one_one_Code_natural ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % bit_iff_and_drop_bit_eq_1
% 0.33/0.61 thf(fact_4901_bits__ident,axiom,
% 0.33/0.61 ! [N2: nat,A: code_integer] :
% 0.33/0.61 ( ( plus_p5714425477246183910nteger @ ( bit_se7788150548672797655nteger @ N2 @ ( bit_se3928097537394005634nteger @ N2 @ A ) ) @ ( bit_se1745604003318907178nteger @ N2 @ A ) )
% 0.33/0.61 = A ) ).
% 0.33/0.61
% 0.33/0.61 % bits_ident
% 0.33/0.61 thf(fact_4902_bits__ident,axiom,
% 0.33/0.61 ! [N2: nat,A: int] :
% 0.33/0.61 ( ( plus_plus_int @ ( bit_se545348938243370406it_int @ N2 @ ( bit_se8568078237143864401it_int @ N2 @ A ) ) @ ( bit_se2923211474154528505it_int @ N2 @ A ) )
% 0.33/0.61 = A ) ).
% 0.33/0.61
% 0.33/0.61 % bits_ident
% 0.33/0.61 thf(fact_4903_bits__ident,axiom,
% 0.33/0.61 ! [N2: nat,A: nat] :
% 0.33/0.61 ( ( plus_plus_nat @ ( bit_se547839408752420682it_nat @ N2 @ ( bit_se8570568707652914677it_nat @ N2 @ A ) ) @ ( bit_se2925701944663578781it_nat @ N2 @ A ) )
% 0.33/0.61 = A ) ).
% 0.33/0.61
% 0.33/0.61 % bits_ident
% 0.33/0.61 thf(fact_4904_bits__ident,axiom,
% 0.33/0.61 ! [N2: nat,A: code_natural] :
% 0.33/0.61 ( ( plus_p4538020629002901425atural @ ( bit_se6611745700429515170atural @ N2 @ ( bit_se2751692689150723149atural @ N2 @ A ) ) @ ( bit_se569199155075624693atural @ N2 @ A ) )
% 0.33/0.61 = A ) ).
% 0.33/0.61
% 0.33/0.61 % bits_ident
% 0.33/0.61 thf(fact_4905_slice__eq__mask,axiom,
% 0.33/0.61 ! [N2: nat,M2: nat,A: code_integer] :
% 0.33/0.61 ( ( bit_se7788150548672797655nteger @ N2 @ ( bit_se1745604003318907178nteger @ M2 @ ( bit_se3928097537394005634nteger @ N2 @ A ) ) )
% 0.33/0.61 = ( bit_se3949692690581998587nteger @ A @ ( bit_se3949692690581998587nteger @ ( bit_se2119862282449309892nteger @ ( plus_plus_nat @ M2 @ N2 ) ) @ ( bit_ri7632146776885996613nteger @ ( bit_se2119862282449309892nteger @ N2 ) ) ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % slice_eq_mask
% 0.33/0.61 thf(fact_4906_slice__eq__mask,axiom,
% 0.33/0.61 ! [N2: nat,M2: nat,A: int] :
% 0.33/0.61 ( ( bit_se545348938243370406it_int @ N2 @ ( bit_se2923211474154528505it_int @ M2 @ ( bit_se8568078237143864401it_int @ N2 @ A ) ) )
% 0.33/0.61 = ( bit_se725231765392027082nd_int @ A @ ( bit_se725231765392027082nd_int @ ( bit_se2000444600071755411sk_int @ ( plus_plus_nat @ M2 @ N2 ) ) @ ( bit_ri7919022796975470100ot_int @ ( bit_se2000444600071755411sk_int @ N2 ) ) ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % slice_eq_mask
% 0.33/0.61 thf(fact_4907_image__add__0,axiom,
% 0.33/0.61 ! [S2: set_Code_integer] :
% 0.33/0.61 ( ( image_4470545334726330049nteger @ ( plus_p5714425477246183910nteger @ zero_z3403309356797280102nteger ) @ S2 )
% 0.33/0.61 = S2 ) ).
% 0.33/0.61
% 0.33/0.61 % image_add_0
% 0.33/0.61 thf(fact_4908_image__add__0,axiom,
% 0.33/0.61 ! [S2: set_mu2057375006010111271at_nat] :
% 0.33/0.61 ( ( image_2516384619306764229at_nat @ ( plus_p7104986032573967614at_nat @ zero_z1048942125864253310at_nat ) @ S2 )
% 0.33/0.61 = S2 ) ).
% 0.33/0.61
% 0.33/0.61 % image_add_0
% 0.33/0.61 thf(fact_4909_image__add__0,axiom,
% 0.33/0.61 ! [S2: set_rat] :
% 0.33/0.61 ( ( image_rat_rat @ ( plus_plus_rat @ zero_zero_rat ) @ S2 )
% 0.33/0.61 = S2 ) ).
% 0.33/0.61
% 0.33/0.61 % image_add_0
% 0.33/0.61 thf(fact_4910_image__add__0,axiom,
% 0.33/0.61 ! [S2: set_nat] :
% 0.33/0.61 ( ( image_nat_nat @ ( plus_plus_nat @ zero_zero_nat ) @ S2 )
% 0.33/0.61 = S2 ) ).
% 0.33/0.61
% 0.33/0.61 % image_add_0
% 0.33/0.61 thf(fact_4911_image__add__0,axiom,
% 0.33/0.61 ! [S2: set_int] :
% 0.33/0.61 ( ( image_int_int @ ( plus_plus_int @ zero_zero_int ) @ S2 )
% 0.33/0.61 = S2 ) ).
% 0.33/0.61
% 0.33/0.61 % image_add_0
% 0.33/0.61 thf(fact_4912_times__int__def,axiom,
% 0.33/0.61 ( times_times_int
% 0.33/0.61 = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 0.33/0.61 @ ( produc27273713700761075at_nat
% 0.33/0.61 @ ^ [X3: nat,Y3: nat] :
% 0.33/0.61 ( produc2626176000494625587at_nat
% 0.33/0.61 @ ^ [U2: nat,V2: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X3 @ U2 ) @ ( times_times_nat @ Y3 @ V2 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X3 @ V2 ) @ ( times_times_nat @ Y3 @ U2 ) ) ) ) ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % times_int_def
% 0.33/0.61 thf(fact_4913_minus__int__def,axiom,
% 0.33/0.61 ( minus_minus_int
% 0.33/0.61 = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 0.33/0.61 @ ( produc27273713700761075at_nat
% 0.33/0.61 @ ^ [X3: nat,Y3: nat] :
% 0.33/0.61 ( produc2626176000494625587at_nat
% 0.33/0.61 @ ^ [U2: nat,V2: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X3 @ V2 ) @ ( plus_plus_nat @ Y3 @ U2 ) ) ) ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % minus_int_def
% 0.33/0.61 thf(fact_4914_plus__int__def,axiom,
% 0.33/0.61 ( plus_plus_int
% 0.33/0.61 = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 0.33/0.61 @ ( produc27273713700761075at_nat
% 0.33/0.61 @ ^ [X3: nat,Y3: nat] :
% 0.33/0.61 ( produc2626176000494625587at_nat
% 0.33/0.61 @ ^ [U2: nat,V2: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X3 @ U2 ) @ ( plus_plus_nat @ Y3 @ V2 ) ) ) ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % plus_int_def
% 0.33/0.61 thf(fact_4915_rat__minus__code,axiom,
% 0.33/0.61 ! [P4: rat,Q3: rat] :
% 0.33/0.61 ( ( quotient_of @ ( minus_minus_rat @ P4 @ Q3 ) )
% 0.33/0.61 = ( produc4245557441103728435nt_int
% 0.33/0.61 @ ^ [A5: int,C2: int] :
% 0.33/0.61 ( produc4245557441103728435nt_int
% 0.33/0.61 @ ^ [B4: int,D4: int] : ( normalize @ ( product_Pair_int_int @ ( minus_minus_int @ ( times_times_int @ A5 @ D4 ) @ ( times_times_int @ B4 @ C2 ) ) @ ( times_times_int @ C2 @ D4 ) ) )
% 0.33/0.61 @ ( quotient_of @ Q3 ) )
% 0.33/0.61 @ ( quotient_of @ P4 ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % rat_minus_code
% 0.33/0.61 thf(fact_4916_rat__plus__code,axiom,
% 0.33/0.61 ! [P4: rat,Q3: rat] :
% 0.33/0.61 ( ( quotient_of @ ( plus_plus_rat @ P4 @ Q3 ) )
% 0.33/0.61 = ( produc4245557441103728435nt_int
% 0.33/0.61 @ ^ [A5: int,C2: int] :
% 0.33/0.61 ( produc4245557441103728435nt_int
% 0.33/0.61 @ ^ [B4: int,D4: int] : ( normalize @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ A5 @ D4 ) @ ( times_times_int @ B4 @ C2 ) ) @ ( times_times_int @ C2 @ D4 ) ) )
% 0.33/0.61 @ ( quotient_of @ Q3 ) )
% 0.33/0.61 @ ( quotient_of @ P4 ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % rat_plus_code
% 0.33/0.61 thf(fact_4917_image__Suc__atLeastAtMost,axiom,
% 0.33/0.61 ! [I: nat,J: nat] :
% 0.33/0.61 ( ( image_nat_nat @ suc @ ( set_or1269000886237332187st_nat @ I @ J ) )
% 0.33/0.61 = ( set_or1269000886237332187st_nat @ ( suc @ I ) @ ( suc @ J ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % image_Suc_atLeastAtMost
% 0.33/0.61 thf(fact_4918_image__Suc__atLeastLessThan,axiom,
% 0.33/0.61 ! [I: nat,J: nat] :
% 0.33/0.61 ( ( image_nat_nat @ suc @ ( set_or4665077453230672383an_nat @ I @ J ) )
% 0.33/0.61 = ( set_or4665077453230672383an_nat @ ( suc @ I ) @ ( suc @ J ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % image_Suc_atLeastLessThan
% 0.33/0.61 thf(fact_4919_in__inv__image,axiom,
% 0.33/0.61 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,R2: set_Pr4329608150637261639at_nat,F: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat] :
% 0.33/0.61 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ ( inv_im7023619800666061458at_nat @ R2 @ F ) )
% 0.33/0.61 = ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( F @ X ) @ ( F @ Y ) ) @ R2 ) ) ).
% 0.33/0.61
% 0.33/0.61 % in_inv_image
% 0.33/0.61 thf(fact_4920_in__inv__image,axiom,
% 0.33/0.61 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,R2: set_Pr1261947904930325089at_nat,F: set_Pr1261947904930325089at_nat > nat] :
% 0.33/0.61 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ ( inv_im6750873321330482877at_nat @ R2 @ F ) )
% 0.33/0.61 = ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ ( F @ X ) @ ( F @ Y ) ) @ R2 ) ) ).
% 0.33/0.61
% 0.33/0.61 % in_inv_image
% 0.33/0.61 thf(fact_4921_in__inv__image,axiom,
% 0.33/0.61 ! [X: nat,Y: nat,R2: set_Pr4329608150637261639at_nat,F: nat > set_Pr1261947904930325089at_nat] :
% 0.33/0.61 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( inv_im4437241714082187487at_nat @ R2 @ F ) )
% 0.33/0.61 = ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( F @ X ) @ ( F @ Y ) ) @ R2 ) ) ).
% 0.33/0.61
% 0.33/0.61 % in_inv_image
% 0.33/0.61 thf(fact_4922_in__inv__image,axiom,
% 0.33/0.61 ! [X: nat,Y: nat,R2: set_Pr1261947904930325089at_nat,F: nat > nat] :
% 0.33/0.61 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( inv_image_nat_nat @ R2 @ F ) )
% 0.33/0.61 = ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ ( F @ X ) @ ( F @ Y ) ) @ R2 ) ) ).
% 0.33/0.61
% 0.33/0.61 % in_inv_image
% 0.33/0.61 thf(fact_4923_pair__imageI,axiom,
% 0.33/0.61 ! [A: nat,B: nat,A2: set_Pr1261947904930325089at_nat,F: nat > nat > $o] :
% 0.33/0.61 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ A2 )
% 0.33/0.61 => ( member_o @ ( F @ A @ B ) @ ( image_3693632289388996572_nat_o @ ( produc6081775807080527818_nat_o @ F ) @ A2 ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % pair_imageI
% 0.33/0.61 thf(fact_4924_pair__imageI,axiom,
% 0.33/0.61 ! [A: nat,B: nat,A2: set_Pr1261947904930325089at_nat,F: nat > nat > int] :
% 0.33/0.61 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ A2 )
% 0.33/0.61 => ( member_int @ ( F @ A @ B ) @ ( image_2483585944268220136at_int @ ( produc6840382203811409530at_int @ F ) @ A2 ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % pair_imageI
% 0.33/0.61 thf(fact_4925_pair__imageI,axiom,
% 0.33/0.61 ! [A: nat,B: nat,A2: set_Pr1261947904930325089at_nat,F: nat > nat > nat] :
% 0.33/0.61 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ A2 )
% 0.33/0.61 => ( member_nat @ ( F @ A @ B ) @ ( image_2486076414777270412at_nat @ ( produc6842872674320459806at_nat @ F ) @ A2 ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % pair_imageI
% 0.33/0.61 thf(fact_4926_pair__imageI,axiom,
% 0.33/0.61 ! [A: int,B: int,A2: set_Pr958786334691620121nt_int,F: int > int > int] :
% 0.33/0.61 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ A2 )
% 0.33/0.61 => ( member_int @ ( F @ A @ B ) @ ( image_5042161079198086560nt_int @ ( produc8211389475949308722nt_int @ F ) @ A2 ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % pair_imageI
% 0.33/0.61 thf(fact_4927_pair__imageI,axiom,
% 0.33/0.61 ! [A: nat,B: nat,A2: set_Pr1261947904930325089at_nat,F: nat > nat > product_prod_nat_nat] :
% 0.33/0.61 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ A2 )
% 0.33/0.61 => ( member8440522571783428010at_nat @ ( F @ A @ B ) @ ( image_5168914502847457605at_nat @ ( produc2626176000494625587at_nat @ F ) @ A2 ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % pair_imageI
% 0.33/0.61 thf(fact_4928_pair__imageI,axiom,
% 0.33/0.61 ! [A: int,B: int,A2: set_Pr958786334691620121nt_int,F: int > int > product_prod_int_int] :
% 0.33/0.61 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ A2 )
% 0.33/0.61 => ( member5262025264175285858nt_int @ ( F @ A @ B ) @ ( image_2653370878348428101nt_int @ ( produc4245557441103728435nt_int @ F ) @ A2 ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % pair_imageI
% 0.33/0.61 thf(fact_4929_pair__imageI,axiom,
% 0.33/0.61 ! [A: nat,B: nat,A2: set_Pr1261947904930325089at_nat,F: nat > nat > product_prod_nat_nat > $o] :
% 0.33/0.61 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ A2 )
% 0.33/0.61 => ( member2006080708140975699_nat_o @ ( F @ A @ B ) @ ( image_2972642778337070200_nat_o @ ( produc8739625826339149834_nat_o @ F ) @ A2 ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % pair_imageI
% 0.33/0.61 thf(fact_4930_pair__imageI,axiom,
% 0.33/0.61 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,A2: set_Pr4329608150637261639at_nat,F: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o] :
% 0.33/0.61 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ B ) @ A2 )
% 0.33/0.61 => ( member_o @ ( F @ A @ B ) @ ( image_3500134854233901558_nat_o @ ( produc410239310623530412_nat_o @ F ) @ A2 ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % pair_imageI
% 0.33/0.61 thf(fact_4931_pair__imageI,axiom,
% 0.33/0.61 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,A2: set_Pr4329608150637261639at_nat,F: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > nat] :
% 0.33/0.61 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ B ) @ A2 )
% 0.33/0.61 => ( member_nat @ ( F @ A @ B ) @ ( image_3198525501578754290at_nat @ ( produc4001655692221972156at_nat @ F ) @ A2 ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % pair_imageI
% 0.33/0.61 thf(fact_4932_pair__imageI,axiom,
% 0.33/0.61 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,A2: set_Pr4329608150637261639at_nat,F: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > int] :
% 0.33/0.61 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ B ) @ A2 )
% 0.33/0.61 => ( member_int @ ( F @ A @ B ) @ ( image_3196035031069704014at_int @ ( produc3999165221712921880at_int @ F ) @ A2 ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % pair_imageI
% 0.33/0.61 thf(fact_4933_int__of__integer__max,axiom,
% 0.33/0.61 ! [K: code_integer,L: code_integer] :
% 0.33/0.61 ( ( code_int_of_integer @ ( ord_max_Code_integer @ K @ L ) )
% 0.33/0.61 = ( ord_max_int @ ( code_int_of_integer @ K ) @ ( code_int_of_integer @ L ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % int_of_integer_max
% 0.33/0.61 thf(fact_4934_rat__one__code,axiom,
% 0.33/0.61 ( ( quotient_of @ one_one_rat )
% 0.33/0.61 = ( product_Pair_int_int @ one_one_int @ one_one_int ) ) ).
% 0.33/0.61
% 0.33/0.61 % rat_one_code
% 0.33/0.61 thf(fact_4935_of__nat__of__integer,axiom,
% 0.33/0.61 ! [K: code_integer] :
% 0.33/0.61 ( ( semiri4939895301339042750nteger @ ( code_nat_of_integer @ K ) )
% 0.33/0.61 = ( ord_max_Code_integer @ zero_z3403309356797280102nteger @ K ) ) ).
% 0.33/0.61
% 0.33/0.61 % of_nat_of_integer
% 0.33/0.61 thf(fact_4936_rat__zero__code,axiom,
% 0.33/0.61 ( ( quotient_of @ zero_zero_rat )
% 0.33/0.61 = ( product_Pair_int_int @ zero_zero_int @ one_one_int ) ) ).
% 0.33/0.61
% 0.33/0.61 % rat_zero_code
% 0.33/0.61 thf(fact_4937_quotient__of__number_I3_J,axiom,
% 0.33/0.61 ! [K: num] :
% 0.33/0.61 ( ( quotient_of @ ( numeral_numeral_rat @ K ) )
% 0.33/0.61 = ( product_Pair_int_int @ ( numeral_numeral_int @ K ) @ one_one_int ) ) ).
% 0.33/0.61
% 0.33/0.61 % quotient_of_number(3)
% 0.33/0.61 thf(fact_4938_quotient__of__number_I4_J,axiom,
% 0.33/0.61 ( ( quotient_of @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.33/0.61 = ( product_Pair_int_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ) ) ).
% 0.33/0.61
% 0.33/0.61 % quotient_of_number(4)
% 0.33/0.61 thf(fact_4939_quotient__of__number_I5_J,axiom,
% 0.33/0.61 ! [K: num] :
% 0.33/0.61 ( ( quotient_of @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 0.33/0.61 = ( product_Pair_int_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) ).
% 0.33/0.61
% 0.33/0.61 % quotient_of_number(5)
% 0.33/0.61 thf(fact_4940_diff__rat__def,axiom,
% 0.33/0.61 ( minus_minus_rat
% 0.33/0.61 = ( ^ [Q5: rat,R3: rat] : ( plus_plus_rat @ Q5 @ ( uminus_uminus_rat @ R3 ) ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % diff_rat_def
% 0.33/0.61 thf(fact_4941_quotient__of__div,axiom,
% 0.33/0.61 ! [R2: rat,N2: int,D2: int] :
% 0.33/0.61 ( ( ( quotient_of @ R2 )
% 0.33/0.61 = ( product_Pair_int_int @ N2 @ D2 ) )
% 0.33/0.61 => ( R2
% 0.33/0.61 = ( divide_divide_rat @ ( ring_1_of_int_rat @ N2 ) @ ( ring_1_of_int_rat @ D2 ) ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % quotient_of_div
% 0.33/0.61 thf(fact_4942_zero__notin__Suc__image,axiom,
% 0.33/0.61 ! [A2: set_nat] :
% 0.33/0.61 ~ ( member_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ A2 ) ) ).
% 0.33/0.61
% 0.33/0.61 % zero_notin_Suc_image
% 0.33/0.61 thf(fact_4943_None__notin__image__Some,axiom,
% 0.33/0.61 ! [A2: set_Pr5142436192348053284it_nat] :
% 0.33/0.61 ~ ( member3517700364412436275it_nat @ none_P2587165478634041381it_nat @ ( image_4799632500972785611it_nat @ some_P6105628898608307625it_nat @ A2 ) ) ).
% 0.33/0.61
% 0.33/0.61 % None_notin_image_Some
% 0.33/0.61 thf(fact_4944_None__notin__image__Some,axiom,
% 0.33/0.61 ! [A2: set_num] :
% 0.33/0.61 ~ ( member_option_num @ none_num @ ( image_num_option_num @ some_num @ A2 ) ) ).
% 0.33/0.61
% 0.33/0.61 % None_notin_image_Some
% 0.33/0.61 thf(fact_4945_None__notin__image__Some,axiom,
% 0.33/0.61 ! [A2: set_Pr1354866905816374718it_nat] :
% 0.33/0.61 ~ ( member5596548051065438575it_nat @ none_P9117596204409417319it_nat @ ( image_3455408117458022631it_nat @ some_P1914260805536162275it_nat @ A2 ) ) ).
% 0.33/0.61
% 0.33/0.61 % None_notin_image_Some
% 0.33/0.61 thf(fact_4946_plus__integer__def,axiom,
% 0.33/0.61 ( plus_p5714425477246183910nteger
% 0.33/0.61 = ( map_fu8272188784021352819nteger @ code_int_of_integer @ ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int ) @ plus_plus_int ) ) ).
% 0.33/0.61
% 0.33/0.61 % plus_integer_def
% 0.33/0.61 thf(fact_4947_times__integer__def,axiom,
% 0.33/0.61 ( times_3573771949741848930nteger
% 0.33/0.61 = ( map_fu8272188784021352819nteger @ code_int_of_integer @ ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int ) @ times_times_int ) ) ).
% 0.33/0.61
% 0.33/0.61 % times_integer_def
% 0.33/0.61 thf(fact_4948_minus__integer__def,axiom,
% 0.33/0.61 ( minus_8373710615458151222nteger
% 0.33/0.61 = ( map_fu8272188784021352819nteger @ code_int_of_integer @ ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int ) @ minus_minus_int ) ) ).
% 0.33/0.61
% 0.33/0.61 % minus_integer_def
% 0.33/0.61 thf(fact_4949_divide__integer__def,axiom,
% 0.33/0.61 ( divide6298287555418463151nteger
% 0.33/0.61 = ( map_fu8272188784021352819nteger @ code_int_of_integer @ ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int ) @ divide_divide_int ) ) ).
% 0.33/0.61
% 0.33/0.61 % divide_integer_def
% 0.33/0.61 thf(fact_4950_modulo__integer__def,axiom,
% 0.33/0.61 ( modulo364778990260209775nteger
% 0.33/0.61 = ( map_fu8272188784021352819nteger @ code_int_of_integer @ ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int ) @ modulo_modulo_int ) ) ).
% 0.33/0.61
% 0.33/0.61 % modulo_integer_def
% 0.33/0.61 thf(fact_4951_and__integer__def,axiom,
% 0.33/0.61 ( bit_se3949692690581998587nteger
% 0.33/0.61 = ( map_fu8272188784021352819nteger @ code_int_of_integer @ ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int ) @ bit_se725231765392027082nd_int ) ) ).
% 0.33/0.61
% 0.33/0.61 % and_integer_def
% 0.33/0.61 thf(fact_4952_or__integer__def,axiom,
% 0.33/0.61 ( bit_se1080825931792720795nteger
% 0.33/0.61 = ( map_fu8272188784021352819nteger @ code_int_of_integer @ ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int ) @ bit_se1409905431419307370or_int ) ) ).
% 0.33/0.61
% 0.33/0.61 % or_integer_def
% 0.33/0.61 thf(fact_4953_xor__integer__def,axiom,
% 0.33/0.61 ( bit_se3222712562003087583nteger
% 0.33/0.61 = ( map_fu8272188784021352819nteger @ code_int_of_integer @ ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int ) @ bit_se6526347334894502574or_int ) ) ).
% 0.33/0.61
% 0.33/0.61 % xor_integer_def
% 0.33/0.61 thf(fact_4954_image__int__atLeastAtMost,axiom,
% 0.33/0.61 ! [A: nat,B: nat] :
% 0.33/0.61 ( ( image_nat_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 0.33/0.61 = ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % image_int_atLeastAtMost
% 0.33/0.61 thf(fact_4955_image__int__atLeastLessThan,axiom,
% 0.33/0.61 ! [A: nat,B: nat] :
% 0.33/0.61 ( ( image_nat_int @ semiri1314217659103216013at_int @ ( set_or4665077453230672383an_nat @ A @ B ) )
% 0.33/0.61 = ( set_or4662586982721622107an_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % image_int_atLeastLessThan
% 0.33/0.61 thf(fact_4956_quotient__of__denom__pos,axiom,
% 0.33/0.61 ! [R2: rat,P4: int,Q3: int] :
% 0.33/0.61 ( ( ( quotient_of @ R2 )
% 0.33/0.61 = ( product_Pair_int_int @ P4 @ Q3 ) )
% 0.33/0.61 => ( ord_less_int @ zero_zero_int @ Q3 ) ) ).
% 0.33/0.61
% 0.33/0.61 % quotient_of_denom_pos
% 0.33/0.61 thf(fact_4957_image__Suc__atMost,axiom,
% 0.33/0.61 ! [N2: nat] :
% 0.33/0.61 ( ( image_nat_nat @ suc @ ( set_ord_atMost_nat @ N2 ) )
% 0.33/0.61 = ( set_or1269000886237332187st_nat @ one_one_nat @ ( suc @ N2 ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % image_Suc_atMost
% 0.33/0.61 thf(fact_4958_image__Suc__lessThan,axiom,
% 0.33/0.61 ! [N2: nat] :
% 0.33/0.61 ( ( image_nat_nat @ suc @ ( set_ord_lessThan_nat @ N2 ) )
% 0.33/0.61 = ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) ) ).
% 0.33/0.61
% 0.33/0.61 % image_Suc_lessThan
% 0.33/0.61 thf(fact_4959_rat__uminus__code,axiom,
% 0.33/0.61 ! [P4: rat] :
% 0.33/0.61 ( ( quotient_of @ ( uminus_uminus_rat @ P4 ) )
% 0.33/0.61 = ( produc4245557441103728435nt_int
% 0.33/0.61 @ ^ [A5: int] : ( product_Pair_int_int @ ( uminus_uminus_int @ A5 ) )
% 0.33/0.61 @ ( quotient_of @ P4 ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % rat_uminus_code
% 0.33/0.61 thf(fact_4960_rat__abs__code,axiom,
% 0.33/0.61 ! [P4: rat] :
% 0.33/0.61 ( ( quotient_of @ ( abs_abs_rat @ P4 ) )
% 0.33/0.61 = ( produc4245557441103728435nt_int
% 0.33/0.61 @ ^ [A5: int] : ( product_Pair_int_int @ ( abs_abs_int @ A5 ) )
% 0.33/0.61 @ ( quotient_of @ P4 ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % rat_abs_code
% 0.33/0.61 thf(fact_4961_uminus__integer__def,axiom,
% 0.33/0.61 ( uminus1351360451143612070nteger
% 0.33/0.61 = ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int @ uminus_uminus_int ) ) ).
% 0.33/0.61
% 0.33/0.61 % uminus_integer_def
% 0.33/0.61 thf(fact_4962_abs__integer__def,axiom,
% 0.33/0.61 ( abs_abs_Code_integer
% 0.33/0.61 = ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int @ abs_abs_int ) ) ).
% 0.33/0.61
% 0.33/0.61 % abs_integer_def
% 0.33/0.61 thf(fact_4963_image__add__int__atLeastLessThan,axiom,
% 0.33/0.61 ! [L: int,U: int] :
% 0.33/0.61 ( ( image_int_int
% 0.33/0.61 @ ^ [X3: int] : ( plus_plus_int @ X3 @ L )
% 0.33/0.61 @ ( set_or4662586982721622107an_int @ zero_zero_int @ ( minus_minus_int @ U @ L ) ) )
% 0.33/0.61 = ( set_or4662586982721622107an_int @ L @ U ) ) ).
% 0.33/0.61
% 0.33/0.61 % image_add_int_atLeastLessThan
% 0.33/0.61 thf(fact_4964_sgn__integer__def,axiom,
% 0.33/0.61 ( sgn_sgn_Code_integer
% 0.33/0.61 = ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int @ sgn_sgn_int ) ) ).
% 0.33/0.61
% 0.33/0.61 % sgn_integer_def
% 0.33/0.61 thf(fact_4965_not__integer__def,axiom,
% 0.33/0.61 ( bit_ri7632146776885996613nteger
% 0.33/0.61 = ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int @ bit_ri7919022796975470100ot_int ) ) ).
% 0.33/0.61
% 0.33/0.61 % not_integer_def
% 0.33/0.61 thf(fact_4966_image__add__integer__atLeastLessThan,axiom,
% 0.33/0.61 ! [L: code_integer,U: code_integer] :
% 0.33/0.61 ( ( image_4470545334726330049nteger
% 0.33/0.61 @ ^ [X3: code_integer] : ( plus_p5714425477246183910nteger @ X3 @ L )
% 0.33/0.61 @ ( set_or8404916559141939852nteger @ zero_z3403309356797280102nteger @ ( minus_8373710615458151222nteger @ U @ L ) ) )
% 0.33/0.61 = ( set_or8404916559141939852nteger @ L @ U ) ) ).
% 0.33/0.61
% 0.33/0.61 % image_add_integer_atLeastLessThan
% 0.33/0.61 thf(fact_4967_rat__times__code,axiom,
% 0.33/0.61 ! [P4: rat,Q3: rat] :
% 0.33/0.61 ( ( quotient_of @ ( times_times_rat @ P4 @ Q3 ) )
% 0.33/0.61 = ( produc4245557441103728435nt_int
% 0.33/0.61 @ ^ [A5: int,C2: int] :
% 0.33/0.61 ( produc4245557441103728435nt_int
% 0.33/0.61 @ ^ [B4: int,D4: int] : ( normalize @ ( product_Pair_int_int @ ( times_times_int @ A5 @ B4 ) @ ( times_times_int @ C2 @ D4 ) ) )
% 0.33/0.61 @ ( quotient_of @ Q3 ) )
% 0.33/0.61 @ ( quotient_of @ P4 ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % rat_times_code
% 0.33/0.61 thf(fact_4968_rat__divide__code,axiom,
% 0.33/0.61 ! [P4: rat,Q3: rat] :
% 0.33/0.61 ( ( quotient_of @ ( divide_divide_rat @ P4 @ Q3 ) )
% 0.33/0.61 = ( produc4245557441103728435nt_int
% 0.33/0.61 @ ^ [A5: int,C2: int] :
% 0.33/0.61 ( produc4245557441103728435nt_int
% 0.33/0.61 @ ^ [B4: int,D4: int] : ( normalize @ ( product_Pair_int_int @ ( times_times_int @ A5 @ D4 ) @ ( times_times_int @ C2 @ B4 ) ) )
% 0.33/0.61 @ ( quotient_of @ Q3 ) )
% 0.33/0.61 @ ( quotient_of @ P4 ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % rat_divide_code
% 0.33/0.61 thf(fact_4969_image__atLeastZeroLessThan__int,axiom,
% 0.33/0.61 ! [U: int] :
% 0.33/0.61 ( ( ord_less_eq_int @ zero_zero_int @ U )
% 0.33/0.61 => ( ( set_or4662586982721622107an_int @ zero_zero_int @ U )
% 0.33/0.61 = ( image_nat_int @ semiri1314217659103216013at_int @ ( set_ord_lessThan_nat @ ( nat2 @ U ) ) ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % image_atLeastZeroLessThan_int
% 0.33/0.61 thf(fact_4970_quotient__of__int,axiom,
% 0.33/0.61 ! [A: int] :
% 0.33/0.61 ( ( quotient_of @ ( of_int @ A ) )
% 0.33/0.61 = ( product_Pair_int_int @ A @ one_one_int ) ) ).
% 0.33/0.61
% 0.33/0.61 % quotient_of_int
% 0.33/0.61 thf(fact_4971_rat__inverse__code,axiom,
% 0.33/0.61 ! [P4: rat] :
% 0.33/0.61 ( ( quotient_of @ ( inverse_inverse_rat @ P4 ) )
% 0.33/0.61 = ( produc4245557441103728435nt_int
% 0.33/0.61 @ ^ [A5: int,B4: int] : ( if_Pro3027730157355071871nt_int @ ( A5 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ ( times_times_int @ ( sgn_sgn_int @ A5 ) @ B4 ) @ ( abs_abs_int @ A5 ) ) )
% 0.33/0.61 @ ( quotient_of @ P4 ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % rat_inverse_code
% 0.33/0.61 thf(fact_4972_diff__numeral__special_I8_J,axiom,
% 0.33/0.61 ! [M2: num] :
% 0.33/0.61 ( ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( uminus_uminus_int @ one_one_int ) )
% 0.33/0.61 = ( neg_numeral_sub_int @ one @ M2 ) ) ).
% 0.33/0.61
% 0.33/0.61 % diff_numeral_special(8)
% 0.33/0.61 thf(fact_4973_diff__numeral__special_I8_J,axiom,
% 0.33/0.61 ! [M2: num] :
% 0.33/0.61 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.33/0.61 = ( neg_nu5755505904847501662nteger @ one @ M2 ) ) ).
% 0.33/0.61
% 0.33/0.61 % diff_numeral_special(8)
% 0.33/0.61 thf(fact_4974_diff__numeral__special_I8_J,axiom,
% 0.33/0.61 ! [M2: num] :
% 0.33/0.61 ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.33/0.61 = ( neg_numeral_sub_rat @ one @ M2 ) ) ).
% 0.33/0.61
% 0.33/0.61 % diff_numeral_special(8)
% 0.33/0.61 thf(fact_4975_diff__numeral__special_I7_J,axiom,
% 0.33/0.61 ! [N2: num] :
% 0.33/0.61 ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 0.33/0.61 = ( neg_numeral_sub_int @ N2 @ one ) ) ).
% 0.33/0.61
% 0.33/0.61 % diff_numeral_special(7)
% 0.33/0.61 thf(fact_4976_diff__numeral__special_I7_J,axiom,
% 0.33/0.61 ! [N2: num] :
% 0.33/0.61 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 0.33/0.61 = ( neg_nu5755505904847501662nteger @ N2 @ one ) ) ).
% 0.33/0.61
% 0.33/0.61 % diff_numeral_special(7)
% 0.33/0.61 thf(fact_4977_diff__numeral__special_I7_J,axiom,
% 0.33/0.61 ! [N2: num] :
% 0.33/0.61 ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 0.33/0.61 = ( neg_numeral_sub_rat @ N2 @ one ) ) ).
% 0.33/0.61
% 0.33/0.61 % diff_numeral_special(7)
% 0.33/0.61 thf(fact_4978_minus__sub__one__diff__one,axiom,
% 0.33/0.61 ! [M2: num] :
% 0.33/0.61 ( ( minus_minus_int @ ( uminus_uminus_int @ ( neg_numeral_sub_int @ M2 @ one ) ) @ one_one_int )
% 0.33/0.61 = ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % minus_sub_one_diff_one
% 0.33/0.61 thf(fact_4979_minus__sub__one__diff__one,axiom,
% 0.33/0.61 ! [M2: num] :
% 0.33/0.61 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ ( neg_nu5755505904847501662nteger @ M2 @ one ) ) @ one_one_Code_integer )
% 0.33/0.61 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % minus_sub_one_diff_one
% 0.33/0.61 thf(fact_4980_minus__sub__one__diff__one,axiom,
% 0.33/0.61 ! [M2: num] :
% 0.33/0.61 ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( neg_numeral_sub_rat @ M2 @ one ) ) @ one_one_rat )
% 0.33/0.61 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % minus_sub_one_diff_one
% 0.33/0.61 thf(fact_4981_add__neg__numeral__special_I4_J,axiom,
% 0.33/0.61 ! [N2: num] :
% 0.33/0.61 ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N2 ) )
% 0.33/0.61 = ( neg_numeral_sub_int @ N2 @ one ) ) ).
% 0.33/0.61
% 0.33/0.61 % add_neg_numeral_special(4)
% 0.33/0.61 thf(fact_4982_add__neg__numeral__special_I4_J,axiom,
% 0.33/0.61 ! [N2: num] :
% 0.33/0.61 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ N2 ) )
% 0.33/0.61 = ( neg_nu5755505904847501662nteger @ N2 @ one ) ) ).
% 0.33/0.61
% 0.33/0.61 % add_neg_numeral_special(4)
% 0.33/0.61 thf(fact_4983_add__neg__numeral__special_I4_J,axiom,
% 0.33/0.61 ! [N2: num] :
% 0.33/0.61 ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ N2 ) )
% 0.33/0.61 = ( neg_numeral_sub_rat @ N2 @ one ) ) ).
% 0.33/0.61
% 0.33/0.61 % add_neg_numeral_special(4)
% 0.33/0.61 thf(fact_4984_int__of__integer__sub,axiom,
% 0.33/0.61 ! [K: num,L: num] :
% 0.33/0.61 ( ( code_int_of_integer @ ( neg_nu5755505904847501662nteger @ K @ L ) )
% 0.33/0.61 = ( neg_numeral_sub_int @ K @ L ) ) ).
% 0.33/0.61
% 0.33/0.61 % int_of_integer_sub
% 0.33/0.61 thf(fact_4985_inverse__1,axiom,
% 0.33/0.61 ( ( inverse_inverse_rat @ one_one_rat )
% 0.33/0.61 = one_one_rat ) ).
% 0.33/0.61
% 0.33/0.61 % inverse_1
% 0.33/0.61 thf(fact_4986_inverse__eq__1__iff,axiom,
% 0.33/0.61 ! [X: rat] :
% 0.33/0.61 ( ( ( inverse_inverse_rat @ X )
% 0.33/0.61 = one_one_rat )
% 0.33/0.61 = ( X = one_one_rat ) ) ).
% 0.33/0.61
% 0.33/0.61 % inverse_eq_1_iff
% 0.33/0.61 thf(fact_4987_right__inverse,axiom,
% 0.33/0.61 ! [A: rat] :
% 0.33/0.61 ( ( A != zero_zero_rat )
% 0.33/0.61 => ( ( times_times_rat @ A @ ( inverse_inverse_rat @ A ) )
% 0.33/0.61 = one_one_rat ) ) ).
% 0.33/0.61
% 0.33/0.61 % right_inverse
% 0.33/0.61 thf(fact_4988_left__inverse,axiom,
% 0.33/0.61 ! [A: rat] :
% 0.33/0.61 ( ( A != zero_zero_rat )
% 0.33/0.61 => ( ( times_times_rat @ ( inverse_inverse_rat @ A ) @ A )
% 0.33/0.61 = one_one_rat ) ) ).
% 0.33/0.61
% 0.33/0.61 % left_inverse
% 0.33/0.61 thf(fact_4989_inverse__eq__divide__numeral,axiom,
% 0.33/0.61 ! [W: num] :
% 0.33/0.61 ( ( inverse_inverse_rat @ ( numeral_numeral_rat @ W ) )
% 0.33/0.61 = ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ W ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % inverse_eq_divide_numeral
% 0.33/0.61 thf(fact_4990_add__neg__numeral__simps_I2_J,axiom,
% 0.33/0.61 ! [M2: num,N2: num] :
% 0.33/0.61 ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( numeral_numeral_int @ N2 ) )
% 0.33/0.61 = ( neg_numeral_sub_int @ N2 @ M2 ) ) ).
% 0.33/0.61
% 0.33/0.61 % add_neg_numeral_simps(2)
% 0.33/0.61 thf(fact_4991_add__neg__numeral__simps_I2_J,axiom,
% 0.33/0.61 ! [M2: num,N2: num] :
% 0.33/0.61 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ ( numera6620942414471956472nteger @ N2 ) )
% 0.33/0.61 = ( neg_nu5755505904847501662nteger @ N2 @ M2 ) ) ).
% 0.33/0.61
% 0.33/0.61 % add_neg_numeral_simps(2)
% 0.33/0.61 thf(fact_4992_add__neg__numeral__simps_I2_J,axiom,
% 0.33/0.61 ! [M2: num,N2: num] :
% 0.33/0.61 ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ ( numeral_numeral_rat @ N2 ) )
% 0.33/0.61 = ( neg_numeral_sub_rat @ N2 @ M2 ) ) ).
% 0.33/0.61
% 0.33/0.61 % add_neg_numeral_simps(2)
% 0.33/0.61 thf(fact_4993_add__neg__numeral__simps_I1_J,axiom,
% 0.33/0.61 ! [M2: num,N2: num] :
% 0.33/0.61 ( ( plus_plus_int @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 0.33/0.61 = ( neg_numeral_sub_int @ M2 @ N2 ) ) ).
% 0.33/0.61
% 0.33/0.61 % add_neg_numeral_simps(1)
% 0.33/0.61 thf(fact_4994_add__neg__numeral__simps_I1_J,axiom,
% 0.33/0.61 ! [M2: num,N2: num] :
% 0.33/0.61 ( ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ M2 ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 0.33/0.61 = ( neg_nu5755505904847501662nteger @ M2 @ N2 ) ) ).
% 0.33/0.61
% 0.33/0.61 % add_neg_numeral_simps(1)
% 0.33/0.61 thf(fact_4995_add__neg__numeral__simps_I1_J,axiom,
% 0.33/0.61 ! [M2: num,N2: num] :
% 0.33/0.61 ( ( plus_plus_rat @ ( numeral_numeral_rat @ M2 ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 0.33/0.61 = ( neg_numeral_sub_rat @ M2 @ N2 ) ) ).
% 0.33/0.61
% 0.33/0.61 % add_neg_numeral_simps(1)
% 0.33/0.61 thf(fact_4996_semiring__norm_I166_J,axiom,
% 0.33/0.61 ! [V: num,W: num,Y: int] :
% 0.33/0.61 ( ( plus_plus_int @ ( numeral_numeral_int @ V ) @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ Y ) )
% 0.33/0.61 = ( plus_plus_int @ ( neg_numeral_sub_int @ V @ W ) @ Y ) ) ).
% 0.33/0.61
% 0.33/0.61 % semiring_norm(166)
% 0.33/0.61 thf(fact_4997_semiring__norm_I166_J,axiom,
% 0.33/0.61 ! [V: num,W: num,Y: code_integer] :
% 0.33/0.61 ( ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ V ) @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) @ Y ) )
% 0.33/0.61 = ( plus_p5714425477246183910nteger @ ( neg_nu5755505904847501662nteger @ V @ W ) @ Y ) ) ).
% 0.33/0.61
% 0.33/0.61 % semiring_norm(166)
% 0.33/0.61 thf(fact_4998_semiring__norm_I166_J,axiom,
% 0.33/0.61 ! [V: num,W: num,Y: rat] :
% 0.33/0.61 ( ( plus_plus_rat @ ( numeral_numeral_rat @ V ) @ ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ Y ) )
% 0.33/0.61 = ( plus_plus_rat @ ( neg_numeral_sub_rat @ V @ W ) @ Y ) ) ).
% 0.33/0.61
% 0.33/0.61 % semiring_norm(166)
% 0.33/0.61 thf(fact_4999_semiring__norm_I167_J,axiom,
% 0.33/0.61 ! [V: num,W: num,Y: int] :
% 0.33/0.61 ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( plus_plus_int @ ( numeral_numeral_int @ W ) @ Y ) )
% 0.33/0.61 = ( plus_plus_int @ ( neg_numeral_sub_int @ W @ V ) @ Y ) ) ).
% 0.33/0.61
% 0.33/0.61 % semiring_norm(167)
% 0.33/0.61 thf(fact_5000_semiring__norm_I167_J,axiom,
% 0.33/0.61 ! [V: num,W: num,Y: code_integer] :
% 0.33/0.61 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ W ) @ Y ) )
% 0.33/0.61 = ( plus_p5714425477246183910nteger @ ( neg_nu5755505904847501662nteger @ W @ V ) @ Y ) ) ).
% 0.33/0.61
% 0.33/0.61 % semiring_norm(167)
% 0.33/0.61 thf(fact_5001_semiring__norm_I167_J,axiom,
% 0.33/0.61 ! [V: num,W: num,Y: rat] :
% 0.33/0.61 ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ ( plus_plus_rat @ ( numeral_numeral_rat @ W ) @ Y ) )
% 0.33/0.61 = ( plus_plus_rat @ ( neg_numeral_sub_rat @ W @ V ) @ Y ) ) ).
% 0.33/0.61
% 0.33/0.61 % semiring_norm(167)
% 0.33/0.61 thf(fact_5002_inverse__eq__divide__neg__numeral,axiom,
% 0.33/0.61 ! [W: num] :
% 0.33/0.61 ( ( inverse_inverse_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 0.33/0.61 = ( divide_divide_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % inverse_eq_divide_neg_numeral
% 0.33/0.61 thf(fact_5003_diff__numeral__special_I2_J,axiom,
% 0.33/0.61 ! [M2: num] :
% 0.33/0.61 ( ( minus_minus_int @ ( numeral_numeral_int @ M2 ) @ one_one_int )
% 0.33/0.61 = ( neg_numeral_sub_int @ M2 @ one ) ) ).
% 0.33/0.61
% 0.33/0.61 % diff_numeral_special(2)
% 0.33/0.61 thf(fact_5004_diff__numeral__special_I2_J,axiom,
% 0.33/0.61 ! [M2: num] :
% 0.33/0.61 ( ( minus_8373710615458151222nteger @ ( numera6620942414471956472nteger @ M2 ) @ one_one_Code_integer )
% 0.33/0.61 = ( neg_nu5755505904847501662nteger @ M2 @ one ) ) ).
% 0.33/0.61
% 0.33/0.61 % diff_numeral_special(2)
% 0.33/0.61 thf(fact_5005_diff__numeral__special_I2_J,axiom,
% 0.33/0.61 ! [M2: num] :
% 0.33/0.61 ( ( minus_minus_rat @ ( numeral_numeral_rat @ M2 ) @ one_one_rat )
% 0.33/0.61 = ( neg_numeral_sub_rat @ M2 @ one ) ) ).
% 0.33/0.61
% 0.33/0.61 % diff_numeral_special(2)
% 0.33/0.61 thf(fact_5006_diff__numeral__special_I1_J,axiom,
% 0.33/0.61 ! [N2: num] :
% 0.33/0.61 ( ( minus_minus_int @ one_one_int @ ( numeral_numeral_int @ N2 ) )
% 0.33/0.61 = ( neg_numeral_sub_int @ one @ N2 ) ) ).
% 0.33/0.61
% 0.33/0.61 % diff_numeral_special(1)
% 0.33/0.61 thf(fact_5007_diff__numeral__special_I1_J,axiom,
% 0.33/0.61 ! [N2: num] :
% 0.33/0.61 ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ N2 ) )
% 0.33/0.61 = ( neg_nu5755505904847501662nteger @ one @ N2 ) ) ).
% 0.33/0.61
% 0.33/0.61 % diff_numeral_special(1)
% 0.33/0.61 thf(fact_5008_diff__numeral__special_I1_J,axiom,
% 0.33/0.61 ! [N2: num] :
% 0.33/0.61 ( ( minus_minus_rat @ one_one_rat @ ( numeral_numeral_rat @ N2 ) )
% 0.33/0.61 = ( neg_numeral_sub_rat @ one @ N2 ) ) ).
% 0.33/0.61
% 0.33/0.61 % diff_numeral_special(1)
% 0.33/0.61 thf(fact_5009_add__neg__numeral__special_I1_J,axiom,
% 0.33/0.61 ! [M2: num] :
% 0.33/0.61 ( ( plus_plus_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) )
% 0.33/0.61 = ( neg_numeral_sub_int @ one @ M2 ) ) ).
% 0.33/0.61
% 0.33/0.61 % add_neg_numeral_special(1)
% 0.33/0.61 thf(fact_5010_add__neg__numeral__special_I1_J,axiom,
% 0.33/0.61 ! [M2: num] :
% 0.33/0.61 ( ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) )
% 0.33/0.61 = ( neg_nu5755505904847501662nteger @ one @ M2 ) ) ).
% 0.33/0.61
% 0.33/0.61 % add_neg_numeral_special(1)
% 0.33/0.61 thf(fact_5011_add__neg__numeral__special_I1_J,axiom,
% 0.33/0.61 ! [M2: num] :
% 0.33/0.61 ( ( plus_plus_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) )
% 0.33/0.61 = ( neg_numeral_sub_rat @ one @ M2 ) ) ).
% 0.33/0.61
% 0.33/0.61 % add_neg_numeral_special(1)
% 0.33/0.61 thf(fact_5012_add__neg__numeral__special_I2_J,axiom,
% 0.33/0.61 ! [M2: num] :
% 0.33/0.61 ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ one_one_int )
% 0.33/0.61 = ( neg_numeral_sub_int @ one @ M2 ) ) ).
% 0.33/0.61
% 0.33/0.61 % add_neg_numeral_special(2)
% 0.33/0.61 thf(fact_5013_add__neg__numeral__special_I2_J,axiom,
% 0.33/0.61 ! [M2: num] :
% 0.33/0.61 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ one_one_Code_integer )
% 0.33/0.61 = ( neg_nu5755505904847501662nteger @ one @ M2 ) ) ).
% 0.33/0.61
% 0.33/0.61 % add_neg_numeral_special(2)
% 0.33/0.61 thf(fact_5014_add__neg__numeral__special_I2_J,axiom,
% 0.33/0.61 ! [M2: num] :
% 0.33/0.61 ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ one_one_rat )
% 0.33/0.61 = ( neg_numeral_sub_rat @ one @ M2 ) ) ).
% 0.33/0.61
% 0.33/0.61 % add_neg_numeral_special(2)
% 0.33/0.61 thf(fact_5015_add__neg__numeral__special_I3_J,axiom,
% 0.33/0.61 ! [M2: num] :
% 0.33/0.61 ( ( plus_plus_int @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ one_one_int ) )
% 0.33/0.61 = ( neg_numeral_sub_int @ M2 @ one ) ) ).
% 0.33/0.61
% 0.33/0.61 % add_neg_numeral_special(3)
% 0.33/0.61 thf(fact_5016_add__neg__numeral__special_I3_J,axiom,
% 0.33/0.61 ! [M2: num] :
% 0.33/0.61 ( ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ M2 ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.33/0.61 = ( neg_nu5755505904847501662nteger @ M2 @ one ) ) ).
% 0.33/0.61
% 0.33/0.61 % add_neg_numeral_special(3)
% 0.33/0.61 thf(fact_5017_add__neg__numeral__special_I3_J,axiom,
% 0.33/0.61 ! [M2: num] :
% 0.33/0.61 ( ( plus_plus_rat @ ( numeral_numeral_rat @ M2 ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.33/0.61 = ( neg_numeral_sub_rat @ M2 @ one ) ) ).
% 0.33/0.61
% 0.33/0.61 % add_neg_numeral_special(3)
% 0.33/0.61 thf(fact_5018_inverse__unique,axiom,
% 0.33/0.61 ! [A: rat,B: rat] :
% 0.33/0.61 ( ( ( times_times_rat @ A @ B )
% 0.33/0.61 = one_one_rat )
% 0.33/0.61 => ( ( inverse_inverse_rat @ A )
% 0.33/0.61 = B ) ) ).
% 0.33/0.61
% 0.33/0.61 % inverse_unique
% 0.33/0.61 thf(fact_5019_inverse__eq__divide,axiom,
% 0.33/0.61 ( inverse_inverse_rat
% 0.33/0.61 = ( divide_divide_rat @ one_one_rat ) ) ).
% 0.33/0.61
% 0.33/0.61 % inverse_eq_divide
% 0.33/0.61 thf(fact_5020_inverse__le__1__iff,axiom,
% 0.33/0.61 ! [X: rat] :
% 0.33/0.61 ( ( ord_less_eq_rat @ ( inverse_inverse_rat @ X ) @ one_one_rat )
% 0.33/0.61 = ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 0.33/0.61 | ( ord_less_eq_rat @ one_one_rat @ X ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % inverse_le_1_iff
% 0.33/0.61 thf(fact_5021_one__less__inverse__iff,axiom,
% 0.33/0.61 ! [X: rat] :
% 0.33/0.61 ( ( ord_less_rat @ one_one_rat @ ( inverse_inverse_rat @ X ) )
% 0.33/0.61 = ( ( ord_less_rat @ zero_zero_rat @ X )
% 0.33/0.61 & ( ord_less_rat @ X @ one_one_rat ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % one_less_inverse_iff
% 0.33/0.61 thf(fact_5022_one__less__inverse,axiom,
% 0.33/0.61 ! [A: rat] :
% 0.33/0.61 ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.33/0.61 => ( ( ord_less_rat @ A @ one_one_rat )
% 0.33/0.61 => ( ord_less_rat @ one_one_rat @ ( inverse_inverse_rat @ A ) ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % one_less_inverse
% 0.33/0.61 thf(fact_5023_division__ring__inverse__add,axiom,
% 0.33/0.61 ! [A: rat,B: rat] :
% 0.33/0.61 ( ( A != zero_zero_rat )
% 0.33/0.61 => ( ( B != zero_zero_rat )
% 0.33/0.61 => ( ( plus_plus_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 0.33/0.61 = ( times_times_rat @ ( times_times_rat @ ( inverse_inverse_rat @ A ) @ ( plus_plus_rat @ A @ B ) ) @ ( inverse_inverse_rat @ B ) ) ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % division_ring_inverse_add
% 0.33/0.61 thf(fact_5024_inverse__add,axiom,
% 0.33/0.61 ! [A: rat,B: rat] :
% 0.33/0.61 ( ( A != zero_zero_rat )
% 0.33/0.61 => ( ( B != zero_zero_rat )
% 0.33/0.61 => ( ( plus_plus_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 0.33/0.61 = ( times_times_rat @ ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ ( inverse_inverse_rat @ A ) ) @ ( inverse_inverse_rat @ B ) ) ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % inverse_add
% 0.33/0.61 thf(fact_5025_field__class_Ofield__inverse,axiom,
% 0.33/0.61 ! [A: rat] :
% 0.33/0.61 ( ( A != zero_zero_rat )
% 0.33/0.61 => ( ( times_times_rat @ ( inverse_inverse_rat @ A ) @ A )
% 0.33/0.61 = one_one_rat ) ) ).
% 0.33/0.61
% 0.33/0.61 % field_class.field_inverse
% 0.33/0.61 thf(fact_5026_nonzero__inverse__eq__divide,axiom,
% 0.33/0.61 ! [A: rat] :
% 0.33/0.61 ( ( A != zero_zero_rat )
% 0.33/0.61 => ( ( inverse_inverse_rat @ A )
% 0.33/0.61 = ( divide_divide_rat @ one_one_rat @ A ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % nonzero_inverse_eq_divide
% 0.33/0.61 thf(fact_5027_one__le__inverse__iff,axiom,
% 0.33/0.61 ! [X: rat] :
% 0.33/0.61 ( ( ord_less_eq_rat @ one_one_rat @ ( inverse_inverse_rat @ X ) )
% 0.33/0.61 = ( ( ord_less_rat @ zero_zero_rat @ X )
% 0.33/0.61 & ( ord_less_eq_rat @ X @ one_one_rat ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % one_le_inverse_iff
% 0.33/0.61 thf(fact_5028_inverse__less__1__iff,axiom,
% 0.33/0.61 ! [X: rat] :
% 0.33/0.61 ( ( ord_less_rat @ ( inverse_inverse_rat @ X ) @ one_one_rat )
% 0.33/0.61 = ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 0.33/0.61 | ( ord_less_rat @ one_one_rat @ X ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % inverse_less_1_iff
% 0.33/0.61 thf(fact_5029_one__le__inverse,axiom,
% 0.33/0.61 ! [A: rat] :
% 0.33/0.61 ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.33/0.61 => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 0.33/0.61 => ( ord_less_eq_rat @ one_one_rat @ ( inverse_inverse_rat @ A ) ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % one_le_inverse
% 0.33/0.61 thf(fact_5030_Frct__code__post_I5_J,axiom,
% 0.33/0.61 ! [K: num] :
% 0.33/0.61 ( ( frct @ ( product_Pair_int_int @ one_one_int @ ( numeral_numeral_int @ K ) ) )
% 0.33/0.61 = ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ K ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % Frct_code_post(5)
% 0.33/0.61 thf(fact_5031_Code__Numeral_Odup__def,axiom,
% 0.33/0.61 ( code_dup
% 0.33/0.61 = ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int
% 0.33/0.61 @ ^ [K4: int] : ( plus_plus_int @ K4 @ K4 ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % Code_Numeral.dup_def
% 0.33/0.61 thf(fact_5032_Frct__code__post_I6_J,axiom,
% 0.33/0.61 ! [K: num,L: num] :
% 0.33/0.61 ( ( frct @ ( product_Pair_int_int @ ( numeral_numeral_int @ K ) @ ( numeral_numeral_int @ L ) ) )
% 0.33/0.61 = ( divide_divide_rat @ ( numeral_numeral_rat @ K ) @ ( numeral_numeral_rat @ L ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % Frct_code_post(6)
% 0.33/0.61 thf(fact_5033_Frct__code__post_I4_J,axiom,
% 0.33/0.61 ! [K: num] :
% 0.33/0.61 ( ( frct @ ( product_Pair_int_int @ ( numeral_numeral_int @ K ) @ one_one_int ) )
% 0.33/0.61 = ( numeral_numeral_rat @ K ) ) ).
% 0.33/0.61
% 0.33/0.61 % Frct_code_post(4)
% 0.33/0.61 thf(fact_5034_eq__numeral__iff__iszero_I8_J,axiom,
% 0.33/0.61 ! [Y: num] :
% 0.33/0.61 ( ( one_one_int
% 0.33/0.61 = ( uminus_uminus_int @ ( numeral_numeral_int @ Y ) ) )
% 0.33/0.61 = ( ring_1_iszero_int @ ( numeral_numeral_int @ ( plus_plus_num @ one @ Y ) ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % eq_numeral_iff_iszero(8)
% 0.33/0.61 thf(fact_5035_eq__numeral__iff__iszero_I8_J,axiom,
% 0.33/0.61 ! [Y: num] :
% 0.33/0.61 ( ( one_one_Code_integer
% 0.33/0.61 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ Y ) ) )
% 0.33/0.61 = ( ring_16219924574208605041nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ one @ Y ) ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % eq_numeral_iff_iszero(8)
% 0.33/0.61 thf(fact_5036_eq__numeral__iff__iszero_I8_J,axiom,
% 0.33/0.61 ! [Y: num] :
% 0.33/0.61 ( ( one_one_rat
% 0.33/0.61 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ Y ) ) )
% 0.33/0.61 = ( ring_1_iszero_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ one @ Y ) ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % eq_numeral_iff_iszero(8)
% 0.33/0.61 thf(fact_5037_eq__numeral__iff__iszero_I7_J,axiom,
% 0.33/0.61 ! [X: num] :
% 0.33/0.61 ( ( ( uminus_uminus_int @ ( numeral_numeral_int @ X ) )
% 0.33/0.61 = one_one_int )
% 0.33/0.61 = ( ring_1_iszero_int @ ( numeral_numeral_int @ ( plus_plus_num @ X @ one ) ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % eq_numeral_iff_iszero(7)
% 0.33/0.61 thf(fact_5038_eq__numeral__iff__iszero_I7_J,axiom,
% 0.33/0.61 ! [X: num] :
% 0.33/0.61 ( ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) )
% 0.33/0.61 = one_one_Code_integer )
% 0.33/0.61 = ( ring_16219924574208605041nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ X @ one ) ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % eq_numeral_iff_iszero(7)
% 0.33/0.61 thf(fact_5039_eq__numeral__iff__iszero_I7_J,axiom,
% 0.33/0.61 ! [X: num] :
% 0.33/0.61 ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) )
% 0.33/0.61 = one_one_rat )
% 0.33/0.61 = ( ring_1_iszero_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ X @ one ) ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % eq_numeral_iff_iszero(7)
% 0.33/0.61 thf(fact_5040_Inf_OINF__image,axiom,
% 0.33/0.61 ! [Inf: set_Code_integer > code_integer,G: code_integer > code_integer,F: num > code_integer,A2: set_num] :
% 0.33/0.61 ( ( Inf @ ( image_4470545334726330049nteger @ G @ ( image_8379761247532268670nteger @ F @ A2 ) ) )
% 0.33/0.61 = ( Inf @ ( image_8379761247532268670nteger @ ( comp_C3531382070062128313er_num @ G @ F ) @ A2 ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % Inf.INF_image
% 0.33/0.61 thf(fact_5041_Inf_OINF__image,axiom,
% 0.33/0.61 ! [Inf: set_num > num,G: nat > num,F: int > nat,A2: set_int] :
% 0.33/0.61 ( ( Inf @ ( image_nat_num @ G @ ( image_int_nat @ F @ A2 ) ) )
% 0.33/0.61 = ( Inf @ ( image_int_num @ ( comp_nat_num_int @ G @ F ) @ A2 ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % Inf.INF_image
% 0.33/0.61 thf(fact_5042_Inf_OINF__image,axiom,
% 0.33/0.61 ! [Inf: set_Code_integer > code_integer,G: code_integer > code_integer,F: nat > code_integer,A2: set_nat] :
% 0.33/0.61 ( ( Inf @ ( image_4470545334726330049nteger @ G @ ( image_1215581382706833972nteger @ F @ A2 ) ) )
% 0.33/0.61 = ( Inf @ ( image_1215581382706833972nteger @ ( comp_C6974050283906349679er_nat @ G @ F ) @ A2 ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % Inf.INF_image
% 0.33/0.61 thf(fact_5043_Inf_OINF__image,axiom,
% 0.33/0.61 ! [Inf: set_nat > nat,G: code_integer > nat,F: nat > code_integer,A2: set_nat] :
% 0.33/0.61 ( ( Inf @ ( image_951025933927791156er_nat @ G @ ( image_1215581382706833972nteger @ F @ A2 ) ) )
% 0.33/0.61 = ( Inf @ ( image_nat_nat @ ( comp_C4049556595663050210at_nat @ G @ F ) @ A2 ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % Inf.INF_image
% 0.33/0.61 thf(fact_5044_Inf_OINF__image,axiom,
% 0.33/0.61 ! [Inf: set_int > int,G: code_integer > int,F: nat > code_integer,A2: set_nat] :
% 0.33/0.61 ( ( Inf @ ( image_948535463418740880er_int @ G @ ( image_1215581382706833972nteger @ F @ A2 ) ) )
% 0.33/0.61 = ( Inf @ ( image_nat_int @ ( comp_C5048910307564104766nt_nat @ G @ F ) @ A2 ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % Inf.INF_image
% 0.33/0.61 thf(fact_5045_Inf_OINF__image,axiom,
% 0.33/0.61 ! [Inf: set_Code_integer > code_integer,G: int > code_integer,F: nat > int,A2: set_nat] :
% 0.33/0.61 ( ( Inf @ ( image_1587234942943678608nteger @ G @ ( image_nat_int @ F @ A2 ) ) )
% 0.33/0.61 = ( Inf @ ( image_1215581382706833972nteger @ ( comp_i1588355021709917246er_nat @ G @ F ) @ A2 ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % Inf.INF_image
% 0.33/0.61 thf(fact_5046_Inf_OINF__image,axiom,
% 0.33/0.61 ! [Inf: set_nat > nat,G: int > nat,F: nat > int,A2: set_nat] :
% 0.33/0.61 ( ( Inf @ ( image_int_nat @ G @ ( image_nat_int @ F @ A2 ) ) )
% 0.33/0.61 = ( Inf @ ( image_nat_nat @ ( comp_int_nat_nat @ G @ F ) @ A2 ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % Inf.INF_image
% 0.33/0.61 thf(fact_5047_Inf_OINF__image,axiom,
% 0.33/0.61 ! [Inf: set_Code_integer > code_integer,G: nat > code_integer,F: nat > nat,A2: set_nat] :
% 0.33/0.61 ( ( Inf @ ( image_1215581382706833972nteger @ G @ ( image_nat_nat @ F @ A2 ) ) )
% 0.33/0.61 = ( Inf @ ( image_1215581382706833972nteger @ ( comp_n3898172953802868194er_nat @ G @ F ) @ A2 ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % Inf.INF_image
% 0.33/0.61 thf(fact_5048_Inf_OINF__image,axiom,
% 0.33/0.61 ! [Inf: set_nat > nat,G: nat > nat,F: nat > nat,A2: set_nat] :
% 0.33/0.61 ( ( Inf @ ( image_nat_nat @ G @ ( image_nat_nat @ F @ A2 ) ) )
% 0.33/0.61 = ( Inf @ ( image_nat_nat @ ( comp_nat_nat_nat @ G @ F ) @ A2 ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % Inf.INF_image
% 0.33/0.61 thf(fact_5049_Inf_OINF__image,axiom,
% 0.33/0.61 ! [Inf: set_int > int,G: nat > int,F: int > nat,A2: set_int] :
% 0.33/0.61 ( ( Inf @ ( image_nat_int @ G @ ( image_int_nat @ F @ A2 ) ) )
% 0.33/0.61 = ( Inf @ ( image_int_int @ ( comp_nat_int_int @ G @ F ) @ A2 ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % Inf.INF_image
% 0.33/0.61 thf(fact_5050_not__iszero__1,axiom,
% 0.33/0.61 ~ ( ring_16219924574208605041nteger @ one_one_Code_integer ) ).
% 0.33/0.61
% 0.33/0.61 % not_iszero_1
% 0.33/0.61 thf(fact_5051_not__iszero__1,axiom,
% 0.33/0.61 ~ ( ring_1_iszero_rat @ one_one_rat ) ).
% 0.33/0.61
% 0.33/0.61 % not_iszero_1
% 0.33/0.61 thf(fact_5052_not__iszero__1,axiom,
% 0.33/0.61 ~ ( ring_1_iszero_int @ one_one_int ) ).
% 0.33/0.61
% 0.33/0.61 % not_iszero_1
% 0.33/0.61 thf(fact_5053_Code__Numeral_Odup__code_I1_J,axiom,
% 0.33/0.61 ( ( code_dup @ zero_z3403309356797280102nteger )
% 0.33/0.61 = zero_z3403309356797280102nteger ) ).
% 0.33/0.61
% 0.33/0.61 % Code_Numeral.dup_code(1)
% 0.33/0.61 thf(fact_5054_not__iszero__neg__1,axiom,
% 0.33/0.61 ~ ( ring_1_iszero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 0.33/0.61
% 0.33/0.61 % not_iszero_neg_1
% 0.33/0.61 thf(fact_5055_not__iszero__neg__1,axiom,
% 0.33/0.61 ~ ( ring_16219924574208605041nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.33/0.61
% 0.33/0.61 % not_iszero_neg_1
% 0.33/0.61 thf(fact_5056_not__iszero__neg__1,axiom,
% 0.33/0.61 ~ ( ring_1_iszero_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.33/0.61
% 0.33/0.61 % not_iszero_neg_1
% 0.33/0.61 thf(fact_5057_dup_Orep__eq,axiom,
% 0.33/0.61 ! [X: code_integer] :
% 0.33/0.61 ( ( code_int_of_integer @ ( code_dup @ X ) )
% 0.33/0.61 = ( plus_plus_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ X ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % dup.rep_eq
% 0.33/0.61 thf(fact_5058_dup_Oabs__eq,axiom,
% 0.33/0.61 ! [X: int] :
% 0.33/0.61 ( ( code_dup @ ( code_integer_of_int @ X ) )
% 0.33/0.61 = ( code_integer_of_int @ ( plus_plus_int @ X @ X ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % dup.abs_eq
% 0.33/0.61 thf(fact_5059_eq__numeral__iff__iszero_I2_J,axiom,
% 0.33/0.61 ! [X: num,Y: num] :
% 0.33/0.61 ( ( ( numeral_numeral_int @ X )
% 0.33/0.61 = ( uminus_uminus_int @ ( numeral_numeral_int @ Y ) ) )
% 0.33/0.61 = ( ring_1_iszero_int @ ( numeral_numeral_int @ ( plus_plus_num @ X @ Y ) ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % eq_numeral_iff_iszero(2)
% 0.33/0.61 thf(fact_5060_eq__numeral__iff__iszero_I2_J,axiom,
% 0.33/0.61 ! [X: num,Y: num] :
% 0.33/0.61 ( ( ( numera6620942414471956472nteger @ X )
% 0.33/0.61 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ Y ) ) )
% 0.33/0.61 = ( ring_16219924574208605041nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ X @ Y ) ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % eq_numeral_iff_iszero(2)
% 0.33/0.61 thf(fact_5061_eq__numeral__iff__iszero_I2_J,axiom,
% 0.33/0.61 ! [X: num,Y: num] :
% 0.33/0.61 ( ( ( numeral_numeral_rat @ X )
% 0.33/0.61 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ Y ) ) )
% 0.33/0.61 = ( ring_1_iszero_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ X @ Y ) ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % eq_numeral_iff_iszero(2)
% 0.33/0.61 thf(fact_5062_eq__numeral__iff__iszero_I3_J,axiom,
% 0.33/0.61 ! [X: num,Y: num] :
% 0.33/0.61 ( ( ( uminus_uminus_int @ ( numeral_numeral_int @ X ) )
% 0.33/0.61 = ( numeral_numeral_int @ Y ) )
% 0.33/0.61 = ( ring_1_iszero_int @ ( numeral_numeral_int @ ( plus_plus_num @ X @ Y ) ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % eq_numeral_iff_iszero(3)
% 0.33/0.61 thf(fact_5063_eq__numeral__iff__iszero_I3_J,axiom,
% 0.33/0.61 ! [X: num,Y: num] :
% 0.33/0.61 ( ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) )
% 0.33/0.61 = ( numera6620942414471956472nteger @ Y ) )
% 0.33/0.61 = ( ring_16219924574208605041nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ X @ Y ) ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % eq_numeral_iff_iszero(3)
% 0.33/0.61 thf(fact_5064_eq__numeral__iff__iszero_I3_J,axiom,
% 0.33/0.61 ! [X: num,Y: num] :
% 0.33/0.61 ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) )
% 0.33/0.61 = ( numeral_numeral_rat @ Y ) )
% 0.33/0.61 = ( ring_1_iszero_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ X @ Y ) ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % eq_numeral_iff_iszero(3)
% 0.33/0.61 thf(fact_5065_Frct__code__post_I2_J,axiom,
% 0.33/0.61 ! [A: int] :
% 0.33/0.61 ( ( frct @ ( product_Pair_int_int @ A @ zero_zero_int ) )
% 0.33/0.61 = zero_zero_rat ) ).
% 0.33/0.61
% 0.33/0.61 % Frct_code_post(2)
% 0.33/0.61 thf(fact_5066_Frct__code__post_I1_J,axiom,
% 0.33/0.61 ! [A: int] :
% 0.33/0.61 ( ( frct @ ( product_Pair_int_int @ zero_zero_int @ A ) )
% 0.33/0.61 = zero_zero_rat ) ).
% 0.33/0.61
% 0.33/0.61 % Frct_code_post(1)
% 0.33/0.61 thf(fact_5067_Frct__code__post_I3_J,axiom,
% 0.33/0.61 ( ( frct @ ( product_Pair_int_int @ one_one_int @ one_one_int ) )
% 0.33/0.61 = one_one_rat ) ).
% 0.33/0.61
% 0.33/0.61 % Frct_code_post(3)
% 0.33/0.61 thf(fact_5068_eq__numeral__iff__iszero_I6_J,axiom,
% 0.33/0.61 ! [Y: num] :
% 0.33/0.61 ( ( one_one_int
% 0.33/0.61 = ( numeral_numeral_int @ Y ) )
% 0.33/0.61 = ( ring_1_iszero_int @ ( neg_numeral_sub_int @ one @ Y ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % eq_numeral_iff_iszero(6)
% 0.33/0.61 thf(fact_5069_eq__numeral__iff__iszero_I6_J,axiom,
% 0.33/0.61 ! [Y: num] :
% 0.33/0.61 ( ( one_one_Code_integer
% 0.33/0.61 = ( numera6620942414471956472nteger @ Y ) )
% 0.33/0.61 = ( ring_16219924574208605041nteger @ ( neg_nu5755505904847501662nteger @ one @ Y ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % eq_numeral_iff_iszero(6)
% 0.33/0.61 thf(fact_5070_eq__numeral__iff__iszero_I6_J,axiom,
% 0.33/0.61 ! [Y: num] :
% 0.33/0.61 ( ( one_one_rat
% 0.33/0.61 = ( numeral_numeral_rat @ Y ) )
% 0.33/0.61 = ( ring_1_iszero_rat @ ( neg_numeral_sub_rat @ one @ Y ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % eq_numeral_iff_iszero(6)
% 0.33/0.61 thf(fact_5071_eq__numeral__iff__iszero_I5_J,axiom,
% 0.33/0.61 ! [X: num] :
% 0.33/0.61 ( ( ( numeral_numeral_int @ X )
% 0.33/0.61 = one_one_int )
% 0.33/0.61 = ( ring_1_iszero_int @ ( neg_numeral_sub_int @ X @ one ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % eq_numeral_iff_iszero(5)
% 0.33/0.61 thf(fact_5072_eq__numeral__iff__iszero_I5_J,axiom,
% 0.33/0.61 ! [X: num] :
% 0.33/0.61 ( ( ( numera6620942414471956472nteger @ X )
% 0.33/0.61 = one_one_Code_integer )
% 0.33/0.61 = ( ring_16219924574208605041nteger @ ( neg_nu5755505904847501662nteger @ X @ one ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % eq_numeral_iff_iszero(5)
% 0.33/0.61 thf(fact_5073_eq__numeral__iff__iszero_I5_J,axiom,
% 0.33/0.61 ! [X: num] :
% 0.33/0.61 ( ( ( numeral_numeral_rat @ X )
% 0.33/0.61 = one_one_rat )
% 0.33/0.61 = ( ring_1_iszero_rat @ ( neg_numeral_sub_rat @ X @ one ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % eq_numeral_iff_iszero(5)
% 0.33/0.61 thf(fact_5074_Frct__code__post_I7_J,axiom,
% 0.33/0.61 ! [A: int,B: int] :
% 0.33/0.61 ( ( frct @ ( product_Pair_int_int @ ( uminus_uminus_int @ A ) @ B ) )
% 0.33/0.61 = ( uminus_uminus_rat @ ( frct @ ( product_Pair_int_int @ A @ B ) ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % Frct_code_post(7)
% 0.33/0.61 thf(fact_5075_Frct__code__post_I8_J,axiom,
% 0.33/0.61 ! [A: int,B: int] :
% 0.33/0.61 ( ( frct @ ( product_Pair_int_int @ A @ ( uminus_uminus_int @ B ) ) )
% 0.33/0.61 = ( uminus_uminus_rat @ ( frct @ ( product_Pair_int_int @ A @ B ) ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % Frct_code_post(8)
% 0.33/0.61 thf(fact_5076_Sup_OSUP__image,axiom,
% 0.33/0.61 ! [Sup: set_Code_integer > code_integer,G: code_integer > code_integer,F: num > code_integer,A2: set_num] :
% 0.33/0.61 ( ( Sup @ ( image_4470545334726330049nteger @ G @ ( image_8379761247532268670nteger @ F @ A2 ) ) )
% 0.33/0.61 = ( Sup @ ( image_8379761247532268670nteger @ ( comp_C3531382070062128313er_num @ G @ F ) @ A2 ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % Sup.SUP_image
% 0.33/0.61 thf(fact_5077_Sup_OSUP__image,axiom,
% 0.33/0.61 ! [Sup: set_num > num,G: nat > num,F: int > nat,A2: set_int] :
% 0.33/0.61 ( ( Sup @ ( image_nat_num @ G @ ( image_int_nat @ F @ A2 ) ) )
% 0.33/0.61 = ( Sup @ ( image_int_num @ ( comp_nat_num_int @ G @ F ) @ A2 ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % Sup.SUP_image
% 0.33/0.61 thf(fact_5078_Sup_OSUP__image,axiom,
% 0.33/0.61 ! [Sup: set_Code_integer > code_integer,G: code_integer > code_integer,F: nat > code_integer,A2: set_nat] :
% 0.33/0.61 ( ( Sup @ ( image_4470545334726330049nteger @ G @ ( image_1215581382706833972nteger @ F @ A2 ) ) )
% 0.33/0.61 = ( Sup @ ( image_1215581382706833972nteger @ ( comp_C6974050283906349679er_nat @ G @ F ) @ A2 ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % Sup.SUP_image
% 0.33/0.61 thf(fact_5079_Sup_OSUP__image,axiom,
% 0.33/0.61 ! [Sup: set_nat > nat,G: code_integer > nat,F: nat > code_integer,A2: set_nat] :
% 0.33/0.61 ( ( Sup @ ( image_951025933927791156er_nat @ G @ ( image_1215581382706833972nteger @ F @ A2 ) ) )
% 0.33/0.61 = ( Sup @ ( image_nat_nat @ ( comp_C4049556595663050210at_nat @ G @ F ) @ A2 ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % Sup.SUP_image
% 0.33/0.61 thf(fact_5080_Sup_OSUP__image,axiom,
% 0.33/0.61 ! [Sup: set_int > int,G: code_integer > int,F: nat > code_integer,A2: set_nat] :
% 0.33/0.61 ( ( Sup @ ( image_948535463418740880er_int @ G @ ( image_1215581382706833972nteger @ F @ A2 ) ) )
% 0.33/0.61 = ( Sup @ ( image_nat_int @ ( comp_C5048910307564104766nt_nat @ G @ F ) @ A2 ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % Sup.SUP_image
% 0.33/0.61 thf(fact_5081_Sup_OSUP__image,axiom,
% 0.33/0.61 ! [Sup: set_Code_integer > code_integer,G: int > code_integer,F: nat > int,A2: set_nat] :
% 0.33/0.61 ( ( Sup @ ( image_1587234942943678608nteger @ G @ ( image_nat_int @ F @ A2 ) ) )
% 0.33/0.61 = ( Sup @ ( image_1215581382706833972nteger @ ( comp_i1588355021709917246er_nat @ G @ F ) @ A2 ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % Sup.SUP_image
% 0.33/0.61 thf(fact_5082_Sup_OSUP__image,axiom,
% 0.33/0.61 ! [Sup: set_nat > nat,G: int > nat,F: nat > int,A2: set_nat] :
% 0.33/0.61 ( ( Sup @ ( image_int_nat @ G @ ( image_nat_int @ F @ A2 ) ) )
% 0.33/0.61 = ( Sup @ ( image_nat_nat @ ( comp_int_nat_nat @ G @ F ) @ A2 ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % Sup.SUP_image
% 0.33/0.61 thf(fact_5083_Sup_OSUP__image,axiom,
% 0.33/0.61 ! [Sup: set_Code_integer > code_integer,G: nat > code_integer,F: nat > nat,A2: set_nat] :
% 0.33/0.61 ( ( Sup @ ( image_1215581382706833972nteger @ G @ ( image_nat_nat @ F @ A2 ) ) )
% 0.33/0.61 = ( Sup @ ( image_1215581382706833972nteger @ ( comp_n3898172953802868194er_nat @ G @ F ) @ A2 ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % Sup.SUP_image
% 0.33/0.61 thf(fact_5084_Sup_OSUP__image,axiom,
% 0.33/0.61 ! [Sup: set_nat > nat,G: nat > nat,F: nat > nat,A2: set_nat] :
% 0.33/0.61 ( ( Sup @ ( image_nat_nat @ G @ ( image_nat_nat @ F @ A2 ) ) )
% 0.33/0.61 = ( Sup @ ( image_nat_nat @ ( comp_nat_nat_nat @ G @ F ) @ A2 ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % Sup.SUP_image
% 0.33/0.61 thf(fact_5085_Sup_OSUP__image,axiom,
% 0.33/0.61 ! [Sup: set_int > int,G: nat > int,F: int > nat,A2: set_int] :
% 0.33/0.61 ( ( Sup @ ( image_nat_int @ G @ ( image_int_nat @ F @ A2 ) ) )
% 0.33/0.61 = ( Sup @ ( image_int_int @ ( comp_nat_int_int @ G @ F ) @ A2 ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % Sup.SUP_image
% 0.33/0.61 thf(fact_5086_Code__Numeral_Osub__code_I9_J,axiom,
% 0.33/0.61 ! [M2: num,N2: num] :
% 0.33/0.61 ( ( code_sub @ ( bit0 @ M2 ) @ ( bit1 @ N2 ) )
% 0.33/0.61 = ( minus_8373710615458151222nteger @ ( code_dup @ ( code_sub @ M2 @ N2 ) ) @ one_one_Code_integer ) ) ).
% 0.33/0.61
% 0.33/0.61 % Code_Numeral.sub_code(9)
% 0.33/0.61 thf(fact_5087_Code__Numeral_Osub__code_I8_J,axiom,
% 0.33/0.61 ! [M2: num,N2: num] :
% 0.33/0.61 ( ( code_sub @ ( bit1 @ M2 ) @ ( bit0 @ N2 ) )
% 0.33/0.61 = ( plus_p5714425477246183910nteger @ ( code_dup @ ( code_sub @ M2 @ N2 ) ) @ one_one_Code_integer ) ) ).
% 0.33/0.61
% 0.33/0.61 % Code_Numeral.sub_code(8)
% 0.33/0.61 thf(fact_5088_less__eq__int__def,axiom,
% 0.33/0.61 ( ord_less_eq_int
% 0.33/0.61 = ( map_fu434086159418415080_int_o @ rep_Integ @ ( map_fu4826362097070443709at_o_o @ rep_Integ @ id_o )
% 0.33/0.61 @ ( produc8739625826339149834_nat_o
% 0.33/0.61 @ ^ [X3: nat,Y3: nat] :
% 0.33/0.61 ( produc6081775807080527818_nat_o
% 0.33/0.61 @ ^ [U2: nat,V2: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X3 @ V2 ) @ ( plus_plus_nat @ U2 @ Y3 ) ) ) ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % less_eq_int_def
% 0.33/0.61 thf(fact_5089_less__int__def,axiom,
% 0.33/0.61 ( ord_less_int
% 0.33/0.61 = ( map_fu434086159418415080_int_o @ rep_Integ @ ( map_fu4826362097070443709at_o_o @ rep_Integ @ id_o )
% 0.33/0.61 @ ( produc8739625826339149834_nat_o
% 0.33/0.61 @ ^ [X3: nat,Y3: nat] :
% 0.33/0.61 ( produc6081775807080527818_nat_o
% 0.33/0.61 @ ^ [U2: nat,V2: nat] : ( ord_less_nat @ ( plus_plus_nat @ X3 @ V2 ) @ ( plus_plus_nat @ U2 @ Y3 ) ) ) ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % less_int_def
% 0.33/0.61 thf(fact_5090_image__affinity__atLeastAtMost__div__diff,axiom,
% 0.33/0.61 ! [A: rat,B: rat,M2: rat,C: rat] :
% 0.33/0.61 ( ( ( ( set_or633870826150836451st_rat @ A @ B )
% 0.33/0.61 = bot_bot_set_rat )
% 0.33/0.61 => ( ( image_rat_rat
% 0.33/0.61 @ ^ [X3: rat] : ( minus_minus_rat @ ( divide_divide_rat @ X3 @ M2 ) @ C )
% 0.33/0.61 @ ( set_or633870826150836451st_rat @ A @ B ) )
% 0.33/0.61 = bot_bot_set_rat ) )
% 0.33/0.61 & ( ( ( set_or633870826150836451st_rat @ A @ B )
% 0.33/0.61 != bot_bot_set_rat )
% 0.33/0.61 => ( ( ( ord_less_eq_rat @ zero_zero_rat @ M2 )
% 0.33/0.61 => ( ( image_rat_rat
% 0.33/0.61 @ ^ [X3: rat] : ( minus_minus_rat @ ( divide_divide_rat @ X3 @ M2 ) @ C )
% 0.33/0.61 @ ( set_or633870826150836451st_rat @ A @ B ) )
% 0.33/0.61 = ( set_or633870826150836451st_rat @ ( minus_minus_rat @ ( divide_divide_rat @ A @ M2 ) @ C ) @ ( minus_minus_rat @ ( divide_divide_rat @ B @ M2 ) @ C ) ) ) )
% 0.33/0.61 & ( ~ ( ord_less_eq_rat @ zero_zero_rat @ M2 )
% 0.33/0.61 => ( ( image_rat_rat
% 0.33/0.61 @ ^ [X3: rat] : ( minus_minus_rat @ ( divide_divide_rat @ X3 @ M2 ) @ C )
% 0.33/0.61 @ ( set_or633870826150836451st_rat @ A @ B ) )
% 0.33/0.61 = ( set_or633870826150836451st_rat @ ( minus_minus_rat @ ( divide_divide_rat @ B @ M2 ) @ C ) @ ( minus_minus_rat @ ( divide_divide_rat @ A @ M2 ) @ C ) ) ) ) ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % image_affinity_atLeastAtMost_div_diff
% 0.33/0.61 thf(fact_5091_image__affinity__atLeastAtMost__div,axiom,
% 0.33/0.61 ! [A: rat,B: rat,M2: rat,C: rat] :
% 0.33/0.61 ( ( ( ( set_or633870826150836451st_rat @ A @ B )
% 0.33/0.61 = bot_bot_set_rat )
% 0.33/0.61 => ( ( image_rat_rat
% 0.33/0.61 @ ^ [X3: rat] : ( plus_plus_rat @ ( divide_divide_rat @ X3 @ M2 ) @ C )
% 0.33/0.61 @ ( set_or633870826150836451st_rat @ A @ B ) )
% 0.33/0.61 = bot_bot_set_rat ) )
% 0.33/0.61 & ( ( ( set_or633870826150836451st_rat @ A @ B )
% 0.33/0.61 != bot_bot_set_rat )
% 0.33/0.61 => ( ( ( ord_less_eq_rat @ zero_zero_rat @ M2 )
% 0.33/0.61 => ( ( image_rat_rat
% 0.33/0.61 @ ^ [X3: rat] : ( plus_plus_rat @ ( divide_divide_rat @ X3 @ M2 ) @ C )
% 0.33/0.61 @ ( set_or633870826150836451st_rat @ A @ B ) )
% 0.33/0.61 = ( set_or633870826150836451st_rat @ ( plus_plus_rat @ ( divide_divide_rat @ A @ M2 ) @ C ) @ ( plus_plus_rat @ ( divide_divide_rat @ B @ M2 ) @ C ) ) ) )
% 0.33/0.61 & ( ~ ( ord_less_eq_rat @ zero_zero_rat @ M2 )
% 0.33/0.61 => ( ( image_rat_rat
% 0.33/0.61 @ ^ [X3: rat] : ( plus_plus_rat @ ( divide_divide_rat @ X3 @ M2 ) @ C )
% 0.33/0.61 @ ( set_or633870826150836451st_rat @ A @ B ) )
% 0.33/0.61 = ( set_or633870826150836451st_rat @ ( plus_plus_rat @ ( divide_divide_rat @ B @ M2 ) @ C ) @ ( plus_plus_rat @ ( divide_divide_rat @ A @ M2 ) @ C ) ) ) ) ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % image_affinity_atLeastAtMost_div
% 0.33/0.61 thf(fact_5092_image__affinity__atLeastAtMost__diff,axiom,
% 0.33/0.61 ! [A: rat,B: rat,M2: rat,C: rat] :
% 0.33/0.61 ( ( ( ( set_or633870826150836451st_rat @ A @ B )
% 0.33/0.61 = bot_bot_set_rat )
% 0.33/0.61 => ( ( image_rat_rat
% 0.33/0.61 @ ^ [X3: rat] : ( minus_minus_rat @ ( times_times_rat @ M2 @ X3 ) @ C )
% 0.33/0.61 @ ( set_or633870826150836451st_rat @ A @ B ) )
% 0.33/0.61 = bot_bot_set_rat ) )
% 0.33/0.61 & ( ( ( set_or633870826150836451st_rat @ A @ B )
% 0.33/0.61 != bot_bot_set_rat )
% 0.33/0.61 => ( ( ( ord_less_eq_rat @ zero_zero_rat @ M2 )
% 0.33/0.61 => ( ( image_rat_rat
% 0.33/0.61 @ ^ [X3: rat] : ( minus_minus_rat @ ( times_times_rat @ M2 @ X3 ) @ C )
% 0.33/0.61 @ ( set_or633870826150836451st_rat @ A @ B ) )
% 0.33/0.61 = ( set_or633870826150836451st_rat @ ( minus_minus_rat @ ( times_times_rat @ M2 @ A ) @ C ) @ ( minus_minus_rat @ ( times_times_rat @ M2 @ B ) @ C ) ) ) )
% 0.33/0.61 & ( ~ ( ord_less_eq_rat @ zero_zero_rat @ M2 )
% 0.33/0.61 => ( ( image_rat_rat
% 0.33/0.61 @ ^ [X3: rat] : ( minus_minus_rat @ ( times_times_rat @ M2 @ X3 ) @ C )
% 0.33/0.61 @ ( set_or633870826150836451st_rat @ A @ B ) )
% 0.33/0.61 = ( set_or633870826150836451st_rat @ ( minus_minus_rat @ ( times_times_rat @ M2 @ B ) @ C ) @ ( minus_minus_rat @ ( times_times_rat @ M2 @ A ) @ C ) ) ) ) ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % image_affinity_atLeastAtMost_diff
% 0.33/0.61 thf(fact_5093_id__apply,axiom,
% 0.33/0.61 ( id_o
% 0.33/0.61 = ( ^ [X3: $o] : X3 ) ) ).
% 0.33/0.61
% 0.33/0.61 % id_apply
% 0.33/0.61 thf(fact_5094_id__apply,axiom,
% 0.33/0.61 ( id_nat
% 0.33/0.61 = ( ^ [X3: nat] : X3 ) ) ).
% 0.33/0.61
% 0.33/0.61 % id_apply
% 0.33/0.61 thf(fact_5095_id__apply,axiom,
% 0.33/0.61 ( id_nat_o
% 0.33/0.61 = ( ^ [X3: nat > $o] : X3 ) ) ).
% 0.33/0.61
% 0.33/0.61 % id_apply
% 0.33/0.61 thf(fact_5096_id__apply,axiom,
% 0.33/0.61 ( id_num
% 0.33/0.61 = ( ^ [X3: num] : X3 ) ) ).
% 0.33/0.61
% 0.33/0.61 % id_apply
% 0.33/0.61 thf(fact_5097_id__apply,axiom,
% 0.33/0.61 ( id_int
% 0.33/0.61 = ( ^ [X3: int] : X3 ) ) ).
% 0.33/0.61
% 0.33/0.61 % id_apply
% 0.33/0.61 thf(fact_5098_bijective__Empty,axiom,
% 0.33/0.61 biject3388518990857851981at_nat @ bot_bo228742789529271731at_nat ).
% 0.33/0.61
% 0.33/0.61 % bijective_Empty
% 0.33/0.61 thf(fact_5099_bijective__Empty,axiom,
% 0.33/0.61 bijective_nat_nat @ bot_bo2099793752762293965at_nat ).
% 0.33/0.61
% 0.33/0.61 % bijective_Empty
% 0.33/0.61 thf(fact_5100_image__id,axiom,
% 0.33/0.61 ( ( image_o_o @ id_o )
% 0.33/0.61 = id_set_o ) ).
% 0.33/0.61
% 0.33/0.61 % image_id
% 0.33/0.61 thf(fact_5101_image__id,axiom,
% 0.33/0.61 ( ( image_nat_o_nat_o @ id_nat_o )
% 0.33/0.61 = id_set_nat_o ) ).
% 0.33/0.61
% 0.33/0.61 % image_id
% 0.33/0.61 thf(fact_5102_image__id,axiom,
% 0.33/0.61 ( ( image_num_num @ id_num )
% 0.33/0.61 = id_set_num ) ).
% 0.33/0.61
% 0.33/0.61 % image_id
% 0.33/0.61 thf(fact_5103_image__id,axiom,
% 0.33/0.61 ( ( image_nat_nat @ id_nat )
% 0.33/0.61 = id_set_nat ) ).
% 0.33/0.61
% 0.33/0.61 % image_id
% 0.33/0.61 thf(fact_5104_image__id,axiom,
% 0.33/0.61 ( ( image_int_int @ id_int )
% 0.33/0.61 = id_set_int ) ).
% 0.33/0.61
% 0.33/0.61 % image_id
% 0.33/0.61 thf(fact_5105_fun_Omap__id,axiom,
% 0.33/0.61 ! [T: num > code_integer] :
% 0.33/0.61 ( ( comp_C3531382070062128313er_num @ id_Code_integer @ T )
% 0.33/0.61 = T ) ).
% 0.33/0.61
% 0.33/0.61 % fun.map_id
% 0.33/0.61 thf(fact_5106_id__comp,axiom,
% 0.33/0.61 ! [G: num > code_integer] :
% 0.33/0.61 ( ( comp_C3531382070062128313er_num @ id_Code_integer @ G )
% 0.33/0.61 = G ) ).
% 0.33/0.61
% 0.33/0.61 % id_comp
% 0.33/0.61 thf(fact_5107_comp__id,axiom,
% 0.33/0.61 ! [F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 0.33/0.61 ( ( comp_C1593894019821074884nteger @ F @ id_Code_integer )
% 0.33/0.61 = F ) ).
% 0.33/0.61
% 0.33/0.61 % comp_id
% 0.33/0.61 thf(fact_5108_lessThan__0,axiom,
% 0.33/0.61 ( ( set_ord_lessThan_nat @ zero_zero_nat )
% 0.33/0.61 = bot_bot_set_nat ) ).
% 0.33/0.61
% 0.33/0.61 % lessThan_0
% 0.33/0.61 thf(fact_5109_apsnd__id,axiom,
% 0.33/0.61 ( ( produc6499014454317279255nteger @ id_Code_integer )
% 0.33/0.61 = id_Pro2309048762231606924nteger ) ).
% 0.33/0.61
% 0.33/0.61 % apsnd_id
% 0.33/0.61 thf(fact_5110_set__to__map__empty,axiom,
% 0.33/0.61 ( ( set_to4447731662395764663at_nat @ bot_bo228742789529271731at_nat )
% 0.33/0.61 = ( ^ [X3: set_Pr1261947904930325089at_nat] : none_s625347054029921090at_nat ) ) ).
% 0.33/0.61
% 0.33/0.61 % set_to_map_empty
% 0.33/0.61 thf(fact_5111_set__to__map__empty,axiom,
% 0.33/0.61 ( ( set_to_map_nat_nat @ bot_bo2099793752762293965at_nat )
% 0.33/0.61 = ( ^ [X3: nat] : none_nat ) ) ).
% 0.33/0.61
% 0.33/0.61 % set_to_map_empty
% 0.33/0.61 thf(fact_5112_atLeastatMost__empty__iff2,axiom,
% 0.33/0.61 ! [A: $o,B: $o] :
% 0.33/0.61 ( ( bot_bot_set_o
% 0.33/0.61 = ( set_or8904488021354931149Most_o @ A @ B ) )
% 0.33/0.61 = ( ~ ( ord_less_eq_o @ A @ B ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % atLeastatMost_empty_iff2
% 0.33/0.61 thf(fact_5113_atLeastatMost__empty__iff2,axiom,
% 0.33/0.61 ! [A: set_nat,B: set_nat] :
% 0.33/0.61 ( ( bot_bot_set_set_nat
% 0.33/0.61 = ( set_or4548717258645045905et_nat @ A @ B ) )
% 0.33/0.61 = ( ~ ( ord_less_eq_set_nat @ A @ B ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % atLeastatMost_empty_iff2
% 0.33/0.61 thf(fact_5114_atLeastatMost__empty__iff2,axiom,
% 0.33/0.61 ! [A: rat,B: rat] :
% 0.33/0.61 ( ( bot_bot_set_rat
% 0.33/0.61 = ( set_or633870826150836451st_rat @ A @ B ) )
% 0.33/0.61 = ( ~ ( ord_less_eq_rat @ A @ B ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % atLeastatMost_empty_iff2
% 0.33/0.61 thf(fact_5115_atLeastatMost__empty__iff2,axiom,
% 0.33/0.61 ! [A: num,B: num] :
% 0.33/0.61 ( ( bot_bot_set_num
% 0.33/0.61 = ( set_or7049704709247886629st_num @ A @ B ) )
% 0.33/0.61 = ( ~ ( ord_less_eq_num @ A @ B ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % atLeastatMost_empty_iff2
% 0.33/0.61 thf(fact_5116_atLeastatMost__empty__iff2,axiom,
% 0.33/0.61 ! [A: int,B: int] :
% 0.33/0.61 ( ( bot_bot_set_int
% 0.33/0.61 = ( set_or1266510415728281911st_int @ A @ B ) )
% 0.33/0.61 = ( ~ ( ord_less_eq_int @ A @ B ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % atLeastatMost_empty_iff2
% 0.33/0.61 thf(fact_5117_atLeastatMost__empty__iff2,axiom,
% 0.33/0.61 ! [A: nat,B: nat] :
% 0.33/0.61 ( ( bot_bot_set_nat
% 0.33/0.61 = ( set_or1269000886237332187st_nat @ A @ B ) )
% 0.33/0.61 = ( ~ ( ord_less_eq_nat @ A @ B ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % atLeastatMost_empty_iff2
% 0.33/0.61 thf(fact_5118_atLeastatMost__empty__iff2,axiom,
% 0.33/0.61 ! [A: code_integer,B: code_integer] :
% 0.33/0.61 ( ( bot_bo3990330152332043303nteger
% 0.33/0.61 = ( set_or189985376899183464nteger @ A @ B ) )
% 0.33/0.61 = ( ~ ( ord_le3102999989581377725nteger @ A @ B ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % atLeastatMost_empty_iff2
% 0.33/0.61 thf(fact_5119_atLeastatMost__empty__iff,axiom,
% 0.33/0.61 ! [A: $o,B: $o] :
% 0.33/0.61 ( ( ( set_or8904488021354931149Most_o @ A @ B )
% 0.33/0.61 = bot_bot_set_o )
% 0.33/0.61 = ( ~ ( ord_less_eq_o @ A @ B ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % atLeastatMost_empty_iff
% 0.33/0.61 thf(fact_5120_atLeastatMost__empty__iff,axiom,
% 0.33/0.61 ! [A: set_nat,B: set_nat] :
% 0.33/0.61 ( ( ( set_or4548717258645045905et_nat @ A @ B )
% 0.33/0.61 = bot_bot_set_set_nat )
% 0.33/0.61 = ( ~ ( ord_less_eq_set_nat @ A @ B ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % atLeastatMost_empty_iff
% 0.33/0.61 thf(fact_5121_atLeastatMost__empty__iff,axiom,
% 0.33/0.61 ! [A: rat,B: rat] :
% 0.33/0.61 ( ( ( set_or633870826150836451st_rat @ A @ B )
% 0.33/0.61 = bot_bot_set_rat )
% 0.33/0.61 = ( ~ ( ord_less_eq_rat @ A @ B ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % atLeastatMost_empty_iff
% 0.33/0.61 thf(fact_5122_atLeastatMost__empty__iff,axiom,
% 0.33/0.61 ! [A: num,B: num] :
% 0.33/0.61 ( ( ( set_or7049704709247886629st_num @ A @ B )
% 0.33/0.61 = bot_bot_set_num )
% 0.33/0.61 = ( ~ ( ord_less_eq_num @ A @ B ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % atLeastatMost_empty_iff
% 0.33/0.61 thf(fact_5123_atLeastatMost__empty__iff,axiom,
% 0.33/0.61 ! [A: int,B: int] :
% 0.33/0.61 ( ( ( set_or1266510415728281911st_int @ A @ B )
% 0.33/0.61 = bot_bot_set_int )
% 0.33/0.61 = ( ~ ( ord_less_eq_int @ A @ B ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % atLeastatMost_empty_iff
% 0.33/0.61 thf(fact_5124_atLeastatMost__empty__iff,axiom,
% 0.33/0.61 ! [A: nat,B: nat] :
% 0.33/0.61 ( ( ( set_or1269000886237332187st_nat @ A @ B )
% 0.33/0.61 = bot_bot_set_nat )
% 0.33/0.61 = ( ~ ( ord_less_eq_nat @ A @ B ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % atLeastatMost_empty_iff
% 0.33/0.61 thf(fact_5125_atLeastatMost__empty__iff,axiom,
% 0.33/0.61 ! [A: code_integer,B: code_integer] :
% 0.33/0.61 ( ( ( set_or189985376899183464nteger @ A @ B )
% 0.33/0.61 = bot_bo3990330152332043303nteger )
% 0.33/0.61 = ( ~ ( ord_le3102999989581377725nteger @ A @ B ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % atLeastatMost_empty_iff
% 0.33/0.61 thf(fact_5126_atLeastatMost__empty,axiom,
% 0.33/0.61 ! [B: $o,A: $o] :
% 0.33/0.61 ( ( ord_less_o @ B @ A )
% 0.33/0.61 => ( ( set_or8904488021354931149Most_o @ A @ B )
% 0.33/0.61 = bot_bot_set_o ) ) ).
% 0.33/0.61
% 0.33/0.61 % atLeastatMost_empty
% 0.33/0.61 thf(fact_5127_atLeastatMost__empty,axiom,
% 0.33/0.61 ! [B: rat,A: rat] :
% 0.33/0.61 ( ( ord_less_rat @ B @ A )
% 0.33/0.61 => ( ( set_or633870826150836451st_rat @ A @ B )
% 0.33/0.61 = bot_bot_set_rat ) ) ).
% 0.33/0.61
% 0.33/0.61 % atLeastatMost_empty
% 0.33/0.61 thf(fact_5128_atLeastatMost__empty,axiom,
% 0.33/0.61 ! [B: num,A: num] :
% 0.33/0.61 ( ( ord_less_num @ B @ A )
% 0.33/0.61 => ( ( set_or7049704709247886629st_num @ A @ B )
% 0.33/0.61 = bot_bot_set_num ) ) ).
% 0.33/0.61
% 0.33/0.61 % atLeastatMost_empty
% 0.33/0.61 thf(fact_5129_atLeastatMost__empty,axiom,
% 0.33/0.61 ! [B: int,A: int] :
% 0.33/0.61 ( ( ord_less_int @ B @ A )
% 0.33/0.61 => ( ( set_or1266510415728281911st_int @ A @ B )
% 0.33/0.61 = bot_bot_set_int ) ) ).
% 0.33/0.61
% 0.33/0.61 % atLeastatMost_empty
% 0.33/0.61 thf(fact_5130_atLeastatMost__empty,axiom,
% 0.33/0.61 ! [B: nat,A: nat] :
% 0.33/0.61 ( ( ord_less_nat @ B @ A )
% 0.33/0.61 => ( ( set_or1269000886237332187st_nat @ A @ B )
% 0.33/0.61 = bot_bot_set_nat ) ) ).
% 0.33/0.61
% 0.33/0.61 % atLeastatMost_empty
% 0.33/0.61 thf(fact_5131_atLeastatMost__empty,axiom,
% 0.33/0.61 ! [B: code_integer,A: code_integer] :
% 0.33/0.61 ( ( ord_le6747313008572928689nteger @ B @ A )
% 0.33/0.61 => ( ( set_or189985376899183464nteger @ A @ B )
% 0.33/0.61 = bot_bo3990330152332043303nteger ) ) ).
% 0.33/0.61
% 0.33/0.61 % atLeastatMost_empty
% 0.33/0.61 thf(fact_5132_atLeastLessThan__empty,axiom,
% 0.33/0.61 ! [B: $o,A: $o] :
% 0.33/0.61 ( ( ord_less_eq_o @ B @ A )
% 0.33/0.61 => ( ( set_or7139685690850216873Than_o @ A @ B )
% 0.33/0.61 = bot_bot_set_o ) ) ).
% 0.33/0.61
% 0.33/0.61 % atLeastLessThan_empty
% 0.33/0.61 thf(fact_5133_atLeastLessThan__empty,axiom,
% 0.33/0.61 ! [B: set_nat,A: set_nat] :
% 0.33/0.61 ( ( ord_less_eq_set_nat @ B @ A )
% 0.33/0.61 => ( ( set_or3540276404033026485et_nat @ A @ B )
% 0.33/0.61 = bot_bot_set_set_nat ) ) ).
% 0.33/0.61
% 0.33/0.61 % atLeastLessThan_empty
% 0.33/0.61 thf(fact_5134_atLeastLessThan__empty,axiom,
% 0.33/0.61 ! [B: rat,A: rat] :
% 0.33/0.61 ( ( ord_less_eq_rat @ B @ A )
% 0.33/0.61 => ( ( set_or4029947393144176647an_rat @ A @ B )
% 0.33/0.61 = bot_bot_set_rat ) ) ).
% 0.33/0.61
% 0.33/0.61 % atLeastLessThan_empty
% 0.33/0.61 thf(fact_5135_atLeastLessThan__empty,axiom,
% 0.33/0.61 ! [B: num,A: num] :
% 0.33/0.61 ( ( ord_less_eq_num @ B @ A )
% 0.33/0.61 => ( ( set_or1222409239386451017an_num @ A @ B )
% 0.33/0.61 = bot_bot_set_num ) ) ).
% 0.33/0.61
% 0.33/0.61 % atLeastLessThan_empty
% 0.33/0.61 thf(fact_5136_atLeastLessThan__empty,axiom,
% 0.33/0.61 ! [B: nat,A: nat] :
% 0.33/0.61 ( ( ord_less_eq_nat @ B @ A )
% 0.33/0.61 => ( ( set_or4665077453230672383an_nat @ A @ B )
% 0.33/0.61 = bot_bot_set_nat ) ) ).
% 0.33/0.61
% 0.33/0.61 % atLeastLessThan_empty
% 0.33/0.61 thf(fact_5137_atLeastLessThan__empty,axiom,
% 0.33/0.61 ! [B: code_integer,A: code_integer] :
% 0.33/0.61 ( ( ord_le3102999989581377725nteger @ B @ A )
% 0.33/0.61 => ( ( set_or8404916559141939852nteger @ A @ B )
% 0.33/0.61 = bot_bo3990330152332043303nteger ) ) ).
% 0.33/0.61
% 0.33/0.61 % atLeastLessThan_empty
% 0.33/0.61 thf(fact_5138_atLeastLessThan__empty,axiom,
% 0.33/0.61 ! [B: int,A: int] :
% 0.33/0.61 ( ( ord_less_eq_int @ B @ A )
% 0.33/0.61 => ( ( set_or4662586982721622107an_int @ A @ B )
% 0.33/0.61 = bot_bot_set_int ) ) ).
% 0.33/0.61
% 0.33/0.61 % atLeastLessThan_empty
% 0.33/0.61 thf(fact_5139_atLeastLessThan__empty__iff,axiom,
% 0.33/0.61 ! [A: $o,B: $o] :
% 0.33/0.61 ( ( ( set_or7139685690850216873Than_o @ A @ B )
% 0.33/0.61 = bot_bot_set_o )
% 0.33/0.61 = ( ~ ( ord_less_o @ A @ B ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % atLeastLessThan_empty_iff
% 0.33/0.61 thf(fact_5140_atLeastLessThan__empty__iff,axiom,
% 0.33/0.61 ! [A: rat,B: rat] :
% 0.33/0.61 ( ( ( set_or4029947393144176647an_rat @ A @ B )
% 0.33/0.61 = bot_bot_set_rat )
% 0.33/0.61 = ( ~ ( ord_less_rat @ A @ B ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % atLeastLessThan_empty_iff
% 0.33/0.61 thf(fact_5141_atLeastLessThan__empty__iff,axiom,
% 0.33/0.61 ! [A: num,B: num] :
% 0.33/0.61 ( ( ( set_or1222409239386451017an_num @ A @ B )
% 0.33/0.61 = bot_bot_set_num )
% 0.33/0.61 = ( ~ ( ord_less_num @ A @ B ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % atLeastLessThan_empty_iff
% 0.33/0.61 thf(fact_5142_atLeastLessThan__empty__iff,axiom,
% 0.33/0.61 ! [A: nat,B: nat] :
% 0.33/0.61 ( ( ( set_or4665077453230672383an_nat @ A @ B )
% 0.33/0.61 = bot_bot_set_nat )
% 0.33/0.61 = ( ~ ( ord_less_nat @ A @ B ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % atLeastLessThan_empty_iff
% 0.33/0.61 thf(fact_5143_atLeastLessThan__empty__iff,axiom,
% 0.33/0.61 ! [A: code_integer,B: code_integer] :
% 0.33/0.61 ( ( ( set_or8404916559141939852nteger @ A @ B )
% 0.33/0.61 = bot_bo3990330152332043303nteger )
% 0.33/0.61 = ( ~ ( ord_le6747313008572928689nteger @ A @ B ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % atLeastLessThan_empty_iff
% 0.33/0.61 thf(fact_5144_atLeastLessThan__empty__iff,axiom,
% 0.33/0.61 ! [A: int,B: int] :
% 0.33/0.61 ( ( ( set_or4662586982721622107an_int @ A @ B )
% 0.33/0.61 = bot_bot_set_int )
% 0.33/0.61 = ( ~ ( ord_less_int @ A @ B ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % atLeastLessThan_empty_iff
% 0.33/0.61 thf(fact_5145_atLeastLessThan__empty__iff2,axiom,
% 0.33/0.61 ! [A: $o,B: $o] :
% 0.33/0.61 ( ( bot_bot_set_o
% 0.33/0.61 = ( set_or7139685690850216873Than_o @ A @ B ) )
% 0.33/0.61 = ( ~ ( ord_less_o @ A @ B ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % atLeastLessThan_empty_iff2
% 0.33/0.61 thf(fact_5146_atLeastLessThan__empty__iff2,axiom,
% 0.33/0.61 ! [A: rat,B: rat] :
% 0.33/0.61 ( ( bot_bot_set_rat
% 0.33/0.61 = ( set_or4029947393144176647an_rat @ A @ B ) )
% 0.33/0.61 = ( ~ ( ord_less_rat @ A @ B ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % atLeastLessThan_empty_iff2
% 0.33/0.61 thf(fact_5147_atLeastLessThan__empty__iff2,axiom,
% 0.33/0.61 ! [A: num,B: num] :
% 0.33/0.61 ( ( bot_bot_set_num
% 0.33/0.61 = ( set_or1222409239386451017an_num @ A @ B ) )
% 0.33/0.61 = ( ~ ( ord_less_num @ A @ B ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % atLeastLessThan_empty_iff2
% 0.33/0.61 thf(fact_5148_atLeastLessThan__empty__iff2,axiom,
% 0.33/0.61 ! [A: nat,B: nat] :
% 0.33/0.61 ( ( bot_bot_set_nat
% 0.33/0.61 = ( set_or4665077453230672383an_nat @ A @ B ) )
% 0.33/0.61 = ( ~ ( ord_less_nat @ A @ B ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % atLeastLessThan_empty_iff2
% 0.33/0.61 thf(fact_5149_atLeastLessThan__empty__iff2,axiom,
% 0.33/0.61 ! [A: code_integer,B: code_integer] :
% 0.33/0.61 ( ( bot_bo3990330152332043303nteger
% 0.33/0.61 = ( set_or8404916559141939852nteger @ A @ B ) )
% 0.33/0.61 = ( ~ ( ord_le6747313008572928689nteger @ A @ B ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % atLeastLessThan_empty_iff2
% 0.33/0.61 thf(fact_5150_atLeastLessThan__empty__iff2,axiom,
% 0.33/0.61 ! [A: int,B: int] :
% 0.33/0.61 ( ( bot_bot_set_int
% 0.33/0.61 = ( set_or4662586982721622107an_int @ A @ B ) )
% 0.33/0.61 = ( ~ ( ord_less_int @ A @ B ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % atLeastLessThan_empty_iff2
% 0.33/0.61 thf(fact_5151_prod_Oempty,axiom,
% 0.33/0.61 ! [G: $o > code_integer] :
% 0.33/0.61 ( ( groups7694694392188491536nteger @ G @ bot_bot_set_o )
% 0.33/0.61 = one_one_Code_integer ) ).
% 0.33/0.61
% 0.33/0.61 % prod.empty
% 0.33/0.61 thf(fact_5152_prod_Oempty,axiom,
% 0.33/0.61 ! [G: $o > assn] :
% 0.33/0.61 ( ( groups5301882518646026715o_assn @ G @ bot_bot_set_o )
% 0.33/0.61 = one_one_assn ) ).
% 0.33/0.61
% 0.33/0.61 % prod.empty
% 0.33/0.61 thf(fact_5153_prod_Oempty,axiom,
% 0.33/0.61 ! [G: $o > rat] :
% 0.33/0.61 ( ( groups2869687844427037835_o_rat @ G @ bot_bot_set_o )
% 0.33/0.61 = one_one_rat ) ).
% 0.33/0.61
% 0.33/0.61 % prod.empty
% 0.33/0.61 thf(fact_5154_prod_Oempty,axiom,
% 0.33/0.61 ! [G: $o > nat] :
% 0.33/0.61 ( ( groups3504817904513533571_o_nat @ G @ bot_bot_set_o )
% 0.33/0.61 = one_one_nat ) ).
% 0.33/0.61
% 0.33/0.61 % prod.empty
% 0.33/0.61 thf(fact_5155_prod_Oempty,axiom,
% 0.33/0.61 ! [G: $o > int] :
% 0.33/0.61 ( ( groups3502327434004483295_o_int @ G @ bot_bot_set_o )
% 0.33/0.61 = one_one_int ) ).
% 0.33/0.61
% 0.33/0.61 % prod.empty
% 0.33/0.61 thf(fact_5156_prod_Oempty,axiom,
% 0.33/0.61 ! [G: nat > code_integer] :
% 0.33/0.61 ( ( groups3455450783089532116nteger @ G @ bot_bot_set_nat )
% 0.33/0.61 = one_one_Code_integer ) ).
% 0.33/0.61
% 0.33/0.61 % prod.empty
% 0.33/0.61 thf(fact_5157_prod_Oempty,axiom,
% 0.33/0.61 ! [G: nat > assn] :
% 0.33/0.61 ( ( groups6906906614972039071t_assn @ G @ bot_bot_set_nat )
% 0.33/0.61 = one_one_assn ) ).
% 0.33/0.61
% 0.33/0.61 % prod.empty
% 0.33/0.61 thf(fact_5158_prod_Oempty,axiom,
% 0.33/0.61 ! [G: nat > rat] :
% 0.33/0.61 ( ( groups73079841787564623at_rat @ G @ bot_bot_set_nat )
% 0.33/0.61 = one_one_rat ) ).
% 0.33/0.61
% 0.33/0.61 % prod.empty
% 0.33/0.61 thf(fact_5159_prod_Oempty,axiom,
% 0.33/0.61 ! [G: int > code_integer] :
% 0.33/0.61 ( ( groups3827104343326376752nteger @ G @ bot_bot_set_int )
% 0.33/0.61 = one_one_Code_integer ) ).
% 0.33/0.61
% 0.33/0.61 % prod.empty
% 0.33/0.61 thf(fact_5160_prod_Oempty,axiom,
% 0.33/0.61 ! [G: int > assn] :
% 0.33/0.61 ( ( groups7882442080178216443t_assn @ G @ bot_bot_set_int )
% 0.33/0.61 = one_one_assn ) ).
% 0.33/0.61
% 0.33/0.61 % prod.empty
% 0.33/0.61 thf(fact_5161_group__add__class_Ominus__comp__minus,axiom,
% 0.33/0.61 ( ( comp_int_int_int @ uminus_uminus_int @ uminus_uminus_int )
% 0.33/0.61 = id_int ) ).
% 0.33/0.61
% 0.33/0.61 % group_add_class.minus_comp_minus
% 0.33/0.61 thf(fact_5162_group__add__class_Ominus__comp__minus,axiom,
% 0.33/0.61 ( ( comp_C7449957260575251196nteger @ uminus1351360451143612070nteger @ uminus1351360451143612070nteger )
% 0.33/0.61 = id_Code_integer ) ).
% 0.33/0.61
% 0.33/0.61 % group_add_class.minus_comp_minus
% 0.33/0.61 thf(fact_5163_group__add__class_Ominus__comp__minus,axiom,
% 0.33/0.61 ( ( comp_rat_rat_rat @ uminus_uminus_rat @ uminus_uminus_rat )
% 0.33/0.61 = id_rat ) ).
% 0.33/0.61
% 0.33/0.61 % group_add_class.minus_comp_minus
% 0.33/0.61 thf(fact_5164_boolean__algebra__class_Ominus__comp__minus,axiom,
% 0.33/0.61 ( ( comp_o_o_o @ uminus_uminus_o @ uminus_uminus_o )
% 0.33/0.61 = id_o ) ).
% 0.33/0.61
% 0.33/0.61 % boolean_algebra_class.minus_comp_minus
% 0.33/0.61 thf(fact_5165_boolean__algebra__class_Ominus__comp__minus,axiom,
% 0.33/0.61 ( ( comp_n5656820349209612572_nat_o @ uminus_uminus_nat_o @ uminus_uminus_nat_o )
% 0.33/0.61 = id_nat_o ) ).
% 0.33/0.61
% 0.33/0.61 % boolean_algebra_class.minus_comp_minus
% 0.33/0.61 thf(fact_5166_boolean__algebra__class_Ominus__comp__minus,axiom,
% 0.33/0.61 ( ( comp_P7645380973975430442t_unit @ uminus2952777764628376836t_unit @ uminus2952777764628376836t_unit )
% 0.33/0.61 = id_Product_unit ) ).
% 0.33/0.61
% 0.33/0.61 % boolean_algebra_class.minus_comp_minus
% 0.33/0.61 thf(fact_5167_rel__of__empty,axiom,
% 0.33/0.61 ! [P: produc3843707927480180839at_nat > $o] :
% 0.33/0.61 ( ( rel_of6563097375766832824at_nat
% 0.33/0.61 @ ^ [X3: set_Pr1261947904930325089at_nat] : none_s625347054029921090at_nat
% 0.33/0.61 @ P )
% 0.33/0.61 = bot_bo228742789529271731at_nat ) ).
% 0.33/0.61
% 0.33/0.61 % rel_of_empty
% 0.33/0.61 thf(fact_5168_rel__of__empty,axiom,
% 0.33/0.61 ! [P: product_prod_nat_nat > $o] :
% 0.33/0.61 ( ( rel_of_nat_nat
% 0.33/0.61 @ ^ [X3: nat] : none_nat
% 0.33/0.61 @ P )
% 0.33/0.61 = bot_bo2099793752762293965at_nat ) ).
% 0.33/0.61
% 0.33/0.61 % rel_of_empty
% 0.33/0.61 thf(fact_5169_comp__the__Some,axiom,
% 0.33/0.61 ( ( comp_option_o_o_o @ the_o @ some_o )
% 0.33/0.61 = id_o ) ).
% 0.33/0.61
% 0.33/0.61 % comp_the_Some
% 0.33/0.61 thf(fact_5170_comp__the__Some,axiom,
% 0.33/0.61 ( ( comp_o4663963155070737957at_nat @ the_nat @ some_nat )
% 0.33/0.61 = id_nat ) ).
% 0.33/0.61
% 0.33/0.61 % comp_the_Some
% 0.33/0.61 thf(fact_5171_comp__the__Some,axiom,
% 0.33/0.61 ( ( comp_o8860755393669798242_nat_o @ the_nat_o @ some_nat_o )
% 0.33/0.61 = id_nat_o ) ).
% 0.33/0.61
% 0.33/0.61 % comp_the_Some
% 0.33/0.61 thf(fact_5172_comp__the__Some,axiom,
% 0.33/0.61 ( ( comp_o2446264010603541305nt_int @ the_int2 @ some_int )
% 0.33/0.61 = id_int ) ).
% 0.33/0.61
% 0.33/0.61 % comp_the_Some
% 0.33/0.61 thf(fact_5173_comp__the__Some,axiom,
% 0.33/0.61 ( ( comp_o6342398210560591875um_num @ the_num @ some_num )
% 0.33/0.61 = id_num ) ).
% 0.33/0.61
% 0.33/0.61 % comp_the_Some
% 0.33/0.61 thf(fact_5174_comp__the__Some,axiom,
% 0.33/0.61 ( ( comp_o279924169626513613it_nat @ the_Pr7776125533777466484it_nat @ some_P1914260805536162275it_nat )
% 0.33/0.61 = id_Pro1159712480615372887it_nat ) ).
% 0.33/0.61
% 0.33/0.61 % comp_the_Some
% 0.33/0.61 thf(fact_5175_fun_Omap__id0,axiom,
% 0.33/0.61 ( ( comp_o_o_nat @ id_o )
% 0.33/0.61 = id_nat_o ) ).
% 0.33/0.61
% 0.33/0.61 % fun.map_id0
% 0.33/0.61 thf(fact_5176_fun_Omap__id0,axiom,
% 0.33/0.61 ( ( comp_C3531382070062128313er_num @ id_Code_integer )
% 0.33/0.61 = id_num_Code_integer ) ).
% 0.33/0.61
% 0.33/0.61 % fun.map_id0
% 0.33/0.61 thf(fact_5177_Iio__eq__empty__iff,axiom,
% 0.33/0.61 ! [N2: $o] :
% 0.33/0.61 ( ( ( set_ord_lessThan_o @ N2 )
% 0.33/0.61 = bot_bot_set_o )
% 0.33/0.61 = ( N2 = bot_bot_o ) ) ).
% 0.33/0.61
% 0.33/0.61 % Iio_eq_empty_iff
% 0.33/0.61 thf(fact_5178_Iio__eq__empty__iff,axiom,
% 0.33/0.61 ! [N2: nat] :
% 0.33/0.61 ( ( ( set_ord_lessThan_nat @ N2 )
% 0.33/0.61 = bot_bot_set_nat )
% 0.33/0.61 = ( N2 = bot_bot_nat ) ) ).
% 0.33/0.61
% 0.33/0.61 % Iio_eq_empty_iff
% 0.33/0.61 thf(fact_5179_option_Omap__id0,axiom,
% 0.33/0.61 ( ( map_option_o_o @ id_o )
% 0.33/0.61 = id_option_o ) ).
% 0.33/0.61
% 0.33/0.61 % option.map_id0
% 0.33/0.61 thf(fact_5180_option_Omap__id0,axiom,
% 0.33/0.61 ( ( map_option_nat_nat @ id_nat )
% 0.33/0.61 = id_option_nat ) ).
% 0.33/0.61
% 0.33/0.61 % option.map_id0
% 0.33/0.61 thf(fact_5181_option_Omap__id0,axiom,
% 0.33/0.61 ( ( map_op6424164270877473355_nat_o @ id_nat_o )
% 0.33/0.61 = id_option_nat_o ) ).
% 0.33/0.61
% 0.33/0.61 % option.map_id0
% 0.33/0.61 thf(fact_5182_option_Omap__id0,axiom,
% 0.33/0.61 ( ( map_option_int_int @ id_int )
% 0.33/0.61 = id_option_int ) ).
% 0.33/0.61
% 0.33/0.61 % option.map_id0
% 0.33/0.61 thf(fact_5183_option_Omap__id0,axiom,
% 0.33/0.61 ( ( map_option_num_num @ id_num )
% 0.33/0.61 = id_option_num ) ).
% 0.33/0.61
% 0.33/0.61 % option.map_id0
% 0.33/0.61 thf(fact_5184_set__notEmptyE,axiom,
% 0.33/0.61 ! [S2: set_Pr4329608150637261639at_nat] :
% 0.33/0.61 ( ( S2 != bot_bo228742789529271731at_nat )
% 0.33/0.61 => ~ ! [X4: produc3843707927480180839at_nat] :
% 0.33/0.61 ~ ( member8757157785044589968at_nat @ X4 @ S2 ) ) ).
% 0.33/0.61
% 0.33/0.61 % set_notEmptyE
% 0.33/0.61 thf(fact_5185_set__notEmptyE,axiom,
% 0.33/0.61 ! [S2: set_Pr1261947904930325089at_nat] :
% 0.33/0.61 ( ( S2 != bot_bo2099793752762293965at_nat )
% 0.33/0.61 => ~ ! [X4: product_prod_nat_nat] :
% 0.33/0.61 ~ ( member8440522571783428010at_nat @ X4 @ S2 ) ) ).
% 0.33/0.61
% 0.33/0.61 % set_notEmptyE
% 0.33/0.61 thf(fact_5186_set__notEmptyE,axiom,
% 0.33/0.61 ! [S2: set_o] :
% 0.33/0.61 ( ( S2 != bot_bot_set_o )
% 0.33/0.61 => ~ ! [X4: $o] :
% 0.33/0.61 ~ ( member_o @ X4 @ S2 ) ) ).
% 0.33/0.61
% 0.33/0.61 % set_notEmptyE
% 0.33/0.61 thf(fact_5187_set__notEmptyE,axiom,
% 0.33/0.61 ! [S2: set_nat] :
% 0.33/0.61 ( ( S2 != bot_bot_set_nat )
% 0.33/0.61 => ~ ! [X4: nat] :
% 0.33/0.61 ~ ( member_nat @ X4 @ S2 ) ) ).
% 0.33/0.61
% 0.33/0.61 % set_notEmptyE
% 0.33/0.61 thf(fact_5188_set__notEmptyE,axiom,
% 0.33/0.61 ! [S2: set_int] :
% 0.33/0.61 ( ( S2 != bot_bot_set_int )
% 0.33/0.61 => ~ ! [X4: int] :
% 0.33/0.61 ~ ( member_int @ X4 @ S2 ) ) ).
% 0.33/0.61
% 0.33/0.61 % set_notEmptyE
% 0.33/0.61 thf(fact_5189_memb__imp__not__empty,axiom,
% 0.33/0.61 ! [X: produc3843707927480180839at_nat,S2: set_Pr4329608150637261639at_nat] :
% 0.33/0.61 ( ( member8757157785044589968at_nat @ X @ S2 )
% 0.33/0.61 => ( S2 != bot_bo228742789529271731at_nat ) ) ).
% 0.33/0.61
% 0.33/0.61 % memb_imp_not_empty
% 0.33/0.61 thf(fact_5190_memb__imp__not__empty,axiom,
% 0.33/0.61 ! [X: product_prod_nat_nat,S2: set_Pr1261947904930325089at_nat] :
% 0.33/0.61 ( ( member8440522571783428010at_nat @ X @ S2 )
% 0.33/0.61 => ( S2 != bot_bo2099793752762293965at_nat ) ) ).
% 0.33/0.61
% 0.33/0.61 % memb_imp_not_empty
% 0.33/0.61 thf(fact_5191_memb__imp__not__empty,axiom,
% 0.33/0.61 ! [X: $o,S2: set_o] :
% 0.33/0.61 ( ( member_o @ X @ S2 )
% 0.33/0.61 => ( S2 != bot_bot_set_o ) ) ).
% 0.33/0.61
% 0.33/0.61 % memb_imp_not_empty
% 0.33/0.61 thf(fact_5192_memb__imp__not__empty,axiom,
% 0.33/0.61 ! [X: nat,S2: set_nat] :
% 0.33/0.61 ( ( member_nat @ X @ S2 )
% 0.33/0.61 => ( S2 != bot_bot_set_nat ) ) ).
% 0.33/0.61
% 0.33/0.61 % memb_imp_not_empty
% 0.33/0.61 thf(fact_5193_memb__imp__not__empty,axiom,
% 0.33/0.61 ! [X: int,S2: set_int] :
% 0.33/0.61 ( ( member_int @ X @ S2 )
% 0.33/0.61 => ( S2 != bot_bot_set_int ) ) ).
% 0.33/0.61
% 0.33/0.61 % memb_imp_not_empty
% 0.33/0.61 thf(fact_5194_id__def,axiom,
% 0.33/0.61 ( id_o
% 0.33/0.61 = ( ^ [X3: $o] : X3 ) ) ).
% 0.33/0.61
% 0.33/0.61 % id_def
% 0.33/0.61 thf(fact_5195_id__def,axiom,
% 0.33/0.61 ( id_nat
% 0.33/0.61 = ( ^ [X3: nat] : X3 ) ) ).
% 0.33/0.61
% 0.33/0.61 % id_def
% 0.33/0.61 thf(fact_5196_id__def,axiom,
% 0.33/0.61 ( id_nat_o
% 0.33/0.61 = ( ^ [X3: nat > $o] : X3 ) ) ).
% 0.33/0.61
% 0.33/0.61 % id_def
% 0.33/0.61 thf(fact_5197_id__def,axiom,
% 0.33/0.61 ( id_num
% 0.33/0.61 = ( ^ [X3: num] : X3 ) ) ).
% 0.33/0.61
% 0.33/0.61 % id_def
% 0.33/0.61 thf(fact_5198_id__def,axiom,
% 0.33/0.61 ( id_int
% 0.33/0.61 = ( ^ [X3: int] : X3 ) ) ).
% 0.33/0.61
% 0.33/0.61 % id_def
% 0.33/0.61 thf(fact_5199_eq__id__iff,axiom,
% 0.33/0.61 ! [F: $o > $o] :
% 0.33/0.61 ( ( ! [X3: $o] :
% 0.33/0.61 ( ( F @ X3 )
% 0.33/0.61 = X3 ) )
% 0.33/0.61 = ( F = id_o ) ) ).
% 0.33/0.61
% 0.33/0.61 % eq_id_iff
% 0.33/0.61 thf(fact_5200_eq__id__iff,axiom,
% 0.33/0.61 ! [F: nat > nat] :
% 0.33/0.61 ( ( ! [X3: nat] :
% 0.33/0.61 ( ( F @ X3 )
% 0.33/0.61 = X3 ) )
% 0.33/0.61 = ( F = id_nat ) ) ).
% 0.33/0.61
% 0.33/0.61 % eq_id_iff
% 0.33/0.61 thf(fact_5201_eq__id__iff,axiom,
% 0.33/0.61 ! [F: ( nat > $o ) > nat > $o] :
% 0.33/0.61 ( ( ! [X3: nat > $o] :
% 0.33/0.61 ( ( F @ X3 )
% 0.33/0.61 = X3 ) )
% 0.33/0.61 = ( F = id_nat_o ) ) ).
% 0.33/0.61
% 0.33/0.61 % eq_id_iff
% 0.33/0.61 thf(fact_5202_eq__id__iff,axiom,
% 0.33/0.61 ! [F: num > num] :
% 0.33/0.61 ( ( ! [X3: num] :
% 0.33/0.61 ( ( F @ X3 )
% 0.33/0.61 = X3 ) )
% 0.33/0.61 = ( F = id_num ) ) ).
% 0.33/0.61
% 0.33/0.61 % eq_id_iff
% 0.33/0.61 thf(fact_5203_eq__id__iff,axiom,
% 0.33/0.61 ! [F: int > int] :
% 0.33/0.61 ( ( ! [X3: int] :
% 0.33/0.61 ( ( F @ X3 )
% 0.33/0.61 = X3 ) )
% 0.33/0.61 = ( F = id_int ) ) ).
% 0.33/0.61
% 0.33/0.61 % eq_id_iff
% 0.33/0.61 thf(fact_5204_comp__eq__id__dest,axiom,
% 0.33/0.61 ! [A: code_integer > code_integer,B: num > code_integer,C: num > code_integer,V: num] :
% 0.33/0.61 ( ( ( comp_C3531382070062128313er_num @ A @ B )
% 0.33/0.61 = ( comp_C3531382070062128313er_num @ id_Code_integer @ C ) )
% 0.33/0.61 => ( ( A @ ( B @ V ) )
% 0.33/0.61 = ( C @ V ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % comp_eq_id_dest
% 0.33/0.61 thf(fact_5205_comp__eq__id__dest,axiom,
% 0.33/0.61 ! [A: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,B: code_integer > code_integer,C: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,V: code_integer] :
% 0.33/0.61 ( ( ( comp_C1593894019821074884nteger @ A @ B )
% 0.33/0.61 = ( comp_P3928908779438215820nteger @ id_Pro496765588584934260nteger @ C ) )
% 0.33/0.61 => ( ( A @ ( B @ V ) )
% 0.33/0.61 = ( C @ V ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % comp_eq_id_dest
% 0.33/0.61 thf(fact_5206_comp__eq__id__dest,axiom,
% 0.33/0.61 ! [A: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,B: code_integer > code_integer > code_integer,C: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,V: code_integer] :
% 0.33/0.61 ( ( ( comp_C8797469213163452608nteger @ A @ B )
% 0.33/0.61 = ( comp_P3928908779438215820nteger @ id_Pro496765588584934260nteger @ C ) )
% 0.33/0.61 => ( ( A @ ( B @ V ) )
% 0.33/0.61 = ( C @ V ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % comp_eq_id_dest
% 0.33/0.61 thf(fact_5207_comp__eq__id__dest,axiom,
% 0.33/0.61 ! [A: nat > num,B: int > nat,C: int > num,V: int] :
% 0.33/0.61 ( ( ( comp_nat_num_int @ A @ B )
% 0.33/0.61 = ( comp_num_num_int @ id_num @ C ) )
% 0.33/0.61 => ( ( A @ ( B @ V ) )
% 0.33/0.61 = ( C @ V ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % comp_eq_id_dest
% 0.33/0.61 thf(fact_5208_option_Omap__id,axiom,
% 0.33/0.61 ! [T: option_o] :
% 0.33/0.61 ( ( map_option_o_o @ id_o @ T )
% 0.33/0.61 = T ) ).
% 0.33/0.61
% 0.33/0.61 % option.map_id
% 0.33/0.61 thf(fact_5209_option_Omap__id,axiom,
% 0.33/0.61 ! [T: option_nat] :
% 0.33/0.61 ( ( map_option_nat_nat @ id_nat @ T )
% 0.33/0.61 = T ) ).
% 0.33/0.61
% 0.33/0.61 % option.map_id
% 0.33/0.61 thf(fact_5210_option_Omap__id,axiom,
% 0.33/0.61 ! [T: option_nat_o] :
% 0.33/0.61 ( ( map_op6424164270877473355_nat_o @ id_nat_o @ T )
% 0.33/0.61 = T ) ).
% 0.33/0.61
% 0.33/0.61 % option.map_id
% 0.33/0.61 thf(fact_5211_option_Omap__id,axiom,
% 0.33/0.61 ! [T: option_int] :
% 0.33/0.61 ( ( map_option_int_int @ id_int @ T )
% 0.33/0.61 = T ) ).
% 0.33/0.61
% 0.33/0.61 % option.map_id
% 0.33/0.61 thf(fact_5212_option_Omap__id,axiom,
% 0.33/0.61 ! [T: option_num] :
% 0.33/0.61 ( ( map_option_num_num @ id_num @ T )
% 0.33/0.61 = T ) ).
% 0.33/0.61
% 0.33/0.61 % option.map_id
% 0.33/0.61 thf(fact_5213_not__empty__eq__Iic__eq__empty,axiom,
% 0.33/0.61 ! [H3: $o] :
% 0.33/0.61 ( bot_bot_set_o
% 0.33/0.61 != ( set_ord_atMost_o @ H3 ) ) ).
% 0.33/0.61
% 0.33/0.61 % not_empty_eq_Iic_eq_empty
% 0.33/0.61 thf(fact_5214_not__empty__eq__Iic__eq__empty,axiom,
% 0.33/0.61 ! [H3: int] :
% 0.33/0.61 ( bot_bot_set_int
% 0.33/0.61 != ( set_ord_atMost_int @ H3 ) ) ).
% 0.33/0.61
% 0.33/0.61 % not_empty_eq_Iic_eq_empty
% 0.33/0.61 thf(fact_5215_not__empty__eq__Iic__eq__empty,axiom,
% 0.33/0.61 ! [H3: nat] :
% 0.33/0.61 ( bot_bot_set_nat
% 0.33/0.61 != ( set_ord_atMost_nat @ H3 ) ) ).
% 0.33/0.61
% 0.33/0.61 % not_empty_eq_Iic_eq_empty
% 0.33/0.61 thf(fact_5216_lessThan__non__empty,axiom,
% 0.33/0.61 ! [X: int] :
% 0.33/0.61 ( ( set_ord_lessThan_int @ X )
% 0.33/0.61 != bot_bot_set_int ) ).
% 0.33/0.61
% 0.33/0.61 % lessThan_non_empty
% 0.33/0.61 thf(fact_5217_subset__minus__empty,axiom,
% 0.33/0.61 ! [A2: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat] :
% 0.33/0.61 ( ( ord_le1268244103169919719at_nat @ A2 @ B5 )
% 0.33/0.61 => ( ( minus_3314409938677909166at_nat @ A2 @ B5 )
% 0.33/0.61 = bot_bo228742789529271731at_nat ) ) ).
% 0.33/0.61
% 0.33/0.61 % subset_minus_empty
% 0.33/0.61 thf(fact_5218_subset__minus__empty,axiom,
% 0.33/0.61 ! [A2: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 0.33/0.61 ( ( ord_le3146513528884898305at_nat @ A2 @ B5 )
% 0.33/0.61 => ( ( minus_1356011639430497352at_nat @ A2 @ B5 )
% 0.33/0.61 = bot_bo2099793752762293965at_nat ) ) ).
% 0.33/0.61
% 0.33/0.61 % subset_minus_empty
% 0.33/0.61 thf(fact_5219_subset__minus__empty,axiom,
% 0.33/0.61 ! [A2: set_o,B5: set_o] :
% 0.33/0.61 ( ( ord_less_eq_set_o @ A2 @ B5 )
% 0.33/0.61 => ( ( minus_minus_set_o @ A2 @ B5 )
% 0.33/0.61 = bot_bot_set_o ) ) ).
% 0.33/0.61
% 0.33/0.61 % subset_minus_empty
% 0.33/0.61 thf(fact_5220_subset__minus__empty,axiom,
% 0.33/0.61 ! [A2: set_int,B5: set_int] :
% 0.33/0.61 ( ( ord_less_eq_set_int @ A2 @ B5 )
% 0.33/0.61 => ( ( minus_minus_set_int @ A2 @ B5 )
% 0.33/0.61 = bot_bot_set_int ) ) ).
% 0.33/0.61
% 0.33/0.61 % subset_minus_empty
% 0.33/0.61 thf(fact_5221_subset__minus__empty,axiom,
% 0.33/0.61 ! [A2: set_nat,B5: set_nat] :
% 0.33/0.61 ( ( ord_less_eq_set_nat @ A2 @ B5 )
% 0.33/0.61 => ( ( minus_minus_set_nat @ A2 @ B5 )
% 0.33/0.61 = bot_bot_set_nat ) ) ).
% 0.33/0.61
% 0.33/0.61 % subset_minus_empty
% 0.33/0.61 thf(fact_5222_atLeastLessThan0,axiom,
% 0.33/0.61 ! [M2: nat] :
% 0.33/0.61 ( ( set_or4665077453230672383an_nat @ M2 @ zero_zero_nat )
% 0.33/0.61 = bot_bot_set_nat ) ).
% 0.33/0.61
% 0.33/0.61 % atLeastLessThan0
% 0.33/0.61 thf(fact_5223_lessThan__empty__iff,axiom,
% 0.33/0.61 ! [N2: nat] :
% 0.33/0.61 ( ( ( set_ord_lessThan_nat @ N2 )
% 0.33/0.61 = bot_bot_set_nat )
% 0.33/0.61 = ( N2 = zero_zero_nat ) ) ).
% 0.33/0.61
% 0.33/0.61 % lessThan_empty_iff
% 0.33/0.61 thf(fact_5224_set__to__map__empty__iff_I1_J,axiom,
% 0.33/0.61 ! [S2: set_Pr4329608150637261639at_nat] :
% 0.33/0.61 ( ( ( set_to4447731662395764663at_nat @ S2 )
% 0.33/0.61 = ( ^ [X3: set_Pr1261947904930325089at_nat] : none_s625347054029921090at_nat ) )
% 0.33/0.61 = ( S2 = bot_bo228742789529271731at_nat ) ) ).
% 0.33/0.61
% 0.33/0.61 % set_to_map_empty_iff(1)
% 0.33/0.61 thf(fact_5225_set__to__map__empty__iff_I1_J,axiom,
% 0.33/0.61 ! [S2: set_Pr1261947904930325089at_nat] :
% 0.33/0.61 ( ( ( set_to_map_nat_nat @ S2 )
% 0.33/0.61 = ( ^ [X3: nat] : none_nat ) )
% 0.33/0.61 = ( S2 = bot_bo2099793752762293965at_nat ) ) ).
% 0.33/0.61
% 0.33/0.61 % set_to_map_empty_iff(1)
% 0.33/0.61 thf(fact_5226_Code__Numeral_Osub__code_I1_J,axiom,
% 0.33/0.61 ( ( code_sub @ one @ one )
% 0.33/0.61 = zero_z3403309356797280102nteger ) ).
% 0.33/0.61
% 0.33/0.61 % Code_Numeral.sub_code(1)
% 0.33/0.61 thf(fact_5227_set__to__map__empty__iff_I2_J,axiom,
% 0.33/0.61 ! [S2: set_Pr4329608150637261639at_nat] :
% 0.33/0.61 ( ( ( ^ [X3: set_Pr1261947904930325089at_nat] : none_s625347054029921090at_nat )
% 0.33/0.61 = ( set_to4447731662395764663at_nat @ S2 ) )
% 0.33/0.61 = ( S2 = bot_bo228742789529271731at_nat ) ) ).
% 0.33/0.61
% 0.33/0.61 % set_to_map_empty_iff(2)
% 0.33/0.61 thf(fact_5228_set__to__map__empty__iff_I2_J,axiom,
% 0.33/0.61 ! [S2: set_Pr1261947904930325089at_nat] :
% 0.33/0.61 ( ( ( ^ [X3: nat] : none_nat )
% 0.33/0.61 = ( set_to_map_nat_nat @ S2 ) )
% 0.33/0.61 = ( S2 = bot_bo2099793752762293965at_nat ) ) ).
% 0.33/0.61
% 0.33/0.61 % set_to_map_empty_iff(2)
% 0.33/0.61 thf(fact_5229_less__integer__def,axiom,
% 0.33/0.61 ( ord_le6747313008572928689nteger
% 0.33/0.61 = ( map_fu2496120808607739376eger_o @ code_int_of_integer @ ( map_fu6957801986076833569nt_o_o @ code_int_of_integer @ id_o ) @ ord_less_int ) ) ).
% 0.33/0.61
% 0.33/0.61 % less_integer_def
% 0.33/0.61 thf(fact_5230_less__eq__integer__def,axiom,
% 0.33/0.61 ( ord_le3102999989581377725nteger
% 0.33/0.61 = ( map_fu2496120808607739376eger_o @ code_int_of_integer @ ( map_fu6957801986076833569nt_o_o @ code_int_of_integer @ id_o ) @ ord_less_eq_int ) ) ).
% 0.33/0.61
% 0.33/0.61 % less_eq_integer_def
% 0.33/0.61 thf(fact_5231_Code__Numeral_Osub__code_I6_J,axiom,
% 0.33/0.61 ! [M2: num,N2: num] :
% 0.33/0.61 ( ( code_sub @ ( bit0 @ M2 ) @ ( bit0 @ N2 ) )
% 0.33/0.61 = ( code_dup @ ( code_sub @ M2 @ N2 ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % Code_Numeral.sub_code(6)
% 0.33/0.61 thf(fact_5232_Code__Numeral_Osub__code_I7_J,axiom,
% 0.33/0.61 ! [M2: num,N2: num] :
% 0.33/0.61 ( ( code_sub @ ( bit1 @ M2 ) @ ( bit1 @ N2 ) )
% 0.33/0.61 = ( code_dup @ ( code_sub @ M2 @ N2 ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % Code_Numeral.sub_code(7)
% 0.33/0.61 thf(fact_5233_sub_Orep__eq,axiom,
% 0.33/0.61 ! [X: num,Xa: num] :
% 0.33/0.61 ( ( code_int_of_integer @ ( code_sub @ X @ Xa ) )
% 0.33/0.61 = ( minus_minus_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Xa ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % sub.rep_eq
% 0.33/0.61 thf(fact_5234_sub_Oabs__eq,axiom,
% 0.33/0.61 ( code_sub
% 0.33/0.61 = ( ^ [Xa4: num,X3: num] : ( code_integer_of_int @ ( minus_minus_int @ ( numeral_numeral_int @ Xa4 ) @ ( numeral_numeral_int @ X3 ) ) ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % sub.abs_eq
% 0.33/0.61 thf(fact_5235_image__mult__atLeastAtMost__if,axiom,
% 0.33/0.61 ! [C: rat,X: rat,Y: rat] :
% 0.33/0.61 ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.33/0.61 => ( ( image_rat_rat @ ( times_times_rat @ C ) @ ( set_or633870826150836451st_rat @ X @ Y ) )
% 0.33/0.61 = ( set_or633870826150836451st_rat @ ( times_times_rat @ C @ X ) @ ( times_times_rat @ C @ Y ) ) ) )
% 0.33/0.61 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.33/0.61 => ( ( ( ord_less_eq_rat @ X @ Y )
% 0.33/0.61 => ( ( image_rat_rat @ ( times_times_rat @ C ) @ ( set_or633870826150836451st_rat @ X @ Y ) )
% 0.33/0.61 = ( set_or633870826150836451st_rat @ ( times_times_rat @ C @ Y ) @ ( times_times_rat @ C @ X ) ) ) )
% 0.33/0.61 & ( ~ ( ord_less_eq_rat @ X @ Y )
% 0.33/0.61 => ( ( image_rat_rat @ ( times_times_rat @ C ) @ ( set_or633870826150836451st_rat @ X @ Y ) )
% 0.33/0.61 = bot_bot_set_rat ) ) ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % image_mult_atLeastAtMost_if
% 0.33/0.61 thf(fact_5236_image__mult__atLeastAtMost__if_H,axiom,
% 0.33/0.61 ! [X: rat,Y: rat,C: rat] :
% 0.33/0.61 ( ( ( ord_less_eq_rat @ X @ Y )
% 0.33/0.61 => ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.33/0.61 => ( ( image_rat_rat
% 0.33/0.61 @ ^ [X3: rat] : ( times_times_rat @ X3 @ C )
% 0.33/0.61 @ ( set_or633870826150836451st_rat @ X @ Y ) )
% 0.33/0.61 = ( set_or633870826150836451st_rat @ ( times_times_rat @ X @ C ) @ ( times_times_rat @ Y @ C ) ) ) )
% 0.33/0.61 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.33/0.61 => ( ( image_rat_rat
% 0.33/0.61 @ ^ [X3: rat] : ( times_times_rat @ X3 @ C )
% 0.33/0.61 @ ( set_or633870826150836451st_rat @ X @ Y ) )
% 0.33/0.61 = ( set_or633870826150836451st_rat @ ( times_times_rat @ Y @ C ) @ ( times_times_rat @ X @ C ) ) ) ) ) )
% 0.33/0.61 & ( ~ ( ord_less_eq_rat @ X @ Y )
% 0.33/0.61 => ( ( image_rat_rat
% 0.33/0.61 @ ^ [X3: rat] : ( times_times_rat @ X3 @ C )
% 0.33/0.61 @ ( set_or633870826150836451st_rat @ X @ Y ) )
% 0.33/0.61 = bot_bot_set_rat ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % image_mult_atLeastAtMost_if'
% 0.33/0.61 thf(fact_5237_image__affinity__atLeastAtMost,axiom,
% 0.33/0.61 ! [A: rat,B: rat,M2: rat,C: rat] :
% 0.33/0.61 ( ( ( ( set_or633870826150836451st_rat @ A @ B )
% 0.33/0.61 = bot_bot_set_rat )
% 0.33/0.61 => ( ( image_rat_rat
% 0.33/0.61 @ ^ [X3: rat] : ( plus_plus_rat @ ( times_times_rat @ M2 @ X3 ) @ C )
% 0.33/0.61 @ ( set_or633870826150836451st_rat @ A @ B ) )
% 0.33/0.61 = bot_bot_set_rat ) )
% 0.33/0.61 & ( ( ( set_or633870826150836451st_rat @ A @ B )
% 0.33/0.61 != bot_bot_set_rat )
% 0.33/0.61 => ( ( ( ord_less_eq_rat @ zero_zero_rat @ M2 )
% 0.33/0.61 => ( ( image_rat_rat
% 0.33/0.61 @ ^ [X3: rat] : ( plus_plus_rat @ ( times_times_rat @ M2 @ X3 ) @ C )
% 0.33/0.61 @ ( set_or633870826150836451st_rat @ A @ B ) )
% 0.33/0.61 = ( set_or633870826150836451st_rat @ ( plus_plus_rat @ ( times_times_rat @ M2 @ A ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ M2 @ B ) @ C ) ) ) )
% 0.33/0.61 & ( ~ ( ord_less_eq_rat @ zero_zero_rat @ M2 )
% 0.33/0.61 => ( ( image_rat_rat
% 0.33/0.61 @ ^ [X3: rat] : ( plus_plus_rat @ ( times_times_rat @ M2 @ X3 ) @ C )
% 0.33/0.61 @ ( set_or633870826150836451st_rat @ A @ B ) )
% 0.33/0.61 = ( set_or633870826150836451st_rat @ ( plus_plus_rat @ ( times_times_rat @ M2 @ B ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ M2 @ A ) @ C ) ) ) ) ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % image_affinity_atLeastAtMost
% 0.33/0.61 thf(fact_5238_and__int_Osimps,axiom,
% 0.33/0.61 ( bit_se725231765392027082nd_int
% 0.33/0.61 = ( ^ [K4: int,L3: int] :
% 0.33/0.61 ( if_int
% 0.33/0.61 @ ( ( member_int @ K4 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 0.33/0.61 & ( member_int @ L3 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 0.33/0.61 @ ( uminus_uminus_int
% 0.33/0.61 @ ( zero_n2684676970156552555ol_int
% 0.33/0.61 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K4 )
% 0.33/0.61 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L3 ) ) ) )
% 0.33/0.61 @ ( plus_plus_int
% 0.33/0.61 @ ( zero_n2684676970156552555ol_int
% 0.33/0.61 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K4 )
% 0.33/0.61 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L3 ) ) )
% 0.33/0.61 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % and_int.simps
% 0.33/0.61 thf(fact_5239_and__int_Oelims,axiom,
% 0.33/0.61 ! [X: int,Xa: int,Y: int] :
% 0.33/0.61 ( ( ( bit_se725231765392027082nd_int @ X @ Xa )
% 0.33/0.61 = Y )
% 0.33/0.61 => ( ( ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 0.33/0.61 & ( member_int @ Xa @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 0.33/0.61 => ( Y
% 0.33/0.61 = ( uminus_uminus_int
% 0.33/0.61 @ ( zero_n2684676970156552555ol_int
% 0.33/0.61 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 0.33/0.61 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa ) ) ) ) ) )
% 0.33/0.61 & ( ~ ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 0.33/0.61 & ( member_int @ Xa @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 0.33/0.61 => ( Y
% 0.33/0.61 = ( plus_plus_int
% 0.33/0.61 @ ( zero_n2684676970156552555ol_int
% 0.33/0.61 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 0.33/0.61 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa ) ) )
% 0.33/0.61 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ X @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ Xa @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % and_int.elims
% 0.33/0.61 thf(fact_5240_and__int_Opelims,axiom,
% 0.33/0.61 ! [X: int,Xa: int,Y: int] :
% 0.33/0.61 ( ( ( bit_se725231765392027082nd_int @ X @ Xa )
% 0.33/0.61 = Y )
% 0.33/0.61 => ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X @ Xa ) )
% 0.33/0.61 => ~ ( ( ( ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 0.33/0.61 & ( member_int @ Xa @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 0.33/0.61 => ( Y
% 0.33/0.61 = ( uminus_uminus_int
% 0.33/0.61 @ ( zero_n2684676970156552555ol_int
% 0.33/0.61 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 0.33/0.61 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa ) ) ) ) ) )
% 0.33/0.61 & ( ~ ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 0.33/0.61 & ( member_int @ Xa @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 0.33/0.61 => ( Y
% 0.33/0.61 = ( plus_plus_int
% 0.33/0.61 @ ( zero_n2684676970156552555ol_int
% 0.33/0.61 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 0.33/0.61 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa ) ) )
% 0.33/0.61 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ X @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ Xa @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 0.33/0.61 => ~ ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X @ Xa ) ) ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % and_int.pelims
% 0.33/0.61 thf(fact_5241_and__int_Opsimps,axiom,
% 0.33/0.61 ! [K: int,L: int] :
% 0.33/0.61 ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ K @ L ) )
% 0.33/0.61 => ( ( ( ( member_int @ K @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 0.33/0.61 & ( member_int @ L @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 0.33/0.61 => ( ( bit_se725231765392027082nd_int @ K @ L )
% 0.33/0.61 = ( uminus_uminus_int
% 0.33/0.61 @ ( zero_n2684676970156552555ol_int
% 0.33/0.61 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 0.33/0.61 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) ) ) ) )
% 0.33/0.61 & ( ~ ( ( member_int @ K @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 0.33/0.61 & ( member_int @ L @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 0.33/0.61 => ( ( bit_se725231765392027082nd_int @ K @ L )
% 0.33/0.61 = ( plus_plus_int
% 0.33/0.61 @ ( zero_n2684676970156552555ol_int
% 0.33/0.61 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 0.33/0.61 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) )
% 0.33/0.61 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % and_int.psimps
% 0.33/0.61 thf(fact_5242_and__int_Opinduct,axiom,
% 0.33/0.61 ! [A0: int,A1: int,P: int > int > $o] :
% 0.33/0.61 ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ A0 @ A1 ) )
% 0.33/0.61 => ( ! [K5: int,L5: int] :
% 0.33/0.61 ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ K5 @ L5 ) )
% 0.33/0.61 => ( ( ~ ( ( member_int @ K5 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 0.33/0.61 & ( member_int @ L5 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 0.33/0.61 => ( P @ ( divide_divide_int @ K5 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L5 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 0.33/0.61 => ( P @ K5 @ L5 ) ) )
% 0.33/0.61 => ( P @ A0 @ A1 ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % and_int.pinduct
% 0.33/0.61 thf(fact_5243_mask__mod__exp,axiom,
% 0.33/0.61 ! [N2: nat,M2: nat] :
% 0.33/0.61 ( ( modulo_modulo_int @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ one_one_int ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 ) )
% 0.33/0.61 = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( ord_min_nat @ M2 @ N2 ) ) @ one_one_int ) ) ).
% 0.33/0.61
% 0.33/0.61 % mask_mod_exp
% 0.33/0.61 thf(fact_5244_mask__mod__exp,axiom,
% 0.33/0.61 ! [N2: nat,M2: nat] :
% 0.33/0.61 ( ( modulo_modulo_nat @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 0.33/0.61 = ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( ord_min_nat @ M2 @ N2 ) ) @ one_one_nat ) ) ).
% 0.33/0.61
% 0.33/0.61 % mask_mod_exp
% 0.33/0.61 thf(fact_5245_mask__mod__exp,axiom,
% 0.33/0.61 ! [N2: nat,M2: nat] :
% 0.33/0.61 ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) @ one_one_Code_integer ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M2 ) )
% 0.33/0.61 = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( ord_min_nat @ M2 @ N2 ) ) @ one_one_Code_integer ) ) ).
% 0.33/0.61
% 0.33/0.61 % mask_mod_exp
% 0.33/0.61 thf(fact_5246_mask__mod__exp,axiom,
% 0.33/0.61 ! [N2: nat,M2: nat] :
% 0.33/0.61 ( ( modulo8411746178871703098atural @ ( minus_7197305767214868737atural @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N2 ) @ one_one_Code_natural ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ M2 ) )
% 0.33/0.61 = ( minus_7197305767214868737atural @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( ord_min_nat @ M2 @ N2 ) ) @ one_one_Code_natural ) ) ).
% 0.33/0.61
% 0.33/0.61 % mask_mod_exp
% 0.33/0.61 thf(fact_5247_pair__leqI2,axiom,
% 0.33/0.61 ! [A: nat,B: nat,S: nat,T: nat] :
% 0.33/0.61 ( ( ord_less_eq_nat @ A @ B )
% 0.33/0.61 => ( ( ord_less_eq_nat @ S @ T )
% 0.33/0.61 => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A @ S ) @ ( product_Pair_nat_nat @ B @ T ) ) @ fun_pair_leq ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % pair_leqI2
% 0.33/0.61 thf(fact_5248_min__eq__arg_I1_J,axiom,
% 0.33/0.61 ! [M2: code_integer,N2: code_integer] :
% 0.33/0.61 ( ( ( ord_min_Code_integer @ M2 @ N2 )
% 0.33/0.61 = M2 )
% 0.33/0.61 = ( ord_le3102999989581377725nteger @ M2 @ N2 ) ) ).
% 0.33/0.61
% 0.33/0.61 % min_eq_arg(1)
% 0.33/0.61 thf(fact_5249_min__eq__arg_I1_J,axiom,
% 0.33/0.61 ! [M2: code_natural,N2: code_natural] :
% 0.33/0.61 ( ( ( ord_min_Code_natural @ M2 @ N2 )
% 0.33/0.61 = M2 )
% 0.33/0.61 = ( ord_le1926595141338095240atural @ M2 @ N2 ) ) ).
% 0.33/0.61
% 0.33/0.61 % min_eq_arg(1)
% 0.33/0.61 thf(fact_5250_min__eq__arg_I1_J,axiom,
% 0.33/0.61 ! [M2: rat,N2: rat] :
% 0.33/0.61 ( ( ( ord_min_rat @ M2 @ N2 )
% 0.33/0.61 = M2 )
% 0.33/0.61 = ( ord_less_eq_rat @ M2 @ N2 ) ) ).
% 0.33/0.61
% 0.33/0.61 % min_eq_arg(1)
% 0.33/0.61 thf(fact_5251_min__eq__arg_I1_J,axiom,
% 0.33/0.61 ! [M2: num,N2: num] :
% 0.33/0.61 ( ( ( ord_min_num @ M2 @ N2 )
% 0.33/0.61 = M2 )
% 0.33/0.61 = ( ord_less_eq_num @ M2 @ N2 ) ) ).
% 0.33/0.61
% 0.33/0.61 % min_eq_arg(1)
% 0.33/0.61 thf(fact_5252_min__eq__arg_I1_J,axiom,
% 0.33/0.61 ! [M2: nat,N2: nat] :
% 0.33/0.61 ( ( ( ord_min_nat @ M2 @ N2 )
% 0.33/0.61 = M2 )
% 0.33/0.61 = ( ord_less_eq_nat @ M2 @ N2 ) ) ).
% 0.33/0.61
% 0.33/0.61 % min_eq_arg(1)
% 0.33/0.61 thf(fact_5253_min__eq__arg_I1_J,axiom,
% 0.33/0.61 ! [M2: int,N2: int] :
% 0.33/0.61 ( ( ( ord_min_int @ M2 @ N2 )
% 0.33/0.61 = M2 )
% 0.33/0.61 = ( ord_less_eq_int @ M2 @ N2 ) ) ).
% 0.33/0.61
% 0.33/0.61 % min_eq_arg(1)
% 0.33/0.61 thf(fact_5254_min__eq__arg_I2_J,axiom,
% 0.33/0.61 ! [M2: code_integer,N2: code_integer] :
% 0.33/0.61 ( ( ( ord_min_Code_integer @ M2 @ N2 )
% 0.33/0.61 = N2 )
% 0.33/0.61 = ( ord_le3102999989581377725nteger @ N2 @ M2 ) ) ).
% 0.33/0.61
% 0.33/0.61 % min_eq_arg(2)
% 0.33/0.61 thf(fact_5255_min__eq__arg_I2_J,axiom,
% 0.33/0.61 ! [M2: code_natural,N2: code_natural] :
% 0.33/0.61 ( ( ( ord_min_Code_natural @ M2 @ N2 )
% 0.33/0.61 = N2 )
% 0.33/0.61 = ( ord_le1926595141338095240atural @ N2 @ M2 ) ) ).
% 0.33/0.61
% 0.33/0.61 % min_eq_arg(2)
% 0.33/0.61 thf(fact_5256_min__eq__arg_I2_J,axiom,
% 0.33/0.61 ! [M2: rat,N2: rat] :
% 0.33/0.61 ( ( ( ord_min_rat @ M2 @ N2 )
% 0.33/0.61 = N2 )
% 0.33/0.61 = ( ord_less_eq_rat @ N2 @ M2 ) ) ).
% 0.33/0.61
% 0.33/0.61 % min_eq_arg(2)
% 0.33/0.61 thf(fact_5257_min__eq__arg_I2_J,axiom,
% 0.33/0.61 ! [M2: num,N2: num] :
% 0.33/0.61 ( ( ( ord_min_num @ M2 @ N2 )
% 0.33/0.61 = N2 )
% 0.33/0.61 = ( ord_less_eq_num @ N2 @ M2 ) ) ).
% 0.33/0.61
% 0.33/0.61 % min_eq_arg(2)
% 0.33/0.61 thf(fact_5258_min__eq__arg_I2_J,axiom,
% 0.33/0.61 ! [M2: nat,N2: nat] :
% 0.33/0.61 ( ( ( ord_min_nat @ M2 @ N2 )
% 0.33/0.61 = N2 )
% 0.33/0.61 = ( ord_less_eq_nat @ N2 @ M2 ) ) ).
% 0.33/0.61
% 0.33/0.61 % min_eq_arg(2)
% 0.33/0.61 thf(fact_5259_min__eq__arg_I2_J,axiom,
% 0.33/0.61 ! [M2: int,N2: int] :
% 0.33/0.61 ( ( ( ord_min_int @ M2 @ N2 )
% 0.33/0.61 = N2 )
% 0.33/0.61 = ( ord_less_eq_int @ N2 @ M2 ) ) ).
% 0.33/0.61
% 0.33/0.61 % min_eq_arg(2)
% 0.33/0.61 thf(fact_5260_min__arg__le_I1_J,axiom,
% 0.33/0.61 ! [N2: code_integer,M2: code_integer] :
% 0.33/0.61 ( ( ord_le3102999989581377725nteger @ N2 @ ( ord_min_Code_integer @ M2 @ N2 ) )
% 0.33/0.61 = ( ( ord_min_Code_integer @ M2 @ N2 )
% 0.33/0.61 = N2 ) ) ).
% 0.33/0.61
% 0.33/0.61 % min_arg_le(1)
% 0.33/0.61 thf(fact_5261_min__arg__le_I1_J,axiom,
% 0.33/0.61 ! [N2: code_natural,M2: code_natural] :
% 0.33/0.61 ( ( ord_le1926595141338095240atural @ N2 @ ( ord_min_Code_natural @ M2 @ N2 ) )
% 0.33/0.61 = ( ( ord_min_Code_natural @ M2 @ N2 )
% 0.33/0.61 = N2 ) ) ).
% 0.33/0.61
% 0.33/0.61 % min_arg_le(1)
% 0.33/0.61 thf(fact_5262_min__arg__le_I1_J,axiom,
% 0.33/0.61 ! [N2: set_nat,M2: set_nat] :
% 0.33/0.61 ( ( ord_less_eq_set_nat @ N2 @ ( ord_min_set_nat @ M2 @ N2 ) )
% 0.33/0.61 = ( ( ord_min_set_nat @ M2 @ N2 )
% 0.33/0.61 = N2 ) ) ).
% 0.33/0.61
% 0.33/0.61 % min_arg_le(1)
% 0.33/0.61 thf(fact_5263_min__arg__le_I1_J,axiom,
% 0.33/0.61 ! [N2: rat,M2: rat] :
% 0.33/0.61 ( ( ord_less_eq_rat @ N2 @ ( ord_min_rat @ M2 @ N2 ) )
% 0.33/0.61 = ( ( ord_min_rat @ M2 @ N2 )
% 0.33/0.61 = N2 ) ) ).
% 0.33/0.61
% 0.33/0.61 % min_arg_le(1)
% 0.33/0.61 thf(fact_5264_min__arg__le_I1_J,axiom,
% 0.33/0.61 ! [N2: num,M2: num] :
% 0.33/0.61 ( ( ord_less_eq_num @ N2 @ ( ord_min_num @ M2 @ N2 ) )
% 0.33/0.61 = ( ( ord_min_num @ M2 @ N2 )
% 0.33/0.61 = N2 ) ) ).
% 0.33/0.61
% 0.33/0.61 % min_arg_le(1)
% 0.33/0.61 thf(fact_5265_min__arg__le_I1_J,axiom,
% 0.33/0.61 ! [N2: nat,M2: nat] :
% 0.33/0.61 ( ( ord_less_eq_nat @ N2 @ ( ord_min_nat @ M2 @ N2 ) )
% 0.33/0.61 = ( ( ord_min_nat @ M2 @ N2 )
% 0.33/0.61 = N2 ) ) ).
% 0.33/0.61
% 0.33/0.61 % min_arg_le(1)
% 0.33/0.61 thf(fact_5266_min__arg__le_I1_J,axiom,
% 0.33/0.61 ! [N2: int,M2: int] :
% 0.33/0.61 ( ( ord_less_eq_int @ N2 @ ( ord_min_int @ M2 @ N2 ) )
% 0.33/0.61 = ( ( ord_min_int @ M2 @ N2 )
% 0.33/0.61 = N2 ) ) ).
% 0.33/0.61
% 0.33/0.61 % min_arg_le(1)
% 0.33/0.61 thf(fact_5267_min__arg__le_I2_J,axiom,
% 0.33/0.61 ! [M2: code_integer,N2: code_integer] :
% 0.33/0.61 ( ( ord_le3102999989581377725nteger @ M2 @ ( ord_min_Code_integer @ M2 @ N2 ) )
% 0.33/0.61 = ( ( ord_min_Code_integer @ M2 @ N2 )
% 0.33/0.61 = M2 ) ) ).
% 0.33/0.61
% 0.33/0.61 % min_arg_le(2)
% 0.33/0.61 thf(fact_5268_min__arg__le_I2_J,axiom,
% 0.33/0.61 ! [M2: code_natural,N2: code_natural] :
% 0.33/0.61 ( ( ord_le1926595141338095240atural @ M2 @ ( ord_min_Code_natural @ M2 @ N2 ) )
% 0.33/0.61 = ( ( ord_min_Code_natural @ M2 @ N2 )
% 0.33/0.61 = M2 ) ) ).
% 0.33/0.61
% 0.33/0.61 % min_arg_le(2)
% 0.33/0.61 thf(fact_5269_min__arg__le_I2_J,axiom,
% 0.33/0.61 ! [M2: set_nat,N2: set_nat] :
% 0.33/0.61 ( ( ord_less_eq_set_nat @ M2 @ ( ord_min_set_nat @ M2 @ N2 ) )
% 0.33/0.61 = ( ( ord_min_set_nat @ M2 @ N2 )
% 0.33/0.61 = M2 ) ) ).
% 0.33/0.61
% 0.33/0.61 % min_arg_le(2)
% 0.33/0.61 thf(fact_5270_min__arg__le_I2_J,axiom,
% 0.33/0.61 ! [M2: rat,N2: rat] :
% 0.33/0.61 ( ( ord_less_eq_rat @ M2 @ ( ord_min_rat @ M2 @ N2 ) )
% 0.33/0.61 = ( ( ord_min_rat @ M2 @ N2 )
% 0.33/0.61 = M2 ) ) ).
% 0.33/0.61
% 0.33/0.61 % min_arg_le(2)
% 0.33/0.61 thf(fact_5271_min__arg__le_I2_J,axiom,
% 0.33/0.61 ! [M2: num,N2: num] :
% 0.33/0.61 ( ( ord_less_eq_num @ M2 @ ( ord_min_num @ M2 @ N2 ) )
% 0.33/0.61 = ( ( ord_min_num @ M2 @ N2 )
% 0.33/0.61 = M2 ) ) ).
% 0.33/0.61
% 0.33/0.61 % min_arg_le(2)
% 0.33/0.61 thf(fact_5272_min__arg__le_I2_J,axiom,
% 0.33/0.61 ! [M2: nat,N2: nat] :
% 0.33/0.61 ( ( ord_less_eq_nat @ M2 @ ( ord_min_nat @ M2 @ N2 ) )
% 0.33/0.61 = ( ( ord_min_nat @ M2 @ N2 )
% 0.33/0.61 = M2 ) ) ).
% 0.33/0.61
% 0.33/0.61 % min_arg_le(2)
% 0.33/0.61 thf(fact_5273_min__arg__le_I2_J,axiom,
% 0.33/0.61 ! [M2: int,N2: int] :
% 0.33/0.61 ( ( ord_less_eq_int @ M2 @ ( ord_min_int @ M2 @ N2 ) )
% 0.33/0.61 = ( ( ord_min_int @ M2 @ N2 )
% 0.33/0.61 = M2 ) ) ).
% 0.33/0.61
% 0.33/0.61 % min_arg_le(2)
% 0.33/0.61 thf(fact_5274_min__arg__not__ge_I1_J,axiom,
% 0.33/0.61 ! [M2: code_natural,N2: code_natural] :
% 0.33/0.61 ( ( ~ ( ord_le5570908160329646204atural @ ( ord_min_Code_natural @ M2 @ N2 ) @ M2 ) )
% 0.33/0.61 = ( ( ord_min_Code_natural @ M2 @ N2 )
% 0.33/0.61 = M2 ) ) ).
% 0.33/0.61
% 0.33/0.61 % min_arg_not_ge(1)
% 0.33/0.61 thf(fact_5275_min__arg__not__ge_I1_J,axiom,
% 0.33/0.61 ! [M2: code_integer,N2: code_integer] :
% 0.33/0.61 ( ( ~ ( ord_le6747313008572928689nteger @ ( ord_min_Code_integer @ M2 @ N2 ) @ M2 ) )
% 0.33/0.61 = ( ( ord_min_Code_integer @ M2 @ N2 )
% 0.33/0.61 = M2 ) ) ).
% 0.33/0.61
% 0.33/0.61 % min_arg_not_ge(1)
% 0.33/0.61 thf(fact_5276_min__arg__not__ge_I1_J,axiom,
% 0.33/0.61 ! [M2: rat,N2: rat] :
% 0.33/0.61 ( ( ~ ( ord_less_rat @ ( ord_min_rat @ M2 @ N2 ) @ M2 ) )
% 0.33/0.61 = ( ( ord_min_rat @ M2 @ N2 )
% 0.33/0.61 = M2 ) ) ).
% 0.33/0.61
% 0.33/0.61 % min_arg_not_ge(1)
% 0.33/0.61 thf(fact_5277_min__arg__not__ge_I1_J,axiom,
% 0.33/0.61 ! [M2: num,N2: num] :
% 0.33/0.61 ( ( ~ ( ord_less_num @ ( ord_min_num @ M2 @ N2 ) @ M2 ) )
% 0.33/0.61 = ( ( ord_min_num @ M2 @ N2 )
% 0.33/0.61 = M2 ) ) ).
% 0.33/0.61
% 0.33/0.61 % min_arg_not_ge(1)
% 0.33/0.61 thf(fact_5278_min__arg__not__ge_I1_J,axiom,
% 0.33/0.61 ! [M2: nat,N2: nat] :
% 0.33/0.61 ( ( ~ ( ord_less_nat @ ( ord_min_nat @ M2 @ N2 ) @ M2 ) )
% 0.33/0.61 = ( ( ord_min_nat @ M2 @ N2 )
% 0.33/0.61 = M2 ) ) ).
% 0.33/0.61
% 0.33/0.61 % min_arg_not_ge(1)
% 0.33/0.61 thf(fact_5279_min__arg__not__ge_I1_J,axiom,
% 0.33/0.61 ! [M2: int,N2: int] :
% 0.33/0.61 ( ( ~ ( ord_less_int @ ( ord_min_int @ M2 @ N2 ) @ M2 ) )
% 0.33/0.61 = ( ( ord_min_int @ M2 @ N2 )
% 0.33/0.61 = M2 ) ) ).
% 0.33/0.61
% 0.33/0.61 % min_arg_not_ge(1)
% 0.33/0.61 thf(fact_5280_min__arg__not__ge_I2_J,axiom,
% 0.33/0.61 ! [M2: code_natural,N2: code_natural] :
% 0.33/0.61 ( ( ~ ( ord_le5570908160329646204atural @ ( ord_min_Code_natural @ M2 @ N2 ) @ N2 ) )
% 0.33/0.61 = ( ( ord_min_Code_natural @ M2 @ N2 )
% 0.33/0.61 = N2 ) ) ).
% 0.33/0.61
% 0.33/0.61 % min_arg_not_ge(2)
% 0.33/0.61 thf(fact_5281_min__arg__not__ge_I2_J,axiom,
% 0.33/0.61 ! [M2: code_integer,N2: code_integer] :
% 0.33/0.61 ( ( ~ ( ord_le6747313008572928689nteger @ ( ord_min_Code_integer @ M2 @ N2 ) @ N2 ) )
% 0.33/0.61 = ( ( ord_min_Code_integer @ M2 @ N2 )
% 0.33/0.61 = N2 ) ) ).
% 0.33/0.61
% 0.33/0.61 % min_arg_not_ge(2)
% 0.33/0.61 thf(fact_5282_min__arg__not__ge_I2_J,axiom,
% 0.33/0.61 ! [M2: rat,N2: rat] :
% 0.33/0.61 ( ( ~ ( ord_less_rat @ ( ord_min_rat @ M2 @ N2 ) @ N2 ) )
% 0.33/0.61 = ( ( ord_min_rat @ M2 @ N2 )
% 0.33/0.61 = N2 ) ) ).
% 0.33/0.61
% 0.33/0.61 % min_arg_not_ge(2)
% 0.33/0.61 thf(fact_5283_min__arg__not__ge_I2_J,axiom,
% 0.33/0.61 ! [M2: num,N2: num] :
% 0.33/0.61 ( ( ~ ( ord_less_num @ ( ord_min_num @ M2 @ N2 ) @ N2 ) )
% 0.33/0.61 = ( ( ord_min_num @ M2 @ N2 )
% 0.33/0.61 = N2 ) ) ).
% 0.33/0.61
% 0.33/0.61 % min_arg_not_ge(2)
% 0.33/0.61 thf(fact_5284_min__arg__not__ge_I2_J,axiom,
% 0.33/0.61 ! [M2: nat,N2: nat] :
% 0.33/0.61 ( ( ~ ( ord_less_nat @ ( ord_min_nat @ M2 @ N2 ) @ N2 ) )
% 0.33/0.61 = ( ( ord_min_nat @ M2 @ N2 )
% 0.33/0.61 = N2 ) ) ).
% 0.33/0.61
% 0.33/0.61 % min_arg_not_ge(2)
% 0.33/0.61 thf(fact_5285_min__arg__not__ge_I2_J,axiom,
% 0.33/0.61 ! [M2: int,N2: int] :
% 0.33/0.61 ( ( ~ ( ord_less_int @ ( ord_min_int @ M2 @ N2 ) @ N2 ) )
% 0.33/0.61 = ( ( ord_min_int @ M2 @ N2 )
% 0.33/0.61 = N2 ) ) ).
% 0.33/0.61
% 0.33/0.61 % min_arg_not_ge(2)
% 0.33/0.61 thf(fact_5286_min__less__self__conv_I1_J,axiom,
% 0.33/0.61 ! [A: code_natural,B: code_natural] :
% 0.33/0.61 ( ( ord_le5570908160329646204atural @ ( ord_min_Code_natural @ A @ B ) @ A )
% 0.33/0.61 = ( ord_le5570908160329646204atural @ B @ A ) ) ).
% 0.33/0.61
% 0.33/0.61 % min_less_self_conv(1)
% 0.33/0.61 thf(fact_5287_min__less__self__conv_I1_J,axiom,
% 0.33/0.61 ! [A: code_integer,B: code_integer] :
% 0.33/0.61 ( ( ord_le6747313008572928689nteger @ ( ord_min_Code_integer @ A @ B ) @ A )
% 0.33/0.61 = ( ord_le6747313008572928689nteger @ B @ A ) ) ).
% 0.33/0.61
% 0.33/0.61 % min_less_self_conv(1)
% 0.33/0.61 thf(fact_5288_min__less__self__conv_I1_J,axiom,
% 0.33/0.61 ! [A: rat,B: rat] :
% 0.33/0.61 ( ( ord_less_rat @ ( ord_min_rat @ A @ B ) @ A )
% 0.33/0.61 = ( ord_less_rat @ B @ A ) ) ).
% 0.33/0.61
% 0.33/0.61 % min_less_self_conv(1)
% 0.33/0.61 thf(fact_5289_min__less__self__conv_I1_J,axiom,
% 0.33/0.61 ! [A: num,B: num] :
% 0.33/0.61 ( ( ord_less_num @ ( ord_min_num @ A @ B ) @ A )
% 0.33/0.61 = ( ord_less_num @ B @ A ) ) ).
% 0.33/0.61
% 0.33/0.61 % min_less_self_conv(1)
% 0.33/0.61 thf(fact_5290_min__less__self__conv_I1_J,axiom,
% 0.33/0.61 ! [A: nat,B: nat] :
% 0.33/0.61 ( ( ord_less_nat @ ( ord_min_nat @ A @ B ) @ A )
% 0.33/0.61 = ( ord_less_nat @ B @ A ) ) ).
% 0.33/0.61
% 0.33/0.61 % min_less_self_conv(1)
% 0.33/0.61 thf(fact_5291_min__less__self__conv_I1_J,axiom,
% 0.33/0.61 ! [A: int,B: int] :
% 0.33/0.61 ( ( ord_less_int @ ( ord_min_int @ A @ B ) @ A )
% 0.33/0.61 = ( ord_less_int @ B @ A ) ) ).
% 0.33/0.61
% 0.33/0.61 % min_less_self_conv(1)
% 0.33/0.61 thf(fact_5292_min__less__self__conv_I2_J,axiom,
% 0.33/0.61 ! [A: code_natural,B: code_natural] :
% 0.33/0.61 ( ( ord_le5570908160329646204atural @ ( ord_min_Code_natural @ A @ B ) @ B )
% 0.33/0.61 = ( ord_le5570908160329646204atural @ A @ B ) ) ).
% 0.33/0.61
% 0.33/0.61 % min_less_self_conv(2)
% 0.33/0.61 thf(fact_5293_min__less__self__conv_I2_J,axiom,
% 0.33/0.61 ! [A: code_integer,B: code_integer] :
% 0.33/0.61 ( ( ord_le6747313008572928689nteger @ ( ord_min_Code_integer @ A @ B ) @ B )
% 0.33/0.61 = ( ord_le6747313008572928689nteger @ A @ B ) ) ).
% 0.33/0.61
% 0.33/0.61 % min_less_self_conv(2)
% 0.33/0.61 thf(fact_5294_min__less__self__conv_I2_J,axiom,
% 0.33/0.61 ! [A: rat,B: rat] :
% 0.33/0.61 ( ( ord_less_rat @ ( ord_min_rat @ A @ B ) @ B )
% 0.33/0.61 = ( ord_less_rat @ A @ B ) ) ).
% 0.33/0.61
% 0.33/0.61 % min_less_self_conv(2)
% 0.33/0.61 thf(fact_5295_min__less__self__conv_I2_J,axiom,
% 0.33/0.61 ! [A: num,B: num] :
% 0.33/0.61 ( ( ord_less_num @ ( ord_min_num @ A @ B ) @ B )
% 0.33/0.61 = ( ord_less_num @ A @ B ) ) ).
% 0.33/0.61
% 0.33/0.61 % min_less_self_conv(2)
% 0.33/0.61 thf(fact_5296_min__less__self__conv_I2_J,axiom,
% 0.33/0.61 ! [A: nat,B: nat] :
% 0.33/0.61 ( ( ord_less_nat @ ( ord_min_nat @ A @ B ) @ B )
% 0.33/0.61 = ( ord_less_nat @ A @ B ) ) ).
% 0.33/0.61
% 0.33/0.61 % min_less_self_conv(2)
% 0.33/0.61 thf(fact_5297_min__less__self__conv_I2_J,axiom,
% 0.33/0.61 ! [A: int,B: int] :
% 0.33/0.61 ( ( ord_less_int @ ( ord_min_int @ A @ B ) @ B )
% 0.33/0.61 = ( ord_less_int @ A @ B ) ) ).
% 0.33/0.61
% 0.33/0.61 % min_less_self_conv(2)
% 0.33/0.61 thf(fact_5298_min__simps_I1_J,axiom,
% 0.33/0.61 ! [A: code_natural,B: code_natural] :
% 0.33/0.61 ( ( ord_le5570908160329646204atural @ A @ B )
% 0.33/0.61 => ( ( ord_min_Code_natural @ A @ B )
% 0.33/0.61 = A ) ) ).
% 0.33/0.61
% 0.33/0.61 % min_simps(1)
% 0.33/0.61 thf(fact_5299_min__simps_I1_J,axiom,
% 0.33/0.61 ! [A: code_integer,B: code_integer] :
% 0.33/0.61 ( ( ord_le6747313008572928689nteger @ A @ B )
% 0.33/0.61 => ( ( ord_min_Code_integer @ A @ B )
% 0.33/0.61 = A ) ) ).
% 0.33/0.61
% 0.33/0.61 % min_simps(1)
% 0.33/0.61 thf(fact_5300_min__simps_I1_J,axiom,
% 0.33/0.61 ! [A: rat,B: rat] :
% 0.33/0.61 ( ( ord_less_rat @ A @ B )
% 0.33/0.61 => ( ( ord_min_rat @ A @ B )
% 0.33/0.61 = A ) ) ).
% 0.33/0.61
% 0.33/0.61 % min_simps(1)
% 0.33/0.61 thf(fact_5301_min__simps_I1_J,axiom,
% 0.33/0.61 ! [A: num,B: num] :
% 0.33/0.61 ( ( ord_less_num @ A @ B )
% 0.33/0.61 => ( ( ord_min_num @ A @ B )
% 0.33/0.61 = A ) ) ).
% 0.33/0.61
% 0.33/0.61 % min_simps(1)
% 0.33/0.61 thf(fact_5302_min__simps_I1_J,axiom,
% 0.33/0.61 ! [A: nat,B: nat] :
% 0.33/0.61 ( ( ord_less_nat @ A @ B )
% 0.33/0.61 => ( ( ord_min_nat @ A @ B )
% 0.33/0.61 = A ) ) ).
% 0.33/0.61
% 0.33/0.61 % min_simps(1)
% 0.33/0.61 thf(fact_5303_min__simps_I1_J,axiom,
% 0.33/0.61 ! [A: int,B: int] :
% 0.33/0.61 ( ( ord_less_int @ A @ B )
% 0.33/0.61 => ( ( ord_min_int @ A @ B )
% 0.33/0.61 = A ) ) ).
% 0.33/0.61
% 0.33/0.61 % min_simps(1)
% 0.33/0.61 thf(fact_5304_min__simps_I2_J,axiom,
% 0.33/0.61 ! [B: code_natural,A: code_natural] :
% 0.33/0.61 ( ( ord_le5570908160329646204atural @ B @ A )
% 0.33/0.61 => ( ( ord_min_Code_natural @ A @ B )
% 0.33/0.61 = B ) ) ).
% 0.33/0.61
% 0.33/0.61 % min_simps(2)
% 0.33/0.61 thf(fact_5305_min__simps_I2_J,axiom,
% 0.33/0.61 ! [B: code_integer,A: code_integer] :
% 0.33/0.61 ( ( ord_le6747313008572928689nteger @ B @ A )
% 0.33/0.61 => ( ( ord_min_Code_integer @ A @ B )
% 0.33/0.61 = B ) ) ).
% 0.33/0.61
% 0.33/0.61 % min_simps(2)
% 0.33/0.61 thf(fact_5306_min__simps_I2_J,axiom,
% 0.33/0.61 ! [B: rat,A: rat] :
% 0.33/0.61 ( ( ord_less_rat @ B @ A )
% 0.33/0.61 => ( ( ord_min_rat @ A @ B )
% 0.33/0.61 = B ) ) ).
% 0.33/0.61
% 0.33/0.61 % min_simps(2)
% 0.33/0.61 thf(fact_5307_min__simps_I2_J,axiom,
% 0.33/0.61 ! [B: num,A: num] :
% 0.33/0.61 ( ( ord_less_num @ B @ A )
% 0.33/0.61 => ( ( ord_min_num @ A @ B )
% 0.33/0.61 = B ) ) ).
% 0.33/0.61
% 0.33/0.61 % min_simps(2)
% 0.33/0.61 thf(fact_5308_min__simps_I2_J,axiom,
% 0.33/0.61 ! [B: nat,A: nat] :
% 0.33/0.61 ( ( ord_less_nat @ B @ A )
% 0.33/0.61 => ( ( ord_min_nat @ A @ B )
% 0.33/0.61 = B ) ) ).
% 0.33/0.61
% 0.33/0.61 % min_simps(2)
% 0.33/0.61 thf(fact_5309_min__simps_I2_J,axiom,
% 0.33/0.61 ! [B: int,A: int] :
% 0.33/0.61 ( ( ord_less_int @ B @ A )
% 0.33/0.61 => ( ( ord_min_int @ A @ B )
% 0.33/0.61 = B ) ) ).
% 0.33/0.61
% 0.33/0.61 % min_simps(2)
% 0.33/0.61 thf(fact_5310_min__0__1_I2_J,axiom,
% 0.33/0.61 ( ( ord_min_rat @ one_one_rat @ zero_zero_rat )
% 0.33/0.61 = zero_zero_rat ) ).
% 0.33/0.61
% 0.33/0.61 % min_0_1(2)
% 0.33/0.61 thf(fact_5311_min__0__1_I2_J,axiom,
% 0.33/0.61 ( ( ord_min_nat @ one_one_nat @ zero_zero_nat )
% 0.33/0.61 = zero_zero_nat ) ).
% 0.33/0.61
% 0.33/0.61 % min_0_1(2)
% 0.33/0.61 thf(fact_5312_min__0__1_I2_J,axiom,
% 0.33/0.61 ( ( ord_min_Code_integer @ one_one_Code_integer @ zero_z3403309356797280102nteger )
% 0.33/0.61 = zero_z3403309356797280102nteger ) ).
% 0.33/0.61
% 0.33/0.61 % min_0_1(2)
% 0.33/0.61 thf(fact_5313_min__0__1_I2_J,axiom,
% 0.33/0.61 ( ( ord_min_int @ one_one_int @ zero_zero_int )
% 0.33/0.61 = zero_zero_int ) ).
% 0.33/0.61
% 0.33/0.61 % min_0_1(2)
% 0.33/0.61 thf(fact_5314_min__0__1_I2_J,axiom,
% 0.33/0.61 ( ( ord_min_Code_natural @ one_one_Code_natural @ zero_z2226904508553997617atural )
% 0.33/0.61 = zero_z2226904508553997617atural ) ).
% 0.33/0.61
% 0.33/0.61 % min_0_1(2)
% 0.33/0.61 thf(fact_5315_min__0__1_I1_J,axiom,
% 0.33/0.61 ( ( ord_min_rat @ zero_zero_rat @ one_one_rat )
% 0.33/0.61 = zero_zero_rat ) ).
% 0.33/0.61
% 0.33/0.61 % min_0_1(1)
% 0.33/0.61 thf(fact_5316_min__0__1_I1_J,axiom,
% 0.33/0.61 ( ( ord_min_nat @ zero_zero_nat @ one_one_nat )
% 0.33/0.61 = zero_zero_nat ) ).
% 0.33/0.61
% 0.33/0.61 % min_0_1(1)
% 0.33/0.61 thf(fact_5317_min__0__1_I1_J,axiom,
% 0.33/0.61 ( ( ord_min_Code_integer @ zero_z3403309356797280102nteger @ one_one_Code_integer )
% 0.33/0.61 = zero_z3403309356797280102nteger ) ).
% 0.33/0.61
% 0.33/0.61 % min_0_1(1)
% 0.33/0.61 thf(fact_5318_min__0__1_I1_J,axiom,
% 0.33/0.61 ( ( ord_min_int @ zero_zero_int @ one_one_int )
% 0.33/0.61 = zero_zero_int ) ).
% 0.33/0.61
% 0.33/0.61 % min_0_1(1)
% 0.33/0.61 thf(fact_5319_min__0__1_I1_J,axiom,
% 0.33/0.61 ( ( ord_min_Code_natural @ zero_z2226904508553997617atural @ one_one_Code_natural )
% 0.33/0.61 = zero_z2226904508553997617atural ) ).
% 0.33/0.61
% 0.33/0.61 % min_0_1(1)
% 0.33/0.61 thf(fact_5320_min__0__1_I5_J,axiom,
% 0.33/0.61 ! [X: num] :
% 0.33/0.61 ( ( ord_min_nat @ one_one_nat @ ( numeral_numeral_nat @ X ) )
% 0.33/0.61 = one_one_nat ) ).
% 0.33/0.61
% 0.33/0.61 % min_0_1(5)
% 0.33/0.61 thf(fact_5321_min__0__1_I5_J,axiom,
% 0.33/0.61 ! [X: num] :
% 0.33/0.61 ( ( ord_min_int @ one_one_int @ ( numeral_numeral_int @ X ) )
% 0.33/0.61 = one_one_int ) ).
% 0.33/0.61
% 0.33/0.61 % min_0_1(5)
% 0.33/0.61 thf(fact_5322_min__0__1_I5_J,axiom,
% 0.33/0.61 ! [X: num] :
% 0.33/0.61 ( ( ord_min_Code_integer @ one_one_Code_integer @ ( numera6620942414471956472nteger @ X ) )
% 0.33/0.61 = one_one_Code_integer ) ).
% 0.33/0.61
% 0.33/0.61 % min_0_1(5)
% 0.33/0.61 thf(fact_5323_min__0__1_I5_J,axiom,
% 0.33/0.61 ! [X: num] :
% 0.33/0.61 ( ( ord_min_rat @ one_one_rat @ ( numeral_numeral_rat @ X ) )
% 0.33/0.61 = one_one_rat ) ).
% 0.33/0.61
% 0.33/0.61 % min_0_1(5)
% 0.33/0.61 thf(fact_5324_min__0__1_I5_J,axiom,
% 0.33/0.61 ! [X: num] :
% 0.33/0.61 ( ( ord_min_Code_natural @ one_one_Code_natural @ ( numera5444537566228673987atural @ X ) )
% 0.33/0.61 = one_one_Code_natural ) ).
% 0.33/0.61
% 0.33/0.61 % min_0_1(5)
% 0.33/0.61 thf(fact_5325_min__0__1_I6_J,axiom,
% 0.33/0.61 ! [X: num] :
% 0.33/0.61 ( ( ord_min_nat @ ( numeral_numeral_nat @ X ) @ one_one_nat )
% 0.33/0.61 = one_one_nat ) ).
% 0.33/0.61
% 0.33/0.61 % min_0_1(6)
% 0.33/0.61 thf(fact_5326_min__0__1_I6_J,axiom,
% 0.33/0.61 ! [X: num] :
% 0.33/0.61 ( ( ord_min_int @ ( numeral_numeral_int @ X ) @ one_one_int )
% 0.33/0.61 = one_one_int ) ).
% 0.33/0.61
% 0.33/0.61 % min_0_1(6)
% 0.33/0.61 thf(fact_5327_min__0__1_I6_J,axiom,
% 0.33/0.61 ! [X: num] :
% 0.33/0.61 ( ( ord_min_Code_integer @ ( numera6620942414471956472nteger @ X ) @ one_one_Code_integer )
% 0.33/0.61 = one_one_Code_integer ) ).
% 0.33/0.61
% 0.33/0.61 % min_0_1(6)
% 0.33/0.61 thf(fact_5328_min__0__1_I6_J,axiom,
% 0.33/0.61 ! [X: num] :
% 0.33/0.61 ( ( ord_min_rat @ ( numeral_numeral_rat @ X ) @ one_one_rat )
% 0.33/0.61 = one_one_rat ) ).
% 0.33/0.61
% 0.33/0.61 % min_0_1(6)
% 0.33/0.61 thf(fact_5329_min__0__1_I6_J,axiom,
% 0.33/0.61 ! [X: num] :
% 0.33/0.61 ( ( ord_min_Code_natural @ ( numera5444537566228673987atural @ X ) @ one_one_Code_natural )
% 0.33/0.61 = one_one_Code_natural ) ).
% 0.33/0.61
% 0.33/0.61 % min_0_1(6)
% 0.33/0.61 thf(fact_5330_atLeastAtMost__singleton__iff,axiom,
% 0.33/0.61 ! [A: $o,B: $o,C: $o] :
% 0.33/0.61 ( ( ( set_or8904488021354931149Most_o @ A @ B )
% 0.33/0.61 = ( insert_o @ C @ bot_bot_set_o ) )
% 0.33/0.61 = ( ( A = B )
% 0.33/0.61 & ( B = C ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % atLeastAtMost_singleton_iff
% 0.33/0.61 thf(fact_5331_atLeastAtMost__singleton__iff,axiom,
% 0.33/0.61 ! [A: int,B: int,C: int] :
% 0.33/0.61 ( ( ( set_or1266510415728281911st_int @ A @ B )
% 0.33/0.61 = ( insert_int @ C @ bot_bot_set_int ) )
% 0.33/0.61 = ( ( A = B )
% 0.33/0.61 & ( B = C ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % atLeastAtMost_singleton_iff
% 0.33/0.61 thf(fact_5332_atLeastAtMost__singleton__iff,axiom,
% 0.33/0.61 ! [A: nat,B: nat,C: nat] :
% 0.33/0.61 ( ( ( set_or1269000886237332187st_nat @ A @ B )
% 0.33/0.61 = ( insert_nat @ C @ bot_bot_set_nat ) )
% 0.33/0.61 = ( ( A = B )
% 0.33/0.61 & ( B = C ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % atLeastAtMost_singleton_iff
% 0.33/0.61 thf(fact_5333_atLeastAtMost__singleton__iff,axiom,
% 0.33/0.61 ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.33/0.61 ( ( ( set_or189985376899183464nteger @ A @ B )
% 0.33/0.61 = ( insert_Code_integer @ C @ bot_bo3990330152332043303nteger ) )
% 0.33/0.61 = ( ( A = B )
% 0.33/0.61 & ( B = C ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % atLeastAtMost_singleton_iff
% 0.33/0.61 thf(fact_5334_atLeastAtMost__singleton,axiom,
% 0.33/0.61 ! [A: $o] :
% 0.33/0.61 ( ( set_or8904488021354931149Most_o @ A @ A )
% 0.33/0.61 = ( insert_o @ A @ bot_bot_set_o ) ) ).
% 0.33/0.61
% 0.33/0.61 % atLeastAtMost_singleton
% 0.33/0.61 thf(fact_5335_atLeastAtMost__singleton,axiom,
% 0.33/0.61 ! [A: int] :
% 0.33/0.61 ( ( set_or1266510415728281911st_int @ A @ A )
% 0.33/0.61 = ( insert_int @ A @ bot_bot_set_int ) ) ).
% 0.33/0.61
% 0.33/0.61 % atLeastAtMost_singleton
% 0.33/0.61 thf(fact_5336_atLeastAtMost__singleton,axiom,
% 0.33/0.61 ! [A: nat] :
% 0.33/0.61 ( ( set_or1269000886237332187st_nat @ A @ A )
% 0.33/0.61 = ( insert_nat @ A @ bot_bot_set_nat ) ) ).
% 0.33/0.61
% 0.33/0.61 % atLeastAtMost_singleton
% 0.33/0.61 thf(fact_5337_atLeastAtMost__singleton,axiom,
% 0.33/0.61 ! [A: code_integer] :
% 0.33/0.61 ( ( set_or189985376899183464nteger @ A @ A )
% 0.33/0.61 = ( insert_Code_integer @ A @ bot_bo3990330152332043303nteger ) ) ).
% 0.33/0.61
% 0.33/0.61 % atLeastAtMost_singleton
% 0.33/0.61 thf(fact_5338_min__Suc__gt_I2_J,axiom,
% 0.33/0.61 ! [A: nat,B: nat] :
% 0.33/0.61 ( ( ord_less_nat @ A @ B )
% 0.33/0.61 => ( ( ord_min_nat @ B @ ( suc @ A ) )
% 0.33/0.61 = ( suc @ A ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % min_Suc_gt(2)
% 0.33/0.61 thf(fact_5339_min__Suc__gt_I1_J,axiom,
% 0.33/0.61 ! [A: nat,B: nat] :
% 0.33/0.61 ( ( ord_less_nat @ A @ B )
% 0.33/0.61 => ( ( ord_min_nat @ ( suc @ A ) @ B )
% 0.33/0.61 = ( suc @ A ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % min_Suc_gt(1)
% 0.33/0.61 thf(fact_5340_case__prod__Pair,axiom,
% 0.33/0.61 ( ( produc6512950862096126219nteger @ produc8603105652947943368nteger )
% 0.33/0.61 = id_Pro1379270990444177765nteger ) ).
% 0.33/0.61
% 0.33/0.61 % case_prod_Pair
% 0.33/0.61 thf(fact_5341_case__prod__Pair,axiom,
% 0.33/0.61 ( ( produc4058941399401191971et_nat @ produc5001842942810119800et_nat )
% 0.33/0.61 = id_Pro1888964116897856973et_nat ) ).
% 0.33/0.61
% 0.33/0.61 % case_prod_Pair
% 0.33/0.61 thf(fact_5342_case__prod__Pair,axiom,
% 0.33/0.61 ( ( produc2377985495875741467et_nat @ produc2245416461498447860et_nat )
% 0.33/0.61 = id_Pro1297863087923562825et_nat ) ).
% 0.33/0.61
% 0.33/0.61 % case_prod_Pair
% 0.33/0.61 thf(fact_5343_case__prod__Pair,axiom,
% 0.33/0.61 ( ( produc8492565224438309093nt_int @ produc5700946648718959541nt_int )
% 0.33/0.61 = id_Pro5422067691592394322nt_int ) ).
% 0.33/0.61
% 0.33/0.61 % case_prod_Pair
% 0.33/0.61 thf(fact_5344_case__prod__Pair,axiom,
% 0.33/0.61 ( ( produc5122537100556696953nt_int @ produc4305682042979456191nt_int )
% 0.33/0.61 = id_Pro3923183700162330716nt_int ) ).
% 0.33/0.61
% 0.33/0.61 % case_prod_Pair
% 0.33/0.61 thf(fact_5345_case__prod__Pair,axiom,
% 0.33/0.61 ( ( produc4245557441103728435nt_int @ product_Pair_int_int )
% 0.33/0.61 = id_Pro4381231610383771306nt_int ) ).
% 0.33/0.61
% 0.33/0.61 % case_prod_Pair
% 0.33/0.61 thf(fact_5346_single__Diff__lessThan,axiom,
% 0.33/0.61 ! [K: $o] :
% 0.33/0.61 ( ( minus_minus_set_o @ ( insert_o @ K @ bot_bot_set_o ) @ ( set_ord_lessThan_o @ K ) )
% 0.33/0.61 = ( insert_o @ K @ bot_bot_set_o ) ) ).
% 0.33/0.61
% 0.33/0.61 % single_Diff_lessThan
% 0.33/0.61 thf(fact_5347_single__Diff__lessThan,axiom,
% 0.33/0.61 ! [K: int] :
% 0.33/0.61 ( ( minus_minus_set_int @ ( insert_int @ K @ bot_bot_set_int ) @ ( set_ord_lessThan_int @ K ) )
% 0.33/0.61 = ( insert_int @ K @ bot_bot_set_int ) ) ).
% 0.33/0.61
% 0.33/0.61 % single_Diff_lessThan
% 0.33/0.61 thf(fact_5348_single__Diff__lessThan,axiom,
% 0.33/0.61 ! [K: nat] :
% 0.33/0.61 ( ( minus_minus_set_nat @ ( insert_nat @ K @ bot_bot_set_nat ) @ ( set_ord_lessThan_nat @ K ) )
% 0.33/0.61 = ( insert_nat @ K @ bot_bot_set_nat ) ) ).
% 0.33/0.61
% 0.33/0.61 % single_Diff_lessThan
% 0.33/0.61 thf(fact_5349_min__add__distrib__right,axiom,
% 0.33/0.61 ! [X: rat,Y: rat,Z: rat] :
% 0.33/0.61 ( ( plus_plus_rat @ X @ ( ord_min_rat @ Y @ Z ) )
% 0.33/0.61 = ( ord_min_rat @ ( plus_plus_rat @ X @ Y ) @ ( plus_plus_rat @ X @ Z ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % min_add_distrib_right
% 0.33/0.61 thf(fact_5350_min__add__distrib__right,axiom,
% 0.33/0.61 ! [X: nat,Y: nat,Z: nat] :
% 0.33/0.61 ( ( plus_plus_nat @ X @ ( ord_min_nat @ Y @ Z ) )
% 0.33/0.61 = ( ord_min_nat @ ( plus_plus_nat @ X @ Y ) @ ( plus_plus_nat @ X @ Z ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % min_add_distrib_right
% 0.33/0.61 thf(fact_5351_min__add__distrib__right,axiom,
% 0.33/0.61 ! [X: code_integer,Y: code_integer,Z: code_integer] :
% 0.33/0.61 ( ( plus_p5714425477246183910nteger @ X @ ( ord_min_Code_integer @ Y @ Z ) )
% 0.33/0.61 = ( ord_min_Code_integer @ ( plus_p5714425477246183910nteger @ X @ Y ) @ ( plus_p5714425477246183910nteger @ X @ Z ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % min_add_distrib_right
% 0.33/0.61 thf(fact_5352_min__add__distrib__right,axiom,
% 0.33/0.61 ! [X: int,Y: int,Z: int] :
% 0.33/0.61 ( ( plus_plus_int @ X @ ( ord_min_int @ Y @ Z ) )
% 0.33/0.61 = ( ord_min_int @ ( plus_plus_int @ X @ Y ) @ ( plus_plus_int @ X @ Z ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % min_add_distrib_right
% 0.33/0.61 thf(fact_5353_min__add__distrib__right,axiom,
% 0.33/0.61 ! [X: code_natural,Y: code_natural,Z: code_natural] :
% 0.33/0.61 ( ( plus_p4538020629002901425atural @ X @ ( ord_min_Code_natural @ Y @ Z ) )
% 0.33/0.61 = ( ord_min_Code_natural @ ( plus_p4538020629002901425atural @ X @ Y ) @ ( plus_p4538020629002901425atural @ X @ Z ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % min_add_distrib_right
% 0.33/0.61 thf(fact_5354_min__add__distrib__left,axiom,
% 0.33/0.61 ! [X: rat,Y: rat,Z: rat] :
% 0.33/0.61 ( ( plus_plus_rat @ ( ord_min_rat @ X @ Y ) @ Z )
% 0.33/0.61 = ( ord_min_rat @ ( plus_plus_rat @ X @ Z ) @ ( plus_plus_rat @ Y @ Z ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % min_add_distrib_left
% 0.33/0.61 thf(fact_5355_min__add__distrib__left,axiom,
% 0.33/0.61 ! [X: nat,Y: nat,Z: nat] :
% 0.33/0.61 ( ( plus_plus_nat @ ( ord_min_nat @ X @ Y ) @ Z )
% 0.33/0.61 = ( ord_min_nat @ ( plus_plus_nat @ X @ Z ) @ ( plus_plus_nat @ Y @ Z ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % min_add_distrib_left
% 0.33/0.61 thf(fact_5356_min__add__distrib__left,axiom,
% 0.33/0.61 ! [X: code_integer,Y: code_integer,Z: code_integer] :
% 0.33/0.61 ( ( plus_p5714425477246183910nteger @ ( ord_min_Code_integer @ X @ Y ) @ Z )
% 0.33/0.61 = ( ord_min_Code_integer @ ( plus_p5714425477246183910nteger @ X @ Z ) @ ( plus_p5714425477246183910nteger @ Y @ Z ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % min_add_distrib_left
% 0.33/0.61 thf(fact_5357_min__add__distrib__left,axiom,
% 0.33/0.61 ! [X: int,Y: int,Z: int] :
% 0.33/0.61 ( ( plus_plus_int @ ( ord_min_int @ X @ Y ) @ Z )
% 0.33/0.61 = ( ord_min_int @ ( plus_plus_int @ X @ Z ) @ ( plus_plus_int @ Y @ Z ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % min_add_distrib_left
% 0.33/0.61 thf(fact_5358_min__add__distrib__left,axiom,
% 0.33/0.61 ! [X: code_natural,Y: code_natural,Z: code_natural] :
% 0.33/0.61 ( ( plus_p4538020629002901425atural @ ( ord_min_Code_natural @ X @ Y ) @ Z )
% 0.33/0.61 = ( ord_min_Code_natural @ ( plus_p4538020629002901425atural @ X @ Z ) @ ( plus_p4538020629002901425atural @ Y @ Z ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % min_add_distrib_left
% 0.33/0.61 thf(fact_5359_min__diff__distrib__left,axiom,
% 0.33/0.61 ! [X: code_integer,Y: code_integer,Z: code_integer] :
% 0.33/0.61 ( ( minus_8373710615458151222nteger @ ( ord_min_Code_integer @ X @ Y ) @ Z )
% 0.33/0.61 = ( ord_min_Code_integer @ ( minus_8373710615458151222nteger @ X @ Z ) @ ( minus_8373710615458151222nteger @ Y @ Z ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % min_diff_distrib_left
% 0.33/0.61 thf(fact_5360_min__diff__distrib__left,axiom,
% 0.33/0.61 ! [X: rat,Y: rat,Z: rat] :
% 0.33/0.61 ( ( minus_minus_rat @ ( ord_min_rat @ X @ Y ) @ Z )
% 0.33/0.61 = ( ord_min_rat @ ( minus_minus_rat @ X @ Z ) @ ( minus_minus_rat @ Y @ Z ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % min_diff_distrib_left
% 0.33/0.61 thf(fact_5361_min__diff__distrib__left,axiom,
% 0.33/0.61 ! [X: int,Y: int,Z: int] :
% 0.33/0.61 ( ( minus_minus_int @ ( ord_min_int @ X @ Y ) @ Z )
% 0.33/0.61 = ( ord_min_int @ ( minus_minus_int @ X @ Z ) @ ( minus_minus_int @ Y @ Z ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % min_diff_distrib_left
% 0.33/0.61 thf(fact_5362_bot__option__def,axiom,
% 0.33/0.61 bot_bot_option_num = none_num ).
% 0.33/0.61
% 0.33/0.61 % bot_option_def
% 0.33/0.61 thf(fact_5363_bot__empty__eq2,axiom,
% 0.33/0.61 ( bot_bo3000040243691356879eger_o
% 0.33/0.61 = ( ^ [X3: produc6241069584506657477e_term > option6357759511663192854e_term,Y3: produc8923325533196201883nteger] : ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X3 @ Y3 ) @ bot_bo5443222936135328352nteger ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % bot_empty_eq2
% 0.33/0.61 thf(fact_5364_bot__empty__eq2,axiom,
% 0.33/0.61 ( bot_bo5580076615179976505_nat_o
% 0.33/0.61 = ( ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3658429121746597890et_nat] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X3 @ Y3 ) @ bot_bo1481135142794719944et_nat ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % bot_empty_eq2
% 0.33/0.61 thf(fact_5365_bot__empty__eq2,axiom,
% 0.33/0.61 ( bot_bo3790638025767943357_nat_o
% 0.33/0.61 = ( ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3925858234332021118et_nat] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X3 @ Y3 ) @ bot_bo5635537948650799172et_nat ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % bot_empty_eq2
% 0.33/0.61 thf(fact_5366_bot__empty__eq2,axiom,
% 0.33/0.61 ( bot_bo8662317086119403298_int_o
% 0.33/0.61 = ( ^ [X3: produc8551481072490612790e_term > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X3 @ Y3 ) @ bot_bo572930865798478029nt_int ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % bot_empty_eq2
% 0.33/0.61 thf(fact_5367_bot__empty__eq2,axiom,
% 0.33/0.61 ( bot_bo1403522918969695512_int_o
% 0.33/0.61 = ( ^ [X3: int > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X3 @ Y3 ) @ bot_bo4508923176915781079nt_int ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % bot_empty_eq2
% 0.33/0.61 thf(fact_5368_bot__empty__eq2,axiom,
% 0.33/0.61 ( bot_bo394778441745866138_nat_o
% 0.33/0.61 = ( ^ [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ Y3 ) @ bot_bo228742789529271731at_nat ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % bot_empty_eq2
% 0.33/0.61 thf(fact_5369_bot__empty__eq2,axiom,
% 0.33/0.61 ( bot_bot_nat_nat_o
% 0.33/0.61 = ( ^ [X3: nat,Y3: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y3 ) @ bot_bo2099793752762293965at_nat ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % bot_empty_eq2
% 0.33/0.61 thf(fact_5370_map__fun_Oidentity,axiom,
% 0.33/0.61 ( ( map_fun_nat_nat_o_o
% 0.33/0.61 @ ^ [X3: nat] : X3
% 0.33/0.61 @ ^ [X3: $o] : X3 )
% 0.33/0.61 = id_nat_o ) ).
% 0.33/0.61
% 0.33/0.61 % map_fun.identity
% 0.33/0.61 thf(fact_5371_map__option_Oidentity,axiom,
% 0.33/0.61 ( ( map_option_num_num
% 0.33/0.61 @ ^ [X3: num] : X3 )
% 0.33/0.61 = id_option_num ) ).
% 0.33/0.61
% 0.33/0.61 % map_option.identity
% 0.33/0.61 thf(fact_5372_minus__max__eq__min,axiom,
% 0.33/0.61 ! [X: int,Y: int] :
% 0.33/0.61 ( ( uminus_uminus_int @ ( ord_max_int @ X @ Y ) )
% 0.33/0.61 = ( ord_min_int @ ( uminus_uminus_int @ X ) @ ( uminus_uminus_int @ Y ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % minus_max_eq_min
% 0.33/0.61 thf(fact_5373_minus__max__eq__min,axiom,
% 0.33/0.61 ! [X: code_integer,Y: code_integer] :
% 0.33/0.61 ( ( uminus1351360451143612070nteger @ ( ord_max_Code_integer @ X @ Y ) )
% 0.33/0.61 = ( ord_min_Code_integer @ ( uminus1351360451143612070nteger @ X ) @ ( uminus1351360451143612070nteger @ Y ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % minus_max_eq_min
% 0.33/0.61 thf(fact_5374_minus__max__eq__min,axiom,
% 0.33/0.61 ! [X: rat,Y: rat] :
% 0.33/0.61 ( ( uminus_uminus_rat @ ( ord_max_rat @ X @ Y ) )
% 0.33/0.61 = ( ord_min_rat @ ( uminus_uminus_rat @ X ) @ ( uminus_uminus_rat @ Y ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % minus_max_eq_min
% 0.33/0.61 thf(fact_5375_minus__min__eq__max,axiom,
% 0.33/0.61 ! [X: int,Y: int] :
% 0.33/0.61 ( ( uminus_uminus_int @ ( ord_min_int @ X @ Y ) )
% 0.33/0.61 = ( ord_max_int @ ( uminus_uminus_int @ X ) @ ( uminus_uminus_int @ Y ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % minus_min_eq_max
% 0.33/0.61 thf(fact_5376_minus__min__eq__max,axiom,
% 0.33/0.61 ! [X: code_integer,Y: code_integer] :
% 0.33/0.61 ( ( uminus1351360451143612070nteger @ ( ord_min_Code_integer @ X @ Y ) )
% 0.33/0.61 = ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ X ) @ ( uminus1351360451143612070nteger @ Y ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % minus_min_eq_max
% 0.33/0.61 thf(fact_5377_minus__min__eq__max,axiom,
% 0.33/0.61 ! [X: rat,Y: rat] :
% 0.33/0.61 ( ( uminus_uminus_rat @ ( ord_min_rat @ X @ Y ) )
% 0.33/0.61 = ( ord_max_rat @ ( uminus_uminus_rat @ X ) @ ( uminus_uminus_rat @ Y ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % minus_min_eq_max
% 0.33/0.61 thf(fact_5378_insert__minus__eq,axiom,
% 0.33/0.61 ! [X: produc3843707927480180839at_nat,Y: produc3843707927480180839at_nat,A2: set_Pr4329608150637261639at_nat] :
% 0.33/0.61 ( ( X != Y )
% 0.33/0.61 => ( ( minus_3314409938677909166at_nat @ ( insert9069300056098147895at_nat @ X @ A2 ) @ ( insert9069300056098147895at_nat @ Y @ bot_bo228742789529271731at_nat ) )
% 0.33/0.61 = ( insert9069300056098147895at_nat @ X @ ( minus_3314409938677909166at_nat @ A2 @ ( insert9069300056098147895at_nat @ Y @ bot_bo228742789529271731at_nat ) ) ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % insert_minus_eq
% 0.33/0.61 thf(fact_5379_insert__minus__eq,axiom,
% 0.33/0.61 ! [X: product_prod_nat_nat,Y: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat] :
% 0.33/0.61 ( ( X != Y )
% 0.33/0.61 => ( ( minus_1356011639430497352at_nat @ ( insert8211810215607154385at_nat @ X @ A2 ) @ ( insert8211810215607154385at_nat @ Y @ bot_bo2099793752762293965at_nat ) )
% 0.33/0.61 = ( insert8211810215607154385at_nat @ X @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ Y @ bot_bo2099793752762293965at_nat ) ) ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % insert_minus_eq
% 0.33/0.61 thf(fact_5380_insert__minus__eq,axiom,
% 0.33/0.61 ! [X: $o,Y: $o,A2: set_o] :
% 0.33/0.61 ( ( X != Y )
% 0.33/0.61 => ( ( minus_minus_set_o @ ( insert_o @ X @ A2 ) @ ( insert_o @ Y @ bot_bot_set_o ) )
% 0.33/0.61 = ( insert_o @ X @ ( minus_minus_set_o @ A2 @ ( insert_o @ Y @ bot_bot_set_o ) ) ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % insert_minus_eq
% 0.33/0.61 thf(fact_5381_insert__minus__eq,axiom,
% 0.33/0.61 ! [X: int,Y: int,A2: set_int] :
% 0.33/0.61 ( ( X != Y )
% 0.33/0.61 => ( ( minus_minus_set_int @ ( insert_int @ X @ A2 ) @ ( insert_int @ Y @ bot_bot_set_int ) )
% 0.33/0.61 = ( insert_int @ X @ ( minus_minus_set_int @ A2 @ ( insert_int @ Y @ bot_bot_set_int ) ) ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % insert_minus_eq
% 0.33/0.61 thf(fact_5382_insert__minus__eq,axiom,
% 0.33/0.61 ! [X: nat,Y: nat,A2: set_nat] :
% 0.33/0.61 ( ( X != Y )
% 0.33/0.61 => ( ( minus_minus_set_nat @ ( insert_nat @ X @ A2 ) @ ( insert_nat @ Y @ bot_bot_set_nat ) )
% 0.33/0.61 = ( insert_nat @ X @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ Y @ bot_bot_set_nat ) ) ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % insert_minus_eq
% 0.33/0.61 thf(fact_5383_set__minus__singleton__eq,axiom,
% 0.33/0.61 ! [X: produc3843707927480180839at_nat,X11: set_Pr4329608150637261639at_nat] :
% 0.33/0.61 ( ~ ( member8757157785044589968at_nat @ X @ X11 )
% 0.33/0.61 => ( ( minus_3314409938677909166at_nat @ X11 @ ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) )
% 0.33/0.61 = X11 ) ) ).
% 0.33/0.61
% 0.33/0.61 % set_minus_singleton_eq
% 0.33/0.61 thf(fact_5384_set__minus__singleton__eq,axiom,
% 0.33/0.61 ! [X: product_prod_nat_nat,X11: set_Pr1261947904930325089at_nat] :
% 0.33/0.61 ( ~ ( member8440522571783428010at_nat @ X @ X11 )
% 0.33/0.61 => ( ( minus_1356011639430497352at_nat @ X11 @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) )
% 0.33/0.61 = X11 ) ) ).
% 0.33/0.61
% 0.33/0.61 % set_minus_singleton_eq
% 0.33/0.61 thf(fact_5385_set__minus__singleton__eq,axiom,
% 0.33/0.61 ! [X: $o,X11: set_o] :
% 0.33/0.61 ( ~ ( member_o @ X @ X11 )
% 0.33/0.61 => ( ( minus_minus_set_o @ X11 @ ( insert_o @ X @ bot_bot_set_o ) )
% 0.33/0.61 = X11 ) ) ).
% 0.33/0.61
% 0.33/0.61 % set_minus_singleton_eq
% 0.33/0.61 thf(fact_5386_set__minus__singleton__eq,axiom,
% 0.33/0.61 ! [X: int,X11: set_int] :
% 0.33/0.61 ( ~ ( member_int @ X @ X11 )
% 0.33/0.61 => ( ( minus_minus_set_int @ X11 @ ( insert_int @ X @ bot_bot_set_int ) )
% 0.33/0.61 = X11 ) ) ).
% 0.33/0.61
% 0.33/0.61 % set_minus_singleton_eq
% 0.33/0.61 thf(fact_5387_set__minus__singleton__eq,axiom,
% 0.33/0.61 ! [X: nat,X11: set_nat] :
% 0.33/0.61 ( ~ ( member_nat @ X @ X11 )
% 0.33/0.61 => ( ( minus_minus_set_nat @ X11 @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 0.33/0.61 = X11 ) ) ).
% 0.33/0.61
% 0.33/0.61 % set_minus_singleton_eq
% 0.33/0.61 thf(fact_5388_atLeastAtMost__singleton_H,axiom,
% 0.33/0.61 ! [A: $o,B: $o] :
% 0.33/0.61 ( ( A = B )
% 0.33/0.61 => ( ( set_or8904488021354931149Most_o @ A @ B )
% 0.33/0.61 = ( insert_o @ A @ bot_bot_set_o ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % atLeastAtMost_singleton'
% 0.33/0.61 thf(fact_5389_atLeastAtMost__singleton_H,axiom,
% 0.33/0.61 ! [A: int,B: int] :
% 0.33/0.61 ( ( A = B )
% 0.33/0.61 => ( ( set_or1266510415728281911st_int @ A @ B )
% 0.33/0.61 = ( insert_int @ A @ bot_bot_set_int ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % atLeastAtMost_singleton'
% 0.33/0.61 thf(fact_5390_atLeastAtMost__singleton_H,axiom,
% 0.33/0.61 ! [A: nat,B: nat] :
% 0.33/0.61 ( ( A = B )
% 0.33/0.61 => ( ( set_or1269000886237332187st_nat @ A @ B )
% 0.33/0.61 = ( insert_nat @ A @ bot_bot_set_nat ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % atLeastAtMost_singleton'
% 0.33/0.61 thf(fact_5391_atLeastAtMost__singleton_H,axiom,
% 0.33/0.61 ! [A: code_integer,B: code_integer] :
% 0.33/0.61 ( ( A = B )
% 0.33/0.61 => ( ( set_or189985376899183464nteger @ A @ B )
% 0.33/0.61 = ( insert_Code_integer @ A @ bot_bo3990330152332043303nteger ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % atLeastAtMost_singleton'
% 0.33/0.61 thf(fact_5392_remove__subset,axiom,
% 0.33/0.61 ! [X: produc3843707927480180839at_nat,S2: set_Pr4329608150637261639at_nat] :
% 0.33/0.61 ( ( member8757157785044589968at_nat @ X @ S2 )
% 0.33/0.61 => ( ord_le2604355607129572851at_nat @ ( minus_3314409938677909166at_nat @ S2 @ ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) ) @ S2 ) ) ).
% 0.33/0.61
% 0.33/0.61 % remove_subset
% 0.33/0.61 thf(fact_5393_remove__subset,axiom,
% 0.33/0.61 ! [X: product_prod_nat_nat,S2: set_Pr1261947904930325089at_nat] :
% 0.33/0.61 ( ( member8440522571783428010at_nat @ X @ S2 )
% 0.33/0.61 => ( ord_le7866589430770878221at_nat @ ( minus_1356011639430497352at_nat @ S2 @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) @ S2 ) ) ).
% 0.33/0.61
% 0.33/0.61 % remove_subset
% 0.33/0.61 thf(fact_5394_remove__subset,axiom,
% 0.33/0.61 ! [X: $o,S2: set_o] :
% 0.33/0.61 ( ( member_o @ X @ S2 )
% 0.33/0.61 => ( ord_less_set_o @ ( minus_minus_set_o @ S2 @ ( insert_o @ X @ bot_bot_set_o ) ) @ S2 ) ) ).
% 0.33/0.61
% 0.33/0.61 % remove_subset
% 0.33/0.61 thf(fact_5395_remove__subset,axiom,
% 0.33/0.61 ! [X: int,S2: set_int] :
% 0.33/0.61 ( ( member_int @ X @ S2 )
% 0.33/0.61 => ( ord_less_set_int @ ( minus_minus_set_int @ S2 @ ( insert_int @ X @ bot_bot_set_int ) ) @ S2 ) ) ).
% 0.33/0.61
% 0.33/0.61 % remove_subset
% 0.33/0.61 thf(fact_5396_remove__subset,axiom,
% 0.33/0.61 ! [X: nat,S2: set_nat] :
% 0.33/0.61 ( ( member_nat @ X @ S2 )
% 0.33/0.61 => ( ord_less_set_nat @ ( minus_minus_set_nat @ S2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) @ S2 ) ) ).
% 0.33/0.61
% 0.33/0.61 % remove_subset
% 0.33/0.61 thf(fact_5397_nat__of__integer__def,axiom,
% 0.33/0.61 ( code_nat_of_integer
% 0.33/0.61 = ( map_fu6539832666145259331at_nat @ code_int_of_integer @ id_nat @ nat2 ) ) ).
% 0.33/0.61
% 0.33/0.61 % nat_of_integer_def
% 0.33/0.61 thf(fact_5398_bit__integer__def,axiom,
% 0.33/0.61 ( bit_se9216721137139052372nteger
% 0.33/0.61 = ( map_fu186220595405829473_nat_o @ code_int_of_integer @ id_nat_o @ bit_se1146084159140164899it_int ) ) ).
% 0.33/0.61
% 0.33/0.61 % bit_integer_def
% 0.33/0.61 thf(fact_5399_mask__integer__def,axiom,
% 0.33/0.61 ( bit_se2119862282449309892nteger
% 0.33/0.61 = ( map_fu6290471996055670595nteger @ id_nat @ code_integer_of_int @ bit_se2000444600071755411sk_int ) ) ).
% 0.33/0.61
% 0.33/0.61 % mask_integer_def
% 0.33/0.61 thf(fact_5400_atLeastLessThan__eq__atLeastAtMost__diff,axiom,
% 0.33/0.61 ( set_or7139685690850216873Than_o
% 0.33/0.61 = ( ^ [A5: $o,B4: $o] : ( minus_minus_set_o @ ( set_or8904488021354931149Most_o @ A5 @ B4 ) @ ( insert_o @ B4 @ bot_bot_set_o ) ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % atLeastLessThan_eq_atLeastAtMost_diff
% 0.33/0.61 thf(fact_5401_atLeastLessThan__eq__atLeastAtMost__diff,axiom,
% 0.33/0.61 ( set_or4665077453230672383an_nat
% 0.33/0.61 = ( ^ [A5: nat,B4: nat] : ( minus_minus_set_nat @ ( set_or1269000886237332187st_nat @ A5 @ B4 ) @ ( insert_nat @ B4 @ bot_bot_set_nat ) ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % atLeastLessThan_eq_atLeastAtMost_diff
% 0.33/0.61 thf(fact_5402_atLeastLessThan__eq__atLeastAtMost__diff,axiom,
% 0.33/0.61 ( set_or8404916559141939852nteger
% 0.33/0.61 = ( ^ [A5: code_integer,B4: code_integer] : ( minus_2355218937544613996nteger @ ( set_or189985376899183464nteger @ A5 @ B4 ) @ ( insert_Code_integer @ B4 @ bot_bo3990330152332043303nteger ) ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % atLeastLessThan_eq_atLeastAtMost_diff
% 0.33/0.61 thf(fact_5403_atLeastLessThan__eq__atLeastAtMost__diff,axiom,
% 0.33/0.61 ( set_or4662586982721622107an_int
% 0.33/0.61 = ( ^ [A5: int,B4: int] : ( minus_minus_set_int @ ( set_or1266510415728281911st_int @ A5 @ B4 ) @ ( insert_int @ B4 @ bot_bot_set_int ) ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % atLeastLessThan_eq_atLeastAtMost_diff
% 0.33/0.61 thf(fact_5404_atLeastAtMostPlus1__int__conv,axiom,
% 0.33/0.61 ! [M2: int,N2: int] :
% 0.33/0.61 ( ( ord_less_eq_int @ M2 @ ( plus_plus_int @ one_one_int @ N2 ) )
% 0.33/0.61 => ( ( set_or1266510415728281911st_int @ M2 @ ( plus_plus_int @ one_one_int @ N2 ) )
% 0.33/0.61 = ( insert_int @ ( plus_plus_int @ one_one_int @ N2 ) @ ( set_or1266510415728281911st_int @ M2 @ N2 ) ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % atLeastAtMostPlus1_int_conv
% 0.33/0.61 thf(fact_5405_simp__from__to,axiom,
% 0.33/0.61 ( set_or1266510415728281911st_int
% 0.33/0.61 = ( ^ [I3: int,J2: int] : ( if_set_int @ ( ord_less_int @ J2 @ I3 ) @ bot_bot_set_int @ ( insert_int @ I3 @ ( set_or1266510415728281911st_int @ ( plus_plus_int @ I3 @ one_one_int ) @ J2 ) ) ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % simp_from_to
% 0.33/0.61 thf(fact_5406_Code__Numeral_Osub__def,axiom,
% 0.33/0.61 ( code_sub
% 0.33/0.61 = ( map_fu6891787308814931657nteger @ id_num @ ( map_fu8638147718074629079nteger @ id_num @ code_integer_of_int )
% 0.33/0.61 @ ^ [M: num,N4: num] : ( minus_minus_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N4 ) ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % Code_Numeral.sub_def
% 0.33/0.61 thf(fact_5407_num__of__integer__def,axiom,
% 0.33/0.61 ( code_num_of_integer
% 0.33/0.61 = ( map_fu1227494855608507351um_num @ code_int_of_integer @ id_num @ ( comp_nat_num_int @ num_of_nat @ nat2 ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % num_of_integer_def
% 0.33/0.61 thf(fact_5408_take__bit__integer__def,axiom,
% 0.33/0.61 ( bit_se1745604003318907178nteger
% 0.33/0.61 = ( map_fu8224359078269604234nteger @ id_nat @ ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int ) @ bit_se2923211474154528505it_int ) ) ).
% 0.33/0.61
% 0.33/0.61 % take_bit_integer_def
% 0.33/0.61 thf(fact_5409_drop__bit__integer__def,axiom,
% 0.33/0.61 ( bit_se3928097537394005634nteger
% 0.33/0.61 = ( map_fu8224359078269604234nteger @ id_nat @ ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int ) @ bit_se8568078237143864401it_int ) ) ).
% 0.33/0.61
% 0.33/0.61 % drop_bit_integer_def
% 0.33/0.61 thf(fact_5410_push__bit__integer__def,axiom,
% 0.33/0.61 ( bit_se7788150548672797655nteger
% 0.33/0.61 = ( map_fu8224359078269604234nteger @ id_nat @ ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int ) @ bit_se545348938243370406it_int ) ) ).
% 0.33/0.61
% 0.33/0.61 % push_bit_integer_def
% 0.33/0.61 thf(fact_5411_unset__bit__integer__def,axiom,
% 0.33/0.61 ( bit_se8260200283734997820nteger
% 0.33/0.61 = ( map_fu8224359078269604234nteger @ id_nat @ ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int ) @ bit_se4203085406695923979it_int ) ) ).
% 0.33/0.61
% 0.33/0.61 % unset_bit_integer_def
% 0.33/0.61 thf(fact_5412_set__bit__integer__def,axiom,
% 0.33/0.61 ( bit_se2793503036327961859nteger
% 0.33/0.61 = ( map_fu8224359078269604234nteger @ id_nat @ ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int ) @ bit_se7879613467334960850it_int ) ) ).
% 0.33/0.61
% 0.33/0.61 % set_bit_integer_def
% 0.33/0.61 thf(fact_5413_flip__bit__integer__def,axiom,
% 0.33/0.61 ( bit_se1345352211410354436nteger
% 0.33/0.61 = ( map_fu8224359078269604234nteger @ id_nat @ ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int ) @ bit_se2159334234014336723it_int ) ) ).
% 0.33/0.61
% 0.33/0.61 % flip_bit_integer_def
% 0.33/0.61 thf(fact_5414_pair__leqI1,axiom,
% 0.33/0.61 ! [A: nat,B: nat,S: nat,T: nat] :
% 0.33/0.61 ( ( ord_less_nat @ A @ B )
% 0.33/0.61 => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A @ S ) @ ( product_Pair_nat_nat @ B @ T ) ) @ fun_pair_leq ) ) ).
% 0.33/0.61
% 0.33/0.61 % pair_leqI1
% 0.33/0.61 thf(fact_5415_image__minus__const__atLeastLessThan__nat,axiom,
% 0.33/0.61 ! [C: nat,Y: nat,X: nat] :
% 0.33/0.61 ( ( ( ord_less_nat @ C @ Y )
% 0.33/0.61 => ( ( image_nat_nat
% 0.33/0.61 @ ^ [I3: nat] : ( minus_minus_nat @ I3 @ C )
% 0.33/0.61 @ ( set_or4665077453230672383an_nat @ X @ Y ) )
% 0.33/0.61 = ( set_or4665077453230672383an_nat @ ( minus_minus_nat @ X @ C ) @ ( minus_minus_nat @ Y @ C ) ) ) )
% 0.33/0.61 & ( ~ ( ord_less_nat @ C @ Y )
% 0.33/0.61 => ( ( ( ord_less_nat @ X @ Y )
% 0.33/0.61 => ( ( image_nat_nat
% 0.33/0.61 @ ^ [I3: nat] : ( minus_minus_nat @ I3 @ C )
% 0.33/0.61 @ ( set_or4665077453230672383an_nat @ X @ Y ) )
% 0.33/0.61 = ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) )
% 0.33/0.61 & ( ~ ( ord_less_nat @ X @ Y )
% 0.33/0.61 => ( ( image_nat_nat
% 0.33/0.61 @ ^ [I3: nat] : ( minus_minus_nat @ I3 @ C )
% 0.33/0.61 @ ( set_or4665077453230672383an_nat @ X @ Y ) )
% 0.33/0.61 = bot_bot_set_nat ) ) ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % image_minus_const_atLeastLessThan_nat
% 0.33/0.61 thf(fact_5416_card__atLeastAtMost__int,axiom,
% 0.33/0.61 ! [L: int,U: int] :
% 0.33/0.61 ( ( finite_card_int @ ( set_or1266510415728281911st_int @ L @ U ) )
% 0.33/0.61 = ( nat2 @ ( plus_plus_int @ ( minus_minus_int @ U @ L ) @ one_one_int ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % card_atLeastAtMost_int
% 0.33/0.61 thf(fact_5417_range__mod,axiom,
% 0.33/0.61 ! [N2: nat] :
% 0.33/0.61 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.33/0.61 => ( ( image_nat_nat
% 0.33/0.61 @ ^ [M: nat] : ( modulo_modulo_nat @ M @ N2 )
% 0.33/0.61 @ top_top_set_nat )
% 0.33/0.61 = ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % range_mod
% 0.33/0.61 thf(fact_5418_Some__image__these__eq,axiom,
% 0.33/0.61 ! [A2: set_op3940070208846178154it_nat] :
% 0.33/0.61 ( ( image_4799632500972785611it_nat @ some_P6105628898608307625it_nat @ ( these_6645423997822192641it_nat @ A2 ) )
% 0.33/0.61 = ( collec8141831914148684149it_nat
% 0.33/0.61 @ ^ [X3: option3216581401566546698it_nat] :
% 0.33/0.61 ( ( member3517700364412436275it_nat @ X3 @ A2 )
% 0.33/0.61 & ( X3 != none_P2587165478634041381it_nat ) ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % Some_image_these_eq
% 0.33/0.61 thf(fact_5419_Some__image__these__eq,axiom,
% 0.33/0.61 ! [A2: set_option_num] :
% 0.33/0.61 ( ( image_num_option_num @ some_num @ ( these_num @ A2 ) )
% 0.33/0.61 = ( collect_option_num
% 0.33/0.61 @ ^ [X3: option_num] :
% 0.33/0.61 ( ( member_option_num @ X3 @ A2 )
% 0.33/0.61 & ( X3 != none_num ) ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % Some_image_these_eq
% 0.33/0.61 thf(fact_5420_Some__image__these__eq,axiom,
% 0.33/0.61 ! [A2: set_op239864471688321678it_nat] :
% 0.33/0.61 ( ( image_3455408117458022631it_nat @ some_P1914260805536162275it_nat @ ( these_3407724651694999947it_nat @ A2 ) )
% 0.33/0.61 = ( collec5742531119322951597it_nat
% 0.33/0.61 @ ^ [X3: option8956607266484857688it_nat] :
% 0.33/0.61 ( ( member5596548051065438575it_nat @ X3 @ A2 )
% 0.33/0.61 & ( X3 != none_P9117596204409417319it_nat ) ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % Some_image_these_eq
% 0.33/0.61 thf(fact_5421_prod__mono2,axiom,
% 0.33/0.61 ! [B5: set_o,A2: set_o,F: $o > code_integer] :
% 0.33/0.61 ( ( finite_finite_o @ B5 )
% 0.33/0.61 => ( ( ord_less_eq_set_o @ A2 @ B5 )
% 0.33/0.61 => ( ! [B2: $o] :
% 0.33/0.61 ( ( member_o @ B2 @ ( minus_minus_set_o @ B5 @ A2 ) )
% 0.33/0.61 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F @ B2 ) ) )
% 0.33/0.61 => ( ! [A3: $o] :
% 0.33/0.61 ( ( member_o @ A3 @ A2 )
% 0.33/0.61 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ A3 ) ) )
% 0.33/0.61 => ( ord_le3102999989581377725nteger @ ( groups7694694392188491536nteger @ F @ A2 ) @ ( groups7694694392188491536nteger @ F @ B5 ) ) ) ) ) ) ).
% 0.33/0.61
% 0.33/0.61 % prod_mono2
% 0.33/0.61 thf(fact_5422_prod__mono2,axiom,
% 0.33/0.61 ! [B5: set_int,A2: set_int,F: int > code_integer] :
% 0.33/0.61 ( ( finite_finite_int @ B5 )
% 0.33/0.61 => ( ( ord_less_eq_set_int @ A2 @ B5 )
% 0.33/0.61 => ( ! [B2: int] :
% 0.33/0.62 ( ( member_int @ B2 @ ( minus_minus_set_int @ B5 @ A2 ) )
% 0.33/0.62 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F @ B2 ) ) )
% 0.33/0.62 => ( ! [A3: int] :
% 0.33/0.62 ( ( member_int @ A3 @ A2 )
% 0.33/0.62 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ A3 ) ) )
% 0.33/0.62 => ( ord_le3102999989581377725nteger @ ( groups3827104343326376752nteger @ F @ A2 ) @ ( groups3827104343326376752nteger @ F @ B5 ) ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % prod_mono2
% 0.33/0.62 thf(fact_5423_prod__mono2,axiom,
% 0.33/0.62 ! [B5: set_Code_integer,A2: set_Code_integer,F: code_integer > code_integer] :
% 0.33/0.62 ( ( finite6017078050557962740nteger @ B5 )
% 0.33/0.62 => ( ( ord_le7084787975880047091nteger @ A2 @ B5 )
% 0.33/0.62 => ( ! [B2: code_integer] :
% 0.33/0.62 ( ( member_Code_integer @ B2 @ ( minus_2355218937544613996nteger @ B5 @ A2 ) )
% 0.33/0.62 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F @ B2 ) ) )
% 0.33/0.62 => ( ! [A3: code_integer] :
% 0.33/0.62 ( ( member_Code_integer @ A3 @ A2 )
% 0.33/0.62 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ A3 ) ) )
% 0.33/0.62 => ( ord_le3102999989581377725nteger @ ( groups3674199335183972705nteger @ F @ A2 ) @ ( groups3674199335183972705nteger @ F @ B5 ) ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % prod_mono2
% 0.33/0.62 thf(fact_5424_prod__mono2,axiom,
% 0.33/0.62 ! [B5: set_o,A2: set_o,F: $o > rat] :
% 0.33/0.62 ( ( finite_finite_o @ B5 )
% 0.33/0.62 => ( ( ord_less_eq_set_o @ A2 @ B5 )
% 0.33/0.62 => ( ! [B2: $o] :
% 0.33/0.62 ( ( member_o @ B2 @ ( minus_minus_set_o @ B5 @ A2 ) )
% 0.33/0.62 => ( ord_less_eq_rat @ one_one_rat @ ( F @ B2 ) ) )
% 0.33/0.62 => ( ! [A3: $o] :
% 0.33/0.62 ( ( member_o @ A3 @ A2 )
% 0.33/0.62 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ A3 ) ) )
% 0.33/0.62 => ( ord_less_eq_rat @ ( groups2869687844427037835_o_rat @ F @ A2 ) @ ( groups2869687844427037835_o_rat @ F @ B5 ) ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % prod_mono2
% 0.33/0.62 thf(fact_5425_prod__mono2,axiom,
% 0.33/0.62 ! [B5: set_int,A2: set_int,F: int > rat] :
% 0.33/0.62 ( ( finite_finite_int @ B5 )
% 0.33/0.62 => ( ( ord_less_eq_set_int @ A2 @ B5 )
% 0.33/0.62 => ( ! [B2: int] :
% 0.33/0.62 ( ( member_int @ B2 @ ( minus_minus_set_int @ B5 @ A2 ) )
% 0.33/0.62 => ( ord_less_eq_rat @ one_one_rat @ ( F @ B2 ) ) )
% 0.33/0.62 => ( ! [A3: int] :
% 0.33/0.62 ( ( member_int @ A3 @ A2 )
% 0.33/0.62 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ A3 ) ) )
% 0.33/0.62 => ( ord_less_eq_rat @ ( groups1072433553688619179nt_rat @ F @ A2 ) @ ( groups1072433553688619179nt_rat @ F @ B5 ) ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % prod_mono2
% 0.33/0.62 thf(fact_5426_prod__mono2,axiom,
% 0.33/0.62 ! [B5: set_Code_integer,A2: set_Code_integer,F: code_integer > rat] :
% 0.33/0.62 ( ( finite6017078050557962740nteger @ B5 )
% 0.33/0.62 => ( ( ord_le7084787975880047091nteger @ A2 @ B5 )
% 0.33/0.62 => ( ! [B2: code_integer] :
% 0.33/0.62 ( ( member_Code_integer @ B2 @ ( minus_2355218937544613996nteger @ B5 @ A2 ) )
% 0.33/0.62 => ( ord_less_eq_rat @ one_one_rat @ ( F @ B2 ) ) )
% 0.33/0.62 => ( ! [A3: code_integer] :
% 0.33/0.62 ( ( member_Code_integer @ A3 @ A2 )
% 0.33/0.62 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ A3 ) ) )
% 0.33/0.62 => ( ord_less_eq_rat @ ( groups2555765274223993564er_rat @ F @ A2 ) @ ( groups2555765274223993564er_rat @ F @ B5 ) ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % prod_mono2
% 0.33/0.62 thf(fact_5427_prod__mono2,axiom,
% 0.33/0.62 ! [B5: set_o,A2: set_o,F: $o > int] :
% 0.33/0.62 ( ( finite_finite_o @ B5 )
% 0.33/0.62 => ( ( ord_less_eq_set_o @ A2 @ B5 )
% 0.33/0.62 => ( ! [B2: $o] :
% 0.33/0.62 ( ( member_o @ B2 @ ( minus_minus_set_o @ B5 @ A2 ) )
% 0.33/0.62 => ( ord_less_eq_int @ one_one_int @ ( F @ B2 ) ) )
% 0.33/0.62 => ( ! [A3: $o] :
% 0.33/0.62 ( ( member_o @ A3 @ A2 )
% 0.33/0.62 => ( ord_less_eq_int @ zero_zero_int @ ( F @ A3 ) ) )
% 0.33/0.62 => ( ord_less_eq_int @ ( groups3502327434004483295_o_int @ F @ A2 ) @ ( groups3502327434004483295_o_int @ F @ B5 ) ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % prod_mono2
% 0.33/0.62 thf(fact_5428_prod__mono2,axiom,
% 0.33/0.62 ! [B5: set_Code_integer,A2: set_Code_integer,F: code_integer > int] :
% 0.33/0.62 ( ( finite6017078050557962740nteger @ B5 )
% 0.33/0.62 => ( ( ord_le7084787975880047091nteger @ A2 @ B5 )
% 0.33/0.62 => ( ! [B2: code_integer] :
% 0.33/0.62 ( ( member_Code_integer @ B2 @ ( minus_2355218937544613996nteger @ B5 @ A2 ) )
% 0.33/0.62 => ( ord_less_eq_int @ one_one_int @ ( F @ B2 ) ) )
% 0.33/0.62 => ( ! [A3: code_integer] :
% 0.33/0.62 ( ( member_Code_integer @ A3 @ A2 )
% 0.33/0.62 => ( ord_less_eq_int @ zero_zero_int @ ( F @ A3 ) ) )
% 0.33/0.62 => ( ord_less_eq_int @ ( groups3188404863801439024er_int @ F @ A2 ) @ ( groups3188404863801439024er_int @ F @ B5 ) ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % prod_mono2
% 0.33/0.62 thf(fact_5429_prod__mono2,axiom,
% 0.33/0.62 ! [B5: set_nat,A2: set_nat,F: nat > code_integer] :
% 0.33/0.62 ( ( finite_finite_nat @ B5 )
% 0.33/0.62 => ( ( ord_less_eq_set_nat @ A2 @ B5 )
% 0.33/0.62 => ( ! [B2: nat] :
% 0.33/0.62 ( ( member_nat @ B2 @ ( minus_minus_set_nat @ B5 @ A2 ) )
% 0.33/0.62 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F @ B2 ) ) )
% 0.33/0.62 => ( ! [A3: nat] :
% 0.33/0.62 ( ( member_nat @ A3 @ A2 )
% 0.33/0.62 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ A3 ) ) )
% 0.33/0.62 => ( ord_le3102999989581377725nteger @ ( groups3455450783089532116nteger @ F @ A2 ) @ ( groups3455450783089532116nteger @ F @ B5 ) ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % prod_mono2
% 0.33/0.62 thf(fact_5430_prod__mono2,axiom,
% 0.33/0.62 ! [B5: set_nat,A2: set_nat,F: nat > rat] :
% 0.33/0.62 ( ( finite_finite_nat @ B5 )
% 0.33/0.62 => ( ( ord_less_eq_set_nat @ A2 @ B5 )
% 0.33/0.62 => ( ! [B2: nat] :
% 0.33/0.62 ( ( member_nat @ B2 @ ( minus_minus_set_nat @ B5 @ A2 ) )
% 0.33/0.62 => ( ord_less_eq_rat @ one_one_rat @ ( F @ B2 ) ) )
% 0.33/0.62 => ( ! [A3: nat] :
% 0.33/0.62 ( ( member_nat @ A3 @ A2 )
% 0.33/0.62 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ A3 ) ) )
% 0.33/0.62 => ( ord_less_eq_rat @ ( groups73079841787564623at_rat @ F @ A2 ) @ ( groups73079841787564623at_rat @ F @ B5 ) ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % prod_mono2
% 0.33/0.62 thf(fact_5431_the__dflt__None__nonempty,axiom,
% 0.33/0.62 ! [S2: set_Pr4329608150637261639at_nat] :
% 0.33/0.62 ( ( S2 != bot_bo228742789529271731at_nat )
% 0.33/0.62 => ( ( dflt_N3208751546879591902at_nat @ S2 )
% 0.33/0.62 = ( some_s5890477192898017836at_nat @ S2 ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % the_dflt_None_nonempty
% 0.33/0.62 thf(fact_5432_the__dflt__None__nonempty,axiom,
% 0.33/0.62 ! [S2: set_Pr1261947904930325089at_nat] :
% 0.33/0.62 ( ( S2 != bot_bo2099793752762293965at_nat )
% 0.33/0.62 => ( ( dflt_N6592383573632408824at_nat @ S2 )
% 0.33/0.62 = ( some_s147305329494351046at_nat @ S2 ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % the_dflt_None_nonempty
% 0.33/0.62 thf(fact_5433_the__dflt__None__nonempty,axiom,
% 0.33/0.62 ! [S2: set_o] :
% 0.33/0.62 ( ( S2 != bot_bot_set_o )
% 0.33/0.62 => ( ( dflt_None_set_o @ S2 )
% 0.33/0.62 = ( some_set_o @ S2 ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % the_dflt_None_nonempty
% 0.33/0.62 thf(fact_5434_the__dflt__None__nonempty,axiom,
% 0.33/0.62 ! [S2: set_nat] :
% 0.33/0.62 ( ( S2 != bot_bot_set_nat )
% 0.33/0.62 => ( ( dflt_None_set_nat @ S2 )
% 0.33/0.62 = ( some_set_nat @ S2 ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % the_dflt_None_nonempty
% 0.33/0.62 thf(fact_5435_the__dflt__None__nonempty,axiom,
% 0.33/0.62 ! [S2: set_int] :
% 0.33/0.62 ( ( S2 != bot_bot_set_int )
% 0.33/0.62 => ( ( dflt_None_set_int @ S2 )
% 0.33/0.62 = ( some_set_int @ S2 ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % the_dflt_None_nonempty
% 0.33/0.62 thf(fact_5436_the__dflt__None__empty,axiom,
% 0.33/0.62 ( ( dflt_N3208751546879591902at_nat @ bot_bo228742789529271731at_nat )
% 0.33/0.62 = none_s6518873173954064040at_nat ) ).
% 0.33/0.62
% 0.33/0.62 % the_dflt_None_empty
% 0.33/0.62 thf(fact_5437_the__dflt__None__empty,axiom,
% 0.33/0.62 ( ( dflt_N6592383573632408824at_nat @ bot_bo2099793752762293965at_nat )
% 0.33/0.62 = none_s625347054029921090at_nat ) ).
% 0.33/0.62
% 0.33/0.62 % the_dflt_None_empty
% 0.33/0.62 thf(fact_5438_the__dflt__None__empty,axiom,
% 0.33/0.62 ( ( dflt_None_set_o @ bot_bot_set_o )
% 0.33/0.62 = none_set_o ) ).
% 0.33/0.62
% 0.33/0.62 % the_dflt_None_empty
% 0.33/0.62 thf(fact_5439_the__dflt__None__empty,axiom,
% 0.33/0.62 ( ( dflt_None_set_nat @ bot_bot_set_nat )
% 0.33/0.62 = none_set_nat ) ).
% 0.33/0.62
% 0.33/0.62 % the_dflt_None_empty
% 0.33/0.62 thf(fact_5440_the__dflt__None__empty,axiom,
% 0.33/0.62 ( ( dflt_None_set_int @ bot_bot_set_int )
% 0.33/0.62 = none_set_int ) ).
% 0.33/0.62
% 0.33/0.62 % the_dflt_None_empty
% 0.33/0.62 thf(fact_5441_atMost__UNIV__triv,axiom,
% 0.33/0.62 ( ( set_or4236626031148496127et_nat @ top_top_set_nat )
% 0.33/0.62 = top_top_set_set_nat ) ).
% 0.33/0.62
% 0.33/0.62 % atMost_UNIV_triv
% 0.33/0.62 thf(fact_5442_atMost__UNIV__triv,axiom,
% 0.33/0.62 ( ( set_or2827140217781692084t_unit @ top_to1996260823553986621t_unit )
% 0.33/0.62 = top_to1767297665138865437t_unit ) ).
% 0.33/0.62
% 0.33/0.62 % atMost_UNIV_triv
% 0.33/0.62 thf(fact_5443_atMost__UNIV__triv,axiom,
% 0.33/0.62 ( ( set_or58775011639299419et_int @ top_top_set_int )
% 0.33/0.62 = top_top_set_set_int ) ).
% 0.33/0.62
% 0.33/0.62 % atMost_UNIV_triv
% 0.33/0.62 thf(fact_5444_finite__atLeastAtMost,axiom,
% 0.33/0.62 ! [L: nat,U: nat] : ( finite_finite_nat @ ( set_or1269000886237332187st_nat @ L @ U ) ) ).
% 0.33/0.62
% 0.33/0.62 % finite_atLeastAtMost
% 0.33/0.62 thf(fact_5445_finite__atLeastLessThan,axiom,
% 0.33/0.62 ! [L: nat,U: nat] : ( finite_finite_nat @ ( set_or4665077453230672383an_nat @ L @ U ) ) ).
% 0.33/0.62
% 0.33/0.62 % finite_atLeastLessThan
% 0.33/0.62 thf(fact_5446_int__of__integer__min,axiom,
% 0.33/0.62 ! [K: code_integer,L: code_integer] :
% 0.33/0.62 ( ( code_int_of_integer @ ( ord_min_Code_integer @ K @ L ) )
% 0.33/0.62 = ( ord_min_int @ ( code_int_of_integer @ K ) @ ( code_int_of_integer @ L ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % int_of_integer_min
% 0.33/0.62 thf(fact_5447_finite__atMost,axiom,
% 0.33/0.62 ! [K: nat] : ( finite_finite_nat @ ( set_ord_atMost_nat @ K ) ) ).
% 0.33/0.62
% 0.33/0.62 % finite_atMost
% 0.33/0.62 thf(fact_5448_finite__lessThan,axiom,
% 0.33/0.62 ! [K: nat] : ( finite_finite_nat @ ( set_ord_lessThan_nat @ K ) ) ).
% 0.33/0.62
% 0.33/0.62 % finite_lessThan
% 0.33/0.62 thf(fact_5449_finite__atLeastAtMost__int,axiom,
% 0.33/0.62 ! [L: int,U: int] : ( finite_finite_int @ ( set_or1266510415728281911st_int @ L @ U ) ) ).
% 0.33/0.62
% 0.33/0.62 % finite_atLeastAtMost_int
% 0.33/0.62 thf(fact_5450_finite__atLeastLessThan__int,axiom,
% 0.33/0.62 ! [L: int,U: int] : ( finite_finite_int @ ( set_or4662586982721622107an_int @ L @ U ) ) ).
% 0.33/0.62
% 0.33/0.62 % finite_atLeastLessThan_int
% 0.33/0.62 thf(fact_5451_finite__atLeastLessThan__integer,axiom,
% 0.33/0.62 ! [L: code_integer,U: code_integer] : ( finite6017078050557962740nteger @ ( set_or8404916559141939852nteger @ L @ U ) ) ).
% 0.33/0.62
% 0.33/0.62 % finite_atLeastLessThan_integer
% 0.33/0.62 thf(fact_5452_finite__atLeastAtMost__integer,axiom,
% 0.33/0.62 ! [L: code_integer,U: code_integer] : ( finite6017078050557962740nteger @ ( set_or189985376899183464nteger @ L @ U ) ) ).
% 0.33/0.62
% 0.33/0.62 % finite_atLeastAtMost_integer
% 0.33/0.62 thf(fact_5453_finite__option__UNIV,axiom,
% 0.33/0.62 ( ( finite6785661671136154180nteger @ top_to5929521628599800467nteger )
% 0.33/0.62 = ( finite6017078050557962740nteger @ top_to4645266643341252675nteger ) ) ).
% 0.33/0.62
% 0.33/0.62 % finite_option_UNIV
% 0.33/0.62 thf(fact_5454_finite__option__UNIV,axiom,
% 0.33/0.62 ( ( finite6732403688824079472at_nat @ top_to3251141154256563319at_nat )
% 0.33/0.62 = ( finite6177210948735845034at_nat @ top_to4669805908274784177at_nat ) ) ).
% 0.33/0.62
% 0.33/0.62 % finite_option_UNIV
% 0.33/0.62 thf(fact_5455_finite__option__UNIV,axiom,
% 0.33/0.62 ( ( finite5523153139673422903on_nat @ top_to8920198386146353926on_nat )
% 0.33/0.62 = ( finite_finite_nat @ top_top_set_nat ) ) ).
% 0.33/0.62
% 0.33/0.62 % finite_option_UNIV
% 0.33/0.62 thf(fact_5456_finite__option__UNIV,axiom,
% 0.33/0.62 ( ( finite1445617369574913404t_unit @ top_to2690860209552263555t_unit )
% 0.33/0.62 = ( finite4290736615968046902t_unit @ top_to1996260823553986621t_unit ) ) ).
% 0.33/0.62
% 0.33/0.62 % finite_option_UNIV
% 0.33/0.62 thf(fact_5457_finite__option__UNIV,axiom,
% 0.33/0.62 ( ( finite1345302120164226195on_int @ top_to6430115241214627170on_int )
% 0.33/0.62 = ( finite_finite_int @ top_top_set_int ) ) ).
% 0.33/0.62
% 0.33/0.62 % finite_option_UNIV
% 0.33/0.62 thf(fact_5458_card__eq__UNIV,axiom,
% 0.33/0.62 ! [S2: set_Product_unit] :
% 0.33/0.62 ( ( ( finite410649719033368117t_unit @ S2 )
% 0.33/0.62 = ( finite410649719033368117t_unit @ top_to1996260823553986621t_unit ) )
% 0.33/0.62 = ( S2 = top_to1996260823553986621t_unit ) ) ).
% 0.33/0.62
% 0.33/0.62 % card_eq_UNIV
% 0.33/0.62 thf(fact_5459_card__eq__UNIV2,axiom,
% 0.33/0.62 ! [S2: set_Product_unit] :
% 0.33/0.62 ( ( ( finite410649719033368117t_unit @ top_to1996260823553986621t_unit )
% 0.33/0.62 = ( finite410649719033368117t_unit @ S2 ) )
% 0.33/0.62 = ( S2 = top_to1996260823553986621t_unit ) ) ).
% 0.33/0.62
% 0.33/0.62 % card_eq_UNIV2
% 0.33/0.62 thf(fact_5460_these__empty,axiom,
% 0.33/0.62 ( ( these_1872268174106123684at_nat @ bot_bo1471150103859235065at_nat )
% 0.33/0.62 = bot_bo228742789529271731at_nat ) ).
% 0.33/0.62
% 0.33/0.62 % these_empty
% 0.33/0.62 thf(fact_5461_these__empty,axiom,
% 0.33/0.62 ( ( these_8061402112538453438at_nat @ bot_bo3414888551220300179at_nat )
% 0.33/0.62 = bot_bo2099793752762293965at_nat ) ).
% 0.33/0.62
% 0.33/0.62 % these_empty
% 0.33/0.62 thf(fact_5462_these__empty,axiom,
% 0.33/0.62 ( ( these_o @ bot_bot_set_option_o )
% 0.33/0.62 = bot_bot_set_o ) ).
% 0.33/0.62
% 0.33/0.62 % these_empty
% 0.33/0.62 thf(fact_5463_these__empty,axiom,
% 0.33/0.62 ( ( these_nat @ bot_bo5009843511495006442on_nat )
% 0.33/0.62 = bot_bot_set_nat ) ).
% 0.33/0.62
% 0.33/0.62 % these_empty
% 0.33/0.62 thf(fact_5464_these__empty,axiom,
% 0.33/0.62 ( ( these_int @ bot_bo2519760366563279686on_int )
% 0.33/0.62 = bot_bot_set_int ) ).
% 0.33/0.62
% 0.33/0.62 % these_empty
% 0.33/0.62 thf(fact_5465_these__insert__None,axiom,
% 0.33/0.62 ! [A2: set_op3940070208846178154it_nat] :
% 0.33/0.62 ( ( these_6645423997822192641it_nat @ ( insert7468008629046257882it_nat @ none_P2587165478634041381it_nat @ A2 ) )
% 0.33/0.62 = ( these_6645423997822192641it_nat @ A2 ) ) ).
% 0.33/0.62
% 0.33/0.62 % these_insert_None
% 0.33/0.62 thf(fact_5466_these__insert__None,axiom,
% 0.33/0.62 ! [A2: set_option_num] :
% 0.33/0.62 ( ( these_num @ ( insert_option_num @ none_num @ A2 ) )
% 0.33/0.62 = ( these_num @ A2 ) ) ).
% 0.33/0.62
% 0.33/0.62 % these_insert_None
% 0.33/0.62 thf(fact_5467_these__insert__None,axiom,
% 0.33/0.62 ! [A2: set_op239864471688321678it_nat] :
% 0.33/0.62 ( ( these_3407724651694999947it_nat @ ( insert2007652293347934600it_nat @ none_P9117596204409417319it_nat @ A2 ) )
% 0.33/0.62 = ( these_3407724651694999947it_nat @ A2 ) ) ).
% 0.33/0.62
% 0.33/0.62 % these_insert_None
% 0.33/0.62 thf(fact_5468_the__dflt__None__set,axiom,
% 0.33/0.62 ! [X: set_Pr4329608150637261639at_nat] :
% 0.33/0.62 ( ( the_de6830073021511528542at_nat @ bot_bo228742789529271731at_nat @ ( dflt_N3208751546879591902at_nat @ X ) )
% 0.33/0.62 = X ) ).
% 0.33/0.62
% 0.33/0.62 % the_dflt_None_set
% 0.33/0.62 thf(fact_5469_the__dflt__None__set,axiom,
% 0.33/0.62 ! [X: set_Pr1261947904930325089at_nat] :
% 0.33/0.62 ( ( the_de3668382347305825784at_nat @ bot_bo2099793752762293965at_nat @ ( dflt_N6592383573632408824at_nat @ X ) )
% 0.33/0.62 = X ) ).
% 0.33/0.62
% 0.33/0.62 % the_dflt_None_set
% 0.33/0.62 thf(fact_5470_the__dflt__None__set,axiom,
% 0.33/0.62 ! [X: set_o] :
% 0.33/0.62 ( ( the_default_set_o @ bot_bot_set_o @ ( dflt_None_set_o @ X ) )
% 0.33/0.62 = X ) ).
% 0.33/0.62
% 0.33/0.62 % the_dflt_None_set
% 0.33/0.62 thf(fact_5471_the__dflt__None__set,axiom,
% 0.33/0.62 ! [X: set_nat] :
% 0.33/0.62 ( ( the_default_set_nat @ bot_bot_set_nat @ ( dflt_None_set_nat @ X ) )
% 0.33/0.62 = X ) ).
% 0.33/0.62
% 0.33/0.62 % the_dflt_None_set
% 0.33/0.62 thf(fact_5472_the__dflt__None__set,axiom,
% 0.33/0.62 ! [X: set_int] :
% 0.33/0.62 ( ( the_default_set_int @ bot_bot_set_int @ ( dflt_None_set_int @ X ) )
% 0.33/0.62 = X ) ).
% 0.33/0.62
% 0.33/0.62 % the_dflt_None_set
% 0.33/0.62 thf(fact_5473_surj__plus,axiom,
% 0.33/0.62 ! [A: rat] :
% 0.33/0.62 ( ( image_rat_rat @ ( plus_plus_rat @ A ) @ top_top_set_rat )
% 0.33/0.62 = top_top_set_rat ) ).
% 0.33/0.62
% 0.33/0.62 % surj_plus
% 0.33/0.62 thf(fact_5474_surj__plus,axiom,
% 0.33/0.62 ! [A: int] :
% 0.33/0.62 ( ( image_int_int @ ( plus_plus_int @ A ) @ top_top_set_int )
% 0.33/0.62 = top_top_set_int ) ).
% 0.33/0.62
% 0.33/0.62 % surj_plus
% 0.33/0.62 thf(fact_5475_infinite__Icc__iff,axiom,
% 0.33/0.62 ! [A: rat,B: rat] :
% 0.33/0.62 ( ( ~ ( finite_finite_rat @ ( set_or633870826150836451st_rat @ A @ B ) ) )
% 0.33/0.62 = ( ord_less_rat @ A @ B ) ) ).
% 0.33/0.62
% 0.33/0.62 % infinite_Icc_iff
% 0.33/0.62 thf(fact_5476_infinite__Ico__iff,axiom,
% 0.33/0.62 ! [A: rat,B: rat] :
% 0.33/0.62 ( ( ~ ( finite_finite_rat @ ( set_or4029947393144176647an_rat @ A @ B ) ) )
% 0.33/0.62 = ( ord_less_rat @ A @ B ) ) ).
% 0.33/0.62
% 0.33/0.62 % infinite_Ico_iff
% 0.33/0.62 thf(fact_5477_prod_Oinfinite,axiom,
% 0.33/0.62 ! [A2: set_nat,G: nat > code_integer] :
% 0.33/0.62 ( ~ ( finite_finite_nat @ A2 )
% 0.33/0.62 => ( ( groups3455450783089532116nteger @ G @ A2 )
% 0.33/0.62 = one_one_Code_integer ) ) ).
% 0.33/0.62
% 0.33/0.62 % prod.infinite
% 0.33/0.62 thf(fact_5478_prod_Oinfinite,axiom,
% 0.33/0.62 ! [A2: set_int,G: int > code_integer] :
% 0.33/0.62 ( ~ ( finite_finite_int @ A2 )
% 0.33/0.62 => ( ( groups3827104343326376752nteger @ G @ A2 )
% 0.33/0.62 = one_one_Code_integer ) ) ).
% 0.33/0.62
% 0.33/0.62 % prod.infinite
% 0.33/0.62 thf(fact_5479_prod_Oinfinite,axiom,
% 0.33/0.62 ! [A2: set_Code_integer,G: code_integer > code_integer] :
% 0.33/0.62 ( ~ ( finite6017078050557962740nteger @ A2 )
% 0.33/0.62 => ( ( groups3674199335183972705nteger @ G @ A2 )
% 0.33/0.62 = one_one_Code_integer ) ) ).
% 0.33/0.62
% 0.33/0.62 % prod.infinite
% 0.33/0.62 thf(fact_5480_prod_Oinfinite,axiom,
% 0.33/0.62 ! [A2: set_nat,G: nat > assn] :
% 0.33/0.62 ( ~ ( finite_finite_nat @ A2 )
% 0.33/0.62 => ( ( groups6906906614972039071t_assn @ G @ A2 )
% 0.33/0.62 = one_one_assn ) ) ).
% 0.33/0.62
% 0.33/0.62 % prod.infinite
% 0.33/0.62 thf(fact_5481_prod_Oinfinite,axiom,
% 0.33/0.62 ! [A2: set_int,G: int > assn] :
% 0.33/0.62 ( ~ ( finite_finite_int @ A2 )
% 0.33/0.62 => ( ( groups7882442080178216443t_assn @ G @ A2 )
% 0.33/0.62 = one_one_assn ) ) ).
% 0.33/0.62
% 0.33/0.62 % prod.infinite
% 0.33/0.62 thf(fact_5482_prod_Oinfinite,axiom,
% 0.33/0.62 ! [A2: set_Code_integer,G: code_integer > assn] :
% 0.33/0.62 ( ~ ( finite6017078050557962740nteger @ A2 )
% 0.33/0.62 => ( ( groups1304777262505850412r_assn @ G @ A2 )
% 0.33/0.62 = one_one_assn ) ) ).
% 0.33/0.62
% 0.33/0.62 % prod.infinite
% 0.33/0.62 thf(fact_5483_prod_Oinfinite,axiom,
% 0.33/0.62 ! [A2: set_nat,G: nat > rat] :
% 0.33/0.62 ( ~ ( finite_finite_nat @ A2 )
% 0.33/0.62 => ( ( groups73079841787564623at_rat @ G @ A2 )
% 0.33/0.62 = one_one_rat ) ) ).
% 0.33/0.62
% 0.33/0.62 % prod.infinite
% 0.33/0.62 thf(fact_5484_prod_Oinfinite,axiom,
% 0.33/0.62 ! [A2: set_int,G: int > rat] :
% 0.33/0.62 ( ~ ( finite_finite_int @ A2 )
% 0.33/0.62 => ( ( groups1072433553688619179nt_rat @ G @ A2 )
% 0.33/0.62 = one_one_rat ) ) ).
% 0.33/0.62
% 0.33/0.62 % prod.infinite
% 0.33/0.62 thf(fact_5485_prod_Oinfinite,axiom,
% 0.33/0.62 ! [A2: set_Code_integer,G: code_integer > rat] :
% 0.33/0.62 ( ~ ( finite6017078050557962740nteger @ A2 )
% 0.33/0.62 => ( ( groups2555765274223993564er_rat @ G @ A2 )
% 0.33/0.62 = one_one_rat ) ) ).
% 0.33/0.62
% 0.33/0.62 % prod.infinite
% 0.33/0.62 thf(fact_5486_prod_Oinfinite,axiom,
% 0.33/0.62 ! [A2: set_int,G: int > nat] :
% 0.33/0.62 ( ~ ( finite_finite_int @ A2 )
% 0.33/0.62 => ( ( groups1707563613775114915nt_nat @ G @ A2 )
% 0.33/0.62 = one_one_nat ) ) ).
% 0.33/0.62
% 0.33/0.62 % prod.infinite
% 0.33/0.62 thf(fact_5487_card__ge__UNIV,axiom,
% 0.33/0.62 ! [S2: set_Product_unit] :
% 0.33/0.62 ( ( ord_less_eq_nat @ ( finite410649719033368117t_unit @ top_to1996260823553986621t_unit ) @ ( finite410649719033368117t_unit @ S2 ) )
% 0.33/0.62 = ( S2 = top_to1996260823553986621t_unit ) ) ).
% 0.33/0.62
% 0.33/0.62 % card_ge_UNIV
% 0.33/0.62 thf(fact_5488_surj__diff__right,axiom,
% 0.33/0.62 ! [A: code_integer] :
% 0.33/0.62 ( ( image_4470545334726330049nteger
% 0.33/0.62 @ ^ [X3: code_integer] : ( minus_8373710615458151222nteger @ X3 @ A )
% 0.33/0.62 @ top_to4645266643341252675nteger )
% 0.33/0.62 = top_to4645266643341252675nteger ) ).
% 0.33/0.62
% 0.33/0.62 % surj_diff_right
% 0.33/0.62 thf(fact_5489_surj__diff__right,axiom,
% 0.33/0.62 ! [A: rat] :
% 0.33/0.62 ( ( image_rat_rat
% 0.33/0.62 @ ^ [X3: rat] : ( minus_minus_rat @ X3 @ A )
% 0.33/0.62 @ top_top_set_rat )
% 0.33/0.62 = top_top_set_rat ) ).
% 0.33/0.62
% 0.33/0.62 % surj_diff_right
% 0.33/0.62 thf(fact_5490_surj__diff__right,axiom,
% 0.33/0.62 ! [A: int] :
% 0.33/0.62 ( ( image_int_int
% 0.33/0.62 @ ^ [X3: int] : ( minus_minus_int @ X3 @ A )
% 0.33/0.62 @ top_top_set_int )
% 0.33/0.62 = top_top_set_int ) ).
% 0.33/0.62
% 0.33/0.62 % surj_diff_right
% 0.33/0.62 thf(fact_5491_prod__eq__1__iff,axiom,
% 0.33/0.62 ! [A2: set_int,F: int > nat] :
% 0.33/0.62 ( ( finite_finite_int @ A2 )
% 0.33/0.62 => ( ( ( groups1707563613775114915nt_nat @ F @ A2 )
% 0.33/0.62 = one_one_nat )
% 0.33/0.62 = ( ! [X3: int] :
% 0.33/0.62 ( ( member_int @ X3 @ A2 )
% 0.33/0.62 => ( ( F @ X3 )
% 0.33/0.62 = one_one_nat ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % prod_eq_1_iff
% 0.33/0.62 thf(fact_5492_prod__eq__1__iff,axiom,
% 0.33/0.62 ! [A2: set_Code_integer,F: code_integer > nat] :
% 0.33/0.62 ( ( finite6017078050557962740nteger @ A2 )
% 0.33/0.62 => ( ( ( groups3190895334310489300er_nat @ F @ A2 )
% 0.33/0.62 = one_one_nat )
% 0.33/0.62 = ( ! [X3: code_integer] :
% 0.33/0.62 ( ( member_Code_integer @ X3 @ A2 )
% 0.33/0.62 => ( ( F @ X3 )
% 0.33/0.62 = one_one_nat ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % prod_eq_1_iff
% 0.33/0.62 thf(fact_5493_prod__eq__1__iff,axiom,
% 0.33/0.62 ! [A2: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > nat] :
% 0.33/0.62 ( ( finite6177210948735845034at_nat @ A2 )
% 0.33/0.62 => ( ( ( groups4077766827762148844at_nat @ F @ A2 )
% 0.33/0.62 = one_one_nat )
% 0.33/0.62 = ( ! [X3: product_prod_nat_nat] :
% 0.33/0.62 ( ( member8440522571783428010at_nat @ X3 @ A2 )
% 0.33/0.62 => ( ( F @ X3 )
% 0.33/0.62 = one_one_nat ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % prod_eq_1_iff
% 0.33/0.62 thf(fact_5494_prod__eq__1__iff,axiom,
% 0.33/0.62 ! [A2: set_nat,F: nat > nat] :
% 0.33/0.62 ( ( finite_finite_nat @ A2 )
% 0.33/0.62 => ( ( ( groups708209901874060359at_nat @ F @ A2 )
% 0.33/0.62 = one_one_nat )
% 0.33/0.62 = ( ! [X3: nat] :
% 0.33/0.62 ( ( member_nat @ X3 @ A2 )
% 0.33/0.62 => ( ( F @ X3 )
% 0.33/0.62 = one_one_nat ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % prod_eq_1_iff
% 0.33/0.62 thf(fact_5495_prod_Odelta,axiom,
% 0.33/0.62 ! [S2: set_o,A: $o,B: $o > code_integer] :
% 0.33/0.62 ( ( finite_finite_o @ S2 )
% 0.33/0.62 => ( ( ( member_o @ A @ S2 )
% 0.33/0.62 => ( ( groups7694694392188491536nteger
% 0.33/0.62 @ ^ [K4: $o] : ( if_Code_integer @ ( K4 = A ) @ ( B @ K4 ) @ one_one_Code_integer )
% 0.33/0.62 @ S2 )
% 0.33/0.62 = ( B @ A ) ) )
% 0.33/0.62 & ( ~ ( member_o @ A @ S2 )
% 0.33/0.62 => ( ( groups7694694392188491536nteger
% 0.33/0.62 @ ^ [K4: $o] : ( if_Code_integer @ ( K4 = A ) @ ( B @ K4 ) @ one_one_Code_integer )
% 0.33/0.62 @ S2 )
% 0.33/0.62 = one_one_Code_integer ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % prod.delta
% 0.33/0.62 thf(fact_5496_prod_Odelta,axiom,
% 0.33/0.62 ! [S2: set_nat,A: nat,B: nat > code_integer] :
% 0.33/0.62 ( ( finite_finite_nat @ S2 )
% 0.33/0.62 => ( ( ( member_nat @ A @ S2 )
% 0.33/0.62 => ( ( groups3455450783089532116nteger
% 0.33/0.62 @ ^ [K4: nat] : ( if_Code_integer @ ( K4 = A ) @ ( B @ K4 ) @ one_one_Code_integer )
% 0.33/0.62 @ S2 )
% 0.33/0.62 = ( B @ A ) ) )
% 0.33/0.62 & ( ~ ( member_nat @ A @ S2 )
% 0.33/0.62 => ( ( groups3455450783089532116nteger
% 0.33/0.62 @ ^ [K4: nat] : ( if_Code_integer @ ( K4 = A ) @ ( B @ K4 ) @ one_one_Code_integer )
% 0.33/0.62 @ S2 )
% 0.33/0.62 = one_one_Code_integer ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % prod.delta
% 0.33/0.62 thf(fact_5497_prod_Odelta,axiom,
% 0.33/0.62 ! [S2: set_int,A: int,B: int > code_integer] :
% 0.33/0.62 ( ( finite_finite_int @ S2 )
% 0.33/0.62 => ( ( ( member_int @ A @ S2 )
% 0.33/0.62 => ( ( groups3827104343326376752nteger
% 0.33/0.62 @ ^ [K4: int] : ( if_Code_integer @ ( K4 = A ) @ ( B @ K4 ) @ one_one_Code_integer )
% 0.33/0.62 @ S2 )
% 0.33/0.62 = ( B @ A ) ) )
% 0.33/0.62 & ( ~ ( member_int @ A @ S2 )
% 0.33/0.62 => ( ( groups3827104343326376752nteger
% 0.33/0.62 @ ^ [K4: int] : ( if_Code_integer @ ( K4 = A ) @ ( B @ K4 ) @ one_one_Code_integer )
% 0.33/0.62 @ S2 )
% 0.33/0.62 = one_one_Code_integer ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % prod.delta
% 0.33/0.62 thf(fact_5498_prod_Odelta,axiom,
% 0.33/0.62 ! [S2: set_Code_integer,A: code_integer,B: code_integer > code_integer] :
% 0.33/0.62 ( ( finite6017078050557962740nteger @ S2 )
% 0.33/0.62 => ( ( ( member_Code_integer @ A @ S2 )
% 0.33/0.62 => ( ( groups3674199335183972705nteger
% 0.33/0.62 @ ^ [K4: code_integer] : ( if_Code_integer @ ( K4 = A ) @ ( B @ K4 ) @ one_one_Code_integer )
% 0.33/0.62 @ S2 )
% 0.33/0.62 = ( B @ A ) ) )
% 0.33/0.62 & ( ~ ( member_Code_integer @ A @ S2 )
% 0.33/0.62 => ( ( groups3674199335183972705nteger
% 0.33/0.62 @ ^ [K4: code_integer] : ( if_Code_integer @ ( K4 = A ) @ ( B @ K4 ) @ one_one_Code_integer )
% 0.33/0.62 @ S2 )
% 0.33/0.62 = one_one_Code_integer ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % prod.delta
% 0.33/0.62 thf(fact_5499_prod_Odelta,axiom,
% 0.33/0.62 ! [S2: set_o,A: $o,B: $o > assn] :
% 0.33/0.62 ( ( finite_finite_o @ S2 )
% 0.33/0.62 => ( ( ( member_o @ A @ S2 )
% 0.33/0.62 => ( ( groups5301882518646026715o_assn
% 0.33/0.62 @ ^ [K4: $o] : ( if_assn @ ( K4 = A ) @ ( B @ K4 ) @ one_one_assn )
% 0.33/0.62 @ S2 )
% 0.33/0.62 = ( B @ A ) ) )
% 0.33/0.62 & ( ~ ( member_o @ A @ S2 )
% 0.33/0.62 => ( ( groups5301882518646026715o_assn
% 0.33/0.62 @ ^ [K4: $o] : ( if_assn @ ( K4 = A ) @ ( B @ K4 ) @ one_one_assn )
% 0.33/0.62 @ S2 )
% 0.33/0.62 = one_one_assn ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % prod.delta
% 0.33/0.62 thf(fact_5500_prod_Odelta,axiom,
% 0.33/0.62 ! [S2: set_nat,A: nat,B: nat > assn] :
% 0.33/0.62 ( ( finite_finite_nat @ S2 )
% 0.33/0.62 => ( ( ( member_nat @ A @ S2 )
% 0.33/0.62 => ( ( groups6906906614972039071t_assn
% 0.33/0.62 @ ^ [K4: nat] : ( if_assn @ ( K4 = A ) @ ( B @ K4 ) @ one_one_assn )
% 0.33/0.62 @ S2 )
% 0.33/0.62 = ( B @ A ) ) )
% 0.33/0.62 & ( ~ ( member_nat @ A @ S2 )
% 0.33/0.62 => ( ( groups6906906614972039071t_assn
% 0.33/0.62 @ ^ [K4: nat] : ( if_assn @ ( K4 = A ) @ ( B @ K4 ) @ one_one_assn )
% 0.33/0.62 @ S2 )
% 0.33/0.62 = one_one_assn ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % prod.delta
% 0.33/0.62 thf(fact_5501_prod_Odelta,axiom,
% 0.33/0.62 ! [S2: set_int,A: int,B: int > assn] :
% 0.33/0.62 ( ( finite_finite_int @ S2 )
% 0.33/0.62 => ( ( ( member_int @ A @ S2 )
% 0.33/0.62 => ( ( groups7882442080178216443t_assn
% 0.33/0.62 @ ^ [K4: int] : ( if_assn @ ( K4 = A ) @ ( B @ K4 ) @ one_one_assn )
% 0.33/0.62 @ S2 )
% 0.33/0.62 = ( B @ A ) ) )
% 0.33/0.62 & ( ~ ( member_int @ A @ S2 )
% 0.33/0.62 => ( ( groups7882442080178216443t_assn
% 0.33/0.62 @ ^ [K4: int] : ( if_assn @ ( K4 = A ) @ ( B @ K4 ) @ one_one_assn )
% 0.33/0.62 @ S2 )
% 0.33/0.62 = one_one_assn ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % prod.delta
% 0.33/0.62 thf(fact_5502_prod_Odelta,axiom,
% 0.33/0.62 ! [S2: set_Code_integer,A: code_integer,B: code_integer > assn] :
% 0.33/0.62 ( ( finite6017078050557962740nteger @ S2 )
% 0.33/0.62 => ( ( ( member_Code_integer @ A @ S2 )
% 0.33/0.62 => ( ( groups1304777262505850412r_assn
% 0.33/0.62 @ ^ [K4: code_integer] : ( if_assn @ ( K4 = A ) @ ( B @ K4 ) @ one_one_assn )
% 0.33/0.62 @ S2 )
% 0.33/0.62 = ( B @ A ) ) )
% 0.33/0.62 & ( ~ ( member_Code_integer @ A @ S2 )
% 0.33/0.62 => ( ( groups1304777262505850412r_assn
% 0.33/0.62 @ ^ [K4: code_integer] : ( if_assn @ ( K4 = A ) @ ( B @ K4 ) @ one_one_assn )
% 0.33/0.62 @ S2 )
% 0.33/0.62 = one_one_assn ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % prod.delta
% 0.33/0.62 thf(fact_5503_prod_Odelta,axiom,
% 0.33/0.62 ! [S2: set_o,A: $o,B: $o > rat] :
% 0.33/0.62 ( ( finite_finite_o @ S2 )
% 0.33/0.62 => ( ( ( member_o @ A @ S2 )
% 0.33/0.62 => ( ( groups2869687844427037835_o_rat
% 0.33/0.62 @ ^ [K4: $o] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ one_one_rat )
% 0.33/0.62 @ S2 )
% 0.33/0.62 = ( B @ A ) ) )
% 0.33/0.62 & ( ~ ( member_o @ A @ S2 )
% 0.33/0.62 => ( ( groups2869687844427037835_o_rat
% 0.33/0.62 @ ^ [K4: $o] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ one_one_rat )
% 0.33/0.62 @ S2 )
% 0.33/0.62 = one_one_rat ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % prod.delta
% 0.33/0.62 thf(fact_5504_prod_Odelta,axiom,
% 0.33/0.62 ! [S2: set_nat,A: nat,B: nat > rat] :
% 0.33/0.62 ( ( finite_finite_nat @ S2 )
% 0.33/0.62 => ( ( ( member_nat @ A @ S2 )
% 0.33/0.62 => ( ( groups73079841787564623at_rat
% 0.33/0.62 @ ^ [K4: nat] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ one_one_rat )
% 0.33/0.62 @ S2 )
% 0.33/0.62 = ( B @ A ) ) )
% 0.33/0.62 & ( ~ ( member_nat @ A @ S2 )
% 0.33/0.62 => ( ( groups73079841787564623at_rat
% 0.33/0.62 @ ^ [K4: nat] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ one_one_rat )
% 0.33/0.62 @ S2 )
% 0.33/0.62 = one_one_rat ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % prod.delta
% 0.33/0.62 thf(fact_5505_prod_Odelta_H,axiom,
% 0.33/0.62 ! [S2: set_o,A: $o,B: $o > code_integer] :
% 0.33/0.62 ( ( finite_finite_o @ S2 )
% 0.33/0.62 => ( ( ( member_o @ A @ S2 )
% 0.33/0.62 => ( ( groups7694694392188491536nteger
% 0.33/0.62 @ ^ [K4: $o] : ( if_Code_integer @ ( A = K4 ) @ ( B @ K4 ) @ one_one_Code_integer )
% 0.33/0.62 @ S2 )
% 0.33/0.62 = ( B @ A ) ) )
% 0.33/0.62 & ( ~ ( member_o @ A @ S2 )
% 0.33/0.62 => ( ( groups7694694392188491536nteger
% 0.33/0.62 @ ^ [K4: $o] : ( if_Code_integer @ ( A = K4 ) @ ( B @ K4 ) @ one_one_Code_integer )
% 0.33/0.62 @ S2 )
% 0.33/0.62 = one_one_Code_integer ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % prod.delta'
% 0.33/0.62 thf(fact_5506_prod_Odelta_H,axiom,
% 0.33/0.62 ! [S2: set_nat,A: nat,B: nat > code_integer] :
% 0.33/0.62 ( ( finite_finite_nat @ S2 )
% 0.33/0.62 => ( ( ( member_nat @ A @ S2 )
% 0.33/0.62 => ( ( groups3455450783089532116nteger
% 0.33/0.62 @ ^ [K4: nat] : ( if_Code_integer @ ( A = K4 ) @ ( B @ K4 ) @ one_one_Code_integer )
% 0.33/0.62 @ S2 )
% 0.33/0.62 = ( B @ A ) ) )
% 0.33/0.62 & ( ~ ( member_nat @ A @ S2 )
% 0.33/0.62 => ( ( groups3455450783089532116nteger
% 0.33/0.62 @ ^ [K4: nat] : ( if_Code_integer @ ( A = K4 ) @ ( B @ K4 ) @ one_one_Code_integer )
% 0.33/0.62 @ S2 )
% 0.33/0.62 = one_one_Code_integer ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % prod.delta'
% 0.33/0.62 thf(fact_5507_prod_Odelta_H,axiom,
% 0.33/0.62 ! [S2: set_int,A: int,B: int > code_integer] :
% 0.33/0.62 ( ( finite_finite_int @ S2 )
% 0.33/0.62 => ( ( ( member_int @ A @ S2 )
% 0.33/0.62 => ( ( groups3827104343326376752nteger
% 0.33/0.62 @ ^ [K4: int] : ( if_Code_integer @ ( A = K4 ) @ ( B @ K4 ) @ one_one_Code_integer )
% 0.33/0.62 @ S2 )
% 0.33/0.62 = ( B @ A ) ) )
% 0.33/0.62 & ( ~ ( member_int @ A @ S2 )
% 0.33/0.62 => ( ( groups3827104343326376752nteger
% 0.33/0.62 @ ^ [K4: int] : ( if_Code_integer @ ( A = K4 ) @ ( B @ K4 ) @ one_one_Code_integer )
% 0.33/0.62 @ S2 )
% 0.33/0.62 = one_one_Code_integer ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % prod.delta'
% 0.33/0.62 thf(fact_5508_prod_Odelta_H,axiom,
% 0.33/0.62 ! [S2: set_Code_integer,A: code_integer,B: code_integer > code_integer] :
% 0.33/0.62 ( ( finite6017078050557962740nteger @ S2 )
% 0.33/0.62 => ( ( ( member_Code_integer @ A @ S2 )
% 0.33/0.62 => ( ( groups3674199335183972705nteger
% 0.33/0.62 @ ^ [K4: code_integer] : ( if_Code_integer @ ( A = K4 ) @ ( B @ K4 ) @ one_one_Code_integer )
% 0.33/0.62 @ S2 )
% 0.33/0.62 = ( B @ A ) ) )
% 0.33/0.62 & ( ~ ( member_Code_integer @ A @ S2 )
% 0.33/0.62 => ( ( groups3674199335183972705nteger
% 0.33/0.62 @ ^ [K4: code_integer] : ( if_Code_integer @ ( A = K4 ) @ ( B @ K4 ) @ one_one_Code_integer )
% 0.33/0.62 @ S2 )
% 0.33/0.62 = one_one_Code_integer ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % prod.delta'
% 0.33/0.62 thf(fact_5509_prod_Odelta_H,axiom,
% 0.33/0.62 ! [S2: set_o,A: $o,B: $o > assn] :
% 0.33/0.62 ( ( finite_finite_o @ S2 )
% 0.33/0.62 => ( ( ( member_o @ A @ S2 )
% 0.33/0.62 => ( ( groups5301882518646026715o_assn
% 0.33/0.62 @ ^ [K4: $o] : ( if_assn @ ( A = K4 ) @ ( B @ K4 ) @ one_one_assn )
% 0.33/0.62 @ S2 )
% 0.33/0.62 = ( B @ A ) ) )
% 0.33/0.62 & ( ~ ( member_o @ A @ S2 )
% 0.33/0.62 => ( ( groups5301882518646026715o_assn
% 0.33/0.62 @ ^ [K4: $o] : ( if_assn @ ( A = K4 ) @ ( B @ K4 ) @ one_one_assn )
% 0.33/0.62 @ S2 )
% 0.33/0.62 = one_one_assn ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % prod.delta'
% 0.33/0.62 thf(fact_5510_prod_Odelta_H,axiom,
% 0.33/0.62 ! [S2: set_nat,A: nat,B: nat > assn] :
% 0.33/0.62 ( ( finite_finite_nat @ S2 )
% 0.33/0.62 => ( ( ( member_nat @ A @ S2 )
% 0.33/0.62 => ( ( groups6906906614972039071t_assn
% 0.33/0.62 @ ^ [K4: nat] : ( if_assn @ ( A = K4 ) @ ( B @ K4 ) @ one_one_assn )
% 0.33/0.62 @ S2 )
% 0.33/0.62 = ( B @ A ) ) )
% 0.33/0.62 & ( ~ ( member_nat @ A @ S2 )
% 0.33/0.62 => ( ( groups6906906614972039071t_assn
% 0.33/0.62 @ ^ [K4: nat] : ( if_assn @ ( A = K4 ) @ ( B @ K4 ) @ one_one_assn )
% 0.33/0.62 @ S2 )
% 0.33/0.62 = one_one_assn ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % prod.delta'
% 0.33/0.62 thf(fact_5511_prod_Odelta_H,axiom,
% 0.33/0.62 ! [S2: set_int,A: int,B: int > assn] :
% 0.33/0.62 ( ( finite_finite_int @ S2 )
% 0.33/0.62 => ( ( ( member_int @ A @ S2 )
% 0.33/0.62 => ( ( groups7882442080178216443t_assn
% 0.33/0.62 @ ^ [K4: int] : ( if_assn @ ( A = K4 ) @ ( B @ K4 ) @ one_one_assn )
% 0.33/0.62 @ S2 )
% 0.33/0.62 = ( B @ A ) ) )
% 0.33/0.62 & ( ~ ( member_int @ A @ S2 )
% 0.33/0.62 => ( ( groups7882442080178216443t_assn
% 0.33/0.62 @ ^ [K4: int] : ( if_assn @ ( A = K4 ) @ ( B @ K4 ) @ one_one_assn )
% 0.33/0.62 @ S2 )
% 0.33/0.62 = one_one_assn ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % prod.delta'
% 0.33/0.62 thf(fact_5512_prod_Odelta_H,axiom,
% 0.33/0.62 ! [S2: set_Code_integer,A: code_integer,B: code_integer > assn] :
% 0.33/0.62 ( ( finite6017078050557962740nteger @ S2 )
% 0.33/0.62 => ( ( ( member_Code_integer @ A @ S2 )
% 0.33/0.62 => ( ( groups1304777262505850412r_assn
% 0.33/0.62 @ ^ [K4: code_integer] : ( if_assn @ ( A = K4 ) @ ( B @ K4 ) @ one_one_assn )
% 0.33/0.62 @ S2 )
% 0.33/0.62 = ( B @ A ) ) )
% 0.33/0.62 & ( ~ ( member_Code_integer @ A @ S2 )
% 0.33/0.62 => ( ( groups1304777262505850412r_assn
% 0.33/0.62 @ ^ [K4: code_integer] : ( if_assn @ ( A = K4 ) @ ( B @ K4 ) @ one_one_assn )
% 0.33/0.62 @ S2 )
% 0.33/0.62 = one_one_assn ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % prod.delta'
% 0.33/0.62 thf(fact_5513_prod_Odelta_H,axiom,
% 0.33/0.62 ! [S2: set_o,A: $o,B: $o > rat] :
% 0.33/0.62 ( ( finite_finite_o @ S2 )
% 0.33/0.62 => ( ( ( member_o @ A @ S2 )
% 0.33/0.62 => ( ( groups2869687844427037835_o_rat
% 0.33/0.62 @ ^ [K4: $o] : ( if_rat @ ( A = K4 ) @ ( B @ K4 ) @ one_one_rat )
% 0.33/0.62 @ S2 )
% 0.33/0.62 = ( B @ A ) ) )
% 0.33/0.62 & ( ~ ( member_o @ A @ S2 )
% 0.33/0.62 => ( ( groups2869687844427037835_o_rat
% 0.33/0.62 @ ^ [K4: $o] : ( if_rat @ ( A = K4 ) @ ( B @ K4 ) @ one_one_rat )
% 0.33/0.62 @ S2 )
% 0.33/0.62 = one_one_rat ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % prod.delta'
% 0.33/0.62 thf(fact_5514_prod_Odelta_H,axiom,
% 0.33/0.62 ! [S2: set_nat,A: nat,B: nat > rat] :
% 0.33/0.62 ( ( finite_finite_nat @ S2 )
% 0.33/0.62 => ( ( ( member_nat @ A @ S2 )
% 0.33/0.62 => ( ( groups73079841787564623at_rat
% 0.33/0.62 @ ^ [K4: nat] : ( if_rat @ ( A = K4 ) @ ( B @ K4 ) @ one_one_rat )
% 0.33/0.62 @ S2 )
% 0.33/0.62 = ( B @ A ) ) )
% 0.33/0.62 & ( ~ ( member_nat @ A @ S2 )
% 0.33/0.62 => ( ( groups73079841787564623at_rat
% 0.33/0.62 @ ^ [K4: nat] : ( if_rat @ ( A = K4 ) @ ( B @ K4 ) @ one_one_rat )
% 0.33/0.62 @ S2 )
% 0.33/0.62 = one_one_rat ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % prod.delta'
% 0.33/0.62 thf(fact_5515_these__insert__Some,axiom,
% 0.33/0.62 ! [X: produc3843707927480180839at_nat,A2: set_op989438649584373901at_nat] :
% 0.33/0.62 ( ( these_1872268174106123684at_nat @ ( insert6833468608972679677at_nat @ ( some_P131194445498448716at_nat @ X ) @ A2 ) )
% 0.33/0.62 = ( insert9069300056098147895at_nat @ X @ ( these_1872268174106123684at_nat @ A2 ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % these_insert_Some
% 0.33/0.62 thf(fact_5516_these__insert__Some,axiom,
% 0.33/0.62 ! [X: product_prod_nat_nat,A2: set_op4508134149509766951at_nat] :
% 0.33/0.62 ( ( these_8061402112538453438at_nat @ ( insert6842972033726296599at_nat @ ( some_P7363390416028606310at_nat @ X ) @ A2 ) )
% 0.33/0.62 = ( insert8211810215607154385at_nat @ X @ ( these_8061402112538453438at_nat @ A2 ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % these_insert_Some
% 0.33/0.62 thf(fact_5517_these__insert__Some,axiom,
% 0.33/0.62 ! [X: $o,A2: set_option_o] :
% 0.33/0.62 ( ( these_o @ ( insert_option_o @ ( some_o @ X ) @ A2 ) )
% 0.33/0.62 = ( insert_o @ X @ ( these_o @ A2 ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % these_insert_Some
% 0.33/0.62 thf(fact_5518_these__insert__Some,axiom,
% 0.33/0.62 ! [X: nat,A2: set_option_nat] :
% 0.33/0.62 ( ( these_nat @ ( insert_option_nat @ ( some_nat @ X ) @ A2 ) )
% 0.33/0.62 = ( insert_nat @ X @ ( these_nat @ A2 ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % these_insert_Some
% 0.33/0.62 thf(fact_5519_these__insert__Some,axiom,
% 0.33/0.62 ! [X: int,A2: set_option_int] :
% 0.33/0.62 ( ( these_int @ ( insert_option_int @ ( some_int @ X ) @ A2 ) )
% 0.33/0.62 = ( insert_int @ X @ ( these_int @ A2 ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % these_insert_Some
% 0.33/0.62 thf(fact_5520_these__insert__Some,axiom,
% 0.33/0.62 ! [X: num,A2: set_option_num] :
% 0.33/0.62 ( ( these_num @ ( insert_option_num @ ( some_num @ X ) @ A2 ) )
% 0.33/0.62 = ( insert_num @ X @ ( these_num @ A2 ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % these_insert_Some
% 0.33/0.62 thf(fact_5521_these__insert__Some,axiom,
% 0.33/0.62 ! [X: produc8664842809031399944it_nat,A2: set_op239864471688321678it_nat] :
% 0.33/0.62 ( ( these_3407724651694999947it_nat @ ( insert2007652293347934600it_nat @ ( some_P1914260805536162275it_nat @ X ) @ A2 ) )
% 0.33/0.62 = ( insert5940566491043231800it_nat @ X @ ( these_3407724651694999947it_nat @ A2 ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % these_insert_Some
% 0.33/0.62 thf(fact_5522_these__image__Some__eq,axiom,
% 0.33/0.62 ! [A2: set_num] :
% 0.33/0.62 ( ( these_num @ ( image_num_option_num @ some_num @ A2 ) )
% 0.33/0.62 = A2 ) ).
% 0.33/0.62
% 0.33/0.62 % these_image_Some_eq
% 0.33/0.62 thf(fact_5523_these__image__Some__eq,axiom,
% 0.33/0.62 ! [A2: set_Pr1354866905816374718it_nat] :
% 0.33/0.62 ( ( these_3407724651694999947it_nat @ ( image_3455408117458022631it_nat @ some_P1914260805536162275it_nat @ A2 ) )
% 0.33/0.62 = A2 ) ).
% 0.33/0.62
% 0.33/0.62 % these_image_Some_eq
% 0.33/0.62 thf(fact_5524_sum_Oinsert,axiom,
% 0.33/0.62 ! [A2: set_o,X: $o,G: $o > rat] :
% 0.33/0.62 ( ( finite_finite_o @ A2 )
% 0.33/0.62 => ( ~ ( member_o @ X @ A2 )
% 0.33/0.62 => ( ( groups7872700643590313910_o_rat @ G @ ( insert_o @ X @ A2 ) )
% 0.33/0.62 = ( plus_plus_rat @ ( G @ X ) @ ( groups7872700643590313910_o_rat @ G @ A2 ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % sum.insert
% 0.33/0.62 thf(fact_5525_sum_Oinsert,axiom,
% 0.33/0.62 ! [A2: set_nat,X: nat,G: nat > rat] :
% 0.33/0.62 ( ( finite_finite_nat @ A2 )
% 0.33/0.62 => ( ~ ( member_nat @ X @ A2 )
% 0.33/0.62 => ( ( groups2906978787729119204at_rat @ G @ ( insert_nat @ X @ A2 ) )
% 0.33/0.62 = ( plus_plus_rat @ ( G @ X ) @ ( groups2906978787729119204at_rat @ G @ A2 ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % sum.insert
% 0.33/0.62 thf(fact_5526_sum_Oinsert,axiom,
% 0.33/0.62 ! [A2: set_int,X: int,G: int > rat] :
% 0.33/0.62 ( ( finite_finite_int @ A2 )
% 0.33/0.62 => ( ~ ( member_int @ X @ A2 )
% 0.33/0.62 => ( ( groups3906332499630173760nt_rat @ G @ ( insert_int @ X @ A2 ) )
% 0.33/0.62 = ( plus_plus_rat @ ( G @ X ) @ ( groups3906332499630173760nt_rat @ G @ A2 ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % sum.insert
% 0.33/0.62 thf(fact_5527_sum_Oinsert,axiom,
% 0.33/0.62 ! [A2: set_Code_integer,X: code_integer,G: code_integer > rat] :
% 0.33/0.62 ( ( finite6017078050557962740nteger @ A2 )
% 0.33/0.62 => ( ~ ( member_Code_integer @ X @ A2 )
% 0.33/0.62 => ( ( groups6602215022474089585er_rat @ G @ ( insert_Code_integer @ X @ A2 ) )
% 0.33/0.62 = ( plus_plus_rat @ ( G @ X ) @ ( groups6602215022474089585er_rat @ G @ A2 ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % sum.insert
% 0.33/0.62 thf(fact_5528_sum_Oinsert,axiom,
% 0.33/0.62 ! [A2: set_o,X: $o,G: $o > nat] :
% 0.33/0.62 ( ( finite_finite_o @ A2 )
% 0.33/0.62 => ( ~ ( member_o @ X @ A2 )
% 0.33/0.62 => ( ( groups8507830703676809646_o_nat @ G @ ( insert_o @ X @ A2 ) )
% 0.33/0.62 = ( plus_plus_nat @ ( G @ X ) @ ( groups8507830703676809646_o_nat @ G @ A2 ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % sum.insert
% 0.33/0.62 thf(fact_5529_sum_Oinsert,axiom,
% 0.33/0.62 ! [A2: set_int,X: int,G: int > nat] :
% 0.33/0.62 ( ( finite_finite_int @ A2 )
% 0.33/0.62 => ( ~ ( member_int @ X @ A2 )
% 0.33/0.62 => ( ( groups4541462559716669496nt_nat @ G @ ( insert_int @ X @ A2 ) )
% 0.33/0.62 = ( plus_plus_nat @ ( G @ X ) @ ( groups4541462559716669496nt_nat @ G @ A2 ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % sum.insert
% 0.33/0.62 thf(fact_5530_sum_Oinsert,axiom,
% 0.33/0.62 ! [A2: set_Code_integer,X: code_integer,G: code_integer > nat] :
% 0.33/0.62 ( ( finite6017078050557962740nteger @ A2 )
% 0.33/0.62 => ( ~ ( member_Code_integer @ X @ A2 )
% 0.33/0.62 => ( ( groups7237345082560585321er_nat @ G @ ( insert_Code_integer @ X @ A2 ) )
% 0.33/0.62 = ( plus_plus_nat @ ( G @ X ) @ ( groups7237345082560585321er_nat @ G @ A2 ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % sum.insert
% 0.33/0.62 thf(fact_5531_sum_Oinsert,axiom,
% 0.33/0.62 ! [A2: set_o,X: $o,G: $o > int] :
% 0.33/0.62 ( ( finite_finite_o @ A2 )
% 0.33/0.62 => ( ~ ( member_o @ X @ A2 )
% 0.33/0.62 => ( ( groups8505340233167759370_o_int @ G @ ( insert_o @ X @ A2 ) )
% 0.33/0.62 = ( plus_plus_int @ ( G @ X ) @ ( groups8505340233167759370_o_int @ G @ A2 ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % sum.insert
% 0.33/0.62 thf(fact_5532_sum_Oinsert,axiom,
% 0.33/0.62 ! [A2: set_nat,X: nat,G: nat > int] :
% 0.33/0.62 ( ( finite_finite_nat @ A2 )
% 0.33/0.62 => ( ~ ( member_nat @ X @ A2 )
% 0.33/0.62 => ( ( groups3539618377306564664at_int @ G @ ( insert_nat @ X @ A2 ) )
% 0.33/0.62 = ( plus_plus_int @ ( G @ X ) @ ( groups3539618377306564664at_int @ G @ A2 ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % sum.insert
% 0.33/0.62 thf(fact_5533_sum_Oinsert,axiom,
% 0.33/0.62 ! [A2: set_Code_integer,X: code_integer,G: code_integer > int] :
% 0.33/0.62 ( ( finite6017078050557962740nteger @ A2 )
% 0.33/0.62 => ( ~ ( member_Code_integer @ X @ A2 )
% 0.33/0.62 => ( ( groups7234854612051535045er_int @ G @ ( insert_Code_integer @ X @ A2 ) )
% 0.33/0.62 = ( plus_plus_int @ ( G @ X ) @ ( groups7234854612051535045er_int @ G @ A2 ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % sum.insert
% 0.33/0.62 thf(fact_5534_atLeastLessThan__singleton,axiom,
% 0.33/0.62 ! [M2: nat] :
% 0.33/0.62 ( ( set_or4665077453230672383an_nat @ M2 @ ( suc @ M2 ) )
% 0.33/0.62 = ( insert_nat @ M2 @ bot_bot_set_nat ) ) ).
% 0.33/0.62
% 0.33/0.62 % atLeastLessThan_singleton
% 0.33/0.62 thf(fact_5535_atMost__0,axiom,
% 0.33/0.62 ( ( set_ord_atMost_nat @ zero_zero_nat )
% 0.33/0.62 = ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ).
% 0.33/0.62
% 0.33/0.62 % atMost_0
% 0.33/0.62 thf(fact_5536_card__atLeastLessThan__int,axiom,
% 0.33/0.62 ! [L: int,U: int] :
% 0.33/0.62 ( ( finite_card_int @ ( set_or4662586982721622107an_int @ L @ U ) )
% 0.33/0.62 = ( nat2 @ ( minus_minus_int @ U @ L ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % card_atLeastLessThan_int
% 0.33/0.62 thf(fact_5537_card__doubleton__eq__2__iff,axiom,
% 0.33/0.62 ! [A: product_unit,B: product_unit] :
% 0.33/0.62 ( ( ( finite410649719033368117t_unit @ ( insert_Product_unit @ A @ ( insert_Product_unit @ B @ bot_bo3957492148770167129t_unit ) ) )
% 0.33/0.62 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.33/0.62 = ( A != B ) ) ).
% 0.33/0.62
% 0.33/0.62 % card_doubleton_eq_2_iff
% 0.33/0.62 thf(fact_5538_card__doubleton__eq__2__iff,axiom,
% 0.33/0.62 ! [A: list_nat,B: list_nat] :
% 0.33/0.62 ( ( ( finite_card_list_nat @ ( insert_list_nat @ A @ ( insert_list_nat @ B @ bot_bot_set_list_nat ) ) )
% 0.33/0.62 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.33/0.62 = ( A != B ) ) ).
% 0.33/0.62
% 0.33/0.62 % card_doubleton_eq_2_iff
% 0.33/0.62 thf(fact_5539_card__doubleton__eq__2__iff,axiom,
% 0.33/0.62 ! [A: produc3843707927480180839at_nat,B: produc3843707927480180839at_nat] :
% 0.33/0.62 ( ( ( finite3771342082235030671at_nat @ ( insert9069300056098147895at_nat @ A @ ( insert9069300056098147895at_nat @ B @ bot_bo228742789529271731at_nat ) ) )
% 0.33/0.62 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.33/0.62 = ( A != B ) ) ).
% 0.33/0.62
% 0.33/0.62 % card_doubleton_eq_2_iff
% 0.33/0.62 thf(fact_5540_card__doubleton__eq__2__iff,axiom,
% 0.33/0.62 ! [A: product_prod_nat_nat,B: product_prod_nat_nat] :
% 0.33/0.62 ( ( ( finite711546835091564841at_nat @ ( insert8211810215607154385at_nat @ A @ ( insert8211810215607154385at_nat @ B @ bot_bo2099793752762293965at_nat ) ) )
% 0.33/0.62 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.33/0.62 = ( A != B ) ) ).
% 0.33/0.62
% 0.33/0.62 % card_doubleton_eq_2_iff
% 0.33/0.62 thf(fact_5541_card__doubleton__eq__2__iff,axiom,
% 0.33/0.62 ! [A: $o,B: $o] :
% 0.33/0.62 ( ( ( finite_card_o @ ( insert_o @ A @ ( insert_o @ B @ bot_bot_set_o ) ) )
% 0.33/0.62 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.33/0.62 = ( A != B ) ) ).
% 0.33/0.62
% 0.33/0.62 % card_doubleton_eq_2_iff
% 0.33/0.62 thf(fact_5542_card__doubleton__eq__2__iff,axiom,
% 0.33/0.62 ! [A: nat,B: nat] :
% 0.33/0.62 ( ( ( finite_card_nat @ ( insert_nat @ A @ ( insert_nat @ B @ bot_bot_set_nat ) ) )
% 0.33/0.62 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.33/0.62 = ( A != B ) ) ).
% 0.33/0.62
% 0.33/0.62 % card_doubleton_eq_2_iff
% 0.33/0.62 thf(fact_5543_card__doubleton__eq__2__iff,axiom,
% 0.33/0.62 ! [A: int,B: int] :
% 0.33/0.62 ( ( ( finite_card_int @ ( insert_int @ A @ ( insert_int @ B @ bot_bot_set_int ) ) )
% 0.33/0.62 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.33/0.62 = ( A != B ) ) ).
% 0.33/0.62
% 0.33/0.62 % card_doubleton_eq_2_iff
% 0.33/0.62 thf(fact_5544_atMost__eq__UNIV__iff,axiom,
% 0.33/0.62 ! [X: set_nat] :
% 0.33/0.62 ( ( ( set_or4236626031148496127et_nat @ X )
% 0.33/0.62 = top_top_set_set_nat )
% 0.33/0.62 = ( X = top_top_set_nat ) ) ).
% 0.33/0.62
% 0.33/0.62 % atMost_eq_UNIV_iff
% 0.33/0.62 thf(fact_5545_atMost__eq__UNIV__iff,axiom,
% 0.33/0.62 ! [X: set_Product_unit] :
% 0.33/0.62 ( ( ( set_or2827140217781692084t_unit @ X )
% 0.33/0.62 = top_to1767297665138865437t_unit )
% 0.33/0.62 = ( X = top_to1996260823553986621t_unit ) ) ).
% 0.33/0.62
% 0.33/0.62 % atMost_eq_UNIV_iff
% 0.33/0.62 thf(fact_5546_atMost__eq__UNIV__iff,axiom,
% 0.33/0.62 ! [X: set_int] :
% 0.33/0.62 ( ( ( set_or58775011639299419et_int @ X )
% 0.33/0.62 = top_top_set_set_int )
% 0.33/0.62 = ( X = top_top_set_int ) ) ).
% 0.33/0.62
% 0.33/0.62 % atMost_eq_UNIV_iff
% 0.33/0.62 thf(fact_5547_atMost__eq__UNIV__iff,axiom,
% 0.33/0.62 ! [X: assn] :
% 0.33/0.62 ( ( ( set_ord_atMost_assn @ X )
% 0.33/0.62 = top_top_set_assn )
% 0.33/0.62 = ( X = top_top_assn ) ) ).
% 0.33/0.62
% 0.33/0.62 % atMost_eq_UNIV_iff
% 0.33/0.62 thf(fact_5548_atMost__eq__UNIV__iff,axiom,
% 0.33/0.62 ! [X: product_unit] :
% 0.33/0.62 ( ( ( set_or8621721900777396692t_unit @ X )
% 0.33/0.62 = top_to1996260823553986621t_unit )
% 0.33/0.62 = ( X = top_top_Product_unit ) ) ).
% 0.33/0.62
% 0.33/0.62 % atMost_eq_UNIV_iff
% 0.33/0.62 thf(fact_5549_card__le__if__inj__on__rel,axiom,
% 0.33/0.62 ! [B5: set_o,A2: set_o,R2: $o > $o > $o] :
% 0.33/0.62 ( ( finite_finite_o @ B5 )
% 0.33/0.62 => ( ! [A3: $o] :
% 0.33/0.62 ( ( member_o @ A3 @ A2 )
% 0.33/0.62 => ? [B7: $o] :
% 0.33/0.62 ( ( member_o @ B7 @ B5 )
% 0.33/0.62 & ( R2 @ A3 @ B7 ) ) )
% 0.33/0.62 => ( ! [A13: $o,A24: $o,B2: $o] :
% 0.33/0.62 ( ( member_o @ A13 @ A2 )
% 0.33/0.62 => ( ( member_o @ A24 @ A2 )
% 0.33/0.62 => ( ( member_o @ B2 @ B5 )
% 0.33/0.62 => ( ( R2 @ A13 @ B2 )
% 0.33/0.62 => ( ( R2 @ A24 @ B2 )
% 0.33/0.62 => ( A13 = A24 ) ) ) ) ) )
% 0.33/0.62 => ( ord_less_eq_nat @ ( finite_card_o @ A2 ) @ ( finite_card_o @ B5 ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % card_le_if_inj_on_rel
% 0.33/0.62 thf(fact_5550_card__le__if__inj__on__rel,axiom,
% 0.33/0.62 ! [B5: set_Product_unit,A2: set_o,R2: $o > product_unit > $o] :
% 0.33/0.62 ( ( finite4290736615968046902t_unit @ B5 )
% 0.33/0.62 => ( ! [A3: $o] :
% 0.33/0.62 ( ( member_o @ A3 @ A2 )
% 0.33/0.62 => ? [B7: product_unit] :
% 0.33/0.62 ( ( member_Product_unit @ B7 @ B5 )
% 0.33/0.62 & ( R2 @ A3 @ B7 ) ) )
% 0.33/0.62 => ( ! [A13: $o,A24: $o,B2: product_unit] :
% 0.33/0.62 ( ( member_o @ A13 @ A2 )
% 0.33/0.62 => ( ( member_o @ A24 @ A2 )
% 0.33/0.62 => ( ( member_Product_unit @ B2 @ B5 )
% 0.33/0.62 => ( ( R2 @ A13 @ B2 )
% 0.33/0.62 => ( ( R2 @ A24 @ B2 )
% 0.33/0.62 => ( A13 = A24 ) ) ) ) ) )
% 0.33/0.62 => ( ord_less_eq_nat @ ( finite_card_o @ A2 ) @ ( finite410649719033368117t_unit @ B5 ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % card_le_if_inj_on_rel
% 0.33/0.62 thf(fact_5551_card__le__if__inj__on__rel,axiom,
% 0.33/0.62 ! [B5: set_o,A2: set_int,R2: int > $o > $o] :
% 0.33/0.62 ( ( finite_finite_o @ B5 )
% 0.33/0.62 => ( ! [A3: int] :
% 0.33/0.62 ( ( member_int @ A3 @ A2 )
% 0.33/0.62 => ? [B7: $o] :
% 0.33/0.62 ( ( member_o @ B7 @ B5 )
% 0.33/0.62 & ( R2 @ A3 @ B7 ) ) )
% 0.33/0.62 => ( ! [A13: int,A24: int,B2: $o] :
% 0.33/0.62 ( ( member_int @ A13 @ A2 )
% 0.33/0.62 => ( ( member_int @ A24 @ A2 )
% 0.33/0.62 => ( ( member_o @ B2 @ B5 )
% 0.33/0.62 => ( ( R2 @ A13 @ B2 )
% 0.33/0.62 => ( ( R2 @ A24 @ B2 )
% 0.33/0.62 => ( A13 = A24 ) ) ) ) ) )
% 0.33/0.62 => ( ord_less_eq_nat @ ( finite_card_int @ A2 ) @ ( finite_card_o @ B5 ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % card_le_if_inj_on_rel
% 0.33/0.62 thf(fact_5552_card__le__if__inj__on__rel,axiom,
% 0.33/0.62 ! [B5: set_Product_unit,A2: set_int,R2: int > product_unit > $o] :
% 0.33/0.62 ( ( finite4290736615968046902t_unit @ B5 )
% 0.33/0.62 => ( ! [A3: int] :
% 0.33/0.62 ( ( member_int @ A3 @ A2 )
% 0.33/0.62 => ? [B7: product_unit] :
% 0.33/0.62 ( ( member_Product_unit @ B7 @ B5 )
% 0.33/0.62 & ( R2 @ A3 @ B7 ) ) )
% 0.33/0.62 => ( ! [A13: int,A24: int,B2: product_unit] :
% 0.33/0.62 ( ( member_int @ A13 @ A2 )
% 0.33/0.62 => ( ( member_int @ A24 @ A2 )
% 0.33/0.62 => ( ( member_Product_unit @ B2 @ B5 )
% 0.33/0.62 => ( ( R2 @ A13 @ B2 )
% 0.33/0.62 => ( ( R2 @ A24 @ B2 )
% 0.33/0.62 => ( A13 = A24 ) ) ) ) ) )
% 0.33/0.62 => ( ord_less_eq_nat @ ( finite_card_int @ A2 ) @ ( finite410649719033368117t_unit @ B5 ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % card_le_if_inj_on_rel
% 0.33/0.62 thf(fact_5553_card__le__if__inj__on__rel,axiom,
% 0.33/0.62 ! [B5: set_o,A2: set_Product_unit,R2: product_unit > $o > $o] :
% 0.33/0.62 ( ( finite_finite_o @ B5 )
% 0.33/0.62 => ( ! [A3: product_unit] :
% 0.33/0.62 ( ( member_Product_unit @ A3 @ A2 )
% 0.33/0.62 => ? [B7: $o] :
% 0.33/0.62 ( ( member_o @ B7 @ B5 )
% 0.33/0.62 & ( R2 @ A3 @ B7 ) ) )
% 0.33/0.62 => ( ! [A13: product_unit,A24: product_unit,B2: $o] :
% 0.33/0.62 ( ( member_Product_unit @ A13 @ A2 )
% 0.33/0.62 => ( ( member_Product_unit @ A24 @ A2 )
% 0.33/0.62 => ( ( member_o @ B2 @ B5 )
% 0.33/0.62 => ( ( R2 @ A13 @ B2 )
% 0.33/0.62 => ( ( R2 @ A24 @ B2 )
% 0.33/0.62 => ( A13 = A24 ) ) ) ) ) )
% 0.33/0.62 => ( ord_less_eq_nat @ ( finite410649719033368117t_unit @ A2 ) @ ( finite_card_o @ B5 ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % card_le_if_inj_on_rel
% 0.33/0.62 thf(fact_5554_card__le__if__inj__on__rel,axiom,
% 0.33/0.62 ! [B5: set_Product_unit,A2: set_Product_unit,R2: product_unit > product_unit > $o] :
% 0.33/0.62 ( ( finite4290736615968046902t_unit @ B5 )
% 0.33/0.62 => ( ! [A3: product_unit] :
% 0.33/0.62 ( ( member_Product_unit @ A3 @ A2 )
% 0.33/0.62 => ? [B7: product_unit] :
% 0.33/0.62 ( ( member_Product_unit @ B7 @ B5 )
% 0.33/0.62 & ( R2 @ A3 @ B7 ) ) )
% 0.33/0.62 => ( ! [A13: product_unit,A24: product_unit,B2: product_unit] :
% 0.33/0.62 ( ( member_Product_unit @ A13 @ A2 )
% 0.33/0.62 => ( ( member_Product_unit @ A24 @ A2 )
% 0.33/0.62 => ( ( member_Product_unit @ B2 @ B5 )
% 0.33/0.62 => ( ( R2 @ A13 @ B2 )
% 0.33/0.62 => ( ( R2 @ A24 @ B2 )
% 0.33/0.62 => ( A13 = A24 ) ) ) ) ) )
% 0.33/0.62 => ( ord_less_eq_nat @ ( finite410649719033368117t_unit @ A2 ) @ ( finite410649719033368117t_unit @ B5 ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % card_le_if_inj_on_rel
% 0.33/0.62 thf(fact_5555_card__le__if__inj__on__rel,axiom,
% 0.33/0.62 ! [B5: set_o,A2: set_nat,R2: nat > $o > $o] :
% 0.33/0.62 ( ( finite_finite_o @ B5 )
% 0.33/0.62 => ( ! [A3: nat] :
% 0.33/0.62 ( ( member_nat @ A3 @ A2 )
% 0.33/0.62 => ? [B7: $o] :
% 0.33/0.62 ( ( member_o @ B7 @ B5 )
% 0.33/0.62 & ( R2 @ A3 @ B7 ) ) )
% 0.33/0.62 => ( ! [A13: nat,A24: nat,B2: $o] :
% 0.33/0.62 ( ( member_nat @ A13 @ A2 )
% 0.33/0.62 => ( ( member_nat @ A24 @ A2 )
% 0.33/0.62 => ( ( member_o @ B2 @ B5 )
% 0.33/0.62 => ( ( R2 @ A13 @ B2 )
% 0.33/0.62 => ( ( R2 @ A24 @ B2 )
% 0.33/0.62 => ( A13 = A24 ) ) ) ) ) )
% 0.33/0.62 => ( ord_less_eq_nat @ ( finite_card_nat @ A2 ) @ ( finite_card_o @ B5 ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % card_le_if_inj_on_rel
% 0.33/0.62 thf(fact_5556_card__le__if__inj__on__rel,axiom,
% 0.33/0.62 ! [B5: set_Product_unit,A2: set_nat,R2: nat > product_unit > $o] :
% 0.33/0.62 ( ( finite4290736615968046902t_unit @ B5 )
% 0.33/0.62 => ( ! [A3: nat] :
% 0.33/0.62 ( ( member_nat @ A3 @ A2 )
% 0.33/0.62 => ? [B7: product_unit] :
% 0.33/0.62 ( ( member_Product_unit @ B7 @ B5 )
% 0.33/0.62 & ( R2 @ A3 @ B7 ) ) )
% 0.33/0.62 => ( ! [A13: nat,A24: nat,B2: product_unit] :
% 0.33/0.62 ( ( member_nat @ A13 @ A2 )
% 0.33/0.62 => ( ( member_nat @ A24 @ A2 )
% 0.33/0.62 => ( ( member_Product_unit @ B2 @ B5 )
% 0.33/0.62 => ( ( R2 @ A13 @ B2 )
% 0.33/0.62 => ( ( R2 @ A24 @ B2 )
% 0.33/0.62 => ( A13 = A24 ) ) ) ) ) )
% 0.33/0.62 => ( ord_less_eq_nat @ ( finite_card_nat @ A2 ) @ ( finite410649719033368117t_unit @ B5 ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % card_le_if_inj_on_rel
% 0.33/0.62 thf(fact_5557_card__le__if__inj__on__rel,axiom,
% 0.33/0.62 ! [B5: set_nat,A2: set_o,R2: $o > nat > $o] :
% 0.33/0.62 ( ( finite_finite_nat @ B5 )
% 0.33/0.62 => ( ! [A3: $o] :
% 0.33/0.62 ( ( member_o @ A3 @ A2 )
% 0.33/0.62 => ? [B7: nat] :
% 0.33/0.62 ( ( member_nat @ B7 @ B5 )
% 0.33/0.62 & ( R2 @ A3 @ B7 ) ) )
% 0.33/0.62 => ( ! [A13: $o,A24: $o,B2: nat] :
% 0.33/0.62 ( ( member_o @ A13 @ A2 )
% 0.33/0.62 => ( ( member_o @ A24 @ A2 )
% 0.33/0.62 => ( ( member_nat @ B2 @ B5 )
% 0.33/0.62 => ( ( R2 @ A13 @ B2 )
% 0.33/0.62 => ( ( R2 @ A24 @ B2 )
% 0.33/0.62 => ( A13 = A24 ) ) ) ) ) )
% 0.33/0.62 => ( ord_less_eq_nat @ ( finite_card_o @ A2 ) @ ( finite_card_nat @ B5 ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % card_le_if_inj_on_rel
% 0.33/0.62 thf(fact_5558_card__le__if__inj__on__rel,axiom,
% 0.33/0.62 ! [B5: set_nat,A2: set_int,R2: int > nat > $o] :
% 0.33/0.62 ( ( finite_finite_nat @ B5 )
% 0.33/0.62 => ( ! [A3: int] :
% 0.33/0.62 ( ( member_int @ A3 @ A2 )
% 0.33/0.62 => ? [B7: nat] :
% 0.33/0.62 ( ( member_nat @ B7 @ B5 )
% 0.33/0.62 & ( R2 @ A3 @ B7 ) ) )
% 0.33/0.62 => ( ! [A13: int,A24: int,B2: nat] :
% 0.33/0.62 ( ( member_int @ A13 @ A2 )
% 0.33/0.62 => ( ( member_int @ A24 @ A2 )
% 0.33/0.62 => ( ( member_nat @ B2 @ B5 )
% 0.33/0.62 => ( ( R2 @ A13 @ B2 )
% 0.33/0.62 => ( ( R2 @ A24 @ B2 )
% 0.33/0.62 => ( A13 = A24 ) ) ) ) ) )
% 0.33/0.62 => ( ord_less_eq_nat @ ( finite_card_int @ A2 ) @ ( finite_card_nat @ B5 ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % card_le_if_inj_on_rel
% 0.33/0.62 thf(fact_5559_top__option__def,axiom,
% 0.33/0.62 ( top_to4826455019444611206et_nat
% 0.33/0.62 = ( some_set_nat @ top_top_set_nat ) ) ).
% 0.33/0.62
% 0.33/0.62 % top_option_def
% 0.33/0.62 thf(fact_5560_top__option__def,axiom,
% 0.33/0.62 ( top_to7662761140297458691t_unit
% 0.33/0.62 = ( some_s8043159101241848530t_unit @ top_to1996260823553986621t_unit ) ) ).
% 0.33/0.62
% 0.33/0.62 % top_option_def
% 0.33/0.62 thf(fact_5561_top__option__def,axiom,
% 0.33/0.62 ( top_to2336371874512884450et_int
% 0.33/0.62 = ( some_set_int @ top_top_set_int ) ) ).
% 0.33/0.62
% 0.33/0.62 % top_option_def
% 0.33/0.62 thf(fact_5562_top__option__def,axiom,
% 0.33/0.62 ( top_to4322782652514146083t_unit
% 0.33/0.62 = ( some_Product_unit @ top_top_Product_unit ) ) ).
% 0.33/0.62
% 0.33/0.62 % top_option_def
% 0.33/0.62 thf(fact_5563_top__option__def,axiom,
% 0.33/0.62 ( top_top_option_assn
% 0.33/0.62 = ( some_assn @ top_top_assn ) ) ).
% 0.33/0.62
% 0.33/0.62 % top_option_def
% 0.33/0.62 thf(fact_5564_finite__if__eq__beyond__finite,axiom,
% 0.33/0.62 ! [S2: set_int,S3: set_int] :
% 0.33/0.62 ( ( finite_finite_int @ S2 )
% 0.33/0.62 => ( finite6197958912794628473et_int
% 0.33/0.62 @ ( collect_set_int
% 0.33/0.62 @ ^ [S4: set_int] :
% 0.33/0.62 ( ( minus_minus_set_int @ S4 @ S2 )
% 0.33/0.62 = ( minus_minus_set_int @ S3 @ S2 ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % finite_if_eq_beyond_finite
% 0.33/0.62 thf(fact_5565_finite__if__eq__beyond__finite,axiom,
% 0.33/0.62 ! [S2: set_Code_integer,S3: set_Code_integer] :
% 0.33/0.62 ( ( finite6017078050557962740nteger @ S2 )
% 0.33/0.62 => ( finite6931041176100689706nteger
% 0.33/0.62 @ ( collec574505750873337192nteger
% 0.33/0.62 @ ^ [S4: set_Code_integer] :
% 0.33/0.62 ( ( minus_2355218937544613996nteger @ S4 @ S2 )
% 0.33/0.62 = ( minus_2355218937544613996nteger @ S3 @ S2 ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % finite_if_eq_beyond_finite
% 0.33/0.62 thf(fact_5566_finite__if__eq__beyond__finite,axiom,
% 0.33/0.62 ! [S2: set_Pr1261947904930325089at_nat,S3: set_Pr1261947904930325089at_nat] :
% 0.33/0.62 ( ( finite6177210948735845034at_nat @ S2 )
% 0.33/0.62 => ( finite9047747110432174090at_nat
% 0.33/0.62 @ ( collec5514110066124741708at_nat
% 0.33/0.62 @ ^ [S4: set_Pr1261947904930325089at_nat] :
% 0.33/0.62 ( ( minus_1356011639430497352at_nat @ S4 @ S2 )
% 0.33/0.62 = ( minus_1356011639430497352at_nat @ S3 @ S2 ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % finite_if_eq_beyond_finite
% 0.33/0.62 thf(fact_5567_finite__if__eq__beyond__finite,axiom,
% 0.33/0.62 ! [S2: set_nat,S3: set_nat] :
% 0.33/0.62 ( ( finite_finite_nat @ S2 )
% 0.33/0.62 => ( finite1152437895449049373et_nat
% 0.33/0.62 @ ( collect_set_nat
% 0.33/0.62 @ ^ [S4: set_nat] :
% 0.33/0.62 ( ( minus_minus_set_nat @ S4 @ S2 )
% 0.33/0.62 = ( minus_minus_set_nat @ S3 @ S2 ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % finite_if_eq_beyond_finite
% 0.33/0.62 thf(fact_5568_finite__range__Some,axiom,
% 0.33/0.62 ( ( finite6785661671136154180nteger @ ( image_8960079959263999889nteger @ some_Code_integer @ top_to4645266643341252675nteger ) )
% 0.33/0.62 = ( finite6017078050557962740nteger @ top_to4645266643341252675nteger ) ) ).
% 0.33/0.62
% 0.33/0.62 % finite_range_Some
% 0.33/0.62 thf(fact_5569_finite__range__Some,axiom,
% 0.33/0.62 ( ( finite6732403688824079472at_nat @ ( image_4198897800814241419at_nat @ some_P7363390416028606310at_nat @ top_to4669805908274784177at_nat ) )
% 0.33/0.62 = ( finite6177210948735845034at_nat @ top_to4669805908274784177at_nat ) ) ).
% 0.33/0.62
% 0.33/0.62 % finite_range_Some
% 0.33/0.62 thf(fact_5570_finite__range__Some,axiom,
% 0.33/0.62 ( ( finite6231397076622260609on_num @ ( image_num_option_num @ some_num @ top_top_set_num ) )
% 0.33/0.62 = ( finite_finite_num @ top_top_set_num ) ) ).
% 0.33/0.62
% 0.33/0.62 % finite_range_Some
% 0.33/0.62 thf(fact_5571_finite__range__Some,axiom,
% 0.33/0.62 ( ( finite6292238467249657455it_nat @ ( image_3455408117458022631it_nat @ some_P1914260805536162275it_nat @ top_to4082048134677576814it_nat ) )
% 0.33/0.62 = ( finite6446286893012251551it_nat @ top_to4082048134677576814it_nat ) ) ).
% 0.33/0.62
% 0.33/0.62 % finite_range_Some
% 0.33/0.62 thf(fact_5572_finite__range__Some,axiom,
% 0.33/0.62 ( ( finite5523153139673422903on_nat @ ( image_nat_option_nat @ some_nat @ top_top_set_nat ) )
% 0.33/0.62 = ( finite_finite_nat @ top_top_set_nat ) ) ).
% 0.33/0.62
% 0.33/0.62 % finite_range_Some
% 0.33/0.62 thf(fact_5573_finite__range__Some,axiom,
% 0.33/0.62 ( ( finite1445617369574913404t_unit @ ( image_7094380055901048587t_unit @ some_Product_unit @ top_to1996260823553986621t_unit ) )
% 0.33/0.62 = ( finite4290736615968046902t_unit @ top_to1996260823553986621t_unit ) ) ).
% 0.33/0.62
% 0.33/0.62 % finite_range_Some
% 0.33/0.62 thf(fact_5574_finite__range__Some,axiom,
% 0.33/0.62 ( ( finite1345302120164226195on_int @ ( image_int_option_int @ some_int @ top_top_set_int ) )
% 0.33/0.62 = ( finite_finite_int @ top_top_set_int ) ) ).
% 0.33/0.62
% 0.33/0.62 % finite_range_Some
% 0.33/0.62 thf(fact_5575_obtain__subset__with__card__n,axiom,
% 0.33/0.62 ! [N2: nat,S2: set_Product_unit] :
% 0.33/0.62 ( ( ord_less_eq_nat @ N2 @ ( finite410649719033368117t_unit @ S2 ) )
% 0.33/0.62 => ~ ! [T3: set_Product_unit] :
% 0.33/0.62 ( ( ord_le3507040750410214029t_unit @ T3 @ S2 )
% 0.33/0.62 => ( ( ( finite410649719033368117t_unit @ T3 )
% 0.33/0.62 = N2 )
% 0.33/0.62 => ~ ( finite4290736615968046902t_unit @ T3 ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % obtain_subset_with_card_n
% 0.33/0.62 thf(fact_5576_obtain__subset__with__card__n,axiom,
% 0.33/0.62 ! [N2: nat,S2: set_list_nat] :
% 0.33/0.62 ( ( ord_less_eq_nat @ N2 @ ( finite_card_list_nat @ S2 ) )
% 0.33/0.62 => ~ ! [T3: set_list_nat] :
% 0.33/0.62 ( ( ord_le6045566169113846134st_nat @ T3 @ S2 )
% 0.33/0.62 => ( ( ( finite_card_list_nat @ T3 )
% 0.33/0.62 = N2 )
% 0.33/0.62 => ~ ( finite8100373058378681591st_nat @ T3 ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % obtain_subset_with_card_n
% 0.33/0.62 thf(fact_5577_obtain__subset__with__card__n,axiom,
% 0.33/0.62 ! [N2: nat,S2: set_int] :
% 0.33/0.62 ( ( ord_less_eq_nat @ N2 @ ( finite_card_int @ S2 ) )
% 0.33/0.62 => ~ ! [T3: set_int] :
% 0.33/0.62 ( ( ord_less_eq_set_int @ T3 @ S2 )
% 0.33/0.62 => ( ( ( finite_card_int @ T3 )
% 0.33/0.62 = N2 )
% 0.33/0.62 => ~ ( finite_finite_int @ T3 ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % obtain_subset_with_card_n
% 0.33/0.62 thf(fact_5578_obtain__subset__with__card__n,axiom,
% 0.33/0.62 ! [N2: nat,S2: set_Code_integer] :
% 0.33/0.62 ( ( ord_less_eq_nat @ N2 @ ( finite4902975817058060853nteger @ S2 ) )
% 0.33/0.62 => ~ ! [T3: set_Code_integer] :
% 0.33/0.62 ( ( ord_le7084787975880047091nteger @ T3 @ S2 )
% 0.33/0.62 => ( ( ( finite4902975817058060853nteger @ T3 )
% 0.33/0.62 = N2 )
% 0.33/0.62 => ~ ( finite6017078050557962740nteger @ T3 ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % obtain_subset_with_card_n
% 0.33/0.62 thf(fact_5579_obtain__subset__with__card__n,axiom,
% 0.33/0.62 ! [N2: nat,S2: set_Pr1261947904930325089at_nat] :
% 0.33/0.62 ( ( ord_less_eq_nat @ N2 @ ( finite711546835091564841at_nat @ S2 ) )
% 0.33/0.62 => ~ ! [T3: set_Pr1261947904930325089at_nat] :
% 0.33/0.62 ( ( ord_le3146513528884898305at_nat @ T3 @ S2 )
% 0.33/0.62 => ( ( ( finite711546835091564841at_nat @ T3 )
% 0.33/0.62 = N2 )
% 0.33/0.62 => ~ ( finite6177210948735845034at_nat @ T3 ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % obtain_subset_with_card_n
% 0.33/0.62 thf(fact_5580_obtain__subset__with__card__n,axiom,
% 0.33/0.62 ! [N2: nat,S2: set_nat] :
% 0.33/0.62 ( ( ord_less_eq_nat @ N2 @ ( finite_card_nat @ S2 ) )
% 0.33/0.62 => ~ ! [T3: set_nat] :
% 0.33/0.62 ( ( ord_less_eq_set_nat @ T3 @ S2 )
% 0.33/0.62 => ( ( ( finite_card_nat @ T3 )
% 0.33/0.62 = N2 )
% 0.33/0.62 => ~ ( finite_finite_nat @ T3 ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % obtain_subset_with_card_n
% 0.33/0.62 thf(fact_5581_atLeastAtMost__eq__UNIV__iff,axiom,
% 0.33/0.62 ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat] :
% 0.33/0.62 ( ( ( set_or4049648398082403068at_nat @ X @ Y )
% 0.33/0.62 = top_to1754375979021635447at_nat )
% 0.33/0.62 = ( ( X = bot_bo228742789529271731at_nat )
% 0.33/0.62 & ( Y = top_to6833984726390702231at_nat ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % atLeastAtMost_eq_UNIV_iff
% 0.33/0.62 thf(fact_5582_atLeastAtMost__eq__UNIV__iff,axiom,
% 0.33/0.62 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 0.33/0.62 ( ( ( set_or2784603332384507286at_nat @ X @ Y )
% 0.33/0.62 = top_to7629004291339433233at_nat )
% 0.33/0.62 = ( ( X = bot_bo2099793752762293965at_nat )
% 0.33/0.62 & ( Y = top_to4669805908274784177at_nat ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % atLeastAtMost_eq_UNIV_iff
% 0.33/0.62 thf(fact_5583_atLeastAtMost__eq__UNIV__iff,axiom,
% 0.33/0.62 ! [X: set_o,Y: set_o] :
% 0.33/0.62 ( ( ( set_or266616469461849773_set_o @ X @ Y )
% 0.33/0.62 = top_top_set_set_o )
% 0.33/0.62 = ( ( X = bot_bot_set_o )
% 0.33/0.62 & ( Y = top_top_set_o ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % atLeastAtMost_eq_UNIV_iff
% 0.33/0.62 thf(fact_5584_atLeastAtMost__eq__UNIV__iff,axiom,
% 0.33/0.62 ! [X: set_nat,Y: set_nat] :
% 0.33/0.62 ( ( ( set_or4548717258645045905et_nat @ X @ Y )
% 0.33/0.62 = top_top_set_set_nat )
% 0.33/0.62 = ( ( X = bot_bot_set_nat )
% 0.33/0.62 & ( Y = top_top_set_nat ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % atLeastAtMost_eq_UNIV_iff
% 0.33/0.62 thf(fact_5585_atLeastAtMost__eq__UNIV__iff,axiom,
% 0.33/0.62 ! [X: set_Product_unit,Y: set_Product_unit] :
% 0.33/0.62 ( ( ( set_or269330187037242274t_unit @ X @ Y )
% 0.33/0.62 = top_to1767297665138865437t_unit )
% 0.33/0.62 = ( ( X = bot_bo3957492148770167129t_unit )
% 0.33/0.62 & ( Y = top_to1996260823553986621t_unit ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % atLeastAtMost_eq_UNIV_iff
% 0.33/0.62 thf(fact_5586_atLeastAtMost__eq__UNIV__iff,axiom,
% 0.33/0.62 ! [X: set_int,Y: set_int] :
% 0.33/0.62 ( ( ( set_or370866239135849197et_int @ X @ Y )
% 0.33/0.62 = top_top_set_set_int )
% 0.33/0.62 = ( ( X = bot_bot_set_int )
% 0.33/0.62 & ( Y = top_top_set_int ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % atLeastAtMost_eq_UNIV_iff
% 0.33/0.62 thf(fact_5587_atLeastAtMost__eq__UNIV__iff,axiom,
% 0.33/0.62 ! [X: assn,Y: assn] :
% 0.33/0.62 ( ( ( set_or7959216805967363635t_assn @ X @ Y )
% 0.33/0.62 = top_top_set_assn )
% 0.33/0.62 = ( ( X = bot_bot_assn )
% 0.33/0.62 & ( Y = top_top_assn ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % atLeastAtMost_eq_UNIV_iff
% 0.33/0.62 thf(fact_5588_atLeastAtMost__eq__UNIV__iff,axiom,
% 0.33/0.62 ! [X: product_unit,Y: product_unit] :
% 0.33/0.62 ( ( ( set_or5692540242118139586t_unit @ X @ Y )
% 0.33/0.62 = top_to1996260823553986621t_unit )
% 0.33/0.62 = ( ( X = bot_bot_Product_unit )
% 0.33/0.62 & ( Y = top_top_Product_unit ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % atLeastAtMost_eq_UNIV_iff
% 0.33/0.62 thf(fact_5589_UNIV__option__conv,axiom,
% 0.33/0.62 ( top_to7137183367772546234it_nat
% 0.33/0.62 = ( insert7468008629046257882it_nat @ none_P2587165478634041381it_nat @ ( image_4799632500972785611it_nat @ some_P6105628898608307625it_nat @ top_to3995162779041354868it_nat ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % UNIV_option_conv
% 0.33/0.62 thf(fact_5590_UNIV__option__conv,axiom,
% 0.33/0.62 ( top_to4635417975585700688on_num
% 0.33/0.62 = ( insert_option_num @ none_num @ ( image_num_option_num @ some_num @ top_top_set_num ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % UNIV_option_conv
% 0.33/0.62 thf(fact_5591_UNIV__option__conv,axiom,
% 0.33/0.62 ( top_to6632602878615679294it_nat
% 0.33/0.62 = ( insert2007652293347934600it_nat @ none_P9117596204409417319it_nat @ ( image_3455408117458022631it_nat @ some_P1914260805536162275it_nat @ top_to4082048134677576814it_nat ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % UNIV_option_conv
% 0.33/0.62 thf(fact_5592_UNIV__option__conv,axiom,
% 0.33/0.62 ( top_to8920198386146353926on_nat
% 0.33/0.62 = ( insert_option_nat @ none_nat @ ( image_nat_option_nat @ some_nat @ top_top_set_nat ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % UNIV_option_conv
% 0.33/0.62 thf(fact_5593_UNIV__option__conv,axiom,
% 0.33/0.62 ( top_to2690860209552263555t_unit
% 0.33/0.62 = ( insert2866144167138965411t_unit @ none_Product_unit @ ( image_7094380055901048587t_unit @ some_Product_unit @ top_to1996260823553986621t_unit ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % UNIV_option_conv
% 0.33/0.62 thf(fact_5594_UNIV__option__conv,axiom,
% 0.33/0.62 ( top_to6430115241214627170on_int
% 0.33/0.62 = ( insert_option_int @ none_int @ ( image_int_option_int @ some_int @ top_top_set_int ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % UNIV_option_conv
% 0.33/0.62 thf(fact_5595_bounded__nat__set__is__finite,axiom,
% 0.33/0.62 ! [N6: set_nat,N2: nat] :
% 0.33/0.62 ( ! [X4: nat] :
% 0.33/0.62 ( ( member_nat @ X4 @ N6 )
% 0.33/0.62 => ( ord_less_nat @ X4 @ N2 ) )
% 0.33/0.62 => ( finite_finite_nat @ N6 ) ) ).
% 0.33/0.62
% 0.33/0.62 % bounded_nat_set_is_finite
% 0.33/0.62 thf(fact_5596_finite__nat__set__iff__bounded,axiom,
% 0.33/0.62 ( finite_finite_nat
% 0.33/0.62 = ( ^ [N9: set_nat] :
% 0.33/0.62 ? [M: nat] :
% 0.33/0.62 ! [X3: nat] :
% 0.33/0.62 ( ( member_nat @ X3 @ N9 )
% 0.33/0.62 => ( ord_less_nat @ X3 @ M ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % finite_nat_set_iff_bounded
% 0.33/0.62 thf(fact_5597_finite__nat__set__iff__bounded__le,axiom,
% 0.33/0.62 ( finite_finite_nat
% 0.33/0.62 = ( ^ [N9: set_nat] :
% 0.33/0.62 ? [M: nat] :
% 0.33/0.62 ! [X3: nat] :
% 0.33/0.62 ( ( member_nat @ X3 @ N9 )
% 0.33/0.62 => ( ord_less_eq_nat @ X3 @ M ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % finite_nat_set_iff_bounded_le
% 0.33/0.62 thf(fact_5598_surjD,axiom,
% 0.33/0.62 ! [F: nat > code_integer,Y: code_integer] :
% 0.33/0.62 ( ( ( image_1215581382706833972nteger @ F @ top_top_set_nat )
% 0.33/0.62 = top_to4645266643341252675nteger )
% 0.33/0.62 => ? [X4: nat] :
% 0.33/0.62 ( Y
% 0.33/0.62 = ( F @ X4 ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % surjD
% 0.33/0.62 thf(fact_5599_surjD,axiom,
% 0.33/0.62 ! [F: nat > nat,Y: nat] :
% 0.33/0.62 ( ( ( image_nat_nat @ F @ top_top_set_nat )
% 0.33/0.62 = top_top_set_nat )
% 0.33/0.62 => ? [X4: nat] :
% 0.33/0.62 ( Y
% 0.33/0.62 = ( F @ X4 ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % surjD
% 0.33/0.62 thf(fact_5600_surjD,axiom,
% 0.33/0.62 ! [F: nat > product_unit,Y: product_unit] :
% 0.33/0.62 ( ( ( image_8730104196221521654t_unit @ F @ top_top_set_nat )
% 0.33/0.62 = top_to1996260823553986621t_unit )
% 0.33/0.62 => ? [X4: nat] :
% 0.33/0.62 ( Y
% 0.33/0.62 = ( F @ X4 ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % surjD
% 0.33/0.62 thf(fact_5601_surjD,axiom,
% 0.33/0.62 ! [F: nat > int,Y: int] :
% 0.33/0.62 ( ( ( image_nat_int @ F @ top_top_set_nat )
% 0.33/0.62 = top_top_set_int )
% 0.33/0.62 => ? [X4: nat] :
% 0.33/0.62 ( Y
% 0.33/0.62 = ( F @ X4 ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % surjD
% 0.33/0.62 thf(fact_5602_surjD,axiom,
% 0.33/0.62 ! [F: product_unit > nat,Y: nat] :
% 0.33/0.62 ( ( ( image_875570014554754200it_nat @ F @ top_to1996260823553986621t_unit )
% 0.33/0.62 = top_top_set_nat )
% 0.33/0.62 => ? [X4: product_unit] :
% 0.33/0.62 ( Y
% 0.33/0.62 = ( F @ X4 ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % surjD
% 0.33/0.62 thf(fact_5603_surjD,axiom,
% 0.33/0.62 ! [F: product_unit > product_unit,Y: product_unit] :
% 0.33/0.62 ( ( ( image_405062704495631173t_unit @ F @ top_to1996260823553986621t_unit )
% 0.33/0.62 = top_to1996260823553986621t_unit )
% 0.33/0.62 => ? [X4: product_unit] :
% 0.33/0.62 ( Y
% 0.33/0.62 = ( F @ X4 ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % surjD
% 0.33/0.62 thf(fact_5604_surjD,axiom,
% 0.33/0.62 ! [F: product_unit > int,Y: int] :
% 0.33/0.62 ( ( ( image_873079544045703924it_int @ F @ top_to1996260823553986621t_unit )
% 0.33/0.62 = top_top_set_int )
% 0.33/0.62 => ? [X4: product_unit] :
% 0.33/0.62 ( Y
% 0.33/0.62 = ( F @ X4 ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % surjD
% 0.33/0.62 thf(fact_5605_surjD,axiom,
% 0.33/0.62 ! [F: int > nat,Y: nat] :
% 0.33/0.62 ( ( ( image_int_nat @ F @ top_top_set_int )
% 0.33/0.62 = top_top_set_nat )
% 0.33/0.62 => ? [X4: int] :
% 0.33/0.62 ( Y
% 0.33/0.62 = ( F @ X4 ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % surjD
% 0.33/0.62 thf(fact_5606_surjD,axiom,
% 0.33/0.62 ! [F: int > product_unit,Y: product_unit] :
% 0.33/0.62 ( ( ( image_5846526143423701914t_unit @ F @ top_top_set_int )
% 0.33/0.62 = top_to1996260823553986621t_unit )
% 0.33/0.62 => ? [X4: int] :
% 0.33/0.62 ( Y
% 0.33/0.62 = ( F @ X4 ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % surjD
% 0.33/0.62 thf(fact_5607_surjD,axiom,
% 0.33/0.62 ! [F: int > int,Y: int] :
% 0.33/0.62 ( ( ( image_int_int @ F @ top_top_set_int )
% 0.33/0.62 = top_top_set_int )
% 0.33/0.62 => ? [X4: int] :
% 0.33/0.62 ( Y
% 0.33/0.62 = ( F @ X4 ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % surjD
% 0.33/0.62 thf(fact_5608_surjE,axiom,
% 0.33/0.62 ! [F: nat > code_integer,Y: code_integer] :
% 0.33/0.62 ( ( ( image_1215581382706833972nteger @ F @ top_top_set_nat )
% 0.33/0.62 = top_to4645266643341252675nteger )
% 0.33/0.62 => ~ ! [X4: nat] :
% 0.33/0.62 ( Y
% 0.33/0.62 != ( F @ X4 ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % surjE
% 0.33/0.62 thf(fact_5609_surjE,axiom,
% 0.33/0.62 ! [F: nat > nat,Y: nat] :
% 0.33/0.62 ( ( ( image_nat_nat @ F @ top_top_set_nat )
% 0.33/0.62 = top_top_set_nat )
% 0.33/0.62 => ~ ! [X4: nat] :
% 0.33/0.62 ( Y
% 0.33/0.62 != ( F @ X4 ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % surjE
% 0.33/0.62 thf(fact_5610_surjE,axiom,
% 0.33/0.62 ! [F: nat > product_unit,Y: product_unit] :
% 0.33/0.62 ( ( ( image_8730104196221521654t_unit @ F @ top_top_set_nat )
% 0.33/0.62 = top_to1996260823553986621t_unit )
% 0.33/0.62 => ~ ! [X4: nat] :
% 0.33/0.62 ( Y
% 0.33/0.62 != ( F @ X4 ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % surjE
% 0.33/0.62 thf(fact_5611_surjE,axiom,
% 0.33/0.62 ! [F: nat > int,Y: int] :
% 0.33/0.62 ( ( ( image_nat_int @ F @ top_top_set_nat )
% 0.33/0.62 = top_top_set_int )
% 0.33/0.62 => ~ ! [X4: nat] :
% 0.33/0.62 ( Y
% 0.33/0.62 != ( F @ X4 ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % surjE
% 0.33/0.62 thf(fact_5612_surjE,axiom,
% 0.33/0.62 ! [F: product_unit > nat,Y: nat] :
% 0.33/0.62 ( ( ( image_875570014554754200it_nat @ F @ top_to1996260823553986621t_unit )
% 0.33/0.62 = top_top_set_nat )
% 0.33/0.62 => ~ ! [X4: product_unit] :
% 0.33/0.62 ( Y
% 0.33/0.62 != ( F @ X4 ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % surjE
% 0.33/0.62 thf(fact_5613_surjE,axiom,
% 0.33/0.62 ! [F: product_unit > product_unit,Y: product_unit] :
% 0.33/0.62 ( ( ( image_405062704495631173t_unit @ F @ top_to1996260823553986621t_unit )
% 0.33/0.62 = top_to1996260823553986621t_unit )
% 0.33/0.62 => ~ ! [X4: product_unit] :
% 0.33/0.62 ( Y
% 0.33/0.62 != ( F @ X4 ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % surjE
% 0.33/0.62 thf(fact_5614_surjE,axiom,
% 0.33/0.62 ! [F: product_unit > int,Y: int] :
% 0.33/0.62 ( ( ( image_873079544045703924it_int @ F @ top_to1996260823553986621t_unit )
% 0.33/0.62 = top_top_set_int )
% 0.33/0.62 => ~ ! [X4: product_unit] :
% 0.33/0.62 ( Y
% 0.33/0.62 != ( F @ X4 ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % surjE
% 0.33/0.62 thf(fact_5615_surjE,axiom,
% 0.33/0.62 ! [F: int > nat,Y: nat] :
% 0.33/0.62 ( ( ( image_int_nat @ F @ top_top_set_int )
% 0.33/0.62 = top_top_set_nat )
% 0.33/0.62 => ~ ! [X4: int] :
% 0.33/0.62 ( Y
% 0.33/0.62 != ( F @ X4 ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % surjE
% 0.33/0.62 thf(fact_5616_surjE,axiom,
% 0.33/0.62 ! [F: int > product_unit,Y: product_unit] :
% 0.33/0.62 ( ( ( image_5846526143423701914t_unit @ F @ top_top_set_int )
% 0.33/0.62 = top_to1996260823553986621t_unit )
% 0.33/0.62 => ~ ! [X4: int] :
% 0.33/0.62 ( Y
% 0.33/0.62 != ( F @ X4 ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % surjE
% 0.33/0.62 thf(fact_5617_surjE,axiom,
% 0.33/0.62 ! [F: int > int,Y: int] :
% 0.33/0.62 ( ( ( image_int_int @ F @ top_top_set_int )
% 0.33/0.62 = top_top_set_int )
% 0.33/0.62 => ~ ! [X4: int] :
% 0.33/0.62 ( Y
% 0.33/0.62 != ( F @ X4 ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % surjE
% 0.33/0.62 thf(fact_5618_surjI,axiom,
% 0.33/0.62 ! [G: nat > code_integer,F: code_integer > nat] :
% 0.33/0.62 ( ! [X4: code_integer] :
% 0.33/0.62 ( ( G @ ( F @ X4 ) )
% 0.33/0.62 = X4 )
% 0.33/0.62 => ( ( image_1215581382706833972nteger @ G @ top_top_set_nat )
% 0.33/0.62 = top_to4645266643341252675nteger ) ) ).
% 0.33/0.62
% 0.33/0.62 % surjI
% 0.33/0.62 thf(fact_5619_surjI,axiom,
% 0.33/0.62 ! [G: nat > nat,F: nat > nat] :
% 0.33/0.62 ( ! [X4: nat] :
% 0.33/0.62 ( ( G @ ( F @ X4 ) )
% 0.33/0.62 = X4 )
% 0.33/0.62 => ( ( image_nat_nat @ G @ top_top_set_nat )
% 0.33/0.62 = top_top_set_nat ) ) ).
% 0.33/0.62
% 0.33/0.62 % surjI
% 0.33/0.62 thf(fact_5620_surjI,axiom,
% 0.33/0.62 ! [G: nat > product_unit,F: product_unit > nat] :
% 0.33/0.62 ( ! [X4: product_unit] :
% 0.33/0.62 ( ( G @ ( F @ X4 ) )
% 0.33/0.62 = X4 )
% 0.33/0.62 => ( ( image_8730104196221521654t_unit @ G @ top_top_set_nat )
% 0.33/0.62 = top_to1996260823553986621t_unit ) ) ).
% 0.33/0.62
% 0.33/0.62 % surjI
% 0.33/0.62 thf(fact_5621_surjI,axiom,
% 0.33/0.62 ! [G: nat > int,F: int > nat] :
% 0.33/0.62 ( ! [X4: int] :
% 0.33/0.62 ( ( G @ ( F @ X4 ) )
% 0.33/0.62 = X4 )
% 0.33/0.62 => ( ( image_nat_int @ G @ top_top_set_nat )
% 0.33/0.62 = top_top_set_int ) ) ).
% 0.33/0.62
% 0.33/0.62 % surjI
% 0.33/0.62 thf(fact_5622_surjI,axiom,
% 0.33/0.62 ! [G: product_unit > nat,F: nat > product_unit] :
% 0.33/0.62 ( ! [X4: nat] :
% 0.33/0.62 ( ( G @ ( F @ X4 ) )
% 0.33/0.62 = X4 )
% 0.33/0.62 => ( ( image_875570014554754200it_nat @ G @ top_to1996260823553986621t_unit )
% 0.33/0.62 = top_top_set_nat ) ) ).
% 0.33/0.62
% 0.33/0.62 % surjI
% 0.33/0.62 thf(fact_5623_surjI,axiom,
% 0.33/0.62 ! [G: product_unit > product_unit,F: product_unit > product_unit] :
% 0.33/0.62 ( ! [X4: product_unit] :
% 0.33/0.62 ( ( G @ ( F @ X4 ) )
% 0.33/0.62 = X4 )
% 0.33/0.62 => ( ( image_405062704495631173t_unit @ G @ top_to1996260823553986621t_unit )
% 0.33/0.62 = top_to1996260823553986621t_unit ) ) ).
% 0.33/0.62
% 0.33/0.62 % surjI
% 0.33/0.62 thf(fact_5624_surjI,axiom,
% 0.33/0.62 ! [G: product_unit > int,F: int > product_unit] :
% 0.33/0.62 ( ! [X4: int] :
% 0.33/0.62 ( ( G @ ( F @ X4 ) )
% 0.33/0.62 = X4 )
% 0.33/0.62 => ( ( image_873079544045703924it_int @ G @ top_to1996260823553986621t_unit )
% 0.33/0.62 = top_top_set_int ) ) ).
% 0.33/0.62
% 0.33/0.62 % surjI
% 0.33/0.62 thf(fact_5625_surjI,axiom,
% 0.33/0.62 ! [G: int > nat,F: nat > int] :
% 0.33/0.62 ( ! [X4: nat] :
% 0.33/0.62 ( ( G @ ( F @ X4 ) )
% 0.33/0.62 = X4 )
% 0.33/0.62 => ( ( image_int_nat @ G @ top_top_set_int )
% 0.33/0.62 = top_top_set_nat ) ) ).
% 0.33/0.62
% 0.33/0.62 % surjI
% 0.33/0.62 thf(fact_5626_surjI,axiom,
% 0.33/0.62 ! [G: int > product_unit,F: product_unit > int] :
% 0.33/0.62 ( ! [X4: product_unit] :
% 0.33/0.62 ( ( G @ ( F @ X4 ) )
% 0.33/0.62 = X4 )
% 0.33/0.62 => ( ( image_5846526143423701914t_unit @ G @ top_top_set_int )
% 0.33/0.62 = top_to1996260823553986621t_unit ) ) ).
% 0.33/0.62
% 0.33/0.62 % surjI
% 0.33/0.62 thf(fact_5627_surjI,axiom,
% 0.33/0.62 ! [G: int > int,F: int > int] :
% 0.33/0.62 ( ! [X4: int] :
% 0.33/0.62 ( ( G @ ( F @ X4 ) )
% 0.33/0.62 = X4 )
% 0.33/0.62 => ( ( image_int_int @ G @ top_top_set_int )
% 0.33/0.62 = top_top_set_int ) ) ).
% 0.33/0.62
% 0.33/0.62 % surjI
% 0.33/0.62 thf(fact_5628_surj__def,axiom,
% 0.33/0.62 ! [F: nat > code_integer] :
% 0.33/0.62 ( ( ( image_1215581382706833972nteger @ F @ top_top_set_nat )
% 0.33/0.62 = top_to4645266643341252675nteger )
% 0.33/0.62 = ( ! [Y3: code_integer] :
% 0.33/0.62 ? [X3: nat] :
% 0.33/0.62 ( Y3
% 0.33/0.62 = ( F @ X3 ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % surj_def
% 0.33/0.62 thf(fact_5629_surj__def,axiom,
% 0.33/0.62 ! [F: nat > nat] :
% 0.33/0.62 ( ( ( image_nat_nat @ F @ top_top_set_nat )
% 0.33/0.62 = top_top_set_nat )
% 0.33/0.62 = ( ! [Y3: nat] :
% 0.33/0.62 ? [X3: nat] :
% 0.33/0.62 ( Y3
% 0.33/0.62 = ( F @ X3 ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % surj_def
% 0.33/0.62 thf(fact_5630_surj__def,axiom,
% 0.33/0.62 ! [F: nat > product_unit] :
% 0.33/0.62 ( ( ( image_8730104196221521654t_unit @ F @ top_top_set_nat )
% 0.33/0.62 = top_to1996260823553986621t_unit )
% 0.33/0.62 = ( ! [Y3: product_unit] :
% 0.33/0.62 ? [X3: nat] :
% 0.33/0.62 ( Y3
% 0.33/0.62 = ( F @ X3 ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % surj_def
% 0.33/0.62 thf(fact_5631_surj__def,axiom,
% 0.33/0.62 ! [F: nat > int] :
% 0.33/0.62 ( ( ( image_nat_int @ F @ top_top_set_nat )
% 0.33/0.62 = top_top_set_int )
% 0.33/0.62 = ( ! [Y3: int] :
% 0.33/0.62 ? [X3: nat] :
% 0.33/0.62 ( Y3
% 0.33/0.62 = ( F @ X3 ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % surj_def
% 0.33/0.62 thf(fact_5632_surj__def,axiom,
% 0.33/0.62 ! [F: product_unit > nat] :
% 0.33/0.62 ( ( ( image_875570014554754200it_nat @ F @ top_to1996260823553986621t_unit )
% 0.33/0.62 = top_top_set_nat )
% 0.33/0.62 = ( ! [Y3: nat] :
% 0.33/0.62 ? [X3: product_unit] :
% 0.33/0.62 ( Y3
% 0.33/0.62 = ( F @ X3 ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % surj_def
% 0.33/0.62 thf(fact_5633_surj__def,axiom,
% 0.33/0.62 ! [F: product_unit > product_unit] :
% 0.33/0.62 ( ( ( image_405062704495631173t_unit @ F @ top_to1996260823553986621t_unit )
% 0.33/0.62 = top_to1996260823553986621t_unit )
% 0.33/0.62 = ( ! [Y3: product_unit] :
% 0.33/0.62 ? [X3: product_unit] :
% 0.33/0.62 ( Y3
% 0.33/0.62 = ( F @ X3 ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % surj_def
% 0.33/0.62 thf(fact_5634_surj__def,axiom,
% 0.33/0.62 ! [F: product_unit > int] :
% 0.33/0.62 ( ( ( image_873079544045703924it_int @ F @ top_to1996260823553986621t_unit )
% 0.33/0.62 = top_top_set_int )
% 0.33/0.62 = ( ! [Y3: int] :
% 0.33/0.62 ? [X3: product_unit] :
% 0.33/0.62 ( Y3
% 0.33/0.62 = ( F @ X3 ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % surj_def
% 0.33/0.62 thf(fact_5635_surj__def,axiom,
% 0.33/0.62 ! [F: int > nat] :
% 0.33/0.62 ( ( ( image_int_nat @ F @ top_top_set_int )
% 0.33/0.62 = top_top_set_nat )
% 0.33/0.62 = ( ! [Y3: nat] :
% 0.33/0.62 ? [X3: int] :
% 0.33/0.62 ( Y3
% 0.33/0.62 = ( F @ X3 ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % surj_def
% 0.33/0.62 thf(fact_5636_surj__def,axiom,
% 0.33/0.62 ! [F: int > product_unit] :
% 0.33/0.62 ( ( ( image_5846526143423701914t_unit @ F @ top_top_set_int )
% 0.33/0.62 = top_to1996260823553986621t_unit )
% 0.33/0.62 = ( ! [Y3: product_unit] :
% 0.33/0.62 ? [X3: int] :
% 0.33/0.62 ( Y3
% 0.33/0.62 = ( F @ X3 ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % surj_def
% 0.33/0.62 thf(fact_5637_surj__def,axiom,
% 0.33/0.62 ! [F: int > int] :
% 0.33/0.62 ( ( ( image_int_int @ F @ top_top_set_int )
% 0.33/0.62 = top_top_set_int )
% 0.33/0.62 = ( ! [Y3: int] :
% 0.33/0.62 ? [X3: int] :
% 0.33/0.62 ( Y3
% 0.33/0.62 = ( F @ X3 ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % surj_def
% 0.33/0.62 thf(fact_5638_these__empty__eq,axiom,
% 0.33/0.62 ! [B5: set_op3940070208846178154it_nat] :
% 0.33/0.62 ( ( ( these_6645423997822192641it_nat @ B5 )
% 0.33/0.62 = bot_bo6361524548789211024it_nat )
% 0.33/0.62 = ( ( B5 = bot_bo8185009268211221974it_nat )
% 0.33/0.62 | ( B5
% 0.33/0.62 = ( insert7468008629046257882it_nat @ none_P2587165478634041381it_nat @ bot_bo8185009268211221974it_nat ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % these_empty_eq
% 0.33/0.62 thf(fact_5639_these__empty__eq,axiom,
% 0.33/0.62 ! [B5: set_option_num] :
% 0.33/0.62 ( ( ( these_num @ B5 )
% 0.33/0.62 = bot_bot_set_num )
% 0.33/0.62 = ( ( B5 = bot_bo725063100934353204on_num )
% 0.33/0.62 | ( B5
% 0.33/0.62 = ( insert_option_num @ none_num @ bot_bo725063100934353204on_num ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % these_empty_eq
% 0.33/0.62 thf(fact_5640_these__empty__eq,axiom,
% 0.33/0.62 ! [B5: set_op239864471688321678it_nat] :
% 0.33/0.62 ( ( ( these_3407724651694999947it_nat @ B5 )
% 0.33/0.62 = bot_bo5696401558416705618it_nat )
% 0.33/0.62 = ( ( B5 = bot_bo1172055076661450530it_nat )
% 0.33/0.62 | ( B5
% 0.33/0.62 = ( insert2007652293347934600it_nat @ none_P9117596204409417319it_nat @ bot_bo1172055076661450530it_nat ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % these_empty_eq
% 0.33/0.62 thf(fact_5641_these__empty__eq,axiom,
% 0.33/0.62 ! [B5: set_op989438649584373901at_nat] :
% 0.33/0.62 ( ( ( these_1872268174106123684at_nat @ B5 )
% 0.33/0.62 = bot_bo228742789529271731at_nat )
% 0.33/0.62 = ( ( B5 = bot_bo1471150103859235065at_nat )
% 0.33/0.62 | ( B5
% 0.33/0.62 = ( insert6833468608972679677at_nat @ none_P5811896708078067656at_nat @ bot_bo1471150103859235065at_nat ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % these_empty_eq
% 0.33/0.62 thf(fact_5642_these__empty__eq,axiom,
% 0.33/0.62 ! [B5: set_op4508134149509766951at_nat] :
% 0.33/0.62 ( ( ( these_8061402112538453438at_nat @ B5 )
% 0.33/0.62 = bot_bo2099793752762293965at_nat )
% 0.33/0.62 = ( ( B5 = bot_bo3414888551220300179at_nat )
% 0.33/0.62 | ( B5
% 0.33/0.62 = ( insert6842972033726296599at_nat @ none_P5556105721700978146at_nat @ bot_bo3414888551220300179at_nat ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % these_empty_eq
% 0.33/0.62 thf(fact_5643_these__empty__eq,axiom,
% 0.33/0.62 ! [B5: set_option_o] :
% 0.33/0.62 ( ( ( these_o @ B5 )
% 0.33/0.62 = bot_bot_set_o )
% 0.33/0.62 = ( ( B5 = bot_bot_set_option_o )
% 0.33/0.62 | ( B5
% 0.33/0.62 = ( insert_option_o @ none_o @ bot_bot_set_option_o ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % these_empty_eq
% 0.33/0.62 thf(fact_5644_these__empty__eq,axiom,
% 0.33/0.62 ! [B5: set_option_nat] :
% 0.33/0.62 ( ( ( these_nat @ B5 )
% 0.33/0.62 = bot_bot_set_nat )
% 0.33/0.62 = ( ( B5 = bot_bo5009843511495006442on_nat )
% 0.33/0.62 | ( B5
% 0.33/0.62 = ( insert_option_nat @ none_nat @ bot_bo5009843511495006442on_nat ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % these_empty_eq
% 0.33/0.62 thf(fact_5645_these__empty__eq,axiom,
% 0.33/0.62 ! [B5: set_option_int] :
% 0.33/0.62 ( ( ( these_int @ B5 )
% 0.33/0.62 = bot_bot_set_int )
% 0.33/0.62 = ( ( B5 = bot_bo2519760366563279686on_int )
% 0.33/0.62 | ( B5
% 0.33/0.62 = ( insert_option_int @ none_int @ bot_bo2519760366563279686on_int ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % these_empty_eq
% 0.33/0.62 thf(fact_5646_these__not__empty__eq,axiom,
% 0.33/0.62 ! [B5: set_op3940070208846178154it_nat] :
% 0.33/0.62 ( ( ( these_6645423997822192641it_nat @ B5 )
% 0.33/0.62 != bot_bo6361524548789211024it_nat )
% 0.33/0.62 = ( ( B5 != bot_bo8185009268211221974it_nat )
% 0.33/0.62 & ( B5
% 0.33/0.62 != ( insert7468008629046257882it_nat @ none_P2587165478634041381it_nat @ bot_bo8185009268211221974it_nat ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % these_not_empty_eq
% 0.33/0.62 thf(fact_5647_these__not__empty__eq,axiom,
% 0.33/0.62 ! [B5: set_option_num] :
% 0.33/0.62 ( ( ( these_num @ B5 )
% 0.33/0.62 != bot_bot_set_num )
% 0.33/0.62 = ( ( B5 != bot_bo725063100934353204on_num )
% 0.33/0.62 & ( B5
% 0.33/0.62 != ( insert_option_num @ none_num @ bot_bo725063100934353204on_num ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % these_not_empty_eq
% 0.33/0.62 thf(fact_5648_these__not__empty__eq,axiom,
% 0.33/0.62 ! [B5: set_op239864471688321678it_nat] :
% 0.33/0.62 ( ( ( these_3407724651694999947it_nat @ B5 )
% 0.33/0.62 != bot_bo5696401558416705618it_nat )
% 0.33/0.62 = ( ( B5 != bot_bo1172055076661450530it_nat )
% 0.33/0.62 & ( B5
% 0.33/0.62 != ( insert2007652293347934600it_nat @ none_P9117596204409417319it_nat @ bot_bo1172055076661450530it_nat ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % these_not_empty_eq
% 0.33/0.62 thf(fact_5649_these__not__empty__eq,axiom,
% 0.33/0.62 ! [B5: set_op989438649584373901at_nat] :
% 0.33/0.62 ( ( ( these_1872268174106123684at_nat @ B5 )
% 0.33/0.62 != bot_bo228742789529271731at_nat )
% 0.33/0.62 = ( ( B5 != bot_bo1471150103859235065at_nat )
% 0.33/0.62 & ( B5
% 0.33/0.62 != ( insert6833468608972679677at_nat @ none_P5811896708078067656at_nat @ bot_bo1471150103859235065at_nat ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % these_not_empty_eq
% 0.33/0.62 thf(fact_5650_these__not__empty__eq,axiom,
% 0.33/0.62 ! [B5: set_op4508134149509766951at_nat] :
% 0.33/0.62 ( ( ( these_8061402112538453438at_nat @ B5 )
% 0.33/0.62 != bot_bo2099793752762293965at_nat )
% 0.33/0.62 = ( ( B5 != bot_bo3414888551220300179at_nat )
% 0.33/0.62 & ( B5
% 0.33/0.62 != ( insert6842972033726296599at_nat @ none_P5556105721700978146at_nat @ bot_bo3414888551220300179at_nat ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % these_not_empty_eq
% 0.33/0.62 thf(fact_5651_these__not__empty__eq,axiom,
% 0.33/0.62 ! [B5: set_option_o] :
% 0.33/0.62 ( ( ( these_o @ B5 )
% 0.33/0.62 != bot_bot_set_o )
% 0.33/0.62 = ( ( B5 != bot_bot_set_option_o )
% 0.33/0.62 & ( B5
% 0.33/0.62 != ( insert_option_o @ none_o @ bot_bot_set_option_o ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % these_not_empty_eq
% 0.33/0.62 thf(fact_5652_these__not__empty__eq,axiom,
% 0.33/0.62 ! [B5: set_option_nat] :
% 0.33/0.62 ( ( ( these_nat @ B5 )
% 0.33/0.62 != bot_bot_set_nat )
% 0.33/0.62 = ( ( B5 != bot_bo5009843511495006442on_nat )
% 0.33/0.62 & ( B5
% 0.33/0.62 != ( insert_option_nat @ none_nat @ bot_bo5009843511495006442on_nat ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % these_not_empty_eq
% 0.33/0.62 thf(fact_5653_these__not__empty__eq,axiom,
% 0.33/0.62 ! [B5: set_option_int] :
% 0.33/0.62 ( ( ( these_int @ B5 )
% 0.33/0.62 != bot_bot_set_int )
% 0.33/0.62 = ( ( B5 != bot_bo2519760366563279686on_int )
% 0.33/0.62 & ( B5
% 0.33/0.62 != ( insert_option_int @ none_int @ bot_bo2519760366563279686on_int ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % these_not_empty_eq
% 0.33/0.62 thf(fact_5654_not__UNIV__eq__Icc,axiom,
% 0.33/0.62 ! [L4: int,H5: int] :
% 0.33/0.62 ( top_top_set_int
% 0.33/0.62 != ( set_or1266510415728281911st_int @ L4 @ H5 ) ) ).
% 0.33/0.62
% 0.33/0.62 % not_UNIV_eq_Icc
% 0.33/0.62 thf(fact_5655_not__UNIV__eq__Icc,axiom,
% 0.33/0.62 ! [L4: nat,H5: nat] :
% 0.33/0.62 ( top_top_set_nat
% 0.33/0.62 != ( set_or1269000886237332187st_nat @ L4 @ H5 ) ) ).
% 0.33/0.62
% 0.33/0.62 % not_UNIV_eq_Icc
% 0.33/0.62 thf(fact_5656_infinite__Iic,axiom,
% 0.33/0.62 ! [A: int] :
% 0.33/0.62 ~ ( finite_finite_int @ ( set_ord_atMost_int @ A ) ) ).
% 0.33/0.62
% 0.33/0.62 % infinite_Iic
% 0.33/0.62 thf(fact_5657_infinite__Iio,axiom,
% 0.33/0.62 ! [A: int] :
% 0.33/0.62 ~ ( finite_finite_int @ ( set_ord_lessThan_int @ A ) ) ).
% 0.33/0.62
% 0.33/0.62 % infinite_Iio
% 0.33/0.62 thf(fact_5658_not__UNIV__eq__Iic,axiom,
% 0.33/0.62 ! [H5: int] :
% 0.33/0.62 ( top_top_set_int
% 0.33/0.62 != ( set_ord_atMost_int @ H5 ) ) ).
% 0.33/0.62
% 0.33/0.62 % not_UNIV_eq_Iic
% 0.33/0.62 thf(fact_5659_not__UNIV__eq__Iic,axiom,
% 0.33/0.62 ! [H5: nat] :
% 0.33/0.62 ( top_top_set_nat
% 0.33/0.62 != ( set_ord_atMost_nat @ H5 ) ) ).
% 0.33/0.62
% 0.33/0.62 % not_UNIV_eq_Iic
% 0.33/0.62 thf(fact_5660_card__1__singletonI,axiom,
% 0.33/0.62 ! [S2: set_Product_unit,X: product_unit] :
% 0.33/0.62 ( ( finite4290736615968046902t_unit @ S2 )
% 0.33/0.62 => ( ( ( finite410649719033368117t_unit @ S2 )
% 0.33/0.62 = one_one_nat )
% 0.33/0.62 => ( ( member_Product_unit @ X @ S2 )
% 0.33/0.62 => ( S2
% 0.33/0.62 = ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % card_1_singletonI
% 0.33/0.62 thf(fact_5661_card__1__singletonI,axiom,
% 0.33/0.62 ! [S2: set_list_nat,X: list_nat] :
% 0.33/0.62 ( ( finite8100373058378681591st_nat @ S2 )
% 0.33/0.62 => ( ( ( finite_card_list_nat @ S2 )
% 0.33/0.62 = one_one_nat )
% 0.33/0.62 => ( ( member_list_nat @ X @ S2 )
% 0.33/0.62 => ( S2
% 0.33/0.62 = ( insert_list_nat @ X @ bot_bot_set_list_nat ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % card_1_singletonI
% 0.33/0.62 thf(fact_5662_card__1__singletonI,axiom,
% 0.33/0.62 ! [S2: set_Code_integer,X: code_integer] :
% 0.33/0.62 ( ( finite6017078050557962740nteger @ S2 )
% 0.33/0.62 => ( ( ( finite4902975817058060853nteger @ S2 )
% 0.33/0.62 = one_one_nat )
% 0.33/0.62 => ( ( member_Code_integer @ X @ S2 )
% 0.33/0.62 => ( S2
% 0.33/0.62 = ( insert_Code_integer @ X @ bot_bo3990330152332043303nteger ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % card_1_singletonI
% 0.33/0.62 thf(fact_5663_card__1__singletonI,axiom,
% 0.33/0.62 ! [S2: set_Pr4329608150637261639at_nat,X: produc3843707927480180839at_nat] :
% 0.33/0.62 ( ( finite4343798906461161616at_nat @ S2 )
% 0.33/0.62 => ( ( ( finite3771342082235030671at_nat @ S2 )
% 0.33/0.62 = one_one_nat )
% 0.33/0.62 => ( ( member8757157785044589968at_nat @ X @ S2 )
% 0.33/0.62 => ( S2
% 0.33/0.62 = ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % card_1_singletonI
% 0.33/0.62 thf(fact_5664_card__1__singletonI,axiom,
% 0.33/0.62 ! [S2: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat] :
% 0.33/0.62 ( ( finite6177210948735845034at_nat @ S2 )
% 0.33/0.62 => ( ( ( finite711546835091564841at_nat @ S2 )
% 0.33/0.62 = one_one_nat )
% 0.33/0.62 => ( ( member8440522571783428010at_nat @ X @ S2 )
% 0.33/0.62 => ( S2
% 0.33/0.62 = ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % card_1_singletonI
% 0.33/0.62 thf(fact_5665_card__1__singletonI,axiom,
% 0.33/0.62 ! [S2: set_o,X: $o] :
% 0.33/0.62 ( ( finite_finite_o @ S2 )
% 0.33/0.62 => ( ( ( finite_card_o @ S2 )
% 0.33/0.62 = one_one_nat )
% 0.33/0.62 => ( ( member_o @ X @ S2 )
% 0.33/0.62 => ( S2
% 0.33/0.62 = ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % card_1_singletonI
% 0.33/0.62 thf(fact_5666_card__1__singletonI,axiom,
% 0.33/0.62 ! [S2: set_nat,X: nat] :
% 0.33/0.62 ( ( finite_finite_nat @ S2 )
% 0.33/0.62 => ( ( ( finite_card_nat @ S2 )
% 0.33/0.62 = one_one_nat )
% 0.33/0.62 => ( ( member_nat @ X @ S2 )
% 0.33/0.62 => ( S2
% 0.33/0.62 = ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % card_1_singletonI
% 0.33/0.62 thf(fact_5667_card__1__singletonI,axiom,
% 0.33/0.62 ! [S2: set_int,X: int] :
% 0.33/0.62 ( ( finite_finite_int @ S2 )
% 0.33/0.62 => ( ( ( finite_card_int @ S2 )
% 0.33/0.62 = one_one_nat )
% 0.33/0.62 => ( ( member_int @ X @ S2 )
% 0.33/0.62 => ( S2
% 0.33/0.62 = ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % card_1_singletonI
% 0.33/0.62 thf(fact_5668_finite__M__bounded__by__nat,axiom,
% 0.33/0.62 ! [P: nat > $o,I: nat] :
% 0.33/0.62 ( finite_finite_nat
% 0.33/0.62 @ ( collect_nat
% 0.33/0.62 @ ^ [K4: nat] :
% 0.33/0.62 ( ( P @ K4 )
% 0.33/0.62 & ( ord_less_nat @ K4 @ I ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % finite_M_bounded_by_nat
% 0.33/0.62 thf(fact_5669_finite__less__ub,axiom,
% 0.33/0.62 ! [F: nat > nat,U: nat] :
% 0.33/0.62 ( ! [N: nat] : ( ord_less_eq_nat @ N @ ( F @ N ) )
% 0.33/0.62 => ( finite_finite_nat
% 0.33/0.62 @ ( collect_nat
% 0.33/0.62 @ ^ [N4: nat] : ( ord_less_eq_nat @ ( F @ N4 ) @ U ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % finite_less_ub
% 0.33/0.62 thf(fact_5670_card__insert__disjoint_H,axiom,
% 0.33/0.62 ! [A2: set_Pr4329608150637261639at_nat,X: produc3843707927480180839at_nat] :
% 0.33/0.62 ( ( finite4343798906461161616at_nat @ A2 )
% 0.33/0.62 => ( ~ ( member8757157785044589968at_nat @ X @ A2 )
% 0.33/0.62 => ( ( minus_minus_nat @ ( finite3771342082235030671at_nat @ ( insert9069300056098147895at_nat @ X @ A2 ) ) @ ( suc @ zero_zero_nat ) )
% 0.33/0.62 = ( finite3771342082235030671at_nat @ A2 ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % card_insert_disjoint'
% 0.33/0.62 thf(fact_5671_card__insert__disjoint_H,axiom,
% 0.33/0.62 ! [A2: set_o,X: $o] :
% 0.33/0.62 ( ( finite_finite_o @ A2 )
% 0.33/0.62 => ( ~ ( member_o @ X @ A2 )
% 0.33/0.62 => ( ( minus_minus_nat @ ( finite_card_o @ ( insert_o @ X @ A2 ) ) @ ( suc @ zero_zero_nat ) )
% 0.33/0.62 = ( finite_card_o @ A2 ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % card_insert_disjoint'
% 0.33/0.62 thf(fact_5672_card__insert__disjoint_H,axiom,
% 0.33/0.62 ! [A2: set_Product_unit,X: product_unit] :
% 0.33/0.62 ( ( finite4290736615968046902t_unit @ A2 )
% 0.33/0.62 => ( ~ ( member_Product_unit @ X @ A2 )
% 0.33/0.62 => ( ( minus_minus_nat @ ( finite410649719033368117t_unit @ ( insert_Product_unit @ X @ A2 ) ) @ ( suc @ zero_zero_nat ) )
% 0.33/0.62 = ( finite410649719033368117t_unit @ A2 ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % card_insert_disjoint'
% 0.33/0.62 thf(fact_5673_card__insert__disjoint_H,axiom,
% 0.33/0.62 ! [A2: set_list_nat,X: list_nat] :
% 0.33/0.62 ( ( finite8100373058378681591st_nat @ A2 )
% 0.33/0.62 => ( ~ ( member_list_nat @ X @ A2 )
% 0.33/0.62 => ( ( minus_minus_nat @ ( finite_card_list_nat @ ( insert_list_nat @ X @ A2 ) ) @ ( suc @ zero_zero_nat ) )
% 0.33/0.62 = ( finite_card_list_nat @ A2 ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % card_insert_disjoint'
% 0.33/0.62 thf(fact_5674_card__insert__disjoint_H,axiom,
% 0.33/0.62 ! [A2: set_nat,X: nat] :
% 0.33/0.62 ( ( finite_finite_nat @ A2 )
% 0.33/0.62 => ( ~ ( member_nat @ X @ A2 )
% 0.33/0.62 => ( ( minus_minus_nat @ ( finite_card_nat @ ( insert_nat @ X @ A2 ) ) @ ( suc @ zero_zero_nat ) )
% 0.33/0.62 = ( finite_card_nat @ A2 ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % card_insert_disjoint'
% 0.33/0.62 thf(fact_5675_card__insert__disjoint_H,axiom,
% 0.33/0.62 ! [A2: set_int,X: int] :
% 0.33/0.62 ( ( finite_finite_int @ A2 )
% 0.33/0.62 => ( ~ ( member_int @ X @ A2 )
% 0.33/0.62 => ( ( minus_minus_nat @ ( finite_card_int @ ( insert_int @ X @ A2 ) ) @ ( suc @ zero_zero_nat ) )
% 0.33/0.62 = ( finite_card_int @ A2 ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % card_insert_disjoint'
% 0.33/0.62 thf(fact_5676_card__insert__disjoint_H,axiom,
% 0.33/0.62 ! [A2: set_Code_integer,X: code_integer] :
% 0.33/0.62 ( ( finite6017078050557962740nteger @ A2 )
% 0.33/0.62 => ( ~ ( member_Code_integer @ X @ A2 )
% 0.33/0.62 => ( ( minus_minus_nat @ ( finite4902975817058060853nteger @ ( insert_Code_integer @ X @ A2 ) ) @ ( suc @ zero_zero_nat ) )
% 0.33/0.62 = ( finite4902975817058060853nteger @ A2 ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % card_insert_disjoint'
% 0.33/0.62 thf(fact_5677_card__insert__disjoint_H,axiom,
% 0.33/0.62 ! [A2: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat] :
% 0.33/0.62 ( ( finite6177210948735845034at_nat @ A2 )
% 0.33/0.62 => ( ~ ( member8440522571783428010at_nat @ X @ A2 )
% 0.33/0.62 => ( ( minus_minus_nat @ ( finite711546835091564841at_nat @ ( insert8211810215607154385at_nat @ X @ A2 ) ) @ ( suc @ zero_zero_nat ) )
% 0.33/0.62 = ( finite711546835091564841at_nat @ A2 ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % card_insert_disjoint'
% 0.33/0.62 thf(fact_5678_in__these__eq,axiom,
% 0.33/0.62 ! [X: produc3843707927480180839at_nat,A2: set_op989438649584373901at_nat] :
% 0.33/0.62 ( ( member8757157785044589968at_nat @ X @ ( these_1872268174106123684at_nat @ A2 ) )
% 0.33/0.62 = ( member4288423094740844502at_nat @ ( some_P131194445498448716at_nat @ X ) @ A2 ) ) ).
% 0.33/0.62
% 0.33/0.62 % in_these_eq
% 0.33/0.62 thf(fact_5679_in__these__eq,axiom,
% 0.33/0.62 ! [X: product_prod_nat_nat,A2: set_op4508134149509766951at_nat] :
% 0.33/0.62 ( ( member8440522571783428010at_nat @ X @ ( these_8061402112538453438at_nat @ A2 ) )
% 0.33/0.62 = ( member3954567711264315760at_nat @ ( some_P7363390416028606310at_nat @ X ) @ A2 ) ) ).
% 0.33/0.62
% 0.33/0.62 % in_these_eq
% 0.33/0.62 thf(fact_5680_in__these__eq,axiom,
% 0.33/0.62 ! [X: $o,A2: set_option_o] :
% 0.33/0.62 ( ( member_o @ X @ ( these_o @ A2 ) )
% 0.33/0.62 = ( member_option_o @ ( some_o @ X ) @ A2 ) ) ).
% 0.33/0.62
% 0.33/0.62 % in_these_eq
% 0.33/0.62 thf(fact_5681_in__these__eq,axiom,
% 0.33/0.62 ! [X: nat,A2: set_option_nat] :
% 0.33/0.62 ( ( member_nat @ X @ ( these_nat @ A2 ) )
% 0.33/0.62 = ( member_option_nat @ ( some_nat @ X ) @ A2 ) ) ).
% 0.33/0.62
% 0.33/0.62 % in_these_eq
% 0.33/0.62 thf(fact_5682_in__these__eq,axiom,
% 0.33/0.62 ! [X: int,A2: set_option_int] :
% 0.33/0.62 ( ( member_int @ X @ ( these_int @ A2 ) )
% 0.33/0.62 = ( member_option_int @ ( some_int @ X ) @ A2 ) ) ).
% 0.33/0.62
% 0.33/0.62 % in_these_eq
% 0.33/0.62 thf(fact_5683_in__these__eq,axiom,
% 0.33/0.62 ! [X: num,A2: set_option_num] :
% 0.33/0.62 ( ( member_num @ X @ ( these_num @ A2 ) )
% 0.33/0.62 = ( member_option_num @ ( some_num @ X ) @ A2 ) ) ).
% 0.33/0.62
% 0.33/0.62 % in_these_eq
% 0.33/0.62 thf(fact_5684_in__these__eq,axiom,
% 0.33/0.62 ! [X: produc8664842809031399944it_nat,A2: set_op239864471688321678it_nat] :
% 0.33/0.62 ( ( member3421417852355157663it_nat @ X @ ( these_3407724651694999947it_nat @ A2 ) )
% 0.33/0.62 = ( member5596548051065438575it_nat @ ( some_P1914260805536162275it_nat @ X ) @ A2 ) ) ).
% 0.33/0.62
% 0.33/0.62 % in_these_eq
% 0.33/0.62 thf(fact_5685_infinite__Icc,axiom,
% 0.33/0.62 ! [A: rat,B: rat] :
% 0.33/0.62 ( ( ord_less_rat @ A @ B )
% 0.33/0.62 => ~ ( finite_finite_rat @ ( set_or633870826150836451st_rat @ A @ B ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % infinite_Icc
% 0.33/0.62 thf(fact_5686_infinite__Ico,axiom,
% 0.33/0.62 ! [A: rat,B: rat] :
% 0.33/0.62 ( ( ord_less_rat @ A @ B )
% 0.33/0.62 => ~ ( finite_finite_rat @ ( set_or4029947393144176647an_rat @ A @ B ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % infinite_Ico
% 0.33/0.62 thf(fact_5687_subset__eq__atLeast0__atMost__finite,axiom,
% 0.33/0.62 ! [N6: set_nat,N2: nat] :
% 0.33/0.62 ( ( ord_less_eq_set_nat @ N6 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 0.33/0.62 => ( finite_finite_nat @ N6 ) ) ).
% 0.33/0.62
% 0.33/0.62 % subset_eq_atLeast0_atMost_finite
% 0.33/0.62 thf(fact_5688_subset__eq__atLeast0__lessThan__finite,axiom,
% 0.33/0.62 ! [N6: set_nat,N2: nat] :
% 0.33/0.62 ( ( ord_less_eq_set_nat @ N6 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) )
% 0.33/0.62 => ( finite_finite_nat @ N6 ) ) ).
% 0.33/0.62
% 0.33/0.62 % subset_eq_atLeast0_lessThan_finite
% 0.33/0.62 thf(fact_5689_atMost__Suc,axiom,
% 0.33/0.62 ! [K: nat] :
% 0.33/0.62 ( ( set_ord_atMost_nat @ ( suc @ K ) )
% 0.33/0.62 = ( insert_nat @ ( suc @ K ) @ ( set_ord_atMost_nat @ K ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % atMost_Suc
% 0.33/0.62 thf(fact_5690_surj__fun__eq,axiom,
% 0.33/0.62 ! [F: num > code_integer,X11: set_num,G1: code_integer > code_integer,G22: code_integer > code_integer] :
% 0.33/0.62 ( ( ( image_8379761247532268670nteger @ F @ X11 )
% 0.33/0.62 = top_to4645266643341252675nteger )
% 0.33/0.62 => ( ! [X4: num] :
% 0.33/0.62 ( ( member_num @ X4 @ X11 )
% 0.33/0.62 => ( ( comp_C3531382070062128313er_num @ G1 @ F @ X4 )
% 0.33/0.62 = ( comp_C3531382070062128313er_num @ G22 @ F @ X4 ) ) )
% 0.33/0.62 => ( G1 = G22 ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % surj_fun_eq
% 0.33/0.62 thf(fact_5691_surj__fun__eq,axiom,
% 0.33/0.62 ! [F: code_integer > code_integer,X11: set_Code_integer,G1: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,G22: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 0.33/0.62 ( ( ( image_4470545334726330049nteger @ F @ X11 )
% 0.33/0.62 = top_to4645266643341252675nteger )
% 0.33/0.62 => ( ! [X4: code_integer] :
% 0.33/0.62 ( ( member_Code_integer @ X4 @ X11 )
% 0.33/0.62 => ( ( comp_C1593894019821074884nteger @ G1 @ F @ X4 )
% 0.33/0.62 = ( comp_C1593894019821074884nteger @ G22 @ F @ X4 ) ) )
% 0.33/0.62 => ( G1 = G22 ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % surj_fun_eq
% 0.33/0.62 thf(fact_5692_surj__fun__eq,axiom,
% 0.33/0.62 ! [F: code_integer > code_integer > code_integer,X11: set_Code_integer,G1: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G22: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 0.33/0.62 ( ( ( image_2177946750938214461nteger @ F @ X11 )
% 0.33/0.62 = top_to3804862627464599871nteger )
% 0.33/0.62 => ( ! [X4: code_integer] :
% 0.33/0.62 ( ( member_Code_integer @ X4 @ X11 )
% 0.33/0.62 => ( ( comp_C8797469213163452608nteger @ G1 @ F @ X4 )
% 0.33/0.62 = ( comp_C8797469213163452608nteger @ G22 @ F @ X4 ) ) )
% 0.33/0.62 => ( G1 = G22 ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % surj_fun_eq
% 0.33/0.62 thf(fact_5693_surj__fun__eq,axiom,
% 0.33/0.62 ! [F: int > nat,X11: set_int,G1: nat > num,G22: nat > num] :
% 0.33/0.62 ( ( ( image_int_nat @ F @ X11 )
% 0.33/0.62 = top_top_set_nat )
% 0.33/0.62 => ( ! [X4: int] :
% 0.33/0.62 ( ( member_int @ X4 @ X11 )
% 0.33/0.62 => ( ( comp_nat_num_int @ G1 @ F @ X4 )
% 0.33/0.62 = ( comp_nat_num_int @ G22 @ F @ X4 ) ) )
% 0.33/0.62 => ( G1 = G22 ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % surj_fun_eq
% 0.33/0.62 thf(fact_5694_comp__surj,axiom,
% 0.33/0.62 ! [F: num > code_integer,G: code_integer > code_integer] :
% 0.33/0.62 ( ( ( image_8379761247532268670nteger @ F @ top_top_set_num )
% 0.33/0.62 = top_to4645266643341252675nteger )
% 0.33/0.62 => ( ( ( image_4470545334726330049nteger @ G @ top_to4645266643341252675nteger )
% 0.33/0.62 = top_to4645266643341252675nteger )
% 0.33/0.62 => ( ( image_8379761247532268670nteger @ ( comp_C3531382070062128313er_num @ G @ F ) @ top_top_set_num )
% 0.33/0.62 = top_to4645266643341252675nteger ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % comp_surj
% 0.33/0.62 thf(fact_5695_comp__surj,axiom,
% 0.33/0.62 ! [F: nat > code_integer,G: code_integer > code_integer] :
% 0.33/0.62 ( ( ( image_1215581382706833972nteger @ F @ top_top_set_nat )
% 0.33/0.62 = top_to4645266643341252675nteger )
% 0.33/0.62 => ( ( ( image_4470545334726330049nteger @ G @ top_to4645266643341252675nteger )
% 0.33/0.62 = top_to4645266643341252675nteger )
% 0.33/0.62 => ( ( image_1215581382706833972nteger @ ( comp_C6974050283906349679er_nat @ G @ F ) @ top_top_set_nat )
% 0.33/0.62 = top_to4645266643341252675nteger ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % comp_surj
% 0.33/0.62 thf(fact_5696_comp__surj,axiom,
% 0.33/0.62 ! [F: nat > code_integer,G: code_integer > nat] :
% 0.33/0.62 ( ( ( image_1215581382706833972nteger @ F @ top_top_set_nat )
% 0.33/0.62 = top_to4645266643341252675nteger )
% 0.33/0.62 => ( ( ( image_951025933927791156er_nat @ G @ top_to4645266643341252675nteger )
% 0.33/0.62 = top_top_set_nat )
% 0.33/0.62 => ( ( image_nat_nat @ ( comp_C4049556595663050210at_nat @ G @ F ) @ top_top_set_nat )
% 0.33/0.62 = top_top_set_nat ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % comp_surj
% 0.33/0.62 thf(fact_5697_comp__surj,axiom,
% 0.33/0.62 ! [F: nat > code_integer,G: code_integer > product_unit] :
% 0.33/0.62 ( ( ( image_1215581382706833972nteger @ F @ top_top_set_nat )
% 0.33/0.62 = top_to4645266643341252675nteger )
% 0.33/0.62 => ( ( ( image_7182656606676592809t_unit @ G @ top_to4645266643341252675nteger )
% 0.33/0.62 = top_to1996260823553986621t_unit )
% 0.33/0.62 => ( ( image_8730104196221521654t_unit @ ( comp_C8086623346886033437it_nat @ G @ F ) @ top_top_set_nat )
% 0.33/0.62 = top_to1996260823553986621t_unit ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % comp_surj
% 0.33/0.62 thf(fact_5698_comp__surj,axiom,
% 0.33/0.62 ! [F: nat > code_integer,G: code_integer > int] :
% 0.33/0.62 ( ( ( image_1215581382706833972nteger @ F @ top_top_set_nat )
% 0.33/0.62 = top_to4645266643341252675nteger )
% 0.33/0.62 => ( ( ( image_948535463418740880er_int @ G @ top_to4645266643341252675nteger )
% 0.33/0.62 = top_top_set_int )
% 0.33/0.62 => ( ( image_nat_int @ ( comp_C5048910307564104766nt_nat @ G @ F ) @ top_top_set_nat )
% 0.33/0.62 = top_top_set_int ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % comp_surj
% 0.33/0.62 thf(fact_5699_comp__surj,axiom,
% 0.33/0.62 ! [F: nat > nat,G: nat > code_integer] :
% 0.33/0.62 ( ( ( image_nat_nat @ F @ top_top_set_nat )
% 0.33/0.62 = top_top_set_nat )
% 0.33/0.62 => ( ( ( image_1215581382706833972nteger @ G @ top_top_set_nat )
% 0.33/0.62 = top_to4645266643341252675nteger )
% 0.33/0.62 => ( ( image_1215581382706833972nteger @ ( comp_n3898172953802868194er_nat @ G @ F ) @ top_top_set_nat )
% 0.33/0.62 = top_to4645266643341252675nteger ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % comp_surj
% 0.33/0.62 thf(fact_5700_comp__surj,axiom,
% 0.33/0.62 ! [F: nat > nat,G: nat > nat] :
% 0.33/0.62 ( ( ( image_nat_nat @ F @ top_top_set_nat )
% 0.33/0.62 = top_top_set_nat )
% 0.33/0.62 => ( ( ( image_nat_nat @ G @ top_top_set_nat )
% 0.33/0.62 = top_top_set_nat )
% 0.33/0.62 => ( ( image_nat_nat @ ( comp_nat_nat_nat @ G @ F ) @ top_top_set_nat )
% 0.33/0.62 = top_top_set_nat ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % comp_surj
% 0.33/0.62 thf(fact_5701_comp__surj,axiom,
% 0.33/0.62 ! [F: nat > nat,G: nat > product_unit] :
% 0.33/0.62 ( ( ( image_nat_nat @ F @ top_top_set_nat )
% 0.33/0.62 = top_top_set_nat )
% 0.33/0.62 => ( ( ( image_8730104196221521654t_unit @ G @ top_top_set_nat )
% 0.33/0.62 = top_to1996260823553986621t_unit )
% 0.33/0.62 => ( ( image_8730104196221521654t_unit @ ( comp_n9025697279074352746it_nat @ G @ F ) @ top_top_set_nat )
% 0.33/0.62 = top_to1996260823553986621t_unit ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % comp_surj
% 0.33/0.62 thf(fact_5702_comp__surj,axiom,
% 0.33/0.62 ! [F: nat > nat,G: nat > int] :
% 0.33/0.62 ( ( ( image_nat_nat @ F @ top_top_set_nat )
% 0.33/0.62 = top_top_set_nat )
% 0.33/0.62 => ( ( ( image_nat_int @ G @ top_top_set_nat )
% 0.33/0.62 = top_top_set_int )
% 0.33/0.62 => ( ( image_nat_int @ ( comp_nat_int_nat @ G @ F ) @ top_top_set_nat )
% 0.33/0.62 = top_top_set_int ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % comp_surj
% 0.33/0.62 thf(fact_5703_comp__surj,axiom,
% 0.33/0.62 ! [F: nat > product_unit,G: product_unit > code_integer] :
% 0.33/0.62 ( ( ( image_8730104196221521654t_unit @ F @ top_top_set_nat )
% 0.33/0.62 = top_to1996260823553986621t_unit )
% 0.33/0.62 => ( ( ( image_3815118110082124069nteger @ G @ top_to1996260823553986621t_unit )
% 0.33/0.62 = top_to4645266643341252675nteger )
% 0.33/0.62 => ( ( image_1215581382706833972nteger @ ( comp_P756492639069434009er_nat @ G @ F ) @ top_top_set_nat )
% 0.33/0.62 = top_to4645266643341252675nteger ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % comp_surj
% 0.33/0.62 thf(fact_5704_fun_Oset__map,axiom,
% 0.33/0.62 ! [F: code_integer > code_integer,V: num > code_integer] :
% 0.33/0.62 ( ( image_8379761247532268670nteger @ ( comp_C3531382070062128313er_num @ F @ V ) @ top_top_set_num )
% 0.33/0.62 = ( image_4470545334726330049nteger @ F @ ( image_8379761247532268670nteger @ V @ top_top_set_num ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % fun.set_map
% 0.33/0.62 thf(fact_5705_fun_Oset__map,axiom,
% 0.33/0.62 ! [F: code_integer > code_integer,V: nat > code_integer] :
% 0.33/0.62 ( ( image_1215581382706833972nteger @ ( comp_C6974050283906349679er_nat @ F @ V ) @ top_top_set_nat )
% 0.33/0.62 = ( image_4470545334726330049nteger @ F @ ( image_1215581382706833972nteger @ V @ top_top_set_nat ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % fun.set_map
% 0.33/0.62 thf(fact_5706_fun_Oset__map,axiom,
% 0.33/0.62 ! [F: int > code_integer,V: nat > int] :
% 0.33/0.62 ( ( image_1215581382706833972nteger @ ( comp_i1588355021709917246er_nat @ F @ V ) @ top_top_set_nat )
% 0.33/0.62 = ( image_1587234942943678608nteger @ F @ ( image_nat_int @ V @ top_top_set_nat ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % fun.set_map
% 0.33/0.62 thf(fact_5707_fun_Oset__map,axiom,
% 0.33/0.62 ! [F: nat > code_integer,V: nat > nat] :
% 0.33/0.62 ( ( image_1215581382706833972nteger @ ( comp_n3898172953802868194er_nat @ F @ V ) @ top_top_set_nat )
% 0.33/0.62 = ( image_1215581382706833972nteger @ F @ ( image_nat_nat @ V @ top_top_set_nat ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % fun.set_map
% 0.33/0.62 thf(fact_5708_fun_Oset__map,axiom,
% 0.33/0.62 ! [F: code_integer > nat,V: nat > code_integer] :
% 0.33/0.62 ( ( image_nat_nat @ ( comp_C4049556595663050210at_nat @ F @ V ) @ top_top_set_nat )
% 0.33/0.62 = ( image_951025933927791156er_nat @ F @ ( image_1215581382706833972nteger @ V @ top_top_set_nat ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % fun.set_map
% 0.33/0.62 thf(fact_5709_fun_Oset__map,axiom,
% 0.33/0.62 ! [F: int > nat,V: nat > int] :
% 0.33/0.62 ( ( image_nat_nat @ ( comp_int_nat_nat @ F @ V ) @ top_top_set_nat )
% 0.33/0.62 = ( image_int_nat @ F @ ( image_nat_int @ V @ top_top_set_nat ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % fun.set_map
% 0.33/0.62 thf(fact_5710_fun_Oset__map,axiom,
% 0.33/0.62 ! [F: nat > nat,V: nat > nat] :
% 0.33/0.62 ( ( image_nat_nat @ ( comp_nat_nat_nat @ F @ V ) @ top_top_set_nat )
% 0.33/0.62 = ( image_nat_nat @ F @ ( image_nat_nat @ V @ top_top_set_nat ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % fun.set_map
% 0.33/0.62 thf(fact_5711_fun_Oset__map,axiom,
% 0.33/0.62 ! [F: code_integer > int,V: nat > code_integer] :
% 0.33/0.62 ( ( image_nat_int @ ( comp_C5048910307564104766nt_nat @ F @ V ) @ top_top_set_nat )
% 0.33/0.62 = ( image_948535463418740880er_int @ F @ ( image_1215581382706833972nteger @ V @ top_top_set_nat ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % fun.set_map
% 0.33/0.62 thf(fact_5712_fun_Oset__map,axiom,
% 0.33/0.62 ! [F: nat > int,V: nat > nat] :
% 0.33/0.62 ( ( image_nat_int @ ( comp_nat_int_nat @ F @ V ) @ top_top_set_nat )
% 0.33/0.62 = ( image_nat_int @ F @ ( image_nat_nat @ V @ top_top_set_nat ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % fun.set_map
% 0.33/0.62 thf(fact_5713_fun_Oset__map,axiom,
% 0.33/0.62 ! [F: int > int,V: nat > int] :
% 0.33/0.62 ( ( image_nat_int @ ( comp_int_int_nat @ F @ V ) @ top_top_set_nat )
% 0.33/0.62 = ( image_int_int @ F @ ( image_nat_int @ V @ top_top_set_nat ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % fun.set_map
% 0.33/0.62 thf(fact_5714_fun_Omap__cong,axiom,
% 0.33/0.62 ! [X: num > code_integer,Ya: num > code_integer,F: code_integer > code_integer,G: code_integer > code_integer] :
% 0.33/0.62 ( ( X = Ya )
% 0.33/0.62 => ( ! [Z3: code_integer] :
% 0.33/0.62 ( ( member_Code_integer @ Z3 @ ( image_8379761247532268670nteger @ Ya @ top_top_set_num ) )
% 0.33/0.62 => ( ( F @ Z3 )
% 0.33/0.62 = ( G @ Z3 ) ) )
% 0.33/0.62 => ( ( comp_C3531382070062128313er_num @ F @ X )
% 0.33/0.62 = ( comp_C3531382070062128313er_num @ G @ Ya ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % fun.map_cong
% 0.33/0.62 thf(fact_5715_fun_Omap__cong,axiom,
% 0.33/0.62 ! [X: code_integer > code_integer,Ya: code_integer > code_integer,F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 0.33/0.62 ( ( X = Ya )
% 0.33/0.62 => ( ! [Z3: code_integer] :
% 0.33/0.62 ( ( member_Code_integer @ Z3 @ ( image_4470545334726330049nteger @ Ya @ top_to4645266643341252675nteger ) )
% 0.33/0.62 => ( ( F @ Z3 )
% 0.33/0.62 = ( G @ Z3 ) ) )
% 0.33/0.62 => ( ( comp_C1593894019821074884nteger @ F @ X )
% 0.33/0.62 = ( comp_C1593894019821074884nteger @ G @ Ya ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % fun.map_cong
% 0.33/0.62 thf(fact_5716_fun_Omap__cong,axiom,
% 0.33/0.62 ! [X: code_integer > code_integer > code_integer,Ya: code_integer > code_integer > code_integer,F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 0.33/0.62 ( ( X = Ya )
% 0.33/0.62 => ( ! [Z3: code_integer > code_integer] :
% 0.33/0.62 ( ( member2790140394383616496nteger @ Z3 @ ( image_2177946750938214461nteger @ Ya @ top_to4645266643341252675nteger ) )
% 0.33/0.62 => ( ( F @ Z3 )
% 0.33/0.62 = ( G @ Z3 ) ) )
% 0.33/0.62 => ( ( comp_C8797469213163452608nteger @ F @ X )
% 0.33/0.62 = ( comp_C8797469213163452608nteger @ G @ Ya ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % fun.map_cong
% 0.33/0.62 thf(fact_5717_fun_Omap__cong,axiom,
% 0.33/0.62 ! [X: int > nat,Ya: int > nat,F: nat > num,G: nat > num] :
% 0.33/0.62 ( ( X = Ya )
% 0.33/0.62 => ( ! [Z3: nat] :
% 0.33/0.62 ( ( member_nat @ Z3 @ ( image_int_nat @ Ya @ top_top_set_int ) )
% 0.33/0.62 => ( ( F @ Z3 )
% 0.33/0.62 = ( G @ Z3 ) ) )
% 0.33/0.62 => ( ( comp_nat_num_int @ F @ X )
% 0.33/0.62 = ( comp_nat_num_int @ G @ Ya ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % fun.map_cong
% 0.33/0.62 thf(fact_5718_fun_Omap__cong0,axiom,
% 0.33/0.62 ! [X: num > code_integer,F: code_integer > code_integer,G: code_integer > code_integer] :
% 0.33/0.62 ( ! [Z3: code_integer] :
% 0.33/0.62 ( ( member_Code_integer @ Z3 @ ( image_8379761247532268670nteger @ X @ top_top_set_num ) )
% 0.33/0.62 => ( ( F @ Z3 )
% 0.33/0.62 = ( G @ Z3 ) ) )
% 0.33/0.62 => ( ( comp_C3531382070062128313er_num @ F @ X )
% 0.33/0.62 = ( comp_C3531382070062128313er_num @ G @ X ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % fun.map_cong0
% 0.33/0.62 thf(fact_5719_fun_Omap__cong0,axiom,
% 0.33/0.62 ! [X: code_integer > code_integer,F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 0.33/0.62 ( ! [Z3: code_integer] :
% 0.33/0.62 ( ( member_Code_integer @ Z3 @ ( image_4470545334726330049nteger @ X @ top_to4645266643341252675nteger ) )
% 0.33/0.62 => ( ( F @ Z3 )
% 0.33/0.62 = ( G @ Z3 ) ) )
% 0.33/0.62 => ( ( comp_C1593894019821074884nteger @ F @ X )
% 0.33/0.62 = ( comp_C1593894019821074884nteger @ G @ X ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % fun.map_cong0
% 0.33/0.62 thf(fact_5720_fun_Omap__cong0,axiom,
% 0.33/0.62 ! [X: code_integer > code_integer > code_integer,F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 0.33/0.62 ( ! [Z3: code_integer > code_integer] :
% 0.33/0.62 ( ( member2790140394383616496nteger @ Z3 @ ( image_2177946750938214461nteger @ X @ top_to4645266643341252675nteger ) )
% 0.33/0.62 => ( ( F @ Z3 )
% 0.33/0.62 = ( G @ Z3 ) ) )
% 0.33/0.62 => ( ( comp_C8797469213163452608nteger @ F @ X )
% 0.33/0.62 = ( comp_C8797469213163452608nteger @ G @ X ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % fun.map_cong0
% 0.33/0.62 thf(fact_5721_fun_Omap__cong0,axiom,
% 0.33/0.62 ! [X: int > nat,F: nat > num,G: nat > num] :
% 0.33/0.62 ( ! [Z3: nat] :
% 0.33/0.62 ( ( member_nat @ Z3 @ ( image_int_nat @ X @ top_top_set_int ) )
% 0.33/0.62 => ( ( F @ Z3 )
% 0.33/0.62 = ( G @ Z3 ) ) )
% 0.33/0.62 => ( ( comp_nat_num_int @ F @ X )
% 0.33/0.62 = ( comp_nat_num_int @ G @ X ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % fun.map_cong0
% 0.33/0.62 thf(fact_5722_fun_Oinj__map__strong,axiom,
% 0.33/0.62 ! [X: num > code_integer,Xa: num > code_integer,F: code_integer > code_integer,Fa: code_integer > code_integer] :
% 0.33/0.62 ( ! [Z3: code_integer,Za: code_integer] :
% 0.33/0.62 ( ( member_Code_integer @ Z3 @ ( image_8379761247532268670nteger @ X @ top_top_set_num ) )
% 0.33/0.62 => ( ( member_Code_integer @ Za @ ( image_8379761247532268670nteger @ Xa @ top_top_set_num ) )
% 0.33/0.62 => ( ( ( F @ Z3 )
% 0.33/0.62 = ( Fa @ Za ) )
% 0.33/0.62 => ( Z3 = Za ) ) ) )
% 0.33/0.62 => ( ( ( comp_C3531382070062128313er_num @ F @ X )
% 0.33/0.62 = ( comp_C3531382070062128313er_num @ Fa @ Xa ) )
% 0.33/0.62 => ( X = Xa ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % fun.inj_map_strong
% 0.33/0.62 thf(fact_5723_fun_Oinj__map__strong,axiom,
% 0.33/0.62 ! [X: code_integer > code_integer,Xa: code_integer > code_integer,F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,Fa: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 0.33/0.62 ( ! [Z3: code_integer,Za: code_integer] :
% 0.33/0.62 ( ( member_Code_integer @ Z3 @ ( image_4470545334726330049nteger @ X @ top_to4645266643341252675nteger ) )
% 0.33/0.62 => ( ( member_Code_integer @ Za @ ( image_4470545334726330049nteger @ Xa @ top_to4645266643341252675nteger ) )
% 0.33/0.62 => ( ( ( F @ Z3 )
% 0.33/0.62 = ( Fa @ Za ) )
% 0.33/0.62 => ( Z3 = Za ) ) ) )
% 0.33/0.62 => ( ( ( comp_C1593894019821074884nteger @ F @ X )
% 0.33/0.62 = ( comp_C1593894019821074884nteger @ Fa @ Xa ) )
% 0.33/0.62 => ( X = Xa ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % fun.inj_map_strong
% 0.33/0.62 thf(fact_5724_fun_Oinj__map__strong,axiom,
% 0.33/0.62 ! [X: code_integer > code_integer > code_integer,Xa: code_integer > code_integer > code_integer,F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,Fa: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 0.33/0.62 ( ! [Z3: code_integer > code_integer,Za: code_integer > code_integer] :
% 0.33/0.62 ( ( member2790140394383616496nteger @ Z3 @ ( image_2177946750938214461nteger @ X @ top_to4645266643341252675nteger ) )
% 0.33/0.62 => ( ( member2790140394383616496nteger @ Za @ ( image_2177946750938214461nteger @ Xa @ top_to4645266643341252675nteger ) )
% 0.33/0.62 => ( ( ( F @ Z3 )
% 0.33/0.62 = ( Fa @ Za ) )
% 0.33/0.62 => ( Z3 = Za ) ) ) )
% 0.33/0.62 => ( ( ( comp_C8797469213163452608nteger @ F @ X )
% 0.33/0.62 = ( comp_C8797469213163452608nteger @ Fa @ Xa ) )
% 0.33/0.62 => ( X = Xa ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % fun.inj_map_strong
% 0.33/0.62 thf(fact_5725_fun_Oinj__map__strong,axiom,
% 0.33/0.62 ! [X: int > nat,Xa: int > nat,F: nat > num,Fa: nat > num] :
% 0.33/0.62 ( ! [Z3: nat,Za: nat] :
% 0.33/0.62 ( ( member_nat @ Z3 @ ( image_int_nat @ X @ top_top_set_int ) )
% 0.33/0.62 => ( ( member_nat @ Za @ ( image_int_nat @ Xa @ top_top_set_int ) )
% 0.33/0.62 => ( ( ( F @ Z3 )
% 0.33/0.62 = ( Fa @ Za ) )
% 0.33/0.62 => ( Z3 = Za ) ) ) )
% 0.33/0.62 => ( ( ( comp_nat_num_int @ F @ X )
% 0.33/0.62 = ( comp_nat_num_int @ Fa @ Xa ) )
% 0.33/0.62 => ( X = Xa ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % fun.inj_map_strong
% 0.33/0.62 thf(fact_5726_lessThan__Suc,axiom,
% 0.33/0.62 ! [K: nat] :
% 0.33/0.62 ( ( set_ord_lessThan_nat @ ( suc @ K ) )
% 0.33/0.62 = ( insert_nat @ K @ ( set_ord_lessThan_nat @ K ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % lessThan_Suc
% 0.33/0.62 thf(fact_5727_not__UNIV__le__Icc,axiom,
% 0.33/0.62 ! [L: int,H3: int] :
% 0.33/0.62 ~ ( ord_less_eq_set_int @ top_top_set_int @ ( set_or1266510415728281911st_int @ L @ H3 ) ) ).
% 0.33/0.62
% 0.33/0.62 % not_UNIV_le_Icc
% 0.33/0.62 thf(fact_5728_not__UNIV__le__Icc,axiom,
% 0.33/0.62 ! [L: nat,H3: nat] :
% 0.33/0.62 ~ ( ord_less_eq_set_nat @ top_top_set_nat @ ( set_or1269000886237332187st_nat @ L @ H3 ) ) ).
% 0.33/0.62
% 0.33/0.62 % not_UNIV_le_Icc
% 0.33/0.62 thf(fact_5729_surj__id,axiom,
% 0.33/0.62 ( ( image_o_o @ id_o @ top_top_set_o )
% 0.33/0.62 = top_top_set_o ) ).
% 0.33/0.62
% 0.33/0.62 % surj_id
% 0.33/0.62 thf(fact_5730_surj__id,axiom,
% 0.33/0.62 ( ( image_nat_o_nat_o @ id_nat_o @ top_top_set_nat_o )
% 0.33/0.62 = top_top_set_nat_o ) ).
% 0.33/0.62
% 0.33/0.62 % surj_id
% 0.33/0.62 thf(fact_5731_surj__id,axiom,
% 0.33/0.62 ( ( image_num_num @ id_num @ top_top_set_num )
% 0.33/0.62 = top_top_set_num ) ).
% 0.33/0.62
% 0.33/0.62 % surj_id
% 0.33/0.62 thf(fact_5732_surj__id,axiom,
% 0.33/0.62 ( ( image_nat_nat @ id_nat @ top_top_set_nat )
% 0.33/0.62 = top_top_set_nat ) ).
% 0.33/0.62
% 0.33/0.62 % surj_id
% 0.33/0.62 thf(fact_5733_surj__id,axiom,
% 0.33/0.62 ( ( image_405062704495631173t_unit @ id_Product_unit @ top_to1996260823553986621t_unit )
% 0.33/0.62 = top_to1996260823553986621t_unit ) ).
% 0.33/0.62
% 0.33/0.62 % surj_id
% 0.33/0.62 thf(fact_5734_surj__id,axiom,
% 0.33/0.62 ( ( image_int_int @ id_int @ top_top_set_int )
% 0.33/0.62 = top_top_set_int ) ).
% 0.33/0.62
% 0.33/0.62 % surj_id
% 0.33/0.62 thf(fact_5735_not__UNIV__le__Iic,axiom,
% 0.33/0.62 ! [H3: int] :
% 0.33/0.62 ~ ( ord_less_eq_set_int @ top_top_set_int @ ( set_ord_atMost_int @ H3 ) ) ).
% 0.33/0.62
% 0.33/0.62 % not_UNIV_le_Iic
% 0.33/0.62 thf(fact_5736_not__UNIV__le__Iic,axiom,
% 0.33/0.62 ! [H3: nat] :
% 0.33/0.62 ~ ( ord_less_eq_set_nat @ top_top_set_nat @ ( set_ord_atMost_nat @ H3 ) ) ).
% 0.33/0.62
% 0.33/0.62 % not_UNIV_le_Iic
% 0.33/0.62 thf(fact_5737_sum_Ofinite__Collect__op,axiom,
% 0.33/0.62 ! [I4: set_o,X: $o > code_integer,Y: $o > code_integer] :
% 0.33/0.62 ( ( finite_finite_o
% 0.33/0.62 @ ( collect_o
% 0.33/0.62 @ ^ [I3: $o] :
% 0.33/0.62 ( ( member_o @ I3 @ I4 )
% 0.33/0.62 & ( ( X @ I3 )
% 0.33/0.62 != zero_z3403309356797280102nteger ) ) ) )
% 0.33/0.62 => ( ( finite_finite_o
% 0.33/0.62 @ ( collect_o
% 0.33/0.62 @ ^ [I3: $o] :
% 0.33/0.62 ( ( member_o @ I3 @ I4 )
% 0.33/0.62 & ( ( Y @ I3 )
% 0.33/0.62 != zero_z3403309356797280102nteger ) ) ) )
% 0.33/0.62 => ( finite_finite_o
% 0.33/0.62 @ ( collect_o
% 0.33/0.62 @ ^ [I3: $o] :
% 0.33/0.62 ( ( member_o @ I3 @ I4 )
% 0.33/0.62 & ( ( plus_p5714425477246183910nteger @ ( X @ I3 ) @ ( Y @ I3 ) )
% 0.33/0.62 != zero_z3403309356797280102nteger ) ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % sum.finite_Collect_op
% 0.33/0.62 thf(fact_5738_sum_Ofinite__Collect__op,axiom,
% 0.33/0.62 ! [I4: set_nat,X: nat > code_integer,Y: nat > code_integer] :
% 0.33/0.62 ( ( finite_finite_nat
% 0.33/0.62 @ ( collect_nat
% 0.33/0.62 @ ^ [I3: nat] :
% 0.33/0.62 ( ( member_nat @ I3 @ I4 )
% 0.33/0.62 & ( ( X @ I3 )
% 0.33/0.62 != zero_z3403309356797280102nteger ) ) ) )
% 0.33/0.62 => ( ( finite_finite_nat
% 0.33/0.62 @ ( collect_nat
% 0.33/0.62 @ ^ [I3: nat] :
% 0.33/0.62 ( ( member_nat @ I3 @ I4 )
% 0.33/0.62 & ( ( Y @ I3 )
% 0.33/0.62 != zero_z3403309356797280102nteger ) ) ) )
% 0.33/0.62 => ( finite_finite_nat
% 0.33/0.62 @ ( collect_nat
% 0.33/0.62 @ ^ [I3: nat] :
% 0.33/0.62 ( ( member_nat @ I3 @ I4 )
% 0.33/0.62 & ( ( plus_p5714425477246183910nteger @ ( X @ I3 ) @ ( Y @ I3 ) )
% 0.33/0.62 != zero_z3403309356797280102nteger ) ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % sum.finite_Collect_op
% 0.33/0.62 thf(fact_5739_sum_Ofinite__Collect__op,axiom,
% 0.33/0.62 ! [I4: set_int,X: int > code_integer,Y: int > code_integer] :
% 0.33/0.62 ( ( finite_finite_int
% 0.33/0.62 @ ( collect_int
% 0.33/0.62 @ ^ [I3: int] :
% 0.33/0.62 ( ( member_int @ I3 @ I4 )
% 0.33/0.62 & ( ( X @ I3 )
% 0.33/0.62 != zero_z3403309356797280102nteger ) ) ) )
% 0.33/0.62 => ( ( finite_finite_int
% 0.33/0.62 @ ( collect_int
% 0.33/0.62 @ ^ [I3: int] :
% 0.33/0.62 ( ( member_int @ I3 @ I4 )
% 0.33/0.62 & ( ( Y @ I3 )
% 0.33/0.62 != zero_z3403309356797280102nteger ) ) ) )
% 0.33/0.62 => ( finite_finite_int
% 0.33/0.62 @ ( collect_int
% 0.33/0.62 @ ^ [I3: int] :
% 0.33/0.62 ( ( member_int @ I3 @ I4 )
% 0.33/0.62 & ( ( plus_p5714425477246183910nteger @ ( X @ I3 ) @ ( Y @ I3 ) )
% 0.33/0.62 != zero_z3403309356797280102nteger ) ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % sum.finite_Collect_op
% 0.33/0.62 thf(fact_5740_sum_Ofinite__Collect__op,axiom,
% 0.33/0.62 ! [I4: set_Code_integer,X: code_integer > code_integer,Y: code_integer > code_integer] :
% 0.33/0.62 ( ( finite6017078050557962740nteger
% 0.33/0.62 @ ( collect_Code_integer
% 0.33/0.62 @ ^ [I3: code_integer] :
% 0.33/0.62 ( ( member_Code_integer @ I3 @ I4 )
% 0.33/0.62 & ( ( X @ I3 )
% 0.33/0.62 != zero_z3403309356797280102nteger ) ) ) )
% 0.33/0.62 => ( ( finite6017078050557962740nteger
% 0.33/0.62 @ ( collect_Code_integer
% 0.33/0.62 @ ^ [I3: code_integer] :
% 0.33/0.62 ( ( member_Code_integer @ I3 @ I4 )
% 0.33/0.62 & ( ( Y @ I3 )
% 0.33/0.62 != zero_z3403309356797280102nteger ) ) ) )
% 0.33/0.62 => ( finite6017078050557962740nteger
% 0.33/0.62 @ ( collect_Code_integer
% 0.33/0.62 @ ^ [I3: code_integer] :
% 0.33/0.62 ( ( member_Code_integer @ I3 @ I4 )
% 0.33/0.62 & ( ( plus_p5714425477246183910nteger @ ( X @ I3 ) @ ( Y @ I3 ) )
% 0.33/0.62 != zero_z3403309356797280102nteger ) ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % sum.finite_Collect_op
% 0.33/0.62 thf(fact_5741_sum_Ofinite__Collect__op,axiom,
% 0.33/0.62 ! [I4: set_o,X: $o > rat,Y: $o > rat] :
% 0.33/0.62 ( ( finite_finite_o
% 0.33/0.62 @ ( collect_o
% 0.33/0.62 @ ^ [I3: $o] :
% 0.33/0.62 ( ( member_o @ I3 @ I4 )
% 0.33/0.62 & ( ( X @ I3 )
% 0.33/0.62 != zero_zero_rat ) ) ) )
% 0.33/0.62 => ( ( finite_finite_o
% 0.33/0.62 @ ( collect_o
% 0.33/0.62 @ ^ [I3: $o] :
% 0.33/0.62 ( ( member_o @ I3 @ I4 )
% 0.33/0.62 & ( ( Y @ I3 )
% 0.33/0.62 != zero_zero_rat ) ) ) )
% 0.33/0.62 => ( finite_finite_o
% 0.33/0.62 @ ( collect_o
% 0.33/0.62 @ ^ [I3: $o] :
% 0.33/0.62 ( ( member_o @ I3 @ I4 )
% 0.33/0.62 & ( ( plus_plus_rat @ ( X @ I3 ) @ ( Y @ I3 ) )
% 0.33/0.62 != zero_zero_rat ) ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % sum.finite_Collect_op
% 0.33/0.62 thf(fact_5742_sum_Ofinite__Collect__op,axiom,
% 0.33/0.62 ! [I4: set_nat,X: nat > rat,Y: nat > rat] :
% 0.33/0.62 ( ( finite_finite_nat
% 0.33/0.62 @ ( collect_nat
% 0.33/0.62 @ ^ [I3: nat] :
% 0.33/0.62 ( ( member_nat @ I3 @ I4 )
% 0.33/0.62 & ( ( X @ I3 )
% 0.33/0.62 != zero_zero_rat ) ) ) )
% 0.33/0.62 => ( ( finite_finite_nat
% 0.33/0.62 @ ( collect_nat
% 0.33/0.62 @ ^ [I3: nat] :
% 0.33/0.62 ( ( member_nat @ I3 @ I4 )
% 0.33/0.62 & ( ( Y @ I3 )
% 0.33/0.62 != zero_zero_rat ) ) ) )
% 0.33/0.62 => ( finite_finite_nat
% 0.33/0.62 @ ( collect_nat
% 0.33/0.62 @ ^ [I3: nat] :
% 0.33/0.62 ( ( member_nat @ I3 @ I4 )
% 0.33/0.62 & ( ( plus_plus_rat @ ( X @ I3 ) @ ( Y @ I3 ) )
% 0.33/0.62 != zero_zero_rat ) ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % sum.finite_Collect_op
% 0.33/0.62 thf(fact_5743_sum_Ofinite__Collect__op,axiom,
% 0.33/0.62 ! [I4: set_int,X: int > rat,Y: int > rat] :
% 0.33/0.62 ( ( finite_finite_int
% 0.33/0.62 @ ( collect_int
% 0.33/0.62 @ ^ [I3: int] :
% 0.33/0.62 ( ( member_int @ I3 @ I4 )
% 0.33/0.62 & ( ( X @ I3 )
% 0.33/0.62 != zero_zero_rat ) ) ) )
% 0.33/0.62 => ( ( finite_finite_int
% 0.33/0.62 @ ( collect_int
% 0.33/0.62 @ ^ [I3: int] :
% 0.33/0.62 ( ( member_int @ I3 @ I4 )
% 0.33/0.62 & ( ( Y @ I3 )
% 0.33/0.62 != zero_zero_rat ) ) ) )
% 0.33/0.62 => ( finite_finite_int
% 0.33/0.62 @ ( collect_int
% 0.33/0.62 @ ^ [I3: int] :
% 0.33/0.62 ( ( member_int @ I3 @ I4 )
% 0.33/0.62 & ( ( plus_plus_rat @ ( X @ I3 ) @ ( Y @ I3 ) )
% 0.33/0.62 != zero_zero_rat ) ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % sum.finite_Collect_op
% 0.33/0.62 thf(fact_5744_sum_Ofinite__Collect__op,axiom,
% 0.33/0.62 ! [I4: set_Code_integer,X: code_integer > rat,Y: code_integer > rat] :
% 0.33/0.62 ( ( finite6017078050557962740nteger
% 0.33/0.62 @ ( collect_Code_integer
% 0.33/0.62 @ ^ [I3: code_integer] :
% 0.33/0.62 ( ( member_Code_integer @ I3 @ I4 )
% 0.33/0.62 & ( ( X @ I3 )
% 0.33/0.62 != zero_zero_rat ) ) ) )
% 0.33/0.62 => ( ( finite6017078050557962740nteger
% 0.33/0.62 @ ( collect_Code_integer
% 0.33/0.62 @ ^ [I3: code_integer] :
% 0.33/0.62 ( ( member_Code_integer @ I3 @ I4 )
% 0.33/0.62 & ( ( Y @ I3 )
% 0.33/0.62 != zero_zero_rat ) ) ) )
% 0.33/0.62 => ( finite6017078050557962740nteger
% 0.33/0.62 @ ( collect_Code_integer
% 0.33/0.62 @ ^ [I3: code_integer] :
% 0.33/0.62 ( ( member_Code_integer @ I3 @ I4 )
% 0.33/0.62 & ( ( plus_plus_rat @ ( X @ I3 ) @ ( Y @ I3 ) )
% 0.33/0.62 != zero_zero_rat ) ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % sum.finite_Collect_op
% 0.33/0.62 thf(fact_5745_sum_Ofinite__Collect__op,axiom,
% 0.33/0.62 ! [I4: set_o,X: $o > nat,Y: $o > nat] :
% 0.33/0.62 ( ( finite_finite_o
% 0.33/0.62 @ ( collect_o
% 0.33/0.62 @ ^ [I3: $o] :
% 0.33/0.62 ( ( member_o @ I3 @ I4 )
% 0.33/0.62 & ( ( X @ I3 )
% 0.33/0.62 != zero_zero_nat ) ) ) )
% 0.33/0.62 => ( ( finite_finite_o
% 0.33/0.62 @ ( collect_o
% 0.33/0.62 @ ^ [I3: $o] :
% 0.33/0.62 ( ( member_o @ I3 @ I4 )
% 0.33/0.62 & ( ( Y @ I3 )
% 0.33/0.62 != zero_zero_nat ) ) ) )
% 0.33/0.62 => ( finite_finite_o
% 0.33/0.62 @ ( collect_o
% 0.33/0.62 @ ^ [I3: $o] :
% 0.33/0.62 ( ( member_o @ I3 @ I4 )
% 0.33/0.62 & ( ( plus_plus_nat @ ( X @ I3 ) @ ( Y @ I3 ) )
% 0.33/0.62 != zero_zero_nat ) ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % sum.finite_Collect_op
% 0.33/0.62 thf(fact_5746_sum_Ofinite__Collect__op,axiom,
% 0.33/0.62 ! [I4: set_nat,X: nat > nat,Y: nat > nat] :
% 0.33/0.62 ( ( finite_finite_nat
% 0.33/0.62 @ ( collect_nat
% 0.33/0.62 @ ^ [I3: nat] :
% 0.33/0.62 ( ( member_nat @ I3 @ I4 )
% 0.33/0.62 & ( ( X @ I3 )
% 0.33/0.62 != zero_zero_nat ) ) ) )
% 0.33/0.62 => ( ( finite_finite_nat
% 0.33/0.62 @ ( collect_nat
% 0.33/0.62 @ ^ [I3: nat] :
% 0.33/0.62 ( ( member_nat @ I3 @ I4 )
% 0.33/0.62 & ( ( Y @ I3 )
% 0.33/0.62 != zero_zero_nat ) ) ) )
% 0.33/0.62 => ( finite_finite_nat
% 0.33/0.62 @ ( collect_nat
% 0.33/0.62 @ ^ [I3: nat] :
% 0.33/0.62 ( ( member_nat @ I3 @ I4 )
% 0.33/0.62 & ( ( plus_plus_nat @ ( X @ I3 ) @ ( Y @ I3 ) )
% 0.33/0.62 != zero_zero_nat ) ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % sum.finite_Collect_op
% 0.33/0.62 thf(fact_5747_prod_Ofinite__Collect__op,axiom,
% 0.33/0.62 ! [I4: set_o,X: $o > code_integer,Y: $o > code_integer] :
% 0.33/0.62 ( ( finite_finite_o
% 0.33/0.62 @ ( collect_o
% 0.33/0.62 @ ^ [I3: $o] :
% 0.33/0.62 ( ( member_o @ I3 @ I4 )
% 0.33/0.62 & ( ( X @ I3 )
% 0.33/0.62 != one_one_Code_integer ) ) ) )
% 0.33/0.62 => ( ( finite_finite_o
% 0.33/0.62 @ ( collect_o
% 0.33/0.62 @ ^ [I3: $o] :
% 0.33/0.62 ( ( member_o @ I3 @ I4 )
% 0.33/0.62 & ( ( Y @ I3 )
% 0.33/0.62 != one_one_Code_integer ) ) ) )
% 0.33/0.62 => ( finite_finite_o
% 0.33/0.62 @ ( collect_o
% 0.33/0.62 @ ^ [I3: $o] :
% 0.33/0.62 ( ( member_o @ I3 @ I4 )
% 0.33/0.62 & ( ( times_3573771949741848930nteger @ ( X @ I3 ) @ ( Y @ I3 ) )
% 0.33/0.62 != one_one_Code_integer ) ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % prod.finite_Collect_op
% 0.33/0.62 thf(fact_5748_prod_Ofinite__Collect__op,axiom,
% 0.33/0.62 ! [I4: set_nat,X: nat > code_integer,Y: nat > code_integer] :
% 0.33/0.62 ( ( finite_finite_nat
% 0.33/0.62 @ ( collect_nat
% 0.33/0.62 @ ^ [I3: nat] :
% 0.33/0.62 ( ( member_nat @ I3 @ I4 )
% 0.33/0.62 & ( ( X @ I3 )
% 0.33/0.62 != one_one_Code_integer ) ) ) )
% 0.33/0.62 => ( ( finite_finite_nat
% 0.33/0.62 @ ( collect_nat
% 0.33/0.62 @ ^ [I3: nat] :
% 0.33/0.62 ( ( member_nat @ I3 @ I4 )
% 0.33/0.62 & ( ( Y @ I3 )
% 0.33/0.62 != one_one_Code_integer ) ) ) )
% 0.33/0.62 => ( finite_finite_nat
% 0.33/0.62 @ ( collect_nat
% 0.33/0.62 @ ^ [I3: nat] :
% 0.33/0.62 ( ( member_nat @ I3 @ I4 )
% 0.33/0.62 & ( ( times_3573771949741848930nteger @ ( X @ I3 ) @ ( Y @ I3 ) )
% 0.33/0.62 != one_one_Code_integer ) ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % prod.finite_Collect_op
% 0.33/0.62 thf(fact_5749_prod_Ofinite__Collect__op,axiom,
% 0.33/0.62 ! [I4: set_int,X: int > code_integer,Y: int > code_integer] :
% 0.33/0.62 ( ( finite_finite_int
% 0.33/0.62 @ ( collect_int
% 0.33/0.62 @ ^ [I3: int] :
% 0.33/0.62 ( ( member_int @ I3 @ I4 )
% 0.33/0.62 & ( ( X @ I3 )
% 0.33/0.62 != one_one_Code_integer ) ) ) )
% 0.33/0.62 => ( ( finite_finite_int
% 0.33/0.62 @ ( collect_int
% 0.33/0.62 @ ^ [I3: int] :
% 0.33/0.62 ( ( member_int @ I3 @ I4 )
% 0.33/0.62 & ( ( Y @ I3 )
% 0.33/0.62 != one_one_Code_integer ) ) ) )
% 0.33/0.62 => ( finite_finite_int
% 0.33/0.62 @ ( collect_int
% 0.33/0.62 @ ^ [I3: int] :
% 0.33/0.62 ( ( member_int @ I3 @ I4 )
% 0.33/0.62 & ( ( times_3573771949741848930nteger @ ( X @ I3 ) @ ( Y @ I3 ) )
% 0.33/0.62 != one_one_Code_integer ) ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % prod.finite_Collect_op
% 0.33/0.62 thf(fact_5750_prod_Ofinite__Collect__op,axiom,
% 0.33/0.62 ! [I4: set_Code_integer,X: code_integer > code_integer,Y: code_integer > code_integer] :
% 0.33/0.62 ( ( finite6017078050557962740nteger
% 0.33/0.62 @ ( collect_Code_integer
% 0.33/0.62 @ ^ [I3: code_integer] :
% 0.33/0.62 ( ( member_Code_integer @ I3 @ I4 )
% 0.33/0.62 & ( ( X @ I3 )
% 0.33/0.62 != one_one_Code_integer ) ) ) )
% 0.33/0.62 => ( ( finite6017078050557962740nteger
% 0.33/0.62 @ ( collect_Code_integer
% 0.33/0.62 @ ^ [I3: code_integer] :
% 0.33/0.62 ( ( member_Code_integer @ I3 @ I4 )
% 0.33/0.62 & ( ( Y @ I3 )
% 0.33/0.62 != one_one_Code_integer ) ) ) )
% 0.33/0.62 => ( finite6017078050557962740nteger
% 0.33/0.62 @ ( collect_Code_integer
% 0.33/0.62 @ ^ [I3: code_integer] :
% 0.33/0.62 ( ( member_Code_integer @ I3 @ I4 )
% 0.33/0.62 & ( ( times_3573771949741848930nteger @ ( X @ I3 ) @ ( Y @ I3 ) )
% 0.33/0.62 != one_one_Code_integer ) ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % prod.finite_Collect_op
% 0.33/0.62 thf(fact_5751_prod_Ofinite__Collect__op,axiom,
% 0.33/0.62 ! [I4: set_o,X: $o > assn,Y: $o > assn] :
% 0.33/0.62 ( ( finite_finite_o
% 0.33/0.62 @ ( collect_o
% 0.33/0.62 @ ^ [I3: $o] :
% 0.33/0.62 ( ( member_o @ I3 @ I4 )
% 0.33/0.62 & ( ( X @ I3 )
% 0.33/0.62 != one_one_assn ) ) ) )
% 0.33/0.62 => ( ( finite_finite_o
% 0.33/0.62 @ ( collect_o
% 0.33/0.62 @ ^ [I3: $o] :
% 0.33/0.62 ( ( member_o @ I3 @ I4 )
% 0.33/0.62 & ( ( Y @ I3 )
% 0.33/0.62 != one_one_assn ) ) ) )
% 0.33/0.62 => ( finite_finite_o
% 0.33/0.62 @ ( collect_o
% 0.33/0.62 @ ^ [I3: $o] :
% 0.33/0.62 ( ( member_o @ I3 @ I4 )
% 0.33/0.62 & ( ( times_times_assn @ ( X @ I3 ) @ ( Y @ I3 ) )
% 0.33/0.62 != one_one_assn ) ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % prod.finite_Collect_op
% 0.33/0.62 thf(fact_5752_prod_Ofinite__Collect__op,axiom,
% 0.33/0.62 ! [I4: set_nat,X: nat > assn,Y: nat > assn] :
% 0.33/0.62 ( ( finite_finite_nat
% 0.33/0.62 @ ( collect_nat
% 0.33/0.62 @ ^ [I3: nat] :
% 0.33/0.62 ( ( member_nat @ I3 @ I4 )
% 0.33/0.62 & ( ( X @ I3 )
% 0.33/0.62 != one_one_assn ) ) ) )
% 0.33/0.62 => ( ( finite_finite_nat
% 0.33/0.62 @ ( collect_nat
% 0.33/0.62 @ ^ [I3: nat] :
% 0.33/0.62 ( ( member_nat @ I3 @ I4 )
% 0.33/0.62 & ( ( Y @ I3 )
% 0.33/0.62 != one_one_assn ) ) ) )
% 0.33/0.62 => ( finite_finite_nat
% 0.33/0.62 @ ( collect_nat
% 0.33/0.62 @ ^ [I3: nat] :
% 0.33/0.62 ( ( member_nat @ I3 @ I4 )
% 0.33/0.62 & ( ( times_times_assn @ ( X @ I3 ) @ ( Y @ I3 ) )
% 0.33/0.62 != one_one_assn ) ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % prod.finite_Collect_op
% 0.33/0.62 thf(fact_5753_prod_Ofinite__Collect__op,axiom,
% 0.33/0.62 ! [I4: set_int,X: int > assn,Y: int > assn] :
% 0.33/0.62 ( ( finite_finite_int
% 0.33/0.62 @ ( collect_int
% 0.33/0.62 @ ^ [I3: int] :
% 0.33/0.62 ( ( member_int @ I3 @ I4 )
% 0.33/0.62 & ( ( X @ I3 )
% 0.33/0.62 != one_one_assn ) ) ) )
% 0.33/0.62 => ( ( finite_finite_int
% 0.33/0.62 @ ( collect_int
% 0.33/0.62 @ ^ [I3: int] :
% 0.33/0.62 ( ( member_int @ I3 @ I4 )
% 0.33/0.62 & ( ( Y @ I3 )
% 0.33/0.62 != one_one_assn ) ) ) )
% 0.33/0.62 => ( finite_finite_int
% 0.33/0.62 @ ( collect_int
% 0.33/0.62 @ ^ [I3: int] :
% 0.33/0.62 ( ( member_int @ I3 @ I4 )
% 0.33/0.62 & ( ( times_times_assn @ ( X @ I3 ) @ ( Y @ I3 ) )
% 0.33/0.62 != one_one_assn ) ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % prod.finite_Collect_op
% 0.33/0.62 thf(fact_5754_prod_Ofinite__Collect__op,axiom,
% 0.33/0.62 ! [I4: set_Code_integer,X: code_integer > assn,Y: code_integer > assn] :
% 0.33/0.62 ( ( finite6017078050557962740nteger
% 0.33/0.62 @ ( collect_Code_integer
% 0.33/0.62 @ ^ [I3: code_integer] :
% 0.33/0.62 ( ( member_Code_integer @ I3 @ I4 )
% 0.33/0.62 & ( ( X @ I3 )
% 0.33/0.62 != one_one_assn ) ) ) )
% 0.33/0.62 => ( ( finite6017078050557962740nteger
% 0.33/0.62 @ ( collect_Code_integer
% 0.33/0.62 @ ^ [I3: code_integer] :
% 0.33/0.62 ( ( member_Code_integer @ I3 @ I4 )
% 0.33/0.62 & ( ( Y @ I3 )
% 0.33/0.62 != one_one_assn ) ) ) )
% 0.33/0.62 => ( finite6017078050557962740nteger
% 0.33/0.62 @ ( collect_Code_integer
% 0.33/0.62 @ ^ [I3: code_integer] :
% 0.33/0.62 ( ( member_Code_integer @ I3 @ I4 )
% 0.33/0.62 & ( ( times_times_assn @ ( X @ I3 ) @ ( Y @ I3 ) )
% 0.33/0.62 != one_one_assn ) ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % prod.finite_Collect_op
% 0.33/0.62 thf(fact_5755_prod_Ofinite__Collect__op,axiom,
% 0.33/0.62 ! [I4: set_o,X: $o > rat,Y: $o > rat] :
% 0.33/0.62 ( ( finite_finite_o
% 0.33/0.62 @ ( collect_o
% 0.33/0.62 @ ^ [I3: $o] :
% 0.33/0.62 ( ( member_o @ I3 @ I4 )
% 0.33/0.62 & ( ( X @ I3 )
% 0.33/0.62 != one_one_rat ) ) ) )
% 0.33/0.62 => ( ( finite_finite_o
% 0.33/0.62 @ ( collect_o
% 0.33/0.62 @ ^ [I3: $o] :
% 0.33/0.62 ( ( member_o @ I3 @ I4 )
% 0.33/0.62 & ( ( Y @ I3 )
% 0.33/0.62 != one_one_rat ) ) ) )
% 0.33/0.62 => ( finite_finite_o
% 0.33/0.62 @ ( collect_o
% 0.33/0.62 @ ^ [I3: $o] :
% 0.33/0.62 ( ( member_o @ I3 @ I4 )
% 0.33/0.62 & ( ( times_times_rat @ ( X @ I3 ) @ ( Y @ I3 ) )
% 0.33/0.62 != one_one_rat ) ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % prod.finite_Collect_op
% 0.33/0.62 thf(fact_5756_prod_Ofinite__Collect__op,axiom,
% 0.33/0.62 ! [I4: set_nat,X: nat > rat,Y: nat > rat] :
% 0.33/0.62 ( ( finite_finite_nat
% 0.33/0.62 @ ( collect_nat
% 0.33/0.62 @ ^ [I3: nat] :
% 0.33/0.62 ( ( member_nat @ I3 @ I4 )
% 0.33/0.62 & ( ( X @ I3 )
% 0.33/0.62 != one_one_rat ) ) ) )
% 0.33/0.62 => ( ( finite_finite_nat
% 0.33/0.62 @ ( collect_nat
% 0.33/0.62 @ ^ [I3: nat] :
% 0.33/0.62 ( ( member_nat @ I3 @ I4 )
% 0.33/0.62 & ( ( Y @ I3 )
% 0.33/0.62 != one_one_rat ) ) ) )
% 0.33/0.62 => ( finite_finite_nat
% 0.33/0.62 @ ( collect_nat
% 0.33/0.62 @ ^ [I3: nat] :
% 0.33/0.62 ( ( member_nat @ I3 @ I4 )
% 0.33/0.62 & ( ( times_times_rat @ ( X @ I3 ) @ ( Y @ I3 ) )
% 0.33/0.62 != one_one_rat ) ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % prod.finite_Collect_op
% 0.33/0.62 thf(fact_5757_finite__atLeastZeroLessThan__int,axiom,
% 0.33/0.62 ! [U: int] : ( finite_finite_int @ ( set_or4662586982721622107an_int @ zero_zero_int @ U ) ) ).
% 0.33/0.62
% 0.33/0.62 % finite_atLeastZeroLessThan_int
% 0.33/0.62 thf(fact_5758_card__eq__sum,axiom,
% 0.33/0.62 ( finite_card_int
% 0.33/0.62 = ( groups4541462559716669496nt_nat
% 0.33/0.62 @ ^ [X3: int] : one_one_nat ) ) ).
% 0.33/0.62
% 0.33/0.62 % card_eq_sum
% 0.33/0.62 thf(fact_5759_card__eq__sum,axiom,
% 0.33/0.62 ( finite410649719033368117t_unit
% 0.33/0.62 = ( groups8766797177574957219it_nat
% 0.33/0.62 @ ^ [X3: product_unit] : one_one_nat ) ) ).
% 0.33/0.62
% 0.33/0.62 % card_eq_sum
% 0.33/0.62 thf(fact_5760_card__eq__sum,axiom,
% 0.33/0.62 ( finite_card_list_nat
% 0.33/0.62 = ( groups4396056296759096172at_nat
% 0.33/0.62 @ ^ [X3: list_nat] : one_one_nat ) ) ).
% 0.33/0.62
% 0.33/0.62 % card_eq_sum
% 0.33/0.62 thf(fact_5761_card__eq__sum,axiom,
% 0.33/0.62 ( finite_card_nat
% 0.33/0.62 = ( groups3542108847815614940at_nat
% 0.33/0.62 @ ^ [X3: nat] : one_one_nat ) ) ).
% 0.33/0.62
% 0.33/0.62 % card_eq_sum
% 0.33/0.62 thf(fact_5762_prod_Ointer__filter,axiom,
% 0.33/0.62 ! [A2: set_o,G: $o > code_integer,P: $o > $o] :
% 0.33/0.62 ( ( finite_finite_o @ A2 )
% 0.33/0.62 => ( ( groups7694694392188491536nteger @ G
% 0.33/0.62 @ ( collect_o
% 0.33/0.62 @ ^ [X3: $o] :
% 0.33/0.62 ( ( member_o @ X3 @ A2 )
% 0.33/0.62 & ( P @ X3 ) ) ) )
% 0.33/0.62 = ( groups7694694392188491536nteger
% 0.33/0.62 @ ^ [X3: $o] : ( if_Code_integer @ ( P @ X3 ) @ ( G @ X3 ) @ one_one_Code_integer )
% 0.33/0.62 @ A2 ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % prod.inter_filter
% 0.33/0.62 thf(fact_5763_prod_Ointer__filter,axiom,
% 0.33/0.62 ! [A2: set_nat,G: nat > code_integer,P: nat > $o] :
% 0.33/0.62 ( ( finite_finite_nat @ A2 )
% 0.33/0.62 => ( ( groups3455450783089532116nteger @ G
% 0.33/0.62 @ ( collect_nat
% 0.33/0.62 @ ^ [X3: nat] :
% 0.33/0.62 ( ( member_nat @ X3 @ A2 )
% 0.33/0.62 & ( P @ X3 ) ) ) )
% 0.33/0.62 = ( groups3455450783089532116nteger
% 0.33/0.62 @ ^ [X3: nat] : ( if_Code_integer @ ( P @ X3 ) @ ( G @ X3 ) @ one_one_Code_integer )
% 0.33/0.62 @ A2 ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % prod.inter_filter
% 0.33/0.62 thf(fact_5764_prod_Ointer__filter,axiom,
% 0.33/0.62 ! [A2: set_int,G: int > code_integer,P: int > $o] :
% 0.33/0.62 ( ( finite_finite_int @ A2 )
% 0.33/0.62 => ( ( groups3827104343326376752nteger @ G
% 0.33/0.62 @ ( collect_int
% 0.33/0.62 @ ^ [X3: int] :
% 0.33/0.62 ( ( member_int @ X3 @ A2 )
% 0.33/0.62 & ( P @ X3 ) ) ) )
% 0.33/0.62 = ( groups3827104343326376752nteger
% 0.33/0.62 @ ^ [X3: int] : ( if_Code_integer @ ( P @ X3 ) @ ( G @ X3 ) @ one_one_Code_integer )
% 0.33/0.62 @ A2 ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % prod.inter_filter
% 0.33/0.62 thf(fact_5765_prod_Ointer__filter,axiom,
% 0.33/0.62 ! [A2: set_Code_integer,G: code_integer > code_integer,P: code_integer > $o] :
% 0.33/0.62 ( ( finite6017078050557962740nteger @ A2 )
% 0.33/0.62 => ( ( groups3674199335183972705nteger @ G
% 0.33/0.62 @ ( collect_Code_integer
% 0.33/0.62 @ ^ [X3: code_integer] :
% 0.33/0.62 ( ( member_Code_integer @ X3 @ A2 )
% 0.33/0.62 & ( P @ X3 ) ) ) )
% 0.33/0.62 = ( groups3674199335183972705nteger
% 0.33/0.62 @ ^ [X3: code_integer] : ( if_Code_integer @ ( P @ X3 ) @ ( G @ X3 ) @ one_one_Code_integer )
% 0.33/0.62 @ A2 ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % prod.inter_filter
% 0.33/0.62 thf(fact_5766_prod_Ointer__filter,axiom,
% 0.33/0.62 ! [A2: set_o,G: $o > assn,P: $o > $o] :
% 0.33/0.62 ( ( finite_finite_o @ A2 )
% 0.33/0.62 => ( ( groups5301882518646026715o_assn @ G
% 0.33/0.62 @ ( collect_o
% 0.33/0.62 @ ^ [X3: $o] :
% 0.33/0.62 ( ( member_o @ X3 @ A2 )
% 0.33/0.62 & ( P @ X3 ) ) ) )
% 0.33/0.62 = ( groups5301882518646026715o_assn
% 0.33/0.62 @ ^ [X3: $o] : ( if_assn @ ( P @ X3 ) @ ( G @ X3 ) @ one_one_assn )
% 0.33/0.62 @ A2 ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % prod.inter_filter
% 0.33/0.62 thf(fact_5767_prod_Ointer__filter,axiom,
% 0.33/0.62 ! [A2: set_nat,G: nat > assn,P: nat > $o] :
% 0.33/0.62 ( ( finite_finite_nat @ A2 )
% 0.33/0.62 => ( ( groups6906906614972039071t_assn @ G
% 0.33/0.62 @ ( collect_nat
% 0.33/0.62 @ ^ [X3: nat] :
% 0.33/0.62 ( ( member_nat @ X3 @ A2 )
% 0.33/0.62 & ( P @ X3 ) ) ) )
% 0.33/0.62 = ( groups6906906614972039071t_assn
% 0.33/0.62 @ ^ [X3: nat] : ( if_assn @ ( P @ X3 ) @ ( G @ X3 ) @ one_one_assn )
% 0.33/0.62 @ A2 ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % prod.inter_filter
% 0.33/0.62 thf(fact_5768_prod_Ointer__filter,axiom,
% 0.33/0.62 ! [A2: set_int,G: int > assn,P: int > $o] :
% 0.33/0.62 ( ( finite_finite_int @ A2 )
% 0.33/0.62 => ( ( groups7882442080178216443t_assn @ G
% 0.33/0.62 @ ( collect_int
% 0.33/0.62 @ ^ [X3: int] :
% 0.33/0.62 ( ( member_int @ X3 @ A2 )
% 0.33/0.62 & ( P @ X3 ) ) ) )
% 0.33/0.62 = ( groups7882442080178216443t_assn
% 0.33/0.62 @ ^ [X3: int] : ( if_assn @ ( P @ X3 ) @ ( G @ X3 ) @ one_one_assn )
% 0.33/0.62 @ A2 ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % prod.inter_filter
% 0.33/0.62 thf(fact_5769_prod_Ointer__filter,axiom,
% 0.33/0.62 ! [A2: set_Code_integer,G: code_integer > assn,P: code_integer > $o] :
% 0.33/0.62 ( ( finite6017078050557962740nteger @ A2 )
% 0.33/0.62 => ( ( groups1304777262505850412r_assn @ G
% 0.33/0.62 @ ( collect_Code_integer
% 0.33/0.62 @ ^ [X3: code_integer] :
% 0.33/0.62 ( ( member_Code_integer @ X3 @ A2 )
% 0.33/0.62 & ( P @ X3 ) ) ) )
% 0.33/0.62 = ( groups1304777262505850412r_assn
% 0.33/0.62 @ ^ [X3: code_integer] : ( if_assn @ ( P @ X3 ) @ ( G @ X3 ) @ one_one_assn )
% 0.33/0.62 @ A2 ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % prod.inter_filter
% 0.33/0.62 thf(fact_5770_prod_Ointer__filter,axiom,
% 0.33/0.62 ! [A2: set_o,G: $o > rat,P: $o > $o] :
% 0.33/0.62 ( ( finite_finite_o @ A2 )
% 0.33/0.62 => ( ( groups2869687844427037835_o_rat @ G
% 0.33/0.62 @ ( collect_o
% 0.33/0.62 @ ^ [X3: $o] :
% 0.33/0.62 ( ( member_o @ X3 @ A2 )
% 0.33/0.62 & ( P @ X3 ) ) ) )
% 0.33/0.62 = ( groups2869687844427037835_o_rat
% 0.33/0.62 @ ^ [X3: $o] : ( if_rat @ ( P @ X3 ) @ ( G @ X3 ) @ one_one_rat )
% 0.33/0.62 @ A2 ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % prod.inter_filter
% 0.33/0.62 thf(fact_5771_prod_Ointer__filter,axiom,
% 0.33/0.62 ! [A2: set_nat,G: nat > rat,P: nat > $o] :
% 0.33/0.62 ( ( finite_finite_nat @ A2 )
% 0.33/0.62 => ( ( groups73079841787564623at_rat @ G
% 0.33/0.62 @ ( collect_nat
% 0.33/0.62 @ ^ [X3: nat] :
% 0.33/0.62 ( ( member_nat @ X3 @ A2 )
% 0.33/0.62 & ( P @ X3 ) ) ) )
% 0.33/0.62 = ( groups73079841787564623at_rat
% 0.33/0.62 @ ^ [X3: nat] : ( if_rat @ ( P @ X3 ) @ ( G @ X3 ) @ one_one_rat )
% 0.33/0.62 @ A2 ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % prod.inter_filter
% 0.33/0.62 thf(fact_5772_prod__gen__delta,axiom,
% 0.33/0.62 ! [S2: set_o,A: $o,B: $o > assn,C: assn] :
% 0.33/0.62 ( ( finite_finite_o @ S2 )
% 0.33/0.62 => ( ( ( member_o @ A @ S2 )
% 0.33/0.62 => ( ( groups5301882518646026715o_assn
% 0.33/0.62 @ ^ [K4: $o] : ( if_assn @ ( K4 = A ) @ ( B @ K4 ) @ C )
% 0.33/0.62 @ S2 )
% 0.33/0.62 = ( times_times_assn @ ( B @ A ) @ ( power_power_assn @ C @ ( minus_minus_nat @ ( finite_card_o @ S2 ) @ one_one_nat ) ) ) ) )
% 0.33/0.62 & ( ~ ( member_o @ A @ S2 )
% 0.33/0.62 => ( ( groups5301882518646026715o_assn
% 0.33/0.62 @ ^ [K4: $o] : ( if_assn @ ( K4 = A ) @ ( B @ K4 ) @ C )
% 0.33/0.62 @ S2 )
% 0.33/0.62 = ( power_power_assn @ C @ ( finite_card_o @ S2 ) ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % prod_gen_delta
% 0.33/0.62 thf(fact_5773_prod__gen__delta,axiom,
% 0.33/0.62 ! [S2: set_Product_unit,A: product_unit,B: product_unit > assn,C: assn] :
% 0.33/0.62 ( ( finite4290736615968046902t_unit @ S2 )
% 0.33/0.62 => ( ( ( member_Product_unit @ A @ S2 )
% 0.33/0.62 => ( ( groups5360233303959380816t_assn
% 0.33/0.62 @ ^ [K4: product_unit] : ( if_assn @ ( K4 = A ) @ ( B @ K4 ) @ C )
% 0.33/0.62 @ S2 )
% 0.33/0.62 = ( times_times_assn @ ( B @ A ) @ ( power_power_assn @ C @ ( minus_minus_nat @ ( finite410649719033368117t_unit @ S2 ) @ one_one_nat ) ) ) ) )
% 0.33/0.62 & ( ~ ( member_Product_unit @ A @ S2 )
% 0.33/0.62 => ( ( groups5360233303959380816t_assn
% 0.33/0.62 @ ^ [K4: product_unit] : ( if_assn @ ( K4 = A ) @ ( B @ K4 ) @ C )
% 0.33/0.62 @ S2 )
% 0.33/0.62 = ( power_power_assn @ C @ ( finite410649719033368117t_unit @ S2 ) ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % prod_gen_delta
% 0.33/0.62 thf(fact_5774_prod__gen__delta,axiom,
% 0.33/0.62 ! [S2: set_nat,A: nat,B: nat > assn,C: assn] :
% 0.33/0.62 ( ( finite_finite_nat @ S2 )
% 0.33/0.62 => ( ( ( member_nat @ A @ S2 )
% 0.33/0.62 => ( ( groups6906906614972039071t_assn
% 0.33/0.62 @ ^ [K4: nat] : ( if_assn @ ( K4 = A ) @ ( B @ K4 ) @ C )
% 0.33/0.62 @ S2 )
% 0.33/0.62 = ( times_times_assn @ ( B @ A ) @ ( power_power_assn @ C @ ( minus_minus_nat @ ( finite_card_nat @ S2 ) @ one_one_nat ) ) ) ) )
% 0.33/0.62 & ( ~ ( member_nat @ A @ S2 )
% 0.33/0.62 => ( ( groups6906906614972039071t_assn
% 0.33/0.62 @ ^ [K4: nat] : ( if_assn @ ( K4 = A ) @ ( B @ K4 ) @ C )
% 0.33/0.62 @ S2 )
% 0.33/0.62 = ( power_power_assn @ C @ ( finite_card_nat @ S2 ) ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % prod_gen_delta
% 0.33/0.62 thf(fact_5775_prod__gen__delta,axiom,
% 0.33/0.62 ! [S2: set_int,A: int,B: int > assn,C: assn] :
% 0.33/0.62 ( ( finite_finite_int @ S2 )
% 0.33/0.62 => ( ( ( member_int @ A @ S2 )
% 0.33/0.62 => ( ( groups7882442080178216443t_assn
% 0.33/0.62 @ ^ [K4: int] : ( if_assn @ ( K4 = A ) @ ( B @ K4 ) @ C )
% 0.33/0.62 @ S2 )
% 0.33/0.62 = ( times_times_assn @ ( B @ A ) @ ( power_power_assn @ C @ ( minus_minus_nat @ ( finite_card_int @ S2 ) @ one_one_nat ) ) ) ) )
% 0.33/0.62 & ( ~ ( member_int @ A @ S2 )
% 0.33/0.62 => ( ( groups7882442080178216443t_assn
% 0.33/0.62 @ ^ [K4: int] : ( if_assn @ ( K4 = A ) @ ( B @ K4 ) @ C )
% 0.33/0.62 @ S2 )
% 0.33/0.62 = ( power_power_assn @ C @ ( finite_card_int @ S2 ) ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % prod_gen_delta
% 0.33/0.62 thf(fact_5776_prod__gen__delta,axiom,
% 0.33/0.62 ! [S2: set_Code_integer,A: code_integer,B: code_integer > assn,C: assn] :
% 0.33/0.62 ( ( finite6017078050557962740nteger @ S2 )
% 0.33/0.62 => ( ( ( member_Code_integer @ A @ S2 )
% 0.33/0.62 => ( ( groups1304777262505850412r_assn
% 0.33/0.62 @ ^ [K4: code_integer] : ( if_assn @ ( K4 = A ) @ ( B @ K4 ) @ C )
% 0.33/0.62 @ S2 )
% 0.33/0.62 = ( times_times_assn @ ( B @ A ) @ ( power_power_assn @ C @ ( minus_minus_nat @ ( finite4902975817058060853nteger @ S2 ) @ one_one_nat ) ) ) ) )
% 0.33/0.62 & ( ~ ( member_Code_integer @ A @ S2 )
% 0.33/0.62 => ( ( groups1304777262505850412r_assn
% 0.33/0.62 @ ^ [K4: code_integer] : ( if_assn @ ( K4 = A ) @ ( B @ K4 ) @ C )
% 0.33/0.62 @ S2 )
% 0.33/0.62 = ( power_power_assn @ C @ ( finite4902975817058060853nteger @ S2 ) ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % prod_gen_delta
% 0.33/0.62 thf(fact_5777_prod__gen__delta,axiom,
% 0.33/0.62 ! [S2: set_o,A: $o,B: $o > rat,C: rat] :
% 0.33/0.62 ( ( finite_finite_o @ S2 )
% 0.33/0.62 => ( ( ( member_o @ A @ S2 )
% 0.33/0.62 => ( ( groups2869687844427037835_o_rat
% 0.33/0.62 @ ^ [K4: $o] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ C )
% 0.33/0.62 @ S2 )
% 0.33/0.62 = ( times_times_rat @ ( B @ A ) @ ( power_power_rat @ C @ ( minus_minus_nat @ ( finite_card_o @ S2 ) @ one_one_nat ) ) ) ) )
% 0.33/0.62 & ( ~ ( member_o @ A @ S2 )
% 0.33/0.62 => ( ( groups2869687844427037835_o_rat
% 0.33/0.62 @ ^ [K4: $o] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ C )
% 0.33/0.62 @ S2 )
% 0.33/0.62 = ( power_power_rat @ C @ ( finite_card_o @ S2 ) ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % prod_gen_delta
% 0.33/0.62 thf(fact_5778_prod__gen__delta,axiom,
% 0.33/0.62 ! [S2: set_Product_unit,A: product_unit,B: product_unit > rat,C: rat] :
% 0.33/0.62 ( ( finite4290736615968046902t_unit @ S2 )
% 0.33/0.62 => ( ( ( member_Product_unit @ A @ S2 )
% 0.33/0.62 => ( ( groups8984663225794451456it_rat
% 0.33/0.62 @ ^ [K4: product_unit] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ C )
% 0.33/0.62 @ S2 )
% 0.33/0.62 = ( times_times_rat @ ( B @ A ) @ ( power_power_rat @ C @ ( minus_minus_nat @ ( finite410649719033368117t_unit @ S2 ) @ one_one_nat ) ) ) ) )
% 0.33/0.62 & ( ~ ( member_Product_unit @ A @ S2 )
% 0.33/0.62 => ( ( groups8984663225794451456it_rat
% 0.33/0.62 @ ^ [K4: product_unit] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ C )
% 0.33/0.62 @ S2 )
% 0.33/0.62 = ( power_power_rat @ C @ ( finite410649719033368117t_unit @ S2 ) ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % prod_gen_delta
% 0.33/0.62 thf(fact_5779_prod__gen__delta,axiom,
% 0.33/0.62 ! [S2: set_nat,A: nat,B: nat > rat,C: rat] :
% 0.33/0.62 ( ( finite_finite_nat @ S2 )
% 0.33/0.62 => ( ( ( member_nat @ A @ S2 )
% 0.33/0.62 => ( ( groups73079841787564623at_rat
% 0.33/0.62 @ ^ [K4: nat] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ C )
% 0.33/0.62 @ S2 )
% 0.33/0.62 = ( times_times_rat @ ( B @ A ) @ ( power_power_rat @ C @ ( minus_minus_nat @ ( finite_card_nat @ S2 ) @ one_one_nat ) ) ) ) )
% 0.33/0.62 & ( ~ ( member_nat @ A @ S2 )
% 0.33/0.62 => ( ( groups73079841787564623at_rat
% 0.33/0.62 @ ^ [K4: nat] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ C )
% 0.33/0.62 @ S2 )
% 0.33/0.62 = ( power_power_rat @ C @ ( finite_card_nat @ S2 ) ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % prod_gen_delta
% 0.33/0.62 thf(fact_5780_prod__gen__delta,axiom,
% 0.33/0.62 ! [S2: set_int,A: int,B: int > rat,C: rat] :
% 0.33/0.62 ( ( finite_finite_int @ S2 )
% 0.33/0.62 => ( ( ( member_int @ A @ S2 )
% 0.33/0.62 => ( ( groups1072433553688619179nt_rat
% 0.33/0.62 @ ^ [K4: int] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ C )
% 0.33/0.62 @ S2 )
% 0.33/0.62 = ( times_times_rat @ ( B @ A ) @ ( power_power_rat @ C @ ( minus_minus_nat @ ( finite_card_int @ S2 ) @ one_one_nat ) ) ) ) )
% 0.33/0.62 & ( ~ ( member_int @ A @ S2 )
% 0.33/0.62 => ( ( groups1072433553688619179nt_rat
% 0.33/0.62 @ ^ [K4: int] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ C )
% 0.33/0.62 @ S2 )
% 0.33/0.62 = ( power_power_rat @ C @ ( finite_card_int @ S2 ) ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % prod_gen_delta
% 0.33/0.62 thf(fact_5781_prod__gen__delta,axiom,
% 0.33/0.62 ! [S2: set_Code_integer,A: code_integer,B: code_integer > rat,C: rat] :
% 0.33/0.62 ( ( finite6017078050557962740nteger @ S2 )
% 0.33/0.62 => ( ( ( member_Code_integer @ A @ S2 )
% 0.33/0.62 => ( ( groups2555765274223993564er_rat
% 0.33/0.62 @ ^ [K4: code_integer] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ C )
% 0.33/0.62 @ S2 )
% 0.33/0.62 = ( times_times_rat @ ( B @ A ) @ ( power_power_rat @ C @ ( minus_minus_nat @ ( finite4902975817058060853nteger @ S2 ) @ one_one_nat ) ) ) ) )
% 0.33/0.62 & ( ~ ( member_Code_integer @ A @ S2 )
% 0.33/0.62 => ( ( groups2555765274223993564er_rat
% 0.33/0.62 @ ^ [K4: code_integer] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ C )
% 0.33/0.62 @ S2 )
% 0.33/0.62 = ( power_power_rat @ C @ ( finite4902975817058060853nteger @ S2 ) ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % prod_gen_delta
% 0.33/0.62 thf(fact_5782_finite__atLeastZeroLessThan__integer,axiom,
% 0.33/0.62 ! [U: code_integer] : ( finite6017078050557962740nteger @ ( set_or8404916559141939852nteger @ zero_z3403309356797280102nteger @ U ) ) ).
% 0.33/0.62
% 0.33/0.62 % finite_atLeastZeroLessThan_integer
% 0.33/0.62 thf(fact_5783_card__2__iff_H,axiom,
% 0.33/0.62 ! [S2: set_int] :
% 0.33/0.62 ( ( ( finite_card_int @ S2 )
% 0.33/0.62 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.33/0.62 = ( ? [X3: int] :
% 0.33/0.62 ( ( member_int @ X3 @ S2 )
% 0.33/0.62 & ? [Y3: int] :
% 0.33/0.62 ( ( member_int @ Y3 @ S2 )
% 0.33/0.62 & ( X3 != Y3 )
% 0.33/0.62 & ! [Z4: int] :
% 0.33/0.62 ( ( member_int @ Z4 @ S2 )
% 0.33/0.62 => ( ( Z4 = X3 )
% 0.33/0.62 | ( Z4 = Y3 ) ) ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % card_2_iff'
% 0.33/0.62 thf(fact_5784_card__2__iff_H,axiom,
% 0.33/0.62 ! [S2: set_Product_unit] :
% 0.33/0.62 ( ( ( finite410649719033368117t_unit @ S2 )
% 0.33/0.62 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.33/0.62 = ( ? [X3: product_unit] :
% 0.33/0.62 ( ( member_Product_unit @ X3 @ S2 )
% 0.33/0.62 & ? [Y3: product_unit] :
% 0.33/0.62 ( ( member_Product_unit @ Y3 @ S2 )
% 0.33/0.62 & ( X3 != Y3 )
% 0.33/0.62 & ! [Z4: product_unit] :
% 0.33/0.62 ( ( member_Product_unit @ Z4 @ S2 )
% 0.33/0.62 => ( ( Z4 = X3 )
% 0.33/0.62 | ( Z4 = Y3 ) ) ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % card_2_iff'
% 0.33/0.62 thf(fact_5785_card__2__iff_H,axiom,
% 0.33/0.62 ! [S2: set_nat] :
% 0.33/0.62 ( ( ( finite_card_nat @ S2 )
% 0.33/0.62 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.33/0.62 = ( ? [X3: nat] :
% 0.33/0.62 ( ( member_nat @ X3 @ S2 )
% 0.33/0.62 & ? [Y3: nat] :
% 0.33/0.62 ( ( member_nat @ Y3 @ S2 )
% 0.33/0.62 & ( X3 != Y3 )
% 0.33/0.62 & ! [Z4: nat] :
% 0.33/0.62 ( ( member_nat @ Z4 @ S2 )
% 0.33/0.62 => ( ( Z4 = X3 )
% 0.33/0.62 | ( Z4 = Y3 ) ) ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % card_2_iff'
% 0.33/0.62 thf(fact_5786_card__2__iff_H,axiom,
% 0.33/0.62 ! [S2: set_list_nat] :
% 0.33/0.62 ( ( ( finite_card_list_nat @ S2 )
% 0.33/0.62 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.33/0.62 = ( ? [X3: list_nat] :
% 0.33/0.62 ( ( member_list_nat @ X3 @ S2 )
% 0.33/0.62 & ? [Y3: list_nat] :
% 0.33/0.62 ( ( member_list_nat @ Y3 @ S2 )
% 0.33/0.62 & ( X3 != Y3 )
% 0.33/0.62 & ! [Z4: list_nat] :
% 0.33/0.62 ( ( member_list_nat @ Z4 @ S2 )
% 0.33/0.62 => ( ( Z4 = X3 )
% 0.33/0.62 | ( Z4 = Y3 ) ) ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % card_2_iff'
% 0.33/0.62 thf(fact_5787_sum_Orelated,axiom,
% 0.33/0.62 ! [R4: code_integer > code_integer > $o,S2: set_nat,H3: nat > code_integer,G: nat > code_integer] :
% 0.33/0.62 ( ( R4 @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 0.33/0.62 => ( ! [X13: code_integer,Y12: code_integer,X22: code_integer,Y22: code_integer] :
% 0.33/0.62 ( ( ( R4 @ X13 @ X22 )
% 0.33/0.62 & ( R4 @ Y12 @ Y22 ) )
% 0.33/0.62 => ( R4 @ ( plus_p5714425477246183910nteger @ X13 @ Y12 ) @ ( plus_p5714425477246183910nteger @ X22 @ Y22 ) ) )
% 0.33/0.62 => ( ( finite_finite_nat @ S2 )
% 0.33/0.62 => ( ! [X4: nat] :
% 0.33/0.62 ( ( member_nat @ X4 @ S2 )
% 0.33/0.62 => ( R4 @ ( H3 @ X4 ) @ ( G @ X4 ) ) )
% 0.33/0.62 => ( R4 @ ( groups7501900531339628137nteger @ H3 @ S2 ) @ ( groups7501900531339628137nteger @ G @ S2 ) ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % sum.related
% 0.33/0.62 thf(fact_5788_sum_Orelated,axiom,
% 0.33/0.62 ! [R4: code_integer > code_integer > $o,S2: set_int,H3: int > code_integer,G: int > code_integer] :
% 0.33/0.62 ( ( R4 @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 0.33/0.62 => ( ! [X13: code_integer,Y12: code_integer,X22: code_integer,Y22: code_integer] :
% 0.33/0.62 ( ( ( R4 @ X13 @ X22 )
% 0.33/0.62 & ( R4 @ Y12 @ Y22 ) )
% 0.33/0.62 => ( R4 @ ( plus_p5714425477246183910nteger @ X13 @ Y12 ) @ ( plus_p5714425477246183910nteger @ X22 @ Y22 ) ) )
% 0.33/0.62 => ( ( finite_finite_int @ S2 )
% 0.33/0.62 => ( ! [X4: int] :
% 0.33/0.62 ( ( member_int @ X4 @ S2 )
% 0.33/0.62 => ( R4 @ ( H3 @ X4 ) @ ( G @ X4 ) ) )
% 0.33/0.62 => ( R4 @ ( groups7873554091576472773nteger @ H3 @ S2 ) @ ( groups7873554091576472773nteger @ G @ S2 ) ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % sum.related
% 0.33/0.62 thf(fact_5789_sum_Orelated,axiom,
% 0.33/0.62 ! [R4: code_integer > code_integer > $o,S2: set_Code_integer,H3: code_integer > code_integer,G: code_integer > code_integer] :
% 0.33/0.62 ( ( R4 @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 0.33/0.62 => ( ! [X13: code_integer,Y12: code_integer,X22: code_integer,Y22: code_integer] :
% 0.33/0.62 ( ( ( R4 @ X13 @ X22 )
% 0.33/0.62 & ( R4 @ Y12 @ Y22 ) )
% 0.33/0.62 => ( R4 @ ( plus_p5714425477246183910nteger @ X13 @ Y12 ) @ ( plus_p5714425477246183910nteger @ X22 @ Y22 ) ) )
% 0.33/0.62 => ( ( finite6017078050557962740nteger @ S2 )
% 0.33/0.62 => ( ! [X4: code_integer] :
% 0.33/0.62 ( ( member_Code_integer @ X4 @ S2 )
% 0.33/0.62 => ( R4 @ ( H3 @ X4 ) @ ( G @ X4 ) ) )
% 0.33/0.62 => ( R4 @ ( groups879477027807139574nteger @ H3 @ S2 ) @ ( groups879477027807139574nteger @ G @ S2 ) ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % sum.related
% 0.33/0.62 thf(fact_5790_sum_Orelated,axiom,
% 0.33/0.62 ! [R4: rat > rat > $o,S2: set_nat,H3: nat > rat,G: nat > rat] :
% 0.33/0.62 ( ( R4 @ zero_zero_rat @ zero_zero_rat )
% 0.33/0.62 => ( ! [X13: rat,Y12: rat,X22: rat,Y22: rat] :
% 0.33/0.62 ( ( ( R4 @ X13 @ X22 )
% 0.33/0.62 & ( R4 @ Y12 @ Y22 ) )
% 0.33/0.62 => ( R4 @ ( plus_plus_rat @ X13 @ Y12 ) @ ( plus_plus_rat @ X22 @ Y22 ) ) )
% 0.33/0.62 => ( ( finite_finite_nat @ S2 )
% 0.33/0.62 => ( ! [X4: nat] :
% 0.33/0.62 ( ( member_nat @ X4 @ S2 )
% 0.33/0.62 => ( R4 @ ( H3 @ X4 ) @ ( G @ X4 ) ) )
% 0.33/0.62 => ( R4 @ ( groups2906978787729119204at_rat @ H3 @ S2 ) @ ( groups2906978787729119204at_rat @ G @ S2 ) ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % sum.related
% 0.33/0.62 thf(fact_5791_sum_Orelated,axiom,
% 0.33/0.62 ! [R4: rat > rat > $o,S2: set_int,H3: int > rat,G: int > rat] :
% 0.33/0.62 ( ( R4 @ zero_zero_rat @ zero_zero_rat )
% 0.33/0.62 => ( ! [X13: rat,Y12: rat,X22: rat,Y22: rat] :
% 0.33/0.62 ( ( ( R4 @ X13 @ X22 )
% 0.33/0.62 & ( R4 @ Y12 @ Y22 ) )
% 0.33/0.62 => ( R4 @ ( plus_plus_rat @ X13 @ Y12 ) @ ( plus_plus_rat @ X22 @ Y22 ) ) )
% 0.33/0.62 => ( ( finite_finite_int @ S2 )
% 0.33/0.62 => ( ! [X4: int] :
% 0.33/0.62 ( ( member_int @ X4 @ S2 )
% 0.33/0.62 => ( R4 @ ( H3 @ X4 ) @ ( G @ X4 ) ) )
% 0.33/0.62 => ( R4 @ ( groups3906332499630173760nt_rat @ H3 @ S2 ) @ ( groups3906332499630173760nt_rat @ G @ S2 ) ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % sum.related
% 0.33/0.62 thf(fact_5792_sum_Orelated,axiom,
% 0.33/0.62 ! [R4: rat > rat > $o,S2: set_Code_integer,H3: code_integer > rat,G: code_integer > rat] :
% 0.33/0.62 ( ( R4 @ zero_zero_rat @ zero_zero_rat )
% 0.33/0.62 => ( ! [X13: rat,Y12: rat,X22: rat,Y22: rat] :
% 0.33/0.62 ( ( ( R4 @ X13 @ X22 )
% 0.33/0.62 & ( R4 @ Y12 @ Y22 ) )
% 0.33/0.62 => ( R4 @ ( plus_plus_rat @ X13 @ Y12 ) @ ( plus_plus_rat @ X22 @ Y22 ) ) )
% 0.33/0.62 => ( ( finite6017078050557962740nteger @ S2 )
% 0.33/0.62 => ( ! [X4: code_integer] :
% 0.33/0.62 ( ( member_Code_integer @ X4 @ S2 )
% 0.33/0.62 => ( R4 @ ( H3 @ X4 ) @ ( G @ X4 ) ) )
% 0.33/0.62 => ( R4 @ ( groups6602215022474089585er_rat @ H3 @ S2 ) @ ( groups6602215022474089585er_rat @ G @ S2 ) ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % sum.related
% 0.33/0.62 thf(fact_5793_sum_Orelated,axiom,
% 0.33/0.62 ! [R4: nat > nat > $o,S2: set_int,H3: int > nat,G: int > nat] :
% 0.33/0.62 ( ( R4 @ zero_zero_nat @ zero_zero_nat )
% 0.33/0.62 => ( ! [X13: nat,Y12: nat,X22: nat,Y22: nat] :
% 0.33/0.62 ( ( ( R4 @ X13 @ X22 )
% 0.33/0.62 & ( R4 @ Y12 @ Y22 ) )
% 0.33/0.62 => ( R4 @ ( plus_plus_nat @ X13 @ Y12 ) @ ( plus_plus_nat @ X22 @ Y22 ) ) )
% 0.33/0.62 => ( ( finite_finite_int @ S2 )
% 0.33/0.62 => ( ! [X4: int] :
% 0.33/0.62 ( ( member_int @ X4 @ S2 )
% 0.33/0.62 => ( R4 @ ( H3 @ X4 ) @ ( G @ X4 ) ) )
% 0.33/0.62 => ( R4 @ ( groups4541462559716669496nt_nat @ H3 @ S2 ) @ ( groups4541462559716669496nt_nat @ G @ S2 ) ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % sum.related
% 0.33/0.62 thf(fact_5794_sum_Orelated,axiom,
% 0.33/0.62 ! [R4: nat > nat > $o,S2: set_Code_integer,H3: code_integer > nat,G: code_integer > nat] :
% 0.33/0.62 ( ( R4 @ zero_zero_nat @ zero_zero_nat )
% 0.33/0.62 => ( ! [X13: nat,Y12: nat,X22: nat,Y22: nat] :
% 0.33/0.62 ( ( ( R4 @ X13 @ X22 )
% 0.33/0.62 & ( R4 @ Y12 @ Y22 ) )
% 0.33/0.62 => ( R4 @ ( plus_plus_nat @ X13 @ Y12 ) @ ( plus_plus_nat @ X22 @ Y22 ) ) )
% 0.33/0.62 => ( ( finite6017078050557962740nteger @ S2 )
% 0.33/0.62 => ( ! [X4: code_integer] :
% 0.33/0.62 ( ( member_Code_integer @ X4 @ S2 )
% 0.33/0.62 => ( R4 @ ( H3 @ X4 ) @ ( G @ X4 ) ) )
% 0.33/0.62 => ( R4 @ ( groups7237345082560585321er_nat @ H3 @ S2 ) @ ( groups7237345082560585321er_nat @ G @ S2 ) ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % sum.related
% 0.33/0.62 thf(fact_5795_sum_Orelated,axiom,
% 0.33/0.62 ! [R4: int > int > $o,S2: set_nat,H3: nat > int,G: nat > int] :
% 0.33/0.62 ( ( R4 @ zero_zero_int @ zero_zero_int )
% 0.33/0.62 => ( ! [X13: int,Y12: int,X22: int,Y22: int] :
% 0.33/0.62 ( ( ( R4 @ X13 @ X22 )
% 0.33/0.62 & ( R4 @ Y12 @ Y22 ) )
% 0.33/0.62 => ( R4 @ ( plus_plus_int @ X13 @ Y12 ) @ ( plus_plus_int @ X22 @ Y22 ) ) )
% 0.33/0.62 => ( ( finite_finite_nat @ S2 )
% 0.33/0.62 => ( ! [X4: nat] :
% 0.33/0.62 ( ( member_nat @ X4 @ S2 )
% 0.33/0.62 => ( R4 @ ( H3 @ X4 ) @ ( G @ X4 ) ) )
% 0.33/0.62 => ( R4 @ ( groups3539618377306564664at_int @ H3 @ S2 ) @ ( groups3539618377306564664at_int @ G @ S2 ) ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % sum.related
% 0.33/0.62 thf(fact_5796_sum_Orelated,axiom,
% 0.33/0.62 ! [R4: int > int > $o,S2: set_Code_integer,H3: code_integer > int,G: code_integer > int] :
% 0.33/0.62 ( ( R4 @ zero_zero_int @ zero_zero_int )
% 0.33/0.62 => ( ! [X13: int,Y12: int,X22: int,Y22: int] :
% 0.33/0.62 ( ( ( R4 @ X13 @ X22 )
% 0.33/0.62 & ( R4 @ Y12 @ Y22 ) )
% 0.33/0.62 => ( R4 @ ( plus_plus_int @ X13 @ Y12 ) @ ( plus_plus_int @ X22 @ Y22 ) ) )
% 0.33/0.62 => ( ( finite6017078050557962740nteger @ S2 )
% 0.33/0.62 => ( ! [X4: code_integer] :
% 0.33/0.62 ( ( member_Code_integer @ X4 @ S2 )
% 0.33/0.62 => ( R4 @ ( H3 @ X4 ) @ ( G @ X4 ) ) )
% 0.33/0.62 => ( R4 @ ( groups7234854612051535045er_int @ H3 @ S2 ) @ ( groups7234854612051535045er_int @ G @ S2 ) ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % sum.related
% 0.33/0.62 thf(fact_5797_prod_Orelated,axiom,
% 0.33/0.62 ! [R4: code_integer > code_integer > $o,S2: set_nat,H3: nat > code_integer,G: nat > code_integer] :
% 0.33/0.62 ( ( R4 @ one_one_Code_integer @ one_one_Code_integer )
% 0.33/0.62 => ( ! [X13: code_integer,Y12: code_integer,X22: code_integer,Y22: code_integer] :
% 0.33/0.62 ( ( ( R4 @ X13 @ X22 )
% 0.33/0.62 & ( R4 @ Y12 @ Y22 ) )
% 0.33/0.62 => ( R4 @ ( times_3573771949741848930nteger @ X13 @ Y12 ) @ ( times_3573771949741848930nteger @ X22 @ Y22 ) ) )
% 0.33/0.62 => ( ( finite_finite_nat @ S2 )
% 0.33/0.62 => ( ! [X4: nat] :
% 0.33/0.62 ( ( member_nat @ X4 @ S2 )
% 0.33/0.62 => ( R4 @ ( H3 @ X4 ) @ ( G @ X4 ) ) )
% 0.33/0.62 => ( R4 @ ( groups3455450783089532116nteger @ H3 @ S2 ) @ ( groups3455450783089532116nteger @ G @ S2 ) ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % prod.related
% 0.33/0.62 thf(fact_5798_prod_Orelated,axiom,
% 0.33/0.62 ! [R4: code_integer > code_integer > $o,S2: set_int,H3: int > code_integer,G: int > code_integer] :
% 0.33/0.62 ( ( R4 @ one_one_Code_integer @ one_one_Code_integer )
% 0.33/0.62 => ( ! [X13: code_integer,Y12: code_integer,X22: code_integer,Y22: code_integer] :
% 0.33/0.62 ( ( ( R4 @ X13 @ X22 )
% 0.33/0.62 & ( R4 @ Y12 @ Y22 ) )
% 0.33/0.62 => ( R4 @ ( times_3573771949741848930nteger @ X13 @ Y12 ) @ ( times_3573771949741848930nteger @ X22 @ Y22 ) ) )
% 0.33/0.62 => ( ( finite_finite_int @ S2 )
% 0.33/0.62 => ( ! [X4: int] :
% 0.33/0.62 ( ( member_int @ X4 @ S2 )
% 0.33/0.62 => ( R4 @ ( H3 @ X4 ) @ ( G @ X4 ) ) )
% 0.33/0.62 => ( R4 @ ( groups3827104343326376752nteger @ H3 @ S2 ) @ ( groups3827104343326376752nteger @ G @ S2 ) ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % prod.related
% 0.33/0.62 thf(fact_5799_prod_Orelated,axiom,
% 0.33/0.62 ! [R4: code_integer > code_integer > $o,S2: set_Code_integer,H3: code_integer > code_integer,G: code_integer > code_integer] :
% 0.33/0.62 ( ( R4 @ one_one_Code_integer @ one_one_Code_integer )
% 0.33/0.62 => ( ! [X13: code_integer,Y12: code_integer,X22: code_integer,Y22: code_integer] :
% 0.33/0.62 ( ( ( R4 @ X13 @ X22 )
% 0.33/0.62 & ( R4 @ Y12 @ Y22 ) )
% 0.33/0.62 => ( R4 @ ( times_3573771949741848930nteger @ X13 @ Y12 ) @ ( times_3573771949741848930nteger @ X22 @ Y22 ) ) )
% 0.33/0.62 => ( ( finite6017078050557962740nteger @ S2 )
% 0.33/0.62 => ( ! [X4: code_integer] :
% 0.33/0.62 ( ( member_Code_integer @ X4 @ S2 )
% 0.33/0.62 => ( R4 @ ( H3 @ X4 ) @ ( G @ X4 ) ) )
% 0.33/0.62 => ( R4 @ ( groups3674199335183972705nteger @ H3 @ S2 ) @ ( groups3674199335183972705nteger @ G @ S2 ) ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % prod.related
% 0.33/0.62 thf(fact_5800_prod_Orelated,axiom,
% 0.33/0.62 ! [R4: assn > assn > $o,S2: set_nat,H3: nat > assn,G: nat > assn] :
% 0.33/0.62 ( ( R4 @ one_one_assn @ one_one_assn )
% 0.33/0.62 => ( ! [X13: assn,Y12: assn,X22: assn,Y22: assn] :
% 0.33/0.62 ( ( ( R4 @ X13 @ X22 )
% 0.33/0.62 & ( R4 @ Y12 @ Y22 ) )
% 0.33/0.62 => ( R4 @ ( times_times_assn @ X13 @ Y12 ) @ ( times_times_assn @ X22 @ Y22 ) ) )
% 0.33/0.62 => ( ( finite_finite_nat @ S2 )
% 0.33/0.62 => ( ! [X4: nat] :
% 0.33/0.62 ( ( member_nat @ X4 @ S2 )
% 0.33/0.62 => ( R4 @ ( H3 @ X4 ) @ ( G @ X4 ) ) )
% 0.33/0.62 => ( R4 @ ( groups6906906614972039071t_assn @ H3 @ S2 ) @ ( groups6906906614972039071t_assn @ G @ S2 ) ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % prod.related
% 0.33/0.62 thf(fact_5801_prod_Orelated,axiom,
% 0.33/0.62 ! [R4: assn > assn > $o,S2: set_int,H3: int > assn,G: int > assn] :
% 0.33/0.62 ( ( R4 @ one_one_assn @ one_one_assn )
% 0.33/0.62 => ( ! [X13: assn,Y12: assn,X22: assn,Y22: assn] :
% 0.33/0.62 ( ( ( R4 @ X13 @ X22 )
% 0.33/0.62 & ( R4 @ Y12 @ Y22 ) )
% 0.33/0.62 => ( R4 @ ( times_times_assn @ X13 @ Y12 ) @ ( times_times_assn @ X22 @ Y22 ) ) )
% 0.33/0.62 => ( ( finite_finite_int @ S2 )
% 0.33/0.62 => ( ! [X4: int] :
% 0.33/0.62 ( ( member_int @ X4 @ S2 )
% 0.33/0.62 => ( R4 @ ( H3 @ X4 ) @ ( G @ X4 ) ) )
% 0.33/0.62 => ( R4 @ ( groups7882442080178216443t_assn @ H3 @ S2 ) @ ( groups7882442080178216443t_assn @ G @ S2 ) ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % prod.related
% 0.33/0.62 thf(fact_5802_prod_Orelated,axiom,
% 0.33/0.62 ! [R4: assn > assn > $o,S2: set_Code_integer,H3: code_integer > assn,G: code_integer > assn] :
% 0.33/0.62 ( ( R4 @ one_one_assn @ one_one_assn )
% 0.33/0.62 => ( ! [X13: assn,Y12: assn,X22: assn,Y22: assn] :
% 0.33/0.62 ( ( ( R4 @ X13 @ X22 )
% 0.33/0.62 & ( R4 @ Y12 @ Y22 ) )
% 0.33/0.62 => ( R4 @ ( times_times_assn @ X13 @ Y12 ) @ ( times_times_assn @ X22 @ Y22 ) ) )
% 0.33/0.62 => ( ( finite6017078050557962740nteger @ S2 )
% 0.33/0.62 => ( ! [X4: code_integer] :
% 0.33/0.62 ( ( member_Code_integer @ X4 @ S2 )
% 0.33/0.62 => ( R4 @ ( H3 @ X4 ) @ ( G @ X4 ) ) )
% 0.33/0.62 => ( R4 @ ( groups1304777262505850412r_assn @ H3 @ S2 ) @ ( groups1304777262505850412r_assn @ G @ S2 ) ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % prod.related
% 0.33/0.62 thf(fact_5803_prod_Orelated,axiom,
% 0.33/0.62 ! [R4: rat > rat > $o,S2: set_nat,H3: nat > rat,G: nat > rat] :
% 0.33/0.62 ( ( R4 @ one_one_rat @ one_one_rat )
% 0.33/0.62 => ( ! [X13: rat,Y12: rat,X22: rat,Y22: rat] :
% 0.33/0.62 ( ( ( R4 @ X13 @ X22 )
% 0.33/0.62 & ( R4 @ Y12 @ Y22 ) )
% 0.33/0.62 => ( R4 @ ( times_times_rat @ X13 @ Y12 ) @ ( times_times_rat @ X22 @ Y22 ) ) )
% 0.33/0.62 => ( ( finite_finite_nat @ S2 )
% 0.33/0.62 => ( ! [X4: nat] :
% 0.33/0.62 ( ( member_nat @ X4 @ S2 )
% 0.33/0.62 => ( R4 @ ( H3 @ X4 ) @ ( G @ X4 ) ) )
% 0.33/0.62 => ( R4 @ ( groups73079841787564623at_rat @ H3 @ S2 ) @ ( groups73079841787564623at_rat @ G @ S2 ) ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % prod.related
% 0.33/0.62 thf(fact_5804_prod_Orelated,axiom,
% 0.33/0.62 ! [R4: rat > rat > $o,S2: set_int,H3: int > rat,G: int > rat] :
% 0.33/0.62 ( ( R4 @ one_one_rat @ one_one_rat )
% 0.33/0.62 => ( ! [X13: rat,Y12: rat,X22: rat,Y22: rat] :
% 0.33/0.62 ( ( ( R4 @ X13 @ X22 )
% 0.33/0.62 & ( R4 @ Y12 @ Y22 ) )
% 0.33/0.62 => ( R4 @ ( times_times_rat @ X13 @ Y12 ) @ ( times_times_rat @ X22 @ Y22 ) ) )
% 0.33/0.62 => ( ( finite_finite_int @ S2 )
% 0.33/0.62 => ( ! [X4: int] :
% 0.33/0.62 ( ( member_int @ X4 @ S2 )
% 0.33/0.62 => ( R4 @ ( H3 @ X4 ) @ ( G @ X4 ) ) )
% 0.33/0.62 => ( R4 @ ( groups1072433553688619179nt_rat @ H3 @ S2 ) @ ( groups1072433553688619179nt_rat @ G @ S2 ) ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % prod.related
% 0.33/0.62 thf(fact_5805_prod_Orelated,axiom,
% 0.33/0.62 ! [R4: rat > rat > $o,S2: set_Code_integer,H3: code_integer > rat,G: code_integer > rat] :
% 0.33/0.62 ( ( R4 @ one_one_rat @ one_one_rat )
% 0.33/0.62 => ( ! [X13: rat,Y12: rat,X22: rat,Y22: rat] :
% 0.33/0.62 ( ( ( R4 @ X13 @ X22 )
% 0.33/0.62 & ( R4 @ Y12 @ Y22 ) )
% 0.33/0.62 => ( R4 @ ( times_times_rat @ X13 @ Y12 ) @ ( times_times_rat @ X22 @ Y22 ) ) )
% 0.33/0.62 => ( ( finite6017078050557962740nteger @ S2 )
% 0.33/0.62 => ( ! [X4: code_integer] :
% 0.33/0.62 ( ( member_Code_integer @ X4 @ S2 )
% 0.33/0.62 => ( R4 @ ( H3 @ X4 ) @ ( G @ X4 ) ) )
% 0.33/0.62 => ( R4 @ ( groups2555765274223993564er_rat @ H3 @ S2 ) @ ( groups2555765274223993564er_rat @ G @ S2 ) ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % prod.related
% 0.33/0.62 thf(fact_5806_prod_Orelated,axiom,
% 0.33/0.62 ! [R4: nat > nat > $o,S2: set_int,H3: int > nat,G: int > nat] :
% 0.33/0.62 ( ( R4 @ one_one_nat @ one_one_nat )
% 0.33/0.62 => ( ! [X13: nat,Y12: nat,X22: nat,Y22: nat] :
% 0.33/0.62 ( ( ( R4 @ X13 @ X22 )
% 0.33/0.62 & ( R4 @ Y12 @ Y22 ) )
% 0.33/0.62 => ( R4 @ ( times_times_nat @ X13 @ Y12 ) @ ( times_times_nat @ X22 @ Y22 ) ) )
% 0.33/0.62 => ( ( finite_finite_int @ S2 )
% 0.33/0.62 => ( ! [X4: int] :
% 0.33/0.62 ( ( member_int @ X4 @ S2 )
% 0.33/0.62 => ( R4 @ ( H3 @ X4 ) @ ( G @ X4 ) ) )
% 0.33/0.62 => ( R4 @ ( groups1707563613775114915nt_nat @ H3 @ S2 ) @ ( groups1707563613775114915nt_nat @ G @ S2 ) ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % prod.related
% 0.33/0.62 thf(fact_5807_sum_Oinsert__if,axiom,
% 0.33/0.62 ! [A2: set_o,X: $o,G: $o > rat] :
% 0.33/0.62 ( ( finite_finite_o @ A2 )
% 0.33/0.62 => ( ( ( member_o @ X @ A2 )
% 0.33/0.62 => ( ( groups7872700643590313910_o_rat @ G @ ( insert_o @ X @ A2 ) )
% 0.33/0.62 = ( groups7872700643590313910_o_rat @ G @ A2 ) ) )
% 0.33/0.62 & ( ~ ( member_o @ X @ A2 )
% 0.33/0.62 => ( ( groups7872700643590313910_o_rat @ G @ ( insert_o @ X @ A2 ) )
% 0.33/0.62 = ( plus_plus_rat @ ( G @ X ) @ ( groups7872700643590313910_o_rat @ G @ A2 ) ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % sum.insert_if
% 0.33/0.62 thf(fact_5808_sum_Oinsert__if,axiom,
% 0.33/0.62 ! [A2: set_nat,X: nat,G: nat > rat] :
% 0.33/0.62 ( ( finite_finite_nat @ A2 )
% 0.33/0.62 => ( ( ( member_nat @ X @ A2 )
% 0.33/0.62 => ( ( groups2906978787729119204at_rat @ G @ ( insert_nat @ X @ A2 ) )
% 0.33/0.62 = ( groups2906978787729119204at_rat @ G @ A2 ) ) )
% 0.33/0.62 & ( ~ ( member_nat @ X @ A2 )
% 0.33/0.62 => ( ( groups2906978787729119204at_rat @ G @ ( insert_nat @ X @ A2 ) )
% 0.33/0.62 = ( plus_plus_rat @ ( G @ X ) @ ( groups2906978787729119204at_rat @ G @ A2 ) ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % sum.insert_if
% 0.33/0.62 thf(fact_5809_sum_Oinsert__if,axiom,
% 0.33/0.62 ! [A2: set_int,X: int,G: int > rat] :
% 0.33/0.62 ( ( finite_finite_int @ A2 )
% 0.33/0.62 => ( ( ( member_int @ X @ A2 )
% 0.33/0.62 => ( ( groups3906332499630173760nt_rat @ G @ ( insert_int @ X @ A2 ) )
% 0.33/0.62 = ( groups3906332499630173760nt_rat @ G @ A2 ) ) )
% 0.33/0.62 & ( ~ ( member_int @ X @ A2 )
% 0.33/0.62 => ( ( groups3906332499630173760nt_rat @ G @ ( insert_int @ X @ A2 ) )
% 0.33/0.62 = ( plus_plus_rat @ ( G @ X ) @ ( groups3906332499630173760nt_rat @ G @ A2 ) ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % sum.insert_if
% 0.33/0.62 thf(fact_5810_sum_Oinsert__if,axiom,
% 0.33/0.62 ! [A2: set_Code_integer,X: code_integer,G: code_integer > rat] :
% 0.33/0.62 ( ( finite6017078050557962740nteger @ A2 )
% 0.33/0.62 => ( ( ( member_Code_integer @ X @ A2 )
% 0.33/0.62 => ( ( groups6602215022474089585er_rat @ G @ ( insert_Code_integer @ X @ A2 ) )
% 0.33/0.62 = ( groups6602215022474089585er_rat @ G @ A2 ) ) )
% 0.33/0.62 & ( ~ ( member_Code_integer @ X @ A2 )
% 0.33/0.62 => ( ( groups6602215022474089585er_rat @ G @ ( insert_Code_integer @ X @ A2 ) )
% 0.33/0.62 = ( plus_plus_rat @ ( G @ X ) @ ( groups6602215022474089585er_rat @ G @ A2 ) ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % sum.insert_if
% 0.33/0.62 thf(fact_5811_sum_Oinsert__if,axiom,
% 0.33/0.62 ! [A2: set_o,X: $o,G: $o > nat] :
% 0.33/0.62 ( ( finite_finite_o @ A2 )
% 0.33/0.62 => ( ( ( member_o @ X @ A2 )
% 0.33/0.62 => ( ( groups8507830703676809646_o_nat @ G @ ( insert_o @ X @ A2 ) )
% 0.33/0.62 = ( groups8507830703676809646_o_nat @ G @ A2 ) ) )
% 0.33/0.62 & ( ~ ( member_o @ X @ A2 )
% 0.33/0.62 => ( ( groups8507830703676809646_o_nat @ G @ ( insert_o @ X @ A2 ) )
% 0.33/0.62 = ( plus_plus_nat @ ( G @ X ) @ ( groups8507830703676809646_o_nat @ G @ A2 ) ) ) ) ) ) ).
% 0.33/0.62
% 0.33/0.62 % sum.insert_if
% 0.33/0.62 thf(fact_5812_sum_Oinsert__if,axiom,
% 0.33/0.62 ! [A2: set_int,X: int,G: int > nat] :
% 0.33/0.63 ( ( finite_finite_int @ A2 )
% 0.33/0.63 => ( ( ( member_int @ X @ A2 )
% 0.33/0.63 => ( ( groups4541462559716669496nt_nat @ G @ ( insert_int @ X @ A2 ) )
% 0.33/0.63 = ( groups4541462559716669496nt_nat @ G @ A2 ) ) )
% 0.33/0.63 & ( ~ ( member_int @ X @ A2 )
% 0.33/0.63 => ( ( groups4541462559716669496nt_nat @ G @ ( insert_int @ X @ A2 ) )
% 0.33/0.63 = ( plus_plus_nat @ ( G @ X ) @ ( groups4541462559716669496nt_nat @ G @ A2 ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % sum.insert_if
% 0.33/0.63 thf(fact_5813_sum_Oinsert__if,axiom,
% 0.33/0.63 ! [A2: set_Code_integer,X: code_integer,G: code_integer > nat] :
% 0.33/0.63 ( ( finite6017078050557962740nteger @ A2 )
% 0.33/0.63 => ( ( ( member_Code_integer @ X @ A2 )
% 0.33/0.63 => ( ( groups7237345082560585321er_nat @ G @ ( insert_Code_integer @ X @ A2 ) )
% 0.33/0.63 = ( groups7237345082560585321er_nat @ G @ A2 ) ) )
% 0.33/0.63 & ( ~ ( member_Code_integer @ X @ A2 )
% 0.33/0.63 => ( ( groups7237345082560585321er_nat @ G @ ( insert_Code_integer @ X @ A2 ) )
% 0.33/0.63 = ( plus_plus_nat @ ( G @ X ) @ ( groups7237345082560585321er_nat @ G @ A2 ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % sum.insert_if
% 0.33/0.63 thf(fact_5814_sum_Oinsert__if,axiom,
% 0.33/0.63 ! [A2: set_o,X: $o,G: $o > int] :
% 0.33/0.63 ( ( finite_finite_o @ A2 )
% 0.33/0.63 => ( ( ( member_o @ X @ A2 )
% 0.33/0.63 => ( ( groups8505340233167759370_o_int @ G @ ( insert_o @ X @ A2 ) )
% 0.33/0.63 = ( groups8505340233167759370_o_int @ G @ A2 ) ) )
% 0.33/0.63 & ( ~ ( member_o @ X @ A2 )
% 0.33/0.63 => ( ( groups8505340233167759370_o_int @ G @ ( insert_o @ X @ A2 ) )
% 0.33/0.63 = ( plus_plus_int @ ( G @ X ) @ ( groups8505340233167759370_o_int @ G @ A2 ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % sum.insert_if
% 0.33/0.63 thf(fact_5815_sum_Oinsert__if,axiom,
% 0.33/0.63 ! [A2: set_nat,X: nat,G: nat > int] :
% 0.33/0.63 ( ( finite_finite_nat @ A2 )
% 0.33/0.63 => ( ( ( member_nat @ X @ A2 )
% 0.33/0.63 => ( ( groups3539618377306564664at_int @ G @ ( insert_nat @ X @ A2 ) )
% 0.33/0.63 = ( groups3539618377306564664at_int @ G @ A2 ) ) )
% 0.33/0.63 & ( ~ ( member_nat @ X @ A2 )
% 0.33/0.63 => ( ( groups3539618377306564664at_int @ G @ ( insert_nat @ X @ A2 ) )
% 0.33/0.63 = ( plus_plus_int @ ( G @ X ) @ ( groups3539618377306564664at_int @ G @ A2 ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % sum.insert_if
% 0.33/0.63 thf(fact_5816_sum_Oinsert__if,axiom,
% 0.33/0.63 ! [A2: set_Code_integer,X: code_integer,G: code_integer > int] :
% 0.33/0.63 ( ( finite6017078050557962740nteger @ A2 )
% 0.33/0.63 => ( ( ( member_Code_integer @ X @ A2 )
% 0.33/0.63 => ( ( groups7234854612051535045er_int @ G @ ( insert_Code_integer @ X @ A2 ) )
% 0.33/0.63 = ( groups7234854612051535045er_int @ G @ A2 ) ) )
% 0.33/0.63 & ( ~ ( member_Code_integer @ X @ A2 )
% 0.33/0.63 => ( ( groups7234854612051535045er_int @ G @ ( insert_Code_integer @ X @ A2 ) )
% 0.33/0.63 = ( plus_plus_int @ ( G @ X ) @ ( groups7234854612051535045er_int @ G @ A2 ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % sum.insert_if
% 0.33/0.63 thf(fact_5817_atLeast0__atMost__Suc,axiom,
% 0.33/0.63 ! [N2: nat] :
% 0.33/0.63 ( ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) )
% 0.33/0.63 = ( insert_nat @ ( suc @ N2 ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % atLeast0_atMost_Suc
% 0.33/0.63 thf(fact_5818_atLeast0__lessThan__Suc,axiom,
% 0.33/0.63 ! [N2: nat] :
% 0.33/0.63 ( ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N2 ) )
% 0.33/0.63 = ( insert_nat @ N2 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % atLeast0_lessThan_Suc
% 0.33/0.63 thf(fact_5819_Icc__eq__insert__lb__nat,axiom,
% 0.33/0.63 ! [M2: nat,N2: nat] :
% 0.33/0.63 ( ( ord_less_eq_nat @ M2 @ N2 )
% 0.33/0.63 => ( ( set_or1269000886237332187st_nat @ M2 @ N2 )
% 0.33/0.63 = ( insert_nat @ M2 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N2 ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % Icc_eq_insert_lb_nat
% 0.33/0.63 thf(fact_5820_atLeastAtMostSuc__conv,axiom,
% 0.33/0.63 ! [M2: nat,N2: nat] :
% 0.33/0.63 ( ( ord_less_eq_nat @ M2 @ ( suc @ N2 ) )
% 0.33/0.63 => ( ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N2 ) )
% 0.33/0.63 = ( insert_nat @ ( suc @ N2 ) @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % atLeastAtMostSuc_conv
% 0.33/0.63 thf(fact_5821_atLeastAtMost__insertL,axiom,
% 0.33/0.63 ! [M2: nat,N2: nat] :
% 0.33/0.63 ( ( ord_less_eq_nat @ M2 @ N2 )
% 0.33/0.63 => ( ( insert_nat @ M2 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N2 ) )
% 0.33/0.63 = ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % atLeastAtMost_insertL
% 0.33/0.63 thf(fact_5822_prod_Oreindex__bij__witness__not__neutral,axiom,
% 0.33/0.63 ! [S7: set_o,T4: set_o,S2: set_o,I: $o > $o,J: $o > $o,T5: set_o,G: $o > code_integer,H3: $o > code_integer] :
% 0.33/0.63 ( ( finite_finite_o @ S7 )
% 0.33/0.63 => ( ( finite_finite_o @ T4 )
% 0.33/0.63 => ( ! [A3: $o] :
% 0.33/0.63 ( ( member_o @ A3 @ ( minus_minus_set_o @ S2 @ S7 ) )
% 0.33/0.63 => ( ( I @ ( J @ A3 ) )
% 0.33/0.63 = A3 ) )
% 0.33/0.63 => ( ! [A3: $o] :
% 0.33/0.63 ( ( member_o @ A3 @ ( minus_minus_set_o @ S2 @ S7 ) )
% 0.33/0.63 => ( member_o @ ( J @ A3 ) @ ( minus_minus_set_o @ T5 @ T4 ) ) )
% 0.33/0.63 => ( ! [B2: $o] :
% 0.33/0.63 ( ( member_o @ B2 @ ( minus_minus_set_o @ T5 @ T4 ) )
% 0.33/0.63 => ( ( J @ ( I @ B2 ) )
% 0.33/0.63 = B2 ) )
% 0.33/0.63 => ( ! [B2: $o] :
% 0.33/0.63 ( ( member_o @ B2 @ ( minus_minus_set_o @ T5 @ T4 ) )
% 0.33/0.63 => ( member_o @ ( I @ B2 ) @ ( minus_minus_set_o @ S2 @ S7 ) ) )
% 0.33/0.63 => ( ! [A3: $o] :
% 0.33/0.63 ( ( member_o @ A3 @ S7 )
% 0.33/0.63 => ( ( G @ A3 )
% 0.33/0.63 = one_one_Code_integer ) )
% 0.33/0.63 => ( ! [B2: $o] :
% 0.33/0.63 ( ( member_o @ B2 @ T4 )
% 0.33/0.63 => ( ( H3 @ B2 )
% 0.33/0.63 = one_one_Code_integer ) )
% 0.33/0.63 => ( ! [A3: $o] :
% 0.33/0.63 ( ( member_o @ A3 @ S2 )
% 0.33/0.63 => ( ( H3 @ ( J @ A3 ) )
% 0.33/0.63 = ( G @ A3 ) ) )
% 0.33/0.63 => ( ( groups7694694392188491536nteger @ G @ S2 )
% 0.33/0.63 = ( groups7694694392188491536nteger @ H3 @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.reindex_bij_witness_not_neutral
% 0.33/0.63 thf(fact_5823_prod_Oreindex__bij__witness__not__neutral,axiom,
% 0.33/0.63 ! [S7: set_o,T4: set_int,S2: set_o,I: int > $o,J: $o > int,T5: set_int,G: $o > code_integer,H3: int > code_integer] :
% 0.33/0.63 ( ( finite_finite_o @ S7 )
% 0.33/0.63 => ( ( finite_finite_int @ T4 )
% 0.33/0.63 => ( ! [A3: $o] :
% 0.33/0.63 ( ( member_o @ A3 @ ( minus_minus_set_o @ S2 @ S7 ) )
% 0.33/0.63 => ( ( I @ ( J @ A3 ) )
% 0.33/0.63 = A3 ) )
% 0.33/0.63 => ( ! [A3: $o] :
% 0.33/0.63 ( ( member_o @ A3 @ ( minus_minus_set_o @ S2 @ S7 ) )
% 0.33/0.63 => ( member_int @ ( J @ A3 ) @ ( minus_minus_set_int @ T5 @ T4 ) ) )
% 0.33/0.63 => ( ! [B2: int] :
% 0.33/0.63 ( ( member_int @ B2 @ ( minus_minus_set_int @ T5 @ T4 ) )
% 0.33/0.63 => ( ( J @ ( I @ B2 ) )
% 0.33/0.63 = B2 ) )
% 0.33/0.63 => ( ! [B2: int] :
% 0.33/0.63 ( ( member_int @ B2 @ ( minus_minus_set_int @ T5 @ T4 ) )
% 0.33/0.63 => ( member_o @ ( I @ B2 ) @ ( minus_minus_set_o @ S2 @ S7 ) ) )
% 0.33/0.63 => ( ! [A3: $o] :
% 0.33/0.63 ( ( member_o @ A3 @ S7 )
% 0.33/0.63 => ( ( G @ A3 )
% 0.33/0.63 = one_one_Code_integer ) )
% 0.33/0.63 => ( ! [B2: int] :
% 0.33/0.63 ( ( member_int @ B2 @ T4 )
% 0.33/0.63 => ( ( H3 @ B2 )
% 0.33/0.63 = one_one_Code_integer ) )
% 0.33/0.63 => ( ! [A3: $o] :
% 0.33/0.63 ( ( member_o @ A3 @ S2 )
% 0.33/0.63 => ( ( H3 @ ( J @ A3 ) )
% 0.33/0.63 = ( G @ A3 ) ) )
% 0.33/0.63 => ( ( groups7694694392188491536nteger @ G @ S2 )
% 0.33/0.63 = ( groups3827104343326376752nteger @ H3 @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.reindex_bij_witness_not_neutral
% 0.33/0.63 thf(fact_5824_prod_Oreindex__bij__witness__not__neutral,axiom,
% 0.33/0.63 ! [S7: set_o,T4: set_Code_integer,S2: set_o,I: code_integer > $o,J: $o > code_integer,T5: set_Code_integer,G: $o > code_integer,H3: code_integer > code_integer] :
% 0.33/0.63 ( ( finite_finite_o @ S7 )
% 0.33/0.63 => ( ( finite6017078050557962740nteger @ T4 )
% 0.33/0.63 => ( ! [A3: $o] :
% 0.33/0.63 ( ( member_o @ A3 @ ( minus_minus_set_o @ S2 @ S7 ) )
% 0.33/0.63 => ( ( I @ ( J @ A3 ) )
% 0.33/0.63 = A3 ) )
% 0.33/0.63 => ( ! [A3: $o] :
% 0.33/0.63 ( ( member_o @ A3 @ ( minus_minus_set_o @ S2 @ S7 ) )
% 0.33/0.63 => ( member_Code_integer @ ( J @ A3 ) @ ( minus_2355218937544613996nteger @ T5 @ T4 ) ) )
% 0.33/0.63 => ( ! [B2: code_integer] :
% 0.33/0.63 ( ( member_Code_integer @ B2 @ ( minus_2355218937544613996nteger @ T5 @ T4 ) )
% 0.33/0.63 => ( ( J @ ( I @ B2 ) )
% 0.33/0.63 = B2 ) )
% 0.33/0.63 => ( ! [B2: code_integer] :
% 0.33/0.63 ( ( member_Code_integer @ B2 @ ( minus_2355218937544613996nteger @ T5 @ T4 ) )
% 0.33/0.63 => ( member_o @ ( I @ B2 ) @ ( minus_minus_set_o @ S2 @ S7 ) ) )
% 0.33/0.63 => ( ! [A3: $o] :
% 0.33/0.63 ( ( member_o @ A3 @ S7 )
% 0.33/0.63 => ( ( G @ A3 )
% 0.33/0.63 = one_one_Code_integer ) )
% 0.33/0.63 => ( ! [B2: code_integer] :
% 0.33/0.63 ( ( member_Code_integer @ B2 @ T4 )
% 0.33/0.63 => ( ( H3 @ B2 )
% 0.33/0.63 = one_one_Code_integer ) )
% 0.33/0.63 => ( ! [A3: $o] :
% 0.33/0.63 ( ( member_o @ A3 @ S2 )
% 0.33/0.63 => ( ( H3 @ ( J @ A3 ) )
% 0.33/0.63 = ( G @ A3 ) ) )
% 0.33/0.63 => ( ( groups7694694392188491536nteger @ G @ S2 )
% 0.33/0.63 = ( groups3674199335183972705nteger @ H3 @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.reindex_bij_witness_not_neutral
% 0.33/0.63 thf(fact_5825_prod_Oreindex__bij__witness__not__neutral,axiom,
% 0.33/0.63 ! [S7: set_int,T4: set_o,S2: set_int,I: $o > int,J: int > $o,T5: set_o,G: int > code_integer,H3: $o > code_integer] :
% 0.33/0.63 ( ( finite_finite_int @ S7 )
% 0.33/0.63 => ( ( finite_finite_o @ T4 )
% 0.33/0.63 => ( ! [A3: int] :
% 0.33/0.63 ( ( member_int @ A3 @ ( minus_minus_set_int @ S2 @ S7 ) )
% 0.33/0.63 => ( ( I @ ( J @ A3 ) )
% 0.33/0.63 = A3 ) )
% 0.33/0.63 => ( ! [A3: int] :
% 0.33/0.63 ( ( member_int @ A3 @ ( minus_minus_set_int @ S2 @ S7 ) )
% 0.33/0.63 => ( member_o @ ( J @ A3 ) @ ( minus_minus_set_o @ T5 @ T4 ) ) )
% 0.33/0.63 => ( ! [B2: $o] :
% 0.33/0.63 ( ( member_o @ B2 @ ( minus_minus_set_o @ T5 @ T4 ) )
% 0.33/0.63 => ( ( J @ ( I @ B2 ) )
% 0.33/0.63 = B2 ) )
% 0.33/0.63 => ( ! [B2: $o] :
% 0.33/0.63 ( ( member_o @ B2 @ ( minus_minus_set_o @ T5 @ T4 ) )
% 0.33/0.63 => ( member_int @ ( I @ B2 ) @ ( minus_minus_set_int @ S2 @ S7 ) ) )
% 0.33/0.63 => ( ! [A3: int] :
% 0.33/0.63 ( ( member_int @ A3 @ S7 )
% 0.33/0.63 => ( ( G @ A3 )
% 0.33/0.63 = one_one_Code_integer ) )
% 0.33/0.63 => ( ! [B2: $o] :
% 0.33/0.63 ( ( member_o @ B2 @ T4 )
% 0.33/0.63 => ( ( H3 @ B2 )
% 0.33/0.63 = one_one_Code_integer ) )
% 0.33/0.63 => ( ! [A3: int] :
% 0.33/0.63 ( ( member_int @ A3 @ S2 )
% 0.33/0.63 => ( ( H3 @ ( J @ A3 ) )
% 0.33/0.63 = ( G @ A3 ) ) )
% 0.33/0.63 => ( ( groups3827104343326376752nteger @ G @ S2 )
% 0.33/0.63 = ( groups7694694392188491536nteger @ H3 @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.reindex_bij_witness_not_neutral
% 0.33/0.63 thf(fact_5826_prod_Oreindex__bij__witness__not__neutral,axiom,
% 0.33/0.63 ! [S7: set_int,T4: set_int,S2: set_int,I: int > int,J: int > int,T5: set_int,G: int > code_integer,H3: int > code_integer] :
% 0.33/0.63 ( ( finite_finite_int @ S7 )
% 0.33/0.63 => ( ( finite_finite_int @ T4 )
% 0.33/0.63 => ( ! [A3: int] :
% 0.33/0.63 ( ( member_int @ A3 @ ( minus_minus_set_int @ S2 @ S7 ) )
% 0.33/0.63 => ( ( I @ ( J @ A3 ) )
% 0.33/0.63 = A3 ) )
% 0.33/0.63 => ( ! [A3: int] :
% 0.33/0.63 ( ( member_int @ A3 @ ( minus_minus_set_int @ S2 @ S7 ) )
% 0.33/0.63 => ( member_int @ ( J @ A3 ) @ ( minus_minus_set_int @ T5 @ T4 ) ) )
% 0.33/0.63 => ( ! [B2: int] :
% 0.33/0.63 ( ( member_int @ B2 @ ( minus_minus_set_int @ T5 @ T4 ) )
% 0.33/0.63 => ( ( J @ ( I @ B2 ) )
% 0.33/0.63 = B2 ) )
% 0.33/0.63 => ( ! [B2: int] :
% 0.33/0.63 ( ( member_int @ B2 @ ( minus_minus_set_int @ T5 @ T4 ) )
% 0.33/0.63 => ( member_int @ ( I @ B2 ) @ ( minus_minus_set_int @ S2 @ S7 ) ) )
% 0.33/0.63 => ( ! [A3: int] :
% 0.33/0.63 ( ( member_int @ A3 @ S7 )
% 0.33/0.63 => ( ( G @ A3 )
% 0.33/0.63 = one_one_Code_integer ) )
% 0.33/0.63 => ( ! [B2: int] :
% 0.33/0.63 ( ( member_int @ B2 @ T4 )
% 0.33/0.63 => ( ( H3 @ B2 )
% 0.33/0.63 = one_one_Code_integer ) )
% 0.33/0.63 => ( ! [A3: int] :
% 0.33/0.63 ( ( member_int @ A3 @ S2 )
% 0.33/0.63 => ( ( H3 @ ( J @ A3 ) )
% 0.33/0.63 = ( G @ A3 ) ) )
% 0.33/0.63 => ( ( groups3827104343326376752nteger @ G @ S2 )
% 0.33/0.63 = ( groups3827104343326376752nteger @ H3 @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.reindex_bij_witness_not_neutral
% 0.33/0.63 thf(fact_5827_prod_Oreindex__bij__witness__not__neutral,axiom,
% 0.33/0.63 ! [S7: set_int,T4: set_Code_integer,S2: set_int,I: code_integer > int,J: int > code_integer,T5: set_Code_integer,G: int > code_integer,H3: code_integer > code_integer] :
% 0.33/0.63 ( ( finite_finite_int @ S7 )
% 0.33/0.63 => ( ( finite6017078050557962740nteger @ T4 )
% 0.33/0.63 => ( ! [A3: int] :
% 0.33/0.63 ( ( member_int @ A3 @ ( minus_minus_set_int @ S2 @ S7 ) )
% 0.33/0.63 => ( ( I @ ( J @ A3 ) )
% 0.33/0.63 = A3 ) )
% 0.33/0.63 => ( ! [A3: int] :
% 0.33/0.63 ( ( member_int @ A3 @ ( minus_minus_set_int @ S2 @ S7 ) )
% 0.33/0.63 => ( member_Code_integer @ ( J @ A3 ) @ ( minus_2355218937544613996nteger @ T5 @ T4 ) ) )
% 0.33/0.63 => ( ! [B2: code_integer] :
% 0.33/0.63 ( ( member_Code_integer @ B2 @ ( minus_2355218937544613996nteger @ T5 @ T4 ) )
% 0.33/0.63 => ( ( J @ ( I @ B2 ) )
% 0.33/0.63 = B2 ) )
% 0.33/0.63 => ( ! [B2: code_integer] :
% 0.33/0.63 ( ( member_Code_integer @ B2 @ ( minus_2355218937544613996nteger @ T5 @ T4 ) )
% 0.33/0.63 => ( member_int @ ( I @ B2 ) @ ( minus_minus_set_int @ S2 @ S7 ) ) )
% 0.33/0.63 => ( ! [A3: int] :
% 0.33/0.63 ( ( member_int @ A3 @ S7 )
% 0.33/0.63 => ( ( G @ A3 )
% 0.33/0.63 = one_one_Code_integer ) )
% 0.33/0.63 => ( ! [B2: code_integer] :
% 0.33/0.63 ( ( member_Code_integer @ B2 @ T4 )
% 0.33/0.63 => ( ( H3 @ B2 )
% 0.33/0.63 = one_one_Code_integer ) )
% 0.33/0.63 => ( ! [A3: int] :
% 0.33/0.63 ( ( member_int @ A3 @ S2 )
% 0.33/0.63 => ( ( H3 @ ( J @ A3 ) )
% 0.33/0.63 = ( G @ A3 ) ) )
% 0.33/0.63 => ( ( groups3827104343326376752nteger @ G @ S2 )
% 0.33/0.63 = ( groups3674199335183972705nteger @ H3 @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.reindex_bij_witness_not_neutral
% 0.33/0.63 thf(fact_5828_prod_Oreindex__bij__witness__not__neutral,axiom,
% 0.33/0.63 ! [S7: set_Code_integer,T4: set_o,S2: set_Code_integer,I: $o > code_integer,J: code_integer > $o,T5: set_o,G: code_integer > code_integer,H3: $o > code_integer] :
% 0.33/0.63 ( ( finite6017078050557962740nteger @ S7 )
% 0.33/0.63 => ( ( finite_finite_o @ T4 )
% 0.33/0.63 => ( ! [A3: code_integer] :
% 0.33/0.63 ( ( member_Code_integer @ A3 @ ( minus_2355218937544613996nteger @ S2 @ S7 ) )
% 0.33/0.63 => ( ( I @ ( J @ A3 ) )
% 0.33/0.63 = A3 ) )
% 0.33/0.63 => ( ! [A3: code_integer] :
% 0.33/0.63 ( ( member_Code_integer @ A3 @ ( minus_2355218937544613996nteger @ S2 @ S7 ) )
% 0.33/0.63 => ( member_o @ ( J @ A3 ) @ ( minus_minus_set_o @ T5 @ T4 ) ) )
% 0.33/0.63 => ( ! [B2: $o] :
% 0.33/0.63 ( ( member_o @ B2 @ ( minus_minus_set_o @ T5 @ T4 ) )
% 0.33/0.63 => ( ( J @ ( I @ B2 ) )
% 0.33/0.63 = B2 ) )
% 0.33/0.63 => ( ! [B2: $o] :
% 0.33/0.63 ( ( member_o @ B2 @ ( minus_minus_set_o @ T5 @ T4 ) )
% 0.33/0.63 => ( member_Code_integer @ ( I @ B2 ) @ ( minus_2355218937544613996nteger @ S2 @ S7 ) ) )
% 0.33/0.63 => ( ! [A3: code_integer] :
% 0.33/0.63 ( ( member_Code_integer @ A3 @ S7 )
% 0.33/0.63 => ( ( G @ A3 )
% 0.33/0.63 = one_one_Code_integer ) )
% 0.33/0.63 => ( ! [B2: $o] :
% 0.33/0.63 ( ( member_o @ B2 @ T4 )
% 0.33/0.63 => ( ( H3 @ B2 )
% 0.33/0.63 = one_one_Code_integer ) )
% 0.33/0.63 => ( ! [A3: code_integer] :
% 0.33/0.63 ( ( member_Code_integer @ A3 @ S2 )
% 0.33/0.63 => ( ( H3 @ ( J @ A3 ) )
% 0.33/0.63 = ( G @ A3 ) ) )
% 0.33/0.63 => ( ( groups3674199335183972705nteger @ G @ S2 )
% 0.33/0.63 = ( groups7694694392188491536nteger @ H3 @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.reindex_bij_witness_not_neutral
% 0.33/0.63 thf(fact_5829_prod_Oreindex__bij__witness__not__neutral,axiom,
% 0.33/0.63 ! [S7: set_Code_integer,T4: set_int,S2: set_Code_integer,I: int > code_integer,J: code_integer > int,T5: set_int,G: code_integer > code_integer,H3: int > code_integer] :
% 0.33/0.63 ( ( finite6017078050557962740nteger @ S7 )
% 0.33/0.63 => ( ( finite_finite_int @ T4 )
% 0.33/0.63 => ( ! [A3: code_integer] :
% 0.33/0.63 ( ( member_Code_integer @ A3 @ ( minus_2355218937544613996nteger @ S2 @ S7 ) )
% 0.33/0.63 => ( ( I @ ( J @ A3 ) )
% 0.33/0.63 = A3 ) )
% 0.33/0.63 => ( ! [A3: code_integer] :
% 0.33/0.63 ( ( member_Code_integer @ A3 @ ( minus_2355218937544613996nteger @ S2 @ S7 ) )
% 0.33/0.63 => ( member_int @ ( J @ A3 ) @ ( minus_minus_set_int @ T5 @ T4 ) ) )
% 0.33/0.63 => ( ! [B2: int] :
% 0.33/0.63 ( ( member_int @ B2 @ ( minus_minus_set_int @ T5 @ T4 ) )
% 0.33/0.63 => ( ( J @ ( I @ B2 ) )
% 0.33/0.63 = B2 ) )
% 0.33/0.63 => ( ! [B2: int] :
% 0.33/0.63 ( ( member_int @ B2 @ ( minus_minus_set_int @ T5 @ T4 ) )
% 0.33/0.63 => ( member_Code_integer @ ( I @ B2 ) @ ( minus_2355218937544613996nteger @ S2 @ S7 ) ) )
% 0.33/0.63 => ( ! [A3: code_integer] :
% 0.33/0.63 ( ( member_Code_integer @ A3 @ S7 )
% 0.33/0.63 => ( ( G @ A3 )
% 0.33/0.63 = one_one_Code_integer ) )
% 0.33/0.63 => ( ! [B2: int] :
% 0.33/0.63 ( ( member_int @ B2 @ T4 )
% 0.33/0.63 => ( ( H3 @ B2 )
% 0.33/0.63 = one_one_Code_integer ) )
% 0.33/0.63 => ( ! [A3: code_integer] :
% 0.33/0.63 ( ( member_Code_integer @ A3 @ S2 )
% 0.33/0.63 => ( ( H3 @ ( J @ A3 ) )
% 0.33/0.63 = ( G @ A3 ) ) )
% 0.33/0.63 => ( ( groups3674199335183972705nteger @ G @ S2 )
% 0.33/0.63 = ( groups3827104343326376752nteger @ H3 @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.reindex_bij_witness_not_neutral
% 0.33/0.63 thf(fact_5830_prod_Oreindex__bij__witness__not__neutral,axiom,
% 0.33/0.63 ! [S7: set_Code_integer,T4: set_Code_integer,S2: set_Code_integer,I: code_integer > code_integer,J: code_integer > code_integer,T5: set_Code_integer,G: code_integer > code_integer,H3: code_integer > code_integer] :
% 0.33/0.63 ( ( finite6017078050557962740nteger @ S7 )
% 0.33/0.63 => ( ( finite6017078050557962740nteger @ T4 )
% 0.33/0.63 => ( ! [A3: code_integer] :
% 0.33/0.63 ( ( member_Code_integer @ A3 @ ( minus_2355218937544613996nteger @ S2 @ S7 ) )
% 0.33/0.63 => ( ( I @ ( J @ A3 ) )
% 0.33/0.63 = A3 ) )
% 0.33/0.63 => ( ! [A3: code_integer] :
% 0.33/0.63 ( ( member_Code_integer @ A3 @ ( minus_2355218937544613996nteger @ S2 @ S7 ) )
% 0.33/0.63 => ( member_Code_integer @ ( J @ A3 ) @ ( minus_2355218937544613996nteger @ T5 @ T4 ) ) )
% 0.33/0.63 => ( ! [B2: code_integer] :
% 0.33/0.63 ( ( member_Code_integer @ B2 @ ( minus_2355218937544613996nteger @ T5 @ T4 ) )
% 0.33/0.63 => ( ( J @ ( I @ B2 ) )
% 0.33/0.63 = B2 ) )
% 0.33/0.63 => ( ! [B2: code_integer] :
% 0.33/0.63 ( ( member_Code_integer @ B2 @ ( minus_2355218937544613996nteger @ T5 @ T4 ) )
% 0.33/0.63 => ( member_Code_integer @ ( I @ B2 ) @ ( minus_2355218937544613996nteger @ S2 @ S7 ) ) )
% 0.33/0.63 => ( ! [A3: code_integer] :
% 0.33/0.63 ( ( member_Code_integer @ A3 @ S7 )
% 0.33/0.63 => ( ( G @ A3 )
% 0.33/0.63 = one_one_Code_integer ) )
% 0.33/0.63 => ( ! [B2: code_integer] :
% 0.33/0.63 ( ( member_Code_integer @ B2 @ T4 )
% 0.33/0.63 => ( ( H3 @ B2 )
% 0.33/0.63 = one_one_Code_integer ) )
% 0.33/0.63 => ( ! [A3: code_integer] :
% 0.33/0.63 ( ( member_Code_integer @ A3 @ S2 )
% 0.33/0.63 => ( ( H3 @ ( J @ A3 ) )
% 0.33/0.63 = ( G @ A3 ) ) )
% 0.33/0.63 => ( ( groups3674199335183972705nteger @ G @ S2 )
% 0.33/0.63 = ( groups3674199335183972705nteger @ H3 @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.reindex_bij_witness_not_neutral
% 0.33/0.63 thf(fact_5831_prod_Oreindex__bij__witness__not__neutral,axiom,
% 0.33/0.63 ! [S7: set_o,T4: set_o,S2: set_o,I: $o > $o,J: $o > $o,T5: set_o,G: $o > assn,H3: $o > assn] :
% 0.33/0.63 ( ( finite_finite_o @ S7 )
% 0.33/0.63 => ( ( finite_finite_o @ T4 )
% 0.33/0.63 => ( ! [A3: $o] :
% 0.33/0.63 ( ( member_o @ A3 @ ( minus_minus_set_o @ S2 @ S7 ) )
% 0.33/0.63 => ( ( I @ ( J @ A3 ) )
% 0.33/0.63 = A3 ) )
% 0.33/0.63 => ( ! [A3: $o] :
% 0.33/0.63 ( ( member_o @ A3 @ ( minus_minus_set_o @ S2 @ S7 ) )
% 0.33/0.63 => ( member_o @ ( J @ A3 ) @ ( minus_minus_set_o @ T5 @ T4 ) ) )
% 0.33/0.63 => ( ! [B2: $o] :
% 0.33/0.63 ( ( member_o @ B2 @ ( minus_minus_set_o @ T5 @ T4 ) )
% 0.33/0.63 => ( ( J @ ( I @ B2 ) )
% 0.33/0.63 = B2 ) )
% 0.33/0.63 => ( ! [B2: $o] :
% 0.33/0.63 ( ( member_o @ B2 @ ( minus_minus_set_o @ T5 @ T4 ) )
% 0.33/0.63 => ( member_o @ ( I @ B2 ) @ ( minus_minus_set_o @ S2 @ S7 ) ) )
% 0.33/0.63 => ( ! [A3: $o] :
% 0.33/0.63 ( ( member_o @ A3 @ S7 )
% 0.33/0.63 => ( ( G @ A3 )
% 0.33/0.63 = one_one_assn ) )
% 0.33/0.63 => ( ! [B2: $o] :
% 0.33/0.63 ( ( member_o @ B2 @ T4 )
% 0.33/0.63 => ( ( H3 @ B2 )
% 0.33/0.63 = one_one_assn ) )
% 0.33/0.63 => ( ! [A3: $o] :
% 0.33/0.63 ( ( member_o @ A3 @ S2 )
% 0.33/0.63 => ( ( H3 @ ( J @ A3 ) )
% 0.33/0.63 = ( G @ A3 ) ) )
% 0.33/0.63 => ( ( groups5301882518646026715o_assn @ G @ S2 )
% 0.33/0.63 = ( groups5301882518646026715o_assn @ H3 @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.reindex_bij_witness_not_neutral
% 0.33/0.63 thf(fact_5832_dflt__None__set__def,axiom,
% 0.33/0.63 ( dflt_N3208751546879591902at_nat
% 0.33/0.63 = ( ^ [S5: set_Pr4329608150637261639at_nat] : ( if_opt5121585740920863443at_nat @ ( S5 = bot_bo228742789529271731at_nat ) @ none_s6518873173954064040at_nat @ ( some_s5890477192898017836at_nat @ S5 ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % dflt_None_set_def
% 0.33/0.63 thf(fact_5833_dflt__None__set__def,axiom,
% 0.33/0.63 ( dflt_N6592383573632408824at_nat
% 0.33/0.63 = ( ^ [S5: set_Pr1261947904930325089at_nat] : ( if_opt7704869406773131885at_nat @ ( S5 = bot_bo2099793752762293965at_nat ) @ none_s625347054029921090at_nat @ ( some_s147305329494351046at_nat @ S5 ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % dflt_None_set_def
% 0.33/0.63 thf(fact_5834_dflt__None__set__def,axiom,
% 0.33/0.63 ( dflt_None_set_o
% 0.33/0.63 = ( ^ [S5: set_o] : ( if_option_set_o @ ( S5 = bot_bot_set_o ) @ none_set_o @ ( some_set_o @ S5 ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % dflt_None_set_def
% 0.33/0.63 thf(fact_5835_dflt__None__set__def,axiom,
% 0.33/0.63 ( dflt_None_set_nat
% 0.33/0.63 = ( ^ [S5: set_nat] : ( if_option_set_nat @ ( S5 = bot_bot_set_nat ) @ none_set_nat @ ( some_set_nat @ S5 ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % dflt_None_set_def
% 0.33/0.63 thf(fact_5836_dflt__None__set__def,axiom,
% 0.33/0.63 ( dflt_None_set_int
% 0.33/0.63 = ( ^ [S5: set_int] : ( if_option_set_int @ ( S5 = bot_bot_set_int ) @ none_set_int @ ( some_set_int @ S5 ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % dflt_None_set_def
% 0.33/0.63 thf(fact_5837_sum__eq__1__iff,axiom,
% 0.33/0.63 ! [A2: set_int,F: int > nat] :
% 0.33/0.63 ( ( finite_finite_int @ A2 )
% 0.33/0.63 => ( ( ( groups4541462559716669496nt_nat @ F @ A2 )
% 0.33/0.63 = one_one_nat )
% 0.33/0.63 = ( ? [X3: int] :
% 0.33/0.63 ( ( member_int @ X3 @ A2 )
% 0.33/0.63 & ( ( F @ X3 )
% 0.33/0.63 = one_one_nat )
% 0.33/0.63 & ! [Y3: int] :
% 0.33/0.63 ( ( member_int @ Y3 @ A2 )
% 0.33/0.63 => ( ( X3 != Y3 )
% 0.33/0.63 => ( ( F @ Y3 )
% 0.33/0.63 = zero_zero_nat ) ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % sum_eq_1_iff
% 0.33/0.63 thf(fact_5838_sum__eq__1__iff,axiom,
% 0.33/0.63 ! [A2: set_Code_integer,F: code_integer > nat] :
% 0.33/0.63 ( ( finite6017078050557962740nteger @ A2 )
% 0.33/0.63 => ( ( ( groups7237345082560585321er_nat @ F @ A2 )
% 0.33/0.63 = one_one_nat )
% 0.33/0.63 = ( ? [X3: code_integer] :
% 0.33/0.63 ( ( member_Code_integer @ X3 @ A2 )
% 0.33/0.63 & ( ( F @ X3 )
% 0.33/0.63 = one_one_nat )
% 0.33/0.63 & ! [Y3: code_integer] :
% 0.33/0.63 ( ( member_Code_integer @ Y3 @ A2 )
% 0.33/0.63 => ( ( X3 != Y3 )
% 0.33/0.63 => ( ( F @ Y3 )
% 0.33/0.63 = zero_zero_nat ) ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % sum_eq_1_iff
% 0.33/0.63 thf(fact_5839_sum__eq__1__iff,axiom,
% 0.33/0.63 ! [A2: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > nat] :
% 0.33/0.63 ( ( finite6177210948735845034at_nat @ A2 )
% 0.33/0.63 => ( ( ( groups977919841031483927at_nat @ F @ A2 )
% 0.33/0.63 = one_one_nat )
% 0.33/0.63 = ( ? [X3: product_prod_nat_nat] :
% 0.33/0.63 ( ( member8440522571783428010at_nat @ X3 @ A2 )
% 0.33/0.63 & ( ( F @ X3 )
% 0.33/0.63 = one_one_nat )
% 0.33/0.63 & ! [Y3: product_prod_nat_nat] :
% 0.33/0.63 ( ( member8440522571783428010at_nat @ Y3 @ A2 )
% 0.33/0.63 => ( ( X3 != Y3 )
% 0.33/0.63 => ( ( F @ Y3 )
% 0.33/0.63 = zero_zero_nat ) ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % sum_eq_1_iff
% 0.33/0.63 thf(fact_5840_sum__eq__1__iff,axiom,
% 0.33/0.63 ! [A2: set_nat,F: nat > nat] :
% 0.33/0.63 ( ( finite_finite_nat @ A2 )
% 0.33/0.63 => ( ( ( groups3542108847815614940at_nat @ F @ A2 )
% 0.33/0.63 = one_one_nat )
% 0.33/0.63 = ( ? [X3: nat] :
% 0.33/0.63 ( ( member_nat @ X3 @ A2 )
% 0.33/0.63 & ( ( F @ X3 )
% 0.33/0.63 = one_one_nat )
% 0.33/0.63 & ! [Y3: nat] :
% 0.33/0.63 ( ( member_nat @ Y3 @ A2 )
% 0.33/0.63 => ( ( X3 != Y3 )
% 0.33/0.63 => ( ( F @ Y3 )
% 0.33/0.63 = zero_zero_nat ) ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % sum_eq_1_iff
% 0.33/0.63 thf(fact_5841_surj__Compl__image__subset,axiom,
% 0.33/0.63 ! [F: nat > code_integer,A2: set_nat] :
% 0.33/0.63 ( ( ( image_1215581382706833972nteger @ F @ top_top_set_nat )
% 0.33/0.63 = top_to4645266643341252675nteger )
% 0.33/0.63 => ( ord_le7084787975880047091nteger @ ( uminus804700908173204444nteger @ ( image_1215581382706833972nteger @ F @ A2 ) ) @ ( image_1215581382706833972nteger @ F @ ( uminus5710092332889474511et_nat @ A2 ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % surj_Compl_image_subset
% 0.33/0.63 thf(fact_5842_surj__Compl__image__subset,axiom,
% 0.33/0.63 ! [F: nat > product_unit,A2: set_nat] :
% 0.33/0.63 ( ( ( image_8730104196221521654t_unit @ F @ top_top_set_nat )
% 0.33/0.63 = top_to1996260823553986621t_unit )
% 0.33/0.63 => ( ord_le3507040750410214029t_unit @ ( uminus5944136376168626660t_unit @ ( image_8730104196221521654t_unit @ F @ A2 ) ) @ ( image_8730104196221521654t_unit @ F @ ( uminus5710092332889474511et_nat @ A2 ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % surj_Compl_image_subset
% 0.33/0.63 thf(fact_5843_surj__Compl__image__subset,axiom,
% 0.33/0.63 ! [F: nat > int,A2: set_nat] :
% 0.33/0.63 ( ( ( image_nat_int @ F @ top_top_set_nat )
% 0.33/0.63 = top_top_set_int )
% 0.33/0.63 => ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ ( image_nat_int @ F @ A2 ) ) @ ( image_nat_int @ F @ ( uminus5710092332889474511et_nat @ A2 ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % surj_Compl_image_subset
% 0.33/0.63 thf(fact_5844_surj__Compl__image__subset,axiom,
% 0.33/0.63 ! [F: product_unit > product_unit,A2: set_Product_unit] :
% 0.33/0.63 ( ( ( image_405062704495631173t_unit @ F @ top_to1996260823553986621t_unit )
% 0.33/0.63 = top_to1996260823553986621t_unit )
% 0.33/0.63 => ( ord_le3507040750410214029t_unit @ ( uminus5944136376168626660t_unit @ ( image_405062704495631173t_unit @ F @ A2 ) ) @ ( image_405062704495631173t_unit @ F @ ( uminus5944136376168626660t_unit @ A2 ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % surj_Compl_image_subset
% 0.33/0.63 thf(fact_5845_surj__Compl__image__subset,axiom,
% 0.33/0.63 ! [F: product_unit > int,A2: set_Product_unit] :
% 0.33/0.63 ( ( ( image_873079544045703924it_int @ F @ top_to1996260823553986621t_unit )
% 0.33/0.63 = top_top_set_int )
% 0.33/0.63 => ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ ( image_873079544045703924it_int @ F @ A2 ) ) @ ( image_873079544045703924it_int @ F @ ( uminus5944136376168626660t_unit @ A2 ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % surj_Compl_image_subset
% 0.33/0.63 thf(fact_5846_surj__Compl__image__subset,axiom,
% 0.33/0.63 ! [F: int > product_unit,A2: set_int] :
% 0.33/0.63 ( ( ( image_5846526143423701914t_unit @ F @ top_top_set_int )
% 0.33/0.63 = top_to1996260823553986621t_unit )
% 0.33/0.63 => ( ord_le3507040750410214029t_unit @ ( uminus5944136376168626660t_unit @ ( image_5846526143423701914t_unit @ F @ A2 ) ) @ ( image_5846526143423701914t_unit @ F @ ( uminus1532241313380277803et_int @ A2 ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % surj_Compl_image_subset
% 0.33/0.63 thf(fact_5847_surj__Compl__image__subset,axiom,
% 0.33/0.63 ! [F: int > int,A2: set_int] :
% 0.33/0.63 ( ( ( image_int_int @ F @ top_top_set_int )
% 0.33/0.63 = top_top_set_int )
% 0.33/0.63 => ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ ( image_int_int @ F @ A2 ) ) @ ( image_int_int @ F @ ( uminus1532241313380277803et_int @ A2 ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % surj_Compl_image_subset
% 0.33/0.63 thf(fact_5848_surj__Compl__image__subset,axiom,
% 0.33/0.63 ! [F: nat > nat,A2: set_nat] :
% 0.33/0.63 ( ( ( image_nat_nat @ F @ top_top_set_nat )
% 0.33/0.63 = top_top_set_nat )
% 0.33/0.63 => ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ ( image_nat_nat @ F @ A2 ) ) @ ( image_nat_nat @ F @ ( uminus5710092332889474511et_nat @ A2 ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % surj_Compl_image_subset
% 0.33/0.63 thf(fact_5849_surj__Compl__image__subset,axiom,
% 0.33/0.63 ! [F: product_unit > nat,A2: set_Product_unit] :
% 0.33/0.63 ( ( ( image_875570014554754200it_nat @ F @ top_to1996260823553986621t_unit )
% 0.33/0.63 = top_top_set_nat )
% 0.33/0.63 => ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ ( image_875570014554754200it_nat @ F @ A2 ) ) @ ( image_875570014554754200it_nat @ F @ ( uminus5944136376168626660t_unit @ A2 ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % surj_Compl_image_subset
% 0.33/0.63 thf(fact_5850_surj__Compl__image__subset,axiom,
% 0.33/0.63 ! [F: int > nat,A2: set_int] :
% 0.33/0.63 ( ( ( image_int_nat @ F @ top_top_set_int )
% 0.33/0.63 = top_top_set_nat )
% 0.33/0.63 => ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ ( image_int_nat @ F @ A2 ) ) @ ( image_int_nat @ F @ ( uminus1532241313380277803et_int @ A2 ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % surj_Compl_image_subset
% 0.33/0.63 thf(fact_5851_card__atLeastZeroLessThan__int,axiom,
% 0.33/0.63 ! [U: int] :
% 0.33/0.63 ( ( finite_card_int @ ( set_or4662586982721622107an_int @ zero_zero_int @ U ) )
% 0.33/0.63 = ( nat2 @ U ) ) ).
% 0.33/0.63
% 0.33/0.63 % card_atLeastZeroLessThan_int
% 0.33/0.63 thf(fact_5852_atMost__nat__numeral,axiom,
% 0.33/0.63 ! [K: num] :
% 0.33/0.63 ( ( set_ord_atMost_nat @ ( numeral_numeral_nat @ K ) )
% 0.33/0.63 = ( insert_nat @ ( numeral_numeral_nat @ K ) @ ( set_ord_atMost_nat @ ( pred_numeral @ K ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % atMost_nat_numeral
% 0.33/0.63 thf(fact_5853_lessThan__nat__numeral,axiom,
% 0.33/0.63 ! [K: num] :
% 0.33/0.63 ( ( set_ord_lessThan_nat @ ( numeral_numeral_nat @ K ) )
% 0.33/0.63 = ( insert_nat @ ( pred_numeral @ K ) @ ( set_ord_lessThan_nat @ ( pred_numeral @ K ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % lessThan_nat_numeral
% 0.33/0.63 thf(fact_5854_sum__Suc,axiom,
% 0.33/0.63 ! [F: int > nat,A2: set_int] :
% 0.33/0.63 ( ( groups4541462559716669496nt_nat
% 0.33/0.63 @ ^ [X3: int] : ( suc @ ( F @ X3 ) )
% 0.33/0.63 @ A2 )
% 0.33/0.63 = ( plus_plus_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ ( finite_card_int @ A2 ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % sum_Suc
% 0.33/0.63 thf(fact_5855_sum__Suc,axiom,
% 0.33/0.63 ! [F: product_unit > nat,A2: set_Product_unit] :
% 0.33/0.63 ( ( groups8766797177574957219it_nat
% 0.33/0.63 @ ^ [X3: product_unit] : ( suc @ ( F @ X3 ) )
% 0.33/0.63 @ A2 )
% 0.33/0.63 = ( plus_plus_nat @ ( groups8766797177574957219it_nat @ F @ A2 ) @ ( finite410649719033368117t_unit @ A2 ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % sum_Suc
% 0.33/0.63 thf(fact_5856_sum__Suc,axiom,
% 0.33/0.63 ! [F: list_nat > nat,A2: set_list_nat] :
% 0.33/0.63 ( ( groups4396056296759096172at_nat
% 0.33/0.63 @ ^ [X3: list_nat] : ( suc @ ( F @ X3 ) )
% 0.33/0.63 @ A2 )
% 0.33/0.63 = ( plus_plus_nat @ ( groups4396056296759096172at_nat @ F @ A2 ) @ ( finite_card_list_nat @ A2 ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % sum_Suc
% 0.33/0.63 thf(fact_5857_sum__Suc,axiom,
% 0.33/0.63 ! [F: nat > nat,A2: set_nat] :
% 0.33/0.63 ( ( groups3542108847815614940at_nat
% 0.33/0.63 @ ^ [X3: nat] : ( suc @ ( F @ X3 ) )
% 0.33/0.63 @ A2 )
% 0.33/0.63 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ ( finite_card_nat @ A2 ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % sum_Suc
% 0.33/0.63 thf(fact_5858_prod_Osetdiff__irrelevant,axiom,
% 0.33/0.63 ! [A2: set_int,G: int > code_integer] :
% 0.33/0.63 ( ( finite_finite_int @ A2 )
% 0.33/0.63 => ( ( groups3827104343326376752nteger @ G
% 0.33/0.63 @ ( minus_minus_set_int @ A2
% 0.33/0.63 @ ( collect_int
% 0.33/0.63 @ ^ [X3: int] :
% 0.33/0.63 ( ( G @ X3 )
% 0.33/0.63 = one_one_Code_integer ) ) ) )
% 0.33/0.63 = ( groups3827104343326376752nteger @ G @ A2 ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.setdiff_irrelevant
% 0.33/0.63 thf(fact_5859_prod_Osetdiff__irrelevant,axiom,
% 0.33/0.63 ! [A2: set_Code_integer,G: code_integer > code_integer] :
% 0.33/0.63 ( ( finite6017078050557962740nteger @ A2 )
% 0.33/0.63 => ( ( groups3674199335183972705nteger @ G
% 0.33/0.63 @ ( minus_2355218937544613996nteger @ A2
% 0.33/0.63 @ ( collect_Code_integer
% 0.33/0.63 @ ^ [X3: code_integer] :
% 0.33/0.63 ( ( G @ X3 )
% 0.33/0.63 = one_one_Code_integer ) ) ) )
% 0.33/0.63 = ( groups3674199335183972705nteger @ G @ A2 ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.setdiff_irrelevant
% 0.33/0.63 thf(fact_5860_prod_Osetdiff__irrelevant,axiom,
% 0.33/0.63 ! [A2: set_int,G: int > assn] :
% 0.33/0.63 ( ( finite_finite_int @ A2 )
% 0.33/0.63 => ( ( groups7882442080178216443t_assn @ G
% 0.33/0.63 @ ( minus_minus_set_int @ A2
% 0.33/0.63 @ ( collect_int
% 0.33/0.63 @ ^ [X3: int] :
% 0.33/0.63 ( ( G @ X3 )
% 0.33/0.63 = one_one_assn ) ) ) )
% 0.33/0.63 = ( groups7882442080178216443t_assn @ G @ A2 ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.setdiff_irrelevant
% 0.33/0.63 thf(fact_5861_prod_Osetdiff__irrelevant,axiom,
% 0.33/0.63 ! [A2: set_Code_integer,G: code_integer > assn] :
% 0.33/0.63 ( ( finite6017078050557962740nteger @ A2 )
% 0.33/0.63 => ( ( groups1304777262505850412r_assn @ G
% 0.33/0.63 @ ( minus_2355218937544613996nteger @ A2
% 0.33/0.63 @ ( collect_Code_integer
% 0.33/0.63 @ ^ [X3: code_integer] :
% 0.33/0.63 ( ( G @ X3 )
% 0.33/0.63 = one_one_assn ) ) ) )
% 0.33/0.63 = ( groups1304777262505850412r_assn @ G @ A2 ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.setdiff_irrelevant
% 0.33/0.63 thf(fact_5862_prod_Osetdiff__irrelevant,axiom,
% 0.33/0.63 ! [A2: set_int,G: int > rat] :
% 0.33/0.63 ( ( finite_finite_int @ A2 )
% 0.33/0.63 => ( ( groups1072433553688619179nt_rat @ G
% 0.33/0.63 @ ( minus_minus_set_int @ A2
% 0.33/0.63 @ ( collect_int
% 0.33/0.63 @ ^ [X3: int] :
% 0.33/0.63 ( ( G @ X3 )
% 0.33/0.63 = one_one_rat ) ) ) )
% 0.33/0.63 = ( groups1072433553688619179nt_rat @ G @ A2 ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.setdiff_irrelevant
% 0.33/0.63 thf(fact_5863_prod_Osetdiff__irrelevant,axiom,
% 0.33/0.63 ! [A2: set_Code_integer,G: code_integer > rat] :
% 0.33/0.63 ( ( finite6017078050557962740nteger @ A2 )
% 0.33/0.63 => ( ( groups2555765274223993564er_rat @ G
% 0.33/0.63 @ ( minus_2355218937544613996nteger @ A2
% 0.33/0.63 @ ( collect_Code_integer
% 0.33/0.63 @ ^ [X3: code_integer] :
% 0.33/0.63 ( ( G @ X3 )
% 0.33/0.63 = one_one_rat ) ) ) )
% 0.33/0.63 = ( groups2555765274223993564er_rat @ G @ A2 ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.setdiff_irrelevant
% 0.33/0.63 thf(fact_5864_prod_Osetdiff__irrelevant,axiom,
% 0.33/0.63 ! [A2: set_int,G: int > nat] :
% 0.33/0.63 ( ( finite_finite_int @ A2 )
% 0.33/0.63 => ( ( groups1707563613775114915nt_nat @ G
% 0.33/0.63 @ ( minus_minus_set_int @ A2
% 0.33/0.63 @ ( collect_int
% 0.33/0.63 @ ^ [X3: int] :
% 0.33/0.63 ( ( G @ X3 )
% 0.33/0.63 = one_one_nat ) ) ) )
% 0.33/0.63 = ( groups1707563613775114915nt_nat @ G @ A2 ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.setdiff_irrelevant
% 0.33/0.63 thf(fact_5865_prod_Osetdiff__irrelevant,axiom,
% 0.33/0.63 ! [A2: set_Code_integer,G: code_integer > nat] :
% 0.33/0.63 ( ( finite6017078050557962740nteger @ A2 )
% 0.33/0.63 => ( ( groups3190895334310489300er_nat @ G
% 0.33/0.63 @ ( minus_2355218937544613996nteger @ A2
% 0.33/0.63 @ ( collect_Code_integer
% 0.33/0.63 @ ^ [X3: code_integer] :
% 0.33/0.63 ( ( G @ X3 )
% 0.33/0.63 = one_one_nat ) ) ) )
% 0.33/0.63 = ( groups3190895334310489300er_nat @ G @ A2 ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.setdiff_irrelevant
% 0.33/0.63 thf(fact_5866_prod_Osetdiff__irrelevant,axiom,
% 0.33/0.63 ! [A2: set_Code_integer,G: code_integer > int] :
% 0.33/0.63 ( ( finite6017078050557962740nteger @ A2 )
% 0.33/0.63 => ( ( groups3188404863801439024er_int @ G
% 0.33/0.63 @ ( minus_2355218937544613996nteger @ A2
% 0.33/0.63 @ ( collect_Code_integer
% 0.33/0.63 @ ^ [X3: code_integer] :
% 0.33/0.63 ( ( G @ X3 )
% 0.33/0.63 = one_one_int ) ) ) )
% 0.33/0.63 = ( groups3188404863801439024er_int @ G @ A2 ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.setdiff_irrelevant
% 0.33/0.63 thf(fact_5867_prod_Osetdiff__irrelevant,axiom,
% 0.33/0.63 ! [A2: set_nat,G: nat > code_integer] :
% 0.33/0.63 ( ( finite_finite_nat @ A2 )
% 0.33/0.63 => ( ( groups3455450783089532116nteger @ G
% 0.33/0.63 @ ( minus_minus_set_nat @ A2
% 0.33/0.63 @ ( collect_nat
% 0.33/0.63 @ ^ [X3: nat] :
% 0.33/0.63 ( ( G @ X3 )
% 0.33/0.63 = one_one_Code_integer ) ) ) )
% 0.33/0.63 = ( groups3455450783089532116nteger @ G @ A2 ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.setdiff_irrelevant
% 0.33/0.63 thf(fact_5868_notin__range__Some,axiom,
% 0.33/0.63 ! [X: option3216581401566546698it_nat] :
% 0.33/0.63 ( ( ~ ( member3517700364412436275it_nat @ X @ ( image_4799632500972785611it_nat @ some_P6105628898608307625it_nat @ top_to3995162779041354868it_nat ) ) )
% 0.33/0.63 = ( X = none_P2587165478634041381it_nat ) ) ).
% 0.33/0.63
% 0.33/0.63 % notin_range_Some
% 0.33/0.63 thf(fact_5869_notin__range__Some,axiom,
% 0.33/0.63 ! [X: option_num] :
% 0.33/0.63 ( ( ~ ( member_option_num @ X @ ( image_num_option_num @ some_num @ top_top_set_num ) ) )
% 0.33/0.63 = ( X = none_num ) ) ).
% 0.33/0.63
% 0.33/0.63 % notin_range_Some
% 0.33/0.63 thf(fact_5870_notin__range__Some,axiom,
% 0.33/0.63 ! [X: option8956607266484857688it_nat] :
% 0.33/0.63 ( ( ~ ( member5596548051065438575it_nat @ X @ ( image_3455408117458022631it_nat @ some_P1914260805536162275it_nat @ top_to4082048134677576814it_nat ) ) )
% 0.33/0.63 = ( X = none_P9117596204409417319it_nat ) ) ).
% 0.33/0.63
% 0.33/0.63 % notin_range_Some
% 0.33/0.63 thf(fact_5871_notin__range__Some,axiom,
% 0.33/0.63 ! [X: option_nat] :
% 0.33/0.63 ( ( ~ ( member_option_nat @ X @ ( image_nat_option_nat @ some_nat @ top_top_set_nat ) ) )
% 0.33/0.63 = ( X = none_nat ) ) ).
% 0.33/0.63
% 0.33/0.63 % notin_range_Some
% 0.33/0.63 thf(fact_5872_notin__range__Some,axiom,
% 0.33/0.63 ! [X: option_Product_unit] :
% 0.33/0.63 ( ( ~ ( member1378114217278917244t_unit @ X @ ( image_7094380055901048587t_unit @ some_Product_unit @ top_to1996260823553986621t_unit ) ) )
% 0.33/0.63 = ( X = none_Product_unit ) ) ).
% 0.33/0.63
% 0.33/0.63 % notin_range_Some
% 0.33/0.63 thf(fact_5873_notin__range__Some,axiom,
% 0.33/0.63 ! [X: option_int] :
% 0.33/0.63 ( ( ~ ( member_option_int @ X @ ( image_int_option_int @ some_int @ top_top_set_int ) ) )
% 0.33/0.63 = ( X = none_int ) ) ).
% 0.33/0.63
% 0.33/0.63 % notin_range_Some
% 0.33/0.63 thf(fact_5874_less__1__prod2,axiom,
% 0.33/0.63 ! [I4: set_o,I: $o,F: $o > code_integer] :
% 0.33/0.63 ( ( finite_finite_o @ I4 )
% 0.33/0.63 => ( ( member_o @ I @ I4 )
% 0.33/0.63 => ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( F @ I ) )
% 0.33/0.63 => ( ! [I2: $o] :
% 0.33/0.63 ( ( member_o @ I2 @ I4 )
% 0.33/0.63 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F @ I2 ) ) )
% 0.33/0.63 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( groups7694694392188491536nteger @ F @ I4 ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % less_1_prod2
% 0.33/0.63 thf(fact_5875_less__1__prod2,axiom,
% 0.33/0.63 ! [I4: set_nat,I: nat,F: nat > code_integer] :
% 0.33/0.63 ( ( finite_finite_nat @ I4 )
% 0.33/0.63 => ( ( member_nat @ I @ I4 )
% 0.33/0.63 => ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( F @ I ) )
% 0.33/0.63 => ( ! [I2: nat] :
% 0.33/0.63 ( ( member_nat @ I2 @ I4 )
% 0.33/0.63 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F @ I2 ) ) )
% 0.33/0.63 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( groups3455450783089532116nteger @ F @ I4 ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % less_1_prod2
% 0.33/0.63 thf(fact_5876_less__1__prod2,axiom,
% 0.33/0.63 ! [I4: set_int,I: int,F: int > code_integer] :
% 0.33/0.63 ( ( finite_finite_int @ I4 )
% 0.33/0.63 => ( ( member_int @ I @ I4 )
% 0.33/0.63 => ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( F @ I ) )
% 0.33/0.63 => ( ! [I2: int] :
% 0.33/0.63 ( ( member_int @ I2 @ I4 )
% 0.33/0.63 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F @ I2 ) ) )
% 0.33/0.63 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( groups3827104343326376752nteger @ F @ I4 ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % less_1_prod2
% 0.33/0.63 thf(fact_5877_less__1__prod2,axiom,
% 0.33/0.63 ! [I4: set_Code_integer,I: code_integer,F: code_integer > code_integer] :
% 0.33/0.63 ( ( finite6017078050557962740nteger @ I4 )
% 0.33/0.63 => ( ( member_Code_integer @ I @ I4 )
% 0.33/0.63 => ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( F @ I ) )
% 0.33/0.63 => ( ! [I2: code_integer] :
% 0.33/0.63 ( ( member_Code_integer @ I2 @ I4 )
% 0.33/0.63 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F @ I2 ) ) )
% 0.33/0.63 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( groups3674199335183972705nteger @ F @ I4 ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % less_1_prod2
% 0.33/0.63 thf(fact_5878_less__1__prod2,axiom,
% 0.33/0.63 ! [I4: set_o,I: $o,F: $o > rat] :
% 0.33/0.63 ( ( finite_finite_o @ I4 )
% 0.33/0.63 => ( ( member_o @ I @ I4 )
% 0.33/0.63 => ( ( ord_less_rat @ one_one_rat @ ( F @ I ) )
% 0.33/0.63 => ( ! [I2: $o] :
% 0.33/0.63 ( ( member_o @ I2 @ I4 )
% 0.33/0.63 => ( ord_less_eq_rat @ one_one_rat @ ( F @ I2 ) ) )
% 0.33/0.63 => ( ord_less_rat @ one_one_rat @ ( groups2869687844427037835_o_rat @ F @ I4 ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % less_1_prod2
% 0.33/0.63 thf(fact_5879_less__1__prod2,axiom,
% 0.33/0.63 ! [I4: set_nat,I: nat,F: nat > rat] :
% 0.33/0.63 ( ( finite_finite_nat @ I4 )
% 0.33/0.63 => ( ( member_nat @ I @ I4 )
% 0.33/0.63 => ( ( ord_less_rat @ one_one_rat @ ( F @ I ) )
% 0.33/0.63 => ( ! [I2: nat] :
% 0.33/0.63 ( ( member_nat @ I2 @ I4 )
% 0.33/0.63 => ( ord_less_eq_rat @ one_one_rat @ ( F @ I2 ) ) )
% 0.33/0.63 => ( ord_less_rat @ one_one_rat @ ( groups73079841787564623at_rat @ F @ I4 ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % less_1_prod2
% 0.33/0.63 thf(fact_5880_less__1__prod2,axiom,
% 0.33/0.63 ! [I4: set_int,I: int,F: int > rat] :
% 0.33/0.63 ( ( finite_finite_int @ I4 )
% 0.33/0.63 => ( ( member_int @ I @ I4 )
% 0.33/0.63 => ( ( ord_less_rat @ one_one_rat @ ( F @ I ) )
% 0.33/0.63 => ( ! [I2: int] :
% 0.33/0.63 ( ( member_int @ I2 @ I4 )
% 0.33/0.63 => ( ord_less_eq_rat @ one_one_rat @ ( F @ I2 ) ) )
% 0.33/0.63 => ( ord_less_rat @ one_one_rat @ ( groups1072433553688619179nt_rat @ F @ I4 ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % less_1_prod2
% 0.33/0.63 thf(fact_5881_less__1__prod2,axiom,
% 0.33/0.63 ! [I4: set_Code_integer,I: code_integer,F: code_integer > rat] :
% 0.33/0.63 ( ( finite6017078050557962740nteger @ I4 )
% 0.33/0.63 => ( ( member_Code_integer @ I @ I4 )
% 0.33/0.63 => ( ( ord_less_rat @ one_one_rat @ ( F @ I ) )
% 0.33/0.63 => ( ! [I2: code_integer] :
% 0.33/0.63 ( ( member_Code_integer @ I2 @ I4 )
% 0.33/0.63 => ( ord_less_eq_rat @ one_one_rat @ ( F @ I2 ) ) )
% 0.33/0.63 => ( ord_less_rat @ one_one_rat @ ( groups2555765274223993564er_rat @ F @ I4 ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % less_1_prod2
% 0.33/0.63 thf(fact_5882_less__1__prod2,axiom,
% 0.33/0.63 ! [I4: set_o,I: $o,F: $o > int] :
% 0.33/0.63 ( ( finite_finite_o @ I4 )
% 0.33/0.63 => ( ( member_o @ I @ I4 )
% 0.33/0.63 => ( ( ord_less_int @ one_one_int @ ( F @ I ) )
% 0.33/0.63 => ( ! [I2: $o] :
% 0.33/0.63 ( ( member_o @ I2 @ I4 )
% 0.33/0.63 => ( ord_less_eq_int @ one_one_int @ ( F @ I2 ) ) )
% 0.33/0.63 => ( ord_less_int @ one_one_int @ ( groups3502327434004483295_o_int @ F @ I4 ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % less_1_prod2
% 0.33/0.63 thf(fact_5883_less__1__prod2,axiom,
% 0.33/0.63 ! [I4: set_Code_integer,I: code_integer,F: code_integer > int] :
% 0.33/0.63 ( ( finite6017078050557962740nteger @ I4 )
% 0.33/0.63 => ( ( member_Code_integer @ I @ I4 )
% 0.33/0.63 => ( ( ord_less_int @ one_one_int @ ( F @ I ) )
% 0.33/0.63 => ( ! [I2: code_integer] :
% 0.33/0.63 ( ( member_Code_integer @ I2 @ I4 )
% 0.33/0.63 => ( ord_less_eq_int @ one_one_int @ ( F @ I2 ) ) )
% 0.33/0.63 => ( ord_less_int @ one_one_int @ ( groups3188404863801439024er_int @ F @ I4 ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % less_1_prod2
% 0.33/0.63 thf(fact_5884_less__1__prod,axiom,
% 0.33/0.63 ! [I4: set_Code_integer,F: code_integer > code_integer] :
% 0.33/0.63 ( ( finite6017078050557962740nteger @ I4 )
% 0.33/0.63 => ( ( I4 != bot_bo3990330152332043303nteger )
% 0.33/0.63 => ( ! [I2: code_integer] :
% 0.33/0.63 ( ( member_Code_integer @ I2 @ I4 )
% 0.33/0.63 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( F @ I2 ) ) )
% 0.33/0.63 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( groups3674199335183972705nteger @ F @ I4 ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % less_1_prod
% 0.33/0.63 thf(fact_5885_less__1__prod,axiom,
% 0.33/0.63 ! [I4: set_o,F: $o > code_integer] :
% 0.33/0.63 ( ( finite_finite_o @ I4 )
% 0.33/0.63 => ( ( I4 != bot_bot_set_o )
% 0.33/0.63 => ( ! [I2: $o] :
% 0.33/0.63 ( ( member_o @ I2 @ I4 )
% 0.33/0.63 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( F @ I2 ) ) )
% 0.33/0.63 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( groups7694694392188491536nteger @ F @ I4 ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % less_1_prod
% 0.33/0.63 thf(fact_5886_less__1__prod,axiom,
% 0.33/0.63 ! [I4: set_nat,F: nat > code_integer] :
% 0.33/0.63 ( ( finite_finite_nat @ I4 )
% 0.33/0.63 => ( ( I4 != bot_bot_set_nat )
% 0.33/0.63 => ( ! [I2: nat] :
% 0.33/0.63 ( ( member_nat @ I2 @ I4 )
% 0.33/0.63 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( F @ I2 ) ) )
% 0.33/0.63 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( groups3455450783089532116nteger @ F @ I4 ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % less_1_prod
% 0.33/0.63 thf(fact_5887_less__1__prod,axiom,
% 0.33/0.63 ! [I4: set_int,F: int > code_integer] :
% 0.33/0.63 ( ( finite_finite_int @ I4 )
% 0.33/0.63 => ( ( I4 != bot_bot_set_int )
% 0.33/0.63 => ( ! [I2: int] :
% 0.33/0.63 ( ( member_int @ I2 @ I4 )
% 0.33/0.63 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( F @ I2 ) ) )
% 0.33/0.63 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( groups3827104343326376752nteger @ F @ I4 ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % less_1_prod
% 0.33/0.63 thf(fact_5888_less__1__prod,axiom,
% 0.33/0.63 ! [I4: set_Code_integer,F: code_integer > rat] :
% 0.33/0.63 ( ( finite6017078050557962740nteger @ I4 )
% 0.33/0.63 => ( ( I4 != bot_bo3990330152332043303nteger )
% 0.33/0.63 => ( ! [I2: code_integer] :
% 0.33/0.63 ( ( member_Code_integer @ I2 @ I4 )
% 0.33/0.63 => ( ord_less_rat @ one_one_rat @ ( F @ I2 ) ) )
% 0.33/0.63 => ( ord_less_rat @ one_one_rat @ ( groups2555765274223993564er_rat @ F @ I4 ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % less_1_prod
% 0.33/0.63 thf(fact_5889_less__1__prod,axiom,
% 0.33/0.63 ! [I4: set_o,F: $o > rat] :
% 0.33/0.63 ( ( finite_finite_o @ I4 )
% 0.33/0.63 => ( ( I4 != bot_bot_set_o )
% 0.33/0.63 => ( ! [I2: $o] :
% 0.33/0.63 ( ( member_o @ I2 @ I4 )
% 0.33/0.63 => ( ord_less_rat @ one_one_rat @ ( F @ I2 ) ) )
% 0.33/0.63 => ( ord_less_rat @ one_one_rat @ ( groups2869687844427037835_o_rat @ F @ I4 ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % less_1_prod
% 0.33/0.63 thf(fact_5890_less__1__prod,axiom,
% 0.33/0.63 ! [I4: set_nat,F: nat > rat] :
% 0.33/0.63 ( ( finite_finite_nat @ I4 )
% 0.33/0.63 => ( ( I4 != bot_bot_set_nat )
% 0.33/0.63 => ( ! [I2: nat] :
% 0.33/0.63 ( ( member_nat @ I2 @ I4 )
% 0.33/0.63 => ( ord_less_rat @ one_one_rat @ ( F @ I2 ) ) )
% 0.33/0.63 => ( ord_less_rat @ one_one_rat @ ( groups73079841787564623at_rat @ F @ I4 ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % less_1_prod
% 0.33/0.63 thf(fact_5891_less__1__prod,axiom,
% 0.33/0.63 ! [I4: set_int,F: int > rat] :
% 0.33/0.63 ( ( finite_finite_int @ I4 )
% 0.33/0.63 => ( ( I4 != bot_bot_set_int )
% 0.33/0.63 => ( ! [I2: int] :
% 0.33/0.63 ( ( member_int @ I2 @ I4 )
% 0.33/0.63 => ( ord_less_rat @ one_one_rat @ ( F @ I2 ) ) )
% 0.33/0.63 => ( ord_less_rat @ one_one_rat @ ( groups1072433553688619179nt_rat @ F @ I4 ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % less_1_prod
% 0.33/0.63 thf(fact_5892_less__1__prod,axiom,
% 0.33/0.63 ! [I4: set_Code_integer,F: code_integer > int] :
% 0.33/0.63 ( ( finite6017078050557962740nteger @ I4 )
% 0.33/0.63 => ( ( I4 != bot_bo3990330152332043303nteger )
% 0.33/0.63 => ( ! [I2: code_integer] :
% 0.33/0.63 ( ( member_Code_integer @ I2 @ I4 )
% 0.33/0.63 => ( ord_less_int @ one_one_int @ ( F @ I2 ) ) )
% 0.33/0.63 => ( ord_less_int @ one_one_int @ ( groups3188404863801439024er_int @ F @ I4 ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % less_1_prod
% 0.33/0.63 thf(fact_5893_less__1__prod,axiom,
% 0.33/0.63 ! [I4: set_o,F: $o > int] :
% 0.33/0.63 ( ( finite_finite_o @ I4 )
% 0.33/0.63 => ( ( I4 != bot_bot_set_o )
% 0.33/0.63 => ( ! [I2: $o] :
% 0.33/0.63 ( ( member_o @ I2 @ I4 )
% 0.33/0.63 => ( ord_less_int @ one_one_int @ ( F @ I2 ) ) )
% 0.33/0.63 => ( ord_less_int @ one_one_int @ ( groups3502327434004483295_o_int @ F @ I4 ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % less_1_prod
% 0.33/0.63 thf(fact_5894_sum_Oreindex__nontrivial,axiom,
% 0.33/0.63 ! [A2: set_num,H3: num > code_integer,G: code_integer > code_integer] :
% 0.33/0.63 ( ( finite_finite_num @ A2 )
% 0.33/0.63 => ( ! [X4: num,Y5: num] :
% 0.33/0.63 ( ( member_num @ X4 @ A2 )
% 0.33/0.63 => ( ( member_num @ Y5 @ A2 )
% 0.33/0.63 => ( ( X4 != Y5 )
% 0.33/0.63 => ( ( ( H3 @ X4 )
% 0.33/0.63 = ( H3 @ Y5 ) )
% 0.33/0.63 => ( ( G @ ( H3 @ X4 ) )
% 0.33/0.63 = zero_z3403309356797280102nteger ) ) ) ) )
% 0.33/0.63 => ( ( groups879477027807139574nteger @ G @ ( image_8379761247532268670nteger @ H3 @ A2 ) )
% 0.33/0.63 = ( groups5442708359310287027nteger @ ( comp_C3531382070062128313er_num @ G @ H3 ) @ A2 ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % sum.reindex_nontrivial
% 0.33/0.63 thf(fact_5895_sum_Oreindex__nontrivial,axiom,
% 0.33/0.63 ! [A2: set_nat,H3: nat > code_integer,G: code_integer > code_integer] :
% 0.33/0.63 ( ( finite_finite_nat @ A2 )
% 0.33/0.63 => ( ! [X4: nat,Y5: nat] :
% 0.33/0.63 ( ( member_nat @ X4 @ A2 )
% 0.33/0.63 => ( ( member_nat @ Y5 @ A2 )
% 0.33/0.63 => ( ( X4 != Y5 )
% 0.33/0.63 => ( ( ( H3 @ X4 )
% 0.33/0.63 = ( H3 @ Y5 ) )
% 0.33/0.63 => ( ( G @ ( H3 @ X4 ) )
% 0.33/0.63 = zero_z3403309356797280102nteger ) ) ) ) )
% 0.33/0.63 => ( ( groups879477027807139574nteger @ G @ ( image_1215581382706833972nteger @ H3 @ A2 ) )
% 0.33/0.63 = ( groups7501900531339628137nteger @ ( comp_C6974050283906349679er_nat @ G @ H3 ) @ A2 ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % sum.reindex_nontrivial
% 0.33/0.63 thf(fact_5896_sum_Oreindex__nontrivial,axiom,
% 0.33/0.63 ! [A2: set_nat,H3: nat > nat,G: nat > code_integer] :
% 0.33/0.63 ( ( finite_finite_nat @ A2 )
% 0.33/0.63 => ( ! [X4: nat,Y5: nat] :
% 0.33/0.63 ( ( member_nat @ X4 @ A2 )
% 0.33/0.63 => ( ( member_nat @ Y5 @ A2 )
% 0.33/0.63 => ( ( X4 != Y5 )
% 0.33/0.63 => ( ( ( H3 @ X4 )
% 0.33/0.63 = ( H3 @ Y5 ) )
% 0.33/0.63 => ( ( G @ ( H3 @ X4 ) )
% 0.33/0.63 = zero_z3403309356797280102nteger ) ) ) ) )
% 0.33/0.63 => ( ( groups7501900531339628137nteger @ G @ ( image_nat_nat @ H3 @ A2 ) )
% 0.33/0.63 = ( groups7501900531339628137nteger @ ( comp_n3898172953802868194er_nat @ G @ H3 ) @ A2 ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % sum.reindex_nontrivial
% 0.33/0.63 thf(fact_5897_sum_Oreindex__nontrivial,axiom,
% 0.33/0.63 ! [A2: set_nat,H3: nat > int,G: int > code_integer] :
% 0.33/0.63 ( ( finite_finite_nat @ A2 )
% 0.33/0.63 => ( ! [X4: nat,Y5: nat] :
% 0.33/0.63 ( ( member_nat @ X4 @ A2 )
% 0.33/0.63 => ( ( member_nat @ Y5 @ A2 )
% 0.33/0.63 => ( ( X4 != Y5 )
% 0.33/0.63 => ( ( ( H3 @ X4 )
% 0.33/0.63 = ( H3 @ Y5 ) )
% 0.33/0.63 => ( ( G @ ( H3 @ X4 ) )
% 0.33/0.63 = zero_z3403309356797280102nteger ) ) ) ) )
% 0.33/0.63 => ( ( groups7873554091576472773nteger @ G @ ( image_nat_int @ H3 @ A2 ) )
% 0.33/0.63 = ( groups7501900531339628137nteger @ ( comp_i1588355021709917246er_nat @ G @ H3 ) @ A2 ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % sum.reindex_nontrivial
% 0.33/0.63 thf(fact_5898_sum_Oreindex__nontrivial,axiom,
% 0.33/0.63 ! [A2: set_int,H3: int > int,G: int > code_integer] :
% 0.33/0.63 ( ( finite_finite_int @ A2 )
% 0.33/0.63 => ( ! [X4: int,Y5: int] :
% 0.33/0.63 ( ( member_int @ X4 @ A2 )
% 0.33/0.63 => ( ( member_int @ Y5 @ A2 )
% 0.33/0.63 => ( ( X4 != Y5 )
% 0.33/0.63 => ( ( ( H3 @ X4 )
% 0.33/0.63 = ( H3 @ Y5 ) )
% 0.33/0.63 => ( ( G @ ( H3 @ X4 ) )
% 0.33/0.63 = zero_z3403309356797280102nteger ) ) ) ) )
% 0.33/0.63 => ( ( groups7873554091576472773nteger @ G @ ( image_int_int @ H3 @ A2 ) )
% 0.33/0.63 = ( groups7873554091576472773nteger @ ( comp_i1585864551200866970er_int @ G @ H3 ) @ A2 ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % sum.reindex_nontrivial
% 0.33/0.63 thf(fact_5899_sum_Oreindex__nontrivial,axiom,
% 0.33/0.63 ! [A2: set_nat,H3: nat > code_integer,G: code_integer > rat] :
% 0.33/0.63 ( ( finite_finite_nat @ A2 )
% 0.33/0.63 => ( ! [X4: nat,Y5: nat] :
% 0.33/0.63 ( ( member_nat @ X4 @ A2 )
% 0.33/0.63 => ( ( member_nat @ Y5 @ A2 )
% 0.33/0.63 => ( ( X4 != Y5 )
% 0.33/0.63 => ( ( ( H3 @ X4 )
% 0.33/0.63 = ( H3 @ Y5 ) )
% 0.33/0.63 => ( ( G @ ( H3 @ X4 ) )
% 0.33/0.63 = zero_zero_rat ) ) ) ) )
% 0.33/0.63 => ( ( groups6602215022474089585er_rat @ G @ ( image_1215581382706833972nteger @ H3 @ A2 ) )
% 0.33/0.63 = ( groups2906978787729119204at_rat @ ( comp_C3733001951728184298at_nat @ G @ H3 ) @ A2 ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % sum.reindex_nontrivial
% 0.33/0.63 thf(fact_5900_sum_Oreindex__nontrivial,axiom,
% 0.33/0.63 ! [A2: set_nat,H3: nat > nat,G: nat > rat] :
% 0.33/0.63 ( ( finite_finite_nat @ A2 )
% 0.33/0.63 => ( ! [X4: nat,Y5: nat] :
% 0.33/0.63 ( ( member_nat @ X4 @ A2 )
% 0.33/0.63 => ( ( member_nat @ Y5 @ A2 )
% 0.33/0.63 => ( ( X4 != Y5 )
% 0.33/0.63 => ( ( ( H3 @ X4 )
% 0.33/0.63 = ( H3 @ Y5 ) )
% 0.33/0.63 => ( ( G @ ( H3 @ X4 ) )
% 0.33/0.63 = zero_zero_rat ) ) ) ) )
% 0.33/0.63 => ( ( groups2906978787729119204at_rat @ G @ ( image_nat_nat @ H3 @ A2 ) )
% 0.33/0.63 = ( groups2906978787729119204at_rat @ ( comp_nat_rat_nat @ G @ H3 ) @ A2 ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % sum.reindex_nontrivial
% 0.33/0.63 thf(fact_5901_sum_Oreindex__nontrivial,axiom,
% 0.33/0.63 ! [A2: set_nat,H3: nat > int,G: int > rat] :
% 0.33/0.63 ( ( finite_finite_nat @ A2 )
% 0.33/0.63 => ( ! [X4: nat,Y5: nat] :
% 0.33/0.63 ( ( member_nat @ X4 @ A2 )
% 0.33/0.63 => ( ( member_nat @ Y5 @ A2 )
% 0.33/0.63 => ( ( X4 != Y5 )
% 0.33/0.63 => ( ( ( H3 @ X4 )
% 0.33/0.63 = ( H3 @ Y5 ) )
% 0.33/0.63 => ( ( G @ ( H3 @ X4 ) )
% 0.33/0.63 = zero_zero_rat ) ) ) ) )
% 0.33/0.63 => ( ( groups3906332499630173760nt_rat @ G @ ( image_nat_int @ H3 @ A2 ) )
% 0.33/0.63 = ( groups2906978787729119204at_rat @ ( comp_int_rat_nat @ G @ H3 ) @ A2 ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % sum.reindex_nontrivial
% 0.33/0.63 thf(fact_5902_sum_Oreindex__nontrivial,axiom,
% 0.33/0.63 ! [A2: set_int,H3: int > int,G: int > rat] :
% 0.33/0.63 ( ( finite_finite_int @ A2 )
% 0.33/0.63 => ( ! [X4: int,Y5: int] :
% 0.33/0.63 ( ( member_int @ X4 @ A2 )
% 0.33/0.63 => ( ( member_int @ Y5 @ A2 )
% 0.33/0.63 => ( ( X4 != Y5 )
% 0.33/0.63 => ( ( ( H3 @ X4 )
% 0.33/0.63 = ( H3 @ Y5 ) )
% 0.33/0.63 => ( ( G @ ( H3 @ X4 ) )
% 0.33/0.63 = zero_zero_rat ) ) ) ) )
% 0.33/0.63 => ( ( groups3906332499630173760nt_rat @ G @ ( image_int_int @ H3 @ A2 ) )
% 0.33/0.63 = ( groups3906332499630173760nt_rat @ ( comp_int_rat_int @ G @ H3 ) @ A2 ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % sum.reindex_nontrivial
% 0.33/0.63 thf(fact_5903_sum_Oreindex__nontrivial,axiom,
% 0.33/0.63 ! [A2: set_int,H3: int > int,G: int > nat] :
% 0.33/0.63 ( ( finite_finite_int @ A2 )
% 0.33/0.63 => ( ! [X4: int,Y5: int] :
% 0.33/0.63 ( ( member_int @ X4 @ A2 )
% 0.33/0.63 => ( ( member_int @ Y5 @ A2 )
% 0.33/0.63 => ( ( X4 != Y5 )
% 0.33/0.63 => ( ( ( H3 @ X4 )
% 0.33/0.63 = ( H3 @ Y5 ) )
% 0.33/0.63 => ( ( G @ ( H3 @ X4 ) )
% 0.33/0.63 = zero_zero_nat ) ) ) ) )
% 0.33/0.63 => ( ( groups4541462559716669496nt_nat @ G @ ( image_int_int @ H3 @ A2 ) )
% 0.33/0.63 = ( groups4541462559716669496nt_nat @ ( comp_int_nat_int @ G @ H3 ) @ A2 ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % sum.reindex_nontrivial
% 0.33/0.63 thf(fact_5904_prod_Oreindex__nontrivial,axiom,
% 0.33/0.63 ! [A2: set_num,H3: num > code_integer,G: code_integer > code_integer] :
% 0.33/0.63 ( ( finite_finite_num @ A2 )
% 0.33/0.63 => ( ! [X4: num,Y5: num] :
% 0.33/0.63 ( ( member_num @ X4 @ A2 )
% 0.33/0.63 => ( ( member_num @ Y5 @ A2 )
% 0.33/0.63 => ( ( X4 != Y5 )
% 0.33/0.63 => ( ( ( H3 @ X4 )
% 0.33/0.63 = ( H3 @ Y5 ) )
% 0.33/0.63 => ( ( G @ ( H3 @ X4 ) )
% 0.33/0.63 = one_one_Code_integer ) ) ) ) )
% 0.33/0.63 => ( ( groups3674199335183972705nteger @ G @ ( image_8379761247532268670nteger @ H3 @ A2 ) )
% 0.33/0.63 = ( groups1396258611060191006nteger @ ( comp_C3531382070062128313er_num @ G @ H3 ) @ A2 ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.reindex_nontrivial
% 0.33/0.63 thf(fact_5905_prod_Oreindex__nontrivial,axiom,
% 0.33/0.63 ! [A2: set_nat,H3: nat > code_integer,G: code_integer > code_integer] :
% 0.33/0.63 ( ( finite_finite_nat @ A2 )
% 0.33/0.63 => ( ! [X4: nat,Y5: nat] :
% 0.33/0.63 ( ( member_nat @ X4 @ A2 )
% 0.33/0.63 => ( ( member_nat @ Y5 @ A2 )
% 0.33/0.63 => ( ( X4 != Y5 )
% 0.33/0.63 => ( ( ( H3 @ X4 )
% 0.33/0.63 = ( H3 @ Y5 ) )
% 0.33/0.63 => ( ( G @ ( H3 @ X4 ) )
% 0.33/0.63 = one_one_Code_integer ) ) ) ) )
% 0.33/0.63 => ( ( groups3674199335183972705nteger @ G @ ( image_1215581382706833972nteger @ H3 @ A2 ) )
% 0.33/0.63 = ( groups3455450783089532116nteger @ ( comp_C6974050283906349679er_nat @ G @ H3 ) @ A2 ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.reindex_nontrivial
% 0.33/0.63 thf(fact_5906_prod_Oreindex__nontrivial,axiom,
% 0.33/0.63 ! [A2: set_nat,H3: nat > nat,G: nat > code_integer] :
% 0.33/0.63 ( ( finite_finite_nat @ A2 )
% 0.33/0.63 => ( ! [X4: nat,Y5: nat] :
% 0.33/0.63 ( ( member_nat @ X4 @ A2 )
% 0.33/0.63 => ( ( member_nat @ Y5 @ A2 )
% 0.33/0.63 => ( ( X4 != Y5 )
% 0.33/0.63 => ( ( ( H3 @ X4 )
% 0.33/0.63 = ( H3 @ Y5 ) )
% 0.33/0.63 => ( ( G @ ( H3 @ X4 ) )
% 0.33/0.63 = one_one_Code_integer ) ) ) ) )
% 0.33/0.63 => ( ( groups3455450783089532116nteger @ G @ ( image_nat_nat @ H3 @ A2 ) )
% 0.33/0.63 = ( groups3455450783089532116nteger @ ( comp_n3898172953802868194er_nat @ G @ H3 ) @ A2 ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.reindex_nontrivial
% 0.33/0.63 thf(fact_5907_prod_Oreindex__nontrivial,axiom,
% 0.33/0.63 ! [A2: set_nat,H3: nat > int,G: int > code_integer] :
% 0.33/0.63 ( ( finite_finite_nat @ A2 )
% 0.33/0.63 => ( ! [X4: nat,Y5: nat] :
% 0.33/0.63 ( ( member_nat @ X4 @ A2 )
% 0.33/0.63 => ( ( member_nat @ Y5 @ A2 )
% 0.33/0.63 => ( ( X4 != Y5 )
% 0.33/0.63 => ( ( ( H3 @ X4 )
% 0.33/0.63 = ( H3 @ Y5 ) )
% 0.33/0.63 => ( ( G @ ( H3 @ X4 ) )
% 0.33/0.63 = one_one_Code_integer ) ) ) ) )
% 0.33/0.63 => ( ( groups3827104343326376752nteger @ G @ ( image_nat_int @ H3 @ A2 ) )
% 0.33/0.63 = ( groups3455450783089532116nteger @ ( comp_i1588355021709917246er_nat @ G @ H3 ) @ A2 ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.reindex_nontrivial
% 0.33/0.63 thf(fact_5908_prod_Oreindex__nontrivial,axiom,
% 0.33/0.63 ! [A2: set_int,H3: int > int,G: int > code_integer] :
% 0.33/0.63 ( ( finite_finite_int @ A2 )
% 0.33/0.63 => ( ! [X4: int,Y5: int] :
% 0.33/0.63 ( ( member_int @ X4 @ A2 )
% 0.33/0.63 => ( ( member_int @ Y5 @ A2 )
% 0.33/0.63 => ( ( X4 != Y5 )
% 0.33/0.63 => ( ( ( H3 @ X4 )
% 0.33/0.63 = ( H3 @ Y5 ) )
% 0.33/0.63 => ( ( G @ ( H3 @ X4 ) )
% 0.33/0.63 = one_one_Code_integer ) ) ) ) )
% 0.33/0.63 => ( ( groups3827104343326376752nteger @ G @ ( image_int_int @ H3 @ A2 ) )
% 0.33/0.63 = ( groups3827104343326376752nteger @ ( comp_i1585864551200866970er_int @ G @ H3 ) @ A2 ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.reindex_nontrivial
% 0.33/0.63 thf(fact_5909_prod_Oreindex__nontrivial,axiom,
% 0.33/0.63 ! [A2: set_nat,H3: nat > code_integer,G: code_integer > assn] :
% 0.33/0.63 ( ( finite_finite_nat @ A2 )
% 0.33/0.63 => ( ! [X4: nat,Y5: nat] :
% 0.33/0.63 ( ( member_nat @ X4 @ A2 )
% 0.33/0.63 => ( ( member_nat @ Y5 @ A2 )
% 0.33/0.63 => ( ( X4 != Y5 )
% 0.33/0.63 => ( ( ( H3 @ X4 )
% 0.33/0.63 = ( H3 @ Y5 ) )
% 0.33/0.63 => ( ( G @ ( H3 @ X4 ) )
% 0.33/0.63 = one_one_assn ) ) ) ) )
% 0.33/0.63 => ( ( groups1304777262505850412r_assn @ G @ ( image_1215581382706833972nteger @ H3 @ A2 ) )
% 0.33/0.63 = ( groups6906906614972039071t_assn @ ( comp_C8462447471145125178sn_nat @ G @ H3 ) @ A2 ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.reindex_nontrivial
% 0.33/0.63 thf(fact_5910_prod_Oreindex__nontrivial,axiom,
% 0.33/0.63 ! [A2: set_nat,H3: nat > nat,G: nat > assn] :
% 0.33/0.63 ( ( finite_finite_nat @ A2 )
% 0.33/0.63 => ( ! [X4: nat,Y5: nat] :
% 0.33/0.63 ( ( member_nat @ X4 @ A2 )
% 0.33/0.63 => ( ( member_nat @ Y5 @ A2 )
% 0.33/0.63 => ( ( X4 != Y5 )
% 0.33/0.63 => ( ( ( H3 @ X4 )
% 0.33/0.63 = ( H3 @ Y5 ) )
% 0.33/0.63 => ( ( G @ ( H3 @ X4 ) )
% 0.33/0.63 = one_one_assn ) ) ) ) )
% 0.33/0.63 => ( ( groups6906906614972039071t_assn @ G @ ( image_nat_nat @ H3 @ A2 ) )
% 0.33/0.63 = ( groups6906906614972039071t_assn @ ( comp_nat_assn_nat @ G @ H3 ) @ A2 ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.reindex_nontrivial
% 0.33/0.63 thf(fact_5911_prod_Oreindex__nontrivial,axiom,
% 0.33/0.63 ! [A2: set_nat,H3: nat > int,G: int > assn] :
% 0.33/0.63 ( ( finite_finite_nat @ A2 )
% 0.33/0.63 => ( ! [X4: nat,Y5: nat] :
% 0.33/0.63 ( ( member_nat @ X4 @ A2 )
% 0.33/0.63 => ( ( member_nat @ Y5 @ A2 )
% 0.33/0.63 => ( ( X4 != Y5 )
% 0.33/0.63 => ( ( ( H3 @ X4 )
% 0.33/0.63 = ( H3 @ Y5 ) )
% 0.33/0.63 => ( ( G @ ( H3 @ X4 ) )
% 0.33/0.63 = one_one_assn ) ) ) ) )
% 0.33/0.63 => ( ( groups7882442080178216443t_assn @ G @ ( image_nat_int @ H3 @ A2 ) )
% 0.33/0.63 = ( groups6906906614972039071t_assn @ ( comp_int_assn_nat @ G @ H3 ) @ A2 ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.reindex_nontrivial
% 0.33/0.63 thf(fact_5912_prod_Oreindex__nontrivial,axiom,
% 0.33/0.63 ! [A2: set_int,H3: int > int,G: int > assn] :
% 0.33/0.63 ( ( finite_finite_int @ A2 )
% 0.33/0.63 => ( ! [X4: int,Y5: int] :
% 0.33/0.63 ( ( member_int @ X4 @ A2 )
% 0.33/0.63 => ( ( member_int @ Y5 @ A2 )
% 0.33/0.63 => ( ( X4 != Y5 )
% 0.33/0.63 => ( ( ( H3 @ X4 )
% 0.33/0.63 = ( H3 @ Y5 ) )
% 0.33/0.63 => ( ( G @ ( H3 @ X4 ) )
% 0.33/0.63 = one_one_assn ) ) ) ) )
% 0.33/0.63 => ( ( groups7882442080178216443t_assn @ G @ ( image_int_int @ H3 @ A2 ) )
% 0.33/0.63 = ( groups7882442080178216443t_assn @ ( comp_int_assn_int @ G @ H3 ) @ A2 ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.reindex_nontrivial
% 0.33/0.63 thf(fact_5913_prod_Oreindex__nontrivial,axiom,
% 0.33/0.63 ! [A2: set_nat,H3: nat > code_integer,G: code_integer > rat] :
% 0.33/0.63 ( ( finite_finite_nat @ A2 )
% 0.33/0.63 => ( ! [X4: nat,Y5: nat] :
% 0.33/0.63 ( ( member_nat @ X4 @ A2 )
% 0.33/0.63 => ( ( member_nat @ Y5 @ A2 )
% 0.33/0.63 => ( ( X4 != Y5 )
% 0.33/0.63 => ( ( ( H3 @ X4 )
% 0.33/0.63 = ( H3 @ Y5 ) )
% 0.33/0.63 => ( ( G @ ( H3 @ X4 ) )
% 0.33/0.63 = one_one_rat ) ) ) ) )
% 0.33/0.63 => ( ( groups2555765274223993564er_rat @ G @ ( image_1215581382706833972nteger @ H3 @ A2 ) )
% 0.33/0.63 = ( groups73079841787564623at_rat @ ( comp_C3733001951728184298at_nat @ G @ H3 ) @ A2 ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.reindex_nontrivial
% 0.33/0.63 thf(fact_5914_sum_Osubset__diff,axiom,
% 0.33/0.63 ! [B5: set_int,A2: set_int,G: int > rat] :
% 0.33/0.63 ( ( ord_less_eq_set_int @ B5 @ A2 )
% 0.33/0.63 => ( ( finite_finite_int @ A2 )
% 0.33/0.63 => ( ( groups3906332499630173760nt_rat @ G @ A2 )
% 0.33/0.63 = ( plus_plus_rat @ ( groups3906332499630173760nt_rat @ G @ ( minus_minus_set_int @ A2 @ B5 ) ) @ ( groups3906332499630173760nt_rat @ G @ B5 ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % sum.subset_diff
% 0.33/0.63 thf(fact_5915_sum_Osubset__diff,axiom,
% 0.33/0.63 ! [B5: set_Code_integer,A2: set_Code_integer,G: code_integer > rat] :
% 0.33/0.63 ( ( ord_le7084787975880047091nteger @ B5 @ A2 )
% 0.33/0.63 => ( ( finite6017078050557962740nteger @ A2 )
% 0.33/0.63 => ( ( groups6602215022474089585er_rat @ G @ A2 )
% 0.33/0.63 = ( plus_plus_rat @ ( groups6602215022474089585er_rat @ G @ ( minus_2355218937544613996nteger @ A2 @ B5 ) ) @ ( groups6602215022474089585er_rat @ G @ B5 ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % sum.subset_diff
% 0.33/0.63 thf(fact_5916_sum_Osubset__diff,axiom,
% 0.33/0.63 ! [B5: set_int,A2: set_int,G: int > nat] :
% 0.33/0.63 ( ( ord_less_eq_set_int @ B5 @ A2 )
% 0.33/0.63 => ( ( finite_finite_int @ A2 )
% 0.33/0.63 => ( ( groups4541462559716669496nt_nat @ G @ A2 )
% 0.33/0.63 = ( plus_plus_nat @ ( groups4541462559716669496nt_nat @ G @ ( minus_minus_set_int @ A2 @ B5 ) ) @ ( groups4541462559716669496nt_nat @ G @ B5 ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % sum.subset_diff
% 0.33/0.63 thf(fact_5917_sum_Osubset__diff,axiom,
% 0.33/0.63 ! [B5: set_Code_integer,A2: set_Code_integer,G: code_integer > nat] :
% 0.33/0.63 ( ( ord_le7084787975880047091nteger @ B5 @ A2 )
% 0.33/0.63 => ( ( finite6017078050557962740nteger @ A2 )
% 0.33/0.63 => ( ( groups7237345082560585321er_nat @ G @ A2 )
% 0.33/0.63 = ( plus_plus_nat @ ( groups7237345082560585321er_nat @ G @ ( minus_2355218937544613996nteger @ A2 @ B5 ) ) @ ( groups7237345082560585321er_nat @ G @ B5 ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % sum.subset_diff
% 0.33/0.63 thf(fact_5918_sum_Osubset__diff,axiom,
% 0.33/0.63 ! [B5: set_Code_integer,A2: set_Code_integer,G: code_integer > int] :
% 0.33/0.63 ( ( ord_le7084787975880047091nteger @ B5 @ A2 )
% 0.33/0.63 => ( ( finite6017078050557962740nteger @ A2 )
% 0.33/0.63 => ( ( groups7234854612051535045er_int @ G @ A2 )
% 0.33/0.63 = ( plus_plus_int @ ( groups7234854612051535045er_int @ G @ ( minus_2355218937544613996nteger @ A2 @ B5 ) ) @ ( groups7234854612051535045er_int @ G @ B5 ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % sum.subset_diff
% 0.33/0.63 thf(fact_5919_sum_Osubset__diff,axiom,
% 0.33/0.63 ! [B5: set_nat,A2: set_nat,G: nat > rat] :
% 0.33/0.63 ( ( ord_less_eq_set_nat @ B5 @ A2 )
% 0.33/0.63 => ( ( finite_finite_nat @ A2 )
% 0.33/0.63 => ( ( groups2906978787729119204at_rat @ G @ A2 )
% 0.33/0.63 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( minus_minus_set_nat @ A2 @ B5 ) ) @ ( groups2906978787729119204at_rat @ G @ B5 ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % sum.subset_diff
% 0.33/0.63 thf(fact_5920_sum_Osubset__diff,axiom,
% 0.33/0.63 ! [B5: set_nat,A2: set_nat,G: nat > int] :
% 0.33/0.63 ( ( ord_less_eq_set_nat @ B5 @ A2 )
% 0.33/0.63 => ( ( finite_finite_nat @ A2 )
% 0.33/0.63 => ( ( groups3539618377306564664at_int @ G @ A2 )
% 0.33/0.63 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( minus_minus_set_nat @ A2 @ B5 ) ) @ ( groups3539618377306564664at_int @ G @ B5 ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % sum.subset_diff
% 0.33/0.63 thf(fact_5921_sum_Osubset__diff,axiom,
% 0.33/0.63 ! [B5: set_nat,A2: set_nat,G: nat > nat] :
% 0.33/0.63 ( ( ord_less_eq_set_nat @ B5 @ A2 )
% 0.33/0.63 => ( ( finite_finite_nat @ A2 )
% 0.33/0.63 => ( ( groups3542108847815614940at_nat @ G @ A2 )
% 0.33/0.63 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( minus_minus_set_nat @ A2 @ B5 ) ) @ ( groups3542108847815614940at_nat @ G @ B5 ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % sum.subset_diff
% 0.33/0.63 thf(fact_5922_sum_Osubset__diff,axiom,
% 0.33/0.63 ! [B5: set_int,A2: set_int,G: int > int] :
% 0.33/0.63 ( ( ord_less_eq_set_int @ B5 @ A2 )
% 0.33/0.63 => ( ( finite_finite_int @ A2 )
% 0.33/0.63 => ( ( groups4538972089207619220nt_int @ G @ A2 )
% 0.33/0.63 = ( plus_plus_int @ ( groups4538972089207619220nt_int @ G @ ( minus_minus_set_int @ A2 @ B5 ) ) @ ( groups4538972089207619220nt_int @ G @ B5 ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % sum.subset_diff
% 0.33/0.63 thf(fact_5923_sum_Osubset__diff,axiom,
% 0.33/0.63 ! [B5: set_Pr1261947904930325089at_nat,A2: set_Pr1261947904930325089at_nat,G: product_prod_nat_nat > rat] :
% 0.33/0.63 ( ( ord_le3146513528884898305at_nat @ B5 @ A2 )
% 0.33/0.63 => ( ( finite6177210948735845034at_nat @ A2 )
% 0.33/0.63 => ( ( groups342789780944988191at_rat @ G @ A2 )
% 0.33/0.63 = ( plus_plus_rat @ ( groups342789780944988191at_rat @ G @ ( minus_1356011639430497352at_nat @ A2 @ B5 ) ) @ ( groups342789780944988191at_rat @ G @ B5 ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % sum.subset_diff
% 0.33/0.63 thf(fact_5924_prod_Osame__carrier,axiom,
% 0.33/0.63 ! [C4: set_o,A2: set_o,B5: set_o,G: $o > code_integer,H3: $o > code_integer] :
% 0.33/0.63 ( ( finite_finite_o @ C4 )
% 0.33/0.63 => ( ( ord_less_eq_set_o @ A2 @ C4 )
% 0.33/0.63 => ( ( ord_less_eq_set_o @ B5 @ C4 )
% 0.33/0.63 => ( ! [A3: $o] :
% 0.33/0.63 ( ( member_o @ A3 @ ( minus_minus_set_o @ C4 @ A2 ) )
% 0.33/0.63 => ( ( G @ A3 )
% 0.33/0.63 = one_one_Code_integer ) )
% 0.33/0.63 => ( ! [B2: $o] :
% 0.33/0.63 ( ( member_o @ B2 @ ( minus_minus_set_o @ C4 @ B5 ) )
% 0.33/0.63 => ( ( H3 @ B2 )
% 0.33/0.63 = one_one_Code_integer ) )
% 0.33/0.63 => ( ( ( groups7694694392188491536nteger @ G @ A2 )
% 0.33/0.63 = ( groups7694694392188491536nteger @ H3 @ B5 ) )
% 0.33/0.63 = ( ( groups7694694392188491536nteger @ G @ C4 )
% 0.33/0.63 = ( groups7694694392188491536nteger @ H3 @ C4 ) ) ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.same_carrier
% 0.33/0.63 thf(fact_5925_prod_Osame__carrier,axiom,
% 0.33/0.63 ! [C4: set_int,A2: set_int,B5: set_int,G: int > code_integer,H3: int > code_integer] :
% 0.33/0.63 ( ( finite_finite_int @ C4 )
% 0.33/0.63 => ( ( ord_less_eq_set_int @ A2 @ C4 )
% 0.33/0.63 => ( ( ord_less_eq_set_int @ B5 @ C4 )
% 0.33/0.63 => ( ! [A3: int] :
% 0.33/0.63 ( ( member_int @ A3 @ ( minus_minus_set_int @ C4 @ A2 ) )
% 0.33/0.63 => ( ( G @ A3 )
% 0.33/0.63 = one_one_Code_integer ) )
% 0.33/0.63 => ( ! [B2: int] :
% 0.33/0.63 ( ( member_int @ B2 @ ( minus_minus_set_int @ C4 @ B5 ) )
% 0.33/0.63 => ( ( H3 @ B2 )
% 0.33/0.63 = one_one_Code_integer ) )
% 0.33/0.63 => ( ( ( groups3827104343326376752nteger @ G @ A2 )
% 0.33/0.63 = ( groups3827104343326376752nteger @ H3 @ B5 ) )
% 0.33/0.63 = ( ( groups3827104343326376752nteger @ G @ C4 )
% 0.33/0.63 = ( groups3827104343326376752nteger @ H3 @ C4 ) ) ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.same_carrier
% 0.33/0.63 thf(fact_5926_prod_Osame__carrier,axiom,
% 0.33/0.63 ! [C4: set_Code_integer,A2: set_Code_integer,B5: set_Code_integer,G: code_integer > code_integer,H3: code_integer > code_integer] :
% 0.33/0.63 ( ( finite6017078050557962740nteger @ C4 )
% 0.33/0.63 => ( ( ord_le7084787975880047091nteger @ A2 @ C4 )
% 0.33/0.63 => ( ( ord_le7084787975880047091nteger @ B5 @ C4 )
% 0.33/0.63 => ( ! [A3: code_integer] :
% 0.33/0.63 ( ( member_Code_integer @ A3 @ ( minus_2355218937544613996nteger @ C4 @ A2 ) )
% 0.33/0.63 => ( ( G @ A3 )
% 0.33/0.63 = one_one_Code_integer ) )
% 0.33/0.63 => ( ! [B2: code_integer] :
% 0.33/0.63 ( ( member_Code_integer @ B2 @ ( minus_2355218937544613996nteger @ C4 @ B5 ) )
% 0.33/0.63 => ( ( H3 @ B2 )
% 0.33/0.63 = one_one_Code_integer ) )
% 0.33/0.63 => ( ( ( groups3674199335183972705nteger @ G @ A2 )
% 0.33/0.63 = ( groups3674199335183972705nteger @ H3 @ B5 ) )
% 0.33/0.63 = ( ( groups3674199335183972705nteger @ G @ C4 )
% 0.33/0.63 = ( groups3674199335183972705nteger @ H3 @ C4 ) ) ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.same_carrier
% 0.33/0.63 thf(fact_5927_prod_Osame__carrier,axiom,
% 0.33/0.63 ! [C4: set_o,A2: set_o,B5: set_o,G: $o > assn,H3: $o > assn] :
% 0.33/0.63 ( ( finite_finite_o @ C4 )
% 0.33/0.63 => ( ( ord_less_eq_set_o @ A2 @ C4 )
% 0.33/0.63 => ( ( ord_less_eq_set_o @ B5 @ C4 )
% 0.33/0.63 => ( ! [A3: $o] :
% 0.33/0.63 ( ( member_o @ A3 @ ( minus_minus_set_o @ C4 @ A2 ) )
% 0.33/0.63 => ( ( G @ A3 )
% 0.33/0.63 = one_one_assn ) )
% 0.33/0.63 => ( ! [B2: $o] :
% 0.33/0.63 ( ( member_o @ B2 @ ( minus_minus_set_o @ C4 @ B5 ) )
% 0.33/0.63 => ( ( H3 @ B2 )
% 0.33/0.63 = one_one_assn ) )
% 0.33/0.63 => ( ( ( groups5301882518646026715o_assn @ G @ A2 )
% 0.33/0.63 = ( groups5301882518646026715o_assn @ H3 @ B5 ) )
% 0.33/0.63 = ( ( groups5301882518646026715o_assn @ G @ C4 )
% 0.33/0.63 = ( groups5301882518646026715o_assn @ H3 @ C4 ) ) ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.same_carrier
% 0.33/0.63 thf(fact_5928_prod_Osame__carrier,axiom,
% 0.33/0.63 ! [C4: set_int,A2: set_int,B5: set_int,G: int > assn,H3: int > assn] :
% 0.33/0.63 ( ( finite_finite_int @ C4 )
% 0.33/0.63 => ( ( ord_less_eq_set_int @ A2 @ C4 )
% 0.33/0.63 => ( ( ord_less_eq_set_int @ B5 @ C4 )
% 0.33/0.63 => ( ! [A3: int] :
% 0.33/0.63 ( ( member_int @ A3 @ ( minus_minus_set_int @ C4 @ A2 ) )
% 0.33/0.63 => ( ( G @ A3 )
% 0.33/0.63 = one_one_assn ) )
% 0.33/0.63 => ( ! [B2: int] :
% 0.33/0.63 ( ( member_int @ B2 @ ( minus_minus_set_int @ C4 @ B5 ) )
% 0.33/0.63 => ( ( H3 @ B2 )
% 0.33/0.63 = one_one_assn ) )
% 0.33/0.63 => ( ( ( groups7882442080178216443t_assn @ G @ A2 )
% 0.33/0.63 = ( groups7882442080178216443t_assn @ H3 @ B5 ) )
% 0.33/0.63 = ( ( groups7882442080178216443t_assn @ G @ C4 )
% 0.33/0.63 = ( groups7882442080178216443t_assn @ H3 @ C4 ) ) ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.same_carrier
% 0.33/0.63 thf(fact_5929_prod_Osame__carrier,axiom,
% 0.33/0.63 ! [C4: set_Code_integer,A2: set_Code_integer,B5: set_Code_integer,G: code_integer > assn,H3: code_integer > assn] :
% 0.33/0.63 ( ( finite6017078050557962740nteger @ C4 )
% 0.33/0.63 => ( ( ord_le7084787975880047091nteger @ A2 @ C4 )
% 0.33/0.63 => ( ( ord_le7084787975880047091nteger @ B5 @ C4 )
% 0.33/0.63 => ( ! [A3: code_integer] :
% 0.33/0.63 ( ( member_Code_integer @ A3 @ ( minus_2355218937544613996nteger @ C4 @ A2 ) )
% 0.33/0.63 => ( ( G @ A3 )
% 0.33/0.63 = one_one_assn ) )
% 0.33/0.63 => ( ! [B2: code_integer] :
% 0.33/0.63 ( ( member_Code_integer @ B2 @ ( minus_2355218937544613996nteger @ C4 @ B5 ) )
% 0.33/0.63 => ( ( H3 @ B2 )
% 0.33/0.63 = one_one_assn ) )
% 0.33/0.63 => ( ( ( groups1304777262505850412r_assn @ G @ A2 )
% 0.33/0.63 = ( groups1304777262505850412r_assn @ H3 @ B5 ) )
% 0.33/0.63 = ( ( groups1304777262505850412r_assn @ G @ C4 )
% 0.33/0.63 = ( groups1304777262505850412r_assn @ H3 @ C4 ) ) ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.same_carrier
% 0.33/0.63 thf(fact_5930_prod_Osame__carrier,axiom,
% 0.33/0.63 ! [C4: set_o,A2: set_o,B5: set_o,G: $o > rat,H3: $o > rat] :
% 0.33/0.63 ( ( finite_finite_o @ C4 )
% 0.33/0.63 => ( ( ord_less_eq_set_o @ A2 @ C4 )
% 0.33/0.63 => ( ( ord_less_eq_set_o @ B5 @ C4 )
% 0.33/0.63 => ( ! [A3: $o] :
% 0.33/0.63 ( ( member_o @ A3 @ ( minus_minus_set_o @ C4 @ A2 ) )
% 0.33/0.63 => ( ( G @ A3 )
% 0.33/0.63 = one_one_rat ) )
% 0.33/0.63 => ( ! [B2: $o] :
% 0.33/0.63 ( ( member_o @ B2 @ ( minus_minus_set_o @ C4 @ B5 ) )
% 0.33/0.63 => ( ( H3 @ B2 )
% 0.33/0.63 = one_one_rat ) )
% 0.33/0.63 => ( ( ( groups2869687844427037835_o_rat @ G @ A2 )
% 0.33/0.63 = ( groups2869687844427037835_o_rat @ H3 @ B5 ) )
% 0.33/0.63 = ( ( groups2869687844427037835_o_rat @ G @ C4 )
% 0.33/0.63 = ( groups2869687844427037835_o_rat @ H3 @ C4 ) ) ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.same_carrier
% 0.33/0.63 thf(fact_5931_prod_Osame__carrier,axiom,
% 0.33/0.63 ! [C4: set_int,A2: set_int,B5: set_int,G: int > rat,H3: int > rat] :
% 0.33/0.63 ( ( finite_finite_int @ C4 )
% 0.33/0.63 => ( ( ord_less_eq_set_int @ A2 @ C4 )
% 0.33/0.63 => ( ( ord_less_eq_set_int @ B5 @ C4 )
% 0.33/0.63 => ( ! [A3: int] :
% 0.33/0.63 ( ( member_int @ A3 @ ( minus_minus_set_int @ C4 @ A2 ) )
% 0.33/0.63 => ( ( G @ A3 )
% 0.33/0.63 = one_one_rat ) )
% 0.33/0.63 => ( ! [B2: int] :
% 0.33/0.63 ( ( member_int @ B2 @ ( minus_minus_set_int @ C4 @ B5 ) )
% 0.33/0.63 => ( ( H3 @ B2 )
% 0.33/0.63 = one_one_rat ) )
% 0.33/0.63 => ( ( ( groups1072433553688619179nt_rat @ G @ A2 )
% 0.33/0.63 = ( groups1072433553688619179nt_rat @ H3 @ B5 ) )
% 0.33/0.63 = ( ( groups1072433553688619179nt_rat @ G @ C4 )
% 0.33/0.63 = ( groups1072433553688619179nt_rat @ H3 @ C4 ) ) ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.same_carrier
% 0.33/0.63 thf(fact_5932_prod_Osame__carrier,axiom,
% 0.33/0.63 ! [C4: set_Code_integer,A2: set_Code_integer,B5: set_Code_integer,G: code_integer > rat,H3: code_integer > rat] :
% 0.33/0.63 ( ( finite6017078050557962740nteger @ C4 )
% 0.33/0.63 => ( ( ord_le7084787975880047091nteger @ A2 @ C4 )
% 0.33/0.63 => ( ( ord_le7084787975880047091nteger @ B5 @ C4 )
% 0.33/0.63 => ( ! [A3: code_integer] :
% 0.33/0.63 ( ( member_Code_integer @ A3 @ ( minus_2355218937544613996nteger @ C4 @ A2 ) )
% 0.33/0.63 => ( ( G @ A3 )
% 0.33/0.63 = one_one_rat ) )
% 0.33/0.63 => ( ! [B2: code_integer] :
% 0.33/0.63 ( ( member_Code_integer @ B2 @ ( minus_2355218937544613996nteger @ C4 @ B5 ) )
% 0.33/0.63 => ( ( H3 @ B2 )
% 0.33/0.63 = one_one_rat ) )
% 0.33/0.63 => ( ( ( groups2555765274223993564er_rat @ G @ A2 )
% 0.33/0.63 = ( groups2555765274223993564er_rat @ H3 @ B5 ) )
% 0.33/0.63 = ( ( groups2555765274223993564er_rat @ G @ C4 )
% 0.33/0.63 = ( groups2555765274223993564er_rat @ H3 @ C4 ) ) ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.same_carrier
% 0.33/0.63 thf(fact_5933_prod_Osame__carrier,axiom,
% 0.33/0.63 ! [C4: set_o,A2: set_o,B5: set_o,G: $o > nat,H3: $o > nat] :
% 0.33/0.63 ( ( finite_finite_o @ C4 )
% 0.33/0.63 => ( ( ord_less_eq_set_o @ A2 @ C4 )
% 0.33/0.63 => ( ( ord_less_eq_set_o @ B5 @ C4 )
% 0.33/0.63 => ( ! [A3: $o] :
% 0.33/0.63 ( ( member_o @ A3 @ ( minus_minus_set_o @ C4 @ A2 ) )
% 0.33/0.63 => ( ( G @ A3 )
% 0.33/0.63 = one_one_nat ) )
% 0.33/0.63 => ( ! [B2: $o] :
% 0.33/0.63 ( ( member_o @ B2 @ ( minus_minus_set_o @ C4 @ B5 ) )
% 0.33/0.63 => ( ( H3 @ B2 )
% 0.33/0.63 = one_one_nat ) )
% 0.33/0.63 => ( ( ( groups3504817904513533571_o_nat @ G @ A2 )
% 0.33/0.63 = ( groups3504817904513533571_o_nat @ H3 @ B5 ) )
% 0.33/0.63 = ( ( groups3504817904513533571_o_nat @ G @ C4 )
% 0.33/0.63 = ( groups3504817904513533571_o_nat @ H3 @ C4 ) ) ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.same_carrier
% 0.33/0.63 thf(fact_5934_prod_Osame__carrierI,axiom,
% 0.33/0.63 ! [C4: set_o,A2: set_o,B5: set_o,G: $o > code_integer,H3: $o > code_integer] :
% 0.33/0.63 ( ( finite_finite_o @ C4 )
% 0.33/0.63 => ( ( ord_less_eq_set_o @ A2 @ C4 )
% 0.33/0.63 => ( ( ord_less_eq_set_o @ B5 @ C4 )
% 0.33/0.63 => ( ! [A3: $o] :
% 0.33/0.63 ( ( member_o @ A3 @ ( minus_minus_set_o @ C4 @ A2 ) )
% 0.33/0.63 => ( ( G @ A3 )
% 0.33/0.63 = one_one_Code_integer ) )
% 0.33/0.63 => ( ! [B2: $o] :
% 0.33/0.63 ( ( member_o @ B2 @ ( minus_minus_set_o @ C4 @ B5 ) )
% 0.33/0.63 => ( ( H3 @ B2 )
% 0.33/0.63 = one_one_Code_integer ) )
% 0.33/0.63 => ( ( ( groups7694694392188491536nteger @ G @ C4 )
% 0.33/0.63 = ( groups7694694392188491536nteger @ H3 @ C4 ) )
% 0.33/0.63 => ( ( groups7694694392188491536nteger @ G @ A2 )
% 0.33/0.63 = ( groups7694694392188491536nteger @ H3 @ B5 ) ) ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.same_carrierI
% 0.33/0.63 thf(fact_5935_prod_Osame__carrierI,axiom,
% 0.33/0.63 ! [C4: set_int,A2: set_int,B5: set_int,G: int > code_integer,H3: int > code_integer] :
% 0.33/0.63 ( ( finite_finite_int @ C4 )
% 0.33/0.63 => ( ( ord_less_eq_set_int @ A2 @ C4 )
% 0.33/0.63 => ( ( ord_less_eq_set_int @ B5 @ C4 )
% 0.33/0.63 => ( ! [A3: int] :
% 0.33/0.63 ( ( member_int @ A3 @ ( minus_minus_set_int @ C4 @ A2 ) )
% 0.33/0.63 => ( ( G @ A3 )
% 0.33/0.63 = one_one_Code_integer ) )
% 0.33/0.63 => ( ! [B2: int] :
% 0.33/0.63 ( ( member_int @ B2 @ ( minus_minus_set_int @ C4 @ B5 ) )
% 0.33/0.63 => ( ( H3 @ B2 )
% 0.33/0.63 = one_one_Code_integer ) )
% 0.33/0.63 => ( ( ( groups3827104343326376752nteger @ G @ C4 )
% 0.33/0.63 = ( groups3827104343326376752nteger @ H3 @ C4 ) )
% 0.33/0.63 => ( ( groups3827104343326376752nteger @ G @ A2 )
% 0.33/0.63 = ( groups3827104343326376752nteger @ H3 @ B5 ) ) ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.same_carrierI
% 0.33/0.63 thf(fact_5936_prod_Osame__carrierI,axiom,
% 0.33/0.63 ! [C4: set_Code_integer,A2: set_Code_integer,B5: set_Code_integer,G: code_integer > code_integer,H3: code_integer > code_integer] :
% 0.33/0.63 ( ( finite6017078050557962740nteger @ C4 )
% 0.33/0.63 => ( ( ord_le7084787975880047091nteger @ A2 @ C4 )
% 0.33/0.63 => ( ( ord_le7084787975880047091nteger @ B5 @ C4 )
% 0.33/0.63 => ( ! [A3: code_integer] :
% 0.33/0.63 ( ( member_Code_integer @ A3 @ ( minus_2355218937544613996nteger @ C4 @ A2 ) )
% 0.33/0.63 => ( ( G @ A3 )
% 0.33/0.63 = one_one_Code_integer ) )
% 0.33/0.63 => ( ! [B2: code_integer] :
% 0.33/0.63 ( ( member_Code_integer @ B2 @ ( minus_2355218937544613996nteger @ C4 @ B5 ) )
% 0.33/0.63 => ( ( H3 @ B2 )
% 0.33/0.63 = one_one_Code_integer ) )
% 0.33/0.63 => ( ( ( groups3674199335183972705nteger @ G @ C4 )
% 0.33/0.63 = ( groups3674199335183972705nteger @ H3 @ C4 ) )
% 0.33/0.63 => ( ( groups3674199335183972705nteger @ G @ A2 )
% 0.33/0.63 = ( groups3674199335183972705nteger @ H3 @ B5 ) ) ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.same_carrierI
% 0.33/0.63 thf(fact_5937_prod_Osame__carrierI,axiom,
% 0.33/0.63 ! [C4: set_o,A2: set_o,B5: set_o,G: $o > assn,H3: $o > assn] :
% 0.33/0.63 ( ( finite_finite_o @ C4 )
% 0.33/0.63 => ( ( ord_less_eq_set_o @ A2 @ C4 )
% 0.33/0.63 => ( ( ord_less_eq_set_o @ B5 @ C4 )
% 0.33/0.63 => ( ! [A3: $o] :
% 0.33/0.63 ( ( member_o @ A3 @ ( minus_minus_set_o @ C4 @ A2 ) )
% 0.33/0.63 => ( ( G @ A3 )
% 0.33/0.63 = one_one_assn ) )
% 0.33/0.63 => ( ! [B2: $o] :
% 0.33/0.63 ( ( member_o @ B2 @ ( minus_minus_set_o @ C4 @ B5 ) )
% 0.33/0.63 => ( ( H3 @ B2 )
% 0.33/0.63 = one_one_assn ) )
% 0.33/0.63 => ( ( ( groups5301882518646026715o_assn @ G @ C4 )
% 0.33/0.63 = ( groups5301882518646026715o_assn @ H3 @ C4 ) )
% 0.33/0.63 => ( ( groups5301882518646026715o_assn @ G @ A2 )
% 0.33/0.63 = ( groups5301882518646026715o_assn @ H3 @ B5 ) ) ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.same_carrierI
% 0.33/0.63 thf(fact_5938_prod_Osame__carrierI,axiom,
% 0.33/0.63 ! [C4: set_int,A2: set_int,B5: set_int,G: int > assn,H3: int > assn] :
% 0.33/0.63 ( ( finite_finite_int @ C4 )
% 0.33/0.63 => ( ( ord_less_eq_set_int @ A2 @ C4 )
% 0.33/0.63 => ( ( ord_less_eq_set_int @ B5 @ C4 )
% 0.33/0.63 => ( ! [A3: int] :
% 0.33/0.63 ( ( member_int @ A3 @ ( minus_minus_set_int @ C4 @ A2 ) )
% 0.33/0.63 => ( ( G @ A3 )
% 0.33/0.63 = one_one_assn ) )
% 0.33/0.63 => ( ! [B2: int] :
% 0.33/0.63 ( ( member_int @ B2 @ ( minus_minus_set_int @ C4 @ B5 ) )
% 0.33/0.63 => ( ( H3 @ B2 )
% 0.33/0.63 = one_one_assn ) )
% 0.33/0.63 => ( ( ( groups7882442080178216443t_assn @ G @ C4 )
% 0.33/0.63 = ( groups7882442080178216443t_assn @ H3 @ C4 ) )
% 0.33/0.63 => ( ( groups7882442080178216443t_assn @ G @ A2 )
% 0.33/0.63 = ( groups7882442080178216443t_assn @ H3 @ B5 ) ) ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.same_carrierI
% 0.33/0.63 thf(fact_5939_prod_Osame__carrierI,axiom,
% 0.33/0.63 ! [C4: set_Code_integer,A2: set_Code_integer,B5: set_Code_integer,G: code_integer > assn,H3: code_integer > assn] :
% 0.33/0.63 ( ( finite6017078050557962740nteger @ C4 )
% 0.33/0.63 => ( ( ord_le7084787975880047091nteger @ A2 @ C4 )
% 0.33/0.63 => ( ( ord_le7084787975880047091nteger @ B5 @ C4 )
% 0.33/0.63 => ( ! [A3: code_integer] :
% 0.33/0.63 ( ( member_Code_integer @ A3 @ ( minus_2355218937544613996nteger @ C4 @ A2 ) )
% 0.33/0.63 => ( ( G @ A3 )
% 0.33/0.63 = one_one_assn ) )
% 0.33/0.63 => ( ! [B2: code_integer] :
% 0.33/0.63 ( ( member_Code_integer @ B2 @ ( minus_2355218937544613996nteger @ C4 @ B5 ) )
% 0.33/0.63 => ( ( H3 @ B2 )
% 0.33/0.63 = one_one_assn ) )
% 0.33/0.63 => ( ( ( groups1304777262505850412r_assn @ G @ C4 )
% 0.33/0.63 = ( groups1304777262505850412r_assn @ H3 @ C4 ) )
% 0.33/0.63 => ( ( groups1304777262505850412r_assn @ G @ A2 )
% 0.33/0.63 = ( groups1304777262505850412r_assn @ H3 @ B5 ) ) ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.same_carrierI
% 0.33/0.63 thf(fact_5940_prod_Osame__carrierI,axiom,
% 0.33/0.63 ! [C4: set_o,A2: set_o,B5: set_o,G: $o > rat,H3: $o > rat] :
% 0.33/0.63 ( ( finite_finite_o @ C4 )
% 0.33/0.63 => ( ( ord_less_eq_set_o @ A2 @ C4 )
% 0.33/0.63 => ( ( ord_less_eq_set_o @ B5 @ C4 )
% 0.33/0.63 => ( ! [A3: $o] :
% 0.33/0.63 ( ( member_o @ A3 @ ( minus_minus_set_o @ C4 @ A2 ) )
% 0.33/0.63 => ( ( G @ A3 )
% 0.33/0.63 = one_one_rat ) )
% 0.33/0.63 => ( ! [B2: $o] :
% 0.33/0.63 ( ( member_o @ B2 @ ( minus_minus_set_o @ C4 @ B5 ) )
% 0.33/0.63 => ( ( H3 @ B2 )
% 0.33/0.63 = one_one_rat ) )
% 0.33/0.63 => ( ( ( groups2869687844427037835_o_rat @ G @ C4 )
% 0.33/0.63 = ( groups2869687844427037835_o_rat @ H3 @ C4 ) )
% 0.33/0.63 => ( ( groups2869687844427037835_o_rat @ G @ A2 )
% 0.33/0.63 = ( groups2869687844427037835_o_rat @ H3 @ B5 ) ) ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.same_carrierI
% 0.33/0.63 thf(fact_5941_prod_Osame__carrierI,axiom,
% 0.33/0.63 ! [C4: set_int,A2: set_int,B5: set_int,G: int > rat,H3: int > rat] :
% 0.33/0.63 ( ( finite_finite_int @ C4 )
% 0.33/0.63 => ( ( ord_less_eq_set_int @ A2 @ C4 )
% 0.33/0.63 => ( ( ord_less_eq_set_int @ B5 @ C4 )
% 0.33/0.63 => ( ! [A3: int] :
% 0.33/0.63 ( ( member_int @ A3 @ ( minus_minus_set_int @ C4 @ A2 ) )
% 0.33/0.63 => ( ( G @ A3 )
% 0.33/0.63 = one_one_rat ) )
% 0.33/0.63 => ( ! [B2: int] :
% 0.33/0.63 ( ( member_int @ B2 @ ( minus_minus_set_int @ C4 @ B5 ) )
% 0.33/0.63 => ( ( H3 @ B2 )
% 0.33/0.63 = one_one_rat ) )
% 0.33/0.63 => ( ( ( groups1072433553688619179nt_rat @ G @ C4 )
% 0.33/0.63 = ( groups1072433553688619179nt_rat @ H3 @ C4 ) )
% 0.33/0.63 => ( ( groups1072433553688619179nt_rat @ G @ A2 )
% 0.33/0.63 = ( groups1072433553688619179nt_rat @ H3 @ B5 ) ) ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.same_carrierI
% 0.33/0.63 thf(fact_5942_prod_Osame__carrierI,axiom,
% 0.33/0.63 ! [C4: set_Code_integer,A2: set_Code_integer,B5: set_Code_integer,G: code_integer > rat,H3: code_integer > rat] :
% 0.33/0.63 ( ( finite6017078050557962740nteger @ C4 )
% 0.33/0.63 => ( ( ord_le7084787975880047091nteger @ A2 @ C4 )
% 0.33/0.63 => ( ( ord_le7084787975880047091nteger @ B5 @ C4 )
% 0.33/0.63 => ( ! [A3: code_integer] :
% 0.33/0.63 ( ( member_Code_integer @ A3 @ ( minus_2355218937544613996nteger @ C4 @ A2 ) )
% 0.33/0.63 => ( ( G @ A3 )
% 0.33/0.63 = one_one_rat ) )
% 0.33/0.63 => ( ! [B2: code_integer] :
% 0.33/0.63 ( ( member_Code_integer @ B2 @ ( minus_2355218937544613996nteger @ C4 @ B5 ) )
% 0.33/0.63 => ( ( H3 @ B2 )
% 0.33/0.63 = one_one_rat ) )
% 0.33/0.63 => ( ( ( groups2555765274223993564er_rat @ G @ C4 )
% 0.33/0.63 = ( groups2555765274223993564er_rat @ H3 @ C4 ) )
% 0.33/0.63 => ( ( groups2555765274223993564er_rat @ G @ A2 )
% 0.33/0.63 = ( groups2555765274223993564er_rat @ H3 @ B5 ) ) ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.same_carrierI
% 0.33/0.63 thf(fact_5943_prod_Osame__carrierI,axiom,
% 0.33/0.63 ! [C4: set_o,A2: set_o,B5: set_o,G: $o > nat,H3: $o > nat] :
% 0.33/0.63 ( ( finite_finite_o @ C4 )
% 0.33/0.63 => ( ( ord_less_eq_set_o @ A2 @ C4 )
% 0.33/0.63 => ( ( ord_less_eq_set_o @ B5 @ C4 )
% 0.33/0.63 => ( ! [A3: $o] :
% 0.33/0.63 ( ( member_o @ A3 @ ( minus_minus_set_o @ C4 @ A2 ) )
% 0.33/0.63 => ( ( G @ A3 )
% 0.33/0.63 = one_one_nat ) )
% 0.33/0.63 => ( ! [B2: $o] :
% 0.33/0.63 ( ( member_o @ B2 @ ( minus_minus_set_o @ C4 @ B5 ) )
% 0.33/0.63 => ( ( H3 @ B2 )
% 0.33/0.63 = one_one_nat ) )
% 0.33/0.63 => ( ( ( groups3504817904513533571_o_nat @ G @ C4 )
% 0.33/0.63 = ( groups3504817904513533571_o_nat @ H3 @ C4 ) )
% 0.33/0.63 => ( ( groups3504817904513533571_o_nat @ G @ A2 )
% 0.33/0.63 = ( groups3504817904513533571_o_nat @ H3 @ B5 ) ) ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.same_carrierI
% 0.33/0.63 thf(fact_5944_prod_Omono__neutral__left,axiom,
% 0.33/0.63 ! [T5: set_int,S2: set_int,G: int > code_integer] :
% 0.33/0.63 ( ( finite_finite_int @ T5 )
% 0.33/0.63 => ( ( ord_less_eq_set_int @ S2 @ T5 )
% 0.33/0.63 => ( ! [X4: int] :
% 0.33/0.63 ( ( member_int @ X4 @ ( minus_minus_set_int @ T5 @ S2 ) )
% 0.33/0.63 => ( ( G @ X4 )
% 0.33/0.63 = one_one_Code_integer ) )
% 0.33/0.63 => ( ( groups3827104343326376752nteger @ G @ S2 )
% 0.33/0.63 = ( groups3827104343326376752nteger @ G @ T5 ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.mono_neutral_left
% 0.33/0.63 thf(fact_5945_prod_Omono__neutral__left,axiom,
% 0.33/0.63 ! [T5: set_Code_integer,S2: set_Code_integer,G: code_integer > code_integer] :
% 0.33/0.63 ( ( finite6017078050557962740nteger @ T5 )
% 0.33/0.63 => ( ( ord_le7084787975880047091nteger @ S2 @ T5 )
% 0.33/0.63 => ( ! [X4: code_integer] :
% 0.33/0.63 ( ( member_Code_integer @ X4 @ ( minus_2355218937544613996nteger @ T5 @ S2 ) )
% 0.33/0.63 => ( ( G @ X4 )
% 0.33/0.63 = one_one_Code_integer ) )
% 0.33/0.63 => ( ( groups3674199335183972705nteger @ G @ S2 )
% 0.33/0.63 = ( groups3674199335183972705nteger @ G @ T5 ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.mono_neutral_left
% 0.33/0.63 thf(fact_5946_prod_Omono__neutral__left,axiom,
% 0.33/0.63 ! [T5: set_int,S2: set_int,G: int > assn] :
% 0.33/0.63 ( ( finite_finite_int @ T5 )
% 0.33/0.63 => ( ( ord_less_eq_set_int @ S2 @ T5 )
% 0.33/0.63 => ( ! [X4: int] :
% 0.33/0.63 ( ( member_int @ X4 @ ( minus_minus_set_int @ T5 @ S2 ) )
% 0.33/0.63 => ( ( G @ X4 )
% 0.33/0.63 = one_one_assn ) )
% 0.33/0.63 => ( ( groups7882442080178216443t_assn @ G @ S2 )
% 0.33/0.63 = ( groups7882442080178216443t_assn @ G @ T5 ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.mono_neutral_left
% 0.33/0.63 thf(fact_5947_prod_Omono__neutral__left,axiom,
% 0.33/0.63 ! [T5: set_Code_integer,S2: set_Code_integer,G: code_integer > assn] :
% 0.33/0.63 ( ( finite6017078050557962740nteger @ T5 )
% 0.33/0.63 => ( ( ord_le7084787975880047091nteger @ S2 @ T5 )
% 0.33/0.63 => ( ! [X4: code_integer] :
% 0.33/0.63 ( ( member_Code_integer @ X4 @ ( minus_2355218937544613996nteger @ T5 @ S2 ) )
% 0.33/0.63 => ( ( G @ X4 )
% 0.33/0.63 = one_one_assn ) )
% 0.33/0.63 => ( ( groups1304777262505850412r_assn @ G @ S2 )
% 0.33/0.63 = ( groups1304777262505850412r_assn @ G @ T5 ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.mono_neutral_left
% 0.33/0.63 thf(fact_5948_prod_Omono__neutral__left,axiom,
% 0.33/0.63 ! [T5: set_int,S2: set_int,G: int > rat] :
% 0.33/0.63 ( ( finite_finite_int @ T5 )
% 0.33/0.63 => ( ( ord_less_eq_set_int @ S2 @ T5 )
% 0.33/0.63 => ( ! [X4: int] :
% 0.33/0.63 ( ( member_int @ X4 @ ( minus_minus_set_int @ T5 @ S2 ) )
% 0.33/0.63 => ( ( G @ X4 )
% 0.33/0.63 = one_one_rat ) )
% 0.33/0.63 => ( ( groups1072433553688619179nt_rat @ G @ S2 )
% 0.33/0.63 = ( groups1072433553688619179nt_rat @ G @ T5 ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.mono_neutral_left
% 0.33/0.63 thf(fact_5949_prod_Omono__neutral__left,axiom,
% 0.33/0.63 ! [T5: set_Code_integer,S2: set_Code_integer,G: code_integer > rat] :
% 0.33/0.63 ( ( finite6017078050557962740nteger @ T5 )
% 0.33/0.63 => ( ( ord_le7084787975880047091nteger @ S2 @ T5 )
% 0.33/0.63 => ( ! [X4: code_integer] :
% 0.33/0.63 ( ( member_Code_integer @ X4 @ ( minus_2355218937544613996nteger @ T5 @ S2 ) )
% 0.33/0.63 => ( ( G @ X4 )
% 0.33/0.63 = one_one_rat ) )
% 0.33/0.63 => ( ( groups2555765274223993564er_rat @ G @ S2 )
% 0.33/0.63 = ( groups2555765274223993564er_rat @ G @ T5 ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.mono_neutral_left
% 0.33/0.63 thf(fact_5950_prod_Omono__neutral__left,axiom,
% 0.33/0.63 ! [T5: set_int,S2: set_int,G: int > nat] :
% 0.33/0.63 ( ( finite_finite_int @ T5 )
% 0.33/0.63 => ( ( ord_less_eq_set_int @ S2 @ T5 )
% 0.33/0.63 => ( ! [X4: int] :
% 0.33/0.63 ( ( member_int @ X4 @ ( minus_minus_set_int @ T5 @ S2 ) )
% 0.33/0.63 => ( ( G @ X4 )
% 0.33/0.63 = one_one_nat ) )
% 0.33/0.63 => ( ( groups1707563613775114915nt_nat @ G @ S2 )
% 0.33/0.63 = ( groups1707563613775114915nt_nat @ G @ T5 ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.mono_neutral_left
% 0.33/0.63 thf(fact_5951_prod_Omono__neutral__left,axiom,
% 0.33/0.63 ! [T5: set_Code_integer,S2: set_Code_integer,G: code_integer > nat] :
% 0.33/0.63 ( ( finite6017078050557962740nteger @ T5 )
% 0.33/0.63 => ( ( ord_le7084787975880047091nteger @ S2 @ T5 )
% 0.33/0.63 => ( ! [X4: code_integer] :
% 0.33/0.63 ( ( member_Code_integer @ X4 @ ( minus_2355218937544613996nteger @ T5 @ S2 ) )
% 0.33/0.63 => ( ( G @ X4 )
% 0.33/0.63 = one_one_nat ) )
% 0.33/0.63 => ( ( groups3190895334310489300er_nat @ G @ S2 )
% 0.33/0.63 = ( groups3190895334310489300er_nat @ G @ T5 ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.mono_neutral_left
% 0.33/0.63 thf(fact_5952_prod_Omono__neutral__left,axiom,
% 0.33/0.63 ! [T5: set_Code_integer,S2: set_Code_integer,G: code_integer > int] :
% 0.33/0.63 ( ( finite6017078050557962740nteger @ T5 )
% 0.33/0.63 => ( ( ord_le7084787975880047091nteger @ S2 @ T5 )
% 0.33/0.63 => ( ! [X4: code_integer] :
% 0.33/0.63 ( ( member_Code_integer @ X4 @ ( minus_2355218937544613996nteger @ T5 @ S2 ) )
% 0.33/0.63 => ( ( G @ X4 )
% 0.33/0.63 = one_one_int ) )
% 0.33/0.63 => ( ( groups3188404863801439024er_int @ G @ S2 )
% 0.33/0.63 = ( groups3188404863801439024er_int @ G @ T5 ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.mono_neutral_left
% 0.33/0.63 thf(fact_5953_prod_Omono__neutral__left,axiom,
% 0.33/0.63 ! [T5: set_nat,S2: set_nat,G: nat > code_integer] :
% 0.33/0.63 ( ( finite_finite_nat @ T5 )
% 0.33/0.63 => ( ( ord_less_eq_set_nat @ S2 @ T5 )
% 0.33/0.63 => ( ! [X4: nat] :
% 0.33/0.63 ( ( member_nat @ X4 @ ( minus_minus_set_nat @ T5 @ S2 ) )
% 0.33/0.63 => ( ( G @ X4 )
% 0.33/0.63 = one_one_Code_integer ) )
% 0.33/0.63 => ( ( groups3455450783089532116nteger @ G @ S2 )
% 0.33/0.63 = ( groups3455450783089532116nteger @ G @ T5 ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.mono_neutral_left
% 0.33/0.63 thf(fact_5954_prod_Omono__neutral__right,axiom,
% 0.33/0.63 ! [T5: set_int,S2: set_int,G: int > code_integer] :
% 0.33/0.63 ( ( finite_finite_int @ T5 )
% 0.33/0.63 => ( ( ord_less_eq_set_int @ S2 @ T5 )
% 0.33/0.63 => ( ! [X4: int] :
% 0.33/0.63 ( ( member_int @ X4 @ ( minus_minus_set_int @ T5 @ S2 ) )
% 0.33/0.63 => ( ( G @ X4 )
% 0.33/0.63 = one_one_Code_integer ) )
% 0.33/0.63 => ( ( groups3827104343326376752nteger @ G @ T5 )
% 0.33/0.63 = ( groups3827104343326376752nteger @ G @ S2 ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.mono_neutral_right
% 0.33/0.63 thf(fact_5955_prod_Omono__neutral__right,axiom,
% 0.33/0.63 ! [T5: set_Code_integer,S2: set_Code_integer,G: code_integer > code_integer] :
% 0.33/0.63 ( ( finite6017078050557962740nteger @ T5 )
% 0.33/0.63 => ( ( ord_le7084787975880047091nteger @ S2 @ T5 )
% 0.33/0.63 => ( ! [X4: code_integer] :
% 0.33/0.63 ( ( member_Code_integer @ X4 @ ( minus_2355218937544613996nteger @ T5 @ S2 ) )
% 0.33/0.63 => ( ( G @ X4 )
% 0.33/0.63 = one_one_Code_integer ) )
% 0.33/0.63 => ( ( groups3674199335183972705nteger @ G @ T5 )
% 0.33/0.63 = ( groups3674199335183972705nteger @ G @ S2 ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.mono_neutral_right
% 0.33/0.63 thf(fact_5956_prod_Omono__neutral__right,axiom,
% 0.33/0.63 ! [T5: set_int,S2: set_int,G: int > assn] :
% 0.33/0.63 ( ( finite_finite_int @ T5 )
% 0.33/0.63 => ( ( ord_less_eq_set_int @ S2 @ T5 )
% 0.33/0.63 => ( ! [X4: int] :
% 0.33/0.63 ( ( member_int @ X4 @ ( minus_minus_set_int @ T5 @ S2 ) )
% 0.33/0.63 => ( ( G @ X4 )
% 0.33/0.63 = one_one_assn ) )
% 0.33/0.63 => ( ( groups7882442080178216443t_assn @ G @ T5 )
% 0.33/0.63 = ( groups7882442080178216443t_assn @ G @ S2 ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.mono_neutral_right
% 0.33/0.63 thf(fact_5957_prod_Omono__neutral__right,axiom,
% 0.33/0.63 ! [T5: set_Code_integer,S2: set_Code_integer,G: code_integer > assn] :
% 0.33/0.63 ( ( finite6017078050557962740nteger @ T5 )
% 0.33/0.63 => ( ( ord_le7084787975880047091nteger @ S2 @ T5 )
% 0.33/0.63 => ( ! [X4: code_integer] :
% 0.33/0.63 ( ( member_Code_integer @ X4 @ ( minus_2355218937544613996nteger @ T5 @ S2 ) )
% 0.33/0.63 => ( ( G @ X4 )
% 0.33/0.63 = one_one_assn ) )
% 0.33/0.63 => ( ( groups1304777262505850412r_assn @ G @ T5 )
% 0.33/0.63 = ( groups1304777262505850412r_assn @ G @ S2 ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.mono_neutral_right
% 0.33/0.63 thf(fact_5958_prod_Omono__neutral__right,axiom,
% 0.33/0.63 ! [T5: set_int,S2: set_int,G: int > rat] :
% 0.33/0.63 ( ( finite_finite_int @ T5 )
% 0.33/0.63 => ( ( ord_less_eq_set_int @ S2 @ T5 )
% 0.33/0.63 => ( ! [X4: int] :
% 0.33/0.63 ( ( member_int @ X4 @ ( minus_minus_set_int @ T5 @ S2 ) )
% 0.33/0.63 => ( ( G @ X4 )
% 0.33/0.63 = one_one_rat ) )
% 0.33/0.63 => ( ( groups1072433553688619179nt_rat @ G @ T5 )
% 0.33/0.63 = ( groups1072433553688619179nt_rat @ G @ S2 ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.mono_neutral_right
% 0.33/0.63 thf(fact_5959_prod_Omono__neutral__right,axiom,
% 0.33/0.63 ! [T5: set_Code_integer,S2: set_Code_integer,G: code_integer > rat] :
% 0.33/0.63 ( ( finite6017078050557962740nteger @ T5 )
% 0.33/0.63 => ( ( ord_le7084787975880047091nteger @ S2 @ T5 )
% 0.33/0.63 => ( ! [X4: code_integer] :
% 0.33/0.63 ( ( member_Code_integer @ X4 @ ( minus_2355218937544613996nteger @ T5 @ S2 ) )
% 0.33/0.63 => ( ( G @ X4 )
% 0.33/0.63 = one_one_rat ) )
% 0.33/0.63 => ( ( groups2555765274223993564er_rat @ G @ T5 )
% 0.33/0.63 = ( groups2555765274223993564er_rat @ G @ S2 ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.mono_neutral_right
% 0.33/0.63 thf(fact_5960_prod_Omono__neutral__right,axiom,
% 0.33/0.63 ! [T5: set_int,S2: set_int,G: int > nat] :
% 0.33/0.63 ( ( finite_finite_int @ T5 )
% 0.33/0.63 => ( ( ord_less_eq_set_int @ S2 @ T5 )
% 0.33/0.63 => ( ! [X4: int] :
% 0.33/0.63 ( ( member_int @ X4 @ ( minus_minus_set_int @ T5 @ S2 ) )
% 0.33/0.63 => ( ( G @ X4 )
% 0.33/0.63 = one_one_nat ) )
% 0.33/0.63 => ( ( groups1707563613775114915nt_nat @ G @ T5 )
% 0.33/0.63 = ( groups1707563613775114915nt_nat @ G @ S2 ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.mono_neutral_right
% 0.33/0.63 thf(fact_5961_prod_Omono__neutral__right,axiom,
% 0.33/0.63 ! [T5: set_Code_integer,S2: set_Code_integer,G: code_integer > nat] :
% 0.33/0.63 ( ( finite6017078050557962740nteger @ T5 )
% 0.33/0.63 => ( ( ord_le7084787975880047091nteger @ S2 @ T5 )
% 0.33/0.63 => ( ! [X4: code_integer] :
% 0.33/0.63 ( ( member_Code_integer @ X4 @ ( minus_2355218937544613996nteger @ T5 @ S2 ) )
% 0.33/0.63 => ( ( G @ X4 )
% 0.33/0.63 = one_one_nat ) )
% 0.33/0.63 => ( ( groups3190895334310489300er_nat @ G @ T5 )
% 0.33/0.63 = ( groups3190895334310489300er_nat @ G @ S2 ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.mono_neutral_right
% 0.33/0.63 thf(fact_5962_prod_Omono__neutral__right,axiom,
% 0.33/0.63 ! [T5: set_Code_integer,S2: set_Code_integer,G: code_integer > int] :
% 0.33/0.63 ( ( finite6017078050557962740nteger @ T5 )
% 0.33/0.63 => ( ( ord_le7084787975880047091nteger @ S2 @ T5 )
% 0.33/0.63 => ( ! [X4: code_integer] :
% 0.33/0.63 ( ( member_Code_integer @ X4 @ ( minus_2355218937544613996nteger @ T5 @ S2 ) )
% 0.33/0.63 => ( ( G @ X4 )
% 0.33/0.63 = one_one_int ) )
% 0.33/0.63 => ( ( groups3188404863801439024er_int @ G @ T5 )
% 0.33/0.63 = ( groups3188404863801439024er_int @ G @ S2 ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.mono_neutral_right
% 0.33/0.63 thf(fact_5963_prod_Omono__neutral__right,axiom,
% 0.33/0.63 ! [T5: set_nat,S2: set_nat,G: nat > code_integer] :
% 0.33/0.63 ( ( finite_finite_nat @ T5 )
% 0.33/0.63 => ( ( ord_less_eq_set_nat @ S2 @ T5 )
% 0.33/0.63 => ( ! [X4: nat] :
% 0.33/0.63 ( ( member_nat @ X4 @ ( minus_minus_set_nat @ T5 @ S2 ) )
% 0.33/0.63 => ( ( G @ X4 )
% 0.33/0.63 = one_one_Code_integer ) )
% 0.33/0.63 => ( ( groups3455450783089532116nteger @ G @ T5 )
% 0.33/0.63 = ( groups3455450783089532116nteger @ G @ S2 ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.mono_neutral_right
% 0.33/0.63 thf(fact_5964_prod_Omono__neutral__cong__left,axiom,
% 0.33/0.63 ! [T5: set_o,S2: set_o,H3: $o > code_integer,G: $o > code_integer] :
% 0.33/0.63 ( ( finite_finite_o @ T5 )
% 0.33/0.63 => ( ( ord_less_eq_set_o @ S2 @ T5 )
% 0.33/0.63 => ( ! [X4: $o] :
% 0.33/0.63 ( ( member_o @ X4 @ ( minus_minus_set_o @ T5 @ S2 ) )
% 0.33/0.63 => ( ( H3 @ X4 )
% 0.33/0.63 = one_one_Code_integer ) )
% 0.33/0.63 => ( ! [X4: $o] :
% 0.33/0.63 ( ( member_o @ X4 @ S2 )
% 0.33/0.63 => ( ( G @ X4 )
% 0.33/0.63 = ( H3 @ X4 ) ) )
% 0.33/0.63 => ( ( groups7694694392188491536nteger @ G @ S2 )
% 0.33/0.63 = ( groups7694694392188491536nteger @ H3 @ T5 ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.mono_neutral_cong_left
% 0.33/0.63 thf(fact_5965_prod_Omono__neutral__cong__left,axiom,
% 0.33/0.63 ! [T5: set_int,S2: set_int,H3: int > code_integer,G: int > code_integer] :
% 0.33/0.63 ( ( finite_finite_int @ T5 )
% 0.33/0.63 => ( ( ord_less_eq_set_int @ S2 @ T5 )
% 0.33/0.63 => ( ! [X4: int] :
% 0.33/0.63 ( ( member_int @ X4 @ ( minus_minus_set_int @ T5 @ S2 ) )
% 0.33/0.63 => ( ( H3 @ X4 )
% 0.33/0.63 = one_one_Code_integer ) )
% 0.33/0.63 => ( ! [X4: int] :
% 0.33/0.63 ( ( member_int @ X4 @ S2 )
% 0.33/0.63 => ( ( G @ X4 )
% 0.33/0.63 = ( H3 @ X4 ) ) )
% 0.33/0.63 => ( ( groups3827104343326376752nteger @ G @ S2 )
% 0.33/0.63 = ( groups3827104343326376752nteger @ H3 @ T5 ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.mono_neutral_cong_left
% 0.33/0.63 thf(fact_5966_prod_Omono__neutral__cong__left,axiom,
% 0.33/0.63 ! [T5: set_Code_integer,S2: set_Code_integer,H3: code_integer > code_integer,G: code_integer > code_integer] :
% 0.33/0.63 ( ( finite6017078050557962740nteger @ T5 )
% 0.33/0.63 => ( ( ord_le7084787975880047091nteger @ S2 @ T5 )
% 0.33/0.63 => ( ! [X4: code_integer] :
% 0.33/0.63 ( ( member_Code_integer @ X4 @ ( minus_2355218937544613996nteger @ T5 @ S2 ) )
% 0.33/0.63 => ( ( H3 @ X4 )
% 0.33/0.63 = one_one_Code_integer ) )
% 0.33/0.63 => ( ! [X4: code_integer] :
% 0.33/0.63 ( ( member_Code_integer @ X4 @ S2 )
% 0.33/0.63 => ( ( G @ X4 )
% 0.33/0.63 = ( H3 @ X4 ) ) )
% 0.33/0.63 => ( ( groups3674199335183972705nteger @ G @ S2 )
% 0.33/0.63 = ( groups3674199335183972705nteger @ H3 @ T5 ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.mono_neutral_cong_left
% 0.33/0.63 thf(fact_5967_prod_Omono__neutral__cong__left,axiom,
% 0.33/0.63 ! [T5: set_o,S2: set_o,H3: $o > assn,G: $o > assn] :
% 0.33/0.63 ( ( finite_finite_o @ T5 )
% 0.33/0.63 => ( ( ord_less_eq_set_o @ S2 @ T5 )
% 0.33/0.63 => ( ! [X4: $o] :
% 0.33/0.63 ( ( member_o @ X4 @ ( minus_minus_set_o @ T5 @ S2 ) )
% 0.33/0.63 => ( ( H3 @ X4 )
% 0.33/0.63 = one_one_assn ) )
% 0.33/0.63 => ( ! [X4: $o] :
% 0.33/0.63 ( ( member_o @ X4 @ S2 )
% 0.33/0.63 => ( ( G @ X4 )
% 0.33/0.63 = ( H3 @ X4 ) ) )
% 0.33/0.63 => ( ( groups5301882518646026715o_assn @ G @ S2 )
% 0.33/0.63 = ( groups5301882518646026715o_assn @ H3 @ T5 ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.mono_neutral_cong_left
% 0.33/0.63 thf(fact_5968_prod_Omono__neutral__cong__left,axiom,
% 0.33/0.63 ! [T5: set_int,S2: set_int,H3: int > assn,G: int > assn] :
% 0.33/0.63 ( ( finite_finite_int @ T5 )
% 0.33/0.63 => ( ( ord_less_eq_set_int @ S2 @ T5 )
% 0.33/0.63 => ( ! [X4: int] :
% 0.33/0.63 ( ( member_int @ X4 @ ( minus_minus_set_int @ T5 @ S2 ) )
% 0.33/0.63 => ( ( H3 @ X4 )
% 0.33/0.63 = one_one_assn ) )
% 0.33/0.63 => ( ! [X4: int] :
% 0.33/0.63 ( ( member_int @ X4 @ S2 )
% 0.33/0.63 => ( ( G @ X4 )
% 0.33/0.63 = ( H3 @ X4 ) ) )
% 0.33/0.63 => ( ( groups7882442080178216443t_assn @ G @ S2 )
% 0.33/0.63 = ( groups7882442080178216443t_assn @ H3 @ T5 ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.mono_neutral_cong_left
% 0.33/0.63 thf(fact_5969_prod_Omono__neutral__cong__left,axiom,
% 0.33/0.63 ! [T5: set_Code_integer,S2: set_Code_integer,H3: code_integer > assn,G: code_integer > assn] :
% 0.33/0.63 ( ( finite6017078050557962740nteger @ T5 )
% 0.33/0.63 => ( ( ord_le7084787975880047091nteger @ S2 @ T5 )
% 0.33/0.63 => ( ! [X4: code_integer] :
% 0.33/0.63 ( ( member_Code_integer @ X4 @ ( minus_2355218937544613996nteger @ T5 @ S2 ) )
% 0.33/0.63 => ( ( H3 @ X4 )
% 0.33/0.63 = one_one_assn ) )
% 0.33/0.63 => ( ! [X4: code_integer] :
% 0.33/0.63 ( ( member_Code_integer @ X4 @ S2 )
% 0.33/0.63 => ( ( G @ X4 )
% 0.33/0.63 = ( H3 @ X4 ) ) )
% 0.33/0.63 => ( ( groups1304777262505850412r_assn @ G @ S2 )
% 0.33/0.63 = ( groups1304777262505850412r_assn @ H3 @ T5 ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.mono_neutral_cong_left
% 0.33/0.63 thf(fact_5970_prod_Omono__neutral__cong__left,axiom,
% 0.33/0.63 ! [T5: set_o,S2: set_o,H3: $o > rat,G: $o > rat] :
% 0.33/0.63 ( ( finite_finite_o @ T5 )
% 0.33/0.63 => ( ( ord_less_eq_set_o @ S2 @ T5 )
% 0.33/0.63 => ( ! [X4: $o] :
% 0.33/0.63 ( ( member_o @ X4 @ ( minus_minus_set_o @ T5 @ S2 ) )
% 0.33/0.63 => ( ( H3 @ X4 )
% 0.33/0.63 = one_one_rat ) )
% 0.33/0.63 => ( ! [X4: $o] :
% 0.33/0.63 ( ( member_o @ X4 @ S2 )
% 0.33/0.63 => ( ( G @ X4 )
% 0.33/0.63 = ( H3 @ X4 ) ) )
% 0.33/0.63 => ( ( groups2869687844427037835_o_rat @ G @ S2 )
% 0.33/0.63 = ( groups2869687844427037835_o_rat @ H3 @ T5 ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.mono_neutral_cong_left
% 0.33/0.63 thf(fact_5971_prod_Omono__neutral__cong__left,axiom,
% 0.33/0.63 ! [T5: set_int,S2: set_int,H3: int > rat,G: int > rat] :
% 0.33/0.63 ( ( finite_finite_int @ T5 )
% 0.33/0.63 => ( ( ord_less_eq_set_int @ S2 @ T5 )
% 0.33/0.63 => ( ! [X4: int] :
% 0.33/0.63 ( ( member_int @ X4 @ ( minus_minus_set_int @ T5 @ S2 ) )
% 0.33/0.63 => ( ( H3 @ X4 )
% 0.33/0.63 = one_one_rat ) )
% 0.33/0.63 => ( ! [X4: int] :
% 0.33/0.63 ( ( member_int @ X4 @ S2 )
% 0.33/0.63 => ( ( G @ X4 )
% 0.33/0.63 = ( H3 @ X4 ) ) )
% 0.33/0.63 => ( ( groups1072433553688619179nt_rat @ G @ S2 )
% 0.33/0.63 = ( groups1072433553688619179nt_rat @ H3 @ T5 ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.mono_neutral_cong_left
% 0.33/0.63 thf(fact_5972_prod_Omono__neutral__cong__left,axiom,
% 0.33/0.63 ! [T5: set_Code_integer,S2: set_Code_integer,H3: code_integer > rat,G: code_integer > rat] :
% 0.33/0.63 ( ( finite6017078050557962740nteger @ T5 )
% 0.33/0.63 => ( ( ord_le7084787975880047091nteger @ S2 @ T5 )
% 0.33/0.63 => ( ! [X4: code_integer] :
% 0.33/0.63 ( ( member_Code_integer @ X4 @ ( minus_2355218937544613996nteger @ T5 @ S2 ) )
% 0.33/0.63 => ( ( H3 @ X4 )
% 0.33/0.63 = one_one_rat ) )
% 0.33/0.63 => ( ! [X4: code_integer] :
% 0.33/0.63 ( ( member_Code_integer @ X4 @ S2 )
% 0.33/0.63 => ( ( G @ X4 )
% 0.33/0.63 = ( H3 @ X4 ) ) )
% 0.33/0.63 => ( ( groups2555765274223993564er_rat @ G @ S2 )
% 0.33/0.63 = ( groups2555765274223993564er_rat @ H3 @ T5 ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.mono_neutral_cong_left
% 0.33/0.63 thf(fact_5973_prod_Omono__neutral__cong__left,axiom,
% 0.33/0.63 ! [T5: set_o,S2: set_o,H3: $o > nat,G: $o > nat] :
% 0.33/0.63 ( ( finite_finite_o @ T5 )
% 0.33/0.63 => ( ( ord_less_eq_set_o @ S2 @ T5 )
% 0.33/0.63 => ( ! [X4: $o] :
% 0.33/0.63 ( ( member_o @ X4 @ ( minus_minus_set_o @ T5 @ S2 ) )
% 0.33/0.63 => ( ( H3 @ X4 )
% 0.33/0.63 = one_one_nat ) )
% 0.33/0.63 => ( ! [X4: $o] :
% 0.33/0.63 ( ( member_o @ X4 @ S2 )
% 0.33/0.63 => ( ( G @ X4 )
% 0.33/0.63 = ( H3 @ X4 ) ) )
% 0.33/0.63 => ( ( groups3504817904513533571_o_nat @ G @ S2 )
% 0.33/0.63 = ( groups3504817904513533571_o_nat @ H3 @ T5 ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.mono_neutral_cong_left
% 0.33/0.63 thf(fact_5974_prod_Omono__neutral__cong__right,axiom,
% 0.33/0.63 ! [T5: set_o,S2: set_o,G: $o > code_integer,H3: $o > code_integer] :
% 0.33/0.63 ( ( finite_finite_o @ T5 )
% 0.33/0.63 => ( ( ord_less_eq_set_o @ S2 @ T5 )
% 0.33/0.63 => ( ! [X4: $o] :
% 0.33/0.63 ( ( member_o @ X4 @ ( minus_minus_set_o @ T5 @ S2 ) )
% 0.33/0.63 => ( ( G @ X4 )
% 0.33/0.63 = one_one_Code_integer ) )
% 0.33/0.63 => ( ! [X4: $o] :
% 0.33/0.63 ( ( member_o @ X4 @ S2 )
% 0.33/0.63 => ( ( G @ X4 )
% 0.33/0.63 = ( H3 @ X4 ) ) )
% 0.33/0.63 => ( ( groups7694694392188491536nteger @ G @ T5 )
% 0.33/0.63 = ( groups7694694392188491536nteger @ H3 @ S2 ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.mono_neutral_cong_right
% 0.33/0.63 thf(fact_5975_prod_Omono__neutral__cong__right,axiom,
% 0.33/0.63 ! [T5: set_int,S2: set_int,G: int > code_integer,H3: int > code_integer] :
% 0.33/0.63 ( ( finite_finite_int @ T5 )
% 0.33/0.63 => ( ( ord_less_eq_set_int @ S2 @ T5 )
% 0.33/0.63 => ( ! [X4: int] :
% 0.33/0.63 ( ( member_int @ X4 @ ( minus_minus_set_int @ T5 @ S2 ) )
% 0.33/0.63 => ( ( G @ X4 )
% 0.33/0.63 = one_one_Code_integer ) )
% 0.33/0.63 => ( ! [X4: int] :
% 0.33/0.63 ( ( member_int @ X4 @ S2 )
% 0.33/0.63 => ( ( G @ X4 )
% 0.33/0.63 = ( H3 @ X4 ) ) )
% 0.33/0.63 => ( ( groups3827104343326376752nteger @ G @ T5 )
% 0.33/0.63 = ( groups3827104343326376752nteger @ H3 @ S2 ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.mono_neutral_cong_right
% 0.33/0.63 thf(fact_5976_prod_Omono__neutral__cong__right,axiom,
% 0.33/0.63 ! [T5: set_Code_integer,S2: set_Code_integer,G: code_integer > code_integer,H3: code_integer > code_integer] :
% 0.33/0.63 ( ( finite6017078050557962740nteger @ T5 )
% 0.33/0.63 => ( ( ord_le7084787975880047091nteger @ S2 @ T5 )
% 0.33/0.63 => ( ! [X4: code_integer] :
% 0.33/0.63 ( ( member_Code_integer @ X4 @ ( minus_2355218937544613996nteger @ T5 @ S2 ) )
% 0.33/0.63 => ( ( G @ X4 )
% 0.33/0.63 = one_one_Code_integer ) )
% 0.33/0.63 => ( ! [X4: code_integer] :
% 0.33/0.63 ( ( member_Code_integer @ X4 @ S2 )
% 0.33/0.63 => ( ( G @ X4 )
% 0.33/0.63 = ( H3 @ X4 ) ) )
% 0.33/0.63 => ( ( groups3674199335183972705nteger @ G @ T5 )
% 0.33/0.63 = ( groups3674199335183972705nteger @ H3 @ S2 ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.mono_neutral_cong_right
% 0.33/0.63 thf(fact_5977_prod_Omono__neutral__cong__right,axiom,
% 0.33/0.63 ! [T5: set_o,S2: set_o,G: $o > assn,H3: $o > assn] :
% 0.33/0.63 ( ( finite_finite_o @ T5 )
% 0.33/0.63 => ( ( ord_less_eq_set_o @ S2 @ T5 )
% 0.33/0.63 => ( ! [X4: $o] :
% 0.33/0.63 ( ( member_o @ X4 @ ( minus_minus_set_o @ T5 @ S2 ) )
% 0.33/0.63 => ( ( G @ X4 )
% 0.33/0.63 = one_one_assn ) )
% 0.33/0.63 => ( ! [X4: $o] :
% 0.33/0.63 ( ( member_o @ X4 @ S2 )
% 0.33/0.63 => ( ( G @ X4 )
% 0.33/0.63 = ( H3 @ X4 ) ) )
% 0.33/0.63 => ( ( groups5301882518646026715o_assn @ G @ T5 )
% 0.33/0.63 = ( groups5301882518646026715o_assn @ H3 @ S2 ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.mono_neutral_cong_right
% 0.33/0.63 thf(fact_5978_prod_Omono__neutral__cong__right,axiom,
% 0.33/0.63 ! [T5: set_int,S2: set_int,G: int > assn,H3: int > assn] :
% 0.33/0.63 ( ( finite_finite_int @ T5 )
% 0.33/0.63 => ( ( ord_less_eq_set_int @ S2 @ T5 )
% 0.33/0.63 => ( ! [X4: int] :
% 0.33/0.63 ( ( member_int @ X4 @ ( minus_minus_set_int @ T5 @ S2 ) )
% 0.33/0.63 => ( ( G @ X4 )
% 0.33/0.63 = one_one_assn ) )
% 0.33/0.63 => ( ! [X4: int] :
% 0.33/0.63 ( ( member_int @ X4 @ S2 )
% 0.33/0.63 => ( ( G @ X4 )
% 0.33/0.63 = ( H3 @ X4 ) ) )
% 0.33/0.63 => ( ( groups7882442080178216443t_assn @ G @ T5 )
% 0.33/0.63 = ( groups7882442080178216443t_assn @ H3 @ S2 ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.mono_neutral_cong_right
% 0.33/0.63 thf(fact_5979_prod_Omono__neutral__cong__right,axiom,
% 0.33/0.63 ! [T5: set_Code_integer,S2: set_Code_integer,G: code_integer > assn,H3: code_integer > assn] :
% 0.33/0.63 ( ( finite6017078050557962740nteger @ T5 )
% 0.33/0.63 => ( ( ord_le7084787975880047091nteger @ S2 @ T5 )
% 0.33/0.63 => ( ! [X4: code_integer] :
% 0.33/0.63 ( ( member_Code_integer @ X4 @ ( minus_2355218937544613996nteger @ T5 @ S2 ) )
% 0.33/0.63 => ( ( G @ X4 )
% 0.33/0.63 = one_one_assn ) )
% 0.33/0.63 => ( ! [X4: code_integer] :
% 0.33/0.63 ( ( member_Code_integer @ X4 @ S2 )
% 0.33/0.63 => ( ( G @ X4 )
% 0.33/0.63 = ( H3 @ X4 ) ) )
% 0.33/0.63 => ( ( groups1304777262505850412r_assn @ G @ T5 )
% 0.33/0.63 = ( groups1304777262505850412r_assn @ H3 @ S2 ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.mono_neutral_cong_right
% 0.33/0.63 thf(fact_5980_prod_Omono__neutral__cong__right,axiom,
% 0.33/0.63 ! [T5: set_o,S2: set_o,G: $o > rat,H3: $o > rat] :
% 0.33/0.63 ( ( finite_finite_o @ T5 )
% 0.33/0.63 => ( ( ord_less_eq_set_o @ S2 @ T5 )
% 0.33/0.63 => ( ! [X4: $o] :
% 0.33/0.63 ( ( member_o @ X4 @ ( minus_minus_set_o @ T5 @ S2 ) )
% 0.33/0.63 => ( ( G @ X4 )
% 0.33/0.63 = one_one_rat ) )
% 0.33/0.63 => ( ! [X4: $o] :
% 0.33/0.63 ( ( member_o @ X4 @ S2 )
% 0.33/0.63 => ( ( G @ X4 )
% 0.33/0.63 = ( H3 @ X4 ) ) )
% 0.33/0.63 => ( ( groups2869687844427037835_o_rat @ G @ T5 )
% 0.33/0.63 = ( groups2869687844427037835_o_rat @ H3 @ S2 ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.mono_neutral_cong_right
% 0.33/0.63 thf(fact_5981_prod_Omono__neutral__cong__right,axiom,
% 0.33/0.63 ! [T5: set_int,S2: set_int,G: int > rat,H3: int > rat] :
% 0.33/0.63 ( ( finite_finite_int @ T5 )
% 0.33/0.63 => ( ( ord_less_eq_set_int @ S2 @ T5 )
% 0.33/0.63 => ( ! [X4: int] :
% 0.33/0.63 ( ( member_int @ X4 @ ( minus_minus_set_int @ T5 @ S2 ) )
% 0.33/0.63 => ( ( G @ X4 )
% 0.33/0.63 = one_one_rat ) )
% 0.33/0.63 => ( ! [X4: int] :
% 0.33/0.63 ( ( member_int @ X4 @ S2 )
% 0.33/0.63 => ( ( G @ X4 )
% 0.33/0.63 = ( H3 @ X4 ) ) )
% 0.33/0.63 => ( ( groups1072433553688619179nt_rat @ G @ T5 )
% 0.33/0.63 = ( groups1072433553688619179nt_rat @ H3 @ S2 ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.mono_neutral_cong_right
% 0.33/0.63 thf(fact_5982_prod_Omono__neutral__cong__right,axiom,
% 0.33/0.63 ! [T5: set_Code_integer,S2: set_Code_integer,G: code_integer > rat,H3: code_integer > rat] :
% 0.33/0.63 ( ( finite6017078050557962740nteger @ T5 )
% 0.33/0.63 => ( ( ord_le7084787975880047091nteger @ S2 @ T5 )
% 0.33/0.63 => ( ! [X4: code_integer] :
% 0.33/0.63 ( ( member_Code_integer @ X4 @ ( minus_2355218937544613996nteger @ T5 @ S2 ) )
% 0.33/0.63 => ( ( G @ X4 )
% 0.33/0.63 = one_one_rat ) )
% 0.33/0.63 => ( ! [X4: code_integer] :
% 0.33/0.63 ( ( member_Code_integer @ X4 @ S2 )
% 0.33/0.63 => ( ( G @ X4 )
% 0.33/0.63 = ( H3 @ X4 ) ) )
% 0.33/0.63 => ( ( groups2555765274223993564er_rat @ G @ T5 )
% 0.33/0.63 = ( groups2555765274223993564er_rat @ H3 @ S2 ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.mono_neutral_cong_right
% 0.33/0.63 thf(fact_5983_prod_Omono__neutral__cong__right,axiom,
% 0.33/0.63 ! [T5: set_o,S2: set_o,G: $o > nat,H3: $o > nat] :
% 0.33/0.63 ( ( finite_finite_o @ T5 )
% 0.33/0.63 => ( ( ord_less_eq_set_o @ S2 @ T5 )
% 0.33/0.63 => ( ! [X4: $o] :
% 0.33/0.63 ( ( member_o @ X4 @ ( minus_minus_set_o @ T5 @ S2 ) )
% 0.33/0.63 => ( ( G @ X4 )
% 0.33/0.63 = one_one_nat ) )
% 0.33/0.63 => ( ! [X4: $o] :
% 0.33/0.63 ( ( member_o @ X4 @ S2 )
% 0.33/0.63 => ( ( G @ X4 )
% 0.33/0.63 = ( H3 @ X4 ) ) )
% 0.33/0.63 => ( ( groups3504817904513533571_o_nat @ G @ T5 )
% 0.33/0.63 = ( groups3504817904513533571_o_nat @ H3 @ S2 ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.mono_neutral_cong_right
% 0.33/0.63 thf(fact_5984_atLeastLessThanSuc,axiom,
% 0.33/0.63 ! [M2: nat,N2: nat] :
% 0.33/0.63 ( ( ( ord_less_eq_nat @ M2 @ N2 )
% 0.33/0.63 => ( ( set_or4665077453230672383an_nat @ M2 @ ( suc @ N2 ) )
% 0.33/0.63 = ( insert_nat @ N2 @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) ) )
% 0.33/0.63 & ( ~ ( ord_less_eq_nat @ M2 @ N2 )
% 0.33/0.63 => ( ( set_or4665077453230672383an_nat @ M2 @ ( suc @ N2 ) )
% 0.33/0.63 = bot_bot_set_nat ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % atLeastLessThanSuc
% 0.33/0.63 thf(fact_5985_Option_Othese__def,axiom,
% 0.33/0.63 ( these_6645423997822192641it_nat
% 0.33/0.63 = ( ^ [A7: set_op3940070208846178154it_nat] :
% 0.33/0.63 ( image_5549452628634654015it_nat @ the_Pr5856008525237892824it_nat
% 0.33/0.63 @ ( collec8141831914148684149it_nat
% 0.33/0.63 @ ^ [X3: option3216581401566546698it_nat] :
% 0.33/0.63 ( ( member3517700364412436275it_nat @ X3 @ A7 )
% 0.33/0.63 & ( X3 != none_P2587165478634041381it_nat ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % Option.these_def
% 0.33/0.63 thf(fact_5986_Option_Othese__def,axiom,
% 0.33/0.63 ( these_num
% 0.33/0.63 = ( ^ [A7: set_option_num] :
% 0.33/0.63 ( image_option_num_num @ the_num
% 0.33/0.63 @ ( collect_option_num
% 0.33/0.63 @ ^ [X3: option_num] :
% 0.33/0.63 ( ( member_option_num @ X3 @ A7 )
% 0.33/0.63 & ( X3 != none_num ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % Option.these_def
% 0.33/0.63 thf(fact_5987_Option_Othese__def,axiom,
% 0.33/0.63 ( these_3407724651694999947it_nat
% 0.33/0.63 = ( ^ [A7: set_op239864471688321678it_nat] :
% 0.33/0.63 ( image_1237920015125996135it_nat @ the_Pr7776125533777466484it_nat
% 0.33/0.63 @ ( collec5742531119322951597it_nat
% 0.33/0.63 @ ^ [X3: option8956607266484857688it_nat] :
% 0.33/0.63 ( ( member5596548051065438575it_nat @ X3 @ A7 )
% 0.33/0.63 & ( X3 != none_P9117596204409417319it_nat ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % Option.these_def
% 0.33/0.63 thf(fact_5988_atLeast0__atMost__Suc__eq__insert__0,axiom,
% 0.33/0.63 ! [N2: nat] :
% 0.33/0.63 ( ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) )
% 0.33/0.63 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % atLeast0_atMost_Suc_eq_insert_0
% 0.33/0.63 thf(fact_5989_atLeast0__lessThan__Suc__eq__insert__0,axiom,
% 0.33/0.63 ! [N2: nat] :
% 0.33/0.63 ( ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N2 ) )
% 0.33/0.63 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % atLeast0_lessThan_Suc_eq_insert_0
% 0.33/0.63 thf(fact_5990_atMost__Suc__eq__insert__0,axiom,
% 0.33/0.63 ! [N2: nat] :
% 0.33/0.63 ( ( set_ord_atMost_nat @ ( suc @ N2 ) )
% 0.33/0.63 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % atMost_Suc_eq_insert_0
% 0.33/0.63 thf(fact_5991_lessThan__Suc__eq__insert__0,axiom,
% 0.33/0.63 ! [N2: nat] :
% 0.33/0.63 ( ( set_ord_lessThan_nat @ ( suc @ N2 ) )
% 0.33/0.63 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % lessThan_Suc_eq_insert_0
% 0.33/0.63 thf(fact_5992_card__2__iff,axiom,
% 0.33/0.63 ! [S2: set_Product_unit] :
% 0.33/0.63 ( ( ( finite410649719033368117t_unit @ S2 )
% 0.33/0.63 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.33/0.63 = ( ? [X3: product_unit,Y3: product_unit] :
% 0.33/0.63 ( ( S2
% 0.33/0.63 = ( insert_Product_unit @ X3 @ ( insert_Product_unit @ Y3 @ bot_bo3957492148770167129t_unit ) ) )
% 0.33/0.63 & ( X3 != Y3 ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % card_2_iff
% 0.33/0.63 thf(fact_5993_card__2__iff,axiom,
% 0.33/0.63 ! [S2: set_list_nat] :
% 0.33/0.63 ( ( ( finite_card_list_nat @ S2 )
% 0.33/0.63 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.33/0.63 = ( ? [X3: list_nat,Y3: list_nat] :
% 0.33/0.63 ( ( S2
% 0.33/0.63 = ( insert_list_nat @ X3 @ ( insert_list_nat @ Y3 @ bot_bot_set_list_nat ) ) )
% 0.33/0.63 & ( X3 != Y3 ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % card_2_iff
% 0.33/0.63 thf(fact_5994_card__2__iff,axiom,
% 0.33/0.63 ! [S2: set_Pr4329608150637261639at_nat] :
% 0.33/0.63 ( ( ( finite3771342082235030671at_nat @ S2 )
% 0.33/0.63 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.33/0.63 = ( ? [X3: produc3843707927480180839at_nat,Y3: produc3843707927480180839at_nat] :
% 0.33/0.63 ( ( S2
% 0.33/0.63 = ( insert9069300056098147895at_nat @ X3 @ ( insert9069300056098147895at_nat @ Y3 @ bot_bo228742789529271731at_nat ) ) )
% 0.33/0.63 & ( X3 != Y3 ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % card_2_iff
% 0.33/0.63 thf(fact_5995_card__2__iff,axiom,
% 0.33/0.63 ! [S2: set_Pr1261947904930325089at_nat] :
% 0.33/0.63 ( ( ( finite711546835091564841at_nat @ S2 )
% 0.33/0.63 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.33/0.63 = ( ? [X3: product_prod_nat_nat,Y3: product_prod_nat_nat] :
% 0.33/0.63 ( ( S2
% 0.33/0.63 = ( insert8211810215607154385at_nat @ X3 @ ( insert8211810215607154385at_nat @ Y3 @ bot_bo2099793752762293965at_nat ) ) )
% 0.33/0.63 & ( X3 != Y3 ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % card_2_iff
% 0.33/0.63 thf(fact_5996_card__2__iff,axiom,
% 0.33/0.63 ! [S2: set_o] :
% 0.33/0.63 ( ( ( finite_card_o @ S2 )
% 0.33/0.63 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.33/0.63 = ( ? [X3: $o,Y3: $o] :
% 0.33/0.63 ( ( S2
% 0.33/0.63 = ( insert_o @ X3 @ ( insert_o @ Y3 @ bot_bot_set_o ) ) )
% 0.33/0.63 & ( X3 != Y3 ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % card_2_iff
% 0.33/0.63 thf(fact_5997_card__2__iff,axiom,
% 0.33/0.63 ! [S2: set_nat] :
% 0.33/0.63 ( ( ( finite_card_nat @ S2 )
% 0.33/0.63 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.33/0.63 = ( ? [X3: nat,Y3: nat] :
% 0.33/0.63 ( ( S2
% 0.33/0.63 = ( insert_nat @ X3 @ ( insert_nat @ Y3 @ bot_bot_set_nat ) ) )
% 0.33/0.63 & ( X3 != Y3 ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % card_2_iff
% 0.33/0.63 thf(fact_5998_card__2__iff,axiom,
% 0.33/0.63 ! [S2: set_int] :
% 0.33/0.63 ( ( ( finite_card_int @ S2 )
% 0.33/0.63 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.33/0.63 = ( ? [X3: int,Y3: int] :
% 0.33/0.63 ( ( S2
% 0.33/0.63 = ( insert_int @ X3 @ ( insert_int @ Y3 @ bot_bot_set_int ) ) )
% 0.33/0.63 & ( X3 != Y3 ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % card_2_iff
% 0.33/0.63 thf(fact_5999_card__3__iff,axiom,
% 0.33/0.63 ! [S2: set_Product_unit] :
% 0.33/0.63 ( ( ( finite410649719033368117t_unit @ S2 )
% 0.33/0.63 = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 0.33/0.63 = ( ? [X3: product_unit,Y3: product_unit,Z4: product_unit] :
% 0.33/0.63 ( ( S2
% 0.33/0.63 = ( insert_Product_unit @ X3 @ ( insert_Product_unit @ Y3 @ ( insert_Product_unit @ Z4 @ bot_bo3957492148770167129t_unit ) ) ) )
% 0.33/0.63 & ( X3 != Y3 )
% 0.33/0.63 & ( Y3 != Z4 )
% 0.33/0.63 & ( X3 != Z4 ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % card_3_iff
% 0.33/0.63 thf(fact_6000_card__3__iff,axiom,
% 0.33/0.63 ! [S2: set_list_nat] :
% 0.33/0.63 ( ( ( finite_card_list_nat @ S2 )
% 0.33/0.63 = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 0.33/0.63 = ( ? [X3: list_nat,Y3: list_nat,Z4: list_nat] :
% 0.33/0.63 ( ( S2
% 0.33/0.63 = ( insert_list_nat @ X3 @ ( insert_list_nat @ Y3 @ ( insert_list_nat @ Z4 @ bot_bot_set_list_nat ) ) ) )
% 0.33/0.63 & ( X3 != Y3 )
% 0.33/0.63 & ( Y3 != Z4 )
% 0.33/0.63 & ( X3 != Z4 ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % card_3_iff
% 0.33/0.63 thf(fact_6001_card__3__iff,axiom,
% 0.33/0.63 ! [S2: set_Pr4329608150637261639at_nat] :
% 0.33/0.63 ( ( ( finite3771342082235030671at_nat @ S2 )
% 0.33/0.63 = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 0.33/0.63 = ( ? [X3: produc3843707927480180839at_nat,Y3: produc3843707927480180839at_nat,Z4: produc3843707927480180839at_nat] :
% 0.33/0.63 ( ( S2
% 0.33/0.63 = ( insert9069300056098147895at_nat @ X3 @ ( insert9069300056098147895at_nat @ Y3 @ ( insert9069300056098147895at_nat @ Z4 @ bot_bo228742789529271731at_nat ) ) ) )
% 0.33/0.63 & ( X3 != Y3 )
% 0.33/0.63 & ( Y3 != Z4 )
% 0.33/0.63 & ( X3 != Z4 ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % card_3_iff
% 0.33/0.63 thf(fact_6002_card__3__iff,axiom,
% 0.33/0.63 ! [S2: set_Pr1261947904930325089at_nat] :
% 0.33/0.63 ( ( ( finite711546835091564841at_nat @ S2 )
% 0.33/0.63 = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 0.33/0.63 = ( ? [X3: product_prod_nat_nat,Y3: product_prod_nat_nat,Z4: product_prod_nat_nat] :
% 0.33/0.63 ( ( S2
% 0.33/0.63 = ( insert8211810215607154385at_nat @ X3 @ ( insert8211810215607154385at_nat @ Y3 @ ( insert8211810215607154385at_nat @ Z4 @ bot_bo2099793752762293965at_nat ) ) ) )
% 0.33/0.63 & ( X3 != Y3 )
% 0.33/0.63 & ( Y3 != Z4 )
% 0.33/0.63 & ( X3 != Z4 ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % card_3_iff
% 0.33/0.63 thf(fact_6003_card__3__iff,axiom,
% 0.33/0.63 ! [S2: set_o] :
% 0.33/0.63 ( ( ( finite_card_o @ S2 )
% 0.33/0.63 = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 0.33/0.63 = ( ? [X3: $o,Y3: $o,Z4: $o] :
% 0.33/0.63 ( ( S2
% 0.33/0.63 = ( insert_o @ X3 @ ( insert_o @ Y3 @ ( insert_o @ Z4 @ bot_bot_set_o ) ) ) )
% 0.33/0.63 & ( X3 != Y3 )
% 0.33/0.63 & ( Y3 != Z4 )
% 0.33/0.63 & ( X3 != Z4 ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % card_3_iff
% 0.33/0.63 thf(fact_6004_card__3__iff,axiom,
% 0.33/0.63 ! [S2: set_nat] :
% 0.33/0.63 ( ( ( finite_card_nat @ S2 )
% 0.33/0.63 = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 0.33/0.63 = ( ? [X3: nat,Y3: nat,Z4: nat] :
% 0.33/0.63 ( ( S2
% 0.33/0.63 = ( insert_nat @ X3 @ ( insert_nat @ Y3 @ ( insert_nat @ Z4 @ bot_bot_set_nat ) ) ) )
% 0.33/0.63 & ( X3 != Y3 )
% 0.33/0.63 & ( Y3 != Z4 )
% 0.33/0.63 & ( X3 != Z4 ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % card_3_iff
% 0.33/0.63 thf(fact_6005_card__3__iff,axiom,
% 0.33/0.63 ! [S2: set_int] :
% 0.33/0.63 ( ( ( finite_card_int @ S2 )
% 0.33/0.63 = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 0.33/0.63 = ( ? [X3: int,Y3: int,Z4: int] :
% 0.33/0.63 ( ( S2
% 0.33/0.63 = ( insert_int @ X3 @ ( insert_int @ Y3 @ ( insert_int @ Z4 @ bot_bot_set_int ) ) ) )
% 0.33/0.63 & ( X3 != Y3 )
% 0.33/0.63 & ( Y3 != Z4 )
% 0.33/0.63 & ( X3 != Z4 ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % card_3_iff
% 0.33/0.63 thf(fact_6006_sum__image__le,axiom,
% 0.33/0.63 ! [I4: set_num,G: code_integer > code_integer,F: num > code_integer] :
% 0.33/0.63 ( ( finite_finite_num @ I4 )
% 0.33/0.63 => ( ! [I2: num] :
% 0.33/0.63 ( ( member_num @ I2 @ I4 )
% 0.33/0.63 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( G @ ( F @ I2 ) ) ) )
% 0.33/0.63 => ( ord_le3102999989581377725nteger @ ( groups879477027807139574nteger @ G @ ( image_8379761247532268670nteger @ F @ I4 ) ) @ ( groups5442708359310287027nteger @ ( comp_C3531382070062128313er_num @ G @ F ) @ I4 ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % sum_image_le
% 0.33/0.63 thf(fact_6007_sum__image__le,axiom,
% 0.33/0.63 ! [I4: set_nat,G: code_integer > code_integer,F: nat > code_integer] :
% 0.33/0.63 ( ( finite_finite_nat @ I4 )
% 0.33/0.63 => ( ! [I2: nat] :
% 0.33/0.63 ( ( member_nat @ I2 @ I4 )
% 0.33/0.63 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( G @ ( F @ I2 ) ) ) )
% 0.33/0.63 => ( ord_le3102999989581377725nteger @ ( groups879477027807139574nteger @ G @ ( image_1215581382706833972nteger @ F @ I4 ) ) @ ( groups7501900531339628137nteger @ ( comp_C6974050283906349679er_nat @ G @ F ) @ I4 ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % sum_image_le
% 0.33/0.63 thf(fact_6008_sum__image__le,axiom,
% 0.33/0.63 ! [I4: set_nat,G: nat > code_integer,F: nat > nat] :
% 0.33/0.63 ( ( finite_finite_nat @ I4 )
% 0.33/0.63 => ( ! [I2: nat] :
% 0.33/0.63 ( ( member_nat @ I2 @ I4 )
% 0.33/0.63 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( G @ ( F @ I2 ) ) ) )
% 0.33/0.63 => ( ord_le3102999989581377725nteger @ ( groups7501900531339628137nteger @ G @ ( image_nat_nat @ F @ I4 ) ) @ ( groups7501900531339628137nteger @ ( comp_n3898172953802868194er_nat @ G @ F ) @ I4 ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % sum_image_le
% 0.33/0.63 thf(fact_6009_sum__image__le,axiom,
% 0.33/0.63 ! [I4: set_nat,G: int > code_integer,F: nat > int] :
% 0.33/0.63 ( ( finite_finite_nat @ I4 )
% 0.33/0.63 => ( ! [I2: nat] :
% 0.33/0.63 ( ( member_nat @ I2 @ I4 )
% 0.33/0.63 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( G @ ( F @ I2 ) ) ) )
% 0.33/0.63 => ( ord_le3102999989581377725nteger @ ( groups7873554091576472773nteger @ G @ ( image_nat_int @ F @ I4 ) ) @ ( groups7501900531339628137nteger @ ( comp_i1588355021709917246er_nat @ G @ F ) @ I4 ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % sum_image_le
% 0.33/0.63 thf(fact_6010_sum__image__le,axiom,
% 0.33/0.63 ! [I4: set_int,G: int > code_integer,F: int > int] :
% 0.33/0.63 ( ( finite_finite_int @ I4 )
% 0.33/0.63 => ( ! [I2: int] :
% 0.33/0.63 ( ( member_int @ I2 @ I4 )
% 0.33/0.63 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( G @ ( F @ I2 ) ) ) )
% 0.33/0.63 => ( ord_le3102999989581377725nteger @ ( groups7873554091576472773nteger @ G @ ( image_int_int @ F @ I4 ) ) @ ( groups7873554091576472773nteger @ ( comp_i1585864551200866970er_int @ G @ F ) @ I4 ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % sum_image_le
% 0.33/0.63 thf(fact_6011_sum__image__le,axiom,
% 0.33/0.63 ! [I4: set_nat,G: code_integer > rat,F: nat > code_integer] :
% 0.33/0.63 ( ( finite_finite_nat @ I4 )
% 0.33/0.63 => ( ! [I2: nat] :
% 0.33/0.63 ( ( member_nat @ I2 @ I4 )
% 0.33/0.63 => ( ord_less_eq_rat @ zero_zero_rat @ ( G @ ( F @ I2 ) ) ) )
% 0.33/0.63 => ( ord_less_eq_rat @ ( groups6602215022474089585er_rat @ G @ ( image_1215581382706833972nteger @ F @ I4 ) ) @ ( groups2906978787729119204at_rat @ ( comp_C3733001951728184298at_nat @ G @ F ) @ I4 ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % sum_image_le
% 0.33/0.63 thf(fact_6012_sum__image__le,axiom,
% 0.33/0.63 ! [I4: set_nat,G: nat > rat,F: nat > nat] :
% 0.33/0.63 ( ( finite_finite_nat @ I4 )
% 0.33/0.63 => ( ! [I2: nat] :
% 0.33/0.63 ( ( member_nat @ I2 @ I4 )
% 0.33/0.63 => ( ord_less_eq_rat @ zero_zero_rat @ ( G @ ( F @ I2 ) ) ) )
% 0.33/0.63 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ G @ ( image_nat_nat @ F @ I4 ) ) @ ( groups2906978787729119204at_rat @ ( comp_nat_rat_nat @ G @ F ) @ I4 ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % sum_image_le
% 0.33/0.63 thf(fact_6013_sum__image__le,axiom,
% 0.33/0.63 ! [I4: set_nat,G: int > rat,F: nat > int] :
% 0.33/0.63 ( ( finite_finite_nat @ I4 )
% 0.33/0.63 => ( ! [I2: nat] :
% 0.33/0.63 ( ( member_nat @ I2 @ I4 )
% 0.33/0.63 => ( ord_less_eq_rat @ zero_zero_rat @ ( G @ ( F @ I2 ) ) ) )
% 0.33/0.63 => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ G @ ( image_nat_int @ F @ I4 ) ) @ ( groups2906978787729119204at_rat @ ( comp_int_rat_nat @ G @ F ) @ I4 ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % sum_image_le
% 0.33/0.63 thf(fact_6014_sum__image__le,axiom,
% 0.33/0.63 ! [I4: set_int,G: int > rat,F: int > int] :
% 0.33/0.63 ( ( finite_finite_int @ I4 )
% 0.33/0.63 => ( ! [I2: int] :
% 0.33/0.63 ( ( member_int @ I2 @ I4 )
% 0.33/0.63 => ( ord_less_eq_rat @ zero_zero_rat @ ( G @ ( F @ I2 ) ) ) )
% 0.33/0.63 => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ G @ ( image_int_int @ F @ I4 ) ) @ ( groups3906332499630173760nt_rat @ ( comp_int_rat_int @ G @ F ) @ I4 ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % sum_image_le
% 0.33/0.63 thf(fact_6015_sum__image__le,axiom,
% 0.33/0.63 ! [I4: set_int,G: int > nat,F: int > int] :
% 0.33/0.63 ( ( finite_finite_int @ I4 )
% 0.33/0.63 => ( ! [I2: int] :
% 0.33/0.63 ( ( member_int @ I2 @ I4 )
% 0.33/0.63 => ( ord_less_eq_nat @ zero_zero_nat @ ( G @ ( F @ I2 ) ) ) )
% 0.33/0.63 => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ G @ ( image_int_int @ F @ I4 ) ) @ ( groups4541462559716669496nt_nat @ ( comp_int_nat_int @ G @ F ) @ I4 ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % sum_image_le
% 0.33/0.63 thf(fact_6016_sum_Oremove,axiom,
% 0.33/0.63 ! [A2: set_Code_integer,X: code_integer,G: code_integer > rat] :
% 0.33/0.63 ( ( finite6017078050557962740nteger @ A2 )
% 0.33/0.63 => ( ( member_Code_integer @ X @ A2 )
% 0.33/0.63 => ( ( groups6602215022474089585er_rat @ G @ A2 )
% 0.33/0.63 = ( plus_plus_rat @ ( G @ X ) @ ( groups6602215022474089585er_rat @ G @ ( minus_2355218937544613996nteger @ A2 @ ( insert_Code_integer @ X @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % sum.remove
% 0.33/0.63 thf(fact_6017_sum_Oremove,axiom,
% 0.33/0.63 ! [A2: set_Code_integer,X: code_integer,G: code_integer > nat] :
% 0.33/0.63 ( ( finite6017078050557962740nteger @ A2 )
% 0.33/0.63 => ( ( member_Code_integer @ X @ A2 )
% 0.33/0.63 => ( ( groups7237345082560585321er_nat @ G @ A2 )
% 0.33/0.63 = ( plus_plus_nat @ ( G @ X ) @ ( groups7237345082560585321er_nat @ G @ ( minus_2355218937544613996nteger @ A2 @ ( insert_Code_integer @ X @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % sum.remove
% 0.33/0.63 thf(fact_6018_sum_Oremove,axiom,
% 0.33/0.63 ! [A2: set_Code_integer,X: code_integer,G: code_integer > int] :
% 0.33/0.63 ( ( finite6017078050557962740nteger @ A2 )
% 0.33/0.63 => ( ( member_Code_integer @ X @ A2 )
% 0.33/0.63 => ( ( groups7234854612051535045er_int @ G @ A2 )
% 0.33/0.63 = ( plus_plus_int @ ( G @ X ) @ ( groups7234854612051535045er_int @ G @ ( minus_2355218937544613996nteger @ A2 @ ( insert_Code_integer @ X @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % sum.remove
% 0.33/0.63 thf(fact_6019_sum_Oremove,axiom,
% 0.33/0.63 ! [A2: set_o,X: $o,G: $o > rat] :
% 0.33/0.63 ( ( finite_finite_o @ A2 )
% 0.33/0.63 => ( ( member_o @ X @ A2 )
% 0.33/0.63 => ( ( groups7872700643590313910_o_rat @ G @ A2 )
% 0.33/0.63 = ( plus_plus_rat @ ( G @ X ) @ ( groups7872700643590313910_o_rat @ G @ ( minus_minus_set_o @ A2 @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % sum.remove
% 0.33/0.63 thf(fact_6020_sum_Oremove,axiom,
% 0.33/0.63 ! [A2: set_o,X: $o,G: $o > nat] :
% 0.33/0.63 ( ( finite_finite_o @ A2 )
% 0.33/0.63 => ( ( member_o @ X @ A2 )
% 0.33/0.63 => ( ( groups8507830703676809646_o_nat @ G @ A2 )
% 0.33/0.63 = ( plus_plus_nat @ ( G @ X ) @ ( groups8507830703676809646_o_nat @ G @ ( minus_minus_set_o @ A2 @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % sum.remove
% 0.33/0.63 thf(fact_6021_sum_Oremove,axiom,
% 0.33/0.63 ! [A2: set_o,X: $o,G: $o > int] :
% 0.33/0.63 ( ( finite_finite_o @ A2 )
% 0.33/0.63 => ( ( member_o @ X @ A2 )
% 0.33/0.63 => ( ( groups8505340233167759370_o_int @ G @ A2 )
% 0.33/0.63 = ( plus_plus_int @ ( G @ X ) @ ( groups8505340233167759370_o_int @ G @ ( minus_minus_set_o @ A2 @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % sum.remove
% 0.33/0.63 thf(fact_6022_sum_Oremove,axiom,
% 0.33/0.63 ! [A2: set_int,X: int,G: int > rat] :
% 0.33/0.63 ( ( finite_finite_int @ A2 )
% 0.33/0.63 => ( ( member_int @ X @ A2 )
% 0.33/0.63 => ( ( groups3906332499630173760nt_rat @ G @ A2 )
% 0.33/0.63 = ( plus_plus_rat @ ( G @ X ) @ ( groups3906332499630173760nt_rat @ G @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % sum.remove
% 0.33/0.63 thf(fact_6023_sum_Oremove,axiom,
% 0.33/0.63 ! [A2: set_int,X: int,G: int > nat] :
% 0.33/0.63 ( ( finite_finite_int @ A2 )
% 0.33/0.63 => ( ( member_int @ X @ A2 )
% 0.33/0.63 => ( ( groups4541462559716669496nt_nat @ G @ A2 )
% 0.33/0.63 = ( plus_plus_nat @ ( G @ X ) @ ( groups4541462559716669496nt_nat @ G @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % sum.remove
% 0.33/0.63 thf(fact_6024_sum_Oremove,axiom,
% 0.33/0.63 ! [A2: set_nat,X: nat,G: nat > rat] :
% 0.33/0.63 ( ( finite_finite_nat @ A2 )
% 0.33/0.63 => ( ( member_nat @ X @ A2 )
% 0.33/0.63 => ( ( groups2906978787729119204at_rat @ G @ A2 )
% 0.33/0.63 = ( plus_plus_rat @ ( G @ X ) @ ( groups2906978787729119204at_rat @ G @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % sum.remove
% 0.33/0.63 thf(fact_6025_sum_Oremove,axiom,
% 0.33/0.63 ! [A2: set_nat,X: nat,G: nat > int] :
% 0.33/0.63 ( ( finite_finite_nat @ A2 )
% 0.33/0.63 => ( ( member_nat @ X @ A2 )
% 0.33/0.63 => ( ( groups3539618377306564664at_int @ G @ A2 )
% 0.33/0.63 = ( plus_plus_int @ ( G @ X ) @ ( groups3539618377306564664at_int @ G @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % sum.remove
% 0.33/0.63 thf(fact_6026_sum_Oinsert__remove,axiom,
% 0.33/0.63 ! [A2: set_Code_integer,G: code_integer > rat,X: code_integer] :
% 0.33/0.63 ( ( finite6017078050557962740nteger @ A2 )
% 0.33/0.63 => ( ( groups6602215022474089585er_rat @ G @ ( insert_Code_integer @ X @ A2 ) )
% 0.33/0.63 = ( plus_plus_rat @ ( G @ X ) @ ( groups6602215022474089585er_rat @ G @ ( minus_2355218937544613996nteger @ A2 @ ( insert_Code_integer @ X @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % sum.insert_remove
% 0.33/0.63 thf(fact_6027_sum_Oinsert__remove,axiom,
% 0.33/0.63 ! [A2: set_Code_integer,G: code_integer > nat,X: code_integer] :
% 0.33/0.63 ( ( finite6017078050557962740nteger @ A2 )
% 0.33/0.63 => ( ( groups7237345082560585321er_nat @ G @ ( insert_Code_integer @ X @ A2 ) )
% 0.33/0.63 = ( plus_plus_nat @ ( G @ X ) @ ( groups7237345082560585321er_nat @ G @ ( minus_2355218937544613996nteger @ A2 @ ( insert_Code_integer @ X @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % sum.insert_remove
% 0.33/0.63 thf(fact_6028_sum_Oinsert__remove,axiom,
% 0.33/0.63 ! [A2: set_Code_integer,G: code_integer > int,X: code_integer] :
% 0.33/0.63 ( ( finite6017078050557962740nteger @ A2 )
% 0.33/0.63 => ( ( groups7234854612051535045er_int @ G @ ( insert_Code_integer @ X @ A2 ) )
% 0.33/0.63 = ( plus_plus_int @ ( G @ X ) @ ( groups7234854612051535045er_int @ G @ ( minus_2355218937544613996nteger @ A2 @ ( insert_Code_integer @ X @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % sum.insert_remove
% 0.33/0.63 thf(fact_6029_sum_Oinsert__remove,axiom,
% 0.33/0.63 ! [A2: set_o,G: $o > rat,X: $o] :
% 0.33/0.63 ( ( finite_finite_o @ A2 )
% 0.33/0.63 => ( ( groups7872700643590313910_o_rat @ G @ ( insert_o @ X @ A2 ) )
% 0.33/0.63 = ( plus_plus_rat @ ( G @ X ) @ ( groups7872700643590313910_o_rat @ G @ ( minus_minus_set_o @ A2 @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % sum.insert_remove
% 0.33/0.63 thf(fact_6030_sum_Oinsert__remove,axiom,
% 0.33/0.63 ! [A2: set_o,G: $o > nat,X: $o] :
% 0.33/0.63 ( ( finite_finite_o @ A2 )
% 0.33/0.63 => ( ( groups8507830703676809646_o_nat @ G @ ( insert_o @ X @ A2 ) )
% 0.33/0.63 = ( plus_plus_nat @ ( G @ X ) @ ( groups8507830703676809646_o_nat @ G @ ( minus_minus_set_o @ A2 @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % sum.insert_remove
% 0.33/0.63 thf(fact_6031_sum_Oinsert__remove,axiom,
% 0.33/0.63 ! [A2: set_o,G: $o > int,X: $o] :
% 0.33/0.63 ( ( finite_finite_o @ A2 )
% 0.33/0.63 => ( ( groups8505340233167759370_o_int @ G @ ( insert_o @ X @ A2 ) )
% 0.33/0.63 = ( plus_plus_int @ ( G @ X ) @ ( groups8505340233167759370_o_int @ G @ ( minus_minus_set_o @ A2 @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % sum.insert_remove
% 0.33/0.63 thf(fact_6032_sum_Oinsert__remove,axiom,
% 0.33/0.63 ! [A2: set_int,G: int > rat,X: int] :
% 0.33/0.63 ( ( finite_finite_int @ A2 )
% 0.33/0.63 => ( ( groups3906332499630173760nt_rat @ G @ ( insert_int @ X @ A2 ) )
% 0.33/0.63 = ( plus_plus_rat @ ( G @ X ) @ ( groups3906332499630173760nt_rat @ G @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % sum.insert_remove
% 0.33/0.63 thf(fact_6033_sum_Oinsert__remove,axiom,
% 0.33/0.63 ! [A2: set_int,G: int > nat,X: int] :
% 0.33/0.63 ( ( finite_finite_int @ A2 )
% 0.33/0.63 => ( ( groups4541462559716669496nt_nat @ G @ ( insert_int @ X @ A2 ) )
% 0.33/0.63 = ( plus_plus_nat @ ( G @ X ) @ ( groups4541462559716669496nt_nat @ G @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % sum.insert_remove
% 0.33/0.63 thf(fact_6034_sum_Oinsert__remove,axiom,
% 0.33/0.63 ! [A2: set_nat,G: nat > rat,X: nat] :
% 0.33/0.63 ( ( finite_finite_nat @ A2 )
% 0.33/0.63 => ( ( groups2906978787729119204at_rat @ G @ ( insert_nat @ X @ A2 ) )
% 0.33/0.63 = ( plus_plus_rat @ ( G @ X ) @ ( groups2906978787729119204at_rat @ G @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % sum.insert_remove
% 0.33/0.63 thf(fact_6035_sum_Oinsert__remove,axiom,
% 0.33/0.63 ! [A2: set_nat,G: nat > int,X: nat] :
% 0.33/0.63 ( ( finite_finite_nat @ A2 )
% 0.33/0.63 => ( ( groups3539618377306564664at_int @ G @ ( insert_nat @ X @ A2 ) )
% 0.33/0.63 = ( plus_plus_int @ ( G @ X ) @ ( groups3539618377306564664at_int @ G @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % sum.insert_remove
% 0.33/0.63 thf(fact_6036_atLeast1__atMost__eq__remove0,axiom,
% 0.33/0.63 ! [N2: nat] :
% 0.33/0.63 ( ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 0.33/0.63 = ( minus_minus_set_nat @ ( set_ord_atMost_nat @ N2 ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % atLeast1_atMost_eq_remove0
% 0.33/0.63 thf(fact_6037_atLeast1__lessThan__eq__remove0,axiom,
% 0.33/0.63 ! [N2: nat] :
% 0.33/0.63 ( ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 0.33/0.63 = ( minus_minus_set_nat @ ( set_ord_lessThan_nat @ N2 ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % atLeast1_lessThan_eq_remove0
% 0.33/0.63 thf(fact_6038_atLeastLessThan__nat__numeral,axiom,
% 0.33/0.63 ! [M2: nat,K: num] :
% 0.33/0.63 ( ( ( ord_less_eq_nat @ M2 @ ( pred_numeral @ K ) )
% 0.33/0.63 => ( ( set_or4665077453230672383an_nat @ M2 @ ( numeral_numeral_nat @ K ) )
% 0.33/0.63 = ( insert_nat @ ( pred_numeral @ K ) @ ( set_or4665077453230672383an_nat @ M2 @ ( pred_numeral @ K ) ) ) ) )
% 0.33/0.63 & ( ~ ( ord_less_eq_nat @ M2 @ ( pred_numeral @ K ) )
% 0.33/0.63 => ( ( set_or4665077453230672383an_nat @ M2 @ ( numeral_numeral_nat @ K ) )
% 0.33/0.63 = bot_bot_set_nat ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % atLeastLessThan_nat_numeral
% 0.33/0.63 thf(fact_6039_sum_Odelta__remove,axiom,
% 0.33/0.63 ! [S2: set_Code_integer,A: code_integer,B: code_integer > rat,C: code_integer > rat] :
% 0.33/0.63 ( ( finite6017078050557962740nteger @ S2 )
% 0.33/0.63 => ( ( ( member_Code_integer @ A @ S2 )
% 0.33/0.63 => ( ( groups6602215022474089585er_rat
% 0.33/0.63 @ ^ [K4: code_integer] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 0.33/0.63 @ S2 )
% 0.33/0.63 = ( plus_plus_rat @ ( B @ A ) @ ( groups6602215022474089585er_rat @ C @ ( minus_2355218937544613996nteger @ S2 @ ( insert_Code_integer @ A @ bot_bo3990330152332043303nteger ) ) ) ) ) )
% 0.33/0.63 & ( ~ ( member_Code_integer @ A @ S2 )
% 0.33/0.63 => ( ( groups6602215022474089585er_rat
% 0.33/0.63 @ ^ [K4: code_integer] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 0.33/0.63 @ S2 )
% 0.33/0.63 = ( groups6602215022474089585er_rat @ C @ ( minus_2355218937544613996nteger @ S2 @ ( insert_Code_integer @ A @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % sum.delta_remove
% 0.33/0.63 thf(fact_6040_sum_Odelta__remove,axiom,
% 0.33/0.63 ! [S2: set_Code_integer,A: code_integer,B: code_integer > nat,C: code_integer > nat] :
% 0.33/0.63 ( ( finite6017078050557962740nteger @ S2 )
% 0.33/0.63 => ( ( ( member_Code_integer @ A @ S2 )
% 0.33/0.63 => ( ( groups7237345082560585321er_nat
% 0.33/0.63 @ ^ [K4: code_integer] : ( if_nat @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 0.33/0.63 @ S2 )
% 0.33/0.63 = ( plus_plus_nat @ ( B @ A ) @ ( groups7237345082560585321er_nat @ C @ ( minus_2355218937544613996nteger @ S2 @ ( insert_Code_integer @ A @ bot_bo3990330152332043303nteger ) ) ) ) ) )
% 0.33/0.63 & ( ~ ( member_Code_integer @ A @ S2 )
% 0.33/0.63 => ( ( groups7237345082560585321er_nat
% 0.33/0.63 @ ^ [K4: code_integer] : ( if_nat @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 0.33/0.63 @ S2 )
% 0.33/0.63 = ( groups7237345082560585321er_nat @ C @ ( minus_2355218937544613996nteger @ S2 @ ( insert_Code_integer @ A @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % sum.delta_remove
% 0.33/0.63 thf(fact_6041_sum_Odelta__remove,axiom,
% 0.33/0.63 ! [S2: set_Code_integer,A: code_integer,B: code_integer > int,C: code_integer > int] :
% 0.33/0.63 ( ( finite6017078050557962740nteger @ S2 )
% 0.33/0.63 => ( ( ( member_Code_integer @ A @ S2 )
% 0.33/0.63 => ( ( groups7234854612051535045er_int
% 0.33/0.63 @ ^ [K4: code_integer] : ( if_int @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 0.33/0.63 @ S2 )
% 0.33/0.63 = ( plus_plus_int @ ( B @ A ) @ ( groups7234854612051535045er_int @ C @ ( minus_2355218937544613996nteger @ S2 @ ( insert_Code_integer @ A @ bot_bo3990330152332043303nteger ) ) ) ) ) )
% 0.33/0.63 & ( ~ ( member_Code_integer @ A @ S2 )
% 0.33/0.63 => ( ( groups7234854612051535045er_int
% 0.33/0.63 @ ^ [K4: code_integer] : ( if_int @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 0.33/0.63 @ S2 )
% 0.33/0.63 = ( groups7234854612051535045er_int @ C @ ( minus_2355218937544613996nteger @ S2 @ ( insert_Code_integer @ A @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % sum.delta_remove
% 0.33/0.63 thf(fact_6042_sum_Odelta__remove,axiom,
% 0.33/0.63 ! [S2: set_o,A: $o,B: $o > rat,C: $o > rat] :
% 0.33/0.63 ( ( finite_finite_o @ S2 )
% 0.33/0.63 => ( ( ( member_o @ A @ S2 )
% 0.33/0.63 => ( ( groups7872700643590313910_o_rat
% 0.33/0.63 @ ^ [K4: $o] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 0.33/0.63 @ S2 )
% 0.33/0.63 = ( plus_plus_rat @ ( B @ A ) @ ( groups7872700643590313910_o_rat @ C @ ( minus_minus_set_o @ S2 @ ( insert_o @ A @ bot_bot_set_o ) ) ) ) ) )
% 0.33/0.63 & ( ~ ( member_o @ A @ S2 )
% 0.33/0.63 => ( ( groups7872700643590313910_o_rat
% 0.33/0.63 @ ^ [K4: $o] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 0.33/0.63 @ S2 )
% 0.33/0.63 = ( groups7872700643590313910_o_rat @ C @ ( minus_minus_set_o @ S2 @ ( insert_o @ A @ bot_bot_set_o ) ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % sum.delta_remove
% 0.33/0.63 thf(fact_6043_sum_Odelta__remove,axiom,
% 0.33/0.63 ! [S2: set_o,A: $o,B: $o > nat,C: $o > nat] :
% 0.33/0.63 ( ( finite_finite_o @ S2 )
% 0.33/0.63 => ( ( ( member_o @ A @ S2 )
% 0.33/0.63 => ( ( groups8507830703676809646_o_nat
% 0.33/0.63 @ ^ [K4: $o] : ( if_nat @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 0.33/0.63 @ S2 )
% 0.33/0.63 = ( plus_plus_nat @ ( B @ A ) @ ( groups8507830703676809646_o_nat @ C @ ( minus_minus_set_o @ S2 @ ( insert_o @ A @ bot_bot_set_o ) ) ) ) ) )
% 0.33/0.63 & ( ~ ( member_o @ A @ S2 )
% 0.33/0.63 => ( ( groups8507830703676809646_o_nat
% 0.33/0.63 @ ^ [K4: $o] : ( if_nat @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 0.33/0.63 @ S2 )
% 0.33/0.63 = ( groups8507830703676809646_o_nat @ C @ ( minus_minus_set_o @ S2 @ ( insert_o @ A @ bot_bot_set_o ) ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % sum.delta_remove
% 0.33/0.63 thf(fact_6044_sum_Odelta__remove,axiom,
% 0.33/0.63 ! [S2: set_o,A: $o,B: $o > int,C: $o > int] :
% 0.33/0.63 ( ( finite_finite_o @ S2 )
% 0.33/0.63 => ( ( ( member_o @ A @ S2 )
% 0.33/0.63 => ( ( groups8505340233167759370_o_int
% 0.33/0.63 @ ^ [K4: $o] : ( if_int @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 0.33/0.63 @ S2 )
% 0.33/0.63 = ( plus_plus_int @ ( B @ A ) @ ( groups8505340233167759370_o_int @ C @ ( minus_minus_set_o @ S2 @ ( insert_o @ A @ bot_bot_set_o ) ) ) ) ) )
% 0.33/0.63 & ( ~ ( member_o @ A @ S2 )
% 0.33/0.63 => ( ( groups8505340233167759370_o_int
% 0.33/0.63 @ ^ [K4: $o] : ( if_int @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 0.33/0.63 @ S2 )
% 0.33/0.63 = ( groups8505340233167759370_o_int @ C @ ( minus_minus_set_o @ S2 @ ( insert_o @ A @ bot_bot_set_o ) ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % sum.delta_remove
% 0.33/0.63 thf(fact_6045_sum_Odelta__remove,axiom,
% 0.33/0.63 ! [S2: set_int,A: int,B: int > rat,C: int > rat] :
% 0.33/0.63 ( ( finite_finite_int @ S2 )
% 0.33/0.63 => ( ( ( member_int @ A @ S2 )
% 0.33/0.63 => ( ( groups3906332499630173760nt_rat
% 0.33/0.63 @ ^ [K4: int] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 0.33/0.63 @ S2 )
% 0.33/0.63 = ( plus_plus_rat @ ( B @ A ) @ ( groups3906332499630173760nt_rat @ C @ ( minus_minus_set_int @ S2 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) )
% 0.33/0.63 & ( ~ ( member_int @ A @ S2 )
% 0.33/0.63 => ( ( groups3906332499630173760nt_rat
% 0.33/0.63 @ ^ [K4: int] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 0.33/0.63 @ S2 )
% 0.33/0.63 = ( groups3906332499630173760nt_rat @ C @ ( minus_minus_set_int @ S2 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % sum.delta_remove
% 0.33/0.63 thf(fact_6046_sum_Odelta__remove,axiom,
% 0.33/0.63 ! [S2: set_int,A: int,B: int > nat,C: int > nat] :
% 0.33/0.63 ( ( finite_finite_int @ S2 )
% 0.33/0.63 => ( ( ( member_int @ A @ S2 )
% 0.33/0.63 => ( ( groups4541462559716669496nt_nat
% 0.33/0.63 @ ^ [K4: int] : ( if_nat @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 0.33/0.63 @ S2 )
% 0.33/0.63 = ( plus_plus_nat @ ( B @ A ) @ ( groups4541462559716669496nt_nat @ C @ ( minus_minus_set_int @ S2 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) )
% 0.33/0.63 & ( ~ ( member_int @ A @ S2 )
% 0.33/0.63 => ( ( groups4541462559716669496nt_nat
% 0.33/0.63 @ ^ [K4: int] : ( if_nat @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 0.33/0.63 @ S2 )
% 0.33/0.63 = ( groups4541462559716669496nt_nat @ C @ ( minus_minus_set_int @ S2 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % sum.delta_remove
% 0.33/0.63 thf(fact_6047_sum_Odelta__remove,axiom,
% 0.33/0.63 ! [S2: set_nat,A: nat,B: nat > rat,C: nat > rat] :
% 0.33/0.63 ( ( finite_finite_nat @ S2 )
% 0.33/0.63 => ( ( ( member_nat @ A @ S2 )
% 0.33/0.63 => ( ( groups2906978787729119204at_rat
% 0.33/0.63 @ ^ [K4: nat] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 0.33/0.63 @ S2 )
% 0.33/0.63 = ( plus_plus_rat @ ( B @ A ) @ ( groups2906978787729119204at_rat @ C @ ( minus_minus_set_nat @ S2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ) )
% 0.33/0.63 & ( ~ ( member_nat @ A @ S2 )
% 0.33/0.63 => ( ( groups2906978787729119204at_rat
% 0.33/0.63 @ ^ [K4: nat] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 0.33/0.63 @ S2 )
% 0.33/0.63 = ( groups2906978787729119204at_rat @ C @ ( minus_minus_set_nat @ S2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % sum.delta_remove
% 0.33/0.63 thf(fact_6048_sum_Odelta__remove,axiom,
% 0.33/0.63 ! [S2: set_nat,A: nat,B: nat > int,C: nat > int] :
% 0.33/0.63 ( ( finite_finite_nat @ S2 )
% 0.33/0.63 => ( ( ( member_nat @ A @ S2 )
% 0.33/0.63 => ( ( groups3539618377306564664at_int
% 0.33/0.63 @ ^ [K4: nat] : ( if_int @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 0.33/0.63 @ S2 )
% 0.33/0.63 = ( plus_plus_int @ ( B @ A ) @ ( groups3539618377306564664at_int @ C @ ( minus_minus_set_nat @ S2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ) )
% 0.33/0.63 & ( ~ ( member_nat @ A @ S2 )
% 0.33/0.63 => ( ( groups3539618377306564664at_int
% 0.33/0.63 @ ^ [K4: nat] : ( if_int @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 0.33/0.63 @ S2 )
% 0.33/0.63 = ( groups3539618377306564664at_int @ C @ ( minus_minus_set_nat @ S2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % sum.delta_remove
% 0.33/0.63 thf(fact_6049_prod__le__power,axiom,
% 0.33/0.63 ! [A2: set_o,F: $o > code_integer,N2: code_integer,K: nat] :
% 0.33/0.63 ( ! [I2: $o] :
% 0.33/0.63 ( ( member_o @ I2 @ A2 )
% 0.33/0.63 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ I2 ) )
% 0.33/0.63 & ( ord_le3102999989581377725nteger @ ( F @ I2 ) @ N2 ) ) )
% 0.33/0.63 => ( ( ord_less_eq_nat @ ( finite_card_o @ A2 ) @ K )
% 0.33/0.63 => ( ( ord_le3102999989581377725nteger @ one_one_Code_integer @ N2 )
% 0.33/0.63 => ( ord_le3102999989581377725nteger @ ( groups7694694392188491536nteger @ F @ A2 ) @ ( power_8256067586552552935nteger @ N2 @ K ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod_le_power
% 0.33/0.63 thf(fact_6050_prod__le__power,axiom,
% 0.33/0.63 ! [A2: set_int,F: int > code_integer,N2: code_integer,K: nat] :
% 0.33/0.63 ( ! [I2: int] :
% 0.33/0.63 ( ( member_int @ I2 @ A2 )
% 0.33/0.63 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ I2 ) )
% 0.33/0.63 & ( ord_le3102999989581377725nteger @ ( F @ I2 ) @ N2 ) ) )
% 0.33/0.63 => ( ( ord_less_eq_nat @ ( finite_card_int @ A2 ) @ K )
% 0.33/0.63 => ( ( ord_le3102999989581377725nteger @ one_one_Code_integer @ N2 )
% 0.33/0.63 => ( ord_le3102999989581377725nteger @ ( groups3827104343326376752nteger @ F @ A2 ) @ ( power_8256067586552552935nteger @ N2 @ K ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod_le_power
% 0.33/0.63 thf(fact_6051_prod__le__power,axiom,
% 0.33/0.63 ! [A2: set_Product_unit,F: product_unit > code_integer,N2: code_integer,K: nat] :
% 0.33/0.63 ( ! [I2: product_unit] :
% 0.33/0.63 ( ( member_Product_unit @ I2 @ A2 )
% 0.33/0.63 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ I2 ) )
% 0.33/0.63 & ( ord_le3102999989581377725nteger @ ( F @ I2 ) @ N2 ) ) )
% 0.33/0.63 => ( ( ord_less_eq_nat @ ( finite410649719033368117t_unit @ A2 ) @ K )
% 0.33/0.63 => ( ( ord_le3102999989581377725nteger @ one_one_Code_integer @ N2 )
% 0.33/0.63 => ( ord_le3102999989581377725nteger @ ( groups8185359811944078981nteger @ F @ A2 ) @ ( power_8256067586552552935nteger @ N2 @ K ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod_le_power
% 0.33/0.63 thf(fact_6052_prod__le__power,axiom,
% 0.33/0.63 ! [A2: set_nat,F: nat > code_integer,N2: code_integer,K: nat] :
% 0.33/0.63 ( ! [I2: nat] :
% 0.33/0.63 ( ( member_nat @ I2 @ A2 )
% 0.33/0.63 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ I2 ) )
% 0.33/0.63 & ( ord_le3102999989581377725nteger @ ( F @ I2 ) @ N2 ) ) )
% 0.33/0.63 => ( ( ord_less_eq_nat @ ( finite_card_nat @ A2 ) @ K )
% 0.33/0.63 => ( ( ord_le3102999989581377725nteger @ one_one_Code_integer @ N2 )
% 0.33/0.63 => ( ord_le3102999989581377725nteger @ ( groups3455450783089532116nteger @ F @ A2 ) @ ( power_8256067586552552935nteger @ N2 @ K ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod_le_power
% 0.33/0.63 thf(fact_6053_prod__le__power,axiom,
% 0.33/0.63 ! [A2: set_o,F: $o > rat,N2: rat,K: nat] :
% 0.33/0.63 ( ! [I2: $o] :
% 0.33/0.63 ( ( member_o @ I2 @ A2 )
% 0.33/0.63 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) )
% 0.33/0.63 & ( ord_less_eq_rat @ ( F @ I2 ) @ N2 ) ) )
% 0.33/0.63 => ( ( ord_less_eq_nat @ ( finite_card_o @ A2 ) @ K )
% 0.33/0.63 => ( ( ord_less_eq_rat @ one_one_rat @ N2 )
% 0.33/0.63 => ( ord_less_eq_rat @ ( groups2869687844427037835_o_rat @ F @ A2 ) @ ( power_power_rat @ N2 @ K ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod_le_power
% 0.33/0.63 thf(fact_6054_prod__le__power,axiom,
% 0.33/0.63 ! [A2: set_int,F: int > rat,N2: rat,K: nat] :
% 0.33/0.63 ( ! [I2: int] :
% 0.33/0.63 ( ( member_int @ I2 @ A2 )
% 0.33/0.63 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) )
% 0.33/0.63 & ( ord_less_eq_rat @ ( F @ I2 ) @ N2 ) ) )
% 0.33/0.63 => ( ( ord_less_eq_nat @ ( finite_card_int @ A2 ) @ K )
% 0.33/0.63 => ( ( ord_less_eq_rat @ one_one_rat @ N2 )
% 0.33/0.63 => ( ord_less_eq_rat @ ( groups1072433553688619179nt_rat @ F @ A2 ) @ ( power_power_rat @ N2 @ K ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod_le_power
% 0.33/0.63 thf(fact_6055_prod__le__power,axiom,
% 0.33/0.63 ! [A2: set_Product_unit,F: product_unit > rat,N2: rat,K: nat] :
% 0.33/0.63 ( ! [I2: product_unit] :
% 0.33/0.63 ( ( member_Product_unit @ I2 @ A2 )
% 0.33/0.63 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) )
% 0.33/0.63 & ( ord_less_eq_rat @ ( F @ I2 ) @ N2 ) ) )
% 0.33/0.63 => ( ( ord_less_eq_nat @ ( finite410649719033368117t_unit @ A2 ) @ K )
% 0.33/0.63 => ( ( ord_less_eq_rat @ one_one_rat @ N2 )
% 0.33/0.63 => ( ord_less_eq_rat @ ( groups8984663225794451456it_rat @ F @ A2 ) @ ( power_power_rat @ N2 @ K ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod_le_power
% 0.33/0.63 thf(fact_6056_prod__le__power,axiom,
% 0.33/0.63 ! [A2: set_nat,F: nat > rat,N2: rat,K: nat] :
% 0.33/0.63 ( ! [I2: nat] :
% 0.33/0.63 ( ( member_nat @ I2 @ A2 )
% 0.33/0.63 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) )
% 0.33/0.63 & ( ord_less_eq_rat @ ( F @ I2 ) @ N2 ) ) )
% 0.33/0.63 => ( ( ord_less_eq_nat @ ( finite_card_nat @ A2 ) @ K )
% 0.33/0.63 => ( ( ord_less_eq_rat @ one_one_rat @ N2 )
% 0.33/0.63 => ( ord_less_eq_rat @ ( groups73079841787564623at_rat @ F @ A2 ) @ ( power_power_rat @ N2 @ K ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod_le_power
% 0.33/0.63 thf(fact_6057_prod__le__power,axiom,
% 0.33/0.63 ! [A2: set_o,F: $o > nat,N2: nat,K: nat] :
% 0.33/0.63 ( ! [I2: $o] :
% 0.33/0.63 ( ( member_o @ I2 @ A2 )
% 0.33/0.63 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I2 ) )
% 0.33/0.63 & ( ord_less_eq_nat @ ( F @ I2 ) @ N2 ) ) )
% 0.33/0.63 => ( ( ord_less_eq_nat @ ( finite_card_o @ A2 ) @ K )
% 0.33/0.63 => ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 0.33/0.63 => ( ord_less_eq_nat @ ( groups3504817904513533571_o_nat @ F @ A2 ) @ ( power_power_nat @ N2 @ K ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod_le_power
% 0.33/0.63 thf(fact_6058_prod__le__power,axiom,
% 0.33/0.63 ! [A2: set_int,F: int > nat,N2: nat,K: nat] :
% 0.33/0.63 ( ! [I2: int] :
% 0.33/0.63 ( ( member_int @ I2 @ A2 )
% 0.33/0.63 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I2 ) )
% 0.33/0.63 & ( ord_less_eq_nat @ ( F @ I2 ) @ N2 ) ) )
% 0.33/0.63 => ( ( ord_less_eq_nat @ ( finite_card_int @ A2 ) @ K )
% 0.33/0.63 => ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 0.33/0.63 => ( ord_less_eq_nat @ ( groups1707563613775114915nt_nat @ F @ A2 ) @ ( power_power_nat @ N2 @ K ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod_le_power
% 0.33/0.63 thf(fact_6059_card__Diff__insert,axiom,
% 0.33/0.63 ! [A: produc3843707927480180839at_nat,A2: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat] :
% 0.33/0.63 ( ( member8757157785044589968at_nat @ A @ A2 )
% 0.33/0.63 => ( ~ ( member8757157785044589968at_nat @ A @ B5 )
% 0.33/0.63 => ( ( finite3771342082235030671at_nat @ ( minus_3314409938677909166at_nat @ A2 @ ( insert9069300056098147895at_nat @ A @ B5 ) ) )
% 0.33/0.63 = ( minus_minus_nat @ ( finite3771342082235030671at_nat @ ( minus_3314409938677909166at_nat @ A2 @ B5 ) ) @ one_one_nat ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % card_Diff_insert
% 0.33/0.63 thf(fact_6060_card__Diff__insert,axiom,
% 0.33/0.63 ! [A: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 0.33/0.63 ( ( member8440522571783428010at_nat @ A @ A2 )
% 0.33/0.63 => ( ~ ( member8440522571783428010at_nat @ A @ B5 )
% 0.33/0.63 => ( ( finite711546835091564841at_nat @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ A @ B5 ) ) )
% 0.33/0.63 = ( minus_minus_nat @ ( finite711546835091564841at_nat @ ( minus_1356011639430497352at_nat @ A2 @ B5 ) ) @ one_one_nat ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % card_Diff_insert
% 0.33/0.63 thf(fact_6061_card__Diff__insert,axiom,
% 0.33/0.63 ! [A: $o,A2: set_o,B5: set_o] :
% 0.33/0.63 ( ( member_o @ A @ A2 )
% 0.33/0.63 => ( ~ ( member_o @ A @ B5 )
% 0.33/0.63 => ( ( finite_card_o @ ( minus_minus_set_o @ A2 @ ( insert_o @ A @ B5 ) ) )
% 0.33/0.63 = ( minus_minus_nat @ ( finite_card_o @ ( minus_minus_set_o @ A2 @ B5 ) ) @ one_one_nat ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % card_Diff_insert
% 0.33/0.63 thf(fact_6062_card__Diff__insert,axiom,
% 0.33/0.63 ! [A: int,A2: set_int,B5: set_int] :
% 0.33/0.63 ( ( member_int @ A @ A2 )
% 0.33/0.63 => ( ~ ( member_int @ A @ B5 )
% 0.33/0.63 => ( ( finite_card_int @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ B5 ) ) )
% 0.33/0.63 = ( minus_minus_nat @ ( finite_card_int @ ( minus_minus_set_int @ A2 @ B5 ) ) @ one_one_nat ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % card_Diff_insert
% 0.33/0.63 thf(fact_6063_card__Diff__insert,axiom,
% 0.33/0.63 ! [A: product_unit,A2: set_Product_unit,B5: set_Product_unit] :
% 0.33/0.63 ( ( member_Product_unit @ A @ A2 )
% 0.33/0.63 => ( ~ ( member_Product_unit @ A @ B5 )
% 0.33/0.63 => ( ( finite410649719033368117t_unit @ ( minus_6452836326544984404t_unit @ A2 @ ( insert_Product_unit @ A @ B5 ) ) )
% 0.33/0.63 = ( minus_minus_nat @ ( finite410649719033368117t_unit @ ( minus_6452836326544984404t_unit @ A2 @ B5 ) ) @ one_one_nat ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % card_Diff_insert
% 0.33/0.63 thf(fact_6064_card__Diff__insert,axiom,
% 0.33/0.63 ! [A: list_nat,A2: set_list_nat,B5: set_list_nat] :
% 0.33/0.63 ( ( member_list_nat @ A @ A2 )
% 0.33/0.63 => ( ~ ( member_list_nat @ A @ B5 )
% 0.33/0.63 => ( ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A2 @ ( insert_list_nat @ A @ B5 ) ) )
% 0.33/0.63 = ( minus_minus_nat @ ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A2 @ B5 ) ) @ one_one_nat ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % card_Diff_insert
% 0.33/0.63 thf(fact_6065_card__Diff__insert,axiom,
% 0.33/0.63 ! [A: nat,A2: set_nat,B5: set_nat] :
% 0.33/0.63 ( ( member_nat @ A @ A2 )
% 0.33/0.63 => ( ~ ( member_nat @ A @ B5 )
% 0.33/0.63 => ( ( finite_card_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ B5 ) ) )
% 0.33/0.63 = ( minus_minus_nat @ ( finite_card_nat @ ( minus_minus_set_nat @ A2 @ B5 ) ) @ one_one_nat ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % card_Diff_insert
% 0.33/0.63 thf(fact_6066_card__insert__le__m1,axiom,
% 0.33/0.63 ! [N2: nat,Y: set_Pr4329608150637261639at_nat,X: produc3843707927480180839at_nat] :
% 0.33/0.63 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.33/0.63 => ( ( ord_less_eq_nat @ ( finite3771342082235030671at_nat @ Y ) @ ( minus_minus_nat @ N2 @ one_one_nat ) )
% 0.33/0.63 => ( ord_less_eq_nat @ ( finite3771342082235030671at_nat @ ( insert9069300056098147895at_nat @ X @ Y ) ) @ N2 ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % card_insert_le_m1
% 0.33/0.63 thf(fact_6067_card__insert__le__m1,axiom,
% 0.33/0.63 ! [N2: nat,Y: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat] :
% 0.33/0.63 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.33/0.63 => ( ( ord_less_eq_nat @ ( finite711546835091564841at_nat @ Y ) @ ( minus_minus_nat @ N2 @ one_one_nat ) )
% 0.33/0.63 => ( ord_less_eq_nat @ ( finite711546835091564841at_nat @ ( insert8211810215607154385at_nat @ X @ Y ) ) @ N2 ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % card_insert_le_m1
% 0.33/0.63 thf(fact_6068_card__insert__le__m1,axiom,
% 0.33/0.63 ! [N2: nat,Y: set_o,X: $o] :
% 0.33/0.63 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.33/0.63 => ( ( ord_less_eq_nat @ ( finite_card_o @ Y ) @ ( minus_minus_nat @ N2 @ one_one_nat ) )
% 0.33/0.63 => ( ord_less_eq_nat @ ( finite_card_o @ ( insert_o @ X @ Y ) ) @ N2 ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % card_insert_le_m1
% 0.33/0.63 thf(fact_6069_card__insert__le__m1,axiom,
% 0.33/0.63 ! [N2: nat,Y: set_int,X: int] :
% 0.33/0.63 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.33/0.63 => ( ( ord_less_eq_nat @ ( finite_card_int @ Y ) @ ( minus_minus_nat @ N2 @ one_one_nat ) )
% 0.33/0.63 => ( ord_less_eq_nat @ ( finite_card_int @ ( insert_int @ X @ Y ) ) @ N2 ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % card_insert_le_m1
% 0.33/0.63 thf(fact_6070_card__insert__le__m1,axiom,
% 0.33/0.63 ! [N2: nat,Y: set_Product_unit,X: product_unit] :
% 0.33/0.63 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.33/0.63 => ( ( ord_less_eq_nat @ ( finite410649719033368117t_unit @ Y ) @ ( minus_minus_nat @ N2 @ one_one_nat ) )
% 0.33/0.63 => ( ord_less_eq_nat @ ( finite410649719033368117t_unit @ ( insert_Product_unit @ X @ Y ) ) @ N2 ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % card_insert_le_m1
% 0.33/0.63 thf(fact_6071_card__insert__le__m1,axiom,
% 0.33/0.63 ! [N2: nat,Y: set_nat,X: nat] :
% 0.33/0.63 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.33/0.63 => ( ( ord_less_eq_nat @ ( finite_card_nat @ Y ) @ ( minus_minus_nat @ N2 @ one_one_nat ) )
% 0.33/0.63 => ( ord_less_eq_nat @ ( finite_card_nat @ ( insert_nat @ X @ Y ) ) @ N2 ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % card_insert_le_m1
% 0.33/0.63 thf(fact_6072_card__insert__le__m1,axiom,
% 0.33/0.63 ! [N2: nat,Y: set_list_nat,X: list_nat] :
% 0.33/0.63 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.33/0.63 => ( ( ord_less_eq_nat @ ( finite_card_list_nat @ Y ) @ ( minus_minus_nat @ N2 @ one_one_nat ) )
% 0.33/0.63 => ( ord_less_eq_nat @ ( finite_card_list_nat @ ( insert_list_nat @ X @ Y ) ) @ N2 ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % card_insert_le_m1
% 0.33/0.63 thf(fact_6073_card__Diff__singleton__if,axiom,
% 0.33/0.63 ! [X: product_unit,A2: set_Product_unit] :
% 0.33/0.63 ( ( ( member_Product_unit @ X @ A2 )
% 0.33/0.63 => ( ( finite410649719033368117t_unit @ ( minus_6452836326544984404t_unit @ A2 @ ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) ) )
% 0.33/0.63 = ( minus_minus_nat @ ( finite410649719033368117t_unit @ A2 ) @ one_one_nat ) ) )
% 0.33/0.63 & ( ~ ( member_Product_unit @ X @ A2 )
% 0.33/0.63 => ( ( finite410649719033368117t_unit @ ( minus_6452836326544984404t_unit @ A2 @ ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) ) )
% 0.33/0.63 = ( finite410649719033368117t_unit @ A2 ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % card_Diff_singleton_if
% 0.33/0.63 thf(fact_6074_card__Diff__singleton__if,axiom,
% 0.33/0.63 ! [X: list_nat,A2: set_list_nat] :
% 0.33/0.63 ( ( ( member_list_nat @ X @ A2 )
% 0.33/0.63 => ( ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A2 @ ( insert_list_nat @ X @ bot_bot_set_list_nat ) ) )
% 0.33/0.63 = ( minus_minus_nat @ ( finite_card_list_nat @ A2 ) @ one_one_nat ) ) )
% 0.33/0.63 & ( ~ ( member_list_nat @ X @ A2 )
% 0.33/0.63 => ( ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A2 @ ( insert_list_nat @ X @ bot_bot_set_list_nat ) ) )
% 0.33/0.63 = ( finite_card_list_nat @ A2 ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % card_Diff_singleton_if
% 0.33/0.63 thf(fact_6075_card__Diff__singleton__if,axiom,
% 0.33/0.63 ! [X: produc3843707927480180839at_nat,A2: set_Pr4329608150637261639at_nat] :
% 0.33/0.63 ( ( ( member8757157785044589968at_nat @ X @ A2 )
% 0.33/0.63 => ( ( finite3771342082235030671at_nat @ ( minus_3314409938677909166at_nat @ A2 @ ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) ) )
% 0.33/0.63 = ( minus_minus_nat @ ( finite3771342082235030671at_nat @ A2 ) @ one_one_nat ) ) )
% 0.33/0.63 & ( ~ ( member8757157785044589968at_nat @ X @ A2 )
% 0.33/0.63 => ( ( finite3771342082235030671at_nat @ ( minus_3314409938677909166at_nat @ A2 @ ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) ) )
% 0.33/0.63 = ( finite3771342082235030671at_nat @ A2 ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % card_Diff_singleton_if
% 0.33/0.63 thf(fact_6076_card__Diff__singleton__if,axiom,
% 0.33/0.63 ! [X: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat] :
% 0.33/0.63 ( ( ( member8440522571783428010at_nat @ X @ A2 )
% 0.33/0.63 => ( ( finite711546835091564841at_nat @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) )
% 0.33/0.63 = ( minus_minus_nat @ ( finite711546835091564841at_nat @ A2 ) @ one_one_nat ) ) )
% 0.33/0.63 & ( ~ ( member8440522571783428010at_nat @ X @ A2 )
% 0.33/0.63 => ( ( finite711546835091564841at_nat @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) )
% 0.33/0.63 = ( finite711546835091564841at_nat @ A2 ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % card_Diff_singleton_if
% 0.33/0.63 thf(fact_6077_card__Diff__singleton__if,axiom,
% 0.33/0.63 ! [X: $o,A2: set_o] :
% 0.33/0.63 ( ( ( member_o @ X @ A2 )
% 0.33/0.63 => ( ( finite_card_o @ ( minus_minus_set_o @ A2 @ ( insert_o @ X @ bot_bot_set_o ) ) )
% 0.33/0.63 = ( minus_minus_nat @ ( finite_card_o @ A2 ) @ one_one_nat ) ) )
% 0.33/0.63 & ( ~ ( member_o @ X @ A2 )
% 0.33/0.63 => ( ( finite_card_o @ ( minus_minus_set_o @ A2 @ ( insert_o @ X @ bot_bot_set_o ) ) )
% 0.33/0.63 = ( finite_card_o @ A2 ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % card_Diff_singleton_if
% 0.33/0.63 thf(fact_6078_card__Diff__singleton__if,axiom,
% 0.33/0.63 ! [X: int,A2: set_int] :
% 0.33/0.63 ( ( ( member_int @ X @ A2 )
% 0.33/0.63 => ( ( finite_card_int @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) )
% 0.33/0.63 = ( minus_minus_nat @ ( finite_card_int @ A2 ) @ one_one_nat ) ) )
% 0.33/0.63 & ( ~ ( member_int @ X @ A2 )
% 0.33/0.63 => ( ( finite_card_int @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) )
% 0.33/0.63 = ( finite_card_int @ A2 ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % card_Diff_singleton_if
% 0.33/0.63 thf(fact_6079_card__Diff__singleton__if,axiom,
% 0.33/0.63 ! [X: nat,A2: set_nat] :
% 0.33/0.63 ( ( ( member_nat @ X @ A2 )
% 0.33/0.63 => ( ( finite_card_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) )
% 0.33/0.63 = ( minus_minus_nat @ ( finite_card_nat @ A2 ) @ one_one_nat ) ) )
% 0.33/0.63 & ( ~ ( member_nat @ X @ A2 )
% 0.33/0.63 => ( ( finite_card_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) )
% 0.33/0.63 = ( finite_card_nat @ A2 ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % card_Diff_singleton_if
% 0.33/0.63 thf(fact_6080_card__Diff__singleton,axiom,
% 0.33/0.63 ! [X: product_unit,A2: set_Product_unit] :
% 0.33/0.63 ( ( member_Product_unit @ X @ A2 )
% 0.33/0.63 => ( ( finite410649719033368117t_unit @ ( minus_6452836326544984404t_unit @ A2 @ ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) ) )
% 0.33/0.63 = ( minus_minus_nat @ ( finite410649719033368117t_unit @ A2 ) @ one_one_nat ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % card_Diff_singleton
% 0.33/0.63 thf(fact_6081_card__Diff__singleton,axiom,
% 0.33/0.63 ! [X: list_nat,A2: set_list_nat] :
% 0.33/0.63 ( ( member_list_nat @ X @ A2 )
% 0.33/0.63 => ( ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A2 @ ( insert_list_nat @ X @ bot_bot_set_list_nat ) ) )
% 0.33/0.63 = ( minus_minus_nat @ ( finite_card_list_nat @ A2 ) @ one_one_nat ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % card_Diff_singleton
% 0.33/0.63 thf(fact_6082_card__Diff__singleton,axiom,
% 0.33/0.63 ! [X: produc3843707927480180839at_nat,A2: set_Pr4329608150637261639at_nat] :
% 0.33/0.63 ( ( member8757157785044589968at_nat @ X @ A2 )
% 0.33/0.63 => ( ( finite3771342082235030671at_nat @ ( minus_3314409938677909166at_nat @ A2 @ ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) ) )
% 0.33/0.63 = ( minus_minus_nat @ ( finite3771342082235030671at_nat @ A2 ) @ one_one_nat ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % card_Diff_singleton
% 0.33/0.63 thf(fact_6083_card__Diff__singleton,axiom,
% 0.33/0.63 ! [X: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat] :
% 0.33/0.63 ( ( member8440522571783428010at_nat @ X @ A2 )
% 0.33/0.63 => ( ( finite711546835091564841at_nat @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) )
% 0.33/0.63 = ( minus_minus_nat @ ( finite711546835091564841at_nat @ A2 ) @ one_one_nat ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % card_Diff_singleton
% 0.33/0.63 thf(fact_6084_card__Diff__singleton,axiom,
% 0.33/0.63 ! [X: $o,A2: set_o] :
% 0.33/0.63 ( ( member_o @ X @ A2 )
% 0.33/0.63 => ( ( finite_card_o @ ( minus_minus_set_o @ A2 @ ( insert_o @ X @ bot_bot_set_o ) ) )
% 0.33/0.63 = ( minus_minus_nat @ ( finite_card_o @ A2 ) @ one_one_nat ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % card_Diff_singleton
% 0.33/0.63 thf(fact_6085_card__Diff__singleton,axiom,
% 0.33/0.63 ! [X: int,A2: set_int] :
% 0.33/0.63 ( ( member_int @ X @ A2 )
% 0.33/0.63 => ( ( finite_card_int @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) )
% 0.33/0.63 = ( minus_minus_nat @ ( finite_card_int @ A2 ) @ one_one_nat ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % card_Diff_singleton
% 0.33/0.63 thf(fact_6086_card__Diff__singleton,axiom,
% 0.33/0.63 ! [X: nat,A2: set_nat] :
% 0.33/0.63 ( ( member_nat @ X @ A2 )
% 0.33/0.63 => ( ( finite_card_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) )
% 0.33/0.63 = ( minus_minus_nat @ ( finite_card_nat @ A2 ) @ one_one_nat ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % card_Diff_singleton
% 0.33/0.63 thf(fact_6087_in__finite__psubset,axiom,
% 0.33/0.63 ! [A2: set_nat,B5: set_nat] :
% 0.33/0.63 ( ( member8277197624267554838et_nat @ ( produc4532415448927165861et_nat @ A2 @ B5 ) @ finite_psubset_nat )
% 0.33/0.63 = ( ( ord_less_set_nat @ A2 @ B5 )
% 0.33/0.63 & ( finite_finite_nat @ B5 ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % in_finite_psubset
% 0.33/0.63 thf(fact_6088_in__finite__psubset,axiom,
% 0.33/0.63 ! [A2: set_int,B5: set_int] :
% 0.33/0.63 ( ( member2572552093476627150et_int @ ( produc6363374080413544029et_int @ A2 @ B5 ) @ finite_psubset_int )
% 0.33/0.63 = ( ( ord_less_set_int @ A2 @ B5 )
% 0.33/0.63 & ( finite_finite_int @ B5 ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % in_finite_psubset
% 0.33/0.63 thf(fact_6089_in__finite__psubset,axiom,
% 0.33/0.63 ! [A2: set_Code_integer,B5: set_Code_integer] :
% 0.33/0.63 ( ( member4307123515891402160nteger @ ( produc7443773368509356479nteger @ A2 @ B5 ) @ finite2416775604798480986nteger )
% 0.33/0.63 = ( ( ord_le1307284697595431911nteger @ A2 @ B5 )
% 0.33/0.63 & ( finite6017078050557962740nteger @ B5 ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % in_finite_psubset
% 0.33/0.63 thf(fact_6090_in__finite__psubset,axiom,
% 0.33/0.63 ! [A2: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 0.33/0.63 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A2 @ B5 ) @ finite469560695537375940at_nat )
% 0.33/0.63 = ( ( ord_le7866589430770878221at_nat @ A2 @ B5 )
% 0.33/0.63 & ( finite6177210948735845034at_nat @ B5 ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % in_finite_psubset
% 0.33/0.63 thf(fact_6091_card__1__singletonE,axiom,
% 0.33/0.63 ! [A2: set_Product_unit] :
% 0.33/0.63 ( ( ( finite410649719033368117t_unit @ A2 )
% 0.33/0.63 = one_one_nat )
% 0.33/0.63 => ~ ! [X4: product_unit] :
% 0.33/0.63 ( A2
% 0.33/0.63 != ( insert_Product_unit @ X4 @ bot_bo3957492148770167129t_unit ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % card_1_singletonE
% 0.33/0.63 thf(fact_6092_card__1__singletonE,axiom,
% 0.33/0.63 ! [A2: set_list_nat] :
% 0.33/0.63 ( ( ( finite_card_list_nat @ A2 )
% 0.33/0.63 = one_one_nat )
% 0.33/0.63 => ~ ! [X4: list_nat] :
% 0.33/0.63 ( A2
% 0.33/0.63 != ( insert_list_nat @ X4 @ bot_bot_set_list_nat ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % card_1_singletonE
% 0.33/0.63 thf(fact_6093_card__1__singletonE,axiom,
% 0.33/0.63 ! [A2: set_Pr4329608150637261639at_nat] :
% 0.33/0.63 ( ( ( finite3771342082235030671at_nat @ A2 )
% 0.33/0.63 = one_one_nat )
% 0.33/0.63 => ~ ! [X4: produc3843707927480180839at_nat] :
% 0.33/0.63 ( A2
% 0.33/0.63 != ( insert9069300056098147895at_nat @ X4 @ bot_bo228742789529271731at_nat ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % card_1_singletonE
% 0.33/0.63 thf(fact_6094_card__1__singletonE,axiom,
% 0.33/0.63 ! [A2: set_Pr1261947904930325089at_nat] :
% 0.33/0.63 ( ( ( finite711546835091564841at_nat @ A2 )
% 0.33/0.63 = one_one_nat )
% 0.33/0.63 => ~ ! [X4: product_prod_nat_nat] :
% 0.33/0.63 ( A2
% 0.33/0.63 != ( insert8211810215607154385at_nat @ X4 @ bot_bo2099793752762293965at_nat ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % card_1_singletonE
% 0.33/0.63 thf(fact_6095_card__1__singletonE,axiom,
% 0.33/0.63 ! [A2: set_o] :
% 0.33/0.63 ( ( ( finite_card_o @ A2 )
% 0.33/0.63 = one_one_nat )
% 0.33/0.63 => ~ ! [X4: $o] :
% 0.33/0.63 ( A2
% 0.33/0.63 != ( insert_o @ X4 @ bot_bot_set_o ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % card_1_singletonE
% 0.33/0.63 thf(fact_6096_card__1__singletonE,axiom,
% 0.33/0.63 ! [A2: set_nat] :
% 0.33/0.63 ( ( ( finite_card_nat @ A2 )
% 0.33/0.63 = one_one_nat )
% 0.33/0.63 => ~ ! [X4: nat] :
% 0.33/0.63 ( A2
% 0.33/0.63 != ( insert_nat @ X4 @ bot_bot_set_nat ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % card_1_singletonE
% 0.33/0.63 thf(fact_6097_card__1__singletonE,axiom,
% 0.33/0.63 ! [A2: set_int] :
% 0.33/0.63 ( ( ( finite_card_int @ A2 )
% 0.33/0.63 = one_one_nat )
% 0.33/0.63 => ~ ! [X4: int] :
% 0.33/0.63 ( A2
% 0.33/0.63 != ( insert_int @ X4 @ bot_bot_set_int ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % card_1_singletonE
% 0.33/0.63 thf(fact_6098_integer__of__nat__def,axiom,
% 0.33/0.63 ( code_integer_of_nat
% 0.33/0.63 = ( map_fu6290471996055670595nteger @ id_nat @ code_integer_of_int @ semiri1314217659103216013at_int ) ) ).
% 0.33/0.63
% 0.33/0.63 % integer_of_nat_def
% 0.33/0.63 thf(fact_6099_card__UNIV__unit,axiom,
% 0.33/0.63 ( ( finite410649719033368117t_unit @ top_to1996260823553986621t_unit )
% 0.33/0.63 = one_one_nat ) ).
% 0.33/0.63
% 0.33/0.63 % card_UNIV_unit
% 0.33/0.63 thf(fact_6100_card__lessThan,axiom,
% 0.33/0.63 ! [U: nat] :
% 0.33/0.63 ( ( finite_card_nat @ ( set_ord_lessThan_nat @ U ) )
% 0.33/0.63 = U ) ).
% 0.33/0.63
% 0.33/0.63 % card_lessThan
% 0.33/0.63 thf(fact_6101_card__atLeastLessThan,axiom,
% 0.33/0.63 ! [L: nat,U: nat] :
% 0.33/0.63 ( ( finite_card_nat @ ( set_or4665077453230672383an_nat @ L @ U ) )
% 0.33/0.63 = ( minus_minus_nat @ U @ L ) ) ).
% 0.33/0.63
% 0.33/0.63 % card_atLeastLessThan
% 0.33/0.63 thf(fact_6102_card__atMost,axiom,
% 0.33/0.63 ! [U: nat] :
% 0.33/0.63 ( ( finite_card_nat @ ( set_ord_atMost_nat @ U ) )
% 0.33/0.63 = ( suc @ U ) ) ).
% 0.33/0.63
% 0.33/0.63 % card_atMost
% 0.33/0.63 thf(fact_6103_Collect__const__case__prod,axiom,
% 0.33/0.63 ! [P: $o] :
% 0.33/0.63 ( ( P
% 0.33/0.63 => ( ( collec6321179662152712658at_nat
% 0.33/0.63 @ ( produc410239310623530412_nat_o
% 0.33/0.63 @ ^ [A5: set_Pr1261947904930325089at_nat,B4: set_Pr1261947904930325089at_nat] : P ) )
% 0.33/0.63 = top_to6833984726390702231at_nat ) )
% 0.33/0.63 & ( ~ P
% 0.33/0.63 => ( ( collec6321179662152712658at_nat
% 0.33/0.63 @ ( produc410239310623530412_nat_o
% 0.33/0.63 @ ^ [A5: set_Pr1261947904930325089at_nat,B4: set_Pr1261947904930325089at_nat] : P ) )
% 0.33/0.63 = bot_bo228742789529271731at_nat ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % Collect_const_case_prod
% 0.33/0.63 thf(fact_6104_Collect__const__case__prod,axiom,
% 0.33/0.63 ! [P: $o] :
% 0.33/0.63 ( ( P
% 0.33/0.63 => ( ( collec3392354462482085612at_nat
% 0.33/0.63 @ ( produc6081775807080527818_nat_o
% 0.33/0.63 @ ^ [A5: nat,B4: nat] : P ) )
% 0.33/0.63 = top_to4669805908274784177at_nat ) )
% 0.33/0.63 & ( ~ P
% 0.33/0.63 => ( ( collec3392354462482085612at_nat
% 0.33/0.63 @ ( produc6081775807080527818_nat_o
% 0.33/0.63 @ ^ [A5: nat,B4: nat] : P ) )
% 0.33/0.63 = bot_bo2099793752762293965at_nat ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % Collect_const_case_prod
% 0.33/0.63 thf(fact_6105_nat__of__integer__integer__of__nat,axiom,
% 0.33/0.63 ! [N2: nat] :
% 0.33/0.63 ( ( code_nat_of_integer @ ( code_integer_of_nat @ N2 ) )
% 0.33/0.63 = N2 ) ).
% 0.33/0.63
% 0.33/0.63 % nat_of_integer_integer_of_nat
% 0.33/0.63 thf(fact_6106_card__atLeastAtMost,axiom,
% 0.33/0.63 ! [L: nat,U: nat] :
% 0.33/0.63 ( ( finite_card_nat @ ( set_or1269000886237332187st_nat @ L @ U ) )
% 0.33/0.63 = ( minus_minus_nat @ ( suc @ U ) @ L ) ) ).
% 0.33/0.63
% 0.33/0.63 % card_atLeastAtMost
% 0.33/0.63 thf(fact_6107_integer__of__nat_Orep__eq,axiom,
% 0.33/0.63 ! [X: nat] :
% 0.33/0.63 ( ( code_int_of_integer @ ( code_integer_of_nat @ X ) )
% 0.33/0.63 = ( semiri1314217659103216013at_int @ X ) ) ).
% 0.33/0.63
% 0.33/0.63 % integer_of_nat.rep_eq
% 0.33/0.63 thf(fact_6108_int__of__integer__integer__of__nat,axiom,
% 0.33/0.63 ! [N2: nat] :
% 0.33/0.63 ( ( code_int_of_integer @ ( code_integer_of_nat @ N2 ) )
% 0.33/0.63 = ( semiri1314217659103216013at_int @ N2 ) ) ).
% 0.33/0.63
% 0.33/0.63 % int_of_integer_integer_of_nat
% 0.33/0.63 thf(fact_6109_top__empty__eq2,axiom,
% 0.33/0.63 ( top_to8903224817164384382_nat_o
% 0.33/0.63 = ( ^ [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ Y3 ) @ top_to6833984726390702231at_nat ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % top_empty_eq2
% 0.33/0.63 thf(fact_6110_top__empty__eq2,axiom,
% 0.33/0.63 ( top_top_nat_nat_o
% 0.33/0.63 = ( ^ [X3: nat,Y3: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y3 ) @ top_to4669805908274784177at_nat ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % top_empty_eq2
% 0.33/0.63 thf(fact_6111_top__empty__eq2,axiom,
% 0.33/0.63 ( top_to8112647782992986859eger_o
% 0.33/0.63 = ( ^ [X3: produc6241069584506657477e_term > option6357759511663192854e_term,Y3: produc8923325533196201883nteger] : ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X3 @ Y3 ) @ top_to7512759353274530428nteger ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % top_empty_eq2
% 0.33/0.63 thf(fact_6112_top__empty__eq2,axiom,
% 0.33/0.63 ( top_to2428096842796733269_nat_o
% 0.33/0.63 = ( ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3658429121746597890et_nat] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X3 @ Y3 ) @ top_to8753217654552796900et_nat ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % top_empty_eq2
% 0.33/0.63 thf(fact_6113_top__empty__eq2,axiom,
% 0.33/0.63 ( top_to7190503160269336793_nat_o
% 0.33/0.63 = ( ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3925858234332021118et_nat] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X3 @ Y3 ) @ top_to1599102959340997728et_nat ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % top_empty_eq2
% 0.33/0.63 thf(fact_6114_top__empty__eq2,axiom,
% 0.33/0.63 ( top_to6261655714344447806_int_o
% 0.33/0.63 = ( ^ [X3: produc8551481072490612790e_term > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X3 @ Y3 ) @ top_to3181862456159035625nt_int ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % top_empty_eq2
% 0.33/0.63 thf(fact_6115_top__empty__eq2,axiom,
% 0.33/0.63 ( top_to6513043852502318900_int_o
% 0.33/0.63 = ( ^ [X3: int > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X3 @ Y3 ) @ top_to2069137843433766899nt_int ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % top_empty_eq2
% 0.33/0.63 thf(fact_6116_int__of__integer__induct,axiom,
% 0.33/0.63 ! [Y: int,P: int > $o] :
% 0.33/0.63 ( ( member_int @ Y @ top_top_set_int )
% 0.33/0.63 => ( ! [X4: code_integer] : ( P @ ( code_int_of_integer @ X4 ) )
% 0.33/0.63 => ( P @ Y ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % int_of_integer_induct
% 0.33/0.63 thf(fact_6117_int__of__integer__cases,axiom,
% 0.33/0.63 ! [Y: int] :
% 0.33/0.63 ( ( member_int @ Y @ top_top_set_int )
% 0.33/0.63 => ~ ! [X4: code_integer] :
% 0.33/0.63 ( Y
% 0.33/0.63 != ( code_int_of_integer @ X4 ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % int_of_integer_cases
% 0.33/0.63 thf(fact_6118_int__of__integer,axiom,
% 0.33/0.63 ! [X: code_integer] : ( member_int @ ( code_int_of_integer @ X ) @ top_top_set_int ) ).
% 0.33/0.63
% 0.33/0.63 % int_of_integer
% 0.33/0.63 thf(fact_6119_integer__of__int__inject,axiom,
% 0.33/0.63 ! [X: int,Y: int] :
% 0.33/0.63 ( ( member_int @ X @ top_top_set_int )
% 0.33/0.63 => ( ( member_int @ Y @ top_top_set_int )
% 0.33/0.63 => ( ( ( code_integer_of_int @ X )
% 0.33/0.63 = ( code_integer_of_int @ Y ) )
% 0.33/0.63 = ( X = Y ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % integer_of_int_inject
% 0.33/0.63 thf(fact_6120_integer__of__int__induct,axiom,
% 0.33/0.63 ! [P: code_integer > $o,X: code_integer] :
% 0.33/0.63 ( ! [Y5: int] :
% 0.33/0.63 ( ( member_int @ Y5 @ top_top_set_int )
% 0.33/0.63 => ( P @ ( code_integer_of_int @ Y5 ) ) )
% 0.33/0.63 => ( P @ X ) ) ).
% 0.33/0.63
% 0.33/0.63 % integer_of_int_induct
% 0.33/0.63 thf(fact_6121_integer__of__int__cases,axiom,
% 0.33/0.63 ! [X: code_integer] :
% 0.33/0.63 ~ ! [Y5: int] :
% 0.33/0.63 ( ( X
% 0.33/0.63 = ( code_integer_of_int @ Y5 ) )
% 0.33/0.63 => ~ ( member_int @ Y5 @ top_top_set_int ) ) ).
% 0.33/0.63
% 0.33/0.63 % integer_of_int_cases
% 0.33/0.63 thf(fact_6122_subset__card__intvl__is__intvl,axiom,
% 0.33/0.63 ! [A2: set_nat,K: nat] :
% 0.33/0.63 ( ( ord_less_eq_set_nat @ A2 @ ( set_or4665077453230672383an_nat @ K @ ( plus_plus_nat @ K @ ( finite_card_nat @ A2 ) ) ) )
% 0.33/0.63 => ( A2
% 0.33/0.63 = ( set_or4665077453230672383an_nat @ K @ ( plus_plus_nat @ K @ ( finite_card_nat @ A2 ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % subset_card_intvl_is_intvl
% 0.33/0.63 thf(fact_6123_integer__of__int__inverse,axiom,
% 0.33/0.63 ! [Y: int] :
% 0.33/0.63 ( ( member_int @ Y @ top_top_set_int )
% 0.33/0.63 => ( ( code_int_of_integer @ ( code_integer_of_int @ Y ) )
% 0.33/0.63 = Y ) ) ).
% 0.33/0.63
% 0.33/0.63 % integer_of_int_inverse
% 0.33/0.63 thf(fact_6124_subset__eq__atLeast0__lessThan__card,axiom,
% 0.33/0.63 ! [N6: set_nat,N2: nat] :
% 0.33/0.63 ( ( ord_less_eq_set_nat @ N6 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) )
% 0.33/0.63 => ( ord_less_eq_nat @ ( finite_card_nat @ N6 ) @ N2 ) ) ).
% 0.33/0.63
% 0.33/0.63 % subset_eq_atLeast0_lessThan_card
% 0.33/0.63 thf(fact_6125_integer__of__nat__eq__of__nat,axiom,
% 0.33/0.63 code_integer_of_nat = semiri4939895301339042750nteger ).
% 0.33/0.63
% 0.33/0.63 % integer_of_nat_eq_of_nat
% 0.33/0.63 thf(fact_6126_card__less__Suc2,axiom,
% 0.33/0.63 ! [M3: set_nat,I: nat] :
% 0.33/0.63 ( ~ ( member_nat @ zero_zero_nat @ M3 )
% 0.33/0.63 => ( ( finite_card_nat
% 0.33/0.63 @ ( collect_nat
% 0.33/0.63 @ ^ [K4: nat] :
% 0.33/0.63 ( ( member_nat @ ( suc @ K4 ) @ M3 )
% 0.33/0.63 & ( ord_less_nat @ K4 @ I ) ) ) )
% 0.33/0.63 = ( finite_card_nat
% 0.33/0.63 @ ( collect_nat
% 0.33/0.63 @ ^ [K4: nat] :
% 0.33/0.63 ( ( member_nat @ K4 @ M3 )
% 0.33/0.63 & ( ord_less_nat @ K4 @ ( suc @ I ) ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % card_less_Suc2
% 0.33/0.63 thf(fact_6127_card__less__Suc,axiom,
% 0.33/0.63 ! [M3: set_nat,I: nat] :
% 0.33/0.63 ( ( member_nat @ zero_zero_nat @ M3 )
% 0.33/0.63 => ( ( suc
% 0.33/0.63 @ ( finite_card_nat
% 0.33/0.63 @ ( collect_nat
% 0.33/0.63 @ ^ [K4: nat] :
% 0.33/0.63 ( ( member_nat @ ( suc @ K4 ) @ M3 )
% 0.33/0.63 & ( ord_less_nat @ K4 @ I ) ) ) ) )
% 0.33/0.63 = ( finite_card_nat
% 0.33/0.63 @ ( collect_nat
% 0.33/0.63 @ ^ [K4: nat] :
% 0.33/0.63 ( ( member_nat @ K4 @ M3 )
% 0.33/0.63 & ( ord_less_nat @ K4 @ ( suc @ I ) ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % card_less_Suc
% 0.33/0.63 thf(fact_6128_card__less,axiom,
% 0.33/0.63 ! [M3: set_nat,I: nat] :
% 0.33/0.63 ( ( member_nat @ zero_zero_nat @ M3 )
% 0.33/0.63 => ( ( finite_card_nat
% 0.33/0.63 @ ( collect_nat
% 0.33/0.63 @ ^ [K4: nat] :
% 0.33/0.63 ( ( member_nat @ K4 @ M3 )
% 0.33/0.63 & ( ord_less_nat @ K4 @ ( suc @ I ) ) ) ) )
% 0.33/0.63 != zero_zero_nat ) ) ).
% 0.33/0.63
% 0.33/0.63 % card_less
% 0.33/0.63 thf(fact_6129_integer__of__nat__0,axiom,
% 0.33/0.63 ( ( code_integer_of_nat @ zero_zero_nat )
% 0.33/0.63 = zero_z3403309356797280102nteger ) ).
% 0.33/0.63
% 0.33/0.63 % integer_of_nat_0
% 0.33/0.63 thf(fact_6130_integer__of__nat_Oabs__eq,axiom,
% 0.33/0.63 ( code_integer_of_nat
% 0.33/0.63 = ( ^ [X3: nat] : ( code_integer_of_int @ ( semiri1314217659103216013at_int @ X3 ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % integer_of_nat.abs_eq
% 0.33/0.63 thf(fact_6131_integer__of__nat__numeral,axiom,
% 0.33/0.63 ! [N2: num] :
% 0.33/0.63 ( ( code_integer_of_nat @ ( numeral_numeral_nat @ N2 ) )
% 0.33/0.63 = ( numera6620942414471956472nteger @ N2 ) ) ).
% 0.33/0.63
% 0.33/0.63 % integer_of_nat_numeral
% 0.33/0.63 thf(fact_6132_integer__of__nat__1,axiom,
% 0.33/0.63 ( ( code_integer_of_nat @ one_one_nat )
% 0.33/0.63 = one_one_Code_integer ) ).
% 0.33/0.63
% 0.33/0.63 % integer_of_nat_1
% 0.33/0.63 thf(fact_6133_card__sum__le__nat__sum,axiom,
% 0.33/0.63 ! [S2: set_nat] :
% 0.33/0.63 ( ord_less_eq_nat
% 0.33/0.63 @ ( groups3542108847815614940at_nat
% 0.33/0.63 @ ^ [X3: nat] : X3
% 0.33/0.63 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( finite_card_nat @ S2 ) ) )
% 0.33/0.63 @ ( groups3542108847815614940at_nat
% 0.33/0.63 @ ^ [X3: nat] : X3
% 0.33/0.63 @ S2 ) ) ).
% 0.33/0.63
% 0.33/0.63 % card_sum_le_nat_sum
% 0.33/0.63 thf(fact_6134_set__encode__insert,axiom,
% 0.33/0.63 ! [A2: set_nat,N2: nat] :
% 0.33/0.63 ( ( finite_finite_nat @ A2 )
% 0.33/0.63 => ( ~ ( member_nat @ N2 @ A2 )
% 0.33/0.63 => ( ( nat_set_encode @ ( insert_nat @ N2 @ A2 ) )
% 0.33/0.63 = ( plus_plus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ ( nat_set_encode @ A2 ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % set_encode_insert
% 0.33/0.63 thf(fact_6135_card__greaterThanLessThan__int,axiom,
% 0.33/0.63 ! [L: int,U: int] :
% 0.33/0.63 ( ( finite_card_int @ ( set_or5832277885323065728an_int @ L @ U ) )
% 0.33/0.63 = ( nat2 @ ( minus_minus_int @ U @ ( plus_plus_int @ L @ one_one_int ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % card_greaterThanLessThan_int
% 0.33/0.63 thf(fact_6136_wmax__insertI,axiom,
% 0.33/0.63 ! [Y: product_prod_nat_nat,YS: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat,XS: set_Pr1261947904930325089at_nat] :
% 0.33/0.63 ( ( member8440522571783428010at_nat @ Y @ YS )
% 0.33/0.63 => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X @ Y ) @ fun_pair_leq )
% 0.33/0.63 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ XS @ YS ) @ fun_max_weak )
% 0.33/0.63 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( insert8211810215607154385at_nat @ X @ XS ) @ YS ) @ fun_max_weak ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % wmax_insertI
% 0.33/0.63 thf(fact_6137_wmin__insertI,axiom,
% 0.33/0.63 ! [X: product_prod_nat_nat,XS: set_Pr1261947904930325089at_nat,Y: product_prod_nat_nat,YS: set_Pr1261947904930325089at_nat] :
% 0.33/0.63 ( ( member8440522571783428010at_nat @ X @ XS )
% 0.33/0.63 => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X @ Y ) @ fun_pair_leq )
% 0.33/0.63 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ XS @ YS ) @ fun_min_weak )
% 0.33/0.63 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ XS @ ( insert8211810215607154385at_nat @ Y @ YS ) ) @ fun_min_weak ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % wmin_insertI
% 0.33/0.63 thf(fact_6138_smin__insertI,axiom,
% 0.33/0.63 ! [X: product_prod_nat_nat,XS: set_Pr1261947904930325089at_nat,Y: product_prod_nat_nat,YS: set_Pr1261947904930325089at_nat] :
% 0.33/0.63 ( ( member8440522571783428010at_nat @ X @ XS )
% 0.33/0.63 => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X @ Y ) @ fun_pair_less )
% 0.33/0.63 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ XS @ YS ) @ fun_min_strict )
% 0.33/0.63 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ XS @ ( insert8211810215607154385at_nat @ Y @ YS ) ) @ fun_min_strict ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % smin_insertI
% 0.33/0.63 thf(fact_6139_prod_Oinsert_H,axiom,
% 0.33/0.63 ! [I4: set_o,P4: $o > code_integer,I: $o] :
% 0.33/0.63 ( ( finite_finite_o
% 0.33/0.63 @ ( collect_o
% 0.33/0.63 @ ^ [X3: $o] :
% 0.33/0.63 ( ( member_o @ X3 @ I4 )
% 0.33/0.63 & ( ( P4 @ X3 )
% 0.33/0.63 != one_one_Code_integer ) ) ) )
% 0.33/0.63 => ( ( ( member_o @ I @ I4 )
% 0.33/0.63 => ( ( groups2836416601086271911nteger @ P4 @ ( insert_o @ I @ I4 ) )
% 0.33/0.63 = ( groups2836416601086271911nteger @ P4 @ I4 ) ) )
% 0.33/0.63 & ( ~ ( member_o @ I @ I4 )
% 0.33/0.63 => ( ( groups2836416601086271911nteger @ P4 @ ( insert_o @ I @ I4 ) )
% 0.33/0.63 = ( times_3573771949741848930nteger @ ( P4 @ I ) @ ( groups2836416601086271911nteger @ P4 @ I4 ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.insert'
% 0.33/0.63 thf(fact_6140_prod_Oinsert_H,axiom,
% 0.33/0.63 ! [I4: set_nat,P4: nat > code_integer,I: nat] :
% 0.33/0.63 ( ( finite_finite_nat
% 0.33/0.63 @ ( collect_nat
% 0.33/0.63 @ ^ [X3: nat] :
% 0.33/0.63 ( ( member_nat @ X3 @ I4 )
% 0.33/0.63 & ( ( P4 @ X3 )
% 0.33/0.63 != one_one_Code_integer ) ) ) )
% 0.33/0.63 => ( ( ( member_nat @ I @ I4 )
% 0.33/0.63 => ( ( groups8290090294887179773nteger @ P4 @ ( insert_nat @ I @ I4 ) )
% 0.33/0.63 = ( groups8290090294887179773nteger @ P4 @ I4 ) ) )
% 0.33/0.63 & ( ~ ( member_nat @ I @ I4 )
% 0.33/0.63 => ( ( groups8290090294887179773nteger @ P4 @ ( insert_nat @ I @ I4 ) )
% 0.33/0.63 = ( times_3573771949741848930nteger @ ( P4 @ I ) @ ( groups8290090294887179773nteger @ P4 @ I4 ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.insert'
% 0.33/0.63 thf(fact_6141_prod_Oinsert_H,axiom,
% 0.33/0.63 ! [I4: set_int,P4: int > code_integer,I: int] :
% 0.33/0.63 ( ( finite_finite_int
% 0.33/0.63 @ ( collect_int
% 0.33/0.63 @ ^ [X3: int] :
% 0.33/0.63 ( ( member_int @ X3 @ I4 )
% 0.33/0.63 & ( ( P4 @ X3 )
% 0.33/0.63 != one_one_Code_integer ) ) ) )
% 0.33/0.63 => ( ( ( member_int @ I @ I4 )
% 0.33/0.63 => ( ( groups8661743855124024409nteger @ P4 @ ( insert_int @ I @ I4 ) )
% 0.33/0.63 = ( groups8661743855124024409nteger @ P4 @ I4 ) ) )
% 0.33/0.63 & ( ~ ( member_int @ I @ I4 )
% 0.33/0.63 => ( ( groups8661743855124024409nteger @ P4 @ ( insert_int @ I @ I4 ) )
% 0.33/0.63 = ( times_3573771949741848930nteger @ ( P4 @ I ) @ ( groups8661743855124024409nteger @ P4 @ I4 ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.insert'
% 0.33/0.63 thf(fact_6142_prod_Oinsert_H,axiom,
% 0.33/0.63 ! [I4: set_Code_integer,P4: code_integer > code_integer,I: code_integer] :
% 0.33/0.63 ( ( finite6017078050557962740nteger
% 0.33/0.63 @ ( collect_Code_integer
% 0.33/0.63 @ ^ [X3: code_integer] :
% 0.33/0.63 ( ( member_Code_integer @ X3 @ I4 )
% 0.33/0.63 & ( ( P4 @ X3 )
% 0.33/0.63 != one_one_Code_integer ) ) ) )
% 0.33/0.63 => ( ( ( member_Code_integer @ I @ I4 )
% 0.33/0.63 => ( ( groups7219916603568234122nteger @ P4 @ ( insert_Code_integer @ I @ I4 ) )
% 0.33/0.63 = ( groups7219916603568234122nteger @ P4 @ I4 ) ) )
% 0.33/0.63 & ( ~ ( member_Code_integer @ I @ I4 )
% 0.33/0.63 => ( ( groups7219916603568234122nteger @ P4 @ ( insert_Code_integer @ I @ I4 ) )
% 0.33/0.63 = ( times_3573771949741848930nteger @ ( P4 @ I ) @ ( groups7219916603568234122nteger @ P4 @ I4 ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.insert'
% 0.33/0.63 thf(fact_6143_prod_Oinsert_H,axiom,
% 0.33/0.63 ! [I4: set_o,P4: $o > assn,I: $o] :
% 0.33/0.63 ( ( finite_finite_o
% 0.33/0.63 @ ( collect_o
% 0.33/0.63 @ ^ [X3: $o] :
% 0.33/0.63 ( ( member_o @ X3 @ I4 )
% 0.33/0.63 & ( ( P4 @ X3 )
% 0.33/0.63 != one_one_assn ) ) ) )
% 0.33/0.63 => ( ( ( member_o @ I @ I4 )
% 0.33/0.63 => ( ( groups12625163056032370o_assn @ P4 @ ( insert_o @ I @ I4 ) )
% 0.33/0.63 = ( groups12625163056032370o_assn @ P4 @ I4 ) ) )
% 0.33/0.63 & ( ~ ( member_o @ I @ I4 )
% 0.33/0.63 => ( ( groups12625163056032370o_assn @ P4 @ ( insert_o @ I @ I4 ) )
% 0.33/0.63 = ( times_times_assn @ ( P4 @ I ) @ ( groups12625163056032370o_assn @ P4 @ I4 ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.insert'
% 0.33/0.63 thf(fact_6144_prod_Oinsert_H,axiom,
% 0.33/0.63 ! [I4: set_nat,P4: nat > assn,I: nat] :
% 0.33/0.63 ( ( finite_finite_nat
% 0.33/0.63 @ ( collect_nat
% 0.33/0.63 @ ^ [X3: nat] :
% 0.33/0.63 ( ( member_nat @ X3 @ I4 )
% 0.33/0.63 & ( ( P4 @ X3 )
% 0.33/0.63 != one_one_assn ) ) ) )
% 0.33/0.63 => ( ( ( member_nat @ I @ I4 )
% 0.33/0.63 => ( ( groups3916077543535352520t_assn @ P4 @ ( insert_nat @ I @ I4 ) )
% 0.33/0.63 = ( groups3916077543535352520t_assn @ P4 @ I4 ) ) )
% 0.33/0.63 & ( ~ ( member_nat @ I @ I4 )
% 0.33/0.63 => ( ( groups3916077543535352520t_assn @ P4 @ ( insert_nat @ I @ I4 ) )
% 0.33/0.63 = ( times_times_assn @ ( P4 @ I ) @ ( groups3916077543535352520t_assn @ P4 @ I4 ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.insert'
% 0.33/0.63 thf(fact_6145_prod_Oinsert_H,axiom,
% 0.33/0.63 ! [I4: set_int,P4: int > assn,I: int] :
% 0.33/0.63 ( ( finite_finite_int
% 0.33/0.63 @ ( collect_int
% 0.33/0.63 @ ^ [X3: int] :
% 0.33/0.63 ( ( member_int @ X3 @ I4 )
% 0.33/0.63 & ( ( P4 @ X3 )
% 0.33/0.63 != one_one_assn ) ) ) )
% 0.33/0.63 => ( ( ( member_int @ I @ I4 )
% 0.33/0.63 => ( ( groups4891613008741529892t_assn @ P4 @ ( insert_int @ I @ I4 ) )
% 0.33/0.63 = ( groups4891613008741529892t_assn @ P4 @ I4 ) ) )
% 0.33/0.63 & ( ~ ( member_int @ I @ I4 )
% 0.33/0.63 => ( ( groups4891613008741529892t_assn @ P4 @ ( insert_int @ I @ I4 ) )
% 0.33/0.63 = ( times_times_assn @ ( P4 @ I ) @ ( groups4891613008741529892t_assn @ P4 @ I4 ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.insert'
% 0.33/0.63 thf(fact_6146_prod_Oinsert_H,axiom,
% 0.33/0.63 ! [I4: set_Code_integer,P4: code_integer > assn,I: code_integer] :
% 0.33/0.63 ( ( finite6017078050557962740nteger
% 0.33/0.63 @ ( collect_Code_integer
% 0.33/0.63 @ ^ [X3: code_integer] :
% 0.33/0.63 ( ( member_Code_integer @ X3 @ I4 )
% 0.33/0.63 & ( ( P4 @ X3 )
% 0.33/0.63 != one_one_assn ) ) ) )
% 0.33/0.63 => ( ( ( member_Code_integer @ I @ I4 )
% 0.33/0.63 => ( ( groups980104329299799381r_assn @ P4 @ ( insert_Code_integer @ I @ I4 ) )
% 0.33/0.63 = ( groups980104329299799381r_assn @ P4 @ I4 ) ) )
% 0.33/0.63 & ( ~ ( member_Code_integer @ I @ I4 )
% 0.33/0.63 => ( ( groups980104329299799381r_assn @ P4 @ ( insert_Code_integer @ I @ I4 ) )
% 0.33/0.63 = ( times_times_assn @ ( P4 @ I ) @ ( groups980104329299799381r_assn @ P4 @ I4 ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.insert'
% 0.33/0.63 thf(fact_6147_prod_Oinsert_H,axiom,
% 0.33/0.63 ! [I4: set_o,P4: $o > rat,I: $o] :
% 0.33/0.63 ( ( finite_finite_o
% 0.33/0.63 @ ( collect_o
% 0.33/0.63 @ ^ [X3: $o] :
% 0.33/0.63 ( ( member_o @ X3 @ I4 )
% 0.33/0.63 & ( ( P4 @ X3 )
% 0.33/0.63 != one_one_rat ) ) ) )
% 0.33/0.63 => ( ( ( member_o @ I @ I4 )
% 0.33/0.63 => ( ( groups4688112016125141794_o_rat @ P4 @ ( insert_o @ I @ I4 ) )
% 0.33/0.63 = ( groups4688112016125141794_o_rat @ P4 @ I4 ) ) )
% 0.33/0.63 & ( ~ ( member_o @ I @ I4 )
% 0.33/0.63 => ( ( groups4688112016125141794_o_rat @ P4 @ ( insert_o @ I @ I4 ) )
% 0.33/0.63 = ( times_times_rat @ ( P4 @ I ) @ ( groups4688112016125141794_o_rat @ P4 @ I4 ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.insert'
% 0.33/0.63 thf(fact_6148_prod_Oinsert_H,axiom,
% 0.33/0.63 ! [I4: set_nat,P4: nat > rat,I: nat] :
% 0.33/0.63 ( ( finite_finite_nat
% 0.33/0.63 @ ( collect_nat
% 0.33/0.63 @ ^ [X3: nat] :
% 0.33/0.63 ( ( member_nat @ X3 @ I4 )
% 0.33/0.63 & ( ( P4 @ X3 )
% 0.33/0.63 != one_one_rat ) ) ) )
% 0.33/0.63 => ( ( ( member_nat @ I @ I4 )
% 0.33/0.63 => ( ( groups4112464933559648120at_rat @ P4 @ ( insert_nat @ I @ I4 ) )
% 0.33/0.63 = ( groups4112464933559648120at_rat @ P4 @ I4 ) ) )
% 0.33/0.63 & ( ~ ( member_nat @ I @ I4 )
% 0.33/0.63 => ( ( groups4112464933559648120at_rat @ P4 @ ( insert_nat @ I @ I4 ) )
% 0.33/0.63 = ( times_times_rat @ ( P4 @ I ) @ ( groups4112464933559648120at_rat @ P4 @ I4 ) ) ) ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % prod.insert'
% 0.33/0.63 thf(fact_6149_greaterThanLessThan__iff,axiom,
% 0.33/0.63 ! [I: $o,L: $o,U: $o] :
% 0.33/0.63 ( ( member_o @ I @ ( set_or1716231572884733764Than_o @ L @ U ) )
% 0.33/0.63 = ( ( ord_less_o @ L @ I )
% 0.33/0.63 & ( ord_less_o @ I @ U ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % greaterThanLessThan_iff
% 0.33/0.63 thf(fact_6150_greaterThanLessThan__iff,axiom,
% 0.33/0.63 ! [I: rat,L: rat,U: rat] :
% 0.33/0.63 ( ( member_rat @ I @ ( set_or5199638295745620268an_rat @ L @ U ) )
% 0.33/0.63 = ( ( ord_less_rat @ L @ I )
% 0.33/0.63 & ( ord_less_rat @ I @ U ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % greaterThanLessThan_iff
% 0.33/0.63 thf(fact_6151_greaterThanLessThan__iff,axiom,
% 0.33/0.63 ! [I: num,L: num,U: num] :
% 0.33/0.63 ( ( member_num @ I @ ( set_or2392100141987894638an_num @ L @ U ) )
% 0.33/0.63 = ( ( ord_less_num @ L @ I )
% 0.33/0.63 & ( ord_less_num @ I @ U ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % greaterThanLessThan_iff
% 0.33/0.63 thf(fact_6152_greaterThanLessThan__iff,axiom,
% 0.33/0.63 ! [I: int,L: int,U: int] :
% 0.33/0.63 ( ( member_int @ I @ ( set_or5832277885323065728an_int @ L @ U ) )
% 0.33/0.63 = ( ( ord_less_int @ L @ I )
% 0.33/0.63 & ( ord_less_int @ I @ U ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % greaterThanLessThan_iff
% 0.33/0.63 thf(fact_6153_greaterThanLessThan__iff,axiom,
% 0.33/0.63 ! [I: nat,L: nat,U: nat] :
% 0.33/0.63 ( ( member_nat @ I @ ( set_or5834768355832116004an_nat @ L @ U ) )
% 0.33/0.63 = ( ( ord_less_nat @ L @ I )
% 0.33/0.63 & ( ord_less_nat @ I @ U ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % greaterThanLessThan_iff
% 0.33/0.63 thf(fact_6154_greaterThanLessThan__iff,axiom,
% 0.33/0.63 ! [I: code_integer,L: code_integer,U: code_integer] :
% 0.33/0.63 ( ( member_Code_integer @ I @ ( set_or4266950643985792945nteger @ L @ U ) )
% 0.33/0.63 = ( ( ord_le6747313008572928689nteger @ L @ I )
% 0.33/0.63 & ( ord_le6747313008572928689nteger @ I @ U ) ) ) ).
% 0.33/0.63
% 0.33/0.63 % greaterThanLessThan_iff
% 0.33/0.63 thf(fact_6155_finite__greaterThanLessThan__int,axiom,
% 0.33/0.63 ! [L: int,U: int] : ( finite_finite_int @ ( set_or5832277885323065728an_int @ L @ U ) ) ).
% 0.33/0.63
% 0.33/0.63 % finite_greaterThanLessThan_int
% 0.33/0.63 thf(fact_6156_greaterThanLessThan__empty__iff2,axiom,
% 0.33/0.63 ! [A: rat,B: rat] :
% 0.33/0.63 ( ( bot_bot_set_rat
% 0.33/0.63 = ( set_or5199638295745620268an_rat @ A @ B ) )
% 0.33/0.63 = ( ord_less_eq_rat @ B @ A ) ) ).
% 0.33/0.63
% 0.33/0.63 % greaterThanLessThan_empty_iff2
% 0.33/0.63 thf(fact_6157_greaterThanLessThan__empty__iff,axiom,
% 0.33/0.63 ! [A: rat,B: rat] :
% 0.33/0.63 ( ( ( set_or5199638295745620268an_rat @ A @ B )
% 0.33/0.63 = bot_bot_set_rat )
% 0.33/0.63 = ( ord_less_eq_rat @ B @ A ) ) ).
% 0.33/0.63
% 0.33/0.63 % greaterThanLessThan_empty_iff
% 0.33/0.63 thf(fact_6158_greaterThanLessThan__empty,axiom,
% 0.33/0.63 ! [L: $o,K: $o] :
% 0.33/0.63 ( ( ord_less_eq_o @ L @ K )
% 0.33/0.63 => ( ( set_or1716231572884733764Than_o @ K @ L )
% 0.33/0.63 = bot_bot_set_o ) ) ).
% 0.33/0.63
% 0.33/0.63 % greaterThanLessThan_empty
% 0.33/0.63 thf(fact_6159_greaterThanLessThan__empty,axiom,
% 0.33/0.63 ! [L: set_nat,K: set_nat] :
% 0.33/0.63 ( ( ord_less_eq_set_nat @ L @ K )
% 0.33/0.63 => ( ( set_or8625682525731655386et_nat @ K @ L )
% 0.33/0.63 = bot_bot_set_set_nat ) ) ).
% 0.33/0.64
% 0.33/0.64 % greaterThanLessThan_empty
% 0.33/0.64 thf(fact_6160_greaterThanLessThan__empty,axiom,
% 0.33/0.64 ! [L: rat,K: rat] :
% 0.33/0.64 ( ( ord_less_eq_rat @ L @ K )
% 0.33/0.64 => ( ( set_or5199638295745620268an_rat @ K @ L )
% 0.33/0.64 = bot_bot_set_rat ) ) ).
% 0.33/0.64
% 0.33/0.64 % greaterThanLessThan_empty
% 0.33/0.64 thf(fact_6161_greaterThanLessThan__empty,axiom,
% 0.33/0.64 ! [L: num,K: num] :
% 0.33/0.64 ( ( ord_less_eq_num @ L @ K )
% 0.33/0.64 => ( ( set_or2392100141987894638an_num @ K @ L )
% 0.33/0.64 = bot_bot_set_num ) ) ).
% 0.33/0.64
% 0.33/0.64 % greaterThanLessThan_empty
% 0.33/0.64 thf(fact_6162_greaterThanLessThan__empty,axiom,
% 0.33/0.64 ! [L: int,K: int] :
% 0.33/0.64 ( ( ord_less_eq_int @ L @ K )
% 0.33/0.64 => ( ( set_or5832277885323065728an_int @ K @ L )
% 0.33/0.64 = bot_bot_set_int ) ) ).
% 0.33/0.64
% 0.33/0.64 % greaterThanLessThan_empty
% 0.33/0.64 thf(fact_6163_greaterThanLessThan__empty,axiom,
% 0.33/0.64 ! [L: nat,K: nat] :
% 0.33/0.64 ( ( ord_less_eq_nat @ L @ K )
% 0.33/0.64 => ( ( set_or5834768355832116004an_nat @ K @ L )
% 0.33/0.64 = bot_bot_set_nat ) ) ).
% 0.33/0.64
% 0.33/0.64 % greaterThanLessThan_empty
% 0.33/0.64 thf(fact_6164_greaterThanLessThan__empty,axiom,
% 0.33/0.64 ! [L: code_integer,K: code_integer] :
% 0.33/0.64 ( ( ord_le3102999989581377725nteger @ L @ K )
% 0.33/0.64 => ( ( set_or4266950643985792945nteger @ K @ L )
% 0.33/0.64 = bot_bo3990330152332043303nteger ) ) ).
% 0.33/0.64
% 0.33/0.64 % greaterThanLessThan_empty
% 0.33/0.64 thf(fact_6165_infinite__Ioo__iff,axiom,
% 0.33/0.64 ! [A: rat,B: rat] :
% 0.33/0.64 ( ( ~ ( finite_finite_rat @ ( set_or5199638295745620268an_rat @ A @ B ) ) )
% 0.33/0.64 = ( ord_less_rat @ A @ B ) ) ).
% 0.33/0.64
% 0.33/0.64 % infinite_Ioo_iff
% 0.33/0.64 thf(fact_6166_image__uminus__greaterThanLessThan,axiom,
% 0.33/0.64 ! [X: rat,Y: rat] :
% 0.33/0.64 ( ( image_rat_rat @ uminus_uminus_rat @ ( set_or5199638295745620268an_rat @ X @ Y ) )
% 0.33/0.64 = ( set_or5199638295745620268an_rat @ ( uminus_uminus_rat @ Y ) @ ( uminus_uminus_rat @ X ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % image_uminus_greaterThanLessThan
% 0.33/0.64 thf(fact_6167_image__uminus__greaterThanLessThan,axiom,
% 0.33/0.64 ! [X: int,Y: int] :
% 0.33/0.64 ( ( image_int_int @ uminus_uminus_int @ ( set_or5832277885323065728an_int @ X @ Y ) )
% 0.33/0.64 = ( set_or5832277885323065728an_int @ ( uminus_uminus_int @ Y ) @ ( uminus_uminus_int @ X ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % image_uminus_greaterThanLessThan
% 0.33/0.64 thf(fact_6168_image__uminus__greaterThanLessThan,axiom,
% 0.33/0.64 ! [X: code_integer,Y: code_integer] :
% 0.33/0.64 ( ( image_4470545334726330049nteger @ uminus1351360451143612070nteger @ ( set_or4266950643985792945nteger @ X @ Y ) )
% 0.33/0.64 = ( set_or4266950643985792945nteger @ ( uminus1351360451143612070nteger @ Y ) @ ( uminus1351360451143612070nteger @ X ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % image_uminus_greaterThanLessThan
% 0.33/0.64 thf(fact_6169_prod_Oempty_H,axiom,
% 0.33/0.64 ! [P4: $o > code_integer] :
% 0.33/0.64 ( ( groups2836416601086271911nteger @ P4 @ bot_bot_set_o )
% 0.33/0.64 = one_one_Code_integer ) ).
% 0.33/0.64
% 0.33/0.64 % prod.empty'
% 0.33/0.64 thf(fact_6170_prod_Oempty_H,axiom,
% 0.33/0.64 ! [P4: $o > assn] :
% 0.33/0.64 ( ( groups12625163056032370o_assn @ P4 @ bot_bot_set_o )
% 0.33/0.64 = one_one_assn ) ).
% 0.33/0.64
% 0.33/0.64 % prod.empty'
% 0.33/0.64 thf(fact_6171_prod_Oempty_H,axiom,
% 0.33/0.64 ! [P4: $o > rat] :
% 0.33/0.64 ( ( groups4688112016125141794_o_rat @ P4 @ bot_bot_set_o )
% 0.33/0.64 = one_one_rat ) ).
% 0.33/0.64
% 0.33/0.64 % prod.empty'
% 0.33/0.64 thf(fact_6172_prod_Oempty_H,axiom,
% 0.33/0.64 ! [P4: $o > nat] :
% 0.33/0.64 ( ( groups5323242076211637530_o_nat @ P4 @ bot_bot_set_o )
% 0.33/0.64 = one_one_nat ) ).
% 0.33/0.64
% 0.33/0.64 % prod.empty'
% 0.33/0.64 thf(fact_6173_prod_Oempty_H,axiom,
% 0.33/0.64 ! [P4: $o > int] :
% 0.33/0.64 ( ( groups5320751605702587254_o_int @ P4 @ bot_bot_set_o )
% 0.33/0.64 = one_one_int ) ).
% 0.33/0.64
% 0.33/0.64 % prod.empty'
% 0.33/0.64 thf(fact_6174_prod_Oempty_H,axiom,
% 0.33/0.64 ! [P4: nat > code_integer] :
% 0.33/0.64 ( ( groups8290090294887179773nteger @ P4 @ bot_bot_set_nat )
% 0.33/0.64 = one_one_Code_integer ) ).
% 0.33/0.64
% 0.33/0.64 % prod.empty'
% 0.33/0.64 thf(fact_6175_prod_Oempty_H,axiom,
% 0.33/0.64 ! [P4: nat > assn] :
% 0.33/0.64 ( ( groups3916077543535352520t_assn @ P4 @ bot_bot_set_nat )
% 0.33/0.64 = one_one_assn ) ).
% 0.33/0.64
% 0.33/0.64 % prod.empty'
% 0.33/0.64 thf(fact_6176_prod_Oempty_H,axiom,
% 0.33/0.64 ! [P4: nat > rat] :
% 0.33/0.64 ( ( groups4112464933559648120at_rat @ P4 @ bot_bot_set_nat )
% 0.33/0.64 = one_one_rat ) ).
% 0.33/0.64
% 0.33/0.64 % prod.empty'
% 0.33/0.64 thf(fact_6177_prod_Oempty_H,axiom,
% 0.33/0.64 ! [P4: nat > nat] :
% 0.33/0.64 ( ( groups4747594993646143856at_nat @ P4 @ bot_bot_set_nat )
% 0.33/0.64 = one_one_nat ) ).
% 0.33/0.64
% 0.33/0.64 % prod.empty'
% 0.33/0.64 thf(fact_6178_prod_Oempty_H,axiom,
% 0.33/0.64 ! [P4: nat > int] :
% 0.33/0.64 ( ( groups4745104523137093580at_int @ P4 @ bot_bot_set_nat )
% 0.33/0.64 = one_one_int ) ).
% 0.33/0.64
% 0.33/0.64 % prod.empty'
% 0.33/0.64 thf(fact_6179_smin__emptyI,axiom,
% 0.33/0.64 ! [X11: set_Pr1261947904930325089at_nat] :
% 0.33/0.64 ( ( X11 != bot_bo2099793752762293965at_nat )
% 0.33/0.64 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X11 @ bot_bo2099793752762293965at_nat ) @ fun_min_strict ) ) ).
% 0.33/0.64
% 0.33/0.64 % smin_emptyI
% 0.33/0.64 thf(fact_6180_wmax__emptyI,axiom,
% 0.33/0.64 ! [X11: set_Pr1261947904930325089at_nat] :
% 0.33/0.64 ( ( finite6177210948735845034at_nat @ X11 )
% 0.33/0.64 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ bot_bo2099793752762293965at_nat @ X11 ) @ fun_max_weak ) ) ).
% 0.33/0.64
% 0.33/0.64 % wmax_emptyI
% 0.33/0.64 thf(fact_6181_wmin__emptyI,axiom,
% 0.33/0.64 ! [X11: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X11 @ bot_bo2099793752762293965at_nat ) @ fun_min_weak ) ).
% 0.33/0.64
% 0.33/0.64 % wmin_emptyI
% 0.33/0.64 thf(fact_6182_prod_Onon__neutral_H,axiom,
% 0.33/0.64 ! [G: $o > code_integer,I4: set_o] :
% 0.33/0.64 ( ( groups2836416601086271911nteger @ G
% 0.33/0.64 @ ( collect_o
% 0.33/0.64 @ ^ [X3: $o] :
% 0.33/0.64 ( ( member_o @ X3 @ I4 )
% 0.33/0.64 & ( ( G @ X3 )
% 0.33/0.64 != one_one_Code_integer ) ) ) )
% 0.33/0.64 = ( groups2836416601086271911nteger @ G @ I4 ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod.non_neutral'
% 0.33/0.64 thf(fact_6183_prod_Onon__neutral_H,axiom,
% 0.33/0.64 ! [G: int > code_integer,I4: set_int] :
% 0.33/0.64 ( ( groups8661743855124024409nteger @ G
% 0.33/0.64 @ ( collect_int
% 0.33/0.64 @ ^ [X3: int] :
% 0.33/0.64 ( ( member_int @ X3 @ I4 )
% 0.33/0.64 & ( ( G @ X3 )
% 0.33/0.64 != one_one_Code_integer ) ) ) )
% 0.33/0.64 = ( groups8661743855124024409nteger @ G @ I4 ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod.non_neutral'
% 0.33/0.64 thf(fact_6184_prod_Onon__neutral_H,axiom,
% 0.33/0.64 ! [G: nat > code_integer,I4: set_nat] :
% 0.33/0.64 ( ( groups8290090294887179773nteger @ G
% 0.33/0.64 @ ( collect_nat
% 0.33/0.64 @ ^ [X3: nat] :
% 0.33/0.64 ( ( member_nat @ X3 @ I4 )
% 0.33/0.64 & ( ( G @ X3 )
% 0.33/0.64 != one_one_Code_integer ) ) ) )
% 0.33/0.64 = ( groups8290090294887179773nteger @ G @ I4 ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod.non_neutral'
% 0.33/0.64 thf(fact_6185_prod_Onon__neutral_H,axiom,
% 0.33/0.64 ! [G: $o > assn,I4: set_o] :
% 0.33/0.64 ( ( groups12625163056032370o_assn @ G
% 0.33/0.64 @ ( collect_o
% 0.33/0.64 @ ^ [X3: $o] :
% 0.33/0.64 ( ( member_o @ X3 @ I4 )
% 0.33/0.64 & ( ( G @ X3 )
% 0.33/0.64 != one_one_assn ) ) ) )
% 0.33/0.64 = ( groups12625163056032370o_assn @ G @ I4 ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod.non_neutral'
% 0.33/0.64 thf(fact_6186_prod_Onon__neutral_H,axiom,
% 0.33/0.64 ! [G: int > assn,I4: set_int] :
% 0.33/0.64 ( ( groups4891613008741529892t_assn @ G
% 0.33/0.64 @ ( collect_int
% 0.33/0.64 @ ^ [X3: int] :
% 0.33/0.64 ( ( member_int @ X3 @ I4 )
% 0.33/0.64 & ( ( G @ X3 )
% 0.33/0.64 != one_one_assn ) ) ) )
% 0.33/0.64 = ( groups4891613008741529892t_assn @ G @ I4 ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod.non_neutral'
% 0.33/0.64 thf(fact_6187_prod_Onon__neutral_H,axiom,
% 0.33/0.64 ! [G: nat > assn,I4: set_nat] :
% 0.33/0.64 ( ( groups3916077543535352520t_assn @ G
% 0.33/0.64 @ ( collect_nat
% 0.33/0.64 @ ^ [X3: nat] :
% 0.33/0.64 ( ( member_nat @ X3 @ I4 )
% 0.33/0.64 & ( ( G @ X3 )
% 0.33/0.64 != one_one_assn ) ) ) )
% 0.33/0.64 = ( groups3916077543535352520t_assn @ G @ I4 ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod.non_neutral'
% 0.33/0.64 thf(fact_6188_prod_Onon__neutral_H,axiom,
% 0.33/0.64 ! [G: $o > rat,I4: set_o] :
% 0.33/0.64 ( ( groups4688112016125141794_o_rat @ G
% 0.33/0.64 @ ( collect_o
% 0.33/0.64 @ ^ [X3: $o] :
% 0.33/0.64 ( ( member_o @ X3 @ I4 )
% 0.33/0.64 & ( ( G @ X3 )
% 0.33/0.64 != one_one_rat ) ) ) )
% 0.33/0.64 = ( groups4688112016125141794_o_rat @ G @ I4 ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod.non_neutral'
% 0.33/0.64 thf(fact_6189_prod_Onon__neutral_H,axiom,
% 0.33/0.64 ! [G: int > rat,I4: set_int] :
% 0.33/0.64 ( ( groups5111818645460702676nt_rat @ G
% 0.33/0.64 @ ( collect_int
% 0.33/0.64 @ ^ [X3: int] :
% 0.33/0.64 ( ( member_int @ X3 @ I4 )
% 0.33/0.64 & ( ( G @ X3 )
% 0.33/0.64 != one_one_rat ) ) ) )
% 0.33/0.64 = ( groups5111818645460702676nt_rat @ G @ I4 ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod.non_neutral'
% 0.33/0.64 thf(fact_6190_prod_Onon__neutral_H,axiom,
% 0.33/0.64 ! [G: nat > rat,I4: set_nat] :
% 0.33/0.64 ( ( groups4112464933559648120at_rat @ G
% 0.33/0.64 @ ( collect_nat
% 0.33/0.64 @ ^ [X3: nat] :
% 0.33/0.64 ( ( member_nat @ X3 @ I4 )
% 0.33/0.64 & ( ( G @ X3 )
% 0.33/0.64 != one_one_rat ) ) ) )
% 0.33/0.64 = ( groups4112464933559648120at_rat @ G @ I4 ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod.non_neutral'
% 0.33/0.64 thf(fact_6191_prod_Onon__neutral_H,axiom,
% 0.33/0.64 ! [G: $o > nat,I4: set_o] :
% 0.33/0.64 ( ( groups5323242076211637530_o_nat @ G
% 0.33/0.64 @ ( collect_o
% 0.33/0.64 @ ^ [X3: $o] :
% 0.33/0.64 ( ( member_o @ X3 @ I4 )
% 0.33/0.64 & ( ( G @ X3 )
% 0.33/0.64 != one_one_nat ) ) ) )
% 0.33/0.64 = ( groups5323242076211637530_o_nat @ G @ I4 ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod.non_neutral'
% 0.33/0.64 thf(fact_6192_infinite__Ioo,axiom,
% 0.33/0.64 ! [A: rat,B: rat] :
% 0.33/0.64 ( ( ord_less_rat @ A @ B )
% 0.33/0.64 => ~ ( finite_finite_rat @ ( set_or5199638295745620268an_rat @ A @ B ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % infinite_Ioo
% 0.33/0.64 thf(fact_6193_greaterThanLessThan__subseteq__greaterThanLessThan,axiom,
% 0.33/0.64 ! [A: rat,B: rat,C: rat,D2: rat] :
% 0.33/0.64 ( ( ord_less_eq_set_rat @ ( set_or5199638295745620268an_rat @ A @ B ) @ ( set_or5199638295745620268an_rat @ C @ D2 ) )
% 0.33/0.64 = ( ( ord_less_rat @ A @ B )
% 0.33/0.64 => ( ( ord_less_eq_rat @ C @ A )
% 0.33/0.64 & ( ord_less_eq_rat @ B @ D2 ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % greaterThanLessThan_subseteq_greaterThanLessThan
% 0.33/0.64 thf(fact_6194_prod__decode__aux_Ocases,axiom,
% 0.33/0.64 ! [X: product_prod_nat_nat] :
% 0.33/0.64 ~ ! [K5: nat,M5: nat] :
% 0.33/0.64 ( X
% 0.33/0.64 != ( product_Pair_nat_nat @ K5 @ M5 ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod_decode_aux.cases
% 0.33/0.64 thf(fact_6195_atLeastPlusOneLessThan__greaterThanLessThan__int,axiom,
% 0.33/0.64 ! [L: int,U: int] :
% 0.33/0.64 ( ( set_or4662586982721622107an_int @ ( plus_plus_int @ L @ one_one_int ) @ U )
% 0.33/0.64 = ( set_or5832277885323065728an_int @ L @ U ) ) ).
% 0.33/0.64
% 0.33/0.64 % atLeastPlusOneLessThan_greaterThanLessThan_int
% 0.33/0.64 thf(fact_6196_prod_Omono__neutral__left_H,axiom,
% 0.33/0.64 ! [S2: set_nat,T5: set_nat,G: nat > code_integer] :
% 0.33/0.64 ( ( ord_less_eq_set_nat @ S2 @ T5 )
% 0.33/0.64 => ( ! [X4: nat] :
% 0.33/0.64 ( ( member_nat @ X4 @ ( minus_minus_set_nat @ T5 @ S2 ) )
% 0.33/0.64 => ( ( G @ X4 )
% 0.33/0.64 = one_one_Code_integer ) )
% 0.33/0.64 => ( ( groups8290090294887179773nteger @ G @ S2 )
% 0.33/0.64 = ( groups8290090294887179773nteger @ G @ T5 ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod.mono_neutral_left'
% 0.33/0.64 thf(fact_6197_prod_Omono__neutral__left_H,axiom,
% 0.33/0.64 ! [S2: set_nat,T5: set_nat,G: nat > assn] :
% 0.33/0.64 ( ( ord_less_eq_set_nat @ S2 @ T5 )
% 0.33/0.64 => ( ! [X4: nat] :
% 0.33/0.64 ( ( member_nat @ X4 @ ( minus_minus_set_nat @ T5 @ S2 ) )
% 0.33/0.64 => ( ( G @ X4 )
% 0.33/0.64 = one_one_assn ) )
% 0.33/0.64 => ( ( groups3916077543535352520t_assn @ G @ S2 )
% 0.33/0.64 = ( groups3916077543535352520t_assn @ G @ T5 ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod.mono_neutral_left'
% 0.33/0.64 thf(fact_6198_prod_Omono__neutral__left_H,axiom,
% 0.33/0.64 ! [S2: set_nat,T5: set_nat,G: nat > rat] :
% 0.33/0.64 ( ( ord_less_eq_set_nat @ S2 @ T5 )
% 0.33/0.64 => ( ! [X4: nat] :
% 0.33/0.64 ( ( member_nat @ X4 @ ( minus_minus_set_nat @ T5 @ S2 ) )
% 0.33/0.64 => ( ( G @ X4 )
% 0.33/0.64 = one_one_rat ) )
% 0.33/0.64 => ( ( groups4112464933559648120at_rat @ G @ S2 )
% 0.33/0.64 = ( groups4112464933559648120at_rat @ G @ T5 ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod.mono_neutral_left'
% 0.33/0.64 thf(fact_6199_prod_Omono__neutral__left_H,axiom,
% 0.33/0.64 ! [S2: set_nat,T5: set_nat,G: nat > nat] :
% 0.33/0.64 ( ( ord_less_eq_set_nat @ S2 @ T5 )
% 0.33/0.64 => ( ! [X4: nat] :
% 0.33/0.64 ( ( member_nat @ X4 @ ( minus_minus_set_nat @ T5 @ S2 ) )
% 0.33/0.64 => ( ( G @ X4 )
% 0.33/0.64 = one_one_nat ) )
% 0.33/0.64 => ( ( groups4747594993646143856at_nat @ G @ S2 )
% 0.33/0.64 = ( groups4747594993646143856at_nat @ G @ T5 ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod.mono_neutral_left'
% 0.33/0.64 thf(fact_6200_prod_Omono__neutral__left_H,axiom,
% 0.33/0.64 ! [S2: set_nat,T5: set_nat,G: nat > int] :
% 0.33/0.64 ( ( ord_less_eq_set_nat @ S2 @ T5 )
% 0.33/0.64 => ( ! [X4: nat] :
% 0.33/0.64 ( ( member_nat @ X4 @ ( minus_minus_set_nat @ T5 @ S2 ) )
% 0.33/0.64 => ( ( G @ X4 )
% 0.33/0.64 = one_one_int ) )
% 0.33/0.64 => ( ( groups4745104523137093580at_int @ G @ S2 )
% 0.33/0.64 = ( groups4745104523137093580at_int @ G @ T5 ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod.mono_neutral_left'
% 0.33/0.64 thf(fact_6201_prod_Omono__neutral__right_H,axiom,
% 0.33/0.64 ! [S2: set_nat,T5: set_nat,G: nat > code_integer] :
% 0.33/0.64 ( ( ord_less_eq_set_nat @ S2 @ T5 )
% 0.33/0.64 => ( ! [X4: nat] :
% 0.33/0.64 ( ( member_nat @ X4 @ ( minus_minus_set_nat @ T5 @ S2 ) )
% 0.33/0.64 => ( ( G @ X4 )
% 0.33/0.64 = one_one_Code_integer ) )
% 0.33/0.64 => ( ( groups8290090294887179773nteger @ G @ T5 )
% 0.33/0.64 = ( groups8290090294887179773nteger @ G @ S2 ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod.mono_neutral_right'
% 0.33/0.64 thf(fact_6202_prod_Omono__neutral__right_H,axiom,
% 0.33/0.64 ! [S2: set_nat,T5: set_nat,G: nat > assn] :
% 0.33/0.64 ( ( ord_less_eq_set_nat @ S2 @ T5 )
% 0.33/0.64 => ( ! [X4: nat] :
% 0.33/0.64 ( ( member_nat @ X4 @ ( minus_minus_set_nat @ T5 @ S2 ) )
% 0.33/0.64 => ( ( G @ X4 )
% 0.33/0.64 = one_one_assn ) )
% 0.33/0.64 => ( ( groups3916077543535352520t_assn @ G @ T5 )
% 0.33/0.64 = ( groups3916077543535352520t_assn @ G @ S2 ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod.mono_neutral_right'
% 0.33/0.64 thf(fact_6203_prod_Omono__neutral__right_H,axiom,
% 0.33/0.64 ! [S2: set_nat,T5: set_nat,G: nat > rat] :
% 0.33/0.64 ( ( ord_less_eq_set_nat @ S2 @ T5 )
% 0.33/0.64 => ( ! [X4: nat] :
% 0.33/0.64 ( ( member_nat @ X4 @ ( minus_minus_set_nat @ T5 @ S2 ) )
% 0.33/0.64 => ( ( G @ X4 )
% 0.33/0.64 = one_one_rat ) )
% 0.33/0.64 => ( ( groups4112464933559648120at_rat @ G @ T5 )
% 0.33/0.64 = ( groups4112464933559648120at_rat @ G @ S2 ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod.mono_neutral_right'
% 0.33/0.64 thf(fact_6204_prod_Omono__neutral__right_H,axiom,
% 0.33/0.64 ! [S2: set_nat,T5: set_nat,G: nat > nat] :
% 0.33/0.64 ( ( ord_less_eq_set_nat @ S2 @ T5 )
% 0.33/0.64 => ( ! [X4: nat] :
% 0.33/0.64 ( ( member_nat @ X4 @ ( minus_minus_set_nat @ T5 @ S2 ) )
% 0.33/0.64 => ( ( G @ X4 )
% 0.33/0.64 = one_one_nat ) )
% 0.33/0.64 => ( ( groups4747594993646143856at_nat @ G @ T5 )
% 0.33/0.64 = ( groups4747594993646143856at_nat @ G @ S2 ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod.mono_neutral_right'
% 0.33/0.64 thf(fact_6205_prod_Omono__neutral__right_H,axiom,
% 0.33/0.64 ! [S2: set_nat,T5: set_nat,G: nat > int] :
% 0.33/0.64 ( ( ord_less_eq_set_nat @ S2 @ T5 )
% 0.33/0.64 => ( ! [X4: nat] :
% 0.33/0.64 ( ( member_nat @ X4 @ ( minus_minus_set_nat @ T5 @ S2 ) )
% 0.33/0.64 => ( ( G @ X4 )
% 0.33/0.64 = one_one_int ) )
% 0.33/0.64 => ( ( groups4745104523137093580at_int @ G @ T5 )
% 0.33/0.64 = ( groups4745104523137093580at_int @ G @ S2 ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod.mono_neutral_right'
% 0.33/0.64 thf(fact_6206_prod_Omono__neutral__cong__left_H,axiom,
% 0.33/0.64 ! [S2: set_o,T5: set_o,H3: $o > code_integer,G: $o > code_integer] :
% 0.33/0.64 ( ( ord_less_eq_set_o @ S2 @ T5 )
% 0.33/0.64 => ( ! [I2: $o] :
% 0.33/0.64 ( ( member_o @ I2 @ ( minus_minus_set_o @ T5 @ S2 ) )
% 0.33/0.64 => ( ( H3 @ I2 )
% 0.33/0.64 = one_one_Code_integer ) )
% 0.33/0.64 => ( ! [X4: $o] :
% 0.33/0.64 ( ( member_o @ X4 @ S2 )
% 0.33/0.64 => ( ( G @ X4 )
% 0.33/0.64 = ( H3 @ X4 ) ) )
% 0.33/0.64 => ( ( groups2836416601086271911nteger @ G @ S2 )
% 0.33/0.64 = ( groups2836416601086271911nteger @ H3 @ T5 ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod.mono_neutral_cong_left'
% 0.33/0.64 thf(fact_6207_prod_Omono__neutral__cong__left_H,axiom,
% 0.33/0.64 ! [S2: set_int,T5: set_int,H3: int > code_integer,G: int > code_integer] :
% 0.33/0.64 ( ( ord_less_eq_set_int @ S2 @ T5 )
% 0.33/0.64 => ( ! [I2: int] :
% 0.33/0.64 ( ( member_int @ I2 @ ( minus_minus_set_int @ T5 @ S2 ) )
% 0.33/0.64 => ( ( H3 @ I2 )
% 0.33/0.64 = one_one_Code_integer ) )
% 0.33/0.64 => ( ! [X4: int] :
% 0.33/0.64 ( ( member_int @ X4 @ S2 )
% 0.33/0.64 => ( ( G @ X4 )
% 0.33/0.64 = ( H3 @ X4 ) ) )
% 0.33/0.64 => ( ( groups8661743855124024409nteger @ G @ S2 )
% 0.33/0.64 = ( groups8661743855124024409nteger @ H3 @ T5 ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod.mono_neutral_cong_left'
% 0.33/0.64 thf(fact_6208_prod_Omono__neutral__cong__left_H,axiom,
% 0.33/0.64 ! [S2: set_o,T5: set_o,H3: $o > assn,G: $o > assn] :
% 0.33/0.64 ( ( ord_less_eq_set_o @ S2 @ T5 )
% 0.33/0.64 => ( ! [I2: $o] :
% 0.33/0.64 ( ( member_o @ I2 @ ( minus_minus_set_o @ T5 @ S2 ) )
% 0.33/0.64 => ( ( H3 @ I2 )
% 0.33/0.64 = one_one_assn ) )
% 0.33/0.64 => ( ! [X4: $o] :
% 0.33/0.64 ( ( member_o @ X4 @ S2 )
% 0.33/0.64 => ( ( G @ X4 )
% 0.33/0.64 = ( H3 @ X4 ) ) )
% 0.33/0.64 => ( ( groups12625163056032370o_assn @ G @ S2 )
% 0.33/0.64 = ( groups12625163056032370o_assn @ H3 @ T5 ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod.mono_neutral_cong_left'
% 0.33/0.64 thf(fact_6209_prod_Omono__neutral__cong__left_H,axiom,
% 0.33/0.64 ! [S2: set_int,T5: set_int,H3: int > assn,G: int > assn] :
% 0.33/0.64 ( ( ord_less_eq_set_int @ S2 @ T5 )
% 0.33/0.64 => ( ! [I2: int] :
% 0.33/0.64 ( ( member_int @ I2 @ ( minus_minus_set_int @ T5 @ S2 ) )
% 0.33/0.64 => ( ( H3 @ I2 )
% 0.33/0.64 = one_one_assn ) )
% 0.33/0.64 => ( ! [X4: int] :
% 0.33/0.64 ( ( member_int @ X4 @ S2 )
% 0.33/0.64 => ( ( G @ X4 )
% 0.33/0.64 = ( H3 @ X4 ) ) )
% 0.33/0.64 => ( ( groups4891613008741529892t_assn @ G @ S2 )
% 0.33/0.64 = ( groups4891613008741529892t_assn @ H3 @ T5 ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod.mono_neutral_cong_left'
% 0.33/0.64 thf(fact_6210_prod_Omono__neutral__cong__left_H,axiom,
% 0.33/0.64 ! [S2: set_o,T5: set_o,H3: $o > rat,G: $o > rat] :
% 0.33/0.64 ( ( ord_less_eq_set_o @ S2 @ T5 )
% 0.33/0.64 => ( ! [I2: $o] :
% 0.33/0.64 ( ( member_o @ I2 @ ( minus_minus_set_o @ T5 @ S2 ) )
% 0.33/0.64 => ( ( H3 @ I2 )
% 0.33/0.64 = one_one_rat ) )
% 0.33/0.64 => ( ! [X4: $o] :
% 0.33/0.64 ( ( member_o @ X4 @ S2 )
% 0.33/0.64 => ( ( G @ X4 )
% 0.33/0.64 = ( H3 @ X4 ) ) )
% 0.33/0.64 => ( ( groups4688112016125141794_o_rat @ G @ S2 )
% 0.33/0.64 = ( groups4688112016125141794_o_rat @ H3 @ T5 ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod.mono_neutral_cong_left'
% 0.33/0.64 thf(fact_6211_prod_Omono__neutral__cong__left_H,axiom,
% 0.33/0.64 ! [S2: set_int,T5: set_int,H3: int > rat,G: int > rat] :
% 0.33/0.64 ( ( ord_less_eq_set_int @ S2 @ T5 )
% 0.33/0.64 => ( ! [I2: int] :
% 0.33/0.64 ( ( member_int @ I2 @ ( minus_minus_set_int @ T5 @ S2 ) )
% 0.33/0.64 => ( ( H3 @ I2 )
% 0.33/0.64 = one_one_rat ) )
% 0.33/0.64 => ( ! [X4: int] :
% 0.33/0.64 ( ( member_int @ X4 @ S2 )
% 0.33/0.64 => ( ( G @ X4 )
% 0.33/0.64 = ( H3 @ X4 ) ) )
% 0.33/0.64 => ( ( groups5111818645460702676nt_rat @ G @ S2 )
% 0.33/0.64 = ( groups5111818645460702676nt_rat @ H3 @ T5 ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod.mono_neutral_cong_left'
% 0.33/0.64 thf(fact_6212_prod_Omono__neutral__cong__left_H,axiom,
% 0.33/0.64 ! [S2: set_o,T5: set_o,H3: $o > nat,G: $o > nat] :
% 0.33/0.64 ( ( ord_less_eq_set_o @ S2 @ T5 )
% 0.33/0.64 => ( ! [I2: $o] :
% 0.33/0.64 ( ( member_o @ I2 @ ( minus_minus_set_o @ T5 @ S2 ) )
% 0.33/0.64 => ( ( H3 @ I2 )
% 0.33/0.64 = one_one_nat ) )
% 0.33/0.64 => ( ! [X4: $o] :
% 0.33/0.64 ( ( member_o @ X4 @ S2 )
% 0.33/0.64 => ( ( G @ X4 )
% 0.33/0.64 = ( H3 @ X4 ) ) )
% 0.33/0.64 => ( ( groups5323242076211637530_o_nat @ G @ S2 )
% 0.33/0.64 = ( groups5323242076211637530_o_nat @ H3 @ T5 ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod.mono_neutral_cong_left'
% 0.33/0.64 thf(fact_6213_prod_Omono__neutral__cong__left_H,axiom,
% 0.33/0.64 ! [S2: set_int,T5: set_int,H3: int > nat,G: int > nat] :
% 0.33/0.64 ( ( ord_less_eq_set_int @ S2 @ T5 )
% 0.33/0.64 => ( ! [I2: int] :
% 0.33/0.64 ( ( member_int @ I2 @ ( minus_minus_set_int @ T5 @ S2 ) )
% 0.33/0.64 => ( ( H3 @ I2 )
% 0.33/0.64 = one_one_nat ) )
% 0.33/0.64 => ( ! [X4: int] :
% 0.33/0.64 ( ( member_int @ X4 @ S2 )
% 0.33/0.64 => ( ( G @ X4 )
% 0.33/0.64 = ( H3 @ X4 ) ) )
% 0.33/0.64 => ( ( groups5746948705547198412nt_nat @ G @ S2 )
% 0.33/0.64 = ( groups5746948705547198412nt_nat @ H3 @ T5 ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod.mono_neutral_cong_left'
% 0.33/0.64 thf(fact_6214_prod_Omono__neutral__cong__left_H,axiom,
% 0.33/0.64 ! [S2: set_o,T5: set_o,H3: $o > int,G: $o > int] :
% 0.33/0.64 ( ( ord_less_eq_set_o @ S2 @ T5 )
% 0.33/0.64 => ( ! [I2: $o] :
% 0.33/0.64 ( ( member_o @ I2 @ ( minus_minus_set_o @ T5 @ S2 ) )
% 0.33/0.64 => ( ( H3 @ I2 )
% 0.33/0.64 = one_one_int ) )
% 0.33/0.64 => ( ! [X4: $o] :
% 0.33/0.64 ( ( member_o @ X4 @ S2 )
% 0.33/0.64 => ( ( G @ X4 )
% 0.33/0.64 = ( H3 @ X4 ) ) )
% 0.33/0.64 => ( ( groups5320751605702587254_o_int @ G @ S2 )
% 0.33/0.64 = ( groups5320751605702587254_o_int @ H3 @ T5 ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod.mono_neutral_cong_left'
% 0.33/0.64 thf(fact_6215_prod_Omono__neutral__cong__left_H,axiom,
% 0.33/0.64 ! [S2: set_int,T5: set_int,H3: int > int,G: int > int] :
% 0.33/0.64 ( ( ord_less_eq_set_int @ S2 @ T5 )
% 0.33/0.64 => ( ! [I2: int] :
% 0.33/0.64 ( ( member_int @ I2 @ ( minus_minus_set_int @ T5 @ S2 ) )
% 0.33/0.64 => ( ( H3 @ I2 )
% 0.33/0.64 = one_one_int ) )
% 0.33/0.64 => ( ! [X4: int] :
% 0.33/0.64 ( ( member_int @ X4 @ S2 )
% 0.33/0.64 => ( ( G @ X4 )
% 0.33/0.64 = ( H3 @ X4 ) ) )
% 0.33/0.64 => ( ( groups5744458235038148136nt_int @ G @ S2 )
% 0.33/0.64 = ( groups5744458235038148136nt_int @ H3 @ T5 ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod.mono_neutral_cong_left'
% 0.33/0.64 thf(fact_6216_prod_Omono__neutral__cong__right_H,axiom,
% 0.33/0.64 ! [S2: set_o,T5: set_o,G: $o > code_integer,H3: $o > code_integer] :
% 0.33/0.64 ( ( ord_less_eq_set_o @ S2 @ T5 )
% 0.33/0.64 => ( ! [X4: $o] :
% 0.33/0.64 ( ( member_o @ X4 @ ( minus_minus_set_o @ T5 @ S2 ) )
% 0.33/0.64 => ( ( G @ X4 )
% 0.33/0.64 = one_one_Code_integer ) )
% 0.33/0.64 => ( ! [X4: $o] :
% 0.33/0.64 ( ( member_o @ X4 @ S2 )
% 0.33/0.64 => ( ( G @ X4 )
% 0.33/0.64 = ( H3 @ X4 ) ) )
% 0.33/0.64 => ( ( groups2836416601086271911nteger @ G @ T5 )
% 0.33/0.64 = ( groups2836416601086271911nteger @ H3 @ S2 ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod.mono_neutral_cong_right'
% 0.33/0.64 thf(fact_6217_prod_Omono__neutral__cong__right_H,axiom,
% 0.33/0.64 ! [S2: set_int,T5: set_int,G: int > code_integer,H3: int > code_integer] :
% 0.33/0.64 ( ( ord_less_eq_set_int @ S2 @ T5 )
% 0.33/0.64 => ( ! [X4: int] :
% 0.33/0.64 ( ( member_int @ X4 @ ( minus_minus_set_int @ T5 @ S2 ) )
% 0.33/0.64 => ( ( G @ X4 )
% 0.33/0.64 = one_one_Code_integer ) )
% 0.33/0.64 => ( ! [X4: int] :
% 0.33/0.64 ( ( member_int @ X4 @ S2 )
% 0.33/0.64 => ( ( G @ X4 )
% 0.33/0.64 = ( H3 @ X4 ) ) )
% 0.33/0.64 => ( ( groups8661743855124024409nteger @ G @ T5 )
% 0.33/0.64 = ( groups8661743855124024409nteger @ H3 @ S2 ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod.mono_neutral_cong_right'
% 0.33/0.64 thf(fact_6218_prod_Omono__neutral__cong__right_H,axiom,
% 0.33/0.64 ! [S2: set_o,T5: set_o,G: $o > assn,H3: $o > assn] :
% 0.33/0.64 ( ( ord_less_eq_set_o @ S2 @ T5 )
% 0.33/0.64 => ( ! [X4: $o] :
% 0.33/0.64 ( ( member_o @ X4 @ ( minus_minus_set_o @ T5 @ S2 ) )
% 0.33/0.64 => ( ( G @ X4 )
% 0.33/0.64 = one_one_assn ) )
% 0.33/0.64 => ( ! [X4: $o] :
% 0.33/0.64 ( ( member_o @ X4 @ S2 )
% 0.33/0.64 => ( ( G @ X4 )
% 0.33/0.64 = ( H3 @ X4 ) ) )
% 0.33/0.64 => ( ( groups12625163056032370o_assn @ G @ T5 )
% 0.33/0.64 = ( groups12625163056032370o_assn @ H3 @ S2 ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod.mono_neutral_cong_right'
% 0.33/0.64 thf(fact_6219_prod_Omono__neutral__cong__right_H,axiom,
% 0.33/0.64 ! [S2: set_int,T5: set_int,G: int > assn,H3: int > assn] :
% 0.33/0.64 ( ( ord_less_eq_set_int @ S2 @ T5 )
% 0.33/0.64 => ( ! [X4: int] :
% 0.33/0.64 ( ( member_int @ X4 @ ( minus_minus_set_int @ T5 @ S2 ) )
% 0.33/0.64 => ( ( G @ X4 )
% 0.33/0.64 = one_one_assn ) )
% 0.33/0.64 => ( ! [X4: int] :
% 0.33/0.64 ( ( member_int @ X4 @ S2 )
% 0.33/0.64 => ( ( G @ X4 )
% 0.33/0.64 = ( H3 @ X4 ) ) )
% 0.33/0.64 => ( ( groups4891613008741529892t_assn @ G @ T5 )
% 0.33/0.64 = ( groups4891613008741529892t_assn @ H3 @ S2 ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod.mono_neutral_cong_right'
% 0.33/0.64 thf(fact_6220_prod_Omono__neutral__cong__right_H,axiom,
% 0.33/0.64 ! [S2: set_o,T5: set_o,G: $o > rat,H3: $o > rat] :
% 0.33/0.64 ( ( ord_less_eq_set_o @ S2 @ T5 )
% 0.33/0.64 => ( ! [X4: $o] :
% 0.33/0.64 ( ( member_o @ X4 @ ( minus_minus_set_o @ T5 @ S2 ) )
% 0.33/0.64 => ( ( G @ X4 )
% 0.33/0.64 = one_one_rat ) )
% 0.33/0.64 => ( ! [X4: $o] :
% 0.33/0.64 ( ( member_o @ X4 @ S2 )
% 0.33/0.64 => ( ( G @ X4 )
% 0.33/0.64 = ( H3 @ X4 ) ) )
% 0.33/0.64 => ( ( groups4688112016125141794_o_rat @ G @ T5 )
% 0.33/0.64 = ( groups4688112016125141794_o_rat @ H3 @ S2 ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod.mono_neutral_cong_right'
% 0.33/0.64 thf(fact_6221_prod_Omono__neutral__cong__right_H,axiom,
% 0.33/0.64 ! [S2: set_int,T5: set_int,G: int > rat,H3: int > rat] :
% 0.33/0.64 ( ( ord_less_eq_set_int @ S2 @ T5 )
% 0.33/0.64 => ( ! [X4: int] :
% 0.33/0.64 ( ( member_int @ X4 @ ( minus_minus_set_int @ T5 @ S2 ) )
% 0.33/0.64 => ( ( G @ X4 )
% 0.33/0.64 = one_one_rat ) )
% 0.33/0.64 => ( ! [X4: int] :
% 0.33/0.64 ( ( member_int @ X4 @ S2 )
% 0.33/0.64 => ( ( G @ X4 )
% 0.33/0.64 = ( H3 @ X4 ) ) )
% 0.33/0.64 => ( ( groups5111818645460702676nt_rat @ G @ T5 )
% 0.33/0.64 = ( groups5111818645460702676nt_rat @ H3 @ S2 ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod.mono_neutral_cong_right'
% 0.33/0.64 thf(fact_6222_prod_Omono__neutral__cong__right_H,axiom,
% 0.33/0.64 ! [S2: set_o,T5: set_o,G: $o > nat,H3: $o > nat] :
% 0.33/0.64 ( ( ord_less_eq_set_o @ S2 @ T5 )
% 0.33/0.64 => ( ! [X4: $o] :
% 0.33/0.64 ( ( member_o @ X4 @ ( minus_minus_set_o @ T5 @ S2 ) )
% 0.33/0.64 => ( ( G @ X4 )
% 0.33/0.64 = one_one_nat ) )
% 0.33/0.64 => ( ! [X4: $o] :
% 0.33/0.64 ( ( member_o @ X4 @ S2 )
% 0.33/0.64 => ( ( G @ X4 )
% 0.33/0.64 = ( H3 @ X4 ) ) )
% 0.33/0.64 => ( ( groups5323242076211637530_o_nat @ G @ T5 )
% 0.33/0.64 = ( groups5323242076211637530_o_nat @ H3 @ S2 ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod.mono_neutral_cong_right'
% 0.33/0.64 thf(fact_6223_prod_Omono__neutral__cong__right_H,axiom,
% 0.33/0.64 ! [S2: set_int,T5: set_int,G: int > nat,H3: int > nat] :
% 0.33/0.64 ( ( ord_less_eq_set_int @ S2 @ T5 )
% 0.33/0.64 => ( ! [X4: int] :
% 0.33/0.64 ( ( member_int @ X4 @ ( minus_minus_set_int @ T5 @ S2 ) )
% 0.33/0.64 => ( ( G @ X4 )
% 0.33/0.64 = one_one_nat ) )
% 0.33/0.64 => ( ! [X4: int] :
% 0.33/0.64 ( ( member_int @ X4 @ S2 )
% 0.33/0.64 => ( ( G @ X4 )
% 0.33/0.64 = ( H3 @ X4 ) ) )
% 0.33/0.64 => ( ( groups5746948705547198412nt_nat @ G @ T5 )
% 0.33/0.64 = ( groups5746948705547198412nt_nat @ H3 @ S2 ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod.mono_neutral_cong_right'
% 0.33/0.64 thf(fact_6224_prod_Omono__neutral__cong__right_H,axiom,
% 0.33/0.64 ! [S2: set_o,T5: set_o,G: $o > int,H3: $o > int] :
% 0.33/0.64 ( ( ord_less_eq_set_o @ S2 @ T5 )
% 0.33/0.64 => ( ! [X4: $o] :
% 0.33/0.64 ( ( member_o @ X4 @ ( minus_minus_set_o @ T5 @ S2 ) )
% 0.33/0.64 => ( ( G @ X4 )
% 0.33/0.64 = one_one_int ) )
% 0.33/0.64 => ( ! [X4: $o] :
% 0.33/0.64 ( ( member_o @ X4 @ S2 )
% 0.33/0.64 => ( ( G @ X4 )
% 0.33/0.64 = ( H3 @ X4 ) ) )
% 0.33/0.64 => ( ( groups5320751605702587254_o_int @ G @ T5 )
% 0.33/0.64 = ( groups5320751605702587254_o_int @ H3 @ S2 ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod.mono_neutral_cong_right'
% 0.33/0.64 thf(fact_6225_prod_Omono__neutral__cong__right_H,axiom,
% 0.33/0.64 ! [S2: set_int,T5: set_int,G: int > int,H3: int > int] :
% 0.33/0.64 ( ( ord_less_eq_set_int @ S2 @ T5 )
% 0.33/0.64 => ( ! [X4: int] :
% 0.33/0.64 ( ( member_int @ X4 @ ( minus_minus_set_int @ T5 @ S2 ) )
% 0.33/0.64 => ( ( G @ X4 )
% 0.33/0.64 = one_one_int ) )
% 0.33/0.64 => ( ! [X4: int] :
% 0.33/0.64 ( ( member_int @ X4 @ S2 )
% 0.33/0.64 => ( ( G @ X4 )
% 0.33/0.64 = ( H3 @ X4 ) ) )
% 0.33/0.64 => ( ( groups5744458235038148136nt_int @ G @ T5 )
% 0.33/0.64 = ( groups5744458235038148136nt_int @ H3 @ S2 ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod.mono_neutral_cong_right'
% 0.33/0.64 thf(fact_6226_prod_Odistrib_H,axiom,
% 0.33/0.64 ! [I4: set_o,G: $o > code_integer,H3: $o > code_integer] :
% 0.33/0.64 ( ( finite_finite_o
% 0.33/0.64 @ ( collect_o
% 0.33/0.64 @ ^ [X3: $o] :
% 0.33/0.64 ( ( member_o @ X3 @ I4 )
% 0.33/0.64 & ( ( G @ X3 )
% 0.33/0.64 != one_one_Code_integer ) ) ) )
% 0.33/0.64 => ( ( finite_finite_o
% 0.33/0.64 @ ( collect_o
% 0.33/0.64 @ ^ [X3: $o] :
% 0.33/0.64 ( ( member_o @ X3 @ I4 )
% 0.33/0.64 & ( ( H3 @ X3 )
% 0.33/0.64 != one_one_Code_integer ) ) ) )
% 0.33/0.64 => ( ( groups2836416601086271911nteger
% 0.33/0.64 @ ^ [I3: $o] : ( times_3573771949741848930nteger @ ( G @ I3 ) @ ( H3 @ I3 ) )
% 0.33/0.64 @ I4 )
% 0.33/0.64 = ( times_3573771949741848930nteger @ ( groups2836416601086271911nteger @ G @ I4 ) @ ( groups2836416601086271911nteger @ H3 @ I4 ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod.distrib'
% 0.33/0.64 thf(fact_6227_prod_Odistrib_H,axiom,
% 0.33/0.64 ! [I4: set_nat,G: nat > code_integer,H3: nat > code_integer] :
% 0.33/0.64 ( ( finite_finite_nat
% 0.33/0.64 @ ( collect_nat
% 0.33/0.64 @ ^ [X3: nat] :
% 0.33/0.64 ( ( member_nat @ X3 @ I4 )
% 0.33/0.64 & ( ( G @ X3 )
% 0.33/0.64 != one_one_Code_integer ) ) ) )
% 0.33/0.64 => ( ( finite_finite_nat
% 0.33/0.64 @ ( collect_nat
% 0.33/0.64 @ ^ [X3: nat] :
% 0.33/0.64 ( ( member_nat @ X3 @ I4 )
% 0.33/0.64 & ( ( H3 @ X3 )
% 0.33/0.64 != one_one_Code_integer ) ) ) )
% 0.33/0.64 => ( ( groups8290090294887179773nteger
% 0.33/0.64 @ ^ [I3: nat] : ( times_3573771949741848930nteger @ ( G @ I3 ) @ ( H3 @ I3 ) )
% 0.33/0.64 @ I4 )
% 0.33/0.64 = ( times_3573771949741848930nteger @ ( groups8290090294887179773nteger @ G @ I4 ) @ ( groups8290090294887179773nteger @ H3 @ I4 ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod.distrib'
% 0.33/0.64 thf(fact_6228_prod_Odistrib_H,axiom,
% 0.33/0.64 ! [I4: set_int,G: int > code_integer,H3: int > code_integer] :
% 0.33/0.64 ( ( finite_finite_int
% 0.33/0.64 @ ( collect_int
% 0.33/0.64 @ ^ [X3: int] :
% 0.33/0.64 ( ( member_int @ X3 @ I4 )
% 0.33/0.64 & ( ( G @ X3 )
% 0.33/0.64 != one_one_Code_integer ) ) ) )
% 0.33/0.64 => ( ( finite_finite_int
% 0.33/0.64 @ ( collect_int
% 0.33/0.64 @ ^ [X3: int] :
% 0.33/0.64 ( ( member_int @ X3 @ I4 )
% 0.33/0.64 & ( ( H3 @ X3 )
% 0.33/0.64 != one_one_Code_integer ) ) ) )
% 0.33/0.64 => ( ( groups8661743855124024409nteger
% 0.33/0.64 @ ^ [I3: int] : ( times_3573771949741848930nteger @ ( G @ I3 ) @ ( H3 @ I3 ) )
% 0.33/0.64 @ I4 )
% 0.33/0.64 = ( times_3573771949741848930nteger @ ( groups8661743855124024409nteger @ G @ I4 ) @ ( groups8661743855124024409nteger @ H3 @ I4 ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod.distrib'
% 0.33/0.64 thf(fact_6229_prod_Odistrib_H,axiom,
% 0.33/0.64 ! [I4: set_Code_integer,G: code_integer > code_integer,H3: code_integer > code_integer] :
% 0.33/0.64 ( ( finite6017078050557962740nteger
% 0.33/0.64 @ ( collect_Code_integer
% 0.33/0.64 @ ^ [X3: code_integer] :
% 0.33/0.64 ( ( member_Code_integer @ X3 @ I4 )
% 0.33/0.64 & ( ( G @ X3 )
% 0.33/0.64 != one_one_Code_integer ) ) ) )
% 0.33/0.64 => ( ( finite6017078050557962740nteger
% 0.33/0.64 @ ( collect_Code_integer
% 0.33/0.64 @ ^ [X3: code_integer] :
% 0.33/0.64 ( ( member_Code_integer @ X3 @ I4 )
% 0.33/0.64 & ( ( H3 @ X3 )
% 0.33/0.64 != one_one_Code_integer ) ) ) )
% 0.33/0.64 => ( ( groups7219916603568234122nteger
% 0.33/0.64 @ ^ [I3: code_integer] : ( times_3573771949741848930nteger @ ( G @ I3 ) @ ( H3 @ I3 ) )
% 0.33/0.64 @ I4 )
% 0.33/0.64 = ( times_3573771949741848930nteger @ ( groups7219916603568234122nteger @ G @ I4 ) @ ( groups7219916603568234122nteger @ H3 @ I4 ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod.distrib'
% 0.33/0.64 thf(fact_6230_prod_Odistrib_H,axiom,
% 0.33/0.64 ! [I4: set_o,G: $o > assn,H3: $o > assn] :
% 0.33/0.64 ( ( finite_finite_o
% 0.33/0.64 @ ( collect_o
% 0.33/0.64 @ ^ [X3: $o] :
% 0.33/0.64 ( ( member_o @ X3 @ I4 )
% 0.33/0.64 & ( ( G @ X3 )
% 0.33/0.64 != one_one_assn ) ) ) )
% 0.33/0.64 => ( ( finite_finite_o
% 0.33/0.64 @ ( collect_o
% 0.33/0.64 @ ^ [X3: $o] :
% 0.33/0.64 ( ( member_o @ X3 @ I4 )
% 0.33/0.64 & ( ( H3 @ X3 )
% 0.33/0.64 != one_one_assn ) ) ) )
% 0.33/0.64 => ( ( groups12625163056032370o_assn
% 0.33/0.64 @ ^ [I3: $o] : ( times_times_assn @ ( G @ I3 ) @ ( H3 @ I3 ) )
% 0.33/0.64 @ I4 )
% 0.33/0.64 = ( times_times_assn @ ( groups12625163056032370o_assn @ G @ I4 ) @ ( groups12625163056032370o_assn @ H3 @ I4 ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod.distrib'
% 0.33/0.64 thf(fact_6231_prod_Odistrib_H,axiom,
% 0.33/0.64 ! [I4: set_nat,G: nat > assn,H3: nat > assn] :
% 0.33/0.64 ( ( finite_finite_nat
% 0.33/0.64 @ ( collect_nat
% 0.33/0.64 @ ^ [X3: nat] :
% 0.33/0.64 ( ( member_nat @ X3 @ I4 )
% 0.33/0.64 & ( ( G @ X3 )
% 0.33/0.64 != one_one_assn ) ) ) )
% 0.33/0.64 => ( ( finite_finite_nat
% 0.33/0.64 @ ( collect_nat
% 0.33/0.64 @ ^ [X3: nat] :
% 0.33/0.64 ( ( member_nat @ X3 @ I4 )
% 0.33/0.64 & ( ( H3 @ X3 )
% 0.33/0.64 != one_one_assn ) ) ) )
% 0.33/0.64 => ( ( groups3916077543535352520t_assn
% 0.33/0.64 @ ^ [I3: nat] : ( times_times_assn @ ( G @ I3 ) @ ( H3 @ I3 ) )
% 0.33/0.64 @ I4 )
% 0.33/0.64 = ( times_times_assn @ ( groups3916077543535352520t_assn @ G @ I4 ) @ ( groups3916077543535352520t_assn @ H3 @ I4 ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod.distrib'
% 0.33/0.64 thf(fact_6232_prod_Odistrib_H,axiom,
% 0.33/0.64 ! [I4: set_int,G: int > assn,H3: int > assn] :
% 0.33/0.64 ( ( finite_finite_int
% 0.33/0.64 @ ( collect_int
% 0.33/0.64 @ ^ [X3: int] :
% 0.33/0.64 ( ( member_int @ X3 @ I4 )
% 0.33/0.64 & ( ( G @ X3 )
% 0.33/0.64 != one_one_assn ) ) ) )
% 0.33/0.64 => ( ( finite_finite_int
% 0.33/0.64 @ ( collect_int
% 0.33/0.64 @ ^ [X3: int] :
% 0.33/0.64 ( ( member_int @ X3 @ I4 )
% 0.33/0.64 & ( ( H3 @ X3 )
% 0.33/0.64 != one_one_assn ) ) ) )
% 0.33/0.64 => ( ( groups4891613008741529892t_assn
% 0.33/0.64 @ ^ [I3: int] : ( times_times_assn @ ( G @ I3 ) @ ( H3 @ I3 ) )
% 0.33/0.64 @ I4 )
% 0.33/0.64 = ( times_times_assn @ ( groups4891613008741529892t_assn @ G @ I4 ) @ ( groups4891613008741529892t_assn @ H3 @ I4 ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod.distrib'
% 0.33/0.64 thf(fact_6233_prod_Odistrib_H,axiom,
% 0.33/0.64 ! [I4: set_Code_integer,G: code_integer > assn,H3: code_integer > assn] :
% 0.33/0.64 ( ( finite6017078050557962740nteger
% 0.33/0.64 @ ( collect_Code_integer
% 0.33/0.64 @ ^ [X3: code_integer] :
% 0.33/0.64 ( ( member_Code_integer @ X3 @ I4 )
% 0.33/0.64 & ( ( G @ X3 )
% 0.33/0.64 != one_one_assn ) ) ) )
% 0.33/0.64 => ( ( finite6017078050557962740nteger
% 0.33/0.64 @ ( collect_Code_integer
% 0.33/0.64 @ ^ [X3: code_integer] :
% 0.33/0.64 ( ( member_Code_integer @ X3 @ I4 )
% 0.33/0.64 & ( ( H3 @ X3 )
% 0.33/0.64 != one_one_assn ) ) ) )
% 0.33/0.64 => ( ( groups980104329299799381r_assn
% 0.33/0.64 @ ^ [I3: code_integer] : ( times_times_assn @ ( G @ I3 ) @ ( H3 @ I3 ) )
% 0.33/0.64 @ I4 )
% 0.33/0.64 = ( times_times_assn @ ( groups980104329299799381r_assn @ G @ I4 ) @ ( groups980104329299799381r_assn @ H3 @ I4 ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod.distrib'
% 0.33/0.64 thf(fact_6234_prod_Odistrib_H,axiom,
% 0.33/0.64 ! [I4: set_o,G: $o > rat,H3: $o > rat] :
% 0.33/0.64 ( ( finite_finite_o
% 0.33/0.64 @ ( collect_o
% 0.33/0.64 @ ^ [X3: $o] :
% 0.33/0.64 ( ( member_o @ X3 @ I4 )
% 0.33/0.64 & ( ( G @ X3 )
% 0.33/0.64 != one_one_rat ) ) ) )
% 0.33/0.64 => ( ( finite_finite_o
% 0.33/0.64 @ ( collect_o
% 0.33/0.64 @ ^ [X3: $o] :
% 0.33/0.64 ( ( member_o @ X3 @ I4 )
% 0.33/0.64 & ( ( H3 @ X3 )
% 0.33/0.64 != one_one_rat ) ) ) )
% 0.33/0.64 => ( ( groups4688112016125141794_o_rat
% 0.33/0.64 @ ^ [I3: $o] : ( times_times_rat @ ( G @ I3 ) @ ( H3 @ I3 ) )
% 0.33/0.64 @ I4 )
% 0.33/0.64 = ( times_times_rat @ ( groups4688112016125141794_o_rat @ G @ I4 ) @ ( groups4688112016125141794_o_rat @ H3 @ I4 ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod.distrib'
% 0.33/0.64 thf(fact_6235_prod_Odistrib_H,axiom,
% 0.33/0.64 ! [I4: set_nat,G: nat > rat,H3: nat > rat] :
% 0.33/0.64 ( ( finite_finite_nat
% 0.33/0.64 @ ( collect_nat
% 0.33/0.64 @ ^ [X3: nat] :
% 0.33/0.64 ( ( member_nat @ X3 @ I4 )
% 0.33/0.64 & ( ( G @ X3 )
% 0.33/0.64 != one_one_rat ) ) ) )
% 0.33/0.64 => ( ( finite_finite_nat
% 0.33/0.64 @ ( collect_nat
% 0.33/0.64 @ ^ [X3: nat] :
% 0.33/0.64 ( ( member_nat @ X3 @ I4 )
% 0.33/0.64 & ( ( H3 @ X3 )
% 0.33/0.64 != one_one_rat ) ) ) )
% 0.33/0.64 => ( ( groups4112464933559648120at_rat
% 0.33/0.64 @ ^ [I3: nat] : ( times_times_rat @ ( G @ I3 ) @ ( H3 @ I3 ) )
% 0.33/0.64 @ I4 )
% 0.33/0.64 = ( times_times_rat @ ( groups4112464933559648120at_rat @ G @ I4 ) @ ( groups4112464933559648120at_rat @ H3 @ I4 ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod.distrib'
% 0.33/0.64 thf(fact_6236_prod_OG__def,axiom,
% 0.33/0.64 ( groups2836416601086271911nteger
% 0.33/0.64 = ( ^ [P6: $o > code_integer,I5: set_o] :
% 0.33/0.64 ( if_Code_integer
% 0.33/0.64 @ ( finite_finite_o
% 0.33/0.64 @ ( collect_o
% 0.33/0.64 @ ^ [X3: $o] :
% 0.33/0.64 ( ( member_o @ X3 @ I5 )
% 0.33/0.64 & ( ( P6 @ X3 )
% 0.33/0.64 != one_one_Code_integer ) ) ) )
% 0.33/0.64 @ ( groups7694694392188491536nteger @ P6
% 0.33/0.64 @ ( collect_o
% 0.33/0.64 @ ^ [X3: $o] :
% 0.33/0.64 ( ( member_o @ X3 @ I5 )
% 0.33/0.64 & ( ( P6 @ X3 )
% 0.33/0.64 != one_one_Code_integer ) ) ) )
% 0.33/0.64 @ one_one_Code_integer ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod.G_def
% 0.33/0.64 thf(fact_6237_prod_OG__def,axiom,
% 0.33/0.64 ( groups8290090294887179773nteger
% 0.33/0.64 = ( ^ [P6: nat > code_integer,I5: set_nat] :
% 0.33/0.64 ( if_Code_integer
% 0.33/0.64 @ ( finite_finite_nat
% 0.33/0.64 @ ( collect_nat
% 0.33/0.64 @ ^ [X3: nat] :
% 0.33/0.64 ( ( member_nat @ X3 @ I5 )
% 0.33/0.64 & ( ( P6 @ X3 )
% 0.33/0.64 != one_one_Code_integer ) ) ) )
% 0.33/0.64 @ ( groups3455450783089532116nteger @ P6
% 0.33/0.64 @ ( collect_nat
% 0.33/0.64 @ ^ [X3: nat] :
% 0.33/0.64 ( ( member_nat @ X3 @ I5 )
% 0.33/0.64 & ( ( P6 @ X3 )
% 0.33/0.64 != one_one_Code_integer ) ) ) )
% 0.33/0.64 @ one_one_Code_integer ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod.G_def
% 0.33/0.64 thf(fact_6238_prod_OG__def,axiom,
% 0.33/0.64 ( groups8661743855124024409nteger
% 0.33/0.64 = ( ^ [P6: int > code_integer,I5: set_int] :
% 0.33/0.64 ( if_Code_integer
% 0.33/0.64 @ ( finite_finite_int
% 0.33/0.64 @ ( collect_int
% 0.33/0.64 @ ^ [X3: int] :
% 0.33/0.64 ( ( member_int @ X3 @ I5 )
% 0.33/0.64 & ( ( P6 @ X3 )
% 0.33/0.64 != one_one_Code_integer ) ) ) )
% 0.33/0.64 @ ( groups3827104343326376752nteger @ P6
% 0.33/0.64 @ ( collect_int
% 0.33/0.64 @ ^ [X3: int] :
% 0.33/0.64 ( ( member_int @ X3 @ I5 )
% 0.33/0.64 & ( ( P6 @ X3 )
% 0.33/0.64 != one_one_Code_integer ) ) ) )
% 0.33/0.64 @ one_one_Code_integer ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod.G_def
% 0.33/0.64 thf(fact_6239_prod_OG__def,axiom,
% 0.33/0.64 ( groups7219916603568234122nteger
% 0.33/0.64 = ( ^ [P6: code_integer > code_integer,I5: set_Code_integer] :
% 0.33/0.64 ( if_Code_integer
% 0.33/0.64 @ ( finite6017078050557962740nteger
% 0.33/0.64 @ ( collect_Code_integer
% 0.33/0.64 @ ^ [X3: code_integer] :
% 0.33/0.64 ( ( member_Code_integer @ X3 @ I5 )
% 0.33/0.64 & ( ( P6 @ X3 )
% 0.33/0.64 != one_one_Code_integer ) ) ) )
% 0.33/0.64 @ ( groups3674199335183972705nteger @ P6
% 0.33/0.64 @ ( collect_Code_integer
% 0.33/0.64 @ ^ [X3: code_integer] :
% 0.33/0.64 ( ( member_Code_integer @ X3 @ I5 )
% 0.33/0.64 & ( ( P6 @ X3 )
% 0.33/0.64 != one_one_Code_integer ) ) ) )
% 0.33/0.64 @ one_one_Code_integer ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod.G_def
% 0.33/0.64 thf(fact_6240_prod_OG__def,axiom,
% 0.33/0.64 ( groups12625163056032370o_assn
% 0.33/0.64 = ( ^ [P6: $o > assn,I5: set_o] :
% 0.33/0.64 ( if_assn
% 0.33/0.64 @ ( finite_finite_o
% 0.33/0.64 @ ( collect_o
% 0.33/0.64 @ ^ [X3: $o] :
% 0.33/0.64 ( ( member_o @ X3 @ I5 )
% 0.33/0.64 & ( ( P6 @ X3 )
% 0.33/0.64 != one_one_assn ) ) ) )
% 0.33/0.64 @ ( groups5301882518646026715o_assn @ P6
% 0.33/0.64 @ ( collect_o
% 0.33/0.64 @ ^ [X3: $o] :
% 0.33/0.64 ( ( member_o @ X3 @ I5 )
% 0.33/0.64 & ( ( P6 @ X3 )
% 0.33/0.64 != one_one_assn ) ) ) )
% 0.33/0.64 @ one_one_assn ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod.G_def
% 0.33/0.64 thf(fact_6241_prod_OG__def,axiom,
% 0.33/0.64 ( groups3916077543535352520t_assn
% 0.33/0.64 = ( ^ [P6: nat > assn,I5: set_nat] :
% 0.33/0.64 ( if_assn
% 0.33/0.64 @ ( finite_finite_nat
% 0.33/0.64 @ ( collect_nat
% 0.33/0.64 @ ^ [X3: nat] :
% 0.33/0.64 ( ( member_nat @ X3 @ I5 )
% 0.33/0.64 & ( ( P6 @ X3 )
% 0.33/0.64 != one_one_assn ) ) ) )
% 0.33/0.64 @ ( groups6906906614972039071t_assn @ P6
% 0.33/0.64 @ ( collect_nat
% 0.33/0.64 @ ^ [X3: nat] :
% 0.33/0.64 ( ( member_nat @ X3 @ I5 )
% 0.33/0.64 & ( ( P6 @ X3 )
% 0.33/0.64 != one_one_assn ) ) ) )
% 0.33/0.64 @ one_one_assn ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod.G_def
% 0.33/0.64 thf(fact_6242_prod_OG__def,axiom,
% 0.33/0.64 ( groups4891613008741529892t_assn
% 0.33/0.64 = ( ^ [P6: int > assn,I5: set_int] :
% 0.33/0.64 ( if_assn
% 0.33/0.64 @ ( finite_finite_int
% 0.33/0.64 @ ( collect_int
% 0.33/0.64 @ ^ [X3: int] :
% 0.33/0.64 ( ( member_int @ X3 @ I5 )
% 0.33/0.64 & ( ( P6 @ X3 )
% 0.33/0.64 != one_one_assn ) ) ) )
% 0.33/0.64 @ ( groups7882442080178216443t_assn @ P6
% 0.33/0.64 @ ( collect_int
% 0.33/0.64 @ ^ [X3: int] :
% 0.33/0.64 ( ( member_int @ X3 @ I5 )
% 0.33/0.64 & ( ( P6 @ X3 )
% 0.33/0.64 != one_one_assn ) ) ) )
% 0.33/0.64 @ one_one_assn ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod.G_def
% 0.33/0.64 thf(fact_6243_prod_OG__def,axiom,
% 0.33/0.64 ( groups980104329299799381r_assn
% 0.33/0.64 = ( ^ [P6: code_integer > assn,I5: set_Code_integer] :
% 0.33/0.64 ( if_assn
% 0.33/0.64 @ ( finite6017078050557962740nteger
% 0.33/0.64 @ ( collect_Code_integer
% 0.33/0.64 @ ^ [X3: code_integer] :
% 0.33/0.64 ( ( member_Code_integer @ X3 @ I5 )
% 0.33/0.64 & ( ( P6 @ X3 )
% 0.33/0.64 != one_one_assn ) ) ) )
% 0.33/0.64 @ ( groups1304777262505850412r_assn @ P6
% 0.33/0.64 @ ( collect_Code_integer
% 0.33/0.64 @ ^ [X3: code_integer] :
% 0.33/0.64 ( ( member_Code_integer @ X3 @ I5 )
% 0.33/0.64 & ( ( P6 @ X3 )
% 0.33/0.64 != one_one_assn ) ) ) )
% 0.33/0.64 @ one_one_assn ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod.G_def
% 0.33/0.64 thf(fact_6244_prod_OG__def,axiom,
% 0.33/0.64 ( groups4688112016125141794_o_rat
% 0.33/0.64 = ( ^ [P6: $o > rat,I5: set_o] :
% 0.33/0.64 ( if_rat
% 0.33/0.64 @ ( finite_finite_o
% 0.33/0.64 @ ( collect_o
% 0.33/0.64 @ ^ [X3: $o] :
% 0.33/0.64 ( ( member_o @ X3 @ I5 )
% 0.33/0.64 & ( ( P6 @ X3 )
% 0.33/0.64 != one_one_rat ) ) ) )
% 0.33/0.64 @ ( groups2869687844427037835_o_rat @ P6
% 0.33/0.64 @ ( collect_o
% 0.33/0.64 @ ^ [X3: $o] :
% 0.33/0.64 ( ( member_o @ X3 @ I5 )
% 0.33/0.64 & ( ( P6 @ X3 )
% 0.33/0.64 != one_one_rat ) ) ) )
% 0.33/0.64 @ one_one_rat ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod.G_def
% 0.33/0.64 thf(fact_6245_prod_OG__def,axiom,
% 0.33/0.64 ( groups4112464933559648120at_rat
% 0.33/0.64 = ( ^ [P6: nat > rat,I5: set_nat] :
% 0.33/0.64 ( if_rat
% 0.33/0.64 @ ( finite_finite_nat
% 0.33/0.64 @ ( collect_nat
% 0.33/0.64 @ ^ [X3: nat] :
% 0.33/0.64 ( ( member_nat @ X3 @ I5 )
% 0.33/0.64 & ( ( P6 @ X3 )
% 0.33/0.64 != one_one_rat ) ) ) )
% 0.33/0.64 @ ( groups73079841787564623at_rat @ P6
% 0.33/0.64 @ ( collect_nat
% 0.33/0.64 @ ^ [X3: nat] :
% 0.33/0.64 ( ( member_nat @ X3 @ I5 )
% 0.33/0.64 & ( ( P6 @ X3 )
% 0.33/0.64 != one_one_rat ) ) ) )
% 0.33/0.64 @ one_one_rat ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod.G_def
% 0.33/0.64 thf(fact_6246_greaterThanLessThan__subseteq__atLeastAtMost__iff,axiom,
% 0.33/0.64 ! [A: rat,B: rat,C: rat,D2: rat] :
% 0.33/0.64 ( ( ord_less_eq_set_rat @ ( set_or5199638295745620268an_rat @ A @ B ) @ ( set_or633870826150836451st_rat @ C @ D2 ) )
% 0.33/0.64 = ( ( ord_less_rat @ A @ B )
% 0.33/0.64 => ( ( ord_less_eq_rat @ C @ A )
% 0.33/0.64 & ( ord_less_eq_rat @ B @ D2 ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % greaterThanLessThan_subseteq_atLeastAtMost_iff
% 0.33/0.64 thf(fact_6247_greaterThanLessThan__subseteq__atLeastLessThan__iff,axiom,
% 0.33/0.64 ! [A: rat,B: rat,C: rat,D2: rat] :
% 0.33/0.64 ( ( ord_less_eq_set_rat @ ( set_or5199638295745620268an_rat @ A @ B ) @ ( set_or4029947393144176647an_rat @ C @ D2 ) )
% 0.33/0.64 = ( ( ord_less_rat @ A @ B )
% 0.33/0.64 => ( ( ord_less_eq_rat @ C @ A )
% 0.33/0.64 & ( ord_less_eq_rat @ B @ D2 ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % greaterThanLessThan_subseteq_atLeastLessThan_iff
% 0.33/0.64 thf(fact_6248_atLeastAtMost__diff__ends,axiom,
% 0.33/0.64 ! [A: $o,B: $o] :
% 0.33/0.64 ( ( minus_minus_set_o @ ( set_or8904488021354931149Most_o @ A @ B ) @ ( insert_o @ A @ ( insert_o @ B @ bot_bot_set_o ) ) )
% 0.33/0.64 = ( set_or1716231572884733764Than_o @ A @ B ) ) ).
% 0.33/0.64
% 0.33/0.64 % atLeastAtMost_diff_ends
% 0.33/0.64 thf(fact_6249_atLeastAtMost__diff__ends,axiom,
% 0.33/0.64 ! [A: int,B: int] :
% 0.33/0.64 ( ( minus_minus_set_int @ ( set_or1266510415728281911st_int @ A @ B ) @ ( insert_int @ A @ ( insert_int @ B @ bot_bot_set_int ) ) )
% 0.33/0.64 = ( set_or5832277885323065728an_int @ A @ B ) ) ).
% 0.33/0.64
% 0.33/0.64 % atLeastAtMost_diff_ends
% 0.33/0.64 thf(fact_6250_atLeastAtMost__diff__ends,axiom,
% 0.33/0.64 ! [A: nat,B: nat] :
% 0.33/0.64 ( ( minus_minus_set_nat @ ( set_or1269000886237332187st_nat @ A @ B ) @ ( insert_nat @ A @ ( insert_nat @ B @ bot_bot_set_nat ) ) )
% 0.33/0.64 = ( set_or5834768355832116004an_nat @ A @ B ) ) ).
% 0.33/0.64
% 0.33/0.64 % atLeastAtMost_diff_ends
% 0.33/0.64 thf(fact_6251_atLeastAtMost__diff__ends,axiom,
% 0.33/0.64 ! [A: code_integer,B: code_integer] :
% 0.33/0.64 ( ( minus_2355218937544613996nteger @ ( set_or189985376899183464nteger @ A @ B ) @ ( insert_Code_integer @ A @ ( insert_Code_integer @ B @ bot_bo3990330152332043303nteger ) ) )
% 0.33/0.64 = ( set_or4266950643985792945nteger @ A @ B ) ) ).
% 0.33/0.64
% 0.33/0.64 % atLeastAtMost_diff_ends
% 0.33/0.64 thf(fact_6252_smax__insertI,axiom,
% 0.33/0.64 ! [Y: product_prod_nat_nat,Y9: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat,X11: set_Pr1261947904930325089at_nat] :
% 0.33/0.64 ( ( member8440522571783428010at_nat @ Y @ Y9 )
% 0.33/0.64 => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X @ Y ) @ fun_pair_less )
% 0.33/0.64 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X11 @ Y9 ) @ fun_max_strict )
% 0.33/0.64 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( insert8211810215607154385at_nat @ X @ X11 ) @ Y9 ) @ fun_max_strict ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % smax_insertI
% 0.33/0.64 thf(fact_6253_set__decode__plus__power__2,axiom,
% 0.33/0.64 ! [N2: nat,Z: nat] :
% 0.33/0.64 ( ~ ( member_nat @ N2 @ ( nat_set_decode @ Z ) )
% 0.33/0.64 => ( ( nat_set_decode @ ( plus_plus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ Z ) )
% 0.33/0.64 = ( insert_nat @ N2 @ ( nat_set_decode @ Z ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % set_decode_plus_power_2
% 0.33/0.64 thf(fact_6254_prod__decode__aux_Osimps,axiom,
% 0.33/0.64 ( nat_prod_decode_aux
% 0.33/0.64 = ( ^ [K4: nat,M: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ M @ K4 ) @ ( product_Pair_nat_nat @ M @ ( minus_minus_nat @ K4 @ M ) ) @ ( nat_prod_decode_aux @ ( suc @ K4 ) @ ( minus_minus_nat @ M @ ( suc @ K4 ) ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod_decode_aux.simps
% 0.33/0.64 thf(fact_6255_prod__decode__aux_Oelims,axiom,
% 0.33/0.64 ! [X: nat,Xa: nat,Y: product_prod_nat_nat] :
% 0.33/0.64 ( ( ( nat_prod_decode_aux @ X @ Xa )
% 0.33/0.64 = Y )
% 0.33/0.64 => ( ( ( ord_less_eq_nat @ Xa @ X )
% 0.33/0.64 => ( Y
% 0.33/0.64 = ( product_Pair_nat_nat @ Xa @ ( minus_minus_nat @ X @ Xa ) ) ) )
% 0.33/0.64 & ( ~ ( ord_less_eq_nat @ Xa @ X )
% 0.33/0.64 => ( Y
% 0.33/0.64 = ( nat_prod_decode_aux @ ( suc @ X ) @ ( minus_minus_nat @ Xa @ ( suc @ X ) ) ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod_decode_aux.elims
% 0.33/0.64 thf(fact_6256_min__rpair__set,axiom,
% 0.33/0.64 fun_re2478310338295953701at_nat @ ( produc9060074326276436823at_nat @ fun_min_strict @ fun_min_weak ) ).
% 0.33/0.64
% 0.33/0.64 % min_rpair_set
% 0.33/0.64 thf(fact_6257_triangle__Suc,axiom,
% 0.33/0.64 ! [N2: nat] :
% 0.33/0.64 ( ( nat_triangle @ ( suc @ N2 ) )
% 0.33/0.64 = ( plus_plus_nat @ ( nat_triangle @ N2 ) @ ( suc @ N2 ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % triangle_Suc
% 0.33/0.64 thf(fact_6258_finite__greaterThanLessThan,axiom,
% 0.33/0.64 ! [L: nat,U: nat] : ( finite_finite_nat @ ( set_or5834768355832116004an_nat @ L @ U ) ) ).
% 0.33/0.64
% 0.33/0.64 % finite_greaterThanLessThan
% 0.33/0.64 thf(fact_6259_finite__greaterThanLessThan__integer,axiom,
% 0.33/0.64 ! [L: code_integer,U: code_integer] : ( finite6017078050557962740nteger @ ( set_or4266950643985792945nteger @ L @ U ) ) ).
% 0.33/0.64
% 0.33/0.64 % finite_greaterThanLessThan_integer
% 0.33/0.64 thf(fact_6260_card__greaterThanLessThan,axiom,
% 0.33/0.64 ! [L: nat,U: nat] :
% 0.33/0.64 ( ( finite_card_nat @ ( set_or5834768355832116004an_nat @ L @ U ) )
% 0.33/0.64 = ( minus_minus_nat @ U @ ( suc @ L ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % card_greaterThanLessThan
% 0.33/0.64 thf(fact_6261_max__rpair__set,axiom,
% 0.33/0.64 fun_re2478310338295953701at_nat @ ( produc9060074326276436823at_nat @ fun_max_strict @ fun_max_weak ) ).
% 0.33/0.64
% 0.33/0.64 % max_rpair_set
% 0.33/0.64 thf(fact_6262_atLeastSucLessThan__greaterThanLessThan,axiom,
% 0.33/0.64 ! [L: nat,U: nat] :
% 0.33/0.64 ( ( set_or4665077453230672383an_nat @ ( suc @ L ) @ U )
% 0.33/0.64 = ( set_or5834768355832116004an_nat @ L @ U ) ) ).
% 0.33/0.64
% 0.33/0.64 % atLeastSucLessThan_greaterThanLessThan
% 0.33/0.64 thf(fact_6263_smax__emptyI,axiom,
% 0.33/0.64 ! [Y9: set_Pr1261947904930325089at_nat] :
% 0.33/0.64 ( ( finite6177210948735845034at_nat @ Y9 )
% 0.33/0.64 => ( ( Y9 != bot_bo2099793752762293965at_nat )
% 0.33/0.64 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ bot_bo2099793752762293965at_nat @ Y9 ) @ fun_max_strict ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % smax_emptyI
% 0.33/0.64 thf(fact_6264_atLeastPlusOneLessThan__greaterThanLessThan__integer,axiom,
% 0.33/0.64 ! [L: code_integer,U: code_integer] :
% 0.33/0.64 ( ( set_or8404916559141939852nteger @ ( plus_p5714425477246183910nteger @ L @ one_one_Code_integer ) @ U )
% 0.33/0.64 = ( set_or4266950643985792945nteger @ L @ U ) ) ).
% 0.33/0.64
% 0.33/0.64 % atLeastPlusOneLessThan_greaterThanLessThan_integer
% 0.33/0.64 thf(fact_6265_prod__decode__aux_Opelims,axiom,
% 0.33/0.64 ! [X: nat,Xa: nat,Y: product_prod_nat_nat] :
% 0.33/0.64 ( ( ( nat_prod_decode_aux @ X @ Xa )
% 0.33/0.64 = Y )
% 0.33/0.64 => ( ( accp_P4275260045618599050at_nat @ nat_pr5047031295181774490ux_rel @ ( product_Pair_nat_nat @ X @ Xa ) )
% 0.33/0.64 => ~ ( ( ( ( ord_less_eq_nat @ Xa @ X )
% 0.33/0.64 => ( Y
% 0.33/0.64 = ( product_Pair_nat_nat @ Xa @ ( minus_minus_nat @ X @ Xa ) ) ) )
% 0.33/0.64 & ( ~ ( ord_less_eq_nat @ Xa @ X )
% 0.33/0.64 => ( Y
% 0.33/0.64 = ( nat_prod_decode_aux @ ( suc @ X ) @ ( minus_minus_nat @ Xa @ ( suc @ X ) ) ) ) ) )
% 0.33/0.64 => ~ ( accp_P4275260045618599050at_nat @ nat_pr5047031295181774490ux_rel @ ( product_Pair_nat_nat @ X @ Xa ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod_decode_aux.pelims
% 0.33/0.64 thf(fact_6266_total__on__singleton,axiom,
% 0.33/0.64 ! [X: set_Pr1261947904930325089at_nat] : ( total_7212417256332265445at_nat @ ( insert9200635055090092081at_nat @ X @ bot_bo3083307316010499117at_nat ) @ ( insert9069300056098147895at_nat @ ( produc2922128104949294807at_nat @ X @ X ) @ bot_bo228742789529271731at_nat ) ) ).
% 0.33/0.64
% 0.33/0.64 % total_on_singleton
% 0.33/0.64 thf(fact_6267_total__on__singleton,axiom,
% 0.33/0.64 ! [X: produc3843707927480180839at_nat] : ( total_1513685709984341995at_nat @ ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) @ ( insert398606708087465655at_nat @ ( produc2335810615602371415at_nat @ X @ X ) @ bot_bo7193250159860175667at_nat ) ) ).
% 0.33/0.64
% 0.33/0.64 % total_on_singleton
% 0.33/0.64 thf(fact_6268_total__on__singleton,axiom,
% 0.33/0.64 ! [X: product_prod_nat_nat] : ( total_3592101749530773125at_nat @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) @ ( insert5050368324300391991at_nat @ ( produc6161850002892822231at_nat @ X @ X ) @ bot_bo5327735625951526323at_nat ) ) ).
% 0.33/0.64
% 0.33/0.64 % total_on_singleton
% 0.33/0.64 thf(fact_6269_total__on__singleton,axiom,
% 0.33/0.64 ! [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 ) ) ).
% 0.33/0.64
% 0.33/0.64 % total_on_singleton
% 0.33/0.64 thf(fact_6270_total__on__singleton,axiom,
% 0.33/0.64 ! [X: nat] : ( total_on_nat @ ( insert_nat @ X @ bot_bot_set_nat ) @ ( insert8211810215607154385at_nat @ ( product_Pair_nat_nat @ X @ X ) @ bot_bo2099793752762293965at_nat ) ) ).
% 0.33/0.64
% 0.33/0.64 % total_on_singleton
% 0.33/0.64 thf(fact_6271_total__on__singleton,axiom,
% 0.33/0.64 ! [X: int] : ( total_on_int @ ( insert_int @ X @ bot_bot_set_int ) @ ( insert5033312907999012233nt_int @ ( product_Pair_int_int @ X @ X ) @ bot_bo1796632182523588997nt_int ) ) ).
% 0.33/0.64
% 0.33/0.64 % total_on_singleton
% 0.33/0.64 thf(fact_6272_prod__encode__prod__decode__aux,axiom,
% 0.33/0.64 ! [K: nat,M2: nat] :
% 0.33/0.64 ( ( nat_prod_encode @ ( nat_prod_decode_aux @ K @ M2 ) )
% 0.33/0.64 = ( plus_plus_nat @ ( nat_triangle @ K ) @ M2 ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod_encode_prod_decode_aux
% 0.33/0.64 thf(fact_6273_sum_Oinsert_H,axiom,
% 0.33/0.64 ! [I4: set_o,P4: $o > code_integer,I: $o] :
% 0.33/0.64 ( ( finite_finite_o
% 0.33/0.64 @ ( collect_o
% 0.33/0.64 @ ^ [X3: $o] :
% 0.33/0.64 ( ( member_o @ X3 @ I4 )
% 0.33/0.64 & ( ( P4 @ X3 )
% 0.33/0.64 != zero_z3403309356797280102nteger ) ) ) )
% 0.33/0.64 => ( ( ( member_o @ I @ I4 )
% 0.33/0.64 => ( ( groups1402912129352969042nteger @ P4 @ ( insert_o @ I @ I4 ) )
% 0.33/0.64 = ( groups1402912129352969042nteger @ P4 @ I4 ) ) )
% 0.33/0.64 & ( ~ ( member_o @ I @ I4 )
% 0.33/0.64 => ( ( groups1402912129352969042nteger @ P4 @ ( insert_o @ I @ I4 ) )
% 0.33/0.64 = ( plus_p5714425477246183910nteger @ ( P4 @ I ) @ ( groups1402912129352969042nteger @ P4 @ I4 ) ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % sum.insert'
% 0.33/0.64 thf(fact_6274_sum_Oinsert_H,axiom,
% 0.33/0.64 ! [I4: set_nat,P4: nat > code_integer,I: nat] :
% 0.33/0.64 ( ( finite_finite_nat
% 0.33/0.64 @ ( collect_nat
% 0.33/0.64 @ ^ [X3: nat] :
% 0.33/0.64 ( ( member_nat @ X3 @ I4 )
% 0.33/0.64 & ( ( P4 @ X3 )
% 0.33/0.64 != zero_z3403309356797280102nteger ) ) ) )
% 0.33/0.64 => ( ( ( member_nat @ I @ I4 )
% 0.33/0.64 => ( ( groups555127423416065298nteger @ P4 @ ( insert_nat @ I @ I4 ) )
% 0.33/0.64 = ( groups555127423416065298nteger @ P4 @ I4 ) ) )
% 0.33/0.64 & ( ~ ( member_nat @ I @ I4 )
% 0.33/0.64 => ( ( groups555127423416065298nteger @ P4 @ ( insert_nat @ I @ I4 ) )
% 0.33/0.64 = ( plus_p5714425477246183910nteger @ ( P4 @ I ) @ ( groups555127423416065298nteger @ P4 @ I4 ) ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % sum.insert'
% 0.33/0.64 thf(fact_6275_sum_Oinsert_H,axiom,
% 0.33/0.64 ! [I4: set_int,P4: int > code_integer,I: int] :
% 0.33/0.64 ( ( finite_finite_int
% 0.33/0.64 @ ( collect_int
% 0.33/0.64 @ ^ [X3: int] :
% 0.33/0.64 ( ( member_int @ X3 @ I4 )
% 0.33/0.64 & ( ( P4 @ X3 )
% 0.33/0.64 != zero_z3403309356797280102nteger ) ) ) )
% 0.33/0.64 => ( ( ( member_int @ I @ I4 )
% 0.33/0.64 => ( ( groups926780983652909934nteger @ P4 @ ( insert_int @ I @ I4 ) )
% 0.33/0.64 = ( groups926780983652909934nteger @ P4 @ I4 ) ) )
% 0.33/0.64 & ( ~ ( member_int @ I @ I4 )
% 0.33/0.64 => ( ( groups926780983652909934nteger @ P4 @ ( insert_int @ I @ I4 ) )
% 0.33/0.64 = ( plus_p5714425477246183910nteger @ ( P4 @ I ) @ ( groups926780983652909934nteger @ P4 @ I4 ) ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % sum.insert'
% 0.33/0.64 thf(fact_6276_sum_Oinsert_H,axiom,
% 0.33/0.64 ! [I4: set_Code_integer,P4: code_integer > code_integer,I: code_integer] :
% 0.33/0.64 ( ( finite6017078050557962740nteger
% 0.33/0.64 @ ( collect_Code_integer
% 0.33/0.64 @ ^ [X3: code_integer] :
% 0.33/0.64 ( ( member_Code_integer @ X3 @ I4 )
% 0.33/0.64 & ( ( P4 @ X3 )
% 0.33/0.64 != zero_z3403309356797280102nteger ) ) ) )
% 0.33/0.64 => ( ( ( member_Code_integer @ I @ I4 )
% 0.33/0.64 => ( ( groups910942671188738463nteger @ P4 @ ( insert_Code_integer @ I @ I4 ) )
% 0.33/0.64 = ( groups910942671188738463nteger @ P4 @ I4 ) ) )
% 0.33/0.64 & ( ~ ( member_Code_integer @ I @ I4 )
% 0.33/0.64 => ( ( groups910942671188738463nteger @ P4 @ ( insert_Code_integer @ I @ I4 ) )
% 0.33/0.64 = ( plus_p5714425477246183910nteger @ ( P4 @ I ) @ ( groups910942671188738463nteger @ P4 @ I4 ) ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % sum.insert'
% 0.33/0.64 thf(fact_6277_sum_Oinsert_H,axiom,
% 0.33/0.64 ! [I4: set_o,P4: $o > rat,I: $o] :
% 0.33/0.64 ( ( finite_finite_o
% 0.33/0.64 @ ( collect_o
% 0.33/0.64 @ ^ [X3: $o] :
% 0.33/0.64 ( ( member_o @ X3 @ I4 )
% 0.33/0.64 & ( ( P4 @ X3 )
% 0.33/0.64 != zero_zero_rat ) ) ) )
% 0.33/0.64 => ( ( ( member_o @ I @ I4 )
% 0.33/0.64 => ( ( groups3921277224699582669_o_rat @ P4 @ ( insert_o @ I @ I4 ) )
% 0.33/0.64 = ( groups3921277224699582669_o_rat @ P4 @ I4 ) ) )
% 0.33/0.64 & ( ~ ( member_o @ I @ I4 )
% 0.33/0.64 => ( ( groups3921277224699582669_o_rat @ P4 @ ( insert_o @ I @ I4 ) )
% 0.33/0.64 = ( plus_plus_rat @ ( P4 @ I ) @ ( groups3921277224699582669_o_rat @ P4 @ I4 ) ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % sum.insert'
% 0.33/0.64 thf(fact_6278_sum_Oinsert_H,axiom,
% 0.33/0.64 ! [I4: set_nat,P4: nat > rat,I: nat] :
% 0.33/0.64 ( ( finite_finite_nat
% 0.33/0.64 @ ( collect_nat
% 0.33/0.64 @ ^ [X3: nat] :
% 0.33/0.64 ( ( member_nat @ X3 @ I4 )
% 0.33/0.64 & ( ( P4 @ X3 )
% 0.33/0.64 != zero_zero_rat ) ) ) )
% 0.33/0.64 => ( ( ( member_nat @ I @ I4 )
% 0.33/0.64 => ( ( groups1351286907653491341at_rat @ P4 @ ( insert_nat @ I @ I4 ) )
% 0.33/0.64 = ( groups1351286907653491341at_rat @ P4 @ I4 ) ) )
% 0.33/0.64 & ( ~ ( member_nat @ I @ I4 )
% 0.33/0.64 => ( ( groups1351286907653491341at_rat @ P4 @ ( insert_nat @ I @ I4 ) )
% 0.33/0.64 = ( plus_plus_rat @ ( P4 @ I ) @ ( groups1351286907653491341at_rat @ P4 @ I4 ) ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % sum.insert'
% 0.33/0.64 thf(fact_6279_sum_Oinsert_H,axiom,
% 0.33/0.64 ! [I4: set_int,P4: int > rat,I: int] :
% 0.33/0.64 ( ( finite_finite_int
% 0.33/0.64 @ ( collect_int
% 0.33/0.64 @ ^ [X3: int] :
% 0.33/0.64 ( ( member_int @ X3 @ I4 )
% 0.33/0.64 & ( ( P4 @ X3 )
% 0.33/0.64 != zero_zero_rat ) ) ) )
% 0.33/0.64 => ( ( ( member_int @ I @ I4 )
% 0.33/0.64 => ( ( groups2350640619554545897nt_rat @ P4 @ ( insert_int @ I @ I4 ) )
% 0.33/0.64 = ( groups2350640619554545897nt_rat @ P4 @ I4 ) ) )
% 0.33/0.64 & ( ~ ( member_int @ I @ I4 )
% 0.33/0.64 => ( ( groups2350640619554545897nt_rat @ P4 @ ( insert_int @ I @ I4 ) )
% 0.33/0.64 = ( plus_plus_rat @ ( P4 @ I ) @ ( groups2350640619554545897nt_rat @ P4 @ I4 ) ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % sum.insert'
% 0.33/0.64 thf(fact_6280_sum_Oinsert_H,axiom,
% 0.33/0.64 ! [I4: set_Code_integer,P4: code_integer > rat,I: code_integer] :
% 0.33/0.64 ( ( finite6017078050557962740nteger
% 0.33/0.64 @ ( collect_Code_integer
% 0.33/0.64 @ ^ [X3: code_integer] :
% 0.33/0.64 ( ( member_Code_integer @ X3 @ I4 )
% 0.33/0.64 & ( ( P4 @ X3 )
% 0.33/0.64 != zero_zero_rat ) ) ) )
% 0.33/0.64 => ( ( ( member_Code_integer @ I @ I4 )
% 0.33/0.64 => ( ( groups8878813951405302554er_rat @ P4 @ ( insert_Code_integer @ I @ I4 ) )
% 0.33/0.64 = ( groups8878813951405302554er_rat @ P4 @ I4 ) ) )
% 0.33/0.64 & ( ~ ( member_Code_integer @ I @ I4 )
% 0.33/0.64 => ( ( groups8878813951405302554er_rat @ P4 @ ( insert_Code_integer @ I @ I4 ) )
% 0.33/0.64 = ( plus_plus_rat @ ( P4 @ I ) @ ( groups8878813951405302554er_rat @ P4 @ I4 ) ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % sum.insert'
% 0.33/0.64 thf(fact_6281_sum_Oinsert_H,axiom,
% 0.33/0.64 ! [I4: set_o,P4: $o > nat,I: $o] :
% 0.33/0.64 ( ( finite_finite_o
% 0.33/0.64 @ ( collect_o
% 0.33/0.64 @ ^ [X3: $o] :
% 0.33/0.64 ( ( member_o @ X3 @ I4 )
% 0.33/0.64 & ( ( P4 @ X3 )
% 0.33/0.64 != zero_zero_nat ) ) ) )
% 0.33/0.64 => ( ( ( member_o @ I @ I4 )
% 0.33/0.64 => ( ( groups4556407284786078405_o_nat @ P4 @ ( insert_o @ I @ I4 ) )
% 0.33/0.64 = ( groups4556407284786078405_o_nat @ P4 @ I4 ) ) )
% 0.33/0.64 & ( ~ ( member_o @ I @ I4 )
% 0.33/0.64 => ( ( groups4556407284786078405_o_nat @ P4 @ ( insert_o @ I @ I4 ) )
% 0.33/0.64 = ( plus_plus_nat @ ( P4 @ I ) @ ( groups4556407284786078405_o_nat @ P4 @ I4 ) ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % sum.insert'
% 0.33/0.64 thf(fact_6282_sum_Oinsert_H,axiom,
% 0.33/0.64 ! [I4: set_nat,P4: nat > nat,I: nat] :
% 0.33/0.64 ( ( finite_finite_nat
% 0.33/0.64 @ ( collect_nat
% 0.33/0.64 @ ^ [X3: nat] :
% 0.33/0.64 ( ( member_nat @ X3 @ I4 )
% 0.33/0.64 & ( ( P4 @ X3 )
% 0.33/0.64 != zero_zero_nat ) ) ) )
% 0.33/0.64 => ( ( ( member_nat @ I @ I4 )
% 0.33/0.64 => ( ( groups1986416967739987077at_nat @ P4 @ ( insert_nat @ I @ I4 ) )
% 0.33/0.64 = ( groups1986416967739987077at_nat @ P4 @ I4 ) ) )
% 0.33/0.64 & ( ~ ( member_nat @ I @ I4 )
% 0.33/0.64 => ( ( groups1986416967739987077at_nat @ P4 @ ( insert_nat @ I @ I4 ) )
% 0.33/0.64 = ( plus_plus_nat @ ( P4 @ I ) @ ( groups1986416967739987077at_nat @ P4 @ I4 ) ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % sum.insert'
% 0.33/0.64 thf(fact_6283_max__ext_Omax__extI,axiom,
% 0.33/0.64 ! [X11: set_se7855581050983116737at_nat,Y9: set_se7855581050983116737at_nat,R4: set_Pr4329608150637261639at_nat] :
% 0.33/0.64 ( ( finite9047747110432174090at_nat @ X11 )
% 0.33/0.64 => ( ( finite9047747110432174090at_nat @ Y9 )
% 0.33/0.64 => ( ( Y9 != bot_bo3083307316010499117at_nat )
% 0.33/0.64 => ( ! [X4: set_Pr1261947904930325089at_nat] :
% 0.33/0.64 ( ( member2643936169264416010at_nat @ X4 @ X11 )
% 0.33/0.64 => ? [Xa2: set_Pr1261947904930325089at_nat] :
% 0.33/0.64 ( ( member2643936169264416010at_nat @ Xa2 @ Y9 )
% 0.33/0.64 & ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X4 @ Xa2 ) @ R4 ) ) )
% 0.33/0.64 => ( member4300370950623927696at_nat @ ( produc7462898802507495127at_nat @ X11 @ Y9 ) @ ( max_ex4535816423174879388at_nat @ R4 ) ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % max_ext.max_extI
% 0.33/0.64 thf(fact_6284_max__ext_Omax__extI,axiom,
% 0.33/0.64 ! [X11: set_Code_integer,Y9: set_Code_integer,R4: set_Pr4811707699266497531nteger] :
% 0.33/0.64 ( ( finite6017078050557962740nteger @ X11 )
% 0.33/0.64 => ( ( finite6017078050557962740nteger @ Y9 )
% 0.33/0.64 => ( ( Y9 != bot_bo3990330152332043303nteger )
% 0.33/0.64 => ( ! [X4: code_integer] :
% 0.33/0.64 ( ( member_Code_integer @ X4 @ X11 )
% 0.33/0.64 => ? [Xa2: code_integer] :
% 0.33/0.64 ( ( member_Code_integer @ Xa2 @ Y9 )
% 0.33/0.64 & ( member157494554546826820nteger @ ( produc1086072967326762835nteger @ X4 @ Xa2 ) @ R4 ) ) )
% 0.33/0.64 => ( member4307123515891402160nteger @ ( produc7443773368509356479nteger @ X11 @ Y9 ) @ ( max_ext_Code_integer @ R4 ) ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % max_ext.max_extI
% 0.33/0.64 thf(fact_6285_max__ext_Omax__extI,axiom,
% 0.33/0.64 ! [X11: set_Pr4329608150637261639at_nat,Y9: set_Pr4329608150637261639at_nat,R4: set_Pr5564308138774400199at_nat] :
% 0.33/0.64 ( ( finite4343798906461161616at_nat @ X11 )
% 0.33/0.64 => ( ( finite4343798906461161616at_nat @ Y9 )
% 0.33/0.64 => ( ( Y9 != bot_bo228742789529271731at_nat )
% 0.33/0.64 => ( ! [X4: produc3843707927480180839at_nat] :
% 0.33/0.64 ( ( member8757157785044589968at_nat @ X4 @ X11 )
% 0.33/0.64 => ? [Xa2: produc3843707927480180839at_nat] :
% 0.33/0.64 ( ( member8757157785044589968at_nat @ Xa2 @ Y9 )
% 0.33/0.64 & ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ X4 @ Xa2 ) @ R4 ) ) )
% 0.33/0.64 => ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ X11 @ Y9 ) @ ( max_ex8833738776070432290at_nat @ R4 ) ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % max_ext.max_extI
% 0.33/0.64 thf(fact_6286_max__ext_Omax__extI,axiom,
% 0.33/0.64 ! [X11: set_Pr1261947904930325089at_nat,Y9: set_Pr1261947904930325089at_nat,R4: set_Pr8693737435421807431at_nat] :
% 0.33/0.64 ( ( finite6177210948735845034at_nat @ X11 )
% 0.33/0.64 => ( ( finite6177210948735845034at_nat @ Y9 )
% 0.33/0.64 => ( ( Y9 != bot_bo2099793752762293965at_nat )
% 0.33/0.64 => ( ! [X4: product_prod_nat_nat] :
% 0.33/0.64 ( ( member8440522571783428010at_nat @ X4 @ X11 )
% 0.33/0.64 => ? [Xa2: product_prod_nat_nat] :
% 0.33/0.64 ( ( member8440522571783428010at_nat @ Xa2 @ Y9 )
% 0.33/0.64 & ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X4 @ Xa2 ) @ R4 ) ) )
% 0.33/0.64 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X11 @ Y9 ) @ ( max_ex8135407076693332796at_nat @ R4 ) ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % max_ext.max_extI
% 0.33/0.64 thf(fact_6287_max__ext_Omax__extI,axiom,
% 0.33/0.64 ! [X11: set_o,Y9: set_o,R4: set_Product_prod_o_o] :
% 0.33/0.64 ( ( finite_finite_o @ X11 )
% 0.33/0.64 => ( ( finite_finite_o @ Y9 )
% 0.33/0.64 => ( ( Y9 != bot_bot_set_o )
% 0.33/0.64 => ( ! [X4: $o] :
% 0.33/0.64 ( ( member_o @ X4 @ X11 )
% 0.33/0.64 => ? [Xa2: $o] :
% 0.33/0.64 ( ( member_o @ Xa2 @ Y9 )
% 0.33/0.64 & ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ X4 @ Xa2 ) @ R4 ) ) )
% 0.33/0.64 => ( member9116954335612470352_set_o @ ( produc5838405689764958487_set_o @ X11 @ Y9 ) @ ( max_ext_o @ R4 ) ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % max_ext.max_extI
% 0.33/0.64 thf(fact_6288_max__ext_Omax__extI,axiom,
% 0.33/0.64 ! [X11: set_nat,Y9: set_nat,R4: set_Pr1261947904930325089at_nat] :
% 0.33/0.64 ( ( finite_finite_nat @ X11 )
% 0.33/0.64 => ( ( finite_finite_nat @ Y9 )
% 0.33/0.64 => ( ( Y9 != bot_bot_set_nat )
% 0.33/0.64 => ( ! [X4: nat] :
% 0.33/0.64 ( ( member_nat @ X4 @ X11 )
% 0.33/0.64 => ? [Xa2: nat] :
% 0.33/0.64 ( ( member_nat @ Xa2 @ Y9 )
% 0.33/0.64 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Xa2 ) @ R4 ) ) )
% 0.33/0.64 => ( member8277197624267554838et_nat @ ( produc4532415448927165861et_nat @ X11 @ Y9 ) @ ( max_ext_nat @ R4 ) ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % max_ext.max_extI
% 0.33/0.64 thf(fact_6289_max__ext_Omax__extI,axiom,
% 0.33/0.64 ! [X11: set_int,Y9: set_int,R4: set_Pr958786334691620121nt_int] :
% 0.33/0.64 ( ( finite_finite_int @ X11 )
% 0.33/0.64 => ( ( finite_finite_int @ Y9 )
% 0.33/0.64 => ( ( Y9 != bot_bot_set_int )
% 0.33/0.64 => ( ! [X4: int] :
% 0.33/0.64 ( ( member_int @ X4 @ X11 )
% 0.33/0.64 => ? [Xa2: int] :
% 0.33/0.64 ( ( member_int @ Xa2 @ Y9 )
% 0.33/0.64 & ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Xa2 ) @ R4 ) ) )
% 0.33/0.64 => ( member2572552093476627150et_int @ ( produc6363374080413544029et_int @ X11 @ Y9 ) @ ( max_ext_int @ R4 ) ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % max_ext.max_extI
% 0.33/0.64 thf(fact_6290_total__on__def,axiom,
% 0.33/0.64 ( total_7212417256332265445at_nat
% 0.33/0.64 = ( ^ [A7: set_se7855581050983116737at_nat,R3: set_Pr4329608150637261639at_nat] :
% 0.33/0.64 ! [X3: set_Pr1261947904930325089at_nat] :
% 0.33/0.64 ( ( member2643936169264416010at_nat @ X3 @ A7 )
% 0.33/0.64 => ! [Y3: set_Pr1261947904930325089at_nat] :
% 0.33/0.64 ( ( member2643936169264416010at_nat @ Y3 @ A7 )
% 0.33/0.64 => ( ( X3 != Y3 )
% 0.33/0.64 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ Y3 ) @ R3 )
% 0.33/0.64 | ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ Y3 @ X3 ) @ R3 ) ) ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % total_on_def
% 0.33/0.64 thf(fact_6291_total__on__def,axiom,
% 0.33/0.64 ( total_on_nat
% 0.33/0.64 = ( ^ [A7: set_nat,R3: set_Pr1261947904930325089at_nat] :
% 0.33/0.64 ! [X3: nat] :
% 0.33/0.64 ( ( member_nat @ X3 @ A7 )
% 0.33/0.64 => ! [Y3: nat] :
% 0.33/0.64 ( ( member_nat @ Y3 @ A7 )
% 0.33/0.64 => ( ( X3 != Y3 )
% 0.33/0.64 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y3 ) @ R3 )
% 0.33/0.64 | ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y3 @ X3 ) @ R3 ) ) ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % total_on_def
% 0.33/0.64 thf(fact_6292_total__onI,axiom,
% 0.33/0.64 ! [A2: set_se7855581050983116737at_nat,R2: set_Pr4329608150637261639at_nat] :
% 0.33/0.64 ( ! [X4: set_Pr1261947904930325089at_nat,Y5: set_Pr1261947904930325089at_nat] :
% 0.33/0.64 ( ( member2643936169264416010at_nat @ X4 @ A2 )
% 0.33/0.64 => ( ( member2643936169264416010at_nat @ Y5 @ A2 )
% 0.33/0.64 => ( ( X4 != Y5 )
% 0.33/0.64 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X4 @ Y5 ) @ R2 )
% 0.33/0.64 | ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ Y5 @ X4 ) @ R2 ) ) ) ) )
% 0.33/0.64 => ( total_7212417256332265445at_nat @ A2 @ R2 ) ) ).
% 0.33/0.64
% 0.33/0.64 % total_onI
% 0.33/0.64 thf(fact_6293_total__onI,axiom,
% 0.33/0.64 ! [A2: set_Pr4329608150637261639at_nat,R2: set_Pr5564308138774400199at_nat] :
% 0.33/0.64 ( ! [X4: produc3843707927480180839at_nat,Y5: produc3843707927480180839at_nat] :
% 0.33/0.64 ( ( member8757157785044589968at_nat @ X4 @ A2 )
% 0.33/0.64 => ( ( member8757157785044589968at_nat @ Y5 @ A2 )
% 0.33/0.64 => ( ( X4 != Y5 )
% 0.33/0.64 => ( ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ X4 @ Y5 ) @ R2 )
% 0.33/0.64 | ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ Y5 @ X4 ) @ R2 ) ) ) ) )
% 0.33/0.64 => ( total_1513685709984341995at_nat @ A2 @ R2 ) ) ).
% 0.33/0.64
% 0.33/0.64 % total_onI
% 0.33/0.64 thf(fact_6294_total__onI,axiom,
% 0.33/0.64 ! [A2: set_Pr1261947904930325089at_nat,R2: set_Pr8693737435421807431at_nat] :
% 0.33/0.64 ( ! [X4: product_prod_nat_nat,Y5: product_prod_nat_nat] :
% 0.33/0.64 ( ( member8440522571783428010at_nat @ X4 @ A2 )
% 0.33/0.64 => ( ( member8440522571783428010at_nat @ Y5 @ A2 )
% 0.33/0.64 => ( ( X4 != Y5 )
% 0.33/0.64 => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X4 @ Y5 ) @ R2 )
% 0.33/0.64 | ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ Y5 @ X4 ) @ R2 ) ) ) ) )
% 0.33/0.64 => ( total_3592101749530773125at_nat @ A2 @ R2 ) ) ).
% 0.33/0.64
% 0.33/0.64 % total_onI
% 0.33/0.64 thf(fact_6295_total__onI,axiom,
% 0.33/0.64 ! [A2: set_o,R2: set_Product_prod_o_o] :
% 0.33/0.64 ( ! [X4: $o,Y5: $o] :
% 0.33/0.64 ( ( member_o @ X4 @ A2 )
% 0.33/0.64 => ( ( member_o @ Y5 @ A2 )
% 0.33/0.64 => ( ( X4 != Y5 )
% 0.33/0.64 => ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ X4 @ Y5 ) @ R2 )
% 0.33/0.64 | ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ Y5 @ X4 ) @ R2 ) ) ) ) )
% 0.33/0.64 => ( total_on_o @ A2 @ R2 ) ) ).
% 0.33/0.64
% 0.33/0.64 % total_onI
% 0.33/0.64 thf(fact_6296_total__onI,axiom,
% 0.33/0.64 ! [A2: set_nat,R2: set_Pr1261947904930325089at_nat] :
% 0.33/0.64 ( ! [X4: nat,Y5: nat] :
% 0.33/0.64 ( ( member_nat @ X4 @ A2 )
% 0.33/0.64 => ( ( member_nat @ Y5 @ A2 )
% 0.33/0.64 => ( ( X4 != Y5 )
% 0.33/0.64 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Y5 ) @ R2 )
% 0.33/0.64 | ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y5 @ X4 ) @ R2 ) ) ) ) )
% 0.33/0.64 => ( total_on_nat @ A2 @ R2 ) ) ).
% 0.33/0.64
% 0.33/0.64 % total_onI
% 0.33/0.64 thf(fact_6297_total__onI,axiom,
% 0.33/0.64 ! [A2: set_int,R2: set_Pr958786334691620121nt_int] :
% 0.33/0.64 ( ! [X4: int,Y5: int] :
% 0.33/0.64 ( ( member_int @ X4 @ A2 )
% 0.33/0.64 => ( ( member_int @ Y5 @ A2 )
% 0.33/0.64 => ( ( X4 != Y5 )
% 0.33/0.64 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Y5 ) @ R2 )
% 0.33/0.64 | ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Y5 @ X4 ) @ R2 ) ) ) ) )
% 0.33/0.64 => ( total_on_int @ A2 @ R2 ) ) ).
% 0.33/0.64
% 0.33/0.64 % total_onI
% 0.33/0.64 thf(fact_6298_sum_Odistrib__triv_H,axiom,
% 0.33/0.64 ! [I4: set_nat,G: nat > rat,H3: nat > rat] :
% 0.33/0.64 ( ( finite_finite_nat @ I4 )
% 0.33/0.64 => ( ( groups1351286907653491341at_rat
% 0.33/0.64 @ ^ [I3: nat] : ( plus_plus_rat @ ( G @ I3 ) @ ( H3 @ I3 ) )
% 0.33/0.64 @ I4 )
% 0.33/0.64 = ( plus_plus_rat @ ( groups1351286907653491341at_rat @ G @ I4 ) @ ( groups1351286907653491341at_rat @ H3 @ I4 ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % sum.distrib_triv'
% 0.33/0.64 thf(fact_6299_sum_Odistrib__triv_H,axiom,
% 0.33/0.64 ! [I4: set_int,G: int > rat,H3: int > rat] :
% 0.33/0.64 ( ( finite_finite_int @ I4 )
% 0.33/0.64 => ( ( groups2350640619554545897nt_rat
% 0.33/0.64 @ ^ [I3: int] : ( plus_plus_rat @ ( G @ I3 ) @ ( H3 @ I3 ) )
% 0.33/0.64 @ I4 )
% 0.33/0.64 = ( plus_plus_rat @ ( groups2350640619554545897nt_rat @ G @ I4 ) @ ( groups2350640619554545897nt_rat @ H3 @ I4 ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % sum.distrib_triv'
% 0.33/0.64 thf(fact_6300_sum_Odistrib__triv_H,axiom,
% 0.33/0.64 ! [I4: set_Code_integer,G: code_integer > rat,H3: code_integer > rat] :
% 0.33/0.64 ( ( finite6017078050557962740nteger @ I4 )
% 0.33/0.64 => ( ( groups8878813951405302554er_rat
% 0.33/0.64 @ ^ [I3: code_integer] : ( plus_plus_rat @ ( G @ I3 ) @ ( H3 @ I3 ) )
% 0.33/0.64 @ I4 )
% 0.33/0.64 = ( plus_plus_rat @ ( groups8878813951405302554er_rat @ G @ I4 ) @ ( groups8878813951405302554er_rat @ H3 @ I4 ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % sum.distrib_triv'
% 0.33/0.64 thf(fact_6301_sum_Odistrib__triv_H,axiom,
% 0.33/0.64 ! [I4: set_nat,G: nat > nat,H3: nat > nat] :
% 0.33/0.64 ( ( finite_finite_nat @ I4 )
% 0.33/0.64 => ( ( groups1986416967739987077at_nat
% 0.33/0.64 @ ^ [I3: nat] : ( plus_plus_nat @ ( G @ I3 ) @ ( H3 @ I3 ) )
% 0.33/0.64 @ I4 )
% 0.33/0.64 = ( plus_plus_nat @ ( groups1986416967739987077at_nat @ G @ I4 ) @ ( groups1986416967739987077at_nat @ H3 @ I4 ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % sum.distrib_triv'
% 0.33/0.64 thf(fact_6302_sum_Odistrib__triv_H,axiom,
% 0.33/0.64 ! [I4: set_int,G: int > nat,H3: int > nat] :
% 0.33/0.64 ( ( finite_finite_int @ I4 )
% 0.33/0.64 => ( ( groups2985770679641041633nt_nat
% 0.33/0.64 @ ^ [I3: int] : ( plus_plus_nat @ ( G @ I3 ) @ ( H3 @ I3 ) )
% 0.33/0.64 @ I4 )
% 0.33/0.64 = ( plus_plus_nat @ ( groups2985770679641041633nt_nat @ G @ I4 ) @ ( groups2985770679641041633nt_nat @ H3 @ I4 ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % sum.distrib_triv'
% 0.33/0.64 thf(fact_6303_sum_Odistrib__triv_H,axiom,
% 0.33/0.64 ! [I4: set_Code_integer,G: code_integer > nat,H3: code_integer > nat] :
% 0.33/0.64 ( ( finite6017078050557962740nteger @ I4 )
% 0.33/0.64 => ( ( groups290571974637022482er_nat
% 0.33/0.64 @ ^ [I3: code_integer] : ( plus_plus_nat @ ( G @ I3 ) @ ( H3 @ I3 ) )
% 0.33/0.64 @ I4 )
% 0.33/0.64 = ( plus_plus_nat @ ( groups290571974637022482er_nat @ G @ I4 ) @ ( groups290571974637022482er_nat @ H3 @ I4 ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % sum.distrib_triv'
% 0.33/0.64 thf(fact_6304_sum_Odistrib__triv_H,axiom,
% 0.33/0.64 ! [I4: set_nat,G: nat > int,H3: nat > int] :
% 0.33/0.64 ( ( finite_finite_nat @ I4 )
% 0.33/0.64 => ( ( groups1983926497230936801at_int
% 0.33/0.64 @ ^ [I3: nat] : ( plus_plus_int @ ( G @ I3 ) @ ( H3 @ I3 ) )
% 0.33/0.64 @ I4 )
% 0.33/0.64 = ( plus_plus_int @ ( groups1983926497230936801at_int @ G @ I4 ) @ ( groups1983926497230936801at_int @ H3 @ I4 ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % sum.distrib_triv'
% 0.33/0.64 thf(fact_6305_sum_Odistrib__triv_H,axiom,
% 0.33/0.64 ! [I4: set_int,G: int > int,H3: int > int] :
% 0.33/0.64 ( ( finite_finite_int @ I4 )
% 0.33/0.64 => ( ( groups2983280209131991357nt_int
% 0.33/0.64 @ ^ [I3: int] : ( plus_plus_int @ ( G @ I3 ) @ ( H3 @ I3 ) )
% 0.33/0.64 @ I4 )
% 0.33/0.64 = ( plus_plus_int @ ( groups2983280209131991357nt_int @ G @ I4 ) @ ( groups2983280209131991357nt_int @ H3 @ I4 ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % sum.distrib_triv'
% 0.33/0.64 thf(fact_6306_sum_Odistrib__triv_H,axiom,
% 0.33/0.64 ! [I4: set_Code_integer,G: code_integer > int,H3: code_integer > int] :
% 0.33/0.64 ( ( finite6017078050557962740nteger @ I4 )
% 0.33/0.64 => ( ( groups288081504127972206er_int
% 0.33/0.64 @ ^ [I3: code_integer] : ( plus_plus_int @ ( G @ I3 ) @ ( H3 @ I3 ) )
% 0.33/0.64 @ I4 )
% 0.33/0.64 = ( plus_plus_int @ ( groups288081504127972206er_int @ G @ I4 ) @ ( groups288081504127972206er_int @ H3 @ I4 ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % sum.distrib_triv'
% 0.33/0.64 thf(fact_6307_sum_Odistrib__triv_H,axiom,
% 0.33/0.64 ! [I4: set_Pr1261947904930325089at_nat,G: product_prod_nat_nat > rat,H3: product_prod_nat_nat > rat] :
% 0.33/0.64 ( ( finite6177210948735845034at_nat @ I4 )
% 0.33/0.64 => ( ( groups3328076802468863542at_rat
% 0.33/0.64 @ ^ [I3: product_prod_nat_nat] : ( plus_plus_rat @ ( G @ I3 ) @ ( H3 @ I3 ) )
% 0.33/0.64 @ I4 )
% 0.33/0.64 = ( plus_plus_rat @ ( groups3328076802468863542at_rat @ G @ I4 ) @ ( groups3328076802468863542at_rat @ H3 @ I4 ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % sum.distrib_triv'
% 0.33/0.64 thf(fact_6308_le__prod__encode__1,axiom,
% 0.33/0.64 ! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( nat_prod_encode @ ( product_Pair_nat_nat @ A @ B ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % le_prod_encode_1
% 0.33/0.64 thf(fact_6309_le__prod__encode__2,axiom,
% 0.33/0.64 ! [B: nat,A: nat] : ( ord_less_eq_nat @ B @ ( nat_prod_encode @ ( product_Pair_nat_nat @ A @ B ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % le_prod_encode_2
% 0.33/0.64 thf(fact_6310_sum_Odistrib_H,axiom,
% 0.33/0.64 ! [I4: set_o,G: $o > code_integer,H3: $o > code_integer] :
% 0.33/0.64 ( ( finite_finite_o
% 0.33/0.64 @ ( collect_o
% 0.33/0.64 @ ^ [X3: $o] :
% 0.33/0.64 ( ( member_o @ X3 @ I4 )
% 0.33/0.64 & ( ( G @ X3 )
% 0.33/0.64 != zero_z3403309356797280102nteger ) ) ) )
% 0.33/0.64 => ( ( finite_finite_o
% 0.33/0.64 @ ( collect_o
% 0.33/0.64 @ ^ [X3: $o] :
% 0.33/0.64 ( ( member_o @ X3 @ I4 )
% 0.33/0.64 & ( ( H3 @ X3 )
% 0.33/0.64 != zero_z3403309356797280102nteger ) ) ) )
% 0.33/0.64 => ( ( groups1402912129352969042nteger
% 0.33/0.64 @ ^ [I3: $o] : ( plus_p5714425477246183910nteger @ ( G @ I3 ) @ ( H3 @ I3 ) )
% 0.33/0.64 @ I4 )
% 0.33/0.64 = ( plus_p5714425477246183910nteger @ ( groups1402912129352969042nteger @ G @ I4 ) @ ( groups1402912129352969042nteger @ H3 @ I4 ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % sum.distrib'
% 0.33/0.64 thf(fact_6311_sum_Odistrib_H,axiom,
% 0.33/0.64 ! [I4: set_nat,G: nat > code_integer,H3: nat > code_integer] :
% 0.33/0.64 ( ( finite_finite_nat
% 0.33/0.64 @ ( collect_nat
% 0.33/0.64 @ ^ [X3: nat] :
% 0.33/0.64 ( ( member_nat @ X3 @ I4 )
% 0.33/0.64 & ( ( G @ X3 )
% 0.33/0.64 != zero_z3403309356797280102nteger ) ) ) )
% 0.33/0.64 => ( ( finite_finite_nat
% 0.33/0.64 @ ( collect_nat
% 0.33/0.64 @ ^ [X3: nat] :
% 0.33/0.64 ( ( member_nat @ X3 @ I4 )
% 0.33/0.64 & ( ( H3 @ X3 )
% 0.33/0.64 != zero_z3403309356797280102nteger ) ) ) )
% 0.33/0.64 => ( ( groups555127423416065298nteger
% 0.33/0.64 @ ^ [I3: nat] : ( plus_p5714425477246183910nteger @ ( G @ I3 ) @ ( H3 @ I3 ) )
% 0.33/0.64 @ I4 )
% 0.33/0.64 = ( plus_p5714425477246183910nteger @ ( groups555127423416065298nteger @ G @ I4 ) @ ( groups555127423416065298nteger @ H3 @ I4 ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % sum.distrib'
% 0.33/0.64 thf(fact_6312_sum_Odistrib_H,axiom,
% 0.33/0.64 ! [I4: set_int,G: int > code_integer,H3: int > code_integer] :
% 0.33/0.64 ( ( finite_finite_int
% 0.33/0.64 @ ( collect_int
% 0.33/0.64 @ ^ [X3: int] :
% 0.33/0.64 ( ( member_int @ X3 @ I4 )
% 0.33/0.64 & ( ( G @ X3 )
% 0.33/0.64 != zero_z3403309356797280102nteger ) ) ) )
% 0.33/0.64 => ( ( finite_finite_int
% 0.33/0.64 @ ( collect_int
% 0.33/0.64 @ ^ [X3: int] :
% 0.33/0.64 ( ( member_int @ X3 @ I4 )
% 0.33/0.64 & ( ( H3 @ X3 )
% 0.33/0.64 != zero_z3403309356797280102nteger ) ) ) )
% 0.33/0.64 => ( ( groups926780983652909934nteger
% 0.33/0.64 @ ^ [I3: int] : ( plus_p5714425477246183910nteger @ ( G @ I3 ) @ ( H3 @ I3 ) )
% 0.33/0.64 @ I4 )
% 0.33/0.64 = ( plus_p5714425477246183910nteger @ ( groups926780983652909934nteger @ G @ I4 ) @ ( groups926780983652909934nteger @ H3 @ I4 ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % sum.distrib'
% 0.33/0.64 thf(fact_6313_sum_Odistrib_H,axiom,
% 0.33/0.64 ! [I4: set_Code_integer,G: code_integer > code_integer,H3: code_integer > code_integer] :
% 0.33/0.64 ( ( finite6017078050557962740nteger
% 0.33/0.64 @ ( collect_Code_integer
% 0.33/0.64 @ ^ [X3: code_integer] :
% 0.33/0.64 ( ( member_Code_integer @ X3 @ I4 )
% 0.33/0.64 & ( ( G @ X3 )
% 0.33/0.64 != zero_z3403309356797280102nteger ) ) ) )
% 0.33/0.64 => ( ( finite6017078050557962740nteger
% 0.33/0.64 @ ( collect_Code_integer
% 0.33/0.64 @ ^ [X3: code_integer] :
% 0.33/0.64 ( ( member_Code_integer @ X3 @ I4 )
% 0.33/0.64 & ( ( H3 @ X3 )
% 0.33/0.64 != zero_z3403309356797280102nteger ) ) ) )
% 0.33/0.64 => ( ( groups910942671188738463nteger
% 0.33/0.64 @ ^ [I3: code_integer] : ( plus_p5714425477246183910nteger @ ( G @ I3 ) @ ( H3 @ I3 ) )
% 0.33/0.64 @ I4 )
% 0.33/0.64 = ( plus_p5714425477246183910nteger @ ( groups910942671188738463nteger @ G @ I4 ) @ ( groups910942671188738463nteger @ H3 @ I4 ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % sum.distrib'
% 0.33/0.64 thf(fact_6314_sum_Odistrib_H,axiom,
% 0.33/0.64 ! [I4: set_o,G: $o > rat,H3: $o > rat] :
% 0.33/0.64 ( ( finite_finite_o
% 0.33/0.64 @ ( collect_o
% 0.33/0.64 @ ^ [X3: $o] :
% 0.33/0.64 ( ( member_o @ X3 @ I4 )
% 0.33/0.64 & ( ( G @ X3 )
% 0.33/0.64 != zero_zero_rat ) ) ) )
% 0.33/0.64 => ( ( finite_finite_o
% 0.33/0.64 @ ( collect_o
% 0.33/0.64 @ ^ [X3: $o] :
% 0.33/0.64 ( ( member_o @ X3 @ I4 )
% 0.33/0.64 & ( ( H3 @ X3 )
% 0.33/0.64 != zero_zero_rat ) ) ) )
% 0.33/0.64 => ( ( groups3921277224699582669_o_rat
% 0.33/0.64 @ ^ [I3: $o] : ( plus_plus_rat @ ( G @ I3 ) @ ( H3 @ I3 ) )
% 0.33/0.64 @ I4 )
% 0.33/0.64 = ( plus_plus_rat @ ( groups3921277224699582669_o_rat @ G @ I4 ) @ ( groups3921277224699582669_o_rat @ H3 @ I4 ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % sum.distrib'
% 0.33/0.64 thf(fact_6315_sum_Odistrib_H,axiom,
% 0.33/0.64 ! [I4: set_nat,G: nat > rat,H3: nat > rat] :
% 0.33/0.64 ( ( finite_finite_nat
% 0.33/0.64 @ ( collect_nat
% 0.33/0.64 @ ^ [X3: nat] :
% 0.33/0.64 ( ( member_nat @ X3 @ I4 )
% 0.33/0.64 & ( ( G @ X3 )
% 0.33/0.64 != zero_zero_rat ) ) ) )
% 0.33/0.64 => ( ( finite_finite_nat
% 0.33/0.64 @ ( collect_nat
% 0.33/0.64 @ ^ [X3: nat] :
% 0.33/0.64 ( ( member_nat @ X3 @ I4 )
% 0.33/0.64 & ( ( H3 @ X3 )
% 0.33/0.64 != zero_zero_rat ) ) ) )
% 0.33/0.64 => ( ( groups1351286907653491341at_rat
% 0.33/0.64 @ ^ [I3: nat] : ( plus_plus_rat @ ( G @ I3 ) @ ( H3 @ I3 ) )
% 0.33/0.64 @ I4 )
% 0.33/0.64 = ( plus_plus_rat @ ( groups1351286907653491341at_rat @ G @ I4 ) @ ( groups1351286907653491341at_rat @ H3 @ I4 ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % sum.distrib'
% 0.33/0.64 thf(fact_6316_sum_Odistrib_H,axiom,
% 0.33/0.64 ! [I4: set_int,G: int > rat,H3: int > rat] :
% 0.33/0.64 ( ( finite_finite_int
% 0.33/0.64 @ ( collect_int
% 0.33/0.64 @ ^ [X3: int] :
% 0.33/0.64 ( ( member_int @ X3 @ I4 )
% 0.33/0.64 & ( ( G @ X3 )
% 0.33/0.64 != zero_zero_rat ) ) ) )
% 0.33/0.64 => ( ( finite_finite_int
% 0.33/0.64 @ ( collect_int
% 0.33/0.64 @ ^ [X3: int] :
% 0.33/0.64 ( ( member_int @ X3 @ I4 )
% 0.33/0.64 & ( ( H3 @ X3 )
% 0.33/0.64 != zero_zero_rat ) ) ) )
% 0.33/0.64 => ( ( groups2350640619554545897nt_rat
% 0.33/0.64 @ ^ [I3: int] : ( plus_plus_rat @ ( G @ I3 ) @ ( H3 @ I3 ) )
% 0.33/0.64 @ I4 )
% 0.33/0.64 = ( plus_plus_rat @ ( groups2350640619554545897nt_rat @ G @ I4 ) @ ( groups2350640619554545897nt_rat @ H3 @ I4 ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % sum.distrib'
% 0.33/0.64 thf(fact_6317_sum_Odistrib_H,axiom,
% 0.33/0.64 ! [I4: set_Code_integer,G: code_integer > rat,H3: code_integer > rat] :
% 0.33/0.64 ( ( finite6017078050557962740nteger
% 0.33/0.64 @ ( collect_Code_integer
% 0.33/0.64 @ ^ [X3: code_integer] :
% 0.33/0.64 ( ( member_Code_integer @ X3 @ I4 )
% 0.33/0.64 & ( ( G @ X3 )
% 0.33/0.64 != zero_zero_rat ) ) ) )
% 0.33/0.64 => ( ( finite6017078050557962740nteger
% 0.33/0.64 @ ( collect_Code_integer
% 0.33/0.64 @ ^ [X3: code_integer] :
% 0.33/0.64 ( ( member_Code_integer @ X3 @ I4 )
% 0.33/0.64 & ( ( H3 @ X3 )
% 0.33/0.64 != zero_zero_rat ) ) ) )
% 0.33/0.64 => ( ( groups8878813951405302554er_rat
% 0.33/0.64 @ ^ [I3: code_integer] : ( plus_plus_rat @ ( G @ I3 ) @ ( H3 @ I3 ) )
% 0.33/0.64 @ I4 )
% 0.33/0.64 = ( plus_plus_rat @ ( groups8878813951405302554er_rat @ G @ I4 ) @ ( groups8878813951405302554er_rat @ H3 @ I4 ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % sum.distrib'
% 0.33/0.64 thf(fact_6318_sum_Odistrib_H,axiom,
% 0.33/0.64 ! [I4: set_o,G: $o > nat,H3: $o > nat] :
% 0.33/0.64 ( ( finite_finite_o
% 0.33/0.64 @ ( collect_o
% 0.33/0.64 @ ^ [X3: $o] :
% 0.33/0.64 ( ( member_o @ X3 @ I4 )
% 0.33/0.64 & ( ( G @ X3 )
% 0.33/0.64 != zero_zero_nat ) ) ) )
% 0.33/0.64 => ( ( finite_finite_o
% 0.33/0.64 @ ( collect_o
% 0.33/0.64 @ ^ [X3: $o] :
% 0.33/0.64 ( ( member_o @ X3 @ I4 )
% 0.33/0.64 & ( ( H3 @ X3 )
% 0.33/0.64 != zero_zero_nat ) ) ) )
% 0.33/0.64 => ( ( groups4556407284786078405_o_nat
% 0.33/0.64 @ ^ [I3: $o] : ( plus_plus_nat @ ( G @ I3 ) @ ( H3 @ I3 ) )
% 0.33/0.64 @ I4 )
% 0.33/0.64 = ( plus_plus_nat @ ( groups4556407284786078405_o_nat @ G @ I4 ) @ ( groups4556407284786078405_o_nat @ H3 @ I4 ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % sum.distrib'
% 0.33/0.64 thf(fact_6319_sum_Odistrib_H,axiom,
% 0.33/0.64 ! [I4: set_nat,G: nat > nat,H3: nat > nat] :
% 0.33/0.64 ( ( finite_finite_nat
% 0.33/0.64 @ ( collect_nat
% 0.33/0.64 @ ^ [X3: nat] :
% 0.33/0.64 ( ( member_nat @ X3 @ I4 )
% 0.33/0.64 & ( ( G @ X3 )
% 0.33/0.64 != zero_zero_nat ) ) ) )
% 0.33/0.64 => ( ( finite_finite_nat
% 0.33/0.64 @ ( collect_nat
% 0.33/0.64 @ ^ [X3: nat] :
% 0.33/0.64 ( ( member_nat @ X3 @ I4 )
% 0.33/0.64 & ( ( H3 @ X3 )
% 0.33/0.64 != zero_zero_nat ) ) ) )
% 0.33/0.64 => ( ( groups1986416967739987077at_nat
% 0.33/0.64 @ ^ [I3: nat] : ( plus_plus_nat @ ( G @ I3 ) @ ( H3 @ I3 ) )
% 0.33/0.64 @ I4 )
% 0.33/0.64 = ( plus_plus_nat @ ( groups1986416967739987077at_nat @ G @ I4 ) @ ( groups1986416967739987077at_nat @ H3 @ I4 ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % sum.distrib'
% 0.33/0.64 thf(fact_6320_prod__encode__def,axiom,
% 0.33/0.64 ( nat_prod_encode
% 0.33/0.64 = ( produc6842872674320459806at_nat
% 0.33/0.64 @ ^ [M: nat,N4: nat] : ( plus_plus_nat @ ( nat_triangle @ ( plus_plus_nat @ M @ N4 ) ) @ M ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod_encode_def
% 0.33/0.64 thf(fact_6321_max__ext_Ocases,axiom,
% 0.33/0.64 ! [A1: set_se7855581050983116737at_nat,A23: set_se7855581050983116737at_nat,R4: set_Pr4329608150637261639at_nat] :
% 0.33/0.64 ( ( member4300370950623927696at_nat @ ( produc7462898802507495127at_nat @ A1 @ A23 ) @ ( max_ex4535816423174879388at_nat @ R4 ) )
% 0.33/0.64 => ~ ( ( finite9047747110432174090at_nat @ A1 )
% 0.33/0.64 => ( ( finite9047747110432174090at_nat @ A23 )
% 0.33/0.64 => ( ( A23 != bot_bo3083307316010499117at_nat )
% 0.33/0.64 => ~ ! [X8: set_Pr1261947904930325089at_nat] :
% 0.33/0.64 ( ( member2643936169264416010at_nat @ X8 @ A1 )
% 0.33/0.64 => ? [Xa3: set_Pr1261947904930325089at_nat] :
% 0.33/0.64 ( ( member2643936169264416010at_nat @ Xa3 @ A23 )
% 0.33/0.64 & ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X8 @ Xa3 ) @ R4 ) ) ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % max_ext.cases
% 0.33/0.64 thf(fact_6322_max__ext_Ocases,axiom,
% 0.33/0.64 ! [A1: set_Code_integer,A23: set_Code_integer,R4: set_Pr4811707699266497531nteger] :
% 0.33/0.64 ( ( member4307123515891402160nteger @ ( produc7443773368509356479nteger @ A1 @ A23 ) @ ( max_ext_Code_integer @ R4 ) )
% 0.33/0.64 => ~ ( ( finite6017078050557962740nteger @ A1 )
% 0.33/0.64 => ( ( finite6017078050557962740nteger @ A23 )
% 0.33/0.64 => ( ( A23 != bot_bo3990330152332043303nteger )
% 0.33/0.64 => ~ ! [X8: code_integer] :
% 0.33/0.64 ( ( member_Code_integer @ X8 @ A1 )
% 0.33/0.64 => ? [Xa3: code_integer] :
% 0.33/0.64 ( ( member_Code_integer @ Xa3 @ A23 )
% 0.33/0.64 & ( member157494554546826820nteger @ ( produc1086072967326762835nteger @ X8 @ Xa3 ) @ R4 ) ) ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % max_ext.cases
% 0.33/0.64 thf(fact_6323_max__ext_Ocases,axiom,
% 0.33/0.64 ! [A1: set_Pr4329608150637261639at_nat,A23: set_Pr4329608150637261639at_nat,R4: set_Pr5564308138774400199at_nat] :
% 0.33/0.64 ( ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ A1 @ A23 ) @ ( max_ex8833738776070432290at_nat @ R4 ) )
% 0.33/0.64 => ~ ( ( finite4343798906461161616at_nat @ A1 )
% 0.33/0.64 => ( ( finite4343798906461161616at_nat @ A23 )
% 0.33/0.64 => ( ( A23 != bot_bo228742789529271731at_nat )
% 0.33/0.64 => ~ ! [X8: produc3843707927480180839at_nat] :
% 0.33/0.64 ( ( member8757157785044589968at_nat @ X8 @ A1 )
% 0.33/0.64 => ? [Xa3: produc3843707927480180839at_nat] :
% 0.33/0.64 ( ( member8757157785044589968at_nat @ Xa3 @ A23 )
% 0.33/0.64 & ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ X8 @ Xa3 ) @ R4 ) ) ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % max_ext.cases
% 0.33/0.64 thf(fact_6324_max__ext_Ocases,axiom,
% 0.33/0.64 ! [A1: set_Pr1261947904930325089at_nat,A23: set_Pr1261947904930325089at_nat,R4: set_Pr8693737435421807431at_nat] :
% 0.33/0.64 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A1 @ A23 ) @ ( max_ex8135407076693332796at_nat @ R4 ) )
% 0.33/0.64 => ~ ( ( finite6177210948735845034at_nat @ A1 )
% 0.33/0.64 => ( ( finite6177210948735845034at_nat @ A23 )
% 0.33/0.64 => ( ( A23 != bot_bo2099793752762293965at_nat )
% 0.33/0.64 => ~ ! [X8: product_prod_nat_nat] :
% 0.33/0.64 ( ( member8440522571783428010at_nat @ X8 @ A1 )
% 0.33/0.64 => ? [Xa3: product_prod_nat_nat] :
% 0.33/0.64 ( ( member8440522571783428010at_nat @ Xa3 @ A23 )
% 0.33/0.64 & ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X8 @ Xa3 ) @ R4 ) ) ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % max_ext.cases
% 0.33/0.64 thf(fact_6325_max__ext_Ocases,axiom,
% 0.33/0.64 ! [A1: set_o,A23: set_o,R4: set_Product_prod_o_o] :
% 0.33/0.64 ( ( member9116954335612470352_set_o @ ( produc5838405689764958487_set_o @ A1 @ A23 ) @ ( max_ext_o @ R4 ) )
% 0.33/0.64 => ~ ( ( finite_finite_o @ A1 )
% 0.33/0.64 => ( ( finite_finite_o @ A23 )
% 0.33/0.64 => ( ( A23 != bot_bot_set_o )
% 0.33/0.64 => ~ ! [X8: $o] :
% 0.33/0.64 ( ( member_o @ X8 @ A1 )
% 0.33/0.64 => ? [Xa3: $o] :
% 0.33/0.64 ( ( member_o @ Xa3 @ A23 )
% 0.33/0.64 & ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ X8 @ Xa3 ) @ R4 ) ) ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % max_ext.cases
% 0.33/0.64 thf(fact_6326_max__ext_Ocases,axiom,
% 0.33/0.64 ! [A1: set_nat,A23: set_nat,R4: set_Pr1261947904930325089at_nat] :
% 0.33/0.64 ( ( member8277197624267554838et_nat @ ( produc4532415448927165861et_nat @ A1 @ A23 ) @ ( max_ext_nat @ R4 ) )
% 0.33/0.64 => ~ ( ( finite_finite_nat @ A1 )
% 0.33/0.64 => ( ( finite_finite_nat @ A23 )
% 0.33/0.64 => ( ( A23 != bot_bot_set_nat )
% 0.33/0.64 => ~ ! [X8: nat] :
% 0.33/0.64 ( ( member_nat @ X8 @ A1 )
% 0.33/0.64 => ? [Xa3: nat] :
% 0.33/0.64 ( ( member_nat @ Xa3 @ A23 )
% 0.33/0.64 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X8 @ Xa3 ) @ R4 ) ) ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % max_ext.cases
% 0.33/0.64 thf(fact_6327_max__ext_Ocases,axiom,
% 0.33/0.64 ! [A1: set_int,A23: set_int,R4: set_Pr958786334691620121nt_int] :
% 0.33/0.64 ( ( member2572552093476627150et_int @ ( produc6363374080413544029et_int @ A1 @ A23 ) @ ( max_ext_int @ R4 ) )
% 0.33/0.64 => ~ ( ( finite_finite_int @ A1 )
% 0.33/0.64 => ( ( finite_finite_int @ A23 )
% 0.33/0.64 => ( ( A23 != bot_bot_set_int )
% 0.33/0.64 => ~ ! [X8: int] :
% 0.33/0.64 ( ( member_int @ X8 @ A1 )
% 0.33/0.64 => ? [Xa3: int] :
% 0.33/0.64 ( ( member_int @ Xa3 @ A23 )
% 0.33/0.64 & ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X8 @ Xa3 ) @ R4 ) ) ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % max_ext.cases
% 0.33/0.64 thf(fact_6328_max__ext_Osimps,axiom,
% 0.33/0.64 ! [A1: set_se7855581050983116737at_nat,A23: set_se7855581050983116737at_nat,R4: set_Pr4329608150637261639at_nat] :
% 0.33/0.64 ( ( member4300370950623927696at_nat @ ( produc7462898802507495127at_nat @ A1 @ A23 ) @ ( max_ex4535816423174879388at_nat @ R4 ) )
% 0.33/0.64 = ( ( finite9047747110432174090at_nat @ A1 )
% 0.33/0.64 & ( finite9047747110432174090at_nat @ A23 )
% 0.33/0.64 & ( A23 != bot_bo3083307316010499117at_nat )
% 0.33/0.64 & ! [X3: set_Pr1261947904930325089at_nat] :
% 0.33/0.64 ( ( member2643936169264416010at_nat @ X3 @ A1 )
% 0.33/0.64 => ? [Y3: set_Pr1261947904930325089at_nat] :
% 0.33/0.64 ( ( member2643936169264416010at_nat @ Y3 @ A23 )
% 0.33/0.64 & ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ Y3 ) @ R4 ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % max_ext.simps
% 0.33/0.64 thf(fact_6329_max__ext_Osimps,axiom,
% 0.33/0.64 ! [A1: set_Code_integer,A23: set_Code_integer,R4: set_Pr4811707699266497531nteger] :
% 0.33/0.64 ( ( member4307123515891402160nteger @ ( produc7443773368509356479nteger @ A1 @ A23 ) @ ( max_ext_Code_integer @ R4 ) )
% 0.33/0.64 = ( ( finite6017078050557962740nteger @ A1 )
% 0.33/0.64 & ( finite6017078050557962740nteger @ A23 )
% 0.33/0.64 & ( A23 != bot_bo3990330152332043303nteger )
% 0.33/0.64 & ! [X3: code_integer] :
% 0.33/0.64 ( ( member_Code_integer @ X3 @ A1 )
% 0.33/0.64 => ? [Y3: code_integer] :
% 0.33/0.64 ( ( member_Code_integer @ Y3 @ A23 )
% 0.33/0.64 & ( member157494554546826820nteger @ ( produc1086072967326762835nteger @ X3 @ Y3 ) @ R4 ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % max_ext.simps
% 0.33/0.64 thf(fact_6330_max__ext_Osimps,axiom,
% 0.33/0.64 ! [A1: set_Pr4329608150637261639at_nat,A23: set_Pr4329608150637261639at_nat,R4: set_Pr5564308138774400199at_nat] :
% 0.33/0.64 ( ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ A1 @ A23 ) @ ( max_ex8833738776070432290at_nat @ R4 ) )
% 0.33/0.64 = ( ( finite4343798906461161616at_nat @ A1 )
% 0.33/0.64 & ( finite4343798906461161616at_nat @ A23 )
% 0.33/0.64 & ( A23 != bot_bo228742789529271731at_nat )
% 0.33/0.64 & ! [X3: produc3843707927480180839at_nat] :
% 0.33/0.64 ( ( member8757157785044589968at_nat @ X3 @ A1 )
% 0.33/0.64 => ? [Y3: produc3843707927480180839at_nat] :
% 0.33/0.64 ( ( member8757157785044589968at_nat @ Y3 @ A23 )
% 0.33/0.64 & ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ X3 @ Y3 ) @ R4 ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % max_ext.simps
% 0.33/0.64 thf(fact_6331_max__ext_Osimps,axiom,
% 0.33/0.64 ! [A1: set_Pr1261947904930325089at_nat,A23: set_Pr1261947904930325089at_nat,R4: set_Pr8693737435421807431at_nat] :
% 0.33/0.64 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A1 @ A23 ) @ ( max_ex8135407076693332796at_nat @ R4 ) )
% 0.33/0.64 = ( ( finite6177210948735845034at_nat @ A1 )
% 0.33/0.64 & ( finite6177210948735845034at_nat @ A23 )
% 0.33/0.64 & ( A23 != bot_bo2099793752762293965at_nat )
% 0.33/0.64 & ! [X3: product_prod_nat_nat] :
% 0.33/0.64 ( ( member8440522571783428010at_nat @ X3 @ A1 )
% 0.33/0.64 => ? [Y3: product_prod_nat_nat] :
% 0.33/0.64 ( ( member8440522571783428010at_nat @ Y3 @ A23 )
% 0.33/0.64 & ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X3 @ Y3 ) @ R4 ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % max_ext.simps
% 0.33/0.64 thf(fact_6332_max__ext_Osimps,axiom,
% 0.33/0.64 ! [A1: set_o,A23: set_o,R4: set_Product_prod_o_o] :
% 0.33/0.64 ( ( member9116954335612470352_set_o @ ( produc5838405689764958487_set_o @ A1 @ A23 ) @ ( max_ext_o @ R4 ) )
% 0.33/0.64 = ( ( finite_finite_o @ A1 )
% 0.33/0.64 & ( finite_finite_o @ A23 )
% 0.33/0.64 & ( A23 != bot_bot_set_o )
% 0.33/0.64 & ! [X3: $o] :
% 0.33/0.64 ( ( member_o @ X3 @ A1 )
% 0.33/0.64 => ? [Y3: $o] :
% 0.33/0.64 ( ( member_o @ Y3 @ A23 )
% 0.33/0.64 & ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ X3 @ Y3 ) @ R4 ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % max_ext.simps
% 0.33/0.64 thf(fact_6333_max__ext_Osimps,axiom,
% 0.33/0.64 ! [A1: set_nat,A23: set_nat,R4: set_Pr1261947904930325089at_nat] :
% 0.33/0.64 ( ( member8277197624267554838et_nat @ ( produc4532415448927165861et_nat @ A1 @ A23 ) @ ( max_ext_nat @ R4 ) )
% 0.33/0.64 = ( ( finite_finite_nat @ A1 )
% 0.33/0.64 & ( finite_finite_nat @ A23 )
% 0.33/0.64 & ( A23 != bot_bot_set_nat )
% 0.33/0.64 & ! [X3: nat] :
% 0.33/0.64 ( ( member_nat @ X3 @ A1 )
% 0.33/0.64 => ? [Y3: nat] :
% 0.33/0.64 ( ( member_nat @ Y3 @ A23 )
% 0.33/0.64 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y3 ) @ R4 ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % max_ext.simps
% 0.33/0.64 thf(fact_6334_max__ext_Osimps,axiom,
% 0.33/0.64 ! [A1: set_int,A23: set_int,R4: set_Pr958786334691620121nt_int] :
% 0.33/0.64 ( ( member2572552093476627150et_int @ ( produc6363374080413544029et_int @ A1 @ A23 ) @ ( max_ext_int @ R4 ) )
% 0.33/0.64 = ( ( finite_finite_int @ A1 )
% 0.33/0.64 & ( finite_finite_int @ A23 )
% 0.33/0.64 & ( A23 != bot_bot_set_int )
% 0.33/0.64 & ! [X3: int] :
% 0.33/0.64 ( ( member_int @ X3 @ A1 )
% 0.33/0.64 => ? [Y3: int] :
% 0.33/0.64 ( ( member_int @ Y3 @ A23 )
% 0.33/0.64 & ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X3 @ Y3 ) @ R4 ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % max_ext.simps
% 0.33/0.64 thf(fact_6335_max__extp__eq,axiom,
% 0.33/0.64 ( max_ex4864111882549613972at_nat
% 0.33/0.64 = ( ^ [R3: product_prod_nat_nat > product_prod_nat_nat > $o,X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ Y3 ) @ ( max_ex8135407076693332796at_nat @ ( collec7088162979684241874at_nat @ ( produc6590410687421337004_nat_o @ R3 ) ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % max_extp_eq
% 0.33/0.64 thf(fact_6336_max__extp__max__ext__eq,axiom,
% 0.33/0.64 ! [R4: set_Pr4329608150637261639at_nat] :
% 0.33/0.64 ( ( max_ex4845989503969680116at_nat
% 0.33/0.64 @ ^ [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ Y3 ) @ R4 ) )
% 0.33/0.64 = ( ^ [X3: set_se7855581050983116737at_nat,Y3: set_se7855581050983116737at_nat] : ( member4300370950623927696at_nat @ ( produc7462898802507495127at_nat @ X3 @ Y3 ) @ ( max_ex4535816423174879388at_nat @ R4 ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % max_extp_max_ext_eq
% 0.33/0.64 thf(fact_6337_max__extp__max__ext__eq,axiom,
% 0.33/0.64 ! [R4: set_Pr1261947904930325089at_nat] :
% 0.33/0.64 ( ( max_extp_nat
% 0.33/0.64 @ ^ [X3: nat,Y3: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y3 ) @ R4 ) )
% 0.33/0.64 = ( ^ [X3: set_nat,Y3: set_nat] : ( member8277197624267554838et_nat @ ( produc4532415448927165861et_nat @ X3 @ Y3 ) @ ( max_ext_nat @ R4 ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % max_extp_max_ext_eq
% 0.33/0.64 thf(fact_6338_max__extp__max__ext__eq,axiom,
% 0.33/0.64 ! [R4: set_Pr8693737435421807431at_nat] :
% 0.33/0.64 ( ( max_ex4864111882549613972at_nat
% 0.33/0.64 @ ^ [X3: product_prod_nat_nat,Y3: product_prod_nat_nat] : ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X3 @ Y3 ) @ R4 ) )
% 0.33/0.64 = ( ^ [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ Y3 ) @ ( max_ex8135407076693332796at_nat @ R4 ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % max_extp_max_ext_eq
% 0.33/0.64 thf(fact_6339_one__div__numeral,axiom,
% 0.33/0.64 ! [N2: num] :
% 0.33/0.64 ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ N2 ) )
% 0.33/0.64 = ( produc8508995932063986495nteger @ ( unique3479559517661332726nteger @ one @ N2 ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % one_div_numeral
% 0.33/0.64 thf(fact_6340_one__div__numeral,axiom,
% 0.33/0.64 ! [N2: num] :
% 0.33/0.64 ( ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ N2 ) )
% 0.33/0.64 = ( product_fst_int_int @ ( unique5052692396658037445od_int @ one @ N2 ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % one_div_numeral
% 0.33/0.64 thf(fact_6341_one__div__numeral,axiom,
% 0.33/0.64 ! [N2: num] :
% 0.33/0.64 ( ( divide_divide_nat @ one_one_nat @ ( numeral_numeral_nat @ N2 ) )
% 0.33/0.64 = ( product_fst_nat_nat @ ( unique5055182867167087721od_nat @ one @ N2 ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % one_div_numeral
% 0.33/0.64 thf(fact_6342_sqr_Osimps_I3_J,axiom,
% 0.33/0.64 ! [N2: num] :
% 0.33/0.64 ( ( sqr @ ( bit1 @ N2 ) )
% 0.33/0.64 = ( bit1 @ ( bit0 @ ( plus_plus_num @ ( sqr @ N2 ) @ N2 ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % sqr.simps(3)
% 0.33/0.64 thf(fact_6343_one__mod__numeral,axiom,
% 0.33/0.64 ! [N2: num] :
% 0.33/0.64 ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ N2 ) )
% 0.33/0.64 = ( produc6174133586879617921nteger @ ( unique3479559517661332726nteger @ one @ N2 ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % one_mod_numeral
% 0.33/0.64 thf(fact_6344_one__mod__numeral,axiom,
% 0.33/0.64 ! [N2: num] :
% 0.33/0.64 ( ( modulo_modulo_int @ one_one_int @ ( numeral_numeral_int @ N2 ) )
% 0.33/0.64 = ( product_snd_int_int @ ( unique5052692396658037445od_int @ one @ N2 ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % one_mod_numeral
% 0.33/0.64 thf(fact_6345_one__mod__numeral,axiom,
% 0.33/0.64 ! [N2: num] :
% 0.33/0.64 ( ( modulo_modulo_nat @ one_one_nat @ ( numeral_numeral_nat @ N2 ) )
% 0.33/0.64 = ( product_snd_nat_nat @ ( unique5055182867167087721od_nat @ one @ N2 ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % one_mod_numeral
% 0.33/0.64 thf(fact_6346_card__UNION,axiom,
% 0.33/0.64 ! [A2: set_set_Product_unit] :
% 0.33/0.64 ( ( finite1772178364199683094t_unit @ A2 )
% 0.33/0.64 => ( ! [X4: set_Product_unit] :
% 0.33/0.64 ( ( member5877623283571906838t_unit @ X4 @ A2 )
% 0.33/0.64 => ( finite4290736615968046902t_unit @ X4 ) )
% 0.33/0.64 => ( ( finite410649719033368117t_unit @ ( comple3349607820504768346t_unit @ A2 ) )
% 0.33/0.64 = ( nat2
% 0.33/0.64 @ ( groups9212676010950626495it_int
% 0.33/0.64 @ ^ [I5: set_set_Product_unit] : ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( plus_plus_nat @ ( finite22775419188893461t_unit @ I5 ) @ one_one_nat ) ) @ ( semiri1314217659103216013at_int @ ( finite410649719033368117t_unit @ ( comple7216939928495492468t_unit @ I5 ) ) ) )
% 0.33/0.64 @ ( collec4600646233855244344t_unit
% 0.33/0.64 @ ^ [I5: set_set_Product_unit] :
% 0.33/0.64 ( ( ord_le3674001228145610605t_unit @ I5 @ A2 )
% 0.33/0.64 & ( I5 != bot_bo6284674557190688313t_unit ) ) ) ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % card_UNION
% 0.33/0.64 thf(fact_6347_card__UNION,axiom,
% 0.33/0.64 ! [A2: set_set_list_nat] :
% 0.33/0.64 ( ( finite7047420756378620717st_nat @ A2 )
% 0.33/0.64 => ( ! [X4: set_list_nat] :
% 0.33/0.64 ( ( member_set_list_nat @ X4 @ A2 )
% 0.33/0.64 => ( finite8100373058378681591st_nat @ X4 ) )
% 0.33/0.64 => ( ( finite_card_list_nat @ ( comple8404747032580312297st_nat @ A2 ) )
% 0.33/0.64 = ( nat2
% 0.33/0.64 @ ( groups7004213669654646580at_int
% 0.33/0.64 @ ^ [I5: set_set_list_nat] : ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( plus_plus_nat @ ( finite2364142230527598318st_nat @ I5 ) @ one_one_nat ) ) @ ( semiri1314217659103216013at_int @ ( finite_card_list_nat @ ( comple184543376406953807st_nat @ I5 ) ) ) )
% 0.33/0.64 @ ( collec4691811733418234273st_nat
% 0.33/0.64 @ ^ [I5: set_set_list_nat] :
% 0.33/0.64 ( ( ord_le1068707526560357548st_nat @ I5 @ A2 )
% 0.33/0.64 & ( I5 != bot_bo3886227569956363488st_nat ) ) ) ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % card_UNION
% 0.33/0.64 thf(fact_6348_card__UNION,axiom,
% 0.33/0.64 ! [A2: set_set_int] :
% 0.33/0.64 ( ( finite6197958912794628473et_int @ A2 )
% 0.33/0.64 => ( ! [X4: set_int] :
% 0.33/0.64 ( ( member_set_int @ X4 @ A2 )
% 0.33/0.64 => ( finite_finite_int @ X4 ) )
% 0.33/0.64 => ( ( finite_card_int @ ( comple3221217463730067765et_int @ A2 ) )
% 0.33/0.64 = ( nat2
% 0.33/0.64 @ ( groups1080061135233207040nt_int
% 0.33/0.64 @ ^ [I5: set_set_int] : ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( plus_plus_nat @ ( finite_card_set_int @ I5 ) @ one_one_nat ) ) @ ( semiri1314217659103216013at_int @ ( finite_card_int @ ( comple3628384868704368283et_int @ I5 ) ) ) )
% 0.33/0.64 @ ( collect_set_set_int
% 0.33/0.64 @ ^ [I5: set_set_int] :
% 0.33/0.64 ( ( ord_le4403425263959731960et_int @ I5 @ A2 )
% 0.33/0.64 & ( I5 != bot_bot_set_set_int ) ) ) ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % card_UNION
% 0.33/0.64 thf(fact_6349_card__UNION,axiom,
% 0.33/0.64 ! [A2: set_set_Code_integer] :
% 0.33/0.64 ( ( finite6931041176100689706nteger @ A2 )
% 0.33/0.64 => ( ! [X4: set_Code_integer] :
% 0.33/0.64 ( ( member1834298987299537450nteger @ X4 @ A2 )
% 0.33/0.64 => ( finite6017078050557962740nteger @ X4 ) )
% 0.33/0.64 => ( ( finite4902975817058060853nteger @ ( comple739944243200306918nteger @ A2 ) )
% 0.33/0.64 = ( nat2
% 0.33/0.64 @ ( groups2416162284031854641er_int
% 0.33/0.64 @ ^ [I5: set_set_Code_integer] : ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( plus_plus_nat @ ( finite1340570857867686763nteger @ I5 ) @ one_one_nat ) ) @ ( semiri1314217659103216013at_int @ ( finite4902975817058060853nteger @ ( comple1256288197631046732nteger @ I5 ) ) ) )
% 0.33/0.64 @ ( collec9208119312383884190nteger
% 0.33/0.64 @ ^ [I5: set_set_Code_integer] :
% 0.33/0.64 ( ( ord_le1914454125413604393nteger @ I5 @ A2 )
% 0.33/0.64 & ( I5 != bot_bo9204850693367297629nteger ) ) ) ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % card_UNION
% 0.33/0.64 thf(fact_6350_card__UNION,axiom,
% 0.33/0.64 ! [A2: set_se7855581050983116737at_nat] :
% 0.33/0.64 ( ( finite9047747110432174090at_nat @ A2 )
% 0.33/0.64 => ( ! [X4: set_Pr1261947904930325089at_nat] :
% 0.33/0.64 ( ( member2643936169264416010at_nat @ X4 @ A2 )
% 0.33/0.64 => ( finite6177210948735845034at_nat @ X4 ) )
% 0.33/0.64 => ( ( finite711546835091564841at_nat @ ( comple5685304695842803022at_nat @ A2 ) )
% 0.33/0.64 = ( nat2
% 0.33/0.64 @ ( groups1759609815103008563at_int
% 0.33/0.64 @ ^ [I5: set_se7855581050983116737at_nat] : ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( plus_plus_nat @ ( finite4356350796350151305at_nat @ I5 ) @ one_one_nat ) ) @ ( semiri1314217659103216013at_int @ ( finite711546835091564841at_nat @ ( comple1930127330929219688at_nat @ I5 ) ) ) )
% 0.33/0.64 @ ( collec6698286964019821996at_nat
% 0.33/0.64 @ ^ [I5: set_se7855581050983116737at_nat] :
% 0.33/0.64 ( ( ord_le2077887516847798113at_nat @ I5 @ A2 )
% 0.33/0.64 & ( I5 != bot_bo3083307316010499117at_nat ) ) ) ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % card_UNION
% 0.33/0.64 thf(fact_6351_card__UNION,axiom,
% 0.33/0.64 ! [A2: set_set_nat] :
% 0.33/0.64 ( ( finite1152437895449049373et_nat @ A2 )
% 0.33/0.64 => ( ! [X4: set_nat] :
% 0.33/0.64 ( ( member_set_nat @ X4 @ A2 )
% 0.33/0.64 => ( finite_finite_nat @ X4 ) )
% 0.33/0.64 => ( ( finite_card_nat @ ( comple7399068483239264473et_nat @ A2 ) )
% 0.33/0.64 = ( nat2
% 0.33/0.64 @ ( groups7084729577923612836at_int
% 0.33/0.64 @ ^ [I5: set_set_nat] : ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( plus_plus_nat @ ( finite_card_set_nat @ I5 ) @ one_one_nat ) ) @ ( semiri1314217659103216013at_int @ ( finite_card_nat @ ( comple7806235888213564991et_nat @ I5 ) ) ) )
% 0.33/0.64 @ ( collect_set_set_nat
% 0.33/0.64 @ ^ [I5: set_set_nat] :
% 0.33/0.64 ( ( ord_le6893508408891458716et_nat @ I5 @ A2 )
% 0.33/0.64 & ( I5 != bot_bot_set_set_nat ) ) ) ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % card_UNION
% 0.33/0.64 thf(fact_6352_Sup__atMost,axiom,
% 0.33/0.64 ! [Y: set_nat] :
% 0.33/0.64 ( ( comple7399068483239264473et_nat @ ( set_or4236626031148496127et_nat @ Y ) )
% 0.33/0.64 = Y ) ).
% 0.33/0.64
% 0.33/0.64 % Sup_atMost
% 0.33/0.64 thf(fact_6353_Sup__atMost,axiom,
% 0.33/0.64 ! [Y: product_unit] :
% 0.33/0.64 ( ( comple4687483117567863418t_unit @ ( set_or8621721900777396692t_unit @ Y ) )
% 0.33/0.64 = Y ) ).
% 0.33/0.64
% 0.33/0.64 % Sup_atMost
% 0.33/0.64 thf(fact_6354_fst__apsnd,axiom,
% 0.33/0.64 ! [F: code_integer > code_integer,X: produc8923325533196201883nteger] :
% 0.33/0.64 ( ( produc8508995932063986495nteger @ ( produc6499014454317279255nteger @ F @ X ) )
% 0.33/0.64 = ( produc8508995932063986495nteger @ X ) ) ).
% 0.33/0.64
% 0.33/0.64 % fst_apsnd
% 0.33/0.64 thf(fact_6355_fst__apsnd,axiom,
% 0.33/0.64 ! [F: int > int,X: product_prod_int_int] :
% 0.33/0.64 ( ( product_fst_int_int @ ( produc4463282112584876420nt_int @ F @ X ) )
% 0.33/0.64 = ( product_fst_int_int @ X ) ) ).
% 0.33/0.64
% 0.33/0.64 % fst_apsnd
% 0.33/0.64 thf(fact_6356_fst__comp__apsnd,axiom,
% 0.33/0.64 ! [F: code_integer > code_integer] :
% 0.33/0.64 ( ( comp_P3428181540658402820nteger @ produc8508995932063986495nteger @ ( produc6499014454317279255nteger @ F ) )
% 0.33/0.64 = produc8508995932063986495nteger ) ).
% 0.33/0.64
% 0.33/0.64 % fst_comp_apsnd
% 0.33/0.64 thf(fact_6357_fst__comp__apsnd,axiom,
% 0.33/0.64 ! [F: int > int] :
% 0.33/0.64 ( ( comp_P5356232565778667509nt_int @ product_fst_int_int @ ( produc4463282112584876420nt_int @ F ) )
% 0.33/0.64 = product_fst_int_int ) ).
% 0.33/0.64
% 0.33/0.64 % fst_comp_apsnd
% 0.33/0.64 thf(fact_6358_apsnd__eq__conv,axiom,
% 0.33/0.64 ! [F: code_integer > code_integer,X: produc8923325533196201883nteger,G: code_integer > code_integer] :
% 0.33/0.64 ( ( ( produc6499014454317279255nteger @ F @ X )
% 0.33/0.64 = ( produc6499014454317279255nteger @ G @ X ) )
% 0.33/0.64 = ( ( F @ ( produc6174133586879617921nteger @ X ) )
% 0.33/0.64 = ( G @ ( produc6174133586879617921nteger @ X ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % apsnd_eq_conv
% 0.33/0.64 thf(fact_6359_snd__apsnd,axiom,
% 0.33/0.64 ! [F: code_integer > code_integer,X: produc8923325533196201883nteger] :
% 0.33/0.64 ( ( produc6174133586879617921nteger @ ( produc6499014454317279255nteger @ F @ X ) )
% 0.33/0.64 = ( F @ ( produc6174133586879617921nteger @ X ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % snd_apsnd
% 0.33/0.64 thf(fact_6360_snd__apsnd,axiom,
% 0.33/0.64 ! [F: int > int,X: product_prod_int_int] :
% 0.33/0.64 ( ( product_snd_int_int @ ( produc4463282112584876420nt_int @ F @ X ) )
% 0.33/0.64 = ( F @ ( product_snd_int_int @ X ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % snd_apsnd
% 0.33/0.64 thf(fact_6361_snd__apsnd,axiom,
% 0.33/0.64 ! [F: produc7822875418678951345atural > produc7822875418678951345atural,X: produc5835291356934675326atural] :
% 0.33/0.64 ( ( produc6591912806276919810atural @ ( produc4464772112783624294atural @ F @ X ) )
% 0.33/0.64 = ( F @ ( produc6591912806276919810atural @ X ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % snd_apsnd
% 0.33/0.64 thf(fact_6362_snd__comp__apsnd,axiom,
% 0.33/0.64 ! [F: code_integer > code_integer] :
% 0.33/0.64 ( ( comp_P3428181540658402820nteger @ produc6174133586879617921nteger @ ( produc6499014454317279255nteger @ F ) )
% 0.33/0.64 = ( comp_C1043215000170864188nteger @ F @ produc6174133586879617921nteger ) ) ).
% 0.33/0.64
% 0.33/0.64 % snd_comp_apsnd
% 0.33/0.64 thf(fact_6363_snd__comp__apsnd,axiom,
% 0.33/0.64 ! [F: int > int] :
% 0.33/0.64 ( ( comp_P5356232565778667509nt_int @ product_snd_int_int @ ( produc4463282112584876420nt_int @ F ) )
% 0.33/0.64 = ( comp_i4330622015127193916nt_int @ F @ product_snd_int_int ) ) ).
% 0.33/0.64
% 0.33/0.64 % snd_comp_apsnd
% 0.33/0.64 thf(fact_6364_snd__comp__apsnd,axiom,
% 0.33/0.64 ! [F: produc7822875418678951345atural > produc7822875418678951345atural] :
% 0.33/0.64 ( ( comp_P7610810914149544718atural @ produc6591912806276919810atural @ ( produc4464772112783624294atural @ F ) )
% 0.33/0.64 = ( comp_P3067963646784605345atural @ F @ produc6591912806276919810atural ) ) ).
% 0.33/0.64
% 0.33/0.64 % snd_comp_apsnd
% 0.33/0.64 thf(fact_6365_fst__divmod__integer,axiom,
% 0.33/0.64 ! [K: code_integer,L: code_integer] :
% 0.33/0.64 ( ( produc8508995932063986495nteger @ ( code_divmod_integer @ K @ L ) )
% 0.33/0.64 = ( divide6298287555418463151nteger @ K @ L ) ) ).
% 0.33/0.64
% 0.33/0.64 % fst_divmod_integer
% 0.33/0.64 thf(fact_6366_snd__divmod__integer,axiom,
% 0.33/0.64 ! [K: code_integer,L: code_integer] :
% 0.33/0.64 ( ( produc6174133586879617921nteger @ ( code_divmod_integer @ K @ L ) )
% 0.33/0.64 = ( modulo364778990260209775nteger @ K @ L ) ) ).
% 0.33/0.64
% 0.33/0.64 % snd_divmod_integer
% 0.33/0.64 thf(fact_6367_Sup__atLeastAtMost,axiom,
% 0.33/0.64 ! [X: set_nat,Y: set_nat] :
% 0.33/0.64 ( ( ord_less_eq_set_nat @ X @ Y )
% 0.33/0.64 => ( ( comple7399068483239264473et_nat @ ( set_or4548717258645045905et_nat @ X @ Y ) )
% 0.33/0.64 = Y ) ) ).
% 0.33/0.64
% 0.33/0.64 % Sup_atLeastAtMost
% 0.33/0.64 thf(fact_6368_Sup__atLeastAtMost,axiom,
% 0.33/0.64 ! [X: product_unit,Y: product_unit] :
% 0.33/0.64 ( ( ord_le3221252021190050221t_unit @ X @ Y )
% 0.33/0.64 => ( ( comple4687483117567863418t_unit @ ( set_or5692540242118139586t_unit @ X @ Y ) )
% 0.33/0.64 = Y ) ) ).
% 0.33/0.64
% 0.33/0.64 % Sup_atLeastAtMost
% 0.33/0.64 thf(fact_6369_Inf__atLeastAtMost,axiom,
% 0.33/0.64 ! [X: set_nat,Y: set_nat] :
% 0.33/0.64 ( ( ord_less_eq_set_nat @ X @ Y )
% 0.33/0.64 => ( ( comple7806235888213564991et_nat @ ( set_or4548717258645045905et_nat @ X @ Y ) )
% 0.33/0.64 = X ) ) ).
% 0.33/0.64
% 0.33/0.64 % Inf_atLeastAtMost
% 0.33/0.64 thf(fact_6370_Inf__atLeastAtMost,axiom,
% 0.33/0.64 ! [X: product_unit,Y: product_unit] :
% 0.33/0.64 ( ( ord_le3221252021190050221t_unit @ X @ Y )
% 0.33/0.64 => ( ( comple2584293577114468500t_unit @ ( set_or5692540242118139586t_unit @ X @ Y ) )
% 0.33/0.64 = X ) ) ).
% 0.33/0.64
% 0.33/0.64 % Inf_atLeastAtMost
% 0.33/0.64 thf(fact_6371_Inf__atLeastLessThan,axiom,
% 0.33/0.64 ! [X: set_nat,Y: set_nat] :
% 0.33/0.64 ( ( ord_less_set_nat @ X @ Y )
% 0.33/0.64 => ( ( comple7806235888213564991et_nat @ ( set_or3540276404033026485et_nat @ X @ Y ) )
% 0.33/0.64 = X ) ) ).
% 0.33/0.64
% 0.33/0.64 % Inf_atLeastLessThan
% 0.33/0.64 thf(fact_6372_Inf__atLeastLessThan,axiom,
% 0.33/0.64 ! [X: product_unit,Y: product_unit] :
% 0.33/0.64 ( ( ord_le361264281704409273t_unit @ X @ Y )
% 0.33/0.64 => ( ( comple2584293577114468500t_unit @ ( set_or4663484573592751262t_unit @ X @ Y ) )
% 0.33/0.64 = X ) ) ).
% 0.33/0.64
% 0.33/0.64 % Inf_atLeastLessThan
% 0.33/0.64 thf(fact_6373_prod_Ocollapse,axiom,
% 0.33/0.64 ! [Prod: produc1908205239877642774nteger] :
% 0.33/0.64 ( ( produc8603105652947943368nteger @ ( produc7822682618958472924nteger @ Prod ) @ ( produc7856867400915047194nteger @ Prod ) )
% 0.33/0.64 = Prod ) ).
% 0.33/0.64
% 0.33/0.64 % prod.collapse
% 0.33/0.64 thf(fact_6374_prod_Ocollapse,axiom,
% 0.33/0.64 ! [Prod: produc3925858234332021118et_nat] :
% 0.33/0.64 ( ( produc5001842942810119800et_nat @ ( produc995936583742144908et_nat @ Prod ) @ ( produc4011572625026189258et_nat @ Prod ) )
% 0.33/0.64 = Prod ) ).
% 0.33/0.64
% 0.33/0.64 % prod.collapse
% 0.33/0.64 thf(fact_6375_prod_Ocollapse,axiom,
% 0.33/0.64 ! [Prod: produc2732055786443039994et_nat] :
% 0.33/0.64 ( ( produc2245416461498447860et_nat @ ( produc180342877477747464et_nat @ Prod ) @ ( produc5374455773327741254et_nat @ Prod ) )
% 0.33/0.64 = Prod ) ).
% 0.33/0.64
% 0.33/0.64 % prod.collapse
% 0.33/0.64 thf(fact_6376_prod_Ocollapse,axiom,
% 0.33/0.64 ! [Prod: produc2285326912895808259nt_int] :
% 0.33/0.64 ( ( produc5700946648718959541nt_int @ ( produc6816164490631068361nt_int @ Prod ) @ ( produc7328097813583171335nt_int @ Prod ) )
% 0.33/0.64 = Prod ) ).
% 0.33/0.64
% 0.33/0.64 % prod.collapse
% 0.33/0.64 thf(fact_6377_prod_Ocollapse,axiom,
% 0.33/0.64 ! [Prod: produc7773217078559923341nt_int] :
% 0.33/0.64 ( ( produc4305682042979456191nt_int @ ( produc6230002227079971283nt_int @ Prod ) @ ( produc3162348030201620241nt_int @ Prod ) )
% 0.33/0.64 = Prod ) ).
% 0.33/0.64
% 0.33/0.64 % prod.collapse
% 0.33/0.64 thf(fact_6378_prod_Ocollapse,axiom,
% 0.33/0.64 ! [Prod: produc8923325533196201883nteger] :
% 0.33/0.64 ( ( produc1086072967326762835nteger @ ( produc8508995932063986495nteger @ Prod ) @ ( produc6174133586879617921nteger @ Prod ) )
% 0.33/0.64 = Prod ) ).
% 0.33/0.64
% 0.33/0.64 % prod.collapse
% 0.33/0.64 thf(fact_6379_prod_Ocollapse,axiom,
% 0.33/0.64 ! [Prod: product_prod_int_int] :
% 0.33/0.64 ( ( product_Pair_int_int @ ( product_fst_int_int @ Prod ) @ ( product_snd_int_int @ Prod ) )
% 0.33/0.64 = Prod ) ).
% 0.33/0.64
% 0.33/0.64 % prod.collapse
% 0.33/0.64 thf(fact_6380_prod_Ocollapse,axiom,
% 0.33/0.64 ! [Prod: produc5835291356934675326atural] :
% 0.33/0.64 ( ( produc6639722614265839536atural @ ( produc497848011034438852atural @ Prod ) @ ( produc6591912806276919810atural @ Prod ) )
% 0.33/0.64 = Prod ) ).
% 0.33/0.64
% 0.33/0.64 % prod.collapse
% 0.33/0.64 thf(fact_6381_Inf__atMost,axiom,
% 0.33/0.64 ! [X: set_Pr4329608150637261639at_nat] :
% 0.33/0.64 ( ( comple6751905152567503566at_nat @ ( set_or4071486571221009422at_nat @ X ) )
% 0.33/0.64 = bot_bo228742789529271731at_nat ) ).
% 0.33/0.64
% 0.33/0.64 % Inf_atMost
% 0.33/0.64 thf(fact_6382_Inf__atMost,axiom,
% 0.33/0.64 ! [X: set_Pr1261947904930325089at_nat] :
% 0.33/0.64 ( ( comple1930127330929219688at_nat @ ( set_or2762583123196137896at_nat @ X ) )
% 0.33/0.64 = bot_bo2099793752762293965at_nat ) ).
% 0.33/0.64
% 0.33/0.64 % Inf_atMost
% 0.33/0.64 thf(fact_6383_Inf__atMost,axiom,
% 0.33/0.64 ! [X: set_o] :
% 0.33/0.64 ( ( comple3063163877087187839_set_o @ ( set_ord_atMost_set_o @ X ) )
% 0.33/0.64 = bot_bot_set_o ) ).
% 0.33/0.64
% 0.33/0.64 % Inf_atMost
% 0.33/0.64 thf(fact_6384_Inf__atMost,axiom,
% 0.33/0.64 ! [X: set_int] :
% 0.33/0.64 ( ( comple3628384868704368283et_int @ ( set_or58775011639299419et_int @ X ) )
% 0.33/0.64 = bot_bot_set_int ) ).
% 0.33/0.64
% 0.33/0.64 % Inf_atMost
% 0.33/0.64 thf(fact_6385_Inf__atMost,axiom,
% 0.33/0.64 ! [X: set_nat] :
% 0.33/0.64 ( ( comple7806235888213564991et_nat @ ( set_or4236626031148496127et_nat @ X ) )
% 0.33/0.64 = bot_bot_set_nat ) ).
% 0.33/0.64
% 0.33/0.64 % Inf_atMost
% 0.33/0.64 thf(fact_6386_Inf__atMost,axiom,
% 0.33/0.64 ! [X: product_unit] :
% 0.33/0.64 ( ( comple2584293577114468500t_unit @ ( set_or8621721900777396692t_unit @ X ) )
% 0.33/0.64 = bot_bot_Product_unit ) ).
% 0.33/0.64
% 0.33/0.64 % Inf_atMost
% 0.33/0.64 thf(fact_6387_img__fst,axiom,
% 0.33/0.64 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,S2: set_Pr4329608150637261639at_nat] :
% 0.33/0.64 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ B ) @ S2 )
% 0.33/0.64 => ( member2643936169264416010at_nat @ A @ ( image_7979982168039674559at_nat @ produc6011863565407846595at_nat @ S2 ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % img_fst
% 0.33/0.64 thf(fact_6388_img__fst,axiom,
% 0.33/0.64 ! [A: nat,B: nat,S2: set_Pr1261947904930325089at_nat] :
% 0.33/0.64 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ S2 )
% 0.33/0.64 => ( member_nat @ A @ ( image_2486076414777270412at_nat @ product_fst_nat_nat @ S2 ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % img_fst
% 0.33/0.64 thf(fact_6389_img__fst,axiom,
% 0.33/0.64 ! [A: produc6241069584506657477e_term > option6357759511663192854e_term,B: produc8923325533196201883nteger,S2: set_Pr1281608226676607948nteger] :
% 0.33/0.64 ( ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ A @ B ) @ S2 )
% 0.33/0.64 => ( member4242434998011752849e_term @ A @ ( image_4436781500471753239e_term @ produc7822682618958472924nteger @ S2 ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % img_fst
% 0.33/0.64 thf(fact_6390_img__fst,axiom,
% 0.33/0.64 ! [A: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat,S2: set_Pr3286484037609594932et_nat] :
% 0.33/0.64 ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ A @ B ) @ S2 )
% 0.33/0.64 => ( member6576561426505652726_nat_o @ A @ ( image_6802380912191114376_nat_o @ produc995936583742144908et_nat @ S2 ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % img_fst
% 0.33/0.64 thf(fact_6391_img__fst,axiom,
% 0.33/0.64 ! [A: produc3658429121746597890et_nat > $o,B: produc3925858234332021118et_nat,S2: set_Pr8536935166611901872et_nat] :
% 0.33/0.64 ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ A @ B ) @ S2 )
% 0.33/0.64 => ( member6576561426505652726_nat_o @ A @ ( image_2517677226577294348_nat_o @ produc180342877477747464et_nat @ S2 ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % img_fst
% 0.33/0.64 thf(fact_6392_img__fst,axiom,
% 0.33/0.64 ! [A: produc8551481072490612790e_term > option6357759511663192854e_term,B: product_prod_int_int,S2: set_Pr9222295170931077689nt_int] :
% 0.33/0.64 ( ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ A @ B ) @ S2 )
% 0.33/0.64 => ( member3222579708246209666e_term @ A @ ( image_142517975987106933e_term @ produc6816164490631068361nt_int @ S2 ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % img_fst
% 0.33/0.64 thf(fact_6393_img__fst,axiom,
% 0.33/0.64 ! [A: int > option6357759511663192854e_term,B: product_prod_int_int,S2: set_Pr1872883991513573699nt_int] :
% 0.33/0.64 ( ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ A @ B ) @ S2 )
% 0.33/0.64 => ( member8845023287901829240e_term @ A @ ( image_4217645046469565813e_term @ produc6230002227079971283nt_int @ S2 ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % img_fst
% 0.33/0.64 thf(fact_6394_img__fst,axiom,
% 0.33/0.64 ! [A: code_integer,B: code_integer,S2: set_Pr4811707699266497531nteger] :
% 0.33/0.64 ( ( member157494554546826820nteger @ ( produc1086072967326762835nteger @ A @ B ) @ S2 )
% 0.33/0.64 => ( member_Code_integer @ A @ ( image_6316824473203919795nteger @ produc8508995932063986495nteger @ S2 ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % img_fst
% 0.33/0.64 thf(fact_6395_img__fst,axiom,
% 0.33/0.64 ! [A: int,B: int,S2: set_Pr958786334691620121nt_int] :
% 0.33/0.64 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ S2 )
% 0.33/0.64 => ( member_int @ A @ ( image_5042161079198086560nt_int @ product_fst_int_int @ S2 ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % img_fst
% 0.33/0.64 thf(fact_6396_img__snd,axiom,
% 0.33/0.64 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,S2: set_Pr4329608150637261639at_nat] :
% 0.33/0.64 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ B ) @ S2 )
% 0.33/0.64 => ( member2643936169264416010at_nat @ B @ ( image_7979982168039674559at_nat @ produc2937545259423399429at_nat @ S2 ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % img_snd
% 0.33/0.64 thf(fact_6397_img__snd,axiom,
% 0.33/0.64 ! [A: nat,B: nat,S2: set_Pr1261947904930325089at_nat] :
% 0.33/0.64 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ S2 )
% 0.33/0.64 => ( member_nat @ B @ ( image_2486076414777270412at_nat @ product_snd_nat_nat @ S2 ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % img_snd
% 0.33/0.64 thf(fact_6398_img__snd,axiom,
% 0.33/0.64 ! [A: produc6241069584506657477e_term > option6357759511663192854e_term,B: produc8923325533196201883nteger,S2: set_Pr1281608226676607948nteger] :
% 0.33/0.64 ( ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ A @ B ) @ S2 )
% 0.33/0.64 => ( member157494554546826820nteger @ B @ ( image_3141030398089242942nteger @ produc7856867400915047194nteger @ S2 ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % img_snd
% 0.33/0.64 thf(fact_6399_img__snd,axiom,
% 0.33/0.64 ! [A: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat,S2: set_Pr3286484037609594932et_nat] :
% 0.33/0.64 ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ A @ B ) @ S2 )
% 0.33/0.64 => ( member6260224972018164377et_nat @ B @ ( image_4390311411407041927et_nat @ produc4011572625026189258et_nat @ S2 ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % img_snd
% 0.33/0.64 thf(fact_6400_img__snd,axiom,
% 0.33/0.64 ! [A: produc3658429121746597890et_nat > $o,B: produc3925858234332021118et_nat,S2: set_Pr8536935166611901872et_nat] :
% 0.33/0.64 ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ A @ B ) @ S2 )
% 0.33/0.64 => ( member1996754912294343701et_nat @ B @ ( image_4557310310409863807et_nat @ produc5374455773327741254et_nat @ S2 ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % img_snd
% 0.33/0.64 thf(fact_6401_img__snd,axiom,
% 0.33/0.64 ! [A: produc8551481072490612790e_term > option6357759511663192854e_term,B: product_prod_int_int,S2: set_Pr9222295170931077689nt_int] :
% 0.33/0.64 ( ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ A @ B ) @ S2 )
% 0.33/0.64 => ( member5262025264175285858nt_int @ B @ ( image_3915291023682402351nt_int @ produc7328097813583171335nt_int @ S2 ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % img_snd
% 0.33/0.64 thf(fact_6402_img__snd,axiom,
% 0.33/0.64 ! [A: int > option6357759511663192854e_term,B: product_prod_int_int,S2: set_Pr1872883991513573699nt_int] :
% 0.33/0.64 ( ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ A @ B ) @ S2 )
% 0.33/0.64 => ( member5262025264175285858nt_int @ B @ ( image_3108077152341812517nt_int @ produc3162348030201620241nt_int @ S2 ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % img_snd
% 0.33/0.64 thf(fact_6403_img__snd,axiom,
% 0.33/0.64 ! [A: code_integer,B: code_integer,S2: set_Pr4811707699266497531nteger] :
% 0.33/0.64 ( ( member157494554546826820nteger @ ( produc1086072967326762835nteger @ A @ B ) @ S2 )
% 0.33/0.64 => ( member_Code_integer @ B @ ( image_6316824473203919795nteger @ produc6174133586879617921nteger @ S2 ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % img_snd
% 0.33/0.64 thf(fact_6404_img__snd,axiom,
% 0.33/0.64 ! [A: int,B: int,S2: set_Pr958786334691620121nt_int] :
% 0.33/0.64 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ S2 )
% 0.33/0.64 => ( member_int @ B @ ( image_5042161079198086560nt_int @ product_snd_int_int @ S2 ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % img_snd
% 0.33/0.64 thf(fact_6405_img__snd,axiom,
% 0.33/0.64 ! [A: code_natural,B: produc7822875418678951345atural,S2: set_Pr2352657477744078772atural] :
% 0.33/0.64 ( ( member2108296798382401941atural @ ( produc6639722614265839536atural @ A @ B ) @ S2 )
% 0.33/0.64 => ( member8280416476884352090atural @ B @ ( image_3837677093542026988atural @ produc6591912806276919810atural @ S2 ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % img_snd
% 0.33/0.64 thf(fact_6406_fst__divmod__abs,axiom,
% 0.33/0.64 ! [K: code_integer,L: code_integer] :
% 0.33/0.64 ( ( produc8508995932063986495nteger @ ( code_divmod_abs @ K @ L ) )
% 0.33/0.64 = ( divide6298287555418463151nteger @ ( abs_abs_Code_integer @ K ) @ ( abs_abs_Code_integer @ L ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % fst_divmod_abs
% 0.33/0.64 thf(fact_6407_snd__divmod__abs,axiom,
% 0.33/0.64 ! [K: code_integer,L: code_integer] :
% 0.33/0.64 ( ( produc6174133586879617921nteger @ ( code_divmod_abs @ K @ L ) )
% 0.33/0.64 = ( modulo364778990260209775nteger @ ( abs_abs_Code_integer @ K ) @ ( abs_abs_Code_integer @ L ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % snd_divmod_abs
% 0.33/0.64 thf(fact_6408_Inf__atMostLessThan,axiom,
% 0.33/0.64 ! [X: set_Pr4329608150637261639at_nat] :
% 0.33/0.64 ( ( ord_le2604355607129572851at_nat @ top_to6833984726390702231at_nat @ X )
% 0.33/0.64 => ( ( comple6751905152567503566at_nat @ ( set_or2137699863726836970at_nat @ X ) )
% 0.33/0.64 = bot_bo228742789529271731at_nat ) ) ).
% 0.33/0.64
% 0.33/0.64 % Inf_atMostLessThan
% 0.33/0.64 thf(fact_6409_Inf__atMostLessThan,axiom,
% 0.33/0.64 ! [X: set_Pr1261947904930325089at_nat] :
% 0.33/0.64 ( ( ord_le7866589430770878221at_nat @ top_to4669805908274784177at_nat @ X )
% 0.33/0.64 => ( ( comple1930127330929219688at_nat @ ( set_or5243998310507771012at_nat @ X ) )
% 0.33/0.64 = bot_bo2099793752762293965at_nat ) ) ).
% 0.33/0.64
% 0.33/0.64 % Inf_atMostLessThan
% 0.33/0.64 thf(fact_6410_Inf__atMostLessThan,axiom,
% 0.33/0.64 ! [X: set_o] :
% 0.33/0.64 ( ( ord_less_set_o @ top_top_set_o @ X )
% 0.33/0.64 => ( ( comple3063163877087187839_set_o @ ( set_or3489638696441961371_set_o @ X ) )
% 0.33/0.64 = bot_bot_set_o ) ) ).
% 0.33/0.64
% 0.33/0.64 % Inf_atMostLessThan
% 0.33/0.64 thf(fact_6411_Inf__atMostLessThan,axiom,
% 0.33/0.64 ! [X: set_Product_unit] :
% 0.33/0.64 ( ( ord_le8056459307392131481t_unit @ top_to1996260823553986621t_unit @ X )
% 0.33/0.64 => ( ( comple7216939928495492468t_unit @ ( set_or3324826255835560848t_unit @ X ) )
% 0.33/0.64 = bot_bo3957492148770167129t_unit ) ) ).
% 0.33/0.64
% 0.33/0.64 % Inf_atMostLessThan
% 0.33/0.64 thf(fact_6412_Inf__atMostLessThan,axiom,
% 0.33/0.64 ! [X: set_int] :
% 0.33/0.64 ( ( ord_less_set_int @ top_top_set_int @ X )
% 0.33/0.64 => ( ( comple3628384868704368283et_int @ ( set_or5935648273017318783et_int @ X ) )
% 0.33/0.64 = bot_bot_set_int ) ) ).
% 0.33/0.64
% 0.33/0.64 % Inf_atMostLessThan
% 0.33/0.64 thf(fact_6413_Inf__atMostLessThan,axiom,
% 0.33/0.64 ! [X: set_nat] :
% 0.33/0.64 ( ( ord_less_set_nat @ top_top_set_nat @ X )
% 0.33/0.64 => ( ( comple7806235888213564991et_nat @ ( set_or890127255671739683et_nat @ X ) )
% 0.33/0.64 = bot_bot_set_nat ) ) ).
% 0.33/0.64
% 0.33/0.64 % Inf_atMostLessThan
% 0.33/0.64 thf(fact_6414_Inf__atMostLessThan,axiom,
% 0.33/0.64 ! [X: product_unit] :
% 0.33/0.64 ( ( ord_le361264281704409273t_unit @ top_top_Product_unit @ X )
% 0.33/0.64 => ( ( comple2584293577114468500t_unit @ ( set_or8708608758551125680t_unit @ X ) )
% 0.33/0.64 = bot_bot_Product_unit ) ) ).
% 0.33/0.64
% 0.33/0.64 % Inf_atMostLessThan
% 0.33/0.64 thf(fact_6415_case__prod__beta_H,axiom,
% 0.33/0.64 ( produc6842872674320459806at_nat
% 0.33/0.64 = ( ^ [F2: nat > nat > nat,X3: product_prod_nat_nat] : ( F2 @ ( product_fst_nat_nat @ X3 ) @ ( product_snd_nat_nat @ X3 ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % case_prod_beta'
% 0.33/0.64 thf(fact_6416_case__prod__beta_H,axiom,
% 0.33/0.64 ( produc27273713700761075at_nat
% 0.33/0.64 = ( ^ [F2: nat > nat > product_prod_nat_nat > product_prod_nat_nat,X3: product_prod_nat_nat] : ( F2 @ ( product_fst_nat_nat @ X3 ) @ ( product_snd_nat_nat @ X3 ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % case_prod_beta'
% 0.33/0.64 thf(fact_6417_case__prod__beta_H,axiom,
% 0.33/0.64 ( produc8739625826339149834_nat_o
% 0.33/0.64 = ( ^ [F2: nat > nat > product_prod_nat_nat > $o,X3: product_prod_nat_nat] : ( F2 @ ( product_fst_nat_nat @ X3 ) @ ( product_snd_nat_nat @ X3 ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % case_prod_beta'
% 0.33/0.64 thf(fact_6418_case__prod__beta_H,axiom,
% 0.33/0.64 ( produc4245557441103728435nt_int
% 0.33/0.64 = ( ^ [F2: int > int > product_prod_int_int,X3: product_prod_int_int] : ( F2 @ ( product_fst_int_int @ X3 ) @ ( product_snd_int_int @ X3 ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % case_prod_beta'
% 0.33/0.64 thf(fact_6419_case__prod__beta_H,axiom,
% 0.33/0.64 ( produc8211389475949308722nt_int
% 0.33/0.64 = ( ^ [F2: int > int > int,X3: product_prod_int_int] : ( F2 @ ( product_fst_int_int @ X3 ) @ ( product_snd_int_int @ X3 ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % case_prod_beta'
% 0.33/0.64 thf(fact_6420_case__prod__unfold,axiom,
% 0.33/0.64 ( produc6842872674320459806at_nat
% 0.33/0.64 = ( ^ [C2: nat > nat > nat,P6: product_prod_nat_nat] : ( C2 @ ( product_fst_nat_nat @ P6 ) @ ( product_snd_nat_nat @ P6 ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % case_prod_unfold
% 0.33/0.64 thf(fact_6421_case__prod__unfold,axiom,
% 0.33/0.64 ( produc27273713700761075at_nat
% 0.33/0.64 = ( ^ [C2: nat > nat > product_prod_nat_nat > product_prod_nat_nat,P6: product_prod_nat_nat] : ( C2 @ ( product_fst_nat_nat @ P6 ) @ ( product_snd_nat_nat @ P6 ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % case_prod_unfold
% 0.33/0.64 thf(fact_6422_case__prod__unfold,axiom,
% 0.33/0.64 ( produc8739625826339149834_nat_o
% 0.33/0.64 = ( ^ [C2: nat > nat > product_prod_nat_nat > $o,P6: product_prod_nat_nat] : ( C2 @ ( product_fst_nat_nat @ P6 ) @ ( product_snd_nat_nat @ P6 ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % case_prod_unfold
% 0.33/0.64 thf(fact_6423_case__prod__unfold,axiom,
% 0.33/0.64 ( produc4245557441103728435nt_int
% 0.33/0.64 = ( ^ [C2: int > int > product_prod_int_int,P6: product_prod_int_int] : ( C2 @ ( product_fst_int_int @ P6 ) @ ( product_snd_int_int @ P6 ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % case_prod_unfold
% 0.33/0.64 thf(fact_6424_case__prod__unfold,axiom,
% 0.33/0.64 ( produc8211389475949308722nt_int
% 0.33/0.64 = ( ^ [C2: int > int > int,P6: product_prod_int_int] : ( C2 @ ( product_fst_int_int @ P6 ) @ ( product_snd_int_int @ P6 ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % case_prod_unfold
% 0.33/0.64 thf(fact_6425_Product__Type_OCollect__case__prodD,axiom,
% 0.33/0.64 ! [X: produc3843707927480180839at_nat,A2: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o] :
% 0.33/0.64 ( ( member8757157785044589968at_nat @ X @ ( collec6321179662152712658at_nat @ ( produc410239310623530412_nat_o @ A2 ) ) )
% 0.33/0.64 => ( A2 @ ( produc6011863565407846595at_nat @ X ) @ ( produc2937545259423399429at_nat @ X ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % Product_Type.Collect_case_prodD
% 0.33/0.64 thf(fact_6426_Product__Type_OCollect__case__prodD,axiom,
% 0.33/0.64 ! [X: product_prod_nat_nat,A2: nat > nat > $o] :
% 0.33/0.64 ( ( member8440522571783428010at_nat @ X @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ A2 ) ) )
% 0.33/0.64 => ( A2 @ ( product_fst_nat_nat @ X ) @ ( product_snd_nat_nat @ X ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % Product_Type.Collect_case_prodD
% 0.33/0.64 thf(fact_6427_Product__Type_OCollect__case__prodD,axiom,
% 0.33/0.64 ! [X: produc8923325533196201883nteger,A2: code_integer > code_integer > $o] :
% 0.33/0.64 ( ( member157494554546826820nteger @ X @ ( collec7766031446232907142nteger @ ( produc2066375834425727024eger_o @ A2 ) ) )
% 0.33/0.64 => ( A2 @ ( produc8508995932063986495nteger @ X ) @ ( produc6174133586879617921nteger @ X ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % Product_Type.Collect_case_prodD
% 0.33/0.64 thf(fact_6428_Product__Type_OCollect__case__prodD,axiom,
% 0.33/0.64 ! [X: product_prod_int_int,A2: int > int > $o] :
% 0.33/0.64 ( ( member5262025264175285858nt_int @ X @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ A2 ) ) )
% 0.33/0.64 => ( A2 @ ( product_fst_int_int @ X ) @ ( product_snd_int_int @ X ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % Product_Type.Collect_case_prodD
% 0.33/0.64 thf(fact_6429_Product__Type_OCollect__case__prodD,axiom,
% 0.33/0.64 ! [X: produc5835291356934675326atural,A2: code_natural > produc7822875418678951345atural > $o] :
% 0.33/0.64 ( ( member2108296798382401941atural @ X @ ( collec1991479681304692691atural @ ( produc7358226366420480123ural_o @ A2 ) ) )
% 0.33/0.64 => ( A2 @ ( produc497848011034438852atural @ X ) @ ( produc6591912806276919810atural @ X ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % Product_Type.Collect_case_prodD
% 0.33/0.64 thf(fact_6430_case__prod__beta,axiom,
% 0.33/0.64 ( produc6842872674320459806at_nat
% 0.33/0.64 = ( ^ [F2: nat > nat > nat,P6: product_prod_nat_nat] : ( F2 @ ( product_fst_nat_nat @ P6 ) @ ( product_snd_nat_nat @ P6 ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % case_prod_beta
% 0.33/0.64 thf(fact_6431_case__prod__beta,axiom,
% 0.33/0.64 ( produc27273713700761075at_nat
% 0.33/0.64 = ( ^ [F2: nat > nat > product_prod_nat_nat > product_prod_nat_nat,P6: product_prod_nat_nat] : ( F2 @ ( product_fst_nat_nat @ P6 ) @ ( product_snd_nat_nat @ P6 ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % case_prod_beta
% 0.33/0.64 thf(fact_6432_case__prod__beta,axiom,
% 0.33/0.64 ( produc8739625826339149834_nat_o
% 0.33/0.64 = ( ^ [F2: nat > nat > product_prod_nat_nat > $o,P6: product_prod_nat_nat] : ( F2 @ ( product_fst_nat_nat @ P6 ) @ ( product_snd_nat_nat @ P6 ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % case_prod_beta
% 0.33/0.64 thf(fact_6433_case__prod__beta,axiom,
% 0.33/0.64 ( produc4245557441103728435nt_int
% 0.33/0.64 = ( ^ [F2: int > int > product_prod_int_int,P6: product_prod_int_int] : ( F2 @ ( product_fst_int_int @ P6 ) @ ( product_snd_int_int @ P6 ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % case_prod_beta
% 0.33/0.64 thf(fact_6434_case__prod__beta,axiom,
% 0.33/0.64 ( produc8211389475949308722nt_int
% 0.33/0.64 = ( ^ [F2: int > int > int,P6: product_prod_int_int] : ( F2 @ ( product_fst_int_int @ P6 ) @ ( product_snd_int_int @ P6 ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % case_prod_beta
% 0.33/0.64 thf(fact_6435_split__beta,axiom,
% 0.33/0.64 ( produc6842872674320459806at_nat
% 0.33/0.64 = ( ^ [F2: nat > nat > nat,Prod2: product_prod_nat_nat] : ( F2 @ ( product_fst_nat_nat @ Prod2 ) @ ( product_snd_nat_nat @ Prod2 ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % split_beta
% 0.33/0.64 thf(fact_6436_split__beta,axiom,
% 0.33/0.64 ( produc27273713700761075at_nat
% 0.33/0.64 = ( ^ [F2: nat > nat > product_prod_nat_nat > product_prod_nat_nat,Prod2: product_prod_nat_nat] : ( F2 @ ( product_fst_nat_nat @ Prod2 ) @ ( product_snd_nat_nat @ Prod2 ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % split_beta
% 0.33/0.64 thf(fact_6437_split__beta,axiom,
% 0.33/0.64 ( produc8739625826339149834_nat_o
% 0.33/0.64 = ( ^ [F2: nat > nat > product_prod_nat_nat > $o,Prod2: product_prod_nat_nat] : ( F2 @ ( product_fst_nat_nat @ Prod2 ) @ ( product_snd_nat_nat @ Prod2 ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % split_beta
% 0.33/0.64 thf(fact_6438_split__beta,axiom,
% 0.33/0.64 ( produc4245557441103728435nt_int
% 0.33/0.64 = ( ^ [F2: int > int > product_prod_int_int,Prod2: product_prod_int_int] : ( F2 @ ( product_fst_int_int @ Prod2 ) @ ( product_snd_int_int @ Prod2 ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % split_beta
% 0.33/0.64 thf(fact_6439_split__beta,axiom,
% 0.33/0.64 ( produc8211389475949308722nt_int
% 0.33/0.64 = ( ^ [F2: int > int > int,Prod2: product_prod_int_int] : ( F2 @ ( product_fst_int_int @ Prod2 ) @ ( product_snd_int_int @ Prod2 ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % split_beta
% 0.33/0.64 thf(fact_6440_effect__guardI,axiom,
% 0.33/0.64 ! [P: heap_e7401611519738050253t_unit > $o,H3: heap_e7401611519738050253t_unit,H5: heap_e7401611519738050253t_unit,F: heap_e7401611519738050253t_unit > produc8664842809031399944it_nat,N2: nat,R2: product_unit] :
% 0.33/0.64 ( ( P @ H3 )
% 0.33/0.64 => ( ( H5
% 0.33/0.64 = ( produc2838810277069100634it_nat @ ( produc8604850587836428116it_nat @ ( F @ H3 ) ) ) )
% 0.33/0.64 => ( ( N2
% 0.33/0.64 = ( produc2594868675584459928it_nat @ ( produc8604850587836428116it_nat @ ( F @ H3 ) ) ) )
% 0.33/0.64 => ( ( R2
% 0.33/0.64 = ( produc4530234641508181270it_nat @ ( F @ H3 ) ) )
% 0.33/0.64 => ( heap_T6553295506729943825t_unit @ ( heap_T8440541562793052209t_unit @ P @ F ) @ H3 @ H5 @ R2 @ N2 ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % effect_guardI
% 0.33/0.64 thf(fact_6441_effect__guardI,axiom,
% 0.33/0.64 ! [P: heap_e7401611519738050253t_unit > $o,H3: heap_e7401611519738050253t_unit,H5: heap_e7401611519738050253t_unit,F: heap_e7401611519738050253t_unit > produc6714399278180371524it_nat,N2: nat,R2: array_a] :
% 0.33/0.64 ( ( P @ H3 )
% 0.33/0.64 => ( ( H5
% 0.33/0.64 = ( produc2838810277069100634it_nat @ ( produc6991280839920081578it_nat @ ( F @ H3 ) ) ) )
% 0.33/0.64 => ( ( N2
% 0.33/0.64 = ( produc2594868675584459928it_nat @ ( produc6991280839920081578it_nat @ ( F @ H3 ) ) ) )
% 0.33/0.64 => ( ( R2
% 0.33/0.64 = ( produc491454361838572648it_nat @ ( F @ H3 ) ) )
% 0.33/0.64 => ( heap_T5830633491639066771rray_a @ ( heap_T7685628758766326643rray_a @ P @ F ) @ H3 @ H5 @ R2 @ N2 ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % effect_guardI
% 0.33/0.64 thf(fact_6442_effect__guardE,axiom,
% 0.33/0.64 ! [P: heap_e7401611519738050253t_unit > $o,F: heap_e7401611519738050253t_unit > produc8664842809031399944it_nat,H3: heap_e7401611519738050253t_unit,H5: heap_e7401611519738050253t_unit,R2: product_unit,N2: nat] :
% 0.33/0.64 ( ( heap_T6553295506729943825t_unit @ ( heap_T8440541562793052209t_unit @ P @ F ) @ H3 @ H5 @ R2 @ N2 )
% 0.33/0.64 => ~ ( ( H5
% 0.33/0.64 = ( produc2838810277069100634it_nat @ ( produc8604850587836428116it_nat @ ( F @ H3 ) ) ) )
% 0.33/0.64 => ( ( N2
% 0.33/0.64 = ( produc2594868675584459928it_nat @ ( produc8604850587836428116it_nat @ ( F @ H3 ) ) ) )
% 0.33/0.64 => ( ( R2
% 0.33/0.64 = ( produc4530234641508181270it_nat @ ( F @ H3 ) ) )
% 0.33/0.64 => ~ ( P @ H3 ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % effect_guardE
% 0.33/0.64 thf(fact_6443_effect__guardE,axiom,
% 0.33/0.64 ! [P: heap_e7401611519738050253t_unit > $o,F: heap_e7401611519738050253t_unit > produc6714399278180371524it_nat,H3: heap_e7401611519738050253t_unit,H5: heap_e7401611519738050253t_unit,R2: array_a,N2: nat] :
% 0.33/0.64 ( ( heap_T5830633491639066771rray_a @ ( heap_T7685628758766326643rray_a @ P @ F ) @ H3 @ H5 @ R2 @ N2 )
% 0.33/0.64 => ~ ( ( H5
% 0.33/0.64 = ( produc2838810277069100634it_nat @ ( produc6991280839920081578it_nat @ ( F @ H3 ) ) ) )
% 0.33/0.64 => ( ( N2
% 0.33/0.64 = ( produc2594868675584459928it_nat @ ( produc6991280839920081578it_nat @ ( F @ H3 ) ) ) )
% 0.33/0.64 => ( ( R2
% 0.33/0.64 = ( produc491454361838572648it_nat @ ( F @ H3 ) ) )
% 0.33/0.64 => ~ ( P @ H3 ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % effect_guardE
% 0.33/0.64 thf(fact_6444_effectE,axiom,
% 0.33/0.64 ! [C: heap_T5738788834812785303t_unit,H3: heap_e7401611519738050253t_unit,H5: heap_e7401611519738050253t_unit,R2: product_unit,N2: nat] :
% 0.33/0.64 ( ( heap_T6553295506729943825t_unit @ C @ H3 @ H5 @ R2 @ N2 )
% 0.33/0.64 => ~ ( ( R2
% 0.33/0.64 = ( produc4530234641508181270it_nat @ ( the_Pr7776125533777466484it_nat @ ( heap_T875086893843062177t_unit @ C @ H3 ) ) ) )
% 0.33/0.64 => ( ( H5
% 0.33/0.64 = ( produc2838810277069100634it_nat @ ( produc8604850587836428116it_nat @ ( the_Pr7776125533777466484it_nat @ ( heap_T875086893843062177t_unit @ C @ H3 ) ) ) ) )
% 0.33/0.64 => ( ( N2
% 0.33/0.64 = ( produc2594868675584459928it_nat @ ( produc8604850587836428116it_nat @ ( the_Pr7776125533777466484it_nat @ ( heap_T875086893843062177t_unit @ C @ H3 ) ) ) ) )
% 0.33/0.64 => ~ ( heap_T584514906347983379t_unit @ C @ H3 ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % effectE
% 0.33/0.64 thf(fact_6445_effectE,axiom,
% 0.33/0.64 ! [C: heap_T6362127782908069795rray_a,H3: heap_e7401611519738050253t_unit,H5: heap_e7401611519738050253t_unit,R2: array_a,N2: nat] :
% 0.33/0.64 ( ( heap_T5830633491639066771rray_a @ C @ H3 @ H5 @ R2 @ N2 )
% 0.33/0.64 => ~ ( ( R2
% 0.33/0.64 = ( produc491454361838572648it_nat @ ( the_Pr5856008525237892824it_nat @ ( heap_T5591663578999710211rray_a @ C @ H3 ) ) ) )
% 0.33/0.64 => ( ( H5
% 0.33/0.64 = ( produc2838810277069100634it_nat @ ( produc6991280839920081578it_nat @ ( the_Pr5856008525237892824it_nat @ ( heap_T5591663578999710211rray_a @ C @ H3 ) ) ) ) )
% 0.33/0.64 => ( ( N2
% 0.33/0.64 = ( produc2594868675584459928it_nat @ ( produc6991280839920081578it_nat @ ( the_Pr5856008525237892824it_nat @ ( heap_T5591663578999710211rray_a @ C @ H3 ) ) ) ) )
% 0.33/0.64 => ~ ( heap_T6932021131025641745rray_a @ C @ H3 ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % effectE
% 0.33/0.64 thf(fact_6446_prod__eq__iff,axiom,
% 0.33/0.64 ( ( ^ [Y4: produc8923325533196201883nteger,Z2: produc8923325533196201883nteger] : ( Y4 = Z2 ) )
% 0.33/0.64 = ( ^ [S4: produc8923325533196201883nteger,T2: produc8923325533196201883nteger] :
% 0.33/0.64 ( ( ( produc8508995932063986495nteger @ S4 )
% 0.33/0.64 = ( produc8508995932063986495nteger @ T2 ) )
% 0.33/0.64 & ( ( produc6174133586879617921nteger @ S4 )
% 0.33/0.64 = ( produc6174133586879617921nteger @ T2 ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod_eq_iff
% 0.33/0.64 thf(fact_6447_prod__eq__iff,axiom,
% 0.33/0.64 ( ( ^ [Y4: product_prod_int_int,Z2: product_prod_int_int] : ( Y4 = Z2 ) )
% 0.33/0.64 = ( ^ [S4: product_prod_int_int,T2: product_prod_int_int] :
% 0.33/0.64 ( ( ( product_fst_int_int @ S4 )
% 0.33/0.64 = ( product_fst_int_int @ T2 ) )
% 0.33/0.64 & ( ( product_snd_int_int @ S4 )
% 0.33/0.64 = ( product_snd_int_int @ T2 ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod_eq_iff
% 0.33/0.64 thf(fact_6448_prod__eq__iff,axiom,
% 0.33/0.64 ( ( ^ [Y4: produc5835291356934675326atural,Z2: produc5835291356934675326atural] : ( Y4 = Z2 ) )
% 0.33/0.64 = ( ^ [S4: produc5835291356934675326atural,T2: produc5835291356934675326atural] :
% 0.33/0.64 ( ( ( produc497848011034438852atural @ S4 )
% 0.33/0.64 = ( produc497848011034438852atural @ T2 ) )
% 0.33/0.64 & ( ( produc6591912806276919810atural @ S4 )
% 0.33/0.64 = ( produc6591912806276919810atural @ T2 ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod_eq_iff
% 0.33/0.64 thf(fact_6449_prod__eqI,axiom,
% 0.33/0.64 ! [P4: produc8923325533196201883nteger,Q3: produc8923325533196201883nteger] :
% 0.33/0.64 ( ( ( produc8508995932063986495nteger @ P4 )
% 0.33/0.64 = ( produc8508995932063986495nteger @ Q3 ) )
% 0.33/0.64 => ( ( ( produc6174133586879617921nteger @ P4 )
% 0.33/0.64 = ( produc6174133586879617921nteger @ Q3 ) )
% 0.33/0.64 => ( P4 = Q3 ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod_eqI
% 0.33/0.64 thf(fact_6450_prod__eqI,axiom,
% 0.33/0.64 ! [P4: product_prod_int_int,Q3: product_prod_int_int] :
% 0.33/0.64 ( ( ( product_fst_int_int @ P4 )
% 0.33/0.64 = ( product_fst_int_int @ Q3 ) )
% 0.33/0.64 => ( ( ( product_snd_int_int @ P4 )
% 0.33/0.64 = ( product_snd_int_int @ Q3 ) )
% 0.33/0.64 => ( P4 = Q3 ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod_eqI
% 0.33/0.64 thf(fact_6451_prod__eqI,axiom,
% 0.33/0.64 ! [P4: produc5835291356934675326atural,Q3: produc5835291356934675326atural] :
% 0.33/0.64 ( ( ( produc497848011034438852atural @ P4 )
% 0.33/0.64 = ( produc497848011034438852atural @ Q3 ) )
% 0.33/0.64 => ( ( ( produc6591912806276919810atural @ P4 )
% 0.33/0.64 = ( produc6591912806276919810atural @ Q3 ) )
% 0.33/0.64 => ( P4 = Q3 ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod_eqI
% 0.33/0.64 thf(fact_6452_prod_Oexpand,axiom,
% 0.33/0.64 ! [Prod: produc8923325533196201883nteger,Prod3: produc8923325533196201883nteger] :
% 0.33/0.64 ( ( ( ( produc8508995932063986495nteger @ Prod )
% 0.33/0.64 = ( produc8508995932063986495nteger @ Prod3 ) )
% 0.33/0.64 & ( ( produc6174133586879617921nteger @ Prod )
% 0.33/0.64 = ( produc6174133586879617921nteger @ Prod3 ) ) )
% 0.33/0.64 => ( Prod = Prod3 ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod.expand
% 0.33/0.64 thf(fact_6453_prod_Oexpand,axiom,
% 0.33/0.64 ! [Prod: product_prod_int_int,Prod3: product_prod_int_int] :
% 0.33/0.64 ( ( ( ( product_fst_int_int @ Prod )
% 0.33/0.64 = ( product_fst_int_int @ Prod3 ) )
% 0.33/0.64 & ( ( product_snd_int_int @ Prod )
% 0.33/0.64 = ( product_snd_int_int @ Prod3 ) ) )
% 0.33/0.64 => ( Prod = Prod3 ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod.expand
% 0.33/0.64 thf(fact_6454_prod_Oexpand,axiom,
% 0.33/0.64 ! [Prod: produc5835291356934675326atural,Prod3: produc5835291356934675326atural] :
% 0.33/0.64 ( ( ( ( produc497848011034438852atural @ Prod )
% 0.33/0.64 = ( produc497848011034438852atural @ Prod3 ) )
% 0.33/0.64 & ( ( produc6591912806276919810atural @ Prod )
% 0.33/0.64 = ( produc6591912806276919810atural @ Prod3 ) ) )
% 0.33/0.64 => ( Prod = Prod3 ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod.expand
% 0.33/0.64 thf(fact_6455_All__prod__contract,axiom,
% 0.33/0.64 ! [P: code_integer > code_integer > $o] :
% 0.33/0.64 ( ( ! [A5: code_integer,X9: code_integer] : ( P @ A5 @ X9 ) )
% 0.33/0.64 = ( ! [Z4: produc8923325533196201883nteger] : ( P @ ( produc8508995932063986495nteger @ Z4 ) @ ( produc6174133586879617921nteger @ Z4 ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % All_prod_contract
% 0.33/0.64 thf(fact_6456_All__prod__contract,axiom,
% 0.33/0.64 ! [P: int > int > $o] :
% 0.33/0.64 ( ( ! [A5: int,X9: int] : ( P @ A5 @ X9 ) )
% 0.33/0.64 = ( ! [Z4: product_prod_int_int] : ( P @ ( product_fst_int_int @ Z4 ) @ ( product_snd_int_int @ Z4 ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % All_prod_contract
% 0.33/0.64 thf(fact_6457_All__prod__contract,axiom,
% 0.33/0.64 ! [P: code_natural > produc7822875418678951345atural > $o] :
% 0.33/0.64 ( ( ! [A5: code_natural,X9: produc7822875418678951345atural] : ( P @ A5 @ X9 ) )
% 0.33/0.64 = ( ! [Z4: produc5835291356934675326atural] : ( P @ ( produc497848011034438852atural @ Z4 ) @ ( produc6591912806276919810atural @ Z4 ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % All_prod_contract
% 0.33/0.64 thf(fact_6458_Ex__prod__contract,axiom,
% 0.33/0.64 ! [P: code_integer > code_integer > $o] :
% 0.33/0.64 ( ( ? [A5: code_integer,X9: code_integer] : ( P @ A5 @ X9 ) )
% 0.33/0.64 = ( ? [Z4: produc8923325533196201883nteger] : ( P @ ( produc8508995932063986495nteger @ Z4 ) @ ( produc6174133586879617921nteger @ Z4 ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % Ex_prod_contract
% 0.33/0.64 thf(fact_6459_Ex__prod__contract,axiom,
% 0.33/0.64 ! [P: int > int > $o] :
% 0.33/0.64 ( ( ? [A5: int,X9: int] : ( P @ A5 @ X9 ) )
% 0.33/0.64 = ( ? [Z4: product_prod_int_int] : ( P @ ( product_fst_int_int @ Z4 ) @ ( product_snd_int_int @ Z4 ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % Ex_prod_contract
% 0.33/0.64 thf(fact_6460_Ex__prod__contract,axiom,
% 0.33/0.64 ! [P: code_natural > produc7822875418678951345atural > $o] :
% 0.33/0.64 ( ( ? [A5: code_natural,X9: produc7822875418678951345atural] : ( P @ A5 @ X9 ) )
% 0.33/0.64 = ( ? [Z4: produc5835291356934675326atural] : ( P @ ( produc497848011034438852atural @ Z4 ) @ ( produc6591912806276919810atural @ Z4 ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % Ex_prod_contract
% 0.33/0.64 thf(fact_6461_prod_Osplit__sel,axiom,
% 0.33/0.64 ! [P: nat > $o,F: nat > nat > nat,Prod: product_prod_nat_nat] :
% 0.33/0.64 ( ( P @ ( produc6842872674320459806at_nat @ F @ Prod ) )
% 0.33/0.64 = ( ( Prod
% 0.33/0.64 = ( product_Pair_nat_nat @ ( product_fst_nat_nat @ Prod ) @ ( product_snd_nat_nat @ Prod ) ) )
% 0.33/0.64 => ( P @ ( F @ ( product_fst_nat_nat @ Prod ) @ ( product_snd_nat_nat @ Prod ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod.split_sel
% 0.33/0.64 thf(fact_6462_prod_Osplit__sel,axiom,
% 0.33/0.64 ! [P: ( product_prod_nat_nat > product_prod_nat_nat ) > $o,F: nat > nat > product_prod_nat_nat > product_prod_nat_nat,Prod: product_prod_nat_nat] :
% 0.33/0.64 ( ( P @ ( produc27273713700761075at_nat @ F @ Prod ) )
% 0.33/0.64 = ( ( Prod
% 0.33/0.64 = ( product_Pair_nat_nat @ ( product_fst_nat_nat @ Prod ) @ ( product_snd_nat_nat @ Prod ) ) )
% 0.33/0.64 => ( P @ ( F @ ( product_fst_nat_nat @ Prod ) @ ( product_snd_nat_nat @ Prod ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod.split_sel
% 0.33/0.64 thf(fact_6463_prod_Osplit__sel,axiom,
% 0.33/0.64 ! [P: ( product_prod_nat_nat > $o ) > $o,F: nat > nat > product_prod_nat_nat > $o,Prod: product_prod_nat_nat] :
% 0.33/0.64 ( ( P @ ( produc8739625826339149834_nat_o @ F @ Prod ) )
% 0.33/0.64 = ( ( Prod
% 0.33/0.64 = ( product_Pair_nat_nat @ ( product_fst_nat_nat @ Prod ) @ ( product_snd_nat_nat @ Prod ) ) )
% 0.33/0.64 => ( P @ ( F @ ( product_fst_nat_nat @ Prod ) @ ( product_snd_nat_nat @ Prod ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod.split_sel
% 0.33/0.64 thf(fact_6464_prod_Osplit__sel,axiom,
% 0.33/0.64 ! [P: product_prod_int_int > $o,F: int > int > product_prod_int_int,Prod: product_prod_int_int] :
% 0.33/0.64 ( ( P @ ( produc4245557441103728435nt_int @ F @ Prod ) )
% 0.33/0.64 = ( ( Prod
% 0.33/0.64 = ( product_Pair_int_int @ ( product_fst_int_int @ Prod ) @ ( product_snd_int_int @ Prod ) ) )
% 0.33/0.64 => ( P @ ( F @ ( product_fst_int_int @ Prod ) @ ( product_snd_int_int @ Prod ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod.split_sel
% 0.33/0.64 thf(fact_6465_prod_Osplit__sel,axiom,
% 0.33/0.64 ! [P: int > $o,F: int > int > int,Prod: product_prod_int_int] :
% 0.33/0.64 ( ( P @ ( produc8211389475949308722nt_int @ F @ Prod ) )
% 0.33/0.64 = ( ( Prod
% 0.33/0.64 = ( product_Pair_int_int @ ( product_fst_int_int @ Prod ) @ ( product_snd_int_int @ Prod ) ) )
% 0.33/0.64 => ( P @ ( F @ ( product_fst_int_int @ Prod ) @ ( product_snd_int_int @ Prod ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod.split_sel
% 0.33/0.64 thf(fact_6466_prod_Osplit__sel__asm,axiom,
% 0.33/0.64 ! [P: nat > $o,F: nat > nat > nat,Prod: product_prod_nat_nat] :
% 0.33/0.64 ( ( P @ ( produc6842872674320459806at_nat @ F @ Prod ) )
% 0.33/0.64 = ( ~ ( ( Prod
% 0.33/0.64 = ( product_Pair_nat_nat @ ( product_fst_nat_nat @ Prod ) @ ( product_snd_nat_nat @ Prod ) ) )
% 0.33/0.64 & ~ ( P @ ( F @ ( product_fst_nat_nat @ Prod ) @ ( product_snd_nat_nat @ Prod ) ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod.split_sel_asm
% 0.33/0.64 thf(fact_6467_prod_Osplit__sel__asm,axiom,
% 0.33/0.64 ! [P: ( product_prod_nat_nat > product_prod_nat_nat ) > $o,F: nat > nat > product_prod_nat_nat > product_prod_nat_nat,Prod: product_prod_nat_nat] :
% 0.33/0.64 ( ( P @ ( produc27273713700761075at_nat @ F @ Prod ) )
% 0.33/0.64 = ( ~ ( ( Prod
% 0.33/0.64 = ( product_Pair_nat_nat @ ( product_fst_nat_nat @ Prod ) @ ( product_snd_nat_nat @ Prod ) ) )
% 0.33/0.64 & ~ ( P @ ( F @ ( product_fst_nat_nat @ Prod ) @ ( product_snd_nat_nat @ Prod ) ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod.split_sel_asm
% 0.33/0.64 thf(fact_6468_prod_Osplit__sel__asm,axiom,
% 0.33/0.64 ! [P: ( product_prod_nat_nat > $o ) > $o,F: nat > nat > product_prod_nat_nat > $o,Prod: product_prod_nat_nat] :
% 0.33/0.64 ( ( P @ ( produc8739625826339149834_nat_o @ F @ Prod ) )
% 0.33/0.64 = ( ~ ( ( Prod
% 0.33/0.64 = ( product_Pair_nat_nat @ ( product_fst_nat_nat @ Prod ) @ ( product_snd_nat_nat @ Prod ) ) )
% 0.33/0.64 & ~ ( P @ ( F @ ( product_fst_nat_nat @ Prod ) @ ( product_snd_nat_nat @ Prod ) ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod.split_sel_asm
% 0.33/0.64 thf(fact_6469_prod_Osplit__sel__asm,axiom,
% 0.33/0.64 ! [P: product_prod_int_int > $o,F: int > int > product_prod_int_int,Prod: product_prod_int_int] :
% 0.33/0.64 ( ( P @ ( produc4245557441103728435nt_int @ F @ Prod ) )
% 0.33/0.64 = ( ~ ( ( Prod
% 0.33/0.64 = ( product_Pair_int_int @ ( product_fst_int_int @ Prod ) @ ( product_snd_int_int @ Prod ) ) )
% 0.33/0.64 & ~ ( P @ ( F @ ( product_fst_int_int @ Prod ) @ ( product_snd_int_int @ Prod ) ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod.split_sel_asm
% 0.33/0.64 thf(fact_6470_prod_Osplit__sel__asm,axiom,
% 0.33/0.64 ! [P: int > $o,F: int > int > int,Prod: product_prod_int_int] :
% 0.33/0.64 ( ( P @ ( produc8211389475949308722nt_int @ F @ Prod ) )
% 0.33/0.64 = ( ~ ( ( Prod
% 0.33/0.64 = ( product_Pair_int_int @ ( product_fst_int_int @ Prod ) @ ( product_snd_int_int @ Prod ) ) )
% 0.33/0.64 & ~ ( P @ ( F @ ( product_fst_int_int @ Prod ) @ ( product_snd_int_int @ Prod ) ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod.split_sel_asm
% 0.33/0.64 thf(fact_6471_surjective__pairing,axiom,
% 0.33/0.64 ! [T: produc1908205239877642774nteger] :
% 0.33/0.64 ( T
% 0.33/0.64 = ( produc8603105652947943368nteger @ ( produc7822682618958472924nteger @ T ) @ ( produc7856867400915047194nteger @ T ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % surjective_pairing
% 0.33/0.64 thf(fact_6472_surjective__pairing,axiom,
% 0.33/0.64 ! [T: produc3925858234332021118et_nat] :
% 0.33/0.64 ( T
% 0.33/0.64 = ( produc5001842942810119800et_nat @ ( produc995936583742144908et_nat @ T ) @ ( produc4011572625026189258et_nat @ T ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % surjective_pairing
% 0.33/0.64 thf(fact_6473_surjective__pairing,axiom,
% 0.33/0.64 ! [T: produc2732055786443039994et_nat] :
% 0.33/0.64 ( T
% 0.33/0.64 = ( produc2245416461498447860et_nat @ ( produc180342877477747464et_nat @ T ) @ ( produc5374455773327741254et_nat @ T ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % surjective_pairing
% 0.33/0.64 thf(fact_6474_surjective__pairing,axiom,
% 0.33/0.64 ! [T: produc2285326912895808259nt_int] :
% 0.33/0.64 ( T
% 0.33/0.64 = ( produc5700946648718959541nt_int @ ( produc6816164490631068361nt_int @ T ) @ ( produc7328097813583171335nt_int @ T ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % surjective_pairing
% 0.33/0.64 thf(fact_6475_surjective__pairing,axiom,
% 0.33/0.64 ! [T: produc7773217078559923341nt_int] :
% 0.33/0.64 ( T
% 0.33/0.64 = ( produc4305682042979456191nt_int @ ( produc6230002227079971283nt_int @ T ) @ ( produc3162348030201620241nt_int @ T ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % surjective_pairing
% 0.33/0.64 thf(fact_6476_surjective__pairing,axiom,
% 0.33/0.64 ! [T: produc8923325533196201883nteger] :
% 0.33/0.64 ( T
% 0.33/0.64 = ( produc1086072967326762835nteger @ ( produc8508995932063986495nteger @ T ) @ ( produc6174133586879617921nteger @ T ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % surjective_pairing
% 0.33/0.64 thf(fact_6477_surjective__pairing,axiom,
% 0.33/0.64 ! [T: product_prod_int_int] :
% 0.33/0.64 ( T
% 0.33/0.64 = ( product_Pair_int_int @ ( product_fst_int_int @ T ) @ ( product_snd_int_int @ T ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % surjective_pairing
% 0.33/0.64 thf(fact_6478_surjective__pairing,axiom,
% 0.33/0.64 ! [T: produc5835291356934675326atural] :
% 0.33/0.64 ( T
% 0.33/0.64 = ( produc6639722614265839536atural @ ( produc497848011034438852atural @ T ) @ ( produc6591912806276919810atural @ T ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % surjective_pairing
% 0.33/0.64 thf(fact_6479_prod_Oexhaust__sel,axiom,
% 0.33/0.64 ! [Prod: produc1908205239877642774nteger] :
% 0.33/0.64 ( Prod
% 0.33/0.64 = ( produc8603105652947943368nteger @ ( produc7822682618958472924nteger @ Prod ) @ ( produc7856867400915047194nteger @ Prod ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod.exhaust_sel
% 0.33/0.64 thf(fact_6480_prod_Oexhaust__sel,axiom,
% 0.33/0.64 ! [Prod: produc3925858234332021118et_nat] :
% 0.33/0.64 ( Prod
% 0.33/0.64 = ( produc5001842942810119800et_nat @ ( produc995936583742144908et_nat @ Prod ) @ ( produc4011572625026189258et_nat @ Prod ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod.exhaust_sel
% 0.33/0.64 thf(fact_6481_prod_Oexhaust__sel,axiom,
% 0.33/0.64 ! [Prod: produc2732055786443039994et_nat] :
% 0.33/0.64 ( Prod
% 0.33/0.64 = ( produc2245416461498447860et_nat @ ( produc180342877477747464et_nat @ Prod ) @ ( produc5374455773327741254et_nat @ Prod ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod.exhaust_sel
% 0.33/0.64 thf(fact_6482_prod_Oexhaust__sel,axiom,
% 0.33/0.64 ! [Prod: produc2285326912895808259nt_int] :
% 0.33/0.64 ( Prod
% 0.33/0.64 = ( produc5700946648718959541nt_int @ ( produc6816164490631068361nt_int @ Prod ) @ ( produc7328097813583171335nt_int @ Prod ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod.exhaust_sel
% 0.33/0.64 thf(fact_6483_prod_Oexhaust__sel,axiom,
% 0.33/0.64 ! [Prod: produc7773217078559923341nt_int] :
% 0.33/0.64 ( Prod
% 0.33/0.64 = ( produc4305682042979456191nt_int @ ( produc6230002227079971283nt_int @ Prod ) @ ( produc3162348030201620241nt_int @ Prod ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod.exhaust_sel
% 0.33/0.64 thf(fact_6484_prod_Oexhaust__sel,axiom,
% 0.33/0.64 ! [Prod: produc8923325533196201883nteger] :
% 0.33/0.64 ( Prod
% 0.33/0.64 = ( produc1086072967326762835nteger @ ( produc8508995932063986495nteger @ Prod ) @ ( produc6174133586879617921nteger @ Prod ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod.exhaust_sel
% 0.33/0.64 thf(fact_6485_prod_Oexhaust__sel,axiom,
% 0.33/0.64 ! [Prod: product_prod_int_int] :
% 0.33/0.64 ( Prod
% 0.33/0.64 = ( product_Pair_int_int @ ( product_fst_int_int @ Prod ) @ ( product_snd_int_int @ Prod ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod.exhaust_sel
% 0.33/0.64 thf(fact_6486_prod_Oexhaust__sel,axiom,
% 0.33/0.64 ! [Prod: produc5835291356934675326atural] :
% 0.33/0.64 ( Prod
% 0.33/0.64 = ( produc6639722614265839536atural @ ( produc497848011034438852atural @ Prod ) @ ( produc6591912806276919810atural @ Prod ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % prod.exhaust_sel
% 0.33/0.64 thf(fact_6487_exI__realizer,axiom,
% 0.33/0.64 ! [P: produc8923325533196201883nteger > ( produc6241069584506657477e_term > option6357759511663192854e_term ) > $o,Y: produc8923325533196201883nteger,X: produc6241069584506657477e_term > option6357759511663192854e_term] :
% 0.33/0.64 ( ( P @ Y @ X )
% 0.33/0.64 => ( P @ ( produc7856867400915047194nteger @ ( produc8603105652947943368nteger @ X @ Y ) ) @ ( produc7822682618958472924nteger @ ( produc8603105652947943368nteger @ X @ Y ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % exI_realizer
% 0.33/0.64 thf(fact_6488_exI__realizer,axiom,
% 0.33/0.64 ! [P: produc3658429121746597890et_nat > ( produc3658429121746597890et_nat > $o ) > $o,Y: produc3658429121746597890et_nat,X: produc3658429121746597890et_nat > $o] :
% 0.33/0.64 ( ( P @ Y @ X )
% 0.33/0.64 => ( P @ ( produc4011572625026189258et_nat @ ( produc5001842942810119800et_nat @ X @ Y ) ) @ ( produc995936583742144908et_nat @ ( produc5001842942810119800et_nat @ X @ Y ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % exI_realizer
% 0.33/0.64 thf(fact_6489_exI__realizer,axiom,
% 0.33/0.64 ! [P: produc3925858234332021118et_nat > ( produc3658429121746597890et_nat > $o ) > $o,Y: produc3925858234332021118et_nat,X: produc3658429121746597890et_nat > $o] :
% 0.33/0.64 ( ( P @ Y @ X )
% 0.33/0.64 => ( P @ ( produc5374455773327741254et_nat @ ( produc2245416461498447860et_nat @ X @ Y ) ) @ ( produc180342877477747464et_nat @ ( produc2245416461498447860et_nat @ X @ Y ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % exI_realizer
% 0.33/0.64 thf(fact_6490_exI__realizer,axiom,
% 0.33/0.64 ! [P: product_prod_int_int > ( produc8551481072490612790e_term > option6357759511663192854e_term ) > $o,Y: product_prod_int_int,X: produc8551481072490612790e_term > option6357759511663192854e_term] :
% 0.33/0.64 ( ( P @ Y @ X )
% 0.33/0.64 => ( P @ ( produc7328097813583171335nt_int @ ( produc5700946648718959541nt_int @ X @ Y ) ) @ ( produc6816164490631068361nt_int @ ( produc5700946648718959541nt_int @ X @ Y ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % exI_realizer
% 0.33/0.64 thf(fact_6491_exI__realizer,axiom,
% 0.33/0.64 ! [P: product_prod_int_int > ( int > option6357759511663192854e_term ) > $o,Y: product_prod_int_int,X: int > option6357759511663192854e_term] :
% 0.33/0.64 ( ( P @ Y @ X )
% 0.33/0.64 => ( P @ ( produc3162348030201620241nt_int @ ( produc4305682042979456191nt_int @ X @ Y ) ) @ ( produc6230002227079971283nt_int @ ( produc4305682042979456191nt_int @ X @ Y ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % exI_realizer
% 0.33/0.64 thf(fact_6492_exI__realizer,axiom,
% 0.33/0.64 ! [P: code_integer > code_integer > $o,Y: code_integer,X: code_integer] :
% 0.33/0.64 ( ( P @ Y @ X )
% 0.33/0.64 => ( P @ ( produc6174133586879617921nteger @ ( produc1086072967326762835nteger @ X @ Y ) ) @ ( produc8508995932063986495nteger @ ( produc1086072967326762835nteger @ X @ Y ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % exI_realizer
% 0.33/0.64 thf(fact_6493_exI__realizer,axiom,
% 0.33/0.64 ! [P: int > int > $o,Y: int,X: int] :
% 0.33/0.64 ( ( P @ Y @ X )
% 0.33/0.64 => ( P @ ( product_snd_int_int @ ( product_Pair_int_int @ X @ Y ) ) @ ( product_fst_int_int @ ( product_Pair_int_int @ X @ Y ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % exI_realizer
% 0.33/0.64 thf(fact_6494_exI__realizer,axiom,
% 0.33/0.64 ! [P: produc7822875418678951345atural > code_natural > $o,Y: produc7822875418678951345atural,X: code_natural] :
% 0.33/0.64 ( ( P @ Y @ X )
% 0.33/0.64 => ( P @ ( produc6591912806276919810atural @ ( produc6639722614265839536atural @ X @ Y ) ) @ ( produc497848011034438852atural @ ( produc6639722614265839536atural @ X @ Y ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % exI_realizer
% 0.33/0.64 thf(fact_6495_conjI__realizer,axiom,
% 0.33/0.64 ! [P: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > $o,P4: produc6241069584506657477e_term > option6357759511663192854e_term,Q: produc8923325533196201883nteger > $o,Q3: produc8923325533196201883nteger] :
% 0.33/0.64 ( ( P @ P4 )
% 0.33/0.64 => ( ( Q @ Q3 )
% 0.33/0.64 => ( ( P @ ( produc7822682618958472924nteger @ ( produc8603105652947943368nteger @ P4 @ Q3 ) ) )
% 0.33/0.64 & ( Q @ ( produc7856867400915047194nteger @ ( produc8603105652947943368nteger @ P4 @ Q3 ) ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % conjI_realizer
% 0.33/0.64 thf(fact_6496_conjI__realizer,axiom,
% 0.33/0.64 ! [P: ( produc3658429121746597890et_nat > $o ) > $o,P4: produc3658429121746597890et_nat > $o,Q: produc3658429121746597890et_nat > $o,Q3: produc3658429121746597890et_nat] :
% 0.33/0.64 ( ( P @ P4 )
% 0.33/0.64 => ( ( Q @ Q3 )
% 0.33/0.64 => ( ( P @ ( produc995936583742144908et_nat @ ( produc5001842942810119800et_nat @ P4 @ Q3 ) ) )
% 0.33/0.64 & ( Q @ ( produc4011572625026189258et_nat @ ( produc5001842942810119800et_nat @ P4 @ Q3 ) ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % conjI_realizer
% 0.33/0.64 thf(fact_6497_conjI__realizer,axiom,
% 0.33/0.64 ! [P: ( produc3658429121746597890et_nat > $o ) > $o,P4: produc3658429121746597890et_nat > $o,Q: produc3925858234332021118et_nat > $o,Q3: produc3925858234332021118et_nat] :
% 0.33/0.64 ( ( P @ P4 )
% 0.33/0.64 => ( ( Q @ Q3 )
% 0.33/0.64 => ( ( P @ ( produc180342877477747464et_nat @ ( produc2245416461498447860et_nat @ P4 @ Q3 ) ) )
% 0.33/0.64 & ( Q @ ( produc5374455773327741254et_nat @ ( produc2245416461498447860et_nat @ P4 @ Q3 ) ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % conjI_realizer
% 0.33/0.64 thf(fact_6498_conjI__realizer,axiom,
% 0.33/0.64 ! [P: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > $o,P4: produc8551481072490612790e_term > option6357759511663192854e_term,Q: product_prod_int_int > $o,Q3: product_prod_int_int] :
% 0.33/0.64 ( ( P @ P4 )
% 0.33/0.64 => ( ( Q @ Q3 )
% 0.33/0.64 => ( ( P @ ( produc6816164490631068361nt_int @ ( produc5700946648718959541nt_int @ P4 @ Q3 ) ) )
% 0.33/0.64 & ( Q @ ( produc7328097813583171335nt_int @ ( produc5700946648718959541nt_int @ P4 @ Q3 ) ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % conjI_realizer
% 0.33/0.64 thf(fact_6499_conjI__realizer,axiom,
% 0.33/0.64 ! [P: ( int > option6357759511663192854e_term ) > $o,P4: int > option6357759511663192854e_term,Q: product_prod_int_int > $o,Q3: product_prod_int_int] :
% 0.33/0.64 ( ( P @ P4 )
% 0.33/0.64 => ( ( Q @ Q3 )
% 0.33/0.64 => ( ( P @ ( produc6230002227079971283nt_int @ ( produc4305682042979456191nt_int @ P4 @ Q3 ) ) )
% 0.33/0.64 & ( Q @ ( produc3162348030201620241nt_int @ ( produc4305682042979456191nt_int @ P4 @ Q3 ) ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % conjI_realizer
% 0.33/0.64 thf(fact_6500_conjI__realizer,axiom,
% 0.33/0.64 ! [P: code_integer > $o,P4: code_integer,Q: code_integer > $o,Q3: code_integer] :
% 0.33/0.64 ( ( P @ P4 )
% 0.33/0.64 => ( ( Q @ Q3 )
% 0.33/0.64 => ( ( P @ ( produc8508995932063986495nteger @ ( produc1086072967326762835nteger @ P4 @ Q3 ) ) )
% 0.33/0.64 & ( Q @ ( produc6174133586879617921nteger @ ( produc1086072967326762835nteger @ P4 @ Q3 ) ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % conjI_realizer
% 0.33/0.64 thf(fact_6501_conjI__realizer,axiom,
% 0.33/0.64 ! [P: int > $o,P4: int,Q: int > $o,Q3: int] :
% 0.33/0.64 ( ( P @ P4 )
% 0.33/0.64 => ( ( Q @ Q3 )
% 0.33/0.64 => ( ( P @ ( product_fst_int_int @ ( product_Pair_int_int @ P4 @ Q3 ) ) )
% 0.33/0.64 & ( Q @ ( product_snd_int_int @ ( product_Pair_int_int @ P4 @ Q3 ) ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % conjI_realizer
% 0.33/0.64 thf(fact_6502_conjI__realizer,axiom,
% 0.33/0.64 ! [P: code_natural > $o,P4: code_natural,Q: produc7822875418678951345atural > $o,Q3: produc7822875418678951345atural] :
% 0.33/0.64 ( ( P @ P4 )
% 0.33/0.64 => ( ( Q @ Q3 )
% 0.33/0.64 => ( ( P @ ( produc497848011034438852atural @ ( produc6639722614265839536atural @ P4 @ Q3 ) ) )
% 0.33/0.64 & ( Q @ ( produc6591912806276919810atural @ ( produc6639722614265839536atural @ P4 @ Q3 ) ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % conjI_realizer
% 0.33/0.64 thf(fact_6503_execute__bind__success,axiom,
% 0.33/0.64 ! [F: heap_T5738788834812785303t_unit,H3: heap_e7401611519738050253t_unit,G: product_unit > heap_T6362127782908069795rray_a] :
% 0.33/0.64 ( ( heap_T584514906347983379t_unit @ F @ H3 )
% 0.33/0.64 => ( ( heap_T5591663578999710211rray_a @ ( heap_T7158140910958840029rray_a @ F @ G ) @ H3 )
% 0.33/0.64 = ( heap_T531568236820715630rray_a @ ( produc2594868675584459928it_nat @ ( produc8604850587836428116it_nat @ ( the_Pr7776125533777466484it_nat @ ( heap_T875086893843062177t_unit @ F @ H3 ) ) ) ) @ ( heap_T5591663578999710211rray_a @ ( G @ ( produc4530234641508181270it_nat @ ( the_Pr7776125533777466484it_nat @ ( heap_T875086893843062177t_unit @ F @ H3 ) ) ) ) @ ( produc2838810277069100634it_nat @ ( produc8604850587836428116it_nat @ ( the_Pr7776125533777466484it_nat @ ( heap_T875086893843062177t_unit @ F @ H3 ) ) ) ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % execute_bind_success
% 0.33/0.64 thf(fact_6504_execute__bind__success,axiom,
% 0.33/0.64 ! [F: heap_T5738788834812785303t_unit,H3: heap_e7401611519738050253t_unit,G: product_unit > heap_T5738788834812785303t_unit] :
% 0.33/0.64 ( ( heap_T584514906347983379t_unit @ F @ H3 )
% 0.33/0.64 => ( ( heap_T875086893843062177t_unit @ ( heap_T2633723481742716231t_unit @ F @ G ) @ H3 )
% 0.33/0.64 = ( heap_T3616969660504097270t_unit @ ( produc2594868675584459928it_nat @ ( produc8604850587836428116it_nat @ ( the_Pr7776125533777466484it_nat @ ( heap_T875086893843062177t_unit @ F @ H3 ) ) ) ) @ ( heap_T875086893843062177t_unit @ ( G @ ( produc4530234641508181270it_nat @ ( the_Pr7776125533777466484it_nat @ ( heap_T875086893843062177t_unit @ F @ H3 ) ) ) ) @ ( produc2838810277069100634it_nat @ ( produc8604850587836428116it_nat @ ( the_Pr7776125533777466484it_nat @ ( heap_T875086893843062177t_unit @ F @ H3 ) ) ) ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % execute_bind_success
% 0.33/0.64 thf(fact_6505_execute__bind__success,axiom,
% 0.33/0.64 ! [F: heap_T6362127782908069795rray_a,H3: heap_e7401611519738050253t_unit,G: array_a > heap_T6362127782908069795rray_a] :
% 0.33/0.64 ( ( heap_T6932021131025641745rray_a @ F @ H3 )
% 0.33/0.64 => ( ( heap_T5591663578999710211rray_a @ ( heap_T2407400398799471159rray_a @ F @ G ) @ H3 )
% 0.33/0.64 = ( heap_T531568236820715630rray_a @ ( produc2594868675584459928it_nat @ ( produc6991280839920081578it_nat @ ( the_Pr5856008525237892824it_nat @ ( heap_T5591663578999710211rray_a @ F @ H3 ) ) ) ) @ ( heap_T5591663578999710211rray_a @ ( G @ ( produc491454361838572648it_nat @ ( the_Pr5856008525237892824it_nat @ ( heap_T5591663578999710211rray_a @ F @ H3 ) ) ) ) @ ( produc2838810277069100634it_nat @ ( produc6991280839920081578it_nat @ ( the_Pr5856008525237892824it_nat @ ( heap_T5591663578999710211rray_a @ F @ H3 ) ) ) ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % execute_bind_success
% 0.33/0.64 thf(fact_6506_execute__bind__success,axiom,
% 0.33/0.64 ! [F: heap_T6362127782908069795rray_a,H3: heap_e7401611519738050253t_unit,G: array_a > heap_T5738788834812785303t_unit] :
% 0.33/0.64 ( ( heap_T6932021131025641745rray_a @ F @ H3 )
% 0.33/0.64 => ( ( heap_T875086893843062177t_unit @ ( heap_T7324619625323989613t_unit @ F @ G ) @ H3 )
% 0.33/0.64 = ( heap_T3616969660504097270t_unit @ ( produc2594868675584459928it_nat @ ( produc6991280839920081578it_nat @ ( the_Pr5856008525237892824it_nat @ ( heap_T5591663578999710211rray_a @ F @ H3 ) ) ) ) @ ( heap_T875086893843062177t_unit @ ( G @ ( produc491454361838572648it_nat @ ( the_Pr5856008525237892824it_nat @ ( heap_T5591663578999710211rray_a @ F @ H3 ) ) ) ) @ ( produc2838810277069100634it_nat @ ( produc6991280839920081578it_nat @ ( the_Pr5856008525237892824it_nat @ ( heap_T5591663578999710211rray_a @ F @ H3 ) ) ) ) ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % execute_bind_success
% 0.33/0.64 thf(fact_6507_sndI,axiom,
% 0.33/0.64 ! [X: produc1908205239877642774nteger,Y: produc6241069584506657477e_term > option6357759511663192854e_term,Z: produc8923325533196201883nteger] :
% 0.33/0.64 ( ( X
% 0.33/0.64 = ( produc8603105652947943368nteger @ Y @ Z ) )
% 0.33/0.64 => ( ( produc7856867400915047194nteger @ X )
% 0.33/0.64 = Z ) ) ).
% 0.33/0.64
% 0.33/0.64 % sndI
% 0.33/0.64 thf(fact_6508_sndI,axiom,
% 0.33/0.64 ! [X: produc3925858234332021118et_nat,Y: produc3658429121746597890et_nat > $o,Z: produc3658429121746597890et_nat] :
% 0.33/0.64 ( ( X
% 0.33/0.64 = ( produc5001842942810119800et_nat @ Y @ Z ) )
% 0.33/0.64 => ( ( produc4011572625026189258et_nat @ X )
% 0.33/0.64 = Z ) ) ).
% 0.33/0.64
% 0.33/0.64 % sndI
% 0.33/0.64 thf(fact_6509_sndI,axiom,
% 0.33/0.64 ! [X: produc2732055786443039994et_nat,Y: produc3658429121746597890et_nat > $o,Z: produc3925858234332021118et_nat] :
% 0.33/0.64 ( ( X
% 0.33/0.64 = ( produc2245416461498447860et_nat @ Y @ Z ) )
% 0.33/0.64 => ( ( produc5374455773327741254et_nat @ X )
% 0.33/0.64 = Z ) ) ).
% 0.33/0.64
% 0.33/0.64 % sndI
% 0.33/0.64 thf(fact_6510_sndI,axiom,
% 0.33/0.64 ! [X: produc2285326912895808259nt_int,Y: produc8551481072490612790e_term > option6357759511663192854e_term,Z: product_prod_int_int] :
% 0.33/0.64 ( ( X
% 0.33/0.64 = ( produc5700946648718959541nt_int @ Y @ Z ) )
% 0.33/0.64 => ( ( produc7328097813583171335nt_int @ X )
% 0.33/0.64 = Z ) ) ).
% 0.33/0.64
% 0.33/0.64 % sndI
% 0.33/0.64 thf(fact_6511_sndI,axiom,
% 0.33/0.64 ! [X: produc7773217078559923341nt_int,Y: int > option6357759511663192854e_term,Z: product_prod_int_int] :
% 0.33/0.64 ( ( X
% 0.33/0.64 = ( produc4305682042979456191nt_int @ Y @ Z ) )
% 0.33/0.64 => ( ( produc3162348030201620241nt_int @ X )
% 0.33/0.64 = Z ) ) ).
% 0.33/0.64
% 0.33/0.64 % sndI
% 0.33/0.64 thf(fact_6512_sndI,axiom,
% 0.33/0.64 ! [X: produc8923325533196201883nteger,Y: code_integer,Z: code_integer] :
% 0.33/0.64 ( ( X
% 0.33/0.64 = ( produc1086072967326762835nteger @ Y @ Z ) )
% 0.33/0.64 => ( ( produc6174133586879617921nteger @ X )
% 0.33/0.64 = Z ) ) ).
% 0.33/0.64
% 0.33/0.64 % sndI
% 0.33/0.64 thf(fact_6513_sndI,axiom,
% 0.33/0.64 ! [X: product_prod_int_int,Y: int,Z: int] :
% 0.33/0.64 ( ( X
% 0.33/0.64 = ( product_Pair_int_int @ Y @ Z ) )
% 0.33/0.64 => ( ( product_snd_int_int @ X )
% 0.33/0.64 = Z ) ) ).
% 0.33/0.64
% 0.33/0.64 % sndI
% 0.33/0.64 thf(fact_6514_sndI,axiom,
% 0.33/0.64 ! [X: produc5835291356934675326atural,Y: code_natural,Z: produc7822875418678951345atural] :
% 0.33/0.64 ( ( X
% 0.33/0.64 = ( produc6639722614265839536atural @ Y @ Z ) )
% 0.33/0.64 => ( ( produc6591912806276919810atural @ X )
% 0.33/0.64 = Z ) ) ).
% 0.33/0.64
% 0.33/0.64 % sndI
% 0.33/0.64 thf(fact_6515_sndE,axiom,
% 0.33/0.64 ! [X: produc1908205239877642774nteger,A: produc6241069584506657477e_term > option6357759511663192854e_term,B: produc8923325533196201883nteger,P: produc8923325533196201883nteger > $o] :
% 0.33/0.64 ( ( X
% 0.33/0.64 = ( produc8603105652947943368nteger @ A @ B ) )
% 0.33/0.64 => ( ( P @ ( produc7856867400915047194nteger @ X ) )
% 0.33/0.64 => ( P @ B ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % sndE
% 0.33/0.64 thf(fact_6516_sndE,axiom,
% 0.33/0.64 ! [X: produc3925858234332021118et_nat,A: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat,P: produc3658429121746597890et_nat > $o] :
% 0.33/0.64 ( ( X
% 0.33/0.64 = ( produc5001842942810119800et_nat @ A @ B ) )
% 0.33/0.64 => ( ( P @ ( produc4011572625026189258et_nat @ X ) )
% 0.33/0.64 => ( P @ B ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % sndE
% 0.33/0.64 thf(fact_6517_sndE,axiom,
% 0.33/0.64 ! [X: produc2732055786443039994et_nat,A: produc3658429121746597890et_nat > $o,B: produc3925858234332021118et_nat,P: produc3925858234332021118et_nat > $o] :
% 0.33/0.64 ( ( X
% 0.33/0.64 = ( produc2245416461498447860et_nat @ A @ B ) )
% 0.33/0.64 => ( ( P @ ( produc5374455773327741254et_nat @ X ) )
% 0.33/0.64 => ( P @ B ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % sndE
% 0.33/0.64 thf(fact_6518_sndE,axiom,
% 0.33/0.64 ! [X: produc2285326912895808259nt_int,A: produc8551481072490612790e_term > option6357759511663192854e_term,B: product_prod_int_int,P: product_prod_int_int > $o] :
% 0.33/0.64 ( ( X
% 0.33/0.64 = ( produc5700946648718959541nt_int @ A @ B ) )
% 0.33/0.64 => ( ( P @ ( produc7328097813583171335nt_int @ X ) )
% 0.33/0.64 => ( P @ B ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % sndE
% 0.33/0.64 thf(fact_6519_sndE,axiom,
% 0.33/0.64 ! [X: produc7773217078559923341nt_int,A: int > option6357759511663192854e_term,B: product_prod_int_int,P: product_prod_int_int > $o] :
% 0.33/0.64 ( ( X
% 0.33/0.64 = ( produc4305682042979456191nt_int @ A @ B ) )
% 0.33/0.64 => ( ( P @ ( produc3162348030201620241nt_int @ X ) )
% 0.33/0.64 => ( P @ B ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % sndE
% 0.33/0.64 thf(fact_6520_sndE,axiom,
% 0.33/0.64 ! [X: produc8923325533196201883nteger,A: code_integer,B: code_integer,P: code_integer > $o] :
% 0.33/0.64 ( ( X
% 0.33/0.64 = ( produc1086072967326762835nteger @ A @ B ) )
% 0.33/0.64 => ( ( P @ ( produc6174133586879617921nteger @ X ) )
% 0.33/0.64 => ( P @ B ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % sndE
% 0.33/0.64 thf(fact_6521_sndE,axiom,
% 0.33/0.64 ! [X: product_prod_int_int,A: int,B: int,P: int > $o] :
% 0.33/0.64 ( ( X
% 0.33/0.64 = ( product_Pair_int_int @ A @ B ) )
% 0.33/0.64 => ( ( P @ ( product_snd_int_int @ X ) )
% 0.33/0.64 => ( P @ B ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % sndE
% 0.33/0.64 thf(fact_6522_sndE,axiom,
% 0.33/0.64 ! [X: produc5835291356934675326atural,A: code_natural,B: produc7822875418678951345atural,P: produc7822875418678951345atural > $o] :
% 0.33/0.64 ( ( X
% 0.33/0.64 = ( produc6639722614265839536atural @ A @ B ) )
% 0.33/0.64 => ( ( P @ ( produc6591912806276919810atural @ X ) )
% 0.33/0.64 => ( P @ B ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % sndE
% 0.33/0.64 thf(fact_6523_snd__eqD,axiom,
% 0.33/0.64 ! [X: produc6241069584506657477e_term > option6357759511663192854e_term,Y: produc8923325533196201883nteger,A: produc8923325533196201883nteger] :
% 0.33/0.64 ( ( ( produc7856867400915047194nteger @ ( produc8603105652947943368nteger @ X @ Y ) )
% 0.33/0.64 = A )
% 0.33/0.64 => ( Y = A ) ) ).
% 0.33/0.64
% 0.33/0.64 % snd_eqD
% 0.33/0.64 thf(fact_6524_snd__eqD,axiom,
% 0.33/0.64 ! [X: produc3658429121746597890et_nat > $o,Y: produc3658429121746597890et_nat,A: produc3658429121746597890et_nat] :
% 0.33/0.64 ( ( ( produc4011572625026189258et_nat @ ( produc5001842942810119800et_nat @ X @ Y ) )
% 0.33/0.64 = A )
% 0.33/0.64 => ( Y = A ) ) ).
% 0.33/0.64
% 0.33/0.64 % snd_eqD
% 0.33/0.64 thf(fact_6525_snd__eqD,axiom,
% 0.33/0.64 ! [X: produc3658429121746597890et_nat > $o,Y: produc3925858234332021118et_nat,A: produc3925858234332021118et_nat] :
% 0.33/0.64 ( ( ( produc5374455773327741254et_nat @ ( produc2245416461498447860et_nat @ X @ Y ) )
% 0.33/0.64 = A )
% 0.33/0.64 => ( Y = A ) ) ).
% 0.33/0.64
% 0.33/0.64 % snd_eqD
% 0.33/0.64 thf(fact_6526_snd__eqD,axiom,
% 0.33/0.64 ! [X: produc8551481072490612790e_term > option6357759511663192854e_term,Y: product_prod_int_int,A: product_prod_int_int] :
% 0.33/0.64 ( ( ( produc7328097813583171335nt_int @ ( produc5700946648718959541nt_int @ X @ Y ) )
% 0.33/0.64 = A )
% 0.33/0.64 => ( Y = A ) ) ).
% 0.33/0.64
% 0.33/0.64 % snd_eqD
% 0.33/0.64 thf(fact_6527_snd__eqD,axiom,
% 0.33/0.64 ! [X: int > option6357759511663192854e_term,Y: product_prod_int_int,A: product_prod_int_int] :
% 0.33/0.64 ( ( ( produc3162348030201620241nt_int @ ( produc4305682042979456191nt_int @ X @ Y ) )
% 0.33/0.64 = A )
% 0.33/0.64 => ( Y = A ) ) ).
% 0.33/0.64
% 0.33/0.64 % snd_eqD
% 0.33/0.64 thf(fact_6528_snd__eqD,axiom,
% 0.33/0.64 ! [X: code_integer,Y: code_integer,A: code_integer] :
% 0.33/0.64 ( ( ( produc6174133586879617921nteger @ ( produc1086072967326762835nteger @ X @ Y ) )
% 0.33/0.64 = A )
% 0.33/0.64 => ( Y = A ) ) ).
% 0.33/0.64
% 0.33/0.64 % snd_eqD
% 0.33/0.64 thf(fact_6529_snd__eqD,axiom,
% 0.33/0.64 ! [X: int,Y: int,A: int] :
% 0.33/0.64 ( ( ( product_snd_int_int @ ( product_Pair_int_int @ X @ Y ) )
% 0.33/0.64 = A )
% 0.33/0.64 => ( Y = A ) ) ).
% 0.33/0.64
% 0.33/0.64 % snd_eqD
% 0.33/0.64 thf(fact_6530_snd__eqD,axiom,
% 0.33/0.64 ! [X: code_natural,Y: produc7822875418678951345atural,A: produc7822875418678951345atural] :
% 0.33/0.64 ( ( ( produc6591912806276919810atural @ ( produc6639722614265839536atural @ X @ Y ) )
% 0.33/0.64 = A )
% 0.33/0.64 => ( Y = A ) ) ).
% 0.33/0.64
% 0.33/0.64 % snd_eqD
% 0.33/0.64 thf(fact_6531_snd__conv,axiom,
% 0.33/0.64 ! [X1: produc6241069584506657477e_term > option6357759511663192854e_term,X2: produc8923325533196201883nteger] :
% 0.33/0.64 ( ( produc7856867400915047194nteger @ ( produc8603105652947943368nteger @ X1 @ X2 ) )
% 0.33/0.64 = X2 ) ).
% 0.33/0.64
% 0.33/0.64 % snd_conv
% 0.33/0.64 thf(fact_6532_snd__conv,axiom,
% 0.33/0.64 ! [X1: produc3658429121746597890et_nat > $o,X2: produc3658429121746597890et_nat] :
% 0.33/0.64 ( ( produc4011572625026189258et_nat @ ( produc5001842942810119800et_nat @ X1 @ X2 ) )
% 0.33/0.64 = X2 ) ).
% 0.33/0.64
% 0.33/0.64 % snd_conv
% 0.33/0.64 thf(fact_6533_snd__conv,axiom,
% 0.33/0.64 ! [X1: produc3658429121746597890et_nat > $o,X2: produc3925858234332021118et_nat] :
% 0.33/0.64 ( ( produc5374455773327741254et_nat @ ( produc2245416461498447860et_nat @ X1 @ X2 ) )
% 0.33/0.64 = X2 ) ).
% 0.33/0.64
% 0.33/0.64 % snd_conv
% 0.33/0.64 thf(fact_6534_snd__conv,axiom,
% 0.33/0.64 ! [X1: produc8551481072490612790e_term > option6357759511663192854e_term,X2: product_prod_int_int] :
% 0.33/0.64 ( ( produc7328097813583171335nt_int @ ( produc5700946648718959541nt_int @ X1 @ X2 ) )
% 0.33/0.64 = X2 ) ).
% 0.33/0.64
% 0.33/0.64 % snd_conv
% 0.33/0.64 thf(fact_6535_snd__conv,axiom,
% 0.33/0.64 ! [X1: int > option6357759511663192854e_term,X2: product_prod_int_int] :
% 0.33/0.64 ( ( produc3162348030201620241nt_int @ ( produc4305682042979456191nt_int @ X1 @ X2 ) )
% 0.33/0.64 = X2 ) ).
% 0.33/0.64
% 0.33/0.64 % snd_conv
% 0.33/0.64 thf(fact_6536_snd__conv,axiom,
% 0.33/0.64 ! [X1: code_integer,X2: code_integer] :
% 0.33/0.64 ( ( produc6174133586879617921nteger @ ( produc1086072967326762835nteger @ X1 @ X2 ) )
% 0.33/0.64 = X2 ) ).
% 0.33/0.64
% 0.33/0.64 % snd_conv
% 0.33/0.64 thf(fact_6537_snd__conv,axiom,
% 0.33/0.64 ! [X1: int,X2: int] :
% 0.33/0.64 ( ( product_snd_int_int @ ( product_Pair_int_int @ X1 @ X2 ) )
% 0.33/0.64 = X2 ) ).
% 0.33/0.64
% 0.33/0.64 % snd_conv
% 0.33/0.64 thf(fact_6538_snd__conv,axiom,
% 0.33/0.64 ! [X1: code_natural,X2: produc7822875418678951345atural] :
% 0.33/0.64 ( ( produc6591912806276919810atural @ ( produc6639722614265839536atural @ X1 @ X2 ) )
% 0.33/0.64 = X2 ) ).
% 0.33/0.64
% 0.33/0.64 % snd_conv
% 0.33/0.64 thf(fact_6539_Some__Inf,axiom,
% 0.33/0.64 ! [A2: set_set_nat] :
% 0.33/0.64 ( ( some_set_nat @ ( comple7806235888213564991et_nat @ A2 ) )
% 0.33/0.64 = ( comple3446467376476514063et_nat @ ( image_838307146230912995et_nat @ some_set_nat @ A2 ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % Some_Inf
% 0.33/0.64 thf(fact_6540_Some__Inf,axiom,
% 0.33/0.64 ! [A2: set_Product_unit] :
% 0.33/0.64 ( ( some_Product_unit @ ( comple2584293577114468500t_unit @ A2 ) )
% 0.33/0.64 = ( comple5564859526659248602t_unit @ ( image_7094380055901048587t_unit @ some_Product_unit @ A2 ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % Some_Inf
% 0.33/0.64 thf(fact_6541_fstI,axiom,
% 0.33/0.64 ! [X: produc1908205239877642774nteger,Y: produc6241069584506657477e_term > option6357759511663192854e_term,Z: produc8923325533196201883nteger] :
% 0.33/0.64 ( ( X
% 0.33/0.64 = ( produc8603105652947943368nteger @ Y @ Z ) )
% 0.33/0.64 => ( ( produc7822682618958472924nteger @ X )
% 0.33/0.64 = Y ) ) ).
% 0.33/0.64
% 0.33/0.64 % fstI
% 0.33/0.64 thf(fact_6542_fstI,axiom,
% 0.33/0.64 ! [X: produc3925858234332021118et_nat,Y: produc3658429121746597890et_nat > $o,Z: produc3658429121746597890et_nat] :
% 0.33/0.64 ( ( X
% 0.33/0.64 = ( produc5001842942810119800et_nat @ Y @ Z ) )
% 0.33/0.64 => ( ( produc995936583742144908et_nat @ X )
% 0.33/0.64 = Y ) ) ).
% 0.33/0.64
% 0.33/0.64 % fstI
% 0.33/0.64 thf(fact_6543_fstI,axiom,
% 0.33/0.64 ! [X: produc2732055786443039994et_nat,Y: produc3658429121746597890et_nat > $o,Z: produc3925858234332021118et_nat] :
% 0.33/0.64 ( ( X
% 0.33/0.64 = ( produc2245416461498447860et_nat @ Y @ Z ) )
% 0.33/0.64 => ( ( produc180342877477747464et_nat @ X )
% 0.33/0.64 = Y ) ) ).
% 0.33/0.64
% 0.33/0.64 % fstI
% 0.33/0.64 thf(fact_6544_fstI,axiom,
% 0.33/0.64 ! [X: produc2285326912895808259nt_int,Y: produc8551481072490612790e_term > option6357759511663192854e_term,Z: product_prod_int_int] :
% 0.33/0.64 ( ( X
% 0.33/0.64 = ( produc5700946648718959541nt_int @ Y @ Z ) )
% 0.33/0.64 => ( ( produc6816164490631068361nt_int @ X )
% 0.33/0.64 = Y ) ) ).
% 0.33/0.64
% 0.33/0.64 % fstI
% 0.33/0.64 thf(fact_6545_fstI,axiom,
% 0.33/0.64 ! [X: produc7773217078559923341nt_int,Y: int > option6357759511663192854e_term,Z: product_prod_int_int] :
% 0.33/0.64 ( ( X
% 0.33/0.64 = ( produc4305682042979456191nt_int @ Y @ Z ) )
% 0.33/0.64 => ( ( produc6230002227079971283nt_int @ X )
% 0.33/0.64 = Y ) ) ).
% 0.33/0.64
% 0.33/0.64 % fstI
% 0.33/0.64 thf(fact_6546_fstI,axiom,
% 0.33/0.64 ! [X: produc8923325533196201883nteger,Y: code_integer,Z: code_integer] :
% 0.33/0.64 ( ( X
% 0.33/0.64 = ( produc1086072967326762835nteger @ Y @ Z ) )
% 0.33/0.64 => ( ( produc8508995932063986495nteger @ X )
% 0.33/0.64 = Y ) ) ).
% 0.33/0.64
% 0.33/0.64 % fstI
% 0.33/0.64 thf(fact_6547_fstI,axiom,
% 0.33/0.64 ! [X: product_prod_int_int,Y: int,Z: int] :
% 0.33/0.64 ( ( X
% 0.33/0.64 = ( product_Pair_int_int @ Y @ Z ) )
% 0.33/0.64 => ( ( product_fst_int_int @ X )
% 0.33/0.64 = Y ) ) ).
% 0.33/0.64
% 0.33/0.64 % fstI
% 0.33/0.64 thf(fact_6548_fstE,axiom,
% 0.33/0.64 ! [X: produc1908205239877642774nteger,A: produc6241069584506657477e_term > option6357759511663192854e_term,B: produc8923325533196201883nteger,P: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > $o] :
% 0.33/0.64 ( ( X
% 0.33/0.64 = ( produc8603105652947943368nteger @ A @ B ) )
% 0.33/0.64 => ( ( P @ ( produc7822682618958472924nteger @ X ) )
% 0.33/0.64 => ( P @ A ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % fstE
% 0.33/0.64 thf(fact_6549_fstE,axiom,
% 0.33/0.64 ! [X: produc3925858234332021118et_nat,A: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat,P: ( produc3658429121746597890et_nat > $o ) > $o] :
% 0.33/0.64 ( ( X
% 0.33/0.64 = ( produc5001842942810119800et_nat @ A @ B ) )
% 0.33/0.64 => ( ( P @ ( produc995936583742144908et_nat @ X ) )
% 0.33/0.64 => ( P @ A ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % fstE
% 0.33/0.64 thf(fact_6550_fstE,axiom,
% 0.33/0.64 ! [X: produc2732055786443039994et_nat,A: produc3658429121746597890et_nat > $o,B: produc3925858234332021118et_nat,P: ( produc3658429121746597890et_nat > $o ) > $o] :
% 0.33/0.64 ( ( X
% 0.33/0.64 = ( produc2245416461498447860et_nat @ A @ B ) )
% 0.33/0.64 => ( ( P @ ( produc180342877477747464et_nat @ X ) )
% 0.33/0.64 => ( P @ A ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % fstE
% 0.33/0.64 thf(fact_6551_fstE,axiom,
% 0.33/0.64 ! [X: produc2285326912895808259nt_int,A: produc8551481072490612790e_term > option6357759511663192854e_term,B: product_prod_int_int,P: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > $o] :
% 0.33/0.64 ( ( X
% 0.33/0.64 = ( produc5700946648718959541nt_int @ A @ B ) )
% 0.33/0.64 => ( ( P @ ( produc6816164490631068361nt_int @ X ) )
% 0.33/0.64 => ( P @ A ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % fstE
% 0.33/0.64 thf(fact_6552_fstE,axiom,
% 0.33/0.64 ! [X: produc7773217078559923341nt_int,A: int > option6357759511663192854e_term,B: product_prod_int_int,P: ( int > option6357759511663192854e_term ) > $o] :
% 0.33/0.64 ( ( X
% 0.33/0.64 = ( produc4305682042979456191nt_int @ A @ B ) )
% 0.33/0.64 => ( ( P @ ( produc6230002227079971283nt_int @ X ) )
% 0.33/0.64 => ( P @ A ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % fstE
% 0.33/0.64 thf(fact_6553_fstE,axiom,
% 0.33/0.64 ! [X: produc8923325533196201883nteger,A: code_integer,B: code_integer,P: code_integer > $o] :
% 0.33/0.64 ( ( X
% 0.33/0.64 = ( produc1086072967326762835nteger @ A @ B ) )
% 0.33/0.64 => ( ( P @ ( produc8508995932063986495nteger @ X ) )
% 0.33/0.64 => ( P @ A ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % fstE
% 0.33/0.64 thf(fact_6554_fstE,axiom,
% 0.33/0.64 ! [X: product_prod_int_int,A: int,B: int,P: int > $o] :
% 0.33/0.64 ( ( X
% 0.33/0.64 = ( product_Pair_int_int @ A @ B ) )
% 0.33/0.64 => ( ( P @ ( product_fst_int_int @ X ) )
% 0.33/0.64 => ( P @ A ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % fstE
% 0.33/0.64 thf(fact_6555_fst__eqD,axiom,
% 0.33/0.64 ! [X: produc6241069584506657477e_term > option6357759511663192854e_term,Y: produc8923325533196201883nteger,A: produc6241069584506657477e_term > option6357759511663192854e_term] :
% 0.33/0.64 ( ( ( produc7822682618958472924nteger @ ( produc8603105652947943368nteger @ X @ Y ) )
% 0.33/0.64 = A )
% 0.33/0.64 => ( X = A ) ) ).
% 0.33/0.64
% 0.33/0.64 % fst_eqD
% 0.33/0.64 thf(fact_6556_fst__eqD,axiom,
% 0.33/0.64 ! [X: produc3658429121746597890et_nat > $o,Y: produc3658429121746597890et_nat,A: produc3658429121746597890et_nat > $o] :
% 0.33/0.64 ( ( ( produc995936583742144908et_nat @ ( produc5001842942810119800et_nat @ X @ Y ) )
% 0.33/0.64 = A )
% 0.33/0.64 => ( X = A ) ) ).
% 0.33/0.64
% 0.33/0.64 % fst_eqD
% 0.33/0.64 thf(fact_6557_fst__eqD,axiom,
% 0.33/0.64 ! [X: produc3658429121746597890et_nat > $o,Y: produc3925858234332021118et_nat,A: produc3658429121746597890et_nat > $o] :
% 0.33/0.64 ( ( ( produc180342877477747464et_nat @ ( produc2245416461498447860et_nat @ X @ Y ) )
% 0.33/0.64 = A )
% 0.33/0.64 => ( X = A ) ) ).
% 0.33/0.64
% 0.33/0.64 % fst_eqD
% 0.33/0.64 thf(fact_6558_fst__eqD,axiom,
% 0.33/0.64 ! [X: produc8551481072490612790e_term > option6357759511663192854e_term,Y: product_prod_int_int,A: produc8551481072490612790e_term > option6357759511663192854e_term] :
% 0.33/0.64 ( ( ( produc6816164490631068361nt_int @ ( produc5700946648718959541nt_int @ X @ Y ) )
% 0.33/0.64 = A )
% 0.33/0.64 => ( X = A ) ) ).
% 0.33/0.64
% 0.33/0.64 % fst_eqD
% 0.33/0.64 thf(fact_6559_fst__eqD,axiom,
% 0.33/0.64 ! [X: int > option6357759511663192854e_term,Y: product_prod_int_int,A: int > option6357759511663192854e_term] :
% 0.33/0.64 ( ( ( produc6230002227079971283nt_int @ ( produc4305682042979456191nt_int @ X @ Y ) )
% 0.33/0.64 = A )
% 0.33/0.64 => ( X = A ) ) ).
% 0.33/0.64
% 0.33/0.64 % fst_eqD
% 0.33/0.64 thf(fact_6560_fst__eqD,axiom,
% 0.33/0.64 ! [X: code_integer,Y: code_integer,A: code_integer] :
% 0.33/0.64 ( ( ( produc8508995932063986495nteger @ ( produc1086072967326762835nteger @ X @ Y ) )
% 0.33/0.64 = A )
% 0.33/0.64 => ( X = A ) ) ).
% 0.33/0.64
% 0.33/0.64 % fst_eqD
% 0.33/0.64 thf(fact_6561_fst__eqD,axiom,
% 0.33/0.64 ! [X: int,Y: int,A: int] :
% 0.33/0.64 ( ( ( product_fst_int_int @ ( product_Pair_int_int @ X @ Y ) )
% 0.33/0.64 = A )
% 0.33/0.64 => ( X = A ) ) ).
% 0.33/0.64
% 0.33/0.64 % fst_eqD
% 0.33/0.64 thf(fact_6562_fst__conv,axiom,
% 0.33/0.64 ! [X1: produc6241069584506657477e_term > option6357759511663192854e_term,X2: produc8923325533196201883nteger] :
% 0.33/0.64 ( ( produc7822682618958472924nteger @ ( produc8603105652947943368nteger @ X1 @ X2 ) )
% 0.33/0.64 = X1 ) ).
% 0.33/0.64
% 0.33/0.64 % fst_conv
% 0.33/0.64 thf(fact_6563_fst__conv,axiom,
% 0.33/0.64 ! [X1: produc3658429121746597890et_nat > $o,X2: produc3658429121746597890et_nat] :
% 0.33/0.64 ( ( produc995936583742144908et_nat @ ( produc5001842942810119800et_nat @ X1 @ X2 ) )
% 0.33/0.64 = X1 ) ).
% 0.33/0.64
% 0.33/0.64 % fst_conv
% 0.33/0.64 thf(fact_6564_fst__conv,axiom,
% 0.33/0.64 ! [X1: produc3658429121746597890et_nat > $o,X2: produc3925858234332021118et_nat] :
% 0.33/0.64 ( ( produc180342877477747464et_nat @ ( produc2245416461498447860et_nat @ X1 @ X2 ) )
% 0.33/0.64 = X1 ) ).
% 0.33/0.64
% 0.33/0.64 % fst_conv
% 0.33/0.64 thf(fact_6565_fst__conv,axiom,
% 0.33/0.64 ! [X1: produc8551481072490612790e_term > option6357759511663192854e_term,X2: product_prod_int_int] :
% 0.33/0.64 ( ( produc6816164490631068361nt_int @ ( produc5700946648718959541nt_int @ X1 @ X2 ) )
% 0.33/0.64 = X1 ) ).
% 0.33/0.64
% 0.33/0.64 % fst_conv
% 0.33/0.64 thf(fact_6566_fst__conv,axiom,
% 0.33/0.64 ! [X1: int > option6357759511663192854e_term,X2: product_prod_int_int] :
% 0.33/0.64 ( ( produc6230002227079971283nt_int @ ( produc4305682042979456191nt_int @ X1 @ X2 ) )
% 0.33/0.64 = X1 ) ).
% 0.33/0.64
% 0.33/0.64 % fst_conv
% 0.33/0.64 thf(fact_6567_fst__conv,axiom,
% 0.33/0.64 ! [X1: code_integer,X2: code_integer] :
% 0.33/0.64 ( ( produc8508995932063986495nteger @ ( produc1086072967326762835nteger @ X1 @ X2 ) )
% 0.33/0.64 = X1 ) ).
% 0.33/0.64
% 0.33/0.64 % fst_conv
% 0.33/0.64 thf(fact_6568_fst__conv,axiom,
% 0.33/0.64 ! [X1: int,X2: int] :
% 0.33/0.64 ( ( product_fst_int_int @ ( product_Pair_int_int @ X1 @ X2 ) )
% 0.33/0.64 = X1 ) ).
% 0.33/0.64
% 0.33/0.64 % fst_conv
% 0.33/0.64 thf(fact_6569_snd__fst__flip,axiom,
% 0.33/0.64 ( produc1152141638515386128e_term
% 0.33/0.64 = ( comp_P8650103696410638905e_term @ produc7822682618958472924nteger
% 0.33/0.64 @ ( produc5068368601420144385nteger
% 0.33/0.64 @ ^ [X3: produc8923325533196201883nteger,Y3: produc6241069584506657477e_term > option6357759511663192854e_term] : ( produc8603105652947943368nteger @ Y3 @ X3 ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % snd_fst_flip
% 0.33/0.64 thf(fact_6570_snd__fst__flip,axiom,
% 0.33/0.64 ( produc1838968430882301508_nat_o
% 0.33/0.64 = ( comp_P1110778729668777324_nat_o @ produc995936583742144908et_nat
% 0.33/0.64 @ ( produc5206072795621629085et_nat
% 0.33/0.64 @ ^ [X3: produc3658429121746597890et_nat,Y3: produc3658429121746597890et_nat > $o] : ( produc5001842942810119800et_nat @ Y3 @ X3 ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % snd_fst_flip
% 0.33/0.64 thf(fact_6571_snd__fst__flip,axiom,
% 0.33/0.64 ( produc6803565743942592456_nat_o
% 0.33/0.64 = ( comp_P4355506512671352436_nat_o @ produc180342877477747464et_nat
% 0.33/0.64 @ ( produc9203276081649983901et_nat
% 0.33/0.64 @ ^ [X3: produc3925858234332021118et_nat,Y3: produc3658429121746597890et_nat > $o] : ( produc2245416461498447860et_nat @ Y3 @ X3 ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % snd_fst_flip
% 0.33/0.64 thf(fact_6572_snd__fst__flip,axiom,
% 0.33/0.64 ( produc6847057335086834975e_term
% 0.33/0.64 = ( comp_P8577347034251779110e_term @ produc6816164490631068361nt_int
% 0.33/0.64 @ ( produc199769199162113789nt_int
% 0.33/0.64 @ ^ [X3: product_prod_int_int,Y3: produc8551481072490612790e_term > option6357759511663192854e_term] : ( produc5700946648718959541nt_int @ Y3 @ X3 ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % snd_fst_flip
% 0.33/0.64 thf(fact_6573_snd__fst__flip,axiom,
% 0.33/0.64 ( produc6373639247523685013e_term
% 0.33/0.64 = ( comp_P1875353012086385820e_term @ produc6230002227079971283nt_int
% 0.33/0.64 @ ( produc3478612561300218621nt_int
% 0.33/0.64 @ ^ [X3: product_prod_int_int,Y3: int > option6357759511663192854e_term] : ( produc4305682042979456191nt_int @ Y3 @ X3 ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % snd_fst_flip
% 0.33/0.64 thf(fact_6574_snd__fst__flip,axiom,
% 0.33/0.64 ( produc6174133586879617921nteger
% 0.33/0.64 = ( comp_P3428181540658402820nteger @ produc8508995932063986495nteger
% 0.33/0.64 @ ( produc6916734918728496179nteger
% 0.33/0.64 @ ^ [X3: code_integer,Y3: code_integer] : ( produc1086072967326762835nteger @ Y3 @ X3 ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % snd_fst_flip
% 0.33/0.64 thf(fact_6575_snd__fst__flip,axiom,
% 0.33/0.64 ( produc6591912806276919810atural
% 0.33/0.64 = ( comp_P3887058762840424708atural @ produc4353917038236142998atural
% 0.33/0.64 @ ( produc6785097126449100389atural
% 0.33/0.64 @ ^ [X3: code_natural,Y3: produc7822875418678951345atural] : ( produc1272419604612767874atural @ Y3 @ X3 ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % snd_fst_flip
% 0.33/0.64 thf(fact_6576_snd__fst__flip,axiom,
% 0.33/0.64 ( product_snd_int_int
% 0.33/0.64 = ( comp_P5356232565778667509nt_int @ product_fst_int_int
% 0.33/0.64 @ ( produc4245557441103728435nt_int
% 0.33/0.64 @ ^ [X3: int,Y3: int] : ( product_Pair_int_int @ Y3 @ X3 ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % snd_fst_flip
% 0.33/0.64 thf(fact_6577_fst__snd__flip,axiom,
% 0.33/0.64 ( produc1117956856558811858e_term
% 0.33/0.64 = ( comp_P1663382703091044646e_term @ produc7856867400915047194nteger
% 0.33/0.64 @ ( produc5068368601420144385nteger
% 0.33/0.64 @ ^ [X3: produc8923325533196201883nteger,Y3: produc6241069584506657477e_term > option6357759511663192854e_term] : ( produc8603105652947943368nteger @ Y3 @ X3 ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % fst_snd_flip
% 0.33/0.64 thf(fact_6578_fst__snd__flip,axiom,
% 0.33/0.64 ( produc8046704426453032966_nat_o
% 0.33/0.64 = ( comp_P5089495125153697957_nat_o @ produc4011572625026189258et_nat
% 0.33/0.64 @ ( produc5206072795621629085et_nat
% 0.33/0.64 @ ^ [X3: produc3658429121746597890et_nat,Y3: produc3658429121746597890et_nat > $o] : ( produc5001842942810119800et_nat @ Y3 @ X3 ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % fst_snd_flip
% 0.33/0.64 thf(fact_6579_fst__snd__flip,axiom,
% 0.33/0.64 ( produc1609452848092598666_nat_o
% 0.33/0.64 = ( comp_P9183373265949749025_nat_o @ produc5374455773327741254et_nat
% 0.33/0.64 @ ( produc9203276081649983901et_nat
% 0.33/0.64 @ ^ [X3: produc3925858234332021118et_nat,Y3: produc3658429121746597890et_nat > $o] : ( produc2245416461498447860et_nat @ Y3 @ X3 ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % fst_snd_flip
% 0.33/0.64 thf(fact_6580_fst__snd__flip,axiom,
% 0.33/0.64 ( produc6335124012134732001e_term
% 0.33/0.64 = ( comp_P4057098934159210662e_term @ produc7328097813583171335nt_int
% 0.33/0.64 @ ( produc199769199162113789nt_int
% 0.33/0.64 @ ^ [X3: product_prod_int_int,Y3: produc8551481072490612790e_term > option6357759511663192854e_term] : ( produc5700946648718959541nt_int @ Y3 @ X3 ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % fst_snd_flip
% 0.33/0.64 thf(fact_6581_fst__snd__flip,axiom,
% 0.33/0.64 ( produc217921407547260247e_term
% 0.33/0.64 = ( comp_P5363713469694551954e_term @ produc3162348030201620241nt_int
% 0.33/0.64 @ ( produc3478612561300218621nt_int
% 0.33/0.64 @ ^ [X3: product_prod_int_int,Y3: int > option6357759511663192854e_term] : ( produc4305682042979456191nt_int @ Y3 @ X3 ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % fst_snd_flip
% 0.33/0.64 thf(fact_6582_fst__snd__flip,axiom,
% 0.33/0.64 ( produc8508995932063986495nteger
% 0.33/0.64 = ( comp_P3428181540658402820nteger @ produc6174133586879617921nteger
% 0.33/0.64 @ ( produc6916734918728496179nteger
% 0.33/0.64 @ ^ [X3: code_integer,Y3: code_integer] : ( produc1086072967326762835nteger @ Y3 @ X3 ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % fst_snd_flip
% 0.33/0.64 thf(fact_6583_fst__snd__flip,axiom,
% 0.33/0.64 ( produc4353917038236142998atural
% 0.33/0.64 = ( comp_P5756991293874479000atural @ produc6591912806276919810atural
% 0.33/0.64 @ ( produc1198152457851389869atural
% 0.33/0.64 @ ^ [X3: produc7822875418678951345atural,Y3: code_natural] : ( produc6639722614265839536atural @ Y3 @ X3 ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % fst_snd_flip
% 0.33/0.64 thf(fact_6584_fst__snd__flip,axiom,
% 0.33/0.64 ( product_fst_int_int
% 0.33/0.64 = ( comp_P5356232565778667509nt_int @ product_snd_int_int
% 0.33/0.64 @ ( produc4245557441103728435nt_int
% 0.33/0.64 @ ^ [X3: int,Y3: int] : ( product_Pair_int_int @ Y3 @ X3 ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % fst_snd_flip
% 0.33/0.64 thf(fact_6585_finite__UNION__then__finite,axiom,
% 0.33/0.64 ! [B5: $o > set_int,A2: set_o,A: $o] :
% 0.33/0.64 ( ( finite_finite_int @ ( comple3221217463730067765et_int @ ( image_o_set_int @ B5 @ A2 ) ) )
% 0.33/0.64 => ( ( member_o @ A @ A2 )
% 0.33/0.64 => ( finite_finite_int @ ( B5 @ A ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % finite_UNION_then_finite
% 0.33/0.64 thf(fact_6586_finite__UNION__then__finite,axiom,
% 0.33/0.64 ! [B5: nat > set_int,A2: set_nat,A: nat] :
% 0.33/0.64 ( ( finite_finite_int @ ( comple3221217463730067765et_int @ ( image_nat_set_int @ B5 @ A2 ) ) )
% 0.33/0.64 => ( ( member_nat @ A @ A2 )
% 0.33/0.64 => ( finite_finite_int @ ( B5 @ A ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % finite_UNION_then_finite
% 0.33/0.64 thf(fact_6587_finite__UNION__then__finite,axiom,
% 0.33/0.64 ! [B5: int > set_int,A2: set_int,A: int] :
% 0.33/0.64 ( ( finite_finite_int @ ( comple3221217463730067765et_int @ ( image_int_set_int @ B5 @ A2 ) ) )
% 0.33/0.64 => ( ( member_int @ A @ A2 )
% 0.33/0.64 => ( finite_finite_int @ ( B5 @ A ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % finite_UNION_then_finite
% 0.33/0.64 thf(fact_6588_finite__UNION__then__finite,axiom,
% 0.33/0.64 ! [B5: $o > set_Code_integer,A2: set_o,A: $o] :
% 0.33/0.64 ( ( finite6017078050557962740nteger @ ( comple739944243200306918nteger @ ( image_6491638074533506790nteger @ B5 @ A2 ) ) )
% 0.33/0.64 => ( ( member_o @ A @ A2 )
% 0.33/0.64 => ( finite6017078050557962740nteger @ ( B5 @ A ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % finite_UNION_then_finite
% 0.33/0.64 thf(fact_6589_finite__UNION__then__finite,axiom,
% 0.33/0.64 ! [B5: nat > set_Code_integer,A2: set_nat,A: nat] :
% 0.33/0.64 ( ( finite6017078050557962740nteger @ ( comple739944243200306918nteger @ ( image_2385391725447763818nteger @ B5 @ A2 ) ) )
% 0.33/0.64 => ( ( member_nat @ A @ A2 )
% 0.33/0.64 => ( finite6017078050557962740nteger @ ( B5 @ A ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % finite_UNION_then_finite
% 0.33/0.64 thf(fact_6590_finite__UNION__then__finite,axiom,
% 0.33/0.64 ! [B5: int > set_Code_integer,A2: set_int,A: int] :
% 0.33/0.64 ( ( finite6017078050557962740nteger @ ( comple739944243200306918nteger @ ( image_75573793354812870nteger @ B5 @ A2 ) ) )
% 0.33/0.64 => ( ( member_int @ A @ A2 )
% 0.33/0.64 => ( finite6017078050557962740nteger @ ( B5 @ A ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % finite_UNION_then_finite
% 0.33/0.64 thf(fact_6591_finite__UNION__then__finite,axiom,
% 0.33/0.64 ! [B5: $o > set_nat,A2: set_o,A: $o] :
% 0.33/0.64 ( ( finite_finite_nat @ ( comple7399068483239264473et_nat @ ( image_o_set_nat @ B5 @ A2 ) ) )
% 0.33/0.64 => ( ( member_o @ A @ A2 )
% 0.33/0.64 => ( finite_finite_nat @ ( B5 @ A ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % finite_UNION_then_finite
% 0.33/0.64 thf(fact_6592_finite__UNION__then__finite,axiom,
% 0.33/0.64 ! [B5: nat > set_nat,A2: set_nat,A: nat] :
% 0.33/0.64 ( ( finite_finite_nat @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ B5 @ A2 ) ) )
% 0.33/0.64 => ( ( member_nat @ A @ A2 )
% 0.33/0.64 => ( finite_finite_nat @ ( B5 @ A ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % finite_UNION_then_finite
% 0.33/0.64 thf(fact_6593_finite__UNION__then__finite,axiom,
% 0.33/0.64 ! [B5: int > set_nat,A2: set_int,A: int] :
% 0.33/0.64 ( ( finite_finite_nat @ ( comple7399068483239264473et_nat @ ( image_int_set_nat @ B5 @ A2 ) ) )
% 0.33/0.64 => ( ( member_int @ A @ A2 )
% 0.33/0.64 => ( finite_finite_nat @ ( B5 @ A ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % finite_UNION_then_finite
% 0.33/0.64 thf(fact_6594_finite__UNION__then__finite,axiom,
% 0.33/0.64 ! [B5: product_prod_nat_nat > set_int,A2: set_Pr1261947904930325089at_nat,A: product_prod_nat_nat] :
% 0.33/0.64 ( ( finite_finite_int @ ( comple3221217463730067765et_int @ ( image_5061345727057949854et_int @ B5 @ A2 ) ) )
% 0.33/0.64 => ( ( member8440522571783428010at_nat @ A @ A2 )
% 0.33/0.64 => ( finite_finite_int @ ( B5 @ A ) ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % finite_UNION_then_finite
% 0.33/0.64 thf(fact_6595_case__prod__comp,axiom,
% 0.33/0.64 ! [F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer,X: produc3346328345660746739nteger] :
% 0.33/0.64 ( ( produc4281629032016041417nteger @ ( comp_C1593894019821074884nteger @ F @ G ) @ X )
% 0.33/0.64 = ( F @ ( G @ ( produc1861665112190112313nteger @ X ) ) @ ( produc7955729907432593271nteger @ X ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % case_prod_comp
% 0.33/0.64 thf(fact_6596_case__prod__comp,axiom,
% 0.33/0.64 ! [F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer > code_integer,X: produc3346328345660746739nteger] :
% 0.33/0.64 ( ( produc4281629032016041417nteger @ ( comp_C8797469213163452608nteger @ F @ G ) @ X )
% 0.33/0.64 = ( F @ ( G @ ( produc1861665112190112313nteger @ X ) ) @ ( produc7955729907432593271nteger @ X ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % case_prod_comp
% 0.33/0.64 thf(fact_6597_fn__snd__conv,axiom,
% 0.33/0.64 ! [F: nat > nat] :
% 0.33/0.64 ( ( ^ [X3: product_prod_nat_nat] : ( F @ ( product_snd_nat_nat @ X3 ) ) )
% 0.33/0.64 = ( produc6842872674320459806at_nat
% 0.33/0.64 @ ^ [Uu: nat] : F ) ) ).
% 0.33/0.64
% 0.33/0.64 % fn_snd_conv
% 0.33/0.64 thf(fact_6598_fn__snd__conv,axiom,
% 0.33/0.64 ! [F: nat > product_prod_nat_nat > product_prod_nat_nat] :
% 0.33/0.64 ( ( ^ [X3: product_prod_nat_nat] : ( F @ ( product_snd_nat_nat @ X3 ) ) )
% 0.33/0.64 = ( produc27273713700761075at_nat
% 0.33/0.64 @ ^ [Uu: nat] : F ) ) ).
% 0.33/0.64
% 0.33/0.64 % fn_snd_conv
% 0.33/0.64 thf(fact_6599_fn__snd__conv,axiom,
% 0.33/0.64 ! [F: nat > product_prod_nat_nat > $o] :
% 0.33/0.64 ( ( ^ [X3: product_prod_nat_nat] : ( F @ ( product_snd_nat_nat @ X3 ) ) )
% 0.33/0.64 = ( produc8739625826339149834_nat_o
% 0.33/0.64 @ ^ [Uu: nat] : F ) ) ).
% 0.33/0.64
% 0.33/0.64 % fn_snd_conv
% 0.33/0.64 thf(fact_6600_fn__snd__conv,axiom,
% 0.33/0.64 ! [F: int > product_prod_int_int] :
% 0.33/0.64 ( ( ^ [X3: product_prod_int_int] : ( F @ ( product_snd_int_int @ X3 ) ) )
% 0.33/0.64 = ( produc4245557441103728435nt_int
% 0.33/0.64 @ ^ [Uu: int] : F ) ) ).
% 0.33/0.64
% 0.33/0.64 % fn_snd_conv
% 0.33/0.64 thf(fact_6601_fn__snd__conv,axiom,
% 0.33/0.64 ! [F: int > int] :
% 0.33/0.64 ( ( ^ [X3: product_prod_int_int] : ( F @ ( product_snd_int_int @ X3 ) ) )
% 0.33/0.64 = ( produc8211389475949308722nt_int
% 0.33/0.64 @ ^ [Uu: int] : F ) ) ).
% 0.33/0.64
% 0.33/0.64 % fn_snd_conv
% 0.33/0.64 thf(fact_6602_snd__def,axiom,
% 0.33/0.64 ( produc6174133586879617921nteger
% 0.33/0.64 = ( produc7469247390737344965nteger
% 0.33/0.64 @ ^ [X12: code_integer,X23: code_integer] : X23 ) ) ).
% 0.33/0.64
% 0.33/0.64 % snd_def
% 0.33/0.64 thf(fact_6603_snd__def,axiom,
% 0.33/0.64 ( produc6591912806276919810atural
% 0.33/0.64 = ( produc6302656368764539796atural
% 0.33/0.64 @ ^ [X12: code_natural,X23: produc7822875418678951345atural] : X23 ) ) ).
% 0.33/0.64
% 0.33/0.64 % snd_def
% 0.33/0.64 thf(fact_6604_snd__def,axiom,
% 0.33/0.64 ( product_snd_nat_nat
% 0.33/0.64 = ( produc6842872674320459806at_nat
% 0.33/0.64 @ ^ [X12: nat,X23: nat] : X23 ) ) ).
% 0.33/0.64
% 0.33/0.64 % snd_def
% 0.33/0.64 thf(fact_6605_snd__def,axiom,
% 0.33/0.64 ( product_snd_int_int
% 0.33/0.64 = ( produc8211389475949308722nt_int
% 0.33/0.64 @ ^ [X12: int,X23: int] : X23 ) ) ).
% 0.33/0.64
% 0.33/0.64 % snd_def
% 0.33/0.64 thf(fact_6606_fn__fst__conv,axiom,
% 0.33/0.64 ! [F: nat > nat] :
% 0.33/0.64 ( ( ^ [X3: product_prod_nat_nat] : ( F @ ( product_fst_nat_nat @ X3 ) ) )
% 0.33/0.64 = ( produc6842872674320459806at_nat
% 0.33/0.64 @ ^ [A5: nat,Uu: nat] : ( F @ A5 ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % fn_fst_conv
% 0.33/0.64 thf(fact_6607_fn__fst__conv,axiom,
% 0.33/0.64 ! [F: nat > product_prod_nat_nat > product_prod_nat_nat] :
% 0.33/0.64 ( ( ^ [X3: product_prod_nat_nat] : ( F @ ( product_fst_nat_nat @ X3 ) ) )
% 0.33/0.64 = ( produc27273713700761075at_nat
% 0.33/0.64 @ ^ [A5: nat,Uu: nat] : ( F @ A5 ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % fn_fst_conv
% 0.33/0.64 thf(fact_6608_fn__fst__conv,axiom,
% 0.33/0.64 ! [F: nat > product_prod_nat_nat > $o] :
% 0.33/0.64 ( ( ^ [X3: product_prod_nat_nat] : ( F @ ( product_fst_nat_nat @ X3 ) ) )
% 0.33/0.64 = ( produc8739625826339149834_nat_o
% 0.33/0.64 @ ^ [A5: nat,Uu: nat] : ( F @ A5 ) ) ) ).
% 0.33/0.64
% 0.33/0.64 % fn_fst_conv
% 0.33/0.64 thf(fact_6609_fn__fst__conv,axiom,
% 0.33/0.64 ! [F: int > product_prod_int_int] :
% 0.33/0.64 ( ( ^ [X3: product_prod_int_int] : ( F @ ( product_fst_int_int @ X3 ) ) )
% 0.33/0.64 = ( produc4245557441103728435nt_int
% 0.33/0.64 @ ^ [A5: int,Uu: int] : ( F @ A5 ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % fn_fst_conv
% 0.33/0.65 thf(fact_6610_fn__fst__conv,axiom,
% 0.33/0.65 ! [F: int > int] :
% 0.33/0.65 ( ( ^ [X3: product_prod_int_int] : ( F @ ( product_fst_int_int @ X3 ) ) )
% 0.33/0.65 = ( produc8211389475949308722nt_int
% 0.33/0.65 @ ^ [A5: int,Uu: int] : ( F @ A5 ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % fn_fst_conv
% 0.33/0.65 thf(fact_6611_fst__def,axiom,
% 0.33/0.65 ( produc8508995932063986495nteger
% 0.33/0.65 = ( produc7469247390737344965nteger
% 0.33/0.65 @ ^ [X12: code_integer,X23: code_integer] : X12 ) ) ).
% 0.33/0.65
% 0.33/0.65 % fst_def
% 0.33/0.65 thf(fact_6612_fst__def,axiom,
% 0.33/0.65 ( product_fst_nat_nat
% 0.33/0.65 = ( produc6842872674320459806at_nat
% 0.33/0.65 @ ^ [X12: nat,X23: nat] : X12 ) ) ).
% 0.33/0.65
% 0.33/0.65 % fst_def
% 0.33/0.65 thf(fact_6613_fst__def,axiom,
% 0.33/0.65 ( product_fst_int_int
% 0.33/0.65 = ( produc8211389475949308722nt_int
% 0.33/0.65 @ ^ [X12: int,X23: int] : X12 ) ) ).
% 0.33/0.65
% 0.33/0.65 % fst_def
% 0.33/0.65 thf(fact_6614_Collect__split__mono__strong,axiom,
% 0.33/0.65 ! [X11: set_Code_integer,A2: set_Pr4811707699266497531nteger,Y9: set_Code_integer,P: code_integer > code_integer > $o,Q: code_integer > code_integer > $o] :
% 0.33/0.65 ( ( X11
% 0.33/0.65 = ( image_6316824473203919795nteger @ produc8508995932063986495nteger @ A2 ) )
% 0.33/0.65 => ( ( Y9
% 0.33/0.65 = ( image_6316824473203919795nteger @ produc6174133586879617921nteger @ A2 ) )
% 0.33/0.65 => ( ! [X4: code_integer] :
% 0.33/0.65 ( ( member_Code_integer @ X4 @ X11 )
% 0.33/0.65 => ! [Xa3: code_integer] :
% 0.33/0.65 ( ( member_Code_integer @ Xa3 @ Y9 )
% 0.33/0.65 => ( ( P @ X4 @ Xa3 )
% 0.33/0.65 => ( Q @ X4 @ Xa3 ) ) ) )
% 0.33/0.65 => ( ( ord_le3725938330318615451nteger @ A2 @ ( collec7766031446232907142nteger @ ( produc2066375834425727024eger_o @ P ) ) )
% 0.33/0.65 => ( ord_le3725938330318615451nteger @ A2 @ ( collec7766031446232907142nteger @ ( produc2066375834425727024eger_o @ Q ) ) ) ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % Collect_split_mono_strong
% 0.33/0.65 thf(fact_6615_Collect__split__mono__strong,axiom,
% 0.33/0.65 ! [X11: set_int,A2: set_Pr958786334691620121nt_int,Y9: set_int,P: int > int > $o,Q: int > int > $o] :
% 0.33/0.65 ( ( X11
% 0.33/0.65 = ( image_5042161079198086560nt_int @ product_fst_int_int @ A2 ) )
% 0.33/0.65 => ( ( Y9
% 0.33/0.65 = ( image_5042161079198086560nt_int @ product_snd_int_int @ A2 ) )
% 0.33/0.65 => ( ! [X4: int] :
% 0.33/0.65 ( ( member_int @ X4 @ X11 )
% 0.33/0.65 => ! [Xa3: int] :
% 0.33/0.65 ( ( member_int @ Xa3 @ Y9 )
% 0.33/0.65 => ( ( P @ X4 @ Xa3 )
% 0.33/0.65 => ( Q @ X4 @ Xa3 ) ) ) )
% 0.33/0.65 => ( ( ord_le2843351958646193337nt_int @ A2 @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ P ) ) )
% 0.33/0.65 => ( ord_le2843351958646193337nt_int @ A2 @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ Q ) ) ) ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % Collect_split_mono_strong
% 0.33/0.65 thf(fact_6616_Collect__split__mono__strong,axiom,
% 0.33/0.65 ! [X11: set_Code_natural,A2: set_Pr2352657477744078772atural,Y9: set_Pr7564037697178849041atural,P: code_natural > produc7822875418678951345atural > $o,Q: code_natural > produc7822875418678951345atural > $o] :
% 0.33/0.65 ( ( X11
% 0.33/0.65 = ( image_8194678751871465133atural @ produc497848011034438852atural @ A2 ) )
% 0.33/0.65 => ( ( Y9
% 0.33/0.65 = ( image_3837677093542026988atural @ produc6591912806276919810atural @ A2 ) )
% 0.33/0.65 => ( ! [X4: code_natural] :
% 0.33/0.65 ( ( member_Code_natural @ X4 @ X11 )
% 0.33/0.65 => ! [Xa3: produc7822875418678951345atural] :
% 0.33/0.65 ( ( member8280416476884352090atural @ Xa3 @ Y9 )
% 0.33/0.65 => ( ( P @ X4 @ Xa3 )
% 0.33/0.65 => ( Q @ X4 @ Xa3 ) ) ) )
% 0.33/0.65 => ( ( ord_le2202040463148982292atural @ A2 @ ( collec1991479681304692691atural @ ( produc7358226366420480123ural_o @ P ) ) )
% 0.33/0.65 => ( ord_le2202040463148982292atural @ A2 @ ( collec1991479681304692691atural @ ( produc7358226366420480123ural_o @ Q ) ) ) ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % Collect_split_mono_strong
% 0.33/0.65 thf(fact_6617_Some__Sup,axiom,
% 0.33/0.65 ! [A2: set_o] :
% 0.33/0.65 ( ( A2 != bot_bot_set_o )
% 0.33/0.65 => ( ( some_o @ ( complete_Sup_Sup_o @ A2 ) )
% 0.33/0.65 = ( comple4490649148004324043tion_o @ ( image_o_option_o @ some_o @ A2 ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % Some_Sup
% 0.33/0.65 thf(fact_6618_Some__Sup,axiom,
% 0.33/0.65 ! [A2: set_set_nat] :
% 0.33/0.65 ( ( A2 != bot_bot_set_set_nat )
% 0.33/0.65 => ( ( some_set_nat @ ( comple7399068483239264473et_nat @ A2 ) )
% 0.33/0.65 = ( comple8455683388168444585et_nat @ ( image_838307146230912995et_nat @ some_set_nat @ A2 ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % Some_Sup
% 0.33/0.65 thf(fact_6619_Some__Sup,axiom,
% 0.33/0.65 ! [A2: set_Product_unit] :
% 0.33/0.65 ( ( A2 != bot_bo3957492148770167129t_unit )
% 0.33/0.65 => ( ( some_Product_unit @ ( comple4687483117567863418t_unit @ A2 ) )
% 0.33/0.65 = ( comple7481738165189995200t_unit @ ( image_7094380055901048587t_unit @ some_Product_unit @ A2 ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % Some_Sup
% 0.33/0.65 thf(fact_6620_Inf__option__def,axiom,
% 0.33/0.65 ( comple3446467376476514063et_nat
% 0.33/0.65 = ( ^ [A7: set_option_set_nat] : ( if_option_set_nat @ ( member8989860449721436141et_nat @ none_set_nat @ A7 ) @ none_set_nat @ ( some_set_nat @ ( comple7806235888213564991et_nat @ ( these_set_nat @ A7 ) ) ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % Inf_option_def
% 0.33/0.65 thf(fact_6621_Inf__option__def,axiom,
% 0.33/0.65 ( comple5564859526659248602t_unit
% 0.33/0.65 = ( ^ [A7: set_op3165557761946182707t_unit] : ( if_opt6227717841141446553t_unit @ ( member1378114217278917244t_unit @ none_Product_unit @ A7 ) @ none_Product_unit @ ( some_Product_unit @ ( comple2584293577114468500t_unit @ ( these_Product_unit @ A7 ) ) ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % Inf_option_def
% 0.33/0.65 thf(fact_6622_Some__INF,axiom,
% 0.33/0.65 ! [F: nat > set_nat,A2: set_nat] :
% 0.33/0.65 ( ( some_set_nat @ ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ F @ A2 ) ) )
% 0.33/0.65 = ( comple3446467376476514063et_nat
% 0.33/0.65 @ ( image_1085372205585808685et_nat
% 0.33/0.65 @ ^ [X3: nat] : ( some_set_nat @ ( F @ X3 ) )
% 0.33/0.65 @ A2 ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % Some_INF
% 0.33/0.65 thf(fact_6623_INF__image,axiom,
% 0.33/0.65 ! [G: code_integer > nat,F: nat > code_integer,A2: set_nat] :
% 0.33/0.65 ( ( complete_Inf_Inf_nat @ ( image_951025933927791156er_nat @ G @ ( image_1215581382706833972nteger @ F @ A2 ) ) )
% 0.33/0.65 = ( complete_Inf_Inf_nat @ ( image_nat_nat @ ( comp_C4049556595663050210at_nat @ G @ F ) @ A2 ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % INF_image
% 0.33/0.65 thf(fact_6624_INF__image,axiom,
% 0.33/0.65 ! [G: code_integer > int,F: nat > code_integer,A2: set_nat] :
% 0.33/0.65 ( ( complete_Inf_Inf_int @ ( image_948535463418740880er_int @ G @ ( image_1215581382706833972nteger @ F @ A2 ) ) )
% 0.33/0.65 = ( complete_Inf_Inf_int @ ( image_nat_int @ ( comp_C5048910307564104766nt_nat @ G @ F ) @ A2 ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % INF_image
% 0.33/0.65 thf(fact_6625_INF__image,axiom,
% 0.33/0.65 ! [G: int > nat,F: nat > int,A2: set_nat] :
% 0.33/0.65 ( ( complete_Inf_Inf_nat @ ( image_int_nat @ G @ ( image_nat_int @ F @ A2 ) ) )
% 0.33/0.65 = ( complete_Inf_Inf_nat @ ( image_nat_nat @ ( comp_int_nat_nat @ G @ F ) @ A2 ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % INF_image
% 0.33/0.65 thf(fact_6626_INF__image,axiom,
% 0.33/0.65 ! [G: nat > nat,F: nat > nat,A2: set_nat] :
% 0.33/0.65 ( ( complete_Inf_Inf_nat @ ( image_nat_nat @ G @ ( image_nat_nat @ F @ A2 ) ) )
% 0.33/0.65 = ( complete_Inf_Inf_nat @ ( image_nat_nat @ ( comp_nat_nat_nat @ G @ F ) @ A2 ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % INF_image
% 0.33/0.65 thf(fact_6627_INF__image,axiom,
% 0.33/0.65 ! [G: nat > int,F: int > nat,A2: set_int] :
% 0.33/0.65 ( ( complete_Inf_Inf_int @ ( image_nat_int @ G @ ( image_int_nat @ F @ A2 ) ) )
% 0.33/0.65 = ( complete_Inf_Inf_int @ ( image_int_int @ ( comp_nat_int_int @ G @ F ) @ A2 ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % INF_image
% 0.33/0.65 thf(fact_6628_INF__image,axiom,
% 0.33/0.65 ! [G: nat > int,F: nat > nat,A2: set_nat] :
% 0.33/0.65 ( ( complete_Inf_Inf_int @ ( image_nat_int @ G @ ( image_nat_nat @ F @ A2 ) ) )
% 0.33/0.65 = ( complete_Inf_Inf_int @ ( image_nat_int @ ( comp_nat_int_nat @ G @ F ) @ A2 ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % INF_image
% 0.33/0.65 thf(fact_6629_INF__image,axiom,
% 0.33/0.65 ! [G: int > int,F: nat > int,A2: set_nat] :
% 0.33/0.65 ( ( complete_Inf_Inf_int @ ( image_int_int @ G @ ( image_nat_int @ F @ A2 ) ) )
% 0.33/0.65 = ( complete_Inf_Inf_int @ ( image_nat_int @ ( comp_int_int_nat @ G @ F ) @ A2 ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % INF_image
% 0.33/0.65 thf(fact_6630_INF__image,axiom,
% 0.33/0.65 ! [G: int > int,F: int > int,A2: set_int] :
% 0.33/0.65 ( ( complete_Inf_Inf_int @ ( image_int_int @ G @ ( image_int_int @ F @ A2 ) ) )
% 0.33/0.65 = ( complete_Inf_Inf_int @ ( image_int_int @ ( comp_int_int_int @ G @ F ) @ A2 ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % INF_image
% 0.33/0.65 thf(fact_6631_INF__image,axiom,
% 0.33/0.65 ! [G: code_integer > product_unit,F: nat > code_integer,A2: set_nat] :
% 0.33/0.65 ( ( comple2584293577114468500t_unit @ ( image_7182656606676592809t_unit @ G @ ( image_1215581382706833972nteger @ F @ A2 ) ) )
% 0.33/0.65 = ( comple2584293577114468500t_unit @ ( image_8730104196221521654t_unit @ ( comp_C8086623346886033437it_nat @ G @ F ) @ A2 ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % INF_image
% 0.33/0.65 thf(fact_6632_INF__image,axiom,
% 0.33/0.65 ! [G: nat > product_unit,F: nat > nat,A2: set_nat] :
% 0.33/0.65 ( ( comple2584293577114468500t_unit @ ( image_8730104196221521654t_unit @ G @ ( image_nat_nat @ F @ A2 ) ) )
% 0.33/0.65 = ( comple2584293577114468500t_unit @ ( image_8730104196221521654t_unit @ ( comp_n9025697279074352746it_nat @ G @ F ) @ A2 ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % INF_image
% 0.33/0.65 thf(fact_6633_SUP__image,axiom,
% 0.33/0.65 ! [G: code_integer > nat,F: nat > code_integer,A2: set_nat] :
% 0.33/0.65 ( ( complete_Sup_Sup_nat @ ( image_951025933927791156er_nat @ G @ ( image_1215581382706833972nteger @ F @ A2 ) ) )
% 0.33/0.65 = ( complete_Sup_Sup_nat @ ( image_nat_nat @ ( comp_C4049556595663050210at_nat @ G @ F ) @ A2 ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % SUP_image
% 0.33/0.65 thf(fact_6634_SUP__image,axiom,
% 0.33/0.65 ! [G: code_integer > int,F: nat > code_integer,A2: set_nat] :
% 0.33/0.65 ( ( complete_Sup_Sup_int @ ( image_948535463418740880er_int @ G @ ( image_1215581382706833972nteger @ F @ A2 ) ) )
% 0.33/0.65 = ( complete_Sup_Sup_int @ ( image_nat_int @ ( comp_C5048910307564104766nt_nat @ G @ F ) @ A2 ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % SUP_image
% 0.33/0.65 thf(fact_6635_SUP__image,axiom,
% 0.33/0.65 ! [G: int > nat,F: nat > int,A2: set_nat] :
% 0.33/0.65 ( ( complete_Sup_Sup_nat @ ( image_int_nat @ G @ ( image_nat_int @ F @ A2 ) ) )
% 0.33/0.65 = ( complete_Sup_Sup_nat @ ( image_nat_nat @ ( comp_int_nat_nat @ G @ F ) @ A2 ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % SUP_image
% 0.33/0.65 thf(fact_6636_SUP__image,axiom,
% 0.33/0.65 ! [G: nat > nat,F: nat > nat,A2: set_nat] :
% 0.33/0.65 ( ( complete_Sup_Sup_nat @ ( image_nat_nat @ G @ ( image_nat_nat @ F @ A2 ) ) )
% 0.33/0.65 = ( complete_Sup_Sup_nat @ ( image_nat_nat @ ( comp_nat_nat_nat @ G @ F ) @ A2 ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % SUP_image
% 0.33/0.65 thf(fact_6637_SUP__image,axiom,
% 0.33/0.65 ! [G: nat > int,F: int > nat,A2: set_int] :
% 0.33/0.65 ( ( complete_Sup_Sup_int @ ( image_nat_int @ G @ ( image_int_nat @ F @ A2 ) ) )
% 0.33/0.65 = ( complete_Sup_Sup_int @ ( image_int_int @ ( comp_nat_int_int @ G @ F ) @ A2 ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % SUP_image
% 0.33/0.65 thf(fact_6638_SUP__image,axiom,
% 0.33/0.65 ! [G: nat > int,F: nat > nat,A2: set_nat] :
% 0.33/0.65 ( ( complete_Sup_Sup_int @ ( image_nat_int @ G @ ( image_nat_nat @ F @ A2 ) ) )
% 0.33/0.65 = ( complete_Sup_Sup_int @ ( image_nat_int @ ( comp_nat_int_nat @ G @ F ) @ A2 ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % SUP_image
% 0.33/0.65 thf(fact_6639_SUP__image,axiom,
% 0.33/0.65 ! [G: int > int,F: nat > int,A2: set_nat] :
% 0.33/0.65 ( ( complete_Sup_Sup_int @ ( image_int_int @ G @ ( image_nat_int @ F @ A2 ) ) )
% 0.33/0.65 = ( complete_Sup_Sup_int @ ( image_nat_int @ ( comp_int_int_nat @ G @ F ) @ A2 ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % SUP_image
% 0.33/0.65 thf(fact_6640_SUP__image,axiom,
% 0.33/0.65 ! [G: int > int,F: int > int,A2: set_int] :
% 0.33/0.65 ( ( complete_Sup_Sup_int @ ( image_int_int @ G @ ( image_int_int @ F @ A2 ) ) )
% 0.33/0.65 = ( complete_Sup_Sup_int @ ( image_int_int @ ( comp_int_int_int @ G @ F ) @ A2 ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % SUP_image
% 0.33/0.65 thf(fact_6641_SUP__image,axiom,
% 0.33/0.65 ! [G: code_integer > product_unit,F: nat > code_integer,A2: set_nat] :
% 0.33/0.65 ( ( comple4687483117567863418t_unit @ ( image_7182656606676592809t_unit @ G @ ( image_1215581382706833972nteger @ F @ A2 ) ) )
% 0.33/0.65 = ( comple4687483117567863418t_unit @ ( image_8730104196221521654t_unit @ ( comp_C8086623346886033437it_nat @ G @ F ) @ A2 ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % SUP_image
% 0.33/0.65 thf(fact_6642_SUP__image,axiom,
% 0.33/0.65 ! [G: nat > product_unit,F: nat > nat,A2: set_nat] :
% 0.33/0.65 ( ( comple4687483117567863418t_unit @ ( image_8730104196221521654t_unit @ G @ ( image_nat_nat @ F @ A2 ) ) )
% 0.33/0.65 = ( comple4687483117567863418t_unit @ ( image_8730104196221521654t_unit @ ( comp_n9025697279074352746it_nat @ G @ F ) @ A2 ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % SUP_image
% 0.33/0.65 thf(fact_6643_in__snd__imageE,axiom,
% 0.33/0.65 ! [Y: set_Pr1261947904930325089at_nat,S2: set_Pr4329608150637261639at_nat] :
% 0.33/0.65 ( ( member2643936169264416010at_nat @ Y @ ( image_7979982168039674559at_nat @ produc2937545259423399429at_nat @ S2 ) )
% 0.33/0.65 => ~ ! [X4: set_Pr1261947904930325089at_nat] :
% 0.33/0.65 ~ ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X4 @ Y ) @ S2 ) ) ).
% 0.33/0.65
% 0.33/0.65 % in_snd_imageE
% 0.33/0.65 thf(fact_6644_in__snd__imageE,axiom,
% 0.33/0.65 ! [Y: nat,S2: set_Pr1261947904930325089at_nat] :
% 0.33/0.65 ( ( member_nat @ Y @ ( image_2486076414777270412at_nat @ product_snd_nat_nat @ S2 ) )
% 0.33/0.65 => ~ ! [X4: nat] :
% 0.33/0.65 ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Y ) @ S2 ) ) ).
% 0.33/0.65
% 0.33/0.65 % in_snd_imageE
% 0.33/0.65 thf(fact_6645_in__snd__imageE,axiom,
% 0.33/0.65 ! [Y: produc8923325533196201883nteger,S2: set_Pr1281608226676607948nteger] :
% 0.33/0.65 ( ( member157494554546826820nteger @ Y @ ( image_3141030398089242942nteger @ produc7856867400915047194nteger @ S2 ) )
% 0.33/0.65 => ~ ! [X4: produc6241069584506657477e_term > option6357759511663192854e_term] :
% 0.33/0.65 ~ ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X4 @ Y ) @ S2 ) ) ).
% 0.33/0.65
% 0.33/0.65 % in_snd_imageE
% 0.33/0.65 thf(fact_6646_in__snd__imageE,axiom,
% 0.33/0.65 ! [Y: produc3658429121746597890et_nat,S2: set_Pr3286484037609594932et_nat] :
% 0.33/0.65 ( ( member6260224972018164377et_nat @ Y @ ( image_4390311411407041927et_nat @ produc4011572625026189258et_nat @ S2 ) )
% 0.33/0.65 => ~ ! [X4: produc3658429121746597890et_nat > $o] :
% 0.33/0.65 ~ ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X4 @ Y ) @ S2 ) ) ).
% 0.33/0.65
% 0.33/0.65 % in_snd_imageE
% 0.33/0.65 thf(fact_6647_in__snd__imageE,axiom,
% 0.33/0.65 ! [Y: produc3925858234332021118et_nat,S2: set_Pr8536935166611901872et_nat] :
% 0.33/0.65 ( ( member1996754912294343701et_nat @ Y @ ( image_4557310310409863807et_nat @ produc5374455773327741254et_nat @ S2 ) )
% 0.33/0.65 => ~ ! [X4: produc3658429121746597890et_nat > $o] :
% 0.33/0.65 ~ ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X4 @ Y ) @ S2 ) ) ).
% 0.33/0.65
% 0.33/0.65 % in_snd_imageE
% 0.33/0.65 thf(fact_6648_in__snd__imageE,axiom,
% 0.33/0.65 ! [Y: product_prod_int_int,S2: set_Pr9222295170931077689nt_int] :
% 0.33/0.65 ( ( member5262025264175285858nt_int @ Y @ ( image_3915291023682402351nt_int @ produc7328097813583171335nt_int @ S2 ) )
% 0.33/0.65 => ~ ! [X4: produc8551481072490612790e_term > option6357759511663192854e_term] :
% 0.33/0.65 ~ ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X4 @ Y ) @ S2 ) ) ).
% 0.33/0.65
% 0.33/0.65 % in_snd_imageE
% 0.33/0.65 thf(fact_6649_in__snd__imageE,axiom,
% 0.33/0.65 ! [Y: product_prod_int_int,S2: set_Pr1872883991513573699nt_int] :
% 0.33/0.65 ( ( member5262025264175285858nt_int @ Y @ ( image_3108077152341812517nt_int @ produc3162348030201620241nt_int @ S2 ) )
% 0.33/0.65 => ~ ! [X4: int > option6357759511663192854e_term] :
% 0.33/0.65 ~ ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X4 @ Y ) @ S2 ) ) ).
% 0.33/0.65
% 0.33/0.65 % in_snd_imageE
% 0.33/0.65 thf(fact_6650_in__snd__imageE,axiom,
% 0.33/0.65 ! [Y: code_integer,S2: set_Pr4811707699266497531nteger] :
% 0.33/0.65 ( ( member_Code_integer @ Y @ ( image_6316824473203919795nteger @ produc6174133586879617921nteger @ S2 ) )
% 0.33/0.65 => ~ ! [X4: code_integer] :
% 0.33/0.65 ~ ( member157494554546826820nteger @ ( produc1086072967326762835nteger @ X4 @ Y ) @ S2 ) ) ).
% 0.33/0.65
% 0.33/0.65 % in_snd_imageE
% 0.33/0.65 thf(fact_6651_in__snd__imageE,axiom,
% 0.33/0.65 ! [Y: int,S2: set_Pr958786334691620121nt_int] :
% 0.33/0.65 ( ( member_int @ Y @ ( image_5042161079198086560nt_int @ product_snd_int_int @ S2 ) )
% 0.33/0.65 => ~ ! [X4: int] :
% 0.33/0.65 ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Y ) @ S2 ) ) ).
% 0.33/0.65
% 0.33/0.65 % in_snd_imageE
% 0.33/0.65 thf(fact_6652_in__snd__imageE,axiom,
% 0.33/0.65 ! [Y: produc7822875418678951345atural,S2: set_Pr2352657477744078772atural] :
% 0.33/0.65 ( ( member8280416476884352090atural @ Y @ ( image_3837677093542026988atural @ produc6591912806276919810atural @ S2 ) )
% 0.33/0.65 => ~ ! [X4: code_natural] :
% 0.33/0.65 ~ ( member2108296798382401941atural @ ( produc6639722614265839536atural @ X4 @ Y ) @ S2 ) ) ).
% 0.33/0.65
% 0.33/0.65 % in_snd_imageE
% 0.33/0.65 thf(fact_6653_in__fst__imageE,axiom,
% 0.33/0.65 ! [X: set_Pr1261947904930325089at_nat,S2: set_Pr4329608150637261639at_nat] :
% 0.33/0.65 ( ( member2643936169264416010at_nat @ X @ ( image_7979982168039674559at_nat @ produc6011863565407846595at_nat @ S2 ) )
% 0.33/0.65 => ~ ! [Y5: set_Pr1261947904930325089at_nat] :
% 0.33/0.65 ~ ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y5 ) @ S2 ) ) ).
% 0.33/0.65
% 0.33/0.65 % in_fst_imageE
% 0.33/0.65 thf(fact_6654_in__fst__imageE,axiom,
% 0.33/0.65 ! [X: nat,S2: set_Pr1261947904930325089at_nat] :
% 0.33/0.65 ( ( member_nat @ X @ ( image_2486076414777270412at_nat @ product_fst_nat_nat @ S2 ) )
% 0.33/0.65 => ~ ! [Y5: nat] :
% 0.33/0.65 ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y5 ) @ S2 ) ) ).
% 0.33/0.65
% 0.33/0.65 % in_fst_imageE
% 0.33/0.65 thf(fact_6655_in__fst__imageE,axiom,
% 0.33/0.65 ! [X: produc6241069584506657477e_term > option6357759511663192854e_term,S2: set_Pr1281608226676607948nteger] :
% 0.33/0.65 ( ( member4242434998011752849e_term @ X @ ( image_4436781500471753239e_term @ produc7822682618958472924nteger @ S2 ) )
% 0.33/0.65 => ~ ! [Y5: produc8923325533196201883nteger] :
% 0.33/0.65 ~ ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X @ Y5 ) @ S2 ) ) ).
% 0.33/0.65
% 0.33/0.65 % in_fst_imageE
% 0.33/0.65 thf(fact_6656_in__fst__imageE,axiom,
% 0.33/0.65 ! [X: produc3658429121746597890et_nat > $o,S2: set_Pr3286484037609594932et_nat] :
% 0.33/0.65 ( ( member6576561426505652726_nat_o @ X @ ( image_6802380912191114376_nat_o @ produc995936583742144908et_nat @ S2 ) )
% 0.33/0.65 => ~ ! [Y5: produc3658429121746597890et_nat] :
% 0.33/0.65 ~ ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X @ Y5 ) @ S2 ) ) ).
% 0.33/0.65
% 0.33/0.65 % in_fst_imageE
% 0.33/0.65 thf(fact_6657_in__fst__imageE,axiom,
% 0.33/0.65 ! [X: produc3658429121746597890et_nat > $o,S2: set_Pr8536935166611901872et_nat] :
% 0.33/0.65 ( ( member6576561426505652726_nat_o @ X @ ( image_2517677226577294348_nat_o @ produc180342877477747464et_nat @ S2 ) )
% 0.33/0.65 => ~ ! [Y5: produc3925858234332021118et_nat] :
% 0.33/0.65 ~ ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X @ Y5 ) @ S2 ) ) ).
% 0.33/0.65
% 0.33/0.65 % in_fst_imageE
% 0.33/0.65 thf(fact_6658_in__fst__imageE,axiom,
% 0.33/0.65 ! [X: produc8551481072490612790e_term > option6357759511663192854e_term,S2: set_Pr9222295170931077689nt_int] :
% 0.33/0.65 ( ( member3222579708246209666e_term @ X @ ( image_142517975987106933e_term @ produc6816164490631068361nt_int @ S2 ) )
% 0.33/0.65 => ~ ! [Y5: product_prod_int_int] :
% 0.33/0.65 ~ ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X @ Y5 ) @ S2 ) ) ).
% 0.33/0.65
% 0.33/0.65 % in_fst_imageE
% 0.33/0.65 thf(fact_6659_in__fst__imageE,axiom,
% 0.33/0.65 ! [X: int > option6357759511663192854e_term,S2: set_Pr1872883991513573699nt_int] :
% 0.33/0.65 ( ( member8845023287901829240e_term @ X @ ( image_4217645046469565813e_term @ produc6230002227079971283nt_int @ S2 ) )
% 0.33/0.65 => ~ ! [Y5: product_prod_int_int] :
% 0.33/0.65 ~ ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X @ Y5 ) @ S2 ) ) ).
% 0.33/0.65
% 0.33/0.65 % in_fst_imageE
% 0.33/0.65 thf(fact_6660_in__fst__imageE,axiom,
% 0.33/0.65 ! [X: code_integer,S2: set_Pr4811707699266497531nteger] :
% 0.33/0.65 ( ( member_Code_integer @ X @ ( image_6316824473203919795nteger @ produc8508995932063986495nteger @ S2 ) )
% 0.33/0.65 => ~ ! [Y5: code_integer] :
% 0.33/0.65 ~ ( member157494554546826820nteger @ ( produc1086072967326762835nteger @ X @ Y5 ) @ S2 ) ) ).
% 0.33/0.65
% 0.33/0.65 % in_fst_imageE
% 0.33/0.65 thf(fact_6661_in__fst__imageE,axiom,
% 0.33/0.65 ! [X: int,S2: set_Pr958786334691620121nt_int] :
% 0.33/0.65 ( ( member_int @ X @ ( image_5042161079198086560nt_int @ product_fst_int_int @ S2 ) )
% 0.33/0.65 => ~ ! [Y5: int] :
% 0.33/0.65 ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y5 ) @ S2 ) ) ).
% 0.33/0.65
% 0.33/0.65 % in_fst_imageE
% 0.33/0.65 thf(fact_6662_Some__SUP,axiom,
% 0.33/0.65 ! [A2: set_Pr4329608150637261639at_nat,F: produc3843707927480180839at_nat > set_nat] :
% 0.33/0.65 ( ( A2 != bot_bo228742789529271731at_nat )
% 0.33/0.65 => ( ( some_set_nat @ ( comple7399068483239264473et_nat @ ( image_3160451284896210088et_nat @ F @ A2 ) ) )
% 0.33/0.65 = ( comple8455683388168444585et_nat
% 0.33/0.65 @ ( image_934083234596377592et_nat
% 0.33/0.65 @ ^ [X3: produc3843707927480180839at_nat] : ( some_set_nat @ ( F @ X3 ) )
% 0.33/0.65 @ A2 ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % Some_SUP
% 0.33/0.65 thf(fact_6663_Some__SUP,axiom,
% 0.33/0.65 ! [A2: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > set_nat] :
% 0.33/0.65 ( ( A2 != bot_bo2099793752762293965at_nat )
% 0.33/0.65 => ( ( some_set_nat @ ( comple7399068483239264473et_nat @ ( image_15824709712370754et_nat @ F @ A2 ) ) )
% 0.33/0.65 = ( comple8455683388168444585et_nat
% 0.33/0.65 @ ( image_7383884694314771602et_nat
% 0.33/0.65 @ ^ [X3: product_prod_nat_nat] : ( some_set_nat @ ( F @ X3 ) )
% 0.33/0.65 @ A2 ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % Some_SUP
% 0.33/0.65 thf(fact_6664_Some__SUP,axiom,
% 0.33/0.65 ! [A2: set_o,F: $o > set_nat] :
% 0.33/0.65 ( ( A2 != bot_bot_set_o )
% 0.33/0.65 => ( ( some_set_nat @ ( comple7399068483239264473et_nat @ ( image_o_set_nat @ F @ A2 ) ) )
% 0.33/0.65 = ( comple8455683388168444585et_nat
% 0.33/0.65 @ ( image_966425688229763753et_nat
% 0.33/0.65 @ ^ [X3: $o] : ( some_set_nat @ ( F @ X3 ) )
% 0.33/0.65 @ A2 ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % Some_SUP
% 0.33/0.65 thf(fact_6665_Some__SUP,axiom,
% 0.33/0.65 ! [A2: set_nat,F: nat > set_nat] :
% 0.33/0.65 ( ( A2 != bot_bot_set_nat )
% 0.33/0.65 => ( ( some_set_nat @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ F @ A2 ) ) )
% 0.33/0.65 = ( comple8455683388168444585et_nat
% 0.33/0.65 @ ( image_1085372205585808685et_nat
% 0.33/0.65 @ ^ [X3: nat] : ( some_set_nat @ ( F @ X3 ) )
% 0.33/0.65 @ A2 ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % Some_SUP
% 0.33/0.65 thf(fact_6666_Some__SUP,axiom,
% 0.33/0.65 ! [A2: set_int,F: int > set_nat] :
% 0.33/0.65 ( ( A2 != bot_bot_set_int )
% 0.33/0.65 => ( ( some_set_nat @ ( comple7399068483239264473et_nat @ ( image_int_set_nat @ F @ A2 ) ) )
% 0.33/0.65 = ( comple8455683388168444585et_nat
% 0.33/0.65 @ ( image_2293489338514188681et_nat
% 0.33/0.65 @ ^ [X3: int] : ( some_set_nat @ ( F @ X3 ) )
% 0.33/0.65 @ A2 ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % Some_SUP
% 0.33/0.65 thf(fact_6667_Some__SUP,axiom,
% 0.33/0.65 ! [A2: set_Pr4329608150637261639at_nat,F: produc3843707927480180839at_nat > product_unit] :
% 0.33/0.65 ( ( A2 != bot_bo228742789529271731at_nat )
% 0.33/0.65 => ( ( some_Product_unit @ ( comple4687483117567863418t_unit @ ( image_7082456443403096939t_unit @ F @ A2 ) ) )
% 0.33/0.65 = ( comple7481738165189995200t_unit
% 0.33/0.65 @ ( image_8585598761158579761t_unit
% 0.33/0.65 @ ^ [X3: produc3843707927480180839at_nat] : ( some_Product_unit @ ( F @ X3 ) )
% 0.33/0.65 @ A2 ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % Some_SUP
% 0.33/0.65 thf(fact_6668_Some__SUP,axiom,
% 0.33/0.65 ! [A2: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > product_unit] :
% 0.33/0.65 ( ( A2 != bot_bo2099793752762293965at_nat )
% 0.33/0.65 => ( ( some_Product_unit @ ( comple4687483117567863418t_unit @ ( image_6169909464789311569t_unit @ F @ A2 ) ) )
% 0.33/0.65 = ( comple7481738165189995200t_unit
% 0.33/0.65 @ ( image_7548311901266006551t_unit
% 0.33/0.65 @ ^ [X3: product_prod_nat_nat] : ( some_Product_unit @ ( F @ X3 ) )
% 0.33/0.65 @ A2 ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % Some_SUP
% 0.33/0.65 thf(fact_6669_Some__SUP,axiom,
% 0.33/0.65 ! [A2: set_o,F: $o > product_unit] :
% 0.33/0.65 ( ( A2 != bot_bot_set_o )
% 0.33/0.65 => ( ( some_Product_unit @ ( comple4687483117567863418t_unit @ ( image_o_Product_unit @ F @ A2 ) ) )
% 0.33/0.65 = ( comple7481738165189995200t_unit
% 0.33/0.65 @ ( image_4415570909310888640t_unit
% 0.33/0.65 @ ^ [X3: $o] : ( some_Product_unit @ ( F @ X3 ) )
% 0.33/0.65 @ A2 ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % Some_SUP
% 0.33/0.65 thf(fact_6670_Some__SUP,axiom,
% 0.33/0.65 ! [A2: set_nat,F: nat > product_unit] :
% 0.33/0.65 ( ( A2 != bot_bot_set_nat )
% 0.33/0.65 => ( ( some_Product_unit @ ( comple4687483117567863418t_unit @ ( image_8730104196221521654t_unit @ F @ A2 ) ) )
% 0.33/0.65 = ( comple7481738165189995200t_unit
% 0.33/0.65 @ ( image_1497621718204147004t_unit
% 0.33/0.65 @ ^ [X3: nat] : ( some_Product_unit @ ( F @ X3 ) )
% 0.33/0.65 @ A2 ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % Some_SUP
% 0.33/0.65 thf(fact_6671_Some__SUP,axiom,
% 0.33/0.65 ! [A2: set_int,F: int > product_unit] :
% 0.33/0.65 ( ( A2 != bot_bot_set_int )
% 0.33/0.65 => ( ( some_Product_unit @ ( comple4687483117567863418t_unit @ ( image_5846526143423701914t_unit @ F @ A2 ) ) )
% 0.33/0.65 = ( comple7481738165189995200t_unit
% 0.33/0.65 @ ( image_1735198859854722016t_unit
% 0.33/0.65 @ ^ [X3: int] : ( some_Product_unit @ ( F @ X3 ) )
% 0.33/0.65 @ A2 ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % Some_SUP
% 0.33/0.65 thf(fact_6672_finite__range__prod,axiom,
% 0.33/0.65 ! [F: nat > product_prod_nat_nat] :
% 0.33/0.65 ( ( finite_finite_nat @ ( image_nat_nat @ ( comp_P1955610211387027840at_nat @ product_fst_nat_nat @ F ) @ top_top_set_nat ) )
% 0.33/0.65 => ( ( finite_finite_nat @ ( image_nat_nat @ ( comp_P1955610211387027840at_nat @ product_snd_nat_nat @ F ) @ top_top_set_nat ) )
% 0.33/0.65 => ( finite6177210948735845034at_nat @ ( image_5846123807819985514at_nat @ F @ top_top_set_nat ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % finite_range_prod
% 0.33/0.65 thf(fact_6673_finite__range__prod,axiom,
% 0.33/0.65 ! [F: nat > product_prod_nat_int] :
% 0.33/0.65 ( ( finite_finite_nat @ ( image_nat_nat @ ( comp_P7964419862382602716at_nat @ product_fst_nat_int @ F ) @ top_top_set_nat ) )
% 0.33/0.65 => ( ( finite_finite_int @ ( image_nat_int @ ( comp_P8963773574283657272nt_nat @ product_snd_nat_int @ F ) @ top_top_set_nat ) )
% 0.33/0.65 => ( finite1999359929226648326at_int @ ( image_1668272788310788806at_int @ F @ top_top_set_nat ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % finite_range_prod
% 0.33/0.65 thf(fact_6674_finite__range__prod,axiom,
% 0.33/0.65 ! [F: nat > produc2591615631378489102nteger] :
% 0.33/0.65 ( ( finite_finite_nat @ ( image_nat_nat @ ( comp_P9144323761349829517at_nat @ produc8897218493789310642nteger @ F ) @ top_top_set_nat ) )
% 0.33/0.65 => ( ( finite6017078050557962740nteger @ ( image_1215581382706833972nteger @ ( comp_P5461341465284484122er_nat @ produc1781891006948753140nteger @ F ) @ top_top_set_nat ) )
% 0.33/0.65 => ( finite1154042800025562295nteger @ ( image_8507997478476487799nteger @ F @ top_top_set_nat ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % finite_range_prod
% 0.33/0.65 thf(fact_6675_finite__range__prod,axiom,
% 0.33/0.65 ! [F: nat > product_prod_int_nat] :
% 0.33/0.65 ( ( finite_finite_int @ ( image_nat_int @ ( comp_P645145991195131448nt_nat @ product_fst_int_nat @ F ) @ top_top_set_nat ) )
% 0.33/0.65 => ( ( finite_finite_nat @ ( image_nat_nat @ ( comp_P8869164316148852700at_nat @ product_snd_int_nat @ F ) @ top_top_set_nat ) )
% 0.33/0.65 => ( finite7176564660636899590nt_nat @ ( image_6845477519721040070nt_nat @ F @ top_top_set_nat ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % finite_range_prod
% 0.33/0.65 thf(fact_6676_finite__range__prod,axiom,
% 0.33/0.65 ! [F: nat > produc2963269191615333738nteger] :
% 0.33/0.65 ( ( finite_finite_int @ ( image_nat_int @ ( comp_P59025373045620805nt_nat @ produc45500017171379470nteger @ F ) @ top_top_set_nat ) )
% 0.33/0.65 => ( ( finite6017078050557962740nteger @ ( image_1215581382706833972nteger @ ( comp_P6870028373966156406er_nat @ produc2153544567185597776nteger @ F ) @ top_top_set_nat ) )
% 0.33/0.65 => ( finite1525696360262406931nteger @ ( image_8879651038713332435nteger @ F @ top_top_set_nat ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % finite_range_prod
% 0.33/0.65 thf(fact_6677_finite__range__prod,axiom,
% 0.33/0.65 ! [F: nat > produc6433947425880249742er_nat] :
% 0.33/0.65 ( ( finite6017078050557962740nteger @ ( image_1215581382706833972nteger @ ( comp_P5700178199414968986er_nat @ produc8632663045010267826er_nat @ F ) @ top_top_set_nat ) )
% 0.33/0.65 => ( ( finite_finite_nat @ ( image_nat_nat @ ( comp_P1337767177661389325at_nat @ produc1517335558169710324er_nat @ F ) @ top_top_set_nat ) )
% 0.33/0.65 => ( finite4996374594527322935er_nat @ ( image_3126957236123472631er_nat @ F @ top_top_set_nat ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % finite_range_prod
% 0.33/0.65 thf(fact_6678_finite__range__prod,axiom,
% 0.33/0.65 ! [F: nat > produc2256096406371053034er_int] :
% 0.33/0.65 ( ( finite6017078050557962740nteger @ ( image_1215581382706833972nteger @ ( comp_P2475326853202991862er_nat @ produc8630172574501217550er_int @ F ) @ top_top_set_nat ) )
% 0.33/0.65 => ( ( finite_finite_int @ ( image_nat_int @ ( comp_P8345930540558018757nt_nat @ produc1514845087660660048er_int @ F ) @ top_top_set_nat ) )
% 0.33/0.65 => ( finite818523575018126227er_int @ ( image_8172478253469051731er_int @ F @ top_top_set_nat ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % finite_range_prod
% 0.33/0.65 thf(fact_6679_finite__range__prod,axiom,
% 0.33/0.65 ! [F: nat > produc8923325533196201883nteger] :
% 0.33/0.65 ( ( finite6017078050557962740nteger @ ( image_1215581382706833972nteger @ ( comp_P3109732533133679783er_nat @ produc8508995932063986495nteger @ F ) @ top_top_set_nat ) )
% 0.33/0.65 => ( ( finite6017078050557962740nteger @ ( image_1215581382706833972nteger @ ( comp_P3109732533133679783er_nat @ produc6174133586879617921nteger @ F ) @ top_top_set_nat ) )
% 0.33/0.65 => ( finite2154694888287295812nteger @ ( image_4272405876590741764nteger @ F @ top_top_set_nat ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % finite_range_prod
% 0.33/0.65 thf(fact_6680_finite__range__prod,axiom,
% 0.33/0.65 ! [F: nat > product_prod_int_int] :
% 0.33/0.65 ( ( finite_finite_int @ ( image_nat_int @ ( comp_P6653955642190706324nt_nat @ product_fst_int_int @ F ) @ top_top_set_nat ) )
% 0.33/0.65 => ( ( finite_finite_int @ ( image_nat_int @ ( comp_P6653955642190706324nt_nat @ product_snd_int_int @ F ) @ top_top_set_nat ) )
% 0.33/0.65 => ( finite2998713641127702882nt_int @ ( image_2667626500211843362nt_int @ F @ top_top_set_nat ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % finite_range_prod
% 0.33/0.65 thf(fact_6681_finite__range__prod,axiom,
% 0.33/0.65 ! [F: product_unit > product_prod_nat_nat] :
% 0.33/0.65 ( ( finite_finite_nat @ ( image_875570014554754200it_nat @ ( comp_P2980510830910040157t_unit @ product_fst_nat_nat @ F ) @ top_to1996260823553986621t_unit ) )
% 0.33/0.65 => ( ( finite_finite_nat @ ( image_875570014554754200it_nat @ ( comp_P2980510830910040157t_unit @ product_snd_nat_nat @ F ) @ top_to1996260823553986621t_unit ) )
% 0.33/0.65 => ( finite6177210948735845034at_nat @ ( image_7281959405765017145at_nat @ F @ top_to1996260823553986621t_unit ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % finite_range_prod
% 0.33/0.65 thf(fact_6682_UN__atMost__UNIV,axiom,
% 0.33/0.65 ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ set_ord_atMost_nat @ top_top_set_nat ) )
% 0.33/0.65 = top_top_set_nat ) ).
% 0.33/0.65
% 0.33/0.65 % UN_atMost_UNIV
% 0.33/0.65 thf(fact_6683_UN__lessThan__UNIV,axiom,
% 0.33/0.65 ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ set_ord_lessThan_nat @ top_top_set_nat ) )
% 0.33/0.65 = top_top_set_nat ) ).
% 0.33/0.65
% 0.33/0.65 % UN_lessThan_UNIV
% 0.33/0.65 thf(fact_6684_Sup__option__def,axiom,
% 0.33/0.65 ( comple8455683388168444585et_nat
% 0.33/0.65 = ( ^ [A7: set_option_set_nat] :
% 0.33/0.65 ( if_option_set_nat
% 0.33/0.65 @ ( ( A7 = bot_bo5650944848895983264et_nat )
% 0.33/0.65 | ( A7
% 0.33/0.65 = ( insert6281397740311767046et_nat @ none_set_nat @ bot_bo5650944848895983264et_nat ) ) )
% 0.33/0.65 @ none_set_nat
% 0.33/0.65 @ ( some_set_nat @ ( comple7399068483239264473et_nat @ ( these_set_nat @ A7 ) ) ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % Sup_option_def
% 0.33/0.65 thf(fact_6685_Sup__option__def,axiom,
% 0.33/0.65 ( comple7481738165189995200t_unit
% 0.33/0.65 = ( ^ [A7: set_op3165557761946182707t_unit] :
% 0.33/0.65 ( if_opt6227717841141446553t_unit
% 0.33/0.65 @ ( ( A7 = bot_bo2792743115866486943t_unit )
% 0.33/0.65 | ( A7
% 0.33/0.65 = ( insert2866144167138965411t_unit @ none_Product_unit @ bot_bo2792743115866486943t_unit ) ) )
% 0.33/0.65 @ none_Product_unit
% 0.33/0.65 @ ( some_Product_unit @ ( comple4687483117567863418t_unit @ ( these_Product_unit @ A7 ) ) ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % Sup_option_def
% 0.33/0.65 thf(fact_6686_snd__image__mp,axiom,
% 0.33/0.65 ! [A2: set_Pr4329608150637261639at_nat,B5: set_se7855581050983116737at_nat,X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 0.33/0.65 ( ( ord_le2077887516847798113at_nat @ ( image_7979982168039674559at_nat @ produc2937545259423399429at_nat @ A2 ) @ B5 )
% 0.33/0.65 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ A2 )
% 0.33/0.65 => ( member2643936169264416010at_nat @ Y @ B5 ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % snd_image_mp
% 0.33/0.65 thf(fact_6687_snd__image__mp,axiom,
% 0.33/0.65 ! [A2: set_Pr1281608226676607948nteger,B5: set_Pr4811707699266497531nteger,X: produc6241069584506657477e_term > option6357759511663192854e_term,Y: produc8923325533196201883nteger] :
% 0.33/0.65 ( ( ord_le3725938330318615451nteger @ ( image_3141030398089242942nteger @ produc7856867400915047194nteger @ A2 ) @ B5 )
% 0.33/0.65 => ( ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X @ Y ) @ A2 )
% 0.33/0.65 => ( member157494554546826820nteger @ Y @ B5 ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % snd_image_mp
% 0.33/0.65 thf(fact_6688_snd__image__mp,axiom,
% 0.33/0.65 ! [A2: set_Pr3286484037609594932et_nat,B5: set_Pr3948176798113811640et_nat,X: produc3658429121746597890et_nat > $o,Y: produc3658429121746597890et_nat] :
% 0.33/0.65 ( ( ord_le8090042543978450200et_nat @ ( image_4390311411407041927et_nat @ produc4011572625026189258et_nat @ A2 ) @ B5 )
% 0.33/0.65 => ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X @ Y ) @ A2 )
% 0.33/0.65 => ( member6260224972018164377et_nat @ Y @ B5 ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % snd_image_mp
% 0.33/0.65 thf(fact_6689_snd__image__mp,axiom,
% 0.33/0.65 ! [A2: set_Pr8536935166611901872et_nat,B5: set_Pr3286484037609594932et_nat,X: produc3658429121746597890et_nat > $o,Y: produc3925858234332021118et_nat] :
% 0.33/0.65 ( ( ord_le5966269811547037844et_nat @ ( image_4557310310409863807et_nat @ produc5374455773327741254et_nat @ A2 ) @ B5 )
% 0.33/0.65 => ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X @ Y ) @ A2 )
% 0.33/0.65 => ( member1996754912294343701et_nat @ Y @ B5 ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % snd_image_mp
% 0.33/0.65 thf(fact_6690_snd__image__mp,axiom,
% 0.33/0.65 ! [A2: set_Pr9222295170931077689nt_int,B5: set_Pr958786334691620121nt_int,X: produc8551481072490612790e_term > option6357759511663192854e_term,Y: product_prod_int_int] :
% 0.33/0.65 ( ( ord_le2843351958646193337nt_int @ ( image_3915291023682402351nt_int @ produc7328097813583171335nt_int @ A2 ) @ B5 )
% 0.33/0.65 => ( ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X @ Y ) @ A2 )
% 0.33/0.65 => ( member5262025264175285858nt_int @ Y @ B5 ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % snd_image_mp
% 0.33/0.65 thf(fact_6691_snd__image__mp,axiom,
% 0.33/0.65 ! [A2: set_Pr1872883991513573699nt_int,B5: set_Pr958786334691620121nt_int,X: int > option6357759511663192854e_term,Y: product_prod_int_int] :
% 0.33/0.65 ( ( ord_le2843351958646193337nt_int @ ( image_3108077152341812517nt_int @ produc3162348030201620241nt_int @ A2 ) @ B5 )
% 0.33/0.65 => ( ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X @ Y ) @ A2 )
% 0.33/0.65 => ( member5262025264175285858nt_int @ Y @ B5 ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % snd_image_mp
% 0.33/0.65 thf(fact_6692_snd__image__mp,axiom,
% 0.33/0.65 ! [A2: set_Pr4811707699266497531nteger,B5: set_Code_integer,X: code_integer,Y: code_integer] :
% 0.33/0.65 ( ( ord_le7084787975880047091nteger @ ( image_6316824473203919795nteger @ produc6174133586879617921nteger @ A2 ) @ B5 )
% 0.33/0.65 => ( ( member157494554546826820nteger @ ( produc1086072967326762835nteger @ X @ Y ) @ A2 )
% 0.33/0.65 => ( member_Code_integer @ Y @ B5 ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % snd_image_mp
% 0.33/0.65 thf(fact_6693_snd__image__mp,axiom,
% 0.33/0.65 ! [A2: set_Pr958786334691620121nt_int,B5: set_int,X: int,Y: int] :
% 0.33/0.65 ( ( ord_less_eq_set_int @ ( image_5042161079198086560nt_int @ product_snd_int_int @ A2 ) @ B5 )
% 0.33/0.65 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ A2 )
% 0.33/0.65 => ( member_int @ Y @ B5 ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % snd_image_mp
% 0.33/0.65 thf(fact_6694_snd__image__mp,axiom,
% 0.33/0.65 ! [A2: set_Pr2352657477744078772atural,B5: set_Pr7564037697178849041atural,X: code_natural,Y: produc7822875418678951345atural] :
% 0.33/0.65 ( ( ord_le6478268328230966961atural @ ( image_3837677093542026988atural @ produc6591912806276919810atural @ A2 ) @ B5 )
% 0.33/0.65 => ( ( member2108296798382401941atural @ ( produc6639722614265839536atural @ X @ Y ) @ A2 )
% 0.33/0.65 => ( member8280416476884352090atural @ Y @ B5 ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % snd_image_mp
% 0.33/0.65 thf(fact_6695_snd__image__mp,axiom,
% 0.33/0.65 ! [A2: set_Pr1261947904930325089at_nat,B5: set_nat,X: nat,Y: nat] :
% 0.33/0.65 ( ( ord_less_eq_set_nat @ ( image_2486076414777270412at_nat @ product_snd_nat_nat @ A2 ) @ B5 )
% 0.33/0.65 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ A2 )
% 0.33/0.65 => ( member_nat @ Y @ B5 ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % snd_image_mp
% 0.33/0.65 thf(fact_6696_fst__image__mp,axiom,
% 0.33/0.65 ! [A2: set_Pr4329608150637261639at_nat,B5: set_se7855581050983116737at_nat,X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 0.33/0.65 ( ( ord_le2077887516847798113at_nat @ ( image_7979982168039674559at_nat @ produc6011863565407846595at_nat @ A2 ) @ B5 )
% 0.33/0.65 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ A2 )
% 0.33/0.65 => ( member2643936169264416010at_nat @ X @ B5 ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % fst_image_mp
% 0.33/0.65 thf(fact_6697_fst__image__mp,axiom,
% 0.33/0.65 ! [A2: set_Pr1281608226676607948nteger,B5: set_Pr7604974323444597168e_term,X: produc6241069584506657477e_term > option6357759511663192854e_term,Y: produc8923325533196201883nteger] :
% 0.33/0.65 ( ( ord_le7106919388332126736e_term @ ( image_4436781500471753239e_term @ produc7822682618958472924nteger @ A2 ) @ B5 )
% 0.33/0.65 => ( ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X @ Y ) @ A2 )
% 0.33/0.65 => ( member4242434998011752849e_term @ X @ B5 ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % fst_image_mp
% 0.33/0.65 thf(fact_6698_fst__image__mp,axiom,
% 0.33/0.65 ! [A2: set_Pr3286484037609594932et_nat,B5: set_Pr4532377907799695533_nat_o,X: produc3658429121746597890et_nat > $o,Y: produc3658429121746597890et_nat] :
% 0.33/0.65 ( ( ord_le2965882846123202637_nat_o @ ( image_6802380912191114376_nat_o @ produc995936583742144908et_nat @ A2 ) @ B5 )
% 0.33/0.65 => ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X @ Y ) @ A2 )
% 0.33/0.65 => ( member6576561426505652726_nat_o @ X @ B5 ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % fst_image_mp
% 0.33/0.65 thf(fact_6699_fst__image__mp,axiom,
% 0.33/0.65 ! [A2: set_Pr8536935166611901872et_nat,B5: set_Pr4532377907799695533_nat_o,X: produc3658429121746597890et_nat > $o,Y: produc3925858234332021118et_nat] :
% 0.33/0.65 ( ( ord_le2965882846123202637_nat_o @ ( image_2517677226577294348_nat_o @ produc180342877477747464et_nat @ A2 ) @ B5 )
% 0.33/0.65 => ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X @ Y ) @ A2 )
% 0.33/0.65 => ( member6576561426505652726_nat_o @ X @ B5 ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % fst_image_mp
% 0.33/0.65 thf(fact_6700_fst__image__mp,axiom,
% 0.33/0.65 ! [A2: set_Pr9222295170931077689nt_int,B5: set_Pr3642885161833720865e_term,X: produc8551481072490612790e_term > option6357759511663192854e_term,Y: product_prod_int_int] :
% 0.33/0.65 ( ( ord_le4129093240937979009e_term @ ( image_142517975987106933e_term @ produc6816164490631068361nt_int @ A2 ) @ B5 )
% 0.33/0.65 => ( ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X @ Y ) @ A2 )
% 0.33/0.65 => ( member3222579708246209666e_term @ X @ B5 ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % fst_image_mp
% 0.33/0.65 thf(fact_6701_fst__image__mp,axiom,
% 0.33/0.65 ! [A2: set_Pr1872883991513573699nt_int,B5: set_in3461395444621081367e_term,X: int > option6357759511663192854e_term,Y: product_prod_int_int] :
% 0.33/0.65 ( ( ord_le567748327753481079e_term @ ( image_4217645046469565813e_term @ produc6230002227079971283nt_int @ A2 ) @ B5 )
% 0.33/0.65 => ( ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X @ Y ) @ A2 )
% 0.33/0.65 => ( member8845023287901829240e_term @ X @ B5 ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % fst_image_mp
% 0.33/0.65 thf(fact_6702_fst__image__mp,axiom,
% 0.33/0.65 ! [A2: set_Pr4811707699266497531nteger,B5: set_Code_integer,X: code_integer,Y: code_integer] :
% 0.33/0.65 ( ( ord_le7084787975880047091nteger @ ( image_6316824473203919795nteger @ produc8508995932063986495nteger @ A2 ) @ B5 )
% 0.33/0.65 => ( ( member157494554546826820nteger @ ( produc1086072967326762835nteger @ X @ Y ) @ A2 )
% 0.33/0.65 => ( member_Code_integer @ X @ B5 ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % fst_image_mp
% 0.33/0.65 thf(fact_6703_fst__image__mp,axiom,
% 0.33/0.65 ! [A2: set_Pr958786334691620121nt_int,B5: set_int,X: int,Y: int] :
% 0.33/0.65 ( ( ord_less_eq_set_int @ ( image_5042161079198086560nt_int @ product_fst_int_int @ A2 ) @ B5 )
% 0.33/0.65 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ A2 )
% 0.33/0.65 => ( member_int @ X @ B5 ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % fst_image_mp
% 0.33/0.65 thf(fact_6704_fst__image__mp,axiom,
% 0.33/0.65 ! [A2: set_Pr1261947904930325089at_nat,B5: set_nat,X: nat,Y: nat] :
% 0.33/0.65 ( ( ord_less_eq_set_nat @ ( image_2486076414777270412at_nat @ product_fst_nat_nat @ A2 ) @ B5 )
% 0.33/0.65 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ A2 )
% 0.33/0.65 => ( member_nat @ X @ B5 ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % fst_image_mp
% 0.33/0.65 thf(fact_6705_prod_OUnion__comp,axiom,
% 0.33/0.65 ! [B5: set_set_o,G: $o > code_integer] :
% 0.33/0.65 ( ! [X4: set_o] :
% 0.33/0.65 ( ( member_set_o @ X4 @ B5 )
% 0.33/0.65 => ( finite_finite_o @ X4 ) )
% 0.33/0.65 => ( ! [A14: set_o] :
% 0.33/0.65 ( ( member_set_o @ A14 @ B5 )
% 0.33/0.65 => ! [A25: set_o] :
% 0.33/0.65 ( ( member_set_o @ A25 @ B5 )
% 0.33/0.65 => ( ( A14 != A25 )
% 0.33/0.65 => ! [X4: $o] :
% 0.33/0.65 ( ( member_o @ X4 @ A14 )
% 0.33/0.65 => ( ( member_o @ X4 @ A25 )
% 0.33/0.65 => ( ( G @ X4 )
% 0.33/0.65 = one_one_Code_integer ) ) ) ) ) )
% 0.33/0.65 => ( ( groups7694694392188491536nteger @ G @ ( comple90263536869209701_set_o @ B5 ) )
% 0.33/0.65 = ( comp_s262121120021782499nteger @ groups8987389756002350576nteger @ groups7694694392188491536nteger @ G @ B5 ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % prod.Union_comp
% 0.33/0.65 thf(fact_6706_prod_OUnion__comp,axiom,
% 0.33/0.65 ! [B5: set_set_int,G: int > code_integer] :
% 0.33/0.65 ( ! [X4: set_int] :
% 0.33/0.65 ( ( member_set_int @ X4 @ B5 )
% 0.33/0.65 => ( finite_finite_int @ X4 ) )
% 0.33/0.65 => ( ! [A14: set_int] :
% 0.33/0.65 ( ( member_set_int @ A14 @ B5 )
% 0.33/0.65 => ! [A25: set_int] :
% 0.33/0.65 ( ( member_set_int @ A25 @ B5 )
% 0.33/0.65 => ( ( A14 != A25 )
% 0.33/0.65 => ! [X4: int] :
% 0.33/0.65 ( ( member_int @ X4 @ A14 )
% 0.33/0.65 => ( ( member_int @ X4 @ A25 )
% 0.33/0.65 => ( ( G @ X4 )
% 0.33/0.65 = one_one_Code_integer ) ) ) ) ) )
% 0.33/0.65 => ( ( groups3827104343326376752nteger @ G @ ( comple3221217463730067765et_int @ B5 ) )
% 0.33/0.65 = ( comp_s7646638485285982975nteger @ groups8770619586034088166nteger @ groups3827104343326376752nteger @ G @ B5 ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % prod.Union_comp
% 0.33/0.65 thf(fact_6707_prod_OUnion__comp,axiom,
% 0.33/0.65 ! [B5: set_set_Code_integer,G: code_integer > code_integer] :
% 0.33/0.65 ( ! [X4: set_Code_integer] :
% 0.33/0.65 ( ( member1834298987299537450nteger @ X4 @ B5 )
% 0.33/0.65 => ( finite6017078050557962740nteger @ X4 ) )
% 0.33/0.65 => ( ! [A14: set_Code_integer] :
% 0.33/0.65 ( ( member1834298987299537450nteger @ A14 @ B5 )
% 0.33/0.65 => ! [A25: set_Code_integer] :
% 0.33/0.65 ( ( member1834298987299537450nteger @ A25 @ B5 )
% 0.33/0.65 => ( ( A14 != A25 )
% 0.33/0.65 => ! [X4: code_integer] :
% 0.33/0.65 ( ( member_Code_integer @ X4 @ A14 )
% 0.33/0.65 => ( ( member_Code_integer @ X4 @ A25 )
% 0.33/0.65 => ( ( G @ X4 )
% 0.33/0.65 = one_one_Code_integer ) ) ) ) ) )
% 0.33/0.65 => ( ( groups3674199335183972705nteger @ G @ ( comple739944243200306918nteger @ B5 ) )
% 0.33/0.65 = ( comp_s8484400498494363538nteger @ groups1474571732273379991nteger @ groups3674199335183972705nteger @ G @ B5 ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % prod.Union_comp
% 0.33/0.65 thf(fact_6708_prod_OUnion__comp,axiom,
% 0.33/0.65 ! [B5: set_set_o,G: $o > assn] :
% 0.33/0.65 ( ! [X4: set_o] :
% 0.33/0.65 ( ( member_set_o @ X4 @ B5 )
% 0.33/0.65 => ( finite_finite_o @ X4 ) )
% 0.33/0.65 => ( ! [A14: set_o] :
% 0.33/0.65 ( ( member_set_o @ A14 @ B5 )
% 0.33/0.65 => ! [A25: set_o] :
% 0.33/0.65 ( ( member_set_o @ A25 @ B5 )
% 0.33/0.65 => ( ( A14 != A25 )
% 0.33/0.65 => ! [X4: $o] :
% 0.33/0.65 ( ( member_o @ X4 @ A14 )
% 0.33/0.65 => ( ( member_o @ X4 @ A25 )
% 0.33/0.65 => ( ( G @ X4 )
% 0.33/0.65 = one_one_assn ) ) ) ) ) )
% 0.33/0.65 => ( ( groups5301882518646026715o_assn @ G @ ( comple90263536869209701_set_o @ B5 ) )
% 0.33/0.65 = ( comp_s518380907012905326o_assn @ groups6963733262650904763o_assn @ groups5301882518646026715o_assn @ G @ B5 ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % prod.Union_comp
% 0.33/0.65 thf(fact_6709_prod_OUnion__comp,axiom,
% 0.33/0.65 ! [B5: set_set_int,G: int > assn] :
% 0.33/0.65 ( ! [X4: set_int] :
% 0.33/0.65 ( ( member_set_int @ X4 @ B5 )
% 0.33/0.65 => ( finite_finite_int @ X4 ) )
% 0.33/0.65 => ( ! [A14: set_int] :
% 0.33/0.65 ( ( member_set_int @ A14 @ B5 )
% 0.33/0.65 => ! [A25: set_int] :
% 0.33/0.65 ( ( member_set_int @ A25 @ B5 )
% 0.33/0.65 => ( ( A14 != A25 )
% 0.33/0.65 => ! [X4: int] :
% 0.33/0.65 ( ( member_int @ X4 @ A14 )
% 0.33/0.65 => ( ( member_int @ X4 @ A25 )
% 0.33/0.65 => ( ( G @ X4 )
% 0.33/0.65 = one_one_assn ) ) ) ) ) )
% 0.33/0.65 => ( ( groups7882442080178216443t_assn @ G @ ( comple3221217463730067765et_int @ B5 ) )
% 0.33/0.65 = ( comp_s4595925057662634336t_assn @ groups5950967880310095793t_assn @ groups7882442080178216443t_assn @ G @ B5 ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % prod.Union_comp
% 0.33/0.65 thf(fact_6710_prod_OUnion__comp,axiom,
% 0.33/0.65 ! [B5: set_set_Code_integer,G: code_integer > assn] :
% 0.33/0.65 ( ! [X4: set_Code_integer] :
% 0.33/0.65 ( ( member1834298987299537450nteger @ X4 @ B5 )
% 0.33/0.65 => ( finite6017078050557962740nteger @ X4 ) )
% 0.33/0.65 => ( ! [A14: set_Code_integer] :
% 0.33/0.65 ( ( member1834298987299537450nteger @ A14 @ B5 )
% 0.33/0.65 => ! [A25: set_Code_integer] :
% 0.33/0.65 ( ( member1834298987299537450nteger @ A25 @ B5 )
% 0.33/0.65 => ( ( A14 != A25 )
% 0.33/0.65 => ! [X4: code_integer] :
% 0.33/0.65 ( ( member_Code_integer @ X4 @ A14 )
% 0.33/0.65 => ( ( member_Code_integer @ X4 @ A25 )
% 0.33/0.65 => ( ( G @ X4 )
% 0.33/0.65 = one_one_assn ) ) ) ) ) )
% 0.33/0.65 => ( ( groups1304777262505850412r_assn @ G @ ( comple739944243200306918nteger @ B5 ) )
% 0.33/0.65 = ( comp_s3531641609786562035r_assn @ groups4245288774754739042r_assn @ groups1304777262505850412r_assn @ G @ B5 ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % prod.Union_comp
% 0.33/0.65 thf(fact_6711_prod_OUnion__comp,axiom,
% 0.33/0.65 ! [B5: set_set_o,G: $o > rat] :
% 0.33/0.65 ( ! [X4: set_o] :
% 0.33/0.65 ( ( member_set_o @ X4 @ B5 )
% 0.33/0.65 => ( finite_finite_o @ X4 ) )
% 0.33/0.65 => ( ! [A14: set_o] :
% 0.33/0.65 ( ( member_set_o @ A14 @ B5 )
% 0.33/0.65 => ! [A25: set_o] :
% 0.33/0.65 ( ( member_set_o @ A25 @ B5 )
% 0.33/0.65 => ( ( A14 != A25 )
% 0.33/0.65 => ! [X4: $o] :
% 0.33/0.65 ( ( member_o @ X4 @ A14 )
% 0.33/0.65 => ( ( member_o @ X4 @ A25 )
% 0.33/0.65 => ( ( G @ X4 )
% 0.33/0.65 = one_one_rat ) ) ) ) ) )
% 0.33/0.65 => ( ( groups2869687844427037835_o_rat @ G @ ( comple90263536869209701_set_o @ B5 ) )
% 0.33/0.65 = ( comp_s1265507639253661726_o_rat @ groups4233643617323539307_o_rat @ groups2869687844427037835_o_rat @ G @ B5 ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % prod.Union_comp
% 0.33/0.65 thf(fact_6712_prod_OUnion__comp,axiom,
% 0.33/0.65 ! [B5: set_set_int,G: int > rat] :
% 0.33/0.65 ( ! [X4: set_int] :
% 0.33/0.65 ( ( member_set_int @ X4 @ B5 )
% 0.33/0.65 => ( finite_finite_int @ X4 ) )
% 0.33/0.65 => ( ! [A14: set_int] :
% 0.33/0.65 ( ( member_set_int @ A14 @ B5 )
% 0.33/0.65 => ! [A25: set_int] :
% 0.33/0.65 ( ( member_set_int @ A25 @ B5 )
% 0.33/0.65 => ( ( A14 != A25 )
% 0.33/0.65 => ! [X4: int] :
% 0.33/0.65 ( ( member_int @ X4 @ A14 )
% 0.33/0.65 => ( ( member_int @ X4 @ A25 )
% 0.33/0.65 => ( ( G @ X4 )
% 0.33/0.65 = one_one_rat ) ) ) ) ) )
% 0.33/0.65 => ( ( groups1072433553688619179nt_rat @ G @ ( comple3221217463730067765et_int @ B5 ) )
% 0.33/0.65 = ( comp_s4088261402702255472nt_rat @ groups5800339274786551393nt_rat @ groups1072433553688619179nt_rat @ G @ B5 ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % prod.Union_comp
% 0.33/0.65 thf(fact_6713_prod_OUnion__comp,axiom,
% 0.33/0.65 ! [B5: set_set_Code_integer,G: code_integer > rat] :
% 0.33/0.65 ( ! [X4: set_Code_integer] :
% 0.33/0.65 ( ( member1834298987299537450nteger @ X4 @ B5 )
% 0.33/0.65 => ( finite6017078050557962740nteger @ X4 ) )
% 0.33/0.65 => ( ! [A14: set_Code_integer] :
% 0.33/0.65 ( ( member1834298987299537450nteger @ A14 @ B5 )
% 0.33/0.65 => ! [A25: set_Code_integer] :
% 0.33/0.65 ( ( member1834298987299537450nteger @ A25 @ B5 )
% 0.33/0.65 => ( ( A14 != A25 )
% 0.33/0.65 => ! [X4: code_integer] :
% 0.33/0.65 ( ( member_Code_integer @ X4 @ A14 )
% 0.33/0.65 => ( ( member_Code_integer @ X4 @ A25 )
% 0.33/0.65 => ( ( G @ X4 )
% 0.33/0.65 = one_one_rat ) ) ) ) ) )
% 0.33/0.65 => ( ( groups2555765274223993564er_rat @ G @ ( comple739944243200306918nteger @ B5 ) )
% 0.33/0.65 = ( comp_s9045439038509510147er_rat @ groups5409254039008640018er_rat @ groups2555765274223993564er_rat @ G @ B5 ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % prod.Union_comp
% 0.33/0.65 thf(fact_6714_prod_OUnion__comp,axiom,
% 0.33/0.65 ! [B5: set_set_o,G: $o > nat] :
% 0.33/0.65 ( ! [X4: set_o] :
% 0.33/0.65 ( ( member_set_o @ X4 @ B5 )
% 0.33/0.65 => ( finite_finite_o @ X4 ) )
% 0.33/0.65 => ( ! [A14: set_o] :
% 0.33/0.65 ( ( member_set_o @ A14 @ B5 )
% 0.33/0.65 => ! [A25: set_o] :
% 0.33/0.65 ( ( member_set_o @ A25 @ B5 )
% 0.33/0.65 => ( ( A14 != A25 )
% 0.33/0.65 => ! [X4: $o] :
% 0.33/0.65 ( ( member_o @ X4 @ A14 )
% 0.33/0.65 => ( ( member_o @ X4 @ A25 )
% 0.33/0.65 => ( ( G @ X4 )
% 0.33/0.65 = one_one_nat ) ) ) ) ) )
% 0.33/0.65 => ( ( groups3504817904513533571_o_nat @ G @ ( comple90263536869209701_set_o @ B5 ) )
% 0.33/0.65 = ( comp_s6084864194472624150_o_nat @ groups4868773677410035043_o_nat @ groups3504817904513533571_o_nat @ G @ B5 ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % prod.Union_comp
% 0.33/0.65 thf(fact_6715_UN__UN__finite__eq,axiom,
% 0.33/0.65 ! [A2: nat > set_nat] :
% 0.33/0.65 ( ( comple7399068483239264473et_nat
% 0.33/0.65 @ ( image_nat_set_nat
% 0.33/0.65 @ ^ [N4: nat] : ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ A2 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N4 ) ) )
% 0.33/0.65 @ top_top_set_nat ) )
% 0.33/0.65 = ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ A2 @ top_top_set_nat ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % UN_UN_finite_eq
% 0.33/0.65 thf(fact_6716_UN__le__add__shift,axiom,
% 0.33/0.65 ! [M3: nat > set_nat,K: nat,N2: nat] :
% 0.33/0.65 ( ( comple7399068483239264473et_nat
% 0.33/0.65 @ ( image_nat_set_nat
% 0.33/0.65 @ ^ [I3: nat] : ( M3 @ ( plus_plus_nat @ I3 @ K ) )
% 0.33/0.65 @ ( set_ord_atMost_nat @ N2 ) ) )
% 0.33/0.65 = ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ M3 @ ( set_or1269000886237332187st_nat @ K @ ( plus_plus_nat @ N2 @ K ) ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % UN_le_add_shift
% 0.33/0.65 thf(fact_6717_UN__le__add__shift__strict,axiom,
% 0.33/0.65 ! [M3: nat > set_nat,K: nat,N2: nat] :
% 0.33/0.65 ( ( comple7399068483239264473et_nat
% 0.33/0.65 @ ( image_nat_set_nat
% 0.33/0.65 @ ^ [I3: nat] : ( M3 @ ( plus_plus_nat @ I3 @ K ) )
% 0.33/0.65 @ ( set_ord_lessThan_nat @ N2 ) ) )
% 0.33/0.65 = ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ M3 @ ( set_or4665077453230672383an_nat @ K @ ( plus_plus_nat @ N2 @ K ) ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % UN_le_add_shift_strict
% 0.33/0.65 thf(fact_6718_rat__sgn__code,axiom,
% 0.33/0.65 ! [P4: rat] :
% 0.33/0.65 ( ( quotient_of @ ( sgn_sgn_rat @ P4 ) )
% 0.33/0.65 = ( product_Pair_int_int @ ( sgn_sgn_int @ ( product_fst_int_int @ ( quotient_of @ P4 ) ) ) @ one_one_int ) ) ).
% 0.33/0.65
% 0.33/0.65 % rat_sgn_code
% 0.33/0.65 thf(fact_6719_bezw__non__0,axiom,
% 0.33/0.65 ! [Y: nat,X: nat] :
% 0.33/0.65 ( ( ord_less_nat @ zero_zero_nat @ Y )
% 0.33/0.65 => ( ( bezw @ X @ Y )
% 0.33/0.65 = ( 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 ) ) ) ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % bezw_non_0
% 0.33/0.65 thf(fact_6720_UN__finite__subset,axiom,
% 0.33/0.65 ! [A2: nat > set_nat,C4: set_nat] :
% 0.33/0.65 ( ! [N: nat] : ( ord_less_eq_set_nat @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ A2 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) @ C4 )
% 0.33/0.65 => ( ord_less_eq_set_nat @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ A2 @ top_top_set_nat ) ) @ C4 ) ) ).
% 0.33/0.65
% 0.33/0.65 % UN_finite_subset
% 0.33/0.65 thf(fact_6721_UN__finite2__eq,axiom,
% 0.33/0.65 ! [A2: nat > set_nat,B5: nat > set_nat,K: nat] :
% 0.33/0.65 ( ! [N: nat] :
% 0.33/0.65 ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ A2 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) )
% 0.33/0.65 = ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ B5 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( plus_plus_nat @ N @ K ) ) ) ) )
% 0.33/0.65 => ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ A2 @ top_top_set_nat ) )
% 0.33/0.65 = ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ B5 @ top_top_set_nat ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % UN_finite2_eq
% 0.33/0.65 thf(fact_6722_bezw_Oelims,axiom,
% 0.33/0.65 ! [X: nat,Xa: nat,Y: product_prod_int_int] :
% 0.33/0.65 ( ( ( bezw @ X @ Xa )
% 0.33/0.65 = Y )
% 0.33/0.65 => ( ( ( Xa = zero_zero_nat )
% 0.33/0.65 => ( Y
% 0.33/0.65 = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) )
% 0.33/0.65 & ( ( Xa != zero_zero_nat )
% 0.33/0.65 => ( Y
% 0.33/0.65 = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X @ Xa ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X @ Xa ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X @ Xa ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X @ Xa ) ) ) ) ) ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % bezw.elims
% 0.33/0.65 thf(fact_6723_bezw_Osimps,axiom,
% 0.33/0.65 ( bezw
% 0.33/0.65 = ( ^ [X3: nat,Y3: nat] : ( if_Pro3027730157355071871nt_int @ ( Y3 = zero_zero_nat ) @ ( product_Pair_int_int @ one_one_int @ zero_zero_int ) @ ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Y3 @ ( modulo_modulo_nat @ X3 @ Y3 ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Y3 @ ( modulo_modulo_nat @ X3 @ Y3 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Y3 @ ( modulo_modulo_nat @ X3 @ Y3 ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X3 @ Y3 ) ) ) ) ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % bezw.simps
% 0.33/0.65 thf(fact_6724_max__ext__def,axiom,
% 0.33/0.65 ( max_ex4535816423174879388at_nat
% 0.33/0.65 = ( ^ [R5: set_Pr4329608150637261639at_nat] :
% 0.33/0.65 ( collec2601550354786890194at_nat
% 0.33/0.65 @ ( produc1491100424724016556_nat_o
% 0.33/0.65 @ ( max_ex4845989503969680116at_nat
% 0.33/0.65 @ ^ [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ Y3 ) @ R5 ) ) ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % max_ext_def
% 0.33/0.65 thf(fact_6725_max__ext__def,axiom,
% 0.33/0.65 ( max_ext_nat
% 0.33/0.65 = ( ^ [R5: set_Pr1261947904930325089at_nat] :
% 0.33/0.65 ( collec6662362479098859352et_nat
% 0.33/0.65 @ ( produc6247414631856714078_nat_o
% 0.33/0.65 @ ( max_extp_nat
% 0.33/0.65 @ ^ [X3: nat,Y3: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y3 ) @ R5 ) ) ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % max_ext_def
% 0.33/0.65 thf(fact_6726_max__ext__def,axiom,
% 0.33/0.65 ( max_ex8135407076693332796at_nat
% 0.33/0.65 = ( ^ [R5: set_Pr8693737435421807431at_nat] :
% 0.33/0.65 ( collec6321179662152712658at_nat
% 0.33/0.65 @ ( produc410239310623530412_nat_o
% 0.33/0.65 @ ( max_ex4864111882549613972at_nat
% 0.33/0.65 @ ^ [X3: product_prod_nat_nat,Y3: product_prod_nat_nat] : ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X3 @ Y3 ) @ R5 ) ) ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % max_ext_def
% 0.33/0.65 thf(fact_6727_UN__finite2__subset,axiom,
% 0.33/0.65 ! [A2: nat > set_nat,B5: nat > set_nat,K: nat] :
% 0.33/0.65 ( ! [N: nat] : ( ord_less_eq_set_nat @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ A2 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ B5 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( plus_plus_nat @ N @ K ) ) ) ) )
% 0.33/0.65 => ( ord_less_eq_set_nat @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ A2 @ top_top_set_nat ) ) @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ B5 @ top_top_set_nat ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % UN_finite2_subset
% 0.33/0.65 thf(fact_6728_bezw_Opelims,axiom,
% 0.33/0.65 ! [X: nat,Xa: nat,Y: product_prod_int_int] :
% 0.33/0.65 ( ( ( bezw @ X @ Xa )
% 0.33/0.65 = Y )
% 0.33/0.65 => ( ( accp_P4275260045618599050at_nat @ bezw_rel @ ( product_Pair_nat_nat @ X @ Xa ) )
% 0.33/0.65 => ~ ( ( ( ( Xa = zero_zero_nat )
% 0.33/0.65 => ( Y
% 0.33/0.65 = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) )
% 0.33/0.65 & ( ( Xa != zero_zero_nat )
% 0.33/0.65 => ( Y
% 0.33/0.65 = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X @ Xa ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X @ Xa ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X @ Xa ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X @ Xa ) ) ) ) ) ) ) )
% 0.33/0.65 => ~ ( accp_P4275260045618599050at_nat @ bezw_rel @ ( product_Pair_nat_nat @ X @ Xa ) ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % bezw.pelims
% 0.33/0.65 thf(fact_6729_snd__diag__id,axiom,
% 0.33/0.65 ! [Z: $o] :
% 0.33/0.65 ( ( comp_P2137996956111167876_o_o_o @ product_snd_o_o
% 0.33/0.65 @ ^ [X3: $o] : ( product_Pair_o_o @ X3 @ X3 )
% 0.33/0.65 @ Z )
% 0.33/0.65 = ( id_o @ Z ) ) ).
% 0.33/0.65
% 0.33/0.65 % snd_diag_id
% 0.33/0.65 thf(fact_6730_snd__diag__id,axiom,
% 0.33/0.65 ! [Z: nat] :
% 0.33/0.65 ( ( comp_P1955610211387027840at_nat @ product_snd_nat_nat
% 0.33/0.65 @ ^ [X3: nat] : ( product_Pair_nat_nat @ X3 @ X3 )
% 0.33/0.65 @ Z )
% 0.33/0.65 = ( id_nat @ Z ) ) ).
% 0.33/0.65
% 0.33/0.65 % snd_diag_id
% 0.33/0.65 thf(fact_6731_snd__diag__id,axiom,
% 0.33/0.65 ! [Z: nat > $o] :
% 0.33/0.65 ( ( comp_P8312345242777556868_nat_o @ produc6795044007072221829_nat_o
% 0.33/0.65 @ ^ [X3: nat > $o] : ( produc5701653931590357335_nat_o @ X3 @ X3 )
% 0.33/0.65 @ Z )
% 0.33/0.65 = ( id_nat_o @ Z ) ) ).
% 0.33/0.65
% 0.33/0.65 % snd_diag_id
% 0.33/0.65 thf(fact_6732_snd__diag__id,axiom,
% 0.33/0.65 ! [Z: num] :
% 0.33/0.65 ( ( comp_P864883071962432936um_num @ product_snd_num_num
% 0.33/0.65 @ ^ [X3: num] : ( product_Pair_num_num @ X3 @ X3 )
% 0.33/0.65 @ Z )
% 0.33/0.65 = ( id_num @ Z ) ) ).
% 0.33/0.65
% 0.33/0.65 % snd_diag_id
% 0.33/0.65 thf(fact_6733_snd__diag__id,axiom,
% 0.33/0.65 ! [Z: code_integer] :
% 0.33/0.65 ( ( comp_P7111796090210262324nteger @ produc6174133586879617921nteger
% 0.33/0.65 @ ^ [X3: code_integer] : ( produc1086072967326762835nteger @ X3 @ X3 )
% 0.33/0.65 @ Z )
% 0.33/0.65 = ( id_Code_integer @ Z ) ) ).
% 0.33/0.65
% 0.33/0.65 % snd_diag_id
% 0.33/0.65 thf(fact_6734_snd__diag__id,axiom,
% 0.33/0.65 ! [Z: int] :
% 0.33/0.65 ( ( comp_P6651465171681656048nt_int @ product_snd_int_int
% 0.33/0.65 @ ^ [X3: int] : ( product_Pair_int_int @ X3 @ X3 )
% 0.33/0.65 @ Z )
% 0.33/0.65 = ( id_int @ Z ) ) ).
% 0.33/0.65
% 0.33/0.65 % snd_diag_id
% 0.33/0.65 thf(fact_6735_fst__diag__id,axiom,
% 0.33/0.65 ! [Z: $o] :
% 0.33/0.65 ( ( comp_P2137996956111167876_o_o_o @ product_fst_o_o
% 0.33/0.65 @ ^ [X3: $o] : ( product_Pair_o_o @ X3 @ X3 )
% 0.33/0.65 @ Z )
% 0.33/0.65 = ( id_o @ Z ) ) ).
% 0.33/0.65
% 0.33/0.65 % fst_diag_id
% 0.33/0.65 thf(fact_6736_fst__diag__id,axiom,
% 0.33/0.65 ! [Z: nat] :
% 0.33/0.65 ( ( comp_P1955610211387027840at_nat @ product_fst_nat_nat
% 0.33/0.65 @ ^ [X3: nat] : ( product_Pair_nat_nat @ X3 @ X3 )
% 0.33/0.65 @ Z )
% 0.33/0.65 = ( id_nat @ Z ) ) ).
% 0.33/0.65
% 0.33/0.65 % fst_diag_id
% 0.33/0.65 thf(fact_6737_fst__diag__id,axiom,
% 0.33/0.65 ! [Z: nat > $o] :
% 0.33/0.65 ( ( comp_P8312345242777556868_nat_o @ produc6972895793295859523_nat_o
% 0.33/0.65 @ ^ [X3: nat > $o] : ( produc5701653931590357335_nat_o @ X3 @ X3 )
% 0.33/0.65 @ Z )
% 0.33/0.65 = ( id_nat_o @ Z ) ) ).
% 0.33/0.65
% 0.33/0.65 % fst_diag_id
% 0.33/0.65 thf(fact_6738_fst__diag__id,axiom,
% 0.33/0.65 ! [Z: num] :
% 0.33/0.65 ( ( comp_P864883071962432936um_num @ product_fst_num_num
% 0.33/0.65 @ ^ [X3: num] : ( product_Pair_num_num @ X3 @ X3 )
% 0.33/0.65 @ Z )
% 0.33/0.65 = ( id_num @ Z ) ) ).
% 0.33/0.65
% 0.33/0.65 % fst_diag_id
% 0.33/0.65 thf(fact_6739_fst__diag__id,axiom,
% 0.33/0.65 ! [Z: code_integer] :
% 0.33/0.65 ( ( comp_P7111796090210262324nteger @ produc8508995932063986495nteger
% 0.33/0.65 @ ^ [X3: code_integer] : ( produc1086072967326762835nteger @ X3 @ X3 )
% 0.33/0.65 @ Z )
% 0.33/0.65 = ( id_Code_integer @ Z ) ) ).
% 0.33/0.65
% 0.33/0.65 % fst_diag_id
% 0.33/0.65 thf(fact_6740_fst__diag__id,axiom,
% 0.33/0.65 ! [Z: int] :
% 0.33/0.65 ( ( comp_P6651465171681656048nt_int @ product_fst_int_int
% 0.33/0.65 @ ^ [X3: int] : ( product_Pair_int_int @ X3 @ X3 )
% 0.33/0.65 @ Z )
% 0.33/0.65 = ( id_int @ Z ) ) ).
% 0.33/0.65
% 0.33/0.65 % fst_diag_id
% 0.33/0.65 thf(fact_6741_size__prod__simp,axiom,
% 0.33/0.65 ( basic_7565498685090299632nteger
% 0.33/0.65 = ( ^ [F2: code_integer > nat,G2: code_integer > nat,P6: produc8923325533196201883nteger] : ( plus_plus_nat @ ( plus_plus_nat @ ( F2 @ ( produc8508995932063986495nteger @ P6 ) ) @ ( G2 @ ( produc6174133586879617921nteger @ P6 ) ) ) @ ( suc @ zero_zero_nat ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % size_prod_simp
% 0.33/0.65 thf(fact_6742_size__prod__simp,axiom,
% 0.33/0.65 ( basic_1872990034501187214nt_int
% 0.33/0.65 = ( ^ [F2: int > nat,G2: int > nat,P6: product_prod_int_int] : ( plus_plus_nat @ ( plus_plus_nat @ ( F2 @ ( product_fst_int_int @ P6 ) ) @ ( G2 @ ( product_snd_int_int @ P6 ) ) ) @ ( suc @ zero_zero_nat ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % size_prod_simp
% 0.33/0.65 thf(fact_6743_size__prod__simp,axiom,
% 0.33/0.65 ( basic_8185638495112405971atural
% 0.33/0.65 = ( ^ [F2: code_natural > nat,G2: produc7822875418678951345atural > nat,P6: produc5835291356934675326atural] : ( plus_plus_nat @ ( plus_plus_nat @ ( F2 @ ( produc497848011034438852atural @ P6 ) ) @ ( G2 @ ( produc6591912806276919810atural @ P6 ) ) ) @ ( suc @ zero_zero_nat ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % size_prod_simp
% 0.33/0.65 thf(fact_6744_fst__diag__snd,axiom,
% 0.33/0.65 ( ( comp_P3428181540658402820nteger @ produc8508995932063986495nteger
% 0.33/0.65 @ ( comp_C2277306503614464128nteger
% 0.33/0.65 @ ^ [X3: code_integer] : ( produc1086072967326762835nteger @ X3 @ X3 )
% 0.33/0.65 @ produc6174133586879617921nteger ) )
% 0.33/0.65 = produc6174133586879617921nteger ) ).
% 0.33/0.65
% 0.33/0.65 % fst_diag_snd
% 0.33/0.65 thf(fact_6745_fst__diag__snd,axiom,
% 0.33/0.65 ( ( comp_P5356232565778667509nt_int @ product_fst_int_int
% 0.33/0.65 @ ( comp_i5941103828406351439nt_int
% 0.33/0.65 @ ^ [X3: int] : ( product_Pair_int_int @ X3 @ X3 )
% 0.33/0.65 @ product_snd_int_int ) )
% 0.33/0.65 = product_snd_int_int ) ).
% 0.33/0.65
% 0.33/0.65 % fst_diag_snd
% 0.33/0.65 thf(fact_6746_fst__diag__snd,axiom,
% 0.33/0.65 ( ( comp_P230220204662055659atural @ produc1537665297809786051atural
% 0.33/0.65 @ ( comp_P4943825737035310295atural
% 0.33/0.65 @ ^ [X3: produc7822875418678951345atural] : ( produc4480994950612372183atural @ X3 @ X3 )
% 0.33/0.65 @ produc6591912806276919810atural ) )
% 0.33/0.65 = produc6591912806276919810atural ) ).
% 0.33/0.65
% 0.33/0.65 % fst_diag_snd
% 0.33/0.65 thf(fact_6747_snd__diag__fst,axiom,
% 0.33/0.65 ( ( comp_P3428181540658402820nteger @ produc6174133586879617921nteger
% 0.33/0.65 @ ( comp_C2277306503614464128nteger
% 0.33/0.65 @ ^ [X3: code_integer] : ( produc1086072967326762835nteger @ X3 @ X3 )
% 0.33/0.65 @ produc8508995932063986495nteger ) )
% 0.33/0.65 = produc8508995932063986495nteger ) ).
% 0.33/0.65
% 0.33/0.65 % snd_diag_fst
% 0.33/0.65 thf(fact_6748_snd__diag__fst,axiom,
% 0.33/0.65 ( ( comp_P5356232565778667509nt_int @ product_snd_int_int
% 0.33/0.65 @ ( comp_i5941103828406351439nt_int
% 0.33/0.65 @ ^ [X3: int] : ( product_Pair_int_int @ X3 @ X3 )
% 0.33/0.65 @ product_fst_int_int ) )
% 0.33/0.65 = product_fst_int_int ) ).
% 0.33/0.65
% 0.33/0.65 % snd_diag_fst
% 0.33/0.65 thf(fact_6749_INF__Int__eq2,axiom,
% 0.33/0.65 ! [S2: set_se5479201105039950375at_nat] :
% 0.33/0.65 ( ( comple8322679762649017525_nat_o
% 0.33/0.65 @ ( image_6595146019508340652_nat_o
% 0.33/0.65 @ ^ [I3: set_Pr4329608150637261639at_nat,X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ Y3 ) @ I3 )
% 0.33/0.65 @ S2 ) )
% 0.33/0.65 = ( ^ [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ Y3 ) @ ( comple6751905152567503566at_nat @ S2 ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % INF_Int_eq2
% 0.33/0.65 thf(fact_6750_INF__Int__eq2,axiom,
% 0.33/0.65 ! [S2: set_se7855581050983116737at_nat] :
% 0.33/0.65 ( ( comple1675732732025788397_nat_o
% 0.33/0.65 @ ( image_6923511907955291850_nat_o
% 0.33/0.65 @ ^ [I3: set_Pr1261947904930325089at_nat,X3: nat,Y3: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y3 ) @ I3 )
% 0.33/0.65 @ S2 ) )
% 0.33/0.65 = ( ^ [X3: nat,Y3: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y3 ) @ ( comple1930127330929219688at_nat @ S2 ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % INF_Int_eq2
% 0.33/0.65 thf(fact_6751_INF__Int__eq2,axiom,
% 0.33/0.65 ! [S2: set_se124295367203800706nteger] :
% 0.33/0.65 ( ( comple797978290332539892eger_o
% 0.33/0.65 @ ( image_3377504002992083726eger_o
% 0.33/0.65 @ ^ [I3: set_Pr1281608226676607948nteger,X3: produc6241069584506657477e_term > option6357759511663192854e_term,Y3: produc8923325533196201883nteger] : ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X3 @ Y3 ) @ I3 )
% 0.33/0.65 @ S2 ) )
% 0.33/0.65 = ( ^ [X3: produc6241069584506657477e_term > option6357759511663192854e_term,Y3: produc8923325533196201883nteger] : ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X3 @ Y3 ) @ ( comple141797230998674821nteger @ S2 ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % INF_Int_eq2
% 0.33/0.65 thf(fact_6752_INF__Int__eq2,axiom,
% 0.33/0.65 ! [S2: set_se8543413830569400298et_nat] :
% 0.33/0.65 ( ( comple4401490224799119198_nat_o
% 0.33/0.65 @ ( image_1071233342602175200_nat_o
% 0.33/0.65 @ ^ [I3: set_Pr3286484037609594932et_nat,X3: produc3658429121746597890et_nat > $o,Y3: produc3658429121746597890et_nat] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X3 @ Y3 ) @ I3 )
% 0.33/0.65 @ S2 ) )
% 0.33/0.65 = ( ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3658429121746597890et_nat] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X3 @ Y3 ) @ ( comple8712884055654468845et_nat @ S2 ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % INF_Int_eq2
% 0.33/0.65 thf(fact_6753_INF__Int__eq2,axiom,
% 0.33/0.65 ! [S2: set_se5120235452707311462et_nat] :
% 0.33/0.65 ( ( comple1647972170925272290_nat_o
% 0.33/0.65 @ ( image_6856364241397052896_nat_o
% 0.33/0.65 @ ^ [I3: set_Pr8536935166611901872et_nat,X3: produc3658429121746597890et_nat > $o,Y3: produc3925858234332021118et_nat] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X3 @ Y3 ) @ I3 )
% 0.33/0.65 @ S2 ) )
% 0.33/0.65 = ( ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3925858234332021118et_nat] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X3 @ Y3 ) @ ( comple8400030738448405097et_nat @ S2 ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % INF_Int_eq2
% 0.33/0.65 thf(fact_6754_INF__Int__eq2,axiom,
% 0.33/0.65 ! [S2: set_se2364587433798273647nt_int] :
% 0.33/0.65 ( ( comple2375672059646964807_int_o
% 0.33/0.65 @ ( image_5684251269295653582_int_o
% 0.33/0.65 @ ^ [I3: set_Pr9222295170931077689nt_int,X3: produc8551481072490612790e_term > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X3 @ Y3 ) @ I3 )
% 0.33/0.65 @ S2 ) )
% 0.33/0.65 = ( ^ [X3: produc8551481072490612790e_term > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X3 @ Y3 ) @ ( comple6065809805536145394nt_int @ S2 ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % INF_Int_eq2
% 0.33/0.65 thf(fact_6755_INF__Int__eq2,axiom,
% 0.33/0.65 ! [S2: set_se7394616247590735609nt_int] :
% 0.33/0.65 ( ( comple7280212863790966717_int_o
% 0.33/0.65 @ ( image_1744818337813142478_int_o
% 0.33/0.65 @ ^ [I3: set_Pr1872883991513573699nt_int,X3: int > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X3 @ Y3 ) @ I3 )
% 0.33/0.65 @ S2 ) )
% 0.33/0.65 = ( ^ [X3: int > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X3 @ Y3 ) @ ( comple2057271477292249724nt_int @ S2 ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % INF_Int_eq2
% 0.33/0.65 thf(fact_6756_SUP__Sup__eq2,axiom,
% 0.33/0.65 ! [S2: set_se5479201105039950375at_nat] :
% 0.33/0.65 ( ( comple493620192902636699_nat_o
% 0.33/0.65 @ ( image_6595146019508340652_nat_o
% 0.33/0.65 @ ^ [I3: set_Pr4329608150637261639at_nat,X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ Y3 ) @ I3 )
% 0.33/0.65 @ S2 ) )
% 0.33/0.65 = ( ^ [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ Y3 ) @ ( comple4364388969068068532at_nat @ S2 ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % SUP_Sup_eq2
% 0.33/0.65 thf(fact_6757_SUP__Sup__eq2,axiom,
% 0.33/0.65 ! [S2: set_se7855581050983116737at_nat] :
% 0.33/0.65 ( ( comple3592611370556534995_nat_o
% 0.33/0.65 @ ( image_6923511907955291850_nat_o
% 0.33/0.65 @ ^ [I3: set_Pr1261947904930325089at_nat,X3: nat,Y3: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y3 ) @ I3 )
% 0.33/0.65 @ S2 ) )
% 0.33/0.65 = ( ^ [X3: nat,Y3: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y3 ) @ ( comple5685304695842803022at_nat @ S2 ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % SUP_Sup_eq2
% 0.33/0.65 thf(fact_6758_SUP__Sup__eq2,axiom,
% 0.33/0.65 ! [S2: set_se124295367203800706nteger] :
% 0.33/0.65 ( ( comple6692557002573936782eger_o
% 0.33/0.65 @ ( image_3377504002992083726eger_o
% 0.33/0.65 @ ^ [I3: set_Pr1281608226676607948nteger,X3: produc6241069584506657477e_term > option6357759511663192854e_term,Y3: produc8923325533196201883nteger] : ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X3 @ Y3 ) @ I3 )
% 0.33/0.65 @ S2 ) )
% 0.33/0.65 = ( ^ [X3: produc6241069584506657477e_term > option6357759511663192854e_term,Y3: produc8923325533196201883nteger] : ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X3 @ Y3 ) @ ( comple1324685164916153887nteger @ S2 ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % SUP_Sup_eq2
% 0.33/0.65 thf(fact_6759_SUP__Sup__eq2,axiom,
% 0.33/0.65 ! [S2: set_se8543413830569400298et_nat] :
% 0.33/0.65 ( ( comple2736776311324672504_nat_o
% 0.33/0.65 @ ( image_1071233342602175200_nat_o
% 0.33/0.65 @ ^ [I3: set_Pr3286484037609594932et_nat,X3: produc3658429121746597890et_nat > $o,Y3: produc3658429121746597890et_nat] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X3 @ Y3 ) @ I3 )
% 0.33/0.65 @ S2 ) )
% 0.33/0.65 = ( ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3658429121746597890et_nat] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X3 @ Y3 ) @ ( comple4849024849677941639et_nat @ S2 ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % SUP_Sup_eq2
% 0.33/0.65 thf(fact_6760_SUP__Sup__eq2,axiom,
% 0.33/0.65 ! [S2: set_se5120235452707311462et_nat] :
% 0.33/0.65 ( ( comple5542144468884744060_nat_o
% 0.33/0.65 @ ( image_6856364241397052896_nat_o
% 0.33/0.65 @ ^ [I3: set_Pr8536935166611901872et_nat,X3: produc3658429121746597890et_nat > $o,Y3: produc3925858234332021118et_nat] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X3 @ Y3 ) @ I3 )
% 0.33/0.65 @ S2 ) )
% 0.33/0.65 = ( ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3925858234332021118et_nat] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X3 @ Y3 ) @ ( comple5063570841203093763et_nat @ S2 ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % SUP_Sup_eq2
% 0.33/0.65 thf(fact_6761_SUP__Sup__eq2,axiom,
% 0.33/0.65 ! [S2: set_se2364587433798273647nt_int] :
% 0.33/0.65 ( ( comple7735192718774405345_int_o
% 0.33/0.65 @ ( image_5684251269295653582_int_o
% 0.33/0.65 @ ^ [I3: set_Pr9222295170931077689nt_int,X3: produc8551481072490612790e_term > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X3 @ Y3 ) @ I3 )
% 0.33/0.65 @ S2 ) )
% 0.33/0.65 = ( ^ [X3: produc8551481072490612790e_term > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X3 @ Y3 ) @ ( comple6871990601243273356nt_int @ S2 ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % SUP_Sup_eq2
% 0.33/0.65 thf(fact_6762_SUP__Sup__eq2,axiom,
% 0.33/0.65 ! [S2: set_se7394616247590735609nt_int] :
% 0.33/0.65 ( ( comple8902563120744349527_int_o
% 0.33/0.65 @ ( image_1744818337813142478_int_o
% 0.33/0.65 @ ^ [I3: set_Pr1872883991513573699nt_int,X3: int > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X3 @ Y3 ) @ I3 )
% 0.33/0.65 @ S2 ) )
% 0.33/0.65 = ( ^ [X3: int > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X3 @ Y3 ) @ ( comple5772984051336441366nt_int @ S2 ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % SUP_Sup_eq2
% 0.33/0.65 thf(fact_6763_Inf__INT__eq2,axiom,
% 0.33/0.65 ( comple8322679762649017525_nat_o
% 0.33/0.65 = ( ^ [S5: set_se9180647916752606350_nat_o,X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ Y3 ) @ ( comple6751905152567503566at_nat @ ( image_4902389024228248874at_nat @ collec6321179662152712658at_nat @ ( image_6226802281960588479_nat_o @ produc410239310623530412_nat_o @ S5 ) ) ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % Inf_INT_eq2
% 0.33/0.65 thf(fact_6764_Inf__INT__eq2,axiom,
% 0.33/0.65 ( comple1675732732025788397_nat_o
% 0.33/0.65 = ( ^ [S5: set_nat_nat_o,X3: nat,Y3: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y3 ) @ ( comple1930127330929219688at_nat @ ( image_7124889717316225246at_nat @ collec3392354462482085612at_nat @ ( image_7429393840292777309_nat_o @ produc6081775807080527818_nat_o @ S5 ) ) ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % Inf_INT_eq2
% 0.33/0.65 thf(fact_6765_Inf__INT__eq2,axiom,
% 0.33/0.65 ( comple797978290332539892eger_o
% 0.33/0.65 = ( ^ [S5: set_Pr8914822823351560561eger_o,X3: produc6241069584506657477e_term > option6357759511663192854e_term,Y3: produc8923325533196201883nteger] : ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X3 @ Y3 ) @ ( comple141797230998674821nteger @ ( image_2691561895000378432nteger @ collec6950949345391930603nteger @ ( image_5214523798439755767eger_o @ produc6253627499356882019eger_o @ S5 ) ) ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % Inf_INT_eq2
% 0.33/0.65 thf(fact_6766_Inf__INT__eq2,axiom,
% 0.33/0.65 ( comple4401490224799119198_nat_o
% 0.33/0.65 = ( ^ [S5: set_Pr8208987589773510107_nat_o,X3: produc3658429121746597890et_nat > $o,Y3: produc3658429121746597890et_nat] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X3 @ Y3 ) @ ( comple8712884055654468845et_nat @ ( image_8138495846740763712et_nat @ collec1402215087704437587et_nat @ ( image_8189751627993580965_nat_o @ produc1437786849005270451_nat_o @ S5 ) ) ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % Inf_INT_eq2
% 0.33/0.65 thf(fact_6767_Inf__INT__eq2,axiom,
% 0.33/0.65 ( comple1647972170925272290_nat_o
% 0.33/0.65 = ( ^ [S5: set_Pr1457143144315775327_nat_o,X3: produc3658429121746597890et_nat > $o,Y3: produc3925858234332021118et_nat] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X3 @ Y3 ) @ ( comple8400030738448405097et_nat @ ( image_3321512208570918720et_nat @ collec5543584681430388431et_nat @ ( image_1033581555836824229_nat_o @ produc838355143741117751_nat_o @ S5 ) ) ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % Inf_INT_eq2
% 0.33/0.65 thf(fact_6768_Inf__INT__eq2,axiom,
% 0.33/0.65 ( comple2375672059646964807_int_o
% 0.33/0.65 = ( ^ [S5: set_Pr5050529186185961540_int_o,X3: produc8551481072490612790e_term > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X3 @ Y3 ) @ ( comple6065809805536145394nt_int @ ( image_7643917626522560896nt_int @ collec1790188477890212312nt_int @ ( image_7631425643974863415_int_o @ produc1573362020775583542_int_o @ S5 ) ) ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % Inf_INT_eq2
% 0.33/0.65 thf(fact_6769_Inf__INT__eq2,axiom,
% 0.33/0.65 ( comple7280212863790966717_int_o
% 0.33/0.65 = ( ^ [S5: set_in8474487674441654202_int_o,X3: int > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X3 @ Y3 ) @ ( comple2057271477292249724nt_int @ ( image_2770089787918713472nt_int @ collec506566255779805410nt_int @ ( image_7670822187664137143_int_o @ produc2558449545302689196_int_o @ S5 ) ) ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % Inf_INT_eq2
% 0.33/0.65 thf(fact_6770_Sup__SUP__eq2,axiom,
% 0.33/0.65 ( comple493620192902636699_nat_o
% 0.33/0.65 = ( ^ [S5: set_se9180647916752606350_nat_o,X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ Y3 ) @ ( comple4364388969068068532at_nat @ ( image_4902389024228248874at_nat @ collec6321179662152712658at_nat @ ( image_6226802281960588479_nat_o @ produc410239310623530412_nat_o @ S5 ) ) ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % Sup_SUP_eq2
% 0.33/0.65 thf(fact_6771_Sup__SUP__eq2,axiom,
% 0.33/0.65 ( comple3592611370556534995_nat_o
% 0.33/0.65 = ( ^ [S5: set_nat_nat_o,X3: nat,Y3: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y3 ) @ ( comple5685304695842803022at_nat @ ( image_7124889717316225246at_nat @ collec3392354462482085612at_nat @ ( image_7429393840292777309_nat_o @ produc6081775807080527818_nat_o @ S5 ) ) ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % Sup_SUP_eq2
% 0.33/0.65 thf(fact_6772_Sup__SUP__eq2,axiom,
% 0.33/0.65 ( comple6692557002573936782eger_o
% 0.33/0.65 = ( ^ [S5: set_Pr8914822823351560561eger_o,X3: produc6241069584506657477e_term > option6357759511663192854e_term,Y3: produc8923325533196201883nteger] : ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X3 @ Y3 ) @ ( comple1324685164916153887nteger @ ( image_2691561895000378432nteger @ collec6950949345391930603nteger @ ( image_5214523798439755767eger_o @ produc6253627499356882019eger_o @ S5 ) ) ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % Sup_SUP_eq2
% 0.33/0.65 thf(fact_6773_Sup__SUP__eq2,axiom,
% 0.33/0.65 ( comple2736776311324672504_nat_o
% 0.33/0.65 = ( ^ [S5: set_Pr8208987589773510107_nat_o,X3: produc3658429121746597890et_nat > $o,Y3: produc3658429121746597890et_nat] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X3 @ Y3 ) @ ( comple4849024849677941639et_nat @ ( image_8138495846740763712et_nat @ collec1402215087704437587et_nat @ ( image_8189751627993580965_nat_o @ produc1437786849005270451_nat_o @ S5 ) ) ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % Sup_SUP_eq2
% 0.33/0.65 thf(fact_6774_Sup__SUP__eq2,axiom,
% 0.33/0.65 ( comple5542144468884744060_nat_o
% 0.33/0.65 = ( ^ [S5: set_Pr1457143144315775327_nat_o,X3: produc3658429121746597890et_nat > $o,Y3: produc3925858234332021118et_nat] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X3 @ Y3 ) @ ( comple5063570841203093763et_nat @ ( image_3321512208570918720et_nat @ collec5543584681430388431et_nat @ ( image_1033581555836824229_nat_o @ produc838355143741117751_nat_o @ S5 ) ) ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % Sup_SUP_eq2
% 0.33/0.65 thf(fact_6775_Sup__SUP__eq2,axiom,
% 0.33/0.65 ( comple7735192718774405345_int_o
% 0.33/0.65 = ( ^ [S5: set_Pr5050529186185961540_int_o,X3: produc8551481072490612790e_term > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X3 @ Y3 ) @ ( comple6871990601243273356nt_int @ ( image_7643917626522560896nt_int @ collec1790188477890212312nt_int @ ( image_7631425643974863415_int_o @ produc1573362020775583542_int_o @ S5 ) ) ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % Sup_SUP_eq2
% 0.33/0.65 thf(fact_6776_Sup__SUP__eq2,axiom,
% 0.33/0.65 ( comple8902563120744349527_int_o
% 0.33/0.65 = ( ^ [S5: set_in8474487674441654202_int_o,X3: int > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X3 @ Y3 ) @ ( comple5772984051336441366nt_int @ ( image_2770089787918713472nt_int @ collec506566255779805410nt_int @ ( image_7670822187664137143_int_o @ produc2558449545302689196_int_o @ S5 ) ) ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % Sup_SUP_eq2
% 0.33/0.65 thf(fact_6777_fst__diag__fst,axiom,
% 0.33/0.65 ( ( comp_P3428181540658402820nteger @ produc8508995932063986495nteger
% 0.33/0.65 @ ( comp_C2277306503614464128nteger
% 0.33/0.65 @ ^ [X3: code_integer] : ( produc1086072967326762835nteger @ X3 @ X3 )
% 0.33/0.65 @ produc8508995932063986495nteger ) )
% 0.33/0.65 = produc8508995932063986495nteger ) ).
% 0.33/0.65
% 0.33/0.65 % fst_diag_fst
% 0.33/0.65 thf(fact_6778_fst__diag__fst,axiom,
% 0.33/0.65 ( ( comp_P5356232565778667509nt_int @ product_fst_int_int
% 0.33/0.65 @ ( comp_i5941103828406351439nt_int
% 0.33/0.65 @ ^ [X3: int] : ( product_Pair_int_int @ X3 @ X3 )
% 0.33/0.65 @ product_fst_int_int ) )
% 0.33/0.65 = product_fst_int_int ) ).
% 0.33/0.65
% 0.33/0.65 % fst_diag_fst
% 0.33/0.65 thf(fact_6779_snd__diag__snd,axiom,
% 0.33/0.65 ( ( comp_P230220204662055659atural @ produc7455300194457530885atural
% 0.33/0.65 @ ( comp_P4943825737035310295atural
% 0.33/0.65 @ ^ [X3: produc7822875418678951345atural] : ( produc4480994950612372183atural @ X3 @ X3 )
% 0.33/0.65 @ produc6591912806276919810atural ) )
% 0.33/0.65 = produc6591912806276919810atural ) ).
% 0.33/0.65
% 0.33/0.65 % snd_diag_snd
% 0.33/0.65 thf(fact_6780_snd__diag__snd,axiom,
% 0.33/0.65 ( ( comp_P3428181540658402820nteger @ produc6174133586879617921nteger
% 0.33/0.65 @ ( comp_C2277306503614464128nteger
% 0.33/0.65 @ ^ [X3: code_integer] : ( produc1086072967326762835nteger @ X3 @ X3 )
% 0.33/0.65 @ produc6174133586879617921nteger ) )
% 0.33/0.65 = produc6174133586879617921nteger ) ).
% 0.33/0.65
% 0.33/0.65 % snd_diag_snd
% 0.33/0.65 thf(fact_6781_snd__diag__snd,axiom,
% 0.33/0.65 ( ( comp_P5356232565778667509nt_int @ product_snd_int_int
% 0.33/0.65 @ ( comp_i5941103828406351439nt_int
% 0.33/0.65 @ ^ [X3: int] : ( product_Pair_int_int @ X3 @ X3 )
% 0.33/0.65 @ product_snd_int_int ) )
% 0.33/0.65 = product_snd_int_int ) ).
% 0.33/0.65
% 0.33/0.65 % snd_diag_snd
% 0.33/0.65 thf(fact_6782_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 0.33/0.65 ! [P: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o,X: produc6241069584506657477e_term > option6357759511663192854e_term,Y: produc8923325533196201883nteger,A: produc1908205239877642774nteger] :
% 0.33/0.65 ( ( P @ X @ Y )
% 0.33/0.65 => ( ( A
% 0.33/0.65 = ( produc8603105652947943368nteger @ X @ Y ) )
% 0.33/0.65 => ( P @ ( produc7822682618958472924nteger @ A ) @ ( produc7856867400915047194nteger @ A ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % BNF_Greatest_Fixpoint.subst_Pair
% 0.33/0.65 thf(fact_6783_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 0.33/0.65 ! [P: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o,X: produc3658429121746597890et_nat > $o,Y: produc3658429121746597890et_nat,A: produc3925858234332021118et_nat] :
% 0.33/0.65 ( ( P @ X @ Y )
% 0.33/0.65 => ( ( A
% 0.33/0.65 = ( produc5001842942810119800et_nat @ X @ Y ) )
% 0.33/0.65 => ( P @ ( produc995936583742144908et_nat @ A ) @ ( produc4011572625026189258et_nat @ A ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % BNF_Greatest_Fixpoint.subst_Pair
% 0.33/0.65 thf(fact_6784_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 0.33/0.65 ! [P: ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o,X: produc3658429121746597890et_nat > $o,Y: produc3925858234332021118et_nat,A: produc2732055786443039994et_nat] :
% 0.33/0.65 ( ( P @ X @ Y )
% 0.33/0.65 => ( ( A
% 0.33/0.65 = ( produc2245416461498447860et_nat @ X @ Y ) )
% 0.33/0.65 => ( P @ ( produc180342877477747464et_nat @ A ) @ ( produc5374455773327741254et_nat @ A ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % BNF_Greatest_Fixpoint.subst_Pair
% 0.33/0.65 thf(fact_6785_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 0.33/0.65 ! [P: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o,X: produc8551481072490612790e_term > option6357759511663192854e_term,Y: product_prod_int_int,A: produc2285326912895808259nt_int] :
% 0.33/0.65 ( ( P @ X @ Y )
% 0.33/0.65 => ( ( A
% 0.33/0.65 = ( produc5700946648718959541nt_int @ X @ Y ) )
% 0.33/0.65 => ( P @ ( produc6816164490631068361nt_int @ A ) @ ( produc7328097813583171335nt_int @ A ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % BNF_Greatest_Fixpoint.subst_Pair
% 0.33/0.65 thf(fact_6786_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 0.33/0.65 ! [P: ( int > option6357759511663192854e_term ) > product_prod_int_int > $o,X: int > option6357759511663192854e_term,Y: product_prod_int_int,A: produc7773217078559923341nt_int] :
% 0.33/0.65 ( ( P @ X @ Y )
% 0.33/0.65 => ( ( A
% 0.33/0.65 = ( produc4305682042979456191nt_int @ X @ Y ) )
% 0.33/0.65 => ( P @ ( produc6230002227079971283nt_int @ A ) @ ( produc3162348030201620241nt_int @ A ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % BNF_Greatest_Fixpoint.subst_Pair
% 0.33/0.65 thf(fact_6787_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 0.33/0.65 ! [P: code_integer > code_integer > $o,X: code_integer,Y: code_integer,A: produc8923325533196201883nteger] :
% 0.33/0.65 ( ( P @ X @ Y )
% 0.33/0.65 => ( ( A
% 0.33/0.65 = ( produc1086072967326762835nteger @ X @ Y ) )
% 0.33/0.65 => ( P @ ( produc8508995932063986495nteger @ A ) @ ( produc6174133586879617921nteger @ A ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % BNF_Greatest_Fixpoint.subst_Pair
% 0.33/0.65 thf(fact_6788_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 0.33/0.65 ! [P: int > int > $o,X: int,Y: int,A: product_prod_int_int] :
% 0.33/0.65 ( ( P @ X @ Y )
% 0.33/0.65 => ( ( A
% 0.33/0.65 = ( product_Pair_int_int @ X @ Y ) )
% 0.33/0.65 => ( P @ ( product_fst_int_int @ A ) @ ( product_snd_int_int @ A ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % BNF_Greatest_Fixpoint.subst_Pair
% 0.33/0.65 thf(fact_6789_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 0.33/0.65 ! [P: code_natural > produc7822875418678951345atural > $o,X: code_natural,Y: produc7822875418678951345atural,A: produc5835291356934675326atural] :
% 0.33/0.65 ( ( P @ X @ Y )
% 0.33/0.65 => ( ( A
% 0.33/0.65 = ( produc6639722614265839536atural @ X @ Y ) )
% 0.33/0.65 => ( P @ ( produc497848011034438852atural @ A ) @ ( produc6591912806276919810atural @ A ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % BNF_Greatest_Fixpoint.subst_Pair
% 0.33/0.65 thf(fact_6790_normalize__def,axiom,
% 0.33/0.65 ( normalize
% 0.33/0.65 = ( ^ [P6: product_prod_int_int] :
% 0.33/0.65 ( if_Pro3027730157355071871nt_int @ ( ord_less_int @ zero_zero_int @ ( product_snd_int_int @ P6 ) ) @ ( product_Pair_int_int @ ( divide_divide_int @ ( product_fst_int_int @ P6 ) @ ( gcd_gcd_int @ ( product_fst_int_int @ P6 ) @ ( product_snd_int_int @ P6 ) ) ) @ ( divide_divide_int @ ( product_snd_int_int @ P6 ) @ ( gcd_gcd_int @ ( product_fst_int_int @ P6 ) @ ( product_snd_int_int @ P6 ) ) ) )
% 0.33/0.65 @ ( if_Pro3027730157355071871nt_int
% 0.33/0.65 @ ( ( product_snd_int_int @ P6 )
% 0.33/0.65 = zero_zero_int )
% 0.33/0.65 @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 0.33/0.65 @ ( product_Pair_int_int @ ( divide_divide_int @ ( product_fst_int_int @ P6 ) @ ( uminus_uminus_int @ ( gcd_gcd_int @ ( product_fst_int_int @ P6 ) @ ( product_snd_int_int @ P6 ) ) ) ) @ ( divide_divide_int @ ( product_snd_int_int @ P6 ) @ ( uminus_uminus_int @ ( gcd_gcd_int @ ( product_fst_int_int @ P6 ) @ ( product_snd_int_int @ P6 ) ) ) ) ) ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % normalize_def
% 0.33/0.65 thf(fact_6791_range__prod,axiom,
% 0.33/0.65 ! [F: nat > produc6433947425880249742er_nat] :
% 0.33/0.65 ( ord_le3209295114279298062er_nat @ ( image_3126957236123472631er_nat @ F @ top_top_set_nat )
% 0.33/0.65 @ ( produc4260658192689636599er_nat @ ( image_1215581382706833972nteger @ ( comp_P5700178199414968986er_nat @ produc8632663045010267826er_nat @ F ) @ top_top_set_nat )
% 0.33/0.65 @ ^ [Uu: code_integer] : ( image_nat_nat @ ( comp_P1337767177661389325at_nat @ produc1517335558169710324er_nat @ F ) @ top_top_set_nat ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % range_prod
% 0.33/0.65 thf(fact_6792_range__prod,axiom,
% 0.33/0.65 ! [F: nat > produc2256096406371053034er_int] :
% 0.33/0.65 ( ord_le719211969347571306er_int @ ( image_8172478253469051731er_int @ F @ top_top_set_nat )
% 0.33/0.65 @ ( produc4258167722180586323er_int @ ( image_1215581382706833972nteger @ ( comp_P2475326853202991862er_nat @ produc8630172574501217550er_int @ F ) @ top_top_set_nat )
% 0.33/0.65 @ ^ [Uu: code_integer] : ( image_nat_int @ ( comp_P8345930540558018757nt_nat @ produc1514845087660660048er_int @ F ) @ top_top_set_nat ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % range_prod
% 0.33/0.65 thf(fact_6793_range__prod,axiom,
% 0.33/0.65 ! [F: nat > produc2591615631378489102nteger] :
% 0.33/0.65 ( ord_le5852610332322655630nteger @ ( image_8507997478476487799nteger @ F @ top_top_set_nat )
% 0.33/0.65 @ ( produc4525213641468679415nteger @ ( image_nat_nat @ ( comp_P9144323761349829517at_nat @ produc8897218493789310642nteger @ F ) @ top_top_set_nat )
% 0.33/0.65 @ ^ [Uu: nat] : ( image_1215581382706833972nteger @ ( comp_P5461341465284484122er_nat @ produc1781891006948753140nteger @ F ) @ top_top_set_nat ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % range_prod
% 0.33/0.65 thf(fact_6794_range__prod,axiom,
% 0.33/0.65 ! [F: nat > product_prod_nat_nat] :
% 0.33/0.65 ( ord_le3146513528884898305at_nat @ ( image_5846123807819985514at_nat @ F @ top_top_set_nat )
% 0.33/0.65 @ ( produc457027306803732586at_nat @ ( image_nat_nat @ ( comp_P1955610211387027840at_nat @ product_fst_nat_nat @ F ) @ top_top_set_nat )
% 0.33/0.65 @ ^ [Uu: nat] : ( image_nat_nat @ ( comp_P1955610211387027840at_nat @ product_snd_nat_nat @ F ) @ top_top_set_nat ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % range_prod
% 0.33/0.65 thf(fact_6795_range__prod,axiom,
% 0.33/0.65 ! [F: nat > product_prod_nat_int] :
% 0.33/0.65 ( ord_le656430383953171549at_int @ ( image_1668272788310788806at_int @ F @ top_top_set_nat )
% 0.33/0.65 @ ( produc454536836294682310at_int @ ( image_nat_nat @ ( comp_P7964419862382602716at_nat @ product_fst_nat_int @ F ) @ top_top_set_nat )
% 0.33/0.65 @ ^ [Uu: nat] : ( image_nat_int @ ( comp_P8963773574283657272nt_nat @ product_snd_nat_int @ F ) @ top_top_set_nat ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % range_prod
% 0.33/0.65 thf(fact_6796_range__prod,axiom,
% 0.33/0.65 ! [F: nat > produc2963269191615333738nteger] :
% 0.33/0.65 ( ord_le2638047946463454698nteger @ ( image_8879651038713332435nteger @ F @ top_top_set_nat )
% 0.33/0.65 @ ( produc4896867201705524051nteger @ ( image_nat_int @ ( comp_P59025373045620805nt_nat @ produc45500017171379470nteger @ F ) @ top_top_set_nat )
% 0.33/0.65 @ ^ [Uu: int] : ( image_1215581382706833972nteger @ ( comp_P6870028373966156406er_nat @ produc2153544567185597776nteger @ F ) @ top_top_set_nat ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % range_prod
% 0.33/0.65 thf(fact_6797_range__prod,axiom,
% 0.33/0.65 ! [F: nat > product_prod_int_nat] :
% 0.33/0.65 ( ord_le5333435103577920093nt_nat @ ( image_6845477519721040070nt_nat @ F @ top_top_set_nat )
% 0.33/0.65 @ ( produc1456381018704787142nt_nat @ ( image_nat_int @ ( comp_P645145991195131448nt_nat @ product_fst_int_nat @ F ) @ top_top_set_nat )
% 0.33/0.65 @ ^ [Uu: int] : ( image_nat_nat @ ( comp_P8869164316148852700at_nat @ product_snd_int_nat @ F ) @ top_top_set_nat ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % range_prod
% 0.33/0.65 thf(fact_6798_range__prod,axiom,
% 0.33/0.65 ! [F: nat > produc8923325533196201883nteger] :
% 0.33/0.65 ( ord_le3725938330318615451nteger @ ( image_4272405876590741764nteger @ F @ top_top_set_nat )
% 0.33/0.65 @ ( produc5882431272649516420nteger @ ( image_1215581382706833972nteger @ ( comp_P3109732533133679783er_nat @ produc8508995932063986495nteger @ F ) @ top_top_set_nat )
% 0.33/0.65 @ ^ [Uu: code_integer] : ( image_1215581382706833972nteger @ ( comp_P3109732533133679783er_nat @ produc6174133586879617921nteger @ F ) @ top_top_set_nat ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % range_prod
% 0.33/0.65 thf(fact_6799_range__prod,axiom,
% 0.33/0.65 ! [F: nat > product_prod_int_int] :
% 0.33/0.65 ( ord_le2843351958646193337nt_int @ ( image_2667626500211843362nt_int @ F @ top_top_set_nat )
% 0.33/0.65 @ ( produc1453890548195736866nt_int @ ( image_nat_int @ ( comp_P6653955642190706324nt_nat @ product_fst_int_int @ F ) @ top_top_set_nat )
% 0.33/0.65 @ ^ [Uu: int] : ( image_nat_int @ ( comp_P6653955642190706324nt_nat @ product_snd_int_int @ F ) @ top_top_set_nat ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % range_prod
% 0.33/0.65 thf(fact_6800_range__prod,axiom,
% 0.33/0.65 ! [F: product_unit > produc8923325533196201883nteger] :
% 0.33/0.65 ( ord_le3725938330318615451nteger @ ( image_8089323762101378259nteger @ F @ top_to1996260823553986621t_unit )
% 0.33/0.65 @ ( produc5882431272649516420nteger @ ( image_3815118110082124069nteger @ ( comp_P659088277599099894t_unit @ produc8508995932063986495nteger @ F ) @ top_to1996260823553986621t_unit )
% 0.33/0.65 @ ^ [Uu: code_integer] : ( image_3815118110082124069nteger @ ( comp_P659088277599099894t_unit @ produc6174133586879617921nteger @ F ) @ top_to1996260823553986621t_unit ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % range_prod
% 0.33/0.65 thf(fact_6801_fun_Oin__rel,axiom,
% 0.33/0.65 ! [R4: code_integer > code_integer > $o,A: nat > code_integer,B: nat > code_integer] :
% 0.33/0.65 ( ( bNF_re1236659899165691067nteger
% 0.33/0.65 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.65 @ R4
% 0.33/0.65 @ A
% 0.33/0.65 @ B )
% 0.33/0.65 = ( ? [Z4: nat > produc8923325533196201883nteger] :
% 0.33/0.65 ( ( member1326526067935671339nteger @ Z4
% 0.33/0.65 @ ( collec7299664631084759149nteger
% 0.33/0.65 @ ^ [X3: nat > produc8923325533196201883nteger] : ( ord_le3725938330318615451nteger @ ( image_4272405876590741764nteger @ X3 @ top_top_set_nat ) @ ( collec7766031446232907142nteger @ ( produc2066375834425727024eger_o @ R4 ) ) ) ) )
% 0.33/0.65 & ( ( comp_P3109732533133679783er_nat @ produc8508995932063986495nteger @ Z4 )
% 0.33/0.65 = A )
% 0.33/0.65 & ( ( comp_P3109732533133679783er_nat @ produc6174133586879617921nteger @ Z4 )
% 0.33/0.65 = B ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % fun.in_rel
% 0.33/0.65 thf(fact_6802_fun_Oin__rel,axiom,
% 0.33/0.65 ! [R4: int > int > $o,A: nat > int,B: nat > int] :
% 0.33/0.65 ( ( bNF_re6650684261131312217nt_int
% 0.33/0.65 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.65 @ R4
% 0.33/0.65 @ A
% 0.33/0.65 @ B )
% 0.33/0.65 = ( ? [Z4: nat > product_prod_int_int] :
% 0.33/0.65 ( ( member6440191985751670089nt_int @ Z4
% 0.33/0.65 @ ( collec8414850927317488011nt_int
% 0.33/0.65 @ ^ [X3: nat > product_prod_int_int] : ( ord_le2843351958646193337nt_int @ ( image_2667626500211843362nt_int @ X3 @ top_top_set_nat ) @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ R4 ) ) ) ) )
% 0.33/0.65 & ( ( comp_P6653955642190706324nt_nat @ product_fst_int_int @ Z4 )
% 0.33/0.65 = A )
% 0.33/0.65 & ( ( comp_P6653955642190706324nt_nat @ product_snd_int_int @ Z4 )
% 0.33/0.65 = B ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % fun.in_rel
% 0.33/0.65 thf(fact_6803_fun_Oin__rel,axiom,
% 0.33/0.65 ! [R4: code_integer > code_integer > $o,A: product_unit > code_integer,B: product_unit > code_integer] :
% 0.33/0.65 ( ( bNF_re8417623677625516633nteger
% 0.33/0.65 @ ^ [Y4: product_unit,Z2: product_unit] : ( Y4 = Z2 )
% 0.33/0.65 @ R4
% 0.33/0.65 @ A
% 0.33/0.65 @ B )
% 0.33/0.65 = ( ? [Z4: product_unit > produc8923325533196201883nteger] :
% 0.33/0.65 ( ( member2837767709637065162nteger @ Z4
% 0.33/0.65 @ ( collec492036462967229448nteger
% 0.33/0.65 @ ^ [X3: product_unit > produc8923325533196201883nteger] : ( ord_le3725938330318615451nteger @ ( image_8089323762101378259nteger @ X3 @ top_to1996260823553986621t_unit ) @ ( collec7766031446232907142nteger @ ( produc2066375834425727024eger_o @ R4 ) ) ) ) )
% 0.33/0.65 & ( ( comp_P659088277599099894t_unit @ produc8508995932063986495nteger @ Z4 )
% 0.33/0.65 = A )
% 0.33/0.65 & ( ( comp_P659088277599099894t_unit @ produc6174133586879617921nteger @ Z4 )
% 0.33/0.65 = B ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % fun.in_rel
% 0.33/0.65 thf(fact_6804_fun_Oin__rel,axiom,
% 0.33/0.65 ! [R4: int > int > $o,A: product_unit > int,B: product_unit > int] :
% 0.33/0.65 ( ( bNF_re8422471777688076791nt_int
% 0.33/0.65 @ ^ [Y4: product_unit,Z2: product_unit] : ( Y4 = Z2 )
% 0.33/0.65 @ R4
% 0.33/0.65 @ A
% 0.33/0.65 @ B )
% 0.33/0.65 = ( ? [Z4: product_unit > product_prod_int_int] :
% 0.33/0.65 ( ( member5541948317052402408nt_int @ Z4
% 0.33/0.65 @ ( collec2513708037538135334nt_int
% 0.33/0.65 @ ^ [X3: product_unit > product_prod_int_int] : ( ord_le2843351958646193337nt_int @ ( image_4103462098156874993nt_int @ X3 @ top_to1996260823553986621t_unit ) @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ R4 ) ) ) ) )
% 0.33/0.65 & ( ( comp_P6796073005956588617t_unit @ product_fst_int_int @ Z4 )
% 0.33/0.65 = A )
% 0.33/0.65 & ( ( comp_P6796073005956588617t_unit @ product_snd_int_int @ Z4 )
% 0.33/0.65 = B ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % fun.in_rel
% 0.33/0.65 thf(fact_6805_fun_Oin__rel,axiom,
% 0.33/0.65 ! [R4: code_integer > code_integer > $o,A: int > code_integer,B: int > code_integer] :
% 0.33/0.65 ( ( bNF_re1784066744496875891nteger
% 0.33/0.65 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.65 @ R4
% 0.33/0.65 @ A
% 0.33/0.65 @ B )
% 0.33/0.65 = ( ? [Z4: int > produc8923325533196201883nteger] :
% 0.33/0.65 ( ( member2248416676132969167nteger @ Z4
% 0.33/0.65 @ ( collec8221555239282056977nteger
% 0.33/0.65 @ ^ [X3: int > produc8923325533196201883nteger] : ( ord_le3725938330318615451nteger @ ( image_5194296484788039592nteger @ X3 @ top_top_set_int ) @ ( collec7766031446232907142nteger @ ( produc2066375834425727024eger_o @ R4 ) ) ) ) )
% 0.33/0.65 & ( ( comp_P3107242062624629507er_int @ produc8508995932063986495nteger @ Z4 )
% 0.33/0.65 = A )
% 0.33/0.65 & ( ( comp_P3107242062624629507er_int @ produc6174133586879617921nteger @ Z4 )
% 0.33/0.65 = B ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % fun.in_rel
% 0.33/0.65 thf(fact_6806_fun_Oin__rel,axiom,
% 0.33/0.65 ! [R4: int > int > $o,A: int > int,B: int > int] :
% 0.33/0.65 ( ( bNF_re4712519889275205905nt_int
% 0.33/0.65 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.65 @ R4
% 0.33/0.65 @ A
% 0.33/0.65 @ B )
% 0.33/0.65 = ( ? [Z4: int > product_prod_int_int] :
% 0.33/0.65 ( ( member254662033361028077nt_int @ Z4
% 0.33/0.65 @ ( collec2229320974926845999nt_int
% 0.33/0.65 @ ^ [X3: int > product_prod_int_int] : ( ord_le2843351958646193337nt_int @ ( image_5705468584675977158nt_int @ X3 @ top_top_set_int ) @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ R4 ) ) ) ) )
% 0.33/0.65 & ( ( comp_P6651465171681656048nt_int @ product_fst_int_int @ Z4 )
% 0.33/0.65 = A )
% 0.33/0.65 & ( ( comp_P6651465171681656048nt_int @ product_snd_int_int @ Z4 )
% 0.33/0.65 = B ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % fun.in_rel
% 0.33/0.65 thf(fact_6807_fun_Oin__rel,axiom,
% 0.33/0.65 ! [R4: code_natural > produc7822875418678951345atural > $o,A: nat > code_natural,B: nat > produc7822875418678951345atural] :
% 0.33/0.65 ( ( bNF_re6101645755646507080atural
% 0.33/0.65 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.65 @ R4
% 0.33/0.65 @ A
% 0.33/0.65 @ B )
% 0.33/0.65 = ( ? [Z4: nat > produc5835291356934675326atural] :
% 0.33/0.65 ( ( member528921174545443716atural @ Z4
% 0.33/0.65 @ ( collec3197714919839585474atural
% 0.33/0.65 @ ^ [X3: nat > produc5835291356934675326atural] : ( ord_le2202040463148982292atural @ ( image_4072043198136622805atural @ X3 @ top_top_set_nat ) @ ( collec1991479681304692691atural @ ( produc7358226366420480123ural_o @ R4 ) ) ) ) )
% 0.33/0.65 & ( ( comp_P5592315970379621083al_nat @ produc497848011034438852atural @ Z4 )
% 0.33/0.65 = A )
% 0.33/0.65 & ( ( comp_P8477885140431536992al_nat @ produc6591912806276919810atural @ Z4 )
% 0.33/0.65 = B ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % fun.in_rel
% 0.33/0.65 thf(fact_6808_fun_Oin__rel,axiom,
% 0.33/0.65 ! [R4: code_natural > produc7822875418678951345atural > $o,A: product_unit > code_natural,B: product_unit > produc7822875418678951345atural] :
% 0.33/0.65 ( ( bNF_re5641277236161133866atural
% 0.33/0.65 @ ^ [Y4: product_unit,Z2: product_unit] : ( Y4 = Z2 )
% 0.33/0.65 @ R4
% 0.33/0.65 @ A
% 0.33/0.65 @ B )
% 0.33/0.65 = ( ? [Z4: product_unit > produc5835291356934675326atural] :
% 0.33/0.65 ( ( member4946248492122881829atural @ Z4
% 0.33/0.65 @ ( collec3282430933710331751atural
% 0.33/0.65 @ ^ [X3: product_unit > produc5835291356934675326atural] : ( ord_le2202040463148982292atural @ ( image_220848230107539526atural @ X3 @ top_to1996260823553986621t_unit ) @ ( collec1991479681304692691atural @ ( produc7358226366420480123ural_o @ R4 ) ) ) ) )
% 0.33/0.65 & ( ( comp_P210409258367696578t_unit @ produc497848011034438852atural @ Z4 )
% 0.33/0.65 = A )
% 0.33/0.65 & ( ( comp_P1945487127105810045t_unit @ produc6591912806276919810atural @ Z4 )
% 0.33/0.65 = B ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % fun.in_rel
% 0.33/0.65 thf(fact_6809_fun_Oin__rel,axiom,
% 0.33/0.65 ! [R4: code_natural > produc7822875418678951345atural > $o,A: int > code_natural,B: int > produc7822875418678951345atural] :
% 0.33/0.65 ( ( bNF_re6290619412732081552atural
% 0.33/0.65 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.65 @ R4
% 0.33/0.65 @ A
% 0.33/0.65 @ B )
% 0.33/0.65 = ( ? [Z4: int > produc5835291356934675326atural] :
% 0.33/0.65 ( ( member3292482584629245920atural @ Z4
% 0.33/0.65 @ ( collec5961276329923387678atural
% 0.33/0.65 @ ^ [X3: int > produc5835291356934675326atural] : ( ord_le2202040463148982292atural @ ( image_6835604608220425009atural @ X3 @ top_top_set_int ) @ ( collec1991479681304692691atural @ ( produc7358226366420480123ural_o @ R4 ) ) ) ) )
% 0.33/0.65 & ( ( comp_P5589825499870570807al_int @ produc497848011034438852atural @ Z4 )
% 0.33/0.65 = A )
% 0.33/0.65 & ( ( comp_P8475394669922486716al_int @ produc6591912806276919810atural @ Z4 )
% 0.33/0.65 = B ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % fun.in_rel
% 0.33/0.65 thf(fact_6810_fun_Oin__rel,axiom,
% 0.33/0.65 ! [R4: ( nat > $o ) > ( nat > $o ) > $o,A: int > nat > $o,B: int > nat > $o] :
% 0.33/0.65 ( ( bNF_re3376528473927230327_nat_o
% 0.33/0.65 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.65 @ R4
% 0.33/0.65 @ A
% 0.33/0.65 @ B )
% 0.33/0.65 = ( ? [Z4: int > produc7360885484439884007_nat_o] :
% 0.33/0.65 ( ( member7306185171444233115_nat_o @ Z4
% 0.33/0.65 @ ( collec2839945811840875229_nat_o
% 0.33/0.65 @ ^ [X3: int > produc7360885484439884007_nat_o] : ( ord_le3745675095661657703_nat_o @ ( image_259982842891744372_nat_o @ X3 @ top_top_set_int ) @ ( collec5110290359514967890_nat_o @ ( produc2845945524848125740at_o_o @ R4 ) ) ) ) )
% 0.33/0.65 & ( ( comp_P1075760313067033319_o_int @ produc6972895793295859523_nat_o @ Z4 )
% 0.33/0.65 = A )
% 0.33/0.65 & ( ( comp_P1075760313067033319_o_int @ produc6795044007072221829_nat_o @ Z4 )
% 0.33/0.65 = B ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % fun.in_rel
% 0.33/0.65 thf(fact_6811_apfst__apsnd,axiom,
% 0.33/0.65 ! [F: code_integer > int > option6357759511663192854e_term,G: code_integer > product_prod_int_int,X: produc8923325533196201883nteger] :
% 0.33/0.65 ( ( produc5167107986097539517nt_int @ F @ ( produc3535056655957556987nteger @ G @ X ) )
% 0.33/0.65 = ( produc4305682042979456191nt_int @ ( F @ ( produc8508995932063986495nteger @ X ) ) @ ( G @ ( produc6174133586879617921nteger @ X ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % apfst_apsnd
% 0.33/0.65 thf(fact_6812_apfst__apsnd,axiom,
% 0.33/0.65 ! [F: int > int > option6357759511663192854e_term,G: int > product_prod_int_int,X: product_prod_int_int] :
% 0.33/0.65 ( ( produc7862092043137183022nt_int @ F @ ( produc6100211334659168315nt_int @ G @ X ) )
% 0.33/0.65 = ( produc4305682042979456191nt_int @ ( F @ ( product_fst_int_int @ X ) ) @ ( G @ ( product_snd_int_int @ X ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % apfst_apsnd
% 0.33/0.65 thf(fact_6813_apfst__apsnd,axiom,
% 0.33/0.65 ! [F: code_integer > produc3658429121746597890et_nat > $o,G: code_integer > produc3658429121746597890et_nat,X: produc8923325533196201883nteger] :
% 0.33/0.65 ( ( produc4644964300586701942et_nat @ F @ ( produc7246245855585345468nteger @ G @ X ) )
% 0.33/0.65 = ( produc5001842942810119800et_nat @ ( F @ ( produc8508995932063986495nteger @ X ) ) @ ( G @ ( produc6174133586879617921nteger @ X ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % apfst_apsnd
% 0.33/0.65 thf(fact_6814_apfst__apsnd,axiom,
% 0.33/0.65 ! [F: int > produc3658429121746597890et_nat > $o,G: int > produc3658429121746597890et_nat,X: product_prod_int_int] :
% 0.33/0.65 ( ( produc5259063908904861543et_nat @ F @ ( produc9121118195053341018at_int @ G @ X ) )
% 0.33/0.65 = ( produc5001842942810119800et_nat @ ( F @ ( product_fst_int_int @ X ) ) @ ( G @ ( product_snd_int_int @ X ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % apfst_apsnd
% 0.33/0.65 thf(fact_6815_apfst__apsnd,axiom,
% 0.33/0.65 ! [F: code_natural > int > option6357759511663192854e_term,G: produc7822875418678951345atural > product_prod_int_int,X: produc5835291356934675326atural] :
% 0.33/0.65 ( ( produc7347430915296828978nt_int @ F @ ( produc5167862320620071534atural @ G @ X ) )
% 0.33/0.65 = ( produc4305682042979456191nt_int @ ( F @ ( produc497848011034438852atural @ X ) ) @ ( G @ ( produc6591912806276919810atural @ X ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % apfst_apsnd
% 0.33/0.65 thf(fact_6816_apfst__apsnd,axiom,
% 0.33/0.65 ! [F: code_integer > produc6241069584506657477e_term > option6357759511663192854e_term,G: code_integer > produc8923325533196201883nteger,X: produc8923325533196201883nteger] :
% 0.33/0.65 ( ( produc5215714788235631558nteger @ F @ ( produc7166930624044334813nteger @ G @ X ) )
% 0.33/0.65 = ( produc8603105652947943368nteger @ ( F @ ( produc8508995932063986495nteger @ X ) ) @ ( G @ ( produc6174133586879617921nteger @ X ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % apfst_apsnd
% 0.33/0.65 thf(fact_6817_apfst__apsnd,axiom,
% 0.33/0.65 ! [F: code_integer > produc8551481072490612790e_term > option6357759511663192854e_term,G: code_integer > product_prod_int_int,X: produc8923325533196201883nteger] :
% 0.33/0.65 ( ( produc7725767832589379507nt_int @ F @ ( produc3535056655957556987nteger @ G @ X ) )
% 0.33/0.65 = ( produc5700946648718959541nt_int @ ( F @ ( produc8508995932063986495nteger @ X ) ) @ ( G @ ( produc6174133586879617921nteger @ X ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % apfst_apsnd
% 0.33/0.65 thf(fact_6818_apfst__apsnd,axiom,
% 0.33/0.65 ! [F: int > produc6241069584506657477e_term > option6357759511663192854e_term,G: int > produc8923325533196201883nteger,X: product_prod_int_int] :
% 0.33/0.65 ( ( produc5502177047915545527nteger @ F @ ( produc2935421404040714269er_int @ G @ X ) )
% 0.33/0.65 = ( produc8603105652947943368nteger @ ( F @ ( product_fst_int_int @ X ) ) @ ( G @ ( product_snd_int_int @ X ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % apfst_apsnd
% 0.33/0.65 thf(fact_6819_apfst__apsnd,axiom,
% 0.33/0.65 ! [F: int > produc8551481072490612790e_term > option6357759511663192854e_term,G: int > product_prod_int_int,X: product_prod_int_int] :
% 0.33/0.65 ( ( produc9204274687749184420nt_int @ F @ ( produc6100211334659168315nt_int @ G @ X ) )
% 0.33/0.65 = ( produc5700946648718959541nt_int @ ( F @ ( product_fst_int_int @ X ) ) @ ( G @ ( product_snd_int_int @ X ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % apfst_apsnd
% 0.33/0.65 thf(fact_6820_apfst__apsnd,axiom,
% 0.33/0.65 ! [F: code_natural > produc3658429121746597890et_nat > $o,G: produc7822875418678951345atural > produc3658429121746597890et_nat,X: produc5835291356934675326atural] :
% 0.33/0.65 ( ( produc7618241212158389867et_nat @ F @ ( produc1304257963789341151atural @ G @ X ) )
% 0.33/0.65 = ( produc5001842942810119800et_nat @ ( F @ ( produc497848011034438852atural @ X ) ) @ ( G @ ( produc6591912806276919810atural @ X ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % apfst_apsnd
% 0.33/0.65 thf(fact_6821_apsnd__apfst,axiom,
% 0.33/0.65 ! [F: code_integer > code_integer,G: code_integer > code_integer,X: produc8923325533196201883nteger] :
% 0.33/0.65 ( ( produc6499014454317279255nteger @ F @ ( produc3195571438000033749nteger @ G @ X ) )
% 0.33/0.65 = ( produc1086072967326762835nteger @ ( G @ ( produc8508995932063986495nteger @ X ) ) @ ( F @ ( produc6174133586879617921nteger @ X ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % apsnd_apfst
% 0.33/0.65 thf(fact_6822_apsnd__apfst,axiom,
% 0.33/0.65 ! [F: code_integer > product_prod_int_int,G: code_integer > int > option6357759511663192854e_term,X: produc8923325533196201883nteger] :
% 0.33/0.65 ( ( produc8992176017387436671e_term @ F @ ( produc3207347198985423705nteger @ G @ X ) )
% 0.33/0.65 = ( produc4305682042979456191nt_int @ ( G @ ( produc8508995932063986495nteger @ X ) ) @ ( F @ ( produc6174133586879617921nteger @ X ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % apsnd_apfst
% 0.33/0.65 thf(fact_6823_apsnd__apfst,axiom,
% 0.33/0.65 ! [F: int > product_prod_int_int,G: int > int > option6357759511663192854e_term,X: product_prod_int_int] :
% 0.33/0.65 ( ( produc3260485439724623344e_term @ F @ ( produc2895628470685950711rm_int @ G @ X ) )
% 0.33/0.65 = ( produc4305682042979456191nt_int @ ( G @ ( product_fst_int_int @ X ) ) @ ( F @ ( product_snd_int_int @ X ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % apsnd_apfst
% 0.33/0.65 thf(fact_6824_apsnd__apfst,axiom,
% 0.33/0.65 ! [F: code_integer > produc3658429121746597890et_nat,G: code_integer > produc3658429121746597890et_nat > $o,X: produc8923325533196201883nteger] :
% 0.33/0.65 ( ( produc898583841617791278_nat_o @ F @ ( produc7528800376889492689nteger @ G @ X ) )
% 0.33/0.65 = ( produc5001842942810119800et_nat @ ( G @ ( produc8508995932063986495nteger @ X ) ) @ ( F @ ( produc6174133586879617921nteger @ X ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % apsnd_apfst
% 0.33/0.65 thf(fact_6825_apsnd__apfst,axiom,
% 0.33/0.65 ! [F: int > produc3658429121746597890et_nat,G: int > produc3658429121746597890et_nat > $o,X: product_prod_int_int] :
% 0.33/0.65 ( ( produc3447581998352395295_nat_o @ F @ ( produc1933289243015553937_o_int @ G @ X ) )
% 0.33/0.65 = ( produc5001842942810119800et_nat @ ( G @ ( product_fst_int_int @ X ) ) @ ( F @ ( product_snd_int_int @ X ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % apsnd_apfst
% 0.33/0.65 thf(fact_6826_apsnd__apfst,axiom,
% 0.33/0.65 ! [F: produc7822875418678951345atural > product_prod_int_int,G: code_natural > int > option6357759511663192854e_term,X: produc5835291356934675326atural] :
% 0.33/0.65 ( ( produc7977970570655791143e_term @ F @ ( produc8323928115967317034atural @ G @ X ) )
% 0.33/0.65 = ( produc4305682042979456191nt_int @ ( G @ ( produc497848011034438852atural @ X ) ) @ ( F @ ( produc6591912806276919810atural @ X ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % apsnd_apfst
% 0.33/0.65 thf(fact_6827_apsnd__apfst,axiom,
% 0.33/0.65 ! [F: code_integer > produc8923325533196201883nteger,G: code_integer > produc6241069584506657477e_term > option6357759511663192854e_term,X: produc8923325533196201883nteger] :
% 0.33/0.65 ( ( produc4047920161794714618e_term @ F @ ( produc7628915689858001394nteger @ G @ X ) )
% 0.33/0.65 = ( produc8603105652947943368nteger @ ( G @ ( produc8508995932063986495nteger @ X ) ) @ ( F @ ( produc6174133586879617921nteger @ X ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % apsnd_apfst
% 0.33/0.65 thf(fact_6828_apsnd__apfst,axiom,
% 0.33/0.65 ! [F: code_integer > product_prod_int_int,G: code_integer > produc8551481072490612790e_term > option6357759511663192854e_term,X: produc8923325533196201883nteger] :
% 0.33/0.65 ( ( produc6067092816631456265e_term @ F @ ( produc7602971101079744739nteger @ G @ X ) )
% 0.33/0.65 = ( produc5700946648718959541nt_int @ ( G @ ( produc8508995932063986495nteger @ X ) ) @ ( F @ ( produc6174133586879617921nteger @ X ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % apsnd_apfst
% 0.33/0.65 thf(fact_6829_apsnd__apfst,axiom,
% 0.33/0.65 ! [F: int > produc8923325533196201883nteger,G: int > produc6241069584506657477e_term > option6357759511663192854e_term,X: product_prod_int_int] :
% 0.33/0.65 ( ( produc552091674517523435e_term @ F @ ( produc7344697412356995344rm_int @ G @ X ) )
% 0.33/0.65 = ( produc8603105652947943368nteger @ ( G @ ( product_fst_int_int @ X ) ) @ ( F @ ( product_snd_int_int @ X ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % apsnd_apfst
% 0.33/0.65 thf(fact_6830_apsnd__apfst,axiom,
% 0.33/0.65 ! [F: int > product_prod_int_int,G: int > produc8551481072490612790e_term > option6357759511663192854e_term,X: product_prod_int_int] :
% 0.33/0.65 ( ( produc189803804368834042e_term @ F @ ( produc212012705979908097rm_int @ G @ X ) )
% 0.33/0.65 = ( produc5700946648718959541nt_int @ ( G @ ( product_fst_int_int @ X ) ) @ ( F @ ( product_snd_int_int @ X ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % apsnd_apfst
% 0.33/0.65 thf(fact_6831_eq__snd__iff,axiom,
% 0.33/0.65 ! [B: produc8923325533196201883nteger,P4: produc1908205239877642774nteger] :
% 0.33/0.65 ( ( B
% 0.33/0.65 = ( produc7856867400915047194nteger @ P4 ) )
% 0.33/0.65 = ( ? [A5: produc6241069584506657477e_term > option6357759511663192854e_term] :
% 0.33/0.65 ( P4
% 0.33/0.65 = ( produc8603105652947943368nteger @ A5 @ B ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % eq_snd_iff
% 0.33/0.65 thf(fact_6832_eq__snd__iff,axiom,
% 0.33/0.65 ! [B: produc3658429121746597890et_nat,P4: produc3925858234332021118et_nat] :
% 0.33/0.65 ( ( B
% 0.33/0.65 = ( produc4011572625026189258et_nat @ P4 ) )
% 0.33/0.65 = ( ? [A5: produc3658429121746597890et_nat > $o] :
% 0.33/0.65 ( P4
% 0.33/0.65 = ( produc5001842942810119800et_nat @ A5 @ B ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % eq_snd_iff
% 0.33/0.65 thf(fact_6833_eq__snd__iff,axiom,
% 0.33/0.65 ! [B: produc3925858234332021118et_nat,P4: produc2732055786443039994et_nat] :
% 0.33/0.65 ( ( B
% 0.33/0.65 = ( produc5374455773327741254et_nat @ P4 ) )
% 0.33/0.65 = ( ? [A5: produc3658429121746597890et_nat > $o] :
% 0.33/0.65 ( P4
% 0.33/0.65 = ( produc2245416461498447860et_nat @ A5 @ B ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % eq_snd_iff
% 0.33/0.65 thf(fact_6834_eq__snd__iff,axiom,
% 0.33/0.65 ! [B: product_prod_int_int,P4: produc2285326912895808259nt_int] :
% 0.33/0.65 ( ( B
% 0.33/0.65 = ( produc7328097813583171335nt_int @ P4 ) )
% 0.33/0.65 = ( ? [A5: produc8551481072490612790e_term > option6357759511663192854e_term] :
% 0.33/0.65 ( P4
% 0.33/0.65 = ( produc5700946648718959541nt_int @ A5 @ B ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % eq_snd_iff
% 0.33/0.65 thf(fact_6835_eq__snd__iff,axiom,
% 0.33/0.65 ! [B: product_prod_int_int,P4: produc7773217078559923341nt_int] :
% 0.33/0.65 ( ( B
% 0.33/0.65 = ( produc3162348030201620241nt_int @ P4 ) )
% 0.33/0.65 = ( ? [A5: int > option6357759511663192854e_term] :
% 0.33/0.65 ( P4
% 0.33/0.65 = ( produc4305682042979456191nt_int @ A5 @ B ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % eq_snd_iff
% 0.33/0.65 thf(fact_6836_eq__snd__iff,axiom,
% 0.33/0.65 ! [B: code_integer,P4: produc8923325533196201883nteger] :
% 0.33/0.65 ( ( B
% 0.33/0.65 = ( produc6174133586879617921nteger @ P4 ) )
% 0.33/0.65 = ( ? [A5: code_integer] :
% 0.33/0.65 ( P4
% 0.33/0.65 = ( produc1086072967326762835nteger @ A5 @ B ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % eq_snd_iff
% 0.33/0.65 thf(fact_6837_eq__snd__iff,axiom,
% 0.33/0.65 ! [B: int,P4: product_prod_int_int] :
% 0.33/0.65 ( ( B
% 0.33/0.65 = ( product_snd_int_int @ P4 ) )
% 0.33/0.65 = ( ? [A5: int] :
% 0.33/0.65 ( P4
% 0.33/0.65 = ( product_Pair_int_int @ A5 @ B ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % eq_snd_iff
% 0.33/0.65 thf(fact_6838_eq__snd__iff,axiom,
% 0.33/0.65 ! [B: produc7822875418678951345atural,P4: produc5835291356934675326atural] :
% 0.33/0.65 ( ( B
% 0.33/0.65 = ( produc6591912806276919810atural @ P4 ) )
% 0.33/0.65 = ( ? [A5: code_natural] :
% 0.33/0.65 ( P4
% 0.33/0.65 = ( produc6639722614265839536atural @ A5 @ B ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % eq_snd_iff
% 0.33/0.65 thf(fact_6839_SigmaI,axiom,
% 0.33/0.65 ! [A: $o,A2: set_o,B: $o,B5: $o > set_o] :
% 0.33/0.65 ( ( member_o @ A @ A2 )
% 0.33/0.65 => ( ( member_o @ B @ ( B5 @ A ) )
% 0.33/0.65 => ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ A @ B ) @ ( product_Sigma_o_o @ A2 @ B5 ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % SigmaI
% 0.33/0.65 thf(fact_6840_SigmaI,axiom,
% 0.33/0.65 ! [A: $o,A2: set_o,B: nat,B5: $o > set_nat] :
% 0.33/0.65 ( ( member_o @ A @ A2 )
% 0.33/0.65 => ( ( member_nat @ B @ ( B5 @ A ) )
% 0.33/0.65 => ( member2802428098988154798_o_nat @ ( product_Pair_o_nat @ A @ B ) @ ( product_Sigma_o_nat @ A2 @ B5 ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % SigmaI
% 0.33/0.65 thf(fact_6841_SigmaI,axiom,
% 0.33/0.65 ! [A: $o,A2: set_o,B: int,B5: $o > set_int] :
% 0.33/0.65 ( ( member_o @ A @ A2 )
% 0.33/0.65 => ( ( member_int @ B @ ( B5 @ A ) )
% 0.33/0.65 => ( member7847949116333733898_o_int @ ( product_Pair_o_int @ A @ B ) @ ( product_Sigma_o_int @ A2 @ B5 ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % SigmaI
% 0.33/0.65 thf(fact_6842_SigmaI,axiom,
% 0.33/0.65 ! [A: nat,A2: set_nat,B: $o,B5: nat > set_o] :
% 0.33/0.65 ( ( member_nat @ A @ A2 )
% 0.33/0.65 => ( ( member_o @ B @ ( B5 @ A ) )
% 0.33/0.65 => ( member6310962623043647828_nat_o @ ( product_Pair_nat_o @ A @ B ) @ ( product_Sigma_nat_o @ A2 @ B5 ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % SigmaI
% 0.33/0.65 thf(fact_6843_SigmaI,axiom,
% 0.33/0.65 ! [A: nat,A2: set_nat,B: nat,B5: nat > set_nat] :
% 0.33/0.65 ( ( member_nat @ A @ A2 )
% 0.33/0.65 => ( ( member_nat @ B @ ( B5 @ A ) )
% 0.33/0.65 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ ( produc457027306803732586at_nat @ A2 @ B5 ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % SigmaI
% 0.33/0.65 thf(fact_6844_SigmaI,axiom,
% 0.33/0.65 ! [A: nat,A2: set_nat,B: int,B5: nat > set_int] :
% 0.33/0.65 ( ( member_nat @ A @ A2 )
% 0.33/0.65 => ( ( member_int @ B @ ( B5 @ A ) )
% 0.33/0.65 => ( member4262671552274231302at_int @ ( product_Pair_nat_int @ A @ B ) @ ( produc454536836294682310at_int @ A2 @ B5 ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % SigmaI
% 0.33/0.65 thf(fact_6845_SigmaI,axiom,
% 0.33/0.65 ! [A: int,A2: set_int,B: $o,B5: int > set_o] :
% 0.33/0.65 ( ( member_int @ A @ A2 )
% 0.33/0.65 => ( ( member_o @ B @ ( B5 @ A ) )
% 0.33/0.65 => ( member4489920277610959864_int_o @ ( product_Pair_int_o @ A @ B ) @ ( product_Sigma_int_o @ A2 @ B5 ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % SigmaI
% 0.33/0.65 thf(fact_6846_SigmaI,axiom,
% 0.33/0.65 ! [A: int,A2: set_int,B: nat,B5: int > set_nat] :
% 0.33/0.65 ( ( member_int @ A @ A2 )
% 0.33/0.65 => ( ( member_nat @ B @ ( B5 @ A ) )
% 0.33/0.65 => ( member216504246829706758nt_nat @ ( product_Pair_int_nat @ A @ B ) @ ( produc1456381018704787142nt_nat @ A2 @ B5 ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % SigmaI
% 0.33/0.65 thf(fact_6847_SigmaI,axiom,
% 0.33/0.65 ! [A: int,A2: set_int,B: int,B5: int > set_int] :
% 0.33/0.65 ( ( member_int @ A @ A2 )
% 0.33/0.65 => ( ( member_int @ B @ ( B5 @ A ) )
% 0.33/0.65 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ ( produc1453890548195736866nt_int @ A2 @ B5 ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % SigmaI
% 0.33/0.65 thf(fact_6848_SigmaI,axiom,
% 0.33/0.65 ! [A: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,B: $o,B5: product_prod_nat_nat > set_o] :
% 0.33/0.65 ( ( member8440522571783428010at_nat @ A @ A2 )
% 0.33/0.65 => ( ( member_o @ B @ ( B5 @ A ) )
% 0.33/0.65 => ( member2200362271989506215_nat_o @ ( produc855456346497908590_nat_o @ A @ B ) @ ( produc203973861852599583_nat_o @ A2 @ B5 ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % SigmaI
% 0.33/0.65 thf(fact_6849_mem__Sigma__iff,axiom,
% 0.33/0.65 ! [A: $o,B: $o,A2: set_o,B5: $o > set_o] :
% 0.33/0.65 ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ A @ B ) @ ( product_Sigma_o_o @ A2 @ B5 ) )
% 0.33/0.65 = ( ( member_o @ A @ A2 )
% 0.33/0.65 & ( member_o @ B @ ( B5 @ A ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % mem_Sigma_iff
% 0.33/0.65 thf(fact_6850_mem__Sigma__iff,axiom,
% 0.33/0.65 ! [A: $o,B: nat,A2: set_o,B5: $o > set_nat] :
% 0.33/0.65 ( ( member2802428098988154798_o_nat @ ( product_Pair_o_nat @ A @ B ) @ ( product_Sigma_o_nat @ A2 @ B5 ) )
% 0.33/0.65 = ( ( member_o @ A @ A2 )
% 0.33/0.65 & ( member_nat @ B @ ( B5 @ A ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % mem_Sigma_iff
% 0.33/0.65 thf(fact_6851_mem__Sigma__iff,axiom,
% 0.33/0.65 ! [A: $o,B: int,A2: set_o,B5: $o > set_int] :
% 0.33/0.65 ( ( member7847949116333733898_o_int @ ( product_Pair_o_int @ A @ B ) @ ( product_Sigma_o_int @ A2 @ B5 ) )
% 0.33/0.65 = ( ( member_o @ A @ A2 )
% 0.33/0.65 & ( member_int @ B @ ( B5 @ A ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % mem_Sigma_iff
% 0.33/0.65 thf(fact_6852_mem__Sigma__iff,axiom,
% 0.33/0.65 ! [A: nat,B: $o,A2: set_nat,B5: nat > set_o] :
% 0.33/0.65 ( ( member6310962623043647828_nat_o @ ( product_Pair_nat_o @ A @ B ) @ ( product_Sigma_nat_o @ A2 @ B5 ) )
% 0.33/0.65 = ( ( member_nat @ A @ A2 )
% 0.33/0.65 & ( member_o @ B @ ( B5 @ A ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % mem_Sigma_iff
% 0.33/0.65 thf(fact_6853_mem__Sigma__iff,axiom,
% 0.33/0.65 ! [A: nat,B: int,A2: set_nat,B5: nat > set_int] :
% 0.33/0.65 ( ( member4262671552274231302at_int @ ( product_Pair_nat_int @ A @ B ) @ ( produc454536836294682310at_int @ A2 @ B5 ) )
% 0.33/0.65 = ( ( member_nat @ A @ A2 )
% 0.33/0.65 & ( member_int @ B @ ( B5 @ A ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % mem_Sigma_iff
% 0.33/0.65 thf(fact_6854_mem__Sigma__iff,axiom,
% 0.33/0.65 ! [A: int,B: $o,A2: set_int,B5: int > set_o] :
% 0.33/0.65 ( ( member4489920277610959864_int_o @ ( product_Pair_int_o @ A @ B ) @ ( product_Sigma_int_o @ A2 @ B5 ) )
% 0.33/0.65 = ( ( member_int @ A @ A2 )
% 0.33/0.65 & ( member_o @ B @ ( B5 @ A ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % mem_Sigma_iff
% 0.33/0.65 thf(fact_6855_mem__Sigma__iff,axiom,
% 0.33/0.65 ! [A: int,B: nat,A2: set_int,B5: int > set_nat] :
% 0.33/0.65 ( ( member216504246829706758nt_nat @ ( product_Pair_int_nat @ A @ B ) @ ( produc1456381018704787142nt_nat @ A2 @ B5 ) )
% 0.33/0.65 = ( ( member_int @ A @ A2 )
% 0.33/0.65 & ( member_nat @ B @ ( B5 @ A ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % mem_Sigma_iff
% 0.33/0.65 thf(fact_6856_mem__Sigma__iff,axiom,
% 0.33/0.65 ! [A: int,B: int,A2: set_int,B5: int > set_int] :
% 0.33/0.65 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ ( produc1453890548195736866nt_int @ A2 @ B5 ) )
% 0.33/0.65 = ( ( member_int @ A @ A2 )
% 0.33/0.65 & ( member_int @ B @ ( B5 @ A ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % mem_Sigma_iff
% 0.33/0.65 thf(fact_6857_mem__Sigma__iff,axiom,
% 0.33/0.65 ! [A: nat,B: nat,A2: set_nat,B5: nat > set_nat] :
% 0.33/0.65 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ ( produc457027306803732586at_nat @ A2 @ B5 ) )
% 0.33/0.65 = ( ( member_nat @ A @ A2 )
% 0.33/0.65 & ( member_nat @ B @ ( B5 @ A ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % mem_Sigma_iff
% 0.33/0.65 thf(fact_6858_mem__Sigma__iff,axiom,
% 0.33/0.65 ! [A: product_prod_nat_nat,B: $o,A2: set_Pr1261947904930325089at_nat,B5: product_prod_nat_nat > set_o] :
% 0.33/0.65 ( ( member2200362271989506215_nat_o @ ( produc855456346497908590_nat_o @ A @ B ) @ ( produc203973861852599583_nat_o @ A2 @ B5 ) )
% 0.33/0.65 = ( ( member8440522571783428010at_nat @ A @ A2 )
% 0.33/0.65 & ( member_o @ B @ ( B5 @ A ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % mem_Sigma_iff
% 0.33/0.65 thf(fact_6859_gcd__add1,axiom,
% 0.33/0.65 ! [M2: nat,N2: nat] :
% 0.33/0.65 ( ( gcd_gcd_nat @ ( plus_plus_nat @ M2 @ N2 ) @ N2 )
% 0.33/0.65 = ( gcd_gcd_nat @ M2 @ N2 ) ) ).
% 0.33/0.65
% 0.33/0.65 % gcd_add1
% 0.33/0.65 thf(fact_6860_gcd__add1,axiom,
% 0.33/0.65 ! [M2: int,N2: int] :
% 0.33/0.65 ( ( gcd_gcd_int @ ( plus_plus_int @ M2 @ N2 ) @ N2 )
% 0.33/0.65 = ( gcd_gcd_int @ M2 @ N2 ) ) ).
% 0.33/0.65
% 0.33/0.65 % gcd_add1
% 0.33/0.65 thf(fact_6861_gcd__add2,axiom,
% 0.33/0.65 ! [M2: nat,N2: nat] :
% 0.33/0.65 ( ( gcd_gcd_nat @ M2 @ ( plus_plus_nat @ M2 @ N2 ) )
% 0.33/0.65 = ( gcd_gcd_nat @ M2 @ N2 ) ) ).
% 0.33/0.65
% 0.33/0.65 % gcd_add2
% 0.33/0.65 thf(fact_6862_gcd__add2,axiom,
% 0.33/0.65 ! [M2: int,N2: int] :
% 0.33/0.65 ( ( gcd_gcd_int @ M2 @ ( plus_plus_int @ M2 @ N2 ) )
% 0.33/0.65 = ( gcd_gcd_int @ M2 @ N2 ) ) ).
% 0.33/0.65
% 0.33/0.65 % gcd_add2
% 0.33/0.65 thf(fact_6863_gcd_Obottom__left__bottom,axiom,
% 0.33/0.65 ! [A: nat] :
% 0.33/0.65 ( ( gcd_gcd_nat @ one_one_nat @ A )
% 0.33/0.65 = one_one_nat ) ).
% 0.33/0.65
% 0.33/0.65 % gcd.bottom_left_bottom
% 0.33/0.65 thf(fact_6864_gcd_Obottom__left__bottom,axiom,
% 0.33/0.65 ! [A: int] :
% 0.33/0.65 ( ( gcd_gcd_int @ one_one_int @ A )
% 0.33/0.65 = one_one_int ) ).
% 0.33/0.65
% 0.33/0.65 % gcd.bottom_left_bottom
% 0.33/0.65 thf(fact_6865_gcd_Obottom__right__bottom,axiom,
% 0.33/0.65 ! [A: nat] :
% 0.33/0.65 ( ( gcd_gcd_nat @ A @ one_one_nat )
% 0.33/0.65 = one_one_nat ) ).
% 0.33/0.65
% 0.33/0.65 % gcd.bottom_right_bottom
% 0.33/0.65 thf(fact_6866_gcd_Obottom__right__bottom,axiom,
% 0.33/0.65 ! [A: int] :
% 0.33/0.65 ( ( gcd_gcd_int @ A @ one_one_int )
% 0.33/0.65 = one_one_int ) ).
% 0.33/0.65
% 0.33/0.65 % gcd.bottom_right_bottom
% 0.33/0.65 thf(fact_6867_apfst__conv,axiom,
% 0.33/0.65 ! [F: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc6241069584506657477e_term > option6357759511663192854e_term,X: produc6241069584506657477e_term > option6357759511663192854e_term,Y: produc8923325533196201883nteger] :
% 0.33/0.65 ( ( produc2515316116081422825nteger @ F @ ( produc8603105652947943368nteger @ X @ Y ) )
% 0.33/0.65 = ( produc8603105652947943368nteger @ ( F @ X ) @ Y ) ) ).
% 0.33/0.65
% 0.33/0.65 % apfst_conv
% 0.33/0.65 thf(fact_6868_apfst__conv,axiom,
% 0.33/0.65 ! [F: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o,X: produc3658429121746597890et_nat > $o,Y: produc3658429121746597890et_nat] :
% 0.33/0.65 ( ( produc3198230245617193214et_nat @ F @ ( produc5001842942810119800et_nat @ X @ Y ) )
% 0.33/0.65 = ( produc5001842942810119800et_nat @ ( F @ X ) @ Y ) ) ).
% 0.33/0.65
% 0.33/0.65 % apfst_conv
% 0.33/0.65 thf(fact_6869_apfst__conv,axiom,
% 0.33/0.65 ! [F: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o,X: produc3658429121746597890et_nat > $o,Y: produc3925858234332021118et_nat] :
% 0.33/0.65 ( ( produc1442628905706551930et_nat @ F @ ( produc2245416461498447860et_nat @ X @ Y ) )
% 0.33/0.65 = ( produc2245416461498447860et_nat @ ( F @ X ) @ Y ) ) ).
% 0.33/0.65
% 0.33/0.65 % apfst_conv
% 0.33/0.65 thf(fact_6870_apfst__conv,axiom,
% 0.33/0.65 ! [F: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > produc8551481072490612790e_term > option6357759511663192854e_term,X: produc8551481072490612790e_term > option6357759511663192854e_term,Y: product_prod_int_int] :
% 0.33/0.65 ( ( produc7277921532047535397nt_int @ F @ ( produc5700946648718959541nt_int @ X @ Y ) )
% 0.33/0.65 = ( produc5700946648718959541nt_int @ ( F @ X ) @ Y ) ) ).
% 0.33/0.65
% 0.33/0.65 % apfst_conv
% 0.33/0.65 thf(fact_6871_apfst__conv,axiom,
% 0.33/0.65 ! [F: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > int > option6357759511663192854e_term,X: produc8551481072490612790e_term > option6357759511663192854e_term,Y: product_prod_int_int] :
% 0.33/0.65 ( ( produc6919319362177967663nt_int @ F @ ( produc5700946648718959541nt_int @ X @ Y ) )
% 0.33/0.65 = ( produc4305682042979456191nt_int @ ( F @ X ) @ Y ) ) ).
% 0.33/0.65
% 0.33/0.65 % apfst_conv
% 0.33/0.65 thf(fact_6872_apfst__conv,axiom,
% 0.33/0.65 ! [F: ( int > option6357759511663192854e_term ) > produc8551481072490612790e_term > option6357759511663192854e_term,X: int > option6357759511663192854e_term,Y: product_prod_int_int] :
% 0.33/0.65 ( ( produc6067946493426971951nt_int @ F @ ( produc4305682042979456191nt_int @ X @ Y ) )
% 0.33/0.65 = ( produc5700946648718959541nt_int @ ( F @ X ) @ Y ) ) ).
% 0.33/0.65
% 0.33/0.65 % apfst_conv
% 0.33/0.65 thf(fact_6873_apfst__conv,axiom,
% 0.33/0.65 ! [F: ( int > option6357759511663192854e_term ) > int > option6357759511663192854e_term,X: int > option6357759511663192854e_term,Y: product_prod_int_int] :
% 0.33/0.65 ( ( produc7131893314732144953nt_int @ F @ ( produc4305682042979456191nt_int @ X @ Y ) )
% 0.33/0.65 = ( produc4305682042979456191nt_int @ ( F @ X ) @ Y ) ) ).
% 0.33/0.65
% 0.33/0.65 % apfst_conv
% 0.33/0.65 thf(fact_6874_fst__apfst,axiom,
% 0.33/0.65 ! [F: code_integer > code_integer,X: produc8923325533196201883nteger] :
% 0.33/0.65 ( ( produc8508995932063986495nteger @ ( produc3195571438000033749nteger @ F @ X ) )
% 0.33/0.65 = ( F @ ( produc8508995932063986495nteger @ X ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % fst_apfst
% 0.33/0.65 thf(fact_6875_fst__apfst,axiom,
% 0.33/0.65 ! [F: int > int,X: product_prod_int_int] :
% 0.33/0.65 ( ( product_fst_int_int @ ( produc2355237562570658114nt_int @ F @ X ) )
% 0.33/0.65 = ( F @ ( product_fst_int_int @ X ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % fst_apfst
% 0.33/0.65 thf(fact_6876_snd__apfst,axiom,
% 0.33/0.65 ! [F: code_integer > code_integer,X: produc8923325533196201883nteger] :
% 0.33/0.65 ( ( produc6174133586879617921nteger @ ( produc3195571438000033749nteger @ F @ X ) )
% 0.33/0.65 = ( produc6174133586879617921nteger @ X ) ) ).
% 0.33/0.65
% 0.33/0.65 % snd_apfst
% 0.33/0.65 thf(fact_6877_snd__apfst,axiom,
% 0.33/0.65 ! [F: int > int,X: product_prod_int_int] :
% 0.33/0.65 ( ( product_snd_int_int @ ( produc2355237562570658114nt_int @ F @ X ) )
% 0.33/0.65 = ( product_snd_int_int @ X ) ) ).
% 0.33/0.65
% 0.33/0.65 % snd_apfst
% 0.33/0.65 thf(fact_6878_snd__apfst,axiom,
% 0.33/0.65 ! [F: code_natural > code_natural,X: produc5835291356934675326atural] :
% 0.33/0.65 ( ( produc6591912806276919810atural @ ( produc4623092060929046819atural @ F @ X ) )
% 0.33/0.65 = ( produc6591912806276919810atural @ X ) ) ).
% 0.33/0.65
% 0.33/0.65 % snd_apfst
% 0.33/0.65 thf(fact_6879_Collect__case__prod,axiom,
% 0.33/0.65 ! [P: nat > $o,Q: nat > $o] :
% 0.33/0.65 ( ( collec3392354462482085612at_nat
% 0.33/0.65 @ ( produc6081775807080527818_nat_o
% 0.33/0.65 @ ^ [A5: nat,B4: nat] :
% 0.33/0.65 ( ( P @ A5 )
% 0.33/0.65 & ( Q @ B4 ) ) ) )
% 0.33/0.65 = ( produc457027306803732586at_nat @ ( collect_nat @ P )
% 0.33/0.65 @ ^ [Uu: nat] : ( collect_nat @ Q ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % Collect_case_prod
% 0.33/0.65 thf(fact_6880_Collect__case__prod,axiom,
% 0.33/0.65 ! [P: nat > $o,Q: list_nat > $o] :
% 0.33/0.65 ( ( collec1907656820224499068st_nat
% 0.33/0.65 @ ( produc5265810065896090426_nat_o
% 0.33/0.65 @ ^ [A5: nat,B4: list_nat] :
% 0.33/0.65 ( ( P @ A5 )
% 0.33/0.65 & ( Q @ B4 ) ) ) )
% 0.33/0.65 = ( produc5227933103413159546st_nat @ ( collect_nat @ P )
% 0.33/0.65 @ ^ [Uu: nat] : ( collect_list_nat @ Q ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % Collect_case_prod
% 0.33/0.65 thf(fact_6881_Collect__case__prod,axiom,
% 0.33/0.65 ! [P: list_nat > $o,Q: nat > $o] :
% 0.33/0.65 ( ( collec8096645339561496572at_nat
% 0.33/0.65 @ ( produc7308574044827705018_nat_o
% 0.33/0.65 @ ^ [A5: list_nat,B4: nat] :
% 0.33/0.65 ( ( P @ A5 )
% 0.33/0.65 & ( Q @ B4 ) ) ) )
% 0.33/0.65 = ( produc7466890150575444730at_nat @ ( collect_list_nat @ P )
% 0.33/0.65 @ ^ [Uu: list_nat] : ( collect_nat @ Q ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % Collect_case_prod
% 0.33/0.65 thf(fact_6882_Collect__case__prod,axiom,
% 0.33/0.65 ! [P: list_nat > $o,Q: list_nat > $o] :
% 0.33/0.65 ( ( collec1570431334306492044st_nat
% 0.33/0.65 @ ( produc6382697403170970154_nat_o
% 0.33/0.65 @ ^ [A5: list_nat,B4: list_nat] :
% 0.33/0.65 ( ( P @ A5 )
% 0.33/0.65 & ( Q @ B4 ) ) ) )
% 0.33/0.65 = ( produc6850429418872557834st_nat @ ( collect_list_nat @ P )
% 0.33/0.65 @ ^ [Uu: list_nat] : ( collect_list_nat @ Q ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % Collect_case_prod
% 0.33/0.65 thf(fact_6883_is__unit__gcd__iff,axiom,
% 0.33/0.65 ! [A: nat,B: nat] :
% 0.33/0.65 ( ( dvd_dvd_nat @ ( gcd_gcd_nat @ A @ B ) @ one_one_nat )
% 0.33/0.65 = ( ( gcd_gcd_nat @ A @ B )
% 0.33/0.65 = one_one_nat ) ) ).
% 0.33/0.65
% 0.33/0.65 % is_unit_gcd_iff
% 0.33/0.65 thf(fact_6884_is__unit__gcd__iff,axiom,
% 0.33/0.65 ! [A: int,B: int] :
% 0.33/0.65 ( ( dvd_dvd_int @ ( gcd_gcd_int @ A @ B ) @ one_one_int )
% 0.33/0.65 = ( ( gcd_gcd_int @ A @ B )
% 0.33/0.65 = one_one_int ) ) ).
% 0.33/0.65
% 0.33/0.65 % is_unit_gcd_iff
% 0.33/0.65 thf(fact_6885_Sigma__empty1,axiom,
% 0.33/0.65 ! [B5: set_Pr1261947904930325089at_nat > set_se7855581050983116737at_nat] :
% 0.33/0.65 ( ( produc7726050920695093128at_nat @ bot_bo3083307316010499117at_nat @ B5 )
% 0.33/0.65 = bot_bo228742789529271731at_nat ) ).
% 0.33/0.65
% 0.33/0.65 % Sigma_empty1
% 0.33/0.65 thf(fact_6886_Sigma__empty1,axiom,
% 0.33/0.65 ! [B5: nat > set_nat] :
% 0.33/0.65 ( ( produc457027306803732586at_nat @ bot_bot_set_nat @ B5 )
% 0.33/0.65 = bot_bo2099793752762293965at_nat ) ).
% 0.33/0.65
% 0.33/0.65 % Sigma_empty1
% 0.33/0.65 thf(fact_6887_Sigma__empty2,axiom,
% 0.33/0.65 ! [A2: set_se7855581050983116737at_nat] :
% 0.33/0.65 ( ( produc7726050920695093128at_nat @ A2
% 0.33/0.65 @ ^ [Uu: set_Pr1261947904930325089at_nat] : bot_bo3083307316010499117at_nat )
% 0.33/0.65 = bot_bo228742789529271731at_nat ) ).
% 0.33/0.65
% 0.33/0.65 % Sigma_empty2
% 0.33/0.65 thf(fact_6888_Sigma__empty2,axiom,
% 0.33/0.65 ! [A2: set_nat] :
% 0.33/0.65 ( ( produc457027306803732586at_nat @ A2
% 0.33/0.65 @ ^ [Uu: nat] : bot_bot_set_nat )
% 0.33/0.65 = bot_bo2099793752762293965at_nat ) ).
% 0.33/0.65
% 0.33/0.65 % Sigma_empty2
% 0.33/0.65 thf(fact_6889_Times__empty,axiom,
% 0.33/0.65 ! [A2: set_o,B5: set_o] :
% 0.33/0.65 ( ( ( product_Sigma_o_o @ A2
% 0.33/0.65 @ ^ [Uu: $o] : B5 )
% 0.33/0.65 = bot_bo7073875226086086771od_o_o )
% 0.33/0.65 = ( ( A2 = bot_bot_set_o )
% 0.33/0.65 | ( B5 = bot_bot_set_o ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % Times_empty
% 0.33/0.65 thf(fact_6890_Times__empty,axiom,
% 0.33/0.65 ! [A2: set_o,B5: set_nat] :
% 0.33/0.65 ( ( ( product_Sigma_o_nat @ A2
% 0.33/0.65 @ ^ [Uu: $o] : B5 )
% 0.33/0.65 = bot_bo66526543525301729_o_nat )
% 0.33/0.65 = ( ( A2 = bot_bot_set_o )
% 0.33/0.65 | ( B5 = bot_bot_set_nat ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % Times_empty
% 0.33/0.65 thf(fact_6891_Times__empty,axiom,
% 0.33/0.65 ! [A2: set_o,B5: set_int] :
% 0.33/0.65 ( ( ( product_Sigma_o_int @ A2
% 0.33/0.65 @ ^ [Uu: $o] : B5 )
% 0.33/0.65 = bot_bo6799815435448350781_o_int )
% 0.33/0.65 = ( ( A2 = bot_bot_set_o )
% 0.33/0.65 | ( B5 = bot_bot_set_int ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % Times_empty
% 0.33/0.65 thf(fact_6892_Times__empty,axiom,
% 0.33/0.65 ! [A2: set_nat,B5: set_o] :
% 0.33/0.65 ( ( ( product_Sigma_nat_o @ A2
% 0.33/0.65 @ ^ [Uu: nat] : B5 )
% 0.33/0.65 = bot_bo1114129665703605383_nat_o )
% 0.33/0.65 = ( ( A2 = bot_bot_set_nat )
% 0.33/0.65 | ( B5 = bot_bot_set_o ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % Times_empty
% 0.33/0.65 thf(fact_6893_Times__empty,axiom,
% 0.33/0.65 ! [A2: set_nat,B5: set_int] :
% 0.33/0.65 ( ( ( produc454536836294682310at_int @ A2
% 0.33/0.65 @ ^ [Uu: nat] : B5 )
% 0.33/0.65 = bot_bo8833082644685343017at_int )
% 0.33/0.65 = ( ( A2 = bot_bot_set_nat )
% 0.33/0.65 | ( B5 = bot_bot_set_int ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % Times_empty
% 0.33/0.65 thf(fact_6894_Times__empty,axiom,
% 0.33/0.65 ! [A2: set_int,B5: set_o] :
% 0.33/0.65 ( ( ( product_Sigma_int_o @ A2
% 0.33/0.65 @ ^ [Uu: int] : B5 )
% 0.33/0.65 = bot_bo8092356734887935275_int_o )
% 0.33/0.65 = ( ( A2 = bot_bot_set_int )
% 0.33/0.65 | ( B5 = bot_bot_set_o ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % Times_empty
% 0.33/0.65 thf(fact_6895_Times__empty,axiom,
% 0.33/0.65 ! [A2: set_int,B5: set_nat] :
% 0.33/0.65 ( ( ( produc1456381018704787142nt_nat @ A2
% 0.33/0.65 @ ^ [Uu: int] : B5 )
% 0.33/0.65 = bot_bo4286715327455315753nt_nat )
% 0.33/0.65 = ( ( A2 = bot_bot_set_int )
% 0.33/0.65 | ( B5 = bot_bot_set_nat ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % Times_empty
% 0.33/0.65 thf(fact_6896_Times__empty,axiom,
% 0.33/0.65 ! [A2: set_int,B5: set_int] :
% 0.33/0.65 ( ( ( produc1453890548195736866nt_int @ A2
% 0.33/0.65 @ ^ [Uu: int] : B5 )
% 0.33/0.65 = bot_bo1796632182523588997nt_int )
% 0.33/0.65 = ( ( A2 = bot_bot_set_int )
% 0.33/0.65 | ( B5 = bot_bot_set_int ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % Times_empty
% 0.33/0.65 thf(fact_6897_Times__empty,axiom,
% 0.33/0.65 ! [A2: set_nat,B5: set_nat] :
% 0.33/0.65 ( ( ( produc457027306803732586at_nat @ A2
% 0.33/0.65 @ ^ [Uu: nat] : B5 )
% 0.33/0.65 = bot_bo2099793752762293965at_nat )
% 0.33/0.65 = ( ( A2 = bot_bot_set_nat )
% 0.33/0.65 | ( B5 = bot_bot_set_nat ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % Times_empty
% 0.33/0.65 thf(fact_6898_Times__empty,axiom,
% 0.33/0.65 ! [A2: set_Pr1261947904930325089at_nat,B5: set_o] :
% 0.33/0.65 ( ( ( produc203973861852599583_nat_o @ A2
% 0.33/0.65 @ ^ [Uu: product_prod_nat_nat] : B5 )
% 0.33/0.65 = bot_bo5454027612061941066_nat_o )
% 0.33/0.65 = ( ( A2 = bot_bo2099793752762293965at_nat )
% 0.33/0.65 | ( B5 = bot_bot_set_o ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % Times_empty
% 0.33/0.65 thf(fact_6899_Sigma__UNIV__cancel,axiom,
% 0.33/0.65 ! [A2: set_se7855581050983116737at_nat,X11: set_se7855581050983116737at_nat] :
% 0.33/0.65 ( ( minus_3314409938677909166at_nat
% 0.33/0.65 @ ( produc7726050920695093128at_nat @ A2
% 0.33/0.65 @ ^ [Uu: set_Pr1261947904930325089at_nat] : X11 )
% 0.33/0.65 @ ( produc7726050920695093128at_nat @ A2
% 0.33/0.65 @ ^ [Uu: set_Pr1261947904930325089at_nat] : top_to7629004291339433233at_nat ) )
% 0.33/0.65 = bot_bo228742789529271731at_nat ) ).
% 0.33/0.65
% 0.33/0.65 % Sigma_UNIV_cancel
% 0.33/0.65 thf(fact_6900_Sigma__UNIV__cancel,axiom,
% 0.33/0.65 ! [A2: set_nat,X11: set_nat] :
% 0.33/0.65 ( ( minus_1356011639430497352at_nat
% 0.33/0.65 @ ( produc457027306803732586at_nat @ A2
% 0.33/0.65 @ ^ [Uu: nat] : X11 )
% 0.33/0.65 @ ( produc457027306803732586at_nat @ A2
% 0.33/0.65 @ ^ [Uu: nat] : top_top_set_nat ) )
% 0.33/0.65 = bot_bo2099793752762293965at_nat ) ).
% 0.33/0.65
% 0.33/0.65 % Sigma_UNIV_cancel
% 0.33/0.65 thf(fact_6901_snd__comp__apfst,axiom,
% 0.33/0.65 ! [F: code_integer > code_integer] :
% 0.33/0.65 ( ( comp_P3428181540658402820nteger @ produc6174133586879617921nteger @ ( produc3195571438000033749nteger @ F ) )
% 0.33/0.65 = produc6174133586879617921nteger ) ).
% 0.33/0.65
% 0.33/0.65 % snd_comp_apfst
% 0.33/0.65 thf(fact_6902_snd__comp__apfst,axiom,
% 0.33/0.65 ! [F: int > int] :
% 0.33/0.65 ( ( comp_P5356232565778667509nt_int @ product_snd_int_int @ ( produc2355237562570658114nt_int @ F ) )
% 0.33/0.65 = product_snd_int_int ) ).
% 0.33/0.65
% 0.33/0.65 % snd_comp_apfst
% 0.33/0.65 thf(fact_6903_snd__comp__apfst,axiom,
% 0.33/0.65 ! [F: code_natural > code_natural] :
% 0.33/0.65 ( ( comp_P7610810914149544718atural @ produc6591912806276919810atural @ ( produc4623092060929046819atural @ F ) )
% 0.33/0.65 = produc6591912806276919810atural ) ).
% 0.33/0.65
% 0.33/0.65 % snd_comp_apfst
% 0.33/0.65 thf(fact_6904_UNIV__Times__UNIV,axiom,
% 0.33/0.65 ( ( produc457027306803732586at_nat @ top_top_set_nat
% 0.33/0.65 @ ^ [Uu: nat] : top_top_set_nat )
% 0.33/0.65 = top_to4669805908274784177at_nat ) ).
% 0.33/0.65
% 0.33/0.65 % UNIV_Times_UNIV
% 0.33/0.65 thf(fact_6905_UNIV__Times__UNIV,axiom,
% 0.33/0.65 ( ( produc5506539147108004339t_unit @ top_top_set_nat
% 0.33/0.65 @ ^ [Uu: nat] : top_to1996260823553986621t_unit )
% 0.33/0.65 = top_to8544742955230171288t_unit ) ).
% 0.33/0.65
% 0.33/0.65 % UNIV_Times_UNIV
% 0.33/0.65 thf(fact_6906_UNIV__Times__UNIV,axiom,
% 0.33/0.65 ( ( produc454536836294682310at_int @ top_top_set_nat
% 0.33/0.65 @ ^ [Uu: nat] : top_top_set_int )
% 0.33/0.65 = top_to2179722763343057421at_int ) ).
% 0.33/0.65
% 0.33/0.65 % UNIV_Times_UNIV
% 0.33/0.65 thf(fact_6907_UNIV__Times__UNIV,axiom,
% 0.33/0.65 ( ( produc6875377002296012693it_nat @ top_to1996260823553986621t_unit
% 0.33/0.65 @ ^ [Uu: product_unit] : top_top_set_nat )
% 0.33/0.65 = top_to5974110478112770290it_nat ) ).
% 0.33/0.65
% 0.33/0.65 % UNIV_Times_UNIV
% 0.33/0.65 thf(fact_6908_UNIV__Times__UNIV,axiom,
% 0.33/0.65 ( ( produc6121607364029222536t_unit @ top_to1996260823553986621t_unit
% 0.33/0.65 @ ^ [Uu: product_unit] : top_to1996260823553986621t_unit )
% 0.33/0.65 = top_to1835807148980544151t_unit ) ).
% 0.33/0.65
% 0.33/0.65 % UNIV_Times_UNIV
% 0.33/0.65 thf(fact_6909_UNIV__Times__UNIV,axiom,
% 0.33/0.65 ( ( produc6872886531786962417it_int @ top_to1996260823553986621t_unit
% 0.33/0.65 @ ^ [Uu: product_unit] : top_top_set_int )
% 0.33/0.65 = top_to3484027333181043534it_int ) ).
% 0.33/0.65
% 0.33/0.65 % UNIV_Times_UNIV
% 0.33/0.65 thf(fact_6910_UNIV__Times__UNIV,axiom,
% 0.33/0.65 ( ( produc1456381018704787142nt_nat @ top_top_set_int
% 0.33/0.65 @ ^ [Uu: int] : top_top_set_nat )
% 0.33/0.65 = top_to6856727482967805965nt_nat ) ).
% 0.33/0.65
% 0.33/0.65 % UNIV_Times_UNIV
% 0.33/0.65 thf(fact_6911_UNIV__Times__UNIV,axiom,
% 0.33/0.65 ( ( produc2622961094310184599t_unit @ top_top_set_int
% 0.33/0.65 @ ^ [Uu: int] : top_to1996260823553986621t_unit )
% 0.33/0.65 = top_to876157113852465980t_unit ) ).
% 0.33/0.65
% 0.33/0.65 % UNIV_Times_UNIV
% 0.33/0.65 thf(fact_6912_UNIV__Times__UNIV,axiom,
% 0.33/0.65 ( ( produc1453890548195736866nt_int @ top_top_set_int
% 0.33/0.65 @ ^ [Uu: int] : top_top_set_int )
% 0.33/0.65 = top_to4366644338036079209nt_int ) ).
% 0.33/0.65
% 0.33/0.65 % UNIV_Times_UNIV
% 0.33/0.65 thf(fact_6913_pairself__image__cart,axiom,
% 0.33/0.65 ! [F: nat > code_integer,A2: set_nat,B5: set_nat] :
% 0.33/0.65 ( ( image_5669961043262023647nteger @ ( pairse4825235148789309005nteger @ F )
% 0.33/0.65 @ ( produc457027306803732586at_nat @ A2
% 0.33/0.65 @ ^ [Uu: nat] : B5 ) )
% 0.33/0.65 = ( produc5882431272649516420nteger @ ( image_1215581382706833972nteger @ F @ A2 )
% 0.33/0.65 @ ^ [Uu: code_integer] : ( image_1215581382706833972nteger @ F @ B5 ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % pairself_image_cart
% 0.33/0.65 thf(fact_6914_pairself__image__cart,axiom,
% 0.33/0.65 ! [F: nat > set_nat,A2: set_nat,B5: set_nat] :
% 0.33/0.65 ( ( image_4566292076127975857et_nat @ ( pairself_nat_set_nat @ F )
% 0.33/0.65 @ ( produc457027306803732586at_nat @ A2
% 0.33/0.65 @ ^ [Uu: nat] : B5 ) )
% 0.33/0.65 = ( produc105401717395143638et_nat @ ( image_nat_set_nat @ F @ A2 )
% 0.33/0.65 @ ^ [Uu: set_nat] : ( image_nat_set_nat @ F @ B5 ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % pairself_image_cart
% 0.33/0.65 thf(fact_6915_pairself__image__cart,axiom,
% 0.33/0.65 ! [F: nat > nat,A2: set_nat,B5: set_nat] :
% 0.33/0.65 ( ( image_5168914502847457605at_nat @ ( pairself_nat_nat @ F )
% 0.33/0.65 @ ( produc457027306803732586at_nat @ A2
% 0.33/0.65 @ ^ [Uu: nat] : B5 ) )
% 0.33/0.65 = ( produc457027306803732586at_nat @ ( image_nat_nat @ F @ A2 )
% 0.33/0.65 @ ^ [Uu: nat] : ( image_nat_nat @ F @ B5 ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % pairself_image_cart
% 0.33/0.65 thf(fact_6916_pairself__image__cart,axiom,
% 0.33/0.65 ! [F: nat > int,A2: set_nat,B5: set_nat] :
% 0.33/0.65 ( ( image_1990417195239315453nt_int @ ( pairself_nat_int @ F )
% 0.33/0.65 @ ( produc457027306803732586at_nat @ A2
% 0.33/0.65 @ ^ [Uu: nat] : B5 ) )
% 0.33/0.65 = ( produc1453890548195736866nt_int @ ( image_nat_int @ F @ A2 )
% 0.33/0.65 @ ^ [Uu: int] : ( image_nat_int @ F @ B5 ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % pairself_image_cart
% 0.33/0.65 thf(fact_6917_pairself__image__cart,axiom,
% 0.33/0.65 ! [F: int > int,A2: set_int,B5: set_int] :
% 0.33/0.65 ( ( image_2653370878348428101nt_int @ ( pairself_int_int @ F )
% 0.33/0.65 @ ( produc1453890548195736866nt_int @ A2
% 0.33/0.65 @ ^ [Uu: int] : B5 ) )
% 0.33/0.65 = ( produc1453890548195736866nt_int @ ( image_int_int @ F @ A2 )
% 0.33/0.65 @ ^ [Uu: int] : ( image_int_int @ F @ B5 ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % pairself_image_cart
% 0.33/0.65 thf(fact_6918_fst__image__times,axiom,
% 0.33/0.65 ! [B5: set_Code_integer,A2: set_Code_integer] :
% 0.33/0.65 ( ( ( B5 = bot_bo3990330152332043303nteger )
% 0.33/0.65 => ( ( image_6316824473203919795nteger @ produc8508995932063986495nteger
% 0.33/0.65 @ ( produc5882431272649516420nteger @ A2
% 0.33/0.65 @ ^ [Uu: code_integer] : B5 ) )
% 0.33/0.65 = bot_bo3990330152332043303nteger ) )
% 0.33/0.65 & ( ( B5 != bot_bo3990330152332043303nteger )
% 0.33/0.65 => ( ( image_6316824473203919795nteger @ produc8508995932063986495nteger
% 0.33/0.65 @ ( produc5882431272649516420nteger @ A2
% 0.33/0.65 @ ^ [Uu: code_integer] : B5 ) )
% 0.33/0.65 = A2 ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % fst_image_times
% 0.33/0.65 thf(fact_6919_fst__image__times,axiom,
% 0.33/0.65 ! [B5: set_o,A2: set_o] :
% 0.33/0.65 ( ( ( B5 = bot_bot_set_o )
% 0.33/0.65 => ( ( image_7896445794123959606_o_o_o @ product_fst_o_o
% 0.33/0.65 @ ( product_Sigma_o_o @ A2
% 0.33/0.65 @ ^ [Uu: $o] : B5 ) )
% 0.33/0.65 = bot_bot_set_o ) )
% 0.33/0.65 & ( ( B5 != bot_bot_set_o )
% 0.33/0.65 => ( ( image_7896445794123959606_o_o_o @ product_fst_o_o
% 0.33/0.65 @ ( product_Sigma_o_o @ A2
% 0.33/0.65 @ ^ [Uu: $o] : B5 ) )
% 0.33/0.65 = A2 ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % fst_image_times
% 0.33/0.65 thf(fact_6920_fst__image__times,axiom,
% 0.33/0.65 ! [B5: set_o,A2: set_nat] :
% 0.33/0.65 ( ( ( B5 = bot_bot_set_o )
% 0.33/0.65 => ( ( image_8629803608462650132_o_nat @ product_fst_nat_o
% 0.33/0.65 @ ( product_Sigma_nat_o @ A2
% 0.33/0.65 @ ^ [Uu: nat] : B5 ) )
% 0.33/0.65 = bot_bot_set_nat ) )
% 0.33/0.65 & ( ( B5 != bot_bot_set_o )
% 0.33/0.65 => ( ( image_8629803608462650132_o_nat @ product_fst_nat_o
% 0.33/0.65 @ ( product_Sigma_nat_o @ A2
% 0.33/0.65 @ ^ [Uu: nat] : B5 ) )
% 0.33/0.65 = A2 ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % fst_image_times
% 0.33/0.65 thf(fact_6921_fst__image__times,axiom,
% 0.33/0.65 ! [B5: set_o,A2: set_int] :
% 0.33/0.65 ( ( ( B5 = bot_bot_set_o )
% 0.33/0.65 => ( ( image_90517134139374612_o_int @ product_fst_int_o
% 0.33/0.65 @ ( product_Sigma_int_o @ A2
% 0.33/0.65 @ ^ [Uu: int] : B5 ) )
% 0.33/0.65 = bot_bot_set_int ) )
% 0.33/0.65 & ( ( B5 != bot_bot_set_o )
% 0.33/0.65 => ( ( image_90517134139374612_o_int @ product_fst_int_o
% 0.33/0.65 @ ( product_Sigma_int_o @ A2
% 0.33/0.65 @ ^ [Uu: int] : B5 ) )
% 0.33/0.65 = A2 ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % fst_image_times
% 0.33/0.65 thf(fact_6922_fst__image__times,axiom,
% 0.33/0.65 ! [B5: set_nat,A2: set_o] :
% 0.33/0.65 ( ( ( B5 = bot_bot_set_nat )
% 0.33/0.65 => ( ( image_8105710389281276538_nat_o @ product_fst_o_nat
% 0.33/0.65 @ ( product_Sigma_o_nat @ A2
% 0.33/0.65 @ ^ [Uu: $o] : B5 ) )
% 0.33/0.65 = bot_bot_set_o ) )
% 0.33/0.65 & ( ( B5 != bot_bot_set_nat )
% 0.33/0.65 => ( ( image_8105710389281276538_nat_o @ product_fst_o_nat
% 0.33/0.65 @ ( product_Sigma_o_nat @ A2
% 0.33/0.65 @ ^ [Uu: $o] : B5 ) )
% 0.33/0.65 = A2 ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % fst_image_times
% 0.33/0.65 thf(fact_6923_fst__image__times,axiom,
% 0.33/0.65 ! [B5: set_nat,A2: set_nat] :
% 0.33/0.65 ( ( ( B5 = bot_bot_set_nat )
% 0.33/0.65 => ( ( image_2486076414777270412at_nat @ product_fst_nat_nat
% 0.33/0.65 @ ( produc457027306803732586at_nat @ A2
% 0.33/0.65 @ ^ [Uu: nat] : B5 ) )
% 0.33/0.65 = bot_bot_set_nat ) )
% 0.33/0.65 & ( ( B5 != bot_bot_set_nat )
% 0.33/0.65 => ( ( image_2486076414777270412at_nat @ product_fst_nat_nat
% 0.33/0.65 @ ( produc457027306803732586at_nat @ A2
% 0.33/0.65 @ ^ [Uu: nat] : B5 ) )
% 0.33/0.65 = A2 ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % fst_image_times
% 0.33/0.65 thf(fact_6924_fst__image__times,axiom,
% 0.33/0.65 ! [B5: set_nat,A2: set_int] :
% 0.33/0.65 ( ( ( B5 = bot_bot_set_nat )
% 0.33/0.65 => ( ( image_2855239504505064772at_int @ product_fst_int_nat
% 0.33/0.65 @ ( produc1456381018704787142nt_nat @ A2
% 0.33/0.65 @ ^ [Uu: int] : B5 ) )
% 0.33/0.65 = bot_bot_set_int ) )
% 0.33/0.65 & ( ( B5 != bot_bot_set_nat )
% 0.33/0.65 => ( ( image_2855239504505064772at_int @ product_fst_int_nat
% 0.33/0.65 @ ( produc1456381018704787142nt_nat @ A2
% 0.33/0.65 @ ^ [Uu: int] : B5 ) )
% 0.33/0.65 = A2 ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % fst_image_times
% 0.33/0.65 thf(fact_6925_fst__image__times,axiom,
% 0.33/0.65 ! [B5: set_int,A2: set_o] :
% 0.33/0.65 ( ( ( B5 = bot_bot_set_int )
% 0.33/0.65 => ( ( image_5860565421610830622_int_o @ product_fst_o_int
% 0.33/0.65 @ ( product_Sigma_o_int @ A2
% 0.33/0.65 @ ^ [Uu: $o] : B5 ) )
% 0.33/0.65 = bot_bot_set_o ) )
% 0.33/0.65 & ( ( B5 != bot_bot_set_int )
% 0.33/0.65 => ( ( image_5860565421610830622_int_o @ product_fst_o_int
% 0.33/0.65 @ ( product_Sigma_o_int @ A2
% 0.33/0.65 @ ^ [Uu: $o] : B5 ) )
% 0.33/0.65 = A2 ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % fst_image_times
% 0.33/0.65 thf(fact_6926_fst__image__times,axiom,
% 0.33/0.65 ! [B5: set_int,A2: set_nat] :
% 0.33/0.65 ( ( ( B5 = bot_bot_set_int )
% 0.33/0.65 => ( ( image_4672997989470292200nt_nat @ product_fst_nat_int
% 0.33/0.65 @ ( produc454536836294682310at_int @ A2
% 0.33/0.65 @ ^ [Uu: nat] : B5 ) )
% 0.33/0.65 = bot_bot_set_nat ) )
% 0.33/0.65 & ( ( B5 != bot_bot_set_int )
% 0.33/0.65 => ( ( image_4672997989470292200nt_nat @ product_fst_nat_int
% 0.33/0.65 @ ( produc454536836294682310at_int @ A2
% 0.33/0.65 @ ^ [Uu: nat] : B5 ) )
% 0.33/0.65 = A2 ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % fst_image_times
% 0.33/0.65 thf(fact_6927_fst__image__times,axiom,
% 0.33/0.65 ! [B5: set_int,A2: set_int] :
% 0.33/0.65 ( ( ( B5 = bot_bot_set_int )
% 0.33/0.65 => ( ( image_5042161079198086560nt_int @ product_fst_int_int
% 0.33/0.65 @ ( produc1453890548195736866nt_int @ A2
% 0.33/0.65 @ ^ [Uu: int] : B5 ) )
% 0.33/0.65 = bot_bot_set_int ) )
% 0.33/0.65 & ( ( B5 != bot_bot_set_int )
% 0.33/0.65 => ( ( image_5042161079198086560nt_int @ product_fst_int_int
% 0.33/0.65 @ ( produc1453890548195736866nt_int @ A2
% 0.33/0.65 @ ^ [Uu: int] : B5 ) )
% 0.33/0.65 = A2 ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % fst_image_times
% 0.33/0.65 thf(fact_6928_snd__image__times,axiom,
% 0.33/0.65 ! [A2: set_Code_integer,B5: set_Code_integer] :
% 0.33/0.65 ( ( ( A2 = bot_bo3990330152332043303nteger )
% 0.33/0.65 => ( ( image_6316824473203919795nteger @ produc6174133586879617921nteger
% 0.33/0.65 @ ( produc5882431272649516420nteger @ A2
% 0.33/0.65 @ ^ [Uu: code_integer] : B5 ) )
% 0.33/0.65 = bot_bo3990330152332043303nteger ) )
% 0.33/0.65 & ( ( A2 != bot_bo3990330152332043303nteger )
% 0.33/0.65 => ( ( image_6316824473203919795nteger @ produc6174133586879617921nteger
% 0.33/0.65 @ ( produc5882431272649516420nteger @ A2
% 0.33/0.65 @ ^ [Uu: code_integer] : B5 ) )
% 0.33/0.65 = B5 ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % snd_image_times
% 0.33/0.65 thf(fact_6929_snd__image__times,axiom,
% 0.33/0.65 ! [A2: set_o,B5: set_o] :
% 0.33/0.65 ( ( ( A2 = bot_bot_set_o )
% 0.33/0.65 => ( ( image_7896445794123959606_o_o_o @ product_snd_o_o
% 0.33/0.65 @ ( product_Sigma_o_o @ A2
% 0.33/0.65 @ ^ [Uu: $o] : B5 ) )
% 0.33/0.65 = bot_bot_set_o ) )
% 0.33/0.65 & ( ( A2 != bot_bot_set_o )
% 0.33/0.65 => ( ( image_7896445794123959606_o_o_o @ product_snd_o_o
% 0.33/0.65 @ ( product_Sigma_o_o @ A2
% 0.33/0.65 @ ^ [Uu: $o] : B5 ) )
% 0.33/0.65 = B5 ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % snd_image_times
% 0.33/0.65 thf(fact_6930_snd__image__times,axiom,
% 0.33/0.65 ! [A2: set_o,B5: set_nat] :
% 0.33/0.65 ( ( ( A2 = bot_bot_set_o )
% 0.33/0.65 => ( ( image_4888532181312399726at_nat @ product_snd_o_nat
% 0.33/0.65 @ ( product_Sigma_o_nat @ A2
% 0.33/0.65 @ ^ [Uu: $o] : B5 ) )
% 0.33/0.65 = bot_bot_set_nat ) )
% 0.33/0.65 & ( ( A2 != bot_bot_set_o )
% 0.33/0.65 => ( ( image_4888532181312399726at_nat @ product_snd_o_nat
% 0.33/0.65 @ ( product_Sigma_o_nat @ A2
% 0.33/0.65 @ ^ [Uu: $o] : B5 ) )
% 0.33/0.65 = B5 ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % snd_image_times
% 0.33/0.65 thf(fact_6931_snd__image__times,axiom,
% 0.33/0.65 ! [A2: set_o,B5: set_int] :
% 0.33/0.65 ( ( ( A2 = bot_bot_set_o )
% 0.33/0.65 => ( ( image_7072963285496371238nt_int @ product_snd_o_int
% 0.33/0.65 @ ( product_Sigma_o_int @ A2
% 0.33/0.65 @ ^ [Uu: $o] : B5 ) )
% 0.33/0.65 = bot_bot_set_int ) )
% 0.33/0.65 & ( ( A2 != bot_bot_set_o )
% 0.33/0.65 => ( ( image_7072963285496371238nt_int @ product_snd_o_int
% 0.33/0.65 @ ( product_Sigma_o_int @ A2
% 0.33/0.65 @ ^ [Uu: $o] : B5 ) )
% 0.33/0.65 = B5 ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % snd_image_times
% 0.33/0.65 thf(fact_6932_snd__image__times,axiom,
% 0.33/0.65 ! [A2: set_nat,B5: set_o] :
% 0.33/0.65 ( ( ( A2 = bot_bot_set_nat )
% 0.33/0.65 => ( ( image_7478392465989118804at_o_o @ product_snd_nat_o
% 0.33/0.65 @ ( product_Sigma_nat_o @ A2
% 0.33/0.65 @ ^ [Uu: nat] : B5 ) )
% 0.33/0.65 = bot_bot_set_o ) )
% 0.33/0.65 & ( ( A2 != bot_bot_set_nat )
% 0.33/0.65 => ( ( image_7478392465989118804at_o_o @ product_snd_nat_o
% 0.33/0.65 @ ( product_Sigma_nat_o @ A2
% 0.33/0.65 @ ^ [Uu: nat] : B5 ) )
% 0.33/0.65 = B5 ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % snd_image_times
% 0.33/0.65 thf(fact_6933_snd__image__times,axiom,
% 0.33/0.65 ! [A2: set_nat,B5: set_nat] :
% 0.33/0.65 ( ( ( A2 = bot_bot_set_nat )
% 0.33/0.65 => ( ( image_2486076414777270412at_nat @ product_snd_nat_nat
% 0.33/0.65 @ ( produc457027306803732586at_nat @ A2
% 0.33/0.65 @ ^ [Uu: nat] : B5 ) )
% 0.33/0.65 = bot_bot_set_nat ) )
% 0.33/0.65 & ( ( A2 != bot_bot_set_nat )
% 0.33/0.65 => ( ( image_2486076414777270412at_nat @ product_snd_nat_nat
% 0.33/0.65 @ ( produc457027306803732586at_nat @ A2
% 0.33/0.65 @ ^ [Uu: nat] : B5 ) )
% 0.33/0.65 = B5 ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % snd_image_times
% 0.33/0.65 thf(fact_6934_snd__image__times,axiom,
% 0.33/0.65 ! [A2: set_nat,B5: set_int] :
% 0.33/0.65 ( ( ( A2 = bot_bot_set_nat )
% 0.33/0.65 => ( ( image_4670507518961241924nt_int @ product_snd_nat_int
% 0.33/0.65 @ ( produc454536836294682310at_int @ A2
% 0.33/0.65 @ ^ [Uu: nat] : B5 ) )
% 0.33/0.65 = bot_bot_set_int ) )
% 0.33/0.65 & ( ( A2 != bot_bot_set_nat )
% 0.33/0.65 => ( ( image_4670507518961241924nt_int @ product_snd_nat_int
% 0.33/0.65 @ ( produc454536836294682310at_int @ A2
% 0.33/0.65 @ ^ [Uu: nat] : B5 ) )
% 0.33/0.65 = B5 ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % snd_image_times
% 0.33/0.65 thf(fact_6935_snd__image__times,axiom,
% 0.33/0.65 ! [A2: set_int,B5: set_o] :
% 0.33/0.65 ( ( ( A2 = bot_bot_set_int )
% 0.33/0.65 => ( ( image_5561579847027142576nt_o_o @ product_snd_int_o
% 0.33/0.65 @ ( product_Sigma_int_o @ A2
% 0.33/0.65 @ ^ [Uu: int] : B5 ) )
% 0.33/0.65 = bot_bot_set_o ) )
% 0.33/0.65 & ( ( A2 != bot_bot_set_int )
% 0.33/0.65 => ( ( image_5561579847027142576nt_o_o @ product_snd_int_o
% 0.33/0.65 @ ( product_Sigma_int_o @ A2
% 0.33/0.65 @ ^ [Uu: int] : B5 ) )
% 0.33/0.65 = B5 ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % snd_image_times
% 0.33/0.65 thf(fact_6936_snd__image__times,axiom,
% 0.33/0.65 ! [A2: set_int,B5: set_nat] :
% 0.33/0.65 ( ( ( A2 = bot_bot_set_int )
% 0.33/0.65 => ( ( image_2857729975014115048at_nat @ product_snd_int_nat
% 0.33/0.65 @ ( produc1456381018704787142nt_nat @ A2
% 0.33/0.65 @ ^ [Uu: int] : B5 ) )
% 0.33/0.65 = bot_bot_set_nat ) )
% 0.33/0.65 & ( ( A2 != bot_bot_set_int )
% 0.33/0.65 => ( ( image_2857729975014115048at_nat @ product_snd_int_nat
% 0.33/0.65 @ ( produc1456381018704787142nt_nat @ A2
% 0.33/0.65 @ ^ [Uu: int] : B5 ) )
% 0.33/0.65 = B5 ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % snd_image_times
% 0.33/0.65 thf(fact_6937_snd__image__times,axiom,
% 0.33/0.65 ! [A2: set_int,B5: set_int] :
% 0.33/0.65 ( ( ( A2 = bot_bot_set_int )
% 0.33/0.65 => ( ( image_5042161079198086560nt_int @ product_snd_int_int
% 0.33/0.65 @ ( produc1453890548195736866nt_int @ A2
% 0.33/0.65 @ ^ [Uu: int] : B5 ) )
% 0.33/0.65 = bot_bot_set_int ) )
% 0.33/0.65 & ( ( A2 != bot_bot_set_int )
% 0.33/0.65 => ( ( image_5042161079198086560nt_int @ product_snd_int_int
% 0.33/0.65 @ ( produc1453890548195736866nt_int @ A2
% 0.33/0.65 @ ^ [Uu: int] : B5 ) )
% 0.33/0.65 = B5 ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % snd_image_times
% 0.33/0.65 thf(fact_6938_fst__comp__apfst,axiom,
% 0.33/0.65 ! [F: code_integer > code_integer] :
% 0.33/0.65 ( ( comp_P3428181540658402820nteger @ produc8508995932063986495nteger @ ( produc3195571438000033749nteger @ F ) )
% 0.33/0.65 = ( comp_C1043215000170864188nteger @ F @ produc8508995932063986495nteger ) ) ).
% 0.33/0.65
% 0.33/0.65 % fst_comp_apfst
% 0.33/0.65 thf(fact_6939_fst__comp__apfst,axiom,
% 0.33/0.65 ! [F: int > int] :
% 0.33/0.65 ( ( comp_P5356232565778667509nt_int @ product_fst_int_int @ ( produc2355237562570658114nt_int @ F ) )
% 0.33/0.65 = ( comp_i4330622015127193916nt_int @ F @ product_fst_int_int ) ) ).
% 0.33/0.65
% 0.33/0.65 % fst_comp_apfst
% 0.33/0.65 thf(fact_6940_fun_Omap__transfer,axiom,
% 0.33/0.65 ! [Rb2: code_integer > code_integer > $o,Sd: code_integer > code_integer > $o] :
% 0.33/0.65 ( bNF_re5979881370344185769nteger @ ( bNF_re1062419521925302741nteger @ Rb2 @ Sd )
% 0.33/0.65 @ ( bNF_re6097285183634142137nteger
% 0.33/0.65 @ ( bNF_re6741283560065411407nteger
% 0.33/0.65 @ ^ [Y4: num,Z2: num] : ( Y4 = Z2 )
% 0.33/0.65 @ Rb2 )
% 0.33/0.65 @ ( bNF_re6741283560065411407nteger
% 0.33/0.65 @ ^ [Y4: num,Z2: num] : ( Y4 = Z2 )
% 0.33/0.65 @ Sd ) )
% 0.33/0.65 @ comp_C3531382070062128313er_num
% 0.33/0.65 @ comp_C3531382070062128313er_num ) ).
% 0.33/0.65
% 0.33/0.65 % fun.map_transfer
% 0.33/0.65 thf(fact_6941_fun_Omap__transfer,axiom,
% 0.33/0.65 ! [Rb2: nat > nat > $o,Sd: num > num > $o] :
% 0.33/0.65 ( bNF_re3846787885862361009nt_num @ ( bNF_re341483209202555957um_num @ Rb2 @ Sd )
% 0.33/0.65 @ ( bNF_re9099949428469764705nt_num
% 0.33/0.65 @ ( bNF_re3715656647883201625at_nat
% 0.33/0.65 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.65 @ Rb2 )
% 0.33/0.65 @ ( bNF_re7626690874201225453um_num
% 0.33/0.65 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.65 @ Sd ) )
% 0.33/0.65 @ comp_nat_num_int
% 0.33/0.65 @ comp_nat_num_int ) ).
% 0.33/0.65
% 0.33/0.65 % fun.map_transfer
% 0.33/0.65 thf(fact_6942_fun_Omap__transfer,axiom,
% 0.33/0.65 ! [Rb2: int > int > $o,Sd: ( nat > $o ) > ( nat > $o ) > $o] :
% 0.33/0.65 ( bNF_re7908124382625962333_nat_o @ ( bNF_re3376528473927230327_nat_o @ Rb2 @ Sd )
% 0.33/0.65 @ ( bNF_re6033114333830760525_nat_o
% 0.33/0.65 @ ( bNF_re4712519889275205905nt_int
% 0.33/0.65 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.65 @ Rb2 )
% 0.33/0.65 @ ( bNF_re3376528473927230327_nat_o
% 0.33/0.65 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.65 @ Sd ) )
% 0.33/0.65 @ comp_int_nat_o_int
% 0.33/0.65 @ comp_int_nat_o_int ) ).
% 0.33/0.65
% 0.33/0.65 % fun.map_transfer
% 0.33/0.65 thf(fact_6943_fun_Omap__transfer,axiom,
% 0.33/0.65 ! [Rb2: int > int > $o,Sd: ( int > $o ) > ( int > $o ) > $o] :
% 0.33/0.65 ( bNF_re1900612664124570461_int_o @ ( bNF_re3403563459893282935_int_o @ Rb2 @ Sd )
% 0.33/0.65 @ ( bNF_re3014639844587090765_int_o
% 0.33/0.65 @ ( bNF_re4712519889275205905nt_int
% 0.33/0.65 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.65 @ Rb2 )
% 0.33/0.65 @ ( bNF_re3403563459893282935_int_o
% 0.33/0.65 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.65 @ Sd ) )
% 0.33/0.65 @ comp_int_int_o_int
% 0.33/0.65 @ comp_int_int_o_int ) ).
% 0.33/0.65
% 0.33/0.65 % fun.map_transfer
% 0.33/0.65 thf(fact_6944_fun_Omap__transfer,axiom,
% 0.33/0.65 ! [Rb2: int > int > $o,Sd: ( int > int ) > ( int > int ) > $o] :
% 0.33/0.65 ( bNF_re4984751527058004117nt_int @ ( bNF_re711492959462206631nt_int @ Rb2 @ Sd )
% 0.33/0.65 @ ( bNF_re724639330072410579nt_int
% 0.33/0.65 @ ( bNF_re4712519889275205905nt_int
% 0.33/0.65 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.65 @ Rb2 )
% 0.33/0.65 @ ( bNF_re711492959462206631nt_int
% 0.33/0.65 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.65 @ Sd ) )
% 0.33/0.65 @ comp_int_int_int_int
% 0.33/0.65 @ comp_int_int_int_int ) ).
% 0.33/0.65
% 0.33/0.65 % fun.map_transfer
% 0.33/0.65 thf(fact_6945_fun_Omap__transfer,axiom,
% 0.33/0.65 ! [Rb2: int > int > $o,Sd: ( int > product_prod_int_int ) > ( int > rat ) > $o] :
% 0.33/0.65 ( bNF_re62019127700022579nt_rat @ ( bNF_re3461391660133120880nt_rat @ Rb2 @ Sd )
% 0.33/0.65 @ ( bNF_re949775918795716016nt_rat
% 0.33/0.65 @ ( bNF_re4712519889275205905nt_int
% 0.33/0.65 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.65 @ Rb2 )
% 0.33/0.65 @ ( bNF_re3461391660133120880nt_rat
% 0.33/0.65 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.65 @ Sd ) )
% 0.33/0.65 @ comp_i87437609017934369nt_int
% 0.33/0.65 @ comp_int_int_rat_int ) ).
% 0.33/0.65
% 0.33/0.65 % fun.map_transfer
% 0.33/0.65 thf(fact_6946_fun_Omap__transfer,axiom,
% 0.33/0.65 ! [Rb2: ( nat > $o ) > ( nat > $o ) > $o,Sd: ( nat > $o ) > ( nat > $o ) > $o] :
% 0.33/0.65 ( bNF_re1550856938216548981_nat_o @ ( bNF_re2697311982885662685_nat_o @ Rb2 @ Sd )
% 0.33/0.65 @ ( bNF_re5673586069474677853_nat_o
% 0.33/0.65 @ ( bNF_re3376528473927230327_nat_o
% 0.33/0.65 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.65 @ Rb2 )
% 0.33/0.65 @ ( bNF_re3376528473927230327_nat_o
% 0.33/0.65 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.65 @ Sd ) )
% 0.33/0.65 @ comp_nat_o_nat_o_int
% 0.33/0.65 @ comp_nat_o_nat_o_int ) ).
% 0.33/0.65
% 0.33/0.65 % fun.map_transfer
% 0.33/0.65 thf(fact_6947_fun_Omap__transfer,axiom,
% 0.33/0.65 ! [Rb2: ( nat > $o ) > ( nat > $o ) > $o,Sd: ( int > $o ) > ( int > $o ) > $o] :
% 0.33/0.65 ( bNF_re3491090157995142405_int_o @ ( bNF_re2724346968851715293_int_o @ Rb2 @ Sd )
% 0.33/0.65 @ ( bNF_re2655111580231008093_int_o
% 0.33/0.65 @ ( bNF_re3376528473927230327_nat_o
% 0.33/0.65 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.65 @ Rb2 )
% 0.33/0.65 @ ( bNF_re3403563459893282935_int_o
% 0.33/0.65 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.65 @ Sd ) )
% 0.33/0.65 @ comp_nat_o_int_o_int
% 0.33/0.65 @ comp_nat_o_int_o_int ) ).
% 0.33/0.65
% 0.33/0.65 % fun.map_transfer
% 0.33/0.65 thf(fact_6948_fun_Omap__transfer,axiom,
% 0.33/0.65 ! [Rb2: ( nat > $o ) > ( nat > $o ) > $o,Sd: ( int > int ) > ( int > int ) > $o] :
% 0.33/0.65 ( bNF_re5539255234643219293nt_int @ ( bNF_re7183634743573646861nt_int @ Rb2 @ Sd )
% 0.33/0.65 @ ( bNF_re7395152722673581539nt_int
% 0.33/0.65 @ ( bNF_re3376528473927230327_nat_o
% 0.33/0.65 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.65 @ Rb2 )
% 0.33/0.65 @ ( bNF_re711492959462206631nt_int
% 0.33/0.65 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.65 @ Sd ) )
% 0.33/0.65 @ comp_n3090169619561918849nt_int
% 0.33/0.65 @ comp_n3090169619561918849nt_int ) ).
% 0.33/0.65
% 0.33/0.65 % fun.map_transfer
% 0.33/0.65 thf(fact_6949_fun_Omap__transfer,axiom,
% 0.33/0.65 ! [Rb2: ( int > $o ) > ( int > $o ) > $o,Sd: ( nat > $o ) > ( nat > $o ) > $o] :
% 0.33/0.65 ( bNF_re615132412071444453_nat_o @ ( bNF_re2535741173671728349_nat_o @ Rb2 @ Sd )
% 0.33/0.65 @ ( bNF_re2446162618891206493_nat_o
% 0.33/0.65 @ ( bNF_re3403563459893282935_int_o
% 0.33/0.65 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.65 @ Rb2 )
% 0.33/0.65 @ ( bNF_re3376528473927230327_nat_o
% 0.33/0.65 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.65 @ Sd ) )
% 0.33/0.65 @ comp_int_o_nat_o_int
% 0.33/0.65 @ comp_int_o_nat_o_int ) ).
% 0.33/0.65
% 0.33/0.65 % fun.map_transfer
% 0.33/0.65 thf(fact_6950_comp__transfer,axiom,
% 0.33/0.65 ! [B5: code_integer > code_integer > $o,C4: code_integer > code_integer > $o,A2: num > num > $o] : ( bNF_re5979881370344185769nteger @ ( bNF_re1062419521925302741nteger @ B5 @ C4 ) @ ( bNF_re6097285183634142137nteger @ ( bNF_re6741283560065411407nteger @ A2 @ B5 ) @ ( bNF_re6741283560065411407nteger @ A2 @ C4 ) ) @ comp_C3531382070062128313er_num @ comp_C3531382070062128313er_num ) ).
% 0.33/0.65
% 0.33/0.65 % comp_transfer
% 0.33/0.65 thf(fact_6951_comp__transfer,axiom,
% 0.33/0.65 ! [B5: code_integer > nat > $o,C4: code_integer > num > $o,A2: num > int > $o] : ( bNF_re5469402333911078061nt_num @ ( bNF_re1758498617148825349er_num @ B5 @ C4 ) @ ( bNF_re1151383970801924621nt_num @ ( bNF_re6324211044263125204er_nat @ A2 @ B5 ) @ ( bNF_re2881542830418903838er_num @ A2 @ C4 ) ) @ comp_C3531382070062128313er_num @ comp_nat_num_int ) ).
% 0.33/0.65
% 0.33/0.65 % comp_transfer
% 0.33/0.65 thf(fact_6952_comp__transfer,axiom,
% 0.33/0.65 ! [B5: nat > code_integer > $o,C4: num > code_integer > $o,A2: int > num > $o] : ( bNF_re2163612987331707565nteger @ ( bNF_re8763372240999575301nteger @ B5 @ C4 ) @ ( bNF_re8894579221946749965nteger @ ( bNF_re151304249936775380nteger @ A2 @ B5 ) @ ( bNF_re7315484114762210078nteger @ A2 @ C4 ) ) @ comp_nat_num_int @ comp_C3531382070062128313er_num ) ).
% 0.33/0.65
% 0.33/0.65 % comp_transfer
% 0.33/0.65 thf(fact_6953_comp__transfer,axiom,
% 0.33/0.65 ! [B5: nat > nat > $o,C4: num > num > $o,A2: int > int > $o] : ( bNF_re3846787885862361009nt_num @ ( bNF_re341483209202555957um_num @ B5 @ C4 ) @ ( bNF_re9099949428469764705nt_num @ ( bNF_re3715656647883201625at_nat @ A2 @ B5 ) @ ( bNF_re7626690874201225453um_num @ A2 @ C4 ) ) @ comp_nat_num_int @ comp_nat_num_int ) ).
% 0.33/0.65
% 0.33/0.65 % comp_transfer
% 0.33/0.65 thf(fact_6954_comp__transfer,axiom,
% 0.33/0.65 ! [B5: int > int > $o,C4: ( nat > $o ) > ( nat > $o ) > $o,A2: int > int > $o] : ( bNF_re7908124382625962333_nat_o @ ( bNF_re3376528473927230327_nat_o @ B5 @ C4 ) @ ( bNF_re6033114333830760525_nat_o @ ( bNF_re4712519889275205905nt_int @ A2 @ B5 ) @ ( bNF_re3376528473927230327_nat_o @ A2 @ C4 ) ) @ comp_int_nat_o_int @ comp_int_nat_o_int ) ).
% 0.33/0.65
% 0.33/0.65 % comp_transfer
% 0.33/0.65 thf(fact_6955_comp__transfer,axiom,
% 0.33/0.65 ! [B5: int > int > $o,C4: ( int > $o ) > ( int > $o ) > $o,A2: int > int > $o] : ( bNF_re1900612664124570461_int_o @ ( bNF_re3403563459893282935_int_o @ B5 @ C4 ) @ ( bNF_re3014639844587090765_int_o @ ( bNF_re4712519889275205905nt_int @ A2 @ B5 ) @ ( bNF_re3403563459893282935_int_o @ A2 @ C4 ) ) @ comp_int_int_o_int @ comp_int_int_o_int ) ).
% 0.33/0.65
% 0.33/0.65 % comp_transfer
% 0.33/0.65 thf(fact_6956_comp__transfer,axiom,
% 0.33/0.65 ! [B5: int > int > $o,C4: ( int > int ) > ( int > int ) > $o,A2: int > int > $o] : ( bNF_re4984751527058004117nt_int @ ( bNF_re711492959462206631nt_int @ B5 @ C4 ) @ ( bNF_re724639330072410579nt_int @ ( bNF_re4712519889275205905nt_int @ A2 @ B5 ) @ ( bNF_re711492959462206631nt_int @ A2 @ C4 ) ) @ comp_int_int_int_int @ comp_int_int_int_int ) ).
% 0.33/0.65
% 0.33/0.65 % comp_transfer
% 0.33/0.65 thf(fact_6957_comp__transfer,axiom,
% 0.33/0.65 ! [B5: code_integer > code_integer > $o,C4: code_integer > ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > $o,A2: num > code_integer > $o] : ( bNF_re8134695817916415679nteger @ ( bNF_re3370092614548195229nteger @ B5 @ C4 ) @ ( bNF_re2439920061672227847nteger @ ( bNF_re5202476307641864082nteger @ A2 @ B5 ) @ ( bNF_re5031869190687302234nteger @ A2 @ C4 ) ) @ comp_C3531382070062128313er_num @ comp_C1593894019821074884nteger ) ).
% 0.33/0.65
% 0.33/0.65 % comp_transfer
% 0.33/0.65 thf(fact_6958_comp__transfer,axiom,
% 0.33/0.65 ! [B5: code_integer > code_integer > $o,C4: ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > code_integer > $o,A2: code_integer > num > $o] : ( bNF_re4919612610145136063nteger @ ( bNF_re4341081746073172381nteger @ B5 @ C4 ) @ ( bNF_re6724329528997265415nteger @ ( bNF_re7350422212947406738nteger @ A2 @ B5 ) @ ( bNF_re166502229267952730nteger @ A2 @ C4 ) ) @ comp_C1593894019821074884nteger @ comp_C3531382070062128313er_num ) ).
% 0.33/0.65
% 0.33/0.65 % comp_transfer
% 0.33/0.65 thf(fact_6959_comp__transfer,axiom,
% 0.33/0.65 ! [B5: code_integer > nat > $o,C4: ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > num > $o,A2: code_integer > int > $o] : ( bNF_re1890273300020150979nt_num @ ( bNF_re7119966052990372301er_num @ B5 @ C4 ) @ ( bNF_re5190287125156074331nt_num @ ( bNF_re2891348898900095767er_nat @ A2 @ B5 ) @ ( bNF_re8127238762813979689er_num @ A2 @ C4 ) ) @ comp_C1593894019821074884nteger @ comp_nat_num_int ) ).
% 0.33/0.65
% 0.33/0.65 % comp_transfer
% 0.33/0.65 thf(fact_6960_power__transfer,axiom,
% 0.33/0.65 ! [R4: code_integer > code_integer > $o] :
% 0.33/0.65 ( ( R4 @ one_one_Code_integer @ one_one_Code_integer )
% 0.33/0.65 => ( ( bNF_re122555440370955213nteger @ R4 @ ( bNF_re1062419521925302741nteger @ R4 @ R4 ) @ times_3573771949741848930nteger @ times_3573771949741848930nteger )
% 0.33/0.65 => ( bNF_re5462749793222359603nteger @ R4
% 0.33/0.65 @ ( bNF_re1236659899165691067nteger
% 0.33/0.65 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.65 @ R4 )
% 0.33/0.65 @ power_8256067586552552935nteger
% 0.33/0.65 @ power_8256067586552552935nteger ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % power_transfer
% 0.33/0.65 thf(fact_6961_power__transfer,axiom,
% 0.33/0.65 ! [R4: code_integer > assn > $o] :
% 0.33/0.65 ( ( R4 @ one_one_Code_integer @ one_one_assn )
% 0.33/0.65 => ( ( bNF_re7789648203153440174n_assn @ R4 @ ( bNF_re1475883931861434731r_assn @ R4 @ R4 ) @ times_3573771949741848930nteger @ times_times_assn )
% 0.33/0.65 => ( bNF_re2546461910754330953t_assn @ R4
% 0.33/0.65 @ ( bNF_re2692373401909853574r_assn
% 0.33/0.65 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.65 @ R4 )
% 0.33/0.65 @ power_8256067586552552935nteger
% 0.33/0.65 @ power_power_assn ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % power_transfer
% 0.33/0.65 thf(fact_6962_power__transfer,axiom,
% 0.33/0.65 ! [R4: code_integer > rat > $o] :
% 0.33/0.65 ( ( R4 @ one_one_Code_integer @ one_one_rat )
% 0.33/0.65 => ( ( bNF_re2976496150901874110at_rat @ R4 @ ( bNF_re4698098036185532619er_rat @ R4 @ R4 ) @ times_3573771949741848930nteger @ times_times_rat )
% 0.33/0.65 => ( bNF_re1167376069379428009at_rat @ R4
% 0.33/0.65 @ ( bNF_re2882060999336173110er_rat
% 0.33/0.65 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.65 @ R4 )
% 0.33/0.65 @ power_8256067586552552935nteger
% 0.33/0.65 @ power_power_rat ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % power_transfer
% 0.33/0.65 thf(fact_6963_power__transfer,axiom,
% 0.33/0.65 ! [R4: code_integer > nat > $o] :
% 0.33/0.65 ( ( R4 @ one_one_Code_integer @ one_one_nat )
% 0.33/0.65 => ( ( bNF_re3981674901896804262at_nat @ R4 @ ( bNF_re5201166830993046715er_nat @ R4 @ R4 ) @ times_3573771949741848930nteger @ times_times_nat )
% 0.33/0.65 => ( bNF_re4269568176766901913at_nat @ R4
% 0.33/0.65 @ ( bNF_re3517191059422668846er_nat
% 0.33/0.65 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.65 @ R4 )
% 0.33/0.65 @ power_8256067586552552935nteger
% 0.33/0.65 @ power_power_nat ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % power_transfer
% 0.33/0.65 thf(fact_6964_power__transfer,axiom,
% 0.33/0.65 ! [R4: code_integer > int > $o] :
% 0.33/0.65 ( ( R4 @ one_one_Code_integer @ one_one_int )
% 0.33/0.65 => ( ( bNF_re8304916493157054650nt_int @ R4 @ ( bNF_re2888858428391045491er_int @ R4 @ R4 ) @ times_3573771949741848930nteger @ times_times_int )
% 0.33/0.65 => ( bNF_re6766650671887726929at_int @ R4
% 0.33/0.65 @ ( bNF_re3514700588913618570er_int
% 0.33/0.65 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.65 @ R4 )
% 0.33/0.65 @ power_8256067586552552935nteger
% 0.33/0.65 @ power_power_int ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % power_transfer
% 0.33/0.65 thf(fact_6965_power__transfer,axiom,
% 0.33/0.65 ! [R4: assn > code_integer > $o] :
% 0.33/0.65 ( ( R4 @ one_one_assn @ one_one_Code_integer )
% 0.33/0.65 => ( ( bNF_re5822757241383739566nteger @ R4 @ ( bNF_re4134162077946812779nteger @ R4 @ R4 ) @ times_times_assn @ times_3573771949741848930nteger )
% 0.33/0.65 => ( bNF_re2102180915162216137nteger @ R4
% 0.33/0.65 @ ( bNF_re1831131418152741254nteger
% 0.33/0.65 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.65 @ R4 )
% 0.33/0.65 @ power_power_assn
% 0.33/0.65 @ power_8256067586552552935nteger ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % power_transfer
% 0.33/0.65 thf(fact_6966_power__transfer,axiom,
% 0.33/0.65 ! [R4: assn > assn > $o] :
% 0.33/0.65 ( ( R4 @ one_one_assn @ one_one_assn )
% 0.33/0.65 => ( ( bNF_re9137223911888007311n_assn @ R4 @ ( bNF_re1143782165119297793n_assn @ R4 @ R4 ) @ times_times_assn @ times_times_assn )
% 0.33/0.65 => ( bNF_re3650450707543776735t_assn @ R4
% 0.33/0.65 @ ( bNF_re4051817429369991249n_assn
% 0.33/0.65 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.65 @ R4 )
% 0.33/0.65 @ power_power_assn
% 0.33/0.65 @ power_power_assn ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % power_transfer
% 0.33/0.65 thf(fact_6967_power__transfer,axiom,
% 0.33/0.65 ! [R4: assn > rat > $o] :
% 0.33/0.65 ( ( R4 @ one_one_assn @ one_one_rat )
% 0.33/0.65 => ( ( bNF_re967558844708792991at_rat @ R4 @ ( bNF_re9003240792272343649sn_rat @ R4 @ R4 ) @ times_times_assn @ times_times_rat )
% 0.33/0.65 => ( bNF_re6138836914430330175at_rat @ R4
% 0.33/0.65 @ ( bNF_re4159627890580825857sn_rat
% 0.33/0.65 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.65 @ R4 )
% 0.33/0.65 @ power_power_assn
% 0.33/0.65 @ power_power_rat ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % power_transfer
% 0.33/0.65 thf(fact_6968_power__transfer,axiom,
% 0.33/0.65 ! [R4: assn > nat > $o] :
% 0.33/0.65 ( ( R4 @ one_one_assn @ one_one_nat )
% 0.33/0.65 => ( ( bNF_re4386305596031132807at_nat @ R4 @ ( bNF_re6742580585434904145sn_nat @ R4 @ R4 ) @ times_times_assn @ times_times_nat )
% 0.33/0.65 => ( bNF_re8560028565313717551at_nat @ R4
% 0.33/0.65 @ ( bNF_re4794757950667321593sn_nat
% 0.33/0.65 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.65 @ R4 )
% 0.33/0.65 @ power_power_assn
% 0.33/0.65 @ power_power_nat ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % power_transfer
% 0.33/0.65 thf(fact_6969_power__transfer,axiom,
% 0.33/0.65 ! [R4: assn > int > $o] :
% 0.33/0.65 ( ( R4 @ one_one_assn @ one_one_int )
% 0.33/0.65 => ( ( bNF_re7882741803053012379nt_int @ R4 @ ( bNF_re2927800259774540553sn_int @ R4 @ R4 ) @ times_times_assn @ times_times_int )
% 0.33/0.65 => ( bNF_re185025794348816359at_int @ R4
% 0.33/0.65 @ ( bNF_re4792267480158271317sn_int
% 0.33/0.65 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.65 @ R4 )
% 0.33/0.65 @ power_power_assn
% 0.33/0.65 @ power_power_int ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % power_transfer
% 0.33/0.65 thf(fact_6970_times__integer_Orsp,axiom,
% 0.33/0.65 ( bNF_re711492959462206631nt_int
% 0.33/0.65 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.65 @ ( bNF_re4712519889275205905nt_int
% 0.33/0.65 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.65 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 ) )
% 0.33/0.65 @ times_times_int
% 0.33/0.65 @ times_times_int ) ).
% 0.33/0.65
% 0.33/0.65 % times_integer.rsp
% 0.33/0.65 thf(fact_6971_times__natural_Orsp,axiom,
% 0.33/0.65 ( bNF_re1345281282404953727at_nat
% 0.33/0.65 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.65 @ ( bNF_re5653821019739307937at_nat
% 0.33/0.65 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.65 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 ) )
% 0.33/0.65 @ times_times_nat
% 0.33/0.65 @ times_times_nat ) ).
% 0.33/0.65
% 0.33/0.65 % times_natural.rsp
% 0.33/0.65 thf(fact_6972_divide__natural_Orsp,axiom,
% 0.33/0.65 ( bNF_re1345281282404953727at_nat
% 0.33/0.65 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.65 @ ( bNF_re5653821019739307937at_nat
% 0.33/0.65 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.65 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 ) )
% 0.33/0.65 @ divide_divide_nat
% 0.33/0.65 @ divide_divide_nat ) ).
% 0.33/0.65
% 0.33/0.65 % divide_natural.rsp
% 0.33/0.65 thf(fact_6973_divide__integer_Orsp,axiom,
% 0.33/0.65 ( bNF_re711492959462206631nt_int
% 0.33/0.65 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.65 @ ( bNF_re4712519889275205905nt_int
% 0.33/0.65 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.65 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 ) )
% 0.33/0.65 @ divide_divide_int
% 0.33/0.65 @ divide_divide_int ) ).
% 0.33/0.65
% 0.33/0.65 % divide_integer.rsp
% 0.33/0.65 thf(fact_6974_or__natural_Orsp,axiom,
% 0.33/0.65 ( bNF_re1345281282404953727at_nat
% 0.33/0.65 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.65 @ ( bNF_re5653821019739307937at_nat
% 0.33/0.65 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.65 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 ) )
% 0.33/0.65 @ bit_se1412395901928357646or_nat
% 0.33/0.65 @ bit_se1412395901928357646or_nat ) ).
% 0.33/0.65
% 0.33/0.65 % or_natural.rsp
% 0.33/0.65 thf(fact_6975_or__integer_Orsp,axiom,
% 0.33/0.65 ( bNF_re711492959462206631nt_int
% 0.33/0.65 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.65 @ ( bNF_re4712519889275205905nt_int
% 0.33/0.65 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.65 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 ) )
% 0.33/0.65 @ bit_se1409905431419307370or_int
% 0.33/0.65 @ bit_se1409905431419307370or_int ) ).
% 0.33/0.65
% 0.33/0.65 % or_integer.rsp
% 0.33/0.65 thf(fact_6976_set__bit__integer_Orsp,axiom,
% 0.33/0.65 ( bNF_re4785983289428654063nt_int
% 0.33/0.65 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.65 @ ( bNF_re4712519889275205905nt_int
% 0.33/0.65 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.65 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 ) )
% 0.33/0.65 @ bit_se7879613467334960850it_int
% 0.33/0.65 @ bit_se7879613467334960850it_int ) ).
% 0.33/0.65
% 0.33/0.65 % set_bit_integer.rsp
% 0.33/0.65 thf(fact_6977_set__bit__natural_Orsp,axiom,
% 0.33/0.65 ( bNF_re1345281282404953727at_nat
% 0.33/0.65 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.65 @ ( bNF_re5653821019739307937at_nat
% 0.33/0.65 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.65 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 ) )
% 0.33/0.65 @ bit_se7882103937844011126it_nat
% 0.33/0.65 @ bit_se7882103937844011126it_nat ) ).
% 0.33/0.65
% 0.33/0.65 % set_bit_natural.rsp
% 0.33/0.65 thf(fact_6978_xor__integer_Orsp,axiom,
% 0.33/0.65 ( bNF_re711492959462206631nt_int
% 0.33/0.65 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.65 @ ( bNF_re4712519889275205905nt_int
% 0.33/0.65 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.65 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 ) )
% 0.33/0.65 @ bit_se6526347334894502574or_int
% 0.33/0.65 @ bit_se6526347334894502574or_int ) ).
% 0.33/0.65
% 0.33/0.65 % xor_integer.rsp
% 0.33/0.65 thf(fact_6979_xor__natural_Orsp,axiom,
% 0.33/0.65 ( bNF_re1345281282404953727at_nat
% 0.33/0.65 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.65 @ ( bNF_re5653821019739307937at_nat
% 0.33/0.65 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.65 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 ) )
% 0.33/0.65 @ bit_se6528837805403552850or_nat
% 0.33/0.65 @ bit_se6528837805403552850or_nat ) ).
% 0.33/0.65
% 0.33/0.65 % xor_natural.rsp
% 0.33/0.65 thf(fact_6980_and__integer_Orsp,axiom,
% 0.33/0.65 ( bNF_re711492959462206631nt_int
% 0.33/0.65 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.65 @ ( bNF_re4712519889275205905nt_int
% 0.33/0.65 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.65 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 ) )
% 0.33/0.65 @ bit_se725231765392027082nd_int
% 0.33/0.65 @ bit_se725231765392027082nd_int ) ).
% 0.33/0.65
% 0.33/0.65 % and_integer.rsp
% 0.33/0.65 thf(fact_6981_and__natural_Orsp,axiom,
% 0.33/0.65 ( bNF_re1345281282404953727at_nat
% 0.33/0.65 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.65 @ ( bNF_re5653821019739307937at_nat
% 0.33/0.65 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.65 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 ) )
% 0.33/0.65 @ bit_se727722235901077358nd_nat
% 0.33/0.65 @ bit_se727722235901077358nd_nat ) ).
% 0.33/0.65
% 0.33/0.65 % and_natural.rsp
% 0.33/0.65 thf(fact_6982_modulo__integer_Orsp,axiom,
% 0.33/0.65 ( bNF_re711492959462206631nt_int
% 0.33/0.65 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.65 @ ( bNF_re4712519889275205905nt_int
% 0.33/0.65 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.65 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 ) )
% 0.33/0.65 @ modulo_modulo_int
% 0.33/0.65 @ modulo_modulo_int ) ).
% 0.33/0.65
% 0.33/0.65 % modulo_integer.rsp
% 0.33/0.65 thf(fact_6983_modulo__natural_Orsp,axiom,
% 0.33/0.65 ( bNF_re1345281282404953727at_nat
% 0.33/0.65 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.65 @ ( bNF_re5653821019739307937at_nat
% 0.33/0.65 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.65 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 ) )
% 0.33/0.65 @ modulo_modulo_nat
% 0.33/0.65 @ modulo_modulo_nat ) ).
% 0.33/0.65
% 0.33/0.65 % modulo_natural.rsp
% 0.33/0.65 thf(fact_6984_less__integer_Orsp,axiom,
% 0.33/0.65 ( bNF_re3403563459893282935_int_o
% 0.33/0.65 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.65 @ ( bNF_re5089333283451836215nt_o_o
% 0.33/0.65 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.65 @ ^ [Y4: $o,Z2: $o] : ( Y4 = Z2 ) )
% 0.33/0.65 @ ord_less_int
% 0.33/0.65 @ ord_less_int ) ).
% 0.33/0.65
% 0.33/0.65 % less_integer.rsp
% 0.33/0.65 thf(fact_6985_less__natural_Orsp,axiom,
% 0.33/0.65 ( bNF_re578469030762574527_nat_o
% 0.33/0.65 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.65 @ ( bNF_re4705727531993890431at_o_o
% 0.33/0.65 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.65 @ ^ [Y4: $o,Z2: $o] : ( Y4 = Z2 ) )
% 0.33/0.65 @ ord_less_nat
% 0.33/0.65 @ ord_less_nat ) ).
% 0.33/0.65
% 0.33/0.65 % less_natural.rsp
% 0.33/0.65 thf(fact_6986_unset__bit__integer_Orsp,axiom,
% 0.33/0.65 ( bNF_re4785983289428654063nt_int
% 0.33/0.65 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.65 @ ( bNF_re4712519889275205905nt_int
% 0.33/0.65 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.65 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 ) )
% 0.33/0.65 @ bit_se4203085406695923979it_int
% 0.33/0.65 @ bit_se4203085406695923979it_int ) ).
% 0.33/0.65
% 0.33/0.65 % unset_bit_integer.rsp
% 0.33/0.65 thf(fact_6987_take__bit__integer_Orsp,axiom,
% 0.33/0.65 ( bNF_re4785983289428654063nt_int
% 0.33/0.65 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.65 @ ( bNF_re4712519889275205905nt_int
% 0.33/0.65 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.65 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 ) )
% 0.33/0.65 @ bit_se2923211474154528505it_int
% 0.33/0.65 @ bit_se2923211474154528505it_int ) ).
% 0.33/0.65
% 0.33/0.65 % take_bit_integer.rsp
% 0.33/0.65 thf(fact_6988_flip__bit__integer_Orsp,axiom,
% 0.33/0.65 ( bNF_re4785983289428654063nt_int
% 0.33/0.65 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.65 @ ( bNF_re4712519889275205905nt_int
% 0.33/0.65 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.65 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 ) )
% 0.33/0.65 @ bit_se2159334234014336723it_int
% 0.33/0.65 @ bit_se2159334234014336723it_int ) ).
% 0.33/0.65
% 0.33/0.65 % flip_bit_integer.rsp
% 0.33/0.65 thf(fact_6989_flip__bit__natural_Orsp,axiom,
% 0.33/0.65 ( bNF_re1345281282404953727at_nat
% 0.33/0.65 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.65 @ ( bNF_re5653821019739307937at_nat
% 0.33/0.65 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.65 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 ) )
% 0.33/0.65 @ bit_se2161824704523386999it_nat
% 0.33/0.65 @ bit_se2161824704523386999it_nat ) ).
% 0.33/0.65
% 0.33/0.65 % flip_bit_natural.rsp
% 0.33/0.65 thf(fact_6990_push__bit__natural_Orsp,axiom,
% 0.33/0.65 ( bNF_re1345281282404953727at_nat
% 0.33/0.65 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.65 @ ( bNF_re5653821019739307937at_nat
% 0.33/0.65 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.65 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 ) )
% 0.33/0.65 @ bit_se547839408752420682it_nat
% 0.33/0.65 @ bit_se547839408752420682it_nat ) ).
% 0.33/0.65
% 0.33/0.65 % push_bit_natural.rsp
% 0.33/0.65 thf(fact_6991_push__bit__integer_Orsp,axiom,
% 0.33/0.65 ( bNF_re4785983289428654063nt_int
% 0.33/0.65 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.65 @ ( bNF_re4712519889275205905nt_int
% 0.33/0.65 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.65 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 ) )
% 0.33/0.65 @ bit_se545348938243370406it_int
% 0.33/0.65 @ bit_se545348938243370406it_int ) ).
% 0.33/0.65
% 0.33/0.65 % push_bit_integer.rsp
% 0.33/0.65 thf(fact_6992_plus__integer_Orsp,axiom,
% 0.33/0.65 ( bNF_re711492959462206631nt_int
% 0.33/0.65 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.65 @ ( bNF_re4712519889275205905nt_int
% 0.33/0.65 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.65 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 ) )
% 0.33/0.65 @ plus_plus_int
% 0.33/0.65 @ plus_plus_int ) ).
% 0.33/0.65
% 0.33/0.65 % plus_integer.rsp
% 0.33/0.65 thf(fact_6993_plus__natural_Orsp,axiom,
% 0.33/0.65 ( bNF_re1345281282404953727at_nat
% 0.33/0.65 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.65 @ ( bNF_re5653821019739307937at_nat
% 0.33/0.65 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.65 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 ) )
% 0.33/0.65 @ plus_plus_nat
% 0.33/0.65 @ plus_plus_nat ) ).
% 0.33/0.65
% 0.33/0.65 % plus_natural.rsp
% 0.33/0.65 thf(fact_6994_drop__bit__integer_Orsp,axiom,
% 0.33/0.65 ( bNF_re4785983289428654063nt_int
% 0.33/0.65 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.65 @ ( bNF_re4712519889275205905nt_int
% 0.33/0.65 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.65 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 ) )
% 0.33/0.65 @ bit_se8568078237143864401it_int
% 0.33/0.65 @ bit_se8568078237143864401it_int ) ).
% 0.33/0.65
% 0.33/0.65 % drop_bit_integer.rsp
% 0.33/0.65 thf(fact_6995_minus__natural_Orsp,axiom,
% 0.33/0.65 ( bNF_re1345281282404953727at_nat
% 0.33/0.65 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.65 @ ( bNF_re5653821019739307937at_nat
% 0.33/0.65 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.65 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 ) )
% 0.33/0.65 @ minus_minus_nat
% 0.33/0.65 @ minus_minus_nat ) ).
% 0.33/0.65
% 0.33/0.65 % minus_natural.rsp
% 0.33/0.65 thf(fact_6996_minus__integer_Orsp,axiom,
% 0.33/0.65 ( bNF_re711492959462206631nt_int
% 0.33/0.65 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.65 @ ( bNF_re4712519889275205905nt_int
% 0.33/0.65 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.65 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 ) )
% 0.33/0.65 @ minus_minus_int
% 0.33/0.65 @ minus_minus_int ) ).
% 0.33/0.65
% 0.33/0.65 % minus_integer.rsp
% 0.33/0.65 thf(fact_6997_less__eq__integer_Orsp,axiom,
% 0.33/0.65 ( bNF_re3403563459893282935_int_o
% 0.33/0.65 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.65 @ ( bNF_re5089333283451836215nt_o_o
% 0.33/0.65 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.65 @ ^ [Y4: $o,Z2: $o] : ( Y4 = Z2 ) )
% 0.33/0.65 @ ord_less_eq_int
% 0.33/0.65 @ ord_less_eq_int ) ).
% 0.33/0.65
% 0.33/0.65 % less_eq_integer.rsp
% 0.33/0.65 thf(fact_6998_less__eq__natural_Orsp,axiom,
% 0.33/0.65 ( bNF_re578469030762574527_nat_o
% 0.33/0.65 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.65 @ ( bNF_re4705727531993890431at_o_o
% 0.33/0.65 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.65 @ ^ [Y4: $o,Z2: $o] : ( Y4 = Z2 ) )
% 0.33/0.65 @ ord_less_eq_nat
% 0.33/0.65 @ ord_less_eq_nat ) ).
% 0.33/0.65
% 0.33/0.65 % less_eq_natural.rsp
% 0.33/0.65 thf(fact_6999_SigmaE,axiom,
% 0.33/0.65 ! [C: product_prod_o_o,A2: set_o,B5: $o > set_o] :
% 0.33/0.65 ( ( member7466972457876170832od_o_o @ C @ ( product_Sigma_o_o @ A2 @ B5 ) )
% 0.33/0.65 => ~ ! [X4: $o] :
% 0.33/0.65 ( ( member_o @ X4 @ A2 )
% 0.33/0.65 => ! [Y5: $o] :
% 0.33/0.65 ( ( member_o @ Y5 @ ( B5 @ X4 ) )
% 0.33/0.65 => ( C
% 0.33/0.65 != ( product_Pair_o_o @ X4 @ Y5 ) ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % SigmaE
% 0.33/0.65 thf(fact_7000_SigmaE,axiom,
% 0.33/0.65 ! [C: product_prod_o_nat,A2: set_o,B5: $o > set_nat] :
% 0.33/0.65 ( ( member2802428098988154798_o_nat @ C @ ( product_Sigma_o_nat @ A2 @ B5 ) )
% 0.33/0.65 => ~ ! [X4: $o] :
% 0.33/0.65 ( ( member_o @ X4 @ A2 )
% 0.33/0.65 => ! [Y5: nat] :
% 0.33/0.65 ( ( member_nat @ Y5 @ ( B5 @ X4 ) )
% 0.33/0.65 => ( C
% 0.33/0.65 != ( product_Pair_o_nat @ X4 @ Y5 ) ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % SigmaE
% 0.33/0.65 thf(fact_7001_SigmaE,axiom,
% 0.33/0.65 ! [C: product_prod_o_int,A2: set_o,B5: $o > set_int] :
% 0.33/0.65 ( ( member7847949116333733898_o_int @ C @ ( product_Sigma_o_int @ A2 @ B5 ) )
% 0.33/0.65 => ~ ! [X4: $o] :
% 0.33/0.65 ( ( member_o @ X4 @ A2 )
% 0.33/0.65 => ! [Y5: int] :
% 0.33/0.65 ( ( member_int @ Y5 @ ( B5 @ X4 ) )
% 0.33/0.65 => ( C
% 0.33/0.65 != ( product_Pair_o_int @ X4 @ Y5 ) ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % SigmaE
% 0.33/0.65 thf(fact_7002_SigmaE,axiom,
% 0.33/0.65 ! [C: product_prod_nat_o,A2: set_nat,B5: nat > set_o] :
% 0.33/0.65 ( ( member6310962623043647828_nat_o @ C @ ( product_Sigma_nat_o @ A2 @ B5 ) )
% 0.33/0.65 => ~ ! [X4: nat] :
% 0.33/0.65 ( ( member_nat @ X4 @ A2 )
% 0.33/0.65 => ! [Y5: $o] :
% 0.33/0.65 ( ( member_o @ Y5 @ ( B5 @ X4 ) )
% 0.33/0.65 => ( C
% 0.33/0.65 != ( product_Pair_nat_o @ X4 @ Y5 ) ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % SigmaE
% 0.33/0.65 thf(fact_7003_SigmaE,axiom,
% 0.33/0.65 ! [C: product_prod_nat_int,A2: set_nat,B5: nat > set_int] :
% 0.33/0.65 ( ( member4262671552274231302at_int @ C @ ( produc454536836294682310at_int @ A2 @ B5 ) )
% 0.33/0.65 => ~ ! [X4: nat] :
% 0.33/0.65 ( ( member_nat @ X4 @ A2 )
% 0.33/0.65 => ! [Y5: int] :
% 0.33/0.65 ( ( member_int @ Y5 @ ( B5 @ X4 ) )
% 0.33/0.65 => ( C
% 0.33/0.65 != ( product_Pair_nat_int @ X4 @ Y5 ) ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % SigmaE
% 0.33/0.65 thf(fact_7004_SigmaE,axiom,
% 0.33/0.65 ! [C: product_prod_int_o,A2: set_int,B5: int > set_o] :
% 0.33/0.65 ( ( member4489920277610959864_int_o @ C @ ( product_Sigma_int_o @ A2 @ B5 ) )
% 0.33/0.65 => ~ ! [X4: int] :
% 0.33/0.65 ( ( member_int @ X4 @ A2 )
% 0.33/0.65 => ! [Y5: $o] :
% 0.33/0.65 ( ( member_o @ Y5 @ ( B5 @ X4 ) )
% 0.33/0.65 => ( C
% 0.33/0.65 != ( product_Pair_int_o @ X4 @ Y5 ) ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % SigmaE
% 0.33/0.65 thf(fact_7005_SigmaE,axiom,
% 0.33/0.65 ! [C: product_prod_int_nat,A2: set_int,B5: int > set_nat] :
% 0.33/0.65 ( ( member216504246829706758nt_nat @ C @ ( produc1456381018704787142nt_nat @ A2 @ B5 ) )
% 0.33/0.65 => ~ ! [X4: int] :
% 0.33/0.65 ( ( member_int @ X4 @ A2 )
% 0.33/0.65 => ! [Y5: nat] :
% 0.33/0.65 ( ( member_nat @ Y5 @ ( B5 @ X4 ) )
% 0.33/0.65 => ( C
% 0.33/0.65 != ( product_Pair_int_nat @ X4 @ Y5 ) ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % SigmaE
% 0.33/0.65 thf(fact_7006_SigmaE,axiom,
% 0.33/0.65 ! [C: product_prod_int_int,A2: set_int,B5: int > set_int] :
% 0.33/0.65 ( ( member5262025264175285858nt_int @ C @ ( produc1453890548195736866nt_int @ A2 @ B5 ) )
% 0.33/0.65 => ~ ! [X4: int] :
% 0.33/0.65 ( ( member_int @ X4 @ A2 )
% 0.33/0.65 => ! [Y5: int] :
% 0.33/0.65 ( ( member_int @ Y5 @ ( B5 @ X4 ) )
% 0.33/0.65 => ( C
% 0.33/0.65 != ( product_Pair_int_int @ X4 @ Y5 ) ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % SigmaE
% 0.33/0.65 thf(fact_7007_SigmaE,axiom,
% 0.33/0.65 ! [C: product_prod_nat_nat,A2: set_nat,B5: nat > set_nat] :
% 0.33/0.65 ( ( member8440522571783428010at_nat @ C @ ( produc457027306803732586at_nat @ A2 @ B5 ) )
% 0.33/0.65 => ~ ! [X4: nat] :
% 0.33/0.65 ( ( member_nat @ X4 @ A2 )
% 0.33/0.65 => ! [Y5: nat] :
% 0.33/0.65 ( ( member_nat @ Y5 @ ( B5 @ X4 ) )
% 0.33/0.65 => ( C
% 0.33/0.65 != ( product_Pair_nat_nat @ X4 @ Y5 ) ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % SigmaE
% 0.33/0.65 thf(fact_7008_SigmaE,axiom,
% 0.33/0.65 ! [C: produc652263959640188542_nat_o,A2: set_Pr1261947904930325089at_nat,B5: product_prod_nat_nat > set_o] :
% 0.33/0.65 ( ( member2200362271989506215_nat_o @ C @ ( produc203973861852599583_nat_o @ A2 @ B5 ) )
% 0.33/0.65 => ~ ! [X4: product_prod_nat_nat] :
% 0.33/0.65 ( ( member8440522571783428010at_nat @ X4 @ A2 )
% 0.33/0.65 => ! [Y5: $o] :
% 0.33/0.65 ( ( member_o @ Y5 @ ( B5 @ X4 ) )
% 0.33/0.65 => ( C
% 0.33/0.65 != ( produc855456346497908590_nat_o @ X4 @ Y5 ) ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % SigmaE
% 0.33/0.65 thf(fact_7009_SigmaD1,axiom,
% 0.33/0.65 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,A2: set_se7855581050983116737at_nat,B5: set_Pr1261947904930325089at_nat > set_se7855581050983116737at_nat] :
% 0.33/0.65 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ B ) @ ( produc7726050920695093128at_nat @ A2 @ B5 ) )
% 0.33/0.65 => ( member2643936169264416010at_nat @ A @ A2 ) ) ).
% 0.33/0.65
% 0.33/0.65 % SigmaD1
% 0.33/0.65 thf(fact_7010_SigmaD1,axiom,
% 0.33/0.65 ! [A: nat,B: nat,A2: set_nat,B5: nat > set_nat] :
% 0.33/0.65 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ ( produc457027306803732586at_nat @ A2 @ B5 ) )
% 0.33/0.65 => ( member_nat @ A @ A2 ) ) ).
% 0.33/0.65
% 0.33/0.65 % SigmaD1
% 0.33/0.65 thf(fact_7011_SigmaD1,axiom,
% 0.33/0.65 ! [A: produc6241069584506657477e_term > option6357759511663192854e_term,B: produc8923325533196201883nteger,A2: set_Pr7604974323444597168e_term,B5: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > set_Pr4811707699266497531nteger] :
% 0.33/0.65 ( ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ A @ B ) @ ( produc7256824055837167575nteger @ A2 @ B5 ) )
% 0.33/0.65 => ( member4242434998011752849e_term @ A @ A2 ) ) ).
% 0.33/0.65
% 0.33/0.65 % SigmaD1
% 0.33/0.65 thf(fact_7012_SigmaD1,axiom,
% 0.33/0.65 ! [A: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat,A2: set_Pr4532377907799695533_nat_o,B5: ( produc3658429121746597890et_nat > $o ) > set_Pr3948176798113811640et_nat] :
% 0.33/0.65 ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ A @ B ) @ ( produc8052021730408606599et_nat @ A2 @ B5 ) )
% 0.33/0.65 => ( member6576561426505652726_nat_o @ A @ A2 ) ) ).
% 0.33/0.65
% 0.33/0.65 % SigmaD1
% 0.33/0.65 thf(fact_7013_SigmaD1,axiom,
% 0.33/0.65 ! [A: produc3658429121746597890et_nat > $o,B: produc3925858234332021118et_nat,A2: set_Pr4532377907799695533_nat_o,B5: ( produc3658429121746597890et_nat > $o ) > set_Pr3286484037609594932et_nat] :
% 0.33/0.65 ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ A @ B ) @ ( produc7016705354093686019et_nat @ A2 @ B5 ) )
% 0.33/0.65 => ( member6576561426505652726_nat_o @ A @ A2 ) ) ).
% 0.33/0.65
% 0.33/0.65 % SigmaD1
% 0.33/0.65 thf(fact_7014_SigmaD1,axiom,
% 0.33/0.65 ! [A: produc8551481072490612790e_term > option6357759511663192854e_term,B: product_prod_int_int,A2: set_Pr3642885161833720865e_term,B5: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > set_Pr958786334691620121nt_int] :
% 0.33/0.65 ( ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ A @ B ) @ ( produc5808185664642557892nt_int @ A2 @ B5 ) )
% 0.33/0.65 => ( member3222579708246209666e_term @ A @ A2 ) ) ).
% 0.33/0.65
% 0.33/0.65 % SigmaD1
% 0.33/0.65 thf(fact_7015_SigmaD1,axiom,
% 0.33/0.65 ! [A: int > option6357759511663192854e_term,B: product_prod_int_int,A2: set_in3461395444621081367e_term,B5: ( int > option6357759511663192854e_term ) > set_Pr958786334691620121nt_int] :
% 0.33/0.65 ( ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ A @ B ) @ ( produc1318478031590598990nt_int @ A2 @ B5 ) )
% 0.33/0.65 => ( member8845023287901829240e_term @ A @ A2 ) ) ).
% 0.33/0.65
% 0.33/0.65 % SigmaD1
% 0.33/0.65 thf(fact_7016_SigmaD2,axiom,
% 0.33/0.65 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,A2: set_se7855581050983116737at_nat,B5: set_Pr1261947904930325089at_nat > set_se7855581050983116737at_nat] :
% 0.33/0.65 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ B ) @ ( produc7726050920695093128at_nat @ A2 @ B5 ) )
% 0.33/0.65 => ( member2643936169264416010at_nat @ B @ ( B5 @ A ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % SigmaD2
% 0.33/0.65 thf(fact_7017_SigmaD2,axiom,
% 0.33/0.65 ! [A: nat,B: nat,A2: set_nat,B5: nat > set_nat] :
% 0.33/0.65 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ ( produc457027306803732586at_nat @ A2 @ B5 ) )
% 0.33/0.65 => ( member_nat @ B @ ( B5 @ A ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % SigmaD2
% 0.33/0.65 thf(fact_7018_SigmaD2,axiom,
% 0.33/0.65 ! [A: produc6241069584506657477e_term > option6357759511663192854e_term,B: produc8923325533196201883nteger,A2: set_Pr7604974323444597168e_term,B5: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > set_Pr4811707699266497531nteger] :
% 0.33/0.65 ( ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ A @ B ) @ ( produc7256824055837167575nteger @ A2 @ B5 ) )
% 0.33/0.65 => ( member157494554546826820nteger @ B @ ( B5 @ A ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % SigmaD2
% 0.33/0.65 thf(fact_7019_SigmaD2,axiom,
% 0.33/0.65 ! [A: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat,A2: set_Pr4532377907799695533_nat_o,B5: ( produc3658429121746597890et_nat > $o ) > set_Pr3948176798113811640et_nat] :
% 0.33/0.65 ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ A @ B ) @ ( produc8052021730408606599et_nat @ A2 @ B5 ) )
% 0.33/0.65 => ( member6260224972018164377et_nat @ B @ ( B5 @ A ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % SigmaD2
% 0.33/0.65 thf(fact_7020_SigmaD2,axiom,
% 0.33/0.65 ! [A: produc3658429121746597890et_nat > $o,B: produc3925858234332021118et_nat,A2: set_Pr4532377907799695533_nat_o,B5: ( produc3658429121746597890et_nat > $o ) > set_Pr3286484037609594932et_nat] :
% 0.33/0.65 ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ A @ B ) @ ( produc7016705354093686019et_nat @ A2 @ B5 ) )
% 0.33/0.65 => ( member1996754912294343701et_nat @ B @ ( B5 @ A ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % SigmaD2
% 0.33/0.65 thf(fact_7021_SigmaD2,axiom,
% 0.33/0.65 ! [A: produc8551481072490612790e_term > option6357759511663192854e_term,B: product_prod_int_int,A2: set_Pr3642885161833720865e_term,B5: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > set_Pr958786334691620121nt_int] :
% 0.33/0.65 ( ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ A @ B ) @ ( produc5808185664642557892nt_int @ A2 @ B5 ) )
% 0.33/0.65 => ( member5262025264175285858nt_int @ B @ ( B5 @ A ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % SigmaD2
% 0.33/0.65 thf(fact_7022_SigmaD2,axiom,
% 0.33/0.65 ! [A: int > option6357759511663192854e_term,B: product_prod_int_int,A2: set_in3461395444621081367e_term,B5: ( int > option6357759511663192854e_term ) > set_Pr958786334691620121nt_int] :
% 0.33/0.65 ( ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ A @ B ) @ ( produc1318478031590598990nt_int @ A2 @ B5 ) )
% 0.33/0.65 => ( member5262025264175285858nt_int @ B @ ( B5 @ A ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % SigmaD2
% 0.33/0.65 thf(fact_7023_SigmaE2,axiom,
% 0.33/0.65 ! [A: $o,B: $o,A2: set_o,B5: $o > set_o] :
% 0.33/0.65 ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ A @ B ) @ ( product_Sigma_o_o @ A2 @ B5 ) )
% 0.33/0.65 => ~ ( ( member_o @ A @ A2 )
% 0.33/0.65 => ~ ( member_o @ B @ ( B5 @ A ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % SigmaE2
% 0.33/0.65 thf(fact_7024_SigmaE2,axiom,
% 0.33/0.65 ! [A: $o,B: nat,A2: set_o,B5: $o > set_nat] :
% 0.33/0.65 ( ( member2802428098988154798_o_nat @ ( product_Pair_o_nat @ A @ B ) @ ( product_Sigma_o_nat @ A2 @ B5 ) )
% 0.33/0.65 => ~ ( ( member_o @ A @ A2 )
% 0.33/0.65 => ~ ( member_nat @ B @ ( B5 @ A ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % SigmaE2
% 0.33/0.65 thf(fact_7025_SigmaE2,axiom,
% 0.33/0.65 ! [A: $o,B: int,A2: set_o,B5: $o > set_int] :
% 0.33/0.65 ( ( member7847949116333733898_o_int @ ( product_Pair_o_int @ A @ B ) @ ( product_Sigma_o_int @ A2 @ B5 ) )
% 0.33/0.65 => ~ ( ( member_o @ A @ A2 )
% 0.33/0.65 => ~ ( member_int @ B @ ( B5 @ A ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % SigmaE2
% 0.33/0.65 thf(fact_7026_SigmaE2,axiom,
% 0.33/0.65 ! [A: nat,B: $o,A2: set_nat,B5: nat > set_o] :
% 0.33/0.65 ( ( member6310962623043647828_nat_o @ ( product_Pair_nat_o @ A @ B ) @ ( product_Sigma_nat_o @ A2 @ B5 ) )
% 0.33/0.65 => ~ ( ( member_nat @ A @ A2 )
% 0.33/0.65 => ~ ( member_o @ B @ ( B5 @ A ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % SigmaE2
% 0.33/0.65 thf(fact_7027_SigmaE2,axiom,
% 0.33/0.65 ! [A: nat,B: int,A2: set_nat,B5: nat > set_int] :
% 0.33/0.65 ( ( member4262671552274231302at_int @ ( product_Pair_nat_int @ A @ B ) @ ( produc454536836294682310at_int @ A2 @ B5 ) )
% 0.33/0.65 => ~ ( ( member_nat @ A @ A2 )
% 0.33/0.65 => ~ ( member_int @ B @ ( B5 @ A ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % SigmaE2
% 0.33/0.65 thf(fact_7028_SigmaE2,axiom,
% 0.33/0.65 ! [A: int,B: $o,A2: set_int,B5: int > set_o] :
% 0.33/0.65 ( ( member4489920277610959864_int_o @ ( product_Pair_int_o @ A @ B ) @ ( product_Sigma_int_o @ A2 @ B5 ) )
% 0.33/0.65 => ~ ( ( member_int @ A @ A2 )
% 0.33/0.65 => ~ ( member_o @ B @ ( B5 @ A ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % SigmaE2
% 0.33/0.65 thf(fact_7029_SigmaE2,axiom,
% 0.33/0.65 ! [A: int,B: nat,A2: set_int,B5: int > set_nat] :
% 0.33/0.65 ( ( member216504246829706758nt_nat @ ( product_Pair_int_nat @ A @ B ) @ ( produc1456381018704787142nt_nat @ A2 @ B5 ) )
% 0.33/0.65 => ~ ( ( member_int @ A @ A2 )
% 0.33/0.65 => ~ ( member_nat @ B @ ( B5 @ A ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % SigmaE2
% 0.33/0.65 thf(fact_7030_SigmaE2,axiom,
% 0.33/0.65 ! [A: int,B: int,A2: set_int,B5: int > set_int] :
% 0.33/0.65 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ ( produc1453890548195736866nt_int @ A2 @ B5 ) )
% 0.33/0.65 => ~ ( ( member_int @ A @ A2 )
% 0.33/0.65 => ~ ( member_int @ B @ ( B5 @ A ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % SigmaE2
% 0.33/0.65 thf(fact_7031_SigmaE2,axiom,
% 0.33/0.65 ! [A: nat,B: nat,A2: set_nat,B5: nat > set_nat] :
% 0.33/0.65 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ ( produc457027306803732586at_nat @ A2 @ B5 ) )
% 0.33/0.65 => ~ ( ( member_nat @ A @ A2 )
% 0.33/0.65 => ~ ( member_nat @ B @ ( B5 @ A ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % SigmaE2
% 0.33/0.65 thf(fact_7032_SigmaE2,axiom,
% 0.33/0.65 ! [A: product_prod_nat_nat,B: $o,A2: set_Pr1261947904930325089at_nat,B5: product_prod_nat_nat > set_o] :
% 0.33/0.65 ( ( member2200362271989506215_nat_o @ ( produc855456346497908590_nat_o @ A @ B ) @ ( produc203973861852599583_nat_o @ A2 @ B5 ) )
% 0.33/0.65 => ~ ( ( member8440522571783428010at_nat @ A @ A2 )
% 0.33/0.65 => ~ ( member_o @ B @ ( B5 @ A ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % SigmaE2
% 0.33/0.65 thf(fact_7033_Suc_Orsp,axiom,
% 0.33/0.65 ( bNF_re5653821019739307937at_nat
% 0.33/0.65 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.65 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.65 @ suc
% 0.33/0.65 @ suc ) ).
% 0.33/0.65
% 0.33/0.65 % Suc.rsp
% 0.33/0.65 thf(fact_7034_sub_Orsp,axiom,
% 0.33/0.65 ( bNF_re8402795839162346335um_int
% 0.33/0.65 @ ^ [Y4: num,Z2: num] : ( Y4 = Z2 )
% 0.33/0.65 @ ( bNF_re1822329894187522285nt_int
% 0.33/0.65 @ ^ [Y4: num,Z2: num] : ( Y4 = Z2 )
% 0.33/0.65 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 ) )
% 0.33/0.65 @ ^ [M: num,N4: num] : ( minus_minus_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N4 ) )
% 0.33/0.65 @ ^ [M: num,N4: num] : ( minus_minus_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N4 ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % sub.rsp
% 0.33/0.65 thf(fact_7035_transfer__rule__numeral,axiom,
% 0.33/0.65 ! [R4: nat > nat > $o] :
% 0.33/0.65 ( ( R4 @ zero_zero_nat @ zero_zero_nat )
% 0.33/0.65 => ( ( R4 @ one_one_nat @ one_one_nat )
% 0.33/0.65 => ( ( bNF_re1345281282404953727at_nat @ R4 @ ( bNF_re5653821019739307937at_nat @ R4 @ R4 ) @ plus_plus_nat @ plus_plus_nat )
% 0.33/0.65 => ( bNF_re825466652795518005at_nat
% 0.33/0.65 @ ^ [Y4: num,Z2: num] : ( Y4 = Z2 )
% 0.33/0.65 @ R4
% 0.33/0.65 @ numeral_numeral_nat
% 0.33/0.65 @ numeral_numeral_nat ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % transfer_rule_numeral
% 0.33/0.65 thf(fact_7036_transfer__rule__numeral,axiom,
% 0.33/0.65 ! [R4: nat > int > $o] :
% 0.33/0.65 ( ( R4 @ zero_zero_nat @ zero_zero_int )
% 0.33/0.65 => ( ( R4 @ one_one_nat @ one_one_int )
% 0.33/0.65 => ( ( bNF_re5864104203909894035nt_int @ R4 @ ( bNF_re6022984109467102297at_int @ R4 @ R4 ) @ plus_plus_nat @ plus_plus_int )
% 0.33/0.65 => ( bNF_re822976182286467729at_int
% 0.33/0.65 @ ^ [Y4: num,Z2: num] : ( Y4 = Z2 )
% 0.33/0.65 @ R4
% 0.33/0.65 @ numeral_numeral_nat
% 0.33/0.65 @ numeral_numeral_int ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % transfer_rule_numeral
% 0.33/0.65 thf(fact_7037_transfer__rule__numeral,axiom,
% 0.33/0.65 ! [R4: nat > code_integer > $o] :
% 0.33/0.65 ( ( R4 @ zero_zero_nat @ zero_z3403309356797280102nteger )
% 0.33/0.65 => ( ( R4 @ one_one_nat @ one_one_Code_integer )
% 0.33/0.65 => ( ( bNF_re7367609096550055590nteger @ R4 @ ( bNF_re1599192376174140603nteger @ R4 @ R4 ) @ plus_plus_nat @ plus_p5714425477246183910nteger )
% 0.33/0.65 => ( bNF_re6129422230220670146nteger
% 0.33/0.65 @ ^ [Y4: num,Z2: num] : ( Y4 = Z2 )
% 0.33/0.65 @ R4
% 0.33/0.65 @ numeral_numeral_nat
% 0.33/0.65 @ numera6620942414471956472nteger ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % transfer_rule_numeral
% 0.33/0.65 thf(fact_7038_transfer__rule__numeral,axiom,
% 0.33/0.65 ! [R4: nat > rat > $o] :
% 0.33/0.65 ( ( R4 @ zero_zero_nat @ zero_zero_rat )
% 0.33/0.65 => ( ( R4 @ one_one_nat @ one_one_rat )
% 0.33/0.65 => ( ( bNF_re3590448190763046039at_rat @ R4 @ ( bNF_re5790763769214331825at_rat @ R4 @ R4 ) @ plus_plus_nat @ plus_plus_rat )
% 0.33/0.65 => ( bNF_re190336592709022269at_rat
% 0.33/0.65 @ ^ [Y4: num,Z2: num] : ( Y4 = Z2 )
% 0.33/0.65 @ R4
% 0.33/0.65 @ numeral_numeral_nat
% 0.33/0.65 @ numeral_numeral_rat ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % transfer_rule_numeral
% 0.33/0.65 thf(fact_7039_transfer__rule__numeral,axiom,
% 0.33/0.65 ! [R4: nat > code_natural > $o] :
% 0.33/0.65 ( ( R4 @ zero_zero_nat @ zero_z2226904508553997617atural )
% 0.33/0.65 => ( ( R4 @ one_one_nat @ one_one_Code_natural )
% 0.33/0.65 => ( ( bNF_re88643428490162567atural @ R4 @ ( bNF_re3704215830270325841atural @ R4 @ R4 ) @ plus_plus_nat @ plus_p4538020629002901425atural )
% 0.33/0.65 => ( bNF_re4953017381977387661atural
% 0.33/0.65 @ ^ [Y4: num,Z2: num] : ( Y4 = Z2 )
% 0.33/0.65 @ R4
% 0.33/0.65 @ numeral_numeral_nat
% 0.33/0.65 @ numera5444537566228673987atural ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % transfer_rule_numeral
% 0.33/0.65 thf(fact_7040_transfer__rule__numeral,axiom,
% 0.33/0.65 ! [R4: int > nat > $o] :
% 0.33/0.65 ( ( R4 @ zero_zero_int @ zero_zero_nat )
% 0.33/0.65 => ( ( R4 @ one_one_int @ one_one_nat )
% 0.33/0.65 => ( ( bNF_re5416042074812042131at_nat @ R4 @ ( bNF_re4343356799547411545nt_nat @ R4 @ R4 ) @ plus_plus_int @ plus_plus_nat )
% 0.33/0.65 => ( bNF_re1824820364696572561nt_nat
% 0.33/0.65 @ ^ [Y4: num,Z2: num] : ( Y4 = Z2 )
% 0.33/0.65 @ R4
% 0.33/0.65 @ numeral_numeral_int
% 0.33/0.65 @ numeral_numeral_nat ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % transfer_rule_numeral
% 0.33/0.65 thf(fact_7041_transfer__rule__numeral,axiom,
% 0.33/0.65 ! [R4: int > int > $o] :
% 0.33/0.65 ( ( R4 @ zero_zero_int @ zero_zero_int )
% 0.33/0.65 => ( ( R4 @ one_one_int @ one_one_int )
% 0.33/0.65 => ( ( bNF_re711492959462206631nt_int @ R4 @ ( bNF_re4712519889275205905nt_int @ R4 @ R4 ) @ plus_plus_int @ plus_plus_int )
% 0.33/0.65 => ( bNF_re1822329894187522285nt_int
% 0.33/0.65 @ ^ [Y4: num,Z2: num] : ( Y4 = Z2 )
% 0.33/0.65 @ R4
% 0.33/0.65 @ numeral_numeral_int
% 0.33/0.65 @ numeral_numeral_int ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % transfer_rule_numeral
% 0.33/0.65 thf(fact_7042_transfer__rule__numeral,axiom,
% 0.33/0.65 ! [R4: int > code_integer > $o] :
% 0.33/0.65 ( ( R4 @ zero_zero_int @ zero_z3403309356797280102nteger )
% 0.33/0.65 => ( ( R4 @ one_one_int @ one_one_Code_integer )
% 0.33/0.65 => ( ( bNF_re398004352372739002nteger @ R4 @ ( bNF_re3379532845092657523nteger @ R4 @ R4 ) @ plus_plus_int @ plus_p5714425477246183910nteger )
% 0.33/0.65 => ( bNF_re6501075790457514782nteger
% 0.33/0.65 @ ^ [Y4: num,Z2: num] : ( Y4 = Z2 )
% 0.33/0.65 @ R4
% 0.33/0.65 @ numeral_numeral_int
% 0.33/0.65 @ numera6620942414471956472nteger ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % transfer_rule_numeral
% 0.33/0.65 thf(fact_7043_transfer__rule__numeral,axiom,
% 0.33/0.65 ! [R4: int > rat > $o] :
% 0.33/0.65 ( ( R4 @ zero_zero_int @ zero_zero_rat )
% 0.33/0.65 => ( ( R4 @ one_one_int @ one_one_rat )
% 0.33/0.65 => ( ( bNF_re7661208983170134443at_rat @ R4 @ ( bNF_re4480299549022435433nt_rat @ R4 @ R4 ) @ plus_plus_int @ plus_plus_rat )
% 0.33/0.65 => ( bNF_re1189690304610076825nt_rat
% 0.33/0.65 @ ^ [Y4: num,Z2: num] : ( Y4 = Z2 )
% 0.33/0.65 @ R4
% 0.33/0.65 @ numeral_numeral_int
% 0.33/0.65 @ numeral_numeral_rat ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % transfer_rule_numeral
% 0.33/0.65 thf(fact_7044_transfer__rule__numeral,axiom,
% 0.33/0.65 ! [R4: int > code_natural > $o] :
% 0.33/0.65 ( ( R4 @ zero_zero_int @ zero_z2226904508553997617atural )
% 0.33/0.65 => ( ( R4 @ one_one_int @ one_one_Code_natural )
% 0.33/0.65 => ( ( bNF_re2342410721167621787atural @ R4 @ ( bNF_re5484556299188842761atural @ R4 @ R4 ) @ plus_plus_int @ plus_p4538020629002901425atural )
% 0.33/0.65 => ( bNF_re5324670942214232297atural
% 0.33/0.65 @ ^ [Y4: num,Z2: num] : ( Y4 = Z2 )
% 0.33/0.65 @ R4
% 0.33/0.65 @ numeral_numeral_int
% 0.33/0.65 @ numera5444537566228673987atural ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % transfer_rule_numeral
% 0.33/0.65 thf(fact_7045_uminus__integer_Orsp,axiom,
% 0.33/0.65 ( bNF_re4712519889275205905nt_int
% 0.33/0.65 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.65 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.65 @ uminus_uminus_int
% 0.33/0.65 @ uminus_uminus_int ) ).
% 0.33/0.65
% 0.33/0.65 % uminus_integer.rsp
% 0.33/0.65 thf(fact_7046_integer__of__natural_Orsp,axiom,
% 0.33/0.65 ( bNF_re6650684261131312217nt_int
% 0.33/0.65 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.65 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.65 @ semiri1314217659103216013at_int
% 0.33/0.65 @ semiri1314217659103216013at_int ) ).
% 0.33/0.65
% 0.33/0.65 % integer_of_natural.rsp
% 0.33/0.65 thf(fact_7047_natural__of__integer_Orsp,axiom,
% 0.33/0.65 ( bNF_re3715656647883201625at_nat
% 0.33/0.65 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.65 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.65 @ nat2
% 0.33/0.65 @ nat2 ) ).
% 0.33/0.65
% 0.33/0.65 % natural_of_integer.rsp
% 0.33/0.65 thf(fact_7048_abs__integer_Orsp,axiom,
% 0.33/0.65 ( bNF_re4712519889275205905nt_int
% 0.33/0.65 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.65 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.65 @ abs_abs_int
% 0.33/0.65 @ abs_abs_int ) ).
% 0.33/0.65
% 0.33/0.65 % abs_integer.rsp
% 0.33/0.65 thf(fact_7049_bit__integer_Orsp,axiom,
% 0.33/0.65 ( bNF_re3376528473927230327_nat_o
% 0.33/0.65 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.65 @ ^ [Y4: nat > $o,Z2: nat > $o] : ( Y4 = Z2 )
% 0.33/0.65 @ bit_se1146084159140164899it_int
% 0.33/0.65 @ bit_se1146084159140164899it_int ) ).
% 0.33/0.65
% 0.33/0.65 % bit_integer.rsp
% 0.33/0.65 thf(fact_7050_not__integer_Orsp,axiom,
% 0.33/0.65 ( bNF_re4712519889275205905nt_int
% 0.33/0.65 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.65 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.65 @ bit_ri7919022796975470100ot_int
% 0.33/0.65 @ bit_ri7919022796975470100ot_int ) ).
% 0.33/0.65
% 0.33/0.65 % not_integer.rsp
% 0.33/0.65 thf(fact_7051_sgn__integer_Orsp,axiom,
% 0.33/0.65 ( bNF_re4712519889275205905nt_int
% 0.33/0.65 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.65 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.65 @ sgn_sgn_int
% 0.33/0.65 @ sgn_sgn_int ) ).
% 0.33/0.65
% 0.33/0.65 % sgn_integer.rsp
% 0.33/0.65 thf(fact_7052_mask__integer_Orsp,axiom,
% 0.33/0.65 ( bNF_re6650684261131312217nt_int
% 0.33/0.65 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.65 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.65 @ bit_se2000444600071755411sk_int
% 0.33/0.65 @ bit_se2000444600071755411sk_int ) ).
% 0.33/0.65
% 0.33/0.65 % mask_integer.rsp
% 0.33/0.65 thf(fact_7053_mask__natural_Orsp,axiom,
% 0.33/0.65 ( bNF_re5653821019739307937at_nat
% 0.33/0.65 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.65 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.65 @ bit_se2002935070580805687sk_nat
% 0.33/0.65 @ bit_se2002935070580805687sk_nat ) ).
% 0.33/0.65
% 0.33/0.65 % mask_natural.rsp
% 0.33/0.65 thf(fact_7054_transfer__rule__of__int,axiom,
% 0.33/0.65 ! [R4: int > int > $o] :
% 0.33/0.65 ( ( R4 @ zero_zero_int @ zero_zero_int )
% 0.33/0.65 => ( ( R4 @ one_one_int @ one_one_int )
% 0.33/0.65 => ( ( bNF_re711492959462206631nt_int @ R4 @ ( bNF_re4712519889275205905nt_int @ R4 @ R4 ) @ plus_plus_int @ plus_plus_int )
% 0.33/0.65 => ( ( bNF_re4712519889275205905nt_int @ R4 @ R4 @ uminus_uminus_int @ uminus_uminus_int )
% 0.33/0.65 => ( bNF_re4712519889275205905nt_int
% 0.33/0.65 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.65 @ R4
% 0.33/0.65 @ ring_1_of_int_int
% 0.33/0.65 @ ring_1_of_int_int ) ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % transfer_rule_of_int
% 0.33/0.65 thf(fact_7055_transfer__rule__of__int,axiom,
% 0.33/0.65 ! [R4: int > code_integer > $o] :
% 0.33/0.65 ( ( R4 @ zero_zero_int @ zero_z3403309356797280102nteger )
% 0.33/0.65 => ( ( R4 @ one_one_int @ one_one_Code_integer )
% 0.33/0.65 => ( ( bNF_re398004352372739002nteger @ R4 @ ( bNF_re3379532845092657523nteger @ R4 @ R4 ) @ plus_plus_int @ plus_p5714425477246183910nteger )
% 0.33/0.65 => ( ( bNF_re3379532845092657523nteger @ R4 @ R4 @ uminus_uminus_int @ uminus1351360451143612070nteger )
% 0.33/0.65 => ( bNF_re982302072995117890nteger
% 0.33/0.65 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.65 @ R4
% 0.33/0.65 @ ring_1_of_int_int
% 0.33/0.65 @ ring_18347121197199848620nteger ) ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % transfer_rule_of_int
% 0.33/0.65 thf(fact_7056_transfer__rule__of__int,axiom,
% 0.33/0.65 ! [R4: int > rat > $o] :
% 0.33/0.65 ( ( R4 @ zero_zero_int @ zero_zero_rat )
% 0.33/0.65 => ( ( R4 @ one_one_int @ one_one_rat )
% 0.33/0.65 => ( ( bNF_re7661208983170134443at_rat @ R4 @ ( bNF_re4480299549022435433nt_rat @ R4 @ R4 ) @ plus_plus_int @ plus_plus_rat )
% 0.33/0.65 => ( ( bNF_re4480299549022435433nt_rat @ R4 @ R4 @ uminus_uminus_int @ uminus_uminus_rat )
% 0.33/0.65 => ( bNF_re4079880299697760445nt_rat
% 0.33/0.65 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.65 @ R4
% 0.33/0.65 @ ring_1_of_int_int
% 0.33/0.65 @ ring_1_of_int_rat ) ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % transfer_rule_of_int
% 0.33/0.65 thf(fact_7057_transfer__rule__of__int,axiom,
% 0.33/0.65 ! [R4: code_integer > int > $o] :
% 0.33/0.65 ( ( R4 @ zero_z3403309356797280102nteger @ zero_zero_int )
% 0.33/0.65 => ( ( R4 @ one_one_Code_integer @ one_one_int )
% 0.33/0.65 => ( ( bNF_re8304916493157054650nt_int @ R4 @ ( bNF_re2888858428391045491er_int @ R4 @ R4 ) @ plus_p5714425477246183910nteger @ plus_plus_int )
% 0.33/0.65 => ( ( bNF_re2888858428391045491er_int @ R4 @ R4 @ uminus1351360451143612070nteger @ uminus_uminus_int )
% 0.33/0.65 => ( bNF_re343602593470180162er_int
% 0.33/0.65 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.65 @ R4
% 0.33/0.65 @ ring_18347121197199848620nteger
% 0.33/0.65 @ ring_1_of_int_int ) ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % transfer_rule_of_int
% 0.33/0.65 thf(fact_7058_transfer__rule__of__int,axiom,
% 0.33/0.65 ! [R4: code_integer > code_integer > $o] :
% 0.33/0.65 ( ( R4 @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 0.33/0.65 => ( ( R4 @ one_one_Code_integer @ one_one_Code_integer )
% 0.33/0.65 => ( ( bNF_re122555440370955213nteger @ R4 @ ( bNF_re1062419521925302741nteger @ R4 @ R4 ) @ plus_p5714425477246183910nteger @ plus_p5714425477246183910nteger )
% 0.33/0.65 => ( ( bNF_re1062419521925302741nteger @ R4 @ R4 @ uminus1351360451143612070nteger @ uminus1351360451143612070nteger )
% 0.33/0.65 => ( bNF_re1784066744496875891nteger
% 0.33/0.65 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.65 @ R4
% 0.33/0.65 @ ring_18347121197199848620nteger
% 0.33/0.65 @ ring_18347121197199848620nteger ) ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % transfer_rule_of_int
% 0.33/0.65 thf(fact_7059_transfer__rule__of__int,axiom,
% 0.33/0.65 ! [R4: code_integer > rat > $o] :
% 0.33/0.65 ( ( R4 @ zero_z3403309356797280102nteger @ zero_zero_rat )
% 0.33/0.65 => ( ( R4 @ one_one_Code_integer @ one_one_rat )
% 0.33/0.65 => ( ( bNF_re2976496150901874110at_rat @ R4 @ ( bNF_re4698098036185532619er_rat @ R4 @ R4 ) @ plus_p5714425477246183910nteger @ plus_plus_rat )
% 0.33/0.65 => ( ( bNF_re4698098036185532619er_rat @ R4 @ R4 @ uminus1351360451143612070nteger @ uminus_uminus_rat )
% 0.33/0.65 => ( bNF_re8934335040747510510er_rat
% 0.33/0.65 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.65 @ R4
% 0.33/0.65 @ ring_18347121197199848620nteger
% 0.33/0.65 @ ring_1_of_int_rat ) ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % transfer_rule_of_int
% 0.33/0.65 thf(fact_7060_transfer__rule__of__int,axiom,
% 0.33/0.65 ! [R4: rat > int > $o] :
% 0.33/0.65 ( ( R4 @ zero_zero_rat @ zero_zero_int )
% 0.33/0.65 => ( ( R4 @ one_one_rat @ one_one_int )
% 0.33/0.65 => ( ( bNF_re8876735282041863595nt_int @ R4 @ ( bNF_re5838490730811218025at_int @ R4 @ R4 ) @ plus_plus_rat @ plus_plus_int )
% 0.33/0.65 => ( ( bNF_re5838490730811218025at_int @ R4 @ R4 @ uminus_uminus_rat @ uminus_uminus_int )
% 0.33/0.65 => ( bNF_re3396611533439285437at_int
% 0.33/0.65 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.65 @ R4
% 0.33/0.65 @ ring_1_of_int_rat
% 0.33/0.65 @ ring_1_of_int_int ) ) ) ) ) ).
% 0.33/0.65
% 0.33/0.65 % transfer_rule_of_int
% 0.33/0.65 thf(fact_7061_transfer__rule__of__int,axiom,
% 0.33/0.65 ! [R4: rat > code_integer > $o] :
% 0.33/0.65 ( ( R4 @ zero_zero_rat @ zero_z3403309356797280102nteger )
% 0.33/0.65 => ( ( R4 @ one_one_rat @ one_one_Code_integer )
% 0.33/0.65 => ( ( bNF_re4307939118855507134nteger @ R4 @ ( bNF_re2328245411608324299nteger @ R4 @ R4 ) @ plus_plus_rat @ plus_p5714425477246183910nteger )
% 0.33/0.65 => ( ( bNF_re2328245411608324299nteger @ R4 @ R4 @ uminus_uminus_rat @ uminus1351360451143612070nteger )
% 0.33/0.65 => ( bNF_re1382721322319792878nteger
% 0.33/0.65 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.66 @ R4
% 0.33/0.66 @ ring_1_of_int_rat
% 0.33/0.66 @ ring_18347121197199848620nteger ) ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % transfer_rule_of_int
% 0.33/0.66 thf(fact_7062_transfer__rule__of__int,axiom,
% 0.33/0.66 ! [R4: rat > rat > $o] :
% 0.33/0.66 ( ( R4 @ zero_zero_rat @ zero_zero_rat )
% 0.33/0.66 => ( ( R4 @ one_one_rat @ one_one_rat )
% 0.33/0.66 => ( ( bNF_re6603079268895015599at_rat @ R4 @ ( bNF_re5606270390558447553at_rat @ R4 @ R4 ) @ plus_plus_rat @ plus_plus_rat )
% 0.33/0.66 => ( ( bNF_re5606270390558447553at_rat @ R4 @ R4 @ uminus_uminus_rat @ uminus_uminus_rat )
% 0.33/0.66 => ( bNF_re2763971943861839977at_rat
% 0.33/0.66 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.66 @ R4
% 0.33/0.66 @ ring_1_of_int_rat
% 0.33/0.66 @ ring_1_of_int_rat ) ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % transfer_rule_of_int
% 0.33/0.66 thf(fact_7063_fun_Orel__map_I1_J,axiom,
% 0.33/0.66 ! [Sb: ( nat > $o ) > ( nat > $o ) > $o,I: ( nat > $o ) > nat > $o,X: int > nat > $o,Y: int > nat > $o] :
% 0.33/0.66 ( ( bNF_re3376528473927230327_nat_o
% 0.33/0.66 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.66 @ Sb
% 0.33/0.66 @ ( comp_nat_o_nat_o_int @ I @ X )
% 0.33/0.66 @ Y )
% 0.33/0.66 = ( bNF_re3376528473927230327_nat_o
% 0.33/0.66 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.66 @ ^ [X3: nat > $o] : ( Sb @ ( I @ X3 ) )
% 0.33/0.66 @ X
% 0.33/0.66 @ Y ) ) ).
% 0.33/0.66
% 0.33/0.66 % fun.rel_map(1)
% 0.33/0.66 thf(fact_7064_fun_Orel__map_I1_J,axiom,
% 0.33/0.66 ! [Sb: ( int > product_prod_int_int ) > ( int > product_prod_int_int ) > $o,I: ( int > product_prod_int_int ) > int > product_prod_int_int,X: int > int > product_prod_int_int,Y: int > int > product_prod_int_int] :
% 0.33/0.66 ( ( bNF_re157797125943740599nt_int
% 0.33/0.66 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.66 @ Sb
% 0.33/0.66 @ ( comp_i1790862786758963855nt_int @ I @ X )
% 0.33/0.66 @ Y )
% 0.33/0.66 = ( bNF_re157797125943740599nt_int
% 0.33/0.66 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.66 @ ^ [X3: int > product_prod_int_int] : ( Sb @ ( I @ X3 ) )
% 0.33/0.66 @ X
% 0.33/0.66 @ Y ) ) ).
% 0.33/0.66
% 0.33/0.66 % fun.rel_map(1)
% 0.33/0.66 thf(fact_7065_fun_Orel__map_I1_J,axiom,
% 0.33/0.66 ! [Sb: ( int > product_prod_int_int ) > ( int > rat ) > $o,I: ( int > product_prod_int_int ) > int > product_prod_int_int,X: int > int > product_prod_int_int,Y: int > int > rat] :
% 0.33/0.66 ( ( bNF_re3461391660133120880nt_rat
% 0.33/0.66 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.66 @ Sb
% 0.33/0.66 @ ( comp_i1790862786758963855nt_int @ I @ X )
% 0.33/0.66 @ Y )
% 0.33/0.66 = ( bNF_re3461391660133120880nt_rat
% 0.33/0.66 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.66 @ ^ [X3: int > product_prod_int_int] : ( Sb @ ( I @ X3 ) )
% 0.33/0.66 @ X
% 0.33/0.66 @ Y ) ) ).
% 0.33/0.66
% 0.33/0.66 % fun.rel_map(1)
% 0.33/0.66 thf(fact_7066_fun_Orel__map_I1_J,axiom,
% 0.33/0.66 ! [Sb: ( int > $o ) > ( int > $o ) > $o,I: ( int > $o ) > int > $o,X: int > int > $o,Y: int > int > $o] :
% 0.33/0.66 ( ( bNF_re3403563459893282935_int_o
% 0.33/0.66 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.66 @ Sb
% 0.33/0.66 @ ( comp_int_o_int_o_int @ I @ X )
% 0.33/0.66 @ Y )
% 0.33/0.66 = ( bNF_re3403563459893282935_int_o
% 0.33/0.66 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.66 @ ^ [X3: int > $o] : ( Sb @ ( I @ X3 ) )
% 0.33/0.66 @ X
% 0.33/0.66 @ Y ) ) ).
% 0.33/0.66
% 0.33/0.66 % fun.rel_map(1)
% 0.33/0.66 thf(fact_7067_fun_Orel__map_I1_J,axiom,
% 0.33/0.66 ! [Sb: ( int > int ) > ( int > int ) > $o,I: ( int > int ) > int > int,X: int > int > int,Y: int > int > int] :
% 0.33/0.66 ( ( bNF_re711492959462206631nt_int
% 0.33/0.66 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.66 @ Sb
% 0.33/0.66 @ ( comp_i1129928922100200191nt_int @ I @ X )
% 0.33/0.66 @ Y )
% 0.33/0.66 = ( bNF_re711492959462206631nt_int
% 0.33/0.66 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.66 @ ^ [X3: int > int] : ( Sb @ ( I @ X3 ) )
% 0.33/0.66 @ X
% 0.33/0.66 @ Y ) ) ).
% 0.33/0.66
% 0.33/0.66 % fun.rel_map(1)
% 0.33/0.66 thf(fact_7068_fun_Orel__map_I2_J,axiom,
% 0.33/0.66 ! [Sa: ( nat > $o ) > ( nat > $o ) > $o,X: int > nat > $o,G: ( nat > $o ) > nat > $o,Y: int > nat > $o] :
% 0.33/0.66 ( ( bNF_re3376528473927230327_nat_o
% 0.33/0.66 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.66 @ Sa
% 0.33/0.66 @ X
% 0.33/0.66 @ ( comp_nat_o_nat_o_int @ G @ Y ) )
% 0.33/0.66 = ( bNF_re3376528473927230327_nat_o
% 0.33/0.66 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.66 @ ^ [X3: nat > $o,Y3: nat > $o] : ( Sa @ X3 @ ( G @ Y3 ) )
% 0.33/0.66 @ X
% 0.33/0.66 @ Y ) ) ).
% 0.33/0.66
% 0.33/0.66 % fun.rel_map(2)
% 0.33/0.66 thf(fact_7069_fun_Orel__map_I2_J,axiom,
% 0.33/0.66 ! [Sa: ( int > product_prod_int_int ) > ( int > product_prod_int_int ) > $o,X: int > int > product_prod_int_int,G: ( int > product_prod_int_int ) > int > product_prod_int_int,Y: int > int > product_prod_int_int] :
% 0.33/0.66 ( ( bNF_re157797125943740599nt_int
% 0.33/0.66 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.66 @ Sa
% 0.33/0.66 @ X
% 0.33/0.66 @ ( comp_i1790862786758963855nt_int @ G @ Y ) )
% 0.33/0.66 = ( bNF_re157797125943740599nt_int
% 0.33/0.66 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.66 @ ^ [X3: int > product_prod_int_int,Y3: int > product_prod_int_int] : ( Sa @ X3 @ ( G @ Y3 ) )
% 0.33/0.66 @ X
% 0.33/0.66 @ Y ) ) ).
% 0.33/0.66
% 0.33/0.66 % fun.rel_map(2)
% 0.33/0.66 thf(fact_7070_fun_Orel__map_I2_J,axiom,
% 0.33/0.66 ! [Sa: ( int > product_prod_int_int ) > ( int > product_prod_int_int ) > $o,X: int > int > product_prod_int_int,G: ( int > rat ) > int > product_prod_int_int,Y: int > int > rat] :
% 0.33/0.66 ( ( bNF_re157797125943740599nt_int
% 0.33/0.66 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.66 @ Sa
% 0.33/0.66 @ X
% 0.33/0.66 @ ( comp_i929186717396404458nt_int @ G @ Y ) )
% 0.33/0.66 = ( bNF_re3461391660133120880nt_rat
% 0.33/0.66 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.66 @ ^ [X3: int > product_prod_int_int,Y3: int > rat] : ( Sa @ X3 @ ( G @ Y3 ) )
% 0.33/0.66 @ X
% 0.33/0.66 @ Y ) ) ).
% 0.33/0.66
% 0.33/0.66 % fun.rel_map(2)
% 0.33/0.66 thf(fact_7071_fun_Orel__map_I2_J,axiom,
% 0.33/0.66 ! [Sa: ( int > product_prod_int_int ) > ( int > rat ) > $o,X: int > int > product_prod_int_int,G: ( int > product_prod_int_int ) > int > rat,Y: int > int > product_prod_int_int] :
% 0.33/0.66 ( ( bNF_re3461391660133120880nt_rat
% 0.33/0.66 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.66 @ Sa
% 0.33/0.66 @ X
% 0.33/0.66 @ ( comp_i1302866070986779890at_int @ G @ Y ) )
% 0.33/0.66 = ( bNF_re157797125943740599nt_int
% 0.33/0.66 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.66 @ ^ [X3: int > product_prod_int_int,Y3: int > product_prod_int_int] : ( Sa @ X3 @ ( G @ Y3 ) )
% 0.33/0.66 @ X
% 0.33/0.66 @ Y ) ) ).
% 0.33/0.66
% 0.33/0.66 % fun.rel_map(2)
% 0.33/0.66 thf(fact_7072_fun_Orel__map_I2_J,axiom,
% 0.33/0.66 ! [Sa: ( int > product_prod_int_int ) > ( int > rat ) > $o,X: int > int > product_prod_int_int,G: ( int > rat ) > int > rat,Y: int > int > rat] :
% 0.33/0.66 ( ( bNF_re3461391660133120880nt_rat
% 0.33/0.66 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.66 @ Sa
% 0.33/0.66 @ X
% 0.33/0.66 @ ( comp_i8258899369942393943at_int @ G @ Y ) )
% 0.33/0.66 = ( bNF_re3461391660133120880nt_rat
% 0.33/0.66 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.66 @ ^ [X3: int > product_prod_int_int,Y3: int > rat] : ( Sa @ X3 @ ( G @ Y3 ) )
% 0.33/0.66 @ X
% 0.33/0.66 @ Y ) ) ).
% 0.33/0.66
% 0.33/0.66 % fun.rel_map(2)
% 0.33/0.66 thf(fact_7073_fun_Orel__map_I2_J,axiom,
% 0.33/0.66 ! [Sa: ( int > $o ) > ( int > $o ) > $o,X: int > int > $o,G: ( int > $o ) > int > $o,Y: int > int > $o] :
% 0.33/0.66 ( ( bNF_re3403563459893282935_int_o
% 0.33/0.66 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.66 @ Sa
% 0.33/0.66 @ X
% 0.33/0.66 @ ( comp_int_o_int_o_int @ G @ Y ) )
% 0.33/0.66 = ( bNF_re3403563459893282935_int_o
% 0.33/0.66 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.66 @ ^ [X3: int > $o,Y3: int > $o] : ( Sa @ X3 @ ( G @ Y3 ) )
% 0.33/0.66 @ X
% 0.33/0.66 @ Y ) ) ).
% 0.33/0.66
% 0.33/0.66 % fun.rel_map(2)
% 0.33/0.66 thf(fact_7074_fun_Orel__map_I2_J,axiom,
% 0.33/0.66 ! [Sa: ( int > int ) > ( int > int ) > $o,X: int > int > int,G: ( int > int ) > int > int,Y: int > int > int] :
% 0.33/0.66 ( ( bNF_re711492959462206631nt_int
% 0.33/0.66 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.66 @ Sa
% 0.33/0.66 @ X
% 0.33/0.66 @ ( comp_i1129928922100200191nt_int @ G @ Y ) )
% 0.33/0.66 = ( bNF_re711492959462206631nt_int
% 0.33/0.66 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.66 @ ^ [X3: int > int,Y3: int > int] : ( Sa @ X3 @ ( G @ Y3 ) )
% 0.33/0.66 @ X
% 0.33/0.66 @ Y ) ) ).
% 0.33/0.66
% 0.33/0.66 % fun.rel_map(2)
% 0.33/0.66 thf(fact_7075_times__eq__iff,axiom,
% 0.33/0.66 ! [A2: set_o,B5: set_o,C4: set_o,D3: set_o] :
% 0.33/0.66 ( ( ( product_Sigma_o_o @ A2
% 0.33/0.66 @ ^ [Uu: $o] : B5 )
% 0.33/0.66 = ( product_Sigma_o_o @ C4
% 0.33/0.66 @ ^ [Uu: $o] : D3 ) )
% 0.33/0.66 = ( ( ( A2 = C4 )
% 0.33/0.66 & ( B5 = D3 ) )
% 0.33/0.66 | ( ( ( A2 = bot_bot_set_o )
% 0.33/0.66 | ( B5 = bot_bot_set_o ) )
% 0.33/0.66 & ( ( C4 = bot_bot_set_o )
% 0.33/0.66 | ( D3 = bot_bot_set_o ) ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % times_eq_iff
% 0.33/0.66 thf(fact_7076_times__eq__iff,axiom,
% 0.33/0.66 ! [A2: set_o,B5: set_nat,C4: set_o,D3: set_nat] :
% 0.33/0.66 ( ( ( product_Sigma_o_nat @ A2
% 0.33/0.66 @ ^ [Uu: $o] : B5 )
% 0.33/0.66 = ( product_Sigma_o_nat @ C4
% 0.33/0.66 @ ^ [Uu: $o] : D3 ) )
% 0.33/0.66 = ( ( ( A2 = C4 )
% 0.33/0.66 & ( B5 = D3 ) )
% 0.33/0.66 | ( ( ( A2 = bot_bot_set_o )
% 0.33/0.66 | ( B5 = bot_bot_set_nat ) )
% 0.33/0.66 & ( ( C4 = bot_bot_set_o )
% 0.33/0.66 | ( D3 = bot_bot_set_nat ) ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % times_eq_iff
% 0.33/0.66 thf(fact_7077_times__eq__iff,axiom,
% 0.33/0.66 ! [A2: set_o,B5: set_int,C4: set_o,D3: set_int] :
% 0.33/0.66 ( ( ( product_Sigma_o_int @ A2
% 0.33/0.66 @ ^ [Uu: $o] : B5 )
% 0.33/0.66 = ( product_Sigma_o_int @ C4
% 0.33/0.66 @ ^ [Uu: $o] : D3 ) )
% 0.33/0.66 = ( ( ( A2 = C4 )
% 0.33/0.66 & ( B5 = D3 ) )
% 0.33/0.66 | ( ( ( A2 = bot_bot_set_o )
% 0.33/0.66 | ( B5 = bot_bot_set_int ) )
% 0.33/0.66 & ( ( C4 = bot_bot_set_o )
% 0.33/0.66 | ( D3 = bot_bot_set_int ) ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % times_eq_iff
% 0.33/0.66 thf(fact_7078_times__eq__iff,axiom,
% 0.33/0.66 ! [A2: set_nat,B5: set_o,C4: set_nat,D3: set_o] :
% 0.33/0.66 ( ( ( product_Sigma_nat_o @ A2
% 0.33/0.66 @ ^ [Uu: nat] : B5 )
% 0.33/0.66 = ( product_Sigma_nat_o @ C4
% 0.33/0.66 @ ^ [Uu: nat] : D3 ) )
% 0.33/0.66 = ( ( ( A2 = C4 )
% 0.33/0.66 & ( B5 = D3 ) )
% 0.33/0.66 | ( ( ( A2 = bot_bot_set_nat )
% 0.33/0.66 | ( B5 = bot_bot_set_o ) )
% 0.33/0.66 & ( ( C4 = bot_bot_set_nat )
% 0.33/0.66 | ( D3 = bot_bot_set_o ) ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % times_eq_iff
% 0.33/0.66 thf(fact_7079_times__eq__iff,axiom,
% 0.33/0.66 ! [A2: set_nat,B5: set_nat,C4: set_nat,D3: set_nat] :
% 0.33/0.66 ( ( ( produc457027306803732586at_nat @ A2
% 0.33/0.66 @ ^ [Uu: nat] : B5 )
% 0.33/0.66 = ( produc457027306803732586at_nat @ C4
% 0.33/0.66 @ ^ [Uu: nat] : D3 ) )
% 0.33/0.66 = ( ( ( A2 = C4 )
% 0.33/0.66 & ( B5 = D3 ) )
% 0.33/0.66 | ( ( ( A2 = bot_bot_set_nat )
% 0.33/0.66 | ( B5 = bot_bot_set_nat ) )
% 0.33/0.66 & ( ( C4 = bot_bot_set_nat )
% 0.33/0.66 | ( D3 = bot_bot_set_nat ) ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % times_eq_iff
% 0.33/0.66 thf(fact_7080_times__eq__iff,axiom,
% 0.33/0.66 ! [A2: set_nat,B5: set_int,C4: set_nat,D3: set_int] :
% 0.33/0.66 ( ( ( produc454536836294682310at_int @ A2
% 0.33/0.66 @ ^ [Uu: nat] : B5 )
% 0.33/0.66 = ( produc454536836294682310at_int @ C4
% 0.33/0.66 @ ^ [Uu: nat] : D3 ) )
% 0.33/0.66 = ( ( ( A2 = C4 )
% 0.33/0.66 & ( B5 = D3 ) )
% 0.33/0.66 | ( ( ( A2 = bot_bot_set_nat )
% 0.33/0.66 | ( B5 = bot_bot_set_int ) )
% 0.33/0.66 & ( ( C4 = bot_bot_set_nat )
% 0.33/0.66 | ( D3 = bot_bot_set_int ) ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % times_eq_iff
% 0.33/0.66 thf(fact_7081_times__eq__iff,axiom,
% 0.33/0.66 ! [A2: set_int,B5: set_o,C4: set_int,D3: set_o] :
% 0.33/0.66 ( ( ( product_Sigma_int_o @ A2
% 0.33/0.66 @ ^ [Uu: int] : B5 )
% 0.33/0.66 = ( product_Sigma_int_o @ C4
% 0.33/0.66 @ ^ [Uu: int] : D3 ) )
% 0.33/0.66 = ( ( ( A2 = C4 )
% 0.33/0.66 & ( B5 = D3 ) )
% 0.33/0.66 | ( ( ( A2 = bot_bot_set_int )
% 0.33/0.66 | ( B5 = bot_bot_set_o ) )
% 0.33/0.66 & ( ( C4 = bot_bot_set_int )
% 0.33/0.66 | ( D3 = bot_bot_set_o ) ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % times_eq_iff
% 0.33/0.66 thf(fact_7082_times__eq__iff,axiom,
% 0.33/0.66 ! [A2: set_int,B5: set_nat,C4: set_int,D3: set_nat] :
% 0.33/0.66 ( ( ( produc1456381018704787142nt_nat @ A2
% 0.33/0.66 @ ^ [Uu: int] : B5 )
% 0.33/0.66 = ( produc1456381018704787142nt_nat @ C4
% 0.33/0.66 @ ^ [Uu: int] : D3 ) )
% 0.33/0.66 = ( ( ( A2 = C4 )
% 0.33/0.66 & ( B5 = D3 ) )
% 0.33/0.66 | ( ( ( A2 = bot_bot_set_int )
% 0.33/0.66 | ( B5 = bot_bot_set_nat ) )
% 0.33/0.66 & ( ( C4 = bot_bot_set_int )
% 0.33/0.66 | ( D3 = bot_bot_set_nat ) ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % times_eq_iff
% 0.33/0.66 thf(fact_7083_times__eq__iff,axiom,
% 0.33/0.66 ! [A2: set_int,B5: set_int,C4: set_int,D3: set_int] :
% 0.33/0.66 ( ( ( produc1453890548195736866nt_int @ A2
% 0.33/0.66 @ ^ [Uu: int] : B5 )
% 0.33/0.66 = ( produc1453890548195736866nt_int @ C4
% 0.33/0.66 @ ^ [Uu: int] : D3 ) )
% 0.33/0.66 = ( ( ( A2 = C4 )
% 0.33/0.66 & ( B5 = D3 ) )
% 0.33/0.66 | ( ( ( A2 = bot_bot_set_int )
% 0.33/0.66 | ( B5 = bot_bot_set_int ) )
% 0.33/0.66 & ( ( C4 = bot_bot_set_int )
% 0.33/0.66 | ( D3 = bot_bot_set_int ) ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % times_eq_iff
% 0.33/0.66 thf(fact_7084_times__eq__iff,axiom,
% 0.33/0.66 ! [A2: set_Pr1261947904930325089at_nat,B5: set_o,C4: set_Pr1261947904930325089at_nat,D3: set_o] :
% 0.33/0.66 ( ( ( produc203973861852599583_nat_o @ A2
% 0.33/0.66 @ ^ [Uu: product_prod_nat_nat] : B5 )
% 0.33/0.66 = ( produc203973861852599583_nat_o @ C4
% 0.33/0.66 @ ^ [Uu: product_prod_nat_nat] : D3 ) )
% 0.33/0.66 = ( ( ( A2 = C4 )
% 0.33/0.66 & ( B5 = D3 ) )
% 0.33/0.66 | ( ( ( A2 = bot_bo2099793752762293965at_nat )
% 0.33/0.66 | ( B5 = bot_bot_set_o ) )
% 0.33/0.66 & ( ( C4 = bot_bo2099793752762293965at_nat )
% 0.33/0.66 | ( D3 = bot_bot_set_o ) ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % times_eq_iff
% 0.33/0.66 thf(fact_7085_dup_Orsp,axiom,
% 0.33/0.66 ( bNF_re4712519889275205905nt_int
% 0.33/0.66 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.66 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.66 @ ^ [K4: int] : ( plus_plus_int @ K4 @ K4 )
% 0.33/0.66 @ ^ [K4: int] : ( plus_plus_int @ K4 @ K4 ) ) ).
% 0.33/0.66
% 0.33/0.66 % dup.rsp
% 0.33/0.66 thf(fact_7086_Collect__case__prod__Sigma,axiom,
% 0.33/0.66 ! [P: nat > $o,Q: nat > nat > $o] :
% 0.33/0.66 ( ( collec3392354462482085612at_nat
% 0.33/0.66 @ ( produc6081775807080527818_nat_o
% 0.33/0.66 @ ^ [X3: nat,Y3: nat] :
% 0.33/0.66 ( ( P @ X3 )
% 0.33/0.66 & ( Q @ X3 @ Y3 ) ) ) )
% 0.33/0.66 = ( produc457027306803732586at_nat @ ( collect_nat @ P )
% 0.33/0.66 @ ^ [X3: nat] : ( collect_nat @ ( Q @ X3 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % Collect_case_prod_Sigma
% 0.33/0.66 thf(fact_7087_Collect__case__prod__Sigma,axiom,
% 0.33/0.66 ! [P: nat > $o,Q: nat > list_nat > $o] :
% 0.33/0.66 ( ( collec1907656820224499068st_nat
% 0.33/0.66 @ ( produc5265810065896090426_nat_o
% 0.33/0.66 @ ^ [X3: nat,Y3: list_nat] :
% 0.33/0.66 ( ( P @ X3 )
% 0.33/0.66 & ( Q @ X3 @ Y3 ) ) ) )
% 0.33/0.66 = ( produc5227933103413159546st_nat @ ( collect_nat @ P )
% 0.33/0.66 @ ^ [X3: nat] : ( collect_list_nat @ ( Q @ X3 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % Collect_case_prod_Sigma
% 0.33/0.66 thf(fact_7088_Collect__case__prod__Sigma,axiom,
% 0.33/0.66 ! [P: list_nat > $o,Q: list_nat > nat > $o] :
% 0.33/0.66 ( ( collec8096645339561496572at_nat
% 0.33/0.66 @ ( produc7308574044827705018_nat_o
% 0.33/0.66 @ ^ [X3: list_nat,Y3: nat] :
% 0.33/0.66 ( ( P @ X3 )
% 0.33/0.66 & ( Q @ X3 @ Y3 ) ) ) )
% 0.33/0.66 = ( produc7466890150575444730at_nat @ ( collect_list_nat @ P )
% 0.33/0.66 @ ^ [X3: list_nat] : ( collect_nat @ ( Q @ X3 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % Collect_case_prod_Sigma
% 0.33/0.66 thf(fact_7089_Collect__case__prod__Sigma,axiom,
% 0.33/0.66 ! [P: list_nat > $o,Q: list_nat > list_nat > $o] :
% 0.33/0.66 ( ( collec1570431334306492044st_nat
% 0.33/0.66 @ ( produc6382697403170970154_nat_o
% 0.33/0.66 @ ^ [X3: list_nat,Y3: list_nat] :
% 0.33/0.66 ( ( P @ X3 )
% 0.33/0.66 & ( Q @ X3 @ Y3 ) ) ) )
% 0.33/0.66 = ( produc6850429418872557834st_nat @ ( collect_list_nat @ P )
% 0.33/0.66 @ ^ [X3: list_nat] : ( collect_list_nat @ ( Q @ X3 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % Collect_case_prod_Sigma
% 0.33/0.66 thf(fact_7090_apsnd__apfst__commute,axiom,
% 0.33/0.66 ! [F: code_integer > code_integer,G: code_integer > code_integer,P4: produc8923325533196201883nteger] :
% 0.33/0.66 ( ( produc6499014454317279255nteger @ F @ ( produc3195571438000033749nteger @ G @ P4 ) )
% 0.33/0.66 = ( produc3195571438000033749nteger @ G @ ( produc6499014454317279255nteger @ F @ P4 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % apsnd_apfst_commute
% 0.33/0.66 thf(fact_7091_gcd__add__mult,axiom,
% 0.33/0.66 ! [M2: nat,K: nat,N2: nat] :
% 0.33/0.66 ( ( gcd_gcd_nat @ M2 @ ( plus_plus_nat @ ( times_times_nat @ K @ M2 ) @ N2 ) )
% 0.33/0.66 = ( gcd_gcd_nat @ M2 @ N2 ) ) ).
% 0.33/0.66
% 0.33/0.66 % gcd_add_mult
% 0.33/0.66 thf(fact_7092_gcd__add__mult,axiom,
% 0.33/0.66 ! [M2: int,K: int,N2: int] :
% 0.33/0.66 ( ( gcd_gcd_int @ M2 @ ( plus_plus_int @ ( times_times_int @ K @ M2 ) @ N2 ) )
% 0.33/0.66 = ( gcd_gcd_int @ M2 @ N2 ) ) ).
% 0.33/0.66
% 0.33/0.66 % gcd_add_mult
% 0.33/0.66 thf(fact_7093_Sigma__mono,axiom,
% 0.33/0.66 ! [A2: set_Pr4329608150637261639at_nat,C4: set_Pr4329608150637261639at_nat,B5: produc3843707927480180839at_nat > set_nat,D3: produc3843707927480180839at_nat > set_nat] :
% 0.33/0.66 ( ( ord_le1268244103169919719at_nat @ A2 @ C4 )
% 0.33/0.66 => ( ! [X4: produc3843707927480180839at_nat] :
% 0.33/0.66 ( ( member8757157785044589968at_nat @ X4 @ A2 )
% 0.33/0.66 => ( ord_less_eq_set_nat @ ( B5 @ X4 ) @ ( D3 @ X4 ) ) )
% 0.33/0.66 => ( ord_le2145644191787020796at_nat @ ( produc1095920968030776047at_nat @ A2 @ B5 ) @ ( produc1095920968030776047at_nat @ C4 @ D3 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % Sigma_mono
% 0.33/0.66 thf(fact_7094_Sigma__mono,axiom,
% 0.33/0.66 ! [A2: set_Pr1261947904930325089at_nat,C4: set_Pr1261947904930325089at_nat,B5: product_prod_nat_nat > set_nat,D3: product_prod_nat_nat > set_nat] :
% 0.33/0.66 ( ( ord_le3146513528884898305at_nat @ A2 @ C4 )
% 0.33/0.66 => ( ! [X4: product_prod_nat_nat] :
% 0.33/0.66 ( ( member8440522571783428010at_nat @ X4 @ A2 )
% 0.33/0.66 => ( ord_less_eq_set_nat @ ( B5 @ X4 ) @ ( D3 @ X4 ) ) )
% 0.33/0.66 => ( ord_le7094820750414311574at_nat @ ( produc7672662199629908489at_nat @ A2 @ B5 ) @ ( produc7672662199629908489at_nat @ C4 @ D3 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % Sigma_mono
% 0.33/0.66 thf(fact_7095_Sigma__mono,axiom,
% 0.33/0.66 ! [A2: set_o,C4: set_o,B5: $o > set_nat,D3: $o > set_nat] :
% 0.33/0.66 ( ( ord_less_eq_set_o @ A2 @ C4 )
% 0.33/0.66 => ( ! [X4: $o] :
% 0.33/0.66 ( ( member_o @ X4 @ A2 )
% 0.33/0.66 => ( ord_less_eq_set_nat @ ( B5 @ X4 ) @ ( D3 @ X4 ) ) )
% 0.33/0.66 => ( ord_le6472378536984071597_o_nat @ ( product_Sigma_o_nat @ A2 @ B5 ) @ ( product_Sigma_o_nat @ C4 @ D3 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % Sigma_mono
% 0.33/0.66 thf(fact_7096_Sigma__mono,axiom,
% 0.33/0.66 ! [A2: set_int,C4: set_int,B5: int > set_nat,D3: int > set_nat] :
% 0.33/0.66 ( ( ord_less_eq_set_int @ A2 @ C4 )
% 0.33/0.66 => ( ! [X4: int] :
% 0.33/0.66 ( ( member_int @ X4 @ A2 )
% 0.33/0.66 => ( ord_less_eq_set_nat @ ( B5 @ X4 ) @ ( D3 @ X4 ) ) )
% 0.33/0.66 => ( ord_le5333435103577920093nt_nat @ ( produc1456381018704787142nt_nat @ A2 @ B5 ) @ ( produc1456381018704787142nt_nat @ C4 @ D3 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % Sigma_mono
% 0.33/0.66 thf(fact_7097_Sigma__mono,axiom,
% 0.33/0.66 ! [A2: set_nat,C4: set_nat,B5: nat > set_nat,D3: nat > set_nat] :
% 0.33/0.66 ( ( ord_less_eq_set_nat @ A2 @ C4 )
% 0.33/0.66 => ( ! [X4: nat] :
% 0.33/0.66 ( ( member_nat @ X4 @ A2 )
% 0.33/0.66 => ( ord_less_eq_set_nat @ ( B5 @ X4 ) @ ( D3 @ X4 ) ) )
% 0.33/0.66 => ( ord_le3146513528884898305at_nat @ ( produc457027306803732586at_nat @ A2 @ B5 ) @ ( produc457027306803732586at_nat @ C4 @ D3 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % Sigma_mono
% 0.33/0.66 thf(fact_7098_bezout__int,axiom,
% 0.33/0.66 ! [X: int,Y: int] :
% 0.33/0.66 ? [U3: int,V4: int] :
% 0.33/0.66 ( ( plus_plus_int @ ( times_times_int @ U3 @ X ) @ ( times_times_int @ V4 @ Y ) )
% 0.33/0.66 = ( gcd_gcd_int @ X @ Y ) ) ).
% 0.33/0.66
% 0.33/0.66 % bezout_int
% 0.33/0.66 thf(fact_7099_Times__subset__cancel2,axiom,
% 0.33/0.66 ! [X: produc3843707927480180839at_nat,C4: set_Pr4329608150637261639at_nat,A2: set_nat,B5: set_nat] :
% 0.33/0.66 ( ( member8757157785044589968at_nat @ X @ C4 )
% 0.33/0.66 => ( ( ord_le3218026494883419554at_nat
% 0.33/0.66 @ ( produc396409126344608333at_nat @ A2
% 0.33/0.66 @ ^ [Uu: nat] : C4 )
% 0.33/0.66 @ ( produc396409126344608333at_nat @ B5
% 0.33/0.66 @ ^ [Uu: nat] : C4 ) )
% 0.33/0.66 = ( ord_less_eq_set_nat @ A2 @ B5 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % Times_subset_cancel2
% 0.33/0.66 thf(fact_7100_Times__subset__cancel2,axiom,
% 0.33/0.66 ! [X: product_prod_nat_nat,C4: set_Pr1261947904930325089at_nat,A2: set_nat,B5: set_nat] :
% 0.33/0.66 ( ( member8440522571783428010at_nat @ X @ C4 )
% 0.33/0.66 => ( ( ord_le3050193496395145148at_nat
% 0.33/0.66 @ ( produc1809337555817847783at_nat @ A2
% 0.33/0.66 @ ^ [Uu: nat] : C4 )
% 0.33/0.66 @ ( produc1809337555817847783at_nat @ B5
% 0.33/0.66 @ ^ [Uu: nat] : C4 ) )
% 0.33/0.66 = ( ord_less_eq_set_nat @ A2 @ B5 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % Times_subset_cancel2
% 0.33/0.66 thf(fact_7101_Times__subset__cancel2,axiom,
% 0.33/0.66 ! [X: $o,C4: set_o,A2: set_nat,B5: set_nat] :
% 0.33/0.66 ( ( member_o @ X @ C4 )
% 0.33/0.66 => ( ( ord_le7519981659162375251_nat_o
% 0.33/0.66 @ ( product_Sigma_nat_o @ A2
% 0.33/0.66 @ ^ [Uu: nat] : C4 )
% 0.33/0.66 @ ( product_Sigma_nat_o @ B5
% 0.33/0.66 @ ^ [Uu: nat] : C4 ) )
% 0.33/0.66 = ( ord_less_eq_set_nat @ A2 @ B5 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % Times_subset_cancel2
% 0.33/0.66 thf(fact_7102_Times__subset__cancel2,axiom,
% 0.33/0.66 ! [X: nat,C4: set_nat,A2: set_nat,B5: set_nat] :
% 0.33/0.66 ( ( member_nat @ X @ C4 )
% 0.33/0.66 => ( ( ord_le3146513528884898305at_nat
% 0.33/0.66 @ ( produc457027306803732586at_nat @ A2
% 0.33/0.66 @ ^ [Uu: nat] : C4 )
% 0.33/0.66 @ ( produc457027306803732586at_nat @ B5
% 0.33/0.66 @ ^ [Uu: nat] : C4 ) )
% 0.33/0.66 = ( ord_less_eq_set_nat @ A2 @ B5 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % Times_subset_cancel2
% 0.33/0.66 thf(fact_7103_Times__subset__cancel2,axiom,
% 0.33/0.66 ! [X: int,C4: set_int,A2: set_nat,B5: set_nat] :
% 0.33/0.66 ( ( member_int @ X @ C4 )
% 0.33/0.66 => ( ( ord_le656430383953171549at_int
% 0.33/0.66 @ ( produc454536836294682310at_int @ A2
% 0.33/0.66 @ ^ [Uu: nat] : C4 )
% 0.33/0.66 @ ( produc454536836294682310at_int @ B5
% 0.33/0.66 @ ^ [Uu: nat] : C4 ) )
% 0.33/0.66 = ( ord_less_eq_set_nat @ A2 @ B5 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % Times_subset_cancel2
% 0.33/0.66 thf(fact_7104_UN__Times__distrib,axiom,
% 0.33/0.66 ! [E3: nat > set_nat,F5: nat > set_nat,A2: set_nat,B5: set_nat] :
% 0.33/0.66 ( ( comple5685304695842803022at_nat
% 0.33/0.66 @ ( image_5423882813909314213at_nat
% 0.33/0.66 @ ( produc8197505143624133779at_nat
% 0.33/0.66 @ ^ [A5: nat,B4: nat] :
% 0.33/0.66 ( produc457027306803732586at_nat @ ( E3 @ A5 )
% 0.33/0.66 @ ^ [Uu: nat] : ( F5 @ B4 ) ) )
% 0.33/0.66 @ ( produc457027306803732586at_nat @ A2
% 0.33/0.66 @ ^ [Uu: nat] : B5 ) ) )
% 0.33/0.66 = ( produc457027306803732586at_nat @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ E3 @ A2 ) )
% 0.33/0.66 @ ^ [Uu: nat] : ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ F5 @ B5 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % UN_Times_distrib
% 0.33/0.66 thf(fact_7105_mem__Times__iff,axiom,
% 0.33/0.66 ! [X: product_prod_o_o,A2: set_o,B5: set_o] :
% 0.33/0.66 ( ( member7466972457876170832od_o_o @ X
% 0.33/0.66 @ ( product_Sigma_o_o @ A2
% 0.33/0.66 @ ^ [Uu: $o] : B5 ) )
% 0.33/0.66 = ( ( member_o @ ( product_fst_o_o @ X ) @ A2 )
% 0.33/0.66 & ( member_o @ ( product_snd_o_o @ X ) @ B5 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % mem_Times_iff
% 0.33/0.66 thf(fact_7106_mem__Times__iff,axiom,
% 0.33/0.66 ! [X: product_prod_o_nat,A2: set_o,B5: set_nat] :
% 0.33/0.66 ( ( member2802428098988154798_o_nat @ X
% 0.33/0.66 @ ( product_Sigma_o_nat @ A2
% 0.33/0.66 @ ^ [Uu: $o] : B5 ) )
% 0.33/0.66 = ( ( member_o @ ( product_fst_o_nat @ X ) @ A2 )
% 0.33/0.66 & ( member_nat @ ( product_snd_o_nat @ X ) @ B5 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % mem_Times_iff
% 0.33/0.66 thf(fact_7107_mem__Times__iff,axiom,
% 0.33/0.66 ! [X: product_prod_o_int,A2: set_o,B5: set_int] :
% 0.33/0.66 ( ( member7847949116333733898_o_int @ X
% 0.33/0.66 @ ( product_Sigma_o_int @ A2
% 0.33/0.66 @ ^ [Uu: $o] : B5 ) )
% 0.33/0.66 = ( ( member_o @ ( product_fst_o_int @ X ) @ A2 )
% 0.33/0.66 & ( member_int @ ( product_snd_o_int @ X ) @ B5 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % mem_Times_iff
% 0.33/0.66 thf(fact_7108_mem__Times__iff,axiom,
% 0.33/0.66 ! [X: product_prod_nat_o,A2: set_nat,B5: set_o] :
% 0.33/0.66 ( ( member6310962623043647828_nat_o @ X
% 0.33/0.66 @ ( product_Sigma_nat_o @ A2
% 0.33/0.66 @ ^ [Uu: nat] : B5 ) )
% 0.33/0.66 = ( ( member_nat @ ( product_fst_nat_o @ X ) @ A2 )
% 0.33/0.66 & ( member_o @ ( product_snd_nat_o @ X ) @ B5 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % mem_Times_iff
% 0.33/0.66 thf(fact_7109_mem__Times__iff,axiom,
% 0.33/0.66 ! [X: product_prod_nat_int,A2: set_nat,B5: set_int] :
% 0.33/0.66 ( ( member4262671552274231302at_int @ X
% 0.33/0.66 @ ( produc454536836294682310at_int @ A2
% 0.33/0.66 @ ^ [Uu: nat] : B5 ) )
% 0.33/0.66 = ( ( member_nat @ ( product_fst_nat_int @ X ) @ A2 )
% 0.33/0.66 & ( member_int @ ( product_snd_nat_int @ X ) @ B5 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % mem_Times_iff
% 0.33/0.66 thf(fact_7110_mem__Times__iff,axiom,
% 0.33/0.66 ! [X: product_prod_int_o,A2: set_int,B5: set_o] :
% 0.33/0.66 ( ( member4489920277610959864_int_o @ X
% 0.33/0.66 @ ( product_Sigma_int_o @ A2
% 0.33/0.66 @ ^ [Uu: int] : B5 ) )
% 0.33/0.66 = ( ( member_int @ ( product_fst_int_o @ X ) @ A2 )
% 0.33/0.66 & ( member_o @ ( product_snd_int_o @ X ) @ B5 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % mem_Times_iff
% 0.33/0.66 thf(fact_7111_mem__Times__iff,axiom,
% 0.33/0.66 ! [X: product_prod_int_nat,A2: set_int,B5: set_nat] :
% 0.33/0.66 ( ( member216504246829706758nt_nat @ X
% 0.33/0.66 @ ( produc1456381018704787142nt_nat @ A2
% 0.33/0.66 @ ^ [Uu: int] : B5 ) )
% 0.33/0.66 = ( ( member_int @ ( product_fst_int_nat @ X ) @ A2 )
% 0.33/0.66 & ( member_nat @ ( product_snd_int_nat @ X ) @ B5 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % mem_Times_iff
% 0.33/0.66 thf(fact_7112_mem__Times__iff,axiom,
% 0.33/0.66 ! [X: product_prod_nat_nat,A2: set_nat,B5: set_nat] :
% 0.33/0.66 ( ( member8440522571783428010at_nat @ X
% 0.33/0.66 @ ( produc457027306803732586at_nat @ A2
% 0.33/0.66 @ ^ [Uu: nat] : B5 ) )
% 0.33/0.66 = ( ( member_nat @ ( product_fst_nat_nat @ X ) @ A2 )
% 0.33/0.66 & ( member_nat @ ( product_snd_nat_nat @ X ) @ B5 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % mem_Times_iff
% 0.33/0.66 thf(fact_7113_mem__Times__iff,axiom,
% 0.33/0.66 ! [X: produc8923325533196201883nteger,A2: set_Code_integer,B5: set_Code_integer] :
% 0.33/0.66 ( ( member157494554546826820nteger @ X
% 0.33/0.66 @ ( produc5882431272649516420nteger @ A2
% 0.33/0.66 @ ^ [Uu: code_integer] : B5 ) )
% 0.33/0.66 = ( ( member_Code_integer @ ( produc8508995932063986495nteger @ X ) @ A2 )
% 0.33/0.66 & ( member_Code_integer @ ( produc6174133586879617921nteger @ X ) @ B5 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % mem_Times_iff
% 0.33/0.66 thf(fact_7114_mem__Times__iff,axiom,
% 0.33/0.66 ! [X: product_prod_int_int,A2: set_int,B5: set_int] :
% 0.33/0.66 ( ( member5262025264175285858nt_int @ X
% 0.33/0.66 @ ( produc1453890548195736866nt_int @ A2
% 0.33/0.66 @ ^ [Uu: int] : B5 ) )
% 0.33/0.66 = ( ( member_int @ ( product_fst_int_int @ X ) @ A2 )
% 0.33/0.66 & ( member_int @ ( product_snd_int_int @ X ) @ B5 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % mem_Times_iff
% 0.33/0.66 thf(fact_7115_in__prod__fst__sndI,axiom,
% 0.33/0.66 ! [X: product_prod_o_o,A2: set_o,B5: set_o] :
% 0.33/0.66 ( ( member_o @ ( product_fst_o_o @ X ) @ A2 )
% 0.33/0.66 => ( ( member_o @ ( product_snd_o_o @ X ) @ B5 )
% 0.33/0.66 => ( member7466972457876170832od_o_o @ X
% 0.33/0.66 @ ( product_Sigma_o_o @ A2
% 0.33/0.66 @ ^ [Uu: $o] : B5 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % in_prod_fst_sndI
% 0.33/0.66 thf(fact_7116_in__prod__fst__sndI,axiom,
% 0.33/0.66 ! [X: product_prod_o_nat,A2: set_o,B5: set_nat] :
% 0.33/0.66 ( ( member_o @ ( product_fst_o_nat @ X ) @ A2 )
% 0.33/0.66 => ( ( member_nat @ ( product_snd_o_nat @ X ) @ B5 )
% 0.33/0.66 => ( member2802428098988154798_o_nat @ X
% 0.33/0.66 @ ( product_Sigma_o_nat @ A2
% 0.33/0.66 @ ^ [Uu: $o] : B5 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % in_prod_fst_sndI
% 0.33/0.66 thf(fact_7117_in__prod__fst__sndI,axiom,
% 0.33/0.66 ! [X: product_prod_o_int,A2: set_o,B5: set_int] :
% 0.33/0.66 ( ( member_o @ ( product_fst_o_int @ X ) @ A2 )
% 0.33/0.66 => ( ( member_int @ ( product_snd_o_int @ X ) @ B5 )
% 0.33/0.66 => ( member7847949116333733898_o_int @ X
% 0.33/0.66 @ ( product_Sigma_o_int @ A2
% 0.33/0.66 @ ^ [Uu: $o] : B5 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % in_prod_fst_sndI
% 0.33/0.66 thf(fact_7118_in__prod__fst__sndI,axiom,
% 0.33/0.66 ! [X: product_prod_nat_o,A2: set_nat,B5: set_o] :
% 0.33/0.66 ( ( member_nat @ ( product_fst_nat_o @ X ) @ A2 )
% 0.33/0.66 => ( ( member_o @ ( product_snd_nat_o @ X ) @ B5 )
% 0.33/0.66 => ( member6310962623043647828_nat_o @ X
% 0.33/0.66 @ ( product_Sigma_nat_o @ A2
% 0.33/0.66 @ ^ [Uu: nat] : B5 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % in_prod_fst_sndI
% 0.33/0.66 thf(fact_7119_in__prod__fst__sndI,axiom,
% 0.33/0.66 ! [X: product_prod_nat_nat,A2: set_nat,B5: set_nat] :
% 0.33/0.66 ( ( member_nat @ ( product_fst_nat_nat @ X ) @ A2 )
% 0.33/0.66 => ( ( member_nat @ ( product_snd_nat_nat @ X ) @ B5 )
% 0.33/0.66 => ( member8440522571783428010at_nat @ X
% 0.33/0.66 @ ( produc457027306803732586at_nat @ A2
% 0.33/0.66 @ ^ [Uu: nat] : B5 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % in_prod_fst_sndI
% 0.33/0.66 thf(fact_7120_in__prod__fst__sndI,axiom,
% 0.33/0.66 ! [X: product_prod_nat_int,A2: set_nat,B5: set_int] :
% 0.33/0.66 ( ( member_nat @ ( product_fst_nat_int @ X ) @ A2 )
% 0.33/0.66 => ( ( member_int @ ( product_snd_nat_int @ X ) @ B5 )
% 0.33/0.66 => ( member4262671552274231302at_int @ X
% 0.33/0.66 @ ( produc454536836294682310at_int @ A2
% 0.33/0.66 @ ^ [Uu: nat] : B5 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % in_prod_fst_sndI
% 0.33/0.66 thf(fact_7121_in__prod__fst__sndI,axiom,
% 0.33/0.66 ! [X: product_prod_int_o,A2: set_int,B5: set_o] :
% 0.33/0.66 ( ( member_int @ ( product_fst_int_o @ X ) @ A2 )
% 0.33/0.66 => ( ( member_o @ ( product_snd_int_o @ X ) @ B5 )
% 0.33/0.66 => ( member4489920277610959864_int_o @ X
% 0.33/0.66 @ ( product_Sigma_int_o @ A2
% 0.33/0.66 @ ^ [Uu: int] : B5 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % in_prod_fst_sndI
% 0.33/0.66 thf(fact_7122_in__prod__fst__sndI,axiom,
% 0.33/0.66 ! [X: product_prod_int_nat,A2: set_int,B5: set_nat] :
% 0.33/0.66 ( ( member_int @ ( product_fst_int_nat @ X ) @ A2 )
% 0.33/0.66 => ( ( member_nat @ ( product_snd_int_nat @ X ) @ B5 )
% 0.33/0.66 => ( member216504246829706758nt_nat @ X
% 0.33/0.66 @ ( produc1456381018704787142nt_nat @ A2
% 0.33/0.66 @ ^ [Uu: int] : B5 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % in_prod_fst_sndI
% 0.33/0.66 thf(fact_7123_in__prod__fst__sndI,axiom,
% 0.33/0.66 ! [X: produc8923325533196201883nteger,A2: set_Code_integer,B5: set_Code_integer] :
% 0.33/0.66 ( ( member_Code_integer @ ( produc8508995932063986495nteger @ X ) @ A2 )
% 0.33/0.66 => ( ( member_Code_integer @ ( produc6174133586879617921nteger @ X ) @ B5 )
% 0.33/0.66 => ( member157494554546826820nteger @ X
% 0.33/0.66 @ ( produc5882431272649516420nteger @ A2
% 0.33/0.66 @ ^ [Uu: code_integer] : B5 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % in_prod_fst_sndI
% 0.33/0.66 thf(fact_7124_in__prod__fst__sndI,axiom,
% 0.33/0.66 ! [X: product_prod_int_int,A2: set_int,B5: set_int] :
% 0.33/0.66 ( ( member_int @ ( product_fst_int_int @ X ) @ A2 )
% 0.33/0.66 => ( ( member_int @ ( product_snd_int_int @ X ) @ B5 )
% 0.33/0.66 => ( member5262025264175285858nt_int @ X
% 0.33/0.66 @ ( produc1453890548195736866nt_int @ A2
% 0.33/0.66 @ ^ [Uu: int] : B5 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % in_prod_fst_sndI
% 0.33/0.66 thf(fact_7125_swap__product,axiom,
% 0.33/0.66 ! [A2: set_Pr4811707699266497531nteger,B5: set_Pr7604974323444597168e_term] :
% 0.33/0.66 ( ( image_8159590125932948193nteger
% 0.33/0.66 @ ( produc5068368601420144385nteger
% 0.33/0.66 @ ^ [I3: produc8923325533196201883nteger,J2: produc6241069584506657477e_term > option6357759511663192854e_term] : ( produc8603105652947943368nteger @ J2 @ I3 ) )
% 0.33/0.66 @ ( produc552098293437506509e_term @ A2
% 0.33/0.66 @ ^ [Uu: produc8923325533196201883nteger] : B5 ) )
% 0.33/0.66 = ( produc7256824055837167575nteger @ B5
% 0.33/0.66 @ ^ [Uu: produc6241069584506657477e_term > option6357759511663192854e_term] : A2 ) ) ).
% 0.33/0.66
% 0.33/0.66 % swap_product
% 0.33/0.66 thf(fact_7126_swap__product,axiom,
% 0.33/0.66 ! [A2: set_Pr3948176798113811640et_nat,B5: set_Pr4532377907799695533_nat_o] :
% 0.33/0.66 ( ( image_4501728140019976901et_nat
% 0.33/0.66 @ ( produc5206072795621629085et_nat
% 0.33/0.66 @ ^ [I3: produc3658429121746597890et_nat,J2: produc3658429121746597890et_nat > $o] : ( produc5001842942810119800et_nat @ J2 @ I3 ) )
% 0.33/0.66 @ ( produc5879417536264718849_nat_o @ A2
% 0.33/0.66 @ ^ [Uu: produc3658429121746597890et_nat] : B5 ) )
% 0.33/0.66 = ( produc8052021730408606599et_nat @ B5
% 0.33/0.66 @ ^ [Uu: produc3658429121746597890et_nat > $o] : A2 ) ) ).
% 0.33/0.66
% 0.33/0.66 % swap_product
% 0.33/0.66 thf(fact_7127_swap__product,axiom,
% 0.33/0.66 ! [A2: set_Pr3286484037609594932et_nat,B5: set_Pr4532377907799695533_nat_o] :
% 0.33/0.66 ( ( image_7255662321850427333et_nat
% 0.33/0.66 @ ( produc9203276081649983901et_nat
% 0.33/0.66 @ ^ [I3: produc3925858234332021118et_nat,J2: produc3658429121746597890et_nat > $o] : ( produc2245416461498447860et_nat @ J2 @ I3 ) )
% 0.33/0.66 @ ( produc8445815324708537221_nat_o @ A2
% 0.33/0.66 @ ^ [Uu: produc3925858234332021118et_nat] : B5 ) )
% 0.33/0.66 = ( produc7016705354093686019et_nat @ B5
% 0.33/0.66 @ ^ [Uu: produc3658429121746597890et_nat > $o] : A2 ) ) ).
% 0.33/0.66
% 0.33/0.66 % swap_product
% 0.33/0.66 thf(fact_7128_swap__product,axiom,
% 0.33/0.66 ! [A2: set_Pr958786334691620121nt_int,B5: set_Pr3642885161833720865e_term] :
% 0.33/0.66 ( ( image_1640129903684976221nt_int
% 0.33/0.66 @ ( produc199769199162113789nt_int
% 0.33/0.66 @ ^ [I3: product_prod_int_int,J2: produc8551481072490612790e_term > option6357759511663192854e_term] : ( produc5700946648718959541nt_int @ J2 @ I3 ) )
% 0.33/0.66 @ ( produc5327145186146221532e_term @ A2
% 0.33/0.66 @ ^ [Uu: product_prod_int_int] : B5 ) )
% 0.33/0.66 = ( produc5808185664642557892nt_int @ B5
% 0.33/0.66 @ ^ [Uu: produc8551481072490612790e_term > option6357759511663192854e_term] : A2 ) ) ).
% 0.33/0.66
% 0.33/0.66 % swap_product
% 0.33/0.66 thf(fact_7129_swap__product,axiom,
% 0.33/0.66 ! [A2: set_Pr958786334691620121nt_int,B5: set_in3461395444621081367e_term] :
% 0.33/0.66 ( ( image_1292712855239066845nt_int
% 0.33/0.66 @ ( produc3478612561300218621nt_int
% 0.33/0.66 @ ^ [I3: product_prod_int_int,J2: int > option6357759511663192854e_term] : ( produc4305682042979456191nt_int @ J2 @ I3 ) )
% 0.33/0.66 @ ( produc4529769248912663762e_term @ A2
% 0.33/0.66 @ ^ [Uu: product_prod_int_int] : B5 ) )
% 0.33/0.66 = ( produc1318478031590598990nt_int @ B5
% 0.33/0.66 @ ^ [Uu: int > option6357759511663192854e_term] : A2 ) ) ).
% 0.33/0.66
% 0.33/0.66 % swap_product
% 0.33/0.66 thf(fact_7130_swap__product,axiom,
% 0.33/0.66 ! [A2: set_int,B5: set_int] :
% 0.33/0.66 ( ( image_2653370878348428101nt_int
% 0.33/0.66 @ ( produc4245557441103728435nt_int
% 0.33/0.66 @ ^ [I3: int,J2: int] : ( product_Pair_int_int @ J2 @ I3 ) )
% 0.33/0.66 @ ( produc1453890548195736866nt_int @ A2
% 0.33/0.66 @ ^ [Uu: int] : B5 ) )
% 0.33/0.66 = ( produc1453890548195736866nt_int @ B5
% 0.33/0.66 @ ^ [Uu: int] : A2 ) ) ).
% 0.33/0.66
% 0.33/0.66 % swap_product
% 0.33/0.66 thf(fact_7131_Sigma__empty__iff,axiom,
% 0.33/0.66 ! [I4: set_se7855581050983116737at_nat,X11: set_Pr1261947904930325089at_nat > set_se7855581050983116737at_nat] :
% 0.33/0.66 ( ( ( produc7726050920695093128at_nat @ I4 @ X11 )
% 0.33/0.66 = bot_bo228742789529271731at_nat )
% 0.33/0.66 = ( ! [X3: set_Pr1261947904930325089at_nat] :
% 0.33/0.66 ( ( member2643936169264416010at_nat @ X3 @ I4 )
% 0.33/0.66 => ( ( X11 @ X3 )
% 0.33/0.66 = bot_bo3083307316010499117at_nat ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % Sigma_empty_iff
% 0.33/0.66 thf(fact_7132_Sigma__empty__iff,axiom,
% 0.33/0.66 ! [I4: set_nat,X11: nat > set_nat] :
% 0.33/0.66 ( ( ( produc457027306803732586at_nat @ I4 @ X11 )
% 0.33/0.66 = bot_bo2099793752762293965at_nat )
% 0.33/0.66 = ( ! [X3: nat] :
% 0.33/0.66 ( ( member_nat @ X3 @ I4 )
% 0.33/0.66 => ( ( X11 @ X3 )
% 0.33/0.66 = bot_bot_set_nat ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % Sigma_empty_iff
% 0.33/0.66 thf(fact_7133_gcd__mult__unit2,axiom,
% 0.33/0.66 ! [A: nat,B: nat,C: nat] :
% 0.33/0.66 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.33/0.66 => ( ( gcd_gcd_nat @ B @ ( times_times_nat @ C @ A ) )
% 0.33/0.66 = ( gcd_gcd_nat @ B @ C ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % gcd_mult_unit2
% 0.33/0.66 thf(fact_7134_gcd__mult__unit2,axiom,
% 0.33/0.66 ! [A: int,B: int,C: int] :
% 0.33/0.66 ( ( dvd_dvd_int @ A @ one_one_int )
% 0.33/0.66 => ( ( gcd_gcd_int @ B @ ( times_times_int @ C @ A ) )
% 0.33/0.66 = ( gcd_gcd_int @ B @ C ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % gcd_mult_unit2
% 0.33/0.66 thf(fact_7135_gcd__mult__unit1,axiom,
% 0.33/0.66 ! [A: nat,B: nat,C: nat] :
% 0.33/0.66 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.33/0.66 => ( ( gcd_gcd_nat @ ( times_times_nat @ B @ A ) @ C )
% 0.33/0.66 = ( gcd_gcd_nat @ B @ C ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % gcd_mult_unit1
% 0.33/0.66 thf(fact_7136_gcd__mult__unit1,axiom,
% 0.33/0.66 ! [A: int,B: int,C: int] :
% 0.33/0.66 ( ( dvd_dvd_int @ A @ one_one_int )
% 0.33/0.66 => ( ( gcd_gcd_int @ ( times_times_int @ B @ A ) @ C )
% 0.33/0.66 = ( gcd_gcd_int @ B @ C ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % gcd_mult_unit1
% 0.33/0.66 thf(fact_7137_gcd__div__unit1,axiom,
% 0.33/0.66 ! [A: int,B: int,C: int] :
% 0.33/0.66 ( ( dvd_dvd_int @ A @ one_one_int )
% 0.33/0.66 => ( ( gcd_gcd_int @ ( divide_divide_int @ B @ A ) @ C )
% 0.33/0.66 = ( gcd_gcd_int @ B @ C ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % gcd_div_unit1
% 0.33/0.66 thf(fact_7138_gcd__div__unit1,axiom,
% 0.33/0.66 ! [A: nat,B: nat,C: nat] :
% 0.33/0.66 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.33/0.66 => ( ( gcd_gcd_nat @ ( divide_divide_nat @ B @ A ) @ C )
% 0.33/0.66 = ( gcd_gcd_nat @ B @ C ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % gcd_div_unit1
% 0.33/0.66 thf(fact_7139_gcd__div__unit2,axiom,
% 0.33/0.66 ! [A: int,B: int,C: int] :
% 0.33/0.66 ( ( dvd_dvd_int @ A @ one_one_int )
% 0.33/0.66 => ( ( gcd_gcd_int @ B @ ( divide_divide_int @ C @ A ) )
% 0.33/0.66 = ( gcd_gcd_int @ B @ C ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % gcd_div_unit2
% 0.33/0.66 thf(fact_7140_gcd__div__unit2,axiom,
% 0.33/0.66 ! [A: nat,B: nat,C: nat] :
% 0.33/0.66 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.33/0.66 => ( ( gcd_gcd_nat @ B @ ( divide_divide_nat @ C @ A ) )
% 0.33/0.66 = ( gcd_gcd_nat @ B @ C ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % gcd_div_unit2
% 0.33/0.66 thf(fact_7141_less__int_Otransfer,axiom,
% 0.33/0.66 ( bNF_re717283939379294677_int_o @ pcr_int
% 0.33/0.66 @ ( bNF_re6644619430987730960nt_o_o @ pcr_int
% 0.33/0.66 @ ^ [Y4: $o,Z2: $o] : ( Y4 = Z2 ) )
% 0.33/0.66 @ ( produc8739625826339149834_nat_o
% 0.33/0.66 @ ^ [X3: nat,Y3: nat] :
% 0.33/0.66 ( produc6081775807080527818_nat_o
% 0.33/0.66 @ ^ [U2: nat,V2: nat] : ( ord_less_nat @ ( plus_plus_nat @ X3 @ V2 ) @ ( plus_plus_nat @ U2 @ Y3 ) ) ) )
% 0.33/0.66 @ ord_less_int ) ).
% 0.33/0.66
% 0.33/0.66 % less_int.transfer
% 0.33/0.66 thf(fact_7142_less__eq__int_Otransfer,axiom,
% 0.33/0.66 ( bNF_re717283939379294677_int_o @ pcr_int
% 0.33/0.66 @ ( bNF_re6644619430987730960nt_o_o @ pcr_int
% 0.33/0.66 @ ^ [Y4: $o,Z2: $o] : ( Y4 = Z2 ) )
% 0.33/0.66 @ ( produc8739625826339149834_nat_o
% 0.33/0.66 @ ^ [X3: nat,Y3: nat] :
% 0.33/0.66 ( produc6081775807080527818_nat_o
% 0.33/0.66 @ ^ [U2: nat,V2: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X3 @ V2 ) @ ( plus_plus_nat @ U2 @ Y3 ) ) ) )
% 0.33/0.66 @ ord_less_eq_int ) ).
% 0.33/0.66
% 0.33/0.66 % less_eq_int.transfer
% 0.33/0.66 thf(fact_7143_plus__int_Otransfer,axiom,
% 0.33/0.66 ( bNF_re7408651293131936558nt_int @ pcr_int @ ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int )
% 0.33/0.66 @ ( produc27273713700761075at_nat
% 0.33/0.66 @ ^ [X3: nat,Y3: nat] :
% 0.33/0.66 ( produc2626176000494625587at_nat
% 0.33/0.66 @ ^ [U2: nat,V2: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X3 @ U2 ) @ ( plus_plus_nat @ Y3 @ V2 ) ) ) )
% 0.33/0.66 @ plus_plus_int ) ).
% 0.33/0.66
% 0.33/0.66 % plus_int.transfer
% 0.33/0.66 thf(fact_7144_minus__int_Otransfer,axiom,
% 0.33/0.66 ( bNF_re7408651293131936558nt_int @ pcr_int @ ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int )
% 0.33/0.66 @ ( produc27273713700761075at_nat
% 0.33/0.66 @ ^ [X3: nat,Y3: nat] :
% 0.33/0.66 ( produc2626176000494625587at_nat
% 0.33/0.66 @ ^ [U2: nat,V2: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X3 @ V2 ) @ ( plus_plus_nat @ Y3 @ U2 ) ) ) )
% 0.33/0.66 @ minus_minus_int ) ).
% 0.33/0.66
% 0.33/0.66 % minus_int.transfer
% 0.33/0.66 thf(fact_7145_times__subset__iff,axiom,
% 0.33/0.66 ! [A2: set_o,C4: set_o,B5: set_o,D3: set_o] :
% 0.33/0.66 ( ( ord_le192195778054999463od_o_o
% 0.33/0.66 @ ( product_Sigma_o_o @ A2
% 0.33/0.66 @ ^ [Uu: $o] : C4 )
% 0.33/0.66 @ ( product_Sigma_o_o @ B5
% 0.33/0.66 @ ^ [Uu: $o] : D3 ) )
% 0.33/0.66 = ( ( A2 = bot_bot_set_o )
% 0.33/0.66 | ( C4 = bot_bot_set_o )
% 0.33/0.66 | ( ( ord_less_eq_set_o @ A2 @ B5 )
% 0.33/0.66 & ( ord_less_eq_set_o @ C4 @ D3 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % times_subset_iff
% 0.33/0.66 thf(fact_7146_times__subset__iff,axiom,
% 0.33/0.66 ! [A2: set_o,C4: set_int,B5: set_o,D3: set_int] :
% 0.33/0.66 ( ( ord_le3982295392052344841_o_int
% 0.33/0.66 @ ( product_Sigma_o_int @ A2
% 0.33/0.66 @ ^ [Uu: $o] : C4 )
% 0.33/0.66 @ ( product_Sigma_o_int @ B5
% 0.33/0.66 @ ^ [Uu: $o] : D3 ) )
% 0.33/0.66 = ( ( A2 = bot_bot_set_o )
% 0.33/0.66 | ( C4 = bot_bot_set_int )
% 0.33/0.66 | ( ( ord_less_eq_set_o @ A2 @ B5 )
% 0.33/0.66 & ( ord_less_eq_set_int @ C4 @ D3 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % times_subset_iff
% 0.33/0.66 thf(fact_7147_times__subset__iff,axiom,
% 0.33/0.66 ! [A2: set_int,C4: set_o,B5: set_int,D3: set_o] :
% 0.33/0.66 ( ( ord_le5274836691491929335_int_o
% 0.33/0.66 @ ( product_Sigma_int_o @ A2
% 0.33/0.66 @ ^ [Uu: int] : C4 )
% 0.33/0.66 @ ( product_Sigma_int_o @ B5
% 0.33/0.66 @ ^ [Uu: int] : D3 ) )
% 0.33/0.66 = ( ( A2 = bot_bot_set_int )
% 0.33/0.66 | ( C4 = bot_bot_set_o )
% 0.33/0.66 | ( ( ord_less_eq_set_int @ A2 @ B5 )
% 0.33/0.66 & ( ord_less_eq_set_o @ C4 @ D3 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % times_subset_iff
% 0.33/0.66 thf(fact_7148_times__subset__iff,axiom,
% 0.33/0.66 ! [A2: set_int,C4: set_int,B5: set_int,D3: set_int] :
% 0.33/0.66 ( ( ord_le2843351958646193337nt_int
% 0.33/0.66 @ ( produc1453890548195736866nt_int @ A2
% 0.33/0.66 @ ^ [Uu: int] : C4 )
% 0.33/0.66 @ ( produc1453890548195736866nt_int @ B5
% 0.33/0.66 @ ^ [Uu: int] : D3 ) )
% 0.33/0.66 = ( ( A2 = bot_bot_set_int )
% 0.33/0.66 | ( C4 = bot_bot_set_int )
% 0.33/0.66 | ( ( ord_less_eq_set_int @ A2 @ B5 )
% 0.33/0.66 & ( ord_less_eq_set_int @ C4 @ D3 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % times_subset_iff
% 0.33/0.66 thf(fact_7149_times__subset__iff,axiom,
% 0.33/0.66 ! [A2: set_o,C4: set_nat,B5: set_o,D3: set_nat] :
% 0.33/0.66 ( ( ord_le6472378536984071597_o_nat
% 0.33/0.66 @ ( product_Sigma_o_nat @ A2
% 0.33/0.66 @ ^ [Uu: $o] : C4 )
% 0.33/0.66 @ ( product_Sigma_o_nat @ B5
% 0.33/0.66 @ ^ [Uu: $o] : D3 ) )
% 0.33/0.66 = ( ( A2 = bot_bot_set_o )
% 0.33/0.66 | ( C4 = bot_bot_set_nat )
% 0.33/0.66 | ( ( ord_less_eq_set_o @ A2 @ B5 )
% 0.33/0.66 & ( ord_less_eq_set_nat @ C4 @ D3 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % times_subset_iff
% 0.33/0.66 thf(fact_7150_times__subset__iff,axiom,
% 0.33/0.66 ! [A2: set_int,C4: set_nat,B5: set_int,D3: set_nat] :
% 0.33/0.66 ( ( ord_le5333435103577920093nt_nat
% 0.33/0.66 @ ( produc1456381018704787142nt_nat @ A2
% 0.33/0.66 @ ^ [Uu: int] : C4 )
% 0.33/0.66 @ ( produc1456381018704787142nt_nat @ B5
% 0.33/0.66 @ ^ [Uu: int] : D3 ) )
% 0.33/0.66 = ( ( A2 = bot_bot_set_int )
% 0.33/0.66 | ( C4 = bot_bot_set_nat )
% 0.33/0.66 | ( ( ord_less_eq_set_int @ A2 @ B5 )
% 0.33/0.66 & ( ord_less_eq_set_nat @ C4 @ D3 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % times_subset_iff
% 0.33/0.66 thf(fact_7151_times__subset__iff,axiom,
% 0.33/0.66 ! [A2: set_nat,C4: set_o,B5: set_nat,D3: set_o] :
% 0.33/0.66 ( ( ord_le7519981659162375251_nat_o
% 0.33/0.66 @ ( product_Sigma_nat_o @ A2
% 0.33/0.66 @ ^ [Uu: nat] : C4 )
% 0.33/0.66 @ ( product_Sigma_nat_o @ B5
% 0.33/0.66 @ ^ [Uu: nat] : D3 ) )
% 0.33/0.66 = ( ( A2 = bot_bot_set_nat )
% 0.33/0.66 | ( C4 = bot_bot_set_o )
% 0.33/0.66 | ( ( ord_less_eq_set_nat @ A2 @ B5 )
% 0.33/0.66 & ( ord_less_eq_set_o @ C4 @ D3 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % times_subset_iff
% 0.33/0.66 thf(fact_7152_times__subset__iff,axiom,
% 0.33/0.66 ! [A2: set_nat,C4: set_int,B5: set_nat,D3: set_int] :
% 0.33/0.66 ( ( ord_le656430383953171549at_int
% 0.33/0.66 @ ( produc454536836294682310at_int @ A2
% 0.33/0.66 @ ^ [Uu: nat] : C4 )
% 0.33/0.66 @ ( produc454536836294682310at_int @ B5
% 0.33/0.66 @ ^ [Uu: nat] : D3 ) )
% 0.33/0.66 = ( ( A2 = bot_bot_set_nat )
% 0.33/0.66 | ( C4 = bot_bot_set_int )
% 0.33/0.66 | ( ( ord_less_eq_set_nat @ A2 @ B5 )
% 0.33/0.66 & ( ord_less_eq_set_int @ C4 @ D3 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % times_subset_iff
% 0.33/0.66 thf(fact_7153_times__subset__iff,axiom,
% 0.33/0.66 ! [A2: set_nat,C4: set_nat,B5: set_nat,D3: set_nat] :
% 0.33/0.66 ( ( ord_le3146513528884898305at_nat
% 0.33/0.66 @ ( produc457027306803732586at_nat @ A2
% 0.33/0.66 @ ^ [Uu: nat] : C4 )
% 0.33/0.66 @ ( produc457027306803732586at_nat @ B5
% 0.33/0.66 @ ^ [Uu: nat] : D3 ) )
% 0.33/0.66 = ( ( A2 = bot_bot_set_nat )
% 0.33/0.66 | ( C4 = bot_bot_set_nat )
% 0.33/0.66 | ( ( ord_less_eq_set_nat @ A2 @ B5 )
% 0.33/0.66 & ( ord_less_eq_set_nat @ C4 @ D3 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % times_subset_iff
% 0.33/0.66 thf(fact_7154_times__subset__iff,axiom,
% 0.33/0.66 ! [A2: set_Pr1261947904930325089at_nat,C4: set_o,B5: set_Pr1261947904930325089at_nat,D3: set_o] :
% 0.33/0.66 ( ( ord_le5919393503700438654_nat_o
% 0.33/0.66 @ ( produc203973861852599583_nat_o @ A2
% 0.33/0.66 @ ^ [Uu: product_prod_nat_nat] : C4 )
% 0.33/0.66 @ ( produc203973861852599583_nat_o @ B5
% 0.33/0.66 @ ^ [Uu: product_prod_nat_nat] : D3 ) )
% 0.33/0.66 = ( ( A2 = bot_bo2099793752762293965at_nat )
% 0.33/0.66 | ( C4 = bot_bot_set_o )
% 0.33/0.66 | ( ( ord_le3146513528884898305at_nat @ A2 @ B5 )
% 0.33/0.66 & ( ord_less_eq_set_o @ C4 @ D3 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % times_subset_iff
% 0.33/0.66 thf(fact_7155_image__paired__Times,axiom,
% 0.33/0.66 ! [F: nat > code_integer,G: nat > code_integer,A2: set_nat,B5: set_nat] :
% 0.33/0.66 ( ( image_5669961043262023647nteger
% 0.33/0.66 @ ( produc39701218431283661nteger
% 0.33/0.66 @ ^ [X3: nat,Y3: nat] : ( produc1086072967326762835nteger @ ( F @ X3 ) @ ( G @ Y3 ) ) )
% 0.33/0.66 @ ( produc457027306803732586at_nat @ A2
% 0.33/0.66 @ ^ [Uu: nat] : B5 ) )
% 0.33/0.66 = ( produc5882431272649516420nteger @ ( image_1215581382706833972nteger @ F @ A2 )
% 0.33/0.66 @ ^ [Uu: code_integer] : ( image_1215581382706833972nteger @ G @ B5 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % image_paired_Times
% 0.33/0.66 thf(fact_7156_image__paired__Times,axiom,
% 0.33/0.66 ! [F: nat > code_integer,G: nat > nat,A2: set_nat,B5: set_nat] :
% 0.33/0.66 ( ( image_1372510298004463058er_nat
% 0.33/0.66 @ ( produc4146132627719282624er_nat
% 0.33/0.66 @ ^ [X3: nat,Y3: nat] : ( produc8807591364040884934er_nat @ ( F @ X3 ) @ ( G @ Y3 ) ) )
% 0.33/0.66 @ ( produc457027306803732586at_nat @ A2
% 0.33/0.66 @ ^ [Uu: nat] : B5 ) )
% 0.33/0.66 = ( produc4260658192689636599er_nat @ ( image_1215581382706833972nteger @ F @ A2 )
% 0.33/0.66 @ ^ [Uu: code_integer] : ( image_nat_nat @ G @ B5 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % image_paired_Times
% 0.33/0.66 thf(fact_7157_image__paired__Times,axiom,
% 0.33/0.66 ! [F: nat > code_integer,G: nat > int,A2: set_nat,B5: set_nat] :
% 0.33/0.66 ( ( image_6418031315350042158er_int
% 0.33/0.66 @ ( produc9191653645064861724er_int
% 0.33/0.66 @ ^ [X3: nat,Y3: nat] : ( produc8805100893531834658er_int @ ( F @ X3 ) @ ( G @ Y3 ) ) )
% 0.33/0.66 @ ( produc457027306803732586at_nat @ A2
% 0.33/0.66 @ ^ [Uu: nat] : B5 ) )
% 0.33/0.66 = ( produc4258167722180586323er_int @ ( image_1215581382706833972nteger @ F @ A2 )
% 0.33/0.66 @ ^ [Uu: code_integer] : ( image_nat_int @ G @ B5 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % image_paired_Times
% 0.33/0.66 thf(fact_7158_image__paired__Times,axiom,
% 0.33/0.66 ! [F: nat > code_integer,G: int > int,A2: set_nat,B5: set_int] :
% 0.33/0.66 ( ( image_202211252889950930er_int
% 0.33/0.66 @ ( produc1728318271963197120er_int
% 0.33/0.66 @ ^ [X3: nat,Y3: int] : ( produc8805100893531834658er_int @ ( F @ X3 ) @ ( G @ Y3 ) ) )
% 0.33/0.66 @ ( produc454536836294682310at_int @ A2
% 0.33/0.66 @ ^ [Uu: nat] : B5 ) )
% 0.33/0.66 = ( produc4258167722180586323er_int @ ( image_1215581382706833972nteger @ F @ A2 )
% 0.33/0.66 @ ^ [Uu: code_integer] : ( image_int_int @ G @ B5 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % image_paired_Times
% 0.33/0.66 thf(fact_7159_image__paired__Times,axiom,
% 0.33/0.66 ! [F: nat > nat,G: nat > code_integer,A2: set_nat,B5: set_nat] :
% 0.33/0.66 ( ( image_6753550540357478226nteger
% 0.33/0.66 @ ( produc303800833217521984nteger
% 0.33/0.66 @ ^ [X3: nat,Y3: nat] : ( produc9072146812819927750nteger @ ( F @ X3 ) @ ( G @ Y3 ) ) )
% 0.33/0.66 @ ( produc457027306803732586at_nat @ A2
% 0.33/0.66 @ ^ [Uu: nat] : B5 ) )
% 0.33/0.66 = ( produc4525213641468679415nteger @ ( image_nat_nat @ F @ A2 )
% 0.33/0.66 @ ^ [Uu: nat] : ( image_1215581382706833972nteger @ G @ B5 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % image_paired_Times
% 0.33/0.66 thf(fact_7160_image__paired__Times,axiom,
% 0.33/0.66 ! [F: nat > nat,G: nat > nat,A2: set_nat,B5: set_nat] :
% 0.33/0.66 ( ( image_5168914502847457605at_nat
% 0.33/0.66 @ ( produc2626176000494625587at_nat
% 0.33/0.66 @ ^ [X3: nat,Y3: nat] : ( product_Pair_nat_nat @ ( F @ X3 ) @ ( G @ Y3 ) ) )
% 0.33/0.66 @ ( produc457027306803732586at_nat @ A2
% 0.33/0.66 @ ^ [Uu: nat] : B5 ) )
% 0.33/0.66 = ( produc457027306803732586at_nat @ ( image_nat_nat @ F @ A2 )
% 0.33/0.66 @ ^ [Uu: nat] : ( image_nat_nat @ G @ B5 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % image_paired_Times
% 0.33/0.66 thf(fact_7161_image__paired__Times,axiom,
% 0.33/0.66 ! [F: nat > nat,G: nat > int,A2: set_nat,B5: set_nat] :
% 0.33/0.66 ( ( image_991063483338260897at_int
% 0.33/0.66 @ ( produc7671697017840204687at_int
% 0.33/0.66 @ ^ [X3: nat,Y3: nat] : ( product_Pair_nat_int @ ( F @ X3 ) @ ( G @ Y3 ) ) )
% 0.33/0.66 @ ( produc457027306803732586at_nat @ A2
% 0.33/0.66 @ ^ [Uu: nat] : B5 ) )
% 0.33/0.66 = ( produc454536836294682310at_int @ ( image_nat_nat @ F @ A2 )
% 0.33/0.66 @ ^ [Uu: nat] : ( image_nat_int @ G @ B5 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % image_paired_Times
% 0.33/0.66 thf(fact_7162_image__paired__Times,axiom,
% 0.33/0.66 ! [F: nat > nat,G: int > int,A2: set_nat,B5: set_int] :
% 0.33/0.66 ( ( image_9117352539549038149at_int
% 0.33/0.66 @ ( produc1486167065449562675at_int
% 0.33/0.66 @ ^ [X3: nat,Y3: int] : ( product_Pair_nat_int @ ( F @ X3 ) @ ( G @ Y3 ) ) )
% 0.33/0.66 @ ( produc454536836294682310at_int @ A2
% 0.33/0.66 @ ^ [Uu: nat] : B5 ) )
% 0.33/0.66 = ( produc454536836294682310at_int @ ( image_nat_nat @ F @ A2 )
% 0.33/0.66 @ ^ [Uu: nat] : ( image_int_int @ G @ B5 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % image_paired_Times
% 0.33/0.66 thf(fact_7163_image__paired__Times,axiom,
% 0.33/0.66 ! [F: nat > int,G: nat > code_integer,A2: set_nat,B5: set_nat] :
% 0.33/0.66 ( ( image_7125204100594322862nteger
% 0.33/0.66 @ ( produc675454393454366620nteger
% 0.33/0.66 @ ^ [X3: nat,Y3: nat] : ( produc220428336201996578nteger @ ( F @ X3 ) @ ( G @ Y3 ) ) )
% 0.33/0.66 @ ( produc457027306803732586at_nat @ A2
% 0.33/0.66 @ ^ [Uu: nat] : B5 ) )
% 0.33/0.66 = ( produc4896867201705524051nteger @ ( image_nat_int @ F @ A2 )
% 0.33/0.66 @ ^ [Uu: int] : ( image_1215581382706833972nteger @ G @ B5 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % image_paired_Times
% 0.33/0.66 thf(fact_7164_image__paired__Times,axiom,
% 0.33/0.66 ! [F: nat > int,G: nat > nat,A2: set_nat,B5: set_nat] :
% 0.33/0.66 ( ( image_6168268214748512161nt_nat
% 0.33/0.66 @ ( produc3625529712395680143nt_nat
% 0.33/0.66 @ ^ [X3: nat,Y3: nat] : ( product_Pair_int_nat @ ( F @ X3 ) @ ( G @ Y3 ) ) )
% 0.33/0.66 @ ( produc457027306803732586at_nat @ A2
% 0.33/0.66 @ ^ [Uu: nat] : B5 ) )
% 0.33/0.66 = ( produc1456381018704787142nt_nat @ ( image_nat_int @ F @ A2 )
% 0.33/0.66 @ ^ [Uu: int] : ( image_nat_nat @ G @ B5 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % image_paired_Times
% 0.33/0.66 thf(fact_7165_fst__image__Sigma,axiom,
% 0.33/0.66 ! [A2: set_Code_integer,B5: code_integer > set_Code_integer] :
% 0.33/0.66 ( ( image_6316824473203919795nteger @ produc8508995932063986495nteger @ ( produc5882431272649516420nteger @ A2 @ B5 ) )
% 0.33/0.66 = ( collect_Code_integer
% 0.33/0.66 @ ^ [X3: code_integer] :
% 0.33/0.66 ( ( member_Code_integer @ X3 @ A2 )
% 0.33/0.66 & ( ( B5 @ X3 )
% 0.33/0.66 != bot_bo3990330152332043303nteger ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % fst_image_Sigma
% 0.33/0.66 thf(fact_7166_fst__image__Sigma,axiom,
% 0.33/0.66 ! [A2: set_o,B5: $o > set_o] :
% 0.33/0.66 ( ( image_7896445794123959606_o_o_o @ product_fst_o_o @ ( product_Sigma_o_o @ A2 @ B5 ) )
% 0.33/0.66 = ( collect_o
% 0.33/0.66 @ ^ [X3: $o] :
% 0.33/0.66 ( ( member_o @ X3 @ A2 )
% 0.33/0.66 & ( ( B5 @ X3 )
% 0.33/0.66 != bot_bot_set_o ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % fst_image_Sigma
% 0.33/0.66 thf(fact_7167_fst__image__Sigma,axiom,
% 0.33/0.66 ! [A2: set_int,B5: int > set_o] :
% 0.33/0.66 ( ( image_90517134139374612_o_int @ product_fst_int_o @ ( product_Sigma_int_o @ A2 @ B5 ) )
% 0.33/0.66 = ( collect_int
% 0.33/0.66 @ ^ [X3: int] :
% 0.33/0.66 ( ( member_int @ X3 @ A2 )
% 0.33/0.66 & ( ( B5 @ X3 )
% 0.33/0.66 != bot_bot_set_o ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % fst_image_Sigma
% 0.33/0.66 thf(fact_7168_fst__image__Sigma,axiom,
% 0.33/0.66 ! [A2: set_nat,B5: nat > set_o] :
% 0.33/0.66 ( ( image_8629803608462650132_o_nat @ product_fst_nat_o @ ( product_Sigma_nat_o @ A2 @ B5 ) )
% 0.33/0.66 = ( collect_nat
% 0.33/0.66 @ ^ [X3: nat] :
% 0.33/0.66 ( ( member_nat @ X3 @ A2 )
% 0.33/0.66 & ( ( B5 @ X3 )
% 0.33/0.66 != bot_bot_set_o ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % fst_image_Sigma
% 0.33/0.66 thf(fact_7169_fst__image__Sigma,axiom,
% 0.33/0.66 ! [A2: set_o,B5: $o > set_nat] :
% 0.33/0.66 ( ( image_8105710389281276538_nat_o @ product_fst_o_nat @ ( product_Sigma_o_nat @ A2 @ B5 ) )
% 0.33/0.66 = ( collect_o
% 0.33/0.66 @ ^ [X3: $o] :
% 0.33/0.66 ( ( member_o @ X3 @ A2 )
% 0.33/0.66 & ( ( B5 @ X3 )
% 0.33/0.66 != bot_bot_set_nat ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % fst_image_Sigma
% 0.33/0.66 thf(fact_7170_fst__image__Sigma,axiom,
% 0.33/0.66 ! [A2: set_int,B5: int > set_nat] :
% 0.33/0.66 ( ( image_2855239504505064772at_int @ product_fst_int_nat @ ( produc1456381018704787142nt_nat @ A2 @ B5 ) )
% 0.33/0.66 = ( collect_int
% 0.33/0.66 @ ^ [X3: int] :
% 0.33/0.66 ( ( member_int @ X3 @ A2 )
% 0.33/0.66 & ( ( B5 @ X3 )
% 0.33/0.66 != bot_bot_set_nat ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % fst_image_Sigma
% 0.33/0.66 thf(fact_7171_fst__image__Sigma,axiom,
% 0.33/0.66 ! [A2: set_nat,B5: nat > set_nat] :
% 0.33/0.66 ( ( image_2486076414777270412at_nat @ product_fst_nat_nat @ ( produc457027306803732586at_nat @ A2 @ B5 ) )
% 0.33/0.66 = ( collect_nat
% 0.33/0.66 @ ^ [X3: nat] :
% 0.33/0.66 ( ( member_nat @ X3 @ A2 )
% 0.33/0.66 & ( ( B5 @ X3 )
% 0.33/0.66 != bot_bot_set_nat ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % fst_image_Sigma
% 0.33/0.66 thf(fact_7172_fst__image__Sigma,axiom,
% 0.33/0.66 ! [A2: set_o,B5: $o > set_int] :
% 0.33/0.66 ( ( image_5860565421610830622_int_o @ product_fst_o_int @ ( product_Sigma_o_int @ A2 @ B5 ) )
% 0.33/0.66 = ( collect_o
% 0.33/0.66 @ ^ [X3: $o] :
% 0.33/0.66 ( ( member_o @ X3 @ A2 )
% 0.33/0.66 & ( ( B5 @ X3 )
% 0.33/0.66 != bot_bot_set_int ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % fst_image_Sigma
% 0.33/0.66 thf(fact_7173_fst__image__Sigma,axiom,
% 0.33/0.66 ! [A2: set_nat,B5: nat > set_int] :
% 0.33/0.66 ( ( image_4672997989470292200nt_nat @ product_fst_nat_int @ ( produc454536836294682310at_int @ A2 @ B5 ) )
% 0.33/0.66 = ( collect_nat
% 0.33/0.66 @ ^ [X3: nat] :
% 0.33/0.66 ( ( member_nat @ X3 @ A2 )
% 0.33/0.66 & ( ( B5 @ X3 )
% 0.33/0.66 != bot_bot_set_int ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % fst_image_Sigma
% 0.33/0.66 thf(fact_7174_fst__image__Sigma,axiom,
% 0.33/0.66 ! [A2: set_int,B5: int > set_int] :
% 0.33/0.66 ( ( image_5042161079198086560nt_int @ product_fst_int_int @ ( produc1453890548195736866nt_int @ A2 @ B5 ) )
% 0.33/0.66 = ( collect_int
% 0.33/0.66 @ ^ [X3: int] :
% 0.33/0.66 ( ( member_int @ X3 @ A2 )
% 0.33/0.66 & ( ( B5 @ X3 )
% 0.33/0.66 != bot_bot_set_int ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % fst_image_Sigma
% 0.33/0.66 thf(fact_7175_Sigma__def,axiom,
% 0.33/0.66 ( produc7256824055837167575nteger
% 0.33/0.66 = ( ^ [A7: set_Pr7604974323444597168e_term,B8: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > set_Pr4811707699266497531nteger] :
% 0.33/0.66 ( comple1324685164916153887nteger
% 0.33/0.66 @ ( image_3218922492622835021nteger
% 0.33/0.66 @ ^ [X3: produc6241069584506657477e_term > option6357759511663192854e_term] :
% 0.33/0.66 ( comple1324685164916153887nteger
% 0.33/0.66 @ ( image_5715966689554962722nteger
% 0.33/0.66 @ ^ [Y3: produc8923325533196201883nteger] : ( insert4245756632806152262nteger @ ( produc8603105652947943368nteger @ X3 @ Y3 ) @ bot_bo5443222936135328352nteger )
% 0.33/0.66 @ ( B8 @ X3 ) ) )
% 0.33/0.66 @ A7 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % Sigma_def
% 0.33/0.66 thf(fact_7176_Sigma__def,axiom,
% 0.33/0.66 ( produc8052021730408606599et_nat
% 0.33/0.66 = ( ^ [A7: set_Pr4532377907799695533_nat_o,B8: ( produc3658429121746597890et_nat > $o ) > set_Pr3948176798113811640et_nat] :
% 0.33/0.66 ( comple4849024849677941639et_nat
% 0.33/0.66 @ ( image_1916054815030244540et_nat
% 0.33/0.66 @ ^ [X3: produc3658429121746597890et_nat > $o] :
% 0.33/0.66 ( comple4849024849677941639et_nat
% 0.33/0.66 @ ( image_15228131989405757et_nat
% 0.33/0.66 @ ^ [Y3: produc3658429121746597890et_nat] : ( insert3111075074545270702et_nat @ ( produc5001842942810119800et_nat @ X3 @ Y3 ) @ bot_bo1481135142794719944et_nat )
% 0.33/0.66 @ ( B8 @ X3 ) ) )
% 0.33/0.66 @ A7 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % Sigma_def
% 0.33/0.66 thf(fact_7177_Sigma__def,axiom,
% 0.33/0.66 ( produc7016705354093686019et_nat
% 0.33/0.66 = ( ^ [A7: set_Pr4532377907799695533_nat_o,B8: ( produc3658429121746597890et_nat > $o ) > set_Pr3286484037609594932et_nat] :
% 0.33/0.66 ( comple5063570841203093763et_nat
% 0.33/0.66 @ ( image_4127253568139551288et_nat
% 0.33/0.66 @ ^ [X3: produc3658429121746597890et_nat > $o] :
% 0.33/0.66 ( comple5063570841203093763et_nat
% 0.33/0.66 @ ( image_8189767104526903093et_nat
% 0.33/0.66 @ ^ [Y3: produc3925858234332021118et_nat] : ( insert8297122186708525866et_nat @ ( produc2245416461498447860et_nat @ X3 @ Y3 ) @ bot_bo5635537948650799172et_nat )
% 0.33/0.66 @ ( B8 @ X3 ) ) )
% 0.33/0.66 @ A7 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % Sigma_def
% 0.33/0.66 thf(fact_7178_Sigma__def,axiom,
% 0.33/0.66 ( produc5808185664642557892nt_int
% 0.33/0.66 = ( ^ [A7: set_Pr3642885161833720865e_term,B8: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > set_Pr958786334691620121nt_int] :
% 0.33/0.66 ( comple6871990601243273356nt_int
% 0.33/0.66 @ ( image_5111841350319496619nt_int
% 0.33/0.66 @ ^ [X3: produc8551481072490612790e_term > option6357759511663192854e_term] :
% 0.33/0.66 ( comple6871990601243273356nt_int
% 0.33/0.66 @ ( image_815654828163180973nt_int
% 0.33/0.66 @ ^ [Y3: product_prod_int_int] : ( insert984290209421517107nt_int @ ( produc5700946648718959541nt_int @ X3 @ Y3 ) @ bot_bo572930865798478029nt_int )
% 0.33/0.66 @ ( B8 @ X3 ) ) )
% 0.33/0.66 @ A7 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % Sigma_def
% 0.33/0.66 thf(fact_7179_Sigma__def,axiom,
% 0.33/0.66 ( produc1318478031590598990nt_int
% 0.33/0.66 = ( ^ [A7: set_in3461395444621081367e_term,B8: ( int > option6357759511663192854e_term ) > set_Pr958786334691620121nt_int] :
% 0.33/0.66 ( comple5772984051336441366nt_int
% 0.33/0.66 @ ( image_7708985414016646955nt_int
% 0.33/0.66 @ ^ [X3: int > option6357759511663192854e_term] :
% 0.33/0.66 ( comple5772984051336441366nt_int
% 0.33/0.66 @ ( image_5963362749323609783nt_int
% 0.33/0.66 @ ^ [Y3: product_prod_int_int] : ( insert750232675644355261nt_int @ ( produc4305682042979456191nt_int @ X3 @ Y3 ) @ bot_bo4508923176915781079nt_int )
% 0.33/0.66 @ ( B8 @ X3 ) ) )
% 0.33/0.66 @ A7 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % Sigma_def
% 0.33/0.66 thf(fact_7180_Sigma__def,axiom,
% 0.33/0.66 ( produc7726050920695093128at_nat
% 0.33/0.66 = ( ^ [A7: set_se7855581050983116737at_nat,B8: set_Pr1261947904930325089at_nat > set_se7855581050983116737at_nat] :
% 0.33/0.66 ( comple4364388969068068532at_nat
% 0.33/0.66 @ ( image_6898982319499645995at_nat
% 0.33/0.66 @ ^ [X3: set_Pr1261947904930325089at_nat] :
% 0.33/0.66 ( comple4364388969068068532at_nat
% 0.33/0.66 @ ( image_6898982319499645995at_nat
% 0.33/0.66 @ ^ [Y3: set_Pr1261947904930325089at_nat] : ( insert9069300056098147895at_nat @ ( produc2922128104949294807at_nat @ X3 @ Y3 ) @ bot_bo228742789529271731at_nat )
% 0.33/0.66 @ ( B8 @ X3 ) ) )
% 0.33/0.66 @ A7 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % Sigma_def
% 0.33/0.66 thf(fact_7181_Sigma__def,axiom,
% 0.33/0.66 ( produc457027306803732586at_nat
% 0.33/0.66 = ( ^ [A7: set_nat,B8: nat > set_nat] :
% 0.33/0.66 ( comple5685304695842803022at_nat
% 0.33/0.66 @ ( image_7178329752028323786at_nat
% 0.33/0.66 @ ^ [X3: nat] :
% 0.33/0.66 ( comple5685304695842803022at_nat
% 0.33/0.66 @ ( image_7178329752028323786at_nat
% 0.33/0.66 @ ^ [Y3: nat] : ( insert8211810215607154385at_nat @ ( product_Pair_nat_nat @ X3 @ Y3 ) @ bot_bo2099793752762293965at_nat )
% 0.33/0.66 @ ( B8 @ X3 ) ) )
% 0.33/0.66 @ A7 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % Sigma_def
% 0.33/0.66 thf(fact_7182_times__int_Otransfer,axiom,
% 0.33/0.66 ( bNF_re7408651293131936558nt_int @ pcr_int @ ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int )
% 0.33/0.66 @ ( produc27273713700761075at_nat
% 0.33/0.66 @ ^ [X3: nat,Y3: nat] :
% 0.33/0.66 ( produc2626176000494625587at_nat
% 0.33/0.66 @ ^ [U2: nat,V2: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X3 @ U2 ) @ ( times_times_nat @ Y3 @ V2 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X3 @ V2 ) @ ( times_times_nat @ Y3 @ U2 ) ) ) ) )
% 0.33/0.66 @ times_times_int ) ).
% 0.33/0.66
% 0.33/0.66 % times_int.transfer
% 0.33/0.66 thf(fact_7183_num__of__integer_Orsp,axiom,
% 0.33/0.66 ( bNF_re7626690874201225453um_num
% 0.33/0.66 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.66 @ ^ [Y4: num,Z2: num] : ( Y4 = Z2 )
% 0.33/0.66 @ ( comp_nat_num_int @ num_of_nat @ nat2 )
% 0.33/0.66 @ ( comp_nat_num_int @ num_of_nat @ nat2 ) ) ).
% 0.33/0.66
% 0.33/0.66 % num_of_integer.rsp
% 0.33/0.66 thf(fact_7184_snd__image__Sigma,axiom,
% 0.33/0.66 ! [A2: set_Code_integer,B5: code_integer > set_Code_integer] :
% 0.33/0.66 ( ( image_6316824473203919795nteger @ produc6174133586879617921nteger @ ( produc5882431272649516420nteger @ A2 @ B5 ) )
% 0.33/0.66 = ( comple739944243200306918nteger @ ( image_2291390168754192375nteger @ B5 @ A2 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % snd_image_Sigma
% 0.33/0.66 thf(fact_7185_snd__image__Sigma,axiom,
% 0.33/0.66 ! [A2: set_int,B5: int > set_int] :
% 0.33/0.66 ( ( image_5042161079198086560nt_int @ product_snd_int_int @ ( produc1453890548195736866nt_int @ A2 @ B5 ) )
% 0.33/0.66 = ( comple3221217463730067765et_int @ ( image_int_set_int @ B5 @ A2 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % snd_image_Sigma
% 0.33/0.66 thf(fact_7186_snd__image__Sigma,axiom,
% 0.33/0.66 ! [A2: set_Code_natural,B5: code_natural > set_Pr7564037697178849041atural] :
% 0.33/0.66 ( ( image_3837677093542026988atural @ produc6591912806276919810atural @ ( produc6231535905537262655atural @ A2 @ B5 ) )
% 0.33/0.66 = ( comple4956303571586142718atural @ ( image_3530315724569248802atural @ B5 @ A2 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % snd_image_Sigma
% 0.33/0.66 thf(fact_7187_snd__image__Sigma,axiom,
% 0.33/0.66 ! [A2: set_nat,B5: nat > set_nat] :
% 0.33/0.66 ( ( image_2486076414777270412at_nat @ product_snd_nat_nat @ ( produc457027306803732586at_nat @ A2 @ B5 ) )
% 0.33/0.66 = ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ B5 @ A2 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % snd_image_Sigma
% 0.33/0.66 thf(fact_7188_subset__fst__snd,axiom,
% 0.33/0.66 ! [A2: set_Pr4811707699266497531nteger] :
% 0.33/0.66 ( ord_le3725938330318615451nteger @ A2
% 0.33/0.66 @ ( produc5882431272649516420nteger @ ( image_6316824473203919795nteger @ produc8508995932063986495nteger @ A2 )
% 0.33/0.66 @ ^ [Uu: code_integer] : ( image_6316824473203919795nteger @ produc6174133586879617921nteger @ A2 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % subset_fst_snd
% 0.33/0.66 thf(fact_7189_subset__fst__snd,axiom,
% 0.33/0.66 ! [A2: set_Pr958786334691620121nt_int] :
% 0.33/0.66 ( ord_le2843351958646193337nt_int @ A2
% 0.33/0.66 @ ( produc1453890548195736866nt_int @ ( image_5042161079198086560nt_int @ product_fst_int_int @ A2 )
% 0.33/0.66 @ ^ [Uu: int] : ( image_5042161079198086560nt_int @ product_snd_int_int @ A2 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % subset_fst_snd
% 0.33/0.66 thf(fact_7190_subset__fst__snd,axiom,
% 0.33/0.66 ! [A2: set_Pr2352657477744078772atural] :
% 0.33/0.66 ( ord_le2202040463148982292atural @ A2
% 0.33/0.66 @ ( produc6231535905537262655atural @ ( image_8194678751871465133atural @ produc497848011034438852atural @ A2 )
% 0.33/0.66 @ ^ [Uu: code_natural] : ( image_3837677093542026988atural @ produc6591912806276919810atural @ A2 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % subset_fst_snd
% 0.33/0.66 thf(fact_7191_int__transfer,axiom,
% 0.33/0.66 ( bNF_re6830278522597306478at_int
% 0.33/0.66 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.66 @ pcr_int
% 0.33/0.66 @ ^ [N4: nat] : ( product_Pair_nat_nat @ N4 @ zero_zero_nat )
% 0.33/0.66 @ semiri1314217659103216013at_int ) ).
% 0.33/0.66
% 0.33/0.66 % int_transfer
% 0.33/0.66 thf(fact_7192_uminus__int_Otransfer,axiom,
% 0.33/0.66 ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int
% 0.33/0.66 @ ( produc2626176000494625587at_nat
% 0.33/0.66 @ ^ [X3: nat,Y3: nat] : ( product_Pair_nat_nat @ Y3 @ X3 ) )
% 0.33/0.66 @ uminus_uminus_int ) ).
% 0.33/0.66
% 0.33/0.66 % uminus_int.transfer
% 0.33/0.66 thf(fact_7193_eq__fst__iff,axiom,
% 0.33/0.66 ! [A: produc6241069584506657477e_term > option6357759511663192854e_term,P4: produc1908205239877642774nteger] :
% 0.33/0.66 ( ( A
% 0.33/0.66 = ( produc7822682618958472924nteger @ P4 ) )
% 0.33/0.66 = ( ? [B4: produc8923325533196201883nteger] :
% 0.33/0.66 ( P4
% 0.33/0.66 = ( produc8603105652947943368nteger @ A @ B4 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % eq_fst_iff
% 0.33/0.66 thf(fact_7194_eq__fst__iff,axiom,
% 0.33/0.66 ! [A: produc3658429121746597890et_nat > $o,P4: produc3925858234332021118et_nat] :
% 0.33/0.66 ( ( A
% 0.33/0.66 = ( produc995936583742144908et_nat @ P4 ) )
% 0.33/0.66 = ( ? [B4: produc3658429121746597890et_nat] :
% 0.33/0.66 ( P4
% 0.33/0.66 = ( produc5001842942810119800et_nat @ A @ B4 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % eq_fst_iff
% 0.33/0.66 thf(fact_7195_eq__fst__iff,axiom,
% 0.33/0.66 ! [A: produc3658429121746597890et_nat > $o,P4: produc2732055786443039994et_nat] :
% 0.33/0.66 ( ( A
% 0.33/0.66 = ( produc180342877477747464et_nat @ P4 ) )
% 0.33/0.66 = ( ? [B4: produc3925858234332021118et_nat] :
% 0.33/0.66 ( P4
% 0.33/0.66 = ( produc2245416461498447860et_nat @ A @ B4 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % eq_fst_iff
% 0.33/0.66 thf(fact_7196_eq__fst__iff,axiom,
% 0.33/0.66 ! [A: produc8551481072490612790e_term > option6357759511663192854e_term,P4: produc2285326912895808259nt_int] :
% 0.33/0.66 ( ( A
% 0.33/0.66 = ( produc6816164490631068361nt_int @ P4 ) )
% 0.33/0.66 = ( ? [B4: product_prod_int_int] :
% 0.33/0.66 ( P4
% 0.33/0.66 = ( produc5700946648718959541nt_int @ A @ B4 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % eq_fst_iff
% 0.33/0.66 thf(fact_7197_eq__fst__iff,axiom,
% 0.33/0.66 ! [A: int > option6357759511663192854e_term,P4: produc7773217078559923341nt_int] :
% 0.33/0.66 ( ( A
% 0.33/0.66 = ( produc6230002227079971283nt_int @ P4 ) )
% 0.33/0.66 = ( ? [B4: product_prod_int_int] :
% 0.33/0.66 ( P4
% 0.33/0.66 = ( produc4305682042979456191nt_int @ A @ B4 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % eq_fst_iff
% 0.33/0.66 thf(fact_7198_eq__fst__iff,axiom,
% 0.33/0.66 ! [A: code_integer,P4: produc8923325533196201883nteger] :
% 0.33/0.66 ( ( A
% 0.33/0.66 = ( produc8508995932063986495nteger @ P4 ) )
% 0.33/0.66 = ( ? [B4: code_integer] :
% 0.33/0.66 ( P4
% 0.33/0.66 = ( produc1086072967326762835nteger @ A @ B4 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % eq_fst_iff
% 0.33/0.66 thf(fact_7199_eq__fst__iff,axiom,
% 0.33/0.66 ! [A: int,P4: product_prod_int_int] :
% 0.33/0.66 ( ( A
% 0.33/0.66 = ( product_fst_int_int @ P4 ) )
% 0.33/0.66 = ( ? [B4: int] :
% 0.33/0.66 ( P4
% 0.33/0.66 = ( product_Pair_int_int @ A @ B4 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % eq_fst_iff
% 0.33/0.66 thf(fact_7200_transfer__rule__of__nat,axiom,
% 0.33/0.66 ! [R4: rat > rat > $o] :
% 0.33/0.66 ( ( R4 @ zero_zero_rat @ zero_zero_rat )
% 0.33/0.66 => ( ( R4 @ one_one_rat @ one_one_rat )
% 0.33/0.66 => ( ( bNF_re6603079268895015599at_rat @ R4 @ ( bNF_re5606270390558447553at_rat @ R4 @ R4 ) @ plus_plus_rat @ plus_plus_rat )
% 0.33/0.66 => ( bNF_re4702136315717946289at_rat
% 0.33/0.66 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.66 @ R4
% 0.33/0.66 @ semiri681578069525770553at_rat
% 0.33/0.66 @ semiri681578069525770553at_rat ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % transfer_rule_of_nat
% 0.33/0.66 thf(fact_7201_transfer__rule__of__nat,axiom,
% 0.33/0.66 ! [R4: rat > int > $o] :
% 0.33/0.66 ( ( R4 @ zero_zero_rat @ zero_zero_int )
% 0.33/0.66 => ( ( R4 @ one_one_rat @ one_one_int )
% 0.33/0.66 => ( ( bNF_re8876735282041863595nt_int @ R4 @ ( bNF_re5838490730811218025at_int @ R4 @ R4 ) @ plus_plus_rat @ plus_plus_int )
% 0.33/0.66 => ( bNF_re5334775905295391749at_int
% 0.33/0.66 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.66 @ R4
% 0.33/0.66 @ semiri681578069525770553at_rat
% 0.33/0.66 @ semiri1314217659103216013at_int ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % transfer_rule_of_nat
% 0.33/0.66 thf(fact_7202_transfer__rule__of__nat,axiom,
% 0.33/0.66 ! [R4: rat > nat > $o] :
% 0.33/0.66 ( ( R4 @ zero_zero_rat @ zero_zero_nat )
% 0.33/0.66 => ( ( R4 @ one_one_rat @ one_one_nat )
% 0.33/0.66 => ( ( bNF_re4357912360536923287at_nat @ R4 @ ( bNF_re5469327641083423665at_nat @ R4 @ R4 ) @ plus_plus_rat @ plus_plus_nat )
% 0.33/0.66 => ( bNF_re5337266375804442025at_nat
% 0.33/0.66 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.66 @ R4
% 0.33/0.66 @ semiri681578069525770553at_rat
% 0.33/0.66 @ semiri1316708129612266289at_nat ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % transfer_rule_of_nat
% 0.33/0.66 thf(fact_7203_transfer__rule__of__nat,axiom,
% 0.33/0.66 ! [R4: rat > code_integer > $o] :
% 0.33/0.66 ( ( R4 @ zero_zero_rat @ zero_z3403309356797280102nteger )
% 0.33/0.66 => ( ( R4 @ one_one_rat @ one_one_Code_integer )
% 0.33/0.66 => ( ( bNF_re4307939118855507134nteger @ R4 @ ( bNF_re2328245411608324299nteger @ R4 @ R4 ) @ plus_plus_rat @ plus_p5714425477246183910nteger )
% 0.33/0.66 => ( bNF_re4553819317763231286nteger
% 0.33/0.66 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.66 @ R4
% 0.33/0.66 @ semiri681578069525770553at_rat
% 0.33/0.66 @ semiri4939895301339042750nteger ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % transfer_rule_of_nat
% 0.33/0.66 thf(fact_7204_transfer__rule__of__nat,axiom,
% 0.33/0.66 ! [R4: rat > code_natural > $o] :
% 0.33/0.66 ( ( R4 @ zero_zero_rat @ zero_z2226904508553997617atural )
% 0.33/0.66 => ( ( R4 @ one_one_rat @ one_one_Code_natural )
% 0.33/0.66 => ( ( bNF_re6252345487650389919atural @ R4 @ ( bNF_re4433268865704509537atural @ R4 @ R4 ) @ plus_plus_rat @ plus_p4538020629002901425atural )
% 0.33/0.66 => ( bNF_re3377414469519948801atural
% 0.33/0.66 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.66 @ R4
% 0.33/0.66 @ semiri681578069525770553at_rat
% 0.33/0.66 @ semiri3763490453095760265atural ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % transfer_rule_of_nat
% 0.33/0.66 thf(fact_7205_transfer__rule__of__nat,axiom,
% 0.33/0.66 ! [R4: int > rat > $o] :
% 0.33/0.66 ( ( R4 @ zero_zero_int @ zero_zero_rat )
% 0.33/0.66 => ( ( R4 @ one_one_int @ one_one_rat )
% 0.33/0.66 => ( ( bNF_re7661208983170134443at_rat @ R4 @ ( bNF_re4480299549022435433nt_rat @ R4 @ R4 ) @ plus_plus_int @ plus_plus_rat )
% 0.33/0.66 => ( bNF_re6018044671553866757nt_rat
% 0.33/0.66 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.66 @ R4
% 0.33/0.66 @ semiri1314217659103216013at_int
% 0.33/0.66 @ semiri681578069525770553at_rat ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % transfer_rule_of_nat
% 0.33/0.66 thf(fact_7206_transfer__rule__of__nat,axiom,
% 0.33/0.66 ! [R4: int > int > $o] :
% 0.33/0.66 ( ( R4 @ zero_zero_int @ zero_zero_int )
% 0.33/0.66 => ( ( R4 @ one_one_int @ one_one_int )
% 0.33/0.66 => ( ( bNF_re711492959462206631nt_int @ R4 @ ( bNF_re4712519889275205905nt_int @ R4 @ R4 ) @ plus_plus_int @ plus_plus_int )
% 0.33/0.66 => ( bNF_re6650684261131312217nt_int
% 0.33/0.66 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.66 @ R4
% 0.33/0.66 @ semiri1314217659103216013at_int
% 0.33/0.66 @ semiri1314217659103216013at_int ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % transfer_rule_of_nat
% 0.33/0.66 thf(fact_7207_transfer__rule__of__nat,axiom,
% 0.33/0.66 ! [R4: int > nat > $o] :
% 0.33/0.66 ( ( R4 @ zero_zero_int @ zero_zero_nat )
% 0.33/0.66 => ( ( R4 @ one_one_int @ one_one_nat )
% 0.33/0.66 => ( ( bNF_re5416042074812042131at_nat @ R4 @ ( bNF_re4343356799547411545nt_nat @ R4 @ R4 ) @ plus_plus_int @ plus_plus_nat )
% 0.33/0.66 => ( bNF_re6653174731640362493nt_nat
% 0.33/0.66 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.66 @ R4
% 0.33/0.66 @ semiri1314217659103216013at_int
% 0.33/0.66 @ semiri1316708129612266289at_nat ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % transfer_rule_of_nat
% 0.33/0.66 thf(fact_7208_transfer__rule__of__nat,axiom,
% 0.33/0.66 ! [R4: int > code_integer > $o] :
% 0.33/0.66 ( ( R4 @ zero_zero_int @ zero_z3403309356797280102nteger )
% 0.33/0.66 => ( ( R4 @ one_one_int @ one_one_Code_integer )
% 0.33/0.66 => ( ( bNF_re398004352372739002nteger @ R4 @ ( bNF_re3379532845092657523nteger @ R4 @ R4 ) @ plus_plus_int @ plus_p5714425477246183910nteger )
% 0.33/0.66 => ( bNF_re4153400068438556298nteger
% 0.33/0.66 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.66 @ R4
% 0.33/0.66 @ semiri1314217659103216013at_int
% 0.33/0.66 @ semiri4939895301339042750nteger ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % transfer_rule_of_nat
% 0.33/0.66 thf(fact_7209_transfer__rule__of__nat,axiom,
% 0.33/0.66 ! [R4: int > code_natural > $o] :
% 0.33/0.66 ( ( R4 @ zero_zero_int @ zero_z2226904508553997617atural )
% 0.33/0.66 => ( ( R4 @ one_one_int @ one_one_Code_natural )
% 0.33/0.66 => ( ( bNF_re2342410721167621787atural @ R4 @ ( bNF_re5484556299188842761atural @ R4 @ R4 ) @ plus_plus_int @ plus_p4538020629002901425atural )
% 0.33/0.66 => ( bNF_re2976995220195273813atural
% 0.33/0.66 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.66 @ R4
% 0.33/0.66 @ semiri1314217659103216013at_int
% 0.33/0.66 @ semiri3763490453095760265atural ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % transfer_rule_of_nat
% 0.33/0.66 thf(fact_7210_transfer__rule__of__bool,axiom,
% 0.33/0.66 ! [R4: rat > rat > $o] :
% 0.33/0.66 ( ( R4 @ zero_zero_rat @ zero_zero_rat )
% 0.33/0.66 => ( ( R4 @ one_one_rat @ one_one_rat )
% 0.33/0.66 => ( bNF_re8824113547921424783at_rat
% 0.33/0.66 @ ^ [Y4: $o,Z2: $o] : ( Y4 = Z2 )
% 0.33/0.66 @ R4
% 0.33/0.66 @ zero_n2052037380579107095ol_rat
% 0.33/0.66 @ zero_n2052037380579107095ol_rat ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % transfer_rule_of_bool
% 0.33/0.66 thf(fact_7211_transfer__rule__of__bool,axiom,
% 0.33/0.66 ! [R4: rat > nat > $o] :
% 0.33/0.66 ( ( R4 @ zero_zero_rat @ zero_zero_nat )
% 0.33/0.66 => ( ( R4 @ one_one_rat @ one_one_nat )
% 0.33/0.66 => ( bNF_re235871571153144711at_nat
% 0.33/0.66 @ ^ [Y4: $o,Z2: $o] : ( Y4 = Z2 )
% 0.33/0.66 @ R4
% 0.33/0.66 @ zero_n2052037380579107095ol_rat
% 0.33/0.66 @ zero_n2687167440665602831ol_nat ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % transfer_rule_of_bool
% 0.33/0.66 thf(fact_7212_transfer__rule__of__bool,axiom,
% 0.33/0.66 ! [R4: rat > int > $o] :
% 0.33/0.66 ( ( R4 @ zero_zero_rat @ zero_zero_int )
% 0.33/0.66 => ( ( R4 @ one_one_rat @ one_one_int )
% 0.33/0.66 => ( bNF_re233381100644094435at_int
% 0.33/0.66 @ ^ [Y4: $o,Z2: $o] : ( Y4 = Z2 )
% 0.33/0.66 @ R4
% 0.33/0.66 @ zero_n2052037380579107095ol_rat
% 0.33/0.66 @ zero_n2684676970156552555ol_int ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % transfer_rule_of_bool
% 0.33/0.66 thf(fact_7213_transfer__rule__of__bool,axiom,
% 0.33/0.66 ! [R4: rat > code_integer > $o] :
% 0.33/0.66 ( ( R4 @ zero_zero_rat @ zero_z3403309356797280102nteger )
% 0.33/0.66 => ( ( R4 @ one_one_rat @ one_one_Code_integer )
% 0.33/0.66 => ( bNF_re5635613845597506580nteger
% 0.33/0.66 @ ^ [Y4: $o,Z2: $o] : ( Y4 = Z2 )
% 0.33/0.66 @ R4
% 0.33/0.66 @ zero_n2052037380579107095ol_rat
% 0.33/0.66 @ zero_n356916108424825756nteger ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % transfer_rule_of_bool
% 0.33/0.66 thf(fact_7214_transfer__rule__of__bool,axiom,
% 0.33/0.66 ! [R4: nat > rat > $o] :
% 0.33/0.66 ( ( R4 @ zero_zero_nat @ zero_zero_rat )
% 0.33/0.66 => ( ( R4 @ one_one_nat @ one_one_rat )
% 0.33/0.66 => ( bNF_re9140668191856290695at_rat
% 0.33/0.66 @ ^ [Y4: $o,Z2: $o] : ( Y4 = Z2 )
% 0.33/0.66 @ R4
% 0.33/0.66 @ zero_n2687167440665602831ol_nat
% 0.33/0.66 @ zero_n2052037380579107095ol_rat ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % transfer_rule_of_bool
% 0.33/0.66 thf(fact_7215_transfer__rule__of__bool,axiom,
% 0.33/0.66 ! [R4: nat > nat > $o] :
% 0.33/0.66 ( ( R4 @ zero_zero_nat @ zero_zero_nat )
% 0.33/0.66 => ( ( R4 @ one_one_nat @ one_one_nat )
% 0.33/0.66 => ( bNF_re552426215088010623at_nat
% 0.33/0.66 @ ^ [Y4: $o,Z2: $o] : ( Y4 = Z2 )
% 0.33/0.66 @ R4
% 0.33/0.66 @ zero_n2687167440665602831ol_nat
% 0.33/0.66 @ zero_n2687167440665602831ol_nat ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % transfer_rule_of_bool
% 0.33/0.66 thf(fact_7216_transfer__rule__of__bool,axiom,
% 0.33/0.66 ! [R4: nat > int > $o] :
% 0.33/0.66 ( ( R4 @ zero_zero_nat @ zero_zero_int )
% 0.33/0.66 => ( ( R4 @ one_one_nat @ one_one_int )
% 0.33/0.66 => ( bNF_re549935744578960347at_int
% 0.33/0.66 @ ^ [Y4: $o,Z2: $o] : ( Y4 = Z2 )
% 0.33/0.66 @ R4
% 0.33/0.66 @ zero_n2687167440665602831ol_nat
% 0.33/0.66 @ zero_n2684676970156552555ol_int ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % transfer_rule_of_bool
% 0.33/0.66 thf(fact_7217_transfer__rule__of__bool,axiom,
% 0.33/0.66 ! [R4: nat > code_integer > $o] :
% 0.33/0.66 ( ( R4 @ zero_zero_nat @ zero_z3403309356797280102nteger )
% 0.33/0.66 => ( ( R4 @ one_one_nat @ one_one_Code_integer )
% 0.33/0.66 => ( bNF_re4863541036035986956nteger
% 0.33/0.66 @ ^ [Y4: $o,Z2: $o] : ( Y4 = Z2 )
% 0.33/0.66 @ R4
% 0.33/0.66 @ zero_n2687167440665602831ol_nat
% 0.33/0.66 @ zero_n356916108424825756nteger ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % transfer_rule_of_bool
% 0.33/0.66 thf(fact_7218_transfer__rule__of__bool,axiom,
% 0.33/0.66 ! [R4: int > rat > $o] :
% 0.33/0.66 ( ( R4 @ zero_zero_int @ zero_zero_rat )
% 0.33/0.66 => ( ( R4 @ one_one_int @ one_one_rat )
% 0.33/0.66 => ( bNF_re916649866902569443nt_rat
% 0.33/0.66 @ ^ [Y4: $o,Z2: $o] : ( Y4 = Z2 )
% 0.33/0.66 @ R4
% 0.33/0.66 @ zero_n2684676970156552555ol_int
% 0.33/0.66 @ zero_n2052037380579107095ol_rat ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % transfer_rule_of_bool
% 0.33/0.66 thf(fact_7219_transfer__rule__of__bool,axiom,
% 0.33/0.66 ! [R4: int > nat > $o] :
% 0.33/0.66 ( ( R4 @ zero_zero_int @ zero_zero_nat )
% 0.33/0.66 => ( ( R4 @ one_one_int @ one_one_nat )
% 0.33/0.66 => ( bNF_re1551779926989065179nt_nat
% 0.33/0.66 @ ^ [Y4: $o,Z2: $o] : ( Y4 = Z2 )
% 0.33/0.66 @ R4
% 0.33/0.66 @ zero_n2684676970156552555ol_int
% 0.33/0.66 @ zero_n2687167440665602831ol_nat ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % transfer_rule_of_bool
% 0.33/0.66 thf(fact_7220_plus__rat_Otransfer,axiom,
% 0.33/0.66 ( bNF_re7627151682743391978at_rat @ pcr_rat @ ( bNF_re8279943556446156061nt_rat @ pcr_rat @ pcr_rat )
% 0.33/0.66 @ ^ [X3: product_prod_int_int,Y3: product_prod_int_int] : ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ X3 ) @ ( product_snd_int_int @ Y3 ) ) @ ( times_times_int @ ( product_fst_int_int @ Y3 ) @ ( product_snd_int_int @ X3 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ X3 ) @ ( product_snd_int_int @ Y3 ) ) )
% 0.33/0.66 @ plus_plus_rat ) ).
% 0.33/0.66
% 0.33/0.66 % plus_rat.transfer
% 0.33/0.66 thf(fact_7221_inverse__rat_Otransfer,axiom,
% 0.33/0.66 ( bNF_re8279943556446156061nt_rat @ pcr_rat @ pcr_rat
% 0.33/0.66 @ ^ [X3: product_prod_int_int] :
% 0.33/0.66 ( if_Pro3027730157355071871nt_int
% 0.33/0.66 @ ( ( product_fst_int_int @ X3 )
% 0.33/0.66 = zero_zero_int )
% 0.33/0.66 @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 0.33/0.66 @ ( product_Pair_int_int @ ( product_snd_int_int @ X3 ) @ ( product_fst_int_int @ X3 ) ) )
% 0.33/0.66 @ inverse_inverse_rat ) ).
% 0.33/0.66
% 0.33/0.66 % inverse_rat.transfer
% 0.33/0.66 thf(fact_7222_Id__on__def,axiom,
% 0.33/0.66 ( id_on_6713504163309144702at_nat
% 0.33/0.66 = ( ^ [A7: set_se7855581050983116737at_nat] :
% 0.33/0.66 ( comple4364388969068068532at_nat
% 0.33/0.66 @ ( image_6898982319499645995at_nat
% 0.33/0.66 @ ^ [X3: set_Pr1261947904930325089at_nat] : ( insert9069300056098147895at_nat @ ( produc2922128104949294807at_nat @ X3 @ X3 ) @ bot_bo228742789529271731at_nat )
% 0.33/0.66 @ A7 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % Id_on_def
% 0.33/0.66 thf(fact_7223_Id__on__def,axiom,
% 0.33/0.66 ( id_on_nat
% 0.33/0.66 = ( ^ [A7: set_nat] :
% 0.33/0.66 ( comple5685304695842803022at_nat
% 0.33/0.66 @ ( image_7178329752028323786at_nat
% 0.33/0.66 @ ^ [X3: nat] : ( insert8211810215607154385at_nat @ ( product_Pair_nat_nat @ X3 @ X3 ) @ bot_bo2099793752762293965at_nat )
% 0.33/0.66 @ A7 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % Id_on_def
% 0.33/0.66 thf(fact_7224_times__rat_Otransfer,axiom,
% 0.33/0.66 ( bNF_re7627151682743391978at_rat @ pcr_rat @ ( bNF_re8279943556446156061nt_rat @ pcr_rat @ pcr_rat )
% 0.33/0.66 @ ^ [X3: product_prod_int_int,Y3: product_prod_int_int] : ( product_Pair_int_int @ ( times_times_int @ ( product_fst_int_int @ X3 ) @ ( product_fst_int_int @ Y3 ) ) @ ( times_times_int @ ( product_snd_int_int @ X3 ) @ ( product_snd_int_int @ Y3 ) ) )
% 0.33/0.66 @ times_times_rat ) ).
% 0.33/0.66
% 0.33/0.66 % times_rat.transfer
% 0.33/0.66 thf(fact_7225_gcd__1__nat,axiom,
% 0.33/0.66 ! [M2: nat] :
% 0.33/0.66 ( ( gcd_gcd_nat @ M2 @ one_one_nat )
% 0.33/0.66 = one_one_nat ) ).
% 0.33/0.66
% 0.33/0.66 % gcd_1_nat
% 0.33/0.66 thf(fact_7226_Id__onI,axiom,
% 0.33/0.66 ! [A: set_Pr1261947904930325089at_nat,A2: set_se7855581050983116737at_nat] :
% 0.33/0.66 ( ( member2643936169264416010at_nat @ A @ A2 )
% 0.33/0.66 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ A ) @ ( id_on_6713504163309144702at_nat @ A2 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % Id_onI
% 0.33/0.66 thf(fact_7227_Id__onI,axiom,
% 0.33/0.66 ! [A: produc3843707927480180839at_nat,A2: set_Pr4329608150637261639at_nat] :
% 0.33/0.66 ( ( member8757157785044589968at_nat @ A @ A2 )
% 0.33/0.66 => ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ A @ A ) @ ( id_on_7869290023980668164at_nat @ A2 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % Id_onI
% 0.33/0.66 thf(fact_7228_Id__onI,axiom,
% 0.33/0.66 ! [A: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat] :
% 0.33/0.66 ( ( member8440522571783428010at_nat @ A @ A2 )
% 0.33/0.66 => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ A @ A ) @ ( id_on_2554058798563519774at_nat @ A2 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % Id_onI
% 0.33/0.66 thf(fact_7229_Id__onI,axiom,
% 0.33/0.66 ! [A: $o,A2: set_o] :
% 0.33/0.66 ( ( member_o @ A @ A2 )
% 0.33/0.66 => ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ A @ A ) @ ( id_on_o @ A2 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % Id_onI
% 0.33/0.66 thf(fact_7230_Id__onI,axiom,
% 0.33/0.66 ! [A: nat,A2: set_nat] :
% 0.33/0.66 ( ( member_nat @ A @ A2 )
% 0.33/0.66 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ A ) @ ( id_on_nat @ A2 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % Id_onI
% 0.33/0.66 thf(fact_7231_Id__onI,axiom,
% 0.33/0.66 ! [A: int,A2: set_int] :
% 0.33/0.66 ( ( member_int @ A @ A2 )
% 0.33/0.66 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ A ) @ ( id_on_int @ A2 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % Id_onI
% 0.33/0.66 thf(fact_7232_unset__bit__natural_Orsp,axiom,
% 0.33/0.66 ( bNF_re1345281282404953727at_nat
% 0.33/0.66 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.66 @ ( bNF_re5653821019739307937at_nat
% 0.33/0.66 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.66 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 ) )
% 0.33/0.66 @ bit_se4205575877204974255it_nat
% 0.33/0.66 @ bit_se4205575877204974255it_nat ) ).
% 0.33/0.66
% 0.33/0.66 % unset_bit_natural.rsp
% 0.33/0.66 thf(fact_7233_take__bit__natural_Orsp,axiom,
% 0.33/0.66 ( bNF_re1345281282404953727at_nat
% 0.33/0.66 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.66 @ ( bNF_re5653821019739307937at_nat
% 0.33/0.66 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.66 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 ) )
% 0.33/0.66 @ bit_se2925701944663578781it_nat
% 0.33/0.66 @ bit_se2925701944663578781it_nat ) ).
% 0.33/0.66
% 0.33/0.66 % take_bit_natural.rsp
% 0.33/0.66 thf(fact_7234_bit__natural_Orsp,axiom,
% 0.33/0.66 ( bNF_re578469030762574527_nat_o
% 0.33/0.66 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.66 @ ^ [Y4: nat > $o,Z2: nat > $o] : ( Y4 = Z2 )
% 0.33/0.66 @ bit_se1148574629649215175it_nat
% 0.33/0.66 @ bit_se1148574629649215175it_nat ) ).
% 0.33/0.66
% 0.33/0.66 % bit_natural.rsp
% 0.33/0.66 thf(fact_7235_drop__bit__natural_Orsp,axiom,
% 0.33/0.66 ( bNF_re1345281282404953727at_nat
% 0.33/0.66 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.66 @ ( bNF_re5653821019739307937at_nat
% 0.33/0.66 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.66 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 ) )
% 0.33/0.66 @ bit_se8570568707652914677it_nat
% 0.33/0.66 @ bit_se8570568707652914677it_nat ) ).
% 0.33/0.66
% 0.33/0.66 % drop_bit_natural.rsp
% 0.33/0.66 thf(fact_7236_Id__on__iff,axiom,
% 0.33/0.66 ! [X: produc3843707927480180839at_nat,Y: produc3843707927480180839at_nat,A2: set_Pr4329608150637261639at_nat] :
% 0.33/0.66 ( ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ X @ Y ) @ ( id_on_7869290023980668164at_nat @ A2 ) )
% 0.33/0.66 = ( ( X = Y )
% 0.33/0.66 & ( member8757157785044589968at_nat @ X @ A2 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % Id_on_iff
% 0.33/0.66 thf(fact_7237_Id__on__iff,axiom,
% 0.33/0.66 ! [X: product_prod_nat_nat,Y: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat] :
% 0.33/0.66 ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X @ Y ) @ ( id_on_2554058798563519774at_nat @ A2 ) )
% 0.33/0.66 = ( ( X = Y )
% 0.33/0.66 & ( member8440522571783428010at_nat @ X @ A2 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % Id_on_iff
% 0.33/0.66 thf(fact_7238_Id__on__iff,axiom,
% 0.33/0.66 ! [X: $o,Y: $o,A2: set_o] :
% 0.33/0.66 ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ X @ Y ) @ ( id_on_o @ A2 ) )
% 0.33/0.66 = ( ( X = Y )
% 0.33/0.66 & ( member_o @ X @ A2 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % Id_on_iff
% 0.33/0.66 thf(fact_7239_Id__on__iff,axiom,
% 0.33/0.66 ! [X: int,Y: int,A2: set_int] :
% 0.33/0.66 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( id_on_int @ A2 ) )
% 0.33/0.66 = ( ( X = Y )
% 0.33/0.66 & ( member_int @ X @ A2 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % Id_on_iff
% 0.33/0.66 thf(fact_7240_Id__on__iff,axiom,
% 0.33/0.66 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,A2: set_se7855581050983116737at_nat] :
% 0.33/0.66 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ ( id_on_6713504163309144702at_nat @ A2 ) )
% 0.33/0.66 = ( ( X = Y )
% 0.33/0.66 & ( member2643936169264416010at_nat @ X @ A2 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % Id_on_iff
% 0.33/0.66 thf(fact_7241_Id__on__iff,axiom,
% 0.33/0.66 ! [X: nat,Y: nat,A2: set_nat] :
% 0.33/0.66 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( id_on_nat @ A2 ) )
% 0.33/0.66 = ( ( X = Y )
% 0.33/0.66 & ( member_nat @ X @ A2 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % Id_on_iff
% 0.33/0.66 thf(fact_7242_Id__on__eqI,axiom,
% 0.33/0.66 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,A2: set_se7855581050983116737at_nat] :
% 0.33/0.66 ( ( A = B )
% 0.33/0.66 => ( ( member2643936169264416010at_nat @ A @ A2 )
% 0.33/0.66 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ B ) @ ( id_on_6713504163309144702at_nat @ A2 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % Id_on_eqI
% 0.33/0.66 thf(fact_7243_Id__on__eqI,axiom,
% 0.33/0.66 ! [A: produc3843707927480180839at_nat,B: produc3843707927480180839at_nat,A2: set_Pr4329608150637261639at_nat] :
% 0.33/0.66 ( ( A = B )
% 0.33/0.66 => ( ( member8757157785044589968at_nat @ A @ A2 )
% 0.33/0.66 => ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ A @ B ) @ ( id_on_7869290023980668164at_nat @ A2 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % Id_on_eqI
% 0.33/0.66 thf(fact_7244_Id__on__eqI,axiom,
% 0.33/0.66 ! [A: product_prod_nat_nat,B: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat] :
% 0.33/0.66 ( ( A = B )
% 0.33/0.66 => ( ( member8440522571783428010at_nat @ A @ A2 )
% 0.33/0.66 => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ A @ B ) @ ( id_on_2554058798563519774at_nat @ A2 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % Id_on_eqI
% 0.33/0.66 thf(fact_7245_Id__on__eqI,axiom,
% 0.33/0.66 ! [A: $o,B: $o,A2: set_o] :
% 0.33/0.66 ( ( A = B )
% 0.33/0.66 => ( ( member_o @ A @ A2 )
% 0.33/0.66 => ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ A @ B ) @ ( id_on_o @ A2 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % Id_on_eqI
% 0.33/0.66 thf(fact_7246_Id__on__eqI,axiom,
% 0.33/0.66 ! [A: nat,B: nat,A2: set_nat] :
% 0.33/0.66 ( ( A = B )
% 0.33/0.66 => ( ( member_nat @ A @ A2 )
% 0.33/0.66 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ ( id_on_nat @ A2 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % Id_on_eqI
% 0.33/0.66 thf(fact_7247_Id__on__eqI,axiom,
% 0.33/0.66 ! [A: int,B: int,A2: set_int] :
% 0.33/0.66 ( ( A = B )
% 0.33/0.66 => ( ( member_int @ A @ A2 )
% 0.33/0.66 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ ( id_on_int @ A2 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % Id_on_eqI
% 0.33/0.66 thf(fact_7248_Id__onE,axiom,
% 0.33/0.66 ! [C: produc1906917888121415911at_nat,A2: set_Pr4329608150637261639at_nat] :
% 0.33/0.66 ( ( member6009668390874684176at_nat @ C @ ( id_on_7869290023980668164at_nat @ A2 ) )
% 0.33/0.66 => ~ ! [X4: produc3843707927480180839at_nat] :
% 0.33/0.66 ( ( member8757157785044589968at_nat @ X4 @ A2 )
% 0.33/0.66 => ( C
% 0.33/0.66 != ( produc2335810615602371415at_nat @ X4 @ X4 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % Id_onE
% 0.33/0.66 thf(fact_7249_Id__onE,axiom,
% 0.33/0.66 ! [C: produc859450856879609959at_nat,A2: set_Pr1261947904930325089at_nat] :
% 0.33/0.66 ( ( member8206827879206165904at_nat @ C @ ( id_on_2554058798563519774at_nat @ A2 ) )
% 0.33/0.66 => ~ ! [X4: product_prod_nat_nat] :
% 0.33/0.66 ( ( member8440522571783428010at_nat @ X4 @ A2 )
% 0.33/0.66 => ( C
% 0.33/0.66 != ( produc6161850002892822231at_nat @ X4 @ X4 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % Id_onE
% 0.33/0.66 thf(fact_7250_Id__onE,axiom,
% 0.33/0.66 ! [C: product_prod_o_o,A2: set_o] :
% 0.33/0.66 ( ( member7466972457876170832od_o_o @ C @ ( id_on_o @ A2 ) )
% 0.33/0.66 => ~ ! [X4: $o] :
% 0.33/0.66 ( ( member_o @ X4 @ A2 )
% 0.33/0.66 => ( C
% 0.33/0.66 != ( product_Pair_o_o @ X4 @ X4 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % Id_onE
% 0.33/0.66 thf(fact_7251_Id__onE,axiom,
% 0.33/0.66 ! [C: product_prod_int_int,A2: set_int] :
% 0.33/0.66 ( ( member5262025264175285858nt_int @ C @ ( id_on_int @ A2 ) )
% 0.33/0.66 => ~ ! [X4: int] :
% 0.33/0.66 ( ( member_int @ X4 @ A2 )
% 0.33/0.66 => ( C
% 0.33/0.66 != ( product_Pair_int_int @ X4 @ X4 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % Id_onE
% 0.33/0.66 thf(fact_7252_Id__onE,axiom,
% 0.33/0.66 ! [C: produc3843707927480180839at_nat,A2: set_se7855581050983116737at_nat] :
% 0.33/0.66 ( ( member8757157785044589968at_nat @ C @ ( id_on_6713504163309144702at_nat @ A2 ) )
% 0.33/0.66 => ~ ! [X4: set_Pr1261947904930325089at_nat] :
% 0.33/0.66 ( ( member2643936169264416010at_nat @ X4 @ A2 )
% 0.33/0.66 => ( C
% 0.33/0.66 != ( produc2922128104949294807at_nat @ X4 @ X4 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % Id_onE
% 0.33/0.66 thf(fact_7253_Id__onE,axiom,
% 0.33/0.66 ! [C: product_prod_nat_nat,A2: set_nat] :
% 0.33/0.66 ( ( member8440522571783428010at_nat @ C @ ( id_on_nat @ A2 ) )
% 0.33/0.66 => ~ ! [X4: nat] :
% 0.33/0.66 ( ( member_nat @ X4 @ A2 )
% 0.33/0.66 => ( C
% 0.33/0.66 != ( product_Pair_nat_nat @ X4 @ X4 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % Id_onE
% 0.33/0.66 thf(fact_7254_bezout__nat,axiom,
% 0.33/0.66 ! [A: nat,B: nat] :
% 0.33/0.66 ( ( A != zero_zero_nat )
% 0.33/0.66 => ? [X4: nat,Y5: nat] :
% 0.33/0.66 ( ( times_times_nat @ A @ X4 )
% 0.33/0.66 = ( plus_plus_nat @ ( times_times_nat @ B @ Y5 ) @ ( gcd_gcd_nat @ A @ B ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % bezout_nat
% 0.33/0.66 thf(fact_7255_one__rat_Otransfer,axiom,
% 0.33/0.66 pcr_rat @ ( product_Pair_int_int @ one_one_int @ one_one_int ) @ one_one_rat ).
% 0.33/0.66
% 0.33/0.66 % one_rat.transfer
% 0.33/0.66 thf(fact_7256_zero__rat_Otransfer,axiom,
% 0.33/0.66 pcr_rat @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ zero_zero_rat ).
% 0.33/0.66
% 0.33/0.66 % zero_rat.transfer
% 0.33/0.66 thf(fact_7257_bezw__aux,axiom,
% 0.33/0.66 ! [X: nat,Y: nat] :
% 0.33/0.66 ( ( semiri1314217659103216013at_int @ ( gcd_gcd_nat @ X @ Y ) )
% 0.33/0.66 = ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ ( bezw @ X @ Y ) ) @ ( semiri1314217659103216013at_int @ X ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ X @ Y ) ) @ ( semiri1314217659103216013at_int @ Y ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % bezw_aux
% 0.33/0.66 thf(fact_7258_uminus__rat_Otransfer,axiom,
% 0.33/0.66 ( bNF_re8279943556446156061nt_rat @ pcr_rat @ pcr_rat
% 0.33/0.66 @ ^ [X3: product_prod_int_int] : ( product_Pair_int_int @ ( uminus_uminus_int @ ( product_fst_int_int @ X3 ) ) @ ( product_snd_int_int @ X3 ) )
% 0.33/0.66 @ uminus_uminus_rat ) ).
% 0.33/0.66
% 0.33/0.66 % uminus_rat.transfer
% 0.33/0.66 thf(fact_7259_gcd__nat_Opelims,axiom,
% 0.33/0.66 ! [X: nat,Xa: nat,Y: nat] :
% 0.33/0.66 ( ( ( gcd_gcd_nat @ X @ Xa )
% 0.33/0.66 = Y )
% 0.33/0.66 => ( ( accp_P4275260045618599050at_nat @ gcd_nat_rel @ ( product_Pair_nat_nat @ X @ Xa ) )
% 0.33/0.66 => ~ ( ( ( ( Xa = zero_zero_nat )
% 0.33/0.66 => ( Y = X ) )
% 0.33/0.66 & ( ( Xa != zero_zero_nat )
% 0.33/0.66 => ( Y
% 0.33/0.66 = ( gcd_gcd_nat @ Xa @ ( modulo_modulo_nat @ X @ Xa ) ) ) ) )
% 0.33/0.66 => ~ ( accp_P4275260045618599050at_nat @ gcd_nat_rel @ ( product_Pair_nat_nat @ X @ Xa ) ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % gcd_nat.pelims
% 0.33/0.66 thf(fact_7260_o__rsp_I1_J,axiom,
% 0.33/0.66 ! [R23: code_integer > code_integer > $o,R32: code_integer > code_integer > $o,R12: num > num > $o] : ( bNF_re5979881370344185769nteger @ ( bNF_re1062419521925302741nteger @ R23 @ R32 ) @ ( bNF_re6097285183634142137nteger @ ( bNF_re6741283560065411407nteger @ R12 @ R23 ) @ ( bNF_re6741283560065411407nteger @ R12 @ R32 ) ) @ comp_C3531382070062128313er_num @ comp_C3531382070062128313er_num ) ).
% 0.33/0.66
% 0.33/0.66 % o_rsp(1)
% 0.33/0.66 thf(fact_7261_o__rsp_I1_J,axiom,
% 0.33/0.66 ! [R23: code_integer > nat > $o,R32: code_integer > num > $o,R12: num > int > $o] : ( bNF_re5469402333911078061nt_num @ ( bNF_re1758498617148825349er_num @ R23 @ R32 ) @ ( bNF_re1151383970801924621nt_num @ ( bNF_re6324211044263125204er_nat @ R12 @ R23 ) @ ( bNF_re2881542830418903838er_num @ R12 @ R32 ) ) @ comp_C3531382070062128313er_num @ comp_nat_num_int ) ).
% 0.33/0.66
% 0.33/0.66 % o_rsp(1)
% 0.33/0.66 thf(fact_7262_o__rsp_I1_J,axiom,
% 0.33/0.66 ! [R23: nat > code_integer > $o,R32: num > code_integer > $o,R12: int > num > $o] : ( bNF_re2163612987331707565nteger @ ( bNF_re8763372240999575301nteger @ R23 @ R32 ) @ ( bNF_re8894579221946749965nteger @ ( bNF_re151304249936775380nteger @ R12 @ R23 ) @ ( bNF_re7315484114762210078nteger @ R12 @ R32 ) ) @ comp_nat_num_int @ comp_C3531382070062128313er_num ) ).
% 0.33/0.66
% 0.33/0.66 % o_rsp(1)
% 0.33/0.66 thf(fact_7263_o__rsp_I1_J,axiom,
% 0.33/0.66 ! [R23: nat > nat > $o,R32: num > num > $o,R12: int > int > $o] : ( bNF_re3846787885862361009nt_num @ ( bNF_re341483209202555957um_num @ R23 @ R32 ) @ ( bNF_re9099949428469764705nt_num @ ( bNF_re3715656647883201625at_nat @ R12 @ R23 ) @ ( bNF_re7626690874201225453um_num @ R12 @ R32 ) ) @ comp_nat_num_int @ comp_nat_num_int ) ).
% 0.33/0.66
% 0.33/0.66 % o_rsp(1)
% 0.33/0.66 thf(fact_7264_o__rsp_I1_J,axiom,
% 0.33/0.66 ! [R23: int > int > $o,R32: ( nat > $o ) > ( nat > $o ) > $o,R12: int > int > $o] : ( bNF_re7908124382625962333_nat_o @ ( bNF_re3376528473927230327_nat_o @ R23 @ R32 ) @ ( bNF_re6033114333830760525_nat_o @ ( bNF_re4712519889275205905nt_int @ R12 @ R23 ) @ ( bNF_re3376528473927230327_nat_o @ R12 @ R32 ) ) @ comp_int_nat_o_int @ comp_int_nat_o_int ) ).
% 0.33/0.66
% 0.33/0.66 % o_rsp(1)
% 0.33/0.66 thf(fact_7265_o__rsp_I1_J,axiom,
% 0.33/0.66 ! [R23: int > int > $o,R32: ( int > $o ) > ( int > $o ) > $o,R12: int > int > $o] : ( bNF_re1900612664124570461_int_o @ ( bNF_re3403563459893282935_int_o @ R23 @ R32 ) @ ( bNF_re3014639844587090765_int_o @ ( bNF_re4712519889275205905nt_int @ R12 @ R23 ) @ ( bNF_re3403563459893282935_int_o @ R12 @ R32 ) ) @ comp_int_int_o_int @ comp_int_int_o_int ) ).
% 0.33/0.66
% 0.33/0.66 % o_rsp(1)
% 0.33/0.66 thf(fact_7266_o__rsp_I1_J,axiom,
% 0.33/0.66 ! [R23: int > int > $o,R32: ( int > int ) > ( int > int ) > $o,R12: int > int > $o] : ( bNF_re4984751527058004117nt_int @ ( bNF_re711492959462206631nt_int @ R23 @ R32 ) @ ( bNF_re724639330072410579nt_int @ ( bNF_re4712519889275205905nt_int @ R12 @ R23 ) @ ( bNF_re711492959462206631nt_int @ R12 @ R32 ) ) @ comp_int_int_int_int @ comp_int_int_int_int ) ).
% 0.33/0.66
% 0.33/0.66 % o_rsp(1)
% 0.33/0.66 thf(fact_7267_o__rsp_I1_J,axiom,
% 0.33/0.66 ! [R23: code_integer > code_integer > $o,R32: code_integer > ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > $o,R12: num > code_integer > $o] : ( bNF_re8134695817916415679nteger @ ( bNF_re3370092614548195229nteger @ R23 @ R32 ) @ ( bNF_re2439920061672227847nteger @ ( bNF_re5202476307641864082nteger @ R12 @ R23 ) @ ( bNF_re5031869190687302234nteger @ R12 @ R32 ) ) @ comp_C3531382070062128313er_num @ comp_C1593894019821074884nteger ) ).
% 0.33/0.66
% 0.33/0.66 % o_rsp(1)
% 0.33/0.66 thf(fact_7268_o__rsp_I1_J,axiom,
% 0.33/0.66 ! [R23: code_integer > code_integer > $o,R32: ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > code_integer > $o,R12: code_integer > num > $o] : ( bNF_re4919612610145136063nteger @ ( bNF_re4341081746073172381nteger @ R23 @ R32 ) @ ( bNF_re6724329528997265415nteger @ ( bNF_re7350422212947406738nteger @ R12 @ R23 ) @ ( bNF_re166502229267952730nteger @ R12 @ R32 ) ) @ comp_C1593894019821074884nteger @ comp_C3531382070062128313er_num ) ).
% 0.33/0.66
% 0.33/0.66 % o_rsp(1)
% 0.33/0.66 thf(fact_7269_o__rsp_I1_J,axiom,
% 0.33/0.66 ! [R23: code_integer > nat > $o,R32: ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > num > $o,R12: code_integer > int > $o] : ( bNF_re1890273300020150979nt_num @ ( bNF_re7119966052990372301er_num @ R23 @ R32 ) @ ( bNF_re5190287125156074331nt_num @ ( bNF_re2891348898900095767er_nat @ R12 @ R23 ) @ ( bNF_re8127238762813979689er_num @ R12 @ R32 ) ) @ comp_C1593894019821074884nteger @ comp_nat_num_int ) ).
% 0.33/0.66
% 0.33/0.66 % o_rsp(1)
% 0.33/0.66 thf(fact_7270_o__rsp_I2_J,axiom,
% 0.33/0.66 ! [R12: num > num > $o] :
% 0.33/0.66 ( bNF_re5979881370344185769nteger
% 0.33/0.66 @ ^ [Y4: code_integer > code_integer,Z2: code_integer > code_integer] : ( Y4 = Z2 )
% 0.33/0.66 @ ( bNF_re6097285183634142137nteger
% 0.33/0.66 @ ( bNF_re6741283560065411407nteger @ R12
% 0.33/0.66 @ ^ [Y4: code_integer,Z2: code_integer] : ( Y4 = Z2 ) )
% 0.33/0.66 @ ( bNF_re6741283560065411407nteger @ R12
% 0.33/0.66 @ ^ [Y4: code_integer,Z2: code_integer] : ( Y4 = Z2 ) ) )
% 0.33/0.66 @ comp_C3531382070062128313er_num
% 0.33/0.66 @ comp_C3531382070062128313er_num ) ).
% 0.33/0.66
% 0.33/0.66 % o_rsp(2)
% 0.33/0.66 thf(fact_7271_o__rsp_I2_J,axiom,
% 0.33/0.66 ! [R12: int > int > $o] :
% 0.33/0.66 ( bNF_re3846787885862361009nt_num
% 0.33/0.66 @ ^ [Y4: nat > num,Z2: nat > num] : ( Y4 = Z2 )
% 0.33/0.66 @ ( bNF_re9099949428469764705nt_num
% 0.33/0.66 @ ( bNF_re3715656647883201625at_nat @ R12
% 0.33/0.66 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 ) )
% 0.33/0.66 @ ( bNF_re7626690874201225453um_num @ R12
% 0.33/0.66 @ ^ [Y4: num,Z2: num] : ( Y4 = Z2 ) ) )
% 0.33/0.66 @ comp_nat_num_int
% 0.33/0.66 @ comp_nat_num_int ) ).
% 0.33/0.66
% 0.33/0.66 % o_rsp(2)
% 0.33/0.66 thf(fact_7272_o__rsp_I2_J,axiom,
% 0.33/0.66 ! [R12: int > int > $o] :
% 0.33/0.66 ( bNF_re1550856938216548981_nat_o
% 0.33/0.66 @ ^ [Y4: ( nat > $o ) > nat > $o,Z2: ( nat > $o ) > nat > $o] : ( Y4 = Z2 )
% 0.33/0.66 @ ( bNF_re5673586069474677853_nat_o
% 0.33/0.66 @ ( bNF_re3376528473927230327_nat_o @ R12
% 0.33/0.66 @ ^ [Y4: nat > $o,Z2: nat > $o] : ( Y4 = Z2 ) )
% 0.33/0.66 @ ( bNF_re3376528473927230327_nat_o @ R12
% 0.33/0.66 @ ^ [Y4: nat > $o,Z2: nat > $o] : ( Y4 = Z2 ) ) )
% 0.33/0.66 @ comp_nat_o_nat_o_int
% 0.33/0.66 @ comp_nat_o_nat_o_int ) ).
% 0.33/0.66
% 0.33/0.66 % o_rsp(2)
% 0.33/0.66 thf(fact_7273_o__rsp_I2_J,axiom,
% 0.33/0.66 ! [R12: int > int > $o] :
% 0.33/0.66 ( bNF_re3491090157995142405_int_o
% 0.33/0.66 @ ^ [Y4: ( nat > $o ) > int > $o,Z2: ( nat > $o ) > int > $o] : ( Y4 = Z2 )
% 0.33/0.66 @ ( bNF_re2655111580231008093_int_o
% 0.33/0.66 @ ( bNF_re3376528473927230327_nat_o @ R12
% 0.33/0.66 @ ^ [Y4: nat > $o,Z2: nat > $o] : ( Y4 = Z2 ) )
% 0.33/0.66 @ ( bNF_re3403563459893282935_int_o @ R12
% 0.33/0.66 @ ^ [Y4: int > $o,Z2: int > $o] : ( Y4 = Z2 ) ) )
% 0.33/0.66 @ comp_nat_o_int_o_int
% 0.33/0.66 @ comp_nat_o_int_o_int ) ).
% 0.33/0.66
% 0.33/0.66 % o_rsp(2)
% 0.33/0.66 thf(fact_7274_o__rsp_I2_J,axiom,
% 0.33/0.66 ! [R12: int > int > $o] :
% 0.33/0.66 ( bNF_re5539255234643219293nt_int
% 0.33/0.66 @ ^ [Y4: ( nat > $o ) > int > int,Z2: ( nat > $o ) > int > int] : ( Y4 = Z2 )
% 0.33/0.66 @ ( bNF_re7395152722673581539nt_int
% 0.33/0.66 @ ( bNF_re3376528473927230327_nat_o @ R12
% 0.33/0.66 @ ^ [Y4: nat > $o,Z2: nat > $o] : ( Y4 = Z2 ) )
% 0.33/0.66 @ ( bNF_re711492959462206631nt_int @ R12
% 0.33/0.66 @ ^ [Y4: int > int,Z2: int > int] : ( Y4 = Z2 ) ) )
% 0.33/0.66 @ comp_n3090169619561918849nt_int
% 0.33/0.66 @ comp_n3090169619561918849nt_int ) ).
% 0.33/0.66
% 0.33/0.66 % o_rsp(2)
% 0.33/0.66 thf(fact_7275_o__rsp_I2_J,axiom,
% 0.33/0.66 ! [R12: int > int > $o] :
% 0.33/0.66 ( bNF_re615132412071444453_nat_o
% 0.33/0.66 @ ^ [Y4: ( int > $o ) > nat > $o,Z2: ( int > $o ) > nat > $o] : ( Y4 = Z2 )
% 0.33/0.66 @ ( bNF_re2446162618891206493_nat_o
% 0.33/0.66 @ ( bNF_re3403563459893282935_int_o @ R12
% 0.33/0.66 @ ^ [Y4: int > $o,Z2: int > $o] : ( Y4 = Z2 ) )
% 0.33/0.66 @ ( bNF_re3376528473927230327_nat_o @ R12
% 0.33/0.66 @ ^ [Y4: nat > $o,Z2: nat > $o] : ( Y4 = Z2 ) ) )
% 0.33/0.66 @ comp_int_o_nat_o_int
% 0.33/0.66 @ comp_int_o_nat_o_int ) ).
% 0.33/0.66
% 0.33/0.66 % o_rsp(2)
% 0.33/0.66 thf(fact_7276_o__rsp_I2_J,axiom,
% 0.33/0.66 ! [R12: int > int > $o] :
% 0.33/0.66 ( bNF_re2555365631850037877_int_o
% 0.33/0.66 @ ^ [Y4: ( int > $o ) > int > $o,Z2: ( int > $o ) > int > $o] : ( Y4 = Z2 )
% 0.33/0.66 @ ( bNF_re8651060166502312541_int_o
% 0.33/0.66 @ ( bNF_re3403563459893282935_int_o @ R12
% 0.33/0.66 @ ^ [Y4: int > $o,Z2: int > $o] : ( Y4 = Z2 ) )
% 0.33/0.66 @ ( bNF_re3403563459893282935_int_o @ R12
% 0.33/0.66 @ ^ [Y4: int > $o,Z2: int > $o] : ( Y4 = Z2 ) ) )
% 0.33/0.66 @ comp_int_o_int_o_int
% 0.33/0.66 @ comp_int_o_int_o_int ) ).
% 0.33/0.66
% 0.33/0.66 % o_rsp(2)
% 0.33/0.66 thf(fact_7277_o__rsp_I2_J,axiom,
% 0.33/0.66 ! [R12: int > int > $o] :
% 0.33/0.66 ( bNF_re5051145820034318685nt_int
% 0.33/0.66 @ ^ [Y4: ( int > $o ) > int > int,Z2: ( int > $o ) > int > int] : ( Y4 = Z2 )
% 0.33/0.66 @ ( bNF_re7462748251485907171nt_int
% 0.33/0.66 @ ( bNF_re3403563459893282935_int_o @ R12
% 0.33/0.66 @ ^ [Y4: int > $o,Z2: int > $o] : ( Y4 = Z2 ) )
% 0.33/0.66 @ ( bNF_re711492959462206631nt_int @ R12
% 0.33/0.66 @ ^ [Y4: int > int,Z2: int > int] : ( Y4 = Z2 ) ) )
% 0.33/0.66 @ comp_i1993086638917920293nt_int
% 0.33/0.66 @ comp_i1993086638917920293nt_int ) ).
% 0.33/0.66
% 0.33/0.66 % o_rsp(2)
% 0.33/0.66 thf(fact_7278_o__rsp_I2_J,axiom,
% 0.33/0.66 ! [R12: int > int > $o] :
% 0.33/0.66 ( bNF_re4659646225794970589_nat_o
% 0.33/0.66 @ ^ [Y4: ( int > int ) > nat > $o,Z2: ( int > int ) > nat > $o] : ( Y4 = Z2 )
% 0.33/0.66 @ ( bNF_re4332408551980016867_nat_o
% 0.33/0.66 @ ( bNF_re711492959462206631nt_int @ R12
% 0.33/0.66 @ ^ [Y4: int > int,Z2: int > int] : ( Y4 = Z2 ) )
% 0.33/0.66 @ ( bNF_re3376528473927230327_nat_o @ R12
% 0.33/0.66 @ ^ [Y4: nat > $o,Z2: nat > $o] : ( Y4 = Z2 ) ) )
% 0.33/0.66 @ comp_i4411980392712547921_o_int
% 0.33/0.66 @ comp_i4411980392712547921_o_int ) ).
% 0.33/0.66
% 0.33/0.66 % o_rsp(2)
% 0.33/0.66 thf(fact_7279_o__rsp_I2_J,axiom,
% 0.33/0.66 ! [R12: int > int > $o] :
% 0.33/0.66 ( bNF_re3161894838932316637_int_o
% 0.33/0.66 @ ^ [Y4: ( int > int ) > int > $o,Z2: ( int > int ) > int > $o] : ( Y4 = Z2 )
% 0.33/0.66 @ ( bNF_re1313934062736347107_int_o
% 0.33/0.66 @ ( bNF_re711492959462206631nt_int @ R12
% 0.33/0.66 @ ^ [Y4: int > int,Z2: int > int] : ( Y4 = Z2 ) )
% 0.33/0.66 @ ( bNF_re3403563459893282935_int_o @ R12
% 0.33/0.66 @ ^ [Y4: int > $o,Z2: int > $o] : ( Y4 = Z2 ) ) )
% 0.33/0.66 @ comp_i5098556425753098485_o_int
% 0.33/0.66 @ comp_i5098556425753098485_o_int ) ).
% 0.33/0.66
% 0.33/0.66 % o_rsp(2)
% 0.33/0.66 thf(fact_7280_apfst__convE,axiom,
% 0.33/0.66 ! [Q3: produc1908205239877642774nteger,F: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc6241069584506657477e_term > option6357759511663192854e_term,P4: produc1908205239877642774nteger] :
% 0.33/0.66 ( ( Q3
% 0.33/0.66 = ( produc2515316116081422825nteger @ F @ P4 ) )
% 0.33/0.66 => ~ ! [X4: produc6241069584506657477e_term > option6357759511663192854e_term,Y5: produc8923325533196201883nteger] :
% 0.33/0.66 ( ( P4
% 0.33/0.66 = ( produc8603105652947943368nteger @ X4 @ Y5 ) )
% 0.33/0.66 => ( Q3
% 0.33/0.66 != ( produc8603105652947943368nteger @ ( F @ X4 ) @ Y5 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % apfst_convE
% 0.33/0.66 thf(fact_7281_apfst__convE,axiom,
% 0.33/0.66 ! [Q3: produc3925858234332021118et_nat,F: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o,P4: produc3925858234332021118et_nat] :
% 0.33/0.66 ( ( Q3
% 0.33/0.66 = ( produc3198230245617193214et_nat @ F @ P4 ) )
% 0.33/0.66 => ~ ! [X4: produc3658429121746597890et_nat > $o,Y5: produc3658429121746597890et_nat] :
% 0.33/0.66 ( ( P4
% 0.33/0.66 = ( produc5001842942810119800et_nat @ X4 @ Y5 ) )
% 0.33/0.66 => ( Q3
% 0.33/0.66 != ( produc5001842942810119800et_nat @ ( F @ X4 ) @ Y5 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % apfst_convE
% 0.33/0.66 thf(fact_7282_apfst__convE,axiom,
% 0.33/0.66 ! [Q3: produc2732055786443039994et_nat,F: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o,P4: produc2732055786443039994et_nat] :
% 0.33/0.66 ( ( Q3
% 0.33/0.66 = ( produc1442628905706551930et_nat @ F @ P4 ) )
% 0.33/0.66 => ~ ! [X4: produc3658429121746597890et_nat > $o,Y5: produc3925858234332021118et_nat] :
% 0.33/0.66 ( ( P4
% 0.33/0.66 = ( produc2245416461498447860et_nat @ X4 @ Y5 ) )
% 0.33/0.66 => ( Q3
% 0.33/0.66 != ( produc2245416461498447860et_nat @ ( F @ X4 ) @ Y5 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % apfst_convE
% 0.33/0.66 thf(fact_7283_apfst__convE,axiom,
% 0.33/0.66 ! [Q3: produc2285326912895808259nt_int,F: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > produc8551481072490612790e_term > option6357759511663192854e_term,P4: produc2285326912895808259nt_int] :
% 0.33/0.66 ( ( Q3
% 0.33/0.66 = ( produc7277921532047535397nt_int @ F @ P4 ) )
% 0.33/0.66 => ~ ! [X4: produc8551481072490612790e_term > option6357759511663192854e_term,Y5: product_prod_int_int] :
% 0.33/0.66 ( ( P4
% 0.33/0.66 = ( produc5700946648718959541nt_int @ X4 @ Y5 ) )
% 0.33/0.66 => ( Q3
% 0.33/0.66 != ( produc5700946648718959541nt_int @ ( F @ X4 ) @ Y5 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % apfst_convE
% 0.33/0.66 thf(fact_7284_apfst__convE,axiom,
% 0.33/0.66 ! [Q3: produc7773217078559923341nt_int,F: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > int > option6357759511663192854e_term,P4: produc2285326912895808259nt_int] :
% 0.33/0.66 ( ( Q3
% 0.33/0.66 = ( produc6919319362177967663nt_int @ F @ P4 ) )
% 0.33/0.66 => ~ ! [X4: produc8551481072490612790e_term > option6357759511663192854e_term,Y5: product_prod_int_int] :
% 0.33/0.66 ( ( P4
% 0.33/0.66 = ( produc5700946648718959541nt_int @ X4 @ Y5 ) )
% 0.33/0.66 => ( Q3
% 0.33/0.66 != ( produc4305682042979456191nt_int @ ( F @ X4 ) @ Y5 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % apfst_convE
% 0.33/0.66 thf(fact_7285_apfst__convE,axiom,
% 0.33/0.66 ! [Q3: produc2285326912895808259nt_int,F: ( int > option6357759511663192854e_term ) > produc8551481072490612790e_term > option6357759511663192854e_term,P4: produc7773217078559923341nt_int] :
% 0.33/0.66 ( ( Q3
% 0.33/0.66 = ( produc6067946493426971951nt_int @ F @ P4 ) )
% 0.33/0.66 => ~ ! [X4: int > option6357759511663192854e_term,Y5: product_prod_int_int] :
% 0.33/0.66 ( ( P4
% 0.33/0.66 = ( produc4305682042979456191nt_int @ X4 @ Y5 ) )
% 0.33/0.66 => ( Q3
% 0.33/0.66 != ( produc5700946648718959541nt_int @ ( F @ X4 ) @ Y5 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % apfst_convE
% 0.33/0.66 thf(fact_7286_apfst__convE,axiom,
% 0.33/0.66 ! [Q3: produc7773217078559923341nt_int,F: ( int > option6357759511663192854e_term ) > int > option6357759511663192854e_term,P4: produc7773217078559923341nt_int] :
% 0.33/0.66 ( ( Q3
% 0.33/0.66 = ( produc7131893314732144953nt_int @ F @ P4 ) )
% 0.33/0.66 => ~ ! [X4: int > option6357759511663192854e_term,Y5: product_prod_int_int] :
% 0.33/0.66 ( ( P4
% 0.33/0.66 = ( produc4305682042979456191nt_int @ X4 @ Y5 ) )
% 0.33/0.66 => ( Q3
% 0.33/0.66 != ( produc4305682042979456191nt_int @ ( F @ X4 ) @ Y5 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % apfst_convE
% 0.33/0.66 thf(fact_7287_UN__le__eq__Un0,axiom,
% 0.33/0.66 ! [M3: nat > set_Pr4329608150637261639at_nat,N2: nat] :
% 0.33/0.66 ( ( comple4364388969068068532at_nat @ ( image_1087905878993176368at_nat @ M3 @ ( set_ord_atMost_nat @ N2 ) ) )
% 0.33/0.66 = ( sup_su5525570899277871387at_nat @ ( comple4364388969068068532at_nat @ ( image_1087905878993176368at_nat @ M3 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) ) ) @ ( M3 @ zero_zero_nat ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % UN_le_eq_Un0
% 0.33/0.66 thf(fact_7288_UN__le__eq__Un0,axiom,
% 0.33/0.66 ! [M3: nat > set_nat,N2: nat] :
% 0.33/0.66 ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ M3 @ ( set_ord_atMost_nat @ N2 ) ) )
% 0.33/0.66 = ( sup_sup_set_nat @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ M3 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) ) ) @ ( M3 @ zero_zero_nat ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % UN_le_eq_Un0
% 0.33/0.66 thf(fact_7289_times__int_Orsp,axiom,
% 0.33/0.66 ( bNF_re3099431351363272937at_nat @ intrel @ ( bNF_re2241393799969408733at_nat @ intrel @ intrel )
% 0.33/0.66 @ ( produc27273713700761075at_nat
% 0.33/0.66 @ ^ [X3: nat,Y3: nat] :
% 0.33/0.66 ( produc2626176000494625587at_nat
% 0.33/0.66 @ ^ [U2: nat,V2: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X3 @ U2 ) @ ( times_times_nat @ Y3 @ V2 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X3 @ V2 ) @ ( times_times_nat @ Y3 @ U2 ) ) ) ) )
% 0.33/0.66 @ ( produc27273713700761075at_nat
% 0.33/0.66 @ ^ [X3: nat,Y3: nat] :
% 0.33/0.66 ( produc2626176000494625587at_nat
% 0.33/0.66 @ ^ [U2: nat,V2: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X3 @ U2 ) @ ( times_times_nat @ Y3 @ V2 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X3 @ V2 ) @ ( times_times_nat @ Y3 @ U2 ) ) ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % times_int.rsp
% 0.33/0.66 thf(fact_7290_sup__Some,axiom,
% 0.33/0.66 ! [X: set_nat,Y: set_nat] :
% 0.33/0.66 ( ( sup_su3598758113090618626et_nat @ ( some_set_nat @ X ) @ ( some_set_nat @ Y ) )
% 0.33/0.66 = ( some_set_nat @ ( sup_sup_set_nat @ X @ Y ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % sup_Some
% 0.33/0.66 thf(fact_7291_sup__Some,axiom,
% 0.33/0.66 ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat] :
% 0.33/0.66 ( ( sup_su2273273666271716065at_nat @ ( some_s5890477192898017836at_nat @ X ) @ ( some_s5890477192898017836at_nat @ Y ) )
% 0.33/0.66 = ( some_s5890477192898017836at_nat @ ( sup_su5525570899277871387at_nat @ X @ Y ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % sup_Some
% 0.33/0.66 thf(fact_7292_sup__Some,axiom,
% 0.33/0.66 ! [X: product_unit,Y: product_unit] :
% 0.33/0.66 ( ( sup_su7717485023253700007t_unit @ ( some_Product_unit @ X ) @ ( some_Product_unit @ Y ) )
% 0.33/0.66 = ( some_Product_unit @ ( sup_sup_Product_unit @ X @ Y ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % sup_Some
% 0.33/0.66 thf(fact_7293_sup__Some,axiom,
% 0.33/0.66 ! [X: assn,Y: assn] :
% 0.33/0.66 ( ( sup_sup_option_assn @ ( some_assn @ X ) @ ( some_assn @ Y ) )
% 0.33/0.66 = ( some_assn @ ( sup_sup_assn @ X @ Y ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % sup_Some
% 0.33/0.66 thf(fact_7294_intrel__iff,axiom,
% 0.33/0.66 ! [X: nat,Y: nat,U: nat,V: nat] :
% 0.33/0.66 ( ( intrel @ ( product_Pair_nat_nat @ X @ Y ) @ ( product_Pair_nat_nat @ U @ V ) )
% 0.33/0.66 = ( ( plus_plus_nat @ X @ V )
% 0.33/0.66 = ( plus_plus_nat @ U @ Y ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % intrel_iff
% 0.33/0.66 thf(fact_7295_insert__Times__insert,axiom,
% 0.33/0.66 ! [A: $o,A2: set_o,B: $o,B5: set_o] :
% 0.33/0.66 ( ( product_Sigma_o_o @ ( insert_o @ A @ A2 )
% 0.33/0.66 @ ^ [Uu: $o] : ( insert_o @ B @ B5 ) )
% 0.33/0.66 = ( insert6201435330877294327od_o_o @ ( product_Pair_o_o @ A @ B )
% 0.33/0.66 @ ( sup_su5769328420594410459od_o_o
% 0.33/0.66 @ ( product_Sigma_o_o @ A2
% 0.33/0.66 @ ^ [Uu: $o] : ( insert_o @ B @ B5 ) )
% 0.33/0.66 @ ( product_Sigma_o_o @ ( insert_o @ A @ A2 )
% 0.33/0.66 @ ^ [Uu: $o] : B5 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % insert_Times_insert
% 0.33/0.66 thf(fact_7296_insert__Times__insert,axiom,
% 0.33/0.66 ! [A: $o,A2: set_o,B: nat,B5: set_nat] :
% 0.33/0.66 ( ( product_Sigma_o_nat @ ( insert_o @ A @ A2 )
% 0.33/0.66 @ ^ [Uu: $o] : ( insert_nat @ B @ B5 ) )
% 0.33/0.66 = ( insert7948214739558299847_o_nat @ ( product_Pair_o_nat @ A @ B )
% 0.33/0.66 @ ( sup_su8679140417860611193_o_nat
% 0.33/0.66 @ ( product_Sigma_o_nat @ A2
% 0.33/0.66 @ ^ [Uu: $o] : ( insert_nat @ B @ B5 ) )
% 0.33/0.66 @ ( product_Sigma_o_nat @ ( insert_o @ A @ A2 )
% 0.33/0.66 @ ^ [Uu: $o] : B5 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % insert_Times_insert
% 0.33/0.66 thf(fact_7297_insert__Times__insert,axiom,
% 0.33/0.66 ! [A: $o,A2: set_o,B: int,B5: set_int] :
% 0.33/0.66 ( ( product_Sigma_o_int @ ( insert_o @ A @ A2 )
% 0.33/0.66 @ ^ [Uu: $o] : ( insert_int @ B @ B5 ) )
% 0.33/0.66 = ( insert3770363720049103139_o_int @ ( product_Pair_o_int @ A @ B )
% 0.33/0.66 @ ( sup_su6189057272928884437_o_int
% 0.33/0.66 @ ( product_Sigma_o_int @ A2
% 0.33/0.66 @ ^ [Uu: $o] : ( insert_int @ B @ B5 ) )
% 0.33/0.66 @ ( product_Sigma_o_int @ ( insert_o @ A @ A2 )
% 0.33/0.66 @ ^ [Uu: $o] : B5 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % insert_Times_insert
% 0.33/0.66 thf(fact_7298_insert__Times__insert,axiom,
% 0.33/0.66 ! [A: nat,A2: set_nat,B: $o,B5: set_o] :
% 0.33/0.66 ( ( product_Sigma_nat_o @ ( insert_nat @ A @ A2 )
% 0.33/0.66 @ ^ [Uu: nat] : ( insert_o @ B @ B5 ) )
% 0.33/0.66 = ( insert2233377226759017069_nat_o @ ( product_Pair_nat_o @ A @ B )
% 0.33/0.66 @ ( sup_su503371503184139039_nat_o
% 0.33/0.66 @ ( product_Sigma_nat_o @ A2
% 0.33/0.66 @ ^ [Uu: nat] : ( insert_o @ B @ B5 ) )
% 0.33/0.66 @ ( product_Sigma_nat_o @ ( insert_nat @ A @ A2 )
% 0.33/0.66 @ ^ [Uu: nat] : B5 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % insert_Times_insert
% 0.33/0.66 thf(fact_7299_insert__Times__insert,axiom,
% 0.33/0.66 ! [A: nat,A2: set_nat,B: nat,B5: set_nat] :
% 0.33/0.66 ( ( produc457027306803732586at_nat @ ( insert_nat @ A @ A2 )
% 0.33/0.66 @ ^ [Uu: nat] : ( insert_nat @ B @ B5 ) )
% 0.33/0.66 = ( insert8211810215607154385at_nat @ ( product_Pair_nat_nat @ A @ B )
% 0.33/0.66 @ ( sup_su6327502436637775413at_nat
% 0.33/0.66 @ ( produc457027306803732586at_nat @ A2
% 0.33/0.66 @ ^ [Uu: nat] : ( insert_nat @ B @ B5 ) )
% 0.33/0.66 @ ( produc457027306803732586at_nat @ ( insert_nat @ A @ A2 )
% 0.33/0.66 @ ^ [Uu: nat] : B5 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % insert_Times_insert
% 0.33/0.66 thf(fact_7300_insert__Times__insert,axiom,
% 0.33/0.66 ! [A: nat,A2: set_nat,B: int,B5: set_int] :
% 0.33/0.66 ( ( produc454536836294682310at_int @ ( insert_nat @ A @ A2 )
% 0.33/0.66 @ ^ [Uu: nat] : ( insert_int @ B @ B5 ) )
% 0.33/0.66 = ( insert4033959196097957677at_int @ ( product_Pair_nat_int @ A @ B )
% 0.33/0.66 @ ( sup_su3837419291706048657at_int
% 0.33/0.66 @ ( produc454536836294682310at_int @ A2
% 0.33/0.66 @ ^ [Uu: nat] : ( insert_int @ B @ B5 ) )
% 0.33/0.66 @ ( produc454536836294682310at_int @ ( insert_nat @ A @ A2 )
% 0.33/0.66 @ ^ [Uu: nat] : B5 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % insert_Times_insert
% 0.33/0.66 thf(fact_7301_insert__Times__insert,axiom,
% 0.33/0.66 ! [A: int,A2: set_int,B: $o,B5: set_o] :
% 0.33/0.66 ( ( product_Sigma_int_o @ ( insert_int @ A @ A2 )
% 0.33/0.66 @ ^ [Uu: int] : ( insert_o @ B @ B5 ) )
% 0.33/0.66 = ( insert412334881326329105_int_o @ ( product_Pair_int_o @ A @ B )
% 0.33/0.66 @ ( sup_su7481598572368468931_int_o
% 0.33/0.66 @ ( product_Sigma_int_o @ A2
% 0.33/0.66 @ ^ [Uu: int] : ( insert_o @ B @ B5 ) )
% 0.33/0.66 @ ( product_Sigma_int_o @ ( insert_int @ A @ A2 )
% 0.33/0.66 @ ^ [Uu: int] : B5 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % insert_Times_insert
% 0.33/0.66 thf(fact_7302_insert__Times__insert,axiom,
% 0.33/0.66 ! [A: int,A2: set_int,B: nat,B5: set_nat] :
% 0.33/0.66 ( ( produc1456381018704787142nt_nat @ ( insert_int @ A @ A2 )
% 0.33/0.66 @ ^ [Uu: int] : ( insert_nat @ B @ B5 ) )
% 0.33/0.66 = ( insert9211163927508208941nt_nat @ ( product_Pair_int_nat @ A @ B )
% 0.33/0.66 @ ( sup_su8514424011330797201nt_nat
% 0.33/0.66 @ ( produc1456381018704787142nt_nat @ A2
% 0.33/0.66 @ ^ [Uu: int] : ( insert_nat @ B @ B5 ) )
% 0.33/0.66 @ ( produc1456381018704787142nt_nat @ ( insert_int @ A @ A2 )
% 0.33/0.66 @ ^ [Uu: int] : B5 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % insert_Times_insert
% 0.33/0.66 thf(fact_7303_insert__Times__insert,axiom,
% 0.33/0.66 ! [A: int,A2: set_int,B: int,B5: set_int] :
% 0.33/0.66 ( ( produc1453890548195736866nt_int @ ( insert_int @ A @ A2 )
% 0.33/0.66 @ ^ [Uu: int] : ( insert_int @ B @ B5 ) )
% 0.33/0.66 = ( insert5033312907999012233nt_int @ ( product_Pair_int_int @ A @ B )
% 0.33/0.66 @ ( sup_su6024340866399070445nt_int
% 0.33/0.66 @ ( produc1453890548195736866nt_int @ A2
% 0.33/0.66 @ ^ [Uu: int] : ( insert_int @ B @ B5 ) )
% 0.33/0.66 @ ( produc1453890548195736866nt_int @ ( insert_int @ A @ A2 )
% 0.33/0.66 @ ^ [Uu: int] : B5 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % insert_Times_insert
% 0.33/0.66 thf(fact_7304_insert__Times__insert,axiom,
% 0.33/0.66 ! [A: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,B: $o,B5: set_o] :
% 0.33/0.66 ( ( produc203973861852599583_nat_o @ ( insert8211810215607154385at_nat @ A @ A2 )
% 0.33/0.66 @ ^ [Uu: product_prod_nat_nat] : ( insert_o @ B @ B5 ) )
% 0.33/0.66 = ( insert2126339615020983374_nat_o @ ( produc855456346497908590_nat_o @ A @ B )
% 0.33/0.66 @ ( sup_su5921324857680904370_nat_o
% 0.33/0.66 @ ( produc203973861852599583_nat_o @ A2
% 0.33/0.66 @ ^ [Uu: product_prod_nat_nat] : ( insert_o @ B @ B5 ) )
% 0.33/0.66 @ ( produc203973861852599583_nat_o @ ( insert8211810215607154385at_nat @ A @ A2 )
% 0.33/0.66 @ ^ [Uu: product_prod_nat_nat] : B5 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % insert_Times_insert
% 0.33/0.66 thf(fact_7305_Sigma__Un__distrib1,axiom,
% 0.33/0.66 ! [I4: set_se7855581050983116737at_nat,J4: set_se7855581050983116737at_nat,C4: set_Pr1261947904930325089at_nat > set_se7855581050983116737at_nat] :
% 0.33/0.66 ( ( produc7726050920695093128at_nat @ ( sup_su3642409539654194069at_nat @ I4 @ J4 ) @ C4 )
% 0.33/0.66 = ( sup_su5525570899277871387at_nat @ ( produc7726050920695093128at_nat @ I4 @ C4 ) @ ( produc7726050920695093128at_nat @ J4 @ C4 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % Sigma_Un_distrib1
% 0.33/0.66 thf(fact_7306_Sigma__Un__distrib2,axiom,
% 0.33/0.66 ! [I4: set_se7855581050983116737at_nat,A2: set_Pr1261947904930325089at_nat > set_se7855581050983116737at_nat,B5: set_Pr1261947904930325089at_nat > set_se7855581050983116737at_nat] :
% 0.33/0.66 ( ( produc7726050920695093128at_nat @ I4
% 0.33/0.66 @ ^ [I3: set_Pr1261947904930325089at_nat] : ( sup_su3642409539654194069at_nat @ ( A2 @ I3 ) @ ( B5 @ I3 ) ) )
% 0.33/0.66 = ( sup_su5525570899277871387at_nat @ ( produc7726050920695093128at_nat @ I4 @ A2 ) @ ( produc7726050920695093128at_nat @ I4 @ B5 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % Sigma_Un_distrib2
% 0.33/0.66 thf(fact_7307_Times__Un__distrib1,axiom,
% 0.33/0.66 ! [A2: set_se7855581050983116737at_nat,B5: set_se7855581050983116737at_nat,C4: set_se7855581050983116737at_nat] :
% 0.33/0.66 ( ( produc7726050920695093128at_nat @ ( sup_su3642409539654194069at_nat @ A2 @ B5 )
% 0.33/0.66 @ ^ [Uu: set_Pr1261947904930325089at_nat] : C4 )
% 0.33/0.66 = ( sup_su5525570899277871387at_nat
% 0.33/0.66 @ ( produc7726050920695093128at_nat @ A2
% 0.33/0.66 @ ^ [Uu: set_Pr1261947904930325089at_nat] : C4 )
% 0.33/0.66 @ ( produc7726050920695093128at_nat @ B5
% 0.33/0.66 @ ^ [Uu: set_Pr1261947904930325089at_nat] : C4 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % Times_Un_distrib1
% 0.33/0.66 thf(fact_7308_set__diff__diff__left,axiom,
% 0.33/0.66 ! [A2: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat,C4: set_Pr4329608150637261639at_nat] :
% 0.33/0.66 ( ( minus_3314409938677909166at_nat @ ( minus_3314409938677909166at_nat @ A2 @ B5 ) @ C4 )
% 0.33/0.66 = ( minus_3314409938677909166at_nat @ A2 @ ( sup_su5525570899277871387at_nat @ B5 @ C4 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % set_diff_diff_left
% 0.33/0.66 thf(fact_7309_set__diff__diff__left,axiom,
% 0.33/0.66 ! [A2: set_nat,B5: set_nat,C4: set_nat] :
% 0.33/0.66 ( ( minus_minus_set_nat @ ( minus_minus_set_nat @ A2 @ B5 ) @ C4 )
% 0.33/0.66 = ( minus_minus_set_nat @ A2 @ ( sup_sup_set_nat @ B5 @ C4 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % set_diff_diff_left
% 0.33/0.66 thf(fact_7310_sup__option__def,axiom,
% 0.33/0.66 ( sup_su3598758113090618626et_nat
% 0.33/0.66 = ( ^ [X3: option_set_nat,Y3: option_set_nat] :
% 0.33/0.66 ( case_o4054078431260844265et_nat @ Y3
% 0.33/0.66 @ ^ [X10: set_nat] :
% 0.33/0.66 ( case_o4054078431260844265et_nat @ X3
% 0.33/0.66 @ ^ [Z4: set_nat] : ( some_set_nat @ ( sup_sup_set_nat @ X10 @ Z4 ) )
% 0.33/0.66 @ Y3 )
% 0.33/0.66 @ X3 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % sup_option_def
% 0.33/0.66 thf(fact_7311_sup__option__def,axiom,
% 0.33/0.66 ( sup_su2273273666271716065at_nat
% 0.33/0.66 = ( ^ [X3: option1583680563626158861at_nat,Y3: option1583680563626158861at_nat] :
% 0.33/0.66 ( case_o9080059180780454917at_nat @ Y3
% 0.33/0.66 @ ^ [X10: set_Pr4329608150637261639at_nat] :
% 0.33/0.66 ( case_o9080059180780454917at_nat @ X3
% 0.33/0.66 @ ^ [Z4: set_Pr4329608150637261639at_nat] : ( some_s5890477192898017836at_nat @ ( sup_su5525570899277871387at_nat @ X10 @ Z4 ) )
% 0.33/0.66 @ Y3 )
% 0.33/0.66 @ X3 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % sup_option_def
% 0.33/0.66 thf(fact_7312_sup__option__def,axiom,
% 0.33/0.66 ( sup_su7717485023253700007t_unit
% 0.33/0.66 = ( ^ [X3: option_Product_unit,Y3: option_Product_unit] :
% 0.33/0.66 ( case_o2985186191577459077t_unit @ Y3
% 0.33/0.66 @ ^ [X10: product_unit] :
% 0.33/0.66 ( case_o2985186191577459077t_unit @ X3
% 0.33/0.66 @ ^ [Z4: product_unit] : ( some_Product_unit @ ( sup_sup_Product_unit @ X10 @ Z4 ) )
% 0.33/0.66 @ Y3 )
% 0.33/0.66 @ X3 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % sup_option_def
% 0.33/0.66 thf(fact_7313_sup__option__def,axiom,
% 0.33/0.66 ( sup_sup_option_assn
% 0.33/0.66 = ( ^ [X3: option_assn,Y3: option_assn] :
% 0.33/0.66 ( case_o4484465799723439917n_assn @ Y3
% 0.33/0.66 @ ^ [X10: assn] :
% 0.33/0.66 ( case_o4484465799723439917n_assn @ X3
% 0.33/0.66 @ ^ [Z4: assn] : ( some_assn @ ( sup_sup_assn @ X10 @ Z4 ) )
% 0.33/0.66 @ Y3 )
% 0.33/0.66 @ X3 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % sup_option_def
% 0.33/0.66 thf(fact_7314_ivl__disj__un__two__touch_I4_J,axiom,
% 0.33/0.66 ! [L: rat,M2: rat,U: rat] :
% 0.33/0.66 ( ( ord_less_eq_rat @ L @ M2 )
% 0.33/0.66 => ( ( ord_less_eq_rat @ M2 @ U )
% 0.33/0.66 => ( ( sup_sup_set_rat @ ( set_or633870826150836451st_rat @ L @ M2 ) @ ( set_or633870826150836451st_rat @ M2 @ U ) )
% 0.33/0.66 = ( set_or633870826150836451st_rat @ L @ U ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % ivl_disj_un_two_touch(4)
% 0.33/0.66 thf(fact_7315_ivl__disj__un__two__touch_I4_J,axiom,
% 0.33/0.66 ! [L: num,M2: num,U: num] :
% 0.33/0.66 ( ( ord_less_eq_num @ L @ M2 )
% 0.33/0.66 => ( ( ord_less_eq_num @ M2 @ U )
% 0.33/0.66 => ( ( sup_sup_set_num @ ( set_or7049704709247886629st_num @ L @ M2 ) @ ( set_or7049704709247886629st_num @ M2 @ U ) )
% 0.33/0.66 = ( set_or7049704709247886629st_num @ L @ U ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % ivl_disj_un_two_touch(4)
% 0.33/0.66 thf(fact_7316_ivl__disj__un__two__touch_I4_J,axiom,
% 0.33/0.66 ! [L: int,M2: int,U: int] :
% 0.33/0.66 ( ( ord_less_eq_int @ L @ M2 )
% 0.33/0.66 => ( ( ord_less_eq_int @ M2 @ U )
% 0.33/0.66 => ( ( sup_sup_set_int @ ( set_or1266510415728281911st_int @ L @ M2 ) @ ( set_or1266510415728281911st_int @ M2 @ U ) )
% 0.33/0.66 = ( set_or1266510415728281911st_int @ L @ U ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % ivl_disj_un_two_touch(4)
% 0.33/0.66 thf(fact_7317_ivl__disj__un__two__touch_I4_J,axiom,
% 0.33/0.66 ! [L: nat,M2: nat,U: nat] :
% 0.33/0.66 ( ( ord_less_eq_nat @ L @ M2 )
% 0.33/0.66 => ( ( ord_less_eq_nat @ M2 @ U )
% 0.33/0.66 => ( ( sup_sup_set_nat @ ( set_or1269000886237332187st_nat @ L @ M2 ) @ ( set_or1269000886237332187st_nat @ M2 @ U ) )
% 0.33/0.66 = ( set_or1269000886237332187st_nat @ L @ U ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % ivl_disj_un_two_touch(4)
% 0.33/0.66 thf(fact_7318_ivl__disj__un__two__touch_I4_J,axiom,
% 0.33/0.66 ! [L: code_integer,M2: code_integer,U: code_integer] :
% 0.33/0.66 ( ( ord_le3102999989581377725nteger @ L @ M2 )
% 0.33/0.66 => ( ( ord_le3102999989581377725nteger @ M2 @ U )
% 0.33/0.66 => ( ( sup_su848401254843788991nteger @ ( set_or189985376899183464nteger @ L @ M2 ) @ ( set_or189985376899183464nteger @ M2 @ U ) )
% 0.33/0.66 = ( set_or189985376899183464nteger @ L @ U ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % ivl_disj_un_two_touch(4)
% 0.33/0.66 thf(fact_7319_ivl__disj__un__two_I3_J,axiom,
% 0.33/0.66 ! [L: rat,M2: rat,U: rat] :
% 0.33/0.66 ( ( ord_less_eq_rat @ L @ M2 )
% 0.33/0.66 => ( ( ord_less_eq_rat @ M2 @ U )
% 0.33/0.66 => ( ( sup_sup_set_rat @ ( set_or4029947393144176647an_rat @ L @ M2 ) @ ( set_or4029947393144176647an_rat @ M2 @ U ) )
% 0.33/0.66 = ( set_or4029947393144176647an_rat @ L @ U ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % ivl_disj_un_two(3)
% 0.33/0.66 thf(fact_7320_ivl__disj__un__two_I3_J,axiom,
% 0.33/0.66 ! [L: num,M2: num,U: num] :
% 0.33/0.66 ( ( ord_less_eq_num @ L @ M2 )
% 0.33/0.66 => ( ( ord_less_eq_num @ M2 @ U )
% 0.33/0.66 => ( ( sup_sup_set_num @ ( set_or1222409239386451017an_num @ L @ M2 ) @ ( set_or1222409239386451017an_num @ M2 @ U ) )
% 0.33/0.66 = ( set_or1222409239386451017an_num @ L @ U ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % ivl_disj_un_two(3)
% 0.33/0.66 thf(fact_7321_ivl__disj__un__two_I3_J,axiom,
% 0.33/0.66 ! [L: nat,M2: nat,U: nat] :
% 0.33/0.66 ( ( ord_less_eq_nat @ L @ M2 )
% 0.33/0.66 => ( ( ord_less_eq_nat @ M2 @ U )
% 0.33/0.66 => ( ( sup_sup_set_nat @ ( set_or4665077453230672383an_nat @ L @ M2 ) @ ( set_or4665077453230672383an_nat @ M2 @ U ) )
% 0.33/0.66 = ( set_or4665077453230672383an_nat @ L @ U ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % ivl_disj_un_two(3)
% 0.33/0.66 thf(fact_7322_ivl__disj__un__two_I3_J,axiom,
% 0.33/0.66 ! [L: code_integer,M2: code_integer,U: code_integer] :
% 0.33/0.66 ( ( ord_le3102999989581377725nteger @ L @ M2 )
% 0.33/0.66 => ( ( ord_le3102999989581377725nteger @ M2 @ U )
% 0.33/0.66 => ( ( sup_su848401254843788991nteger @ ( set_or8404916559141939852nteger @ L @ M2 ) @ ( set_or8404916559141939852nteger @ M2 @ U ) )
% 0.33/0.66 = ( set_or8404916559141939852nteger @ L @ U ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % ivl_disj_un_two(3)
% 0.33/0.66 thf(fact_7323_ivl__disj__un__two_I3_J,axiom,
% 0.33/0.66 ! [L: int,M2: int,U: int] :
% 0.33/0.66 ( ( ord_less_eq_int @ L @ M2 )
% 0.33/0.66 => ( ( ord_less_eq_int @ M2 @ U )
% 0.33/0.66 => ( ( sup_sup_set_int @ ( set_or4662586982721622107an_int @ L @ M2 ) @ ( set_or4662586982721622107an_int @ M2 @ U ) )
% 0.33/0.66 = ( set_or4662586982721622107an_int @ L @ U ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % ivl_disj_un_two(3)
% 0.33/0.66 thf(fact_7324_max__ext__additive,axiom,
% 0.33/0.66 ! [A2: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat,R4: set_Pr8693737435421807431at_nat,C4: set_Pr1261947904930325089at_nat,D3: set_Pr1261947904930325089at_nat] :
% 0.33/0.66 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A2 @ B5 ) @ ( max_ex8135407076693332796at_nat @ R4 ) )
% 0.33/0.66 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ C4 @ D3 ) @ ( max_ex8135407076693332796at_nat @ R4 ) )
% 0.33/0.66 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( sup_su6327502436637775413at_nat @ A2 @ C4 ) @ ( sup_su6327502436637775413at_nat @ B5 @ D3 ) ) @ ( max_ex8135407076693332796at_nat @ R4 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % max_ext_additive
% 0.33/0.66 thf(fact_7325_max__ext__additive,axiom,
% 0.33/0.66 ! [A2: set_nat,B5: set_nat,R4: set_Pr1261947904930325089at_nat,C4: set_nat,D3: set_nat] :
% 0.33/0.66 ( ( member8277197624267554838et_nat @ ( produc4532415448927165861et_nat @ A2 @ B5 ) @ ( max_ext_nat @ R4 ) )
% 0.33/0.66 => ( ( member8277197624267554838et_nat @ ( produc4532415448927165861et_nat @ C4 @ D3 ) @ ( max_ext_nat @ R4 ) )
% 0.33/0.66 => ( member8277197624267554838et_nat @ ( produc4532415448927165861et_nat @ ( sup_sup_set_nat @ A2 @ C4 ) @ ( sup_sup_set_nat @ B5 @ D3 ) ) @ ( max_ext_nat @ R4 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % max_ext_additive
% 0.33/0.66 thf(fact_7326_max__ext__additive,axiom,
% 0.33/0.66 ! [A2: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat,R4: set_Pr5564308138774400199at_nat,C4: set_Pr4329608150637261639at_nat,D3: set_Pr4329608150637261639at_nat] :
% 0.33/0.66 ( ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ A2 @ B5 ) @ ( max_ex8833738776070432290at_nat @ R4 ) )
% 0.33/0.66 => ( ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ C4 @ D3 ) @ ( max_ex8833738776070432290at_nat @ R4 ) )
% 0.33/0.66 => ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ ( sup_su5525570899277871387at_nat @ A2 @ C4 ) @ ( sup_su5525570899277871387at_nat @ B5 @ D3 ) ) @ ( max_ex8833738776070432290at_nat @ R4 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % max_ext_additive
% 0.33/0.66 thf(fact_7327_zero__int_Orsp,axiom,
% 0.33/0.66 intrel @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ).
% 0.33/0.66
% 0.33/0.66 % zero_int.rsp
% 0.33/0.66 thf(fact_7328_ivl__disj__un__two_I7_J,axiom,
% 0.33/0.66 ! [L: rat,M2: rat,U: rat] :
% 0.33/0.66 ( ( ord_less_eq_rat @ L @ M2 )
% 0.33/0.66 => ( ( ord_less_eq_rat @ M2 @ U )
% 0.33/0.66 => ( ( sup_sup_set_rat @ ( set_or4029947393144176647an_rat @ L @ M2 ) @ ( set_or633870826150836451st_rat @ M2 @ U ) )
% 0.33/0.66 = ( set_or633870826150836451st_rat @ L @ U ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % ivl_disj_un_two(7)
% 0.33/0.66 thf(fact_7329_ivl__disj__un__two_I7_J,axiom,
% 0.33/0.66 ! [L: num,M2: num,U: num] :
% 0.33/0.66 ( ( ord_less_eq_num @ L @ M2 )
% 0.33/0.66 => ( ( ord_less_eq_num @ M2 @ U )
% 0.33/0.66 => ( ( sup_sup_set_num @ ( set_or1222409239386451017an_num @ L @ M2 ) @ ( set_or7049704709247886629st_num @ M2 @ U ) )
% 0.33/0.66 = ( set_or7049704709247886629st_num @ L @ U ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % ivl_disj_un_two(7)
% 0.33/0.66 thf(fact_7330_ivl__disj__un__two_I7_J,axiom,
% 0.33/0.66 ! [L: nat,M2: nat,U: nat] :
% 0.33/0.66 ( ( ord_less_eq_nat @ L @ M2 )
% 0.33/0.66 => ( ( ord_less_eq_nat @ M2 @ U )
% 0.33/0.66 => ( ( sup_sup_set_nat @ ( set_or4665077453230672383an_nat @ L @ M2 ) @ ( set_or1269000886237332187st_nat @ M2 @ U ) )
% 0.33/0.66 = ( set_or1269000886237332187st_nat @ L @ U ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % ivl_disj_un_two(7)
% 0.33/0.66 thf(fact_7331_ivl__disj__un__two_I7_J,axiom,
% 0.33/0.66 ! [L: code_integer,M2: code_integer,U: code_integer] :
% 0.33/0.66 ( ( ord_le3102999989581377725nteger @ L @ M2 )
% 0.33/0.66 => ( ( ord_le3102999989581377725nteger @ M2 @ U )
% 0.33/0.66 => ( ( sup_su848401254843788991nteger @ ( set_or8404916559141939852nteger @ L @ M2 ) @ ( set_or189985376899183464nteger @ M2 @ U ) )
% 0.33/0.66 = ( set_or189985376899183464nteger @ L @ U ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % ivl_disj_un_two(7)
% 0.33/0.66 thf(fact_7332_ivl__disj__un__two_I7_J,axiom,
% 0.33/0.66 ! [L: int,M2: int,U: int] :
% 0.33/0.66 ( ( ord_less_eq_int @ L @ M2 )
% 0.33/0.66 => ( ( ord_less_eq_int @ M2 @ U )
% 0.33/0.66 => ( ( sup_sup_set_int @ ( set_or4662586982721622107an_int @ L @ M2 ) @ ( set_or1266510415728281911st_int @ M2 @ U ) )
% 0.33/0.66 = ( set_or1266510415728281911st_int @ L @ U ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % ivl_disj_un_two(7)
% 0.33/0.66 thf(fact_7333_card__Un__le,axiom,
% 0.33/0.66 ! [A2: set_int,B5: set_int] : ( ord_less_eq_nat @ ( finite_card_int @ ( sup_sup_set_int @ A2 @ B5 ) ) @ ( plus_plus_nat @ ( finite_card_int @ A2 ) @ ( finite_card_int @ B5 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % card_Un_le
% 0.33/0.66 thf(fact_7334_card__Un__le,axiom,
% 0.33/0.66 ! [A2: set_Product_unit,B5: set_Product_unit] : ( ord_less_eq_nat @ ( finite410649719033368117t_unit @ ( sup_su793286257634532545t_unit @ A2 @ B5 ) ) @ ( plus_plus_nat @ ( finite410649719033368117t_unit @ A2 ) @ ( finite410649719033368117t_unit @ B5 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % card_Un_le
% 0.33/0.66 thf(fact_7335_card__Un__le,axiom,
% 0.33/0.66 ! [A2: set_list_nat,B5: set_list_nat] : ( ord_less_eq_nat @ ( finite_card_list_nat @ ( sup_sup_set_list_nat @ A2 @ B5 ) ) @ ( plus_plus_nat @ ( finite_card_list_nat @ A2 ) @ ( finite_card_list_nat @ B5 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % card_Un_le
% 0.33/0.66 thf(fact_7336_card__Un__le,axiom,
% 0.33/0.66 ! [A2: set_nat,B5: set_nat] : ( ord_less_eq_nat @ ( finite_card_nat @ ( sup_sup_set_nat @ A2 @ B5 ) ) @ ( plus_plus_nat @ ( finite_card_nat @ A2 ) @ ( finite_card_nat @ B5 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % card_Un_le
% 0.33/0.66 thf(fact_7337_card__Un__le,axiom,
% 0.33/0.66 ! [A2: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat] : ( ord_less_eq_nat @ ( finite3771342082235030671at_nat @ ( sup_su5525570899277871387at_nat @ A2 @ B5 ) ) @ ( plus_plus_nat @ ( finite3771342082235030671at_nat @ A2 ) @ ( finite3771342082235030671at_nat @ B5 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % card_Un_le
% 0.33/0.66 thf(fact_7338_ivl__disj__un__one_I2_J,axiom,
% 0.33/0.66 ! [L: rat,U: rat] :
% 0.33/0.66 ( ( ord_less_eq_rat @ L @ U )
% 0.33/0.66 => ( ( sup_sup_set_rat @ ( set_ord_lessThan_rat @ L ) @ ( set_or4029947393144176647an_rat @ L @ U ) )
% 0.33/0.66 = ( set_ord_lessThan_rat @ U ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % ivl_disj_un_one(2)
% 0.33/0.66 thf(fact_7339_ivl__disj__un__one_I2_J,axiom,
% 0.33/0.66 ! [L: num,U: num] :
% 0.33/0.66 ( ( ord_less_eq_num @ L @ U )
% 0.33/0.66 => ( ( sup_sup_set_num @ ( set_ord_lessThan_num @ L ) @ ( set_or1222409239386451017an_num @ L @ U ) )
% 0.33/0.66 = ( set_ord_lessThan_num @ U ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % ivl_disj_un_one(2)
% 0.33/0.66 thf(fact_7340_ivl__disj__un__one_I2_J,axiom,
% 0.33/0.66 ! [L: nat,U: nat] :
% 0.33/0.66 ( ( ord_less_eq_nat @ L @ U )
% 0.33/0.66 => ( ( sup_sup_set_nat @ ( set_ord_lessThan_nat @ L ) @ ( set_or4665077453230672383an_nat @ L @ U ) )
% 0.33/0.66 = ( set_ord_lessThan_nat @ U ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % ivl_disj_un_one(2)
% 0.33/0.66 thf(fact_7341_ivl__disj__un__one_I2_J,axiom,
% 0.33/0.66 ! [L: code_integer,U: code_integer] :
% 0.33/0.66 ( ( ord_le3102999989581377725nteger @ L @ U )
% 0.33/0.66 => ( ( sup_su848401254843788991nteger @ ( set_or5754767410780653050nteger @ L ) @ ( set_or8404916559141939852nteger @ L @ U ) )
% 0.33/0.66 = ( set_or5754767410780653050nteger @ U ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % ivl_disj_un_one(2)
% 0.33/0.66 thf(fact_7342_ivl__disj__un__one_I2_J,axiom,
% 0.33/0.66 ! [L: int,U: int] :
% 0.33/0.66 ( ( ord_less_eq_int @ L @ U )
% 0.33/0.66 => ( ( sup_sup_set_int @ ( set_ord_lessThan_int @ L ) @ ( set_or4662586982721622107an_int @ L @ U ) )
% 0.33/0.66 = ( set_ord_lessThan_int @ U ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % ivl_disj_un_one(2)
% 0.33/0.66 thf(fact_7343_atLeastLessThan__add__Un,axiom,
% 0.33/0.66 ! [I: nat,J: nat,K: nat] :
% 0.33/0.66 ( ( ord_less_eq_nat @ I @ J )
% 0.33/0.66 => ( ( set_or4665077453230672383an_nat @ I @ ( plus_plus_nat @ J @ K ) )
% 0.33/0.66 = ( sup_sup_set_nat @ ( set_or4665077453230672383an_nat @ I @ J ) @ ( set_or4665077453230672383an_nat @ J @ ( plus_plus_nat @ J @ K ) ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % atLeastLessThan_add_Un
% 0.33/0.66 thf(fact_7344_uminus__int_Orsp,axiom,
% 0.33/0.66 ( bNF_re2241393799969408733at_nat @ intrel @ intrel
% 0.33/0.66 @ ( produc2626176000494625587at_nat
% 0.33/0.66 @ ^ [X3: nat,Y3: nat] : ( product_Pair_nat_nat @ Y3 @ X3 ) )
% 0.33/0.66 @ ( produc2626176000494625587at_nat
% 0.33/0.66 @ ^ [X3: nat,Y3: nat] : ( product_Pair_nat_nat @ Y3 @ X3 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % uminus_int.rsp
% 0.33/0.66 thf(fact_7345_one__int_Orsp,axiom,
% 0.33/0.66 intrel @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) ).
% 0.33/0.66
% 0.33/0.66 % one_int.rsp
% 0.33/0.66 thf(fact_7346_ivl__disj__un__two__touch_I2_J,axiom,
% 0.33/0.66 ! [L: rat,M2: rat,U: rat] :
% 0.33/0.66 ( ( ord_less_eq_rat @ L @ M2 )
% 0.33/0.66 => ( ( ord_less_rat @ M2 @ U )
% 0.33/0.66 => ( ( sup_sup_set_rat @ ( set_or633870826150836451st_rat @ L @ M2 ) @ ( set_or4029947393144176647an_rat @ M2 @ U ) )
% 0.33/0.66 = ( set_or4029947393144176647an_rat @ L @ U ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % ivl_disj_un_two_touch(2)
% 0.33/0.66 thf(fact_7347_ivl__disj__un__two__touch_I2_J,axiom,
% 0.33/0.66 ! [L: num,M2: num,U: num] :
% 0.33/0.66 ( ( ord_less_eq_num @ L @ M2 )
% 0.33/0.66 => ( ( ord_less_num @ M2 @ U )
% 0.33/0.66 => ( ( sup_sup_set_num @ ( set_or7049704709247886629st_num @ L @ M2 ) @ ( set_or1222409239386451017an_num @ M2 @ U ) )
% 0.33/0.66 = ( set_or1222409239386451017an_num @ L @ U ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % ivl_disj_un_two_touch(2)
% 0.33/0.66 thf(fact_7348_ivl__disj__un__two__touch_I2_J,axiom,
% 0.33/0.66 ! [L: nat,M2: nat,U: nat] :
% 0.33/0.66 ( ( ord_less_eq_nat @ L @ M2 )
% 0.33/0.66 => ( ( ord_less_nat @ M2 @ U )
% 0.33/0.66 => ( ( sup_sup_set_nat @ ( set_or1269000886237332187st_nat @ L @ M2 ) @ ( set_or4665077453230672383an_nat @ M2 @ U ) )
% 0.33/0.66 = ( set_or4665077453230672383an_nat @ L @ U ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % ivl_disj_un_two_touch(2)
% 0.33/0.66 thf(fact_7349_ivl__disj__un__two__touch_I2_J,axiom,
% 0.33/0.66 ! [L: code_integer,M2: code_integer,U: code_integer] :
% 0.33/0.66 ( ( ord_le3102999989581377725nteger @ L @ M2 )
% 0.33/0.66 => ( ( ord_le6747313008572928689nteger @ M2 @ U )
% 0.33/0.66 => ( ( sup_su848401254843788991nteger @ ( set_or189985376899183464nteger @ L @ M2 ) @ ( set_or8404916559141939852nteger @ M2 @ U ) )
% 0.33/0.66 = ( set_or8404916559141939852nteger @ L @ U ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % ivl_disj_un_two_touch(2)
% 0.33/0.66 thf(fact_7350_ivl__disj__un__two__touch_I2_J,axiom,
% 0.33/0.66 ! [L: int,M2: int,U: int] :
% 0.33/0.66 ( ( ord_less_eq_int @ L @ M2 )
% 0.33/0.66 => ( ( ord_less_int @ M2 @ U )
% 0.33/0.66 => ( ( sup_sup_set_int @ ( set_or1266510415728281911st_int @ L @ M2 ) @ ( set_or4662586982721622107an_int @ M2 @ U ) )
% 0.33/0.66 = ( set_or4662586982721622107an_int @ L @ U ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % ivl_disj_un_two_touch(2)
% 0.33/0.66 thf(fact_7351_ivl__disj__un__two_I1_J,axiom,
% 0.33/0.66 ! [L: rat,M2: rat,U: rat] :
% 0.33/0.66 ( ( ord_less_rat @ L @ M2 )
% 0.33/0.66 => ( ( ord_less_eq_rat @ M2 @ U )
% 0.33/0.66 => ( ( sup_sup_set_rat @ ( set_or5199638295745620268an_rat @ L @ M2 ) @ ( set_or4029947393144176647an_rat @ M2 @ U ) )
% 0.33/0.66 = ( set_or5199638295745620268an_rat @ L @ U ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % ivl_disj_un_two(1)
% 0.33/0.66 thf(fact_7352_ivl__disj__un__two_I1_J,axiom,
% 0.33/0.66 ! [L: num,M2: num,U: num] :
% 0.33/0.66 ( ( ord_less_num @ L @ M2 )
% 0.33/0.66 => ( ( ord_less_eq_num @ M2 @ U )
% 0.33/0.66 => ( ( sup_sup_set_num @ ( set_or2392100141987894638an_num @ L @ M2 ) @ ( set_or1222409239386451017an_num @ M2 @ U ) )
% 0.33/0.66 = ( set_or2392100141987894638an_num @ L @ U ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % ivl_disj_un_two(1)
% 0.33/0.66 thf(fact_7353_ivl__disj__un__two_I1_J,axiom,
% 0.33/0.66 ! [L: int,M2: int,U: int] :
% 0.33/0.66 ( ( ord_less_int @ L @ M2 )
% 0.33/0.66 => ( ( ord_less_eq_int @ M2 @ U )
% 0.33/0.66 => ( ( sup_sup_set_int @ ( set_or5832277885323065728an_int @ L @ M2 ) @ ( set_or4662586982721622107an_int @ M2 @ U ) )
% 0.33/0.66 = ( set_or5832277885323065728an_int @ L @ U ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % ivl_disj_un_two(1)
% 0.33/0.66 thf(fact_7354_ivl__disj__un__two_I1_J,axiom,
% 0.33/0.66 ! [L: nat,M2: nat,U: nat] :
% 0.33/0.66 ( ( ord_less_nat @ L @ M2 )
% 0.33/0.66 => ( ( ord_less_eq_nat @ M2 @ U )
% 0.33/0.66 => ( ( sup_sup_set_nat @ ( set_or5834768355832116004an_nat @ L @ M2 ) @ ( set_or4665077453230672383an_nat @ M2 @ U ) )
% 0.33/0.66 = ( set_or5834768355832116004an_nat @ L @ U ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % ivl_disj_un_two(1)
% 0.33/0.66 thf(fact_7355_ivl__disj__un__two_I1_J,axiom,
% 0.33/0.66 ! [L: code_integer,M2: code_integer,U: code_integer] :
% 0.33/0.66 ( ( ord_le6747313008572928689nteger @ L @ M2 )
% 0.33/0.66 => ( ( ord_le3102999989581377725nteger @ M2 @ U )
% 0.33/0.66 => ( ( sup_su848401254843788991nteger @ ( set_or4266950643985792945nteger @ L @ M2 ) @ ( set_or8404916559141939852nteger @ M2 @ U ) )
% 0.33/0.66 = ( set_or4266950643985792945nteger @ L @ U ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % ivl_disj_un_two(1)
% 0.33/0.66 thf(fact_7356_ivl__disj__un__singleton_I2_J,axiom,
% 0.33/0.66 ! [U: $o] :
% 0.33/0.66 ( ( sup_sup_set_o @ ( set_ord_lessThan_o @ U ) @ ( insert_o @ U @ bot_bot_set_o ) )
% 0.33/0.66 = ( set_ord_atMost_o @ U ) ) ).
% 0.33/0.66
% 0.33/0.66 % ivl_disj_un_singleton(2)
% 0.33/0.66 thf(fact_7357_ivl__disj__un__singleton_I2_J,axiom,
% 0.33/0.66 ! [U: int] :
% 0.33/0.66 ( ( sup_sup_set_int @ ( set_ord_lessThan_int @ U ) @ ( insert_int @ U @ bot_bot_set_int ) )
% 0.33/0.66 = ( set_ord_atMost_int @ U ) ) ).
% 0.33/0.66
% 0.33/0.66 % ivl_disj_un_singleton(2)
% 0.33/0.66 thf(fact_7358_ivl__disj__un__singleton_I2_J,axiom,
% 0.33/0.66 ! [U: nat] :
% 0.33/0.66 ( ( sup_sup_set_nat @ ( set_ord_lessThan_nat @ U ) @ ( insert_nat @ U @ bot_bot_set_nat ) )
% 0.33/0.66 = ( set_ord_atMost_nat @ U ) ) ).
% 0.33/0.66
% 0.33/0.66 % ivl_disj_un_singleton(2)
% 0.33/0.66 thf(fact_7359_ivl__disj__un__one_I4_J,axiom,
% 0.33/0.66 ! [L: rat,U: rat] :
% 0.33/0.66 ( ( ord_less_eq_rat @ L @ U )
% 0.33/0.66 => ( ( sup_sup_set_rat @ ( set_ord_lessThan_rat @ L ) @ ( set_or633870826150836451st_rat @ L @ U ) )
% 0.33/0.66 = ( set_ord_atMost_rat @ U ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % ivl_disj_un_one(4)
% 0.33/0.66 thf(fact_7360_ivl__disj__un__one_I4_J,axiom,
% 0.33/0.66 ! [L: num,U: num] :
% 0.33/0.66 ( ( ord_less_eq_num @ L @ U )
% 0.33/0.66 => ( ( sup_sup_set_num @ ( set_ord_lessThan_num @ L ) @ ( set_or7049704709247886629st_num @ L @ U ) )
% 0.33/0.66 = ( set_ord_atMost_num @ U ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % ivl_disj_un_one(4)
% 0.33/0.66 thf(fact_7361_ivl__disj__un__one_I4_J,axiom,
% 0.33/0.66 ! [L: int,U: int] :
% 0.33/0.66 ( ( ord_less_eq_int @ L @ U )
% 0.33/0.66 => ( ( sup_sup_set_int @ ( set_ord_lessThan_int @ L ) @ ( set_or1266510415728281911st_int @ L @ U ) )
% 0.33/0.66 = ( set_ord_atMost_int @ U ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % ivl_disj_un_one(4)
% 0.33/0.66 thf(fact_7362_ivl__disj__un__one_I4_J,axiom,
% 0.33/0.66 ! [L: nat,U: nat] :
% 0.33/0.66 ( ( ord_less_eq_nat @ L @ U )
% 0.33/0.66 => ( ( sup_sup_set_nat @ ( set_ord_lessThan_nat @ L ) @ ( set_or1269000886237332187st_nat @ L @ U ) )
% 0.33/0.66 = ( set_ord_atMost_nat @ U ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % ivl_disj_un_one(4)
% 0.33/0.66 thf(fact_7363_ivl__disj__un__one_I4_J,axiom,
% 0.33/0.66 ! [L: code_integer,U: code_integer] :
% 0.33/0.66 ( ( ord_le3102999989581377725nteger @ L @ U )
% 0.33/0.66 => ( ( sup_su848401254843788991nteger @ ( set_or5754767410780653050nteger @ L ) @ ( set_or189985376899183464nteger @ L @ U ) )
% 0.33/0.66 = ( set_or9101266186257409494nteger @ U ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % ivl_disj_un_one(4)
% 0.33/0.66 thf(fact_7364_ivl__disj__un__one_I1_J,axiom,
% 0.33/0.66 ! [L: rat,U: rat] :
% 0.33/0.66 ( ( ord_less_rat @ L @ U )
% 0.33/0.66 => ( ( sup_sup_set_rat @ ( set_ord_atMost_rat @ L ) @ ( set_or5199638295745620268an_rat @ L @ U ) )
% 0.33/0.66 = ( set_ord_lessThan_rat @ U ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % ivl_disj_un_one(1)
% 0.33/0.66 thf(fact_7365_ivl__disj__un__one_I1_J,axiom,
% 0.33/0.66 ! [L: num,U: num] :
% 0.33/0.66 ( ( ord_less_num @ L @ U )
% 0.33/0.66 => ( ( sup_sup_set_num @ ( set_ord_atMost_num @ L ) @ ( set_or2392100141987894638an_num @ L @ U ) )
% 0.33/0.66 = ( set_ord_lessThan_num @ U ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % ivl_disj_un_one(1)
% 0.33/0.66 thf(fact_7366_ivl__disj__un__one_I1_J,axiom,
% 0.33/0.66 ! [L: int,U: int] :
% 0.33/0.66 ( ( ord_less_int @ L @ U )
% 0.33/0.66 => ( ( sup_sup_set_int @ ( set_ord_atMost_int @ L ) @ ( set_or5832277885323065728an_int @ L @ U ) )
% 0.33/0.66 = ( set_ord_lessThan_int @ U ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % ivl_disj_un_one(1)
% 0.33/0.66 thf(fact_7367_ivl__disj__un__one_I1_J,axiom,
% 0.33/0.66 ! [L: nat,U: nat] :
% 0.33/0.66 ( ( ord_less_nat @ L @ U )
% 0.33/0.66 => ( ( sup_sup_set_nat @ ( set_ord_atMost_nat @ L ) @ ( set_or5834768355832116004an_nat @ L @ U ) )
% 0.33/0.66 = ( set_ord_lessThan_nat @ U ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % ivl_disj_un_one(1)
% 0.33/0.66 thf(fact_7368_ivl__disj__un__one_I1_J,axiom,
% 0.33/0.66 ! [L: code_integer,U: code_integer] :
% 0.33/0.66 ( ( ord_le6747313008572928689nteger @ L @ U )
% 0.33/0.66 => ( ( sup_su848401254843788991nteger @ ( set_or9101266186257409494nteger @ L ) @ ( set_or4266950643985792945nteger @ L @ U ) )
% 0.33/0.66 = ( set_or5754767410780653050nteger @ U ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % ivl_disj_un_one(1)
% 0.33/0.66 thf(fact_7369_intrel__def,axiom,
% 0.33/0.66 ( intrel
% 0.33/0.66 = ( produc8739625826339149834_nat_o
% 0.33/0.66 @ ^ [X3: nat,Y3: nat] :
% 0.33/0.66 ( produc6081775807080527818_nat_o
% 0.33/0.66 @ ^ [U2: nat,V2: nat] :
% 0.33/0.66 ( ( plus_plus_nat @ X3 @ V2 )
% 0.33/0.66 = ( plus_plus_nat @ U2 @ Y3 ) ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % intrel_def
% 0.33/0.66 thf(fact_7370_ivl__disj__un__singleton_I6_J,axiom,
% 0.33/0.66 ! [L: $o,U: $o] :
% 0.33/0.66 ( ( ord_less_eq_o @ L @ U )
% 0.33/0.66 => ( ( sup_sup_set_o @ ( set_or7139685690850216873Than_o @ L @ U ) @ ( insert_o @ U @ bot_bot_set_o ) )
% 0.33/0.66 = ( set_or8904488021354931149Most_o @ L @ U ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % ivl_disj_un_singleton(6)
% 0.33/0.66 thf(fact_7371_ivl__disj__un__singleton_I6_J,axiom,
% 0.33/0.66 ! [L: rat,U: rat] :
% 0.33/0.66 ( ( ord_less_eq_rat @ L @ U )
% 0.33/0.66 => ( ( sup_sup_set_rat @ ( set_or4029947393144176647an_rat @ L @ U ) @ ( insert_rat @ U @ bot_bot_set_rat ) )
% 0.33/0.66 = ( set_or633870826150836451st_rat @ L @ U ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % ivl_disj_un_singleton(6)
% 0.33/0.66 thf(fact_7372_ivl__disj__un__singleton_I6_J,axiom,
% 0.33/0.66 ! [L: num,U: num] :
% 0.33/0.66 ( ( ord_less_eq_num @ L @ U )
% 0.33/0.66 => ( ( sup_sup_set_num @ ( set_or1222409239386451017an_num @ L @ U ) @ ( insert_num @ U @ bot_bot_set_num ) )
% 0.33/0.66 = ( set_or7049704709247886629st_num @ L @ U ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % ivl_disj_un_singleton(6)
% 0.33/0.66 thf(fact_7373_ivl__disj__un__singleton_I6_J,axiom,
% 0.33/0.66 ! [L: nat,U: nat] :
% 0.33/0.66 ( ( ord_less_eq_nat @ L @ U )
% 0.33/0.66 => ( ( sup_sup_set_nat @ ( set_or4665077453230672383an_nat @ L @ U ) @ ( insert_nat @ U @ bot_bot_set_nat ) )
% 0.33/0.66 = ( set_or1269000886237332187st_nat @ L @ U ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % ivl_disj_un_singleton(6)
% 0.33/0.66 thf(fact_7374_ivl__disj__un__singleton_I6_J,axiom,
% 0.33/0.66 ! [L: code_integer,U: code_integer] :
% 0.33/0.66 ( ( ord_le3102999989581377725nteger @ L @ U )
% 0.33/0.66 => ( ( sup_su848401254843788991nteger @ ( set_or8404916559141939852nteger @ L @ U ) @ ( insert_Code_integer @ U @ bot_bo3990330152332043303nteger ) )
% 0.33/0.66 = ( set_or189985376899183464nteger @ L @ U ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % ivl_disj_un_singleton(6)
% 0.33/0.66 thf(fact_7375_ivl__disj__un__singleton_I6_J,axiom,
% 0.33/0.66 ! [L: int,U: int] :
% 0.33/0.66 ( ( ord_less_eq_int @ L @ U )
% 0.33/0.66 => ( ( sup_sup_set_int @ ( set_or4662586982721622107an_int @ L @ U ) @ ( insert_int @ U @ bot_bot_set_int ) )
% 0.33/0.66 = ( set_or1266510415728281911st_int @ L @ U ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % ivl_disj_un_singleton(6)
% 0.33/0.66 thf(fact_7376_ivl__disj__un__singleton_I3_J,axiom,
% 0.33/0.66 ! [L: $o,U: $o] :
% 0.33/0.66 ( ( ord_less_o @ L @ U )
% 0.33/0.66 => ( ( sup_sup_set_o @ ( insert_o @ L @ bot_bot_set_o ) @ ( set_or1716231572884733764Than_o @ L @ U ) )
% 0.33/0.66 = ( set_or7139685690850216873Than_o @ L @ U ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % ivl_disj_un_singleton(3)
% 0.33/0.66 thf(fact_7377_ivl__disj__un__singleton_I3_J,axiom,
% 0.33/0.66 ! [L: rat,U: rat] :
% 0.33/0.66 ( ( ord_less_rat @ L @ U )
% 0.33/0.66 => ( ( sup_sup_set_rat @ ( insert_rat @ L @ bot_bot_set_rat ) @ ( set_or5199638295745620268an_rat @ L @ U ) )
% 0.33/0.66 = ( set_or4029947393144176647an_rat @ L @ U ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % ivl_disj_un_singleton(3)
% 0.33/0.66 thf(fact_7378_ivl__disj__un__singleton_I3_J,axiom,
% 0.33/0.66 ! [L: num,U: num] :
% 0.33/0.66 ( ( ord_less_num @ L @ U )
% 0.33/0.66 => ( ( sup_sup_set_num @ ( insert_num @ L @ bot_bot_set_num ) @ ( set_or2392100141987894638an_num @ L @ U ) )
% 0.33/0.66 = ( set_or1222409239386451017an_num @ L @ U ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % ivl_disj_un_singleton(3)
% 0.33/0.66 thf(fact_7379_ivl__disj__un__singleton_I3_J,axiom,
% 0.33/0.66 ! [L: int,U: int] :
% 0.33/0.66 ( ( ord_less_int @ L @ U )
% 0.33/0.66 => ( ( sup_sup_set_int @ ( insert_int @ L @ bot_bot_set_int ) @ ( set_or5832277885323065728an_int @ L @ U ) )
% 0.33/0.66 = ( set_or4662586982721622107an_int @ L @ U ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % ivl_disj_un_singleton(3)
% 0.33/0.66 thf(fact_7380_ivl__disj__un__singleton_I3_J,axiom,
% 0.33/0.66 ! [L: nat,U: nat] :
% 0.33/0.66 ( ( ord_less_nat @ L @ U )
% 0.33/0.66 => ( ( sup_sup_set_nat @ ( insert_nat @ L @ bot_bot_set_nat ) @ ( set_or5834768355832116004an_nat @ L @ U ) )
% 0.33/0.66 = ( set_or4665077453230672383an_nat @ L @ U ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % ivl_disj_un_singleton(3)
% 0.33/0.66 thf(fact_7381_ivl__disj__un__singleton_I3_J,axiom,
% 0.33/0.66 ! [L: code_integer,U: code_integer] :
% 0.33/0.66 ( ( ord_le6747313008572928689nteger @ L @ U )
% 0.33/0.66 => ( ( sup_su848401254843788991nteger @ ( insert_Code_integer @ L @ bot_bo3990330152332043303nteger ) @ ( set_or4266950643985792945nteger @ L @ U ) )
% 0.33/0.66 = ( set_or8404916559141939852nteger @ L @ U ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % ivl_disj_un_singleton(3)
% 0.33/0.66 thf(fact_7382_ivl__disj__un__two_I4_J,axiom,
% 0.33/0.66 ! [L: rat,M2: rat,U: rat] :
% 0.33/0.66 ( ( ord_less_eq_rat @ L @ M2 )
% 0.33/0.66 => ( ( ord_less_rat @ M2 @ U )
% 0.33/0.66 => ( ( sup_sup_set_rat @ ( set_or633870826150836451st_rat @ L @ M2 ) @ ( set_or5199638295745620268an_rat @ M2 @ U ) )
% 0.33/0.66 = ( set_or4029947393144176647an_rat @ L @ U ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % ivl_disj_un_two(4)
% 0.33/0.66 thf(fact_7383_ivl__disj__un__two_I4_J,axiom,
% 0.33/0.66 ! [L: num,M2: num,U: num] :
% 0.33/0.66 ( ( ord_less_eq_num @ L @ M2 )
% 0.33/0.66 => ( ( ord_less_num @ M2 @ U )
% 0.33/0.66 => ( ( sup_sup_set_num @ ( set_or7049704709247886629st_num @ L @ M2 ) @ ( set_or2392100141987894638an_num @ M2 @ U ) )
% 0.33/0.66 = ( set_or1222409239386451017an_num @ L @ U ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % ivl_disj_un_two(4)
% 0.33/0.66 thf(fact_7384_ivl__disj__un__two_I4_J,axiom,
% 0.33/0.66 ! [L: int,M2: int,U: int] :
% 0.33/0.66 ( ( ord_less_eq_int @ L @ M2 )
% 0.33/0.66 => ( ( ord_less_int @ M2 @ U )
% 0.33/0.66 => ( ( sup_sup_set_int @ ( set_or1266510415728281911st_int @ L @ M2 ) @ ( set_or5832277885323065728an_int @ M2 @ U ) )
% 0.33/0.66 = ( set_or4662586982721622107an_int @ L @ U ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % ivl_disj_un_two(4)
% 0.33/0.66 thf(fact_7385_ivl__disj__un__two_I4_J,axiom,
% 0.33/0.66 ! [L: nat,M2: nat,U: nat] :
% 0.33/0.66 ( ( ord_less_eq_nat @ L @ M2 )
% 0.33/0.66 => ( ( ord_less_nat @ M2 @ U )
% 0.33/0.66 => ( ( sup_sup_set_nat @ ( set_or1269000886237332187st_nat @ L @ M2 ) @ ( set_or5834768355832116004an_nat @ M2 @ U ) )
% 0.33/0.66 = ( set_or4665077453230672383an_nat @ L @ U ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % ivl_disj_un_two(4)
% 0.33/0.66 thf(fact_7386_ivl__disj__un__two_I4_J,axiom,
% 0.33/0.66 ! [L: code_integer,M2: code_integer,U: code_integer] :
% 0.33/0.66 ( ( ord_le3102999989581377725nteger @ L @ M2 )
% 0.33/0.66 => ( ( ord_le6747313008572928689nteger @ M2 @ U )
% 0.33/0.66 => ( ( sup_su848401254843788991nteger @ ( set_or189985376899183464nteger @ L @ M2 ) @ ( set_or4266950643985792945nteger @ M2 @ U ) )
% 0.33/0.66 = ( set_or8404916559141939852nteger @ L @ U ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % ivl_disj_un_two(4)
% 0.33/0.66 thf(fact_7387_less__int_Orsp,axiom,
% 0.33/0.66 ( bNF_re4202695980764964119_nat_o @ intrel
% 0.33/0.66 @ ( bNF_re3666534408544137501at_o_o @ intrel
% 0.33/0.66 @ ^ [Y4: $o,Z2: $o] : ( Y4 = Z2 ) )
% 0.33/0.66 @ ( produc8739625826339149834_nat_o
% 0.33/0.66 @ ^ [X3: nat,Y3: nat] :
% 0.33/0.66 ( produc6081775807080527818_nat_o
% 0.33/0.66 @ ^ [U2: nat,V2: nat] : ( ord_less_nat @ ( plus_plus_nat @ X3 @ V2 ) @ ( plus_plus_nat @ U2 @ Y3 ) ) ) )
% 0.33/0.66 @ ( produc8739625826339149834_nat_o
% 0.33/0.66 @ ^ [X3: nat,Y3: nat] :
% 0.33/0.66 ( produc6081775807080527818_nat_o
% 0.33/0.66 @ ^ [U2: nat,V2: nat] : ( ord_less_nat @ ( plus_plus_nat @ X3 @ V2 ) @ ( plus_plus_nat @ U2 @ Y3 ) ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % less_int.rsp
% 0.33/0.66 thf(fact_7388_less__eq__int_Orsp,axiom,
% 0.33/0.66 ( bNF_re4202695980764964119_nat_o @ intrel
% 0.33/0.66 @ ( bNF_re3666534408544137501at_o_o @ intrel
% 0.33/0.66 @ ^ [Y4: $o,Z2: $o] : ( Y4 = Z2 ) )
% 0.33/0.66 @ ( produc8739625826339149834_nat_o
% 0.33/0.66 @ ^ [X3: nat,Y3: nat] :
% 0.33/0.66 ( produc6081775807080527818_nat_o
% 0.33/0.66 @ ^ [U2: nat,V2: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X3 @ V2 ) @ ( plus_plus_nat @ U2 @ Y3 ) ) ) )
% 0.33/0.66 @ ( produc8739625826339149834_nat_o
% 0.33/0.66 @ ^ [X3: nat,Y3: nat] :
% 0.33/0.66 ( produc6081775807080527818_nat_o
% 0.33/0.66 @ ^ [U2: nat,V2: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X3 @ V2 ) @ ( plus_plus_nat @ U2 @ Y3 ) ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % less_eq_int.rsp
% 0.33/0.66 thf(fact_7389_plus__int_Orsp,axiom,
% 0.33/0.66 ( bNF_re3099431351363272937at_nat @ intrel @ ( bNF_re2241393799969408733at_nat @ intrel @ intrel )
% 0.33/0.66 @ ( produc27273713700761075at_nat
% 0.33/0.66 @ ^ [X3: nat,Y3: nat] :
% 0.33/0.66 ( produc2626176000494625587at_nat
% 0.33/0.66 @ ^ [U2: nat,V2: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X3 @ U2 ) @ ( plus_plus_nat @ Y3 @ V2 ) ) ) )
% 0.33/0.66 @ ( produc27273713700761075at_nat
% 0.33/0.66 @ ^ [X3: nat,Y3: nat] :
% 0.33/0.66 ( produc2626176000494625587at_nat
% 0.33/0.66 @ ^ [U2: nat,V2: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X3 @ U2 ) @ ( plus_plus_nat @ Y3 @ V2 ) ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % plus_int.rsp
% 0.33/0.66 thf(fact_7390_minus__int_Orsp,axiom,
% 0.33/0.66 ( bNF_re3099431351363272937at_nat @ intrel @ ( bNF_re2241393799969408733at_nat @ intrel @ intrel )
% 0.33/0.66 @ ( produc27273713700761075at_nat
% 0.33/0.66 @ ^ [X3: nat,Y3: nat] :
% 0.33/0.66 ( produc2626176000494625587at_nat
% 0.33/0.66 @ ^ [U2: nat,V2: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X3 @ V2 ) @ ( plus_plus_nat @ Y3 @ U2 ) ) ) )
% 0.33/0.66 @ ( produc27273713700761075at_nat
% 0.33/0.66 @ ^ [X3: nat,Y3: nat] :
% 0.33/0.66 ( produc2626176000494625587at_nat
% 0.33/0.66 @ ^ [U2: nat,V2: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X3 @ V2 ) @ ( plus_plus_nat @ Y3 @ U2 ) ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % minus_int.rsp
% 0.33/0.66 thf(fact_7391_max__weak__def,axiom,
% 0.33/0.66 ( fun_max_weak
% 0.33/0.66 = ( sup_su5525570899277871387at_nat @ ( max_ex8135407076693332796at_nat @ fun_pair_leq ) @ ( insert9069300056098147895at_nat @ ( produc2922128104949294807at_nat @ bot_bo2099793752762293965at_nat @ bot_bo2099793752762293965at_nat ) @ bot_bo228742789529271731at_nat ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % max_weak_def
% 0.33/0.66 thf(fact_7392_min__weak__def,axiom,
% 0.33/0.66 ( fun_min_weak
% 0.33/0.66 = ( sup_su5525570899277871387at_nat @ ( min_ex6901939911449802026at_nat @ fun_pair_leq ) @ ( insert9069300056098147895at_nat @ ( produc2922128104949294807at_nat @ bot_bo2099793752762293965at_nat @ bot_bo2099793752762293965at_nat ) @ bot_bo228742789529271731at_nat ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % min_weak_def
% 0.33/0.66 thf(fact_7393_fold__union__pair,axiom,
% 0.33/0.66 ! [B5: set_Pr4811707699266497531nteger,X: produc6241069584506657477e_term > option6357759511663192854e_term,A2: set_Pr1281608226676607948nteger] :
% 0.33/0.66 ( ( finite2154694888287295812nteger @ B5 )
% 0.33/0.66 => ( ( sup_su4591284015454442744nteger
% 0.33/0.66 @ ( comple1324685164916153887nteger
% 0.33/0.66 @ ( image_5715966689554962722nteger
% 0.33/0.66 @ ^ [Y3: produc8923325533196201883nteger] : ( insert4245756632806152262nteger @ ( produc8603105652947943368nteger @ X @ Y3 ) @ bot_bo5443222936135328352nteger )
% 0.33/0.66 @ B5 ) )
% 0.33/0.66 @ A2 )
% 0.33/0.66 = ( finite7641027033760462367nteger
% 0.33/0.66 @ ^ [Y3: produc8923325533196201883nteger] : ( insert4245756632806152262nteger @ ( produc8603105652947943368nteger @ X @ Y3 ) )
% 0.33/0.66 @ A2
% 0.33/0.66 @ B5 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % fold_union_pair
% 0.33/0.66 thf(fact_7394_fold__union__pair,axiom,
% 0.33/0.66 ! [B5: set_Pr3948176798113811640et_nat,X: produc3658429121746597890et_nat > $o,A2: set_Pr3286484037609594932et_nat] :
% 0.33/0.66 ( ( finite2970523954037356441et_nat @ B5 )
% 0.33/0.66 => ( ( sup_su7128418612487073120et_nat
% 0.33/0.66 @ ( comple4849024849677941639et_nat
% 0.33/0.66 @ ( image_15228131989405757et_nat
% 0.33/0.66 @ ^ [Y3: produc3658429121746597890et_nat] : ( insert3111075074545270702et_nat @ ( produc5001842942810119800et_nat @ X @ Y3 ) @ bot_bo1481135142794719944et_nat )
% 0.33/0.66 @ B5 ) )
% 0.33/0.66 @ A2 )
% 0.33/0.66 = ( finite2494574492299216512et_nat
% 0.33/0.66 @ ^ [Y3: produc3658429121746597890et_nat] : ( insert3111075074545270702et_nat @ ( produc5001842942810119800et_nat @ X @ Y3 ) )
% 0.33/0.66 @ A2
% 0.33/0.66 @ B5 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % fold_union_pair
% 0.33/0.66 thf(fact_7395_fold__union__pair,axiom,
% 0.33/0.66 ! [B5: set_Pr3286484037609594932et_nat,X: produc3658429121746597890et_nat > $o,A2: set_Pr8536935166611901872et_nat] :
% 0.33/0.66 ( ( finite4151335170723375381et_nat @ B5 )
% 0.33/0.66 => ( ( sup_su8975264963432250076et_nat
% 0.33/0.66 @ ( comple5063570841203093763et_nat
% 0.33/0.66 @ ( image_8189767104526903093et_nat
% 0.33/0.66 @ ^ [Y3: produc3925858234332021118et_nat] : ( insert8297122186708525866et_nat @ ( produc2245416461498447860et_nat @ X @ Y3 ) @ bot_bo5635537948650799172et_nat )
% 0.33/0.66 @ B5 ) )
% 0.33/0.66 @ A2 )
% 0.33/0.66 = ( finite8124994865635982712et_nat
% 0.33/0.66 @ ^ [Y3: produc3925858234332021118et_nat] : ( insert8297122186708525866et_nat @ ( produc2245416461498447860et_nat @ X @ Y3 ) )
% 0.33/0.66 @ A2
% 0.33/0.66 @ B5 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % fold_union_pair
% 0.33/0.66 thf(fact_7396_fold__union__pair,axiom,
% 0.33/0.66 ! [B5: set_Pr958786334691620121nt_int,X: produc8551481072490612790e_term > option6357759511663192854e_term,A2: set_Pr9222295170931077689nt_int] :
% 0.33/0.66 ( ( finite2998713641127702882nt_int @ B5 )
% 0.33/0.66 => ( ( sup_su3382966977382714213nt_int
% 0.33/0.66 @ ( comple6871990601243273356nt_int
% 0.33/0.66 @ ( image_815654828163180973nt_int
% 0.33/0.66 @ ^ [Y3: product_prod_int_int] : ( insert984290209421517107nt_int @ ( produc5700946648718959541nt_int @ X @ Y3 ) @ bot_bo572930865798478029nt_int )
% 0.33/0.66 @ B5 ) )
% 0.33/0.66 @ A2 )
% 0.33/0.66 = ( finite1318812335397358250nt_int
% 0.33/0.66 @ ^ [Y3: product_prod_int_int] : ( insert984290209421517107nt_int @ ( produc5700946648718959541nt_int @ X @ Y3 ) )
% 0.33/0.66 @ A2
% 0.33/0.66 @ B5 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % fold_union_pair
% 0.33/0.66 thf(fact_7397_fold__union__pair,axiom,
% 0.33/0.66 ! [B5: set_Pr958786334691620121nt_int,X: int > option6357759511663192854e_term,A2: set_Pr1872883991513573699nt_int] :
% 0.33/0.66 ( ( finite2998713641127702882nt_int @ B5 )
% 0.33/0.66 => ( ( sup_su3298353300217089135nt_int
% 0.33/0.66 @ ( comple5772984051336441366nt_int
% 0.33/0.66 @ ( image_5963362749323609783nt_int
% 0.33/0.66 @ ^ [Y3: product_prod_int_int] : ( insert750232675644355261nt_int @ ( produc4305682042979456191nt_int @ X @ Y3 ) @ bot_bo4508923176915781079nt_int )
% 0.33/0.66 @ B5 ) )
% 0.33/0.66 @ A2 )
% 0.33/0.66 = ( finite5333674244414288180nt_int
% 0.33/0.66 @ ^ [Y3: product_prod_int_int] : ( insert750232675644355261nt_int @ ( produc4305682042979456191nt_int @ X @ Y3 ) )
% 0.33/0.66 @ A2
% 0.33/0.66 @ B5 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % fold_union_pair
% 0.33/0.66 thf(fact_7398_fold__union__pair,axiom,
% 0.33/0.66 ! [B5: set_se7855581050983116737at_nat,X: set_Pr1261947904930325089at_nat,A2: set_Pr4329608150637261639at_nat] :
% 0.33/0.66 ( ( finite9047747110432174090at_nat @ B5 )
% 0.33/0.66 => ( ( sup_su5525570899277871387at_nat
% 0.33/0.66 @ ( comple4364388969068068532at_nat
% 0.33/0.66 @ ( image_6898982319499645995at_nat
% 0.33/0.66 @ ^ [Y3: set_Pr1261947904930325089at_nat] : ( insert9069300056098147895at_nat @ ( produc2922128104949294807at_nat @ X @ Y3 ) @ bot_bo228742789529271731at_nat )
% 0.33/0.66 @ B5 ) )
% 0.33/0.66 @ A2 )
% 0.33/0.66 = ( finite3179781904389220718at_nat
% 0.33/0.66 @ ^ [Y3: set_Pr1261947904930325089at_nat] : ( insert9069300056098147895at_nat @ ( produc2922128104949294807at_nat @ X @ Y3 ) )
% 0.33/0.66 @ A2
% 0.33/0.66 @ B5 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % fold_union_pair
% 0.33/0.66 thf(fact_7399_fold__union__pair,axiom,
% 0.33/0.66 ! [B5: set_nat,X: nat,A2: set_Pr1261947904930325089at_nat] :
% 0.33/0.66 ( ( finite_finite_nat @ B5 )
% 0.33/0.66 => ( ( sup_su6327502436637775413at_nat
% 0.33/0.66 @ ( comple5685304695842803022at_nat
% 0.33/0.66 @ ( image_7178329752028323786at_nat
% 0.33/0.66 @ ^ [Y3: nat] : ( insert8211810215607154385at_nat @ ( product_Pair_nat_nat @ X @ Y3 ) @ bot_bo2099793752762293965at_nat )
% 0.33/0.66 @ B5 ) )
% 0.33/0.66 @ A2 )
% 0.33/0.66 = ( finite3745491028973389255at_nat
% 0.33/0.66 @ ^ [Y3: nat] : ( insert8211810215607154385at_nat @ ( product_Pair_nat_nat @ X @ Y3 ) )
% 0.33/0.66 @ A2
% 0.33/0.66 @ B5 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % fold_union_pair
% 0.33/0.66 thf(fact_7400_Field__insert,axiom,
% 0.33/0.66 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,R2: set_Pr4329608150637261639at_nat] :
% 0.33/0.66 ( ( field_3145993188331922222at_nat @ ( insert9069300056098147895at_nat @ ( produc2922128104949294807at_nat @ A @ B ) @ R2 ) )
% 0.33/0.66 = ( sup_su3642409539654194069at_nat @ ( insert9200635055090092081at_nat @ A @ ( insert9200635055090092081at_nat @ B @ bot_bo3083307316010499117at_nat ) ) @ ( field_3145993188331922222at_nat @ R2 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % Field_insert
% 0.33/0.66 thf(fact_7401_Field__insert,axiom,
% 0.33/0.66 ! [A: produc3843707927480180839at_nat,B: produc3843707927480180839at_nat,R2: set_Pr5564308138774400199at_nat] :
% 0.33/0.66 ( ( field_2862844103579723188at_nat @ ( insert398606708087465655at_nat @ ( produc2335810615602371415at_nat @ A @ B ) @ R2 ) )
% 0.33/0.66 = ( sup_su5525570899277871387at_nat @ ( insert9069300056098147895at_nat @ A @ ( insert9069300056098147895at_nat @ B @ bot_bo228742789529271731at_nat ) ) @ ( field_2862844103579723188at_nat @ R2 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % Field_insert
% 0.33/0.66 thf(fact_7402_Field__insert,axiom,
% 0.33/0.66 ! [A: product_prod_nat_nat,B: product_prod_nat_nat,R2: set_Pr8693737435421807431at_nat] :
% 0.33/0.66 ( ( field_4706345496283612622at_nat @ ( insert5050368324300391991at_nat @ ( produc6161850002892822231at_nat @ A @ B ) @ R2 ) )
% 0.33/0.66 = ( sup_su6327502436637775413at_nat @ ( insert8211810215607154385at_nat @ A @ ( insert8211810215607154385at_nat @ B @ bot_bo2099793752762293965at_nat ) ) @ ( field_4706345496283612622at_nat @ R2 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % Field_insert
% 0.33/0.66 thf(fact_7403_Field__insert,axiom,
% 0.33/0.66 ! [A: $o,B: $o,R2: set_Product_prod_o_o] :
% 0.33/0.66 ( ( field_o @ ( insert6201435330877294327od_o_o @ ( product_Pair_o_o @ A @ B ) @ R2 ) )
% 0.33/0.66 = ( sup_sup_set_o @ ( insert_o @ A @ ( insert_o @ B @ bot_bot_set_o ) ) @ ( field_o @ R2 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % Field_insert
% 0.33/0.66 thf(fact_7404_Field__insert,axiom,
% 0.33/0.66 ! [A: nat,B: nat,R2: set_Pr1261947904930325089at_nat] :
% 0.33/0.66 ( ( field_nat @ ( insert8211810215607154385at_nat @ ( product_Pair_nat_nat @ A @ B ) @ R2 ) )
% 0.33/0.66 = ( sup_sup_set_nat @ ( insert_nat @ A @ ( insert_nat @ B @ bot_bot_set_nat ) ) @ ( field_nat @ R2 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % Field_insert
% 0.33/0.66 thf(fact_7405_Field__insert,axiom,
% 0.33/0.66 ! [A: int,B: int,R2: set_Pr958786334691620121nt_int] :
% 0.33/0.66 ( ( field_int @ ( insert5033312907999012233nt_int @ ( product_Pair_int_int @ A @ B ) @ R2 ) )
% 0.33/0.66 = ( sup_sup_set_int @ ( insert_int @ A @ ( insert_int @ B @ bot_bot_set_int ) ) @ ( field_int @ R2 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % Field_insert
% 0.33/0.66 thf(fact_7406_set__to__map__insert,axiom,
% 0.33/0.66 ! [Kv: product_prod_nat_nat,S2: set_Pr1261947904930325089at_nat] :
% 0.33/0.66 ( ~ ( member_nat @ ( product_fst_nat_nat @ Kv ) @ ( image_2486076414777270412at_nat @ product_fst_nat_nat @ S2 ) )
% 0.33/0.66 => ( ( set_to_map_nat_nat @ ( insert8211810215607154385at_nat @ Kv @ S2 ) )
% 0.33/0.66 = ( fun_up1493157387958331631on_nat @ ( set_to_map_nat_nat @ S2 ) @ ( product_fst_nat_nat @ Kv ) @ ( some_nat @ ( product_snd_nat_nat @ Kv ) ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % set_to_map_insert
% 0.33/0.66 thf(fact_7407_set__to__map__insert,axiom,
% 0.33/0.66 ! [Kv: product_prod_o_num,S2: set_Pr7040061329075590551_o_num] :
% 0.33/0.66 ( ~ ( member_o @ ( product_fst_o_num @ Kv ) @ ( image_8863890952250787504_num_o @ product_fst_o_num @ S2 ) )
% 0.33/0.66 => ( ( set_to_map_o_num @ ( insert8656458676507137553_o_num @ Kv @ S2 ) )
% 0.33/0.66 = ( fun_upd_o_option_num @ ( set_to_map_o_num @ S2 ) @ ( product_fst_o_num @ Kv ) @ ( some_num @ ( product_snd_o_num @ Kv ) ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % set_to_map_insert
% 0.33/0.66 thf(fact_7408_set__to__map__insert,axiom,
% 0.33/0.66 ! [Kv: product_prod_nat_num,S2: set_Pr6200539531224447659at_num] :
% 0.33/0.66 ( ~ ( member_nat @ ( product_fst_nat_num @ Kv ) @ ( image_4504471508743443926um_nat @ product_fst_nat_num @ S2 ) )
% 0.33/0.66 => ( ( set_to_map_nat_num @ ( insert8920054152555992091at_num @ Kv @ S2 ) )
% 0.33/0.66 = ( fun_up2201401324907169337on_num @ ( set_to_map_nat_num @ S2 ) @ ( product_fst_nat_num @ Kv ) @ ( some_num @ ( product_snd_nat_num @ Kv ) ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % set_to_map_insert
% 0.33/0.66 thf(fact_7409_set__to__map__insert,axiom,
% 0.33/0.66 ! [Kv: product_prod_int_num,S2: set_Pr8387461105917469447nt_num] :
% 0.33/0.66 ( ~ ( member_int @ ( product_fst_int_num @ Kv ) @ ( image_4873634598471238286um_int @ product_fst_int_num @ S2 ) )
% 0.33/0.66 => ( ( set_to_map_int_num @ ( insert696035827602270839nt_num @ Kv @ S2 ) )
% 0.33/0.66 = ( fun_up4328768054909231765on_num @ ( set_to_map_int_num @ S2 ) @ ( product_fst_int_num @ Kv ) @ ( some_num @ ( product_snd_int_num @ Kv ) ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % set_to_map_insert
% 0.33/0.66 thf(fact_7410_set__to__map__insert,axiom,
% 0.33/0.66 ! [Kv: produc8923325533196201883nteger,S2: set_Pr4811707699266497531nteger] :
% 0.33/0.66 ( ~ ( member_Code_integer @ ( produc8508995932063986495nteger @ Kv ) @ ( image_6316824473203919795nteger @ produc8508995932063986495nteger @ S2 ) )
% 0.33/0.66 => ( ( set_to6264436334439079987nteger @ ( insert4913895101485356395nteger @ Kv @ S2 ) )
% 0.33/0.66 = ( fun_up6566892301432185865nteger @ ( set_to6264436334439079987nteger @ S2 ) @ ( produc8508995932063986495nteger @ Kv ) @ ( some_Code_integer @ ( produc6174133586879617921nteger @ Kv ) ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % set_to_map_insert
% 0.33/0.66 thf(fact_7411_set__to__map__insert,axiom,
% 0.33/0.66 ! [Kv: product_prod_int_int,S2: set_Pr958786334691620121nt_int] :
% 0.33/0.66 ( ~ ( member_int @ ( product_fst_int_int @ Kv ) @ ( image_5042161079198086560nt_int @ product_fst_int_int @ S2 ) )
% 0.33/0.66 => ( ( set_to_map_int_int @ ( insert5033312907999012233nt_int @ Kv @ S2 ) )
% 0.33/0.66 = ( fun_up8666045135305973159on_int @ ( set_to_map_int_int @ S2 ) @ ( product_fst_int_int @ Kv ) @ ( some_int @ ( product_snd_int_int @ Kv ) ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % set_to_map_insert
% 0.33/0.66 thf(fact_7412_set__to__map__insert,axiom,
% 0.33/0.66 ! [Kv: produc9082142974458947146at_num,S2: set_Pr7477759153910077568at_num] :
% 0.33/0.66 ( ~ ( member8440522571783428010at_nat @ ( produc1179527155093393624at_num @ Kv ) @ ( image_7418169580930627696at_nat @ produc1179527155093393624at_num @ S2 ) )
% 0.33/0.66 => ( ( set_to5081529003106763492at_num @ ( insert2790150385885543546at_num @ Kv @ S2 ) )
% 0.33/0.66 = ( fun_up8025039454679724718on_num @ ( set_to5081529003106763492at_num @ S2 ) @ ( produc1179527155093393624at_num @ Kv ) @ ( some_num @ ( produc8847702614181477910at_num @ Kv ) ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % set_to_map_insert
% 0.33/0.66 thf(fact_7413_set__to__map__insert,axiom,
% 0.33/0.66 ! [Kv: produc5835291356934675326atural,S2: set_Pr2352657477744078772atural] :
% 0.33/0.66 ( ~ ( member_Code_natural @ ( produc497848011034438852atural @ Kv ) @ ( image_8194678751871465133atural @ produc497848011034438852atural @ S2 ) )
% 0.33/0.66 => ( ( set_to6039658477269176016atural @ ( insert6505218763252461998atural @ Kv @ S2 ) )
% 0.33/0.66 = ( fun_up2923169431403285008atural @ ( set_to6039658477269176016atural @ S2 ) @ ( produc497848011034438852atural @ Kv ) @ ( some_P5671840033927537686atural @ ( produc6591912806276919810atural @ Kv ) ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % set_to_map_insert
% 0.33/0.66 thf(fact_7414_set__to__map__insert,axiom,
% 0.33/0.66 ! [Kv: produc2900562427881843919it_nat,S2: set_Pr6777250647868329861it_nat] :
% 0.33/0.66 ( ~ ( member_o @ ( produc1440270732834495325it_nat @ Kv ) @ ( image_5849890305759347266_nat_o @ produc1440270732834495325it_nat @ S2 ) )
% 0.33/0.66 => ( ( set_to3023635543527487849it_nat @ ( insert6915099157023601407it_nat @ Kv @ S2 ) )
% 0.33/0.66 = ( fun_up1288979561775348147it_nat @ ( set_to3023635543527487849it_nat @ S2 ) @ ( produc1440270732834495325it_nat @ Kv ) @ ( some_P1914260805536162275it_nat @ ( produc5978051280710547099it_nat @ Kv ) ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % set_to_map_insert
% 0.33/0.66 thf(fact_7415_set__to__map__insert,axiom,
% 0.33/0.66 ! [Kv: produc3839731585411834681it_nat,S2: set_Pr633603713510679705it_nat] :
% 0.33/0.66 ( ~ ( member_nat @ ( produc5854401122675660893it_nat @ Kv ) @ ( image_5261730836495542980at_nat @ produc5854401122675660893it_nat @ S2 ) )
% 0.33/0.66 => ( ( set_to785951348762482001it_nat @ ( insert2528233410557839625it_nat @ Kv @ S2 ) )
% 0.33/0.66 = ( fun_up4116053422210368295it_nat @ ( set_to785951348762482001it_nat @ S2 ) @ ( produc5854401122675660893it_nat @ Kv ) @ ( some_P1914260805536162275it_nat @ ( produc8417671938598930591it_nat @ Kv ) ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % set_to_map_insert
% 0.33/0.66 thf(fact_7416_plus__rat_Orsp,axiom,
% 0.33/0.66 ( bNF_re5228765855967844073nt_int @ ratrel @ ( bNF_re7145576690424134365nt_int @ ratrel @ ratrel )
% 0.33/0.66 @ ^ [X3: product_prod_int_int,Y3: product_prod_int_int] : ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ X3 ) @ ( product_snd_int_int @ Y3 ) ) @ ( times_times_int @ ( product_fst_int_int @ Y3 ) @ ( product_snd_int_int @ X3 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ X3 ) @ ( product_snd_int_int @ Y3 ) ) )
% 0.33/0.66 @ ^ [X3: product_prod_int_int,Y3: product_prod_int_int] : ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ X3 ) @ ( product_snd_int_int @ Y3 ) ) @ ( times_times_int @ ( product_fst_int_int @ Y3 ) @ ( product_snd_int_int @ X3 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ X3 ) @ ( product_snd_int_int @ Y3 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % plus_rat.rsp
% 0.33/0.66 thf(fact_7417_inverse__rat_Orsp,axiom,
% 0.33/0.66 ( bNF_re7145576690424134365nt_int @ ratrel @ ratrel
% 0.33/0.66 @ ^ [X3: product_prod_int_int] :
% 0.33/0.66 ( if_Pro3027730157355071871nt_int
% 0.33/0.66 @ ( ( product_fst_int_int @ X3 )
% 0.33/0.66 = zero_zero_int )
% 0.33/0.66 @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 0.33/0.66 @ ( product_Pair_int_int @ ( product_snd_int_int @ X3 ) @ ( product_fst_int_int @ X3 ) ) )
% 0.33/0.66 @ ^ [X3: product_prod_int_int] :
% 0.33/0.66 ( if_Pro3027730157355071871nt_int
% 0.33/0.66 @ ( ( product_fst_int_int @ X3 )
% 0.33/0.66 = zero_zero_int )
% 0.33/0.66 @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 0.33/0.66 @ ( product_Pair_int_int @ ( product_snd_int_int @ X3 ) @ ( product_fst_int_int @ X3 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % inverse_rat.rsp
% 0.33/0.66 thf(fact_7418_image__update,axiom,
% 0.33/0.66 ! [X: nat,A2: set_nat,F: nat > code_integer,N2: code_integer] :
% 0.33/0.66 ( ~ ( member_nat @ X @ A2 )
% 0.33/0.66 => ( ( image_1215581382706833972nteger @ ( fun_up3904115110581602988nteger @ F @ X @ N2 ) @ A2 )
% 0.33/0.66 = ( image_1215581382706833972nteger @ F @ A2 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % image_update
% 0.33/0.66 thf(fact_7419_image__update,axiom,
% 0.33/0.66 ! [X: nat,A2: set_nat,F: nat > set_nat,N2: set_nat] :
% 0.33/0.66 ( ~ ( member_nat @ X @ A2 )
% 0.33/0.66 => ( ( image_nat_set_nat @ ( fun_upd_nat_set_nat @ F @ X @ N2 ) @ A2 )
% 0.33/0.66 = ( image_nat_set_nat @ F @ A2 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % image_update
% 0.33/0.66 thf(fact_7420_image__update,axiom,
% 0.33/0.66 ! [X: nat,A2: set_nat,F: nat > nat,N2: nat] :
% 0.33/0.66 ( ~ ( member_nat @ X @ A2 )
% 0.33/0.66 => ( ( image_nat_nat @ ( fun_upd_nat_nat @ F @ X @ N2 ) @ A2 )
% 0.33/0.66 = ( image_nat_nat @ F @ A2 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % image_update
% 0.33/0.66 thf(fact_7421_image__update,axiom,
% 0.33/0.66 ! [X: nat,A2: set_nat,F: nat > int,N2: int] :
% 0.33/0.66 ( ~ ( member_nat @ X @ A2 )
% 0.33/0.66 => ( ( image_nat_int @ ( fun_upd_nat_int @ F @ X @ N2 ) @ A2 )
% 0.33/0.66 = ( image_nat_int @ F @ A2 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % image_update
% 0.33/0.66 thf(fact_7422_image__update,axiom,
% 0.33/0.66 ! [X: int,A2: set_int,F: int > int,N2: int] :
% 0.33/0.66 ( ~ ( member_int @ X @ A2 )
% 0.33/0.66 => ( ( image_int_int @ ( fun_upd_int_int @ F @ X @ N2 ) @ A2 )
% 0.33/0.66 = ( image_int_int @ F @ A2 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % image_update
% 0.33/0.66 thf(fact_7423_finite__Field__eq__finite,axiom,
% 0.33/0.66 ! [R4: set_Product_prod_o_o] :
% 0.33/0.66 ( ( finite_finite_o @ ( field_o @ R4 ) )
% 0.33/0.66 = ( finite6120865539452801872od_o_o @ R4 ) ) ).
% 0.33/0.66
% 0.33/0.66 % finite_Field_eq_finite
% 0.33/0.66 thf(fact_7424_finite__Field__eq__finite,axiom,
% 0.33/0.66 ! [R4: set_Pr1261947904930325089at_nat] :
% 0.33/0.66 ( ( finite_finite_nat @ ( field_nat @ R4 ) )
% 0.33/0.66 = ( finite6177210948735845034at_nat @ R4 ) ) ).
% 0.33/0.66
% 0.33/0.66 % finite_Field_eq_finite
% 0.33/0.66 thf(fact_7425_finite__Field__eq__finite,axiom,
% 0.33/0.66 ! [R4: set_Pr958786334691620121nt_int] :
% 0.33/0.66 ( ( finite_finite_int @ ( field_int @ R4 ) )
% 0.33/0.66 = ( finite2998713641127702882nt_int @ R4 ) ) ).
% 0.33/0.66
% 0.33/0.66 % finite_Field_eq_finite
% 0.33/0.66 thf(fact_7426_finite__Field__eq__finite,axiom,
% 0.33/0.66 ! [R4: set_Pr4811707699266497531nteger] :
% 0.33/0.66 ( ( finite6017078050557962740nteger @ ( field_Code_integer @ R4 ) )
% 0.33/0.66 = ( finite2154694888287295812nteger @ R4 ) ) ).
% 0.33/0.66
% 0.33/0.66 % finite_Field_eq_finite
% 0.33/0.66 thf(fact_7427_finite__Field__eq__finite,axiom,
% 0.33/0.66 ! [R4: set_Pr8693737435421807431at_nat] :
% 0.33/0.66 ( ( finite6177210948735845034at_nat @ ( field_4706345496283612622at_nat @ R4 ) )
% 0.33/0.66 = ( finite4392333629123659920at_nat @ R4 ) ) ).
% 0.33/0.66
% 0.33/0.66 % finite_Field_eq_finite
% 0.33/0.66 thf(fact_7428_image__map__upd,axiom,
% 0.33/0.66 ! [X: produc3843707927480180839at_nat,A2: set_Pr4329608150637261639at_nat,M2: produc3843707927480180839at_nat > option_num,Y: num] :
% 0.33/0.66 ( ~ ( member8757157785044589968at_nat @ X @ A2 )
% 0.33/0.66 => ( ( image_8464016542990802060on_num @ ( fun_up3286109336741039636on_num @ M2 @ X @ ( some_num @ Y ) ) @ A2 )
% 0.33/0.66 = ( image_8464016542990802060on_num @ M2 @ A2 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % image_map_upd
% 0.33/0.66 thf(fact_7429_image__map__upd,axiom,
% 0.33/0.66 ! [X: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,M2: product_prod_nat_nat > option_num,Y: num] :
% 0.33/0.66 ( ~ ( member8440522571783428010at_nat @ X @ A2 )
% 0.33/0.66 => ( ( image_1023191801488348454on_num @ ( fun_up8025039454679724718on_num @ M2 @ X @ ( some_num @ Y ) ) @ A2 )
% 0.33/0.66 = ( image_1023191801488348454on_num @ M2 @ A2 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % image_map_upd
% 0.33/0.66 thf(fact_7430_image__map__upd,axiom,
% 0.33/0.66 ! [X: $o,A2: set_o,M2: $o > option_num,Y: num] :
% 0.33/0.66 ( ~ ( member_o @ X @ A2 )
% 0.33/0.66 => ( ( image_o_option_num @ ( fun_upd_o_option_num @ M2 @ X @ ( some_num @ Y ) ) @ A2 )
% 0.33/0.66 = ( image_o_option_num @ M2 @ A2 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % image_map_upd
% 0.33/0.66 thf(fact_7431_image__map__upd,axiom,
% 0.33/0.66 ! [X: nat,A2: set_nat,M2: nat > option_num,Y: num] :
% 0.33/0.66 ( ~ ( member_nat @ X @ A2 )
% 0.33/0.66 => ( ( image_nat_option_num @ ( fun_up2201401324907169337on_num @ M2 @ X @ ( some_num @ Y ) ) @ A2 )
% 0.33/0.66 = ( image_nat_option_num @ M2 @ A2 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % image_map_upd
% 0.33/0.66 thf(fact_7432_image__map__upd,axiom,
% 0.33/0.66 ! [X: int,A2: set_int,M2: int > option_num,Y: num] :
% 0.33/0.66 ( ~ ( member_int @ X @ A2 )
% 0.33/0.66 => ( ( image_int_option_num @ ( fun_up4328768054909231765on_num @ M2 @ X @ ( some_num @ Y ) ) @ A2 )
% 0.33/0.66 = ( image_int_option_num @ M2 @ A2 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % image_map_upd
% 0.33/0.66 thf(fact_7433_image__map__upd,axiom,
% 0.33/0.66 ! [X: produc3843707927480180839at_nat,A2: set_Pr4329608150637261639at_nat,M2: produc3843707927480180839at_nat > option8956607266484857688it_nat,Y: produc8664842809031399944it_nat] :
% 0.33/0.66 ( ~ ( member8757157785044589968at_nat @ X @ A2 )
% 0.33/0.66 => ( ( image_140351626946063738it_nat @ ( fun_up5549328659429834498it_nat @ M2 @ X @ ( some_P1914260805536162275it_nat @ Y ) ) @ A2 )
% 0.33/0.66 = ( image_140351626946063738it_nat @ M2 @ A2 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % image_map_upd
% 0.33/0.66 thf(fact_7434_image__map__upd,axiom,
% 0.33/0.66 ! [X: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,M2: product_prod_nat_nat > option8956607266484857688it_nat,Y: produc8664842809031399944it_nat] :
% 0.33/0.66 ( ~ ( member8440522571783428010at_nat @ X @ A2 )
% 0.33/0.66 => ( ( image_5755308894823448084it_nat @ ( fun_up3996838528606387100it_nat @ M2 @ X @ ( some_P1914260805536162275it_nat @ Y ) ) @ A2 )
% 0.33/0.66 = ( image_5755308894823448084it_nat @ M2 @ A2 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % image_map_upd
% 0.33/0.66 thf(fact_7435_image__map__upd,axiom,
% 0.33/0.66 ! [X: $o,A2: set_o,M2: $o > option8956607266484857688it_nat,Y: produc8664842809031399944it_nat] :
% 0.33/0.66 ( ~ ( member_o @ X @ A2 )
% 0.33/0.66 => ( ( image_5849929686412825643it_nat @ ( fun_up1288979561775348147it_nat @ M2 @ X @ ( some_P1914260805536162275it_nat @ Y ) ) @ A2 )
% 0.33/0.66 = ( image_5849929686412825643it_nat @ M2 @ A2 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % image_map_upd
% 0.33/0.66 thf(fact_7436_image__map__upd,axiom,
% 0.33/0.66 ! [X: nat,A2: set_nat,M2: nat > option8956607266484857688it_nat,Y: produc8664842809031399944it_nat] :
% 0.33/0.66 ( ~ ( member_nat @ X @ A2 )
% 0.33/0.66 => ( ( image_5028743614110135983it_nat @ ( fun_up4116053422210368295it_nat @ M2 @ X @ ( some_P1914260805536162275it_nat @ Y ) ) @ A2 )
% 0.33/0.66 = ( image_5028743614110135983it_nat @ M2 @ A2 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % image_map_upd
% 0.33/0.66 thf(fact_7437_image__map__upd,axiom,
% 0.33/0.66 ! [X: int,A2: set_int,M2: int > option8956607266484857688it_nat,Y: produc8664842809031399944it_nat] :
% 0.33/0.66 ( ~ ( member_int @ X @ A2 )
% 0.33/0.66 => ( ( image_7905038228067148555it_nat @ ( fun_up6992348036167380867it_nat @ M2 @ X @ ( some_P1914260805536162275it_nat @ Y ) ) @ A2 )
% 0.33/0.66 = ( image_7905038228067148555it_nat @ M2 @ A2 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % image_map_upd
% 0.33/0.66 thf(fact_7438_FieldI2,axiom,
% 0.33/0.66 ! [I: produc3843707927480180839at_nat,J: produc3843707927480180839at_nat,R4: set_Pr5564308138774400199at_nat] :
% 0.33/0.66 ( ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ I @ J ) @ R4 )
% 0.33/0.66 => ( member8757157785044589968at_nat @ J @ ( field_2862844103579723188at_nat @ R4 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % FieldI2
% 0.33/0.66 thf(fact_7439_FieldI2,axiom,
% 0.33/0.66 ! [I: product_prod_nat_nat,J: product_prod_nat_nat,R4: set_Pr8693737435421807431at_nat] :
% 0.33/0.66 ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ I @ J ) @ R4 )
% 0.33/0.66 => ( member8440522571783428010at_nat @ J @ ( field_4706345496283612622at_nat @ R4 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % FieldI2
% 0.33/0.66 thf(fact_7440_FieldI2,axiom,
% 0.33/0.66 ! [I: int,J: int,R4: set_Pr958786334691620121nt_int] :
% 0.33/0.66 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ I @ J ) @ R4 )
% 0.33/0.66 => ( member_int @ J @ ( field_int @ R4 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % FieldI2
% 0.33/0.66 thf(fact_7441_FieldI2,axiom,
% 0.33/0.66 ! [I: set_Pr1261947904930325089at_nat,J: set_Pr1261947904930325089at_nat,R4: set_Pr4329608150637261639at_nat] :
% 0.33/0.66 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ I @ J ) @ R4 )
% 0.33/0.66 => ( member2643936169264416010at_nat @ J @ ( field_3145993188331922222at_nat @ R4 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % FieldI2
% 0.33/0.66 thf(fact_7442_FieldI2,axiom,
% 0.33/0.66 ! [I: nat,J: nat,R4: set_Pr1261947904930325089at_nat] :
% 0.33/0.66 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ I @ J ) @ R4 )
% 0.33/0.66 => ( member_nat @ J @ ( field_nat @ R4 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % FieldI2
% 0.33/0.66 thf(fact_7443_FieldI2,axiom,
% 0.33/0.66 ! [I: $o,J: $o,R4: set_Product_prod_o_o] :
% 0.33/0.66 ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ I @ J ) @ R4 )
% 0.33/0.66 => ( member_o @ J @ ( field_o @ R4 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % FieldI2
% 0.33/0.66 thf(fact_7444_FieldI1,axiom,
% 0.33/0.66 ! [I: produc3843707927480180839at_nat,J: produc3843707927480180839at_nat,R4: set_Pr5564308138774400199at_nat] :
% 0.33/0.66 ( ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ I @ J ) @ R4 )
% 0.33/0.66 => ( member8757157785044589968at_nat @ I @ ( field_2862844103579723188at_nat @ R4 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % FieldI1
% 0.33/0.66 thf(fact_7445_FieldI1,axiom,
% 0.33/0.66 ! [I: product_prod_nat_nat,J: product_prod_nat_nat,R4: set_Pr8693737435421807431at_nat] :
% 0.33/0.66 ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ I @ J ) @ R4 )
% 0.33/0.66 => ( member8440522571783428010at_nat @ I @ ( field_4706345496283612622at_nat @ R4 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % FieldI1
% 0.33/0.66 thf(fact_7446_FieldI1,axiom,
% 0.33/0.66 ! [I: int,J: int,R4: set_Pr958786334691620121nt_int] :
% 0.33/0.66 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ I @ J ) @ R4 )
% 0.33/0.66 => ( member_int @ I @ ( field_int @ R4 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % FieldI1
% 0.33/0.66 thf(fact_7447_FieldI1,axiom,
% 0.33/0.66 ! [I: set_Pr1261947904930325089at_nat,J: set_Pr1261947904930325089at_nat,R4: set_Pr4329608150637261639at_nat] :
% 0.33/0.66 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ I @ J ) @ R4 )
% 0.33/0.66 => ( member2643936169264416010at_nat @ I @ ( field_3145993188331922222at_nat @ R4 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % FieldI1
% 0.33/0.66 thf(fact_7448_FieldI1,axiom,
% 0.33/0.66 ! [I: nat,J: nat,R4: set_Pr1261947904930325089at_nat] :
% 0.33/0.66 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ I @ J ) @ R4 )
% 0.33/0.66 => ( member_nat @ I @ ( field_nat @ R4 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % FieldI1
% 0.33/0.66 thf(fact_7449_FieldI1,axiom,
% 0.33/0.66 ! [I: $o,J: $o,R4: set_Product_prod_o_o] :
% 0.33/0.66 ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ I @ J ) @ R4 )
% 0.33/0.66 => ( member_o @ I @ ( field_o @ R4 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % FieldI1
% 0.33/0.66 thf(fact_7450_sup__Un__eq2,axiom,
% 0.33/0.66 ! [R4: set_Pr1261947904930325089at_nat,S2: set_Pr1261947904930325089at_nat] :
% 0.33/0.66 ( ( sup_sup_nat_nat_o
% 0.33/0.66 @ ^ [X3: nat,Y3: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y3 ) @ R4 )
% 0.33/0.66 @ ^ [X3: nat,Y3: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y3 ) @ S2 ) )
% 0.33/0.66 = ( ^ [X3: nat,Y3: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y3 ) @ ( sup_su6327502436637775413at_nat @ R4 @ S2 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % sup_Un_eq2
% 0.33/0.66 thf(fact_7451_sup__Un__eq2,axiom,
% 0.33/0.66 ! [R4: set_Pr1281608226676607948nteger,S2: set_Pr1281608226676607948nteger] :
% 0.33/0.66 ( ( sup_su234547053653886311eger_o
% 0.33/0.66 @ ^ [X3: produc6241069584506657477e_term > option6357759511663192854e_term,Y3: produc8923325533196201883nteger] : ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X3 @ Y3 ) @ R4 )
% 0.33/0.66 @ ^ [X3: produc6241069584506657477e_term > option6357759511663192854e_term,Y3: produc8923325533196201883nteger] : ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X3 @ Y3 ) @ S2 ) )
% 0.33/0.66 = ( ^ [X3: produc6241069584506657477e_term > option6357759511663192854e_term,Y3: produc8923325533196201883nteger] : ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X3 @ Y3 ) @ ( sup_su4591284015454442744nteger @ R4 @ S2 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % sup_Un_eq2
% 0.33/0.66 thf(fact_7452_sup__Un__eq2,axiom,
% 0.33/0.66 ! [R4: set_Pr3286484037609594932et_nat,S2: set_Pr3286484037609594932et_nat] :
% 0.33/0.66 ( ( sup_su1630790145277462993_nat_o
% 0.33/0.66 @ ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3658429121746597890et_nat] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X3 @ Y3 ) @ R4 )
% 0.33/0.66 @ ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3658429121746597890et_nat] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X3 @ Y3 ) @ S2 ) )
% 0.33/0.66 = ( ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3658429121746597890et_nat] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X3 @ Y3 ) @ ( sup_su7128418612487073120et_nat @ R4 @ S2 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % sup_Un_eq2
% 0.33/0.66 thf(fact_7453_sup__Un__eq2,axiom,
% 0.33/0.66 ! [R4: set_Pr8536935166611901872et_nat,S2: set_Pr8536935166611901872et_nat] :
% 0.33/0.66 ( ( sup_su6535292691877529429_nat_o
% 0.33/0.66 @ ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3925858234332021118et_nat] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X3 @ Y3 ) @ R4 )
% 0.33/0.66 @ ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3925858234332021118et_nat] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X3 @ Y3 ) @ S2 ) )
% 0.33/0.66 = ( ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3925858234332021118et_nat] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X3 @ Y3 ) @ ( sup_su8975264963432250076et_nat @ R4 @ S2 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % sup_Un_eq2
% 0.33/0.66 thf(fact_7454_sup__Un__eq2,axiom,
% 0.33/0.66 ! [R4: set_Pr9222295170931077689nt_int,S2: set_Pr9222295170931077689nt_int] :
% 0.33/0.66 ( ( sup_su4182031696650224058_int_o
% 0.33/0.66 @ ^ [X3: produc8551481072490612790e_term > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X3 @ Y3 ) @ R4 )
% 0.33/0.66 @ ^ [X3: produc8551481072490612790e_term > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X3 @ Y3 ) @ S2 ) )
% 0.33/0.66 = ( ^ [X3: produc8551481072490612790e_term > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X3 @ Y3 ) @ ( sup_su3382966977382714213nt_int @ R4 @ S2 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % sup_Un_eq2
% 0.33/0.66 thf(fact_7455_sup__Un__eq2,axiom,
% 0.33/0.66 ! [R4: set_Pr1872883991513573699nt_int,S2: set_Pr1872883991513573699nt_int] :
% 0.33/0.66 ( ( sup_su600977994968626096_int_o
% 0.33/0.66 @ ^ [X3: int > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X3 @ Y3 ) @ R4 )
% 0.33/0.66 @ ^ [X3: int > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X3 @ Y3 ) @ S2 ) )
% 0.33/0.66 = ( ^ [X3: int > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X3 @ Y3 ) @ ( sup_su3298353300217089135nt_int @ R4 @ S2 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % sup_Un_eq2
% 0.33/0.66 thf(fact_7456_sup__Un__eq2,axiom,
% 0.33/0.66 ! [R4: set_Pr4329608150637261639at_nat,S2: set_Pr4329608150637261639at_nat] :
% 0.33/0.66 ( ( sup_su7519161239522478338_nat_o
% 0.33/0.66 @ ^ [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ Y3 ) @ R4 )
% 0.33/0.66 @ ^ [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ Y3 ) @ S2 ) )
% 0.33/0.66 = ( ^ [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ Y3 ) @ ( sup_su5525570899277871387at_nat @ R4 @ S2 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % sup_Un_eq2
% 0.33/0.66 thf(fact_7457_fun__upd__comp,axiom,
% 0.33/0.66 ! [F: code_integer > code_integer,G: num > code_integer,X: num,Y: code_integer] :
% 0.33/0.66 ( ( comp_C3531382070062128313er_num @ F @ ( fun_up1844922938552261878nteger @ G @ X @ Y ) )
% 0.33/0.66 = ( fun_up1844922938552261878nteger @ ( comp_C3531382070062128313er_num @ F @ G ) @ X @ ( F @ Y ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % fun_upd_comp
% 0.33/0.66 thf(fact_7458_fun__upd__comp,axiom,
% 0.33/0.66 ! [F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer,X: code_integer,Y: code_integer] :
% 0.33/0.66 ( ( comp_C1593894019821074884nteger @ F @ ( fun_up8355007323143964473nteger @ G @ X @ Y ) )
% 0.33/0.66 = ( fun_up8139772397987072257nteger @ ( comp_C1593894019821074884nteger @ F @ G ) @ X @ ( F @ Y ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % fun_upd_comp
% 0.33/0.66 thf(fact_7459_fun__upd__comp,axiom,
% 0.33/0.66 ! [F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer > code_integer,X: code_integer,Y: code_integer > code_integer] :
% 0.33/0.66 ( ( comp_C8797469213163452608nteger @ F @ ( fun_up8056716234270145717nteger @ G @ X @ Y ) )
% 0.33/0.66 = ( fun_up8139772397987072257nteger @ ( comp_C8797469213163452608nteger @ F @ G ) @ X @ ( F @ Y ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % fun_upd_comp
% 0.33/0.66 thf(fact_7460_fun__upd__comp,axiom,
% 0.33/0.66 ! [F: nat > num,G: int > nat,X: int,Y: nat] :
% 0.33/0.66 ( ( comp_nat_num_int @ F @ ( fun_upd_int_nat @ G @ X @ Y ) )
% 0.33/0.66 = ( fun_upd_int_num @ ( comp_nat_num_int @ F @ G ) @ X @ ( F @ Y ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % fun_upd_comp
% 0.33/0.66 thf(fact_7461_one__rat_Orsp,axiom,
% 0.33/0.66 ratrel @ ( product_Pair_int_int @ one_one_int @ one_one_int ) @ ( product_Pair_int_int @ one_one_int @ one_one_int ) ).
% 0.33/0.66
% 0.33/0.66 % one_rat.rsp
% 0.33/0.66 thf(fact_7462_R__subset__Field,axiom,
% 0.33/0.66 ! [R4: set_Pr1261947904930325089at_nat] :
% 0.33/0.66 ( ord_le3146513528884898305at_nat @ R4
% 0.33/0.66 @ ( produc457027306803732586at_nat @ ( field_nat @ R4 )
% 0.33/0.66 @ ^ [Uu: nat] : ( field_nat @ R4 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % R_subset_Field
% 0.33/0.66 thf(fact_7463_R__subset__Field,axiom,
% 0.33/0.66 ! [R4: set_Product_prod_o_o] :
% 0.33/0.66 ( ord_le192195778054999463od_o_o @ R4
% 0.33/0.66 @ ( product_Sigma_o_o @ ( field_o @ R4 )
% 0.33/0.66 @ ^ [Uu: $o] : ( field_o @ R4 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % R_subset_Field
% 0.33/0.66 thf(fact_7464_fst__in__Field,axiom,
% 0.33/0.66 ! [R4: set_Product_prod_o_o] : ( ord_less_eq_set_o @ ( image_7896445794123959606_o_o_o @ product_fst_o_o @ R4 ) @ ( field_o @ R4 ) ) ).
% 0.33/0.66
% 0.33/0.66 % fst_in_Field
% 0.33/0.66 thf(fact_7465_fst__in__Field,axiom,
% 0.33/0.66 ! [R4: set_Pr4811707699266497531nteger] : ( ord_le7084787975880047091nteger @ ( image_6316824473203919795nteger @ produc8508995932063986495nteger @ R4 ) @ ( field_Code_integer @ R4 ) ) ).
% 0.33/0.66
% 0.33/0.66 % fst_in_Field
% 0.33/0.66 thf(fact_7466_fst__in__Field,axiom,
% 0.33/0.66 ! [R4: set_Pr958786334691620121nt_int] : ( ord_less_eq_set_int @ ( image_5042161079198086560nt_int @ product_fst_int_int @ R4 ) @ ( field_int @ R4 ) ) ).
% 0.33/0.66
% 0.33/0.66 % fst_in_Field
% 0.33/0.66 thf(fact_7467_fst__in__Field,axiom,
% 0.33/0.66 ! [R4: set_Pr1261947904930325089at_nat] : ( ord_less_eq_set_nat @ ( image_2486076414777270412at_nat @ product_fst_nat_nat @ R4 ) @ ( field_nat @ R4 ) ) ).
% 0.33/0.66
% 0.33/0.66 % fst_in_Field
% 0.33/0.66 thf(fact_7468_snd__in__Field,axiom,
% 0.33/0.66 ! [R4: set_Product_prod_o_o] : ( ord_less_eq_set_o @ ( image_7896445794123959606_o_o_o @ product_snd_o_o @ R4 ) @ ( field_o @ R4 ) ) ).
% 0.33/0.66
% 0.33/0.66 % snd_in_Field
% 0.33/0.66 thf(fact_7469_snd__in__Field,axiom,
% 0.33/0.66 ! [R4: set_Pr4811707699266497531nteger] : ( ord_le7084787975880047091nteger @ ( image_6316824473203919795nteger @ produc6174133586879617921nteger @ R4 ) @ ( field_Code_integer @ R4 ) ) ).
% 0.33/0.66
% 0.33/0.66 % snd_in_Field
% 0.33/0.66 thf(fact_7470_snd__in__Field,axiom,
% 0.33/0.66 ! [R4: set_Pr958786334691620121nt_int] : ( ord_less_eq_set_int @ ( image_5042161079198086560nt_int @ product_snd_int_int @ R4 ) @ ( field_int @ R4 ) ) ).
% 0.33/0.66
% 0.33/0.66 % snd_in_Field
% 0.33/0.66 thf(fact_7471_snd__in__Field,axiom,
% 0.33/0.66 ! [R4: set_Pr1261947904930325089at_nat] : ( ord_less_eq_set_nat @ ( image_2486076414777270412at_nat @ product_snd_nat_nat @ R4 ) @ ( field_nat @ R4 ) ) ).
% 0.33/0.66
% 0.33/0.66 % snd_in_Field
% 0.33/0.66 thf(fact_7472_zero__rat_Orsp,axiom,
% 0.33/0.66 ratrel @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) ).
% 0.33/0.66
% 0.33/0.66 % zero_rat.rsp
% 0.33/0.66 thf(fact_7473_Fract_Orsp,axiom,
% 0.33/0.66 ( bNF_re157797125943740599nt_int
% 0.33/0.66 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.66 @ ( bNF_re6250860962936578807nt_int
% 0.33/0.66 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.66 @ ratrel )
% 0.33/0.66 @ ^ [A5: int,B4: int] : ( if_Pro3027730157355071871nt_int @ ( B4 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ A5 @ B4 ) )
% 0.33/0.66 @ ^ [A5: int,B4: int] : ( if_Pro3027730157355071871nt_int @ ( B4 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ A5 @ B4 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % Fract.rsp
% 0.33/0.66 thf(fact_7474_sum_Oeq__fold,axiom,
% 0.33/0.66 ( groups3542108847815614940at_nat
% 0.33/0.66 = ( ^ [G2: nat > nat] : ( finite_fold_nat_nat @ ( comp_nat_nat_nat_nat @ plus_plus_nat @ G2 ) @ zero_zero_nat ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % sum.eq_fold
% 0.33/0.66 thf(fact_7475_sum_Oeq__fold,axiom,
% 0.33/0.66 ( groups4538972089207619220nt_int
% 0.33/0.66 = ( ^ [G2: int > int] : ( finite_fold_int_int @ ( comp_int_int_int_int @ plus_plus_int @ G2 ) @ zero_zero_int ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % sum.eq_fold
% 0.33/0.66 thf(fact_7476_prod_Oeq__fold,axiom,
% 0.33/0.66 ( groups708209901874060359at_nat
% 0.33/0.66 = ( ^ [G2: nat > nat] : ( finite_fold_nat_nat @ ( comp_nat_nat_nat_nat @ times_times_nat @ G2 ) @ one_one_nat ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % prod.eq_fold
% 0.33/0.66 thf(fact_7477_prod_Oeq__fold,axiom,
% 0.33/0.66 ( groups705719431365010083at_int
% 0.33/0.66 = ( ^ [G2: nat > int] : ( finite_fold_nat_int @ ( comp_int_int_int_nat @ times_times_int @ G2 ) @ one_one_int ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % prod.eq_fold
% 0.33/0.66 thf(fact_7478_prod_Oeq__fold,axiom,
% 0.33/0.66 ( groups1705073143266064639nt_int
% 0.33/0.66 = ( ^ [G2: int > int] : ( finite_fold_int_int @ ( comp_int_int_int_int @ times_times_int @ G2 ) @ one_one_int ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % prod.eq_fold
% 0.33/0.66 thf(fact_7479_finite__range__updI,axiom,
% 0.33/0.66 ! [F: nat > option_num,A: nat,B: num] :
% 0.33/0.66 ( ( finite6231397076622260609on_num @ ( image_nat_option_num @ F @ top_top_set_nat ) )
% 0.33/0.66 => ( finite6231397076622260609on_num @ ( image_nat_option_num @ ( fun_up2201401324907169337on_num @ F @ A @ ( some_num @ B ) ) @ top_top_set_nat ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % finite_range_updI
% 0.33/0.66 thf(fact_7480_finite__range__updI,axiom,
% 0.33/0.66 ! [F: nat > option8956607266484857688it_nat,A: nat,B: produc8664842809031399944it_nat] :
% 0.33/0.66 ( ( finite6292238467249657455it_nat @ ( image_5028743614110135983it_nat @ F @ top_top_set_nat ) )
% 0.33/0.66 => ( finite6292238467249657455it_nat @ ( image_5028743614110135983it_nat @ ( fun_up4116053422210368295it_nat @ F @ A @ ( some_P1914260805536162275it_nat @ B ) ) @ top_top_set_nat ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % finite_range_updI
% 0.33/0.66 thf(fact_7481_finite__range__updI,axiom,
% 0.33/0.66 ! [F: product_unit > option_num,A: product_unit,B: num] :
% 0.33/0.66 ( ( finite6231397076622260609on_num @ ( image_5965367930834091826on_num @ F @ top_to1996260823553986621t_unit ) )
% 0.33/0.66 => ( finite6231397076622260609on_num @ ( image_5965367930834091826on_num @ ( fun_up4695802795598371002on_num @ F @ A @ ( some_num @ B ) ) @ top_to1996260823553986621t_unit ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % finite_range_updI
% 0.33/0.66 thf(fact_7482_finite__range__updI,axiom,
% 0.33/0.66 ! [F: product_unit > option8956607266484857688it_nat,A: product_unit,B: produc8664842809031399944it_nat] :
% 0.33/0.66 ( ( finite6292238467249657455it_nat @ ( image_5022536681399171104it_nat @ F @ top_to1996260823553986621t_unit ) )
% 0.33/0.66 => ( finite6292238467249657455it_nat @ ( image_5022536681399171104it_nat @ ( fun_up1973317344121680296it_nat @ F @ A @ ( some_P1914260805536162275it_nat @ B ) ) @ top_to1996260823553986621t_unit ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % finite_range_updI
% 0.33/0.66 thf(fact_7483_finite__range__updI,axiom,
% 0.33/0.66 ! [F: int > option_num,A: int,B: num] :
% 0.33/0.66 ( ( finite6231397076622260609on_num @ ( image_int_option_num @ F @ top_top_set_int ) )
% 0.33/0.66 => ( finite6231397076622260609on_num @ ( image_int_option_num @ ( fun_up4328768054909231765on_num @ F @ A @ ( some_num @ B ) ) @ top_top_set_int ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % finite_range_updI
% 0.33/0.66 thf(fact_7484_finite__range__updI,axiom,
% 0.33/0.66 ! [F: int > option8956607266484857688it_nat,A: int,B: produc8664842809031399944it_nat] :
% 0.33/0.66 ( ( finite6292238467249657455it_nat @ ( image_7905038228067148555it_nat @ F @ top_top_set_int ) )
% 0.33/0.66 => ( finite6292238467249657455it_nat @ ( image_7905038228067148555it_nat @ ( fun_up6992348036167380867it_nat @ F @ A @ ( some_P1914260805536162275it_nat @ B ) ) @ top_top_set_int ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % finite_range_updI
% 0.33/0.66 thf(fact_7485_fun__upd__image,axiom,
% 0.33/0.66 ! [X: $o,A2: set_o,F: $o > $o,Y: $o] :
% 0.33/0.66 ( ( ( member_o @ X @ A2 )
% 0.33/0.66 => ( ( image_o_o @ ( fun_upd_o_o @ F @ X @ Y ) @ A2 )
% 0.33/0.66 = ( insert_o @ Y @ ( image_o_o @ F @ ( minus_minus_set_o @ A2 @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) )
% 0.33/0.66 & ( ~ ( member_o @ X @ A2 )
% 0.33/0.66 => ( ( image_o_o @ ( fun_upd_o_o @ F @ X @ Y ) @ A2 )
% 0.33/0.66 = ( image_o_o @ F @ A2 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % fun_upd_image
% 0.33/0.66 thf(fact_7486_fun__upd__image,axiom,
% 0.33/0.66 ! [X: $o,A2: set_o,F: $o > nat,Y: nat] :
% 0.33/0.66 ( ( ( member_o @ X @ A2 )
% 0.33/0.66 => ( ( image_o_nat @ ( fun_upd_o_nat @ F @ X @ Y ) @ A2 )
% 0.33/0.66 = ( insert_nat @ Y @ ( image_o_nat @ F @ ( minus_minus_set_o @ A2 @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) )
% 0.33/0.66 & ( ~ ( member_o @ X @ A2 )
% 0.33/0.66 => ( ( image_o_nat @ ( fun_upd_o_nat @ F @ X @ Y ) @ A2 )
% 0.33/0.66 = ( image_o_nat @ F @ A2 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % fun_upd_image
% 0.33/0.66 thf(fact_7487_fun__upd__image,axiom,
% 0.33/0.66 ! [X: $o,A2: set_o,F: $o > int,Y: int] :
% 0.33/0.66 ( ( ( member_o @ X @ A2 )
% 0.33/0.66 => ( ( image_o_int @ ( fun_upd_o_int @ F @ X @ Y ) @ A2 )
% 0.33/0.66 = ( insert_int @ Y @ ( image_o_int @ F @ ( minus_minus_set_o @ A2 @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) )
% 0.33/0.66 & ( ~ ( member_o @ X @ A2 )
% 0.33/0.66 => ( ( image_o_int @ ( fun_upd_o_int @ F @ X @ Y ) @ A2 )
% 0.33/0.66 = ( image_o_int @ F @ A2 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % fun_upd_image
% 0.33/0.66 thf(fact_7488_fun__upd__image,axiom,
% 0.33/0.66 ! [X: int,A2: set_int,F: int > $o,Y: $o] :
% 0.33/0.66 ( ( ( member_int @ X @ A2 )
% 0.33/0.66 => ( ( image_int_o @ ( fun_upd_int_o @ F @ X @ Y ) @ A2 )
% 0.33/0.66 = ( insert_o @ Y @ ( image_int_o @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) )
% 0.33/0.66 & ( ~ ( member_int @ X @ A2 )
% 0.33/0.66 => ( ( image_int_o @ ( fun_upd_int_o @ F @ X @ Y ) @ A2 )
% 0.33/0.66 = ( image_int_o @ F @ A2 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % fun_upd_image
% 0.33/0.66 thf(fact_7489_fun__upd__image,axiom,
% 0.33/0.66 ! [X: int,A2: set_int,F: int > nat,Y: nat] :
% 0.33/0.66 ( ( ( member_int @ X @ A2 )
% 0.33/0.66 => ( ( image_int_nat @ ( fun_upd_int_nat @ F @ X @ Y ) @ A2 )
% 0.33/0.66 = ( insert_nat @ Y @ ( image_int_nat @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) )
% 0.33/0.66 & ( ~ ( member_int @ X @ A2 )
% 0.33/0.66 => ( ( image_int_nat @ ( fun_upd_int_nat @ F @ X @ Y ) @ A2 )
% 0.33/0.66 = ( image_int_nat @ F @ A2 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % fun_upd_image
% 0.33/0.66 thf(fact_7490_fun__upd__image,axiom,
% 0.33/0.66 ! [X: int,A2: set_int,F: int > int,Y: int] :
% 0.33/0.66 ( ( ( member_int @ X @ A2 )
% 0.33/0.66 => ( ( image_int_int @ ( fun_upd_int_int @ F @ X @ Y ) @ A2 )
% 0.33/0.66 = ( insert_int @ Y @ ( image_int_int @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) )
% 0.33/0.66 & ( ~ ( member_int @ X @ A2 )
% 0.33/0.66 => ( ( image_int_int @ ( fun_upd_int_int @ F @ X @ Y ) @ A2 )
% 0.33/0.66 = ( image_int_int @ F @ A2 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % fun_upd_image
% 0.33/0.66 thf(fact_7491_fun__upd__image,axiom,
% 0.33/0.66 ! [X: nat,A2: set_nat,F: nat > code_integer,Y: code_integer] :
% 0.33/0.66 ( ( ( member_nat @ X @ A2 )
% 0.33/0.66 => ( ( image_1215581382706833972nteger @ ( fun_up3904115110581602988nteger @ F @ X @ Y ) @ A2 )
% 0.33/0.66 = ( insert_Code_integer @ Y @ ( image_1215581382706833972nteger @ F @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) )
% 0.33/0.66 & ( ~ ( member_nat @ X @ A2 )
% 0.33/0.66 => ( ( image_1215581382706833972nteger @ ( fun_up3904115110581602988nteger @ F @ X @ Y ) @ A2 )
% 0.33/0.66 = ( image_1215581382706833972nteger @ F @ A2 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % fun_upd_image
% 0.33/0.66 thf(fact_7492_fun__upd__image,axiom,
% 0.33/0.66 ! [X: nat,A2: set_nat,F: nat > $o,Y: $o] :
% 0.33/0.66 ( ( ( member_nat @ X @ A2 )
% 0.33/0.66 => ( ( image_nat_o @ ( fun_upd_nat_o @ F @ X @ Y ) @ A2 )
% 0.33/0.66 = ( insert_o @ Y @ ( image_nat_o @ F @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) )
% 0.33/0.66 & ( ~ ( member_nat @ X @ A2 )
% 0.33/0.66 => ( ( image_nat_o @ ( fun_upd_nat_o @ F @ X @ Y ) @ A2 )
% 0.33/0.66 = ( image_nat_o @ F @ A2 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % fun_upd_image
% 0.33/0.66 thf(fact_7493_fun__upd__image,axiom,
% 0.33/0.66 ! [X: nat,A2: set_nat,F: nat > nat,Y: nat] :
% 0.33/0.66 ( ( ( member_nat @ X @ A2 )
% 0.33/0.66 => ( ( image_nat_nat @ ( fun_upd_nat_nat @ F @ X @ Y ) @ A2 )
% 0.33/0.66 = ( insert_nat @ Y @ ( image_nat_nat @ F @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) )
% 0.33/0.66 & ( ~ ( member_nat @ X @ A2 )
% 0.33/0.66 => ( ( image_nat_nat @ ( fun_upd_nat_nat @ F @ X @ Y ) @ A2 )
% 0.33/0.66 = ( image_nat_nat @ F @ A2 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % fun_upd_image
% 0.33/0.66 thf(fact_7494_fun__upd__image,axiom,
% 0.33/0.66 ! [X: nat,A2: set_nat,F: nat > int,Y: int] :
% 0.33/0.66 ( ( ( member_nat @ X @ A2 )
% 0.33/0.66 => ( ( image_nat_int @ ( fun_upd_nat_int @ F @ X @ Y ) @ A2 )
% 0.33/0.66 = ( insert_int @ Y @ ( image_nat_int @ F @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) )
% 0.33/0.66 & ( ~ ( member_nat @ X @ A2 )
% 0.33/0.66 => ( ( image_nat_int @ ( fun_upd_nat_int @ F @ X @ Y ) @ A2 )
% 0.33/0.66 = ( image_nat_int @ F @ A2 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % fun_upd_image
% 0.33/0.66 thf(fact_7495_times__rat_Orsp,axiom,
% 0.33/0.66 ( bNF_re5228765855967844073nt_int @ ratrel @ ( bNF_re7145576690424134365nt_int @ ratrel @ ratrel )
% 0.33/0.66 @ ^ [X3: product_prod_int_int,Y3: product_prod_int_int] : ( product_Pair_int_int @ ( times_times_int @ ( product_fst_int_int @ X3 ) @ ( product_fst_int_int @ Y3 ) ) @ ( times_times_int @ ( product_snd_int_int @ X3 ) @ ( product_snd_int_int @ Y3 ) ) )
% 0.33/0.66 @ ^ [X3: product_prod_int_int,Y3: product_prod_int_int] : ( product_Pair_int_int @ ( times_times_int @ ( product_fst_int_int @ X3 ) @ ( product_fst_int_int @ Y3 ) ) @ ( times_times_int @ ( product_snd_int_int @ X3 ) @ ( product_snd_int_int @ Y3 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % times_rat.rsp
% 0.33/0.66 thf(fact_7496_uminus__rat_Orsp,axiom,
% 0.33/0.66 ( bNF_re7145576690424134365nt_int @ ratrel @ ratrel
% 0.33/0.66 @ ^ [X3: product_prod_int_int] : ( product_Pair_int_int @ ( uminus_uminus_int @ ( product_fst_int_int @ X3 ) ) @ ( product_snd_int_int @ X3 ) )
% 0.33/0.66 @ ^ [X3: product_prod_int_int] : ( product_Pair_int_int @ ( uminus_uminus_int @ ( product_fst_int_int @ X3 ) ) @ ( product_snd_int_int @ X3 ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % uminus_rat.rsp
% 0.33/0.66 thf(fact_7497_plus__rat_Oabs__eq,axiom,
% 0.33/0.66 ! [Xa: product_prod_int_int,X: product_prod_int_int] :
% 0.33/0.66 ( ( ratrel @ Xa @ Xa )
% 0.33/0.66 => ( ( ratrel @ X @ X )
% 0.33/0.66 => ( ( plus_plus_rat @ ( abs_Rat @ Xa ) @ ( abs_Rat @ X ) )
% 0.33/0.66 = ( abs_Rat @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ Xa ) @ ( product_snd_int_int @ X ) ) @ ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_snd_int_int @ Xa ) ) ) @ ( times_times_int @ ( product_snd_int_int @ Xa ) @ ( product_snd_int_int @ X ) ) ) ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % plus_rat.abs_eq
% 0.33/0.66 thf(fact_7498_inverse__rat_Oabs__eq,axiom,
% 0.33/0.66 ! [X: product_prod_int_int] :
% 0.33/0.66 ( ( ratrel @ X @ X )
% 0.33/0.66 => ( ( inverse_inverse_rat @ ( abs_Rat @ X ) )
% 0.33/0.66 = ( abs_Rat
% 0.33/0.66 @ ( if_Pro3027730157355071871nt_int
% 0.33/0.66 @ ( ( product_fst_int_int @ X )
% 0.33/0.66 = zero_zero_int )
% 0.33/0.66 @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 0.33/0.66 @ ( product_Pair_int_int @ ( product_snd_int_int @ X ) @ ( product_fst_int_int @ X ) ) ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % inverse_rat.abs_eq
% 0.33/0.66 thf(fact_7499_times__rat_Oabs__eq,axiom,
% 0.33/0.66 ! [Xa: product_prod_int_int,X: product_prod_int_int] :
% 0.33/0.66 ( ( ratrel @ Xa @ Xa )
% 0.33/0.66 => ( ( ratrel @ X @ X )
% 0.33/0.66 => ( ( times_times_rat @ ( abs_Rat @ Xa ) @ ( abs_Rat @ X ) )
% 0.33/0.66 = ( abs_Rat @ ( product_Pair_int_int @ ( times_times_int @ ( product_fst_int_int @ Xa ) @ ( product_fst_int_int @ X ) ) @ ( times_times_int @ ( product_snd_int_int @ Xa ) @ ( product_snd_int_int @ X ) ) ) ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % times_rat.abs_eq
% 0.33/0.66 thf(fact_7500_uminus__rat_Oabs__eq,axiom,
% 0.33/0.66 ! [X: product_prod_int_int] :
% 0.33/0.66 ( ( ratrel @ X @ X )
% 0.33/0.66 => ( ( uminus_uminus_rat @ ( abs_Rat @ X ) )
% 0.33/0.66 = ( abs_Rat @ ( product_Pair_int_int @ ( uminus_uminus_int @ ( product_fst_int_int @ X ) ) @ ( product_snd_int_int @ X ) ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % uminus_rat.abs_eq
% 0.33/0.66 thf(fact_7501_one__rat__def,axiom,
% 0.33/0.66 ( one_one_rat
% 0.33/0.66 = ( abs_Rat @ ( product_Pair_int_int @ one_one_int @ one_one_int ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % one_rat_def
% 0.33/0.66 thf(fact_7502_zero__rat__def,axiom,
% 0.33/0.66 ( zero_zero_rat
% 0.33/0.66 = ( abs_Rat @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % zero_rat_def
% 0.33/0.66 thf(fact_7503_plus__rat__def,axiom,
% 0.33/0.66 ( plus_plus_rat
% 0.33/0.66 = ( map_fu4333342158222067775at_rat @ rep_Rat @ ( map_fu5673905371560938248nt_rat @ rep_Rat @ abs_Rat )
% 0.33/0.66 @ ^ [X3: product_prod_int_int,Y3: product_prod_int_int] : ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ X3 ) @ ( product_snd_int_int @ Y3 ) ) @ ( times_times_int @ ( product_fst_int_int @ Y3 ) @ ( product_snd_int_int @ X3 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ X3 ) @ ( product_snd_int_int @ Y3 ) ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % plus_rat_def
% 0.33/0.66 thf(fact_7504_inverse__rat__def,axiom,
% 0.33/0.66 ( inverse_inverse_rat
% 0.33/0.66 = ( map_fu5673905371560938248nt_rat @ rep_Rat @ abs_Rat
% 0.33/0.66 @ ^ [X3: product_prod_int_int] :
% 0.33/0.66 ( if_Pro3027730157355071871nt_int
% 0.33/0.66 @ ( ( product_fst_int_int @ X3 )
% 0.33/0.66 = zero_zero_int )
% 0.33/0.66 @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 0.33/0.66 @ ( product_Pair_int_int @ ( product_snd_int_int @ X3 ) @ ( product_fst_int_int @ X3 ) ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % inverse_rat_def
% 0.33/0.66 thf(fact_7505_times__rat__def,axiom,
% 0.33/0.66 ( times_times_rat
% 0.33/0.66 = ( map_fu4333342158222067775at_rat @ rep_Rat @ ( map_fu5673905371560938248nt_rat @ rep_Rat @ abs_Rat )
% 0.33/0.66 @ ^ [X3: product_prod_int_int,Y3: product_prod_int_int] : ( product_Pair_int_int @ ( times_times_int @ ( product_fst_int_int @ X3 ) @ ( product_fst_int_int @ Y3 ) ) @ ( times_times_int @ ( product_snd_int_int @ X3 ) @ ( product_snd_int_int @ Y3 ) ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % times_rat_def
% 0.33/0.66 thf(fact_7506_uminus__rat__def,axiom,
% 0.33/0.66 ( uminus_uminus_rat
% 0.33/0.66 = ( map_fu5673905371560938248nt_rat @ rep_Rat @ abs_Rat
% 0.33/0.66 @ ^ [X3: product_prod_int_int] : ( product_Pair_int_int @ ( uminus_uminus_int @ ( product_fst_int_int @ X3 ) ) @ ( product_snd_int_int @ X3 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % uminus_rat_def
% 0.33/0.66 thf(fact_7507_card__le__Suc__Max,axiom,
% 0.33/0.66 ! [S2: set_nat] :
% 0.33/0.66 ( ( finite_finite_nat @ S2 )
% 0.33/0.66 => ( ord_less_eq_nat @ ( finite_card_nat @ S2 ) @ ( suc @ ( lattic8265883725875713057ax_nat @ S2 ) ) ) ) ).
% 0.33/0.66
% 0.33/0.66 % card_le_Suc_Max
% 0.33/0.66 thf(fact_7508_greaterThan__Suc,axiom,
% 0.33/0.66 ! [K: nat] :
% 0.33/0.66 ( ( set_or1210151606488870762an_nat @ ( suc @ K ) )
% 0.33/0.67 = ( minus_minus_set_nat @ ( set_or1210151606488870762an_nat @ K ) @ ( insert_nat @ ( suc @ K ) @ bot_bot_set_nat ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % greaterThan_Suc
% 0.33/0.67 thf(fact_7509_INT__greaterThan__UNIV,axiom,
% 0.33/0.67 ( ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ set_or1210151606488870762an_nat @ top_top_set_nat ) )
% 0.33/0.67 = bot_bot_set_nat ) ).
% 0.33/0.67
% 0.33/0.67 % INT_greaterThan_UNIV
% 0.33/0.67 thf(fact_7510_greaterThan__0,axiom,
% 0.33/0.67 ( ( set_or1210151606488870762an_nat @ zero_zero_nat )
% 0.33/0.67 = ( image_nat_nat @ suc @ top_top_set_nat ) ) ).
% 0.33/0.67
% 0.33/0.67 % greaterThan_0
% 0.33/0.67 thf(fact_7511_euclidean__size__integer_Orep__eq,axiom,
% 0.33/0.67 ( euclid6377331345833325938nteger
% 0.33/0.67 = ( ^ [X3: code_integer] : ( euclid4774559944035922753ze_int @ ( code_int_of_integer @ X3 ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % euclidean_size_integer.rep_eq
% 0.33/0.67 thf(fact_7512_euclidean__size__integer_Oabs__eq,axiom,
% 0.33/0.67 ! [X: int] :
% 0.33/0.67 ( ( euclid6377331345833325938nteger @ ( code_integer_of_int @ X ) )
% 0.33/0.67 = ( euclid4774559944035922753ze_int @ X ) ) ).
% 0.33/0.67
% 0.33/0.67 % euclidean_size_integer.abs_eq
% 0.33/0.67 thf(fact_7513_euclidean__size__natural_Orsp,axiom,
% 0.33/0.67 ( bNF_re5653821019739307937at_nat
% 0.33/0.67 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.67 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.67 @ euclid4777050414544973029ze_nat
% 0.33/0.67 @ euclid4777050414544973029ze_nat ) ).
% 0.33/0.67
% 0.33/0.67 % euclidean_size_natural.rsp
% 0.33/0.67 thf(fact_7514_euclidean__size__integer__def,axiom,
% 0.33/0.67 ( euclid6377331345833325938nteger
% 0.33/0.67 = ( map_fu6539832666145259331at_nat @ code_int_of_integer @ id_nat @ euclid4774559944035922753ze_int ) ) ).
% 0.33/0.67
% 0.33/0.67 % euclidean_size_integer_def
% 0.33/0.67 thf(fact_7515_euclidean__size__integer_Orsp,axiom,
% 0.33/0.67 ( bNF_re3715656647883201625at_nat
% 0.33/0.67 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.67 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.67 @ euclid4774559944035922753ze_int
% 0.33/0.67 @ euclid4774559944035922753ze_int ) ).
% 0.33/0.67
% 0.33/0.67 % euclidean_size_integer.rsp
% 0.33/0.67 thf(fact_7516_division__segment__integer_Orep__eq,axiom,
% 0.33/0.67 ! [X: code_integer] :
% 0.33/0.67 ( ( code_int_of_integer @ ( euclid6289375185220004616nteger @ X ) )
% 0.33/0.67 = ( euclid3395696857347342551nt_int @ ( code_int_of_integer @ X ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % division_segment_integer.rep_eq
% 0.33/0.67 thf(fact_7517_division__segment__integer_Oabs__eq,axiom,
% 0.33/0.67 ! [X: int] :
% 0.33/0.67 ( ( euclid6289375185220004616nteger @ ( code_integer_of_int @ X ) )
% 0.33/0.67 = ( code_integer_of_int @ ( euclid3395696857347342551nt_int @ X ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % division_segment_integer.abs_eq
% 0.33/0.67 thf(fact_7518_division__segment__nat__def,axiom,
% 0.33/0.67 ( euclid3398187327856392827nt_nat
% 0.33/0.67 = ( ^ [N4: nat] : one_one_nat ) ) ).
% 0.33/0.67
% 0.33/0.67 % division_segment_nat_def
% 0.33/0.67 thf(fact_7519_division__segment__integer_Orsp,axiom,
% 0.33/0.67 ( bNF_re4712519889275205905nt_int
% 0.33/0.67 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.67 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.67 @ euclid3395696857347342551nt_int
% 0.33/0.67 @ euclid3395696857347342551nt_int ) ).
% 0.33/0.67
% 0.33/0.67 % division_segment_integer.rsp
% 0.33/0.67 thf(fact_7520_division__segment__natural_Orsp,axiom,
% 0.33/0.67 ( bNF_re5653821019739307937at_nat
% 0.33/0.67 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.67 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.67 @ euclid3398187327856392827nt_nat
% 0.33/0.67 @ euclid3398187327856392827nt_nat ) ).
% 0.33/0.67
% 0.33/0.67 % division_segment_natural.rsp
% 0.33/0.67 thf(fact_7521_division__segment__integer__def,axiom,
% 0.33/0.67 ( euclid6289375185220004616nteger
% 0.33/0.67 = ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int @ euclid3395696857347342551nt_int ) ) ).
% 0.33/0.67
% 0.33/0.67 % division_segment_integer_def
% 0.33/0.67 thf(fact_7522_finite__greaterThanAtMost,axiom,
% 0.33/0.67 ! [L: nat,U: nat] : ( finite_finite_nat @ ( set_or6659071591806873216st_nat @ L @ U ) ) ).
% 0.33/0.67
% 0.33/0.67 % finite_greaterThanAtMost
% 0.33/0.67 thf(fact_7523_finite__greaterThanAtMost__int,axiom,
% 0.33/0.67 ! [L: int,U: int] : ( finite_finite_int @ ( set_or6656581121297822940st_int @ L @ U ) ) ).
% 0.33/0.67
% 0.33/0.67 % finite_greaterThanAtMost_int
% 0.33/0.67 thf(fact_7524_finite__greaterThanAtMost__integer,axiom,
% 0.33/0.67 ! [L: code_integer,U: code_integer] : ( finite6017078050557962740nteger @ ( set_or2715278749043346189nteger @ L @ U ) ) ).
% 0.33/0.67
% 0.33/0.67 % finite_greaterThanAtMost_integer
% 0.33/0.67 thf(fact_7525_card__greaterThanAtMost,axiom,
% 0.33/0.67 ! [L: nat,U: nat] :
% 0.33/0.67 ( ( finite_card_nat @ ( set_or6659071591806873216st_nat @ L @ U ) )
% 0.33/0.67 = ( minus_minus_nat @ U @ L ) ) ).
% 0.33/0.67
% 0.33/0.67 % card_greaterThanAtMost
% 0.33/0.67 thf(fact_7526_card__greaterThanAtMost__int,axiom,
% 0.33/0.67 ! [L: int,U: int] :
% 0.33/0.67 ( ( finite_card_int @ ( set_or6656581121297822940st_int @ L @ U ) )
% 0.33/0.67 = ( nat2 @ ( minus_minus_int @ U @ L ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % card_greaterThanAtMost_int
% 0.33/0.67 thf(fact_7527_atLeastSucAtMost__greaterThanAtMost,axiom,
% 0.33/0.67 ! [L: nat,U: nat] :
% 0.33/0.67 ( ( set_or1269000886237332187st_nat @ ( suc @ L ) @ U )
% 0.33/0.67 = ( set_or6659071591806873216st_nat @ L @ U ) ) ).
% 0.33/0.67
% 0.33/0.67 % atLeastSucAtMost_greaterThanAtMost
% 0.33/0.67 thf(fact_7528_atLeastPlusOneAtMost__greaterThanAtMost__int,axiom,
% 0.33/0.67 ! [L: int,U: int] :
% 0.33/0.67 ( ( set_or1266510415728281911st_int @ ( plus_plus_int @ L @ one_one_int ) @ U )
% 0.33/0.67 = ( set_or6656581121297822940st_int @ L @ U ) ) ).
% 0.33/0.67
% 0.33/0.67 % atLeastPlusOneAtMost_greaterThanAtMost_int
% 0.33/0.67 thf(fact_7529_atLeastPlusOneAtMost__greaterThanAtMost__integer,axiom,
% 0.33/0.67 ! [L: code_integer,U: code_integer] :
% 0.33/0.67 ( ( set_or189985376899183464nteger @ ( plus_p5714425477246183910nteger @ L @ one_one_Code_integer ) @ U )
% 0.33/0.67 = ( set_or2715278749043346189nteger @ L @ U ) ) ).
% 0.33/0.67
% 0.33/0.67 % atLeastPlusOneAtMost_greaterThanAtMost_integer
% 0.33/0.67 thf(fact_7530_UN__atLeast__UNIV,axiom,
% 0.33/0.67 ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ set_ord_atLeast_nat @ top_top_set_nat ) )
% 0.33/0.67 = top_top_set_nat ) ).
% 0.33/0.67
% 0.33/0.67 % UN_atLeast_UNIV
% 0.33/0.67 thf(fact_7531_atLeast__0,axiom,
% 0.33/0.67 ( ( set_ord_atLeast_nat @ zero_zero_nat )
% 0.33/0.67 = top_top_set_nat ) ).
% 0.33/0.67
% 0.33/0.67 % atLeast_0
% 0.33/0.67 thf(fact_7532_Inf__unit__def,axiom,
% 0.33/0.67 ( comple2584293577114468500t_unit
% 0.33/0.67 = ( ^ [Uu3: set_Product_unit] : product_Unity ) ) ).
% 0.33/0.67
% 0.33/0.67 % Inf_unit_def
% 0.33/0.67 thf(fact_7533_Sup__unit__def,axiom,
% 0.33/0.67 ( comple4687483117567863418t_unit
% 0.33/0.67 = ( ^ [Uu3: set_Product_unit] : product_Unity ) ) ).
% 0.33/0.67
% 0.33/0.67 % Sup_unit_def
% 0.33/0.67 thf(fact_7534_old_Ounit_Oexhaust,axiom,
% 0.33/0.67 ! [Y: product_unit] : ( Y = product_Unity ) ).
% 0.33/0.67
% 0.33/0.67 % old.unit.exhaust
% 0.33/0.67 thf(fact_7535_top__unit__def,axiom,
% 0.33/0.67 top_top_Product_unit = product_Unity ).
% 0.33/0.67
% 0.33/0.67 % top_unit_def
% 0.33/0.67 thf(fact_7536_uminus__unit__def,axiom,
% 0.33/0.67 ( uminus2952777764628376836t_unit
% 0.33/0.67 = ( ^ [Uu3: product_unit] : product_Unity ) ) ).
% 0.33/0.67
% 0.33/0.67 % uminus_unit_def
% 0.33/0.67 thf(fact_7537_bot__unit__def,axiom,
% 0.33/0.67 bot_bot_Product_unit = product_Unity ).
% 0.33/0.67
% 0.33/0.67 % bot_unit_def
% 0.33/0.67 thf(fact_7538_sup__unit__def,axiom,
% 0.33/0.67 ( sup_sup_Product_unit
% 0.33/0.67 = ( ^ [Uu3: product_unit,Uv: product_unit] : product_Unity ) ) ).
% 0.33/0.67
% 0.33/0.67 % sup_unit_def
% 0.33/0.67 thf(fact_7539_UNIV__unit,axiom,
% 0.33/0.67 ( top_to1996260823553986621t_unit
% 0.33/0.67 = ( insert_Product_unit @ product_Unity @ bot_bo3957492148770167129t_unit ) ) ).
% 0.33/0.67
% 0.33/0.67 % UNIV_unit
% 0.33/0.67 thf(fact_7540_atLeast__Suc__greaterThan,axiom,
% 0.33/0.67 ! [K: nat] :
% 0.33/0.67 ( ( set_ord_atLeast_nat @ ( suc @ K ) )
% 0.33/0.67 = ( set_or1210151606488870762an_nat @ K ) ) ).
% 0.33/0.67
% 0.33/0.67 % atLeast_Suc_greaterThan
% 0.33/0.67 thf(fact_7541_wait__def,axiom,
% 0.33/0.67 ( heap_Time_wait
% 0.33/0.67 = ( ^ [N4: nat] :
% 0.33/0.67 ( heap_T6183433275982383450t_unit
% 0.33/0.67 @ ^ [H: heap_e7401611519738050253t_unit] : ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ product_Unity @ ( produc584006145561248582it_nat @ H @ N4 ) ) ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % wait_def
% 0.33/0.67 thf(fact_7542_execute__assert_H,axiom,
% 0.33/0.67 ! [P: $o,H3: heap_e7401611519738050253t_unit] :
% 0.33/0.67 ( ( P
% 0.33/0.67 => ( ( heap_T875086893843062177t_unit @ ( refine_Imp_assert @ P ) @ H3 )
% 0.33/0.67 = ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ product_Unity @ ( produc584006145561248582it_nat @ H3 @ zero_zero_nat ) ) ) ) )
% 0.33/0.67 & ( ~ P
% 0.33/0.67 => ( ( heap_T875086893843062177t_unit @ ( refine_Imp_assert @ P ) @ H3 )
% 0.33/0.67 = none_P9117596204409417319it_nat ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % execute_assert'
% 0.33/0.67 thf(fact_7543_atLeast__Suc,axiom,
% 0.33/0.67 ! [K: nat] :
% 0.33/0.67 ( ( set_ord_atLeast_nat @ ( suc @ K ) )
% 0.33/0.67 = ( minus_minus_set_nat @ ( set_ord_atLeast_nat @ K ) @ ( insert_nat @ K @ bot_bot_set_nat ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % atLeast_Suc
% 0.33/0.67 thf(fact_7544_default__unit__def,axiom,
% 0.33/0.67 defaul566961228789861419t_unit = product_Unity ).
% 0.33/0.67
% 0.33/0.67 % default_unit_def
% 0.33/0.67 thf(fact_7545_inf__unit__def,axiom,
% 0.33/0.67 ( inf_inf_Product_unit
% 0.33/0.67 = ( ^ [Uu3: product_unit,Uv: product_unit] : product_Unity ) ) ).
% 0.33/0.67
% 0.33/0.67 % inf_unit_def
% 0.33/0.67 thf(fact_7546_floor__rat__def,axiom,
% 0.33/0.67 ( archim3151403230148437115or_rat
% 0.33/0.67 = ( ^ [X3: rat] :
% 0.33/0.67 ( the_int
% 0.33/0.67 @ ^ [Z4: int] :
% 0.33/0.67 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z4 ) @ X3 )
% 0.33/0.67 & ( ord_less_rat @ X3 @ ( ring_1_of_int_rat @ ( plus_plus_int @ Z4 @ one_one_int ) ) ) ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % floor_rat_def
% 0.33/0.67 thf(fact_7547_rat__floor__lemma,axiom,
% 0.33/0.67 ! [A: int,B: int] :
% 0.33/0.67 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( divide_divide_int @ A @ B ) ) @ ( fract @ A @ B ) )
% 0.33/0.67 & ( ord_less_rat @ ( fract @ A @ B ) @ ( ring_1_of_int_rat @ ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % rat_floor_lemma
% 0.33/0.67 thf(fact_7548_num__of__integer_Otransfer,axiom,
% 0.33/0.67 ( bNF_re6718328864250387230um_num @ code_pcr_integer
% 0.33/0.67 @ ^ [Y4: num,Z2: num] : ( Y4 = Z2 )
% 0.33/0.67 @ ( comp_nat_num_int @ num_of_nat @ nat2 )
% 0.33/0.67 @ code_num_of_integer ) ).
% 0.33/0.67
% 0.33/0.67 % num_of_integer.transfer
% 0.33/0.67 thf(fact_7549_prod__decode__triangle__add,axiom,
% 0.33/0.67 ! [K: nat,M2: nat] :
% 0.33/0.67 ( ( nat_prod_decode @ ( plus_plus_nat @ ( nat_triangle @ K ) @ M2 ) )
% 0.33/0.67 = ( nat_prod_decode_aux @ K @ M2 ) ) ).
% 0.33/0.67
% 0.33/0.67 % prod_decode_triangle_add
% 0.33/0.67 thf(fact_7550_add__rat,axiom,
% 0.33/0.67 ! [B: int,D2: int,A: int,C: int] :
% 0.33/0.67 ( ( B != zero_zero_int )
% 0.33/0.67 => ( ( D2 != zero_zero_int )
% 0.33/0.67 => ( ( plus_plus_rat @ ( fract @ A @ B ) @ ( fract @ C @ D2 ) )
% 0.33/0.67 = ( fract @ ( plus_plus_int @ ( times_times_int @ A @ D2 ) @ ( times_times_int @ C @ B ) ) @ ( times_times_int @ B @ D2 ) ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % add_rat
% 0.33/0.67 thf(fact_7551_integer_Orep__transfer,axiom,
% 0.33/0.67 ( bNF_re3804157879324367682nt_int @ code_pcr_integer
% 0.33/0.67 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.67 @ ^ [X3: int] : X3
% 0.33/0.67 @ code_int_of_integer ) ).
% 0.33/0.67
% 0.33/0.67 % integer.rep_transfer
% 0.33/0.67 thf(fact_7552_integer_Oid__abs__transfer,axiom,
% 0.33/0.67 ( bNF_re982302072995117890nteger
% 0.33/0.67 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.67 @ code_pcr_integer
% 0.33/0.67 @ ^ [X3: int] : X3
% 0.33/0.67 @ code_integer_of_int ) ).
% 0.33/0.67
% 0.33/0.67 % integer.id_abs_transfer
% 0.33/0.67 thf(fact_7553_zero__integer_Otransfer,axiom,
% 0.33/0.67 code_pcr_integer @ zero_zero_int @ zero_z3403309356797280102nteger ).
% 0.33/0.67
% 0.33/0.67 % zero_integer.transfer
% 0.33/0.67 thf(fact_7554_plus__integer_Otransfer,axiom,
% 0.33/0.67 bNF_re398004352372739002nteger @ code_pcr_integer @ ( bNF_re3379532845092657523nteger @ code_pcr_integer @ code_pcr_integer ) @ plus_plus_int @ plus_p5714425477246183910nteger ).
% 0.33/0.67
% 0.33/0.67 % plus_integer.transfer
% 0.33/0.67 thf(fact_7555_quotient__of__eq,axiom,
% 0.33/0.67 ! [A: int,B: int,P4: int,Q3: int] :
% 0.33/0.67 ( ( ( quotient_of @ ( fract @ A @ B ) )
% 0.33/0.67 = ( product_Pair_int_int @ P4 @ Q3 ) )
% 0.33/0.67 => ( ( fract @ P4 @ Q3 )
% 0.33/0.67 = ( fract @ A @ B ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % quotient_of_eq
% 0.33/0.67 thf(fact_7556_less__integer_Otransfer,axiom,
% 0.33/0.67 ( bNF_re6321650412969554871eger_o @ code_pcr_integer
% 0.33/0.67 @ ( bNF_re6574881592172037608er_o_o @ code_pcr_integer
% 0.33/0.67 @ ^ [Y4: $o,Z2: $o] : ( Y4 = Z2 ) )
% 0.33/0.67 @ ord_less_int
% 0.33/0.67 @ ord_le6747313008572928689nteger ) ).
% 0.33/0.67
% 0.33/0.67 % less_integer.transfer
% 0.33/0.67 thf(fact_7557_one__integer_Otransfer,axiom,
% 0.33/0.67 code_pcr_integer @ one_one_int @ one_one_Code_integer ).
% 0.33/0.67
% 0.33/0.67 % one_integer.transfer
% 0.33/0.67 thf(fact_7558_less__eq__integer_Otransfer,axiom,
% 0.33/0.67 ( bNF_re6321650412969554871eger_o @ code_pcr_integer
% 0.33/0.67 @ ( bNF_re6574881592172037608er_o_o @ code_pcr_integer
% 0.33/0.67 @ ^ [Y4: $o,Z2: $o] : ( Y4 = Z2 ) )
% 0.33/0.67 @ ord_less_eq_int
% 0.33/0.67 @ ord_le3102999989581377725nteger ) ).
% 0.33/0.67
% 0.33/0.67 % less_eq_integer.transfer
% 0.33/0.67 thf(fact_7559_uminus__integer_Otransfer,axiom,
% 0.33/0.67 bNF_re3379532845092657523nteger @ code_pcr_integer @ code_pcr_integer @ uminus_uminus_int @ uminus1351360451143612070nteger ).
% 0.33/0.67
% 0.33/0.67 % uminus_integer.transfer
% 0.33/0.67 thf(fact_7560_times__integer_Otransfer,axiom,
% 0.33/0.67 bNF_re398004352372739002nteger @ code_pcr_integer @ ( bNF_re3379532845092657523nteger @ code_pcr_integer @ code_pcr_integer ) @ times_times_int @ times_3573771949741848930nteger ).
% 0.33/0.67
% 0.33/0.67 % times_integer.transfer
% 0.33/0.67 thf(fact_7561_minus__integer_Otransfer,axiom,
% 0.33/0.67 bNF_re398004352372739002nteger @ code_pcr_integer @ ( bNF_re3379532845092657523nteger @ code_pcr_integer @ code_pcr_integer ) @ minus_minus_int @ minus_8373710615458151222nteger ).
% 0.33/0.67
% 0.33/0.67 % minus_integer.transfer
% 0.33/0.67 thf(fact_7562_abs__integer_Otransfer,axiom,
% 0.33/0.67 bNF_re3379532845092657523nteger @ code_pcr_integer @ code_pcr_integer @ abs_abs_int @ abs_abs_Code_integer ).
% 0.33/0.67
% 0.33/0.67 % abs_integer.transfer
% 0.33/0.67 thf(fact_7563_nat__of__integer_Otransfer,axiom,
% 0.33/0.67 ( bNF_re2807294637932363402at_nat @ code_pcr_integer
% 0.33/0.67 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.67 @ nat2
% 0.33/0.67 @ code_nat_of_integer ) ).
% 0.33/0.67
% 0.33/0.67 % nat_of_integer.transfer
% 0.33/0.67 thf(fact_7564_normalize__eq,axiom,
% 0.33/0.67 ! [A: int,B: int,P4: int,Q3: int] :
% 0.33/0.67 ( ( ( normalize @ ( product_Pair_int_int @ A @ B ) )
% 0.33/0.67 = ( product_Pair_int_int @ P4 @ Q3 ) )
% 0.33/0.67 => ( ( fract @ P4 @ Q3 )
% 0.33/0.67 = ( fract @ A @ B ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % normalize_eq
% 0.33/0.67 thf(fact_7565_integer__of__nat_Otransfer,axiom,
% 0.33/0.67 ( bNF_re4153400068438556298nteger
% 0.33/0.67 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.67 @ code_pcr_integer
% 0.33/0.67 @ semiri1314217659103216013at_int
% 0.33/0.67 @ code_integer_of_nat ) ).
% 0.33/0.67
% 0.33/0.67 % integer_of_nat.transfer
% 0.33/0.67 thf(fact_7566_divide__integer_Otransfer,axiom,
% 0.33/0.67 bNF_re398004352372739002nteger @ code_pcr_integer @ ( bNF_re3379532845092657523nteger @ code_pcr_integer @ code_pcr_integer ) @ divide_divide_int @ divide6298287555418463151nteger ).
% 0.33/0.67
% 0.33/0.67 % divide_integer.transfer
% 0.33/0.67 thf(fact_7567_modulo__integer_Otransfer,axiom,
% 0.33/0.67 bNF_re398004352372739002nteger @ code_pcr_integer @ ( bNF_re3379532845092657523nteger @ code_pcr_integer @ code_pcr_integer ) @ modulo_modulo_int @ modulo364778990260209775nteger ).
% 0.33/0.67
% 0.33/0.67 % modulo_integer.transfer
% 0.33/0.67 thf(fact_7568_sgn__integer_Otransfer,axiom,
% 0.33/0.67 bNF_re3379532845092657523nteger @ code_pcr_integer @ code_pcr_integer @ sgn_sgn_int @ sgn_sgn_Code_integer ).
% 0.33/0.67
% 0.33/0.67 % sgn_integer.transfer
% 0.33/0.67 thf(fact_7569_dup_Otransfer,axiom,
% 0.33/0.67 ( bNF_re3379532845092657523nteger @ code_pcr_integer @ code_pcr_integer
% 0.33/0.67 @ ^ [K4: int] : ( plus_plus_int @ K4 @ K4 )
% 0.33/0.67 @ code_dup ) ).
% 0.33/0.67
% 0.33/0.67 % dup.transfer
% 0.33/0.67 thf(fact_7570_take__bit__integer_Otransfer,axiom,
% 0.33/0.67 ( bNF_re4935368626670024657nteger
% 0.33/0.67 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.67 @ ( bNF_re3379532845092657523nteger @ code_pcr_integer @ code_pcr_integer )
% 0.33/0.67 @ bit_se2923211474154528505it_int
% 0.33/0.67 @ bit_se1745604003318907178nteger ) ).
% 0.33/0.67
% 0.33/0.67 % take_bit_integer.transfer
% 0.33/0.67 thf(fact_7571_not__integer_Otransfer,axiom,
% 0.33/0.67 bNF_re3379532845092657523nteger @ code_pcr_integer @ code_pcr_integer @ bit_ri7919022796975470100ot_int @ bit_ri7632146776885996613nteger ).
% 0.33/0.67
% 0.33/0.67 % not_integer.transfer
% 0.33/0.67 thf(fact_7572_and__integer_Otransfer,axiom,
% 0.33/0.67 bNF_re398004352372739002nteger @ code_pcr_integer @ ( bNF_re3379532845092657523nteger @ code_pcr_integer @ code_pcr_integer ) @ bit_se725231765392027082nd_int @ bit_se3949692690581998587nteger ).
% 0.33/0.67
% 0.33/0.67 % and_integer.transfer
% 0.33/0.67 thf(fact_7573_bit__integer_Otransfer,axiom,
% 0.33/0.67 ( bNF_re4711666741709854504_nat_o @ code_pcr_integer
% 0.33/0.67 @ ^ [Y4: nat > $o,Z2: nat > $o] : ( Y4 = Z2 )
% 0.33/0.67 @ bit_se1146084159140164899it_int
% 0.33/0.67 @ bit_se9216721137139052372nteger ) ).
% 0.33/0.67
% 0.33/0.67 % bit_integer.transfer
% 0.33/0.67 thf(fact_7574_or__integer_Otransfer,axiom,
% 0.33/0.67 bNF_re398004352372739002nteger @ code_pcr_integer @ ( bNF_re3379532845092657523nteger @ code_pcr_integer @ code_pcr_integer ) @ bit_se1409905431419307370or_int @ bit_se1080825931792720795nteger ).
% 0.33/0.67
% 0.33/0.67 % or_integer.transfer
% 0.33/0.67 thf(fact_7575_xor__integer_Otransfer,axiom,
% 0.33/0.67 bNF_re398004352372739002nteger @ code_pcr_integer @ ( bNF_re3379532845092657523nteger @ code_pcr_integer @ code_pcr_integer ) @ bit_se6526347334894502574or_int @ bit_se3222712562003087583nteger ).
% 0.33/0.67
% 0.33/0.67 % xor_integer.transfer
% 0.33/0.67 thf(fact_7576_drop__bit__integer_Otransfer,axiom,
% 0.33/0.67 ( bNF_re4935368626670024657nteger
% 0.33/0.67 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.67 @ ( bNF_re3379532845092657523nteger @ code_pcr_integer @ code_pcr_integer )
% 0.33/0.67 @ bit_se8568078237143864401it_int
% 0.33/0.67 @ bit_se3928097537394005634nteger ) ).
% 0.33/0.67
% 0.33/0.67 % drop_bit_integer.transfer
% 0.33/0.67 thf(fact_7577_push__bit__integer_Otransfer,axiom,
% 0.33/0.67 ( bNF_re4935368626670024657nteger
% 0.33/0.67 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.67 @ ( bNF_re3379532845092657523nteger @ code_pcr_integer @ code_pcr_integer )
% 0.33/0.67 @ bit_se545348938243370406it_int
% 0.33/0.67 @ bit_se7788150548672797655nteger ) ).
% 0.33/0.67
% 0.33/0.67 % push_bit_integer.transfer
% 0.33/0.67 thf(fact_7578_mask__integer_Otransfer,axiom,
% 0.33/0.67 ( bNF_re4153400068438556298nteger
% 0.33/0.67 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.67 @ code_pcr_integer
% 0.33/0.67 @ bit_se2000444600071755411sk_int
% 0.33/0.67 @ bit_se2119862282449309892nteger ) ).
% 0.33/0.67
% 0.33/0.67 % mask_integer.transfer
% 0.33/0.67 thf(fact_7579_unset__bit__integer_Otransfer,axiom,
% 0.33/0.67 ( bNF_re4935368626670024657nteger
% 0.33/0.67 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.67 @ ( bNF_re3379532845092657523nteger @ code_pcr_integer @ code_pcr_integer )
% 0.33/0.67 @ bit_se4203085406695923979it_int
% 0.33/0.67 @ bit_se8260200283734997820nteger ) ).
% 0.33/0.67
% 0.33/0.67 % unset_bit_integer.transfer
% 0.33/0.67 thf(fact_7580_set__bit__integer_Otransfer,axiom,
% 0.33/0.67 ( bNF_re4935368626670024657nteger
% 0.33/0.67 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.67 @ ( bNF_re3379532845092657523nteger @ code_pcr_integer @ code_pcr_integer )
% 0.33/0.67 @ bit_se7879613467334960850it_int
% 0.33/0.67 @ bit_se2793503036327961859nteger ) ).
% 0.33/0.67
% 0.33/0.67 % set_bit_integer.transfer
% 0.33/0.67 thf(fact_7581_division__segment__integer_Otransfer,axiom,
% 0.33/0.67 bNF_re3379532845092657523nteger @ code_pcr_integer @ code_pcr_integer @ euclid3395696857347342551nt_int @ euclid6289375185220004616nteger ).
% 0.33/0.67
% 0.33/0.67 % division_segment_integer.transfer
% 0.33/0.67 thf(fact_7582_flip__bit__integer_Otransfer,axiom,
% 0.33/0.67 ( bNF_re4935368626670024657nteger
% 0.33/0.67 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.67 @ ( bNF_re3379532845092657523nteger @ code_pcr_integer @ code_pcr_integer )
% 0.33/0.67 @ bit_se2159334234014336723it_int
% 0.33/0.67 @ bit_se1345352211410354436nteger ) ).
% 0.33/0.67
% 0.33/0.67 % flip_bit_integer.transfer
% 0.33/0.67 thf(fact_7583_euclidean__size__integer_Otransfer,axiom,
% 0.33/0.67 ( bNF_re2807294637932363402at_nat @ code_pcr_integer
% 0.33/0.67 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.67 @ euclid4774559944035922753ze_int
% 0.33/0.67 @ euclid6377331345833325938nteger ) ).
% 0.33/0.67
% 0.33/0.67 % euclidean_size_integer.transfer
% 0.33/0.67 thf(fact_7584_quotient__of__Fract,axiom,
% 0.33/0.67 ! [A: int,B: int] :
% 0.33/0.67 ( ( quotient_of @ ( fract @ A @ B ) )
% 0.33/0.67 = ( normalize @ ( product_Pair_int_int @ A @ B ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % quotient_of_Fract
% 0.33/0.67 thf(fact_7585_sub_Otransfer,axiom,
% 0.33/0.67 ( bNF_re7876454716742015248nteger
% 0.33/0.67 @ ^ [Y4: num,Z2: num] : ( Y4 = Z2 )
% 0.33/0.67 @ ( bNF_re6501075790457514782nteger
% 0.33/0.67 @ ^ [Y4: num,Z2: num] : ( Y4 = Z2 )
% 0.33/0.67 @ code_pcr_integer )
% 0.33/0.67 @ ^ [M: num,N4: num] : ( minus_minus_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N4 ) )
% 0.33/0.67 @ code_sub ) ).
% 0.33/0.67
% 0.33/0.67 % sub.transfer
% 0.33/0.67 thf(fact_7586_Fract_Oabs__eq,axiom,
% 0.33/0.67 ( fract
% 0.33/0.67 = ( ^ [Xa4: int,X3: int] : ( abs_Rat @ ( if_Pro3027730157355071871nt_int @ ( X3 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ Xa4 @ X3 ) ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % Fract.abs_eq
% 0.33/0.67 thf(fact_7587_Fract_Otransfer,axiom,
% 0.33/0.67 ( bNF_re3461391660133120880nt_rat
% 0.33/0.67 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.67 @ ( bNF_re2214769303045360666nt_rat
% 0.33/0.67 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.67 @ pcr_rat )
% 0.33/0.67 @ ^ [A5: int,B4: int] : ( if_Pro3027730157355071871nt_int @ ( B4 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ A5 @ B4 ) )
% 0.33/0.67 @ fract ) ).
% 0.33/0.67
% 0.33/0.67 % Fract.transfer
% 0.33/0.67 thf(fact_7588_Fract__add__one,axiom,
% 0.33/0.67 ! [N2: int,M2: int] :
% 0.33/0.67 ( ( N2 != zero_zero_int )
% 0.33/0.67 => ( ( fract @ ( plus_plus_int @ M2 @ N2 ) @ N2 )
% 0.33/0.67 = ( plus_plus_rat @ ( fract @ M2 @ N2 ) @ one_one_rat ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % Fract_add_one
% 0.33/0.67 thf(fact_7589_Fract__def,axiom,
% 0.33/0.67 ( fract
% 0.33/0.67 = ( map_fu7831380289885515383nt_rat @ id_int @ ( map_fu3424225382358772769nt_rat @ id_int @ abs_Rat )
% 0.33/0.67 @ ^ [A5: int,B4: int] : ( if_Pro3027730157355071871nt_int @ ( B4 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ A5 @ B4 ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % Fract_def
% 0.33/0.67 thf(fact_7590_list__decode_Opinduct,axiom,
% 0.33/0.67 ! [A0: nat,P: nat > $o] :
% 0.33/0.67 ( ( accp_nat @ nat_list_decode_rel @ A0 )
% 0.33/0.67 => ( ( ( accp_nat @ nat_list_decode_rel @ zero_zero_nat )
% 0.33/0.67 => ( P @ zero_zero_nat ) )
% 0.33/0.67 => ( ! [N: nat] :
% 0.33/0.67 ( ( accp_nat @ nat_list_decode_rel @ ( suc @ N ) )
% 0.33/0.67 => ( ! [X8: nat,Y6: nat] :
% 0.33/0.67 ( ( ( product_Pair_nat_nat @ X8 @ Y6 )
% 0.33/0.67 = ( nat_prod_decode @ N ) )
% 0.33/0.67 => ( P @ Y6 ) )
% 0.33/0.67 => ( P @ ( suc @ N ) ) ) )
% 0.33/0.67 => ( P @ A0 ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % list_decode.pinduct
% 0.33/0.67 thf(fact_7591_type__definition__integer,axiom,
% 0.33/0.67 type_d8366093980585677751er_int @ code_int_of_integer @ code_integer_of_int @ top_top_set_int ).
% 0.33/0.67
% 0.33/0.67 % type_definition_integer
% 0.33/0.67 thf(fact_7592_pred__nat__trancl__eq__le,axiom,
% 0.33/0.67 ! [M2: nat,N2: nat] :
% 0.33/0.67 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ M2 @ N2 ) @ ( transi2905341329935302413cl_nat @ pred_nat ) )
% 0.33/0.67 = ( ord_less_eq_nat @ M2 @ N2 ) ) ).
% 0.33/0.67
% 0.33/0.67 % pred_nat_trancl_eq_le
% 0.33/0.67 thf(fact_7593_less__eq,axiom,
% 0.33/0.67 ! [M2: nat,N2: nat] :
% 0.33/0.67 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ M2 @ N2 ) @ ( transi6264000038957366511cl_nat @ pred_nat ) )
% 0.33/0.67 = ( ord_less_nat @ M2 @ N2 ) ) ).
% 0.33/0.67
% 0.33/0.67 % less_eq
% 0.33/0.67 thf(fact_7594_upt__0__eq__Nil__conv,axiom,
% 0.33/0.67 ! [J: nat] :
% 0.33/0.67 ( ( ( upt @ zero_zero_nat @ J )
% 0.33/0.67 = nil_nat )
% 0.33/0.67 = ( J = zero_zero_nat ) ) ).
% 0.33/0.67
% 0.33/0.67 % upt_0_eq_Nil_conv
% 0.33/0.67 thf(fact_7595_map__add__upt_H,axiom,
% 0.33/0.67 ! [Ofs: nat,A: nat,B: nat] :
% 0.33/0.67 ( ( map_nat_nat
% 0.33/0.67 @ ^ [I3: nat] : ( plus_plus_nat @ I3 @ Ofs )
% 0.33/0.67 @ ( upt @ A @ B ) )
% 0.33/0.67 = ( upt @ ( plus_plus_nat @ A @ Ofs ) @ ( plus_plus_nat @ B @ Ofs ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % map_add_upt'
% 0.33/0.67 thf(fact_7596_map__add__upt,axiom,
% 0.33/0.67 ! [N2: nat,M2: nat] :
% 0.33/0.67 ( ( map_nat_nat
% 0.33/0.67 @ ^ [I3: nat] : ( plus_plus_nat @ I3 @ N2 )
% 0.33/0.67 @ ( upt @ zero_zero_nat @ M2 ) )
% 0.33/0.67 = ( upt @ N2 @ ( plus_plus_nat @ M2 @ N2 ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % map_add_upt
% 0.33/0.67 thf(fact_7597_upt__filter__extend,axiom,
% 0.33/0.67 ! [U: nat,U4: nat,P: nat > $o] :
% 0.33/0.67 ( ( ord_less_eq_nat @ U @ U4 )
% 0.33/0.67 => ( ! [I2: nat] :
% 0.33/0.67 ( ( ( ord_less_eq_nat @ U @ I2 )
% 0.33/0.67 & ( ord_less_nat @ I2 @ U4 ) )
% 0.33/0.67 => ~ ( P @ I2 ) )
% 0.33/0.67 => ( ( filter_nat @ P @ ( upt @ zero_zero_nat @ U ) )
% 0.33/0.67 = ( filter_nat @ P @ ( upt @ zero_zero_nat @ U4 ) ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % upt_filter_extend
% 0.33/0.67 thf(fact_7598_nth__upt,axiom,
% 0.33/0.67 ! [I: nat,K: nat,J: nat] :
% 0.33/0.67 ( ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ J )
% 0.33/0.67 => ( ( nth_nat @ ( upt @ I @ J ) @ K )
% 0.33/0.67 = ( plus_plus_nat @ I @ K ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % nth_upt
% 0.33/0.67 thf(fact_7599_upt__eq__Cons__conv,axiom,
% 0.33/0.67 ! [I: nat,J: nat,X: nat,Xs: list_nat] :
% 0.33/0.67 ( ( ( upt @ I @ J )
% 0.33/0.67 = ( cons_nat @ X @ Xs ) )
% 0.33/0.67 = ( ( ord_less_nat @ I @ J )
% 0.33/0.67 & ( I = X )
% 0.33/0.67 & ( ( upt @ ( plus_plus_nat @ I @ one_one_nat ) @ J )
% 0.33/0.67 = Xs ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % upt_eq_Cons_conv
% 0.33/0.67 thf(fact_7600_list__decode_Opelims,axiom,
% 0.33/0.67 ! [X: nat,Y: list_nat] :
% 0.33/0.67 ( ( ( nat_list_decode @ X )
% 0.33/0.67 = Y )
% 0.33/0.67 => ( ( accp_nat @ nat_list_decode_rel @ X )
% 0.33/0.67 => ( ( ( X = zero_zero_nat )
% 0.33/0.67 => ( ( Y = nil_nat )
% 0.33/0.67 => ~ ( accp_nat @ nat_list_decode_rel @ zero_zero_nat ) ) )
% 0.33/0.67 => ~ ! [N: nat] :
% 0.33/0.67 ( ( X
% 0.33/0.67 = ( suc @ N ) )
% 0.33/0.67 => ( ( Y
% 0.33/0.67 = ( produc2761476792215241774st_nat
% 0.33/0.67 @ ^ [X3: nat,Y3: nat] : ( cons_nat @ X3 @ ( nat_list_decode @ Y3 ) )
% 0.33/0.67 @ ( nat_prod_decode @ N ) ) )
% 0.33/0.67 => ~ ( accp_nat @ nat_list_decode_rel @ ( suc @ N ) ) ) ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % list_decode.pelims
% 0.33/0.67 thf(fact_7601_drop__upt,axiom,
% 0.33/0.67 ! [M2: nat,I: nat,J: nat] :
% 0.33/0.67 ( ( drop_nat @ M2 @ ( upt @ I @ J ) )
% 0.33/0.67 = ( upt @ ( plus_plus_nat @ I @ M2 ) @ J ) ) ).
% 0.33/0.67
% 0.33/0.67 % drop_upt
% 0.33/0.67 thf(fact_7602_natural__zero__minus__one,axiom,
% 0.33/0.67 ( ( minus_7197305767214868737atural @ zero_z2226904508553997617atural @ one_one_Code_natural )
% 0.33/0.67 = zero_z2226904508553997617atural ) ).
% 0.33/0.67
% 0.33/0.67 % natural_zero_minus_one
% 0.33/0.67 thf(fact_7603_list__decode_Opsimps_I1_J,axiom,
% 0.33/0.67 ( ( accp_nat @ nat_list_decode_rel @ zero_zero_nat )
% 0.33/0.67 => ( ( nat_list_decode @ zero_zero_nat )
% 0.33/0.67 = nil_nat ) ) ).
% 0.33/0.67
% 0.33/0.67 % list_decode.psimps(1)
% 0.33/0.67 thf(fact_7604_list__decode_Opsimps_I2_J,axiom,
% 0.33/0.67 ! [N2: nat] :
% 0.33/0.67 ( ( accp_nat @ nat_list_decode_rel @ ( suc @ N2 ) )
% 0.33/0.67 => ( ( nat_list_decode @ ( suc @ N2 ) )
% 0.33/0.67 = ( produc2761476792215241774st_nat
% 0.33/0.67 @ ^ [X3: nat,Y3: nat] : ( cons_nat @ X3 @ ( nat_list_decode @ Y3 ) )
% 0.33/0.67 @ ( nat_prod_decode @ N2 ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % list_decode.psimps(2)
% 0.33/0.67 thf(fact_7605_list__encode_Oelims,axiom,
% 0.33/0.67 ! [X: list_nat,Y: nat] :
% 0.33/0.67 ( ( ( nat_list_encode @ X )
% 0.33/0.67 = Y )
% 0.33/0.67 => ( ( ( X = nil_nat )
% 0.33/0.67 => ( Y != zero_zero_nat ) )
% 0.33/0.67 => ~ ! [X4: nat,Xs2: list_nat] :
% 0.33/0.67 ( ( X
% 0.33/0.67 = ( cons_nat @ X4 @ Xs2 ) )
% 0.33/0.67 => ( Y
% 0.33/0.67 != ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X4 @ ( nat_list_encode @ Xs2 ) ) ) ) ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % list_encode.elims
% 0.33/0.67 thf(fact_7606_upt__merge,axiom,
% 0.33/0.67 ! [I: nat,J: nat,K: nat] :
% 0.33/0.67 ( ( ( ord_less_eq_nat @ I @ J )
% 0.33/0.67 & ( ord_less_eq_nat @ J @ K ) )
% 0.33/0.67 => ( ( append_nat @ ( upt @ I @ J ) @ ( upt @ J @ K ) )
% 0.33/0.67 = ( upt @ I @ K ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % upt_merge
% 0.33/0.67 thf(fact_7607_upt__eq__append__conv,axiom,
% 0.33/0.67 ! [I: nat,J: nat,Xs: list_nat,Ys: list_nat] :
% 0.33/0.67 ( ( ord_less_eq_nat @ I @ J )
% 0.33/0.67 => ( ( ( upt @ I @ J )
% 0.33/0.67 = ( append_nat @ Xs @ Ys ) )
% 0.33/0.67 = ( ? [K4: nat] :
% 0.33/0.67 ( ( ord_less_eq_nat @ I @ K4 )
% 0.33/0.67 & ( ord_less_eq_nat @ K4 @ J )
% 0.33/0.67 & ( ( upt @ I @ K4 )
% 0.33/0.67 = Xs )
% 0.33/0.67 & ( ( upt @ K4 @ J )
% 0.33/0.67 = Ys ) ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % upt_eq_append_conv
% 0.33/0.67 thf(fact_7608_upt__append,axiom,
% 0.33/0.67 ! [I: nat,J: nat] :
% 0.33/0.67 ( ( ord_less_nat @ I @ J )
% 0.33/0.67 => ( ( append_nat @ ( upt @ zero_zero_nat @ I ) @ ( upt @ I @ J ) )
% 0.33/0.67 = ( upt @ zero_zero_nat @ J ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % upt_append
% 0.33/0.67 thf(fact_7609_upt__add__eq__append,axiom,
% 0.33/0.67 ! [I: nat,J: nat,K: nat] :
% 0.33/0.67 ( ( ord_less_eq_nat @ I @ J )
% 0.33/0.67 => ( ( upt @ I @ ( plus_plus_nat @ J @ K ) )
% 0.33/0.67 = ( append_nat @ ( upt @ I @ J ) @ ( upt @ J @ ( plus_plus_nat @ J @ K ) ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % upt_add_eq_append
% 0.33/0.67 thf(fact_7610_upt__eq__lel__conv,axiom,
% 0.33/0.67 ! [L: nat,H3: nat,Is1: list_nat,I: nat,Is2: list_nat] :
% 0.33/0.67 ( ( ( upt @ L @ H3 )
% 0.33/0.67 = ( append_nat @ Is1 @ ( cons_nat @ I @ Is2 ) ) )
% 0.33/0.67 = ( ( Is1
% 0.33/0.67 = ( upt @ L @ I ) )
% 0.33/0.67 & ( Is2
% 0.33/0.67 = ( upt @ ( suc @ I ) @ H3 ) )
% 0.33/0.67 & ( ord_less_eq_nat @ L @ I )
% 0.33/0.67 & ( ord_less_nat @ I @ H3 ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % upt_eq_lel_conv
% 0.33/0.67 thf(fact_7611_list__encode_Osimps_I2_J,axiom,
% 0.33/0.67 ! [X: nat,Xs: list_nat] :
% 0.33/0.67 ( ( nat_list_encode @ ( cons_nat @ X @ Xs ) )
% 0.33/0.67 = ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X @ ( nat_list_encode @ Xs ) ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % list_encode.simps(2)
% 0.33/0.67 thf(fact_7612_list__encode_Opelims,axiom,
% 0.33/0.67 ! [X: list_nat,Y: nat] :
% 0.33/0.67 ( ( ( nat_list_encode @ X )
% 0.33/0.67 = Y )
% 0.33/0.67 => ( ( accp_list_nat @ nat_list_encode_rel @ X )
% 0.33/0.67 => ( ( ( X = nil_nat )
% 0.33/0.67 => ( ( Y = zero_zero_nat )
% 0.33/0.67 => ~ ( accp_list_nat @ nat_list_encode_rel @ nil_nat ) ) )
% 0.33/0.67 => ~ ! [X4: nat,Xs2: list_nat] :
% 0.33/0.67 ( ( X
% 0.33/0.67 = ( cons_nat @ X4 @ Xs2 ) )
% 0.33/0.67 => ( ( Y
% 0.33/0.67 = ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X4 @ ( nat_list_encode @ Xs2 ) ) ) ) )
% 0.33/0.67 => ~ ( accp_list_nat @ nat_list_encode_rel @ ( cons_nat @ X4 @ Xs2 ) ) ) ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % list_encode.pelims
% 0.33/0.67 thf(fact_7613_last__upt,axiom,
% 0.33/0.67 ! [I: nat,J: nat] :
% 0.33/0.67 ( ( ord_less_nat @ I @ J )
% 0.33/0.67 => ( ( last_nat @ ( upt @ I @ J ) )
% 0.33/0.67 = ( minus_minus_nat @ J @ one_one_nat ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % last_upt
% 0.33/0.67 thf(fact_7614_nth__sorted__list__of__set__greaterThanLessThan,axiom,
% 0.33/0.67 ! [N2: nat,J: nat,I: nat] :
% 0.33/0.67 ( ( ord_less_nat @ N2 @ ( minus_minus_nat @ J @ ( suc @ I ) ) )
% 0.33/0.67 => ( ( nth_nat @ ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ I @ J ) ) @ N2 )
% 0.33/0.67 = ( suc @ ( plus_plus_nat @ I @ N2 ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % nth_sorted_list_of_set_greaterThanLessThan
% 0.33/0.67 thf(fact_7615_nth__sorted__list__of__set__greaterThanAtMost,axiom,
% 0.33/0.67 ! [N2: nat,J: nat,I: nat] :
% 0.33/0.67 ( ( ord_less_nat @ N2 @ ( minus_minus_nat @ J @ I ) )
% 0.33/0.67 => ( ( nth_nat @ ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ I @ J ) ) @ N2 )
% 0.33/0.67 = ( suc @ ( plus_plus_nat @ I @ N2 ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % nth_sorted_list_of_set_greaterThanAtMost
% 0.33/0.67 thf(fact_7616_upto_Opelims,axiom,
% 0.33/0.67 ! [X: int,Xa: int,Y: list_int] :
% 0.33/0.67 ( ( ( upto @ X @ Xa )
% 0.33/0.67 = Y )
% 0.33/0.67 => ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ X @ Xa ) )
% 0.33/0.67 => ~ ( ( ( ( ord_less_eq_int @ X @ Xa )
% 0.33/0.67 => ( Y
% 0.33/0.67 = ( cons_int @ X @ ( upto @ ( plus_plus_int @ X @ one_one_int ) @ Xa ) ) ) )
% 0.33/0.67 & ( ~ ( ord_less_eq_int @ X @ Xa )
% 0.33/0.67 => ( Y = nil_int ) ) )
% 0.33/0.67 => ~ ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ X @ Xa ) ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % upto.pelims
% 0.33/0.67 thf(fact_7617_upto_Opsimps,axiom,
% 0.33/0.67 ! [I: int,J: int] :
% 0.33/0.67 ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ I @ J ) )
% 0.33/0.67 => ( ( ( ord_less_eq_int @ I @ J )
% 0.33/0.67 => ( ( upto @ I @ J )
% 0.33/0.67 = ( cons_int @ I @ ( upto @ ( plus_plus_int @ I @ one_one_int ) @ J ) ) ) )
% 0.33/0.67 & ( ~ ( ord_less_eq_int @ I @ J )
% 0.33/0.67 => ( ( upto @ I @ J )
% 0.33/0.67 = nil_int ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % upto.psimps
% 0.33/0.67 thf(fact_7618_nth__upto,axiom,
% 0.33/0.67 ! [I: int,K: nat,J: int] :
% 0.33/0.67 ( ( ord_less_eq_int @ ( plus_plus_int @ I @ ( semiri1314217659103216013at_int @ K ) ) @ J )
% 0.33/0.67 => ( ( nth_int @ ( upto @ I @ J ) @ K )
% 0.33/0.67 = ( plus_plus_int @ I @ ( semiri1314217659103216013at_int @ K ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % nth_upto
% 0.33/0.67 thf(fact_7619_length__upto,axiom,
% 0.33/0.67 ! [I: int,J: int] :
% 0.33/0.67 ( ( size_size_list_int @ ( upto @ I @ J ) )
% 0.33/0.67 = ( nat2 @ ( plus_plus_int @ ( minus_minus_int @ J @ I ) @ one_one_int ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % length_upto
% 0.33/0.67 thf(fact_7620_upto__rec__numeral_I1_J,axiom,
% 0.33/0.67 ! [M2: num,N2: num] :
% 0.33/0.67 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N2 ) )
% 0.33/0.67 => ( ( upto @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N2 ) )
% 0.33/0.67 = ( cons_int @ ( numeral_numeral_int @ M2 ) @ ( upto @ ( plus_plus_int @ ( numeral_numeral_int @ M2 ) @ one_one_int ) @ ( numeral_numeral_int @ N2 ) ) ) ) )
% 0.33/0.67 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N2 ) )
% 0.33/0.67 => ( ( upto @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N2 ) )
% 0.33/0.67 = nil_int ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % upto_rec_numeral(1)
% 0.33/0.67 thf(fact_7621_upto__rec__numeral_I2_J,axiom,
% 0.33/0.67 ! [M2: num,N2: num] :
% 0.33/0.67 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 0.33/0.67 => ( ( upto @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 0.33/0.67 = ( cons_int @ ( numeral_numeral_int @ M2 ) @ ( upto @ ( plus_plus_int @ ( numeral_numeral_int @ M2 ) @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ) ) )
% 0.33/0.67 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 0.33/0.67 => ( ( upto @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 0.33/0.67 = nil_int ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % upto_rec_numeral(2)
% 0.33/0.67 thf(fact_7622_upto__rec__numeral_I3_J,axiom,
% 0.33/0.67 ! [M2: num,N2: num] :
% 0.33/0.67 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( numeral_numeral_int @ N2 ) )
% 0.33/0.67 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( numeral_numeral_int @ N2 ) )
% 0.33/0.67 = ( cons_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( upto @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ one_one_int ) @ ( numeral_numeral_int @ N2 ) ) ) ) )
% 0.33/0.67 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( numeral_numeral_int @ N2 ) )
% 0.33/0.67 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( numeral_numeral_int @ N2 ) )
% 0.33/0.67 = nil_int ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % upto_rec_numeral(3)
% 0.33/0.67 thf(fact_7623_upto__rec__numeral_I4_J,axiom,
% 0.33/0.67 ! [M2: num,N2: num] :
% 0.33/0.67 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 0.33/0.67 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 0.33/0.67 = ( cons_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( upto @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ) ) )
% 0.33/0.67 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 0.33/0.67 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 0.33/0.67 = nil_int ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % upto_rec_numeral(4)
% 0.33/0.67 thf(fact_7624_upto__split2,axiom,
% 0.33/0.67 ! [I: int,J: int,K: int] :
% 0.33/0.67 ( ( ord_less_eq_int @ I @ J )
% 0.33/0.67 => ( ( ord_less_eq_int @ J @ K )
% 0.33/0.67 => ( ( upto @ I @ K )
% 0.33/0.67 = ( append_int @ ( upto @ I @ J ) @ ( upto @ ( plus_plus_int @ J @ one_one_int ) @ K ) ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % upto_split2
% 0.33/0.67 thf(fact_7625_upto__rec1,axiom,
% 0.33/0.67 ! [I: int,J: int] :
% 0.33/0.67 ( ( ord_less_eq_int @ I @ J )
% 0.33/0.67 => ( ( upto @ I @ J )
% 0.33/0.67 = ( cons_int @ I @ ( upto @ ( plus_plus_int @ I @ one_one_int ) @ J ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % upto_rec1
% 0.33/0.67 thf(fact_7626_upto_Osimps,axiom,
% 0.33/0.67 ( upto
% 0.33/0.67 = ( ^ [I3: int,J2: int] : ( if_list_int @ ( ord_less_eq_int @ I3 @ J2 ) @ ( cons_int @ I3 @ ( upto @ ( plus_plus_int @ I3 @ one_one_int ) @ J2 ) ) @ nil_int ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % upto.simps
% 0.33/0.67 thf(fact_7627_upto_Oelims,axiom,
% 0.33/0.67 ! [X: int,Xa: int,Y: list_int] :
% 0.33/0.67 ( ( ( upto @ X @ Xa )
% 0.33/0.67 = Y )
% 0.33/0.67 => ( ( ( ord_less_eq_int @ X @ Xa )
% 0.33/0.67 => ( Y
% 0.33/0.67 = ( cons_int @ X @ ( upto @ ( plus_plus_int @ X @ one_one_int ) @ Xa ) ) ) )
% 0.33/0.67 & ( ~ ( ord_less_eq_int @ X @ Xa )
% 0.33/0.67 => ( Y = nil_int ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % upto.elims
% 0.33/0.67 thf(fact_7628_greaterThanAtMost__upto,axiom,
% 0.33/0.67 ( set_or6656581121297822940st_int
% 0.33/0.67 = ( ^ [I3: int,J2: int] : ( set_int2 @ ( upto @ ( plus_plus_int @ I3 @ one_one_int ) @ J2 ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % greaterThanAtMost_upto
% 0.33/0.67 thf(fact_7629_upto__split3,axiom,
% 0.33/0.67 ! [I: int,J: int,K: int] :
% 0.33/0.67 ( ( ord_less_eq_int @ I @ J )
% 0.33/0.67 => ( ( ord_less_eq_int @ J @ K )
% 0.33/0.67 => ( ( upto @ I @ K )
% 0.33/0.67 = ( append_int @ ( upto @ I @ ( minus_minus_int @ J @ one_one_int ) ) @ ( cons_int @ J @ ( upto @ ( plus_plus_int @ J @ one_one_int ) @ K ) ) ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % upto_split3
% 0.33/0.67 thf(fact_7630_greaterThanLessThan__upto,axiom,
% 0.33/0.67 ( set_or5832277885323065728an_int
% 0.33/0.67 = ( ^ [I3: int,J2: int] : ( set_int2 @ ( upto @ ( plus_plus_int @ I3 @ one_one_int ) @ ( minus_minus_int @ J2 @ one_one_int ) ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % greaterThanLessThan_upto
% 0.33/0.67 thf(fact_7631_take__upt,axiom,
% 0.33/0.67 ! [I: nat,M2: nat,N2: nat] :
% 0.33/0.67 ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ M2 ) @ N2 )
% 0.33/0.67 => ( ( take_nat @ M2 @ ( upt @ I @ N2 ) )
% 0.33/0.67 = ( upt @ I @ ( plus_plus_nat @ I @ M2 ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % take_upt
% 0.33/0.67 thf(fact_7632_butlast__upt,axiom,
% 0.33/0.67 ! [M2: nat,N2: nat] :
% 0.33/0.67 ( ( butlast_nat @ ( upt @ M2 @ N2 ) )
% 0.33/0.67 = ( upt @ M2 @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % butlast_upt
% 0.33/0.67 thf(fact_7633_next_Osimps,axiom,
% 0.33/0.67 ! [V: code_natural,W: code_natural] :
% 0.33/0.67 ( ( next @ ( produc3574140220909816553atural @ V @ W ) )
% 0.33/0.67 = ( produc6639722614265839536atural @ ( plus_p4538020629002901425atural @ ( minus_shift @ ( numera5444537566228673987atural @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( minus_shift @ ( numera5444537566228673987atural @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( times_2397367101498566445atural @ ( modulo8411746178871703098atural @ V @ ( numera5444537566228673987atural @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( numera5444537566228673987atural @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ V @ ( numera5444537566228673987atural @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( numera5444537566228673987atural @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( plus_p4538020629002901425atural @ ( minus_shift @ ( numera5444537566228673987atural @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( times_2397367101498566445atural @ ( modulo8411746178871703098atural @ W @ ( numera5444537566228673987atural @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( numera5444537566228673987atural @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ W @ ( numera5444537566228673987atural @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( numera5444537566228673987atural @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ one_one_Code_natural ) ) @ one_one_Code_natural ) @ ( produc3574140220909816553atural @ ( minus_shift @ ( numera5444537566228673987atural @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( times_2397367101498566445atural @ ( modulo8411746178871703098atural @ V @ ( numera5444537566228673987atural @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( numera5444537566228673987atural @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ V @ ( numera5444537566228673987atural @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( numera5444537566228673987atural @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( minus_shift @ ( numera5444537566228673987atural @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( times_2397367101498566445atural @ ( modulo8411746178871703098atural @ W @ ( numera5444537566228673987atural @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( numera5444537566228673987atural @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ W @ ( numera5444537566228673987atural @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( numera5444537566228673987atural @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % next.simps
% 0.33/0.67 thf(fact_7634_full__exhaustive__natural_H_Ocases,axiom,
% 0.33/0.67 ! [X: produc989692990947075319atural] :
% 0.33/0.67 ~ ! [F3: produc4972180933644002618e_term > option6357759511663192854e_term,D: code_natural,I2: code_natural] :
% 0.33/0.67 ( X
% 0.33/0.67 != ( produc3831813291587773865atural @ F3 @ ( produc3574140220909816553atural @ D @ I2 ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % full_exhaustive_natural'.cases
% 0.33/0.67 thf(fact_7635_exhaustive__natural_H_Ocases,axiom,
% 0.33/0.67 ! [X: produc8731074985263844745atural] :
% 0.33/0.67 ~ ! [F3: code_natural > option6357759511663192854e_term,D: code_natural,I2: code_natural] :
% 0.33/0.67 ( X
% 0.33/0.67 != ( produc2252593628808123835atural @ F3 @ ( produc3574140220909816553atural @ D @ I2 ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % exhaustive_natural'.cases
% 0.33/0.67 thf(fact_7636_log_Ocases,axiom,
% 0.33/0.67 ! [X: produc7822875418678951345atural] :
% 0.33/0.67 ~ ! [B2: code_natural,I2: code_natural] :
% 0.33/0.67 ( X
% 0.33/0.67 != ( produc3574140220909816553atural @ B2 @ I2 ) ) ).
% 0.33/0.67
% 0.33/0.67 % log.cases
% 0.33/0.67 thf(fact_7637_minus__shift__def,axiom,
% 0.33/0.67 ( minus_shift
% 0.33/0.67 = ( ^ [R3: code_natural,K4: code_natural,L3: code_natural] : ( if_Code_natural @ ( ord_le5570908160329646204atural @ K4 @ L3 ) @ ( minus_7197305767214868737atural @ ( plus_p4538020629002901425atural @ R3 @ K4 ) @ L3 ) @ ( minus_7197305767214868737atural @ K4 @ L3 ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % minus_shift_def
% 0.33/0.67 thf(fact_7638_split__seed__def,axiom,
% 0.33/0.67 ( split_seed
% 0.33/0.67 = ( ^ [S4: produc7822875418678951345atural] :
% 0.33/0.67 ( produc8282080750456430313atural
% 0.33/0.67 @ ^ [V2: code_natural,W2: code_natural] :
% 0.33/0.67 ( produc8282080750456430313atural
% 0.33/0.67 @ ^ [V5: code_natural,W3: code_natural] : ( produc4480994950612372183atural @ ( produc3574140220909816553atural @ ( inc_shift @ ( numera5444537566228673987atural @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ V2 ) @ W3 ) @ ( produc3574140220909816553atural @ V5 @ ( inc_shift @ ( numera5444537566228673987atural @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ W2 ) ) )
% 0.33/0.67 @ ( produc6591912806276919810atural @ ( next @ S4 ) ) )
% 0.33/0.67 @ S4 ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % split_seed_def
% 0.33/0.67 thf(fact_7639_log_Osimps,axiom,
% 0.33/0.67 ( log
% 0.33/0.67 = ( ^ [B4: code_natural,I3: code_natural] :
% 0.33/0.67 ( if_Code_natural
% 0.33/0.67 @ ( ( ord_le1926595141338095240atural @ B4 @ one_one_Code_natural )
% 0.33/0.67 | ( ord_le5570908160329646204atural @ I3 @ B4 ) )
% 0.33/0.67 @ one_one_Code_natural
% 0.33/0.67 @ ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( log @ B4 @ ( divide5121882707175180666atural @ I3 @ B4 ) ) ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % log.simps
% 0.33/0.67 thf(fact_7640_log_Oelims,axiom,
% 0.33/0.67 ! [X: code_natural,Xa: code_natural,Y: code_natural] :
% 0.33/0.67 ( ( ( log @ X @ Xa )
% 0.33/0.67 = Y )
% 0.33/0.67 => ( ( ( ( ord_le1926595141338095240atural @ X @ one_one_Code_natural )
% 0.33/0.67 | ( ord_le5570908160329646204atural @ Xa @ X ) )
% 0.33/0.67 => ( Y = one_one_Code_natural ) )
% 0.33/0.67 & ( ~ ( ( ord_le1926595141338095240atural @ X @ one_one_Code_natural )
% 0.33/0.67 | ( ord_le5570908160329646204atural @ Xa @ X ) )
% 0.33/0.67 => ( Y
% 0.33/0.67 = ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( log @ X @ ( divide5121882707175180666atural @ Xa @ X ) ) ) ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % log.elims
% 0.33/0.67 thf(fact_7641_inc__shift__def,axiom,
% 0.33/0.67 ( inc_shift
% 0.33/0.67 = ( ^ [V2: code_natural,K4: code_natural] : ( if_Code_natural @ ( V2 = K4 ) @ one_one_Code_natural @ ( plus_p4538020629002901425atural @ K4 @ one_one_Code_natural ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % inc_shift_def
% 0.33/0.67 thf(fact_7642_log_Opelims,axiom,
% 0.33/0.67 ! [X: code_natural,Xa: code_natural,Y: code_natural] :
% 0.33/0.67 ( ( ( log @ X @ Xa )
% 0.33/0.67 = Y )
% 0.33/0.67 => ( ( accp_P8126237942716283194atural @ log_rel @ ( produc3574140220909816553atural @ X @ Xa ) )
% 0.33/0.67 => ~ ( ( ( ( ( ord_le1926595141338095240atural @ X @ one_one_Code_natural )
% 0.33/0.67 | ( ord_le5570908160329646204atural @ Xa @ X ) )
% 0.33/0.67 => ( Y = one_one_Code_natural ) )
% 0.33/0.67 & ( ~ ( ( ord_le1926595141338095240atural @ X @ one_one_Code_natural )
% 0.33/0.67 | ( ord_le5570908160329646204atural @ Xa @ X ) )
% 0.33/0.67 => ( Y
% 0.33/0.67 = ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( log @ X @ ( divide5121882707175180666atural @ Xa @ X ) ) ) ) ) )
% 0.33/0.67 => ~ ( accp_P8126237942716283194atural @ log_rel @ ( produc3574140220909816553atural @ X @ Xa ) ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % log.pelims
% 0.33/0.67 thf(fact_7643_Random_Orange__def,axiom,
% 0.33/0.67 ( range
% 0.33/0.67 = ( ^ [K4: code_natural] :
% 0.33/0.67 ( produc5538323210962509403atural
% 0.33/0.67 @ ( iterat8892046348760725948atural @ ( log @ ( numera5444537566228673987atural @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ K4 )
% 0.33/0.67 @ ^ [L3: code_natural] :
% 0.33/0.67 ( produc5538323210962509403atural @ next
% 0.33/0.67 @ ^ [V2: code_natural] : ( produc6639722614265839536atural @ ( plus_p4538020629002901425atural @ V2 @ ( times_2397367101498566445atural @ L3 @ ( numera5444537566228673987atural @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 0.33/0.67 @ one_one_Code_natural )
% 0.33/0.67 @ ^ [V2: code_natural] : ( produc6639722614265839536atural @ ( modulo8411746178871703098atural @ V2 @ K4 ) ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % Random.range_def
% 0.33/0.67 thf(fact_7644_wmsI,axiom,
% 0.33/0.67 ! [A2: multis2468970476368604999at_nat,B5: multis2468970476368604999at_nat,Z7: multis2468970476368604999at_nat] :
% 0.33/0.67 ( ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( set_ms8126754132646256062at_nat @ A2 ) @ ( set_ms8126754132646256062at_nat @ B5 ) ) @ fun_max_strict )
% 0.33/0.67 | ( ( A2 = zero_z1048942125864253310at_nat )
% 0.33/0.67 & ( B5 = zero_z1048942125864253310at_nat ) ) )
% 0.33/0.67 => ( member6689249552917799696at_nat @ ( produc4348348721325984599at_nat @ ( plus_p7104986032573967614at_nat @ Z7 @ A2 ) @ ( plus_p7104986032573967614at_nat @ Z7 @ B5 ) ) @ ms_weak ) ) ).
% 0.33/0.67
% 0.33/0.67 % wmsI
% 0.33/0.67 thf(fact_7645_smsI,axiom,
% 0.33/0.67 ! [A2: multis2468970476368604999at_nat,B5: multis2468970476368604999at_nat,Z7: multis2468970476368604999at_nat] :
% 0.33/0.67 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( set_ms8126754132646256062at_nat @ A2 ) @ ( set_ms8126754132646256062at_nat @ B5 ) ) @ fun_max_strict )
% 0.33/0.67 => ( member6689249552917799696at_nat @ ( produc4348348721325984599at_nat @ ( plus_p7104986032573967614at_nat @ Z7 @ A2 ) @ ( plus_p7104986032573967614at_nat @ Z7 @ B5 ) ) @ ms_strict ) ) ).
% 0.33/0.67
% 0.33/0.67 % smsI
% 0.33/0.67 thf(fact_7646_ms__reduction__pair,axiom,
% 0.33/0.67 fun_re7357418987779152907at_nat @ ( produc5245064249948416855at_nat @ ms_strict @ ms_weak ) ).
% 0.33/0.67
% 0.33/0.67 % ms_reduction_pair
% 0.33/0.67 thf(fact_7647_ms__strictI,axiom,
% 0.33/0.67 ! [Z7: multis2468970476368604999at_nat,Z8: multis2468970476368604999at_nat,A2: multis2468970476368604999at_nat,B5: multis2468970476368604999at_nat] :
% 0.33/0.67 ( ( pw_leq @ Z7 @ Z8 )
% 0.33/0.67 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( set_ms8126754132646256062at_nat @ A2 ) @ ( set_ms8126754132646256062at_nat @ B5 ) ) @ fun_max_strict )
% 0.33/0.67 => ( member6689249552917799696at_nat @ ( produc4348348721325984599at_nat @ ( plus_p7104986032573967614at_nat @ Z7 @ A2 ) @ ( plus_p7104986032573967614at_nat @ Z8 @ B5 ) ) @ ms_strict ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % ms_strictI
% 0.33/0.67 thf(fact_7648_ms__weakI1,axiom,
% 0.33/0.67 ! [Z7: multis2468970476368604999at_nat,Z8: multis2468970476368604999at_nat,A2: multis2468970476368604999at_nat,B5: multis2468970476368604999at_nat] :
% 0.33/0.67 ( ( pw_leq @ Z7 @ Z8 )
% 0.33/0.67 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( set_ms8126754132646256062at_nat @ A2 ) @ ( set_ms8126754132646256062at_nat @ B5 ) ) @ fun_max_strict )
% 0.33/0.67 => ( member6689249552917799696at_nat @ ( produc4348348721325984599at_nat @ ( plus_p7104986032573967614at_nat @ Z7 @ A2 ) @ ( plus_p7104986032573967614at_nat @ Z8 @ B5 ) ) @ ms_weak ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % ms_weakI1
% 0.33/0.67 thf(fact_7649_pw__leq__split,axiom,
% 0.33/0.67 ! [X11: multis2468970476368604999at_nat,Y9: multis2468970476368604999at_nat] :
% 0.33/0.67 ( ( pw_leq @ X11 @ Y9 )
% 0.33/0.67 => ? [A8: multis2468970476368604999at_nat,B9: multis2468970476368604999at_nat,Z9: multis2468970476368604999at_nat] :
% 0.33/0.67 ( ( X11
% 0.33/0.67 = ( plus_p7104986032573967614at_nat @ A8 @ Z9 ) )
% 0.33/0.67 & ( Y9
% 0.33/0.67 = ( plus_p7104986032573967614at_nat @ B9 @ Z9 ) )
% 0.33/0.67 & ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( set_ms8126754132646256062at_nat @ A8 ) @ ( set_ms8126754132646256062at_nat @ B9 ) ) @ fun_max_strict )
% 0.33/0.67 | ( ( B9 = zero_z1048942125864253310at_nat )
% 0.33/0.67 & ( A8 = zero_z1048942125864253310at_nat ) ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % pw_leq_split
% 0.33/0.67 thf(fact_7650_ms__weakI2,axiom,
% 0.33/0.67 ! [Z7: multis2468970476368604999at_nat,Z8: multis2468970476368604999at_nat] :
% 0.33/0.67 ( ( pw_leq @ Z7 @ Z8 )
% 0.33/0.67 => ( member6689249552917799696at_nat @ ( produc4348348721325984599at_nat @ ( plus_p7104986032573967614at_nat @ Z7 @ zero_z1048942125864253310at_nat ) @ ( plus_p7104986032573967614at_nat @ Z8 @ zero_z1048942125864253310at_nat ) ) @ ms_weak ) ) ).
% 0.33/0.67
% 0.33/0.67 % ms_weakI2
% 0.33/0.67 thf(fact_7651_pw__leq__lstep,axiom,
% 0.33/0.67 ! [X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 0.33/0.67 ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X @ Y ) @ fun_pair_leq )
% 0.33/0.67 => ( pw_leq @ ( add_ms2612439473150266591at_nat @ X @ zero_z1048942125864253310at_nat ) @ ( add_ms2612439473150266591at_nat @ Y @ zero_z1048942125864253310at_nat ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % pw_leq_lstep
% 0.33/0.67 thf(fact_7652_pw__leq__step,axiom,
% 0.33/0.67 ! [X: product_prod_nat_nat,Y: product_prod_nat_nat,X11: multis2468970476368604999at_nat,Y9: multis2468970476368604999at_nat] :
% 0.33/0.67 ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X @ Y ) @ fun_pair_leq )
% 0.33/0.67 => ( ( pw_leq @ X11 @ Y9 )
% 0.33/0.67 => ( pw_leq @ ( plus_p7104986032573967614at_nat @ ( add_ms2612439473150266591at_nat @ X @ zero_z1048942125864253310at_nat ) @ X11 ) @ ( plus_p7104986032573967614at_nat @ ( add_ms2612439473150266591at_nat @ Y @ zero_z1048942125864253310at_nat ) @ Y9 ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % pw_leq_step
% 0.33/0.67 thf(fact_7653_pw__leq_Osimps,axiom,
% 0.33/0.67 ( pw_leq
% 0.33/0.67 = ( ^ [A12: multis2468970476368604999at_nat,A22: multis2468970476368604999at_nat] :
% 0.33/0.67 ( ( ( A12 = zero_z1048942125864253310at_nat )
% 0.33/0.67 & ( A22 = zero_z1048942125864253310at_nat ) )
% 0.33/0.67 | ? [X3: product_prod_nat_nat,Y3: product_prod_nat_nat,X9: multis2468970476368604999at_nat,Y10: multis2468970476368604999at_nat] :
% 0.33/0.67 ( ( A12
% 0.33/0.67 = ( plus_p7104986032573967614at_nat @ ( add_ms2612439473150266591at_nat @ X3 @ zero_z1048942125864253310at_nat ) @ X9 ) )
% 0.33/0.67 & ( A22
% 0.33/0.67 = ( plus_p7104986032573967614at_nat @ ( add_ms2612439473150266591at_nat @ Y3 @ zero_z1048942125864253310at_nat ) @ Y10 ) )
% 0.33/0.67 & ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X3 @ Y3 ) @ fun_pair_leq )
% 0.33/0.67 & ( pw_leq @ X9 @ Y10 ) ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % pw_leq.simps
% 0.33/0.67 thf(fact_7654_pw__leq_Ocases,axiom,
% 0.33/0.67 ! [A1: multis2468970476368604999at_nat,A23: multis2468970476368604999at_nat] :
% 0.33/0.67 ( ( pw_leq @ A1 @ A23 )
% 0.33/0.67 => ( ( ( A1 = zero_z1048942125864253310at_nat )
% 0.33/0.67 => ( A23 != zero_z1048942125864253310at_nat ) )
% 0.33/0.67 => ~ ! [X4: product_prod_nat_nat,Y5: product_prod_nat_nat,X14: multis2468970476368604999at_nat] :
% 0.33/0.67 ( ( A1
% 0.33/0.67 = ( plus_p7104986032573967614at_nat @ ( add_ms2612439473150266591at_nat @ X4 @ zero_z1048942125864253310at_nat ) @ X14 ) )
% 0.33/0.67 => ! [Y11: multis2468970476368604999at_nat] :
% 0.33/0.67 ( ( A23
% 0.33/0.67 = ( plus_p7104986032573967614at_nat @ ( add_ms2612439473150266591at_nat @ Y5 @ zero_z1048942125864253310at_nat ) @ Y11 ) )
% 0.33/0.67 => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X4 @ Y5 ) @ fun_pair_leq )
% 0.33/0.67 => ~ ( pw_leq @ X14 @ Y11 ) ) ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % pw_leq.cases
% 0.33/0.67 thf(fact_7655_Code__Numeral_Osub__code_I4_J,axiom,
% 0.33/0.67 ! [N2: num] :
% 0.33/0.67 ( ( code_sub @ one @ ( bit0 @ N2 ) )
% 0.33/0.67 = ( code_Neg @ ( bitM @ N2 ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % Code_Numeral.sub_code(4)
% 0.33/0.67 thf(fact_7656_Code__Numeral_Odup__code_I3_J,axiom,
% 0.33/0.67 ! [N2: num] :
% 0.33/0.67 ( ( code_dup @ ( code_Neg @ N2 ) )
% 0.33/0.67 = ( code_Neg @ ( bit0 @ N2 ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % Code_Numeral.dup_code(3)
% 0.33/0.67 thf(fact_7657_less__integer__code_I3_J,axiom,
% 0.33/0.67 ! [L: num] :
% 0.33/0.67 ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( code_Neg @ L ) ) ).
% 0.33/0.67
% 0.33/0.67 % less_integer_code(3)
% 0.33/0.67 thf(fact_7658_less__integer__code_I7_J,axiom,
% 0.33/0.67 ! [K: num] : ( ord_le6747313008572928689nteger @ ( code_Neg @ K ) @ zero_z3403309356797280102nteger ) ).
% 0.33/0.67
% 0.33/0.67 % less_integer_code(7)
% 0.33/0.67 thf(fact_7659_plus__integer__code_I6_J,axiom,
% 0.33/0.67 ! [M2: num,N2: num] :
% 0.33/0.67 ( ( plus_p5714425477246183910nteger @ ( code_Neg @ M2 ) @ ( code_Neg @ N2 ) )
% 0.33/0.67 = ( code_Neg @ ( plus_plus_num @ M2 @ N2 ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % plus_integer_code(6)
% 0.33/0.67 thf(fact_7660_less__eq__integer__code_I7_J,axiom,
% 0.33/0.67 ! [K: num] : ( ord_le3102999989581377725nteger @ ( code_Neg @ K ) @ zero_z3403309356797280102nteger ) ).
% 0.33/0.67
% 0.33/0.67 % less_eq_integer_code(7)
% 0.33/0.67 thf(fact_7661_less__eq__integer__code_I3_J,axiom,
% 0.33/0.67 ! [L: num] :
% 0.33/0.67 ~ ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( code_Neg @ L ) ) ).
% 0.33/0.67
% 0.33/0.67 % less_eq_integer_code(3)
% 0.33/0.67 thf(fact_7662_less__integer__code_I9_J,axiom,
% 0.33/0.67 ! [K: num,L: num] :
% 0.33/0.67 ( ( ord_le6747313008572928689nteger @ ( code_Neg @ K ) @ ( code_Neg @ L ) )
% 0.33/0.67 = ( ord_less_num @ L @ K ) ) ).
% 0.33/0.67
% 0.33/0.67 % less_integer_code(9)
% 0.33/0.67 thf(fact_7663_less__eq__integer__code_I9_J,axiom,
% 0.33/0.67 ! [K: num,L: num] :
% 0.33/0.67 ( ( ord_le3102999989581377725nteger @ ( code_Neg @ K ) @ ( code_Neg @ L ) )
% 0.33/0.67 = ( ord_less_eq_num @ L @ K ) ) ).
% 0.33/0.67
% 0.33/0.67 % less_eq_integer_code(9)
% 0.33/0.67 thf(fact_7664_minus__integer__code_I6_J,axiom,
% 0.33/0.67 ! [M2: num,N2: num] :
% 0.33/0.67 ( ( minus_8373710615458151222nteger @ ( code_Neg @ M2 ) @ ( code_Neg @ N2 ) )
% 0.33/0.67 = ( code_sub @ N2 @ M2 ) ) ).
% 0.33/0.67
% 0.33/0.67 % minus_integer_code(6)
% 0.33/0.67 thf(fact_7665_divmod__abs__code_I2_J,axiom,
% 0.33/0.67 ! [K: num,L: num] :
% 0.33/0.67 ( ( code_divmod_abs @ ( code_Neg @ K ) @ ( code_Neg @ L ) )
% 0.33/0.67 = ( unique3479559517661332726nteger @ K @ L ) ) ).
% 0.33/0.67
% 0.33/0.67 % divmod_abs_code(2)
% 0.33/0.67 thf(fact_7666_Code__Numeral_Osub__code_I5_J,axiom,
% 0.33/0.67 ! [N2: num] :
% 0.33/0.67 ( ( code_sub @ one @ ( bit1 @ N2 ) )
% 0.33/0.67 = ( code_Neg @ ( bit0 @ N2 ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % Code_Numeral.sub_code(5)
% 0.33/0.67 thf(fact_7667_card__length__sum__list__rec,axiom,
% 0.33/0.67 ! [M2: nat,N6: nat] :
% 0.33/0.67 ( ( ord_less_eq_nat @ one_one_nat @ M2 )
% 0.33/0.67 => ( ( finite_card_list_nat
% 0.33/0.67 @ ( collect_list_nat
% 0.33/0.67 @ ^ [L3: list_nat] :
% 0.33/0.67 ( ( ( size_size_list_nat @ L3 )
% 0.33/0.67 = M2 )
% 0.33/0.67 & ( ( groups4561878855575611511st_nat @ L3 )
% 0.33/0.67 = N6 ) ) ) )
% 0.33/0.67 = ( plus_plus_nat
% 0.33/0.67 @ ( finite_card_list_nat
% 0.33/0.67 @ ( collect_list_nat
% 0.33/0.67 @ ^ [L3: list_nat] :
% 0.33/0.67 ( ( ( size_size_list_nat @ L3 )
% 0.33/0.67 = ( minus_minus_nat @ M2 @ one_one_nat ) )
% 0.33/0.67 & ( ( groups4561878855575611511st_nat @ L3 )
% 0.33/0.67 = N6 ) ) ) )
% 0.33/0.67 @ ( finite_card_list_nat
% 0.33/0.67 @ ( collect_list_nat
% 0.33/0.67 @ ^ [L3: list_nat] :
% 0.33/0.67 ( ( ( size_size_list_nat @ L3 )
% 0.33/0.67 = M2 )
% 0.33/0.67 & ( ( plus_plus_nat @ ( groups4561878855575611511st_nat @ L3 ) @ one_one_nat )
% 0.33/0.67 = N6 ) ) ) ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % card_length_sum_list_rec
% 0.33/0.67 thf(fact_7668_card__length__sum__list,axiom,
% 0.33/0.67 ! [M2: nat,N6: nat] :
% 0.33/0.67 ( ( finite_card_list_nat
% 0.33/0.67 @ ( collect_list_nat
% 0.33/0.67 @ ^ [L3: list_nat] :
% 0.33/0.67 ( ( ( size_size_list_nat @ L3 )
% 0.33/0.67 = M2 )
% 0.33/0.67 & ( ( groups4561878855575611511st_nat @ L3 )
% 0.33/0.67 = N6 ) ) ) )
% 0.33/0.67 = ( binomial @ ( minus_minus_nat @ ( plus_plus_nat @ N6 @ M2 ) @ one_one_nat ) @ N6 ) ) ).
% 0.33/0.67
% 0.33/0.67 % card_length_sum_list
% 0.33/0.67 thf(fact_7669_natural__of__nat__of__nat,axiom,
% 0.33/0.67 code_natural_of_nat = semiri3763490453095760265atural ).
% 0.33/0.67
% 0.33/0.67 % natural_of_nat_of_nat
% 0.33/0.67 thf(fact_7670_division__segment__natural_Oabs__eq,axiom,
% 0.33/0.67 ! [X: nat] :
% 0.33/0.67 ( ( euclid5112970336976722131atural @ ( code_natural_of_nat @ X ) )
% 0.33/0.67 = ( code_natural_of_nat @ ( euclid3398187327856392827nt_nat @ X ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % division_segment_natural.abs_eq
% 0.33/0.67 thf(fact_7671_set__bit__natural_Oabs__eq,axiom,
% 0.33/0.67 ! [Xa: nat,X: nat] :
% 0.33/0.67 ( ( bit_se1617098188084679374atural @ Xa @ ( code_natural_of_nat @ X ) )
% 0.33/0.67 = ( code_natural_of_nat @ ( bit_se7882103937844011126it_nat @ Xa @ X ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % set_bit_natural.abs_eq
% 0.33/0.67 thf(fact_7672_flip__bit__natural_Oabs__eq,axiom,
% 0.33/0.67 ! [Xa: nat,X: nat] :
% 0.33/0.67 ( ( bit_se168947363167071951atural @ Xa @ ( code_natural_of_nat @ X ) )
% 0.33/0.67 = ( code_natural_of_nat @ ( bit_se2161824704523386999it_nat @ Xa @ X ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % flip_bit_natural.abs_eq
% 0.33/0.67 thf(fact_7673_unset__bit__natural_Oabs__eq,axiom,
% 0.33/0.67 ! [Xa: nat,X: nat] :
% 0.33/0.67 ( ( bit_se7083795435491715335atural @ Xa @ ( code_natural_of_nat @ X ) )
% 0.33/0.67 = ( code_natural_of_nat @ ( bit_se4205575877204974255it_nat @ Xa @ X ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % unset_bit_natural.abs_eq
% 0.33/0.67 thf(fact_7674_euclidean__size__natural_Oabs__eq,axiom,
% 0.33/0.67 ! [X: nat] :
% 0.33/0.67 ( ( euclid5200926497590043453atural @ ( code_natural_of_nat @ X ) )
% 0.33/0.67 = ( euclid4777050414544973029ze_nat @ X ) ) ).
% 0.33/0.67
% 0.33/0.67 % euclidean_size_natural.abs_eq
% 0.33/0.67 thf(fact_7675_bit__natural_Oabs__eq,axiom,
% 0.33/0.67 ! [X: nat] :
% 0.33/0.67 ( ( bit_se8040316288895769887atural @ ( code_natural_of_nat @ X ) )
% 0.33/0.67 = ( bit_se1148574629649215175it_nat @ X ) ) ).
% 0.33/0.67
% 0.33/0.67 % bit_natural.abs_eq
% 0.33/0.67 thf(fact_7676_natural__of__nat__cases,axiom,
% 0.33/0.67 ! [X: code_natural] :
% 0.33/0.67 ~ ! [Y5: nat] :
% 0.33/0.67 ( ( X
% 0.33/0.67 = ( code_natural_of_nat @ Y5 ) )
% 0.33/0.67 => ~ ( member_nat @ Y5 @ top_top_set_nat ) ) ).
% 0.33/0.67
% 0.33/0.67 % natural_of_nat_cases
% 0.33/0.67 thf(fact_7677_natural__of__nat__induct,axiom,
% 0.33/0.67 ! [P: code_natural > $o,X: code_natural] :
% 0.33/0.67 ( ! [Y5: nat] :
% 0.33/0.67 ( ( member_nat @ Y5 @ top_top_set_nat )
% 0.33/0.67 => ( P @ ( code_natural_of_nat @ Y5 ) ) )
% 0.33/0.67 => ( P @ X ) ) ).
% 0.33/0.67
% 0.33/0.67 % natural_of_nat_induct
% 0.33/0.67 thf(fact_7678_natural__of__nat__inject,axiom,
% 0.33/0.67 ! [X: nat,Y: nat] :
% 0.33/0.67 ( ( member_nat @ X @ top_top_set_nat )
% 0.33/0.67 => ( ( member_nat @ Y @ top_top_set_nat )
% 0.33/0.67 => ( ( ( code_natural_of_nat @ X )
% 0.33/0.67 = ( code_natural_of_nat @ Y ) )
% 0.33/0.67 = ( X = Y ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % natural_of_nat_inject
% 0.33/0.67 thf(fact_7679_take__bit__natural_Oabs__eq,axiom,
% 0.33/0.67 ! [Xa: nat,X: nat] :
% 0.33/0.67 ( ( bit_se569199155075624693atural @ Xa @ ( code_natural_of_nat @ X ) )
% 0.33/0.67 = ( code_natural_of_nat @ ( bit_se2925701944663578781it_nat @ Xa @ X ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % take_bit_natural.abs_eq
% 0.33/0.67 thf(fact_7680_and__natural_Oabs__eq,axiom,
% 0.33/0.67 ! [Xa: nat,X: nat] :
% 0.33/0.67 ( ( bit_se2773287842338716102atural @ ( code_natural_of_nat @ Xa ) @ ( code_natural_of_nat @ X ) )
% 0.33/0.67 = ( code_natural_of_nat @ ( bit_se727722235901077358nd_nat @ Xa @ X ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % and_natural.abs_eq
% 0.33/0.67 thf(fact_7681_xor__natural_Oabs__eq,axiom,
% 0.33/0.67 ! [Xa: nat,X: nat] :
% 0.33/0.67 ( ( bit_se2046307713759805098atural @ ( code_natural_of_nat @ Xa ) @ ( code_natural_of_nat @ X ) )
% 0.33/0.67 = ( code_natural_of_nat @ ( bit_se6528837805403552850or_nat @ Xa @ X ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % xor_natural.abs_eq
% 0.33/0.67 thf(fact_7682_or__natural_Oabs__eq,axiom,
% 0.33/0.67 ! [Xa: nat,X: nat] :
% 0.33/0.67 ( ( bit_se9127793120404214118atural @ ( code_natural_of_nat @ Xa ) @ ( code_natural_of_nat @ X ) )
% 0.33/0.67 = ( code_natural_of_nat @ ( bit_se1412395901928357646or_nat @ Xa @ X ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % or_natural.abs_eq
% 0.33/0.67 thf(fact_7683_mask__natural_Oabs__eq,axiom,
% 0.33/0.67 ( bit_se943457434206027407atural
% 0.33/0.67 = ( ^ [X3: nat] : ( code_natural_of_nat @ ( bit_se2002935070580805687sk_nat @ X3 ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % mask_natural.abs_eq
% 0.33/0.67 thf(fact_7684_push__bit__natural_Oabs__eq,axiom,
% 0.33/0.67 ! [Xa: nat,X: nat] :
% 0.33/0.67 ( ( bit_se6611745700429515170atural @ Xa @ ( code_natural_of_nat @ X ) )
% 0.33/0.67 = ( code_natural_of_nat @ ( bit_se547839408752420682it_nat @ Xa @ X ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % push_bit_natural.abs_eq
% 0.33/0.67 thf(fact_7685_drop__bit__natural_Oabs__eq,axiom,
% 0.33/0.67 ! [Xa: nat,X: nat] :
% 0.33/0.67 ( ( bit_se2751692689150723149atural @ Xa @ ( code_natural_of_nat @ X ) )
% 0.33/0.67 = ( code_natural_of_nat @ ( bit_se8570568707652914677it_nat @ Xa @ X ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % drop_bit_natural.abs_eq
% 0.33/0.67 thf(fact_7686_zero__natural__def,axiom,
% 0.33/0.67 ( zero_z2226904508553997617atural
% 0.33/0.67 = ( code_natural_of_nat @ zero_zero_nat ) ) ).
% 0.33/0.67
% 0.33/0.67 % zero_natural_def
% 0.33/0.67 thf(fact_7687_one__natural__def,axiom,
% 0.33/0.67 ( one_one_Code_natural
% 0.33/0.67 = ( code_natural_of_nat @ one_one_nat ) ) ).
% 0.33/0.67
% 0.33/0.67 % one_natural_def
% 0.33/0.67 thf(fact_7688_less__natural_Oabs__eq,axiom,
% 0.33/0.67 ! [Xa: nat,X: nat] :
% 0.33/0.67 ( ( ord_le5570908160329646204atural @ ( code_natural_of_nat @ Xa ) @ ( code_natural_of_nat @ X ) )
% 0.33/0.67 = ( ord_less_nat @ Xa @ X ) ) ).
% 0.33/0.67
% 0.33/0.67 % less_natural.abs_eq
% 0.33/0.67 thf(fact_7689_plus__natural_Oabs__eq,axiom,
% 0.33/0.67 ! [Xa: nat,X: nat] :
% 0.33/0.67 ( ( plus_p4538020629002901425atural @ ( code_natural_of_nat @ Xa ) @ ( code_natural_of_nat @ X ) )
% 0.33/0.67 = ( code_natural_of_nat @ ( plus_plus_nat @ Xa @ X ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % plus_natural.abs_eq
% 0.33/0.67 thf(fact_7690_minus__natural_Oabs__eq,axiom,
% 0.33/0.67 ! [Xa: nat,X: nat] :
% 0.33/0.67 ( ( minus_7197305767214868737atural @ ( code_natural_of_nat @ Xa ) @ ( code_natural_of_nat @ X ) )
% 0.33/0.67 = ( code_natural_of_nat @ ( minus_minus_nat @ Xa @ X ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % minus_natural.abs_eq
% 0.33/0.67 thf(fact_7691_less__eq__natural_Oabs__eq,axiom,
% 0.33/0.67 ! [Xa: nat,X: nat] :
% 0.33/0.67 ( ( ord_le1926595141338095240atural @ ( code_natural_of_nat @ Xa ) @ ( code_natural_of_nat @ X ) )
% 0.33/0.67 = ( ord_less_eq_nat @ Xa @ X ) ) ).
% 0.33/0.67
% 0.33/0.67 % less_eq_natural.abs_eq
% 0.33/0.67 thf(fact_7692_times__natural_Oabs__eq,axiom,
% 0.33/0.67 ! [Xa: nat,X: nat] :
% 0.33/0.67 ( ( times_2397367101498566445atural @ ( code_natural_of_nat @ Xa ) @ ( code_natural_of_nat @ X ) )
% 0.33/0.67 = ( code_natural_of_nat @ ( times_times_nat @ Xa @ X ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % times_natural.abs_eq
% 0.33/0.67 thf(fact_7693_divide__natural_Oabs__eq,axiom,
% 0.33/0.67 ! [Xa: nat,X: nat] :
% 0.33/0.67 ( ( divide5121882707175180666atural @ ( code_natural_of_nat @ Xa ) @ ( code_natural_of_nat @ X ) )
% 0.33/0.67 = ( code_natural_of_nat @ ( divide_divide_nat @ Xa @ X ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % divide_natural.abs_eq
% 0.33/0.67 thf(fact_7694_mask__natural__def,axiom,
% 0.33/0.67 ( bit_se943457434206027407atural
% 0.33/0.67 = ( map_fu4742413587575543474atural @ id_nat @ code_natural_of_nat @ bit_se2002935070580805687sk_nat ) ) ).
% 0.33/0.67
% 0.33/0.67 % mask_natural_def
% 0.33/0.67 thf(fact_7695_modulo__natural_Oabs__eq,axiom,
% 0.33/0.67 ! [Xa: nat,X: nat] :
% 0.33/0.67 ( ( modulo8411746178871703098atural @ ( code_natural_of_nat @ Xa ) @ ( code_natural_of_nat @ X ) )
% 0.33/0.67 = ( code_natural_of_nat @ ( modulo_modulo_nat @ Xa @ X ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % modulo_natural.abs_eq
% 0.33/0.67 thf(fact_7696_Nat_Oabs__eq,axiom,
% 0.33/0.67 ! [X: int] :
% 0.33/0.67 ( ( code_Nat @ ( code_integer_of_int @ X ) )
% 0.33/0.67 = ( code_natural_of_nat @ ( nat2 @ X ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % Nat.abs_eq
% 0.33/0.67 thf(fact_7697_Nat__def,axiom,
% 0.33/0.67 ( code_Nat
% 0.33/0.67 = ( map_fu1051355602067684763atural @ code_int_of_integer @ code_natural_of_nat @ nat2 ) ) ).
% 0.33/0.67
% 0.33/0.67 % Nat_def
% 0.33/0.67 thf(fact_7698_natural__of__integer_Oabs__eq,axiom,
% 0.33/0.67 ! [X: int] :
% 0.33/0.67 ( ( code_n4118661773612635043nteger @ ( code_integer_of_int @ X ) )
% 0.33/0.67 = ( code_natural_of_nat @ ( nat2 @ X ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % natural_of_integer.abs_eq
% 0.33/0.67 thf(fact_7699_natural__of__nat__of__natural__inverse,axiom,
% 0.33/0.67 ! [N2: code_natural] :
% 0.33/0.67 ( ( code_natural_of_nat @ ( code_nat_of_natural @ N2 ) )
% 0.33/0.67 = N2 ) ).
% 0.33/0.67
% 0.33/0.67 % natural_of_nat_of_natural_inverse
% 0.33/0.67 thf(fact_7700_nat__of__natural__of__nat__inverse,axiom,
% 0.33/0.67 ! [N2: nat] :
% 0.33/0.67 ( ( code_nat_of_natural @ ( code_natural_of_nat @ N2 ) )
% 0.33/0.67 = N2 ) ).
% 0.33/0.67
% 0.33/0.67 % nat_of_natural_of_nat_inverse
% 0.33/0.67 thf(fact_7701_nat__of__natural__inverse,axiom,
% 0.33/0.67 ! [X: code_natural] :
% 0.33/0.67 ( ( code_natural_of_nat @ ( code_nat_of_natural @ X ) )
% 0.33/0.67 = X ) ).
% 0.33/0.67
% 0.33/0.67 % nat_of_natural_inverse
% 0.33/0.67 thf(fact_7702_nat__of__natural__min,axiom,
% 0.33/0.67 ! [K: code_natural,L: code_natural] :
% 0.33/0.67 ( ( code_nat_of_natural @ ( ord_min_Code_natural @ K @ L ) )
% 0.33/0.67 = ( ord_min_nat @ ( code_nat_of_natural @ K ) @ ( code_nat_of_natural @ L ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % nat_of_natural_min
% 0.33/0.67 thf(fact_7703_nat__of__natural__max,axiom,
% 0.33/0.67 ! [K: code_natural,L: code_natural] :
% 0.33/0.67 ( ( code_nat_of_natural @ ( ord_max_Code_natural @ K @ L ) )
% 0.33/0.67 = ( ord_max_nat @ ( code_nat_of_natural @ K ) @ ( code_nat_of_natural @ L ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % nat_of_natural_max
% 0.33/0.67 thf(fact_7704_of__nat__of__natural,axiom,
% 0.33/0.67 ! [N2: code_natural] :
% 0.33/0.67 ( ( semiri3763490453095760265atural @ ( code_nat_of_natural @ N2 ) )
% 0.33/0.67 = N2 ) ).
% 0.33/0.67
% 0.33/0.67 % of_nat_of_natural
% 0.33/0.67 thf(fact_7705_nat__of__natural__of__nat,axiom,
% 0.33/0.67 ! [N2: nat] :
% 0.33/0.67 ( ( code_nat_of_natural @ ( semiri3763490453095760265atural @ N2 ) )
% 0.33/0.67 = N2 ) ).
% 0.33/0.67
% 0.33/0.67 % nat_of_natural_of_nat
% 0.33/0.67 thf(fact_7706_zero__natural_Orep__eq,axiom,
% 0.33/0.67 ( ( code_nat_of_natural @ zero_z2226904508553997617atural )
% 0.33/0.67 = zero_zero_nat ) ).
% 0.33/0.67
% 0.33/0.67 % zero_natural.rep_eq
% 0.33/0.67 thf(fact_7707_one__natural_Orep__eq,axiom,
% 0.33/0.67 ( ( code_nat_of_natural @ one_one_Code_natural )
% 0.33/0.67 = one_one_nat ) ).
% 0.33/0.67
% 0.33/0.67 % one_natural.rep_eq
% 0.33/0.67 thf(fact_7708_plus__natural_Orep__eq,axiom,
% 0.33/0.67 ! [X: code_natural,Xa: code_natural] :
% 0.33/0.67 ( ( code_nat_of_natural @ ( plus_p4538020629002901425atural @ X @ Xa ) )
% 0.33/0.67 = ( plus_plus_nat @ ( code_nat_of_natural @ X ) @ ( code_nat_of_natural @ Xa ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % plus_natural.rep_eq
% 0.33/0.67 thf(fact_7709_minus__natural_Orep__eq,axiom,
% 0.33/0.67 ! [X: code_natural,Xa: code_natural] :
% 0.33/0.67 ( ( code_nat_of_natural @ ( minus_7197305767214868737atural @ X @ Xa ) )
% 0.33/0.67 = ( minus_minus_nat @ ( code_nat_of_natural @ X ) @ ( code_nat_of_natural @ Xa ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % minus_natural.rep_eq
% 0.33/0.67 thf(fact_7710_nat__of__natural__numeral,axiom,
% 0.33/0.67 ! [K: num] :
% 0.33/0.67 ( ( code_nat_of_natural @ ( numera5444537566228673987atural @ K ) )
% 0.33/0.67 = ( numeral_numeral_nat @ K ) ) ).
% 0.33/0.67
% 0.33/0.67 % nat_of_natural_numeral
% 0.33/0.67 thf(fact_7711_times__natural_Orep__eq,axiom,
% 0.33/0.67 ! [X: code_natural,Xa: code_natural] :
% 0.33/0.67 ( ( code_nat_of_natural @ ( times_2397367101498566445atural @ X @ Xa ) )
% 0.33/0.67 = ( times_times_nat @ ( code_nat_of_natural @ X ) @ ( code_nat_of_natural @ Xa ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % times_natural.rep_eq
% 0.33/0.67 thf(fact_7712_divide__natural_Orep__eq,axiom,
% 0.33/0.67 ! [X: code_natural,Xa: code_natural] :
% 0.33/0.67 ( ( code_nat_of_natural @ ( divide5121882707175180666atural @ X @ Xa ) )
% 0.33/0.67 = ( divide_divide_nat @ ( code_nat_of_natural @ X ) @ ( code_nat_of_natural @ Xa ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % divide_natural.rep_eq
% 0.33/0.67 thf(fact_7713_modulo__natural_Orep__eq,axiom,
% 0.33/0.67 ! [X: code_natural,Xa: code_natural] :
% 0.33/0.67 ( ( code_nat_of_natural @ ( modulo8411746178871703098atural @ X @ Xa ) )
% 0.33/0.67 = ( modulo_modulo_nat @ ( code_nat_of_natural @ X ) @ ( code_nat_of_natural @ Xa ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % modulo_natural.rep_eq
% 0.33/0.67 thf(fact_7714_division__segment__natural_Orep__eq,axiom,
% 0.33/0.67 ! [X: code_natural] :
% 0.33/0.67 ( ( code_nat_of_natural @ ( euclid5112970336976722131atural @ X ) )
% 0.33/0.67 = ( euclid3398187327856392827nt_nat @ ( code_nat_of_natural @ X ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % division_segment_natural.rep_eq
% 0.33/0.67 thf(fact_7715_euclidean__size__natural_Orep__eq,axiom,
% 0.33/0.67 ( euclid5200926497590043453atural
% 0.33/0.67 = ( ^ [X3: code_natural] : ( euclid4777050414544973029ze_nat @ ( code_nat_of_natural @ X3 ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % euclidean_size_natural.rep_eq
% 0.33/0.67 thf(fact_7716_unset__bit__natural_Orep__eq,axiom,
% 0.33/0.67 ! [X: nat,Xa: code_natural] :
% 0.33/0.67 ( ( code_nat_of_natural @ ( bit_se7083795435491715335atural @ X @ Xa ) )
% 0.33/0.67 = ( bit_se4205575877204974255it_nat @ X @ ( code_nat_of_natural @ Xa ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % unset_bit_natural.rep_eq
% 0.33/0.67 thf(fact_7717_flip__bit__natural_Orep__eq,axiom,
% 0.33/0.67 ! [X: nat,Xa: code_natural] :
% 0.33/0.67 ( ( code_nat_of_natural @ ( bit_se168947363167071951atural @ X @ Xa ) )
% 0.33/0.67 = ( bit_se2161824704523386999it_nat @ X @ ( code_nat_of_natural @ Xa ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % flip_bit_natural.rep_eq
% 0.33/0.67 thf(fact_7718_set__bit__natural_Orep__eq,axiom,
% 0.33/0.67 ! [X: nat,Xa: code_natural] :
% 0.33/0.67 ( ( code_nat_of_natural @ ( bit_se1617098188084679374atural @ X @ Xa ) )
% 0.33/0.67 = ( bit_se7882103937844011126it_nat @ X @ ( code_nat_of_natural @ Xa ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % set_bit_natural.rep_eq
% 0.33/0.67 thf(fact_7719_Nat_Orep__eq,axiom,
% 0.33/0.67 ! [X: code_integer] :
% 0.33/0.67 ( ( code_nat_of_natural @ ( code_Nat @ X ) )
% 0.33/0.67 = ( nat2 @ ( code_int_of_integer @ X ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % Nat.rep_eq
% 0.33/0.67 thf(fact_7720_push__bit__natural_Orep__eq,axiom,
% 0.33/0.67 ! [X: nat,Xa: code_natural] :
% 0.33/0.67 ( ( code_nat_of_natural @ ( bit_se6611745700429515170atural @ X @ Xa ) )
% 0.33/0.67 = ( bit_se547839408752420682it_nat @ X @ ( code_nat_of_natural @ Xa ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % push_bit_natural.rep_eq
% 0.33/0.67 thf(fact_7721_mask__natural_Orep__eq,axiom,
% 0.33/0.67 ! [X: nat] :
% 0.33/0.67 ( ( code_nat_of_natural @ ( bit_se943457434206027407atural @ X ) )
% 0.33/0.67 = ( bit_se2002935070580805687sk_nat @ X ) ) ).
% 0.33/0.67
% 0.33/0.67 % mask_natural.rep_eq
% 0.33/0.67 thf(fact_7722_and__natural_Orep__eq,axiom,
% 0.33/0.67 ! [X: code_natural,Xa: code_natural] :
% 0.33/0.67 ( ( code_nat_of_natural @ ( bit_se2773287842338716102atural @ X @ Xa ) )
% 0.33/0.67 = ( bit_se727722235901077358nd_nat @ ( code_nat_of_natural @ X ) @ ( code_nat_of_natural @ Xa ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % and_natural.rep_eq
% 0.33/0.67 thf(fact_7723_bit__natural_Orep__eq,axiom,
% 0.33/0.67 ( bit_se8040316288895769887atural
% 0.33/0.67 = ( ^ [X3: code_natural] : ( bit_se1148574629649215175it_nat @ ( code_nat_of_natural @ X3 ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % bit_natural.rep_eq
% 0.33/0.67 thf(fact_7724_nat__of__natural__inject,axiom,
% 0.33/0.67 ! [X: code_natural,Y: code_natural] :
% 0.33/0.67 ( ( ( code_nat_of_natural @ X )
% 0.33/0.67 = ( code_nat_of_natural @ Y ) )
% 0.33/0.67 = ( X = Y ) ) ).
% 0.33/0.67
% 0.33/0.67 % nat_of_natural_inject
% 0.33/0.67 thf(fact_7725_natural__eqI,axiom,
% 0.33/0.67 ! [M2: code_natural,N2: code_natural] :
% 0.33/0.67 ( ( ( code_nat_of_natural @ M2 )
% 0.33/0.67 = ( code_nat_of_natural @ N2 ) )
% 0.33/0.67 => ( M2 = N2 ) ) ).
% 0.33/0.67
% 0.33/0.67 % natural_eqI
% 0.33/0.67 thf(fact_7726_natural__eq__iff,axiom,
% 0.33/0.67 ( ( ^ [Y4: code_natural,Z2: code_natural] : ( Y4 = Z2 ) )
% 0.33/0.67 = ( ^ [M: code_natural,N4: code_natural] :
% 0.33/0.67 ( ( code_nat_of_natural @ M )
% 0.33/0.67 = ( code_nat_of_natural @ N4 ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % natural_eq_iff
% 0.33/0.67 thf(fact_7727_natural__cases,axiom,
% 0.33/0.67 ! [M2: code_natural] :
% 0.33/0.67 ~ ! [N: nat] :
% 0.33/0.67 ( M2
% 0.33/0.67 != ( semiri3763490453095760265atural @ N ) ) ).
% 0.33/0.67
% 0.33/0.67 % natural_cases
% 0.33/0.67 thf(fact_7728_nat__of__natural,axiom,
% 0.33/0.67 ! [X: code_natural] : ( member_nat @ ( code_nat_of_natural @ X ) @ top_top_set_nat ) ).
% 0.33/0.67
% 0.33/0.67 % nat_of_natural
% 0.33/0.67 thf(fact_7729_nat__of__natural__cases,axiom,
% 0.33/0.67 ! [Y: nat] :
% 0.33/0.67 ( ( member_nat @ Y @ top_top_set_nat )
% 0.33/0.67 => ~ ! [X4: code_natural] :
% 0.33/0.67 ( Y
% 0.33/0.67 != ( code_nat_of_natural @ X4 ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % nat_of_natural_cases
% 0.33/0.67 thf(fact_7730_nat__of__natural__induct,axiom,
% 0.33/0.67 ! [Y: nat,P: nat > $o] :
% 0.33/0.67 ( ( member_nat @ Y @ top_top_set_nat )
% 0.33/0.67 => ( ! [X4: code_natural] : ( P @ ( code_nat_of_natural @ X4 ) )
% 0.33/0.67 => ( P @ Y ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % nat_of_natural_induct
% 0.33/0.67 thf(fact_7731_take__bit__natural_Orep__eq,axiom,
% 0.33/0.67 ! [X: nat,Xa: code_natural] :
% 0.33/0.67 ( ( code_nat_of_natural @ ( bit_se569199155075624693atural @ X @ Xa ) )
% 0.33/0.67 = ( bit_se2925701944663578781it_nat @ X @ ( code_nat_of_natural @ Xa ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % take_bit_natural.rep_eq
% 0.33/0.67 thf(fact_7732_or__natural_Orep__eq,axiom,
% 0.33/0.67 ! [X: code_natural,Xa: code_natural] :
% 0.33/0.67 ( ( code_nat_of_natural @ ( bit_se9127793120404214118atural @ X @ Xa ) )
% 0.33/0.67 = ( bit_se1412395901928357646or_nat @ ( code_nat_of_natural @ X ) @ ( code_nat_of_natural @ Xa ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % or_natural.rep_eq
% 0.33/0.67 thf(fact_7733_xor__natural_Orep__eq,axiom,
% 0.33/0.67 ! [X: code_natural,Xa: code_natural] :
% 0.33/0.67 ( ( code_nat_of_natural @ ( bit_se2046307713759805098atural @ X @ Xa ) )
% 0.33/0.67 = ( bit_se6528837805403552850or_nat @ ( code_nat_of_natural @ X ) @ ( code_nat_of_natural @ Xa ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % xor_natural.rep_eq
% 0.33/0.67 thf(fact_7734_drop__bit__natural_Orep__eq,axiom,
% 0.33/0.67 ! [X: nat,Xa: code_natural] :
% 0.33/0.67 ( ( code_nat_of_natural @ ( bit_se2751692689150723149atural @ X @ Xa ) )
% 0.33/0.67 = ( bit_se8570568707652914677it_nat @ X @ ( code_nat_of_natural @ Xa ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % drop_bit_natural.rep_eq
% 0.33/0.67 thf(fact_7735_natural__of__integer_Orep__eq,axiom,
% 0.33/0.67 ! [X: code_integer] :
% 0.33/0.67 ( ( code_nat_of_natural @ ( code_n4118661773612635043nteger @ X ) )
% 0.33/0.67 = ( nat2 @ ( code_int_of_integer @ X ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % natural_of_integer.rep_eq
% 0.33/0.67 thf(fact_7736_less__natural_Orep__eq,axiom,
% 0.33/0.67 ( ord_le5570908160329646204atural
% 0.33/0.67 = ( ^ [X3: code_natural,Xa4: code_natural] : ( ord_less_nat @ ( code_nat_of_natural @ X3 ) @ ( code_nat_of_natural @ Xa4 ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % less_natural.rep_eq
% 0.33/0.67 thf(fact_7737_natural__of__nat__inverse,axiom,
% 0.33/0.67 ! [Y: nat] :
% 0.33/0.67 ( ( member_nat @ Y @ top_top_set_nat )
% 0.33/0.67 => ( ( code_nat_of_natural @ ( code_natural_of_nat @ Y ) )
% 0.33/0.67 = Y ) ) ).
% 0.33/0.67
% 0.33/0.67 % natural_of_nat_inverse
% 0.33/0.67 thf(fact_7738_type__definition__natural,axiom,
% 0.33/0.67 type_d4410041424927559462al_nat @ code_nat_of_natural @ code_natural_of_nat @ top_top_set_nat ).
% 0.33/0.67
% 0.33/0.67 % type_definition_natural
% 0.33/0.67 thf(fact_7739_or__natural__def,axiom,
% 0.33/0.67 ( bit_se9127793120404214118atural
% 0.33/0.67 = ( map_fu6549440983881763648atural @ code_nat_of_natural @ ( map_fu1239815594074539274atural @ code_nat_of_natural @ code_natural_of_nat ) @ bit_se1412395901928357646or_nat ) ) ).
% 0.33/0.67
% 0.33/0.67 % or_natural_def
% 0.33/0.67 thf(fact_7740_xor__natural__def,axiom,
% 0.33/0.67 ( bit_se2046307713759805098atural
% 0.33/0.67 = ( map_fu6549440983881763648atural @ code_nat_of_natural @ ( map_fu1239815594074539274atural @ code_nat_of_natural @ code_natural_of_nat ) @ bit_se6528837805403552850or_nat ) ) ).
% 0.33/0.67
% 0.33/0.67 % xor_natural_def
% 0.33/0.67 thf(fact_7741_and__natural__def,axiom,
% 0.33/0.67 ( bit_se2773287842338716102atural
% 0.33/0.67 = ( map_fu6549440983881763648atural @ code_nat_of_natural @ ( map_fu1239815594074539274atural @ code_nat_of_natural @ code_natural_of_nat ) @ bit_se727722235901077358nd_nat ) ) ).
% 0.33/0.67
% 0.33/0.67 % and_natural_def
% 0.33/0.67 thf(fact_7742_less__eq__natural_Orep__eq,axiom,
% 0.33/0.67 ( ord_le1926595141338095240atural
% 0.33/0.67 = ( ^ [X3: code_natural,Xa4: code_natural] : ( ord_less_eq_nat @ ( code_nat_of_natural @ X3 ) @ ( code_nat_of_natural @ Xa4 ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % less_eq_natural.rep_eq
% 0.33/0.67 thf(fact_7743_division__segment__natural__def,axiom,
% 0.33/0.67 ( euclid5112970336976722131atural
% 0.33/0.67 = ( map_fu1239815594074539274atural @ code_nat_of_natural @ code_natural_of_nat @ euclid3398187327856392827nt_nat ) ) ).
% 0.33/0.67
% 0.33/0.67 % division_segment_natural_def
% 0.33/0.67 thf(fact_7744_euclidean__size__natural__def,axiom,
% 0.33/0.67 ( euclid5200926497590043453atural
% 0.33/0.67 = ( map_fu226235371393106610at_nat @ code_nat_of_natural @ id_nat @ euclid4777050414544973029ze_nat ) ) ).
% 0.33/0.67
% 0.33/0.67 % euclidean_size_natural_def
% 0.33/0.67 thf(fact_7745_plus__natural__def,axiom,
% 0.33/0.67 ( plus_p4538020629002901425atural
% 0.33/0.67 = ( map_fu6549440983881763648atural @ code_nat_of_natural @ ( map_fu1239815594074539274atural @ code_nat_of_natural @ code_natural_of_nat ) @ plus_plus_nat ) ) ).
% 0.33/0.67
% 0.33/0.67 % plus_natural_def
% 0.33/0.67 thf(fact_7746_minus__natural__def,axiom,
% 0.33/0.67 ( minus_7197305767214868737atural
% 0.33/0.67 = ( map_fu6549440983881763648atural @ code_nat_of_natural @ ( map_fu1239815594074539274atural @ code_nat_of_natural @ code_natural_of_nat ) @ minus_minus_nat ) ) ).
% 0.33/0.67
% 0.33/0.67 % minus_natural_def
% 0.33/0.67 thf(fact_7747_bit__natural__def,axiom,
% 0.33/0.67 ( bit_se8040316288895769887atural
% 0.33/0.67 = ( map_fu6244533035418998608_nat_o @ code_nat_of_natural @ id_nat_o @ bit_se1148574629649215175it_nat ) ) ).
% 0.33/0.67
% 0.33/0.67 % bit_natural_def
% 0.33/0.67 thf(fact_7748_less__natural__def,axiom,
% 0.33/0.67 ( ord_le5570908160329646204atural
% 0.33/0.67 = ( map_fu6256889081107267320ural_o @ code_nat_of_natural @ ( map_fu4892316939951275536at_o_o @ code_nat_of_natural @ id_o ) @ ord_less_nat ) ) ).
% 0.33/0.67
% 0.33/0.67 % less_natural_def
% 0.33/0.67 thf(fact_7749_times__natural__def,axiom,
% 0.33/0.67 ( times_2397367101498566445atural
% 0.33/0.67 = ( map_fu6549440983881763648atural @ code_nat_of_natural @ ( map_fu1239815594074539274atural @ code_nat_of_natural @ code_natural_of_nat ) @ times_times_nat ) ) ).
% 0.33/0.67
% 0.33/0.67 % times_natural_def
% 0.33/0.67 thf(fact_7750_divide__natural__def,axiom,
% 0.33/0.67 ( divide5121882707175180666atural
% 0.33/0.67 = ( map_fu6549440983881763648atural @ code_nat_of_natural @ ( map_fu1239815594074539274atural @ code_nat_of_natural @ code_natural_of_nat ) @ divide_divide_nat ) ) ).
% 0.33/0.67
% 0.33/0.67 % divide_natural_def
% 0.33/0.67 thf(fact_7751_take__bit__natural__def,axiom,
% 0.33/0.67 ( bit_se569199155075624693atural
% 0.33/0.67 = ( map_fu6981160461238011112atural @ id_nat @ ( map_fu1239815594074539274atural @ code_nat_of_natural @ code_natural_of_nat ) @ bit_se2925701944663578781it_nat ) ) ).
% 0.33/0.67
% 0.33/0.67 % take_bit_natural_def
% 0.33/0.67 thf(fact_7752_push__bit__natural__def,axiom,
% 0.33/0.67 ( bit_se6611745700429515170atural
% 0.33/0.67 = ( map_fu6981160461238011112atural @ id_nat @ ( map_fu1239815594074539274atural @ code_nat_of_natural @ code_natural_of_nat ) @ bit_se547839408752420682it_nat ) ) ).
% 0.33/0.67
% 0.33/0.67 % push_bit_natural_def
% 0.33/0.67 thf(fact_7753_less__eq__natural__def,axiom,
% 0.33/0.67 ( ord_le1926595141338095240atural
% 0.33/0.67 = ( map_fu6256889081107267320ural_o @ code_nat_of_natural @ ( map_fu4892316939951275536at_o_o @ code_nat_of_natural @ id_o ) @ ord_less_eq_nat ) ) ).
% 0.33/0.67
% 0.33/0.67 % less_eq_natural_def
% 0.33/0.67 thf(fact_7754_modulo__natural__def,axiom,
% 0.33/0.67 ( modulo8411746178871703098atural
% 0.33/0.67 = ( map_fu6549440983881763648atural @ code_nat_of_natural @ ( map_fu1239815594074539274atural @ code_nat_of_natural @ code_natural_of_nat ) @ modulo_modulo_nat ) ) ).
% 0.33/0.67
% 0.33/0.67 % modulo_natural_def
% 0.33/0.67 thf(fact_7755_drop__bit__natural__def,axiom,
% 0.33/0.67 ( bit_se2751692689150723149atural
% 0.33/0.67 = ( map_fu6981160461238011112atural @ id_nat @ ( map_fu1239815594074539274atural @ code_nat_of_natural @ code_natural_of_nat ) @ bit_se8570568707652914677it_nat ) ) ).
% 0.33/0.67
% 0.33/0.67 % drop_bit_natural_def
% 0.33/0.67 thf(fact_7756_unset__bit__natural__def,axiom,
% 0.33/0.67 ( bit_se7083795435491715335atural
% 0.33/0.67 = ( map_fu6981160461238011112atural @ id_nat @ ( map_fu1239815594074539274atural @ code_nat_of_natural @ code_natural_of_nat ) @ bit_se4205575877204974255it_nat ) ) ).
% 0.33/0.67
% 0.33/0.67 % unset_bit_natural_def
% 0.33/0.67 thf(fact_7757_flip__bit__natural__def,axiom,
% 0.33/0.67 ( bit_se168947363167071951atural
% 0.33/0.67 = ( map_fu6981160461238011112atural @ id_nat @ ( map_fu1239815594074539274atural @ code_nat_of_natural @ code_natural_of_nat ) @ bit_se2161824704523386999it_nat ) ) ).
% 0.33/0.67
% 0.33/0.67 % flip_bit_natural_def
% 0.33/0.67 thf(fact_7758_set__bit__natural__def,axiom,
% 0.33/0.67 ( bit_se1617098188084679374atural
% 0.33/0.67 = ( map_fu6981160461238011112atural @ id_nat @ ( map_fu1239815594074539274atural @ code_nat_of_natural @ code_natural_of_nat ) @ bit_se7882103937844011126it_nat ) ) ).
% 0.33/0.67
% 0.33/0.67 % set_bit_natural_def
% 0.33/0.67 thf(fact_7759_natural__decr,axiom,
% 0.33/0.67 ! [N2: code_natural] :
% 0.33/0.67 ( ( N2 != zero_z2226904508553997617atural )
% 0.33/0.67 => ( ord_less_nat @ ( minus_minus_nat @ ( code_nat_of_natural @ N2 ) @ ( suc @ zero_zero_nat ) ) @ ( code_nat_of_natural @ N2 ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % natural_decr
% 0.33/0.67 thf(fact_7760_natural__of__integer__def,axiom,
% 0.33/0.67 ( code_n4118661773612635043nteger
% 0.33/0.67 = ( map_fu1051355602067684763atural @ code_int_of_integer @ code_natural_of_nat @ nat2 ) ) ).
% 0.33/0.67
% 0.33/0.67 % natural_of_integer_def
% 0.33/0.67 thf(fact_7761_integer__of__natural__of__integer,axiom,
% 0.33/0.67 ! [K: code_integer] :
% 0.33/0.67 ( ( code_i5400310926305786745atural @ ( code_n4118661773612635043nteger @ K ) )
% 0.33/0.67 = ( ord_max_Code_integer @ zero_z3403309356797280102nteger @ K ) ) ).
% 0.33/0.67
% 0.33/0.67 % integer_of_natural_of_integer
% 0.33/0.67 thf(fact_7762_integer__of__natural_Orep__eq,axiom,
% 0.33/0.67 ! [X: code_natural] :
% 0.33/0.67 ( ( code_int_of_integer @ ( code_i5400310926305786745atural @ X ) )
% 0.33/0.67 = ( semiri1314217659103216013at_int @ ( code_nat_of_natural @ X ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % integer_of_natural.rep_eq
% 0.33/0.67 thf(fact_7763_int__of__integer__of__natural,axiom,
% 0.33/0.67 ! [N2: code_natural] :
% 0.33/0.67 ( ( code_int_of_integer @ ( code_i5400310926305786745atural @ N2 ) )
% 0.33/0.67 = ( semiri1314217659103216013at_int @ ( code_nat_of_natural @ N2 ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % int_of_integer_of_natural
% 0.33/0.67 thf(fact_7764_integer__of__natural__of__nat,axiom,
% 0.33/0.67 ! [N2: nat] :
% 0.33/0.67 ( ( code_i5400310926305786745atural @ ( semiri3763490453095760265atural @ N2 ) )
% 0.33/0.67 = ( semiri4939895301339042750nteger @ N2 ) ) ).
% 0.33/0.67
% 0.33/0.67 % integer_of_natural_of_nat
% 0.33/0.67 thf(fact_7765_natural__of__integer__of__natural,axiom,
% 0.33/0.67 ! [N2: code_natural] :
% 0.33/0.67 ( ( code_n4118661773612635043nteger @ ( code_i5400310926305786745atural @ N2 ) )
% 0.33/0.67 = N2 ) ).
% 0.33/0.67
% 0.33/0.67 % natural_of_integer_of_natural
% 0.33/0.67 thf(fact_7766_integer__of__natural__def,axiom,
% 0.33/0.67 ( code_i5400310926305786745atural
% 0.33/0.67 = ( map_fu2787874002554666395nteger @ code_nat_of_natural @ code_integer_of_int @ semiri1314217659103216013at_int ) ) ).
% 0.33/0.67
% 0.33/0.67 % integer_of_natural_def
% 0.33/0.67 thf(fact_7767_integer__of__natural_Oabs__eq,axiom,
% 0.33/0.67 ! [X: nat] :
% 0.33/0.67 ( ( code_i5400310926305786745atural @ ( code_natural_of_nat @ X ) )
% 0.33/0.67 = ( code_integer_of_int @ ( semiri1314217659103216013at_int @ X ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % integer_of_natural.abs_eq
% 0.33/0.67 thf(fact_7768_Code__Numeral_Osize__nat__def,axiom,
% 0.33/0.67 code_size_nat = code_nat_of_natural ).
% 0.33/0.67
% 0.33/0.67 % Code_Numeral.size_nat_def
% 0.33/0.67 thf(fact_7769_Code__Numeral_OSuc__def,axiom,
% 0.33/0.67 ( code_Suc
% 0.33/0.67 = ( map_fu1239815594074539274atural @ code_nat_of_natural @ code_natural_of_nat @ suc ) ) ).
% 0.33/0.67
% 0.33/0.67 % Code_Numeral.Suc_def
% 0.33/0.67 thf(fact_7770_natural_Oinject,axiom,
% 0.33/0.67 ! [Natural: code_natural,Natural2: code_natural] :
% 0.33/0.67 ( ( ( code_Suc @ Natural )
% 0.33/0.67 = ( code_Suc @ Natural2 ) )
% 0.33/0.67 = ( Natural = Natural2 ) ) ).
% 0.33/0.67
% 0.33/0.67 % natural.inject
% 0.33/0.67 thf(fact_7771_Suc_Orep__eq,axiom,
% 0.33/0.67 ! [X: code_natural] :
% 0.33/0.67 ( ( code_nat_of_natural @ ( code_Suc @ X ) )
% 0.33/0.67 = ( suc @ ( code_nat_of_natural @ X ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % Suc.rep_eq
% 0.33/0.67 thf(fact_7772_natural_Oexhaust,axiom,
% 0.33/0.67 ! [Y: code_natural] :
% 0.33/0.67 ( ( Y != zero_z2226904508553997617atural )
% 0.33/0.67 => ~ ! [Natural3: code_natural] :
% 0.33/0.67 ( Y
% 0.33/0.67 != ( code_Suc @ Natural3 ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % natural.exhaust
% 0.33/0.67 thf(fact_7773_natural_Odistinct_I1_J,axiom,
% 0.33/0.67 ! [Natural2: code_natural] :
% 0.33/0.67 ( zero_z2226904508553997617atural
% 0.33/0.67 != ( code_Suc @ Natural2 ) ) ).
% 0.33/0.67
% 0.33/0.67 % natural.distinct(1)
% 0.33/0.67 thf(fact_7774_natural_Odistinct_I2_J,axiom,
% 0.33/0.67 ! [Natural2: code_natural] :
% 0.33/0.67 ( ( code_Suc @ Natural2 )
% 0.33/0.67 != zero_z2226904508553997617atural ) ).
% 0.33/0.67
% 0.33/0.67 % natural.distinct(2)
% 0.33/0.67 thf(fact_7775_Suc_Oabs__eq,axiom,
% 0.33/0.67 ! [X: nat] :
% 0.33/0.67 ( ( code_Suc @ ( code_natural_of_nat @ X ) )
% 0.33/0.67 = ( code_natural_of_nat @ ( suc @ X ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % Suc.abs_eq
% 0.33/0.67 thf(fact_7776_Suc__natural__minus__one,axiom,
% 0.33/0.67 ! [N2: code_natural] :
% 0.33/0.67 ( ( minus_7197305767214868737atural @ ( code_Suc @ N2 ) @ one_one_Code_natural )
% 0.33/0.67 = N2 ) ).
% 0.33/0.67
% 0.33/0.67 % Suc_natural_minus_one
% 0.33/0.67 thf(fact_7777_random__aux__set_Ocases,axiom,
% 0.33/0.67 ! [X: produc7822875418678951345atural] :
% 0.33/0.67 ( ! [J3: code_natural] :
% 0.33/0.67 ( X
% 0.33/0.67 != ( produc3574140220909816553atural @ zero_z2226904508553997617atural @ J3 ) )
% 0.33/0.67 => ~ ! [I2: code_natural,J3: code_natural] :
% 0.33/0.67 ( X
% 0.33/0.67 != ( produc3574140220909816553atural @ ( code_Suc @ I2 ) @ J3 ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % random_aux_set.cases
% 0.33/0.67 thf(fact_7778_Code__Numeral_Osub__code_I2_J,axiom,
% 0.33/0.67 ! [M2: num] :
% 0.33/0.67 ( ( code_sub @ ( bit0 @ M2 ) @ one )
% 0.33/0.67 = ( code_Pos @ ( bitM @ M2 ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % Code_Numeral.sub_code(2)
% 0.33/0.67 thf(fact_7779_Code__Numeral_OPos__def,axiom,
% 0.33/0.67 code_Pos = numera6620942414471956472nteger ).
% 0.33/0.67
% 0.33/0.67 % Code_Numeral.Pos_def
% 0.33/0.67 thf(fact_7780_Pos__fold_I2_J,axiom,
% 0.33/0.67 ! [K: num] :
% 0.33/0.67 ( ( numera6620942414471956472nteger @ ( bit0 @ K ) )
% 0.33/0.67 = ( code_Pos @ ( bit0 @ K ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % Pos_fold(2)
% 0.33/0.67 thf(fact_7781_Pos__fold_I1_J,axiom,
% 0.33/0.67 ( ( numera6620942414471956472nteger @ one )
% 0.33/0.67 = ( code_Pos @ one ) ) ).
% 0.33/0.67
% 0.33/0.67 % Pos_fold(1)
% 0.33/0.67 thf(fact_7782_Pos__fold_I3_J,axiom,
% 0.33/0.67 ! [K: num] :
% 0.33/0.67 ( ( numera6620942414471956472nteger @ ( bit1 @ K ) )
% 0.33/0.67 = ( code_Pos @ ( bit1 @ K ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % Pos_fold(3)
% 0.33/0.67 thf(fact_7783_one__integer__code,axiom,
% 0.33/0.67 ( one_one_Code_integer
% 0.33/0.67 = ( code_Pos @ one ) ) ).
% 0.33/0.67
% 0.33/0.67 % one_integer_code
% 0.33/0.67 thf(fact_7784_Code__Numeral_Odup__code_I2_J,axiom,
% 0.33/0.67 ! [N2: num] :
% 0.33/0.67 ( ( code_dup @ ( code_Pos @ N2 ) )
% 0.33/0.67 = ( code_Pos @ ( bit0 @ N2 ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % Code_Numeral.dup_code(2)
% 0.33/0.67 thf(fact_7785_less__integer__code_I4_J,axiom,
% 0.33/0.67 ! [K: num] :
% 0.33/0.67 ~ ( ord_le6747313008572928689nteger @ ( code_Pos @ K ) @ zero_z3403309356797280102nteger ) ).
% 0.33/0.67
% 0.33/0.67 % less_integer_code(4)
% 0.33/0.67 thf(fact_7786_less__integer__code_I2_J,axiom,
% 0.33/0.67 ! [L: num] : ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( code_Pos @ L ) ) ).
% 0.33/0.67
% 0.33/0.67 % less_integer_code(2)
% 0.33/0.67 thf(fact_7787_plus__integer__code_I3_J,axiom,
% 0.33/0.67 ! [M2: num,N2: num] :
% 0.33/0.67 ( ( plus_p5714425477246183910nteger @ ( code_Pos @ M2 ) @ ( code_Pos @ N2 ) )
% 0.33/0.67 = ( code_Pos @ ( plus_plus_num @ M2 @ N2 ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % plus_integer_code(3)
% 0.33/0.67 thf(fact_7788_less__eq__integer__code_I2_J,axiom,
% 0.33/0.67 ! [L: num] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( code_Pos @ L ) ) ).
% 0.33/0.67
% 0.33/0.67 % less_eq_integer_code(2)
% 0.33/0.67 thf(fact_7789_less__eq__integer__code_I4_J,axiom,
% 0.33/0.67 ! [K: num] :
% 0.33/0.67 ~ ( ord_le3102999989581377725nteger @ ( code_Pos @ K ) @ zero_z3403309356797280102nteger ) ).
% 0.33/0.67
% 0.33/0.67 % less_eq_integer_code(4)
% 0.33/0.67 thf(fact_7790_less__integer__code_I8_J,axiom,
% 0.33/0.67 ! [K: num,L: num] : ( ord_le6747313008572928689nteger @ ( code_Neg @ K ) @ ( code_Pos @ L ) ) ).
% 0.33/0.67
% 0.33/0.67 % less_integer_code(8)
% 0.33/0.67 thf(fact_7791_less__integer__code_I6_J,axiom,
% 0.33/0.67 ! [K: num,L: num] :
% 0.33/0.67 ~ ( ord_le6747313008572928689nteger @ ( code_Pos @ K ) @ ( code_Neg @ L ) ) ).
% 0.33/0.67
% 0.33/0.67 % less_integer_code(6)
% 0.33/0.67 thf(fact_7792_uminus__integer__code_I3_J,axiom,
% 0.33/0.67 ! [M2: num] :
% 0.33/0.67 ( ( uminus1351360451143612070nteger @ ( code_Neg @ M2 ) )
% 0.33/0.67 = ( code_Pos @ M2 ) ) ).
% 0.33/0.67
% 0.33/0.67 % uminus_integer_code(3)
% 0.33/0.67 thf(fact_7793_uminus__integer__code_I2_J,axiom,
% 0.33/0.67 ! [M2: num] :
% 0.33/0.67 ( ( uminus1351360451143612070nteger @ ( code_Pos @ M2 ) )
% 0.33/0.67 = ( code_Neg @ M2 ) ) ).
% 0.33/0.67
% 0.33/0.67 % uminus_integer_code(2)
% 0.33/0.67 thf(fact_7794_Code__Numeral_ONeg__def,axiom,
% 0.33/0.67 ( code_Neg
% 0.33/0.67 = ( ^ [N4: num] : ( uminus1351360451143612070nteger @ ( code_Pos @ N4 ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % Code_Numeral.Neg_def
% 0.33/0.67 thf(fact_7795_less__eq__integer__code_I8_J,axiom,
% 0.33/0.67 ! [K: num,L: num] : ( ord_le3102999989581377725nteger @ ( code_Neg @ K ) @ ( code_Pos @ L ) ) ).
% 0.33/0.67
% 0.33/0.67 % less_eq_integer_code(8)
% 0.33/0.67 thf(fact_7796_less__eq__integer__code_I6_J,axiom,
% 0.33/0.67 ! [K: num,L: num] :
% 0.33/0.67 ~ ( ord_le3102999989581377725nteger @ ( code_Pos @ K ) @ ( code_Neg @ L ) ) ).
% 0.33/0.67
% 0.33/0.67 % less_eq_integer_code(6)
% 0.33/0.67 thf(fact_7797_times__integer__code_I3_J,axiom,
% 0.33/0.67 ! [M2: num,N2: num] :
% 0.33/0.67 ( ( times_3573771949741848930nteger @ ( code_Pos @ M2 ) @ ( code_Pos @ N2 ) )
% 0.33/0.67 = ( code_Pos @ ( times_times_num @ M2 @ N2 ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % times_integer_code(3)
% 0.33/0.67 thf(fact_7798_less__integer__code_I5_J,axiom,
% 0.33/0.67 ! [K: num,L: num] :
% 0.33/0.67 ( ( ord_le6747313008572928689nteger @ ( code_Pos @ K ) @ ( code_Pos @ L ) )
% 0.33/0.67 = ( ord_less_num @ K @ L ) ) ).
% 0.33/0.67
% 0.33/0.67 % less_integer_code(5)
% 0.33/0.67 thf(fact_7799_less__eq__integer__code_I5_J,axiom,
% 0.33/0.67 ! [K: num,L: num] :
% 0.33/0.67 ( ( ord_le3102999989581377725nteger @ ( code_Pos @ K ) @ ( code_Pos @ L ) )
% 0.33/0.67 = ( ord_less_eq_num @ K @ L ) ) ).
% 0.33/0.67
% 0.33/0.67 % less_eq_integer_code(5)
% 0.33/0.67 thf(fact_7800_minus__integer__code_I3_J,axiom,
% 0.33/0.67 ! [M2: num,N2: num] :
% 0.33/0.67 ( ( minus_8373710615458151222nteger @ ( code_Pos @ M2 ) @ ( code_Pos @ N2 ) )
% 0.33/0.67 = ( code_sub @ M2 @ N2 ) ) ).
% 0.33/0.67
% 0.33/0.67 % minus_integer_code(3)
% 0.33/0.67 thf(fact_7801_divmod__abs__code_I1_J,axiom,
% 0.33/0.67 ! [K: num,L: num] :
% 0.33/0.67 ( ( code_divmod_abs @ ( code_Pos @ K ) @ ( code_Pos @ L ) )
% 0.33/0.67 = ( unique3479559517661332726nteger @ K @ L ) ) ).
% 0.33/0.67
% 0.33/0.67 % divmod_abs_code(1)
% 0.33/0.67 thf(fact_7802_minus__integer__code_I4_J,axiom,
% 0.33/0.67 ! [M2: num,N2: num] :
% 0.33/0.67 ( ( minus_8373710615458151222nteger @ ( code_Pos @ M2 ) @ ( code_Neg @ N2 ) )
% 0.33/0.67 = ( code_Pos @ ( plus_plus_num @ M2 @ N2 ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % minus_integer_code(4)
% 0.33/0.67 thf(fact_7803_minus__integer__code_I5_J,axiom,
% 0.33/0.67 ! [M2: num,N2: num] :
% 0.33/0.67 ( ( minus_8373710615458151222nteger @ ( code_Neg @ M2 ) @ ( code_Pos @ N2 ) )
% 0.33/0.67 = ( code_Neg @ ( plus_plus_num @ M2 @ N2 ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % minus_integer_code(5)
% 0.33/0.67 thf(fact_7804_times__integer__code_I4_J,axiom,
% 0.33/0.67 ! [M2: num,N2: num] :
% 0.33/0.67 ( ( times_3573771949741848930nteger @ ( code_Pos @ M2 ) @ ( code_Neg @ N2 ) )
% 0.33/0.67 = ( code_Neg @ ( times_times_num @ M2 @ N2 ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % times_integer_code(4)
% 0.33/0.67 thf(fact_7805_times__integer__code_I5_J,axiom,
% 0.33/0.67 ! [M2: num,N2: num] :
% 0.33/0.67 ( ( times_3573771949741848930nteger @ ( code_Neg @ M2 ) @ ( code_Pos @ N2 ) )
% 0.33/0.67 = ( code_Neg @ ( times_times_num @ M2 @ N2 ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % times_integer_code(5)
% 0.33/0.67 thf(fact_7806_times__integer__code_I6_J,axiom,
% 0.33/0.67 ! [M2: num,N2: num] :
% 0.33/0.67 ( ( times_3573771949741848930nteger @ ( code_Neg @ M2 ) @ ( code_Neg @ N2 ) )
% 0.33/0.67 = ( code_Pos @ ( times_times_num @ M2 @ N2 ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % times_integer_code(6)
% 0.33/0.67 thf(fact_7807_plus__integer__code_I4_J,axiom,
% 0.33/0.67 ! [M2: num,N2: num] :
% 0.33/0.67 ( ( plus_p5714425477246183910nteger @ ( code_Pos @ M2 ) @ ( code_Neg @ N2 ) )
% 0.33/0.67 = ( code_sub @ M2 @ N2 ) ) ).
% 0.33/0.67
% 0.33/0.67 % plus_integer_code(4)
% 0.33/0.67 thf(fact_7808_plus__integer__code_I5_J,axiom,
% 0.33/0.67 ! [M2: num,N2: num] :
% 0.33/0.67 ( ( plus_p5714425477246183910nteger @ ( code_Neg @ M2 ) @ ( code_Pos @ N2 ) )
% 0.33/0.67 = ( code_sub @ N2 @ M2 ) ) ).
% 0.33/0.67
% 0.33/0.67 % plus_integer_code(5)
% 0.33/0.67 thf(fact_7809_divmod__abs__code_I3_J,axiom,
% 0.33/0.67 ! [K: num,L: num] :
% 0.33/0.67 ( ( code_divmod_abs @ ( code_Neg @ K ) @ ( code_Pos @ L ) )
% 0.33/0.67 = ( unique3479559517661332726nteger @ K @ L ) ) ).
% 0.33/0.67
% 0.33/0.67 % divmod_abs_code(3)
% 0.33/0.67 thf(fact_7810_divmod__abs__code_I4_J,axiom,
% 0.33/0.67 ! [K: num,L: num] :
% 0.33/0.67 ( ( code_divmod_abs @ ( code_Pos @ K ) @ ( code_Neg @ L ) )
% 0.33/0.67 = ( unique3479559517661332726nteger @ K @ L ) ) ).
% 0.33/0.67
% 0.33/0.67 % divmod_abs_code(4)
% 0.33/0.67 thf(fact_7811_Code__Numeral_Osub__code_I3_J,axiom,
% 0.33/0.67 ! [M2: num] :
% 0.33/0.67 ( ( code_sub @ ( bit1 @ M2 ) @ one )
% 0.33/0.67 = ( code_Pos @ ( bit0 @ M2 ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % Code_Numeral.sub_code(3)
% 0.33/0.67 thf(fact_7812_normalize__stable,axiom,
% 0.33/0.67 ! [Q3: int,P4: int] :
% 0.33/0.67 ( ( ord_less_int @ zero_zero_int @ Q3 )
% 0.33/0.67 => ( ( algebr932160517623751201me_int @ P4 @ Q3 )
% 0.33/0.67 => ( ( normalize @ ( product_Pair_int_int @ P4 @ Q3 ) )
% 0.33/0.67 = ( product_Pair_int_int @ P4 @ Q3 ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % normalize_stable
% 0.33/0.67 thf(fact_7813_quotient__of__coprime,axiom,
% 0.33/0.67 ! [R2: rat,P4: int,Q3: int] :
% 0.33/0.67 ( ( ( quotient_of @ R2 )
% 0.33/0.67 = ( product_Pair_int_int @ P4 @ Q3 ) )
% 0.33/0.67 => ( algebr932160517623751201me_int @ P4 @ Q3 ) ) ).
% 0.33/0.67
% 0.33/0.67 % quotient_of_coprime
% 0.33/0.67 thf(fact_7814_normalize__coprime,axiom,
% 0.33/0.67 ! [R2: product_prod_int_int,P4: int,Q3: int] :
% 0.33/0.67 ( ( ( normalize @ R2 )
% 0.33/0.67 = ( product_Pair_int_int @ P4 @ Q3 ) )
% 0.33/0.67 => ( algebr932160517623751201me_int @ P4 @ Q3 ) ) ).
% 0.33/0.67
% 0.33/0.67 % normalize_coprime
% 0.33/0.67 thf(fact_7815_coprime__common__divisor__nat,axiom,
% 0.33/0.67 ! [A: nat,B: nat,X: nat] :
% 0.33/0.67 ( ( algebr934650988132801477me_nat @ A @ B )
% 0.33/0.67 => ( ( dvd_dvd_nat @ X @ A )
% 0.33/0.67 => ( ( dvd_dvd_nat @ X @ B )
% 0.33/0.67 => ( X = one_one_nat ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % coprime_common_divisor_nat
% 0.33/0.67 thf(fact_7816_coprime__diff__one__right__nat,axiom,
% 0.33/0.67 ! [N2: nat] :
% 0.33/0.67 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.33/0.67 => ( algebr934650988132801477me_nat @ N2 @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % coprime_diff_one_right_nat
% 0.33/0.67 thf(fact_7817_coprime__diff__one__left__nat,axiom,
% 0.33/0.67 ! [N2: nat] :
% 0.33/0.67 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.33/0.67 => ( algebr934650988132801477me_nat @ ( minus_minus_nat @ N2 @ one_one_nat ) @ N2 ) ) ).
% 0.33/0.67
% 0.33/0.67 % coprime_diff_one_left_nat
% 0.33/0.67 thf(fact_7818_integer__of__char__code,axiom,
% 0.33/0.67 ! [B0: $o,B1: $o,B22: $o,B32: $o,B42: $o,B52: $o,B62: $o,B72: $o] :
% 0.33/0.67 ( ( integer_of_char @ ( char2 @ B0 @ B1 @ B22 @ B32 @ B42 @ B52 @ B62 @ B72 ) )
% 0.33/0.67 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ B72 ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B62 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B52 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B42 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B32 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B22 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B1 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B0 ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % integer_of_char_code
% 0.33/0.67 thf(fact_7819_Suc__funpow,axiom,
% 0.33/0.67 ! [N2: nat] :
% 0.33/0.67 ( ( compow_nat_nat @ N2 @ suc )
% 0.33/0.67 = ( plus_plus_nat @ N2 ) ) ).
% 0.33/0.67
% 0.33/0.67 % Suc_funpow
% 0.33/0.67 thf(fact_7820_or__not__num__neg_Opelims,axiom,
% 0.33/0.67 ! [X: num,Xa: num,Y: num] :
% 0.33/0.67 ( ( ( bit_or_not_num_neg @ X @ Xa )
% 0.33/0.67 = Y )
% 0.33/0.67 => ( ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ X @ Xa ) )
% 0.33/0.67 => ( ( ( X = one )
% 0.33/0.67 => ( ( Xa = one )
% 0.33/0.67 => ( ( Y = one )
% 0.33/0.67 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 0.33/0.67 => ( ( ( X = one )
% 0.33/0.67 => ! [M5: num] :
% 0.33/0.67 ( ( Xa
% 0.33/0.67 = ( bit0 @ M5 ) )
% 0.33/0.67 => ( ( Y
% 0.33/0.67 = ( bit1 @ M5 ) )
% 0.33/0.67 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ one @ ( bit0 @ M5 ) ) ) ) ) )
% 0.33/0.67 => ( ( ( X = one )
% 0.33/0.67 => ! [M5: num] :
% 0.33/0.67 ( ( Xa
% 0.33/0.67 = ( bit1 @ M5 ) )
% 0.33/0.67 => ( ( Y
% 0.33/0.67 = ( bit1 @ M5 ) )
% 0.33/0.67 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ one @ ( bit1 @ M5 ) ) ) ) ) )
% 0.33/0.67 => ( ! [N: num] :
% 0.33/0.67 ( ( X
% 0.33/0.67 = ( bit0 @ N ) )
% 0.33/0.67 => ( ( Xa = one )
% 0.33/0.67 => ( ( Y
% 0.33/0.67 = ( bit0 @ one ) )
% 0.33/0.67 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit0 @ N ) @ one ) ) ) ) )
% 0.33/0.67 => ( ! [N: num] :
% 0.33/0.67 ( ( X
% 0.33/0.67 = ( bit0 @ N ) )
% 0.33/0.67 => ! [M5: num] :
% 0.33/0.67 ( ( Xa
% 0.33/0.67 = ( bit0 @ M5 ) )
% 0.33/0.67 => ( ( Y
% 0.33/0.67 = ( bitM @ ( bit_or_not_num_neg @ N @ M5 ) ) )
% 0.33/0.67 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit0 @ N ) @ ( bit0 @ M5 ) ) ) ) ) )
% 0.33/0.67 => ( ! [N: num] :
% 0.33/0.67 ( ( X
% 0.33/0.67 = ( bit0 @ N ) )
% 0.33/0.67 => ! [M5: num] :
% 0.33/0.67 ( ( Xa
% 0.33/0.67 = ( bit1 @ M5 ) )
% 0.33/0.67 => ( ( Y
% 0.33/0.67 = ( bit0 @ ( bit_or_not_num_neg @ N @ M5 ) ) )
% 0.33/0.67 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit0 @ N ) @ ( bit1 @ M5 ) ) ) ) ) )
% 0.33/0.67 => ( ! [N: num] :
% 0.33/0.67 ( ( X
% 0.33/0.67 = ( bit1 @ N ) )
% 0.33/0.67 => ( ( Xa = one )
% 0.33/0.67 => ( ( Y = one )
% 0.33/0.67 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit1 @ N ) @ one ) ) ) ) )
% 0.33/0.67 => ( ! [N: num] :
% 0.33/0.67 ( ( X
% 0.33/0.67 = ( bit1 @ N ) )
% 0.33/0.67 => ! [M5: num] :
% 0.33/0.67 ( ( Xa
% 0.33/0.67 = ( bit0 @ M5 ) )
% 0.33/0.67 => ( ( Y
% 0.33/0.67 = ( bitM @ ( bit_or_not_num_neg @ N @ M5 ) ) )
% 0.33/0.67 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit1 @ N ) @ ( bit0 @ M5 ) ) ) ) ) )
% 0.33/0.67 => ~ ! [N: num] :
% 0.33/0.67 ( ( X
% 0.33/0.67 = ( bit1 @ N ) )
% 0.33/0.67 => ! [M5: num] :
% 0.33/0.67 ( ( Xa
% 0.33/0.67 = ( bit1 @ M5 ) )
% 0.33/0.67 => ( ( Y
% 0.33/0.67 = ( bitM @ ( bit_or_not_num_neg @ N @ M5 ) ) )
% 0.33/0.67 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit1 @ N ) @ ( bit1 @ M5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % or_not_num_neg.pelims
% 0.33/0.67 thf(fact_7821_cr__natural__def,axiom,
% 0.33/0.67 ( code_cr_natural
% 0.33/0.67 = ( ^ [X3: nat,Y3: code_natural] :
% 0.33/0.67 ( X3
% 0.33/0.67 = ( code_nat_of_natural @ Y3 ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % cr_natural_def
% 0.33/0.67 thf(fact_7822_cr__integer__def,axiom,
% 0.33/0.67 ( code_cr_integer
% 0.33/0.67 = ( ^ [X3: int,Y3: code_integer] :
% 0.33/0.67 ( X3
% 0.33/0.67 = ( code_int_of_integer @ Y3 ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % cr_integer_def
% 0.33/0.67 thf(fact_7823_integer_Opcr__cr__eq,axiom,
% 0.33/0.67 code_pcr_integer = code_cr_integer ).
% 0.33/0.67
% 0.33/0.67 % integer.pcr_cr_eq
% 0.33/0.67 thf(fact_7824_unit__factor__simps_I2_J,axiom,
% 0.33/0.67 ! [N2: nat] :
% 0.33/0.67 ( ( unit_f2748546683901255202or_nat @ ( suc @ N2 ) )
% 0.33/0.67 = one_one_nat ) ).
% 0.33/0.67
% 0.33/0.67 % unit_factor_simps(2)
% 0.33/0.67 thf(fact_7825_unit__factor__nat__def,axiom,
% 0.33/0.67 ( unit_f2748546683901255202or_nat
% 0.33/0.67 = ( ^ [N4: nat] : ( if_nat @ ( N4 = zero_zero_nat ) @ zero_zero_nat @ one_one_nat ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % unit_factor_nat_def
% 0.33/0.67 thf(fact_7826_Nat_Otransfer,axiom,
% 0.33/0.67 bNF_re1831474436612530402atural @ code_pcr_integer @ code_pcr_natural @ nat2 @ code_Nat ).
% 0.33/0.67
% 0.33/0.67 % Nat.transfer
% 0.33/0.67 thf(fact_7827_pcr__natural__def,axiom,
% 0.33/0.67 ( code_pcr_natural
% 0.33/0.67 = ( relcom1729257228895983867atural
% 0.33/0.67 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.67 @ code_cr_natural ) ) ).
% 0.33/0.67
% 0.33/0.67 % pcr_natural_def
% 0.33/0.67 thf(fact_7828_natural_Orep__transfer,axiom,
% 0.33/0.67 ( bNF_re7333046803109187065at_nat @ code_pcr_natural
% 0.33/0.67 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.67 @ ^ [X3: nat] : X3
% 0.33/0.67 @ code_nat_of_natural ) ).
% 0.33/0.67
% 0.33/0.67 % natural.rep_transfer
% 0.33/0.67 thf(fact_7829_natural_Oid__abs__transfer,axiom,
% 0.33/0.67 ( bNF_re2605341659958429177atural
% 0.33/0.67 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.67 @ code_pcr_natural
% 0.33/0.67 @ ^ [X3: nat] : X3
% 0.33/0.67 @ code_natural_of_nat ) ).
% 0.33/0.67
% 0.33/0.67 % natural.id_abs_transfer
% 0.33/0.67 thf(fact_7830_natural_Opcr__cr__eq,axiom,
% 0.33/0.67 code_pcr_natural = code_cr_natural ).
% 0.33/0.67
% 0.33/0.67 % natural.pcr_cr_eq
% 0.33/0.67 thf(fact_7831_zero__natural_Otransfer,axiom,
% 0.33/0.67 code_pcr_natural @ zero_zero_nat @ zero_z2226904508553997617atural ).
% 0.33/0.67
% 0.33/0.67 % zero_natural.transfer
% 0.33/0.67 thf(fact_7832_one__natural_Otransfer,axiom,
% 0.33/0.67 code_pcr_natural @ one_one_nat @ one_one_Code_natural ).
% 0.33/0.67
% 0.33/0.67 % one_natural.transfer
% 0.33/0.67 thf(fact_7833_less__natural_Otransfer,axiom,
% 0.33/0.67 ( bNF_re1639080489988575423ural_o @ code_pcr_natural
% 0.33/0.67 @ ( bNF_re2785088596696291543al_o_o @ code_pcr_natural
% 0.33/0.67 @ ^ [Y4: $o,Z2: $o] : ( Y4 = Z2 ) )
% 0.33/0.67 @ ord_less_nat
% 0.33/0.67 @ ord_le5570908160329646204atural ) ).
% 0.33/0.67
% 0.33/0.67 % less_natural.transfer
% 0.33/0.67 thf(fact_7834_plus__natural_Otransfer,axiom,
% 0.33/0.67 bNF_re88643428490162567atural @ code_pcr_natural @ ( bNF_re3704215830270325841atural @ code_pcr_natural @ code_pcr_natural ) @ plus_plus_nat @ plus_p4538020629002901425atural ).
% 0.33/0.67
% 0.33/0.67 % plus_natural.transfer
% 0.33/0.67 thf(fact_7835_Suc_Otransfer,axiom,
% 0.33/0.67 bNF_re3704215830270325841atural @ code_pcr_natural @ code_pcr_natural @ suc @ code_Suc ).
% 0.33/0.67
% 0.33/0.67 % Suc.transfer
% 0.33/0.67 thf(fact_7836_minus__natural_Otransfer,axiom,
% 0.33/0.67 bNF_re88643428490162567atural @ code_pcr_natural @ ( bNF_re3704215830270325841atural @ code_pcr_natural @ code_pcr_natural ) @ minus_minus_nat @ minus_7197305767214868737atural ).
% 0.33/0.67
% 0.33/0.67 % minus_natural.transfer
% 0.33/0.67 thf(fact_7837_pcr__integer__def,axiom,
% 0.33/0.67 ( code_pcr_integer
% 0.33/0.67 = ( relcom967497705283160040nteger
% 0.33/0.67 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.67 @ code_cr_integer ) ) ).
% 0.33/0.67
% 0.33/0.67 % pcr_integer_def
% 0.33/0.67 thf(fact_7838_less__eq__natural_Otransfer,axiom,
% 0.33/0.67 ( bNF_re1639080489988575423ural_o @ code_pcr_natural
% 0.33/0.67 @ ( bNF_re2785088596696291543al_o_o @ code_pcr_natural
% 0.33/0.67 @ ^ [Y4: $o,Z2: $o] : ( Y4 = Z2 ) )
% 0.33/0.67 @ ord_less_eq_nat
% 0.33/0.67 @ ord_le1926595141338095240atural ) ).
% 0.33/0.67
% 0.33/0.67 % less_eq_natural.transfer
% 0.33/0.67 thf(fact_7839_times__natural_Otransfer,axiom,
% 0.33/0.67 bNF_re88643428490162567atural @ code_pcr_natural @ ( bNF_re3704215830270325841atural @ code_pcr_natural @ code_pcr_natural ) @ times_times_nat @ times_2397367101498566445atural ).
% 0.33/0.67
% 0.33/0.67 % times_natural.transfer
% 0.33/0.67 thf(fact_7840_divide__natural_Otransfer,axiom,
% 0.33/0.67 bNF_re88643428490162567atural @ code_pcr_natural @ ( bNF_re3704215830270325841atural @ code_pcr_natural @ code_pcr_natural ) @ divide_divide_nat @ divide5121882707175180666atural ).
% 0.33/0.67
% 0.33/0.67 % divide_natural.transfer
% 0.33/0.67 thf(fact_7841_modulo__natural_Otransfer,axiom,
% 0.33/0.67 bNF_re88643428490162567atural @ code_pcr_natural @ ( bNF_re3704215830270325841atural @ code_pcr_natural @ code_pcr_natural ) @ modulo_modulo_nat @ modulo8411746178871703098atural ).
% 0.33/0.67
% 0.33/0.67 % modulo_natural.transfer
% 0.33/0.67 thf(fact_7842_take__bit__natural_Otransfer,axiom,
% 0.33/0.67 ( bNF_re3692170009638431535atural
% 0.33/0.67 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.67 @ ( bNF_re3704215830270325841atural @ code_pcr_natural @ code_pcr_natural )
% 0.33/0.67 @ bit_se2925701944663578781it_nat
% 0.33/0.67 @ bit_se569199155075624693atural ) ).
% 0.33/0.67
% 0.33/0.67 % take_bit_natural.transfer
% 0.33/0.67 thf(fact_7843_xor__natural_Otransfer,axiom,
% 0.33/0.67 bNF_re88643428490162567atural @ code_pcr_natural @ ( bNF_re3704215830270325841atural @ code_pcr_natural @ code_pcr_natural ) @ bit_se6528837805403552850or_nat @ bit_se2046307713759805098atural ).
% 0.33/0.67
% 0.33/0.67 % xor_natural.transfer
% 0.33/0.67 thf(fact_7844_or__natural_Otransfer,axiom,
% 0.33/0.67 bNF_re88643428490162567atural @ code_pcr_natural @ ( bNF_re3704215830270325841atural @ code_pcr_natural @ code_pcr_natural ) @ bit_se1412395901928357646or_nat @ bit_se9127793120404214118atural ).
% 0.33/0.67
% 0.33/0.67 % or_natural.transfer
% 0.33/0.67 thf(fact_7845_and__natural_Otransfer,axiom,
% 0.33/0.67 bNF_re88643428490162567atural @ code_pcr_natural @ ( bNF_re3704215830270325841atural @ code_pcr_natural @ code_pcr_natural ) @ bit_se727722235901077358nd_nat @ bit_se2773287842338716102atural ).
% 0.33/0.67
% 0.33/0.67 % and_natural.transfer
% 0.33/0.67 thf(fact_7846_bit__natural_Otransfer,axiom,
% 0.33/0.67 ( bNF_re2895713572246619415_nat_o @ code_pcr_natural
% 0.33/0.67 @ ^ [Y4: nat > $o,Z2: nat > $o] : ( Y4 = Z2 )
% 0.33/0.67 @ bit_se1148574629649215175it_nat
% 0.33/0.67 @ bit_se8040316288895769887atural ) ).
% 0.33/0.67
% 0.33/0.67 % bit_natural.transfer
% 0.33/0.67 thf(fact_7847_push__bit__natural_Otransfer,axiom,
% 0.33/0.67 ( bNF_re3692170009638431535atural
% 0.33/0.67 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.67 @ ( bNF_re3704215830270325841atural @ code_pcr_natural @ code_pcr_natural )
% 0.33/0.67 @ bit_se547839408752420682it_nat
% 0.33/0.67 @ bit_se6611745700429515170atural ) ).
% 0.33/0.67
% 0.33/0.67 % push_bit_natural.transfer
% 0.33/0.67 thf(fact_7848_mask__natural_Otransfer,axiom,
% 0.33/0.67 ( bNF_re2605341659958429177atural
% 0.33/0.67 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.67 @ code_pcr_natural
% 0.33/0.67 @ bit_se2002935070580805687sk_nat
% 0.33/0.67 @ bit_se943457434206027407atural ) ).
% 0.33/0.67
% 0.33/0.67 % mask_natural.transfer
% 0.33/0.67 thf(fact_7849_drop__bit__natural_Otransfer,axiom,
% 0.33/0.67 ( bNF_re3692170009638431535atural
% 0.33/0.67 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.67 @ ( bNF_re3704215830270325841atural @ code_pcr_natural @ code_pcr_natural )
% 0.33/0.67 @ bit_se8570568707652914677it_nat
% 0.33/0.67 @ bit_se2751692689150723149atural ) ).
% 0.33/0.67
% 0.33/0.67 % drop_bit_natural.transfer
% 0.33/0.67 thf(fact_7850_division__segment__natural_Otransfer,axiom,
% 0.33/0.67 bNF_re3704215830270325841atural @ code_pcr_natural @ code_pcr_natural @ euclid3398187327856392827nt_nat @ euclid5112970336976722131atural ).
% 0.33/0.67
% 0.33/0.67 % division_segment_natural.transfer
% 0.33/0.67 thf(fact_7851_flip__bit__natural_Otransfer,axiom,
% 0.33/0.67 ( bNF_re3692170009638431535atural
% 0.33/0.67 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.67 @ ( bNF_re3704215830270325841atural @ code_pcr_natural @ code_pcr_natural )
% 0.33/0.67 @ bit_se2161824704523386999it_nat
% 0.33/0.67 @ bit_se168947363167071951atural ) ).
% 0.33/0.67
% 0.33/0.67 % flip_bit_natural.transfer
% 0.33/0.67 thf(fact_7852_set__bit__natural_Otransfer,axiom,
% 0.33/0.67 ( bNF_re3692170009638431535atural
% 0.33/0.67 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.67 @ ( bNF_re3704215830270325841atural @ code_pcr_natural @ code_pcr_natural )
% 0.33/0.67 @ bit_se7882103937844011126it_nat
% 0.33/0.67 @ bit_se1617098188084679374atural ) ).
% 0.33/0.67
% 0.33/0.67 % set_bit_natural.transfer
% 0.33/0.67 thf(fact_7853_unset__bit__natural_Otransfer,axiom,
% 0.33/0.67 ( bNF_re3692170009638431535atural
% 0.33/0.67 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.67 @ ( bNF_re3704215830270325841atural @ code_pcr_natural @ code_pcr_natural )
% 0.33/0.67 @ bit_se4205575877204974255it_nat
% 0.33/0.67 @ bit_se7083795435491715335atural ) ).
% 0.33/0.67
% 0.33/0.67 % unset_bit_natural.transfer
% 0.33/0.67 thf(fact_7854_euclidean__size__natural_Otransfer,axiom,
% 0.33/0.67 ( bNF_re7333046803109187065at_nat @ code_pcr_natural
% 0.33/0.67 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.67 @ euclid4777050414544973029ze_nat
% 0.33/0.67 @ euclid5200926497590043453atural ) ).
% 0.33/0.67
% 0.33/0.67 % euclidean_size_natural.transfer
% 0.33/0.67 thf(fact_7855_integer__of__natural_Otransfer,axiom,
% 0.33/0.67 bNF_re5252274238750452962nteger @ code_pcr_natural @ code_pcr_integer @ semiri1314217659103216013at_int @ code_i5400310926305786745atural ).
% 0.33/0.67
% 0.33/0.67 % integer_of_natural.transfer
% 0.33/0.67 thf(fact_7856_natural__of__integer_Otransfer,axiom,
% 0.33/0.67 bNF_re1831474436612530402atural @ code_pcr_integer @ code_pcr_natural @ nat2 @ code_n4118661773612635043nteger ).
% 0.33/0.67
% 0.33/0.67 % natural_of_integer.transfer
% 0.33/0.67 thf(fact_7857_plus__num__def,axiom,
% 0.33/0.67 ( plus_plus_num
% 0.33/0.67 = ( ^ [M: num,N4: num] : ( num_of_nat @ ( plus_plus_nat @ ( nat_of_num @ M ) @ ( nat_of_num @ N4 ) ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % plus_num_def
% 0.33/0.67 thf(fact_7858_Lcm__nat__empty,axiom,
% 0.33/0.67 ( ( gcd_Lcm_nat @ bot_bot_set_nat )
% 0.33/0.67 = one_one_nat ) ).
% 0.33/0.67
% 0.33/0.67 % Lcm_nat_empty
% 0.33/0.67 thf(fact_7859_nat__of__num_Osimps_I2_J,axiom,
% 0.33/0.67 ! [X: num] :
% 0.33/0.67 ( ( nat_of_num @ ( bit0 @ X ) )
% 0.33/0.67 = ( plus_plus_nat @ ( nat_of_num @ X ) @ ( nat_of_num @ X ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % nat_of_num.simps(2)
% 0.33/0.67 thf(fact_7860_nat__of__num__code_I1_J,axiom,
% 0.33/0.67 ( ( nat_of_num @ one )
% 0.33/0.67 = one_one_nat ) ).
% 0.33/0.67
% 0.33/0.67 % nat_of_num_code(1)
% 0.33/0.67 thf(fact_7861_nat__of__num__add,axiom,
% 0.33/0.67 ! [X: num,Y: num] :
% 0.33/0.67 ( ( nat_of_num @ ( plus_plus_num @ X @ Y ) )
% 0.33/0.67 = ( plus_plus_nat @ ( nat_of_num @ X ) @ ( nat_of_num @ Y ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % nat_of_num_add
% 0.33/0.67 thf(fact_7862_nat__of__num__code_I2_J,axiom,
% 0.33/0.67 ! [N2: num] :
% 0.33/0.67 ( ( nat_of_num @ ( bit0 @ N2 ) )
% 0.33/0.67 = ( plus_plus_nat @ ( nat_of_num @ N2 ) @ ( nat_of_num @ N2 ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % nat_of_num_code(2)
% 0.33/0.67 thf(fact_7863_nat__of__num_Osimps_I3_J,axiom,
% 0.33/0.67 ! [X: num] :
% 0.33/0.67 ( ( nat_of_num @ ( bit1 @ X ) )
% 0.33/0.67 = ( suc @ ( plus_plus_nat @ ( nat_of_num @ X ) @ ( nat_of_num @ X ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % nat_of_num.simps(3)
% 0.33/0.67 thf(fact_7864_nat__of__num__code_I3_J,axiom,
% 0.33/0.67 ! [N2: num] :
% 0.33/0.67 ( ( nat_of_num @ ( bit1 @ N2 ) )
% 0.33/0.67 = ( suc @ ( plus_plus_nat @ ( nat_of_num @ N2 ) @ ( nat_of_num @ N2 ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % nat_of_num_code(3)
% 0.33/0.67 thf(fact_7865_Gcd__nat__eq__one,axiom,
% 0.33/0.67 ! [N6: set_nat] :
% 0.33/0.67 ( ( member_nat @ one_one_nat @ N6 )
% 0.33/0.67 => ( ( gcd_Gcd_nat @ N6 )
% 0.33/0.67 = one_one_nat ) ) ).
% 0.33/0.67
% 0.33/0.67 % Gcd_nat_eq_one
% 0.33/0.67 thf(fact_7866_card__of__Field__natLeq,axiom,
% 0.33/0.67 member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( bNF_Ca3793111618940312692of_nat @ ( field_nat @ bNF_Ca8665028551170535155natLeq ) ) @ bNF_Ca8665028551170535155natLeq ) @ bNF_We5258908940166488438at_nat ).
% 0.33/0.67
% 0.33/0.67 % card_of_Field_natLeq
% 0.33/0.67 thf(fact_7867_card__of__nat,axiom,
% 0.33/0.67 member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( bNF_Ca3793111618940312692of_nat @ top_top_set_nat ) @ bNF_Ca8665028551170535155natLeq ) @ bNF_We5258908940166488438at_nat ).
% 0.33/0.67
% 0.33/0.67 % card_of_nat
% 0.33/0.67 thf(fact_7868_ctwo__Cnotzero,axiom,
% 0.33/0.67 ( ~ ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ bNF_Cardinal_ctwo @ bNF_Cardinal_czero_o ) @ bNF_We2654380646378065620so_o_o )
% 0.33/0.67 & ( bNF_Ca8331644756375544342r_on_o @ ( field_o @ bNF_Cardinal_ctwo ) @ bNF_Cardinal_ctwo ) ) ).
% 0.33/0.67
% 0.33/0.67 % ctwo_Cnotzero
% 0.33/0.67 thf(fact_7869_ctwo__ordLess__natLeq,axiom,
% 0.33/0.67 member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ bNF_Cardinal_ctwo @ bNF_Ca8665028551170535155natLeq ) @ bNF_We8182288985678559134_o_nat ).
% 0.33/0.67
% 0.33/0.67 % ctwo_ordLess_natLeq
% 0.33/0.67 thf(fact_7870_or__num_Opelims,axiom,
% 0.33/0.67 ! [X: num,Xa: num,Y: num] :
% 0.33/0.67 ( ( ( bit_un6697907153464112080or_num @ X @ Xa )
% 0.33/0.67 = Y )
% 0.33/0.67 => ( ( accp_P3113834385874906142um_num @ bit_un4773296044027857193um_rel @ ( product_Pair_num_num @ X @ Xa ) )
% 0.33/0.67 => ( ( ( X = one )
% 0.33/0.67 => ( ( Xa = one )
% 0.33/0.67 => ( ( Y = one )
% 0.33/0.67 => ~ ( accp_P3113834385874906142um_num @ bit_un4773296044027857193um_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 0.33/0.67 => ( ( ( X = one )
% 0.33/0.67 => ! [N: num] :
% 0.33/0.67 ( ( Xa
% 0.33/0.67 = ( bit0 @ N ) )
% 0.33/0.67 => ( ( Y
% 0.33/0.67 = ( bit1 @ N ) )
% 0.33/0.67 => ~ ( accp_P3113834385874906142um_num @ bit_un4773296044027857193um_rel @ ( product_Pair_num_num @ one @ ( bit0 @ N ) ) ) ) ) )
% 0.33/0.67 => ( ( ( X = one )
% 0.33/0.67 => ! [N: num] :
% 0.33/0.67 ( ( Xa
% 0.33/0.67 = ( bit1 @ N ) )
% 0.33/0.67 => ( ( Y
% 0.33/0.67 = ( bit1 @ N ) )
% 0.33/0.67 => ~ ( accp_P3113834385874906142um_num @ bit_un4773296044027857193um_rel @ ( product_Pair_num_num @ one @ ( bit1 @ N ) ) ) ) ) )
% 0.33/0.67 => ( ! [M5: num] :
% 0.33/0.67 ( ( X
% 0.33/0.67 = ( bit0 @ M5 ) )
% 0.33/0.67 => ( ( Xa = one )
% 0.33/0.67 => ( ( Y
% 0.33/0.67 = ( bit1 @ M5 ) )
% 0.33/0.67 => ~ ( accp_P3113834385874906142um_num @ bit_un4773296044027857193um_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ one ) ) ) ) )
% 0.33/0.67 => ( ! [M5: num] :
% 0.33/0.67 ( ( X
% 0.33/0.67 = ( bit0 @ M5 ) )
% 0.33/0.67 => ! [N: num] :
% 0.33/0.67 ( ( Xa
% 0.33/0.67 = ( bit0 @ N ) )
% 0.33/0.67 => ( ( Y
% 0.33/0.67 = ( bit0 @ ( bit_un6697907153464112080or_num @ M5 @ N ) ) )
% 0.33/0.67 => ~ ( accp_P3113834385874906142um_num @ bit_un4773296044027857193um_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ ( bit0 @ N ) ) ) ) ) )
% 0.33/0.67 => ( ! [M5: num] :
% 0.33/0.67 ( ( X
% 0.33/0.67 = ( bit0 @ M5 ) )
% 0.33/0.67 => ! [N: num] :
% 0.33/0.67 ( ( Xa
% 0.33/0.67 = ( bit1 @ N ) )
% 0.33/0.67 => ( ( Y
% 0.33/0.67 = ( bit1 @ ( bit_un6697907153464112080or_num @ M5 @ N ) ) )
% 0.33/0.67 => ~ ( accp_P3113834385874906142um_num @ bit_un4773296044027857193um_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ ( bit1 @ N ) ) ) ) ) )
% 0.33/0.67 => ( ! [M5: num] :
% 0.33/0.67 ( ( X
% 0.33/0.67 = ( bit1 @ M5 ) )
% 0.33/0.67 => ( ( Xa = one )
% 0.33/0.67 => ( ( Y
% 0.33/0.67 = ( bit1 @ M5 ) )
% 0.33/0.67 => ~ ( accp_P3113834385874906142um_num @ bit_un4773296044027857193um_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ one ) ) ) ) )
% 0.33/0.67 => ( ! [M5: num] :
% 0.33/0.67 ( ( X
% 0.33/0.67 = ( bit1 @ M5 ) )
% 0.33/0.67 => ! [N: num] :
% 0.33/0.67 ( ( Xa
% 0.33/0.67 = ( bit0 @ N ) )
% 0.33/0.67 => ( ( Y
% 0.33/0.67 = ( bit1 @ ( bit_un6697907153464112080or_num @ M5 @ N ) ) )
% 0.33/0.67 => ~ ( accp_P3113834385874906142um_num @ bit_un4773296044027857193um_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ ( bit0 @ N ) ) ) ) ) )
% 0.33/0.67 => ~ ! [M5: num] :
% 0.33/0.67 ( ( X
% 0.33/0.67 = ( bit1 @ M5 ) )
% 0.33/0.67 => ! [N: num] :
% 0.33/0.67 ( ( Xa
% 0.33/0.67 = ( bit1 @ N ) )
% 0.33/0.67 => ( ( Y
% 0.33/0.67 = ( bit1 @ ( bit_un6697907153464112080or_num @ M5 @ N ) ) )
% 0.33/0.67 => ~ ( accp_P3113834385874906142um_num @ bit_un4773296044027857193um_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ ( bit1 @ N ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % or_num.pelims
% 0.33/0.67 thf(fact_7871_Quotient__natural,axiom,
% 0.33/0.67 ( quotie743640454666494480atural
% 0.33/0.67 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 0.33/0.67 @ code_natural_of_nat
% 0.33/0.67 @ code_nat_of_natural
% 0.33/0.67 @ code_cr_natural ) ).
% 0.33/0.67
% 0.33/0.67 % Quotient_natural
% 0.33/0.67 thf(fact_7872_Quotient__integer,axiom,
% 0.33/0.67 ( quotie2291698863146621601nteger
% 0.33/0.67 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 0.33/0.67 @ code_integer_of_int
% 0.33/0.67 @ code_int_of_integer
% 0.33/0.67 @ code_cr_integer ) ).
% 0.33/0.67
% 0.33/0.67 % Quotient_integer
% 0.33/0.67 thf(fact_7873_Lcm__nat__def,axiom,
% 0.33/0.67 ( gcd_Lcm_nat
% 0.33/0.67 = ( ^ [M7: set_nat] : ( if_nat @ ( finite_finite_nat @ M7 ) @ ( lattic7826324295020591184_F_nat @ gcd_lcm_nat @ one_one_nat @ M7 ) @ zero_zero_nat ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % Lcm_nat_def
% 0.33/0.67 thf(fact_7874_Lcm__nat__set__eq__fold,axiom,
% 0.33/0.67 ! [Xs: list_nat] :
% 0.33/0.67 ( ( gcd_Lcm_nat @ ( set_nat2 @ Xs ) )
% 0.33/0.67 = ( fold_nat_nat @ gcd_lcm_nat @ Xs @ one_one_nat ) ) ).
% 0.33/0.67
% 0.33/0.67 % Lcm_nat_set_eq_fold
% 0.33/0.67 thf(fact_7875_mod__h__bot__iff_I7_J,axiom,
% 0.33/0.67 ! [P: assn,Q: assn,H3: heap_e7401611519738050253t_unit] :
% 0.33/0.67 ( ( rep_assn @ ( sup_sup_assn @ P @ Q ) @ ( produc7507926704131184380et_nat @ H3 @ bot_bot_set_nat ) )
% 0.33/0.67 = ( ( rep_assn @ P @ ( produc7507926704131184380et_nat @ H3 @ bot_bot_set_nat ) )
% 0.33/0.67 | ( rep_assn @ Q @ ( produc7507926704131184380et_nat @ H3 @ bot_bot_set_nat ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % mod_h_bot_iff(7)
% 0.33/0.67 thf(fact_7876_mod__h__bot__iff_I5_J,axiom,
% 0.33/0.67 ! [P: assn,Q: assn,H3: heap_e7401611519738050253t_unit] :
% 0.33/0.67 ( ( rep_assn @ ( times_times_assn @ P @ Q ) @ ( produc7507926704131184380et_nat @ H3 @ bot_bot_set_nat ) )
% 0.33/0.67 = ( ( rep_assn @ P @ ( produc7507926704131184380et_nat @ H3 @ bot_bot_set_nat ) )
% 0.33/0.67 & ( rep_assn @ Q @ ( produc7507926704131184380et_nat @ H3 @ bot_bot_set_nat ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % mod_h_bot_iff(5)
% 0.33/0.67 thf(fact_7877_mod__h__bot__iff_I6_J,axiom,
% 0.33/0.67 ! [P: assn,Q: assn,H3: heap_e7401611519738050253t_unit] :
% 0.33/0.67 ( ( rep_assn @ ( inf_inf_assn @ P @ Q ) @ ( produc7507926704131184380et_nat @ H3 @ bot_bot_set_nat ) )
% 0.33/0.67 = ( ( rep_assn @ P @ ( produc7507926704131184380et_nat @ H3 @ bot_bot_set_nat ) )
% 0.33/0.67 & ( rep_assn @ Q @ ( produc7507926704131184380et_nat @ H3 @ bot_bot_set_nat ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % mod_h_bot_iff(6)
% 0.33/0.67 thf(fact_7878_mod__h__bot__iff_I2_J,axiom,
% 0.33/0.67 ! [H3: heap_e7401611519738050253t_unit] : ( rep_assn @ top_top_assn @ ( produc7507926704131184380et_nat @ H3 @ bot_bot_set_nat ) ) ).
% 0.33/0.67
% 0.33/0.67 % mod_h_bot_iff(2)
% 0.33/0.67 thf(fact_7879_times__assn__raw_Ocases,axiom,
% 0.33/0.67 ! [X: produc2732055786443039994et_nat] :
% 0.33/0.67 ~ ! [P7: produc3658429121746597890et_nat > $o,Q6: produc3658429121746597890et_nat > $o,H2: heap_e7401611519738050253t_unit,As: set_nat] :
% 0.33/0.67 ( X
% 0.33/0.67 != ( produc2245416461498447860et_nat @ P7 @ ( produc5001842942810119800et_nat @ Q6 @ ( produc7507926704131184380et_nat @ H2 @ As ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % times_assn_raw.cases
% 0.33/0.67 thf(fact_7880_one__assn__raw_Ocases,axiom,
% 0.33/0.67 ! [X: produc3658429121746597890et_nat] :
% 0.33/0.67 ~ ! [H2: heap_e7401611519738050253t_unit,As: set_nat] :
% 0.33/0.67 ( X
% 0.33/0.67 != ( produc7507926704131184380et_nat @ H2 @ As ) ) ).
% 0.33/0.67
% 0.33/0.67 % one_assn_raw.cases
% 0.33/0.67 thf(fact_7881_mod__star__conv,axiom,
% 0.33/0.67 ! [A2: assn,B5: assn,H3: produc3658429121746597890et_nat] :
% 0.33/0.67 ( ( rep_assn @ ( times_times_assn @ A2 @ B5 ) @ H3 )
% 0.33/0.67 = ( ? [Hr: heap_e7401611519738050253t_unit,As1: set_nat,As2: set_nat] :
% 0.33/0.67 ( ( H3
% 0.33/0.67 = ( produc7507926704131184380et_nat @ Hr @ ( sup_sup_set_nat @ As1 @ As2 ) ) )
% 0.33/0.67 & ( ( inf_inf_set_nat @ As1 @ As2 )
% 0.33/0.67 = bot_bot_set_nat )
% 0.33/0.67 & ( rep_assn @ A2 @ ( produc7507926704131184380et_nat @ Hr @ As1 ) )
% 0.33/0.67 & ( rep_assn @ B5 @ ( produc7507926704131184380et_nat @ Hr @ As2 ) ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % mod_star_conv
% 0.33/0.67 thf(fact_7882_star__assnI,axiom,
% 0.33/0.67 ! [P: assn,H3: heap_e7401611519738050253t_unit,As3: set_nat,Q: assn,As4: set_nat] :
% 0.33/0.67 ( ( rep_assn @ P @ ( produc7507926704131184380et_nat @ H3 @ As3 ) )
% 0.33/0.67 => ( ( rep_assn @ Q @ ( produc7507926704131184380et_nat @ H3 @ As4 ) )
% 0.33/0.67 => ( ( ( inf_inf_set_nat @ As3 @ As4 )
% 0.33/0.67 = bot_bot_set_nat )
% 0.33/0.67 => ( rep_assn @ ( times_times_assn @ P @ Q ) @ ( produc7507926704131184380et_nat @ H3 @ ( sup_sup_set_nat @ As3 @ As4 ) ) ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % star_assnI
% 0.33/0.67 thf(fact_7883_mod__emp__simp,axiom,
% 0.33/0.67 ! [H3: heap_e7401611519738050253t_unit] : ( rep_assn @ one_one_assn @ ( produc7507926704131184380et_nat @ H3 @ bot_bot_set_nat ) ) ).
% 0.33/0.67
% 0.33/0.67 % mod_emp_simp
% 0.33/0.67 thf(fact_7884_mod__h__bot__indep,axiom,
% 0.33/0.67 ! [P: assn,H3: heap_e7401611519738050253t_unit,H5: heap_e7401611519738050253t_unit] :
% 0.33/0.67 ( ( rep_assn @ P @ ( produc7507926704131184380et_nat @ H3 @ bot_bot_set_nat ) )
% 0.33/0.67 = ( rep_assn @ P @ ( produc7507926704131184380et_nat @ H5 @ bot_bot_set_nat ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % mod_h_bot_indep
% 0.33/0.67 thf(fact_7885_times__assn__raw_Osimps,axiom,
% 0.33/0.67 ! [P: produc3658429121746597890et_nat > $o,Q: produc3658429121746597890et_nat > $o,H3: heap_e7401611519738050253t_unit,As3: set_nat] :
% 0.33/0.67 ( ( times_assn_raw @ P @ Q @ ( produc7507926704131184380et_nat @ H3 @ As3 ) )
% 0.33/0.67 = ( ? [As1: set_nat,As2: set_nat] :
% 0.33/0.67 ( ( As3
% 0.33/0.67 = ( sup_sup_set_nat @ As1 @ As2 ) )
% 0.33/0.67 & ( ( inf_inf_set_nat @ As1 @ As2 )
% 0.33/0.67 = bot_bot_set_nat )
% 0.33/0.67 & ( P @ ( produc7507926704131184380et_nat @ H3 @ As1 ) )
% 0.33/0.67 & ( Q @ ( produc7507926704131184380et_nat @ H3 @ As2 ) ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % times_assn_raw.simps
% 0.33/0.67 thf(fact_7886_times__assn__raw_Oelims_I3_J,axiom,
% 0.33/0.67 ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat] :
% 0.33/0.67 ( ~ ( times_assn_raw @ X @ Xa @ Xb )
% 0.33/0.67 => ~ ! [H2: heap_e7401611519738050253t_unit,As: set_nat] :
% 0.33/0.67 ( ( Xb
% 0.33/0.67 = ( produc7507926704131184380et_nat @ H2 @ As ) )
% 0.33/0.67 => ? [As12: set_nat,As22: set_nat] :
% 0.33/0.67 ( ( As
% 0.33/0.67 = ( sup_sup_set_nat @ As12 @ As22 ) )
% 0.33/0.67 & ( ( inf_inf_set_nat @ As12 @ As22 )
% 0.33/0.67 = bot_bot_set_nat )
% 0.33/0.67 & ( X @ ( produc7507926704131184380et_nat @ H2 @ As12 ) )
% 0.33/0.67 & ( Xa @ ( produc7507926704131184380et_nat @ H2 @ As22 ) ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % times_assn_raw.elims(3)
% 0.33/0.67 thf(fact_7887_times__assn__raw_Oelims_I2_J,axiom,
% 0.33/0.67 ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat] :
% 0.33/0.67 ( ( times_assn_raw @ X @ Xa @ Xb )
% 0.33/0.67 => ~ ! [H2: heap_e7401611519738050253t_unit,As: set_nat] :
% 0.33/0.67 ( ( Xb
% 0.33/0.67 = ( produc7507926704131184380et_nat @ H2 @ As ) )
% 0.33/0.67 => ~ ? [As13: set_nat,As23: set_nat] :
% 0.33/0.67 ( ( As
% 0.33/0.67 = ( sup_sup_set_nat @ As13 @ As23 ) )
% 0.33/0.67 & ( ( inf_inf_set_nat @ As13 @ As23 )
% 0.33/0.67 = bot_bot_set_nat )
% 0.33/0.67 & ( X @ ( produc7507926704131184380et_nat @ H2 @ As13 ) )
% 0.33/0.67 & ( Xa @ ( produc7507926704131184380et_nat @ H2 @ As23 ) ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % times_assn_raw.elims(2)
% 0.33/0.67 thf(fact_7888_times__assn__raw_Oelims_I1_J,axiom,
% 0.33/0.67 ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat,Y: $o] :
% 0.33/0.67 ( ( ( times_assn_raw @ X @ Xa @ Xb )
% 0.33/0.67 = Y )
% 0.33/0.67 => ~ ! [H2: heap_e7401611519738050253t_unit,As: set_nat] :
% 0.33/0.67 ( ( Xb
% 0.33/0.67 = ( produc7507926704131184380et_nat @ H2 @ As ) )
% 0.33/0.67 => ( Y
% 0.33/0.67 = ( ~ ? [As1: set_nat,As2: set_nat] :
% 0.33/0.67 ( ( As
% 0.33/0.67 = ( sup_sup_set_nat @ As1 @ As2 ) )
% 0.33/0.67 & ( ( inf_inf_set_nat @ As1 @ As2 )
% 0.33/0.67 = bot_bot_set_nat )
% 0.33/0.67 & ( X @ ( produc7507926704131184380et_nat @ H2 @ As1 ) )
% 0.33/0.67 & ( Xa @ ( produc7507926704131184380et_nat @ H2 @ As2 ) ) ) ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % times_assn_raw.elims(1)
% 0.33/0.67 thf(fact_7889_times__assn__raw_Opelims_I1_J,axiom,
% 0.33/0.67 ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat,Y: $o] :
% 0.33/0.67 ( ( ( times_assn_raw @ X @ Xa @ Xb )
% 0.33/0.67 = Y )
% 0.33/0.67 => ( ( accp_P1862375125659990705et_nat @ times_assn_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ Xb ) ) )
% 0.33/0.67 => ~ ! [H2: heap_e7401611519738050253t_unit,As: set_nat] :
% 0.33/0.67 ( ( Xb
% 0.33/0.67 = ( produc7507926704131184380et_nat @ H2 @ As ) )
% 0.33/0.67 => ( ( Y
% 0.33/0.67 = ( ? [As1: set_nat,As2: set_nat] :
% 0.33/0.67 ( ( As
% 0.33/0.67 = ( sup_sup_set_nat @ As1 @ As2 ) )
% 0.33/0.67 & ( ( inf_inf_set_nat @ As1 @ As2 )
% 0.33/0.67 = bot_bot_set_nat )
% 0.33/0.67 & ( X @ ( produc7507926704131184380et_nat @ H2 @ As1 ) )
% 0.33/0.67 & ( Xa @ ( produc7507926704131184380et_nat @ H2 @ As2 ) ) ) ) )
% 0.33/0.67 => ~ ( accp_P1862375125659990705et_nat @ times_assn_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ ( produc7507926704131184380et_nat @ H2 @ As ) ) ) ) ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % times_assn_raw.pelims(1)
% 0.33/0.67 thf(fact_7890_times__assn__raw_Opelims_I2_J,axiom,
% 0.33/0.67 ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat] :
% 0.33/0.67 ( ( times_assn_raw @ X @ Xa @ Xb )
% 0.33/0.67 => ( ( accp_P1862375125659990705et_nat @ times_assn_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ Xb ) ) )
% 0.33/0.67 => ~ ! [H2: heap_e7401611519738050253t_unit,As: set_nat] :
% 0.33/0.67 ( ( Xb
% 0.33/0.67 = ( produc7507926704131184380et_nat @ H2 @ As ) )
% 0.33/0.67 => ( ( accp_P1862375125659990705et_nat @ times_assn_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ ( produc7507926704131184380et_nat @ H2 @ As ) ) ) )
% 0.33/0.67 => ~ ? [As13: set_nat,As23: set_nat] :
% 0.33/0.67 ( ( As
% 0.33/0.67 = ( sup_sup_set_nat @ As13 @ As23 ) )
% 0.33/0.67 & ( ( inf_inf_set_nat @ As13 @ As23 )
% 0.33/0.67 = bot_bot_set_nat )
% 0.33/0.67 & ( X @ ( produc7507926704131184380et_nat @ H2 @ As13 ) )
% 0.33/0.67 & ( Xa @ ( produc7507926704131184380et_nat @ H2 @ As23 ) ) ) ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % times_assn_raw.pelims(2)
% 0.33/0.67 thf(fact_7891_times__assn__raw_Opelims_I3_J,axiom,
% 0.33/0.67 ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat] :
% 0.33/0.67 ( ~ ( times_assn_raw @ X @ Xa @ Xb )
% 0.33/0.67 => ( ( accp_P1862375125659990705et_nat @ times_assn_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ Xb ) ) )
% 0.33/0.67 => ~ ! [H2: heap_e7401611519738050253t_unit,As: set_nat] :
% 0.33/0.67 ( ( Xb
% 0.33/0.67 = ( produc7507926704131184380et_nat @ H2 @ As ) )
% 0.33/0.67 => ( ( accp_P1862375125659990705et_nat @ times_assn_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ ( produc7507926704131184380et_nat @ H2 @ As ) ) ) )
% 0.33/0.67 => ? [As12: set_nat,As22: set_nat] :
% 0.33/0.67 ( ( As
% 0.33/0.67 = ( sup_sup_set_nat @ As12 @ As22 ) )
% 0.33/0.67 & ( ( inf_inf_set_nat @ As12 @ As22 )
% 0.33/0.67 = bot_bot_set_nat )
% 0.33/0.67 & ( X @ ( produc7507926704131184380et_nat @ H2 @ As12 ) )
% 0.33/0.67 & ( Xa @ ( produc7507926704131184380et_nat @ H2 @ As22 ) ) ) ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % times_assn_raw.pelims(3)
% 0.33/0.67 thf(fact_7892_mod__h__bot__iff_I1_J,axiom,
% 0.33/0.67 ! [B: $o,H3: heap_e7401611519738050253t_unit] :
% 0.33/0.67 ( ( rep_assn @ ( pure_assn @ B ) @ ( produc7507926704131184380et_nat @ H3 @ bot_bot_set_nat ) )
% 0.33/0.67 = B ) ).
% 0.33/0.67
% 0.33/0.67 % mod_h_bot_iff(1)
% 0.33/0.67 thf(fact_7893_mod__relH,axiom,
% 0.33/0.67 ! [As3: set_nat,H3: heap_e7401611519738050253t_unit,H5: heap_e7401611519738050253t_unit,P: assn] :
% 0.33/0.67 ( ( relH @ As3 @ H3 @ H5 )
% 0.33/0.67 => ( ( rep_assn @ P @ ( produc7507926704131184380et_nat @ H3 @ As3 ) )
% 0.33/0.67 = ( rep_assn @ P @ ( produc7507926704131184380et_nat @ H5 @ As3 ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % mod_relH
% 0.33/0.67 thf(fact_7894_in__range__empty,axiom,
% 0.33/0.67 ! [H3: heap_e7401611519738050253t_unit] : ( in_range @ ( produc7507926704131184380et_nat @ H3 @ bot_bot_set_nat ) ) ).
% 0.33/0.67
% 0.33/0.67 % in_range_empty
% 0.33/0.67 thf(fact_7895_in__range__dist__union,axiom,
% 0.33/0.67 ! [H3: heap_e7401611519738050253t_unit,As3: set_nat,As4: set_nat] :
% 0.33/0.67 ( ( in_range @ ( produc7507926704131184380et_nat @ H3 @ ( sup_sup_set_nat @ As3 @ As4 ) ) )
% 0.33/0.67 = ( ( in_range @ ( produc7507926704131184380et_nat @ H3 @ As3 ) )
% 0.33/0.67 & ( in_range @ ( produc7507926704131184380et_nat @ H3 @ As4 ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % in_range_dist_union
% 0.33/0.67 thf(fact_7896_relH__refl,axiom,
% 0.33/0.67 ! [H3: heap_e7401611519738050253t_unit,As3: set_nat] :
% 0.33/0.67 ( ( in_range @ ( produc7507926704131184380et_nat @ H3 @ As3 ) )
% 0.33/0.67 => ( relH @ As3 @ H3 @ H3 ) ) ).
% 0.33/0.67
% 0.33/0.67 % relH_refl
% 0.33/0.67 thf(fact_7897_relH__in__rangeI_I1_J,axiom,
% 0.33/0.67 ! [As3: set_nat,H3: heap_e7401611519738050253t_unit,H5: heap_e7401611519738050253t_unit] :
% 0.33/0.67 ( ( relH @ As3 @ H3 @ H5 )
% 0.33/0.67 => ( in_range @ ( produc7507926704131184380et_nat @ H3 @ As3 ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % relH_in_rangeI(1)
% 0.33/0.67 thf(fact_7898_relH__in__rangeI_I2_J,axiom,
% 0.33/0.67 ! [As3: set_nat,H3: heap_e7401611519738050253t_unit,H5: heap_e7401611519738050253t_unit] :
% 0.33/0.67 ( ( relH @ As3 @ H3 @ H5 )
% 0.33/0.67 => ( in_range @ ( produc7507926704131184380et_nat @ H5 @ As3 ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % relH_in_rangeI(2)
% 0.33/0.67 thf(fact_7899_in__range__subset,axiom,
% 0.33/0.67 ! [As3: set_nat,As4: set_nat,H3: heap_e7401611519738050253t_unit] :
% 0.33/0.67 ( ( ord_less_eq_set_nat @ As3 @ As4 )
% 0.33/0.67 => ( ( in_range @ ( produc7507926704131184380et_nat @ H3 @ As4 ) )
% 0.33/0.67 => ( in_range @ ( produc7507926704131184380et_nat @ H3 @ As3 ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % in_range_subset
% 0.33/0.67 thf(fact_7900_in__range_Oelims_I3_J,axiom,
% 0.33/0.67 ! [X: produc3658429121746597890et_nat] :
% 0.33/0.67 ( ~ ( in_range @ X )
% 0.33/0.67 => ~ ! [H2: heap_e7401611519738050253t_unit,As: set_nat] :
% 0.33/0.67 ( ( X
% 0.33/0.67 = ( produc7507926704131184380et_nat @ H2 @ As ) )
% 0.33/0.67 => ! [X4: nat] :
% 0.33/0.67 ( ( member_nat @ X4 @ As )
% 0.33/0.67 => ( ord_less_nat @ X4 @ ( lim_Product_unit @ H2 ) ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % in_range.elims(3)
% 0.33/0.67 thf(fact_7901_in__range_Oelims_I2_J,axiom,
% 0.33/0.67 ! [X: produc3658429121746597890et_nat] :
% 0.33/0.67 ( ( in_range @ X )
% 0.33/0.67 => ~ ! [H2: heap_e7401611519738050253t_unit,As: set_nat] :
% 0.33/0.67 ( ( X
% 0.33/0.67 = ( produc7507926704131184380et_nat @ H2 @ As ) )
% 0.33/0.67 => ~ ! [X8: nat] :
% 0.33/0.67 ( ( member_nat @ X8 @ As )
% 0.33/0.67 => ( ord_less_nat @ X8 @ ( lim_Product_unit @ H2 ) ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % in_range.elims(2)
% 0.33/0.67 thf(fact_7902_in__range_Oelims_I1_J,axiom,
% 0.33/0.67 ! [X: produc3658429121746597890et_nat,Y: $o] :
% 0.33/0.67 ( ( ( in_range @ X )
% 0.33/0.67 = Y )
% 0.33/0.67 => ~ ! [H2: heap_e7401611519738050253t_unit,As: set_nat] :
% 0.33/0.67 ( ( X
% 0.33/0.67 = ( produc7507926704131184380et_nat @ H2 @ As ) )
% 0.33/0.67 => ( Y
% 0.33/0.67 = ( ~ ! [X3: nat] :
% 0.33/0.67 ( ( member_nat @ X3 @ As )
% 0.33/0.67 => ( ord_less_nat @ X3 @ ( lim_Product_unit @ H2 ) ) ) ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % in_range.elims(1)
% 0.33/0.67 thf(fact_7903_in__range_Osimps,axiom,
% 0.33/0.67 ! [H3: heap_e7401611519738050253t_unit,As3: set_nat] :
% 0.33/0.67 ( ( in_range @ ( produc7507926704131184380et_nat @ H3 @ As3 ) )
% 0.33/0.67 = ( ! [X3: nat] :
% 0.33/0.67 ( ( member_nat @ X3 @ As3 )
% 0.33/0.67 => ( ord_less_nat @ X3 @ ( lim_Product_unit @ H3 ) ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % in_range.simps
% 0.33/0.67 thf(fact_7904_wand__assnI,axiom,
% 0.33/0.67 ! [H3: heap_e7401611519738050253t_unit,As3: set_nat,Q: assn,R4: assn] :
% 0.33/0.67 ( ( in_range @ ( produc7507926704131184380et_nat @ H3 @ As3 ) )
% 0.33/0.67 => ( ! [H4: heap_e7401611519738050253t_unit,As5: set_nat] :
% 0.33/0.67 ( ( ( inf_inf_set_nat @ As3 @ As5 )
% 0.33/0.67 = bot_bot_set_nat )
% 0.33/0.67 => ( ( relH @ As3 @ H3 @ H4 )
% 0.33/0.67 => ( ( in_range @ ( produc7507926704131184380et_nat @ H4 @ As3 ) )
% 0.33/0.67 => ( ( rep_assn @ Q @ ( produc7507926704131184380et_nat @ H4 @ As5 ) )
% 0.33/0.67 => ( rep_assn @ R4 @ ( produc7507926704131184380et_nat @ H4 @ ( sup_sup_set_nat @ As3 @ As5 ) ) ) ) ) ) )
% 0.33/0.67 => ( rep_assn @ ( wand_assn @ Q @ R4 ) @ ( produc7507926704131184380et_nat @ H3 @ As3 ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % wand_assnI
% 0.33/0.67 thf(fact_7905_wand__raw_Osimps,axiom,
% 0.33/0.67 ! [P: produc3658429121746597890et_nat > $o,Q: produc3658429121746597890et_nat > $o,H3: heap_e7401611519738050253t_unit,As3: set_nat] :
% 0.33/0.67 ( ( wand_raw @ P @ Q @ ( produc7507926704131184380et_nat @ H3 @ As3 ) )
% 0.33/0.67 = ( ( in_range @ ( produc7507926704131184380et_nat @ H3 @ As3 ) )
% 0.33/0.67 & ! [H6: heap_e7401611519738050253t_unit,As6: set_nat] :
% 0.33/0.67 ( ( ( ( inf_inf_set_nat @ As3 @ As6 )
% 0.33/0.67 = bot_bot_set_nat )
% 0.33/0.67 & ( relH @ As3 @ H3 @ H6 )
% 0.33/0.67 & ( in_range @ ( produc7507926704131184380et_nat @ H6 @ As3 ) )
% 0.33/0.67 & ( P @ ( produc7507926704131184380et_nat @ H6 @ As6 ) ) )
% 0.33/0.67 => ( Q @ ( produc7507926704131184380et_nat @ H6 @ ( sup_sup_set_nat @ As3 @ As6 ) ) ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % wand_raw.simps
% 0.33/0.67 thf(fact_7906_wand__raw_Oelims_I1_J,axiom,
% 0.33/0.67 ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat,Y: $o] :
% 0.33/0.67 ( ( ( wand_raw @ X @ Xa @ Xb )
% 0.33/0.67 = Y )
% 0.33/0.67 => ~ ! [H2: heap_e7401611519738050253t_unit,As: set_nat] :
% 0.33/0.67 ( ( Xb
% 0.33/0.67 = ( produc7507926704131184380et_nat @ H2 @ As ) )
% 0.33/0.67 => ( Y
% 0.33/0.67 = ( ~ ( ( in_range @ ( produc7507926704131184380et_nat @ H2 @ As ) )
% 0.33/0.67 & ! [H6: heap_e7401611519738050253t_unit,As6: set_nat] :
% 0.33/0.67 ( ( ( ( inf_inf_set_nat @ As @ As6 )
% 0.33/0.67 = bot_bot_set_nat )
% 0.33/0.67 & ( relH @ As @ H2 @ H6 )
% 0.33/0.67 & ( in_range @ ( produc7507926704131184380et_nat @ H6 @ As ) )
% 0.33/0.67 & ( X @ ( produc7507926704131184380et_nat @ H6 @ As6 ) ) )
% 0.33/0.67 => ( Xa @ ( produc7507926704131184380et_nat @ H6 @ ( sup_sup_set_nat @ As @ As6 ) ) ) ) ) ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % wand_raw.elims(1)
% 0.33/0.67 thf(fact_7907_wand__raw_Oelims_I3_J,axiom,
% 0.33/0.67 ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat] :
% 0.33/0.67 ( ~ ( wand_raw @ X @ Xa @ Xb )
% 0.33/0.67 => ~ ! [H2: heap_e7401611519738050253t_unit,As: set_nat] :
% 0.33/0.67 ( ( Xb
% 0.33/0.67 = ( produc7507926704131184380et_nat @ H2 @ As ) )
% 0.33/0.67 => ( ( in_range @ ( produc7507926704131184380et_nat @ H2 @ As ) )
% 0.33/0.67 & ! [H4: heap_e7401611519738050253t_unit,As5: set_nat] :
% 0.33/0.67 ( ( ( ( inf_inf_set_nat @ As @ As5 )
% 0.33/0.67 = bot_bot_set_nat )
% 0.33/0.67 & ( relH @ As @ H2 @ H4 )
% 0.33/0.67 & ( in_range @ ( produc7507926704131184380et_nat @ H4 @ As ) )
% 0.33/0.67 & ( X @ ( produc7507926704131184380et_nat @ H4 @ As5 ) ) )
% 0.33/0.67 => ( Xa @ ( produc7507926704131184380et_nat @ H4 @ ( sup_sup_set_nat @ As @ As5 ) ) ) ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % wand_raw.elims(3)
% 0.33/0.67 thf(fact_7908_wand__raw_Oelims_I2_J,axiom,
% 0.33/0.67 ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat] :
% 0.33/0.67 ( ( wand_raw @ X @ Xa @ Xb )
% 0.33/0.67 => ~ ! [H2: heap_e7401611519738050253t_unit,As: set_nat] :
% 0.33/0.67 ( ( Xb
% 0.33/0.67 = ( produc7507926704131184380et_nat @ H2 @ As ) )
% 0.33/0.67 => ~ ( ( in_range @ ( produc7507926704131184380et_nat @ H2 @ As ) )
% 0.33/0.67 & ! [H8: heap_e7401611519738050253t_unit,As7: set_nat] :
% 0.33/0.67 ( ( ( ( inf_inf_set_nat @ As @ As7 )
% 0.33/0.67 = bot_bot_set_nat )
% 0.33/0.67 & ( relH @ As @ H2 @ H8 )
% 0.33/0.67 & ( in_range @ ( produc7507926704131184380et_nat @ H8 @ As ) )
% 0.33/0.67 & ( X @ ( produc7507926704131184380et_nat @ H8 @ As7 ) ) )
% 0.33/0.67 => ( Xa @ ( produc7507926704131184380et_nat @ H8 @ ( sup_sup_set_nat @ As @ As7 ) ) ) ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % wand_raw.elims(2)
% 0.33/0.67 thf(fact_7909_wand__raw_Opelims_I3_J,axiom,
% 0.33/0.67 ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat] :
% 0.33/0.67 ( ~ ( wand_raw @ X @ Xa @ Xb )
% 0.33/0.67 => ( ( accp_P1862375125659990705et_nat @ wand_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ Xb ) ) )
% 0.33/0.67 => ~ ! [H2: heap_e7401611519738050253t_unit,As: set_nat] :
% 0.33/0.67 ( ( Xb
% 0.33/0.67 = ( produc7507926704131184380et_nat @ H2 @ As ) )
% 0.33/0.67 => ( ( accp_P1862375125659990705et_nat @ wand_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ ( produc7507926704131184380et_nat @ H2 @ As ) ) ) )
% 0.33/0.67 => ( ( in_range @ ( produc7507926704131184380et_nat @ H2 @ As ) )
% 0.33/0.67 & ! [H4: heap_e7401611519738050253t_unit,As5: set_nat] :
% 0.33/0.67 ( ( ( ( inf_inf_set_nat @ As @ As5 )
% 0.33/0.67 = bot_bot_set_nat )
% 0.33/0.67 & ( relH @ As @ H2 @ H4 )
% 0.33/0.67 & ( in_range @ ( produc7507926704131184380et_nat @ H4 @ As ) )
% 0.33/0.67 & ( X @ ( produc7507926704131184380et_nat @ H4 @ As5 ) ) )
% 0.33/0.67 => ( Xa @ ( produc7507926704131184380et_nat @ H4 @ ( sup_sup_set_nat @ As @ As5 ) ) ) ) ) ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % wand_raw.pelims(3)
% 0.33/0.67 thf(fact_7910_wand__raw_Opelims_I2_J,axiom,
% 0.33/0.67 ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat] :
% 0.33/0.67 ( ( wand_raw @ X @ Xa @ Xb )
% 0.33/0.67 => ( ( accp_P1862375125659990705et_nat @ wand_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ Xb ) ) )
% 0.33/0.67 => ~ ! [H2: heap_e7401611519738050253t_unit,As: set_nat] :
% 0.33/0.67 ( ( Xb
% 0.33/0.67 = ( produc7507926704131184380et_nat @ H2 @ As ) )
% 0.33/0.67 => ( ( accp_P1862375125659990705et_nat @ wand_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ ( produc7507926704131184380et_nat @ H2 @ As ) ) ) )
% 0.33/0.67 => ~ ( ( in_range @ ( produc7507926704131184380et_nat @ H2 @ As ) )
% 0.33/0.67 & ! [H8: heap_e7401611519738050253t_unit,As7: set_nat] :
% 0.33/0.67 ( ( ( ( inf_inf_set_nat @ As @ As7 )
% 0.33/0.67 = bot_bot_set_nat )
% 0.33/0.67 & ( relH @ As @ H2 @ H8 )
% 0.33/0.67 & ( in_range @ ( produc7507926704131184380et_nat @ H8 @ As ) )
% 0.33/0.67 & ( X @ ( produc7507926704131184380et_nat @ H8 @ As7 ) ) )
% 0.33/0.67 => ( Xa @ ( produc7507926704131184380et_nat @ H8 @ ( sup_sup_set_nat @ As @ As7 ) ) ) ) ) ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % wand_raw.pelims(2)
% 0.33/0.67 thf(fact_7911_wand__raw_Opelims_I1_J,axiom,
% 0.33/0.67 ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat,Y: $o] :
% 0.33/0.67 ( ( ( wand_raw @ X @ Xa @ Xb )
% 0.33/0.67 = Y )
% 0.33/0.67 => ( ( accp_P1862375125659990705et_nat @ wand_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ Xb ) ) )
% 0.33/0.67 => ~ ! [H2: heap_e7401611519738050253t_unit,As: set_nat] :
% 0.33/0.67 ( ( Xb
% 0.33/0.67 = ( produc7507926704131184380et_nat @ H2 @ As ) )
% 0.33/0.67 => ( ( Y
% 0.33/0.67 = ( ( in_range @ ( produc7507926704131184380et_nat @ H2 @ As ) )
% 0.33/0.67 & ! [H6: heap_e7401611519738050253t_unit,As6: set_nat] :
% 0.33/0.67 ( ( ( ( inf_inf_set_nat @ As @ As6 )
% 0.33/0.67 = bot_bot_set_nat )
% 0.33/0.67 & ( relH @ As @ H2 @ H6 )
% 0.33/0.67 & ( in_range @ ( produc7507926704131184380et_nat @ H6 @ As ) )
% 0.33/0.67 & ( X @ ( produc7507926704131184380et_nat @ H6 @ As6 ) ) )
% 0.33/0.67 => ( Xa @ ( produc7507926704131184380et_nat @ H6 @ ( sup_sup_set_nat @ As @ As6 ) ) ) ) ) )
% 0.33/0.67 => ~ ( accp_P1862375125659990705et_nat @ wand_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ ( produc7507926704131184380et_nat @ H2 @ As ) ) ) ) ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % wand_raw.pelims(1)
% 0.33/0.67 thf(fact_7912_in__range_Opelims_I3_J,axiom,
% 0.33/0.67 ! [X: produc3658429121746597890et_nat] :
% 0.33/0.67 ( ~ ( in_range @ X )
% 0.33/0.67 => ( ( accp_P5801069581201407417et_nat @ in_range_rel @ X )
% 0.33/0.67 => ~ ! [H2: heap_e7401611519738050253t_unit,As: set_nat] :
% 0.33/0.67 ( ( X
% 0.33/0.67 = ( produc7507926704131184380et_nat @ H2 @ As ) )
% 0.33/0.67 => ( ( accp_P5801069581201407417et_nat @ in_range_rel @ ( produc7507926704131184380et_nat @ H2 @ As ) )
% 0.33/0.67 => ! [X4: nat] :
% 0.33/0.67 ( ( member_nat @ X4 @ As )
% 0.33/0.67 => ( ord_less_nat @ X4 @ ( lim_Product_unit @ H2 ) ) ) ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % in_range.pelims(3)
% 0.33/0.67 thf(fact_7913_in__range_Opelims_I2_J,axiom,
% 0.33/0.67 ! [X: produc3658429121746597890et_nat] :
% 0.33/0.67 ( ( in_range @ X )
% 0.33/0.67 => ( ( accp_P5801069581201407417et_nat @ in_range_rel @ X )
% 0.33/0.67 => ~ ! [H2: heap_e7401611519738050253t_unit,As: set_nat] :
% 0.33/0.67 ( ( X
% 0.33/0.67 = ( produc7507926704131184380et_nat @ H2 @ As ) )
% 0.33/0.67 => ( ( accp_P5801069581201407417et_nat @ in_range_rel @ ( produc7507926704131184380et_nat @ H2 @ As ) )
% 0.33/0.67 => ~ ! [X8: nat] :
% 0.33/0.67 ( ( member_nat @ X8 @ As )
% 0.33/0.67 => ( ord_less_nat @ X8 @ ( lim_Product_unit @ H2 ) ) ) ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % in_range.pelims(2)
% 0.33/0.67 thf(fact_7914_in__range_Opelims_I1_J,axiom,
% 0.33/0.67 ! [X: produc3658429121746597890et_nat,Y: $o] :
% 0.33/0.67 ( ( ( in_range @ X )
% 0.33/0.67 = Y )
% 0.33/0.67 => ( ( accp_P5801069581201407417et_nat @ in_range_rel @ X )
% 0.33/0.67 => ~ ! [H2: heap_e7401611519738050253t_unit,As: set_nat] :
% 0.33/0.67 ( ( X
% 0.33/0.67 = ( produc7507926704131184380et_nat @ H2 @ As ) )
% 0.33/0.67 => ( ( Y
% 0.33/0.67 = ( ! [X3: nat] :
% 0.33/0.67 ( ( member_nat @ X3 @ As )
% 0.33/0.67 => ( ord_less_nat @ X3 @ ( lim_Product_unit @ H2 ) ) ) ) )
% 0.33/0.67 => ~ ( accp_P5801069581201407417et_nat @ in_range_rel @ ( produc7507926704131184380et_nat @ H2 @ As ) ) ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % in_range.pelims(1)
% 0.33/0.67 thf(fact_7915_one__assn__raw_Oelims_I3_J,axiom,
% 0.33/0.67 ! [X: produc3658429121746597890et_nat] :
% 0.33/0.67 ( ~ ( one_assn_raw @ X )
% 0.33/0.67 => ~ ! [H2: heap_e7401611519738050253t_unit,As: set_nat] :
% 0.33/0.67 ( ( X
% 0.33/0.67 = ( produc7507926704131184380et_nat @ H2 @ As ) )
% 0.33/0.67 => ( As = bot_bot_set_nat ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % one_assn_raw.elims(3)
% 0.33/0.67 thf(fact_7916_one__assn__raw_Oelims_I2_J,axiom,
% 0.33/0.67 ! [X: produc3658429121746597890et_nat] :
% 0.33/0.67 ( ( one_assn_raw @ X )
% 0.33/0.67 => ~ ! [H2: heap_e7401611519738050253t_unit,As: set_nat] :
% 0.33/0.67 ( ( X
% 0.33/0.67 = ( produc7507926704131184380et_nat @ H2 @ As ) )
% 0.33/0.67 => ( As != bot_bot_set_nat ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % one_assn_raw.elims(2)
% 0.33/0.67 thf(fact_7917_one__assn__raw_Oelims_I1_J,axiom,
% 0.33/0.67 ! [X: produc3658429121746597890et_nat,Y: $o] :
% 0.33/0.67 ( ( ( one_assn_raw @ X )
% 0.33/0.67 = Y )
% 0.33/0.67 => ~ ! [H2: heap_e7401611519738050253t_unit,As: set_nat] :
% 0.33/0.67 ( ( X
% 0.33/0.67 = ( produc7507926704131184380et_nat @ H2 @ As ) )
% 0.33/0.67 => ( Y
% 0.33/0.67 = ( As != bot_bot_set_nat ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % one_assn_raw.elims(1)
% 0.33/0.67 thf(fact_7918_one__assn__raw_Osimps,axiom,
% 0.33/0.67 ! [H3: heap_e7401611519738050253t_unit,As3: set_nat] :
% 0.33/0.67 ( ( one_assn_raw @ ( produc7507926704131184380et_nat @ H3 @ As3 ) )
% 0.33/0.67 = ( As3 = bot_bot_set_nat ) ) ).
% 0.33/0.67
% 0.33/0.67 % one_assn_raw.simps
% 0.33/0.67 thf(fact_7919_one__assn__raw_Opelims_I3_J,axiom,
% 0.33/0.67 ! [X: produc3658429121746597890et_nat] :
% 0.33/0.67 ( ~ ( one_assn_raw @ X )
% 0.33/0.67 => ( ( accp_P5801069581201407417et_nat @ one_assn_raw_rel @ X )
% 0.33/0.67 => ~ ! [H2: heap_e7401611519738050253t_unit,As: set_nat] :
% 0.33/0.67 ( ( X
% 0.33/0.67 = ( produc7507926704131184380et_nat @ H2 @ As ) )
% 0.33/0.67 => ( ( accp_P5801069581201407417et_nat @ one_assn_raw_rel @ ( produc7507926704131184380et_nat @ H2 @ As ) )
% 0.33/0.67 => ( As = bot_bot_set_nat ) ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % one_assn_raw.pelims(3)
% 0.33/0.67 thf(fact_7920_one__assn__raw_Opelims_I2_J,axiom,
% 0.33/0.67 ! [X: produc3658429121746597890et_nat] :
% 0.33/0.67 ( ( one_assn_raw @ X )
% 0.33/0.67 => ( ( accp_P5801069581201407417et_nat @ one_assn_raw_rel @ X )
% 0.33/0.67 => ~ ! [H2: heap_e7401611519738050253t_unit,As: set_nat] :
% 0.33/0.67 ( ( X
% 0.33/0.67 = ( produc7507926704131184380et_nat @ H2 @ As ) )
% 0.33/0.67 => ( ( accp_P5801069581201407417et_nat @ one_assn_raw_rel @ ( produc7507926704131184380et_nat @ H2 @ As ) )
% 0.33/0.67 => ( As != bot_bot_set_nat ) ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % one_assn_raw.pelims(2)
% 0.33/0.67 thf(fact_7921_one__assn__raw_Opelims_I1_J,axiom,
% 0.33/0.67 ! [X: produc3658429121746597890et_nat,Y: $o] :
% 0.33/0.67 ( ( ( one_assn_raw @ X )
% 0.33/0.67 = Y )
% 0.33/0.67 => ( ( accp_P5801069581201407417et_nat @ one_assn_raw_rel @ X )
% 0.33/0.67 => ~ ! [H2: heap_e7401611519738050253t_unit,As: set_nat] :
% 0.33/0.67 ( ( X
% 0.33/0.67 = ( produc7507926704131184380et_nat @ H2 @ As ) )
% 0.33/0.67 => ( ( Y
% 0.33/0.67 = ( As = bot_bot_set_nat ) )
% 0.33/0.67 => ~ ( accp_P5801069581201407417et_nat @ one_assn_raw_rel @ ( produc7507926704131184380et_nat @ H2 @ As ) ) ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % one_assn_raw.pelims(1)
% 0.33/0.67 thf(fact_7922_proper__iff,axiom,
% 0.33/0.67 ! [P: produc3658429121746597890et_nat > $o,As3: set_nat,H3: heap_e7401611519738050253t_unit,H5: heap_e7401611519738050253t_unit] :
% 0.33/0.67 ( ( proper @ P )
% 0.33/0.67 => ( ( relH @ As3 @ H3 @ H5 )
% 0.33/0.67 => ( ( in_range @ ( produc7507926704131184380et_nat @ H5 @ As3 ) )
% 0.33/0.67 => ( ( P @ ( produc7507926704131184380et_nat @ H3 @ As3 ) )
% 0.33/0.67 = ( P @ ( produc7507926704131184380et_nat @ H5 @ As3 ) ) ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % proper_iff
% 0.33/0.67 thf(fact_7923_proper__def,axiom,
% 0.33/0.67 ( proper
% 0.33/0.67 = ( ^ [P3: produc3658429121746597890et_nat > $o] :
% 0.33/0.67 ! [H: heap_e7401611519738050253t_unit,H6: heap_e7401611519738050253t_unit,As8: set_nat] :
% 0.33/0.67 ( ( ( P3 @ ( produc7507926704131184380et_nat @ H @ As8 ) )
% 0.33/0.67 => ( in_range @ ( produc7507926704131184380et_nat @ H @ As8 ) ) )
% 0.33/0.67 & ( ( ( P3 @ ( produc7507926704131184380et_nat @ H @ As8 ) )
% 0.33/0.67 & ( relH @ As8 @ H @ H6 )
% 0.33/0.67 & ( in_range @ ( produc7507926704131184380et_nat @ H6 @ As8 ) ) )
% 0.33/0.67 => ( P3 @ ( produc7507926704131184380et_nat @ H6 @ As8 ) ) ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % proper_def
% 0.33/0.67 thf(fact_7924_properD2,axiom,
% 0.33/0.67 ! [P: produc3658429121746597890et_nat > $o,H3: heap_e7401611519738050253t_unit,As3: set_nat,H5: heap_e7401611519738050253t_unit] :
% 0.33/0.67 ( ( proper @ P )
% 0.33/0.67 => ( ( P @ ( produc7507926704131184380et_nat @ H3 @ As3 ) )
% 0.33/0.67 => ( ( relH @ As3 @ H3 @ H5 )
% 0.33/0.67 => ( ( in_range @ ( produc7507926704131184380et_nat @ H5 @ As3 ) )
% 0.33/0.67 => ( P @ ( produc7507926704131184380et_nat @ H5 @ As3 ) ) ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % properD2
% 0.33/0.67 thf(fact_7925_properD1,axiom,
% 0.33/0.67 ! [P: produc3658429121746597890et_nat > $o,H3: heap_e7401611519738050253t_unit,As3: set_nat] :
% 0.33/0.67 ( ( proper @ P )
% 0.33/0.67 => ( ( P @ ( produc7507926704131184380et_nat @ H3 @ As3 ) )
% 0.33/0.67 => ( in_range @ ( produc7507926704131184380et_nat @ H3 @ As3 ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % properD1
% 0.33/0.67 thf(fact_7926_properI,axiom,
% 0.33/0.67 ! [P: produc3658429121746597890et_nat > $o] :
% 0.33/0.67 ( ! [As: set_nat,H2: heap_e7401611519738050253t_unit] :
% 0.33/0.67 ( ( P @ ( produc7507926704131184380et_nat @ H2 @ As ) )
% 0.33/0.67 => ( in_range @ ( produc7507926704131184380et_nat @ H2 @ As ) ) )
% 0.33/0.67 => ( ! [As: set_nat,H2: heap_e7401611519738050253t_unit,H4: heap_e7401611519738050253t_unit] :
% 0.33/0.67 ( ( P @ ( produc7507926704131184380et_nat @ H2 @ As ) )
% 0.33/0.67 => ( ( relH @ As @ H2 @ H4 )
% 0.33/0.67 => ( ( in_range @ ( produc7507926704131184380et_nat @ H4 @ As ) )
% 0.33/0.67 => ( P @ ( produc7507926704131184380et_nat @ H4 @ As ) ) ) ) )
% 0.33/0.67 => ( proper @ P ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % properI
% 0.33/0.67 thf(fact_7927_Int_Osub__code_I8_J,axiom,
% 0.33/0.67 ! [M2: num,N2: num] :
% 0.33/0.67 ( ( sub @ ( bit1 @ M2 ) @ ( bit0 @ N2 ) )
% 0.33/0.67 = ( plus_plus_int @ ( dup @ ( sub @ M2 @ N2 ) ) @ one_one_int ) ) ).
% 0.33/0.67
% 0.33/0.67 % Int.sub_code(8)
% 0.33/0.67 thf(fact_7928_Int_Odup__def,axiom,
% 0.33/0.67 ( dup
% 0.33/0.67 = ( ^ [K4: int] : ( plus_plus_int @ K4 @ K4 ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % Int.dup_def
% 0.33/0.67 thf(fact_7929_relH__def,axiom,
% 0.33/0.67 ( relH
% 0.33/0.67 = ( ^ [As8: set_nat,H: heap_e7401611519738050253t_unit,H6: heap_e7401611519738050253t_unit] :
% 0.33/0.67 ( ( in_range @ ( produc7507926704131184380et_nat @ H @ As8 ) )
% 0.33/0.67 & ( in_range @ ( produc7507926704131184380et_nat @ H6 @ As8 ) )
% 0.33/0.67 & ! [T2: typerep,X3: nat] :
% 0.33/0.67 ( ( member_nat @ X3 @ As8 )
% 0.33/0.67 => ( ( ( refs_Product_unit @ H @ T2 @ X3 )
% 0.33/0.67 = ( refs_Product_unit @ H6 @ T2 @ X3 ) )
% 0.33/0.67 & ( ( arrays_Product_unit @ H @ T2 @ X3 )
% 0.33/0.67 = ( arrays_Product_unit @ H6 @ T2 @ X3 ) ) ) ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % relH_def
% 0.33/0.67 thf(fact_7930_plus__int__code_I6_J,axiom,
% 0.33/0.67 ! [M2: num,N2: num] :
% 0.33/0.67 ( ( plus_plus_int @ ( neg @ M2 ) @ ( neg @ N2 ) )
% 0.33/0.67 = ( neg @ ( plus_plus_num @ M2 @ N2 ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % plus_int_code(6)
% 0.33/0.67 thf(fact_7931_plus__int__code_I5_J,axiom,
% 0.33/0.67 ! [M2: num,N2: num] :
% 0.33/0.67 ( ( plus_plus_int @ ( neg @ M2 ) @ ( pos @ N2 ) )
% 0.33/0.67 = ( sub @ N2 @ M2 ) ) ).
% 0.33/0.67
% 0.33/0.67 % plus_int_code(5)
% 0.33/0.67 thf(fact_7932_plus__int__code_I4_J,axiom,
% 0.33/0.67 ! [M2: num,N2: num] :
% 0.33/0.67 ( ( plus_plus_int @ ( pos @ M2 ) @ ( neg @ N2 ) )
% 0.33/0.67 = ( sub @ M2 @ N2 ) ) ).
% 0.33/0.67
% 0.33/0.67 % plus_int_code(4)
% 0.33/0.67 thf(fact_7933_minus__int__code_I4_J,axiom,
% 0.33/0.67 ! [M2: num,N2: num] :
% 0.33/0.67 ( ( minus_minus_int @ ( pos @ M2 ) @ ( neg @ N2 ) )
% 0.33/0.67 = ( pos @ ( plus_plus_num @ M2 @ N2 ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % minus_int_code(4)
% 0.33/0.67 thf(fact_7934_plus__int__code_I3_J,axiom,
% 0.33/0.67 ! [M2: num,N2: num] :
% 0.33/0.67 ( ( plus_plus_int @ ( pos @ M2 ) @ ( pos @ N2 ) )
% 0.33/0.67 = ( pos @ ( plus_plus_num @ M2 @ N2 ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % plus_int_code(3)
% 0.33/0.67 thf(fact_7935_minus__int__code_I5_J,axiom,
% 0.33/0.67 ! [M2: num,N2: num] :
% 0.33/0.67 ( ( minus_minus_int @ ( neg @ M2 ) @ ( pos @ N2 ) )
% 0.33/0.67 = ( neg @ ( plus_plus_num @ M2 @ N2 ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % minus_int_code(5)
% 0.33/0.67 thf(fact_7936_Unity__def,axiom,
% 0.33/0.67 ( product_Unity
% 0.33/0.67 = ( product_Abs_unit @ $true ) ) ).
% 0.33/0.67
% 0.33/0.67 % Unity_def
% 0.33/0.67 thf(fact_7937_Abs__unit__inject,axiom,
% 0.33/0.67 ! [X: $o,Y: $o] :
% 0.33/0.67 ( ( member_o @ X @ ( insert_o @ $true @ bot_bot_set_o ) )
% 0.33/0.67 => ( ( member_o @ Y @ ( insert_o @ $true @ bot_bot_set_o ) )
% 0.33/0.67 => ( ( ( product_Abs_unit @ X )
% 0.33/0.67 = ( product_Abs_unit @ Y ) )
% 0.33/0.67 = ( X = Y ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % Abs_unit_inject
% 0.33/0.67 thf(fact_7938_Abs__unit__induct,axiom,
% 0.33/0.67 ! [P: product_unit > $o,X: product_unit] :
% 0.33/0.67 ( ! [Y5: $o] :
% 0.33/0.67 ( ( member_o @ Y5 @ ( insert_o @ $true @ bot_bot_set_o ) )
% 0.33/0.67 => ( P @ ( product_Abs_unit @ Y5 ) ) )
% 0.33/0.67 => ( P @ X ) ) ).
% 0.33/0.67
% 0.33/0.67 % Abs_unit_induct
% 0.33/0.67 thf(fact_7939_Abs__unit__cases,axiom,
% 0.33/0.67 ! [X: product_unit] :
% 0.33/0.67 ~ ! [Y5: $o] :
% 0.33/0.67 ( ( X
% 0.33/0.67 = ( product_Abs_unit @ Y5 ) )
% 0.33/0.67 => ~ ( member_o @ Y5 @ ( insert_o @ $true @ bot_bot_set_o ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % Abs_unit_cases
% 0.33/0.67 thf(fact_7940_integer_Odomain,axiom,
% 0.33/0.67 ! [P: int > $o] :
% 0.33/0.67 ( ( ( domainp_int_int
% 0.33/0.67 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 ) )
% 0.33/0.67 = P )
% 0.33/0.67 => ( ( domain452967906960104687nteger @ code_pcr_integer )
% 0.33/0.67 = P ) ) ).
% 0.33/0.67
% 0.33/0.67 % integer.domain
% 0.33/0.67 thf(fact_7941_natural_Odomain,axiom,
% 0.33/0.67 ! [P: nat > $o] :
% 0.33/0.67 ( ( ( domainp_nat_nat
% 0.33/0.67 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 ) )
% 0.33/0.67 = P )
% 0.33/0.67 => ( ( domain8128281535334753374atural @ code_pcr_natural )
% 0.33/0.67 = P ) ) ).
% 0.33/0.67
% 0.33/0.67 % natural.domain
% 0.33/0.67 thf(fact_7942_Abs__unit__inverse,axiom,
% 0.33/0.67 ! [Y: $o] :
% 0.33/0.67 ( ( member_o @ Y @ ( insert_o @ $true @ bot_bot_set_o ) )
% 0.33/0.67 => ( ( product_Rep_unit @ ( product_Abs_unit @ Y ) )
% 0.33/0.67 = Y ) ) ).
% 0.33/0.67
% 0.33/0.67 % Abs_unit_inverse
% 0.33/0.67 thf(fact_7943_type__definition__unit,axiom,
% 0.33/0.67 type_d6188575255521822967unit_o @ product_Rep_unit @ product_Abs_unit @ ( insert_o @ $true @ bot_bot_set_o ) ).
% 0.33/0.67
% 0.33/0.67 % type_definition_unit
% 0.33/0.67 thf(fact_7944_Rep__unit__inverse,axiom,
% 0.33/0.67 ! [X: product_unit] :
% 0.33/0.67 ( ( product_Abs_unit @ ( product_Rep_unit @ X ) )
% 0.33/0.67 = X ) ).
% 0.33/0.67
% 0.33/0.67 % Rep_unit_inverse
% 0.33/0.67 thf(fact_7945_Rep__unit__inject,axiom,
% 0.33/0.67 ! [X: product_unit,Y: product_unit] :
% 0.33/0.67 ( ( ( product_Rep_unit @ X )
% 0.33/0.67 = ( product_Rep_unit @ Y ) )
% 0.33/0.67 = ( X = Y ) ) ).
% 0.33/0.67
% 0.33/0.67 % Rep_unit_inject
% 0.33/0.67 thf(fact_7946_Rep__unit,axiom,
% 0.33/0.67 ! [X: product_unit] : ( member_o @ ( product_Rep_unit @ X ) @ ( insert_o @ $true @ bot_bot_set_o ) ) ).
% 0.33/0.67
% 0.33/0.67 % Rep_unit
% 0.33/0.67 thf(fact_7947_Rep__unit__cases,axiom,
% 0.33/0.67 ! [Y: $o] :
% 0.33/0.67 ( ( member_o @ Y @ ( insert_o @ $true @ bot_bot_set_o ) )
% 0.33/0.67 => ~ ! [X4: product_unit] :
% 0.33/0.67 ( Y
% 0.33/0.67 = ( ~ ( product_Rep_unit @ X4 ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % Rep_unit_cases
% 0.33/0.67 thf(fact_7948_Rep__unit__induct,axiom,
% 0.33/0.67 ! [Y: $o,P: $o > $o] :
% 0.33/0.67 ( ( member_o @ Y @ ( insert_o @ $true @ bot_bot_set_o ) )
% 0.33/0.67 => ( ! [X4: product_unit] : ( P @ ( product_Rep_unit @ X4 ) )
% 0.33/0.67 => ( P @ Y ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % Rep_unit_induct
% 0.33/0.67 thf(fact_7949_positive__add,axiom,
% 0.33/0.67 ! [X: rat,Y: rat] :
% 0.33/0.67 ( ( positive @ X )
% 0.33/0.67 => ( ( positive @ Y )
% 0.33/0.67 => ( positive @ ( plus_plus_rat @ X @ Y ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % positive_add
% 0.33/0.67 thf(fact_7950_nth__item_Opinduct,axiom,
% 0.33/0.67 ! [A0: nat,P: nat > $o] :
% 0.33/0.67 ( ( accp_nat @ nth_item_rel @ A0 )
% 0.33/0.67 => ( ( ( accp_nat @ nth_item_rel @ zero_zero_nat )
% 0.33/0.67 => ( P @ zero_zero_nat ) )
% 0.33/0.67 => ( ! [N: nat] :
% 0.33/0.67 ( ( accp_nat @ nth_item_rel @ ( suc @ N ) )
% 0.33/0.67 => ( ! [A9: nat,Aa2: nat] :
% 0.33/0.67 ( ( ( nat_sum_decode @ N )
% 0.33/0.67 = ( sum_Inl_nat_nat @ A9 ) )
% 0.33/0.67 => ( ( ( nat_sum_decode @ A9 )
% 0.33/0.67 = ( sum_Inl_nat_nat @ Aa2 ) )
% 0.33/0.67 => ( P @ Aa2 ) ) )
% 0.33/0.67 => ( ! [A9: nat,B7: nat] :
% 0.33/0.67 ( ( ( nat_sum_decode @ N )
% 0.33/0.67 = ( sum_Inl_nat_nat @ A9 ) )
% 0.33/0.67 => ( ( ( nat_sum_decode @ A9 )
% 0.33/0.67 = ( sum_Inr_nat_nat @ B7 ) )
% 0.33/0.67 => ( P @ B7 ) ) )
% 0.33/0.67 => ( ! [B7: nat,Ba: nat,X8: nat,Y6: nat] :
% 0.33/0.67 ( ( ( nat_sum_decode @ N )
% 0.33/0.67 = ( sum_Inr_nat_nat @ B7 ) )
% 0.33/0.67 => ( ( ( nat_sum_decode @ B7 )
% 0.33/0.67 = ( sum_Inr_nat_nat @ Ba ) )
% 0.33/0.67 => ( ( ( product_Pair_nat_nat @ X8 @ Y6 )
% 0.33/0.67 = ( nat_prod_decode @ Ba ) )
% 0.33/0.67 => ( P @ X8 ) ) ) )
% 0.33/0.67 => ( ! [B7: nat,Ba: nat,X8: nat,Y6: nat] :
% 0.33/0.67 ( ( ( nat_sum_decode @ N )
% 0.33/0.67 = ( sum_Inr_nat_nat @ B7 ) )
% 0.33/0.67 => ( ( ( nat_sum_decode @ B7 )
% 0.33/0.67 = ( sum_Inr_nat_nat @ Ba ) )
% 0.33/0.67 => ( ( ( product_Pair_nat_nat @ X8 @ Y6 )
% 0.33/0.67 = ( nat_prod_decode @ Ba ) )
% 0.33/0.67 => ( P @ Y6 ) ) ) )
% 0.33/0.67 => ( P @ ( suc @ N ) ) ) ) ) ) )
% 0.33/0.67 => ( P @ A0 ) ) ) ) ).
% 0.33/0.67
% 0.33/0.67 % nth_item.pinduct
% 0.33/0.67
% 0.33/0.67 % Helper facts (51)
% 0.33/0.67 thf(help_If_2_1_If_001t__Int__Oint_T,axiom,
% 0.33/0.67 ! [X: int,Y: int] :
% 0.33/0.67 ( ( if_int @ $false @ X @ Y )
% 0.33/0.67 = Y ) ).
% 0.33/0.67
% 0.33/0.67 thf(help_If_1_1_If_001t__Int__Oint_T,axiom,
% 0.33/0.67 ! [X: int,Y: int] :
% 0.33/0.67 ( ( if_int @ $true @ X @ Y )
% 0.33/0.67 = X ) ).
% 0.33/0.67
% 0.33/0.67 thf(help_If_2_1_If_001t__Nat__Onat_T,axiom,
% 0.33/0.67 ! [X: nat,Y: nat] :
% 0.33/0.67 ( ( if_nat @ $false @ X @ Y )
% 0.33/0.67 = Y ) ).
% 0.33/0.67
% 0.33/0.67 thf(help_If_1_1_If_001t__Nat__Onat_T,axiom,
% 0.33/0.67 ! [X: nat,Y: nat] :
% 0.33/0.67 ( ( if_nat @ $true @ X @ Y )
% 0.33/0.67 = X ) ).
% 0.33/0.67
% 0.33/0.67 thf(help_If_2_1_If_001t__Num__Onum_T,axiom,
% 0.33/0.67 ! [X: num,Y: num] :
% 0.33/0.67 ( ( if_num @ $false @ X @ Y )
% 0.33/0.67 = Y ) ).
% 0.33/0.67
% 0.33/0.67 thf(help_If_1_1_If_001t__Num__Onum_T,axiom,
% 0.33/0.67 ! [X: num,Y: num] :
% 0.33/0.67 ( ( if_num @ $true @ X @ Y )
% 0.33/0.67 = X ) ).
% 0.33/0.67
% 0.33/0.67 thf(help_If_2_1_If_001t__Rat__Orat_T,axiom,
% 0.33/0.67 ! [X: rat,Y: rat] :
% 0.33/0.67 ( ( if_rat @ $false @ X @ Y )
% 0.33/0.67 = Y ) ).
% 0.33/0.67
% 0.33/0.67 thf(help_If_1_1_If_001t__Rat__Orat_T,axiom,
% 0.33/0.67 ! [X: rat,Y: rat] :
% 0.33/0.67 ( ( if_rat @ $true @ X @ Y )
% 0.33/0.67 = X ) ).
% 0.33/0.67
% 0.33/0.67 thf(help_If_2_1_If_001t__Assertions__Oassn_T,axiom,
% 0.33/0.67 ! [X: assn,Y: assn] :
% 0.33/0.67 ( ( if_assn @ $false @ X @ Y )
% 0.33/0.67 = Y ) ).
% 0.33/0.67
% 0.33/0.67 thf(help_If_1_1_If_001t__Assertions__Oassn_T,axiom,
% 0.33/0.67 ! [X: assn,Y: assn] :
% 0.33/0.67 ( ( if_assn @ $true @ X @ Y )
% 0.33/0.67 = X ) ).
% 0.33/0.67
% 0.33/0.67 thf(help_If_2_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 0.33/0.67 ! [X: code_integer,Y: code_integer] :
% 0.33/0.67 ( ( if_Code_integer @ $false @ X @ Y )
% 0.33/0.67 = Y ) ).
% 0.33/0.67
% 0.33/0.67 thf(help_If_1_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 0.33/0.67 ! [X: code_integer,Y: code_integer] :
% 0.33/0.67 ( ( if_Code_integer @ $true @ X @ Y )
% 0.33/0.67 = X ) ).
% 0.33/0.67
% 0.33/0.67 thf(help_If_2_1_If_001t__Code____Numeral__Onatural_T,axiom,
% 0.33/0.67 ! [X: code_natural,Y: code_natural] :
% 0.33/0.67 ( ( if_Code_natural @ $false @ X @ Y )
% 0.33/0.67 = Y ) ).
% 0.33/0.67
% 0.33/0.67 thf(help_If_1_1_If_001t__Code____Numeral__Onatural_T,axiom,
% 0.33/0.67 ! [X: code_natural,Y: code_natural] :
% 0.33/0.67 ( ( if_Code_natural @ $true @ X @ Y )
% 0.33/0.67 = X ) ).
% 0.33/0.67
% 0.33/0.67 thf(help_If_2_1_If_001t__Set__Oset_It__Int__Oint_J_T,axiom,
% 0.33/0.67 ! [X: set_int,Y: set_int] :
% 0.33/0.67 ( ( if_set_int @ $false @ X @ Y )
% 0.33/0.67 = Y ) ).
% 0.33/0.67
% 0.33/0.67 thf(help_If_1_1_If_001t__Set__Oset_It__Int__Oint_J_T,axiom,
% 0.33/0.67 ! [X: set_int,Y: set_int] :
% 0.33/0.67 ( ( if_set_int @ $true @ X @ Y )
% 0.33/0.67 = X ) ).
% 0.33/0.67
% 0.33/0.67 thf(help_If_2_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
% 0.33/0.67 ! [X: list_int,Y: list_int] :
% 0.33/0.67 ( ( if_list_int @ $false @ X @ Y )
% 0.33/0.67 = Y ) ).
% 0.33/0.67
% 0.33/0.67 thf(help_If_1_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
% 0.33/0.67 ! [X: list_int,Y: list_int] :
% 0.33/0.67 ( ( if_list_int @ $true @ X @ Y )
% 0.33/0.67 = X ) ).
% 0.33/0.67
% 0.33/0.67 thf(help_If_2_1_If_001t__Option__Ooption_It__Num__Onum_J_T,axiom,
% 0.33/0.67 ! [X: option_num,Y: option_num] :
% 0.33/0.67 ( ( if_option_num @ $false @ X @ Y )
% 0.33/0.67 = Y ) ).
% 0.33/0.67
% 0.33/0.67 thf(help_If_1_1_If_001t__Option__Ooption_It__Num__Onum_J_T,axiom,
% 0.33/0.67 ! [X: option_num,Y: option_num] :
% 0.33/0.67 ( ( if_option_num @ $true @ X @ Y )
% 0.33/0.67 = X ) ).
% 0.33/0.67
% 0.33/0.67 thf(help_If_2_1_If_001t__Option__Ooption_It__Set__Oset_I_Eo_J_J_T,axiom,
% 0.33/0.67 ! [X: option_set_o,Y: option_set_o] :
% 0.33/0.67 ( ( if_option_set_o @ $false @ X @ Y )
% 0.33/0.67 = Y ) ).
% 0.33/0.67
% 0.33/0.67 thf(help_If_1_1_If_001t__Option__Ooption_It__Set__Oset_I_Eo_J_J_T,axiom,
% 0.33/0.67 ! [X: option_set_o,Y: option_set_o] :
% 0.33/0.67 ( ( if_option_set_o @ $true @ X @ Y )
% 0.33/0.67 = X ) ).
% 0.33/0.67
% 0.33/0.67 thf(help_If_2_1_If_001t__Option__Ooption_It__Product____Type__Ounit_J_T,axiom,
% 0.33/0.67 ! [X: option_Product_unit,Y: option_Product_unit] :
% 0.33/0.67 ( ( if_opt6227717841141446553t_unit @ $false @ X @ Y )
% 0.33/0.67 = Y ) ).
% 0.33/0.67
% 0.33/0.67 thf(help_If_1_1_If_001t__Option__Ooption_It__Product____Type__Ounit_J_T,axiom,
% 0.33/0.67 ! [X: option_Product_unit,Y: option_Product_unit] :
% 0.33/0.67 ( ( if_opt6227717841141446553t_unit @ $true @ X @ Y )
% 0.33/0.67 = X ) ).
% 0.33/0.67
% 0.33/0.67 thf(help_If_2_1_If_001t__Option__Ooption_It__Set__Oset_It__Int__Oint_J_J_T,axiom,
% 0.33/0.67 ! [X: option_set_int,Y: option_set_int] :
% 0.33/0.67 ( ( if_option_set_int @ $false @ X @ Y )
% 0.33/0.67 = Y ) ).
% 0.33/0.67
% 0.33/0.67 thf(help_If_1_1_If_001t__Option__Ooption_It__Set__Oset_It__Int__Oint_J_J_T,axiom,
% 0.33/0.67 ! [X: option_set_int,Y: option_set_int] :
% 0.33/0.67 ( ( if_option_set_int @ $true @ X @ Y )
% 0.33/0.67 = X ) ).
% 0.33/0.67
% 0.33/0.67 thf(help_If_2_1_If_001t__Option__Ooption_It__Set__Oset_It__Nat__Onat_J_J_T,axiom,
% 0.33/0.67 ! [X: option_set_nat,Y: option_set_nat] :
% 0.33/0.67 ( ( if_option_set_nat @ $false @ X @ Y )
% 0.33/0.67 = Y ) ).
% 0.33/0.67
% 0.33/0.67 thf(help_If_1_1_If_001t__Option__Ooption_It__Set__Oset_It__Nat__Onat_J_J_T,axiom,
% 0.33/0.67 ! [X: option_set_nat,Y: option_set_nat] :
% 0.33/0.67 ( ( if_option_set_nat @ $true @ X @ Y )
% 0.33/0.67 = X ) ).
% 0.33/0.67
% 0.33/0.67 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 0.33/0.67 ! [X: product_prod_int_int,Y: product_prod_int_int] :
% 0.33/0.67 ( ( if_Pro3027730157355071871nt_int @ $false @ X @ Y )
% 0.33/0.67 = Y ) ).
% 0.33/0.67
% 0.33/0.67 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 0.33/0.67 ! [X: product_prod_int_int,Y: product_prod_int_int] :
% 0.33/0.67 ( ( if_Pro3027730157355071871nt_int @ $true @ X @ Y )
% 0.33/0.67 = X ) ).
% 0.33/0.67
% 0.33/0.67 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 0.33/0.67 ! [X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 0.33/0.67 ( ( if_Pro6206227464963214023at_nat @ $false @ X @ Y )
% 0.33/0.67 = Y ) ).
% 0.33/0.67
% 0.33/0.67 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 0.33/0.67 ! [X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 0.33/0.67 ( ( if_Pro6206227464963214023at_nat @ $true @ X @ Y )
% 0.33/0.67 = X ) ).
% 0.33/0.67
% 0.33/0.67 thf(help_If_2_1_If_001t__Heap____Time____Monad__OHeap_It__Heap__Oarray_Itf__a_J_J_T,axiom,
% 0.33/0.67 ! [X: heap_T6362127782908069795rray_a,Y: heap_T6362127782908069795rray_a] :
% 0.33/0.67 ( ( if_Hea5896630067203373929rray_a @ $false @ X @ Y )
% 0.33/0.67 = Y ) ).
% 0.33/0.67
% 0.33/0.67 thf(help_If_1_1_If_001t__Heap____Time____Monad__OHeap_It__Heap__Oarray_Itf__a_J_J_T,axiom,
% 0.33/0.67 ! [X: heap_T6362127782908069795rray_a,Y: heap_T6362127782908069795rray_a] :
% 0.33/0.67 ( ( if_Hea5896630067203373929rray_a @ $true @ X @ Y )
% 0.33/0.67 = X ) ).
% 0.33/0.67
% 0.33/0.67 thf(help_If_2_1_If_001t__Heap____Time____Monad__OHeap_It__Product____Type__Ounit_J_T,axiom,
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% See solution above
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% 9.09/5.27 thf(ty_n_t__Set__Oset_It__Option__Ooption_It__Nat__Onat_J_J,type,
% 9.09/5.27 set_option_nat: $tType ).
% 9.09/5.27
% 9.09/5.27 thf(ty_n_t__Set__Oset_It__Option__Ooption_It__Int__Oint_J_J,type,
% 9.09/5.27 set_option_int: $tType ).
% 9.09/5.27
% 9.09/5.27 thf(ty_n_t__Option__Ooption_It__Set__Oset_It__Nat__Onat_J_J,type,
% 9.09/5.27 option_set_nat: $tType ).
% 9.09/5.27
% 9.09/5.27 thf(ty_n_t__Option__Ooption_It__Set__Oset_It__Int__Oint_J_J,type,
% 9.09/5.27 option_set_int: $tType ).
% 9.09/5.27
% 9.09/5.27 thf(ty_n_t__Option__Ooption_It__Code____Numeral__Ointeger_J,type,
% 9.09/5.27 option_Code_integer: $tType ).
% 9.09/5.27
% 9.09/5.27 thf(ty_n_t__Option__Ooption_It__Product____Type__Ounit_J,type,
% 9.09/5.27 option_Product_unit: $tType ).
% 9.09/5.27
% 9.09/5.27 thf(ty_n_t__Option__Ooption_I_062_It__Nat__Onat_M_Eo_J_J,type,
% 9.09/5.27 option_nat_o: $tType ).
% 9.09/5.27
% 9.09/5.27 thf(ty_n_t__Set__Oset_It__List__Olist_It__Nat__Onat_J_J,type,
% 9.09/5.27 set_list_nat: $tType ).
% 9.09/5.27
% 9.09/5.27 thf(ty_n_t__Product____Type__Oprod_It__Nat__Onat_M_Eo_J,type,
% 9.09/5.27 product_prod_nat_o: $tType ).
% 9.09/5.27
% 9.09/5.27 thf(ty_n_t__Product____Type__Oprod_It__Int__Oint_M_Eo_J,type,
% 9.09/5.27 product_prod_int_o: $tType ).
% 9.09/5.27
% 9.09/5.27 thf(ty_n_t__Product____Type__Oprod_I_Eo_Mt__Num__Onum_J,type,
% 9.09/5.27 product_prod_o_num: $tType ).
% 9.09/5.27
% 9.09/5.27 thf(ty_n_t__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J,type,
% 9.09/5.27 product_prod_o_nat: $tType ).
% 9.09/5.27
% 9.09/5.27 thf(ty_n_t__Product____Type__Oprod_I_Eo_Mt__Int__Oint_J,type,
% 9.09/5.27 product_prod_o_int: $tType ).
% 9.09/5.27
% 9.09/5.27 thf(ty_n_t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
% 9.09/5.27 set_set_nat: $tType ).
% 9.09/5.27
% 9.09/5.27 thf(ty_n_t__Set__Oset_It__Set__Oset_It__Int__Oint_J_J,type,
% 9.09/5.27 set_set_int: $tType ).
% 9.09/5.27
% 9.09/5.27 thf(ty_n_t__Set__Oset_It__Code____Numeral__Onatural_J,type,
% 9.09/5.27 set_Code_natural: $tType ).
% 9.09/5.27
% 9.09/5.27 thf(ty_n_t__Set__Oset_It__Code____Numeral__Ointeger_J,type,
% 9.09/5.27 set_Code_integer: $tType ).
% 9.09/5.27
% 9.09/5.27 thf(ty_n_t__Option__Ooption_It__Assertions__Oassn_J,type,
% 9.09/5.27 option_assn: $tType ).
% 9.09/5.27
% 9.09/5.27 thf(ty_n_t__Heap__Oref_It__Product____Type__Ounit_J,type,
% 9.09/5.27 ref_Product_unit: $tType ).
% 9.09/5.27
% 9.09/5.27 thf(ty_n_t__Set__Oset_It__Product____Type__Ounit_J,type,
% 9.09/5.27 set_Product_unit: $tType ).
% 9.09/5.27
% 9.09/5.27 thf(ty_n_t__Set__Oset_It__Option__Ooption_I_Eo_J_J,type,
% 9.09/5.27 set_option_o: $tType ).
% 9.09/5.27
% 9.09/5.27 thf(ty_n_t__Set__Oset_I_062_It__Nat__Onat_M_Eo_J_J,type,
% 9.09/5.27 set_nat_o: $tType ).
% 9.09/5.27
% 9.09/5.27 thf(ty_n_t__Option__Ooption_It__Set__Oset_I_Eo_J_J,type,
% 9.09/5.27 option_set_o: $tType ).
% 9.09/5.27
% 9.09/5.27 thf(ty_n_t__Heap__Oref_It__Heap__Oarray_Itf__a_J_J,type,
% 9.09/5.27 ref_array_a: $tType ).
% 9.09/5.27
% 9.09/5.27 thf(ty_n_t__Product____Type__Oprod_I_Eo_M_Eo_J,type,
% 9.09/5.27 product_prod_o_o: $tType ).
% 9.09/5.27
% 9.09/5.27 thf(ty_n_t__Set__Oset_It__Assertions__Oassn_J,type,
% 9.09/5.27 set_assn: $tType ).
% 9.09/5.27
% 9.09/5.27 thf(ty_n_t__Set__Oset_It__Set__Oset_I_Eo_J_J,type,
% 9.09/5.27 set_set_o: $tType ).
% 9.09/5.27
% 9.09/5.27 thf(ty_n_t__Option__Ooption_It__Rat__Orat_J,type,
% 9.09/5.27 option_rat: $tType ).
% 9.09/5.27
% 9.09/5.27 thf(ty_n_t__Option__Ooption_It__Num__Onum_J,type,
% 9.09/5.27 option_num: $tType ).
% 9.09/5.27
% 9.09/5.27 thf(ty_n_t__Option__Ooption_It__Nat__Onat_J,type,
% 9.09/5.27 option_nat: $tType ).
% 9.09/5.27
% 9.09/5.27 thf(ty_n_t__Option__Ooption_It__Int__Oint_J,type,
% 9.09/5.27 option_int: $tType ).
% 9.09/5.27
% 9.09/5.27 thf(ty_n_t__List__Olist_It__String__Ochar_J,type,
% 9.09/5.27 list_char: $tType ).
% 9.09/5.27
% 9.09/5.27 thf(ty_n_t__List__Olist_It__Nat__Onat_J,type,
% 9.09/5.27 list_nat: $tType ).
% 9.09/5.27
% 9.09/5.27 thf(ty_n_t__List__Olist_It__Int__Oint_J,type,
% 9.09/5.27 list_int: $tType ).
% 9.09/5.27
% 9.09/5.27 thf(ty_n_t__Set__Oset_It__Rat__Orat_J,type,
% 9.09/5.27 set_rat: $tType ).
% 9.09/5.27
% 9.09/5.27 thf(ty_n_t__Set__Oset_It__Num__Onum_J,type,
% 9.09/5.27 set_num: $tType ).
% 9.09/5.27
% 9.09/5.27 thf(ty_n_t__Set__Oset_It__Nat__Onat_J,type,
% 9.09/5.27 set_nat: $tType ).
% 9.09/5.27
% 9.09/5.27 thf(ty_n_t__Set__Oset_It__Int__Oint_J,type,
% 9.09/5.27 set_int: $tType ).
% 9.09/5.27
% 9.09/5.27 thf(ty_n_t__Code____Numeral__Onatural,type,
% 9.09/5.27 code_natural: $tType ).
% 9.09/5.27
% 9.09/5.27 thf(ty_n_t__Code____Numeral__Ointeger,type,
% 9.09/5.27 code_integer: $tType ).
% 9.09/5.27
% 9.09/5.27 thf(ty_n_t__Product____Type__Ounit,type,
% 9.09/5.27 product_unit: $tType ).
% 9.09/5.27
% 9.09/5.27 thf(ty_n_t__Option__Ooption_I_Eo_J,type,
% 9.09/5.27 option_o: $tType ).
% 9.09/5.27
% 9.09/5.27 thf(ty_n_t__Heap__Oarray_Itf__a_J,type,
% 9.09/5.27 array_a: $tType ).
% 9.09/5.27
% 9.09/5.27 thf(ty_n_t__List__Olist_Itf__a_J,type,
% 9.09/5.28 list_a: $tType ).
% 9.09/5.28
% 9.09/5.28 thf(ty_n_t__Typerep__Otyperep,type,
% 9.09/5.28 typerep: $tType ).
% 9.09/5.28
% 9.09/5.28 thf(ty_n_t__Assertions__Oassn,type,
% 9.09/5.28 assn: $tType ).
% 9.09/5.28
% 9.09/5.28 thf(ty_n_t__Set__Oset_I_Eo_J,type,
% 9.09/5.28 set_o: $tType ).
% 9.09/5.28
% 9.09/5.28 thf(ty_n_t__String__Ochar,type,
% 9.09/5.28 char: $tType ).
% 9.09/5.28
% 9.09/5.28 thf(ty_n_t__Rat__Orat,type,
% 9.09/5.28 rat: $tType ).
% 9.09/5.28
% 9.09/5.28 thf(ty_n_t__Num__Onum,type,
% 9.09/5.28 num: $tType ).
% 9.09/5.28
% 9.09/5.28 thf(ty_n_t__Nat__Onat,type,
% 9.09/5.28 nat: $tType ).
% 9.09/5.28
% 9.09/5.28 thf(ty_n_t__Int__Oint,type,
% 9.09/5.28 int: $tType ).
% 9.09/5.28
% 9.09/5.28 thf(ty_n_tf__a,type,
% 9.09/5.28 a: $tType ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Archimedean__Field_Oceiling_001t__Rat__Orat,type,
% 9.09/5.28 archim2889992004027027881ng_rat: rat > int ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Archimedean__Field_Ofloor__ceiling__class_Ofloor_001t__Rat__Orat,type,
% 9.09/5.28 archim3151403230148437115or_rat: rat > int ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Archimedean__Field_Ofrac_001t__Rat__Orat,type,
% 9.09/5.28 archimedean_frac_rat: rat > rat ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Archimedean__Field_Oround_001t__Rat__Orat,type,
% 9.09/5.28 archim7778729529865785530nd_rat: rat > int ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Array__Time_Omake_001tf__a,type,
% 9.09/5.28 array_make_a: nat > ( nat > a ) > heap_T6362127782908069795rray_a ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Array__Time_Onew_001tf__a,type,
% 9.09/5.28 array_new_a: nat > a > heap_T6362127782908069795rray_a ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Array__Time_Oof__list_001tf__a,type,
% 9.09/5.28 array_of_list_a: list_a > heap_T6362127782908069795rray_a ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Assertions_Oassn_ORep__assn,type,
% 9.09/5.28 rep_assn: assn > produc3658429121746597890et_nat > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Assertions_Oin__range,type,
% 9.09/5.28 in_range: produc3658429121746597890et_nat > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Assertions_Oin__range__rel,type,
% 9.09/5.28 in_range_rel: produc3658429121746597890et_nat > produc3658429121746597890et_nat > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Assertions_Oone__assn__raw,type,
% 9.09/5.28 one_assn_raw: produc3658429121746597890et_nat > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Assertions_Oone__assn__raw__rel,type,
% 9.09/5.28 one_assn_raw_rel: produc3658429121746597890et_nat > produc3658429121746597890et_nat > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Assertions_Oproper,type,
% 9.09/5.28 proper: ( produc3658429121746597890et_nat > $o ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Assertions_Opure__assn,type,
% 9.09/5.28 pure_assn: $o > assn ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Assertions_OrelH,type,
% 9.09/5.28 relH: set_nat > heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Assertions_Otimes__assn__raw,type,
% 9.09/5.28 times_assn_raw: ( produc3658429121746597890et_nat > $o ) > ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Assertions_Otimes__assn__raw__rel,type,
% 9.09/5.28 times_assn_raw_rel: produc2732055786443039994et_nat > produc2732055786443039994et_nat > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Assertions_Owand__assn,type,
% 9.09/5.28 wand_assn: assn > assn > assn ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Assertions_Owand__raw,type,
% 9.09/5.28 wand_raw: ( produc3658429121746597890et_nat > $o ) > ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Assertions_Owand__raw__rel,type,
% 9.09/5.28 wand_raw_rel: produc2732055786443039994et_nat > produc2732055786443039994et_nat > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Cardinal__Arithmetic_Octwo,type,
% 9.09/5.28 bNF_Cardinal_ctwo: set_Product_prod_o_o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Cardinal__Arithmetic_Oczero_001_Eo,type,
% 9.09/5.28 bNF_Cardinal_czero_o: set_Product_prod_o_o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Cardinal__Order__Relation_Ocard__of_001t__Nat__Onat,type,
% 9.09/5.28 bNF_Ca3793111618940312692of_nat: set_nat > set_Pr1261947904930325089at_nat ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Cardinal__Order__Relation_Ocard__order__on_001_Eo,type,
% 9.09/5.28 bNF_Ca8331644756375544342r_on_o: set_o > set_Product_prod_o_o > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Cardinal__Order__Relation_OnatLeq,type,
% 9.09/5.28 bNF_Ca8665028551170535155natLeq: set_Pr1261947904930325089at_nat ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001_062_I_062_It__Int__Oint_M_Eo_J_M_062_It__Int__Oint_M_Eo_J_J_001_062_I_062_It__Int__Oint_M_Eo_J_M_062_It__Int__Oint_M_Eo_J_J_001_062_I_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_M_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_J_001_062_I_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_M_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_J,type,
% 9.09/5.28 bNF_re2555365631850037877_int_o: ( ( ( int > $o ) > int > $o ) > ( ( int > $o ) > int > $o ) > $o ) > ( ( ( int > int > $o ) > int > int > $o ) > ( ( int > int > $o ) > int > int > $o ) > $o ) > ( ( ( int > $o ) > int > $o ) > ( int > int > $o ) > int > int > $o ) > ( ( ( int > $o ) > int > $o ) > ( int > int > $o ) > int > int > $o ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001_062_I_062_It__Int__Oint_M_Eo_J_M_062_It__Int__Oint_Mt__Int__Oint_J_J_001_062_I_062_It__Int__Oint_M_Eo_J_M_062_It__Int__Oint_Mt__Int__Oint_J_J_001_062_I_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_M_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J_J_001_062_I_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_M_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
% 9.09/5.28 bNF_re5051145820034318685nt_int: ( ( ( int > $o ) > int > int ) > ( ( int > $o ) > int > int ) > $o ) > ( ( ( int > int > $o ) > int > int > int ) > ( ( int > int > $o ) > int > int > int ) > $o ) > ( ( ( int > $o ) > int > int ) > ( int > int > $o ) > int > int > int ) > ( ( ( int > $o ) > int > int ) > ( int > int > $o ) > int > int > int ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001_062_I_062_It__Int__Oint_M_Eo_J_M_062_It__Nat__Onat_M_Eo_J_J_001_062_I_062_It__Int__Oint_M_Eo_J_M_062_It__Nat__Onat_M_Eo_J_J_001_062_I_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_M_062_It__Int__Oint_M_062_It__Nat__Onat_M_Eo_J_J_J_001_062_I_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_M_062_It__Int__Oint_M_062_It__Nat__Onat_M_Eo_J_J_J,type,
% 9.09/5.28 bNF_re615132412071444453_nat_o: ( ( ( int > $o ) > nat > $o ) > ( ( int > $o ) > nat > $o ) > $o ) > ( ( ( int > int > $o ) > int > nat > $o ) > ( ( int > int > $o ) > int > nat > $o ) > $o ) > ( ( ( int > $o ) > nat > $o ) > ( int > int > $o ) > int > nat > $o ) > ( ( ( int > $o ) > nat > $o ) > ( int > int > $o ) > int > nat > $o ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001_062_I_062_It__Int__Oint_Mt__Int__Oint_J_M_062_It__Int__Oint_M_Eo_J_J_001_062_I_062_It__Int__Oint_Mt__Int__Oint_J_M_062_It__Int__Oint_M_Eo_J_J_001_062_I_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J_M_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_J_001_062_I_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J_M_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_J,type,
% 9.09/5.28 bNF_re3161894838932316637_int_o: ( ( ( int > int ) > int > $o ) > ( ( int > int ) > int > $o ) > $o ) > ( ( ( int > int > int ) > int > int > $o ) > ( ( int > int > int ) > int > int > $o ) > $o ) > ( ( ( int > int ) > int > $o ) > ( int > int > int ) > int > int > $o ) > ( ( ( int > int ) > int > $o ) > ( int > int > int ) > int > int > $o ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001_062_I_062_It__Int__Oint_Mt__Int__Oint_J_M_062_It__Nat__Onat_M_Eo_J_J_001_062_I_062_It__Int__Oint_Mt__Int__Oint_J_M_062_It__Nat__Onat_M_Eo_J_J_001_062_I_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J_M_062_It__Int__Oint_M_062_It__Nat__Onat_M_Eo_J_J_J_001_062_I_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J_M_062_It__Int__Oint_M_062_It__Nat__Onat_M_Eo_J_J_J,type,
% 9.09/5.28 bNF_re4659646225794970589_nat_o: ( ( ( int > int ) > nat > $o ) > ( ( int > int ) > nat > $o ) > $o ) > ( ( ( int > int > int ) > int > nat > $o ) > ( ( int > int > int ) > int > nat > $o ) > $o ) > ( ( ( int > int ) > nat > $o ) > ( int > int > int ) > int > nat > $o ) > ( ( ( int > int ) > nat > $o ) > ( int > int > int ) > int > nat > $o ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001_062_I_062_It__Nat__Onat_M_Eo_J_M_062_It__Int__Oint_M_Eo_J_J_001_062_I_062_It__Nat__Onat_M_Eo_J_M_062_It__Int__Oint_M_Eo_J_J_001_062_I_062_It__Int__Oint_M_062_It__Nat__Onat_M_Eo_J_J_M_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_J_001_062_I_062_It__Int__Oint_M_062_It__Nat__Onat_M_Eo_J_J_M_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_J,type,
% 9.09/5.28 bNF_re3491090157995142405_int_o: ( ( ( nat > $o ) > int > $o ) > ( ( nat > $o ) > int > $o ) > $o ) > ( ( ( int > nat > $o ) > int > int > $o ) > ( ( int > nat > $o ) > int > int > $o ) > $o ) > ( ( ( nat > $o ) > int > $o ) > ( int > nat > $o ) > int > int > $o ) > ( ( ( nat > $o ) > int > $o ) > ( int > nat > $o ) > int > int > $o ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001_062_I_062_It__Nat__Onat_M_Eo_J_M_062_It__Int__Oint_Mt__Int__Oint_J_J_001_062_I_062_It__Nat__Onat_M_Eo_J_M_062_It__Int__Oint_Mt__Int__Oint_J_J_001_062_I_062_It__Int__Oint_M_062_It__Nat__Onat_M_Eo_J_J_M_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J_J_001_062_I_062_It__Int__Oint_M_062_It__Nat__Onat_M_Eo_J_J_M_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
% 9.09/5.28 bNF_re5539255234643219293nt_int: ( ( ( nat > $o ) > int > int ) > ( ( nat > $o ) > int > int ) > $o ) > ( ( ( int > nat > $o ) > int > int > int ) > ( ( int > nat > $o ) > int > int > int ) > $o ) > ( ( ( nat > $o ) > int > int ) > ( int > nat > $o ) > int > int > int ) > ( ( ( nat > $o ) > int > int ) > ( int > nat > $o ) > int > int > int ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001_062_I_062_It__Nat__Onat_M_Eo_J_M_062_It__Nat__Onat_M_Eo_J_J_001_062_I_062_It__Nat__Onat_M_Eo_J_M_062_It__Nat__Onat_M_Eo_J_J_001_062_I_062_It__Int__Oint_M_062_It__Nat__Onat_M_Eo_J_J_M_062_It__Int__Oint_M_062_It__Nat__Onat_M_Eo_J_J_J_001_062_I_062_It__Int__Oint_M_062_It__Nat__Onat_M_Eo_J_J_M_062_It__Int__Oint_M_062_It__Nat__Onat_M_Eo_J_J_J,type,
% 9.09/5.28 bNF_re1550856938216548981_nat_o: ( ( ( nat > $o ) > nat > $o ) > ( ( nat > $o ) > nat > $o ) > $o ) > ( ( ( int > nat > $o ) > int > nat > $o ) > ( ( int > nat > $o ) > int > nat > $o ) > $o ) > ( ( ( nat > $o ) > nat > $o ) > ( int > nat > $o ) > int > nat > $o ) > ( ( ( nat > $o ) > nat > $o ) > ( int > nat > $o ) > int > nat > $o ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Code____Numeral__Ointeger_M_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_J_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001_062_I_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_M_062_It__Code____Numeral__Ointeger_M_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_J_J_001_062_I_062_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_M_062_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_J,type,
% 9.09/5.28 bNF_re4919612610145136063nteger: ( ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer ) > $o ) > ( ( ( code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( ( num > code_integer ) > num > code_integer ) > $o ) > ( ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( ( code_integer > code_integer ) > ( num > code_integer ) > num > code_integer ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Code____Numeral__Ointeger_M_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_J_001_062_It__Nat__Onat_Mt__Num__Onum_J_001_062_I_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_M_062_It__Code____Numeral__Ointeger_M_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_J_J_001_062_I_062_It__Int__Oint_Mt__Nat__Onat_J_M_062_It__Int__Oint_Mt__Num__Onum_J_J,type,
% 9.09/5.28 bNF_re1890273300020150979nt_num: ( ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( nat > num ) > $o ) > ( ( ( code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( ( int > nat ) > int > num ) > $o ) > ( ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( ( nat > num ) > ( int > nat ) > int > num ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001_062_It__Code____Numeral__Ointeger_M_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_J_001_062_I_062_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_M_062_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_J_001_062_I_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_M_062_It__Code____Numeral__Ointeger_M_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_J_J,type,
% 9.09/5.28 bNF_re8134695817916415679nteger: ( ( code_integer > code_integer ) > ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > $o ) > ( ( ( num > code_integer ) > num > code_integer ) > ( ( code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > $o ) > ( ( code_integer > code_integer ) > ( num > code_integer ) > num > code_integer ) > ( ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001_062_I_062_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_M_062_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_J_001_062_I_062_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_M_062_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_J,type,
% 9.09/5.28 bNF_re5979881370344185769nteger: ( ( code_integer > code_integer ) > ( code_integer > code_integer ) > $o ) > ( ( ( num > code_integer ) > num > code_integer ) > ( ( num > code_integer ) > num > code_integer ) > $o ) > ( ( code_integer > code_integer ) > ( num > code_integer ) > num > code_integer ) > ( ( code_integer > code_integer ) > ( num > code_integer ) > num > code_integer ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_It__Code____Numeral__Ointeger_M_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_J_001_062_It__Int__Oint_Mt__Num__Onum_J,type,
% 9.09/5.28 bNF_re5190287125156074331nt_num: ( ( code_integer > code_integer ) > ( int > nat ) > $o ) > ( ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( int > num ) > $o ) > ( ( code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( ( int > nat ) > int > num ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001_062_It__Nat__Onat_Mt__Num__Onum_J_001_062_I_062_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_M_062_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_J_001_062_I_062_It__Int__Oint_Mt__Nat__Onat_J_M_062_It__Int__Oint_Mt__Num__Onum_J_J,type,
% 9.09/5.28 bNF_re5469402333911078061nt_num: ( ( code_integer > code_integer ) > ( nat > num ) > $o ) > ( ( ( num > code_integer ) > num > code_integer ) > ( ( int > nat ) > int > num ) > $o ) > ( ( code_integer > code_integer ) > ( num > code_integer ) > num > code_integer ) > ( ( nat > num ) > ( int > nat ) > int > num ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001_062_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_001_062_It__Code____Numeral__Ointeger_M_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_J_001_062_It__Num__Onum_Mt__Code____Numeral__Ointeger_J,type,
% 9.09/5.28 bNF_re6724329528997265415nteger: ( ( code_integer > code_integer ) > ( num > code_integer ) > $o ) > ( ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( num > code_integer ) > $o ) > ( ( code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( ( num > code_integer ) > num > code_integer ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_001_062_I_062_It__Int__Oint_Mt__Int__Oint_J_M_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_J_001_062_I_062_It__Int__Oint_Mt__Int__Oint_J_M_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_J,type,
% 9.09/5.28 bNF_re1900612664124570461_int_o: ( ( int > int > $o ) > ( int > int > $o ) > $o ) > ( ( ( int > int ) > int > int > $o ) > ( ( int > int ) > int > int > $o ) > $o ) > ( ( int > int > $o ) > ( int > int ) > int > int > $o ) > ( ( int > int > $o ) > ( int > int ) > int > int > $o ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J,type,
% 9.09/5.28 bNF_re8651060166502312541_int_o: ( ( int > int > $o ) > ( int > int > $o ) > $o ) > ( ( int > int > $o ) > ( int > int > $o ) > $o ) > ( ( int > int > $o ) > int > int > $o ) > ( ( int > int > $o ) > int > int > $o ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_001_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J,type,
% 9.09/5.28 bNF_re7462748251485907171nt_int: ( ( int > int > $o ) > ( int > int > $o ) > $o ) > ( ( int > int > int ) > ( int > int > int ) > $o ) > ( ( int > int > $o ) > int > int > int ) > ( ( int > int > $o ) > int > int > int ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_001_062_It__Int__Oint_M_062_It__Nat__Onat_M_Eo_J_J_001_062_It__Int__Oint_M_062_It__Nat__Onat_M_Eo_J_J,type,
% 9.09/5.28 bNF_re2446162618891206493_nat_o: ( ( int > int > $o ) > ( int > int > $o ) > $o ) > ( ( int > nat > $o ) > ( int > nat > $o ) > $o ) > ( ( int > int > $o ) > int > nat > $o ) > ( ( int > int > $o ) > int > nat > $o ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J_001_062_I_062_It__Int__Oint_Mt__Int__Oint_J_M_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J_J_001_062_I_062_It__Int__Oint_Mt__Int__Oint_J_M_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
% 9.09/5.28 bNF_re4984751527058004117nt_int: ( ( int > int > int ) > ( int > int > int ) > $o ) > ( ( ( int > int ) > int > int > int ) > ( ( int > int ) > int > int > int ) > $o ) > ( ( int > int > int ) > ( int > int ) > int > int > int ) > ( ( int > int > int ) > ( int > int ) > int > int > int ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J,type,
% 9.09/5.28 bNF_re1313934062736347107_int_o: ( ( int > int > int ) > ( int > int > int ) > $o ) > ( ( int > int > $o ) > ( int > int > $o ) > $o ) > ( ( int > int > int ) > int > int > $o ) > ( ( int > int > int ) > int > int > $o ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Int__Oint_M_062_It__Nat__Onat_M_Eo_J_J_001_062_It__Int__Oint_M_062_It__Nat__Onat_M_Eo_J_J,type,
% 9.09/5.28 bNF_re4332408551980016867_nat_o: ( ( int > int > int ) > ( int > int > int ) > $o ) > ( ( int > nat > $o ) > ( int > nat > $o ) > $o ) > ( ( int > int > int ) > int > nat > $o ) > ( ( int > int > int ) > int > nat > $o ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J_001_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Rat__Orat_J_J_001_062_I_062_It__Int__Oint_Mt__Int__Oint_J_M_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J_J_001_062_I_062_It__Int__Oint_Mt__Int__Oint_J_M_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Rat__Orat_J_J_J,type,
% 9.09/5.28 bNF_re62019127700022579nt_rat: ( ( int > int > product_prod_int_int ) > ( int > int > rat ) > $o ) > ( ( ( int > int ) > int > int > product_prod_int_int ) > ( ( int > int ) > int > int > rat ) > $o ) > ( ( int > int > product_prod_int_int ) > ( int > int ) > int > int > product_prod_int_int ) > ( ( int > int > rat ) > ( int > int ) > int > int > rat ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_M_062_It__Nat__Onat_M_Eo_J_J_001_062_It__Int__Oint_M_062_It__Nat__Onat_M_Eo_J_J_001_062_I_062_It__Int__Oint_Mt__Int__Oint_J_M_062_It__Int__Oint_M_062_It__Nat__Onat_M_Eo_J_J_J_001_062_I_062_It__Int__Oint_Mt__Int__Oint_J_M_062_It__Int__Oint_M_062_It__Nat__Onat_M_Eo_J_J_J,type,
% 9.09/5.28 bNF_re7908124382625962333_nat_o: ( ( int > nat > $o ) > ( int > nat > $o ) > $o ) > ( ( ( int > int ) > int > nat > $o ) > ( ( int > int ) > int > nat > $o ) > $o ) > ( ( int > nat > $o ) > ( int > int ) > int > nat > $o ) > ( ( int > nat > $o ) > ( int > int ) > int > nat > $o ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_M_062_It__Nat__Onat_M_Eo_J_J_001_062_It__Int__Oint_M_062_It__Nat__Onat_M_Eo_J_J_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J,type,
% 9.09/5.28 bNF_re2655111580231008093_int_o: ( ( int > nat > $o ) > ( int > nat > $o ) > $o ) > ( ( int > int > $o ) > ( int > int > $o ) > $o ) > ( ( int > nat > $o ) > int > int > $o ) > ( ( int > nat > $o ) > int > int > $o ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_M_062_It__Nat__Onat_M_Eo_J_J_001_062_It__Int__Oint_M_062_It__Nat__Onat_M_Eo_J_J_001_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J,type,
% 9.09/5.28 bNF_re7395152722673581539nt_int: ( ( int > nat > $o ) > ( int > nat > $o ) > $o ) > ( ( int > int > int ) > ( int > int > int ) > $o ) > ( ( int > nat > $o ) > int > int > int ) > ( ( int > nat > $o ) > int > int > int ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_M_062_It__Nat__Onat_M_Eo_J_J_001_062_It__Int__Oint_M_062_It__Nat__Onat_M_Eo_J_J_001_062_It__Int__Oint_M_062_It__Nat__Onat_M_Eo_J_J_001_062_It__Int__Oint_M_062_It__Nat__Onat_M_Eo_J_J,type,
% 9.09/5.28 bNF_re5673586069474677853_nat_o: ( ( int > nat > $o ) > ( int > nat > $o ) > $o ) > ( ( int > nat > $o ) > ( int > nat > $o ) > $o ) > ( ( int > nat > $o ) > int > nat > $o ) > ( ( int > nat > $o ) > int > nat > $o ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_M_Eo_J_001_062_It__Int__Oint_M_Eo_J_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Nat__Onat_M_Eo_J,type,
% 9.09/5.28 bNF_re2535741173671728349_nat_o: ( ( int > $o ) > ( int > $o ) > $o ) > ( ( nat > $o ) > ( nat > $o ) > $o ) > ( ( int > $o ) > nat > $o ) > ( ( int > $o ) > nat > $o ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J,type,
% 9.09/5.28 bNF_re3014639844587090765_int_o: ( ( int > int ) > ( int > int ) > $o ) > ( ( int > int > $o ) > ( int > int > $o ) > $o ) > ( ( int > int ) > int > int > $o ) > ( ( int > int ) > int > int > $o ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J,type,
% 9.09/5.28 bNF_re724639330072410579nt_int: ( ( int > int ) > ( int > int ) > $o ) > ( ( int > int > int ) > ( int > int > int ) > $o ) > ( ( int > int ) > int > int > int ) > ( ( int > int ) > int > int > int ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J_001_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Rat__Orat_J_J,type,
% 9.09/5.28 bNF_re949775918795716016nt_rat: ( ( int > int ) > ( int > int ) > $o ) > ( ( int > int > product_prod_int_int ) > ( int > int > rat ) > $o ) > ( ( int > int ) > int > int > product_prod_int_int ) > ( ( int > int ) > int > int > rat ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Int__Oint_M_062_It__Nat__Onat_M_Eo_J_J_001_062_It__Int__Oint_M_062_It__Nat__Onat_M_Eo_J_J,type,
% 9.09/5.28 bNF_re6033114333830760525_nat_o: ( ( int > int ) > ( int > int ) > $o ) > ( ( int > nat > $o ) > ( int > nat > $o ) > $o ) > ( ( int > int ) > int > nat > $o ) > ( ( int > int ) > int > nat > $o ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_It__Int__Oint_Mt__Num__Onum_J_001_062_It__Int__Oint_Mt__Num__Onum_J,type,
% 9.09/5.28 bNF_re9099949428469764705nt_num: ( ( int > nat ) > ( int > nat ) > $o ) > ( ( int > num ) > ( int > num ) > $o ) > ( ( int > nat ) > int > num ) > ( ( int > nat ) > int > num ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_001_062_It__Int__Oint_Mt__Num__Onum_J_001_062_It__Num__Onum_Mt__Code____Numeral__Ointeger_J,type,
% 9.09/5.28 bNF_re8894579221946749965nteger: ( ( int > nat ) > ( num > code_integer ) > $o ) > ( ( int > num ) > ( num > code_integer ) > $o ) > ( ( int > nat ) > int > num ) > ( ( num > code_integer ) > num > code_integer ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Int__Oint_M_Eo_J_001_062_It__Int__Oint_M_Eo_J,type,
% 9.09/5.28 bNF_re2724346968851715293_int_o: ( ( nat > $o ) > ( nat > $o ) > $o ) > ( ( int > $o ) > ( int > $o ) > $o ) > ( ( nat > $o ) > int > $o ) > ( ( nat > $o ) > int > $o ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Int__Oint_Mt__Int__Oint_J,type,
% 9.09/5.28 bNF_re7183634743573646861nt_int: ( ( nat > $o ) > ( nat > $o ) > $o ) > ( ( int > int ) > ( int > int ) > $o ) > ( ( nat > $o ) > int > int ) > ( ( nat > $o ) > int > int ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Nat__Onat_M_Eo_J,type,
% 9.09/5.28 bNF_re2697311982885662685_nat_o: ( ( nat > $o ) > ( nat > $o ) > $o ) > ( ( nat > $o ) > ( nat > $o ) > $o ) > ( ( nat > $o ) > nat > $o ) > ( ( nat > $o ) > nat > $o ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Nat__Onat_Mt__Num__Onum_J_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001_062_I_062_It__Int__Oint_Mt__Nat__Onat_J_M_062_It__Int__Oint_Mt__Num__Onum_J_J_001_062_I_062_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_M_062_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_J,type,
% 9.09/5.28 bNF_re2163612987331707565nteger: ( ( nat > num ) > ( code_integer > code_integer ) > $o ) > ( ( ( int > nat ) > int > num ) > ( ( num > code_integer ) > num > code_integer ) > $o ) > ( ( nat > num ) > ( int > nat ) > int > num ) > ( ( code_integer > code_integer ) > ( num > code_integer ) > num > code_integer ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Nat__Onat_Mt__Num__Onum_J_001_062_It__Nat__Onat_Mt__Num__Onum_J_001_062_I_062_It__Int__Oint_Mt__Nat__Onat_J_M_062_It__Int__Oint_Mt__Num__Onum_J_J_001_062_I_062_It__Int__Oint_Mt__Nat__Onat_J_M_062_It__Int__Oint_Mt__Num__Onum_J_J,type,
% 9.09/5.28 bNF_re3846787885862361009nt_num: ( ( nat > num ) > ( nat > num ) > $o ) > ( ( ( int > nat ) > int > num ) > ( ( int > nat ) > int > num ) > $o ) > ( ( nat > num ) > ( int > nat ) > int > num ) > ( ( nat > num ) > ( int > nat ) > int > num ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001_062_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_001_062_It__Code____Numeral__Ointeger_M_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_J,type,
% 9.09/5.28 bNF_re2439920061672227847nteger: ( ( num > code_integer ) > ( code_integer > code_integer ) > $o ) > ( ( num > code_integer ) > ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > $o ) > ( ( num > code_integer ) > num > code_integer ) > ( ( code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_001_062_It__Int__Oint_Mt__Num__Onum_J,type,
% 9.09/5.28 bNF_re1151383970801924621nt_num: ( ( num > code_integer ) > ( int > nat ) > $o ) > ( ( num > code_integer ) > ( int > num ) > $o ) > ( ( num > code_integer ) > num > code_integer ) > ( ( int > nat ) > int > num ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_001_062_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_001_062_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_001_062_It__Num__Onum_Mt__Code____Numeral__Ointeger_J,type,
% 9.09/5.28 bNF_re6097285183634142137nteger: ( ( num > code_integer ) > ( num > code_integer ) > $o ) > ( ( num > code_integer ) > ( num > code_integer ) > $o ) > ( ( num > code_integer ) > num > code_integer ) > ( ( num > code_integer ) > num > code_integer ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001_Eo_001_Eo_001t__Int__Oint_001t__Nat__Onat,type,
% 9.09/5.28 bNF_re1551779926989065179nt_nat: ( $o > $o > $o ) > ( int > nat > $o ) > ( $o > int ) > ( $o > nat ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001_Eo_001_Eo_001t__Int__Oint_001t__Rat__Orat,type,
% 9.09/5.28 bNF_re916649866902569443nt_rat: ( $o > $o > $o ) > ( int > rat > $o ) > ( $o > int ) > ( $o > rat ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001_Eo_001_Eo_001t__Nat__Onat_001t__Code____Numeral__Ointeger,type,
% 9.09/5.28 bNF_re4863541036035986956nteger: ( $o > $o > $o ) > ( nat > code_integer > $o ) > ( $o > nat ) > ( $o > code_integer ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001_Eo_001_Eo_001t__Nat__Onat_001t__Int__Oint,type,
% 9.09/5.28 bNF_re549935744578960347at_int: ( $o > $o > $o ) > ( nat > int > $o ) > ( $o > nat ) > ( $o > int ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001_Eo_001_Eo_001t__Nat__Onat_001t__Nat__Onat,type,
% 9.09/5.28 bNF_re552426215088010623at_nat: ( $o > $o > $o ) > ( nat > nat > $o ) > ( $o > nat ) > ( $o > nat ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001_Eo_001_Eo_001t__Nat__Onat_001t__Rat__Orat,type,
% 9.09/5.28 bNF_re9140668191856290695at_rat: ( $o > $o > $o ) > ( nat > rat > $o ) > ( $o > nat ) > ( $o > rat ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001_Eo_001_Eo_001t__Rat__Orat_001t__Code____Numeral__Ointeger,type,
% 9.09/5.28 bNF_re5635613845597506580nteger: ( $o > $o > $o ) > ( rat > code_integer > $o ) > ( $o > rat ) > ( $o > code_integer ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001_Eo_001_Eo_001t__Rat__Orat_001t__Int__Oint,type,
% 9.09/5.28 bNF_re233381100644094435at_int: ( $o > $o > $o ) > ( rat > int > $o ) > ( $o > rat ) > ( $o > int ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001_Eo_001_Eo_001t__Rat__Orat_001t__Nat__Onat,type,
% 9.09/5.28 bNF_re235871571153144711at_nat: ( $o > $o > $o ) > ( rat > nat > $o ) > ( $o > rat ) > ( $o > nat ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001_Eo_001_Eo_001t__Rat__Orat_001t__Rat__Orat,type,
% 9.09/5.28 bNF_re8824113547921424783at_rat: ( $o > $o > $o ) > ( rat > rat > $o ) > ( $o > rat ) > ( $o > rat ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Assertions__Oassn_001t__Assertions__Oassn_001_062_It__Assertions__Oassn_Mt__Assertions__Oassn_J_001_062_It__Assertions__Oassn_Mt__Assertions__Oassn_J,type,
% 9.09/5.28 bNF_re9137223911888007311n_assn: ( assn > assn > $o ) > ( ( assn > assn ) > ( assn > assn ) > $o ) > ( assn > assn > assn ) > ( assn > assn > assn ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Assertions__Oassn_001t__Assertions__Oassn_001_062_It__Nat__Onat_Mt__Assertions__Oassn_J_001_062_It__Nat__Onat_Mt__Assertions__Oassn_J,type,
% 9.09/5.28 bNF_re3650450707543776735t_assn: ( assn > assn > $o ) > ( ( nat > assn ) > ( nat > assn ) > $o ) > ( assn > nat > assn ) > ( assn > nat > assn ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Assertions__Oassn_001t__Assertions__Oassn_001t__Assertions__Oassn_001t__Assertions__Oassn,type,
% 9.09/5.28 bNF_re1143782165119297793n_assn: ( assn > assn > $o ) > ( assn > assn > $o ) > ( assn > assn ) > ( assn > assn ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Assertions__Oassn_001t__Code____Numeral__Ointeger_001_062_It__Assertions__Oassn_Mt__Assertions__Oassn_J_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 9.09/5.28 bNF_re5822757241383739566nteger: ( assn > code_integer > $o ) > ( ( assn > assn ) > ( code_integer > code_integer ) > $o ) > ( assn > assn > assn ) > ( code_integer > code_integer > code_integer ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Assertions__Oassn_001t__Code____Numeral__Ointeger_001_062_It__Nat__Onat_Mt__Assertions__Oassn_J_001_062_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J,type,
% 9.09/5.28 bNF_re2102180915162216137nteger: ( assn > code_integer > $o ) > ( ( nat > assn ) > ( nat > code_integer ) > $o ) > ( assn > nat > assn ) > ( code_integer > nat > code_integer ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Assertions__Oassn_001t__Code____Numeral__Ointeger_001t__Assertions__Oassn_001t__Code____Numeral__Ointeger,type,
% 9.09/5.28 bNF_re4134162077946812779nteger: ( assn > code_integer > $o ) > ( assn > code_integer > $o ) > ( assn > assn ) > ( code_integer > code_integer ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Assertions__Oassn_001t__Int__Oint_001_062_It__Assertions__Oassn_Mt__Assertions__Oassn_J_001_062_It__Int__Oint_Mt__Int__Oint_J,type,
% 9.09/5.28 bNF_re7882741803053012379nt_int: ( assn > int > $o ) > ( ( assn > assn ) > ( int > int ) > $o ) > ( assn > assn > assn ) > ( int > int > int ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Assertions__Oassn_001t__Int__Oint_001_062_It__Nat__Onat_Mt__Assertions__Oassn_J_001_062_It__Nat__Onat_Mt__Int__Oint_J,type,
% 9.09/5.28 bNF_re185025794348816359at_int: ( assn > int > $o ) > ( ( nat > assn ) > ( nat > int ) > $o ) > ( assn > nat > assn ) > ( int > nat > int ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Assertions__Oassn_001t__Int__Oint_001t__Assertions__Oassn_001t__Int__Oint,type,
% 9.09/5.28 bNF_re2927800259774540553sn_int: ( assn > int > $o ) > ( assn > int > $o ) > ( assn > assn ) > ( int > int ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Assertions__Oassn_001t__Nat__Onat_001_062_It__Assertions__Oassn_Mt__Assertions__Oassn_J_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 9.09/5.28 bNF_re4386305596031132807at_nat: ( assn > nat > $o ) > ( ( assn > assn ) > ( nat > nat ) > $o ) > ( assn > assn > assn ) > ( nat > nat > nat ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Assertions__Oassn_001t__Nat__Onat_001_062_It__Nat__Onat_Mt__Assertions__Oassn_J_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 9.09/5.28 bNF_re8560028565313717551at_nat: ( assn > nat > $o ) > ( ( nat > assn ) > ( nat > nat ) > $o ) > ( assn > nat > assn ) > ( nat > nat > nat ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Assertions__Oassn_001t__Nat__Onat_001t__Assertions__Oassn_001t__Nat__Onat,type,
% 9.09/5.28 bNF_re6742580585434904145sn_nat: ( assn > nat > $o ) > ( assn > nat > $o ) > ( assn > assn ) > ( nat > nat ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Assertions__Oassn_001t__Rat__Orat_001_062_It__Assertions__Oassn_Mt__Assertions__Oassn_J_001_062_It__Rat__Orat_Mt__Rat__Orat_J,type,
% 9.09/5.28 bNF_re967558844708792991at_rat: ( assn > rat > $o ) > ( ( assn > assn ) > ( rat > rat ) > $o ) > ( assn > assn > assn ) > ( rat > rat > rat ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Assertions__Oassn_001t__Rat__Orat_001_062_It__Nat__Onat_Mt__Assertions__Oassn_J_001_062_It__Nat__Onat_Mt__Rat__Orat_J,type,
% 9.09/5.28 bNF_re6138836914430330175at_rat: ( assn > rat > $o ) > ( ( nat > assn ) > ( nat > rat ) > $o ) > ( assn > nat > assn ) > ( rat > nat > rat ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Assertions__Oassn_001t__Rat__Orat_001t__Assertions__Oassn_001t__Rat__Orat,type,
% 9.09/5.28 bNF_re9003240792272343649sn_rat: ( assn > rat > $o ) > ( assn > rat > $o ) > ( assn > assn ) > ( rat > rat ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Code____Numeral__Ointeger_001t__Assertions__Oassn_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001_062_It__Assertions__Oassn_Mt__Assertions__Oassn_J,type,
% 9.09/5.28 bNF_re7789648203153440174n_assn: ( code_integer > assn > $o ) > ( ( code_integer > code_integer ) > ( assn > assn ) > $o ) > ( code_integer > code_integer > code_integer ) > ( assn > assn > assn ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Code____Numeral__Ointeger_001t__Assertions__Oassn_001_062_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J_001_062_It__Nat__Onat_Mt__Assertions__Oassn_J,type,
% 9.09/5.28 bNF_re2546461910754330953t_assn: ( code_integer > assn > $o ) > ( ( nat > code_integer ) > ( nat > assn ) > $o ) > ( code_integer > nat > code_integer ) > ( assn > nat > assn ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Code____Numeral__Ointeger_001t__Assertions__Oassn_001t__Code____Numeral__Ointeger_001t__Assertions__Oassn,type,
% 9.09/5.28 bNF_re1475883931861434731r_assn: ( code_integer > assn > $o ) > ( code_integer > assn > $o ) > ( code_integer > code_integer ) > ( assn > assn ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 9.09/5.28 bNF_re122555440370955213nteger: ( code_integer > code_integer > $o ) > ( ( code_integer > code_integer ) > ( code_integer > code_integer ) > $o ) > ( code_integer > code_integer > code_integer ) > ( code_integer > code_integer > code_integer ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001_062_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J_001_062_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J,type,
% 9.09/5.28 bNF_re5462749793222359603nteger: ( code_integer > code_integer > $o ) > ( ( nat > code_integer ) > ( nat > code_integer ) > $o ) > ( code_integer > nat > code_integer ) > ( code_integer > nat > code_integer ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Code____Numeral__Ointeger_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,
% 9.09/5.28 bNF_re4341081746073172381nteger: ( code_integer > code_integer > $o ) > ( ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > code_integer > $o ) > ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_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,type,
% 9.09/5.28 bNF_re3370092614548195229nteger: ( code_integer > code_integer > $o ) > ( code_integer > ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > $o ) > ( code_integer > code_integer ) > ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 9.09/5.28 bNF_re1062419521925302741nteger: ( code_integer > code_integer > $o ) > ( code_integer > code_integer > $o ) > ( code_integer > code_integer ) > ( code_integer > code_integer ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Code____Numeral__Ointeger_001t__Int__Oint_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001_062_It__Int__Oint_Mt__Int__Oint_J,type,
% 9.09/5.28 bNF_re8304916493157054650nt_int: ( code_integer > int > $o ) > ( ( code_integer > code_integer ) > ( int > int ) > $o ) > ( code_integer > code_integer > code_integer ) > ( int > int > int ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Code____Numeral__Ointeger_001t__Int__Oint_001_062_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J_001_062_It__Nat__Onat_Mt__Int__Oint_J,type,
% 9.09/5.28 bNF_re6766650671887726929at_int: ( code_integer > int > $o ) > ( ( nat > code_integer ) > ( nat > int ) > $o ) > ( code_integer > nat > code_integer ) > ( int > nat > int ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Code____Numeral__Ointeger_001t__Int__Oint_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__Num__Onum,type,
% 9.09/5.28 bNF_re8127238762813979689er_num: ( code_integer > int > $o ) > ( ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > num > $o ) > ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( int > num ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Code____Numeral__Ointeger_001t__Int__Oint_001t__Code____Numeral__Ointeger_001t__Int__Oint,type,
% 9.09/5.28 bNF_re2888858428391045491er_int: ( code_integer > int > $o ) > ( code_integer > int > $o ) > ( code_integer > code_integer ) > ( int > int ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Code____Numeral__Ointeger_001t__Int__Oint_001t__Code____Numeral__Ointeger_001t__Nat__Onat,type,
% 9.09/5.28 bNF_re2891348898900095767er_nat: ( code_integer > int > $o ) > ( code_integer > nat > $o ) > ( code_integer > code_integer ) > ( int > nat ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Code____Numeral__Ointeger_001t__Nat__Onat_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 9.09/5.28 bNF_re3981674901896804262at_nat: ( code_integer > nat > $o ) > ( ( code_integer > code_integer ) > ( nat > nat ) > $o ) > ( code_integer > code_integer > code_integer ) > ( nat > nat > nat ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Code____Numeral__Ointeger_001t__Nat__Onat_001_062_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 9.09/5.28 bNF_re4269568176766901913at_nat: ( code_integer > nat > $o ) > ( ( nat > code_integer ) > ( nat > nat ) > $o ) > ( code_integer > nat > code_integer ) > ( nat > nat > nat ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Code____Numeral__Ointeger_001t__Nat__Onat_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__Num__Onum,type,
% 9.09/5.28 bNF_re7119966052990372301er_num: ( code_integer > nat > $o ) > ( ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > num > $o ) > ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( nat > num ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Code____Numeral__Ointeger_001t__Nat__Onat_001t__Code____Numeral__Ointeger_001t__Nat__Onat,type,
% 9.09/5.28 bNF_re5201166830993046715er_nat: ( code_integer > nat > $o ) > ( code_integer > nat > $o ) > ( code_integer > code_integer ) > ( nat > nat ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Code____Numeral__Ointeger_001t__Nat__Onat_001t__Code____Numeral__Ointeger_001t__Num__Onum,type,
% 9.09/5.28 bNF_re1758498617148825349er_num: ( code_integer > nat > $o ) > ( code_integer > num > $o ) > ( code_integer > code_integer ) > ( nat > num ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Code____Numeral__Ointeger_001t__Num__Onum_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,
% 9.09/5.28 bNF_re166502229267952730nteger: ( code_integer > num > $o ) > ( ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > code_integer > $o ) > ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( num > code_integer ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Code____Numeral__Ointeger_001t__Num__Onum_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 9.09/5.28 bNF_re7350422212947406738nteger: ( code_integer > num > $o ) > ( code_integer > code_integer > $o ) > ( code_integer > code_integer ) > ( num > code_integer ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Code____Numeral__Ointeger_001t__Rat__Orat_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001_062_It__Rat__Orat_Mt__Rat__Orat_J,type,
% 9.09/5.28 bNF_re2976496150901874110at_rat: ( code_integer > rat > $o ) > ( ( code_integer > code_integer ) > ( rat > rat ) > $o ) > ( code_integer > code_integer > code_integer ) > ( rat > rat > rat ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Code____Numeral__Ointeger_001t__Rat__Orat_001_062_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J_001_062_It__Nat__Onat_Mt__Rat__Orat_J,type,
% 9.09/5.28 bNF_re1167376069379428009at_rat: ( code_integer > rat > $o ) > ( ( nat > code_integer ) > ( nat > rat ) > $o ) > ( code_integer > nat > code_integer ) > ( rat > nat > rat ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Code____Numeral__Ointeger_001t__Rat__Orat_001t__Code____Numeral__Ointeger_001t__Rat__Orat,type,
% 9.09/5.28 bNF_re4698098036185532619er_rat: ( code_integer > rat > $o ) > ( code_integer > rat > $o ) > ( code_integer > code_integer ) > ( rat > rat ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Code____Numeral__Ointeger_001_062_It__Int__Oint_M_Eo_J_001_062_It__Code____Numeral__Ointeger_M_Eo_J,type,
% 9.09/5.28 bNF_re6321650412969554871eger_o: ( int > code_integer > $o ) > ( ( int > $o ) > ( code_integer > $o ) > $o ) > ( int > int > $o ) > ( code_integer > code_integer > $o ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Code____Numeral__Ointeger_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 9.09/5.28 bNF_re398004352372739002nteger: ( int > code_integer > $o ) > ( ( int > int ) > ( code_integer > code_integer ) > $o ) > ( int > int > int ) > ( code_integer > code_integer > code_integer ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Code____Numeral__Ointeger_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Nat__Onat_M_Eo_J,type,
% 9.09/5.28 bNF_re4711666741709854504_nat_o: ( int > code_integer > $o ) > ( ( nat > $o ) > ( nat > $o ) > $o ) > ( int > nat > $o ) > ( code_integer > nat > $o ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Code____Numeral__Ointeger_001_Eo_001_Eo,type,
% 9.09/5.28 bNF_re6574881592172037608er_o_o: ( int > code_integer > $o ) > ( $o > $o > $o ) > ( int > $o ) > ( code_integer > $o ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Code____Numeral__Ointeger_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
% 9.09/5.28 bNF_re3379532845092657523nteger: ( int > code_integer > $o ) > ( int > code_integer > $o ) > ( int > int ) > ( code_integer > code_integer ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Code____Numeral__Ointeger_001t__Int__Oint_001t__Int__Oint,type,
% 9.09/5.28 bNF_re3804157879324367682nt_int: ( int > code_integer > $o ) > ( int > int > $o ) > ( int > int ) > ( code_integer > int ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Code____Numeral__Ointeger_001t__Nat__Onat_001t__Code____Numeral__Onatural,type,
% 9.09/5.28 bNF_re1831474436612530402atural: ( int > code_integer > $o ) > ( nat > code_natural > $o ) > ( int > nat ) > ( code_integer > code_natural ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Code____Numeral__Ointeger_001t__Nat__Onat_001t__Nat__Onat,type,
% 9.09/5.28 bNF_re2807294637932363402at_nat: ( int > code_integer > $o ) > ( nat > nat > $o ) > ( int > nat ) > ( code_integer > nat ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Code____Numeral__Ointeger_001t__Num__Onum_001t__Num__Onum,type,
% 9.09/5.28 bNF_re6718328864250387230um_num: ( int > code_integer > $o ) > ( num > num > $o ) > ( int > num ) > ( code_integer > num ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Code____Numeral__Onatural_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J,type,
% 9.09/5.28 bNF_re2342410721167621787atural: ( int > code_natural > $o ) > ( ( int > int ) > ( code_natural > code_natural ) > $o ) > ( int > int > int ) > ( code_natural > code_natural > code_natural ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Code____Numeral__Onatural_001t__Int__Oint_001t__Code____Numeral__Onatural,type,
% 9.09/5.28 bNF_re5484556299188842761atural: ( int > code_natural > $o ) > ( int > code_natural > $o ) > ( int > int ) > ( code_natural > code_natural ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_062_It__Int__Oint_M_Eo_J_001_062_It__Int__Oint_M_Eo_J,type,
% 9.09/5.28 bNF_re3403563459893282935_int_o: ( int > int > $o ) > ( ( int > $o ) > ( int > $o ) > $o ) > ( int > int > $o ) > ( int > int > $o ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Int__Oint_Mt__Int__Oint_J,type,
% 9.09/5.28 bNF_re711492959462206631nt_int: ( int > int > $o ) > ( ( int > int ) > ( int > int ) > $o ) > ( int > int > int ) > ( int > int > int ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_062_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
% 9.09/5.28 bNF_re157797125943740599nt_int: ( int > int > $o ) > ( ( int > product_prod_int_int ) > ( int > product_prod_int_int ) > $o ) > ( int > int > product_prod_int_int ) > ( int > int > product_prod_int_int ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_062_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Int__Oint_Mt__Rat__Orat_J,type,
% 9.09/5.28 bNF_re3461391660133120880nt_rat: ( int > int > $o ) > ( ( int > product_prod_int_int ) > ( int > rat ) > $o ) > ( int > int > product_prod_int_int ) > ( int > int > rat ) > $o ).
% 9.09/5.28
% 9.09/5.28 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,
% 9.09/5.28 bNF_re3376528473927230327_nat_o: ( int > int > $o ) > ( ( nat > $o ) > ( nat > $o ) > $o ) > ( int > nat > $o ) > ( int > nat > $o ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_Eo_001_Eo,type,
% 9.09/5.28 bNF_re5089333283451836215nt_o_o: ( int > int > $o ) > ( $o > $o > $o ) > ( int > $o ) > ( int > $o ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 9.09/5.28 bNF_re1784066744496875891nteger: ( int > int > $o ) > ( code_integer > code_integer > $o ) > ( int > code_integer ) > ( int > code_integer ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Code____Numeral__Ointeger_001t__Int__Oint,type,
% 9.09/5.28 bNF_re343602593470180162er_int: ( int > int > $o ) > ( code_integer > int > $o ) > ( int > code_integer ) > ( int > int ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Code____Numeral__Ointeger_001t__Rat__Orat,type,
% 9.09/5.28 bNF_re8934335040747510510er_rat: ( int > int > $o ) > ( code_integer > rat > $o ) > ( int > code_integer ) > ( int > rat ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Code____Numeral__Onatural_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J,type,
% 9.09/5.28 bNF_re6290619412732081552atural: ( int > int > $o ) > ( code_natural > produc7822875418678951345atural > $o ) > ( int > code_natural ) > ( int > produc7822875418678951345atural ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
% 9.09/5.28 bNF_re982302072995117890nteger: ( int > int > $o ) > ( int > code_integer > $o ) > ( int > int ) > ( int > code_integer ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint,type,
% 9.09/5.28 bNF_re4712519889275205905nt_int: ( int > int > $o ) > ( int > int > $o ) > ( int > int ) > ( int > int ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint_001t__Rat__Orat,type,
% 9.09/5.28 bNF_re4079880299697760445nt_rat: ( int > int > $o ) > ( int > rat > $o ) > ( int > int ) > ( int > rat ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Nat__Onat_001t__Nat__Onat,type,
% 9.09/5.28 bNF_re3715656647883201625at_nat: ( int > int > $o ) > ( nat > nat > $o ) > ( int > nat ) > ( int > nat ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Num__Onum_001t__Num__Onum,type,
% 9.09/5.28 bNF_re7626690874201225453um_num: ( int > int > $o ) > ( num > num > $o ) > ( int > num ) > ( int > num ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 9.09/5.28 bNF_re6250860962936578807nt_int: ( int > int > $o ) > ( product_prod_int_int > product_prod_int_int > $o ) > ( int > product_prod_int_int ) > ( int > product_prod_int_int ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Rat__Orat,type,
% 9.09/5.28 bNF_re2214769303045360666nt_rat: ( int > int > $o ) > ( product_prod_int_int > rat > $o ) > ( int > product_prod_int_int ) > ( int > rat ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Rat__Orat_001t__Code____Numeral__Ointeger,type,
% 9.09/5.28 bNF_re1382721322319792878nteger: ( int > int > $o ) > ( rat > code_integer > $o ) > ( int > rat ) > ( int > code_integer ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Rat__Orat_001t__Int__Oint,type,
% 9.09/5.28 bNF_re3396611533439285437at_int: ( int > int > $o ) > ( rat > int > $o ) > ( int > rat ) > ( int > int ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Rat__Orat_001t__Rat__Orat,type,
% 9.09/5.28 bNF_re2763971943861839977at_rat: ( int > int > $o ) > ( rat > rat > $o ) > ( int > rat ) > ( int > rat ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Nat__Onat_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 9.09/5.28 bNF_re5416042074812042131at_nat: ( int > nat > $o ) > ( ( int > int ) > ( nat > nat ) > $o ) > ( int > int > int ) > ( nat > nat > nat ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Nat__Onat_001t__Int__Oint_001t__Nat__Onat,type,
% 9.09/5.28 bNF_re4343356799547411545nt_nat: ( int > nat > $o ) > ( int > nat > $o ) > ( int > int ) > ( nat > nat ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Num__Onum_001t__Nat__Onat_001t__Code____Numeral__Ointeger,type,
% 9.09/5.28 bNF_re151304249936775380nteger: ( int > num > $o ) > ( nat > code_integer > $o ) > ( int > nat ) > ( num > code_integer ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Num__Onum_001t__Num__Onum_001t__Code____Numeral__Ointeger,type,
% 9.09/5.28 bNF_re7315484114762210078nteger: ( int > num > $o ) > ( num > code_integer > $o ) > ( int > num ) > ( num > code_integer ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Rat__Orat_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Rat__Orat_Mt__Rat__Orat_J,type,
% 9.09/5.28 bNF_re7661208983170134443at_rat: ( int > rat > $o ) > ( ( int > int ) > ( rat > rat ) > $o ) > ( int > int > int ) > ( rat > rat > rat ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Rat__Orat_001t__Int__Oint_001t__Rat__Orat,type,
% 9.09/5.28 bNF_re4480299549022435433nt_rat: ( int > rat > $o ) > ( int > rat > $o ) > ( int > int ) > ( rat > rat ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Code____Numeral__Ointeger_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 9.09/5.28 bNF_re7367609096550055590nteger: ( nat > code_integer > $o ) > ( ( nat > nat ) > ( code_integer > code_integer ) > $o ) > ( nat > nat > nat ) > ( code_integer > code_integer > code_integer ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Code____Numeral__Ointeger_001t__Nat__Onat_001t__Code____Numeral__Ointeger,type,
% 9.09/5.28 bNF_re1599192376174140603nteger: ( nat > code_integer > $o ) > ( nat > code_integer > $o ) > ( nat > nat ) > ( code_integer > code_integer ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Code____Numeral__Ointeger_001t__Num__Onum_001t__Code____Numeral__Ointeger,type,
% 9.09/5.28 bNF_re8763372240999575301nteger: ( nat > code_integer > $o ) > ( num > code_integer > $o ) > ( nat > num ) > ( code_integer > code_integer ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Code____Numeral__Onatural_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Code____Numeral__Onatural_M_Eo_J,type,
% 9.09/5.28 bNF_re1639080489988575423ural_o: ( nat > code_natural > $o ) > ( ( nat > $o ) > ( code_natural > $o ) > $o ) > ( nat > nat > $o ) > ( code_natural > code_natural > $o ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Code____Numeral__Onatural_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Nat__Onat_M_Eo_J,type,
% 9.09/5.28 bNF_re2895713572246619415_nat_o: ( nat > code_natural > $o ) > ( ( nat > $o ) > ( nat > $o ) > $o ) > ( nat > nat > $o ) > ( code_natural > nat > $o ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Code____Numeral__Onatural_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J,type,
% 9.09/5.28 bNF_re88643428490162567atural: ( nat > code_natural > $o ) > ( ( nat > nat ) > ( code_natural > code_natural ) > $o ) > ( nat > nat > nat ) > ( code_natural > code_natural > code_natural ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Code____Numeral__Onatural_001_Eo_001_Eo,type,
% 9.09/5.28 bNF_re2785088596696291543al_o_o: ( nat > code_natural > $o ) > ( $o > $o > $o ) > ( nat > $o ) > ( code_natural > $o ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Code____Numeral__Onatural_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
% 9.09/5.28 bNF_re5252274238750452962nteger: ( nat > code_natural > $o ) > ( int > code_integer > $o ) > ( nat > int ) > ( code_natural > code_integer ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Code____Numeral__Onatural_001t__Nat__Onat_001t__Code____Numeral__Onatural,type,
% 9.09/5.28 bNF_re3704215830270325841atural: ( nat > code_natural > $o ) > ( nat > code_natural > $o ) > ( nat > nat ) > ( code_natural > code_natural ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Code____Numeral__Onatural_001t__Nat__Onat_001t__Nat__Onat,type,
% 9.09/5.28 bNF_re7333046803109187065at_nat: ( nat > code_natural > $o ) > ( nat > nat > $o ) > ( nat > nat ) > ( code_natural > nat ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Int__Oint_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Int__Oint_Mt__Int__Oint_J,type,
% 9.09/5.28 bNF_re5864104203909894035nt_int: ( nat > int > $o ) > ( ( nat > nat ) > ( int > int ) > $o ) > ( nat > nat > nat ) > ( int > int > int ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Int__Oint_001t__Nat__Onat_001t__Int__Oint,type,
% 9.09/5.28 bNF_re6022984109467102297at_int: ( nat > int > $o ) > ( nat > int > $o ) > ( nat > nat ) > ( int > int ) > $o ).
% 9.09/5.28
% 9.09/5.28 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__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 9.09/5.28 bNF_re4935368626670024657nteger: ( nat > nat > $o ) > ( ( int > int ) > ( code_integer > code_integer ) > $o ) > ( nat > int > int ) > ( nat > code_integer > code_integer ) > $o ).
% 9.09/5.28
% 9.09/5.28 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,
% 9.09/5.28 bNF_re4785983289428654063nt_int: ( nat > nat > $o ) > ( ( int > int ) > ( int > int ) > $o ) > ( nat > int > int ) > ( nat > int > int ) > $o ).
% 9.09/5.28
% 9.09/5.28 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,
% 9.09/5.28 bNF_re578469030762574527_nat_o: ( nat > nat > $o ) > ( ( nat > $o ) > ( nat > $o ) > $o ) > ( nat > nat > $o ) > ( nat > nat > $o ) > $o ).
% 9.09/5.28
% 9.09/5.28 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__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J,type,
% 9.09/5.28 bNF_re3692170009638431535atural: ( nat > nat > $o ) > ( ( nat > nat ) > ( code_natural > code_natural ) > $o ) > ( nat > nat > nat ) > ( nat > code_natural > code_natural ) > $o ).
% 9.09/5.28
% 9.09/5.28 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,
% 9.09/5.28 bNF_re1345281282404953727at_nat: ( nat > nat > $o ) > ( ( nat > nat ) > ( nat > nat ) > $o ) > ( nat > nat > nat ) > ( nat > nat > nat ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001_Eo_001_Eo,type,
% 9.09/5.28 bNF_re4705727531993890431at_o_o: ( nat > nat > $o ) > ( $o > $o > $o ) > ( nat > $o ) > ( nat > $o ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Assertions__Oassn_001t__Assertions__Oassn,type,
% 9.09/5.28 bNF_re4051817429369991249n_assn: ( nat > nat > $o ) > ( assn > assn > $o ) > ( nat > assn ) > ( nat > assn ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Assertions__Oassn_001t__Code____Numeral__Ointeger,type,
% 9.09/5.28 bNF_re1831131418152741254nteger: ( nat > nat > $o ) > ( assn > code_integer > $o ) > ( nat > assn ) > ( nat > code_integer ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Assertions__Oassn_001t__Int__Oint,type,
% 9.09/5.28 bNF_re4792267480158271317sn_int: ( nat > nat > $o ) > ( assn > int > $o ) > ( nat > assn ) > ( nat > int ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Assertions__Oassn_001t__Nat__Onat,type,
% 9.09/5.28 bNF_re4794757950667321593sn_nat: ( nat > nat > $o ) > ( assn > nat > $o ) > ( nat > assn ) > ( nat > nat ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Assertions__Oassn_001t__Rat__Orat,type,
% 9.09/5.28 bNF_re4159627890580825857sn_rat: ( nat > nat > $o ) > ( assn > rat > $o ) > ( nat > assn ) > ( nat > rat ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Code____Numeral__Ointeger_001t__Assertions__Oassn,type,
% 9.09/5.28 bNF_re2692373401909853574r_assn: ( nat > nat > $o ) > ( code_integer > assn > $o ) > ( nat > code_integer ) > ( nat > assn ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 9.09/5.28 bNF_re1236659899165691067nteger: ( nat > nat > $o ) > ( code_integer > code_integer > $o ) > ( nat > code_integer ) > ( nat > code_integer ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Code____Numeral__Ointeger_001t__Int__Oint,type,
% 9.09/5.28 bNF_re3514700588913618570er_int: ( nat > nat > $o ) > ( code_integer > int > $o ) > ( nat > code_integer ) > ( nat > int ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Code____Numeral__Ointeger_001t__Nat__Onat,type,
% 9.09/5.28 bNF_re3517191059422668846er_nat: ( nat > nat > $o ) > ( code_integer > nat > $o ) > ( nat > code_integer ) > ( nat > nat ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Code____Numeral__Ointeger_001t__Rat__Orat,type,
% 9.09/5.28 bNF_re2882060999336173110er_rat: ( nat > nat > $o ) > ( code_integer > rat > $o ) > ( nat > code_integer ) > ( nat > rat ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Code____Numeral__Onatural_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J,type,
% 9.09/5.28 bNF_re6101645755646507080atural: ( nat > nat > $o ) > ( code_natural > produc7822875418678951345atural > $o ) > ( nat > code_natural ) > ( nat > produc7822875418678951345atural ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
% 9.09/5.28 bNF_re4153400068438556298nteger: ( nat > nat > $o ) > ( int > code_integer > $o ) > ( nat > int ) > ( nat > code_integer ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Int__Oint_001t__Code____Numeral__Onatural,type,
% 9.09/5.28 bNF_re2976995220195273813atural: ( nat > nat > $o ) > ( int > code_natural > $o ) > ( nat > int ) > ( nat > code_natural ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Int__Oint_001t__Int__Oint,type,
% 9.09/5.28 bNF_re6650684261131312217nt_int: ( nat > nat > $o ) > ( int > int > $o ) > ( nat > int ) > ( nat > int ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Int__Oint_001t__Nat__Onat,type,
% 9.09/5.28 bNF_re6653174731640362493nt_nat: ( nat > nat > $o ) > ( int > nat > $o ) > ( nat > int ) > ( nat > nat ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Int__Oint_001t__Rat__Orat,type,
% 9.09/5.28 bNF_re6018044671553866757nt_rat: ( nat > nat > $o ) > ( int > rat > $o ) > ( nat > int ) > ( nat > rat ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat_001t__Code____Numeral__Onatural,type,
% 9.09/5.28 bNF_re2605341659958429177atural: ( nat > nat > $o ) > ( nat > code_natural > $o ) > ( nat > nat ) > ( nat > code_natural ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
% 9.09/5.28 bNF_re5653821019739307937at_nat: ( nat > nat > $o ) > ( nat > nat > $o ) > ( nat > nat ) > ( nat > nat ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Num__Onum_001t__Num__Onum,type,
% 9.09/5.28 bNF_re341483209202555957um_num: ( nat > nat > $o ) > ( num > num > $o ) > ( nat > num ) > ( nat > num ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint,type,
% 9.09/5.28 bNF_re6830278522597306478at_int: ( nat > nat > $o ) > ( product_prod_nat_nat > int > $o ) > ( nat > product_prod_nat_nat ) > ( nat > int ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Rat__Orat_001t__Code____Numeral__Ointeger,type,
% 9.09/5.28 bNF_re4553819317763231286nteger: ( nat > nat > $o ) > ( rat > code_integer > $o ) > ( nat > rat ) > ( nat > code_integer ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Rat__Orat_001t__Code____Numeral__Onatural,type,
% 9.09/5.28 bNF_re3377414469519948801atural: ( nat > nat > $o ) > ( rat > code_natural > $o ) > ( nat > rat ) > ( nat > code_natural ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Rat__Orat_001t__Int__Oint,type,
% 9.09/5.28 bNF_re5334775905295391749at_int: ( nat > nat > $o ) > ( rat > int > $o ) > ( nat > rat ) > ( nat > int ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Rat__Orat_001t__Nat__Onat,type,
% 9.09/5.28 bNF_re5337266375804442025at_nat: ( nat > nat > $o ) > ( rat > nat > $o ) > ( nat > rat ) > ( nat > nat ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Rat__Orat_001t__Rat__Orat,type,
% 9.09/5.28 bNF_re4702136315717946289at_rat: ( nat > nat > $o ) > ( rat > rat > $o ) > ( nat > rat ) > ( nat > rat ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Rat__Orat_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Rat__Orat_Mt__Rat__Orat_J,type,
% 9.09/5.28 bNF_re3590448190763046039at_rat: ( nat > rat > $o ) > ( ( nat > nat ) > ( rat > rat ) > $o ) > ( nat > nat > nat ) > ( rat > rat > rat ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Rat__Orat_001t__Nat__Onat_001t__Rat__Orat,type,
% 9.09/5.28 bNF_re5790763769214331825at_rat: ( nat > rat > $o ) > ( nat > rat > $o ) > ( nat > nat ) > ( rat > rat ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Num__Onum_001t__Code____Numeral__Ointeger_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,type,
% 9.09/5.28 bNF_re5031869190687302234nteger: ( num > code_integer > $o ) > ( code_integer > ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > $o ) > ( num > code_integer ) > ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Num__Onum_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 9.09/5.28 bNF_re5202476307641864082nteger: ( num > code_integer > $o ) > ( code_integer > code_integer > $o ) > ( num > code_integer ) > ( code_integer > code_integer ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Num__Onum_001t__Int__Oint_001t__Code____Numeral__Ointeger_001t__Nat__Onat,type,
% 9.09/5.28 bNF_re6324211044263125204er_nat: ( num > int > $o ) > ( code_integer > nat > $o ) > ( num > code_integer ) > ( int > nat ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Num__Onum_001t__Int__Oint_001t__Code____Numeral__Ointeger_001t__Num__Onum,type,
% 9.09/5.28 bNF_re2881542830418903838er_num: ( num > int > $o ) > ( code_integer > num > $o ) > ( num > code_integer ) > ( int > num ) > $o ).
% 9.09/5.28
% 9.09/5.28 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__Code____Numeral__Ointeger_J,type,
% 9.09/5.28 bNF_re7876454716742015248nteger: ( num > num > $o ) > ( ( num > int ) > ( num > code_integer ) > $o ) > ( num > num > int ) > ( num > num > code_integer ) > $o ).
% 9.09/5.28
% 9.09/5.28 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,
% 9.09/5.28 bNF_re8402795839162346335um_int: ( num > num > $o ) > ( ( num > int ) > ( num > int ) > $o ) > ( num > num > int ) > ( num > num > int ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Num__Onum_001t__Num__Onum_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 9.09/5.28 bNF_re6741283560065411407nteger: ( num > num > $o ) > ( code_integer > code_integer > $o ) > ( num > code_integer ) > ( num > code_integer ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Num__Onum_001t__Num__Onum_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
% 9.09/5.28 bNF_re6501075790457514782nteger: ( num > num > $o ) > ( int > code_integer > $o ) > ( num > int ) > ( num > code_integer ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Num__Onum_001t__Num__Onum_001t__Int__Oint_001t__Code____Numeral__Onatural,type,
% 9.09/5.28 bNF_re5324670942214232297atural: ( num > num > $o ) > ( int > code_natural > $o ) > ( num > int ) > ( num > code_natural ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Num__Onum_001t__Num__Onum_001t__Int__Oint_001t__Int__Oint,type,
% 9.09/5.28 bNF_re1822329894187522285nt_int: ( num > num > $o ) > ( int > int > $o ) > ( num > int ) > ( num > int ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Num__Onum_001t__Num__Onum_001t__Int__Oint_001t__Nat__Onat,type,
% 9.09/5.28 bNF_re1824820364696572561nt_nat: ( num > num > $o ) > ( int > nat > $o ) > ( num > int ) > ( num > nat ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Num__Onum_001t__Num__Onum_001t__Int__Oint_001t__Rat__Orat,type,
% 9.09/5.28 bNF_re1189690304610076825nt_rat: ( num > num > $o ) > ( int > rat > $o ) > ( num > int ) > ( num > rat ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Num__Onum_001t__Num__Onum_001t__Nat__Onat_001t__Code____Numeral__Ointeger,type,
% 9.09/5.28 bNF_re6129422230220670146nteger: ( num > num > $o ) > ( nat > code_integer > $o ) > ( num > nat ) > ( num > code_integer ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Num__Onum_001t__Num__Onum_001t__Nat__Onat_001t__Code____Numeral__Onatural,type,
% 9.09/5.28 bNF_re4953017381977387661atural: ( num > num > $o ) > ( nat > code_natural > $o ) > ( num > nat ) > ( num > code_natural ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Num__Onum_001t__Num__Onum_001t__Nat__Onat_001t__Int__Oint,type,
% 9.09/5.28 bNF_re822976182286467729at_int: ( num > num > $o ) > ( nat > int > $o ) > ( num > nat ) > ( num > int ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Num__Onum_001t__Num__Onum_001t__Nat__Onat_001t__Nat__Onat,type,
% 9.09/5.28 bNF_re825466652795518005at_nat: ( num > num > $o ) > ( nat > nat > $o ) > ( num > nat ) > ( num > nat ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Num__Onum_001t__Num__Onum_001t__Nat__Onat_001t__Rat__Orat,type,
% 9.09/5.28 bNF_re190336592709022269at_rat: ( num > num > $o ) > ( nat > rat > $o ) > ( num > nat ) > ( num > rat ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
% 9.09/5.28 bNF_re5228765855967844073nt_int: ( product_prod_int_int > product_prod_int_int > $o ) > ( ( product_prod_int_int > product_prod_int_int ) > ( product_prod_int_int > product_prod_int_int ) > $o ) > ( product_prod_int_int > product_prod_int_int > product_prod_int_int ) > ( product_prod_int_int > product_prod_int_int > product_prod_int_int ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 9.09/5.28 bNF_re7145576690424134365nt_int: ( product_prod_int_int > product_prod_int_int > $o ) > ( product_prod_int_int > product_prod_int_int > $o ) > ( product_prod_int_int > product_prod_int_int ) > ( product_prod_int_int > product_prod_int_int ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Rat__Orat_001_062_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Rat__Orat_Mt__Rat__Orat_J,type,
% 9.09/5.28 bNF_re7627151682743391978at_rat: ( product_prod_int_int > rat > $o ) > ( ( product_prod_int_int > product_prod_int_int ) > ( rat > rat ) > $o ) > ( product_prod_int_int > product_prod_int_int > product_prod_int_int ) > ( rat > rat > rat ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Rat__Orat_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Rat__Orat,type,
% 9.09/5.28 bNF_re8279943556446156061nt_rat: ( product_prod_int_int > rat > $o ) > ( product_prod_int_int > rat > $o ) > ( product_prod_int_int > product_prod_int_int ) > ( rat > rat ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_001_062_It__Int__Oint_M_Eo_J,type,
% 9.09/5.28 bNF_re717283939379294677_int_o: ( product_prod_nat_nat > int > $o ) > ( ( product_prod_nat_nat > $o ) > ( int > $o ) > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( int > int > $o ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001_062_It__Int__Oint_Mt__Int__Oint_J,type,
% 9.09/5.28 bNF_re7408651293131936558nt_int: ( product_prod_nat_nat > int > $o ) > ( ( product_prod_nat_nat > product_prod_nat_nat ) > ( int > int ) > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > ( int > int > int ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001_Eo_001_Eo,type,
% 9.09/5.28 bNF_re6644619430987730960nt_o_o: ( product_prod_nat_nat > int > $o ) > ( $o > $o > $o ) > ( product_prod_nat_nat > $o ) > ( int > $o ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint,type,
% 9.09/5.28 bNF_re7400052026677387805at_int: ( product_prod_nat_nat > int > $o ) > ( product_prod_nat_nat > int > $o ) > ( product_prod_nat_nat > product_prod_nat_nat ) > ( int > int ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J,type,
% 9.09/5.28 bNF_re4202695980764964119_nat_o: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( ( product_prod_nat_nat > $o ) > ( product_prod_nat_nat > $o ) > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 9.09/5.28 bNF_re3099431351363272937at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( ( product_prod_nat_nat > product_prod_nat_nat ) > ( product_prod_nat_nat > product_prod_nat_nat ) > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_Eo_001_Eo,type,
% 9.09/5.28 bNF_re3666534408544137501at_o_o: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( $o > $o > $o ) > ( product_prod_nat_nat > $o ) > ( product_prod_nat_nat > $o ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 9.09/5.28 bNF_re2241393799969408733at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > product_prod_nat_nat ) > ( product_prod_nat_nat > product_prod_nat_nat ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Ounit_001t__Product____Type__Ounit_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 9.09/5.28 bNF_re8417623677625516633nteger: ( product_unit > product_unit > $o ) > ( code_integer > code_integer > $o ) > ( product_unit > code_integer ) > ( product_unit > code_integer ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Ounit_001t__Product____Type__Ounit_001t__Code____Numeral__Onatural_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J,type,
% 9.09/5.28 bNF_re5641277236161133866atural: ( product_unit > product_unit > $o ) > ( code_natural > produc7822875418678951345atural > $o ) > ( product_unit > code_natural ) > ( product_unit > produc7822875418678951345atural ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Ounit_001t__Product____Type__Ounit_001t__Int__Oint_001t__Int__Oint,type,
% 9.09/5.28 bNF_re8422471777688076791nt_int: ( product_unit > product_unit > $o ) > ( int > int > $o ) > ( product_unit > int ) > ( product_unit > int ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Rat__Orat_001t__Code____Numeral__Ointeger_001_062_It__Rat__Orat_Mt__Rat__Orat_J_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 9.09/5.28 bNF_re4307939118855507134nteger: ( rat > code_integer > $o ) > ( ( rat > rat ) > ( code_integer > code_integer ) > $o ) > ( rat > rat > rat ) > ( code_integer > code_integer > code_integer ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Rat__Orat_001t__Code____Numeral__Ointeger_001t__Rat__Orat_001t__Code____Numeral__Ointeger,type,
% 9.09/5.28 bNF_re2328245411608324299nteger: ( rat > code_integer > $o ) > ( rat > code_integer > $o ) > ( rat > rat ) > ( code_integer > code_integer ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Rat__Orat_001t__Code____Numeral__Onatural_001_062_It__Rat__Orat_Mt__Rat__Orat_J_001_062_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J,type,
% 9.09/5.28 bNF_re6252345487650389919atural: ( rat > code_natural > $o ) > ( ( rat > rat ) > ( code_natural > code_natural ) > $o ) > ( rat > rat > rat ) > ( code_natural > code_natural > code_natural ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Rat__Orat_001t__Code____Numeral__Onatural_001t__Rat__Orat_001t__Code____Numeral__Onatural,type,
% 9.09/5.28 bNF_re4433268865704509537atural: ( rat > code_natural > $o ) > ( rat > code_natural > $o ) > ( rat > rat ) > ( code_natural > code_natural ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Rat__Orat_001t__Int__Oint_001_062_It__Rat__Orat_Mt__Rat__Orat_J_001_062_It__Int__Oint_Mt__Int__Oint_J,type,
% 9.09/5.28 bNF_re8876735282041863595nt_int: ( rat > int > $o ) > ( ( rat > rat ) > ( int > int ) > $o ) > ( rat > rat > rat ) > ( int > int > int ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Rat__Orat_001t__Int__Oint_001t__Rat__Orat_001t__Int__Oint,type,
% 9.09/5.28 bNF_re5838490730811218025at_int: ( rat > int > $o ) > ( rat > int > $o ) > ( rat > rat ) > ( int > int ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Rat__Orat_001t__Nat__Onat_001_062_It__Rat__Orat_Mt__Rat__Orat_J_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 9.09/5.28 bNF_re4357912360536923287at_nat: ( rat > nat > $o ) > ( ( rat > rat ) > ( nat > nat ) > $o ) > ( rat > rat > rat ) > ( nat > nat > nat ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Rat__Orat_001t__Nat__Onat_001t__Rat__Orat_001t__Nat__Onat,type,
% 9.09/5.28 bNF_re5469327641083423665at_nat: ( rat > nat > $o ) > ( rat > nat > $o ) > ( rat > rat ) > ( nat > nat ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Rat__Orat_001t__Rat__Orat_001_062_It__Rat__Orat_Mt__Rat__Orat_J_001_062_It__Rat__Orat_Mt__Rat__Orat_J,type,
% 9.09/5.28 bNF_re6603079268895015599at_rat: ( rat > rat > $o ) > ( ( rat > rat ) > ( rat > rat ) > $o ) > ( rat > rat > rat ) > ( rat > rat > rat ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Def_Orel__fun_001t__Rat__Orat_001t__Rat__Orat_001t__Rat__Orat_001t__Rat__Orat,type,
% 9.09/5.28 bNF_re5606270390558447553at_rat: ( rat > rat > $o ) > ( rat > rat > $o ) > ( rat > rat ) > ( rat > rat ) > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Wellorder__Constructions_OordIso_001_Eo_001_Eo,type,
% 9.09/5.28 bNF_We2654380646378065620so_o_o: set_Pr1932065953672099015od_o_o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Wellorder__Constructions_OordIso_001t__Nat__Onat_001t__Nat__Onat,type,
% 9.09/5.28 bNF_We5258908940166488438at_nat: set_Pr4329608150637261639at_nat ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_BNF__Wellorder__Constructions_OordLess_001_Eo_001t__Nat__Onat,type,
% 9.09/5.28 bNF_We8182288985678559134_o_nat: set_Pr457366540195662369at_nat ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Basic__BNF__LFPs_Oprod_Osize__prod_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 9.09/5.28 basic_7565498685090299632nteger: ( code_integer > nat ) > ( code_integer > nat ) > produc8923325533196201883nteger > nat ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Basic__BNF__LFPs_Oprod_Osize__prod_001t__Code____Numeral__Onatural_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J,type,
% 9.09/5.28 basic_8185638495112405971atural: ( code_natural > nat ) > ( produc7822875418678951345atural > nat ) > produc5835291356934675326atural > nat ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Basic__BNF__LFPs_Oprod_Osize__prod_001t__Int__Oint_001t__Int__Oint,type,
% 9.09/5.28 basic_1872990034501187214nt_int: ( int > nat ) > ( int > nat ) > product_prod_int_int > nat ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Binomial_Obinomial,type,
% 9.09/5.28 binomial: nat > nat > nat ).
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% 9.09/5.28
% 9.09/5.28 thf(sy_c_Finite__Set_Ofinite_001t__Set__Oset_It__Product____Type__Ounit_J,type,
% 9.09/5.28 finite1772178364199683094t_unit: set_set_Product_unit > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Finite__Set_Ofold_001t__Int__Oint_001t__Int__Oint,type,
% 9.09/5.28 finite_fold_int_int: ( int > int > int ) > int > set_int > int ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Finite__Set_Ofold_001t__Nat__Onat_001t__Int__Oint,type,
% 9.09/5.28 finite_fold_nat_int: ( nat > int > int ) > int > set_nat > int ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Finite__Set_Ofold_001t__Nat__Onat_001t__Nat__Onat,type,
% 9.09/5.28 finite_fold_nat_nat: ( nat > nat > nat ) > nat > set_nat > nat ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Finite__Set_Ofold_001t__Nat__Onat_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 9.09/5.28 finite3745491028973389255at_nat: ( nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ) > set_Pr1261947904930325089at_nat > set_nat > set_Pr1261947904930325089at_nat ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Finite__Set_Ofold_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_001t__Set__Oset_It__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_J,type,
% 9.09/5.28 finite8124994865635982712et_nat: ( produc3925858234332021118et_nat > set_Pr8536935166611901872et_nat > set_Pr8536935166611901872et_nat ) > set_Pr8536935166611901872et_nat > set_Pr3286484037609594932et_nat > set_Pr8536935166611901872et_nat ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Finite__Set_Ofold_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Set__Oset_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J,type,
% 9.09/5.28 finite7641027033760462367nteger: ( produc8923325533196201883nteger > set_Pr1281608226676607948nteger > set_Pr1281608226676607948nteger ) > set_Pr1281608226676607948nteger > set_Pr4811707699266497531nteger > set_Pr1281608226676607948nteger ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Finite__Set_Ofold_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_001t__Set__Oset_It__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,
% 9.09/5.28 finite2494574492299216512et_nat: ( produc3658429121746597890et_nat > set_Pr3286484037609594932et_nat > set_Pr3286484037609594932et_nat ) > set_Pr3286484037609594932et_nat > set_Pr3948176798113811640et_nat > set_Pr3286484037609594932et_nat ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Finite__Set_Ofold_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Set__Oset_It__Product____Type__Oprod_I_062_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
% 9.09/5.28 finite5333674244414288180nt_int: ( product_prod_int_int > set_Pr1872883991513573699nt_int > set_Pr1872883991513573699nt_int ) > set_Pr1872883991513573699nt_int > set_Pr958786334691620121nt_int > set_Pr1872883991513573699nt_int ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Finite__Set_Ofold_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Set__Oset_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Int__Oint_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
% 9.09/5.28 finite1318812335397358250nt_int: ( product_prod_int_int > set_Pr9222295170931077689nt_int > set_Pr9222295170931077689nt_int ) > set_Pr9222295170931077689nt_int > set_Pr958786334691620121nt_int > set_Pr9222295170931077689nt_int ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Finite__Set_Ofold_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
% 9.09/5.28 finite3179781904389220718at_nat: ( set_Pr1261947904930325089at_nat > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat ) > set_Pr4329608150637261639at_nat > set_se7855581050983116737at_nat > set_Pr4329608150637261639at_nat ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001_062_I_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_Mt__Num__Onum_J,type,
% 9.09/5.28 comp_C3959375555751086581er_num: ( ( code_integer > code_integer ) > code_integer > code_integer ) > ( ( ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > num ) > code_integer > code_integer ) > ( ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > num ) > code_integer > code_integer ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Code____Numeral__Ointeger,type,
% 9.09/5.28 comp_C2822359487432382964nteger: ( ( code_integer > code_integer ) > code_integer > code_integer ) > ( code_integer > code_integer > code_integer ) > code_integer > code_integer > code_integer ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001_062_It__Num__Onum_M_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_J_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 9.09/5.28 comp_C5301300457492916725nteger: ( ( code_integer > code_integer ) > num > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( ( code_integer > code_integer ) > code_integer > code_integer ) > ( code_integer > code_integer ) > num > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001_062_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_001_062_It__Code____Numeral__Ointeger_Mt__Num__Onum_J,type,
% 9.09/5.28 comp_C9104104092898552938er_num: ( ( code_integer > code_integer ) > num > code_integer ) > ( ( code_integer > num ) > code_integer > code_integer ) > ( code_integer > num ) > num > code_integer ).
% 9.09/5.28
% 9.09/5.28 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_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 9.09/5.28 comp_C3983183376822107068nteger: ( ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( ( code_integer > code_integer ) > code_integer > code_integer ) > ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 9.09/5.28
% 9.09/5.28 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,
% 9.09/5.28 comp_C8797469213163452608nteger: ( ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 9.09/5.28
% 9.09/5.28 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__Num__Onum,type,
% 9.09/5.28 comp_C8645541002826910333er_num: ( ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( num > code_integer > code_integer ) > num > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 9.09/5.28 comp_C5076291335850163704nteger: ( ( code_integer > code_integer ) > code_integer ) > ( code_integer > code_integer > code_integer ) > code_integer > code_integer ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001_062_It__Code____Numeral__Ointeger_Mt__Nat__Onat_J_001_062_It__Num__Onum_Mt__Num__Onum_J_001_062_It__Code____Numeral__Ointeger_Mt__Int__Oint_J,type,
% 9.09/5.28 comp_C8127656796141369388er_int: ( ( code_integer > nat ) > num > num ) > ( ( code_integer > int ) > code_integer > nat ) > ( code_integer > int ) > num > num ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001_062_It__Int__Oint_M_Eo_J_001_062_It__Int__Oint_M_Eo_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J,type,
% 9.09/5.28 comp_i6226780894115828703_nat_o: ( ( int > $o ) > int > $o ) > ( ( product_prod_nat_nat > $o ) > int > $o ) > ( product_prod_nat_nat > $o ) > int > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001_062_It__Int__Oint_M_Eo_J_001_062_It__Int__Oint_M_Eo_J_001t__Int__Oint,type,
% 9.09/5.28 comp_int_o_int_o_int: ( ( int > $o ) > int > $o ) > ( int > int > $o ) > int > int > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001_062_It__Int__Oint_M_Eo_J_001_062_It__Int__Oint_Mt__Int__Oint_J_001t__Int__Oint,type,
% 9.09/5.28 comp_i1993086638917920293nt_int: ( ( int > $o ) > int > int ) > ( int > int > $o ) > int > int > int ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001_062_It__Int__Oint_M_Eo_J_001_062_It__Nat__Onat_M_Eo_J_001t__Int__Oint,type,
% 9.09/5.28 comp_int_o_nat_o_int: ( ( int > $o ) > nat > $o ) > ( int > int > $o ) > int > nat > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Int__Oint_M_Eo_J_001t__Int__Oint,type,
% 9.09/5.28 comp_i5098556425753098485_o_int: ( ( int > int ) > int > $o ) > ( int > int > int ) > int > int > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Int__Oint_Mt__Int__Oint_J_001t__Int__Oint,type,
% 9.09/5.28 comp_i1129928922100200191nt_int: ( ( int > int ) > int > int ) > ( int > int > int ) > int > int > int ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Nat__Onat_M_Eo_J_001t__Int__Oint,type,
% 9.09/5.28 comp_i4411980392712547921_o_int: ( ( int > int ) > nat > $o ) > ( int > int > int ) > int > nat > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001_062_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001t__Int__Oint,type,
% 9.09/5.28 comp_i1790862786758963855nt_int: ( ( int > product_prod_int_int ) > int > product_prod_int_int ) > ( int > int > product_prod_int_int ) > int > int > product_prod_int_int ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001_062_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Int__Oint_Mt__Rat__Orat_J_001_062_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
% 9.09/5.28 comp_i118865614814752126nt_int: ( ( int > product_prod_int_int ) > int > rat ) > ( ( int > product_prod_int_int ) > int > product_prod_int_int ) > ( int > product_prod_int_int ) > int > rat ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001_062_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Int__Oint_Mt__Rat__Orat_J_001t__Int__Oint,type,
% 9.09/5.28 comp_i1302866070986779890at_int: ( ( int > product_prod_int_int ) > int > rat ) > ( int > int > product_prod_int_int ) > int > int > rat ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001_062_It__Int__Oint_Mt__Rat__Orat_J_001_062_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001t__Int__Oint,type,
% 9.09/5.28 comp_i929186717396404458nt_int: ( ( int > rat ) > int > product_prod_int_int ) > ( int > int > rat ) > int > int > product_prod_int_int ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001_062_It__Int__Oint_Mt__Rat__Orat_J_001_062_It__Int__Oint_Mt__Rat__Orat_J_001_062_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
% 9.09/5.28 comp_i5271019637457297241nt_int: ( ( int > rat ) > int > rat ) > ( ( int > product_prod_int_int ) > int > rat ) > ( int > product_prod_int_int ) > int > rat ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001_062_It__Int__Oint_Mt__Rat__Orat_J_001_062_It__Int__Oint_Mt__Rat__Orat_J_001t__Int__Oint,type,
% 9.09/5.28 comp_i8258899369942393943at_int: ( ( int > rat ) > int > rat ) > ( int > int > rat ) > int > int > rat ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Int__Oint_M_Eo_J_001t__Int__Oint,type,
% 9.09/5.28 comp_nat_o_int_o_int: ( ( nat > $o ) > int > $o ) > ( int > nat > $o ) > int > int > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Int__Oint_Mt__Int__Oint_J_001t__Int__Oint,type,
% 9.09/5.28 comp_n3090169619561918849nt_int: ( ( nat > $o ) > int > int ) > ( int > nat > $o ) > int > int > int ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Nat__Onat_M_Eo_J,type,
% 9.09/5.28 comp_n5656820349209612572_nat_o: ( ( nat > $o ) > nat > $o ) > ( ( nat > $o ) > nat > $o ) > ( nat > $o ) > nat > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Nat__Onat_M_Eo_J_001t__Int__Oint,type,
% 9.09/5.28 comp_nat_o_nat_o_int: ( ( nat > $o ) > nat > $o ) > ( int > nat > $o ) > int > nat > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001_062_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J_001_062_It__Int__Oint_Mt__Code____Numeral__Ointeger_J_001_062_It__Num__Onum_Mt__Num__Onum_J,type,
% 9.09/5.28 comp_n3323228797031117228um_num: ( ( nat > code_integer ) > int > code_integer ) > ( ( num > num ) > nat > code_integer ) > ( num > num ) > int > code_integer ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Int__Oint_Mt__Num__Onum_J_001_062_It__Num__Onum_Mt__Int__Oint_J,type,
% 9.09/5.28 comp_n4765151935410462062um_int: ( ( nat > nat ) > int > num ) > ( ( num > int ) > nat > nat ) > ( num > int ) > int > num ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_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_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,
% 9.09/5.28 comp_P3928908779438215820nteger: ( ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_001_062_It__Int__Oint_M_Eo_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J,type,
% 9.09/5.28 comp_P286844350285437056_nat_o: ( ( product_prod_nat_nat > $o ) > int > $o ) > ( ( product_prod_nat_nat > $o ) > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > $o ) > int > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_001_062_It__Int__Oint_M_Eo_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 9.09/5.28 comp_P9039549498699531069at_nat: ( ( product_prod_nat_nat > $o ) > int > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > int > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001_062_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 9.09/5.28 comp_P1872448293794610368at_nat: ( ( product_prod_nat_nat > product_prod_nat_nat ) > int > int ) > ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > product_prod_nat_nat > int > int ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001_062_It__Set__Oset_I_Eo_J_Mt__Assertions__Oassn_J_001_062_It__Set__Oset_It__Set__Oset_I_Eo_J_J_Mt__Assertions__Oassn_J_001_062_I_Eo_Mt__Assertions__Oassn_J,type,
% 9.09/5.28 comp_s518380907012905326o_assn: ( ( set_o > assn ) > set_set_o > assn ) > ( ( $o > assn ) > set_o > assn ) > ( $o > assn ) > set_set_o > assn ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001_062_It__Set__Oset_I_Eo_J_Mt__Code____Numeral__Ointeger_J_001_062_It__Set__Oset_It__Set__Oset_I_Eo_J_J_Mt__Code____Numeral__Ointeger_J_001_062_I_Eo_Mt__Code____Numeral__Ointeger_J,type,
% 9.09/5.28 comp_s262121120021782499nteger: ( ( set_o > code_integer ) > set_set_o > code_integer ) > ( ( $o > code_integer ) > set_o > code_integer ) > ( $o > code_integer ) > set_set_o > code_integer ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001_062_It__Set__Oset_I_Eo_J_Mt__Nat__Onat_J_001_062_It__Set__Oset_It__Set__Oset_I_Eo_J_J_Mt__Nat__Onat_J_001_062_I_Eo_Mt__Nat__Onat_J,type,
% 9.09/5.28 comp_s6084864194472624150_o_nat: ( ( set_o > nat ) > set_set_o > nat ) > ( ( $o > nat ) > set_o > nat ) > ( $o > nat ) > set_set_o > nat ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001_062_It__Set__Oset_I_Eo_J_Mt__Rat__Orat_J_001_062_It__Set__Oset_It__Set__Oset_I_Eo_J_J_Mt__Rat__Orat_J_001_062_I_Eo_Mt__Rat__Orat_J,type,
% 9.09/5.28 comp_s1265507639253661726_o_rat: ( ( set_o > rat ) > set_set_o > rat ) > ( ( $o > rat ) > set_o > rat ) > ( $o > rat ) > set_set_o > rat ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001_062_It__Set__Oset_It__Code____Numeral__Ointeger_J_Mt__Assertions__Oassn_J_001_062_It__Set__Oset_It__Set__Oset_It__Code____Numeral__Ointeger_J_J_Mt__Assertions__Oassn_J_001_062_It__Code____Numeral__Ointeger_Mt__Assertions__Oassn_J,type,
% 9.09/5.28 comp_s3531641609786562035r_assn: ( ( set_Code_integer > assn ) > set_set_Code_integer > assn ) > ( ( code_integer > assn ) > set_Code_integer > assn ) > ( code_integer > assn ) > set_set_Code_integer > assn ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001_062_It__Set__Oset_It__Code____Numeral__Ointeger_J_Mt__Code____Numeral__Ointeger_J_001_062_It__Set__Oset_It__Set__Oset_It__Code____Numeral__Ointeger_J_J_Mt__Code____Numeral__Ointeger_J_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 9.09/5.28 comp_s8484400498494363538nteger: ( ( set_Code_integer > code_integer ) > set_set_Code_integer > code_integer ) > ( ( code_integer > code_integer ) > set_Code_integer > code_integer ) > ( code_integer > code_integer ) > set_set_Code_integer > code_integer ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001_062_It__Set__Oset_It__Code____Numeral__Ointeger_J_Mt__Rat__Orat_J_001_062_It__Set__Oset_It__Set__Oset_It__Code____Numeral__Ointeger_J_J_Mt__Rat__Orat_J_001_062_It__Code____Numeral__Ointeger_Mt__Rat__Orat_J,type,
% 9.09/5.28 comp_s9045439038509510147er_rat: ( ( set_Code_integer > rat ) > set_set_Code_integer > rat ) > ( ( code_integer > rat ) > set_Code_integer > rat ) > ( code_integer > rat ) > set_set_Code_integer > rat ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001_062_It__Set__Oset_It__Int__Oint_J_Mt__Assertions__Oassn_J_001_062_It__Set__Oset_It__Set__Oset_It__Int__Oint_J_J_Mt__Assertions__Oassn_J_001_062_It__Int__Oint_Mt__Assertions__Oassn_J,type,
% 9.09/5.28 comp_s4595925057662634336t_assn: ( ( set_int > assn ) > set_set_int > assn ) > ( ( int > assn ) > set_int > assn ) > ( int > assn ) > set_set_int > assn ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001_062_It__Set__Oset_It__Int__Oint_J_Mt__Code____Numeral__Ointeger_J_001_062_It__Set__Oset_It__Set__Oset_It__Int__Oint_J_J_Mt__Code____Numeral__Ointeger_J_001_062_It__Int__Oint_Mt__Code____Numeral__Ointeger_J,type,
% 9.09/5.28 comp_s7646638485285982975nteger: ( ( set_int > code_integer ) > set_set_int > code_integer ) > ( ( int > code_integer ) > set_int > code_integer ) > ( int > code_integer ) > set_set_int > code_integer ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001_062_It__Set__Oset_It__Int__Oint_J_Mt__Rat__Orat_J_001_062_It__Set__Oset_It__Set__Oset_It__Int__Oint_J_J_Mt__Rat__Orat_J_001_062_It__Int__Oint_Mt__Rat__Orat_J,type,
% 9.09/5.28 comp_s4088261402702255472nt_rat: ( ( set_int > rat ) > set_set_int > rat ) > ( ( int > rat ) > set_int > rat ) > ( int > rat ) > set_set_int > rat ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001_Eo_001_Eo_001_Eo,type,
% 9.09/5.28 comp_o_o_o: ( $o > $o ) > ( $o > $o ) > $o > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001_Eo_001_Eo_001t__Nat__Onat,type,
% 9.09/5.28 comp_o_o_nat: ( $o > $o ) > ( nat > $o ) > nat > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001_Eo_001_Eo_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 9.09/5.28 comp_o8022916681612831582at_nat: ( $o > $o ) > ( product_prod_nat_nat > $o ) > product_prod_nat_nat > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Code____Numeral__Ointeger,type,
% 9.09/5.28 comp_C2931745410781319416nteger: ( code_integer > code_integer > code_integer ) > ( code_integer > code_integer ) > code_integer > code_integer > code_integer ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Num__Onum,type,
% 9.09/5.28 comp_C3662112809048933045er_num: ( code_integer > code_integer > code_integer ) > ( num > code_integer ) > num > code_integer > code_integer ).
% 9.09/5.28
% 9.09/5.28 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_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 9.09/5.28 comp_C95226695241045696nteger: ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( ( code_integer > code_integer ) > code_integer ) > ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 9.09/5.28
% 9.09/5.28 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,
% 9.09/5.28 comp_C1593894019821074884nteger: ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 9.09/5.28
% 9.09/5.28 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__Num__Onum,type,
% 9.09/5.28 comp_C6617437204949736321er_num: ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( num > code_integer ) > num > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001t__Assertions__Oassn_001t__Nat__Onat,type,
% 9.09/5.28 comp_C8462447471145125178sn_nat: ( code_integer > assn ) > ( nat > code_integer ) > nat > assn ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 9.09/5.28 comp_C7449957260575251196nteger: ( code_integer > code_integer ) > ( code_integer > code_integer ) > code_integer > code_integer ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Nat__Onat,type,
% 9.09/5.28 comp_C6974050283906349679er_nat: ( code_integer > code_integer ) > ( nat > code_integer ) > nat > code_integer ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Num__Onum,type,
% 9.09/5.28 comp_C3531382070062128313er_num: ( code_integer > code_integer ) > ( num > code_integer ) > num > code_integer ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 9.09/5.28 comp_C1043215000170864188nteger: ( code_integer > code_integer ) > ( produc8923325533196201883nteger > code_integer ) > produc8923325533196201883nteger > code_integer ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001t__Int__Oint_001t__Int__Oint,type,
% 9.09/5.28 comp_C5046419837055054490nt_int: ( code_integer > int ) > ( int > code_integer ) > int > int ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001t__Int__Oint_001t__Nat__Onat,type,
% 9.09/5.28 comp_C5048910307564104766nt_nat: ( code_integer > int ) > ( nat > code_integer ) > nat > int ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001t__Nat__Onat_001t__Nat__Onat,type,
% 9.09/5.28 comp_C4049556595663050210at_nat: ( code_integer > nat ) > ( nat > code_integer ) > nat > nat ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 9.09/5.28 comp_C2277306503614464128nteger: ( code_integer > produc8923325533196201883nteger ) > ( produc8923325533196201883nteger > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001t__Product____Type__Ounit_001t__Nat__Onat,type,
% 9.09/5.28 comp_C8086623346886033437it_nat: ( code_integer > product_unit ) > ( nat > code_integer ) > nat > product_unit ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001t__Rat__Orat_001t__Nat__Onat,type,
% 9.09/5.28 comp_C3733001951728184298at_nat: ( code_integer > rat ) > ( nat > code_integer ) > nat > rat ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001_062_It__Int__Oint_M_Eo_J_001t__Int__Oint,type,
% 9.09/5.28 comp_int_int_o_int: ( int > int > $o ) > ( int > int ) > int > int > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001_062_It__Int__Oint_Mt__Int__Oint_J_001t__Int__Oint,type,
% 9.09/5.28 comp_int_int_int_int: ( int > int > int ) > ( int > int ) > int > int > int ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001_062_It__Int__Oint_Mt__Int__Oint_J_001t__Nat__Onat,type,
% 9.09/5.28 comp_int_int_int_nat: ( int > int > int ) > ( nat > int ) > nat > int > int ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001_062_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001t__Int__Oint,type,
% 9.09/5.28 comp_i87437609017934369nt_int: ( int > int > product_prod_int_int ) > ( int > int ) > int > int > product_prod_int_int ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001_062_It__Int__Oint_Mt__Rat__Orat_J_001t__Int__Oint,type,
% 9.09/5.28 comp_int_int_rat_int: ( int > int > rat ) > ( int > int ) > int > int > rat ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001_062_It__Nat__Onat_M_Eo_J_001t__Int__Oint,type,
% 9.09/5.28 comp_int_nat_o_int: ( int > nat > $o ) > ( int > int ) > int > nat > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Assertions__Oassn_001t__Int__Oint,type,
% 9.09/5.28 comp_int_assn_int: ( int > assn ) > ( int > int ) > int > assn ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Assertions__Oassn_001t__Nat__Onat,type,
% 9.09/5.28 comp_int_assn_nat: ( int > assn ) > ( nat > int ) > nat > assn ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Code____Numeral__Ointeger_001t__Int__Oint,type,
% 9.09/5.28 comp_i1585864551200866970er_int: ( int > code_integer ) > ( int > int ) > int > code_integer ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Code____Numeral__Ointeger_001t__Nat__Onat,type,
% 9.09/5.28 comp_i1588355021709917246er_nat: ( int > code_integer ) > ( nat > int ) > nat > code_integer ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint,type,
% 9.09/5.28 comp_int_int_int: ( int > int ) > ( int > int ) > int > int ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Int__Oint_001t__Nat__Onat,type,
% 9.09/5.28 comp_int_int_nat: ( int > int ) > ( nat > int ) > nat > int ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Int__Oint_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 9.09/5.28 comp_i4330622015127193916nt_int: ( int > int ) > ( product_prod_int_int > int ) > product_prod_int_int > int ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Nat__Onat_001t__Int__Oint,type,
% 9.09/5.28 comp_int_nat_int: ( int > nat ) > ( int > int ) > int > nat ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Nat__Onat_001t__Nat__Onat,type,
% 9.09/5.28 comp_int_nat_nat: ( int > nat ) > ( nat > int ) > nat > nat ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Num__Onum_001t__Int__Oint,type,
% 9.09/5.28 comp_int_num_int: ( int > num ) > ( int > int ) > int > num ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 9.09/5.28 comp_i5941103828406351439nt_int: ( int > product_prod_int_int ) > ( product_prod_int_int > int ) > product_prod_int_int > product_prod_int_int ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint,type,
% 9.09/5.28 comp_i1108739374719436894at_int: ( int > product_prod_nat_nat ) > ( int > int ) > int > product_prod_nat_nat ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Rat__Orat_001t__Int__Oint,type,
% 9.09/5.28 comp_int_rat_int: ( int > rat ) > ( int > int ) > int > rat ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Rat__Orat_001t__Nat__Onat,type,
% 9.09/5.28 comp_int_rat_nat: ( int > rat ) > ( nat > int ) > nat > rat ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat,type,
% 9.09/5.28 comp_nat_nat_nat_nat: ( nat > nat > nat ) > ( nat > nat ) > nat > nat > nat ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001_Eo_001t__Nat__Onat,type,
% 9.09/5.28 comp_nat_o_nat: ( nat > $o ) > ( nat > nat ) > nat > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Assertions__Oassn_001t__Nat__Onat,type,
% 9.09/5.28 comp_nat_assn_nat: ( nat > assn ) > ( nat > nat ) > nat > assn ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Code____Numeral__Ointeger_001t__Nat__Onat,type,
% 9.09/5.28 comp_n3898172953802868194er_nat: ( nat > code_integer ) > ( nat > nat ) > nat > code_integer ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Int__Oint_001t__Int__Oint,type,
% 9.09/5.28 comp_nat_int_int: ( nat > int ) > ( int > nat ) > int > int ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Int__Oint_001t__Nat__Onat,type,
% 9.09/5.28 comp_nat_int_nat: ( nat > int ) > ( nat > nat ) > nat > int ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Nat__Onat,type,
% 9.09/5.28 comp_n8698576032424989604at_nat: ( nat > multis2468970476368604999at_nat ) > ( nat > nat ) > nat > multis2468970476368604999at_nat ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Nat__Onat_001t__Int__Oint,type,
% 9.09/5.28 comp_nat_nat_int: ( nat > nat ) > ( int > nat ) > int > nat ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
% 9.09/5.28 comp_nat_nat_nat: ( nat > nat ) > ( nat > nat ) > nat > nat ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Num__Onum_001t__Int__Oint,type,
% 9.09/5.28 comp_nat_num_int: ( nat > num ) > ( int > nat ) > int > num ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Num__Onum_001t__Nat__Onat,type,
% 9.09/5.28 comp_nat_num_nat: ( nat > num ) > ( nat > nat ) > nat > num ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Product____Type__Ounit_001t__Nat__Onat,type,
% 9.09/5.28 comp_n9025697279074352746it_nat: ( nat > product_unit ) > ( nat > nat ) > nat > product_unit ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Rat__Orat_001t__Nat__Onat,type,
% 9.09/5.28 comp_nat_rat_nat: ( nat > rat ) > ( nat > nat ) > nat > rat ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Num__Onum_001t__Code____Numeral__Ointeger_001t__Num__Onum,type,
% 9.09/5.28 comp_n6909714581898973814er_num: ( num > code_integer ) > ( num > num ) > num > code_integer ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Num__Onum_001t__Int__Oint_001t__Num__Onum,type,
% 9.09/5.28 comp_num_int_num: ( num > int ) > ( num > num ) > num > int ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Num__Onum_001t__Nat__Onat_001t__Num__Onum,type,
% 9.09/5.28 comp_num_nat_num: ( num > nat ) > ( num > num ) > num > nat ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Num__Onum_001t__Num__Onum_001t__Int__Oint,type,
% 9.09/5.28 comp_num_num_int: ( num > num ) > ( int > num ) > int > num ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Num__Onum_001t__Num__Onum_001t__Nat__Onat,type,
% 9.09/5.28 comp_num_num_nat: ( num > num ) > ( nat > num ) > nat > num ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Num__Onum_001t__Num__Onum_001t__Num__Onum,type,
% 9.09/5.28 comp_num_num_num: ( num > num ) > ( num > num ) > num > num ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Num__Onum_001t__Option__Ooption_It__Num__Onum_J_001t__Num__Onum,type,
% 9.09/5.28 comp_n6731957995704128387um_num: ( num > option_num ) > ( num > num ) > num > option_num ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Option__Ooption_I_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001t__Option__Ooption_I_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_J_001t__Option__Ooption_It__Code____Numeral__Ointeger_J,type,
% 9.09/5.28 comp_o7188567781464924208nteger: ( option8057788054806935849nteger > option7428179582072448501nteger ) > ( option_Code_integer > option8057788054806935849nteger ) > option_Code_integer > option7428179582072448501nteger ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Option__Ooption_I_062_It__Nat__Onat_M_Eo_J_J_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Nat__Onat_M_Eo_J,type,
% 9.09/5.28 comp_o8860755393669798242_nat_o: ( option_nat_o > nat > $o ) > ( ( nat > $o ) > option_nat_o ) > ( nat > $o ) > nat > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Option__Ooption_I_Eo_J_001_Eo_001_Eo,type,
% 9.09/5.28 comp_option_o_o_o: ( option_o > $o ) > ( $o > option_o ) > $o > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Option__Ooption_It__Code____Numeral__Ointeger_J_001t__Option__Ooption_I_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_J_001t__Option__Ooption_It__Code____Numeral__Ointeger_J,type,
% 9.09/5.28 comp_o9011007105448239796nteger: ( option_Code_integer > option7428179582072448501nteger ) > ( option_Code_integer > option_Code_integer ) > option_Code_integer > option7428179582072448501nteger ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Option__Ooption_It__Code____Numeral__Ointeger_J_001t__Option__Ooption_It__Code____Numeral__Ointeger_J_001t__Option__Ooption_It__Num__Onum_J,type,
% 9.09/5.28 comp_o5321900959263616553on_num: ( option_Code_integer > option_Code_integer ) > ( option_num > option_Code_integer ) > option_num > option_Code_integer ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Option__Ooption_It__Int__Oint_J_001t__Int__Oint_001t__Int__Oint,type,
% 9.09/5.28 comp_o2446264010603541305nt_int: ( option_int > int ) > ( int > option_int ) > int > int ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Option__Ooption_It__Nat__Onat_J_001t__Nat__Onat_001t__Nat__Onat,type,
% 9.09/5.28 comp_o4663963155070737957at_nat: ( option_nat > nat ) > ( nat > option_nat ) > nat > nat ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Option__Ooption_It__Nat__Onat_J_001t__Option__Ooption_It__Num__Onum_J_001t__Option__Ooption_It__Int__Oint_J,type,
% 9.09/5.28 comp_o3128663659858294251on_int: ( option_nat > option_num ) > ( option_int > option_nat ) > option_int > option_num ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Option__Ooption_It__Num__Onum_J_001t__Nat__Onat_001t__Option__Ooption_It__Num__Onum_J,type,
% 9.09/5.28 comp_o6878144249584144265on_num: ( option_num > nat ) > ( option_num > option_num ) > option_num > nat ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Option__Ooption_It__Num__Onum_J_001t__Num__Onum_001t__Num__Onum,type,
% 9.09/5.28 comp_o6342398210560591875um_num: ( option_num > num ) > ( num > option_num ) > num > num ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Option__Ooption_It__Num__Onum_J_001t__Option__Ooption_It__Num__Onum_J_001t__Option__Ooption_It__Num__Onum_J,type,
% 9.09/5.28 comp_o8931257242830428707on_num: ( option_num > option_num ) > ( option_num > option_num ) > option_num > option_num ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 9.09/5.28 comp_o279924169626513613it_nat: ( option8956607266484857688it_nat > produc8664842809031399944it_nat ) > ( produc8664842809031399944it_nat > option8956607266484857688it_nat ) > produc8664842809031399944it_nat > produc8664842809031399944it_nat ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_I_062_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_062_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_J,type,
% 9.09/5.28 comp_P1875353012086385820e_term: ( produc7773217078559923341nt_int > int > option6357759511663192854e_term ) > ( produc3832618445565238089e_term > produc7773217078559923341nt_int ) > produc3832618445565238089e_term > int > option6357759511663192854e_term ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_I_062_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_062_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_J,type,
% 9.09/5.28 comp_P5363713469694551954e_term: ( produc7773217078559923341nt_int > product_prod_int_int ) > ( produc3832618445565238089e_term > produc7773217078559923341nt_int ) > produc3832618445565238089e_term > product_prod_int_int ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_I_062_It__Nat__Onat_M_Eo_J_M_062_It__Nat__Onat_M_Eo_J_J_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Nat__Onat_M_Eo_J,type,
% 9.09/5.28 comp_P8312345242777556868_nat_o: ( produc7360885484439884007_nat_o > nat > $o ) > ( ( nat > $o ) > produc7360885484439884007_nat_o ) > ( nat > $o ) > nat > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_I_062_It__Nat__Onat_M_Eo_J_M_062_It__Nat__Onat_M_Eo_J_J_001_062_It__Nat__Onat_M_Eo_J_001t__Int__Oint,type,
% 9.09/5.28 comp_P1075760313067033319_o_int: ( produc7360885484439884007_nat_o > nat > $o ) > ( int > produc7360885484439884007_nat_o ) > int > nat > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_M_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_J,type,
% 9.09/5.28 comp_P8650103696410638905e_term: ( produc1908205239877642774nteger > produc6241069584506657477e_term > option6357759511663192854e_term ) > ( produc998928222018024388e_term > produc1908205239877642774nteger ) > produc998928222018024388e_term > produc6241069584506657477e_term > option6357759511663192854e_term ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_M_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_J,type,
% 9.09/5.28 comp_P1663382703091044646e_term: ( produc1908205239877642774nteger > produc8923325533196201883nteger ) > ( produc998928222018024388e_term > produc1908205239877642774nteger ) > produc998928222018024388e_term > produc8923325533196201883nteger ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_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_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__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_M_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_J,type,
% 9.09/5.28 comp_P4355506512671352436_nat_o: ( produc2732055786443039994et_nat > produc3658429121746597890et_nat > $o ) > ( produc4962441903510821572_nat_o > produc2732055786443039994et_nat ) > produc4962441903510821572_nat_o > produc3658429121746597890et_nat > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_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_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_001t__Product____Type__Oprod_It__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_M_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_J,type,
% 9.09/5.28 comp_P9183373265949749025_nat_o: ( produc2732055786443039994et_nat > produc3925858234332021118et_nat ) > ( produc4962441903510821572_nat_o > produc2732055786443039994et_nat ) > produc4962441903510821572_nat_o > produc3925858234332021118et_nat ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_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_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__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_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_J,type,
% 9.09/5.28 comp_P1110778729668777324_nat_o: ( produc3925858234332021118et_nat > produc3658429121746597890et_nat > $o ) > ( produc6907119039986491712_nat_o > produc3925858234332021118et_nat ) > produc6907119039986491712_nat_o > produc3658429121746597890et_nat > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_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_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_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_J,type,
% 9.09/5.28 comp_P5089495125153697957_nat_o: ( produc3925858234332021118et_nat > produc3658429121746597890et_nat ) > ( produc6907119039986491712_nat_o > produc3925858234332021118et_nat ) > produc6907119039986491712_nat_o > produc3658429121746597890et_nat ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Int__Oint_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Product____Type__Oprod_It__Int__Oint_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_062_It__Product____Type__Oprod_It__Int__Oint_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_J,type,
% 9.09/5.28 comp_P8577347034251779110e_term: ( produc2285326912895808259nt_int > produc8551481072490612790e_term > option6357759511663192854e_term ) > ( produc1821397396195235155e_term > produc2285326912895808259nt_int ) > produc1821397396195235155e_term > produc8551481072490612790e_term > option6357759511663192854e_term ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Int__Oint_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_062_It__Product____Type__Oprod_It__Int__Oint_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_J,type,
% 9.09/5.28 comp_P4057098934159210662e_term: ( produc2285326912895808259nt_int > product_prod_int_int ) > ( produc1821397396195235155e_term > produc2285326912895808259nt_int ) > produc1821397396195235155e_term > product_prod_int_int ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_I_Eo_M_Eo_J_001_Eo_001_Eo,type,
% 9.09/5.28 comp_P2137996956111167876_o_o_o: ( product_prod_o_o > $o ) > ( $o > product_prod_o_o ) > $o > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 9.09/5.28 comp_P7111796090210262324nteger: ( produc8923325533196201883nteger > code_integer ) > ( code_integer > produc8923325533196201883nteger ) > code_integer > code_integer ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Code____Numeral__Ointeger_001t__Int__Oint,type,
% 9.09/5.28 comp_P3107242062624629507er_int: ( produc8923325533196201883nteger > code_integer ) > ( int > produc8923325533196201883nteger ) > int > code_integer ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Code____Numeral__Ointeger_001t__Nat__Onat,type,
% 9.09/5.28 comp_P3109732533133679783er_nat: ( produc8923325533196201883nteger > code_integer ) > ( nat > produc8923325533196201883nteger ) > nat > code_integer ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Code____Numeral__Ointeger_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 9.09/5.28 comp_P3428181540658402820nteger: ( produc8923325533196201883nteger > code_integer ) > ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > produc8923325533196201883nteger > code_integer ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Code____Numeral__Ointeger_001t__Product____Type__Ounit,type,
% 9.09/5.28 comp_P659088277599099894t_unit: ( produc8923325533196201883nteger > code_integer ) > ( product_unit > produc8923325533196201883nteger ) > product_unit > code_integer ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Int__Oint_J_001t__Code____Numeral__Ointeger_001t__Nat__Onat,type,
% 9.09/5.28 comp_P2475326853202991862er_nat: ( produc2256096406371053034er_int > code_integer ) > ( nat > produc2256096406371053034er_int ) > nat > code_integer ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Int__Oint_J_001t__Int__Oint_001t__Nat__Onat,type,
% 9.09/5.28 comp_P8345930540558018757nt_nat: ( produc2256096406371053034er_int > int ) > ( nat > produc2256096406371053034er_int ) > nat > int ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Nat__Onat_J_001t__Code____Numeral__Ointeger_001t__Nat__Onat,type,
% 9.09/5.28 comp_P5700178199414968986er_nat: ( produc6433947425880249742er_nat > code_integer ) > ( nat > produc6433947425880249742er_nat ) > nat > code_integer ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Nat__Onat_J_001t__Nat__Onat_001t__Nat__Onat,type,
% 9.09/5.28 comp_P1337767177661389325at_nat: ( produc6433947425880249742er_nat > nat ) > ( nat > produc6433947425880249742er_nat ) > nat > nat ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J,type,
% 9.09/5.28 comp_P3067963646784605345atural: ( produc7822875418678951345atural > produc7822875418678951345atural ) > ( produc5835291356934675326atural > produc7822875418678951345atural ) > produc5835291356934675326atural > produc7822875418678951345atural ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J,type,
% 9.09/5.28 comp_P4943825737035310295atural: ( produc7822875418678951345atural > produc6756470014200349799atural ) > ( produc5835291356934675326atural > produc7822875418678951345atural ) > produc5835291356934675326atural > produc6756470014200349799atural ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J_001t__Code____Numeral__Onatural_001t__Int__Oint,type,
% 9.09/5.28 comp_P5589825499870570807al_int: ( produc5835291356934675326atural > code_natural ) > ( int > produc5835291356934675326atural ) > int > code_natural ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J_001t__Code____Numeral__Onatural_001t__Nat__Onat,type,
% 9.09/5.28 comp_P5592315970379621083al_nat: ( produc5835291356934675326atural > code_natural ) > ( nat > produc5835291356934675326atural ) > nat > code_natural ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J_001t__Code____Numeral__Onatural_001t__Product____Type__Ounit,type,
% 9.09/5.28 comp_P210409258367696578t_unit: ( produc5835291356934675326atural > code_natural ) > ( product_unit > produc5835291356934675326atural ) > product_unit > code_natural ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_001t__Int__Oint,type,
% 9.09/5.28 comp_P8475394669922486716al_int: ( produc5835291356934675326atural > produc7822875418678951345atural ) > ( int > produc5835291356934675326atural ) > int > produc7822875418678951345atural ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_001t__Nat__Onat,type,
% 9.09/5.28 comp_P8477885140431536992al_nat: ( produc5835291356934675326atural > produc7822875418678951345atural ) > ( nat > produc5835291356934675326atural ) > nat > produc7822875418678951345atural ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J,type,
% 9.09/5.28 comp_P7610810914149544718atural: ( produc5835291356934675326atural > produc7822875418678951345atural ) > ( produc5835291356934675326atural > produc5835291356934675326atural ) > produc5835291356934675326atural > produc7822875418678951345atural ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_Mt__Code____Numeral__Onatural_J,type,
% 9.09/5.28 comp_P5756991293874479000atural: ( produc5835291356934675326atural > produc7822875418678951345atural ) > ( produc3981471736659609608atural > produc5835291356934675326atural ) > produc3981471736659609608atural > produc7822875418678951345atural ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_001t__Product____Type__Ounit,type,
% 9.09/5.28 comp_P1945487127105810045t_unit: ( produc5835291356934675326atural > produc7822875418678951345atural ) > ( product_unit > produc5835291356934675326atural ) > product_unit > produc7822875418678951345atural ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_001t__Option__Ooption_It__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J,type,
% 9.09/5.28 comp_P2097125496263478628t_unit: ( produc6714399278180371524it_nat > option3216581401566546698it_nat ) > ( heap_e7401611519738050253t_unit > produc6714399278180371524it_nat ) > heap_e7401611519738050253t_unit > option3216581401566546698it_nat ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Int__Oint_Mt__Code____Numeral__Ointeger_J_001t__Code____Numeral__Ointeger_001t__Nat__Onat,type,
% 9.09/5.28 comp_P6870028373966156406er_nat: ( produc2963269191615333738nteger > code_integer ) > ( nat > produc2963269191615333738nteger ) > nat > code_integer ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Int__Oint_Mt__Code____Numeral__Ointeger_J_001t__Int__Oint_001t__Nat__Onat,type,
% 9.09/5.28 comp_P59025373045620805nt_nat: ( produc2963269191615333738nteger > int ) > ( nat > produc2963269191615333738nteger ) > nat > int ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Int__Oint_001t__Int__Oint,type,
% 9.09/5.28 comp_P6651465171681656048nt_int: ( product_prod_int_int > int ) > ( int > product_prod_int_int ) > int > int ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Int__Oint_001t__Nat__Onat,type,
% 9.09/5.28 comp_P6653955642190706324nt_nat: ( product_prod_int_int > int ) > ( nat > product_prod_int_int ) > nat > int ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Int__Oint_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 9.09/5.28 comp_P5356232565778667509nt_int: ( product_prod_int_int > int ) > ( product_prod_int_int > product_prod_int_int ) > product_prod_int_int > int ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Int__Oint_001t__Product____Type__Ounit,type,
% 9.09/5.28 comp_P6796073005956588617t_unit: ( product_prod_int_int > int ) > ( product_unit > product_prod_int_int ) > product_unit > int ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Rat__Orat_001t__Int__Oint,type,
% 9.09/5.28 comp_P5335556815845735580at_int: ( product_prod_int_int > rat ) > ( int > product_prod_int_int ) > int > rat ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Rat__Orat_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 9.09/5.28 comp_P5648219952011055433nt_int: ( product_prod_int_int > rat ) > ( product_prod_int_int > product_prod_int_int ) > product_prod_int_int > rat ).
% 9.09/5.28
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% 9.09/5.28 comp_P645145991195131448nt_nat: ( product_prod_int_nat > int ) > ( nat > product_prod_int_nat ) > nat > int ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Int__Oint_Mt__Nat__Onat_J_001t__Nat__Onat_001t__Nat__Onat,type,
% 9.09/5.28 comp_P8869164316148852700at_nat: ( product_prod_int_nat > nat ) > ( nat > product_prod_int_nat ) > nat > nat ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J_001t__Code____Numeral__Ointeger_001t__Nat__Onat,type,
% 9.09/5.28 comp_P5461341465284484122er_nat: ( produc2591615631378489102nteger > code_integer ) > ( nat > produc2591615631378489102nteger ) > nat > code_integer ).
% 9.09/5.28
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% 9.09/5.28 comp_P9144323761349829517at_nat: ( produc2591615631378489102nteger > nat ) > ( nat > produc2591615631378489102nteger ) > nat > nat ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Int__Oint_J_001t__Int__Oint_001t__Nat__Onat,type,
% 9.09/5.28 comp_P8963773574283657272nt_nat: ( product_prod_nat_int > int ) > ( nat > product_prod_nat_int ) > nat > int ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Int__Oint_J_001t__Nat__Onat_001t__Nat__Onat,type,
% 9.09/5.28 comp_P7964419862382602716at_nat: ( product_prod_nat_int > nat ) > ( nat > product_prod_nat_int ) > nat > nat ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Int__Oint_M_Eo_J_001t__Int__Oint,type,
% 9.09/5.28 comp_P7507668834397697393_o_int: ( product_prod_nat_nat > int > $o ) > ( int > product_prod_nat_nat ) > int > int > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Int__Oint_Mt__Int__Oint_J_001t__Int__Oint,type,
% 9.09/5.28 comp_P1029605119844863363nt_int: ( product_prod_nat_nat > int > int ) > ( int > product_prod_nat_nat ) > int > int > int ).
% 9.09/5.28
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% 9.09/5.28 comp_P1289042343629989734_o_int: ( product_prod_nat_nat > $o ) > ( int > product_prod_nat_nat ) > int > $o ).
% 9.09/5.28
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% 9.09/5.28 comp_P1955610211387027840at_nat: ( product_prod_nat_nat > nat ) > ( nat > product_prod_nat_nat ) > nat > nat ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat_001t__Product____Type__Ounit,type,
% 9.09/5.28 comp_P2980510830910040157t_unit: ( product_prod_nat_nat > nat ) > ( product_unit > product_prod_nat_nat ) > product_unit > nat ).
% 9.09/5.28
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% 9.09/5.28 comp_P7428279379633703887at_int: ( product_prod_nat_nat > product_prod_nat_nat ) > ( int > product_prod_nat_nat ) > int > product_prod_nat_nat ).
% 9.09/5.28
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% 9.09/5.28 comp_P864883071962432936um_num: ( product_prod_num_num > num ) > ( num > product_prod_num_num ) > num > num ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_Mt__Code____Numeral__Onatural_J_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J,type,
% 9.09/5.28 comp_P3887058762840424708atural: ( produc3981471736659609608atural > produc7822875418678951345atural ) > ( produc5835291356934675326atural > produc3981471736659609608atural ) > produc5835291356934675326atural > produc7822875418678951345atural ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J,type,
% 9.09/5.28 comp_P230220204662055659atural: ( produc6756470014200349799atural > produc7822875418678951345atural ) > ( produc5835291356934675326atural > produc6756470014200349799atural ) > produc5835291356934675326atural > produc7822875418678951345atural ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_001t__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J,type,
% 9.09/5.28 comp_P3118722334806803912t_unit: ( produc8664842809031399944it_nat > option8956607266484857688it_nat ) > ( heap_e7401611519738050253t_unit > produc8664842809031399944it_nat ) > heap_e7401611519738050253t_unit > option8956607266484857688it_nat ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Product____Type__Ounit_001t__Code____Numeral__Ointeger_001t__Nat__Onat,type,
% 9.09/5.28 comp_P756492639069434009er_nat: ( product_unit > code_integer ) > ( nat > product_unit ) > nat > code_integer ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Product____Type__Ounit_001t__Product____Type__Ounit_001t__Product____Type__Ounit,type,
% 9.09/5.28 comp_P7645380973975430442t_unit: ( product_unit > product_unit ) > ( product_unit > product_unit ) > product_unit > product_unit ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Rat__Orat_001t__Nat__Onat_001t__Nat__Onat,type,
% 9.09/5.28 comp_rat_nat_nat: ( rat > nat ) > ( nat > rat ) > nat > nat ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Rat__Orat_001t__Rat__Orat_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 9.09/5.28 comp_r4727614531642239972nt_int: ( rat > rat ) > ( product_prod_int_int > rat ) > product_prod_int_int > rat ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ocomp_001t__Rat__Orat_001t__Rat__Orat_001t__Rat__Orat,type,
% 9.09/5.28 comp_rat_rat_rat: ( rat > rat ) > ( rat > rat ) > rat > rat ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ofun__upd_001_Eo_001_Eo,type,
% 9.09/5.28 fun_upd_o_o: ( $o > $o ) > $o > $o > $o > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ofun__upd_001_Eo_001t__Int__Oint,type,
% 9.09/5.28 fun_upd_o_int: ( $o > int ) > $o > int > $o > int ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ofun__upd_001_Eo_001t__Nat__Onat,type,
% 9.09/5.28 fun_upd_o_nat: ( $o > nat ) > $o > nat > $o > nat ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ofun__upd_001_Eo_001t__Option__Ooption_It__Num__Onum_J,type,
% 9.09/5.28 fun_upd_o_option_num: ( $o > option_num ) > $o > option_num > $o > option_num ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ofun__upd_001_Eo_001t__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
% 9.09/5.28 fun_up1288979561775348147it_nat: ( $o > option8956607266484857688it_nat ) > $o > option8956607266484857688it_nat > $o > option8956607266484857688it_nat ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ofun__upd_001t__Code____Numeral__Ointeger_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 9.09/5.28 fun_up8056716234270145717nteger: ( code_integer > code_integer > code_integer ) > code_integer > ( code_integer > code_integer ) > code_integer > code_integer > code_integer ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ofun__upd_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,type,
% 9.09/5.28 fun_up8139772397987072257nteger: ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > code_integer > ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ofun__upd_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 9.09/5.28 fun_up8355007323143964473nteger: ( code_integer > code_integer ) > code_integer > code_integer > code_integer > code_integer ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ofun__upd_001t__Code____Numeral__Ointeger_001t__Option__Ooption_It__Code____Numeral__Ointeger_J,type,
% 9.09/5.28 fun_up6566892301432185865nteger: ( code_integer > option_Code_integer ) > code_integer > option_Code_integer > code_integer > option_Code_integer ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ofun__upd_001t__Code____Numeral__Onatural_001t__Option__Ooption_It__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J,type,
% 9.09/5.28 fun_up2923169431403285008atural: ( code_natural > option5403585828896915703atural ) > code_natural > option5403585828896915703atural > code_natural > option5403585828896915703atural ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ofun__upd_001t__Int__Oint_001_Eo,type,
% 9.09/5.28 fun_upd_int_o: ( int > $o ) > int > $o > int > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ofun__upd_001t__Int__Oint_001t__Int__Oint,type,
% 9.09/5.28 fun_upd_int_int: ( int > int ) > int > int > int > int ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ofun__upd_001t__Int__Oint_001t__Nat__Onat,type,
% 9.09/5.28 fun_upd_int_nat: ( int > nat ) > int > nat > int > nat ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ofun__upd_001t__Int__Oint_001t__Num__Onum,type,
% 9.09/5.28 fun_upd_int_num: ( int > num ) > int > num > int > num ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ofun__upd_001t__Int__Oint_001t__Option__Ooption_It__Int__Oint_J,type,
% 9.09/5.28 fun_up8666045135305973159on_int: ( int > option_int ) > int > option_int > int > option_int ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ofun__upd_001t__Int__Oint_001t__Option__Ooption_It__Num__Onum_J,type,
% 9.09/5.28 fun_up4328768054909231765on_num: ( int > option_num ) > int > option_num > int > option_num ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ofun__upd_001t__Int__Oint_001t__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
% 9.09/5.28 fun_up6992348036167380867it_nat: ( int > option8956607266484857688it_nat ) > int > option8956607266484857688it_nat > int > option8956607266484857688it_nat ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ofun__upd_001t__Nat__Onat_001_Eo,type,
% 9.09/5.28 fun_upd_nat_o: ( nat > $o ) > nat > $o > nat > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ofun__upd_001t__Nat__Onat_001t__Code____Numeral__Ointeger,type,
% 9.09/5.28 fun_up3904115110581602988nteger: ( nat > code_integer ) > nat > code_integer > nat > code_integer ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ofun__upd_001t__Nat__Onat_001t__Int__Oint,type,
% 9.09/5.28 fun_upd_nat_int: ( nat > int ) > nat > int > nat > int ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ofun__upd_001t__Nat__Onat_001t__Nat__Onat,type,
% 9.09/5.28 fun_upd_nat_nat: ( nat > nat ) > nat > nat > nat > nat ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ofun__upd_001t__Nat__Onat_001t__Option__Ooption_It__Nat__Onat_J,type,
% 9.09/5.28 fun_up1493157387958331631on_nat: ( nat > option_nat ) > nat > option_nat > nat > option_nat ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ofun__upd_001t__Nat__Onat_001t__Option__Ooption_It__Num__Onum_J,type,
% 9.09/5.28 fun_up2201401324907169337on_num: ( nat > option_num ) > nat > option_num > nat > option_num ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ofun__upd_001t__Nat__Onat_001t__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
% 9.09/5.28 fun_up4116053422210368295it_nat: ( nat > option8956607266484857688it_nat ) > nat > option8956607266484857688it_nat > nat > option8956607266484857688it_nat ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ofun__upd_001t__Nat__Onat_001t__Set__Oset_It__Nat__Onat_J,type,
% 9.09/5.28 fun_upd_nat_set_nat: ( nat > set_nat ) > nat > set_nat > nat > set_nat ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ofun__upd_001t__Num__Onum_001t__Code____Numeral__Ointeger,type,
% 9.09/5.28 fun_up1844922938552261878nteger: ( num > code_integer ) > num > code_integer > num > code_integer ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ofun__upd_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Option__Ooption_It__Num__Onum_J,type,
% 9.09/5.28 fun_up8025039454679724718on_num: ( product_prod_nat_nat > option_num ) > product_prod_nat_nat > option_num > product_prod_nat_nat > option_num ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ofun__upd_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
% 9.09/5.28 fun_up3996838528606387100it_nat: ( product_prod_nat_nat > option8956607266484857688it_nat ) > product_prod_nat_nat > option8956607266484857688it_nat > product_prod_nat_nat > option8956607266484857688it_nat ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ofun__upd_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__Option__Ooption_It__Num__Onum_J,type,
% 9.09/5.28 fun_up3286109336741039636on_num: ( produc3843707927480180839at_nat > option_num ) > produc3843707927480180839at_nat > option_num > produc3843707927480180839at_nat > option_num ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ofun__upd_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
% 9.09/5.28 fun_up5549328659429834498it_nat: ( produc3843707927480180839at_nat > option8956607266484857688it_nat ) > produc3843707927480180839at_nat > option8956607266484857688it_nat > produc3843707927480180839at_nat > option8956607266484857688it_nat ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ofun__upd_001t__Product____Type__Ounit_001t__Option__Ooption_It__Num__Onum_J,type,
% 9.09/5.28 fun_up4695802795598371002on_num: ( product_unit > option_num ) > product_unit > option_num > product_unit > option_num ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Ofun__upd_001t__Product____Type__Ounit_001t__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
% 9.09/5.28 fun_up1973317344121680296it_nat: ( product_unit > option8956607266484857688it_nat ) > product_unit > option8956607266484857688it_nat > product_unit > option8956607266484857688it_nat ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Oid_001_062_It__Nat__Onat_M_Eo_J,type,
% 9.09/5.28 id_nat_o: ( nat > $o ) > nat > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Oid_001_062_It__Num__Onum_Mt__Code____Numeral__Ointeger_J,type,
% 9.09/5.28 id_num_Code_integer: ( num > code_integer ) > num > code_integer ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Oid_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,type,
% 9.09/5.28 id_Pro496765588584934260nteger: ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Oid_001_Eo,type,
% 9.09/5.28 id_o: $o > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Oid_001t__Code____Numeral__Ointeger,type,
% 9.09/5.28 id_Code_integer: code_integer > code_integer ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Oid_001t__Int__Oint,type,
% 9.09/5.28 id_int: int > int ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Oid_001t__Nat__Onat,type,
% 9.09/5.28 id_nat: nat > nat ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Oid_001t__Num__Onum,type,
% 9.09/5.28 id_num: num > num ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Oid_001t__Option__Ooption_I_062_It__Nat__Onat_M_Eo_J_J,type,
% 9.09/5.28 id_option_nat_o: option_nat_o > option_nat_o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Oid_001t__Option__Ooption_I_Eo_J,type,
% 9.09/5.28 id_option_o: option_o > option_o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Oid_001t__Option__Ooption_It__Int__Oint_J,type,
% 9.09/5.28 id_option_int: option_int > option_int ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Oid_001t__Option__Ooption_It__Nat__Onat_J,type,
% 9.09/5.28 id_option_nat: option_nat > option_nat ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Oid_001t__Option__Ooption_It__Num__Onum_J,type,
% 9.09/5.28 id_option_num: option_num > option_num ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Oid_001t__Product____Type__Oprod_I_062_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
% 9.09/5.28 id_Pro3923183700162330716nt_int: produc7773217078559923341nt_int > produc7773217078559923341nt_int ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Oid_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
% 9.09/5.28 id_Pro1379270990444177765nteger: produc1908205239877642774nteger > produc1908205239877642774nteger ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Oid_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,
% 9.09/5.28 id_Pro1297863087923562825et_nat: produc2732055786443039994et_nat > produc2732055786443039994et_nat ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Oid_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,
% 9.09/5.28 id_Pro1888964116897856973et_nat: produc3925858234332021118et_nat > produc3925858234332021118et_nat ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Oid_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Int__Oint_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
% 9.09/5.28 id_Pro5422067691592394322nt_int: produc2285326912895808259nt_int > produc2285326912895808259nt_int ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Oid_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 9.09/5.28 id_Pro2309048762231606924nteger: produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Oid_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 9.09/5.28 id_Pro4381231610383771306nt_int: product_prod_int_int > product_prod_int_int ).
% 9.09/5.28
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% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Oid_001t__Product____Type__Ounit,type,
% 9.09/5.28 id_Product_unit: product_unit > product_unit ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Oid_001t__Rat__Orat,type,
% 9.09/5.28 id_rat: rat > rat ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Oid_001t__Set__Oset_I_062_It__Nat__Onat_M_Eo_J_J,type,
% 9.09/5.28 id_set_nat_o: set_nat_o > set_nat_o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Oid_001t__Set__Oset_I_Eo_J,type,
% 9.09/5.28 id_set_o: set_o > set_o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Oid_001t__Set__Oset_It__Int__Oint_J,type,
% 9.09/5.28 id_set_int: set_int > set_int ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Oid_001t__Set__Oset_It__Nat__Onat_J,type,
% 9.09/5.28 id_set_nat: set_nat > set_nat ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Oid_001t__Set__Oset_It__Num__Onum_J,type,
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% 9.09/5.28
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% 9.09/5.28 map_fu1335501423231535891nteger: ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( num > code_integer ) > ( ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > num ) > code_integer > code_integer ).
% 9.09/5.28
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% 9.09/5.28 map_fu6423247683660063826nteger: ( code_integer > code_integer ) > ( ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 9.09/5.28
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% 9.09/5.28 map_fu2576242048321985878nteger: ( code_integer > code_integer ) > ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 9.09/5.28
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% 9.09/5.28 map_fu5082455417554595470nteger: ( code_integer > code_integer ) > ( code_integer > code_integer ) > ( code_integer > code_integer ) > code_integer > code_integer ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Omap__fun_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Int__Oint_001t__Nat__Onat,type,
% 9.09/5.28 map_fu5423760287386111952nt_nat: ( code_integer > code_integer ) > ( int > nat ) > ( code_integer > int ) > code_integer > nat ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Omap__fun_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Num__Onum_001t__Code____Numeral__Ointeger,type,
% 9.09/5.28 map_fu603974984455542859nteger: ( code_integer > code_integer ) > ( num > code_integer ) > ( code_integer > num ) > code_integer > code_integer ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Omap__fun_001t__Code____Numeral__Ointeger_001t__Int__Oint_001_062_It__Int__Oint_M_Eo_J_001_062_It__Code____Numeral__Ointeger_M_Eo_J,type,
% 9.09/5.28 map_fu2496120808607739376eger_o: ( code_integer > int ) > ( ( int > $o ) > code_integer > $o ) > ( int > int > $o ) > code_integer > code_integer > $o ).
% 9.09/5.28
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% 9.09/5.28 map_fu8272188784021352819nteger: ( code_integer > int ) > ( ( int > int ) > code_integer > code_integer ) > ( int > int > int ) > code_integer > code_integer > code_integer ).
% 9.09/5.28
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% 9.09/5.28 map_fu186220595405829473_nat_o: ( code_integer > int ) > ( ( nat > $o ) > nat > $o ) > ( int > nat > $o ) > code_integer > nat > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Omap__fun_001t__Code____Numeral__Ointeger_001t__Int__Oint_001_Eo_001_Eo,type,
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% 9.09/5.28
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% 9.09/5.28
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% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Omap__fun_001t__Code____Numeral__Ointeger_001t__Int__Oint_001t__Nat__Onat_001t__Nat__Onat,type,
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% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Omap__fun_001t__Code____Numeral__Ointeger_001t__Int__Oint_001t__Num__Onum_001t__Num__Onum,type,
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% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Omap__fun_001t__Code____Numeral__Onatural_001t__Nat__Onat_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Code____Numeral__Onatural_M_Eo_J,type,
% 9.09/5.28 map_fu6256889081107267320ural_o: ( code_natural > nat ) > ( ( nat > $o ) > code_natural > $o ) > ( nat > nat > $o ) > code_natural > code_natural > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Omap__fun_001t__Code____Numeral__Onatural_001t__Nat__Onat_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Nat__Onat_M_Eo_J,type,
% 9.09/5.28 map_fu6244533035418998608_nat_o: ( code_natural > nat ) > ( ( nat > $o ) > nat > $o ) > ( nat > nat > $o ) > code_natural > nat > $o ).
% 9.09/5.28
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% 9.09/5.28 map_fu6549440983881763648atural: ( code_natural > nat ) > ( ( nat > nat ) > code_natural > code_natural ) > ( nat > nat > nat ) > code_natural > code_natural > code_natural ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Omap__fun_001t__Code____Numeral__Onatural_001t__Nat__Onat_001_Eo_001_Eo,type,
% 9.09/5.28 map_fu4892316939951275536at_o_o: ( code_natural > nat ) > ( $o > $o ) > ( nat > $o ) > code_natural > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Omap__fun_001t__Code____Numeral__Onatural_001t__Nat__Onat_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
% 9.09/5.28 map_fu2787874002554666395nteger: ( code_natural > nat ) > ( int > code_integer ) > ( nat > int ) > code_natural > code_integer ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Omap__fun_001t__Code____Numeral__Onatural_001t__Nat__Onat_001t__Nat__Onat_001t__Code____Numeral__Onatural,type,
% 9.09/5.28 map_fu1239815594074539274atural: ( code_natural > nat ) > ( nat > code_natural ) > ( nat > nat ) > code_natural > code_natural ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Omap__fun_001t__Code____Numeral__Onatural_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
% 9.09/5.28 map_fu226235371393106610at_nat: ( code_natural > nat ) > ( nat > nat ) > ( nat > nat ) > code_natural > nat ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Int__Oint_001_062_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Int__Oint_Mt__Rat__Orat_J,type,
% 9.09/5.28 map_fu7831380289885515383nt_rat: ( int > int ) > ( ( int > product_prod_int_int ) > int > rat ) > ( int > int > product_prod_int_int ) > int > int > rat ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Int__Oint_001_Eo_001_Eo,type,
% 9.09/5.28 map_fun_int_int_o_o: ( int > int ) > ( $o > $o ) > ( int > $o ) > int > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Int__Oint_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 9.09/5.28 map_fu2180209013632630320nt_int: ( int > int ) > ( product_prod_int_int > product_prod_int_int ) > ( int > product_prod_int_int ) > int > product_prod_int_int ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Int__Oint_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Rat__Orat,type,
% 9.09/5.28 map_fu3424225382358772769nt_rat: ( int > int ) > ( product_prod_int_int > rat ) > ( int > product_prod_int_int ) > int > rat ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Int__Oint_001t__Rat__Orat_001t__Rat__Orat,type,
% 9.09/5.28 map_fu6531859369801489698at_rat: ( int > int ) > ( rat > rat ) > ( int > rat ) > int > rat ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Nat__Onat_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 9.09/5.28 map_fu1717202910479192016nteger: ( int > nat ) > ( code_integer > code_integer ) > ( nat > code_integer ) > int > code_integer ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Nat__Onat_001t__Nat__Onat_001t__Num__Onum,type,
% 9.09/5.28 map_fu3669222299741785344at_num: ( int > nat ) > ( nat > num ) > ( nat > nat ) > int > num ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Num__Onum_001t__Int__Oint_001t__Num__Onum,type,
% 9.09/5.28 map_fu2609383839613498790nt_num: ( int > num ) > ( int > num ) > ( num > int ) > int > num ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Num__Onum_001t__Num__Onum_001t__Code____Numeral__Ointeger,type,
% 9.09/5.28 map_fu229184005524548567nteger: ( int > num ) > ( num > code_integer ) > ( num > num ) > int > code_integer ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_001_062_It__Int__Oint_M_Eo_J,type,
% 9.09/5.28 map_fu434086159418415080_int_o: ( int > product_prod_nat_nat ) > ( ( product_prod_nat_nat > $o ) > int > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > int > int > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001_062_It__Int__Oint_Mt__Int__Oint_J,type,
% 9.09/5.28 map_fu4960017516451851995nt_int: ( int > product_prod_nat_nat ) > ( ( product_prod_nat_nat > product_prod_nat_nat ) > int > int ) > ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > int > int > int ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_Eo_001_Eo,type,
% 9.09/5.28 map_fu4826362097070443709at_o_o: ( int > product_prod_nat_nat ) > ( $o > $o ) > ( product_prod_nat_nat > $o ) > int > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint,type,
% 9.09/5.28 map_fu3667384564859982768at_int: ( int > product_prod_nat_nat ) > ( product_prod_nat_nat > int ) > ( product_prod_nat_nat > product_prod_nat_nat ) > int > int ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Omap__fun_001t__Nat__Onat_001t__Nat__Onat_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 9.09/5.28 map_fu8224359078269604234nteger: ( nat > nat ) > ( ( int > int ) > code_integer > code_integer ) > ( nat > int > int ) > nat > code_integer > code_integer ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Omap__fun_001t__Nat__Onat_001t__Nat__Onat_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J,type,
% 9.09/5.28 map_fu6981160461238011112atural: ( nat > nat ) > ( ( nat > nat ) > code_natural > code_natural ) > ( nat > nat > nat ) > nat > code_natural > code_natural ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Omap__fun_001t__Nat__Onat_001t__Nat__Onat_001_Eo_001_Eo,type,
% 9.09/5.28 map_fun_nat_nat_o_o: ( nat > nat ) > ( $o > $o ) > ( nat > $o ) > nat > $o ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Omap__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
% 9.09/5.28 map_fu6290471996055670595nteger: ( nat > nat ) > ( int > code_integer ) > ( nat > int ) > nat > code_integer ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Omap__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat_001t__Code____Numeral__Onatural,type,
% 9.09/5.28 map_fu4742413587575543474atural: ( nat > nat ) > ( nat > code_natural ) > ( nat > nat ) > nat > code_natural ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Omap__fun_001t__Nat__Onat_001t__Num__Onum_001t__Int__Oint_001t__Nat__Onat,type,
% 9.09/5.28 map_fu8361869985550671104nt_nat: ( nat > num ) > ( int > nat ) > ( num > int ) > nat > nat ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Omap__fun_001t__Nat__Onat_001t__Num__Onum_001t__Num__Onum_001t__Code____Numeral__Ointeger,type,
% 9.09/5.28 map_fu1090464068875036027nteger: ( nat > num ) > ( num > code_integer ) > ( num > num ) > nat > code_integer ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Omap__fun_001t__Num__Onum_001t__Code____Numeral__Ointeger_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,type,
% 9.09/5.28 map_fu1235460277957925907nteger: ( num > code_integer ) > ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer ) > num > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Omap__fun_001t__Num__Onum_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 9.09/5.28 map_fu5269526691104299083nteger: ( num > code_integer ) > ( code_integer > code_integer ) > ( code_integer > code_integer ) > num > code_integer ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Omap__fun_001t__Num__Onum_001t__Code____Numeral__Ointeger_001t__Int__Oint_001t__Num__Onum,type,
% 9.09/5.28 map_fu8479170043890205655nt_num: ( num > code_integer ) > ( int > num ) > ( code_integer > int ) > num > num ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Omap__fun_001t__Num__Onum_001t__Code____Numeral__Ointeger_001t__Nat__Onat_001t__Num__Onum,type,
% 9.09/5.28 map_fu7479816331989151099at_num: ( num > code_integer ) > ( nat > num ) > ( code_integer > nat ) > num > num ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Omap__fun_001t__Num__Onum_001t__Code____Numeral__Ointeger_001t__Num__Onum_001t__Code____Numeral__Ointeger,type,
% 9.09/5.28 map_fu8223014087597717000nteger: ( num > code_integer ) > ( num > code_integer ) > ( code_integer > num ) > num > code_integer ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Omap__fun_001t__Num__Onum_001t__Num__Onum_001_062_It__Num__Onum_Mt__Int__Oint_J_001_062_It__Num__Onum_Mt__Code____Numeral__Ointeger_J,type,
% 9.09/5.28 map_fu6891787308814931657nteger: ( num > num ) > ( ( num > int ) > num > code_integer ) > ( num > num > int ) > num > num > code_integer ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Omap__fun_001t__Num__Onum_001t__Num__Onum_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
% 9.09/5.28 map_fu8638147718074629079nteger: ( num > num ) > ( int > code_integer ) > ( num > int ) > num > code_integer ).
% 9.09/5.28
% 9.09/5.28 thf(sy_c_Fun_Omap__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_Eo_001_Eo,type,
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% 9.09/5.29 if_opt7017092727090204112it_nat: $o > option3216581401566546698it_nat > option3216581401566546698it_nat > option3216581401566546698it_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_If_001t__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
% 9.09/5.29 if_opt1729522071442692626it_nat: $o > option8956607266484857688it_nat > option8956607266484857688it_nat > option8956607266484857688it_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_If_001t__Option__Ooption_It__Product____Type__Ounit_J,type,
% 9.09/5.29 if_opt6227717841141446553t_unit: $o > option_Product_unit > option_Product_unit > option_Product_unit ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_If_001t__Option__Ooption_It__Set__Oset_I_Eo_J_J,type,
% 9.09/5.29 if_option_set_o: $o > option_set_o > option_set_o > option_set_o ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_If_001t__Option__Ooption_It__Set__Oset_It__Int__Oint_J_J,type,
% 9.09/5.29 if_option_set_int: $o > option_set_int > option_set_int > option_set_int ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_If_001t__Option__Ooption_It__Set__Oset_It__Nat__Onat_J_J,type,
% 9.09/5.29 if_option_set_nat: $o > option_set_nat > option_set_nat > option_set_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_If_001t__Option__Ooption_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 9.09/5.29 if_opt7704869406773131885at_nat: $o > option8963830502488799655at_nat > option8963830502488799655at_nat > option8963830502488799655at_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_If_001t__Option__Ooption_It__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J,type,
% 9.09/5.29 if_opt5121585740920863443at_nat: $o > option1583680563626158861at_nat > option1583680563626158861at_nat > option1583680563626158861at_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J,type,
% 9.09/5.29 if_Pro5737122678794959658eger_o: $o > produc6271795597528267376eger_o > produc6271795597528267376eger_o > produc6271795597528267376eger_o ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 9.09/5.29 if_Pro6119634080678213985nteger: $o > produc8923325533196201883nteger > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 9.09/5.29 if_Pro3027730157355071871nt_int: $o > product_prod_int_int > product_prod_int_int > product_prod_int_int ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 9.09/5.29 if_Pro6206227464963214023at_nat: $o > product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_If_001t__Rat__Orat,type,
% 9.09/5.29 if_rat: $o > rat > rat > rat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_If_001t__Set__Oset_It__Int__Oint_J,type,
% 9.09/5.29 if_set_int: $o > set_int > set_int > set_int ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Int_OAbs__Integ,type,
% 9.09/5.29 abs_Integ: product_prod_nat_nat > int ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Int_ONeg,type,
% 9.09/5.29 neg: num > int ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Int_OPos,type,
% 9.09/5.29 pos: num > int ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Int_ORep__Integ,type,
% 9.09/5.29 rep_Integ: int > product_prod_nat_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Int_Odup,type,
% 9.09/5.29 dup: int > int ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Int_Ointrel,type,
% 9.09/5.29 intrel: product_prod_nat_nat > product_prod_nat_nat > $o ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Int_Onat,type,
% 9.09/5.29 nat2: int > nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Int_Opcr__int,type,
% 9.09/5.29 pcr_int: product_prod_nat_nat > int > $o ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Int_Oring__1__class_OInts_001t__Code____Numeral__Ointeger,type,
% 9.09/5.29 ring_11222124179247155820nteger: set_Code_integer ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Int_Oring__1__class_OInts_001t__Int__Oint,type,
% 9.09/5.29 ring_1_Ints_int: set_int ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Int_Oring__1__class_OInts_001t__Rat__Orat,type,
% 9.09/5.29 ring_1_Ints_rat: set_rat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Int_Oring__1__class_Oof__int_001t__Code____Numeral__Ointeger,type,
% 9.09/5.29 ring_18347121197199848620nteger: int > code_integer ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Int_Oring__1__class_Oof__int_001t__Int__Oint,type,
% 9.09/5.29 ring_1_of_int_int: int > int ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Int_Oring__1__class_Oof__int_001t__Rat__Orat,type,
% 9.09/5.29 ring_1_of_int_rat: int > rat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Int_Osub,type,
% 9.09/5.29 sub: num > num > int ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Assertions__Oassn,type,
% 9.09/5.29 inf_inf_assn: assn > assn > assn ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Product____Type__Ounit,type,
% 9.09/5.29 inf_inf_Product_unit: product_unit > product_unit > product_unit ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Nat__Onat_J,type,
% 9.09/5.29 inf_inf_set_nat: set_nat > set_nat > set_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Lattices_Osup__class_Osup_001_062_I_062_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_M_062_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J_J,type,
% 9.09/5.29 sup_su600977994968626096_int_o: ( ( int > option6357759511663192854e_term ) > product_prod_int_int > $o ) > ( ( int > option6357759511663192854e_term ) > product_prod_int_int > $o ) > ( int > option6357759511663192854e_term ) > product_prod_int_int > $o ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Lattices_Osup__class_Osup_001_062_I_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_M_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_M_Eo_J_J,type,
% 9.09/5.29 sup_su234547053653886311eger_o: ( ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o ) > ( ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o ) > ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Lattices_Osup__class_Osup_001_062_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_M_062_It__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_M_Eo_J_J,type,
% 9.09/5.29 sup_su6535292691877529429_nat_o: ( ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o ) > ( ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o ) > ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Lattices_Osup__class_Osup_001_062_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_M_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_J,type,
% 9.09/5.29 sup_su1630790145277462993_nat_o: ( ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o ) > ( ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o ) > ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Lattices_Osup__class_Osup_001_062_I_062_It__Product____Type__Oprod_It__Int__Oint_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_M_062_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J_J,type,
% 9.09/5.29 sup_su4182031696650224058_int_o: ( ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o ) > ( ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o ) > ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Lattices_Osup__class_Osup_001_062_It__Nat__Onat_M_062_It__Nat__Onat_M_Eo_J_J,type,
% 9.09/5.29 sup_sup_nat_nat_o: ( nat > nat > $o ) > ( nat > nat > $o ) > nat > nat > $o ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Lattices_Osup__class_Osup_001_062_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_M_062_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_M_Eo_J_J,type,
% 9.09/5.29 sup_su7519161239522478338_nat_o: ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ) > ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ) > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Lattices_Osup__class_Osup_001t__Assertions__Oassn,type,
% 9.09/5.29 sup_sup_assn: assn > assn > assn ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Lattices_Osup__class_Osup_001t__Option__Ooption_It__Assertions__Oassn_J,type,
% 9.09/5.29 sup_sup_option_assn: option_assn > option_assn > option_assn ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Lattices_Osup__class_Osup_001t__Option__Ooption_It__Product____Type__Ounit_J,type,
% 9.09/5.29 sup_su7717485023253700007t_unit: option_Product_unit > option_Product_unit > option_Product_unit ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Lattices_Osup__class_Osup_001t__Option__Ooption_It__Set__Oset_It__Nat__Onat_J_J,type,
% 9.09/5.29 sup_su3598758113090618626et_nat: option_set_nat > option_set_nat > option_set_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Lattices_Osup__class_Osup_001t__Option__Ooption_It__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J,type,
% 9.09/5.29 sup_su2273273666271716065at_nat: option1583680563626158861at_nat > option1583680563626158861at_nat > option1583680563626158861at_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Lattices_Osup__class_Osup_001t__Product____Type__Ounit,type,
% 9.09/5.29 sup_sup_Product_unit: product_unit > product_unit > product_unit ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_I_Eo_J,type,
% 9.09/5.29 sup_sup_set_o: set_o > set_o > set_o ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Code____Numeral__Ointeger_J,type,
% 9.09/5.29 sup_su848401254843788991nteger: set_Code_integer > set_Code_integer > set_Code_integer ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Int__Oint_J,type,
% 9.09/5.29 sup_sup_set_int: set_int > set_int > set_int ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__List__Olist_It__Nat__Onat_J_J,type,
% 9.09/5.29 sup_sup_set_list_nat: set_list_nat > set_list_nat > set_list_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Nat__Onat_J,type,
% 9.09/5.29 sup_sup_set_nat: set_nat > set_nat > set_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Num__Onum_J,type,
% 9.09/5.29 sup_sup_set_num: set_num > set_num > set_num ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_I_062_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
% 9.09/5.29 sup_su3298353300217089135nt_int: set_Pr1872883991513573699nt_int > set_Pr1872883991513573699nt_int > set_Pr1872883991513573699nt_int ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J,type,
% 9.09/5.29 sup_su4591284015454442744nteger: set_Pr1281608226676607948nteger > set_Pr1281608226676607948nteger > set_Pr1281608226676607948nteger ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__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_J,type,
% 9.09/5.29 sup_su8975264963432250076et_nat: set_Pr8536935166611901872et_nat > set_Pr8536935166611901872et_nat > set_Pr8536935166611901872et_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__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,
% 9.09/5.29 sup_su7128418612487073120et_nat: set_Pr3286484037609594932et_nat > set_Pr3286484037609594932et_nat > set_Pr3286484037609594932et_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Int__Oint_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
% 9.09/5.29 sup_su3382966977382714213nt_int: set_Pr9222295170931077689nt_int > set_Pr9222295170931077689nt_int > set_Pr9222295170931077689nt_int ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
% 9.09/5.29 sup_su5769328420594410459od_o_o: set_Product_prod_o_o > set_Product_prod_o_o > set_Product_prod_o_o ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_Mt__Int__Oint_J_J,type,
% 9.09/5.29 sup_su6189057272928884437_o_int: set_Pr8834758594704517033_o_int > set_Pr8834758594704517033_o_int > set_Pr8834758594704517033_o_int ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_J,type,
% 9.09/5.29 sup_su8679140417860611193_o_nat: set_Pr2101469702781467981_o_nat > set_Pr2101469702781467981_o_nat > set_Pr2101469702781467981_o_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_M_Eo_J_J,type,
% 9.09/5.29 sup_su7481598572368468931_int_o: set_Pr903927857289325719_int_o > set_Pr903927857289325719_int_o > set_Pr903927857289325719_int_o ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
% 9.09/5.29 sup_su6024340866399070445nt_int: set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Nat__Onat_J_J,type,
% 9.09/5.29 sup_su8514424011330797201nt_nat: set_Pr3448869479623346877nt_nat > set_Pr3448869479623346877nt_nat > set_Pr3448869479623346877nt_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_M_Eo_J_J,type,
% 9.09/5.29 sup_su503371503184139039_nat_o: set_Pr3149072824959771635_nat_o > set_Pr3149072824959771635_nat_o > set_Pr3149072824959771635_nat_o ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Int__Oint_J_J,type,
% 9.09/5.29 sup_su3837419291706048657at_int: set_Pr7995236796853374141at_int > set_Pr7995236796853374141at_int > set_Pr7995236796853374141at_int ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 9.09/5.29 sup_su6327502436637775413at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_J,type,
% 9.09/5.29 sup_su5921324857680904370_nat_o: set_Pr6558897299634722526_nat_o > set_Pr6558897299634722526_nat_o > set_Pr6558897299634722526_nat_o ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
% 9.09/5.29 sup_su5525570899277871387at_nat: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Ounit_J,type,
% 9.09/5.29 sup_su793286257634532545t_unit: set_Product_unit > set_Product_unit > set_Product_unit ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Rat__Orat_J,type,
% 9.09/5.29 sup_sup_set_rat: set_rat > set_rat > set_rat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 9.09/5.29 sup_su3642409539654194069at_nat: set_se7855581050983116737at_nat > set_se7855581050983116737at_nat > set_se7855581050983116737at_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Lattices__Big_Olinorder__class_OMax_001t__Nat__Onat,type,
% 9.09/5.29 lattic8265883725875713057ax_nat: set_nat > nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Lattices__Big_Osemilattice__neutr__set_OF_001t__Nat__Onat,type,
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% 9.09/5.29
% 9.09/5.29 thf(sy_c_Lifting_OQuotient_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
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% 9.09/5.29
% 9.09/5.29 thf(sy_c_Lifting_OQuotient_001t__Nat__Onat_001t__Code____Numeral__Onatural,type,
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% 9.09/5.29
% 9.09/5.29 thf(sy_c_List_Oappend_001t__Int__Oint,type,
% 9.09/5.29 append_int: list_int > list_int > list_int ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_List_Oappend_001t__Nat__Onat,type,
% 9.09/5.29 append_nat: list_nat > list_nat > list_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_List_Obutlast_001t__Nat__Onat,type,
% 9.09/5.29 butlast_nat: list_nat > list_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_List_Odrop_001t__Nat__Onat,type,
% 9.09/5.29 drop_nat: nat > list_nat > list_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_List_Ofilter_001t__Nat__Onat,type,
% 9.09/5.29 filter_nat: ( nat > $o ) > list_nat > list_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_List_Ofold_001t__Nat__Onat_001t__Nat__Onat,type,
% 9.09/5.29 fold_nat_nat: ( nat > nat > nat ) > list_nat > nat > nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_List_Olast_001t__Nat__Onat,type,
% 9.09/5.29 last_nat: list_nat > nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_List_Olinorder__class_Osorted__list__of__set_001t__Nat__Onat,type,
% 9.09/5.29 linord2614967742042102400et_nat: set_nat > list_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_List_Olist_OCons_001t__Int__Oint,type,
% 9.09/5.29 cons_int: int > list_int > list_int ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_List_Olist_OCons_001t__Nat__Onat,type,
% 9.09/5.29 cons_nat: nat > list_nat > list_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_List_Olist_ONil_001t__Int__Oint,type,
% 9.09/5.29 nil_int: list_int ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_List_Olist_ONil_001t__Nat__Onat,type,
% 9.09/5.29 nil_nat: list_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_List_Olist_Omap_001t__Nat__Onat_001t__Nat__Onat,type,
% 9.09/5.29 map_nat_nat: ( nat > nat ) > list_nat > list_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_List_Olist_Oset_001t__Int__Oint,type,
% 9.09/5.29 set_int2: list_int > set_int ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_List_Olist_Oset_001t__Nat__Onat,type,
% 9.09/5.29 set_nat2: list_nat > set_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_List_Onth_001t__Int__Oint,type,
% 9.09/5.29 nth_int: list_int > nat > int ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_List_Onth_001t__Nat__Onat,type,
% 9.09/5.29 nth_nat: list_nat > nat > nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_List_Otake_001t__Nat__Onat,type,
% 9.09/5.29 take_nat: nat > list_nat > list_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_List_Oupt,type,
% 9.09/5.29 upt: nat > nat > list_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_List_Oupto,type,
% 9.09/5.29 upto: int > int > list_int ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_List_Oupto__rel,type,
% 9.09/5.29 upto_rel: product_prod_int_int > product_prod_int_int > $o ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Misc_OEps__Opt_001t__Nat__Onat,type,
% 9.09/5.29 eps_Opt_nat: ( nat > $o ) > option_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Misc_OEps__Opt_001t__Num__Onum,type,
% 9.09/5.29 eps_Opt_num: ( num > $o ) > option_num ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Misc_OEps__Opt_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,
% 9.09/5.29 eps_Op6423059015816587746et_nat: ( produc3925858234332021118et_nat > $o ) > option5190343406534369742et_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Misc_OEps__Opt_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 9.09/5.29 eps_Op9034888937550303799nteger: ( produc8923325533196201883nteger > $o ) > option2651255830984564193nteger ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Misc_OEps__Opt_001t__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 9.09/5.29 eps_Op1141264490366522080it_nat: ( produc6714399278180371524it_nat > $o ) > option3216581401566546698it_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Misc_OEps__Opt_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J,type,
% 9.09/5.29 eps_Op2013419657081471078et_nat: ( produc3658429121746597890et_nat > $o ) > option936205604648967762et_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Misc_OEps__Opt_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 9.09/5.29 eps_Op2446201859369042517nt_int: ( product_prod_int_int > $o ) > option4624381673175914239nt_int ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Misc_OEps__Opt_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 9.09/5.29 eps_Op3393321821070424684it_nat: ( produc8664842809031399944it_nat > $o ) > option8956607266484857688it_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Misc_OEps__Opt_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 9.09/5.29 eps_Op994234036888646909at_nat: ( set_Pr1261947904930325089at_nat > $o ) > option8963830502488799655at_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Misc_Obijective_001_062_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
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% 9.09/5.29
% 9.09/5.29 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,
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% 9.09/5.29
% 9.09/5.29 thf(sy_c_Misc_Obijective_001_062_It__Product____Type__Oprod_It__Int__Oint_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 9.09/5.29 biject383251550997737151nt_int: set_Pr9222295170931077689nt_int > $o ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Misc_Obijective_001t__Nat__Onat_001t__Nat__Onat,type,
% 9.09/5.29 bijective_nat_nat: set_Pr1261947904930325089at_nat > $o ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Misc_Obijective_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
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% 9.09/5.29
% 9.09/5.29 thf(sy_c_Misc_Odflt__None__set_001_Eo,type,
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% 9.09/5.29
% 9.09/5.29 thf(sy_c_Misc_Odflt__None__set_001t__Int__Oint,type,
% 9.09/5.29 dflt_None_set_int: set_int > option_set_int ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Misc_Odflt__None__set_001t__Nat__Onat,type,
% 9.09/5.29 dflt_None_set_nat: set_nat > option_set_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Misc_Odflt__None__set_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 9.09/5.29 dflt_N6592383573632408824at_nat: set_Pr1261947904930325089at_nat > option8963830502488799655at_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Misc_Odflt__None__set_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 9.09/5.29 dflt_N3208751546879591902at_nat: set_Pr4329608150637261639at_nat > option1583680563626158861at_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Misc_Omap__mmupd_001_Eo_001t__Num__Onum,type,
% 9.09/5.29 map_mmupd_o_num: ( $o > option_num ) > set_o > num > $o > option_num ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Misc_Omap__mmupd_001_Eo_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 9.09/5.29 map_mm4340940675810032635it_nat: ( $o > option8956607266484857688it_nat ) > set_o > produc8664842809031399944it_nat > $o > option8956607266484857688it_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Misc_Omap__mmupd_001t__Int__Oint_001t__Num__Onum,type,
% 9.09/5.29 map_mmupd_int_num: ( int > option_num ) > set_int > num > int > option_num ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Misc_Omap__mmupd_001t__Int__Oint_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 9.09/5.29 map_mm5942422175790858651it_nat: ( int > option8956607266484857688it_nat ) > set_int > produc8664842809031399944it_nat > int > option8956607266484857688it_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Misc_Omap__mmupd_001t__Nat__Onat_001t__Num__Onum,type,
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% 9.09/5.29
% 9.09/5.29 thf(sy_c_Misc_Omap__mmupd_001t__Nat__Onat_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 9.09/5.29 map_mm4316137065318800191it_nat: ( nat > option8956607266484857688it_nat ) > set_nat > produc8664842809031399944it_nat > nat > option8956607266484857688it_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Misc_Omap__mmupd_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Num__Onum,type,
% 9.09/5.29 map_mm6272435474268545910at_num: ( product_prod_nat_nat > option_num ) > set_Pr1261947904930325089at_nat > num > product_prod_nat_nat > option_num ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Misc_Omap__mmupd_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 9.09/5.29 map_mm8925508573636269924it_nat: ( product_prod_nat_nat > option8956607266484857688it_nat ) > set_Pr1261947904930325089at_nat > produc8664842809031399944it_nat > product_prod_nat_nat > option8956607266484857688it_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Misc_Omap__mmupd_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__Num__Onum,type,
% 9.09/5.29 map_mm2124855372588256220at_num: ( produc3843707927480180839at_nat > option_num ) > set_Pr4329608150637261639at_nat > num > produc3843707927480180839at_nat > option_num ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Misc_Omap__mmupd_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 9.09/5.29 map_mm6227321356191524810it_nat: ( produc3843707927480180839at_nat > option8956607266484857688it_nat ) > set_Pr4329608150637261639at_nat > produc8664842809031399944it_nat > produc3843707927480180839at_nat > option8956607266484857688it_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Misc_Opairself_001t__Int__Oint_001t__Int__Oint,type,
% 9.09/5.29 pairself_int_int: ( int > int ) > product_prod_int_int > product_prod_int_int ).
% 9.09/5.29
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% 9.09/5.29 thf(sy_c_Misc_Orel__of_001t__Nat__Onat_001t__Nat__Onat,type,
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% 9.09/5.29 thf(sy_c_Nat_Osize__class_Osize_001t__Heap____Time____Monad__OHeap_It__Product____Type__Ounit_J,type,
% 9.09/5.29 size_s1564113455978345259t_unit: heap_T5738788834812785303t_unit > nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Int__Oint_J,type,
% 9.09/5.29 size_size_list_int: list_int > nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Nat__Onat_J,type,
% 9.09/5.29 size_size_list_nat: list_nat > nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Nat_Osize__class_Osize_001t__Num__Onum,type,
% 9.09/5.29 size_size_num: num > nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Nat_Osize__class_Osize_001t__Option__Ooption_It__Num__Onum_J,type,
% 9.09/5.29 size_size_option_num: option_num > nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Nat_Osize__class_Osize_001t__Option__Ooption_It__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
% 9.09/5.29 size_s6797157356856800118it_nat: option3216581401566546698it_nat > nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Nat_Osize__class_Osize_001t__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
% 9.09/5.29 size_s8766407808098229740it_nat: option8956607266484857688it_nat > nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Nat__Bijection_Olist__decode,type,
% 9.09/5.29 nat_list_decode: nat > list_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Nat__Bijection_Olist__decode__rel,type,
% 9.09/5.29 nat_list_decode_rel: nat > nat > $o ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Nat__Bijection_Olist__encode,type,
% 9.09/5.29 nat_list_encode: list_nat > nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Nat__Bijection_Olist__encode__rel,type,
% 9.09/5.29 nat_list_encode_rel: list_nat > list_nat > $o ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Nat__Bijection_Oprod__decode,type,
% 9.09/5.29 nat_prod_decode: nat > product_prod_nat_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Nat__Bijection_Oprod__decode__aux,type,
% 9.09/5.29 nat_prod_decode_aux: nat > nat > product_prod_nat_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Nat__Bijection_Oprod__decode__aux__rel,type,
% 9.09/5.29 nat_pr5047031295181774490ux_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Nat__Bijection_Oprod__encode,type,
% 9.09/5.29 nat_prod_encode: product_prod_nat_nat > nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Nat__Bijection_Oset__decode,type,
% 9.09/5.29 nat_set_decode: nat > set_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Nat__Bijection_Oset__encode,type,
% 9.09/5.29 nat_set_encode: set_nat > nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Nat__Bijection_Osum__decode,type,
% 9.09/5.29 nat_sum_decode: nat > sum_sum_nat_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Nat__Bijection_Otriangle,type,
% 9.09/5.29 nat_triangle: nat > nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Num_OBitM,type,
% 9.09/5.29 bitM: num > num ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Num_Oinc,type,
% 9.09/5.29 inc: num > num ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Num_Onat__of__num,type,
% 9.09/5.29 nat_of_num: num > nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Code____Numeral__Ointeger,type,
% 9.09/5.29 neg_nu8804712462038260780nteger: code_integer > code_integer ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Int__Oint,type,
% 9.09/5.29 neg_numeral_dbl_int: int > int ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Rat__Orat,type,
% 9.09/5.29 neg_numeral_dbl_rat: rat > rat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Code____Numeral__Ointeger,type,
% 9.09/5.29 neg_nu7757733837767384882nteger: code_integer > code_integer ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Int__Oint,type,
% 9.09/5.29 neg_nu3811975205180677377ec_int: int > int ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Rat__Orat,type,
% 9.09/5.29 neg_nu3179335615603231917ec_rat: rat > rat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Code____Numeral__Ointeger,type,
% 9.09/5.29 neg_nu5831290666863070958nteger: code_integer > code_integer ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Int__Oint,type,
% 9.09/5.29 neg_nu5851722552734809277nc_int: int > int ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Rat__Orat,type,
% 9.09/5.29 neg_nu5219082963157363817nc_rat: rat > rat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Num_Oneg__numeral__class_Ois__num_001t__Code____Numeral__Ointeger,type,
% 9.09/5.29 neg_nu2435721316971906650nteger: code_integer > $o ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Num_Oneg__numeral__class_Ois__num_001t__Int__Oint,type,
% 9.09/5.29 neg_nu7441568979088483369um_int: int > $o ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Num_Oneg__numeral__class_Ois__num_001t__Rat__Orat,type,
% 9.09/5.29 neg_nu6808929389511037909um_rat: rat > $o ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Num_Oneg__numeral__class_Osub_001t__Code____Numeral__Ointeger,type,
% 9.09/5.29 neg_nu5755505904847501662nteger: num > num > code_integer ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Num_Oneg__numeral__class_Osub_001t__Int__Oint,type,
% 9.09/5.29 neg_numeral_sub_int: num > num > int ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Num_Oneg__numeral__class_Osub_001t__Rat__Orat,type,
% 9.09/5.29 neg_numeral_sub_rat: num > num > rat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Num_Onum_OBit0,type,
% 9.09/5.29 bit0: num > num ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Num_Onum_OBit1,type,
% 9.09/5.29 bit1: num > num ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Num_Onum_OOne,type,
% 9.09/5.29 one: num ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Num_Onum_Ocase__num_001t__Option__Ooption_It__Num__Onum_J,type,
% 9.09/5.29 case_num_option_num: option_num > ( num > option_num ) > ( num > option_num ) > num > option_num ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Num_Onum_Osize__num,type,
% 9.09/5.29 size_num: num > nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Num_Onum__of__nat,type,
% 9.09/5.29 num_of_nat: nat > num ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Code____Numeral__Ointeger,type,
% 9.09/5.29 numera6620942414471956472nteger: num > code_integer ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Code____Numeral__Onatural,type,
% 9.09/5.29 numera5444537566228673987atural: num > code_natural ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Int__Oint,type,
% 9.09/5.29 numeral_numeral_int: num > int ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Nat__Onat,type,
% 9.09/5.29 numeral_numeral_nat: num > nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Rat__Orat,type,
% 9.09/5.29 numeral_numeral_rat: num > rat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Num_Opred__numeral,type,
% 9.09/5.29 pred_numeral: num > nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Num_Oring__1__class_Oiszero_001t__Code____Numeral__Ointeger,type,
% 9.09/5.29 ring_16219924574208605041nteger: code_integer > $o ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Num_Oring__1__class_Oiszero_001t__Int__Oint,type,
% 9.09/5.29 ring_1_iszero_int: int > $o ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Num_Oring__1__class_Oiszero_001t__Rat__Orat,type,
% 9.09/5.29 ring_1_iszero_rat: rat > $o ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Num_Osqr,type,
% 9.09/5.29 sqr: num > num ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Option_Obind_001t__Num__Onum_001t__Num__Onum,type,
% 9.09/5.29 bind_num_num: option_num > ( num > option_num ) > option_num ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Option_Obind_001t__Num__Onum_001t__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 9.09/5.29 bind_n6186876254402743274it_nat: option_num > ( num > option3216581401566546698it_nat ) > option3216581401566546698it_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Option_Obind_001t__Num__Onum_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 9.09/5.29 bind_n550516262659884002it_nat: option_num > ( num > option8956607266484857688it_nat ) > option8956607266484857688it_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Option_Obind_001t__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_001t__Num__Onum,type,
% 9.09/5.29 bind_P7816469540982926368at_num: option3216581401566546698it_nat > ( produc6714399278180371524it_nat > option_num ) > option_num ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Option_Obind_001t__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_001t__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 9.09/5.29 bind_P1787608729393679550it_nat: option3216581401566546698it_nat > ( produc6714399278180371524it_nat > option3216581401566546698it_nat ) > option3216581401566546698it_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Option_Obind_001t__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 9.09/5.29 bind_P3087804342168909838it_nat: option3216581401566546698it_nat > ( produc6714399278180371524it_nat > option8956607266484857688it_nat ) > option8956607266484857688it_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Option_Obind_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_001t__Num__Onum,type,
% 9.09/5.29 bind_P4387644102537648098at_num: option8956607266484857688it_nat > ( produc8664842809031399944it_nat > option_num ) > option_num ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Option_Obind_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_001t__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 9.09/5.29 bind_P1106314856888375420it_nat: option8956607266484857688it_nat > ( produc8664842809031399944it_nat > option3216581401566546698it_nat ) > option3216581401566546698it_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Option_Obind_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 9.09/5.29 bind_P7351952464966851536it_nat: option8956607266484857688it_nat > ( produc8664842809031399944it_nat > option8956607266484857688it_nat ) > option8956607266484857688it_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Option_Ocombine__options_001t__Num__Onum,type,
% 9.09/5.29 combine_options_num: ( num > num > num ) > option_num > option_num > option_num ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Option_Ocombine__options_001t__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 9.09/5.29 combin3867838909898076099it_nat: ( produc6714399278180371524it_nat > produc6714399278180371524it_nat > produc6714399278180371524it_nat ) > option3216581401566546698it_nat > option3216581401566546698it_nat > option3216581401566546698it_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Option_Ocombine__options_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 9.09/5.29 combin4318129983670048329it_nat: ( produc8664842809031399944it_nat > produc8664842809031399944it_nat > produc8664842809031399944it_nat ) > option8956607266484857688it_nat > option8956607266484857688it_nat > option8956607266484857688it_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Option_Ooption_ONone_001_Eo,type,
% 9.09/5.29 none_o: option_o ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Option_Ooption_ONone_001t__Int__Oint,type,
% 9.09/5.29 none_int: option_int ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Option_Ooption_ONone_001t__Nat__Onat,type,
% 9.09/5.29 none_nat: option_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Option_Ooption_ONone_001t__Num__Onum,type,
% 9.09/5.29 none_num: option_num ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Option_Ooption_ONone_001t__Product____Type__Oprod_I_062_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
% 9.09/5.29 none_P3773570700014501484nt_int: option4256020574406277085nt_int ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Option_Ooption_ONone_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
% 9.09/5.29 none_P4442379456014020469nteger: option8051342751916580710nteger ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Option_Ooption_ONone_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,
% 9.09/5.29 none_P199884684680593241et_nat: option2860828798490689354et_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Option_Ooption_ONone_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,
% 9.09/5.29 none_P4972525538344268765et_nat: option5190343406534369742et_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Option_Ooption_ONone_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Int__Oint_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
% 9.09/5.29 none_P1286213070022356066nt_int: option7541221861074943443nt_int ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Option_Ooption_ONone_001t__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 9.09/5.29 none_P2587165478634041381it_nat: option3216581401566546698it_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Option_Ooption_ONone_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 9.09/5.29 none_P5556105721700978146at_nat: option4927543243414619207at_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Option_Ooption_ONone_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 9.09/5.29 none_P9117596204409417319it_nat: option8956607266484857688it_nat ).
% 9.09/5.29
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% 9.09/5.29
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% 9.09/5.29 case_o5699750240967658439it_nat: option3216581401566546698it_nat > ( produc8664842809031399944it_nat > option3216581401566546698it_nat ) > option8956607266484857688it_nat > option3216581401566546698it_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Option_Ooption_Ocase__option_001t__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_001t__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 9.09/5.29 case_o3886096569520666655it_nat: option8956607266484857688it_nat > ( produc6714399278180371524it_nat > option8956607266484857688it_nat ) > option3216581401566546698it_nat > option8956607266484857688it_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Option_Ooption_Ocase__option_001t__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 9.09/5.29 case_o2963978774867076333it_nat: option8956607266484857688it_nat > ( produc8664842809031399944it_nat > option8956607266484857688it_nat ) > option8956607266484857688it_nat > option8956607266484857688it_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Option_Ooption_Ocase__option_001t__Option__Ooption_It__Product____Type__Ounit_J_001t__Product____Type__Ounit,type,
% 9.09/5.29 case_o2985186191577459077t_unit: option_Product_unit > ( product_unit > option_Product_unit ) > option_Product_unit > option_Product_unit ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Option_Ooption_Ocase__option_001t__Option__Ooption_It__Set__Oset_It__Nat__Onat_J_J_001t__Set__Oset_It__Nat__Onat_J,type,
% 9.09/5.29 case_o4054078431260844265et_nat: option_set_nat > ( set_nat > option_set_nat ) > option_set_nat > option_set_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Option_Ooption_Ocase__option_001t__Option__Ooption_It__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
% 9.09/5.29 case_o9080059180780454917at_nat: option1583680563626158861at_nat > ( set_Pr4329608150637261639at_nat > option1583680563626158861at_nat ) > option1583680563626158861at_nat > option1583680563626158861at_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Option_Ooption_Ocase__option_001t__Product____Type__Ounit_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 9.09/5.29 case_o9196786658626276042it_nat: product_unit > ( produc8664842809031399944it_nat > product_unit ) > option8956607266484857688it_nat > product_unit ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Option_Ooption_Omap__option_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,type,
% 9.09/5.29 map_op3563471509957180299nteger: ( ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ) > option8057788054806935849nteger > option7428179582072448501nteger ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Option_Ooption_Omap__option_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Nat__Onat_M_Eo_J,type,
% 9.09/5.29 map_op6424164270877473355_nat_o: ( ( nat > $o ) > nat > $o ) > option_nat_o > option_nat_o ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Option_Ooption_Omap__option_001_Eo_001_Eo,type,
% 9.09/5.29 map_option_o_o: ( $o > $o ) > option_o > option_o ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Option_Ooption_Omap__option_001t__Code____Numeral__Ointeger_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 9.09/5.29 map_op370346339404370627nteger: ( code_integer > code_integer > code_integer ) > option_Code_integer > option8057788054806935849nteger ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Option_Ooption_Omap__option_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,type,
% 9.09/5.29 map_op9146685272036663823nteger: ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > option_Code_integer > option7428179582072448501nteger ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Option_Ooption_Omap__option_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 9.09/5.29 map_op3669829223712506439nteger: ( code_integer > code_integer ) > option_Code_integer > option_Code_integer ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Option_Ooption_Omap__option_001t__Int__Oint_001t__Int__Oint,type,
% 9.09/5.29 map_option_int_int: ( int > int ) > option_int > option_int ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Option_Ooption_Omap__option_001t__Int__Oint_001t__Nat__Onat,type,
% 9.09/5.29 map_option_int_nat: ( int > nat ) > option_int > option_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Option_Ooption_Omap__option_001t__Int__Oint_001t__Num__Onum,type,
% 9.09/5.29 map_option_int_num: ( int > num ) > option_int > option_num ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Option_Ooption_Omap__option_001t__Nat__Onat_001t__Nat__Onat,type,
% 9.09/5.29 map_option_nat_nat: ( nat > nat ) > option_nat > option_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Option_Ooption_Omap__option_001t__Nat__Onat_001t__Num__Onum,type,
% 9.09/5.29 map_option_nat_num: ( nat > num ) > option_nat > option_num ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Option_Ooption_Omap__option_001t__Num__Onum_001t__Code____Numeral__Ointeger,type,
% 9.09/5.29 map_op2849635639313731588nteger: ( num > code_integer ) > option_num > option_Code_integer ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Option_Ooption_Omap__option_001t__Num__Onum_001t__Num__Onum,type,
% 9.09/5.29 map_option_num_num: ( num > num ) > option_num > option_num ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Option_Ooption_Omap__option_001t__Num__Onum_001t__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 9.09/5.29 map_op6598675229099881181it_nat: ( num > produc6714399278180371524it_nat ) > option_num > option3216581401566546698it_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Option_Ooption_Omap__option_001t__Num__Onum_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 9.09/5.29 map_op8118133509425879471it_nat: ( num > produc8664842809031399944it_nat ) > option_num > option8956607266484857688it_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Option_Ooption_Omap__option_001t__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_001t__Num__Onum,type,
% 9.09/5.29 map_op8228268515680064275at_num: ( produc6714399278180371524it_nat > num ) > option3216581401566546698it_nat > option_num ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Option_Ooption_Omap__option_001t__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_001t__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 9.09/5.29 map_op6002829699023054091it_nat: ( produc6714399278180371524it_nat > produc6714399278180371524it_nat ) > option3216581401566546698it_nat > option3216581401566546698it_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Option_Ooption_Omap__option_001t__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 9.09/5.29 map_op674526153330701057it_nat: ( produc6714399278180371524it_nat > produc8664842809031399944it_nat ) > option3216581401566546698it_nat > option8956607266484857688it_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Option_Ooption_Omap__option_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_001t__Num__Onum,type,
% 9.09/5.29 map_op2731889312448867759at_num: ( produc8664842809031399944it_nat > num ) > option8956607266484857688it_nat > option_num ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Option_Ooption_Omap__option_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_001t__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 9.09/5.29 map_op7916408704904942447it_nat: ( produc8664842809031399944it_nat > produc6714399278180371524it_nat ) > option8956607266484857688it_nat > option3216581401566546698it_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Option_Ooption_Omap__option_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 9.09/5.29 map_op8673683442680995229it_nat: ( produc8664842809031399944it_nat > produc8664842809031399944it_nat ) > option8956607266484857688it_nat > option8956607266484857688it_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Option_Ooption_Osize__option_001t__Num__Onum,type,
% 9.09/5.29 size_option_num: ( num > nat ) > option_num > nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Option_Ooption_Osize__option_001t__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 9.09/5.29 size_o5312321843473198183it_nat: ( produc6714399278180371524it_nat > nat ) > option3216581401566546698it_nat > nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Option_Ooption_Osize__option_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 9.09/5.29 size_o29782932136985253it_nat: ( produc8664842809031399944it_nat > nat ) > option8956607266484857688it_nat > nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Option_Ooption_Othe_001_062_It__Nat__Onat_M_Eo_J,type,
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% 9.09/5.29
% 9.09/5.29 thf(sy_c_Option_Ooption_Othe_001_Eo,type,
% 9.09/5.29 the_o: option_o > $o ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Option_Ooption_Othe_001t__Int__Oint,type,
% 9.09/5.29 the_int2: option_int > int ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Option_Ooption_Othe_001t__Nat__Onat,type,
% 9.09/5.29 the_nat: option_nat > nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Option_Ooption_Othe_001t__Num__Onum,type,
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% 9.09/5.29
% 9.09/5.29 thf(sy_c_Option_Ooption_Othe_001t__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 9.09/5.29 the_Pr5856008525237892824it_nat: option3216581401566546698it_nat > produc6714399278180371524it_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Option_Ooption_Othe_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 9.09/5.29 the_Pr7776125533777466484it_nat: option8956607266484857688it_nat > produc8664842809031399944it_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Option_Othese_001_Eo,type,
% 9.09/5.29 these_o: set_option_o > set_o ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Option_Othese_001t__Int__Oint,type,
% 9.09/5.29 these_int: set_option_int > set_int ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Option_Othese_001t__Nat__Onat,type,
% 9.09/5.29 these_nat: set_option_nat > set_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Option_Othese_001t__Num__Onum,type,
% 9.09/5.29 these_num: set_option_num > set_num ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Option_Othese_001t__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 9.09/5.29 these_6645423997822192641it_nat: set_op3940070208846178154it_nat > set_Pr5142436192348053284it_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Option_Othese_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 9.09/5.29 these_8061402112538453438at_nat: set_op4508134149509766951at_nat > set_Pr1261947904930325089at_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Option_Othese_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 9.09/5.29 these_3407724651694999947it_nat: set_op239864471688321678it_nat > set_Pr1354866905816374718it_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Option_Othese_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 9.09/5.29 these_1872268174106123684at_nat: set_op989438649584373901at_nat > set_Pr4329608150637261639at_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Option_Othese_001t__Product____Type__Ounit,type,
% 9.09/5.29 these_Product_unit: set_op3165557761946182707t_unit > set_Product_unit ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Option_Othese_001t__Set__Oset_It__Nat__Onat_J,type,
% 9.09/5.29 these_set_nat: set_option_set_nat > set_set_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Orderings_Obot__class_Obot_001_062_I_062_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_M_062_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J_J,type,
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% 9.09/5.29
% 9.09/5.29 thf(sy_c_Orderings_Obot__class_Obot_001_062_I_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_M_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_M_Eo_J_J,type,
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% 9.09/5.29
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% 9.09/5.29
% 9.09/5.29 thf(sy_c_Orderings_Obot__class_Obot_001_062_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_M_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_J,type,
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% 9.09/5.29
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% 9.09/5.29
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% 9.09/5.29
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% 9.09/5.29
% 9.09/5.29 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_001t__Nat__Onat_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J,type,
% 9.09/5.29 produc9092781844693468442t_unit: ( heap_e7401611519738050253t_unit > nat > heap_e7401611519738050253t_unit ) > produc6653097349344004940it_nat > heap_e7401611519738050253t_unit ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_001t__Nat__Onat_001t__Nat__Onat,type,
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% 9.09/5.29
% 9.09/5.29 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_001t__Nat__Onat_001t__Option__Ooption_It__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
% 9.09/5.29 produc921929042997482327it_nat: ( heap_e7401611519738050253t_unit > nat > option3216581401566546698it_nat ) > produc6653097349344004940it_nat > option3216581401566546698it_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_001t__Nat__Onat_001t__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
% 9.09/5.29 produc7488178964372371019it_nat: ( heap_e7401611519738050253t_unit > nat > option8956607266484857688it_nat ) > produc6653097349344004940it_nat > option8956607266484857688it_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_001t__Nat__Onat_001t__Product____Type__Ounit,type,
% 9.09/5.29 produc1863717115126956122t_unit: ( heap_e7401611519738050253t_unit > nat > product_unit ) > produc6653097349344004940it_nat > product_unit ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001_Eo,type,
% 9.09/5.29 produc4947309494688390418_int_o: ( int > int > $o ) > product_prod_int_int > $o ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint,type,
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% 9.09/5.29
% 9.09/5.29 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
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% 9.09/5.29
% 9.09/5.29 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__List__Olist_It__Nat__Onat_J_001t__List__Olist_It__Nat__Onat_J_001_Eo,type,
% 9.09/5.29 produc6382697403170970154_nat_o: ( list_nat > list_nat > $o ) > produc1828647624359046049st_nat > $o ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__List__Olist_It__Nat__Onat_J_001t__Nat__Onat_001_Eo,type,
% 9.09/5.29 produc7308574044827705018_nat_o: ( list_nat > nat > $o ) > produc1540777390238407569at_nat > $o ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Int__Oint_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Int__Oint_J,type,
% 9.09/5.29 produc1728318271963197120er_int: ( nat > int > produc2256096406371053034er_int ) > product_prod_nat_int > produc2256096406371053034er_int ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Int__Oint_J,type,
% 9.09/5.29 produc1486167065449562675at_int: ( nat > int > product_prod_nat_int ) > product_prod_nat_int > product_prod_nat_int ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__List__Olist_It__Nat__Onat_J_001_Eo,type,
% 9.09/5.29 produc5265810065896090426_nat_o: ( nat > list_nat > $o ) > produc4575160907756185873st_nat > $o ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J,type,
% 9.09/5.29 produc8739625826339149834_nat_o: ( nat > nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > product_prod_nat_nat > $o ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 9.09/5.29 produc27273713700761075at_nat: ( nat > nat > product_prod_nat_nat > product_prod_nat_nat ) > product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001_Eo,type,
% 9.09/5.29 produc6081775807080527818_nat_o: ( nat > nat > $o ) > product_prod_nat_nat > $o ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Int__Oint,type,
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% 9.09/5.29
% 9.09/5.29 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__List__Olist_It__Nat__Onat_J,type,
% 9.09/5.29 produc2761476792215241774st_nat: ( nat > nat > list_nat ) > product_prod_nat_nat > list_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
% 9.09/5.29 produc6842872674320459806at_nat: ( nat > nat > nat ) > product_prod_nat_nat > nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 9.09/5.29 produc39701218431283661nteger: ( nat > nat > produc8923325533196201883nteger ) > product_prod_nat_nat > produc8923325533196201883nteger ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Int__Oint_J,type,
% 9.09/5.29 produc9191653645064861724er_int: ( nat > nat > produc2256096406371053034er_int ) > product_prod_nat_nat > produc2256096406371053034er_int ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Nat__Onat_J,type,
% 9.09/5.29 produc4146132627719282624er_nat: ( nat > nat > produc6433947425880249742er_nat ) > product_prod_nat_nat > produc6433947425880249742er_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Product____Type__Oprod_It__Int__Oint_Mt__Code____Numeral__Ointeger_J,type,
% 9.09/5.29 produc675454393454366620nteger: ( nat > nat > produc2963269191615333738nteger ) > product_prod_nat_nat > produc2963269191615333738nteger ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Product____Type__Oprod_It__Int__Oint_Mt__Nat__Onat_J,type,
% 9.09/5.29 produc3625529712395680143nt_nat: ( nat > nat > product_prod_int_nat ) > product_prod_nat_nat > product_prod_int_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J,type,
% 9.09/5.29 produc303800833217521984nteger: ( nat > nat > produc2591615631378489102nteger ) > product_prod_nat_nat > produc2591615631378489102nteger ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Int__Oint_J,type,
% 9.09/5.29 produc7671697017840204687at_int: ( nat > nat > product_prod_nat_int ) > product_prod_nat_nat > product_prod_nat_int ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 9.09/5.29 produc2626176000494625587at_nat: ( nat > nat > product_prod_nat_nat ) > product_prod_nat_nat > product_prod_nat_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 9.09/5.29 produc8197505143624133779at_nat: ( nat > nat > set_Pr1261947904930325089at_nat ) > product_prod_nat_nat > set_Pr1261947904930325089at_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Num__Onum_001t__Option__Ooption_It__Num__Onum_J,type,
% 9.09/5.29 produc478579273971653890on_num: ( nat > num > option_num ) > product_prod_nat_num > option_num ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_M_Eo_J,type,
% 9.09/5.29 produc1908958340173245860_nat_o: ( nat > set_Pr1261947904930325089at_nat > produc3313772616054891654at_nat > $o ) > produc3313772616054891654at_nat > produc3313772616054891654at_nat > $o ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001_Eo,type,
% 9.09/5.29 produc7997411485876045171_nat_o: ( nat > set_Pr1261947904930325089at_nat > $o ) > produc3313772616054891654at_nat > $o ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Product__Type_Oprod_Ocase__prod_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_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_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,
% 9.09/5.29 produc9203276081649983901et_nat: ( produc3925858234332021118et_nat > ( produc3658429121746597890et_nat > $o ) > produc2732055786443039994et_nat ) > produc4962441903510821572_nat_o > produc2732055786443039994et_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
% 9.09/5.29 produc5068368601420144385nteger: ( produc8923325533196201883nteger > ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc1908205239877642774nteger ) > produc998928222018024388e_term > produc1908205239877642774nteger ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_001t__Code____Numeral__Onatural_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J,type,
% 9.09/5.29 produc1198152457851389869atural: ( produc7822875418678951345atural > code_natural > produc5835291356934675326atural ) > produc3981471736659609608atural > produc5835291356934675326atural ).
% 9.09/5.29
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% 9.09/5.29 produc5206072795621629085et_nat: ( produc3658429121746597890et_nat > ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat ) > produc6907119039986491712_nat_o > produc3925858234332021118et_nat ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_I_062_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
% 9.09/5.29 produc3478612561300218621nt_int: ( product_prod_int_int > ( int > option6357759511663192854e_term ) > produc7773217078559923341nt_int ) > produc3832618445565238089e_term > produc7773217078559923341nt_int ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Product____Type__Oprod_It__Int__Oint_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Int__Oint_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
% 9.09/5.29 produc199769199162113789nt_int: ( product_prod_int_int > ( produc8551481072490612790e_term > option6357759511663192854e_term ) > produc2285326912895808259nt_int ) > produc1821397396195235155e_term > produc2285326912895808259nt_int ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_Eo,type,
% 9.09/5.29 produc6590410687421337004_nat_o: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > produc859450856879609959at_nat > $o ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001_Eo,type,
% 9.09/5.29 produc7830147906768200158_nat_o: ( produc3313772616054891654at_nat > produc3313772616054891654at_nat > $o ) > produc2714363965264676845at_nat > $o ).
% 9.09/5.29
% 9.09/5.29 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Nat__Onat_J_001_Eo,type,
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% 9.17/5.30
% 9.17/5.30 thf(sy_c_Set_Oimage_001t__Set__Oset_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Int__Oint_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J_001_062_I_062_It__Product____Type__Oprod_It__Int__Oint_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_M_062_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J_J,type,
% 9.17/5.30 image_5684251269295653582_int_o: ( set_Pr9222295170931077689nt_int > ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o ) > set_se2364587433798273647nt_int > set_Pr5050529186185961540_int_o ).
% 9.17/5.30
% 9.17/5.30 thf(sy_c_Set_Oimage_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001_062_It__Nat__Onat_M_062_It__Nat__Onat_M_Eo_J_J,type,
% 9.17/5.30 image_6923511907955291850_nat_o: ( set_Pr1261947904930325089at_nat > nat > nat > $o ) > set_se7855581050983116737at_nat > set_nat_nat_o ).
% 9.17/5.30
% 9.17/5.30 thf(sy_c_Set_Oimage_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
% 9.17/5.30 image_6898982319499645995at_nat: ( set_Pr1261947904930325089at_nat > set_Pr4329608150637261639at_nat ) > set_se7855581050983116737at_nat > set_se5479201105039950375at_nat ).
% 9.17/5.30
% 9.17/5.30 thf(sy_c_Set_Oimage_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_001_062_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_M_062_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_M_Eo_J_J,type,
% 9.17/5.30 image_6595146019508340652_nat_o: ( set_Pr4329608150637261639at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ) > set_se5479201105039950375at_nat > set_se9180647916752606350_nat_o ).
% 9.17/5.30
% 9.17/5.30 thf(sy_c_Set_Oinsert_001_Eo,type,
% 9.17/5.30 insert_o: $o > set_o > set_o ).
% 9.17/5.30
% 9.17/5.30 thf(sy_c_Set_Oinsert_001t__Code____Numeral__Ointeger,type,
% 9.17/5.30 insert_Code_integer: code_integer > set_Code_integer > set_Code_integer ).
% 9.17/5.30
% 9.17/5.30 thf(sy_c_Set_Oinsert_001t__Int__Oint,type,
% 9.17/5.30 insert_int: int > set_int > set_int ).
% 9.17/5.30
% 9.17/5.30 thf(sy_c_Set_Oinsert_001t__List__Olist_It__Nat__Onat_J,type,
% 9.17/5.30 insert_list_nat: list_nat > set_list_nat > set_list_nat ).
% 9.17/5.30
% 9.17/5.30 thf(sy_c_Set_Oinsert_001t__Nat__Onat,type,
% 9.17/5.30 insert_nat: nat > set_nat > set_nat ).
% 9.17/5.30
% 9.17/5.30 thf(sy_c_Set_Oinsert_001t__Num__Onum,type,
% 9.17/5.30 insert_num: num > set_num > set_num ).
% 9.17/5.30
% 9.17/5.30 thf(sy_c_Set_Oinsert_001t__Option__Ooption_I_Eo_J,type,
% 9.17/5.30 insert_option_o: option_o > set_option_o > set_option_o ).
% 9.17/5.30
% 9.17/5.30 thf(sy_c_Set_Oinsert_001t__Option__Ooption_It__Int__Oint_J,type,
% 9.17/5.30 insert_option_int: option_int > set_option_int > set_option_int ).
% 9.17/5.30
% 9.17/5.30 thf(sy_c_Set_Oinsert_001t__Option__Ooption_It__Nat__Onat_J,type,
% 9.17/5.30 insert_option_nat: option_nat > set_option_nat > set_option_nat ).
% 9.17/5.30
% 9.17/5.30 thf(sy_c_Set_Oinsert_001t__Option__Ooption_It__Num__Onum_J,type,
% 9.17/5.30 insert_option_num: option_num > set_option_num > set_option_num ).
% 9.17/5.30
% 9.17/5.30 thf(sy_c_Set_Oinsert_001t__Option__Ooption_It__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
% 9.17/5.30 insert7468008629046257882it_nat: option3216581401566546698it_nat > set_op3940070208846178154it_nat > set_op3940070208846178154it_nat ).
% 9.17/5.30
% 9.17/5.30 thf(sy_c_Set_Oinsert_001t__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 9.17/5.30 insert6842972033726296599at_nat: option4927543243414619207at_nat > set_op4508134149509766951at_nat > set_op4508134149509766951at_nat ).
% 9.17/5.30
% 9.17/5.30 thf(sy_c_Set_Oinsert_001t__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
% 9.17/5.30 insert2007652293347934600it_nat: option8956607266484857688it_nat > set_op239864471688321678it_nat > set_op239864471688321678it_nat ).
% 9.17/5.30
% 9.17/5.30 thf(sy_c_Set_Oinsert_001t__Option__Ooption_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
% 9.17/5.30 insert6833468608972679677at_nat: option8699557107911914541at_nat > set_op989438649584373901at_nat > set_op989438649584373901at_nat ).
% 9.17/5.30
% 9.17/5.30 thf(sy_c_Set_Oinsert_001t__Option__Ooption_It__Product____Type__Ounit_J,type,
% 9.17/5.30 insert2866144167138965411t_unit: option_Product_unit > set_op3165557761946182707t_unit > set_op3165557761946182707t_unit ).
% 9.17/5.30
% 9.17/5.30 thf(sy_c_Set_Oinsert_001t__Option__Ooption_It__Set__Oset_It__Nat__Onat_J_J,type,
% 9.17/5.30 insert6281397740311767046et_nat: option_set_nat > set_option_set_nat > set_option_set_nat ).
% 9.17/5.30
% 9.17/5.30 thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_I_062_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
% 9.17/5.30 insert750232675644355261nt_int: produc7773217078559923341nt_int > set_Pr1872883991513573699nt_int > set_Pr1872883991513573699nt_int ).
% 9.17/5.30
% 9.17/5.30 thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
% 9.17/5.30 insert4245756632806152262nteger: produc1908205239877642774nteger > set_Pr1281608226676607948nteger > set_Pr1281608226676607948nteger ).
% 9.17/5.30
% 9.17/5.30 thf(sy_c_Set_Oinsert_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,
% 9.17/5.30 insert8297122186708525866et_nat: produc2732055786443039994et_nat > set_Pr8536935166611901872et_nat > set_Pr8536935166611901872et_nat ).
% 9.17/5.30
% 9.17/5.30 thf(sy_c_Set_Oinsert_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,
% 9.17/5.30 insert3111075074545270702et_nat: produc3925858234332021118et_nat > set_Pr3286484037609594932et_nat > set_Pr3286484037609594932et_nat ).
% 9.17/5.30
% 9.17/5.30 thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Int__Oint_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
% 9.17/5.30 insert984290209421517107nt_int: produc2285326912895808259nt_int > set_Pr9222295170931077689nt_int > set_Pr9222295170931077689nt_int ).
% 9.17/5.30
% 9.17/5.30 thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_I_Eo_M_Eo_J,type,
% 9.17/5.30 insert6201435330877294327od_o_o: product_prod_o_o > set_Product_prod_o_o > set_Product_prod_o_o ).
% 9.17/5.30
% 9.17/5.30 thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_I_Eo_Mt__Int__Oint_J,type,
% 9.17/5.30 insert3770363720049103139_o_int: product_prod_o_int > set_Pr8834758594704517033_o_int > set_Pr8834758594704517033_o_int ).
% 9.17/5.30
% 9.17/5.30 thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J,type,
% 9.17/5.30 insert7948214739558299847_o_nat: product_prod_o_nat > set_Pr2101469702781467981_o_nat > set_Pr2101469702781467981_o_nat ).
% 9.17/5.30
% 9.17/5.30 thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_I_Eo_Mt__Num__Onum_J,type,
% 9.17/5.30 insert8656458676507137553_o_num: product_prod_o_num > set_Pr7040061329075590551_o_num > set_Pr7040061329075590551_o_num ).
% 9.17/5.30
% 9.17/5.30 thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_I_Eo_Mt__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
% 9.17/5.30 insert6915099157023601407it_nat: produc2900562427881843919it_nat > set_Pr6777250647868329861it_nat > set_Pr6777250647868329861it_nat ).
% 9.17/5.30
% 9.17/5.30 thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 9.17/5.30 insert4913895101485356395nteger: produc8923325533196201883nteger > set_Pr4811707699266497531nteger > set_Pr4811707699266497531nteger ).
% 9.17/5.30
% 9.17/5.30 thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J,type,
% 9.17/5.30 insert6505218763252461998atural: produc5835291356934675326atural > set_Pr2352657477744078772atural > set_Pr2352657477744078772atural ).
% 9.17/5.30
% 9.17/5.30 thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_It__Int__Oint_M_Eo_J,type,
% 9.17/5.30 insert412334881326329105_int_o: product_prod_int_o > set_Pr903927857289325719_int_o > set_Pr903927857289325719_int_o ).
% 9.17/5.30
% 9.17/5.30 thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 9.17/5.30 insert5033312907999012233nt_int: product_prod_int_int > set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int ).
% 9.17/5.30
% 9.17/5.30 thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_It__Int__Oint_Mt__Nat__Onat_J,type,
% 9.17/5.30 insert9211163927508208941nt_nat: product_prod_int_nat > set_Pr3448869479623346877nt_nat > set_Pr3448869479623346877nt_nat ).
% 9.17/5.30
% 9.17/5.30 thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_It__Int__Oint_Mt__Num__Onum_J,type,
% 9.17/5.30 insert696035827602270839nt_num: product_prod_int_num > set_Pr8387461105917469447nt_num > set_Pr8387461105917469447nt_num ).
% 9.17/5.30
% 9.17/5.30 thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_It__Nat__Onat_M_Eo_J,type,
% 9.17/5.30 insert2233377226759017069_nat_o: product_prod_nat_o > set_Pr3149072824959771635_nat_o > set_Pr3149072824959771635_nat_o ).
% 9.17/5.30
% 9.17/5.30 thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Int__Oint_J,type,
% 9.17/5.30 insert4033959196097957677at_int: product_prod_nat_int > set_Pr7995236796853374141at_int > set_Pr7995236796853374141at_int ).
% 9.17/5.30
% 9.17/5.30 thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 9.17/5.30 insert8211810215607154385at_nat: product_prod_nat_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
% 9.17/5.30
% 9.17/5.30 thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Num__Onum_J,type,
% 9.17/5.30 insert8920054152555992091at_num: product_prod_nat_num > set_Pr6200539531224447659at_num > set_Pr6200539531224447659at_num ).
% 9.17/5.30
% 9.17/5.30 thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
% 9.17/5.30 insert2528233410557839625it_nat: produc3839731585411834681it_nat > set_Pr633603713510679705it_nat > set_Pr633603713510679705it_nat ).
% 9.17/5.30
% 9.17/5.30 thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J,type,
% 9.17/5.30 insert2126339615020983374_nat_o: produc652263959640188542_nat_o > set_Pr6558897299634722526_nat_o > set_Pr6558897299634722526_nat_o ).
% 9.17/5.30
% 9.17/5.30 thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Num__Onum_J,type,
% 9.17/5.30 insert2790150385885543546at_num: produc9082142974458947146at_num > set_Pr7477759153910077568at_num > set_Pr7477759153910077568at_num ).
% 9.17/5.30
% 9.17/5.30 thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 9.17/5.30 insert5050368324300391991at_nat: produc859450856879609959at_nat > set_Pr8693737435421807431at_nat > set_Pr8693737435421807431at_nat ).
% 9.17/5.30
% 9.17/5.30 thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
% 9.17/5.30 insert398606708087465655at_nat: produc1906917888121415911at_nat > set_Pr5564308138774400199at_nat > set_Pr5564308138774400199at_nat ).
% 9.17/5.30
% 9.17/5.30 thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 9.17/5.30 insert5940566491043231800it_nat: produc8664842809031399944it_nat > set_Pr1354866905816374718it_nat > set_Pr1354866905816374718it_nat ).
% 9.17/5.30
% 9.17/5.30 thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 9.17/5.30 insert9069300056098147895at_nat: produc3843707927480180839at_nat > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat ).
% 9.17/5.30
% 9.17/5.30 thf(sy_c_Set_Oinsert_001t__Product____Type__Ounit,type,
% 9.17/5.30 insert_Product_unit: product_unit > set_Product_unit > set_Product_unit ).
% 9.17/5.30
% 9.17/5.30 thf(sy_c_Set_Oinsert_001t__Rat__Orat,type,
% 9.17/5.30 insert_rat: rat > set_rat > set_rat ).
% 9.17/5.30
% 9.17/5.30 thf(sy_c_Set_Oinsert_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 9.17/5.30 insert9200635055090092081at_nat: set_Pr1261947904930325089at_nat > set_se7855581050983116737at_nat > set_se7855581050983116737at_nat ).
% 9.17/5.30
% 9.17/5.30 thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Assertions__Oassn,type,
% 9.17/5.30 set_fo1959793692361082170t_assn: ( nat > assn > assn ) > nat > nat > assn > assn ).
% 9.17/5.30
% 9.17/5.30 thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Code____Numeral__Ointeger,type,
% 9.17/5.30 set_fo1084959871951514735nteger: ( nat > code_integer > code_integer ) > nat > nat > code_integer > code_integer ).
% 9.17/5.30
% 9.17/5.30 thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Code____Numeral__Onatural,type,
% 9.17/5.30 set_fo9131927060563008058atural: ( nat > code_natural > code_natural ) > nat > nat > code_natural > code_natural ).
% 9.17/5.30
% 9.17/5.30 thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Int__Oint,type,
% 9.17/5.30 set_fo2581907887559384638at_int: ( nat > int > int ) > nat > nat > int > int ).
% 9.17/5.30
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% 9.17/5.30
% 9.17/5.30 thf(sy_c_Wellfounded_Ofinite__psubset_001t__Nat__Onat,type,
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% 9.17/5.30
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% 9.17/5.30
% 9.17/5.30 thf(sy_c_Wellfounded_Oless__than,type,
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% 9.17/5.30 thf(sy_c_Wellfounded_Olex__prod_001_062_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
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% 9.17/5.30
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% 9.17/5.30
% 9.17/5.30 thf(sy_c_Wellfounded_Olex__prod_001t__Nat__Onat_001t__Nat__Onat,type,
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% 9.17/5.30
% 9.17/5.30 thf(sy_c_Wellfounded_Omax__ext_001_Eo,type,
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% 9.17/5.30 thf(sy_c_Wellfounded_Omax__ext_001t__Int__Oint,type,
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% 9.17/5.30
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% 9.17/5.30
% 9.17/5.30 thf(sy_c_Wellfounded_Omeasure_001t__Nat__Onat,type,
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% 9.17/5.30
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% 9.17/5.30 thf(sy_c_Wellfounded_Opred__nat,type,
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% 9.17/5.30 ( ( heap_T5591663578999710211rray_a @ F @ H2 )
% 9.17/5.30 = ( heap_T5591663578999710211rray_a @ G @ H2 ) )
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% 9.17/5.30 thf(fact_3_Heap__eqI,axiom,
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% 9.17/5.30 ( ( heap_T875086893843062177t_unit @ F @ H2 )
% 9.17/5.30 = ( heap_T875086893843062177t_unit @ G @ H2 ) )
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% 9.17/5.30 thf(fact_4_execute__raise,axiom,
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% 9.17/5.30 ( ( heap_T5591663578999710211rray_a @ ( heap_T1552190017797416154rray_a @ S ) )
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% 9.17/5.30 ( ( heap_T3039585018531920163rray_a @ X @ Y )
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% 9.17/5.30 => ( ( heap_T5591663578999710211rray_a @ X @ H3 )
% 9.17/5.30 = ( heap_T5591663578999710211rray_a @ Y @ H3 ) ) ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_15_Heap__ordE,axiom,
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% 9.17/5.30 ( ( heap_T499439718319394433t_unit @ X @ Y )
% 9.17/5.30 => ( ( ( heap_T875086893843062177t_unit @ X @ H3 )
% 9.17/5.30 != none_P9117596204409417319it_nat )
% 9.17/5.30 => ( ( heap_T875086893843062177t_unit @ X @ H3 )
% 9.17/5.30 = ( heap_T875086893843062177t_unit @ Y @ H3 ) ) ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_16_Heap__ordI,axiom,
% 9.17/5.30 ! [X: heap_T6362127782908069795rray_a,Y: heap_T6362127782908069795rray_a] :
% 9.17/5.30 ( ! [H2: heap_e7401611519738050253t_unit] :
% 9.17/5.30 ( ( ( heap_T5591663578999710211rray_a @ X @ H2 )
% 9.17/5.30 = none_P2587165478634041381it_nat )
% 9.17/5.30 | ( ( heap_T5591663578999710211rray_a @ X @ H2 )
% 9.17/5.30 = ( heap_T5591663578999710211rray_a @ Y @ H2 ) ) )
% 9.17/5.30 => ( heap_T3039585018531920163rray_a @ X @ Y ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_17_Heap__ordI,axiom,
% 9.17/5.30 ! [X: heap_T5738788834812785303t_unit,Y: heap_T5738788834812785303t_unit] :
% 9.17/5.30 ( ! [H2: heap_e7401611519738050253t_unit] :
% 9.17/5.30 ( ( ( heap_T875086893843062177t_unit @ X @ H2 )
% 9.17/5.30 = none_P9117596204409417319it_nat )
% 9.17/5.30 | ( ( heap_T875086893843062177t_unit @ X @ H2 )
% 9.17/5.30 = ( heap_T875086893843062177t_unit @ Y @ H2 ) ) )
% 9.17/5.30 => ( heap_T499439718319394433t_unit @ X @ Y ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_18_execute__bind_I2_J,axiom,
% 9.17/5.30 ! [F: heap_T6362127782908069795rray_a,H3: heap_e7401611519738050253t_unit,G: array_a > heap_T6362127782908069795rray_a] :
% 9.17/5.30 ( ( ( heap_T5591663578999710211rray_a @ F @ H3 )
% 9.17/5.30 = none_P2587165478634041381it_nat )
% 9.17/5.30 => ( ( heap_T5591663578999710211rray_a @ ( heap_T2407400398799471159rray_a @ F @ G ) @ H3 )
% 9.17/5.30 = none_P2587165478634041381it_nat ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_19_execute__bind_I2_J,axiom,
% 9.17/5.30 ! [F: heap_T6362127782908069795rray_a,H3: heap_e7401611519738050253t_unit,G: array_a > heap_T5738788834812785303t_unit] :
% 9.17/5.30 ( ( ( heap_T5591663578999710211rray_a @ F @ H3 )
% 9.17/5.30 = none_P2587165478634041381it_nat )
% 9.17/5.30 => ( ( heap_T875086893843062177t_unit @ ( heap_T7324619625323989613t_unit @ F @ G ) @ H3 )
% 9.17/5.30 = none_P9117596204409417319it_nat ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_20_execute__bind_I2_J,axiom,
% 9.17/5.30 ! [F: heap_T5738788834812785303t_unit,H3: heap_e7401611519738050253t_unit,G: product_unit > heap_T6362127782908069795rray_a] :
% 9.17/5.30 ( ( ( heap_T875086893843062177t_unit @ F @ H3 )
% 9.17/5.30 = none_P9117596204409417319it_nat )
% 9.17/5.30 => ( ( heap_T5591663578999710211rray_a @ ( heap_T7158140910958840029rray_a @ F @ G ) @ H3 )
% 9.17/5.30 = none_P2587165478634041381it_nat ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_21_execute__bind_I2_J,axiom,
% 9.17/5.30 ! [F: heap_T5738788834812785303t_unit,H3: heap_e7401611519738050253t_unit,G: product_unit > heap_T5738788834812785303t_unit] :
% 9.17/5.30 ( ( ( heap_T875086893843062177t_unit @ F @ H3 )
% 9.17/5.30 = none_P9117596204409417319it_nat )
% 9.17/5.30 => ( ( heap_T875086893843062177t_unit @ ( heap_T2633723481742716231t_unit @ F @ G ) @ H3 )
% 9.17/5.30 = none_P9117596204409417319it_nat ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_22_the__default_Osimps_I2_J,axiom,
% 9.17/5.30 ! [X: produc6714399278180371524it_nat] :
% 9.17/5.30 ( ( the_de8559148246674365659it_nat @ X @ none_P2587165478634041381it_nat )
% 9.17/5.30 = X ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_23_the__default_Osimps_I2_J,axiom,
% 9.17/5.30 ! [X: num] :
% 9.17/5.30 ( ( the_default_num @ X @ none_num )
% 9.17/5.30 = X ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_24_the__default_Osimps_I2_J,axiom,
% 9.17/5.30 ! [X: produc8664842809031399944it_nat] :
% 9.17/5.30 ( ( the_de2487931475039285041it_nat @ X @ none_P9117596204409417319it_nat )
% 9.17/5.30 = X ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_25_raise__bind,axiom,
% 9.17/5.30 ! [E: list_char,F: product_unit > heap_T5738788834812785303t_unit] :
% 9.17/5.30 ( ( heap_T2633723481742716231t_unit @ ( heap_T2927564422264180874t_unit @ E ) @ F )
% 9.17/5.30 = ( heap_T2927564422264180874t_unit @ E ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_26_raise__bind,axiom,
% 9.17/5.30 ! [E: list_char,F: product_unit > heap_T6362127782908069795rray_a] :
% 9.17/5.30 ( ( heap_T7158140910958840029rray_a @ ( heap_T2927564422264180874t_unit @ E ) @ F )
% 9.17/5.30 = ( heap_T1552190017797416154rray_a @ E ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_27_raise__bind,axiom,
% 9.17/5.30 ! [E: list_char,F: array_a > heap_T5738788834812785303t_unit] :
% 9.17/5.30 ( ( heap_T7324619625323989613t_unit @ ( heap_T1552190017797416154rray_a @ E ) @ F )
% 9.17/5.30 = ( heap_T2927564422264180874t_unit @ E ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_28_raise__bind,axiom,
% 9.17/5.30 ! [E: list_char,F: array_a > heap_T6362127782908069795rray_a] :
% 9.17/5.30 ( ( heap_T2407400398799471159rray_a @ ( heap_T1552190017797416154rray_a @ E ) @ F )
% 9.17/5.30 = ( heap_T1552190017797416154rray_a @ E ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_29_heap_Oleq__refl,axiom,
% 9.17/5.30 ! [X: heap_T5738788834812785303t_unit] : ( heap_T499439718319394433t_unit @ X @ X ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_30_heap_Oleq__refl,axiom,
% 9.17/5.30 ! [X: heap_T6362127782908069795rray_a] : ( heap_T3039585018531920163rray_a @ X @ X ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_31_heap_Oleq__trans,axiom,
% 9.17/5.30 ! [X: heap_T5738788834812785303t_unit,Y: heap_T5738788834812785303t_unit,Z: heap_T5738788834812785303t_unit] :
% 9.17/5.30 ( ( heap_T499439718319394433t_unit @ X @ Y )
% 9.17/5.30 => ( ( heap_T499439718319394433t_unit @ Y @ Z )
% 9.17/5.30 => ( heap_T499439718319394433t_unit @ X @ Z ) ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_32_heap_Oleq__trans,axiom,
% 9.17/5.30 ! [X: heap_T6362127782908069795rray_a,Y: heap_T6362127782908069795rray_a,Z: heap_T6362127782908069795rray_a] :
% 9.17/5.30 ( ( heap_T3039585018531920163rray_a @ X @ Y )
% 9.17/5.30 => ( ( heap_T3039585018531920163rray_a @ Y @ Z )
% 9.17/5.30 => ( heap_T3039585018531920163rray_a @ X @ Z ) ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_33_heap_Oleq__antisym,axiom,
% 9.17/5.30 ! [X: heap_T5738788834812785303t_unit,Y: heap_T5738788834812785303t_unit] :
% 9.17/5.30 ( ( heap_T499439718319394433t_unit @ X @ Y )
% 9.17/5.30 => ( ( heap_T499439718319394433t_unit @ Y @ X )
% 9.17/5.30 => ( X = Y ) ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_34_heap_Oleq__antisym,axiom,
% 9.17/5.30 ! [X: heap_T6362127782908069795rray_a,Y: heap_T6362127782908069795rray_a] :
% 9.17/5.30 ( ( heap_T3039585018531920163rray_a @ X @ Y )
% 9.17/5.30 => ( ( heap_T3039585018531920163rray_a @ Y @ X )
% 9.17/5.30 => ( X = Y ) ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_35_success__ifI,axiom,
% 9.17/5.30 ! [C: $o,T: heap_T5738788834812785303t_unit,H3: heap_e7401611519738050253t_unit,E: heap_T5738788834812785303t_unit] :
% 9.17/5.30 ( ( C
% 9.17/5.30 => ( heap_T584514906347983379t_unit @ T @ H3 ) )
% 9.17/5.30 => ( ( ~ C
% 9.17/5.30 => ( heap_T584514906347983379t_unit @ E @ H3 ) )
% 9.17/5.30 => ( heap_T584514906347983379t_unit @ ( if_Hea8138950348631371857t_unit @ C @ T @ E ) @ H3 ) ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_36_success__ifI,axiom,
% 9.17/5.30 ! [C: $o,T: heap_T6362127782908069795rray_a,H3: heap_e7401611519738050253t_unit,E: heap_T6362127782908069795rray_a] :
% 9.17/5.30 ( ( C
% 9.17/5.30 => ( heap_T6932021131025641745rray_a @ T @ H3 ) )
% 9.17/5.30 => ( ( ~ C
% 9.17/5.30 => ( heap_T6932021131025641745rray_a @ E @ H3 ) )
% 9.17/5.30 => ( heap_T6932021131025641745rray_a @ ( if_Hea5896630067203373929rray_a @ C @ T @ E ) @ H3 ) ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_37_success__guardI,axiom,
% 9.17/5.30 ! [P: heap_e7401611519738050253t_unit > $o,H3: heap_e7401611519738050253t_unit,F: heap_e7401611519738050253t_unit > produc8664842809031399944it_nat] :
% 9.17/5.30 ( ( P @ H3 )
% 9.17/5.30 => ( heap_T584514906347983379t_unit @ ( heap_T8440541562793052209t_unit @ P @ F ) @ H3 ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_38_success__guardI,axiom,
% 9.17/5.30 ! [P: heap_e7401611519738050253t_unit > $o,H3: heap_e7401611519738050253t_unit,F: heap_e7401611519738050253t_unit > produc6714399278180371524it_nat] :
% 9.17/5.30 ( ( P @ H3 )
% 9.17/5.30 => ( heap_T6932021131025641745rray_a @ ( heap_T7685628758766326643rray_a @ P @ F ) @ H3 ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_39_success__assertI,axiom,
% 9.17/5.30 ! [P: product_unit > $o,X: product_unit,H3: heap_e7401611519738050253t_unit] :
% 9.17/5.30 ( ( P @ X )
% 9.17/5.30 => ( heap_T584514906347983379t_unit @ ( heap_T4208721593536448476t_unit @ P @ X ) @ H3 ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_40_success__assertI,axiom,
% 9.17/5.30 ! [P: array_a > $o,X: array_a,H3: heap_e7401611519738050253t_unit] :
% 9.17/5.30 ( ( P @ X )
% 9.17/5.30 => ( heap_T6932021131025641745rray_a @ ( heap_T7971689983404357896rray_a @ P @ X ) @ H3 ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_41_fails__bind,axiom,
% 9.17/5.30 ! [M2: heap_T5738788834812785303t_unit,F: product_unit > heap_T5738788834812785303t_unit,H3: heap_e7401611519738050253t_unit] :
% 9.17/5.30 ( ( time_f8834461667527620124t_unit @ ( heap_T2633723481742716231t_unit @ M2 @ F ) @ H3 )
% 9.17/5.30 = ( ~ ( time_f8834461667527620124t_unit @ M2 @ H3 )
% 9.17/5.30 => ( time_f8834461667527620124t_unit @ ( F @ ( time_t2745601220510131320t_unit @ M2 @ H3 ) ) @ ( time_t3350536682685678164t_unit @ M2 @ H3 ) ) ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_42_fails__bind,axiom,
% 9.17/5.30 ! [M2: heap_T6362127782908069795rray_a,F: array_a > heap_T5738788834812785303t_unit,H3: heap_e7401611519738050253t_unit] :
% 9.17/5.30 ( ( time_f8834461667527620124t_unit @ ( heap_T7324619625323989613t_unit @ M2 @ F ) @ H3 )
% 9.17/5.30 = ( ~ ( time_fails_array_a @ M2 @ H3 )
% 9.17/5.30 => ( time_f8834461667527620124t_unit @ ( F @ ( time_the_res_array_a @ M2 @ H3 ) ) @ ( time_t490086488869527696rray_a @ M2 @ H3 ) ) ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_43_fails__bind,axiom,
% 9.17/5.30 ! [M2: heap_T5738788834812785303t_unit,F: product_unit > heap_T6362127782908069795rray_a,H3: heap_e7401611519738050253t_unit] :
% 9.17/5.30 ( ( time_fails_array_a @ ( heap_T7158140910958840029rray_a @ M2 @ F ) @ H3 )
% 9.17/5.30 = ( ~ ( time_f8834461667527620124t_unit @ M2 @ H3 )
% 9.17/5.30 => ( time_fails_array_a @ ( F @ ( time_t2745601220510131320t_unit @ M2 @ H3 ) ) @ ( time_t3350536682685678164t_unit @ M2 @ H3 ) ) ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_44_fails__bind,axiom,
% 9.17/5.30 ! [M2: heap_T6362127782908069795rray_a,F: array_a > heap_T6362127782908069795rray_a,H3: heap_e7401611519738050253t_unit] :
% 9.17/5.30 ( ( time_fails_array_a @ ( heap_T2407400398799471159rray_a @ M2 @ F ) @ H3 )
% 9.17/5.30 = ( ~ ( time_fails_array_a @ M2 @ H3 )
% 9.17/5.30 => ( time_fails_array_a @ ( F @ ( time_the_res_array_a @ M2 @ H3 ) ) @ ( time_t490086488869527696rray_a @ M2 @ H3 ) ) ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_45_success__of__listI,axiom,
% 9.17/5.30 ! [Xs: list_a,H3: heap_e7401611519738050253t_unit] : ( heap_T6932021131025641745rray_a @ ( array_of_list_a @ Xs ) @ H3 ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_46_success__tapI,axiom,
% 9.17/5.30 ! [F: heap_e7401611519738050253t_unit > product_unit,H3: heap_e7401611519738050253t_unit] : ( heap_T584514906347983379t_unit @ ( heap_T560649228465745139t_unit @ F ) @ H3 ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_47_success__tapI,axiom,
% 9.17/5.30 ! [F: heap_e7401611519738050253t_unit > array_a,H3: heap_e7401611519738050253t_unit] : ( heap_T6932021131025641745rray_a @ ( heap_T2055650868554030641rray_a @ F ) @ H3 ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_48_success__heapI,axiom,
% 9.17/5.30 ! [F: heap_e7401611519738050253t_unit > produc8664842809031399944it_nat,H3: heap_e7401611519738050253t_unit] : ( heap_T584514906347983379t_unit @ ( heap_T6927113302350381334t_unit @ F ) @ H3 ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_49_success__heapI,axiom,
% 9.17/5.30 ! [F: heap_e7401611519738050253t_unit > produc6714399278180371524it_nat,H3: heap_e7401611519738050253t_unit] : ( heap_T6932021131025641745rray_a @ ( heap_T7473999186002612558rray_a @ F ) @ H3 ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_50_success__ureturnI,axiom,
% 9.17/5.30 ! [X: product_unit,H3: heap_e7401611519738050253t_unit] : ( heap_T584514906347983379t_unit @ ( heap_T4284346855313245393t_unit @ X ) @ H3 ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_51_success__ureturnI,axiom,
% 9.17/5.30 ! [X: array_a,H3: heap_e7401611519738050253t_unit] : ( heap_T6932021131025641745rray_a @ ( heap_T4328122439115681491rray_a @ X ) @ H3 ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_52_execute__guard_I2_J,axiom,
% 9.17/5.30 ! [P: heap_e7401611519738050253t_unit > $o,H3: heap_e7401611519738050253t_unit,F: heap_e7401611519738050253t_unit > produc6714399278180371524it_nat] :
% 9.17/5.30 ( ( P @ H3 )
% 9.17/5.30 => ( ( heap_T5591663578999710211rray_a @ ( heap_T7685628758766326643rray_a @ P @ F ) @ H3 )
% 9.17/5.30 = ( some_P6105628898608307625it_nat @ ( F @ H3 ) ) ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_53_execute__guard_I2_J,axiom,
% 9.17/5.30 ! [P: heap_e7401611519738050253t_unit > $o,H3: heap_e7401611519738050253t_unit,F: heap_e7401611519738050253t_unit > produc8664842809031399944it_nat] :
% 9.17/5.30 ( ( P @ H3 )
% 9.17/5.30 => ( ( heap_T875086893843062177t_unit @ ( heap_T8440541562793052209t_unit @ P @ F ) @ H3 )
% 9.17/5.30 = ( some_P1914260805536162275it_nat @ ( F @ H3 ) ) ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_54_combine__options__simps_I1_J,axiom,
% 9.17/5.30 ! [F: produc6714399278180371524it_nat > produc6714399278180371524it_nat > produc6714399278180371524it_nat,Y: option3216581401566546698it_nat] :
% 9.17/5.30 ( ( combin3867838909898076099it_nat @ F @ none_P2587165478634041381it_nat @ Y )
% 9.17/5.30 = Y ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_55_combine__options__simps_I1_J,axiom,
% 9.17/5.30 ! [F: num > num > num,Y: option_num] :
% 9.17/5.30 ( ( combine_options_num @ F @ none_num @ Y )
% 9.17/5.30 = Y ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_56_combine__options__simps_I1_J,axiom,
% 9.17/5.30 ! [F: produc8664842809031399944it_nat > produc8664842809031399944it_nat > produc8664842809031399944it_nat,Y: option8956607266484857688it_nat] :
% 9.17/5.30 ( ( combin4318129983670048329it_nat @ F @ none_P9117596204409417319it_nat @ Y )
% 9.17/5.30 = Y ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_57_combine__options__simps_I2_J,axiom,
% 9.17/5.30 ! [F: produc6714399278180371524it_nat > produc6714399278180371524it_nat > produc6714399278180371524it_nat,X: option3216581401566546698it_nat] :
% 9.17/5.30 ( ( combin3867838909898076099it_nat @ F @ X @ none_P2587165478634041381it_nat )
% 9.17/5.30 = X ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_58_combine__options__simps_I2_J,axiom,
% 9.17/5.30 ! [F: num > num > num,X: option_num] :
% 9.17/5.30 ( ( combine_options_num @ F @ X @ none_num )
% 9.17/5.30 = X ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_59_combine__options__simps_I2_J,axiom,
% 9.17/5.30 ! [F: produc8664842809031399944it_nat > produc8664842809031399944it_nat > produc8664842809031399944it_nat,X: option8956607266484857688it_nat] :
% 9.17/5.30 ( ( combin4318129983670048329it_nat @ F @ X @ none_P9117596204409417319it_nat )
% 9.17/5.30 = X ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_60_option_Oinject,axiom,
% 9.17/5.30 ! [X2: num,Y2: num] :
% 9.17/5.30 ( ( ( some_num @ X2 )
% 9.17/5.30 = ( some_num @ Y2 ) )
% 9.17/5.30 = ( X2 = Y2 ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_61_option_Oinject,axiom,
% 9.17/5.30 ! [X2: produc8664842809031399944it_nat,Y2: produc8664842809031399944it_nat] :
% 9.17/5.30 ( ( ( some_P1914260805536162275it_nat @ X2 )
% 9.17/5.30 = ( some_P1914260805536162275it_nat @ Y2 ) )
% 9.17/5.30 = ( X2 = Y2 ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_62_not__None__eq,axiom,
% 9.17/5.30 ! [X: option3216581401566546698it_nat] :
% 9.17/5.30 ( ( X != none_P2587165478634041381it_nat )
% 9.17/5.30 = ( ? [Y3: produc6714399278180371524it_nat] :
% 9.17/5.30 ( X
% 9.17/5.30 = ( some_P6105628898608307625it_nat @ Y3 ) ) ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_63_not__None__eq,axiom,
% 9.17/5.30 ! [X: option_num] :
% 9.17/5.30 ( ( X != none_num )
% 9.17/5.30 = ( ? [Y3: num] :
% 9.17/5.30 ( X
% 9.17/5.30 = ( some_num @ Y3 ) ) ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_64_not__None__eq,axiom,
% 9.17/5.30 ! [X: option8956607266484857688it_nat] :
% 9.17/5.30 ( ( X != none_P9117596204409417319it_nat )
% 9.17/5.30 = ( ? [Y3: produc8664842809031399944it_nat] :
% 9.17/5.30 ( X
% 9.17/5.30 = ( some_P1914260805536162275it_nat @ Y3 ) ) ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_65_not__Some__eq,axiom,
% 9.17/5.30 ! [X: option3216581401566546698it_nat] :
% 9.17/5.30 ( ( ! [Y3: produc6714399278180371524it_nat] :
% 9.17/5.30 ( X
% 9.17/5.30 != ( some_P6105628898608307625it_nat @ Y3 ) ) )
% 9.17/5.30 = ( X = none_P2587165478634041381it_nat ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_66_not__Some__eq,axiom,
% 9.17/5.30 ! [X: option_num] :
% 9.17/5.30 ( ( ! [Y3: num] :
% 9.17/5.30 ( X
% 9.17/5.30 != ( some_num @ Y3 ) ) )
% 9.17/5.30 = ( X = none_num ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_67_not__Some__eq,axiom,
% 9.17/5.30 ! [X: option8956607266484857688it_nat] :
% 9.17/5.30 ( ( ! [Y3: produc8664842809031399944it_nat] :
% 9.17/5.30 ( X
% 9.17/5.30 != ( some_P1914260805536162275it_nat @ Y3 ) ) )
% 9.17/5.30 = ( X = none_P9117596204409417319it_nat ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_68_combine__options__simps_I3_J,axiom,
% 9.17/5.30 ! [F: num > num > num,A: num,B: num] :
% 9.17/5.30 ( ( combine_options_num @ F @ ( some_num @ A ) @ ( some_num @ B ) )
% 9.17/5.30 = ( some_num @ ( F @ A @ B ) ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_69_combine__options__simps_I3_J,axiom,
% 9.17/5.30 ! [F: produc8664842809031399944it_nat > produc8664842809031399944it_nat > produc8664842809031399944it_nat,A: produc8664842809031399944it_nat,B: produc8664842809031399944it_nat] :
% 9.17/5.30 ( ( combin4318129983670048329it_nat @ F @ ( some_P1914260805536162275it_nat @ A ) @ ( some_P1914260805536162275it_nat @ B ) )
% 9.17/5.30 = ( some_P1914260805536162275it_nat @ ( F @ A @ B ) ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_70_mem__Collect__eq,axiom,
% 9.17/5.30 ! [A: produc3843707927480180839at_nat,P: produc3843707927480180839at_nat > $o] :
% 9.17/5.30 ( ( member8757157785044589968at_nat @ A @ ( collec6321179662152712658at_nat @ P ) )
% 9.17/5.30 = ( P @ A ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_71_mem__Collect__eq,axiom,
% 9.17/5.30 ! [A: product_prod_nat_nat,P: product_prod_nat_nat > $o] :
% 9.17/5.30 ( ( member8440522571783428010at_nat @ A @ ( collec3392354462482085612at_nat @ P ) )
% 9.17/5.30 = ( P @ A ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_72_mem__Collect__eq,axiom,
% 9.17/5.30 ! [A: $o,P: $o > $o] :
% 9.17/5.30 ( ( member_o @ A @ ( collect_o @ P ) )
% 9.17/5.30 = ( P @ A ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_73_mem__Collect__eq,axiom,
% 9.17/5.30 ! [A: int,P: int > $o] :
% 9.17/5.30 ( ( member_int @ A @ ( collect_int @ P ) )
% 9.17/5.30 = ( P @ A ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_74_mem__Collect__eq,axiom,
% 9.17/5.30 ! [A: nat,P: nat > $o] :
% 9.17/5.30 ( ( member_nat @ A @ ( collect_nat @ P ) )
% 9.17/5.30 = ( P @ A ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_75_mem__Collect__eq,axiom,
% 9.17/5.30 ! [A: list_nat,P: list_nat > $o] :
% 9.17/5.30 ( ( member_list_nat @ A @ ( collect_list_nat @ P ) )
% 9.17/5.30 = ( P @ A ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_76_Collect__mem__eq,axiom,
% 9.17/5.30 ! [A2: set_Pr4329608150637261639at_nat] :
% 9.17/5.30 ( ( collec6321179662152712658at_nat
% 9.17/5.30 @ ^ [X3: produc3843707927480180839at_nat] : ( member8757157785044589968at_nat @ X3 @ A2 ) )
% 9.17/5.30 = A2 ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_77_Collect__mem__eq,axiom,
% 9.17/5.30 ! [A2: set_Pr1261947904930325089at_nat] :
% 9.17/5.30 ( ( collec3392354462482085612at_nat
% 9.17/5.30 @ ^ [X3: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X3 @ A2 ) )
% 9.17/5.30 = A2 ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_78_Collect__mem__eq,axiom,
% 9.17/5.30 ! [A2: set_o] :
% 9.17/5.30 ( ( collect_o
% 9.17/5.30 @ ^ [X3: $o] : ( member_o @ X3 @ A2 ) )
% 9.17/5.30 = A2 ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_79_Collect__mem__eq,axiom,
% 9.17/5.30 ! [A2: set_int] :
% 9.17/5.30 ( ( collect_int
% 9.17/5.30 @ ^ [X3: int] : ( member_int @ X3 @ A2 ) )
% 9.17/5.30 = A2 ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_80_Collect__mem__eq,axiom,
% 9.17/5.30 ! [A2: set_nat] :
% 9.17/5.30 ( ( collect_nat
% 9.17/5.30 @ ^ [X3: nat] : ( member_nat @ X3 @ A2 ) )
% 9.17/5.30 = A2 ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_81_Collect__mem__eq,axiom,
% 9.17/5.30 ! [A2: set_list_nat] :
% 9.17/5.30 ( ( collect_list_nat
% 9.17/5.30 @ ^ [X3: list_nat] : ( member_list_nat @ X3 @ A2 ) )
% 9.17/5.30 = A2 ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_82_Collect__cong,axiom,
% 9.17/5.30 ! [P: nat > $o,Q: nat > $o] :
% 9.17/5.30 ( ! [X4: nat] :
% 9.17/5.30 ( ( P @ X4 )
% 9.17/5.30 = ( Q @ X4 ) )
% 9.17/5.30 => ( ( collect_nat @ P )
% 9.17/5.30 = ( collect_nat @ Q ) ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_83_Collect__cong,axiom,
% 9.17/5.30 ! [P: list_nat > $o,Q: list_nat > $o] :
% 9.17/5.30 ( ! [X4: list_nat] :
% 9.17/5.30 ( ( P @ X4 )
% 9.17/5.30 = ( Q @ X4 ) )
% 9.17/5.30 => ( ( collect_list_nat @ P )
% 9.17/5.30 = ( collect_list_nat @ Q ) ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_84_option_Odistinct_I1_J,axiom,
% 9.17/5.30 ! [X2: produc6714399278180371524it_nat] :
% 9.17/5.30 ( none_P2587165478634041381it_nat
% 9.17/5.30 != ( some_P6105628898608307625it_nat @ X2 ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_85_option_Odistinct_I1_J,axiom,
% 9.17/5.30 ! [X2: num] :
% 9.17/5.30 ( none_num
% 9.17/5.30 != ( some_num @ X2 ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_86_option_Odistinct_I1_J,axiom,
% 9.17/5.30 ! [X2: produc8664842809031399944it_nat] :
% 9.17/5.30 ( none_P9117596204409417319it_nat
% 9.17/5.30 != ( some_P1914260805536162275it_nat @ X2 ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_87_option_OdiscI,axiom,
% 9.17/5.30 ! [Option: option3216581401566546698it_nat,X2: produc6714399278180371524it_nat] :
% 9.17/5.30 ( ( Option
% 9.17/5.30 = ( some_P6105628898608307625it_nat @ X2 ) )
% 9.17/5.30 => ( Option != none_P2587165478634041381it_nat ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_88_option_OdiscI,axiom,
% 9.17/5.30 ! [Option: option_num,X2: num] :
% 9.17/5.30 ( ( Option
% 9.17/5.30 = ( some_num @ X2 ) )
% 9.17/5.30 => ( Option != none_num ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_89_option_OdiscI,axiom,
% 9.17/5.30 ! [Option: option8956607266484857688it_nat,X2: produc8664842809031399944it_nat] :
% 9.17/5.30 ( ( Option
% 9.17/5.30 = ( some_P1914260805536162275it_nat @ X2 ) )
% 9.17/5.30 => ( Option != none_P9117596204409417319it_nat ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_90_option_Oexhaust,axiom,
% 9.17/5.30 ! [Y: option3216581401566546698it_nat] :
% 9.17/5.30 ( ( Y != none_P2587165478634041381it_nat )
% 9.17/5.30 => ~ ! [X22: produc6714399278180371524it_nat] :
% 9.17/5.30 ( Y
% 9.17/5.30 != ( some_P6105628898608307625it_nat @ X22 ) ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_91_option_Oexhaust,axiom,
% 9.17/5.30 ! [Y: option_num] :
% 9.17/5.30 ( ( Y != none_num )
% 9.17/5.30 => ~ ! [X22: num] :
% 9.17/5.30 ( Y
% 9.17/5.30 != ( some_num @ X22 ) ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_92_option_Oexhaust,axiom,
% 9.17/5.30 ! [Y: option8956607266484857688it_nat] :
% 9.17/5.30 ( ( Y != none_P9117596204409417319it_nat )
% 9.17/5.30 => ~ ! [X22: produc8664842809031399944it_nat] :
% 9.17/5.30 ( Y
% 9.17/5.30 != ( some_P1914260805536162275it_nat @ X22 ) ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_93_split__option__ex,axiom,
% 9.17/5.30 ( ( ^ [P2: option3216581401566546698it_nat > $o] :
% 9.17/5.30 ? [X5: option3216581401566546698it_nat] : ( P2 @ X5 ) )
% 9.17/5.30 = ( ^ [P3: option3216581401566546698it_nat > $o] :
% 9.17/5.30 ( ( P3 @ none_P2587165478634041381it_nat )
% 9.17/5.30 | ? [X3: produc6714399278180371524it_nat] : ( P3 @ ( some_P6105628898608307625it_nat @ X3 ) ) ) ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_94_split__option__ex,axiom,
% 9.17/5.30 ( ( ^ [P2: option_num > $o] :
% 9.17/5.30 ? [X5: option_num] : ( P2 @ X5 ) )
% 9.17/5.30 = ( ^ [P3: option_num > $o] :
% 9.17/5.30 ( ( P3 @ none_num )
% 9.17/5.30 | ? [X3: num] : ( P3 @ ( some_num @ X3 ) ) ) ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_95_split__option__ex,axiom,
% 9.17/5.30 ( ( ^ [P2: option8956607266484857688it_nat > $o] :
% 9.17/5.30 ? [X5: option8956607266484857688it_nat] : ( P2 @ X5 ) )
% 9.17/5.30 = ( ^ [P3: option8956607266484857688it_nat > $o] :
% 9.17/5.30 ( ( P3 @ none_P9117596204409417319it_nat )
% 9.17/5.30 | ? [X3: produc8664842809031399944it_nat] : ( P3 @ ( some_P1914260805536162275it_nat @ X3 ) ) ) ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_96_split__option__all,axiom,
% 9.17/5.30 ( ( ^ [P2: option3216581401566546698it_nat > $o] :
% 9.17/5.30 ! [X5: option3216581401566546698it_nat] : ( P2 @ X5 ) )
% 9.17/5.30 = ( ^ [P3: option3216581401566546698it_nat > $o] :
% 9.17/5.30 ( ( P3 @ none_P2587165478634041381it_nat )
% 9.17/5.30 & ! [X3: produc6714399278180371524it_nat] : ( P3 @ ( some_P6105628898608307625it_nat @ X3 ) ) ) ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_97_split__option__all,axiom,
% 9.17/5.30 ( ( ^ [P2: option_num > $o] :
% 9.17/5.30 ! [X5: option_num] : ( P2 @ X5 ) )
% 9.17/5.30 = ( ^ [P3: option_num > $o] :
% 9.17/5.30 ( ( P3 @ none_num )
% 9.17/5.30 & ! [X3: num] : ( P3 @ ( some_num @ X3 ) ) ) ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_98_split__option__all,axiom,
% 9.17/5.30 ( ( ^ [P2: option8956607266484857688it_nat > $o] :
% 9.17/5.30 ! [X5: option8956607266484857688it_nat] : ( P2 @ X5 ) )
% 9.17/5.30 = ( ^ [P3: option8956607266484857688it_nat > $o] :
% 9.17/5.30 ( ( P3 @ none_P9117596204409417319it_nat )
% 9.17/5.30 & ! [X3: produc8664842809031399944it_nat] : ( P3 @ ( some_P1914260805536162275it_nat @ X3 ) ) ) ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_99_combine__options__cases,axiom,
% 9.17/5.30 ! [X: option3216581401566546698it_nat,P: option3216581401566546698it_nat > option3216581401566546698it_nat > $o,Y: option3216581401566546698it_nat] :
% 9.17/5.30 ( ( ( X = none_P2587165478634041381it_nat )
% 9.17/5.30 => ( P @ X @ Y ) )
% 9.17/5.30 => ( ( ( Y = none_P2587165478634041381it_nat )
% 9.17/5.30 => ( P @ X @ Y ) )
% 9.17/5.30 => ( ! [A3: produc6714399278180371524it_nat,B2: produc6714399278180371524it_nat] :
% 9.17/5.30 ( ( X
% 9.17/5.30 = ( some_P6105628898608307625it_nat @ A3 ) )
% 9.17/5.30 => ( ( Y
% 9.17/5.30 = ( some_P6105628898608307625it_nat @ B2 ) )
% 9.17/5.30 => ( P @ X @ Y ) ) )
% 9.17/5.30 => ( P @ X @ Y ) ) ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_100_combine__options__cases,axiom,
% 9.17/5.30 ! [X: option3216581401566546698it_nat,P: option3216581401566546698it_nat > option_num > $o,Y: option_num] :
% 9.17/5.30 ( ( ( X = none_P2587165478634041381it_nat )
% 9.17/5.30 => ( P @ X @ Y ) )
% 9.17/5.30 => ( ( ( Y = none_num )
% 9.17/5.30 => ( P @ X @ Y ) )
% 9.17/5.30 => ( ! [A3: produc6714399278180371524it_nat,B2: num] :
% 9.17/5.30 ( ( X
% 9.17/5.30 = ( some_P6105628898608307625it_nat @ A3 ) )
% 9.17/5.30 => ( ( Y
% 9.17/5.30 = ( some_num @ B2 ) )
% 9.17/5.30 => ( P @ X @ Y ) ) )
% 9.17/5.30 => ( P @ X @ Y ) ) ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_101_combine__options__cases,axiom,
% 9.17/5.30 ! [X: option3216581401566546698it_nat,P: option3216581401566546698it_nat > option8956607266484857688it_nat > $o,Y: option8956607266484857688it_nat] :
% 9.17/5.30 ( ( ( X = none_P2587165478634041381it_nat )
% 9.17/5.30 => ( P @ X @ Y ) )
% 9.17/5.30 => ( ( ( Y = none_P9117596204409417319it_nat )
% 9.17/5.30 => ( P @ X @ Y ) )
% 9.17/5.30 => ( ! [A3: produc6714399278180371524it_nat,B2: produc8664842809031399944it_nat] :
% 9.17/5.30 ( ( X
% 9.17/5.30 = ( some_P6105628898608307625it_nat @ A3 ) )
% 9.17/5.30 => ( ( Y
% 9.17/5.30 = ( some_P1914260805536162275it_nat @ B2 ) )
% 9.17/5.30 => ( P @ X @ Y ) ) )
% 9.17/5.30 => ( P @ X @ Y ) ) ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_102_combine__options__cases,axiom,
% 9.17/5.30 ! [X: option_num,P: option_num > option3216581401566546698it_nat > $o,Y: option3216581401566546698it_nat] :
% 9.17/5.30 ( ( ( X = none_num )
% 9.17/5.30 => ( P @ X @ Y ) )
% 9.17/5.30 => ( ( ( Y = none_P2587165478634041381it_nat )
% 9.17/5.30 => ( P @ X @ Y ) )
% 9.17/5.30 => ( ! [A3: num,B2: produc6714399278180371524it_nat] :
% 9.17/5.30 ( ( X
% 9.17/5.30 = ( some_num @ A3 ) )
% 9.17/5.30 => ( ( Y
% 9.17/5.30 = ( some_P6105628898608307625it_nat @ B2 ) )
% 9.17/5.30 => ( P @ X @ Y ) ) )
% 9.17/5.30 => ( P @ X @ Y ) ) ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_103_combine__options__cases,axiom,
% 9.17/5.30 ! [X: option_num,P: option_num > option_num > $o,Y: option_num] :
% 9.17/5.30 ( ( ( X = none_num )
% 9.17/5.30 => ( P @ X @ Y ) )
% 9.17/5.30 => ( ( ( Y = none_num )
% 9.17/5.30 => ( P @ X @ Y ) )
% 9.17/5.30 => ( ! [A3: num,B2: num] :
% 9.17/5.30 ( ( X
% 9.17/5.30 = ( some_num @ A3 ) )
% 9.17/5.30 => ( ( Y
% 9.17/5.30 = ( some_num @ B2 ) )
% 9.17/5.30 => ( P @ X @ Y ) ) )
% 9.17/5.30 => ( P @ X @ Y ) ) ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_104_combine__options__cases,axiom,
% 9.17/5.30 ! [X: option_num,P: option_num > option8956607266484857688it_nat > $o,Y: option8956607266484857688it_nat] :
% 9.17/5.30 ( ( ( X = none_num )
% 9.17/5.30 => ( P @ X @ Y ) )
% 9.17/5.30 => ( ( ( Y = none_P9117596204409417319it_nat )
% 9.17/5.30 => ( P @ X @ Y ) )
% 9.17/5.30 => ( ! [A3: num,B2: produc8664842809031399944it_nat] :
% 9.17/5.30 ( ( X
% 9.17/5.30 = ( some_num @ A3 ) )
% 9.17/5.30 => ( ( Y
% 9.17/5.30 = ( some_P1914260805536162275it_nat @ B2 ) )
% 9.17/5.30 => ( P @ X @ Y ) ) )
% 9.17/5.30 => ( P @ X @ Y ) ) ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_105_combine__options__cases,axiom,
% 9.17/5.30 ! [X: option8956607266484857688it_nat,P: option8956607266484857688it_nat > option3216581401566546698it_nat > $o,Y: option3216581401566546698it_nat] :
% 9.17/5.30 ( ( ( X = none_P9117596204409417319it_nat )
% 9.17/5.30 => ( P @ X @ Y ) )
% 9.17/5.30 => ( ( ( Y = none_P2587165478634041381it_nat )
% 9.17/5.30 => ( P @ X @ Y ) )
% 9.17/5.30 => ( ! [A3: produc8664842809031399944it_nat,B2: produc6714399278180371524it_nat] :
% 9.17/5.30 ( ( X
% 9.17/5.30 = ( some_P1914260805536162275it_nat @ A3 ) )
% 9.17/5.30 => ( ( Y
% 9.17/5.30 = ( some_P6105628898608307625it_nat @ B2 ) )
% 9.17/5.30 => ( P @ X @ Y ) ) )
% 9.17/5.30 => ( P @ X @ Y ) ) ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_106_combine__options__cases,axiom,
% 9.17/5.30 ! [X: option8956607266484857688it_nat,P: option8956607266484857688it_nat > option_num > $o,Y: option_num] :
% 9.17/5.30 ( ( ( X = none_P9117596204409417319it_nat )
% 9.17/5.30 => ( P @ X @ Y ) )
% 9.17/5.30 => ( ( ( Y = none_num )
% 9.17/5.30 => ( P @ X @ Y ) )
% 9.17/5.30 => ( ! [A3: produc8664842809031399944it_nat,B2: num] :
% 9.17/5.30 ( ( X
% 9.17/5.30 = ( some_P1914260805536162275it_nat @ A3 ) )
% 9.17/5.30 => ( ( Y
% 9.17/5.30 = ( some_num @ B2 ) )
% 9.17/5.30 => ( P @ X @ Y ) ) )
% 9.17/5.30 => ( P @ X @ Y ) ) ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_107_combine__options__cases,axiom,
% 9.17/5.30 ! [X: option8956607266484857688it_nat,P: option8956607266484857688it_nat > option8956607266484857688it_nat > $o,Y: option8956607266484857688it_nat] :
% 9.17/5.30 ( ( ( X = none_P9117596204409417319it_nat )
% 9.17/5.30 => ( P @ X @ Y ) )
% 9.17/5.30 => ( ( ( Y = none_P9117596204409417319it_nat )
% 9.17/5.30 => ( P @ X @ Y ) )
% 9.17/5.30 => ( ! [A3: produc8664842809031399944it_nat,B2: produc8664842809031399944it_nat] :
% 9.17/5.30 ( ( X
% 9.17/5.30 = ( some_P1914260805536162275it_nat @ A3 ) )
% 9.17/5.30 => ( ( Y
% 9.17/5.30 = ( some_P1914260805536162275it_nat @ B2 ) )
% 9.17/5.30 => ( P @ X @ Y ) ) )
% 9.17/5.30 => ( P @ X @ Y ) ) ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_108_success__effectE,axiom,
% 9.17/5.30 ! [C: heap_T5738788834812785303t_unit,H3: heap_e7401611519738050253t_unit] :
% 9.17/5.30 ( ( heap_T584514906347983379t_unit @ C @ H3 )
% 9.17/5.30 => ~ ! [R: product_unit,H4: heap_e7401611519738050253t_unit,N: nat] :
% 9.17/5.30 ~ ( heap_T6553295506729943825t_unit @ C @ H3 @ H4 @ R @ N ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_109_success__effectE,axiom,
% 9.17/5.30 ! [C: heap_T6362127782908069795rray_a,H3: heap_e7401611519738050253t_unit] :
% 9.17/5.30 ( ( heap_T6932021131025641745rray_a @ C @ H3 )
% 9.17/5.30 => ~ ! [R: array_a,H4: heap_e7401611519738050253t_unit,N: nat] :
% 9.17/5.30 ~ ( heap_T5830633491639066771rray_a @ C @ H3 @ H4 @ R @ N ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_110_effect__success,axiom,
% 9.17/5.30 ! [C: heap_T5738788834812785303t_unit,H3: heap_e7401611519738050253t_unit,H5: heap_e7401611519738050253t_unit,R2: product_unit,N2: nat] :
% 9.17/5.30 ( ( heap_T6553295506729943825t_unit @ C @ H3 @ H5 @ R2 @ N2 )
% 9.17/5.30 => ( heap_T584514906347983379t_unit @ C @ H3 ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_111_effect__success,axiom,
% 9.17/5.30 ! [C: heap_T6362127782908069795rray_a,H3: heap_e7401611519738050253t_unit,H5: heap_e7401611519738050253t_unit,R2: array_a,N2: nat] :
% 9.17/5.30 ( ( heap_T5830633491639066771rray_a @ C @ H3 @ H5 @ R2 @ N2 )
% 9.17/5.30 => ( heap_T6932021131025641745rray_a @ C @ H3 ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_112_effect__raiseE,axiom,
% 9.17/5.30 ! [X: list_char,H3: heap_e7401611519738050253t_unit,H5: heap_e7401611519738050253t_unit,R2: product_unit,N2: nat] :
% 9.17/5.30 ~ ( heap_T6553295506729943825t_unit @ ( heap_T2927564422264180874t_unit @ X ) @ H3 @ H5 @ R2 @ N2 ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_113_effect__raiseE,axiom,
% 9.17/5.30 ! [X: list_char,H3: heap_e7401611519738050253t_unit,H5: heap_e7401611519738050253t_unit,R2: array_a,N2: nat] :
% 9.17/5.30 ~ ( heap_T5830633491639066771rray_a @ ( heap_T1552190017797416154rray_a @ X ) @ H3 @ H5 @ R2 @ N2 ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_114_the__default_Osimps_I1_J,axiom,
% 9.17/5.30 ! [Uu2: num,X: num] :
% 9.17/5.30 ( ( the_default_num @ Uu2 @ ( some_num @ X ) )
% 9.17/5.30 = X ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_115_the__default_Osimps_I1_J,axiom,
% 9.17/5.30 ! [Uu2: produc8664842809031399944it_nat,X: produc8664842809031399944it_nat] :
% 9.17/5.30 ( ( the_de2487931475039285041it_nat @ Uu2 @ ( some_P1914260805536162275it_nat @ X ) )
% 9.17/5.30 = X ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_116_Heap__cases,axiom,
% 9.17/5.30 ! [F: heap_T6362127782908069795rray_a,H3: heap_e7401611519738050253t_unit] :
% 9.17/5.30 ( ! [X4: array_a,H4: produc6653097349344004940it_nat] :
% 9.17/5.30 ( ( heap_T5591663578999710211rray_a @ F @ H3 )
% 9.17/5.30 != ( some_P6105628898608307625it_nat @ ( produc1733996804261680252it_nat @ X4 @ H4 ) ) )
% 9.17/5.30 => ( ( heap_T5591663578999710211rray_a @ F @ H3 )
% 9.17/5.30 = none_P2587165478634041381it_nat ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_117_Heap__cases,axiom,
% 9.17/5.30 ! [F: heap_T5738788834812785303t_unit,H3: heap_e7401611519738050253t_unit] :
% 9.17/5.30 ( ! [X4: product_unit,H4: produc6653097349344004940it_nat] :
% 9.17/5.30 ( ( heap_T875086893843062177t_unit @ F @ H3 )
% 9.17/5.30 != ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ X4 @ H4 ) ) )
% 9.17/5.30 => ( ( heap_T875086893843062177t_unit @ F @ H3 )
% 9.17/5.30 = none_P9117596204409417319it_nat ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_118_successE,axiom,
% 9.17/5.30 ! [F: heap_T5738788834812785303t_unit,H3: heap_e7401611519738050253t_unit] :
% 9.17/5.30 ( ( heap_T584514906347983379t_unit @ F @ H3 )
% 9.17/5.30 => ~ ! [R: product_unit,H4: produc6653097349344004940it_nat] :
% 9.17/5.30 ( ( heap_T875086893843062177t_unit @ F @ H3 )
% 9.17/5.30 != ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ R @ H4 ) ) ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_119_successE,axiom,
% 9.17/5.30 ! [F: heap_T6362127782908069795rray_a,H3: heap_e7401611519738050253t_unit] :
% 9.17/5.30 ( ( heap_T6932021131025641745rray_a @ F @ H3 )
% 9.17/5.30 => ~ ! [R: array_a,H4: produc6653097349344004940it_nat] :
% 9.17/5.30 ( ( heap_T5591663578999710211rray_a @ F @ H3 )
% 9.17/5.30 != ( some_P6105628898608307625it_nat @ ( produc1733996804261680252it_nat @ R @ H4 ) ) ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_120_execute__heap,axiom,
% 9.17/5.30 ! [F: heap_e7401611519738050253t_unit > produc6714399278180371524it_nat] :
% 9.17/5.30 ( ( heap_T5591663578999710211rray_a @ ( heap_T7473999186002612558rray_a @ F ) )
% 9.17/5.30 = ( comp_P2097125496263478628t_unit @ some_P6105628898608307625it_nat @ F ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_121_execute__heap,axiom,
% 9.17/5.30 ! [F: heap_e7401611519738050253t_unit > produc8664842809031399944it_nat] :
% 9.17/5.30 ( ( heap_T875086893843062177t_unit @ ( heap_T6927113302350381334t_unit @ F ) )
% 9.17/5.30 = ( comp_P3118722334806803912t_unit @ some_P1914260805536162275it_nat @ F ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_122_some__opt__sym__eq__trivial,axiom,
% 9.17/5.30 ! [X: num] :
% 9.17/5.30 ( ( eps_Opt_num
% 9.17/5.30 @ ( ^ [Y4: num,Z2: num] : ( Y4 = Z2 )
% 9.17/5.30 @ X ) )
% 9.17/5.30 = ( some_num @ X ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_123_some__opt__sym__eq__trivial,axiom,
% 9.17/5.30 ! [X: produc8664842809031399944it_nat] :
% 9.17/5.30 ( ( eps_Op3393321821070424684it_nat
% 9.17/5.30 @ ( ^ [Y4: produc8664842809031399944it_nat,Z2: produc8664842809031399944it_nat] : ( Y4 = Z2 )
% 9.17/5.30 @ X ) )
% 9.17/5.30 = ( some_P1914260805536162275it_nat @ X ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_124_success__newI,axiom,
% 9.17/5.30 ! [N2: nat,X: a,H3: heap_e7401611519738050253t_unit] : ( heap_T6932021131025641745rray_a @ ( array_new_a @ N2 @ X ) @ H3 ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_125_success__makeI,axiom,
% 9.17/5.30 ! [N2: nat,F: nat > a,H3: heap_e7401611519738050253t_unit] : ( heap_T6932021131025641745rray_a @ ( array_make_a @ N2 @ F ) @ H3 ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_126_mmupd__in__upd,axiom,
% 9.17/5.30 ! [K: produc3843707927480180839at_nat,K2: set_Pr4329608150637261639at_nat,M2: produc3843707927480180839at_nat > option_num,V: num] :
% 9.17/5.30 ( ( member8757157785044589968at_nat @ K @ K2 )
% 9.17/5.30 => ( ( map_mm2124855372588256220at_num @ M2 @ K2 @ V @ K )
% 9.17/5.30 = ( some_num @ V ) ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_127_mmupd__in__upd,axiom,
% 9.17/5.30 ! [K: product_prod_nat_nat,K2: set_Pr1261947904930325089at_nat,M2: product_prod_nat_nat > option_num,V: num] :
% 9.17/5.30 ( ( member8440522571783428010at_nat @ K @ K2 )
% 9.17/5.30 => ( ( map_mm6272435474268545910at_num @ M2 @ K2 @ V @ K )
% 9.17/5.30 = ( some_num @ V ) ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_128_mmupd__in__upd,axiom,
% 9.17/5.30 ! [K: $o,K2: set_o,M2: $o > option_num,V: num] :
% 9.17/5.30 ( ( member_o @ K @ K2 )
% 9.17/5.30 => ( ( map_mmupd_o_num @ M2 @ K2 @ V @ K )
% 9.17/5.30 = ( some_num @ V ) ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_129_mmupd__in__upd,axiom,
% 9.17/5.30 ! [K: nat,K2: set_nat,M2: nat > option_num,V: num] :
% 9.17/5.30 ( ( member_nat @ K @ K2 )
% 9.17/5.30 => ( ( map_mmupd_nat_num @ M2 @ K2 @ V @ K )
% 9.17/5.30 = ( some_num @ V ) ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_130_mmupd__in__upd,axiom,
% 9.17/5.30 ! [K: int,K2: set_int,M2: int > option_num,V: num] :
% 9.17/5.30 ( ( member_int @ K @ K2 )
% 9.17/5.30 => ( ( map_mmupd_int_num @ M2 @ K2 @ V @ K )
% 9.17/5.30 = ( some_num @ V ) ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_131_mmupd__in__upd,axiom,
% 9.17/5.30 ! [K: produc3843707927480180839at_nat,K2: set_Pr4329608150637261639at_nat,M2: produc3843707927480180839at_nat > option8956607266484857688it_nat,V: produc8664842809031399944it_nat] :
% 9.17/5.30 ( ( member8757157785044589968at_nat @ K @ K2 )
% 9.17/5.30 => ( ( map_mm6227321356191524810it_nat @ M2 @ K2 @ V @ K )
% 9.17/5.30 = ( some_P1914260805536162275it_nat @ V ) ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_132_mmupd__in__upd,axiom,
% 9.17/5.30 ! [K: product_prod_nat_nat,K2: set_Pr1261947904930325089at_nat,M2: product_prod_nat_nat > option8956607266484857688it_nat,V: produc8664842809031399944it_nat] :
% 9.17/5.30 ( ( member8440522571783428010at_nat @ K @ K2 )
% 9.17/5.30 => ( ( map_mm8925508573636269924it_nat @ M2 @ K2 @ V @ K )
% 9.17/5.30 = ( some_P1914260805536162275it_nat @ V ) ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_133_mmupd__in__upd,axiom,
% 9.17/5.30 ! [K: $o,K2: set_o,M2: $o > option8956607266484857688it_nat,V: produc8664842809031399944it_nat] :
% 9.17/5.30 ( ( member_o @ K @ K2 )
% 9.17/5.30 => ( ( map_mm4340940675810032635it_nat @ M2 @ K2 @ V @ K )
% 9.17/5.30 = ( some_P1914260805536162275it_nat @ V ) ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_134_mmupd__in__upd,axiom,
% 9.17/5.30 ! [K: nat,K2: set_nat,M2: nat > option8956607266484857688it_nat,V: produc8664842809031399944it_nat] :
% 9.17/5.30 ( ( member_nat @ K @ K2 )
% 9.17/5.30 => ( ( map_mm4316137065318800191it_nat @ M2 @ K2 @ V @ K )
% 9.17/5.30 = ( some_P1914260805536162275it_nat @ V ) ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_135_mmupd__in__upd,axiom,
% 9.17/5.30 ! [K: int,K2: set_int,M2: int > option8956607266484857688it_nat,V: produc8664842809031399944it_nat] :
% 9.17/5.30 ( ( member_int @ K @ K2 )
% 9.17/5.30 => ( ( map_mm5942422175790858651it_nat @ M2 @ K2 @ V @ K )
% 9.17/5.30 = ( some_P1914260805536162275it_nat @ V ) ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_136_option_Ocollapse,axiom,
% 9.17/5.30 ! [Option: option3216581401566546698it_nat] :
% 9.17/5.30 ( ( Option != none_P2587165478634041381it_nat )
% 9.17/5.30 => ( ( some_P6105628898608307625it_nat @ ( the_Pr5856008525237892824it_nat @ Option ) )
% 9.17/5.30 = Option ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_137_option_Ocollapse,axiom,
% 9.17/5.30 ! [Option: option_num] :
% 9.17/5.30 ( ( Option != none_num )
% 9.17/5.30 => ( ( some_num @ ( the_num @ Option ) )
% 9.17/5.30 = Option ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_138_option_Ocollapse,axiom,
% 9.17/5.30 ! [Option: option8956607266484857688it_nat] :
% 9.17/5.30 ( ( Option != none_P9117596204409417319it_nat )
% 9.17/5.30 => ( ( some_P1914260805536162275it_nat @ ( the_Pr7776125533777466484it_nat @ Option ) )
% 9.17/5.30 = Option ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_139_not__Some__eq2,axiom,
% 9.17/5.30 ! [V: option8051342751916580710nteger] :
% 9.17/5.30 ( ( ! [X3: produc6241069584506657477e_term > option6357759511663192854e_term,Y3: produc8923325533196201883nteger] :
% 9.17/5.30 ( V
% 9.17/5.30 != ( some_P1462369734362851057nteger @ ( produc8603105652947943368nteger @ X3 @ Y3 ) ) ) )
% 9.17/5.30 = ( V = none_P4442379456014020469nteger ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_140_not__Some__eq2,axiom,
% 9.17/5.30 ! [V: option5190343406534369742et_nat] :
% 9.17/5.30 ( ( ! [X3: produc3658429121746597890et_nat > $o,Y3: produc3658429121746597890et_nat] :
% 9.17/5.30 ( V
% 9.17/5.30 != ( some_P750831030444334937et_nat @ ( produc5001842942810119800et_nat @ X3 @ Y3 ) ) ) )
% 9.17/5.30 = ( V = none_P4972525538344268765et_nat ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_141_not__Some__eq2,axiom,
% 9.17/5.30 ! [V: option2860828798490689354et_nat] :
% 9.17/5.30 ( ( ! [X3: produc3658429121746597890et_nat > $o,Y3: produc3925858234332021118et_nat] :
% 9.17/5.30 ( V
% 9.17/5.30 != ( some_P1630309045189364437et_nat @ ( produc2245416461498447860et_nat @ X3 @ Y3 ) ) ) )
% 9.17/5.30 = ( V = none_P199884684680593241et_nat ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_142_not__Some__eq2,axiom,
% 9.17/5.30 ! [V: option7541221861074943443nt_int] :
% 9.17/5.30 ( ( ! [X3: produc8551481072490612790e_term > option6357759511663192854e_term,Y3: product_prod_int_int] :
% 9.17/5.30 ( V
% 9.17/5.30 != ( some_P2355398578364412894nt_int @ ( produc5700946648718959541nt_int @ X3 @ Y3 ) ) ) )
% 9.17/5.30 = ( V = none_P1286213070022356066nt_int ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_143_not__Some__eq2,axiom,
% 9.17/5.30 ! [V: option4256020574406277085nt_int] :
% 9.17/5.30 ( ( ! [X3: int > option6357759511663192854e_term,Y3: product_prod_int_int] :
% 9.17/5.30 ( V
% 9.17/5.30 != ( some_P7455497367792166888nt_int @ ( produc4305682042979456191nt_int @ X3 @ Y3 ) ) ) )
% 9.17/5.30 = ( V = none_P3773570700014501484nt_int ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_144_not__Some__eq2,axiom,
% 9.17/5.30 ! [V: option3216581401566546698it_nat] :
% 9.17/5.30 ( ( ! [X3: array_a,Y3: produc6653097349344004940it_nat] :
% 9.17/5.30 ( V
% 9.17/5.30 != ( some_P6105628898608307625it_nat @ ( produc1733996804261680252it_nat @ X3 @ Y3 ) ) ) )
% 9.17/5.30 = ( V = none_P2587165478634041381it_nat ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_145_not__Some__eq2,axiom,
% 9.17/5.30 ! [V: option8956607266484857688it_nat] :
% 9.17/5.30 ( ( ! [X3: product_unit,Y3: produc6653097349344004940it_nat] :
% 9.17/5.30 ( V
% 9.17/5.30 != ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ X3 @ Y3 ) ) ) )
% 9.17/5.30 = ( V = none_P9117596204409417319it_nat ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_146_effect__assertI,axiom,
% 9.17/5.30 ! [P: product_unit > $o,X: product_unit,H5: heap_e7401611519738050253t_unit,H3: heap_e7401611519738050253t_unit,R2: product_unit,N2: nat] :
% 9.17/5.30 ( ( P @ X )
% 9.17/5.30 => ( ( H5 = H3 )
% 9.17/5.30 => ( ( R2 = X )
% 9.17/5.30 => ( ( N2 = one_one_nat )
% 9.17/5.30 => ( heap_T6553295506729943825t_unit @ ( heap_T4208721593536448476t_unit @ P @ X ) @ H3 @ H5 @ R2 @ N2 ) ) ) ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_147_effect__assertI,axiom,
% 9.17/5.30 ! [P: array_a > $o,X: array_a,H5: heap_e7401611519738050253t_unit,H3: heap_e7401611519738050253t_unit,R2: array_a,N2: nat] :
% 9.17/5.30 ( ( P @ X )
% 9.17/5.30 => ( ( H5 = H3 )
% 9.17/5.30 => ( ( R2 = X )
% 9.17/5.30 => ( ( N2 = one_one_nat )
% 9.17/5.30 => ( heap_T5830633491639066771rray_a @ ( heap_T7971689983404357896rray_a @ P @ X ) @ H3 @ H5 @ R2 @ N2 ) ) ) ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_148_fun__comp__eq__conv,axiom,
% 9.17/5.30 ! [F: code_integer > code_integer,G: num > code_integer,Fg: num > code_integer] :
% 9.17/5.30 ( ( ( comp_C3531382070062128313er_num @ F @ G )
% 9.17/5.30 = Fg )
% 9.17/5.30 = ( ! [X3: num] :
% 9.17/5.30 ( ( F @ ( G @ X3 ) )
% 9.17/5.30 = ( Fg @ X3 ) ) ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_149_fun__comp__eq__conv,axiom,
% 9.17/5.30 ! [F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer,Fg: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 9.17/5.30 ( ( ( comp_C1593894019821074884nteger @ F @ G )
% 9.17/5.30 = Fg )
% 9.17/5.30 = ( ! [X3: code_integer] :
% 9.17/5.30 ( ( F @ ( G @ X3 ) )
% 9.17/5.30 = ( Fg @ X3 ) ) ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_150_fun__comp__eq__conv,axiom,
% 9.17/5.30 ! [F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer > code_integer,Fg: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 9.17/5.30 ( ( ( comp_C8797469213163452608nteger @ F @ G )
% 9.17/5.30 = Fg )
% 9.17/5.30 = ( ! [X3: code_integer] :
% 9.17/5.30 ( ( F @ ( G @ X3 ) )
% 9.17/5.30 = ( Fg @ X3 ) ) ) ) ).
% 9.17/5.30
% 9.17/5.30 thf(fact_151_fun__comp__eq__conv,axiom,
% 9.17/5.30 ! [F: nat > num,G: int > nat,Fg: int > num] :
% 9.17/5.30 ( ( ( comp_nat_num_int @ F @ G )
% 9.17/5.30 = Fg )
% 9.17/5.30 = ( ! [X3: int] :
% 9.17/5.30 ( ( F @ ( G @ X3 ) )
% 9.17/5.31 = ( Fg @ X3 ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_152_comp__cong__right,axiom,
% 9.17/5.31 ! [X: num > code_integer,Y: num > code_integer,F: code_integer > code_integer] :
% 9.17/5.31 ( ( X = Y )
% 9.17/5.31 => ( ( comp_C3531382070062128313er_num @ F @ X )
% 9.17/5.31 = ( comp_C3531382070062128313er_num @ F @ Y ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_153_comp__cong__right,axiom,
% 9.17/5.31 ! [X: code_integer > code_integer,Y: code_integer > code_integer,F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 9.17/5.31 ( ( X = Y )
% 9.17/5.31 => ( ( comp_C1593894019821074884nteger @ F @ X )
% 9.17/5.31 = ( comp_C1593894019821074884nteger @ F @ Y ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_154_comp__cong__right,axiom,
% 9.17/5.31 ! [X: code_integer > code_integer > code_integer,Y: code_integer > code_integer > code_integer,F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 9.17/5.31 ( ( X = Y )
% 9.17/5.31 => ( ( comp_C8797469213163452608nteger @ F @ X )
% 9.17/5.31 = ( comp_C8797469213163452608nteger @ F @ Y ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_155_comp__cong__right,axiom,
% 9.17/5.31 ! [X: int > nat,Y: int > nat,F: nat > num] :
% 9.17/5.31 ( ( X = Y )
% 9.17/5.31 => ( ( comp_nat_num_int @ F @ X )
% 9.17/5.31 = ( comp_nat_num_int @ F @ Y ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_156_comp__cong__left,axiom,
% 9.17/5.31 ! [X: code_integer > code_integer,Y: code_integer > code_integer,F: num > code_integer] :
% 9.17/5.31 ( ( X = Y )
% 9.17/5.31 => ( ( comp_C3531382070062128313er_num @ X @ F )
% 9.17/5.31 = ( comp_C3531382070062128313er_num @ Y @ F ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_157_comp__cong__left,axiom,
% 9.17/5.31 ! [X: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,Y: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,F: code_integer > code_integer] :
% 9.17/5.31 ( ( X = Y )
% 9.17/5.31 => ( ( comp_C1593894019821074884nteger @ X @ F )
% 9.17/5.31 = ( comp_C1593894019821074884nteger @ Y @ F ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_158_comp__cong__left,axiom,
% 9.17/5.31 ! [X: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,Y: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,F: code_integer > code_integer > code_integer] :
% 9.17/5.31 ( ( X = Y )
% 9.17/5.31 => ( ( comp_C8797469213163452608nteger @ X @ F )
% 9.17/5.31 = ( comp_C8797469213163452608nteger @ Y @ F ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_159_comp__cong__left,axiom,
% 9.17/5.31 ! [X: nat > num,Y: nat > num,F: int > nat] :
% 9.17/5.31 ( ( X = Y )
% 9.17/5.31 => ( ( comp_nat_num_int @ X @ F )
% 9.17/5.31 = ( comp_nat_num_int @ Y @ F ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_160_bex2I,axiom,
% 9.17/5.31 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,S2: set_Pr4329608150637261639at_nat,P: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o] :
% 9.17/5.31 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ B ) @ S2 )
% 9.17/5.31 => ( ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ B ) @ S2 )
% 9.17/5.31 => ( P @ A @ B ) )
% 9.17/5.31 => ? [A3: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 9.17/5.31 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A3 @ B2 ) @ S2 )
% 9.17/5.31 & ( P @ A3 @ B2 ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_161_bex2I,axiom,
% 9.17/5.31 ! [A: nat,B: nat,S2: set_Pr1261947904930325089at_nat,P: nat > nat > $o] :
% 9.17/5.31 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ S2 )
% 9.17/5.31 => ( ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ S2 )
% 9.17/5.31 => ( P @ A @ B ) )
% 9.17/5.31 => ? [A3: nat,B2: nat] :
% 9.17/5.31 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A3 @ B2 ) @ S2 )
% 9.17/5.31 & ( P @ A3 @ B2 ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_162_bex2I,axiom,
% 9.17/5.31 ! [A: produc6241069584506657477e_term > option6357759511663192854e_term,B: produc8923325533196201883nteger,S2: set_Pr1281608226676607948nteger,P: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o] :
% 9.17/5.31 ( ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ A @ B ) @ S2 )
% 9.17/5.31 => ( ( ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ A @ B ) @ S2 )
% 9.17/5.31 => ( P @ A @ B ) )
% 9.17/5.31 => ? [A3: produc6241069584506657477e_term > option6357759511663192854e_term,B2: produc8923325533196201883nteger] :
% 9.17/5.31 ( ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ A3 @ B2 ) @ S2 )
% 9.17/5.31 & ( P @ A3 @ B2 ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_163_bex2I,axiom,
% 9.17/5.31 ! [A: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat,S2: set_Pr3286484037609594932et_nat,P: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o] :
% 9.17/5.31 ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ A @ B ) @ S2 )
% 9.17/5.31 => ( ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ A @ B ) @ S2 )
% 9.17/5.31 => ( P @ A @ B ) )
% 9.17/5.31 => ? [A3: produc3658429121746597890et_nat > $o,B2: produc3658429121746597890et_nat] :
% 9.17/5.31 ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ A3 @ B2 ) @ S2 )
% 9.17/5.31 & ( P @ A3 @ B2 ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_164_bex2I,axiom,
% 9.17/5.31 ! [A: produc3658429121746597890et_nat > $o,B: produc3925858234332021118et_nat,S2: set_Pr8536935166611901872et_nat,P: ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o] :
% 9.17/5.31 ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ A @ B ) @ S2 )
% 9.17/5.31 => ( ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ A @ B ) @ S2 )
% 9.17/5.31 => ( P @ A @ B ) )
% 9.17/5.31 => ? [A3: produc3658429121746597890et_nat > $o,B2: produc3925858234332021118et_nat] :
% 9.17/5.31 ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ A3 @ B2 ) @ S2 )
% 9.17/5.31 & ( P @ A3 @ B2 ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_165_bex2I,axiom,
% 9.17/5.31 ! [A: produc8551481072490612790e_term > option6357759511663192854e_term,B: product_prod_int_int,S2: set_Pr9222295170931077689nt_int,P: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o] :
% 9.17/5.31 ( ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ A @ B ) @ S2 )
% 9.17/5.31 => ( ( ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ A @ B ) @ S2 )
% 9.17/5.31 => ( P @ A @ B ) )
% 9.17/5.31 => ? [A3: produc8551481072490612790e_term > option6357759511663192854e_term,B2: product_prod_int_int] :
% 9.17/5.31 ( ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ A3 @ B2 ) @ S2 )
% 9.17/5.31 & ( P @ A3 @ B2 ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_166_bex2I,axiom,
% 9.17/5.31 ! [A: int > option6357759511663192854e_term,B: product_prod_int_int,S2: set_Pr1872883991513573699nt_int,P: ( int > option6357759511663192854e_term ) > product_prod_int_int > $o] :
% 9.17/5.31 ( ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ A @ B ) @ S2 )
% 9.17/5.31 => ( ( ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ A @ B ) @ S2 )
% 9.17/5.31 => ( P @ A @ B ) )
% 9.17/5.31 => ? [A3: int > option6357759511663192854e_term,B2: product_prod_int_int] :
% 9.17/5.31 ( ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ A3 @ B2 ) @ S2 )
% 9.17/5.31 & ( P @ A3 @ B2 ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_167_pairself_Ocases,axiom,
% 9.17/5.31 ! [X: produc7773217078559923341nt_int] :
% 9.17/5.31 ~ ! [F3: int > option6357759511663192854e_term,A3: int,B2: int] :
% 9.17/5.31 ( X
% 9.17/5.31 != ( produc4305682042979456191nt_int @ F3 @ ( product_Pair_int_int @ A3 @ B2 ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_168_fails__array__new,axiom,
% 9.17/5.31 ! [N2: nat,X: a,H3: heap_e7401611519738050253t_unit] :
% 9.17/5.31 ~ ( time_fails_array_a @ ( array_new_a @ N2 @ X ) @ H3 ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_169_timeFrame_Ocases,axiom,
% 9.17/5.31 ! [X: produc2867611627572283311it_nat] :
% 9.17/5.31 ( ! [N: nat,R: array_a,H2: heap_e7401611519738050253t_unit,N3: nat] :
% 9.17/5.31 ( X
% 9.17/5.31 != ( produc3378006678175723489it_nat @ N @ ( some_P6105628898608307625it_nat @ ( produc1733996804261680252it_nat @ R @ ( produc584006145561248582it_nat @ H2 @ N3 ) ) ) ) )
% 9.17/5.31 => ~ ! [N: nat] :
% 9.17/5.31 ( X
% 9.17/5.31 != ( produc3378006678175723489it_nat @ N @ none_P2587165478634041381it_nat ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_170_timeFrame_Ocases,axiom,
% 9.17/5.31 ! [X: produc3911288613690379145it_nat] :
% 9.17/5.31 ( ! [N: nat,R: product_unit,H2: heap_e7401611519738050253t_unit,N3: nat] :
% 9.17/5.31 ( X
% 9.17/5.31 != ( produc638857205735767105it_nat @ N @ ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ R @ ( produc584006145561248582it_nat @ H2 @ N3 ) ) ) ) )
% 9.17/5.31 => ~ ! [N: nat] :
% 9.17/5.31 ( X
% 9.17/5.31 != ( produc638857205735767105it_nat @ N @ none_P9117596204409417319it_nat ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_171_execute__assert_I1_J,axiom,
% 9.17/5.31 ! [P: array_a > $o,X: array_a,H3: heap_e7401611519738050253t_unit] :
% 9.17/5.31 ( ( P @ X )
% 9.17/5.31 => ( ( heap_T5591663578999710211rray_a @ ( heap_T7971689983404357896rray_a @ P @ X ) @ H3 )
% 9.17/5.31 = ( some_P6105628898608307625it_nat @ ( produc1733996804261680252it_nat @ X @ ( produc584006145561248582it_nat @ H3 @ one_one_nat ) ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_172_execute__assert_I1_J,axiom,
% 9.17/5.31 ! [P: product_unit > $o,X: product_unit,H3: heap_e7401611519738050253t_unit] :
% 9.17/5.31 ( ( P @ X )
% 9.17/5.31 => ( ( heap_T875086893843062177t_unit @ ( heap_T4208721593536448476t_unit @ P @ X ) @ H3 )
% 9.17/5.31 = ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ X @ ( produc584006145561248582it_nat @ H3 @ one_one_nat ) ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_173_execute__tap,axiom,
% 9.17/5.31 ! [F: heap_e7401611519738050253t_unit > array_a,H3: heap_e7401611519738050253t_unit] :
% 9.17/5.31 ( ( heap_T5591663578999710211rray_a @ ( heap_T2055650868554030641rray_a @ F ) @ H3 )
% 9.17/5.31 = ( some_P6105628898608307625it_nat @ ( produc1733996804261680252it_nat @ ( F @ H3 ) @ ( produc584006145561248582it_nat @ H3 @ one_one_nat ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_174_execute__tap,axiom,
% 9.17/5.31 ! [F: heap_e7401611519738050253t_unit > product_unit,H3: heap_e7401611519738050253t_unit] :
% 9.17/5.31 ( ( heap_T875086893843062177t_unit @ ( heap_T560649228465745139t_unit @ F ) @ H3 )
% 9.17/5.31 = ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ ( F @ H3 ) @ ( produc584006145561248582it_nat @ H3 @ one_one_nat ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_175_option_Osel,axiom,
% 9.17/5.31 ! [X2: num] :
% 9.17/5.31 ( ( the_num @ ( some_num @ X2 ) )
% 9.17/5.31 = X2 ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_176_option_Osel,axiom,
% 9.17/5.31 ! [X2: produc8664842809031399944it_nat] :
% 9.17/5.31 ( ( the_Pr7776125533777466484it_nat @ ( some_P1914260805536162275it_nat @ X2 ) )
% 9.17/5.31 = X2 ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_177_option_Oexpand,axiom,
% 9.17/5.31 ! [Option: option3216581401566546698it_nat,Option2: option3216581401566546698it_nat] :
% 9.17/5.31 ( ( ( Option = none_P2587165478634041381it_nat )
% 9.17/5.31 = ( Option2 = none_P2587165478634041381it_nat ) )
% 9.17/5.31 => ( ( ( Option != none_P2587165478634041381it_nat )
% 9.17/5.31 => ( ( Option2 != none_P2587165478634041381it_nat )
% 9.17/5.31 => ( ( the_Pr5856008525237892824it_nat @ Option )
% 9.17/5.31 = ( the_Pr5856008525237892824it_nat @ Option2 ) ) ) )
% 9.17/5.31 => ( Option = Option2 ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_178_option_Oexpand,axiom,
% 9.17/5.31 ! [Option: option_num,Option2: option_num] :
% 9.17/5.31 ( ( ( Option = none_num )
% 9.17/5.31 = ( Option2 = none_num ) )
% 9.17/5.31 => ( ( ( Option != none_num )
% 9.17/5.31 => ( ( Option2 != none_num )
% 9.17/5.31 => ( ( the_num @ Option )
% 9.17/5.31 = ( the_num @ Option2 ) ) ) )
% 9.17/5.31 => ( Option = Option2 ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_179_option_Oexpand,axiom,
% 9.17/5.31 ! [Option: option8956607266484857688it_nat,Option2: option8956607266484857688it_nat] :
% 9.17/5.31 ( ( ( Option = none_P9117596204409417319it_nat )
% 9.17/5.31 = ( Option2 = none_P9117596204409417319it_nat ) )
% 9.17/5.31 => ( ( ( Option != none_P9117596204409417319it_nat )
% 9.17/5.31 => ( ( Option2 != none_P9117596204409417319it_nat )
% 9.17/5.31 => ( ( the_Pr7776125533777466484it_nat @ Option )
% 9.17/5.31 = ( the_Pr7776125533777466484it_nat @ Option2 ) ) ) )
% 9.17/5.31 => ( Option = Option2 ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_180_effect__def,axiom,
% 9.17/5.31 ( heap_T5830633491639066771rray_a
% 9.17/5.31 = ( ^ [C2: heap_T6362127782908069795rray_a,H: heap_e7401611519738050253t_unit,H6: heap_e7401611519738050253t_unit,R3: array_a,N4: nat] :
% 9.17/5.31 ( ( heap_T5591663578999710211rray_a @ C2 @ H )
% 9.17/5.31 = ( some_P6105628898608307625it_nat @ ( produc1733996804261680252it_nat @ R3 @ ( produc584006145561248582it_nat @ H6 @ N4 ) ) ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_181_effect__def,axiom,
% 9.17/5.31 ( heap_T6553295506729943825t_unit
% 9.17/5.31 = ( ^ [C2: heap_T5738788834812785303t_unit,H: heap_e7401611519738050253t_unit,H6: heap_e7401611519738050253t_unit,R3: product_unit,N4: nat] :
% 9.17/5.31 ( ( heap_T875086893843062177t_unit @ C2 @ H )
% 9.17/5.31 = ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ R3 @ ( produc584006145561248582it_nat @ H6 @ N4 ) ) ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_182_effectI,axiom,
% 9.17/5.31 ! [C: heap_T6362127782908069795rray_a,H3: heap_e7401611519738050253t_unit,R2: array_a,H5: heap_e7401611519738050253t_unit,N2: nat] :
% 9.17/5.31 ( ( ( heap_T5591663578999710211rray_a @ C @ H3 )
% 9.17/5.31 = ( some_P6105628898608307625it_nat @ ( produc1733996804261680252it_nat @ R2 @ ( produc584006145561248582it_nat @ H5 @ N2 ) ) ) )
% 9.17/5.31 => ( heap_T5830633491639066771rray_a @ C @ H3 @ H5 @ R2 @ N2 ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_183_effectI,axiom,
% 9.17/5.31 ! [C: heap_T5738788834812785303t_unit,H3: heap_e7401611519738050253t_unit,R2: product_unit,H5: heap_e7401611519738050253t_unit,N2: nat] :
% 9.17/5.31 ( ( ( heap_T875086893843062177t_unit @ C @ H3 )
% 9.17/5.31 = ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ R2 @ ( produc584006145561248582it_nat @ H5 @ N2 ) ) ) )
% 9.17/5.31 => ( heap_T6553295506729943825t_unit @ C @ H3 @ H5 @ R2 @ N2 ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_184_map__mmupd__def,axiom,
% 9.17/5.31 ( map_mm2124855372588256220at_num
% 9.17/5.31 = ( ^ [M: produc3843707927480180839at_nat > option_num,K3: set_Pr4329608150637261639at_nat,V2: num,K4: produc3843707927480180839at_nat] : ( if_option_num @ ( member8757157785044589968at_nat @ K4 @ K3 ) @ ( some_num @ V2 ) @ ( M @ K4 ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_185_map__mmupd__def,axiom,
% 9.17/5.31 ( map_mm6272435474268545910at_num
% 9.17/5.31 = ( ^ [M: product_prod_nat_nat > option_num,K3: set_Pr1261947904930325089at_nat,V2: num,K4: product_prod_nat_nat] : ( if_option_num @ ( member8440522571783428010at_nat @ K4 @ K3 ) @ ( some_num @ V2 ) @ ( M @ K4 ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_186_map__mmupd__def,axiom,
% 9.17/5.31 ( map_mmupd_o_num
% 9.17/5.31 = ( ^ [M: $o > option_num,K3: set_o,V2: num,K4: $o] : ( if_option_num @ ( member_o @ K4 @ K3 ) @ ( some_num @ V2 ) @ ( M @ K4 ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_187_map__mmupd__def,axiom,
% 9.17/5.31 ( map_mmupd_nat_num
% 9.17/5.31 = ( ^ [M: nat > option_num,K3: set_nat,V2: num,K4: nat] : ( if_option_num @ ( member_nat @ K4 @ K3 ) @ ( some_num @ V2 ) @ ( M @ K4 ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_188_map__mmupd__def,axiom,
% 9.17/5.31 ( map_mmupd_int_num
% 9.17/5.31 = ( ^ [M: int > option_num,K3: set_int,V2: num,K4: int] : ( if_option_num @ ( member_int @ K4 @ K3 ) @ ( some_num @ V2 ) @ ( M @ K4 ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_189_map__mmupd__def,axiom,
% 9.17/5.31 ( map_mm6227321356191524810it_nat
% 9.17/5.31 = ( ^ [M: produc3843707927480180839at_nat > option8956607266484857688it_nat,K3: set_Pr4329608150637261639at_nat,V2: produc8664842809031399944it_nat,K4: produc3843707927480180839at_nat] : ( if_opt1729522071442692626it_nat @ ( member8757157785044589968at_nat @ K4 @ K3 ) @ ( some_P1914260805536162275it_nat @ V2 ) @ ( M @ K4 ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_190_map__mmupd__def,axiom,
% 9.17/5.31 ( map_mm8925508573636269924it_nat
% 9.17/5.31 = ( ^ [M: product_prod_nat_nat > option8956607266484857688it_nat,K3: set_Pr1261947904930325089at_nat,V2: produc8664842809031399944it_nat,K4: product_prod_nat_nat] : ( if_opt1729522071442692626it_nat @ ( member8440522571783428010at_nat @ K4 @ K3 ) @ ( some_P1914260805536162275it_nat @ V2 ) @ ( M @ K4 ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_191_map__mmupd__def,axiom,
% 9.17/5.31 ( map_mm4340940675810032635it_nat
% 9.17/5.31 = ( ^ [M: $o > option8956607266484857688it_nat,K3: set_o,V2: produc8664842809031399944it_nat,K4: $o] : ( if_opt1729522071442692626it_nat @ ( member_o @ K4 @ K3 ) @ ( some_P1914260805536162275it_nat @ V2 ) @ ( M @ K4 ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_192_map__mmupd__def,axiom,
% 9.17/5.31 ( map_mm4316137065318800191it_nat
% 9.17/5.31 = ( ^ [M: nat > option8956607266484857688it_nat,K3: set_nat,V2: produc8664842809031399944it_nat,K4: nat] : ( if_opt1729522071442692626it_nat @ ( member_nat @ K4 @ K3 ) @ ( some_P1914260805536162275it_nat @ V2 ) @ ( M @ K4 ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_193_map__mmupd__def,axiom,
% 9.17/5.31 ( map_mm5942422175790858651it_nat
% 9.17/5.31 = ( ^ [M: int > option8956607266484857688it_nat,K3: set_int,V2: produc8664842809031399944it_nat,K4: int] : ( if_opt1729522071442692626it_nat @ ( member_int @ K4 @ K3 ) @ ( some_P1914260805536162275it_nat @ V2 ) @ ( M @ K4 ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_194_map__mmupdE,axiom,
% 9.17/5.31 ! [M2: produc3843707927480180839at_nat > option_num,K2: set_Pr4329608150637261639at_nat,V: num,K: produc3843707927480180839at_nat,X: num] :
% 9.17/5.31 ( ( ( map_mm2124855372588256220at_num @ M2 @ K2 @ V @ K )
% 9.17/5.31 = ( some_num @ X ) )
% 9.17/5.31 => ( ( ~ ( member8757157785044589968at_nat @ K @ K2 )
% 9.17/5.31 => ( ( M2 @ K )
% 9.17/5.31 != ( some_num @ X ) ) )
% 9.17/5.31 => ~ ( ( member8757157785044589968at_nat @ K @ K2 )
% 9.17/5.31 => ( X != V ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_195_map__mmupdE,axiom,
% 9.17/5.31 ! [M2: product_prod_nat_nat > option_num,K2: set_Pr1261947904930325089at_nat,V: num,K: product_prod_nat_nat,X: num] :
% 9.17/5.31 ( ( ( map_mm6272435474268545910at_num @ M2 @ K2 @ V @ K )
% 9.17/5.31 = ( some_num @ X ) )
% 9.17/5.31 => ( ( ~ ( member8440522571783428010at_nat @ K @ K2 )
% 9.17/5.31 => ( ( M2 @ K )
% 9.17/5.31 != ( some_num @ X ) ) )
% 9.17/5.31 => ~ ( ( member8440522571783428010at_nat @ K @ K2 )
% 9.17/5.31 => ( X != V ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_196_map__mmupdE,axiom,
% 9.17/5.31 ! [M2: $o > option_num,K2: set_o,V: num,K: $o,X: num] :
% 9.17/5.31 ( ( ( map_mmupd_o_num @ M2 @ K2 @ V @ K )
% 9.17/5.31 = ( some_num @ X ) )
% 9.17/5.31 => ( ( ~ ( member_o @ K @ K2 )
% 9.17/5.31 => ( ( M2 @ K )
% 9.17/5.31 != ( some_num @ X ) ) )
% 9.17/5.31 => ~ ( ( member_o @ K @ K2 )
% 9.17/5.31 => ( X != V ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_197_map__mmupdE,axiom,
% 9.17/5.31 ! [M2: nat > option_num,K2: set_nat,V: num,K: nat,X: num] :
% 9.17/5.31 ( ( ( map_mmupd_nat_num @ M2 @ K2 @ V @ K )
% 9.17/5.31 = ( some_num @ X ) )
% 9.17/5.31 => ( ( ~ ( member_nat @ K @ K2 )
% 9.17/5.31 => ( ( M2 @ K )
% 9.17/5.31 != ( some_num @ X ) ) )
% 9.17/5.31 => ~ ( ( member_nat @ K @ K2 )
% 9.17/5.31 => ( X != V ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_198_map__mmupdE,axiom,
% 9.17/5.31 ! [M2: int > option_num,K2: set_int,V: num,K: int,X: num] :
% 9.17/5.31 ( ( ( map_mmupd_int_num @ M2 @ K2 @ V @ K )
% 9.17/5.31 = ( some_num @ X ) )
% 9.17/5.31 => ( ( ~ ( member_int @ K @ K2 )
% 9.17/5.31 => ( ( M2 @ K )
% 9.17/5.31 != ( some_num @ X ) ) )
% 9.17/5.31 => ~ ( ( member_int @ K @ K2 )
% 9.17/5.31 => ( X != V ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_199_map__mmupdE,axiom,
% 9.17/5.31 ! [M2: produc3843707927480180839at_nat > option8956607266484857688it_nat,K2: set_Pr4329608150637261639at_nat,V: produc8664842809031399944it_nat,K: produc3843707927480180839at_nat,X: produc8664842809031399944it_nat] :
% 9.17/5.31 ( ( ( map_mm6227321356191524810it_nat @ M2 @ K2 @ V @ K )
% 9.17/5.31 = ( some_P1914260805536162275it_nat @ X ) )
% 9.17/5.31 => ( ( ~ ( member8757157785044589968at_nat @ K @ K2 )
% 9.17/5.31 => ( ( M2 @ K )
% 9.17/5.31 != ( some_P1914260805536162275it_nat @ X ) ) )
% 9.17/5.31 => ~ ( ( member8757157785044589968at_nat @ K @ K2 )
% 9.17/5.31 => ( X != V ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_200_map__mmupdE,axiom,
% 9.17/5.31 ! [M2: product_prod_nat_nat > option8956607266484857688it_nat,K2: set_Pr1261947904930325089at_nat,V: produc8664842809031399944it_nat,K: product_prod_nat_nat,X: produc8664842809031399944it_nat] :
% 9.17/5.31 ( ( ( map_mm8925508573636269924it_nat @ M2 @ K2 @ V @ K )
% 9.17/5.31 = ( some_P1914260805536162275it_nat @ X ) )
% 9.17/5.31 => ( ( ~ ( member8440522571783428010at_nat @ K @ K2 )
% 9.17/5.31 => ( ( M2 @ K )
% 9.17/5.31 != ( some_P1914260805536162275it_nat @ X ) ) )
% 9.17/5.31 => ~ ( ( member8440522571783428010at_nat @ K @ K2 )
% 9.17/5.31 => ( X != V ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_201_map__mmupdE,axiom,
% 9.17/5.31 ! [M2: $o > option8956607266484857688it_nat,K2: set_o,V: produc8664842809031399944it_nat,K: $o,X: produc8664842809031399944it_nat] :
% 9.17/5.31 ( ( ( map_mm4340940675810032635it_nat @ M2 @ K2 @ V @ K )
% 9.17/5.31 = ( some_P1914260805536162275it_nat @ X ) )
% 9.17/5.31 => ( ( ~ ( member_o @ K @ K2 )
% 9.17/5.31 => ( ( M2 @ K )
% 9.17/5.31 != ( some_P1914260805536162275it_nat @ X ) ) )
% 9.17/5.31 => ~ ( ( member_o @ K @ K2 )
% 9.17/5.31 => ( X != V ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_202_map__mmupdE,axiom,
% 9.17/5.31 ! [M2: nat > option8956607266484857688it_nat,K2: set_nat,V: produc8664842809031399944it_nat,K: nat,X: produc8664842809031399944it_nat] :
% 9.17/5.31 ( ( ( map_mm4316137065318800191it_nat @ M2 @ K2 @ V @ K )
% 9.17/5.31 = ( some_P1914260805536162275it_nat @ X ) )
% 9.17/5.31 => ( ( ~ ( member_nat @ K @ K2 )
% 9.17/5.31 => ( ( M2 @ K )
% 9.17/5.31 != ( some_P1914260805536162275it_nat @ X ) ) )
% 9.17/5.31 => ~ ( ( member_nat @ K @ K2 )
% 9.17/5.31 => ( X != V ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_203_map__mmupdE,axiom,
% 9.17/5.31 ! [M2: int > option8956607266484857688it_nat,K2: set_int,V: produc8664842809031399944it_nat,K: int,X: produc8664842809031399944it_nat] :
% 9.17/5.31 ( ( ( map_mm5942422175790858651it_nat @ M2 @ K2 @ V @ K )
% 9.17/5.31 = ( some_P1914260805536162275it_nat @ X ) )
% 9.17/5.31 => ( ( ~ ( member_int @ K @ K2 )
% 9.17/5.31 => ( ( M2 @ K )
% 9.17/5.31 != ( some_P1914260805536162275it_nat @ X ) ) )
% 9.17/5.31 => ~ ( ( member_int @ K @ K2 )
% 9.17/5.31 => ( X != V ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_204_success__bind__executeI,axiom,
% 9.17/5.31 ! [F: heap_T6362127782908069795rray_a,H3: heap_e7401611519738050253t_unit,X: array_a,H5: heap_e7401611519738050253t_unit,N2: nat,G: array_a > heap_T5738788834812785303t_unit] :
% 9.17/5.31 ( ( ( heap_T5591663578999710211rray_a @ F @ H3 )
% 9.17/5.31 = ( some_P6105628898608307625it_nat @ ( produc1733996804261680252it_nat @ X @ ( produc584006145561248582it_nat @ H5 @ N2 ) ) ) )
% 9.17/5.31 => ( ( heap_T584514906347983379t_unit @ ( G @ X ) @ H5 )
% 9.17/5.31 => ( heap_T584514906347983379t_unit @ ( heap_T7324619625323989613t_unit @ F @ G ) @ H3 ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_205_success__bind__executeI,axiom,
% 9.17/5.31 ! [F: heap_T5738788834812785303t_unit,H3: heap_e7401611519738050253t_unit,X: product_unit,H5: heap_e7401611519738050253t_unit,N2: nat,G: product_unit > heap_T5738788834812785303t_unit] :
% 9.17/5.31 ( ( ( heap_T875086893843062177t_unit @ F @ H3 )
% 9.17/5.31 = ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ X @ ( produc584006145561248582it_nat @ H5 @ N2 ) ) ) )
% 9.17/5.31 => ( ( heap_T584514906347983379t_unit @ ( G @ X ) @ H5 )
% 9.17/5.31 => ( heap_T584514906347983379t_unit @ ( heap_T2633723481742716231t_unit @ F @ G ) @ H3 ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_206_success__bind__executeI,axiom,
% 9.17/5.31 ! [F: heap_T6362127782908069795rray_a,H3: heap_e7401611519738050253t_unit,X: array_a,H5: heap_e7401611519738050253t_unit,N2: nat,G: array_a > heap_T6362127782908069795rray_a] :
% 9.17/5.31 ( ( ( heap_T5591663578999710211rray_a @ F @ H3 )
% 9.17/5.31 = ( some_P6105628898608307625it_nat @ ( produc1733996804261680252it_nat @ X @ ( produc584006145561248582it_nat @ H5 @ N2 ) ) ) )
% 9.17/5.31 => ( ( heap_T6932021131025641745rray_a @ ( G @ X ) @ H5 )
% 9.17/5.31 => ( heap_T6932021131025641745rray_a @ ( heap_T2407400398799471159rray_a @ F @ G ) @ H3 ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_207_success__bind__executeI,axiom,
% 9.17/5.31 ! [F: heap_T5738788834812785303t_unit,H3: heap_e7401611519738050253t_unit,X: product_unit,H5: heap_e7401611519738050253t_unit,N2: nat,G: product_unit > heap_T6362127782908069795rray_a] :
% 9.17/5.31 ( ( ( heap_T875086893843062177t_unit @ F @ H3 )
% 9.17/5.31 = ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ X @ ( produc584006145561248582it_nat @ H5 @ N2 ) ) ) )
% 9.17/5.31 => ( ( heap_T6932021131025641745rray_a @ ( G @ X ) @ H5 )
% 9.17/5.31 => ( heap_T6932021131025641745rray_a @ ( heap_T7158140910958840029rray_a @ F @ G ) @ H3 ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_208_Eps__Opt__eq__Some__implies,axiom,
% 9.17/5.31 ! [P: num > $o,X: num] :
% 9.17/5.31 ( ( ( eps_Opt_num @ P )
% 9.17/5.31 = ( some_num @ X ) )
% 9.17/5.31 => ( P @ X ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_209_Eps__Opt__eq__Some__implies,axiom,
% 9.17/5.31 ! [P: produc8664842809031399944it_nat > $o,X: produc8664842809031399944it_nat] :
% 9.17/5.31 ( ( ( eps_Op3393321821070424684it_nat @ P )
% 9.17/5.31 = ( some_P1914260805536162275it_nat @ X ) )
% 9.17/5.31 => ( P @ X ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_210_Eps__Opt__eq__Some,axiom,
% 9.17/5.31 ! [P: num > $o,X: num] :
% 9.17/5.31 ( ! [X6: num] :
% 9.17/5.31 ( ( P @ X )
% 9.17/5.31 => ( ( P @ X6 )
% 9.17/5.31 => ( X6 = X ) ) )
% 9.17/5.31 => ( ( ( eps_Opt_num @ P )
% 9.17/5.31 = ( some_num @ X ) )
% 9.17/5.31 = ( P @ X ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_211_Eps__Opt__eq__Some,axiom,
% 9.17/5.31 ! [P: produc8664842809031399944it_nat > $o,X: produc8664842809031399944it_nat] :
% 9.17/5.31 ( ! [X6: produc8664842809031399944it_nat] :
% 9.17/5.31 ( ( P @ X )
% 9.17/5.31 => ( ( P @ X6 )
% 9.17/5.31 => ( X6 = X ) ) )
% 9.17/5.31 => ( ( ( eps_Op3393321821070424684it_nat @ P )
% 9.17/5.31 = ( some_P1914260805536162275it_nat @ X ) )
% 9.17/5.31 = ( P @ X ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_212_option_Oexhaust__sel,axiom,
% 9.17/5.31 ! [Option: option3216581401566546698it_nat] :
% 9.17/5.31 ( ( Option != none_P2587165478634041381it_nat )
% 9.17/5.31 => ( Option
% 9.17/5.31 = ( some_P6105628898608307625it_nat @ ( the_Pr5856008525237892824it_nat @ Option ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_213_option_Oexhaust__sel,axiom,
% 9.17/5.31 ! [Option: option_num] :
% 9.17/5.31 ( ( Option != none_num )
% 9.17/5.31 => ( Option
% 9.17/5.31 = ( some_num @ ( the_num @ Option ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_214_option_Oexhaust__sel,axiom,
% 9.17/5.31 ! [Option: option8956607266484857688it_nat] :
% 9.17/5.31 ( ( Option != none_P9117596204409417319it_nat )
% 9.17/5.31 => ( Option
% 9.17/5.31 = ( some_P1914260805536162275it_nat @ ( the_Pr7776125533777466484it_nat @ Option ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_215_effect__assertE,axiom,
% 9.17/5.31 ! [P: product_unit > $o,X: product_unit,H3: heap_e7401611519738050253t_unit,H5: heap_e7401611519738050253t_unit,R2: product_unit,N2: nat] :
% 9.17/5.31 ( ( heap_T6553295506729943825t_unit @ ( heap_T4208721593536448476t_unit @ P @ X ) @ H3 @ H5 @ R2 @ N2 )
% 9.17/5.31 => ~ ( ( P @ X )
% 9.17/5.31 => ( ( R2 = X )
% 9.17/5.31 => ( ( H5 = H3 )
% 9.17/5.31 => ( N2 != one_one_nat ) ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_216_effect__assertE,axiom,
% 9.17/5.31 ! [P: array_a > $o,X: array_a,H3: heap_e7401611519738050253t_unit,H5: heap_e7401611519738050253t_unit,R2: array_a,N2: nat] :
% 9.17/5.31 ( ( heap_T5830633491639066771rray_a @ ( heap_T7971689983404357896rray_a @ P @ X ) @ H3 @ H5 @ R2 @ N2 )
% 9.17/5.31 => ~ ( ( P @ X )
% 9.17/5.31 => ( ( R2 = X )
% 9.17/5.31 => ( ( H5 = H3 )
% 9.17/5.31 => ( N2 != one_one_nat ) ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_217_comp__apply,axiom,
% 9.17/5.31 ( comp_C3531382070062128313er_num
% 9.17/5.31 = ( ^ [F2: code_integer > code_integer,G2: num > code_integer,X3: num] : ( F2 @ ( G2 @ X3 ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_218_comp__apply,axiom,
% 9.17/5.31 ( comp_C1593894019821074884nteger
% 9.17/5.31 = ( ^ [F2: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,G2: code_integer > code_integer,X3: code_integer] : ( F2 @ ( G2 @ X3 ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_219_comp__apply,axiom,
% 9.17/5.31 ( comp_C8797469213163452608nteger
% 9.17/5.31 = ( ^ [F2: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G2: code_integer > code_integer > code_integer,X3: code_integer] : ( F2 @ ( G2 @ X3 ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_220_comp__apply,axiom,
% 9.17/5.31 ( comp_nat_num_int
% 9.17/5.31 = ( ^ [F2: nat > num,G2: int > nat,X3: int] : ( F2 @ ( G2 @ X3 ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_221_prod_Oinject,axiom,
% 9.17/5.31 ! [X1: produc6241069584506657477e_term > option6357759511663192854e_term,X2: produc8923325533196201883nteger,Y1: produc6241069584506657477e_term > option6357759511663192854e_term,Y2: produc8923325533196201883nteger] :
% 9.17/5.31 ( ( ( produc8603105652947943368nteger @ X1 @ X2 )
% 9.17/5.31 = ( produc8603105652947943368nteger @ Y1 @ Y2 ) )
% 9.17/5.31 = ( ( X1 = Y1 )
% 9.17/5.31 & ( X2 = Y2 ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_222_prod_Oinject,axiom,
% 9.17/5.31 ! [X1: produc3658429121746597890et_nat > $o,X2: produc3658429121746597890et_nat,Y1: produc3658429121746597890et_nat > $o,Y2: produc3658429121746597890et_nat] :
% 9.17/5.31 ( ( ( produc5001842942810119800et_nat @ X1 @ X2 )
% 9.17/5.31 = ( produc5001842942810119800et_nat @ Y1 @ Y2 ) )
% 9.17/5.31 = ( ( X1 = Y1 )
% 9.17/5.31 & ( X2 = Y2 ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_223_prod_Oinject,axiom,
% 9.17/5.31 ! [X1: produc3658429121746597890et_nat > $o,X2: produc3925858234332021118et_nat,Y1: produc3658429121746597890et_nat > $o,Y2: produc3925858234332021118et_nat] :
% 9.17/5.31 ( ( ( produc2245416461498447860et_nat @ X1 @ X2 )
% 9.17/5.31 = ( produc2245416461498447860et_nat @ Y1 @ Y2 ) )
% 9.17/5.31 = ( ( X1 = Y1 )
% 9.17/5.31 & ( X2 = Y2 ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_224_prod_Oinject,axiom,
% 9.17/5.31 ! [X1: produc8551481072490612790e_term > option6357759511663192854e_term,X2: product_prod_int_int,Y1: produc8551481072490612790e_term > option6357759511663192854e_term,Y2: product_prod_int_int] :
% 9.17/5.31 ( ( ( produc5700946648718959541nt_int @ X1 @ X2 )
% 9.17/5.31 = ( produc5700946648718959541nt_int @ Y1 @ Y2 ) )
% 9.17/5.31 = ( ( X1 = Y1 )
% 9.17/5.31 & ( X2 = Y2 ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_225_prod_Oinject,axiom,
% 9.17/5.31 ! [X1: int > option6357759511663192854e_term,X2: product_prod_int_int,Y1: int > option6357759511663192854e_term,Y2: product_prod_int_int] :
% 9.17/5.31 ( ( ( produc4305682042979456191nt_int @ X1 @ X2 )
% 9.17/5.31 = ( produc4305682042979456191nt_int @ Y1 @ Y2 ) )
% 9.17/5.31 = ( ( X1 = Y1 )
% 9.17/5.31 & ( X2 = Y2 ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_226_old_Oprod_Oinject,axiom,
% 9.17/5.31 ! [A: produc6241069584506657477e_term > option6357759511663192854e_term,B: produc8923325533196201883nteger,A4: produc6241069584506657477e_term > option6357759511663192854e_term,B3: produc8923325533196201883nteger] :
% 9.17/5.31 ( ( ( produc8603105652947943368nteger @ A @ B )
% 9.17/5.31 = ( produc8603105652947943368nteger @ A4 @ B3 ) )
% 9.17/5.31 = ( ( A = A4 )
% 9.17/5.31 & ( B = B3 ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_227_old_Oprod_Oinject,axiom,
% 9.17/5.31 ! [A: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat,A4: produc3658429121746597890et_nat > $o,B3: produc3658429121746597890et_nat] :
% 9.17/5.31 ( ( ( produc5001842942810119800et_nat @ A @ B )
% 9.17/5.31 = ( produc5001842942810119800et_nat @ A4 @ B3 ) )
% 9.17/5.31 = ( ( A = A4 )
% 9.17/5.31 & ( B = B3 ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_228_old_Oprod_Oinject,axiom,
% 9.17/5.31 ! [A: produc3658429121746597890et_nat > $o,B: produc3925858234332021118et_nat,A4: produc3658429121746597890et_nat > $o,B3: produc3925858234332021118et_nat] :
% 9.17/5.31 ( ( ( produc2245416461498447860et_nat @ A @ B )
% 9.17/5.31 = ( produc2245416461498447860et_nat @ A4 @ B3 ) )
% 9.17/5.31 = ( ( A = A4 )
% 9.17/5.31 & ( B = B3 ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_229_old_Oprod_Oinject,axiom,
% 9.17/5.31 ! [A: produc8551481072490612790e_term > option6357759511663192854e_term,B: product_prod_int_int,A4: produc8551481072490612790e_term > option6357759511663192854e_term,B3: product_prod_int_int] :
% 9.17/5.31 ( ( ( produc5700946648718959541nt_int @ A @ B )
% 9.17/5.31 = ( produc5700946648718959541nt_int @ A4 @ B3 ) )
% 9.17/5.31 = ( ( A = A4 )
% 9.17/5.31 & ( B = B3 ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_230_old_Oprod_Oinject,axiom,
% 9.17/5.31 ! [A: int > option6357759511663192854e_term,B: product_prod_int_int,A4: int > option6357759511663192854e_term,B3: product_prod_int_int] :
% 9.17/5.31 ( ( ( produc4305682042979456191nt_int @ A @ B )
% 9.17/5.31 = ( produc4305682042979456191nt_int @ A4 @ B3 ) )
% 9.17/5.31 = ( ( A = A4 )
% 9.17/5.31 & ( B = B3 ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_231_execute__bind_I1_J,axiom,
% 9.17/5.31 ! [F: heap_T6362127782908069795rray_a,H3: heap_e7401611519738050253t_unit,X: array_a,H5: heap_e7401611519738050253t_unit,N2: nat,G: array_a > heap_T6362127782908069795rray_a] :
% 9.17/5.31 ( ( ( heap_T5591663578999710211rray_a @ F @ H3 )
% 9.17/5.31 = ( some_P6105628898608307625it_nat @ ( produc1733996804261680252it_nat @ X @ ( produc584006145561248582it_nat @ H5 @ N2 ) ) ) )
% 9.17/5.31 => ( ( heap_T5591663578999710211rray_a @ ( heap_T2407400398799471159rray_a @ F @ G ) @ H3 )
% 9.17/5.31 = ( heap_T531568236820715630rray_a @ N2 @ ( heap_T5591663578999710211rray_a @ ( G @ X ) @ H5 ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_232_execute__bind_I1_J,axiom,
% 9.17/5.31 ! [F: heap_T6362127782908069795rray_a,H3: heap_e7401611519738050253t_unit,X: array_a,H5: heap_e7401611519738050253t_unit,N2: nat,G: array_a > heap_T5738788834812785303t_unit] :
% 9.17/5.31 ( ( ( heap_T5591663578999710211rray_a @ F @ H3 )
% 9.17/5.31 = ( some_P6105628898608307625it_nat @ ( produc1733996804261680252it_nat @ X @ ( produc584006145561248582it_nat @ H5 @ N2 ) ) ) )
% 9.17/5.31 => ( ( heap_T875086893843062177t_unit @ ( heap_T7324619625323989613t_unit @ F @ G ) @ H3 )
% 9.17/5.31 = ( heap_T3616969660504097270t_unit @ N2 @ ( heap_T875086893843062177t_unit @ ( G @ X ) @ H5 ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_233_execute__bind_I1_J,axiom,
% 9.17/5.31 ! [F: heap_T5738788834812785303t_unit,H3: heap_e7401611519738050253t_unit,X: product_unit,H5: heap_e7401611519738050253t_unit,N2: nat,G: product_unit > heap_T6362127782908069795rray_a] :
% 9.17/5.31 ( ( ( heap_T875086893843062177t_unit @ F @ H3 )
% 9.17/5.31 = ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ X @ ( produc584006145561248582it_nat @ H5 @ N2 ) ) ) )
% 9.17/5.31 => ( ( heap_T5591663578999710211rray_a @ ( heap_T7158140910958840029rray_a @ F @ G ) @ H3 )
% 9.17/5.31 = ( heap_T531568236820715630rray_a @ N2 @ ( heap_T5591663578999710211rray_a @ ( G @ X ) @ H5 ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_234_execute__bind_I1_J,axiom,
% 9.17/5.31 ! [F: heap_T5738788834812785303t_unit,H3: heap_e7401611519738050253t_unit,X: product_unit,H5: heap_e7401611519738050253t_unit,N2: nat,G: product_unit > heap_T5738788834812785303t_unit] :
% 9.17/5.31 ( ( ( heap_T875086893843062177t_unit @ F @ H3 )
% 9.17/5.31 = ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ X @ ( produc584006145561248582it_nat @ H5 @ N2 ) ) ) )
% 9.17/5.31 => ( ( heap_T875086893843062177t_unit @ ( heap_T2633723481742716231t_unit @ F @ G ) @ H3 )
% 9.17/5.31 = ( heap_T3616969660504097270t_unit @ N2 @ ( heap_T875086893843062177t_unit @ ( G @ X ) @ H5 ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_235_prod__cases3,axiom,
% 9.17/5.31 ! [Y: produc1908205239877642774nteger] :
% 9.17/5.31 ~ ! [A3: produc6241069584506657477e_term > option6357759511663192854e_term,B2: code_integer,C3: code_integer] :
% 9.17/5.31 ( Y
% 9.17/5.31 != ( produc8603105652947943368nteger @ A3 @ ( produc1086072967326762835nteger @ B2 @ C3 ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_236_prod__cases3,axiom,
% 9.17/5.31 ! [Y: produc3925858234332021118et_nat] :
% 9.17/5.31 ~ ! [A3: produc3658429121746597890et_nat > $o,B2: heap_e7401611519738050253t_unit,C3: set_nat] :
% 9.17/5.31 ( Y
% 9.17/5.31 != ( produc5001842942810119800et_nat @ A3 @ ( produc7507926704131184380et_nat @ B2 @ C3 ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_237_prod__cases3,axiom,
% 9.17/5.31 ! [Y: produc2732055786443039994et_nat] :
% 9.17/5.31 ~ ! [A3: produc3658429121746597890et_nat > $o,B2: produc3658429121746597890et_nat > $o,C3: produc3658429121746597890et_nat] :
% 9.17/5.31 ( Y
% 9.17/5.31 != ( produc2245416461498447860et_nat @ A3 @ ( produc5001842942810119800et_nat @ B2 @ C3 ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_238_prod__cases3,axiom,
% 9.17/5.31 ! [Y: produc2285326912895808259nt_int] :
% 9.17/5.31 ~ ! [A3: produc8551481072490612790e_term > option6357759511663192854e_term,B2: int,C3: int] :
% 9.17/5.31 ( Y
% 9.17/5.31 != ( produc5700946648718959541nt_int @ A3 @ ( product_Pair_int_int @ B2 @ C3 ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_239_prod__cases3,axiom,
% 9.17/5.31 ! [Y: produc7773217078559923341nt_int] :
% 9.17/5.31 ~ ! [A3: int > option6357759511663192854e_term,B2: int,C3: int] :
% 9.17/5.31 ( Y
% 9.17/5.31 != ( produc4305682042979456191nt_int @ A3 @ ( product_Pair_int_int @ B2 @ C3 ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_240_prod__cases4,axiom,
% 9.17/5.31 ! [Y: produc2732055786443039994et_nat] :
% 9.17/5.31 ~ ! [A3: produc3658429121746597890et_nat > $o,B2: produc3658429121746597890et_nat > $o,C3: heap_e7401611519738050253t_unit,D: set_nat] :
% 9.17/5.31 ( Y
% 9.17/5.31 != ( produc2245416461498447860et_nat @ A3 @ ( produc5001842942810119800et_nat @ B2 @ ( produc7507926704131184380et_nat @ C3 @ D ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_241_prod__induct3,axiom,
% 9.17/5.31 ! [P: produc1908205239877642774nteger > $o,X: produc1908205239877642774nteger] :
% 9.17/5.31 ( ! [A3: produc6241069584506657477e_term > option6357759511663192854e_term,B2: code_integer,C3: code_integer] : ( P @ ( produc8603105652947943368nteger @ A3 @ ( produc1086072967326762835nteger @ B2 @ C3 ) ) )
% 9.17/5.31 => ( P @ X ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_242_prod__induct3,axiom,
% 9.17/5.31 ! [P: produc3925858234332021118et_nat > $o,X: produc3925858234332021118et_nat] :
% 9.17/5.31 ( ! [A3: produc3658429121746597890et_nat > $o,B2: heap_e7401611519738050253t_unit,C3: set_nat] : ( P @ ( produc5001842942810119800et_nat @ A3 @ ( produc7507926704131184380et_nat @ B2 @ C3 ) ) )
% 9.17/5.31 => ( P @ X ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_243_prod__induct3,axiom,
% 9.17/5.31 ! [P: produc2732055786443039994et_nat > $o,X: produc2732055786443039994et_nat] :
% 9.17/5.31 ( ! [A3: produc3658429121746597890et_nat > $o,B2: produc3658429121746597890et_nat > $o,C3: produc3658429121746597890et_nat] : ( P @ ( produc2245416461498447860et_nat @ A3 @ ( produc5001842942810119800et_nat @ B2 @ C3 ) ) )
% 9.17/5.31 => ( P @ X ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_244_prod__induct3,axiom,
% 9.17/5.31 ! [P: produc2285326912895808259nt_int > $o,X: produc2285326912895808259nt_int] :
% 9.17/5.31 ( ! [A3: produc8551481072490612790e_term > option6357759511663192854e_term,B2: int,C3: int] : ( P @ ( produc5700946648718959541nt_int @ A3 @ ( product_Pair_int_int @ B2 @ C3 ) ) )
% 9.17/5.31 => ( P @ X ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_245_prod__induct3,axiom,
% 9.17/5.31 ! [P: produc7773217078559923341nt_int > $o,X: produc7773217078559923341nt_int] :
% 9.17/5.31 ( ! [A3: int > option6357759511663192854e_term,B2: int,C3: int] : ( P @ ( produc4305682042979456191nt_int @ A3 @ ( product_Pair_int_int @ B2 @ C3 ) ) )
% 9.17/5.31 => ( P @ X ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_246_prod__induct4,axiom,
% 9.17/5.31 ! [P: produc2732055786443039994et_nat > $o,X: produc2732055786443039994et_nat] :
% 9.17/5.31 ( ! [A3: produc3658429121746597890et_nat > $o,B2: produc3658429121746597890et_nat > $o,C3: heap_e7401611519738050253t_unit,D: set_nat] : ( P @ ( produc2245416461498447860et_nat @ A3 @ ( produc5001842942810119800et_nat @ B2 @ ( produc7507926704131184380et_nat @ C3 @ D ) ) ) )
% 9.17/5.31 => ( P @ X ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_247_timeFrame_Osimps_I2_J,axiom,
% 9.17/5.31 ! [N2: nat] :
% 9.17/5.31 ( ( heap_T531568236820715630rray_a @ N2 @ none_P2587165478634041381it_nat )
% 9.17/5.31 = none_P2587165478634041381it_nat ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_248_timeFrame_Osimps_I2_J,axiom,
% 9.17/5.31 ! [N2: nat] :
% 9.17/5.31 ( ( heap_T3616969660504097270t_unit @ N2 @ none_P9117596204409417319it_nat )
% 9.17/5.31 = none_P9117596204409417319it_nat ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_249_Pair__inject,axiom,
% 9.17/5.31 ! [A: produc6241069584506657477e_term > option6357759511663192854e_term,B: produc8923325533196201883nteger,A4: produc6241069584506657477e_term > option6357759511663192854e_term,B3: produc8923325533196201883nteger] :
% 9.17/5.31 ( ( ( produc8603105652947943368nteger @ A @ B )
% 9.17/5.31 = ( produc8603105652947943368nteger @ A4 @ B3 ) )
% 9.17/5.31 => ~ ( ( A = A4 )
% 9.17/5.31 => ( B != B3 ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_250_Pair__inject,axiom,
% 9.17/5.31 ! [A: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat,A4: produc3658429121746597890et_nat > $o,B3: produc3658429121746597890et_nat] :
% 9.17/5.31 ( ( ( produc5001842942810119800et_nat @ A @ B )
% 9.17/5.31 = ( produc5001842942810119800et_nat @ A4 @ B3 ) )
% 9.17/5.31 => ~ ( ( A = A4 )
% 9.17/5.31 => ( B != B3 ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_251_Pair__inject,axiom,
% 9.17/5.31 ! [A: produc3658429121746597890et_nat > $o,B: produc3925858234332021118et_nat,A4: produc3658429121746597890et_nat > $o,B3: produc3925858234332021118et_nat] :
% 9.17/5.31 ( ( ( produc2245416461498447860et_nat @ A @ B )
% 9.17/5.31 = ( produc2245416461498447860et_nat @ A4 @ B3 ) )
% 9.17/5.31 => ~ ( ( A = A4 )
% 9.17/5.31 => ( B != B3 ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_252_Pair__inject,axiom,
% 9.17/5.31 ! [A: produc8551481072490612790e_term > option6357759511663192854e_term,B: product_prod_int_int,A4: produc8551481072490612790e_term > option6357759511663192854e_term,B3: product_prod_int_int] :
% 9.17/5.31 ( ( ( produc5700946648718959541nt_int @ A @ B )
% 9.17/5.31 = ( produc5700946648718959541nt_int @ A4 @ B3 ) )
% 9.17/5.31 => ~ ( ( A = A4 )
% 9.17/5.31 => ( B != B3 ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_253_Pair__inject,axiom,
% 9.17/5.31 ! [A: int > option6357759511663192854e_term,B: product_prod_int_int,A4: int > option6357759511663192854e_term,B3: product_prod_int_int] :
% 9.17/5.31 ( ( ( produc4305682042979456191nt_int @ A @ B )
% 9.17/5.31 = ( produc4305682042979456191nt_int @ A4 @ B3 ) )
% 9.17/5.31 => ~ ( ( A = A4 )
% 9.17/5.31 => ( B != B3 ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_254_prod__cases,axiom,
% 9.17/5.31 ! [P: produc1908205239877642774nteger > $o,P4: produc1908205239877642774nteger] :
% 9.17/5.31 ( ! [A3: produc6241069584506657477e_term > option6357759511663192854e_term,B2: produc8923325533196201883nteger] : ( P @ ( produc8603105652947943368nteger @ A3 @ B2 ) )
% 9.17/5.31 => ( P @ P4 ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_255_prod__cases,axiom,
% 9.17/5.31 ! [P: produc3925858234332021118et_nat > $o,P4: produc3925858234332021118et_nat] :
% 9.17/5.31 ( ! [A3: produc3658429121746597890et_nat > $o,B2: produc3658429121746597890et_nat] : ( P @ ( produc5001842942810119800et_nat @ A3 @ B2 ) )
% 9.17/5.31 => ( P @ P4 ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_256_prod__cases,axiom,
% 9.17/5.31 ! [P: produc2732055786443039994et_nat > $o,P4: produc2732055786443039994et_nat] :
% 9.17/5.31 ( ! [A3: produc3658429121746597890et_nat > $o,B2: produc3925858234332021118et_nat] : ( P @ ( produc2245416461498447860et_nat @ A3 @ B2 ) )
% 9.17/5.31 => ( P @ P4 ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_257_prod__cases,axiom,
% 9.17/5.31 ! [P: produc2285326912895808259nt_int > $o,P4: produc2285326912895808259nt_int] :
% 9.17/5.31 ( ! [A3: produc8551481072490612790e_term > option6357759511663192854e_term,B2: product_prod_int_int] : ( P @ ( produc5700946648718959541nt_int @ A3 @ B2 ) )
% 9.17/5.31 => ( P @ P4 ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_258_prod__cases,axiom,
% 9.17/5.31 ! [P: produc7773217078559923341nt_int > $o,P4: produc7773217078559923341nt_int] :
% 9.17/5.31 ( ! [A3: int > option6357759511663192854e_term,B2: product_prod_int_int] : ( P @ ( produc4305682042979456191nt_int @ A3 @ B2 ) )
% 9.17/5.31 => ( P @ P4 ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_259_surj__pair,axiom,
% 9.17/5.31 ! [P4: produc1908205239877642774nteger] :
% 9.17/5.31 ? [X4: produc6241069584506657477e_term > option6357759511663192854e_term,Y5: produc8923325533196201883nteger] :
% 9.17/5.31 ( P4
% 9.17/5.31 = ( produc8603105652947943368nteger @ X4 @ Y5 ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_260_surj__pair,axiom,
% 9.17/5.31 ! [P4: produc3925858234332021118et_nat] :
% 9.17/5.31 ? [X4: produc3658429121746597890et_nat > $o,Y5: produc3658429121746597890et_nat] :
% 9.17/5.31 ( P4
% 9.17/5.31 = ( produc5001842942810119800et_nat @ X4 @ Y5 ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_261_surj__pair,axiom,
% 9.17/5.31 ! [P4: produc2732055786443039994et_nat] :
% 9.17/5.31 ? [X4: produc3658429121746597890et_nat > $o,Y5: produc3925858234332021118et_nat] :
% 9.17/5.31 ( P4
% 9.17/5.31 = ( produc2245416461498447860et_nat @ X4 @ Y5 ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_262_surj__pair,axiom,
% 9.17/5.31 ! [P4: produc2285326912895808259nt_int] :
% 9.17/5.31 ? [X4: produc8551481072490612790e_term > option6357759511663192854e_term,Y5: product_prod_int_int] :
% 9.17/5.31 ( P4
% 9.17/5.31 = ( produc5700946648718959541nt_int @ X4 @ Y5 ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_263_surj__pair,axiom,
% 9.17/5.31 ! [P4: produc7773217078559923341nt_int] :
% 9.17/5.31 ? [X4: int > option6357759511663192854e_term,Y5: product_prod_int_int] :
% 9.17/5.31 ( P4
% 9.17/5.31 = ( produc4305682042979456191nt_int @ X4 @ Y5 ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_264_old_Oprod_Oexhaust,axiom,
% 9.17/5.31 ! [Y: produc1908205239877642774nteger] :
% 9.17/5.31 ~ ! [A3: produc6241069584506657477e_term > option6357759511663192854e_term,B2: produc8923325533196201883nteger] :
% 9.17/5.31 ( Y
% 9.17/5.31 != ( produc8603105652947943368nteger @ A3 @ B2 ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_265_old_Oprod_Oexhaust,axiom,
% 9.17/5.31 ! [Y: produc3925858234332021118et_nat] :
% 9.17/5.31 ~ ! [A3: produc3658429121746597890et_nat > $o,B2: produc3658429121746597890et_nat] :
% 9.17/5.31 ( Y
% 9.17/5.31 != ( produc5001842942810119800et_nat @ A3 @ B2 ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_266_old_Oprod_Oexhaust,axiom,
% 9.17/5.31 ! [Y: produc2732055786443039994et_nat] :
% 9.17/5.31 ~ ! [A3: produc3658429121746597890et_nat > $o,B2: produc3925858234332021118et_nat] :
% 9.17/5.31 ( Y
% 9.17/5.31 != ( produc2245416461498447860et_nat @ A3 @ B2 ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_267_old_Oprod_Oexhaust,axiom,
% 9.17/5.31 ! [Y: produc2285326912895808259nt_int] :
% 9.17/5.31 ~ ! [A3: produc8551481072490612790e_term > option6357759511663192854e_term,B2: product_prod_int_int] :
% 9.17/5.31 ( Y
% 9.17/5.31 != ( produc5700946648718959541nt_int @ A3 @ B2 ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_268_old_Oprod_Oexhaust,axiom,
% 9.17/5.31 ! [Y: produc7773217078559923341nt_int] :
% 9.17/5.31 ~ ! [A3: int > option6357759511663192854e_term,B2: product_prod_int_int] :
% 9.17/5.31 ( Y
% 9.17/5.31 != ( produc4305682042979456191nt_int @ A3 @ B2 ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_269_one__reorient,axiom,
% 9.17/5.31 ! [X: code_integer] :
% 9.17/5.31 ( ( one_one_Code_integer = X )
% 9.17/5.31 = ( X = one_one_Code_integer ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_270_one__reorient,axiom,
% 9.17/5.31 ! [X: assn] :
% 9.17/5.31 ( ( one_one_assn = X )
% 9.17/5.31 = ( X = one_one_assn ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_271_one__reorient,axiom,
% 9.17/5.31 ! [X: rat] :
% 9.17/5.31 ( ( one_one_rat = X )
% 9.17/5.31 = ( X = one_one_rat ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_272_one__reorient,axiom,
% 9.17/5.31 ! [X: nat] :
% 9.17/5.31 ( ( one_one_nat = X )
% 9.17/5.31 = ( X = one_one_nat ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_273_one__reorient,axiom,
% 9.17/5.31 ! [X: int] :
% 9.17/5.31 ( ( one_one_int = X )
% 9.17/5.31 = ( X = one_one_int ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_274_comp__eq__dest__lhs,axiom,
% 9.17/5.31 ! [A: code_integer > code_integer,B: num > code_integer,C: num > code_integer,V: num] :
% 9.17/5.31 ( ( ( comp_C3531382070062128313er_num @ A @ B )
% 9.17/5.31 = C )
% 9.17/5.31 => ( ( A @ ( B @ V ) )
% 9.17/5.31 = ( C @ V ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_275_comp__eq__dest__lhs,axiom,
% 9.17/5.31 ! [A: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,B: code_integer > code_integer,C: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,V: code_integer] :
% 9.17/5.31 ( ( ( comp_C1593894019821074884nteger @ A @ B )
% 9.17/5.31 = C )
% 9.17/5.31 => ( ( A @ ( B @ V ) )
% 9.17/5.31 = ( C @ V ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_276_comp__eq__dest__lhs,axiom,
% 9.17/5.31 ! [A: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,B: code_integer > code_integer > code_integer,C: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,V: code_integer] :
% 9.17/5.31 ( ( ( comp_C8797469213163452608nteger @ A @ B )
% 9.17/5.31 = C )
% 9.17/5.31 => ( ( A @ ( B @ V ) )
% 9.17/5.31 = ( C @ V ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_277_comp__eq__dest__lhs,axiom,
% 9.17/5.31 ! [A: nat > num,B: int > nat,C: int > num,V: int] :
% 9.17/5.31 ( ( ( comp_nat_num_int @ A @ B )
% 9.17/5.31 = C )
% 9.17/5.31 => ( ( A @ ( B @ V ) )
% 9.17/5.31 = ( C @ V ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_278_comp__eq__elim,axiom,
% 9.17/5.31 ! [A: code_integer > code_integer,B: num > code_integer,C: code_integer > code_integer,D2: num > code_integer] :
% 9.17/5.31 ( ( ( comp_C3531382070062128313er_num @ A @ B )
% 9.17/5.31 = ( comp_C3531382070062128313er_num @ C @ D2 ) )
% 9.17/5.31 => ! [V3: num] :
% 9.17/5.31 ( ( A @ ( B @ V3 ) )
% 9.17/5.31 = ( C @ ( D2 @ V3 ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_279_comp__eq__elim,axiom,
% 9.17/5.31 ! [A: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,B: code_integer > code_integer,C: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,D2: code_integer > code_integer] :
% 9.17/5.31 ( ( ( comp_C1593894019821074884nteger @ A @ B )
% 9.17/5.31 = ( comp_C1593894019821074884nteger @ C @ D2 ) )
% 9.17/5.31 => ! [V3: code_integer] :
% 9.17/5.31 ( ( A @ ( B @ V3 ) )
% 9.17/5.31 = ( C @ ( D2 @ V3 ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_280_comp__eq__elim,axiom,
% 9.17/5.31 ! [A: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,B: code_integer > code_integer,C: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,D2: code_integer > code_integer > code_integer] :
% 9.17/5.31 ( ( ( comp_C1593894019821074884nteger @ A @ B )
% 9.17/5.31 = ( comp_C8797469213163452608nteger @ C @ D2 ) )
% 9.17/5.31 => ! [V3: code_integer] :
% 9.17/5.31 ( ( A @ ( B @ V3 ) )
% 9.17/5.31 = ( C @ ( D2 @ V3 ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_281_comp__eq__elim,axiom,
% 9.17/5.31 ! [A: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,B: code_integer > code_integer > code_integer,C: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,D2: code_integer > code_integer] :
% 9.17/5.31 ( ( ( comp_C8797469213163452608nteger @ A @ B )
% 9.17/5.31 = ( comp_C1593894019821074884nteger @ C @ D2 ) )
% 9.17/5.31 => ! [V3: code_integer] :
% 9.17/5.31 ( ( A @ ( B @ V3 ) )
% 9.17/5.31 = ( C @ ( D2 @ V3 ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_282_comp__eq__elim,axiom,
% 9.17/5.31 ! [A: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,B: code_integer > code_integer > code_integer,C: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,D2: code_integer > code_integer > code_integer] :
% 9.17/5.31 ( ( ( comp_C8797469213163452608nteger @ A @ B )
% 9.17/5.31 = ( comp_C8797469213163452608nteger @ C @ D2 ) )
% 9.17/5.31 => ! [V3: code_integer] :
% 9.17/5.31 ( ( A @ ( B @ V3 ) )
% 9.17/5.31 = ( C @ ( D2 @ V3 ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_283_comp__eq__elim,axiom,
% 9.17/5.31 ! [A: nat > num,B: int > nat,C: nat > num,D2: int > nat] :
% 9.17/5.31 ( ( ( comp_nat_num_int @ A @ B )
% 9.17/5.31 = ( comp_nat_num_int @ C @ D2 ) )
% 9.17/5.31 => ! [V3: int] :
% 9.17/5.31 ( ( A @ ( B @ V3 ) )
% 9.17/5.31 = ( C @ ( D2 @ V3 ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_284_comp__eq__dest,axiom,
% 9.17/5.31 ! [A: code_integer > code_integer,B: num > code_integer,C: code_integer > code_integer,D2: num > code_integer,V: num] :
% 9.17/5.31 ( ( ( comp_C3531382070062128313er_num @ A @ B )
% 9.17/5.31 = ( comp_C3531382070062128313er_num @ C @ D2 ) )
% 9.17/5.31 => ( ( A @ ( B @ V ) )
% 9.17/5.31 = ( C @ ( D2 @ V ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_285_comp__eq__dest,axiom,
% 9.17/5.31 ! [A: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,B: code_integer > code_integer,C: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,D2: code_integer > code_integer,V: code_integer] :
% 9.17/5.31 ( ( ( comp_C1593894019821074884nteger @ A @ B )
% 9.17/5.31 = ( comp_C1593894019821074884nteger @ C @ D2 ) )
% 9.17/5.31 => ( ( A @ ( B @ V ) )
% 9.17/5.31 = ( C @ ( D2 @ V ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_286_comp__eq__dest,axiom,
% 9.17/5.31 ! [A: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,B: code_integer > code_integer,C: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,D2: code_integer > code_integer > code_integer,V: code_integer] :
% 9.17/5.31 ( ( ( comp_C1593894019821074884nteger @ A @ B )
% 9.17/5.31 = ( comp_C8797469213163452608nteger @ C @ D2 ) )
% 9.17/5.31 => ( ( A @ ( B @ V ) )
% 9.17/5.31 = ( C @ ( D2 @ V ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_287_comp__eq__dest,axiom,
% 9.17/5.31 ! [A: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,B: code_integer > code_integer > code_integer,C: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,D2: code_integer > code_integer,V: code_integer] :
% 9.17/5.31 ( ( ( comp_C8797469213163452608nteger @ A @ B )
% 9.17/5.31 = ( comp_C1593894019821074884nteger @ C @ D2 ) )
% 9.17/5.31 => ( ( A @ ( B @ V ) )
% 9.17/5.31 = ( C @ ( D2 @ V ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_288_comp__eq__dest,axiom,
% 9.17/5.31 ! [A: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,B: code_integer > code_integer > code_integer,C: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,D2: code_integer > code_integer > code_integer,V: code_integer] :
% 9.17/5.31 ( ( ( comp_C8797469213163452608nteger @ A @ B )
% 9.17/5.31 = ( comp_C8797469213163452608nteger @ C @ D2 ) )
% 9.17/5.31 => ( ( A @ ( B @ V ) )
% 9.17/5.31 = ( C @ ( D2 @ V ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_289_comp__eq__dest,axiom,
% 9.17/5.31 ! [A: nat > num,B: int > nat,C: nat > num,D2: int > nat,V: int] :
% 9.17/5.31 ( ( ( comp_nat_num_int @ A @ B )
% 9.17/5.31 = ( comp_nat_num_int @ C @ D2 ) )
% 9.17/5.31 => ( ( A @ ( B @ V ) )
% 9.17/5.31 = ( C @ ( D2 @ V ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_290_comp__assoc,axiom,
% 9.17/5.31 ! [F: code_integer > code_integer,G: num > code_integer,H3: num > num] :
% 9.17/5.31 ( ( comp_n6909714581898973814er_num @ ( comp_C3531382070062128313er_num @ F @ G ) @ H3 )
% 9.17/5.31 = ( comp_C3531382070062128313er_num @ F @ ( comp_n6909714581898973814er_num @ G @ H3 ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_291_comp__assoc,axiom,
% 9.17/5.31 ! [F: nat > num,G: int > nat,H3: int > int] :
% 9.17/5.31 ( ( comp_int_num_int @ ( comp_nat_num_int @ F @ G ) @ H3 )
% 9.17/5.31 = ( comp_nat_num_int @ F @ ( comp_int_nat_int @ G @ H3 ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_292_comp__assoc,axiom,
% 9.17/5.31 ! [F: code_integer > code_integer,G: code_integer > code_integer,H3: num > code_integer] :
% 9.17/5.31 ( ( comp_C3531382070062128313er_num @ ( comp_C7449957260575251196nteger @ F @ G ) @ H3 )
% 9.17/5.31 = ( comp_C3531382070062128313er_num @ F @ ( comp_C3531382070062128313er_num @ G @ H3 ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_293_comp__assoc,axiom,
% 9.17/5.31 ! [F: num > num,G: nat > num,H3: int > nat] :
% 9.17/5.31 ( ( comp_nat_num_int @ ( comp_num_num_nat @ F @ G ) @ H3 )
% 9.17/5.31 = ( comp_num_num_int @ F @ ( comp_nat_num_int @ G @ H3 ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_294_comp__assoc,axiom,
% 9.17/5.31 ! [F: nat > num,G: nat > nat,H3: int > nat] :
% 9.17/5.31 ( ( comp_nat_num_int @ ( comp_nat_num_nat @ F @ G ) @ H3 )
% 9.17/5.31 = ( comp_nat_num_int @ F @ ( comp_nat_nat_int @ G @ H3 ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_295_comp__assoc,axiom,
% 9.17/5.31 ! [F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer,H3: num > code_integer] :
% 9.17/5.31 ( ( comp_C6617437204949736321er_num @ ( comp_C1593894019821074884nteger @ F @ G ) @ H3 )
% 9.17/5.31 = ( comp_C6617437204949736321er_num @ F @ ( comp_C3531382070062128313er_num @ G @ H3 ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_296_comp__assoc,axiom,
% 9.17/5.31 ! [F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer,H3: code_integer > code_integer] :
% 9.17/5.31 ( ( comp_C1593894019821074884nteger @ ( comp_C1593894019821074884nteger @ F @ G ) @ H3 )
% 9.17/5.31 = ( comp_C1593894019821074884nteger @ F @ ( comp_C7449957260575251196nteger @ G @ H3 ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_297_comp__assoc,axiom,
% 9.17/5.31 ! [F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer > code_integer,H3: code_integer > code_integer] :
% 9.17/5.31 ( ( comp_C1593894019821074884nteger @ ( comp_C8797469213163452608nteger @ F @ G ) @ H3 )
% 9.17/5.31 = ( comp_C8797469213163452608nteger @ F @ ( comp_C2931745410781319416nteger @ G @ H3 ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_298_comp__assoc,axiom,
% 9.17/5.31 ! [F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,G: ( code_integer > code_integer ) > code_integer,H3: code_integer > code_integer > code_integer] :
% 9.17/5.31 ( ( comp_C8797469213163452608nteger @ ( comp_C95226695241045696nteger @ F @ G ) @ H3 )
% 9.17/5.31 = ( comp_C1593894019821074884nteger @ F @ ( comp_C5076291335850163704nteger @ G @ H3 ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_299_comp__assoc,axiom,
% 9.17/5.31 ! [F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G: ( code_integer > code_integer ) > code_integer > code_integer,H3: code_integer > code_integer > code_integer] :
% 9.17/5.31 ( ( comp_C8797469213163452608nteger @ ( comp_C3983183376822107068nteger @ F @ G ) @ H3 )
% 9.17/5.31 = ( comp_C8797469213163452608nteger @ F @ ( comp_C2822359487432382964nteger @ G @ H3 ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_300_comp__def,axiom,
% 9.17/5.31 ( comp_C3531382070062128313er_num
% 9.17/5.31 = ( ^ [F2: code_integer > code_integer,G2: num > code_integer,X3: num] : ( F2 @ ( G2 @ X3 ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_301_comp__def,axiom,
% 9.17/5.31 ( comp_C1593894019821074884nteger
% 9.17/5.31 = ( ^ [F2: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,G2: code_integer > code_integer,X3: code_integer] : ( F2 @ ( G2 @ X3 ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_302_comp__def,axiom,
% 9.17/5.31 ( comp_C8797469213163452608nteger
% 9.17/5.31 = ( ^ [F2: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G2: code_integer > code_integer > code_integer,X3: code_integer] : ( F2 @ ( G2 @ X3 ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_303_comp__def,axiom,
% 9.17/5.31 ( comp_nat_num_int
% 9.17/5.31 = ( ^ [F2: nat > num,G2: int > nat,X3: int] : ( F2 @ ( G2 @ X3 ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_304_timeFrame_Oelims,axiom,
% 9.17/5.31 ! [X: nat,Xa: option3216581401566546698it_nat,Y: option3216581401566546698it_nat] :
% 9.17/5.31 ( ( ( heap_T531568236820715630rray_a @ X @ Xa )
% 9.17/5.31 = Y )
% 9.17/5.31 => ( ! [R: array_a,H2: heap_e7401611519738050253t_unit,N3: nat] :
% 9.17/5.31 ( ( Xa
% 9.17/5.31 = ( some_P6105628898608307625it_nat @ ( produc1733996804261680252it_nat @ R @ ( produc584006145561248582it_nat @ H2 @ N3 ) ) ) )
% 9.17/5.31 => ( Y
% 9.17/5.31 != ( some_P6105628898608307625it_nat @ ( produc1733996804261680252it_nat @ R @ ( produc584006145561248582it_nat @ H2 @ ( plus_plus_nat @ X @ N3 ) ) ) ) ) )
% 9.17/5.31 => ~ ( ( Xa = none_P2587165478634041381it_nat )
% 9.17/5.31 => ( Y != none_P2587165478634041381it_nat ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_305_timeFrame_Oelims,axiom,
% 9.17/5.31 ! [X: nat,Xa: option8956607266484857688it_nat,Y: option8956607266484857688it_nat] :
% 9.17/5.31 ( ( ( heap_T3616969660504097270t_unit @ X @ Xa )
% 9.17/5.31 = Y )
% 9.17/5.31 => ( ! [R: product_unit,H2: heap_e7401611519738050253t_unit,N3: nat] :
% 9.17/5.31 ( ( Xa
% 9.17/5.31 = ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ R @ ( produc584006145561248582it_nat @ H2 @ N3 ) ) ) )
% 9.17/5.31 => ( Y
% 9.17/5.31 != ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ R @ ( produc584006145561248582it_nat @ H2 @ ( plus_plus_nat @ X @ N3 ) ) ) ) ) )
% 9.17/5.31 => ~ ( ( Xa = none_P9117596204409417319it_nat )
% 9.17/5.31 => ( Y != none_P9117596204409417319it_nat ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_306_execute__bind__eq__SomeI,axiom,
% 9.17/5.31 ! [F: heap_T6362127782908069795rray_a,H3: heap_e7401611519738050253t_unit,X: array_a,H5: heap_e7401611519738050253t_unit,N2: nat,G: array_a > heap_T6362127782908069795rray_a,Y: array_a,H7: heap_e7401611519738050253t_unit,N5: nat] :
% 9.17/5.31 ( ( ( heap_T5591663578999710211rray_a @ F @ H3 )
% 9.17/5.31 = ( some_P6105628898608307625it_nat @ ( produc1733996804261680252it_nat @ X @ ( produc584006145561248582it_nat @ H5 @ N2 ) ) ) )
% 9.17/5.31 => ( ( ( heap_T5591663578999710211rray_a @ ( G @ X ) @ H5 )
% 9.17/5.31 = ( some_P6105628898608307625it_nat @ ( produc1733996804261680252it_nat @ Y @ ( produc584006145561248582it_nat @ H7 @ N5 ) ) ) )
% 9.17/5.31 => ( ( heap_T5591663578999710211rray_a @ ( heap_T2407400398799471159rray_a @ F @ G ) @ H3 )
% 9.17/5.31 = ( some_P6105628898608307625it_nat @ ( produc1733996804261680252it_nat @ Y @ ( produc584006145561248582it_nat @ H7 @ ( plus_plus_nat @ N2 @ N5 ) ) ) ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_307_execute__bind__eq__SomeI,axiom,
% 9.17/5.31 ! [F: heap_T6362127782908069795rray_a,H3: heap_e7401611519738050253t_unit,X: array_a,H5: heap_e7401611519738050253t_unit,N2: nat,G: array_a > heap_T5738788834812785303t_unit,Y: product_unit,H7: heap_e7401611519738050253t_unit,N5: nat] :
% 9.17/5.31 ( ( ( heap_T5591663578999710211rray_a @ F @ H3 )
% 9.17/5.31 = ( some_P6105628898608307625it_nat @ ( produc1733996804261680252it_nat @ X @ ( produc584006145561248582it_nat @ H5 @ N2 ) ) ) )
% 9.17/5.31 => ( ( ( heap_T875086893843062177t_unit @ ( G @ X ) @ H5 )
% 9.17/5.31 = ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ Y @ ( produc584006145561248582it_nat @ H7 @ N5 ) ) ) )
% 9.17/5.31 => ( ( heap_T875086893843062177t_unit @ ( heap_T7324619625323989613t_unit @ F @ G ) @ H3 )
% 9.17/5.31 = ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ Y @ ( produc584006145561248582it_nat @ H7 @ ( plus_plus_nat @ N2 @ N5 ) ) ) ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_308_execute__bind__eq__SomeI,axiom,
% 9.17/5.31 ! [F: heap_T5738788834812785303t_unit,H3: heap_e7401611519738050253t_unit,X: product_unit,H5: heap_e7401611519738050253t_unit,N2: nat,G: product_unit > heap_T6362127782908069795rray_a,Y: array_a,H7: heap_e7401611519738050253t_unit,N5: nat] :
% 9.17/5.31 ( ( ( heap_T875086893843062177t_unit @ F @ H3 )
% 9.17/5.31 = ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ X @ ( produc584006145561248582it_nat @ H5 @ N2 ) ) ) )
% 9.17/5.31 => ( ( ( heap_T5591663578999710211rray_a @ ( G @ X ) @ H5 )
% 9.17/5.31 = ( some_P6105628898608307625it_nat @ ( produc1733996804261680252it_nat @ Y @ ( produc584006145561248582it_nat @ H7 @ N5 ) ) ) )
% 9.17/5.31 => ( ( heap_T5591663578999710211rray_a @ ( heap_T7158140910958840029rray_a @ F @ G ) @ H3 )
% 9.17/5.31 = ( some_P6105628898608307625it_nat @ ( produc1733996804261680252it_nat @ Y @ ( produc584006145561248582it_nat @ H7 @ ( plus_plus_nat @ N2 @ N5 ) ) ) ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_309_execute__bind__eq__SomeI,axiom,
% 9.17/5.31 ! [F: heap_T5738788834812785303t_unit,H3: heap_e7401611519738050253t_unit,X: product_unit,H5: heap_e7401611519738050253t_unit,N2: nat,G: product_unit > heap_T5738788834812785303t_unit,Y: product_unit,H7: heap_e7401611519738050253t_unit,N5: nat] :
% 9.17/5.31 ( ( ( heap_T875086893843062177t_unit @ F @ H3 )
% 9.17/5.31 = ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ X @ ( produc584006145561248582it_nat @ H5 @ N2 ) ) ) )
% 9.17/5.31 => ( ( ( heap_T875086893843062177t_unit @ ( G @ X ) @ H5 )
% 9.17/5.31 = ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ Y @ ( produc584006145561248582it_nat @ H7 @ N5 ) ) ) )
% 9.17/5.31 => ( ( heap_T875086893843062177t_unit @ ( heap_T2633723481742716231t_unit @ F @ G ) @ H3 )
% 9.17/5.31 = ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ Y @ ( produc584006145561248582it_nat @ H7 @ ( plus_plus_nat @ N2 @ N5 ) ) ) ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_310_timeFrame_Osimps_I1_J,axiom,
% 9.17/5.31 ! [N2: nat,R2: product_unit,H3: heap_e7401611519738050253t_unit,N5: nat] :
% 9.17/5.31 ( ( heap_T3616969660504097270t_unit @ N2 @ ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ R2 @ ( produc584006145561248582it_nat @ H3 @ N5 ) ) ) )
% 9.17/5.31 = ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ R2 @ ( produc584006145561248582it_nat @ H3 @ ( plus_plus_nat @ N2 @ N5 ) ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_311_heap__def,axiom,
% 9.17/5.31 ( heap_T6927113302350381334t_unit
% 9.17/5.31 = ( ^ [F2: heap_e7401611519738050253t_unit > produc8664842809031399944it_nat] : ( heap_T6183433275982383450t_unit @ ( comp_P3118722334806803912t_unit @ some_P1914260805536162275it_nat @ F2 ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_312_option_Osplit__sel,axiom,
% 9.17/5.31 ! [P: int > $o,F1: int,F22: num > int,Option: option_num] :
% 9.17/5.31 ( ( P @ ( case_option_int_num @ F1 @ F22 @ Option ) )
% 9.17/5.31 = ( ( ( Option = none_num )
% 9.17/5.31 => ( P @ F1 ) )
% 9.17/5.31 & ( ( Option
% 9.17/5.31 = ( some_num @ ( the_num @ Option ) ) )
% 9.17/5.31 => ( P @ ( F22 @ ( the_num @ Option ) ) ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_313_option_Osplit__sel,axiom,
% 9.17/5.31 ! [P: option_num > $o,F1: option_num,F22: num > option_num,Option: option_num] :
% 9.17/5.31 ( ( P @ ( case_o6005452278849405969um_num @ F1 @ F22 @ Option ) )
% 9.17/5.31 = ( ( ( Option = none_num )
% 9.17/5.31 => ( P @ F1 ) )
% 9.17/5.31 & ( ( Option
% 9.17/5.31 = ( some_num @ ( the_num @ Option ) ) )
% 9.17/5.31 => ( P @ ( F22 @ ( the_num @ Option ) ) ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_314_option_Osplit__sel,axiom,
% 9.17/5.31 ! [P: num > $o,F1: num,F22: num > num,Option: option_num] :
% 9.17/5.31 ( ( P @ ( case_option_num_num @ F1 @ F22 @ Option ) )
% 9.17/5.31 = ( ( ( Option = none_num )
% 9.17/5.31 => ( P @ F1 ) )
% 9.17/5.31 & ( ( Option
% 9.17/5.31 = ( some_num @ ( the_num @ Option ) ) )
% 9.17/5.31 => ( P @ ( F22 @ ( the_num @ Option ) ) ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_315_option_Osplit__sel__asm,axiom,
% 9.17/5.31 ! [P: int > $o,F1: int,F22: num > int,Option: option_num] :
% 9.17/5.31 ( ( P @ ( case_option_int_num @ F1 @ F22 @ Option ) )
% 9.17/5.31 = ( ~ ( ( ( Option = none_num )
% 9.17/5.31 & ~ ( P @ F1 ) )
% 9.17/5.31 | ( ( Option
% 9.17/5.31 = ( some_num @ ( the_num @ Option ) ) )
% 9.17/5.31 & ~ ( P @ ( F22 @ ( the_num @ Option ) ) ) ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_316_option_Osplit__sel__asm,axiom,
% 9.17/5.31 ! [P: option_num > $o,F1: option_num,F22: num > option_num,Option: option_num] :
% 9.17/5.31 ( ( P @ ( case_o6005452278849405969um_num @ F1 @ F22 @ Option ) )
% 9.17/5.31 = ( ~ ( ( ( Option = none_num )
% 9.17/5.31 & ~ ( P @ F1 ) )
% 9.17/5.31 | ( ( Option
% 9.17/5.31 = ( some_num @ ( the_num @ Option ) ) )
% 9.17/5.31 & ~ ( P @ ( F22 @ ( the_num @ Option ) ) ) ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_317_option_Osplit__sel__asm,axiom,
% 9.17/5.31 ! [P: num > $o,F1: num,F22: num > num,Option: option_num] :
% 9.17/5.31 ( ( P @ ( case_option_num_num @ F1 @ F22 @ Option ) )
% 9.17/5.31 = ( ~ ( ( ( Option = none_num )
% 9.17/5.31 & ~ ( P @ F1 ) )
% 9.17/5.31 | ( ( Option
% 9.17/5.31 = ( some_num @ ( the_num @ Option ) ) )
% 9.17/5.31 & ~ ( P @ ( F22 @ ( the_num @ Option ) ) ) ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_318_one__natural_Orsp,axiom,
% 9.17/5.31 one_one_nat = one_one_nat ).
% 9.17/5.31
% 9.17/5.31 thf(fact_319_timeFrame_Opelims,axiom,
% 9.17/5.31 ! [X: nat,Xa: option3216581401566546698it_nat,Y: option3216581401566546698it_nat] :
% 9.17/5.31 ( ( ( heap_T531568236820715630rray_a @ X @ Xa )
% 9.17/5.31 = Y )
% 9.17/5.31 => ( ( accp_P8948468358075348838it_nat @ heap_T6578553156929092987rray_a @ ( produc3378006678175723489it_nat @ X @ Xa ) )
% 9.17/5.31 => ( ! [R: array_a,H2: heap_e7401611519738050253t_unit,N3: nat] :
% 9.17/5.31 ( ( Xa
% 9.17/5.31 = ( some_P6105628898608307625it_nat @ ( produc1733996804261680252it_nat @ R @ ( produc584006145561248582it_nat @ H2 @ N3 ) ) ) )
% 9.17/5.31 => ( ( Y
% 9.17/5.31 = ( some_P6105628898608307625it_nat @ ( produc1733996804261680252it_nat @ R @ ( produc584006145561248582it_nat @ H2 @ ( plus_plus_nat @ X @ N3 ) ) ) ) )
% 9.17/5.31 => ~ ( accp_P8948468358075348838it_nat @ heap_T6578553156929092987rray_a @ ( produc3378006678175723489it_nat @ X @ ( some_P6105628898608307625it_nat @ ( produc1733996804261680252it_nat @ R @ ( produc584006145561248582it_nat @ H2 @ N3 ) ) ) ) ) ) )
% 9.17/5.31 => ~ ( ( Xa = none_P2587165478634041381it_nat )
% 9.17/5.31 => ( ( Y = none_P2587165478634041381it_nat )
% 9.17/5.31 => ~ ( accp_P8948468358075348838it_nat @ heap_T6578553156929092987rray_a @ ( produc3378006678175723489it_nat @ X @ none_P2587165478634041381it_nat ) ) ) ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_320_timeFrame_Opelims,axiom,
% 9.17/5.31 ! [X: nat,Xa: option8956607266484857688it_nat,Y: option8956607266484857688it_nat] :
% 9.17/5.31 ( ( ( heap_T3616969660504097270t_unit @ X @ Xa )
% 9.17/5.31 = Y )
% 9.17/5.31 => ( ( accp_P414730952086964626it_nat @ heap_T996182799752388649t_unit @ ( produc638857205735767105it_nat @ X @ Xa ) )
% 9.17/5.31 => ( ! [R: product_unit,H2: heap_e7401611519738050253t_unit,N3: nat] :
% 9.17/5.31 ( ( Xa
% 9.17/5.31 = ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ R @ ( produc584006145561248582it_nat @ H2 @ N3 ) ) ) )
% 9.17/5.31 => ( ( Y
% 9.17/5.31 = ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ R @ ( produc584006145561248582it_nat @ H2 @ ( plus_plus_nat @ X @ N3 ) ) ) ) )
% 9.17/5.31 => ~ ( accp_P414730952086964626it_nat @ heap_T996182799752388649t_unit @ ( produc638857205735767105it_nat @ X @ ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ R @ ( produc584006145561248582it_nat @ H2 @ N3 ) ) ) ) ) ) )
% 9.17/5.31 => ~ ( ( Xa = none_P9117596204409417319it_nat )
% 9.17/5.31 => ( ( Y = none_P9117596204409417319it_nat )
% 9.17/5.31 => ~ ( accp_P414730952086964626it_nat @ heap_T996182799752388649t_unit @ ( produc638857205735767105it_nat @ X @ none_P9117596204409417319it_nat ) ) ) ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_321_add__right__cancel,axiom,
% 9.17/5.31 ! [B: multis2468970476368604999at_nat,A: multis2468970476368604999at_nat,C: multis2468970476368604999at_nat] :
% 9.17/5.31 ( ( ( plus_p7104986032573967614at_nat @ B @ A )
% 9.17/5.31 = ( plus_p7104986032573967614at_nat @ C @ A ) )
% 9.17/5.31 = ( B = C ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_322_add__right__cancel,axiom,
% 9.17/5.31 ! [B: rat,A: rat,C: rat] :
% 9.17/5.31 ( ( ( plus_plus_rat @ B @ A )
% 9.17/5.31 = ( plus_plus_rat @ C @ A ) )
% 9.17/5.31 = ( B = C ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_323_add__right__cancel,axiom,
% 9.17/5.31 ! [B: nat,A: nat,C: nat] :
% 9.17/5.31 ( ( ( plus_plus_nat @ B @ A )
% 9.17/5.31 = ( plus_plus_nat @ C @ A ) )
% 9.17/5.31 = ( B = C ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_324_add__right__cancel,axiom,
% 9.17/5.31 ! [B: int,A: int,C: int] :
% 9.17/5.31 ( ( ( plus_plus_int @ B @ A )
% 9.17/5.31 = ( plus_plus_int @ C @ A ) )
% 9.17/5.31 = ( B = C ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_325_add__left__cancel,axiom,
% 9.17/5.31 ! [A: multis2468970476368604999at_nat,B: multis2468970476368604999at_nat,C: multis2468970476368604999at_nat] :
% 9.17/5.31 ( ( ( plus_p7104986032573967614at_nat @ A @ B )
% 9.17/5.31 = ( plus_p7104986032573967614at_nat @ A @ C ) )
% 9.17/5.31 = ( B = C ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_326_add__left__cancel,axiom,
% 9.17/5.31 ! [A: rat,B: rat,C: rat] :
% 9.17/5.31 ( ( ( plus_plus_rat @ A @ B )
% 9.17/5.31 = ( plus_plus_rat @ A @ C ) )
% 9.17/5.31 = ( B = C ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_327_add__left__cancel,axiom,
% 9.17/5.31 ! [A: nat,B: nat,C: nat] :
% 9.17/5.31 ( ( ( plus_plus_nat @ A @ B )
% 9.17/5.31 = ( plus_plus_nat @ A @ C ) )
% 9.17/5.31 = ( B = C ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_328_add__left__cancel,axiom,
% 9.17/5.31 ! [A: int,B: int,C: int] :
% 9.17/5.31 ( ( ( plus_plus_int @ A @ B )
% 9.17/5.31 = ( plus_plus_int @ A @ C ) )
% 9.17/5.31 = ( B = C ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_329_Heap_Oinject,axiom,
% 9.17/5.31 ! [X: heap_e7401611519738050253t_unit > option8956607266484857688it_nat,Ya: heap_e7401611519738050253t_unit > option8956607266484857688it_nat] :
% 9.17/5.31 ( ( ( heap_T6183433275982383450t_unit @ X )
% 9.17/5.31 = ( heap_T6183433275982383450t_unit @ Ya ) )
% 9.17/5.31 = ( X = Ya ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_330_Heap__execute,axiom,
% 9.17/5.31 ! [F: heap_T6362127782908069795rray_a] :
% 9.17/5.31 ( ( heap_T1488828001306802186rray_a @ ( heap_T5591663578999710211rray_a @ F ) )
% 9.17/5.31 = F ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_331_Heap__execute,axiom,
% 9.17/5.31 ! [F: heap_T5738788834812785303t_unit] :
% 9.17/5.31 ( ( heap_T6183433275982383450t_unit @ ( heap_T875086893843062177t_unit @ F ) )
% 9.17/5.31 = F ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_332_add__right__imp__eq,axiom,
% 9.17/5.31 ! [B: multis2468970476368604999at_nat,A: multis2468970476368604999at_nat,C: multis2468970476368604999at_nat] :
% 9.17/5.31 ( ( ( plus_p7104986032573967614at_nat @ B @ A )
% 9.17/5.31 = ( plus_p7104986032573967614at_nat @ C @ A ) )
% 9.17/5.31 => ( B = C ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_333_add__right__imp__eq,axiom,
% 9.17/5.31 ! [B: rat,A: rat,C: rat] :
% 9.17/5.31 ( ( ( plus_plus_rat @ B @ A )
% 9.17/5.31 = ( plus_plus_rat @ C @ A ) )
% 9.17/5.31 => ( B = C ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_334_add__right__imp__eq,axiom,
% 9.17/5.31 ! [B: nat,A: nat,C: nat] :
% 9.17/5.31 ( ( ( plus_plus_nat @ B @ A )
% 9.17/5.31 = ( plus_plus_nat @ C @ A ) )
% 9.17/5.31 => ( B = C ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_335_add__right__imp__eq,axiom,
% 9.17/5.31 ! [B: int,A: int,C: int] :
% 9.17/5.31 ( ( ( plus_plus_int @ B @ A )
% 9.17/5.31 = ( plus_plus_int @ C @ A ) )
% 9.17/5.31 => ( B = C ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_336_add__left__imp__eq,axiom,
% 9.17/5.31 ! [A: multis2468970476368604999at_nat,B: multis2468970476368604999at_nat,C: multis2468970476368604999at_nat] :
% 9.17/5.31 ( ( ( plus_p7104986032573967614at_nat @ A @ B )
% 9.17/5.31 = ( plus_p7104986032573967614at_nat @ A @ C ) )
% 9.17/5.31 => ( B = C ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_337_add__left__imp__eq,axiom,
% 9.17/5.31 ! [A: rat,B: rat,C: rat] :
% 9.17/5.31 ( ( ( plus_plus_rat @ A @ B )
% 9.17/5.31 = ( plus_plus_rat @ A @ C ) )
% 9.17/5.31 => ( B = C ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_338_add__left__imp__eq,axiom,
% 9.17/5.31 ! [A: nat,B: nat,C: nat] :
% 9.17/5.31 ( ( ( plus_plus_nat @ A @ B )
% 9.17/5.31 = ( plus_plus_nat @ A @ C ) )
% 9.17/5.31 => ( B = C ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_339_add__left__imp__eq,axiom,
% 9.17/5.31 ! [A: int,B: int,C: int] :
% 9.17/5.31 ( ( ( plus_plus_int @ A @ B )
% 9.17/5.31 = ( plus_plus_int @ A @ C ) )
% 9.17/5.31 => ( B = C ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_340_ab__semigroup__add__class_Oadd_Oleft__commute,axiom,
% 9.17/5.31 ! [B: multis2468970476368604999at_nat,A: multis2468970476368604999at_nat,C: multis2468970476368604999at_nat] :
% 9.17/5.31 ( ( plus_p7104986032573967614at_nat @ B @ ( plus_p7104986032573967614at_nat @ A @ C ) )
% 9.17/5.31 = ( plus_p7104986032573967614at_nat @ A @ ( plus_p7104986032573967614at_nat @ B @ C ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_341_ab__semigroup__add__class_Oadd_Oleft__commute,axiom,
% 9.17/5.31 ! [B: rat,A: rat,C: rat] :
% 9.17/5.31 ( ( plus_plus_rat @ B @ ( plus_plus_rat @ A @ C ) )
% 9.17/5.31 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_342_ab__semigroup__add__class_Oadd_Oleft__commute,axiom,
% 9.17/5.31 ! [B: nat,A: nat,C: nat] :
% 9.17/5.31 ( ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C ) )
% 9.17/5.31 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_343_ab__semigroup__add__class_Oadd_Oleft__commute,axiom,
% 9.17/5.31 ! [B: int,A: int,C: int] :
% 9.17/5.31 ( ( plus_plus_int @ B @ ( plus_plus_int @ A @ C ) )
% 9.17/5.31 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_344_ab__semigroup__add__class_Oadd_Ocommute,axiom,
% 9.17/5.31 ( plus_p7104986032573967614at_nat
% 9.17/5.31 = ( ^ [A5: multis2468970476368604999at_nat,B4: multis2468970476368604999at_nat] : ( plus_p7104986032573967614at_nat @ B4 @ A5 ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_345_ab__semigroup__add__class_Oadd_Ocommute,axiom,
% 9.17/5.31 ( plus_plus_rat
% 9.17/5.31 = ( ^ [A5: rat,B4: rat] : ( plus_plus_rat @ B4 @ A5 ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_346_ab__semigroup__add__class_Oadd_Ocommute,axiom,
% 9.17/5.31 ( plus_plus_nat
% 9.17/5.31 = ( ^ [A5: nat,B4: nat] : ( plus_plus_nat @ B4 @ A5 ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_347_ab__semigroup__add__class_Oadd_Ocommute,axiom,
% 9.17/5.31 ( plus_plus_int
% 9.17/5.31 = ( ^ [A5: int,B4: int] : ( plus_plus_int @ B4 @ A5 ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_348_add_Oright__cancel,axiom,
% 9.17/5.31 ! [B: rat,A: rat,C: rat] :
% 9.17/5.31 ( ( ( plus_plus_rat @ B @ A )
% 9.17/5.31 = ( plus_plus_rat @ C @ A ) )
% 9.17/5.31 = ( B = C ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_349_add_Oright__cancel,axiom,
% 9.17/5.31 ! [B: int,A: int,C: int] :
% 9.17/5.31 ( ( ( plus_plus_int @ B @ A )
% 9.17/5.31 = ( plus_plus_int @ C @ A ) )
% 9.17/5.31 = ( B = C ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_350_add_Oleft__cancel,axiom,
% 9.17/5.31 ! [A: rat,B: rat,C: rat] :
% 9.17/5.31 ( ( ( plus_plus_rat @ A @ B )
% 9.17/5.31 = ( plus_plus_rat @ A @ C ) )
% 9.17/5.31 = ( B = C ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_351_add_Oleft__cancel,axiom,
% 9.17/5.31 ! [A: int,B: int,C: int] :
% 9.17/5.31 ( ( ( plus_plus_int @ A @ B )
% 9.17/5.31 = ( plus_plus_int @ A @ C ) )
% 9.17/5.31 = ( B = C ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_352_add_Oassoc,axiom,
% 9.17/5.31 ! [A: multis2468970476368604999at_nat,B: multis2468970476368604999at_nat,C: multis2468970476368604999at_nat] :
% 9.17/5.31 ( ( plus_p7104986032573967614at_nat @ ( plus_p7104986032573967614at_nat @ A @ B ) @ C )
% 9.17/5.31 = ( plus_p7104986032573967614at_nat @ A @ ( plus_p7104986032573967614at_nat @ B @ C ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_353_add_Oassoc,axiom,
% 9.17/5.31 ! [A: rat,B: rat,C: rat] :
% 9.17/5.31 ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 9.17/5.31 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_354_add_Oassoc,axiom,
% 9.17/5.31 ! [A: nat,B: nat,C: nat] :
% 9.17/5.31 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 9.17/5.31 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_355_add_Oassoc,axiom,
% 9.17/5.31 ! [A: int,B: int,C: int] :
% 9.17/5.31 ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 9.17/5.31 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_356_group__cancel_Oadd2,axiom,
% 9.17/5.31 ! [B5: multis2468970476368604999at_nat,K: multis2468970476368604999at_nat,B: multis2468970476368604999at_nat,A: multis2468970476368604999at_nat] :
% 9.17/5.31 ( ( B5
% 9.17/5.31 = ( plus_p7104986032573967614at_nat @ K @ B ) )
% 9.17/5.31 => ( ( plus_p7104986032573967614at_nat @ A @ B5 )
% 9.17/5.31 = ( plus_p7104986032573967614at_nat @ K @ ( plus_p7104986032573967614at_nat @ A @ B ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_357_group__cancel_Oadd2,axiom,
% 9.17/5.31 ! [B5: rat,K: rat,B: rat,A: rat] :
% 9.17/5.31 ( ( B5
% 9.17/5.31 = ( plus_plus_rat @ K @ B ) )
% 9.17/5.31 => ( ( plus_plus_rat @ A @ B5 )
% 9.17/5.31 = ( plus_plus_rat @ K @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_358_group__cancel_Oadd2,axiom,
% 9.17/5.31 ! [B5: nat,K: nat,B: nat,A: nat] :
% 9.17/5.31 ( ( B5
% 9.17/5.31 = ( plus_plus_nat @ K @ B ) )
% 9.17/5.31 => ( ( plus_plus_nat @ A @ B5 )
% 9.17/5.31 = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_359_group__cancel_Oadd2,axiom,
% 9.17/5.31 ! [B5: int,K: int,B: int,A: int] :
% 9.17/5.31 ( ( B5
% 9.17/5.31 = ( plus_plus_int @ K @ B ) )
% 9.17/5.31 => ( ( plus_plus_int @ A @ B5 )
% 9.17/5.31 = ( plus_plus_int @ K @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_360_group__cancel_Oadd1,axiom,
% 9.17/5.31 ! [A2: multis2468970476368604999at_nat,K: multis2468970476368604999at_nat,A: multis2468970476368604999at_nat,B: multis2468970476368604999at_nat] :
% 9.17/5.31 ( ( A2
% 9.17/5.31 = ( plus_p7104986032573967614at_nat @ K @ A ) )
% 9.17/5.31 => ( ( plus_p7104986032573967614at_nat @ A2 @ B )
% 9.17/5.31 = ( plus_p7104986032573967614at_nat @ K @ ( plus_p7104986032573967614at_nat @ A @ B ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_361_group__cancel_Oadd1,axiom,
% 9.17/5.31 ! [A2: rat,K: rat,A: rat,B: rat] :
% 9.17/5.31 ( ( A2
% 9.17/5.31 = ( plus_plus_rat @ K @ A ) )
% 9.17/5.31 => ( ( plus_plus_rat @ A2 @ B )
% 9.17/5.31 = ( plus_plus_rat @ K @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_362_group__cancel_Oadd1,axiom,
% 9.17/5.31 ! [A2: nat,K: nat,A: nat,B: nat] :
% 9.17/5.31 ( ( A2
% 9.17/5.31 = ( plus_plus_nat @ K @ A ) )
% 9.17/5.31 => ( ( plus_plus_nat @ A2 @ B )
% 9.17/5.31 = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_363_group__cancel_Oadd1,axiom,
% 9.17/5.31 ! [A2: int,K: int,A: int,B: int] :
% 9.17/5.31 ( ( A2
% 9.17/5.31 = ( plus_plus_int @ K @ A ) )
% 9.17/5.31 => ( ( plus_plus_int @ A2 @ B )
% 9.17/5.31 = ( plus_plus_int @ K @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_364_add__mono__thms__linordered__semiring_I4_J,axiom,
% 9.17/5.31 ! [I: rat,J: rat,K: rat,L: rat] :
% 9.17/5.31 ( ( ( I = J )
% 9.17/5.31 & ( K = L ) )
% 9.17/5.31 => ( ( plus_plus_rat @ I @ K )
% 9.17/5.31 = ( plus_plus_rat @ J @ L ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_365_add__mono__thms__linordered__semiring_I4_J,axiom,
% 9.17/5.31 ! [I: nat,J: nat,K: nat,L: nat] :
% 9.17/5.31 ( ( ( I = J )
% 9.17/5.31 & ( K = L ) )
% 9.17/5.31 => ( ( plus_plus_nat @ I @ K )
% 9.17/5.31 = ( plus_plus_nat @ J @ L ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_366_add__mono__thms__linordered__semiring_I4_J,axiom,
% 9.17/5.31 ! [I: int,J: int,K: int,L: int] :
% 9.17/5.31 ( ( ( I = J )
% 9.17/5.31 & ( K = L ) )
% 9.17/5.31 => ( ( plus_plus_int @ I @ K )
% 9.17/5.31 = ( plus_plus_int @ J @ L ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_367_Heap_Oexhaust,axiom,
% 9.17/5.31 ! [Y: heap_T5738788834812785303t_unit] :
% 9.17/5.31 ~ ! [X4: heap_e7401611519738050253t_unit > option8956607266484857688it_nat] :
% 9.17/5.31 ( Y
% 9.17/5.31 != ( heap_T6183433275982383450t_unit @ X4 ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_368_execute_Osimps,axiom,
% 9.17/5.31 ! [F: heap_e7401611519738050253t_unit > option3216581401566546698it_nat] :
% 9.17/5.31 ( ( heap_T5591663578999710211rray_a @ ( heap_T1488828001306802186rray_a @ F ) )
% 9.17/5.31 = F ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_369_execute_Osimps,axiom,
% 9.17/5.31 ! [F: heap_e7401611519738050253t_unit > option8956607266484857688it_nat] :
% 9.17/5.31 ( ( heap_T875086893843062177t_unit @ ( heap_T6183433275982383450t_unit @ F ) )
% 9.17/5.31 = F ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_370_option_Osimps_I5_J,axiom,
% 9.17/5.31 ! [F1: int,F22: num > int,X2: num] :
% 9.17/5.31 ( ( case_option_int_num @ F1 @ F22 @ ( some_num @ X2 ) )
% 9.17/5.31 = ( F22 @ X2 ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_371_option_Osimps_I5_J,axiom,
% 9.17/5.31 ! [F1: option_num,F22: num > option_num,X2: num] :
% 9.17/5.31 ( ( case_o6005452278849405969um_num @ F1 @ F22 @ ( some_num @ X2 ) )
% 9.17/5.31 = ( F22 @ X2 ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_372_option_Osimps_I5_J,axiom,
% 9.17/5.31 ! [F1: num,F22: num > num,X2: num] :
% 9.17/5.31 ( ( case_option_num_num @ F1 @ F22 @ ( some_num @ X2 ) )
% 9.17/5.31 = ( F22 @ X2 ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_373_option_Osimps_I4_J,axiom,
% 9.17/5.31 ! [F1: int,F22: num > int] :
% 9.17/5.31 ( ( case_option_int_num @ F1 @ F22 @ none_num )
% 9.17/5.31 = F1 ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_374_option_Osimps_I4_J,axiom,
% 9.17/5.31 ! [F1: option_num,F22: num > option_num] :
% 9.17/5.31 ( ( case_o6005452278849405969um_num @ F1 @ F22 @ none_num )
% 9.17/5.31 = F1 ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_375_option_Osimps_I4_J,axiom,
% 9.17/5.31 ! [F1: num,F22: num > num] :
% 9.17/5.31 ( ( case_option_num_num @ F1 @ F22 @ none_num )
% 9.17/5.31 = F1 ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_376_option_Ocase__eq__if,axiom,
% 9.17/5.31 ( case_option_int_num
% 9.17/5.31 = ( ^ [F12: int,F23: num > int,Option3: option_num] : ( if_int @ ( Option3 = none_num ) @ F12 @ ( F23 @ ( the_num @ Option3 ) ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_377_option_Ocase__eq__if,axiom,
% 9.17/5.31 ( case_o6005452278849405969um_num
% 9.17/5.31 = ( ^ [F12: option_num,F23: num > option_num,Option3: option_num] : ( if_option_num @ ( Option3 = none_num ) @ F12 @ ( F23 @ ( the_num @ Option3 ) ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_378_option_Ocase__eq__if,axiom,
% 9.17/5.31 ( case_option_num_num
% 9.17/5.31 = ( ^ [F12: num,F23: num > num,Option3: option_num] : ( if_num @ ( Option3 = none_num ) @ F12 @ ( F23 @ ( the_num @ Option3 ) ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_379_accp_Ocases,axiom,
% 9.17/5.31 ! [R2: product_prod_nat_nat > product_prod_nat_nat > $o,A: product_prod_nat_nat] :
% 9.17/5.31 ( ( accp_P4275260045618599050at_nat @ R2 @ A )
% 9.17/5.31 => ! [Y6: product_prod_nat_nat] :
% 9.17/5.31 ( ( R2 @ Y6 @ A )
% 9.17/5.31 => ( accp_P4275260045618599050at_nat @ R2 @ Y6 ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_380_accp_Ocases,axiom,
% 9.17/5.31 ! [R2: product_prod_int_int > product_prod_int_int > $o,A: product_prod_int_int] :
% 9.17/5.31 ( ( accp_P1096762738010456898nt_int @ R2 @ A )
% 9.17/5.31 => ! [Y6: product_prod_int_int] :
% 9.17/5.31 ( ( R2 @ Y6 @ A )
% 9.17/5.31 => ( accp_P1096762738010456898nt_int @ R2 @ Y6 ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_381_accp_Ocases,axiom,
% 9.17/5.31 ! [R2: produc2732055786443039994et_nat > produc2732055786443039994et_nat > $o,A: produc2732055786443039994et_nat] :
% 9.17/5.31 ( ( accp_P1862375125659990705et_nat @ R2 @ A )
% 9.17/5.31 => ! [Y6: produc2732055786443039994et_nat] :
% 9.17/5.31 ( ( R2 @ Y6 @ A )
% 9.17/5.31 => ( accp_P1862375125659990705et_nat @ R2 @ Y6 ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_382_accp_Ocases,axiom,
% 9.17/5.31 ! [R2: list_nat > list_nat > $o,A: list_nat] :
% 9.17/5.31 ( ( accp_list_nat @ R2 @ A )
% 9.17/5.31 => ! [Y6: list_nat] :
% 9.17/5.31 ( ( R2 @ Y6 @ A )
% 9.17/5.31 => ( accp_list_nat @ R2 @ Y6 ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_383_accp_Ocases,axiom,
% 9.17/5.31 ! [R2: nat > nat > $o,A: nat] :
% 9.17/5.31 ( ( accp_nat @ R2 @ A )
% 9.17/5.31 => ! [Y6: nat] :
% 9.17/5.31 ( ( R2 @ Y6 @ A )
% 9.17/5.31 => ( accp_nat @ R2 @ Y6 ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_384_accp_Osimps,axiom,
% 9.17/5.31 ( accp_P4275260045618599050at_nat
% 9.17/5.31 = ( ^ [R3: product_prod_nat_nat > product_prod_nat_nat > $o,A5: product_prod_nat_nat] :
% 9.17/5.31 ? [X3: product_prod_nat_nat] :
% 9.17/5.31 ( ( A5 = X3 )
% 9.17/5.31 & ! [Y3: product_prod_nat_nat] :
% 9.17/5.31 ( ( R3 @ Y3 @ X3 )
% 9.17/5.31 => ( accp_P4275260045618599050at_nat @ R3 @ Y3 ) ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_385_accp_Osimps,axiom,
% 9.17/5.31 ( accp_P1096762738010456898nt_int
% 9.17/5.31 = ( ^ [R3: product_prod_int_int > product_prod_int_int > $o,A5: product_prod_int_int] :
% 9.17/5.31 ? [X3: product_prod_int_int] :
% 9.17/5.31 ( ( A5 = X3 )
% 9.17/5.31 & ! [Y3: product_prod_int_int] :
% 9.17/5.31 ( ( R3 @ Y3 @ X3 )
% 9.17/5.31 => ( accp_P1096762738010456898nt_int @ R3 @ Y3 ) ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_386_accp_Osimps,axiom,
% 9.17/5.31 ( accp_P1862375125659990705et_nat
% 9.17/5.31 = ( ^ [R3: produc2732055786443039994et_nat > produc2732055786443039994et_nat > $o,A5: produc2732055786443039994et_nat] :
% 9.17/5.31 ? [X3: produc2732055786443039994et_nat] :
% 9.17/5.31 ( ( A5 = X3 )
% 9.17/5.31 & ! [Y3: produc2732055786443039994et_nat] :
% 9.17/5.31 ( ( R3 @ Y3 @ X3 )
% 9.17/5.31 => ( accp_P1862375125659990705et_nat @ R3 @ Y3 ) ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_387_accp_Osimps,axiom,
% 9.17/5.31 ( accp_list_nat
% 9.17/5.31 = ( ^ [R3: list_nat > list_nat > $o,A5: list_nat] :
% 9.17/5.31 ? [X3: list_nat] :
% 9.17/5.31 ( ( A5 = X3 )
% 9.17/5.31 & ! [Y3: list_nat] :
% 9.17/5.31 ( ( R3 @ Y3 @ X3 )
% 9.17/5.31 => ( accp_list_nat @ R3 @ Y3 ) ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_388_accp_Osimps,axiom,
% 9.17/5.31 ( accp_nat
% 9.17/5.31 = ( ^ [R3: nat > nat > $o,A5: nat] :
% 9.17/5.31 ? [X3: nat] :
% 9.17/5.31 ( ( A5 = X3 )
% 9.17/5.31 & ! [Y3: nat] :
% 9.17/5.31 ( ( R3 @ Y3 @ X3 )
% 9.17/5.31 => ( accp_nat @ R3 @ Y3 ) ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_389_accpI,axiom,
% 9.17/5.31 ! [R2: product_prod_nat_nat > product_prod_nat_nat > $o,X: product_prod_nat_nat] :
% 9.17/5.31 ( ! [Y5: product_prod_nat_nat] :
% 9.17/5.31 ( ( R2 @ Y5 @ X )
% 9.17/5.31 => ( accp_P4275260045618599050at_nat @ R2 @ Y5 ) )
% 9.17/5.31 => ( accp_P4275260045618599050at_nat @ R2 @ X ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_390_accpI,axiom,
% 9.17/5.31 ! [R2: product_prod_int_int > product_prod_int_int > $o,X: product_prod_int_int] :
% 9.17/5.31 ( ! [Y5: product_prod_int_int] :
% 9.17/5.31 ( ( R2 @ Y5 @ X )
% 9.17/5.31 => ( accp_P1096762738010456898nt_int @ R2 @ Y5 ) )
% 9.17/5.31 => ( accp_P1096762738010456898nt_int @ R2 @ X ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_391_accpI,axiom,
% 9.17/5.31 ! [R2: produc2732055786443039994et_nat > produc2732055786443039994et_nat > $o,X: produc2732055786443039994et_nat] :
% 9.17/5.31 ( ! [Y5: produc2732055786443039994et_nat] :
% 9.17/5.31 ( ( R2 @ Y5 @ X )
% 9.17/5.31 => ( accp_P1862375125659990705et_nat @ R2 @ Y5 ) )
% 9.17/5.31 => ( accp_P1862375125659990705et_nat @ R2 @ X ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_392_accpI,axiom,
% 9.17/5.31 ! [R2: list_nat > list_nat > $o,X: list_nat] :
% 9.17/5.31 ( ! [Y5: list_nat] :
% 9.17/5.31 ( ( R2 @ Y5 @ X )
% 9.17/5.31 => ( accp_list_nat @ R2 @ Y5 ) )
% 9.17/5.31 => ( accp_list_nat @ R2 @ X ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_393_accpI,axiom,
% 9.17/5.31 ! [R2: nat > nat > $o,X: nat] :
% 9.17/5.31 ( ! [Y5: nat] :
% 9.17/5.31 ( ( R2 @ Y5 @ X )
% 9.17/5.31 => ( accp_nat @ R2 @ Y5 ) )
% 9.17/5.31 => ( accp_nat @ R2 @ X ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_394_accp__induct,axiom,
% 9.17/5.31 ! [R2: product_prod_nat_nat > product_prod_nat_nat > $o,A: product_prod_nat_nat,P: product_prod_nat_nat > $o] :
% 9.17/5.31 ( ( accp_P4275260045618599050at_nat @ R2 @ A )
% 9.17/5.31 => ( ! [X4: product_prod_nat_nat] :
% 9.17/5.31 ( ( accp_P4275260045618599050at_nat @ R2 @ X4 )
% 9.17/5.31 => ( ! [Y6: product_prod_nat_nat] :
% 9.17/5.31 ( ( R2 @ Y6 @ X4 )
% 9.17/5.31 => ( P @ Y6 ) )
% 9.17/5.31 => ( P @ X4 ) ) )
% 9.17/5.31 => ( P @ A ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_395_accp__induct,axiom,
% 9.17/5.31 ! [R2: product_prod_int_int > product_prod_int_int > $o,A: product_prod_int_int,P: product_prod_int_int > $o] :
% 9.17/5.31 ( ( accp_P1096762738010456898nt_int @ R2 @ A )
% 9.17/5.31 => ( ! [X4: product_prod_int_int] :
% 9.17/5.31 ( ( accp_P1096762738010456898nt_int @ R2 @ X4 )
% 9.17/5.31 => ( ! [Y6: product_prod_int_int] :
% 9.17/5.31 ( ( R2 @ Y6 @ X4 )
% 9.17/5.31 => ( P @ Y6 ) )
% 9.17/5.31 => ( P @ X4 ) ) )
% 9.17/5.31 => ( P @ A ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_396_accp__induct,axiom,
% 9.17/5.31 ! [R2: produc2732055786443039994et_nat > produc2732055786443039994et_nat > $o,A: produc2732055786443039994et_nat,P: produc2732055786443039994et_nat > $o] :
% 9.17/5.31 ( ( accp_P1862375125659990705et_nat @ R2 @ A )
% 9.17/5.31 => ( ! [X4: produc2732055786443039994et_nat] :
% 9.17/5.31 ( ( accp_P1862375125659990705et_nat @ R2 @ X4 )
% 9.17/5.31 => ( ! [Y6: produc2732055786443039994et_nat] :
% 9.17/5.31 ( ( R2 @ Y6 @ X4 )
% 9.17/5.31 => ( P @ Y6 ) )
% 9.17/5.31 => ( P @ X4 ) ) )
% 9.17/5.31 => ( P @ A ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_397_accp__induct,axiom,
% 9.17/5.31 ! [R2: list_nat > list_nat > $o,A: list_nat,P: list_nat > $o] :
% 9.17/5.31 ( ( accp_list_nat @ R2 @ A )
% 9.17/5.31 => ( ! [X4: list_nat] :
% 9.17/5.31 ( ( accp_list_nat @ R2 @ X4 )
% 9.17/5.31 => ( ! [Y6: list_nat] :
% 9.17/5.31 ( ( R2 @ Y6 @ X4 )
% 9.17/5.31 => ( P @ Y6 ) )
% 9.17/5.31 => ( P @ X4 ) ) )
% 9.17/5.31 => ( P @ A ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_398_accp__induct,axiom,
% 9.17/5.31 ! [R2: nat > nat > $o,A: nat,P: nat > $o] :
% 9.17/5.31 ( ( accp_nat @ R2 @ A )
% 9.17/5.31 => ( ! [X4: nat] :
% 9.17/5.31 ( ( accp_nat @ R2 @ X4 )
% 9.17/5.31 => ( ! [Y6: nat] :
% 9.17/5.31 ( ( R2 @ Y6 @ X4 )
% 9.17/5.31 => ( P @ Y6 ) )
% 9.17/5.31 => ( P @ X4 ) ) )
% 9.17/5.31 => ( P @ A ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_399_accp__downward,axiom,
% 9.17/5.31 ! [R2: product_prod_nat_nat > product_prod_nat_nat > $o,B: product_prod_nat_nat,A: product_prod_nat_nat] :
% 9.17/5.31 ( ( accp_P4275260045618599050at_nat @ R2 @ B )
% 9.17/5.31 => ( ( R2 @ A @ B )
% 9.17/5.31 => ( accp_P4275260045618599050at_nat @ R2 @ A ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_400_accp__downward,axiom,
% 9.17/5.31 ! [R2: product_prod_int_int > product_prod_int_int > $o,B: product_prod_int_int,A: product_prod_int_int] :
% 9.17/5.31 ( ( accp_P1096762738010456898nt_int @ R2 @ B )
% 9.17/5.31 => ( ( R2 @ A @ B )
% 9.17/5.31 => ( accp_P1096762738010456898nt_int @ R2 @ A ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_401_accp__downward,axiom,
% 9.17/5.31 ! [R2: produc2732055786443039994et_nat > produc2732055786443039994et_nat > $o,B: produc2732055786443039994et_nat,A: produc2732055786443039994et_nat] :
% 9.17/5.31 ( ( accp_P1862375125659990705et_nat @ R2 @ B )
% 9.17/5.31 => ( ( R2 @ A @ B )
% 9.17/5.31 => ( accp_P1862375125659990705et_nat @ R2 @ A ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_402_accp__downward,axiom,
% 9.17/5.31 ! [R2: list_nat > list_nat > $o,B: list_nat,A: list_nat] :
% 9.17/5.31 ( ( accp_list_nat @ R2 @ B )
% 9.17/5.31 => ( ( R2 @ A @ B )
% 9.17/5.31 => ( accp_list_nat @ R2 @ A ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_403_accp__downward,axiom,
% 9.17/5.31 ! [R2: nat > nat > $o,B: nat,A: nat] :
% 9.17/5.31 ( ( accp_nat @ R2 @ B )
% 9.17/5.31 => ( ( R2 @ A @ B )
% 9.17/5.31 => ( accp_nat @ R2 @ A ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_404_not__accp__down,axiom,
% 9.17/5.31 ! [R4: product_prod_nat_nat > product_prod_nat_nat > $o,X: product_prod_nat_nat] :
% 9.17/5.31 ( ~ ( accp_P4275260045618599050at_nat @ R4 @ X )
% 9.17/5.31 => ~ ! [Z3: product_prod_nat_nat] :
% 9.17/5.31 ( ( R4 @ Z3 @ X )
% 9.17/5.31 => ( accp_P4275260045618599050at_nat @ R4 @ Z3 ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_405_not__accp__down,axiom,
% 9.17/5.31 ! [R4: product_prod_int_int > product_prod_int_int > $o,X: product_prod_int_int] :
% 9.17/5.31 ( ~ ( accp_P1096762738010456898nt_int @ R4 @ X )
% 9.17/5.31 => ~ ! [Z3: product_prod_int_int] :
% 9.17/5.31 ( ( R4 @ Z3 @ X )
% 9.17/5.31 => ( accp_P1096762738010456898nt_int @ R4 @ Z3 ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_406_not__accp__down,axiom,
% 9.17/5.31 ! [R4: produc2732055786443039994et_nat > produc2732055786443039994et_nat > $o,X: produc2732055786443039994et_nat] :
% 9.17/5.31 ( ~ ( accp_P1862375125659990705et_nat @ R4 @ X )
% 9.17/5.31 => ~ ! [Z3: produc2732055786443039994et_nat] :
% 9.17/5.31 ( ( R4 @ Z3 @ X )
% 9.17/5.31 => ( accp_P1862375125659990705et_nat @ R4 @ Z3 ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_407_not__accp__down,axiom,
% 9.17/5.31 ! [R4: list_nat > list_nat > $o,X: list_nat] :
% 9.17/5.31 ( ~ ( accp_list_nat @ R4 @ X )
% 9.17/5.31 => ~ ! [Z3: list_nat] :
% 9.17/5.31 ( ( R4 @ Z3 @ X )
% 9.17/5.31 => ( accp_list_nat @ R4 @ Z3 ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_408_not__accp__down,axiom,
% 9.17/5.31 ! [R4: nat > nat > $o,X: nat] :
% 9.17/5.31 ( ~ ( accp_nat @ R4 @ X )
% 9.17/5.31 => ~ ! [Z3: nat] :
% 9.17/5.31 ( ( R4 @ Z3 @ X )
% 9.17/5.31 => ( accp_nat @ R4 @ Z3 ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_409_accp__induct__rule,axiom,
% 9.17/5.31 ! [R2: product_prod_nat_nat > product_prod_nat_nat > $o,A: product_prod_nat_nat,P: product_prod_nat_nat > $o] :
% 9.17/5.31 ( ( accp_P4275260045618599050at_nat @ R2 @ A )
% 9.17/5.31 => ( ! [X4: product_prod_nat_nat] :
% 9.17/5.31 ( ( accp_P4275260045618599050at_nat @ R2 @ X4 )
% 9.17/5.31 => ( ! [Y6: product_prod_nat_nat] :
% 9.17/5.31 ( ( R2 @ Y6 @ X4 )
% 9.17/5.31 => ( P @ Y6 ) )
% 9.17/5.31 => ( P @ X4 ) ) )
% 9.17/5.31 => ( P @ A ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_410_accp__induct__rule,axiom,
% 9.17/5.31 ! [R2: product_prod_int_int > product_prod_int_int > $o,A: product_prod_int_int,P: product_prod_int_int > $o] :
% 9.17/5.31 ( ( accp_P1096762738010456898nt_int @ R2 @ A )
% 9.17/5.31 => ( ! [X4: product_prod_int_int] :
% 9.17/5.31 ( ( accp_P1096762738010456898nt_int @ R2 @ X4 )
% 9.17/5.31 => ( ! [Y6: product_prod_int_int] :
% 9.17/5.31 ( ( R2 @ Y6 @ X4 )
% 9.17/5.31 => ( P @ Y6 ) )
% 9.17/5.31 => ( P @ X4 ) ) )
% 9.17/5.31 => ( P @ A ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_411_accp__induct__rule,axiom,
% 9.17/5.31 ! [R2: produc2732055786443039994et_nat > produc2732055786443039994et_nat > $o,A: produc2732055786443039994et_nat,P: produc2732055786443039994et_nat > $o] :
% 9.17/5.31 ( ( accp_P1862375125659990705et_nat @ R2 @ A )
% 9.17/5.31 => ( ! [X4: produc2732055786443039994et_nat] :
% 9.17/5.31 ( ( accp_P1862375125659990705et_nat @ R2 @ X4 )
% 9.17/5.31 => ( ! [Y6: produc2732055786443039994et_nat] :
% 9.17/5.31 ( ( R2 @ Y6 @ X4 )
% 9.17/5.31 => ( P @ Y6 ) )
% 9.17/5.31 => ( P @ X4 ) ) )
% 9.17/5.31 => ( P @ A ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_412_accp__induct__rule,axiom,
% 9.17/5.31 ! [R2: list_nat > list_nat > $o,A: list_nat,P: list_nat > $o] :
% 9.17/5.31 ( ( accp_list_nat @ R2 @ A )
% 9.17/5.31 => ( ! [X4: list_nat] :
% 9.17/5.31 ( ( accp_list_nat @ R2 @ X4 )
% 9.17/5.31 => ( ! [Y6: list_nat] :
% 9.17/5.31 ( ( R2 @ Y6 @ X4 )
% 9.17/5.31 => ( P @ Y6 ) )
% 9.17/5.31 => ( P @ X4 ) ) )
% 9.17/5.31 => ( P @ A ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_413_accp__induct__rule,axiom,
% 9.17/5.31 ! [R2: nat > nat > $o,A: nat,P: nat > $o] :
% 9.17/5.31 ( ( accp_nat @ R2 @ A )
% 9.17/5.31 => ( ! [X4: nat] :
% 9.17/5.31 ( ( accp_nat @ R2 @ X4 )
% 9.17/5.31 => ( ! [Y6: nat] :
% 9.17/5.31 ( ( R2 @ Y6 @ X4 )
% 9.17/5.31 => ( P @ Y6 ) )
% 9.17/5.31 => ( P @ X4 ) ) )
% 9.17/5.31 => ( P @ A ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_414_fun_Omap__comp,axiom,
% 9.17/5.31 ! [G: num > num,F: nat > num,V: int > nat] :
% 9.17/5.31 ( ( comp_num_num_int @ G @ ( comp_nat_num_int @ F @ V ) )
% 9.17/5.31 = ( comp_nat_num_int @ ( comp_num_num_nat @ G @ F ) @ V ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_415_fun_Omap__comp,axiom,
% 9.17/5.31 ! [G: code_integer > code_integer,F: num > code_integer,V: num > num] :
% 9.17/5.31 ( ( comp_C3531382070062128313er_num @ G @ ( comp_n6909714581898973814er_num @ F @ V ) )
% 9.17/5.31 = ( comp_n6909714581898973814er_num @ ( comp_C3531382070062128313er_num @ G @ F ) @ V ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_416_fun_Omap__comp,axiom,
% 9.17/5.31 ! [G: code_integer > code_integer,F: code_integer > code_integer,V: num > code_integer] :
% 9.17/5.31 ( ( comp_C3531382070062128313er_num @ G @ ( comp_C3531382070062128313er_num @ F @ V ) )
% 9.17/5.31 = ( comp_C3531382070062128313er_num @ ( comp_C7449957260575251196nteger @ G @ F ) @ V ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_417_fun_Omap__comp,axiom,
% 9.17/5.31 ! [G: nat > num,F: int > nat,V: int > int] :
% 9.17/5.31 ( ( comp_nat_num_int @ G @ ( comp_int_nat_int @ F @ V ) )
% 9.17/5.31 = ( comp_int_num_int @ ( comp_nat_num_int @ G @ F ) @ V ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_418_fun_Omap__comp,axiom,
% 9.17/5.31 ! [G: nat > num,F: nat > nat,V: int > nat] :
% 9.17/5.31 ( ( comp_nat_num_int @ G @ ( comp_nat_nat_int @ F @ V ) )
% 9.17/5.31 = ( comp_nat_num_int @ ( comp_nat_num_nat @ G @ F ) @ V ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_419_fun_Omap__comp,axiom,
% 9.17/5.31 ! [G: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,F: code_integer > code_integer,V: num > code_integer] :
% 9.17/5.31 ( ( comp_C6617437204949736321er_num @ G @ ( comp_C3531382070062128313er_num @ F @ V ) )
% 9.17/5.31 = ( comp_C6617437204949736321er_num @ ( comp_C1593894019821074884nteger @ G @ F ) @ V ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_420_fun_Omap__comp,axiom,
% 9.17/5.31 ! [G: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,F: code_integer > code_integer,V: code_integer > code_integer] :
% 9.17/5.31 ( ( comp_C1593894019821074884nteger @ G @ ( comp_C7449957260575251196nteger @ F @ V ) )
% 9.17/5.31 = ( comp_C1593894019821074884nteger @ ( comp_C1593894019821074884nteger @ G @ F ) @ V ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_421_fun_Omap__comp,axiom,
% 9.17/5.31 ! [G: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,F: ( code_integer > code_integer ) > code_integer,V: code_integer > code_integer > code_integer] :
% 9.17/5.31 ( ( comp_C1593894019821074884nteger @ G @ ( comp_C5076291335850163704nteger @ F @ V ) )
% 9.17/5.31 = ( comp_C8797469213163452608nteger @ ( comp_C95226695241045696nteger @ G @ F ) @ V ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_422_fun_Omap__comp,axiom,
% 9.17/5.31 ! [G: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,F: code_integer > code_integer > code_integer,V: code_integer > code_integer] :
% 9.17/5.31 ( ( comp_C8797469213163452608nteger @ G @ ( comp_C2931745410781319416nteger @ F @ V ) )
% 9.17/5.31 = ( comp_C1593894019821074884nteger @ ( comp_C8797469213163452608nteger @ G @ F ) @ V ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_423_fun_Omap__comp,axiom,
% 9.17/5.31 ! [G: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,F: ( code_integer > code_integer ) > code_integer > code_integer,V: code_integer > code_integer > code_integer] :
% 9.17/5.31 ( ( comp_C8797469213163452608nteger @ G @ ( comp_C2822359487432382964nteger @ F @ V ) )
% 9.17/5.31 = ( comp_C8797469213163452608nteger @ ( comp_C3983183376822107068nteger @ G @ F ) @ V ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_424_comp__cong,axiom,
% 9.17/5.31 ! [F: code_integer > code_integer,G: num > code_integer,X: num,F4: code_integer > code_integer,G3: num > code_integer,X7: num] :
% 9.17/5.31 ( ( ( F @ ( G @ X ) )
% 9.17/5.31 = ( F4 @ ( G3 @ X7 ) ) )
% 9.17/5.31 => ( ( comp_C3531382070062128313er_num @ F @ G @ X )
% 9.17/5.31 = ( comp_C3531382070062128313er_num @ F4 @ G3 @ X7 ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_425_comp__cong,axiom,
% 9.17/5.31 ! [F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer,X: code_integer,F4: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,G3: code_integer > code_integer,X7: code_integer] :
% 9.17/5.31 ( ( ( F @ ( G @ X ) )
% 9.17/5.31 = ( F4 @ ( G3 @ X7 ) ) )
% 9.17/5.31 => ( ( comp_C1593894019821074884nteger @ F @ G @ X )
% 9.17/5.31 = ( comp_C1593894019821074884nteger @ F4 @ G3 @ X7 ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_426_comp__cong,axiom,
% 9.17/5.31 ! [F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer,X: code_integer,F4: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G3: code_integer > code_integer > code_integer,X7: code_integer] :
% 9.17/5.31 ( ( ( F @ ( G @ X ) )
% 9.17/5.31 = ( F4 @ ( G3 @ X7 ) ) )
% 9.17/5.31 => ( ( comp_C1593894019821074884nteger @ F @ G @ X )
% 9.17/5.31 = ( comp_C8797469213163452608nteger @ F4 @ G3 @ X7 ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_427_comp__cong,axiom,
% 9.17/5.31 ! [F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer > code_integer,X: code_integer,F4: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,G3: code_integer > code_integer,X7: code_integer] :
% 9.17/5.31 ( ( ( F @ ( G @ X ) )
% 9.17/5.31 = ( F4 @ ( G3 @ X7 ) ) )
% 9.17/5.31 => ( ( comp_C8797469213163452608nteger @ F @ G @ X )
% 9.17/5.31 = ( comp_C1593894019821074884nteger @ F4 @ G3 @ X7 ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_428_comp__cong,axiom,
% 9.17/5.31 ! [F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer > code_integer,X: code_integer,F4: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G3: code_integer > code_integer > code_integer,X7: code_integer] :
% 9.17/5.31 ( ( ( F @ ( G @ X ) )
% 9.17/5.31 = ( F4 @ ( G3 @ X7 ) ) )
% 9.17/5.31 => ( ( comp_C8797469213163452608nteger @ F @ G @ X )
% 9.17/5.31 = ( comp_C8797469213163452608nteger @ F4 @ G3 @ X7 ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_429_comp__cong,axiom,
% 9.17/5.31 ! [F: nat > num,G: int > nat,X: int,F4: nat > num,G3: int > nat,X7: int] :
% 9.17/5.31 ( ( ( F @ ( G @ X ) )
% 9.17/5.31 = ( F4 @ ( G3 @ X7 ) ) )
% 9.17/5.31 => ( ( comp_nat_num_int @ F @ G @ X )
% 9.17/5.31 = ( comp_nat_num_int @ F4 @ G3 @ X7 ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_430_curryI,axiom,
% 9.17/5.31 ! [F: produc1908205239877642774nteger > $o,A: produc6241069584506657477e_term > option6357759511663192854e_term,B: produc8923325533196201883nteger] :
% 9.17/5.31 ( ( F @ ( produc8603105652947943368nteger @ A @ B ) )
% 9.17/5.31 => ( produc1217013493180205570eger_o @ F @ A @ B ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_431_curryI,axiom,
% 9.17/5.31 ! [F: produc3925858234332021118et_nat > $o,A: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat] :
% 9.17/5.31 ( ( F @ ( produc5001842942810119800et_nat @ A @ B ) )
% 9.17/5.31 => ( produc6216949301066131538_nat_o @ F @ A @ B ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_432_curryI,axiom,
% 9.17/5.31 ! [F: produc2732055786443039994et_nat > $o,A: produc3658429121746597890et_nat > $o,B: produc3925858234332021118et_nat] :
% 9.17/5.31 ( ( F @ ( produc2245416461498447860et_nat @ A @ B ) )
% 9.17/5.31 => ( produc5101573711933517782_nat_o @ F @ A @ B ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_433_curryI,axiom,
% 9.17/5.31 ! [F: produc2285326912895808259nt_int > $o,A: produc8551481072490612790e_term > option6357759511663192854e_term,B: product_prod_int_int] :
% 9.17/5.31 ( ( F @ ( produc5700946648718959541nt_int @ A @ B ) )
% 9.17/5.31 => ( produc730925184835016917_int_o @ F @ A @ B ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_434_curryI,axiom,
% 9.17/5.31 ! [F: produc7773217078559923341nt_int > $o,A: int > option6357759511663192854e_term,B: product_prod_int_int] :
% 9.17/5.31 ( ( F @ ( produc4305682042979456191nt_int @ A @ B ) )
% 9.17/5.31 => ( produc9098658269643458507_int_o @ F @ A @ B ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_435_curryE,axiom,
% 9.17/5.31 ! [F: produc1908205239877642774nteger > $o,A: produc6241069584506657477e_term > option6357759511663192854e_term,B: produc8923325533196201883nteger] :
% 9.17/5.31 ( ( produc1217013493180205570eger_o @ F @ A @ B )
% 9.17/5.31 => ( F @ ( produc8603105652947943368nteger @ A @ B ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_436_curryE,axiom,
% 9.17/5.31 ! [F: produc3925858234332021118et_nat > $o,A: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat] :
% 9.17/5.31 ( ( produc6216949301066131538_nat_o @ F @ A @ B )
% 9.17/5.31 => ( F @ ( produc5001842942810119800et_nat @ A @ B ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_437_curryE,axiom,
% 9.17/5.31 ! [F: produc2732055786443039994et_nat > $o,A: produc3658429121746597890et_nat > $o,B: produc3925858234332021118et_nat] :
% 9.17/5.31 ( ( produc5101573711933517782_nat_o @ F @ A @ B )
% 9.17/5.31 => ( F @ ( produc2245416461498447860et_nat @ A @ B ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_438_curryE,axiom,
% 9.17/5.31 ! [F: produc2285326912895808259nt_int > $o,A: produc8551481072490612790e_term > option6357759511663192854e_term,B: product_prod_int_int] :
% 9.17/5.31 ( ( produc730925184835016917_int_o @ F @ A @ B )
% 9.17/5.31 => ( F @ ( produc5700946648718959541nt_int @ A @ B ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_439_curryE,axiom,
% 9.17/5.31 ! [F: produc7773217078559923341nt_int > $o,A: int > option6357759511663192854e_term,B: product_prod_int_int] :
% 9.17/5.31 ( ( produc9098658269643458507_int_o @ F @ A @ B )
% 9.17/5.31 => ( F @ ( produc4305682042979456191nt_int @ A @ B ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_440_curryD,axiom,
% 9.17/5.31 ! [F: produc1908205239877642774nteger > $o,A: produc6241069584506657477e_term > option6357759511663192854e_term,B: produc8923325533196201883nteger] :
% 9.17/5.31 ( ( produc1217013493180205570eger_o @ F @ A @ B )
% 9.17/5.31 => ( F @ ( produc8603105652947943368nteger @ A @ B ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_441_curryD,axiom,
% 9.17/5.31 ! [F: produc3925858234332021118et_nat > $o,A: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat] :
% 9.17/5.31 ( ( produc6216949301066131538_nat_o @ F @ A @ B )
% 9.17/5.31 => ( F @ ( produc5001842942810119800et_nat @ A @ B ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_442_curryD,axiom,
% 9.17/5.31 ! [F: produc2732055786443039994et_nat > $o,A: produc3658429121746597890et_nat > $o,B: produc3925858234332021118et_nat] :
% 9.17/5.31 ( ( produc5101573711933517782_nat_o @ F @ A @ B )
% 9.17/5.31 => ( F @ ( produc2245416461498447860et_nat @ A @ B ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_443_curryD,axiom,
% 9.17/5.31 ! [F: produc2285326912895808259nt_int > $o,A: produc8551481072490612790e_term > option6357759511663192854e_term,B: product_prod_int_int] :
% 9.17/5.31 ( ( produc730925184835016917_int_o @ F @ A @ B )
% 9.17/5.31 => ( F @ ( produc5700946648718959541nt_int @ A @ B ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_444_curryD,axiom,
% 9.17/5.31 ! [F: produc7773217078559923341nt_int > $o,A: int > option6357759511663192854e_term,B: product_prod_int_int] :
% 9.17/5.31 ( ( produc9098658269643458507_int_o @ F @ A @ B )
% 9.17/5.31 => ( F @ ( produc4305682042979456191nt_int @ A @ B ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_445_in__lex__prod,axiom,
% 9.17/5.31 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,A4: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat,R2: set_Pr4329608150637261639at_nat,S: set_Pr4329608150637261639at_nat] :
% 9.17/5.31 ( ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ ( produc2922128104949294807at_nat @ A @ B ) @ ( produc2922128104949294807at_nat @ A4 @ B3 ) ) @ ( lex_pr8000699672184251119at_nat @ R2 @ S ) )
% 9.17/5.31 = ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ A4 ) @ R2 )
% 9.17/5.31 | ( ( A = A4 )
% 9.17/5.31 & ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ B @ B3 ) @ S ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_446_in__lex__prod,axiom,
% 9.17/5.31 ! [A: set_Pr1261947904930325089at_nat,B: nat,A4: set_Pr1261947904930325089at_nat,B3: nat,R2: set_Pr4329608150637261639at_nat,S: set_Pr1261947904930325089at_nat] :
% 9.17/5.31 ( ( member3480088626692287306at_nat @ ( produc3585720979125124569at_nat @ ( produc3149970401713881818at_nat @ A @ B ) @ ( produc3149970401713881818at_nat @ A4 @ B3 ) ) @ ( lex_pr1951919194703979714at_nat @ R2 @ S ) )
% 9.17/5.31 = ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ A4 ) @ R2 )
% 9.17/5.31 | ( ( A = A4 )
% 9.17/5.31 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ B @ B3 ) @ S ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_447_in__lex__prod,axiom,
% 9.17/5.31 ! [A: nat,B: set_Pr1261947904930325089at_nat,A4: nat,B3: set_Pr1261947904930325089at_nat,R2: set_Pr1261947904930325089at_nat,S: set_Pr4329608150637261639at_nat] :
% 9.17/5.31 ( ( member4107301959146914710at_nat @ ( produc8824474337961625893at_nat @ ( produc5463602008962177208at_nat @ A @ B ) @ ( produc5463602008962177208at_nat @ A4 @ B3 ) ) @ ( lex_pr4265550801952275104at_nat @ R2 @ S ) )
% 9.17/5.31 = ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ A4 ) @ R2 )
% 9.17/5.31 | ( ( A = A4 )
% 9.17/5.31 & ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ B @ B3 ) @ S ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_448_in__lex__prod,axiom,
% 9.17/5.31 ! [A: nat,B: nat,A4: nat,B3: nat,R2: set_Pr1261947904930325089at_nat,S: set_Pr1261947904930325089at_nat] :
% 9.17/5.31 ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A @ B ) @ ( product_Pair_nat_nat @ A4 @ B3 ) ) @ ( lex_prod_nat_nat @ R2 @ S ) )
% 9.17/5.31 = ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ A4 ) @ R2 )
% 9.17/5.31 | ( ( A = A4 )
% 9.17/5.31 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ B @ B3 ) @ S ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_449_in__lex__prod,axiom,
% 9.17/5.31 ! [A: produc6241069584506657477e_term > option6357759511663192854e_term,B: produc8923325533196201883nteger,A4: produc6241069584506657477e_term > option6357759511663192854e_term,B3: produc8923325533196201883nteger,R2: set_Pr6418322821503574069e_term,S: set_Pr5052581263052047815nteger] :
% 9.17/5.31 ( ( member2446009503569356342nteger @ ( produc7954516348491987909nteger @ ( produc8603105652947943368nteger @ A @ B ) @ ( produc8603105652947943368nteger @ A4 @ B3 ) ) @ ( lex_pr3763927252266284464nteger @ R2 @ S ) )
% 9.17/5.31 = ( ( member6786453453753086846e_term @ ( produc6915061378690470669e_term @ A @ A4 ) @ R2 )
% 9.17/5.31 | ( ( A = A4 )
% 9.17/5.31 & ( member335077259223437328nteger @ ( produc4911887526399440471nteger @ B @ B3 ) @ S ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_450_in__lex__prod,axiom,
% 9.17/5.31 ! [A: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat,A4: produc3658429121746597890et_nat > $o,B3: produc3658429121746597890et_nat,R2: set_Pr2161125870931222855_nat_o,S: set_Pr719794911490849221et_nat] :
% 9.17/5.31 ( ( member4763271486408492550et_nat @ ( produc8599840265553166229et_nat @ ( produc5001842942810119800et_nat @ A @ B ) @ ( produc5001842942810119800et_nat @ A4 @ B3 ) ) @ ( lex_pr5340572901959109728et_nat @ R2 @ S ) )
% 9.17/5.31 = ( ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ A @ A4 ) @ R2 )
% 9.17/5.31 | ( ( A = A4 )
% 9.17/5.31 & ( member6099555550032318734et_nat @ ( produc8199053930788261021et_nat @ B @ B3 ) @ S ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_451_in__lex__prod,axiom,
% 9.17/5.31 ! [A: produc3658429121746597890et_nat > $o,B: produc3925858234332021118et_nat,A4: produc3658429121746597890et_nat > $o,B3: produc3925858234332021118et_nat,R2: set_Pr2161125870931222855_nat_o,S: set_Pr7928877670098842301et_nat] :
% 9.17/5.31 ( ( member6341495586645257982et_nat @ ( produc1940133919992309389et_nat @ ( produc2245416461498447860et_nat @ A @ B ) @ ( produc2245416461498447860et_nat @ A4 @ B3 ) ) @ ( lex_pr4722427456421979612et_nat @ R2 @ S ) )
% 9.17/5.31 = ( ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ A @ A4 ) @ R2 )
% 9.17/5.31 | ( ( A = A4 )
% 9.17/5.31 & ( member4763271486408492550et_nat @ ( produc8599840265553166229et_nat @ B @ B3 ) @ S ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_452_in__lex__prod,axiom,
% 9.17/5.31 ! [A: produc8551481072490612790e_term > option6357759511663192854e_term,B: product_prod_int_int,A4: produc8551481072490612790e_term > option6357759511663192854e_term,B3: product_prod_int_int,R2: set_Pr4675205556198584599e_term,S: set_Pr2560585780119916871nt_int] :
% 9.17/5.31 ( ( member6582457606847315088nt_int @ ( produc7601053194514725023nt_int @ ( produc5700946648718959541nt_int @ A @ B ) @ ( produc5700946648718959541nt_int @ A4 @ B3 ) ) @ ( lex_pr4548132154224949661nt_int @ R2 @ S ) )
% 9.17/5.31 = ( ( member8796044733138646368e_term @ ( produc8124735558134971759e_term @ A @ A4 ) @ R2 )
% 9.17/5.31 | ( ( A = A4 )
% 9.17/5.31 & ( member8566619992076573584nt_int @ ( produc3646306378393792727nt_int @ B @ B3 ) @ S ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_453_in__lex__prod,axiom,
% 9.17/5.31 ! [A: int > option6357759511663192854e_term,B: product_prod_int_int,A4: int > option6357759511663192854e_term,B3: product_prod_int_int,R2: set_Pr7140365069852192003e_term,S: set_Pr2560585780119916871nt_int] :
% 9.17/5.31 ( ( member4085533954029916580nt_int @ ( produc8406175334058502835nt_int @ ( produc4305682042979456191nt_int @ A @ B ) @ ( produc4305682042979456191nt_int @ A4 @ B3 ) ) @ ( lex_pr7234932505866811047nt_int @ R2 @ S ) )
% 9.17/5.31 = ( ( member6538663773838357324e_term @ ( produc4510790414113558107e_term @ A @ A4 ) @ R2 )
% 9.17/5.31 | ( ( A = A4 )
% 9.17/5.31 & ( member8566619992076573584nt_int @ ( produc3646306378393792727nt_int @ B @ B3 ) @ S ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_454_rewriteR__comp__comp2,axiom,
% 9.17/5.31 ! [G: int > nat,H3: int > int,R1: nat > nat,R22: int > nat,F: nat > num,L: nat > num] :
% 9.17/5.31 ( ( ( comp_int_nat_int @ G @ H3 )
% 9.17/5.31 = ( comp_nat_nat_int @ R1 @ R22 ) )
% 9.17/5.31 => ( ( ( comp_nat_num_nat @ F @ R1 )
% 9.17/5.31 = L )
% 9.17/5.31 => ( ( comp_int_num_int @ ( comp_nat_num_int @ F @ G ) @ H3 )
% 9.17/5.31 = ( comp_nat_num_int @ L @ R22 ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_455_rewriteR__comp__comp2,axiom,
% 9.17/5.31 ! [G: nat > nat,H3: int > nat,R1: int > nat,R22: int > int,F: nat > num,L: int > num] :
% 9.17/5.31 ( ( ( comp_nat_nat_int @ G @ H3 )
% 9.17/5.31 = ( comp_int_nat_int @ R1 @ R22 ) )
% 9.17/5.31 => ( ( ( comp_nat_num_int @ F @ R1 )
% 9.17/5.31 = L )
% 9.17/5.31 => ( ( comp_nat_num_int @ ( comp_nat_num_nat @ F @ G ) @ H3 )
% 9.17/5.31 = ( comp_int_num_int @ L @ R22 ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_456_rewriteR__comp__comp2,axiom,
% 9.17/5.31 ! [G: num > code_integer,H3: num > num,R1: code_integer > code_integer,R22: num > code_integer,F: code_integer > code_integer,L: code_integer > code_integer] :
% 9.17/5.31 ( ( ( comp_n6909714581898973814er_num @ G @ H3 )
% 9.17/5.31 = ( comp_C3531382070062128313er_num @ R1 @ R22 ) )
% 9.17/5.31 => ( ( ( comp_C7449957260575251196nteger @ F @ R1 )
% 9.17/5.31 = L )
% 9.17/5.31 => ( ( comp_n6909714581898973814er_num @ ( comp_C3531382070062128313er_num @ F @ G ) @ H3 )
% 9.17/5.31 = ( comp_C3531382070062128313er_num @ L @ R22 ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_457_rewriteR__comp__comp2,axiom,
% 9.17/5.31 ! [G: code_integer > code_integer,H3: num > code_integer,R1: num > code_integer,R22: num > num,F: code_integer > code_integer,L: num > code_integer] :
% 9.17/5.31 ( ( ( comp_C3531382070062128313er_num @ G @ H3 )
% 9.17/5.31 = ( comp_n6909714581898973814er_num @ R1 @ R22 ) )
% 9.17/5.31 => ( ( ( comp_C3531382070062128313er_num @ F @ R1 )
% 9.17/5.31 = L )
% 9.17/5.31 => ( ( comp_C3531382070062128313er_num @ ( comp_C7449957260575251196nteger @ F @ G ) @ H3 )
% 9.17/5.31 = ( comp_n6909714581898973814er_num @ L @ R22 ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_458_rewriteR__comp__comp2,axiom,
% 9.17/5.31 ! [G: code_integer > code_integer,H3: num > code_integer,R1: code_integer > code_integer,R22: num > code_integer,F: code_integer > code_integer,L: code_integer > code_integer] :
% 9.17/5.31 ( ( ( comp_C3531382070062128313er_num @ G @ H3 )
% 9.17/5.31 = ( comp_C3531382070062128313er_num @ R1 @ R22 ) )
% 9.17/5.31 => ( ( ( comp_C7449957260575251196nteger @ F @ R1 )
% 9.17/5.31 = L )
% 9.17/5.31 => ( ( comp_C3531382070062128313er_num @ ( comp_C7449957260575251196nteger @ F @ G ) @ H3 )
% 9.17/5.31 = ( comp_C3531382070062128313er_num @ L @ R22 ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_459_rewriteR__comp__comp2,axiom,
% 9.17/5.31 ! [G: nat > num,H3: int > nat,R1: nat > num,R22: int > nat,F: num > num,L: nat > num] :
% 9.17/5.31 ( ( ( comp_nat_num_int @ G @ H3 )
% 9.17/5.31 = ( comp_nat_num_int @ R1 @ R22 ) )
% 9.17/5.31 => ( ( ( comp_num_num_nat @ F @ R1 )
% 9.17/5.31 = L )
% 9.17/5.31 => ( ( comp_nat_num_int @ ( comp_num_num_nat @ F @ G ) @ H3 )
% 9.17/5.31 = ( comp_nat_num_int @ L @ R22 ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_460_rewriteR__comp__comp2,axiom,
% 9.17/5.31 ! [G: code_integer > code_integer,H3: code_integer > code_integer,R1: code_integer > code_integer,R22: code_integer > code_integer,F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,L: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 9.17/5.31 ( ( ( comp_C7449957260575251196nteger @ G @ H3 )
% 9.17/5.31 = ( comp_C7449957260575251196nteger @ R1 @ R22 ) )
% 9.17/5.31 => ( ( ( comp_C1593894019821074884nteger @ F @ R1 )
% 9.17/5.31 = L )
% 9.17/5.31 => ( ( comp_C1593894019821074884nteger @ ( comp_C1593894019821074884nteger @ F @ G ) @ H3 )
% 9.17/5.31 = ( comp_C1593894019821074884nteger @ L @ R22 ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_461_rewriteR__comp__comp2,axiom,
% 9.17/5.31 ! [G: code_integer > code_integer,H3: num > code_integer,R1: code_integer > code_integer,R22: num > code_integer,F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,L: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 9.17/5.31 ( ( ( comp_C3531382070062128313er_num @ G @ H3 )
% 9.17/5.31 = ( comp_C3531382070062128313er_num @ R1 @ R22 ) )
% 9.17/5.31 => ( ( ( comp_C1593894019821074884nteger @ F @ R1 )
% 9.17/5.31 = L )
% 9.17/5.31 => ( ( comp_C6617437204949736321er_num @ ( comp_C1593894019821074884nteger @ F @ G ) @ H3 )
% 9.17/5.31 = ( comp_C6617437204949736321er_num @ L @ R22 ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_462_rewriteR__comp__comp2,axiom,
% 9.17/5.31 ! [G: code_integer > code_integer,H3: code_integer > code_integer,R1: ( code_integer > code_integer ) > code_integer,R22: code_integer > code_integer > code_integer,F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,L: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 9.17/5.31 ( ( ( comp_C7449957260575251196nteger @ G @ H3 )
% 9.17/5.31 = ( comp_C5076291335850163704nteger @ R1 @ R22 ) )
% 9.17/5.31 => ( ( ( comp_C95226695241045696nteger @ F @ R1 )
% 9.17/5.31 = L )
% 9.17/5.31 => ( ( comp_C1593894019821074884nteger @ ( comp_C1593894019821074884nteger @ F @ G ) @ H3 )
% 9.17/5.31 = ( comp_C8797469213163452608nteger @ L @ R22 ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_463_rewriteR__comp__comp2,axiom,
% 9.17/5.31 ! [G: ( code_integer > code_integer ) > code_integer,H3: code_integer > code_integer > code_integer,R1: code_integer > code_integer,R22: code_integer > code_integer,F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,L: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 9.17/5.31 ( ( ( comp_C5076291335850163704nteger @ G @ H3 )
% 9.17/5.31 = ( comp_C7449957260575251196nteger @ R1 @ R22 ) )
% 9.17/5.31 => ( ( ( comp_C1593894019821074884nteger @ F @ R1 )
% 9.17/5.31 = L )
% 9.17/5.31 => ( ( comp_C8797469213163452608nteger @ ( comp_C95226695241045696nteger @ F @ G ) @ H3 )
% 9.17/5.31 = ( comp_C1593894019821074884nteger @ L @ R22 ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_464_rewriteL__comp__comp2,axiom,
% 9.17/5.31 ! [F: num > num,G: nat > num,L1: nat > num,L2: nat > nat,H3: int > nat,R2: int > nat] :
% 9.17/5.31 ( ( ( comp_num_num_nat @ F @ G )
% 9.17/5.31 = ( comp_nat_num_nat @ L1 @ L2 ) )
% 9.17/5.31 => ( ( ( comp_nat_nat_int @ L2 @ H3 )
% 9.17/5.31 = R2 )
% 9.17/5.31 => ( ( comp_num_num_int @ F @ ( comp_nat_num_int @ G @ H3 ) )
% 9.17/5.31 = ( comp_nat_num_int @ L1 @ R2 ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_465_rewriteL__comp__comp2,axiom,
% 9.17/5.31 ! [F: code_integer > code_integer,G: code_integer > code_integer,L1: code_integer > code_integer,L2: code_integer > code_integer,H3: num > code_integer,R2: num > code_integer] :
% 9.17/5.31 ( ( ( comp_C7449957260575251196nteger @ F @ G )
% 9.17/5.31 = ( comp_C7449957260575251196nteger @ L1 @ L2 ) )
% 9.17/5.31 => ( ( ( comp_C3531382070062128313er_num @ L2 @ H3 )
% 9.17/5.31 = R2 )
% 9.17/5.31 => ( ( comp_C3531382070062128313er_num @ F @ ( comp_C3531382070062128313er_num @ G @ H3 ) )
% 9.17/5.31 = ( comp_C3531382070062128313er_num @ L1 @ R2 ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_466_rewriteL__comp__comp2,axiom,
% 9.17/5.31 ! [F: nat > num,G: nat > nat,L1: num > num,L2: nat > num,H3: int > nat,R2: int > num] :
% 9.17/5.31 ( ( ( comp_nat_num_nat @ F @ G )
% 9.17/5.31 = ( comp_num_num_nat @ L1 @ L2 ) )
% 9.17/5.31 => ( ( ( comp_nat_num_int @ L2 @ H3 )
% 9.17/5.31 = R2 )
% 9.17/5.31 => ( ( comp_nat_num_int @ F @ ( comp_nat_nat_int @ G @ H3 ) )
% 9.17/5.31 = ( comp_num_num_int @ L1 @ R2 ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_467_rewriteL__comp__comp2,axiom,
% 9.17/5.31 ! [F: code_integer > code_integer,G: num > code_integer,L1: code_integer > code_integer,L2: num > code_integer,H3: num > num,R2: num > code_integer] :
% 9.17/5.31 ( ( ( comp_C3531382070062128313er_num @ F @ G )
% 9.17/5.31 = ( comp_C3531382070062128313er_num @ L1 @ L2 ) )
% 9.17/5.31 => ( ( ( comp_n6909714581898973814er_num @ L2 @ H3 )
% 9.17/5.31 = R2 )
% 9.17/5.31 => ( ( comp_C3531382070062128313er_num @ F @ ( comp_n6909714581898973814er_num @ G @ H3 ) )
% 9.17/5.31 = ( comp_C3531382070062128313er_num @ L1 @ R2 ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_468_rewriteL__comp__comp2,axiom,
% 9.17/5.31 ! [F: nat > num,G: int > nat,L1: nat > num,L2: int > nat,H3: int > int,R2: int > nat] :
% 9.17/5.31 ( ( ( comp_nat_num_int @ F @ G )
% 9.17/5.31 = ( comp_nat_num_int @ L1 @ L2 ) )
% 9.17/5.31 => ( ( ( comp_int_nat_int @ L2 @ H3 )
% 9.17/5.31 = R2 )
% 9.17/5.31 => ( ( comp_nat_num_int @ F @ ( comp_int_nat_int @ G @ H3 ) )
% 9.17/5.31 = ( comp_nat_num_int @ L1 @ R2 ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_469_rewriteL__comp__comp2,axiom,
% 9.17/5.31 ! [F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer,L1: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,L2: code_integer > code_integer,H3: code_integer > code_integer,R2: code_integer > code_integer] :
% 9.17/5.31 ( ( ( comp_C1593894019821074884nteger @ F @ G )
% 9.17/5.31 = ( comp_C1593894019821074884nteger @ L1 @ L2 ) )
% 9.17/5.31 => ( ( ( comp_C7449957260575251196nteger @ L2 @ H3 )
% 9.17/5.31 = R2 )
% 9.17/5.31 => ( ( comp_C1593894019821074884nteger @ F @ ( comp_C7449957260575251196nteger @ G @ H3 ) )
% 9.17/5.31 = ( comp_C1593894019821074884nteger @ L1 @ R2 ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_470_rewriteL__comp__comp2,axiom,
% 9.17/5.31 ! [F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer,L1: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,L2: code_integer > code_integer,H3: num > code_integer,R2: num > code_integer] :
% 9.17/5.31 ( ( ( comp_C1593894019821074884nteger @ F @ G )
% 9.17/5.31 = ( comp_C1593894019821074884nteger @ L1 @ L2 ) )
% 9.17/5.31 => ( ( ( comp_C3531382070062128313er_num @ L2 @ H3 )
% 9.17/5.31 = R2 )
% 9.17/5.31 => ( ( comp_C6617437204949736321er_num @ F @ ( comp_C3531382070062128313er_num @ G @ H3 ) )
% 9.17/5.31 = ( comp_C6617437204949736321er_num @ L1 @ R2 ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_471_rewriteL__comp__comp2,axiom,
% 9.17/5.31 ! [F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer,L1: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,L2: code_integer > code_integer > code_integer,H3: num > code_integer,R2: num > code_integer > code_integer] :
% 9.17/5.31 ( ( ( comp_C1593894019821074884nteger @ F @ G )
% 9.17/5.31 = ( comp_C8797469213163452608nteger @ L1 @ L2 ) )
% 9.17/5.31 => ( ( ( comp_C3662112809048933045er_num @ L2 @ H3 )
% 9.17/5.31 = R2 )
% 9.17/5.31 => ( ( comp_C6617437204949736321er_num @ F @ ( comp_C3531382070062128313er_num @ G @ H3 ) )
% 9.17/5.31 = ( comp_C8645541002826910333er_num @ L1 @ R2 ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_472_rewriteL__comp__comp2,axiom,
% 9.17/5.31 ! [F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer,L1: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,L2: code_integer > code_integer > code_integer,H3: code_integer > code_integer,R2: code_integer > code_integer > code_integer] :
% 9.17/5.31 ( ( ( comp_C1593894019821074884nteger @ F @ G )
% 9.17/5.31 = ( comp_C8797469213163452608nteger @ L1 @ L2 ) )
% 9.17/5.31 => ( ( ( comp_C2931745410781319416nteger @ L2 @ H3 )
% 9.17/5.31 = R2 )
% 9.17/5.31 => ( ( comp_C1593894019821074884nteger @ F @ ( comp_C7449957260575251196nteger @ G @ H3 ) )
% 9.17/5.31 = ( comp_C8797469213163452608nteger @ L1 @ R2 ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_473_rewriteL__comp__comp2,axiom,
% 9.17/5.31 ! [F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer > code_integer,L1: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,L2: code_integer > code_integer,H3: code_integer > code_integer,R2: code_integer > code_integer] :
% 9.17/5.31 ( ( ( comp_C8797469213163452608nteger @ F @ G )
% 9.17/5.31 = ( comp_C1593894019821074884nteger @ L1 @ L2 ) )
% 9.17/5.31 => ( ( ( comp_C7449957260575251196nteger @ L2 @ H3 )
% 9.17/5.31 = R2 )
% 9.17/5.31 => ( ( comp_C8797469213163452608nteger @ F @ ( comp_C2931745410781319416nteger @ G @ H3 ) )
% 9.17/5.31 = ( comp_C1593894019821074884nteger @ L1 @ R2 ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_474_rewriteR__comp__comp,axiom,
% 9.17/5.31 ! [G: num > code_integer,H3: num > num,R2: num > code_integer,F: code_integer > code_integer] :
% 9.17/5.31 ( ( ( comp_n6909714581898973814er_num @ G @ H3 )
% 9.17/5.31 = R2 )
% 9.17/5.31 => ( ( comp_n6909714581898973814er_num @ ( comp_C3531382070062128313er_num @ F @ G ) @ H3 )
% 9.17/5.31 = ( comp_C3531382070062128313er_num @ F @ R2 ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_475_rewriteR__comp__comp,axiom,
% 9.17/5.31 ! [G: int > nat,H3: int > int,R2: int > nat,F: nat > num] :
% 9.17/5.31 ( ( ( comp_int_nat_int @ G @ H3 )
% 9.17/5.31 = R2 )
% 9.17/5.31 => ( ( comp_int_num_int @ ( comp_nat_num_int @ F @ G ) @ H3 )
% 9.17/5.31 = ( comp_nat_num_int @ F @ R2 ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_476_rewriteR__comp__comp,axiom,
% 9.17/5.31 ! [G: nat > nat,H3: int > nat,R2: int > nat,F: nat > num] :
% 9.17/5.31 ( ( ( comp_nat_nat_int @ G @ H3 )
% 9.17/5.31 = R2 )
% 9.17/5.31 => ( ( comp_nat_num_int @ ( comp_nat_num_nat @ F @ G ) @ H3 )
% 9.17/5.31 = ( comp_nat_num_int @ F @ R2 ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_477_rewriteR__comp__comp,axiom,
% 9.17/5.31 ! [G: code_integer > code_integer,H3: num > code_integer,R2: num > code_integer,F: code_integer > code_integer] :
% 9.17/5.31 ( ( ( comp_C3531382070062128313er_num @ G @ H3 )
% 9.17/5.31 = R2 )
% 9.17/5.31 => ( ( comp_C3531382070062128313er_num @ ( comp_C7449957260575251196nteger @ F @ G ) @ H3 )
% 9.17/5.31 = ( comp_C3531382070062128313er_num @ F @ R2 ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_478_rewriteR__comp__comp,axiom,
% 9.17/5.31 ! [G: nat > num,H3: int > nat,R2: int > num,F: num > num] :
% 9.17/5.31 ( ( ( comp_nat_num_int @ G @ H3 )
% 9.17/5.31 = R2 )
% 9.17/5.31 => ( ( comp_nat_num_int @ ( comp_num_num_nat @ F @ G ) @ H3 )
% 9.17/5.31 = ( comp_num_num_int @ F @ R2 ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_479_rewriteR__comp__comp,axiom,
% 9.17/5.31 ! [G: code_integer > code_integer,H3: code_integer > code_integer,R2: code_integer > code_integer,F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 9.17/5.31 ( ( ( comp_C7449957260575251196nteger @ G @ H3 )
% 9.17/5.31 = R2 )
% 9.17/5.31 => ( ( comp_C1593894019821074884nteger @ ( comp_C1593894019821074884nteger @ F @ G ) @ H3 )
% 9.17/5.31 = ( comp_C1593894019821074884nteger @ F @ R2 ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_480_rewriteR__comp__comp,axiom,
% 9.17/5.31 ! [G: code_integer > code_integer,H3: num > code_integer,R2: num > code_integer,F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 9.17/5.31 ( ( ( comp_C3531382070062128313er_num @ G @ H3 )
% 9.17/5.31 = R2 )
% 9.17/5.31 => ( ( comp_C6617437204949736321er_num @ ( comp_C1593894019821074884nteger @ F @ G ) @ H3 )
% 9.17/5.31 = ( comp_C6617437204949736321er_num @ F @ R2 ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_481_rewriteR__comp__comp,axiom,
% 9.17/5.31 ! [G: code_integer > code_integer > code_integer,H3: code_integer > code_integer,R2: code_integer > code_integer > code_integer,F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 9.17/5.31 ( ( ( comp_C2931745410781319416nteger @ G @ H3 )
% 9.17/5.31 = R2 )
% 9.17/5.31 => ( ( comp_C1593894019821074884nteger @ ( comp_C8797469213163452608nteger @ F @ G ) @ H3 )
% 9.17/5.31 = ( comp_C8797469213163452608nteger @ F @ R2 ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_482_rewriteR__comp__comp,axiom,
% 9.17/5.31 ! [G: ( code_integer > code_integer ) > code_integer,H3: code_integer > code_integer > code_integer,R2: code_integer > code_integer,F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 9.17/5.31 ( ( ( comp_C5076291335850163704nteger @ G @ H3 )
% 9.17/5.31 = R2 )
% 9.17/5.31 => ( ( comp_C8797469213163452608nteger @ ( comp_C95226695241045696nteger @ F @ G ) @ H3 )
% 9.17/5.31 = ( comp_C1593894019821074884nteger @ F @ R2 ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_483_rewriteR__comp__comp,axiom,
% 9.17/5.31 ! [G: ( code_integer > code_integer ) > code_integer > code_integer,H3: code_integer > code_integer > code_integer,R2: code_integer > code_integer > code_integer,F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 9.17/5.31 ( ( ( comp_C2822359487432382964nteger @ G @ H3 )
% 9.17/5.31 = R2 )
% 9.17/5.31 => ( ( comp_C8797469213163452608nteger @ ( comp_C3983183376822107068nteger @ F @ G ) @ H3 )
% 9.17/5.31 = ( comp_C8797469213163452608nteger @ F @ R2 ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_484_rewriteL__comp__comp,axiom,
% 9.17/5.31 ! [F: num > num,G: nat > num,L: nat > num,H3: int > nat] :
% 9.17/5.31 ( ( ( comp_num_num_nat @ F @ G )
% 9.17/5.31 = L )
% 9.17/5.31 => ( ( comp_num_num_int @ F @ ( comp_nat_num_int @ G @ H3 ) )
% 9.17/5.31 = ( comp_nat_num_int @ L @ H3 ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_485_rewriteL__comp__comp,axiom,
% 9.17/5.31 ! [F: code_integer > code_integer,G: code_integer > code_integer,L: code_integer > code_integer,H3: num > code_integer] :
% 9.17/5.31 ( ( ( comp_C7449957260575251196nteger @ F @ G )
% 9.17/5.31 = L )
% 9.17/5.31 => ( ( comp_C3531382070062128313er_num @ F @ ( comp_C3531382070062128313er_num @ G @ H3 ) )
% 9.17/5.31 = ( comp_C3531382070062128313er_num @ L @ H3 ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_486_rewriteL__comp__comp,axiom,
% 9.17/5.31 ! [F: nat > num,G: nat > nat,L: nat > num,H3: int > nat] :
% 9.17/5.31 ( ( ( comp_nat_num_nat @ F @ G )
% 9.17/5.31 = L )
% 9.17/5.31 => ( ( comp_nat_num_int @ F @ ( comp_nat_nat_int @ G @ H3 ) )
% 9.17/5.31 = ( comp_nat_num_int @ L @ H3 ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_487_rewriteL__comp__comp,axiom,
% 9.17/5.31 ! [F: code_integer > code_integer,G: num > code_integer,L: num > code_integer,H3: num > num] :
% 9.17/5.31 ( ( ( comp_C3531382070062128313er_num @ F @ G )
% 9.17/5.31 = L )
% 9.17/5.31 => ( ( comp_C3531382070062128313er_num @ F @ ( comp_n6909714581898973814er_num @ G @ H3 ) )
% 9.17/5.31 = ( comp_n6909714581898973814er_num @ L @ H3 ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_488_rewriteL__comp__comp,axiom,
% 9.17/5.31 ! [F: nat > num,G: int > nat,L: int > num,H3: int > int] :
% 9.17/5.31 ( ( ( comp_nat_num_int @ F @ G )
% 9.17/5.31 = L )
% 9.17/5.31 => ( ( comp_nat_num_int @ F @ ( comp_int_nat_int @ G @ H3 ) )
% 9.17/5.31 = ( comp_int_num_int @ L @ H3 ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_489_rewriteL__comp__comp,axiom,
% 9.17/5.31 ! [F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer,L: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,H3: num > code_integer] :
% 9.17/5.31 ( ( ( comp_C1593894019821074884nteger @ F @ G )
% 9.17/5.31 = L )
% 9.17/5.31 => ( ( comp_C6617437204949736321er_num @ F @ ( comp_C3531382070062128313er_num @ G @ H3 ) )
% 9.17/5.31 = ( comp_C6617437204949736321er_num @ L @ H3 ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_490_rewriteL__comp__comp,axiom,
% 9.17/5.31 ! [F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer,L: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,H3: code_integer > code_integer] :
% 9.17/5.31 ( ( ( comp_C1593894019821074884nteger @ F @ G )
% 9.17/5.31 = L )
% 9.17/5.31 => ( ( comp_C1593894019821074884nteger @ F @ ( comp_C7449957260575251196nteger @ G @ H3 ) )
% 9.17/5.31 = ( comp_C1593894019821074884nteger @ L @ H3 ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_491_rewriteL__comp__comp,axiom,
% 9.17/5.31 ! [F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,G: ( code_integer > code_integer ) > code_integer,L: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,H3: code_integer > code_integer > code_integer] :
% 9.17/5.31 ( ( ( comp_C95226695241045696nteger @ F @ G )
% 9.17/5.31 = L )
% 9.17/5.31 => ( ( comp_C1593894019821074884nteger @ F @ ( comp_C5076291335850163704nteger @ G @ H3 ) )
% 9.17/5.31 = ( comp_C8797469213163452608nteger @ L @ H3 ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_492_rewriteL__comp__comp,axiom,
% 9.17/5.31 ! [F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer > code_integer,L: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,H3: code_integer > code_integer] :
% 9.17/5.31 ( ( ( comp_C8797469213163452608nteger @ F @ G )
% 9.17/5.31 = L )
% 9.17/5.31 => ( ( comp_C8797469213163452608nteger @ F @ ( comp_C2931745410781319416nteger @ G @ H3 ) )
% 9.17/5.31 = ( comp_C1593894019821074884nteger @ L @ H3 ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_493_rewriteL__comp__comp,axiom,
% 9.17/5.31 ! [F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G: ( code_integer > code_integer ) > code_integer > code_integer,L: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,H3: code_integer > code_integer > code_integer] :
% 9.17/5.31 ( ( ( comp_C3983183376822107068nteger @ F @ G )
% 9.17/5.31 = L )
% 9.17/5.31 => ( ( comp_C8797469213163452608nteger @ F @ ( comp_C2822359487432382964nteger @ G @ H3 ) )
% 9.17/5.31 = ( comp_C8797469213163452608nteger @ L @ H3 ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_494_type__copy__map__cong0,axiom,
% 9.17/5.31 ! [M3: num > code_integer,G: num > num,X: num,N6: code_integer > code_integer,H3: num > code_integer,F: code_integer > code_integer] :
% 9.17/5.31 ( ( ( M3 @ ( G @ X ) )
% 9.17/5.31 = ( N6 @ ( H3 @ X ) ) )
% 9.17/5.31 => ( ( comp_n6909714581898973814er_num @ ( comp_C3531382070062128313er_num @ F @ M3 ) @ G @ X )
% 9.17/5.31 = ( comp_C3531382070062128313er_num @ ( comp_C7449957260575251196nteger @ F @ N6 ) @ H3 @ X ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_495_type__copy__map__cong0,axiom,
% 9.17/5.31 ! [M3: int > nat,G: int > int,X: int,N6: nat > nat,H3: int > nat,F: nat > num] :
% 9.17/5.31 ( ( ( M3 @ ( G @ X ) )
% 9.17/5.31 = ( N6 @ ( H3 @ X ) ) )
% 9.17/5.31 => ( ( comp_int_num_int @ ( comp_nat_num_int @ F @ M3 ) @ G @ X )
% 9.17/5.31 = ( comp_nat_num_int @ ( comp_nat_num_nat @ F @ N6 ) @ H3 @ X ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_496_type__copy__map__cong0,axiom,
% 9.17/5.31 ! [M3: code_integer > code_integer,G: num > code_integer,X: num,N6: num > code_integer,H3: num > num,F: code_integer > code_integer] :
% 9.17/5.31 ( ( ( M3 @ ( G @ X ) )
% 9.17/5.31 = ( N6 @ ( H3 @ X ) ) )
% 9.17/5.31 => ( ( comp_C3531382070062128313er_num @ ( comp_C7449957260575251196nteger @ F @ M3 ) @ G @ X )
% 9.17/5.31 = ( comp_n6909714581898973814er_num @ ( comp_C3531382070062128313er_num @ F @ N6 ) @ H3 @ X ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_497_type__copy__map__cong0,axiom,
% 9.17/5.31 ! [M3: code_integer > code_integer,G: code_integer > code_integer,X: code_integer,N6: code_integer > code_integer,H3: code_integer > code_integer,F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 9.17/5.31 ( ( ( M3 @ ( G @ X ) )
% 9.17/5.31 = ( N6 @ ( H3 @ X ) ) )
% 9.17/5.31 => ( ( comp_C1593894019821074884nteger @ ( comp_C1593894019821074884nteger @ F @ M3 ) @ G @ X )
% 9.17/5.31 = ( comp_C1593894019821074884nteger @ ( comp_C1593894019821074884nteger @ F @ N6 ) @ H3 @ X ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_498_type__copy__map__cong0,axiom,
% 9.17/5.31 ! [M3: code_integer > code_integer,G: code_integer > code_integer,X: code_integer,N6: ( code_integer > code_integer ) > code_integer,H3: code_integer > code_integer > code_integer,F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 9.17/5.31 ( ( ( M3 @ ( G @ X ) )
% 9.17/5.31 = ( N6 @ ( H3 @ X ) ) )
% 9.17/5.31 => ( ( comp_C1593894019821074884nteger @ ( comp_C1593894019821074884nteger @ F @ M3 ) @ G @ X )
% 9.17/5.31 = ( comp_C8797469213163452608nteger @ ( comp_C95226695241045696nteger @ F @ N6 ) @ H3 @ X ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_499_type__copy__map__cong0,axiom,
% 9.17/5.31 ! [M3: code_integer > code_integer > code_integer,G: code_integer > code_integer,X: code_integer,N6: code_integer > code_integer > code_integer,H3: code_integer > code_integer,F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 9.17/5.31 ( ( ( M3 @ ( G @ X ) )
% 9.17/5.31 = ( N6 @ ( H3 @ X ) ) )
% 9.17/5.31 => ( ( comp_C1593894019821074884nteger @ ( comp_C8797469213163452608nteger @ F @ M3 ) @ G @ X )
% 9.17/5.31 = ( comp_C1593894019821074884nteger @ ( comp_C8797469213163452608nteger @ F @ N6 ) @ H3 @ X ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_500_type__copy__map__cong0,axiom,
% 9.17/5.31 ! [M3: code_integer > code_integer > code_integer,G: code_integer > code_integer,X: code_integer,N6: ( code_integer > code_integer ) > code_integer > code_integer,H3: code_integer > code_integer > code_integer,F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 9.17/5.31 ( ( ( M3 @ ( G @ X ) )
% 9.17/5.31 = ( N6 @ ( H3 @ X ) ) )
% 9.17/5.31 => ( ( comp_C1593894019821074884nteger @ ( comp_C8797469213163452608nteger @ F @ M3 ) @ G @ X )
% 9.17/5.31 = ( comp_C8797469213163452608nteger @ ( comp_C3983183376822107068nteger @ F @ N6 ) @ H3 @ X ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_501_type__copy__map__cong0,axiom,
% 9.17/5.31 ! [M3: ( code_integer > code_integer ) > code_integer,G: code_integer > code_integer > code_integer,X: code_integer,N6: code_integer > code_integer,H3: code_integer > code_integer,F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 9.17/5.31 ( ( ( M3 @ ( G @ X ) )
% 9.17/5.31 = ( N6 @ ( H3 @ X ) ) )
% 9.17/5.31 => ( ( comp_C8797469213163452608nteger @ ( comp_C95226695241045696nteger @ F @ M3 ) @ G @ X )
% 9.17/5.31 = ( comp_C1593894019821074884nteger @ ( comp_C1593894019821074884nteger @ F @ N6 ) @ H3 @ X ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_502_type__copy__map__cong0,axiom,
% 9.17/5.31 ! [M3: ( code_integer > code_integer ) > code_integer > code_integer,G: code_integer > code_integer > code_integer,X: code_integer,N6: code_integer > code_integer > code_integer,H3: code_integer > code_integer,F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 9.17/5.31 ( ( ( M3 @ ( G @ X ) )
% 9.17/5.31 = ( N6 @ ( H3 @ X ) ) )
% 9.17/5.31 => ( ( comp_C8797469213163452608nteger @ ( comp_C3983183376822107068nteger @ F @ M3 ) @ G @ X )
% 9.17/5.31 = ( comp_C1593894019821074884nteger @ ( comp_C8797469213163452608nteger @ F @ N6 ) @ H3 @ X ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_503_type__copy__map__cong0,axiom,
% 9.17/5.31 ! [M3: nat > nat,G: int > nat,X: int,N6: int > nat,H3: int > int,F: nat > num] :
% 9.17/5.31 ( ( ( M3 @ ( G @ X ) )
% 9.17/5.31 = ( N6 @ ( H3 @ X ) ) )
% 9.17/5.31 => ( ( comp_nat_num_int @ ( comp_nat_num_nat @ F @ M3 ) @ G @ X )
% 9.17/5.31 = ( comp_int_num_int @ ( comp_nat_num_int @ F @ N6 ) @ H3 @ X ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_504_comp__apply__eq,axiom,
% 9.17/5.31 ! [F: code_integer > code_integer,G: num > code_integer,X: num,H3: code_integer > code_integer,K: num > code_integer] :
% 9.17/5.31 ( ( ( F @ ( G @ X ) )
% 9.17/5.31 = ( H3 @ ( K @ X ) ) )
% 9.17/5.31 => ( ( comp_C3531382070062128313er_num @ F @ G @ X )
% 9.17/5.31 = ( comp_C3531382070062128313er_num @ H3 @ K @ X ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_505_comp__apply__eq,axiom,
% 9.17/5.31 ! [F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer,X: code_integer,H3: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,K: code_integer > code_integer] :
% 9.17/5.31 ( ( ( F @ ( G @ X ) )
% 9.17/5.31 = ( H3 @ ( K @ X ) ) )
% 9.17/5.31 => ( ( comp_C1593894019821074884nteger @ F @ G @ X )
% 9.17/5.31 = ( comp_C1593894019821074884nteger @ H3 @ K @ X ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_506_comp__apply__eq,axiom,
% 9.17/5.31 ! [F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer,X: code_integer,H3: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,K: code_integer > code_integer > code_integer] :
% 9.17/5.31 ( ( ( F @ ( G @ X ) )
% 9.17/5.31 = ( H3 @ ( K @ X ) ) )
% 9.17/5.31 => ( ( comp_C1593894019821074884nteger @ F @ G @ X )
% 9.17/5.31 = ( comp_C8797469213163452608nteger @ H3 @ K @ X ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_507_comp__apply__eq,axiom,
% 9.17/5.31 ! [F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer > code_integer,X: code_integer,H3: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,K: code_integer > code_integer] :
% 9.17/5.31 ( ( ( F @ ( G @ X ) )
% 9.17/5.31 = ( H3 @ ( K @ X ) ) )
% 9.17/5.31 => ( ( comp_C8797469213163452608nteger @ F @ G @ X )
% 9.17/5.31 = ( comp_C1593894019821074884nteger @ H3 @ K @ X ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_508_comp__apply__eq,axiom,
% 9.17/5.31 ! [F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer > code_integer,X: code_integer,H3: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,K: code_integer > code_integer > code_integer] :
% 9.17/5.31 ( ( ( F @ ( G @ X ) )
% 9.17/5.31 = ( H3 @ ( K @ X ) ) )
% 9.17/5.31 => ( ( comp_C8797469213163452608nteger @ F @ G @ X )
% 9.17/5.31 = ( comp_C8797469213163452608nteger @ H3 @ K @ X ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_509_comp__apply__eq,axiom,
% 9.17/5.31 ! [F: nat > num,G: int > nat,X: int,H3: nat > num,K: int > nat] :
% 9.17/5.31 ( ( ( F @ ( G @ X ) )
% 9.17/5.31 = ( H3 @ ( K @ X ) ) )
% 9.17/5.31 => ( ( comp_nat_num_int @ F @ G @ X )
% 9.17/5.31 = ( comp_nat_num_int @ H3 @ K @ X ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_510_add_Oright__commute,axiom,
% 9.17/5.31 ! [A: multis2468970476368604999at_nat,B: multis2468970476368604999at_nat,C: multis2468970476368604999at_nat] :
% 9.17/5.31 ( ( plus_p7104986032573967614at_nat @ ( plus_p7104986032573967614at_nat @ A @ B ) @ C )
% 9.17/5.31 = ( plus_p7104986032573967614at_nat @ ( plus_p7104986032573967614at_nat @ A @ C ) @ B ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_511_add_Oright__commute,axiom,
% 9.17/5.31 ! [A: rat,B: rat,C: rat] :
% 9.17/5.31 ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 9.17/5.31 = ( plus_plus_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_512_add_Oright__commute,axiom,
% 9.17/5.31 ! [A: nat,B: nat,C: nat] :
% 9.17/5.31 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 9.17/5.31 = ( plus_plus_nat @ ( plus_plus_nat @ A @ C ) @ B ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_513_add_Oright__commute,axiom,
% 9.17/5.31 ! [A: int,B: int,C: int] :
% 9.17/5.31 ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 9.17/5.31 = ( plus_plus_int @ ( plus_plus_int @ A @ C ) @ B ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_514_add__less__cancel__right,axiom,
% 9.17/5.31 ! [A: code_integer,C: code_integer,B: code_integer] :
% 9.17/5.31 ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ C ) @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 9.17/5.31 = ( ord_le6747313008572928689nteger @ A @ B ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_515_add__less__cancel__right,axiom,
% 9.17/5.31 ! [A: rat,C: rat,B: rat] :
% 9.17/5.31 ( ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 9.17/5.31 = ( ord_less_rat @ A @ B ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_516_add__less__cancel__right,axiom,
% 9.17/5.31 ! [A: nat,C: nat,B: nat] :
% 9.17/5.31 ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 9.17/5.31 = ( ord_less_nat @ A @ B ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_517_add__less__cancel__right,axiom,
% 9.17/5.31 ! [A: int,C: int,B: int] :
% 9.17/5.31 ( ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 9.17/5.31 = ( ord_less_int @ A @ B ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_518_add__less__cancel__left,axiom,
% 9.17/5.31 ! [C: code_integer,A: code_integer,B: code_integer] :
% 9.17/5.31 ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ C @ A ) @ ( plus_p5714425477246183910nteger @ C @ B ) )
% 9.17/5.31 = ( ord_le6747313008572928689nteger @ A @ B ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_519_add__less__cancel__left,axiom,
% 9.17/5.31 ! [C: rat,A: rat,B: rat] :
% 9.17/5.31 ( ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 9.17/5.31 = ( ord_less_rat @ A @ B ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_520_add__less__cancel__left,axiom,
% 9.17/5.31 ! [C: nat,A: nat,B: nat] :
% 9.17/5.31 ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 9.17/5.31 = ( ord_less_nat @ A @ B ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_521_add__less__cancel__left,axiom,
% 9.17/5.31 ! [C: int,A: int,B: int] :
% 9.17/5.31 ( ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 9.17/5.31 = ( ord_less_int @ A @ B ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_522_add__less__imp__less__right,axiom,
% 9.17/5.31 ! [A: code_integer,C: code_integer,B: code_integer] :
% 9.17/5.31 ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ C ) @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 9.17/5.31 => ( ord_le6747313008572928689nteger @ A @ B ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_523_add__less__imp__less__right,axiom,
% 9.17/5.31 ! [A: rat,C: rat,B: rat] :
% 9.17/5.31 ( ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 9.17/5.31 => ( ord_less_rat @ A @ B ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_524_add__less__imp__less__right,axiom,
% 9.17/5.31 ! [A: nat,C: nat,B: nat] :
% 9.17/5.31 ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 9.17/5.31 => ( ord_less_nat @ A @ B ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_525_add__less__imp__less__right,axiom,
% 9.17/5.31 ! [A: int,C: int,B: int] :
% 9.17/5.31 ( ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 9.17/5.31 => ( ord_less_int @ A @ B ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_526_add__less__imp__less__left,axiom,
% 9.17/5.31 ! [C: code_integer,A: code_integer,B: code_integer] :
% 9.17/5.31 ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ C @ A ) @ ( plus_p5714425477246183910nteger @ C @ B ) )
% 9.17/5.31 => ( ord_le6747313008572928689nteger @ A @ B ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_527_add__less__imp__less__left,axiom,
% 9.17/5.31 ! [C: rat,A: rat,B: rat] :
% 9.17/5.31 ( ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 9.17/5.31 => ( ord_less_rat @ A @ B ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_528_add__less__imp__less__left,axiom,
% 9.17/5.31 ! [C: nat,A: nat,B: nat] :
% 9.17/5.31 ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 9.17/5.31 => ( ord_less_nat @ A @ B ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_529_add__less__imp__less__left,axiom,
% 9.17/5.31 ! [C: int,A: int,B: int] :
% 9.17/5.31 ( ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 9.17/5.31 => ( ord_less_int @ A @ B ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_530_add__strict__right__mono,axiom,
% 9.17/5.31 ! [A: code_integer,B: code_integer,C: code_integer] :
% 9.17/5.31 ( ( ord_le6747313008572928689nteger @ A @ B )
% 9.17/5.31 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ C ) @ ( plus_p5714425477246183910nteger @ B @ C ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_531_add__strict__right__mono,axiom,
% 9.17/5.31 ! [A: rat,B: rat,C: rat] :
% 9.17/5.31 ( ( ord_less_rat @ A @ B )
% 9.17/5.31 => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_532_add__strict__right__mono,axiom,
% 9.17/5.31 ! [A: nat,B: nat,C: nat] :
% 9.17/5.31 ( ( ord_less_nat @ A @ B )
% 9.17/5.31 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_533_add__strict__right__mono,axiom,
% 9.17/5.31 ! [A: int,B: int,C: int] :
% 9.17/5.31 ( ( ord_less_int @ A @ B )
% 9.17/5.31 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_534_add__strict__left__mono,axiom,
% 9.17/5.31 ! [A: code_integer,B: code_integer,C: code_integer] :
% 9.17/5.31 ( ( ord_le6747313008572928689nteger @ A @ B )
% 9.17/5.31 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ C @ A ) @ ( plus_p5714425477246183910nteger @ C @ B ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_535_add__strict__left__mono,axiom,
% 9.17/5.31 ! [A: rat,B: rat,C: rat] :
% 9.17/5.31 ( ( ord_less_rat @ A @ B )
% 9.17/5.31 => ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_536_add__strict__left__mono,axiom,
% 9.17/5.31 ! [A: nat,B: nat,C: nat] :
% 9.17/5.31 ( ( ord_less_nat @ A @ B )
% 9.17/5.31 => ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_537_add__strict__left__mono,axiom,
% 9.17/5.31 ! [A: int,B: int,C: int] :
% 9.17/5.31 ( ( ord_less_int @ A @ B )
% 9.17/5.31 => ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_538_add__strict__mono,axiom,
% 9.17/5.31 ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 9.17/5.31 ( ( ord_le6747313008572928689nteger @ A @ B )
% 9.17/5.31 => ( ( ord_le6747313008572928689nteger @ C @ D2 )
% 9.17/5.31 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ C ) @ ( plus_p5714425477246183910nteger @ B @ D2 ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_539_add__strict__mono,axiom,
% 9.17/5.31 ! [A: rat,B: rat,C: rat,D2: rat] :
% 9.17/5.31 ( ( ord_less_rat @ A @ B )
% 9.17/5.31 => ( ( ord_less_rat @ C @ D2 )
% 9.17/5.31 => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D2 ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_540_add__strict__mono,axiom,
% 9.17/5.31 ! [A: nat,B: nat,C: nat,D2: nat] :
% 9.17/5.31 ( ( ord_less_nat @ A @ B )
% 9.17/5.31 => ( ( ord_less_nat @ C @ D2 )
% 9.17/5.31 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D2 ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_541_add__strict__mono,axiom,
% 9.17/5.31 ! [A: int,B: int,C: int,D2: int] :
% 9.17/5.31 ( ( ord_less_int @ A @ B )
% 9.17/5.31 => ( ( ord_less_int @ C @ D2 )
% 9.17/5.31 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D2 ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_542_add__mono__thms__linordered__field_I1_J,axiom,
% 9.17/5.31 ! [I: code_integer,J: code_integer,K: code_integer,L: code_integer] :
% 9.17/5.31 ( ( ( ord_le6747313008572928689nteger @ I @ J )
% 9.17/5.31 & ( K = L ) )
% 9.17/5.31 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ I @ K ) @ ( plus_p5714425477246183910nteger @ J @ L ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_543_add__mono__thms__linordered__field_I1_J,axiom,
% 9.17/5.31 ! [I: rat,J: rat,K: rat,L: rat] :
% 9.17/5.31 ( ( ( ord_less_rat @ I @ J )
% 9.17/5.31 & ( K = L ) )
% 9.17/5.31 => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_544_add__mono__thms__linordered__field_I1_J,axiom,
% 9.17/5.31 ! [I: nat,J: nat,K: nat,L: nat] :
% 9.17/5.31 ( ( ( ord_less_nat @ I @ J )
% 9.17/5.31 & ( K = L ) )
% 9.17/5.31 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_545_add__mono__thms__linordered__field_I1_J,axiom,
% 9.17/5.31 ! [I: int,J: int,K: int,L: int] :
% 9.17/5.31 ( ( ( ord_less_int @ I @ J )
% 9.17/5.31 & ( K = L ) )
% 9.17/5.31 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_546_add__mono__thms__linordered__field_I2_J,axiom,
% 9.17/5.31 ! [I: code_integer,J: code_integer,K: code_integer,L: code_integer] :
% 9.17/5.31 ( ( ( I = J )
% 9.17/5.31 & ( ord_le6747313008572928689nteger @ K @ L ) )
% 9.17/5.31 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ I @ K ) @ ( plus_p5714425477246183910nteger @ J @ L ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_547_add__mono__thms__linordered__field_I2_J,axiom,
% 9.17/5.31 ! [I: rat,J: rat,K: rat,L: rat] :
% 9.17/5.31 ( ( ( I = J )
% 9.17/5.31 & ( ord_less_rat @ K @ L ) )
% 9.17/5.31 => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_548_add__mono__thms__linordered__field_I2_J,axiom,
% 9.17/5.31 ! [I: nat,J: nat,K: nat,L: nat] :
% 9.17/5.31 ( ( ( I = J )
% 9.17/5.31 & ( ord_less_nat @ K @ L ) )
% 9.17/5.31 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_549_add__mono__thms__linordered__field_I2_J,axiom,
% 9.17/5.31 ! [I: int,J: int,K: int,L: int] :
% 9.17/5.31 ( ( ( I = J )
% 9.17/5.31 & ( ord_less_int @ K @ L ) )
% 9.17/5.31 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_550_add__mono__thms__linordered__field_I5_J,axiom,
% 9.17/5.31 ! [I: code_integer,J: code_integer,K: code_integer,L: code_integer] :
% 9.17/5.31 ( ( ( ord_le6747313008572928689nteger @ I @ J )
% 9.17/5.31 & ( ord_le6747313008572928689nteger @ K @ L ) )
% 9.17/5.31 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ I @ K ) @ ( plus_p5714425477246183910nteger @ J @ L ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_551_add__mono__thms__linordered__field_I5_J,axiom,
% 9.17/5.31 ! [I: rat,J: rat,K: rat,L: rat] :
% 9.17/5.31 ( ( ( ord_less_rat @ I @ J )
% 9.17/5.31 & ( ord_less_rat @ K @ L ) )
% 9.17/5.31 => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_552_add__mono__thms__linordered__field_I5_J,axiom,
% 9.17/5.31 ! [I: nat,J: nat,K: nat,L: nat] :
% 9.17/5.31 ( ( ( ord_less_nat @ I @ J )
% 9.17/5.31 & ( ord_less_nat @ K @ L ) )
% 9.17/5.31 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_553_add__mono__thms__linordered__field_I5_J,axiom,
% 9.17/5.31 ! [I: int,J: int,K: int,L: int] :
% 9.17/5.31 ( ( ( ord_less_int @ I @ J )
% 9.17/5.31 & ( ord_less_int @ K @ L ) )
% 9.17/5.31 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_554_success__returnI,axiom,
% 9.17/5.31 ! [X: product_unit,H3: heap_e7401611519738050253t_unit] : ( heap_T584514906347983379t_unit @ ( heap_T7507251653302230130t_unit @ X ) @ H3 ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_555_success__returnI,axiom,
% 9.17/5.31 ! [X: array_a,H3: heap_e7401611519738050253t_unit] : ( heap_T6932021131025641745rray_a @ ( heap_T4896204969850773234rray_a @ X ) @ H3 ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_556_fails__return,axiom,
% 9.17/5.31 ! [X: product_unit,H3: heap_e7401611519738050253t_unit] :
% 9.17/5.31 ~ ( time_f8834461667527620124t_unit @ ( heap_T7507251653302230130t_unit @ X ) @ H3 ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_557_fails__return,axiom,
% 9.17/5.31 ! [X: array_a,H3: heap_e7401611519738050253t_unit] :
% 9.17/5.31 ~ ( time_fails_array_a @ ( heap_T4896204969850773234rray_a @ X ) @ H3 ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_558_add_Oright__assoc,axiom,
% 9.17/5.31 ! [A: multis2468970476368604999at_nat,B: multis2468970476368604999at_nat,C: multis2468970476368604999at_nat] :
% 9.17/5.31 ( ( plus_p7104986032573967614at_nat @ ( plus_p7104986032573967614at_nat @ A @ B ) @ C )
% 9.17/5.31 = ( plus_p7104986032573967614at_nat @ A @ ( plus_p7104986032573967614at_nat @ B @ C ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_559_add_Oright__assoc,axiom,
% 9.17/5.31 ! [A: rat,B: rat,C: rat] :
% 9.17/5.31 ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 9.17/5.31 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_560_add_Oright__assoc,axiom,
% 9.17/5.31 ! [A: nat,B: nat,C: nat] :
% 9.17/5.31 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 9.17/5.31 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_561_add_Oright__assoc,axiom,
% 9.17/5.31 ! [A: int,B: int,C: int] :
% 9.17/5.31 ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 9.17/5.31 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_562_nat__add__left__cancel__less,axiom,
% 9.17/5.31 ! [K: nat,M2: nat,N2: nat] :
% 9.17/5.31 ( ( ord_less_nat @ ( plus_plus_nat @ K @ M2 ) @ ( plus_plus_nat @ K @ N2 ) )
% 9.17/5.31 = ( ord_less_nat @ M2 @ N2 ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_563_less__option__Some,axiom,
% 9.17/5.31 ! [X: code_integer,Y: code_integer] :
% 9.17/5.31 ( ( ord_le7113747843092208513nteger @ ( some_Code_integer @ X ) @ ( some_Code_integer @ Y ) )
% 9.17/5.31 = ( ord_le6747313008572928689nteger @ X @ Y ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_564_less__option__Some,axiom,
% 9.17/5.31 ! [X: rat,Y: rat] :
% 9.17/5.31 ( ( ord_less_option_rat @ ( some_rat @ X ) @ ( some_rat @ Y ) )
% 9.17/5.31 = ( ord_less_rat @ X @ Y ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_565_less__option__Some,axiom,
% 9.17/5.31 ! [X: num,Y: num] :
% 9.17/5.31 ( ( ord_less_option_num @ ( some_num @ X ) @ ( some_num @ Y ) )
% 9.17/5.31 = ( ord_less_num @ X @ Y ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_566_less__option__Some,axiom,
% 9.17/5.31 ! [X: nat,Y: nat] :
% 9.17/5.31 ( ( ord_less_option_nat @ ( some_nat @ X ) @ ( some_nat @ Y ) )
% 9.17/5.31 = ( ord_less_nat @ X @ Y ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_567_less__option__Some,axiom,
% 9.17/5.31 ! [X: int,Y: int] :
% 9.17/5.31 ( ( ord_less_option_int @ ( some_int @ X ) @ ( some_int @ Y ) )
% 9.17/5.31 = ( ord_less_int @ X @ Y ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_568_fold__atLeastAtMost__nat_Opelims,axiom,
% 9.17/5.31 ! [X: nat > nat > nat,Xa: nat,Xb: nat,Xc: nat,Y: nat] :
% 9.17/5.31 ( ( ( set_fo2584398358068434914at_nat @ X @ Xa @ Xb @ Xc )
% 9.17/5.31 = Y )
% 9.17/5.31 => ( ( accp_P6019419558468335806at_nat @ set_fo3699595496184130361el_nat @ ( produc3209952032786966637at_nat @ X @ ( produc487386426758144856at_nat @ Xa @ ( product_Pair_nat_nat @ Xb @ Xc ) ) ) )
% 9.17/5.31 => ~ ( ( ( ( ord_less_nat @ Xb @ Xa )
% 9.17/5.31 => ( Y = Xc ) )
% 9.17/5.31 & ( ~ ( ord_less_nat @ Xb @ Xa )
% 9.17/5.31 => ( Y
% 9.17/5.31 = ( set_fo2584398358068434914at_nat @ X @ ( plus_plus_nat @ Xa @ one_one_nat ) @ Xb @ ( X @ Xa @ Xc ) ) ) ) )
% 9.17/5.31 => ~ ( accp_P6019419558468335806at_nat @ set_fo3699595496184130361el_nat @ ( produc3209952032786966637at_nat @ X @ ( produc487386426758144856at_nat @ Xa @ ( product_Pair_nat_nat @ Xb @ Xc ) ) ) ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_569_fold__atLeastAtMost__nat_Opsimps,axiom,
% 9.17/5.31 ! [F: nat > nat > nat,A: nat,B: nat,Acc: nat] :
% 9.17/5.31 ( ( accp_P6019419558468335806at_nat @ set_fo3699595496184130361el_nat @ ( produc3209952032786966637at_nat @ F @ ( produc487386426758144856at_nat @ A @ ( product_Pair_nat_nat @ B @ Acc ) ) ) )
% 9.17/5.31 => ( ( ( ord_less_nat @ B @ A )
% 9.17/5.31 => ( ( set_fo2584398358068434914at_nat @ F @ A @ B @ Acc )
% 9.17/5.31 = Acc ) )
% 9.17/5.31 & ( ~ ( ord_less_nat @ B @ A )
% 9.17/5.31 => ( ( set_fo2584398358068434914at_nat @ F @ A @ B @ Acc )
% 9.17/5.31 = ( set_fo2584398358068434914at_nat @ F @ ( plus_plus_nat @ A @ one_one_nat ) @ B @ ( F @ A @ Acc ) ) ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_570_in__measure,axiom,
% 9.17/5.31 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,F: set_Pr1261947904930325089at_nat > nat] :
% 9.17/5.31 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ ( measur1827424007717751593at_nat @ F ) )
% 9.17/5.31 = ( ord_less_nat @ ( F @ X ) @ ( F @ Y ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_571_in__measure,axiom,
% 9.17/5.31 ! [X: nat,Y: nat,F: nat > nat] :
% 9.17/5.31 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( measure_nat @ F ) )
% 9.17/5.31 = ( ord_less_nat @ ( F @ X ) @ ( F @ Y ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_572_less__add__one,axiom,
% 9.17/5.31 ! [A: code_integer] : ( ord_le6747313008572928689nteger @ A @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_573_less__add__one,axiom,
% 9.17/5.31 ! [A: rat] : ( ord_less_rat @ A @ ( plus_plus_rat @ A @ one_one_rat ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_574_less__add__one,axiom,
% 9.17/5.31 ! [A: nat] : ( ord_less_nat @ A @ ( plus_plus_nat @ A @ one_one_nat ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_575_less__add__one,axiom,
% 9.17/5.31 ! [A: int] : ( ord_less_int @ A @ ( plus_plus_int @ A @ one_one_int ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_576_add__mono1,axiom,
% 9.17/5.31 ! [A: code_integer,B: code_integer] :
% 9.17/5.31 ( ( ord_le6747313008572928689nteger @ A @ B )
% 9.17/5.31 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) @ ( plus_p5714425477246183910nteger @ B @ one_one_Code_integer ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_577_add__mono1,axiom,
% 9.17/5.31 ! [A: rat,B: rat] :
% 9.17/5.31 ( ( ord_less_rat @ A @ B )
% 9.17/5.31 => ( ord_less_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( plus_plus_rat @ B @ one_one_rat ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_578_add__mono1,axiom,
% 9.17/5.31 ! [A: nat,B: nat] :
% 9.17/5.31 ( ( ord_less_nat @ A @ B )
% 9.17/5.31 => ( ord_less_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( plus_plus_nat @ B @ one_one_nat ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_579_add__mono1,axiom,
% 9.17/5.31 ! [A: int,B: int] :
% 9.17/5.31 ( ( ord_less_int @ A @ B )
% 9.17/5.31 => ( ord_less_int @ ( plus_plus_int @ A @ one_one_int ) @ ( plus_plus_int @ B @ one_one_int ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_580_add__lessD1,axiom,
% 9.17/5.31 ! [I: nat,J: nat,K: nat] :
% 9.17/5.31 ( ( ord_less_nat @ ( plus_plus_nat @ I @ J ) @ K )
% 9.17/5.31 => ( ord_less_nat @ I @ K ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_581_add__less__mono,axiom,
% 9.17/5.31 ! [I: nat,J: nat,K: nat,L: nat] :
% 9.17/5.31 ( ( ord_less_nat @ I @ J )
% 9.17/5.31 => ( ( ord_less_nat @ K @ L )
% 9.17/5.31 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_582_not__add__less1,axiom,
% 9.17/5.31 ! [I: nat,J: nat] :
% 9.17/5.31 ~ ( ord_less_nat @ ( plus_plus_nat @ I @ J ) @ I ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_583_less__option__None,axiom,
% 9.17/5.31 ! [X: option_num] :
% 9.17/5.31 ~ ( ord_less_option_num @ X @ none_num ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_584_less__option__None__Some__code,axiom,
% 9.17/5.31 ! [X: num] : ( ord_less_option_num @ none_num @ ( some_num @ X ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_585_less__option__None__Some,axiom,
% 9.17/5.31 ! [X: num] : ( ord_less_option_num @ none_num @ ( some_num @ X ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_586_less__option__None__is__Some,axiom,
% 9.17/5.31 ! [X: option_num] :
% 9.17/5.31 ( ( ord_less_option_num @ none_num @ X )
% 9.17/5.31 => ? [Z3: num] :
% 9.17/5.31 ( X
% 9.17/5.31 = ( some_num @ Z3 ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_587_fold__atLeastAtMost__nat_Osimps,axiom,
% 9.17/5.31 ( set_fo2584398358068434914at_nat
% 9.17/5.31 = ( ^ [F2: nat > nat > nat,A5: nat,B4: nat,Acc2: nat] : ( if_nat @ ( ord_less_nat @ B4 @ A5 ) @ Acc2 @ ( set_fo2584398358068434914at_nat @ F2 @ ( plus_plus_nat @ A5 @ one_one_nat ) @ B4 @ ( F2 @ A5 @ Acc2 ) ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_588_fold__atLeastAtMost__nat_Oelims,axiom,
% 9.17/5.31 ! [X: nat > nat > nat,Xa: nat,Xb: nat,Xc: nat,Y: nat] :
% 9.17/5.31 ( ( ( set_fo2584398358068434914at_nat @ X @ Xa @ Xb @ Xc )
% 9.17/5.31 = Y )
% 9.17/5.31 => ( ( ( ord_less_nat @ Xb @ Xa )
% 9.17/5.31 => ( Y = Xc ) )
% 9.17/5.31 & ( ~ ( ord_less_nat @ Xb @ Xa )
% 9.17/5.31 => ( Y
% 9.17/5.31 = ( set_fo2584398358068434914at_nat @ X @ ( plus_plus_nat @ Xa @ one_one_nat ) @ Xb @ ( X @ Xa @ Xc ) ) ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_589_less__add__eq__less,axiom,
% 9.17/5.31 ! [K: nat,L: nat,M2: nat,N2: nat] :
% 9.17/5.31 ( ( ord_less_nat @ K @ L )
% 9.17/5.31 => ( ( ( plus_plus_nat @ M2 @ L )
% 9.17/5.31 = ( plus_plus_nat @ K @ N2 ) )
% 9.17/5.31 => ( ord_less_nat @ M2 @ N2 ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_590_trans__less__add2,axiom,
% 9.17/5.31 ! [I: nat,J: nat,M2: nat] :
% 9.17/5.31 ( ( ord_less_nat @ I @ J )
% 9.17/5.31 => ( ord_less_nat @ I @ ( plus_plus_nat @ M2 @ J ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_591_trans__less__add1,axiom,
% 9.17/5.31 ! [I: nat,J: nat,M2: nat] :
% 9.17/5.31 ( ( ord_less_nat @ I @ J )
% 9.17/5.31 => ( ord_less_nat @ I @ ( plus_plus_nat @ J @ M2 ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_592_add__less__mono1,axiom,
% 9.17/5.31 ! [I: nat,J: nat,K: nat] :
% 9.17/5.31 ( ( ord_less_nat @ I @ J )
% 9.17/5.31 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_593_not__add__less2,axiom,
% 9.17/5.31 ! [J: nat,I: nat] :
% 9.17/5.31 ~ ( ord_less_nat @ ( plus_plus_nat @ J @ I ) @ I ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_594_less__numeral__extra_I4_J,axiom,
% 9.17/5.31 ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ one_one_Code_integer ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_595_less__numeral__extra_I4_J,axiom,
% 9.17/5.31 ~ ( ord_less_rat @ one_one_rat @ one_one_rat ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_596_less__numeral__extra_I4_J,axiom,
% 9.17/5.31 ~ ( ord_less_nat @ one_one_nat @ one_one_nat ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_597_less__numeral__extra_I4_J,axiom,
% 9.17/5.31 ~ ( ord_less_int @ one_one_int @ one_one_int ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_598_mlex__iff,axiom,
% 9.17/5.31 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,F: set_Pr1261947904930325089at_nat > nat,R4: set_Pr4329608150637261639at_nat] :
% 9.17/5.31 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ ( mlex_p3502713205431853936at_nat @ F @ R4 ) )
% 9.17/5.31 = ( ( ord_less_nat @ ( F @ X ) @ ( F @ Y ) )
% 9.17/5.31 | ( ( ( F @ X )
% 9.17/5.31 = ( F @ Y ) )
% 9.17/5.31 & ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ R4 ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_599_mlex__iff,axiom,
% 9.17/5.31 ! [X: nat,Y: nat,F: nat > nat,R4: set_Pr1261947904930325089at_nat] :
% 9.17/5.31 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( mlex_prod_nat @ F @ R4 ) )
% 9.17/5.31 = ( ( ord_less_nat @ ( F @ X ) @ ( F @ Y ) )
% 9.17/5.31 | ( ( ( F @ X )
% 9.17/5.31 = ( F @ Y ) )
% 9.17/5.31 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ R4 ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_600_mlex__less,axiom,
% 9.17/5.31 ! [F: set_Pr1261947904930325089at_nat > nat,X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,R4: set_Pr4329608150637261639at_nat] :
% 9.17/5.31 ( ( ord_less_nat @ ( F @ X ) @ ( F @ Y ) )
% 9.17/5.31 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ ( mlex_p3502713205431853936at_nat @ F @ R4 ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_601_mlex__less,axiom,
% 9.17/5.31 ! [F: nat > nat,X: nat,Y: nat,R4: set_Pr1261947904930325089at_nat] :
% 9.17/5.31 ( ( ord_less_nat @ ( F @ X ) @ ( F @ Y ) )
% 9.17/5.31 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( mlex_prod_nat @ F @ R4 ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_602_pairself_Opelims,axiom,
% 9.17/5.31 ! [X: int > option6357759511663192854e_term,Xa: product_prod_int_int,Y: produc6576344331059438605e_term] :
% 9.17/5.31 ( ( ( pairse3534876335208825186e_term @ X @ Xa )
% 9.17/5.31 = Y )
% 9.17/5.31 => ( ( accp_P8928870874622223812nt_int @ pairse6848479906795794847e_term @ ( produc4305682042979456191nt_int @ X @ Xa ) )
% 9.17/5.31 => ~ ! [A3: int,B2: int] :
% 9.17/5.31 ( ( Xa
% 9.17/5.31 = ( product_Pair_int_int @ A3 @ B2 ) )
% 9.17/5.31 => ( ( Y
% 9.17/5.31 = ( produc5950683997804057413e_term @ ( X @ A3 ) @ ( X @ B2 ) ) )
% 9.17/5.31 => ~ ( accp_P8928870874622223812nt_int @ pairse6848479906795794847e_term @ ( produc4305682042979456191nt_int @ X @ ( product_Pair_int_int @ A3 @ B2 ) ) ) ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_603_execute__return,axiom,
% 9.17/5.31 ! [X: array_a] :
% 9.17/5.31 ( ( heap_T5591663578999710211rray_a @ ( heap_T4896204969850773234rray_a @ X ) )
% 9.17/5.31 = ( comp_P2097125496263478628t_unit @ some_P6105628898608307625it_nat
% 9.17/5.31 @ ^ [H: heap_e7401611519738050253t_unit] : ( produc1733996804261680252it_nat @ X @ ( produc584006145561248582it_nat @ H @ one_one_nat ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_604_execute__return,axiom,
% 9.17/5.31 ! [X: product_unit] :
% 9.17/5.31 ( ( heap_T875086893843062177t_unit @ ( heap_T7507251653302230130t_unit @ X ) )
% 9.17/5.31 = ( comp_P3118722334806803912t_unit @ some_P1914260805536162275it_nat
% 9.17/5.31 @ ^ [H: heap_e7401611519738050253t_unit] : ( produc7133225469290080770it_nat @ X @ ( produc584006145561248582it_nat @ H @ one_one_nat ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_605_same__fstI,axiom,
% 9.17/5.31 ! [P: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > $o,X: produc6241069584506657477e_term > option6357759511663192854e_term,Y7: produc8923325533196201883nteger,Y: produc8923325533196201883nteger,R4: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > set_Pr5052581263052047815nteger] :
% 9.17/5.31 ( ( P @ X )
% 9.17/5.31 => ( ( member335077259223437328nteger @ ( produc4911887526399440471nteger @ Y7 @ Y ) @ ( R4 @ X ) )
% 9.17/5.31 => ( member2446009503569356342nteger @ ( produc7954516348491987909nteger @ ( produc8603105652947943368nteger @ X @ Y7 ) @ ( produc8603105652947943368nteger @ X @ Y ) ) @ ( same_f8038803414157382067nteger @ P @ R4 ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_606_same__fstI,axiom,
% 9.17/5.31 ! [P: ( produc3658429121746597890et_nat > $o ) > $o,X: produc3658429121746597890et_nat > $o,Y7: produc3658429121746597890et_nat,Y: produc3658429121746597890et_nat,R4: ( produc3658429121746597890et_nat > $o ) > set_Pr719794911490849221et_nat] :
% 9.17/5.31 ( ( P @ X )
% 9.17/5.31 => ( ( member6099555550032318734et_nat @ ( produc8199053930788261021et_nat @ Y7 @ Y ) @ ( R4 @ X ) )
% 9.17/5.31 => ( member4763271486408492550et_nat @ ( produc8599840265553166229et_nat @ ( produc5001842942810119800et_nat @ X @ Y7 ) @ ( produc5001842942810119800et_nat @ X @ Y ) ) @ ( same_f7251492184213700963et_nat @ P @ R4 ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_607_same__fstI,axiom,
% 9.17/5.31 ! [P: ( produc3658429121746597890et_nat > $o ) > $o,X: produc3658429121746597890et_nat > $o,Y7: produc3925858234332021118et_nat,Y: produc3925858234332021118et_nat,R4: ( produc3658429121746597890et_nat > $o ) > set_Pr7928877670098842301et_nat] :
% 9.17/5.31 ( ( P @ X )
% 9.17/5.31 => ( ( member4763271486408492550et_nat @ ( produc8599840265553166229et_nat @ Y7 @ Y ) @ ( R4 @ X ) )
% 9.17/5.31 => ( member6341495586645257982et_nat @ ( produc1940133919992309389et_nat @ ( produc2245416461498447860et_nat @ X @ Y7 ) @ ( produc2245416461498447860et_nat @ X @ Y ) ) @ ( same_f1912051055550046943et_nat @ P @ R4 ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_608_same__fstI,axiom,
% 9.17/5.31 ! [P: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > $o,X: produc8551481072490612790e_term > option6357759511663192854e_term,Y7: product_prod_int_int,Y: product_prod_int_int,R4: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > set_Pr2560585780119916871nt_int] :
% 9.17/5.31 ( ( P @ X )
% 9.17/5.31 => ( ( member8566619992076573584nt_int @ ( produc3646306378393792727nt_int @ Y7 @ Y ) @ ( R4 @ X ) )
% 9.17/5.31 => ( member6582457606847315088nt_int @ ( produc7601053194514725023nt_int @ ( produc5700946648718959541nt_int @ X @ Y7 ) @ ( produc5700946648718959541nt_int @ X @ Y ) ) @ ( same_f5472592420709775776nt_int @ P @ R4 ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_609_same__fstI,axiom,
% 9.17/5.31 ! [P: ( int > option6357759511663192854e_term ) > $o,X: int > option6357759511663192854e_term,Y7: product_prod_int_int,Y: product_prod_int_int,R4: ( int > option6357759511663192854e_term ) > set_Pr2560585780119916871nt_int] :
% 9.17/5.31 ( ( P @ X )
% 9.17/5.31 => ( ( member8566619992076573584nt_int @ ( produc3646306378393792727nt_int @ Y7 @ Y ) @ ( R4 @ X ) )
% 9.17/5.31 => ( member4085533954029916580nt_int @ ( produc8406175334058502835nt_int @ ( produc4305682042979456191nt_int @ X @ Y7 ) @ ( produc4305682042979456191nt_int @ X @ Y ) ) @ ( same_f6662725367016992042nt_int @ P @ R4 ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_610_zero__less__two,axiom,
% 9.17/5.31 ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ one_one_Code_integer ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_611_zero__less__two,axiom,
% 9.17/5.31 ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_612_zero__less__two,axiom,
% 9.17/5.31 ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_613_zero__less__two,axiom,
% 9.17/5.31 ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ one_one_int ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_614_is__num__normalize_I1_J,axiom,
% 9.17/5.31 ! [A: rat,B: rat,C: rat] :
% 9.17/5.31 ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 9.17/5.31 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_615_is__num__normalize_I1_J,axiom,
% 9.17/5.31 ! [A: int,B: int,C: int] :
% 9.17/5.31 ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 9.17/5.31 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_616_add_Osafe__commute,axiom,
% 9.17/5.31 ! [X: multis2468970476368604999at_nat,Y: multis2468970476368604999at_nat,A: multis2468970476368604999at_nat,B: multis2468970476368604999at_nat] :
% 9.17/5.31 ( ( syntax5084084251851430274at_nat @ ( plus_p7104986032573967614at_nat @ X @ Y ) @ A )
% 9.17/5.31 => ( ( plus_p7104986032573967614at_nat @ A @ B )
% 9.17/5.31 = ( plus_p7104986032573967614at_nat @ B @ A ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_617_add_Osafe__commute,axiom,
% 9.17/5.31 ! [X: rat,Y: rat,A: rat,B: rat] :
% 9.17/5.31 ( ( syntax3730441303064801268at_rat @ ( plus_plus_rat @ X @ Y ) @ A )
% 9.17/5.31 => ( ( plus_plus_rat @ A @ B )
% 9.17/5.31 = ( plus_plus_rat @ B @ A ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_618_add_Osafe__commute,axiom,
% 9.17/5.31 ! [X: nat,Y: nat,A: nat,B: nat] :
% 9.17/5.31 ( ( syntax4682126007086162916at_nat @ ( plus_plus_nat @ X @ Y ) @ A )
% 9.17/5.31 => ( ( plus_plus_nat @ A @ B )
% 9.17/5.31 = ( plus_plus_nat @ B @ A ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_619_add_Osafe__commute,axiom,
% 9.17/5.31 ! [X: int,Y: int,A: int,B: int] :
% 9.17/5.31 ( ( syntax5678989248478167196nt_int @ ( plus_plus_int @ X @ Y ) @ A )
% 9.17/5.31 => ( ( plus_plus_int @ A @ B )
% 9.17/5.31 = ( plus_plus_int @ B @ A ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_620_bijective__def,axiom,
% 9.17/5.31 ( biject3388518990857851981at_nat
% 9.17/5.31 = ( ^ [R5: set_Pr4329608150637261639at_nat] :
% 9.17/5.31 ( ! [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat,Z4: set_Pr1261947904930325089at_nat] :
% 9.17/5.31 ( ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ Y3 ) @ R5 )
% 9.17/5.31 & ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ Z4 ) @ R5 ) )
% 9.17/5.31 => ( Y3 = Z4 ) )
% 9.17/5.31 & ! [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat,Z4: set_Pr1261947904930325089at_nat] :
% 9.17/5.31 ( ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ Z4 ) @ R5 )
% 9.17/5.31 & ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ Y3 @ Z4 ) @ R5 ) )
% 9.17/5.31 => ( X3 = Y3 ) ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_621_bijective__def,axiom,
% 9.17/5.31 ( bijective_nat_nat
% 9.17/5.31 = ( ^ [R5: set_Pr1261947904930325089at_nat] :
% 9.17/5.31 ( ! [X3: nat,Y3: nat,Z4: nat] :
% 9.17/5.31 ( ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y3 ) @ R5 )
% 9.17/5.31 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Z4 ) @ R5 ) )
% 9.17/5.31 => ( Y3 = Z4 ) )
% 9.17/5.31 & ! [X3: nat,Y3: nat,Z4: nat] :
% 9.17/5.31 ( ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Z4 ) @ R5 )
% 9.17/5.31 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y3 @ Z4 ) @ R5 ) )
% 9.17/5.31 => ( X3 = Y3 ) ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_622_bijective__def,axiom,
% 9.17/5.31 ( biject9051520373387432658nteger
% 9.17/5.31 = ( ^ [R5: set_Pr1281608226676607948nteger] :
% 9.17/5.31 ( ! [X3: produc6241069584506657477e_term > option6357759511663192854e_term,Y3: produc8923325533196201883nteger,Z4: produc8923325533196201883nteger] :
% 9.17/5.31 ( ( ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X3 @ Y3 ) @ R5 )
% 9.17/5.31 & ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X3 @ Z4 ) @ R5 ) )
% 9.17/5.31 => ( Y3 = Z4 ) )
% 9.17/5.31 & ! [X3: produc6241069584506657477e_term > option6357759511663192854e_term,Y3: produc6241069584506657477e_term > option6357759511663192854e_term,Z4: produc8923325533196201883nteger] :
% 9.17/5.31 ( ( ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X3 @ Z4 ) @ R5 )
% 9.17/5.31 & ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ Y3 @ Z4 ) @ R5 ) )
% 9.17/5.31 => ( X3 = Y3 ) ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_623_bijective__def,axiom,
% 9.17/5.31 ( biject2615096655818420098et_nat
% 9.17/5.31 = ( ^ [R5: set_Pr3286484037609594932et_nat] :
% 9.17/5.31 ( ! [X3: produc3658429121746597890et_nat > $o,Y3: produc3658429121746597890et_nat,Z4: produc3658429121746597890et_nat] :
% 9.17/5.31 ( ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X3 @ Y3 ) @ R5 )
% 9.17/5.31 & ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X3 @ Z4 ) @ R5 ) )
% 9.17/5.31 => ( Y3 = Z4 ) )
% 9.17/5.31 & ! [X3: produc3658429121746597890et_nat > $o,Y3: produc3658429121746597890et_nat > $o,Z4: produc3658429121746597890et_nat] :
% 9.17/5.31 ( ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X3 @ Z4 ) @ R5 )
% 9.17/5.31 & ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ Y3 @ Z4 ) @ R5 ) )
% 9.17/5.31 => ( X3 = Y3 ) ) ) ) ) ).
% 9.17/5.31
% 9.17/5.31 thf(fact_624_bijective__def,axiom,
% 9.17/5.32 ( biject1468766312547416318et_nat
% 9.17/5.32 = ( ^ [R5: set_Pr8536935166611901872et_nat] :
% 9.17/5.32 ( ! [X3: produc3658429121746597890et_nat > $o,Y3: produc3925858234332021118et_nat,Z4: produc3925858234332021118et_nat] :
% 9.17/5.32 ( ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X3 @ Y3 ) @ R5 )
% 9.17/5.32 & ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X3 @ Z4 ) @ R5 ) )
% 9.17/5.32 => ( Y3 = Z4 ) )
% 9.17/5.32 & ! [X3: produc3658429121746597890et_nat > $o,Y3: produc3658429121746597890et_nat > $o,Z4: produc3925858234332021118et_nat] :
% 9.17/5.32 ( ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X3 @ Z4 ) @ R5 )
% 9.17/5.32 & ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ Y3 @ Z4 ) @ R5 ) )
% 9.17/5.32 => ( X3 = Y3 ) ) ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_625_bijective__def,axiom,
% 9.17/5.32 ( biject383251550997737151nt_int
% 9.17/5.32 = ( ^ [R5: set_Pr9222295170931077689nt_int] :
% 9.17/5.32 ( ! [X3: produc8551481072490612790e_term > option6357759511663192854e_term,Y3: product_prod_int_int,Z4: product_prod_int_int] :
% 9.17/5.32 ( ( ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X3 @ Y3 ) @ R5 )
% 9.17/5.32 & ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X3 @ Z4 ) @ R5 ) )
% 9.17/5.32 => ( Y3 = Z4 ) )
% 9.17/5.32 & ! [X3: produc8551481072490612790e_term > option6357759511663192854e_term,Y3: produc8551481072490612790e_term > option6357759511663192854e_term,Z4: product_prod_int_int] :
% 9.17/5.32 ( ( ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X3 @ Z4 ) @ R5 )
% 9.17/5.32 & ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ Y3 @ Z4 ) @ R5 ) )
% 9.17/5.32 => ( X3 = Y3 ) ) ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_626_bijective__def,axiom,
% 9.17/5.32 ( biject576505603616484041nt_int
% 9.17/5.32 = ( ^ [R5: set_Pr1872883991513573699nt_int] :
% 9.17/5.32 ( ! [X3: int > option6357759511663192854e_term,Y3: product_prod_int_int,Z4: product_prod_int_int] :
% 9.17/5.32 ( ( ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X3 @ Y3 ) @ R5 )
% 9.17/5.32 & ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X3 @ Z4 ) @ R5 ) )
% 9.17/5.32 => ( Y3 = Z4 ) )
% 9.17/5.32 & ! [X3: int > option6357759511663192854e_term,Y3: int > option6357759511663192854e_term,Z4: product_prod_int_int] :
% 9.17/5.32 ( ( ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X3 @ Z4 ) @ R5 )
% 9.17/5.32 & ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ Y3 @ Z4 ) @ R5 ) )
% 9.17/5.32 => ( X3 = Y3 ) ) ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_627_ssubst__Pair__rhs,axiom,
% 9.17/5.32 ! [R2: set_Pr1261947904930325089at_nat,S: set_Pr1261947904930325089at_nat,R4: set_Pr4329608150637261639at_nat,S3: set_Pr1261947904930325089at_nat] :
% 9.17/5.32 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ R2 @ S ) @ R4 )
% 9.17/5.32 => ( ( S3 = S )
% 9.17/5.32 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ R2 @ S3 ) @ R4 ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_628_ssubst__Pair__rhs,axiom,
% 9.17/5.32 ! [R2: nat,S: nat,R4: set_Pr1261947904930325089at_nat,S3: nat] :
% 9.17/5.32 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ R2 @ S ) @ R4 )
% 9.17/5.32 => ( ( S3 = S )
% 9.17/5.32 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ R2 @ S3 ) @ R4 ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_629_ssubst__Pair__rhs,axiom,
% 9.17/5.32 ! [R2: produc6241069584506657477e_term > option6357759511663192854e_term,S: produc8923325533196201883nteger,R4: set_Pr1281608226676607948nteger,S3: produc8923325533196201883nteger] :
% 9.17/5.32 ( ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ R2 @ S ) @ R4 )
% 9.17/5.32 => ( ( S3 = S )
% 9.17/5.32 => ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ R2 @ S3 ) @ R4 ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_630_ssubst__Pair__rhs,axiom,
% 9.17/5.32 ! [R2: produc3658429121746597890et_nat > $o,S: produc3658429121746597890et_nat,R4: set_Pr3286484037609594932et_nat,S3: produc3658429121746597890et_nat] :
% 9.17/5.32 ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ R2 @ S ) @ R4 )
% 9.17/5.32 => ( ( S3 = S )
% 9.17/5.32 => ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ R2 @ S3 ) @ R4 ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_631_ssubst__Pair__rhs,axiom,
% 9.17/5.32 ! [R2: produc3658429121746597890et_nat > $o,S: produc3925858234332021118et_nat,R4: set_Pr8536935166611901872et_nat,S3: produc3925858234332021118et_nat] :
% 9.17/5.32 ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ R2 @ S ) @ R4 )
% 9.17/5.32 => ( ( S3 = S )
% 9.17/5.32 => ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ R2 @ S3 ) @ R4 ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_632_ssubst__Pair__rhs,axiom,
% 9.17/5.32 ! [R2: produc8551481072490612790e_term > option6357759511663192854e_term,S: product_prod_int_int,R4: set_Pr9222295170931077689nt_int,S3: product_prod_int_int] :
% 9.17/5.32 ( ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ R2 @ S ) @ R4 )
% 9.17/5.32 => ( ( S3 = S )
% 9.17/5.32 => ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ R2 @ S3 ) @ R4 ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_633_ssubst__Pair__rhs,axiom,
% 9.17/5.32 ! [R2: int > option6357759511663192854e_term,S: product_prod_int_int,R4: set_Pr1872883991513573699nt_int,S3: product_prod_int_int] :
% 9.17/5.32 ( ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ R2 @ S ) @ R4 )
% 9.17/5.32 => ( ( S3 = S )
% 9.17/5.32 => ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ R2 @ S3 ) @ R4 ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_634_add__is__0,axiom,
% 9.17/5.32 ! [M2: nat,N2: nat] :
% 9.17/5.32 ( ( ( plus_plus_nat @ M2 @ N2 )
% 9.17/5.32 = zero_zero_nat )
% 9.17/5.32 = ( ( M2 = zero_zero_nat )
% 9.17/5.32 & ( N2 = zero_zero_nat ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_635_Nat_Oadd__0__right,axiom,
% 9.17/5.32 ! [M2: nat] :
% 9.17/5.32 ( ( plus_plus_nat @ M2 @ zero_zero_nat )
% 9.17/5.32 = M2 ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_636_not__gr__zero,axiom,
% 9.17/5.32 ! [N2: nat] :
% 9.17/5.32 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N2 ) )
% 9.17/5.32 = ( N2 = zero_zero_nat ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_637_add__0,axiom,
% 9.17/5.32 ! [A: code_integer] :
% 9.17/5.32 ( ( plus_p5714425477246183910nteger @ zero_z3403309356797280102nteger @ A )
% 9.17/5.32 = A ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_638_add__0,axiom,
% 9.17/5.32 ! [A: multis2468970476368604999at_nat] :
% 9.17/5.32 ( ( plus_p7104986032573967614at_nat @ zero_z1048942125864253310at_nat @ A )
% 9.17/5.32 = A ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_639_add__0,axiom,
% 9.17/5.32 ! [A: rat] :
% 9.17/5.32 ( ( plus_plus_rat @ zero_zero_rat @ A )
% 9.17/5.32 = A ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_640_add__0,axiom,
% 9.17/5.32 ! [A: nat] :
% 9.17/5.32 ( ( plus_plus_nat @ zero_zero_nat @ A )
% 9.17/5.32 = A ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_641_add__0,axiom,
% 9.17/5.32 ! [A: int] :
% 9.17/5.32 ( ( plus_plus_int @ zero_zero_int @ A )
% 9.17/5.32 = A ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_642_zero__eq__add__iff__both__eq__0,axiom,
% 9.17/5.32 ! [X: nat,Y: nat] :
% 9.17/5.32 ( ( zero_zero_nat
% 9.17/5.32 = ( plus_plus_nat @ X @ Y ) )
% 9.17/5.32 = ( ( X = zero_zero_nat )
% 9.17/5.32 & ( Y = zero_zero_nat ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_643_add__eq__0__iff__both__eq__0,axiom,
% 9.17/5.32 ! [X: nat,Y: nat] :
% 9.17/5.32 ( ( ( plus_plus_nat @ X @ Y )
% 9.17/5.32 = zero_zero_nat )
% 9.17/5.32 = ( ( X = zero_zero_nat )
% 9.17/5.32 & ( Y = zero_zero_nat ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_644_add__cancel__right__right,axiom,
% 9.17/5.32 ! [A: code_integer,B: code_integer] :
% 9.17/5.32 ( ( A
% 9.17/5.32 = ( plus_p5714425477246183910nteger @ A @ B ) )
% 9.17/5.32 = ( B = zero_z3403309356797280102nteger ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_645_add__cancel__right__right,axiom,
% 9.17/5.32 ! [A: multis2468970476368604999at_nat,B: multis2468970476368604999at_nat] :
% 9.17/5.32 ( ( A
% 9.17/5.32 = ( plus_p7104986032573967614at_nat @ A @ B ) )
% 9.17/5.32 = ( B = zero_z1048942125864253310at_nat ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_646_add__cancel__right__right,axiom,
% 9.17/5.32 ! [A: rat,B: rat] :
% 9.17/5.32 ( ( A
% 9.17/5.32 = ( plus_plus_rat @ A @ B ) )
% 9.17/5.32 = ( B = zero_zero_rat ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_647_add__cancel__right__right,axiom,
% 9.17/5.32 ! [A: nat,B: nat] :
% 9.17/5.32 ( ( A
% 9.17/5.32 = ( plus_plus_nat @ A @ B ) )
% 9.17/5.32 = ( B = zero_zero_nat ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_648_add__cancel__right__right,axiom,
% 9.17/5.32 ! [A: int,B: int] :
% 9.17/5.32 ( ( A
% 9.17/5.32 = ( plus_plus_int @ A @ B ) )
% 9.17/5.32 = ( B = zero_zero_int ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_649_add__cancel__right__left,axiom,
% 9.17/5.32 ! [A: code_integer,B: code_integer] :
% 9.17/5.32 ( ( A
% 9.17/5.32 = ( plus_p5714425477246183910nteger @ B @ A ) )
% 9.17/5.32 = ( B = zero_z3403309356797280102nteger ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_650_add__cancel__right__left,axiom,
% 9.17/5.32 ! [A: multis2468970476368604999at_nat,B: multis2468970476368604999at_nat] :
% 9.17/5.32 ( ( A
% 9.17/5.32 = ( plus_p7104986032573967614at_nat @ B @ A ) )
% 9.17/5.32 = ( B = zero_z1048942125864253310at_nat ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_651_add__cancel__right__left,axiom,
% 9.17/5.32 ! [A: rat,B: rat] :
% 9.17/5.32 ( ( A
% 9.17/5.32 = ( plus_plus_rat @ B @ A ) )
% 9.17/5.32 = ( B = zero_zero_rat ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_652_add__cancel__right__left,axiom,
% 9.17/5.32 ! [A: nat,B: nat] :
% 9.17/5.32 ( ( A
% 9.17/5.32 = ( plus_plus_nat @ B @ A ) )
% 9.17/5.32 = ( B = zero_zero_nat ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_653_add__cancel__right__left,axiom,
% 9.17/5.32 ! [A: int,B: int] :
% 9.17/5.32 ( ( A
% 9.17/5.32 = ( plus_plus_int @ B @ A ) )
% 9.17/5.32 = ( B = zero_zero_int ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_654_add__cancel__left__right,axiom,
% 9.17/5.32 ! [A: code_integer,B: code_integer] :
% 9.17/5.32 ( ( ( plus_p5714425477246183910nteger @ A @ B )
% 9.17/5.32 = A )
% 9.17/5.32 = ( B = zero_z3403309356797280102nteger ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_655_add__cancel__left__right,axiom,
% 9.17/5.32 ! [A: multis2468970476368604999at_nat,B: multis2468970476368604999at_nat] :
% 9.17/5.32 ( ( ( plus_p7104986032573967614at_nat @ A @ B )
% 9.17/5.32 = A )
% 9.17/5.32 = ( B = zero_z1048942125864253310at_nat ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_656_add__cancel__left__right,axiom,
% 9.17/5.32 ! [A: rat,B: rat] :
% 9.17/5.32 ( ( ( plus_plus_rat @ A @ B )
% 9.17/5.32 = A )
% 9.17/5.32 = ( B = zero_zero_rat ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_657_add__cancel__left__right,axiom,
% 9.17/5.32 ! [A: nat,B: nat] :
% 9.17/5.32 ( ( ( plus_plus_nat @ A @ B )
% 9.17/5.32 = A )
% 9.17/5.32 = ( B = zero_zero_nat ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_658_add__cancel__left__right,axiom,
% 9.17/5.32 ! [A: int,B: int] :
% 9.17/5.32 ( ( ( plus_plus_int @ A @ B )
% 9.17/5.32 = A )
% 9.17/5.32 = ( B = zero_zero_int ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_659_add__cancel__left__left,axiom,
% 9.17/5.32 ! [B: code_integer,A: code_integer] :
% 9.17/5.32 ( ( ( plus_p5714425477246183910nteger @ B @ A )
% 9.17/5.32 = A )
% 9.17/5.32 = ( B = zero_z3403309356797280102nteger ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_660_add__cancel__left__left,axiom,
% 9.17/5.32 ! [B: multis2468970476368604999at_nat,A: multis2468970476368604999at_nat] :
% 9.17/5.32 ( ( ( plus_p7104986032573967614at_nat @ B @ A )
% 9.17/5.32 = A )
% 9.17/5.32 = ( B = zero_z1048942125864253310at_nat ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_661_add__cancel__left__left,axiom,
% 9.17/5.32 ! [B: rat,A: rat] :
% 9.17/5.32 ( ( ( plus_plus_rat @ B @ A )
% 9.17/5.32 = A )
% 9.17/5.32 = ( B = zero_zero_rat ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_662_add__cancel__left__left,axiom,
% 9.17/5.32 ! [B: nat,A: nat] :
% 9.17/5.32 ( ( ( plus_plus_nat @ B @ A )
% 9.17/5.32 = A )
% 9.17/5.32 = ( B = zero_zero_nat ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_663_add__cancel__left__left,axiom,
% 9.17/5.32 ! [B: int,A: int] :
% 9.17/5.32 ( ( ( plus_plus_int @ B @ A )
% 9.17/5.32 = A )
% 9.17/5.32 = ( B = zero_zero_int ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_664_double__zero__sym,axiom,
% 9.17/5.32 ! [A: code_integer] :
% 9.17/5.32 ( ( zero_z3403309356797280102nteger
% 9.17/5.32 = ( plus_p5714425477246183910nteger @ A @ A ) )
% 9.17/5.32 = ( A = zero_z3403309356797280102nteger ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_665_double__zero__sym,axiom,
% 9.17/5.32 ! [A: rat] :
% 9.17/5.32 ( ( zero_zero_rat
% 9.17/5.32 = ( plus_plus_rat @ A @ A ) )
% 9.17/5.32 = ( A = zero_zero_rat ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_666_double__zero__sym,axiom,
% 9.17/5.32 ! [A: int] :
% 9.17/5.32 ( ( zero_zero_int
% 9.17/5.32 = ( plus_plus_int @ A @ A ) )
% 9.17/5.32 = ( A = zero_zero_int ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_667_add_Oright__neutral,axiom,
% 9.17/5.32 ! [A: code_integer] :
% 9.17/5.32 ( ( plus_p5714425477246183910nteger @ A @ zero_z3403309356797280102nteger )
% 9.17/5.32 = A ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_668_add_Oright__neutral,axiom,
% 9.17/5.32 ! [A: multis2468970476368604999at_nat] :
% 9.17/5.32 ( ( plus_p7104986032573967614at_nat @ A @ zero_z1048942125864253310at_nat )
% 9.17/5.32 = A ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_669_add_Oright__neutral,axiom,
% 9.17/5.32 ! [A: rat] :
% 9.17/5.32 ( ( plus_plus_rat @ A @ zero_zero_rat )
% 9.17/5.32 = A ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_670_add_Oright__neutral,axiom,
% 9.17/5.32 ! [A: nat] :
% 9.17/5.32 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 9.17/5.32 = A ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_671_add_Oright__neutral,axiom,
% 9.17/5.32 ! [A: int] :
% 9.17/5.32 ( ( plus_plus_int @ A @ zero_zero_int )
% 9.17/5.32 = A ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_672_add__gr__0,axiom,
% 9.17/5.32 ! [M2: nat,N2: nat] :
% 9.17/5.32 ( ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ M2 @ N2 ) )
% 9.17/5.32 = ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 9.17/5.32 | ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_673_less__one,axiom,
% 9.17/5.32 ! [N2: nat] :
% 9.17/5.32 ( ( ord_less_nat @ N2 @ one_one_nat )
% 9.17/5.32 = ( N2 = zero_zero_nat ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_674_some__opt__eq__trivial,axiom,
% 9.17/5.32 ! [X: num] :
% 9.17/5.32 ( ( eps_Opt_num
% 9.17/5.32 @ ^ [Y3: num] : ( Y3 = X ) )
% 9.17/5.32 = ( some_num @ X ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_675_some__opt__eq__trivial,axiom,
% 9.17/5.32 ! [X: produc8664842809031399944it_nat] :
% 9.17/5.32 ( ( eps_Op3393321821070424684it_nat
% 9.17/5.32 @ ^ [Y3: produc8664842809031399944it_nat] : ( Y3 = X ) )
% 9.17/5.32 = ( some_P1914260805536162275it_nat @ X ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_676_zero__less__double__add__iff__zero__less__single__add,axiom,
% 9.17/5.32 ! [A: code_integer] :
% 9.17/5.32 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ A @ A ) )
% 9.17/5.32 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_677_zero__less__double__add__iff__zero__less__single__add,axiom,
% 9.17/5.32 ! [A: rat] :
% 9.17/5.32 ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ A ) )
% 9.17/5.32 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_678_zero__less__double__add__iff__zero__less__single__add,axiom,
% 9.17/5.32 ! [A: int] :
% 9.17/5.32 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
% 9.17/5.32 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_679_double__add__less__zero__iff__single__add__less__zero,axiom,
% 9.17/5.32 ! [A: code_integer] :
% 9.17/5.32 ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ A ) @ zero_z3403309356797280102nteger )
% 9.17/5.32 = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_680_double__add__less__zero__iff__single__add__less__zero,axiom,
% 9.17/5.32 ! [A: rat] :
% 9.17/5.32 ( ( ord_less_rat @ ( plus_plus_rat @ A @ A ) @ zero_zero_rat )
% 9.17/5.32 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_681_double__add__less__zero__iff__single__add__less__zero,axiom,
% 9.17/5.32 ! [A: int] :
% 9.17/5.32 ( ( ord_less_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
% 9.17/5.32 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_682_less__add__same__cancel2,axiom,
% 9.17/5.32 ! [A: code_integer,B: code_integer] :
% 9.17/5.32 ( ( ord_le6747313008572928689nteger @ A @ ( plus_p5714425477246183910nteger @ B @ A ) )
% 9.17/5.32 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_683_less__add__same__cancel2,axiom,
% 9.17/5.32 ! [A: rat,B: rat] :
% 9.17/5.32 ( ( ord_less_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 9.17/5.32 = ( ord_less_rat @ zero_zero_rat @ B ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_684_less__add__same__cancel2,axiom,
% 9.17/5.32 ! [A: nat,B: nat] :
% 9.17/5.32 ( ( ord_less_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 9.17/5.32 = ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_685_less__add__same__cancel2,axiom,
% 9.17/5.32 ! [A: int,B: int] :
% 9.17/5.32 ( ( ord_less_int @ A @ ( plus_plus_int @ B @ A ) )
% 9.17/5.32 = ( ord_less_int @ zero_zero_int @ B ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_686_less__add__same__cancel1,axiom,
% 9.17/5.32 ! [A: code_integer,B: code_integer] :
% 9.17/5.32 ( ( ord_le6747313008572928689nteger @ A @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 9.17/5.32 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_687_less__add__same__cancel1,axiom,
% 9.17/5.32 ! [A: rat,B: rat] :
% 9.17/5.32 ( ( ord_less_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 9.17/5.32 = ( ord_less_rat @ zero_zero_rat @ B ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_688_less__add__same__cancel1,axiom,
% 9.17/5.32 ! [A: nat,B: nat] :
% 9.17/5.32 ( ( ord_less_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 9.17/5.32 = ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_689_less__add__same__cancel1,axiom,
% 9.17/5.32 ! [A: int,B: int] :
% 9.17/5.32 ( ( ord_less_int @ A @ ( plus_plus_int @ A @ B ) )
% 9.17/5.32 = ( ord_less_int @ zero_zero_int @ B ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_690_add__less__same__cancel2,axiom,
% 9.17/5.32 ! [A: code_integer,B: code_integer] :
% 9.17/5.32 ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ B )
% 9.17/5.32 = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_691_add__less__same__cancel2,axiom,
% 9.17/5.32 ! [A: rat,B: rat] :
% 9.17/5.32 ( ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 9.17/5.32 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_692_add__less__same__cancel2,axiom,
% 9.17/5.32 ! [A: nat,B: nat] :
% 9.17/5.32 ( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 9.17/5.32 = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_693_add__less__same__cancel2,axiom,
% 9.17/5.32 ! [A: int,B: int] :
% 9.17/5.32 ( ( ord_less_int @ ( plus_plus_int @ A @ B ) @ B )
% 9.17/5.32 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_694_add__less__same__cancel1,axiom,
% 9.17/5.32 ! [B: code_integer,A: code_integer] :
% 9.17/5.32 ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ B @ A ) @ B )
% 9.17/5.32 = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_695_add__less__same__cancel1,axiom,
% 9.17/5.32 ! [B: rat,A: rat] :
% 9.17/5.32 ( ( ord_less_rat @ ( plus_plus_rat @ B @ A ) @ B )
% 9.17/5.32 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_696_add__less__same__cancel1,axiom,
% 9.17/5.32 ! [B: nat,A: nat] :
% 9.17/5.32 ( ( ord_less_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 9.17/5.32 = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_697_add__less__same__cancel1,axiom,
% 9.17/5.32 ! [B: int,A: int] :
% 9.17/5.32 ( ( ord_less_int @ ( plus_plus_int @ B @ A ) @ B )
% 9.17/5.32 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_698_some__opt__false__trivial,axiom,
% 9.17/5.32 ( ( eps_Op1141264490366522080it_nat
% 9.17/5.32 @ ^ [Uu: produc6714399278180371524it_nat] : $false )
% 9.17/5.32 = none_P2587165478634041381it_nat ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_699_some__opt__false__trivial,axiom,
% 9.17/5.32 ( ( eps_Opt_num
% 9.17/5.32 @ ^ [Uu: num] : $false )
% 9.17/5.32 = none_num ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_700_some__opt__false__trivial,axiom,
% 9.17/5.32 ( ( eps_Op3393321821070424684it_nat
% 9.17/5.32 @ ^ [Uu: produc8664842809031399944it_nat] : $false )
% 9.17/5.32 = none_P9117596204409417319it_nat ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_701_zero__reorient,axiom,
% 9.17/5.32 ! [X: code_integer] :
% 9.17/5.32 ( ( zero_z3403309356797280102nteger = X )
% 9.17/5.32 = ( X = zero_z3403309356797280102nteger ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_702_zero__reorient,axiom,
% 9.17/5.32 ! [X: multis2468970476368604999at_nat] :
% 9.17/5.32 ( ( zero_z1048942125864253310at_nat = X )
% 9.17/5.32 = ( X = zero_z1048942125864253310at_nat ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_703_zero__reorient,axiom,
% 9.17/5.32 ! [X: rat] :
% 9.17/5.32 ( ( zero_zero_rat = X )
% 9.17/5.32 = ( X = zero_zero_rat ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_704_zero__reorient,axiom,
% 9.17/5.32 ! [X: nat] :
% 9.17/5.32 ( ( zero_zero_nat = X )
% 9.17/5.32 = ( X = zero_zero_nat ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_705_zero__reorient,axiom,
% 9.17/5.32 ! [X: int] :
% 9.17/5.32 ( ( zero_zero_int = X )
% 9.17/5.32 = ( X = zero_zero_int ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_706_fun_Omap__ident,axiom,
% 9.17/5.32 ! [T: num > code_integer] :
% 9.17/5.32 ( ( comp_C3531382070062128313er_num
% 9.17/5.32 @ ^ [X3: code_integer] : X3
% 9.17/5.32 @ T )
% 9.17/5.32 = T ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_707_option_Odisc__eq__case_I2_J,axiom,
% 9.17/5.32 ! [Option: option3216581401566546698it_nat] :
% 9.17/5.32 ( ( Option != none_P2587165478634041381it_nat )
% 9.17/5.32 = ( case_o2169478532838437047it_nat @ $false
% 9.17/5.32 @ ^ [Uu: produc6714399278180371524it_nat] : $true
% 9.17/5.32 @ Option ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_708_option_Odisc__eq__case_I2_J,axiom,
% 9.17/5.32 ! [Option: option_num] :
% 9.17/5.32 ( ( Option != none_num )
% 9.17/5.32 = ( case_option_o_num @ $false
% 9.17/5.32 @ ^ [Uu: num] : $true
% 9.17/5.32 @ Option ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_709_option_Odisc__eq__case_I2_J,axiom,
% 9.17/5.32 ! [Option: option8956607266484857688it_nat] :
% 9.17/5.32 ( ( Option != none_P9117596204409417319it_nat )
% 9.17/5.32 = ( case_o2686588417244861013it_nat @ $false
% 9.17/5.32 @ ^ [Uu: produc8664842809031399944it_nat] : $true
% 9.17/5.32 @ Option ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_710_option_Odisc__eq__case_I1_J,axiom,
% 9.17/5.32 ! [Option: option3216581401566546698it_nat] :
% 9.17/5.32 ( ( Option = none_P2587165478634041381it_nat )
% 9.17/5.32 = ( case_o2169478532838437047it_nat @ $true
% 9.17/5.32 @ ^ [Uu: produc6714399278180371524it_nat] : $false
% 9.17/5.32 @ Option ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_711_option_Odisc__eq__case_I1_J,axiom,
% 9.17/5.32 ! [Option: option_num] :
% 9.17/5.32 ( ( Option = none_num )
% 9.17/5.32 = ( case_option_o_num @ $true
% 9.17/5.32 @ ^ [Uu: num] : $false
% 9.17/5.32 @ Option ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_712_option_Odisc__eq__case_I1_J,axiom,
% 9.17/5.32 ! [Option: option8956607266484857688it_nat] :
% 9.17/5.32 ( ( Option = none_P9117596204409417319it_nat )
% 9.17/5.32 = ( case_o2686588417244861013it_nat @ $true
% 9.17/5.32 @ ^ [Uu: produc8664842809031399944it_nat] : $false
% 9.17/5.32 @ Option ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_713_option_Ocase__distrib,axiom,
% 9.17/5.32 ! [H3: int > int,F1: int,F22: num > int,Option: option_num] :
% 9.17/5.32 ( ( H3 @ ( case_option_int_num @ F1 @ F22 @ Option ) )
% 9.17/5.32 = ( case_option_int_num @ ( H3 @ F1 )
% 9.17/5.32 @ ^ [X3: num] : ( H3 @ ( F22 @ X3 ) )
% 9.17/5.32 @ Option ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_714_option_Ocase__distrib,axiom,
% 9.17/5.32 ! [H3: int > option_num,F1: int,F22: num > int,Option: option_num] :
% 9.17/5.32 ( ( H3 @ ( case_option_int_num @ F1 @ F22 @ Option ) )
% 9.17/5.32 = ( case_o6005452278849405969um_num @ ( H3 @ F1 )
% 9.17/5.32 @ ^ [X3: num] : ( H3 @ ( F22 @ X3 ) )
% 9.17/5.32 @ Option ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_715_option_Ocase__distrib,axiom,
% 9.17/5.32 ! [H3: int > num,F1: int,F22: num > int,Option: option_num] :
% 9.17/5.32 ( ( H3 @ ( case_option_int_num @ F1 @ F22 @ Option ) )
% 9.17/5.32 = ( case_option_num_num @ ( H3 @ F1 )
% 9.17/5.32 @ ^ [X3: num] : ( H3 @ ( F22 @ X3 ) )
% 9.17/5.32 @ Option ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_716_option_Ocase__distrib,axiom,
% 9.17/5.32 ! [H3: option_num > int,F1: option_num,F22: num > option_num,Option: option_num] :
% 9.17/5.32 ( ( H3 @ ( case_o6005452278849405969um_num @ F1 @ F22 @ Option ) )
% 9.17/5.32 = ( case_option_int_num @ ( H3 @ F1 )
% 9.17/5.32 @ ^ [X3: num] : ( H3 @ ( F22 @ X3 ) )
% 9.17/5.32 @ Option ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_717_option_Ocase__distrib,axiom,
% 9.17/5.32 ! [H3: option_num > option_num,F1: option_num,F22: num > option_num,Option: option_num] :
% 9.17/5.32 ( ( H3 @ ( case_o6005452278849405969um_num @ F1 @ F22 @ Option ) )
% 9.17/5.32 = ( case_o6005452278849405969um_num @ ( H3 @ F1 )
% 9.17/5.32 @ ^ [X3: num] : ( H3 @ ( F22 @ X3 ) )
% 9.17/5.32 @ Option ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_718_option_Ocase__distrib,axiom,
% 9.17/5.32 ! [H3: option_num > num,F1: option_num,F22: num > option_num,Option: option_num] :
% 9.17/5.32 ( ( H3 @ ( case_o6005452278849405969um_num @ F1 @ F22 @ Option ) )
% 9.17/5.32 = ( case_option_num_num @ ( H3 @ F1 )
% 9.17/5.32 @ ^ [X3: num] : ( H3 @ ( F22 @ X3 ) )
% 9.17/5.32 @ Option ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_719_option_Ocase__distrib,axiom,
% 9.17/5.32 ! [H3: num > int,F1: num,F22: num > num,Option: option_num] :
% 9.17/5.32 ( ( H3 @ ( case_option_num_num @ F1 @ F22 @ Option ) )
% 9.17/5.32 = ( case_option_int_num @ ( H3 @ F1 )
% 9.17/5.32 @ ^ [X3: num] : ( H3 @ ( F22 @ X3 ) )
% 9.17/5.32 @ Option ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_720_option_Ocase__distrib,axiom,
% 9.17/5.32 ! [H3: num > option_num,F1: num,F22: num > num,Option: option_num] :
% 9.17/5.32 ( ( H3 @ ( case_option_num_num @ F1 @ F22 @ Option ) )
% 9.17/5.32 = ( case_o6005452278849405969um_num @ ( H3 @ F1 )
% 9.17/5.32 @ ^ [X3: num] : ( H3 @ ( F22 @ X3 ) )
% 9.17/5.32 @ Option ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_721_option_Ocase__distrib,axiom,
% 9.17/5.32 ! [H3: num > num,F1: num,F22: num > num,Option: option_num] :
% 9.17/5.32 ( ( H3 @ ( case_option_num_num @ F1 @ F22 @ Option ) )
% 9.17/5.32 = ( case_option_num_num @ ( H3 @ F1 )
% 9.17/5.32 @ ^ [X3: num] : ( H3 @ ( F22 @ X3 ) )
% 9.17/5.32 @ Option ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_722_case__optionE,axiom,
% 9.17/5.32 ! [P: $o,Q: produc6714399278180371524it_nat > $o,X: option3216581401566546698it_nat] :
% 9.17/5.32 ( ( case_o2169478532838437047it_nat @ P @ Q @ X )
% 9.17/5.32 => ( ( ( X = none_P2587165478634041381it_nat )
% 9.17/5.32 => ~ P )
% 9.17/5.32 => ~ ! [Y5: produc6714399278180371524it_nat] :
% 9.17/5.32 ( ( X
% 9.17/5.32 = ( some_P6105628898608307625it_nat @ Y5 ) )
% 9.17/5.32 => ~ ( Q @ Y5 ) ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_723_case__optionE,axiom,
% 9.17/5.32 ! [P: $o,Q: num > $o,X: option_num] :
% 9.17/5.32 ( ( case_option_o_num @ P @ Q @ X )
% 9.17/5.32 => ( ( ( X = none_num )
% 9.17/5.32 => ~ P )
% 9.17/5.32 => ~ ! [Y5: num] :
% 9.17/5.32 ( ( X
% 9.17/5.32 = ( some_num @ Y5 ) )
% 9.17/5.32 => ~ ( Q @ Y5 ) ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_724_case__optionE,axiom,
% 9.17/5.32 ! [P: $o,Q: produc8664842809031399944it_nat > $o,X: option8956607266484857688it_nat] :
% 9.17/5.32 ( ( case_o2686588417244861013it_nat @ P @ Q @ X )
% 9.17/5.32 => ( ( ( X = none_P9117596204409417319it_nat )
% 9.17/5.32 => ~ P )
% 9.17/5.32 => ~ ! [Y5: produc8664842809031399944it_nat] :
% 9.17/5.32 ( ( X
% 9.17/5.32 = ( some_P1914260805536162275it_nat @ Y5 ) )
% 9.17/5.32 => ~ ( Q @ Y5 ) ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_725_combine__options__def,axiom,
% 9.17/5.32 ( combin4318129983670048329it_nat
% 9.17/5.32 = ( ^ [F2: produc8664842809031399944it_nat > produc8664842809031399944it_nat > produc8664842809031399944it_nat,X3: option8956607266484857688it_nat,Y3: option8956607266484857688it_nat] :
% 9.17/5.32 ( case_o2963978774867076333it_nat @ Y3
% 9.17/5.32 @ ^ [Z4: produc8664842809031399944it_nat] :
% 9.17/5.32 ( case_o2963978774867076333it_nat @ ( some_P1914260805536162275it_nat @ Z4 )
% 9.17/5.32 @ ^ [Aa: produc8664842809031399944it_nat] : ( some_P1914260805536162275it_nat @ ( F2 @ Z4 @ Aa ) )
% 9.17/5.32 @ Y3 )
% 9.17/5.32 @ X3 ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_726_combine__options__def,axiom,
% 9.17/5.32 ( combine_options_num
% 9.17/5.32 = ( ^ [F2: num > num > num,X3: option_num,Y3: option_num] :
% 9.17/5.32 ( case_o6005452278849405969um_num @ Y3
% 9.17/5.32 @ ^ [Z4: num] :
% 9.17/5.32 ( case_o6005452278849405969um_num @ ( some_num @ Z4 )
% 9.17/5.32 @ ^ [Aa: num] : ( some_num @ ( F2 @ Z4 @ Aa ) )
% 9.17/5.32 @ Y3 )
% 9.17/5.32 @ X3 ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_727_less__option__def,axiom,
% 9.17/5.32 ( ord_le7113747843092208513nteger
% 9.17/5.32 = ( ^ [X3: option_Code_integer] :
% 9.17/5.32 ( case_o43118980978444458nteger @ $false
% 9.17/5.32 @ ^ [Y3: code_integer] :
% 9.17/5.32 ( case_o43118980978444458nteger @ $true
% 9.17/5.32 @ ^ [Z4: code_integer] : ( ord_le6747313008572928689nteger @ Z4 @ Y3 )
% 9.17/5.32 @ X3 ) ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_728_less__option__def,axiom,
% 9.17/5.32 ( ord_less_option_rat
% 9.17/5.32 = ( ^ [X3: option_rat] :
% 9.17/5.32 ( case_option_o_rat @ $false
% 9.17/5.32 @ ^ [Y3: rat] :
% 9.17/5.32 ( case_option_o_rat @ $true
% 9.17/5.32 @ ^ [Z4: rat] : ( ord_less_rat @ Z4 @ Y3 )
% 9.17/5.32 @ X3 ) ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_729_less__option__def,axiom,
% 9.17/5.32 ( ord_less_option_num
% 9.17/5.32 = ( ^ [X3: option_num] :
% 9.17/5.32 ( case_option_o_num @ $false
% 9.17/5.32 @ ^ [Y3: num] :
% 9.17/5.32 ( case_option_o_num @ $true
% 9.17/5.32 @ ^ [Z4: num] : ( ord_less_num @ Z4 @ Y3 )
% 9.17/5.32 @ X3 ) ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_730_less__option__def,axiom,
% 9.17/5.32 ( ord_less_option_nat
% 9.17/5.32 = ( ^ [X3: option_nat] :
% 9.17/5.32 ( case_option_o_nat @ $false
% 9.17/5.32 @ ^ [Y3: nat] :
% 9.17/5.32 ( case_option_o_nat @ $true
% 9.17/5.32 @ ^ [Z4: nat] : ( ord_less_nat @ Z4 @ Y3 )
% 9.17/5.32 @ X3 ) ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_731_less__option__def,axiom,
% 9.17/5.32 ( ord_less_option_int
% 9.17/5.32 = ( ^ [X3: option_int] :
% 9.17/5.32 ( case_option_o_int @ $false
% 9.17/5.32 @ ^ [Y3: int] :
% 9.17/5.32 ( case_option_o_int @ $true
% 9.17/5.32 @ ^ [Z4: int] : ( ord_less_int @ Z4 @ Y3 )
% 9.17/5.32 @ X3 ) ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_732_zero__less__iff__neq__zero,axiom,
% 9.17/5.32 ! [N2: nat] :
% 9.17/5.32 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 9.17/5.32 = ( N2 != zero_zero_nat ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_733_gr__implies__not__zero,axiom,
% 9.17/5.32 ! [M2: nat,N2: nat] :
% 9.17/5.32 ( ( ord_less_nat @ M2 @ N2 )
% 9.17/5.32 => ( N2 != zero_zero_nat ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_734_not__less__zero,axiom,
% 9.17/5.32 ! [N2: nat] :
% 9.17/5.32 ~ ( ord_less_nat @ N2 @ zero_zero_nat ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_735_gr__zeroI,axiom,
% 9.17/5.32 ! [N2: nat] :
% 9.17/5.32 ( ( N2 != zero_zero_nat )
% 9.17/5.32 => ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_736_add_Ogroup__left__neutral,axiom,
% 9.17/5.32 ! [A: code_integer] :
% 9.17/5.32 ( ( plus_p5714425477246183910nteger @ zero_z3403309356797280102nteger @ A )
% 9.17/5.32 = A ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_737_add_Ogroup__left__neutral,axiom,
% 9.17/5.32 ! [A: rat] :
% 9.17/5.32 ( ( plus_plus_rat @ zero_zero_rat @ A )
% 9.17/5.32 = A ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_738_add_Ogroup__left__neutral,axiom,
% 9.17/5.32 ! [A: int] :
% 9.17/5.32 ( ( plus_plus_int @ zero_zero_int @ A )
% 9.17/5.32 = A ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_739_add_Ocomm__neutral,axiom,
% 9.17/5.32 ! [A: code_integer] :
% 9.17/5.32 ( ( plus_p5714425477246183910nteger @ A @ zero_z3403309356797280102nteger )
% 9.17/5.32 = A ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_740_add_Ocomm__neutral,axiom,
% 9.17/5.32 ! [A: multis2468970476368604999at_nat] :
% 9.17/5.32 ( ( plus_p7104986032573967614at_nat @ A @ zero_z1048942125864253310at_nat )
% 9.17/5.32 = A ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_741_add_Ocomm__neutral,axiom,
% 9.17/5.32 ! [A: rat] :
% 9.17/5.32 ( ( plus_plus_rat @ A @ zero_zero_rat )
% 9.17/5.32 = A ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_742_add_Ocomm__neutral,axiom,
% 9.17/5.32 ! [A: nat] :
% 9.17/5.32 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 9.17/5.32 = A ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_743_add_Ocomm__neutral,axiom,
% 9.17/5.32 ! [A: int] :
% 9.17/5.32 ( ( plus_plus_int @ A @ zero_zero_int )
% 9.17/5.32 = A ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_744_comm__monoid__add__class_Oadd__0,axiom,
% 9.17/5.32 ! [A: code_integer] :
% 9.17/5.32 ( ( plus_p5714425477246183910nteger @ zero_z3403309356797280102nteger @ A )
% 9.17/5.32 = A ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_745_comm__monoid__add__class_Oadd__0,axiom,
% 9.17/5.32 ! [A: multis2468970476368604999at_nat] :
% 9.17/5.32 ( ( plus_p7104986032573967614at_nat @ zero_z1048942125864253310at_nat @ A )
% 9.17/5.32 = A ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_746_comm__monoid__add__class_Oadd__0,axiom,
% 9.17/5.32 ! [A: rat] :
% 9.17/5.32 ( ( plus_plus_rat @ zero_zero_rat @ A )
% 9.17/5.32 = A ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_747_comm__monoid__add__class_Oadd__0,axiom,
% 9.17/5.32 ! [A: nat] :
% 9.17/5.32 ( ( plus_plus_nat @ zero_zero_nat @ A )
% 9.17/5.32 = A ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_748_comm__monoid__add__class_Oadd__0,axiom,
% 9.17/5.32 ! [A: int] :
% 9.17/5.32 ( ( plus_plus_int @ zero_zero_int @ A )
% 9.17/5.32 = A ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_749_zero__neq__one,axiom,
% 9.17/5.32 zero_z3403309356797280102nteger != one_one_Code_integer ).
% 9.17/5.32
% 9.17/5.32 thf(fact_750_zero__neq__one,axiom,
% 9.17/5.32 zero_zero_rat != one_one_rat ).
% 9.17/5.32
% 9.17/5.32 thf(fact_751_zero__neq__one,axiom,
% 9.17/5.32 zero_zero_nat != one_one_nat ).
% 9.17/5.32
% 9.17/5.32 thf(fact_752_zero__neq__one,axiom,
% 9.17/5.32 zero_zero_int != one_one_int ).
% 9.17/5.32
% 9.17/5.32 thf(fact_753_plus__nat_Oadd__0,axiom,
% 9.17/5.32 ! [N2: nat] :
% 9.17/5.32 ( ( plus_plus_nat @ zero_zero_nat @ N2 )
% 9.17/5.32 = N2 ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_754_add__eq__self__zero,axiom,
% 9.17/5.32 ! [M2: nat,N2: nat] :
% 9.17/5.32 ( ( ( plus_plus_nat @ M2 @ N2 )
% 9.17/5.32 = M2 )
% 9.17/5.32 => ( N2 = zero_zero_nat ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_755_less__numeral__extra_I1_J,axiom,
% 9.17/5.32 ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ one_one_Code_integer ).
% 9.17/5.32
% 9.17/5.32 thf(fact_756_less__numeral__extra_I1_J,axiom,
% 9.17/5.32 ord_less_rat @ zero_zero_rat @ one_one_rat ).
% 9.17/5.32
% 9.17/5.32 thf(fact_757_less__numeral__extra_I1_J,axiom,
% 9.17/5.32 ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 9.17/5.32
% 9.17/5.32 thf(fact_758_less__numeral__extra_I1_J,axiom,
% 9.17/5.32 ord_less_int @ zero_zero_int @ one_one_int ).
% 9.17/5.32
% 9.17/5.32 thf(fact_759_raise__def,axiom,
% 9.17/5.32 ( heap_T1552190017797416154rray_a
% 9.17/5.32 = ( ^ [S4: list_char] :
% 9.17/5.32 ( heap_T1488828001306802186rray_a
% 9.17/5.32 @ ^ [Uu: heap_e7401611519738050253t_unit] : none_P2587165478634041381it_nat ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_760_raise__def,axiom,
% 9.17/5.32 ( heap_T2927564422264180874t_unit
% 9.17/5.32 = ( ^ [S4: list_char] :
% 9.17/5.32 ( heap_T6183433275982383450t_unit
% 9.17/5.32 @ ^ [Uu: heap_e7401611519738050253t_unit] : none_P9117596204409417319it_nat ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_761_guard__def,axiom,
% 9.17/5.32 ( heap_T7685628758766326643rray_a
% 9.17/5.32 = ( ^ [P3: heap_e7401611519738050253t_unit > $o,F2: heap_e7401611519738050253t_unit > produc6714399278180371524it_nat] :
% 9.17/5.32 ( heap_T1488828001306802186rray_a
% 9.17/5.32 @ ^ [H: heap_e7401611519738050253t_unit] : ( if_opt7017092727090204112it_nat @ ( P3 @ H ) @ ( some_P6105628898608307625it_nat @ ( F2 @ H ) ) @ none_P2587165478634041381it_nat ) ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_762_guard__def,axiom,
% 9.17/5.32 ( heap_T8440541562793052209t_unit
% 9.17/5.32 = ( ^ [P3: heap_e7401611519738050253t_unit > $o,F2: heap_e7401611519738050253t_unit > produc8664842809031399944it_nat] :
% 9.17/5.32 ( heap_T6183433275982383450t_unit
% 9.17/5.32 @ ^ [H: heap_e7401611519738050253t_unit] : ( if_opt1729522071442692626it_nat @ ( P3 @ H ) @ ( some_P1914260805536162275it_nat @ ( F2 @ H ) ) @ none_P9117596204409417319it_nat ) ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_763_pos__add__strict,axiom,
% 9.17/5.32 ! [A: code_integer,B: code_integer,C: code_integer] :
% 9.17/5.32 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 9.17/5.32 => ( ( ord_le6747313008572928689nteger @ B @ C )
% 9.17/5.32 => ( ord_le6747313008572928689nteger @ B @ ( plus_p5714425477246183910nteger @ A @ C ) ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_764_pos__add__strict,axiom,
% 9.17/5.32 ! [A: rat,B: rat,C: rat] :
% 9.17/5.32 ( ( ord_less_rat @ zero_zero_rat @ A )
% 9.17/5.32 => ( ( ord_less_rat @ B @ C )
% 9.17/5.32 => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_765_pos__add__strict,axiom,
% 9.17/5.32 ! [A: nat,B: nat,C: nat] :
% 9.17/5.32 ( ( ord_less_nat @ zero_zero_nat @ A )
% 9.17/5.32 => ( ( ord_less_nat @ B @ C )
% 9.17/5.32 => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_766_pos__add__strict,axiom,
% 9.17/5.32 ! [A: int,B: int,C: int] :
% 9.17/5.32 ( ( ord_less_int @ zero_zero_int @ A )
% 9.17/5.32 => ( ( ord_less_int @ B @ C )
% 9.17/5.32 => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_767_canonically__ordered__monoid__add__class_OlessE,axiom,
% 9.17/5.32 ! [A: nat,B: nat] :
% 9.17/5.32 ( ( ord_less_nat @ A @ B )
% 9.17/5.32 => ~ ! [C3: nat] :
% 9.17/5.32 ( ( B
% 9.17/5.32 = ( plus_plus_nat @ A @ C3 ) )
% 9.17/5.32 => ( C3 = zero_zero_nat ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_768_add__pos__pos,axiom,
% 9.17/5.32 ! [A: code_integer,B: code_integer] :
% 9.17/5.32 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 9.17/5.32 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 9.17/5.32 => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_769_add__pos__pos,axiom,
% 9.17/5.32 ! [A: rat,B: rat] :
% 9.17/5.32 ( ( ord_less_rat @ zero_zero_rat @ A )
% 9.17/5.32 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 9.17/5.32 => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_770_add__pos__pos,axiom,
% 9.17/5.32 ! [A: nat,B: nat] :
% 9.17/5.32 ( ( ord_less_nat @ zero_zero_nat @ A )
% 9.17/5.32 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 9.17/5.32 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_771_add__pos__pos,axiom,
% 9.17/5.32 ! [A: int,B: int] :
% 9.17/5.32 ( ( ord_less_int @ zero_zero_int @ A )
% 9.17/5.32 => ( ( ord_less_int @ zero_zero_int @ B )
% 9.17/5.32 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_772_add__neg__neg,axiom,
% 9.17/5.32 ! [A: code_integer,B: code_integer] :
% 9.17/5.32 ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 9.17/5.32 => ( ( ord_le6747313008572928689nteger @ B @ zero_z3403309356797280102nteger )
% 9.17/5.32 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ zero_z3403309356797280102nteger ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_773_add__neg__neg,axiom,
% 9.17/5.32 ! [A: rat,B: rat] :
% 9.17/5.32 ( ( ord_less_rat @ A @ zero_zero_rat )
% 9.17/5.32 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 9.17/5.32 => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_774_add__neg__neg,axiom,
% 9.17/5.32 ! [A: nat,B: nat] :
% 9.17/5.32 ( ( ord_less_nat @ A @ zero_zero_nat )
% 9.17/5.32 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 9.17/5.32 => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_775_add__neg__neg,axiom,
% 9.17/5.32 ! [A: int,B: int] :
% 9.17/5.32 ( ( ord_less_int @ A @ zero_zero_int )
% 9.17/5.32 => ( ( ord_less_int @ B @ zero_zero_int )
% 9.17/5.32 => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_776_add__less__zeroD,axiom,
% 9.17/5.32 ! [X: code_integer,Y: code_integer] :
% 9.17/5.32 ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ X @ Y ) @ zero_z3403309356797280102nteger )
% 9.17/5.32 => ( ( ord_le6747313008572928689nteger @ X @ zero_z3403309356797280102nteger )
% 9.17/5.32 | ( ord_le6747313008572928689nteger @ Y @ zero_z3403309356797280102nteger ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_777_add__less__zeroD,axiom,
% 9.17/5.32 ! [X: rat,Y: rat] :
% 9.17/5.32 ( ( ord_less_rat @ ( plus_plus_rat @ X @ Y ) @ zero_zero_rat )
% 9.17/5.32 => ( ( ord_less_rat @ X @ zero_zero_rat )
% 9.17/5.32 | ( ord_less_rat @ Y @ zero_zero_rat ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_778_add__less__zeroD,axiom,
% 9.17/5.32 ! [X: int,Y: int] :
% 9.17/5.32 ( ( ord_less_int @ ( plus_plus_int @ X @ Y ) @ zero_zero_int )
% 9.17/5.32 => ( ( ord_less_int @ X @ zero_zero_int )
% 9.17/5.32 | ( ord_less_int @ Y @ zero_zero_int ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_779_zero__less__one,axiom,
% 9.17/5.32 ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ one_one_Code_integer ).
% 9.17/5.32
% 9.17/5.32 thf(fact_780_zero__less__one,axiom,
% 9.17/5.32 ord_less_rat @ zero_zero_rat @ one_one_rat ).
% 9.17/5.32
% 9.17/5.32 thf(fact_781_zero__less__one,axiom,
% 9.17/5.32 ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 9.17/5.32
% 9.17/5.32 thf(fact_782_zero__less__one,axiom,
% 9.17/5.32 ord_less_int @ zero_zero_int @ one_one_int ).
% 9.17/5.32
% 9.17/5.32 thf(fact_783_not__one__less__zero,axiom,
% 9.17/5.32 ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ zero_z3403309356797280102nteger ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_784_not__one__less__zero,axiom,
% 9.17/5.32 ~ ( ord_less_rat @ one_one_rat @ zero_zero_rat ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_785_not__one__less__zero,axiom,
% 9.17/5.32 ~ ( ord_less_nat @ one_one_nat @ zero_zero_nat ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_786_not__one__less__zero,axiom,
% 9.17/5.32 ~ ( ord_less_int @ one_one_int @ zero_zero_int ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_787_execute__ureturn,axiom,
% 9.17/5.32 ! [X: array_a] :
% 9.17/5.32 ( ( heap_T5591663578999710211rray_a @ ( heap_T4328122439115681491rray_a @ X ) )
% 9.17/5.32 = ( comp_P2097125496263478628t_unit @ some_P6105628898608307625it_nat
% 9.17/5.32 @ ^ [H: heap_e7401611519738050253t_unit] : ( produc1733996804261680252it_nat @ X @ ( produc584006145561248582it_nat @ H @ zero_zero_nat ) ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_788_execute__ureturn,axiom,
% 9.17/5.32 ! [X: product_unit] :
% 9.17/5.32 ( ( heap_T875086893843062177t_unit @ ( heap_T4284346855313245393t_unit @ X ) )
% 9.17/5.32 = ( comp_P3118722334806803912t_unit @ some_P1914260805536162275it_nat
% 9.17/5.32 @ ^ [H: heap_e7401611519738050253t_unit] : ( produc7133225469290080770it_nat @ X @ ( produc584006145561248582it_nat @ H @ zero_zero_nat ) ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_789_less__imp__add__positive,axiom,
% 9.17/5.32 ! [I: nat,J: nat] :
% 9.17/5.32 ( ( ord_less_nat @ I @ J )
% 9.17/5.32 => ? [K5: nat] :
% 9.17/5.32 ( ( ord_less_nat @ zero_zero_nat @ K5 )
% 9.17/5.32 & ( ( plus_plus_nat @ I @ K5 )
% 9.17/5.32 = J ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_790_tap__def,axiom,
% 9.17/5.32 ( heap_T560649228465745139t_unit
% 9.17/5.32 = ( ^ [F2: heap_e7401611519738050253t_unit > product_unit] :
% 9.17/5.32 ( heap_T6183433275982383450t_unit
% 9.17/5.32 @ ^ [H: heap_e7401611519738050253t_unit] : ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ ( F2 @ H ) @ ( produc584006145561248582it_nat @ H @ one_one_nat ) ) ) ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_791_double__eq__0__iff,axiom,
% 9.17/5.32 ! [A: code_integer] :
% 9.17/5.32 ( ( ( plus_p5714425477246183910nteger @ A @ A )
% 9.17/5.32 = zero_z3403309356797280102nteger )
% 9.17/5.32 = ( A = zero_z3403309356797280102nteger ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_792_double__eq__0__iff,axiom,
% 9.17/5.32 ! [A: rat] :
% 9.17/5.32 ( ( ( plus_plus_rat @ A @ A )
% 9.17/5.32 = zero_zero_rat )
% 9.17/5.32 = ( A = zero_zero_rat ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_793_double__eq__0__iff,axiom,
% 9.17/5.32 ! [A: int] :
% 9.17/5.32 ( ( ( plus_plus_int @ A @ A )
% 9.17/5.32 = zero_zero_int )
% 9.17/5.32 = ( A = zero_zero_int ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_794_add__0__iff,axiom,
% 9.17/5.32 ! [B: code_integer,A: code_integer] :
% 9.17/5.32 ( ( B
% 9.17/5.32 = ( plus_p5714425477246183910nteger @ B @ A ) )
% 9.17/5.32 = ( A = zero_z3403309356797280102nteger ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_795_add__0__iff,axiom,
% 9.17/5.32 ! [B: rat,A: rat] :
% 9.17/5.32 ( ( B
% 9.17/5.32 = ( plus_plus_rat @ B @ A ) )
% 9.17/5.32 = ( A = zero_zero_rat ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_796_add__0__iff,axiom,
% 9.17/5.32 ! [B: nat,A: nat] :
% 9.17/5.32 ( ( B
% 9.17/5.32 = ( plus_plus_nat @ B @ A ) )
% 9.17/5.32 = ( A = zero_zero_nat ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_797_add__0__iff,axiom,
% 9.17/5.32 ! [B: int,A: int] :
% 9.17/5.32 ( ( B
% 9.17/5.32 = ( plus_plus_int @ B @ A ) )
% 9.17/5.32 = ( A = zero_zero_int ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_798_verit__sum__simplify,axiom,
% 9.17/5.32 ! [A: code_integer] :
% 9.17/5.32 ( ( plus_p5714425477246183910nteger @ A @ zero_z3403309356797280102nteger )
% 9.17/5.32 = A ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_799_verit__sum__simplify,axiom,
% 9.17/5.32 ! [A: multis2468970476368604999at_nat] :
% 9.17/5.32 ( ( plus_p7104986032573967614at_nat @ A @ zero_z1048942125864253310at_nat )
% 9.17/5.32 = A ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_800_verit__sum__simplify,axiom,
% 9.17/5.32 ! [A: rat] :
% 9.17/5.32 ( ( plus_plus_rat @ A @ zero_zero_rat )
% 9.17/5.32 = A ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_801_verit__sum__simplify,axiom,
% 9.17/5.32 ! [A: nat] :
% 9.17/5.32 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 9.17/5.32 = A ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_802_verit__sum__simplify,axiom,
% 9.17/5.32 ! [A: int] :
% 9.17/5.32 ( ( plus_plus_int @ A @ zero_zero_int )
% 9.17/5.32 = A ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_803_dbl__inc__simps_I2_J,axiom,
% 9.17/5.32 ( ( neg_nu5831290666863070958nteger @ zero_z3403309356797280102nteger )
% 9.17/5.32 = one_one_Code_integer ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_804_dbl__inc__simps_I2_J,axiom,
% 9.17/5.32 ( ( neg_nu5219082963157363817nc_rat @ zero_zero_rat )
% 9.17/5.32 = one_one_rat ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_805_dbl__inc__simps_I2_J,axiom,
% 9.17/5.32 ( ( neg_nu5851722552734809277nc_int @ zero_zero_int )
% 9.17/5.32 = one_one_int ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_806_disjE__realizer2,axiom,
% 9.17/5.32 ! [P: $o,Q: num > $o,X: option_num,R4: int > $o,F: int,G: num > int] :
% 9.17/5.32 ( ( case_option_o_num @ P @ Q @ X )
% 9.17/5.32 => ( ( P
% 9.17/5.32 => ( R4 @ F ) )
% 9.17/5.32 => ( ! [Q2: num] :
% 9.17/5.32 ( ( Q @ Q2 )
% 9.17/5.32 => ( R4 @ ( G @ Q2 ) ) )
% 9.17/5.32 => ( R4 @ ( case_option_int_num @ F @ G @ X ) ) ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_807_disjE__realizer2,axiom,
% 9.17/5.32 ! [P: $o,Q: num > $o,X: option_num,R4: option_num > $o,F: option_num,G: num > option_num] :
% 9.17/5.32 ( ( case_option_o_num @ P @ Q @ X )
% 9.17/5.32 => ( ( P
% 9.17/5.32 => ( R4 @ F ) )
% 9.17/5.32 => ( ! [Q2: num] :
% 9.17/5.32 ( ( Q @ Q2 )
% 9.17/5.32 => ( R4 @ ( G @ Q2 ) ) )
% 9.17/5.32 => ( R4 @ ( case_o6005452278849405969um_num @ F @ G @ X ) ) ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_808_disjE__realizer2,axiom,
% 9.17/5.32 ! [P: $o,Q: num > $o,X: option_num,R4: num > $o,F: num,G: num > num] :
% 9.17/5.32 ( ( case_option_o_num @ P @ Q @ X )
% 9.17/5.32 => ( ( P
% 9.17/5.32 => ( R4 @ F ) )
% 9.17/5.32 => ( ! [Q2: num] :
% 9.17/5.32 ( ( Q @ Q2 )
% 9.17/5.32 => ( R4 @ ( G @ Q2 ) ) )
% 9.17/5.32 => ( R4 @ ( case_option_num_num @ F @ G @ X ) ) ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_809_set__to__map__def,axiom,
% 9.17/5.32 ( set_to4447731662395764663at_nat
% 9.17/5.32 = ( ^ [S5: set_Pr4329608150637261639at_nat,K4: set_Pr1261947904930325089at_nat] :
% 9.17/5.32 ( eps_Op994234036888646909at_nat
% 9.17/5.32 @ ^ [V2: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ K4 @ V2 ) @ S5 ) ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_810_set__to__map__def,axiom,
% 9.17/5.32 ( set_to_map_nat_nat
% 9.17/5.32 = ( ^ [S5: set_Pr1261947904930325089at_nat,K4: nat] :
% 9.17/5.32 ( eps_Opt_nat
% 9.17/5.32 @ ^ [V2: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ K4 @ V2 ) @ S5 ) ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_811_set__to__map__def,axiom,
% 9.17/5.32 ( set_to680829756418416360nteger
% 9.17/5.32 = ( ^ [S5: set_Pr1281608226676607948nteger,K4: produc6241069584506657477e_term > option6357759511663192854e_term] :
% 9.17/5.32 ( eps_Op9034888937550303799nteger
% 9.17/5.32 @ ^ [V2: produc8923325533196201883nteger] : ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ K4 @ V2 ) @ S5 ) ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_812_set__to__map__def,axiom,
% 9.17/5.32 ( set_to6040779677306527128et_nat
% 9.17/5.32 = ( ^ [S5: set_Pr3286484037609594932et_nat,K4: produc3658429121746597890et_nat > $o] :
% 9.17/5.32 ( eps_Op2013419657081471078et_nat
% 9.17/5.32 @ ^ [V2: produc3658429121746597890et_nat] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ K4 @ V2 ) @ S5 ) ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_813_set__to__map__def,axiom,
% 9.17/5.32 ( set_to2047380710992656148et_nat
% 9.17/5.32 = ( ^ [S5: set_Pr8536935166611901872et_nat,K4: produc3658429121746597890et_nat > $o] :
% 9.17/5.32 ( eps_Op6423059015816587746et_nat
% 9.17/5.32 @ ^ [V2: produc3925858234332021118et_nat] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ K4 @ V2 ) @ S5 ) ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_814_set__to__map__def,axiom,
% 9.17/5.32 ( set_to6585427216324510421nt_int
% 9.17/5.32 = ( ^ [S5: set_Pr9222295170931077689nt_int,K4: produc8551481072490612790e_term > option6357759511663192854e_term] :
% 9.17/5.32 ( eps_Op2446201859369042517nt_int
% 9.17/5.32 @ ^ [V2: product_prod_int_int] : ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ K4 @ V2 ) @ S5 ) ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_815_set__to__map__def,axiom,
% 9.17/5.32 ( set_to1653371902132773855nt_int
% 9.17/5.32 = ( ^ [S5: set_Pr1872883991513573699nt_int,K4: int > option6357759511663192854e_term] :
% 9.17/5.32 ( eps_Op2446201859369042517nt_int
% 9.17/5.32 @ ^ [V2: product_prod_int_int] : ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ K4 @ V2 ) @ S5 ) ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_816_K__record__comp,axiom,
% 9.17/5.32 ! [C: code_integer,F: num > code_integer] :
% 9.17/5.32 ( ( comp_C3531382070062128313er_num
% 9.17/5.32 @ ^ [X3: code_integer] : C
% 9.17/5.32 @ F )
% 9.17/5.32 = ( ^ [X3: num] : C ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_817_K__record__comp,axiom,
% 9.17/5.32 ! [C: produc8923325533196201883nteger > produc8923325533196201883nteger,F: code_integer > code_integer] :
% 9.17/5.32 ( ( comp_C1593894019821074884nteger
% 9.17/5.32 @ ^ [X3: code_integer] : C
% 9.17/5.32 @ F )
% 9.17/5.32 = ( ^ [X3: code_integer] : C ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_818_K__record__comp,axiom,
% 9.17/5.32 ! [C: produc8923325533196201883nteger > produc8923325533196201883nteger,F: code_integer > code_integer > code_integer] :
% 9.17/5.32 ( ( comp_C8797469213163452608nteger
% 9.17/5.32 @ ^ [X3: code_integer > code_integer] : C
% 9.17/5.32 @ F )
% 9.17/5.32 = ( ^ [X3: code_integer] : C ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_819_K__record__comp,axiom,
% 9.17/5.32 ! [C: num,F: int > nat] :
% 9.17/5.32 ( ( comp_nat_num_int
% 9.17/5.32 @ ^ [X3: nat] : C
% 9.17/5.32 @ F )
% 9.17/5.32 = ( ^ [X3: int] : C ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_820_pred__equals__eq2,axiom,
% 9.17/5.32 ! [R4: set_Pr4329608150637261639at_nat,S2: set_Pr4329608150637261639at_nat] :
% 9.17/5.32 ( ( ( ^ [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ Y3 ) @ R4 ) )
% 9.17/5.32 = ( ^ [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ Y3 ) @ S2 ) ) )
% 9.17/5.32 = ( R4 = S2 ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_821_pred__equals__eq2,axiom,
% 9.17/5.32 ! [R4: set_Pr1261947904930325089at_nat,S2: set_Pr1261947904930325089at_nat] :
% 9.17/5.32 ( ( ( ^ [X3: nat,Y3: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y3 ) @ R4 ) )
% 9.17/5.32 = ( ^ [X3: nat,Y3: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y3 ) @ S2 ) ) )
% 9.17/5.32 = ( R4 = S2 ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_822_pred__equals__eq2,axiom,
% 9.17/5.32 ! [R4: set_Pr1281608226676607948nteger,S2: set_Pr1281608226676607948nteger] :
% 9.17/5.32 ( ( ( ^ [X3: produc6241069584506657477e_term > option6357759511663192854e_term,Y3: produc8923325533196201883nteger] : ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X3 @ Y3 ) @ R4 ) )
% 9.17/5.32 = ( ^ [X3: produc6241069584506657477e_term > option6357759511663192854e_term,Y3: produc8923325533196201883nteger] : ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X3 @ Y3 ) @ S2 ) ) )
% 9.17/5.32 = ( R4 = S2 ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_823_pred__equals__eq2,axiom,
% 9.17/5.32 ! [R4: set_Pr3286484037609594932et_nat,S2: set_Pr3286484037609594932et_nat] :
% 9.17/5.32 ( ( ( ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3658429121746597890et_nat] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X3 @ Y3 ) @ R4 ) )
% 9.17/5.32 = ( ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3658429121746597890et_nat] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X3 @ Y3 ) @ S2 ) ) )
% 9.17/5.32 = ( R4 = S2 ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_824_pred__equals__eq2,axiom,
% 9.17/5.32 ! [R4: set_Pr8536935166611901872et_nat,S2: set_Pr8536935166611901872et_nat] :
% 9.17/5.32 ( ( ( ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3925858234332021118et_nat] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X3 @ Y3 ) @ R4 ) )
% 9.17/5.32 = ( ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3925858234332021118et_nat] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X3 @ Y3 ) @ S2 ) ) )
% 9.17/5.32 = ( R4 = S2 ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_825_pred__equals__eq2,axiom,
% 9.17/5.32 ! [R4: set_Pr9222295170931077689nt_int,S2: set_Pr9222295170931077689nt_int] :
% 9.17/5.32 ( ( ( ^ [X3: produc8551481072490612790e_term > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X3 @ Y3 ) @ R4 ) )
% 9.17/5.32 = ( ^ [X3: produc8551481072490612790e_term > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X3 @ Y3 ) @ S2 ) ) )
% 9.17/5.32 = ( R4 = S2 ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_826_pred__equals__eq2,axiom,
% 9.17/5.32 ! [R4: set_Pr1872883991513573699nt_int,S2: set_Pr1872883991513573699nt_int] :
% 9.17/5.32 ( ( ( ^ [X3: int > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X3 @ Y3 ) @ R4 ) )
% 9.17/5.32 = ( ^ [X3: int > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X3 @ Y3 ) @ S2 ) ) )
% 9.17/5.32 = ( R4 = S2 ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_827_dbl__inc__def,axiom,
% 9.17/5.32 ( neg_nu5831290666863070958nteger
% 9.17/5.32 = ( ^ [X3: code_integer] : ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ X3 @ X3 ) @ one_one_Code_integer ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_828_dbl__inc__def,axiom,
% 9.17/5.32 ( neg_nu5219082963157363817nc_rat
% 9.17/5.32 = ( ^ [X3: rat] : ( plus_plus_rat @ ( plus_plus_rat @ X3 @ X3 ) @ one_one_rat ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_829_dbl__inc__def,axiom,
% 9.17/5.32 ( neg_nu5851722552734809277nc_int
% 9.17/5.32 = ( ^ [X3: int] : ( plus_plus_int @ ( plus_plus_int @ X3 @ X3 ) @ one_one_int ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_830_zero__natural_Orsp,axiom,
% 9.17/5.32 zero_zero_nat = zero_zero_nat ).
% 9.17/5.32
% 9.17/5.32 thf(fact_831_fails__wait,axiom,
% 9.17/5.32 ! [X: nat,H3: heap_e7401611519738050253t_unit] :
% 9.17/5.32 ~ ( time_f8834461667527620124t_unit @ ( heap_Time_wait @ X ) @ H3 ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_832_Euclid__induct,axiom,
% 9.17/5.32 ! [P: nat > nat > $o,A: nat,B: nat] :
% 9.17/5.32 ( ! [A3: nat,B2: nat] :
% 9.17/5.32 ( ( P @ A3 @ B2 )
% 9.17/5.32 = ( P @ B2 @ A3 ) )
% 9.17/5.32 => ( ! [A3: nat] : ( P @ A3 @ zero_zero_nat )
% 9.17/5.32 => ( ! [A3: nat,B2: nat] :
% 9.17/5.32 ( ( P @ A3 @ B2 )
% 9.17/5.32 => ( P @ A3 @ ( plus_plus_nat @ A3 @ B2 ) ) )
% 9.17/5.32 => ( P @ A @ B ) ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_833_Ints__odd__less__0,axiom,
% 9.17/5.32 ! [A: code_integer] :
% 9.17/5.32 ( ( member_Code_integer @ A @ ring_11222124179247155820nteger )
% 9.17/5.32 => ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ A ) @ zero_z3403309356797280102nteger )
% 9.17/5.32 = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_834_Ints__odd__less__0,axiom,
% 9.17/5.32 ! [A: rat] :
% 9.17/5.32 ( ( member_rat @ A @ ring_1_Ints_rat )
% 9.17/5.32 => ( ( ord_less_rat @ ( plus_plus_rat @ ( plus_plus_rat @ one_one_rat @ A ) @ A ) @ zero_zero_rat )
% 9.17/5.32 = ( ord_less_rat @ A @ zero_zero_rat ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_835_Ints__odd__less__0,axiom,
% 9.17/5.32 ! [A: int] :
% 9.17/5.32 ( ( member_int @ A @ ring_1_Ints_int )
% 9.17/5.32 => ( ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ A ) @ A ) @ zero_zero_int )
% 9.17/5.32 = ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_836_num__of__nat__plus__distrib,axiom,
% 9.17/5.32 ! [M2: nat,N2: nat] :
% 9.17/5.32 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 9.17/5.32 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 9.17/5.32 => ( ( num_of_nat @ ( plus_plus_nat @ M2 @ N2 ) )
% 9.17/5.32 = ( plus_plus_num @ ( num_of_nat @ M2 ) @ ( num_of_nat @ N2 ) ) ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_837_divides__aux__eq,axiom,
% 9.17/5.32 ! [Q3: code_integer,R2: code_integer] :
% 9.17/5.32 ( ( unique5706413561485394159nteger @ ( produc1086072967326762835nteger @ Q3 @ R2 ) )
% 9.17/5.32 = ( R2 = zero_z3403309356797280102nteger ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_838_divides__aux__eq,axiom,
% 9.17/5.32 ! [Q3: nat,R2: nat] :
% 9.17/5.32 ( ( unique6322359934112328802ux_nat @ ( product_Pair_nat_nat @ Q3 @ R2 ) )
% 9.17/5.32 = ( R2 = zero_zero_nat ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_839_divides__aux__eq,axiom,
% 9.17/5.32 ! [Q3: int,R2: int] :
% 9.17/5.32 ( ( unique6319869463603278526ux_int @ ( product_Pair_int_int @ Q3 @ R2 ) )
% 9.17/5.32 = ( R2 = zero_zero_int ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_840_sgn__pos,axiom,
% 9.17/5.32 ! [A: code_integer] :
% 9.17/5.32 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 9.17/5.32 => ( ( sgn_sgn_Code_integer @ A )
% 9.17/5.32 = one_one_Code_integer ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_841_sgn__pos,axiom,
% 9.17/5.32 ! [A: rat] :
% 9.17/5.32 ( ( ord_less_rat @ zero_zero_rat @ A )
% 9.17/5.32 => ( ( sgn_sgn_rat @ A )
% 9.17/5.32 = one_one_rat ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_842_sgn__pos,axiom,
% 9.17/5.32 ! [A: int] :
% 9.17/5.32 ( ( ord_less_int @ zero_zero_int @ A )
% 9.17/5.32 => ( ( sgn_sgn_int @ A )
% 9.17/5.32 = one_one_int ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_843_abs__add__one__gt__zero,axiom,
% 9.17/5.32 ! [X: code_integer] : ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( abs_abs_Code_integer @ X ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_844_abs__add__one__gt__zero,axiom,
% 9.17/5.32 ! [X: rat] : ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ one_one_rat @ ( abs_abs_rat @ X ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_845_abs__add__one__gt__zero,axiom,
% 9.17/5.32 ! [X: int] : ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ ( abs_abs_int @ X ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_846_map__option__case,axiom,
% 9.17/5.32 ( map_option_num_num
% 9.17/5.32 = ( ^ [F2: num > num] :
% 9.17/5.32 ( case_o6005452278849405969um_num @ none_num
% 9.17/5.32 @ ^ [X3: num] : ( some_num @ ( F2 @ X3 ) ) ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_847_add__neg__numeral__special_I7_J,axiom,
% 9.17/5.32 ( ( plus_plus_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) )
% 9.17/5.32 = zero_zero_int ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_848_add__neg__numeral__special_I7_J,axiom,
% 9.17/5.32 ( ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.17/5.32 = zero_z3403309356797280102nteger ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_849_add__neg__numeral__special_I7_J,axiom,
% 9.17/5.32 ( ( plus_plus_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 9.17/5.32 = zero_zero_rat ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_850_add__neg__numeral__special_I8_J,axiom,
% 9.17/5.32 ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 9.17/5.32 = zero_zero_int ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_851_add__neg__numeral__special_I8_J,axiom,
% 9.17/5.32 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer )
% 9.17/5.32 = zero_z3403309356797280102nteger ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_852_add__neg__numeral__special_I8_J,axiom,
% 9.17/5.32 ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat )
% 9.17/5.32 = zero_zero_rat ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_853_dbl__dec__simps_I3_J,axiom,
% 9.17/5.32 ( ( neg_nu7757733837767384882nteger @ one_one_Code_integer )
% 9.17/5.32 = one_one_Code_integer ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_854_dbl__dec__simps_I3_J,axiom,
% 9.17/5.32 ( ( neg_nu3179335615603231917ec_rat @ one_one_rat )
% 9.17/5.32 = one_one_rat ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_855_dbl__dec__simps_I3_J,axiom,
% 9.17/5.32 ( ( neg_nu3811975205180677377ec_int @ one_one_int )
% 9.17/5.32 = one_one_int ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_856_neg__equal__iff__equal,axiom,
% 9.17/5.32 ! [A: int,B: int] :
% 9.17/5.32 ( ( ( uminus_uminus_int @ A )
% 9.17/5.32 = ( uminus_uminus_int @ B ) )
% 9.17/5.32 = ( A = B ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_857_neg__equal__iff__equal,axiom,
% 9.17/5.32 ! [A: code_integer,B: code_integer] :
% 9.17/5.32 ( ( ( uminus1351360451143612070nteger @ A )
% 9.17/5.32 = ( uminus1351360451143612070nteger @ B ) )
% 9.17/5.32 = ( A = B ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_858_neg__equal__iff__equal,axiom,
% 9.17/5.32 ! [A: rat,B: rat] :
% 9.17/5.32 ( ( ( uminus_uminus_rat @ A )
% 9.17/5.32 = ( uminus_uminus_rat @ B ) )
% 9.17/5.32 = ( A = B ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_859_add_Oinverse__inverse,axiom,
% 9.17/5.32 ! [A: int] :
% 9.17/5.32 ( ( uminus_uminus_int @ ( uminus_uminus_int @ A ) )
% 9.17/5.32 = A ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_860_add_Oinverse__inverse,axiom,
% 9.17/5.32 ! [A: code_integer] :
% 9.17/5.32 ( ( uminus1351360451143612070nteger @ ( uminus1351360451143612070nteger @ A ) )
% 9.17/5.32 = A ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_861_add_Oinverse__inverse,axiom,
% 9.17/5.32 ! [A: rat] :
% 9.17/5.32 ( ( uminus_uminus_rat @ ( uminus_uminus_rat @ A ) )
% 9.17/5.32 = A ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_862_abs__idempotent,axiom,
% 9.17/5.32 ! [A: int] :
% 9.17/5.32 ( ( abs_abs_int @ ( abs_abs_int @ A ) )
% 9.17/5.32 = ( abs_abs_int @ A ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_863_abs__idempotent,axiom,
% 9.17/5.32 ! [A: code_integer] :
% 9.17/5.32 ( ( abs_abs_Code_integer @ ( abs_abs_Code_integer @ A ) )
% 9.17/5.32 = ( abs_abs_Code_integer @ A ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_864_abs__idempotent,axiom,
% 9.17/5.32 ! [A: rat] :
% 9.17/5.32 ( ( abs_abs_rat @ ( abs_abs_rat @ A ) )
% 9.17/5.32 = ( abs_abs_rat @ A ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_865_neg__equal__zero,axiom,
% 9.17/5.32 ! [A: int] :
% 9.17/5.32 ( ( ( uminus_uminus_int @ A )
% 9.17/5.32 = A )
% 9.17/5.32 = ( A = zero_zero_int ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_866_neg__equal__zero,axiom,
% 9.17/5.32 ! [A: code_integer] :
% 9.17/5.32 ( ( ( uminus1351360451143612070nteger @ A )
% 9.17/5.32 = A )
% 9.17/5.32 = ( A = zero_z3403309356797280102nteger ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_867_neg__equal__zero,axiom,
% 9.17/5.32 ! [A: rat] :
% 9.17/5.32 ( ( ( uminus_uminus_rat @ A )
% 9.17/5.32 = A )
% 9.17/5.32 = ( A = zero_zero_rat ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_868_equal__neg__zero,axiom,
% 9.17/5.32 ! [A: int] :
% 9.17/5.32 ( ( A
% 9.17/5.32 = ( uminus_uminus_int @ A ) )
% 9.17/5.32 = ( A = zero_zero_int ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_869_equal__neg__zero,axiom,
% 9.17/5.32 ! [A: code_integer] :
% 9.17/5.32 ( ( A
% 9.17/5.32 = ( uminus1351360451143612070nteger @ A ) )
% 9.17/5.32 = ( A = zero_z3403309356797280102nteger ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_870_equal__neg__zero,axiom,
% 9.17/5.32 ! [A: rat] :
% 9.17/5.32 ( ( A
% 9.17/5.32 = ( uminus_uminus_rat @ A ) )
% 9.17/5.32 = ( A = zero_zero_rat ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_871_neg__equal__0__iff__equal,axiom,
% 9.17/5.32 ! [A: int] :
% 9.17/5.32 ( ( ( uminus_uminus_int @ A )
% 9.17/5.32 = zero_zero_int )
% 9.17/5.32 = ( A = zero_zero_int ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_872_neg__equal__0__iff__equal,axiom,
% 9.17/5.32 ! [A: code_integer] :
% 9.17/5.32 ( ( ( uminus1351360451143612070nteger @ A )
% 9.17/5.32 = zero_z3403309356797280102nteger )
% 9.17/5.32 = ( A = zero_z3403309356797280102nteger ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_873_neg__equal__0__iff__equal,axiom,
% 9.17/5.32 ! [A: rat] :
% 9.17/5.32 ( ( ( uminus_uminus_rat @ A )
% 9.17/5.32 = zero_zero_rat )
% 9.17/5.32 = ( A = zero_zero_rat ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_874_neg__0__equal__iff__equal,axiom,
% 9.17/5.32 ! [A: int] :
% 9.17/5.32 ( ( zero_zero_int
% 9.17/5.32 = ( uminus_uminus_int @ A ) )
% 9.17/5.32 = ( zero_zero_int = A ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_875_neg__0__equal__iff__equal,axiom,
% 9.17/5.32 ! [A: code_integer] :
% 9.17/5.32 ( ( zero_z3403309356797280102nteger
% 9.17/5.32 = ( uminus1351360451143612070nteger @ A ) )
% 9.17/5.32 = ( zero_z3403309356797280102nteger = A ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_876_neg__0__equal__iff__equal,axiom,
% 9.17/5.32 ! [A: rat] :
% 9.17/5.32 ( ( zero_zero_rat
% 9.17/5.32 = ( uminus_uminus_rat @ A ) )
% 9.17/5.32 = ( zero_zero_rat = A ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_877_add_Oinverse__neutral,axiom,
% 9.17/5.32 ( ( uminus_uminus_int @ zero_zero_int )
% 9.17/5.32 = zero_zero_int ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_878_add_Oinverse__neutral,axiom,
% 9.17/5.32 ( ( uminus1351360451143612070nteger @ zero_z3403309356797280102nteger )
% 9.17/5.32 = zero_z3403309356797280102nteger ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_879_add_Oinverse__neutral,axiom,
% 9.17/5.32 ( ( uminus_uminus_rat @ zero_zero_rat )
% 9.17/5.32 = zero_zero_rat ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_880_neg__less__iff__less,axiom,
% 9.17/5.32 ! [B: int,A: int] :
% 9.17/5.32 ( ( ord_less_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) )
% 9.17/5.32 = ( ord_less_int @ A @ B ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_881_neg__less__iff__less,axiom,
% 9.17/5.32 ! [B: code_integer,A: code_integer] :
% 9.17/5.32 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) )
% 9.17/5.32 = ( ord_le6747313008572928689nteger @ A @ B ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_882_neg__less__iff__less,axiom,
% 9.17/5.32 ! [B: rat,A: rat] :
% 9.17/5.32 ( ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) )
% 9.17/5.32 = ( ord_less_rat @ A @ B ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_883_minus__add__distrib,axiom,
% 9.17/5.32 ! [A: int,B: int] :
% 9.17/5.32 ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 9.17/5.32 = ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_884_minus__add__distrib,axiom,
% 9.17/5.32 ! [A: code_integer,B: code_integer] :
% 9.17/5.32 ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 9.17/5.32 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_885_minus__add__distrib,axiom,
% 9.17/5.32 ! [A: rat,B: rat] :
% 9.17/5.32 ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 9.17/5.32 = ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_886_minus__add__cancel,axiom,
% 9.17/5.32 ! [A: int,B: int] :
% 9.17/5.32 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( plus_plus_int @ A @ B ) )
% 9.17/5.32 = B ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_887_minus__add__cancel,axiom,
% 9.17/5.32 ! [A: code_integer,B: code_integer] :
% 9.17/5.32 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 9.17/5.32 = B ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_888_minus__add__cancel,axiom,
% 9.17/5.32 ! [A: rat,B: rat] :
% 9.17/5.32 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( plus_plus_rat @ A @ B ) )
% 9.17/5.32 = B ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_889_add__minus__cancel,axiom,
% 9.17/5.32 ! [A: int,B: int] :
% 9.17/5.32 ( ( plus_plus_int @ A @ ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B ) )
% 9.17/5.32 = B ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_890_add__minus__cancel,axiom,
% 9.17/5.32 ! [A: code_integer,B: code_integer] :
% 9.17/5.32 ( ( plus_p5714425477246183910nteger @ A @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) )
% 9.17/5.32 = B ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_891_add__minus__cancel,axiom,
% 9.17/5.32 ! [A: rat,B: rat] :
% 9.17/5.32 ( ( plus_plus_rat @ A @ ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ B ) )
% 9.17/5.32 = B ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_892_abs__zero,axiom,
% 9.17/5.32 ( ( abs_abs_Code_integer @ zero_z3403309356797280102nteger )
% 9.17/5.32 = zero_z3403309356797280102nteger ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_893_abs__zero,axiom,
% 9.17/5.32 ( ( abs_abs_rat @ zero_zero_rat )
% 9.17/5.32 = zero_zero_rat ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_894_abs__zero,axiom,
% 9.17/5.32 ( ( abs_abs_int @ zero_zero_int )
% 9.17/5.32 = zero_zero_int ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_895_abs__eq__0,axiom,
% 9.17/5.32 ! [A: code_integer] :
% 9.17/5.32 ( ( ( abs_abs_Code_integer @ A )
% 9.17/5.32 = zero_z3403309356797280102nteger )
% 9.17/5.32 = ( A = zero_z3403309356797280102nteger ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_896_abs__eq__0,axiom,
% 9.17/5.32 ! [A: rat] :
% 9.17/5.32 ( ( ( abs_abs_rat @ A )
% 9.17/5.32 = zero_zero_rat )
% 9.17/5.32 = ( A = zero_zero_rat ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_897_abs__eq__0,axiom,
% 9.17/5.32 ! [A: int] :
% 9.17/5.32 ( ( ( abs_abs_int @ A )
% 9.17/5.32 = zero_zero_int )
% 9.17/5.32 = ( A = zero_zero_int ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_898_abs__0__eq,axiom,
% 9.17/5.32 ! [A: code_integer] :
% 9.17/5.32 ( ( zero_z3403309356797280102nteger
% 9.17/5.32 = ( abs_abs_Code_integer @ A ) )
% 9.17/5.32 = ( A = zero_z3403309356797280102nteger ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_899_abs__0__eq,axiom,
% 9.17/5.32 ! [A: rat] :
% 9.17/5.32 ( ( zero_zero_rat
% 9.17/5.32 = ( abs_abs_rat @ A ) )
% 9.17/5.32 = ( A = zero_zero_rat ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_900_abs__0__eq,axiom,
% 9.17/5.32 ! [A: int] :
% 9.17/5.32 ( ( zero_zero_int
% 9.17/5.32 = ( abs_abs_int @ A ) )
% 9.17/5.32 = ( A = zero_zero_int ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_901_abs__add__abs,axiom,
% 9.17/5.32 ! [A: code_integer,B: code_integer] :
% 9.17/5.32 ( ( abs_abs_Code_integer @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) )
% 9.17/5.32 = ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_902_abs__add__abs,axiom,
% 9.17/5.32 ! [A: rat,B: rat] :
% 9.17/5.32 ( ( abs_abs_rat @ ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) )
% 9.17/5.32 = ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_903_abs__add__abs,axiom,
% 9.17/5.32 ! [A: int,B: int] :
% 9.17/5.32 ( ( abs_abs_int @ ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) )
% 9.17/5.32 = ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_904_abs__1,axiom,
% 9.17/5.32 ( ( abs_abs_Code_integer @ one_one_Code_integer )
% 9.17/5.32 = one_one_Code_integer ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_905_abs__1,axiom,
% 9.17/5.32 ( ( abs_abs_rat @ one_one_rat )
% 9.17/5.32 = one_one_rat ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_906_abs__1,axiom,
% 9.17/5.32 ( ( abs_abs_int @ one_one_int )
% 9.17/5.32 = one_one_int ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_907_abs__minus__cancel,axiom,
% 9.17/5.32 ! [A: int] :
% 9.17/5.32 ( ( abs_abs_int @ ( uminus_uminus_int @ A ) )
% 9.17/5.32 = ( abs_abs_int @ A ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_908_abs__minus__cancel,axiom,
% 9.17/5.32 ! [A: code_integer] :
% 9.17/5.32 ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ A ) )
% 9.17/5.32 = ( abs_abs_Code_integer @ A ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_909_abs__minus__cancel,axiom,
% 9.17/5.32 ! [A: rat] :
% 9.17/5.32 ( ( abs_abs_rat @ ( uminus_uminus_rat @ A ) )
% 9.17/5.32 = ( abs_abs_rat @ A ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_910_sgn__1,axiom,
% 9.17/5.32 ( ( sgn_sgn_int @ one_one_int )
% 9.17/5.32 = one_one_int ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_911_sgn__1,axiom,
% 9.17/5.32 ( ( sgn_sgn_Code_integer @ one_one_Code_integer )
% 9.17/5.32 = one_one_Code_integer ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_912_sgn__1,axiom,
% 9.17/5.32 ( ( sgn_sgn_rat @ one_one_rat )
% 9.17/5.32 = one_one_rat ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_913_map__option__eq__Some,axiom,
% 9.17/5.32 ! [F: produc8664842809031399944it_nat > num,Xo: option8956607266484857688it_nat,Y: num] :
% 9.17/5.32 ( ( ( map_op2731889312448867759at_num @ F @ Xo )
% 9.17/5.32 = ( some_num @ Y ) )
% 9.17/5.32 = ( ? [Z4: produc8664842809031399944it_nat] :
% 9.17/5.32 ( ( Xo
% 9.17/5.32 = ( some_P1914260805536162275it_nat @ Z4 ) )
% 9.17/5.32 & ( ( F @ Z4 )
% 9.17/5.32 = Y ) ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_914_map__option__eq__Some,axiom,
% 9.17/5.32 ! [F: num > produc8664842809031399944it_nat,Xo: option_num,Y: produc8664842809031399944it_nat] :
% 9.17/5.32 ( ( ( map_op8118133509425879471it_nat @ F @ Xo )
% 9.17/5.32 = ( some_P1914260805536162275it_nat @ Y ) )
% 9.17/5.32 = ( ? [Z4: num] :
% 9.17/5.32 ( ( Xo
% 9.17/5.32 = ( some_num @ Z4 ) )
% 9.17/5.32 & ( ( F @ Z4 )
% 9.17/5.32 = Y ) ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_915_map__option__eq__Some,axiom,
% 9.17/5.32 ! [F: produc8664842809031399944it_nat > produc8664842809031399944it_nat,Xo: option8956607266484857688it_nat,Y: produc8664842809031399944it_nat] :
% 9.17/5.32 ( ( ( map_op8673683442680995229it_nat @ F @ Xo )
% 9.17/5.32 = ( some_P1914260805536162275it_nat @ Y ) )
% 9.17/5.32 = ( ? [Z4: produc8664842809031399944it_nat] :
% 9.17/5.32 ( ( Xo
% 9.17/5.32 = ( some_P1914260805536162275it_nat @ Z4 ) )
% 9.17/5.32 & ( ( F @ Z4 )
% 9.17/5.32 = Y ) ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_916_map__option__eq__Some,axiom,
% 9.17/5.32 ! [F: num > num,Xo: option_num,Y: num] :
% 9.17/5.32 ( ( ( map_option_num_num @ F @ Xo )
% 9.17/5.32 = ( some_num @ Y ) )
% 9.17/5.32 = ( ? [Z4: num] :
% 9.17/5.32 ( ( Xo
% 9.17/5.32 = ( some_num @ Z4 ) )
% 9.17/5.32 & ( ( F @ Z4 )
% 9.17/5.32 = Y ) ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_917_None__eq__map__option__iff,axiom,
% 9.17/5.32 ! [F: produc6714399278180371524it_nat > produc6714399278180371524it_nat,X: option3216581401566546698it_nat] :
% 9.17/5.32 ( ( none_P2587165478634041381it_nat
% 9.17/5.32 = ( map_op6002829699023054091it_nat @ F @ X ) )
% 9.17/5.32 = ( X = none_P2587165478634041381it_nat ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_918_None__eq__map__option__iff,axiom,
% 9.17/5.32 ! [F: num > produc6714399278180371524it_nat,X: option_num] :
% 9.17/5.32 ( ( none_P2587165478634041381it_nat
% 9.17/5.32 = ( map_op6598675229099881181it_nat @ F @ X ) )
% 9.17/5.32 = ( X = none_num ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_919_None__eq__map__option__iff,axiom,
% 9.17/5.32 ! [F: produc8664842809031399944it_nat > produc6714399278180371524it_nat,X: option8956607266484857688it_nat] :
% 9.17/5.32 ( ( none_P2587165478634041381it_nat
% 9.17/5.32 = ( map_op7916408704904942447it_nat @ F @ X ) )
% 9.17/5.32 = ( X = none_P9117596204409417319it_nat ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_920_None__eq__map__option__iff,axiom,
% 9.17/5.32 ! [F: produc6714399278180371524it_nat > num,X: option3216581401566546698it_nat] :
% 9.17/5.32 ( ( none_num
% 9.17/5.32 = ( map_op8228268515680064275at_num @ F @ X ) )
% 9.17/5.32 = ( X = none_P2587165478634041381it_nat ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_921_None__eq__map__option__iff,axiom,
% 9.17/5.32 ! [F: produc8664842809031399944it_nat > num,X: option8956607266484857688it_nat] :
% 9.17/5.32 ( ( none_num
% 9.17/5.32 = ( map_op2731889312448867759at_num @ F @ X ) )
% 9.17/5.32 = ( X = none_P9117596204409417319it_nat ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_922_None__eq__map__option__iff,axiom,
% 9.17/5.32 ! [F: produc6714399278180371524it_nat > produc8664842809031399944it_nat,X: option3216581401566546698it_nat] :
% 9.17/5.32 ( ( none_P9117596204409417319it_nat
% 9.17/5.32 = ( map_op674526153330701057it_nat @ F @ X ) )
% 9.17/5.32 = ( X = none_P2587165478634041381it_nat ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_923_None__eq__map__option__iff,axiom,
% 9.17/5.32 ! [F: num > produc8664842809031399944it_nat,X: option_num] :
% 9.17/5.32 ( ( none_P9117596204409417319it_nat
% 9.17/5.32 = ( map_op8118133509425879471it_nat @ F @ X ) )
% 9.17/5.32 = ( X = none_num ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_924_None__eq__map__option__iff,axiom,
% 9.17/5.32 ! [F: produc8664842809031399944it_nat > produc8664842809031399944it_nat,X: option8956607266484857688it_nat] :
% 9.17/5.32 ( ( none_P9117596204409417319it_nat
% 9.17/5.32 = ( map_op8673683442680995229it_nat @ F @ X ) )
% 9.17/5.32 = ( X = none_P9117596204409417319it_nat ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_925_None__eq__map__option__iff,axiom,
% 9.17/5.32 ! [F: num > num,X: option_num] :
% 9.17/5.32 ( ( none_num
% 9.17/5.32 = ( map_option_num_num @ F @ X ) )
% 9.17/5.32 = ( X = none_num ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_926_map__option__is__None,axiom,
% 9.17/5.32 ! [F: produc6714399278180371524it_nat > produc6714399278180371524it_nat,Opt: option3216581401566546698it_nat] :
% 9.17/5.32 ( ( ( map_op6002829699023054091it_nat @ F @ Opt )
% 9.17/5.32 = none_P2587165478634041381it_nat )
% 9.17/5.32 = ( Opt = none_P2587165478634041381it_nat ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_927_map__option__is__None,axiom,
% 9.17/5.32 ! [F: num > produc6714399278180371524it_nat,Opt: option_num] :
% 9.17/5.32 ( ( ( map_op6598675229099881181it_nat @ F @ Opt )
% 9.17/5.32 = none_P2587165478634041381it_nat )
% 9.17/5.32 = ( Opt = none_num ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_928_map__option__is__None,axiom,
% 9.17/5.32 ! [F: produc8664842809031399944it_nat > produc6714399278180371524it_nat,Opt: option8956607266484857688it_nat] :
% 9.17/5.32 ( ( ( map_op7916408704904942447it_nat @ F @ Opt )
% 9.17/5.32 = none_P2587165478634041381it_nat )
% 9.17/5.32 = ( Opt = none_P9117596204409417319it_nat ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_929_map__option__is__None,axiom,
% 9.17/5.32 ! [F: produc6714399278180371524it_nat > num,Opt: option3216581401566546698it_nat] :
% 9.17/5.32 ( ( ( map_op8228268515680064275at_num @ F @ Opt )
% 9.17/5.32 = none_num )
% 9.17/5.32 = ( Opt = none_P2587165478634041381it_nat ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_930_map__option__is__None,axiom,
% 9.17/5.32 ! [F: produc8664842809031399944it_nat > num,Opt: option8956607266484857688it_nat] :
% 9.17/5.32 ( ( ( map_op2731889312448867759at_num @ F @ Opt )
% 9.17/5.32 = none_num )
% 9.17/5.32 = ( Opt = none_P9117596204409417319it_nat ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_931_map__option__is__None,axiom,
% 9.17/5.32 ! [F: produc6714399278180371524it_nat > produc8664842809031399944it_nat,Opt: option3216581401566546698it_nat] :
% 9.17/5.32 ( ( ( map_op674526153330701057it_nat @ F @ Opt )
% 9.17/5.32 = none_P9117596204409417319it_nat )
% 9.17/5.32 = ( Opt = none_P2587165478634041381it_nat ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_932_map__option__is__None,axiom,
% 9.17/5.32 ! [F: num > produc8664842809031399944it_nat,Opt: option_num] :
% 9.17/5.32 ( ( ( map_op8118133509425879471it_nat @ F @ Opt )
% 9.17/5.32 = none_P9117596204409417319it_nat )
% 9.17/5.32 = ( Opt = none_num ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_933_map__option__is__None,axiom,
% 9.17/5.32 ! [F: produc8664842809031399944it_nat > produc8664842809031399944it_nat,Opt: option8956607266484857688it_nat] :
% 9.17/5.32 ( ( ( map_op8673683442680995229it_nat @ F @ Opt )
% 9.17/5.32 = none_P9117596204409417319it_nat )
% 9.17/5.32 = ( Opt = none_P9117596204409417319it_nat ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_934_map__option__is__None,axiom,
% 9.17/5.32 ! [F: num > num,Opt: option_num] :
% 9.17/5.32 ( ( ( map_option_num_num @ F @ Opt )
% 9.17/5.32 = none_num )
% 9.17/5.32 = ( Opt = none_num ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_935_option_Omap__disc__iff,axiom,
% 9.17/5.32 ! [F: produc6714399278180371524it_nat > produc6714399278180371524it_nat,A: option3216581401566546698it_nat] :
% 9.17/5.32 ( ( ( map_op6002829699023054091it_nat @ F @ A )
% 9.17/5.32 = none_P2587165478634041381it_nat )
% 9.17/5.32 = ( A = none_P2587165478634041381it_nat ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_936_option_Omap__disc__iff,axiom,
% 9.17/5.32 ! [F: num > produc6714399278180371524it_nat,A: option_num] :
% 9.17/5.32 ( ( ( map_op6598675229099881181it_nat @ F @ A )
% 9.17/5.32 = none_P2587165478634041381it_nat )
% 9.17/5.32 = ( A = none_num ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_937_option_Omap__disc__iff,axiom,
% 9.17/5.32 ! [F: produc8664842809031399944it_nat > produc6714399278180371524it_nat,A: option8956607266484857688it_nat] :
% 9.17/5.32 ( ( ( map_op7916408704904942447it_nat @ F @ A )
% 9.17/5.32 = none_P2587165478634041381it_nat )
% 9.17/5.32 = ( A = none_P9117596204409417319it_nat ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_938_option_Omap__disc__iff,axiom,
% 9.17/5.32 ! [F: produc6714399278180371524it_nat > num,A: option3216581401566546698it_nat] :
% 9.17/5.32 ( ( ( map_op8228268515680064275at_num @ F @ A )
% 9.17/5.32 = none_num )
% 9.17/5.32 = ( A = none_P2587165478634041381it_nat ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_939_option_Omap__disc__iff,axiom,
% 9.17/5.32 ! [F: produc8664842809031399944it_nat > num,A: option8956607266484857688it_nat] :
% 9.17/5.32 ( ( ( map_op2731889312448867759at_num @ F @ A )
% 9.17/5.32 = none_num )
% 9.17/5.32 = ( A = none_P9117596204409417319it_nat ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_940_option_Omap__disc__iff,axiom,
% 9.17/5.32 ! [F: produc6714399278180371524it_nat > produc8664842809031399944it_nat,A: option3216581401566546698it_nat] :
% 9.17/5.32 ( ( ( map_op674526153330701057it_nat @ F @ A )
% 9.17/5.32 = none_P9117596204409417319it_nat )
% 9.17/5.32 = ( A = none_P2587165478634041381it_nat ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_941_option_Omap__disc__iff,axiom,
% 9.17/5.32 ! [F: num > produc8664842809031399944it_nat,A: option_num] :
% 9.17/5.32 ( ( ( map_op8118133509425879471it_nat @ F @ A )
% 9.17/5.32 = none_P9117596204409417319it_nat )
% 9.17/5.32 = ( A = none_num ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_942_option_Omap__disc__iff,axiom,
% 9.17/5.32 ! [F: produc8664842809031399944it_nat > produc8664842809031399944it_nat,A: option8956607266484857688it_nat] :
% 9.17/5.32 ( ( ( map_op8673683442680995229it_nat @ F @ A )
% 9.17/5.32 = none_P9117596204409417319it_nat )
% 9.17/5.32 = ( A = none_P9117596204409417319it_nat ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_943_option_Omap__disc__iff,axiom,
% 9.17/5.32 ! [F: num > num,A: option_num] :
% 9.17/5.32 ( ( ( map_option_num_num @ F @ A )
% 9.17/5.32 = none_num )
% 9.17/5.32 = ( A = none_num ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_944_neg__less__0__iff__less,axiom,
% 9.17/5.32 ! [A: int] :
% 9.17/5.32 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 9.17/5.32 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_945_neg__less__0__iff__less,axiom,
% 9.17/5.32 ! [A: code_integer] :
% 9.17/5.32 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ zero_z3403309356797280102nteger )
% 9.17/5.32 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_946_neg__less__0__iff__less,axiom,
% 9.17/5.32 ! [A: rat] :
% 9.17/5.32 ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ zero_zero_rat )
% 9.17/5.32 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_947_neg__0__less__iff__less,axiom,
% 9.17/5.32 ! [A: int] :
% 9.17/5.32 ( ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 9.17/5.32 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_948_neg__0__less__iff__less,axiom,
% 9.17/5.32 ! [A: code_integer] :
% 9.17/5.32 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ A ) )
% 9.17/5.32 = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_949_neg__0__less__iff__less,axiom,
% 9.17/5.32 ! [A: rat] :
% 9.17/5.32 ( ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ A ) )
% 9.17/5.32 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_950_neg__less__pos,axiom,
% 9.17/5.32 ! [A: int] :
% 9.17/5.32 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ A )
% 9.17/5.32 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_951_neg__less__pos,axiom,
% 9.17/5.32 ! [A: code_integer] :
% 9.17/5.32 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 9.17/5.32 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_952_neg__less__pos,axiom,
% 9.17/5.32 ! [A: rat] :
% 9.17/5.32 ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ A )
% 9.17/5.32 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_953_less__neg__neg,axiom,
% 9.17/5.32 ! [A: int] :
% 9.17/5.32 ( ( ord_less_int @ A @ ( uminus_uminus_int @ A ) )
% 9.17/5.32 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_954_less__neg__neg,axiom,
% 9.17/5.32 ! [A: code_integer] :
% 9.17/5.32 ( ( ord_le6747313008572928689nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 9.17/5.32 = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_955_less__neg__neg,axiom,
% 9.17/5.32 ! [A: rat] :
% 9.17/5.32 ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ A ) )
% 9.17/5.32 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_956_ab__left__minus,axiom,
% 9.17/5.32 ! [A: int] :
% 9.17/5.32 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ A )
% 9.17/5.32 = zero_zero_int ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_957_ab__left__minus,axiom,
% 9.17/5.32 ! [A: code_integer] :
% 9.17/5.32 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 9.17/5.32 = zero_z3403309356797280102nteger ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_958_ab__left__minus,axiom,
% 9.17/5.32 ! [A: rat] :
% 9.17/5.32 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ A )
% 9.17/5.32 = zero_zero_rat ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_959_add_Oright__inverse,axiom,
% 9.17/5.32 ! [A: int] :
% 9.17/5.32 ( ( plus_plus_int @ A @ ( uminus_uminus_int @ A ) )
% 9.17/5.32 = zero_zero_int ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_960_add_Oright__inverse,axiom,
% 9.17/5.32 ! [A: code_integer] :
% 9.17/5.32 ( ( plus_p5714425477246183910nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 9.17/5.32 = zero_z3403309356797280102nteger ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_961_add_Oright__inverse,axiom,
% 9.17/5.32 ! [A: rat] :
% 9.17/5.32 ( ( plus_plus_rat @ A @ ( uminus_uminus_rat @ A ) )
% 9.17/5.32 = zero_zero_rat ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_962_zero__less__abs__iff,axiom,
% 9.17/5.32 ! [A: code_integer] :
% 9.17/5.32 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ A ) )
% 9.17/5.32 = ( A != zero_z3403309356797280102nteger ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_963_zero__less__abs__iff,axiom,
% 9.17/5.32 ! [A: rat] :
% 9.17/5.32 ( ( ord_less_rat @ zero_zero_rat @ ( abs_abs_rat @ A ) )
% 9.17/5.32 = ( A != zero_zero_rat ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_964_zero__less__abs__iff,axiom,
% 9.17/5.32 ! [A: int] :
% 9.17/5.32 ( ( ord_less_int @ zero_zero_int @ ( abs_abs_int @ A ) )
% 9.17/5.32 = ( A != zero_zero_int ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_965_abs__neg__one,axiom,
% 9.17/5.32 ( ( abs_abs_int @ ( uminus_uminus_int @ one_one_int ) )
% 9.17/5.32 = one_one_int ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_966_abs__neg__one,axiom,
% 9.17/5.32 ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.17/5.32 = one_one_Code_integer ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_967_abs__neg__one,axiom,
% 9.17/5.32 ( ( abs_abs_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 9.17/5.32 = one_one_rat ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_968_case__map__option,axiom,
% 9.17/5.32 ! [G: code_integer,H3: code_integer > code_integer,F: num > code_integer,X: option_num] :
% 9.17/5.32 ( ( case_o9049918639272118855nteger @ G @ H3 @ ( map_op2849635639313731588nteger @ F @ X ) )
% 9.17/5.32 = ( case_o356765784539232260er_num @ G @ ( comp_C3531382070062128313er_num @ H3 @ F ) @ X ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_969_case__map__option,axiom,
% 9.17/5.32 ! [G: produc8923325533196201883nteger > produc8923325533196201883nteger,H3: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,F: code_integer > code_integer,X: option_Code_integer] :
% 9.17/5.32 ( ( case_o7134296353695833103nteger @ G @ H3 @ ( map_op3669829223712506439nteger @ F @ X ) )
% 9.17/5.32 = ( case_o7134296353695833103nteger @ G @ ( comp_C1593894019821074884nteger @ H3 @ F ) @ X ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_970_case__map__option,axiom,
% 9.17/5.32 ! [G: produc8923325533196201883nteger > produc8923325533196201883nteger,H3: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,F: code_integer > code_integer > code_integer,X: option_Code_integer] :
% 9.17/5.32 ( ( case_o1441893360019914891nteger @ G @ H3 @ ( map_op370346339404370627nteger @ F @ X ) )
% 9.17/5.32 = ( case_o7134296353695833103nteger @ G @ ( comp_C8797469213163452608nteger @ H3 @ F ) @ X ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_971_case__map__option,axiom,
% 9.17/5.32 ! [G: num,H3: nat > num,F: int > nat,X: option_int] :
% 9.17/5.32 ( ( case_option_num_nat @ G @ H3 @ ( map_option_int_nat @ F @ X ) )
% 9.17/5.32 = ( case_option_num_int @ G @ ( comp_nat_num_int @ H3 @ F ) @ X ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_972_case__map__option,axiom,
% 9.17/5.32 ! [G: int,H3: num > int,F: num > num,X: option_num] :
% 9.17/5.32 ( ( case_option_int_num @ G @ H3 @ ( map_option_num_num @ F @ X ) )
% 9.17/5.32 = ( case_option_int_num @ G @ ( comp_num_int_num @ H3 @ F ) @ X ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_973_case__map__option,axiom,
% 9.17/5.32 ! [G: option_num,H3: num > option_num,F: num > num,X: option_num] :
% 9.17/5.32 ( ( case_o6005452278849405969um_num @ G @ H3 @ ( map_option_num_num @ F @ X ) )
% 9.17/5.32 = ( case_o6005452278849405969um_num @ G @ ( comp_n6731957995704128387um_num @ H3 @ F ) @ X ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_974_case__map__option,axiom,
% 9.17/5.32 ! [G: num,H3: num > num,F: num > num,X: option_num] :
% 9.17/5.32 ( ( case_option_num_num @ G @ H3 @ ( map_option_num_num @ F @ X ) )
% 9.17/5.32 = ( case_option_num_num @ G @ ( comp_num_num_num @ H3 @ F ) @ X ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_975_dbl__inc__simps_I4_J,axiom,
% 9.17/5.32 ( ( neg_nu5851722552734809277nc_int @ ( uminus_uminus_int @ one_one_int ) )
% 9.17/5.32 = ( uminus_uminus_int @ one_one_int ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_976_dbl__inc__simps_I4_J,axiom,
% 9.17/5.32 ( ( neg_nu5831290666863070958nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.17/5.32 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_977_dbl__inc__simps_I4_J,axiom,
% 9.17/5.32 ( ( neg_nu5219082963157363817nc_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 9.17/5.32 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_978_abs__sgn__eq__1,axiom,
% 9.17/5.32 ! [A: code_integer] :
% 9.17/5.32 ( ( A != zero_z3403309356797280102nteger )
% 9.17/5.32 => ( ( abs_abs_Code_integer @ ( sgn_sgn_Code_integer @ A ) )
% 9.17/5.32 = one_one_Code_integer ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_979_abs__sgn__eq__1,axiom,
% 9.17/5.32 ! [A: rat] :
% 9.17/5.32 ( ( A != zero_zero_rat )
% 9.17/5.32 => ( ( abs_abs_rat @ ( sgn_sgn_rat @ A ) )
% 9.17/5.32 = one_one_rat ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_980_abs__sgn__eq__1,axiom,
% 9.17/5.32 ! [A: int] :
% 9.17/5.32 ( ( A != zero_zero_int )
% 9.17/5.32 => ( ( abs_abs_int @ ( sgn_sgn_int @ A ) )
% 9.17/5.32 = one_one_int ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_981_dbl__dec__simps_I2_J,axiom,
% 9.17/5.32 ( ( neg_nu3811975205180677377ec_int @ zero_zero_int )
% 9.17/5.32 = ( uminus_uminus_int @ one_one_int ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_982_dbl__dec__simps_I2_J,axiom,
% 9.17/5.32 ( ( neg_nu7757733837767384882nteger @ zero_z3403309356797280102nteger )
% 9.17/5.32 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_983_dbl__dec__simps_I2_J,axiom,
% 9.17/5.32 ( ( neg_nu3179335615603231917ec_rat @ zero_zero_rat )
% 9.17/5.32 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_984_sgn__neg,axiom,
% 9.17/5.32 ! [A: int] :
% 9.17/5.32 ( ( ord_less_int @ A @ zero_zero_int )
% 9.17/5.32 => ( ( sgn_sgn_int @ A )
% 9.17/5.32 = ( uminus_uminus_int @ one_one_int ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_985_sgn__neg,axiom,
% 9.17/5.32 ! [A: code_integer] :
% 9.17/5.32 ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 9.17/5.32 => ( ( sgn_sgn_Code_integer @ A )
% 9.17/5.32 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_986_sgn__neg,axiom,
% 9.17/5.32 ! [A: rat] :
% 9.17/5.32 ( ( ord_less_rat @ A @ zero_zero_rat )
% 9.17/5.32 => ( ( sgn_sgn_rat @ A )
% 9.17/5.32 = ( uminus_uminus_rat @ one_one_rat ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_987_minus__equation__iff,axiom,
% 9.17/5.32 ! [A: int,B: int] :
% 9.17/5.32 ( ( ( uminus_uminus_int @ A )
% 9.17/5.32 = B )
% 9.17/5.32 = ( ( uminus_uminus_int @ B )
% 9.17/5.32 = A ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_988_minus__equation__iff,axiom,
% 9.17/5.32 ! [A: code_integer,B: code_integer] :
% 9.17/5.32 ( ( ( uminus1351360451143612070nteger @ A )
% 9.17/5.32 = B )
% 9.17/5.32 = ( ( uminus1351360451143612070nteger @ B )
% 9.17/5.32 = A ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_989_minus__equation__iff,axiom,
% 9.17/5.32 ! [A: rat,B: rat] :
% 9.17/5.32 ( ( ( uminus_uminus_rat @ A )
% 9.17/5.32 = B )
% 9.17/5.32 = ( ( uminus_uminus_rat @ B )
% 9.17/5.32 = A ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_990_equation__minus__iff,axiom,
% 9.17/5.32 ! [A: int,B: int] :
% 9.17/5.32 ( ( A
% 9.17/5.32 = ( uminus_uminus_int @ B ) )
% 9.17/5.32 = ( B
% 9.17/5.32 = ( uminus_uminus_int @ A ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_991_equation__minus__iff,axiom,
% 9.17/5.32 ! [A: code_integer,B: code_integer] :
% 9.17/5.32 ( ( A
% 9.17/5.32 = ( uminus1351360451143612070nteger @ B ) )
% 9.17/5.32 = ( B
% 9.17/5.32 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_992_equation__minus__iff,axiom,
% 9.17/5.32 ! [A: rat,B: rat] :
% 9.17/5.32 ( ( A
% 9.17/5.32 = ( uminus_uminus_rat @ B ) )
% 9.17/5.32 = ( B
% 9.17/5.32 = ( uminus_uminus_rat @ A ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_993_same__sgn__abs__add,axiom,
% 9.17/5.32 ! [B: code_integer,A: code_integer] :
% 9.17/5.32 ( ( ( sgn_sgn_Code_integer @ B )
% 9.17/5.32 = ( sgn_sgn_Code_integer @ A ) )
% 9.17/5.32 => ( ( abs_abs_Code_integer @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 9.17/5.32 = ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_994_same__sgn__abs__add,axiom,
% 9.17/5.32 ! [B: rat,A: rat] :
% 9.17/5.32 ( ( ( sgn_sgn_rat @ B )
% 9.17/5.32 = ( sgn_sgn_rat @ A ) )
% 9.17/5.32 => ( ( abs_abs_rat @ ( plus_plus_rat @ A @ B ) )
% 9.17/5.32 = ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_995_same__sgn__abs__add,axiom,
% 9.17/5.32 ! [B: int,A: int] :
% 9.17/5.32 ( ( ( sgn_sgn_int @ B )
% 9.17/5.32 = ( sgn_sgn_int @ A ) )
% 9.17/5.32 => ( ( abs_abs_int @ ( plus_plus_int @ A @ B ) )
% 9.17/5.32 = ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_996_sgn__minus__1,axiom,
% 9.17/5.32 ( ( sgn_sgn_int @ ( uminus_uminus_int @ one_one_int ) )
% 9.17/5.32 = ( uminus_uminus_int @ one_one_int ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_997_sgn__minus__1,axiom,
% 9.17/5.32 ( ( sgn_sgn_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.17/5.32 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_998_sgn__minus__1,axiom,
% 9.17/5.32 ( ( sgn_sgn_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 9.17/5.32 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_999_option_Omap__ident,axiom,
% 9.17/5.32 ! [T: option_num] :
% 9.17/5.32 ( ( map_option_num_num
% 9.17/5.32 @ ^ [X3: num] : X3
% 9.17/5.32 @ T )
% 9.17/5.32 = T ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1000_abs__of__neg,axiom,
% 9.17/5.32 ! [A: int] :
% 9.17/5.32 ( ( ord_less_int @ A @ zero_zero_int )
% 9.17/5.32 => ( ( abs_abs_int @ A )
% 9.17/5.32 = ( uminus_uminus_int @ A ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1001_abs__of__neg,axiom,
% 9.17/5.32 ! [A: code_integer] :
% 9.17/5.32 ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 9.17/5.32 => ( ( abs_abs_Code_integer @ A )
% 9.17/5.32 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1002_abs__of__neg,axiom,
% 9.17/5.32 ! [A: rat] :
% 9.17/5.32 ( ( ord_less_rat @ A @ zero_zero_rat )
% 9.17/5.32 => ( ( abs_abs_rat @ A )
% 9.17/5.32 = ( uminus_uminus_rat @ A ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1003_abs__sgn__eq,axiom,
% 9.17/5.32 ! [A: code_integer] :
% 9.17/5.32 ( ( ( A = zero_z3403309356797280102nteger )
% 9.17/5.32 => ( ( abs_abs_Code_integer @ ( sgn_sgn_Code_integer @ A ) )
% 9.17/5.32 = zero_z3403309356797280102nteger ) )
% 9.17/5.32 & ( ( A != zero_z3403309356797280102nteger )
% 9.17/5.32 => ( ( abs_abs_Code_integer @ ( sgn_sgn_Code_integer @ A ) )
% 9.17/5.32 = one_one_Code_integer ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1004_abs__sgn__eq,axiom,
% 9.17/5.32 ! [A: rat] :
% 9.17/5.32 ( ( ( A = zero_zero_rat )
% 9.17/5.32 => ( ( abs_abs_rat @ ( sgn_sgn_rat @ A ) )
% 9.17/5.32 = zero_zero_rat ) )
% 9.17/5.32 & ( ( A != zero_zero_rat )
% 9.17/5.32 => ( ( abs_abs_rat @ ( sgn_sgn_rat @ A ) )
% 9.17/5.32 = one_one_rat ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1005_abs__sgn__eq,axiom,
% 9.17/5.32 ! [A: int] :
% 9.17/5.32 ( ( ( A = zero_zero_int )
% 9.17/5.32 => ( ( abs_abs_int @ ( sgn_sgn_int @ A ) )
% 9.17/5.32 = zero_zero_int ) )
% 9.17/5.32 & ( ( A != zero_zero_int )
% 9.17/5.32 => ( ( abs_abs_int @ ( sgn_sgn_int @ A ) )
% 9.17/5.32 = one_one_int ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1006_abs__one,axiom,
% 9.17/5.32 ( ( abs_abs_Code_integer @ one_one_Code_integer )
% 9.17/5.32 = one_one_Code_integer ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1007_abs__one,axiom,
% 9.17/5.32 ( ( abs_abs_rat @ one_one_rat )
% 9.17/5.32 = one_one_rat ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1008_abs__one,axiom,
% 9.17/5.32 ( ( abs_abs_int @ one_one_int )
% 9.17/5.32 = one_one_int ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1009_map__option_Ocompositionality,axiom,
% 9.17/5.32 ! [F: code_integer > code_integer,G: num > code_integer,Option: option_num] :
% 9.17/5.32 ( ( map_op3669829223712506439nteger @ F @ ( map_op2849635639313731588nteger @ G @ Option ) )
% 9.17/5.32 = ( map_op2849635639313731588nteger @ ( comp_C3531382070062128313er_num @ F @ G ) @ Option ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1010_map__option_Ocompositionality,axiom,
% 9.17/5.32 ! [F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer,Option: option_Code_integer] :
% 9.17/5.32 ( ( map_op9146685272036663823nteger @ F @ ( map_op3669829223712506439nteger @ G @ Option ) )
% 9.17/5.32 = ( map_op9146685272036663823nteger @ ( comp_C1593894019821074884nteger @ F @ G ) @ Option ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1011_map__option_Ocompositionality,axiom,
% 9.17/5.32 ! [F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer > code_integer,Option: option_Code_integer] :
% 9.17/5.32 ( ( map_op3563471509957180299nteger @ F @ ( map_op370346339404370627nteger @ G @ Option ) )
% 9.17/5.32 = ( map_op9146685272036663823nteger @ ( comp_C8797469213163452608nteger @ F @ G ) @ Option ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1012_map__option_Ocompositionality,axiom,
% 9.17/5.32 ! [F: nat > num,G: int > nat,Option: option_int] :
% 9.17/5.32 ( ( map_option_nat_num @ F @ ( map_option_int_nat @ G @ Option ) )
% 9.17/5.32 = ( map_option_int_num @ ( comp_nat_num_int @ F @ G ) @ Option ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1013_map__option_Ocompositionality,axiom,
% 9.17/5.32 ! [F: num > num,G: num > num,Option: option_num] :
% 9.17/5.32 ( ( map_option_num_num @ F @ ( map_option_num_num @ G @ Option ) )
% 9.17/5.32 = ( map_option_num_num @ ( comp_num_num_num @ F @ G ) @ Option ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1014_option_Omap__comp,axiom,
% 9.17/5.32 ! [G: code_integer > code_integer,F: num > code_integer,V: option_num] :
% 9.17/5.32 ( ( map_op3669829223712506439nteger @ G @ ( map_op2849635639313731588nteger @ F @ V ) )
% 9.17/5.32 = ( map_op2849635639313731588nteger @ ( comp_C3531382070062128313er_num @ G @ F ) @ V ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1015_option_Omap__comp,axiom,
% 9.17/5.32 ! [G: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,F: code_integer > code_integer,V: option_Code_integer] :
% 9.17/5.32 ( ( map_op9146685272036663823nteger @ G @ ( map_op3669829223712506439nteger @ F @ V ) )
% 9.17/5.32 = ( map_op9146685272036663823nteger @ ( comp_C1593894019821074884nteger @ G @ F ) @ V ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1016_option_Omap__comp,axiom,
% 9.17/5.32 ! [G: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,F: code_integer > code_integer > code_integer,V: option_Code_integer] :
% 9.17/5.32 ( ( map_op3563471509957180299nteger @ G @ ( map_op370346339404370627nteger @ F @ V ) )
% 9.17/5.32 = ( map_op9146685272036663823nteger @ ( comp_C8797469213163452608nteger @ G @ F ) @ V ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1017_option_Omap__comp,axiom,
% 9.17/5.32 ! [G: nat > num,F: int > nat,V: option_int] :
% 9.17/5.32 ( ( map_option_nat_num @ G @ ( map_option_int_nat @ F @ V ) )
% 9.17/5.32 = ( map_option_int_num @ ( comp_nat_num_int @ G @ F ) @ V ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1018_option_Omap__comp,axiom,
% 9.17/5.32 ! [G: num > num,F: num > num,V: option_num] :
% 9.17/5.32 ( ( map_option_num_num @ G @ ( map_option_num_num @ F @ V ) )
% 9.17/5.32 = ( map_option_num_num @ ( comp_num_num_num @ G @ F ) @ V ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1019_map__option_Ocomp,axiom,
% 9.17/5.32 ! [F: code_integer > code_integer,G: num > code_integer] :
% 9.17/5.32 ( ( comp_o5321900959263616553on_num @ ( map_op3669829223712506439nteger @ F ) @ ( map_op2849635639313731588nteger @ G ) )
% 9.17/5.32 = ( map_op2849635639313731588nteger @ ( comp_C3531382070062128313er_num @ F @ G ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1020_map__option_Ocomp,axiom,
% 9.17/5.32 ! [F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer] :
% 9.17/5.32 ( ( comp_o9011007105448239796nteger @ ( map_op9146685272036663823nteger @ F ) @ ( map_op3669829223712506439nteger @ G ) )
% 9.17/5.32 = ( map_op9146685272036663823nteger @ ( comp_C1593894019821074884nteger @ F @ G ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1021_map__option_Ocomp,axiom,
% 9.17/5.32 ! [F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer > code_integer] :
% 9.17/5.32 ( ( comp_o7188567781464924208nteger @ ( map_op3563471509957180299nteger @ F ) @ ( map_op370346339404370627nteger @ G ) )
% 9.17/5.32 = ( map_op9146685272036663823nteger @ ( comp_C8797469213163452608nteger @ F @ G ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1022_map__option_Ocomp,axiom,
% 9.17/5.32 ! [F: nat > num,G: int > nat] :
% 9.17/5.32 ( ( comp_o3128663659858294251on_int @ ( map_option_nat_num @ F ) @ ( map_option_int_nat @ G ) )
% 9.17/5.32 = ( map_option_int_num @ ( comp_nat_num_int @ F @ G ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1023_map__option_Ocomp,axiom,
% 9.17/5.32 ! [F: num > num,G: num > num] :
% 9.17/5.32 ( ( comp_o8931257242830428707on_num @ ( map_option_num_num @ F ) @ ( map_option_num_num @ G ) )
% 9.17/5.32 = ( map_option_num_num @ ( comp_num_num_num @ F @ G ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1024_minus__less__iff,axiom,
% 9.17/5.32 ! [A: int,B: int] :
% 9.17/5.32 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ B )
% 9.17/5.32 = ( ord_less_int @ ( uminus_uminus_int @ B ) @ A ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1025_minus__less__iff,axiom,
% 9.17/5.32 ! [A: code_integer,B: code_integer] :
% 9.17/5.32 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 9.17/5.32 = ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ A ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1026_minus__less__iff,axiom,
% 9.17/5.32 ! [A: rat,B: rat] :
% 9.17/5.32 ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ B )
% 9.17/5.32 = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ A ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1027_less__minus__iff,axiom,
% 9.17/5.32 ! [A: int,B: int] :
% 9.17/5.32 ( ( ord_less_int @ A @ ( uminus_uminus_int @ B ) )
% 9.17/5.32 = ( ord_less_int @ B @ ( uminus_uminus_int @ A ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1028_less__minus__iff,axiom,
% 9.17/5.32 ! [A: code_integer,B: code_integer] :
% 9.17/5.32 ( ( ord_le6747313008572928689nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 9.17/5.32 = ( ord_le6747313008572928689nteger @ B @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1029_less__minus__iff,axiom,
% 9.17/5.32 ! [A: rat,B: rat] :
% 9.17/5.32 ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ B ) )
% 9.17/5.32 = ( ord_less_rat @ B @ ( uminus_uminus_rat @ A ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1030_is__num__normalize_I8_J,axiom,
% 9.17/5.32 ! [A: int,B: int] :
% 9.17/5.32 ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 9.17/5.32 = ( plus_plus_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1031_is__num__normalize_I8_J,axiom,
% 9.17/5.32 ! [A: code_integer,B: code_integer] :
% 9.17/5.32 ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 9.17/5.32 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1032_is__num__normalize_I8_J,axiom,
% 9.17/5.32 ! [A: rat,B: rat] :
% 9.17/5.32 ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 9.17/5.32 = ( plus_plus_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1033_add_Oinverse__distrib__swap,axiom,
% 9.17/5.32 ! [A: int,B: int] :
% 9.17/5.32 ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 9.17/5.32 = ( plus_plus_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1034_add_Oinverse__distrib__swap,axiom,
% 9.17/5.32 ! [A: code_integer,B: code_integer] :
% 9.17/5.32 ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 9.17/5.32 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1035_add_Oinverse__distrib__swap,axiom,
% 9.17/5.32 ! [A: rat,B: rat] :
% 9.17/5.32 ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 9.17/5.32 = ( plus_plus_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1036_group__cancel_Oneg1,axiom,
% 9.17/5.32 ! [A2: int,K: int,A: int] :
% 9.17/5.32 ( ( A2
% 9.17/5.32 = ( plus_plus_int @ K @ A ) )
% 9.17/5.32 => ( ( uminus_uminus_int @ A2 )
% 9.17/5.32 = ( plus_plus_int @ ( uminus_uminus_int @ K ) @ ( uminus_uminus_int @ A ) ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1037_group__cancel_Oneg1,axiom,
% 9.17/5.32 ! [A2: code_integer,K: code_integer,A: code_integer] :
% 9.17/5.32 ( ( A2
% 9.17/5.32 = ( plus_p5714425477246183910nteger @ K @ A ) )
% 9.17/5.32 => ( ( uminus1351360451143612070nteger @ A2 )
% 9.17/5.32 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ K ) @ ( uminus1351360451143612070nteger @ A ) ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1038_group__cancel_Oneg1,axiom,
% 9.17/5.32 ! [A2: rat,K: rat,A: rat] :
% 9.17/5.32 ( ( A2
% 9.17/5.32 = ( plus_plus_rat @ K @ A ) )
% 9.17/5.32 => ( ( uminus_uminus_rat @ A2 )
% 9.17/5.32 = ( plus_plus_rat @ ( uminus_uminus_rat @ K ) @ ( uminus_uminus_rat @ A ) ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1039_one__neq__neg__one,axiom,
% 9.17/5.32 ( one_one_int
% 9.17/5.32 != ( uminus_uminus_int @ one_one_int ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1040_one__neq__neg__one,axiom,
% 9.17/5.32 ( one_one_Code_integer
% 9.17/5.32 != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1041_one__neq__neg__one,axiom,
% 9.17/5.32 ( one_one_rat
% 9.17/5.32 != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1042_map__option__cong,axiom,
% 9.17/5.32 ! [X: option_num,Y: option_num,F: num > num,G: num > num] :
% 9.17/5.32 ( ( X = Y )
% 9.17/5.32 => ( ! [A3: num] :
% 9.17/5.32 ( ( Y
% 9.17/5.32 = ( some_num @ A3 ) )
% 9.17/5.32 => ( ( F @ A3 )
% 9.17/5.32 = ( G @ A3 ) ) )
% 9.17/5.32 => ( ( map_option_num_num @ F @ X )
% 9.17/5.32 = ( map_option_num_num @ G @ Y ) ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1043_option_Osimps_I9_J,axiom,
% 9.17/5.32 ! [F: num > produc8664842809031399944it_nat,X2: num] :
% 9.17/5.32 ( ( map_op8118133509425879471it_nat @ F @ ( some_num @ X2 ) )
% 9.17/5.32 = ( some_P1914260805536162275it_nat @ ( F @ X2 ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1044_option_Osimps_I9_J,axiom,
% 9.17/5.32 ! [F: produc8664842809031399944it_nat > num,X2: produc8664842809031399944it_nat] :
% 9.17/5.32 ( ( map_op2731889312448867759at_num @ F @ ( some_P1914260805536162275it_nat @ X2 ) )
% 9.17/5.32 = ( some_num @ ( F @ X2 ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1045_option_Osimps_I9_J,axiom,
% 9.17/5.32 ! [F: produc8664842809031399944it_nat > produc8664842809031399944it_nat,X2: produc8664842809031399944it_nat] :
% 9.17/5.32 ( ( map_op8673683442680995229it_nat @ F @ ( some_P1914260805536162275it_nat @ X2 ) )
% 9.17/5.32 = ( some_P1914260805536162275it_nat @ ( F @ X2 ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1046_option_Osimps_I9_J,axiom,
% 9.17/5.32 ! [F: num > num,X2: num] :
% 9.17/5.32 ( ( map_option_num_num @ F @ ( some_num @ X2 ) )
% 9.17/5.32 = ( some_num @ ( F @ X2 ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1047_option_Osimps_I8_J,axiom,
% 9.17/5.32 ! [F: produc6714399278180371524it_nat > produc6714399278180371524it_nat] :
% 9.17/5.32 ( ( map_op6002829699023054091it_nat @ F @ none_P2587165478634041381it_nat )
% 9.17/5.32 = none_P2587165478634041381it_nat ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1048_option_Osimps_I8_J,axiom,
% 9.17/5.32 ! [F: produc6714399278180371524it_nat > num] :
% 9.17/5.32 ( ( map_op8228268515680064275at_num @ F @ none_P2587165478634041381it_nat )
% 9.17/5.32 = none_num ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1049_option_Osimps_I8_J,axiom,
% 9.17/5.32 ! [F: produc6714399278180371524it_nat > produc8664842809031399944it_nat] :
% 9.17/5.32 ( ( map_op674526153330701057it_nat @ F @ none_P2587165478634041381it_nat )
% 9.17/5.32 = none_P9117596204409417319it_nat ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1050_option_Osimps_I8_J,axiom,
% 9.17/5.32 ! [F: num > produc6714399278180371524it_nat] :
% 9.17/5.32 ( ( map_op6598675229099881181it_nat @ F @ none_num )
% 9.17/5.32 = none_P2587165478634041381it_nat ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1051_option_Osimps_I8_J,axiom,
% 9.17/5.32 ! [F: num > produc8664842809031399944it_nat] :
% 9.17/5.32 ( ( map_op8118133509425879471it_nat @ F @ none_num )
% 9.17/5.32 = none_P9117596204409417319it_nat ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1052_option_Osimps_I8_J,axiom,
% 9.17/5.32 ! [F: produc8664842809031399944it_nat > produc6714399278180371524it_nat] :
% 9.17/5.32 ( ( map_op7916408704904942447it_nat @ F @ none_P9117596204409417319it_nat )
% 9.17/5.32 = none_P2587165478634041381it_nat ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1053_option_Osimps_I8_J,axiom,
% 9.17/5.32 ! [F: produc8664842809031399944it_nat > num] :
% 9.17/5.32 ( ( map_op2731889312448867759at_num @ F @ none_P9117596204409417319it_nat )
% 9.17/5.32 = none_num ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1054_option_Osimps_I8_J,axiom,
% 9.17/5.32 ! [F: produc8664842809031399944it_nat > produc8664842809031399944it_nat] :
% 9.17/5.32 ( ( map_op8673683442680995229it_nat @ F @ none_P9117596204409417319it_nat )
% 9.17/5.32 = none_P9117596204409417319it_nat ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1055_option_Osimps_I8_J,axiom,
% 9.17/5.32 ! [F: num > num] :
% 9.17/5.32 ( ( map_option_num_num @ F @ none_num )
% 9.17/5.32 = none_num ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1056_same__sgn__sgn__add,axiom,
% 9.17/5.32 ! [B: code_integer,A: code_integer] :
% 9.17/5.32 ( ( ( sgn_sgn_Code_integer @ B )
% 9.17/5.32 = ( sgn_sgn_Code_integer @ A ) )
% 9.17/5.32 => ( ( sgn_sgn_Code_integer @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 9.17/5.32 = ( sgn_sgn_Code_integer @ A ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1057_same__sgn__sgn__add,axiom,
% 9.17/5.32 ! [B: rat,A: rat] :
% 9.17/5.32 ( ( ( sgn_sgn_rat @ B )
% 9.17/5.32 = ( sgn_sgn_rat @ A ) )
% 9.17/5.32 => ( ( sgn_sgn_rat @ ( plus_plus_rat @ A @ B ) )
% 9.17/5.32 = ( sgn_sgn_rat @ A ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1058_same__sgn__sgn__add,axiom,
% 9.17/5.32 ! [B: int,A: int] :
% 9.17/5.32 ( ( ( sgn_sgn_int @ B )
% 9.17/5.32 = ( sgn_sgn_int @ A ) )
% 9.17/5.32 => ( ( sgn_sgn_int @ ( plus_plus_int @ A @ B ) )
% 9.17/5.32 = ( sgn_sgn_int @ A ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1059_Ints__add,axiom,
% 9.17/5.32 ! [A: rat,B: rat] :
% 9.17/5.32 ( ( member_rat @ A @ ring_1_Ints_rat )
% 9.17/5.32 => ( ( member_rat @ B @ ring_1_Ints_rat )
% 9.17/5.32 => ( member_rat @ ( plus_plus_rat @ A @ B ) @ ring_1_Ints_rat ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1060_Ints__add,axiom,
% 9.17/5.32 ! [A: int,B: int] :
% 9.17/5.32 ( ( member_int @ A @ ring_1_Ints_int )
% 9.17/5.32 => ( ( member_int @ B @ ring_1_Ints_int )
% 9.17/5.32 => ( member_int @ ( plus_plus_int @ A @ B ) @ ring_1_Ints_int ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1061_success__lookupI,axiom,
% 9.17/5.32 ! [R2: ref_Product_unit,H3: heap_e7401611519738050253t_unit] : ( heap_T584514906347983379t_unit @ ( ref_lo7930775386976318366t_unit @ R2 ) @ H3 ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1062_success__lookupI,axiom,
% 9.17/5.32 ! [R2: ref_array_a,H3: heap_e7401611519738050253t_unit] : ( heap_T6932021131025641745rray_a @ ( ref_lookup_array_a @ R2 ) @ H3 ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1063_Ints__1,axiom,
% 9.17/5.32 member_Code_integer @ one_one_Code_integer @ ring_11222124179247155820nteger ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1064_Ints__1,axiom,
% 9.17/5.32 member_rat @ one_one_rat @ ring_1_Ints_rat ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1065_Ints__1,axiom,
% 9.17/5.32 member_int @ one_one_int @ ring_1_Ints_int ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1066_Ints__nonzero__abs__less1,axiom,
% 9.17/5.32 ! [X: code_integer] :
% 9.17/5.32 ( ( member_Code_integer @ X @ ring_11222124179247155820nteger )
% 9.17/5.32 => ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ X ) @ one_one_Code_integer )
% 9.17/5.32 => ( X = zero_z3403309356797280102nteger ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1067_Ints__nonzero__abs__less1,axiom,
% 9.17/5.32 ! [X: rat] :
% 9.17/5.32 ( ( member_rat @ X @ ring_1_Ints_rat )
% 9.17/5.32 => ( ( ord_less_rat @ ( abs_abs_rat @ X ) @ one_one_rat )
% 9.17/5.32 => ( X = zero_zero_rat ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1068_Ints__nonzero__abs__less1,axiom,
% 9.17/5.32 ! [X: int] :
% 9.17/5.32 ( ( member_int @ X @ ring_1_Ints_int )
% 9.17/5.32 => ( ( ord_less_int @ ( abs_abs_int @ X ) @ one_one_int )
% 9.17/5.32 => ( X = zero_zero_int ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1069_sgn__if,axiom,
% 9.17/5.32 ( sgn_sgn_int
% 9.17/5.32 = ( ^ [X3: int] : ( if_int @ ( X3 = zero_zero_int ) @ zero_zero_int @ ( if_int @ ( ord_less_int @ zero_zero_int @ X3 ) @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1070_sgn__if,axiom,
% 9.17/5.32 ( sgn_sgn_Code_integer
% 9.17/5.32 = ( ^ [X3: code_integer] : ( if_Code_integer @ ( X3 = zero_z3403309356797280102nteger ) @ zero_z3403309356797280102nteger @ ( if_Code_integer @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ X3 ) @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1071_sgn__if,axiom,
% 9.17/5.32 ( sgn_sgn_rat
% 9.17/5.32 = ( ^ [X3: rat] : ( if_rat @ ( X3 = zero_zero_rat ) @ zero_zero_rat @ ( if_rat @ ( ord_less_rat @ zero_zero_rat @ X3 ) @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1072_sgn__1__neg,axiom,
% 9.17/5.32 ! [A: int] :
% 9.17/5.32 ( ( ( sgn_sgn_int @ A )
% 9.17/5.32 = ( uminus_uminus_int @ one_one_int ) )
% 9.17/5.32 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1073_sgn__1__neg,axiom,
% 9.17/5.32 ! [A: code_integer] :
% 9.17/5.32 ( ( ( sgn_sgn_Code_integer @ A )
% 9.17/5.32 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.17/5.32 = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1074_sgn__1__neg,axiom,
% 9.17/5.32 ! [A: rat] :
% 9.17/5.32 ( ( ( sgn_sgn_rat @ A )
% 9.17/5.32 = ( uminus_uminus_rat @ one_one_rat ) )
% 9.17/5.32 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1075_abs__not__less__zero,axiom,
% 9.17/5.32 ! [A: code_integer] :
% 9.17/5.32 ~ ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ zero_z3403309356797280102nteger ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1076_abs__not__less__zero,axiom,
% 9.17/5.32 ! [A: rat] :
% 9.17/5.32 ~ ( ord_less_rat @ ( abs_abs_rat @ A ) @ zero_zero_rat ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1077_abs__not__less__zero,axiom,
% 9.17/5.32 ! [A: int] :
% 9.17/5.32 ~ ( ord_less_int @ ( abs_abs_int @ A ) @ zero_zero_int ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1078_abs__of__pos,axiom,
% 9.17/5.32 ! [A: code_integer] :
% 9.17/5.32 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 9.17/5.32 => ( ( abs_abs_Code_integer @ A )
% 9.17/5.32 = A ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1079_abs__of__pos,axiom,
% 9.17/5.32 ! [A: rat] :
% 9.17/5.32 ( ( ord_less_rat @ zero_zero_rat @ A )
% 9.17/5.32 => ( ( abs_abs_rat @ A )
% 9.17/5.32 = A ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1080_abs__of__pos,axiom,
% 9.17/5.32 ! [A: int] :
% 9.17/5.32 ( ( ord_less_int @ zero_zero_int @ A )
% 9.17/5.32 => ( ( abs_abs_int @ A )
% 9.17/5.32 = A ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1081_neg__eq__iff__add__eq__0,axiom,
% 9.17/5.32 ! [A: int,B: int] :
% 9.17/5.32 ( ( ( uminus_uminus_int @ A )
% 9.17/5.32 = B )
% 9.17/5.32 = ( ( plus_plus_int @ A @ B )
% 9.17/5.32 = zero_zero_int ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1082_neg__eq__iff__add__eq__0,axiom,
% 9.17/5.32 ! [A: code_integer,B: code_integer] :
% 9.17/5.32 ( ( ( uminus1351360451143612070nteger @ A )
% 9.17/5.32 = B )
% 9.17/5.32 = ( ( plus_p5714425477246183910nteger @ A @ B )
% 9.17/5.32 = zero_z3403309356797280102nteger ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1083_neg__eq__iff__add__eq__0,axiom,
% 9.17/5.32 ! [A: rat,B: rat] :
% 9.17/5.32 ( ( ( uminus_uminus_rat @ A )
% 9.17/5.32 = B )
% 9.17/5.32 = ( ( plus_plus_rat @ A @ B )
% 9.17/5.32 = zero_zero_rat ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1084_eq__neg__iff__add__eq__0,axiom,
% 9.17/5.32 ! [A: int,B: int] :
% 9.17/5.32 ( ( A
% 9.17/5.32 = ( uminus_uminus_int @ B ) )
% 9.17/5.32 = ( ( plus_plus_int @ A @ B )
% 9.17/5.32 = zero_zero_int ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1085_eq__neg__iff__add__eq__0,axiom,
% 9.17/5.32 ! [A: code_integer,B: code_integer] :
% 9.17/5.32 ( ( A
% 9.17/5.32 = ( uminus1351360451143612070nteger @ B ) )
% 9.17/5.32 = ( ( plus_p5714425477246183910nteger @ A @ B )
% 9.17/5.32 = zero_z3403309356797280102nteger ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1086_eq__neg__iff__add__eq__0,axiom,
% 9.17/5.32 ! [A: rat,B: rat] :
% 9.17/5.32 ( ( A
% 9.17/5.32 = ( uminus_uminus_rat @ B ) )
% 9.17/5.32 = ( ( plus_plus_rat @ A @ B )
% 9.17/5.32 = zero_zero_rat ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1087_add_Oinverse__unique,axiom,
% 9.17/5.32 ! [A: int,B: int] :
% 9.17/5.32 ( ( ( plus_plus_int @ A @ B )
% 9.17/5.32 = zero_zero_int )
% 9.17/5.32 => ( ( uminus_uminus_int @ A )
% 9.17/5.32 = B ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1088_add_Oinverse__unique,axiom,
% 9.17/5.32 ! [A: code_integer,B: code_integer] :
% 9.17/5.32 ( ( ( plus_p5714425477246183910nteger @ A @ B )
% 9.17/5.32 = zero_z3403309356797280102nteger )
% 9.17/5.32 => ( ( uminus1351360451143612070nteger @ A )
% 9.17/5.32 = B ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1089_add_Oinverse__unique,axiom,
% 9.17/5.32 ! [A: rat,B: rat] :
% 9.17/5.32 ( ( ( plus_plus_rat @ A @ B )
% 9.17/5.32 = zero_zero_rat )
% 9.17/5.32 => ( ( uminus_uminus_rat @ A )
% 9.17/5.32 = B ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1090_ab__group__add__class_Oab__left__minus,axiom,
% 9.17/5.32 ! [A: int] :
% 9.17/5.32 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ A )
% 9.17/5.32 = zero_zero_int ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1091_ab__group__add__class_Oab__left__minus,axiom,
% 9.17/5.32 ! [A: code_integer] :
% 9.17/5.32 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 9.17/5.32 = zero_z3403309356797280102nteger ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1092_ab__group__add__class_Oab__left__minus,axiom,
% 9.17/5.32 ! [A: rat] :
% 9.17/5.32 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ A )
% 9.17/5.32 = zero_zero_rat ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1093_add__eq__0__iff,axiom,
% 9.17/5.32 ! [A: int,B: int] :
% 9.17/5.32 ( ( ( plus_plus_int @ A @ B )
% 9.17/5.32 = zero_zero_int )
% 9.17/5.32 = ( B
% 9.17/5.32 = ( uminus_uminus_int @ A ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1094_add__eq__0__iff,axiom,
% 9.17/5.32 ! [A: code_integer,B: code_integer] :
% 9.17/5.32 ( ( ( plus_p5714425477246183910nteger @ A @ B )
% 9.17/5.32 = zero_z3403309356797280102nteger )
% 9.17/5.32 = ( B
% 9.17/5.32 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1095_add__eq__0__iff,axiom,
% 9.17/5.32 ! [A: rat,B: rat] :
% 9.17/5.32 ( ( ( plus_plus_rat @ A @ B )
% 9.17/5.32 = zero_zero_rat )
% 9.17/5.32 = ( B
% 9.17/5.32 = ( uminus_uminus_rat @ A ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1096_zero__neq__neg__one,axiom,
% 9.17/5.32 ( zero_zero_int
% 9.17/5.32 != ( uminus_uminus_int @ one_one_int ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1097_zero__neq__neg__one,axiom,
% 9.17/5.32 ( zero_z3403309356797280102nteger
% 9.17/5.32 != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1098_zero__neq__neg__one,axiom,
% 9.17/5.32 ( zero_zero_rat
% 9.17/5.32 != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1099_less__minus__one__simps_I4_J,axiom,
% 9.17/5.32 ~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1100_less__minus__one__simps_I4_J,axiom,
% 9.17/5.32 ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1101_less__minus__one__simps_I4_J,axiom,
% 9.17/5.32 ~ ( ord_less_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1102_less__minus__one__simps_I2_J,axiom,
% 9.17/5.32 ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1103_less__minus__one__simps_I2_J,axiom,
% 9.17/5.32 ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1104_less__minus__one__simps_I2_J,axiom,
% 9.17/5.32 ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1105_option_Omap__sel,axiom,
% 9.17/5.32 ! [A: option_num,F: num > num] :
% 9.17/5.32 ( ( A != none_num )
% 9.17/5.32 => ( ( the_num @ ( map_option_num_num @ F @ A ) )
% 9.17/5.32 = ( F @ ( the_num @ A ) ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1106_Ints__double__eq__0__iff,axiom,
% 9.17/5.32 ! [A: code_integer] :
% 9.17/5.32 ( ( member_Code_integer @ A @ ring_11222124179247155820nteger )
% 9.17/5.32 => ( ( ( plus_p5714425477246183910nteger @ A @ A )
% 9.17/5.32 = zero_z3403309356797280102nteger )
% 9.17/5.32 = ( A = zero_z3403309356797280102nteger ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1107_Ints__double__eq__0__iff,axiom,
% 9.17/5.32 ! [A: rat] :
% 9.17/5.32 ( ( member_rat @ A @ ring_1_Ints_rat )
% 9.17/5.32 => ( ( ( plus_plus_rat @ A @ A )
% 9.17/5.32 = zero_zero_rat )
% 9.17/5.32 = ( A = zero_zero_rat ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1108_Ints__double__eq__0__iff,axiom,
% 9.17/5.32 ! [A: int] :
% 9.17/5.32 ( ( member_int @ A @ ring_1_Ints_int )
% 9.17/5.32 => ( ( ( plus_plus_int @ A @ A )
% 9.17/5.32 = zero_zero_int )
% 9.17/5.32 = ( A = zero_zero_int ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1109_less__minus__one__simps_I3_J,axiom,
% 9.17/5.32 ~ ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1110_less__minus__one__simps_I3_J,axiom,
% 9.17/5.32 ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1111_less__minus__one__simps_I3_J,axiom,
% 9.17/5.32 ~ ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1112_less__minus__one__simps_I1_J,axiom,
% 9.17/5.32 ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1113_less__minus__one__simps_I1_J,axiom,
% 9.17/5.32 ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ zero_z3403309356797280102nteger ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1114_less__minus__one__simps_I1_J,axiom,
% 9.17/5.32 ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ zero_zero_rat ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1115_sgn__1__pos,axiom,
% 9.17/5.32 ! [A: code_integer] :
% 9.17/5.32 ( ( ( sgn_sgn_Code_integer @ A )
% 9.17/5.32 = one_one_Code_integer )
% 9.17/5.32 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1116_sgn__1__pos,axiom,
% 9.17/5.32 ! [A: rat] :
% 9.17/5.32 ( ( ( sgn_sgn_rat @ A )
% 9.17/5.32 = one_one_rat )
% 9.17/5.32 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1117_sgn__1__pos,axiom,
% 9.17/5.32 ! [A: int] :
% 9.17/5.32 ( ( ( sgn_sgn_int @ A )
% 9.17/5.32 = one_one_int )
% 9.17/5.32 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1118_Ints__odd__nonzero,axiom,
% 9.17/5.32 ! [A: code_integer] :
% 9.17/5.32 ( ( member_Code_integer @ A @ ring_11222124179247155820nteger )
% 9.17/5.32 => ( ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ A )
% 9.17/5.32 != zero_z3403309356797280102nteger ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1119_Ints__odd__nonzero,axiom,
% 9.17/5.32 ! [A: rat] :
% 9.17/5.32 ( ( member_rat @ A @ ring_1_Ints_rat )
% 9.17/5.32 => ( ( plus_plus_rat @ ( plus_plus_rat @ one_one_rat @ A ) @ A )
% 9.17/5.32 != zero_zero_rat ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1120_Ints__odd__nonzero,axiom,
% 9.17/5.32 ! [A: int] :
% 9.17/5.32 ( ( member_int @ A @ ring_1_Ints_int )
% 9.17/5.32 => ( ( plus_plus_int @ ( plus_plus_int @ one_one_int @ A ) @ A )
% 9.17/5.32 != zero_zero_int ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1121_execute__lookup,axiom,
% 9.17/5.32 ! [R2: ref_array_a,H3: heap_e7401611519738050253t_unit] :
% 9.17/5.32 ( ( heap_T5591663578999710211rray_a @ ( ref_lookup_array_a @ R2 ) @ H3 )
% 9.17/5.32 = ( some_P6105628898608307625it_nat @ ( produc1733996804261680252it_nat @ ( ref_get_array_a @ H3 @ R2 ) @ ( produc584006145561248582it_nat @ H3 @ one_one_nat ) ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1122_execute__lookup,axiom,
% 9.17/5.32 ! [R2: ref_Product_unit,H3: heap_e7401611519738050253t_unit] :
% 9.17/5.32 ( ( heap_T875086893843062177t_unit @ ( ref_lo7930775386976318366t_unit @ R2 ) @ H3 )
% 9.17/5.32 = ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ ( ref_get_Product_unit @ H3 @ R2 ) @ ( produc584006145561248582it_nat @ H3 @ one_one_nat ) ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1123_fails__assert_H,axiom,
% 9.17/5.32 ! [P: $o,H3: heap_e7401611519738050253t_unit] :
% 9.17/5.32 ( ( time_f8834461667527620124t_unit @ ( refine_Imp_assert @ P ) @ H3 )
% 9.17/5.32 = ~ P ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1124_add_Ogroup__axioms,axiom,
% 9.17/5.32 group_int @ plus_plus_int @ zero_zero_int @ uminus_uminus_int ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1125_add_Ogroup__axioms,axiom,
% 9.17/5.32 group_Code_integer @ plus_p5714425477246183910nteger @ zero_z3403309356797280102nteger @ uminus1351360451143612070nteger ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1126_add_Ogroup__axioms,axiom,
% 9.17/5.32 group_rat @ plus_plus_rat @ zero_zero_rat @ uminus_uminus_rat ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1127_num__of__nat__double,axiom,
% 9.17/5.32 ! [N2: nat] :
% 9.17/5.32 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 9.17/5.32 => ( ( num_of_nat @ ( plus_plus_nat @ N2 @ N2 ) )
% 9.17/5.32 = ( bit0 @ ( num_of_nat @ N2 ) ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1128_Ints__nonzero__abs__ge1,axiom,
% 9.17/5.32 ! [X: code_integer] :
% 9.17/5.32 ( ( member_Code_integer @ X @ ring_11222124179247155820nteger )
% 9.17/5.32 => ( ( X != zero_z3403309356797280102nteger )
% 9.17/5.32 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( abs_abs_Code_integer @ X ) ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1129_Ints__nonzero__abs__ge1,axiom,
% 9.17/5.32 ! [X: rat] :
% 9.17/5.32 ( ( member_rat @ X @ ring_1_Ints_rat )
% 9.17/5.32 => ( ( X != zero_zero_rat )
% 9.17/5.32 => ( ord_less_eq_rat @ one_one_rat @ ( abs_abs_rat @ X ) ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1130_Ints__nonzero__abs__ge1,axiom,
% 9.17/5.32 ! [X: int] :
% 9.17/5.32 ( ( member_int @ X @ ring_1_Ints_int )
% 9.17/5.32 => ( ( X != zero_zero_int )
% 9.17/5.32 => ( ord_less_eq_int @ one_one_int @ ( abs_abs_int @ X ) ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1131_map__conv__bind__option,axiom,
% 9.17/5.32 ( map_option_num_num
% 9.17/5.32 = ( ^ [F2: num > num,X3: option_num] : ( bind_num_num @ X3 @ ( comp_n6731957995704128387um_num @ some_num @ F2 ) ) ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1132_nat__add__left__cancel__le,axiom,
% 9.17/5.32 ! [K: nat,M2: nat,N2: nat] :
% 9.17/5.32 ( ( ord_less_eq_nat @ ( plus_plus_nat @ K @ M2 ) @ ( plus_plus_nat @ K @ N2 ) )
% 9.17/5.32 = ( ord_less_eq_nat @ M2 @ N2 ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1133_less__eq__option__None__code,axiom,
% 9.17/5.32 ! [X: option_num] : ( ord_le6622620407824499402on_num @ none_num @ X ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1134_le__zero__eq,axiom,
% 9.17/5.32 ! [N2: nat] :
% 9.17/5.32 ( ( ord_less_eq_nat @ N2 @ zero_zero_nat )
% 9.17/5.32 = ( N2 = zero_zero_nat ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1135_add__le__cancel__left,axiom,
% 9.17/5.32 ! [C: rat,A: rat,B: rat] :
% 9.17/5.32 ( ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 9.17/5.32 = ( ord_less_eq_rat @ A @ B ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1136_add__le__cancel__left,axiom,
% 9.17/5.32 ! [C: nat,A: nat,B: nat] :
% 9.17/5.32 ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 9.17/5.32 = ( ord_less_eq_nat @ A @ B ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1137_add__le__cancel__left,axiom,
% 9.17/5.32 ! [C: int,A: int,B: int] :
% 9.17/5.32 ( ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 9.17/5.32 = ( ord_less_eq_int @ A @ B ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1138_add__le__cancel__right,axiom,
% 9.17/5.32 ! [A: rat,C: rat,B: rat] :
% 9.17/5.32 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 9.17/5.32 = ( ord_less_eq_rat @ A @ B ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1139_add__le__cancel__right,axiom,
% 9.17/5.32 ! [A: nat,C: nat,B: nat] :
% 9.17/5.32 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 9.17/5.32 = ( ord_less_eq_nat @ A @ B ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1140_add__le__cancel__right,axiom,
% 9.17/5.32 ! [A: int,C: int,B: int] :
% 9.17/5.32 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 9.17/5.32 = ( ord_less_eq_int @ A @ B ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1141_neg__le__iff__le,axiom,
% 9.17/5.32 ! [B: code_integer,A: code_integer] :
% 9.17/5.32 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) )
% 9.17/5.32 = ( ord_le3102999989581377725nteger @ A @ B ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1142_neg__le__iff__le,axiom,
% 9.17/5.32 ! [B: rat,A: rat] :
% 9.17/5.32 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) )
% 9.17/5.32 = ( ord_less_eq_rat @ A @ B ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1143_neg__le__iff__le,axiom,
% 9.17/5.32 ! [B: int,A: int] :
% 9.17/5.32 ( ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) )
% 9.17/5.32 = ( ord_less_eq_int @ A @ B ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1144_less__eq__option__Some,axiom,
% 9.17/5.32 ! [X: set_nat,Y: set_nat] :
% 9.17/5.32 ( ( ord_le2843612097646854710et_nat @ ( some_set_nat @ X ) @ ( some_set_nat @ Y ) )
% 9.17/5.32 = ( ord_less_eq_set_nat @ X @ Y ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1145_less__eq__option__Some,axiom,
% 9.17/5.32 ! [X: rat,Y: rat] :
% 9.17/5.32 ( ( ord_le2406147912482264968on_rat @ ( some_rat @ X ) @ ( some_rat @ Y ) )
% 9.17/5.32 = ( ord_less_eq_rat @ X @ Y ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1146_less__eq__option__Some,axiom,
% 9.17/5.32 ! [X: num,Y: num] :
% 9.17/5.32 ( ( ord_le6622620407824499402on_num @ ( some_num @ X ) @ ( some_num @ Y ) )
% 9.17/5.32 = ( ord_less_eq_num @ X @ Y ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1147_less__eq__option__Some,axiom,
% 9.17/5.32 ! [X: nat,Y: nat] :
% 9.17/5.32 ( ( ord_le5914376470875661696on_nat @ ( some_nat @ X ) @ ( some_nat @ Y ) )
% 9.17/5.32 = ( ord_less_eq_nat @ X @ Y ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1148_less__eq__option__Some,axiom,
% 9.17/5.32 ! [X: int,Y: int] :
% 9.17/5.32 ( ( ord_le1736525451366464988on_int @ ( some_int @ X ) @ ( some_int @ Y ) )
% 9.17/5.32 = ( ord_less_eq_int @ X @ Y ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1149_less__eq__option__Some__None,axiom,
% 9.17/5.32 ! [X: num] :
% 9.17/5.32 ~ ( ord_le6622620407824499402on_num @ ( some_num @ X ) @ none_num ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1150_bind__runit,axiom,
% 9.17/5.32 ! [X: option_num] :
% 9.17/5.32 ( ( bind_num_num @ X @ some_num )
% 9.17/5.32 = X ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1151_bind__runit,axiom,
% 9.17/5.32 ! [X: option8956607266484857688it_nat] :
% 9.17/5.32 ( ( bind_P7351952464966851536it_nat @ X @ some_P1914260805536162275it_nat )
% 9.17/5.32 = X ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1152_add__le__same__cancel1,axiom,
% 9.17/5.32 ! [B: code_integer,A: code_integer] :
% 9.17/5.32 ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ B @ A ) @ B )
% 9.17/5.32 = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1153_add__le__same__cancel1,axiom,
% 9.17/5.32 ! [B: rat,A: rat] :
% 9.17/5.32 ( ( ord_less_eq_rat @ ( plus_plus_rat @ B @ A ) @ B )
% 9.17/5.32 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1154_add__le__same__cancel1,axiom,
% 9.17/5.32 ! [B: nat,A: nat] :
% 9.17/5.32 ( ( ord_less_eq_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 9.17/5.32 = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1155_add__le__same__cancel1,axiom,
% 9.17/5.32 ! [B: int,A: int] :
% 9.17/5.32 ( ( ord_less_eq_int @ ( plus_plus_int @ B @ A ) @ B )
% 9.17/5.32 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1156_add__le__same__cancel2,axiom,
% 9.17/5.32 ! [A: code_integer,B: code_integer] :
% 9.17/5.32 ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ B )
% 9.17/5.32 = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1157_add__le__same__cancel2,axiom,
% 9.17/5.32 ! [A: rat,B: rat] :
% 9.17/5.32 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 9.17/5.32 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1158_add__le__same__cancel2,axiom,
% 9.17/5.32 ! [A: nat,B: nat] :
% 9.17/5.32 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 9.17/5.32 = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1159_add__le__same__cancel2,axiom,
% 9.17/5.32 ! [A: int,B: int] :
% 9.17/5.32 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ B )
% 9.17/5.32 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1160_le__add__same__cancel1,axiom,
% 9.17/5.32 ! [A: code_integer,B: code_integer] :
% 9.17/5.32 ( ( ord_le3102999989581377725nteger @ A @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 9.17/5.32 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1161_le__add__same__cancel1,axiom,
% 9.17/5.32 ! [A: rat,B: rat] :
% 9.17/5.32 ( ( ord_less_eq_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 9.17/5.32 = ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1162_le__add__same__cancel1,axiom,
% 9.17/5.32 ! [A: nat,B: nat] :
% 9.17/5.32 ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 9.17/5.32 = ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1163_le__add__same__cancel1,axiom,
% 9.17/5.32 ! [A: int,B: int] :
% 9.17/5.32 ( ( ord_less_eq_int @ A @ ( plus_plus_int @ A @ B ) )
% 9.17/5.32 = ( ord_less_eq_int @ zero_zero_int @ B ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1164_le__add__same__cancel2,axiom,
% 9.17/5.32 ! [A: code_integer,B: code_integer] :
% 9.17/5.32 ( ( ord_le3102999989581377725nteger @ A @ ( plus_p5714425477246183910nteger @ B @ A ) )
% 9.17/5.32 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1165_le__add__same__cancel2,axiom,
% 9.17/5.32 ! [A: rat,B: rat] :
% 9.17/5.32 ( ( ord_less_eq_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 9.17/5.32 = ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1166_le__add__same__cancel2,axiom,
% 9.17/5.32 ! [A: nat,B: nat] :
% 9.17/5.32 ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 9.17/5.32 = ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1167_le__add__same__cancel2,axiom,
% 9.17/5.32 ! [A: int,B: int] :
% 9.17/5.32 ( ( ord_less_eq_int @ A @ ( plus_plus_int @ B @ A ) )
% 9.17/5.32 = ( ord_less_eq_int @ zero_zero_int @ B ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1168_double__add__le__zero__iff__single__add__le__zero,axiom,
% 9.17/5.32 ! [A: code_integer] :
% 9.17/5.32 ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ A @ A ) @ zero_z3403309356797280102nteger )
% 9.17/5.32 = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1169_double__add__le__zero__iff__single__add__le__zero,axiom,
% 9.17/5.32 ! [A: rat] :
% 9.17/5.32 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ A ) @ zero_zero_rat )
% 9.17/5.32 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1170_double__add__le__zero__iff__single__add__le__zero,axiom,
% 9.17/5.32 ! [A: int] :
% 9.17/5.32 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
% 9.17/5.32 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1171_zero__le__double__add__iff__zero__le__single__add,axiom,
% 9.17/5.32 ! [A: code_integer] :
% 9.17/5.32 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ A @ A ) )
% 9.17/5.32 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1172_zero__le__double__add__iff__zero__le__single__add,axiom,
% 9.17/5.32 ! [A: rat] :
% 9.17/5.32 ( ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ A ) )
% 9.17/5.32 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1173_zero__le__double__add__iff__zero__le__single__add,axiom,
% 9.17/5.32 ! [A: int] :
% 9.17/5.32 ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
% 9.17/5.32 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1174_neg__0__le__iff__le,axiom,
% 9.17/5.32 ! [A: code_integer] :
% 9.17/5.32 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ A ) )
% 9.17/5.32 = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1175_neg__0__le__iff__le,axiom,
% 9.17/5.32 ! [A: rat] :
% 9.17/5.32 ( ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ A ) )
% 9.17/5.32 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1176_neg__0__le__iff__le,axiom,
% 9.17/5.32 ! [A: int] :
% 9.17/5.32 ( ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 9.17/5.32 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1177_neg__le__0__iff__le,axiom,
% 9.17/5.32 ! [A: code_integer] :
% 9.17/5.32 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ zero_z3403309356797280102nteger )
% 9.17/5.32 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1178_neg__le__0__iff__le,axiom,
% 9.17/5.32 ! [A: rat] :
% 9.17/5.32 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ zero_zero_rat )
% 9.17/5.32 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1179_neg__le__0__iff__le,axiom,
% 9.17/5.32 ! [A: int] :
% 9.17/5.32 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 9.17/5.32 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1180_less__eq__neg__nonpos,axiom,
% 9.17/5.32 ! [A: code_integer] :
% 9.17/5.32 ( ( ord_le3102999989581377725nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 9.17/5.32 = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1181_less__eq__neg__nonpos,axiom,
% 9.17/5.32 ! [A: rat] :
% 9.17/5.32 ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ A ) )
% 9.17/5.32 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1182_less__eq__neg__nonpos,axiom,
% 9.17/5.32 ! [A: int] :
% 9.17/5.32 ( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ A ) )
% 9.17/5.32 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1183_neg__less__eq__nonneg,axiom,
% 9.17/5.32 ! [A: code_integer] :
% 9.17/5.32 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 9.17/5.32 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1184_neg__less__eq__nonneg,axiom,
% 9.17/5.32 ! [A: rat] :
% 9.17/5.32 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ A )
% 9.17/5.32 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1185_neg__less__eq__nonneg,axiom,
% 9.17/5.32 ! [A: int] :
% 9.17/5.32 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ A )
% 9.17/5.32 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1186_abs__of__nonneg,axiom,
% 9.17/5.32 ! [A: code_integer] :
% 9.17/5.32 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 9.17/5.32 => ( ( abs_abs_Code_integer @ A )
% 9.17/5.32 = A ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1187_abs__of__nonneg,axiom,
% 9.17/5.32 ! [A: rat] :
% 9.17/5.32 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 9.17/5.32 => ( ( abs_abs_rat @ A )
% 9.17/5.32 = A ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1188_abs__of__nonneg,axiom,
% 9.17/5.32 ! [A: int] :
% 9.17/5.32 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 9.17/5.32 => ( ( abs_abs_int @ A )
% 9.17/5.32 = A ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1189_abs__le__self__iff,axiom,
% 9.17/5.32 ! [A: code_integer] :
% 9.17/5.32 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ A )
% 9.17/5.32 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 9.17/5.32
% 9.17/5.32 thf(fact_1190_abs__le__self__iff,axiom,
% 9.17/5.32 ! [A: rat] :
% 9.17/5.32 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ A )
% 9.17/5.33 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1191_abs__le__self__iff,axiom,
% 9.17/5.33 ! [A: int] :
% 9.17/5.33 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ A )
% 9.17/5.33 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1192_abs__le__zero__iff,axiom,
% 9.17/5.33 ! [A: code_integer] :
% 9.17/5.33 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ zero_z3403309356797280102nteger )
% 9.17/5.33 = ( A = zero_z3403309356797280102nteger ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1193_abs__le__zero__iff,axiom,
% 9.17/5.33 ! [A: rat] :
% 9.17/5.33 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ zero_zero_rat )
% 9.17/5.33 = ( A = zero_zero_rat ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1194_abs__le__zero__iff,axiom,
% 9.17/5.33 ! [A: int] :
% 9.17/5.33 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ zero_zero_int )
% 9.17/5.33 = ( A = zero_zero_int ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1195_abs__of__nonpos,axiom,
% 9.17/5.33 ! [A: code_integer] :
% 9.17/5.33 ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 9.17/5.33 => ( ( abs_abs_Code_integer @ A )
% 9.17/5.33 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1196_abs__of__nonpos,axiom,
% 9.17/5.33 ! [A: rat] :
% 9.17/5.33 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 9.17/5.33 => ( ( abs_abs_rat @ A )
% 9.17/5.33 = ( uminus_uminus_rat @ A ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1197_abs__of__nonpos,axiom,
% 9.17/5.33 ! [A: int] :
% 9.17/5.33 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 9.17/5.33 => ( ( abs_abs_int @ A )
% 9.17/5.33 = ( uminus_uminus_int @ A ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1198_ord__eq__le__eq__trans,axiom,
% 9.17/5.33 ! [A: set_nat,B: set_nat,C: set_nat,D2: set_nat] :
% 9.17/5.33 ( ( A = B )
% 9.17/5.33 => ( ( ord_less_eq_set_nat @ B @ C )
% 9.17/5.33 => ( ( C = D2 )
% 9.17/5.33 => ( ord_less_eq_set_nat @ A @ D2 ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1199_ord__eq__le__eq__trans,axiom,
% 9.17/5.33 ! [A: rat,B: rat,C: rat,D2: rat] :
% 9.17/5.33 ( ( A = B )
% 9.17/5.33 => ( ( ord_less_eq_rat @ B @ C )
% 9.17/5.33 => ( ( C = D2 )
% 9.17/5.33 => ( ord_less_eq_rat @ A @ D2 ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1200_ord__eq__le__eq__trans,axiom,
% 9.17/5.33 ! [A: num,B: num,C: num,D2: num] :
% 9.17/5.33 ( ( A = B )
% 9.17/5.33 => ( ( ord_less_eq_num @ B @ C )
% 9.17/5.33 => ( ( C = D2 )
% 9.17/5.33 => ( ord_less_eq_num @ A @ D2 ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1201_ord__eq__le__eq__trans,axiom,
% 9.17/5.33 ! [A: nat,B: nat,C: nat,D2: nat] :
% 9.17/5.33 ( ( A = B )
% 9.17/5.33 => ( ( ord_less_eq_nat @ B @ C )
% 9.17/5.33 => ( ( C = D2 )
% 9.17/5.33 => ( ord_less_eq_nat @ A @ D2 ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1202_ord__eq__le__eq__trans,axiom,
% 9.17/5.33 ! [A: int,B: int,C: int,D2: int] :
% 9.17/5.33 ( ( A = B )
% 9.17/5.33 => ( ( ord_less_eq_int @ B @ C )
% 9.17/5.33 => ( ( C = D2 )
% 9.17/5.33 => ( ord_less_eq_int @ A @ D2 ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1203_accp__subset,axiom,
% 9.17/5.33 ! [R12: product_prod_nat_nat > product_prod_nat_nat > $o,R23: product_prod_nat_nat > product_prod_nat_nat > $o] :
% 9.17/5.33 ( ( ord_le5604493270027003598_nat_o @ R12 @ R23 )
% 9.17/5.33 => ( ord_le704812498762024988_nat_o @ ( accp_P4275260045618599050at_nat @ R23 ) @ ( accp_P4275260045618599050at_nat @ R12 ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1204_accp__subset,axiom,
% 9.17/5.33 ! [R12: product_prod_int_int > product_prod_int_int > $o,R23: product_prod_int_int > product_prod_int_int > $o] :
% 9.17/5.33 ( ( ord_le1598226405681992910_int_o @ R12 @ R23 )
% 9.17/5.33 => ( ord_le8369615600986905444_int_o @ ( accp_P1096762738010456898nt_int @ R23 ) @ ( accp_P1096762738010456898nt_int @ R12 ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1205_accp__subset,axiom,
% 9.17/5.33 ! [R12: produc2732055786443039994et_nat > produc2732055786443039994et_nat > $o,R23: produc2732055786443039994et_nat > produc2732055786443039994et_nat > $o] :
% 9.17/5.33 ( ( ord_le7226304311989208114_nat_o @ R12 @ R23 )
% 9.17/5.33 => ( ord_le1658592502415435381_nat_o @ ( accp_P1862375125659990705et_nat @ R23 ) @ ( accp_P1862375125659990705et_nat @ R12 ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1206_accp__subset,axiom,
% 9.17/5.33 ! [R12: list_nat > list_nat > $o,R23: list_nat > list_nat > $o] :
% 9.17/5.33 ( ( ord_le6558929396352911974_nat_o @ R12 @ R23 )
% 9.17/5.33 => ( ord_le1520216061033275535_nat_o @ ( accp_list_nat @ R23 ) @ ( accp_list_nat @ R12 ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1207_accp__subset,axiom,
% 9.17/5.33 ! [R12: nat > nat > $o,R23: nat > nat > $o] :
% 9.17/5.33 ( ( ord_le2646555220125990790_nat_o @ R12 @ R23 )
% 9.17/5.33 => ( ord_less_eq_nat_o @ ( accp_nat @ R23 ) @ ( accp_nat @ R12 ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1208_le__some__optE,axiom,
% 9.17/5.33 ! [M2: set_nat,X: option_set_nat] :
% 9.17/5.33 ( ( ord_le2843612097646854710et_nat @ ( some_set_nat @ M2 ) @ X )
% 9.17/5.33 => ~ ! [M4: set_nat] :
% 9.17/5.33 ( ( X
% 9.17/5.33 = ( some_set_nat @ M4 ) )
% 9.17/5.33 => ~ ( ord_less_eq_set_nat @ M2 @ M4 ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1209_le__some__optE,axiom,
% 9.17/5.33 ! [M2: rat,X: option_rat] :
% 9.17/5.33 ( ( ord_le2406147912482264968on_rat @ ( some_rat @ M2 ) @ X )
% 9.17/5.33 => ~ ! [M4: rat] :
% 9.17/5.33 ( ( X
% 9.17/5.33 = ( some_rat @ M4 ) )
% 9.17/5.33 => ~ ( ord_less_eq_rat @ M2 @ M4 ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1210_le__some__optE,axiom,
% 9.17/5.33 ! [M2: num,X: option_num] :
% 9.17/5.33 ( ( ord_le6622620407824499402on_num @ ( some_num @ M2 ) @ X )
% 9.17/5.33 => ~ ! [M4: num] :
% 9.17/5.33 ( ( X
% 9.17/5.33 = ( some_num @ M4 ) )
% 9.17/5.33 => ~ ( ord_less_eq_num @ M2 @ M4 ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1211_le__some__optE,axiom,
% 9.17/5.33 ! [M2: nat,X: option_nat] :
% 9.17/5.33 ( ( ord_le5914376470875661696on_nat @ ( some_nat @ M2 ) @ X )
% 9.17/5.33 => ~ ! [M4: nat] :
% 9.17/5.33 ( ( X
% 9.17/5.33 = ( some_nat @ M4 ) )
% 9.17/5.33 => ~ ( ord_less_eq_nat @ M2 @ M4 ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1212_le__some__optE,axiom,
% 9.17/5.33 ! [M2: int,X: option_int] :
% 9.17/5.33 ( ( ord_le1736525451366464988on_int @ ( some_int @ M2 ) @ X )
% 9.17/5.33 => ~ ! [M4: int] :
% 9.17/5.33 ( ( X
% 9.17/5.33 = ( some_int @ M4 ) )
% 9.17/5.33 => ~ ( ord_less_eq_int @ M2 @ M4 ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1213_pred__subset__eq2,axiom,
% 9.17/5.33 ! [R4: set_Pr4329608150637261639at_nat,S2: set_Pr4329608150637261639at_nat] :
% 9.17/5.33 ( ( ord_le3935385432712749774_nat_o
% 9.17/5.33 @ ^ [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ Y3 ) @ R4 )
% 9.17/5.33 @ ^ [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ Y3 ) @ S2 ) )
% 9.17/5.33 = ( ord_le1268244103169919719at_nat @ R4 @ S2 ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1214_pred__subset__eq2,axiom,
% 9.17/5.33 ! [R4: set_Pr1261947904930325089at_nat,S2: set_Pr1261947904930325089at_nat] :
% 9.17/5.33 ( ( ord_le2646555220125990790_nat_o
% 9.17/5.33 @ ^ [X3: nat,Y3: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y3 ) @ R4 )
% 9.17/5.33 @ ^ [X3: nat,Y3: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y3 ) @ S2 ) )
% 9.17/5.33 = ( ord_le3146513528884898305at_nat @ R4 @ S2 ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1215_pred__subset__eq2,axiom,
% 9.17/5.33 ! [R4: set_Pr1281608226676607948nteger,S2: set_Pr1281608226676607948nteger] :
% 9.17/5.33 ( ( ord_le4340812435750786203eger_o
% 9.17/5.33 @ ^ [X3: produc6241069584506657477e_term > option6357759511663192854e_term,Y3: produc8923325533196201883nteger] : ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X3 @ Y3 ) @ R4 )
% 9.17/5.33 @ ^ [X3: produc6241069584506657477e_term > option6357759511663192854e_term,Y3: produc8923325533196201883nteger] : ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X3 @ Y3 ) @ S2 ) )
% 9.17/5.33 = ( ord_le653643898420964396nteger @ R4 @ S2 ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1216_pred__subset__eq2,axiom,
% 9.17/5.33 ! [R4: set_Pr3286484037609594932et_nat,S2: set_Pr3286484037609594932et_nat] :
% 9.17/5.33 ( ( ord_le8000401564054156549_nat_o
% 9.17/5.33 @ ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3658429121746597890et_nat] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X3 @ Y3 ) @ R4 )
% 9.17/5.33 @ ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3658429121746597890et_nat] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X3 @ Y3 ) @ S2 ) )
% 9.17/5.33 = ( ord_le5966269811547037844et_nat @ R4 @ S2 ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1217_pred__subset__eq2,axiom,
% 9.17/5.33 ! [R4: set_Pr8536935166611901872et_nat,S2: set_Pr8536935166611901872et_nat] :
% 9.17/5.33 ( ( ord_le6753239538765779593_nat_o
% 9.17/5.33 @ ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3925858234332021118et_nat] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X3 @ Y3 ) @ R4 )
% 9.17/5.33 @ ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3925858234332021118et_nat] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X3 @ Y3 ) @ S2 ) )
% 9.17/5.33 = ( ord_le4763372923235995152et_nat @ R4 @ S2 ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1218_pred__subset__eq2,axiom,
% 9.17/5.33 ! [R4: set_Pr9222295170931077689nt_int,S2: set_Pr9222295170931077689nt_int] :
% 9.17/5.33 ( ( ord_le5643404153117327598_int_o
% 9.17/5.33 @ ^ [X3: produc8551481072490612790e_term > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X3 @ Y3 ) @ R4 )
% 9.17/5.33 @ ^ [X3: produc8551481072490612790e_term > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X3 @ Y3 ) @ S2 ) )
% 9.17/5.33 = ( ord_le8725513860283290265nt_int @ R4 @ S2 ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1219_pred__subset__eq2,axiom,
% 9.17/5.33 ! [R4: set_Pr1872883991513573699nt_int,S2: set_Pr1872883991513573699nt_int] :
% 9.17/5.33 ( ( ord_le2124322318746777828_int_o
% 9.17/5.33 @ ^ [X3: int > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X3 @ Y3 ) @ R4 )
% 9.17/5.33 @ ^ [X3: int > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X3 @ Y3 ) @ S2 ) )
% 9.17/5.33 = ( ord_le135402666524580259nt_int @ R4 @ S2 ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1220_less__eq__option__def,axiom,
% 9.17/5.33 ( ord_le2843612097646854710et_nat
% 9.17/5.33 = ( ^ [X3: option_set_nat,Y3: option_set_nat] :
% 9.17/5.33 ( case_o4401850862724306899et_nat @ $true
% 9.17/5.33 @ ^ [Z4: set_nat] : ( case_o4401850862724306899et_nat @ $false @ ( ord_less_eq_set_nat @ Z4 ) @ Y3 )
% 9.17/5.33 @ X3 ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1221_less__eq__option__def,axiom,
% 9.17/5.33 ( ord_le2406147912482264968on_rat
% 9.17/5.33 = ( ^ [X3: option_rat,Y3: option_rat] :
% 9.17/5.33 ( case_option_o_rat @ $true
% 9.17/5.33 @ ^ [Z4: rat] : ( case_option_o_rat @ $false @ ( ord_less_eq_rat @ Z4 ) @ Y3 )
% 9.17/5.33 @ X3 ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1222_less__eq__option__def,axiom,
% 9.17/5.33 ( ord_le6622620407824499402on_num
% 9.17/5.33 = ( ^ [X3: option_num,Y3: option_num] :
% 9.17/5.33 ( case_option_o_num @ $true
% 9.17/5.33 @ ^ [Z4: num] : ( case_option_o_num @ $false @ ( ord_less_eq_num @ Z4 ) @ Y3 )
% 9.17/5.33 @ X3 ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1223_less__eq__option__def,axiom,
% 9.17/5.33 ( ord_le5914376470875661696on_nat
% 9.17/5.33 = ( ^ [X3: option_nat,Y3: option_nat] :
% 9.17/5.33 ( case_option_o_nat @ $true
% 9.17/5.33 @ ^ [Z4: nat] : ( case_option_o_nat @ $false @ ( ord_less_eq_nat @ Z4 ) @ Y3 )
% 9.17/5.33 @ X3 ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1224_less__eq__option__def,axiom,
% 9.17/5.33 ( ord_le1736525451366464988on_int
% 9.17/5.33 = ( ^ [X3: option_int,Y3: option_int] :
% 9.17/5.33 ( case_option_o_int @ $true
% 9.17/5.33 @ ^ [Z4: int] : ( case_option_o_int @ $false @ ( ord_less_eq_int @ Z4 ) @ Y3 )
% 9.17/5.33 @ X3 ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1225_zero__le,axiom,
% 9.17/5.33 ! [X: nat] : ( ord_less_eq_nat @ zero_zero_nat @ X ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1226_add__mono__thms__linordered__semiring_I3_J,axiom,
% 9.17/5.33 ! [I: rat,J: rat,K: rat,L: rat] :
% 9.17/5.33 ( ( ( ord_less_eq_rat @ I @ J )
% 9.17/5.33 & ( K = L ) )
% 9.17/5.33 => ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1227_add__mono__thms__linordered__semiring_I3_J,axiom,
% 9.17/5.33 ! [I: nat,J: nat,K: nat,L: nat] :
% 9.17/5.33 ( ( ( ord_less_eq_nat @ I @ J )
% 9.17/5.33 & ( K = L ) )
% 9.17/5.33 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1228_add__mono__thms__linordered__semiring_I3_J,axiom,
% 9.17/5.33 ! [I: int,J: int,K: int,L: int] :
% 9.17/5.33 ( ( ( ord_less_eq_int @ I @ J )
% 9.17/5.33 & ( K = L ) )
% 9.17/5.33 => ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1229_add__mono__thms__linordered__semiring_I2_J,axiom,
% 9.17/5.33 ! [I: rat,J: rat,K: rat,L: rat] :
% 9.17/5.33 ( ( ( I = J )
% 9.17/5.33 & ( ord_less_eq_rat @ K @ L ) )
% 9.17/5.33 => ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1230_add__mono__thms__linordered__semiring_I2_J,axiom,
% 9.17/5.33 ! [I: nat,J: nat,K: nat,L: nat] :
% 9.17/5.33 ( ( ( I = J )
% 9.17/5.33 & ( ord_less_eq_nat @ K @ L ) )
% 9.17/5.33 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1231_add__mono__thms__linordered__semiring_I2_J,axiom,
% 9.17/5.33 ! [I: int,J: int,K: int,L: int] :
% 9.17/5.33 ( ( ( I = J )
% 9.17/5.33 & ( ord_less_eq_int @ K @ L ) )
% 9.17/5.33 => ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1232_add__mono__thms__linordered__semiring_I1_J,axiom,
% 9.17/5.33 ! [I: rat,J: rat,K: rat,L: rat] :
% 9.17/5.33 ( ( ( ord_less_eq_rat @ I @ J )
% 9.17/5.33 & ( ord_less_eq_rat @ K @ L ) )
% 9.17/5.33 => ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1233_add__mono__thms__linordered__semiring_I1_J,axiom,
% 9.17/5.33 ! [I: nat,J: nat,K: nat,L: nat] :
% 9.17/5.33 ( ( ( ord_less_eq_nat @ I @ J )
% 9.17/5.33 & ( ord_less_eq_nat @ K @ L ) )
% 9.17/5.33 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1234_add__mono__thms__linordered__semiring_I1_J,axiom,
% 9.17/5.33 ! [I: int,J: int,K: int,L: int] :
% 9.17/5.33 ( ( ( ord_less_eq_int @ I @ J )
% 9.17/5.33 & ( ord_less_eq_int @ K @ L ) )
% 9.17/5.33 => ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1235_add__mono,axiom,
% 9.17/5.33 ! [A: rat,B: rat,C: rat,D2: rat] :
% 9.17/5.33 ( ( ord_less_eq_rat @ A @ B )
% 9.17/5.33 => ( ( ord_less_eq_rat @ C @ D2 )
% 9.17/5.33 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D2 ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1236_add__mono,axiom,
% 9.17/5.33 ! [A: nat,B: nat,C: nat,D2: nat] :
% 9.17/5.33 ( ( ord_less_eq_nat @ A @ B )
% 9.17/5.33 => ( ( ord_less_eq_nat @ C @ D2 )
% 9.17/5.33 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D2 ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1237_add__mono,axiom,
% 9.17/5.33 ! [A: int,B: int,C: int,D2: int] :
% 9.17/5.33 ( ( ord_less_eq_int @ A @ B )
% 9.17/5.33 => ( ( ord_less_eq_int @ C @ D2 )
% 9.17/5.33 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D2 ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1238_add__left__mono,axiom,
% 9.17/5.33 ! [A: rat,B: rat,C: rat] :
% 9.17/5.33 ( ( ord_less_eq_rat @ A @ B )
% 9.17/5.33 => ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1239_add__left__mono,axiom,
% 9.17/5.33 ! [A: nat,B: nat,C: nat] :
% 9.17/5.33 ( ( ord_less_eq_nat @ A @ B )
% 9.17/5.33 => ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1240_add__left__mono,axiom,
% 9.17/5.33 ! [A: int,B: int,C: int] :
% 9.17/5.33 ( ( ord_less_eq_int @ A @ B )
% 9.17/5.33 => ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1241_less__eqE,axiom,
% 9.17/5.33 ! [A: nat,B: nat] :
% 9.17/5.33 ( ( ord_less_eq_nat @ A @ B )
% 9.17/5.33 => ~ ! [C3: nat] :
% 9.17/5.33 ( B
% 9.17/5.33 != ( plus_plus_nat @ A @ C3 ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1242_add__right__mono,axiom,
% 9.17/5.33 ! [A: rat,B: rat,C: rat] :
% 9.17/5.33 ( ( ord_less_eq_rat @ A @ B )
% 9.17/5.33 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1243_add__right__mono,axiom,
% 9.17/5.33 ! [A: nat,B: nat,C: nat] :
% 9.17/5.33 ( ( ord_less_eq_nat @ A @ B )
% 9.17/5.33 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1244_add__right__mono,axiom,
% 9.17/5.33 ! [A: int,B: int,C: int] :
% 9.17/5.33 ( ( ord_less_eq_int @ A @ B )
% 9.17/5.33 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1245_le__iff__add,axiom,
% 9.17/5.33 ( ord_less_eq_nat
% 9.17/5.33 = ( ^ [A5: nat,B4: nat] :
% 9.17/5.33 ? [C2: nat] :
% 9.17/5.33 ( B4
% 9.17/5.33 = ( plus_plus_nat @ A5 @ C2 ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1246_add__le__imp__le__left,axiom,
% 9.17/5.33 ! [C: rat,A: rat,B: rat] :
% 9.17/5.33 ( ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 9.17/5.33 => ( ord_less_eq_rat @ A @ B ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1247_add__le__imp__le__left,axiom,
% 9.17/5.33 ! [C: nat,A: nat,B: nat] :
% 9.17/5.33 ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 9.17/5.33 => ( ord_less_eq_nat @ A @ B ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1248_add__le__imp__le__left,axiom,
% 9.17/5.33 ! [C: int,A: int,B: int] :
% 9.17/5.33 ( ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 9.17/5.33 => ( ord_less_eq_int @ A @ B ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1249_add__le__imp__le__right,axiom,
% 9.17/5.33 ! [A: rat,C: rat,B: rat] :
% 9.17/5.33 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 9.17/5.33 => ( ord_less_eq_rat @ A @ B ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1250_add__le__imp__le__right,axiom,
% 9.17/5.33 ! [A: nat,C: nat,B: nat] :
% 9.17/5.33 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 9.17/5.33 => ( ord_less_eq_nat @ A @ B ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1251_add__le__imp__le__right,axiom,
% 9.17/5.33 ! [A: int,C: int,B: int] :
% 9.17/5.33 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 9.17/5.33 => ( ord_less_eq_int @ A @ B ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1252_accp__subset__induct,axiom,
% 9.17/5.33 ! [D3: product_prod_nat_nat > $o,R4: product_prod_nat_nat > product_prod_nat_nat > $o,X: product_prod_nat_nat,P: product_prod_nat_nat > $o] :
% 9.17/5.33 ( ( ord_le704812498762024988_nat_o @ D3 @ ( accp_P4275260045618599050at_nat @ R4 ) )
% 9.17/5.33 => ( ! [X4: product_prod_nat_nat,Z3: product_prod_nat_nat] :
% 9.17/5.33 ( ( D3 @ X4 )
% 9.17/5.33 => ( ( R4 @ Z3 @ X4 )
% 9.17/5.33 => ( D3 @ Z3 ) ) )
% 9.17/5.33 => ( ( D3 @ X )
% 9.17/5.33 => ( ! [X4: product_prod_nat_nat] :
% 9.17/5.33 ( ( D3 @ X4 )
% 9.17/5.33 => ( ! [Z5: product_prod_nat_nat] :
% 9.17/5.33 ( ( R4 @ Z5 @ X4 )
% 9.17/5.33 => ( P @ Z5 ) )
% 9.17/5.33 => ( P @ X4 ) ) )
% 9.17/5.33 => ( P @ X ) ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1253_accp__subset__induct,axiom,
% 9.17/5.33 ! [D3: product_prod_int_int > $o,R4: product_prod_int_int > product_prod_int_int > $o,X: product_prod_int_int,P: product_prod_int_int > $o] :
% 9.17/5.33 ( ( ord_le8369615600986905444_int_o @ D3 @ ( accp_P1096762738010456898nt_int @ R4 ) )
% 9.17/5.33 => ( ! [X4: product_prod_int_int,Z3: product_prod_int_int] :
% 9.17/5.33 ( ( D3 @ X4 )
% 9.17/5.33 => ( ( R4 @ Z3 @ X4 )
% 9.17/5.33 => ( D3 @ Z3 ) ) )
% 9.17/5.33 => ( ( D3 @ X )
% 9.17/5.33 => ( ! [X4: product_prod_int_int] :
% 9.17/5.33 ( ( D3 @ X4 )
% 9.17/5.33 => ( ! [Z5: product_prod_int_int] :
% 9.17/5.33 ( ( R4 @ Z5 @ X4 )
% 9.17/5.33 => ( P @ Z5 ) )
% 9.17/5.33 => ( P @ X4 ) ) )
% 9.17/5.33 => ( P @ X ) ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1254_accp__subset__induct,axiom,
% 9.17/5.33 ! [D3: produc2732055786443039994et_nat > $o,R4: produc2732055786443039994et_nat > produc2732055786443039994et_nat > $o,X: produc2732055786443039994et_nat,P: produc2732055786443039994et_nat > $o] :
% 9.17/5.33 ( ( ord_le1658592502415435381_nat_o @ D3 @ ( accp_P1862375125659990705et_nat @ R4 ) )
% 9.17/5.33 => ( ! [X4: produc2732055786443039994et_nat,Z3: produc2732055786443039994et_nat] :
% 9.17/5.33 ( ( D3 @ X4 )
% 9.17/5.33 => ( ( R4 @ Z3 @ X4 )
% 9.17/5.33 => ( D3 @ Z3 ) ) )
% 9.17/5.33 => ( ( D3 @ X )
% 9.17/5.33 => ( ! [X4: produc2732055786443039994et_nat] :
% 9.17/5.33 ( ( D3 @ X4 )
% 9.17/5.33 => ( ! [Z5: produc2732055786443039994et_nat] :
% 9.17/5.33 ( ( R4 @ Z5 @ X4 )
% 9.17/5.33 => ( P @ Z5 ) )
% 9.17/5.33 => ( P @ X4 ) ) )
% 9.17/5.33 => ( P @ X ) ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1255_accp__subset__induct,axiom,
% 9.17/5.33 ! [D3: list_nat > $o,R4: list_nat > list_nat > $o,X: list_nat,P: list_nat > $o] :
% 9.17/5.33 ( ( ord_le1520216061033275535_nat_o @ D3 @ ( accp_list_nat @ R4 ) )
% 9.17/5.33 => ( ! [X4: list_nat,Z3: list_nat] :
% 9.17/5.33 ( ( D3 @ X4 )
% 9.17/5.33 => ( ( R4 @ Z3 @ X4 )
% 9.17/5.33 => ( D3 @ Z3 ) ) )
% 9.17/5.33 => ( ( D3 @ X )
% 9.17/5.33 => ( ! [X4: list_nat] :
% 9.17/5.33 ( ( D3 @ X4 )
% 9.17/5.33 => ( ! [Z5: list_nat] :
% 9.17/5.33 ( ( R4 @ Z5 @ X4 )
% 9.17/5.33 => ( P @ Z5 ) )
% 9.17/5.33 => ( P @ X4 ) ) )
% 9.17/5.33 => ( P @ X ) ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1256_accp__subset__induct,axiom,
% 9.17/5.33 ! [D3: nat > $o,R4: nat > nat > $o,X: nat,P: nat > $o] :
% 9.17/5.33 ( ( ord_less_eq_nat_o @ D3 @ ( accp_nat @ R4 ) )
% 9.17/5.33 => ( ! [X4: nat,Z3: nat] :
% 9.17/5.33 ( ( D3 @ X4 )
% 9.17/5.33 => ( ( R4 @ Z3 @ X4 )
% 9.17/5.33 => ( D3 @ Z3 ) ) )
% 9.17/5.33 => ( ( D3 @ X )
% 9.17/5.33 => ( ! [X4: nat] :
% 9.17/5.33 ( ( D3 @ X4 )
% 9.17/5.33 => ( ! [Z5: nat] :
% 9.17/5.33 ( ( R4 @ Z5 @ X4 )
% 9.17/5.33 => ( P @ Z5 ) )
% 9.17/5.33 => ( P @ X4 ) ) )
% 9.17/5.33 => ( P @ X ) ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1257_le__numeral__extra_I4_J,axiom,
% 9.17/5.33 ord_le3102999989581377725nteger @ one_one_Code_integer @ one_one_Code_integer ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1258_le__numeral__extra_I4_J,axiom,
% 9.17/5.33 ord_less_eq_rat @ one_one_rat @ one_one_rat ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1259_le__numeral__extra_I4_J,axiom,
% 9.17/5.33 ord_less_eq_nat @ one_one_nat @ one_one_nat ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1260_le__numeral__extra_I4_J,axiom,
% 9.17/5.33 ord_less_eq_int @ one_one_int @ one_one_int ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1261_subrelI,axiom,
% 9.17/5.33 ! [R2: set_Pr4329608150637261639at_nat,S: set_Pr4329608150637261639at_nat] :
% 9.17/5.33 ( ! [X4: set_Pr1261947904930325089at_nat,Y5: set_Pr1261947904930325089at_nat] :
% 9.17/5.33 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X4 @ Y5 ) @ R2 )
% 9.17/5.33 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X4 @ Y5 ) @ S ) )
% 9.17/5.33 => ( ord_le1268244103169919719at_nat @ R2 @ S ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1262_subrelI,axiom,
% 9.17/5.33 ! [R2: set_Pr1261947904930325089at_nat,S: set_Pr1261947904930325089at_nat] :
% 9.17/5.33 ( ! [X4: nat,Y5: nat] :
% 9.17/5.33 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Y5 ) @ R2 )
% 9.17/5.33 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Y5 ) @ S ) )
% 9.17/5.33 => ( ord_le3146513528884898305at_nat @ R2 @ S ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1263_subrelI,axiom,
% 9.17/5.33 ! [R2: set_Pr1281608226676607948nteger,S: set_Pr1281608226676607948nteger] :
% 9.17/5.33 ( ! [X4: produc6241069584506657477e_term > option6357759511663192854e_term,Y5: produc8923325533196201883nteger] :
% 9.17/5.33 ( ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X4 @ Y5 ) @ R2 )
% 9.17/5.33 => ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X4 @ Y5 ) @ S ) )
% 9.17/5.33 => ( ord_le653643898420964396nteger @ R2 @ S ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1264_subrelI,axiom,
% 9.17/5.33 ! [R2: set_Pr3286484037609594932et_nat,S: set_Pr3286484037609594932et_nat] :
% 9.17/5.33 ( ! [X4: produc3658429121746597890et_nat > $o,Y5: produc3658429121746597890et_nat] :
% 9.17/5.33 ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X4 @ Y5 ) @ R2 )
% 9.17/5.33 => ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X4 @ Y5 ) @ S ) )
% 9.17/5.33 => ( ord_le5966269811547037844et_nat @ R2 @ S ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1265_subrelI,axiom,
% 9.17/5.33 ! [R2: set_Pr8536935166611901872et_nat,S: set_Pr8536935166611901872et_nat] :
% 9.17/5.33 ( ! [X4: produc3658429121746597890et_nat > $o,Y5: produc3925858234332021118et_nat] :
% 9.17/5.33 ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X4 @ Y5 ) @ R2 )
% 9.17/5.33 => ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X4 @ Y5 ) @ S ) )
% 9.17/5.33 => ( ord_le4763372923235995152et_nat @ R2 @ S ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1266_subrelI,axiom,
% 9.17/5.33 ! [R2: set_Pr9222295170931077689nt_int,S: set_Pr9222295170931077689nt_int] :
% 9.17/5.33 ( ! [X4: produc8551481072490612790e_term > option6357759511663192854e_term,Y5: product_prod_int_int] :
% 9.17/5.33 ( ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X4 @ Y5 ) @ R2 )
% 9.17/5.33 => ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X4 @ Y5 ) @ S ) )
% 9.17/5.33 => ( ord_le8725513860283290265nt_int @ R2 @ S ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1267_subrelI,axiom,
% 9.17/5.33 ! [R2: set_Pr1872883991513573699nt_int,S: set_Pr1872883991513573699nt_int] :
% 9.17/5.33 ( ! [X4: int > option6357759511663192854e_term,Y5: product_prod_int_int] :
% 9.17/5.33 ( ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X4 @ Y5 ) @ R2 )
% 9.17/5.33 => ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X4 @ Y5 ) @ S ) )
% 9.17/5.33 => ( ord_le135402666524580259nt_int @ R2 @ S ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1268_le__minus__iff,axiom,
% 9.17/5.33 ! [A: code_integer,B: code_integer] :
% 9.17/5.33 ( ( ord_le3102999989581377725nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 9.17/5.33 = ( ord_le3102999989581377725nteger @ B @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1269_le__minus__iff,axiom,
% 9.17/5.33 ! [A: rat,B: rat] :
% 9.17/5.33 ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ B ) )
% 9.17/5.33 = ( ord_less_eq_rat @ B @ ( uminus_uminus_rat @ A ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1270_le__minus__iff,axiom,
% 9.17/5.33 ! [A: int,B: int] :
% 9.17/5.33 ( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ B ) )
% 9.17/5.33 = ( ord_less_eq_int @ B @ ( uminus_uminus_int @ A ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1271_minus__le__iff,axiom,
% 9.17/5.33 ! [A: code_integer,B: code_integer] :
% 9.17/5.33 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 9.17/5.33 = ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ A ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1272_minus__le__iff,axiom,
% 9.17/5.33 ! [A: rat,B: rat] :
% 9.17/5.33 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B )
% 9.17/5.33 = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ A ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1273_minus__le__iff,axiom,
% 9.17/5.33 ! [A: int,B: int] :
% 9.17/5.33 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B )
% 9.17/5.33 = ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ A ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1274_le__imp__neg__le,axiom,
% 9.17/5.33 ! [A: code_integer,B: code_integer] :
% 9.17/5.33 ( ( ord_le3102999989581377725nteger @ A @ B )
% 9.17/5.33 => ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1275_le__imp__neg__le,axiom,
% 9.17/5.33 ! [A: rat,B: rat] :
% 9.17/5.33 ( ( ord_less_eq_rat @ A @ B )
% 9.17/5.33 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1276_le__imp__neg__le,axiom,
% 9.17/5.33 ! [A: int,B: int] :
% 9.17/5.33 ( ( ord_less_eq_int @ A @ B )
% 9.17/5.33 => ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1277_exists__leI,axiom,
% 9.17/5.33 ! [N2: nat,P: nat > $o] :
% 9.17/5.33 ( ( ! [N7: nat] :
% 9.17/5.33 ( ( ord_less_nat @ N7 @ N2 )
% 9.17/5.33 => ~ ( P @ N7 ) )
% 9.17/5.33 => ( P @ N2 ) )
% 9.17/5.33 => ? [N3: nat] :
% 9.17/5.33 ( ( ord_less_eq_nat @ N3 @ N2 )
% 9.17/5.33 & ( P @ N3 ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1278_nat__le__iff__add,axiom,
% 9.17/5.33 ( ord_less_eq_nat
% 9.17/5.33 = ( ^ [M: nat,N4: nat] :
% 9.17/5.33 ? [K4: nat] :
% 9.17/5.33 ( N4
% 9.17/5.33 = ( plus_plus_nat @ M @ K4 ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1279_trans__le__add2,axiom,
% 9.17/5.33 ! [I: nat,J: nat,M2: nat] :
% 9.17/5.33 ( ( ord_less_eq_nat @ I @ J )
% 9.17/5.33 => ( ord_less_eq_nat @ I @ ( plus_plus_nat @ M2 @ J ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1280_trans__le__add1,axiom,
% 9.17/5.33 ! [I: nat,J: nat,M2: nat] :
% 9.17/5.33 ( ( ord_less_eq_nat @ I @ J )
% 9.17/5.33 => ( ord_less_eq_nat @ I @ ( plus_plus_nat @ J @ M2 ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1281_add__le__mono1,axiom,
% 9.17/5.33 ! [I: nat,J: nat,K: nat] :
% 9.17/5.33 ( ( ord_less_eq_nat @ I @ J )
% 9.17/5.33 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1282_add__le__mono,axiom,
% 9.17/5.33 ! [I: nat,J: nat,K: nat,L: nat] :
% 9.17/5.33 ( ( ord_less_eq_nat @ I @ J )
% 9.17/5.33 => ( ( ord_less_eq_nat @ K @ L )
% 9.17/5.33 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1283_le__Suc__ex,axiom,
% 9.17/5.33 ! [K: nat,L: nat] :
% 9.17/5.33 ( ( ord_less_eq_nat @ K @ L )
% 9.17/5.33 => ? [N: nat] :
% 9.17/5.33 ( L
% 9.17/5.33 = ( plus_plus_nat @ K @ N ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1284_add__leD2,axiom,
% 9.17/5.33 ! [M2: nat,K: nat,N2: nat] :
% 9.17/5.33 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M2 @ K ) @ N2 )
% 9.17/5.33 => ( ord_less_eq_nat @ K @ N2 ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1285_add__leD1,axiom,
% 9.17/5.33 ! [M2: nat,K: nat,N2: nat] :
% 9.17/5.33 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M2 @ K ) @ N2 )
% 9.17/5.33 => ( ord_less_eq_nat @ M2 @ N2 ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1286_le__add2,axiom,
% 9.17/5.33 ! [N2: nat,M2: nat] : ( ord_less_eq_nat @ N2 @ ( plus_plus_nat @ M2 @ N2 ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1287_le__add1,axiom,
% 9.17/5.33 ! [N2: nat,M2: nat] : ( ord_less_eq_nat @ N2 @ ( plus_plus_nat @ N2 @ M2 ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1288_add__leE,axiom,
% 9.17/5.33 ! [M2: nat,K: nat,N2: nat] :
% 9.17/5.33 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M2 @ K ) @ N2 )
% 9.17/5.33 => ~ ( ( ord_less_eq_nat @ M2 @ N2 )
% 9.17/5.33 => ~ ( ord_less_eq_nat @ K @ N2 ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1289_abs__le__D1,axiom,
% 9.17/5.33 ! [A: code_integer,B: code_integer] :
% 9.17/5.33 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 9.17/5.33 => ( ord_le3102999989581377725nteger @ A @ B ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1290_abs__le__D1,axiom,
% 9.17/5.33 ! [A: rat,B: rat] :
% 9.17/5.33 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 9.17/5.33 => ( ord_less_eq_rat @ A @ B ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1291_abs__le__D1,axiom,
% 9.17/5.33 ! [A: int,B: int] :
% 9.17/5.33 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 9.17/5.33 => ( ord_less_eq_int @ A @ B ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1292_abs__ge__self,axiom,
% 9.17/5.33 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ A @ ( abs_abs_Code_integer @ A ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1293_abs__ge__self,axiom,
% 9.17/5.33 ! [A: rat] : ( ord_less_eq_rat @ A @ ( abs_abs_rat @ A ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1294_abs__ge__self,axiom,
% 9.17/5.33 ! [A: int] : ( ord_less_eq_int @ A @ ( abs_abs_int @ A ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1295_less__eq__option__None,axiom,
% 9.17/5.33 ! [X: option_num] : ( ord_le6622620407824499402on_num @ none_num @ X ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1296_less__eq__option__None__is__None,axiom,
% 9.17/5.33 ! [X: option_num] :
% 9.17/5.33 ( ( ord_le6622620407824499402on_num @ X @ none_num )
% 9.17/5.33 => ( X = none_num ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1297_bind__eq__Some__conv,axiom,
% 9.17/5.33 ! [F: option_num,G: num > option_num,X: num] :
% 9.17/5.33 ( ( ( bind_num_num @ F @ G )
% 9.17/5.33 = ( some_num @ X ) )
% 9.17/5.33 = ( ? [Y3: num] :
% 9.17/5.33 ( ( F
% 9.17/5.33 = ( some_num @ Y3 ) )
% 9.17/5.33 & ( ( G @ Y3 )
% 9.17/5.33 = ( some_num @ X ) ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1298_bind__eq__Some__conv,axiom,
% 9.17/5.33 ! [F: option8956607266484857688it_nat,G: produc8664842809031399944it_nat > option_num,X: num] :
% 9.17/5.33 ( ( ( bind_P4387644102537648098at_num @ F @ G )
% 9.17/5.33 = ( some_num @ X ) )
% 9.17/5.33 = ( ? [Y3: produc8664842809031399944it_nat] :
% 9.17/5.33 ( ( F
% 9.17/5.33 = ( some_P1914260805536162275it_nat @ Y3 ) )
% 9.17/5.33 & ( ( G @ Y3 )
% 9.17/5.33 = ( some_num @ X ) ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1299_bind__eq__Some__conv,axiom,
% 9.17/5.33 ! [F: option_num,G: num > option8956607266484857688it_nat,X: produc8664842809031399944it_nat] :
% 9.17/5.33 ( ( ( bind_n550516262659884002it_nat @ F @ G )
% 9.17/5.33 = ( some_P1914260805536162275it_nat @ X ) )
% 9.17/5.33 = ( ? [Y3: num] :
% 9.17/5.33 ( ( F
% 9.17/5.33 = ( some_num @ Y3 ) )
% 9.17/5.33 & ( ( G @ Y3 )
% 9.17/5.33 = ( some_P1914260805536162275it_nat @ X ) ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1300_bind__eq__Some__conv,axiom,
% 9.17/5.33 ! [F: option8956607266484857688it_nat,G: produc8664842809031399944it_nat > option8956607266484857688it_nat,X: produc8664842809031399944it_nat] :
% 9.17/5.33 ( ( ( bind_P7351952464966851536it_nat @ F @ G )
% 9.17/5.33 = ( some_P1914260805536162275it_nat @ X ) )
% 9.17/5.33 = ( ? [Y3: produc8664842809031399944it_nat] :
% 9.17/5.33 ( ( F
% 9.17/5.33 = ( some_P1914260805536162275it_nat @ Y3 ) )
% 9.17/5.33 & ( ( G @ Y3 )
% 9.17/5.33 = ( some_P1914260805536162275it_nat @ X ) ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1301_bind_Obind__lzero,axiom,
% 9.17/5.33 ! [F: produc6714399278180371524it_nat > option3216581401566546698it_nat] :
% 9.17/5.33 ( ( bind_P1787608729393679550it_nat @ none_P2587165478634041381it_nat @ F )
% 9.17/5.33 = none_P2587165478634041381it_nat ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1302_bind_Obind__lzero,axiom,
% 9.17/5.33 ! [F: produc6714399278180371524it_nat > option_num] :
% 9.17/5.33 ( ( bind_P7816469540982926368at_num @ none_P2587165478634041381it_nat @ F )
% 9.17/5.33 = none_num ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1303_bind_Obind__lzero,axiom,
% 9.17/5.33 ! [F: produc6714399278180371524it_nat > option8956607266484857688it_nat] :
% 9.17/5.33 ( ( bind_P3087804342168909838it_nat @ none_P2587165478634041381it_nat @ F )
% 9.17/5.33 = none_P9117596204409417319it_nat ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1304_bind_Obind__lzero,axiom,
% 9.17/5.33 ! [F: num > option3216581401566546698it_nat] :
% 9.17/5.33 ( ( bind_n6186876254402743274it_nat @ none_num @ F )
% 9.17/5.33 = none_P2587165478634041381it_nat ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1305_bind_Obind__lzero,axiom,
% 9.17/5.33 ! [F: num > option_num] :
% 9.17/5.33 ( ( bind_num_num @ none_num @ F )
% 9.17/5.33 = none_num ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1306_bind_Obind__lzero,axiom,
% 9.17/5.33 ! [F: num > option8956607266484857688it_nat] :
% 9.17/5.33 ( ( bind_n550516262659884002it_nat @ none_num @ F )
% 9.17/5.33 = none_P9117596204409417319it_nat ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1307_bind_Obind__lzero,axiom,
% 9.17/5.33 ! [F: produc8664842809031399944it_nat > option3216581401566546698it_nat] :
% 9.17/5.33 ( ( bind_P1106314856888375420it_nat @ none_P9117596204409417319it_nat @ F )
% 9.17/5.33 = none_P2587165478634041381it_nat ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1308_bind_Obind__lzero,axiom,
% 9.17/5.33 ! [F: produc8664842809031399944it_nat > option_num] :
% 9.17/5.33 ( ( bind_P4387644102537648098at_num @ none_P9117596204409417319it_nat @ F )
% 9.17/5.33 = none_num ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1309_bind_Obind__lzero,axiom,
% 9.17/5.33 ! [F: produc8664842809031399944it_nat > option8956607266484857688it_nat] :
% 9.17/5.33 ( ( bind_P7351952464966851536it_nat @ none_P9117596204409417319it_nat @ F )
% 9.17/5.33 = none_P9117596204409417319it_nat ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1310_add__decreasing,axiom,
% 9.17/5.33 ! [A: code_integer,C: code_integer,B: code_integer] :
% 9.17/5.33 ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 9.17/5.33 => ( ( ord_le3102999989581377725nteger @ C @ B )
% 9.17/5.33 => ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ A @ C ) @ B ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1311_add__decreasing,axiom,
% 9.17/5.33 ! [A: rat,C: rat,B: rat] :
% 9.17/5.33 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 9.17/5.33 => ( ( ord_less_eq_rat @ C @ B )
% 9.17/5.33 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1312_add__decreasing,axiom,
% 9.17/5.33 ! [A: nat,C: nat,B: nat] :
% 9.17/5.33 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 9.17/5.33 => ( ( ord_less_eq_nat @ C @ B )
% 9.17/5.33 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ B ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1313_add__decreasing,axiom,
% 9.17/5.33 ! [A: int,C: int,B: int] :
% 9.17/5.33 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 9.17/5.33 => ( ( ord_less_eq_int @ C @ B )
% 9.17/5.33 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ B ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1314_add__increasing,axiom,
% 9.17/5.33 ! [A: code_integer,B: code_integer,C: code_integer] :
% 9.17/5.33 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 9.17/5.33 => ( ( ord_le3102999989581377725nteger @ B @ C )
% 9.17/5.33 => ( ord_le3102999989581377725nteger @ B @ ( plus_p5714425477246183910nteger @ A @ C ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1315_add__increasing,axiom,
% 9.17/5.33 ! [A: rat,B: rat,C: rat] :
% 9.17/5.33 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 9.17/5.33 => ( ( ord_less_eq_rat @ B @ C )
% 9.17/5.33 => ( ord_less_eq_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1316_add__increasing,axiom,
% 9.17/5.33 ! [A: nat,B: nat,C: nat] :
% 9.17/5.33 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 9.17/5.33 => ( ( ord_less_eq_nat @ B @ C )
% 9.17/5.33 => ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1317_add__increasing,axiom,
% 9.17/5.33 ! [A: int,B: int,C: int] :
% 9.17/5.33 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 9.17/5.33 => ( ( ord_less_eq_int @ B @ C )
% 9.17/5.33 => ( ord_less_eq_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1318_add__decreasing2,axiom,
% 9.17/5.33 ! [C: code_integer,A: code_integer,B: code_integer] :
% 9.17/5.33 ( ( ord_le3102999989581377725nteger @ C @ zero_z3403309356797280102nteger )
% 9.17/5.33 => ( ( ord_le3102999989581377725nteger @ A @ B )
% 9.17/5.33 => ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ A @ C ) @ B ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1319_add__decreasing2,axiom,
% 9.17/5.33 ! [C: rat,A: rat,B: rat] :
% 9.17/5.33 ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 9.17/5.33 => ( ( ord_less_eq_rat @ A @ B )
% 9.17/5.33 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1320_add__decreasing2,axiom,
% 9.17/5.33 ! [C: nat,A: nat,B: nat] :
% 9.17/5.33 ( ( ord_less_eq_nat @ C @ zero_zero_nat )
% 9.17/5.33 => ( ( ord_less_eq_nat @ A @ B )
% 9.17/5.33 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ B ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1321_add__decreasing2,axiom,
% 9.17/5.33 ! [C: int,A: int,B: int] :
% 9.17/5.33 ( ( ord_less_eq_int @ C @ zero_zero_int )
% 9.17/5.33 => ( ( ord_less_eq_int @ A @ B )
% 9.17/5.33 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ B ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1322_add__increasing2,axiom,
% 9.17/5.33 ! [C: code_integer,B: code_integer,A: code_integer] :
% 9.17/5.33 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 9.17/5.33 => ( ( ord_le3102999989581377725nteger @ B @ A )
% 9.17/5.33 => ( ord_le3102999989581377725nteger @ B @ ( plus_p5714425477246183910nteger @ A @ C ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1323_add__increasing2,axiom,
% 9.17/5.33 ! [C: rat,B: rat,A: rat] :
% 9.17/5.33 ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 9.17/5.33 => ( ( ord_less_eq_rat @ B @ A )
% 9.17/5.33 => ( ord_less_eq_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1324_add__increasing2,axiom,
% 9.17/5.33 ! [C: nat,B: nat,A: nat] :
% 9.17/5.33 ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 9.17/5.33 => ( ( ord_less_eq_nat @ B @ A )
% 9.17/5.33 => ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1325_add__increasing2,axiom,
% 9.17/5.33 ! [C: int,B: int,A: int] :
% 9.17/5.33 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 9.17/5.33 => ( ( ord_less_eq_int @ B @ A )
% 9.17/5.33 => ( ord_less_eq_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1326_add__nonneg__nonneg,axiom,
% 9.17/5.33 ! [A: code_integer,B: code_integer] :
% 9.17/5.33 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 9.17/5.33 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 9.17/5.33 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1327_add__nonneg__nonneg,axiom,
% 9.17/5.33 ! [A: rat,B: rat] :
% 9.17/5.33 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 9.17/5.33 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 9.17/5.33 => ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1328_add__nonneg__nonneg,axiom,
% 9.17/5.33 ! [A: nat,B: nat] :
% 9.17/5.33 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 9.17/5.33 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 9.17/5.33 => ( ord_less_eq_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1329_add__nonneg__nonneg,axiom,
% 9.17/5.33 ! [A: int,B: int] :
% 9.17/5.33 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 9.17/5.33 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 9.17/5.33 => ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1330_add__nonpos__nonpos,axiom,
% 9.17/5.33 ! [A: code_integer,B: code_integer] :
% 9.17/5.33 ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 9.17/5.33 => ( ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger )
% 9.17/5.33 => ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ zero_z3403309356797280102nteger ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1331_add__nonpos__nonpos,axiom,
% 9.17/5.33 ! [A: rat,B: rat] :
% 9.17/5.33 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 9.17/5.33 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 9.17/5.33 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1332_add__nonpos__nonpos,axiom,
% 9.17/5.33 ! [A: nat,B: nat] :
% 9.17/5.33 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 9.17/5.33 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 9.17/5.33 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1333_add__nonpos__nonpos,axiom,
% 9.17/5.33 ! [A: int,B: int] :
% 9.17/5.33 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 9.17/5.33 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 9.17/5.33 => ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1334_add__nonneg__eq__0__iff,axiom,
% 9.17/5.33 ! [X: code_integer,Y: code_integer] :
% 9.17/5.33 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X )
% 9.17/5.33 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y )
% 9.17/5.33 => ( ( ( plus_p5714425477246183910nteger @ X @ Y )
% 9.17/5.33 = zero_z3403309356797280102nteger )
% 9.17/5.33 = ( ( X = zero_z3403309356797280102nteger )
% 9.17/5.33 & ( Y = zero_z3403309356797280102nteger ) ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1335_add__nonneg__eq__0__iff,axiom,
% 9.17/5.33 ! [X: rat,Y: rat] :
% 9.17/5.33 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 9.17/5.33 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 9.17/5.33 => ( ( ( plus_plus_rat @ X @ Y )
% 9.17/5.33 = zero_zero_rat )
% 9.17/5.33 = ( ( X = zero_zero_rat )
% 9.17/5.33 & ( Y = zero_zero_rat ) ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1336_add__nonneg__eq__0__iff,axiom,
% 9.17/5.33 ! [X: nat,Y: nat] :
% 9.17/5.33 ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 9.17/5.33 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 9.17/5.33 => ( ( ( plus_plus_nat @ X @ Y )
% 9.17/5.33 = zero_zero_nat )
% 9.17/5.33 = ( ( X = zero_zero_nat )
% 9.17/5.33 & ( Y = zero_zero_nat ) ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1337_add__nonneg__eq__0__iff,axiom,
% 9.17/5.33 ! [X: int,Y: int] :
% 9.17/5.33 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 9.17/5.33 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 9.17/5.33 => ( ( ( plus_plus_int @ X @ Y )
% 9.17/5.33 = zero_zero_int )
% 9.17/5.33 = ( ( X = zero_zero_int )
% 9.17/5.33 & ( Y = zero_zero_int ) ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1338_add__nonpos__eq__0__iff,axiom,
% 9.17/5.33 ! [X: code_integer,Y: code_integer] :
% 9.17/5.33 ( ( ord_le3102999989581377725nteger @ X @ zero_z3403309356797280102nteger )
% 9.17/5.33 => ( ( ord_le3102999989581377725nteger @ Y @ zero_z3403309356797280102nteger )
% 9.17/5.33 => ( ( ( plus_p5714425477246183910nteger @ X @ Y )
% 9.17/5.33 = zero_z3403309356797280102nteger )
% 9.17/5.33 = ( ( X = zero_z3403309356797280102nteger )
% 9.17/5.33 & ( Y = zero_z3403309356797280102nteger ) ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1339_add__nonpos__eq__0__iff,axiom,
% 9.17/5.33 ! [X: rat,Y: rat] :
% 9.17/5.33 ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 9.17/5.33 => ( ( ord_less_eq_rat @ Y @ zero_zero_rat )
% 9.17/5.33 => ( ( ( plus_plus_rat @ X @ Y )
% 9.17/5.33 = zero_zero_rat )
% 9.17/5.33 = ( ( X = zero_zero_rat )
% 9.17/5.33 & ( Y = zero_zero_rat ) ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1340_add__nonpos__eq__0__iff,axiom,
% 9.17/5.33 ! [X: nat,Y: nat] :
% 9.17/5.33 ( ( ord_less_eq_nat @ X @ zero_zero_nat )
% 9.17/5.33 => ( ( ord_less_eq_nat @ Y @ zero_zero_nat )
% 9.17/5.33 => ( ( ( plus_plus_nat @ X @ Y )
% 9.17/5.33 = zero_zero_nat )
% 9.17/5.33 = ( ( X = zero_zero_nat )
% 9.17/5.33 & ( Y = zero_zero_nat ) ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1341_add__nonpos__eq__0__iff,axiom,
% 9.17/5.33 ! [X: int,Y: int] :
% 9.17/5.33 ( ( ord_less_eq_int @ X @ zero_zero_int )
% 9.17/5.33 => ( ( ord_less_eq_int @ Y @ zero_zero_int )
% 9.17/5.33 => ( ( ( plus_plus_int @ X @ Y )
% 9.17/5.33 = zero_zero_int )
% 9.17/5.33 = ( ( X = zero_zero_int )
% 9.17/5.33 & ( Y = zero_zero_int ) ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1342_not__one__le__zero,axiom,
% 9.17/5.33 ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ zero_z3403309356797280102nteger ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1343_not__one__le__zero,axiom,
% 9.17/5.33 ~ ( ord_less_eq_rat @ one_one_rat @ zero_zero_rat ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1344_not__one__le__zero,axiom,
% 9.17/5.33 ~ ( ord_less_eq_nat @ one_one_nat @ zero_zero_nat ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1345_not__one__le__zero,axiom,
% 9.17/5.33 ~ ( ord_less_eq_int @ one_one_int @ zero_zero_int ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1346_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 9.17/5.33 ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ one_one_Code_integer ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1347_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 9.17/5.33 ord_less_eq_rat @ zero_zero_rat @ one_one_rat ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1348_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 9.17/5.33 ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1349_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 9.17/5.33 ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1350_zero__less__one__class_Ozero__le__one,axiom,
% 9.17/5.33 ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ one_one_Code_integer ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1351_zero__less__one__class_Ozero__le__one,axiom,
% 9.17/5.33 ord_less_eq_rat @ zero_zero_rat @ one_one_rat ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1352_zero__less__one__class_Ozero__le__one,axiom,
% 9.17/5.33 ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1353_zero__less__one__class_Ozero__le__one,axiom,
% 9.17/5.33 ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1354_add__mono__thms__linordered__field_I4_J,axiom,
% 9.17/5.33 ! [I: code_integer,J: code_integer,K: code_integer,L: code_integer] :
% 9.17/5.33 ( ( ( ord_le3102999989581377725nteger @ I @ J )
% 9.17/5.33 & ( ord_le6747313008572928689nteger @ K @ L ) )
% 9.17/5.33 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ I @ K ) @ ( plus_p5714425477246183910nteger @ J @ L ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1355_add__mono__thms__linordered__field_I4_J,axiom,
% 9.17/5.33 ! [I: rat,J: rat,K: rat,L: rat] :
% 9.17/5.33 ( ( ( ord_less_eq_rat @ I @ J )
% 9.17/5.33 & ( ord_less_rat @ K @ L ) )
% 9.17/5.33 => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1356_add__mono__thms__linordered__field_I4_J,axiom,
% 9.17/5.33 ! [I: nat,J: nat,K: nat,L: nat] :
% 9.17/5.33 ( ( ( ord_less_eq_nat @ I @ J )
% 9.17/5.33 & ( ord_less_nat @ K @ L ) )
% 9.17/5.33 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1357_add__mono__thms__linordered__field_I4_J,axiom,
% 9.17/5.33 ! [I: int,J: int,K: int,L: int] :
% 9.17/5.33 ( ( ( ord_less_eq_int @ I @ J )
% 9.17/5.33 & ( ord_less_int @ K @ L ) )
% 9.17/5.33 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1358_add__mono__thms__linordered__field_I3_J,axiom,
% 9.17/5.33 ! [I: code_integer,J: code_integer,K: code_integer,L: code_integer] :
% 9.17/5.33 ( ( ( ord_le6747313008572928689nteger @ I @ J )
% 9.17/5.33 & ( ord_le3102999989581377725nteger @ K @ L ) )
% 9.17/5.33 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ I @ K ) @ ( plus_p5714425477246183910nteger @ J @ L ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1359_add__mono__thms__linordered__field_I3_J,axiom,
% 9.17/5.33 ! [I: rat,J: rat,K: rat,L: rat] :
% 9.17/5.33 ( ( ( ord_less_rat @ I @ J )
% 9.17/5.33 & ( ord_less_eq_rat @ K @ L ) )
% 9.17/5.33 => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1360_add__mono__thms__linordered__field_I3_J,axiom,
% 9.17/5.33 ! [I: nat,J: nat,K: nat,L: nat] :
% 9.17/5.33 ( ( ( ord_less_nat @ I @ J )
% 9.17/5.33 & ( ord_less_eq_nat @ K @ L ) )
% 9.17/5.33 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1361_add__mono__thms__linordered__field_I3_J,axiom,
% 9.17/5.33 ! [I: int,J: int,K: int,L: int] :
% 9.17/5.33 ( ( ( ord_less_int @ I @ J )
% 9.17/5.33 & ( ord_less_eq_int @ K @ L ) )
% 9.17/5.33 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1362_add__le__less__mono,axiom,
% 9.17/5.33 ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 9.17/5.33 ( ( ord_le3102999989581377725nteger @ A @ B )
% 9.17/5.33 => ( ( ord_le6747313008572928689nteger @ C @ D2 )
% 9.17/5.33 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ C ) @ ( plus_p5714425477246183910nteger @ B @ D2 ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1363_add__le__less__mono,axiom,
% 9.17/5.33 ! [A: rat,B: rat,C: rat,D2: rat] :
% 9.17/5.33 ( ( ord_less_eq_rat @ A @ B )
% 9.17/5.33 => ( ( ord_less_rat @ C @ D2 )
% 9.17/5.33 => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D2 ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1364_add__le__less__mono,axiom,
% 9.17/5.33 ! [A: nat,B: nat,C: nat,D2: nat] :
% 9.17/5.33 ( ( ord_less_eq_nat @ A @ B )
% 9.17/5.33 => ( ( ord_less_nat @ C @ D2 )
% 9.17/5.33 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D2 ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1365_add__le__less__mono,axiom,
% 9.17/5.33 ! [A: int,B: int,C: int,D2: int] :
% 9.17/5.33 ( ( ord_less_eq_int @ A @ B )
% 9.17/5.33 => ( ( ord_less_int @ C @ D2 )
% 9.17/5.33 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D2 ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1366_add__less__le__mono,axiom,
% 9.17/5.33 ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 9.17/5.33 ( ( ord_le6747313008572928689nteger @ A @ B )
% 9.17/5.33 => ( ( ord_le3102999989581377725nteger @ C @ D2 )
% 9.17/5.33 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ C ) @ ( plus_p5714425477246183910nteger @ B @ D2 ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1367_add__less__le__mono,axiom,
% 9.17/5.33 ! [A: rat,B: rat,C: rat,D2: rat] :
% 9.17/5.33 ( ( ord_less_rat @ A @ B )
% 9.17/5.33 => ( ( ord_less_eq_rat @ C @ D2 )
% 9.17/5.33 => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D2 ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1368_add__less__le__mono,axiom,
% 9.17/5.33 ! [A: nat,B: nat,C: nat,D2: nat] :
% 9.17/5.33 ( ( ord_less_nat @ A @ B )
% 9.17/5.33 => ( ( ord_less_eq_nat @ C @ D2 )
% 9.17/5.33 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D2 ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1369_add__less__le__mono,axiom,
% 9.17/5.33 ! [A: int,B: int,C: int,D2: int] :
% 9.17/5.33 ( ( ord_less_int @ A @ B )
% 9.17/5.33 => ( ( ord_less_eq_int @ C @ D2 )
% 9.17/5.33 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D2 ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1370_le__minus__one__simps_I2_J,axiom,
% 9.17/5.33 ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1371_le__minus__one__simps_I2_J,axiom,
% 9.17/5.33 ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1372_le__minus__one__simps_I2_J,axiom,
% 9.17/5.33 ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1373_le__minus__one__simps_I4_J,axiom,
% 9.17/5.33 ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1374_le__minus__one__simps_I4_J,axiom,
% 9.17/5.33 ~ ( ord_less_eq_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1375_le__minus__one__simps_I4_J,axiom,
% 9.17/5.33 ~ ( ord_less_eq_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1376_abs__ge__zero,axiom,
% 9.17/5.33 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ A ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1377_abs__ge__zero,axiom,
% 9.17/5.33 ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( abs_abs_rat @ A ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1378_abs__ge__zero,axiom,
% 9.17/5.33 ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( abs_abs_int @ A ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1379_abs__triangle__ineq,axiom,
% 9.17/5.33 ! [A: code_integer,B: code_integer] : ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( plus_p5714425477246183910nteger @ A @ B ) ) @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1380_abs__triangle__ineq,axiom,
% 9.17/5.33 ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( plus_plus_rat @ A @ B ) ) @ ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1381_abs__triangle__ineq,axiom,
% 9.17/5.33 ! [A: int,B: int] : ( ord_less_eq_int @ ( abs_abs_int @ ( plus_plus_int @ A @ B ) ) @ ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1382_abs__leI,axiom,
% 9.17/5.33 ! [A: code_integer,B: code_integer] :
% 9.17/5.33 ( ( ord_le3102999989581377725nteger @ A @ B )
% 9.17/5.33 => ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 9.17/5.33 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1383_abs__leI,axiom,
% 9.17/5.33 ! [A: rat,B: rat] :
% 9.17/5.33 ( ( ord_less_eq_rat @ A @ B )
% 9.17/5.33 => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B )
% 9.17/5.33 => ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1384_abs__leI,axiom,
% 9.17/5.33 ! [A: int,B: int] :
% 9.17/5.33 ( ( ord_less_eq_int @ A @ B )
% 9.17/5.33 => ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B )
% 9.17/5.33 => ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1385_abs__le__D2,axiom,
% 9.17/5.33 ! [A: code_integer,B: code_integer] :
% 9.17/5.33 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 9.17/5.33 => ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1386_abs__le__D2,axiom,
% 9.17/5.33 ! [A: rat,B: rat] :
% 9.17/5.33 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 9.17/5.33 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1387_abs__le__D2,axiom,
% 9.17/5.33 ! [A: int,B: int] :
% 9.17/5.33 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 9.17/5.33 => ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1388_abs__le__iff,axiom,
% 9.17/5.33 ! [A: code_integer,B: code_integer] :
% 9.17/5.33 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 9.17/5.33 = ( ( ord_le3102999989581377725nteger @ A @ B )
% 9.17/5.33 & ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1389_abs__le__iff,axiom,
% 9.17/5.33 ! [A: rat,B: rat] :
% 9.17/5.33 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 9.17/5.33 = ( ( ord_less_eq_rat @ A @ B )
% 9.17/5.33 & ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1390_abs__le__iff,axiom,
% 9.17/5.33 ! [A: int,B: int] :
% 9.17/5.33 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 9.17/5.33 = ( ( ord_less_eq_int @ A @ B )
% 9.17/5.33 & ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1391_abs__ge__minus__self,axiom,
% 9.17/5.33 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ ( abs_abs_Code_integer @ A ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1392_abs__ge__minus__self,axiom,
% 9.17/5.33 ! [A: rat] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ ( abs_abs_rat @ A ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1393_abs__ge__minus__self,axiom,
% 9.17/5.33 ! [A: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ ( abs_abs_int @ A ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1394_mono__nat__linear__lb,axiom,
% 9.17/5.33 ! [F: nat > nat,M2: nat,K: nat] :
% 9.17/5.33 ( ! [M5: nat,N: nat] :
% 9.17/5.33 ( ( ord_less_nat @ M5 @ N )
% 9.17/5.33 => ( ord_less_nat @ ( F @ M5 ) @ ( F @ N ) ) )
% 9.17/5.33 => ( ord_less_eq_nat @ ( plus_plus_nat @ ( F @ M2 ) @ K ) @ ( F @ ( plus_plus_nat @ M2 @ K ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1395_nat__geq__1__eq__neqz,axiom,
% 9.17/5.33 ! [X: nat] :
% 9.17/5.33 ( ( ord_less_eq_nat @ one_one_nat @ X )
% 9.17/5.33 = ( X != zero_zero_nat ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1396_bind__split__asm,axiom,
% 9.17/5.33 ! [P: option3216581401566546698it_nat > $o,M2: option3216581401566546698it_nat,F: produc6714399278180371524it_nat > option3216581401566546698it_nat] :
% 9.17/5.33 ( ( P @ ( bind_P1787608729393679550it_nat @ M2 @ F ) )
% 9.17/5.33 = ( ~ ( ( ( M2 = none_P2587165478634041381it_nat )
% 9.17/5.33 & ~ ( P @ none_P2587165478634041381it_nat ) )
% 9.17/5.33 | ? [X3: produc6714399278180371524it_nat] :
% 9.17/5.33 ( ( M2
% 9.17/5.33 = ( some_P6105628898608307625it_nat @ X3 ) )
% 9.17/5.33 & ~ ( P @ ( F @ X3 ) ) ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1397_bind__split__asm,axiom,
% 9.17/5.33 ! [P: option_num > $o,M2: option3216581401566546698it_nat,F: produc6714399278180371524it_nat > option_num] :
% 9.17/5.33 ( ( P @ ( bind_P7816469540982926368at_num @ M2 @ F ) )
% 9.17/5.33 = ( ~ ( ( ( M2 = none_P2587165478634041381it_nat )
% 9.17/5.33 & ~ ( P @ none_num ) )
% 9.17/5.33 | ? [X3: produc6714399278180371524it_nat] :
% 9.17/5.33 ( ( M2
% 9.17/5.33 = ( some_P6105628898608307625it_nat @ X3 ) )
% 9.17/5.33 & ~ ( P @ ( F @ X3 ) ) ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1398_bind__split__asm,axiom,
% 9.17/5.33 ! [P: option8956607266484857688it_nat > $o,M2: option3216581401566546698it_nat,F: produc6714399278180371524it_nat > option8956607266484857688it_nat] :
% 9.17/5.33 ( ( P @ ( bind_P3087804342168909838it_nat @ M2 @ F ) )
% 9.17/5.33 = ( ~ ( ( ( M2 = none_P2587165478634041381it_nat )
% 9.17/5.33 & ~ ( P @ none_P9117596204409417319it_nat ) )
% 9.17/5.33 | ? [X3: produc6714399278180371524it_nat] :
% 9.17/5.33 ( ( M2
% 9.17/5.33 = ( some_P6105628898608307625it_nat @ X3 ) )
% 9.17/5.33 & ~ ( P @ ( F @ X3 ) ) ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1399_bind__split__asm,axiom,
% 9.17/5.33 ! [P: option3216581401566546698it_nat > $o,M2: option_num,F: num > option3216581401566546698it_nat] :
% 9.17/5.33 ( ( P @ ( bind_n6186876254402743274it_nat @ M2 @ F ) )
% 9.17/5.33 = ( ~ ( ( ( M2 = none_num )
% 9.17/5.33 & ~ ( P @ none_P2587165478634041381it_nat ) )
% 9.17/5.33 | ? [X3: num] :
% 9.17/5.33 ( ( M2
% 9.17/5.33 = ( some_num @ X3 ) )
% 9.17/5.33 & ~ ( P @ ( F @ X3 ) ) ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1400_bind__split__asm,axiom,
% 9.17/5.33 ! [P: option_num > $o,M2: option_num,F: num > option_num] :
% 9.17/5.33 ( ( P @ ( bind_num_num @ M2 @ F ) )
% 9.17/5.33 = ( ~ ( ( ( M2 = none_num )
% 9.17/5.33 & ~ ( P @ none_num ) )
% 9.17/5.33 | ? [X3: num] :
% 9.17/5.33 ( ( M2
% 9.17/5.33 = ( some_num @ X3 ) )
% 9.17/5.33 & ~ ( P @ ( F @ X3 ) ) ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1401_bind__split__asm,axiom,
% 9.17/5.33 ! [P: option8956607266484857688it_nat > $o,M2: option_num,F: num > option8956607266484857688it_nat] :
% 9.17/5.33 ( ( P @ ( bind_n550516262659884002it_nat @ M2 @ F ) )
% 9.17/5.33 = ( ~ ( ( ( M2 = none_num )
% 9.17/5.33 & ~ ( P @ none_P9117596204409417319it_nat ) )
% 9.17/5.33 | ? [X3: num] :
% 9.17/5.33 ( ( M2
% 9.17/5.33 = ( some_num @ X3 ) )
% 9.17/5.33 & ~ ( P @ ( F @ X3 ) ) ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1402_bind__split__asm,axiom,
% 9.17/5.33 ! [P: option3216581401566546698it_nat > $o,M2: option8956607266484857688it_nat,F: produc8664842809031399944it_nat > option3216581401566546698it_nat] :
% 9.17/5.33 ( ( P @ ( bind_P1106314856888375420it_nat @ M2 @ F ) )
% 9.17/5.33 = ( ~ ( ( ( M2 = none_P9117596204409417319it_nat )
% 9.17/5.33 & ~ ( P @ none_P2587165478634041381it_nat ) )
% 9.17/5.33 | ? [X3: produc8664842809031399944it_nat] :
% 9.17/5.33 ( ( M2
% 9.17/5.33 = ( some_P1914260805536162275it_nat @ X3 ) )
% 9.17/5.33 & ~ ( P @ ( F @ X3 ) ) ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1403_bind__split__asm,axiom,
% 9.17/5.33 ! [P: option_num > $o,M2: option8956607266484857688it_nat,F: produc8664842809031399944it_nat > option_num] :
% 9.17/5.33 ( ( P @ ( bind_P4387644102537648098at_num @ M2 @ F ) )
% 9.17/5.33 = ( ~ ( ( ( M2 = none_P9117596204409417319it_nat )
% 9.17/5.33 & ~ ( P @ none_num ) )
% 9.17/5.33 | ? [X3: produc8664842809031399944it_nat] :
% 9.17/5.33 ( ( M2
% 9.17/5.33 = ( some_P1914260805536162275it_nat @ X3 ) )
% 9.17/5.33 & ~ ( P @ ( F @ X3 ) ) ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1404_bind__split__asm,axiom,
% 9.17/5.33 ! [P: option8956607266484857688it_nat > $o,M2: option8956607266484857688it_nat,F: produc8664842809031399944it_nat > option8956607266484857688it_nat] :
% 9.17/5.33 ( ( P @ ( bind_P7351952464966851536it_nat @ M2 @ F ) )
% 9.17/5.33 = ( ~ ( ( ( M2 = none_P9117596204409417319it_nat )
% 9.17/5.33 & ~ ( P @ none_P9117596204409417319it_nat ) )
% 9.17/5.33 | ? [X3: produc8664842809031399944it_nat] :
% 9.17/5.33 ( ( M2
% 9.17/5.33 = ( some_P1914260805536162275it_nat @ X3 ) )
% 9.17/5.33 & ~ ( P @ ( F @ X3 ) ) ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1405_bind__split,axiom,
% 9.17/5.33 ! [P: option3216581401566546698it_nat > $o,M2: option3216581401566546698it_nat,F: produc6714399278180371524it_nat > option3216581401566546698it_nat] :
% 9.17/5.33 ( ( P @ ( bind_P1787608729393679550it_nat @ M2 @ F ) )
% 9.17/5.33 = ( ( ( M2 = none_P2587165478634041381it_nat )
% 9.17/5.33 => ( P @ none_P2587165478634041381it_nat ) )
% 9.17/5.33 & ! [V2: produc6714399278180371524it_nat] :
% 9.17/5.33 ( ( M2
% 9.17/5.33 = ( some_P6105628898608307625it_nat @ V2 ) )
% 9.17/5.33 => ( P @ ( F @ V2 ) ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1406_bind__split,axiom,
% 9.17/5.33 ! [P: option_num > $o,M2: option3216581401566546698it_nat,F: produc6714399278180371524it_nat > option_num] :
% 9.17/5.33 ( ( P @ ( bind_P7816469540982926368at_num @ M2 @ F ) )
% 9.17/5.33 = ( ( ( M2 = none_P2587165478634041381it_nat )
% 9.17/5.33 => ( P @ none_num ) )
% 9.17/5.33 & ! [V2: produc6714399278180371524it_nat] :
% 9.17/5.33 ( ( M2
% 9.17/5.33 = ( some_P6105628898608307625it_nat @ V2 ) )
% 9.17/5.33 => ( P @ ( F @ V2 ) ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1407_bind__split,axiom,
% 9.17/5.33 ! [P: option8956607266484857688it_nat > $o,M2: option3216581401566546698it_nat,F: produc6714399278180371524it_nat > option8956607266484857688it_nat] :
% 9.17/5.33 ( ( P @ ( bind_P3087804342168909838it_nat @ M2 @ F ) )
% 9.17/5.33 = ( ( ( M2 = none_P2587165478634041381it_nat )
% 9.17/5.33 => ( P @ none_P9117596204409417319it_nat ) )
% 9.17/5.33 & ! [V2: produc6714399278180371524it_nat] :
% 9.17/5.33 ( ( M2
% 9.17/5.33 = ( some_P6105628898608307625it_nat @ V2 ) )
% 9.17/5.33 => ( P @ ( F @ V2 ) ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1408_bind__split,axiom,
% 9.17/5.33 ! [P: option3216581401566546698it_nat > $o,M2: option_num,F: num > option3216581401566546698it_nat] :
% 9.17/5.33 ( ( P @ ( bind_n6186876254402743274it_nat @ M2 @ F ) )
% 9.17/5.33 = ( ( ( M2 = none_num )
% 9.17/5.33 => ( P @ none_P2587165478634041381it_nat ) )
% 9.17/5.33 & ! [V2: num] :
% 9.17/5.33 ( ( M2
% 9.17/5.33 = ( some_num @ V2 ) )
% 9.17/5.33 => ( P @ ( F @ V2 ) ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1409_bind__split,axiom,
% 9.17/5.33 ! [P: option_num > $o,M2: option_num,F: num > option_num] :
% 9.17/5.33 ( ( P @ ( bind_num_num @ M2 @ F ) )
% 9.17/5.33 = ( ( ( M2 = none_num )
% 9.17/5.33 => ( P @ none_num ) )
% 9.17/5.33 & ! [V2: num] :
% 9.17/5.33 ( ( M2
% 9.17/5.33 = ( some_num @ V2 ) )
% 9.17/5.33 => ( P @ ( F @ V2 ) ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1410_bind__split,axiom,
% 9.17/5.33 ! [P: option8956607266484857688it_nat > $o,M2: option_num,F: num > option8956607266484857688it_nat] :
% 9.17/5.33 ( ( P @ ( bind_n550516262659884002it_nat @ M2 @ F ) )
% 9.17/5.33 = ( ( ( M2 = none_num )
% 9.17/5.33 => ( P @ none_P9117596204409417319it_nat ) )
% 9.17/5.33 & ! [V2: num] :
% 9.17/5.33 ( ( M2
% 9.17/5.33 = ( some_num @ V2 ) )
% 9.17/5.33 => ( P @ ( F @ V2 ) ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1411_bind__split,axiom,
% 9.17/5.33 ! [P: option3216581401566546698it_nat > $o,M2: option8956607266484857688it_nat,F: produc8664842809031399944it_nat > option3216581401566546698it_nat] :
% 9.17/5.33 ( ( P @ ( bind_P1106314856888375420it_nat @ M2 @ F ) )
% 9.17/5.33 = ( ( ( M2 = none_P9117596204409417319it_nat )
% 9.17/5.33 => ( P @ none_P2587165478634041381it_nat ) )
% 9.17/5.33 & ! [V2: produc8664842809031399944it_nat] :
% 9.17/5.33 ( ( M2
% 9.17/5.33 = ( some_P1914260805536162275it_nat @ V2 ) )
% 9.17/5.33 => ( P @ ( F @ V2 ) ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1412_bind__split,axiom,
% 9.17/5.33 ! [P: option_num > $o,M2: option8956607266484857688it_nat,F: produc8664842809031399944it_nat > option_num] :
% 9.17/5.33 ( ( P @ ( bind_P4387644102537648098at_num @ M2 @ F ) )
% 9.17/5.33 = ( ( ( M2 = none_P9117596204409417319it_nat )
% 9.17/5.33 => ( P @ none_num ) )
% 9.17/5.33 & ! [V2: produc8664842809031399944it_nat] :
% 9.17/5.33 ( ( M2
% 9.17/5.33 = ( some_P1914260805536162275it_nat @ V2 ) )
% 9.17/5.33 => ( P @ ( F @ V2 ) ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1413_bind__split,axiom,
% 9.17/5.33 ! [P: option8956607266484857688it_nat > $o,M2: option8956607266484857688it_nat,F: produc8664842809031399944it_nat > option8956607266484857688it_nat] :
% 9.17/5.33 ( ( P @ ( bind_P7351952464966851536it_nat @ M2 @ F ) )
% 9.17/5.33 = ( ( ( M2 = none_P9117596204409417319it_nat )
% 9.17/5.33 => ( P @ none_P9117596204409417319it_nat ) )
% 9.17/5.33 & ! [V2: produc8664842809031399944it_nat] :
% 9.17/5.33 ( ( M2
% 9.17/5.33 = ( some_P1914260805536162275it_nat @ V2 ) )
% 9.17/5.33 => ( P @ ( F @ V2 ) ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1414_mlex__leq,axiom,
% 9.17/5.33 ! [F: set_Pr1261947904930325089at_nat > nat,X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,R4: set_Pr4329608150637261639at_nat] :
% 9.17/5.33 ( ( ord_less_eq_nat @ ( F @ X ) @ ( F @ Y ) )
% 9.17/5.33 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ R4 )
% 9.17/5.33 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ ( mlex_p3502713205431853936at_nat @ F @ R4 ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1415_mlex__leq,axiom,
% 9.17/5.33 ! [F: nat > nat,X: nat,Y: nat,R4: set_Pr1261947904930325089at_nat] :
% 9.17/5.33 ( ( ord_less_eq_nat @ ( F @ X ) @ ( F @ Y ) )
% 9.17/5.33 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ R4 )
% 9.17/5.33 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( mlex_prod_nat @ F @ R4 ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1416_bind__eq__None__conv,axiom,
% 9.17/5.33 ! [A: option3216581401566546698it_nat,F: produc6714399278180371524it_nat > option3216581401566546698it_nat] :
% 9.17/5.33 ( ( ( bind_P1787608729393679550it_nat @ A @ F )
% 9.17/5.33 = none_P2587165478634041381it_nat )
% 9.17/5.33 = ( ( A = none_P2587165478634041381it_nat )
% 9.17/5.33 | ( ( F @ ( the_Pr5856008525237892824it_nat @ A ) )
% 9.17/5.33 = none_P2587165478634041381it_nat ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1417_bind__eq__None__conv,axiom,
% 9.17/5.33 ! [A: option_num,F: num > option3216581401566546698it_nat] :
% 9.17/5.33 ( ( ( bind_n6186876254402743274it_nat @ A @ F )
% 9.17/5.33 = none_P2587165478634041381it_nat )
% 9.17/5.33 = ( ( A = none_num )
% 9.17/5.33 | ( ( F @ ( the_num @ A ) )
% 9.17/5.33 = none_P2587165478634041381it_nat ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1418_bind__eq__None__conv,axiom,
% 9.17/5.33 ! [A: option8956607266484857688it_nat,F: produc8664842809031399944it_nat > option3216581401566546698it_nat] :
% 9.17/5.33 ( ( ( bind_P1106314856888375420it_nat @ A @ F )
% 9.17/5.33 = none_P2587165478634041381it_nat )
% 9.17/5.33 = ( ( A = none_P9117596204409417319it_nat )
% 9.17/5.33 | ( ( F @ ( the_Pr7776125533777466484it_nat @ A ) )
% 9.17/5.33 = none_P2587165478634041381it_nat ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1419_bind__eq__None__conv,axiom,
% 9.17/5.33 ! [A: option3216581401566546698it_nat,F: produc6714399278180371524it_nat > option_num] :
% 9.17/5.33 ( ( ( bind_P7816469540982926368at_num @ A @ F )
% 9.17/5.33 = none_num )
% 9.17/5.33 = ( ( A = none_P2587165478634041381it_nat )
% 9.17/5.33 | ( ( F @ ( the_Pr5856008525237892824it_nat @ A ) )
% 9.17/5.33 = none_num ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1420_bind__eq__None__conv,axiom,
% 9.17/5.33 ! [A: option_num,F: num > option_num] :
% 9.17/5.33 ( ( ( bind_num_num @ A @ F )
% 9.17/5.33 = none_num )
% 9.17/5.33 = ( ( A = none_num )
% 9.17/5.33 | ( ( F @ ( the_num @ A ) )
% 9.17/5.33 = none_num ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1421_bind__eq__None__conv,axiom,
% 9.17/5.33 ! [A: option8956607266484857688it_nat,F: produc8664842809031399944it_nat > option_num] :
% 9.17/5.33 ( ( ( bind_P4387644102537648098at_num @ A @ F )
% 9.17/5.33 = none_num )
% 9.17/5.33 = ( ( A = none_P9117596204409417319it_nat )
% 9.17/5.33 | ( ( F @ ( the_Pr7776125533777466484it_nat @ A ) )
% 9.17/5.33 = none_num ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1422_bind__eq__None__conv,axiom,
% 9.17/5.33 ! [A: option3216581401566546698it_nat,F: produc6714399278180371524it_nat > option8956607266484857688it_nat] :
% 9.17/5.33 ( ( ( bind_P3087804342168909838it_nat @ A @ F )
% 9.17/5.33 = none_P9117596204409417319it_nat )
% 9.17/5.33 = ( ( A = none_P2587165478634041381it_nat )
% 9.17/5.33 | ( ( F @ ( the_Pr5856008525237892824it_nat @ A ) )
% 9.17/5.33 = none_P9117596204409417319it_nat ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1423_bind__eq__None__conv,axiom,
% 9.17/5.33 ! [A: option_num,F: num > option8956607266484857688it_nat] :
% 9.17/5.33 ( ( ( bind_n550516262659884002it_nat @ A @ F )
% 9.17/5.33 = none_P9117596204409417319it_nat )
% 9.17/5.33 = ( ( A = none_num )
% 9.17/5.33 | ( ( F @ ( the_num @ A ) )
% 9.17/5.33 = none_P9117596204409417319it_nat ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1424_bind__eq__None__conv,axiom,
% 9.17/5.33 ! [A: option8956607266484857688it_nat,F: produc8664842809031399944it_nat > option8956607266484857688it_nat] :
% 9.17/5.33 ( ( ( bind_P7351952464966851536it_nat @ A @ F )
% 9.17/5.33 = none_P9117596204409417319it_nat )
% 9.17/5.33 = ( ( A = none_P9117596204409417319it_nat )
% 9.17/5.33 | ( ( F @ ( the_Pr7776125533777466484it_nat @ A ) )
% 9.17/5.33 = none_P9117596204409417319it_nat ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1425_add__neg__nonpos,axiom,
% 9.17/5.33 ! [A: code_integer,B: code_integer] :
% 9.17/5.33 ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 9.17/5.33 => ( ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger )
% 9.17/5.33 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ zero_z3403309356797280102nteger ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1426_add__neg__nonpos,axiom,
% 9.17/5.33 ! [A: rat,B: rat] :
% 9.17/5.33 ( ( ord_less_rat @ A @ zero_zero_rat )
% 9.17/5.33 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 9.17/5.33 => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1427_add__neg__nonpos,axiom,
% 9.17/5.33 ! [A: nat,B: nat] :
% 9.17/5.33 ( ( ord_less_nat @ A @ zero_zero_nat )
% 9.17/5.33 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 9.17/5.33 => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1428_add__neg__nonpos,axiom,
% 9.17/5.33 ! [A: int,B: int] :
% 9.17/5.33 ( ( ord_less_int @ A @ zero_zero_int )
% 9.17/5.33 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 9.17/5.33 => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1429_add__nonneg__pos,axiom,
% 9.17/5.33 ! [A: code_integer,B: code_integer] :
% 9.17/5.33 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 9.17/5.33 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 9.17/5.33 => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1430_add__nonneg__pos,axiom,
% 9.17/5.33 ! [A: rat,B: rat] :
% 9.17/5.33 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 9.17/5.33 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 9.17/5.33 => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1431_add__nonneg__pos,axiom,
% 9.17/5.33 ! [A: nat,B: nat] :
% 9.17/5.33 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 9.17/5.33 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 9.17/5.33 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1432_add__nonneg__pos,axiom,
% 9.17/5.33 ! [A: int,B: int] :
% 9.17/5.33 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 9.17/5.33 => ( ( ord_less_int @ zero_zero_int @ B )
% 9.17/5.33 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1433_add__nonpos__neg,axiom,
% 9.17/5.33 ! [A: code_integer,B: code_integer] :
% 9.17/5.33 ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 9.17/5.33 => ( ( ord_le6747313008572928689nteger @ B @ zero_z3403309356797280102nteger )
% 9.17/5.33 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ zero_z3403309356797280102nteger ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1434_add__nonpos__neg,axiom,
% 9.17/5.33 ! [A: rat,B: rat] :
% 9.17/5.33 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 9.17/5.33 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 9.17/5.33 => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1435_add__nonpos__neg,axiom,
% 9.17/5.33 ! [A: nat,B: nat] :
% 9.17/5.33 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 9.17/5.33 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 9.17/5.33 => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1436_add__nonpos__neg,axiom,
% 9.17/5.33 ! [A: int,B: int] :
% 9.17/5.33 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 9.17/5.33 => ( ( ord_less_int @ B @ zero_zero_int )
% 9.17/5.33 => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1437_add__pos__nonneg,axiom,
% 9.17/5.33 ! [A: code_integer,B: code_integer] :
% 9.17/5.33 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 9.17/5.33 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 9.17/5.33 => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1438_add__pos__nonneg,axiom,
% 9.17/5.33 ! [A: rat,B: rat] :
% 9.17/5.33 ( ( ord_less_rat @ zero_zero_rat @ A )
% 9.17/5.33 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 9.17/5.33 => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1439_add__pos__nonneg,axiom,
% 9.17/5.33 ! [A: nat,B: nat] :
% 9.17/5.33 ( ( ord_less_nat @ zero_zero_nat @ A )
% 9.17/5.33 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 9.17/5.33 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1440_add__pos__nonneg,axiom,
% 9.17/5.33 ! [A: int,B: int] :
% 9.17/5.33 ( ( ord_less_int @ zero_zero_int @ A )
% 9.17/5.33 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 9.17/5.33 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1441_add__strict__increasing,axiom,
% 9.17/5.33 ! [A: code_integer,B: code_integer,C: code_integer] :
% 9.17/5.33 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 9.17/5.33 => ( ( ord_le3102999989581377725nteger @ B @ C )
% 9.17/5.33 => ( ord_le6747313008572928689nteger @ B @ ( plus_p5714425477246183910nteger @ A @ C ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1442_add__strict__increasing,axiom,
% 9.17/5.33 ! [A: rat,B: rat,C: rat] :
% 9.17/5.33 ( ( ord_less_rat @ zero_zero_rat @ A )
% 9.17/5.33 => ( ( ord_less_eq_rat @ B @ C )
% 9.17/5.33 => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1443_add__strict__increasing,axiom,
% 9.17/5.33 ! [A: nat,B: nat,C: nat] :
% 9.17/5.33 ( ( ord_less_nat @ zero_zero_nat @ A )
% 9.17/5.33 => ( ( ord_less_eq_nat @ B @ C )
% 9.17/5.33 => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1444_add__strict__increasing,axiom,
% 9.17/5.33 ! [A: int,B: int,C: int] :
% 9.17/5.33 ( ( ord_less_int @ zero_zero_int @ A )
% 9.17/5.33 => ( ( ord_less_eq_int @ B @ C )
% 9.17/5.33 => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1445_add__strict__increasing2,axiom,
% 9.17/5.33 ! [A: code_integer,B: code_integer,C: code_integer] :
% 9.17/5.33 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 9.17/5.33 => ( ( ord_le6747313008572928689nteger @ B @ C )
% 9.17/5.33 => ( ord_le6747313008572928689nteger @ B @ ( plus_p5714425477246183910nteger @ A @ C ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1446_add__strict__increasing2,axiom,
% 9.17/5.33 ! [A: rat,B: rat,C: rat] :
% 9.17/5.33 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 9.17/5.33 => ( ( ord_less_rat @ B @ C )
% 9.17/5.33 => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1447_add__strict__increasing2,axiom,
% 9.17/5.33 ! [A: nat,B: nat,C: nat] :
% 9.17/5.33 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 9.17/5.33 => ( ( ord_less_nat @ B @ C )
% 9.17/5.33 => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1448_add__strict__increasing2,axiom,
% 9.17/5.33 ! [A: int,B: int,C: int] :
% 9.17/5.33 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 9.17/5.33 => ( ( ord_less_int @ B @ C )
% 9.17/5.33 => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1449_discrete,axiom,
% 9.17/5.33 ( ord_le6747313008572928689nteger
% 9.17/5.33 = ( ^ [A5: code_integer] : ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ A5 @ one_one_Code_integer ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1450_discrete,axiom,
% 9.17/5.33 ( ord_less_nat
% 9.17/5.33 = ( ^ [A5: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ A5 @ one_one_nat ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1451_discrete,axiom,
% 9.17/5.33 ( ord_less_int
% 9.17/5.33 = ( ^ [A5: int] : ( ord_less_eq_int @ ( plus_plus_int @ A5 @ one_one_int ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1452_le__minus__one__simps_I1_J,axiom,
% 9.17/5.33 ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ zero_z3403309356797280102nteger ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1453_le__minus__one__simps_I1_J,axiom,
% 9.17/5.33 ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ zero_zero_rat ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1454_le__minus__one__simps_I1_J,axiom,
% 9.17/5.33 ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1455_le__minus__one__simps_I3_J,axiom,
% 9.17/5.33 ~ ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1456_le__minus__one__simps_I3_J,axiom,
% 9.17/5.33 ~ ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1457_le__minus__one__simps_I3_J,axiom,
% 9.17/5.33 ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1458_dense__eq0__I,axiom,
% 9.17/5.33 ! [X: rat] :
% 9.17/5.33 ( ! [E2: rat] :
% 9.17/5.33 ( ( ord_less_rat @ zero_zero_rat @ E2 )
% 9.17/5.33 => ( ord_less_eq_rat @ ( abs_abs_rat @ X ) @ E2 ) )
% 9.17/5.33 => ( X = zero_zero_rat ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1459_abs__minus__le__zero,axiom,
% 9.17/5.33 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( abs_abs_Code_integer @ A ) ) @ zero_z3403309356797280102nteger ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1460_abs__minus__le__zero,axiom,
% 9.17/5.33 ! [A: rat] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( abs_abs_rat @ A ) ) @ zero_zero_rat ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1461_abs__minus__le__zero,axiom,
% 9.17/5.33 ! [A: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( abs_abs_int @ A ) ) @ zero_zero_int ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1462_success__changeI,axiom,
% 9.17/5.33 ! [F: product_unit > product_unit,R2: ref_Product_unit,H3: heap_e7401611519738050253t_unit] : ( heap_T584514906347983379t_unit @ ( ref_ch7259622376331601608t_unit @ F @ R2 ) @ H3 ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1463_success__changeI,axiom,
% 9.17/5.33 ! [F: array_a > array_a,R2: ref_array_a,H3: heap_e7401611519738050253t_unit] : ( heap_T6932021131025641745rray_a @ ( ref_change_array_a @ F @ R2 ) @ H3 ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1464_semiring__norm_I6_J,axiom,
% 9.17/5.33 ! [M2: num,N2: num] :
% 9.17/5.33 ( ( plus_plus_num @ ( bit0 @ M2 ) @ ( bit0 @ N2 ) )
% 9.17/5.33 = ( bit0 @ ( plus_plus_num @ M2 @ N2 ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1465_field__le__epsilon,axiom,
% 9.17/5.33 ! [X: rat,Y: rat] :
% 9.17/5.33 ( ! [E2: rat] :
% 9.17/5.33 ( ( ord_less_rat @ zero_zero_rat @ E2 )
% 9.17/5.33 => ( ord_less_eq_rat @ X @ ( plus_plus_rat @ Y @ E2 ) ) )
% 9.17/5.33 => ( ord_less_eq_rat @ X @ Y ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1466_convex__bound__lt,axiom,
% 9.17/5.33 ! [X: code_integer,A: code_integer,Y: code_integer,U: code_integer,V: code_integer] :
% 9.17/5.33 ( ( ord_le6747313008572928689nteger @ X @ A )
% 9.17/5.33 => ( ( ord_le6747313008572928689nteger @ Y @ A )
% 9.17/5.33 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ U )
% 9.17/5.33 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ V )
% 9.17/5.33 => ( ( ( plus_p5714425477246183910nteger @ U @ V )
% 9.17/5.33 = one_one_Code_integer )
% 9.17/5.33 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ U @ X ) @ ( times_3573771949741848930nteger @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1467_convex__bound__lt,axiom,
% 9.17/5.33 ! [X: rat,A: rat,Y: rat,U: rat,V: rat] :
% 9.17/5.33 ( ( ord_less_rat @ X @ A )
% 9.17/5.33 => ( ( ord_less_rat @ Y @ A )
% 9.17/5.33 => ( ( ord_less_eq_rat @ zero_zero_rat @ U )
% 9.17/5.33 => ( ( ord_less_eq_rat @ zero_zero_rat @ V )
% 9.17/5.33 => ( ( ( plus_plus_rat @ U @ V )
% 9.17/5.33 = one_one_rat )
% 9.17/5.33 => ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ U @ X ) @ ( times_times_rat @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1468_convex__bound__lt,axiom,
% 9.17/5.33 ! [X: int,A: int,Y: int,U: int,V: int] :
% 9.17/5.33 ( ( ord_less_int @ X @ A )
% 9.17/5.33 => ( ( ord_less_int @ Y @ A )
% 9.17/5.33 => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 9.17/5.33 => ( ( ord_less_eq_int @ zero_zero_int @ V )
% 9.17/5.33 => ( ( ( plus_plus_int @ U @ V )
% 9.17/5.33 = one_one_int )
% 9.17/5.33 => ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ U @ X ) @ ( times_times_int @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1469_Ints__eq__abs__less1,axiom,
% 9.17/5.33 ! [X: code_integer,Y: code_integer] :
% 9.17/5.33 ( ( member_Code_integer @ X @ ring_11222124179247155820nteger )
% 9.17/5.33 => ( ( member_Code_integer @ Y @ ring_11222124179247155820nteger )
% 9.17/5.33 => ( ( X = Y )
% 9.17/5.33 = ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ X @ Y ) ) @ one_one_Code_integer ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1470_Ints__eq__abs__less1,axiom,
% 9.17/5.33 ! [X: rat,Y: rat] :
% 9.17/5.33 ( ( member_rat @ X @ ring_1_Ints_rat )
% 9.17/5.33 => ( ( member_rat @ Y @ ring_1_Ints_rat )
% 9.17/5.33 => ( ( X = Y )
% 9.17/5.33 = ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X @ Y ) ) @ one_one_rat ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1471_Ints__eq__abs__less1,axiom,
% 9.17/5.33 ! [X: int,Y: int] :
% 9.17/5.33 ( ( member_int @ X @ ring_1_Ints_int )
% 9.17/5.33 => ( ( member_int @ Y @ ring_1_Ints_int )
% 9.17/5.33 => ( ( X = Y )
% 9.17/5.33 = ( ord_less_int @ ( abs_abs_int @ ( minus_minus_int @ X @ Y ) ) @ one_one_int ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1472_nat0__intermed__int__val,axiom,
% 9.17/5.33 ! [N2: nat,F: nat > int,K: int] :
% 9.17/5.33 ( ! [I2: nat] :
% 9.17/5.33 ( ( ord_less_nat @ I2 @ N2 )
% 9.17/5.33 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( plus_plus_nat @ I2 @ one_one_nat ) ) @ ( F @ I2 ) ) ) @ one_one_int ) )
% 9.17/5.33 => ( ( ord_less_eq_int @ ( F @ zero_zero_nat ) @ K )
% 9.17/5.33 => ( ( ord_less_eq_int @ K @ ( F @ N2 ) )
% 9.17/5.33 => ? [I2: nat] :
% 9.17/5.33 ( ( ord_less_eq_nat @ I2 @ N2 )
% 9.17/5.33 & ( ( F @ I2 )
% 9.17/5.33 = K ) ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1473_diff__diff__left,axiom,
% 9.17/5.33 ! [I: nat,J: nat,K: nat] :
% 9.17/5.33 ( ( minus_minus_nat @ ( minus_minus_nat @ I @ J ) @ K )
% 9.17/5.33 = ( minus_minus_nat @ I @ ( plus_plus_nat @ J @ K ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1474_nat__1__eq__mult__iff,axiom,
% 9.17/5.33 ! [M2: nat,N2: nat] :
% 9.17/5.33 ( ( one_one_nat
% 9.17/5.33 = ( times_times_nat @ M2 @ N2 ) )
% 9.17/5.33 = ( ( M2 = one_one_nat )
% 9.17/5.33 & ( N2 = one_one_nat ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1475_nat__mult__eq__1__iff,axiom,
% 9.17/5.33 ! [M2: nat,N2: nat] :
% 9.17/5.33 ( ( ( times_times_nat @ M2 @ N2 )
% 9.17/5.33 = one_one_nat )
% 9.17/5.33 = ( ( M2 = one_one_nat )
% 9.17/5.33 & ( N2 = one_one_nat ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1476_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 9.17/5.33 ! [A: multis2468970476368604999at_nat] :
% 9.17/5.33 ( ( minus_4286766774447292334at_nat @ A @ A )
% 9.17/5.33 = zero_z1048942125864253310at_nat ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1477_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 9.17/5.33 ! [A: code_integer] :
% 9.17/5.33 ( ( minus_8373710615458151222nteger @ A @ A )
% 9.17/5.33 = zero_z3403309356797280102nteger ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1478_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 9.17/5.33 ! [A: rat] :
% 9.17/5.33 ( ( minus_minus_rat @ A @ A )
% 9.17/5.33 = zero_zero_rat ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1479_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 9.17/5.33 ! [A: nat] :
% 9.17/5.33 ( ( minus_minus_nat @ A @ A )
% 9.17/5.33 = zero_zero_nat ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1480_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 9.17/5.33 ! [A: int] :
% 9.17/5.33 ( ( minus_minus_int @ A @ A )
% 9.17/5.33 = zero_zero_int ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1481_diff__zero,axiom,
% 9.17/5.33 ! [A: multis2468970476368604999at_nat] :
% 9.17/5.33 ( ( minus_4286766774447292334at_nat @ A @ zero_z1048942125864253310at_nat )
% 9.17/5.33 = A ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1482_diff__zero,axiom,
% 9.17/5.33 ! [A: code_integer] :
% 9.17/5.33 ( ( minus_8373710615458151222nteger @ A @ zero_z3403309356797280102nteger )
% 9.17/5.33 = A ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1483_diff__zero,axiom,
% 9.17/5.33 ! [A: rat] :
% 9.17/5.33 ( ( minus_minus_rat @ A @ zero_zero_rat )
% 9.17/5.33 = A ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1484_diff__zero,axiom,
% 9.17/5.33 ! [A: nat] :
% 9.17/5.33 ( ( minus_minus_nat @ A @ zero_zero_nat )
% 9.17/5.33 = A ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1485_diff__zero,axiom,
% 9.17/5.33 ! [A: int] :
% 9.17/5.33 ( ( minus_minus_int @ A @ zero_zero_int )
% 9.17/5.33 = A ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1486_zero__diff,axiom,
% 9.17/5.33 ! [A: multis2468970476368604999at_nat] :
% 9.17/5.33 ( ( minus_4286766774447292334at_nat @ zero_z1048942125864253310at_nat @ A )
% 9.17/5.33 = zero_z1048942125864253310at_nat ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1487_zero__diff,axiom,
% 9.17/5.33 ! [A: nat] :
% 9.17/5.33 ( ( minus_minus_nat @ zero_zero_nat @ A )
% 9.17/5.33 = zero_zero_nat ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1488_diff__0__right,axiom,
% 9.17/5.33 ! [A: code_integer] :
% 9.17/5.33 ( ( minus_8373710615458151222nteger @ A @ zero_z3403309356797280102nteger )
% 9.17/5.33 = A ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1489_diff__0__right,axiom,
% 9.17/5.33 ! [A: rat] :
% 9.17/5.33 ( ( minus_minus_rat @ A @ zero_zero_rat )
% 9.17/5.33 = A ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1490_diff__0__right,axiom,
% 9.17/5.33 ! [A: int] :
% 9.17/5.33 ( ( minus_minus_int @ A @ zero_zero_int )
% 9.17/5.33 = A ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1491_diff__self,axiom,
% 9.17/5.33 ! [A: code_integer] :
% 9.17/5.33 ( ( minus_8373710615458151222nteger @ A @ A )
% 9.17/5.33 = zero_z3403309356797280102nteger ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1492_diff__self,axiom,
% 9.17/5.33 ! [A: rat] :
% 9.17/5.33 ( ( minus_minus_rat @ A @ A )
% 9.17/5.33 = zero_zero_rat ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1493_diff__self,axiom,
% 9.17/5.33 ! [A: int] :
% 9.17/5.33 ( ( minus_minus_int @ A @ A )
% 9.17/5.33 = zero_zero_int ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1494_mult_Oright__neutral,axiom,
% 9.17/5.33 ! [A: code_integer] :
% 9.17/5.33 ( ( times_3573771949741848930nteger @ A @ one_one_Code_integer )
% 9.17/5.33 = A ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1495_mult_Oright__neutral,axiom,
% 9.17/5.33 ! [A: assn] :
% 9.17/5.33 ( ( times_times_assn @ A @ one_one_assn )
% 9.17/5.33 = A ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1496_mult_Oright__neutral,axiom,
% 9.17/5.33 ! [A: rat] :
% 9.17/5.33 ( ( times_times_rat @ A @ one_one_rat )
% 9.17/5.33 = A ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1497_mult_Oright__neutral,axiom,
% 9.17/5.33 ! [A: nat] :
% 9.17/5.33 ( ( times_times_nat @ A @ one_one_nat )
% 9.17/5.33 = A ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1498_mult_Oright__neutral,axiom,
% 9.17/5.33 ! [A: int] :
% 9.17/5.33 ( ( times_times_int @ A @ one_one_int )
% 9.17/5.33 = A ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1499_mult__1,axiom,
% 9.17/5.33 ! [A: code_integer] :
% 9.17/5.33 ( ( times_3573771949741848930nteger @ one_one_Code_integer @ A )
% 9.17/5.33 = A ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1500_mult__1,axiom,
% 9.17/5.33 ! [A: assn] :
% 9.17/5.33 ( ( times_times_assn @ one_one_assn @ A )
% 9.17/5.33 = A ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1501_mult__1,axiom,
% 9.17/5.33 ! [A: rat] :
% 9.17/5.33 ( ( times_times_rat @ one_one_rat @ A )
% 9.17/5.33 = A ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1502_mult__1,axiom,
% 9.17/5.33 ! [A: nat] :
% 9.17/5.33 ( ( times_times_nat @ one_one_nat @ A )
% 9.17/5.33 = A ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1503_mult__1,axiom,
% 9.17/5.33 ! [A: int] :
% 9.17/5.33 ( ( times_times_int @ one_one_int @ A )
% 9.17/5.33 = A ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1504_add__diff__cancel__right_H,axiom,
% 9.17/5.33 ! [A: multis2468970476368604999at_nat,B: multis2468970476368604999at_nat] :
% 9.17/5.33 ( ( minus_4286766774447292334at_nat @ ( plus_p7104986032573967614at_nat @ A @ B ) @ B )
% 9.17/5.33 = A ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1505_add__diff__cancel__right_H,axiom,
% 9.17/5.33 ! [A: code_integer,B: code_integer] :
% 9.17/5.33 ( ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ B )
% 9.17/5.33 = A ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1506_add__diff__cancel__right_H,axiom,
% 9.17/5.33 ! [A: rat,B: rat] :
% 9.17/5.33 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 9.17/5.33 = A ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1507_add__diff__cancel__right_H,axiom,
% 9.17/5.33 ! [A: nat,B: nat] :
% 9.17/5.33 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 9.17/5.33 = A ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1508_add__diff__cancel__right_H,axiom,
% 9.17/5.33 ! [A: int,B: int] :
% 9.17/5.33 ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
% 9.17/5.33 = A ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1509_add__diff__cancel__right,axiom,
% 9.17/5.33 ! [A: multis2468970476368604999at_nat,C: multis2468970476368604999at_nat,B: multis2468970476368604999at_nat] :
% 9.17/5.33 ( ( minus_4286766774447292334at_nat @ ( plus_p7104986032573967614at_nat @ A @ C ) @ ( plus_p7104986032573967614at_nat @ B @ C ) )
% 9.17/5.33 = ( minus_4286766774447292334at_nat @ A @ B ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1510_add__diff__cancel__right,axiom,
% 9.17/5.33 ! [A: code_integer,C: code_integer,B: code_integer] :
% 9.17/5.33 ( ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A @ C ) @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 9.17/5.33 = ( minus_8373710615458151222nteger @ A @ B ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1511_add__diff__cancel__right,axiom,
% 9.17/5.33 ! [A: rat,C: rat,B: rat] :
% 9.17/5.33 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 9.17/5.33 = ( minus_minus_rat @ A @ B ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1512_add__diff__cancel__right,axiom,
% 9.17/5.33 ! [A: nat,C: nat,B: nat] :
% 9.17/5.33 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 9.17/5.33 = ( minus_minus_nat @ A @ B ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1513_add__diff__cancel__right,axiom,
% 9.17/5.33 ! [A: int,C: int,B: int] :
% 9.17/5.33 ( ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 9.17/5.33 = ( minus_minus_int @ A @ B ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1514_add__diff__cancel__left_H,axiom,
% 9.17/5.33 ! [A: multis2468970476368604999at_nat,B: multis2468970476368604999at_nat] :
% 9.17/5.33 ( ( minus_4286766774447292334at_nat @ ( plus_p7104986032573967614at_nat @ A @ B ) @ A )
% 9.17/5.33 = B ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1515_add__diff__cancel__left_H,axiom,
% 9.17/5.33 ! [A: code_integer,B: code_integer] :
% 9.17/5.33 ( ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ A )
% 9.17/5.33 = B ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1516_add__diff__cancel__left_H,axiom,
% 9.17/5.33 ! [A: rat,B: rat] :
% 9.17/5.33 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ A )
% 9.17/5.33 = B ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1517_add__diff__cancel__left_H,axiom,
% 9.17/5.33 ! [A: nat,B: nat] :
% 9.17/5.33 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ A )
% 9.17/5.33 = B ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1518_add__diff__cancel__left_H,axiom,
% 9.17/5.33 ! [A: int,B: int] :
% 9.17/5.33 ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ A )
% 9.17/5.33 = B ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1519_add__diff__cancel__left,axiom,
% 9.17/5.33 ! [C: multis2468970476368604999at_nat,A: multis2468970476368604999at_nat,B: multis2468970476368604999at_nat] :
% 9.17/5.33 ( ( minus_4286766774447292334at_nat @ ( plus_p7104986032573967614at_nat @ C @ A ) @ ( plus_p7104986032573967614at_nat @ C @ B ) )
% 9.17/5.33 = ( minus_4286766774447292334at_nat @ A @ B ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1520_add__diff__cancel__left,axiom,
% 9.17/5.33 ! [C: code_integer,A: code_integer,B: code_integer] :
% 9.17/5.33 ( ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ C @ A ) @ ( plus_p5714425477246183910nteger @ C @ B ) )
% 9.17/5.33 = ( minus_8373710615458151222nteger @ A @ B ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1521_add__diff__cancel__left,axiom,
% 9.17/5.33 ! [C: rat,A: rat,B: rat] :
% 9.17/5.33 ( ( minus_minus_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 9.17/5.33 = ( minus_minus_rat @ A @ B ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1522_add__diff__cancel__left,axiom,
% 9.17/5.33 ! [C: nat,A: nat,B: nat] :
% 9.17/5.33 ( ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 9.17/5.33 = ( minus_minus_nat @ A @ B ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1523_add__diff__cancel__left,axiom,
% 9.17/5.33 ! [C: int,A: int,B: int] :
% 9.17/5.33 ( ( minus_minus_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 9.17/5.33 = ( minus_minus_int @ A @ B ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1524_diff__add__cancel,axiom,
% 9.17/5.33 ! [A: code_integer,B: code_integer] :
% 9.17/5.33 ( ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ B )
% 9.17/5.33 = A ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1525_diff__add__cancel,axiom,
% 9.17/5.33 ! [A: rat,B: rat] :
% 9.17/5.33 ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ B )
% 9.17/5.33 = A ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1526_diff__add__cancel,axiom,
% 9.17/5.33 ! [A: int,B: int] :
% 9.17/5.33 ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
% 9.17/5.33 = A ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1527_add__diff__cancel,axiom,
% 9.17/5.33 ! [A: code_integer,B: code_integer] :
% 9.17/5.33 ( ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ B )
% 9.17/5.33 = A ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1528_add__diff__cancel,axiom,
% 9.17/5.33 ! [A: rat,B: rat] :
% 9.17/5.33 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 9.17/5.33 = A ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1529_add__diff__cancel,axiom,
% 9.17/5.33 ! [A: int,B: int] :
% 9.17/5.33 ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
% 9.17/5.33 = A ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1530_minus__diff__eq,axiom,
% 9.17/5.33 ! [A: int,B: int] :
% 9.17/5.33 ( ( uminus_uminus_int @ ( minus_minus_int @ A @ B ) )
% 9.17/5.33 = ( minus_minus_int @ B @ A ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1531_minus__diff__eq,axiom,
% 9.17/5.33 ! [A: code_integer,B: code_integer] :
% 9.17/5.33 ( ( uminus1351360451143612070nteger @ ( minus_8373710615458151222nteger @ A @ B ) )
% 9.17/5.33 = ( minus_8373710615458151222nteger @ B @ A ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1532_minus__diff__eq,axiom,
% 9.17/5.33 ! [A: rat,B: rat] :
% 9.17/5.33 ( ( uminus_uminus_rat @ ( minus_minus_rat @ A @ B ) )
% 9.17/5.33 = ( minus_minus_rat @ B @ A ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1533_Nat_Oadd__diff__assoc,axiom,
% 9.17/5.33 ! [K: nat,J: nat,I: nat] :
% 9.17/5.33 ( ( ord_less_eq_nat @ K @ J )
% 9.17/5.33 => ( ( plus_plus_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 9.17/5.33 = ( minus_minus_nat @ ( plus_plus_nat @ I @ J ) @ K ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1534_Nat_Oadd__diff__assoc2,axiom,
% 9.17/5.33 ! [K: nat,J: nat,I: nat] :
% 9.17/5.33 ( ( ord_less_eq_nat @ K @ J )
% 9.17/5.33 => ( ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I )
% 9.17/5.33 = ( minus_minus_nat @ ( plus_plus_nat @ J @ I ) @ K ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1535_Nat_Odiff__diff__right,axiom,
% 9.17/5.33 ! [K: nat,J: nat,I: nat] :
% 9.17/5.33 ( ( ord_less_eq_nat @ K @ J )
% 9.17/5.33 => ( ( minus_minus_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 9.17/5.33 = ( minus_minus_nat @ ( plus_plus_nat @ I @ K ) @ J ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1536_zle__add1__eq__le,axiom,
% 9.17/5.33 ! [W: int,Z: int] :
% 9.17/5.33 ( ( ord_less_int @ W @ ( plus_plus_int @ Z @ one_one_int ) )
% 9.17/5.33 = ( ord_less_eq_int @ W @ Z ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1537_diff__ge__0__iff__ge,axiom,
% 9.17/5.33 ! [A: code_integer,B: code_integer] :
% 9.17/5.33 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( minus_8373710615458151222nteger @ A @ B ) )
% 9.17/5.33 = ( ord_le3102999989581377725nteger @ B @ A ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1538_diff__ge__0__iff__ge,axiom,
% 9.17/5.33 ! [A: rat,B: rat] :
% 9.17/5.33 ( ( ord_less_eq_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 9.17/5.33 = ( ord_less_eq_rat @ B @ A ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1539_diff__ge__0__iff__ge,axiom,
% 9.17/5.33 ! [A: int,B: int] :
% 9.17/5.33 ( ( ord_less_eq_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 9.17/5.33 = ( ord_less_eq_int @ B @ A ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1540_zero__comp__diff__simps_I1_J,axiom,
% 9.17/5.33 ! [A: code_integer,B: code_integer] :
% 9.17/5.33 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( minus_8373710615458151222nteger @ A @ B ) )
% 9.17/5.33 = ( ord_le3102999989581377725nteger @ B @ A ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1541_zero__comp__diff__simps_I1_J,axiom,
% 9.17/5.33 ! [A: rat,B: rat] :
% 9.17/5.33 ( ( ord_less_eq_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 9.17/5.33 = ( ord_less_eq_rat @ B @ A ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1542_zero__comp__diff__simps_I1_J,axiom,
% 9.17/5.33 ! [A: int,B: int] :
% 9.17/5.33 ( ( ord_less_eq_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 9.17/5.33 = ( ord_less_eq_int @ B @ A ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1543_diff__gt__0__iff__gt,axiom,
% 9.17/5.33 ! [A: code_integer,B: code_integer] :
% 9.17/5.33 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( minus_8373710615458151222nteger @ A @ B ) )
% 9.17/5.33 = ( ord_le6747313008572928689nteger @ B @ A ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1544_diff__gt__0__iff__gt,axiom,
% 9.17/5.33 ! [A: rat,B: rat] :
% 9.17/5.33 ( ( ord_less_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 9.17/5.33 = ( ord_less_rat @ B @ A ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1545_diff__gt__0__iff__gt,axiom,
% 9.17/5.33 ! [A: int,B: int] :
% 9.17/5.33 ( ( ord_less_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 9.17/5.33 = ( ord_less_int @ B @ A ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1546_zero__comp__diff__simps_I2_J,axiom,
% 9.17/5.33 ! [A: code_integer,B: code_integer] :
% 9.17/5.33 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( minus_8373710615458151222nteger @ A @ B ) )
% 9.17/5.33 = ( ord_le6747313008572928689nteger @ B @ A ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1547_zero__comp__diff__simps_I2_J,axiom,
% 9.17/5.33 ! [A: rat,B: rat] :
% 9.17/5.33 ( ( ord_less_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 9.17/5.33 = ( ord_less_rat @ B @ A ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1548_zero__comp__diff__simps_I2_J,axiom,
% 9.17/5.33 ! [A: int,B: int] :
% 9.17/5.33 ( ( ord_less_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 9.17/5.33 = ( ord_less_int @ B @ A ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1549_le__add__diff__inverse,axiom,
% 9.17/5.33 ! [B: code_integer,A: code_integer] :
% 9.17/5.33 ( ( ord_le3102999989581377725nteger @ B @ A )
% 9.17/5.33 => ( ( plus_p5714425477246183910nteger @ B @ ( minus_8373710615458151222nteger @ A @ B ) )
% 9.17/5.33 = A ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1550_le__add__diff__inverse,axiom,
% 9.17/5.33 ! [B: rat,A: rat] :
% 9.17/5.33 ( ( ord_less_eq_rat @ B @ A )
% 9.17/5.33 => ( ( plus_plus_rat @ B @ ( minus_minus_rat @ A @ B ) )
% 9.17/5.33 = A ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1551_le__add__diff__inverse,axiom,
% 9.17/5.33 ! [B: nat,A: nat] :
% 9.17/5.33 ( ( ord_less_eq_nat @ B @ A )
% 9.17/5.33 => ( ( plus_plus_nat @ B @ ( minus_minus_nat @ A @ B ) )
% 9.17/5.33 = A ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1552_le__add__diff__inverse,axiom,
% 9.17/5.33 ! [B: int,A: int] :
% 9.17/5.33 ( ( ord_less_eq_int @ B @ A )
% 9.17/5.33 => ( ( plus_plus_int @ B @ ( minus_minus_int @ A @ B ) )
% 9.17/5.33 = A ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1553_le__add__diff__inverse2,axiom,
% 9.17/5.33 ! [B: code_integer,A: code_integer] :
% 9.17/5.33 ( ( ord_le3102999989581377725nteger @ B @ A )
% 9.17/5.33 => ( ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ B )
% 9.17/5.33 = A ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1554_le__add__diff__inverse2,axiom,
% 9.17/5.33 ! [B: rat,A: rat] :
% 9.17/5.33 ( ( ord_less_eq_rat @ B @ A )
% 9.17/5.33 => ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ B )
% 9.17/5.33 = A ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1555_le__add__diff__inverse2,axiom,
% 9.17/5.33 ! [B: nat,A: nat] :
% 9.17/5.33 ( ( ord_less_eq_nat @ B @ A )
% 9.17/5.33 => ( ( plus_plus_nat @ ( minus_minus_nat @ A @ B ) @ B )
% 9.17/5.33 = A ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1556_le__add__diff__inverse2,axiom,
% 9.17/5.33 ! [B: int,A: int] :
% 9.17/5.33 ( ( ord_less_eq_int @ B @ A )
% 9.17/5.33 => ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
% 9.17/5.33 = A ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1557_mult__cancel__left1,axiom,
% 9.17/5.33 ! [C: code_integer,B: code_integer] :
% 9.17/5.33 ( ( C
% 9.17/5.33 = ( times_3573771949741848930nteger @ C @ B ) )
% 9.17/5.33 = ( ( C = zero_z3403309356797280102nteger )
% 9.17/5.33 | ( B = one_one_Code_integer ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1558_mult__cancel__left1,axiom,
% 9.17/5.33 ! [C: rat,B: rat] :
% 9.17/5.33 ( ( C
% 9.17/5.33 = ( times_times_rat @ C @ B ) )
% 9.17/5.33 = ( ( C = zero_zero_rat )
% 9.17/5.33 | ( B = one_one_rat ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1559_mult__cancel__left1,axiom,
% 9.17/5.33 ! [C: int,B: int] :
% 9.17/5.33 ( ( C
% 9.17/5.33 = ( times_times_int @ C @ B ) )
% 9.17/5.33 = ( ( C = zero_zero_int )
% 9.17/5.33 | ( B = one_one_int ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1560_mult__cancel__left2,axiom,
% 9.17/5.33 ! [C: code_integer,A: code_integer] :
% 9.17/5.33 ( ( ( times_3573771949741848930nteger @ C @ A )
% 9.17/5.33 = C )
% 9.17/5.33 = ( ( C = zero_z3403309356797280102nteger )
% 9.17/5.33 | ( A = one_one_Code_integer ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1561_mult__cancel__left2,axiom,
% 9.17/5.33 ! [C: rat,A: rat] :
% 9.17/5.33 ( ( ( times_times_rat @ C @ A )
% 9.17/5.33 = C )
% 9.17/5.33 = ( ( C = zero_zero_rat )
% 9.17/5.33 | ( A = one_one_rat ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1562_mult__cancel__left2,axiom,
% 9.17/5.33 ! [C: int,A: int] :
% 9.17/5.33 ( ( ( times_times_int @ C @ A )
% 9.17/5.33 = C )
% 9.17/5.33 = ( ( C = zero_zero_int )
% 9.17/5.33 | ( A = one_one_int ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1563_mult__cancel__right1,axiom,
% 9.17/5.33 ! [C: code_integer,B: code_integer] :
% 9.17/5.33 ( ( C
% 9.17/5.33 = ( times_3573771949741848930nteger @ B @ C ) )
% 9.17/5.33 = ( ( C = zero_z3403309356797280102nteger )
% 9.17/5.33 | ( B = one_one_Code_integer ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1564_mult__cancel__right1,axiom,
% 9.17/5.33 ! [C: rat,B: rat] :
% 9.17/5.33 ( ( C
% 9.17/5.33 = ( times_times_rat @ B @ C ) )
% 9.17/5.33 = ( ( C = zero_zero_rat )
% 9.17/5.33 | ( B = one_one_rat ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1565_mult__cancel__right1,axiom,
% 9.17/5.33 ! [C: int,B: int] :
% 9.17/5.33 ( ( C
% 9.17/5.33 = ( times_times_int @ B @ C ) )
% 9.17/5.33 = ( ( C = zero_zero_int )
% 9.17/5.33 | ( B = one_one_int ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1566_mult__cancel__right2,axiom,
% 9.17/5.33 ! [A: code_integer,C: code_integer] :
% 9.17/5.33 ( ( ( times_3573771949741848930nteger @ A @ C )
% 9.17/5.33 = C )
% 9.17/5.33 = ( ( C = zero_z3403309356797280102nteger )
% 9.17/5.33 | ( A = one_one_Code_integer ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1567_mult__cancel__right2,axiom,
% 9.17/5.33 ! [A: rat,C: rat] :
% 9.17/5.33 ( ( ( times_times_rat @ A @ C )
% 9.17/5.33 = C )
% 9.17/5.33 = ( ( C = zero_zero_rat )
% 9.17/5.33 | ( A = one_one_rat ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1568_mult__cancel__right2,axiom,
% 9.17/5.33 ! [A: int,C: int] :
% 9.17/5.33 ( ( ( times_times_int @ A @ C )
% 9.17/5.33 = C )
% 9.17/5.33 = ( ( C = zero_zero_int )
% 9.17/5.33 | ( A = one_one_int ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1569_diff__add__zero,axiom,
% 9.17/5.33 ! [A: multis2468970476368604999at_nat,B: multis2468970476368604999at_nat] :
% 9.17/5.33 ( ( minus_4286766774447292334at_nat @ A @ ( plus_p7104986032573967614at_nat @ A @ B ) )
% 9.17/5.33 = zero_z1048942125864253310at_nat ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1570_diff__add__zero,axiom,
% 9.17/5.33 ! [A: nat,B: nat] :
% 9.17/5.33 ( ( minus_minus_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 9.17/5.33 = zero_zero_nat ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1571_diff__numeral__special_I9_J,axiom,
% 9.17/5.33 ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ one_one_Code_integer )
% 9.17/5.33 = zero_z3403309356797280102nteger ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1572_diff__numeral__special_I9_J,axiom,
% 9.17/5.33 ( ( minus_minus_rat @ one_one_rat @ one_one_rat )
% 9.17/5.33 = zero_zero_rat ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1573_diff__numeral__special_I9_J,axiom,
% 9.17/5.33 ( ( minus_minus_int @ one_one_int @ one_one_int )
% 9.17/5.33 = zero_zero_int ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1574_diff__0,axiom,
% 9.17/5.33 ! [A: int] :
% 9.17/5.33 ( ( minus_minus_int @ zero_zero_int @ A )
% 9.17/5.33 = ( uminus_uminus_int @ A ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1575_diff__0,axiom,
% 9.17/5.33 ! [A: code_integer] :
% 9.17/5.33 ( ( minus_8373710615458151222nteger @ zero_z3403309356797280102nteger @ A )
% 9.17/5.33 = ( uminus1351360451143612070nteger @ A ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1576_diff__0,axiom,
% 9.17/5.33 ! [A: rat] :
% 9.17/5.33 ( ( minus_minus_rat @ zero_zero_rat @ A )
% 9.17/5.33 = ( uminus_uminus_rat @ A ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1577_mult__minus1,axiom,
% 9.17/5.33 ! [Z: int] :
% 9.17/5.33 ( ( times_times_int @ ( uminus_uminus_int @ one_one_int ) @ Z )
% 9.17/5.33 = ( uminus_uminus_int @ Z ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1578_mult__minus1,axiom,
% 9.17/5.33 ! [Z: code_integer] :
% 9.17/5.33 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ Z )
% 9.17/5.33 = ( uminus1351360451143612070nteger @ Z ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1579_mult__minus1,axiom,
% 9.17/5.33 ! [Z: rat] :
% 9.17/5.33 ( ( times_times_rat @ ( uminus_uminus_rat @ one_one_rat ) @ Z )
% 9.17/5.33 = ( uminus_uminus_rat @ Z ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1580_mult__minus1__right,axiom,
% 9.17/5.33 ! [Z: int] :
% 9.17/5.33 ( ( times_times_int @ Z @ ( uminus_uminus_int @ one_one_int ) )
% 9.17/5.33 = ( uminus_uminus_int @ Z ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1581_mult__minus1__right,axiom,
% 9.17/5.33 ! [Z: code_integer] :
% 9.17/5.33 ( ( times_3573771949741848930nteger @ Z @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.17/5.33 = ( uminus1351360451143612070nteger @ Z ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1582_mult__minus1__right,axiom,
% 9.17/5.33 ! [Z: rat] :
% 9.17/5.33 ( ( times_times_rat @ Z @ ( uminus_uminus_rat @ one_one_rat ) )
% 9.17/5.33 = ( uminus_uminus_rat @ Z ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1583_uminus__add__conv__diff,axiom,
% 9.17/5.33 ! [A: int,B: int] :
% 9.17/5.33 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B )
% 9.17/5.33 = ( minus_minus_int @ B @ A ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1584_uminus__add__conv__diff,axiom,
% 9.17/5.33 ! [A: code_integer,B: code_integer] :
% 9.17/5.33 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 9.17/5.33 = ( minus_8373710615458151222nteger @ B @ A ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1585_uminus__add__conv__diff,axiom,
% 9.17/5.33 ! [A: rat,B: rat] :
% 9.17/5.33 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ B )
% 9.17/5.33 = ( minus_minus_rat @ B @ A ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1586_diff__minus__eq__add,axiom,
% 9.17/5.33 ! [A: int,B: int] :
% 9.17/5.33 ( ( minus_minus_int @ A @ ( uminus_uminus_int @ B ) )
% 9.17/5.33 = ( plus_plus_int @ A @ B ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1587_diff__minus__eq__add,axiom,
% 9.17/5.33 ! [A: code_integer,B: code_integer] :
% 9.17/5.33 ( ( minus_8373710615458151222nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 9.17/5.33 = ( plus_p5714425477246183910nteger @ A @ B ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1588_diff__minus__eq__add,axiom,
% 9.17/5.33 ! [A: rat,B: rat] :
% 9.17/5.33 ( ( minus_minus_rat @ A @ ( uminus_uminus_rat @ B ) )
% 9.17/5.33 = ( plus_plus_rat @ A @ B ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1589_diff__numeral__special_I12_J,axiom,
% 9.17/5.33 ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ one_one_int ) )
% 9.17/5.33 = zero_zero_int ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1590_diff__numeral__special_I12_J,axiom,
% 9.17/5.33 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.17/5.33 = zero_z3403309356797280102nteger ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1591_diff__numeral__special_I12_J,axiom,
% 9.17/5.33 ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 9.17/5.33 = zero_zero_rat ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1592_le__imp__0__less,axiom,
% 9.17/5.33 ! [Z: int] :
% 9.17/5.33 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 9.17/5.33 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ Z ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1593_q__pos__lemma,axiom,
% 9.17/5.33 ! [B3: int,Q4: int,R6: int] :
% 9.17/5.33 ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B3 @ Q4 ) @ R6 ) )
% 9.17/5.33 => ( ( ord_less_int @ R6 @ B3 )
% 9.17/5.33 => ( ( ord_less_int @ zero_zero_int @ B3 )
% 9.17/5.33 => ( ord_less_eq_int @ zero_zero_int @ Q4 ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1594_zdiv__mono2__lemma,axiom,
% 9.17/5.33 ! [B: int,Q3: int,R2: int,B3: int,Q4: int,R6: int] :
% 9.17/5.33 ( ( ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R2 )
% 9.17/5.33 = ( plus_plus_int @ ( times_times_int @ B3 @ Q4 ) @ R6 ) )
% 9.17/5.33 => ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B3 @ Q4 ) @ R6 ) )
% 9.17/5.33 => ( ( ord_less_int @ R6 @ B3 )
% 9.17/5.33 => ( ( ord_less_eq_int @ zero_zero_int @ R2 )
% 9.17/5.33 => ( ( ord_less_int @ zero_zero_int @ B3 )
% 9.17/5.33 => ( ( ord_less_eq_int @ B3 @ B )
% 9.17/5.33 => ( ord_less_eq_int @ Q3 @ Q4 ) ) ) ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1595_zdiv__mono2__neg__lemma,axiom,
% 9.17/5.33 ! [B: int,Q3: int,R2: int,B3: int,Q4: int,R6: int] :
% 9.17/5.33 ( ( ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R2 )
% 9.17/5.33 = ( plus_plus_int @ ( times_times_int @ B3 @ Q4 ) @ R6 ) )
% 9.17/5.33 => ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ B3 @ Q4 ) @ R6 ) @ zero_zero_int )
% 9.17/5.33 => ( ( ord_less_int @ R2 @ B )
% 9.17/5.33 => ( ( ord_less_eq_int @ zero_zero_int @ R6 )
% 9.17/5.33 => ( ( ord_less_int @ zero_zero_int @ B3 )
% 9.17/5.33 => ( ( ord_less_eq_int @ B3 @ B )
% 9.17/5.33 => ( ord_less_eq_int @ Q4 @ Q3 ) ) ) ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1596_unique__quotient__lemma,axiom,
% 9.17/5.33 ! [B: int,Q4: int,R6: int,Q3: int,R2: int] :
% 9.17/5.33 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ Q4 ) @ R6 ) @ ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R2 ) )
% 9.17/5.33 => ( ( ord_less_eq_int @ zero_zero_int @ R6 )
% 9.17/5.33 => ( ( ord_less_int @ R6 @ B )
% 9.17/5.33 => ( ( ord_less_int @ R2 @ B )
% 9.17/5.33 => ( ord_less_eq_int @ Q4 @ Q3 ) ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1597_unique__quotient__lemma__neg,axiom,
% 9.17/5.33 ! [B: int,Q4: int,R6: int,Q3: int,R2: int] :
% 9.17/5.33 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ Q4 ) @ R6 ) @ ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R2 ) )
% 9.17/5.33 => ( ( ord_less_eq_int @ R2 @ zero_zero_int )
% 9.17/5.33 => ( ( ord_less_int @ B @ R2 )
% 9.17/5.33 => ( ( ord_less_int @ B @ R6 )
% 9.17/5.33 => ( ord_less_eq_int @ Q3 @ Q4 ) ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1598_int__ge__induct,axiom,
% 9.17/5.33 ! [K: int,I: int,P: int > $o] :
% 9.17/5.33 ( ( ord_less_eq_int @ K @ I )
% 9.17/5.33 => ( ( P @ K )
% 9.17/5.33 => ( ! [I2: int] :
% 9.17/5.33 ( ( ord_less_eq_int @ K @ I2 )
% 9.17/5.33 => ( ( P @ I2 )
% 9.17/5.33 => ( P @ ( plus_plus_int @ I2 @ one_one_int ) ) ) )
% 9.17/5.33 => ( P @ I ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1599_int__induct,axiom,
% 9.17/5.33 ! [P: int > $o,K: int,I: int] :
% 9.17/5.33 ( ( P @ K )
% 9.17/5.33 => ( ! [I2: int] :
% 9.17/5.33 ( ( ord_less_eq_int @ K @ I2 )
% 9.17/5.33 => ( ( P @ I2 )
% 9.17/5.33 => ( P @ ( plus_plus_int @ I2 @ one_one_int ) ) ) )
% 9.17/5.33 => ( ! [I2: int] :
% 9.17/5.33 ( ( ord_less_eq_int @ I2 @ K )
% 9.17/5.33 => ( ( P @ I2 )
% 9.17/5.33 => ( P @ ( minus_minus_int @ I2 @ one_one_int ) ) ) )
% 9.17/5.33 => ( P @ I ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1600_zless__imp__add1__zle,axiom,
% 9.17/5.33 ! [W: int,Z: int] :
% 9.17/5.33 ( ( ord_less_int @ W @ Z )
% 9.17/5.33 => ( ord_less_eq_int @ ( plus_plus_int @ W @ one_one_int ) @ Z ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1601_add1__zle__eq,axiom,
% 9.17/5.33 ! [W: int,Z: int] :
% 9.17/5.33 ( ( ord_less_eq_int @ ( plus_plus_int @ W @ one_one_int ) @ Z )
% 9.17/5.33 = ( ord_less_int @ W @ Z ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1602_nat__eq__add__iff1,axiom,
% 9.17/5.33 ! [J: nat,I: nat,U: nat,M2: nat,N2: nat] :
% 9.17/5.33 ( ( ord_less_eq_nat @ J @ I )
% 9.17/5.33 => ( ( ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M2 )
% 9.17/5.33 = ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 9.17/5.33 = ( ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M2 )
% 9.17/5.33 = N2 ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1603_nat__eq__add__iff2,axiom,
% 9.17/5.33 ! [I: nat,J: nat,U: nat,M2: nat,N2: nat] :
% 9.17/5.33 ( ( ord_less_eq_nat @ I @ J )
% 9.17/5.33 => ( ( ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M2 )
% 9.17/5.33 = ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 9.17/5.33 = ( M2
% 9.17/5.33 = ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N2 ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1604_nat__le__add__iff1,axiom,
% 9.17/5.33 ! [J: nat,I: nat,U: nat,M2: nat,N2: nat] :
% 9.17/5.33 ( ( ord_less_eq_nat @ J @ I )
% 9.17/5.33 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M2 ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 9.17/5.33 = ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M2 ) @ N2 ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1605_nat__le__add__iff2,axiom,
% 9.17/5.33 ! [I: nat,J: nat,U: nat,M2: nat,N2: nat] :
% 9.17/5.33 ( ( ord_less_eq_nat @ I @ J )
% 9.17/5.33 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M2 ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 9.17/5.33 = ( ord_less_eq_nat @ M2 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N2 ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1606_nat__diff__add__eq1,axiom,
% 9.17/5.33 ! [J: nat,I: nat,U: nat,M2: nat,N2: nat] :
% 9.17/5.33 ( ( ord_less_eq_nat @ J @ I )
% 9.17/5.33 => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M2 ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 9.17/5.33 = ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M2 ) @ N2 ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1607_nat__diff__add__eq2,axiom,
% 9.17/5.33 ! [I: nat,J: nat,U: nat,M2: nat,N2: nat] :
% 9.17/5.33 ( ( ord_less_eq_nat @ I @ J )
% 9.17/5.33 => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M2 ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 9.17/5.33 = ( minus_minus_nat @ M2 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N2 ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1608_bounded__Max__nat,axiom,
% 9.17/5.33 ! [P: nat > $o,X: nat,M3: nat] :
% 9.17/5.33 ( ( P @ X )
% 9.17/5.33 => ( ! [X4: nat] :
% 9.17/5.33 ( ( P @ X4 )
% 9.17/5.33 => ( ord_less_eq_nat @ X4 @ M3 ) )
% 9.17/5.33 => ~ ! [M5: nat] :
% 9.17/5.33 ( ( P @ M5 )
% 9.17/5.33 => ~ ! [X8: nat] :
% 9.17/5.33 ( ( P @ X8 )
% 9.17/5.33 => ( ord_less_eq_nat @ X8 @ M5 ) ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1609_subset__Collect__conv,axiom,
% 9.17/5.33 ! [S2: set_list_nat,P: list_nat > $o] :
% 9.17/5.33 ( ( ord_le6045566169113846134st_nat @ S2 @ ( collect_list_nat @ P ) )
% 9.17/5.33 = ( ! [X3: list_nat] :
% 9.17/5.33 ( ( member_list_nat @ X3 @ S2 )
% 9.17/5.33 => ( P @ X3 ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1610_subset__Collect__conv,axiom,
% 9.17/5.33 ! [S2: set_nat,P: nat > $o] :
% 9.17/5.33 ( ( ord_less_eq_set_nat @ S2 @ ( collect_nat @ P ) )
% 9.17/5.33 = ( ! [X3: nat] :
% 9.17/5.33 ( ( member_nat @ X3 @ S2 )
% 9.17/5.33 => ( P @ X3 ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1611_cancel__ab__semigroup__add__class_Odiff__right__commute,axiom,
% 9.17/5.33 ! [A: code_integer,C: code_integer,B: code_integer] :
% 9.17/5.33 ( ( minus_8373710615458151222nteger @ ( minus_8373710615458151222nteger @ A @ C ) @ B )
% 9.17/5.33 = ( minus_8373710615458151222nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1612_cancel__ab__semigroup__add__class_Odiff__right__commute,axiom,
% 9.17/5.33 ! [A: rat,C: rat,B: rat] :
% 9.17/5.33 ( ( minus_minus_rat @ ( minus_minus_rat @ A @ C ) @ B )
% 9.17/5.33 = ( minus_minus_rat @ ( minus_minus_rat @ A @ B ) @ C ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1613_cancel__ab__semigroup__add__class_Odiff__right__commute,axiom,
% 9.17/5.33 ! [A: nat,C: nat,B: nat] :
% 9.17/5.33 ( ( minus_minus_nat @ ( minus_minus_nat @ A @ C ) @ B )
% 9.17/5.33 = ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1614_cancel__ab__semigroup__add__class_Odiff__right__commute,axiom,
% 9.17/5.33 ! [A: int,C: int,B: int] :
% 9.17/5.33 ( ( minus_minus_int @ ( minus_minus_int @ A @ C ) @ B )
% 9.17/5.33 = ( minus_minus_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1615_ab__semigroup__mult__class_Omult_Oleft__commute,axiom,
% 9.17/5.33 ! [B: assn,A: assn,C: assn] :
% 9.17/5.33 ( ( times_times_assn @ B @ ( times_times_assn @ A @ C ) )
% 9.17/5.33 = ( times_times_assn @ A @ ( times_times_assn @ B @ C ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1616_ab__semigroup__mult__class_Omult_Oleft__commute,axiom,
% 9.17/5.33 ! [B: rat,A: rat,C: rat] :
% 9.17/5.33 ( ( times_times_rat @ B @ ( times_times_rat @ A @ C ) )
% 9.17/5.33 = ( times_times_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1617_ab__semigroup__mult__class_Omult_Oleft__commute,axiom,
% 9.17/5.33 ! [B: nat,A: nat,C: nat] :
% 9.17/5.33 ( ( times_times_nat @ B @ ( times_times_nat @ A @ C ) )
% 9.17/5.33 = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1618_ab__semigroup__mult__class_Omult_Oleft__commute,axiom,
% 9.17/5.33 ! [B: int,A: int,C: int] :
% 9.17/5.33 ( ( times_times_int @ B @ ( times_times_int @ A @ C ) )
% 9.17/5.33 = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1619_ab__semigroup__mult__class_Omult_Ocommute,axiom,
% 9.17/5.33 ( times_times_assn
% 9.17/5.33 = ( ^ [A5: assn,B4: assn] : ( times_times_assn @ B4 @ A5 ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1620_ab__semigroup__mult__class_Omult_Ocommute,axiom,
% 9.17/5.33 ( times_times_rat
% 9.17/5.33 = ( ^ [A5: rat,B4: rat] : ( times_times_rat @ B4 @ A5 ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1621_ab__semigroup__mult__class_Omult_Ocommute,axiom,
% 9.17/5.33 ( times_times_nat
% 9.17/5.33 = ( ^ [A5: nat,B4: nat] : ( times_times_nat @ B4 @ A5 ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1622_ab__semigroup__mult__class_Omult_Ocommute,axiom,
% 9.17/5.33 ( times_times_int
% 9.17/5.33 = ( ^ [A5: int,B4: int] : ( times_times_int @ B4 @ A5 ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1623_mult_Oassoc,axiom,
% 9.17/5.33 ! [A: assn,B: assn,C: assn] :
% 9.17/5.33 ( ( times_times_assn @ ( times_times_assn @ A @ B ) @ C )
% 9.17/5.33 = ( times_times_assn @ A @ ( times_times_assn @ B @ C ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1624_mult_Oassoc,axiom,
% 9.17/5.33 ! [A: rat,B: rat,C: rat] :
% 9.17/5.33 ( ( times_times_rat @ ( times_times_rat @ A @ B ) @ C )
% 9.17/5.33 = ( times_times_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1625_mult_Oassoc,axiom,
% 9.17/5.33 ! [A: nat,B: nat,C: nat] :
% 9.17/5.33 ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
% 9.17/5.33 = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1626_mult_Oassoc,axiom,
% 9.17/5.33 ! [A: int,B: int,C: int] :
% 9.17/5.33 ( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
% 9.17/5.33 = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1627_diff__eq__diff__eq,axiom,
% 9.17/5.33 ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 9.17/5.33 ( ( ( minus_8373710615458151222nteger @ A @ B )
% 9.17/5.33 = ( minus_8373710615458151222nteger @ C @ D2 ) )
% 9.17/5.33 => ( ( A = B )
% 9.17/5.33 = ( C = D2 ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1628_diff__eq__diff__eq,axiom,
% 9.17/5.33 ! [A: rat,B: rat,C: rat,D2: rat] :
% 9.17/5.33 ( ( ( minus_minus_rat @ A @ B )
% 9.17/5.33 = ( minus_minus_rat @ C @ D2 ) )
% 9.17/5.33 => ( ( A = B )
% 9.17/5.33 = ( C = D2 ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1629_diff__eq__diff__eq,axiom,
% 9.17/5.33 ! [A: int,B: int,C: int,D2: int] :
% 9.17/5.33 ( ( ( minus_minus_int @ A @ B )
% 9.17/5.33 = ( minus_minus_int @ C @ D2 ) )
% 9.17/5.33 => ( ( A = B )
% 9.17/5.33 = ( C = D2 ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1630_one__integer_Orsp,axiom,
% 9.17/5.33 one_one_int = one_one_int ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1631_int__gr__induct,axiom,
% 9.17/5.33 ! [K: int,I: int,P: int > $o] :
% 9.17/5.33 ( ( ord_less_int @ K @ I )
% 9.17/5.33 => ( ( P @ ( plus_plus_int @ K @ one_one_int ) )
% 9.17/5.33 => ( ! [I2: int] :
% 9.17/5.33 ( ( ord_less_int @ K @ I2 )
% 9.17/5.33 => ( ( P @ I2 )
% 9.17/5.33 => ( P @ ( plus_plus_int @ I2 @ one_one_int ) ) ) )
% 9.17/5.33 => ( P @ I ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1632_zless__add1__eq,axiom,
% 9.17/5.33 ! [W: int,Z: int] :
% 9.17/5.33 ( ( ord_less_int @ W @ ( plus_plus_int @ Z @ one_one_int ) )
% 9.17/5.33 = ( ( ord_less_int @ W @ Z )
% 9.17/5.33 | ( W = Z ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1633_odd__nonzero,axiom,
% 9.17/5.33 ! [Z: int] :
% 9.17/5.33 ( ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z ) @ Z )
% 9.17/5.33 != zero_zero_int ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1634_odd__less__0__iff,axiom,
% 9.17/5.33 ! [Z: int] :
% 9.17/5.33 ( ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z ) @ Z ) @ zero_zero_int )
% 9.17/5.33 = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1635_eq__add__iff1,axiom,
% 9.17/5.33 ! [A: code_integer,E: code_integer,C: code_integer,B: code_integer,D2: code_integer] :
% 9.17/5.33 ( ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ E ) @ C )
% 9.17/5.33 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ E ) @ D2 ) )
% 9.17/5.33 = ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ E ) @ C )
% 9.17/5.33 = D2 ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1636_eq__add__iff1,axiom,
% 9.17/5.33 ! [A: rat,E: rat,C: rat,B: rat,D2: rat] :
% 9.17/5.33 ( ( ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C )
% 9.17/5.33 = ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D2 ) )
% 9.17/5.33 = ( ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E ) @ C )
% 9.17/5.33 = D2 ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1637_eq__add__iff1,axiom,
% 9.17/5.33 ! [A: int,E: int,C: int,B: int,D2: int] :
% 9.17/5.33 ( ( ( plus_plus_int @ ( times_times_int @ A @ E ) @ C )
% 9.17/5.33 = ( plus_plus_int @ ( times_times_int @ B @ E ) @ D2 ) )
% 9.17/5.33 = ( ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E ) @ C )
% 9.17/5.33 = D2 ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1638_eq__add__iff2,axiom,
% 9.17/5.33 ! [A: code_integer,E: code_integer,C: code_integer,B: code_integer,D2: code_integer] :
% 9.17/5.33 ( ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ E ) @ C )
% 9.17/5.33 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ E ) @ D2 ) )
% 9.17/5.33 = ( C
% 9.17/5.33 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ B @ A ) @ E ) @ D2 ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1639_eq__add__iff2,axiom,
% 9.17/5.33 ! [A: rat,E: rat,C: rat,B: rat,D2: rat] :
% 9.17/5.33 ( ( ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C )
% 9.17/5.33 = ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D2 ) )
% 9.17/5.33 = ( C
% 9.17/5.33 = ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E ) @ D2 ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1640_eq__add__iff2,axiom,
% 9.17/5.33 ! [A: int,E: int,C: int,B: int,D2: int] :
% 9.17/5.33 ( ( ( plus_plus_int @ ( times_times_int @ A @ E ) @ C )
% 9.17/5.33 = ( plus_plus_int @ ( times_times_int @ B @ E ) @ D2 ) )
% 9.17/5.33 = ( C
% 9.17/5.33 = ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E ) @ D2 ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1641_square__diff__square__factored,axiom,
% 9.17/5.33 ! [X: code_integer,Y: code_integer] :
% 9.17/5.33 ( ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ X @ X ) @ ( times_3573771949741848930nteger @ Y @ Y ) )
% 9.17/5.33 = ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ X @ Y ) @ ( minus_8373710615458151222nteger @ X @ Y ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1642_square__diff__square__factored,axiom,
% 9.17/5.33 ! [X: rat,Y: rat] :
% 9.17/5.33 ( ( minus_minus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) )
% 9.17/5.33 = ( times_times_rat @ ( plus_plus_rat @ X @ Y ) @ ( minus_minus_rat @ X @ Y ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1643_square__diff__square__factored,axiom,
% 9.17/5.33 ! [X: int,Y: int] :
% 9.17/5.33 ( ( minus_minus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) )
% 9.17/5.33 = ( times_times_int @ ( plus_plus_int @ X @ Y ) @ ( minus_minus_int @ X @ Y ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1644_left__add__mult__distrib,axiom,
% 9.17/5.33 ! [I: nat,U: nat,J: nat,K: nat] :
% 9.17/5.33 ( ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ K ) )
% 9.17/5.33 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ I @ J ) @ U ) @ K ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1645_nat__less__add__iff1,axiom,
% 9.17/5.33 ! [J: nat,I: nat,U: nat,M2: nat,N2: nat] :
% 9.17/5.33 ( ( ord_less_eq_nat @ J @ I )
% 9.17/5.33 => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M2 ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 9.17/5.33 = ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M2 ) @ N2 ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1646_nat__less__add__iff2,axiom,
% 9.17/5.33 ! [I: nat,J: nat,U: nat,M2: nat,N2: nat] :
% 9.17/5.33 ( ( ord_less_eq_nat @ I @ J )
% 9.17/5.33 => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M2 ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 9.17/5.33 = ( ord_less_nat @ M2 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N2 ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1647_le__add__iff1,axiom,
% 9.17/5.33 ! [A: code_integer,E: code_integer,C: code_integer,B: code_integer,D2: code_integer] :
% 9.17/5.33 ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ E ) @ C ) @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ E ) @ D2 ) )
% 9.17/5.33 = ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ E ) @ C ) @ D2 ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1648_le__add__iff1,axiom,
% 9.17/5.33 ! [A: rat,E: rat,C: rat,B: rat,D2: rat] :
% 9.17/5.33 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D2 ) )
% 9.17/5.33 = ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E ) @ C ) @ D2 ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1649_le__add__iff1,axiom,
% 9.17/5.33 ! [A: int,E: int,C: int,B: int,D2: int] :
% 9.17/5.33 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D2 ) )
% 9.17/5.33 = ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E ) @ C ) @ D2 ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1650_le__add__iff2,axiom,
% 9.17/5.33 ! [A: code_integer,E: code_integer,C: code_integer,B: code_integer,D2: code_integer] :
% 9.17/5.33 ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ E ) @ C ) @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ E ) @ D2 ) )
% 9.17/5.33 = ( ord_le3102999989581377725nteger @ C @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ B @ A ) @ E ) @ D2 ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1651_le__add__iff2,axiom,
% 9.17/5.33 ! [A: rat,E: rat,C: rat,B: rat,D2: rat] :
% 9.17/5.33 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D2 ) )
% 9.17/5.33 = ( ord_less_eq_rat @ C @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E ) @ D2 ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1652_le__add__iff2,axiom,
% 9.17/5.33 ! [A: int,E: int,C: int,B: int,D2: int] :
% 9.17/5.33 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D2 ) )
% 9.17/5.33 = ( ord_less_eq_int @ C @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E ) @ D2 ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1653_less__add__iff1,axiom,
% 9.17/5.33 ! [A: code_integer,E: code_integer,C: code_integer,B: code_integer,D2: code_integer] :
% 9.17/5.33 ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ E ) @ C ) @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ E ) @ D2 ) )
% 9.17/5.33 = ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ E ) @ C ) @ D2 ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1654_less__add__iff1,axiom,
% 9.17/5.33 ! [A: rat,E: rat,C: rat,B: rat,D2: rat] :
% 9.17/5.33 ( ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D2 ) )
% 9.17/5.33 = ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E ) @ C ) @ D2 ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1655_less__add__iff1,axiom,
% 9.17/5.33 ! [A: int,E: int,C: int,B: int,D2: int] :
% 9.17/5.33 ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D2 ) )
% 9.17/5.33 = ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E ) @ C ) @ D2 ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1656_less__add__iff2,axiom,
% 9.17/5.33 ! [A: code_integer,E: code_integer,C: code_integer,B: code_integer,D2: code_integer] :
% 9.17/5.33 ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ E ) @ C ) @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ E ) @ D2 ) )
% 9.17/5.33 = ( ord_le6747313008572928689nteger @ C @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ B @ A ) @ E ) @ D2 ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1657_less__add__iff2,axiom,
% 9.17/5.33 ! [A: rat,E: rat,C: rat,B: rat,D2: rat] :
% 9.17/5.33 ( ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D2 ) )
% 9.17/5.33 = ( ord_less_rat @ C @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E ) @ D2 ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1658_less__add__iff2,axiom,
% 9.17/5.33 ! [A: int,E: int,C: int,B: int,D2: int] :
% 9.17/5.33 ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D2 ) )
% 9.17/5.33 = ( ord_less_int @ C @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E ) @ D2 ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1659_square__diff__one__factored,axiom,
% 9.17/5.33 ! [X: code_integer] :
% 9.17/5.33 ( ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ X @ X ) @ one_one_Code_integer )
% 9.17/5.33 = ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ X @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ X @ one_one_Code_integer ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1660_square__diff__one__factored,axiom,
% 9.17/5.33 ! [X: rat] :
% 9.17/5.33 ( ( minus_minus_rat @ ( times_times_rat @ X @ X ) @ one_one_rat )
% 9.17/5.33 = ( times_times_rat @ ( plus_plus_rat @ X @ one_one_rat ) @ ( minus_minus_rat @ X @ one_one_rat ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1661_square__diff__one__factored,axiom,
% 9.17/5.33 ! [X: int] :
% 9.17/5.33 ( ( minus_minus_int @ ( times_times_int @ X @ X ) @ one_one_int )
% 9.17/5.33 = ( times_times_int @ ( plus_plus_int @ X @ one_one_int ) @ ( minus_minus_int @ X @ one_one_int ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1662_diff__eq__diff__less__eq,axiom,
% 9.17/5.33 ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 9.17/5.33 ( ( ( minus_8373710615458151222nteger @ A @ B )
% 9.17/5.33 = ( minus_8373710615458151222nteger @ C @ D2 ) )
% 9.17/5.33 => ( ( ord_le3102999989581377725nteger @ A @ B )
% 9.17/5.33 = ( ord_le3102999989581377725nteger @ C @ D2 ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1663_diff__eq__diff__less__eq,axiom,
% 9.17/5.33 ! [A: rat,B: rat,C: rat,D2: rat] :
% 9.17/5.33 ( ( ( minus_minus_rat @ A @ B )
% 9.17/5.33 = ( minus_minus_rat @ C @ D2 ) )
% 9.17/5.33 => ( ( ord_less_eq_rat @ A @ B )
% 9.17/5.33 = ( ord_less_eq_rat @ C @ D2 ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1664_diff__eq__diff__less__eq,axiom,
% 9.17/5.33 ! [A: int,B: int,C: int,D2: int] :
% 9.17/5.33 ( ( ( minus_minus_int @ A @ B )
% 9.17/5.33 = ( minus_minus_int @ C @ D2 ) )
% 9.17/5.33 => ( ( ord_less_eq_int @ A @ B )
% 9.17/5.33 = ( ord_less_eq_int @ C @ D2 ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1665_diff__right__mono,axiom,
% 9.17/5.33 ! [A: code_integer,B: code_integer,C: code_integer] :
% 9.17/5.33 ( ( ord_le3102999989581377725nteger @ A @ B )
% 9.17/5.33 => ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ A @ C ) @ ( minus_8373710615458151222nteger @ B @ C ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1666_diff__right__mono,axiom,
% 9.17/5.33 ! [A: rat,B: rat,C: rat] :
% 9.17/5.33 ( ( ord_less_eq_rat @ A @ B )
% 9.17/5.33 => ( ord_less_eq_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ C ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1667_diff__right__mono,axiom,
% 9.17/5.33 ! [A: int,B: int,C: int] :
% 9.17/5.33 ( ( ord_less_eq_int @ A @ B )
% 9.17/5.33 => ( ord_less_eq_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ C ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1668_diff__left__mono,axiom,
% 9.17/5.33 ! [B: code_integer,A: code_integer,C: code_integer] :
% 9.17/5.33 ( ( ord_le3102999989581377725nteger @ B @ A )
% 9.17/5.33 => ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ C @ A ) @ ( minus_8373710615458151222nteger @ C @ B ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1669_diff__left__mono,axiom,
% 9.17/5.33 ! [B: rat,A: rat,C: rat] :
% 9.17/5.33 ( ( ord_less_eq_rat @ B @ A )
% 9.17/5.33 => ( ord_less_eq_rat @ ( minus_minus_rat @ C @ A ) @ ( minus_minus_rat @ C @ B ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1670_diff__left__mono,axiom,
% 9.17/5.33 ! [B: int,A: int,C: int] :
% 9.17/5.33 ( ( ord_less_eq_int @ B @ A )
% 9.17/5.33 => ( ord_less_eq_int @ ( minus_minus_int @ C @ A ) @ ( minus_minus_int @ C @ B ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1671_diff__mono,axiom,
% 9.17/5.33 ! [A: code_integer,B: code_integer,D2: code_integer,C: code_integer] :
% 9.17/5.33 ( ( ord_le3102999989581377725nteger @ A @ B )
% 9.17/5.33 => ( ( ord_le3102999989581377725nteger @ D2 @ C )
% 9.17/5.33 => ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ A @ C ) @ ( minus_8373710615458151222nteger @ B @ D2 ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1672_diff__mono,axiom,
% 9.17/5.33 ! [A: rat,B: rat,D2: rat,C: rat] :
% 9.17/5.33 ( ( ord_less_eq_rat @ A @ B )
% 9.17/5.33 => ( ( ord_less_eq_rat @ D2 @ C )
% 9.17/5.33 => ( ord_less_eq_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ D2 ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1673_diff__mono,axiom,
% 9.17/5.33 ! [A: int,B: int,D2: int,C: int] :
% 9.17/5.33 ( ( ord_less_eq_int @ A @ B )
% 9.17/5.33 => ( ( ord_less_eq_int @ D2 @ C )
% 9.17/5.33 => ( ord_less_eq_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ D2 ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1674_eq__iff__diff__eq__0,axiom,
% 9.17/5.33 ( ( ^ [Y4: code_integer,Z2: code_integer] : ( Y4 = Z2 ) )
% 9.17/5.33 = ( ^ [A5: code_integer,B4: code_integer] :
% 9.17/5.33 ( ( minus_8373710615458151222nteger @ A5 @ B4 )
% 9.17/5.33 = zero_z3403309356797280102nteger ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1675_eq__iff__diff__eq__0,axiom,
% 9.17/5.33 ( ( ^ [Y4: rat,Z2: rat] : ( Y4 = Z2 ) )
% 9.17/5.33 = ( ^ [A5: rat,B4: rat] :
% 9.17/5.33 ( ( minus_minus_rat @ A5 @ B4 )
% 9.17/5.33 = zero_zero_rat ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1676_eq__iff__diff__eq__0,axiom,
% 9.17/5.33 ( ( ^ [Y4: int,Z2: int] : ( Y4 = Z2 ) )
% 9.17/5.33 = ( ^ [A5: int,B4: int] :
% 9.17/5.33 ( ( minus_minus_int @ A5 @ B4 )
% 9.17/5.33 = zero_zero_int ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1677_diff__strict__right__mono,axiom,
% 9.17/5.33 ! [A: code_integer,B: code_integer,C: code_integer] :
% 9.17/5.33 ( ( ord_le6747313008572928689nteger @ A @ B )
% 9.17/5.33 => ( ord_le6747313008572928689nteger @ ( minus_8373710615458151222nteger @ A @ C ) @ ( minus_8373710615458151222nteger @ B @ C ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1678_diff__strict__right__mono,axiom,
% 9.17/5.33 ! [A: rat,B: rat,C: rat] :
% 9.17/5.33 ( ( ord_less_rat @ A @ B )
% 9.17/5.33 => ( ord_less_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ C ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1679_diff__strict__right__mono,axiom,
% 9.17/5.33 ! [A: int,B: int,C: int] :
% 9.17/5.33 ( ( ord_less_int @ A @ B )
% 9.17/5.33 => ( ord_less_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ C ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1680_diff__strict__left__mono,axiom,
% 9.17/5.33 ! [B: code_integer,A: code_integer,C: code_integer] :
% 9.17/5.33 ( ( ord_le6747313008572928689nteger @ B @ A )
% 9.17/5.33 => ( ord_le6747313008572928689nteger @ ( minus_8373710615458151222nteger @ C @ A ) @ ( minus_8373710615458151222nteger @ C @ B ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1681_diff__strict__left__mono,axiom,
% 9.17/5.33 ! [B: rat,A: rat,C: rat] :
% 9.17/5.33 ( ( ord_less_rat @ B @ A )
% 9.17/5.33 => ( ord_less_rat @ ( minus_minus_rat @ C @ A ) @ ( minus_minus_rat @ C @ B ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1682_diff__strict__left__mono,axiom,
% 9.17/5.33 ! [B: int,A: int,C: int] :
% 9.17/5.33 ( ( ord_less_int @ B @ A )
% 9.17/5.33 => ( ord_less_int @ ( minus_minus_int @ C @ A ) @ ( minus_minus_int @ C @ B ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1683_diff__eq__diff__less,axiom,
% 9.17/5.33 ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 9.17/5.33 ( ( ( minus_8373710615458151222nteger @ A @ B )
% 9.17/5.33 = ( minus_8373710615458151222nteger @ C @ D2 ) )
% 9.17/5.33 => ( ( ord_le6747313008572928689nteger @ A @ B )
% 9.17/5.33 = ( ord_le6747313008572928689nteger @ C @ D2 ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1684_diff__eq__diff__less,axiom,
% 9.17/5.33 ! [A: rat,B: rat,C: rat,D2: rat] :
% 9.17/5.33 ( ( ( minus_minus_rat @ A @ B )
% 9.17/5.33 = ( minus_minus_rat @ C @ D2 ) )
% 9.17/5.33 => ( ( ord_less_rat @ A @ B )
% 9.17/5.33 = ( ord_less_rat @ C @ D2 ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1685_diff__eq__diff__less,axiom,
% 9.17/5.33 ! [A: int,B: int,C: int,D2: int] :
% 9.17/5.33 ( ( ( minus_minus_int @ A @ B )
% 9.17/5.33 = ( minus_minus_int @ C @ D2 ) )
% 9.17/5.33 => ( ( ord_less_int @ A @ B )
% 9.17/5.33 = ( ord_less_int @ C @ D2 ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1686_diff__strict__mono,axiom,
% 9.17/5.33 ! [A: code_integer,B: code_integer,D2: code_integer,C: code_integer] :
% 9.17/5.33 ( ( ord_le6747313008572928689nteger @ A @ B )
% 9.17/5.33 => ( ( ord_le6747313008572928689nteger @ D2 @ C )
% 9.17/5.33 => ( ord_le6747313008572928689nteger @ ( minus_8373710615458151222nteger @ A @ C ) @ ( minus_8373710615458151222nteger @ B @ D2 ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1687_diff__strict__mono,axiom,
% 9.17/5.33 ! [A: rat,B: rat,D2: rat,C: rat] :
% 9.17/5.33 ( ( ord_less_rat @ A @ B )
% 9.17/5.33 => ( ( ord_less_rat @ D2 @ C )
% 9.17/5.33 => ( ord_less_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ D2 ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1688_diff__strict__mono,axiom,
% 9.17/5.33 ! [A: int,B: int,D2: int,C: int] :
% 9.17/5.33 ( ( ord_less_int @ A @ B )
% 9.17/5.33 => ( ( ord_less_int @ D2 @ C )
% 9.17/5.33 => ( ord_less_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ D2 ) ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1689_diff__diff__eq,axiom,
% 9.17/5.33 ! [A: multis2468970476368604999at_nat,B: multis2468970476368604999at_nat,C: multis2468970476368604999at_nat] :
% 9.17/5.33 ( ( minus_4286766774447292334at_nat @ ( minus_4286766774447292334at_nat @ A @ B ) @ C )
% 9.17/5.33 = ( minus_4286766774447292334at_nat @ A @ ( plus_p7104986032573967614at_nat @ B @ C ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1690_diff__diff__eq,axiom,
% 9.17/5.33 ! [A: code_integer,B: code_integer,C: code_integer] :
% 9.17/5.33 ( ( minus_8373710615458151222nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C )
% 9.17/5.33 = ( minus_8373710615458151222nteger @ A @ ( plus_p5714425477246183910nteger @ B @ C ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1691_diff__diff__eq,axiom,
% 9.17/5.33 ! [A: rat,B: rat,C: rat] :
% 9.17/5.33 ( ( minus_minus_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 9.17/5.33 = ( minus_minus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1692_diff__diff__eq,axiom,
% 9.17/5.33 ! [A: nat,B: nat,C: nat] :
% 9.17/5.33 ( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C )
% 9.17/5.33 = ( minus_minus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1693_diff__diff__eq,axiom,
% 9.17/5.33 ! [A: int,B: int,C: int] :
% 9.17/5.33 ( ( minus_minus_int @ ( minus_minus_int @ A @ B ) @ C )
% 9.17/5.33 = ( minus_minus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1694_add__implies__diff,axiom,
% 9.17/5.33 ! [C: multis2468970476368604999at_nat,B: multis2468970476368604999at_nat,A: multis2468970476368604999at_nat] :
% 9.17/5.33 ( ( ( plus_p7104986032573967614at_nat @ C @ B )
% 9.17/5.33 = A )
% 9.17/5.33 => ( C
% 9.17/5.33 = ( minus_4286766774447292334at_nat @ A @ B ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1695_add__implies__diff,axiom,
% 9.17/5.33 ! [C: code_integer,B: code_integer,A: code_integer] :
% 9.17/5.33 ( ( ( plus_p5714425477246183910nteger @ C @ B )
% 9.17/5.33 = A )
% 9.17/5.33 => ( C
% 9.17/5.33 = ( minus_8373710615458151222nteger @ A @ B ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1696_add__implies__diff,axiom,
% 9.17/5.33 ! [C: rat,B: rat,A: rat] :
% 9.17/5.33 ( ( ( plus_plus_rat @ C @ B )
% 9.17/5.33 = A )
% 9.17/5.33 => ( C
% 9.17/5.33 = ( minus_minus_rat @ A @ B ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1697_add__implies__diff,axiom,
% 9.17/5.33 ! [C: nat,B: nat,A: nat] :
% 9.17/5.33 ( ( ( plus_plus_nat @ C @ B )
% 9.17/5.33 = A )
% 9.17/5.33 => ( C
% 9.17/5.33 = ( minus_minus_nat @ A @ B ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1698_add__implies__diff,axiom,
% 9.17/5.33 ! [C: int,B: int,A: int] :
% 9.17/5.33 ( ( ( plus_plus_int @ C @ B )
% 9.17/5.33 = A )
% 9.17/5.33 => ( C
% 9.17/5.33 = ( minus_minus_int @ A @ B ) ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1699_diff__add__eq__diff__diff__swap,axiom,
% 9.17/5.33 ! [A: code_integer,B: code_integer,C: code_integer] :
% 9.17/5.33 ( ( minus_8373710615458151222nteger @ A @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 9.17/5.33 = ( minus_8373710615458151222nteger @ ( minus_8373710615458151222nteger @ A @ C ) @ B ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1700_diff__add__eq__diff__diff__swap,axiom,
% 9.17/5.33 ! [A: rat,B: rat,C: rat] :
% 9.17/5.33 ( ( minus_minus_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 9.17/5.33 = ( minus_minus_rat @ ( minus_minus_rat @ A @ C ) @ B ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1701_diff__add__eq__diff__diff__swap,axiom,
% 9.17/5.33 ! [A: int,B: int,C: int] :
% 9.17/5.33 ( ( minus_minus_int @ A @ ( plus_plus_int @ B @ C ) )
% 9.17/5.33 = ( minus_minus_int @ ( minus_minus_int @ A @ C ) @ B ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1702_diff__add__eq,axiom,
% 9.17/5.33 ! [A: code_integer,B: code_integer,C: code_integer] :
% 9.17/5.33 ( ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C )
% 9.17/5.33 = ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A @ C ) @ B ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1703_diff__add__eq,axiom,
% 9.17/5.33 ! [A: rat,B: rat,C: rat] :
% 9.17/5.33 ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 9.17/5.33 = ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1704_diff__add__eq,axiom,
% 9.17/5.33 ! [A: int,B: int,C: int] :
% 9.17/5.33 ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ C )
% 9.17/5.33 = ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ B ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1705_diff__diff__eq2,axiom,
% 9.17/5.33 ! [A: code_integer,B: code_integer,C: code_integer] :
% 9.17/5.33 ( ( minus_8373710615458151222nteger @ A @ ( minus_8373710615458151222nteger @ B @ C ) )
% 9.17/5.33 = ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A @ C ) @ B ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1706_diff__diff__eq2,axiom,
% 9.17/5.33 ! [A: rat,B: rat,C: rat] :
% 9.17/5.33 ( ( minus_minus_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 9.17/5.33 = ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1707_diff__diff__eq2,axiom,
% 9.17/5.33 ! [A: int,B: int,C: int] :
% 9.17/5.33 ( ( minus_minus_int @ A @ ( minus_minus_int @ B @ C ) )
% 9.17/5.33 = ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ B ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1708_add__diff__eq,axiom,
% 9.17/5.33 ! [A: code_integer,B: code_integer,C: code_integer] :
% 9.17/5.33 ( ( plus_p5714425477246183910nteger @ A @ ( minus_8373710615458151222nteger @ B @ C ) )
% 9.17/5.33 = ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1709_add__diff__eq,axiom,
% 9.17/5.33 ! [A: rat,B: rat,C: rat] :
% 9.17/5.33 ( ( plus_plus_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 9.17/5.33 = ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1710_add__diff__eq,axiom,
% 9.17/5.33 ! [A: int,B: int,C: int] :
% 9.17/5.33 ( ( plus_plus_int @ A @ ( minus_minus_int @ B @ C ) )
% 9.17/5.33 = ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1711_eq__diff__eq,axiom,
% 9.17/5.33 ! [A: code_integer,C: code_integer,B: code_integer] :
% 9.17/5.33 ( ( A
% 9.17/5.33 = ( minus_8373710615458151222nteger @ C @ B ) )
% 9.17/5.33 = ( ( plus_p5714425477246183910nteger @ A @ B )
% 9.17/5.33 = C ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1712_eq__diff__eq,axiom,
% 9.17/5.33 ! [A: rat,C: rat,B: rat] :
% 9.17/5.33 ( ( A
% 9.17/5.33 = ( minus_minus_rat @ C @ B ) )
% 9.17/5.33 = ( ( plus_plus_rat @ A @ B )
% 9.17/5.33 = C ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1713_eq__diff__eq,axiom,
% 9.17/5.33 ! [A: int,C: int,B: int] :
% 9.17/5.33 ( ( A
% 9.17/5.33 = ( minus_minus_int @ C @ B ) )
% 9.17/5.33 = ( ( plus_plus_int @ A @ B )
% 9.17/5.33 = C ) ) ).
% 9.17/5.33
% 9.17/5.33 thf(fact_1714_diff__eq__eq,axiom,
% 9.17/5.33 ! [A: code_integer,B: code_integer,C: code_integer] :
% 9.17/5.34 ( ( ( minus_8373710615458151222nteger @ A @ B )
% 9.17/5.34 = C )
% 9.17/5.34 = ( A
% 9.17/5.34 = ( plus_p5714425477246183910nteger @ C @ B ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1715_diff__eq__eq,axiom,
% 9.17/5.34 ! [A: rat,B: rat,C: rat] :
% 9.17/5.34 ( ( ( minus_minus_rat @ A @ B )
% 9.17/5.34 = C )
% 9.17/5.34 = ( A
% 9.17/5.34 = ( plus_plus_rat @ C @ B ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1716_diff__eq__eq,axiom,
% 9.17/5.34 ! [A: int,B: int,C: int] :
% 9.17/5.34 ( ( ( minus_minus_int @ A @ B )
% 9.17/5.34 = C )
% 9.17/5.34 = ( A
% 9.17/5.34 = ( plus_plus_int @ C @ B ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1717_group__cancel_Osub1,axiom,
% 9.17/5.34 ! [A2: code_integer,K: code_integer,A: code_integer,B: code_integer] :
% 9.17/5.34 ( ( A2
% 9.17/5.34 = ( plus_p5714425477246183910nteger @ K @ A ) )
% 9.17/5.34 => ( ( minus_8373710615458151222nteger @ A2 @ B )
% 9.17/5.34 = ( plus_p5714425477246183910nteger @ K @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1718_group__cancel_Osub1,axiom,
% 9.17/5.34 ! [A2: rat,K: rat,A: rat,B: rat] :
% 9.17/5.34 ( ( A2
% 9.17/5.34 = ( plus_plus_rat @ K @ A ) )
% 9.17/5.34 => ( ( minus_minus_rat @ A2 @ B )
% 9.17/5.34 = ( plus_plus_rat @ K @ ( minus_minus_rat @ A @ B ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1719_group__cancel_Osub1,axiom,
% 9.17/5.34 ! [A2: int,K: int,A: int,B: int] :
% 9.17/5.34 ( ( A2
% 9.17/5.34 = ( plus_plus_int @ K @ A ) )
% 9.17/5.34 => ( ( minus_minus_int @ A2 @ B )
% 9.17/5.34 = ( plus_plus_int @ K @ ( minus_minus_int @ A @ B ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1720_minus__diff__commute,axiom,
% 9.17/5.34 ! [B: int,A: int] :
% 9.17/5.34 ( ( minus_minus_int @ ( uminus_uminus_int @ B ) @ A )
% 9.17/5.34 = ( minus_minus_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1721_minus__diff__commute,axiom,
% 9.17/5.34 ! [B: code_integer,A: code_integer] :
% 9.17/5.34 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ B ) @ A )
% 9.17/5.34 = ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1722_minus__diff__commute,axiom,
% 9.17/5.34 ! [B: rat,A: rat] :
% 9.17/5.34 ( ( minus_minus_rat @ ( uminus_uminus_rat @ B ) @ A )
% 9.17/5.34 = ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1723_ring__class_Oring__distribs_I2_J,axiom,
% 9.17/5.34 ! [A: rat,B: rat,C: rat] :
% 9.17/5.34 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 9.17/5.34 = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1724_ring__class_Oring__distribs_I2_J,axiom,
% 9.17/5.34 ! [A: int,B: int,C: int] :
% 9.17/5.34 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 9.17/5.34 = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1725_ring__class_Oring__distribs_I1_J,axiom,
% 9.17/5.34 ! [A: rat,B: rat,C: rat] :
% 9.17/5.34 ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 9.17/5.34 = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1726_ring__class_Oring__distribs_I1_J,axiom,
% 9.17/5.34 ! [A: int,B: int,C: int] :
% 9.17/5.34 ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 9.17/5.34 = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1727_comm__semiring__class_Odistrib,axiom,
% 9.17/5.34 ! [A: rat,B: rat,C: rat] :
% 9.17/5.34 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 9.17/5.34 = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1728_comm__semiring__class_Odistrib,axiom,
% 9.17/5.34 ! [A: nat,B: nat,C: nat] :
% 9.17/5.34 ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 9.17/5.34 = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1729_comm__semiring__class_Odistrib,axiom,
% 9.17/5.34 ! [A: int,B: int,C: int] :
% 9.17/5.34 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 9.17/5.34 = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1730_distrib__left,axiom,
% 9.17/5.34 ! [A: rat,B: rat,C: rat] :
% 9.17/5.34 ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 9.17/5.34 = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1731_distrib__left,axiom,
% 9.17/5.34 ! [A: nat,B: nat,C: nat] :
% 9.17/5.34 ( ( times_times_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 9.17/5.34 = ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1732_distrib__left,axiom,
% 9.17/5.34 ! [A: int,B: int,C: int] :
% 9.17/5.34 ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 9.17/5.34 = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1733_distrib__right,axiom,
% 9.17/5.34 ! [A: rat,B: rat,C: rat] :
% 9.17/5.34 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 9.17/5.34 = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1734_distrib__right,axiom,
% 9.17/5.34 ! [A: nat,B: nat,C: nat] :
% 9.17/5.34 ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 9.17/5.34 = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1735_distrib__right,axiom,
% 9.17/5.34 ! [A: int,B: int,C: int] :
% 9.17/5.34 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 9.17/5.34 = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1736_combine__common__factor,axiom,
% 9.17/5.34 ! [A: rat,E: rat,B: rat,C: rat] :
% 9.17/5.34 ( ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ C ) )
% 9.17/5.34 = ( plus_plus_rat @ ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ E ) @ C ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1737_combine__common__factor,axiom,
% 9.17/5.34 ! [A: nat,E: nat,B: nat,C: nat] :
% 9.17/5.34 ( ( plus_plus_nat @ ( times_times_nat @ A @ E ) @ ( plus_plus_nat @ ( times_times_nat @ B @ E ) @ C ) )
% 9.17/5.34 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ E ) @ C ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1738_combine__common__factor,axiom,
% 9.17/5.34 ! [A: int,E: int,B: int,C: int] :
% 9.17/5.34 ( ( plus_plus_int @ ( times_times_int @ A @ E ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ C ) )
% 9.17/5.34 = ( plus_plus_int @ ( times_times_int @ ( plus_plus_int @ A @ B ) @ E ) @ C ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1739_crossproduct__eq,axiom,
% 9.17/5.34 ! [W: rat,Y: rat,X: rat,Z: rat] :
% 9.17/5.34 ( ( ( plus_plus_rat @ ( times_times_rat @ W @ Y ) @ ( times_times_rat @ X @ Z ) )
% 9.17/5.34 = ( plus_plus_rat @ ( times_times_rat @ W @ Z ) @ ( times_times_rat @ X @ Y ) ) )
% 9.17/5.34 = ( ( W = X )
% 9.17/5.34 | ( Y = Z ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1740_crossproduct__eq,axiom,
% 9.17/5.34 ! [W: nat,Y: nat,X: nat,Z: nat] :
% 9.17/5.34 ( ( ( plus_plus_nat @ ( times_times_nat @ W @ Y ) @ ( times_times_nat @ X @ Z ) )
% 9.17/5.34 = ( plus_plus_nat @ ( times_times_nat @ W @ Z ) @ ( times_times_nat @ X @ Y ) ) )
% 9.17/5.34 = ( ( W = X )
% 9.17/5.34 | ( Y = Z ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1741_crossproduct__eq,axiom,
% 9.17/5.34 ! [W: int,Y: int,X: int,Z: int] :
% 9.17/5.34 ( ( ( plus_plus_int @ ( times_times_int @ W @ Y ) @ ( times_times_int @ X @ Z ) )
% 9.17/5.34 = ( plus_plus_int @ ( times_times_int @ W @ Z ) @ ( times_times_int @ X @ Y ) ) )
% 9.17/5.34 = ( ( W = X )
% 9.17/5.34 | ( Y = Z ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1742_crossproduct__noteq,axiom,
% 9.17/5.34 ! [A: rat,B: rat,C: rat,D2: rat] :
% 9.17/5.34 ( ( ( A != B )
% 9.17/5.34 & ( C != D2 ) )
% 9.17/5.34 = ( ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D2 ) )
% 9.17/5.34 != ( plus_plus_rat @ ( times_times_rat @ A @ D2 ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1743_crossproduct__noteq,axiom,
% 9.17/5.34 ! [A: nat,B: nat,C: nat,D2: nat] :
% 9.17/5.34 ( ( ( A != B )
% 9.17/5.34 & ( C != D2 ) )
% 9.17/5.34 = ( ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D2 ) )
% 9.17/5.34 != ( plus_plus_nat @ ( times_times_nat @ A @ D2 ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1744_crossproduct__noteq,axiom,
% 9.17/5.34 ! [A: int,B: int,C: int,D2: int] :
% 9.17/5.34 ( ( ( A != B )
% 9.17/5.34 & ( C != D2 ) )
% 9.17/5.34 = ( ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D2 ) )
% 9.17/5.34 != ( plus_plus_int @ ( times_times_int @ A @ D2 ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1745_comm__monoid__mult__class_Omult__1,axiom,
% 9.17/5.34 ! [A: code_integer] :
% 9.17/5.34 ( ( times_3573771949741848930nteger @ one_one_Code_integer @ A )
% 9.17/5.34 = A ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1746_comm__monoid__mult__class_Omult__1,axiom,
% 9.17/5.34 ! [A: assn] :
% 9.17/5.34 ( ( times_times_assn @ one_one_assn @ A )
% 9.17/5.34 = A ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1747_comm__monoid__mult__class_Omult__1,axiom,
% 9.17/5.34 ! [A: rat] :
% 9.17/5.34 ( ( times_times_rat @ one_one_rat @ A )
% 9.17/5.34 = A ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1748_comm__monoid__mult__class_Omult__1,axiom,
% 9.17/5.34 ! [A: nat] :
% 9.17/5.34 ( ( times_times_nat @ one_one_nat @ A )
% 9.17/5.34 = A ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1749_comm__monoid__mult__class_Omult__1,axiom,
% 9.17/5.34 ! [A: int] :
% 9.17/5.34 ( ( times_times_int @ one_one_int @ A )
% 9.17/5.34 = A ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1750_mult_Ocomm__neutral,axiom,
% 9.17/5.34 ! [A: code_integer] :
% 9.17/5.34 ( ( times_3573771949741848930nteger @ A @ one_one_Code_integer )
% 9.17/5.34 = A ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1751_mult_Ocomm__neutral,axiom,
% 9.17/5.34 ! [A: assn] :
% 9.17/5.34 ( ( times_times_assn @ A @ one_one_assn )
% 9.17/5.34 = A ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1752_mult_Ocomm__neutral,axiom,
% 9.17/5.34 ! [A: rat] :
% 9.17/5.34 ( ( times_times_rat @ A @ one_one_rat )
% 9.17/5.34 = A ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1753_mult_Ocomm__neutral,axiom,
% 9.17/5.34 ! [A: nat] :
% 9.17/5.34 ( ( times_times_nat @ A @ one_one_nat )
% 9.17/5.34 = A ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1754_mult_Ocomm__neutral,axiom,
% 9.17/5.34 ! [A: int] :
% 9.17/5.34 ( ( times_times_int @ A @ one_one_int )
% 9.17/5.34 = A ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1755_abs__minus__commute,axiom,
% 9.17/5.34 ! [A: code_integer,B: code_integer] :
% 9.17/5.34 ( ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ B ) )
% 9.17/5.34 = ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ B @ A ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1756_abs__minus__commute,axiom,
% 9.17/5.34 ! [A: rat,B: rat] :
% 9.17/5.34 ( ( abs_abs_rat @ ( minus_minus_rat @ A @ B ) )
% 9.17/5.34 = ( abs_abs_rat @ ( minus_minus_rat @ B @ A ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1757_abs__minus__commute,axiom,
% 9.17/5.34 ! [A: int,B: int] :
% 9.17/5.34 ( ( abs_abs_int @ ( minus_minus_int @ A @ B ) )
% 9.17/5.34 = ( abs_abs_int @ ( minus_minus_int @ B @ A ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1758_Nat_Odiff__cancel,axiom,
% 9.17/5.34 ! [K: nat,M2: nat,N2: nat] :
% 9.17/5.34 ( ( minus_minus_nat @ ( plus_plus_nat @ K @ M2 ) @ ( plus_plus_nat @ K @ N2 ) )
% 9.17/5.34 = ( minus_minus_nat @ M2 @ N2 ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1759_diff__cancel2,axiom,
% 9.17/5.34 ! [M2: nat,K: nat,N2: nat] :
% 9.17/5.34 ( ( minus_minus_nat @ ( plus_plus_nat @ M2 @ K ) @ ( plus_plus_nat @ N2 @ K ) )
% 9.17/5.34 = ( minus_minus_nat @ M2 @ N2 ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1760_diff__add__inverse,axiom,
% 9.17/5.34 ! [N2: nat,M2: nat] :
% 9.17/5.34 ( ( minus_minus_nat @ ( plus_plus_nat @ N2 @ M2 ) @ N2 )
% 9.17/5.34 = M2 ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1761_diff__add__inverse2,axiom,
% 9.17/5.34 ! [M2: nat,N2: nat] :
% 9.17/5.34 ( ( minus_minus_nat @ ( plus_plus_nat @ M2 @ N2 ) @ N2 )
% 9.17/5.34 = M2 ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1762_le__diff__conv,axiom,
% 9.17/5.34 ! [J: nat,K: nat,I: nat] :
% 9.17/5.34 ( ( ord_less_eq_nat @ ( minus_minus_nat @ J @ K ) @ I )
% 9.17/5.34 = ( ord_less_eq_nat @ J @ ( plus_plus_nat @ I @ K ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1763_Nat_Ole__diff__conv2,axiom,
% 9.17/5.34 ! [K: nat,J: nat,I: nat] :
% 9.17/5.34 ( ( ord_less_eq_nat @ K @ J )
% 9.17/5.34 => ( ( ord_less_eq_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 9.17/5.34 = ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ J ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1764_Nat_Odiff__add__assoc,axiom,
% 9.17/5.34 ! [K: nat,J: nat,I: nat] :
% 9.17/5.34 ( ( ord_less_eq_nat @ K @ J )
% 9.17/5.34 => ( ( minus_minus_nat @ ( plus_plus_nat @ I @ J ) @ K )
% 9.17/5.34 = ( plus_plus_nat @ I @ ( minus_minus_nat @ J @ K ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1765_Nat_Odiff__add__assoc2,axiom,
% 9.17/5.34 ! [K: nat,J: nat,I: nat] :
% 9.17/5.34 ( ( ord_less_eq_nat @ K @ J )
% 9.17/5.34 => ( ( minus_minus_nat @ ( plus_plus_nat @ J @ I ) @ K )
% 9.17/5.34 = ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1766_Nat_Ole__imp__diff__is__add,axiom,
% 9.17/5.34 ! [I: nat,J: nat,K: nat] :
% 9.17/5.34 ( ( ord_less_eq_nat @ I @ J )
% 9.17/5.34 => ( ( ( minus_minus_nat @ J @ I )
% 9.17/5.34 = K )
% 9.17/5.34 = ( J
% 9.17/5.34 = ( plus_plus_nat @ K @ I ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1767_add__mult__distrib,axiom,
% 9.17/5.34 ! [M2: nat,N2: nat,K: nat] :
% 9.17/5.34 ( ( times_times_nat @ ( plus_plus_nat @ M2 @ N2 ) @ K )
% 9.17/5.34 = ( plus_plus_nat @ ( times_times_nat @ M2 @ K ) @ ( times_times_nat @ N2 @ K ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1768_add__mult__distrib2,axiom,
% 9.17/5.34 ! [K: nat,M2: nat,N2: nat] :
% 9.17/5.34 ( ( times_times_nat @ K @ ( plus_plus_nat @ M2 @ N2 ) )
% 9.17/5.34 = ( plus_plus_nat @ ( times_times_nat @ K @ M2 ) @ ( times_times_nat @ K @ N2 ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1769_mlex__leI,axiom,
% 9.17/5.34 ! [A: nat,A4: nat,B: nat,B3: nat,N6: nat] :
% 9.17/5.34 ( ( ord_less_eq_nat @ A @ A4 )
% 9.17/5.34 => ( ( ord_less_eq_nat @ B @ B3 )
% 9.17/5.34 => ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ A @ N6 ) @ B ) @ ( plus_plus_nat @ ( times_times_nat @ A4 @ N6 ) @ B3 ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1770_nat__mult__1,axiom,
% 9.17/5.34 ! [N2: nat] :
% 9.17/5.34 ( ( times_times_nat @ one_one_nat @ N2 )
% 9.17/5.34 = N2 ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1771_nat__mult__1__right,axiom,
% 9.17/5.34 ! [N2: nat] :
% 9.17/5.34 ( ( times_times_nat @ N2 @ one_one_nat )
% 9.17/5.34 = N2 ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1772_mult__eq__if,axiom,
% 9.17/5.34 ( times_times_nat
% 9.17/5.34 = ( ^ [M: nat,N4: nat] : ( if_nat @ ( M = zero_zero_nat ) @ zero_zero_nat @ ( plus_plus_nat @ N4 @ ( times_times_nat @ ( minus_minus_nat @ M @ one_one_nat ) @ N4 ) ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1773_lambda__one,axiom,
% 9.17/5.34 ( ( ^ [X3: code_integer] : X3 )
% 9.17/5.34 = ( times_3573771949741848930nteger @ one_one_Code_integer ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1774_lambda__one,axiom,
% 9.17/5.34 ( ( ^ [X3: assn] : X3 )
% 9.17/5.34 = ( times_times_assn @ one_one_assn ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1775_lambda__one,axiom,
% 9.17/5.34 ( ( ^ [X3: rat] : X3 )
% 9.17/5.34 = ( times_times_rat @ one_one_rat ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1776_lambda__one,axiom,
% 9.17/5.34 ( ( ^ [X3: nat] : X3 )
% 9.17/5.34 = ( times_times_nat @ one_one_nat ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1777_lambda__one,axiom,
% 9.17/5.34 ( ( ^ [X3: int] : X3 )
% 9.17/5.34 = ( times_times_int @ one_one_int ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1778_is__num__normalize_I6_J,axiom,
% 9.17/5.34 ! [X: rat,Y: rat] :
% 9.17/5.34 ( ( neg_nu6808929389511037909um_rat @ X )
% 9.17/5.34 => ( ( neg_nu6808929389511037909um_rat @ Y )
% 9.17/5.34 => ( neg_nu6808929389511037909um_rat @ ( plus_plus_rat @ X @ Y ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1779_is__num__normalize_I6_J,axiom,
% 9.17/5.34 ! [X: int,Y: int] :
% 9.17/5.34 ( ( neg_nu7441568979088483369um_int @ X )
% 9.17/5.34 => ( ( neg_nu7441568979088483369um_int @ Y )
% 9.17/5.34 => ( neg_nu7441568979088483369um_int @ ( plus_plus_int @ X @ Y ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1780_is__num__add__commute,axiom,
% 9.17/5.34 ! [X: rat,Y: rat] :
% 9.17/5.34 ( ( neg_nu6808929389511037909um_rat @ X )
% 9.17/5.34 => ( ( neg_nu6808929389511037909um_rat @ Y )
% 9.17/5.34 => ( ( plus_plus_rat @ X @ Y )
% 9.17/5.34 = ( plus_plus_rat @ Y @ X ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1781_is__num__add__commute,axiom,
% 9.17/5.34 ! [X: int,Y: int] :
% 9.17/5.34 ( ( neg_nu7441568979088483369um_int @ X )
% 9.17/5.34 => ( ( neg_nu7441568979088483369um_int @ Y )
% 9.17/5.34 => ( ( plus_plus_int @ X @ Y )
% 9.17/5.34 = ( plus_plus_int @ Y @ X ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1782_is__num__add__left__commute,axiom,
% 9.17/5.34 ! [X: rat,Y: rat,Z: rat] :
% 9.17/5.34 ( ( neg_nu6808929389511037909um_rat @ X )
% 9.17/5.34 => ( ( neg_nu6808929389511037909um_rat @ Y )
% 9.17/5.34 => ( ( plus_plus_rat @ X @ ( plus_plus_rat @ Y @ Z ) )
% 9.17/5.34 = ( plus_plus_rat @ Y @ ( plus_plus_rat @ X @ Z ) ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1783_is__num__add__left__commute,axiom,
% 9.17/5.34 ! [X: int,Y: int,Z: int] :
% 9.17/5.34 ( ( neg_nu7441568979088483369um_int @ X )
% 9.17/5.34 => ( ( neg_nu7441568979088483369um_int @ Y )
% 9.17/5.34 => ( ( plus_plus_int @ X @ ( plus_plus_int @ Y @ Z ) )
% 9.17/5.34 = ( plus_plus_int @ Y @ ( plus_plus_int @ X @ Z ) ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1784_is__num__normalize_I4_J,axiom,
% 9.17/5.34 neg_nu2435721316971906650nteger @ one_one_Code_integer ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1785_is__num__normalize_I4_J,axiom,
% 9.17/5.34 neg_nu6808929389511037909um_rat @ one_one_rat ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1786_is__num__normalize_I4_J,axiom,
% 9.17/5.34 neg_nu7441568979088483369um_int @ one_one_int ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1787_le__iff__diff__le__0,axiom,
% 9.17/5.34 ( ord_le3102999989581377725nteger
% 9.17/5.34 = ( ^ [A5: code_integer,B4: code_integer] : ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ A5 @ B4 ) @ zero_z3403309356797280102nteger ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1788_le__iff__diff__le__0,axiom,
% 9.17/5.34 ( ord_less_eq_rat
% 9.17/5.34 = ( ^ [A5: rat,B4: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ A5 @ B4 ) @ zero_zero_rat ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1789_le__iff__diff__le__0,axiom,
% 9.17/5.34 ( ord_less_eq_int
% 9.17/5.34 = ( ^ [A5: int,B4: int] : ( ord_less_eq_int @ ( minus_minus_int @ A5 @ B4 ) @ zero_zero_int ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1790_less__iff__diff__less__0,axiom,
% 9.17/5.34 ( ord_le6747313008572928689nteger
% 9.17/5.34 = ( ^ [A5: code_integer,B4: code_integer] : ( ord_le6747313008572928689nteger @ ( minus_8373710615458151222nteger @ A5 @ B4 ) @ zero_z3403309356797280102nteger ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1791_less__iff__diff__less__0,axiom,
% 9.17/5.34 ( ord_less_rat
% 9.17/5.34 = ( ^ [A5: rat,B4: rat] : ( ord_less_rat @ ( minus_minus_rat @ A5 @ B4 ) @ zero_zero_rat ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1792_less__iff__diff__less__0,axiom,
% 9.17/5.34 ( ord_less_int
% 9.17/5.34 = ( ^ [A5: int,B4: int] : ( ord_less_int @ ( minus_minus_int @ A5 @ B4 ) @ zero_zero_int ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1793_ordered__cancel__comm__monoid__diff__class_Ole__imp__diff__is__add,axiom,
% 9.17/5.34 ! [A: nat,B: nat,C: nat] :
% 9.17/5.34 ( ( ord_less_eq_nat @ A @ B )
% 9.17/5.34 => ( ( ord_less_eq_nat @ A @ B )
% 9.17/5.34 => ( ( ( minus_minus_nat @ B @ A )
% 9.17/5.34 = C )
% 9.17/5.34 = ( B
% 9.17/5.34 = ( plus_plus_nat @ C @ A ) ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1794_ordered__cancel__comm__monoid__diff__class_Oadd__diff__inverse,axiom,
% 9.17/5.34 ! [A: nat,B: nat] :
% 9.17/5.34 ( ( ord_less_eq_nat @ A @ B )
% 9.17/5.34 => ( ( plus_plus_nat @ A @ ( minus_minus_nat @ B @ A ) )
% 9.17/5.34 = B ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1795_ordered__cancel__comm__monoid__diff__class_Odiff__diff__right,axiom,
% 9.17/5.34 ! [A: nat,B: nat,C: nat] :
% 9.17/5.34 ( ( ord_less_eq_nat @ A @ B )
% 9.17/5.34 => ( ( minus_minus_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 9.17/5.34 = ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1796_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc2,axiom,
% 9.17/5.34 ! [A: nat,B: nat,C: nat] :
% 9.17/5.34 ( ( ord_less_eq_nat @ A @ B )
% 9.17/5.34 => ( ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A )
% 9.17/5.34 = ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1797_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc2,axiom,
% 9.17/5.34 ! [A: nat,B: nat,C: nat] :
% 9.17/5.34 ( ( ord_less_eq_nat @ A @ B )
% 9.17/5.34 => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C )
% 9.17/5.34 = ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1798_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc,axiom,
% 9.17/5.34 ! [A: nat,B: nat,C: nat] :
% 9.17/5.34 ( ( ord_less_eq_nat @ A @ B )
% 9.17/5.34 => ( ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A )
% 9.17/5.34 = ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1799_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc,axiom,
% 9.17/5.34 ! [A: nat,B: nat,C: nat] :
% 9.17/5.34 ( ( ord_less_eq_nat @ A @ B )
% 9.17/5.34 => ( ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 9.17/5.34 = ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1800_ordered__cancel__comm__monoid__diff__class_Ole__diff__conv2,axiom,
% 9.17/5.34 ! [A: nat,B: nat,C: nat] :
% 9.17/5.34 ( ( ord_less_eq_nat @ A @ B )
% 9.17/5.34 => ( ( ord_less_eq_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 9.17/5.34 = ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1801_le__add__diff,axiom,
% 9.17/5.34 ! [A: nat,B: nat,C: nat] :
% 9.17/5.34 ( ( ord_less_eq_nat @ A @ B )
% 9.17/5.34 => ( ord_less_eq_nat @ C @ ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1802_ordered__cancel__comm__monoid__diff__class_Odiff__add,axiom,
% 9.17/5.34 ! [A: nat,B: nat] :
% 9.17/5.34 ( ( ord_less_eq_nat @ A @ B )
% 9.17/5.34 => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ A )
% 9.17/5.34 = B ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1803_le__diff__eq,axiom,
% 9.17/5.34 ! [A: code_integer,C: code_integer,B: code_integer] :
% 9.17/5.34 ( ( ord_le3102999989581377725nteger @ A @ ( minus_8373710615458151222nteger @ C @ B ) )
% 9.17/5.34 = ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1804_le__diff__eq,axiom,
% 9.17/5.34 ! [A: rat,C: rat,B: rat] :
% 9.17/5.34 ( ( ord_less_eq_rat @ A @ ( minus_minus_rat @ C @ B ) )
% 9.17/5.34 = ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1805_le__diff__eq,axiom,
% 9.17/5.34 ! [A: int,C: int,B: int] :
% 9.17/5.34 ( ( ord_less_eq_int @ A @ ( minus_minus_int @ C @ B ) )
% 9.17/5.34 = ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1806_diff__le__eq,axiom,
% 9.17/5.34 ! [A: code_integer,B: code_integer,C: code_integer] :
% 9.17/5.34 ( ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C )
% 9.17/5.34 = ( ord_le3102999989581377725nteger @ A @ ( plus_p5714425477246183910nteger @ C @ B ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1807_diff__le__eq,axiom,
% 9.17/5.34 ! [A: rat,B: rat,C: rat] :
% 9.17/5.34 ( ( ord_less_eq_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 9.17/5.34 = ( ord_less_eq_rat @ A @ ( plus_plus_rat @ C @ B ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1808_diff__le__eq,axiom,
% 9.17/5.34 ! [A: int,B: int,C: int] :
% 9.17/5.34 ( ( ord_less_eq_int @ ( minus_minus_int @ A @ B ) @ C )
% 9.17/5.34 = ( ord_less_eq_int @ A @ ( plus_plus_int @ C @ B ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1809_add__le__imp__le__diff,axiom,
% 9.17/5.34 ! [I: code_integer,K: code_integer,N2: code_integer] :
% 9.17/5.34 ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ I @ K ) @ N2 )
% 9.17/5.34 => ( ord_le3102999989581377725nteger @ I @ ( minus_8373710615458151222nteger @ N2 @ K ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1810_add__le__imp__le__diff,axiom,
% 9.17/5.34 ! [I: rat,K: rat,N2: rat] :
% 9.17/5.34 ( ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ N2 )
% 9.17/5.34 => ( ord_less_eq_rat @ I @ ( minus_minus_rat @ N2 @ K ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1811_add__le__imp__le__diff,axiom,
% 9.17/5.34 ! [I: nat,K: nat,N2: nat] :
% 9.17/5.34 ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N2 )
% 9.17/5.34 => ( ord_less_eq_nat @ I @ ( minus_minus_nat @ N2 @ K ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1812_add__le__imp__le__diff,axiom,
% 9.17/5.34 ! [I: int,K: int,N2: int] :
% 9.17/5.34 ( ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ N2 )
% 9.17/5.34 => ( ord_less_eq_int @ I @ ( minus_minus_int @ N2 @ K ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1813_add__le__add__imp__diff__le,axiom,
% 9.17/5.34 ! [I: code_integer,K: code_integer,N2: code_integer,J: code_integer] :
% 9.17/5.34 ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ I @ K ) @ N2 )
% 9.17/5.34 => ( ( ord_le3102999989581377725nteger @ N2 @ ( plus_p5714425477246183910nteger @ J @ K ) )
% 9.17/5.34 => ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ I @ K ) @ N2 )
% 9.17/5.34 => ( ( ord_le3102999989581377725nteger @ N2 @ ( plus_p5714425477246183910nteger @ J @ K ) )
% 9.17/5.34 => ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ N2 @ K ) @ J ) ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1814_add__le__add__imp__diff__le,axiom,
% 9.17/5.34 ! [I: rat,K: rat,N2: rat,J: rat] :
% 9.17/5.34 ( ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ N2 )
% 9.17/5.34 => ( ( ord_less_eq_rat @ N2 @ ( plus_plus_rat @ J @ K ) )
% 9.17/5.34 => ( ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ N2 )
% 9.17/5.34 => ( ( ord_less_eq_rat @ N2 @ ( plus_plus_rat @ J @ K ) )
% 9.17/5.34 => ( ord_less_eq_rat @ ( minus_minus_rat @ N2 @ K ) @ J ) ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1815_add__le__add__imp__diff__le,axiom,
% 9.17/5.34 ! [I: nat,K: nat,N2: nat,J: nat] :
% 9.17/5.34 ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N2 )
% 9.17/5.34 => ( ( ord_less_eq_nat @ N2 @ ( plus_plus_nat @ J @ K ) )
% 9.17/5.34 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N2 )
% 9.17/5.34 => ( ( ord_less_eq_nat @ N2 @ ( plus_plus_nat @ J @ K ) )
% 9.17/5.34 => ( ord_less_eq_nat @ ( minus_minus_nat @ N2 @ K ) @ J ) ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1816_add__le__add__imp__diff__le,axiom,
% 9.17/5.34 ! [I: int,K: int,N2: int,J: int] :
% 9.17/5.34 ( ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ N2 )
% 9.17/5.34 => ( ( ord_less_eq_int @ N2 @ ( plus_plus_int @ J @ K ) )
% 9.17/5.34 => ( ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ N2 )
% 9.17/5.34 => ( ( ord_less_eq_int @ N2 @ ( plus_plus_int @ J @ K ) )
% 9.17/5.34 => ( ord_less_eq_int @ ( minus_minus_int @ N2 @ K ) @ J ) ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1817_less__diff__eq,axiom,
% 9.17/5.34 ! [A: code_integer,C: code_integer,B: code_integer] :
% 9.17/5.34 ( ( ord_le6747313008572928689nteger @ A @ ( minus_8373710615458151222nteger @ C @ B ) )
% 9.17/5.34 = ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1818_less__diff__eq,axiom,
% 9.17/5.34 ! [A: rat,C: rat,B: rat] :
% 9.17/5.34 ( ( ord_less_rat @ A @ ( minus_minus_rat @ C @ B ) )
% 9.17/5.34 = ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1819_less__diff__eq,axiom,
% 9.17/5.34 ! [A: int,C: int,B: int] :
% 9.17/5.34 ( ( ord_less_int @ A @ ( minus_minus_int @ C @ B ) )
% 9.17/5.34 = ( ord_less_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1820_diff__less__eq,axiom,
% 9.17/5.34 ! [A: code_integer,B: code_integer,C: code_integer] :
% 9.17/5.34 ( ( ord_le6747313008572928689nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C )
% 9.17/5.34 = ( ord_le6747313008572928689nteger @ A @ ( plus_p5714425477246183910nteger @ C @ B ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1821_diff__less__eq,axiom,
% 9.17/5.34 ! [A: rat,B: rat,C: rat] :
% 9.17/5.34 ( ( ord_less_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 9.17/5.34 = ( ord_less_rat @ A @ ( plus_plus_rat @ C @ B ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1822_diff__less__eq,axiom,
% 9.17/5.34 ! [A: int,B: int,C: int] :
% 9.17/5.34 ( ( ord_less_int @ ( minus_minus_int @ A @ B ) @ C )
% 9.17/5.34 = ( ord_less_int @ A @ ( plus_plus_int @ C @ B ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1823_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 9.17/5.34 ! [A: code_integer,B: code_integer] :
% 9.17/5.34 ( ~ ( ord_le6747313008572928689nteger @ A @ B )
% 9.17/5.34 => ( ( plus_p5714425477246183910nteger @ B @ ( minus_8373710615458151222nteger @ A @ B ) )
% 9.17/5.34 = A ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1824_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 9.17/5.34 ! [A: rat,B: rat] :
% 9.17/5.34 ( ~ ( ord_less_rat @ A @ B )
% 9.17/5.34 => ( ( plus_plus_rat @ B @ ( minus_minus_rat @ A @ B ) )
% 9.17/5.34 = A ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1825_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 9.17/5.34 ! [A: nat,B: nat] :
% 9.17/5.34 ( ~ ( ord_less_nat @ A @ B )
% 9.17/5.34 => ( ( plus_plus_nat @ B @ ( minus_minus_nat @ A @ B ) )
% 9.17/5.34 = A ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1826_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 9.17/5.34 ! [A: int,B: int] :
% 9.17/5.34 ( ~ ( ord_less_int @ A @ B )
% 9.17/5.34 => ( ( plus_plus_int @ B @ ( minus_minus_int @ A @ B ) )
% 9.17/5.34 = A ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1827_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 9.17/5.34 ( minus_minus_int
% 9.17/5.34 = ( ^ [A5: int,B4: int] : ( plus_plus_int @ A5 @ ( uminus_uminus_int @ B4 ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1828_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 9.17/5.34 ( minus_8373710615458151222nteger
% 9.17/5.34 = ( ^ [A5: code_integer,B4: code_integer] : ( plus_p5714425477246183910nteger @ A5 @ ( uminus1351360451143612070nteger @ B4 ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1829_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 9.17/5.34 ( minus_minus_rat
% 9.17/5.34 = ( ^ [A5: rat,B4: rat] : ( plus_plus_rat @ A5 @ ( uminus_uminus_rat @ B4 ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1830_diff__conv__add__uminus,axiom,
% 9.17/5.34 ( minus_minus_int
% 9.17/5.34 = ( ^ [A5: int,B4: int] : ( plus_plus_int @ A5 @ ( uminus_uminus_int @ B4 ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1831_diff__conv__add__uminus,axiom,
% 9.17/5.34 ( minus_8373710615458151222nteger
% 9.17/5.34 = ( ^ [A5: code_integer,B4: code_integer] : ( plus_p5714425477246183910nteger @ A5 @ ( uminus1351360451143612070nteger @ B4 ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1832_diff__conv__add__uminus,axiom,
% 9.17/5.34 ( minus_minus_rat
% 9.17/5.34 = ( ^ [A5: rat,B4: rat] : ( plus_plus_rat @ A5 @ ( uminus_uminus_rat @ B4 ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1833_group__cancel_Osub2,axiom,
% 9.17/5.34 ! [B5: int,K: int,B: int,A: int] :
% 9.17/5.34 ( ( B5
% 9.17/5.34 = ( plus_plus_int @ K @ B ) )
% 9.17/5.34 => ( ( minus_minus_int @ A @ B5 )
% 9.17/5.34 = ( plus_plus_int @ ( uminus_uminus_int @ K ) @ ( minus_minus_int @ A @ B ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1834_group__cancel_Osub2,axiom,
% 9.17/5.34 ! [B5: code_integer,K: code_integer,B: code_integer,A: code_integer] :
% 9.17/5.34 ( ( B5
% 9.17/5.34 = ( plus_p5714425477246183910nteger @ K @ B ) )
% 9.17/5.34 => ( ( minus_8373710615458151222nteger @ A @ B5 )
% 9.17/5.34 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ K ) @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1835_group__cancel_Osub2,axiom,
% 9.17/5.34 ! [B5: rat,K: rat,B: rat,A: rat] :
% 9.17/5.34 ( ( B5
% 9.17/5.34 = ( plus_plus_rat @ K @ B ) )
% 9.17/5.34 => ( ( minus_minus_rat @ A @ B5 )
% 9.17/5.34 = ( plus_plus_rat @ ( uminus_uminus_rat @ K ) @ ( minus_minus_rat @ A @ B ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1836_abs__triangle__ineq2__sym,axiom,
% 9.17/5.34 ! [A: code_integer,B: code_integer] : ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ B @ A ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1837_abs__triangle__ineq2__sym,axiom,
% 9.17/5.34 ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ B @ A ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1838_abs__triangle__ineq2__sym,axiom,
% 9.17/5.34 ! [A: int,B: int] : ( ord_less_eq_int @ ( minus_minus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) @ ( abs_abs_int @ ( minus_minus_int @ B @ A ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1839_abs__triangle__ineq3,axiom,
% 9.17/5.34 ! [A: code_integer,B: code_integer] : ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1840_abs__triangle__ineq3,axiom,
% 9.17/5.34 ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ A @ B ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1841_abs__triangle__ineq3,axiom,
% 9.17/5.34 ! [A: int,B: int] : ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) @ ( abs_abs_int @ ( minus_minus_int @ A @ B ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1842_abs__triangle__ineq2,axiom,
% 9.17/5.34 ! [A: code_integer,B: code_integer] : ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1843_abs__triangle__ineq2,axiom,
% 9.17/5.34 ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ A @ B ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1844_abs__triangle__ineq2,axiom,
% 9.17/5.34 ! [A: int,B: int] : ( ord_less_eq_int @ ( minus_minus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) @ ( abs_abs_int @ ( minus_minus_int @ A @ B ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1845_add__scale__eq__noteq,axiom,
% 9.17/5.34 ! [R2: code_integer,A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 9.17/5.34 ( ( R2 != zero_z3403309356797280102nteger )
% 9.17/5.34 => ( ( ( A = B )
% 9.17/5.34 & ( C != D2 ) )
% 9.17/5.34 => ( ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ R2 @ C ) )
% 9.17/5.34 != ( plus_p5714425477246183910nteger @ B @ ( times_3573771949741848930nteger @ R2 @ D2 ) ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1846_add__scale__eq__noteq,axiom,
% 9.17/5.34 ! [R2: rat,A: rat,B: rat,C: rat,D2: rat] :
% 9.17/5.34 ( ( R2 != zero_zero_rat )
% 9.17/5.34 => ( ( ( A = B )
% 9.17/5.34 & ( C != D2 ) )
% 9.17/5.34 => ( ( plus_plus_rat @ A @ ( times_times_rat @ R2 @ C ) )
% 9.17/5.34 != ( plus_plus_rat @ B @ ( times_times_rat @ R2 @ D2 ) ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1847_add__scale__eq__noteq,axiom,
% 9.17/5.34 ! [R2: nat,A: nat,B: nat,C: nat,D2: nat] :
% 9.17/5.34 ( ( R2 != zero_zero_nat )
% 9.17/5.34 => ( ( ( A = B )
% 9.17/5.34 & ( C != D2 ) )
% 9.17/5.34 => ( ( plus_plus_nat @ A @ ( times_times_nat @ R2 @ C ) )
% 9.17/5.34 != ( plus_plus_nat @ B @ ( times_times_nat @ R2 @ D2 ) ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1848_add__scale__eq__noteq,axiom,
% 9.17/5.34 ! [R2: int,A: int,B: int,C: int,D2: int] :
% 9.17/5.34 ( ( R2 != zero_zero_int )
% 9.17/5.34 => ( ( ( A = B )
% 9.17/5.34 & ( C != D2 ) )
% 9.17/5.34 => ( ( plus_plus_int @ A @ ( times_times_int @ R2 @ C ) )
% 9.17/5.34 != ( plus_plus_int @ B @ ( times_times_int @ R2 @ D2 ) ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1849_less__1__mult,axiom,
% 9.17/5.34 ! [M2: code_integer,N2: code_integer] :
% 9.17/5.34 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ M2 )
% 9.17/5.34 => ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ N2 )
% 9.17/5.34 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ M2 @ N2 ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1850_less__1__mult,axiom,
% 9.17/5.34 ! [M2: rat,N2: rat] :
% 9.17/5.34 ( ( ord_less_rat @ one_one_rat @ M2 )
% 9.17/5.34 => ( ( ord_less_rat @ one_one_rat @ N2 )
% 9.17/5.34 => ( ord_less_rat @ one_one_rat @ ( times_times_rat @ M2 @ N2 ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1851_less__1__mult,axiom,
% 9.17/5.34 ! [M2: nat,N2: nat] :
% 9.17/5.34 ( ( ord_less_nat @ one_one_nat @ M2 )
% 9.17/5.34 => ( ( ord_less_nat @ one_one_nat @ N2 )
% 9.17/5.34 => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ M2 @ N2 ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1852_less__1__mult,axiom,
% 9.17/5.34 ! [M2: int,N2: int] :
% 9.17/5.34 ( ( ord_less_int @ one_one_int @ M2 )
% 9.17/5.34 => ( ( ord_less_int @ one_one_int @ N2 )
% 9.17/5.34 => ( ord_less_int @ one_one_int @ ( times_times_int @ M2 @ N2 ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1853_square__eq__1__iff,axiom,
% 9.17/5.34 ! [X: int] :
% 9.17/5.34 ( ( ( times_times_int @ X @ X )
% 9.17/5.34 = one_one_int )
% 9.17/5.34 = ( ( X = one_one_int )
% 9.17/5.34 | ( X
% 9.17/5.34 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1854_square__eq__1__iff,axiom,
% 9.17/5.34 ! [X: code_integer] :
% 9.17/5.34 ( ( ( times_3573771949741848930nteger @ X @ X )
% 9.17/5.34 = one_one_Code_integer )
% 9.17/5.34 = ( ( X = one_one_Code_integer )
% 9.17/5.34 | ( X
% 9.17/5.34 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1855_square__eq__1__iff,axiom,
% 9.17/5.34 ! [X: rat] :
% 9.17/5.34 ( ( ( times_times_rat @ X @ X )
% 9.17/5.34 = one_one_rat )
% 9.17/5.34 = ( ( X = one_one_rat )
% 9.17/5.34 | ( X
% 9.17/5.34 = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1856_diff__add__0,axiom,
% 9.17/5.34 ! [N2: nat,M2: nat] :
% 9.17/5.34 ( ( minus_minus_nat @ N2 @ ( plus_plus_nat @ N2 @ M2 ) )
% 9.17/5.34 = zero_zero_nat ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1857_less__diff__conv,axiom,
% 9.17/5.34 ! [I: nat,J: nat,K: nat] :
% 9.17/5.34 ( ( ord_less_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 9.17/5.34 = ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ J ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1858_add__diff__inverse__nat,axiom,
% 9.17/5.34 ! [M2: nat,N2: nat] :
% 9.17/5.34 ( ~ ( ord_less_nat @ M2 @ N2 )
% 9.17/5.34 => ( ( plus_plus_nat @ N2 @ ( minus_minus_nat @ M2 @ N2 ) )
% 9.17/5.34 = M2 ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1859_less__diff__conv2,axiom,
% 9.17/5.34 ! [K: nat,J: nat,I: nat] :
% 9.17/5.34 ( ( ord_less_eq_nat @ K @ J )
% 9.17/5.34 => ( ( ord_less_nat @ ( minus_minus_nat @ J @ K ) @ I )
% 9.17/5.34 = ( ord_less_nat @ J @ ( plus_plus_nat @ I @ K ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1860_mlex__snd__decrI,axiom,
% 9.17/5.34 ! [A: nat,A4: nat,B: nat,B3: nat,N6: nat] :
% 9.17/5.34 ( ( A = A4 )
% 9.17/5.34 => ( ( ord_less_nat @ B @ B3 )
% 9.17/5.34 => ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ A @ N6 ) @ B ) @ ( plus_plus_nat @ ( times_times_nat @ A4 @ N6 ) @ B3 ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1861_mlex__fst__decrI,axiom,
% 9.17/5.34 ! [A: nat,A4: nat,B: nat,N6: nat,B3: nat] :
% 9.17/5.34 ( ( ord_less_nat @ A @ A4 )
% 9.17/5.34 => ( ( ord_less_nat @ B @ N6 )
% 9.17/5.34 => ( ( ord_less_nat @ B3 @ N6 )
% 9.17/5.34 => ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ A @ N6 ) @ B ) @ ( plus_plus_nat @ ( times_times_nat @ A4 @ N6 ) @ B3 ) ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1862_mlex__bound,axiom,
% 9.17/5.34 ! [A: nat,A2: nat,B: nat,N6: nat] :
% 9.17/5.34 ( ( ord_less_nat @ A @ A2 )
% 9.17/5.34 => ( ( ord_less_nat @ B @ N6 )
% 9.17/5.34 => ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ A @ N6 ) @ B ) @ ( times_times_nat @ A2 @ N6 ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1863_mult__eq__self__implies__10,axiom,
% 9.17/5.34 ! [M2: nat,N2: nat] :
% 9.17/5.34 ( ( M2
% 9.17/5.34 = ( times_times_nat @ M2 @ N2 ) )
% 9.17/5.34 => ( ( N2 = one_one_nat )
% 9.17/5.34 | ( M2 = zero_zero_nat ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1864_field__le__mult__one__interval,axiom,
% 9.17/5.34 ! [X: rat,Y: rat] :
% 9.17/5.34 ( ! [Z3: rat] :
% 9.17/5.34 ( ( ord_less_rat @ zero_zero_rat @ Z3 )
% 9.17/5.34 => ( ( ord_less_rat @ Z3 @ one_one_rat )
% 9.17/5.34 => ( ord_less_eq_rat @ ( times_times_rat @ Z3 @ X ) @ Y ) ) )
% 9.17/5.34 => ( ord_less_eq_rat @ X @ Y ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1865_abs__diff__le__iff,axiom,
% 9.17/5.34 ! [X: code_integer,A: code_integer,R2: code_integer] :
% 9.17/5.34 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ X @ A ) ) @ R2 )
% 9.17/5.34 = ( ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ A @ R2 ) @ X )
% 9.17/5.34 & ( ord_le3102999989581377725nteger @ X @ ( plus_p5714425477246183910nteger @ A @ R2 ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1866_abs__diff__le__iff,axiom,
% 9.17/5.34 ! [X: rat,A: rat,R2: rat] :
% 9.17/5.34 ( ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X @ A ) ) @ R2 )
% 9.17/5.34 = ( ( ord_less_eq_rat @ ( minus_minus_rat @ A @ R2 ) @ X )
% 9.17/5.34 & ( ord_less_eq_rat @ X @ ( plus_plus_rat @ A @ R2 ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1867_abs__diff__le__iff,axiom,
% 9.17/5.34 ! [X: int,A: int,R2: int] :
% 9.17/5.34 ( ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ X @ A ) ) @ R2 )
% 9.17/5.34 = ( ( ord_less_eq_int @ ( minus_minus_int @ A @ R2 ) @ X )
% 9.17/5.34 & ( ord_less_eq_int @ X @ ( plus_plus_int @ A @ R2 ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1868_abs__diff__triangle__ineq,axiom,
% 9.17/5.34 ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] : ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ ( plus_p5714425477246183910nteger @ C @ D2 ) ) ) @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ C ) ) @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ B @ D2 ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1869_abs__diff__triangle__ineq,axiom,
% 9.17/5.34 ! [A: rat,B: rat,C: rat,D2: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ C @ D2 ) ) ) @ ( plus_plus_rat @ ( abs_abs_rat @ ( minus_minus_rat @ A @ C ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ B @ D2 ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1870_abs__diff__triangle__ineq,axiom,
% 9.17/5.34 ! [A: int,B: int,C: int,D2: int] : ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ ( plus_plus_int @ C @ D2 ) ) ) @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ A @ C ) ) @ ( abs_abs_int @ ( minus_minus_int @ B @ D2 ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1871_abs__triangle__ineq4,axiom,
% 9.17/5.34 ! [A: code_integer,B: code_integer] : ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ B ) ) @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1872_abs__triangle__ineq4,axiom,
% 9.17/5.34 ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ A @ B ) ) @ ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1873_abs__triangle__ineq4,axiom,
% 9.17/5.34 ! [A: int,B: int] : ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ A @ B ) ) @ ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1874_abs__diff__less__iff,axiom,
% 9.17/5.34 ! [X: code_integer,A: code_integer,R2: code_integer] :
% 9.17/5.34 ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ X @ A ) ) @ R2 )
% 9.17/5.34 = ( ( ord_le6747313008572928689nteger @ ( minus_8373710615458151222nteger @ A @ R2 ) @ X )
% 9.17/5.34 & ( ord_le6747313008572928689nteger @ X @ ( plus_p5714425477246183910nteger @ A @ R2 ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1875_abs__diff__less__iff,axiom,
% 9.17/5.34 ! [X: rat,A: rat,R2: rat] :
% 9.17/5.34 ( ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X @ A ) ) @ R2 )
% 9.17/5.34 = ( ( ord_less_rat @ ( minus_minus_rat @ A @ R2 ) @ X )
% 9.17/5.34 & ( ord_less_rat @ X @ ( plus_plus_rat @ A @ R2 ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1876_abs__diff__less__iff,axiom,
% 9.17/5.34 ! [X: int,A: int,R2: int] :
% 9.17/5.34 ( ( ord_less_int @ ( abs_abs_int @ ( minus_minus_int @ X @ A ) ) @ R2 )
% 9.17/5.34 = ( ( ord_less_int @ ( minus_minus_int @ A @ R2 ) @ X )
% 9.17/5.34 & ( ord_less_int @ X @ ( plus_plus_int @ A @ R2 ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1877_sum__squares__ge__zero,axiom,
% 9.17/5.34 ! [X: code_integer,Y: code_integer] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ X @ X ) @ ( times_3573771949741848930nteger @ Y @ Y ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1878_sum__squares__ge__zero,axiom,
% 9.17/5.34 ! [X: rat,Y: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1879_sum__squares__ge__zero,axiom,
% 9.17/5.34 ! [X: int,Y: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1880_mult__left__le,axiom,
% 9.17/5.34 ! [C: code_integer,A: code_integer] :
% 9.17/5.34 ( ( ord_le3102999989581377725nteger @ C @ one_one_Code_integer )
% 9.17/5.34 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 9.17/5.34 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ C ) @ A ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1881_mult__left__le,axiom,
% 9.17/5.34 ! [C: rat,A: rat] :
% 9.17/5.34 ( ( ord_less_eq_rat @ C @ one_one_rat )
% 9.17/5.34 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 9.17/5.34 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ A ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1882_mult__left__le,axiom,
% 9.17/5.34 ! [C: nat,A: nat] :
% 9.17/5.34 ( ( ord_less_eq_nat @ C @ one_one_nat )
% 9.17/5.34 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 9.17/5.34 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ A ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1883_mult__left__le,axiom,
% 9.17/5.34 ! [C: int,A: int] :
% 9.17/5.34 ( ( ord_less_eq_int @ C @ one_one_int )
% 9.17/5.34 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 9.17/5.34 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ A ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1884_mult__le__one,axiom,
% 9.17/5.34 ! [A: code_integer,B: code_integer] :
% 9.17/5.34 ( ( ord_le3102999989581377725nteger @ A @ one_one_Code_integer )
% 9.17/5.34 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 9.17/5.34 => ( ( ord_le3102999989581377725nteger @ B @ one_one_Code_integer )
% 9.17/5.34 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ B ) @ one_one_Code_integer ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1885_mult__le__one,axiom,
% 9.17/5.34 ! [A: rat,B: rat] :
% 9.17/5.34 ( ( ord_less_eq_rat @ A @ one_one_rat )
% 9.17/5.34 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 9.17/5.34 => ( ( ord_less_eq_rat @ B @ one_one_rat )
% 9.17/5.34 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ one_one_rat ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1886_mult__le__one,axiom,
% 9.17/5.34 ! [A: nat,B: nat] :
% 9.17/5.34 ( ( ord_less_eq_nat @ A @ one_one_nat )
% 9.17/5.34 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 9.17/5.34 => ( ( ord_less_eq_nat @ B @ one_one_nat )
% 9.17/5.34 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ one_one_nat ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1887_mult__le__one,axiom,
% 9.17/5.34 ! [A: int,B: int] :
% 9.17/5.34 ( ( ord_less_eq_int @ A @ one_one_int )
% 9.17/5.34 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 9.17/5.34 => ( ( ord_less_eq_int @ B @ one_one_int )
% 9.17/5.34 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ one_one_int ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1888_mult__right__le__one__le,axiom,
% 9.17/5.34 ! [X: code_integer,Y: code_integer] :
% 9.17/5.34 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X )
% 9.17/5.34 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y )
% 9.17/5.34 => ( ( ord_le3102999989581377725nteger @ Y @ one_one_Code_integer )
% 9.17/5.34 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ X @ Y ) @ X ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1889_mult__right__le__one__le,axiom,
% 9.17/5.34 ! [X: rat,Y: rat] :
% 9.17/5.34 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 9.17/5.34 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 9.17/5.34 => ( ( ord_less_eq_rat @ Y @ one_one_rat )
% 9.17/5.34 => ( ord_less_eq_rat @ ( times_times_rat @ X @ Y ) @ X ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1890_mult__right__le__one__le,axiom,
% 9.17/5.34 ! [X: int,Y: int] :
% 9.17/5.34 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 9.17/5.34 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 9.17/5.34 => ( ( ord_less_eq_int @ Y @ one_one_int )
% 9.17/5.34 => ( ord_less_eq_int @ ( times_times_int @ X @ Y ) @ X ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1891_mult__left__le__one__le,axiom,
% 9.17/5.34 ! [X: code_integer,Y: code_integer] :
% 9.17/5.34 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X )
% 9.17/5.34 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y )
% 9.17/5.34 => ( ( ord_le3102999989581377725nteger @ Y @ one_one_Code_integer )
% 9.17/5.34 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ Y @ X ) @ X ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1892_mult__left__le__one__le,axiom,
% 9.17/5.34 ! [X: rat,Y: rat] :
% 9.17/5.34 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 9.17/5.34 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 9.17/5.34 => ( ( ord_less_eq_rat @ Y @ one_one_rat )
% 9.17/5.34 => ( ord_less_eq_rat @ ( times_times_rat @ Y @ X ) @ X ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1893_mult__left__le__one__le,axiom,
% 9.17/5.34 ! [X: int,Y: int] :
% 9.17/5.34 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 9.17/5.34 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 9.17/5.34 => ( ( ord_less_eq_int @ Y @ one_one_int )
% 9.17/5.34 => ( ord_less_eq_int @ ( times_times_int @ Y @ X ) @ X ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1894_not__sum__squares__lt__zero,axiom,
% 9.17/5.34 ! [X: code_integer,Y: code_integer] :
% 9.17/5.34 ~ ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ X @ X ) @ ( times_3573771949741848930nteger @ Y @ Y ) ) @ zero_z3403309356797280102nteger ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1895_not__sum__squares__lt__zero,axiom,
% 9.17/5.34 ! [X: rat,Y: rat] :
% 9.17/5.34 ~ ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) ) @ zero_zero_rat ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1896_not__sum__squares__lt__zero,axiom,
% 9.17/5.34 ! [X: int,Y: int] :
% 9.17/5.34 ~ ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) @ zero_zero_int ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1897_nat__diff__split,axiom,
% 9.17/5.34 ! [P: nat > $o,A: nat,B: nat] :
% 9.17/5.34 ( ( P @ ( minus_minus_nat @ A @ B ) )
% 9.17/5.34 = ( ( ( ord_less_nat @ A @ B )
% 9.17/5.34 => ( P @ zero_zero_nat ) )
% 9.17/5.34 & ! [D4: nat] :
% 9.17/5.34 ( ( A
% 9.17/5.34 = ( plus_plus_nat @ B @ D4 ) )
% 9.17/5.34 => ( P @ D4 ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1898_nat__diff__split__asm,axiom,
% 9.17/5.34 ! [P: nat > $o,A: nat,B: nat] :
% 9.17/5.34 ( ( P @ ( minus_minus_nat @ A @ B ) )
% 9.17/5.34 = ( ~ ( ( ( ord_less_nat @ A @ B )
% 9.17/5.34 & ~ ( P @ zero_zero_nat ) )
% 9.17/5.34 | ? [D4: nat] :
% 9.17/5.34 ( ( A
% 9.17/5.34 = ( plus_plus_nat @ B @ D4 ) )
% 9.17/5.34 & ~ ( P @ D4 ) ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1899_dbl__dec__def,axiom,
% 9.17/5.34 ( neg_nu7757733837767384882nteger
% 9.17/5.34 = ( ^ [X3: code_integer] : ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ X3 @ X3 ) @ one_one_Code_integer ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1900_dbl__dec__def,axiom,
% 9.17/5.34 ( neg_nu3179335615603231917ec_rat
% 9.17/5.34 = ( ^ [X3: rat] : ( minus_minus_rat @ ( plus_plus_rat @ X3 @ X3 ) @ one_one_rat ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1901_dbl__dec__def,axiom,
% 9.17/5.34 ( neg_nu3811975205180677377ec_int
% 9.17/5.34 = ( ^ [X3: int] : ( minus_minus_int @ ( plus_plus_int @ X3 @ X3 ) @ one_one_int ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1902_mult__le__cancel__left1,axiom,
% 9.17/5.34 ! [C: code_integer,B: code_integer] :
% 9.17/5.34 ( ( ord_le3102999989581377725nteger @ C @ ( times_3573771949741848930nteger @ C @ B ) )
% 9.17/5.34 = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 9.17/5.34 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ B ) )
% 9.17/5.34 & ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 9.17/5.34 => ( ord_le3102999989581377725nteger @ B @ one_one_Code_integer ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1903_mult__le__cancel__left1,axiom,
% 9.17/5.34 ! [C: rat,B: rat] :
% 9.17/5.34 ( ( ord_less_eq_rat @ C @ ( times_times_rat @ C @ B ) )
% 9.17/5.34 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 9.17/5.34 => ( ord_less_eq_rat @ one_one_rat @ B ) )
% 9.17/5.34 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 9.17/5.34 => ( ord_less_eq_rat @ B @ one_one_rat ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1904_mult__le__cancel__left1,axiom,
% 9.17/5.34 ! [C: int,B: int] :
% 9.17/5.34 ( ( ord_less_eq_int @ C @ ( times_times_int @ C @ B ) )
% 9.17/5.34 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 9.17/5.34 => ( ord_less_eq_int @ one_one_int @ B ) )
% 9.17/5.34 & ( ( ord_less_int @ C @ zero_zero_int )
% 9.17/5.34 => ( ord_less_eq_int @ B @ one_one_int ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1905_mult__le__cancel__left2,axiom,
% 9.17/5.34 ! [C: code_integer,A: code_integer] :
% 9.17/5.34 ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ C @ A ) @ C )
% 9.17/5.34 = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 9.17/5.34 => ( ord_le3102999989581377725nteger @ A @ one_one_Code_integer ) )
% 9.17/5.34 & ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 9.17/5.34 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ A ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1906_mult__le__cancel__left2,axiom,
% 9.17/5.34 ! [C: rat,A: rat] :
% 9.17/5.34 ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ C )
% 9.17/5.34 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 9.17/5.34 => ( ord_less_eq_rat @ A @ one_one_rat ) )
% 9.17/5.34 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 9.17/5.34 => ( ord_less_eq_rat @ one_one_rat @ A ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1907_mult__le__cancel__left2,axiom,
% 9.17/5.34 ! [C: int,A: int] :
% 9.17/5.34 ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ C )
% 9.17/5.34 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 9.17/5.34 => ( ord_less_eq_int @ A @ one_one_int ) )
% 9.17/5.34 & ( ( ord_less_int @ C @ zero_zero_int )
% 9.17/5.34 => ( ord_less_eq_int @ one_one_int @ A ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1908_mult__le__cancel__right1,axiom,
% 9.17/5.34 ! [C: code_integer,B: code_integer] :
% 9.17/5.34 ( ( ord_le3102999989581377725nteger @ C @ ( times_3573771949741848930nteger @ B @ C ) )
% 9.17/5.34 = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 9.17/5.34 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ B ) )
% 9.17/5.34 & ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 9.17/5.34 => ( ord_le3102999989581377725nteger @ B @ one_one_Code_integer ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1909_mult__le__cancel__right1,axiom,
% 9.17/5.34 ! [C: rat,B: rat] :
% 9.17/5.34 ( ( ord_less_eq_rat @ C @ ( times_times_rat @ B @ C ) )
% 9.17/5.34 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 9.17/5.34 => ( ord_less_eq_rat @ one_one_rat @ B ) )
% 9.17/5.34 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 9.17/5.34 => ( ord_less_eq_rat @ B @ one_one_rat ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1910_mult__le__cancel__right1,axiom,
% 9.17/5.34 ! [C: int,B: int] :
% 9.17/5.34 ( ( ord_less_eq_int @ C @ ( times_times_int @ B @ C ) )
% 9.17/5.34 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 9.17/5.34 => ( ord_less_eq_int @ one_one_int @ B ) )
% 9.17/5.34 & ( ( ord_less_int @ C @ zero_zero_int )
% 9.17/5.34 => ( ord_less_eq_int @ B @ one_one_int ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1911_mult__le__cancel__right2,axiom,
% 9.17/5.34 ! [A: code_integer,C: code_integer] :
% 9.17/5.34 ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ C ) @ C )
% 9.17/5.34 = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 9.17/5.34 => ( ord_le3102999989581377725nteger @ A @ one_one_Code_integer ) )
% 9.17/5.34 & ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 9.17/5.34 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ A ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1912_mult__le__cancel__right2,axiom,
% 9.17/5.34 ! [A: rat,C: rat] :
% 9.17/5.34 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ C )
% 9.17/5.34 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 9.17/5.34 => ( ord_less_eq_rat @ A @ one_one_rat ) )
% 9.17/5.34 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 9.17/5.34 => ( ord_less_eq_rat @ one_one_rat @ A ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1913_mult__le__cancel__right2,axiom,
% 9.17/5.34 ! [A: int,C: int] :
% 9.17/5.34 ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ C )
% 9.17/5.34 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 9.17/5.34 => ( ord_less_eq_int @ A @ one_one_int ) )
% 9.17/5.34 & ( ( ord_less_int @ C @ zero_zero_int )
% 9.17/5.34 => ( ord_less_eq_int @ one_one_int @ A ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1914_mult__less__cancel__left1,axiom,
% 9.17/5.34 ! [C: code_integer,B: code_integer] :
% 9.17/5.34 ( ( ord_le6747313008572928689nteger @ C @ ( times_3573771949741848930nteger @ C @ B ) )
% 9.17/5.34 = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 9.17/5.34 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ B ) )
% 9.17/5.34 & ( ( ord_le3102999989581377725nteger @ C @ zero_z3403309356797280102nteger )
% 9.17/5.34 => ( ord_le6747313008572928689nteger @ B @ one_one_Code_integer ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1915_mult__less__cancel__left1,axiom,
% 9.17/5.34 ! [C: rat,B: rat] :
% 9.17/5.34 ( ( ord_less_rat @ C @ ( times_times_rat @ C @ B ) )
% 9.17/5.34 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 9.17/5.34 => ( ord_less_rat @ one_one_rat @ B ) )
% 9.17/5.34 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 9.17/5.34 => ( ord_less_rat @ B @ one_one_rat ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1916_mult__less__cancel__left1,axiom,
% 9.17/5.34 ! [C: int,B: int] :
% 9.17/5.34 ( ( ord_less_int @ C @ ( times_times_int @ C @ B ) )
% 9.17/5.34 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 9.17/5.34 => ( ord_less_int @ one_one_int @ B ) )
% 9.17/5.34 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 9.17/5.34 => ( ord_less_int @ B @ one_one_int ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1917_mult__less__cancel__left2,axiom,
% 9.17/5.34 ! [C: code_integer,A: code_integer] :
% 9.17/5.34 ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C @ A ) @ C )
% 9.17/5.34 = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 9.17/5.34 => ( ord_le6747313008572928689nteger @ A @ one_one_Code_integer ) )
% 9.17/5.34 & ( ( ord_le3102999989581377725nteger @ C @ zero_z3403309356797280102nteger )
% 9.17/5.34 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1918_mult__less__cancel__left2,axiom,
% 9.17/5.34 ! [C: rat,A: rat] :
% 9.17/5.34 ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ C )
% 9.17/5.34 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 9.17/5.34 => ( ord_less_rat @ A @ one_one_rat ) )
% 9.17/5.34 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 9.17/5.34 => ( ord_less_rat @ one_one_rat @ A ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1919_mult__less__cancel__left2,axiom,
% 9.17/5.34 ! [C: int,A: int] :
% 9.17/5.34 ( ( ord_less_int @ ( times_times_int @ C @ A ) @ C )
% 9.17/5.34 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 9.17/5.34 => ( ord_less_int @ A @ one_one_int ) )
% 9.17/5.34 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 9.17/5.34 => ( ord_less_int @ one_one_int @ A ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1920_mult__less__cancel__right1,axiom,
% 9.17/5.34 ! [C: code_integer,B: code_integer] :
% 9.17/5.34 ( ( ord_le6747313008572928689nteger @ C @ ( times_3573771949741848930nteger @ B @ C ) )
% 9.17/5.34 = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 9.17/5.34 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ B ) )
% 9.17/5.34 & ( ( ord_le3102999989581377725nteger @ C @ zero_z3403309356797280102nteger )
% 9.17/5.34 => ( ord_le6747313008572928689nteger @ B @ one_one_Code_integer ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1921_mult__less__cancel__right1,axiom,
% 9.17/5.34 ! [C: rat,B: rat] :
% 9.17/5.34 ( ( ord_less_rat @ C @ ( times_times_rat @ B @ C ) )
% 9.17/5.34 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 9.17/5.34 => ( ord_less_rat @ one_one_rat @ B ) )
% 9.17/5.34 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 9.17/5.34 => ( ord_less_rat @ B @ one_one_rat ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1922_mult__less__cancel__right1,axiom,
% 9.17/5.34 ! [C: int,B: int] :
% 9.17/5.34 ( ( ord_less_int @ C @ ( times_times_int @ B @ C ) )
% 9.17/5.34 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 9.17/5.34 => ( ord_less_int @ one_one_int @ B ) )
% 9.17/5.34 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 9.17/5.34 => ( ord_less_int @ B @ one_one_int ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1923_mult__less__cancel__right2,axiom,
% 9.17/5.34 ! [A: code_integer,C: code_integer] :
% 9.17/5.34 ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ C ) @ C )
% 9.17/5.34 = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 9.17/5.34 => ( ord_le6747313008572928689nteger @ A @ one_one_Code_integer ) )
% 9.17/5.34 & ( ( ord_le3102999989581377725nteger @ C @ zero_z3403309356797280102nteger )
% 9.17/5.34 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1924_mult__less__cancel__right2,axiom,
% 9.17/5.34 ! [A: rat,C: rat] :
% 9.17/5.34 ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ C )
% 9.17/5.34 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 9.17/5.34 => ( ord_less_rat @ A @ one_one_rat ) )
% 9.17/5.34 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 9.17/5.34 => ( ord_less_rat @ one_one_rat @ A ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1925_mult__less__cancel__right2,axiom,
% 9.17/5.34 ! [A: int,C: int] :
% 9.17/5.34 ( ( ord_less_int @ ( times_times_int @ A @ C ) @ C )
% 9.17/5.34 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 9.17/5.34 => ( ord_less_int @ A @ one_one_int ) )
% 9.17/5.34 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 9.17/5.34 => ( ord_less_int @ one_one_int @ A ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1926_convex__bound__le,axiom,
% 9.17/5.34 ! [X: code_integer,A: code_integer,Y: code_integer,U: code_integer,V: code_integer] :
% 9.17/5.34 ( ( ord_le3102999989581377725nteger @ X @ A )
% 9.17/5.34 => ( ( ord_le3102999989581377725nteger @ Y @ A )
% 9.17/5.34 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ U )
% 9.17/5.34 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ V )
% 9.17/5.34 => ( ( ( plus_p5714425477246183910nteger @ U @ V )
% 9.17/5.34 = one_one_Code_integer )
% 9.17/5.34 => ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ U @ X ) @ ( times_3573771949741848930nteger @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1927_convex__bound__le,axiom,
% 9.17/5.34 ! [X: rat,A: rat,Y: rat,U: rat,V: rat] :
% 9.17/5.34 ( ( ord_less_eq_rat @ X @ A )
% 9.17/5.34 => ( ( ord_less_eq_rat @ Y @ A )
% 9.17/5.34 => ( ( ord_less_eq_rat @ zero_zero_rat @ U )
% 9.17/5.34 => ( ( ord_less_eq_rat @ zero_zero_rat @ V )
% 9.17/5.34 => ( ( ( plus_plus_rat @ U @ V )
% 9.17/5.34 = one_one_rat )
% 9.17/5.34 => ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ U @ X ) @ ( times_times_rat @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1928_convex__bound__le,axiom,
% 9.17/5.34 ! [X: int,A: int,Y: int,U: int,V: int] :
% 9.17/5.34 ( ( ord_less_eq_int @ X @ A )
% 9.17/5.34 => ( ( ord_less_eq_int @ Y @ A )
% 9.17/5.34 => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 9.17/5.34 => ( ( ord_less_eq_int @ zero_zero_int @ V )
% 9.17/5.34 => ( ( ( plus_plus_int @ U @ V )
% 9.17/5.34 = one_one_int )
% 9.17/5.34 => ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ U @ X ) @ ( times_times_int @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1929_is__num_Ocases,axiom,
% 9.17/5.34 ! [A: int] :
% 9.17/5.34 ( ( neg_nu7441568979088483369um_int @ A )
% 9.17/5.34 => ( ( A != one_one_int )
% 9.17/5.34 => ( ! [X4: int] :
% 9.17/5.34 ( ( A
% 9.17/5.34 = ( uminus_uminus_int @ X4 ) )
% 9.17/5.34 => ~ ( neg_nu7441568979088483369um_int @ X4 ) )
% 9.17/5.34 => ~ ! [X4: int,Y5: int] :
% 9.17/5.34 ( ( A
% 9.17/5.34 = ( plus_plus_int @ X4 @ Y5 ) )
% 9.17/5.34 => ( ( neg_nu7441568979088483369um_int @ X4 )
% 9.17/5.34 => ~ ( neg_nu7441568979088483369um_int @ Y5 ) ) ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1930_is__num_Ocases,axiom,
% 9.17/5.34 ! [A: code_integer] :
% 9.17/5.34 ( ( neg_nu2435721316971906650nteger @ A )
% 9.17/5.34 => ( ( A != one_one_Code_integer )
% 9.17/5.34 => ( ! [X4: code_integer] :
% 9.17/5.34 ( ( A
% 9.17/5.34 = ( uminus1351360451143612070nteger @ X4 ) )
% 9.17/5.34 => ~ ( neg_nu2435721316971906650nteger @ X4 ) )
% 9.17/5.34 => ~ ! [X4: code_integer,Y5: code_integer] :
% 9.17/5.34 ( ( A
% 9.17/5.34 = ( plus_p5714425477246183910nteger @ X4 @ Y5 ) )
% 9.17/5.34 => ( ( neg_nu2435721316971906650nteger @ X4 )
% 9.17/5.34 => ~ ( neg_nu2435721316971906650nteger @ Y5 ) ) ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1931_is__num_Ocases,axiom,
% 9.17/5.34 ! [A: rat] :
% 9.17/5.34 ( ( neg_nu6808929389511037909um_rat @ A )
% 9.17/5.34 => ( ( A != one_one_rat )
% 9.17/5.34 => ( ! [X4: rat] :
% 9.17/5.34 ( ( A
% 9.17/5.34 = ( uminus_uminus_rat @ X4 ) )
% 9.17/5.34 => ~ ( neg_nu6808929389511037909um_rat @ X4 ) )
% 9.17/5.34 => ~ ! [X4: rat,Y5: rat] :
% 9.17/5.34 ( ( A
% 9.17/5.34 = ( plus_plus_rat @ X4 @ Y5 ) )
% 9.17/5.34 => ( ( neg_nu6808929389511037909um_rat @ X4 )
% 9.17/5.34 => ~ ( neg_nu6808929389511037909um_rat @ Y5 ) ) ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1932_is__num_Osimps,axiom,
% 9.17/5.34 ( neg_nu7441568979088483369um_int
% 9.17/5.34 = ( ^ [A5: int] :
% 9.17/5.34 ( ( A5 = one_one_int )
% 9.17/5.34 | ? [X3: int] :
% 9.17/5.34 ( ( A5
% 9.17/5.34 = ( uminus_uminus_int @ X3 ) )
% 9.17/5.34 & ( neg_nu7441568979088483369um_int @ X3 ) )
% 9.17/5.34 | ? [X3: int,Y3: int] :
% 9.17/5.34 ( ( A5
% 9.17/5.34 = ( plus_plus_int @ X3 @ Y3 ) )
% 9.17/5.34 & ( neg_nu7441568979088483369um_int @ X3 )
% 9.17/5.34 & ( neg_nu7441568979088483369um_int @ Y3 ) ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1933_is__num_Osimps,axiom,
% 9.17/5.34 ( neg_nu2435721316971906650nteger
% 9.17/5.34 = ( ^ [A5: code_integer] :
% 9.17/5.34 ( ( A5 = one_one_Code_integer )
% 9.17/5.34 | ? [X3: code_integer] :
% 9.17/5.34 ( ( A5
% 9.17/5.34 = ( uminus1351360451143612070nteger @ X3 ) )
% 9.17/5.34 & ( neg_nu2435721316971906650nteger @ X3 ) )
% 9.17/5.34 | ? [X3: code_integer,Y3: code_integer] :
% 9.17/5.34 ( ( A5
% 9.17/5.34 = ( plus_p5714425477246183910nteger @ X3 @ Y3 ) )
% 9.17/5.34 & ( neg_nu2435721316971906650nteger @ X3 )
% 9.17/5.34 & ( neg_nu2435721316971906650nteger @ Y3 ) ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1934_is__num_Osimps,axiom,
% 9.17/5.34 ( neg_nu6808929389511037909um_rat
% 9.17/5.34 = ( ^ [A5: rat] :
% 9.17/5.34 ( ( A5 = one_one_rat )
% 9.17/5.34 | ? [X3: rat] :
% 9.17/5.34 ( ( A5
% 9.17/5.34 = ( uminus_uminus_rat @ X3 ) )
% 9.17/5.34 & ( neg_nu6808929389511037909um_rat @ X3 ) )
% 9.17/5.34 | ? [X3: rat,Y3: rat] :
% 9.17/5.34 ( ( A5
% 9.17/5.34 = ( plus_plus_rat @ X3 @ Y3 ) )
% 9.17/5.34 & ( neg_nu6808929389511037909um_rat @ X3 )
% 9.17/5.34 & ( neg_nu6808929389511037909um_rat @ Y3 ) ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1935_sum__squares__gt__zero__iff,axiom,
% 9.17/5.34 ! [X: code_integer,Y: code_integer] :
% 9.17/5.34 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ X @ X ) @ ( times_3573771949741848930nteger @ Y @ Y ) ) )
% 9.17/5.34 = ( ( X != zero_z3403309356797280102nteger )
% 9.17/5.34 | ( Y != zero_z3403309356797280102nteger ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1936_sum__squares__gt__zero__iff,axiom,
% 9.17/5.34 ! [X: rat,Y: rat] :
% 9.17/5.34 ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) ) )
% 9.17/5.34 = ( ( X != zero_zero_rat )
% 9.17/5.34 | ( Y != zero_zero_rat ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1937_sum__squares__gt__zero__iff,axiom,
% 9.17/5.34 ! [X: int,Y: int] :
% 9.17/5.34 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) )
% 9.17/5.34 = ( ( X != zero_zero_int )
% 9.17/5.34 | ( Y != zero_zero_int ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1938_sum__squares__le__zero__iff,axiom,
% 9.17/5.34 ! [X: code_integer,Y: code_integer] :
% 9.17/5.34 ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ X @ X ) @ ( times_3573771949741848930nteger @ Y @ Y ) ) @ zero_z3403309356797280102nteger )
% 9.17/5.34 = ( ( X = zero_z3403309356797280102nteger )
% 9.17/5.34 & ( Y = zero_z3403309356797280102nteger ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1939_sum__squares__le__zero__iff,axiom,
% 9.17/5.34 ! [X: rat,Y: rat] :
% 9.17/5.34 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) ) @ zero_zero_rat )
% 9.17/5.34 = ( ( X = zero_zero_rat )
% 9.17/5.34 & ( Y = zero_zero_rat ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1940_sum__squares__le__zero__iff,axiom,
% 9.17/5.34 ! [X: int,Y: int] :
% 9.17/5.34 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) @ zero_zero_int )
% 9.17/5.34 = ( ( X = zero_zero_int )
% 9.17/5.34 & ( Y = zero_zero_int ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1941_incr__lemma,axiom,
% 9.17/5.34 ! [D2: int,Z: int,X: int] :
% 9.17/5.34 ( ( ord_less_int @ zero_zero_int @ D2 )
% 9.17/5.34 => ( 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 ) @ D2 ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1942_decr__lemma,axiom,
% 9.17/5.34 ! [D2: int,X: int,Z: int] :
% 9.17/5.34 ( ( ord_less_int @ zero_zero_int @ D2 )
% 9.17/5.34 => ( ord_less_int @ ( minus_minus_int @ X @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ X @ Z ) ) @ one_one_int ) @ D2 ) ) @ Z ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1943_sum__squares__eq__zero__iff,axiom,
% 9.17/5.34 ! [X: code_integer,Y: code_integer] :
% 9.17/5.34 ( ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ X @ X ) @ ( times_3573771949741848930nteger @ Y @ Y ) )
% 9.17/5.34 = zero_z3403309356797280102nteger )
% 9.17/5.34 = ( ( X = zero_z3403309356797280102nteger )
% 9.17/5.34 & ( Y = zero_z3403309356797280102nteger ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1944_sum__squares__eq__zero__iff,axiom,
% 9.17/5.34 ! [X: rat,Y: rat] :
% 9.17/5.34 ( ( ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) )
% 9.17/5.34 = zero_zero_rat )
% 9.17/5.34 = ( ( X = zero_zero_rat )
% 9.17/5.34 & ( Y = zero_zero_rat ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1945_sum__squares__eq__zero__iff,axiom,
% 9.17/5.34 ! [X: int,Y: int] :
% 9.17/5.34 ( ( ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) )
% 9.17/5.34 = zero_zero_int )
% 9.17/5.34 = ( ( X = zero_zero_int )
% 9.17/5.34 & ( Y = zero_zero_int ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1946_frac__unique__iff,axiom,
% 9.17/5.34 ! [X: rat,A: rat] :
% 9.17/5.34 ( ( ( archimedean_frac_rat @ X )
% 9.17/5.34 = A )
% 9.17/5.34 = ( ( member_rat @ ( minus_minus_rat @ X @ A ) @ ring_1_Ints_rat )
% 9.17/5.34 & ( ord_less_eq_rat @ zero_zero_rat @ A )
% 9.17/5.34 & ( ord_less_rat @ A @ one_one_rat ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1947_scaling__mono,axiom,
% 9.17/5.34 ! [U: rat,V: rat,R2: rat,S: rat] :
% 9.17/5.34 ( ( ord_less_eq_rat @ U @ V )
% 9.17/5.34 => ( ( ord_less_eq_rat @ zero_zero_rat @ R2 )
% 9.17/5.34 => ( ( ord_less_eq_rat @ R2 @ S )
% 9.17/5.34 => ( ord_less_eq_rat @ ( plus_plus_rat @ U @ ( divide_divide_rat @ ( times_times_rat @ R2 @ ( minus_minus_rat @ V @ U ) ) @ S ) ) @ V ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1948_divide__le__eq__1__neg,axiom,
% 9.17/5.34 ! [A: rat,B: rat] :
% 9.17/5.34 ( ( ord_less_rat @ A @ zero_zero_rat )
% 9.17/5.34 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 9.17/5.34 = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1949_divide__le__eq__1__pos,axiom,
% 9.17/5.34 ! [A: rat,B: rat] :
% 9.17/5.34 ( ( ord_less_rat @ zero_zero_rat @ A )
% 9.17/5.34 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 9.17/5.34 = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1950_div__by__1,axiom,
% 9.17/5.34 ! [A: int] :
% 9.17/5.34 ( ( divide_divide_int @ A @ one_one_int )
% 9.17/5.34 = A ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1951_div__by__1,axiom,
% 9.17/5.34 ! [A: nat] :
% 9.17/5.34 ( ( divide_divide_nat @ A @ one_one_nat )
% 9.17/5.34 = A ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1952_div__by__1,axiom,
% 9.17/5.34 ! [A: code_integer] :
% 9.17/5.34 ( ( divide6298287555418463151nteger @ A @ one_one_Code_integer )
% 9.17/5.34 = A ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1953_div__by__1,axiom,
% 9.17/5.34 ! [A: rat] :
% 9.17/5.34 ( ( divide_divide_rat @ A @ one_one_rat )
% 9.17/5.34 = A ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1954_div__by__1,axiom,
% 9.17/5.34 ! [A: code_natural] :
% 9.17/5.34 ( ( divide5121882707175180666atural @ A @ one_one_Code_natural )
% 9.17/5.34 = A ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1955_div__self,axiom,
% 9.17/5.34 ! [A: int] :
% 9.17/5.34 ( ( A != zero_zero_int )
% 9.17/5.34 => ( ( divide_divide_int @ A @ A )
% 9.17/5.34 = one_one_int ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1956_div__self,axiom,
% 9.17/5.34 ! [A: nat] :
% 9.17/5.34 ( ( A != zero_zero_nat )
% 9.17/5.34 => ( ( divide_divide_nat @ A @ A )
% 9.17/5.34 = one_one_nat ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1957_div__self,axiom,
% 9.17/5.34 ! [A: code_integer] :
% 9.17/5.34 ( ( A != zero_z3403309356797280102nteger )
% 9.17/5.34 => ( ( divide6298287555418463151nteger @ A @ A )
% 9.17/5.34 = one_one_Code_integer ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1958_div__self,axiom,
% 9.17/5.34 ! [A: rat] :
% 9.17/5.34 ( ( A != zero_zero_rat )
% 9.17/5.34 => ( ( divide_divide_rat @ A @ A )
% 9.17/5.34 = one_one_rat ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1959_div__self,axiom,
% 9.17/5.34 ! [A: code_natural] :
% 9.17/5.34 ( ( A != zero_z2226904508553997617atural )
% 9.17/5.34 => ( ( divide5121882707175180666atural @ A @ A )
% 9.17/5.34 = one_one_Code_natural ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1960_zero__eq__1__divide__iff,axiom,
% 9.17/5.34 ! [A: rat] :
% 9.17/5.34 ( ( zero_zero_rat
% 9.17/5.34 = ( divide_divide_rat @ one_one_rat @ A ) )
% 9.17/5.34 = ( A = zero_zero_rat ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1961_one__divide__eq__0__iff,axiom,
% 9.17/5.34 ! [A: rat] :
% 9.17/5.34 ( ( ( divide_divide_rat @ one_one_rat @ A )
% 9.17/5.34 = zero_zero_rat )
% 9.17/5.34 = ( A = zero_zero_rat ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1962_eq__divide__eq__1,axiom,
% 9.17/5.34 ! [B: rat,A: rat] :
% 9.17/5.34 ( ( one_one_rat
% 9.17/5.34 = ( divide_divide_rat @ B @ A ) )
% 9.17/5.34 = ( ( A != zero_zero_rat )
% 9.17/5.34 & ( A = B ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1963_divide__eq__eq__1,axiom,
% 9.17/5.34 ! [B: rat,A: rat] :
% 9.17/5.34 ( ( ( divide_divide_rat @ B @ A )
% 9.17/5.34 = one_one_rat )
% 9.17/5.34 = ( ( A != zero_zero_rat )
% 9.17/5.34 & ( A = B ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1964_divide__self__if,axiom,
% 9.17/5.34 ! [A: rat] :
% 9.17/5.34 ( ( ( A = zero_zero_rat )
% 9.17/5.34 => ( ( divide_divide_rat @ A @ A )
% 9.17/5.34 = zero_zero_rat ) )
% 9.17/5.34 & ( ( A != zero_zero_rat )
% 9.17/5.34 => ( ( divide_divide_rat @ A @ A )
% 9.17/5.34 = one_one_rat ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1965_divide__self,axiom,
% 9.17/5.34 ! [A: rat] :
% 9.17/5.34 ( ( A != zero_zero_rat )
% 9.17/5.34 => ( ( divide_divide_rat @ A @ A )
% 9.17/5.34 = one_one_rat ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1966_one__eq__divide__iff,axiom,
% 9.17/5.34 ! [A: rat,B: rat] :
% 9.17/5.34 ( ( one_one_rat
% 9.17/5.34 = ( divide_divide_rat @ A @ B ) )
% 9.17/5.34 = ( ( B != zero_zero_rat )
% 9.17/5.34 & ( A = B ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1967_divide__eq__1__iff,axiom,
% 9.17/5.34 ! [A: rat,B: rat] :
% 9.17/5.34 ( ( ( divide_divide_rat @ A @ B )
% 9.17/5.34 = one_one_rat )
% 9.17/5.34 = ( ( B != zero_zero_rat )
% 9.17/5.34 & ( A = B ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1968_divide__minus1,axiom,
% 9.17/5.34 ! [X: rat] :
% 9.17/5.34 ( ( divide_divide_rat @ X @ ( uminus_uminus_rat @ one_one_rat ) )
% 9.17/5.34 = ( uminus_uminus_rat @ X ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1969_zero__le__divide__1__iff,axiom,
% 9.17/5.34 ! [A: rat] :
% 9.17/5.34 ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ one_one_rat @ A ) )
% 9.17/5.34 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1970_divide__le__0__1__iff,axiom,
% 9.17/5.34 ! [A: rat] :
% 9.17/5.34 ( ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ zero_zero_rat )
% 9.17/5.34 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1971_zero__less__divide__1__iff,axiom,
% 9.17/5.34 ! [A: rat] :
% 9.17/5.34 ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ one_one_rat @ A ) )
% 9.17/5.34 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1972_less__divide__eq__1__pos,axiom,
% 9.17/5.34 ! [A: rat,B: rat] :
% 9.17/5.34 ( ( ord_less_rat @ zero_zero_rat @ A )
% 9.17/5.34 => ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 9.17/5.34 = ( ord_less_rat @ A @ B ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1973_less__divide__eq__1__neg,axiom,
% 9.17/5.34 ! [A: rat,B: rat] :
% 9.17/5.34 ( ( ord_less_rat @ A @ zero_zero_rat )
% 9.17/5.34 => ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 9.17/5.34 = ( ord_less_rat @ B @ A ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1974_divide__less__eq__1__pos,axiom,
% 9.17/5.34 ! [A: rat,B: rat] :
% 9.17/5.34 ( ( ord_less_rat @ zero_zero_rat @ A )
% 9.17/5.34 => ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 9.17/5.34 = ( ord_less_rat @ B @ A ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1975_divide__less__eq__1__neg,axiom,
% 9.17/5.34 ! [A: rat,B: rat] :
% 9.17/5.34 ( ( ord_less_rat @ A @ zero_zero_rat )
% 9.17/5.34 => ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 9.17/5.34 = ( ord_less_rat @ A @ B ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1976_divide__less__0__1__iff,axiom,
% 9.17/5.34 ! [A: rat] :
% 9.17/5.34 ( ( ord_less_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ zero_zero_rat )
% 9.17/5.34 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1977_nonzero__divide__mult__cancel__right,axiom,
% 9.17/5.34 ! [B: rat,A: rat] :
% 9.17/5.34 ( ( B != zero_zero_rat )
% 9.17/5.34 => ( ( divide_divide_rat @ B @ ( times_times_rat @ A @ B ) )
% 9.17/5.34 = ( divide_divide_rat @ one_one_rat @ A ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1978_nonzero__divide__mult__cancel__left,axiom,
% 9.17/5.34 ! [A: rat,B: rat] :
% 9.17/5.34 ( ( A != zero_zero_rat )
% 9.17/5.34 => ( ( divide_divide_rat @ A @ ( times_times_rat @ A @ B ) )
% 9.17/5.34 = ( divide_divide_rat @ one_one_rat @ B ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1979_le__divide__eq__1__pos,axiom,
% 9.17/5.34 ! [A: rat,B: rat] :
% 9.17/5.34 ( ( ord_less_rat @ zero_zero_rat @ A )
% 9.17/5.34 => ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 9.17/5.34 = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1980_le__divide__eq__1__neg,axiom,
% 9.17/5.34 ! [A: rat,B: rat] :
% 9.17/5.34 ( ( ord_less_rat @ A @ zero_zero_rat )
% 9.17/5.34 => ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 9.17/5.34 = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1981_int__distrib_I2_J,axiom,
% 9.17/5.34 ! [W: int,Z1: int,Z22: int] :
% 9.17/5.34 ( ( times_times_int @ W @ ( plus_plus_int @ Z1 @ Z22 ) )
% 9.17/5.34 = ( plus_plus_int @ ( times_times_int @ W @ Z1 ) @ ( times_times_int @ W @ Z22 ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1982_int__distrib_I1_J,axiom,
% 9.17/5.34 ! [Z1: int,Z22: int,W: int] :
% 9.17/5.34 ( ( times_times_int @ ( plus_plus_int @ Z1 @ Z22 ) @ W )
% 9.17/5.34 = ( plus_plus_int @ ( times_times_int @ Z1 @ W ) @ ( times_times_int @ Z22 @ W ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1983_plus__int__code_I2_J,axiom,
% 9.17/5.34 ! [L: int] :
% 9.17/5.34 ( ( plus_plus_int @ zero_zero_int @ L )
% 9.17/5.34 = L ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1984_plus__int__code_I1_J,axiom,
% 9.17/5.34 ! [K: int] :
% 9.17/5.34 ( ( plus_plus_int @ K @ zero_zero_int )
% 9.17/5.34 = K ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1985_zero__integer_Orsp,axiom,
% 9.17/5.34 zero_zero_int = zero_zero_int ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1986_add__divide__distrib,axiom,
% 9.17/5.34 ! [A: rat,B: rat,C: rat] :
% 9.17/5.34 ( ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 9.17/5.34 = ( plus_plus_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1987_int__div__pos__eq,axiom,
% 9.17/5.34 ! [A: int,B: int,Q3: int,R2: int] :
% 9.17/5.34 ( ( A
% 9.17/5.34 = ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R2 ) )
% 9.17/5.34 => ( ( ord_less_eq_int @ zero_zero_int @ R2 )
% 9.17/5.34 => ( ( ord_less_int @ R2 @ B )
% 9.17/5.34 => ( ( divide_divide_int @ A @ B )
% 9.17/5.34 = Q3 ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1988_int__div__neg__eq,axiom,
% 9.17/5.34 ! [A: int,B: int,Q3: int,R2: int] :
% 9.17/5.34 ( ( A
% 9.17/5.34 = ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R2 ) )
% 9.17/5.34 => ( ( ord_less_eq_int @ R2 @ zero_zero_int )
% 9.17/5.34 => ( ( ord_less_int @ B @ R2 )
% 9.17/5.34 => ( ( divide_divide_int @ A @ B )
% 9.17/5.34 = Q3 ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1989_split__zdiv,axiom,
% 9.17/5.34 ! [P: int > $o,N2: int,K: int] :
% 9.17/5.34 ( ( P @ ( divide_divide_int @ N2 @ K ) )
% 9.17/5.34 = ( ( ( K = zero_zero_int )
% 9.17/5.34 => ( P @ zero_zero_int ) )
% 9.17/5.34 & ( ( ord_less_int @ zero_zero_int @ K )
% 9.17/5.34 => ! [I3: int,J2: int] :
% 9.17/5.34 ( ( ( ord_less_eq_int @ zero_zero_int @ J2 )
% 9.17/5.34 & ( ord_less_int @ J2 @ K )
% 9.17/5.34 & ( N2
% 9.17/5.34 = ( plus_plus_int @ ( times_times_int @ K @ I3 ) @ J2 ) ) )
% 9.17/5.34 => ( P @ I3 ) ) )
% 9.17/5.34 & ( ( ord_less_int @ K @ zero_zero_int )
% 9.17/5.34 => ! [I3: int,J2: int] :
% 9.17/5.34 ( ( ( ord_less_int @ K @ J2 )
% 9.17/5.34 & ( ord_less_eq_int @ J2 @ zero_zero_int )
% 9.17/5.34 & ( N2
% 9.17/5.34 = ( plus_plus_int @ ( times_times_int @ K @ I3 ) @ J2 ) ) )
% 9.17/5.34 => ( P @ I3 ) ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1990_frac__lt__1,axiom,
% 9.17/5.34 ! [X: rat] : ( ord_less_rat @ ( archimedean_frac_rat @ X ) @ one_one_rat ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1991_frac__1__eq,axiom,
% 9.17/5.34 ! [X: rat] :
% 9.17/5.34 ( ( archimedean_frac_rat @ ( plus_plus_rat @ X @ one_one_rat ) )
% 9.17/5.34 = ( archimedean_frac_rat @ X ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1992_right__inverse__eq,axiom,
% 9.17/5.34 ! [B: rat,A: rat] :
% 9.17/5.34 ( ( B != zero_zero_rat )
% 9.17/5.34 => ( ( ( divide_divide_rat @ A @ B )
% 9.17/5.34 = one_one_rat )
% 9.17/5.34 = ( A = B ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1993_less__divide__eq__1,axiom,
% 9.17/5.34 ! [B: rat,A: rat] :
% 9.17/5.34 ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 9.17/5.34 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 9.17/5.34 & ( ord_less_rat @ A @ B ) )
% 9.17/5.34 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 9.17/5.34 & ( ord_less_rat @ B @ A ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1994_divide__less__eq__1,axiom,
% 9.17/5.34 ! [B: rat,A: rat] :
% 9.17/5.34 ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 9.17/5.34 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 9.17/5.34 & ( ord_less_rat @ B @ A ) )
% 9.17/5.34 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 9.17/5.34 & ( ord_less_rat @ A @ B ) )
% 9.17/5.34 | ( A = zero_zero_rat ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1995_divide__add__eq__iff,axiom,
% 9.17/5.34 ! [Z: rat,X: rat,Y: rat] :
% 9.17/5.34 ( ( Z != zero_zero_rat )
% 9.17/5.34 => ( ( plus_plus_rat @ ( divide_divide_rat @ X @ Z ) @ Y )
% 9.17/5.34 = ( divide_divide_rat @ ( plus_plus_rat @ X @ ( times_times_rat @ Y @ Z ) ) @ Z ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1996_add__divide__eq__iff,axiom,
% 9.17/5.34 ! [Z: rat,X: rat,Y: rat] :
% 9.17/5.34 ( ( Z != zero_zero_rat )
% 9.17/5.34 => ( ( plus_plus_rat @ X @ ( divide_divide_rat @ Y @ Z ) )
% 9.17/5.34 = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ Z ) @ Y ) @ Z ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1997_add__num__frac,axiom,
% 9.17/5.34 ! [Y: rat,Z: rat,X: rat] :
% 9.17/5.34 ( ( Y != zero_zero_rat )
% 9.17/5.34 => ( ( plus_plus_rat @ Z @ ( divide_divide_rat @ X @ Y ) )
% 9.17/5.34 = ( divide_divide_rat @ ( plus_plus_rat @ X @ ( times_times_rat @ Z @ Y ) ) @ Y ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1998_add__frac__num,axiom,
% 9.17/5.34 ! [Y: rat,X: rat,Z: rat] :
% 9.17/5.34 ( ( Y != zero_zero_rat )
% 9.17/5.34 => ( ( plus_plus_rat @ ( divide_divide_rat @ X @ Y ) @ Z )
% 9.17/5.34 = ( divide_divide_rat @ ( plus_plus_rat @ X @ ( times_times_rat @ Z @ Y ) ) @ Y ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_1999_add__frac__eq,axiom,
% 9.17/5.34 ! [Y: rat,Z: rat,X: rat,W: rat] :
% 9.17/5.34 ( ( Y != zero_zero_rat )
% 9.17/5.34 => ( ( Z != zero_zero_rat )
% 9.17/5.34 => ( ( plus_plus_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ W @ Z ) )
% 9.17/5.34 = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ W @ Y ) ) @ ( times_times_rat @ Y @ Z ) ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2000_add__divide__eq__if__simps_I1_J,axiom,
% 9.17/5.34 ! [Z: rat,A: rat,B: rat] :
% 9.17/5.34 ( ( ( Z = zero_zero_rat )
% 9.17/5.34 => ( ( plus_plus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 9.17/5.34 = A ) )
% 9.17/5.34 & ( ( Z != zero_zero_rat )
% 9.17/5.34 => ( ( plus_plus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 9.17/5.34 = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2001_add__divide__eq__if__simps_I2_J,axiom,
% 9.17/5.34 ! [Z: rat,A: rat,B: rat] :
% 9.17/5.34 ( ( ( Z = zero_zero_rat )
% 9.17/5.34 => ( ( plus_plus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 9.17/5.34 = B ) )
% 9.17/5.34 & ( ( Z != zero_zero_rat )
% 9.17/5.34 => ( ( plus_plus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 9.17/5.34 = ( divide_divide_rat @ ( plus_plus_rat @ A @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2002_less__half__sum,axiom,
% 9.17/5.34 ! [A: rat,B: rat] :
% 9.17/5.34 ( ( ord_less_rat @ A @ B )
% 9.17/5.34 => ( ord_less_rat @ A @ ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2003_gt__half__sum,axiom,
% 9.17/5.34 ! [A: rat,B: rat] :
% 9.17/5.34 ( ( ord_less_rat @ A @ B )
% 9.17/5.34 => ( ord_less_rat @ ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ) @ B ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2004_divide__eq__minus__1__iff,axiom,
% 9.17/5.34 ! [A: rat,B: rat] :
% 9.17/5.34 ( ( ( divide_divide_rat @ A @ B )
% 9.17/5.34 = ( uminus_uminus_rat @ one_one_rat ) )
% 9.17/5.34 = ( ( B != zero_zero_rat )
% 9.17/5.34 & ( A
% 9.17/5.34 = ( uminus_uminus_rat @ B ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2005_div__pos__geq,axiom,
% 9.17/5.34 ! [L: int,K: int] :
% 9.17/5.34 ( ( ord_less_int @ zero_zero_int @ L )
% 9.17/5.34 => ( ( ord_less_eq_int @ L @ K )
% 9.17/5.34 => ( ( divide_divide_int @ K @ L )
% 9.17/5.34 = ( plus_plus_int @ ( divide_divide_int @ ( minus_minus_int @ K @ L ) @ L ) @ one_one_int ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2006_frac__eq,axiom,
% 9.17/5.34 ! [X: rat] :
% 9.17/5.34 ( ( ( archimedean_frac_rat @ X )
% 9.17/5.34 = X )
% 9.17/5.34 = ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 9.17/5.34 & ( ord_less_rat @ X @ one_one_rat ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2007_frac__add,axiom,
% 9.17/5.34 ! [X: rat,Y: rat] :
% 9.17/5.34 ( ( ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X ) @ ( archimedean_frac_rat @ Y ) ) @ one_one_rat )
% 9.17/5.34 => ( ( archimedean_frac_rat @ ( plus_plus_rat @ X @ Y ) )
% 9.17/5.34 = ( plus_plus_rat @ ( archimedean_frac_rat @ X ) @ ( archimedean_frac_rat @ Y ) ) ) )
% 9.17/5.34 & ( ~ ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X ) @ ( archimedean_frac_rat @ Y ) ) @ one_one_rat )
% 9.17/5.34 => ( ( archimedean_frac_rat @ ( plus_plus_rat @ X @ Y ) )
% 9.17/5.34 = ( minus_minus_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X ) @ ( archimedean_frac_rat @ Y ) ) @ one_one_rat ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2008_incr__mult__lemma,axiom,
% 9.17/5.34 ! [D2: int,P: int > $o,K: int] :
% 9.17/5.34 ( ( ord_less_int @ zero_zero_int @ D2 )
% 9.17/5.34 => ( ! [X4: int] :
% 9.17/5.34 ( ( P @ X4 )
% 9.17/5.34 => ( P @ ( plus_plus_int @ X4 @ D2 ) ) )
% 9.17/5.34 => ( ( ord_less_eq_int @ zero_zero_int @ K )
% 9.17/5.34 => ! [X8: int] :
% 9.17/5.34 ( ( P @ X8 )
% 9.17/5.34 => ( P @ ( plus_plus_int @ X8 @ ( times_times_int @ K @ D2 ) ) ) ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2009_divide__le__eq__1,axiom,
% 9.17/5.34 ! [B: rat,A: rat] :
% 9.17/5.34 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 9.17/5.34 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 9.17/5.34 & ( ord_less_eq_rat @ B @ A ) )
% 9.17/5.34 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 9.17/5.34 & ( ord_less_eq_rat @ A @ B ) )
% 9.17/5.34 | ( A = zero_zero_rat ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2010_le__divide__eq__1,axiom,
% 9.17/5.34 ! [B: rat,A: rat] :
% 9.17/5.34 ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 9.17/5.34 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 9.17/5.34 & ( ord_less_eq_rat @ A @ B ) )
% 9.17/5.34 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 9.17/5.34 & ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2011_minus__divide__add__eq__iff,axiom,
% 9.17/5.34 ! [Z: rat,X: rat,Y: rat] :
% 9.17/5.34 ( ( Z != zero_zero_rat )
% 9.17/5.34 => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ X @ Z ) ) @ Y )
% 9.17/5.34 = ( divide_divide_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ X ) @ ( times_times_rat @ Y @ Z ) ) @ Z ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2012_add__divide__eq__if__simps_I3_J,axiom,
% 9.17/5.34 ! [Z: rat,A: rat,B: rat] :
% 9.17/5.34 ( ( ( Z = zero_zero_rat )
% 9.17/5.34 => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 9.17/5.34 = B ) )
% 9.17/5.34 & ( ( Z != zero_zero_rat )
% 9.17/5.34 => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 9.17/5.34 = ( divide_divide_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2013_frac__neg,axiom,
% 9.17/5.34 ! [X: rat] :
% 9.17/5.34 ( ( ( member_rat @ X @ ring_1_Ints_rat )
% 9.17/5.34 => ( ( archimedean_frac_rat @ ( uminus_uminus_rat @ X ) )
% 9.17/5.34 = zero_zero_rat ) )
% 9.17/5.34 & ( ~ ( member_rat @ X @ ring_1_Ints_rat )
% 9.17/5.34 => ( ( archimedean_frac_rat @ ( uminus_uminus_rat @ X ) )
% 9.17/5.34 = ( minus_minus_rat @ one_one_rat @ ( archimedean_frac_rat @ X ) ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2014_div__mult__self4,axiom,
% 9.17/5.34 ! [B: int,C: int,A: int] :
% 9.17/5.34 ( ( B != zero_zero_int )
% 9.17/5.34 => ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ B @ C ) @ A ) @ B )
% 9.17/5.34 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2015_div__mult__self4,axiom,
% 9.17/5.34 ! [B: nat,C: nat,A: nat] :
% 9.17/5.34 ( ( B != zero_zero_nat )
% 9.17/5.34 => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ A ) @ B )
% 9.17/5.34 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2016_div__mult__self4,axiom,
% 9.17/5.34 ! [B: code_integer,C: code_integer,A: code_integer] :
% 9.17/5.34 ( ( B != zero_z3403309356797280102nteger )
% 9.17/5.34 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ C ) @ A ) @ B )
% 9.17/5.34 = ( plus_p5714425477246183910nteger @ C @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2017_div__mult__self4,axiom,
% 9.17/5.34 ! [B: code_natural,C: code_natural,A: code_natural] :
% 9.17/5.34 ( ( B != zero_z2226904508553997617atural )
% 9.17/5.34 => ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ B @ C ) @ A ) @ B )
% 9.17/5.34 = ( plus_p4538020629002901425atural @ C @ ( divide5121882707175180666atural @ A @ B ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2018_div__mult__self3,axiom,
% 9.17/5.34 ! [B: int,C: int,A: int] :
% 9.17/5.34 ( ( B != zero_zero_int )
% 9.17/5.34 => ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ C @ B ) @ A ) @ B )
% 9.17/5.34 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2019_div__mult__self3,axiom,
% 9.17/5.34 ! [B: nat,C: nat,A: nat] :
% 9.17/5.34 ( ( B != zero_zero_nat )
% 9.17/5.34 => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ A ) @ B )
% 9.17/5.34 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2020_div__mult__self3,axiom,
% 9.17/5.34 ! [B: code_integer,C: code_integer,A: code_integer] :
% 9.17/5.34 ( ( B != zero_z3403309356797280102nteger )
% 9.17/5.34 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ C @ B ) @ A ) @ B )
% 9.17/5.34 = ( plus_p5714425477246183910nteger @ C @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2021_div__mult__self3,axiom,
% 9.17/5.34 ! [B: code_natural,C: code_natural,A: code_natural] :
% 9.17/5.34 ( ( B != zero_z2226904508553997617atural )
% 9.17/5.34 => ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ C @ B ) @ A ) @ B )
% 9.17/5.34 = ( plus_p4538020629002901425atural @ C @ ( divide5121882707175180666atural @ A @ B ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2022_div__mult__self2,axiom,
% 9.17/5.34 ! [B: int,A: int,C: int] :
% 9.17/5.34 ( ( B != zero_zero_int )
% 9.17/5.34 => ( ( divide_divide_int @ ( plus_plus_int @ A @ ( times_times_int @ B @ C ) ) @ B )
% 9.17/5.34 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2023_div__mult__self2,axiom,
% 9.17/5.34 ! [B: nat,A: nat,C: nat] :
% 9.17/5.34 ( ( B != zero_zero_nat )
% 9.17/5.34 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ B @ C ) ) @ B )
% 9.17/5.34 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2024_div__mult__self2,axiom,
% 9.17/5.34 ! [B: code_integer,A: code_integer,C: code_integer] :
% 9.17/5.34 ( ( B != zero_z3403309356797280102nteger )
% 9.17/5.34 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) ) @ B )
% 9.17/5.34 = ( plus_p5714425477246183910nteger @ C @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2025_div__mult__self2,axiom,
% 9.17/5.34 ! [B: code_natural,A: code_natural,C: code_natural] :
% 9.17/5.34 ( ( B != zero_z2226904508553997617atural )
% 9.17/5.34 => ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ A @ ( times_2397367101498566445atural @ B @ C ) ) @ B )
% 9.17/5.34 = ( plus_p4538020629002901425atural @ C @ ( divide5121882707175180666atural @ A @ B ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2026_div__mult__self1,axiom,
% 9.17/5.34 ! [B: int,A: int,C: int] :
% 9.17/5.34 ( ( B != zero_zero_int )
% 9.17/5.34 => ( ( divide_divide_int @ ( plus_plus_int @ A @ ( times_times_int @ C @ B ) ) @ B )
% 9.17/5.34 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2027_div__mult__self1,axiom,
% 9.17/5.34 ! [B: nat,A: nat,C: nat] :
% 9.17/5.34 ( ( B != zero_zero_nat )
% 9.17/5.34 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ C @ B ) ) @ B )
% 9.17/5.34 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2028_div__mult__self1,axiom,
% 9.17/5.34 ! [B: code_integer,A: code_integer,C: code_integer] :
% 9.17/5.34 ( ( B != zero_z3403309356797280102nteger )
% 9.17/5.34 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ C @ B ) ) @ B )
% 9.17/5.34 = ( plus_p5714425477246183910nteger @ C @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2029_div__mult__self1,axiom,
% 9.17/5.34 ! [B: code_natural,A: code_natural,C: code_natural] :
% 9.17/5.34 ( ( B != zero_z2226904508553997617atural )
% 9.17/5.34 => ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ A @ ( times_2397367101498566445atural @ C @ B ) ) @ B )
% 9.17/5.34 = ( plus_p4538020629002901425atural @ C @ ( divide5121882707175180666atural @ A @ B ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2030_div__minus1__right,axiom,
% 9.17/5.34 ! [A: int] :
% 9.17/5.34 ( ( divide_divide_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 9.17/5.34 = ( uminus_uminus_int @ A ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2031_div__minus1__right,axiom,
% 9.17/5.34 ! [A: code_integer] :
% 9.17/5.34 ( ( divide6298287555418463151nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.17/5.34 = ( uminus1351360451143612070nteger @ A ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2032_div__pos__neg__trivial,axiom,
% 9.17/5.34 ! [K: int,L: int] :
% 9.17/5.34 ( ( ord_less_int @ zero_zero_int @ K )
% 9.17/5.34 => ( ( ord_less_eq_int @ ( plus_plus_int @ K @ L ) @ zero_zero_int )
% 9.17/5.34 => ( ( divide_divide_int @ K @ L )
% 9.17/5.34 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2033_bits__div__by__1,axiom,
% 9.17/5.34 ! [A: int] :
% 9.17/5.34 ( ( divide_divide_int @ A @ one_one_int )
% 9.17/5.34 = A ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2034_bits__div__by__1,axiom,
% 9.17/5.34 ! [A: nat] :
% 9.17/5.34 ( ( divide_divide_nat @ A @ one_one_nat )
% 9.17/5.34 = A ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2035_bits__div__by__1,axiom,
% 9.17/5.34 ! [A: code_integer] :
% 9.17/5.34 ( ( divide6298287555418463151nteger @ A @ one_one_Code_integer )
% 9.17/5.34 = A ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2036_bits__div__by__1,axiom,
% 9.17/5.34 ! [A: code_natural] :
% 9.17/5.34 ( ( divide5121882707175180666atural @ A @ one_one_Code_natural )
% 9.17/5.34 = A ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2037_dividend__less__times__div,axiom,
% 9.17/5.34 ! [N2: nat,M2: nat] :
% 9.17/5.34 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 9.17/5.34 => ( ord_less_nat @ M2 @ ( plus_plus_nat @ N2 @ ( times_times_nat @ N2 @ ( divide_divide_nat @ M2 @ N2 ) ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2038_dividend__less__div__times,axiom,
% 9.17/5.34 ! [N2: nat,M2: nat] :
% 9.17/5.34 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 9.17/5.34 => ( ord_less_nat @ M2 @ ( plus_plus_nat @ N2 @ ( times_times_nat @ ( divide_divide_nat @ M2 @ N2 ) @ N2 ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2039_split__div,axiom,
% 9.17/5.34 ! [P: nat > $o,M2: nat,N2: nat] :
% 9.17/5.34 ( ( P @ ( divide_divide_nat @ M2 @ N2 ) )
% 9.17/5.34 = ( ( ( N2 = zero_zero_nat )
% 9.17/5.34 => ( P @ zero_zero_nat ) )
% 9.17/5.34 & ( ( N2 != zero_zero_nat )
% 9.17/5.34 => ! [I3: nat,J2: nat] :
% 9.17/5.34 ( ( ord_less_nat @ J2 @ N2 )
% 9.17/5.34 => ( ( M2
% 9.17/5.34 = ( plus_plus_nat @ ( times_times_nat @ N2 @ I3 ) @ J2 ) )
% 9.17/5.34 => ( P @ I3 ) ) ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2040_div__less__dividend,axiom,
% 9.17/5.34 ! [N2: nat,M2: nat] :
% 9.17/5.34 ( ( ord_less_nat @ one_one_nat @ N2 )
% 9.17/5.34 => ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 9.17/5.34 => ( ord_less_nat @ ( divide_divide_nat @ M2 @ N2 ) @ M2 ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2041_div__eq__dividend__iff,axiom,
% 9.17/5.34 ! [M2: nat,N2: nat] :
% 9.17/5.34 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 9.17/5.34 => ( ( ( divide_divide_nat @ M2 @ N2 )
% 9.17/5.34 = M2 )
% 9.17/5.34 = ( N2 = one_one_nat ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2042_div__add__self1,axiom,
% 9.17/5.34 ! [B: int,A: int] :
% 9.17/5.34 ( ( B != zero_zero_int )
% 9.17/5.34 => ( ( divide_divide_int @ ( plus_plus_int @ B @ A ) @ B )
% 9.17/5.34 = ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2043_div__add__self1,axiom,
% 9.17/5.34 ! [B: nat,A: nat] :
% 9.17/5.34 ( ( B != zero_zero_nat )
% 9.17/5.34 => ( ( divide_divide_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 9.17/5.34 = ( plus_plus_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2044_div__add__self1,axiom,
% 9.17/5.34 ! [B: code_integer,A: code_integer] :
% 9.17/5.34 ( ( B != zero_z3403309356797280102nteger )
% 9.17/5.34 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ B @ A ) @ B )
% 9.17/5.34 = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ B ) @ one_one_Code_integer ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2045_div__add__self1,axiom,
% 9.17/5.34 ! [B: code_natural,A: code_natural] :
% 9.17/5.34 ( ( B != zero_z2226904508553997617atural )
% 9.17/5.34 => ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ B @ A ) @ B )
% 9.17/5.34 = ( plus_p4538020629002901425atural @ ( divide5121882707175180666atural @ A @ B ) @ one_one_Code_natural ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2046_div__add__self2,axiom,
% 9.17/5.34 ! [B: int,A: int] :
% 9.17/5.34 ( ( B != zero_zero_int )
% 9.17/5.34 => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ B )
% 9.17/5.34 = ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2047_div__add__self2,axiom,
% 9.17/5.34 ! [B: nat,A: nat] :
% 9.17/5.34 ( ( B != zero_zero_nat )
% 9.17/5.34 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 9.17/5.34 = ( plus_plus_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2048_div__add__self2,axiom,
% 9.17/5.34 ! [B: code_integer,A: code_integer] :
% 9.17/5.34 ( ( B != zero_z3403309356797280102nteger )
% 9.17/5.34 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ B )
% 9.17/5.34 = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ B ) @ one_one_Code_integer ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2049_div__add__self2,axiom,
% 9.17/5.34 ! [B: code_natural,A: code_natural] :
% 9.17/5.34 ( ( B != zero_z2226904508553997617atural )
% 9.17/5.34 => ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ A @ B ) @ B )
% 9.17/5.34 = ( plus_p4538020629002901425atural @ ( divide5121882707175180666atural @ A @ B ) @ one_one_Code_natural ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2050_upto_Opinduct,axiom,
% 9.17/5.34 ! [A0: int,A1: int,P: int > int > $o] :
% 9.17/5.34 ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ A0 @ A1 ) )
% 9.17/5.34 => ( ! [I2: int,J3: int] :
% 9.17/5.34 ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ I2 @ J3 ) )
% 9.17/5.34 => ( ( ( ord_less_eq_int @ I2 @ J3 )
% 9.17/5.34 => ( P @ ( plus_plus_int @ I2 @ one_one_int ) @ J3 ) )
% 9.17/5.34 => ( P @ I2 @ J3 ) ) )
% 9.17/5.34 => ( P @ A0 @ A1 ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2051_eucl__rel__int_Osimps,axiom,
% 9.17/5.34 ( eucl_rel_int
% 9.17/5.34 = ( ^ [A12: int,A22: int,A32: product_prod_int_int] :
% 9.17/5.34 ( ? [K4: int] :
% 9.17/5.34 ( ( A12 = K4 )
% 9.17/5.34 & ( A22 = zero_zero_int )
% 9.17/5.34 & ( A32
% 9.17/5.34 = ( product_Pair_int_int @ zero_zero_int @ K4 ) ) )
% 9.17/5.34 | ? [L3: int,K4: int,Q5: int] :
% 9.17/5.34 ( ( A12 = K4 )
% 9.17/5.34 & ( A22 = L3 )
% 9.17/5.34 & ( A32
% 9.17/5.34 = ( product_Pair_int_int @ Q5 @ zero_zero_int ) )
% 9.17/5.34 & ( L3 != zero_zero_int )
% 9.17/5.34 & ( K4
% 9.17/5.34 = ( times_times_int @ Q5 @ L3 ) ) )
% 9.17/5.34 | ? [R3: int,L3: int,K4: int,Q5: int] :
% 9.17/5.34 ( ( A12 = K4 )
% 9.17/5.34 & ( A22 = L3 )
% 9.17/5.34 & ( A32
% 9.17/5.34 = ( product_Pair_int_int @ Q5 @ R3 ) )
% 9.17/5.34 & ( ( sgn_sgn_int @ R3 )
% 9.17/5.34 = ( sgn_sgn_int @ L3 ) )
% 9.17/5.34 & ( ord_less_int @ ( abs_abs_int @ R3 ) @ ( abs_abs_int @ L3 ) )
% 9.17/5.34 & ( K4
% 9.17/5.34 = ( plus_plus_int @ ( times_times_int @ Q5 @ L3 ) @ R3 ) ) ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2052_eucl__rel__int_Ocases,axiom,
% 9.17/5.34 ! [A1: int,A23: int,A33: product_prod_int_int] :
% 9.17/5.34 ( ( eucl_rel_int @ A1 @ A23 @ A33 )
% 9.17/5.34 => ( ( ( A23 = zero_zero_int )
% 9.17/5.34 => ( A33
% 9.17/5.34 != ( product_Pair_int_int @ zero_zero_int @ A1 ) ) )
% 9.17/5.34 => ( ! [Q2: int] :
% 9.17/5.34 ( ( A33
% 9.17/5.34 = ( product_Pair_int_int @ Q2 @ zero_zero_int ) )
% 9.17/5.34 => ( ( A23 != zero_zero_int )
% 9.17/5.34 => ( A1
% 9.17/5.34 != ( times_times_int @ Q2 @ A23 ) ) ) )
% 9.17/5.34 => ~ ! [R: int,Q2: int] :
% 9.17/5.34 ( ( A33
% 9.17/5.34 = ( product_Pair_int_int @ Q2 @ R ) )
% 9.17/5.34 => ( ( ( sgn_sgn_int @ R )
% 9.17/5.34 = ( sgn_sgn_int @ A23 ) )
% 9.17/5.34 => ( ( ord_less_int @ ( abs_abs_int @ R ) @ ( abs_abs_int @ A23 ) )
% 9.17/5.34 => ( A1
% 9.17/5.34 != ( plus_plus_int @ ( times_times_int @ Q2 @ A23 ) @ R ) ) ) ) ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2053_eucl__rel__int__iff,axiom,
% 9.17/5.34 ! [K: int,L: int,Q3: int,R2: int] :
% 9.17/5.34 ( ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q3 @ R2 ) )
% 9.17/5.34 = ( ( K
% 9.17/5.34 = ( plus_plus_int @ ( times_times_int @ L @ Q3 ) @ R2 ) )
% 9.17/5.34 & ( ( ord_less_int @ zero_zero_int @ L )
% 9.17/5.34 => ( ( ord_less_eq_int @ zero_zero_int @ R2 )
% 9.17/5.34 & ( ord_less_int @ R2 @ L ) ) )
% 9.17/5.34 & ( ~ ( ord_less_int @ zero_zero_int @ L )
% 9.17/5.34 => ( ( ( ord_less_int @ L @ zero_zero_int )
% 9.17/5.34 => ( ( ord_less_int @ L @ R2 )
% 9.17/5.34 & ( ord_less_eq_int @ R2 @ zero_zero_int ) ) )
% 9.17/5.34 & ( ~ ( ord_less_int @ L @ zero_zero_int )
% 9.17/5.34 => ( Q3 = zero_zero_int ) ) ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2054_split__neg__lemma,axiom,
% 9.17/5.34 ! [K: int,P: int > int > $o,N2: int] :
% 9.17/5.34 ( ( ord_less_int @ K @ zero_zero_int )
% 9.17/5.34 => ( ( P @ ( divide_divide_int @ N2 @ K ) @ ( modulo_modulo_int @ N2 @ K ) )
% 9.17/5.34 = ( ! [I3: int,J2: int] :
% 9.17/5.34 ( ( ( ord_less_int @ K @ J2 )
% 9.17/5.34 & ( ord_less_eq_int @ J2 @ zero_zero_int )
% 9.17/5.34 & ( N2
% 9.17/5.34 = ( plus_plus_int @ ( times_times_int @ K @ I3 ) @ J2 ) ) )
% 9.17/5.34 => ( P @ I3 @ J2 ) ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2055_split__pos__lemma,axiom,
% 9.17/5.34 ! [K: int,P: int > int > $o,N2: int] :
% 9.17/5.34 ( ( ord_less_int @ zero_zero_int @ K )
% 9.17/5.34 => ( ( P @ ( divide_divide_int @ N2 @ K ) @ ( modulo_modulo_int @ N2 @ K ) )
% 9.17/5.34 = ( ! [I3: int,J2: int] :
% 9.17/5.34 ( ( ( ord_less_eq_int @ zero_zero_int @ J2 )
% 9.17/5.34 & ( ord_less_int @ J2 @ K )
% 9.17/5.34 & ( N2
% 9.17/5.34 = ( plus_plus_int @ ( times_times_int @ K @ I3 ) @ J2 ) ) )
% 9.17/5.34 => ( P @ I3 @ J2 ) ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2056_mod__add__self2,axiom,
% 9.17/5.34 ! [A: int,B: int] :
% 9.17/5.34 ( ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ B )
% 9.17/5.34 = ( modulo_modulo_int @ A @ B ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2057_mod__add__self2,axiom,
% 9.17/5.34 ! [A: nat,B: nat] :
% 9.17/5.34 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 9.17/5.34 = ( modulo_modulo_nat @ A @ B ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2058_mod__add__self2,axiom,
% 9.17/5.34 ! [A: code_integer,B: code_integer] :
% 9.17/5.34 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ B )
% 9.17/5.34 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2059_mod__add__self2,axiom,
% 9.17/5.34 ! [A: code_natural,B: code_natural] :
% 9.17/5.34 ( ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ A @ B ) @ B )
% 9.17/5.34 = ( modulo8411746178871703098atural @ A @ B ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2060_mod__add__self1,axiom,
% 9.17/5.34 ! [B: int,A: int] :
% 9.17/5.34 ( ( modulo_modulo_int @ ( plus_plus_int @ B @ A ) @ B )
% 9.17/5.34 = ( modulo_modulo_int @ A @ B ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2061_mod__add__self1,axiom,
% 9.17/5.34 ! [B: nat,A: nat] :
% 9.17/5.34 ( ( modulo_modulo_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 9.17/5.34 = ( modulo_modulo_nat @ A @ B ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2062_mod__add__self1,axiom,
% 9.17/5.34 ! [B: code_integer,A: code_integer] :
% 9.17/5.34 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ B @ A ) @ B )
% 9.17/5.34 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2063_mod__add__self1,axiom,
% 9.17/5.34 ! [B: code_natural,A: code_natural] :
% 9.17/5.34 ( ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ B @ A ) @ B )
% 9.17/5.34 = ( modulo8411746178871703098atural @ A @ B ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2064_mod__by__1,axiom,
% 9.17/5.34 ! [A: int] :
% 9.17/5.34 ( ( modulo_modulo_int @ A @ one_one_int )
% 9.17/5.34 = zero_zero_int ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2065_mod__by__1,axiom,
% 9.17/5.34 ! [A: nat] :
% 9.17/5.34 ( ( modulo_modulo_nat @ A @ one_one_nat )
% 9.17/5.34 = zero_zero_nat ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2066_mod__by__1,axiom,
% 9.17/5.34 ! [A: code_integer] :
% 9.17/5.34 ( ( modulo364778990260209775nteger @ A @ one_one_Code_integer )
% 9.17/5.34 = zero_z3403309356797280102nteger ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2067_mod__by__1,axiom,
% 9.17/5.34 ! [A: code_natural] :
% 9.17/5.34 ( ( modulo8411746178871703098atural @ A @ one_one_Code_natural )
% 9.17/5.34 = zero_z2226904508553997617atural ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2068_bits__mod__by__1,axiom,
% 9.17/5.34 ! [A: int] :
% 9.17/5.34 ( ( modulo_modulo_int @ A @ one_one_int )
% 9.17/5.34 = zero_zero_int ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2069_bits__mod__by__1,axiom,
% 9.17/5.34 ! [A: nat] :
% 9.17/5.34 ( ( modulo_modulo_nat @ A @ one_one_nat )
% 9.17/5.34 = zero_zero_nat ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2070_bits__mod__by__1,axiom,
% 9.17/5.34 ! [A: code_integer] :
% 9.17/5.34 ( ( modulo364778990260209775nteger @ A @ one_one_Code_integer )
% 9.17/5.34 = zero_z3403309356797280102nteger ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2071_bits__mod__by__1,axiom,
% 9.17/5.34 ! [A: code_natural] :
% 9.17/5.34 ( ( modulo8411746178871703098atural @ A @ one_one_Code_natural )
% 9.17/5.34 = zero_z2226904508553997617atural ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2072_mod__mult__self1,axiom,
% 9.17/5.34 ! [A: int,C: int,B: int] :
% 9.17/5.34 ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( times_times_int @ C @ B ) ) @ B )
% 9.17/5.34 = ( modulo_modulo_int @ A @ B ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2073_mod__mult__self1,axiom,
% 9.17/5.34 ! [A: nat,C: nat,B: nat] :
% 9.17/5.34 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ C @ B ) ) @ B )
% 9.17/5.34 = ( modulo_modulo_nat @ A @ B ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2074_mod__mult__self1,axiom,
% 9.17/5.34 ! [A: code_integer,C: code_integer,B: code_integer] :
% 9.17/5.34 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ C @ B ) ) @ B )
% 9.17/5.34 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2075_mod__mult__self1,axiom,
% 9.17/5.34 ! [A: code_natural,C: code_natural,B: code_natural] :
% 9.17/5.34 ( ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ A @ ( times_2397367101498566445atural @ C @ B ) ) @ B )
% 9.17/5.34 = ( modulo8411746178871703098atural @ A @ B ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2076_mod__mult__self2,axiom,
% 9.17/5.34 ! [A: int,B: int,C: int] :
% 9.17/5.34 ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( times_times_int @ B @ C ) ) @ B )
% 9.17/5.34 = ( modulo_modulo_int @ A @ B ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2077_mod__mult__self2,axiom,
% 9.17/5.34 ! [A: nat,B: nat,C: nat] :
% 9.17/5.34 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ B @ C ) ) @ B )
% 9.17/5.34 = ( modulo_modulo_nat @ A @ B ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2078_mod__mult__self2,axiom,
% 9.17/5.34 ! [A: code_integer,B: code_integer,C: code_integer] :
% 9.17/5.34 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) ) @ B )
% 9.17/5.34 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2079_mod__mult__self2,axiom,
% 9.17/5.34 ! [A: code_natural,B: code_natural,C: code_natural] :
% 9.17/5.34 ( ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ A @ ( times_2397367101498566445atural @ B @ C ) ) @ B )
% 9.17/5.34 = ( modulo8411746178871703098atural @ A @ B ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2080_mod__mult__self3,axiom,
% 9.17/5.34 ! [C: int,B: int,A: int] :
% 9.17/5.34 ( ( modulo_modulo_int @ ( plus_plus_int @ ( times_times_int @ C @ B ) @ A ) @ B )
% 9.17/5.34 = ( modulo_modulo_int @ A @ B ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2081_mod__mult__self3,axiom,
% 9.17/5.34 ! [C: nat,B: nat,A: nat] :
% 9.17/5.34 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ A ) @ B )
% 9.17/5.34 = ( modulo_modulo_nat @ A @ B ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2082_mod__mult__self3,axiom,
% 9.17/5.34 ! [C: code_integer,B: code_integer,A: code_integer] :
% 9.17/5.34 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ C @ B ) @ A ) @ B )
% 9.17/5.34 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2083_mod__mult__self3,axiom,
% 9.17/5.34 ! [C: code_natural,B: code_natural,A: code_natural] :
% 9.17/5.34 ( ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ C @ B ) @ A ) @ B )
% 9.17/5.34 = ( modulo8411746178871703098atural @ A @ B ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2084_mod__mult__self4,axiom,
% 9.17/5.34 ! [B: int,C: int,A: int] :
% 9.17/5.34 ( ( modulo_modulo_int @ ( plus_plus_int @ ( times_times_int @ B @ C ) @ A ) @ B )
% 9.17/5.34 = ( modulo_modulo_int @ A @ B ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2085_mod__mult__self4,axiom,
% 9.17/5.34 ! [B: nat,C: nat,A: nat] :
% 9.17/5.34 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ A ) @ B )
% 9.17/5.34 = ( modulo_modulo_nat @ A @ B ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2086_mod__mult__self4,axiom,
% 9.17/5.34 ! [B: code_integer,C: code_integer,A: code_integer] :
% 9.17/5.34 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ C ) @ A ) @ B )
% 9.17/5.34 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2087_mod__mult__self4,axiom,
% 9.17/5.34 ! [B: code_natural,C: code_natural,A: code_natural] :
% 9.17/5.34 ( ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ B @ C ) @ A ) @ B )
% 9.17/5.34 = ( modulo8411746178871703098atural @ A @ B ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2088_mod__minus1__right,axiom,
% 9.17/5.34 ! [A: int] :
% 9.17/5.34 ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 9.17/5.34 = zero_zero_int ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2089_mod__minus1__right,axiom,
% 9.17/5.34 ! [A: code_integer] :
% 9.17/5.34 ( ( modulo364778990260209775nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.17/5.34 = zero_z3403309356797280102nteger ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2090_mod__int__unique,axiom,
% 9.17/5.34 ! [K: int,L: int,Q3: int,R2: int] :
% 9.17/5.34 ( ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q3 @ R2 ) )
% 9.17/5.34 => ( ( modulo_modulo_int @ K @ L )
% 9.17/5.34 = R2 ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2091_unique__quotient,axiom,
% 9.17/5.34 ! [A: int,B: int,Q3: int,R2: int,Q4: int,R6: int] :
% 9.17/5.34 ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q3 @ R2 ) )
% 9.17/5.34 => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q4 @ R6 ) )
% 9.17/5.34 => ( Q3 = Q4 ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2092_unique__remainder,axiom,
% 9.17/5.34 ! [A: int,B: int,Q3: int,R2: int,Q4: int,R6: int] :
% 9.17/5.34 ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q3 @ R2 ) )
% 9.17/5.34 => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q4 @ R6 ) )
% 9.17/5.34 => ( R2 = R6 ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2093_full__exhaustive__int_H_Ocases,axiom,
% 9.17/5.34 ! [X: produc2285326912895808259nt_int] :
% 9.17/5.34 ~ ! [F3: produc8551481072490612790e_term > option6357759511663192854e_term,D: int,I2: int] :
% 9.17/5.34 ( X
% 9.17/5.34 != ( produc5700946648718959541nt_int @ F3 @ ( product_Pair_int_int @ D @ I2 ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2094_exhaustive__int_H_Ocases,axiom,
% 9.17/5.34 ! [X: produc7773217078559923341nt_int] :
% 9.17/5.34 ~ ! [F3: int > option6357759511663192854e_term,D: int,I2: int] :
% 9.17/5.34 ( X
% 9.17/5.34 != ( produc4305682042979456191nt_int @ F3 @ ( product_Pair_int_int @ D @ I2 ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2095_small__lazy_H_Ocases,axiom,
% 9.17/5.34 ! [X: product_prod_int_int] :
% 9.17/5.34 ~ ! [D: int,I2: int] :
% 9.17/5.34 ( X
% 9.17/5.34 != ( product_Pair_int_int @ D @ I2 ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2096_eucl__rel__int,axiom,
% 9.17/5.34 ! [K: int,L: int] : ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ ( divide_divide_int @ K @ L ) @ ( modulo_modulo_int @ K @ L ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2097_mod__add__right__eq,axiom,
% 9.17/5.34 ! [A: int,B: int,C: int] :
% 9.17/5.34 ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 9.17/5.34 = ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2098_mod__add__right__eq,axiom,
% 9.17/5.34 ! [A: nat,B: nat,C: nat] :
% 9.17/5.34 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 9.17/5.34 = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2099_mod__add__right__eq,axiom,
% 9.17/5.34 ! [A: code_integer,B: code_integer,C: code_integer] :
% 9.17/5.34 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 9.17/5.34 = ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2100_mod__add__right__eq,axiom,
% 9.17/5.34 ! [A: code_natural,B: code_natural,C: code_natural] :
% 9.17/5.34 ( ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ A @ ( modulo8411746178871703098atural @ B @ C ) ) @ C )
% 9.17/5.34 = ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ A @ B ) @ C ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2101_mod__add__left__eq,axiom,
% 9.17/5.34 ! [A: int,C: int,B: int] :
% 9.17/5.34 ( ( modulo_modulo_int @ ( plus_plus_int @ ( modulo_modulo_int @ A @ C ) @ B ) @ C )
% 9.17/5.34 = ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2102_mod__add__left__eq,axiom,
% 9.17/5.34 ! [A: nat,C: nat,B: nat] :
% 9.17/5.34 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ A @ C ) @ B ) @ C )
% 9.17/5.34 = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2103_mod__add__left__eq,axiom,
% 9.17/5.34 ! [A: code_integer,C: code_integer,B: code_integer] :
% 9.17/5.34 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ C ) @ B ) @ C )
% 9.17/5.34 = ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2104_mod__add__left__eq,axiom,
% 9.17/5.34 ! [A: code_natural,C: code_natural,B: code_natural] :
% 9.17/5.34 ( ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ ( modulo8411746178871703098atural @ A @ C ) @ B ) @ C )
% 9.17/5.34 = ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ A @ B ) @ C ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2105_mod__add__cong,axiom,
% 9.17/5.34 ! [A: int,C: int,A4: int,B: int,B3: int] :
% 9.17/5.34 ( ( ( modulo_modulo_int @ A @ C )
% 9.17/5.34 = ( modulo_modulo_int @ A4 @ C ) )
% 9.17/5.34 => ( ( ( modulo_modulo_int @ B @ C )
% 9.17/5.34 = ( modulo_modulo_int @ B3 @ C ) )
% 9.17/5.34 => ( ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C )
% 9.17/5.34 = ( modulo_modulo_int @ ( plus_plus_int @ A4 @ B3 ) @ C ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2106_mod__add__cong,axiom,
% 9.17/5.34 ! [A: nat,C: nat,A4: nat,B: nat,B3: nat] :
% 9.17/5.34 ( ( ( modulo_modulo_nat @ A @ C )
% 9.17/5.34 = ( modulo_modulo_nat @ A4 @ C ) )
% 9.17/5.34 => ( ( ( modulo_modulo_nat @ B @ C )
% 9.17/5.34 = ( modulo_modulo_nat @ B3 @ C ) )
% 9.17/5.34 => ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 9.17/5.34 = ( modulo_modulo_nat @ ( plus_plus_nat @ A4 @ B3 ) @ C ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2107_mod__add__cong,axiom,
% 9.17/5.34 ! [A: code_integer,C: code_integer,A4: code_integer,B: code_integer,B3: code_integer] :
% 9.17/5.34 ( ( ( modulo364778990260209775nteger @ A @ C )
% 9.17/5.34 = ( modulo364778990260209775nteger @ A4 @ C ) )
% 9.17/5.34 => ( ( ( modulo364778990260209775nteger @ B @ C )
% 9.17/5.34 = ( modulo364778990260209775nteger @ B3 @ C ) )
% 9.17/5.34 => ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 9.17/5.34 = ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A4 @ B3 ) @ C ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2108_mod__add__cong,axiom,
% 9.17/5.34 ! [A: code_natural,C: code_natural,A4: code_natural,B: code_natural,B3: code_natural] :
% 9.17/5.34 ( ( ( modulo8411746178871703098atural @ A @ C )
% 9.17/5.34 = ( modulo8411746178871703098atural @ A4 @ C ) )
% 9.17/5.34 => ( ( ( modulo8411746178871703098atural @ B @ C )
% 9.17/5.34 = ( modulo8411746178871703098atural @ B3 @ C ) )
% 9.17/5.34 => ( ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ A @ B ) @ C )
% 9.17/5.34 = ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ A4 @ B3 ) @ C ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2109_mod__add__eq,axiom,
% 9.17/5.34 ! [A: int,C: int,B: int] :
% 9.17/5.34 ( ( modulo_modulo_int @ ( plus_plus_int @ ( modulo_modulo_int @ A @ C ) @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 9.17/5.34 = ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2110_mod__add__eq,axiom,
% 9.17/5.34 ! [A: nat,C: nat,B: nat] :
% 9.17/5.34 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ A @ C ) @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 9.17/5.34 = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2111_mod__add__eq,axiom,
% 9.17/5.34 ! [A: code_integer,C: code_integer,B: code_integer] :
% 9.17/5.34 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ C ) @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 9.17/5.34 = ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2112_mod__add__eq,axiom,
% 9.17/5.34 ! [A: code_natural,C: code_natural,B: code_natural] :
% 9.17/5.34 ( ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ ( modulo8411746178871703098atural @ A @ C ) @ ( modulo8411746178871703098atural @ B @ C ) ) @ C )
% 9.17/5.34 = ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ A @ B ) @ C ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2113_eucl__rel__int__by0,axiom,
% 9.17/5.34 ! [K: int] : ( eucl_rel_int @ K @ zero_zero_int @ ( product_Pair_int_int @ zero_zero_int @ K ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2114_div__int__unique,axiom,
% 9.17/5.34 ! [K: int,L: int,Q3: int,R2: int] :
% 9.17/5.34 ( ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q3 @ R2 ) )
% 9.17/5.34 => ( ( divide_divide_int @ K @ L )
% 9.17/5.34 = Q3 ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2115_mod__eqE,axiom,
% 9.17/5.34 ! [A: int,C: int,B: int] :
% 9.17/5.34 ( ( ( modulo_modulo_int @ A @ C )
% 9.17/5.34 = ( modulo_modulo_int @ B @ C ) )
% 9.17/5.34 => ~ ! [D: int] :
% 9.17/5.34 ( B
% 9.17/5.34 != ( plus_plus_int @ A @ ( times_times_int @ C @ D ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2116_mod__eqE,axiom,
% 9.17/5.34 ! [A: code_integer,C: code_integer,B: code_integer] :
% 9.17/5.34 ( ( ( modulo364778990260209775nteger @ A @ C )
% 9.17/5.34 = ( modulo364778990260209775nteger @ B @ C ) )
% 9.17/5.34 => ~ ! [D: code_integer] :
% 9.17/5.34 ( B
% 9.17/5.34 != ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ C @ D ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2117_div__add1__eq,axiom,
% 9.17/5.34 ! [A: int,B: int,C: int] :
% 9.17/5.34 ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 9.17/5.34 = ( plus_plus_int @ ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) @ ( divide_divide_int @ ( plus_plus_int @ ( modulo_modulo_int @ A @ C ) @ ( modulo_modulo_int @ B @ C ) ) @ C ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2118_div__add1__eq,axiom,
% 9.17/5.34 ! [A: nat,B: nat,C: nat] :
% 9.17/5.34 ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 9.17/5.34 = ( plus_plus_nat @ ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) @ ( divide_divide_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ A @ C ) @ ( modulo_modulo_nat @ B @ C ) ) @ C ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2119_div__add1__eq,axiom,
% 9.17/5.34 ! [A: code_integer,B: code_integer,C: code_integer] :
% 9.17/5.34 ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 9.17/5.34 = ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) @ ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ C ) @ ( modulo364778990260209775nteger @ B @ C ) ) @ C ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2120_div__add1__eq,axiom,
% 9.17/5.34 ! [A: code_natural,B: code_natural,C: code_natural] :
% 9.17/5.34 ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ A @ B ) @ C )
% 9.17/5.34 = ( plus_p4538020629002901425atural @ ( plus_p4538020629002901425atural @ ( divide5121882707175180666atural @ A @ C ) @ ( divide5121882707175180666atural @ B @ C ) ) @ ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ ( modulo8411746178871703098atural @ A @ C ) @ ( modulo8411746178871703098atural @ B @ C ) ) @ C ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2121_mult__div__mod__eq,axiom,
% 9.17/5.34 ! [B: int,A: int] :
% 9.17/5.34 ( ( plus_plus_int @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) @ ( modulo_modulo_int @ A @ B ) )
% 9.17/5.34 = A ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2122_mult__div__mod__eq,axiom,
% 9.17/5.34 ! [B: nat,A: nat] :
% 9.17/5.34 ( ( plus_plus_nat @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) @ ( modulo_modulo_nat @ A @ B ) )
% 9.17/5.34 = A ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2123_mult__div__mod__eq,axiom,
% 9.17/5.34 ! [B: code_integer,A: code_integer] :
% 9.17/5.34 ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) @ ( modulo364778990260209775nteger @ A @ B ) )
% 9.17/5.34 = A ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2124_mult__div__mod__eq,axiom,
% 9.17/5.34 ! [B: code_natural,A: code_natural] :
% 9.17/5.34 ( ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ B @ ( divide5121882707175180666atural @ A @ B ) ) @ ( modulo8411746178871703098atural @ A @ B ) )
% 9.17/5.34 = A ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2125_mod__mult__div__eq,axiom,
% 9.17/5.34 ! [A: int,B: int] :
% 9.17/5.34 ( ( plus_plus_int @ ( modulo_modulo_int @ A @ B ) @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) )
% 9.17/5.34 = A ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2126_mod__mult__div__eq,axiom,
% 9.17/5.34 ! [A: nat,B: nat] :
% 9.17/5.34 ( ( plus_plus_nat @ ( modulo_modulo_nat @ A @ B ) @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) )
% 9.17/5.34 = A ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2127_mod__mult__div__eq,axiom,
% 9.17/5.34 ! [A: code_integer,B: code_integer] :
% 9.17/5.34 ( ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ B ) @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) )
% 9.17/5.34 = A ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2128_mod__mult__div__eq,axiom,
% 9.17/5.34 ! [A: code_natural,B: code_natural] :
% 9.17/5.34 ( ( plus_p4538020629002901425atural @ ( modulo8411746178871703098atural @ A @ B ) @ ( times_2397367101498566445atural @ B @ ( divide5121882707175180666atural @ A @ B ) ) )
% 9.17/5.34 = A ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2129_mod__div__mult__eq,axiom,
% 9.17/5.34 ! [A: int,B: int] :
% 9.17/5.34 ( ( plus_plus_int @ ( modulo_modulo_int @ A @ B ) @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) )
% 9.17/5.34 = A ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2130_mod__div__mult__eq,axiom,
% 9.17/5.34 ! [A: nat,B: nat] :
% 9.17/5.34 ( ( plus_plus_nat @ ( modulo_modulo_nat @ A @ B ) @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) )
% 9.17/5.34 = A ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2131_mod__div__mult__eq,axiom,
% 9.17/5.34 ! [A: code_integer,B: code_integer] :
% 9.17/5.34 ( ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ B ) @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) )
% 9.17/5.34 = A ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2132_mod__div__mult__eq,axiom,
% 9.17/5.34 ! [A: code_natural,B: code_natural] :
% 9.17/5.34 ( ( plus_p4538020629002901425atural @ ( modulo8411746178871703098atural @ A @ B ) @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ A @ B ) @ B ) )
% 9.17/5.34 = A ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2133_div__mult__mod__eq,axiom,
% 9.17/5.34 ! [A: int,B: int] :
% 9.17/5.34 ( ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) )
% 9.17/5.34 = A ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2134_div__mult__mod__eq,axiom,
% 9.17/5.34 ! [A: nat,B: nat] :
% 9.17/5.34 ( ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) )
% 9.17/5.34 = A ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2135_div__mult__mod__eq,axiom,
% 9.17/5.34 ! [A: code_integer,B: code_integer] :
% 9.17/5.34 ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) @ ( modulo364778990260209775nteger @ A @ B ) )
% 9.17/5.34 = A ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2136_div__mult__mod__eq,axiom,
% 9.17/5.34 ! [A: code_natural,B: code_natural] :
% 9.17/5.34 ( ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ A @ B ) @ B ) @ ( modulo8411746178871703098atural @ A @ B ) )
% 9.17/5.34 = A ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2137_mod__div__decomp,axiom,
% 9.17/5.34 ! [A: int,B: int] :
% 9.17/5.34 ( A
% 9.17/5.34 = ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2138_mod__div__decomp,axiom,
% 9.17/5.34 ! [A: nat,B: nat] :
% 9.17/5.34 ( A
% 9.17/5.34 = ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2139_mod__div__decomp,axiom,
% 9.17/5.34 ! [A: code_integer,B: code_integer] :
% 9.17/5.34 ( A
% 9.17/5.34 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) @ ( modulo364778990260209775nteger @ A @ B ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2140_mod__div__decomp,axiom,
% 9.17/5.34 ! [A: code_natural,B: code_natural] :
% 9.17/5.34 ( A
% 9.17/5.34 = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ A @ B ) @ B ) @ ( modulo8411746178871703098atural @ A @ B ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2141_cancel__div__mod__rules_I1_J,axiom,
% 9.17/5.34 ! [A: int,B: int,C: int] :
% 9.17/5.34 ( ( plus_plus_int @ ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) ) @ C )
% 9.17/5.34 = ( plus_plus_int @ A @ C ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2142_cancel__div__mod__rules_I1_J,axiom,
% 9.17/5.34 ! [A: nat,B: nat,C: nat] :
% 9.17/5.34 ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) ) @ C )
% 9.17/5.34 = ( plus_plus_nat @ A @ C ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2143_cancel__div__mod__rules_I1_J,axiom,
% 9.17/5.34 ! [A: code_integer,B: code_integer,C: code_integer] :
% 9.17/5.34 ( ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) @ ( modulo364778990260209775nteger @ A @ B ) ) @ C )
% 9.17/5.34 = ( plus_p5714425477246183910nteger @ A @ C ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2144_cancel__div__mod__rules_I1_J,axiom,
% 9.17/5.34 ! [A: code_natural,B: code_natural,C: code_natural] :
% 9.17/5.34 ( ( plus_p4538020629002901425atural @ ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ A @ B ) @ B ) @ ( modulo8411746178871703098atural @ A @ B ) ) @ C )
% 9.17/5.34 = ( plus_p4538020629002901425atural @ A @ C ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2145_cancel__div__mod__rules_I2_J,axiom,
% 9.17/5.34 ! [B: int,A: int,C: int] :
% 9.17/5.34 ( ( plus_plus_int @ ( plus_plus_int @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) @ ( modulo_modulo_int @ A @ B ) ) @ C )
% 9.17/5.34 = ( plus_plus_int @ A @ C ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2146_cancel__div__mod__rules_I2_J,axiom,
% 9.17/5.34 ! [B: nat,A: nat,C: nat] :
% 9.17/5.34 ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) @ ( modulo_modulo_nat @ A @ B ) ) @ C )
% 9.17/5.34 = ( plus_plus_nat @ A @ C ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2147_cancel__div__mod__rules_I2_J,axiom,
% 9.17/5.34 ! [B: code_integer,A: code_integer,C: code_integer] :
% 9.17/5.34 ( ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) @ ( modulo364778990260209775nteger @ A @ B ) ) @ C )
% 9.17/5.34 = ( plus_p5714425477246183910nteger @ A @ C ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2148_cancel__div__mod__rules_I2_J,axiom,
% 9.17/5.34 ! [B: code_natural,A: code_natural,C: code_natural] :
% 9.17/5.34 ( ( plus_p4538020629002901425atural @ ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ B @ ( divide5121882707175180666atural @ A @ B ) ) @ ( modulo8411746178871703098atural @ A @ B ) ) @ C )
% 9.17/5.34 = ( plus_p4538020629002901425atural @ A @ C ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2149_div__mult1__eq,axiom,
% 9.17/5.34 ! [A: int,B: int,C: int] :
% 9.17/5.34 ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ C )
% 9.17/5.34 = ( plus_plus_int @ ( times_times_int @ A @ ( divide_divide_int @ B @ C ) ) @ ( divide_divide_int @ ( times_times_int @ A @ ( modulo_modulo_int @ B @ C ) ) @ C ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2150_div__mult1__eq,axiom,
% 9.17/5.34 ! [A: nat,B: nat,C: nat] :
% 9.17/5.34 ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C )
% 9.17/5.34 = ( plus_plus_nat @ ( times_times_nat @ A @ ( divide_divide_nat @ B @ C ) ) @ ( divide_divide_nat @ ( times_times_nat @ A @ ( modulo_modulo_nat @ B @ C ) ) @ C ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2151_div__mult1__eq,axiom,
% 9.17/5.34 ! [A: code_integer,B: code_integer,C: code_integer] :
% 9.17/5.34 ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 9.17/5.34 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) ) @ ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ ( modulo364778990260209775nteger @ B @ C ) ) @ C ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2152_div__mult1__eq,axiom,
% 9.17/5.34 ! [A: code_natural,B: code_natural,C: code_natural] :
% 9.17/5.34 ( ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ A @ B ) @ C )
% 9.17/5.34 = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ A @ ( divide5121882707175180666atural @ B @ C ) ) @ ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ A @ ( modulo8411746178871703098atural @ B @ C ) ) @ C ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2153_eucl__rel__int__dividesI,axiom,
% 9.17/5.34 ! [L: int,K: int,Q3: int] :
% 9.17/5.34 ( ( L != zero_zero_int )
% 9.17/5.34 => ( ( K
% 9.17/5.34 = ( times_times_int @ Q3 @ L ) )
% 9.17/5.34 => ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q3 @ zero_zero_int ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2154_div__mod__decomp__int,axiom,
% 9.17/5.34 ! [A2: int,N2: int] :
% 9.17/5.34 ( A2
% 9.17/5.34 = ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A2 @ N2 ) @ N2 ) @ ( modulo_modulo_int @ A2 @ N2 ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2155_mod__pos__neg__trivial,axiom,
% 9.17/5.34 ! [K: int,L: int] :
% 9.17/5.34 ( ( ord_less_int @ zero_zero_int @ K )
% 9.17/5.34 => ( ( ord_less_eq_int @ ( plus_plus_int @ K @ L ) @ zero_zero_int )
% 9.17/5.34 => ( ( modulo_modulo_int @ K @ L )
% 9.17/5.34 = ( plus_plus_int @ K @ L ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2156_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 9.17/5.34 ! [C: code_integer,A: code_integer,B: code_integer] :
% 9.17/5.34 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 9.17/5.34 => ( ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 9.17/5.34 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ ( modulo364778990260209775nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) @ ( modulo364778990260209775nteger @ A @ B ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2157_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 9.17/5.34 ! [C: nat,A: nat,B: nat] :
% 9.17/5.34 ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 9.17/5.34 => ( ( modulo_modulo_nat @ A @ ( times_times_nat @ B @ C ) )
% 9.17/5.34 = ( plus_plus_nat @ ( times_times_nat @ B @ ( modulo_modulo_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) @ ( modulo_modulo_nat @ A @ B ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2158_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 9.17/5.34 ! [C: int,A: int,B: int] :
% 9.17/5.34 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 9.17/5.34 => ( ( modulo_modulo_int @ A @ ( times_times_int @ B @ C ) )
% 9.17/5.34 = ( plus_plus_int @ ( times_times_int @ B @ ( modulo_modulo_int @ ( divide_divide_int @ A @ B ) @ C ) ) @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2159_int__mod__pos__eq,axiom,
% 9.17/5.34 ! [A: int,B: int,Q3: int,R2: int] :
% 9.17/5.34 ( ( A
% 9.17/5.34 = ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R2 ) )
% 9.17/5.34 => ( ( ord_less_eq_int @ zero_zero_int @ R2 )
% 9.17/5.34 => ( ( ord_less_int @ R2 @ B )
% 9.17/5.34 => ( ( modulo_modulo_int @ A @ B )
% 9.17/5.34 = R2 ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2160_int__mod__neg__eq,axiom,
% 9.17/5.34 ! [A: int,B: int,Q3: int,R2: int] :
% 9.17/5.34 ( ( A
% 9.17/5.34 = ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R2 ) )
% 9.17/5.34 => ( ( ord_less_eq_int @ R2 @ zero_zero_int )
% 9.17/5.34 => ( ( ord_less_int @ B @ R2 )
% 9.17/5.34 => ( ( modulo_modulo_int @ A @ B )
% 9.17/5.34 = R2 ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2161_split__zmod,axiom,
% 9.17/5.34 ! [P: int > $o,N2: int,K: int] :
% 9.17/5.34 ( ( P @ ( modulo_modulo_int @ N2 @ K ) )
% 9.17/5.34 = ( ( ( K = zero_zero_int )
% 9.17/5.34 => ( P @ N2 ) )
% 9.17/5.34 & ( ( ord_less_int @ zero_zero_int @ K )
% 9.17/5.34 => ! [I3: int,J2: int] :
% 9.17/5.34 ( ( ( ord_less_eq_int @ zero_zero_int @ J2 )
% 9.17/5.34 & ( ord_less_int @ J2 @ K )
% 9.17/5.34 & ( N2
% 9.17/5.34 = ( plus_plus_int @ ( times_times_int @ K @ I3 ) @ J2 ) ) )
% 9.17/5.34 => ( P @ J2 ) ) )
% 9.17/5.34 & ( ( ord_less_int @ K @ zero_zero_int )
% 9.17/5.34 => ! [I3: int,J2: int] :
% 9.17/5.34 ( ( ( ord_less_int @ K @ J2 )
% 9.17/5.34 & ( ord_less_eq_int @ J2 @ zero_zero_int )
% 9.17/5.34 & ( N2
% 9.17/5.34 = ( plus_plus_int @ ( times_times_int @ K @ I3 ) @ J2 ) ) )
% 9.17/5.34 => ( P @ J2 ) ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2162_zmod__zmult2__eq,axiom,
% 9.17/5.34 ! [C: int,A: int,B: int] :
% 9.17/5.34 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 9.17/5.34 => ( ( modulo_modulo_int @ A @ ( times_times_int @ B @ C ) )
% 9.17/5.34 = ( plus_plus_int @ ( times_times_int @ B @ ( modulo_modulo_int @ ( divide_divide_int @ A @ B ) @ C ) ) @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2163_zminus1__lemma,axiom,
% 9.17/5.34 ! [A: int,B: int,Q3: int,R2: int] :
% 9.17/5.34 ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q3 @ R2 ) )
% 9.17/5.34 => ( ( B != zero_zero_int )
% 9.17/5.34 => ( eucl_rel_int @ ( uminus_uminus_int @ A ) @ B @ ( product_Pair_int_int @ ( if_int @ ( R2 = zero_zero_int ) @ ( uminus_uminus_int @ Q3 ) @ ( minus_minus_int @ ( uminus_uminus_int @ Q3 ) @ one_one_int ) ) @ ( if_int @ ( R2 = zero_zero_int ) @ zero_zero_int @ ( minus_minus_int @ B @ R2 ) ) ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2164_eucl__rel__int__remainderI,axiom,
% 9.17/5.34 ! [R2: int,L: int,K: int,Q3: int] :
% 9.17/5.34 ( ( ( sgn_sgn_int @ R2 )
% 9.17/5.34 = ( sgn_sgn_int @ L ) )
% 9.17/5.34 => ( ( ord_less_int @ ( abs_abs_int @ R2 ) @ ( abs_abs_int @ L ) )
% 9.17/5.34 => ( ( K
% 9.17/5.34 = ( plus_plus_int @ ( times_times_int @ Q3 @ L ) @ R2 ) )
% 9.17/5.34 => ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q3 @ R2 ) ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2165_verit__le__mono__div__int,axiom,
% 9.17/5.34 ! [A2: int,B5: int,N2: int] :
% 9.17/5.34 ( ( ord_less_int @ A2 @ B5 )
% 9.17/5.34 => ( ( ord_less_int @ zero_zero_int @ N2 )
% 9.17/5.34 => ( ord_less_eq_int
% 9.17/5.34 @ ( plus_plus_int @ ( divide_divide_int @ A2 @ N2 )
% 9.17/5.34 @ ( if_int
% 9.17/5.34 @ ( ( modulo_modulo_int @ B5 @ N2 )
% 9.17/5.34 = zero_zero_int )
% 9.17/5.34 @ one_one_int
% 9.17/5.34 @ zero_zero_int ) )
% 9.17/5.34 @ ( divide_divide_int @ B5 @ N2 ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2166_bezw__0,axiom,
% 9.17/5.34 ! [X: nat] :
% 9.17/5.34 ( ( bezw @ X @ zero_zero_nat )
% 9.17/5.34 = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2167_verit__le__mono__div,axiom,
% 9.17/5.34 ! [A2: nat,B5: nat,N2: nat] :
% 9.17/5.34 ( ( ord_less_nat @ A2 @ B5 )
% 9.17/5.34 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 9.17/5.34 => ( ord_less_eq_nat
% 9.17/5.34 @ ( plus_plus_nat @ ( divide_divide_nat @ A2 @ N2 )
% 9.17/5.34 @ ( if_nat
% 9.17/5.34 @ ( ( modulo_modulo_nat @ B5 @ N2 )
% 9.17/5.34 = zero_zero_nat )
% 9.17/5.34 @ one_one_nat
% 9.17/5.34 @ zero_zero_nat ) )
% 9.17/5.34 @ ( divide_divide_nat @ B5 @ N2 ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2168_zero__le__ceiling,axiom,
% 9.17/5.34 ! [X: rat] :
% 9.17/5.34 ( ( ord_less_eq_int @ zero_zero_int @ ( archim2889992004027027881ng_rat @ X ) )
% 9.17/5.34 = ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ X ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2169_ceiling__less__zero,axiom,
% 9.17/5.34 ! [X: rat] :
% 9.17/5.34 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X ) @ zero_zero_int )
% 9.17/5.34 = ( ord_less_eq_rat @ X @ ( uminus_uminus_rat @ one_one_rat ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2170_floor__add,axiom,
% 9.17/5.34 ! [X: rat,Y: rat] :
% 9.17/5.34 ( ( ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X ) @ ( archimedean_frac_rat @ Y ) ) @ one_one_rat )
% 9.17/5.34 => ( ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X @ Y ) )
% 9.17/5.34 = ( plus_plus_int @ ( archim3151403230148437115or_rat @ X ) @ ( archim3151403230148437115or_rat @ Y ) ) ) )
% 9.17/5.34 & ( ~ ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X ) @ ( archimedean_frac_rat @ Y ) ) @ one_one_rat )
% 9.17/5.34 => ( ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X @ Y ) )
% 9.17/5.34 = ( plus_plus_int @ ( plus_plus_int @ ( archim3151403230148437115or_rat @ X ) @ ( archim3151403230148437115or_rat @ Y ) ) @ one_one_int ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2171_cpmi,axiom,
% 9.17/5.34 ! [D3: int,P: int > $o,P5: int > $o,B5: set_int] :
% 9.17/5.34 ( ( ord_less_int @ zero_zero_int @ D3 )
% 9.17/5.34 => ( ? [Z5: int] :
% 9.17/5.34 ! [X4: int] :
% 9.17/5.34 ( ( ord_less_int @ X4 @ Z5 )
% 9.17/5.34 => ( ( P @ X4 )
% 9.17/5.34 = ( P5 @ X4 ) ) )
% 9.17/5.34 => ( ! [X4: int] :
% 9.17/5.34 ( ! [Xa2: int] :
% 9.17/5.34 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 9.17/5.34 => ! [Xb2: int] :
% 9.17/5.34 ( ( member_int @ Xb2 @ B5 )
% 9.17/5.34 => ( X4
% 9.17/5.34 != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 9.17/5.34 => ( ( P @ X4 )
% 9.17/5.34 => ( P @ ( minus_minus_int @ X4 @ D3 ) ) ) )
% 9.17/5.34 => ( ! [X4: int,K5: int] :
% 9.17/5.34 ( ( P5 @ X4 )
% 9.17/5.34 = ( P5 @ ( minus_minus_int @ X4 @ ( times_times_int @ K5 @ D3 ) ) ) )
% 9.17/5.34 => ( ( ? [X9: int] : ( P @ X9 ) )
% 9.17/5.34 = ( ? [X3: int] :
% 9.17/5.34 ( ( member_int @ X3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 9.17/5.34 & ( P5 @ X3 ) )
% 9.17/5.34 | ? [X3: int] :
% 9.17/5.34 ( ( member_int @ X3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 9.17/5.34 & ? [Y3: int] :
% 9.17/5.34 ( ( member_int @ Y3 @ B5 )
% 9.17/5.34 & ( P @ ( plus_plus_int @ Y3 @ X3 ) ) ) ) ) ) ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2172_cppi,axiom,
% 9.17/5.34 ! [D3: int,P: int > $o,P5: int > $o,A2: set_int] :
% 9.17/5.34 ( ( ord_less_int @ zero_zero_int @ D3 )
% 9.17/5.34 => ( ? [Z5: int] :
% 9.17/5.34 ! [X4: int] :
% 9.17/5.34 ( ( ord_less_int @ Z5 @ X4 )
% 9.17/5.34 => ( ( P @ X4 )
% 9.17/5.34 = ( P5 @ X4 ) ) )
% 9.17/5.34 => ( ! [X4: int] :
% 9.17/5.34 ( ! [Xa2: int] :
% 9.17/5.34 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 9.17/5.34 => ! [Xb2: int] :
% 9.17/5.34 ( ( member_int @ Xb2 @ A2 )
% 9.17/5.34 => ( X4
% 9.17/5.34 != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 9.17/5.34 => ( ( P @ X4 )
% 9.17/5.34 => ( P @ ( plus_plus_int @ X4 @ D3 ) ) ) )
% 9.17/5.34 => ( ! [X4: int,K5: int] :
% 9.17/5.34 ( ( P5 @ X4 )
% 9.17/5.34 = ( P5 @ ( minus_minus_int @ X4 @ ( times_times_int @ K5 @ D3 ) ) ) )
% 9.17/5.34 => ( ( ? [X9: int] : ( P @ X9 ) )
% 9.17/5.34 = ( ? [X3: int] :
% 9.17/5.34 ( ( member_int @ X3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 9.17/5.34 & ( P5 @ X3 ) )
% 9.17/5.34 | ? [X3: int] :
% 9.17/5.34 ( ( member_int @ X3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 9.17/5.34 & ? [Y3: int] :
% 9.17/5.34 ( ( member_int @ Y3 @ A2 )
% 9.17/5.34 & ( P @ ( minus_minus_int @ Y3 @ X3 ) ) ) ) ) ) ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2173_bset_I6_J,axiom,
% 9.17/5.34 ! [D3: int,B5: set_int,T: int] :
% 9.17/5.34 ( ( ord_less_int @ zero_zero_int @ D3 )
% 9.17/5.34 => ! [X8: int] :
% 9.17/5.34 ( ! [Xa3: int] :
% 9.17/5.34 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 9.17/5.34 => ! [Xb3: int] :
% 9.17/5.34 ( ( member_int @ Xb3 @ B5 )
% 9.17/5.34 => ( X8
% 9.17/5.34 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 9.17/5.34 => ( ( ord_less_eq_int @ X8 @ T )
% 9.17/5.34 => ( ord_less_eq_int @ ( minus_minus_int @ X8 @ D3 ) @ T ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2174_bset_I8_J,axiom,
% 9.17/5.34 ! [D3: int,T: int,B5: set_int] :
% 9.17/5.34 ( ( ord_less_int @ zero_zero_int @ D3 )
% 9.17/5.34 => ( ( member_int @ ( minus_minus_int @ T @ one_one_int ) @ B5 )
% 9.17/5.34 => ! [X8: int] :
% 9.17/5.34 ( ! [Xa3: int] :
% 9.17/5.34 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 9.17/5.34 => ! [Xb3: int] :
% 9.17/5.34 ( ( member_int @ Xb3 @ B5 )
% 9.17/5.34 => ( X8
% 9.17/5.34 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 9.17/5.34 => ( ( ord_less_eq_int @ T @ X8 )
% 9.17/5.34 => ( ord_less_eq_int @ T @ ( minus_minus_int @ X8 @ D3 ) ) ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2175_aset_I6_J,axiom,
% 9.17/5.34 ! [D3: int,T: int,A2: set_int] :
% 9.17/5.34 ( ( ord_less_int @ zero_zero_int @ D3 )
% 9.17/5.34 => ( ( member_int @ ( plus_plus_int @ T @ one_one_int ) @ A2 )
% 9.17/5.34 => ! [X8: int] :
% 9.17/5.34 ( ! [Xa3: int] :
% 9.17/5.34 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 9.17/5.34 => ! [Xb3: int] :
% 9.17/5.34 ( ( member_int @ Xb3 @ A2 )
% 9.17/5.34 => ( X8
% 9.17/5.34 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 9.17/5.34 => ( ( ord_less_eq_int @ X8 @ T )
% 9.17/5.34 => ( ord_less_eq_int @ ( plus_plus_int @ X8 @ D3 ) @ T ) ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2176_atLeastAtMost__iff,axiom,
% 9.17/5.34 ! [I: $o,L: $o,U: $o] :
% 9.17/5.34 ( ( member_o @ I @ ( set_or8904488021354931149Most_o @ L @ U ) )
% 9.17/5.34 = ( ( ord_less_eq_o @ L @ I )
% 9.17/5.34 & ( ord_less_eq_o @ I @ U ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2177_atLeastAtMost__iff,axiom,
% 9.17/5.34 ! [I: set_nat,L: set_nat,U: set_nat] :
% 9.17/5.34 ( ( member_set_nat @ I @ ( set_or4548717258645045905et_nat @ L @ U ) )
% 9.17/5.34 = ( ( ord_less_eq_set_nat @ L @ I )
% 9.17/5.34 & ( ord_less_eq_set_nat @ I @ U ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2178_atLeastAtMost__iff,axiom,
% 9.17/5.34 ! [I: rat,L: rat,U: rat] :
% 9.17/5.34 ( ( member_rat @ I @ ( set_or633870826150836451st_rat @ L @ U ) )
% 9.17/5.34 = ( ( ord_less_eq_rat @ L @ I )
% 9.17/5.34 & ( ord_less_eq_rat @ I @ U ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2179_atLeastAtMost__iff,axiom,
% 9.17/5.34 ! [I: num,L: num,U: num] :
% 9.17/5.34 ( ( member_num @ I @ ( set_or7049704709247886629st_num @ L @ U ) )
% 9.17/5.34 = ( ( ord_less_eq_num @ L @ I )
% 9.17/5.34 & ( ord_less_eq_num @ I @ U ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2180_atLeastAtMost__iff,axiom,
% 9.17/5.34 ! [I: int,L: int,U: int] :
% 9.17/5.34 ( ( member_int @ I @ ( set_or1266510415728281911st_int @ L @ U ) )
% 9.17/5.34 = ( ( ord_less_eq_int @ L @ I )
% 9.17/5.34 & ( ord_less_eq_int @ I @ U ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2181_atLeastAtMost__iff,axiom,
% 9.17/5.34 ! [I: nat,L: nat,U: nat] :
% 9.17/5.34 ( ( member_nat @ I @ ( set_or1269000886237332187st_nat @ L @ U ) )
% 9.17/5.34 = ( ( ord_less_eq_nat @ L @ I )
% 9.17/5.34 & ( ord_less_eq_nat @ I @ U ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2182_atLeastAtMost__iff,axiom,
% 9.17/5.34 ! [I: code_integer,L: code_integer,U: code_integer] :
% 9.17/5.34 ( ( member_Code_integer @ I @ ( set_or189985376899183464nteger @ L @ U ) )
% 9.17/5.34 = ( ( ord_le3102999989581377725nteger @ L @ I )
% 9.17/5.34 & ( ord_le3102999989581377725nteger @ I @ U ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2183_Icc__eq__Icc,axiom,
% 9.17/5.34 ! [L: set_nat,H3: set_nat,L4: set_nat,H5: set_nat] :
% 9.17/5.34 ( ( ( set_or4548717258645045905et_nat @ L @ H3 )
% 9.17/5.34 = ( set_or4548717258645045905et_nat @ L4 @ H5 ) )
% 9.17/5.34 = ( ( ( L = L4 )
% 9.17/5.34 & ( H3 = H5 ) )
% 9.17/5.34 | ( ~ ( ord_less_eq_set_nat @ L @ H3 )
% 9.17/5.34 & ~ ( ord_less_eq_set_nat @ L4 @ H5 ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2184_Icc__eq__Icc,axiom,
% 9.17/5.34 ! [L: rat,H3: rat,L4: rat,H5: rat] :
% 9.17/5.34 ( ( ( set_or633870826150836451st_rat @ L @ H3 )
% 9.17/5.34 = ( set_or633870826150836451st_rat @ L4 @ H5 ) )
% 9.17/5.34 = ( ( ( L = L4 )
% 9.17/5.34 & ( H3 = H5 ) )
% 9.17/5.34 | ( ~ ( ord_less_eq_rat @ L @ H3 )
% 9.17/5.34 & ~ ( ord_less_eq_rat @ L4 @ H5 ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2185_Icc__eq__Icc,axiom,
% 9.17/5.34 ! [L: num,H3: num,L4: num,H5: num] :
% 9.17/5.34 ( ( ( set_or7049704709247886629st_num @ L @ H3 )
% 9.17/5.34 = ( set_or7049704709247886629st_num @ L4 @ H5 ) )
% 9.17/5.34 = ( ( ( L = L4 )
% 9.17/5.34 & ( H3 = H5 ) )
% 9.17/5.34 | ( ~ ( ord_less_eq_num @ L @ H3 )
% 9.17/5.34 & ~ ( ord_less_eq_num @ L4 @ H5 ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2186_Icc__eq__Icc,axiom,
% 9.17/5.34 ! [L: int,H3: int,L4: int,H5: int] :
% 9.17/5.34 ( ( ( set_or1266510415728281911st_int @ L @ H3 )
% 9.17/5.34 = ( set_or1266510415728281911st_int @ L4 @ H5 ) )
% 9.17/5.34 = ( ( ( L = L4 )
% 9.17/5.34 & ( H3 = H5 ) )
% 9.17/5.34 | ( ~ ( ord_less_eq_int @ L @ H3 )
% 9.17/5.34 & ~ ( ord_less_eq_int @ L4 @ H5 ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2187_Icc__eq__Icc,axiom,
% 9.17/5.34 ! [L: nat,H3: nat,L4: nat,H5: nat] :
% 9.17/5.34 ( ( ( set_or1269000886237332187st_nat @ L @ H3 )
% 9.17/5.34 = ( set_or1269000886237332187st_nat @ L4 @ H5 ) )
% 9.17/5.34 = ( ( ( L = L4 )
% 9.17/5.34 & ( H3 = H5 ) )
% 9.17/5.34 | ( ~ ( ord_less_eq_nat @ L @ H3 )
% 9.17/5.34 & ~ ( ord_less_eq_nat @ L4 @ H5 ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2188_Icc__eq__Icc,axiom,
% 9.17/5.34 ! [L: code_integer,H3: code_integer,L4: code_integer,H5: code_integer] :
% 9.17/5.34 ( ( ( set_or189985376899183464nteger @ L @ H3 )
% 9.17/5.34 = ( set_or189985376899183464nteger @ L4 @ H5 ) )
% 9.17/5.34 = ( ( ( L = L4 )
% 9.17/5.34 & ( H3 = H5 ) )
% 9.17/5.34 | ( ~ ( ord_le3102999989581377725nteger @ L @ H3 )
% 9.17/5.34 & ~ ( ord_le3102999989581377725nteger @ L4 @ H5 ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2189_atLeastatMost__subset__iff,axiom,
% 9.17/5.34 ! [A: set_nat,B: set_nat,C: set_nat,D2: set_nat] :
% 9.17/5.34 ( ( ord_le6893508408891458716et_nat @ ( set_or4548717258645045905et_nat @ A @ B ) @ ( set_or4548717258645045905et_nat @ C @ D2 ) )
% 9.17/5.34 = ( ~ ( ord_less_eq_set_nat @ A @ B )
% 9.17/5.34 | ( ( ord_less_eq_set_nat @ C @ A )
% 9.17/5.34 & ( ord_less_eq_set_nat @ B @ D2 ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2190_atLeastatMost__subset__iff,axiom,
% 9.17/5.34 ! [A: rat,B: rat,C: rat,D2: rat] :
% 9.17/5.34 ( ( ord_less_eq_set_rat @ ( set_or633870826150836451st_rat @ A @ B ) @ ( set_or633870826150836451st_rat @ C @ D2 ) )
% 9.17/5.34 = ( ~ ( ord_less_eq_rat @ A @ B )
% 9.17/5.34 | ( ( ord_less_eq_rat @ C @ A )
% 9.17/5.34 & ( ord_less_eq_rat @ B @ D2 ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2191_atLeastatMost__subset__iff,axiom,
% 9.17/5.34 ! [A: num,B: num,C: num,D2: num] :
% 9.17/5.34 ( ( ord_less_eq_set_num @ ( set_or7049704709247886629st_num @ A @ B ) @ ( set_or7049704709247886629st_num @ C @ D2 ) )
% 9.17/5.34 = ( ~ ( ord_less_eq_num @ A @ B )
% 9.17/5.34 | ( ( ord_less_eq_num @ C @ A )
% 9.17/5.34 & ( ord_less_eq_num @ B @ D2 ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2192_atLeastatMost__subset__iff,axiom,
% 9.17/5.34 ! [A: int,B: int,C: int,D2: int] :
% 9.17/5.34 ( ( ord_less_eq_set_int @ ( set_or1266510415728281911st_int @ A @ B ) @ ( set_or1266510415728281911st_int @ C @ D2 ) )
% 9.17/5.34 = ( ~ ( ord_less_eq_int @ A @ B )
% 9.17/5.34 | ( ( ord_less_eq_int @ C @ A )
% 9.17/5.34 & ( ord_less_eq_int @ B @ D2 ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2193_atLeastatMost__subset__iff,axiom,
% 9.17/5.34 ! [A: nat,B: nat,C: nat,D2: nat] :
% 9.17/5.34 ( ( ord_less_eq_set_nat @ ( set_or1269000886237332187st_nat @ A @ B ) @ ( set_or1269000886237332187st_nat @ C @ D2 ) )
% 9.17/5.34 = ( ~ ( ord_less_eq_nat @ A @ B )
% 9.17/5.34 | ( ( ord_less_eq_nat @ C @ A )
% 9.17/5.34 & ( ord_less_eq_nat @ B @ D2 ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2194_atLeastatMost__subset__iff,axiom,
% 9.17/5.34 ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 9.17/5.34 ( ( ord_le7084787975880047091nteger @ ( set_or189985376899183464nteger @ A @ B ) @ ( set_or189985376899183464nteger @ C @ D2 ) )
% 9.17/5.34 = ( ~ ( ord_le3102999989581377725nteger @ A @ B )
% 9.17/5.34 | ( ( ord_le3102999989581377725nteger @ C @ A )
% 9.17/5.34 & ( ord_le3102999989581377725nteger @ B @ D2 ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2195_floor__one,axiom,
% 9.17/5.34 ( ( archim3151403230148437115or_rat @ one_one_rat )
% 9.17/5.34 = one_one_int ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2196_ceiling__one,axiom,
% 9.17/5.34 ( ( archim2889992004027027881ng_rat @ one_one_rat )
% 9.17/5.34 = one_one_int ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2197_floor__add2,axiom,
% 9.17/5.34 ! [X: rat,Y: rat] :
% 9.17/5.34 ( ( ( member_rat @ X @ ring_1_Ints_rat )
% 9.17/5.34 | ( member_rat @ Y @ ring_1_Ints_rat ) )
% 9.17/5.34 => ( ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X @ Y ) )
% 9.17/5.34 = ( plus_plus_int @ ( archim3151403230148437115or_rat @ X ) @ ( archim3151403230148437115or_rat @ Y ) ) ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2198_zero__less__floor,axiom,
% 9.17/5.34 ! [X: rat] :
% 9.17/5.34 ( ( ord_less_int @ zero_zero_int @ ( archim3151403230148437115or_rat @ X ) )
% 9.17/5.34 = ( ord_less_eq_rat @ one_one_rat @ X ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2199_floor__le__zero,axiom,
% 9.17/5.34 ! [X: rat] :
% 9.17/5.34 ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X ) @ zero_zero_int )
% 9.17/5.34 = ( ord_less_rat @ X @ one_one_rat ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2200_one__le__floor,axiom,
% 9.17/5.34 ! [X: rat] :
% 9.17/5.34 ( ( ord_less_eq_int @ one_one_int @ ( archim3151403230148437115or_rat @ X ) )
% 9.17/5.34 = ( ord_less_eq_rat @ one_one_rat @ X ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2201_floor__less__one,axiom,
% 9.17/5.34 ! [X: rat] :
% 9.17/5.34 ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X ) @ one_one_int )
% 9.17/5.34 = ( ord_less_rat @ X @ one_one_rat ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2202_ceiling__le__one,axiom,
% 9.17/5.34 ! [X: rat] :
% 9.17/5.34 ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X ) @ one_one_int )
% 9.17/5.34 = ( ord_less_eq_rat @ X @ one_one_rat ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2203_one__less__ceiling,axiom,
% 9.17/5.34 ! [X: rat] :
% 9.17/5.34 ( ( ord_less_int @ one_one_int @ ( archim2889992004027027881ng_rat @ X ) )
% 9.17/5.34 = ( ord_less_rat @ one_one_rat @ X ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2204_ceiling__add__one,axiom,
% 9.17/5.34 ! [X: rat] :
% 9.17/5.34 ( ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X @ one_one_rat ) )
% 9.17/5.34 = ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X ) @ one_one_int ) ) ).
% 9.17/5.34
% 9.17/5.34 thf(fact_2205_floor__diff__one,axiom,
% 9.17/5.34 ! [X: rat] :
% 9.17/5.34 ( ( archim3151403230148437115or_rat @ ( minus_minus_rat @ X @ one_one_rat ) )
% 9.17/5.34 = ( minus_minus_int @ ( archim3151403230148437115or_rat @ X ) @ one_one_int ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2206_ceiling__diff__one,axiom,
% 9.17/5.35 ! [X: rat] :
% 9.17/5.35 ( ( archim2889992004027027881ng_rat @ ( minus_minus_rat @ X @ one_one_rat ) )
% 9.17/5.35 = ( minus_minus_int @ ( archim2889992004027027881ng_rat @ X ) @ one_one_int ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2207_atLeastatMost__psubset__iff,axiom,
% 9.17/5.35 ! [A: set_nat,B: set_nat,C: set_nat,D2: set_nat] :
% 9.17/5.35 ( ( ord_less_set_set_nat @ ( set_or4548717258645045905et_nat @ A @ B ) @ ( set_or4548717258645045905et_nat @ C @ D2 ) )
% 9.17/5.35 = ( ( ~ ( ord_less_eq_set_nat @ A @ B )
% 9.17/5.35 | ( ( ord_less_eq_set_nat @ C @ A )
% 9.17/5.35 & ( ord_less_eq_set_nat @ B @ D2 )
% 9.17/5.35 & ( ( ord_less_set_nat @ C @ A )
% 9.17/5.35 | ( ord_less_set_nat @ B @ D2 ) ) ) )
% 9.17/5.35 & ( ord_less_eq_set_nat @ C @ D2 ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2208_atLeastatMost__psubset__iff,axiom,
% 9.17/5.35 ! [A: rat,B: rat,C: rat,D2: rat] :
% 9.17/5.35 ( ( ord_less_set_rat @ ( set_or633870826150836451st_rat @ A @ B ) @ ( set_or633870826150836451st_rat @ C @ D2 ) )
% 9.17/5.35 = ( ( ~ ( ord_less_eq_rat @ A @ B )
% 9.17/5.35 | ( ( ord_less_eq_rat @ C @ A )
% 9.17/5.35 & ( ord_less_eq_rat @ B @ D2 )
% 9.17/5.35 & ( ( ord_less_rat @ C @ A )
% 9.17/5.35 | ( ord_less_rat @ B @ D2 ) ) ) )
% 9.17/5.35 & ( ord_less_eq_rat @ C @ D2 ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2209_atLeastatMost__psubset__iff,axiom,
% 9.17/5.35 ! [A: num,B: num,C: num,D2: num] :
% 9.17/5.35 ( ( ord_less_set_num @ ( set_or7049704709247886629st_num @ A @ B ) @ ( set_or7049704709247886629st_num @ C @ D2 ) )
% 9.17/5.35 = ( ( ~ ( ord_less_eq_num @ A @ B )
% 9.17/5.35 | ( ( ord_less_eq_num @ C @ A )
% 9.17/5.35 & ( ord_less_eq_num @ B @ D2 )
% 9.17/5.35 & ( ( ord_less_num @ C @ A )
% 9.17/5.35 | ( ord_less_num @ B @ D2 ) ) ) )
% 9.17/5.35 & ( ord_less_eq_num @ C @ D2 ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2210_atLeastatMost__psubset__iff,axiom,
% 9.17/5.35 ! [A: int,B: int,C: int,D2: int] :
% 9.17/5.35 ( ( ord_less_set_int @ ( set_or1266510415728281911st_int @ A @ B ) @ ( set_or1266510415728281911st_int @ C @ D2 ) )
% 9.17/5.35 = ( ( ~ ( ord_less_eq_int @ A @ B )
% 9.17/5.35 | ( ( ord_less_eq_int @ C @ A )
% 9.17/5.35 & ( ord_less_eq_int @ B @ D2 )
% 9.17/5.35 & ( ( ord_less_int @ C @ A )
% 9.17/5.35 | ( ord_less_int @ B @ D2 ) ) ) )
% 9.17/5.35 & ( ord_less_eq_int @ C @ D2 ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2211_atLeastatMost__psubset__iff,axiom,
% 9.17/5.35 ! [A: nat,B: nat,C: nat,D2: nat] :
% 9.17/5.35 ( ( ord_less_set_nat @ ( set_or1269000886237332187st_nat @ A @ B ) @ ( set_or1269000886237332187st_nat @ C @ D2 ) )
% 9.17/5.35 = ( ( ~ ( ord_less_eq_nat @ A @ B )
% 9.17/5.35 | ( ( ord_less_eq_nat @ C @ A )
% 9.17/5.35 & ( ord_less_eq_nat @ B @ D2 )
% 9.17/5.35 & ( ( ord_less_nat @ C @ A )
% 9.17/5.35 | ( ord_less_nat @ B @ D2 ) ) ) )
% 9.17/5.35 & ( ord_less_eq_nat @ C @ D2 ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2212_atLeastatMost__psubset__iff,axiom,
% 9.17/5.35 ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 9.17/5.35 ( ( ord_le1307284697595431911nteger @ ( set_or189985376899183464nteger @ A @ B ) @ ( set_or189985376899183464nteger @ C @ D2 ) )
% 9.17/5.35 = ( ( ~ ( ord_le3102999989581377725nteger @ A @ B )
% 9.17/5.35 | ( ( ord_le3102999989581377725nteger @ C @ A )
% 9.17/5.35 & ( ord_le3102999989581377725nteger @ B @ D2 )
% 9.17/5.35 & ( ( ord_le6747313008572928689nteger @ C @ A )
% 9.17/5.35 | ( ord_le6747313008572928689nteger @ B @ D2 ) ) ) )
% 9.17/5.35 & ( ord_le3102999989581377725nteger @ C @ D2 ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2213_nat__mod__eq__iff,axiom,
% 9.17/5.35 ! [X: nat,N2: nat,Y: nat] :
% 9.17/5.35 ( ( ( modulo_modulo_nat @ X @ N2 )
% 9.17/5.35 = ( modulo_modulo_nat @ Y @ N2 ) )
% 9.17/5.35 = ( ? [Q1: nat,Q22: nat] :
% 9.17/5.35 ( ( plus_plus_nat @ X @ ( times_times_nat @ N2 @ Q1 ) )
% 9.17/5.35 = ( plus_plus_nat @ Y @ ( times_times_nat @ N2 @ Q22 ) ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2214_le__floor__add,axiom,
% 9.17/5.35 ! [X: rat,Y: rat] : ( ord_less_eq_int @ ( plus_plus_int @ ( archim3151403230148437115or_rat @ X ) @ ( archim3151403230148437115or_rat @ Y ) ) @ ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X @ Y ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2215_bset_I1_J,axiom,
% 9.17/5.35 ! [D3: int,B5: set_int,P: int > $o,Q: int > $o] :
% 9.17/5.35 ( ! [X4: int] :
% 9.17/5.35 ( ! [Xa2: int] :
% 9.17/5.35 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 9.17/5.35 => ! [Xb2: int] :
% 9.17/5.35 ( ( member_int @ Xb2 @ B5 )
% 9.17/5.35 => ( X4
% 9.17/5.35 != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 9.17/5.35 => ( ( P @ X4 )
% 9.17/5.35 => ( P @ ( minus_minus_int @ X4 @ D3 ) ) ) )
% 9.17/5.35 => ( ! [X4: int] :
% 9.17/5.35 ( ! [Xa2: int] :
% 9.17/5.35 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 9.17/5.35 => ! [Xb2: int] :
% 9.17/5.35 ( ( member_int @ Xb2 @ B5 )
% 9.17/5.35 => ( X4
% 9.17/5.35 != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 9.17/5.35 => ( ( Q @ X4 )
% 9.17/5.35 => ( Q @ ( minus_minus_int @ X4 @ D3 ) ) ) )
% 9.17/5.35 => ! [X8: int] :
% 9.17/5.35 ( ! [Xa3: int] :
% 9.17/5.35 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 9.17/5.35 => ! [Xb3: int] :
% 9.17/5.35 ( ( member_int @ Xb3 @ B5 )
% 9.17/5.35 => ( X8
% 9.17/5.35 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 9.17/5.35 => ( ( ( P @ X8 )
% 9.17/5.35 & ( Q @ X8 ) )
% 9.17/5.35 => ( ( P @ ( minus_minus_int @ X8 @ D3 ) )
% 9.17/5.35 & ( Q @ ( minus_minus_int @ X8 @ D3 ) ) ) ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2216_bset_I2_J,axiom,
% 9.17/5.35 ! [D3: int,B5: set_int,P: int > $o,Q: int > $o] :
% 9.17/5.35 ( ! [X4: int] :
% 9.17/5.35 ( ! [Xa2: int] :
% 9.17/5.35 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 9.17/5.35 => ! [Xb2: int] :
% 9.17/5.35 ( ( member_int @ Xb2 @ B5 )
% 9.17/5.35 => ( X4
% 9.17/5.35 != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 9.17/5.35 => ( ( P @ X4 )
% 9.17/5.35 => ( P @ ( minus_minus_int @ X4 @ D3 ) ) ) )
% 9.17/5.35 => ( ! [X4: int] :
% 9.17/5.35 ( ! [Xa2: int] :
% 9.17/5.35 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 9.17/5.35 => ! [Xb2: int] :
% 9.17/5.35 ( ( member_int @ Xb2 @ B5 )
% 9.17/5.35 => ( X4
% 9.17/5.35 != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 9.17/5.35 => ( ( Q @ X4 )
% 9.17/5.35 => ( Q @ ( minus_minus_int @ X4 @ D3 ) ) ) )
% 9.17/5.35 => ! [X8: int] :
% 9.17/5.35 ( ! [Xa3: int] :
% 9.17/5.35 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 9.17/5.35 => ! [Xb3: int] :
% 9.17/5.35 ( ( member_int @ Xb3 @ B5 )
% 9.17/5.35 => ( X8
% 9.17/5.35 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 9.17/5.35 => ( ( ( P @ X8 )
% 9.17/5.35 | ( Q @ X8 ) )
% 9.17/5.35 => ( ( P @ ( minus_minus_int @ X8 @ D3 ) )
% 9.17/5.35 | ( Q @ ( minus_minus_int @ X8 @ D3 ) ) ) ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2217_aset_I1_J,axiom,
% 9.17/5.35 ! [D3: int,A2: set_int,P: int > $o,Q: int > $o] :
% 9.17/5.35 ( ! [X4: int] :
% 9.17/5.35 ( ! [Xa2: int] :
% 9.17/5.35 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 9.17/5.35 => ! [Xb2: int] :
% 9.17/5.35 ( ( member_int @ Xb2 @ A2 )
% 9.17/5.35 => ( X4
% 9.17/5.35 != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 9.17/5.35 => ( ( P @ X4 )
% 9.17/5.35 => ( P @ ( plus_plus_int @ X4 @ D3 ) ) ) )
% 9.17/5.35 => ( ! [X4: int] :
% 9.17/5.35 ( ! [Xa2: int] :
% 9.17/5.35 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 9.17/5.35 => ! [Xb2: int] :
% 9.17/5.35 ( ( member_int @ Xb2 @ A2 )
% 9.17/5.35 => ( X4
% 9.17/5.35 != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 9.17/5.35 => ( ( Q @ X4 )
% 9.17/5.35 => ( Q @ ( plus_plus_int @ X4 @ D3 ) ) ) )
% 9.17/5.35 => ! [X8: int] :
% 9.17/5.35 ( ! [Xa3: int] :
% 9.17/5.35 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 9.17/5.35 => ! [Xb3: int] :
% 9.17/5.35 ( ( member_int @ Xb3 @ A2 )
% 9.17/5.35 => ( X8
% 9.17/5.35 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 9.17/5.35 => ( ( ( P @ X8 )
% 9.17/5.35 & ( Q @ X8 ) )
% 9.17/5.35 => ( ( P @ ( plus_plus_int @ X8 @ D3 ) )
% 9.17/5.35 & ( Q @ ( plus_plus_int @ X8 @ D3 ) ) ) ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2218_aset_I2_J,axiom,
% 9.17/5.35 ! [D3: int,A2: set_int,P: int > $o,Q: int > $o] :
% 9.17/5.35 ( ! [X4: int] :
% 9.17/5.35 ( ! [Xa2: int] :
% 9.17/5.35 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 9.17/5.35 => ! [Xb2: int] :
% 9.17/5.35 ( ( member_int @ Xb2 @ A2 )
% 9.17/5.35 => ( X4
% 9.17/5.35 != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 9.17/5.35 => ( ( P @ X4 )
% 9.17/5.35 => ( P @ ( plus_plus_int @ X4 @ D3 ) ) ) )
% 9.17/5.35 => ( ! [X4: int] :
% 9.17/5.35 ( ! [Xa2: int] :
% 9.17/5.35 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 9.17/5.35 => ! [Xb2: int] :
% 9.17/5.35 ( ( member_int @ Xb2 @ A2 )
% 9.17/5.35 => ( X4
% 9.17/5.35 != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 9.17/5.35 => ( ( Q @ X4 )
% 9.17/5.35 => ( Q @ ( plus_plus_int @ X4 @ D3 ) ) ) )
% 9.17/5.35 => ! [X8: int] :
% 9.17/5.35 ( ! [Xa3: int] :
% 9.17/5.35 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 9.17/5.35 => ! [Xb3: int] :
% 9.17/5.35 ( ( member_int @ Xb3 @ A2 )
% 9.17/5.35 => ( X8
% 9.17/5.35 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 9.17/5.35 => ( ( ( P @ X8 )
% 9.17/5.35 | ( Q @ X8 ) )
% 9.17/5.35 => ( ( P @ ( plus_plus_int @ X8 @ D3 ) )
% 9.17/5.35 | ( Q @ ( plus_plus_int @ X8 @ D3 ) ) ) ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2219_nat__mod__eq__lemma,axiom,
% 9.17/5.35 ! [X: nat,N2: nat,Y: nat] :
% 9.17/5.35 ( ( ( modulo_modulo_nat @ X @ N2 )
% 9.17/5.35 = ( modulo_modulo_nat @ Y @ N2 ) )
% 9.17/5.35 => ( ( ord_less_eq_nat @ Y @ X )
% 9.17/5.35 => ? [Q2: nat] :
% 9.17/5.35 ( X
% 9.17/5.35 = ( plus_plus_nat @ Y @ ( times_times_nat @ N2 @ Q2 ) ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2220_mod__eq__nat2E,axiom,
% 9.17/5.35 ! [M2: nat,Q3: nat,N2: nat] :
% 9.17/5.35 ( ( ( modulo_modulo_nat @ M2 @ Q3 )
% 9.17/5.35 = ( modulo_modulo_nat @ N2 @ Q3 ) )
% 9.17/5.35 => ( ( ord_less_eq_nat @ M2 @ N2 )
% 9.17/5.35 => ~ ! [S6: nat] :
% 9.17/5.35 ( N2
% 9.17/5.35 != ( plus_plus_nat @ M2 @ ( times_times_nat @ Q3 @ S6 ) ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2221_mod__eq__nat1E,axiom,
% 9.17/5.35 ! [M2: nat,Q3: nat,N2: nat] :
% 9.17/5.35 ( ( ( modulo_modulo_nat @ M2 @ Q3 )
% 9.17/5.35 = ( modulo_modulo_nat @ N2 @ Q3 ) )
% 9.17/5.35 => ( ( ord_less_eq_nat @ N2 @ M2 )
% 9.17/5.35 => ~ ! [S6: nat] :
% 9.17/5.35 ( M2
% 9.17/5.35 != ( plus_plus_nat @ N2 @ ( times_times_nat @ Q3 @ S6 ) ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2222_ceiling__add__le,axiom,
% 9.17/5.35 ! [X: rat,Y: rat] : ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X @ Y ) ) @ ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X ) @ ( archim2889992004027027881ng_rat @ Y ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2223_mod__mult2__eq,axiom,
% 9.17/5.35 ! [M2: nat,N2: nat,Q3: nat] :
% 9.17/5.35 ( ( modulo_modulo_nat @ M2 @ ( times_times_nat @ N2 @ Q3 ) )
% 9.17/5.35 = ( plus_plus_nat @ ( times_times_nat @ N2 @ ( modulo_modulo_nat @ ( divide_divide_nat @ M2 @ N2 ) @ Q3 ) ) @ ( modulo_modulo_nat @ M2 @ N2 ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2224_div__mod__decomp,axiom,
% 9.17/5.35 ! [A2: nat,N2: nat] :
% 9.17/5.35 ( A2
% 9.17/5.35 = ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A2 @ N2 ) @ N2 ) @ ( modulo_modulo_nat @ A2 @ N2 ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2225_one__add__floor,axiom,
% 9.17/5.35 ! [X: rat] :
% 9.17/5.35 ( ( plus_plus_int @ ( archim3151403230148437115or_rat @ X ) @ one_one_int )
% 9.17/5.35 = ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X @ one_one_rat ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2226_split__mod,axiom,
% 9.17/5.35 ! [P: nat > $o,M2: nat,N2: nat] :
% 9.17/5.35 ( ( P @ ( modulo_modulo_nat @ M2 @ N2 ) )
% 9.17/5.35 = ( ( ( N2 = zero_zero_nat )
% 9.17/5.35 => ( P @ M2 ) )
% 9.17/5.35 & ( ( N2 != zero_zero_nat )
% 9.17/5.35 => ! [I3: nat,J2: nat] :
% 9.17/5.35 ( ( ord_less_nat @ J2 @ N2 )
% 9.17/5.35 => ( ( M2
% 9.17/5.35 = ( plus_plus_nat @ ( times_times_nat @ N2 @ I3 ) @ J2 ) )
% 9.17/5.35 => ( P @ J2 ) ) ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2227_bset_I3_J,axiom,
% 9.17/5.35 ! [D3: int,T: int,B5: set_int] :
% 9.17/5.35 ( ( ord_less_int @ zero_zero_int @ D3 )
% 9.17/5.35 => ( ( member_int @ ( minus_minus_int @ T @ one_one_int ) @ B5 )
% 9.17/5.35 => ! [X8: int] :
% 9.17/5.35 ( ! [Xa3: int] :
% 9.17/5.35 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 9.17/5.35 => ! [Xb3: int] :
% 9.17/5.35 ( ( member_int @ Xb3 @ B5 )
% 9.17/5.35 => ( X8
% 9.17/5.35 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 9.17/5.35 => ( ( X8 = T )
% 9.17/5.35 => ( ( minus_minus_int @ X8 @ D3 )
% 9.17/5.35 = T ) ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2228_bset_I4_J,axiom,
% 9.17/5.35 ! [D3: int,T: int,B5: set_int] :
% 9.17/5.35 ( ( ord_less_int @ zero_zero_int @ D3 )
% 9.17/5.35 => ( ( member_int @ T @ B5 )
% 9.17/5.35 => ! [X8: int] :
% 9.17/5.35 ( ! [Xa3: int] :
% 9.17/5.35 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 9.17/5.35 => ! [Xb3: int] :
% 9.17/5.35 ( ( member_int @ Xb3 @ B5 )
% 9.17/5.35 => ( X8
% 9.17/5.35 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 9.17/5.35 => ( ( X8 != T )
% 9.17/5.35 => ( ( minus_minus_int @ X8 @ D3 )
% 9.17/5.35 != T ) ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2229_bset_I5_J,axiom,
% 9.17/5.35 ! [D3: int,B5: set_int,T: int] :
% 9.17/5.35 ( ( ord_less_int @ zero_zero_int @ D3 )
% 9.17/5.35 => ! [X8: int] :
% 9.17/5.35 ( ! [Xa3: int] :
% 9.17/5.35 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 9.17/5.35 => ! [Xb3: int] :
% 9.17/5.35 ( ( member_int @ Xb3 @ B5 )
% 9.17/5.35 => ( X8
% 9.17/5.35 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 9.17/5.35 => ( ( ord_less_int @ X8 @ T )
% 9.17/5.35 => ( ord_less_int @ ( minus_minus_int @ X8 @ D3 ) @ T ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2230_bset_I7_J,axiom,
% 9.17/5.35 ! [D3: int,T: int,B5: set_int] :
% 9.17/5.35 ( ( ord_less_int @ zero_zero_int @ D3 )
% 9.17/5.35 => ( ( member_int @ T @ B5 )
% 9.17/5.35 => ! [X8: int] :
% 9.17/5.35 ( ! [Xa3: int] :
% 9.17/5.35 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 9.17/5.35 => ! [Xb3: int] :
% 9.17/5.35 ( ( member_int @ Xb3 @ B5 )
% 9.17/5.35 => ( X8
% 9.17/5.35 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 9.17/5.35 => ( ( ord_less_int @ T @ X8 )
% 9.17/5.35 => ( ord_less_int @ T @ ( minus_minus_int @ X8 @ D3 ) ) ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2231_aset_I3_J,axiom,
% 9.17/5.35 ! [D3: int,T: int,A2: set_int] :
% 9.17/5.35 ( ( ord_less_int @ zero_zero_int @ D3 )
% 9.17/5.35 => ( ( member_int @ ( plus_plus_int @ T @ one_one_int ) @ A2 )
% 9.17/5.35 => ! [X8: int] :
% 9.17/5.35 ( ! [Xa3: int] :
% 9.17/5.35 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 9.17/5.35 => ! [Xb3: int] :
% 9.17/5.35 ( ( member_int @ Xb3 @ A2 )
% 9.17/5.35 => ( X8
% 9.17/5.35 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 9.17/5.35 => ( ( X8 = T )
% 9.17/5.35 => ( ( plus_plus_int @ X8 @ D3 )
% 9.17/5.35 = T ) ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2232_aset_I4_J,axiom,
% 9.17/5.35 ! [D3: int,T: int,A2: set_int] :
% 9.17/5.35 ( ( ord_less_int @ zero_zero_int @ D3 )
% 9.17/5.35 => ( ( member_int @ T @ A2 )
% 9.17/5.35 => ! [X8: int] :
% 9.17/5.35 ( ! [Xa3: int] :
% 9.17/5.35 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 9.17/5.35 => ! [Xb3: int] :
% 9.17/5.35 ( ( member_int @ Xb3 @ A2 )
% 9.17/5.35 => ( X8
% 9.17/5.35 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 9.17/5.35 => ( ( X8 != T )
% 9.17/5.35 => ( ( plus_plus_int @ X8 @ D3 )
% 9.17/5.35 != T ) ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2233_aset_I5_J,axiom,
% 9.17/5.35 ! [D3: int,T: int,A2: set_int] :
% 9.17/5.35 ( ( ord_less_int @ zero_zero_int @ D3 )
% 9.17/5.35 => ( ( member_int @ T @ A2 )
% 9.17/5.35 => ! [X8: int] :
% 9.17/5.35 ( ! [Xa3: int] :
% 9.17/5.35 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 9.17/5.35 => ! [Xb3: int] :
% 9.17/5.35 ( ( member_int @ Xb3 @ A2 )
% 9.17/5.35 => ( X8
% 9.17/5.35 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 9.17/5.35 => ( ( ord_less_int @ X8 @ T )
% 9.17/5.35 => ( ord_less_int @ ( plus_plus_int @ X8 @ D3 ) @ T ) ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2234_aset_I7_J,axiom,
% 9.17/5.35 ! [D3: int,A2: set_int,T: int] :
% 9.17/5.35 ( ( ord_less_int @ zero_zero_int @ D3 )
% 9.17/5.35 => ! [X8: int] :
% 9.17/5.35 ( ! [Xa3: int] :
% 9.17/5.35 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 9.17/5.35 => ! [Xb3: int] :
% 9.17/5.35 ( ( member_int @ Xb3 @ A2 )
% 9.17/5.35 => ( X8
% 9.17/5.35 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 9.17/5.35 => ( ( ord_less_int @ T @ X8 )
% 9.17/5.35 => ( ord_less_int @ T @ ( plus_plus_int @ X8 @ D3 ) ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2235_aset_I8_J,axiom,
% 9.17/5.35 ! [D3: int,A2: set_int,T: int] :
% 9.17/5.35 ( ( ord_less_int @ zero_zero_int @ D3 )
% 9.17/5.35 => ! [X8: int] :
% 9.17/5.35 ( ! [Xa3: int] :
% 9.17/5.35 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 9.17/5.35 => ! [Xb3: int] :
% 9.17/5.35 ( ( member_int @ Xb3 @ A2 )
% 9.17/5.35 => ( X8
% 9.17/5.35 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 9.17/5.35 => ( ( ord_less_eq_int @ T @ X8 )
% 9.17/5.35 => ( ord_less_eq_int @ T @ ( plus_plus_int @ X8 @ D3 ) ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2236_ceiling__divide__lower,axiom,
% 9.17/5.35 ! [Q3: rat,P4: rat] :
% 9.17/5.35 ( ( ord_less_rat @ zero_zero_rat @ Q3 )
% 9.17/5.35 => ( ord_less_rat @ ( times_times_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ ( divide_divide_rat @ P4 @ Q3 ) ) ) @ one_one_rat ) @ Q3 ) @ P4 ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2237_floor__divide__upper,axiom,
% 9.17/5.35 ! [Q3: rat,P4: rat] :
% 9.17/5.35 ( ( ord_less_rat @ zero_zero_rat @ Q3 )
% 9.17/5.35 => ( ord_less_rat @ P4 @ ( times_times_rat @ ( plus_plus_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ ( divide_divide_rat @ P4 @ Q3 ) ) ) @ one_one_rat ) @ Q3 ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2238_power__decreasing__iff,axiom,
% 9.17/5.35 ! [B: code_integer,M2: nat,N2: nat] :
% 9.17/5.35 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 9.17/5.35 => ( ( ord_le6747313008572928689nteger @ B @ one_one_Code_integer )
% 9.17/5.35 => ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ B @ M2 ) @ ( power_8256067586552552935nteger @ B @ N2 ) )
% 9.17/5.35 = ( ord_less_eq_nat @ N2 @ M2 ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2239_power__decreasing__iff,axiom,
% 9.17/5.35 ! [B: rat,M2: nat,N2: nat] :
% 9.17/5.35 ( ( ord_less_rat @ zero_zero_rat @ B )
% 9.17/5.35 => ( ( ord_less_rat @ B @ one_one_rat )
% 9.17/5.35 => ( ( ord_less_eq_rat @ ( power_power_rat @ B @ M2 ) @ ( power_power_rat @ B @ N2 ) )
% 9.17/5.35 = ( ord_less_eq_nat @ N2 @ M2 ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2240_power__decreasing__iff,axiom,
% 9.17/5.35 ! [B: nat,M2: nat,N2: nat] :
% 9.17/5.35 ( ( ord_less_nat @ zero_zero_nat @ B )
% 9.17/5.35 => ( ( ord_less_nat @ B @ one_one_nat )
% 9.17/5.35 => ( ( ord_less_eq_nat @ ( power_power_nat @ B @ M2 ) @ ( power_power_nat @ B @ N2 ) )
% 9.17/5.35 = ( ord_less_eq_nat @ N2 @ M2 ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2241_power__decreasing__iff,axiom,
% 9.17/5.35 ! [B: int,M2: nat,N2: nat] :
% 9.17/5.35 ( ( ord_less_int @ zero_zero_int @ B )
% 9.17/5.35 => ( ( ord_less_int @ B @ one_one_int )
% 9.17/5.35 => ( ( ord_less_eq_int @ ( power_power_int @ B @ M2 ) @ ( power_power_int @ B @ N2 ) )
% 9.17/5.35 = ( ord_less_eq_nat @ N2 @ M2 ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2242_divmod__nat__def,axiom,
% 9.17/5.35 ( divmod_nat
% 9.17/5.35 = ( ^ [M: nat,N4: nat] : ( product_Pair_nat_nat @ ( divide_divide_nat @ M @ N4 ) @ ( modulo_modulo_nat @ M @ N4 ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2243_distrib__left__NO__MATCH,axiom,
% 9.17/5.35 ! [X: int,Y: int,A: rat,B: rat,C: rat] :
% 9.17/5.35 ( ( nO_MATCH_int_rat @ ( divide_divide_int @ X @ Y ) @ A )
% 9.17/5.35 => ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 9.17/5.35 = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2244_distrib__left__NO__MATCH,axiom,
% 9.17/5.35 ! [X: int,Y: int,A: nat,B: nat,C: nat] :
% 9.17/5.35 ( ( nO_MATCH_int_nat @ ( divide_divide_int @ X @ Y ) @ A )
% 9.17/5.35 => ( ( times_times_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 9.17/5.35 = ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2245_distrib__left__NO__MATCH,axiom,
% 9.17/5.35 ! [X: int,Y: int,A: int,B: int,C: int] :
% 9.17/5.35 ( ( nO_MATCH_int_int @ ( divide_divide_int @ X @ Y ) @ A )
% 9.17/5.35 => ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 9.17/5.35 = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2246_distrib__left__NO__MATCH,axiom,
% 9.17/5.35 ! [X: nat,Y: nat,A: rat,B: rat,C: rat] :
% 9.17/5.35 ( ( nO_MATCH_nat_rat @ ( divide_divide_nat @ X @ Y ) @ A )
% 9.17/5.35 => ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 9.17/5.35 = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2247_distrib__left__NO__MATCH,axiom,
% 9.17/5.35 ! [X: nat,Y: nat,A: nat,B: nat,C: nat] :
% 9.17/5.35 ( ( nO_MATCH_nat_nat @ ( divide_divide_nat @ X @ Y ) @ A )
% 9.17/5.35 => ( ( times_times_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 9.17/5.35 = ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2248_distrib__left__NO__MATCH,axiom,
% 9.17/5.35 ! [X: nat,Y: nat,A: int,B: int,C: int] :
% 9.17/5.35 ( ( nO_MATCH_nat_int @ ( divide_divide_nat @ X @ Y ) @ A )
% 9.17/5.35 => ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 9.17/5.35 = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2249_distrib__left__NO__MATCH,axiom,
% 9.17/5.35 ! [X: code_integer,Y: code_integer,A: rat,B: rat,C: rat] :
% 9.17/5.35 ( ( nO_MAT7795273704451493282er_rat @ ( divide6298287555418463151nteger @ X @ Y ) @ A )
% 9.17/5.35 => ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 9.17/5.35 = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2250_distrib__left__NO__MATCH,axiom,
% 9.17/5.35 ! [X: code_integer,Y: code_integer,A: nat,B: nat,C: nat] :
% 9.17/5.35 ( ( nO_MAT8430403764537989018er_nat @ ( divide6298287555418463151nteger @ X @ Y ) @ A )
% 9.17/5.35 => ( ( times_times_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 9.17/5.35 = ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2251_distrib__left__NO__MATCH,axiom,
% 9.17/5.35 ! [X: code_integer,Y: code_integer,A: int,B: int,C: int] :
% 9.17/5.35 ( ( nO_MAT8427913294028938742er_int @ ( divide6298287555418463151nteger @ X @ Y ) @ A )
% 9.17/5.35 => ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 9.17/5.35 = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2252_distrib__left__NO__MATCH,axiom,
% 9.17/5.35 ! [X: rat,Y: rat,A: rat,B: rat,C: rat] :
% 9.17/5.35 ( ( nO_MATCH_rat_rat @ ( divide_divide_rat @ X @ Y ) @ A )
% 9.17/5.35 => ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 9.17/5.35 = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2253_distrib__right__NO__MATCH,axiom,
% 9.17/5.35 ! [X: int,Y: int,C: rat,A: rat,B: rat] :
% 9.17/5.35 ( ( nO_MATCH_int_rat @ ( divide_divide_int @ X @ Y ) @ C )
% 9.17/5.35 => ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 9.17/5.35 = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2254_distrib__right__NO__MATCH,axiom,
% 9.17/5.35 ! [X: int,Y: int,C: nat,A: nat,B: nat] :
% 9.17/5.35 ( ( nO_MATCH_int_nat @ ( divide_divide_int @ X @ Y ) @ C )
% 9.17/5.35 => ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 9.17/5.35 = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2255_distrib__right__NO__MATCH,axiom,
% 9.17/5.35 ! [X: int,Y: int,C: int,A: int,B: int] :
% 9.17/5.35 ( ( nO_MATCH_int_int @ ( divide_divide_int @ X @ Y ) @ C )
% 9.17/5.35 => ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 9.17/5.35 = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2256_distrib__right__NO__MATCH,axiom,
% 9.17/5.35 ! [X: nat,Y: nat,C: rat,A: rat,B: rat] :
% 9.17/5.35 ( ( nO_MATCH_nat_rat @ ( divide_divide_nat @ X @ Y ) @ C )
% 9.17/5.35 => ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 9.17/5.35 = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2257_distrib__right__NO__MATCH,axiom,
% 9.17/5.35 ! [X: nat,Y: nat,C: nat,A: nat,B: nat] :
% 9.17/5.35 ( ( nO_MATCH_nat_nat @ ( divide_divide_nat @ X @ Y ) @ C )
% 9.17/5.35 => ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 9.17/5.35 = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2258_distrib__right__NO__MATCH,axiom,
% 9.17/5.35 ! [X: nat,Y: nat,C: int,A: int,B: int] :
% 9.17/5.35 ( ( nO_MATCH_nat_int @ ( divide_divide_nat @ X @ Y ) @ C )
% 9.17/5.35 => ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 9.17/5.35 = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2259_distrib__right__NO__MATCH,axiom,
% 9.17/5.35 ! [X: code_integer,Y: code_integer,C: rat,A: rat,B: rat] :
% 9.17/5.35 ( ( nO_MAT7795273704451493282er_rat @ ( divide6298287555418463151nteger @ X @ Y ) @ C )
% 9.17/5.35 => ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 9.17/5.35 = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2260_distrib__right__NO__MATCH,axiom,
% 9.17/5.35 ! [X: code_integer,Y: code_integer,C: nat,A: nat,B: nat] :
% 9.17/5.35 ( ( nO_MAT8430403764537989018er_nat @ ( divide6298287555418463151nteger @ X @ Y ) @ C )
% 9.17/5.35 => ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 9.17/5.35 = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2261_distrib__right__NO__MATCH,axiom,
% 9.17/5.35 ! [X: code_integer,Y: code_integer,C: int,A: int,B: int] :
% 9.17/5.35 ( ( nO_MAT8427913294028938742er_int @ ( divide6298287555418463151nteger @ X @ Y ) @ C )
% 9.17/5.35 => ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 9.17/5.35 = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2262_distrib__right__NO__MATCH,axiom,
% 9.17/5.35 ! [X: rat,Y: rat,C: rat,A: rat,B: rat] :
% 9.17/5.35 ( ( nO_MATCH_rat_rat @ ( divide_divide_rat @ X @ Y ) @ C )
% 9.17/5.35 => ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 9.17/5.35 = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2263_Suc__times__mod__eq,axiom,
% 9.17/5.35 ! [M2: nat,N2: nat] :
% 9.17/5.35 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M2 )
% 9.17/5.35 => ( ( modulo_modulo_nat @ ( suc @ ( times_times_nat @ M2 @ N2 ) ) @ M2 )
% 9.17/5.35 = one_one_nat ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2264_power__one,axiom,
% 9.17/5.35 ! [N2: nat] :
% 9.17/5.35 ( ( power_8256067586552552935nteger @ one_one_Code_integer @ N2 )
% 9.17/5.35 = one_one_Code_integer ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2265_power__one,axiom,
% 9.17/5.35 ! [N2: nat] :
% 9.17/5.35 ( ( power_power_assn @ one_one_assn @ N2 )
% 9.17/5.35 = one_one_assn ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2266_power__one,axiom,
% 9.17/5.35 ! [N2: nat] :
% 9.17/5.35 ( ( power_power_rat @ one_one_rat @ N2 )
% 9.17/5.35 = one_one_rat ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2267_power__one,axiom,
% 9.17/5.35 ! [N2: nat] :
% 9.17/5.35 ( ( power_power_nat @ one_one_nat @ N2 )
% 9.17/5.35 = one_one_nat ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2268_power__one,axiom,
% 9.17/5.35 ! [N2: nat] :
% 9.17/5.35 ( ( power_power_int @ one_one_int @ N2 )
% 9.17/5.35 = one_one_int ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2269_add__Suc__right,axiom,
% 9.17/5.35 ! [M2: nat,N2: nat] :
% 9.17/5.35 ( ( plus_plus_nat @ M2 @ ( suc @ N2 ) )
% 9.17/5.35 = ( suc @ ( plus_plus_nat @ M2 @ N2 ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2270_power__one__right,axiom,
% 9.17/5.35 ! [A: nat] :
% 9.17/5.35 ( ( power_power_nat @ A @ one_one_nat )
% 9.17/5.35 = A ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2271_power__one__right,axiom,
% 9.17/5.35 ! [A: int] :
% 9.17/5.35 ( ( power_power_int @ A @ one_one_nat )
% 9.17/5.35 = A ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2272_power__inject__exp,axiom,
% 9.17/5.35 ! [A: code_integer,M2: nat,N2: nat] :
% 9.17/5.35 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 9.17/5.35 => ( ( ( power_8256067586552552935nteger @ A @ M2 )
% 9.17/5.35 = ( power_8256067586552552935nteger @ A @ N2 ) )
% 9.17/5.35 = ( M2 = N2 ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2273_power__inject__exp,axiom,
% 9.17/5.35 ! [A: rat,M2: nat,N2: nat] :
% 9.17/5.35 ( ( ord_less_rat @ one_one_rat @ A )
% 9.17/5.35 => ( ( ( power_power_rat @ A @ M2 )
% 9.17/5.35 = ( power_power_rat @ A @ N2 ) )
% 9.17/5.35 = ( M2 = N2 ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2274_power__inject__exp,axiom,
% 9.17/5.35 ! [A: nat,M2: nat,N2: nat] :
% 9.17/5.35 ( ( ord_less_nat @ one_one_nat @ A )
% 9.17/5.35 => ( ( ( power_power_nat @ A @ M2 )
% 9.17/5.35 = ( power_power_nat @ A @ N2 ) )
% 9.17/5.35 = ( M2 = N2 ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2275_power__inject__exp,axiom,
% 9.17/5.35 ! [A: int,M2: nat,N2: nat] :
% 9.17/5.35 ( ( ord_less_int @ one_one_int @ A )
% 9.17/5.35 => ( ( ( power_power_int @ A @ M2 )
% 9.17/5.35 = ( power_power_int @ A @ N2 ) )
% 9.17/5.35 = ( M2 = N2 ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2276_mult__Suc__right,axiom,
% 9.17/5.35 ! [M2: nat,N2: nat] :
% 9.17/5.35 ( ( times_times_nat @ M2 @ ( suc @ N2 ) )
% 9.17/5.35 = ( plus_plus_nat @ M2 @ ( times_times_nat @ M2 @ N2 ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2277_diff__Suc__1,axiom,
% 9.17/5.35 ! [N2: nat] :
% 9.17/5.35 ( ( minus_minus_nat @ ( suc @ N2 ) @ one_one_nat )
% 9.17/5.35 = N2 ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2278_of__int__eq__1__iff,axiom,
% 9.17/5.35 ! [Z: int] :
% 9.17/5.35 ( ( ( ring_1_of_int_int @ Z )
% 9.17/5.35 = one_one_int )
% 9.17/5.35 = ( Z = one_one_int ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2279_of__int__eq__1__iff,axiom,
% 9.17/5.35 ! [Z: int] :
% 9.17/5.35 ( ( ( ring_18347121197199848620nteger @ Z )
% 9.17/5.35 = one_one_Code_integer )
% 9.17/5.35 = ( Z = one_one_int ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2280_of__int__eq__1__iff,axiom,
% 9.17/5.35 ! [Z: int] :
% 9.17/5.35 ( ( ( ring_1_of_int_rat @ Z )
% 9.17/5.35 = one_one_rat )
% 9.17/5.35 = ( Z = one_one_int ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2281_of__int__1,axiom,
% 9.17/5.35 ( ( ring_1_of_int_int @ one_one_int )
% 9.17/5.35 = one_one_int ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2282_of__int__1,axiom,
% 9.17/5.35 ( ( ring_18347121197199848620nteger @ one_one_int )
% 9.17/5.35 = one_one_Code_integer ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2283_of__int__1,axiom,
% 9.17/5.35 ( ( ring_1_of_int_rat @ one_one_int )
% 9.17/5.35 = one_one_rat ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2284_of__int__add,axiom,
% 9.17/5.35 ! [W: int,Z: int] :
% 9.17/5.35 ( ( ring_1_of_int_int @ ( plus_plus_int @ W @ Z ) )
% 9.17/5.35 = ( plus_plus_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2285_of__int__add,axiom,
% 9.17/5.35 ! [W: int,Z: int] :
% 9.17/5.35 ( ( ring_18347121197199848620nteger @ ( plus_plus_int @ W @ Z ) )
% 9.17/5.35 = ( plus_p5714425477246183910nteger @ ( ring_18347121197199848620nteger @ W ) @ ( ring_18347121197199848620nteger @ Z ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2286_of__int__add,axiom,
% 9.17/5.35 ! [W: int,Z: int] :
% 9.17/5.35 ( ( ring_1_of_int_rat @ ( plus_plus_int @ W @ Z ) )
% 9.17/5.35 = ( plus_plus_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2287_power__strict__increasing__iff,axiom,
% 9.17/5.35 ! [B: code_integer,X: nat,Y: nat] :
% 9.17/5.35 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ B )
% 9.17/5.35 => ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ B @ X ) @ ( power_8256067586552552935nteger @ B @ Y ) )
% 9.17/5.35 = ( ord_less_nat @ X @ Y ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2288_power__strict__increasing__iff,axiom,
% 9.17/5.35 ! [B: rat,X: nat,Y: nat] :
% 9.17/5.35 ( ( ord_less_rat @ one_one_rat @ B )
% 9.17/5.35 => ( ( ord_less_rat @ ( power_power_rat @ B @ X ) @ ( power_power_rat @ B @ Y ) )
% 9.17/5.35 = ( ord_less_nat @ X @ Y ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2289_power__strict__increasing__iff,axiom,
% 9.17/5.35 ! [B: nat,X: nat,Y: nat] :
% 9.17/5.35 ( ( ord_less_nat @ one_one_nat @ B )
% 9.17/5.35 => ( ( ord_less_nat @ ( power_power_nat @ B @ X ) @ ( power_power_nat @ B @ Y ) )
% 9.17/5.35 = ( ord_less_nat @ X @ Y ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2290_power__strict__increasing__iff,axiom,
% 9.17/5.35 ! [B: int,X: nat,Y: nat] :
% 9.17/5.35 ( ( ord_less_int @ one_one_int @ B )
% 9.17/5.35 => ( ( ord_less_int @ ( power_power_int @ B @ X ) @ ( power_power_int @ B @ Y ) )
% 9.17/5.35 = ( ord_less_nat @ X @ Y ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2291_left__minus__one__mult__self,axiom,
% 9.17/5.35 ! [N2: nat,A: int] :
% 9.17/5.35 ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 ) @ ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 ) @ A ) )
% 9.17/5.35 = A ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2292_left__minus__one__mult__self,axiom,
% 9.17/5.35 ! [N2: nat,A: code_integer] :
% 9.17/5.35 ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 ) @ ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 ) @ A ) )
% 9.17/5.35 = A ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2293_left__minus__one__mult__self,axiom,
% 9.17/5.35 ! [N2: nat,A: rat] :
% 9.17/5.35 ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 ) @ ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 ) @ A ) )
% 9.17/5.35 = A ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2294_minus__one__mult__self,axiom,
% 9.17/5.35 ! [N2: nat] :
% 9.17/5.35 ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 ) @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 ) )
% 9.17/5.35 = one_one_int ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2295_minus__one__mult__self,axiom,
% 9.17/5.35 ! [N2: nat] :
% 9.17/5.35 ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 ) )
% 9.17/5.35 = one_one_Code_integer ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2296_minus__one__mult__self,axiom,
% 9.17/5.35 ! [N2: nat] :
% 9.17/5.35 ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 ) @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 ) )
% 9.17/5.35 = one_one_rat ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2297_diff__Suc__diff__eq2,axiom,
% 9.17/5.35 ! [K: nat,J: nat,I: nat] :
% 9.17/5.35 ( ( ord_less_eq_nat @ K @ J )
% 9.17/5.35 => ( ( minus_minus_nat @ ( suc @ ( minus_minus_nat @ J @ K ) ) @ I )
% 9.17/5.35 = ( minus_minus_nat @ ( suc @ J ) @ ( plus_plus_nat @ K @ I ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2298_diff__Suc__diff__eq1,axiom,
% 9.17/5.35 ! [K: nat,J: nat,I: nat] :
% 9.17/5.35 ( ( ord_less_eq_nat @ K @ J )
% 9.17/5.35 => ( ( minus_minus_nat @ I @ ( suc @ ( minus_minus_nat @ J @ K ) ) )
% 9.17/5.35 = ( minus_minus_nat @ ( plus_plus_nat @ I @ K ) @ ( suc @ J ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2299_Suc__diff,axiom,
% 9.17/5.35 ! [M2: nat,N2: nat] :
% 9.17/5.35 ( ( ord_less_eq_nat @ M2 @ N2 )
% 9.17/5.35 => ( ( ord_less_eq_nat @ one_one_nat @ M2 )
% 9.17/5.35 => ( ( suc @ ( minus_minus_nat @ N2 @ M2 ) )
% 9.17/5.35 = ( minus_minus_nat @ N2 @ ( minus_minus_nat @ M2 @ one_one_nat ) ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2300_Suc__mod__mult__self4,axiom,
% 9.17/5.35 ! [N2: nat,K: nat,M2: nat] :
% 9.17/5.35 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ ( times_times_nat @ N2 @ K ) @ M2 ) ) @ N2 )
% 9.17/5.35 = ( modulo_modulo_nat @ ( suc @ M2 ) @ N2 ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2301_Suc__mod__mult__self3,axiom,
% 9.17/5.35 ! [K: nat,N2: nat,M2: nat] :
% 9.17/5.35 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ ( times_times_nat @ K @ N2 ) @ M2 ) ) @ N2 )
% 9.17/5.35 = ( modulo_modulo_nat @ ( suc @ M2 ) @ N2 ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2302_Suc__mod__mult__self2,axiom,
% 9.17/5.35 ! [M2: nat,N2: nat,K: nat] :
% 9.17/5.35 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ M2 @ ( times_times_nat @ N2 @ K ) ) ) @ N2 )
% 9.17/5.35 = ( modulo_modulo_nat @ ( suc @ M2 ) @ N2 ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2303_Suc__mod__mult__self1,axiom,
% 9.17/5.35 ! [M2: nat,K: nat,N2: nat] :
% 9.17/5.35 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ M2 @ ( times_times_nat @ K @ N2 ) ) ) @ N2 )
% 9.17/5.35 = ( modulo_modulo_nat @ ( suc @ M2 ) @ N2 ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2304_ceiling__add__of__int,axiom,
% 9.17/5.35 ! [X: rat,Z: int] :
% 9.17/5.35 ( ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X @ ( ring_1_of_int_rat @ Z ) ) )
% 9.17/5.35 = ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X ) @ Z ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2305_power__strict__decreasing__iff,axiom,
% 9.17/5.35 ! [B: code_integer,M2: nat,N2: nat] :
% 9.17/5.35 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 9.17/5.35 => ( ( ord_le6747313008572928689nteger @ B @ one_one_Code_integer )
% 9.17/5.35 => ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ B @ M2 ) @ ( power_8256067586552552935nteger @ B @ N2 ) )
% 9.17/5.35 = ( ord_less_nat @ N2 @ M2 ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2306_power__strict__decreasing__iff,axiom,
% 9.17/5.35 ! [B: rat,M2: nat,N2: nat] :
% 9.17/5.35 ( ( ord_less_rat @ zero_zero_rat @ B )
% 9.17/5.35 => ( ( ord_less_rat @ B @ one_one_rat )
% 9.17/5.35 => ( ( ord_less_rat @ ( power_power_rat @ B @ M2 ) @ ( power_power_rat @ B @ N2 ) )
% 9.17/5.35 = ( ord_less_nat @ N2 @ M2 ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2307_power__strict__decreasing__iff,axiom,
% 9.17/5.35 ! [B: nat,M2: nat,N2: nat] :
% 9.17/5.35 ( ( ord_less_nat @ zero_zero_nat @ B )
% 9.17/5.35 => ( ( ord_less_nat @ B @ one_one_nat )
% 9.17/5.35 => ( ( ord_less_nat @ ( power_power_nat @ B @ M2 ) @ ( power_power_nat @ B @ N2 ) )
% 9.17/5.35 = ( ord_less_nat @ N2 @ M2 ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2308_power__strict__decreasing__iff,axiom,
% 9.17/5.35 ! [B: int,M2: nat,N2: nat] :
% 9.17/5.35 ( ( ord_less_int @ zero_zero_int @ B )
% 9.17/5.35 => ( ( ord_less_int @ B @ one_one_int )
% 9.17/5.35 => ( ( ord_less_int @ ( power_power_int @ B @ M2 ) @ ( power_power_int @ B @ N2 ) )
% 9.17/5.35 = ( ord_less_nat @ N2 @ M2 ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2309_power__increasing__iff,axiom,
% 9.17/5.35 ! [B: code_integer,X: nat,Y: nat] :
% 9.17/5.35 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ B )
% 9.17/5.35 => ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ B @ X ) @ ( power_8256067586552552935nteger @ B @ Y ) )
% 9.17/5.35 = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2310_power__increasing__iff,axiom,
% 9.17/5.35 ! [B: rat,X: nat,Y: nat] :
% 9.17/5.35 ( ( ord_less_rat @ one_one_rat @ B )
% 9.17/5.35 => ( ( ord_less_eq_rat @ ( power_power_rat @ B @ X ) @ ( power_power_rat @ B @ Y ) )
% 9.17/5.35 = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2311_power__increasing__iff,axiom,
% 9.17/5.35 ! [B: nat,X: nat,Y: nat] :
% 9.17/5.35 ( ( ord_less_nat @ one_one_nat @ B )
% 9.17/5.35 => ( ( ord_less_eq_nat @ ( power_power_nat @ B @ X ) @ ( power_power_nat @ B @ Y ) )
% 9.17/5.35 = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2312_power__increasing__iff,axiom,
% 9.17/5.35 ! [B: int,X: nat,Y: nat] :
% 9.17/5.35 ( ( ord_less_int @ one_one_int @ B )
% 9.17/5.35 => ( ( ord_less_eq_int @ ( power_power_int @ B @ X ) @ ( power_power_int @ B @ Y ) )
% 9.17/5.35 = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2313_Suc__diff__1,axiom,
% 9.17/5.35 ! [N2: nat] :
% 9.17/5.35 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 9.17/5.35 => ( ( suc @ ( minus_minus_nat @ N2 @ one_one_nat ) )
% 9.17/5.35 = N2 ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2314_of__int__1__le__iff,axiom,
% 9.17/5.35 ! [Z: int] :
% 9.17/5.35 ( ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( ring_18347121197199848620nteger @ Z ) )
% 9.17/5.35 = ( ord_less_eq_int @ one_one_int @ Z ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2315_of__int__1__le__iff,axiom,
% 9.17/5.35 ! [Z: int] :
% 9.17/5.35 ( ( ord_less_eq_rat @ one_one_rat @ ( ring_1_of_int_rat @ Z ) )
% 9.17/5.35 = ( ord_less_eq_int @ one_one_int @ Z ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2316_of__int__1__le__iff,axiom,
% 9.17/5.35 ! [Z: int] :
% 9.17/5.35 ( ( ord_less_eq_int @ one_one_int @ ( ring_1_of_int_int @ Z ) )
% 9.17/5.35 = ( ord_less_eq_int @ one_one_int @ Z ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2317_of__int__le__1__iff,axiom,
% 9.17/5.35 ! [Z: int] :
% 9.17/5.35 ( ( ord_le3102999989581377725nteger @ ( ring_18347121197199848620nteger @ Z ) @ one_one_Code_integer )
% 9.17/5.35 = ( ord_less_eq_int @ Z @ one_one_int ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2318_of__int__le__1__iff,axiom,
% 9.17/5.35 ! [Z: int] :
% 9.17/5.35 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat )
% 9.17/5.35 = ( ord_less_eq_int @ Z @ one_one_int ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2319_of__int__le__1__iff,axiom,
% 9.17/5.35 ! [Z: int] :
% 9.17/5.35 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z ) @ one_one_int )
% 9.17/5.35 = ( ord_less_eq_int @ Z @ one_one_int ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2320_of__int__less__1__iff,axiom,
% 9.17/5.35 ! [Z: int] :
% 9.17/5.35 ( ( ord_le6747313008572928689nteger @ ( ring_18347121197199848620nteger @ Z ) @ one_one_Code_integer )
% 9.17/5.35 = ( ord_less_int @ Z @ one_one_int ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2321_of__int__less__1__iff,axiom,
% 9.17/5.35 ! [Z: int] :
% 9.17/5.35 ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat )
% 9.17/5.35 = ( ord_less_int @ Z @ one_one_int ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2322_of__int__less__1__iff,axiom,
% 9.17/5.35 ! [Z: int] :
% 9.17/5.35 ( ( ord_less_int @ ( ring_1_of_int_int @ Z ) @ one_one_int )
% 9.17/5.35 = ( ord_less_int @ Z @ one_one_int ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2323_of__int__1__less__iff,axiom,
% 9.17/5.35 ! [Z: int] :
% 9.17/5.35 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( ring_18347121197199848620nteger @ Z ) )
% 9.17/5.35 = ( ord_less_int @ one_one_int @ Z ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2324_of__int__1__less__iff,axiom,
% 9.17/5.35 ! [Z: int] :
% 9.17/5.35 ( ( ord_less_rat @ one_one_rat @ ( ring_1_of_int_rat @ Z ) )
% 9.17/5.35 = ( ord_less_int @ one_one_int @ Z ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2325_of__int__1__less__iff,axiom,
% 9.17/5.35 ! [Z: int] :
% 9.17/5.35 ( ( ord_less_int @ one_one_int @ ( ring_1_of_int_int @ Z ) )
% 9.17/5.35 = ( ord_less_int @ one_one_int @ Z ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2326_power__gt1,axiom,
% 9.17/5.35 ! [A: code_integer,N2: nat] :
% 9.17/5.35 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 9.17/5.35 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ A @ ( suc @ N2 ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2327_power__gt1,axiom,
% 9.17/5.35 ! [A: rat,N2: nat] :
% 9.17/5.35 ( ( ord_less_rat @ one_one_rat @ A )
% 9.17/5.35 => ( ord_less_rat @ one_one_rat @ ( power_power_rat @ A @ ( suc @ N2 ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2328_power__gt1,axiom,
% 9.17/5.35 ! [A: nat,N2: nat] :
% 9.17/5.35 ( ( ord_less_nat @ one_one_nat @ A )
% 9.17/5.35 => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A @ ( suc @ N2 ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2329_power__gt1,axiom,
% 9.17/5.35 ! [A: int,N2: nat] :
% 9.17/5.35 ( ( ord_less_int @ one_one_int @ A )
% 9.17/5.35 => ( ord_less_int @ one_one_int @ ( power_power_int @ A @ ( suc @ N2 ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2330_add__Suc__shift,axiom,
% 9.17/5.35 ! [M2: nat,N2: nat] :
% 9.17/5.35 ( ( plus_plus_nat @ ( suc @ M2 ) @ N2 )
% 9.17/5.35 = ( plus_plus_nat @ M2 @ ( suc @ N2 ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2331_add__Suc,axiom,
% 9.17/5.35 ! [M2: nat,N2: nat] :
% 9.17/5.35 ( ( plus_plus_nat @ ( suc @ M2 ) @ N2 )
% 9.17/5.35 = ( suc @ ( plus_plus_nat @ M2 @ N2 ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2332_nat__arith_Osuc1,axiom,
% 9.17/5.35 ! [A2: nat,K: nat,A: nat] :
% 9.17/5.35 ( ( A2
% 9.17/5.35 = ( plus_plus_nat @ K @ A ) )
% 9.17/5.35 => ( ( suc @ A2 )
% 9.17/5.35 = ( plus_plus_nat @ K @ ( suc @ A ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2333_power__Suc__le__self,axiom,
% 9.17/5.35 ! [A: code_integer,N2: nat] :
% 9.17/5.35 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 9.17/5.35 => ( ( ord_le3102999989581377725nteger @ A @ one_one_Code_integer )
% 9.17/5.35 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ ( suc @ N2 ) ) @ A ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2334_power__Suc__le__self,axiom,
% 9.17/5.35 ! [A: rat,N2: nat] :
% 9.17/5.35 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 9.17/5.35 => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 9.17/5.35 => ( ord_less_eq_rat @ ( power_power_rat @ A @ ( suc @ N2 ) ) @ A ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2335_power__Suc__le__self,axiom,
% 9.17/5.35 ! [A: nat,N2: nat] :
% 9.17/5.35 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 9.17/5.35 => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 9.17/5.35 => ( ord_less_eq_nat @ ( power_power_nat @ A @ ( suc @ N2 ) ) @ A ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2336_power__Suc__le__self,axiom,
% 9.17/5.35 ! [A: int,N2: nat] :
% 9.17/5.35 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 9.17/5.35 => ( ( ord_less_eq_int @ A @ one_one_int )
% 9.17/5.35 => ( ord_less_eq_int @ ( power_power_int @ A @ ( suc @ N2 ) ) @ A ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2337_power__Suc__less__one,axiom,
% 9.17/5.35 ! [A: code_integer,N2: nat] :
% 9.17/5.35 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 9.17/5.35 => ( ( ord_le6747313008572928689nteger @ A @ one_one_Code_integer )
% 9.17/5.35 => ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A @ ( suc @ N2 ) ) @ one_one_Code_integer ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2338_power__Suc__less__one,axiom,
% 9.17/5.35 ! [A: rat,N2: nat] :
% 9.17/5.35 ( ( ord_less_rat @ zero_zero_rat @ A )
% 9.17/5.35 => ( ( ord_less_rat @ A @ one_one_rat )
% 9.17/5.35 => ( ord_less_rat @ ( power_power_rat @ A @ ( suc @ N2 ) ) @ one_one_rat ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2339_power__Suc__less__one,axiom,
% 9.17/5.35 ! [A: nat,N2: nat] :
% 9.17/5.35 ( ( ord_less_nat @ zero_zero_nat @ A )
% 9.17/5.35 => ( ( ord_less_nat @ A @ one_one_nat )
% 9.17/5.35 => ( ord_less_nat @ ( power_power_nat @ A @ ( suc @ N2 ) ) @ one_one_nat ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2340_power__Suc__less__one,axiom,
% 9.17/5.35 ! [A: int,N2: nat] :
% 9.17/5.35 ( ( ord_less_int @ zero_zero_int @ A )
% 9.17/5.35 => ( ( ord_less_int @ A @ one_one_int )
% 9.17/5.35 => ( ord_less_int @ ( power_power_int @ A @ ( suc @ N2 ) ) @ one_one_int ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2341_power__minus_H,axiom,
% 9.17/5.35 ! [X: int,N2: nat] :
% 9.17/5.35 ( ( nO_MATCH_int_int @ one_one_int @ X )
% 9.17/5.35 => ( ( power_power_int @ ( uminus_uminus_int @ X ) @ N2 )
% 9.17/5.35 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 ) @ ( power_power_int @ X @ N2 ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2342_power__minus_H,axiom,
% 9.17/5.35 ! [X: code_integer,N2: nat] :
% 9.17/5.35 ( ( nO_MAT8252062027627875367nteger @ one_one_Code_integer @ X )
% 9.17/5.35 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ X ) @ N2 )
% 9.17/5.35 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 ) @ ( power_8256067586552552935nteger @ X @ N2 ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2343_power__minus_H,axiom,
% 9.17/5.35 ! [X: rat,N2: nat] :
% 9.17/5.35 ( ( nO_MATCH_rat_rat @ one_one_rat @ X )
% 9.17/5.35 => ( ( power_power_rat @ ( uminus_uminus_rat @ X ) @ N2 )
% 9.17/5.35 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 ) @ ( power_power_rat @ X @ N2 ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2344_one__le__power,axiom,
% 9.17/5.35 ! [A: code_integer,N2: nat] :
% 9.17/5.35 ( ( ord_le3102999989581377725nteger @ one_one_Code_integer @ A )
% 9.17/5.35 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ A @ N2 ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2345_one__le__power,axiom,
% 9.17/5.35 ! [A: rat,N2: nat] :
% 9.17/5.35 ( ( ord_less_eq_rat @ one_one_rat @ A )
% 9.17/5.35 => ( ord_less_eq_rat @ one_one_rat @ ( power_power_rat @ A @ N2 ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2346_one__le__power,axiom,
% 9.17/5.35 ! [A: nat,N2: nat] :
% 9.17/5.35 ( ( ord_less_eq_nat @ one_one_nat @ A )
% 9.17/5.35 => ( ord_less_eq_nat @ one_one_nat @ ( power_power_nat @ A @ N2 ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2347_one__le__power,axiom,
% 9.17/5.35 ! [A: int,N2: nat] :
% 9.17/5.35 ( ( ord_less_eq_int @ one_one_int @ A )
% 9.17/5.35 => ( ord_less_eq_int @ one_one_int @ ( power_power_int @ A @ N2 ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2348_left__right__inverse__power,axiom,
% 9.17/5.35 ! [X: code_integer,Y: code_integer,N2: nat] :
% 9.17/5.35 ( ( ( times_3573771949741848930nteger @ X @ Y )
% 9.17/5.35 = one_one_Code_integer )
% 9.17/5.35 => ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ X @ N2 ) @ ( power_8256067586552552935nteger @ Y @ N2 ) )
% 9.17/5.35 = one_one_Code_integer ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2349_left__right__inverse__power,axiom,
% 9.17/5.35 ! [X: assn,Y: assn,N2: nat] :
% 9.17/5.35 ( ( ( times_times_assn @ X @ Y )
% 9.17/5.35 = one_one_assn )
% 9.17/5.35 => ( ( times_times_assn @ ( power_power_assn @ X @ N2 ) @ ( power_power_assn @ Y @ N2 ) )
% 9.17/5.35 = one_one_assn ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2350_left__right__inverse__power,axiom,
% 9.17/5.35 ! [X: rat,Y: rat,N2: nat] :
% 9.17/5.35 ( ( ( times_times_rat @ X @ Y )
% 9.17/5.35 = one_one_rat )
% 9.17/5.35 => ( ( times_times_rat @ ( power_power_rat @ X @ N2 ) @ ( power_power_rat @ Y @ N2 ) )
% 9.17/5.35 = one_one_rat ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2351_left__right__inverse__power,axiom,
% 9.17/5.35 ! [X: nat,Y: nat,N2: nat] :
% 9.17/5.35 ( ( ( times_times_nat @ X @ Y )
% 9.17/5.35 = one_one_nat )
% 9.17/5.35 => ( ( times_times_nat @ ( power_power_nat @ X @ N2 ) @ ( power_power_nat @ Y @ N2 ) )
% 9.17/5.35 = one_one_nat ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2352_left__right__inverse__power,axiom,
% 9.17/5.35 ! [X: int,Y: int,N2: nat] :
% 9.17/5.35 ( ( ( times_times_int @ X @ Y )
% 9.17/5.35 = one_one_int )
% 9.17/5.35 => ( ( times_times_int @ ( power_power_int @ X @ N2 ) @ ( power_power_int @ Y @ N2 ) )
% 9.17/5.35 = one_one_int ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2353_power__0,axiom,
% 9.17/5.35 ! [A: code_integer] :
% 9.17/5.35 ( ( power_8256067586552552935nteger @ A @ zero_zero_nat )
% 9.17/5.35 = one_one_Code_integer ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2354_power__0,axiom,
% 9.17/5.35 ! [A: assn] :
% 9.17/5.35 ( ( power_power_assn @ A @ zero_zero_nat )
% 9.17/5.35 = one_one_assn ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2355_power__0,axiom,
% 9.17/5.35 ! [A: rat] :
% 9.17/5.35 ( ( power_power_rat @ A @ zero_zero_nat )
% 9.17/5.35 = one_one_rat ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2356_power__0,axiom,
% 9.17/5.35 ! [A: nat] :
% 9.17/5.35 ( ( power_power_nat @ A @ zero_zero_nat )
% 9.17/5.35 = one_one_nat ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2357_power__0,axiom,
% 9.17/5.35 ! [A: int] :
% 9.17/5.35 ( ( power_power_int @ A @ zero_zero_nat )
% 9.17/5.35 = one_one_int ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2358_power__one__over,axiom,
% 9.17/5.35 ! [A: rat,N2: nat] :
% 9.17/5.35 ( ( power_power_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ N2 )
% 9.17/5.35 = ( divide_divide_rat @ one_one_rat @ ( power_power_rat @ A @ N2 ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2359_power__add,axiom,
% 9.17/5.35 ! [A: assn,M2: nat,N2: nat] :
% 9.17/5.35 ( ( power_power_assn @ A @ ( plus_plus_nat @ M2 @ N2 ) )
% 9.17/5.35 = ( times_times_assn @ ( power_power_assn @ A @ M2 ) @ ( power_power_assn @ A @ N2 ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2360_power__add,axiom,
% 9.17/5.35 ! [A: rat,M2: nat,N2: nat] :
% 9.17/5.35 ( ( power_power_rat @ A @ ( plus_plus_nat @ M2 @ N2 ) )
% 9.17/5.35 = ( times_times_rat @ ( power_power_rat @ A @ M2 ) @ ( power_power_rat @ A @ N2 ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2361_power__add,axiom,
% 9.17/5.35 ! [A: nat,M2: nat,N2: nat] :
% 9.17/5.35 ( ( power_power_nat @ A @ ( plus_plus_nat @ M2 @ N2 ) )
% 9.17/5.35 = ( times_times_nat @ ( power_power_nat @ A @ M2 ) @ ( power_power_nat @ A @ N2 ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2362_power__add,axiom,
% 9.17/5.35 ! [A: int,M2: nat,N2: nat] :
% 9.17/5.35 ( ( power_power_int @ A @ ( plus_plus_nat @ M2 @ N2 ) )
% 9.17/5.35 = ( times_times_int @ ( power_power_int @ A @ M2 ) @ ( power_power_int @ A @ N2 ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2363_nat__compl__induct_H,axiom,
% 9.17/5.35 ! [P: nat > $o,N2: nat] :
% 9.17/5.35 ( ( P @ zero_zero_nat )
% 9.17/5.35 => ( ! [N: nat] :
% 9.17/5.35 ( ! [Nn: nat] :
% 9.17/5.35 ( ( ord_less_eq_nat @ Nn @ N )
% 9.17/5.35 => ( P @ Nn ) )
% 9.17/5.35 => ( P @ ( suc @ N ) ) )
% 9.17/5.35 => ( P @ N2 ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2364_nat__compl__induct,axiom,
% 9.17/5.35 ! [P: nat > $o,N2: nat] :
% 9.17/5.35 ( ( P @ zero_zero_nat )
% 9.17/5.35 => ( ! [N: nat] :
% 9.17/5.35 ( ! [Nn: nat] :
% 9.17/5.35 ( ( ord_less_eq_nat @ Nn @ N )
% 9.17/5.35 => ( P @ Nn ) )
% 9.17/5.35 => ( P @ ( suc @ N ) ) )
% 9.17/5.35 => ( P @ N2 ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2365_one__is__add,axiom,
% 9.17/5.35 ! [M2: nat,N2: nat] :
% 9.17/5.35 ( ( ( suc @ zero_zero_nat )
% 9.17/5.35 = ( plus_plus_nat @ M2 @ N2 ) )
% 9.17/5.35 = ( ( ( M2
% 9.17/5.35 = ( suc @ zero_zero_nat ) )
% 9.17/5.35 & ( N2 = zero_zero_nat ) )
% 9.17/5.35 | ( ( M2 = zero_zero_nat )
% 9.17/5.35 & ( N2
% 9.17/5.35 = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2366_add__is__1,axiom,
% 9.17/5.35 ! [M2: nat,N2: nat] :
% 9.17/5.35 ( ( ( plus_plus_nat @ M2 @ N2 )
% 9.17/5.35 = ( suc @ zero_zero_nat ) )
% 9.17/5.35 = ( ( ( M2
% 9.17/5.35 = ( suc @ zero_zero_nat ) )
% 9.17/5.35 & ( N2 = zero_zero_nat ) )
% 9.17/5.35 | ( ( M2 = zero_zero_nat )
% 9.17/5.35 & ( N2
% 9.17/5.35 = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2367_nat__in__between__eq_I2_J,axiom,
% 9.17/5.35 ! [A: nat,B: nat] :
% 9.17/5.35 ( ( ( ord_less_eq_nat @ A @ B )
% 9.17/5.35 & ( ord_less_nat @ B @ ( suc @ A ) ) )
% 9.17/5.35 = ( B = A ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2368_nat__in__between__eq_I1_J,axiom,
% 9.17/5.35 ! [A: nat,B: nat] :
% 9.17/5.35 ( ( ( ord_less_nat @ A @ B )
% 9.17/5.35 & ( ord_less_eq_nat @ B @ ( suc @ A ) ) )
% 9.17/5.35 = ( B
% 9.17/5.35 = ( suc @ A ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2369_less__imp__Suc__add,axiom,
% 9.17/5.35 ! [M2: nat,N2: nat] :
% 9.17/5.35 ( ( ord_less_nat @ M2 @ N2 )
% 9.17/5.35 => ? [K5: nat] :
% 9.17/5.35 ( N2
% 9.17/5.35 = ( suc @ ( plus_plus_nat @ M2 @ K5 ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2370_less__iff__Suc__add,axiom,
% 9.17/5.35 ( ord_less_nat
% 9.17/5.35 = ( ^ [M: nat,N4: nat] :
% 9.17/5.35 ? [K4: nat] :
% 9.17/5.35 ( N4
% 9.17/5.35 = ( suc @ ( plus_plus_nat @ M @ K4 ) ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2371_less__add__Suc2,axiom,
% 9.17/5.35 ! [I: nat,M2: nat] : ( ord_less_nat @ I @ ( suc @ ( plus_plus_nat @ M2 @ I ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2372_less__add__Suc1,axiom,
% 9.17/5.35 ! [I: nat,M2: nat] : ( ord_less_nat @ I @ ( suc @ ( plus_plus_nat @ I @ M2 ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2373_less__natE,axiom,
% 9.17/5.35 ! [M2: nat,N2: nat] :
% 9.17/5.35 ( ( ord_less_nat @ M2 @ N2 )
% 9.17/5.35 => ~ ! [Q2: nat] :
% 9.17/5.35 ( N2
% 9.17/5.35 != ( suc @ ( plus_plus_nat @ M2 @ Q2 ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2374_Suc__to__right,axiom,
% 9.17/5.35 ! [N2: nat,M2: nat] :
% 9.17/5.35 ( ( ( suc @ N2 )
% 9.17/5.35 = M2 )
% 9.17/5.35 => ( N2
% 9.17/5.35 = ( minus_minus_nat @ M2 @ ( suc @ zero_zero_nat ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2375_One__nat__def,axiom,
% 9.17/5.35 ( one_one_nat
% 9.17/5.35 = ( suc @ zero_zero_nat ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2376_mult__Suc,axiom,
% 9.17/5.35 ! [M2: nat,N2: nat] :
% 9.17/5.35 ( ( times_times_nat @ ( suc @ M2 ) @ N2 )
% 9.17/5.35 = ( plus_plus_nat @ N2 @ ( times_times_nat @ M2 @ N2 ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2377_Suc__eq__plus1__left,axiom,
% 9.17/5.35 ( suc
% 9.17/5.35 = ( plus_plus_nat @ one_one_nat ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2378_plus__1__eq__Suc,axiom,
% 9.17/5.35 ( ( plus_plus_nat @ one_one_nat )
% 9.17/5.35 = suc ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2379_Suc__eq__plus1,axiom,
% 9.17/5.35 ( suc
% 9.17/5.35 = ( ^ [N4: nat] : ( plus_plus_nat @ N4 @ one_one_nat ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2380_diff__Suc__eq__diff__pred,axiom,
% 9.17/5.35 ! [M2: nat,N2: nat] :
% 9.17/5.35 ( ( minus_minus_nat @ M2 @ ( suc @ N2 ) )
% 9.17/5.35 = ( minus_minus_nat @ ( minus_minus_nat @ M2 @ one_one_nat ) @ N2 ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2381_power__le__one,axiom,
% 9.17/5.35 ! [A: code_integer,N2: nat] :
% 9.17/5.35 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 9.17/5.35 => ( ( ord_le3102999989581377725nteger @ A @ one_one_Code_integer )
% 9.17/5.35 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ N2 ) @ one_one_Code_integer ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2382_power__le__one,axiom,
% 9.17/5.35 ! [A: rat,N2: nat] :
% 9.17/5.35 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 9.17/5.35 => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 9.17/5.35 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N2 ) @ one_one_rat ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2383_power__le__one,axiom,
% 9.17/5.35 ! [A: nat,N2: nat] :
% 9.17/5.35 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 9.17/5.35 => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 9.17/5.35 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N2 ) @ one_one_nat ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2384_power__le__one,axiom,
% 9.17/5.35 ! [A: int,N2: nat] :
% 9.17/5.35 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 9.17/5.35 => ( ( ord_less_eq_int @ A @ one_one_int )
% 9.17/5.35 => ( ord_less_eq_int @ ( power_power_int @ A @ N2 ) @ one_one_int ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2385_power__less__power__Suc,axiom,
% 9.17/5.35 ! [A: code_integer,N2: nat] :
% 9.17/5.35 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 9.17/5.35 => ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A @ N2 ) @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ A @ N2 ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2386_power__less__power__Suc,axiom,
% 9.17/5.35 ! [A: rat,N2: nat] :
% 9.17/5.35 ( ( ord_less_rat @ one_one_rat @ A )
% 9.17/5.35 => ( ord_less_rat @ ( power_power_rat @ A @ N2 ) @ ( times_times_rat @ A @ ( power_power_rat @ A @ N2 ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2387_power__less__power__Suc,axiom,
% 9.17/5.35 ! [A: nat,N2: nat] :
% 9.17/5.35 ( ( ord_less_nat @ one_one_nat @ A )
% 9.17/5.35 => ( ord_less_nat @ ( power_power_nat @ A @ N2 ) @ ( times_times_nat @ A @ ( power_power_nat @ A @ N2 ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2388_power__less__power__Suc,axiom,
% 9.17/5.35 ! [A: int,N2: nat] :
% 9.17/5.35 ( ( ord_less_int @ one_one_int @ A )
% 9.17/5.35 => ( ord_less_int @ ( power_power_int @ A @ N2 ) @ ( times_times_int @ A @ ( power_power_int @ A @ N2 ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2389_power__gt1__lemma,axiom,
% 9.17/5.35 ! [A: code_integer,N2: nat] :
% 9.17/5.35 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 9.17/5.35 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ A @ N2 ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2390_power__gt1__lemma,axiom,
% 9.17/5.35 ! [A: rat,N2: nat] :
% 9.17/5.35 ( ( ord_less_rat @ one_one_rat @ A )
% 9.17/5.35 => ( ord_less_rat @ one_one_rat @ ( times_times_rat @ A @ ( power_power_rat @ A @ N2 ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2391_power__gt1__lemma,axiom,
% 9.17/5.35 ! [A: nat,N2: nat] :
% 9.17/5.35 ( ( ord_less_nat @ one_one_nat @ A )
% 9.17/5.35 => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ A @ ( power_power_nat @ A @ N2 ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2392_power__gt1__lemma,axiom,
% 9.17/5.35 ! [A: int,N2: nat] :
% 9.17/5.35 ( ( ord_less_int @ one_one_int @ A )
% 9.17/5.35 => ( ord_less_int @ one_one_int @ ( times_times_int @ A @ ( power_power_int @ A @ N2 ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2393_power__0__left,axiom,
% 9.17/5.35 ! [N2: nat] :
% 9.17/5.35 ( ( ( N2 = zero_zero_nat )
% 9.17/5.35 => ( ( power_8256067586552552935nteger @ zero_z3403309356797280102nteger @ N2 )
% 9.17/5.35 = one_one_Code_integer ) )
% 9.17/5.35 & ( ( N2 != zero_zero_nat )
% 9.17/5.35 => ( ( power_8256067586552552935nteger @ zero_z3403309356797280102nteger @ N2 )
% 9.17/5.35 = zero_z3403309356797280102nteger ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2394_power__0__left,axiom,
% 9.17/5.35 ! [N2: nat] :
% 9.17/5.35 ( ( ( N2 = zero_zero_nat )
% 9.17/5.35 => ( ( power_power_rat @ zero_zero_rat @ N2 )
% 9.17/5.35 = one_one_rat ) )
% 9.17/5.35 & ( ( N2 != zero_zero_nat )
% 9.17/5.35 => ( ( power_power_rat @ zero_zero_rat @ N2 )
% 9.17/5.35 = zero_zero_rat ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2395_power__0__left,axiom,
% 9.17/5.35 ! [N2: nat] :
% 9.17/5.35 ( ( ( N2 = zero_zero_nat )
% 9.17/5.35 => ( ( power_power_nat @ zero_zero_nat @ N2 )
% 9.17/5.35 = one_one_nat ) )
% 9.17/5.35 & ( ( N2 != zero_zero_nat )
% 9.17/5.35 => ( ( power_power_nat @ zero_zero_nat @ N2 )
% 9.17/5.35 = zero_zero_nat ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2396_power__0__left,axiom,
% 9.17/5.35 ! [N2: nat] :
% 9.17/5.35 ( ( ( N2 = zero_zero_nat )
% 9.17/5.35 => ( ( power_power_int @ zero_zero_int @ N2 )
% 9.17/5.35 = one_one_int ) )
% 9.17/5.35 & ( ( N2 != zero_zero_nat )
% 9.17/5.35 => ( ( power_power_int @ zero_zero_int @ N2 )
% 9.17/5.35 = zero_zero_int ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2397_power__strict__increasing,axiom,
% 9.17/5.35 ! [N2: nat,N6: nat,A: code_integer] :
% 9.17/5.35 ( ( ord_less_nat @ N2 @ N6 )
% 9.17/5.35 => ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 9.17/5.35 => ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A @ N2 ) @ ( power_8256067586552552935nteger @ A @ N6 ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2398_power__strict__increasing,axiom,
% 9.17/5.35 ! [N2: nat,N6: nat,A: rat] :
% 9.17/5.35 ( ( ord_less_nat @ N2 @ N6 )
% 9.17/5.35 => ( ( ord_less_rat @ one_one_rat @ A )
% 9.17/5.35 => ( ord_less_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ A @ N6 ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2399_power__strict__increasing,axiom,
% 9.17/5.35 ! [N2: nat,N6: nat,A: nat] :
% 9.17/5.35 ( ( ord_less_nat @ N2 @ N6 )
% 9.17/5.35 => ( ( ord_less_nat @ one_one_nat @ A )
% 9.17/5.35 => ( ord_less_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ A @ N6 ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2400_power__strict__increasing,axiom,
% 9.17/5.35 ! [N2: nat,N6: nat,A: int] :
% 9.17/5.35 ( ( ord_less_nat @ N2 @ N6 )
% 9.17/5.35 => ( ( ord_less_int @ one_one_int @ A )
% 9.17/5.35 => ( ord_less_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ A @ N6 ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2401_power__less__imp__less__exp,axiom,
% 9.17/5.35 ! [A: code_integer,M2: nat,N2: nat] :
% 9.17/5.35 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 9.17/5.35 => ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A @ M2 ) @ ( power_8256067586552552935nteger @ A @ N2 ) )
% 9.17/5.35 => ( ord_less_nat @ M2 @ N2 ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2402_power__less__imp__less__exp,axiom,
% 9.17/5.35 ! [A: rat,M2: nat,N2: nat] :
% 9.17/5.35 ( ( ord_less_rat @ one_one_rat @ A )
% 9.17/5.35 => ( ( ord_less_rat @ ( power_power_rat @ A @ M2 ) @ ( power_power_rat @ A @ N2 ) )
% 9.17/5.35 => ( ord_less_nat @ M2 @ N2 ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2403_power__less__imp__less__exp,axiom,
% 9.17/5.35 ! [A: nat,M2: nat,N2: nat] :
% 9.17/5.35 ( ( ord_less_nat @ one_one_nat @ A )
% 9.17/5.35 => ( ( ord_less_nat @ ( power_power_nat @ A @ M2 ) @ ( power_power_nat @ A @ N2 ) )
% 9.17/5.35 => ( ord_less_nat @ M2 @ N2 ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2404_power__less__imp__less__exp,axiom,
% 9.17/5.35 ! [A: int,M2: nat,N2: nat] :
% 9.17/5.35 ( ( ord_less_int @ one_one_int @ A )
% 9.17/5.35 => ( ( ord_less_int @ ( power_power_int @ A @ M2 ) @ ( power_power_int @ A @ N2 ) )
% 9.17/5.35 => ( ord_less_nat @ M2 @ N2 ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2405_power__minus,axiom,
% 9.17/5.35 ! [A: int,N2: nat] :
% 9.17/5.35 ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N2 )
% 9.17/5.35 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 ) @ ( power_power_int @ A @ N2 ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2406_power__minus,axiom,
% 9.17/5.35 ! [A: code_integer,N2: nat] :
% 9.17/5.35 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N2 )
% 9.17/5.35 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 ) @ ( power_8256067586552552935nteger @ A @ N2 ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2407_power__minus,axiom,
% 9.17/5.35 ! [A: rat,N2: nat] :
% 9.17/5.35 ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N2 )
% 9.17/5.35 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 ) @ ( power_power_rat @ A @ N2 ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2408_power__increasing,axiom,
% 9.17/5.35 ! [N2: nat,N6: nat,A: code_integer] :
% 9.17/5.35 ( ( ord_less_eq_nat @ N2 @ N6 )
% 9.17/5.35 => ( ( ord_le3102999989581377725nteger @ one_one_Code_integer @ A )
% 9.17/5.35 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ N2 ) @ ( power_8256067586552552935nteger @ A @ N6 ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2409_power__increasing,axiom,
% 9.17/5.35 ! [N2: nat,N6: nat,A: rat] :
% 9.17/5.35 ( ( ord_less_eq_nat @ N2 @ N6 )
% 9.17/5.35 => ( ( ord_less_eq_rat @ one_one_rat @ A )
% 9.17/5.35 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ A @ N6 ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2410_power__increasing,axiom,
% 9.17/5.35 ! [N2: nat,N6: nat,A: nat] :
% 9.17/5.35 ( ( ord_less_eq_nat @ N2 @ N6 )
% 9.17/5.35 => ( ( ord_less_eq_nat @ one_one_nat @ A )
% 9.17/5.35 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ A @ N6 ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2411_power__increasing,axiom,
% 9.17/5.35 ! [N2: nat,N6: nat,A: int] :
% 9.17/5.35 ( ( ord_less_eq_nat @ N2 @ N6 )
% 9.17/5.35 => ( ( ord_less_eq_int @ one_one_int @ A )
% 9.17/5.35 => ( ord_less_eq_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ A @ N6 ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2412_floor__add__int,axiom,
% 9.17/5.35 ! [X: rat,Z: int] :
% 9.17/5.35 ( ( plus_plus_int @ ( archim3151403230148437115or_rat @ X ) @ Z )
% 9.17/5.35 = ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X @ ( ring_1_of_int_rat @ Z ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2413_int__add__floor,axiom,
% 9.17/5.35 ! [Z: int,X: rat] :
% 9.17/5.35 ( ( plus_plus_int @ Z @ ( archim3151403230148437115or_rat @ X ) )
% 9.17/5.35 = ( archim3151403230148437115or_rat @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z ) @ X ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2414_nat__induct__non__zero,axiom,
% 9.17/5.35 ! [N2: nat,P: nat > $o] :
% 9.17/5.35 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 9.17/5.35 => ( ( P @ one_one_nat )
% 9.17/5.35 => ( ! [N: nat] :
% 9.17/5.35 ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.17/5.35 => ( ( P @ N )
% 9.17/5.35 => ( P @ ( suc @ N ) ) ) )
% 9.17/5.35 => ( P @ N2 ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2415_of__int__leD,axiom,
% 9.17/5.35 ! [N2: int,X: code_integer] :
% 9.17/5.35 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( ring_18347121197199848620nteger @ N2 ) ) @ X )
% 9.17/5.35 => ( ( N2 = zero_zero_int )
% 9.17/5.35 | ( ord_le3102999989581377725nteger @ one_one_Code_integer @ X ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2416_of__int__leD,axiom,
% 9.17/5.35 ! [N2: int,X: rat] :
% 9.17/5.35 ( ( ord_less_eq_rat @ ( abs_abs_rat @ ( ring_1_of_int_rat @ N2 ) ) @ X )
% 9.17/5.35 => ( ( N2 = zero_zero_int )
% 9.17/5.35 | ( ord_less_eq_rat @ one_one_rat @ X ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2417_of__int__leD,axiom,
% 9.17/5.35 ! [N2: int,X: int] :
% 9.17/5.35 ( ( ord_less_eq_int @ ( abs_abs_int @ ( ring_1_of_int_int @ N2 ) ) @ X )
% 9.17/5.35 => ( ( N2 = zero_zero_int )
% 9.17/5.35 | ( ord_less_eq_int @ one_one_int @ X ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2418_of__int__lessD,axiom,
% 9.17/5.35 ! [N2: int,X: code_integer] :
% 9.17/5.35 ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ ( ring_18347121197199848620nteger @ N2 ) ) @ X )
% 9.17/5.35 => ( ( N2 = zero_zero_int )
% 9.17/5.35 | ( ord_le6747313008572928689nteger @ one_one_Code_integer @ X ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2419_of__int__lessD,axiom,
% 9.17/5.35 ! [N2: int,X: rat] :
% 9.17/5.35 ( ( ord_less_rat @ ( abs_abs_rat @ ( ring_1_of_int_rat @ N2 ) ) @ X )
% 9.17/5.35 => ( ( N2 = zero_zero_int )
% 9.17/5.35 | ( ord_less_rat @ one_one_rat @ X ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2420_of__int__lessD,axiom,
% 9.17/5.35 ! [N2: int,X: int] :
% 9.17/5.35 ( ( ord_less_int @ ( abs_abs_int @ ( ring_1_of_int_int @ N2 ) ) @ X )
% 9.17/5.35 => ( ( N2 = zero_zero_int )
% 9.17/5.35 | ( ord_less_int @ one_one_int @ X ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2421_floor__exists,axiom,
% 9.17/5.35 ! [X: rat] :
% 9.17/5.35 ? [Z3: int] :
% 9.17/5.35 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z3 ) @ X )
% 9.17/5.35 & ( ord_less_rat @ X @ ( ring_1_of_int_rat @ ( plus_plus_int @ Z3 @ one_one_int ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2422_floor__exists1,axiom,
% 9.17/5.35 ! [X: rat] :
% 9.17/5.35 ? [X4: int] :
% 9.17/5.35 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ X4 ) @ X )
% 9.17/5.35 & ( ord_less_rat @ X @ ( ring_1_of_int_rat @ ( plus_plus_int @ X4 @ one_one_int ) ) )
% 9.17/5.35 & ! [Y6: int] :
% 9.17/5.35 ( ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Y6 ) @ X )
% 9.17/5.35 & ( ord_less_rat @ X @ ( ring_1_of_int_rat @ ( plus_plus_int @ Y6 @ one_one_int ) ) ) )
% 9.17/5.35 => ( Y6 = X4 ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2423_power__Suc__less,axiom,
% 9.17/5.35 ! [A: code_integer,N2: nat] :
% 9.17/5.35 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 9.17/5.35 => ( ( ord_le6747313008572928689nteger @ A @ one_one_Code_integer )
% 9.17/5.35 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ A @ N2 ) ) @ ( power_8256067586552552935nteger @ A @ N2 ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2424_power__Suc__less,axiom,
% 9.17/5.35 ! [A: rat,N2: nat] :
% 9.17/5.35 ( ( ord_less_rat @ zero_zero_rat @ A )
% 9.17/5.35 => ( ( ord_less_rat @ A @ one_one_rat )
% 9.17/5.35 => ( ord_less_rat @ ( times_times_rat @ A @ ( power_power_rat @ A @ N2 ) ) @ ( power_power_rat @ A @ N2 ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2425_power__Suc__less,axiom,
% 9.17/5.35 ! [A: nat,N2: nat] :
% 9.17/5.35 ( ( ord_less_nat @ zero_zero_nat @ A )
% 9.17/5.35 => ( ( ord_less_nat @ A @ one_one_nat )
% 9.17/5.35 => ( ord_less_nat @ ( times_times_nat @ A @ ( power_power_nat @ A @ N2 ) ) @ ( power_power_nat @ A @ N2 ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2426_power__Suc__less,axiom,
% 9.17/5.35 ! [A: int,N2: nat] :
% 9.17/5.35 ( ( ord_less_int @ zero_zero_int @ A )
% 9.17/5.35 => ( ( ord_less_int @ A @ one_one_int )
% 9.17/5.35 => ( ord_less_int @ ( times_times_int @ A @ ( power_power_int @ A @ N2 ) ) @ ( power_power_int @ A @ N2 ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2427_power__strict__decreasing,axiom,
% 9.17/5.35 ! [N2: nat,N6: nat,A: code_integer] :
% 9.17/5.35 ( ( ord_less_nat @ N2 @ N6 )
% 9.17/5.35 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 9.17/5.35 => ( ( ord_le6747313008572928689nteger @ A @ one_one_Code_integer )
% 9.17/5.35 => ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A @ N6 ) @ ( power_8256067586552552935nteger @ A @ N2 ) ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2428_power__strict__decreasing,axiom,
% 9.17/5.35 ! [N2: nat,N6: nat,A: rat] :
% 9.17/5.35 ( ( ord_less_nat @ N2 @ N6 )
% 9.17/5.35 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 9.17/5.35 => ( ( ord_less_rat @ A @ one_one_rat )
% 9.17/5.35 => ( ord_less_rat @ ( power_power_rat @ A @ N6 ) @ ( power_power_rat @ A @ N2 ) ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2429_power__strict__decreasing,axiom,
% 9.17/5.35 ! [N2: nat,N6: nat,A: nat] :
% 9.17/5.35 ( ( ord_less_nat @ N2 @ N6 )
% 9.17/5.35 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 9.17/5.35 => ( ( ord_less_nat @ A @ one_one_nat )
% 9.17/5.35 => ( ord_less_nat @ ( power_power_nat @ A @ N6 ) @ ( power_power_nat @ A @ N2 ) ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2430_power__strict__decreasing,axiom,
% 9.17/5.35 ! [N2: nat,N6: nat,A: int] :
% 9.17/5.35 ( ( ord_less_nat @ N2 @ N6 )
% 9.17/5.35 => ( ( ord_less_int @ zero_zero_int @ A )
% 9.17/5.35 => ( ( ord_less_int @ A @ one_one_int )
% 9.17/5.35 => ( ord_less_int @ ( power_power_int @ A @ N6 ) @ ( power_power_int @ A @ N2 ) ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2431_power__decreasing,axiom,
% 9.17/5.35 ! [N2: nat,N6: nat,A: code_integer] :
% 9.17/5.35 ( ( ord_less_eq_nat @ N2 @ N6 )
% 9.17/5.35 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 9.17/5.35 => ( ( ord_le3102999989581377725nteger @ A @ one_one_Code_integer )
% 9.17/5.35 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ N6 ) @ ( power_8256067586552552935nteger @ A @ N2 ) ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2432_power__decreasing,axiom,
% 9.17/5.35 ! [N2: nat,N6: nat,A: rat] :
% 9.17/5.35 ( ( ord_less_eq_nat @ N2 @ N6 )
% 9.17/5.35 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 9.17/5.35 => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 9.17/5.35 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N6 ) @ ( power_power_rat @ A @ N2 ) ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2433_power__decreasing,axiom,
% 9.17/5.35 ! [N2: nat,N6: nat,A: nat] :
% 9.17/5.35 ( ( ord_less_eq_nat @ N2 @ N6 )
% 9.17/5.35 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 9.17/5.35 => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 9.17/5.35 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N6 ) @ ( power_power_nat @ A @ N2 ) ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2434_power__decreasing,axiom,
% 9.17/5.35 ! [N2: nat,N6: nat,A: int] :
% 9.17/5.35 ( ( ord_less_eq_nat @ N2 @ N6 )
% 9.17/5.35 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 9.17/5.35 => ( ( ord_less_eq_int @ A @ one_one_int )
% 9.17/5.35 => ( ord_less_eq_int @ ( power_power_int @ A @ N6 ) @ ( power_power_int @ A @ N2 ) ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2435_power__le__imp__le__exp,axiom,
% 9.17/5.35 ! [A: code_integer,M2: nat,N2: nat] :
% 9.17/5.35 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 9.17/5.35 => ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ M2 ) @ ( power_8256067586552552935nteger @ A @ N2 ) )
% 9.17/5.35 => ( ord_less_eq_nat @ M2 @ N2 ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2436_power__le__imp__le__exp,axiom,
% 9.17/5.35 ! [A: rat,M2: nat,N2: nat] :
% 9.17/5.35 ( ( ord_less_rat @ one_one_rat @ A )
% 9.17/5.35 => ( ( ord_less_eq_rat @ ( power_power_rat @ A @ M2 ) @ ( power_power_rat @ A @ N2 ) )
% 9.17/5.35 => ( ord_less_eq_nat @ M2 @ N2 ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2437_power__le__imp__le__exp,axiom,
% 9.17/5.35 ! [A: nat,M2: nat,N2: nat] :
% 9.17/5.35 ( ( ord_less_nat @ one_one_nat @ A )
% 9.17/5.35 => ( ( ord_less_eq_nat @ ( power_power_nat @ A @ M2 ) @ ( power_power_nat @ A @ N2 ) )
% 9.17/5.35 => ( ord_less_eq_nat @ M2 @ N2 ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2438_power__le__imp__le__exp,axiom,
% 9.17/5.35 ! [A: int,M2: nat,N2: nat] :
% 9.17/5.35 ( ( ord_less_int @ one_one_int @ A )
% 9.17/5.35 => ( ( ord_less_eq_int @ ( power_power_int @ A @ M2 ) @ ( power_power_int @ A @ N2 ) )
% 9.17/5.35 => ( ord_less_eq_nat @ M2 @ N2 ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2439_self__le__power,axiom,
% 9.17/5.35 ! [A: code_integer,N2: nat] :
% 9.17/5.35 ( ( ord_le3102999989581377725nteger @ one_one_Code_integer @ A )
% 9.17/5.35 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 9.17/5.35 => ( ord_le3102999989581377725nteger @ A @ ( power_8256067586552552935nteger @ A @ N2 ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2440_self__le__power,axiom,
% 9.17/5.35 ! [A: rat,N2: nat] :
% 9.17/5.35 ( ( ord_less_eq_rat @ one_one_rat @ A )
% 9.17/5.35 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 9.17/5.35 => ( ord_less_eq_rat @ A @ ( power_power_rat @ A @ N2 ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2441_self__le__power,axiom,
% 9.17/5.35 ! [A: nat,N2: nat] :
% 9.17/5.35 ( ( ord_less_eq_nat @ one_one_nat @ A )
% 9.17/5.35 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 9.17/5.35 => ( ord_less_eq_nat @ A @ ( power_power_nat @ A @ N2 ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2442_self__le__power,axiom,
% 9.17/5.35 ! [A: int,N2: nat] :
% 9.17/5.35 ( ( ord_less_eq_int @ one_one_int @ A )
% 9.17/5.35 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 9.17/5.35 => ( ord_less_eq_int @ A @ ( power_power_int @ A @ N2 ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2443_one__less__power,axiom,
% 9.17/5.35 ! [A: code_integer,N2: nat] :
% 9.17/5.35 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 9.17/5.35 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 9.17/5.35 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ A @ N2 ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2444_one__less__power,axiom,
% 9.17/5.35 ! [A: rat,N2: nat] :
% 9.17/5.35 ( ( ord_less_rat @ one_one_rat @ A )
% 9.17/5.35 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 9.17/5.35 => ( ord_less_rat @ one_one_rat @ ( power_power_rat @ A @ N2 ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2445_one__less__power,axiom,
% 9.17/5.35 ! [A: nat,N2: nat] :
% 9.17/5.35 ( ( ord_less_nat @ one_one_nat @ A )
% 9.17/5.35 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 9.17/5.35 => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A @ N2 ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2446_one__less__power,axiom,
% 9.17/5.35 ! [A: int,N2: nat] :
% 9.17/5.35 ( ( ord_less_int @ one_one_int @ A )
% 9.17/5.35 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 9.17/5.35 => ( ord_less_int @ one_one_int @ ( power_power_int @ A @ N2 ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2447_nz__le__conv__less,axiom,
% 9.17/5.35 ! [K: nat,M2: nat] :
% 9.17/5.35 ( ( ord_less_nat @ zero_zero_nat @ K )
% 9.17/5.35 => ( ( ord_less_eq_nat @ K @ M2 )
% 9.17/5.35 => ( ord_less_nat @ ( minus_minus_nat @ K @ ( suc @ zero_zero_nat ) ) @ M2 ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2448_ceiling__altdef,axiom,
% 9.17/5.35 ( archim2889992004027027881ng_rat
% 9.17/5.35 = ( ^ [X3: rat] :
% 9.17/5.35 ( if_int
% 9.17/5.35 @ ( X3
% 9.17/5.35 = ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X3 ) ) )
% 9.17/5.35 @ ( archim3151403230148437115or_rat @ X3 )
% 9.17/5.35 @ ( plus_plus_int @ ( archim3151403230148437115or_rat @ X3 ) @ one_one_int ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2449_Suc__diff__eq__diff__pred,axiom,
% 9.17/5.35 ! [N2: nat,M2: nat] :
% 9.17/5.35 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 9.17/5.35 => ( ( minus_minus_nat @ ( suc @ M2 ) @ N2 )
% 9.17/5.35 = ( minus_minus_nat @ M2 @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2450_Suc__pred_H,axiom,
% 9.17/5.35 ! [N2: nat] :
% 9.17/5.35 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 9.17/5.35 => ( N2
% 9.17/5.35 = ( suc @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2451_add__eq__if,axiom,
% 9.17/5.35 ( plus_plus_nat
% 9.17/5.35 = ( ^ [M: nat,N4: nat] : ( if_nat @ ( M = zero_zero_nat ) @ N4 @ ( suc @ ( plus_plus_nat @ ( minus_minus_nat @ M @ one_one_nat ) @ N4 ) ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2452_Suc__n__minus__m__eq,axiom,
% 9.17/5.35 ! [M2: nat,N2: nat] :
% 9.17/5.35 ( ( ord_less_eq_nat @ M2 @ N2 )
% 9.17/5.35 => ( ( ord_less_nat @ one_one_nat @ M2 )
% 9.17/5.35 => ( ( suc @ ( minus_minus_nat @ N2 @ M2 ) )
% 9.17/5.35 = ( minus_minus_nat @ N2 @ ( minus_minus_nat @ M2 @ one_one_nat ) ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2453_floor__unique,axiom,
% 9.17/5.35 ! [Z: int,X: rat] :
% 9.17/5.35 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ X )
% 9.17/5.35 => ( ( ord_less_rat @ X @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) )
% 9.17/5.35 => ( ( archim3151403230148437115or_rat @ X )
% 9.17/5.35 = Z ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2454_floor__eq__iff,axiom,
% 9.17/5.35 ! [X: rat,A: int] :
% 9.17/5.35 ( ( ( archim3151403230148437115or_rat @ X )
% 9.17/5.35 = A )
% 9.17/5.35 = ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ A ) @ X )
% 9.17/5.35 & ( ord_less_rat @ X @ ( plus_plus_rat @ ( ring_1_of_int_rat @ A ) @ one_one_rat ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2455_floor__split,axiom,
% 9.17/5.35 ! [P: int > $o,T: rat] :
% 9.17/5.35 ( ( P @ ( archim3151403230148437115or_rat @ T ) )
% 9.17/5.35 = ( ! [I3: int] :
% 9.17/5.35 ( ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ I3 ) @ T )
% 9.17/5.35 & ( ord_less_rat @ T @ ( plus_plus_rat @ ( ring_1_of_int_rat @ I3 ) @ one_one_rat ) ) )
% 9.17/5.35 => ( P @ I3 ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2456_ceiling__correct,axiom,
% 9.17/5.35 ! [X: rat] :
% 9.17/5.35 ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ X ) ) @ one_one_rat ) @ X )
% 9.17/5.35 & ( ord_less_eq_rat @ X @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ X ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2457_ceiling__unique,axiom,
% 9.17/5.35 ! [Z: int,X: rat] :
% 9.17/5.35 ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) @ X )
% 9.17/5.35 => ( ( ord_less_eq_rat @ X @ ( ring_1_of_int_rat @ Z ) )
% 9.17/5.35 => ( ( archim2889992004027027881ng_rat @ X )
% 9.17/5.35 = Z ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2458_ceiling__eq__iff,axiom,
% 9.17/5.35 ! [X: rat,A: int] :
% 9.17/5.35 ( ( ( archim2889992004027027881ng_rat @ X )
% 9.17/5.35 = A )
% 9.17/5.35 = ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ A ) @ one_one_rat ) @ X )
% 9.17/5.35 & ( ord_less_eq_rat @ X @ ( ring_1_of_int_rat @ A ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2459_ceiling__split,axiom,
% 9.17/5.35 ! [P: int > $o,T: rat] :
% 9.17/5.35 ( ( P @ ( archim2889992004027027881ng_rat @ T ) )
% 9.17/5.35 = ( ! [I3: int] :
% 9.17/5.35 ( ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ I3 ) @ one_one_rat ) @ T )
% 9.17/5.35 & ( ord_less_eq_rat @ T @ ( ring_1_of_int_rat @ I3 ) ) )
% 9.17/5.35 => ( P @ I3 ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2460_less__floor__iff,axiom,
% 9.17/5.35 ! [Z: int,X: rat] :
% 9.17/5.35 ( ( ord_less_int @ Z @ ( archim3151403230148437115or_rat @ X ) )
% 9.17/5.35 = ( ord_less_eq_rat @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) @ X ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2461_floor__le__iff,axiom,
% 9.17/5.35 ! [X: rat,Z: int] :
% 9.17/5.35 ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X ) @ Z )
% 9.17/5.35 = ( ord_less_rat @ X @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2462_ceiling__less__iff,axiom,
% 9.17/5.35 ! [X: rat,Z: int] :
% 9.17/5.35 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X ) @ Z )
% 9.17/5.35 = ( ord_less_eq_rat @ X @ ( minus_minus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2463_le__ceiling__iff,axiom,
% 9.17/5.35 ! [Z: int,X: rat] :
% 9.17/5.35 ( ( ord_less_eq_int @ Z @ ( archim2889992004027027881ng_rat @ X ) )
% 9.17/5.35 = ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) @ X ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2464_floor__correct,axiom,
% 9.17/5.35 ! [X: rat] :
% 9.17/5.35 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X ) ) @ X )
% 9.17/5.35 & ( ord_less_rat @ X @ ( ring_1_of_int_rat @ ( plus_plus_int @ ( archim3151403230148437115or_rat @ X ) @ one_one_int ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2465_power__diff__power__eq,axiom,
% 9.17/5.35 ! [A: int,N2: nat,M2: nat] :
% 9.17/5.35 ( ( A != zero_zero_int )
% 9.17/5.35 => ( ( ( ord_less_eq_nat @ N2 @ M2 )
% 9.17/5.35 => ( ( divide_divide_int @ ( power_power_int @ A @ M2 ) @ ( power_power_int @ A @ N2 ) )
% 9.17/5.35 = ( power_power_int @ A @ ( minus_minus_nat @ M2 @ N2 ) ) ) )
% 9.17/5.35 & ( ~ ( ord_less_eq_nat @ N2 @ M2 )
% 9.17/5.35 => ( ( divide_divide_int @ ( power_power_int @ A @ M2 ) @ ( power_power_int @ A @ N2 ) )
% 9.17/5.35 = ( divide_divide_int @ one_one_int @ ( power_power_int @ A @ ( minus_minus_nat @ N2 @ M2 ) ) ) ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2466_power__diff__power__eq,axiom,
% 9.17/5.35 ! [A: nat,N2: nat,M2: nat] :
% 9.17/5.35 ( ( A != zero_zero_nat )
% 9.17/5.35 => ( ( ( ord_less_eq_nat @ N2 @ M2 )
% 9.17/5.35 => ( ( divide_divide_nat @ ( power_power_nat @ A @ M2 ) @ ( power_power_nat @ A @ N2 ) )
% 9.17/5.35 = ( power_power_nat @ A @ ( minus_minus_nat @ M2 @ N2 ) ) ) )
% 9.17/5.35 & ( ~ ( ord_less_eq_nat @ N2 @ M2 )
% 9.17/5.35 => ( ( divide_divide_nat @ ( power_power_nat @ A @ M2 ) @ ( power_power_nat @ A @ N2 ) )
% 9.17/5.35 = ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ A @ ( minus_minus_nat @ N2 @ M2 ) ) ) ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2467_power__diff__power__eq,axiom,
% 9.17/5.35 ! [A: code_integer,N2: nat,M2: nat] :
% 9.17/5.35 ( ( A != zero_z3403309356797280102nteger )
% 9.17/5.35 => ( ( ( ord_less_eq_nat @ N2 @ M2 )
% 9.17/5.35 => ( ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ A @ M2 ) @ ( power_8256067586552552935nteger @ A @ N2 ) )
% 9.17/5.35 = ( power_8256067586552552935nteger @ A @ ( minus_minus_nat @ M2 @ N2 ) ) ) )
% 9.17/5.35 & ( ~ ( ord_less_eq_nat @ N2 @ M2 )
% 9.17/5.35 => ( ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ A @ M2 ) @ ( power_8256067586552552935nteger @ A @ N2 ) )
% 9.17/5.35 = ( divide6298287555418463151nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ A @ ( minus_minus_nat @ N2 @ M2 ) ) ) ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2468_power__diff__power__eq,axiom,
% 9.17/5.35 ! [A: code_natural,N2: nat,M2: nat] :
% 9.17/5.35 ( ( A != zero_z2226904508553997617atural )
% 9.17/5.35 => ( ( ( ord_less_eq_nat @ N2 @ M2 )
% 9.17/5.35 => ( ( divide5121882707175180666atural @ ( power_7079662738309270450atural @ A @ M2 ) @ ( power_7079662738309270450atural @ A @ N2 ) )
% 9.17/5.35 = ( power_7079662738309270450atural @ A @ ( minus_minus_nat @ M2 @ N2 ) ) ) )
% 9.17/5.35 & ( ~ ( ord_less_eq_nat @ N2 @ M2 )
% 9.17/5.35 => ( ( divide5121882707175180666atural @ ( power_7079662738309270450atural @ A @ M2 ) @ ( power_7079662738309270450atural @ A @ N2 ) )
% 9.17/5.35 = ( divide5121882707175180666atural @ one_one_Code_natural @ ( power_7079662738309270450atural @ A @ ( minus_minus_nat @ N2 @ M2 ) ) ) ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2469_power__eq__if,axiom,
% 9.17/5.35 ( power_8256067586552552935nteger
% 9.17/5.35 = ( ^ [P6: code_integer,M: nat] : ( if_Code_integer @ ( M = zero_zero_nat ) @ one_one_Code_integer @ ( times_3573771949741848930nteger @ P6 @ ( power_8256067586552552935nteger @ P6 @ ( minus_minus_nat @ M @ one_one_nat ) ) ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2470_power__eq__if,axiom,
% 9.17/5.35 ( power_power_assn
% 9.17/5.35 = ( ^ [P6: assn,M: nat] : ( if_assn @ ( M = zero_zero_nat ) @ one_one_assn @ ( times_times_assn @ P6 @ ( power_power_assn @ P6 @ ( minus_minus_nat @ M @ one_one_nat ) ) ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2471_power__eq__if,axiom,
% 9.17/5.35 ( power_power_rat
% 9.17/5.35 = ( ^ [P6: rat,M: nat] : ( if_rat @ ( M = zero_zero_nat ) @ one_one_rat @ ( times_times_rat @ P6 @ ( power_power_rat @ P6 @ ( minus_minus_nat @ M @ one_one_nat ) ) ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2472_power__eq__if,axiom,
% 9.17/5.35 ( power_power_nat
% 9.17/5.35 = ( ^ [P6: nat,M: nat] : ( if_nat @ ( M = zero_zero_nat ) @ one_one_nat @ ( times_times_nat @ P6 @ ( power_power_nat @ P6 @ ( minus_minus_nat @ M @ one_one_nat ) ) ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2473_power__eq__if,axiom,
% 9.17/5.35 ( power_power_int
% 9.17/5.35 = ( ^ [P6: int,M: nat] : ( if_int @ ( M = zero_zero_nat ) @ one_one_int @ ( times_times_int @ P6 @ ( power_power_int @ P6 @ ( minus_minus_nat @ M @ one_one_nat ) ) ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2474_power__minus__mult,axiom,
% 9.17/5.35 ! [N2: nat,A: assn] :
% 9.17/5.35 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 9.17/5.35 => ( ( times_times_assn @ ( power_power_assn @ A @ ( minus_minus_nat @ N2 @ one_one_nat ) ) @ A )
% 9.17/5.35 = ( power_power_assn @ A @ N2 ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2475_power__minus__mult,axiom,
% 9.17/5.35 ! [N2: nat,A: rat] :
% 9.17/5.35 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 9.17/5.35 => ( ( times_times_rat @ ( power_power_rat @ A @ ( minus_minus_nat @ N2 @ one_one_nat ) ) @ A )
% 9.17/5.35 = ( power_power_rat @ A @ N2 ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2476_power__minus__mult,axiom,
% 9.17/5.35 ! [N2: nat,A: nat] :
% 9.17/5.35 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 9.17/5.35 => ( ( times_times_nat @ ( power_power_nat @ A @ ( minus_minus_nat @ N2 @ one_one_nat ) ) @ A )
% 9.17/5.35 = ( power_power_nat @ A @ N2 ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2477_power__minus__mult,axiom,
% 9.17/5.35 ! [N2: nat,A: int] :
% 9.17/5.35 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 9.17/5.35 => ( ( times_times_int @ ( power_power_int @ A @ ( minus_minus_nat @ N2 @ one_one_nat ) ) @ A )
% 9.17/5.35 = ( power_power_int @ A @ N2 ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2478_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 9.17/5.35 ! [K: nat,N2: nat] :
% 9.17/5.35 ( ( ord_less_eq_nat @ K @ N2 )
% 9.17/5.35 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( plus_plus_nat @ N2 @ K ) )
% 9.17/5.35 = ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( minus_minus_nat @ N2 @ K ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2479_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 9.17/5.35 ! [K: nat,N2: nat] :
% 9.17/5.35 ( ( ord_less_eq_nat @ K @ N2 )
% 9.17/5.35 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( plus_plus_nat @ N2 @ K ) )
% 9.17/5.35 = ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( minus_minus_nat @ N2 @ K ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2480_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 9.17/5.35 ! [K: nat,N2: nat] :
% 9.17/5.35 ( ( ord_less_eq_nat @ K @ N2 )
% 9.17/5.35 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( plus_plus_nat @ N2 @ K ) )
% 9.17/5.35 = ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( minus_minus_nat @ N2 @ K ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2481_option_Osize__gen_I2_J,axiom,
% 9.17/5.35 ! [X: num > nat,X2: num] :
% 9.17/5.35 ( ( size_option_num @ X @ ( some_num @ X2 ) )
% 9.17/5.35 = ( plus_plus_nat @ ( X @ X2 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2482_option_Osize__gen_I2_J,axiom,
% 9.17/5.35 ! [X: produc8664842809031399944it_nat > nat,X2: produc8664842809031399944it_nat] :
% 9.17/5.35 ( ( size_o29782932136985253it_nat @ X @ ( some_P1914260805536162275it_nat @ X2 ) )
% 9.17/5.35 = ( plus_plus_nat @ ( X @ X2 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2483_Heap_Osize__gen,axiom,
% 9.17/5.35 ! [Xa: product_unit > nat,X: heap_e7401611519738050253t_unit > option8956607266484857688it_nat] :
% 9.17/5.35 ( ( heap_T4142866422068808505t_unit @ Xa @ ( heap_T6183433275982383450t_unit @ X ) )
% 9.17/5.35 = ( suc @ zero_zero_nat ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2484_num_Osize__gen_I2_J,axiom,
% 9.17/5.35 ! [X2: num] :
% 9.17/5.35 ( ( size_num @ ( bit0 @ X2 ) )
% 9.17/5.35 = ( plus_plus_nat @ ( size_num @ X2 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2485_normalize__negative,axiom,
% 9.17/5.35 ! [Q3: int,P4: int] :
% 9.17/5.35 ( ( ord_less_int @ Q3 @ zero_zero_int )
% 9.17/5.35 => ( ( normalize @ ( product_Pair_int_int @ P4 @ Q3 ) )
% 9.17/5.35 = ( normalize @ ( product_Pair_int_int @ ( uminus_uminus_int @ P4 ) @ ( uminus_uminus_int @ Q3 ) ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2486_option_Osize__gen_I1_J,axiom,
% 9.17/5.35 ! [X: produc6714399278180371524it_nat > nat] :
% 9.17/5.35 ( ( size_o5312321843473198183it_nat @ X @ none_P2587165478634041381it_nat )
% 9.17/5.35 = ( suc @ zero_zero_nat ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2487_option_Osize__gen_I1_J,axiom,
% 9.17/5.35 ! [X: num > nat] :
% 9.17/5.35 ( ( size_option_num @ X @ none_num )
% 9.17/5.35 = ( suc @ zero_zero_nat ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2488_option_Osize__gen_I1_J,axiom,
% 9.17/5.35 ! [X: produc8664842809031399944it_nat > nat] :
% 9.17/5.35 ( ( size_o29782932136985253it_nat @ X @ none_P9117596204409417319it_nat )
% 9.17/5.35 = ( suc @ zero_zero_nat ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2489_Heap_Osize_I2_J,axiom,
% 9.17/5.35 ! [X: heap_e7401611519738050253t_unit > option8956607266484857688it_nat] :
% 9.17/5.35 ( ( size_s1564113455978345259t_unit @ ( heap_T6183433275982383450t_unit @ X ) )
% 9.17/5.35 = ( suc @ zero_zero_nat ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2490_num_Osize_I5_J,axiom,
% 9.17/5.35 ! [X2: num] :
% 9.17/5.35 ( ( size_size_num @ ( bit0 @ X2 ) )
% 9.17/5.35 = ( plus_plus_nat @ ( size_size_num @ X2 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2491_option_Osize_I3_J,axiom,
% 9.17/5.35 ( ( size_s6797157356856800118it_nat @ none_P2587165478634041381it_nat )
% 9.17/5.35 = ( suc @ zero_zero_nat ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2492_option_Osize_I3_J,axiom,
% 9.17/5.35 ( ( size_size_option_num @ none_num )
% 9.17/5.35 = ( suc @ zero_zero_nat ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2493_option_Osize_I3_J,axiom,
% 9.17/5.35 ( ( size_s8766407808098229740it_nat @ none_P9117596204409417319it_nat )
% 9.17/5.35 = ( suc @ zero_zero_nat ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2494_normalize__denom__zero,axiom,
% 9.17/5.35 ! [P4: int] :
% 9.17/5.35 ( ( normalize @ ( product_Pair_int_int @ P4 @ zero_zero_int ) )
% 9.17/5.35 = ( product_Pair_int_int @ zero_zero_int @ one_one_int ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2495_option_Osize__gen__o__map,axiom,
% 9.17/5.35 ! [F: num > nat,G: num > num] :
% 9.17/5.35 ( ( comp_o6878144249584144265on_num @ ( size_option_num @ F ) @ ( map_option_num_num @ G ) )
% 9.17/5.35 = ( size_option_num @ ( comp_num_nat_num @ F @ G ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2496_normalize__denom__pos,axiom,
% 9.17/5.35 ! [R2: product_prod_int_int,P4: int,Q3: int] :
% 9.17/5.35 ( ( ( normalize @ R2 )
% 9.17/5.35 = ( product_Pair_int_int @ P4 @ Q3 ) )
% 9.17/5.35 => ( ord_less_int @ zero_zero_int @ Q3 ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2497_normalize__crossproduct,axiom,
% 9.17/5.35 ! [Q3: int,S: int,P4: int,R2: int] :
% 9.17/5.35 ( ( Q3 != zero_zero_int )
% 9.17/5.35 => ( ( S != zero_zero_int )
% 9.17/5.35 => ( ( ( normalize @ ( product_Pair_int_int @ P4 @ Q3 ) )
% 9.17/5.35 = ( normalize @ ( product_Pair_int_int @ R2 @ S ) ) )
% 9.17/5.35 => ( ( times_times_int @ P4 @ S )
% 9.17/5.35 = ( times_times_int @ R2 @ Q3 ) ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2498_option_Osize_I4_J,axiom,
% 9.17/5.35 ! [X2: num] :
% 9.17/5.35 ( ( size_size_option_num @ ( some_num @ X2 ) )
% 9.17/5.35 = ( suc @ zero_zero_nat ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2499_option_Osize_I4_J,axiom,
% 9.17/5.35 ! [X2: produc8664842809031399944it_nat] :
% 9.17/5.35 ( ( size_s8766407808098229740it_nat @ ( some_P1914260805536162275it_nat @ X2 ) )
% 9.17/5.35 = ( suc @ zero_zero_nat ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2500_divmod__nat__if,axiom,
% 9.17/5.35 ( divmod_nat
% 9.17/5.35 = ( ^ [M: nat,N4: nat] :
% 9.17/5.35 ( if_Pro6206227464963214023at_nat
% 9.17/5.35 @ ( ( N4 = zero_zero_nat )
% 9.17/5.35 | ( ord_less_nat @ M @ N4 ) )
% 9.17/5.35 @ ( product_Pair_nat_nat @ zero_zero_nat @ M )
% 9.17/5.35 @ ( produc2626176000494625587at_nat
% 9.17/5.35 @ ^ [Q5: nat] : ( product_Pair_nat_nat @ ( suc @ Q5 ) )
% 9.17/5.35 @ ( divmod_nat @ ( minus_minus_nat @ M @ N4 ) @ N4 ) ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2501_sum__gp__multiplied,axiom,
% 9.17/5.35 ! [M2: nat,N2: nat,X: code_integer] :
% 9.17/5.35 ( ( ord_less_eq_nat @ M2 @ N2 )
% 9.17/5.35 => ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ one_one_Code_integer @ X ) @ ( groups7501900531339628137nteger @ ( power_8256067586552552935nteger @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) )
% 9.17/5.35 = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ X @ M2 ) @ ( power_8256067586552552935nteger @ X @ ( suc @ N2 ) ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2502_sum__gp__multiplied,axiom,
% 9.17/5.35 ! [M2: nat,N2: nat,X: rat] :
% 9.17/5.35 ( ( ord_less_eq_nat @ M2 @ N2 )
% 9.17/5.35 => ( ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) )
% 9.17/5.35 = ( minus_minus_rat @ ( power_power_rat @ X @ M2 ) @ ( power_power_rat @ X @ ( suc @ N2 ) ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2503_sum__gp__multiplied,axiom,
% 9.17/5.35 ! [M2: nat,N2: nat,X: int] :
% 9.17/5.35 ( ( ord_less_eq_nat @ M2 @ N2 )
% 9.17/5.35 => ( ( times_times_int @ ( minus_minus_int @ one_one_int @ X ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) )
% 9.17/5.35 = ( minus_minus_int @ ( power_power_int @ X @ M2 ) @ ( power_power_int @ X @ ( suc @ N2 ) ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2504_pair__lessI2,axiom,
% 9.17/5.35 ! [A: nat,B: nat,S: nat,T: nat] :
% 9.17/5.35 ( ( ord_less_eq_nat @ A @ B )
% 9.17/5.35 => ( ( ord_less_nat @ S @ T )
% 9.17/5.35 => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A @ S ) @ ( product_Pair_nat_nat @ B @ T ) ) @ fun_pair_less ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2505_pair__less__iff1,axiom,
% 9.17/5.35 ! [X: nat,Y: nat,Z: nat] :
% 9.17/5.35 ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( product_Pair_nat_nat @ X @ Z ) ) @ fun_pair_less )
% 9.17/5.35 = ( ord_less_nat @ Y @ Z ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2506_Suc__times__numeral__mod__eq,axiom,
% 9.17/5.35 ! [K: num,N2: nat] :
% 9.17/5.35 ( ( ( numeral_numeral_nat @ K )
% 9.17/5.35 != one_one_nat )
% 9.17/5.35 => ( ( modulo_modulo_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ K ) @ N2 ) ) @ ( numeral_numeral_nat @ K ) )
% 9.17/5.35 = one_one_nat ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2507_one__int_Otransfer,axiom,
% 9.17/5.35 pcr_int @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) @ one_one_int ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2508_less__than__iff,axiom,
% 9.17/5.35 ! [X: nat,Y: nat] :
% 9.17/5.35 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ less_than )
% 9.17/5.35 = ( ord_less_nat @ X @ Y ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2509_one__int__def,axiom,
% 9.17/5.35 ( one_one_int
% 9.17/5.35 = ( abs_Integ @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2510_sum__telescope_H_H,axiom,
% 9.17/5.35 ! [M2: nat,N2: nat,F: nat > code_integer] :
% 9.17/5.35 ( ( ord_less_eq_nat @ M2 @ N2 )
% 9.17/5.35 => ( ( groups7501900531339628137nteger
% 9.17/5.35 @ ^ [K4: nat] : ( minus_8373710615458151222nteger @ ( F @ K4 ) @ ( F @ ( minus_minus_nat @ K4 @ one_one_nat ) ) )
% 9.17/5.35 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N2 ) )
% 9.17/5.35 = ( minus_8373710615458151222nteger @ ( F @ N2 ) @ ( F @ M2 ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2511_sum__telescope_H_H,axiom,
% 9.17/5.35 ! [M2: nat,N2: nat,F: nat > rat] :
% 9.17/5.35 ( ( ord_less_eq_nat @ M2 @ N2 )
% 9.17/5.35 => ( ( groups2906978787729119204at_rat
% 9.17/5.35 @ ^ [K4: nat] : ( minus_minus_rat @ ( F @ K4 ) @ ( F @ ( minus_minus_nat @ K4 @ one_one_nat ) ) )
% 9.17/5.35 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N2 ) )
% 9.17/5.35 = ( minus_minus_rat @ ( F @ N2 ) @ ( F @ M2 ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2512_sum__telescope_H_H,axiom,
% 9.17/5.35 ! [M2: nat,N2: nat,F: nat > int] :
% 9.17/5.35 ( ( ord_less_eq_nat @ M2 @ N2 )
% 9.17/5.35 => ( ( groups3539618377306564664at_int
% 9.17/5.35 @ ^ [K4: nat] : ( minus_minus_int @ ( F @ K4 ) @ ( F @ ( minus_minus_nat @ K4 @ one_one_nat ) ) )
% 9.17/5.35 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N2 ) )
% 9.17/5.35 = ( minus_minus_int @ ( F @ N2 ) @ ( F @ M2 ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2513_case__prod__conv,axiom,
% 9.17/5.35 ! [F: nat > nat > nat,A: nat,B: nat] :
% 9.17/5.35 ( ( produc6842872674320459806at_nat @ F @ ( product_Pair_nat_nat @ A @ B ) )
% 9.17/5.35 = ( F @ A @ B ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2514_case__prod__conv,axiom,
% 9.17/5.35 ! [F: nat > nat > product_prod_nat_nat > product_prod_nat_nat,A: nat,B: nat] :
% 9.17/5.35 ( ( produc27273713700761075at_nat @ F @ ( product_Pair_nat_nat @ A @ B ) )
% 9.17/5.35 = ( F @ A @ B ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2515_case__prod__conv,axiom,
% 9.17/5.35 ! [F: nat > nat > product_prod_nat_nat > $o,A: nat,B: nat] :
% 9.17/5.35 ( ( produc8739625826339149834_nat_o @ F @ ( product_Pair_nat_nat @ A @ B ) )
% 9.17/5.35 = ( F @ A @ B ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2516_case__prod__conv,axiom,
% 9.17/5.35 ! [F: int > int > product_prod_int_int,A: int,B: int] :
% 9.17/5.35 ( ( produc4245557441103728435nt_int @ F @ ( product_Pair_int_int @ A @ B ) )
% 9.17/5.35 = ( F @ A @ B ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2517_case__prod__conv,axiom,
% 9.17/5.35 ! [F: int > int > int,A: int,B: int] :
% 9.17/5.35 ( ( produc8211389475949308722nt_int @ F @ ( product_Pair_int_int @ A @ B ) )
% 9.17/5.35 = ( F @ A @ B ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2518_case__prod__curry,axiom,
% 9.17/5.35 ! [F: product_prod_nat_nat > nat] :
% 9.17/5.35 ( ( produc6842872674320459806at_nat @ ( produc8871627978511607229at_nat @ F ) )
% 9.17/5.35 = F ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2519_case__prod__curry,axiom,
% 9.17/5.35 ! [F: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat] :
% 9.17/5.35 ( ( produc27273713700761075at_nat @ ( produc3610074571335452306at_nat @ F ) )
% 9.17/5.35 = F ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2520_case__prod__curry,axiom,
% 9.17/5.35 ! [F: product_prod_nat_nat > product_prod_nat_nat > $o] :
% 9.17/5.35 ( ( produc8739625826339149834_nat_o @ ( produc3704529784387675049_nat_o @ F ) )
% 9.17/5.35 = F ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2521_case__prod__curry,axiom,
% 9.17/5.35 ! [F: product_prod_int_int > product_prod_int_int] :
% 9.17/5.35 ( ( produc4245557441103728435nt_int @ ( produc8249235968001453780nt_int @ F ) )
% 9.17/5.35 = F ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2522_case__prod__curry,axiom,
% 9.17/5.35 ! [F: product_prod_int_int > int] :
% 9.17/5.35 ( ( produc8211389475949308722nt_int @ ( produc1016772743285680337nt_int @ F ) )
% 9.17/5.35 = F ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2523_curry__case__prod,axiom,
% 9.17/5.35 ! [F: nat > nat > nat] :
% 9.17/5.35 ( ( produc8871627978511607229at_nat @ ( produc6842872674320459806at_nat @ F ) )
% 9.17/5.35 = F ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2524_curry__case__prod,axiom,
% 9.17/5.35 ! [F: nat > nat > product_prod_nat_nat > product_prod_nat_nat] :
% 9.17/5.35 ( ( produc3610074571335452306at_nat @ ( produc27273713700761075at_nat @ F ) )
% 9.17/5.35 = F ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2525_curry__case__prod,axiom,
% 9.17/5.35 ! [F: nat > nat > product_prod_nat_nat > $o] :
% 9.17/5.35 ( ( produc3704529784387675049_nat_o @ ( produc8739625826339149834_nat_o @ F ) )
% 9.17/5.35 = F ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2526_curry__case__prod,axiom,
% 9.17/5.35 ! [F: int > int > product_prod_int_int] :
% 9.17/5.35 ( ( produc8249235968001453780nt_int @ ( produc4245557441103728435nt_int @ F ) )
% 9.17/5.35 = F ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2527_curry__case__prod,axiom,
% 9.17/5.35 ! [F: int > int > int] :
% 9.17/5.35 ( ( produc1016772743285680337nt_int @ ( produc8211389475949308722nt_int @ F ) )
% 9.17/5.35 = F ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2528_distrib__right__numeral,axiom,
% 9.17/5.35 ! [A: nat,B: nat,V: num] :
% 9.17/5.35 ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ ( numeral_numeral_nat @ V ) )
% 9.17/5.35 = ( plus_plus_nat @ ( times_times_nat @ A @ ( numeral_numeral_nat @ V ) ) @ ( times_times_nat @ B @ ( numeral_numeral_nat @ V ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2529_distrib__right__numeral,axiom,
% 9.17/5.35 ! [A: int,B: int,V: num] :
% 9.17/5.35 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ ( numeral_numeral_int @ V ) )
% 9.17/5.35 = ( plus_plus_int @ ( times_times_int @ A @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ B @ ( numeral_numeral_int @ V ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2530_distrib__right__numeral,axiom,
% 9.17/5.35 ! [A: code_integer,B: code_integer,V: num] :
% 9.17/5.35 ( ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ ( numera6620942414471956472nteger @ V ) )
% 9.17/5.35 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ ( numera6620942414471956472nteger @ V ) ) @ ( times_3573771949741848930nteger @ B @ ( numera6620942414471956472nteger @ V ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2531_distrib__right__numeral,axiom,
% 9.17/5.35 ! [A: rat,B: rat,V: num] :
% 9.17/5.35 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ ( numeral_numeral_rat @ V ) )
% 9.17/5.35 = ( plus_plus_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ B @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2532_distrib__right__numeral,axiom,
% 9.17/5.35 ! [A: code_natural,B: code_natural,V: num] :
% 9.17/5.35 ( ( times_2397367101498566445atural @ ( plus_p4538020629002901425atural @ A @ B ) @ ( numera5444537566228673987atural @ V ) )
% 9.17/5.35 = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ A @ ( numera5444537566228673987atural @ V ) ) @ ( times_2397367101498566445atural @ B @ ( numera5444537566228673987atural @ V ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2533_distrib__left__numeral,axiom,
% 9.17/5.35 ! [V: num,B: nat,C: nat] :
% 9.17/5.35 ( ( times_times_nat @ ( numeral_numeral_nat @ V ) @ ( plus_plus_nat @ B @ C ) )
% 9.17/5.35 = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ V ) @ B ) @ ( times_times_nat @ ( numeral_numeral_nat @ V ) @ C ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2534_distrib__left__numeral,axiom,
% 9.17/5.35 ! [V: num,B: int,C: int] :
% 9.17/5.35 ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( plus_plus_int @ B @ C ) )
% 9.17/5.35 = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ V ) @ B ) @ ( times_times_int @ ( numeral_numeral_int @ V ) @ C ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2535_distrib__left__numeral,axiom,
% 9.17/5.35 ! [V: num,B: code_integer,C: code_integer] :
% 9.17/5.35 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 9.17/5.35 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ B ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ C ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2536_distrib__left__numeral,axiom,
% 9.17/5.35 ! [V: num,B: rat,C: rat] :
% 9.17/5.35 ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( plus_plus_rat @ B @ C ) )
% 9.17/5.35 = ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ B ) @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ C ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2537_distrib__left__numeral,axiom,
% 9.17/5.35 ! [V: num,B: code_natural,C: code_natural] :
% 9.17/5.35 ( ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ V ) @ ( plus_p4538020629002901425atural @ B @ C ) )
% 9.17/5.35 = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ V ) @ B ) @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ V ) @ C ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2538_add__neg__numeral__simps_I3_J,axiom,
% 9.17/5.35 ! [M2: num,N2: num] :
% 9.17/5.35 ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 9.17/5.35 = ( uminus_uminus_int @ ( plus_plus_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N2 ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2539_add__neg__numeral__simps_I3_J,axiom,
% 9.17/5.35 ! [M2: num,N2: num] :
% 9.17/5.35 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 9.17/5.35 = ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ M2 ) @ ( numera6620942414471956472nteger @ N2 ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2540_add__neg__numeral__simps_I3_J,axiom,
% 9.17/5.35 ! [M2: num,N2: num] :
% 9.17/5.35 ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 9.17/5.35 = ( uminus_uminus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ M2 ) @ ( numeral_numeral_rat @ N2 ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2541_add__numeral__left,axiom,
% 9.17/5.35 ! [V: num,W: num,Z: nat] :
% 9.17/5.35 ( ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ W ) @ Z ) )
% 9.17/5.35 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2542_add__numeral__left,axiom,
% 9.17/5.35 ! [V: num,W: num,Z: int] :
% 9.17/5.35 ( ( plus_plus_int @ ( numeral_numeral_int @ V ) @ ( plus_plus_int @ ( numeral_numeral_int @ W ) @ Z ) )
% 9.17/5.35 = ( plus_plus_int @ ( numeral_numeral_int @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2543_add__numeral__left,axiom,
% 9.17/5.35 ! [V: num,W: num,Z: code_integer] :
% 9.17/5.35 ( ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ V ) @ ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ W ) @ Z ) )
% 9.17/5.35 = ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2544_add__numeral__left,axiom,
% 9.17/5.35 ! [V: num,W: num,Z: rat] :
% 9.17/5.35 ( ( plus_plus_rat @ ( numeral_numeral_rat @ V ) @ ( plus_plus_rat @ ( numeral_numeral_rat @ W ) @ Z ) )
% 9.17/5.35 = ( plus_plus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2545_add__numeral__left,axiom,
% 9.17/5.35 ! [V: num,W: num,Z: code_natural] :
% 9.17/5.35 ( ( plus_p4538020629002901425atural @ ( numera5444537566228673987atural @ V ) @ ( plus_p4538020629002901425atural @ ( numera5444537566228673987atural @ W ) @ Z ) )
% 9.17/5.35 = ( plus_p4538020629002901425atural @ ( numera5444537566228673987atural @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2546_numeral__plus__numeral,axiom,
% 9.17/5.35 ! [M2: num,N2: num] :
% 9.17/5.35 ( ( plus_plus_nat @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ N2 ) )
% 9.17/5.35 = ( numeral_numeral_nat @ ( plus_plus_num @ M2 @ N2 ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2547_numeral__plus__numeral,axiom,
% 9.17/5.35 ! [M2: num,N2: num] :
% 9.17/5.35 ( ( plus_plus_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N2 ) )
% 9.17/5.35 = ( numeral_numeral_int @ ( plus_plus_num @ M2 @ N2 ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2548_numeral__plus__numeral,axiom,
% 9.17/5.35 ! [M2: num,N2: num] :
% 9.17/5.35 ( ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ M2 ) @ ( numera6620942414471956472nteger @ N2 ) )
% 9.17/5.35 = ( numera6620942414471956472nteger @ ( plus_plus_num @ M2 @ N2 ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2549_numeral__plus__numeral,axiom,
% 9.17/5.35 ! [M2: num,N2: num] :
% 9.17/5.35 ( ( plus_plus_rat @ ( numeral_numeral_rat @ M2 ) @ ( numeral_numeral_rat @ N2 ) )
% 9.17/5.35 = ( numeral_numeral_rat @ ( plus_plus_num @ M2 @ N2 ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2550_numeral__plus__numeral,axiom,
% 9.17/5.35 ! [M2: num,N2: num] :
% 9.17/5.35 ( ( plus_p4538020629002901425atural @ ( numera5444537566228673987atural @ M2 ) @ ( numera5444537566228673987atural @ N2 ) )
% 9.17/5.35 = ( numera5444537566228673987atural @ ( plus_plus_num @ M2 @ N2 ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2551_semiring__norm_I168_J,axiom,
% 9.17/5.35 ! [V: num,W: num,Y: int] :
% 9.17/5.35 ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ Y ) )
% 9.17/5.35 = ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ V @ W ) ) ) @ Y ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2552_semiring__norm_I168_J,axiom,
% 9.17/5.35 ! [V: num,W: num,Y: code_integer] :
% 9.17/5.35 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) @ Y ) )
% 9.17/5.35 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ V @ W ) ) ) @ Y ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2553_semiring__norm_I168_J,axiom,
% 9.17/5.35 ! [V: num,W: num,Y: rat] :
% 9.17/5.35 ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ Y ) )
% 9.17/5.35 = ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ V @ W ) ) ) @ Y ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2554_diff__numeral__simps_I3_J,axiom,
% 9.17/5.35 ! [M2: num,N2: num] :
% 9.17/5.35 ( ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( numeral_numeral_int @ N2 ) )
% 9.17/5.35 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ M2 @ N2 ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2555_diff__numeral__simps_I3_J,axiom,
% 9.17/5.35 ! [M2: num,N2: num] :
% 9.17/5.35 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ ( numera6620942414471956472nteger @ N2 ) )
% 9.17/5.35 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ M2 @ N2 ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2556_diff__numeral__simps_I3_J,axiom,
% 9.17/5.35 ! [M2: num,N2: num] :
% 9.17/5.35 ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ ( numeral_numeral_rat @ N2 ) )
% 9.17/5.35 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ M2 @ N2 ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2557_diff__numeral__simps_I2_J,axiom,
% 9.17/5.35 ! [M2: num,N2: num] :
% 9.17/5.35 ( ( minus_minus_int @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 9.17/5.35 = ( numeral_numeral_int @ ( plus_plus_num @ M2 @ N2 ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2558_diff__numeral__simps_I2_J,axiom,
% 9.17/5.35 ! [M2: num,N2: num] :
% 9.17/5.35 ( ( minus_8373710615458151222nteger @ ( numera6620942414471956472nteger @ M2 ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 9.17/5.35 = ( numera6620942414471956472nteger @ ( plus_plus_num @ M2 @ N2 ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2559_diff__numeral__simps_I2_J,axiom,
% 9.17/5.35 ! [M2: num,N2: num] :
% 9.17/5.35 ( ( minus_minus_rat @ ( numeral_numeral_rat @ M2 ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 9.17/5.35 = ( numeral_numeral_rat @ ( plus_plus_num @ M2 @ N2 ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2560_ceiling__add__numeral,axiom,
% 9.17/5.35 ! [X: rat,V: num] :
% 9.17/5.35 ( ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X @ ( numeral_numeral_rat @ V ) ) )
% 9.17/5.35 = ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X ) @ ( numeral_numeral_int @ V ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2561_power__add__numeral,axiom,
% 9.17/5.35 ! [A: assn,M2: num,N2: num] :
% 9.17/5.35 ( ( times_times_assn @ ( power_power_assn @ A @ ( numeral_numeral_nat @ M2 ) ) @ ( power_power_assn @ A @ ( numeral_numeral_nat @ N2 ) ) )
% 9.17/5.35 = ( power_power_assn @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M2 @ N2 ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2562_power__add__numeral,axiom,
% 9.17/5.35 ! [A: rat,M2: num,N2: num] :
% 9.17/5.35 ( ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ M2 ) ) @ ( power_power_rat @ A @ ( numeral_numeral_nat @ N2 ) ) )
% 9.17/5.35 = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M2 @ N2 ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2563_power__add__numeral,axiom,
% 9.17/5.35 ! [A: nat,M2: num,N2: num] :
% 9.17/5.35 ( ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M2 ) ) @ ( power_power_nat @ A @ ( numeral_numeral_nat @ N2 ) ) )
% 9.17/5.35 = ( power_power_nat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M2 @ N2 ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2564_power__add__numeral,axiom,
% 9.17/5.35 ! [A: int,M2: num,N2: num] :
% 9.17/5.35 ( ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M2 ) ) @ ( power_power_int @ A @ ( numeral_numeral_nat @ N2 ) ) )
% 9.17/5.35 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M2 @ N2 ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2565_power__add__numeral2,axiom,
% 9.17/5.35 ! [A: assn,M2: num,N2: num,B: assn] :
% 9.17/5.35 ( ( times_times_assn @ ( power_power_assn @ A @ ( numeral_numeral_nat @ M2 ) ) @ ( times_times_assn @ ( power_power_assn @ A @ ( numeral_numeral_nat @ N2 ) ) @ B ) )
% 9.17/5.35 = ( times_times_assn @ ( power_power_assn @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M2 @ N2 ) ) ) @ B ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2566_power__add__numeral2,axiom,
% 9.17/5.35 ! [A: rat,M2: num,N2: num,B: rat] :
% 9.17/5.35 ( ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ M2 ) ) @ ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ N2 ) ) @ B ) )
% 9.17/5.35 = ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M2 @ N2 ) ) ) @ B ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2567_power__add__numeral2,axiom,
% 9.17/5.35 ! [A: nat,M2: num,N2: num,B: nat] :
% 9.17/5.35 ( ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M2 ) ) @ ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ N2 ) ) @ B ) )
% 9.17/5.35 = ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M2 @ N2 ) ) ) @ B ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2568_power__add__numeral2,axiom,
% 9.17/5.35 ! [A: int,M2: num,N2: num,B: int] :
% 9.17/5.35 ( ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M2 ) ) @ ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ N2 ) ) @ B ) )
% 9.17/5.35 = ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M2 @ N2 ) ) ) @ B ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2569_numeral__less__floor,axiom,
% 9.17/5.35 ! [V: num,X: rat] :
% 9.17/5.35 ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim3151403230148437115or_rat @ X ) )
% 9.17/5.35 = ( ord_less_eq_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) @ X ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2570_floor__le__numeral,axiom,
% 9.17/5.35 ! [X: rat,V: num] :
% 9.17/5.35 ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X ) @ ( numeral_numeral_int @ V ) )
% 9.17/5.35 = ( ord_less_rat @ X @ ( plus_plus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2571_sum_Ocl__ivl__Suc,axiom,
% 9.17/5.35 ! [N2: nat,M2: nat,G: nat > code_integer] :
% 9.17/5.35 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M2 )
% 9.17/5.35 => ( ( groups7501900531339628137nteger @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N2 ) ) )
% 9.17/5.35 = zero_z3403309356797280102nteger ) )
% 9.17/5.35 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M2 )
% 9.17/5.35 => ( ( groups7501900531339628137nteger @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N2 ) ) )
% 9.17/5.35 = ( plus_p5714425477246183910nteger @ ( groups7501900531339628137nteger @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2572_sum_Ocl__ivl__Suc,axiom,
% 9.17/5.35 ! [N2: nat,M2: nat,G: nat > multis2468970476368604999at_nat] :
% 9.17/5.35 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M2 )
% 9.17/5.35 => ( ( groups6857163185585827899at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N2 ) ) )
% 9.17/5.35 = zero_z1048942125864253310at_nat ) )
% 9.17/5.35 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M2 )
% 9.17/5.35 => ( ( groups6857163185585827899at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N2 ) ) )
% 9.17/5.35 = ( plus_p7104986032573967614at_nat @ ( groups6857163185585827899at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2573_sum_Ocl__ivl__Suc,axiom,
% 9.17/5.35 ! [N2: nat,M2: nat,G: nat > rat] :
% 9.17/5.35 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M2 )
% 9.17/5.35 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N2 ) ) )
% 9.17/5.35 = zero_zero_rat ) )
% 9.17/5.35 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M2 )
% 9.17/5.35 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N2 ) ) )
% 9.17/5.35 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2574_sum_Ocl__ivl__Suc,axiom,
% 9.17/5.35 ! [N2: nat,M2: nat,G: nat > int] :
% 9.17/5.35 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M2 )
% 9.17/5.35 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N2 ) ) )
% 9.17/5.35 = zero_zero_int ) )
% 9.17/5.35 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M2 )
% 9.17/5.35 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N2 ) ) )
% 9.17/5.35 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2575_sum_Ocl__ivl__Suc,axiom,
% 9.17/5.35 ! [N2: nat,M2: nat,G: nat > nat] :
% 9.17/5.35 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M2 )
% 9.17/5.35 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N2 ) ) )
% 9.17/5.35 = zero_zero_nat ) )
% 9.17/5.35 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M2 )
% 9.17/5.35 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N2 ) ) )
% 9.17/5.35 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2576_ceiling__less__numeral,axiom,
% 9.17/5.35 ! [X: rat,V: num] :
% 9.17/5.35 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X ) @ ( numeral_numeral_int @ V ) )
% 9.17/5.35 = ( ord_less_eq_rat @ X @ ( minus_minus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2577_numeral__le__ceiling,axiom,
% 9.17/5.35 ! [V: num,X: rat] :
% 9.17/5.35 ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim2889992004027027881ng_rat @ X ) )
% 9.17/5.35 = ( ord_less_rat @ ( minus_minus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) @ X ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2578_neg__numeral__less__floor,axiom,
% 9.17/5.35 ! [V: num,X: rat] :
% 9.17/5.35 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim3151403230148437115or_rat @ X ) )
% 9.17/5.35 = ( ord_less_eq_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) @ X ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2579_floor__le__neg__numeral,axiom,
% 9.17/5.35 ! [X: rat,V: num] :
% 9.17/5.35 ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 9.17/5.35 = ( ord_less_rat @ X @ ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2580_ceiling__less__neg__numeral,axiom,
% 9.17/5.35 ! [X: rat,V: num] :
% 9.17/5.35 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 9.17/5.35 = ( ord_less_eq_rat @ X @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2581_neg__numeral__le__ceiling,axiom,
% 9.17/5.35 ! [V: num,X: rat] :
% 9.17/5.35 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim2889992004027027881ng_rat @ X ) )
% 9.17/5.35 = ( ord_less_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) @ X ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2582_nested__case__prod__simp,axiom,
% 9.17/5.35 ( produc27273713700761075at_nat
% 9.17/5.35 = ( ^ [F2: nat > nat > product_prod_nat_nat > product_prod_nat_nat,X3: product_prod_nat_nat,Y3: product_prod_nat_nat] :
% 9.17/5.35 ( produc2626176000494625587at_nat
% 9.17/5.35 @ ^ [A5: nat,B4: nat] : ( F2 @ A5 @ B4 @ Y3 )
% 9.17/5.35 @ X3 ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2583_nested__case__prod__simp,axiom,
% 9.17/5.35 ( produc8739625826339149834_nat_o
% 9.17/5.35 = ( ^ [F2: nat > nat > product_prod_nat_nat > $o,X3: product_prod_nat_nat,Y3: product_prod_nat_nat] :
% 9.17/5.35 ( produc6081775807080527818_nat_o
% 9.17/5.35 @ ^ [A5: nat,B4: nat] : ( F2 @ A5 @ B4 @ Y3 )
% 9.17/5.35 @ X3 ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2584_prod_Ocase__distrib,axiom,
% 9.17/5.35 ! [H3: nat > nat,F: nat > nat > nat,Prod: product_prod_nat_nat] :
% 9.17/5.35 ( ( H3 @ ( produc6842872674320459806at_nat @ F @ Prod ) )
% 9.17/5.35 = ( produc6842872674320459806at_nat
% 9.17/5.35 @ ^ [X12: nat,X23: nat] : ( H3 @ ( F @ X12 @ X23 ) )
% 9.17/5.35 @ Prod ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2585_prod_Ocase__distrib,axiom,
% 9.17/5.35 ! [H3: int > int,F: int > int > int,Prod: product_prod_int_int] :
% 9.17/5.35 ( ( H3 @ ( produc8211389475949308722nt_int @ F @ Prod ) )
% 9.17/5.35 = ( produc8211389475949308722nt_int
% 9.17/5.35 @ ^ [X12: int,X23: int] : ( H3 @ ( F @ X12 @ X23 ) )
% 9.17/5.35 @ Prod ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2586_prod_Ocase__distrib,axiom,
% 9.17/5.35 ! [H3: product_prod_int_int > int,F: int > int > product_prod_int_int,Prod: product_prod_int_int] :
% 9.17/5.35 ( ( H3 @ ( produc4245557441103728435nt_int @ F @ Prod ) )
% 9.17/5.35 = ( produc8211389475949308722nt_int
% 9.17/5.35 @ ^ [X12: int,X23: int] : ( H3 @ ( F @ X12 @ X23 ) )
% 9.17/5.35 @ Prod ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2587_prod_Ocase__distrib,axiom,
% 9.17/5.35 ! [H3: int > product_prod_int_int,F: int > int > int,Prod: product_prod_int_int] :
% 9.17/5.35 ( ( H3 @ ( produc8211389475949308722nt_int @ F @ Prod ) )
% 9.17/5.35 = ( produc4245557441103728435nt_int
% 9.17/5.35 @ ^ [X12: int,X23: int] : ( H3 @ ( F @ X12 @ X23 ) )
% 9.17/5.35 @ Prod ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2588_prod_Ocase__distrib,axiom,
% 9.17/5.35 ! [H3: nat > product_prod_nat_nat > $o,F: nat > nat > nat,Prod: product_prod_nat_nat] :
% 9.17/5.35 ( ( H3 @ ( produc6842872674320459806at_nat @ F @ Prod ) )
% 9.17/5.35 = ( produc8739625826339149834_nat_o
% 9.17/5.35 @ ^ [X12: nat,X23: nat] : ( H3 @ ( F @ X12 @ X23 ) )
% 9.17/5.35 @ Prod ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2589_prod_Ocase__distrib,axiom,
% 9.17/5.35 ! [H3: ( product_prod_nat_nat > $o ) > nat,F: nat > nat > product_prod_nat_nat > $o,Prod: product_prod_nat_nat] :
% 9.17/5.35 ( ( H3 @ ( produc8739625826339149834_nat_o @ F @ Prod ) )
% 9.17/5.35 = ( produc6842872674320459806at_nat
% 9.17/5.35 @ ^ [X12: nat,X23: nat] : ( H3 @ ( F @ X12 @ X23 ) )
% 9.17/5.35 @ Prod ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2590_prod_Ocase__distrib,axiom,
% 9.17/5.35 ! [H3: product_prod_int_int > product_prod_int_int,F: int > int > product_prod_int_int,Prod: product_prod_int_int] :
% 9.17/5.35 ( ( H3 @ ( produc4245557441103728435nt_int @ F @ Prod ) )
% 9.17/5.35 = ( produc4245557441103728435nt_int
% 9.17/5.35 @ ^ [X12: int,X23: int] : ( H3 @ ( F @ X12 @ X23 ) )
% 9.17/5.35 @ Prod ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2591_prod_Ocase__distrib,axiom,
% 9.17/5.35 ! [H3: nat > product_prod_nat_nat > product_prod_nat_nat,F: nat > nat > nat,Prod: product_prod_nat_nat] :
% 9.17/5.35 ( ( H3 @ ( produc6842872674320459806at_nat @ F @ Prod ) )
% 9.17/5.35 = ( produc27273713700761075at_nat
% 9.17/5.35 @ ^ [X12: nat,X23: nat] : ( H3 @ ( F @ X12 @ X23 ) )
% 9.17/5.35 @ Prod ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2592_prod_Ocase__distrib,axiom,
% 9.17/5.35 ! [H3: ( product_prod_nat_nat > product_prod_nat_nat ) > nat,F: nat > nat > product_prod_nat_nat > product_prod_nat_nat,Prod: product_prod_nat_nat] :
% 9.17/5.35 ( ( H3 @ ( produc27273713700761075at_nat @ F @ Prod ) )
% 9.17/5.35 = ( produc6842872674320459806at_nat
% 9.17/5.35 @ ^ [X12: nat,X23: nat] : ( H3 @ ( F @ X12 @ X23 ) )
% 9.17/5.35 @ Prod ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2593_prod_Ocase__distrib,axiom,
% 9.17/5.35 ! [H3: ( product_prod_nat_nat > $o ) > product_prod_nat_nat > $o,F: nat > nat > product_prod_nat_nat > $o,Prod: product_prod_nat_nat] :
% 9.17/5.35 ( ( H3 @ ( produc8739625826339149834_nat_o @ F @ Prod ) )
% 9.17/5.35 = ( produc8739625826339149834_nat_o
% 9.17/5.35 @ ^ [X12: nat,X23: nat] : ( H3 @ ( F @ X12 @ X23 ) )
% 9.17/5.35 @ Prod ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2594_sum_OatLeast__Suc__atMost__Suc__shift,axiom,
% 9.17/5.35 ! [G: nat > nat,M2: nat,N2: nat] :
% 9.17/5.35 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ ( suc @ N2 ) ) )
% 9.17/5.35 = ( groups3542108847815614940at_nat @ ( comp_nat_nat_nat @ G @ suc ) @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2595_sum_OatLeastAtMost__shift__bounds,axiom,
% 9.17/5.35 ! [G: nat > nat,M2: nat,K: nat,N2: nat] :
% 9.17/5.35 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M2 @ K ) @ ( plus_plus_nat @ N2 @ K ) ) )
% 9.17/5.35 = ( groups3542108847815614940at_nat @ ( comp_nat_nat_nat @ G @ ( plus_plus_nat @ K ) ) @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2596_split__cong,axiom,
% 9.17/5.35 ! [Q3: product_prod_nat_nat,F: nat > nat > nat,G: nat > nat > nat,P4: product_prod_nat_nat] :
% 9.17/5.35 ( ! [X4: nat,Y5: nat] :
% 9.17/5.35 ( ( ( product_Pair_nat_nat @ X4 @ Y5 )
% 9.17/5.35 = Q3 )
% 9.17/5.35 => ( ( F @ X4 @ Y5 )
% 9.17/5.35 = ( G @ X4 @ Y5 ) ) )
% 9.17/5.35 => ( ( P4 = Q3 )
% 9.17/5.35 => ( ( produc6842872674320459806at_nat @ F @ P4 )
% 9.17/5.35 = ( produc6842872674320459806at_nat @ G @ Q3 ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2597_split__cong,axiom,
% 9.17/5.35 ! [Q3: product_prod_nat_nat,F: nat > nat > product_prod_nat_nat > product_prod_nat_nat,G: nat > nat > product_prod_nat_nat > product_prod_nat_nat,P4: product_prod_nat_nat] :
% 9.17/5.35 ( ! [X4: nat,Y5: nat] :
% 9.17/5.35 ( ( ( product_Pair_nat_nat @ X4 @ Y5 )
% 9.17/5.35 = Q3 )
% 9.17/5.35 => ( ( F @ X4 @ Y5 )
% 9.17/5.35 = ( G @ X4 @ Y5 ) ) )
% 9.17/5.35 => ( ( P4 = Q3 )
% 9.17/5.35 => ( ( produc27273713700761075at_nat @ F @ P4 )
% 9.17/5.35 = ( produc27273713700761075at_nat @ G @ Q3 ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2598_split__cong,axiom,
% 9.17/5.35 ! [Q3: product_prod_nat_nat,F: nat > nat > product_prod_nat_nat > $o,G: nat > nat > product_prod_nat_nat > $o,P4: product_prod_nat_nat] :
% 9.17/5.35 ( ! [X4: nat,Y5: nat] :
% 9.17/5.35 ( ( ( product_Pair_nat_nat @ X4 @ Y5 )
% 9.17/5.35 = Q3 )
% 9.17/5.35 => ( ( F @ X4 @ Y5 )
% 9.17/5.35 = ( G @ X4 @ Y5 ) ) )
% 9.17/5.35 => ( ( P4 = Q3 )
% 9.17/5.35 => ( ( produc8739625826339149834_nat_o @ F @ P4 )
% 9.17/5.35 = ( produc8739625826339149834_nat_o @ G @ Q3 ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2599_split__cong,axiom,
% 9.17/5.35 ! [Q3: product_prod_int_int,F: int > int > product_prod_int_int,G: int > int > product_prod_int_int,P4: product_prod_int_int] :
% 9.17/5.35 ( ! [X4: int,Y5: int] :
% 9.17/5.35 ( ( ( product_Pair_int_int @ X4 @ Y5 )
% 9.17/5.35 = Q3 )
% 9.17/5.35 => ( ( F @ X4 @ Y5 )
% 9.17/5.35 = ( G @ X4 @ Y5 ) ) )
% 9.17/5.35 => ( ( P4 = Q3 )
% 9.17/5.35 => ( ( produc4245557441103728435nt_int @ F @ P4 )
% 9.17/5.35 = ( produc4245557441103728435nt_int @ G @ Q3 ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2600_split__cong,axiom,
% 9.17/5.35 ! [Q3: product_prod_int_int,F: int > int > int,G: int > int > int,P4: product_prod_int_int] :
% 9.17/5.35 ( ! [X4: int,Y5: int] :
% 9.17/5.35 ( ( ( product_Pair_int_int @ X4 @ Y5 )
% 9.17/5.35 = Q3 )
% 9.17/5.35 => ( ( F @ X4 @ Y5 )
% 9.17/5.35 = ( G @ X4 @ Y5 ) ) )
% 9.17/5.35 => ( ( P4 = Q3 )
% 9.17/5.35 => ( ( produc8211389475949308722nt_int @ F @ P4 )
% 9.17/5.35 = ( produc8211389475949308722nt_int @ G @ Q3 ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2601_old_Oprod_Ocase,axiom,
% 9.17/5.35 ! [F: nat > nat > nat,X1: nat,X2: nat] :
% 9.17/5.35 ( ( produc6842872674320459806at_nat @ F @ ( product_Pair_nat_nat @ X1 @ X2 ) )
% 9.17/5.35 = ( F @ X1 @ X2 ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2602_old_Oprod_Ocase,axiom,
% 9.17/5.35 ! [F: nat > nat > product_prod_nat_nat > product_prod_nat_nat,X1: nat,X2: nat] :
% 9.17/5.35 ( ( produc27273713700761075at_nat @ F @ ( product_Pair_nat_nat @ X1 @ X2 ) )
% 9.17/5.35 = ( F @ X1 @ X2 ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2603_old_Oprod_Ocase,axiom,
% 9.17/5.35 ! [F: nat > nat > product_prod_nat_nat > $o,X1: nat,X2: nat] :
% 9.17/5.35 ( ( produc8739625826339149834_nat_o @ F @ ( product_Pair_nat_nat @ X1 @ X2 ) )
% 9.17/5.35 = ( F @ X1 @ X2 ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2604_old_Oprod_Ocase,axiom,
% 9.17/5.35 ! [F: int > int > product_prod_int_int,X1: int,X2: int] :
% 9.17/5.35 ( ( produc4245557441103728435nt_int @ F @ ( product_Pair_int_int @ X1 @ X2 ) )
% 9.17/5.35 = ( F @ X1 @ X2 ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2605_old_Oprod_Ocase,axiom,
% 9.17/5.35 ! [F: int > int > int,X1: int,X2: int] :
% 9.17/5.35 ( ( produc8211389475949308722nt_int @ F @ ( product_Pair_int_int @ X1 @ X2 ) )
% 9.17/5.35 = ( F @ X1 @ X2 ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2606_uminus__int_Oabs__eq,axiom,
% 9.17/5.35 ! [X: product_prod_nat_nat] :
% 9.17/5.35 ( ( uminus_uminus_int @ ( abs_Integ @ X ) )
% 9.17/5.35 = ( abs_Integ
% 9.17/5.35 @ ( produc2626176000494625587at_nat
% 9.17/5.35 @ ^ [X3: nat,Y3: nat] : ( product_Pair_nat_nat @ Y3 @ X3 )
% 9.17/5.35 @ X ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2607_case__prod__Pair__iden,axiom,
% 9.17/5.35 ! [P4: produc1908205239877642774nteger] :
% 9.17/5.35 ( ( produc6512950862096126219nteger @ produc8603105652947943368nteger @ P4 )
% 9.17/5.35 = P4 ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2608_case__prod__Pair__iden,axiom,
% 9.17/5.35 ! [P4: produc3925858234332021118et_nat] :
% 9.17/5.35 ( ( produc4058941399401191971et_nat @ produc5001842942810119800et_nat @ P4 )
% 9.17/5.35 = P4 ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2609_case__prod__Pair__iden,axiom,
% 9.17/5.35 ! [P4: produc2732055786443039994et_nat] :
% 9.17/5.35 ( ( produc2377985495875741467et_nat @ produc2245416461498447860et_nat @ P4 )
% 9.17/5.35 = P4 ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2610_case__prod__Pair__iden,axiom,
% 9.17/5.35 ! [P4: produc2285326912895808259nt_int] :
% 9.17/5.35 ( ( produc8492565224438309093nt_int @ produc5700946648718959541nt_int @ P4 )
% 9.17/5.35 = P4 ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2611_case__prod__Pair__iden,axiom,
% 9.17/5.35 ! [P4: produc7773217078559923341nt_int] :
% 9.17/5.35 ( ( produc5122537100556696953nt_int @ produc4305682042979456191nt_int @ P4 )
% 9.17/5.35 = P4 ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2612_case__prod__Pair__iden,axiom,
% 9.17/5.35 ! [P4: product_prod_int_int] :
% 9.17/5.35 ( ( produc4245557441103728435nt_int @ product_Pair_int_int @ P4 )
% 9.17/5.35 = P4 ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2613_sum_Oshift__bounds__cl__Suc__ivl,axiom,
% 9.17/5.35 ! [G: nat > nat,M2: nat,N2: nat] :
% 9.17/5.35 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ ( suc @ N2 ) ) )
% 9.17/5.35 = ( groups3542108847815614940at_nat
% 9.17/5.35 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 9.17/5.35 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2614_sum_Oshift__bounds__cl__nat__ivl,axiom,
% 9.17/5.35 ! [G: nat > nat,M2: nat,K: nat,N2: nat] :
% 9.17/5.35 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M2 @ K ) @ ( plus_plus_nat @ N2 @ K ) ) )
% 9.17/5.35 = ( groups3542108847815614940at_nat
% 9.17/5.35 @ ^ [I3: nat] : ( G @ ( plus_plus_nat @ I3 @ K ) )
% 9.17/5.35 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2615_cond__case__prod__eta,axiom,
% 9.17/5.35 ! [F: nat > nat > nat,G: product_prod_nat_nat > nat] :
% 9.17/5.35 ( ! [X4: nat,Y5: nat] :
% 9.17/5.35 ( ( F @ X4 @ Y5 )
% 9.17/5.35 = ( G @ ( product_Pair_nat_nat @ X4 @ Y5 ) ) )
% 9.17/5.35 => ( ( produc6842872674320459806at_nat @ F )
% 9.17/5.35 = G ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2616_cond__case__prod__eta,axiom,
% 9.17/5.35 ! [F: nat > nat > product_prod_nat_nat > product_prod_nat_nat,G: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat] :
% 9.17/5.35 ( ! [X4: nat,Y5: nat] :
% 9.17/5.35 ( ( F @ X4 @ Y5 )
% 9.17/5.35 = ( G @ ( product_Pair_nat_nat @ X4 @ Y5 ) ) )
% 9.17/5.35 => ( ( produc27273713700761075at_nat @ F )
% 9.17/5.35 = G ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2617_cond__case__prod__eta,axiom,
% 9.17/5.35 ! [F: nat > nat > product_prod_nat_nat > $o,G: product_prod_nat_nat > product_prod_nat_nat > $o] :
% 9.17/5.35 ( ! [X4: nat,Y5: nat] :
% 9.17/5.35 ( ( F @ X4 @ Y5 )
% 9.17/5.35 = ( G @ ( product_Pair_nat_nat @ X4 @ Y5 ) ) )
% 9.17/5.35 => ( ( produc8739625826339149834_nat_o @ F )
% 9.17/5.35 = G ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2618_cond__case__prod__eta,axiom,
% 9.17/5.35 ! [F: int > int > product_prod_int_int,G: product_prod_int_int > product_prod_int_int] :
% 9.17/5.35 ( ! [X4: int,Y5: int] :
% 9.17/5.35 ( ( F @ X4 @ Y5 )
% 9.17/5.35 = ( G @ ( product_Pair_int_int @ X4 @ Y5 ) ) )
% 9.17/5.35 => ( ( produc4245557441103728435nt_int @ F )
% 9.17/5.35 = G ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2619_cond__case__prod__eta,axiom,
% 9.17/5.35 ! [F: int > int > int,G: product_prod_int_int > int] :
% 9.17/5.35 ( ! [X4: int,Y5: int] :
% 9.17/5.35 ( ( F @ X4 @ Y5 )
% 9.17/5.35 = ( G @ ( product_Pair_int_int @ X4 @ Y5 ) ) )
% 9.17/5.35 => ( ( produc8211389475949308722nt_int @ F )
% 9.17/5.35 = G ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2620_case__prod__eta,axiom,
% 9.17/5.35 ! [F: product_prod_nat_nat > nat] :
% 9.17/5.35 ( ( produc6842872674320459806at_nat
% 9.17/5.35 @ ^ [X3: nat,Y3: nat] : ( F @ ( product_Pair_nat_nat @ X3 @ Y3 ) ) )
% 9.17/5.35 = F ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2621_case__prod__eta,axiom,
% 9.17/5.35 ! [F: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat] :
% 9.17/5.35 ( ( produc27273713700761075at_nat
% 9.17/5.35 @ ^ [X3: nat,Y3: nat] : ( F @ ( product_Pair_nat_nat @ X3 @ Y3 ) ) )
% 9.17/5.35 = F ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2622_case__prod__eta,axiom,
% 9.17/5.35 ! [F: product_prod_nat_nat > product_prod_nat_nat > $o] :
% 9.17/5.35 ( ( produc8739625826339149834_nat_o
% 9.17/5.35 @ ^ [X3: nat,Y3: nat] : ( F @ ( product_Pair_nat_nat @ X3 @ Y3 ) ) )
% 9.17/5.35 = F ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2623_case__prod__eta,axiom,
% 9.17/5.35 ! [F: product_prod_int_int > product_prod_int_int] :
% 9.17/5.35 ( ( produc4245557441103728435nt_int
% 9.17/5.35 @ ^ [X3: int,Y3: int] : ( F @ ( product_Pair_int_int @ X3 @ Y3 ) ) )
% 9.17/5.35 = F ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2624_case__prod__eta,axiom,
% 9.17/5.35 ! [F: product_prod_int_int > int] :
% 9.17/5.35 ( ( produc8211389475949308722nt_int
% 9.17/5.35 @ ^ [X3: int,Y3: int] : ( F @ ( product_Pair_int_int @ X3 @ Y3 ) ) )
% 9.17/5.35 = F ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2625_case__prodE2,axiom,
% 9.17/5.35 ! [Q: nat > $o,P: nat > nat > nat,Z: product_prod_nat_nat] :
% 9.17/5.35 ( ( Q @ ( produc6842872674320459806at_nat @ P @ Z ) )
% 9.17/5.35 => ~ ! [X4: nat,Y5: nat] :
% 9.17/5.35 ( ( Z
% 9.17/5.35 = ( product_Pair_nat_nat @ X4 @ Y5 ) )
% 9.17/5.35 => ~ ( Q @ ( P @ X4 @ Y5 ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2626_case__prodE2,axiom,
% 9.17/5.35 ! [Q: ( product_prod_nat_nat > product_prod_nat_nat ) > $o,P: nat > nat > product_prod_nat_nat > product_prod_nat_nat,Z: product_prod_nat_nat] :
% 9.17/5.35 ( ( Q @ ( produc27273713700761075at_nat @ P @ Z ) )
% 9.17/5.35 => ~ ! [X4: nat,Y5: nat] :
% 9.17/5.35 ( ( Z
% 9.17/5.35 = ( product_Pair_nat_nat @ X4 @ Y5 ) )
% 9.17/5.35 => ~ ( Q @ ( P @ X4 @ Y5 ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2627_case__prodE2,axiom,
% 9.17/5.35 ! [Q: ( product_prod_nat_nat > $o ) > $o,P: nat > nat > product_prod_nat_nat > $o,Z: product_prod_nat_nat] :
% 9.17/5.35 ( ( Q @ ( produc8739625826339149834_nat_o @ P @ Z ) )
% 9.17/5.35 => ~ ! [X4: nat,Y5: nat] :
% 9.17/5.35 ( ( Z
% 9.17/5.35 = ( product_Pair_nat_nat @ X4 @ Y5 ) )
% 9.17/5.35 => ~ ( Q @ ( P @ X4 @ Y5 ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2628_case__prodE2,axiom,
% 9.17/5.35 ! [Q: product_prod_int_int > $o,P: int > int > product_prod_int_int,Z: product_prod_int_int] :
% 9.17/5.35 ( ( Q @ ( produc4245557441103728435nt_int @ P @ Z ) )
% 9.17/5.35 => ~ ! [X4: int,Y5: int] :
% 9.17/5.35 ( ( Z
% 9.17/5.35 = ( product_Pair_int_int @ X4 @ Y5 ) )
% 9.17/5.35 => ~ ( Q @ ( P @ X4 @ Y5 ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2629_case__prodE2,axiom,
% 9.17/5.35 ! [Q: int > $o,P: int > int > int,Z: product_prod_int_int] :
% 9.17/5.35 ( ( Q @ ( produc8211389475949308722nt_int @ P @ Z ) )
% 9.17/5.35 => ~ ! [X4: int,Y5: int] :
% 9.17/5.35 ( ( Z
% 9.17/5.35 = ( product_Pair_int_int @ X4 @ Y5 ) )
% 9.17/5.35 => ~ ( Q @ ( P @ X4 @ Y5 ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2630_eq__Abs__Integ,axiom,
% 9.17/5.35 ! [Z: int] :
% 9.17/5.35 ~ ! [X4: nat,Y5: nat] :
% 9.17/5.35 ( Z
% 9.17/5.35 != ( abs_Integ @ ( product_Pair_nat_nat @ X4 @ Y5 ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2631_one__le__numeral,axiom,
% 9.17/5.35 ! [N2: num] : ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ N2 ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2632_one__le__numeral,axiom,
% 9.17/5.35 ! [N2: num] : ( ord_le1926595141338095240atural @ one_one_Code_natural @ ( numera5444537566228673987atural @ N2 ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2633_one__le__numeral,axiom,
% 9.17/5.35 ! [N2: num] : ( ord_less_eq_rat @ one_one_rat @ ( numeral_numeral_rat @ N2 ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2634_one__le__numeral,axiom,
% 9.17/5.35 ! [N2: num] : ( ord_less_eq_nat @ one_one_nat @ ( numeral_numeral_nat @ N2 ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2635_one__le__numeral,axiom,
% 9.17/5.35 ! [N2: num] : ( ord_less_eq_int @ one_one_int @ ( numeral_numeral_int @ N2 ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2636_not__numeral__less__one,axiom,
% 9.17/5.35 ! [N2: num] :
% 9.17/5.35 ~ ( ord_less_nat @ ( numeral_numeral_nat @ N2 ) @ one_one_nat ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2637_not__numeral__less__one,axiom,
% 9.17/5.35 ! [N2: num] :
% 9.17/5.35 ~ ( ord_less_int @ ( numeral_numeral_int @ N2 ) @ one_one_int ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2638_not__numeral__less__one,axiom,
% 9.17/5.35 ! [N2: num] :
% 9.17/5.35 ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ N2 ) @ one_one_Code_integer ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2639_not__numeral__less__one,axiom,
% 9.17/5.35 ! [N2: num] :
% 9.17/5.35 ~ ( ord_less_rat @ ( numeral_numeral_rat @ N2 ) @ one_one_rat ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2640_not__numeral__less__one,axiom,
% 9.17/5.35 ! [N2: num] :
% 9.17/5.35 ~ ( ord_le5570908160329646204atural @ ( numera5444537566228673987atural @ N2 ) @ one_one_Code_natural ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2641_one__plus__numeral__commute,axiom,
% 9.17/5.35 ! [X: num] :
% 9.17/5.35 ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ X ) )
% 9.17/5.35 = ( plus_plus_nat @ ( numeral_numeral_nat @ X ) @ one_one_nat ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2642_one__plus__numeral__commute,axiom,
% 9.17/5.35 ! [X: num] :
% 9.17/5.35 ( ( plus_plus_int @ one_one_int @ ( numeral_numeral_int @ X ) )
% 9.17/5.35 = ( plus_plus_int @ ( numeral_numeral_int @ X ) @ one_one_int ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2643_one__plus__numeral__commute,axiom,
% 9.17/5.35 ! [X: num] :
% 9.17/5.35 ( ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ X ) )
% 9.17/5.35 = ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ X ) @ one_one_Code_integer ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2644_one__plus__numeral__commute,axiom,
% 9.17/5.35 ! [X: num] :
% 9.17/5.35 ( ( plus_plus_rat @ one_one_rat @ ( numeral_numeral_rat @ X ) )
% 9.17/5.35 = ( plus_plus_rat @ ( numeral_numeral_rat @ X ) @ one_one_rat ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2645_one__plus__numeral__commute,axiom,
% 9.17/5.35 ! [X: num] :
% 9.17/5.35 ( ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( numera5444537566228673987atural @ X ) )
% 9.17/5.35 = ( plus_p4538020629002901425atural @ ( numera5444537566228673987atural @ X ) @ one_one_Code_natural ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2646_numeral__Bit0,axiom,
% 9.17/5.35 ! [N2: num] :
% 9.17/5.35 ( ( numeral_numeral_nat @ ( bit0 @ N2 ) )
% 9.17/5.35 = ( plus_plus_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ N2 ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2647_numeral__Bit0,axiom,
% 9.17/5.35 ! [N2: num] :
% 9.17/5.35 ( ( numeral_numeral_int @ ( bit0 @ N2 ) )
% 9.17/5.35 = ( plus_plus_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ N2 ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2648_numeral__Bit0,axiom,
% 9.17/5.35 ! [N2: num] :
% 9.17/5.35 ( ( numera6620942414471956472nteger @ ( bit0 @ N2 ) )
% 9.17/5.35 = ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ N2 ) @ ( numera6620942414471956472nteger @ N2 ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2649_numeral__Bit0,axiom,
% 9.17/5.35 ! [N2: num] :
% 9.17/5.35 ( ( numeral_numeral_rat @ ( bit0 @ N2 ) )
% 9.17/5.35 = ( plus_plus_rat @ ( numeral_numeral_rat @ N2 ) @ ( numeral_numeral_rat @ N2 ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2650_numeral__Bit0,axiom,
% 9.17/5.35 ! [N2: num] :
% 9.17/5.35 ( ( numera5444537566228673987atural @ ( bit0 @ N2 ) )
% 9.17/5.35 = ( plus_p4538020629002901425atural @ ( numera5444537566228673987atural @ N2 ) @ ( numera5444537566228673987atural @ N2 ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2651_one__neq__neg__numeral,axiom,
% 9.17/5.35 ! [N2: num] :
% 9.17/5.35 ( one_one_int
% 9.17/5.35 != ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2652_one__neq__neg__numeral,axiom,
% 9.17/5.35 ! [N2: num] :
% 9.17/5.35 ( one_one_Code_integer
% 9.17/5.35 != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2653_one__neq__neg__numeral,axiom,
% 9.17/5.35 ! [N2: num] :
% 9.17/5.35 ( one_one_rat
% 9.17/5.35 != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2654_numeral__neq__neg__one,axiom,
% 9.17/5.35 ! [N2: num] :
% 9.17/5.35 ( ( numeral_numeral_int @ N2 )
% 9.17/5.35 != ( uminus_uminus_int @ one_one_int ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2655_numeral__neq__neg__one,axiom,
% 9.17/5.35 ! [N2: num] :
% 9.17/5.35 ( ( numera6620942414471956472nteger @ N2 )
% 9.17/5.35 != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2656_numeral__neq__neg__one,axiom,
% 9.17/5.35 ! [N2: num] :
% 9.17/5.35 ( ( numeral_numeral_rat @ N2 )
% 9.17/5.35 != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2657_uncurry__def,axiom,
% 9.17/5.35 uncurry_nat_nat_nat = produc6842872674320459806at_nat ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2658_uncurry__def,axiom,
% 9.17/5.35 uncurr8011562610307062878at_nat = produc27273713700761075at_nat ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2659_uncurry__def,axiom,
% 9.17/5.35 uncurr7511940902602773877_nat_o = produc8739625826339149834_nat_o ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2660_uncurry__def,axiom,
% 9.17/5.35 uncurr7650761721940715016nt_int = produc4245557441103728435nt_int ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2661_uncurry__def,axiom,
% 9.17/5.35 uncurry_int_int_int = produc8211389475949308722nt_int ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2662_internal__case__prod__def,axiom,
% 9.17/5.35 produc6557683772455589876at_nat = produc6842872674320459806at_nat ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2663_internal__case__prod__def,axiom,
% 9.17/5.35 produc1854806715440696265at_nat = produc27273713700761075at_nat ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2664_internal__case__prod__def,axiom,
% 9.17/5.35 produc4780622933104268256_nat_o = produc8739625826339149834_nat_o ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2665_internal__case__prod__def,axiom,
% 9.17/5.35 produc297006045350968285nt_int = produc4245557441103728435nt_int ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2666_internal__case__prod__def,axiom,
% 9.17/5.35 produc7926200574084438792nt_int = produc8211389475949308722nt_int ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2667_sum_OatLeastAtMost__rev,axiom,
% 9.17/5.35 ! [G: nat > nat,N2: nat,M2: nat] :
% 9.17/5.35 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ N2 @ M2 ) )
% 9.17/5.35 = ( groups3542108847815614940at_nat
% 9.17/5.35 @ ^ [I3: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M2 @ N2 ) @ I3 ) )
% 9.17/5.35 @ ( set_or1269000886237332187st_nat @ N2 @ M2 ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2668_numeral__code_I2_J,axiom,
% 9.17/5.35 ! [N2: num] :
% 9.17/5.35 ( ( numeral_numeral_nat @ ( bit0 @ N2 ) )
% 9.17/5.35 = ( plus_plus_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ N2 ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2669_numeral__code_I2_J,axiom,
% 9.17/5.35 ! [N2: num] :
% 9.17/5.35 ( ( numeral_numeral_int @ ( bit0 @ N2 ) )
% 9.17/5.35 = ( plus_plus_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ N2 ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2670_numeral__code_I2_J,axiom,
% 9.17/5.35 ! [N2: num] :
% 9.17/5.35 ( ( numera6620942414471956472nteger @ ( bit0 @ N2 ) )
% 9.17/5.35 = ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ N2 ) @ ( numera6620942414471956472nteger @ N2 ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2671_numeral__code_I2_J,axiom,
% 9.17/5.35 ! [N2: num] :
% 9.17/5.35 ( ( numeral_numeral_rat @ ( bit0 @ N2 ) )
% 9.17/5.35 = ( plus_plus_rat @ ( numeral_numeral_rat @ N2 ) @ ( numeral_numeral_rat @ N2 ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2672_numeral__code_I2_J,axiom,
% 9.17/5.35 ! [N2: num] :
% 9.17/5.35 ( ( numera5444537566228673987atural @ ( bit0 @ N2 ) )
% 9.17/5.35 = ( plus_p4538020629002901425atural @ ( numera5444537566228673987atural @ N2 ) @ ( numera5444537566228673987atural @ N2 ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2673_sum__shift__lb__Suc0__0,axiom,
% 9.17/5.35 ! [F: nat > code_integer,K: nat] :
% 9.17/5.35 ( ( ( F @ zero_zero_nat )
% 9.17/5.35 = zero_z3403309356797280102nteger )
% 9.17/5.35 => ( ( groups7501900531339628137nteger @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 9.17/5.35 = ( groups7501900531339628137nteger @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2674_sum__shift__lb__Suc0__0,axiom,
% 9.17/5.35 ! [F: nat > multis2468970476368604999at_nat,K: nat] :
% 9.17/5.35 ( ( ( F @ zero_zero_nat )
% 9.17/5.35 = zero_z1048942125864253310at_nat )
% 9.17/5.35 => ( ( groups6857163185585827899at_nat @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 9.17/5.35 = ( groups6857163185585827899at_nat @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2675_sum__shift__lb__Suc0__0,axiom,
% 9.17/5.35 ! [F: nat > rat,K: nat] :
% 9.17/5.35 ( ( ( F @ zero_zero_nat )
% 9.17/5.35 = zero_zero_rat )
% 9.17/5.35 => ( ( groups2906978787729119204at_rat @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 9.17/5.35 = ( groups2906978787729119204at_rat @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2676_sum__shift__lb__Suc0__0,axiom,
% 9.17/5.35 ! [F: nat > int,K: nat] :
% 9.17/5.35 ( ( ( F @ zero_zero_nat )
% 9.17/5.35 = zero_zero_int )
% 9.17/5.35 => ( ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 9.17/5.35 = ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2677_sum__shift__lb__Suc0__0,axiom,
% 9.17/5.35 ! [F: nat > nat,K: nat] :
% 9.17/5.35 ( ( ( F @ zero_zero_nat )
% 9.17/5.35 = zero_zero_nat )
% 9.17/5.35 => ( ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 9.17/5.35 = ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2678_sum_OatLeast0__atMost__Suc,axiom,
% 9.17/5.35 ! [G: nat > multis2468970476368604999at_nat,N2: nat] :
% 9.17/5.35 ( ( groups6857163185585827899at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 9.17/5.35 = ( plus_p7104986032573967614at_nat @ ( groups6857163185585827899at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2679_sum_OatLeast0__atMost__Suc,axiom,
% 9.17/5.35 ! [G: nat > rat,N2: nat] :
% 9.17/5.35 ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 9.17/5.35 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2680_sum_OatLeast0__atMost__Suc,axiom,
% 9.17/5.35 ! [G: nat > int,N2: nat] :
% 9.17/5.35 ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 9.17/5.35 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2681_sum_OatLeast0__atMost__Suc,axiom,
% 9.17/5.35 ! [G: nat > nat,N2: nat] :
% 9.17/5.35 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 9.17/5.35 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2682_sum_OatLeast0__atMost__Suc__shift,axiom,
% 9.17/5.35 ! [G: nat > multis2468970476368604999at_nat,N2: nat] :
% 9.17/5.35 ( ( groups6857163185585827899at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 9.17/5.35 = ( plus_p7104986032573967614at_nat @ ( G @ zero_zero_nat ) @ ( groups6857163185585827899at_nat @ ( comp_n8698576032424989604at_nat @ G @ suc ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2683_sum_OatLeast0__atMost__Suc__shift,axiom,
% 9.17/5.35 ! [G: nat > rat,N2: nat] :
% 9.17/5.35 ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 9.17/5.35 = ( plus_plus_rat @ ( G @ zero_zero_nat ) @ ( groups2906978787729119204at_rat @ ( comp_nat_rat_nat @ G @ suc ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2684_sum_OatLeast0__atMost__Suc__shift,axiom,
% 9.17/5.35 ! [G: nat > int,N2: nat] :
% 9.17/5.35 ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 9.17/5.35 = ( plus_plus_int @ ( G @ zero_zero_nat ) @ ( groups3539618377306564664at_int @ ( comp_nat_int_nat @ G @ suc ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2685_sum_OatLeast0__atMost__Suc__shift,axiom,
% 9.17/5.35 ! [G: nat > nat,N2: nat] :
% 9.17/5.35 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 9.17/5.35 = ( plus_plus_nat @ ( G @ zero_zero_nat ) @ ( groups3542108847815614940at_nat @ ( comp_nat_nat_nat @ G @ suc ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2686_sum_OatLeast__Suc__atMost,axiom,
% 9.17/5.35 ! [M2: nat,N2: nat,G: nat > multis2468970476368604999at_nat] :
% 9.17/5.35 ( ( ord_less_eq_nat @ M2 @ N2 )
% 9.17/5.35 => ( ( groups6857163185585827899at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 9.17/5.35 = ( plus_p7104986032573967614at_nat @ ( G @ M2 ) @ ( groups6857163185585827899at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N2 ) ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2687_sum_OatLeast__Suc__atMost,axiom,
% 9.17/5.35 ! [M2: nat,N2: nat,G: nat > rat] :
% 9.17/5.35 ( ( ord_less_eq_nat @ M2 @ N2 )
% 9.17/5.35 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 9.17/5.35 = ( plus_plus_rat @ ( G @ M2 ) @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N2 ) ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2688_sum_OatLeast__Suc__atMost,axiom,
% 9.17/5.35 ! [M2: nat,N2: nat,G: nat > int] :
% 9.17/5.35 ( ( ord_less_eq_nat @ M2 @ N2 )
% 9.17/5.35 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 9.17/5.35 = ( plus_plus_int @ ( G @ M2 ) @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N2 ) ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2689_sum_OatLeast__Suc__atMost,axiom,
% 9.17/5.35 ! [M2: nat,N2: nat,G: nat > nat] :
% 9.17/5.35 ( ( ord_less_eq_nat @ M2 @ N2 )
% 9.17/5.35 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 9.17/5.35 = ( plus_plus_nat @ ( G @ M2 ) @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N2 ) ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2690_sum_Onat__ivl__Suc_H,axiom,
% 9.17/5.35 ! [M2: nat,N2: nat,G: nat > multis2468970476368604999at_nat] :
% 9.17/5.35 ( ( ord_less_eq_nat @ M2 @ ( suc @ N2 ) )
% 9.17/5.35 => ( ( groups6857163185585827899at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N2 ) ) )
% 9.17/5.35 = ( plus_p7104986032573967614at_nat @ ( G @ ( suc @ N2 ) ) @ ( groups6857163185585827899at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2691_sum_Onat__ivl__Suc_H,axiom,
% 9.17/5.35 ! [M2: nat,N2: nat,G: nat > rat] :
% 9.17/5.35 ( ( ord_less_eq_nat @ M2 @ ( suc @ N2 ) )
% 9.17/5.35 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N2 ) ) )
% 9.17/5.35 = ( plus_plus_rat @ ( G @ ( suc @ N2 ) ) @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2692_sum_Onat__ivl__Suc_H,axiom,
% 9.17/5.35 ! [M2: nat,N2: nat,G: nat > int] :
% 9.17/5.35 ( ( ord_less_eq_nat @ M2 @ ( suc @ N2 ) )
% 9.17/5.35 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N2 ) ) )
% 9.17/5.35 = ( plus_plus_int @ ( G @ ( suc @ N2 ) ) @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2693_sum_Onat__ivl__Suc_H,axiom,
% 9.17/5.35 ! [M2: nat,N2: nat,G: nat > nat] :
% 9.17/5.35 ( ( ord_less_eq_nat @ M2 @ ( suc @ N2 ) )
% 9.17/5.35 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N2 ) ) )
% 9.17/5.35 = ( plus_plus_nat @ ( G @ ( suc @ N2 ) ) @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2694_neg__numeral__le__one,axiom,
% 9.17/5.35 ! [M2: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ one_one_Code_integer ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2695_neg__numeral__le__one,axiom,
% 9.17/5.35 ! [M2: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ one_one_rat ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2696_neg__numeral__le__one,axiom,
% 9.17/5.35 ! [M2: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ one_one_int ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2697_neg__one__le__numeral,axiom,
% 9.17/5.35 ! [M2: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ M2 ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2698_neg__one__le__numeral,axiom,
% 9.17/5.35 ! [M2: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ M2 ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2699_neg__one__le__numeral,axiom,
% 9.17/5.35 ! [M2: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ M2 ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2700_neg__numeral__le__neg__one,axiom,
% 9.17/5.35 ! [M2: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2701_neg__numeral__le__neg__one,axiom,
% 9.17/5.35 ! [M2: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2702_neg__numeral__le__neg__one,axiom,
% 9.17/5.35 ! [M2: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2703_not__numeral__le__neg__one,axiom,
% 9.17/5.35 ! [M2: num] :
% 9.17/5.35 ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ M2 ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2704_not__numeral__le__neg__one,axiom,
% 9.17/5.35 ! [M2: num] :
% 9.17/5.35 ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ M2 ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2705_not__numeral__le__neg__one,axiom,
% 9.17/5.35 ! [M2: num] :
% 9.17/5.35 ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2706_not__one__le__neg__numeral,axiom,
% 9.17/5.35 ! [M2: num] :
% 9.17/5.35 ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2707_not__one__le__neg__numeral,axiom,
% 9.17/5.35 ! [M2: num] :
% 9.17/5.35 ~ ( ord_less_eq_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2708_not__one__le__neg__numeral,axiom,
% 9.17/5.35 ! [M2: num] :
% 9.17/5.35 ~ ( ord_less_eq_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) ) ).
% 9.17/5.35
% 9.17/5.35 thf(fact_2709_not__neg__one__less__neg__numeral,axiom,
% 9.17/5.36 ! [M2: num] :
% 9.17/5.36 ~ ( ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2710_not__neg__one__less__neg__numeral,axiom,
% 9.17/5.36 ! [M2: num] :
% 9.17/5.36 ~ ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2711_not__neg__one__less__neg__numeral,axiom,
% 9.17/5.36 ! [M2: num] :
% 9.17/5.36 ~ ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2712_not__one__less__neg__numeral,axiom,
% 9.17/5.36 ! [M2: num] :
% 9.17/5.36 ~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2713_not__one__less__neg__numeral,axiom,
% 9.17/5.36 ! [M2: num] :
% 9.17/5.36 ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2714_not__one__less__neg__numeral,axiom,
% 9.17/5.36 ! [M2: num] :
% 9.17/5.36 ~ ( ord_less_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2715_not__numeral__less__neg__one,axiom,
% 9.17/5.36 ! [M2: num] :
% 9.17/5.36 ~ ( ord_less_int @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2716_not__numeral__less__neg__one,axiom,
% 9.17/5.36 ! [M2: num] :
% 9.17/5.36 ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ M2 ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2717_not__numeral__less__neg__one,axiom,
% 9.17/5.36 ! [M2: num] :
% 9.17/5.36 ~ ( ord_less_rat @ ( numeral_numeral_rat @ M2 ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2718_neg__one__less__numeral,axiom,
% 9.17/5.36 ! [M2: num] : ( ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ M2 ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2719_neg__one__less__numeral,axiom,
% 9.17/5.36 ! [M2: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ M2 ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2720_neg__one__less__numeral,axiom,
% 9.17/5.36 ! [M2: num] : ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ M2 ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2721_neg__numeral__less__one,axiom,
% 9.17/5.36 ! [M2: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ one_one_int ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2722_neg__numeral__less__one,axiom,
% 9.17/5.36 ! [M2: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ one_one_Code_integer ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2723_neg__numeral__less__one,axiom,
% 9.17/5.36 ! [M2: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ one_one_rat ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2724_sum_OSuc__reindex__ivl,axiom,
% 9.17/5.36 ! [M2: nat,N2: nat,G: nat > multis2468970476368604999at_nat] :
% 9.17/5.36 ( ( ord_less_eq_nat @ M2 @ N2 )
% 9.17/5.36 => ( ( plus_p7104986032573967614at_nat @ ( groups6857163185585827899at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 9.17/5.36 = ( plus_p7104986032573967614at_nat @ ( G @ M2 )
% 9.17/5.36 @ ( groups6857163185585827899at_nat
% 9.17/5.36 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 9.17/5.36 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2725_sum_OSuc__reindex__ivl,axiom,
% 9.17/5.36 ! [M2: nat,N2: nat,G: nat > rat] :
% 9.17/5.36 ( ( ord_less_eq_nat @ M2 @ N2 )
% 9.17/5.36 => ( ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 9.17/5.36 = ( plus_plus_rat @ ( G @ M2 )
% 9.17/5.36 @ ( groups2906978787729119204at_rat
% 9.17/5.36 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 9.17/5.36 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2726_sum_OSuc__reindex__ivl,axiom,
% 9.17/5.36 ! [M2: nat,N2: nat,G: nat > int] :
% 9.17/5.36 ( ( ord_less_eq_nat @ M2 @ N2 )
% 9.17/5.36 => ( ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 9.17/5.36 = ( plus_plus_int @ ( G @ M2 )
% 9.17/5.36 @ ( groups3539618377306564664at_int
% 9.17/5.36 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 9.17/5.36 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2727_sum_OSuc__reindex__ivl,axiom,
% 9.17/5.36 ! [M2: nat,N2: nat,G: nat > nat] :
% 9.17/5.36 ( ( ord_less_eq_nat @ M2 @ N2 )
% 9.17/5.36 => ( ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 9.17/5.36 = ( plus_plus_nat @ ( G @ M2 )
% 9.17/5.36 @ ( groups3542108847815614940at_nat
% 9.17/5.36 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 9.17/5.36 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2728_sum__Suc__diff,axiom,
% 9.17/5.36 ! [M2: nat,N2: nat,F: nat > code_integer] :
% 9.17/5.36 ( ( ord_less_eq_nat @ M2 @ ( suc @ N2 ) )
% 9.17/5.36 => ( ( groups7501900531339628137nteger
% 9.17/5.36 @ ^ [I3: nat] : ( minus_8373710615458151222nteger @ ( F @ ( suc @ I3 ) ) @ ( F @ I3 ) )
% 9.17/5.36 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 9.17/5.36 = ( minus_8373710615458151222nteger @ ( F @ ( suc @ N2 ) ) @ ( F @ M2 ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2729_sum__Suc__diff,axiom,
% 9.17/5.36 ! [M2: nat,N2: nat,F: nat > rat] :
% 9.17/5.36 ( ( ord_less_eq_nat @ M2 @ ( suc @ N2 ) )
% 9.17/5.36 => ( ( groups2906978787729119204at_rat
% 9.17/5.36 @ ^ [I3: nat] : ( minus_minus_rat @ ( F @ ( suc @ I3 ) ) @ ( F @ I3 ) )
% 9.17/5.36 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 9.17/5.36 = ( minus_minus_rat @ ( F @ ( suc @ N2 ) ) @ ( F @ M2 ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2730_sum__Suc__diff,axiom,
% 9.17/5.36 ! [M2: nat,N2: nat,F: nat > int] :
% 9.17/5.36 ( ( ord_less_eq_nat @ M2 @ ( suc @ N2 ) )
% 9.17/5.36 => ( ( groups3539618377306564664at_int
% 9.17/5.36 @ ^ [I3: nat] : ( minus_minus_int @ ( F @ ( suc @ I3 ) ) @ ( F @ I3 ) )
% 9.17/5.36 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 9.17/5.36 = ( minus_minus_int @ ( F @ ( suc @ N2 ) ) @ ( F @ M2 ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2731_sum__power__add,axiom,
% 9.17/5.36 ! [X: rat,M2: nat,I4: set_nat] :
% 9.17/5.36 ( ( groups2906978787729119204at_rat
% 9.17/5.36 @ ^ [I3: nat] : ( power_power_rat @ X @ ( plus_plus_nat @ M2 @ I3 ) )
% 9.17/5.36 @ I4 )
% 9.17/5.36 = ( times_times_rat @ ( power_power_rat @ X @ M2 ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ I4 ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2732_sum__power__add,axiom,
% 9.17/5.36 ! [X: int,M2: nat,I4: set_nat] :
% 9.17/5.36 ( ( groups3539618377306564664at_int
% 9.17/5.36 @ ^ [I3: nat] : ( power_power_int @ X @ ( plus_plus_nat @ M2 @ I3 ) )
% 9.17/5.36 @ I4 )
% 9.17/5.36 = ( times_times_int @ ( power_power_int @ X @ M2 ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ I4 ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2733_sum_OatLeast__atMost__pred__shift,axiom,
% 9.17/5.36 ! [G: nat > nat,M2: nat,N2: nat] :
% 9.17/5.36 ( ( groups3542108847815614940at_nat
% 9.17/5.36 @ ( comp_nat_nat_nat @ G
% 9.17/5.36 @ ^ [N4: nat] : ( minus_minus_nat @ N4 @ ( suc @ zero_zero_nat ) ) )
% 9.17/5.36 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ ( suc @ N2 ) ) )
% 9.17/5.36 = ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2734_sum__atLeastAtMost__code,axiom,
% 9.17/5.36 ! [F: nat > code_integer,A: nat,B: nat] :
% 9.17/5.36 ( ( groups7501900531339628137nteger @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 9.17/5.36 = ( set_fo1084959871951514735nteger
% 9.17/5.36 @ ^ [A5: nat] : ( plus_p5714425477246183910nteger @ ( F @ A5 ) )
% 9.17/5.36 @ A
% 9.17/5.36 @ B
% 9.17/5.36 @ zero_z3403309356797280102nteger ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2735_sum__atLeastAtMost__code,axiom,
% 9.17/5.36 ! [F: nat > multis2468970476368604999at_nat,A: nat,B: nat] :
% 9.17/5.36 ( ( groups6857163185585827899at_nat @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 9.17/5.36 = ( set_fo4497565046347964853at_nat
% 9.17/5.36 @ ^ [A5: nat] : ( plus_p7104986032573967614at_nat @ ( F @ A5 ) )
% 9.17/5.36 @ A
% 9.17/5.36 @ B
% 9.17/5.36 @ zero_z1048942125864253310at_nat ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2736_sum__atLeastAtMost__code,axiom,
% 9.17/5.36 ! [F: nat > rat,A: nat,B: nat] :
% 9.17/5.36 ( ( groups2906978787729119204at_rat @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 9.17/5.36 = ( set_fo1949268297981939178at_rat
% 9.17/5.36 @ ^ [A5: nat] : ( plus_plus_rat @ ( F @ A5 ) )
% 9.17/5.36 @ A
% 9.17/5.36 @ B
% 9.17/5.36 @ zero_zero_rat ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2737_sum__atLeastAtMost__code,axiom,
% 9.17/5.36 ! [F: nat > int,A: nat,B: nat] :
% 9.17/5.36 ( ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 9.17/5.36 = ( set_fo2581907887559384638at_int
% 9.17/5.36 @ ^ [A5: nat] : ( plus_plus_int @ ( F @ A5 ) )
% 9.17/5.36 @ A
% 9.17/5.36 @ B
% 9.17/5.36 @ zero_zero_int ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2738_sum__atLeastAtMost__code,axiom,
% 9.17/5.36 ! [F: nat > nat,A: nat,B: nat] :
% 9.17/5.36 ( ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 9.17/5.36 = ( set_fo2584398358068434914at_nat
% 9.17/5.36 @ ^ [A5: nat] : ( plus_plus_nat @ ( F @ A5 ) )
% 9.17/5.36 @ A
% 9.17/5.36 @ B
% 9.17/5.36 @ zero_zero_nat ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2739_sum_Oub__add__nat,axiom,
% 9.17/5.36 ! [M2: nat,N2: nat,G: nat > multis2468970476368604999at_nat,P4: nat] :
% 9.17/5.36 ( ( ord_less_eq_nat @ M2 @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 9.17/5.36 => ( ( groups6857163185585827899at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ N2 @ P4 ) ) )
% 9.17/5.36 = ( plus_p7104986032573967614at_nat @ ( groups6857163185585827899at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) @ ( groups6857163185585827899at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ ( plus_plus_nat @ N2 @ P4 ) ) ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2740_sum_Oub__add__nat,axiom,
% 9.17/5.36 ! [M2: nat,N2: nat,G: nat > rat,P4: nat] :
% 9.17/5.36 ( ( ord_less_eq_nat @ M2 @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 9.17/5.36 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ N2 @ P4 ) ) )
% 9.17/5.36 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ ( plus_plus_nat @ N2 @ P4 ) ) ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2741_sum_Oub__add__nat,axiom,
% 9.17/5.36 ! [M2: nat,N2: nat,G: nat > int,P4: nat] :
% 9.17/5.36 ( ( ord_less_eq_nat @ M2 @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 9.17/5.36 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ N2 @ P4 ) ) )
% 9.17/5.36 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ ( plus_plus_nat @ N2 @ P4 ) ) ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2742_sum_Oub__add__nat,axiom,
% 9.17/5.36 ! [M2: nat,N2: nat,G: nat > nat,P4: nat] :
% 9.17/5.36 ( ( ord_less_eq_nat @ M2 @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 9.17/5.36 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ N2 @ P4 ) ) )
% 9.17/5.36 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ ( plus_plus_nat @ N2 @ P4 ) ) ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2743_sum_OatLeastAtMost__shift__0,axiom,
% 9.17/5.36 ! [M2: nat,N2: nat,G: nat > nat] :
% 9.17/5.36 ( ( ord_less_eq_nat @ M2 @ N2 )
% 9.17/5.36 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 9.17/5.36 = ( groups3542108847815614940at_nat @ ( comp_nat_nat_nat @ G @ ( plus_plus_nat @ M2 ) ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( minus_minus_nat @ N2 @ M2 ) ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2744_zero__int__def,axiom,
% 9.17/5.36 ( zero_zero_int
% 9.17/5.36 = ( abs_Integ @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2745_pair__lessI1,axiom,
% 9.17/5.36 ! [A: nat,B: nat,S: nat,T: nat] :
% 9.17/5.36 ( ( ord_less_nat @ A @ B )
% 9.17/5.36 => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A @ S ) @ ( product_Pair_nat_nat @ B @ T ) ) @ fun_pair_less ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2746_zero__int_Otransfer,axiom,
% 9.17/5.36 pcr_int @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) @ zero_zero_int ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2747_sum__natinterval__diff,axiom,
% 9.17/5.36 ! [M2: nat,N2: nat,F: nat > code_integer] :
% 9.17/5.36 ( ( ( ord_less_eq_nat @ M2 @ N2 )
% 9.17/5.36 => ( ( groups7501900531339628137nteger
% 9.17/5.36 @ ^ [K4: nat] : ( minus_8373710615458151222nteger @ ( F @ K4 ) @ ( F @ ( plus_plus_nat @ K4 @ one_one_nat ) ) )
% 9.17/5.36 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 9.17/5.36 = ( minus_8373710615458151222nteger @ ( F @ M2 ) @ ( F @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) )
% 9.17/5.36 & ( ~ ( ord_less_eq_nat @ M2 @ N2 )
% 9.17/5.36 => ( ( groups7501900531339628137nteger
% 9.17/5.36 @ ^ [K4: nat] : ( minus_8373710615458151222nteger @ ( F @ K4 ) @ ( F @ ( plus_plus_nat @ K4 @ one_one_nat ) ) )
% 9.17/5.36 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 9.17/5.36 = zero_z3403309356797280102nteger ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2748_sum__natinterval__diff,axiom,
% 9.17/5.36 ! [M2: nat,N2: nat,F: nat > rat] :
% 9.17/5.36 ( ( ( ord_less_eq_nat @ M2 @ N2 )
% 9.17/5.36 => ( ( groups2906978787729119204at_rat
% 9.17/5.36 @ ^ [K4: nat] : ( minus_minus_rat @ ( F @ K4 ) @ ( F @ ( plus_plus_nat @ K4 @ one_one_nat ) ) )
% 9.17/5.36 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 9.17/5.36 = ( minus_minus_rat @ ( F @ M2 ) @ ( F @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) )
% 9.17/5.36 & ( ~ ( ord_less_eq_nat @ M2 @ N2 )
% 9.17/5.36 => ( ( groups2906978787729119204at_rat
% 9.17/5.36 @ ^ [K4: nat] : ( minus_minus_rat @ ( F @ K4 ) @ ( F @ ( plus_plus_nat @ K4 @ one_one_nat ) ) )
% 9.17/5.36 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 9.17/5.36 = zero_zero_rat ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2749_sum__natinterval__diff,axiom,
% 9.17/5.36 ! [M2: nat,N2: nat,F: nat > int] :
% 9.17/5.36 ( ( ( ord_less_eq_nat @ M2 @ N2 )
% 9.17/5.36 => ( ( groups3539618377306564664at_int
% 9.17/5.36 @ ^ [K4: nat] : ( minus_minus_int @ ( F @ K4 ) @ ( F @ ( plus_plus_nat @ K4 @ one_one_nat ) ) )
% 9.17/5.36 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 9.17/5.36 = ( minus_minus_int @ ( F @ M2 ) @ ( F @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) )
% 9.17/5.36 & ( ~ ( ord_less_eq_nat @ M2 @ N2 )
% 9.17/5.36 => ( ( groups3539618377306564664at_int
% 9.17/5.36 @ ^ [K4: nat] : ( minus_minus_int @ ( F @ K4 ) @ ( F @ ( plus_plus_nat @ K4 @ one_one_nat ) ) )
% 9.17/5.36 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 9.17/5.36 = zero_zero_int ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2750_convex__sum__bound__le,axiom,
% 9.17/5.36 ! [I4: set_o,X: $o > code_integer,A: $o > code_integer,B: code_integer,Delta: code_integer] :
% 9.17/5.36 ( ! [I2: $o] :
% 9.17/5.36 ( ( member_o @ I2 @ I4 )
% 9.17/5.36 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X @ I2 ) ) )
% 9.17/5.36 => ( ( ( groups4406642042086082107nteger @ X @ I4 )
% 9.17/5.36 = one_one_Code_integer )
% 9.17/5.36 => ( ! [I2: $o] :
% 9.17/5.36 ( ( member_o @ I2 @ I4 )
% 9.17/5.36 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I2 ) @ B ) ) @ Delta ) )
% 9.17/5.36 => ( ord_le3102999989581377725nteger
% 9.17/5.36 @ ( abs_abs_Code_integer
% 9.17/5.36 @ ( minus_8373710615458151222nteger
% 9.17/5.36 @ ( groups4406642042086082107nteger
% 9.17/5.36 @ ^ [I3: $o] : ( times_3573771949741848930nteger @ ( A @ I3 ) @ ( X @ I3 ) )
% 9.17/5.36 @ I4 )
% 9.17/5.36 @ B ) )
% 9.17/5.36 @ Delta ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2751_convex__sum__bound__le,axiom,
% 9.17/5.36 ! [I4: set_nat,X: nat > code_integer,A: nat > code_integer,B: code_integer,Delta: code_integer] :
% 9.17/5.36 ( ! [I2: nat] :
% 9.17/5.36 ( ( member_nat @ I2 @ I4 )
% 9.17/5.36 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X @ I2 ) ) )
% 9.17/5.36 => ( ( ( groups7501900531339628137nteger @ X @ I4 )
% 9.17/5.36 = one_one_Code_integer )
% 9.17/5.36 => ( ! [I2: nat] :
% 9.17/5.36 ( ( member_nat @ I2 @ I4 )
% 9.17/5.36 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I2 ) @ B ) ) @ Delta ) )
% 9.17/5.36 => ( ord_le3102999989581377725nteger
% 9.17/5.36 @ ( abs_abs_Code_integer
% 9.17/5.36 @ ( minus_8373710615458151222nteger
% 9.17/5.36 @ ( groups7501900531339628137nteger
% 9.17/5.36 @ ^ [I3: nat] : ( times_3573771949741848930nteger @ ( A @ I3 ) @ ( X @ I3 ) )
% 9.17/5.36 @ I4 )
% 9.17/5.36 @ B ) )
% 9.17/5.36 @ Delta ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2752_convex__sum__bound__le,axiom,
% 9.17/5.36 ! [I4: set_int,X: int > code_integer,A: int > code_integer,B: code_integer,Delta: code_integer] :
% 9.17/5.36 ( ! [I2: int] :
% 9.17/5.36 ( ( member_int @ I2 @ I4 )
% 9.17/5.36 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X @ I2 ) ) )
% 9.17/5.36 => ( ( ( groups7873554091576472773nteger @ X @ I4 )
% 9.17/5.36 = one_one_Code_integer )
% 9.17/5.36 => ( ! [I2: int] :
% 9.17/5.36 ( ( member_int @ I2 @ I4 )
% 9.17/5.36 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I2 ) @ B ) ) @ Delta ) )
% 9.17/5.36 => ( ord_le3102999989581377725nteger
% 9.17/5.36 @ ( abs_abs_Code_integer
% 9.17/5.36 @ ( minus_8373710615458151222nteger
% 9.17/5.36 @ ( groups7873554091576472773nteger
% 9.17/5.36 @ ^ [I3: int] : ( times_3573771949741848930nteger @ ( A @ I3 ) @ ( X @ I3 ) )
% 9.17/5.36 @ I4 )
% 9.17/5.36 @ B ) )
% 9.17/5.36 @ Delta ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2753_convex__sum__bound__le,axiom,
% 9.17/5.36 ! [I4: set_o,X: $o > rat,A: $o > rat,B: rat,Delta: rat] :
% 9.17/5.36 ( ! [I2: $o] :
% 9.17/5.36 ( ( member_o @ I2 @ I4 )
% 9.17/5.36 => ( ord_less_eq_rat @ zero_zero_rat @ ( X @ I2 ) ) )
% 9.17/5.36 => ( ( ( groups7872700643590313910_o_rat @ X @ I4 )
% 9.17/5.36 = one_one_rat )
% 9.17/5.36 => ( ! [I2: $o] :
% 9.17/5.36 ( ( member_o @ I2 @ I4 )
% 9.17/5.36 => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I2 ) @ B ) ) @ Delta ) )
% 9.17/5.36 => ( ord_less_eq_rat
% 9.17/5.36 @ ( abs_abs_rat
% 9.17/5.36 @ ( minus_minus_rat
% 9.17/5.36 @ ( groups7872700643590313910_o_rat
% 9.17/5.36 @ ^ [I3: $o] : ( times_times_rat @ ( A @ I3 ) @ ( X @ I3 ) )
% 9.17/5.36 @ I4 )
% 9.17/5.36 @ B ) )
% 9.17/5.36 @ Delta ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2754_convex__sum__bound__le,axiom,
% 9.17/5.36 ! [I4: set_nat,X: nat > rat,A: nat > rat,B: rat,Delta: rat] :
% 9.17/5.36 ( ! [I2: nat] :
% 9.17/5.36 ( ( member_nat @ I2 @ I4 )
% 9.17/5.36 => ( ord_less_eq_rat @ zero_zero_rat @ ( X @ I2 ) ) )
% 9.17/5.36 => ( ( ( groups2906978787729119204at_rat @ X @ I4 )
% 9.17/5.36 = one_one_rat )
% 9.17/5.36 => ( ! [I2: nat] :
% 9.17/5.36 ( ( member_nat @ I2 @ I4 )
% 9.17/5.36 => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I2 ) @ B ) ) @ Delta ) )
% 9.17/5.36 => ( ord_less_eq_rat
% 9.17/5.36 @ ( abs_abs_rat
% 9.17/5.36 @ ( minus_minus_rat
% 9.17/5.36 @ ( groups2906978787729119204at_rat
% 9.17/5.36 @ ^ [I3: nat] : ( times_times_rat @ ( A @ I3 ) @ ( X @ I3 ) )
% 9.17/5.36 @ I4 )
% 9.17/5.36 @ B ) )
% 9.17/5.36 @ Delta ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2755_convex__sum__bound__le,axiom,
% 9.17/5.36 ! [I4: set_int,X: int > rat,A: int > rat,B: rat,Delta: rat] :
% 9.17/5.36 ( ! [I2: int] :
% 9.17/5.36 ( ( member_int @ I2 @ I4 )
% 9.17/5.36 => ( ord_less_eq_rat @ zero_zero_rat @ ( X @ I2 ) ) )
% 9.17/5.36 => ( ( ( groups3906332499630173760nt_rat @ X @ I4 )
% 9.17/5.36 = one_one_rat )
% 9.17/5.36 => ( ! [I2: int] :
% 9.17/5.36 ( ( member_int @ I2 @ I4 )
% 9.17/5.36 => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I2 ) @ B ) ) @ Delta ) )
% 9.17/5.36 => ( ord_less_eq_rat
% 9.17/5.36 @ ( abs_abs_rat
% 9.17/5.36 @ ( minus_minus_rat
% 9.17/5.36 @ ( groups3906332499630173760nt_rat
% 9.17/5.36 @ ^ [I3: int] : ( times_times_rat @ ( A @ I3 ) @ ( X @ I3 ) )
% 9.17/5.36 @ I4 )
% 9.17/5.36 @ B ) )
% 9.17/5.36 @ Delta ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2756_convex__sum__bound__le,axiom,
% 9.17/5.36 ! [I4: set_o,X: $o > int,A: $o > int,B: int,Delta: int] :
% 9.17/5.36 ( ! [I2: $o] :
% 9.17/5.36 ( ( member_o @ I2 @ I4 )
% 9.17/5.36 => ( ord_less_eq_int @ zero_zero_int @ ( X @ I2 ) ) )
% 9.17/5.36 => ( ( ( groups8505340233167759370_o_int @ X @ I4 )
% 9.17/5.36 = one_one_int )
% 9.17/5.36 => ( ! [I2: $o] :
% 9.17/5.36 ( ( member_o @ I2 @ I4 )
% 9.17/5.36 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( A @ I2 ) @ B ) ) @ Delta ) )
% 9.17/5.36 => ( ord_less_eq_int
% 9.17/5.36 @ ( abs_abs_int
% 9.17/5.36 @ ( minus_minus_int
% 9.17/5.36 @ ( groups8505340233167759370_o_int
% 9.17/5.36 @ ^ [I3: $o] : ( times_times_int @ ( A @ I3 ) @ ( X @ I3 ) )
% 9.17/5.36 @ I4 )
% 9.17/5.36 @ B ) )
% 9.17/5.36 @ Delta ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2757_convex__sum__bound__le,axiom,
% 9.17/5.36 ! [I4: set_nat,X: nat > int,A: nat > int,B: int,Delta: int] :
% 9.17/5.36 ( ! [I2: nat] :
% 9.17/5.36 ( ( member_nat @ I2 @ I4 )
% 9.17/5.36 => ( ord_less_eq_int @ zero_zero_int @ ( X @ I2 ) ) )
% 9.17/5.36 => ( ( ( groups3539618377306564664at_int @ X @ I4 )
% 9.17/5.36 = one_one_int )
% 9.17/5.36 => ( ! [I2: nat] :
% 9.17/5.36 ( ( member_nat @ I2 @ I4 )
% 9.17/5.36 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( A @ I2 ) @ B ) ) @ Delta ) )
% 9.17/5.36 => ( ord_less_eq_int
% 9.17/5.36 @ ( abs_abs_int
% 9.17/5.36 @ ( minus_minus_int
% 9.17/5.36 @ ( groups3539618377306564664at_int
% 9.17/5.36 @ ^ [I3: nat] : ( times_times_int @ ( A @ I3 ) @ ( X @ I3 ) )
% 9.17/5.36 @ I4 )
% 9.17/5.36 @ B ) )
% 9.17/5.36 @ Delta ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2758_convex__sum__bound__le,axiom,
% 9.17/5.36 ! [I4: set_int,X: int > int,A: int > int,B: int,Delta: int] :
% 9.17/5.36 ( ! [I2: int] :
% 9.17/5.36 ( ( member_int @ I2 @ I4 )
% 9.17/5.36 => ( ord_less_eq_int @ zero_zero_int @ ( X @ I2 ) ) )
% 9.17/5.36 => ( ( ( groups4538972089207619220nt_int @ X @ I4 )
% 9.17/5.36 = one_one_int )
% 9.17/5.36 => ( ! [I2: int] :
% 9.17/5.36 ( ( member_int @ I2 @ I4 )
% 9.17/5.36 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( A @ I2 ) @ B ) ) @ Delta ) )
% 9.17/5.36 => ( ord_less_eq_int
% 9.17/5.36 @ ( abs_abs_int
% 9.17/5.36 @ ( minus_minus_int
% 9.17/5.36 @ ( groups4538972089207619220nt_int
% 9.17/5.36 @ ^ [I3: int] : ( times_times_int @ ( A @ I3 ) @ ( X @ I3 ) )
% 9.17/5.36 @ I4 )
% 9.17/5.36 @ B ) )
% 9.17/5.36 @ Delta ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2759_convex__sum__bound__le,axiom,
% 9.17/5.36 ! [I4: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat > code_integer,A: product_prod_nat_nat > code_integer,B: code_integer,Delta: code_integer] :
% 9.17/5.36 ( ! [I2: product_prod_nat_nat] :
% 9.17/5.36 ( ( member8440522571783428010at_nat @ I2 @ I4 )
% 9.17/5.36 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X @ I2 ) ) )
% 9.17/5.36 => ( ( ( groups196832835297161892nteger @ X @ I4 )
% 9.17/5.36 = one_one_Code_integer )
% 9.17/5.36 => ( ! [I2: product_prod_nat_nat] :
% 9.17/5.36 ( ( member8440522571783428010at_nat @ I2 @ I4 )
% 9.17/5.36 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I2 ) @ B ) ) @ Delta ) )
% 9.17/5.36 => ( ord_le3102999989581377725nteger
% 9.17/5.36 @ ( abs_abs_Code_integer
% 9.17/5.36 @ ( minus_8373710615458151222nteger
% 9.17/5.36 @ ( groups196832835297161892nteger
% 9.17/5.36 @ ^ [I3: product_prod_nat_nat] : ( times_3573771949741848930nteger @ ( A @ I3 ) @ ( X @ I3 ) )
% 9.17/5.36 @ I4 )
% 9.17/5.36 @ B ) )
% 9.17/5.36 @ Delta ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2760_sum__comp__morphism,axiom,
% 9.17/5.36 ! [H3: code_integer > code_integer,G: num > code_integer,A2: set_num] :
% 9.17/5.36 ( ( ( H3 @ zero_z3403309356797280102nteger )
% 9.17/5.36 = zero_z3403309356797280102nteger )
% 9.17/5.36 => ( ! [X4: code_integer,Y5: code_integer] :
% 9.17/5.36 ( ( H3 @ ( plus_p5714425477246183910nteger @ X4 @ Y5 ) )
% 9.17/5.36 = ( plus_p5714425477246183910nteger @ ( H3 @ X4 ) @ ( H3 @ Y5 ) ) )
% 9.17/5.36 => ( ( groups5442708359310287027nteger @ ( comp_C3531382070062128313er_num @ H3 @ G ) @ A2 )
% 9.17/5.36 = ( H3 @ ( groups5442708359310287027nteger @ G @ A2 ) ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2761_sum__comp__morphism,axiom,
% 9.17/5.36 ! [H3: nat > code_integer,G: nat > nat,A2: set_nat] :
% 9.17/5.36 ( ( ( H3 @ zero_zero_nat )
% 9.17/5.36 = zero_z3403309356797280102nteger )
% 9.17/5.36 => ( ! [X4: nat,Y5: nat] :
% 9.17/5.36 ( ( H3 @ ( plus_plus_nat @ X4 @ Y5 ) )
% 9.17/5.36 = ( plus_p5714425477246183910nteger @ ( H3 @ X4 ) @ ( H3 @ Y5 ) ) )
% 9.17/5.36 => ( ( groups7501900531339628137nteger @ ( comp_n3898172953802868194er_nat @ H3 @ G ) @ A2 )
% 9.17/5.36 = ( H3 @ ( groups3542108847815614940at_nat @ G @ A2 ) ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2762_sum__comp__morphism,axiom,
% 9.17/5.36 ! [H3: nat > rat,G: nat > nat,A2: set_nat] :
% 9.17/5.36 ( ( ( H3 @ zero_zero_nat )
% 9.17/5.36 = zero_zero_rat )
% 9.17/5.36 => ( ! [X4: nat,Y5: nat] :
% 9.17/5.36 ( ( H3 @ ( plus_plus_nat @ X4 @ Y5 ) )
% 9.17/5.36 = ( plus_plus_rat @ ( H3 @ X4 ) @ ( H3 @ Y5 ) ) )
% 9.17/5.36 => ( ( groups2906978787729119204at_rat @ ( comp_nat_rat_nat @ H3 @ G ) @ A2 )
% 9.17/5.36 = ( H3 @ ( groups3542108847815614940at_nat @ G @ A2 ) ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2763_sum__comp__morphism,axiom,
% 9.17/5.36 ! [H3: nat > int,G: nat > nat,A2: set_nat] :
% 9.17/5.36 ( ( ( H3 @ zero_zero_nat )
% 9.17/5.36 = zero_zero_int )
% 9.17/5.36 => ( ! [X4: nat,Y5: nat] :
% 9.17/5.36 ( ( H3 @ ( plus_plus_nat @ X4 @ Y5 ) )
% 9.17/5.36 = ( plus_plus_int @ ( H3 @ X4 ) @ ( H3 @ Y5 ) ) )
% 9.17/5.36 => ( ( groups3539618377306564664at_int @ ( comp_nat_int_nat @ H3 @ G ) @ A2 )
% 9.17/5.36 = ( H3 @ ( groups3542108847815614940at_nat @ G @ A2 ) ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2764_sum__comp__morphism,axiom,
% 9.17/5.36 ! [H3: int > code_integer,G: int > int,A2: set_int] :
% 9.17/5.36 ( ( ( H3 @ zero_zero_int )
% 9.17/5.36 = zero_z3403309356797280102nteger )
% 9.17/5.36 => ( ! [X4: int,Y5: int] :
% 9.17/5.36 ( ( H3 @ ( plus_plus_int @ X4 @ Y5 ) )
% 9.17/5.36 = ( plus_p5714425477246183910nteger @ ( H3 @ X4 ) @ ( H3 @ Y5 ) ) )
% 9.17/5.36 => ( ( groups7873554091576472773nteger @ ( comp_i1585864551200866970er_int @ H3 @ G ) @ A2 )
% 9.17/5.36 = ( H3 @ ( groups4538972089207619220nt_int @ G @ A2 ) ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2765_sum__comp__morphism,axiom,
% 9.17/5.36 ! [H3: int > rat,G: int > int,A2: set_int] :
% 9.17/5.36 ( ( ( H3 @ zero_zero_int )
% 9.17/5.36 = zero_zero_rat )
% 9.17/5.36 => ( ! [X4: int,Y5: int] :
% 9.17/5.36 ( ( H3 @ ( plus_plus_int @ X4 @ Y5 ) )
% 9.17/5.36 = ( plus_plus_rat @ ( H3 @ X4 ) @ ( H3 @ Y5 ) ) )
% 9.17/5.36 => ( ( groups3906332499630173760nt_rat @ ( comp_int_rat_int @ H3 @ G ) @ A2 )
% 9.17/5.36 = ( H3 @ ( groups4538972089207619220nt_int @ G @ A2 ) ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2766_sum__comp__morphism,axiom,
% 9.17/5.36 ! [H3: int > nat,G: int > int,A2: set_int] :
% 9.17/5.36 ( ( ( H3 @ zero_zero_int )
% 9.17/5.36 = zero_zero_nat )
% 9.17/5.36 => ( ! [X4: int,Y5: int] :
% 9.17/5.36 ( ( H3 @ ( plus_plus_int @ X4 @ Y5 ) )
% 9.17/5.36 = ( plus_plus_nat @ ( H3 @ X4 ) @ ( H3 @ Y5 ) ) )
% 9.17/5.36 => ( ( groups4541462559716669496nt_nat @ ( comp_int_nat_int @ H3 @ G ) @ A2 )
% 9.17/5.36 = ( H3 @ ( groups4538972089207619220nt_int @ G @ A2 ) ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2767_sum__comp__morphism,axiom,
% 9.17/5.36 ! [H3: code_integer > nat,G: nat > code_integer,A2: set_nat] :
% 9.17/5.36 ( ( ( H3 @ zero_z3403309356797280102nteger )
% 9.17/5.36 = zero_zero_nat )
% 9.17/5.36 => ( ! [X4: code_integer,Y5: code_integer] :
% 9.17/5.36 ( ( H3 @ ( plus_p5714425477246183910nteger @ X4 @ Y5 ) )
% 9.17/5.36 = ( plus_plus_nat @ ( H3 @ X4 ) @ ( H3 @ Y5 ) ) )
% 9.17/5.36 => ( ( groups3542108847815614940at_nat @ ( comp_C4049556595663050210at_nat @ H3 @ G ) @ A2 )
% 9.17/5.36 = ( H3 @ ( groups7501900531339628137nteger @ G @ A2 ) ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2768_sum__comp__morphism,axiom,
% 9.17/5.36 ! [H3: rat > nat,G: nat > rat,A2: set_nat] :
% 9.17/5.36 ( ( ( H3 @ zero_zero_rat )
% 9.17/5.36 = zero_zero_nat )
% 9.17/5.36 => ( ! [X4: rat,Y5: rat] :
% 9.17/5.36 ( ( H3 @ ( plus_plus_rat @ X4 @ Y5 ) )
% 9.17/5.36 = ( plus_plus_nat @ ( H3 @ X4 ) @ ( H3 @ Y5 ) ) )
% 9.17/5.36 => ( ( groups3542108847815614940at_nat @ ( comp_rat_nat_nat @ H3 @ G ) @ A2 )
% 9.17/5.36 = ( H3 @ ( groups2906978787729119204at_rat @ G @ A2 ) ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2769_sum__comp__morphism,axiom,
% 9.17/5.36 ! [H3: int > nat,G: nat > int,A2: set_nat] :
% 9.17/5.36 ( ( ( H3 @ zero_zero_int )
% 9.17/5.36 = zero_zero_nat )
% 9.17/5.36 => ( ! [X4: int,Y5: int] :
% 9.17/5.36 ( ( H3 @ ( plus_plus_int @ X4 @ Y5 ) )
% 9.17/5.36 = ( plus_plus_nat @ ( H3 @ X4 ) @ ( H3 @ Y5 ) ) )
% 9.17/5.36 => ( ( groups3542108847815614940at_nat @ ( comp_int_nat_nat @ H3 @ G ) @ A2 )
% 9.17/5.36 = ( H3 @ ( groups3539618377306564664at_int @ G @ A2 ) ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2770_sum__gp,axiom,
% 9.17/5.36 ! [N2: nat,M2: nat,X: rat] :
% 9.17/5.36 ( ( ( ord_less_nat @ N2 @ M2 )
% 9.17/5.36 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 9.17/5.36 = zero_zero_rat ) )
% 9.17/5.36 & ( ~ ( ord_less_nat @ N2 @ M2 )
% 9.17/5.36 => ( ( ( X = one_one_rat )
% 9.17/5.36 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 9.17/5.36 = ( semiri681578069525770553at_rat @ ( minus_minus_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ M2 ) ) ) )
% 9.17/5.36 & ( ( X != one_one_rat )
% 9.17/5.36 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 9.17/5.36 = ( divide_divide_rat @ ( minus_minus_rat @ ( power_power_rat @ X @ M2 ) @ ( power_power_rat @ X @ ( suc @ N2 ) ) ) @ ( minus_minus_rat @ one_one_rat @ X ) ) ) ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2771_divmod__digit__1_I1_J,axiom,
% 9.17/5.36 ! [A: code_integer,B: code_integer] :
% 9.17/5.36 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 9.17/5.36 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 9.17/5.36 => ( ( ord_le3102999989581377725nteger @ B @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) )
% 9.17/5.36 => ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) @ one_one_Code_integer )
% 9.17/5.36 = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2772_divmod__digit__1_I1_J,axiom,
% 9.17/5.36 ! [A: nat,B: nat] :
% 9.17/5.36 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 9.17/5.36 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 9.17/5.36 => ( ( ord_less_eq_nat @ B @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 9.17/5.36 => ( ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) @ one_one_nat )
% 9.17/5.36 = ( divide_divide_nat @ A @ B ) ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2773_divmod__digit__1_I1_J,axiom,
% 9.17/5.36 ! [A: int,B: int] :
% 9.17/5.36 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 9.17/5.36 => ( ( ord_less_int @ zero_zero_int @ B )
% 9.17/5.36 => ( ( ord_less_eq_int @ B @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 9.17/5.36 => ( ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) @ one_one_int )
% 9.17/5.36 = ( divide_divide_int @ A @ B ) ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2774_sum__gp__offset,axiom,
% 9.17/5.36 ! [X: rat,M2: nat,N2: nat] :
% 9.17/5.36 ( ( ( X = one_one_rat )
% 9.17/5.36 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ M2 @ N2 ) ) )
% 9.17/5.36 = ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N2 ) @ one_one_rat ) ) )
% 9.17/5.36 & ( ( X != one_one_rat )
% 9.17/5.36 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ M2 @ N2 ) ) )
% 9.17/5.36 = ( divide_divide_rat @ ( times_times_rat @ ( power_power_rat @ X @ M2 ) @ ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ ( suc @ N2 ) ) ) ) @ ( minus_minus_rat @ one_one_rat @ X ) ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2775_Sum__Icc__nat,axiom,
% 9.17/5.36 ! [M2: nat,N2: nat] :
% 9.17/5.36 ( ( groups3542108847815614940at_nat
% 9.17/5.36 @ ^ [X3: nat] : X3
% 9.17/5.36 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 9.17/5.36 = ( divide_divide_nat @ ( minus_minus_nat @ ( times_times_nat @ N2 @ ( plus_plus_nat @ N2 @ one_one_nat ) ) @ ( times_times_nat @ M2 @ ( minus_minus_nat @ M2 @ one_one_nat ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2776_arith__series__nat,axiom,
% 9.17/5.36 ! [A: nat,D2: nat,N2: nat] :
% 9.17/5.36 ( ( groups3542108847815614940at_nat
% 9.17/5.36 @ ^ [I3: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ I3 @ D2 ) )
% 9.17/5.36 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 9.17/5.36 = ( divide_divide_nat @ ( times_times_nat @ ( suc @ N2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( times_times_nat @ N2 @ D2 ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2777_mod__double__modulus,axiom,
% 9.17/5.36 ! [M2: code_integer,X: code_integer] :
% 9.17/5.36 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ M2 )
% 9.17/5.36 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X )
% 9.17/5.36 => ( ( ( modulo364778990260209775nteger @ X @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M2 ) )
% 9.17/5.36 = ( modulo364778990260209775nteger @ X @ M2 ) )
% 9.17/5.36 | ( ( modulo364778990260209775nteger @ X @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M2 ) )
% 9.17/5.36 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ X @ M2 ) @ M2 ) ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2778_mod__double__modulus,axiom,
% 9.17/5.36 ! [M2: nat,X: nat] :
% 9.17/5.36 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 9.17/5.36 => ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 9.17/5.36 => ( ( ( modulo_modulo_nat @ X @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 9.17/5.36 = ( modulo_modulo_nat @ X @ M2 ) )
% 9.17/5.36 | ( ( modulo_modulo_nat @ X @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 9.17/5.36 = ( plus_plus_nat @ ( modulo_modulo_nat @ X @ M2 ) @ M2 ) ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2779_mod__double__modulus,axiom,
% 9.17/5.36 ! [M2: int,X: int] :
% 9.17/5.36 ( ( ord_less_int @ zero_zero_int @ M2 )
% 9.17/5.36 => ( ( ord_less_eq_int @ zero_zero_int @ X )
% 9.17/5.36 => ( ( ( modulo_modulo_int @ X @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 ) )
% 9.17/5.36 = ( modulo_modulo_int @ X @ M2 ) )
% 9.17/5.36 | ( ( modulo_modulo_int @ X @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 ) )
% 9.17/5.36 = ( plus_plus_int @ ( modulo_modulo_int @ X @ M2 ) @ M2 ) ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2780_sum_Odistrib,axiom,
% 9.17/5.36 ! [G: nat > nat,H3: nat > nat,A2: set_nat] :
% 9.17/5.36 ( ( groups3542108847815614940at_nat
% 9.17/5.36 @ ^ [X3: nat] : ( plus_plus_nat @ ( G @ X3 ) @ ( H3 @ X3 ) )
% 9.17/5.36 @ A2 )
% 9.17/5.36 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ A2 ) @ ( groups3542108847815614940at_nat @ H3 @ A2 ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2781_sum_Odistrib,axiom,
% 9.17/5.36 ! [G: int > int,H3: int > int,A2: set_int] :
% 9.17/5.36 ( ( groups4538972089207619220nt_int
% 9.17/5.36 @ ^ [X3: int] : ( plus_plus_int @ ( G @ X3 ) @ ( H3 @ X3 ) )
% 9.17/5.36 @ A2 )
% 9.17/5.36 = ( plus_plus_int @ ( groups4538972089207619220nt_int @ G @ A2 ) @ ( groups4538972089207619220nt_int @ H3 @ A2 ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2782_case__prodI,axiom,
% 9.17/5.36 ! [F: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o,A: produc6241069584506657477e_term > option6357759511663192854e_term,B: produc8923325533196201883nteger] :
% 9.17/5.36 ( ( F @ A @ B )
% 9.17/5.36 => ( produc6253627499356882019eger_o @ F @ ( produc8603105652947943368nteger @ A @ B ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2783_case__prodI,axiom,
% 9.17/5.36 ! [F: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o,A: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat] :
% 9.17/5.36 ( ( F @ A @ B )
% 9.17/5.36 => ( produc1437786849005270451_nat_o @ F @ ( produc5001842942810119800et_nat @ A @ B ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2784_case__prodI,axiom,
% 9.17/5.36 ! [F: ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o,A: produc3658429121746597890et_nat > $o,B: produc3925858234332021118et_nat] :
% 9.17/5.36 ( ( F @ A @ B )
% 9.17/5.36 => ( produc838355143741117751_nat_o @ F @ ( produc2245416461498447860et_nat @ A @ B ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2785_case__prodI,axiom,
% 9.17/5.36 ! [F: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o,A: produc8551481072490612790e_term > option6357759511663192854e_term,B: product_prod_int_int] :
% 9.17/5.36 ( ( F @ A @ B )
% 9.17/5.36 => ( produc1573362020775583542_int_o @ F @ ( produc5700946648718959541nt_int @ A @ B ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2786_case__prodI,axiom,
% 9.17/5.36 ! [F: ( int > option6357759511663192854e_term ) > product_prod_int_int > $o,A: int > option6357759511663192854e_term,B: product_prod_int_int] :
% 9.17/5.36 ( ( F @ A @ B )
% 9.17/5.36 => ( produc2558449545302689196_int_o @ F @ ( produc4305682042979456191nt_int @ A @ B ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2787_case__prodI2,axiom,
% 9.17/5.36 ! [P4: produc1908205239877642774nteger,C: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o] :
% 9.17/5.36 ( ! [A3: produc6241069584506657477e_term > option6357759511663192854e_term,B2: produc8923325533196201883nteger] :
% 9.17/5.36 ( ( P4
% 9.17/5.36 = ( produc8603105652947943368nteger @ A3 @ B2 ) )
% 9.17/5.36 => ( C @ A3 @ B2 ) )
% 9.17/5.36 => ( produc6253627499356882019eger_o @ C @ P4 ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2788_case__prodI2,axiom,
% 9.17/5.36 ! [P4: produc3925858234332021118et_nat,C: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o] :
% 9.17/5.36 ( ! [A3: produc3658429121746597890et_nat > $o,B2: produc3658429121746597890et_nat] :
% 9.17/5.36 ( ( P4
% 9.17/5.36 = ( produc5001842942810119800et_nat @ A3 @ B2 ) )
% 9.17/5.36 => ( C @ A3 @ B2 ) )
% 9.17/5.36 => ( produc1437786849005270451_nat_o @ C @ P4 ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2789_case__prodI2,axiom,
% 9.17/5.36 ! [P4: produc2732055786443039994et_nat,C: ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o] :
% 9.17/5.36 ( ! [A3: produc3658429121746597890et_nat > $o,B2: produc3925858234332021118et_nat] :
% 9.17/5.36 ( ( P4
% 9.17/5.36 = ( produc2245416461498447860et_nat @ A3 @ B2 ) )
% 9.17/5.36 => ( C @ A3 @ B2 ) )
% 9.17/5.36 => ( produc838355143741117751_nat_o @ C @ P4 ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2790_case__prodI2,axiom,
% 9.17/5.36 ! [P4: produc2285326912895808259nt_int,C: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o] :
% 9.17/5.36 ( ! [A3: produc8551481072490612790e_term > option6357759511663192854e_term,B2: product_prod_int_int] :
% 9.17/5.36 ( ( P4
% 9.17/5.36 = ( produc5700946648718959541nt_int @ A3 @ B2 ) )
% 9.17/5.36 => ( C @ A3 @ B2 ) )
% 9.17/5.36 => ( produc1573362020775583542_int_o @ C @ P4 ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2791_case__prodI2,axiom,
% 9.17/5.36 ! [P4: produc7773217078559923341nt_int,C: ( int > option6357759511663192854e_term ) > product_prod_int_int > $o] :
% 9.17/5.36 ( ! [A3: int > option6357759511663192854e_term,B2: product_prod_int_int] :
% 9.17/5.36 ( ( P4
% 9.17/5.36 = ( produc4305682042979456191nt_int @ A3 @ B2 ) )
% 9.17/5.36 => ( C @ A3 @ B2 ) )
% 9.17/5.36 => ( produc2558449545302689196_int_o @ C @ P4 ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2792_mem__case__prodI,axiom,
% 9.17/5.36 ! [Z: $o,C: ( int > option6357759511663192854e_term ) > product_prod_int_int > set_o,A: int > option6357759511663192854e_term,B: product_prod_int_int] :
% 9.17/5.36 ( ( member_o @ Z @ ( C @ A @ B ) )
% 9.17/5.36 => ( member_o @ Z @ ( produc8646739037753556108_set_o @ C @ ( produc4305682042979456191nt_int @ A @ B ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2793_mem__case__prodI,axiom,
% 9.17/5.36 ! [Z: nat,C: ( int > option6357759511663192854e_term ) > product_prod_int_int > set_nat,A: int > option6357759511663192854e_term,B: product_prod_int_int] :
% 9.17/5.36 ( ( member_nat @ Z @ ( C @ A @ B ) )
% 9.17/5.36 => ( member_nat @ Z @ ( produc8289552606927098482et_nat @ C @ ( produc4305682042979456191nt_int @ A @ B ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2794_mem__case__prodI,axiom,
% 9.17/5.36 ! [Z: int,C: ( int > option6357759511663192854e_term ) > product_prod_int_int > set_int,A: int > option6357759511663192854e_term,B: product_prod_int_int] :
% 9.17/5.36 ( ( member_int @ Z @ ( C @ A @ B ) )
% 9.17/5.36 => ( member_int @ Z @ ( produc4111701587417901774et_int @ C @ ( produc4305682042979456191nt_int @ A @ B ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2795_mem__case__prodI,axiom,
% 9.17/5.36 ! [Z: $o,C: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > set_o,A: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat] :
% 9.17/5.36 ( ( member_o @ Z @ ( C @ A @ B ) )
% 9.17/5.36 => ( member_o @ Z @ ( produc7715693535893868691_set_o @ C @ ( produc5001842942810119800et_nat @ A @ B ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2796_mem__case__prodI,axiom,
% 9.17/5.36 ! [Z: nat,C: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > set_nat,A: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat] :
% 9.17/5.36 ( ( member_nat @ Z @ ( C @ A @ B ) )
% 9.17/5.36 => ( member_nat @ Z @ ( produc8805491454895738411et_nat @ C @ ( produc5001842942810119800et_nat @ A @ B ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2797_mem__case__prodI,axiom,
% 9.17/5.36 ! [Z: int,C: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > set_int,A: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat] :
% 9.17/5.36 ( ( member_int @ Z @ ( C @ A @ B ) )
% 9.17/5.36 => ( member_int @ Z @ ( produc4627640435386541703et_int @ C @ ( produc5001842942810119800et_nat @ A @ B ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2798_mem__case__prodI,axiom,
% 9.17/5.36 ! [Z: product_prod_nat_nat,C: ( int > option6357759511663192854e_term ) > product_prod_int_int > set_Pr1261947904930325089at_nat,A: int > option6357759511663192854e_term,B: product_prod_int_int] :
% 9.17/5.36 ( ( member8440522571783428010at_nat @ Z @ ( C @ A @ B ) )
% 9.17/5.36 => ( member8440522571783428010at_nat @ Z @ ( produc5154663461364529269at_nat @ C @ ( produc4305682042979456191nt_int @ A @ B ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2799_mem__case__prodI,axiom,
% 9.17/5.36 ! [Z: $o,C: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_o,A: produc6241069584506657477e_term > option6357759511663192854e_term,B: produc8923325533196201883nteger] :
% 9.17/5.36 ( ( member_o @ Z @ ( C @ A @ B ) )
% 9.17/5.36 => ( member_o @ Z @ ( produc2373554395599118147_set_o @ C @ ( produc8603105652947943368nteger @ A @ B ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2800_mem__case__prodI,axiom,
% 9.17/5.36 ! [Z: nat,C: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_nat,A: produc6241069584506657477e_term > option6357759511663192854e_term,B: produc8923325533196201883nteger] :
% 9.17/5.36 ( ( member_nat @ Z @ ( C @ A @ B ) )
% 9.17/5.36 => ( member_nat @ Z @ ( produc654622801845291899et_nat @ C @ ( produc8603105652947943368nteger @ A @ B ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2801_mem__case__prodI,axiom,
% 9.17/5.36 ! [Z: int,C: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_int,A: produc6241069584506657477e_term > option6357759511663192854e_term,B: produc8923325533196201883nteger] :
% 9.17/5.36 ( ( member_int @ Z @ ( C @ A @ B ) )
% 9.17/5.36 => ( member_int @ Z @ ( produc5700143819190870999et_int @ C @ ( produc8603105652947943368nteger @ A @ B ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2802_mem__case__prodI2,axiom,
% 9.17/5.36 ! [P4: produc7773217078559923341nt_int,Z: $o,C: ( int > option6357759511663192854e_term ) > product_prod_int_int > set_o] :
% 9.17/5.36 ( ! [A3: int > option6357759511663192854e_term,B2: product_prod_int_int] :
% 9.17/5.36 ( ( P4
% 9.17/5.36 = ( produc4305682042979456191nt_int @ A3 @ B2 ) )
% 9.17/5.36 => ( member_o @ Z @ ( C @ A3 @ B2 ) ) )
% 9.17/5.36 => ( member_o @ Z @ ( produc8646739037753556108_set_o @ C @ P4 ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2803_mem__case__prodI2,axiom,
% 9.17/5.36 ! [P4: produc7773217078559923341nt_int,Z: nat,C: ( int > option6357759511663192854e_term ) > product_prod_int_int > set_nat] :
% 9.17/5.36 ( ! [A3: int > option6357759511663192854e_term,B2: product_prod_int_int] :
% 9.17/5.36 ( ( P4
% 9.17/5.36 = ( produc4305682042979456191nt_int @ A3 @ B2 ) )
% 9.17/5.36 => ( member_nat @ Z @ ( C @ A3 @ B2 ) ) )
% 9.17/5.36 => ( member_nat @ Z @ ( produc8289552606927098482et_nat @ C @ P4 ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2804_mem__case__prodI2,axiom,
% 9.17/5.36 ! [P4: produc7773217078559923341nt_int,Z: int,C: ( int > option6357759511663192854e_term ) > product_prod_int_int > set_int] :
% 9.17/5.36 ( ! [A3: int > option6357759511663192854e_term,B2: product_prod_int_int] :
% 9.17/5.36 ( ( P4
% 9.17/5.36 = ( produc4305682042979456191nt_int @ A3 @ B2 ) )
% 9.17/5.36 => ( member_int @ Z @ ( C @ A3 @ B2 ) ) )
% 9.17/5.36 => ( member_int @ Z @ ( produc4111701587417901774et_int @ C @ P4 ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2805_mem__case__prodI2,axiom,
% 9.17/5.36 ! [P4: produc3925858234332021118et_nat,Z: $o,C: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > set_o] :
% 9.17/5.36 ( ! [A3: produc3658429121746597890et_nat > $o,B2: produc3658429121746597890et_nat] :
% 9.17/5.36 ( ( P4
% 9.17/5.36 = ( produc5001842942810119800et_nat @ A3 @ B2 ) )
% 9.17/5.36 => ( member_o @ Z @ ( C @ A3 @ B2 ) ) )
% 9.17/5.36 => ( member_o @ Z @ ( produc7715693535893868691_set_o @ C @ P4 ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2806_mem__case__prodI2,axiom,
% 9.17/5.36 ! [P4: produc3925858234332021118et_nat,Z: nat,C: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > set_nat] :
% 9.17/5.36 ( ! [A3: produc3658429121746597890et_nat > $o,B2: produc3658429121746597890et_nat] :
% 9.17/5.36 ( ( P4
% 9.17/5.36 = ( produc5001842942810119800et_nat @ A3 @ B2 ) )
% 9.17/5.36 => ( member_nat @ Z @ ( C @ A3 @ B2 ) ) )
% 9.17/5.36 => ( member_nat @ Z @ ( produc8805491454895738411et_nat @ C @ P4 ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2807_mem__case__prodI2,axiom,
% 9.17/5.36 ! [P4: produc3925858234332021118et_nat,Z: int,C: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > set_int] :
% 9.17/5.36 ( ! [A3: produc3658429121746597890et_nat > $o,B2: produc3658429121746597890et_nat] :
% 9.17/5.36 ( ( P4
% 9.17/5.36 = ( produc5001842942810119800et_nat @ A3 @ B2 ) )
% 9.17/5.36 => ( member_int @ Z @ ( C @ A3 @ B2 ) ) )
% 9.17/5.36 => ( member_int @ Z @ ( produc4627640435386541703et_int @ C @ P4 ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2808_mem__case__prodI2,axiom,
% 9.17/5.36 ! [P4: produc7773217078559923341nt_int,Z: product_prod_nat_nat,C: ( int > option6357759511663192854e_term ) > product_prod_int_int > set_Pr1261947904930325089at_nat] :
% 9.17/5.36 ( ! [A3: int > option6357759511663192854e_term,B2: product_prod_int_int] :
% 9.17/5.36 ( ( P4
% 9.17/5.36 = ( produc4305682042979456191nt_int @ A3 @ B2 ) )
% 9.17/5.36 => ( member8440522571783428010at_nat @ Z @ ( C @ A3 @ B2 ) ) )
% 9.17/5.36 => ( member8440522571783428010at_nat @ Z @ ( produc5154663461364529269at_nat @ C @ P4 ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2809_mem__case__prodI2,axiom,
% 9.17/5.36 ! [P4: produc1908205239877642774nteger,Z: $o,C: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_o] :
% 9.17/5.36 ( ! [A3: produc6241069584506657477e_term > option6357759511663192854e_term,B2: produc8923325533196201883nteger] :
% 9.17/5.36 ( ( P4
% 9.17/5.36 = ( produc8603105652947943368nteger @ A3 @ B2 ) )
% 9.17/5.36 => ( member_o @ Z @ ( C @ A3 @ B2 ) ) )
% 9.17/5.36 => ( member_o @ Z @ ( produc2373554395599118147_set_o @ C @ P4 ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2810_mem__case__prodI2,axiom,
% 9.17/5.36 ! [P4: produc1908205239877642774nteger,Z: nat,C: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_nat] :
% 9.17/5.36 ( ! [A3: produc6241069584506657477e_term > option6357759511663192854e_term,B2: produc8923325533196201883nteger] :
% 9.17/5.36 ( ( P4
% 9.17/5.36 = ( produc8603105652947943368nteger @ A3 @ B2 ) )
% 9.17/5.36 => ( member_nat @ Z @ ( C @ A3 @ B2 ) ) )
% 9.17/5.36 => ( member_nat @ Z @ ( produc654622801845291899et_nat @ C @ P4 ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2811_mem__case__prodI2,axiom,
% 9.17/5.36 ! [P4: produc1908205239877642774nteger,Z: int,C: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_int] :
% 9.17/5.36 ( ! [A3: produc6241069584506657477e_term > option6357759511663192854e_term,B2: produc8923325533196201883nteger] :
% 9.17/5.36 ( ( P4
% 9.17/5.36 = ( produc8603105652947943368nteger @ A3 @ B2 ) )
% 9.17/5.36 => ( member_int @ Z @ ( C @ A3 @ B2 ) ) )
% 9.17/5.36 => ( member_int @ Z @ ( produc5700143819190870999et_int @ C @ P4 ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2812_case__prodI2_H,axiom,
% 9.17/5.36 ! [P4: product_prod_nat_nat,C: nat > nat > product_prod_nat_nat > $o,X: product_prod_nat_nat] :
% 9.17/5.36 ( ! [A3: nat,B2: nat] :
% 9.17/5.36 ( ( ( product_Pair_nat_nat @ A3 @ B2 )
% 9.17/5.36 = P4 )
% 9.17/5.36 => ( C @ A3 @ B2 @ X ) )
% 9.17/5.36 => ( produc8739625826339149834_nat_o @ C @ P4 @ X ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2813_one__eq__numeral__iff,axiom,
% 9.17/5.36 ! [N2: num] :
% 9.17/5.36 ( ( one_one_nat
% 9.17/5.36 = ( numeral_numeral_nat @ N2 ) )
% 9.17/5.36 = ( one = N2 ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2814_one__eq__numeral__iff,axiom,
% 9.17/5.36 ! [N2: num] :
% 9.17/5.36 ( ( one_one_int
% 9.17/5.36 = ( numeral_numeral_int @ N2 ) )
% 9.17/5.36 = ( one = N2 ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2815_one__eq__numeral__iff,axiom,
% 9.17/5.36 ! [N2: num] :
% 9.17/5.36 ( ( one_one_Code_integer
% 9.17/5.36 = ( numera6620942414471956472nteger @ N2 ) )
% 9.17/5.36 = ( one = N2 ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2816_one__eq__numeral__iff,axiom,
% 9.17/5.36 ! [N2: num] :
% 9.17/5.36 ( ( one_one_rat
% 9.17/5.36 = ( numeral_numeral_rat @ N2 ) )
% 9.17/5.36 = ( one = N2 ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2817_one__eq__numeral__iff,axiom,
% 9.17/5.36 ! [N2: num] :
% 9.17/5.36 ( ( one_one_Code_natural
% 9.17/5.36 = ( numera5444537566228673987atural @ N2 ) )
% 9.17/5.36 = ( one = N2 ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2818_numeral__eq__one__iff,axiom,
% 9.17/5.36 ! [N2: num] :
% 9.17/5.36 ( ( ( numeral_numeral_nat @ N2 )
% 9.17/5.36 = one_one_nat )
% 9.17/5.36 = ( N2 = one ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2819_numeral__eq__one__iff,axiom,
% 9.17/5.36 ! [N2: num] :
% 9.17/5.36 ( ( ( numeral_numeral_int @ N2 )
% 9.17/5.36 = one_one_int )
% 9.17/5.36 = ( N2 = one ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2820_numeral__eq__one__iff,axiom,
% 9.17/5.36 ! [N2: num] :
% 9.17/5.36 ( ( ( numera6620942414471956472nteger @ N2 )
% 9.17/5.36 = one_one_Code_integer )
% 9.17/5.36 = ( N2 = one ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2821_numeral__eq__one__iff,axiom,
% 9.17/5.36 ! [N2: num] :
% 9.17/5.36 ( ( ( numeral_numeral_rat @ N2 )
% 9.17/5.36 = one_one_rat )
% 9.17/5.36 = ( N2 = one ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2822_numeral__eq__one__iff,axiom,
% 9.17/5.36 ! [N2: num] :
% 9.17/5.36 ( ( ( numera5444537566228673987atural @ N2 )
% 9.17/5.36 = one_one_Code_natural )
% 9.17/5.36 = ( N2 = one ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2823_of__nat__add,axiom,
% 9.17/5.36 ! [M2: nat,N2: nat] :
% 9.17/5.36 ( ( semiri681578069525770553at_rat @ ( plus_plus_nat @ M2 @ N2 ) )
% 9.17/5.36 = ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M2 ) @ ( semiri681578069525770553at_rat @ N2 ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2824_of__nat__add,axiom,
% 9.17/5.36 ! [M2: nat,N2: nat] :
% 9.17/5.36 ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ M2 @ N2 ) )
% 9.17/5.36 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2825_of__nat__add,axiom,
% 9.17/5.36 ! [M2: nat,N2: nat] :
% 9.17/5.36 ( ( semiri1316708129612266289at_nat @ ( plus_plus_nat @ M2 @ N2 ) )
% 9.17/5.36 = ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ M2 ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2826_of__nat__add,axiom,
% 9.17/5.36 ! [M2: nat,N2: nat] :
% 9.17/5.36 ( ( semiri4939895301339042750nteger @ ( plus_plus_nat @ M2 @ N2 ) )
% 9.17/5.36 = ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ M2 ) @ ( semiri4939895301339042750nteger @ N2 ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2827_of__nat__add,axiom,
% 9.17/5.36 ! [M2: nat,N2: nat] :
% 9.17/5.36 ( ( semiri3763490453095760265atural @ ( plus_plus_nat @ M2 @ N2 ) )
% 9.17/5.36 = ( plus_p4538020629002901425atural @ ( semiri3763490453095760265atural @ M2 ) @ ( semiri3763490453095760265atural @ N2 ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2828_of__nat__1,axiom,
% 9.17/5.36 ( ( semiri681578069525770553at_rat @ one_one_nat )
% 9.17/5.36 = one_one_rat ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2829_of__nat__1,axiom,
% 9.17/5.36 ( ( semiri1314217659103216013at_int @ one_one_nat )
% 9.17/5.36 = one_one_int ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2830_of__nat__1,axiom,
% 9.17/5.36 ( ( semiri1316708129612266289at_nat @ one_one_nat )
% 9.17/5.36 = one_one_nat ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2831_of__nat__1,axiom,
% 9.17/5.36 ( ( semiri4939895301339042750nteger @ one_one_nat )
% 9.17/5.36 = one_one_Code_integer ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2832_of__nat__1,axiom,
% 9.17/5.36 ( ( semiri3763490453095760265atural @ one_one_nat )
% 9.17/5.36 = one_one_Code_natural ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2833_of__nat__1__eq__iff,axiom,
% 9.17/5.36 ! [N2: nat] :
% 9.17/5.36 ( ( one_one_rat
% 9.17/5.36 = ( semiri681578069525770553at_rat @ N2 ) )
% 9.17/5.36 = ( N2 = one_one_nat ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2834_of__nat__1__eq__iff,axiom,
% 9.17/5.36 ! [N2: nat] :
% 9.17/5.36 ( ( one_one_int
% 9.17/5.36 = ( semiri1314217659103216013at_int @ N2 ) )
% 9.17/5.36 = ( N2 = one_one_nat ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2835_of__nat__1__eq__iff,axiom,
% 9.17/5.36 ! [N2: nat] :
% 9.17/5.36 ( ( one_one_nat
% 9.17/5.36 = ( semiri1316708129612266289at_nat @ N2 ) )
% 9.17/5.36 = ( N2 = one_one_nat ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2836_of__nat__1__eq__iff,axiom,
% 9.17/5.36 ! [N2: nat] :
% 9.17/5.36 ( ( one_one_Code_integer
% 9.17/5.36 = ( semiri4939895301339042750nteger @ N2 ) )
% 9.17/5.36 = ( N2 = one_one_nat ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2837_of__nat__1__eq__iff,axiom,
% 9.17/5.36 ! [N2: nat] :
% 9.17/5.36 ( ( one_one_Code_natural
% 9.17/5.36 = ( semiri3763490453095760265atural @ N2 ) )
% 9.17/5.36 = ( N2 = one_one_nat ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2838_of__nat__eq__1__iff,axiom,
% 9.17/5.36 ! [N2: nat] :
% 9.17/5.36 ( ( ( semiri681578069525770553at_rat @ N2 )
% 9.17/5.36 = one_one_rat )
% 9.17/5.36 = ( N2 = one_one_nat ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2839_of__nat__eq__1__iff,axiom,
% 9.17/5.36 ! [N2: nat] :
% 9.17/5.36 ( ( ( semiri1314217659103216013at_int @ N2 )
% 9.17/5.36 = one_one_int )
% 9.17/5.36 = ( N2 = one_one_nat ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2840_of__nat__eq__1__iff,axiom,
% 9.17/5.36 ! [N2: nat] :
% 9.17/5.36 ( ( ( semiri1316708129612266289at_nat @ N2 )
% 9.17/5.36 = one_one_nat )
% 9.17/5.36 = ( N2 = one_one_nat ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2841_of__nat__eq__1__iff,axiom,
% 9.17/5.36 ! [N2: nat] :
% 9.17/5.36 ( ( ( semiri4939895301339042750nteger @ N2 )
% 9.17/5.36 = one_one_Code_integer )
% 9.17/5.36 = ( N2 = one_one_nat ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2842_of__nat__eq__1__iff,axiom,
% 9.17/5.36 ! [N2: nat] :
% 9.17/5.36 ( ( ( semiri3763490453095760265atural @ N2 )
% 9.17/5.36 = one_one_Code_natural )
% 9.17/5.36 = ( N2 = one_one_nat ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2843_semiring__norm_I2_J,axiom,
% 9.17/5.36 ( ( plus_plus_num @ one @ one )
% 9.17/5.36 = ( bit0 @ one ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2844_numeral__le__one__iff,axiom,
% 9.17/5.36 ! [N2: num] :
% 9.17/5.36 ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ N2 ) @ one_one_Code_integer )
% 9.17/5.36 = ( ord_less_eq_num @ N2 @ one ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2845_numeral__le__one__iff,axiom,
% 9.17/5.36 ! [N2: num] :
% 9.17/5.36 ( ( ord_le1926595141338095240atural @ ( numera5444537566228673987atural @ N2 ) @ one_one_Code_natural )
% 9.17/5.36 = ( ord_less_eq_num @ N2 @ one ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2846_numeral__le__one__iff,axiom,
% 9.17/5.36 ! [N2: num] :
% 9.17/5.36 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ N2 ) @ one_one_rat )
% 9.17/5.36 = ( ord_less_eq_num @ N2 @ one ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2847_numeral__le__one__iff,axiom,
% 9.17/5.36 ! [N2: num] :
% 9.17/5.36 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ N2 ) @ one_one_nat )
% 9.17/5.36 = ( ord_less_eq_num @ N2 @ one ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2848_numeral__le__one__iff,axiom,
% 9.17/5.36 ! [N2: num] :
% 9.17/5.36 ( ( ord_less_eq_int @ ( numeral_numeral_int @ N2 ) @ one_one_int )
% 9.17/5.36 = ( ord_less_eq_num @ N2 @ one ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2849_one__less__numeral__iff,axiom,
% 9.17/5.36 ! [N2: num] :
% 9.17/5.36 ( ( ord_less_nat @ one_one_nat @ ( numeral_numeral_nat @ N2 ) )
% 9.17/5.36 = ( ord_less_num @ one @ N2 ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2850_one__less__numeral__iff,axiom,
% 9.17/5.36 ! [N2: num] :
% 9.17/5.36 ( ( ord_less_int @ one_one_int @ ( numeral_numeral_int @ N2 ) )
% 9.17/5.36 = ( ord_less_num @ one @ N2 ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2851_one__less__numeral__iff,axiom,
% 9.17/5.36 ! [N2: num] :
% 9.17/5.36 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ N2 ) )
% 9.17/5.36 = ( ord_less_num @ one @ N2 ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2852_one__less__numeral__iff,axiom,
% 9.17/5.36 ! [N2: num] :
% 9.17/5.36 ( ( ord_less_rat @ one_one_rat @ ( numeral_numeral_rat @ N2 ) )
% 9.17/5.36 = ( ord_less_num @ one @ N2 ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2853_one__less__numeral__iff,axiom,
% 9.17/5.36 ! [N2: num] :
% 9.17/5.36 ( ( ord_le5570908160329646204atural @ one_one_Code_natural @ ( numera5444537566228673987atural @ N2 ) )
% 9.17/5.36 = ( ord_less_num @ one @ N2 ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2854_numeral__eq__neg__one__iff,axiom,
% 9.17/5.36 ! [N2: num] :
% 9.17/5.36 ( ( ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) )
% 9.17/5.36 = ( uminus_uminus_int @ one_one_int ) )
% 9.17/5.36 = ( N2 = one ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2855_numeral__eq__neg__one__iff,axiom,
% 9.17/5.36 ! [N2: num] :
% 9.17/5.36 ( ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) )
% 9.17/5.36 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.17/5.36 = ( N2 = one ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2856_numeral__eq__neg__one__iff,axiom,
% 9.17/5.36 ! [N2: num] :
% 9.17/5.36 ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) )
% 9.17/5.36 = ( uminus_uminus_rat @ one_one_rat ) )
% 9.17/5.36 = ( N2 = one ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2857_neg__one__eq__numeral__iff,axiom,
% 9.17/5.36 ! [N2: num] :
% 9.17/5.36 ( ( ( uminus_uminus_int @ one_one_int )
% 9.17/5.36 = ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 9.17/5.36 = ( N2 = one ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2858_neg__one__eq__numeral__iff,axiom,
% 9.17/5.36 ! [N2: num] :
% 9.17/5.36 ( ( ( uminus1351360451143612070nteger @ one_one_Code_integer )
% 9.17/5.36 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 9.17/5.36 = ( N2 = one ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2859_neg__one__eq__numeral__iff,axiom,
% 9.17/5.36 ! [N2: num] :
% 9.17/5.36 ( ( ( uminus_uminus_rat @ one_one_rat )
% 9.17/5.36 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 9.17/5.36 = ( N2 = one ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2860_of__nat__Suc,axiom,
% 9.17/5.36 ! [M2: nat] :
% 9.17/5.36 ( ( semiri681578069525770553at_rat @ ( suc @ M2 ) )
% 9.17/5.36 = ( plus_plus_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ M2 ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2861_of__nat__Suc,axiom,
% 9.17/5.36 ! [M2: nat] :
% 9.17/5.36 ( ( semiri1314217659103216013at_int @ ( suc @ M2 ) )
% 9.17/5.36 = ( plus_plus_int @ one_one_int @ ( semiri1314217659103216013at_int @ M2 ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2862_of__nat__Suc,axiom,
% 9.17/5.36 ! [M2: nat] :
% 9.17/5.36 ( ( semiri1316708129612266289at_nat @ ( suc @ M2 ) )
% 9.17/5.36 = ( plus_plus_nat @ one_one_nat @ ( semiri1316708129612266289at_nat @ M2 ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2863_of__nat__Suc,axiom,
% 9.17/5.36 ! [M2: nat] :
% 9.17/5.36 ( ( semiri4939895301339042750nteger @ ( suc @ M2 ) )
% 9.17/5.36 = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( semiri4939895301339042750nteger @ M2 ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2864_of__nat__Suc,axiom,
% 9.17/5.36 ! [M2: nat] :
% 9.17/5.36 ( ( semiri3763490453095760265atural @ ( suc @ M2 ) )
% 9.17/5.36 = ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( semiri3763490453095760265atural @ M2 ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2865_Suc__numeral,axiom,
% 9.17/5.36 ! [N2: num] :
% 9.17/5.36 ( ( suc @ ( numeral_numeral_nat @ N2 ) )
% 9.17/5.36 = ( numeral_numeral_nat @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2866_not__neg__one__le__neg__numeral__iff,axiom,
% 9.17/5.36 ! [M2: num] :
% 9.17/5.36 ( ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) ) )
% 9.17/5.36 = ( M2 != one ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2867_not__neg__one__le__neg__numeral__iff,axiom,
% 9.17/5.36 ! [M2: num] :
% 9.17/5.36 ( ( ~ ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) ) )
% 9.17/5.36 = ( M2 != one ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2868_not__neg__one__le__neg__numeral__iff,axiom,
% 9.17/5.36 ! [M2: num] :
% 9.17/5.36 ( ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) ) )
% 9.17/5.36 = ( M2 != one ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2869_one__add__one,axiom,
% 9.17/5.36 ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 9.17/5.36 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2870_one__add__one,axiom,
% 9.17/5.36 ( ( plus_plus_int @ one_one_int @ one_one_int )
% 9.17/5.36 = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2871_one__add__one,axiom,
% 9.17/5.36 ( ( plus_p5714425477246183910nteger @ one_one_Code_integer @ one_one_Code_integer )
% 9.17/5.36 = ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2872_one__add__one,axiom,
% 9.17/5.36 ( ( plus_plus_rat @ one_one_rat @ one_one_rat )
% 9.17/5.36 = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2873_one__add__one,axiom,
% 9.17/5.36 ( ( plus_p4538020629002901425atural @ one_one_Code_natural @ one_one_Code_natural )
% 9.17/5.36 = ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2874_neg__numeral__less__neg__one__iff,axiom,
% 9.17/5.36 ! [M2: num] :
% 9.17/5.36 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( uminus_uminus_int @ one_one_int ) )
% 9.17/5.36 = ( M2 != one ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2875_neg__numeral__less__neg__one__iff,axiom,
% 9.17/5.36 ! [M2: num] :
% 9.17/5.36 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.17/5.36 = ( M2 != one ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2876_neg__numeral__less__neg__one__iff,axiom,
% 9.17/5.36 ! [M2: num] :
% 9.17/5.36 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 9.17/5.36 = ( M2 != one ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2877_bits__one__mod__two__eq__one,axiom,
% 9.17/5.36 ( ( modulo_modulo_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.17/5.36 = one_one_int ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2878_bits__one__mod__two__eq__one,axiom,
% 9.17/5.36 ( ( modulo_modulo_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.17/5.36 = one_one_nat ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2879_bits__one__mod__two__eq__one,axiom,
% 9.17/5.36 ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 9.17/5.36 = one_one_Code_integer ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2880_bits__one__mod__two__eq__one,axiom,
% 9.17/5.36 ( ( modulo8411746178871703098atural @ one_one_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 9.17/5.36 = one_one_Code_natural ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2881_one__mod__two__eq__one,axiom,
% 9.17/5.36 ( ( modulo_modulo_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.17/5.36 = one_one_int ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2882_one__mod__two__eq__one,axiom,
% 9.17/5.36 ( ( modulo_modulo_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.17/5.36 = one_one_nat ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2883_one__mod__two__eq__one,axiom,
% 9.17/5.36 ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 9.17/5.36 = one_one_Code_integer ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2884_one__mod__two__eq__one,axiom,
% 9.17/5.36 ( ( modulo8411746178871703098atural @ one_one_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 9.17/5.36 = one_one_Code_natural ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2885_add__2__eq__Suc,axiom,
% 9.17/5.36 ! [N2: nat] :
% 9.17/5.36 ( ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 9.17/5.36 = ( suc @ ( suc @ N2 ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2886_add__2__eq__Suc_H,axiom,
% 9.17/5.36 ! [N2: nat] :
% 9.17/5.36 ( ( plus_plus_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.17/5.36 = ( suc @ ( suc @ N2 ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2887_Suc__1,axiom,
% 9.17/5.36 ( ( suc @ one_one_nat )
% 9.17/5.36 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2888_numeral__plus__one,axiom,
% 9.17/5.36 ! [N2: num] :
% 9.17/5.36 ( ( plus_plus_nat @ ( numeral_numeral_nat @ N2 ) @ one_one_nat )
% 9.17/5.36 = ( numeral_numeral_nat @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2889_numeral__plus__one,axiom,
% 9.17/5.36 ! [N2: num] :
% 9.17/5.36 ( ( plus_plus_int @ ( numeral_numeral_int @ N2 ) @ one_one_int )
% 9.17/5.36 = ( numeral_numeral_int @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2890_numeral__plus__one,axiom,
% 9.17/5.36 ! [N2: num] :
% 9.17/5.36 ( ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ N2 ) @ one_one_Code_integer )
% 9.17/5.36 = ( numera6620942414471956472nteger @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2891_numeral__plus__one,axiom,
% 9.17/5.36 ! [N2: num] :
% 9.17/5.36 ( ( plus_plus_rat @ ( numeral_numeral_rat @ N2 ) @ one_one_rat )
% 9.17/5.36 = ( numeral_numeral_rat @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2892_numeral__plus__one,axiom,
% 9.17/5.36 ! [N2: num] :
% 9.17/5.36 ( ( plus_p4538020629002901425atural @ ( numera5444537566228673987atural @ N2 ) @ one_one_Code_natural )
% 9.17/5.36 = ( numera5444537566228673987atural @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2893_one__plus__numeral,axiom,
% 9.17/5.36 ! [N2: num] :
% 9.17/5.36 ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ N2 ) )
% 9.17/5.36 = ( numeral_numeral_nat @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2894_one__plus__numeral,axiom,
% 9.17/5.36 ! [N2: num] :
% 9.17/5.36 ( ( plus_plus_int @ one_one_int @ ( numeral_numeral_int @ N2 ) )
% 9.17/5.36 = ( numeral_numeral_int @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2895_one__plus__numeral,axiom,
% 9.17/5.36 ! [N2: num] :
% 9.17/5.36 ( ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ N2 ) )
% 9.17/5.36 = ( numera6620942414471956472nteger @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2896_one__plus__numeral,axiom,
% 9.17/5.36 ! [N2: num] :
% 9.17/5.36 ( ( plus_plus_rat @ one_one_rat @ ( numeral_numeral_rat @ N2 ) )
% 9.17/5.36 = ( numeral_numeral_rat @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2897_one__plus__numeral,axiom,
% 9.17/5.36 ! [N2: num] :
% 9.17/5.36 ( ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( numera5444537566228673987atural @ N2 ) )
% 9.17/5.36 = ( numera5444537566228673987atural @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2898_add__self__div__2,axiom,
% 9.17/5.36 ! [M2: nat] :
% 9.17/5.36 ( ( divide_divide_nat @ ( plus_plus_nat @ M2 @ M2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.17/5.36 = M2 ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2899_bits__1__div__2,axiom,
% 9.17/5.36 ( ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.17/5.36 = zero_zero_int ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2900_bits__1__div__2,axiom,
% 9.17/5.36 ( ( divide_divide_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.17/5.36 = zero_zero_nat ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2901_bits__1__div__2,axiom,
% 9.17/5.36 ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 9.17/5.36 = zero_z3403309356797280102nteger ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2902_bits__1__div__2,axiom,
% 9.17/5.36 ( ( divide5121882707175180666atural @ one_one_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 9.17/5.36 = zero_z2226904508553997617atural ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2903_one__div__two__eq__zero,axiom,
% 9.17/5.36 ( ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.17/5.36 = zero_zero_int ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2904_one__div__two__eq__zero,axiom,
% 9.17/5.36 ( ( divide_divide_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.17/5.36 = zero_zero_nat ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2905_one__div__two__eq__zero,axiom,
% 9.17/5.36 ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 9.17/5.36 = zero_z3403309356797280102nteger ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2906_one__div__two__eq__zero,axiom,
% 9.17/5.36 ( ( divide5121882707175180666atural @ one_one_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 9.17/5.36 = zero_z2226904508553997617atural ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2907_add__neg__numeral__special_I9_J,axiom,
% 9.17/5.36 ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ one_one_int ) )
% 9.17/5.36 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2908_add__neg__numeral__special_I9_J,axiom,
% 9.17/5.36 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.17/5.36 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2909_add__neg__numeral__special_I9_J,axiom,
% 9.17/5.36 ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 9.17/5.36 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2910_diff__numeral__special_I11_J,axiom,
% 9.17/5.36 ( ( minus_minus_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) )
% 9.17/5.36 = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2911_diff__numeral__special_I11_J,axiom,
% 9.17/5.36 ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.17/5.36 = ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2912_diff__numeral__special_I11_J,axiom,
% 9.17/5.36 ( ( minus_minus_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 9.17/5.36 = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2913_diff__numeral__special_I10_J,axiom,
% 9.17/5.36 ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 9.17/5.36 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2914_diff__numeral__special_I10_J,axiom,
% 9.17/5.36 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer )
% 9.17/5.36 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2915_diff__numeral__special_I10_J,axiom,
% 9.17/5.36 ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat )
% 9.17/5.36 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2916_not__mod__2__eq__0__eq__1,axiom,
% 9.17/5.36 ! [A: int] :
% 9.17/5.36 ( ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.17/5.36 != zero_zero_int )
% 9.17/5.36 = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.17/5.36 = one_one_int ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2917_not__mod__2__eq__0__eq__1,axiom,
% 9.17/5.36 ! [A: nat] :
% 9.17/5.36 ( ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.17/5.36 != zero_zero_nat )
% 9.17/5.36 = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.17/5.36 = one_one_nat ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2918_not__mod__2__eq__0__eq__1,axiom,
% 9.17/5.36 ! [A: code_integer] :
% 9.17/5.36 ( ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 9.17/5.36 != zero_z3403309356797280102nteger )
% 9.17/5.36 = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 9.17/5.36 = one_one_Code_integer ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2919_not__mod__2__eq__0__eq__1,axiom,
% 9.17/5.36 ! [A: code_natural] :
% 9.17/5.36 ( ( ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 9.17/5.36 != zero_z2226904508553997617atural )
% 9.17/5.36 = ( ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 9.17/5.36 = one_one_Code_natural ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2920_not__mod__2__eq__1__eq__0,axiom,
% 9.17/5.36 ! [A: int] :
% 9.17/5.36 ( ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.17/5.36 != one_one_int )
% 9.17/5.36 = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.17/5.36 = zero_zero_int ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2921_not__mod__2__eq__1__eq__0,axiom,
% 9.17/5.36 ! [A: nat] :
% 9.17/5.36 ( ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.17/5.36 != one_one_nat )
% 9.17/5.36 = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.17/5.36 = zero_zero_nat ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2922_not__mod__2__eq__1__eq__0,axiom,
% 9.17/5.36 ! [A: code_integer] :
% 9.17/5.36 ( ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 9.17/5.36 != one_one_Code_integer )
% 9.17/5.36 = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 9.17/5.36 = zero_z3403309356797280102nteger ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2923_not__mod__2__eq__1__eq__0,axiom,
% 9.17/5.36 ! [A: code_natural] :
% 9.17/5.36 ( ( ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 9.17/5.36 != one_one_Code_natural )
% 9.17/5.36 = ( ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 9.17/5.36 = zero_z2226904508553997617atural ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2924_minus__1__div__2__eq,axiom,
% 9.17/5.36 ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.17/5.36 = ( uminus_uminus_int @ one_one_int ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2925_minus__1__div__2__eq,axiom,
% 9.17/5.36 ( ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 9.17/5.36 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2926_bits__minus__1__mod__2__eq,axiom,
% 9.17/5.36 ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.17/5.36 = one_one_int ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2927_bits__minus__1__mod__2__eq,axiom,
% 9.17/5.36 ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 9.17/5.36 = one_one_Code_integer ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2928_minus__1__mod__2__eq,axiom,
% 9.17/5.36 ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.17/5.36 = one_one_int ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2929_minus__1__mod__2__eq,axiom,
% 9.17/5.36 ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 9.17/5.36 = one_one_Code_integer ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2930_diff__numeral__special_I3_J,axiom,
% 9.17/5.36 ! [N2: num] :
% 9.17/5.36 ( ( minus_minus_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 9.17/5.36 = ( numeral_numeral_int @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2931_diff__numeral__special_I3_J,axiom,
% 9.17/5.36 ! [N2: num] :
% 9.17/5.36 ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 9.17/5.36 = ( numera6620942414471956472nteger @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2932_diff__numeral__special_I3_J,axiom,
% 9.17/5.36 ! [N2: num] :
% 9.17/5.36 ( ( minus_minus_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 9.17/5.36 = ( numeral_numeral_rat @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2933_diff__numeral__special_I4_J,axiom,
% 9.17/5.36 ! [M2: num] :
% 9.17/5.36 ( ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ one_one_int )
% 9.17/5.36 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ M2 @ one ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2934_diff__numeral__special_I4_J,axiom,
% 9.17/5.36 ! [M2: num] :
% 9.17/5.36 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ one_one_Code_integer )
% 9.17/5.36 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ M2 @ one ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2935_diff__numeral__special_I4_J,axiom,
% 9.17/5.36 ! [M2: num] :
% 9.17/5.36 ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ one_one_rat )
% 9.17/5.36 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ M2 @ one ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2936_add__self__mod__2,axiom,
% 9.17/5.36 ! [M2: nat] :
% 9.17/5.36 ( ( modulo_modulo_nat @ ( plus_plus_nat @ M2 @ M2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.17/5.36 = zero_zero_nat ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2937_power__minus1__even,axiom,
% 9.17/5.36 ! [N2: nat] :
% 9.17/5.36 ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 9.17/5.36 = one_one_int ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2938_power__minus1__even,axiom,
% 9.17/5.36 ! [N2: nat] :
% 9.17/5.36 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 9.17/5.36 = one_one_Code_integer ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2939_power__minus1__even,axiom,
% 9.17/5.36 ! [N2: nat] :
% 9.17/5.36 ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 9.17/5.36 = one_one_rat ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2940_mod2__gr__0,axiom,
% 9.17/5.36 ! [M2: nat] :
% 9.17/5.36 ( ( ord_less_nat @ zero_zero_nat @ ( modulo_modulo_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.17/5.36 = ( ( modulo_modulo_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.17/5.36 = one_one_nat ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2941_lex__prod__def,axiom,
% 9.17/5.36 ( lex_pr8000699672184251119at_nat
% 9.17/5.36 = ( ^ [Ra: set_Pr4329608150637261639at_nat,Rb: set_Pr4329608150637261639at_nat] :
% 9.17/5.36 ( collec223960383693904210at_nat
% 9.17/5.36 @ ( produc1561160019221259564_nat_o
% 9.17/5.36 @ ( produc1971064617671185730_nat_o
% 9.17/5.36 @ ^ [A5: set_Pr1261947904930325089at_nat,B4: set_Pr1261947904930325089at_nat] :
% 9.17/5.36 ( produc410239310623530412_nat_o
% 9.17/5.36 @ ^ [A6: set_Pr1261947904930325089at_nat,B6: set_Pr1261947904930325089at_nat] :
% 9.17/5.36 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A5 @ A6 ) @ Ra )
% 9.17/5.36 | ( ( A5 = A6 )
% 9.17/5.36 & ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ B4 @ B6 ) @ Rb ) ) ) ) ) ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2942_lex__prod__def,axiom,
% 9.17/5.36 ( lex_pr1951919194703979714at_nat
% 9.17/5.36 = ( ^ [Ra: set_Pr4329608150637261639at_nat,Rb: set_Pr1261947904930325089at_nat] :
% 9.17/5.36 ( collec1461227866750739596at_nat
% 9.17/5.36 @ ( produc8701595406162815018_nat_o
% 9.17/5.36 @ ( produc7110675705651593384_nat_o
% 9.17/5.36 @ ^ [A5: set_Pr1261947904930325089at_nat,B4: nat] :
% 9.17/5.36 ( produc3595121349294487249_nat_o
% 9.17/5.36 @ ^ [A6: set_Pr1261947904930325089at_nat,B6: nat] :
% 9.17/5.36 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A5 @ A6 ) @ Ra )
% 9.17/5.36 | ( ( A5 = A6 )
% 9.17/5.36 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ B4 @ B6 ) @ Rb ) ) ) ) ) ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2943_lex__prod__def,axiom,
% 9.17/5.36 ( lex_pr4265550801952275104at_nat
% 9.17/5.36 = ( ^ [Ra: set_Pr1261947904930325089at_nat,Rb: set_Pr4329608150637261639at_nat] :
% 9.17/5.36 ( collec2088441199205367000at_nat
% 9.17/5.36 @ ( produc7830147906768200158_nat_o
% 9.17/5.36 @ ( produc1908958340173245860_nat_o
% 9.17/5.36 @ ^ [A5: nat,B4: set_Pr1261947904930325089at_nat] :
% 9.17/5.36 ( produc7997411485876045171_nat_o
% 9.17/5.36 @ ^ [A6: nat,B6: set_Pr1261947904930325089at_nat] :
% 9.17/5.36 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A5 @ A6 ) @ Ra )
% 9.17/5.36 | ( ( A5 = A6 )
% 9.17/5.36 & ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ B4 @ B6 ) @ Rb ) ) ) ) ) ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2944_lex__prod__def,axiom,
% 9.17/5.36 ( lex_prod_nat_nat
% 9.17/5.36 = ( ^ [Ra: set_Pr1261947904930325089at_nat,Rb: set_Pr1261947904930325089at_nat] :
% 9.17/5.36 ( collec7088162979684241874at_nat
% 9.17/5.36 @ ( produc6590410687421337004_nat_o
% 9.17/5.36 @ ( produc8739625826339149834_nat_o
% 9.17/5.36 @ ^ [A5: nat,B4: nat] :
% 9.17/5.36 ( produc6081775807080527818_nat_o
% 9.17/5.36 @ ^ [A6: nat,B6: nat] :
% 9.17/5.36 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A5 @ A6 ) @ Ra )
% 9.17/5.36 | ( ( A5 = A6 )
% 9.17/5.36 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ B4 @ B6 ) @ Rb ) ) ) ) ) ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2945_same__fst__def,axiom,
% 9.17/5.36 ( same_fst_nat_nat
% 9.17/5.36 = ( ^ [P3: nat > $o,R5: nat > set_Pr1261947904930325089at_nat] :
% 9.17/5.36 ( collec7088162979684241874at_nat
% 9.17/5.36 @ ( produc6590410687421337004_nat_o
% 9.17/5.36 @ ( produc8739625826339149834_nat_o
% 9.17/5.36 @ ^ [X10: nat,Y8: nat] :
% 9.17/5.36 ( produc6081775807080527818_nat_o
% 9.17/5.36 @ ^ [X3: nat,Y3: nat] :
% 9.17/5.36 ( ( X10 = X3 )
% 9.17/5.36 & ( P3 @ X3 )
% 9.17/5.36 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y8 @ Y3 ) @ ( R5 @ X3 ) ) ) ) ) ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2946_mem__case__prodE,axiom,
% 9.17/5.36 ! [Z: $o,C: ( int > option6357759511663192854e_term ) > product_prod_int_int > set_o,P4: produc7773217078559923341nt_int] :
% 9.17/5.36 ( ( member_o @ Z @ ( produc8646739037753556108_set_o @ C @ P4 ) )
% 9.17/5.36 => ~ ! [X4: int > option6357759511663192854e_term,Y5: product_prod_int_int] :
% 9.17/5.36 ( ( P4
% 9.17/5.36 = ( produc4305682042979456191nt_int @ X4 @ Y5 ) )
% 9.17/5.36 => ~ ( member_o @ Z @ ( C @ X4 @ Y5 ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2947_mem__case__prodE,axiom,
% 9.17/5.36 ! [Z: nat,C: ( int > option6357759511663192854e_term ) > product_prod_int_int > set_nat,P4: produc7773217078559923341nt_int] :
% 9.17/5.36 ( ( member_nat @ Z @ ( produc8289552606927098482et_nat @ C @ P4 ) )
% 9.17/5.36 => ~ ! [X4: int > option6357759511663192854e_term,Y5: product_prod_int_int] :
% 9.17/5.36 ( ( P4
% 9.17/5.36 = ( produc4305682042979456191nt_int @ X4 @ Y5 ) )
% 9.17/5.36 => ~ ( member_nat @ Z @ ( C @ X4 @ Y5 ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2948_mem__case__prodE,axiom,
% 9.17/5.36 ! [Z: int,C: ( int > option6357759511663192854e_term ) > product_prod_int_int > set_int,P4: produc7773217078559923341nt_int] :
% 9.17/5.36 ( ( member_int @ Z @ ( produc4111701587417901774et_int @ C @ P4 ) )
% 9.17/5.36 => ~ ! [X4: int > option6357759511663192854e_term,Y5: product_prod_int_int] :
% 9.17/5.36 ( ( P4
% 9.17/5.36 = ( produc4305682042979456191nt_int @ X4 @ Y5 ) )
% 9.17/5.36 => ~ ( member_int @ Z @ ( C @ X4 @ Y5 ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2949_mem__case__prodE,axiom,
% 9.17/5.36 ! [Z: $o,C: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > set_o,P4: produc3925858234332021118et_nat] :
% 9.17/5.36 ( ( member_o @ Z @ ( produc7715693535893868691_set_o @ C @ P4 ) )
% 9.17/5.36 => ~ ! [X4: produc3658429121746597890et_nat > $o,Y5: produc3658429121746597890et_nat] :
% 9.17/5.36 ( ( P4
% 9.17/5.36 = ( produc5001842942810119800et_nat @ X4 @ Y5 ) )
% 9.17/5.36 => ~ ( member_o @ Z @ ( C @ X4 @ Y5 ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2950_mem__case__prodE,axiom,
% 9.17/5.36 ! [Z: nat,C: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > set_nat,P4: produc3925858234332021118et_nat] :
% 9.17/5.36 ( ( member_nat @ Z @ ( produc8805491454895738411et_nat @ C @ P4 ) )
% 9.17/5.36 => ~ ! [X4: produc3658429121746597890et_nat > $o,Y5: produc3658429121746597890et_nat] :
% 9.17/5.36 ( ( P4
% 9.17/5.36 = ( produc5001842942810119800et_nat @ X4 @ Y5 ) )
% 9.17/5.36 => ~ ( member_nat @ Z @ ( C @ X4 @ Y5 ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2951_mem__case__prodE,axiom,
% 9.17/5.36 ! [Z: int,C: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > set_int,P4: produc3925858234332021118et_nat] :
% 9.17/5.36 ( ( member_int @ Z @ ( produc4627640435386541703et_int @ C @ P4 ) )
% 9.17/5.36 => ~ ! [X4: produc3658429121746597890et_nat > $o,Y5: produc3658429121746597890et_nat] :
% 9.17/5.36 ( ( P4
% 9.17/5.36 = ( produc5001842942810119800et_nat @ X4 @ Y5 ) )
% 9.17/5.36 => ~ ( member_int @ Z @ ( C @ X4 @ Y5 ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2952_mem__case__prodE,axiom,
% 9.17/5.36 ! [Z: product_prod_nat_nat,C: ( int > option6357759511663192854e_term ) > product_prod_int_int > set_Pr1261947904930325089at_nat,P4: produc7773217078559923341nt_int] :
% 9.17/5.36 ( ( member8440522571783428010at_nat @ Z @ ( produc5154663461364529269at_nat @ C @ P4 ) )
% 9.17/5.36 => ~ ! [X4: int > option6357759511663192854e_term,Y5: product_prod_int_int] :
% 9.17/5.36 ( ( P4
% 9.17/5.36 = ( produc4305682042979456191nt_int @ X4 @ Y5 ) )
% 9.17/5.36 => ~ ( member8440522571783428010at_nat @ Z @ ( C @ X4 @ Y5 ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2953_mem__case__prodE,axiom,
% 9.17/5.36 ! [Z: $o,C: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_o,P4: produc1908205239877642774nteger] :
% 9.17/5.36 ( ( member_o @ Z @ ( produc2373554395599118147_set_o @ C @ P4 ) )
% 9.17/5.36 => ~ ! [X4: produc6241069584506657477e_term > option6357759511663192854e_term,Y5: produc8923325533196201883nteger] :
% 9.17/5.36 ( ( P4
% 9.17/5.36 = ( produc8603105652947943368nteger @ X4 @ Y5 ) )
% 9.17/5.36 => ~ ( member_o @ Z @ ( C @ X4 @ Y5 ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2954_mem__case__prodE,axiom,
% 9.17/5.36 ! [Z: nat,C: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_nat,P4: produc1908205239877642774nteger] :
% 9.17/5.36 ( ( member_nat @ Z @ ( produc654622801845291899et_nat @ C @ P4 ) )
% 9.17/5.36 => ~ ! [X4: produc6241069584506657477e_term > option6357759511663192854e_term,Y5: produc8923325533196201883nteger] :
% 9.17/5.36 ( ( P4
% 9.17/5.36 = ( produc8603105652947943368nteger @ X4 @ Y5 ) )
% 9.17/5.36 => ~ ( member_nat @ Z @ ( C @ X4 @ Y5 ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2955_mem__case__prodE,axiom,
% 9.17/5.36 ! [Z: int,C: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_int,P4: produc1908205239877642774nteger] :
% 9.17/5.36 ( ( member_int @ Z @ ( produc5700143819190870999et_int @ C @ P4 ) )
% 9.17/5.36 => ~ ! [X4: produc6241069584506657477e_term > option6357759511663192854e_term,Y5: produc8923325533196201883nteger] :
% 9.17/5.36 ( ( P4
% 9.17/5.36 = ( produc8603105652947943368nteger @ X4 @ Y5 ) )
% 9.17/5.36 => ~ ( member_int @ Z @ ( C @ X4 @ Y5 ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2956_case__prodD,axiom,
% 9.17/5.36 ! [F: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o,A: produc6241069584506657477e_term > option6357759511663192854e_term,B: produc8923325533196201883nteger] :
% 9.17/5.36 ( ( produc6253627499356882019eger_o @ F @ ( produc8603105652947943368nteger @ A @ B ) )
% 9.17/5.36 => ( F @ A @ B ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2957_case__prodD,axiom,
% 9.17/5.36 ! [F: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o,A: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat] :
% 9.17/5.36 ( ( produc1437786849005270451_nat_o @ F @ ( produc5001842942810119800et_nat @ A @ B ) )
% 9.17/5.36 => ( F @ A @ B ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2958_case__prodD,axiom,
% 9.17/5.36 ! [F: ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o,A: produc3658429121746597890et_nat > $o,B: produc3925858234332021118et_nat] :
% 9.17/5.36 ( ( produc838355143741117751_nat_o @ F @ ( produc2245416461498447860et_nat @ A @ B ) )
% 9.17/5.36 => ( F @ A @ B ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2959_case__prodD,axiom,
% 9.17/5.36 ! [F: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o,A: produc8551481072490612790e_term > option6357759511663192854e_term,B: product_prod_int_int] :
% 9.17/5.36 ( ( produc1573362020775583542_int_o @ F @ ( produc5700946648718959541nt_int @ A @ B ) )
% 9.17/5.36 => ( F @ A @ B ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2960_case__prodD,axiom,
% 9.17/5.36 ! [F: ( int > option6357759511663192854e_term ) > product_prod_int_int > $o,A: int > option6357759511663192854e_term,B: product_prod_int_int] :
% 9.17/5.36 ( ( produc2558449545302689196_int_o @ F @ ( produc4305682042979456191nt_int @ A @ B ) )
% 9.17/5.36 => ( F @ A @ B ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2961_case__prodE,axiom,
% 9.17/5.36 ! [C: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o,P4: produc1908205239877642774nteger] :
% 9.17/5.36 ( ( produc6253627499356882019eger_o @ C @ P4 )
% 9.17/5.36 => ~ ! [X4: produc6241069584506657477e_term > option6357759511663192854e_term,Y5: produc8923325533196201883nteger] :
% 9.17/5.36 ( ( P4
% 9.17/5.36 = ( produc8603105652947943368nteger @ X4 @ Y5 ) )
% 9.17/5.36 => ~ ( C @ X4 @ Y5 ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2962_case__prodE,axiom,
% 9.17/5.36 ! [C: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o,P4: produc3925858234332021118et_nat] :
% 9.17/5.36 ( ( produc1437786849005270451_nat_o @ C @ P4 )
% 9.17/5.36 => ~ ! [X4: produc3658429121746597890et_nat > $o,Y5: produc3658429121746597890et_nat] :
% 9.17/5.36 ( ( P4
% 9.17/5.36 = ( produc5001842942810119800et_nat @ X4 @ Y5 ) )
% 9.17/5.36 => ~ ( C @ X4 @ Y5 ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2963_case__prodE,axiom,
% 9.17/5.36 ! [C: ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o,P4: produc2732055786443039994et_nat] :
% 9.17/5.36 ( ( produc838355143741117751_nat_o @ C @ P4 )
% 9.17/5.36 => ~ ! [X4: produc3658429121746597890et_nat > $o,Y5: produc3925858234332021118et_nat] :
% 9.17/5.36 ( ( P4
% 9.17/5.36 = ( produc2245416461498447860et_nat @ X4 @ Y5 ) )
% 9.17/5.36 => ~ ( C @ X4 @ Y5 ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2964_case__prodE,axiom,
% 9.17/5.36 ! [C: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o,P4: produc2285326912895808259nt_int] :
% 9.17/5.36 ( ( produc1573362020775583542_int_o @ C @ P4 )
% 9.17/5.36 => ~ ! [X4: produc8551481072490612790e_term > option6357759511663192854e_term,Y5: product_prod_int_int] :
% 9.17/5.36 ( ( P4
% 9.17/5.36 = ( produc5700946648718959541nt_int @ X4 @ Y5 ) )
% 9.17/5.36 => ~ ( C @ X4 @ Y5 ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2965_case__prodE,axiom,
% 9.17/5.36 ! [C: ( int > option6357759511663192854e_term ) > product_prod_int_int > $o,P4: produc7773217078559923341nt_int] :
% 9.17/5.36 ( ( produc2558449545302689196_int_o @ C @ P4 )
% 9.17/5.36 => ~ ! [X4: int > option6357759511663192854e_term,Y5: product_prod_int_int] :
% 9.17/5.36 ( ( P4
% 9.17/5.36 = ( produc4305682042979456191nt_int @ X4 @ Y5 ) )
% 9.17/5.36 => ~ ( C @ X4 @ Y5 ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2966_add__One__commute,axiom,
% 9.17/5.36 ! [N2: num] :
% 9.17/5.36 ( ( plus_plus_num @ one @ N2 )
% 9.17/5.36 = ( plus_plus_num @ N2 @ one ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2967_case__prodD_H,axiom,
% 9.17/5.36 ! [R4: nat > nat > product_prod_nat_nat > $o,A: nat,B: nat,C: product_prod_nat_nat] :
% 9.17/5.36 ( ( produc8739625826339149834_nat_o @ R4 @ ( product_Pair_nat_nat @ A @ B ) @ C )
% 9.17/5.36 => ( R4 @ A @ B @ C ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2968_case__prodE_H,axiom,
% 9.17/5.36 ! [C: nat > nat > product_prod_nat_nat > $o,P4: product_prod_nat_nat,Z: product_prod_nat_nat] :
% 9.17/5.36 ( ( produc8739625826339149834_nat_o @ C @ P4 @ Z )
% 9.17/5.36 => ~ ! [X4: nat,Y5: nat] :
% 9.17/5.36 ( ( P4
% 9.17/5.36 = ( product_Pair_nat_nat @ X4 @ Y5 ) )
% 9.17/5.36 => ~ ( C @ X4 @ Y5 @ Z ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2969_sum_OatLeast__int__atMost__int__shift,axiom,
% 9.17/5.36 ! [G: int > nat,M2: nat,N2: nat] :
% 9.17/5.36 ( ( groups4541462559716669496nt_nat @ G @ ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 9.17/5.36 = ( groups3542108847815614940at_nat @ ( comp_int_nat_nat @ G @ semiri1314217659103216013at_int ) @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2970_sum_OatLeast__int__atMost__int__shift,axiom,
% 9.17/5.36 ! [G: int > int,M2: nat,N2: nat] :
% 9.17/5.36 ( ( groups4538972089207619220nt_int @ G @ ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 9.17/5.36 = ( groups3539618377306564664at_int @ ( comp_int_int_nat @ G @ semiri1314217659103216013at_int ) @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2971_less__int_Oabs__eq,axiom,
% 9.17/5.36 ! [Xa: product_prod_nat_nat,X: product_prod_nat_nat] :
% 9.17/5.36 ( ( ord_less_int @ ( abs_Integ @ Xa ) @ ( abs_Integ @ X ) )
% 9.17/5.36 = ( produc8739625826339149834_nat_o
% 9.17/5.36 @ ^ [X3: nat,Y3: nat] :
% 9.17/5.36 ( produc6081775807080527818_nat_o
% 9.17/5.36 @ ^ [U2: nat,V2: nat] : ( ord_less_nat @ ( plus_plus_nat @ X3 @ V2 ) @ ( plus_plus_nat @ U2 @ Y3 ) ) )
% 9.17/5.36 @ Xa
% 9.17/5.36 @ X ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2972_less__eq__int_Oabs__eq,axiom,
% 9.17/5.36 ! [Xa: product_prod_nat_nat,X: product_prod_nat_nat] :
% 9.17/5.36 ( ( ord_less_eq_int @ ( abs_Integ @ Xa ) @ ( abs_Integ @ X ) )
% 9.17/5.36 = ( produc8739625826339149834_nat_o
% 9.17/5.36 @ ^ [X3: nat,Y3: nat] :
% 9.17/5.36 ( produc6081775807080527818_nat_o
% 9.17/5.36 @ ^ [U2: nat,V2: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X3 @ V2 ) @ ( plus_plus_nat @ U2 @ Y3 ) ) )
% 9.17/5.36 @ Xa
% 9.17/5.36 @ X ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2973_zadd__int__left,axiom,
% 9.17/5.36 ! [M2: nat,N2: nat,Z: int] :
% 9.17/5.36 ( ( plus_plus_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ Z ) )
% 9.17/5.36 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ ( plus_plus_nat @ M2 @ N2 ) ) @ Z ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2974_int__plus,axiom,
% 9.17/5.36 ! [N2: nat,M2: nat] :
% 9.17/5.36 ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ N2 @ M2 ) )
% 9.17/5.36 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( semiri1314217659103216013at_int @ M2 ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2975_int__ops_I5_J,axiom,
% 9.17/5.36 ! [A: nat,B: nat] :
% 9.17/5.36 ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ A @ B ) )
% 9.17/5.36 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2976_int__ops_I2_J,axiom,
% 9.17/5.36 ( ( semiri1314217659103216013at_int @ one_one_nat )
% 9.17/5.36 = one_one_int ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2977_zle__iff__zadd,axiom,
% 9.17/5.36 ( ord_less_eq_int
% 9.17/5.36 = ( ^ [W2: int,Z4: int] :
% 9.17/5.36 ? [N4: nat] :
% 9.17/5.36 ( Z4
% 9.17/5.36 = ( plus_plus_int @ W2 @ ( semiri1314217659103216013at_int @ N4 ) ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2978_numeral__One,axiom,
% 9.17/5.36 ( ( numeral_numeral_nat @ one )
% 9.17/5.36 = one_one_nat ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2979_numeral__One,axiom,
% 9.17/5.36 ( ( numeral_numeral_int @ one )
% 9.17/5.36 = one_one_int ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2980_numeral__One,axiom,
% 9.17/5.36 ( ( numera6620942414471956472nteger @ one )
% 9.17/5.36 = one_one_Code_integer ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2981_numeral__One,axiom,
% 9.17/5.36 ( ( numeral_numeral_rat @ one )
% 9.17/5.36 = one_one_rat ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2982_numeral__One,axiom,
% 9.17/5.36 ( ( numera5444537566228673987atural @ one )
% 9.17/5.36 = one_one_Code_natural ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2983_numerals_I1_J,axiom,
% 9.17/5.36 ( ( numeral_numeral_nat @ one )
% 9.17/5.36 = one_one_nat ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2984_execute__bind__case,axiom,
% 9.17/5.36 ! [F: heap_T6362127782908069795rray_a,G: array_a > heap_T6362127782908069795rray_a,H3: heap_e7401611519738050253t_unit] :
% 9.17/5.36 ( ( heap_T5591663578999710211rray_a @ ( heap_T2407400398799471159rray_a @ F @ G ) @ H3 )
% 9.17/5.36 = ( case_o8555119740594961093it_nat @ none_P2587165478634041381it_nat
% 9.17/5.36 @ ( produc8915672860170107321it_nat
% 9.17/5.36 @ ^ [X3: array_a] :
% 9.17/5.36 ( produc921929042997482327it_nat
% 9.17/5.36 @ ^ [H6: heap_e7401611519738050253t_unit,N4: nat] : ( heap_T531568236820715630rray_a @ N4 @ ( heap_T5591663578999710211rray_a @ ( G @ X3 ) @ H6 ) ) ) )
% 9.17/5.36 @ ( heap_T5591663578999710211rray_a @ F @ H3 ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2985_execute__bind__case,axiom,
% 9.17/5.36 ! [F: heap_T5738788834812785303t_unit,G: product_unit > heap_T6362127782908069795rray_a,H3: heap_e7401611519738050253t_unit] :
% 9.17/5.36 ( ( heap_T5591663578999710211rray_a @ ( heap_T7158140910958840029rray_a @ F @ G ) @ H3 )
% 9.17/5.36 = ( case_o5699750240967658439it_nat @ none_P2587165478634041381it_nat
% 9.17/5.36 @ ( produc875294279294635931it_nat
% 9.17/5.36 @ ^ [X3: product_unit] :
% 9.17/5.36 ( produc921929042997482327it_nat
% 9.17/5.36 @ ^ [H6: heap_e7401611519738050253t_unit,N4: nat] : ( heap_T531568236820715630rray_a @ N4 @ ( heap_T5591663578999710211rray_a @ ( G @ X3 ) @ H6 ) ) ) )
% 9.17/5.36 @ ( heap_T875086893843062177t_unit @ F @ H3 ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2986_execute__bind__case,axiom,
% 9.17/5.36 ! [F: heap_T6362127782908069795rray_a,G: array_a > heap_T5738788834812785303t_unit,H3: heap_e7401611519738050253t_unit] :
% 9.17/5.36 ( ( heap_T875086893843062177t_unit @ ( heap_T7324619625323989613t_unit @ F @ G ) @ H3 )
% 9.17/5.36 = ( case_o3886096569520666655it_nat @ none_P9117596204409417319it_nat
% 9.17/5.36 @ ( produc3495058329975564393it_nat
% 9.17/5.36 @ ^ [X3: array_a] :
% 9.17/5.36 ( produc7488178964372371019it_nat
% 9.17/5.36 @ ^ [H6: heap_e7401611519738050253t_unit,N4: nat] : ( heap_T3616969660504097270t_unit @ N4 @ ( heap_T875086893843062177t_unit @ ( G @ X3 ) @ H6 ) ) ) )
% 9.17/5.36 @ ( heap_T5591663578999710211rray_a @ F @ H3 ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2987_execute__bind__case,axiom,
% 9.17/5.36 ! [F: heap_T5738788834812785303t_unit,G: product_unit > heap_T5738788834812785303t_unit,H3: heap_e7401611519738050253t_unit] :
% 9.17/5.36 ( ( heap_T875086893843062177t_unit @ ( heap_T2633723481742716231t_unit @ F @ G ) @ H3 )
% 9.17/5.36 = ( case_o2963978774867076333it_nat @ none_P9117596204409417319it_nat
% 9.17/5.36 @ ( produc1230459020282432263it_nat
% 9.17/5.36 @ ^ [X3: product_unit] :
% 9.17/5.36 ( produc7488178964372371019it_nat
% 9.17/5.36 @ ^ [H6: heap_e7401611519738050253t_unit,N4: nat] : ( heap_T3616969660504097270t_unit @ N4 @ ( heap_T875086893843062177t_unit @ ( G @ X3 ) @ H6 ) ) ) )
% 9.17/5.36 @ ( heap_T875086893843062177t_unit @ F @ H3 ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2988_Sum__Icc__int,axiom,
% 9.17/5.36 ! [M2: int,N2: int] :
% 9.17/5.36 ( ( ord_less_eq_int @ M2 @ N2 )
% 9.17/5.36 => ( ( groups4538972089207619220nt_int
% 9.17/5.36 @ ^ [X3: int] : X3
% 9.17/5.36 @ ( set_or1266510415728281911st_int @ M2 @ N2 ) )
% 9.17/5.36 = ( divide_divide_int @ ( minus_minus_int @ ( times_times_int @ N2 @ ( plus_plus_int @ N2 @ one_one_int ) ) @ ( times_times_int @ M2 @ ( minus_minus_int @ M2 @ one_one_int ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2989_Heap__Time__Monad_Obind__def,axiom,
% 9.17/5.36 ( heap_T2407400398799471159rray_a
% 9.17/5.36 = ( ^ [F2: heap_T6362127782908069795rray_a,G2: array_a > heap_T6362127782908069795rray_a] :
% 9.17/5.36 ( heap_T1488828001306802186rray_a
% 9.17/5.36 @ ^ [H: heap_e7401611519738050253t_unit] :
% 9.17/5.36 ( case_o8555119740594961093it_nat @ none_P2587165478634041381it_nat
% 9.17/5.36 @ ( produc8915672860170107321it_nat
% 9.17/5.36 @ ^ [R3: array_a] :
% 9.17/5.36 ( produc921929042997482327it_nat
% 9.17/5.36 @ ^ [H6: heap_e7401611519738050253t_unit,N4: nat] : ( heap_T531568236820715630rray_a @ N4 @ ( heap_T5591663578999710211rray_a @ ( G2 @ R3 ) @ H6 ) ) ) )
% 9.17/5.36 @ ( heap_T5591663578999710211rray_a @ F2 @ H ) ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2990_Heap__Time__Monad_Obind__def,axiom,
% 9.17/5.36 ( heap_T7158140910958840029rray_a
% 9.17/5.36 = ( ^ [F2: heap_T5738788834812785303t_unit,G2: product_unit > heap_T6362127782908069795rray_a] :
% 9.17/5.36 ( heap_T1488828001306802186rray_a
% 9.17/5.36 @ ^ [H: heap_e7401611519738050253t_unit] :
% 9.17/5.36 ( case_o5699750240967658439it_nat @ none_P2587165478634041381it_nat
% 9.17/5.36 @ ( produc875294279294635931it_nat
% 9.17/5.36 @ ^ [R3: product_unit] :
% 9.17/5.36 ( produc921929042997482327it_nat
% 9.17/5.36 @ ^ [H6: heap_e7401611519738050253t_unit,N4: nat] : ( heap_T531568236820715630rray_a @ N4 @ ( heap_T5591663578999710211rray_a @ ( G2 @ R3 ) @ H6 ) ) ) )
% 9.17/5.36 @ ( heap_T875086893843062177t_unit @ F2 @ H ) ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2991_Heap__Time__Monad_Obind__def,axiom,
% 9.17/5.36 ( heap_T7324619625323989613t_unit
% 9.17/5.36 = ( ^ [F2: heap_T6362127782908069795rray_a,G2: array_a > heap_T5738788834812785303t_unit] :
% 9.17/5.36 ( heap_T6183433275982383450t_unit
% 9.17/5.36 @ ^ [H: heap_e7401611519738050253t_unit] :
% 9.17/5.36 ( case_o3886096569520666655it_nat @ none_P9117596204409417319it_nat
% 9.17/5.36 @ ( produc3495058329975564393it_nat
% 9.17/5.36 @ ^ [R3: array_a] :
% 9.17/5.36 ( produc7488178964372371019it_nat
% 9.17/5.36 @ ^ [H6: heap_e7401611519738050253t_unit,N4: nat] : ( heap_T3616969660504097270t_unit @ N4 @ ( heap_T875086893843062177t_unit @ ( G2 @ R3 ) @ H6 ) ) ) )
% 9.17/5.36 @ ( heap_T5591663578999710211rray_a @ F2 @ H ) ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2992_Heap__Time__Monad_Obind__def,axiom,
% 9.17/5.36 ( heap_T2633723481742716231t_unit
% 9.17/5.36 = ( ^ [F2: heap_T5738788834812785303t_unit,G2: product_unit > heap_T5738788834812785303t_unit] :
% 9.17/5.36 ( heap_T6183433275982383450t_unit
% 9.17/5.36 @ ^ [H: heap_e7401611519738050253t_unit] :
% 9.17/5.36 ( case_o2963978774867076333it_nat @ none_P9117596204409417319it_nat
% 9.17/5.36 @ ( produc1230459020282432263it_nat
% 9.17/5.36 @ ^ [R3: product_unit] :
% 9.17/5.36 ( produc7488178964372371019it_nat
% 9.17/5.36 @ ^ [H6: heap_e7401611519738050253t_unit,N4: nat] : ( heap_T3616969660504097270t_unit @ N4 @ ( heap_T875086893843062177t_unit @ ( G2 @ R3 ) @ H6 ) ) ) )
% 9.17/5.36 @ ( heap_T875086893843062177t_unit @ F2 @ H ) ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2993_zless__iff__Suc__zadd,axiom,
% 9.17/5.36 ( ord_less_int
% 9.17/5.36 = ( ^ [W2: int,Z4: int] :
% 9.17/5.36 ? [N4: nat] :
% 9.17/5.36 ( Z4
% 9.17/5.36 = ( plus_plus_int @ W2 @ ( semiri1314217659103216013at_int @ ( suc @ N4 ) ) ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2994_int__ops_I4_J,axiom,
% 9.17/5.36 ! [A: nat] :
% 9.17/5.36 ( ( semiri1314217659103216013at_int @ ( suc @ A ) )
% 9.17/5.36 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ one_one_int ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2995_int__Suc,axiom,
% 9.17/5.36 ! [N2: nat] :
% 9.17/5.36 ( ( semiri1314217659103216013at_int @ ( suc @ N2 ) )
% 9.17/5.36 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2996_int__bit__induct,axiom,
% 9.17/5.36 ! [P: int > $o,K: int] :
% 9.17/5.36 ( ( P @ zero_zero_int )
% 9.17/5.36 => ( ( P @ ( uminus_uminus_int @ one_one_int ) )
% 9.17/5.36 => ( ! [K5: int] :
% 9.17/5.36 ( ( P @ K5 )
% 9.17/5.36 => ( ( K5 != zero_zero_int )
% 9.17/5.36 => ( P @ ( times_times_int @ K5 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) )
% 9.17/5.36 => ( ! [K5: int] :
% 9.17/5.36 ( ( P @ K5 )
% 9.17/5.36 => ( ( K5
% 9.17/5.36 != ( uminus_uminus_int @ one_one_int ) )
% 9.17/5.36 => ( P @ ( plus_plus_int @ one_one_int @ ( times_times_int @ K5 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) )
% 9.17/5.36 => ( P @ K ) ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2997_uminus__numeral__One,axiom,
% 9.17/5.36 ( ( uminus_uminus_int @ ( numeral_numeral_int @ one ) )
% 9.17/5.36 = ( uminus_uminus_int @ one_one_int ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2998_uminus__numeral__One,axiom,
% 9.17/5.36 ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) )
% 9.17/5.36 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_2999_uminus__numeral__One,axiom,
% 9.17/5.36 ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) )
% 9.17/5.36 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3000_int__def,axiom,
% 9.17/5.36 ( semiri1314217659103216013at_int
% 9.17/5.36 = ( ^ [N4: nat] : ( abs_Integ @ ( product_Pair_nat_nat @ N4 @ zero_zero_nat ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3001_num__of__nat__One,axiom,
% 9.17/5.36 ! [N2: nat] :
% 9.17/5.36 ( ( ord_less_eq_nat @ N2 @ one_one_nat )
% 9.17/5.36 => ( ( num_of_nat @ N2 )
% 9.17/5.36 = one ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3002_neg__zdiv__mult__2,axiom,
% 9.17/5.36 ! [A: int,B: int] :
% 9.17/5.36 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 9.17/5.36 => ( ( 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 ) )
% 9.17/5.36 = ( divide_divide_int @ ( plus_plus_int @ B @ one_one_int ) @ A ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3003_pos__zdiv__mult__2,axiom,
% 9.17/5.36 ! [A: int,B: int] :
% 9.17/5.36 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 9.17/5.36 => ( ( 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 ) )
% 9.17/5.36 = ( divide_divide_int @ B @ A ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3004_pos__zmod__mult__2,axiom,
% 9.17/5.36 ! [A: int,B: int] :
% 9.17/5.36 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 9.17/5.36 => ( ( 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 ) )
% 9.17/5.36 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ B @ A ) ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3005_mod__mult2__eq_H,axiom,
% 9.17/5.36 ! [A: int,M2: nat,N2: nat] :
% 9.17/5.36 ( ( modulo_modulo_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 9.17/5.36 = ( plus_plus_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( modulo_modulo_int @ ( divide_divide_int @ A @ ( semiri1314217659103216013at_int @ M2 ) ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) @ ( modulo_modulo_int @ A @ ( semiri1314217659103216013at_int @ M2 ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3006_mod__mult2__eq_H,axiom,
% 9.17/5.36 ! [A: nat,M2: nat,N2: nat] :
% 9.17/5.36 ( ( modulo_modulo_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M2 ) @ ( semiri1316708129612266289at_nat @ N2 ) ) )
% 9.17/5.36 = ( plus_plus_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M2 ) @ ( modulo_modulo_nat @ ( divide_divide_nat @ A @ ( semiri1316708129612266289at_nat @ M2 ) ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) @ ( modulo_modulo_nat @ A @ ( semiri1316708129612266289at_nat @ M2 ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3007_mod__mult2__eq_H,axiom,
% 9.17/5.36 ! [A: code_integer,M2: nat,N2: nat] :
% 9.17/5.36 ( ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M2 ) @ ( semiri4939895301339042750nteger @ N2 ) ) )
% 9.17/5.36 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M2 ) @ ( modulo364778990260209775nteger @ ( divide6298287555418463151nteger @ A @ ( semiri4939895301339042750nteger @ M2 ) ) @ ( semiri4939895301339042750nteger @ N2 ) ) ) @ ( modulo364778990260209775nteger @ A @ ( semiri4939895301339042750nteger @ M2 ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3008_mod__mult2__eq_H,axiom,
% 9.17/5.36 ! [A: code_natural,M2: nat,N2: nat] :
% 9.17/5.36 ( ( modulo8411746178871703098atural @ A @ ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ M2 ) @ ( semiri3763490453095760265atural @ N2 ) ) )
% 9.17/5.36 = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ M2 ) @ ( modulo8411746178871703098atural @ ( divide5121882707175180666atural @ A @ ( semiri3763490453095760265atural @ M2 ) ) @ ( semiri3763490453095760265atural @ N2 ) ) ) @ ( modulo8411746178871703098atural @ A @ ( semiri3763490453095760265atural @ M2 ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3009_numeral__num__of__nat__unfold,axiom,
% 9.17/5.36 ! [N2: nat] :
% 9.17/5.36 ( ( ( N2 = zero_zero_nat )
% 9.17/5.36 => ( ( numeral_numeral_rat @ ( num_of_nat @ N2 ) )
% 9.17/5.36 = one_one_rat ) )
% 9.17/5.36 & ( ( N2 != zero_zero_nat )
% 9.17/5.36 => ( ( numeral_numeral_rat @ ( num_of_nat @ N2 ) )
% 9.17/5.36 = ( semiri681578069525770553at_rat @ N2 ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3010_numeral__num__of__nat__unfold,axiom,
% 9.17/5.36 ! [N2: nat] :
% 9.17/5.36 ( ( ( N2 = zero_zero_nat )
% 9.17/5.36 => ( ( numeral_numeral_int @ ( num_of_nat @ N2 ) )
% 9.17/5.36 = one_one_int ) )
% 9.17/5.36 & ( ( N2 != zero_zero_nat )
% 9.17/5.36 => ( ( numeral_numeral_int @ ( num_of_nat @ N2 ) )
% 9.17/5.36 = ( semiri1314217659103216013at_int @ N2 ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3011_numeral__num__of__nat__unfold,axiom,
% 9.17/5.36 ! [N2: nat] :
% 9.17/5.36 ( ( ( N2 = zero_zero_nat )
% 9.17/5.36 => ( ( numeral_numeral_nat @ ( num_of_nat @ N2 ) )
% 9.17/5.36 = one_one_nat ) )
% 9.17/5.36 & ( ( N2 != zero_zero_nat )
% 9.17/5.36 => ( ( numeral_numeral_nat @ ( num_of_nat @ N2 ) )
% 9.17/5.36 = ( semiri1316708129612266289at_nat @ N2 ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3012_numeral__num__of__nat__unfold,axiom,
% 9.17/5.36 ! [N2: nat] :
% 9.17/5.36 ( ( ( N2 = zero_zero_nat )
% 9.17/5.36 => ( ( numera6620942414471956472nteger @ ( num_of_nat @ N2 ) )
% 9.17/5.36 = one_one_Code_integer ) )
% 9.17/5.36 & ( ( N2 != zero_zero_nat )
% 9.17/5.36 => ( ( numera6620942414471956472nteger @ ( num_of_nat @ N2 ) )
% 9.17/5.36 = ( semiri4939895301339042750nteger @ N2 ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3013_numeral__num__of__nat__unfold,axiom,
% 9.17/5.36 ! [N2: nat] :
% 9.17/5.36 ( ( ( N2 = zero_zero_nat )
% 9.17/5.36 => ( ( numera5444537566228673987atural @ ( num_of_nat @ N2 ) )
% 9.17/5.36 = one_one_Code_natural ) )
% 9.17/5.36 & ( ( N2 != zero_zero_nat )
% 9.17/5.36 => ( ( numera5444537566228673987atural @ ( num_of_nat @ N2 ) )
% 9.17/5.36 = ( semiri3763490453095760265atural @ N2 ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3014_double__arith__series,axiom,
% 9.17/5.36 ! [A: rat,D2: rat,N2: nat] :
% 9.17/5.36 ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) )
% 9.17/5.36 @ ( groups2906978787729119204at_rat
% 9.17/5.36 @ ^ [I3: nat] : ( plus_plus_rat @ A @ ( times_times_rat @ ( semiri681578069525770553at_rat @ I3 ) @ D2 ) )
% 9.17/5.36 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 9.17/5.36 = ( times_times_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N2 ) @ one_one_rat ) @ ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ A ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N2 ) @ D2 ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3015_double__arith__series,axiom,
% 9.17/5.36 ! [A: int,D2: int,N2: nat] :
% 9.17/5.36 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) )
% 9.17/5.36 @ ( groups3539618377306564664at_int
% 9.17/5.36 @ ^ [I3: nat] : ( plus_plus_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ I3 ) @ D2 ) )
% 9.17/5.36 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 9.17/5.36 = ( times_times_int @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ D2 ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3016_double__arith__series,axiom,
% 9.17/5.36 ! [A: code_integer,D2: code_integer,N2: nat] :
% 9.17/5.36 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) )
% 9.17/5.36 @ ( groups7501900531339628137nteger
% 9.17/5.36 @ ^ [I3: nat] : ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ I3 ) @ D2 ) )
% 9.17/5.36 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 9.17/5.36 = ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N2 ) @ one_one_Code_integer ) @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N2 ) @ D2 ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3017_double__arith__series,axiom,
% 9.17/5.36 ! [A: code_natural,D2: code_natural,N2: nat] :
% 9.17/5.36 ( ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) )
% 9.17/5.36 @ ( groups6325495683096345652atural
% 9.17/5.36 @ ^ [I3: nat] : ( plus_p4538020629002901425atural @ A @ ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ I3 ) @ D2 ) )
% 9.17/5.36 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 9.17/5.36 = ( times_2397367101498566445atural @ ( plus_p4538020629002901425atural @ ( semiri3763490453095760265atural @ N2 ) @ one_one_Code_natural ) @ ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A ) @ ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ N2 ) @ D2 ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3018_double__arith__series,axiom,
% 9.17/5.36 ! [A: nat,D2: nat,N2: nat] :
% 9.17/5.36 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 9.17/5.36 @ ( groups3542108847815614940at_nat
% 9.17/5.36 @ ^ [I3: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ I3 ) @ D2 ) )
% 9.17/5.36 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 9.17/5.36 = ( times_times_nat @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ one_one_nat ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ D2 ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3019_double__gauss__sum,axiom,
% 9.17/5.36 ! [N2: nat] :
% 9.17/5.36 ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( groups2906978787729119204at_rat @ semiri681578069525770553at_rat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 9.17/5.36 = ( times_times_rat @ ( semiri681578069525770553at_rat @ N2 ) @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N2 ) @ one_one_rat ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3020_double__gauss__sum,axiom,
% 9.17/5.36 ! [N2: nat] :
% 9.17/5.36 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 9.17/5.36 = ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3021_double__gauss__sum,axiom,
% 9.17/5.36 ! [N2: nat] :
% 9.17/5.36 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( groups7501900531339628137nteger @ semiri4939895301339042750nteger @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 9.17/5.36 = ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N2 ) @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N2 ) @ one_one_Code_integer ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3022_double__gauss__sum,axiom,
% 9.17/5.36 ! [N2: nat] :
% 9.17/5.36 ( ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( groups6325495683096345652atural @ semiri3763490453095760265atural @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 9.17/5.36 = ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ N2 ) @ ( plus_p4538020629002901425atural @ ( semiri3763490453095760265atural @ N2 ) @ one_one_Code_natural ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3023_double__gauss__sum,axiom,
% 9.17/5.36 ! [N2: nat] :
% 9.17/5.36 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 9.17/5.36 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ one_one_nat ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3024_neg__zmod__mult__2,axiom,
% 9.17/5.36 ! [A: int,B: int] :
% 9.17/5.36 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 9.17/5.36 => ( ( 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 ) )
% 9.17/5.36 = ( 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 ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3025_mult__2,axiom,
% 9.17/5.36 ! [Z: nat] :
% 9.17/5.36 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Z )
% 9.17/5.36 = ( plus_plus_nat @ Z @ Z ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3026_mult__2,axiom,
% 9.17/5.36 ! [Z: int] :
% 9.17/5.36 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Z )
% 9.17/5.36 = ( plus_plus_int @ Z @ Z ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3027_mult__2,axiom,
% 9.17/5.36 ! [Z: code_integer] :
% 9.17/5.36 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Z )
% 9.17/5.36 = ( plus_p5714425477246183910nteger @ Z @ Z ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3028_mult__2,axiom,
% 9.17/5.36 ! [Z: rat] :
% 9.17/5.36 ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ Z )
% 9.17/5.36 = ( plus_plus_rat @ Z @ Z ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3029_mult__2,axiom,
% 9.17/5.36 ! [Z: code_natural] :
% 9.17/5.36 ( ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ Z )
% 9.17/5.36 = ( plus_p4538020629002901425atural @ Z @ Z ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3030_mult__2__right,axiom,
% 9.17/5.36 ! [Z: nat] :
% 9.17/5.36 ( ( times_times_nat @ Z @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.17/5.36 = ( plus_plus_nat @ Z @ Z ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3031_mult__2__right,axiom,
% 9.17/5.36 ! [Z: int] :
% 9.17/5.36 ( ( times_times_int @ Z @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.17/5.36 = ( plus_plus_int @ Z @ Z ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3032_mult__2__right,axiom,
% 9.17/5.36 ! [Z: code_integer] :
% 9.17/5.36 ( ( times_3573771949741848930nteger @ Z @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 9.17/5.36 = ( plus_p5714425477246183910nteger @ Z @ Z ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3033_mult__2__right,axiom,
% 9.17/5.36 ! [Z: rat] :
% 9.17/5.36 ( ( times_times_rat @ Z @ ( numeral_numeral_rat @ ( bit0 @ one ) ) )
% 9.17/5.36 = ( plus_plus_rat @ Z @ Z ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3034_mult__2__right,axiom,
% 9.17/5.36 ! [Z: code_natural] :
% 9.17/5.36 ( ( times_2397367101498566445atural @ Z @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 9.17/5.36 = ( plus_p4538020629002901425atural @ Z @ Z ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3035_left__add__twice,axiom,
% 9.17/5.36 ! [A: nat,B: nat] :
% 9.17/5.36 ( ( plus_plus_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 9.17/5.36 = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3036_left__add__twice,axiom,
% 9.17/5.36 ! [A: int,B: int] :
% 9.17/5.36 ( ( plus_plus_int @ A @ ( plus_plus_int @ A @ B ) )
% 9.17/5.36 = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3037_left__add__twice,axiom,
% 9.17/5.36 ! [A: code_integer,B: code_integer] :
% 9.17/5.36 ( ( plus_p5714425477246183910nteger @ A @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 9.17/5.36 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3038_left__add__twice,axiom,
% 9.17/5.36 ! [A: rat,B: rat] :
% 9.17/5.36 ( ( plus_plus_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 9.17/5.36 = ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3039_left__add__twice,axiom,
% 9.17/5.36 ! [A: code_natural,B: code_natural] :
% 9.17/5.36 ( ( plus_p4538020629002901425atural @ A @ ( plus_p4538020629002901425atural @ A @ B ) )
% 9.17/5.36 = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3040_pos__eucl__rel__int__mult__2,axiom,
% 9.17/5.36 ! [B: int,A: int,Q3: int,R2: int] :
% 9.17/5.36 ( ( ord_less_eq_int @ zero_zero_int @ B )
% 9.17/5.36 => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q3 @ R2 ) )
% 9.17/5.36 => ( 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 ) ) @ R2 ) ) ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3041_one__power2,axiom,
% 9.17/5.36 ( ( power_8256067586552552935nteger @ one_one_Code_integer @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.17/5.36 = one_one_Code_integer ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3042_one__power2,axiom,
% 9.17/5.36 ( ( power_power_rat @ one_one_rat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.17/5.36 = one_one_rat ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3043_one__power2,axiom,
% 9.17/5.36 ( ( power_power_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.17/5.36 = one_one_nat ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3044_one__power2,axiom,
% 9.17/5.36 ( ( power_power_int @ one_one_int @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.17/5.36 = one_one_int ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3045_nat__1__add__1,axiom,
% 9.17/5.36 ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 9.17/5.36 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3046_Suc__nat__number__of__add,axiom,
% 9.17/5.36 ! [V: num,N2: nat] :
% 9.17/5.36 ( ( suc @ ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ N2 ) )
% 9.17/5.36 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ V @ one ) ) @ N2 ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3047_double__gauss__sum__from__Suc__0,axiom,
% 9.17/5.36 ! [N2: nat] :
% 9.17/5.36 ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( groups2906978787729119204at_rat @ semiri681578069525770553at_rat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) )
% 9.17/5.36 = ( times_times_rat @ ( semiri681578069525770553at_rat @ N2 ) @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N2 ) @ one_one_rat ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3048_double__gauss__sum__from__Suc__0,axiom,
% 9.17/5.36 ! [N2: nat] :
% 9.17/5.36 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) )
% 9.17/5.36 = ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3049_double__gauss__sum__from__Suc__0,axiom,
% 9.17/5.36 ! [N2: nat] :
% 9.17/5.36 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( groups7501900531339628137nteger @ semiri4939895301339042750nteger @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) )
% 9.17/5.36 = ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N2 ) @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N2 ) @ one_one_Code_integer ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3050_double__gauss__sum__from__Suc__0,axiom,
% 9.17/5.36 ! [N2: nat] :
% 9.17/5.36 ( ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( groups6325495683096345652atural @ semiri3763490453095760265atural @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) )
% 9.17/5.36 = ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ N2 ) @ ( plus_p4538020629002901425atural @ ( semiri3763490453095760265atural @ N2 ) @ one_one_Code_natural ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3051_double__gauss__sum__from__Suc__0,axiom,
% 9.17/5.36 ! [N2: nat] :
% 9.17/5.36 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) )
% 9.17/5.36 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ one_one_nat ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3052_arith__series,axiom,
% 9.17/5.36 ! [A: int,D2: int,N2: nat] :
% 9.17/5.36 ( ( groups3539618377306564664at_int
% 9.17/5.36 @ ^ [I3: nat] : ( plus_plus_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ I3 ) @ D2 ) )
% 9.17/5.36 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 9.17/5.36 = ( divide_divide_int @ ( times_times_int @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ D2 ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3053_arith__series,axiom,
% 9.17/5.36 ! [A: code_integer,D2: code_integer,N2: nat] :
% 9.17/5.36 ( ( groups7501900531339628137nteger
% 9.17/5.36 @ ^ [I3: nat] : ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ I3 ) @ D2 ) )
% 9.17/5.36 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 9.17/5.36 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N2 ) @ one_one_Code_integer ) @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N2 ) @ D2 ) ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3054_arith__series,axiom,
% 9.17/5.36 ! [A: code_natural,D2: code_natural,N2: nat] :
% 9.17/5.36 ( ( groups6325495683096345652atural
% 9.17/5.36 @ ^ [I3: nat] : ( plus_p4538020629002901425atural @ A @ ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ I3 ) @ D2 ) )
% 9.17/5.36 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 9.17/5.36 = ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ ( plus_p4538020629002901425atural @ ( semiri3763490453095760265atural @ N2 ) @ one_one_Code_natural ) @ ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A ) @ ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ N2 ) @ D2 ) ) ) @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3055_arith__series,axiom,
% 9.17/5.36 ! [A: nat,D2: nat,N2: nat] :
% 9.17/5.36 ( ( groups3542108847815614940at_nat
% 9.17/5.36 @ ^ [I3: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ I3 ) @ D2 ) )
% 9.17/5.36 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 9.17/5.36 = ( divide_divide_nat @ ( times_times_nat @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ one_one_nat ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ D2 ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3056_gauss__sum,axiom,
% 9.17/5.36 ! [N2: nat] :
% 9.17/5.36 ( ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 9.17/5.36 = ( divide_divide_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3057_gauss__sum,axiom,
% 9.17/5.36 ! [N2: nat] :
% 9.17/5.36 ( ( groups7501900531339628137nteger @ semiri4939895301339042750nteger @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 9.17/5.36 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N2 ) @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N2 ) @ one_one_Code_integer ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3058_gauss__sum,axiom,
% 9.17/5.36 ! [N2: nat] :
% 9.17/5.36 ( ( groups6325495683096345652atural @ semiri3763490453095760265atural @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 9.17/5.36 = ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ N2 ) @ ( plus_p4538020629002901425atural @ ( semiri3763490453095760265atural @ N2 ) @ one_one_Code_natural ) ) @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3059_gauss__sum,axiom,
% 9.17/5.36 ! [N2: nat] :
% 9.17/5.36 ( ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 9.17/5.36 = ( divide_divide_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3060_nat__approx__posE,axiom,
% 9.17/5.36 ! [E: rat] :
% 9.17/5.36 ( ( ord_less_rat @ zero_zero_rat @ E )
% 9.17/5.36 => ~ ! [N: nat] :
% 9.17/5.36 ~ ( ord_less_rat @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ ( suc @ N ) ) ) @ E ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3061_neg__eucl__rel__int__mult__2,axiom,
% 9.17/5.36 ! [B: int,A: int,Q3: int,R2: int] :
% 9.17/5.36 ( ( ord_less_eq_int @ B @ zero_zero_int )
% 9.17/5.36 => ( ( eucl_rel_int @ ( plus_plus_int @ A @ one_one_int ) @ B @ ( product_Pair_int_int @ Q3 @ R2 ) )
% 9.17/5.36 => ( 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 ) ) @ R2 ) @ one_one_int ) ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3062_gauss__sum__from__Suc__0,axiom,
% 9.17/5.36 ! [N2: nat] :
% 9.17/5.36 ( ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 9.17/5.36 = ( divide_divide_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3063_gauss__sum__from__Suc__0,axiom,
% 9.17/5.36 ! [N2: nat] :
% 9.17/5.36 ( ( groups7501900531339628137nteger @ semiri4939895301339042750nteger @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 9.17/5.36 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N2 ) @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N2 ) @ one_one_Code_integer ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3064_gauss__sum__from__Suc__0,axiom,
% 9.17/5.36 ! [N2: nat] :
% 9.17/5.36 ( ( groups6325495683096345652atural @ semiri3763490453095760265atural @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 9.17/5.36 = ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ N2 ) @ ( plus_p4538020629002901425atural @ ( semiri3763490453095760265atural @ N2 ) @ one_one_Code_natural ) ) @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3065_gauss__sum__from__Suc__0,axiom,
% 9.17/5.36 ! [N2: nat] :
% 9.17/5.36 ( ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 9.17/5.36 = ( divide_divide_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3066_exp__add__not__zero__imp__right,axiom,
% 9.17/5.36 ! [M2: nat,N2: nat] :
% 9.17/5.36 ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M2 @ N2 ) )
% 9.17/5.36 != zero_zero_nat )
% 9.17/5.36 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 9.17/5.36 != zero_zero_nat ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3067_exp__add__not__zero__imp__right,axiom,
% 9.17/5.36 ! [M2: nat,N2: nat] :
% 9.17/5.36 ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M2 @ N2 ) )
% 9.17/5.36 != zero_zero_int )
% 9.17/5.36 => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 )
% 9.17/5.36 != zero_zero_int ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3068_exp__add__not__zero__imp__right,axiom,
% 9.17/5.36 ! [M2: nat,N2: nat] :
% 9.17/5.36 ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M2 @ N2 ) )
% 9.17/5.36 != zero_z3403309356797280102nteger )
% 9.17/5.36 => ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 )
% 9.17/5.36 != zero_z3403309356797280102nteger ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3069_exp__add__not__zero__imp__right,axiom,
% 9.17/5.36 ! [M2: nat,N2: nat] :
% 9.17/5.36 ( ( ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M2 @ N2 ) )
% 9.17/5.36 != zero_z2226904508553997617atural )
% 9.17/5.36 => ( ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N2 )
% 9.17/5.36 != zero_z2226904508553997617atural ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3070_exp__add__not__zero__imp__left,axiom,
% 9.17/5.36 ! [M2: nat,N2: nat] :
% 9.17/5.36 ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M2 @ N2 ) )
% 9.17/5.36 != zero_zero_nat )
% 9.17/5.36 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 )
% 9.17/5.36 != zero_zero_nat ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3071_exp__add__not__zero__imp__left,axiom,
% 9.17/5.36 ! [M2: nat,N2: nat] :
% 9.17/5.36 ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M2 @ N2 ) )
% 9.17/5.36 != zero_zero_int )
% 9.17/5.36 => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 )
% 9.17/5.36 != zero_zero_int ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3072_exp__add__not__zero__imp__left,axiom,
% 9.17/5.36 ! [M2: nat,N2: nat] :
% 9.17/5.36 ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M2 @ N2 ) )
% 9.17/5.36 != zero_z3403309356797280102nteger )
% 9.17/5.36 => ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M2 )
% 9.17/5.36 != zero_z3403309356797280102nteger ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3073_exp__add__not__zero__imp__left,axiom,
% 9.17/5.36 ! [M2: nat,N2: nat] :
% 9.17/5.36 ( ( ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M2 @ N2 ) )
% 9.17/5.36 != zero_z2226904508553997617atural )
% 9.17/5.36 => ( ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ M2 )
% 9.17/5.36 != zero_z2226904508553997617atural ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3074_sum__power2__eq__zero__iff,axiom,
% 9.17/5.36 ! [X: code_integer,Y: code_integer] :
% 9.17/5.36 ( ( ( plus_p5714425477246183910nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.17/5.36 = zero_z3403309356797280102nteger )
% 9.17/5.36 = ( ( X = zero_z3403309356797280102nteger )
% 9.17/5.36 & ( Y = zero_z3403309356797280102nteger ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3075_sum__power2__eq__zero__iff,axiom,
% 9.17/5.36 ! [X: rat,Y: rat] :
% 9.17/5.36 ( ( ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.17/5.36 = zero_zero_rat )
% 9.17/5.36 = ( ( X = zero_zero_rat )
% 9.17/5.36 & ( Y = zero_zero_rat ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3076_sum__power2__eq__zero__iff,axiom,
% 9.17/5.36 ! [X: int,Y: int] :
% 9.17/5.36 ( ( ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.17/5.36 = zero_zero_int )
% 9.17/5.36 = ( ( X = zero_zero_int )
% 9.17/5.36 & ( Y = zero_zero_int ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3077_div__exp__eq,axiom,
% 9.17/5.36 ! [A: int,M2: nat,N2: nat] :
% 9.17/5.36 ( ( divide_divide_int @ ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 9.17/5.36 = ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M2 @ N2 ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3078_div__exp__eq,axiom,
% 9.17/5.36 ! [A: nat,M2: nat,N2: nat] :
% 9.17/5.36 ( ( divide_divide_nat @ ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 9.17/5.36 = ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M2 @ N2 ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3079_div__exp__eq,axiom,
% 9.17/5.36 ! [A: code_integer,M2: nat,N2: nat] :
% 9.17/5.36 ( ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M2 ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 9.17/5.36 = ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M2 @ N2 ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3080_div__exp__eq,axiom,
% 9.17/5.36 ! [A: code_natural,M2: nat,N2: nat] :
% 9.17/5.36 ( ( divide5121882707175180666atural @ ( divide5121882707175180666atural @ A @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ M2 ) ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N2 ) )
% 9.17/5.36 = ( divide5121882707175180666atural @ A @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M2 @ N2 ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3081_power2__eq__1__iff,axiom,
% 9.17/5.36 ! [A: int] :
% 9.17/5.36 ( ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.17/5.36 = one_one_int )
% 9.17/5.36 = ( ( A = one_one_int )
% 9.17/5.36 | ( A
% 9.17/5.36 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3082_power2__eq__1__iff,axiom,
% 9.17/5.36 ! [A: code_integer] :
% 9.17/5.36 ( ( ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.17/5.36 = one_one_Code_integer )
% 9.17/5.36 = ( ( A = one_one_Code_integer )
% 9.17/5.36 | ( A
% 9.17/5.36 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3083_power2__eq__1__iff,axiom,
% 9.17/5.36 ! [A: rat] :
% 9.17/5.36 ( ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.17/5.36 = one_one_rat )
% 9.17/5.36 = ( ( A = one_one_rat )
% 9.17/5.36 | ( A
% 9.17/5.36 = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3084_plus__int_Oabs__eq,axiom,
% 9.17/5.36 ! [Xa: product_prod_nat_nat,X: product_prod_nat_nat] :
% 9.17/5.36 ( ( plus_plus_int @ ( abs_Integ @ Xa ) @ ( abs_Integ @ X ) )
% 9.17/5.36 = ( abs_Integ
% 9.17/5.36 @ ( produc27273713700761075at_nat
% 9.17/5.36 @ ^ [X3: nat,Y3: nat] :
% 9.17/5.36 ( produc2626176000494625587at_nat
% 9.17/5.36 @ ^ [U2: nat,V2: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X3 @ U2 ) @ ( plus_plus_nat @ Y3 @ V2 ) ) )
% 9.17/5.36 @ Xa
% 9.17/5.36 @ X ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3085_abs__square__eq__1,axiom,
% 9.17/5.36 ! [X: code_integer] :
% 9.17/5.36 ( ( ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.17/5.36 = one_one_Code_integer )
% 9.17/5.36 = ( ( abs_abs_Code_integer @ X )
% 9.17/5.36 = one_one_Code_integer ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3086_abs__square__eq__1,axiom,
% 9.17/5.36 ! [X: rat] :
% 9.17/5.36 ( ( ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.17/5.36 = one_one_rat )
% 9.17/5.36 = ( ( abs_abs_rat @ X )
% 9.17/5.36 = one_one_rat ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3087_abs__square__eq__1,axiom,
% 9.17/5.36 ! [X: int] :
% 9.17/5.36 ( ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.17/5.36 = one_one_int )
% 9.17/5.36 = ( ( abs_abs_int @ X )
% 9.17/5.36 = one_one_int ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3088_minus__int_Oabs__eq,axiom,
% 9.17/5.36 ! [Xa: product_prod_nat_nat,X: product_prod_nat_nat] :
% 9.17/5.36 ( ( minus_minus_int @ ( abs_Integ @ Xa ) @ ( abs_Integ @ X ) )
% 9.17/5.36 = ( abs_Integ
% 9.17/5.36 @ ( produc27273713700761075at_nat
% 9.17/5.36 @ ^ [X3: nat,Y3: nat] :
% 9.17/5.36 ( produc2626176000494625587at_nat
% 9.17/5.36 @ ^ [U2: nat,V2: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X3 @ V2 ) @ ( plus_plus_nat @ Y3 @ U2 ) ) )
% 9.17/5.36 @ Xa
% 9.17/5.36 @ X ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3089_nat__induct2,axiom,
% 9.17/5.36 ! [P: nat > $o,N2: nat] :
% 9.17/5.36 ( ( P @ zero_zero_nat )
% 9.17/5.36 => ( ( P @ one_one_nat )
% 9.17/5.36 => ( ! [N: nat] :
% 9.17/5.36 ( ( P @ N )
% 9.17/5.36 => ( P @ ( plus_plus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 9.17/5.36 => ( P @ N2 ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3090_times__int_Oabs__eq,axiom,
% 9.17/5.36 ! [Xa: product_prod_nat_nat,X: product_prod_nat_nat] :
% 9.17/5.36 ( ( times_times_int @ ( abs_Integ @ Xa ) @ ( abs_Integ @ X ) )
% 9.17/5.36 = ( abs_Integ
% 9.17/5.36 @ ( produc27273713700761075at_nat
% 9.17/5.36 @ ^ [X3: nat,Y3: nat] :
% 9.17/5.36 ( produc2626176000494625587at_nat
% 9.17/5.36 @ ^ [U2: nat,V2: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X3 @ U2 ) @ ( times_times_nat @ Y3 @ V2 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X3 @ V2 ) @ ( times_times_nat @ Y3 @ U2 ) ) ) )
% 9.17/5.36 @ Xa
% 9.17/5.36 @ X ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3091_sum__power2__le__zero__iff,axiom,
% 9.17/5.36 ! [X: code_integer,Y: code_integer] :
% 9.17/5.36 ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_z3403309356797280102nteger )
% 9.17/5.36 = ( ( X = zero_z3403309356797280102nteger )
% 9.17/5.36 & ( Y = zero_z3403309356797280102nteger ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3092_sum__power2__le__zero__iff,axiom,
% 9.17/5.36 ! [X: rat,Y: rat] :
% 9.17/5.36 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_rat )
% 9.17/5.36 = ( ( X = zero_zero_rat )
% 9.17/5.36 & ( Y = zero_zero_rat ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3093_sum__power2__le__zero__iff,axiom,
% 9.17/5.36 ! [X: int,Y: int] :
% 9.17/5.36 ( ( ord_less_eq_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_int )
% 9.17/5.36 = ( ( X = zero_zero_int )
% 9.17/5.36 & ( Y = zero_zero_int ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3094_sum__power2__ge__zero,axiom,
% 9.17/5.36 ! [X: code_integer,Y: code_integer] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3095_sum__power2__ge__zero,axiom,
% 9.17/5.36 ! [X: rat,Y: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3096_sum__power2__ge__zero,axiom,
% 9.17/5.36 ! [X: int,Y: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3097_bits__stable__imp__add__self,axiom,
% 9.17/5.36 ! [A: int] :
% 9.17/5.36 ( ( ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.17/5.36 = A )
% 9.17/5.36 => ( ( plus_plus_int @ A @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 9.17/5.36 = zero_zero_int ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3098_bits__stable__imp__add__self,axiom,
% 9.17/5.36 ! [A: nat] :
% 9.17/5.36 ( ( ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.17/5.36 = A )
% 9.17/5.36 => ( ( plus_plus_nat @ A @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.17/5.36 = zero_zero_nat ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3099_bits__stable__imp__add__self,axiom,
% 9.17/5.36 ! [A: code_integer] :
% 9.17/5.36 ( ( ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 9.17/5.36 = A )
% 9.17/5.36 => ( ( plus_p5714425477246183910nteger @ A @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) )
% 9.17/5.36 = zero_z3403309356797280102nteger ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3100_bits__stable__imp__add__self,axiom,
% 9.17/5.36 ! [A: code_natural] :
% 9.17/5.36 ( ( ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 9.17/5.36 = A )
% 9.17/5.36 => ( ( plus_p4538020629002901425atural @ A @ ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) )
% 9.17/5.36 = zero_z2226904508553997617atural ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3101_not__sum__power2__lt__zero,axiom,
% 9.17/5.36 ! [X: code_integer,Y: code_integer] :
% 9.17/5.36 ~ ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_z3403309356797280102nteger ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3102_not__sum__power2__lt__zero,axiom,
% 9.17/5.36 ! [X: rat,Y: rat] :
% 9.17/5.36 ~ ( ord_less_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_rat ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3103_not__sum__power2__lt__zero,axiom,
% 9.17/5.36 ! [X: int,Y: int] :
% 9.17/5.36 ~ ( ord_less_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_int ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3104_sum__power2__gt__zero__iff,axiom,
% 9.17/5.36 ! [X: code_integer,Y: code_integer] :
% 9.17/5.36 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 9.17/5.36 = ( ( X != zero_z3403309356797280102nteger )
% 9.17/5.36 | ( Y != zero_z3403309356797280102nteger ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3105_sum__power2__gt__zero__iff,axiom,
% 9.17/5.36 ! [X: rat,Y: rat] :
% 9.17/5.36 ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 9.17/5.36 = ( ( X != zero_zero_rat )
% 9.17/5.36 | ( Y != zero_zero_rat ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3106_sum__power2__gt__zero__iff,axiom,
% 9.17/5.36 ! [X: int,Y: int] :
% 9.17/5.36 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 9.17/5.36 = ( ( X != zero_zero_int )
% 9.17/5.36 | ( Y != zero_zero_int ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3107_power2__sum,axiom,
% 9.17/5.36 ! [X: nat,Y: nat] :
% 9.17/5.36 ( ( power_power_nat @ ( plus_plus_nat @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.17/5.36 = ( plus_plus_nat @ ( plus_plus_nat @ ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3108_power2__sum,axiom,
% 9.17/5.36 ! [X: int,Y: int] :
% 9.17/5.36 ( ( power_power_int @ ( plus_plus_int @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.17/5.36 = ( plus_plus_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3109_power2__sum,axiom,
% 9.17/5.36 ! [X: code_integer,Y: code_integer] :
% 9.17/5.36 ( ( power_8256067586552552935nteger @ ( plus_p5714425477246183910nteger @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.17/5.36 = ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3110_power2__sum,axiom,
% 9.17/5.36 ! [X: rat,Y: rat] :
% 9.17/5.36 ( ( power_power_rat @ ( plus_plus_rat @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.17/5.36 = ( plus_plus_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3111_power2__sum,axiom,
% 9.17/5.36 ! [X: code_natural,Y: code_natural] :
% 9.17/5.36 ( ( power_7079662738309270450atural @ ( plus_p4538020629002901425atural @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.17/5.36 = ( plus_p4538020629002901425atural @ ( plus_p4538020629002901425atural @ ( power_7079662738309270450atural @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_7079662738309270450atural @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_2397367101498566445atural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3112_square__le__1,axiom,
% 9.17/5.36 ! [X: code_integer] :
% 9.17/5.36 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ X )
% 9.17/5.36 => ( ( ord_le3102999989581377725nteger @ X @ one_one_Code_integer )
% 9.17/5.36 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3113_square__le__1,axiom,
% 9.17/5.36 ! [X: rat] :
% 9.17/5.36 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ X )
% 9.17/5.36 => ( ( ord_less_eq_rat @ X @ one_one_rat )
% 9.17/5.36 => ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3114_square__le__1,axiom,
% 9.17/5.36 ! [X: int] :
% 9.17/5.36 ( ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ X )
% 9.17/5.36 => ( ( ord_less_eq_int @ X @ one_one_int )
% 9.17/5.36 => ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3115_abs__square__le__1,axiom,
% 9.17/5.36 ! [X: code_integer] :
% 9.17/5.36 ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer )
% 9.17/5.36 = ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X ) @ one_one_Code_integer ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3116_abs__square__le__1,axiom,
% 9.17/5.36 ! [X: rat] :
% 9.17/5.36 ( ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat )
% 9.17/5.36 = ( ord_less_eq_rat @ ( abs_abs_rat @ X ) @ one_one_rat ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3117_abs__square__le__1,axiom,
% 9.17/5.36 ! [X: int] :
% 9.17/5.36 ( ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int )
% 9.17/5.36 = ( ord_less_eq_int @ ( abs_abs_int @ X ) @ one_one_int ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3118_abs__square__less__1,axiom,
% 9.17/5.36 ! [X: code_integer] :
% 9.17/5.36 ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer )
% 9.17/5.36 = ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ X ) @ one_one_Code_integer ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3119_abs__square__less__1,axiom,
% 9.17/5.36 ! [X: rat] :
% 9.17/5.36 ( ( ord_less_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat )
% 9.17/5.36 = ( ord_less_rat @ ( abs_abs_rat @ X ) @ one_one_rat ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3120_abs__square__less__1,axiom,
% 9.17/5.36 ! [X: int] :
% 9.17/5.36 ( ( ord_less_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int )
% 9.17/5.36 = ( ord_less_int @ ( abs_abs_int @ X ) @ one_one_int ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3121_div__exp__mod__exp__eq,axiom,
% 9.17/5.36 ! [A: int,N2: nat,M2: nat] :
% 9.17/5.36 ( ( modulo_modulo_int @ ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 ) )
% 9.17/5.36 = ( divide_divide_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N2 @ M2 ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3122_div__exp__mod__exp__eq,axiom,
% 9.17/5.36 ! [A: nat,N2: nat,M2: nat] :
% 9.17/5.36 ( ( modulo_modulo_nat @ ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 9.17/5.36 = ( divide_divide_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N2 @ M2 ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3123_div__exp__mod__exp__eq,axiom,
% 9.17/5.36 ! [A: code_integer,N2: nat,M2: nat] :
% 9.17/5.36 ( ( modulo364778990260209775nteger @ ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M2 ) )
% 9.17/5.36 = ( divide6298287555418463151nteger @ ( modulo364778990260209775nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N2 @ M2 ) ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3124_div__exp__mod__exp__eq,axiom,
% 9.17/5.36 ! [A: code_natural,N2: nat,M2: nat] :
% 9.17/5.36 ( ( modulo8411746178871703098atural @ ( divide5121882707175180666atural @ A @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N2 ) ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ M2 ) )
% 9.17/5.36 = ( divide5121882707175180666atural @ ( modulo8411746178871703098atural @ A @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N2 @ M2 ) ) ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3125_ex__power__ivl2,axiom,
% 9.17/5.36 ! [B: nat,K: nat] :
% 9.17/5.36 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 9.17/5.36 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 9.17/5.36 => ? [N: nat] :
% 9.17/5.36 ( ( ord_less_nat @ ( power_power_nat @ B @ N ) @ K )
% 9.17/5.36 & ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3126_ex__power__ivl1,axiom,
% 9.17/5.36 ! [B: nat,K: nat] :
% 9.17/5.36 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 9.17/5.36 => ( ( ord_less_eq_nat @ one_one_nat @ K )
% 9.17/5.36 => ? [N: nat] :
% 9.17/5.36 ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N ) @ K )
% 9.17/5.36 & ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3127_power2__diff,axiom,
% 9.17/5.36 ! [X: int,Y: int] :
% 9.17/5.36 ( ( power_power_int @ ( minus_minus_int @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.17/5.36 = ( minus_minus_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3128_power2__diff,axiom,
% 9.17/5.36 ! [X: code_integer,Y: code_integer] :
% 9.17/5.36 ( ( power_8256067586552552935nteger @ ( minus_8373710615458151222nteger @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.17/5.36 = ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3129_power2__diff,axiom,
% 9.17/5.36 ! [X: rat,Y: rat] :
% 9.17/5.36 ( ( power_power_rat @ ( minus_minus_rat @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.17/5.36 = ( minus_minus_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3130_power__minus1__odd,axiom,
% 9.17/5.36 ! [N2: nat] :
% 9.17/5.36 ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 9.17/5.36 = ( uminus_uminus_int @ one_one_int ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3131_power__minus1__odd,axiom,
% 9.17/5.36 ! [N2: nat] :
% 9.17/5.36 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 9.17/5.36 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3132_power__minus1__odd,axiom,
% 9.17/5.36 ! [N2: nat] :
% 9.17/5.36 ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 9.17/5.36 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3133_mask__eq__sum__exp,axiom,
% 9.17/5.36 ! [N2: nat] :
% 9.17/5.36 ( ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ one_one_int )
% 9.17/5.36 = ( groups3539618377306564664at_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.17/5.36 @ ( collect_nat
% 9.17/5.36 @ ^ [Q5: nat] : ( ord_less_nat @ Q5 @ N2 ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3134_mask__eq__sum__exp,axiom,
% 9.17/5.36 ! [N2: nat] :
% 9.17/5.36 ( ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) @ one_one_Code_integer )
% 9.17/5.36 = ( groups7501900531339628137nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 9.17/5.36 @ ( collect_nat
% 9.17/5.36 @ ^ [Q5: nat] : ( ord_less_nat @ Q5 @ N2 ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3135_mask__eq__sum__exp,axiom,
% 9.17/5.36 ! [N2: nat] :
% 9.17/5.36 ( ( minus_7197305767214868737atural @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N2 ) @ one_one_Code_natural )
% 9.17/5.36 = ( groups6325495683096345652atural @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 9.17/5.36 @ ( collect_nat
% 9.17/5.36 @ ^ [Q5: nat] : ( ord_less_nat @ Q5 @ N2 ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3136_mask__eq__sum__exp,axiom,
% 9.17/5.36 ! [N2: nat] :
% 9.17/5.36 ( ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat )
% 9.17/5.36 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.17/5.36 @ ( collect_nat
% 9.17/5.36 @ ^ [Q5: nat] : ( ord_less_nat @ Q5 @ N2 ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3137_sum_Oin__pairs,axiom,
% 9.17/5.36 ! [G: nat > multis2468970476368604999at_nat,M2: nat,N2: nat] :
% 9.17/5.36 ( ( groups6857163185585827899at_nat @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 9.17/5.36 = ( groups6857163185585827899at_nat
% 9.17/5.36 @ ^ [I3: nat] : ( plus_p7104986032573967614at_nat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 9.17/5.36 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3138_sum_Oin__pairs,axiom,
% 9.17/5.36 ! [G: nat > rat,M2: nat,N2: nat] :
% 9.17/5.36 ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 9.17/5.36 = ( groups2906978787729119204at_rat
% 9.17/5.36 @ ^ [I3: nat] : ( plus_plus_rat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 9.17/5.36 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3139_sum_Oin__pairs,axiom,
% 9.17/5.36 ! [G: nat > int,M2: nat,N2: nat] :
% 9.17/5.36 ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 9.17/5.36 = ( groups3539618377306564664at_int
% 9.17/5.36 @ ^ [I3: nat] : ( plus_plus_int @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 9.17/5.36 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3140_sum_Oin__pairs,axiom,
% 9.17/5.36 ! [G: nat > nat,M2: nat,N2: nat] :
% 9.17/5.36 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 9.17/5.36 = ( groups3542108847815614940at_nat
% 9.17/5.36 @ ^ [I3: nat] : ( plus_plus_nat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 9.17/5.36 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3141_gauss__sum__nat,axiom,
% 9.17/5.36 ! [N2: nat] :
% 9.17/5.36 ( ( groups3542108847815614940at_nat
% 9.17/5.36 @ ^ [X3: nat] : X3
% 9.17/5.36 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 9.17/5.36 = ( divide_divide_nat @ ( times_times_nat @ N2 @ ( suc @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3142_divmod__step__eq,axiom,
% 9.17/5.36 ! [L: num,R2: nat,Q3: nat] :
% 9.17/5.36 ( ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ L ) @ R2 )
% 9.17/5.36 => ( ( unique5026877609467782581ep_nat @ L @ ( product_Pair_nat_nat @ Q3 @ R2 ) )
% 9.17/5.36 = ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q3 ) @ one_one_nat ) @ ( minus_minus_nat @ R2 @ ( numeral_numeral_nat @ L ) ) ) ) )
% 9.17/5.36 & ( ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L ) @ R2 )
% 9.17/5.36 => ( ( unique5026877609467782581ep_nat @ L @ ( product_Pair_nat_nat @ Q3 @ R2 ) )
% 9.17/5.36 = ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q3 ) @ R2 ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3143_divmod__step__eq,axiom,
% 9.17/5.36 ! [L: num,R2: int,Q3: int] :
% 9.17/5.36 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ L ) @ R2 )
% 9.17/5.36 => ( ( unique5024387138958732305ep_int @ L @ ( product_Pair_int_int @ Q3 @ R2 ) )
% 9.17/5.36 = ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q3 ) @ one_one_int ) @ ( minus_minus_int @ R2 @ ( numeral_numeral_int @ L ) ) ) ) )
% 9.17/5.36 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ L ) @ R2 )
% 9.17/5.36 => ( ( unique5024387138958732305ep_int @ L @ ( product_Pair_int_int @ Q3 @ R2 ) )
% 9.17/5.36 = ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q3 ) @ R2 ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3144_divmod__step__eq,axiom,
% 9.17/5.36 ! [L: num,R2: code_integer,Q3: code_integer] :
% 9.17/5.36 ( ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L ) @ R2 )
% 9.17/5.36 => ( ( unique4921790084139445826nteger @ L @ ( produc1086072967326762835nteger @ Q3 @ R2 ) )
% 9.17/5.36 = ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q3 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R2 @ ( numera6620942414471956472nteger @ L ) ) ) ) )
% 9.17/5.36 & ( ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L ) @ R2 )
% 9.17/5.36 => ( ( unique4921790084139445826nteger @ L @ ( produc1086072967326762835nteger @ Q3 @ R2 ) )
% 9.17/5.36 = ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q3 ) @ R2 ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3145_divmod__step__def,axiom,
% 9.17/5.36 ( unique5026877609467782581ep_nat
% 9.17/5.36 = ( ^ [L3: num] :
% 9.17/5.36 ( produc2626176000494625587at_nat
% 9.17/5.36 @ ^ [Q5: nat,R3: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L3 ) @ R3 ) @ ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q5 ) @ one_one_nat ) @ ( minus_minus_nat @ R3 @ ( numeral_numeral_nat @ L3 ) ) ) @ ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q5 ) @ R3 ) ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3146_divmod__step__def,axiom,
% 9.17/5.36 ( unique5024387138958732305ep_int
% 9.17/5.36 = ( ^ [L3: num] :
% 9.17/5.36 ( produc4245557441103728435nt_int
% 9.17/5.36 @ ^ [Q5: int,R3: int] : ( if_Pro3027730157355071871nt_int @ ( ord_less_eq_int @ ( numeral_numeral_int @ L3 ) @ R3 ) @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q5 ) @ one_one_int ) @ ( minus_minus_int @ R3 @ ( numeral_numeral_int @ L3 ) ) ) @ ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q5 ) @ R3 ) ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3147_divmod__step__def,axiom,
% 9.17/5.36 ( unique4921790084139445826nteger
% 9.17/5.36 = ( ^ [L3: num] :
% 9.17/5.36 ( produc6916734918728496179nteger
% 9.17/5.36 @ ^ [Q5: code_integer,R3: code_integer] : ( if_Pro6119634080678213985nteger @ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L3 ) @ R3 ) @ ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R3 @ ( numera6620942414471956472nteger @ L3 ) ) ) @ ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q5 ) @ R3 ) ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3148_divmod__step__nat__def,axiom,
% 9.17/5.36 ( unique5026877609467782581ep_nat
% 9.17/5.36 = ( ^ [L3: num] :
% 9.17/5.36 ( produc2626176000494625587at_nat
% 9.17/5.36 @ ^ [Q5: nat,R3: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L3 ) @ R3 ) @ ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q5 ) @ one_one_nat ) @ ( minus_minus_nat @ R3 @ ( numeral_numeral_nat @ L3 ) ) ) @ ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q5 ) @ R3 ) ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3149_divmod__step__int__def,axiom,
% 9.17/5.36 ( unique5024387138958732305ep_int
% 9.17/5.36 = ( ^ [L3: num] :
% 9.17/5.36 ( produc4245557441103728435nt_int
% 9.17/5.36 @ ^ [Q5: int,R3: int] : ( if_Pro3027730157355071871nt_int @ ( ord_less_eq_int @ ( numeral_numeral_int @ L3 ) @ R3 ) @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q5 ) @ one_one_int ) @ ( minus_minus_int @ R3 @ ( numeral_numeral_int @ L3 ) ) ) @ ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q5 ) @ R3 ) ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3150_set__bit__0,axiom,
% 9.17/5.36 ! [A: code_integer] :
% 9.17/5.36 ( ( bit_se2793503036327961859nteger @ zero_zero_nat @ A )
% 9.17/5.36 = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3151_set__bit__0,axiom,
% 9.17/5.36 ! [A: int] :
% 9.17/5.36 ( ( bit_se7879613467334960850it_int @ zero_zero_nat @ A )
% 9.17/5.36 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3152_set__bit__0,axiom,
% 9.17/5.36 ! [A: nat] :
% 9.17/5.36 ( ( bit_se7882103937844011126it_nat @ zero_zero_nat @ A )
% 9.17/5.36 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3153_set__bit__0,axiom,
% 9.17/5.36 ! [A: code_natural] :
% 9.17/5.36 ( ( bit_se1617098188084679374atural @ zero_zero_nat @ A )
% 9.17/5.36 = ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3154_mlex__eq,axiom,
% 9.17/5.36 ( mlex_p3502713205431853936at_nat
% 9.17/5.36 = ( ^ [F2: set_Pr1261947904930325089at_nat > nat,R5: set_Pr4329608150637261639at_nat] :
% 9.17/5.36 ( collec6321179662152712658at_nat
% 9.17/5.36 @ ( produc410239310623530412_nat_o
% 9.17/5.36 @ ^ [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] :
% 9.17/5.36 ( ( ord_less_nat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) )
% 9.17/5.36 | ( ( ord_less_eq_nat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) )
% 9.17/5.36 & ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ Y3 ) @ R5 ) ) ) ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3155_mlex__eq,axiom,
% 9.17/5.36 ( mlex_prod_nat
% 9.17/5.36 = ( ^ [F2: nat > nat,R5: set_Pr1261947904930325089at_nat] :
% 9.17/5.36 ( collec3392354462482085612at_nat
% 9.17/5.36 @ ( produc6081775807080527818_nat_o
% 9.17/5.36 @ ^ [X3: nat,Y3: nat] :
% 9.17/5.36 ( ( ord_less_nat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) )
% 9.17/5.36 | ( ( ord_less_eq_nat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) )
% 9.17/5.36 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y3 ) @ R5 ) ) ) ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3156_unset__bit__Suc,axiom,
% 9.17/5.36 ! [N2: nat,A: code_integer] :
% 9.17/5.36 ( ( bit_se8260200283734997820nteger @ ( suc @ N2 ) @ A )
% 9.17/5.36 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se8260200283734997820nteger @ N2 @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3157_unset__bit__Suc,axiom,
% 9.17/5.36 ! [N2: nat,A: int] :
% 9.17/5.36 ( ( bit_se4203085406695923979it_int @ ( suc @ N2 ) @ A )
% 9.17/5.36 = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se4203085406695923979it_int @ N2 @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3158_unset__bit__Suc,axiom,
% 9.17/5.36 ! [N2: nat,A: nat] :
% 9.17/5.36 ( ( bit_se4205575877204974255it_nat @ ( suc @ N2 ) @ A )
% 9.17/5.36 = ( plus_plus_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se4205575877204974255it_nat @ N2 @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3159_unset__bit__Suc,axiom,
% 9.17/5.36 ! [N2: nat,A: code_natural] :
% 9.17/5.36 ( ( bit_se7083795435491715335atural @ ( suc @ N2 ) @ A )
% 9.17/5.36 = ( plus_p4538020629002901425atural @ ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se7083795435491715335atural @ N2 @ ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3160_flip__bit__Suc,axiom,
% 9.17/5.36 ! [N2: nat,A: code_integer] :
% 9.17/5.36 ( ( bit_se1345352211410354436nteger @ ( suc @ N2 ) @ A )
% 9.17/5.36 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1345352211410354436nteger @ N2 @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3161_flip__bit__Suc,axiom,
% 9.17/5.36 ! [N2: nat,A: int] :
% 9.17/5.36 ( ( bit_se2159334234014336723it_int @ ( suc @ N2 ) @ A )
% 9.17/5.36 = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2159334234014336723it_int @ N2 @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3162_flip__bit__Suc,axiom,
% 9.17/5.36 ! [N2: nat,A: nat] :
% 9.17/5.36 ( ( bit_se2161824704523386999it_nat @ ( suc @ N2 ) @ A )
% 9.17/5.36 = ( plus_plus_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2161824704523386999it_nat @ N2 @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3163_flip__bit__Suc,axiom,
% 9.17/5.36 ! [N2: nat,A: code_natural] :
% 9.17/5.36 ( ( bit_se168947363167071951atural @ ( suc @ N2 ) @ A )
% 9.17/5.36 = ( plus_p4538020629002901425atural @ ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se168947363167071951atural @ N2 @ ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3164_set__bit__Suc,axiom,
% 9.17/5.36 ! [N2: nat,A: code_integer] :
% 9.17/5.36 ( ( bit_se2793503036327961859nteger @ ( suc @ N2 ) @ A )
% 9.17/5.36 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se2793503036327961859nteger @ N2 @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3165_set__bit__Suc,axiom,
% 9.17/5.36 ! [N2: nat,A: int] :
% 9.17/5.36 ( ( bit_se7879613467334960850it_int @ ( suc @ N2 ) @ A )
% 9.17/5.36 = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se7879613467334960850it_int @ N2 @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3166_set__bit__Suc,axiom,
% 9.17/5.36 ! [N2: nat,A: nat] :
% 9.17/5.36 ( ( bit_se7882103937844011126it_nat @ ( suc @ N2 ) @ A )
% 9.17/5.36 = ( plus_plus_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se7882103937844011126it_nat @ N2 @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3167_set__bit__Suc,axiom,
% 9.17/5.36 ! [N2: nat,A: code_natural] :
% 9.17/5.36 ( ( bit_se1617098188084679374atural @ ( suc @ N2 ) @ A )
% 9.17/5.36 = ( plus_p4538020629002901425atural @ ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se1617098188084679374atural @ N2 @ ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3168_divmod__step__integer__def,axiom,
% 9.17/5.36 ( unique4921790084139445826nteger
% 9.17/5.36 = ( ^ [L3: num] :
% 9.17/5.36 ( produc6916734918728496179nteger
% 9.17/5.36 @ ^ [Q5: code_integer,R3: code_integer] : ( if_Pro6119634080678213985nteger @ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L3 ) @ R3 ) @ ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R3 @ ( numera6620942414471956472nteger @ L3 ) ) ) @ ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q5 ) @ R3 ) ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3169_signed__take__bit__rec,axiom,
% 9.17/5.36 ( bit_ri6519982836138164636nteger
% 9.17/5.36 = ( ^ [N4: nat,A5: code_integer] : ( if_Code_integer @ ( N4 = zero_zero_nat ) @ ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A5 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A5 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_ri6519982836138164636nteger @ ( minus_minus_nat @ N4 @ one_one_nat ) @ ( divide6298287555418463151nteger @ A5 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3170_signed__take__bit__rec,axiom,
% 9.17/5.36 ( bit_ri631733984087533419it_int
% 9.17/5.36 = ( ^ [N4: nat,A5: int] : ( if_int @ ( N4 = zero_zero_nat ) @ ( uminus_uminus_int @ ( modulo_modulo_int @ A5 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( plus_plus_int @ ( modulo_modulo_int @ A5 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri631733984087533419it_int @ ( minus_minus_nat @ N4 @ one_one_nat ) @ ( divide_divide_int @ A5 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3171_round__unique,axiom,
% 9.17/5.36 ! [X: rat,Y: int] :
% 9.17/5.36 ( ( ord_less_rat @ ( minus_minus_rat @ X @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_rat @ Y ) )
% 9.17/5.36 => ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Y ) @ ( plus_plus_rat @ X @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) )
% 9.17/5.36 => ( ( archim7778729529865785530nd_rat @ X )
% 9.17/5.36 = Y ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3172_rel__of__def,axiom,
% 9.17/5.36 ( rel_of7835217753297429671nteger
% 9.17/5.36 = ( ^ [M: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > option2651255830984564193nteger,P3: produc1908205239877642774nteger > $o] :
% 9.17/5.36 ( collec6950949345391930603nteger
% 9.17/5.36 @ ( produc6253627499356882019eger_o
% 9.17/5.36 @ ^ [K4: produc6241069584506657477e_term > option6357759511663192854e_term,V2: produc8923325533196201883nteger] :
% 9.17/5.36 ( ( ( M @ K4 )
% 9.17/5.36 = ( some_P6772290148444788224nteger @ V2 ) )
% 9.17/5.36 & ( P3 @ ( produc8603105652947943368nteger @ K4 @ V2 ) ) ) ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3173_rel__of__def,axiom,
% 9.17/5.36 ( rel_of4838799251197538391et_nat
% 9.17/5.36 = ( ^ [M: ( produc3658429121746597890et_nat > $o ) > option936205604648967762et_nat,P3: produc3925858234332021118et_nat > $o] :
% 9.17/5.36 ( collec1402215087704437587et_nat
% 9.17/5.36 @ ( produc1437786849005270451_nat_o
% 9.17/5.36 @ ^ [K4: produc3658429121746597890et_nat > $o,V2: produc3658429121746597890et_nat] :
% 9.17/5.36 ( ( ( M @ K4 )
% 9.17/5.36 = ( some_P624177172695371229et_nat @ V2 ) )
% 9.17/5.36 & ( P3 @ ( produc5001842942810119800et_nat @ K4 @ V2 ) ) ) ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3174_rel__of__def,axiom,
% 9.17/5.36 ( rel_of7774016450764239315et_nat
% 9.17/5.36 = ( ^ [M: ( produc3658429121746597890et_nat > $o ) > option5190343406534369742et_nat,P3: produc2732055786443039994et_nat > $o] :
% 9.17/5.36 ( collec5543584681430388431et_nat
% 9.17/5.36 @ ( produc838355143741117751_nat_o
% 9.17/5.36 @ ^ [K4: produc3658429121746597890et_nat > $o,V2: produc3925858234332021118et_nat] :
% 9.17/5.36 ( ( ( M @ K4 )
% 9.17/5.36 = ( some_P750831030444334937et_nat @ V2 ) )
% 9.17/5.36 & ( P3 @ ( produc2245416461498447860et_nat @ K4 @ V2 ) ) ) ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3175_rel__of__def,axiom,
% 9.17/5.36 ( rel_of8306664904814525588nt_int
% 9.17/5.36 = ( ^ [M: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > option4624381673175914239nt_int,P3: produc2285326912895808259nt_int > $o] :
% 9.17/5.36 ( collec1790188477890212312nt_int
% 9.17/5.36 @ ( produc1573362020775583542_int_o
% 9.17/5.36 @ ^ [K4: produc8551481072490612790e_term > option6357759511663192854e_term,V2: product_prod_int_int] :
% 9.17/5.36 ( ( ( M @ K4 )
% 9.17/5.36 = ( some_P4184893108420464158nt_int @ V2 ) )
% 9.17/5.36 & ( P3 @ ( produc5700946648718959541nt_int @ K4 @ V2 ) ) ) ) ) ) ) ).
% 9.17/5.36
% 9.17/5.36 thf(fact_3176_rel__of__def,axiom,
% 9.17/5.36 ( rel_of5543720577181062686nt_int
% 9.17/5.36 = ( ^ [M: ( int > option6357759511663192854e_term ) > option4624381673175914239nt_int,P3: produc7773217078559923341nt_int > $o] :
% 9.17/5.36 ( collec506566255779805410nt_int
% 9.17/5.36 @ ( produc2558449545302689196_int_o
% 9.17/5.36 @ ^ [K4: int > option6357759511663192854e_term,V2: product_prod_int_int] :
% 9.17/5.37 ( ( ( M @ K4 )
% 9.17/5.37 = ( some_P4184893108420464158nt_int @ V2 ) )
% 9.17/5.37 & ( P3 @ ( produc4305682042979456191nt_int @ K4 @ V2 ) ) ) ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3177_dbl__simps_I4_J,axiom,
% 9.17/5.37 ( ( neg_numeral_dbl_int @ ( uminus_uminus_int @ one_one_int ) )
% 9.17/5.37 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3178_dbl__simps_I4_J,axiom,
% 9.17/5.37 ( ( neg_nu8804712462038260780nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.17/5.37 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3179_dbl__simps_I4_J,axiom,
% 9.17/5.37 ( ( neg_numeral_dbl_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 9.17/5.37 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3180_round__altdef,axiom,
% 9.17/5.37 ( archim7778729529865785530nd_rat
% 9.17/5.37 = ( ^ [X3: rat] : ( if_int @ ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( archimedean_frac_rat @ X3 ) ) @ ( archim2889992004027027881ng_rat @ X3 ) @ ( archim3151403230148437115or_rat @ X3 ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3181_round__unique_H,axiom,
% 9.17/5.37 ! [X: rat,N2: int] :
% 9.17/5.37 ( ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X @ ( ring_1_of_int_rat @ N2 ) ) ) @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 9.17/5.37 => ( ( archim7778729529865785530nd_rat @ X )
% 9.17/5.37 = N2 ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3182_of__int__round__abs__le,axiom,
% 9.17/5.37 ! [X: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X ) ) @ X ) ) @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3183_divmod__algorithm__code_I5_J,axiom,
% 9.17/5.37 ! [M2: num,N2: num] :
% 9.17/5.37 ( ( unique3479559517661332726nteger @ ( bit0 @ M2 ) @ ( bit0 @ N2 ) )
% 9.17/5.37 = ( produc6916734918728496179nteger
% 9.17/5.37 @ ^ [Q5: code_integer,R3: code_integer] : ( produc1086072967326762835nteger @ Q5 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ R3 ) )
% 9.17/5.37 @ ( unique3479559517661332726nteger @ M2 @ N2 ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3184_divmod__algorithm__code_I5_J,axiom,
% 9.17/5.37 ! [M2: num,N2: num] :
% 9.17/5.37 ( ( unique5052692396658037445od_int @ ( bit0 @ M2 ) @ ( bit0 @ N2 ) )
% 9.17/5.37 = ( produc4245557441103728435nt_int
% 9.17/5.37 @ ^ [Q5: int,R3: int] : ( product_Pair_int_int @ Q5 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R3 ) )
% 9.17/5.37 @ ( unique5052692396658037445od_int @ M2 @ N2 ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3185_divmod__algorithm__code_I5_J,axiom,
% 9.17/5.37 ! [M2: num,N2: num] :
% 9.17/5.37 ( ( unique5055182867167087721od_nat @ ( bit0 @ M2 ) @ ( bit0 @ N2 ) )
% 9.17/5.37 = ( produc2626176000494625587at_nat
% 9.17/5.37 @ ^ [Q5: nat,R3: nat] : ( product_Pair_nat_nat @ Q5 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ R3 ) )
% 9.17/5.37 @ ( unique5055182867167087721od_nat @ M2 @ N2 ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3186_signed__take__bit__of__minus__1,axiom,
% 9.17/5.37 ! [N2: nat] :
% 9.17/5.37 ( ( bit_ri6519982836138164636nteger @ N2 @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.17/5.37 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3187_signed__take__bit__of__minus__1,axiom,
% 9.17/5.37 ! [N2: nat] :
% 9.17/5.37 ( ( bit_ri631733984087533419it_int @ N2 @ ( uminus_uminus_int @ one_one_int ) )
% 9.17/5.37 = ( uminus_uminus_int @ one_one_int ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3188_signed__take__bit__Suc__1,axiom,
% 9.17/5.37 ! [N2: nat] :
% 9.17/5.37 ( ( bit_ri6519982836138164636nteger @ ( suc @ N2 ) @ one_one_Code_integer )
% 9.17/5.37 = one_one_Code_integer ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3189_signed__take__bit__Suc__1,axiom,
% 9.17/5.37 ! [N2: nat] :
% 9.17/5.37 ( ( bit_ri631733984087533419it_int @ ( suc @ N2 ) @ one_one_int )
% 9.17/5.37 = one_one_int ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3190_signed__take__bit__numeral__of__1,axiom,
% 9.17/5.37 ! [K: num] :
% 9.17/5.37 ( ( bit_ri6519982836138164636nteger @ ( numeral_numeral_nat @ K ) @ one_one_Code_integer )
% 9.17/5.37 = one_one_Code_integer ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3191_signed__take__bit__numeral__of__1,axiom,
% 9.17/5.37 ! [K: num] :
% 9.17/5.37 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ K ) @ one_one_int )
% 9.17/5.37 = one_one_int ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3192_round__1,axiom,
% 9.17/5.37 ( ( archim7778729529865785530nd_rat @ one_one_rat )
% 9.17/5.37 = one_one_int ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3193_divmod__algorithm__code_I2_J,axiom,
% 9.17/5.37 ! [M2: num] :
% 9.17/5.37 ( ( unique3479559517661332726nteger @ M2 @ one )
% 9.17/5.37 = ( produc1086072967326762835nteger @ ( numera6620942414471956472nteger @ M2 ) @ zero_z3403309356797280102nteger ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3194_divmod__algorithm__code_I2_J,axiom,
% 9.17/5.37 ! [M2: num] :
% 9.17/5.37 ( ( unique5052692396658037445od_int @ M2 @ one )
% 9.17/5.37 = ( product_Pair_int_int @ ( numeral_numeral_int @ M2 ) @ zero_zero_int ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3195_divmod__algorithm__code_I2_J,axiom,
% 9.17/5.37 ! [M2: num] :
% 9.17/5.37 ( ( unique5055182867167087721od_nat @ M2 @ one )
% 9.17/5.37 = ( product_Pair_nat_nat @ ( numeral_numeral_nat @ M2 ) @ zero_zero_nat ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3196_dbl__simps_I3_J,axiom,
% 9.17/5.37 ( ( neg_numeral_dbl_int @ one_one_int )
% 9.17/5.37 = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3197_dbl__simps_I3_J,axiom,
% 9.17/5.37 ( ( neg_nu8804712462038260780nteger @ one_one_Code_integer )
% 9.17/5.37 = ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3198_dbl__simps_I3_J,axiom,
% 9.17/5.37 ( ( neg_numeral_dbl_rat @ one_one_rat )
% 9.17/5.37 = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3199_divmod__algorithm__code_I3_J,axiom,
% 9.17/5.37 ! [N2: num] :
% 9.17/5.37 ( ( unique3479559517661332726nteger @ one @ ( bit0 @ N2 ) )
% 9.17/5.37 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ one ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3200_divmod__algorithm__code_I3_J,axiom,
% 9.17/5.37 ! [N2: num] :
% 9.17/5.37 ( ( unique5052692396658037445od_int @ one @ ( bit0 @ N2 ) )
% 9.17/5.37 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ one ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3201_divmod__algorithm__code_I3_J,axiom,
% 9.17/5.37 ! [N2: num] :
% 9.17/5.37 ( ( unique5055182867167087721od_nat @ one @ ( bit0 @ N2 ) )
% 9.17/5.37 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ one ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3202_less__eq__integer__code_I1_J,axiom,
% 9.17/5.37 ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3203_sgn__integer__code,axiom,
% 9.17/5.37 ( sgn_sgn_Code_integer
% 9.17/5.37 = ( ^ [K4: code_integer] : ( if_Code_integer @ ( K4 = zero_z3403309356797280102nteger ) @ zero_z3403309356797280102nteger @ ( if_Code_integer @ ( ord_le6747313008572928689nteger @ K4 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3204_exhaustive__integer_H_Ocases,axiom,
% 9.17/5.37 ! [X: produc8763457246119570046nteger] :
% 9.17/5.37 ~ ! [F3: code_integer > option6357759511663192854e_term,D: code_integer,I2: code_integer] :
% 9.17/5.37 ( X
% 9.17/5.37 != ( produc6137756002093451184nteger @ F3 @ ( produc1086072967326762835nteger @ D @ I2 ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3205_full__exhaustive__integer_H_Ocases,axiom,
% 9.17/5.37 ! [X: produc1908205239877642774nteger] :
% 9.17/5.37 ~ ! [F3: produc6241069584506657477e_term > option6357759511663192854e_term,D: code_integer,I2: code_integer] :
% 9.17/5.37 ( X
% 9.17/5.37 != ( produc8603105652947943368nteger @ F3 @ ( produc1086072967326762835nteger @ D @ I2 ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3206_times__integer__code_I1_J,axiom,
% 9.17/5.37 ! [K: code_integer] :
% 9.17/5.37 ( ( times_3573771949741848930nteger @ K @ zero_z3403309356797280102nteger )
% 9.17/5.37 = zero_z3403309356797280102nteger ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3207_times__integer__code_I2_J,axiom,
% 9.17/5.37 ! [L: code_integer] :
% 9.17/5.37 ( ( times_3573771949741848930nteger @ zero_z3403309356797280102nteger @ L )
% 9.17/5.37 = zero_z3403309356797280102nteger ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3208_minus__integer__code_I1_J,axiom,
% 9.17/5.37 ! [K: code_integer] :
% 9.17/5.37 ( ( minus_8373710615458151222nteger @ K @ zero_z3403309356797280102nteger )
% 9.17/5.37 = K ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3209_plus__integer__code_I2_J,axiom,
% 9.17/5.37 ! [L: code_integer] :
% 9.17/5.37 ( ( plus_p5714425477246183910nteger @ zero_z3403309356797280102nteger @ L )
% 9.17/5.37 = L ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3210_plus__integer__code_I1_J,axiom,
% 9.17/5.37 ! [K: code_integer] :
% 9.17/5.37 ( ( plus_p5714425477246183910nteger @ K @ zero_z3403309356797280102nteger )
% 9.17/5.37 = K ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3211_minus__integer__code_I2_J,axiom,
% 9.17/5.37 ! [L: code_integer] :
% 9.17/5.37 ( ( minus_8373710615458151222nteger @ zero_z3403309356797280102nteger @ L )
% 9.17/5.37 = ( uminus1351360451143612070nteger @ L ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3212_divmod__integer_H__def,axiom,
% 9.17/5.37 ( unique3479559517661332726nteger
% 9.17/5.37 = ( ^ [M: num,N4: num] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ N4 ) ) @ ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ N4 ) ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3213_signed__take__bit__add,axiom,
% 9.17/5.37 ! [N2: nat,K: int,L: int] :
% 9.17/5.37 ( ( bit_ri631733984087533419it_int @ N2 @ ( plus_plus_int @ ( bit_ri631733984087533419it_int @ N2 @ K ) @ ( bit_ri631733984087533419it_int @ N2 @ L ) ) )
% 9.17/5.37 = ( bit_ri631733984087533419it_int @ N2 @ ( plus_plus_int @ K @ L ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3214_dbl__def,axiom,
% 9.17/5.37 ( neg_numeral_dbl_rat
% 9.17/5.37 = ( ^ [X3: rat] : ( plus_plus_rat @ X3 @ X3 ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3215_dbl__def,axiom,
% 9.17/5.37 ( neg_numeral_dbl_int
% 9.17/5.37 = ( ^ [X3: int] : ( plus_plus_int @ X3 @ X3 ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3216_divmod__int__def,axiom,
% 9.17/5.37 ( unique5052692396658037445od_int
% 9.17/5.37 = ( ^ [M: num,N4: num] : ( product_Pair_int_int @ ( divide_divide_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N4 ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N4 ) ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3217_divmod__def,axiom,
% 9.17/5.37 ( unique3479559517661332726nteger
% 9.17/5.37 = ( ^ [M: num,N4: num] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ N4 ) ) @ ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ N4 ) ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3218_divmod__def,axiom,
% 9.17/5.37 ( unique5052692396658037445od_int
% 9.17/5.37 = ( ^ [M: num,N4: num] : ( product_Pair_int_int @ ( divide_divide_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N4 ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N4 ) ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3219_divmod__def,axiom,
% 9.17/5.37 ( unique5055182867167087721od_nat
% 9.17/5.37 = ( ^ [M: num,N4: num] : ( product_Pair_nat_nat @ ( divide_divide_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N4 ) ) @ ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N4 ) ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3220_divmod_H__nat__def,axiom,
% 9.17/5.37 ( unique5055182867167087721od_nat
% 9.17/5.37 = ( ^ [M: num,N4: num] : ( product_Pair_nat_nat @ ( divide_divide_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N4 ) ) @ ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N4 ) ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3221_signed__take__bit__int__greater__eq,axiom,
% 9.17/5.37 ! [K: int,N2: nat] :
% 9.17/5.37 ( ( ord_less_int @ K @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) )
% 9.17/5.37 => ( ord_less_eq_int @ ( plus_plus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) ) @ ( bit_ri631733984087533419it_int @ N2 @ K ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3222_divmod__divmod__step,axiom,
% 9.17/5.37 ( unique5055182867167087721od_nat
% 9.17/5.37 = ( ^ [M: num,N4: num] : ( if_Pro6206227464963214023at_nat @ ( ord_less_num @ M @ N4 ) @ ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ M ) ) @ ( unique5026877609467782581ep_nat @ N4 @ ( unique5055182867167087721od_nat @ M @ ( bit0 @ N4 ) ) ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3223_divmod__divmod__step,axiom,
% 9.17/5.37 ( unique5052692396658037445od_int
% 9.17/5.37 = ( ^ [M: num,N4: num] : ( if_Pro3027730157355071871nt_int @ ( ord_less_num @ M @ N4 ) @ ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ M ) ) @ ( unique5024387138958732305ep_int @ N4 @ ( unique5052692396658037445od_int @ M @ ( bit0 @ N4 ) ) ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3224_divmod__divmod__step,axiom,
% 9.17/5.37 ( unique3479559517661332726nteger
% 9.17/5.37 = ( ^ [M: num,N4: num] : ( if_Pro6119634080678213985nteger @ ( ord_less_num @ M @ N4 ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( unique4921790084139445826nteger @ N4 @ ( unique3479559517661332726nteger @ M @ ( bit0 @ N4 ) ) ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3225_round__def,axiom,
% 9.17/5.37 ( archim7778729529865785530nd_rat
% 9.17/5.37 = ( ^ [X3: rat] : ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X3 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3226_signed__take__bit__Suc,axiom,
% 9.17/5.37 ! [N2: nat,A: code_integer] :
% 9.17/5.37 ( ( bit_ri6519982836138164636nteger @ ( suc @ N2 ) @ A )
% 9.17/5.37 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_ri6519982836138164636nteger @ N2 @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3227_signed__take__bit__Suc,axiom,
% 9.17/5.37 ! [N2: nat,A: int] :
% 9.17/5.37 ( ( bit_ri631733984087533419it_int @ ( suc @ N2 ) @ A )
% 9.17/5.37 = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri631733984087533419it_int @ N2 @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3228_of__int__round__le,axiom,
% 9.17/5.37 ! [X: rat] : ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X ) ) @ ( plus_plus_rat @ X @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3229_of__int__round__ge,axiom,
% 9.17/5.37 ! [X: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ X @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3230_of__int__round__gt,axiom,
% 9.17/5.37 ! [X: rat] : ( ord_less_rat @ ( minus_minus_rat @ X @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3231_integer__of__int__code,axiom,
% 9.17/5.37 ( code_integer_of_int
% 9.17/5.37 = ( ^ [K4: int] :
% 9.17/5.37 ( if_Code_integer @ ( ord_less_int @ K4 @ zero_zero_int ) @ ( uminus1351360451143612070nteger @ ( code_integer_of_int @ ( uminus_uminus_int @ K4 ) ) )
% 9.17/5.37 @ ( if_Code_integer @ ( K4 = zero_zero_int ) @ zero_z3403309356797280102nteger
% 9.17/5.37 @ ( if_Code_integer
% 9.17/5.37 @ ( ( modulo_modulo_int @ K4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.17/5.37 = zero_zero_int )
% 9.17/5.37 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( code_integer_of_int @ ( divide_divide_int @ K4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 9.17/5.37 @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( code_integer_of_int @ ( divide_divide_int @ K4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_Code_integer ) ) ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3232_divmod__algorithm__code_I6_J,axiom,
% 9.17/5.37 ! [M2: num,N2: num] :
% 9.17/5.37 ( ( unique3479559517661332726nteger @ ( bit1 @ M2 ) @ ( bit0 @ N2 ) )
% 9.17/5.37 = ( produc6916734918728496179nteger
% 9.17/5.37 @ ^ [Q5: code_integer,R3: code_integer] : ( produc1086072967326762835nteger @ Q5 @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ R3 ) @ one_one_Code_integer ) )
% 9.17/5.37 @ ( unique3479559517661332726nteger @ M2 @ N2 ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3233_divmod__algorithm__code_I6_J,axiom,
% 9.17/5.37 ! [M2: num,N2: num] :
% 9.17/5.37 ( ( unique5052692396658037445od_int @ ( bit1 @ M2 ) @ ( bit0 @ N2 ) )
% 9.17/5.37 = ( produc4245557441103728435nt_int
% 9.17/5.37 @ ^ [Q5: int,R3: int] : ( product_Pair_int_int @ Q5 @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R3 ) @ one_one_int ) )
% 9.17/5.37 @ ( unique5052692396658037445od_int @ M2 @ N2 ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3234_divmod__algorithm__code_I6_J,axiom,
% 9.17/5.37 ! [M2: num,N2: num] :
% 9.17/5.37 ( ( unique5055182867167087721od_nat @ ( bit1 @ M2 ) @ ( bit0 @ N2 ) )
% 9.17/5.37 = ( produc2626176000494625587at_nat
% 9.17/5.37 @ ^ [Q5: nat,R3: nat] : ( product_Pair_nat_nat @ Q5 @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ R3 ) @ one_one_nat ) )
% 9.17/5.37 @ ( unique5055182867167087721od_nat @ M2 @ N2 ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3235_of__nat__code,axiom,
% 9.17/5.37 ( semiri681578069525770553at_rat
% 9.17/5.37 = ( ^ [N4: nat] :
% 9.17/5.37 ( semiri7787848453975740701ux_rat
% 9.17/5.37 @ ^ [I3: rat] : ( plus_plus_rat @ I3 @ one_one_rat )
% 9.17/5.37 @ N4
% 9.17/5.37 @ zero_zero_rat ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3236_of__nat__code,axiom,
% 9.17/5.37 ( semiri1314217659103216013at_int
% 9.17/5.37 = ( ^ [N4: nat] :
% 9.17/5.37 ( semiri8420488043553186161ux_int
% 9.17/5.37 @ ^ [I3: int] : ( plus_plus_int @ I3 @ one_one_int )
% 9.17/5.37 @ N4
% 9.17/5.37 @ zero_zero_int ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3237_of__nat__code,axiom,
% 9.17/5.37 ( semiri1316708129612266289at_nat
% 9.17/5.37 = ( ^ [N4: nat] :
% 9.17/5.37 ( semiri8422978514062236437ux_nat
% 9.17/5.37 @ ^ [I3: nat] : ( plus_plus_nat @ I3 @ one_one_nat )
% 9.17/5.37 @ N4
% 9.17/5.37 @ zero_zero_nat ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3238_of__nat__code,axiom,
% 9.17/5.37 ( semiri4939895301339042750nteger
% 9.17/5.37 = ( ^ [N4: nat] :
% 9.17/5.37 ( semiri4055485073559036834nteger
% 9.17/5.37 @ ^ [I3: code_integer] : ( plus_p5714425477246183910nteger @ I3 @ one_one_Code_integer )
% 9.17/5.37 @ N4
% 9.17/5.37 @ zero_z3403309356797280102nteger ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3239_of__nat__code,axiom,
% 9.17/5.37 ( semiri3763490453095760265atural
% 9.17/5.37 = ( ^ [N4: nat] :
% 9.17/5.37 ( semiri2879080225315754349atural
% 9.17/5.37 @ ^ [I3: code_natural] : ( plus_p4538020629002901425atural @ I3 @ one_one_Code_natural )
% 9.17/5.37 @ N4
% 9.17/5.37 @ zero_z2226904508553997617atural ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3240_signed__take__bit__Suc__minus__bit1,axiom,
% 9.17/5.37 ! [N2: nat,K: num] :
% 9.17/5.37 ( ( bit_ri631733984087533419it_int @ ( suc @ N2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 9.17/5.37 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N2 @ ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3241_concat__bit__Suc,axiom,
% 9.17/5.37 ! [N2: nat,K: int,L: int] :
% 9.17/5.37 ( ( bit_concat_bit @ ( suc @ N2 ) @ K @ L )
% 9.17/5.37 = ( plus_plus_int @ ( modulo_modulo_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_concat_bit @ N2 @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ L ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3242_even__succ__mod__exp,axiom,
% 9.17/5.37 ! [A: int,N2: nat] :
% 9.17/5.37 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 9.17/5.37 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 9.17/5.37 => ( ( modulo_modulo_int @ ( plus_plus_int @ one_one_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 9.17/5.37 = ( plus_plus_int @ one_one_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3243_even__succ__mod__exp,axiom,
% 9.17/5.37 ! [A: nat,N2: nat] :
% 9.17/5.37 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 9.17/5.37 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 9.17/5.37 => ( ( modulo_modulo_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 9.17/5.37 = ( plus_plus_nat @ one_one_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3244_even__succ__mod__exp,axiom,
% 9.17/5.37 ! [A: code_integer,N2: nat] :
% 9.17/5.37 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 9.17/5.37 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 9.17/5.37 => ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 9.17/5.37 = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( modulo364778990260209775nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3245_even__succ__mod__exp,axiom,
% 9.17/5.37 ! [A: code_natural,N2: nat] :
% 9.17/5.37 ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 9.17/5.37 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 9.17/5.37 => ( ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ one_one_Code_natural @ A ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N2 ) )
% 9.17/5.37 = ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( modulo8411746178871703098atural @ A @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3246_even__succ__div__exp,axiom,
% 9.17/5.37 ! [A: int,N2: nat] :
% 9.17/5.37 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 9.17/5.37 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 9.17/5.37 => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 9.17/5.37 = ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3247_even__succ__div__exp,axiom,
% 9.17/5.37 ! [A: nat,N2: nat] :
% 9.17/5.37 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 9.17/5.37 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 9.17/5.37 => ( ( divide_divide_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 9.17/5.37 = ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3248_even__succ__div__exp,axiom,
% 9.17/5.37 ! [A: code_integer,N2: nat] :
% 9.17/5.37 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 9.17/5.37 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 9.17/5.37 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 9.17/5.37 = ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3249_even__succ__div__exp,axiom,
% 9.17/5.37 ! [A: code_natural,N2: nat] :
% 9.17/5.37 ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 9.17/5.37 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 9.17/5.37 => ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ one_one_Code_natural @ A ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N2 ) )
% 9.17/5.37 = ( divide5121882707175180666atural @ A @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3250_take__bit__rec,axiom,
% 9.17/5.37 ( bit_se1745604003318907178nteger
% 9.17/5.37 = ( ^ [N4: nat,A5: code_integer] : ( if_Code_integer @ ( N4 = zero_zero_nat ) @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( bit_se1745604003318907178nteger @ ( minus_minus_nat @ N4 @ one_one_nat ) @ ( divide6298287555418463151nteger @ A5 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( modulo364778990260209775nteger @ A5 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3251_take__bit__rec,axiom,
% 9.17/5.37 ( bit_se2923211474154528505it_int
% 9.17/5.37 = ( ^ [N4: nat,A5: int] : ( if_int @ ( N4 = zero_zero_nat ) @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ ( minus_minus_nat @ N4 @ one_one_nat ) @ ( divide_divide_int @ A5 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ A5 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3252_take__bit__rec,axiom,
% 9.17/5.37 ( bit_se2925701944663578781it_nat
% 9.17/5.37 = ( ^ [N4: nat,A5: nat] : ( if_nat @ ( N4 = zero_zero_nat ) @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ ( minus_minus_nat @ N4 @ one_one_nat ) @ ( divide_divide_nat @ A5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ A5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3253_take__bit__rec,axiom,
% 9.17/5.37 ( bit_se569199155075624693atural
% 9.17/5.37 = ( ^ [N4: nat,A5: code_natural] : ( if_Code_natural @ ( N4 = zero_zero_nat ) @ zero_z2226904508553997617atural @ ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( bit_se569199155075624693atural @ ( minus_minus_nat @ N4 @ one_one_nat ) @ ( divide5121882707175180666atural @ A5 @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) @ ( modulo8411746178871703098atural @ A5 @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3254_nat__dvd__1__iff__1,axiom,
% 9.17/5.37 ! [M2: nat] :
% 9.17/5.37 ( ( dvd_dvd_nat @ M2 @ one_one_nat )
% 9.17/5.37 = ( M2 = one_one_nat ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3255_integer__of__int__eq__of__int,axiom,
% 9.17/5.37 code_integer_of_int = ring_18347121197199848620nteger ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3256_dvd__add__triv__right__iff,axiom,
% 9.17/5.37 ! [A: code_integer,B: code_integer] :
% 9.17/5.37 ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ A ) )
% 9.17/5.37 = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3257_dvd__add__triv__right__iff,axiom,
% 9.17/5.37 ! [A: rat,B: rat] :
% 9.17/5.37 ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 9.17/5.37 = ( dvd_dvd_rat @ A @ B ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3258_dvd__add__triv__right__iff,axiom,
% 9.17/5.37 ! [A: nat,B: nat] :
% 9.17/5.37 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 9.17/5.37 = ( dvd_dvd_nat @ A @ B ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3259_dvd__add__triv__right__iff,axiom,
% 9.17/5.37 ! [A: int,B: int] :
% 9.17/5.37 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ A ) )
% 9.17/5.37 = ( dvd_dvd_int @ A @ B ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3260_dvd__add__triv__left__iff,axiom,
% 9.17/5.37 ! [A: code_integer,B: code_integer] :
% 9.17/5.37 ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 9.17/5.37 = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3261_dvd__add__triv__left__iff,axiom,
% 9.17/5.37 ! [A: rat,B: rat] :
% 9.17/5.37 ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 9.17/5.37 = ( dvd_dvd_rat @ A @ B ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3262_dvd__add__triv__left__iff,axiom,
% 9.17/5.37 ! [A: nat,B: nat] :
% 9.17/5.37 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 9.17/5.37 = ( dvd_dvd_nat @ A @ B ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3263_dvd__add__triv__left__iff,axiom,
% 9.17/5.37 ! [A: int,B: int] :
% 9.17/5.37 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ A @ B ) )
% 9.17/5.37 = ( dvd_dvd_int @ A @ B ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3264_dvd__add__times__triv__right__iff,axiom,
% 9.17/5.37 ! [A: code_integer,B: code_integer,C: code_integer] :
% 9.17/5.37 ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ ( times_3573771949741848930nteger @ C @ A ) ) )
% 9.17/5.37 = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3265_dvd__add__times__triv__right__iff,axiom,
% 9.17/5.37 ! [A: rat,B: rat,C: rat] :
% 9.17/5.37 ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ ( times_times_rat @ C @ A ) ) )
% 9.17/5.37 = ( dvd_dvd_rat @ A @ B ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3266_dvd__add__times__triv__right__iff,axiom,
% 9.17/5.37 ! [A: nat,B: nat,C: nat] :
% 9.17/5.37 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ ( times_times_nat @ C @ A ) ) )
% 9.17/5.37 = ( dvd_dvd_nat @ A @ B ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3267_dvd__add__times__triv__right__iff,axiom,
% 9.17/5.37 ! [A: int,B: int,C: int] :
% 9.17/5.37 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ ( times_times_int @ C @ A ) ) )
% 9.17/5.37 = ( dvd_dvd_int @ A @ B ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3268_dvd__add__times__triv__left__iff,axiom,
% 9.17/5.37 ! [A: code_integer,C: code_integer,B: code_integer] :
% 9.17/5.37 ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ C @ A ) @ B ) )
% 9.17/5.37 = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3269_dvd__add__times__triv__left__iff,axiom,
% 9.17/5.37 ! [A: rat,C: rat,B: rat] :
% 9.17/5.37 ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ ( times_times_rat @ C @ A ) @ B ) )
% 9.17/5.37 = ( dvd_dvd_rat @ A @ B ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3270_dvd__add__times__triv__left__iff,axiom,
% 9.17/5.37 ! [A: nat,C: nat,B: nat] :
% 9.17/5.37 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ ( times_times_nat @ C @ A ) @ B ) )
% 9.17/5.37 = ( dvd_dvd_nat @ A @ B ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3271_dvd__add__times__triv__left__iff,axiom,
% 9.17/5.37 ! [A: int,C: int,B: int] :
% 9.17/5.37 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ ( times_times_int @ C @ A ) @ B ) )
% 9.17/5.37 = ( dvd_dvd_int @ A @ B ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3272_unit__prod,axiom,
% 9.17/5.37 ! [A: code_integer,B: code_integer] :
% 9.17/5.37 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 9.17/5.37 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 9.17/5.37 => ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ one_one_Code_integer ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3273_unit__prod,axiom,
% 9.17/5.37 ! [A: nat,B: nat] :
% 9.17/5.37 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 9.17/5.37 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 9.17/5.37 => ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3274_unit__prod,axiom,
% 9.17/5.37 ! [A: int,B: int] :
% 9.17/5.37 ( ( dvd_dvd_int @ A @ one_one_int )
% 9.17/5.37 => ( ( dvd_dvd_int @ B @ one_one_int )
% 9.17/5.37 => ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ one_one_int ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3275_div__add,axiom,
% 9.17/5.37 ! [C: int,A: int,B: int] :
% 9.17/5.37 ( ( dvd_dvd_int @ C @ A )
% 9.17/5.37 => ( ( dvd_dvd_int @ C @ B )
% 9.17/5.37 => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 9.17/5.37 = ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3276_div__add,axiom,
% 9.17/5.37 ! [C: nat,A: nat,B: nat] :
% 9.17/5.37 ( ( dvd_dvd_nat @ C @ A )
% 9.17/5.37 => ( ( dvd_dvd_nat @ C @ B )
% 9.17/5.37 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 9.17/5.37 = ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3277_div__add,axiom,
% 9.17/5.37 ! [C: code_integer,A: code_integer,B: code_integer] :
% 9.17/5.37 ( ( dvd_dvd_Code_integer @ C @ A )
% 9.17/5.37 => ( ( dvd_dvd_Code_integer @ C @ B )
% 9.17/5.37 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 9.17/5.37 = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3278_div__add,axiom,
% 9.17/5.37 ! [C: code_natural,A: code_natural,B: code_natural] :
% 9.17/5.37 ( ( dvd_dvd_Code_natural @ C @ A )
% 9.17/5.37 => ( ( dvd_dvd_Code_natural @ C @ B )
% 9.17/5.37 => ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ A @ B ) @ C )
% 9.17/5.37 = ( plus_p4538020629002901425atural @ ( divide5121882707175180666atural @ A @ C ) @ ( divide5121882707175180666atural @ B @ C ) ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3279_unit__div__1__div__1,axiom,
% 9.17/5.37 ! [A: int] :
% 9.17/5.37 ( ( dvd_dvd_int @ A @ one_one_int )
% 9.17/5.37 => ( ( divide_divide_int @ one_one_int @ ( divide_divide_int @ one_one_int @ A ) )
% 9.17/5.37 = A ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3280_unit__div__1__div__1,axiom,
% 9.17/5.37 ! [A: nat] :
% 9.17/5.37 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 9.17/5.37 => ( ( divide_divide_nat @ one_one_nat @ ( divide_divide_nat @ one_one_nat @ A ) )
% 9.17/5.37 = A ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3281_unit__div__1__div__1,axiom,
% 9.17/5.37 ! [A: code_integer] :
% 9.17/5.37 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 9.17/5.37 => ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( divide6298287555418463151nteger @ one_one_Code_integer @ A ) )
% 9.17/5.37 = A ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3282_unit__div__1__div__1,axiom,
% 9.17/5.37 ! [A: code_natural] :
% 9.17/5.37 ( ( dvd_dvd_Code_natural @ A @ one_one_Code_natural )
% 9.17/5.37 => ( ( divide5121882707175180666atural @ one_one_Code_natural @ ( divide5121882707175180666atural @ one_one_Code_natural @ A ) )
% 9.17/5.37 = A ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3283_unit__div__1__unit,axiom,
% 9.17/5.37 ! [A: int] :
% 9.17/5.37 ( ( dvd_dvd_int @ A @ one_one_int )
% 9.17/5.37 => ( dvd_dvd_int @ ( divide_divide_int @ one_one_int @ A ) @ one_one_int ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3284_unit__div__1__unit,axiom,
% 9.17/5.37 ! [A: nat] :
% 9.17/5.37 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 9.17/5.37 => ( dvd_dvd_nat @ ( divide_divide_nat @ one_one_nat @ A ) @ one_one_nat ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3285_unit__div__1__unit,axiom,
% 9.17/5.37 ! [A: code_integer] :
% 9.17/5.37 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 9.17/5.37 => ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ one_one_Code_integer @ A ) @ one_one_Code_integer ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3286_unit__div__1__unit,axiom,
% 9.17/5.37 ! [A: code_natural] :
% 9.17/5.37 ( ( dvd_dvd_Code_natural @ A @ one_one_Code_natural )
% 9.17/5.37 => ( dvd_dvd_Code_natural @ ( divide5121882707175180666atural @ one_one_Code_natural @ A ) @ one_one_Code_natural ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3287_unit__div,axiom,
% 9.17/5.37 ! [A: int,B: int] :
% 9.17/5.37 ( ( dvd_dvd_int @ A @ one_one_int )
% 9.17/5.37 => ( ( dvd_dvd_int @ B @ one_one_int )
% 9.17/5.37 => ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3288_unit__div,axiom,
% 9.17/5.37 ! [A: nat,B: nat] :
% 9.17/5.37 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 9.17/5.37 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 9.17/5.37 => ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3289_unit__div,axiom,
% 9.17/5.37 ! [A: code_integer,B: code_integer] :
% 9.17/5.37 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 9.17/5.37 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 9.17/5.37 => ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ A @ B ) @ one_one_Code_integer ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3290_unit__div,axiom,
% 9.17/5.37 ! [A: code_natural,B: code_natural] :
% 9.17/5.37 ( ( dvd_dvd_Code_natural @ A @ one_one_Code_natural )
% 9.17/5.37 => ( ( dvd_dvd_Code_natural @ B @ one_one_Code_natural )
% 9.17/5.37 => ( dvd_dvd_Code_natural @ ( divide5121882707175180666atural @ A @ B ) @ one_one_Code_natural ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3291_take__bit__Suc__1,axiom,
% 9.17/5.37 ! [N2: nat] :
% 9.17/5.37 ( ( bit_se1745604003318907178nteger @ ( suc @ N2 ) @ one_one_Code_integer )
% 9.17/5.37 = one_one_Code_integer ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3292_take__bit__Suc__1,axiom,
% 9.17/5.37 ! [N2: nat] :
% 9.17/5.37 ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ one_one_int )
% 9.17/5.37 = one_one_int ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3293_take__bit__Suc__1,axiom,
% 9.17/5.37 ! [N2: nat] :
% 9.17/5.37 ( ( bit_se2925701944663578781it_nat @ ( suc @ N2 ) @ one_one_nat )
% 9.17/5.37 = one_one_nat ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3294_take__bit__Suc__1,axiom,
% 9.17/5.37 ! [N2: nat] :
% 9.17/5.37 ( ( bit_se569199155075624693atural @ ( suc @ N2 ) @ one_one_Code_natural )
% 9.17/5.37 = one_one_Code_natural ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3295_take__bit__numeral__1,axiom,
% 9.17/5.37 ! [L: num] :
% 9.17/5.37 ( ( bit_se1745604003318907178nteger @ ( numeral_numeral_nat @ L ) @ one_one_Code_integer )
% 9.17/5.37 = one_one_Code_integer ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3296_take__bit__numeral__1,axiom,
% 9.17/5.37 ! [L: num] :
% 9.17/5.37 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ one_one_int )
% 9.17/5.37 = one_one_int ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3297_take__bit__numeral__1,axiom,
% 9.17/5.37 ! [L: num] :
% 9.17/5.37 ( ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ L ) @ one_one_nat )
% 9.17/5.37 = one_one_nat ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3298_take__bit__numeral__1,axiom,
% 9.17/5.37 ! [L: num] :
% 9.17/5.37 ( ( bit_se569199155075624693atural @ ( numeral_numeral_nat @ L ) @ one_one_Code_natural )
% 9.17/5.37 = one_one_Code_natural ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3299_semiring__norm_I9_J,axiom,
% 9.17/5.37 ! [M2: num,N2: num] :
% 9.17/5.37 ( ( plus_plus_num @ ( bit1 @ M2 ) @ ( bit0 @ N2 ) )
% 9.17/5.37 = ( bit1 @ ( plus_plus_num @ M2 @ N2 ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3300_semiring__norm_I7_J,axiom,
% 9.17/5.37 ! [M2: num,N2: num] :
% 9.17/5.37 ( ( plus_plus_num @ ( bit0 @ M2 ) @ ( bit1 @ N2 ) )
% 9.17/5.37 = ( bit1 @ ( plus_plus_num @ M2 @ N2 ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3301_semiring__norm_I16_J,axiom,
% 9.17/5.37 ! [M2: num,N2: num] :
% 9.17/5.37 ( ( times_times_num @ ( bit1 @ M2 ) @ ( bit1 @ N2 ) )
% 9.17/5.37 = ( bit1 @ ( plus_plus_num @ ( plus_plus_num @ M2 @ N2 ) @ ( bit0 @ ( times_times_num @ M2 @ N2 ) ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3302_unit__mult__div__div,axiom,
% 9.17/5.37 ! [A: int,B: int] :
% 9.17/5.37 ( ( dvd_dvd_int @ A @ one_one_int )
% 9.17/5.37 => ( ( times_times_int @ B @ ( divide_divide_int @ one_one_int @ A ) )
% 9.17/5.37 = ( divide_divide_int @ B @ A ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3303_unit__mult__div__div,axiom,
% 9.17/5.37 ! [A: nat,B: nat] :
% 9.17/5.37 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 9.17/5.37 => ( ( times_times_nat @ B @ ( divide_divide_nat @ one_one_nat @ A ) )
% 9.17/5.37 = ( divide_divide_nat @ B @ A ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3304_unit__mult__div__div,axiom,
% 9.17/5.37 ! [A: code_integer,B: code_integer] :
% 9.17/5.37 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 9.17/5.37 => ( ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ one_one_Code_integer @ A ) )
% 9.17/5.37 = ( divide6298287555418463151nteger @ B @ A ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3305_unit__mult__div__div,axiom,
% 9.17/5.37 ! [A: code_natural,B: code_natural] :
% 9.17/5.37 ( ( dvd_dvd_Code_natural @ A @ one_one_Code_natural )
% 9.17/5.37 => ( ( times_2397367101498566445atural @ B @ ( divide5121882707175180666atural @ one_one_Code_natural @ A ) )
% 9.17/5.37 = ( divide5121882707175180666atural @ B @ A ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3306_unit__div__mult__self,axiom,
% 9.17/5.37 ! [A: int,B: int] :
% 9.17/5.37 ( ( dvd_dvd_int @ A @ one_one_int )
% 9.17/5.37 => ( ( times_times_int @ ( divide_divide_int @ B @ A ) @ A )
% 9.17/5.37 = B ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3307_unit__div__mult__self,axiom,
% 9.17/5.37 ! [A: nat,B: nat] :
% 9.17/5.37 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 9.17/5.37 => ( ( times_times_nat @ ( divide_divide_nat @ B @ A ) @ A )
% 9.17/5.37 = B ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3308_unit__div__mult__self,axiom,
% 9.17/5.37 ! [A: code_integer,B: code_integer] :
% 9.17/5.37 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 9.17/5.37 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ B @ A ) @ A )
% 9.17/5.37 = B ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3309_unit__div__mult__self,axiom,
% 9.17/5.37 ! [A: code_natural,B: code_natural] :
% 9.17/5.37 ( ( dvd_dvd_Code_natural @ A @ one_one_Code_natural )
% 9.17/5.37 => ( ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ B @ A ) @ A )
% 9.17/5.37 = B ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3310_take__bit__of__1__eq__0__iff,axiom,
% 9.17/5.37 ! [N2: nat] :
% 9.17/5.37 ( ( ( bit_se1745604003318907178nteger @ N2 @ one_one_Code_integer )
% 9.17/5.37 = zero_z3403309356797280102nteger )
% 9.17/5.37 = ( N2 = zero_zero_nat ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3311_take__bit__of__1__eq__0__iff,axiom,
% 9.17/5.37 ! [N2: nat] :
% 9.17/5.37 ( ( ( bit_se2923211474154528505it_int @ N2 @ one_one_int )
% 9.17/5.37 = zero_zero_int )
% 9.17/5.37 = ( N2 = zero_zero_nat ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3312_take__bit__of__1__eq__0__iff,axiom,
% 9.17/5.37 ! [N2: nat] :
% 9.17/5.37 ( ( ( bit_se2925701944663578781it_nat @ N2 @ one_one_nat )
% 9.17/5.37 = zero_zero_nat )
% 9.17/5.37 = ( N2 = zero_zero_nat ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3313_take__bit__of__1__eq__0__iff,axiom,
% 9.17/5.37 ! [N2: nat] :
% 9.17/5.37 ( ( ( bit_se569199155075624693atural @ N2 @ one_one_Code_natural )
% 9.17/5.37 = zero_z2226904508553997617atural )
% 9.17/5.37 = ( N2 = zero_zero_nat ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3314_semiring__norm_I10_J,axiom,
% 9.17/5.37 ! [M2: num,N2: num] :
% 9.17/5.37 ( ( plus_plus_num @ ( bit1 @ M2 ) @ ( bit1 @ N2 ) )
% 9.17/5.37 = ( bit0 @ ( plus_plus_num @ ( plus_plus_num @ M2 @ N2 ) @ one ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3315_semiring__norm_I8_J,axiom,
% 9.17/5.37 ! [M2: num] :
% 9.17/5.37 ( ( plus_plus_num @ ( bit1 @ M2 ) @ one )
% 9.17/5.37 = ( bit0 @ ( plus_plus_num @ M2 @ one ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3316_semiring__norm_I5_J,axiom,
% 9.17/5.37 ! [M2: num] :
% 9.17/5.37 ( ( plus_plus_num @ ( bit0 @ M2 ) @ one )
% 9.17/5.37 = ( bit1 @ M2 ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3317_semiring__norm_I4_J,axiom,
% 9.17/5.37 ! [N2: num] :
% 9.17/5.37 ( ( plus_plus_num @ one @ ( bit1 @ N2 ) )
% 9.17/5.37 = ( bit0 @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3318_semiring__norm_I3_J,axiom,
% 9.17/5.37 ! [N2: num] :
% 9.17/5.37 ( ( plus_plus_num @ one @ ( bit0 @ N2 ) )
% 9.17/5.37 = ( bit1 @ N2 ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3319_odd__add,axiom,
% 9.17/5.37 ! [A: nat,B: nat] :
% 9.17/5.37 ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) ) )
% 9.17/5.37 = ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 9.17/5.37 != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3320_odd__add,axiom,
% 9.17/5.37 ! [A: int,B: int] :
% 9.17/5.37 ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) ) )
% 9.17/5.37 = ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 9.17/5.37 != ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3321_odd__add,axiom,
% 9.17/5.37 ! [A: code_integer,B: code_integer] :
% 9.17/5.37 ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) ) )
% 9.17/5.37 = ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 9.17/5.37 != ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3322_odd__add,axiom,
% 9.17/5.37 ! [A: code_natural,B: code_natural] :
% 9.17/5.37 ( ( ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( plus_p4538020629002901425atural @ A @ B ) ) )
% 9.17/5.37 = ( ( ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A ) )
% 9.17/5.37 != ( ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3323_even__add,axiom,
% 9.17/5.37 ! [A: nat,B: nat] :
% 9.17/5.37 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) )
% 9.17/5.37 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 9.17/5.37 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3324_even__add,axiom,
% 9.17/5.37 ! [A: int,B: int] :
% 9.17/5.37 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) )
% 9.17/5.37 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 9.17/5.37 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3325_even__add,axiom,
% 9.17/5.37 ! [A: code_integer,B: code_integer] :
% 9.17/5.37 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 9.17/5.37 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 9.17/5.37 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3326_even__add,axiom,
% 9.17/5.37 ! [A: code_natural,B: code_natural] :
% 9.17/5.37 ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( plus_p4538020629002901425atural @ A @ B ) )
% 9.17/5.37 = ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 9.17/5.37 = ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ B ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3327_dbl__inc__simps_I3_J,axiom,
% 9.17/5.37 ( ( neg_nu5851722552734809277nc_int @ one_one_int )
% 9.17/5.37 = ( numeral_numeral_int @ ( bit1 @ one ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3328_dbl__inc__simps_I3_J,axiom,
% 9.17/5.37 ( ( neg_nu5831290666863070958nteger @ one_one_Code_integer )
% 9.17/5.37 = ( numera6620942414471956472nteger @ ( bit1 @ one ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3329_dbl__inc__simps_I3_J,axiom,
% 9.17/5.37 ( ( neg_nu5219082963157363817nc_rat @ one_one_rat )
% 9.17/5.37 = ( numeral_numeral_rat @ ( bit1 @ one ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3330_even__plus__one__iff,axiom,
% 9.17/5.37 ! [A: nat] :
% 9.17/5.37 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ one_one_nat ) )
% 9.17/5.37 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3331_even__plus__one__iff,axiom,
% 9.17/5.37 ! [A: int] :
% 9.17/5.37 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ one_one_int ) )
% 9.17/5.37 = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3332_even__plus__one__iff,axiom,
% 9.17/5.37 ! [A: code_integer] :
% 9.17/5.37 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) )
% 9.17/5.37 = ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3333_even__plus__one__iff,axiom,
% 9.17/5.37 ! [A: code_natural] :
% 9.17/5.37 ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( plus_p4538020629002901425atural @ A @ one_one_Code_natural ) )
% 9.17/5.37 = ( ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3334_even__diff,axiom,
% 9.17/5.37 ! [A: int,B: int] :
% 9.17/5.37 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ A @ B ) )
% 9.17/5.37 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3335_even__diff,axiom,
% 9.17/5.37 ! [A: code_integer,B: code_integer] :
% 9.17/5.37 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_8373710615458151222nteger @ A @ B ) )
% 9.17/5.37 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3336_neg__one__even__power,axiom,
% 9.17/5.37 ! [N2: nat] :
% 9.17/5.37 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 9.17/5.37 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 )
% 9.17/5.37 = one_one_int ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3337_neg__one__even__power,axiom,
% 9.17/5.37 ! [N2: nat] :
% 9.17/5.37 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 9.17/5.37 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 )
% 9.17/5.37 = one_one_Code_integer ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3338_neg__one__even__power,axiom,
% 9.17/5.37 ! [N2: nat] :
% 9.17/5.37 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 9.17/5.37 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 )
% 9.17/5.37 = one_one_rat ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3339_neg__one__odd__power,axiom,
% 9.17/5.37 ! [N2: nat] :
% 9.17/5.37 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 9.17/5.37 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 )
% 9.17/5.37 = ( uminus_uminus_int @ one_one_int ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3340_neg__one__odd__power,axiom,
% 9.17/5.37 ! [N2: nat] :
% 9.17/5.37 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 9.17/5.37 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 )
% 9.17/5.37 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3341_neg__one__odd__power,axiom,
% 9.17/5.37 ! [N2: nat] :
% 9.17/5.37 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 9.17/5.37 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 )
% 9.17/5.37 = ( uminus_uminus_rat @ one_one_rat ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3342_even__diff__nat,axiom,
% 9.17/5.37 ! [M2: nat,N2: nat] :
% 9.17/5.37 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M2 @ N2 ) )
% 9.17/5.37 = ( ( ord_less_nat @ M2 @ N2 )
% 9.17/5.37 | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M2 @ N2 ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3343_divmod__algorithm__code_I4_J,axiom,
% 9.17/5.37 ! [N2: num] :
% 9.17/5.37 ( ( unique3479559517661332726nteger @ one @ ( bit1 @ N2 ) )
% 9.17/5.37 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ one ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3344_divmod__algorithm__code_I4_J,axiom,
% 9.17/5.37 ! [N2: num] :
% 9.17/5.37 ( ( unique5052692396658037445od_int @ one @ ( bit1 @ N2 ) )
% 9.17/5.37 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ one ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3345_divmod__algorithm__code_I4_J,axiom,
% 9.17/5.37 ! [N2: num] :
% 9.17/5.37 ( ( unique5055182867167087721od_nat @ one @ ( bit1 @ N2 ) )
% 9.17/5.37 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ one ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3346_mod__Suc__eq__mod__add3,axiom,
% 9.17/5.37 ! [M2: nat,N2: nat] :
% 9.17/5.37 ( ( modulo_modulo_nat @ M2 @ ( suc @ ( suc @ ( suc @ N2 ) ) ) )
% 9.17/5.37 = ( modulo_modulo_nat @ M2 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N2 ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3347_Suc__mod__eq__add3__mod__numeral,axiom,
% 9.17/5.37 ! [M2: nat,V: num] :
% 9.17/5.37 ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( suc @ M2 ) ) ) @ ( numeral_numeral_nat @ V ) )
% 9.17/5.37 = ( modulo_modulo_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M2 ) @ ( numeral_numeral_nat @ V ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3348_div__Suc__eq__div__add3,axiom,
% 9.17/5.37 ! [M2: nat,N2: nat] :
% 9.17/5.37 ( ( divide_divide_nat @ M2 @ ( suc @ ( suc @ ( suc @ N2 ) ) ) )
% 9.17/5.37 = ( divide_divide_nat @ M2 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N2 ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3349_Suc__div__eq__add3__div__numeral,axiom,
% 9.17/5.37 ! [M2: nat,V: num] :
% 9.17/5.37 ( ( divide_divide_nat @ ( suc @ ( suc @ ( suc @ M2 ) ) ) @ ( numeral_numeral_nat @ V ) )
% 9.17/5.37 = ( divide_divide_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M2 ) @ ( numeral_numeral_nat @ V ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3350_dbl__dec__simps_I4_J,axiom,
% 9.17/5.37 ( ( neg_nu3811975205180677377ec_int @ ( uminus_uminus_int @ one_one_int ) )
% 9.17/5.37 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ one ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3351_dbl__dec__simps_I4_J,axiom,
% 9.17/5.37 ( ( neg_nu7757733837767384882nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.17/5.37 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit1 @ one ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3352_dbl__dec__simps_I4_J,axiom,
% 9.17/5.37 ( ( neg_nu3179335615603231917ec_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 9.17/5.37 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit1 @ one ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3353_even__succ__div__2,axiom,
% 9.17/5.37 ! [A: int] :
% 9.17/5.37 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 9.17/5.37 => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ A ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.17/5.37 = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3354_even__succ__div__2,axiom,
% 9.17/5.37 ! [A: nat] :
% 9.17/5.37 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 9.17/5.37 => ( ( divide_divide_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.17/5.37 = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3355_even__succ__div__2,axiom,
% 9.17/5.37 ! [A: code_integer] :
% 9.17/5.37 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 9.17/5.37 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 9.17/5.37 = ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3356_even__succ__div__2,axiom,
% 9.17/5.37 ! [A: code_natural] :
% 9.17/5.37 ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 9.17/5.37 => ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ one_one_Code_natural @ A ) @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 9.17/5.37 = ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3357_odd__succ__div__two,axiom,
% 9.17/5.37 ! [A: int] :
% 9.17/5.37 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 9.17/5.37 => ( ( divide_divide_int @ ( plus_plus_int @ A @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.17/5.37 = ( plus_plus_int @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3358_odd__succ__div__two,axiom,
% 9.17/5.37 ! [A: nat] :
% 9.17/5.37 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 9.17/5.37 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.17/5.37 = ( plus_plus_nat @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3359_odd__succ__div__two,axiom,
% 9.17/5.37 ! [A: code_integer] :
% 9.17/5.37 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 9.17/5.37 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 9.17/5.37 = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ one_one_Code_integer ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3360_odd__succ__div__two,axiom,
% 9.17/5.37 ! [A: code_natural] :
% 9.17/5.37 ( ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 9.17/5.37 => ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ A @ one_one_Code_natural ) @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 9.17/5.37 = ( plus_p4538020629002901425atural @ ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) @ one_one_Code_natural ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3361_even__succ__div__two,axiom,
% 9.17/5.37 ! [A: int] :
% 9.17/5.37 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 9.17/5.37 => ( ( divide_divide_int @ ( plus_plus_int @ A @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.17/5.37 = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3362_even__succ__div__two,axiom,
% 9.17/5.37 ! [A: nat] :
% 9.17/5.37 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 9.17/5.37 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.17/5.37 = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3363_even__succ__div__two,axiom,
% 9.17/5.37 ! [A: code_integer] :
% 9.17/5.37 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 9.17/5.37 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 9.17/5.37 = ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3364_even__succ__div__two,axiom,
% 9.17/5.37 ! [A: code_natural] :
% 9.17/5.37 ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 9.17/5.37 => ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ A @ one_one_Code_natural ) @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 9.17/5.37 = ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3365_odd__two__times__div__two__nat,axiom,
% 9.17/5.37 ! [N2: nat] :
% 9.17/5.37 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 9.17/5.37 => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.17/5.37 = ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3366_odd__two__times__div__two__succ,axiom,
% 9.17/5.37 ! [A: int] :
% 9.17/5.37 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 9.17/5.37 => ( ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ one_one_int )
% 9.17/5.37 = A ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3367_odd__two__times__div__two__succ,axiom,
% 9.17/5.37 ! [A: nat] :
% 9.17/5.37 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 9.17/5.37 => ( ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_nat )
% 9.17/5.37 = A ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3368_odd__two__times__div__two__succ,axiom,
% 9.17/5.37 ! [A: code_integer] :
% 9.17/5.37 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 9.17/5.37 => ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ one_one_Code_integer )
% 9.17/5.37 = A ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3369_odd__two__times__div__two__succ,axiom,
% 9.17/5.37 ! [A: code_natural] :
% 9.17/5.37 ( ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 9.17/5.37 => ( ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) @ one_one_Code_natural )
% 9.17/5.37 = A ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3370_semiring__parity__class_Oeven__mask__iff,axiom,
% 9.17/5.37 ! [N2: nat] :
% 9.17/5.37 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) )
% 9.17/5.37 = ( N2 = zero_zero_nat ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3371_semiring__parity__class_Oeven__mask__iff,axiom,
% 9.17/5.37 ! [N2: nat] :
% 9.17/5.37 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ one_one_int ) )
% 9.17/5.37 = ( N2 = zero_zero_nat ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3372_semiring__parity__class_Oeven__mask__iff,axiom,
% 9.17/5.37 ! [N2: nat] :
% 9.17/5.37 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) @ one_one_Code_integer ) )
% 9.17/5.37 = ( N2 = zero_zero_nat ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3373_semiring__parity__class_Oeven__mask__iff,axiom,
% 9.17/5.37 ! [N2: nat] :
% 9.17/5.37 ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( minus_7197305767214868737atural @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N2 ) @ one_one_Code_natural ) )
% 9.17/5.37 = ( N2 = zero_zero_nat ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3374_zmod__numeral__Bit1,axiom,
% 9.17/5.37 ! [V: num,W: num] :
% 9.17/5.37 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 9.17/5.37 = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) @ one_one_int ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3375_divmod__algorithm__code_I8_J,axiom,
% 9.17/5.37 ! [M2: num,N2: num] :
% 9.17/5.37 ( ( ( ord_less_num @ M2 @ N2 )
% 9.17/5.37 => ( ( unique5055182867167087721od_nat @ ( bit1 @ M2 ) @ ( bit1 @ N2 ) )
% 9.17/5.37 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit1 @ M2 ) ) ) ) )
% 9.17/5.37 & ( ~ ( ord_less_num @ M2 @ N2 )
% 9.17/5.37 => ( ( unique5055182867167087721od_nat @ ( bit1 @ M2 ) @ ( bit1 @ N2 ) )
% 9.17/5.37 = ( unique5026877609467782581ep_nat @ ( bit1 @ N2 ) @ ( unique5055182867167087721od_nat @ ( bit1 @ M2 ) @ ( bit0 @ ( bit1 @ N2 ) ) ) ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3376_divmod__algorithm__code_I8_J,axiom,
% 9.17/5.37 ! [M2: num,N2: num] :
% 9.17/5.37 ( ( ( ord_less_num @ M2 @ N2 )
% 9.17/5.37 => ( ( unique5052692396658037445od_int @ ( bit1 @ M2 ) @ ( bit1 @ N2 ) )
% 9.17/5.37 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ ( bit1 @ M2 ) ) ) ) )
% 9.17/5.37 & ( ~ ( ord_less_num @ M2 @ N2 )
% 9.17/5.37 => ( ( unique5052692396658037445od_int @ ( bit1 @ M2 ) @ ( bit1 @ N2 ) )
% 9.17/5.37 = ( unique5024387138958732305ep_int @ ( bit1 @ N2 ) @ ( unique5052692396658037445od_int @ ( bit1 @ M2 ) @ ( bit0 @ ( bit1 @ N2 ) ) ) ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3377_divmod__algorithm__code_I8_J,axiom,
% 9.17/5.37 ! [M2: num,N2: num] :
% 9.17/5.37 ( ( ( ord_less_num @ M2 @ N2 )
% 9.17/5.37 => ( ( unique3479559517661332726nteger @ ( bit1 @ M2 ) @ ( bit1 @ N2 ) )
% 9.17/5.37 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M2 ) ) ) ) )
% 9.17/5.37 & ( ~ ( ord_less_num @ M2 @ N2 )
% 9.17/5.37 => ( ( unique3479559517661332726nteger @ ( bit1 @ M2 ) @ ( bit1 @ N2 ) )
% 9.17/5.37 = ( unique4921790084139445826nteger @ ( bit1 @ N2 ) @ ( unique3479559517661332726nteger @ ( bit1 @ M2 ) @ ( bit0 @ ( bit1 @ N2 ) ) ) ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3378_divmod__algorithm__code_I7_J,axiom,
% 9.17/5.37 ! [M2: num,N2: num] :
% 9.17/5.37 ( ( ( ord_less_eq_num @ M2 @ N2 )
% 9.17/5.37 => ( ( unique5055182867167087721od_nat @ ( bit0 @ M2 ) @ ( bit1 @ N2 ) )
% 9.17/5.37 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ M2 ) ) ) ) )
% 9.17/5.37 & ( ~ ( ord_less_eq_num @ M2 @ N2 )
% 9.17/5.37 => ( ( unique5055182867167087721od_nat @ ( bit0 @ M2 ) @ ( bit1 @ N2 ) )
% 9.17/5.37 = ( unique5026877609467782581ep_nat @ ( bit1 @ N2 ) @ ( unique5055182867167087721od_nat @ ( bit0 @ M2 ) @ ( bit0 @ ( bit1 @ N2 ) ) ) ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3379_divmod__algorithm__code_I7_J,axiom,
% 9.17/5.37 ! [M2: num,N2: num] :
% 9.17/5.37 ( ( ( ord_less_eq_num @ M2 @ N2 )
% 9.17/5.37 => ( ( unique5052692396658037445od_int @ ( bit0 @ M2 ) @ ( bit1 @ N2 ) )
% 9.17/5.37 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ ( bit0 @ M2 ) ) ) ) )
% 9.17/5.37 & ( ~ ( ord_less_eq_num @ M2 @ N2 )
% 9.17/5.37 => ( ( unique5052692396658037445od_int @ ( bit0 @ M2 ) @ ( bit1 @ N2 ) )
% 9.17/5.37 = ( unique5024387138958732305ep_int @ ( bit1 @ N2 ) @ ( unique5052692396658037445od_int @ ( bit0 @ M2 ) @ ( bit0 @ ( bit1 @ N2 ) ) ) ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3380_divmod__algorithm__code_I7_J,axiom,
% 9.17/5.37 ! [M2: num,N2: num] :
% 9.17/5.37 ( ( ( ord_less_eq_num @ M2 @ N2 )
% 9.17/5.37 => ( ( unique3479559517661332726nteger @ ( bit0 @ M2 ) @ ( bit1 @ N2 ) )
% 9.17/5.37 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M2 ) ) ) ) )
% 9.17/5.37 & ( ~ ( ord_less_eq_num @ M2 @ N2 )
% 9.17/5.37 => ( ( unique3479559517661332726nteger @ ( bit0 @ M2 ) @ ( bit1 @ N2 ) )
% 9.17/5.37 = ( unique4921790084139445826nteger @ ( bit1 @ N2 ) @ ( unique3479559517661332726nteger @ ( bit0 @ M2 ) @ ( bit0 @ ( bit1 @ N2 ) ) ) ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3381_signed__take__bit__Suc__bit1,axiom,
% 9.17/5.37 ! [N2: nat,K: num] :
% 9.17/5.37 ( ( bit_ri631733984087533419it_int @ ( suc @ N2 ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 9.17/5.37 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N2 @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3382_uminus__integer__code_I1_J,axiom,
% 9.17/5.37 ( ( uminus1351360451143612070nteger @ zero_z3403309356797280102nteger )
% 9.17/5.37 = zero_z3403309356797280102nteger ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3383_take__bit__integer_Oabs__eq,axiom,
% 9.17/5.37 ! [Xa: nat,X: int] :
% 9.17/5.37 ( ( bit_se1745604003318907178nteger @ Xa @ ( code_integer_of_int @ X ) )
% 9.17/5.37 = ( code_integer_of_int @ ( bit_se2923211474154528505it_int @ Xa @ X ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3384_abs__integer__code,axiom,
% 9.17/5.37 ( abs_abs_Code_integer
% 9.17/5.37 = ( ^ [K4: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ K4 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ K4 ) @ K4 ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3385_less__integer__code_I1_J,axiom,
% 9.17/5.37 ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3386_unset__bit__integer_Oabs__eq,axiom,
% 9.17/5.37 ! [Xa: nat,X: int] :
% 9.17/5.37 ( ( bit_se8260200283734997820nteger @ Xa @ ( code_integer_of_int @ X ) )
% 9.17/5.37 = ( code_integer_of_int @ ( bit_se4203085406695923979it_int @ Xa @ X ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3387_flip__bit__integer_Oabs__eq,axiom,
% 9.17/5.37 ! [Xa: nat,X: int] :
% 9.17/5.37 ( ( bit_se1345352211410354436nteger @ Xa @ ( code_integer_of_int @ X ) )
% 9.17/5.37 = ( code_integer_of_int @ ( bit_se2159334234014336723it_int @ Xa @ X ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3388_set__bit__integer_Oabs__eq,axiom,
% 9.17/5.37 ! [Xa: nat,X: int] :
% 9.17/5.37 ( ( bit_se2793503036327961859nteger @ Xa @ ( code_integer_of_int @ X ) )
% 9.17/5.37 = ( code_integer_of_int @ ( bit_se7879613467334960850it_int @ Xa @ X ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3389_take__bit__add,axiom,
% 9.17/5.37 ! [N2: nat,A: code_integer,B: code_integer] :
% 9.17/5.37 ( ( bit_se1745604003318907178nteger @ N2 @ ( plus_p5714425477246183910nteger @ ( bit_se1745604003318907178nteger @ N2 @ A ) @ ( bit_se1745604003318907178nteger @ N2 @ B ) ) )
% 9.17/5.37 = ( bit_se1745604003318907178nteger @ N2 @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3390_take__bit__add,axiom,
% 9.17/5.37 ! [N2: nat,A: int,B: int] :
% 9.17/5.37 ( ( bit_se2923211474154528505it_int @ N2 @ ( plus_plus_int @ ( bit_se2923211474154528505it_int @ N2 @ A ) @ ( bit_se2923211474154528505it_int @ N2 @ B ) ) )
% 9.17/5.37 = ( bit_se2923211474154528505it_int @ N2 @ ( plus_plus_int @ A @ B ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3391_take__bit__add,axiom,
% 9.17/5.37 ! [N2: nat,A: nat,B: nat] :
% 9.17/5.37 ( ( bit_se2925701944663578781it_nat @ N2 @ ( plus_plus_nat @ ( bit_se2925701944663578781it_nat @ N2 @ A ) @ ( bit_se2925701944663578781it_nat @ N2 @ B ) ) )
% 9.17/5.37 = ( bit_se2925701944663578781it_nat @ N2 @ ( plus_plus_nat @ A @ B ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3392_take__bit__add,axiom,
% 9.17/5.37 ! [N2: nat,A: code_natural,B: code_natural] :
% 9.17/5.37 ( ( bit_se569199155075624693atural @ N2 @ ( plus_p4538020629002901425atural @ ( bit_se569199155075624693atural @ N2 @ A ) @ ( bit_se569199155075624693atural @ N2 @ B ) ) )
% 9.17/5.37 = ( bit_se569199155075624693atural @ N2 @ ( plus_p4538020629002901425atural @ A @ B ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3393_zero__integer__def,axiom,
% 9.17/5.37 ( zero_z3403309356797280102nteger
% 9.17/5.37 = ( code_integer_of_int @ zero_zero_int ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3394_less__integer_Oabs__eq,axiom,
% 9.17/5.37 ! [Xa: int,X: int] :
% 9.17/5.37 ( ( ord_le6747313008572928689nteger @ ( code_integer_of_int @ Xa ) @ ( code_integer_of_int @ X ) )
% 9.17/5.37 = ( ord_less_int @ Xa @ X ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3395_uminus__integer_Oabs__eq,axiom,
% 9.17/5.37 ! [X: int] :
% 9.17/5.37 ( ( uminus1351360451143612070nteger @ ( code_integer_of_int @ X ) )
% 9.17/5.37 = ( code_integer_of_int @ ( uminus_uminus_int @ X ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3396_abs__integer_Oabs__eq,axiom,
% 9.17/5.37 ! [X: int] :
% 9.17/5.37 ( ( abs_abs_Code_integer @ ( code_integer_of_int @ X ) )
% 9.17/5.37 = ( code_integer_of_int @ ( abs_abs_int @ X ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3397_dvd__add__right__iff,axiom,
% 9.17/5.37 ! [A: code_integer,B: code_integer,C: code_integer] :
% 9.17/5.37 ( ( dvd_dvd_Code_integer @ A @ B )
% 9.17/5.37 => ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 9.17/5.37 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3398_dvd__add__right__iff,axiom,
% 9.17/5.37 ! [A: rat,B: rat,C: rat] :
% 9.17/5.37 ( ( dvd_dvd_rat @ A @ B )
% 9.17/5.37 => ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 9.17/5.37 = ( dvd_dvd_rat @ A @ C ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3399_dvd__add__right__iff,axiom,
% 9.17/5.37 ! [A: nat,B: nat,C: nat] :
% 9.17/5.37 ( ( dvd_dvd_nat @ A @ B )
% 9.17/5.37 => ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 9.17/5.37 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3400_dvd__add__right__iff,axiom,
% 9.17/5.37 ! [A: int,B: int,C: int] :
% 9.17/5.37 ( ( dvd_dvd_int @ A @ B )
% 9.17/5.37 => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ C ) )
% 9.17/5.37 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3401_dvd__add__left__iff,axiom,
% 9.17/5.37 ! [A: code_integer,C: code_integer,B: code_integer] :
% 9.17/5.37 ( ( dvd_dvd_Code_integer @ A @ C )
% 9.17/5.37 => ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 9.17/5.37 = ( dvd_dvd_Code_integer @ A @ B ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3402_dvd__add__left__iff,axiom,
% 9.17/5.37 ! [A: rat,C: rat,B: rat] :
% 9.17/5.37 ( ( dvd_dvd_rat @ A @ C )
% 9.17/5.37 => ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 9.17/5.37 = ( dvd_dvd_rat @ A @ B ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3403_dvd__add__left__iff,axiom,
% 9.17/5.37 ! [A: nat,C: nat,B: nat] :
% 9.17/5.37 ( ( dvd_dvd_nat @ A @ C )
% 9.17/5.37 => ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 9.17/5.37 = ( dvd_dvd_nat @ A @ B ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3404_dvd__add__left__iff,axiom,
% 9.17/5.37 ! [A: int,C: int,B: int] :
% 9.17/5.37 ( ( dvd_dvd_int @ A @ C )
% 9.17/5.37 => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ C ) )
% 9.17/5.37 = ( dvd_dvd_int @ A @ B ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3405_dvd__add,axiom,
% 9.17/5.37 ! [A: code_integer,B: code_integer,C: code_integer] :
% 9.17/5.37 ( ( dvd_dvd_Code_integer @ A @ B )
% 9.17/5.37 => ( ( dvd_dvd_Code_integer @ A @ C )
% 9.17/5.37 => ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ C ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3406_dvd__add,axiom,
% 9.17/5.37 ! [A: rat,B: rat,C: rat] :
% 9.17/5.37 ( ( dvd_dvd_rat @ A @ B )
% 9.17/5.37 => ( ( dvd_dvd_rat @ A @ C )
% 9.17/5.37 => ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3407_dvd__add,axiom,
% 9.17/5.37 ! [A: nat,B: nat,C: nat] :
% 9.17/5.37 ( ( dvd_dvd_nat @ A @ B )
% 9.17/5.37 => ( ( dvd_dvd_nat @ A @ C )
% 9.17/5.37 => ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3408_dvd__add,axiom,
% 9.17/5.37 ! [A: int,B: int,C: int] :
% 9.17/5.37 ( ( dvd_dvd_int @ A @ B )
% 9.17/5.37 => ( ( dvd_dvd_int @ A @ C )
% 9.17/5.37 => ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ C ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3409_divide__integer_Oabs__eq,axiom,
% 9.17/5.37 ! [Xa: int,X: int] :
% 9.17/5.37 ( ( divide6298287555418463151nteger @ ( code_integer_of_int @ Xa ) @ ( code_integer_of_int @ X ) )
% 9.17/5.37 = ( code_integer_of_int @ ( divide_divide_int @ Xa @ X ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3410_dvd__unit__imp__unit,axiom,
% 9.17/5.37 ! [A: code_integer,B: code_integer] :
% 9.17/5.37 ( ( dvd_dvd_Code_integer @ A @ B )
% 9.17/5.37 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 9.17/5.37 => ( dvd_dvd_Code_integer @ A @ one_one_Code_integer ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3411_dvd__unit__imp__unit,axiom,
% 9.17/5.37 ! [A: nat,B: nat] :
% 9.17/5.37 ( ( dvd_dvd_nat @ A @ B )
% 9.17/5.37 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 9.17/5.37 => ( dvd_dvd_nat @ A @ one_one_nat ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3412_dvd__unit__imp__unit,axiom,
% 9.17/5.37 ! [A: int,B: int] :
% 9.17/5.37 ( ( dvd_dvd_int @ A @ B )
% 9.17/5.37 => ( ( dvd_dvd_int @ B @ one_one_int )
% 9.17/5.37 => ( dvd_dvd_int @ A @ one_one_int ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3413_unit__imp__dvd,axiom,
% 9.17/5.37 ! [B: code_integer,A: code_integer] :
% 9.17/5.37 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 9.17/5.37 => ( dvd_dvd_Code_integer @ B @ A ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3414_unit__imp__dvd,axiom,
% 9.17/5.37 ! [B: nat,A: nat] :
% 9.17/5.37 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 9.17/5.37 => ( dvd_dvd_nat @ B @ A ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3415_unit__imp__dvd,axiom,
% 9.17/5.37 ! [B: int,A: int] :
% 9.17/5.37 ( ( dvd_dvd_int @ B @ one_one_int )
% 9.17/5.37 => ( dvd_dvd_int @ B @ A ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3416_one__dvd,axiom,
% 9.17/5.37 ! [A: code_integer] : ( dvd_dvd_Code_integer @ one_one_Code_integer @ A ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3417_one__dvd,axiom,
% 9.17/5.37 ! [A: assn] : ( dvd_dvd_assn @ one_one_assn @ A ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3418_one__dvd,axiom,
% 9.17/5.37 ! [A: rat] : ( dvd_dvd_rat @ one_one_rat @ A ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3419_one__dvd,axiom,
% 9.17/5.37 ! [A: nat] : ( dvd_dvd_nat @ one_one_nat @ A ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3420_one__dvd,axiom,
% 9.17/5.37 ! [A: int] : ( dvd_dvd_int @ one_one_int @ A ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3421_modulo__integer_Oabs__eq,axiom,
% 9.17/5.37 ! [Xa: int,X: int] :
% 9.17/5.37 ( ( modulo364778990260209775nteger @ ( code_integer_of_int @ Xa ) @ ( code_integer_of_int @ X ) )
% 9.17/5.37 = ( code_integer_of_int @ ( modulo_modulo_int @ Xa @ X ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3422_sgn__integer_Oabs__eq,axiom,
% 9.17/5.37 ! [X: int] :
% 9.17/5.37 ( ( sgn_sgn_Code_integer @ ( code_integer_of_int @ X ) )
% 9.17/5.37 = ( code_integer_of_int @ ( sgn_sgn_int @ X ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3423_concat__bit__assoc,axiom,
% 9.17/5.37 ! [N2: nat,K: int,M2: nat,L: int,R2: int] :
% 9.17/5.37 ( ( bit_concat_bit @ N2 @ K @ ( bit_concat_bit @ M2 @ L @ R2 ) )
% 9.17/5.37 = ( bit_concat_bit @ ( plus_plus_nat @ M2 @ N2 ) @ ( bit_concat_bit @ N2 @ K @ L ) @ R2 ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3424_not__is__unit__0,axiom,
% 9.17/5.37 ~ ( dvd_dvd_Code_integer @ zero_z3403309356797280102nteger @ one_one_Code_integer ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3425_not__is__unit__0,axiom,
% 9.17/5.37 ~ ( dvd_dvd_nat @ zero_zero_nat @ one_one_nat ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3426_not__is__unit__0,axiom,
% 9.17/5.37 ~ ( dvd_dvd_int @ zero_zero_int @ one_one_int ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3427_pinf_I9_J,axiom,
% 9.17/5.37 ! [D2: code_integer,S: code_integer] :
% 9.17/5.37 ? [Z3: code_integer] :
% 9.17/5.37 ! [X8: code_integer] :
% 9.17/5.37 ( ( ord_le6747313008572928689nteger @ Z3 @ X8 )
% 9.17/5.37 => ( ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ X8 @ S ) )
% 9.17/5.37 = ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ X8 @ S ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3428_pinf_I9_J,axiom,
% 9.17/5.37 ! [D2: rat,S: rat] :
% 9.17/5.37 ? [Z3: rat] :
% 9.17/5.37 ! [X8: rat] :
% 9.17/5.37 ( ( ord_less_rat @ Z3 @ X8 )
% 9.17/5.37 => ( ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X8 @ S ) )
% 9.17/5.37 = ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X8 @ S ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3429_pinf_I9_J,axiom,
% 9.17/5.37 ! [D2: nat,S: nat] :
% 9.17/5.37 ? [Z3: nat] :
% 9.17/5.37 ! [X8: nat] :
% 9.17/5.37 ( ( ord_less_nat @ Z3 @ X8 )
% 9.17/5.37 => ( ( dvd_dvd_nat @ D2 @ ( plus_plus_nat @ X8 @ S ) )
% 9.17/5.37 = ( dvd_dvd_nat @ D2 @ ( plus_plus_nat @ X8 @ S ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3430_pinf_I9_J,axiom,
% 9.17/5.37 ! [D2: int,S: int] :
% 9.17/5.37 ? [Z3: int] :
% 9.17/5.37 ! [X8: int] :
% 9.17/5.37 ( ( ord_less_int @ Z3 @ X8 )
% 9.17/5.37 => ( ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X8 @ S ) )
% 9.17/5.37 = ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X8 @ S ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3431_pinf_I10_J,axiom,
% 9.17/5.37 ! [D2: code_integer,S: code_integer] :
% 9.17/5.37 ? [Z3: code_integer] :
% 9.17/5.37 ! [X8: code_integer] :
% 9.17/5.37 ( ( ord_le6747313008572928689nteger @ Z3 @ X8 )
% 9.17/5.37 => ( ( ~ ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ X8 @ S ) ) )
% 9.17/5.37 = ( ~ ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ X8 @ S ) ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3432_pinf_I10_J,axiom,
% 9.17/5.37 ! [D2: rat,S: rat] :
% 9.17/5.37 ? [Z3: rat] :
% 9.17/5.37 ! [X8: rat] :
% 9.17/5.37 ( ( ord_less_rat @ Z3 @ X8 )
% 9.17/5.37 => ( ( ~ ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X8 @ S ) ) )
% 9.17/5.37 = ( ~ ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X8 @ S ) ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3433_pinf_I10_J,axiom,
% 9.17/5.37 ! [D2: nat,S: nat] :
% 9.17/5.37 ? [Z3: nat] :
% 9.17/5.37 ! [X8: nat] :
% 9.17/5.37 ( ( ord_less_nat @ Z3 @ X8 )
% 9.17/5.37 => ( ( ~ ( dvd_dvd_nat @ D2 @ ( plus_plus_nat @ X8 @ S ) ) )
% 9.17/5.37 = ( ~ ( dvd_dvd_nat @ D2 @ ( plus_plus_nat @ X8 @ S ) ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3434_pinf_I10_J,axiom,
% 9.17/5.37 ! [D2: int,S: int] :
% 9.17/5.37 ? [Z3: int] :
% 9.17/5.37 ! [X8: int] :
% 9.17/5.37 ( ( ord_less_int @ Z3 @ X8 )
% 9.17/5.37 => ( ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X8 @ S ) ) )
% 9.17/5.37 = ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X8 @ S ) ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3435_minf_I9_J,axiom,
% 9.17/5.37 ! [D2: code_integer,S: code_integer] :
% 9.17/5.37 ? [Z3: code_integer] :
% 9.17/5.37 ! [X8: code_integer] :
% 9.17/5.37 ( ( ord_le6747313008572928689nteger @ X8 @ Z3 )
% 9.17/5.37 => ( ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ X8 @ S ) )
% 9.17/5.37 = ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ X8 @ S ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3436_minf_I9_J,axiom,
% 9.17/5.37 ! [D2: rat,S: rat] :
% 9.17/5.37 ? [Z3: rat] :
% 9.17/5.37 ! [X8: rat] :
% 9.17/5.37 ( ( ord_less_rat @ X8 @ Z3 )
% 9.17/5.37 => ( ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X8 @ S ) )
% 9.17/5.37 = ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X8 @ S ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3437_minf_I9_J,axiom,
% 9.17/5.37 ! [D2: nat,S: nat] :
% 9.17/5.37 ? [Z3: nat] :
% 9.17/5.37 ! [X8: nat] :
% 9.17/5.37 ( ( ord_less_nat @ X8 @ Z3 )
% 9.17/5.37 => ( ( dvd_dvd_nat @ D2 @ ( plus_plus_nat @ X8 @ S ) )
% 9.17/5.37 = ( dvd_dvd_nat @ D2 @ ( plus_plus_nat @ X8 @ S ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3438_minf_I9_J,axiom,
% 9.17/5.37 ! [D2: int,S: int] :
% 9.17/5.37 ? [Z3: int] :
% 9.17/5.37 ! [X8: int] :
% 9.17/5.37 ( ( ord_less_int @ X8 @ Z3 )
% 9.17/5.37 => ( ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X8 @ S ) )
% 9.17/5.37 = ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X8 @ S ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3439_minf_I10_J,axiom,
% 9.17/5.37 ! [D2: code_integer,S: code_integer] :
% 9.17/5.37 ? [Z3: code_integer] :
% 9.17/5.37 ! [X8: code_integer] :
% 9.17/5.37 ( ( ord_le6747313008572928689nteger @ X8 @ Z3 )
% 9.17/5.37 => ( ( ~ ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ X8 @ S ) ) )
% 9.17/5.37 = ( ~ ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ X8 @ S ) ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3440_minf_I10_J,axiom,
% 9.17/5.37 ! [D2: rat,S: rat] :
% 9.17/5.37 ? [Z3: rat] :
% 9.17/5.37 ! [X8: rat] :
% 9.17/5.37 ( ( ord_less_rat @ X8 @ Z3 )
% 9.17/5.37 => ( ( ~ ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X8 @ S ) ) )
% 9.17/5.37 = ( ~ ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X8 @ S ) ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3441_minf_I10_J,axiom,
% 9.17/5.37 ! [D2: nat,S: nat] :
% 9.17/5.37 ? [Z3: nat] :
% 9.17/5.37 ! [X8: nat] :
% 9.17/5.37 ( ( ord_less_nat @ X8 @ Z3 )
% 9.17/5.37 => ( ( ~ ( dvd_dvd_nat @ D2 @ ( plus_plus_nat @ X8 @ S ) ) )
% 9.17/5.37 = ( ~ ( dvd_dvd_nat @ D2 @ ( plus_plus_nat @ X8 @ S ) ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3442_minf_I10_J,axiom,
% 9.17/5.37 ! [D2: int,S: int] :
% 9.17/5.37 ? [Z3: int] :
% 9.17/5.37 ! [X8: int] :
% 9.17/5.37 ( ( ord_less_int @ X8 @ Z3 )
% 9.17/5.37 => ( ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X8 @ S ) ) )
% 9.17/5.37 = ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X8 @ S ) ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3443_unit__mult__right__cancel,axiom,
% 9.17/5.37 ! [A: code_integer,B: code_integer,C: code_integer] :
% 9.17/5.37 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 9.17/5.37 => ( ( ( times_3573771949741848930nteger @ B @ A )
% 9.17/5.37 = ( times_3573771949741848930nteger @ C @ A ) )
% 9.17/5.37 = ( B = C ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3444_unit__mult__right__cancel,axiom,
% 9.17/5.37 ! [A: nat,B: nat,C: nat] :
% 9.17/5.37 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 9.17/5.37 => ( ( ( times_times_nat @ B @ A )
% 9.17/5.37 = ( times_times_nat @ C @ A ) )
% 9.17/5.37 = ( B = C ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3445_unit__mult__right__cancel,axiom,
% 9.17/5.37 ! [A: int,B: int,C: int] :
% 9.17/5.37 ( ( dvd_dvd_int @ A @ one_one_int )
% 9.17/5.37 => ( ( ( times_times_int @ B @ A )
% 9.17/5.37 = ( times_times_int @ C @ A ) )
% 9.17/5.37 = ( B = C ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3446_unit__mult__left__cancel,axiom,
% 9.17/5.37 ! [A: code_integer,B: code_integer,C: code_integer] :
% 9.17/5.37 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 9.17/5.37 => ( ( ( times_3573771949741848930nteger @ A @ B )
% 9.17/5.37 = ( times_3573771949741848930nteger @ A @ C ) )
% 9.17/5.37 = ( B = C ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3447_unit__mult__left__cancel,axiom,
% 9.17/5.37 ! [A: nat,B: nat,C: nat] :
% 9.17/5.37 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 9.17/5.37 => ( ( ( times_times_nat @ A @ B )
% 9.17/5.37 = ( times_times_nat @ A @ C ) )
% 9.17/5.37 = ( B = C ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3448_unit__mult__left__cancel,axiom,
% 9.17/5.37 ! [A: int,B: int,C: int] :
% 9.17/5.37 ( ( dvd_dvd_int @ A @ one_one_int )
% 9.17/5.37 => ( ( ( times_times_int @ A @ B )
% 9.17/5.37 = ( times_times_int @ A @ C ) )
% 9.17/5.37 = ( B = C ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3449_mult__unit__dvd__iff_H,axiom,
% 9.17/5.37 ! [A: code_integer,B: code_integer,C: code_integer] :
% 9.17/5.37 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 9.17/5.37 => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 9.17/5.37 = ( dvd_dvd_Code_integer @ B @ C ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3450_mult__unit__dvd__iff_H,axiom,
% 9.17/5.37 ! [A: nat,B: nat,C: nat] :
% 9.17/5.37 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 9.17/5.37 => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 9.17/5.37 = ( dvd_dvd_nat @ B @ C ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3451_mult__unit__dvd__iff_H,axiom,
% 9.17/5.37 ! [A: int,B: int,C: int] :
% 9.17/5.37 ( ( dvd_dvd_int @ A @ one_one_int )
% 9.17/5.37 => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 9.17/5.37 = ( dvd_dvd_int @ B @ C ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3452_dvd__mult__unit__iff_H,axiom,
% 9.17/5.37 ! [B: code_integer,A: code_integer,C: code_integer] :
% 9.17/5.37 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 9.17/5.37 => ( ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 9.17/5.37 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3453_dvd__mult__unit__iff_H,axiom,
% 9.17/5.37 ! [B: nat,A: nat,C: nat] :
% 9.17/5.37 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 9.17/5.37 => ( ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) )
% 9.17/5.37 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3454_dvd__mult__unit__iff_H,axiom,
% 9.17/5.37 ! [B: int,A: int,C: int] :
% 9.17/5.37 ( ( dvd_dvd_int @ B @ one_one_int )
% 9.17/5.37 => ( ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) )
% 9.17/5.37 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3455_mult__unit__dvd__iff,axiom,
% 9.17/5.37 ! [B: code_integer,A: code_integer,C: code_integer] :
% 9.17/5.37 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 9.17/5.37 => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 9.17/5.37 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3456_mult__unit__dvd__iff,axiom,
% 9.17/5.37 ! [B: nat,A: nat,C: nat] :
% 9.17/5.37 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 9.17/5.37 => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 9.17/5.37 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3457_mult__unit__dvd__iff,axiom,
% 9.17/5.37 ! [B: int,A: int,C: int] :
% 9.17/5.37 ( ( dvd_dvd_int @ B @ one_one_int )
% 9.17/5.37 => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 9.17/5.37 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3458_dvd__mult__unit__iff,axiom,
% 9.17/5.37 ! [B: code_integer,A: code_integer,C: code_integer] :
% 9.17/5.37 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 9.17/5.37 => ( ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ C @ B ) )
% 9.17/5.37 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3459_dvd__mult__unit__iff,axiom,
% 9.17/5.37 ! [B: nat,A: nat,C: nat] :
% 9.17/5.37 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 9.17/5.37 => ( ( dvd_dvd_nat @ A @ ( times_times_nat @ C @ B ) )
% 9.17/5.37 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3460_dvd__mult__unit__iff,axiom,
% 9.17/5.37 ! [B: int,A: int,C: int] :
% 9.17/5.37 ( ( dvd_dvd_int @ B @ one_one_int )
% 9.17/5.37 => ( ( dvd_dvd_int @ A @ ( times_times_int @ C @ B ) )
% 9.17/5.37 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3461_is__unit__mult__iff,axiom,
% 9.17/5.37 ! [A: code_integer,B: code_integer] :
% 9.17/5.37 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ one_one_Code_integer )
% 9.17/5.37 = ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 9.17/5.37 & ( dvd_dvd_Code_integer @ B @ one_one_Code_integer ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3462_is__unit__mult__iff,axiom,
% 9.17/5.37 ! [A: nat,B: nat] :
% 9.17/5.37 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ one_one_nat )
% 9.17/5.37 = ( ( dvd_dvd_nat @ A @ one_one_nat )
% 9.17/5.37 & ( dvd_dvd_nat @ B @ one_one_nat ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3463_is__unit__mult__iff,axiom,
% 9.17/5.37 ! [A: int,B: int] :
% 9.17/5.37 ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ one_one_int )
% 9.17/5.37 = ( ( dvd_dvd_int @ A @ one_one_int )
% 9.17/5.37 & ( dvd_dvd_int @ B @ one_one_int ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3464_div__plus__div__distrib__dvd__left,axiom,
% 9.17/5.37 ! [C: int,A: int,B: int] :
% 9.17/5.37 ( ( dvd_dvd_int @ C @ A )
% 9.17/5.37 => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 9.17/5.37 = ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3465_div__plus__div__distrib__dvd__left,axiom,
% 9.17/5.37 ! [C: nat,A: nat,B: nat] :
% 9.17/5.37 ( ( dvd_dvd_nat @ C @ A )
% 9.17/5.37 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 9.17/5.37 = ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3466_div__plus__div__distrib__dvd__left,axiom,
% 9.17/5.37 ! [C: code_integer,A: code_integer,B: code_integer] :
% 9.17/5.37 ( ( dvd_dvd_Code_integer @ C @ A )
% 9.17/5.37 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 9.17/5.37 = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3467_div__plus__div__distrib__dvd__left,axiom,
% 9.17/5.37 ! [C: code_natural,A: code_natural,B: code_natural] :
% 9.17/5.37 ( ( dvd_dvd_Code_natural @ C @ A )
% 9.17/5.37 => ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ A @ B ) @ C )
% 9.17/5.37 = ( plus_p4538020629002901425atural @ ( divide5121882707175180666atural @ A @ C ) @ ( divide5121882707175180666atural @ B @ C ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3468_div__plus__div__distrib__dvd__right,axiom,
% 9.17/5.37 ! [C: int,B: int,A: int] :
% 9.17/5.37 ( ( dvd_dvd_int @ C @ B )
% 9.17/5.37 => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 9.17/5.37 = ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3469_div__plus__div__distrib__dvd__right,axiom,
% 9.17/5.37 ! [C: nat,B: nat,A: nat] :
% 9.17/5.37 ( ( dvd_dvd_nat @ C @ B )
% 9.17/5.37 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 9.17/5.37 = ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3470_div__plus__div__distrib__dvd__right,axiom,
% 9.17/5.37 ! [C: code_integer,B: code_integer,A: code_integer] :
% 9.17/5.37 ( ( dvd_dvd_Code_integer @ C @ B )
% 9.17/5.37 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 9.17/5.37 = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3471_div__plus__div__distrib__dvd__right,axiom,
% 9.17/5.37 ! [C: code_natural,B: code_natural,A: code_natural] :
% 9.17/5.37 ( ( dvd_dvd_Code_natural @ C @ B )
% 9.17/5.37 => ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ A @ B ) @ C )
% 9.17/5.37 = ( plus_p4538020629002901425atural @ ( divide5121882707175180666atural @ A @ C ) @ ( divide5121882707175180666atural @ B @ C ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3472_unit__div__cancel,axiom,
% 9.17/5.37 ! [A: int,B: int,C: int] :
% 9.17/5.37 ( ( dvd_dvd_int @ A @ one_one_int )
% 9.17/5.37 => ( ( ( divide_divide_int @ B @ A )
% 9.17/5.37 = ( divide_divide_int @ C @ A ) )
% 9.17/5.37 = ( B = C ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3473_unit__div__cancel,axiom,
% 9.17/5.37 ! [A: nat,B: nat,C: nat] :
% 9.17/5.37 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 9.17/5.37 => ( ( ( divide_divide_nat @ B @ A )
% 9.17/5.37 = ( divide_divide_nat @ C @ A ) )
% 9.17/5.37 = ( B = C ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3474_unit__div__cancel,axiom,
% 9.17/5.37 ! [A: code_integer,B: code_integer,C: code_integer] :
% 9.17/5.37 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 9.17/5.37 => ( ( ( divide6298287555418463151nteger @ B @ A )
% 9.17/5.37 = ( divide6298287555418463151nteger @ C @ A ) )
% 9.17/5.37 = ( B = C ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3475_unit__div__cancel,axiom,
% 9.17/5.37 ! [A: code_natural,B: code_natural,C: code_natural] :
% 9.17/5.37 ( ( dvd_dvd_Code_natural @ A @ one_one_Code_natural )
% 9.17/5.37 => ( ( ( divide5121882707175180666atural @ B @ A )
% 9.17/5.37 = ( divide5121882707175180666atural @ C @ A ) )
% 9.17/5.37 = ( B = C ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3476_div__unit__dvd__iff,axiom,
% 9.17/5.37 ! [B: int,A: int,C: int] :
% 9.17/5.37 ( ( dvd_dvd_int @ B @ one_one_int )
% 9.17/5.37 => ( ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ C )
% 9.17/5.37 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3477_div__unit__dvd__iff,axiom,
% 9.17/5.37 ! [B: nat,A: nat,C: nat] :
% 9.17/5.37 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 9.17/5.37 => ( ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ C )
% 9.17/5.37 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3478_div__unit__dvd__iff,axiom,
% 9.17/5.37 ! [B: code_integer,A: code_integer,C: code_integer] :
% 9.17/5.37 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 9.17/5.37 => ( ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ A @ B ) @ C )
% 9.17/5.37 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3479_div__unit__dvd__iff,axiom,
% 9.17/5.37 ! [B: code_natural,A: code_natural,C: code_natural] :
% 9.17/5.37 ( ( dvd_dvd_Code_natural @ B @ one_one_Code_natural )
% 9.17/5.37 => ( ( dvd_dvd_Code_natural @ ( divide5121882707175180666atural @ A @ B ) @ C )
% 9.17/5.37 = ( dvd_dvd_Code_natural @ A @ C ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3480_dvd__div__unit__iff,axiom,
% 9.17/5.37 ! [B: int,A: int,C: int] :
% 9.17/5.37 ( ( dvd_dvd_int @ B @ one_one_int )
% 9.17/5.37 => ( ( dvd_dvd_int @ A @ ( divide_divide_int @ C @ B ) )
% 9.17/5.37 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3481_dvd__div__unit__iff,axiom,
% 9.17/5.37 ! [B: nat,A: nat,C: nat] :
% 9.17/5.37 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 9.17/5.37 => ( ( dvd_dvd_nat @ A @ ( divide_divide_nat @ C @ B ) )
% 9.17/5.37 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3482_dvd__div__unit__iff,axiom,
% 9.17/5.37 ! [B: code_integer,A: code_integer,C: code_integer] :
% 9.17/5.37 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 9.17/5.37 => ( ( dvd_dvd_Code_integer @ A @ ( divide6298287555418463151nteger @ C @ B ) )
% 9.17/5.37 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3483_dvd__div__unit__iff,axiom,
% 9.17/5.37 ! [B: code_natural,A: code_natural,C: code_natural] :
% 9.17/5.37 ( ( dvd_dvd_Code_natural @ B @ one_one_Code_natural )
% 9.17/5.37 => ( ( dvd_dvd_Code_natural @ A @ ( divide5121882707175180666atural @ C @ B ) )
% 9.17/5.37 = ( dvd_dvd_Code_natural @ A @ C ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3484_xor__num_Ocases,axiom,
% 9.17/5.37 ! [X: product_prod_num_num] :
% 9.17/5.37 ( ( X
% 9.17/5.37 != ( product_Pair_num_num @ one @ one ) )
% 9.17/5.37 => ( ! [N: num] :
% 9.17/5.37 ( X
% 9.17/5.37 != ( product_Pair_num_num @ one @ ( bit0 @ N ) ) )
% 9.17/5.37 => ( ! [N: num] :
% 9.17/5.37 ( X
% 9.17/5.37 != ( product_Pair_num_num @ one @ ( bit1 @ N ) ) )
% 9.17/5.37 => ( ! [M5: num] :
% 9.17/5.37 ( X
% 9.17/5.37 != ( product_Pair_num_num @ ( bit0 @ M5 ) @ one ) )
% 9.17/5.37 => ( ! [M5: num,N: num] :
% 9.17/5.37 ( X
% 9.17/5.37 != ( product_Pair_num_num @ ( bit0 @ M5 ) @ ( bit0 @ N ) ) )
% 9.17/5.37 => ( ! [M5: num,N: num] :
% 9.17/5.37 ( X
% 9.17/5.37 != ( product_Pair_num_num @ ( bit0 @ M5 ) @ ( bit1 @ N ) ) )
% 9.17/5.37 => ( ! [M5: num] :
% 9.17/5.37 ( X
% 9.17/5.37 != ( product_Pair_num_num @ ( bit1 @ M5 ) @ one ) )
% 9.17/5.37 => ( ! [M5: num,N: num] :
% 9.17/5.37 ( X
% 9.17/5.37 != ( product_Pair_num_num @ ( bit1 @ M5 ) @ ( bit0 @ N ) ) )
% 9.17/5.37 => ~ ! [M5: num,N: num] :
% 9.17/5.37 ( X
% 9.17/5.37 != ( product_Pair_num_num @ ( bit1 @ M5 ) @ ( bit1 @ N ) ) ) ) ) ) ) ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3485_plus__integer_Oabs__eq,axiom,
% 9.17/5.37 ! [Xa: int,X: int] :
% 9.17/5.37 ( ( plus_p5714425477246183910nteger @ ( code_integer_of_int @ Xa ) @ ( code_integer_of_int @ X ) )
% 9.17/5.37 = ( code_integer_of_int @ ( plus_plus_int @ Xa @ X ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3486_bezout__lemma__nat,axiom,
% 9.17/5.37 ! [D2: nat,A: nat,B: nat,X: nat,Y: nat] :
% 9.17/5.37 ( ( dvd_dvd_nat @ D2 @ A )
% 9.17/5.37 => ( ( dvd_dvd_nat @ D2 @ B )
% 9.17/5.37 => ( ( ( ( times_times_nat @ A @ X )
% 9.17/5.37 = ( plus_plus_nat @ ( times_times_nat @ B @ Y ) @ D2 ) )
% 9.17/5.37 | ( ( times_times_nat @ B @ X )
% 9.17/5.37 = ( plus_plus_nat @ ( times_times_nat @ A @ Y ) @ D2 ) ) )
% 9.17/5.37 => ? [X4: nat,Y5: nat] :
% 9.17/5.37 ( ( dvd_dvd_nat @ D2 @ A )
% 9.17/5.37 & ( dvd_dvd_nat @ D2 @ ( plus_plus_nat @ A @ B ) )
% 9.17/5.37 & ( ( ( times_times_nat @ A @ X4 )
% 9.17/5.37 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ Y5 ) @ D2 ) )
% 9.17/5.37 | ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ X4 )
% 9.17/5.37 = ( plus_plus_nat @ ( times_times_nat @ A @ Y5 ) @ D2 ) ) ) ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3487_bezout__add__nat,axiom,
% 9.17/5.37 ! [A: nat,B: nat] :
% 9.17/5.37 ? [D: nat,X4: nat,Y5: nat] :
% 9.17/5.37 ( ( dvd_dvd_nat @ D @ A )
% 9.17/5.37 & ( dvd_dvd_nat @ D @ B )
% 9.17/5.37 & ( ( ( times_times_nat @ A @ X4 )
% 9.17/5.37 = ( plus_plus_nat @ ( times_times_nat @ B @ Y5 ) @ D ) )
% 9.17/5.37 | ( ( times_times_nat @ B @ X4 )
% 9.17/5.37 = ( plus_plus_nat @ ( times_times_nat @ A @ Y5 ) @ D ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3488_one__integer__def,axiom,
% 9.17/5.37 ( one_one_Code_integer
% 9.17/5.37 = ( code_integer_of_int @ one_one_int ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3489_less__eq__integer_Oabs__eq,axiom,
% 9.17/5.37 ! [Xa: int,X: int] :
% 9.17/5.37 ( ( ord_le3102999989581377725nteger @ ( code_integer_of_int @ Xa ) @ ( code_integer_of_int @ X ) )
% 9.17/5.37 = ( ord_less_eq_int @ Xa @ X ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3490_times__integer_Oabs__eq,axiom,
% 9.17/5.37 ! [Xa: int,X: int] :
% 9.17/5.37 ( ( times_3573771949741848930nteger @ ( code_integer_of_int @ Xa ) @ ( code_integer_of_int @ X ) )
% 9.17/5.37 = ( code_integer_of_int @ ( times_times_int @ Xa @ X ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3491_zdvd__period,axiom,
% 9.17/5.37 ! [A: int,D2: int,X: int,T: int,C: int] :
% 9.17/5.37 ( ( dvd_dvd_int @ A @ D2 )
% 9.17/5.37 => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ X @ T ) )
% 9.17/5.37 = ( dvd_dvd_int @ A @ ( plus_plus_int @ ( plus_plus_int @ X @ ( times_times_int @ C @ D2 ) ) @ T ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3492_zdvd__reduce,axiom,
% 9.17/5.37 ! [K: int,N2: int,M2: int] :
% 9.17/5.37 ( ( dvd_dvd_int @ K @ ( plus_plus_int @ N2 @ ( times_times_int @ K @ M2 ) ) )
% 9.17/5.37 = ( dvd_dvd_int @ K @ N2 ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3493_minus__integer_Oabs__eq,axiom,
% 9.17/5.37 ! [Xa: int,X: int] :
% 9.17/5.37 ( ( minus_8373710615458151222nteger @ ( code_integer_of_int @ Xa ) @ ( code_integer_of_int @ X ) )
% 9.17/5.37 = ( code_integer_of_int @ ( minus_minus_int @ Xa @ X ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3494_unity__coeff__ex,axiom,
% 9.17/5.37 ! [P: code_integer > $o,L: code_integer] :
% 9.17/5.37 ( ( ? [X3: code_integer] : ( P @ ( times_3573771949741848930nteger @ L @ X3 ) ) )
% 9.17/5.37 = ( ? [X3: code_integer] :
% 9.17/5.37 ( ( dvd_dvd_Code_integer @ L @ ( plus_p5714425477246183910nteger @ X3 @ zero_z3403309356797280102nteger ) )
% 9.17/5.37 & ( P @ X3 ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3495_unity__coeff__ex,axiom,
% 9.17/5.37 ! [P: rat > $o,L: rat] :
% 9.17/5.37 ( ( ? [X3: rat] : ( P @ ( times_times_rat @ L @ X3 ) ) )
% 9.17/5.37 = ( ? [X3: rat] :
% 9.17/5.37 ( ( dvd_dvd_rat @ L @ ( plus_plus_rat @ X3 @ zero_zero_rat ) )
% 9.17/5.37 & ( P @ X3 ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3496_unity__coeff__ex,axiom,
% 9.17/5.37 ! [P: nat > $o,L: nat] :
% 9.17/5.37 ( ( ? [X3: nat] : ( P @ ( times_times_nat @ L @ X3 ) ) )
% 9.17/5.37 = ( ? [X3: nat] :
% 9.17/5.37 ( ( dvd_dvd_nat @ L @ ( plus_plus_nat @ X3 @ zero_zero_nat ) )
% 9.17/5.37 & ( P @ X3 ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3497_unity__coeff__ex,axiom,
% 9.17/5.37 ! [P: int > $o,L: int] :
% 9.17/5.37 ( ( ? [X3: int] : ( P @ ( times_times_int @ L @ X3 ) ) )
% 9.17/5.37 = ( ? [X3: int] :
% 9.17/5.37 ( ( dvd_dvd_int @ L @ ( plus_plus_int @ X3 @ zero_zero_int ) )
% 9.17/5.37 & ( P @ X3 ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3498_unit__dvdE,axiom,
% 9.17/5.37 ! [A: code_integer,B: code_integer] :
% 9.17/5.37 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 9.17/5.37 => ~ ( ( A != zero_z3403309356797280102nteger )
% 9.17/5.37 => ! [C3: code_integer] :
% 9.17/5.37 ( B
% 9.17/5.37 != ( times_3573771949741848930nteger @ A @ C3 ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3499_unit__dvdE,axiom,
% 9.17/5.37 ! [A: nat,B: nat] :
% 9.17/5.37 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 9.17/5.37 => ~ ( ( A != zero_zero_nat )
% 9.17/5.37 => ! [C3: nat] :
% 9.17/5.37 ( B
% 9.17/5.37 != ( times_times_nat @ A @ C3 ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3500_unit__dvdE,axiom,
% 9.17/5.37 ! [A: int,B: int] :
% 9.17/5.37 ( ( dvd_dvd_int @ A @ one_one_int )
% 9.17/5.37 => ~ ( ( A != zero_zero_int )
% 9.17/5.37 => ! [C3: int] :
% 9.17/5.37 ( B
% 9.17/5.37 != ( times_times_int @ A @ C3 ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3501_inf__period_I4_J,axiom,
% 9.17/5.37 ! [D2: code_integer,D3: code_integer,T: code_integer] :
% 9.17/5.37 ( ( dvd_dvd_Code_integer @ D2 @ D3 )
% 9.17/5.37 => ! [X8: code_integer,K6: code_integer] :
% 9.17/5.37 ( ( ~ ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ X8 @ T ) ) )
% 9.17/5.37 = ( ~ ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ X8 @ ( times_3573771949741848930nteger @ K6 @ D3 ) ) @ T ) ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3502_inf__period_I4_J,axiom,
% 9.17/5.37 ! [D2: rat,D3: rat,T: rat] :
% 9.17/5.37 ( ( dvd_dvd_rat @ D2 @ D3 )
% 9.17/5.37 => ! [X8: rat,K6: rat] :
% 9.17/5.37 ( ( ~ ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X8 @ T ) ) )
% 9.17/5.37 = ( ~ ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ ( minus_minus_rat @ X8 @ ( times_times_rat @ K6 @ D3 ) ) @ T ) ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3503_inf__period_I4_J,axiom,
% 9.17/5.37 ! [D2: int,D3: int,T: int] :
% 9.17/5.37 ( ( dvd_dvd_int @ D2 @ D3 )
% 9.17/5.37 => ! [X8: int,K6: int] :
% 9.17/5.37 ( ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X8 @ T ) ) )
% 9.17/5.37 = ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ ( minus_minus_int @ X8 @ ( times_times_int @ K6 @ D3 ) ) @ T ) ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3504_inf__period_I3_J,axiom,
% 9.17/5.37 ! [D2: code_integer,D3: code_integer,T: code_integer] :
% 9.17/5.37 ( ( dvd_dvd_Code_integer @ D2 @ D3 )
% 9.17/5.37 => ! [X8: code_integer,K6: code_integer] :
% 9.17/5.37 ( ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ X8 @ T ) )
% 9.17/5.37 = ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ X8 @ ( times_3573771949741848930nteger @ K6 @ D3 ) ) @ T ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3505_inf__period_I3_J,axiom,
% 9.17/5.37 ! [D2: rat,D3: rat,T: rat] :
% 9.17/5.37 ( ( dvd_dvd_rat @ D2 @ D3 )
% 9.17/5.37 => ! [X8: rat,K6: rat] :
% 9.17/5.37 ( ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X8 @ T ) )
% 9.17/5.37 = ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ ( minus_minus_rat @ X8 @ ( times_times_rat @ K6 @ D3 ) ) @ T ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3506_inf__period_I3_J,axiom,
% 9.17/5.37 ! [D2: int,D3: int,T: int] :
% 9.17/5.37 ( ( dvd_dvd_int @ D2 @ D3 )
% 9.17/5.37 => ! [X8: int,K6: int] :
% 9.17/5.37 ( ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X8 @ T ) )
% 9.17/5.37 = ( dvd_dvd_int @ D2 @ ( plus_plus_int @ ( minus_minus_int @ X8 @ ( times_times_int @ K6 @ D3 ) ) @ T ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3507_unit__div__eq__0__iff,axiom,
% 9.17/5.37 ! [B: int,A: int] :
% 9.17/5.37 ( ( dvd_dvd_int @ B @ one_one_int )
% 9.17/5.37 => ( ( ( divide_divide_int @ A @ B )
% 9.17/5.37 = zero_zero_int )
% 9.17/5.37 = ( A = zero_zero_int ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3508_unit__div__eq__0__iff,axiom,
% 9.17/5.37 ! [B: nat,A: nat] :
% 9.17/5.37 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 9.17/5.37 => ( ( ( divide_divide_nat @ A @ B )
% 9.17/5.37 = zero_zero_nat )
% 9.17/5.37 = ( A = zero_zero_nat ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3509_unit__div__eq__0__iff,axiom,
% 9.17/5.37 ! [B: code_integer,A: code_integer] :
% 9.17/5.37 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 9.17/5.37 => ( ( ( divide6298287555418463151nteger @ A @ B )
% 9.17/5.37 = zero_z3403309356797280102nteger )
% 9.17/5.37 = ( A = zero_z3403309356797280102nteger ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3510_unit__div__eq__0__iff,axiom,
% 9.17/5.37 ! [B: code_natural,A: code_natural] :
% 9.17/5.37 ( ( dvd_dvd_Code_natural @ B @ one_one_Code_natural )
% 9.17/5.37 => ( ( ( divide5121882707175180666atural @ A @ B )
% 9.17/5.37 = zero_z2226904508553997617atural )
% 9.17/5.37 = ( A = zero_z2226904508553997617atural ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3511_numeral__Bit1,axiom,
% 9.17/5.37 ! [N2: num] :
% 9.17/5.37 ( ( numeral_numeral_nat @ ( bit1 @ N2 ) )
% 9.17/5.37 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ N2 ) ) @ one_one_nat ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3512_numeral__Bit1,axiom,
% 9.17/5.37 ! [N2: num] :
% 9.17/5.37 ( ( numeral_numeral_int @ ( bit1 @ N2 ) )
% 9.17/5.37 = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ N2 ) ) @ one_one_int ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3513_numeral__Bit1,axiom,
% 9.17/5.37 ! [N2: num] :
% 9.17/5.37 ( ( numera6620942414471956472nteger @ ( bit1 @ N2 ) )
% 9.17/5.37 = ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ N2 ) @ ( numera6620942414471956472nteger @ N2 ) ) @ one_one_Code_integer ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3514_numeral__Bit1,axiom,
% 9.17/5.37 ! [N2: num] :
% 9.17/5.37 ( ( numeral_numeral_rat @ ( bit1 @ N2 ) )
% 9.17/5.37 = ( plus_plus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ N2 ) @ ( numeral_numeral_rat @ N2 ) ) @ one_one_rat ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3515_numeral__Bit1,axiom,
% 9.17/5.37 ! [N2: num] :
% 9.17/5.37 ( ( numera5444537566228673987atural @ ( bit1 @ N2 ) )
% 9.17/5.37 = ( plus_p4538020629002901425atural @ ( plus_p4538020629002901425atural @ ( numera5444537566228673987atural @ N2 ) @ ( numera5444537566228673987atural @ N2 ) ) @ one_one_Code_natural ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3516_unit__eq__div1,axiom,
% 9.17/5.37 ! [B: int,A: int,C: int] :
% 9.17/5.37 ( ( dvd_dvd_int @ B @ one_one_int )
% 9.17/5.37 => ( ( ( divide_divide_int @ A @ B )
% 9.17/5.37 = C )
% 9.17/5.37 = ( A
% 9.17/5.37 = ( times_times_int @ C @ B ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3517_unit__eq__div1,axiom,
% 9.17/5.37 ! [B: nat,A: nat,C: nat] :
% 9.17/5.37 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 9.17/5.37 => ( ( ( divide_divide_nat @ A @ B )
% 9.17/5.37 = C )
% 9.17/5.37 = ( A
% 9.17/5.37 = ( times_times_nat @ C @ B ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3518_unit__eq__div1,axiom,
% 9.17/5.37 ! [B: code_integer,A: code_integer,C: code_integer] :
% 9.17/5.37 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 9.17/5.37 => ( ( ( divide6298287555418463151nteger @ A @ B )
% 9.17/5.37 = C )
% 9.17/5.37 = ( A
% 9.17/5.37 = ( times_3573771949741848930nteger @ C @ B ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3519_unit__eq__div1,axiom,
% 9.17/5.37 ! [B: code_natural,A: code_natural,C: code_natural] :
% 9.17/5.37 ( ( dvd_dvd_Code_natural @ B @ one_one_Code_natural )
% 9.17/5.37 => ( ( ( divide5121882707175180666atural @ A @ B )
% 9.17/5.37 = C )
% 9.17/5.37 = ( A
% 9.17/5.37 = ( times_2397367101498566445atural @ C @ B ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3520_unit__eq__div2,axiom,
% 9.17/5.37 ! [B: int,A: int,C: int] :
% 9.17/5.37 ( ( dvd_dvd_int @ B @ one_one_int )
% 9.17/5.37 => ( ( A
% 9.17/5.37 = ( divide_divide_int @ C @ B ) )
% 9.17/5.37 = ( ( times_times_int @ A @ B )
% 9.17/5.37 = C ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3521_unit__eq__div2,axiom,
% 9.17/5.37 ! [B: nat,A: nat,C: nat] :
% 9.17/5.37 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 9.17/5.37 => ( ( A
% 9.17/5.37 = ( divide_divide_nat @ C @ B ) )
% 9.17/5.37 = ( ( times_times_nat @ A @ B )
% 9.17/5.37 = C ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3522_unit__eq__div2,axiom,
% 9.17/5.37 ! [B: code_integer,A: code_integer,C: code_integer] :
% 9.17/5.37 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 9.17/5.37 => ( ( A
% 9.17/5.37 = ( divide6298287555418463151nteger @ C @ B ) )
% 9.17/5.37 = ( ( times_3573771949741848930nteger @ A @ B )
% 9.17/5.37 = C ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3523_unit__eq__div2,axiom,
% 9.17/5.37 ! [B: code_natural,A: code_natural,C: code_natural] :
% 9.17/5.37 ( ( dvd_dvd_Code_natural @ B @ one_one_Code_natural )
% 9.17/5.37 => ( ( A
% 9.17/5.37 = ( divide5121882707175180666atural @ C @ B ) )
% 9.17/5.37 = ( ( times_2397367101498566445atural @ A @ B )
% 9.17/5.37 = C ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3524_div__mult__unit2,axiom,
% 9.17/5.37 ! [C: int,B: int,A: int] :
% 9.17/5.37 ( ( dvd_dvd_int @ C @ one_one_int )
% 9.17/5.37 => ( ( dvd_dvd_int @ B @ A )
% 9.17/5.37 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 9.17/5.37 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3525_div__mult__unit2,axiom,
% 9.17/5.37 ! [C: nat,B: nat,A: nat] :
% 9.17/5.37 ( ( dvd_dvd_nat @ C @ one_one_nat )
% 9.17/5.37 => ( ( dvd_dvd_nat @ B @ A )
% 9.17/5.37 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 9.17/5.37 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3526_div__mult__unit2,axiom,
% 9.17/5.37 ! [C: code_integer,B: code_integer,A: code_integer] :
% 9.17/5.37 ( ( dvd_dvd_Code_integer @ C @ one_one_Code_integer )
% 9.17/5.37 => ( ( dvd_dvd_Code_integer @ B @ A )
% 9.17/5.37 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 9.17/5.37 = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3527_div__mult__unit2,axiom,
% 9.17/5.37 ! [C: code_natural,B: code_natural,A: code_natural] :
% 9.17/5.37 ( ( dvd_dvd_Code_natural @ C @ one_one_Code_natural )
% 9.17/5.37 => ( ( dvd_dvd_Code_natural @ B @ A )
% 9.17/5.37 => ( ( divide5121882707175180666atural @ A @ ( times_2397367101498566445atural @ B @ C ) )
% 9.17/5.37 = ( divide5121882707175180666atural @ ( divide5121882707175180666atural @ A @ B ) @ C ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3528_unit__div__commute,axiom,
% 9.17/5.37 ! [B: int,A: int,C: int] :
% 9.17/5.37 ( ( dvd_dvd_int @ B @ one_one_int )
% 9.17/5.37 => ( ( times_times_int @ ( divide_divide_int @ A @ B ) @ C )
% 9.17/5.37 = ( divide_divide_int @ ( times_times_int @ A @ C ) @ B ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3529_unit__div__commute,axiom,
% 9.17/5.37 ! [B: nat,A: nat,C: nat] :
% 9.17/5.37 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 9.17/5.37 => ( ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ C )
% 9.17/5.37 = ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ B ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3530_unit__div__commute,axiom,
% 9.17/5.37 ! [B: code_integer,A: code_integer,C: code_integer] :
% 9.17/5.37 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 9.17/5.37 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C )
% 9.17/5.37 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ C ) @ B ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3531_unit__div__commute,axiom,
% 9.17/5.37 ! [B: code_natural,A: code_natural,C: code_natural] :
% 9.17/5.37 ( ( dvd_dvd_Code_natural @ B @ one_one_Code_natural )
% 9.17/5.37 => ( ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ A @ B ) @ C )
% 9.17/5.37 = ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ A @ C ) @ B ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3532_unit__div__mult__swap,axiom,
% 9.17/5.37 ! [C: int,A: int,B: int] :
% 9.17/5.37 ( ( dvd_dvd_int @ C @ one_one_int )
% 9.17/5.37 => ( ( times_times_int @ A @ ( divide_divide_int @ B @ C ) )
% 9.17/5.37 = ( divide_divide_int @ ( times_times_int @ A @ B ) @ C ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3533_unit__div__mult__swap,axiom,
% 9.17/5.37 ! [C: nat,A: nat,B: nat] :
% 9.17/5.37 ( ( dvd_dvd_nat @ C @ one_one_nat )
% 9.17/5.37 => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 9.17/5.37 = ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3534_unit__div__mult__swap,axiom,
% 9.17/5.37 ! [C: code_integer,A: code_integer,B: code_integer] :
% 9.17/5.37 ( ( dvd_dvd_Code_integer @ C @ one_one_Code_integer )
% 9.17/5.37 => ( ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 9.17/5.37 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3535_unit__div__mult__swap,axiom,
% 9.17/5.37 ! [C: code_natural,A: code_natural,B: code_natural] :
% 9.17/5.37 ( ( dvd_dvd_Code_natural @ C @ one_one_Code_natural )
% 9.17/5.37 => ( ( times_2397367101498566445atural @ A @ ( divide5121882707175180666atural @ B @ C ) )
% 9.17/5.37 = ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ A @ B ) @ C ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3536_is__unit__div__mult2__eq,axiom,
% 9.17/5.37 ! [B: int,C: int,A: int] :
% 9.17/5.37 ( ( dvd_dvd_int @ B @ one_one_int )
% 9.17/5.37 => ( ( dvd_dvd_int @ C @ one_one_int )
% 9.17/5.37 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 9.17/5.37 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3537_is__unit__div__mult2__eq,axiom,
% 9.17/5.37 ! [B: nat,C: nat,A: nat] :
% 9.17/5.37 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 9.17/5.37 => ( ( dvd_dvd_nat @ C @ one_one_nat )
% 9.17/5.37 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 9.17/5.37 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3538_is__unit__div__mult2__eq,axiom,
% 9.17/5.37 ! [B: code_integer,C: code_integer,A: code_integer] :
% 9.17/5.37 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 9.17/5.37 => ( ( dvd_dvd_Code_integer @ C @ one_one_Code_integer )
% 9.17/5.37 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 9.17/5.37 = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3539_is__unit__div__mult2__eq,axiom,
% 9.17/5.37 ! [B: code_natural,C: code_natural,A: code_natural] :
% 9.17/5.37 ( ( dvd_dvd_Code_natural @ B @ one_one_Code_natural )
% 9.17/5.37 => ( ( dvd_dvd_Code_natural @ C @ one_one_Code_natural )
% 9.17/5.37 => ( ( divide5121882707175180666atural @ A @ ( times_2397367101498566445atural @ B @ C ) )
% 9.17/5.37 = ( divide5121882707175180666atural @ ( divide5121882707175180666atural @ A @ B ) @ C ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3540_unit__imp__mod__eq__0,axiom,
% 9.17/5.37 ! [B: int,A: int] :
% 9.17/5.37 ( ( dvd_dvd_int @ B @ one_one_int )
% 9.17/5.37 => ( ( modulo_modulo_int @ A @ B )
% 9.17/5.37 = zero_zero_int ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3541_unit__imp__mod__eq__0,axiom,
% 9.17/5.37 ! [B: nat,A: nat] :
% 9.17/5.37 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 9.17/5.37 => ( ( modulo_modulo_nat @ A @ B )
% 9.17/5.37 = zero_zero_nat ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3542_unit__imp__mod__eq__0,axiom,
% 9.17/5.37 ! [B: code_integer,A: code_integer] :
% 9.17/5.37 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 9.17/5.37 => ( ( modulo364778990260209775nteger @ A @ B )
% 9.17/5.37 = zero_z3403309356797280102nteger ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3543_unit__imp__mod__eq__0,axiom,
% 9.17/5.37 ! [B: code_natural,A: code_natural] :
% 9.17/5.37 ( ( dvd_dvd_Code_natural @ B @ one_one_Code_natural )
% 9.17/5.37 => ( ( modulo8411746178871703098atural @ A @ B )
% 9.17/5.37 = zero_z2226904508553997617atural ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3544_is__unit__power__iff,axiom,
% 9.17/5.37 ! [A: code_integer,N2: nat] :
% 9.17/5.37 ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ N2 ) @ one_one_Code_integer )
% 9.17/5.37 = ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 9.17/5.37 | ( N2 = zero_zero_nat ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3545_is__unit__power__iff,axiom,
% 9.17/5.37 ! [A: nat,N2: nat] :
% 9.17/5.37 ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N2 ) @ one_one_nat )
% 9.17/5.37 = ( ( dvd_dvd_nat @ A @ one_one_nat )
% 9.17/5.37 | ( N2 = zero_zero_nat ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3546_is__unit__power__iff,axiom,
% 9.17/5.37 ! [A: int,N2: nat] :
% 9.17/5.37 ( ( dvd_dvd_int @ ( power_power_int @ A @ N2 ) @ one_one_int )
% 9.17/5.37 = ( ( dvd_dvd_int @ A @ one_one_int )
% 9.17/5.37 | ( N2 = zero_zero_nat ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3547_bezout__add__strong__nat,axiom,
% 9.17/5.37 ! [A: nat,B: nat] :
% 9.17/5.37 ( ( A != zero_zero_nat )
% 9.17/5.37 => ? [D: nat,X4: nat,Y5: nat] :
% 9.17/5.37 ( ( dvd_dvd_nat @ D @ A )
% 9.17/5.37 & ( dvd_dvd_nat @ D @ B )
% 9.17/5.37 & ( ( times_times_nat @ A @ X4 )
% 9.17/5.37 = ( plus_plus_nat @ ( times_times_nat @ B @ Y5 ) @ D ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3548_take__bit__Suc__bit1,axiom,
% 9.17/5.37 ! [N2: nat,K: num] :
% 9.17/5.37 ( ( bit_se1745604003318907178nteger @ ( suc @ N2 ) @ ( numera6620942414471956472nteger @ ( bit1 @ K ) ) )
% 9.17/5.37 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( bit_se1745604003318907178nteger @ N2 @ ( numera6620942414471956472nteger @ K ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ one_one_Code_integer ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3549_take__bit__Suc__bit1,axiom,
% 9.17/5.37 ! [N2: nat,K: num] :
% 9.17/5.37 ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 9.17/5.37 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N2 @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3550_take__bit__Suc__bit1,axiom,
% 9.17/5.37 ! [N2: nat,K: num] :
% 9.17/5.37 ( ( bit_se2925701944663578781it_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 9.17/5.37 = ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ N2 @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3551_take__bit__Suc__bit1,axiom,
% 9.17/5.37 ! [N2: nat,K: num] :
% 9.17/5.37 ( ( bit_se569199155075624693atural @ ( suc @ N2 ) @ ( numera5444537566228673987atural @ ( bit1 @ K ) ) )
% 9.17/5.37 = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( bit_se569199155075624693atural @ N2 @ ( numera5444537566228673987atural @ K ) ) @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) @ one_one_Code_natural ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3552_numeral__code_I3_J,axiom,
% 9.17/5.37 ! [N2: num] :
% 9.17/5.37 ( ( numeral_numeral_nat @ ( bit1 @ N2 ) )
% 9.17/5.37 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ N2 ) ) @ one_one_nat ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3553_numeral__code_I3_J,axiom,
% 9.17/5.37 ! [N2: num] :
% 9.17/5.37 ( ( numeral_numeral_int @ ( bit1 @ N2 ) )
% 9.17/5.37 = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ N2 ) ) @ one_one_int ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3554_numeral__code_I3_J,axiom,
% 9.17/5.37 ! [N2: num] :
% 9.17/5.37 ( ( numera6620942414471956472nteger @ ( bit1 @ N2 ) )
% 9.17/5.37 = ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ N2 ) @ ( numera6620942414471956472nteger @ N2 ) ) @ one_one_Code_integer ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3555_numeral__code_I3_J,axiom,
% 9.17/5.37 ! [N2: num] :
% 9.17/5.37 ( ( numeral_numeral_rat @ ( bit1 @ N2 ) )
% 9.17/5.37 = ( plus_plus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ N2 ) @ ( numeral_numeral_rat @ N2 ) ) @ one_one_rat ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3556_numeral__code_I3_J,axiom,
% 9.17/5.37 ! [N2: num] :
% 9.17/5.37 ( ( numera5444537566228673987atural @ ( bit1 @ N2 ) )
% 9.17/5.37 = ( plus_p4538020629002901425atural @ ( plus_p4538020629002901425atural @ ( numera5444537566228673987atural @ N2 ) @ ( numera5444537566228673987atural @ N2 ) ) @ one_one_Code_natural ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3557_stable__imp__take__bit__eq,axiom,
% 9.17/5.37 ! [A: code_integer,N2: nat] :
% 9.17/5.37 ( ( ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 9.17/5.37 = A )
% 9.17/5.37 => ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 9.17/5.37 => ( ( bit_se1745604003318907178nteger @ N2 @ A )
% 9.17/5.37 = zero_z3403309356797280102nteger ) )
% 9.17/5.37 & ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 9.17/5.37 => ( ( bit_se1745604003318907178nteger @ N2 @ A )
% 9.17/5.37 = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) @ one_one_Code_integer ) ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3558_stable__imp__take__bit__eq,axiom,
% 9.17/5.37 ! [A: int,N2: nat] :
% 9.17/5.37 ( ( ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.17/5.37 = A )
% 9.17/5.37 => ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 9.17/5.37 => ( ( bit_se2923211474154528505it_int @ N2 @ A )
% 9.17/5.37 = zero_zero_int ) )
% 9.17/5.37 & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 9.17/5.37 => ( ( bit_se2923211474154528505it_int @ N2 @ A )
% 9.17/5.37 = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ one_one_int ) ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3559_stable__imp__take__bit__eq,axiom,
% 9.17/5.37 ! [A: nat,N2: nat] :
% 9.17/5.37 ( ( ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.17/5.37 = A )
% 9.17/5.37 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 9.17/5.37 => ( ( bit_se2925701944663578781it_nat @ N2 @ A )
% 9.17/5.37 = zero_zero_nat ) )
% 9.17/5.37 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 9.17/5.37 => ( ( bit_se2925701944663578781it_nat @ N2 @ A )
% 9.17/5.37 = ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3560_stable__imp__take__bit__eq,axiom,
% 9.17/5.37 ! [A: code_natural,N2: nat] :
% 9.17/5.37 ( ( ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 9.17/5.37 = A )
% 9.17/5.37 => ( ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 9.17/5.37 => ( ( bit_se569199155075624693atural @ N2 @ A )
% 9.17/5.37 = zero_z2226904508553997617atural ) )
% 9.17/5.37 & ( ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 9.17/5.37 => ( ( bit_se569199155075624693atural @ N2 @ A )
% 9.17/5.37 = ( minus_7197305767214868737atural @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N2 ) @ one_one_Code_natural ) ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3561_is__unitE,axiom,
% 9.17/5.37 ! [A: int,C: int] :
% 9.17/5.37 ( ( dvd_dvd_int @ A @ one_one_int )
% 9.17/5.37 => ~ ( ( A != zero_zero_int )
% 9.17/5.37 => ! [B2: int] :
% 9.17/5.37 ( ( B2 != zero_zero_int )
% 9.17/5.37 => ( ( dvd_dvd_int @ B2 @ one_one_int )
% 9.17/5.37 => ( ( ( divide_divide_int @ one_one_int @ A )
% 9.17/5.37 = B2 )
% 9.17/5.37 => ( ( ( divide_divide_int @ one_one_int @ B2 )
% 9.17/5.37 = A )
% 9.17/5.37 => ( ( ( times_times_int @ A @ B2 )
% 9.17/5.37 = one_one_int )
% 9.17/5.37 => ( ( divide_divide_int @ C @ A )
% 9.17/5.37 != ( times_times_int @ C @ B2 ) ) ) ) ) ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3562_is__unitE,axiom,
% 9.17/5.37 ! [A: nat,C: nat] :
% 9.17/5.37 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 9.17/5.37 => ~ ( ( A != zero_zero_nat )
% 9.17/5.37 => ! [B2: nat] :
% 9.17/5.37 ( ( B2 != zero_zero_nat )
% 9.17/5.37 => ( ( dvd_dvd_nat @ B2 @ one_one_nat )
% 9.17/5.37 => ( ( ( divide_divide_nat @ one_one_nat @ A )
% 9.17/5.37 = B2 )
% 9.17/5.37 => ( ( ( divide_divide_nat @ one_one_nat @ B2 )
% 9.17/5.37 = A )
% 9.17/5.37 => ( ( ( times_times_nat @ A @ B2 )
% 9.17/5.37 = one_one_nat )
% 9.17/5.37 => ( ( divide_divide_nat @ C @ A )
% 9.17/5.37 != ( times_times_nat @ C @ B2 ) ) ) ) ) ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3563_is__unitE,axiom,
% 9.17/5.37 ! [A: code_integer,C: code_integer] :
% 9.17/5.37 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 9.17/5.37 => ~ ( ( A != zero_z3403309356797280102nteger )
% 9.17/5.37 => ! [B2: code_integer] :
% 9.17/5.37 ( ( B2 != zero_z3403309356797280102nteger )
% 9.17/5.37 => ( ( dvd_dvd_Code_integer @ B2 @ one_one_Code_integer )
% 9.17/5.37 => ( ( ( divide6298287555418463151nteger @ one_one_Code_integer @ A )
% 9.17/5.37 = B2 )
% 9.17/5.37 => ( ( ( divide6298287555418463151nteger @ one_one_Code_integer @ B2 )
% 9.17/5.37 = A )
% 9.17/5.37 => ( ( ( times_3573771949741848930nteger @ A @ B2 )
% 9.17/5.37 = one_one_Code_integer )
% 9.17/5.37 => ( ( divide6298287555418463151nteger @ C @ A )
% 9.17/5.37 != ( times_3573771949741848930nteger @ C @ B2 ) ) ) ) ) ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3564_is__unitE,axiom,
% 9.17/5.37 ! [A: code_natural,C: code_natural] :
% 9.17/5.37 ( ( dvd_dvd_Code_natural @ A @ one_one_Code_natural )
% 9.17/5.37 => ~ ( ( A != zero_z2226904508553997617atural )
% 9.17/5.37 => ! [B2: code_natural] :
% 9.17/5.37 ( ( B2 != zero_z2226904508553997617atural )
% 9.17/5.37 => ( ( dvd_dvd_Code_natural @ B2 @ one_one_Code_natural )
% 9.17/5.37 => ( ( ( divide5121882707175180666atural @ one_one_Code_natural @ A )
% 9.17/5.37 = B2 )
% 9.17/5.37 => ( ( ( divide5121882707175180666atural @ one_one_Code_natural @ B2 )
% 9.17/5.37 = A )
% 9.17/5.37 => ( ( ( times_2397367101498566445atural @ A @ B2 )
% 9.17/5.37 = one_one_Code_natural )
% 9.17/5.37 => ( ( divide5121882707175180666atural @ C @ A )
% 9.17/5.37 != ( times_2397367101498566445atural @ C @ B2 ) ) ) ) ) ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3565_is__unit__div__mult__cancel__left,axiom,
% 9.17/5.37 ! [A: int,B: int] :
% 9.17/5.37 ( ( A != zero_zero_int )
% 9.17/5.37 => ( ( dvd_dvd_int @ B @ one_one_int )
% 9.17/5.37 => ( ( divide_divide_int @ A @ ( times_times_int @ A @ B ) )
% 9.17/5.37 = ( divide_divide_int @ one_one_int @ B ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3566_is__unit__div__mult__cancel__left,axiom,
% 9.17/5.37 ! [A: nat,B: nat] :
% 9.17/5.37 ( ( A != zero_zero_nat )
% 9.17/5.37 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 9.17/5.37 => ( ( divide_divide_nat @ A @ ( times_times_nat @ A @ B ) )
% 9.17/5.37 = ( divide_divide_nat @ one_one_nat @ B ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3567_is__unit__div__mult__cancel__left,axiom,
% 9.17/5.37 ! [A: code_integer,B: code_integer] :
% 9.17/5.37 ( ( A != zero_z3403309356797280102nteger )
% 9.17/5.37 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 9.17/5.37 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ A @ B ) )
% 9.17/5.37 = ( divide6298287555418463151nteger @ one_one_Code_integer @ B ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3568_is__unit__div__mult__cancel__left,axiom,
% 9.17/5.37 ! [A: code_natural,B: code_natural] :
% 9.17/5.37 ( ( A != zero_z2226904508553997617atural )
% 9.17/5.37 => ( ( dvd_dvd_Code_natural @ B @ one_one_Code_natural )
% 9.17/5.37 => ( ( divide5121882707175180666atural @ A @ ( times_2397367101498566445atural @ A @ B ) )
% 9.17/5.37 = ( divide5121882707175180666atural @ one_one_Code_natural @ B ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3569_is__unit__div__mult__cancel__right,axiom,
% 9.17/5.37 ! [A: int,B: int] :
% 9.17/5.37 ( ( A != zero_zero_int )
% 9.17/5.37 => ( ( dvd_dvd_int @ B @ one_one_int )
% 9.17/5.37 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ A ) )
% 9.17/5.37 = ( divide_divide_int @ one_one_int @ B ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3570_is__unit__div__mult__cancel__right,axiom,
% 9.17/5.37 ! [A: nat,B: nat] :
% 9.17/5.37 ( ( A != zero_zero_nat )
% 9.17/5.37 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 9.17/5.37 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ A ) )
% 9.17/5.37 = ( divide_divide_nat @ one_one_nat @ B ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3571_is__unit__div__mult__cancel__right,axiom,
% 9.17/5.37 ! [A: code_integer,B: code_integer] :
% 9.17/5.37 ( ( A != zero_z3403309356797280102nteger )
% 9.17/5.37 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 9.17/5.37 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ A ) )
% 9.17/5.37 = ( divide6298287555418463151nteger @ one_one_Code_integer @ B ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3572_is__unit__div__mult__cancel__right,axiom,
% 9.17/5.37 ! [A: code_natural,B: code_natural] :
% 9.17/5.37 ( ( A != zero_z2226904508553997617atural )
% 9.17/5.37 => ( ( dvd_dvd_Code_natural @ B @ one_one_Code_natural )
% 9.17/5.37 => ( ( divide5121882707175180666atural @ A @ ( times_2397367101498566445atural @ B @ A ) )
% 9.17/5.37 = ( divide5121882707175180666atural @ one_one_Code_natural @ B ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3573_odd__even__add,axiom,
% 9.17/5.37 ! [A: nat,B: nat] :
% 9.17/5.37 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 9.17/5.37 => ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 9.17/5.37 => ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3574_odd__even__add,axiom,
% 9.17/5.37 ! [A: int,B: int] :
% 9.17/5.37 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 9.17/5.37 => ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B )
% 9.17/5.37 => ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3575_odd__even__add,axiom,
% 9.17/5.37 ! [A: code_integer,B: code_integer] :
% 9.17/5.37 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 9.17/5.37 => ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B )
% 9.17/5.37 => ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3576_odd__even__add,axiom,
% 9.17/5.37 ! [A: code_natural,B: code_natural] :
% 9.17/5.37 ( ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 9.17/5.37 => ( ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ B )
% 9.17/5.37 => ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( plus_p4538020629002901425atural @ A @ B ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3577_odd__one,axiom,
% 9.17/5.37 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ one_one_nat ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3578_odd__one,axiom,
% 9.17/5.37 ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ one_one_int ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3579_odd__one,axiom,
% 9.17/5.37 ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ one_one_Code_integer ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3580_odd__one,axiom,
% 9.17/5.37 ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ one_one_Code_natural ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3581_dvd__power__iff,axiom,
% 9.17/5.37 ! [X: code_integer,M2: nat,N2: nat] :
% 9.17/5.37 ( ( X != zero_z3403309356797280102nteger )
% 9.17/5.37 => ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ X @ M2 ) @ ( power_8256067586552552935nteger @ X @ N2 ) )
% 9.17/5.37 = ( ( dvd_dvd_Code_integer @ X @ one_one_Code_integer )
% 9.17/5.37 | ( ord_less_eq_nat @ M2 @ N2 ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3582_dvd__power__iff,axiom,
% 9.17/5.37 ! [X: nat,M2: nat,N2: nat] :
% 9.17/5.37 ( ( X != zero_zero_nat )
% 9.17/5.37 => ( ( dvd_dvd_nat @ ( power_power_nat @ X @ M2 ) @ ( power_power_nat @ X @ N2 ) )
% 9.17/5.37 = ( ( dvd_dvd_nat @ X @ one_one_nat )
% 9.17/5.37 | ( ord_less_eq_nat @ M2 @ N2 ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3583_dvd__power__iff,axiom,
% 9.17/5.37 ! [X: int,M2: nat,N2: nat] :
% 9.17/5.37 ( ( X != zero_zero_int )
% 9.17/5.37 => ( ( dvd_dvd_int @ ( power_power_int @ X @ M2 ) @ ( power_power_int @ X @ N2 ) )
% 9.17/5.37 = ( ( dvd_dvd_int @ X @ one_one_int )
% 9.17/5.37 | ( ord_less_eq_nat @ M2 @ N2 ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3584_dvd__power,axiom,
% 9.17/5.37 ! [N2: nat,X: code_integer] :
% 9.17/5.37 ( ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 9.17/5.37 | ( X = one_one_Code_integer ) )
% 9.17/5.37 => ( dvd_dvd_Code_integer @ X @ ( power_8256067586552552935nteger @ X @ N2 ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3585_dvd__power,axiom,
% 9.17/5.37 ! [N2: nat,X: rat] :
% 9.17/5.37 ( ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 9.17/5.37 | ( X = one_one_rat ) )
% 9.17/5.37 => ( dvd_dvd_rat @ X @ ( power_power_rat @ X @ N2 ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3586_dvd__power,axiom,
% 9.17/5.37 ! [N2: nat,X: nat] :
% 9.17/5.37 ( ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 9.17/5.37 | ( X = one_one_nat ) )
% 9.17/5.37 => ( dvd_dvd_nat @ X @ ( power_power_nat @ X @ N2 ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3587_dvd__power,axiom,
% 9.17/5.37 ! [N2: nat,X: int] :
% 9.17/5.37 ( ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 9.17/5.37 | ( X = one_one_int ) )
% 9.17/5.37 => ( dvd_dvd_int @ X @ ( power_power_int @ X @ N2 ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3588_Suc3__eq__add__3,axiom,
% 9.17/5.37 ! [N2: nat] :
% 9.17/5.37 ( ( suc @ ( suc @ ( suc @ N2 ) ) )
% 9.17/5.37 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N2 ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3589_dvd__mult__cancel2,axiom,
% 9.17/5.37 ! [M2: nat,N2: nat] :
% 9.17/5.37 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 9.17/5.37 => ( ( dvd_dvd_nat @ ( times_times_nat @ N2 @ M2 ) @ M2 )
% 9.17/5.37 = ( N2 = one_one_nat ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3590_dvd__mult__cancel1,axiom,
% 9.17/5.37 ! [M2: nat,N2: nat] :
% 9.17/5.37 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 9.17/5.37 => ( ( dvd_dvd_nat @ ( times_times_nat @ M2 @ N2 ) @ M2 )
% 9.17/5.37 = ( N2 = one_one_nat ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3591_dvd__minus__add,axiom,
% 9.17/5.37 ! [Q3: nat,N2: nat,R2: nat,M2: nat] :
% 9.17/5.37 ( ( ord_less_eq_nat @ Q3 @ N2 )
% 9.17/5.37 => ( ( ord_less_eq_nat @ Q3 @ ( times_times_nat @ R2 @ M2 ) )
% 9.17/5.37 => ( ( dvd_dvd_nat @ M2 @ ( minus_minus_nat @ N2 @ Q3 ) )
% 9.17/5.37 = ( dvd_dvd_nat @ M2 @ ( plus_plus_nat @ N2 @ ( minus_minus_nat @ ( times_times_nat @ R2 @ M2 ) @ Q3 ) ) ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3592_power__dvd__imp__le,axiom,
% 9.17/5.37 ! [I: nat,M2: nat,N2: nat] :
% 9.17/5.37 ( ( dvd_dvd_nat @ ( power_power_nat @ I @ M2 ) @ ( power_power_nat @ I @ N2 ) )
% 9.17/5.37 => ( ( ord_less_nat @ one_one_nat @ I )
% 9.17/5.37 => ( ord_less_eq_nat @ M2 @ N2 ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3593_aset_I10_J,axiom,
% 9.17/5.37 ! [D2: int,D3: int,A2: set_int,T: int] :
% 9.17/5.37 ( ( dvd_dvd_int @ D2 @ D3 )
% 9.17/5.37 => ! [X8: int] :
% 9.17/5.37 ( ! [Xa3: int] :
% 9.17/5.37 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 9.17/5.37 => ! [Xb3: int] :
% 9.17/5.37 ( ( member_int @ Xb3 @ A2 )
% 9.17/5.37 => ( X8
% 9.17/5.37 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 9.17/5.37 => ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X8 @ T ) )
% 9.17/5.37 => ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ ( plus_plus_int @ X8 @ D3 ) @ T ) ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3594_aset_I9_J,axiom,
% 9.17/5.37 ! [D2: int,D3: int,A2: set_int,T: int] :
% 9.17/5.37 ( ( dvd_dvd_int @ D2 @ D3 )
% 9.17/5.37 => ! [X8: int] :
% 9.17/5.37 ( ! [Xa3: int] :
% 9.17/5.37 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 9.17/5.37 => ! [Xb3: int] :
% 9.17/5.37 ( ( member_int @ Xb3 @ A2 )
% 9.17/5.37 => ( X8
% 9.17/5.37 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 9.17/5.37 => ( ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X8 @ T ) )
% 9.17/5.37 => ( dvd_dvd_int @ D2 @ ( plus_plus_int @ ( plus_plus_int @ X8 @ D3 ) @ T ) ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3595_bset_I10_J,axiom,
% 9.17/5.37 ! [D2: int,D3: int,B5: set_int,T: int] :
% 9.17/5.37 ( ( dvd_dvd_int @ D2 @ D3 )
% 9.17/5.37 => ! [X8: int] :
% 9.17/5.37 ( ! [Xa3: int] :
% 9.17/5.37 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 9.17/5.37 => ! [Xb3: int] :
% 9.17/5.37 ( ( member_int @ Xb3 @ B5 )
% 9.17/5.37 => ( X8
% 9.17/5.37 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 9.17/5.37 => ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X8 @ T ) )
% 9.17/5.37 => ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ ( minus_minus_int @ X8 @ D3 ) @ T ) ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3596_bset_I9_J,axiom,
% 9.17/5.37 ! [D2: int,D3: int,B5: set_int,T: int] :
% 9.17/5.37 ( ( dvd_dvd_int @ D2 @ D3 )
% 9.17/5.37 => ! [X8: int] :
% 9.17/5.37 ( ! [Xa3: int] :
% 9.17/5.37 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 9.17/5.37 => ! [Xb3: int] :
% 9.17/5.37 ( ( member_int @ Xb3 @ B5 )
% 9.17/5.37 => ( X8
% 9.17/5.37 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 9.17/5.37 => ( ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X8 @ T ) )
% 9.17/5.37 => ( dvd_dvd_int @ D2 @ ( plus_plus_int @ ( minus_minus_int @ X8 @ D3 ) @ T ) ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3597_num_Osize__gen_I3_J,axiom,
% 9.17/5.37 ! [X32: num] :
% 9.17/5.37 ( ( size_num @ ( bit1 @ X32 ) )
% 9.17/5.37 = ( plus_plus_nat @ ( size_num @ X32 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3598_num_Osize_I6_J,axiom,
% 9.17/5.37 ! [X32: num] :
% 9.17/5.37 ( ( size_size_num @ ( bit1 @ X32 ) )
% 9.17/5.37 = ( plus_plus_nat @ ( size_size_num @ X32 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3599_odd__iff__mod__2__eq__one,axiom,
% 9.17/5.37 ! [A: int] :
% 9.17/5.37 ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 9.17/5.37 = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.17/5.37 = one_one_int ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3600_odd__iff__mod__2__eq__one,axiom,
% 9.17/5.37 ! [A: nat] :
% 9.17/5.37 ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 9.17/5.37 = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.17/5.37 = one_one_nat ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3601_odd__iff__mod__2__eq__one,axiom,
% 9.17/5.37 ! [A: code_integer] :
% 9.17/5.37 ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 9.17/5.37 = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 9.17/5.37 = one_one_Code_integer ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3602_odd__iff__mod__2__eq__one,axiom,
% 9.17/5.37 ! [A: code_natural] :
% 9.17/5.37 ( ( ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A ) )
% 9.17/5.37 = ( ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 9.17/5.37 = one_one_Code_natural ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3603_Suc__mod__eq__add3__mod,axiom,
% 9.17/5.37 ! [M2: nat,N2: nat] :
% 9.17/5.37 ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( suc @ M2 ) ) ) @ N2 )
% 9.17/5.37 = ( modulo_modulo_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M2 ) @ N2 ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3604_Suc__div__eq__add3__div,axiom,
% 9.17/5.37 ! [M2: nat,N2: nat] :
% 9.17/5.37 ( ( divide_divide_nat @ ( suc @ ( suc @ ( suc @ M2 ) ) ) @ N2 )
% 9.17/5.37 = ( divide_divide_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M2 ) @ N2 ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3605_even__diff__iff,axiom,
% 9.17/5.37 ! [K: int,L: int] :
% 9.17/5.37 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ K @ L ) )
% 9.17/5.37 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ L ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3606_even__abs__add__iff,axiom,
% 9.17/5.37 ! [K: int,L: int] :
% 9.17/5.37 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ ( abs_abs_int @ K ) @ L ) )
% 9.17/5.37 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ L ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3607_even__add__abs__iff,axiom,
% 9.17/5.37 ! [K: int,L: int] :
% 9.17/5.37 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ ( abs_abs_int @ L ) ) )
% 9.17/5.37 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ L ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3608_signed__take__bit__eq__take__bit__shift,axiom,
% 9.17/5.37 ( bit_ri631733984087533419it_int
% 9.17/5.37 = ( ^ [N4: nat,K4: int] : ( minus_minus_int @ ( bit_se2923211474154528505it_int @ ( suc @ N4 ) @ ( plus_plus_int @ K4 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N4 ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N4 ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3609_take__bit__incr__eq,axiom,
% 9.17/5.37 ! [N2: nat,K: int] :
% 9.17/5.37 ( ( ( bit_se2923211474154528505it_int @ N2 @ K )
% 9.17/5.37 != ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ one_one_int ) )
% 9.17/5.37 => ( ( bit_se2923211474154528505it_int @ N2 @ ( plus_plus_int @ K @ one_one_int ) )
% 9.17/5.37 = ( plus_plus_int @ one_one_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3610_oddE,axiom,
% 9.17/5.37 ! [A: nat] :
% 9.17/5.37 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 9.17/5.37 => ~ ! [B2: nat] :
% 9.17/5.37 ( A
% 9.17/5.37 != ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 ) @ one_one_nat ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3611_oddE,axiom,
% 9.17/5.37 ! [A: int] :
% 9.17/5.37 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 9.17/5.37 => ~ ! [B2: int] :
% 9.17/5.37 ( A
% 9.17/5.37 != ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B2 ) @ one_one_int ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3612_oddE,axiom,
% 9.17/5.37 ! [A: code_integer] :
% 9.17/5.37 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 9.17/5.37 => ~ ! [B2: code_integer] :
% 9.17/5.37 ( A
% 9.17/5.37 != ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B2 ) @ one_one_Code_integer ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3613_oddE,axiom,
% 9.17/5.37 ! [A: code_natural] :
% 9.17/5.37 ( ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 9.17/5.37 => ~ ! [B2: code_natural] :
% 9.17/5.37 ( A
% 9.17/5.37 != ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ B2 ) @ one_one_Code_natural ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3614_parity__cases,axiom,
% 9.17/5.37 ! [A: int] :
% 9.17/5.37 ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 9.17/5.37 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.17/5.37 != zero_zero_int ) )
% 9.17/5.37 => ~ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 9.17/5.37 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.17/5.37 != one_one_int ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3615_parity__cases,axiom,
% 9.17/5.37 ! [A: nat] :
% 9.17/5.37 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 9.17/5.37 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.17/5.37 != zero_zero_nat ) )
% 9.17/5.37 => ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 9.17/5.37 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.17/5.37 != one_one_nat ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3616_parity__cases,axiom,
% 9.17/5.37 ! [A: code_integer] :
% 9.17/5.37 ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 9.17/5.37 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 9.17/5.37 != zero_z3403309356797280102nteger ) )
% 9.17/5.37 => ~ ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 9.17/5.37 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 9.17/5.37 != one_one_Code_integer ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3617_parity__cases,axiom,
% 9.17/5.37 ! [A: code_natural] :
% 9.17/5.37 ( ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 9.17/5.37 => ( ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 9.17/5.37 != zero_z2226904508553997617atural ) )
% 9.17/5.37 => ~ ( ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 9.17/5.37 => ( ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 9.17/5.37 != one_one_Code_natural ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3618_mod2__eq__if,axiom,
% 9.17/5.37 ! [A: int] :
% 9.17/5.37 ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 9.17/5.37 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.17/5.37 = zero_zero_int ) )
% 9.17/5.37 & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 9.17/5.37 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.17/5.37 = one_one_int ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3619_mod2__eq__if,axiom,
% 9.17/5.37 ! [A: nat] :
% 9.17/5.37 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 9.17/5.37 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.17/5.37 = zero_zero_nat ) )
% 9.17/5.37 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 9.17/5.37 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.17/5.37 = one_one_nat ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3620_mod2__eq__if,axiom,
% 9.17/5.37 ! [A: code_integer] :
% 9.17/5.37 ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 9.17/5.37 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 9.17/5.37 = zero_z3403309356797280102nteger ) )
% 9.17/5.37 & ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 9.17/5.37 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 9.17/5.37 = one_one_Code_integer ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3621_mod2__eq__if,axiom,
% 9.17/5.37 ! [A: code_natural] :
% 9.17/5.37 ( ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 9.17/5.37 => ( ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 9.17/5.37 = zero_z2226904508553997617atural ) )
% 9.17/5.37 & ( ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 9.17/5.37 => ( ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 9.17/5.37 = one_one_Code_natural ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3622_minus__one__power__iff,axiom,
% 9.17/5.37 ! [N2: nat] :
% 9.17/5.37 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 9.17/5.37 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 )
% 9.17/5.37 = one_one_int ) )
% 9.17/5.37 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 9.17/5.37 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 )
% 9.17/5.37 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3623_minus__one__power__iff,axiom,
% 9.17/5.37 ! [N2: nat] :
% 9.17/5.37 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 9.17/5.37 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 )
% 9.17/5.37 = one_one_Code_integer ) )
% 9.17/5.37 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 9.17/5.37 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 )
% 9.17/5.37 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3624_minus__one__power__iff,axiom,
% 9.17/5.37 ! [N2: nat] :
% 9.17/5.37 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 9.17/5.37 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 )
% 9.17/5.37 = one_one_rat ) )
% 9.17/5.37 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 9.17/5.37 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 )
% 9.17/5.37 = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3625_take__bit__int__greater__eq,axiom,
% 9.17/5.37 ! [K: int,N2: nat] :
% 9.17/5.37 ( ( ord_less_int @ K @ zero_zero_int )
% 9.17/5.37 => ( ord_less_eq_int @ ( plus_plus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) @ ( bit_se2923211474154528505it_int @ N2 @ K ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3626_take__bit__Suc__minus__1__eq,axiom,
% 9.17/5.37 ! [N2: nat] :
% 9.17/5.37 ( ( bit_se1745604003318907178nteger @ ( suc @ N2 ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.17/5.37 = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) @ one_one_Code_integer ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3627_take__bit__Suc__minus__1__eq,axiom,
% 9.17/5.37 ! [N2: nat] :
% 9.17/5.37 ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ ( uminus_uminus_int @ one_one_int ) )
% 9.17/5.37 = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) @ one_one_int ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3628_take__bit__Suc,axiom,
% 9.17/5.37 ! [N2: nat,A: code_integer] :
% 9.17/5.37 ( ( bit_se1745604003318907178nteger @ ( suc @ N2 ) @ A )
% 9.17/5.37 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( bit_se1745604003318907178nteger @ N2 @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3629_take__bit__Suc,axiom,
% 9.17/5.37 ! [N2: nat,A: int] :
% 9.17/5.37 ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ A )
% 9.17/5.37 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N2 @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3630_take__bit__Suc,axiom,
% 9.17/5.37 ! [N2: nat,A: nat] :
% 9.17/5.37 ( ( bit_se2925701944663578781it_nat @ ( suc @ N2 ) @ A )
% 9.17/5.37 = ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ N2 @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3631_take__bit__Suc,axiom,
% 9.17/5.37 ! [N2: nat,A: code_natural] :
% 9.17/5.37 ( ( bit_se569199155075624693atural @ ( suc @ N2 ) @ A )
% 9.17/5.37 = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( bit_se569199155075624693atural @ N2 @ ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) @ ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3632_take__bit__numeral__minus__1__eq,axiom,
% 9.17/5.37 ! [K: num] :
% 9.17/5.37 ( ( bit_se1745604003318907178nteger @ ( numeral_numeral_nat @ K ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.17/5.37 = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ K ) ) @ one_one_Code_integer ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3633_take__bit__numeral__minus__1__eq,axiom,
% 9.17/5.37 ! [K: num] :
% 9.17/5.37 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ K ) @ ( uminus_uminus_int @ one_one_int ) )
% 9.17/5.37 = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ K ) ) @ one_one_int ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3634_even__mask__div__iff_H,axiom,
% 9.17/5.37 ! [M2: nat,N2: nat] :
% 9.17/5.37 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 ) @ one_one_int ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) )
% 9.17/5.37 = ( ord_less_eq_nat @ M2 @ N2 ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3635_even__mask__div__iff_H,axiom,
% 9.17/5.37 ! [M2: nat,N2: nat] :
% 9.17/5.37 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ one_one_nat ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 9.17/5.37 = ( ord_less_eq_nat @ M2 @ N2 ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3636_even__mask__div__iff_H,axiom,
% 9.17/5.37 ! [M2: nat,N2: nat] :
% 9.17/5.37 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M2 ) @ one_one_Code_integer ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) )
% 9.17/5.37 = ( ord_less_eq_nat @ M2 @ N2 ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3637_even__mask__div__iff_H,axiom,
% 9.17/5.37 ! [M2: nat,N2: nat] :
% 9.17/5.37 ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( divide5121882707175180666atural @ ( minus_7197305767214868737atural @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ M2 ) @ one_one_Code_natural ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N2 ) ) )
% 9.17/5.37 = ( ord_less_eq_nat @ M2 @ N2 ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3638_even__mask__div__iff,axiom,
% 9.17/5.37 ! [M2: nat,N2: nat] :
% 9.17/5.37 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 ) @ one_one_int ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) )
% 9.17/5.37 = ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 )
% 9.17/5.37 = zero_zero_int )
% 9.17/5.37 | ( ord_less_eq_nat @ M2 @ N2 ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3639_even__mask__div__iff,axiom,
% 9.17/5.37 ! [M2: nat,N2: nat] :
% 9.17/5.37 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ one_one_nat ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 9.17/5.37 = ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 9.17/5.37 = zero_zero_nat )
% 9.17/5.37 | ( ord_less_eq_nat @ M2 @ N2 ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3640_even__mask__div__iff,axiom,
% 9.17/5.37 ! [M2: nat,N2: nat] :
% 9.17/5.37 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M2 ) @ one_one_Code_integer ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) )
% 9.17/5.37 = ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 )
% 9.17/5.37 = zero_z3403309356797280102nteger )
% 9.17/5.37 | ( ord_less_eq_nat @ M2 @ N2 ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3641_even__mask__div__iff,axiom,
% 9.17/5.37 ! [M2: nat,N2: nat] :
% 9.17/5.37 ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( divide5121882707175180666atural @ ( minus_7197305767214868737atural @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ M2 ) @ one_one_Code_natural ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N2 ) ) )
% 9.17/5.37 = ( ( ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N2 )
% 9.17/5.37 = zero_z2226904508553997617atural )
% 9.17/5.37 | ( ord_less_eq_nat @ M2 @ N2 ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3642_Code__Numeral_Onegative__def,axiom,
% 9.17/5.37 ( code_negative
% 9.17/5.37 = ( comp_C3531382070062128313er_num @ uminus1351360451143612070nteger @ numera6620942414471956472nteger ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3643_take__bit__numeral__minus__numeral__int,axiom,
% 9.17/5.37 ! [M2: num,N2: num] :
% 9.17/5.37 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ M2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 9.17/5.37 = ( case_option_int_num @ zero_zero_int
% 9.17/5.37 @ ^ [Q5: num] : ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ M2 ) @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ M2 ) ) @ ( numeral_numeral_int @ Q5 ) ) )
% 9.17/5.37 @ ( bit_take_bit_num @ ( numeral_numeral_nat @ M2 ) @ N2 ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3644_signed__take__bit__numeral__minus__bit1,axiom,
% 9.17/5.37 ! [L: num,K: num] :
% 9.17/5.37 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 9.17/5.37 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L ) @ ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3645_execute__change,axiom,
% 9.17/5.37 ! [F: array_a > array_a,R2: ref_array_a,H3: heap_e7401611519738050253t_unit] :
% 9.17/5.37 ( ( heap_T5591663578999710211rray_a @ ( ref_change_array_a @ F @ R2 ) @ H3 )
% 9.17/5.37 = ( some_P6105628898608307625it_nat @ ( produc1733996804261680252it_nat @ ( F @ ( ref_get_array_a @ H3 @ R2 ) ) @ ( produc584006145561248582it_nat @ ( ref_set_array_a @ R2 @ ( F @ ( ref_get_array_a @ H3 @ R2 ) ) @ H3 ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3646_execute__change,axiom,
% 9.17/5.37 ! [F: product_unit > product_unit,R2: ref_Product_unit,H3: heap_e7401611519738050253t_unit] :
% 9.17/5.37 ( ( heap_T875086893843062177t_unit @ ( ref_ch7259622376331601608t_unit @ F @ R2 ) @ H3 )
% 9.17/5.37 = ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ ( F @ ( ref_get_Product_unit @ H3 @ R2 ) ) @ ( produc584006145561248582it_nat @ ( ref_set_Product_unit @ R2 @ ( F @ ( ref_get_Product_unit @ H3 @ R2 ) ) @ H3 ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3647_signed__take__bit__numeral__bit1,axiom,
% 9.17/5.37 ! [L: num,K: num] :
% 9.17/5.37 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 9.17/5.37 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3648_take__bit__Suc__minus__bit1,axiom,
% 9.17/5.37 ! [N2: nat,K: num] :
% 9.17/5.37 ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 9.17/5.37 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3649_divmod__BitM__2__eq,axiom,
% 9.17/5.37 ! [M2: num] :
% 9.17/5.37 ( ( unique5052692396658037445od_int @ ( bitM @ M2 ) @ ( bit0 @ one ) )
% 9.17/5.37 = ( product_Pair_int_int @ ( minus_minus_int @ ( numeral_numeral_int @ M2 ) @ one_one_int ) @ one_one_int ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3650_flip__bit__0,axiom,
% 9.17/5.37 ! [A: code_integer] :
% 9.17/5.37 ( ( bit_se1345352211410354436nteger @ zero_zero_nat @ A )
% 9.17/5.37 = ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3651_flip__bit__0,axiom,
% 9.17/5.37 ! [A: int] :
% 9.17/5.37 ( ( bit_se2159334234014336723it_int @ zero_zero_nat @ A )
% 9.17/5.37 = ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3652_flip__bit__0,axiom,
% 9.17/5.37 ! [A: nat] :
% 9.17/5.37 ( ( bit_se2161824704523386999it_nat @ zero_zero_nat @ A )
% 9.17/5.37 = ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3653_flip__bit__0,axiom,
% 9.17/5.37 ! [A: code_natural] :
% 9.17/5.37 ( ( bit_se168947363167071951atural @ zero_zero_nat @ A )
% 9.17/5.37 = ( plus_p4538020629002901425atural @ ( zero_n8403883297036319079atural @ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A ) ) @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3654_of__bool__eq_I2_J,axiom,
% 9.17/5.37 ( ( zero_n2052037380579107095ol_rat @ $true )
% 9.17/5.37 = one_one_rat ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3655_of__bool__eq_I2_J,axiom,
% 9.17/5.37 ( ( zero_n2687167440665602831ol_nat @ $true )
% 9.17/5.37 = one_one_nat ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3656_of__bool__eq_I2_J,axiom,
% 9.17/5.37 ( ( zero_n2684676970156552555ol_int @ $true )
% 9.17/5.37 = one_one_int ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3657_of__bool__eq_I2_J,axiom,
% 9.17/5.37 ( ( zero_n356916108424825756nteger @ $true )
% 9.17/5.37 = one_one_Code_integer ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3658_of__bool__eq__1__iff,axiom,
% 9.17/5.37 ! [P: $o] :
% 9.17/5.37 ( ( ( zero_n2052037380579107095ol_rat @ P )
% 9.17/5.37 = one_one_rat )
% 9.17/5.37 = P ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3659_of__bool__eq__1__iff,axiom,
% 9.17/5.37 ! [P: $o] :
% 9.17/5.37 ( ( ( zero_n2687167440665602831ol_nat @ P )
% 9.17/5.37 = one_one_nat )
% 9.17/5.37 = P ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3660_of__bool__eq__1__iff,axiom,
% 9.17/5.37 ! [P: $o] :
% 9.17/5.37 ( ( ( zero_n2684676970156552555ol_int @ P )
% 9.17/5.37 = one_one_int )
% 9.17/5.37 = P ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3661_of__bool__eq__1__iff,axiom,
% 9.17/5.37 ! [P: $o] :
% 9.17/5.37 ( ( ( zero_n356916108424825756nteger @ P )
% 9.17/5.37 = one_one_Code_integer )
% 9.17/5.37 = P ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3662_of__bool__less__one__iff,axiom,
% 9.17/5.37 ! [P: $o] :
% 9.17/5.37 ( ( ord_less_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ one_one_rat )
% 9.17/5.37 = ~ P ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3663_of__bool__less__one__iff,axiom,
% 9.17/5.37 ! [P: $o] :
% 9.17/5.37 ( ( ord_less_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ one_one_nat )
% 9.17/5.37 = ~ P ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3664_of__bool__less__one__iff,axiom,
% 9.17/5.37 ! [P: $o] :
% 9.17/5.37 ( ( ord_less_int @ ( zero_n2684676970156552555ol_int @ P ) @ one_one_int )
% 9.17/5.37 = ~ P ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3665_of__bool__less__one__iff,axiom,
% 9.17/5.37 ! [P: $o] :
% 9.17/5.37 ( ( ord_le6747313008572928689nteger @ ( zero_n356916108424825756nteger @ P ) @ one_one_Code_integer )
% 9.17/5.37 = ~ P ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3666_of__bool__not__iff,axiom,
% 9.17/5.37 ! [P: $o] :
% 9.17/5.37 ( ( zero_n2052037380579107095ol_rat @ ~ P )
% 9.17/5.37 = ( minus_minus_rat @ one_one_rat @ ( zero_n2052037380579107095ol_rat @ P ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3667_of__bool__not__iff,axiom,
% 9.17/5.37 ! [P: $o] :
% 9.17/5.37 ( ( zero_n2684676970156552555ol_int @ ~ P )
% 9.17/5.37 = ( minus_minus_int @ one_one_int @ ( zero_n2684676970156552555ol_int @ P ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3668_of__bool__not__iff,axiom,
% 9.17/5.37 ! [P: $o] :
% 9.17/5.37 ( ( zero_n356916108424825756nteger @ ~ P )
% 9.17/5.37 = ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( zero_n356916108424825756nteger @ P ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3669_take__bit__num__simps_I3_J,axiom,
% 9.17/5.37 ! [N2: nat,M2: num] :
% 9.17/5.37 ( ( bit_take_bit_num @ ( suc @ N2 ) @ ( bit0 @ M2 ) )
% 9.17/5.37 = ( case_o6005452278849405969um_num @ none_num
% 9.17/5.37 @ ^ [Q5: num] : ( some_num @ ( bit0 @ Q5 ) )
% 9.17/5.37 @ ( bit_take_bit_num @ N2 @ M2 ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3670_take__bit__num__simps_I4_J,axiom,
% 9.17/5.37 ! [N2: nat,M2: num] :
% 9.17/5.37 ( ( bit_take_bit_num @ ( suc @ N2 ) @ ( bit1 @ M2 ) )
% 9.17/5.37 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ N2 @ M2 ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3671_take__bit__num__simps_I6_J,axiom,
% 9.17/5.37 ! [R2: num,M2: num] :
% 9.17/5.37 ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R2 ) @ ( bit0 @ M2 ) )
% 9.17/5.37 = ( case_o6005452278849405969um_num @ none_num
% 9.17/5.37 @ ^ [Q5: num] : ( some_num @ ( bit0 @ Q5 ) )
% 9.17/5.37 @ ( bit_take_bit_num @ ( pred_numeral @ R2 ) @ M2 ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3672_take__bit__of__1,axiom,
% 9.17/5.37 ! [N2: nat] :
% 9.17/5.37 ( ( bit_se1745604003318907178nteger @ N2 @ one_one_Code_integer )
% 9.17/5.37 = ( zero_n356916108424825756nteger @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3673_take__bit__of__1,axiom,
% 9.17/5.37 ! [N2: nat] :
% 9.17/5.37 ( ( bit_se2923211474154528505it_int @ N2 @ one_one_int )
% 9.17/5.37 = ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3674_take__bit__of__1,axiom,
% 9.17/5.37 ! [N2: nat] :
% 9.17/5.37 ( ( bit_se2925701944663578781it_nat @ N2 @ one_one_nat )
% 9.17/5.37 = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3675_take__bit__of__1,axiom,
% 9.17/5.37 ! [N2: nat] :
% 9.17/5.37 ( ( bit_se569199155075624693atural @ N2 @ one_one_Code_natural )
% 9.17/5.37 = ( zero_n8403883297036319079atural @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3676_add__neg__numeral__special_I6_J,axiom,
% 9.17/5.37 ! [M2: num] :
% 9.17/5.37 ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( uminus_uminus_int @ one_one_int ) )
% 9.17/5.37 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ M2 ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3677_add__neg__numeral__special_I6_J,axiom,
% 9.17/5.37 ! [M2: num] :
% 9.17/5.37 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.17/5.37 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ M2 ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3678_add__neg__numeral__special_I6_J,axiom,
% 9.17/5.37 ! [M2: num] :
% 9.17/5.37 ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 9.17/5.37 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( inc @ M2 ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3679_add__neg__numeral__special_I5_J,axiom,
% 9.17/5.37 ! [N2: num] :
% 9.17/5.37 ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 9.17/5.37 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ N2 ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3680_add__neg__numeral__special_I5_J,axiom,
% 9.17/5.37 ! [N2: num] :
% 9.17/5.37 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 9.17/5.37 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ N2 ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3681_add__neg__numeral__special_I5_J,axiom,
% 9.17/5.37 ! [N2: num] :
% 9.17/5.37 ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 9.17/5.37 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( inc @ N2 ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3682_diff__numeral__special_I5_J,axiom,
% 9.17/5.37 ! [N2: num] :
% 9.17/5.37 ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N2 ) )
% 9.17/5.37 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ N2 ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3683_diff__numeral__special_I5_J,axiom,
% 9.17/5.37 ! [N2: num] :
% 9.17/5.37 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ N2 ) )
% 9.17/5.37 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ N2 ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3684_diff__numeral__special_I5_J,axiom,
% 9.17/5.37 ! [N2: num] :
% 9.17/5.37 ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ N2 ) )
% 9.17/5.37 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( inc @ N2 ) ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3685_diff__numeral__special_I6_J,axiom,
% 9.17/5.37 ! [M2: num] :
% 9.17/5.37 ( ( minus_minus_int @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ one_one_int ) )
% 9.17/5.37 = ( numeral_numeral_int @ ( inc @ M2 ) ) ) ).
% 9.17/5.37
% 9.17/5.37 thf(fact_3686_diff__numeral__special_I6_J,axiom,
% 9.17/5.37 ! [M2: num] :
% 9.17/5.37 ( ( minus_8373710615458151222nteger @ ( numera6620942414471956472nteger @ M2 ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.17/5.37 = ( numera6620942414471956472nteger @ ( inc @ M2 ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3687_diff__numeral__special_I6_J,axiom,
% 9.17/5.38 ! [M2: num] :
% 9.17/5.38 ( ( minus_minus_rat @ ( numeral_numeral_rat @ M2 ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 9.17/5.38 = ( numeral_numeral_rat @ ( inc @ M2 ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3688_take__bit__num__simps_I7_J,axiom,
% 9.17/5.38 ! [R2: num,M2: num] :
% 9.17/5.38 ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R2 ) @ ( bit1 @ M2 ) )
% 9.17/5.38 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ ( pred_numeral @ R2 ) @ M2 ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3689_take__bit__numeral__numeral,axiom,
% 9.17/5.38 ! [M2: num,N2: num] :
% 9.17/5.38 ( ( bit_se1745604003318907178nteger @ ( numeral_numeral_nat @ M2 ) @ ( numera6620942414471956472nteger @ N2 ) )
% 9.17/5.38 = ( case_o356765784539232260er_num @ zero_z3403309356797280102nteger @ numera6620942414471956472nteger @ ( bit_take_bit_num @ ( numeral_numeral_nat @ M2 ) @ N2 ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3690_take__bit__numeral__numeral,axiom,
% 9.17/5.38 ! [M2: num,N2: num] :
% 9.17/5.38 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_int @ N2 ) )
% 9.17/5.38 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_take_bit_num @ ( numeral_numeral_nat @ M2 ) @ N2 ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3691_take__bit__numeral__numeral,axiom,
% 9.17/5.38 ! [M2: num,N2: num] :
% 9.17/5.38 ( ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ N2 ) )
% 9.17/5.38 = ( case_option_nat_num @ zero_zero_nat @ numeral_numeral_nat @ ( bit_take_bit_num @ ( numeral_numeral_nat @ M2 ) @ N2 ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3692_take__bit__numeral__numeral,axiom,
% 9.17/5.38 ! [M2: num,N2: num] :
% 9.17/5.38 ( ( bit_se569199155075624693atural @ ( numeral_numeral_nat @ M2 ) @ ( numera5444537566228673987atural @ N2 ) )
% 9.17/5.38 = ( case_o5621594795226839503al_num @ zero_z2226904508553997617atural @ numera5444537566228673987atural @ ( bit_take_bit_num @ ( numeral_numeral_nat @ M2 ) @ N2 ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3693_bits__1__div__exp,axiom,
% 9.17/5.38 ! [N2: nat] :
% 9.17/5.38 ( ( divide5121882707175180666atural @ one_one_Code_natural @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N2 ) )
% 9.17/5.38 = ( zero_n8403883297036319079atural @ ( N2 = zero_zero_nat ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3694_bits__1__div__exp,axiom,
% 9.17/5.38 ! [N2: nat] :
% 9.17/5.38 ( ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 9.17/5.38 = ( zero_n2687167440665602831ol_nat @ ( N2 = zero_zero_nat ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3695_bits__1__div__exp,axiom,
% 9.17/5.38 ! [N2: nat] :
% 9.17/5.38 ( ( divide_divide_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 9.17/5.38 = ( zero_n2684676970156552555ol_int @ ( N2 = zero_zero_nat ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3696_bits__1__div__exp,axiom,
% 9.17/5.38 ! [N2: nat] :
% 9.17/5.38 ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 9.17/5.38 = ( zero_n356916108424825756nteger @ ( N2 = zero_zero_nat ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3697_one__div__2__pow__eq,axiom,
% 9.17/5.38 ! [N2: nat] :
% 9.17/5.38 ( ( divide5121882707175180666atural @ one_one_Code_natural @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N2 ) )
% 9.17/5.38 = ( zero_n8403883297036319079atural @ ( N2 = zero_zero_nat ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3698_one__div__2__pow__eq,axiom,
% 9.17/5.38 ! [N2: nat] :
% 9.17/5.38 ( ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 9.17/5.38 = ( zero_n2687167440665602831ol_nat @ ( N2 = zero_zero_nat ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3699_one__div__2__pow__eq,axiom,
% 9.17/5.38 ! [N2: nat] :
% 9.17/5.38 ( ( divide_divide_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 9.17/5.38 = ( zero_n2684676970156552555ol_int @ ( N2 = zero_zero_nat ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3700_one__div__2__pow__eq,axiom,
% 9.17/5.38 ! [N2: nat] :
% 9.17/5.38 ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 9.17/5.38 = ( zero_n356916108424825756nteger @ ( N2 = zero_zero_nat ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3701_one__mod__2__pow__eq,axiom,
% 9.17/5.38 ! [N2: nat] :
% 9.17/5.38 ( ( modulo8411746178871703098atural @ one_one_Code_natural @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N2 ) )
% 9.17/5.38 = ( zero_n8403883297036319079atural @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3702_one__mod__2__pow__eq,axiom,
% 9.17/5.38 ! [N2: nat] :
% 9.17/5.38 ( ( modulo_modulo_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 9.17/5.38 = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3703_one__mod__2__pow__eq,axiom,
% 9.17/5.38 ! [N2: nat] :
% 9.17/5.38 ( ( modulo_modulo_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 9.17/5.38 = ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3704_one__mod__2__pow__eq,axiom,
% 9.17/5.38 ! [N2: nat] :
% 9.17/5.38 ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 9.17/5.38 = ( zero_n356916108424825756nteger @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3705_mult__inc,axiom,
% 9.17/5.38 ! [X: num,Y: num] :
% 9.17/5.38 ( ( times_times_num @ X @ ( inc @ Y ) )
% 9.17/5.38 = ( plus_plus_num @ ( times_times_num @ X @ Y ) @ X ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3706_add__inc,axiom,
% 9.17/5.38 ! [X: num,Y: num] :
% 9.17/5.38 ( ( plus_plus_num @ X @ ( inc @ Y ) )
% 9.17/5.38 = ( inc @ ( plus_plus_num @ X @ Y ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3707_of__bool__less__eq__one,axiom,
% 9.17/5.38 ! [P: $o] : ( ord_less_eq_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ one_one_rat ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3708_of__bool__less__eq__one,axiom,
% 9.17/5.38 ! [P: $o] : ( ord_less_eq_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ one_one_nat ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3709_of__bool__less__eq__one,axiom,
% 9.17/5.38 ! [P: $o] : ( ord_less_eq_int @ ( zero_n2684676970156552555ol_int @ P ) @ one_one_int ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3710_of__bool__less__eq__one,axiom,
% 9.17/5.38 ! [P: $o] : ( ord_le3102999989581377725nteger @ ( zero_n356916108424825756nteger @ P ) @ one_one_Code_integer ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3711_of__bool__def,axiom,
% 9.17/5.38 ( zero_n2052037380579107095ol_rat
% 9.17/5.38 = ( ^ [P6: $o] : ( if_rat @ P6 @ one_one_rat @ zero_zero_rat ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3712_of__bool__def,axiom,
% 9.17/5.38 ( zero_n2687167440665602831ol_nat
% 9.17/5.38 = ( ^ [P6: $o] : ( if_nat @ P6 @ one_one_nat @ zero_zero_nat ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3713_of__bool__def,axiom,
% 9.17/5.38 ( zero_n2684676970156552555ol_int
% 9.17/5.38 = ( ^ [P6: $o] : ( if_int @ P6 @ one_one_int @ zero_zero_int ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3714_of__bool__def,axiom,
% 9.17/5.38 ( zero_n356916108424825756nteger
% 9.17/5.38 = ( ^ [P6: $o] : ( if_Code_integer @ P6 @ one_one_Code_integer @ zero_z3403309356797280102nteger ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3715_split__of__bool,axiom,
% 9.17/5.38 ! [P: rat > $o,P4: $o] :
% 9.17/5.38 ( ( P @ ( zero_n2052037380579107095ol_rat @ P4 ) )
% 9.17/5.38 = ( ( P4
% 9.17/5.38 => ( P @ one_one_rat ) )
% 9.17/5.38 & ( ~ P4
% 9.17/5.38 => ( P @ zero_zero_rat ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3716_split__of__bool,axiom,
% 9.17/5.38 ! [P: nat > $o,P4: $o] :
% 9.17/5.38 ( ( P @ ( zero_n2687167440665602831ol_nat @ P4 ) )
% 9.17/5.38 = ( ( P4
% 9.17/5.38 => ( P @ one_one_nat ) )
% 9.17/5.38 & ( ~ P4
% 9.17/5.38 => ( P @ zero_zero_nat ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3717_split__of__bool,axiom,
% 9.17/5.38 ! [P: int > $o,P4: $o] :
% 9.17/5.38 ( ( P @ ( zero_n2684676970156552555ol_int @ P4 ) )
% 9.17/5.38 = ( ( P4
% 9.17/5.38 => ( P @ one_one_int ) )
% 9.17/5.38 & ( ~ P4
% 9.17/5.38 => ( P @ zero_zero_int ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3718_split__of__bool,axiom,
% 9.17/5.38 ! [P: code_integer > $o,P4: $o] :
% 9.17/5.38 ( ( P @ ( zero_n356916108424825756nteger @ P4 ) )
% 9.17/5.38 = ( ( P4
% 9.17/5.38 => ( P @ one_one_Code_integer ) )
% 9.17/5.38 & ( ~ P4
% 9.17/5.38 => ( P @ zero_z3403309356797280102nteger ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3719_split__of__bool__asm,axiom,
% 9.17/5.38 ! [P: rat > $o,P4: $o] :
% 9.17/5.38 ( ( P @ ( zero_n2052037380579107095ol_rat @ P4 ) )
% 9.17/5.38 = ( ~ ( ( P4
% 9.17/5.38 & ~ ( P @ one_one_rat ) )
% 9.17/5.38 | ( ~ P4
% 9.17/5.38 & ~ ( P @ zero_zero_rat ) ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3720_split__of__bool__asm,axiom,
% 9.17/5.38 ! [P: nat > $o,P4: $o] :
% 9.17/5.38 ( ( P @ ( zero_n2687167440665602831ol_nat @ P4 ) )
% 9.17/5.38 = ( ~ ( ( P4
% 9.17/5.38 & ~ ( P @ one_one_nat ) )
% 9.17/5.38 | ( ~ P4
% 9.17/5.38 & ~ ( P @ zero_zero_nat ) ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3721_split__of__bool__asm,axiom,
% 9.17/5.38 ! [P: int > $o,P4: $o] :
% 9.17/5.38 ( ( P @ ( zero_n2684676970156552555ol_int @ P4 ) )
% 9.17/5.38 = ( ~ ( ( P4
% 9.17/5.38 & ~ ( P @ one_one_int ) )
% 9.17/5.38 | ( ~ P4
% 9.17/5.38 & ~ ( P @ zero_zero_int ) ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3722_split__of__bool__asm,axiom,
% 9.17/5.38 ! [P: code_integer > $o,P4: $o] :
% 9.17/5.38 ( ( P @ ( zero_n356916108424825756nteger @ P4 ) )
% 9.17/5.38 = ( ~ ( ( P4
% 9.17/5.38 & ~ ( P @ one_one_Code_integer ) )
% 9.17/5.38 | ( ~ P4
% 9.17/5.38 & ~ ( P @ zero_z3403309356797280102nteger ) ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3723_add__One,axiom,
% 9.17/5.38 ! [X: num] :
% 9.17/5.38 ( ( plus_plus_num @ X @ one )
% 9.17/5.38 = ( inc @ X ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3724_pred__numeral__def,axiom,
% 9.17/5.38 ( pred_numeral
% 9.17/5.38 = ( ^ [K4: num] : ( minus_minus_nat @ ( numeral_numeral_nat @ K4 ) @ one_one_nat ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3725_BitM__plus__one,axiom,
% 9.17/5.38 ! [N2: num] :
% 9.17/5.38 ( ( plus_plus_num @ ( bitM @ N2 ) @ one )
% 9.17/5.38 = ( bit0 @ N2 ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3726_one__plus__BitM,axiom,
% 9.17/5.38 ! [N2: num] :
% 9.17/5.38 ( ( plus_plus_num @ one @ ( bitM @ N2 ) )
% 9.17/5.38 = ( bit0 @ N2 ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3727_numeral__inc,axiom,
% 9.17/5.38 ! [X: num] :
% 9.17/5.38 ( ( numeral_numeral_nat @ ( inc @ X ) )
% 9.17/5.38 = ( plus_plus_nat @ ( numeral_numeral_nat @ X ) @ one_one_nat ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3728_numeral__inc,axiom,
% 9.17/5.38 ! [X: num] :
% 9.17/5.38 ( ( numeral_numeral_int @ ( inc @ X ) )
% 9.17/5.38 = ( plus_plus_int @ ( numeral_numeral_int @ X ) @ one_one_int ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3729_numeral__inc,axiom,
% 9.17/5.38 ! [X: num] :
% 9.17/5.38 ( ( numera6620942414471956472nteger @ ( inc @ X ) )
% 9.17/5.38 = ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ X ) @ one_one_Code_integer ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3730_numeral__inc,axiom,
% 9.17/5.38 ! [X: num] :
% 9.17/5.38 ( ( numeral_numeral_rat @ ( inc @ X ) )
% 9.17/5.38 = ( plus_plus_rat @ ( numeral_numeral_rat @ X ) @ one_one_rat ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3731_numeral__inc,axiom,
% 9.17/5.38 ! [X: num] :
% 9.17/5.38 ( ( numera5444537566228673987atural @ ( inc @ X ) )
% 9.17/5.38 = ( plus_p4538020629002901425atural @ ( numera5444537566228673987atural @ X ) @ one_one_Code_natural ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3732_numeral__BitM,axiom,
% 9.17/5.38 ! [N2: num] :
% 9.17/5.38 ( ( numeral_numeral_int @ ( bitM @ N2 ) )
% 9.17/5.38 = ( minus_minus_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) @ one_one_int ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3733_numeral__BitM,axiom,
% 9.17/5.38 ! [N2: num] :
% 9.17/5.38 ( ( numera6620942414471956472nteger @ ( bitM @ N2 ) )
% 9.17/5.38 = ( minus_8373710615458151222nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N2 ) ) @ one_one_Code_integer ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3734_numeral__BitM,axiom,
% 9.17/5.38 ! [N2: num] :
% 9.17/5.38 ( ( numeral_numeral_rat @ ( bitM @ N2 ) )
% 9.17/5.38 = ( minus_minus_rat @ ( numeral_numeral_rat @ ( bit0 @ N2 ) ) @ one_one_rat ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3735_take__bit__numeral__minus__bit1,axiom,
% 9.17/5.38 ! [L: num,K: num] :
% 9.17/5.38 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 9.17/5.38 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3736_bits__induct,axiom,
% 9.17/5.38 ! [P: code_natural > $o,A: code_natural] :
% 9.17/5.38 ( ! [A3: code_natural] :
% 9.17/5.38 ( ( ( divide5121882707175180666atural @ A3 @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 9.17/5.38 = A3 )
% 9.17/5.38 => ( P @ A3 ) )
% 9.17/5.38 => ( ! [A3: code_natural,B2: $o] :
% 9.17/5.38 ( ( P @ A3 )
% 9.17/5.38 => ( ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ ( zero_n8403883297036319079atural @ B2 ) @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A3 ) ) @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 9.17/5.38 = A3 )
% 9.17/5.38 => ( P @ ( plus_p4538020629002901425atural @ ( zero_n8403883297036319079atural @ B2 ) @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A3 ) ) ) ) )
% 9.17/5.38 => ( P @ A ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3737_bits__induct,axiom,
% 9.17/5.38 ! [P: nat > $o,A: nat] :
% 9.17/5.38 ( ! [A3: nat] :
% 9.17/5.38 ( ( ( divide_divide_nat @ A3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.17/5.38 = A3 )
% 9.17/5.38 => ( P @ A3 ) )
% 9.17/5.38 => ( ! [A3: nat,B2: $o] :
% 9.17/5.38 ( ( P @ A3 )
% 9.17/5.38 => ( ( ( divide_divide_nat @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ B2 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.17/5.38 = A3 )
% 9.17/5.38 => ( P @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ B2 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A3 ) ) ) ) )
% 9.17/5.38 => ( P @ A ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3738_bits__induct,axiom,
% 9.17/5.38 ! [P: int > $o,A: int] :
% 9.17/5.38 ( ! [A3: int] :
% 9.17/5.38 ( ( ( divide_divide_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.17/5.38 = A3 )
% 9.17/5.38 => ( P @ A3 ) )
% 9.17/5.38 => ( ! [A3: int,B2: $o] :
% 9.17/5.38 ( ( P @ A3 )
% 9.17/5.38 => ( ( ( divide_divide_int @ ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ B2 ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A3 ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.17/5.38 = A3 )
% 9.17/5.38 => ( P @ ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ B2 ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A3 ) ) ) ) )
% 9.17/5.38 => ( P @ A ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3739_bits__induct,axiom,
% 9.17/5.38 ! [P: code_integer > $o,A: code_integer] :
% 9.17/5.38 ( ! [A3: code_integer] :
% 9.17/5.38 ( ( ( divide6298287555418463151nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 9.17/5.38 = A3 )
% 9.17/5.38 => ( P @ A3 ) )
% 9.17/5.38 => ( ! [A3: code_integer,B2: $o] :
% 9.17/5.38 ( ( P @ A3 )
% 9.17/5.38 => ( ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ B2 ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A3 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 9.17/5.38 = A3 )
% 9.17/5.38 => ( P @ ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ B2 ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A3 ) ) ) ) )
% 9.17/5.38 => ( P @ A ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3740_divide__int__unfold,axiom,
% 9.17/5.38 ! [L: int,K: int,N2: nat,M2: nat] :
% 9.17/5.38 ( ( ( ( ( sgn_sgn_int @ L )
% 9.17/5.38 = zero_zero_int )
% 9.17/5.38 | ( ( sgn_sgn_int @ K )
% 9.17/5.38 = zero_zero_int )
% 9.17/5.38 | ( N2 = zero_zero_nat ) )
% 9.17/5.38 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M2 ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 9.17/5.38 = zero_zero_int ) )
% 9.17/5.38 & ( ~ ( ( ( sgn_sgn_int @ L )
% 9.17/5.38 = zero_zero_int )
% 9.17/5.38 | ( ( sgn_sgn_int @ K )
% 9.17/5.38 = zero_zero_int )
% 9.17/5.38 | ( N2 = zero_zero_nat ) )
% 9.17/5.38 => ( ( ( ( sgn_sgn_int @ K )
% 9.17/5.38 = ( sgn_sgn_int @ L ) )
% 9.17/5.38 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M2 ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 9.17/5.38 = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M2 @ N2 ) ) ) )
% 9.17/5.38 & ( ( ( sgn_sgn_int @ K )
% 9.17/5.38 != ( sgn_sgn_int @ L ) )
% 9.17/5.38 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M2 ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 9.17/5.38 = ( uminus_uminus_int
% 9.17/5.38 @ ( semiri1314217659103216013at_int
% 9.17/5.38 @ ( plus_plus_nat @ ( divide_divide_nat @ M2 @ N2 )
% 9.17/5.38 @ ( zero_n2687167440665602831ol_nat
% 9.17/5.38 @ ~ ( dvd_dvd_nat @ N2 @ M2 ) ) ) ) ) ) ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3741_take__bit__numeral__bit1,axiom,
% 9.17/5.38 ! [L: num,K: num] :
% 9.17/5.38 ( ( bit_se1745604003318907178nteger @ ( numeral_numeral_nat @ L ) @ ( numera6620942414471956472nteger @ ( bit1 @ K ) ) )
% 9.17/5.38 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( bit_se1745604003318907178nteger @ ( pred_numeral @ L ) @ ( numera6620942414471956472nteger @ K ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ one_one_Code_integer ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3742_take__bit__numeral__bit1,axiom,
% 9.17/5.38 ! [L: num,K: num] :
% 9.17/5.38 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 9.17/5.38 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3743_take__bit__numeral__bit1,axiom,
% 9.17/5.38 ! [L: num,K: num] :
% 9.17/5.38 ( ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 9.17/5.38 = ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ ( pred_numeral @ L ) @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3744_take__bit__numeral__bit1,axiom,
% 9.17/5.38 ! [L: num,K: num] :
% 9.17/5.38 ( ( bit_se569199155075624693atural @ ( numeral_numeral_nat @ L ) @ ( numera5444537566228673987atural @ ( bit1 @ K ) ) )
% 9.17/5.38 = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( bit_se569199155075624693atural @ ( pred_numeral @ L ) @ ( numera5444537566228673987atural @ K ) ) @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) @ one_one_Code_natural ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3745_Divides_Oadjust__div__eq,axiom,
% 9.17/5.38 ! [Q3: int,R2: int] :
% 9.17/5.38 ( ( adjust_div @ ( product_Pair_int_int @ Q3 @ R2 ) )
% 9.17/5.38 = ( plus_plus_int @ Q3 @ ( zero_n2684676970156552555ol_int @ ( R2 != zero_zero_int ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3746_mask__numeral,axiom,
% 9.17/5.38 ! [N2: num] :
% 9.17/5.38 ( ( bit_se2000444600071755411sk_int @ ( numeral_numeral_nat @ N2 ) )
% 9.17/5.38 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2000444600071755411sk_int @ ( pred_numeral @ N2 ) ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3747_mask__numeral,axiom,
% 9.17/5.38 ! [N2: num] :
% 9.17/5.38 ( ( bit_se2119862282449309892nteger @ ( numeral_numeral_nat @ N2 ) )
% 9.17/5.38 = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se2119862282449309892nteger @ ( pred_numeral @ N2 ) ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3748_mask__numeral,axiom,
% 9.17/5.38 ! [N2: num] :
% 9.17/5.38 ( ( bit_se2002935070580805687sk_nat @ ( numeral_numeral_nat @ N2 ) )
% 9.17/5.38 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2002935070580805687sk_nat @ ( pred_numeral @ N2 ) ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3749_mask__numeral,axiom,
% 9.17/5.38 ! [N2: num] :
% 9.17/5.38 ( ( bit_se943457434206027407atural @ ( numeral_numeral_nat @ N2 ) )
% 9.17/5.38 = ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se943457434206027407atural @ ( pred_numeral @ N2 ) ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3750_and__int__unfold,axiom,
% 9.17/5.38 ( bit_se725231765392027082nd_int
% 9.17/5.38 = ( ^ [K4: int,L3: int] :
% 9.17/5.38 ( if_int
% 9.17/5.38 @ ( ( K4 = zero_zero_int )
% 9.17/5.38 | ( L3 = zero_zero_int ) )
% 9.17/5.38 @ zero_zero_int
% 9.17/5.38 @ ( if_int
% 9.17/5.38 @ ( K4
% 9.17/5.38 = ( uminus_uminus_int @ one_one_int ) )
% 9.17/5.38 @ L3
% 9.17/5.38 @ ( if_int
% 9.17/5.38 @ ( L3
% 9.17/5.38 = ( uminus_uminus_int @ one_one_int ) )
% 9.17/5.38 @ K4
% 9.17/5.38 @ ( plus_plus_int @ ( times_times_int @ ( modulo_modulo_int @ K4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ L3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3751_the__res__def,axiom,
% 9.17/5.38 ( time_the_res_array_a
% 9.17/5.38 = ( ^ [M: heap_T6362127782908069795rray_a,H: heap_e7401611519738050253t_unit] :
% 9.17/5.38 ( case_o8314599424437789472it_nat @ undefined_array_a
% 9.17/5.38 @ ( produc8767961711439910440rray_a
% 9.17/5.38 @ ^ [R3: array_a] :
% 9.17/5.38 ( produc2025300630104146186rray_a
% 9.17/5.38 @ ^ [X3: heap_e7401611519738050253t_unit,Xa4: nat] : R3 ) )
% 9.17/5.38 @ ( heap_T5591663578999710211rray_a @ M @ H ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3752_the__res__def,axiom,
% 9.17/5.38 ( time_t2745601220510131320t_unit
% 9.17/5.38 = ( ^ [M: heap_T5738788834812785303t_unit,H: heap_e7401611519738050253t_unit] :
% 9.17/5.38 ( case_o9196786658626276042it_nat @ undefi2974082611360736373t_unit
% 9.17/5.38 @ ( produc5075907435489727646t_unit
% 9.17/5.38 @ ^ [R3: product_unit] :
% 9.17/5.38 ( produc1863717115126956122t_unit
% 9.17/5.38 @ ^ [X3: heap_e7401611519738050253t_unit,Xa4: nat] : R3 ) )
% 9.17/5.38 @ ( heap_T875086893843062177t_unit @ M @ H ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3753_take__bit__eq__mask__iff__exp__dvd,axiom,
% 9.17/5.38 ! [N2: nat,K: int] :
% 9.17/5.38 ( ( ( bit_se2923211474154528505it_int @ N2 @ K )
% 9.17/5.38 = ( bit_se2000444600071755411sk_int @ N2 ) )
% 9.17/5.38 = ( dvd_dvd_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ ( plus_plus_int @ K @ one_one_int ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3754_Code__Numeral_Opositive__def,axiom,
% 9.17/5.38 code_positive = numera6620942414471956472nteger ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3755_divide__int__def,axiom,
% 9.17/5.38 ( divide_divide_int
% 9.17/5.38 = ( ^ [K4: int,L3: int] :
% 9.17/5.38 ( if_int @ ( L3 = zero_zero_int ) @ zero_zero_int
% 9.17/5.38 @ ( if_int
% 9.17/5.38 @ ( ( sgn_sgn_int @ K4 )
% 9.17/5.38 = ( sgn_sgn_int @ L3 ) )
% 9.17/5.38 @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K4 ) ) @ ( nat2 @ ( abs_abs_int @ L3 ) ) ) )
% 9.17/5.38 @ ( uminus_uminus_int
% 9.17/5.38 @ ( semiri1314217659103216013at_int
% 9.17/5.38 @ ( plus_plus_nat @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K4 ) ) @ ( nat2 @ ( abs_abs_int @ L3 ) ) )
% 9.17/5.38 @ ( zero_n2687167440665602831ol_nat
% 9.17/5.38 @ ~ ( dvd_dvd_int @ L3 @ K4 ) ) ) ) ) ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3756_sum__gp0,axiom,
% 9.17/5.38 ! [X: rat,N2: nat] :
% 9.17/5.38 ( ( ( X = one_one_rat )
% 9.17/5.38 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_atMost_nat @ N2 ) )
% 9.17/5.38 = ( semiri681578069525770553at_rat @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) )
% 9.17/5.38 & ( ( X != one_one_rat )
% 9.17/5.38 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_atMost_nat @ N2 ) )
% 9.17/5.38 = ( divide_divide_rat @ ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ ( suc @ N2 ) ) ) @ ( minus_minus_rat @ one_one_rat @ X ) ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3757_atMost__eq__iff,axiom,
% 9.17/5.38 ! [X: nat,Y: nat] :
% 9.17/5.38 ( ( ( set_ord_atMost_nat @ X )
% 9.17/5.38 = ( set_ord_atMost_nat @ Y ) )
% 9.17/5.38 = ( X = Y ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3758_atMost__iff,axiom,
% 9.17/5.38 ! [I: $o,K: $o] :
% 9.17/5.38 ( ( member_o @ I @ ( set_ord_atMost_o @ K ) )
% 9.17/5.38 = ( ord_less_eq_o @ I @ K ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3759_atMost__iff,axiom,
% 9.17/5.38 ! [I: set_nat,K: set_nat] :
% 9.17/5.38 ( ( member_set_nat @ I @ ( set_or4236626031148496127et_nat @ K ) )
% 9.17/5.38 = ( ord_less_eq_set_nat @ I @ K ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3760_atMost__iff,axiom,
% 9.17/5.38 ! [I: rat,K: rat] :
% 9.17/5.38 ( ( member_rat @ I @ ( set_ord_atMost_rat @ K ) )
% 9.17/5.38 = ( ord_less_eq_rat @ I @ K ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3761_atMost__iff,axiom,
% 9.17/5.38 ! [I: num,K: num] :
% 9.17/5.38 ( ( member_num @ I @ ( set_ord_atMost_num @ K ) )
% 9.17/5.38 = ( ord_less_eq_num @ I @ K ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3762_atMost__iff,axiom,
% 9.17/5.38 ! [I: int,K: int] :
% 9.17/5.38 ( ( member_int @ I @ ( set_ord_atMost_int @ K ) )
% 9.17/5.38 = ( ord_less_eq_int @ I @ K ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3763_atMost__iff,axiom,
% 9.17/5.38 ! [I: nat,K: nat] :
% 9.17/5.38 ( ( member_nat @ I @ ( set_ord_atMost_nat @ K ) )
% 9.17/5.38 = ( ord_less_eq_nat @ I @ K ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3764_atMost__subset__iff,axiom,
% 9.17/5.38 ! [X: set_nat,Y: set_nat] :
% 9.17/5.38 ( ( ord_le6893508408891458716et_nat @ ( set_or4236626031148496127et_nat @ X ) @ ( set_or4236626031148496127et_nat @ Y ) )
% 9.17/5.38 = ( ord_less_eq_set_nat @ X @ Y ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3765_atMost__subset__iff,axiom,
% 9.17/5.38 ! [X: rat,Y: rat] :
% 9.17/5.38 ( ( ord_less_eq_set_rat @ ( set_ord_atMost_rat @ X ) @ ( set_ord_atMost_rat @ Y ) )
% 9.17/5.38 = ( ord_less_eq_rat @ X @ Y ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3766_atMost__subset__iff,axiom,
% 9.17/5.38 ! [X: num,Y: num] :
% 9.17/5.38 ( ( ord_less_eq_set_num @ ( set_ord_atMost_num @ X ) @ ( set_ord_atMost_num @ Y ) )
% 9.17/5.38 = ( ord_less_eq_num @ X @ Y ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3767_atMost__subset__iff,axiom,
% 9.17/5.38 ! [X: int,Y: int] :
% 9.17/5.38 ( ( ord_less_eq_set_int @ ( set_ord_atMost_int @ X ) @ ( set_ord_atMost_int @ Y ) )
% 9.17/5.38 = ( ord_less_eq_int @ X @ Y ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3768_atMost__subset__iff,axiom,
% 9.17/5.38 ! [X: nat,Y: nat] :
% 9.17/5.38 ( ( ord_less_eq_set_nat @ ( set_ord_atMost_nat @ X ) @ ( set_ord_atMost_nat @ Y ) )
% 9.17/5.38 = ( ord_less_eq_nat @ X @ Y ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3769_bit_Oconj__one__right,axiom,
% 9.17/5.38 ! [X: int] :
% 9.17/5.38 ( ( bit_se725231765392027082nd_int @ X @ ( uminus_uminus_int @ one_one_int ) )
% 9.17/5.38 = X ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3770_bit_Oconj__one__right,axiom,
% 9.17/5.38 ! [X: code_integer] :
% 9.17/5.38 ( ( bit_se3949692690581998587nteger @ X @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.17/5.38 = X ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3771_and_Oright__neutral,axiom,
% 9.17/5.38 ! [A: int] :
% 9.17/5.38 ( ( bit_se725231765392027082nd_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 9.17/5.38 = A ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3772_and_Oright__neutral,axiom,
% 9.17/5.38 ! [A: code_integer] :
% 9.17/5.38 ( ( bit_se3949692690581998587nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.17/5.38 = A ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3773_and_Oleft__neutral,axiom,
% 9.17/5.38 ! [A: int] :
% 9.17/5.38 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ one_one_int ) @ A )
% 9.17/5.38 = A ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3774_and_Oleft__neutral,axiom,
% 9.17/5.38 ! [A: code_integer] :
% 9.17/5.38 ( ( bit_se3949692690581998587nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ A )
% 9.17/5.38 = A ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3775_and__numerals_I2_J,axiom,
% 9.17/5.38 ! [Y: num] :
% 9.17/5.38 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 9.17/5.38 = one_one_int ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3776_and__numerals_I2_J,axiom,
% 9.17/5.38 ! [Y: num] :
% 9.17/5.38 ( ( bit_se727722235901077358nd_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 9.17/5.38 = one_one_nat ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3777_and__numerals_I2_J,axiom,
% 9.17/5.38 ! [Y: num] :
% 9.17/5.38 ( ( bit_se3949692690581998587nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit1 @ Y ) ) )
% 9.17/5.38 = one_one_Code_integer ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3778_and__numerals_I2_J,axiom,
% 9.17/5.38 ! [Y: num] :
% 9.17/5.38 ( ( bit_se2773287842338716102atural @ one_one_Code_natural @ ( numera5444537566228673987atural @ ( bit1 @ Y ) ) )
% 9.17/5.38 = one_one_Code_natural ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3779_and__numerals_I8_J,axiom,
% 9.17/5.38 ! [X: num] :
% 9.17/5.38 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ one_one_int )
% 9.17/5.38 = one_one_int ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3780_and__numerals_I8_J,axiom,
% 9.17/5.38 ! [X: num] :
% 9.17/5.38 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ one_one_nat )
% 9.17/5.38 = one_one_nat ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3781_and__numerals_I8_J,axiom,
% 9.17/5.38 ! [X: num] :
% 9.17/5.38 ( ( bit_se3949692690581998587nteger @ ( numera6620942414471956472nteger @ ( bit1 @ X ) ) @ one_one_Code_integer )
% 9.17/5.38 = one_one_Code_integer ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3782_and__numerals_I8_J,axiom,
% 9.17/5.38 ! [X: num] :
% 9.17/5.38 ( ( bit_se2773287842338716102atural @ ( numera5444537566228673987atural @ ( bit1 @ X ) ) @ one_one_Code_natural )
% 9.17/5.38 = one_one_Code_natural ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3783_Icc__subset__Iic__iff,axiom,
% 9.17/5.38 ! [L: set_nat,H3: set_nat,H5: set_nat] :
% 9.17/5.38 ( ( ord_le6893508408891458716et_nat @ ( set_or4548717258645045905et_nat @ L @ H3 ) @ ( set_or4236626031148496127et_nat @ H5 ) )
% 9.17/5.38 = ( ~ ( ord_less_eq_set_nat @ L @ H3 )
% 9.17/5.38 | ( ord_less_eq_set_nat @ H3 @ H5 ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3784_Icc__subset__Iic__iff,axiom,
% 9.17/5.38 ! [L: rat,H3: rat,H5: rat] :
% 9.17/5.38 ( ( ord_less_eq_set_rat @ ( set_or633870826150836451st_rat @ L @ H3 ) @ ( set_ord_atMost_rat @ H5 ) )
% 9.17/5.38 = ( ~ ( ord_less_eq_rat @ L @ H3 )
% 9.17/5.38 | ( ord_less_eq_rat @ H3 @ H5 ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3785_Icc__subset__Iic__iff,axiom,
% 9.17/5.38 ! [L: num,H3: num,H5: num] :
% 9.17/5.38 ( ( ord_less_eq_set_num @ ( set_or7049704709247886629st_num @ L @ H3 ) @ ( set_ord_atMost_num @ H5 ) )
% 9.17/5.38 = ( ~ ( ord_less_eq_num @ L @ H3 )
% 9.17/5.38 | ( ord_less_eq_num @ H3 @ H5 ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3786_Icc__subset__Iic__iff,axiom,
% 9.17/5.38 ! [L: int,H3: int,H5: int] :
% 9.17/5.38 ( ( ord_less_eq_set_int @ ( set_or1266510415728281911st_int @ L @ H3 ) @ ( set_ord_atMost_int @ H5 ) )
% 9.17/5.38 = ( ~ ( ord_less_eq_int @ L @ H3 )
% 9.17/5.38 | ( ord_less_eq_int @ H3 @ H5 ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3787_Icc__subset__Iic__iff,axiom,
% 9.17/5.38 ! [L: nat,H3: nat,H5: nat] :
% 9.17/5.38 ( ( ord_less_eq_set_nat @ ( set_or1269000886237332187st_nat @ L @ H3 ) @ ( set_ord_atMost_nat @ H5 ) )
% 9.17/5.38 = ( ~ ( ord_less_eq_nat @ L @ H3 )
% 9.17/5.38 | ( ord_less_eq_nat @ H3 @ H5 ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3788_Icc__subset__Iic__iff,axiom,
% 9.17/5.38 ! [L: code_integer,H3: code_integer,H5: code_integer] :
% 9.17/5.38 ( ( ord_le7084787975880047091nteger @ ( set_or189985376899183464nteger @ L @ H3 ) @ ( set_or9101266186257409494nteger @ H5 ) )
% 9.17/5.38 = ( ~ ( ord_le3102999989581377725nteger @ L @ H3 )
% 9.17/5.38 | ( ord_le3102999989581377725nteger @ H3 @ H5 ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3789_mask__Suc__0,axiom,
% 9.17/5.38 ( ( bit_se2000444600071755411sk_int @ ( suc @ zero_zero_nat ) )
% 9.17/5.38 = one_one_int ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3790_mask__Suc__0,axiom,
% 9.17/5.38 ( ( bit_se2119862282449309892nteger @ ( suc @ zero_zero_nat ) )
% 9.17/5.38 = one_one_Code_integer ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3791_mask__Suc__0,axiom,
% 9.17/5.38 ( ( bit_se2002935070580805687sk_nat @ ( suc @ zero_zero_nat ) )
% 9.17/5.38 = one_one_nat ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3792_mask__Suc__0,axiom,
% 9.17/5.38 ( ( bit_se943457434206027407atural @ ( suc @ zero_zero_nat ) )
% 9.17/5.38 = one_one_Code_natural ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3793_sum_OatMost__Suc,axiom,
% 9.17/5.38 ! [G: nat > multis2468970476368604999at_nat,N2: nat] :
% 9.17/5.38 ( ( groups6857163185585827899at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 9.17/5.38 = ( plus_p7104986032573967614at_nat @ ( groups6857163185585827899at_nat @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3794_sum_OatMost__Suc,axiom,
% 9.17/5.38 ! [G: nat > rat,N2: nat] :
% 9.17/5.38 ( ( groups2906978787729119204at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 9.17/5.38 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3795_sum_OatMost__Suc,axiom,
% 9.17/5.38 ! [G: nat > int,N2: nat] :
% 9.17/5.38 ( ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 9.17/5.38 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3796_sum_OatMost__Suc,axiom,
% 9.17/5.38 ! [G: nat > nat,N2: nat] :
% 9.17/5.38 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 9.17/5.38 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3797_take__bit__minus__one__eq__mask,axiom,
% 9.17/5.38 ! [N2: nat] :
% 9.17/5.38 ( ( bit_se1745604003318907178nteger @ N2 @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.17/5.38 = ( bit_se2119862282449309892nteger @ N2 ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3798_take__bit__minus__one__eq__mask,axiom,
% 9.17/5.38 ! [N2: nat] :
% 9.17/5.38 ( ( bit_se2923211474154528505it_int @ N2 @ ( uminus_uminus_int @ one_one_int ) )
% 9.17/5.38 = ( bit_se2000444600071755411sk_int @ N2 ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3799_and__numerals_I1_J,axiom,
% 9.17/5.38 ! [Y: num] :
% 9.17/5.38 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 9.17/5.38 = zero_zero_int ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3800_and__numerals_I1_J,axiom,
% 9.17/5.38 ! [Y: num] :
% 9.17/5.38 ( ( bit_se727722235901077358nd_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 9.17/5.38 = zero_zero_nat ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3801_and__numerals_I1_J,axiom,
% 9.17/5.38 ! [Y: num] :
% 9.17/5.38 ( ( bit_se3949692690581998587nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ Y ) ) )
% 9.17/5.38 = zero_z3403309356797280102nteger ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3802_and__numerals_I1_J,axiom,
% 9.17/5.38 ! [Y: num] :
% 9.17/5.38 ( ( bit_se2773287842338716102atural @ one_one_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ Y ) ) )
% 9.17/5.38 = zero_z2226904508553997617atural ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3803_and__numerals_I5_J,axiom,
% 9.17/5.38 ! [X: num] :
% 9.17/5.38 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ one_one_int )
% 9.17/5.38 = zero_zero_int ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3804_and__numerals_I5_J,axiom,
% 9.17/5.38 ! [X: num] :
% 9.17/5.38 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ one_one_nat )
% 9.17/5.38 = zero_zero_nat ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3805_and__numerals_I5_J,axiom,
% 9.17/5.38 ! [X: num] :
% 9.17/5.38 ( ( bit_se3949692690581998587nteger @ ( numera6620942414471956472nteger @ ( bit0 @ X ) ) @ one_one_Code_integer )
% 9.17/5.38 = zero_z3403309356797280102nteger ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3806_and__numerals_I5_J,axiom,
% 9.17/5.38 ! [X: num] :
% 9.17/5.38 ( ( bit_se2773287842338716102atural @ ( numera5444537566228673987atural @ ( bit0 @ X ) ) @ one_one_Code_natural )
% 9.17/5.38 = zero_z2226904508553997617atural ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3807_nat__numeral__diff__1,axiom,
% 9.17/5.38 ! [V: num] :
% 9.17/5.38 ( ( minus_minus_nat @ ( numeral_numeral_nat @ V ) @ one_one_nat )
% 9.17/5.38 = ( nat2 @ ( minus_minus_int @ ( numeral_numeral_int @ V ) @ one_one_int ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3808_and__numerals_I7_J,axiom,
% 9.17/5.38 ! [X: num,Y: num] :
% 9.17/5.38 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 9.17/5.38 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3809_and__numerals_I7_J,axiom,
% 9.17/5.38 ! [X: num,Y: num] :
% 9.17/5.38 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 9.17/5.38 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3810_and__numerals_I7_J,axiom,
% 9.17/5.38 ! [X: num,Y: num] :
% 9.17/5.38 ( ( bit_se3949692690581998587nteger @ ( numera6620942414471956472nteger @ ( bit1 @ X ) ) @ ( numera6620942414471956472nteger @ ( bit1 @ Y ) ) )
% 9.17/5.38 = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se3949692690581998587nteger @ ( numera6620942414471956472nteger @ X ) @ ( numera6620942414471956472nteger @ Y ) ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3811_and__numerals_I7_J,axiom,
% 9.17/5.38 ! [X: num,Y: num] :
% 9.17/5.38 ( ( bit_se2773287842338716102atural @ ( numera5444537566228673987atural @ ( bit1 @ X ) ) @ ( numera5444537566228673987atural @ ( bit1 @ Y ) ) )
% 9.17/5.38 = ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se2773287842338716102atural @ ( numera5444537566228673987atural @ X ) @ ( numera5444537566228673987atural @ Y ) ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3812_mask__integer_Oabs__eq,axiom,
% 9.17/5.38 ( bit_se2119862282449309892nteger
% 9.17/5.38 = ( ^ [X3: nat] : ( code_integer_of_int @ ( bit_se2000444600071755411sk_int @ X3 ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3813_not__Iic__eq__Icc,axiom,
% 9.17/5.38 ! [H5: int,L: int,H3: int] :
% 9.17/5.38 ( ( set_ord_atMost_int @ H5 )
% 9.17/5.38 != ( set_or1266510415728281911st_int @ L @ H3 ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3814_atMost__def,axiom,
% 9.17/5.38 ( set_or4236626031148496127et_nat
% 9.17/5.38 = ( ^ [U2: set_nat] :
% 9.17/5.38 ( collect_set_nat
% 9.17/5.38 @ ^ [X3: set_nat] : ( ord_less_eq_set_nat @ X3 @ U2 ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3815_atMost__def,axiom,
% 9.17/5.38 ( set_ord_atMost_rat
% 9.17/5.38 = ( ^ [U2: rat] :
% 9.17/5.38 ( collect_rat
% 9.17/5.38 @ ^ [X3: rat] : ( ord_less_eq_rat @ X3 @ U2 ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3816_atMost__def,axiom,
% 9.17/5.38 ( set_ord_atMost_num
% 9.17/5.38 = ( ^ [U2: num] :
% 9.17/5.38 ( collect_num
% 9.17/5.38 @ ^ [X3: num] : ( ord_less_eq_num @ X3 @ U2 ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3817_atMost__def,axiom,
% 9.17/5.38 ( set_ord_atMost_int
% 9.17/5.38 = ( ^ [U2: int] :
% 9.17/5.38 ( collect_int
% 9.17/5.38 @ ^ [X3: int] : ( ord_less_eq_int @ X3 @ U2 ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3818_atMost__def,axiom,
% 9.17/5.38 ( set_ord_atMost_nat
% 9.17/5.38 = ( ^ [U2: nat] :
% 9.17/5.38 ( collect_nat
% 9.17/5.38 @ ^ [X3: nat] : ( ord_less_eq_nat @ X3 @ U2 ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3819_and__eq__minus__1__iff,axiom,
% 9.17/5.38 ! [A: int,B: int] :
% 9.17/5.38 ( ( ( bit_se725231765392027082nd_int @ A @ B )
% 9.17/5.38 = ( uminus_uminus_int @ one_one_int ) )
% 9.17/5.38 = ( ( A
% 9.17/5.38 = ( uminus_uminus_int @ one_one_int ) )
% 9.17/5.38 & ( B
% 9.17/5.38 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3820_and__eq__minus__1__iff,axiom,
% 9.17/5.38 ! [A: code_integer,B: code_integer] :
% 9.17/5.38 ( ( ( bit_se3949692690581998587nteger @ A @ B )
% 9.17/5.38 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.17/5.38 = ( ( A
% 9.17/5.38 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.17/5.38 & ( B
% 9.17/5.38 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3821_atMost__atLeast0,axiom,
% 9.17/5.38 ( set_ord_atMost_nat
% 9.17/5.38 = ( set_or1269000886237332187st_nat @ zero_zero_nat ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3822_nat__one__as__int,axiom,
% 9.17/5.38 ( one_one_nat
% 9.17/5.38 = ( nat2 @ one_one_int ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3823_not__Iic__le__Icc,axiom,
% 9.17/5.38 ! [H3: int,L4: int,H5: int] :
% 9.17/5.38 ~ ( ord_less_eq_set_int @ ( set_ord_atMost_int @ H3 ) @ ( set_or1266510415728281911st_int @ L4 @ H5 ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3824_nat__int__add,axiom,
% 9.17/5.38 ! [A: nat,B: nat] :
% 9.17/5.38 ( ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) )
% 9.17/5.38 = ( plus_plus_nat @ A @ B ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3825_option_Othe__def,axiom,
% 9.17/5.38 ( the_num
% 9.17/5.38 = ( case_option_num_num @ undefined_num
% 9.17/5.38 @ ^ [X23: num] : X23 ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3826_nat__plus__as__int,axiom,
% 9.17/5.38 ( plus_plus_nat
% 9.17/5.38 = ( ^ [A5: nat,B4: nat] : ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A5 ) @ ( semiri1314217659103216013at_int @ B4 ) ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3827_nat__add__distrib,axiom,
% 9.17/5.38 ! [Z: int,Z6: int] :
% 9.17/5.38 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 9.17/5.38 => ( ( ord_less_eq_int @ zero_zero_int @ Z6 )
% 9.17/5.38 => ( ( nat2 @ ( plus_plus_int @ Z @ Z6 ) )
% 9.17/5.38 = ( plus_plus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z6 ) ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3828_Suc__as__int,axiom,
% 9.17/5.38 ( suc
% 9.17/5.38 = ( ^ [A5: nat] : ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A5 ) @ one_one_int ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3829_nat__abs__triangle__ineq,axiom,
% 9.17/5.38 ! [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 ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3830_sum_OatMost__Suc__shift,axiom,
% 9.17/5.38 ! [G: nat > multis2468970476368604999at_nat,N2: nat] :
% 9.17/5.38 ( ( groups6857163185585827899at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 9.17/5.38 = ( plus_p7104986032573967614at_nat @ ( G @ zero_zero_nat )
% 9.17/5.38 @ ( groups6857163185585827899at_nat
% 9.17/5.38 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 9.17/5.38 @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3831_sum_OatMost__Suc__shift,axiom,
% 9.17/5.38 ! [G: nat > rat,N2: nat] :
% 9.17/5.38 ( ( groups2906978787729119204at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 9.17/5.38 = ( plus_plus_rat @ ( G @ zero_zero_nat )
% 9.17/5.38 @ ( groups2906978787729119204at_rat
% 9.17/5.38 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 9.17/5.38 @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3832_sum_OatMost__Suc__shift,axiom,
% 9.17/5.38 ! [G: nat > int,N2: nat] :
% 9.17/5.38 ( ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 9.17/5.38 = ( plus_plus_int @ ( G @ zero_zero_nat )
% 9.17/5.38 @ ( groups3539618377306564664at_int
% 9.17/5.38 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 9.17/5.38 @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3833_sum_OatMost__Suc__shift,axiom,
% 9.17/5.38 ! [G: nat > nat,N2: nat] :
% 9.17/5.38 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 9.17/5.38 = ( plus_plus_nat @ ( G @ zero_zero_nat )
% 9.17/5.38 @ ( groups3542108847815614940at_nat
% 9.17/5.38 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 9.17/5.38 @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3834_sum__telescope,axiom,
% 9.17/5.38 ! [F: nat > code_integer,I: nat] :
% 9.17/5.38 ( ( groups7501900531339628137nteger
% 9.17/5.38 @ ^ [I3: nat] : ( minus_8373710615458151222nteger @ ( F @ I3 ) @ ( F @ ( suc @ I3 ) ) )
% 9.17/5.38 @ ( set_ord_atMost_nat @ I ) )
% 9.17/5.38 = ( minus_8373710615458151222nteger @ ( F @ zero_zero_nat ) @ ( F @ ( suc @ I ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3835_sum__telescope,axiom,
% 9.17/5.38 ! [F: nat > rat,I: nat] :
% 9.17/5.38 ( ( groups2906978787729119204at_rat
% 9.17/5.38 @ ^ [I3: nat] : ( minus_minus_rat @ ( F @ I3 ) @ ( F @ ( suc @ I3 ) ) )
% 9.17/5.38 @ ( set_ord_atMost_nat @ I ) )
% 9.17/5.38 = ( minus_minus_rat @ ( F @ zero_zero_nat ) @ ( F @ ( suc @ I ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3836_sum__telescope,axiom,
% 9.17/5.38 ! [F: nat > int,I: nat] :
% 9.17/5.38 ( ( groups3539618377306564664at_int
% 9.17/5.38 @ ^ [I3: nat] : ( minus_minus_int @ ( F @ I3 ) @ ( F @ ( suc @ I3 ) ) )
% 9.17/5.38 @ ( set_ord_atMost_nat @ I ) )
% 9.17/5.38 = ( minus_minus_int @ ( F @ zero_zero_nat ) @ ( F @ ( suc @ I ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3837_the__heap__def,axiom,
% 9.17/5.38 ( time_t490086488869527696rray_a
% 9.17/5.38 = ( ^ [M: heap_T6362127782908069795rray_a,H: heap_e7401611519738050253t_unit] :
% 9.17/5.38 ( case_o8180226181140434498it_nat @ undefi8805113437130903861t_unit
% 9.17/5.38 @ ( produc7016084256669755260t_unit
% 9.17/5.38 @ ^ [X3: array_a] :
% 9.17/5.38 ( produc9092781844693468442t_unit
% 9.17/5.38 @ ^ [H6: heap_e7401611519738050253t_unit,Xa4: nat] : H6 ) )
% 9.17/5.38 @ ( heap_T5591663578999710211rray_a @ M @ H ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3838_the__heap__def,axiom,
% 9.17/5.38 ( time_t3350536682685678164t_unit
% 9.17/5.38 = ( ^ [M: heap_T5738788834812785303t_unit,H: heap_e7401611519738050253t_unit] :
% 9.17/5.38 ( case_o2566993838309857162it_nat @ undefi8805113437130903861t_unit
% 9.17/5.38 @ ( produc6568152436032731486t_unit
% 9.17/5.38 @ ^ [X3: product_unit] :
% 9.17/5.38 ( produc9092781844693468442t_unit
% 9.17/5.38 @ ^ [H6: heap_e7401611519738050253t_unit,Xa4: nat] : H6 ) )
% 9.17/5.38 @ ( heap_T875086893843062177t_unit @ M @ H ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3839_and__one__eq,axiom,
% 9.17/5.38 ! [A: int] :
% 9.17/5.38 ( ( bit_se725231765392027082nd_int @ A @ one_one_int )
% 9.17/5.38 = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3840_and__one__eq,axiom,
% 9.17/5.38 ! [A: nat] :
% 9.17/5.38 ( ( bit_se727722235901077358nd_nat @ A @ one_one_nat )
% 9.17/5.38 = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3841_and__one__eq,axiom,
% 9.17/5.38 ! [A: code_integer] :
% 9.17/5.38 ( ( bit_se3949692690581998587nteger @ A @ one_one_Code_integer )
% 9.17/5.38 = ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3842_and__one__eq,axiom,
% 9.17/5.38 ! [A: code_natural] :
% 9.17/5.38 ( ( bit_se2773287842338716102atural @ A @ one_one_Code_natural )
% 9.17/5.38 = ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3843_one__and__eq,axiom,
% 9.17/5.38 ! [A: int] :
% 9.17/5.38 ( ( bit_se725231765392027082nd_int @ one_one_int @ A )
% 9.17/5.38 = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3844_one__and__eq,axiom,
% 9.17/5.38 ! [A: nat] :
% 9.17/5.38 ( ( bit_se727722235901077358nd_nat @ one_one_nat @ A )
% 9.17/5.38 = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3845_one__and__eq,axiom,
% 9.17/5.38 ! [A: code_integer] :
% 9.17/5.38 ( ( bit_se3949692690581998587nteger @ one_one_Code_integer @ A )
% 9.17/5.38 = ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3846_one__and__eq,axiom,
% 9.17/5.38 ! [A: code_natural] :
% 9.17/5.38 ( ( bit_se2773287842338716102atural @ one_one_Code_natural @ A )
% 9.17/5.38 = ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3847_take__bit__eq__mask__iff,axiom,
% 9.17/5.38 ! [N2: nat,K: int] :
% 9.17/5.38 ( ( ( bit_se2923211474154528505it_int @ N2 @ K )
% 9.17/5.38 = ( bit_se2000444600071755411sk_int @ N2 ) )
% 9.17/5.38 = ( ( bit_se2923211474154528505it_int @ N2 @ ( plus_plus_int @ K @ one_one_int ) )
% 9.17/5.38 = zero_zero_int ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3848_Suc__nat__eq__nat__zadd1,axiom,
% 9.17/5.38 ! [Z: int] :
% 9.17/5.38 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 9.17/5.38 => ( ( suc @ ( nat2 @ Z ) )
% 9.17/5.38 = ( nat2 @ ( plus_plus_int @ one_one_int @ Z ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3849_Divides_Oadjust__div__def,axiom,
% 9.17/5.38 ( adjust_div
% 9.17/5.38 = ( produc8211389475949308722nt_int
% 9.17/5.38 @ ^ [Q5: int,R3: int] : ( plus_plus_int @ Q5 @ ( zero_n2684676970156552555ol_int @ ( R3 != zero_zero_int ) ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3850_sum__gp__basic,axiom,
% 9.17/5.38 ! [X: code_integer,N2: nat] :
% 9.17/5.38 ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ one_one_Code_integer @ X ) @ ( groups7501900531339628137nteger @ ( power_8256067586552552935nteger @ X ) @ ( set_ord_atMost_nat @ N2 ) ) )
% 9.17/5.38 = ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ X @ ( suc @ N2 ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3851_sum__gp__basic,axiom,
% 9.17/5.38 ! [X: rat,N2: nat] :
% 9.17/5.38 ( ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_atMost_nat @ N2 ) ) )
% 9.17/5.38 = ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ ( suc @ N2 ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3852_sum__gp__basic,axiom,
% 9.17/5.38 ! [X: int,N2: nat] :
% 9.17/5.38 ( ( times_times_int @ ( minus_minus_int @ one_one_int @ X ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_ord_atMost_nat @ N2 ) ) )
% 9.17/5.38 = ( minus_minus_int @ one_one_int @ ( power_power_int @ X @ ( suc @ N2 ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3853_sum__power__shift,axiom,
% 9.17/5.38 ! [M2: nat,N2: nat,X: rat] :
% 9.17/5.38 ( ( ord_less_eq_nat @ M2 @ N2 )
% 9.17/5.38 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 9.17/5.38 = ( times_times_rat @ ( power_power_rat @ X @ M2 ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_atMost_nat @ ( minus_minus_nat @ N2 @ M2 ) ) ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3854_sum__power__shift,axiom,
% 9.17/5.38 ! [M2: nat,N2: nat,X: int] :
% 9.17/5.38 ( ( ord_less_eq_nat @ M2 @ N2 )
% 9.17/5.38 => ( ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 9.17/5.38 = ( times_times_int @ ( power_power_int @ X @ M2 ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_ord_atMost_nat @ ( minus_minus_nat @ N2 @ M2 ) ) ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3855_sum_Otriangle__reindex__eq,axiom,
% 9.17/5.38 ! [G: nat > nat > nat,N2: nat] :
% 9.17/5.38 ( ( groups977919841031483927at_nat @ ( produc6842872674320459806at_nat @ G )
% 9.17/5.38 @ ( collec3392354462482085612at_nat
% 9.17/5.38 @ ( produc6081775807080527818_nat_o
% 9.17/5.38 @ ^ [I3: nat,J2: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ I3 @ J2 ) @ N2 ) ) ) )
% 9.17/5.38 = ( groups3542108847815614940at_nat
% 9.17/5.38 @ ^ [K4: nat] :
% 9.17/5.38 ( groups3542108847815614940at_nat
% 9.17/5.38 @ ^ [I3: nat] : ( G @ I3 @ ( minus_minus_nat @ K4 @ I3 ) )
% 9.17/5.38 @ ( set_ord_atMost_nat @ K4 ) )
% 9.17/5.38 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3856_and__int__rec,axiom,
% 9.17/5.38 ( bit_se725231765392027082nd_int
% 9.17/5.38 = ( ^ [K4: int,L3: int] :
% 9.17/5.38 ( plus_plus_int
% 9.17/5.38 @ ( zero_n2684676970156552555ol_int
% 9.17/5.38 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K4 )
% 9.17/5.38 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L3 ) ) )
% 9.17/5.38 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3857_mask__half__int,axiom,
% 9.17/5.38 ! [N2: nat] :
% 9.17/5.38 ( ( divide_divide_int @ ( bit_se2000444600071755411sk_int @ N2 ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.17/5.38 = ( bit_se2000444600071755411sk_int @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3858_sum_Oin__pairs__0,axiom,
% 9.17/5.38 ! [G: nat > multis2468970476368604999at_nat,N2: nat] :
% 9.17/5.38 ( ( groups6857163185585827899at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 9.17/5.38 = ( groups6857163185585827899at_nat
% 9.17/5.38 @ ^ [I3: nat] : ( plus_p7104986032573967614at_nat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 9.17/5.38 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3859_sum_Oin__pairs__0,axiom,
% 9.17/5.38 ! [G: nat > rat,N2: nat] :
% 9.17/5.38 ( ( groups2906978787729119204at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 9.17/5.38 = ( groups2906978787729119204at_rat
% 9.17/5.38 @ ^ [I3: nat] : ( plus_plus_rat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 9.17/5.38 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3860_sum_Oin__pairs__0,axiom,
% 9.17/5.38 ! [G: nat > int,N2: nat] :
% 9.17/5.38 ( ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 9.17/5.38 = ( groups3539618377306564664at_int
% 9.17/5.38 @ ^ [I3: nat] : ( plus_plus_int @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 9.17/5.38 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3861_sum_Oin__pairs__0,axiom,
% 9.17/5.38 ! [G: nat > nat,N2: nat] :
% 9.17/5.38 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 9.17/5.38 = ( groups3542108847815614940at_nat
% 9.17/5.38 @ ^ [I3: nat] : ( plus_plus_nat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 9.17/5.38 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3862_mask__nat__def,axiom,
% 9.17/5.38 ( bit_se2002935070580805687sk_nat
% 9.17/5.38 = ( ^ [N4: nat] : ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) @ one_one_nat ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3863_mask__eq__exp__minus__1,axiom,
% 9.17/5.38 ( bit_se2000444600071755411sk_int
% 9.17/5.38 = ( ^ [N4: nat] : ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N4 ) @ one_one_int ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3864_mask__eq__exp__minus__1,axiom,
% 9.17/5.38 ( bit_se2119862282449309892nteger
% 9.17/5.38 = ( ^ [N4: nat] : ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N4 ) @ one_one_Code_integer ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3865_mask__eq__exp__minus__1,axiom,
% 9.17/5.38 ( bit_se2002935070580805687sk_nat
% 9.17/5.38 = ( ^ [N4: nat] : ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) @ one_one_nat ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3866_mask__eq__exp__minus__1,axiom,
% 9.17/5.38 ( bit_se943457434206027407atural
% 9.17/5.38 = ( ^ [N4: nat] : ( minus_7197305767214868737atural @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N4 ) @ one_one_Code_natural ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3867_sum_Ozero__middle,axiom,
% 9.17/5.38 ! [P4: nat,K: nat,G: nat > code_integer,H3: nat > code_integer] :
% 9.17/5.38 ( ( ord_less_eq_nat @ one_one_nat @ P4 )
% 9.17/5.38 => ( ( ord_less_eq_nat @ K @ P4 )
% 9.17/5.38 => ( ( groups7501900531339628137nteger
% 9.17/5.38 @ ^ [J2: nat] : ( if_Code_integer @ ( ord_less_nat @ J2 @ K ) @ ( G @ J2 ) @ ( if_Code_integer @ ( J2 = K ) @ zero_z3403309356797280102nteger @ ( H3 @ ( minus_minus_nat @ J2 @ ( suc @ zero_zero_nat ) ) ) ) )
% 9.17/5.38 @ ( set_ord_atMost_nat @ P4 ) )
% 9.17/5.38 = ( groups7501900531339628137nteger
% 9.17/5.38 @ ^ [J2: nat] : ( if_Code_integer @ ( ord_less_nat @ J2 @ K ) @ ( G @ J2 ) @ ( H3 @ J2 ) )
% 9.17/5.38 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P4 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3868_sum_Ozero__middle,axiom,
% 9.17/5.38 ! [P4: nat,K: nat,G: nat > multis2468970476368604999at_nat,H3: nat > multis2468970476368604999at_nat] :
% 9.17/5.38 ( ( ord_less_eq_nat @ one_one_nat @ P4 )
% 9.17/5.38 => ( ( ord_less_eq_nat @ K @ P4 )
% 9.17/5.38 => ( ( groups6857163185585827899at_nat
% 9.17/5.38 @ ^ [J2: nat] : ( if_mul8430962117462786573at_nat @ ( ord_less_nat @ J2 @ K ) @ ( G @ J2 ) @ ( if_mul8430962117462786573at_nat @ ( J2 = K ) @ zero_z1048942125864253310at_nat @ ( H3 @ ( minus_minus_nat @ J2 @ ( suc @ zero_zero_nat ) ) ) ) )
% 9.17/5.38 @ ( set_ord_atMost_nat @ P4 ) )
% 9.17/5.38 = ( groups6857163185585827899at_nat
% 9.17/5.38 @ ^ [J2: nat] : ( if_mul8430962117462786573at_nat @ ( ord_less_nat @ J2 @ K ) @ ( G @ J2 ) @ ( H3 @ J2 ) )
% 9.17/5.38 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P4 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3869_sum_Ozero__middle,axiom,
% 9.17/5.38 ! [P4: nat,K: nat,G: nat > rat,H3: nat > rat] :
% 9.17/5.38 ( ( ord_less_eq_nat @ one_one_nat @ P4 )
% 9.17/5.38 => ( ( ord_less_eq_nat @ K @ P4 )
% 9.17/5.38 => ( ( groups2906978787729119204at_rat
% 9.17/5.38 @ ^ [J2: nat] : ( if_rat @ ( ord_less_nat @ J2 @ K ) @ ( G @ J2 ) @ ( if_rat @ ( J2 = K ) @ zero_zero_rat @ ( H3 @ ( minus_minus_nat @ J2 @ ( suc @ zero_zero_nat ) ) ) ) )
% 9.17/5.38 @ ( set_ord_atMost_nat @ P4 ) )
% 9.17/5.38 = ( groups2906978787729119204at_rat
% 9.17/5.38 @ ^ [J2: nat] : ( if_rat @ ( ord_less_nat @ J2 @ K ) @ ( G @ J2 ) @ ( H3 @ J2 ) )
% 9.17/5.38 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P4 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3870_sum_Ozero__middle,axiom,
% 9.17/5.38 ! [P4: nat,K: nat,G: nat > int,H3: nat > int] :
% 9.17/5.38 ( ( ord_less_eq_nat @ one_one_nat @ P4 )
% 9.17/5.38 => ( ( ord_less_eq_nat @ K @ P4 )
% 9.17/5.38 => ( ( groups3539618377306564664at_int
% 9.17/5.38 @ ^ [J2: nat] : ( if_int @ ( ord_less_nat @ J2 @ K ) @ ( G @ J2 ) @ ( if_int @ ( J2 = K ) @ zero_zero_int @ ( H3 @ ( minus_minus_nat @ J2 @ ( suc @ zero_zero_nat ) ) ) ) )
% 9.17/5.38 @ ( set_ord_atMost_nat @ P4 ) )
% 9.17/5.38 = ( groups3539618377306564664at_int
% 9.17/5.38 @ ^ [J2: nat] : ( if_int @ ( ord_less_nat @ J2 @ K ) @ ( G @ J2 ) @ ( H3 @ J2 ) )
% 9.17/5.38 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P4 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3871_sum_Ozero__middle,axiom,
% 9.17/5.38 ! [P4: nat,K: nat,G: nat > nat,H3: nat > nat] :
% 9.17/5.38 ( ( ord_less_eq_nat @ one_one_nat @ P4 )
% 9.17/5.38 => ( ( ord_less_eq_nat @ K @ P4 )
% 9.17/5.38 => ( ( groups3542108847815614940at_nat
% 9.17/5.38 @ ^ [J2: nat] : ( if_nat @ ( ord_less_nat @ J2 @ K ) @ ( G @ J2 ) @ ( if_nat @ ( J2 = K ) @ zero_zero_nat @ ( H3 @ ( minus_minus_nat @ J2 @ ( suc @ zero_zero_nat ) ) ) ) )
% 9.17/5.38 @ ( set_ord_atMost_nat @ P4 ) )
% 9.17/5.38 = ( groups3542108847815614940at_nat
% 9.17/5.38 @ ^ [J2: nat] : ( if_nat @ ( ord_less_nat @ J2 @ K ) @ ( G @ J2 ) @ ( H3 @ J2 ) )
% 9.17/5.38 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P4 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3872_and__minus__numerals_I3_J,axiom,
% 9.17/5.38 ! [M2: num,N2: num] :
% 9.17/5.38 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) )
% 9.17/5.38 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M2 @ ( bitM @ N2 ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3873_and__minus__numerals_I7_J,axiom,
% 9.17/5.38 ! [N2: num,M2: num] :
% 9.17/5.38 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) @ ( numeral_numeral_int @ M2 ) )
% 9.17/5.38 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M2 @ ( bitM @ N2 ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3874_and__minus__numerals_I4_J,axiom,
% 9.17/5.38 ! [M2: num,N2: num] :
% 9.17/5.38 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) )
% 9.17/5.38 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M2 @ ( bit0 @ N2 ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3875_and__minus__numerals_I8_J,axiom,
% 9.17/5.38 ! [N2: num,M2: num] :
% 9.17/5.38 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) @ ( numeral_numeral_int @ M2 ) )
% 9.17/5.38 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M2 @ ( bit0 @ N2 ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3876_gbinomial__partial__row__sum,axiom,
% 9.17/5.38 ! [A: rat,M2: nat] :
% 9.17/5.38 ( ( groups2906978787729119204at_rat
% 9.17/5.38 @ ^ [K4: nat] : ( times_times_rat @ ( gbinomial_rat @ A @ K4 ) @ ( minus_minus_rat @ ( divide_divide_rat @ A @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( semiri681578069525770553at_rat @ K4 ) ) )
% 9.17/5.38 @ ( set_ord_atMost_nat @ M2 ) )
% 9.17/5.38 = ( times_times_rat @ ( divide_divide_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M2 ) @ one_one_rat ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( gbinomial_rat @ A @ ( plus_plus_nat @ M2 @ one_one_nat ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3877_gbinomial__r__part__sum,axiom,
% 9.17/5.38 ! [M2: nat] :
% 9.17/5.38 ( ( groups2906978787729119204at_rat @ ( gbinomial_rat @ ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( semiri681578069525770553at_rat @ M2 ) ) @ one_one_rat ) ) @ ( set_ord_atMost_nat @ M2 ) )
% 9.17/5.38 = ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3878_and__num_Oelims,axiom,
% 9.17/5.38 ! [X: num,Xa: num,Y: option_num] :
% 9.17/5.38 ( ( ( bit_un7362597486090784418nd_num @ X @ Xa )
% 9.17/5.38 = Y )
% 9.17/5.38 => ( ( ( X = one )
% 9.17/5.38 => ( ( Xa = one )
% 9.17/5.38 => ( Y
% 9.17/5.38 != ( some_num @ one ) ) ) )
% 9.17/5.38 => ( ( ( X = one )
% 9.17/5.38 => ( ? [N: num] :
% 9.17/5.38 ( Xa
% 9.17/5.38 = ( bit0 @ N ) )
% 9.17/5.38 => ( Y != none_num ) ) )
% 9.17/5.38 => ( ( ( X = one )
% 9.17/5.38 => ( ? [N: num] :
% 9.17/5.38 ( Xa
% 9.17/5.38 = ( bit1 @ N ) )
% 9.17/5.38 => ( Y
% 9.17/5.38 != ( some_num @ one ) ) ) )
% 9.17/5.38 => ( ( ? [M5: num] :
% 9.17/5.38 ( X
% 9.17/5.38 = ( bit0 @ M5 ) )
% 9.17/5.38 => ( ( Xa = one )
% 9.17/5.38 => ( Y != none_num ) ) )
% 9.17/5.38 => ( ! [M5: num] :
% 9.17/5.38 ( ( X
% 9.17/5.38 = ( bit0 @ M5 ) )
% 9.17/5.38 => ! [N: num] :
% 9.17/5.38 ( ( Xa
% 9.17/5.38 = ( bit0 @ N ) )
% 9.17/5.38 => ( Y
% 9.17/5.38 != ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M5 @ N ) ) ) ) )
% 9.17/5.38 => ( ! [M5: num] :
% 9.17/5.38 ( ( X
% 9.17/5.38 = ( bit0 @ M5 ) )
% 9.17/5.38 => ! [N: num] :
% 9.17/5.38 ( ( Xa
% 9.17/5.38 = ( bit1 @ N ) )
% 9.17/5.38 => ( Y
% 9.17/5.38 != ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M5 @ N ) ) ) ) )
% 9.17/5.38 => ( ( ? [M5: num] :
% 9.17/5.38 ( X
% 9.17/5.38 = ( bit1 @ M5 ) )
% 9.17/5.38 => ( ( Xa = one )
% 9.17/5.38 => ( Y
% 9.17/5.38 != ( some_num @ one ) ) ) )
% 9.17/5.38 => ( ! [M5: num] :
% 9.17/5.38 ( ( X
% 9.17/5.38 = ( bit1 @ M5 ) )
% 9.17/5.38 => ! [N: num] :
% 9.17/5.38 ( ( Xa
% 9.17/5.38 = ( bit0 @ N ) )
% 9.17/5.38 => ( Y
% 9.17/5.38 != ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M5 @ N ) ) ) ) )
% 9.17/5.38 => ~ ! [M5: num] :
% 9.17/5.38 ( ( X
% 9.17/5.38 = ( bit1 @ M5 ) )
% 9.17/5.38 => ! [N: num] :
% 9.17/5.38 ( ( Xa
% 9.17/5.38 = ( bit1 @ N ) )
% 9.17/5.38 => ( Y
% 9.17/5.38 != ( case_o6005452278849405969um_num @ ( some_num @ one )
% 9.17/5.38 @ ^ [N8: num] : ( some_num @ ( bit1 @ N8 ) )
% 9.17/5.38 @ ( bit_un7362597486090784418nd_num @ M5 @ N ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3879_take__bit__Suc__from__most,axiom,
% 9.17/5.38 ! [N2: nat,K: int] :
% 9.17/5.38 ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ K )
% 9.17/5.38 = ( plus_plus_int @ ( times_times_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K @ N2 ) ) ) @ ( bit_se2923211474154528505it_int @ N2 @ K ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3880_gbinomial__0_I1_J,axiom,
% 9.17/5.38 ! [A: code_integer] :
% 9.17/5.38 ( ( gbinom8545251970709558553nteger @ A @ zero_zero_nat )
% 9.17/5.38 = one_one_Code_integer ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3881_gbinomial__0_I1_J,axiom,
% 9.17/5.38 ! [A: rat] :
% 9.17/5.38 ( ( gbinomial_rat @ A @ zero_zero_nat )
% 9.17/5.38 = one_one_rat ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3882_gbinomial__0_I1_J,axiom,
% 9.17/5.38 ! [A: nat] :
% 9.17/5.38 ( ( gbinomial_nat @ A @ zero_zero_nat )
% 9.17/5.38 = one_one_nat ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3883_gbinomial__0_I1_J,axiom,
% 9.17/5.38 ! [A: int] :
% 9.17/5.38 ( ( gbinomial_int @ A @ zero_zero_nat )
% 9.17/5.38 = one_one_int ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3884_and__nat__numerals_I2_J,axiom,
% 9.17/5.38 ! [Y: num] :
% 9.17/5.38 ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 9.17/5.38 = one_one_nat ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3885_and__nat__numerals_I4_J,axiom,
% 9.17/5.38 ! [X: num] :
% 9.17/5.38 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 9.17/5.38 = one_one_nat ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3886_bit__disjunctive__add__iff,axiom,
% 9.17/5.38 ! [A: int,B: int,N2: nat] :
% 9.17/5.38 ( ! [N: nat] :
% 9.17/5.38 ( ~ ( bit_se1146084159140164899it_int @ A @ N )
% 9.17/5.38 | ~ ( bit_se1146084159140164899it_int @ B @ N ) )
% 9.17/5.38 => ( ( bit_se1146084159140164899it_int @ ( plus_plus_int @ A @ B ) @ N2 )
% 9.17/5.38 = ( ( bit_se1146084159140164899it_int @ A @ N2 )
% 9.17/5.38 | ( bit_se1146084159140164899it_int @ B @ N2 ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3887_bit__disjunctive__add__iff,axiom,
% 9.17/5.38 ! [A: code_integer,B: code_integer,N2: nat] :
% 9.17/5.38 ( ! [N: nat] :
% 9.17/5.38 ( ~ ( bit_se9216721137139052372nteger @ A @ N )
% 9.17/5.38 | ~ ( bit_se9216721137139052372nteger @ B @ N ) )
% 9.17/5.38 => ( ( bit_se9216721137139052372nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ N2 )
% 9.17/5.38 = ( ( bit_se9216721137139052372nteger @ A @ N2 )
% 9.17/5.38 | ( bit_se9216721137139052372nteger @ B @ N2 ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3888_bit__disjunctive__add__iff,axiom,
% 9.17/5.38 ! [A: nat,B: nat,N2: nat] :
% 9.17/5.38 ( ! [N: nat] :
% 9.17/5.38 ( ~ ( bit_se1148574629649215175it_nat @ A @ N )
% 9.17/5.38 | ~ ( bit_se1148574629649215175it_nat @ B @ N ) )
% 9.17/5.38 => ( ( bit_se1148574629649215175it_nat @ ( plus_plus_nat @ A @ B ) @ N2 )
% 9.17/5.38 = ( ( bit_se1148574629649215175it_nat @ A @ N2 )
% 9.17/5.38 | ( bit_se1148574629649215175it_nat @ B @ N2 ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3889_bit__disjunctive__add__iff,axiom,
% 9.17/5.38 ! [A: code_natural,B: code_natural,N2: nat] :
% 9.17/5.38 ( ! [N: nat] :
% 9.17/5.38 ( ~ ( bit_se8040316288895769887atural @ A @ N )
% 9.17/5.38 | ~ ( bit_se8040316288895769887atural @ B @ N ) )
% 9.17/5.38 => ( ( bit_se8040316288895769887atural @ ( plus_p4538020629002901425atural @ A @ B ) @ N2 )
% 9.17/5.38 = ( ( bit_se8040316288895769887atural @ A @ N2 )
% 9.17/5.38 | ( bit_se8040316288895769887atural @ B @ N2 ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3890_bit__1__iff,axiom,
% 9.17/5.38 ! [N2: nat] :
% 9.17/5.38 ( ( bit_se1146084159140164899it_int @ one_one_int @ N2 )
% 9.17/5.38 = ( N2 = zero_zero_nat ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3891_bit__1__iff,axiom,
% 9.17/5.38 ! [N2: nat] :
% 9.17/5.38 ( ( bit_se9216721137139052372nteger @ one_one_Code_integer @ N2 )
% 9.17/5.38 = ( N2 = zero_zero_nat ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3892_bit__1__iff,axiom,
% 9.17/5.38 ! [N2: nat] :
% 9.17/5.38 ( ( bit_se1148574629649215175it_nat @ one_one_nat @ N2 )
% 9.17/5.38 = ( N2 = zero_zero_nat ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3893_bit__1__iff,axiom,
% 9.17/5.38 ! [N2: nat] :
% 9.17/5.38 ( ( bit_se8040316288895769887atural @ one_one_Code_natural @ N2 )
% 9.17/5.38 = ( N2 = zero_zero_nat ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3894_not__bit__1__Suc,axiom,
% 9.17/5.38 ! [N2: nat] :
% 9.17/5.38 ~ ( bit_se1146084159140164899it_int @ one_one_int @ ( suc @ N2 ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3895_not__bit__1__Suc,axiom,
% 9.17/5.38 ! [N2: nat] :
% 9.17/5.38 ~ ( bit_se9216721137139052372nteger @ one_one_Code_integer @ ( suc @ N2 ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3896_not__bit__1__Suc,axiom,
% 9.17/5.38 ! [N2: nat] :
% 9.17/5.38 ~ ( bit_se1148574629649215175it_nat @ one_one_nat @ ( suc @ N2 ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3897_not__bit__1__Suc,axiom,
% 9.17/5.38 ! [N2: nat] :
% 9.17/5.38 ~ ( bit_se8040316288895769887atural @ one_one_Code_natural @ ( suc @ N2 ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3898_bit__numeral__simps_I1_J,axiom,
% 9.17/5.38 ! [N2: num] :
% 9.17/5.38 ~ ( bit_se1146084159140164899it_int @ one_one_int @ ( numeral_numeral_nat @ N2 ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3899_bit__numeral__simps_I1_J,axiom,
% 9.17/5.38 ! [N2: num] :
% 9.17/5.38 ~ ( bit_se9216721137139052372nteger @ one_one_Code_integer @ ( numeral_numeral_nat @ N2 ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3900_bit__numeral__simps_I1_J,axiom,
% 9.17/5.38 ! [N2: num] :
% 9.17/5.38 ~ ( bit_se1148574629649215175it_nat @ one_one_nat @ ( numeral_numeral_nat @ N2 ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3901_bit__numeral__simps_I1_J,axiom,
% 9.17/5.38 ! [N2: num] :
% 9.17/5.38 ~ ( bit_se8040316288895769887atural @ one_one_Code_natural @ ( numeral_numeral_nat @ N2 ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3902_gbinomial__Suc__Suc,axiom,
% 9.17/5.38 ! [A: rat,K: nat] :
% 9.17/5.38 ( ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) )
% 9.17/5.38 = ( plus_plus_rat @ ( gbinomial_rat @ A @ K ) @ ( gbinomial_rat @ A @ ( suc @ K ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3903_and__integer_Oabs__eq,axiom,
% 9.17/5.38 ! [Xa: int,X: int] :
% 9.17/5.38 ( ( bit_se3949692690581998587nteger @ ( code_integer_of_int @ Xa ) @ ( code_integer_of_int @ X ) )
% 9.17/5.38 = ( code_integer_of_int @ ( bit_se725231765392027082nd_int @ Xa @ X ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3904_gbinomial__addition__formula,axiom,
% 9.17/5.38 ! [A: rat,K: nat] :
% 9.17/5.38 ( ( gbinomial_rat @ A @ ( suc @ K ) )
% 9.17/5.38 = ( plus_plus_rat @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ ( suc @ K ) ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3905_gbinomial__absorb__comp,axiom,
% 9.17/5.38 ! [A: rat,K: nat] :
% 9.17/5.38 ( ( times_times_rat @ ( minus_minus_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ ( gbinomial_rat @ A @ K ) )
% 9.17/5.38 = ( times_times_rat @ A @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3906_gbinomial__mult__1_H,axiom,
% 9.17/5.38 ! [A: rat,K: nat] :
% 9.17/5.38 ( ( times_times_rat @ ( gbinomial_rat @ A @ K ) @ A )
% 9.17/5.38 = ( plus_plus_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ K ) @ ( gbinomial_rat @ A @ K ) ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) @ ( gbinomial_rat @ A @ ( suc @ K ) ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3907_gbinomial__mult__1,axiom,
% 9.17/5.38 ! [A: rat,K: nat] :
% 9.17/5.38 ( ( times_times_rat @ A @ ( gbinomial_rat @ A @ K ) )
% 9.17/5.38 = ( plus_plus_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ K ) @ ( gbinomial_rat @ A @ K ) ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) @ ( gbinomial_rat @ A @ ( suc @ K ) ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3908_Suc__times__gbinomial,axiom,
% 9.17/5.38 ! [K: nat,A: rat] :
% 9.17/5.38 ( ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) @ ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) ) )
% 9.17/5.38 = ( times_times_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( gbinomial_rat @ A @ K ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3909_gbinomial__absorption,axiom,
% 9.17/5.38 ! [K: nat,A: rat] :
% 9.17/5.38 ( ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) @ ( gbinomial_rat @ A @ ( suc @ K ) ) )
% 9.17/5.38 = ( times_times_rat @ A @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3910_gbinomial__parallel__sum,axiom,
% 9.17/5.38 ! [A: rat,N2: nat] :
% 9.17/5.38 ( ( groups2906978787729119204at_rat
% 9.17/5.38 @ ^ [K4: nat] : ( gbinomial_rat @ ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ K4 ) ) @ K4 )
% 9.17/5.38 @ ( set_ord_atMost_nat @ N2 ) )
% 9.17/5.38 = ( gbinomial_rat @ ( plus_plus_rat @ ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ N2 ) ) @ one_one_rat ) @ N2 ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3911_gbinomial__rec,axiom,
% 9.17/5.38 ! [A: rat,K: nat] :
% 9.17/5.38 ( ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) )
% 9.17/5.38 = ( times_times_rat @ ( gbinomial_rat @ A @ K ) @ ( divide_divide_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3912_gbinomial__factors,axiom,
% 9.17/5.38 ! [A: rat,K: nat] :
% 9.17/5.38 ( ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) )
% 9.17/5.38 = ( times_times_rat @ ( divide_divide_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) ) @ ( gbinomial_rat @ A @ K ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3913_gbinomial__negated__upper,axiom,
% 9.17/5.38 ( gbinomial_rat
% 9.17/5.38 = ( ^ [A5: rat,K4: nat] : ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K4 ) @ ( gbinomial_rat @ ( minus_minus_rat @ ( minus_minus_rat @ ( semiri681578069525770553at_rat @ K4 ) @ A5 ) @ one_one_rat ) @ K4 ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3914_gbinomial__index__swap,axiom,
% 9.17/5.38 ! [K: nat,N2: nat] :
% 9.17/5.38 ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K ) @ ( gbinomial_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N2 ) ) @ one_one_rat ) @ K ) )
% 9.17/5.38 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 ) @ ( gbinomial_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ K ) ) @ one_one_rat ) @ N2 ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3915_int__bit__bound,axiom,
% 9.17/5.38 ! [K: int] :
% 9.17/5.38 ~ ! [N: nat] :
% 9.17/5.38 ( ! [M6: nat] :
% 9.17/5.38 ( ( ord_less_eq_nat @ N @ M6 )
% 9.17/5.38 => ( ( bit_se1146084159140164899it_int @ K @ M6 )
% 9.17/5.38 = ( bit_se1146084159140164899it_int @ K @ N ) ) )
% 9.17/5.38 => ~ ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.17/5.38 => ( ( bit_se1146084159140164899it_int @ K @ ( minus_minus_nat @ N @ one_one_nat ) )
% 9.17/5.38 = ( ~ ( bit_se1146084159140164899it_int @ K @ N ) ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3916_gbinomial__minus,axiom,
% 9.17/5.38 ! [A: rat,K: nat] :
% 9.17/5.38 ( ( gbinomial_rat @ ( uminus_uminus_rat @ A ) @ K )
% 9.17/5.38 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K ) @ ( gbinomial_rat @ ( minus_minus_rat @ ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ one_one_rat ) @ K ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3917_gbinomial__reduce__nat,axiom,
% 9.17/5.38 ! [K: nat,A: rat] :
% 9.17/5.38 ( ( ord_less_nat @ zero_zero_nat @ K )
% 9.17/5.38 => ( ( gbinomial_rat @ A @ K )
% 9.17/5.38 = ( plus_plus_rat @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3918_gbinomial__sum__lower__neg,axiom,
% 9.17/5.38 ! [A: rat,M2: nat] :
% 9.17/5.38 ( ( groups2906978787729119204at_rat
% 9.17/5.38 @ ^ [K4: nat] : ( times_times_rat @ ( gbinomial_rat @ A @ K4 ) @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K4 ) )
% 9.17/5.38 @ ( set_ord_atMost_nat @ M2 ) )
% 9.17/5.38 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ M2 ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ M2 ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3919_numeral__and__num,axiom,
% 9.17/5.38 ! [M2: num,N2: num] :
% 9.17/5.38 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N2 ) )
% 9.17/5.38 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_un7362597486090784418nd_num @ M2 @ N2 ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3920_numeral__and__num,axiom,
% 9.17/5.38 ! [M2: num,N2: num] :
% 9.17/5.38 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ N2 ) )
% 9.17/5.38 = ( case_option_nat_num @ zero_zero_nat @ numeral_numeral_nat @ ( bit_un7362597486090784418nd_num @ M2 @ N2 ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3921_numeral__and__num,axiom,
% 9.17/5.38 ! [M2: num,N2: num] :
% 9.17/5.38 ( ( bit_se3949692690581998587nteger @ ( numera6620942414471956472nteger @ M2 ) @ ( numera6620942414471956472nteger @ N2 ) )
% 9.17/5.38 = ( case_o356765784539232260er_num @ zero_z3403309356797280102nteger @ numera6620942414471956472nteger @ ( bit_un7362597486090784418nd_num @ M2 @ N2 ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3922_numeral__and__num,axiom,
% 9.17/5.38 ! [M2: num,N2: num] :
% 9.17/5.38 ( ( bit_se2773287842338716102atural @ ( numera5444537566228673987atural @ M2 ) @ ( numera5444537566228673987atural @ N2 ) )
% 9.17/5.38 = ( case_o5621594795226839503al_num @ zero_z2226904508553997617atural @ numera5444537566228673987atural @ ( bit_un7362597486090784418nd_num @ M2 @ N2 ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3923_gbinomial__sum__up__index,axiom,
% 9.17/5.38 ! [K: nat,N2: nat] :
% 9.17/5.38 ( ( groups2906978787729119204at_rat
% 9.17/5.38 @ ^ [J2: nat] : ( gbinomial_rat @ ( semiri681578069525770553at_rat @ J2 ) @ K )
% 9.17/5.38 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 9.17/5.38 = ( gbinomial_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N2 ) @ one_one_rat ) @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3924_gbinomial__partial__sum__poly,axiom,
% 9.17/5.38 ! [M2: nat,A: rat,X: rat,Y: rat] :
% 9.17/5.38 ( ( groups2906978787729119204at_rat
% 9.17/5.38 @ ^ [K4: nat] : ( times_times_rat @ ( times_times_rat @ ( gbinomial_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M2 ) @ A ) @ K4 ) @ ( power_power_rat @ X @ K4 ) ) @ ( power_power_rat @ Y @ ( minus_minus_nat @ M2 @ K4 ) ) )
% 9.17/5.38 @ ( set_ord_atMost_nat @ M2 ) )
% 9.17/5.38 = ( groups2906978787729119204at_rat
% 9.17/5.38 @ ^ [K4: nat] : ( times_times_rat @ ( times_times_rat @ ( gbinomial_rat @ ( uminus_uminus_rat @ A ) @ K4 ) @ ( power_power_rat @ ( uminus_uminus_rat @ X ) @ K4 ) ) @ ( power_power_rat @ ( plus_plus_rat @ X @ Y ) @ ( minus_minus_nat @ M2 @ K4 ) ) )
% 9.17/5.38 @ ( set_ord_atMost_nat @ M2 ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3925_even__bit__succ__iff,axiom,
% 9.17/5.38 ! [A: int,N2: nat] :
% 9.17/5.38 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 9.17/5.38 => ( ( bit_se1146084159140164899it_int @ ( plus_plus_int @ one_one_int @ A ) @ N2 )
% 9.17/5.38 = ( ( bit_se1146084159140164899it_int @ A @ N2 )
% 9.17/5.38 | ( N2 = zero_zero_nat ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3926_even__bit__succ__iff,axiom,
% 9.17/5.38 ! [A: code_integer,N2: nat] :
% 9.17/5.38 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 9.17/5.38 => ( ( bit_se9216721137139052372nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ N2 )
% 9.17/5.38 = ( ( bit_se9216721137139052372nteger @ A @ N2 )
% 9.17/5.38 | ( N2 = zero_zero_nat ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3927_even__bit__succ__iff,axiom,
% 9.17/5.38 ! [A: nat,N2: nat] :
% 9.17/5.38 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 9.17/5.38 => ( ( bit_se1148574629649215175it_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ N2 )
% 9.17/5.38 = ( ( bit_se1148574629649215175it_nat @ A @ N2 )
% 9.17/5.38 | ( N2 = zero_zero_nat ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3928_even__bit__succ__iff,axiom,
% 9.17/5.38 ! [A: code_natural,N2: nat] :
% 9.17/5.38 ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 9.17/5.38 => ( ( bit_se8040316288895769887atural @ ( plus_p4538020629002901425atural @ one_one_Code_natural @ A ) @ N2 )
% 9.17/5.38 = ( ( bit_se8040316288895769887atural @ A @ N2 )
% 9.17/5.38 | ( N2 = zero_zero_nat ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3929_odd__bit__iff__bit__pred,axiom,
% 9.17/5.38 ! [A: int,N2: nat] :
% 9.17/5.38 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 9.17/5.38 => ( ( bit_se1146084159140164899it_int @ A @ N2 )
% 9.17/5.38 = ( ( bit_se1146084159140164899it_int @ ( minus_minus_int @ A @ one_one_int ) @ N2 )
% 9.17/5.38 | ( N2 = zero_zero_nat ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3930_odd__bit__iff__bit__pred,axiom,
% 9.17/5.38 ! [A: code_integer,N2: nat] :
% 9.17/5.38 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 9.17/5.38 => ( ( bit_se9216721137139052372nteger @ A @ N2 )
% 9.17/5.38 = ( ( bit_se9216721137139052372nteger @ ( minus_8373710615458151222nteger @ A @ one_one_Code_integer ) @ N2 )
% 9.17/5.38 | ( N2 = zero_zero_nat ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3931_odd__bit__iff__bit__pred,axiom,
% 9.17/5.38 ! [A: nat,N2: nat] :
% 9.17/5.38 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 9.17/5.38 => ( ( bit_se1148574629649215175it_nat @ A @ N2 )
% 9.17/5.38 = ( ( bit_se1148574629649215175it_nat @ ( minus_minus_nat @ A @ one_one_nat ) @ N2 )
% 9.17/5.38 | ( N2 = zero_zero_nat ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3932_odd__bit__iff__bit__pred,axiom,
% 9.17/5.38 ! [A: code_natural,N2: nat] :
% 9.17/5.38 ( ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 9.17/5.38 => ( ( bit_se8040316288895769887atural @ A @ N2 )
% 9.17/5.38 = ( ( bit_se8040316288895769887atural @ ( minus_7197305767214868737atural @ A @ one_one_Code_natural ) @ N2 )
% 9.17/5.38 | ( N2 = zero_zero_nat ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3933_and__num_Osimps_I9_J,axiom,
% 9.17/5.38 ! [M2: num,N2: num] :
% 9.17/5.38 ( ( bit_un7362597486090784418nd_num @ ( bit1 @ M2 ) @ ( bit1 @ N2 ) )
% 9.17/5.38 = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 9.17/5.38 @ ^ [N8: num] : ( some_num @ ( bit1 @ N8 ) )
% 9.17/5.38 @ ( bit_un7362597486090784418nd_num @ M2 @ N2 ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3934_gbinomial__absorption_H,axiom,
% 9.17/5.38 ! [K: nat,A: rat] :
% 9.17/5.38 ( ( ord_less_nat @ zero_zero_nat @ K )
% 9.17/5.38 => ( ( gbinomial_rat @ A @ K )
% 9.17/5.38 = ( times_times_rat @ ( divide_divide_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3935_gbinomial__partial__sum__poly__xpos,axiom,
% 9.17/5.38 ! [M2: nat,A: rat,X: rat,Y: rat] :
% 9.17/5.38 ( ( groups2906978787729119204at_rat
% 9.17/5.38 @ ^ [K4: nat] : ( times_times_rat @ ( times_times_rat @ ( gbinomial_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M2 ) @ A ) @ K4 ) @ ( power_power_rat @ X @ K4 ) ) @ ( power_power_rat @ Y @ ( minus_minus_nat @ M2 @ K4 ) ) )
% 9.17/5.38 @ ( set_ord_atMost_nat @ M2 ) )
% 9.17/5.38 = ( groups2906978787729119204at_rat
% 9.17/5.38 @ ^ [K4: nat] : ( times_times_rat @ ( times_times_rat @ ( gbinomial_rat @ ( minus_minus_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ K4 ) @ A ) @ one_one_rat ) @ K4 ) @ ( power_power_rat @ X @ K4 ) ) @ ( power_power_rat @ ( plus_plus_rat @ X @ Y ) @ ( minus_minus_nat @ M2 @ K4 ) ) )
% 9.17/5.38 @ ( set_ord_atMost_nat @ M2 ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3936_gbinomial__sum__nat__pow2,axiom,
% 9.17/5.38 ! [M2: nat] :
% 9.17/5.38 ( ( groups2906978787729119204at_rat
% 9.17/5.38 @ ^ [K4: nat] : ( divide_divide_rat @ ( gbinomial_rat @ ( semiri681578069525770553at_rat @ ( plus_plus_nat @ M2 @ K4 ) ) @ K4 ) @ ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ K4 ) )
% 9.17/5.38 @ ( set_ord_atMost_nat @ M2 ) )
% 9.17/5.38 = ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ M2 ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3937_bit__sum__mult__2__cases,axiom,
% 9.17/5.38 ! [A: int,B: int,N2: nat] :
% 9.17/5.38 ( ! [J3: nat] :
% 9.17/5.38 ~ ( bit_se1146084159140164899it_int @ A @ ( suc @ J3 ) )
% 9.17/5.38 => ( ( bit_se1146084159140164899it_int @ ( plus_plus_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ N2 )
% 9.17/5.38 = ( ( ( N2 = zero_zero_nat )
% 9.17/5.38 => ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 9.17/5.38 & ( ( N2 != zero_zero_nat )
% 9.17/5.38 => ( bit_se1146084159140164899it_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) @ N2 ) ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3938_bit__sum__mult__2__cases,axiom,
% 9.17/5.38 ! [A: code_integer,B: code_integer,N2: nat] :
% 9.17/5.38 ( ! [J3: nat] :
% 9.17/5.38 ~ ( bit_se9216721137139052372nteger @ A @ ( suc @ J3 ) )
% 9.17/5.38 => ( ( bit_se9216721137139052372nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ N2 )
% 9.17/5.38 = ( ( ( N2 = zero_zero_nat )
% 9.17/5.38 => ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 9.17/5.38 & ( ( N2 != zero_zero_nat )
% 9.17/5.38 => ( bit_se9216721137139052372nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) @ N2 ) ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3939_bit__sum__mult__2__cases,axiom,
% 9.17/5.38 ! [A: nat,B: nat,N2: nat] :
% 9.17/5.38 ( ! [J3: nat] :
% 9.17/5.38 ~ ( bit_se1148574629649215175it_nat @ A @ ( suc @ J3 ) )
% 9.17/5.38 => ( ( bit_se1148574629649215175it_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ N2 )
% 9.17/5.38 = ( ( ( N2 = zero_zero_nat )
% 9.17/5.38 => ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 9.17/5.38 & ( ( N2 != zero_zero_nat )
% 9.17/5.38 => ( bit_se1148574629649215175it_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) @ N2 ) ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3940_bit__sum__mult__2__cases,axiom,
% 9.17/5.38 ! [A: code_natural,B: code_natural,N2: nat] :
% 9.17/5.38 ( ! [J3: nat] :
% 9.17/5.38 ~ ( bit_se8040316288895769887atural @ A @ ( suc @ J3 ) )
% 9.17/5.38 => ( ( bit_se8040316288895769887atural @ ( plus_p4538020629002901425atural @ A @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ B ) ) @ N2 )
% 9.17/5.38 = ( ( ( N2 = zero_zero_nat )
% 9.17/5.38 => ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A ) )
% 9.17/5.38 & ( ( N2 != zero_zero_nat )
% 9.17/5.38 => ( bit_se8040316288895769887atural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ B ) @ N2 ) ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3941_and__not__num_Osimps_I8_J,axiom,
% 9.17/5.38 ! [M2: num,N2: num] :
% 9.17/5.38 ( ( bit_and_not_num @ ( bit1 @ M2 ) @ ( bit0 @ N2 ) )
% 9.17/5.38 = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 9.17/5.38 @ ^ [N8: num] : ( some_num @ ( bit1 @ N8 ) )
% 9.17/5.38 @ ( bit_and_not_num @ M2 @ N2 ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3942_bit__rec,axiom,
% 9.17/5.38 ( bit_se1146084159140164899it_int
% 9.17/5.38 = ( ^ [A5: int,N4: nat] :
% 9.17/5.38 ( ( ( N4 = zero_zero_nat )
% 9.17/5.38 => ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A5 ) )
% 9.17/5.38 & ( ( N4 != zero_zero_nat )
% 9.17/5.38 => ( bit_se1146084159140164899it_int @ ( divide_divide_int @ A5 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( minus_minus_nat @ N4 @ one_one_nat ) ) ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3943_bit__rec,axiom,
% 9.17/5.38 ( bit_se9216721137139052372nteger
% 9.17/5.38 = ( ^ [A5: code_integer,N4: nat] :
% 9.17/5.38 ( ( ( N4 = zero_zero_nat )
% 9.17/5.38 => ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A5 ) )
% 9.17/5.38 & ( ( N4 != zero_zero_nat )
% 9.17/5.38 => ( bit_se9216721137139052372nteger @ ( divide6298287555418463151nteger @ A5 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( minus_minus_nat @ N4 @ one_one_nat ) ) ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3944_bit__rec,axiom,
% 9.17/5.38 ( bit_se1148574629649215175it_nat
% 9.17/5.38 = ( ^ [A5: nat,N4: nat] :
% 9.17/5.38 ( ( ( N4 = zero_zero_nat )
% 9.17/5.38 => ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A5 ) )
% 9.17/5.38 & ( ( N4 != zero_zero_nat )
% 9.17/5.38 => ( bit_se1148574629649215175it_nat @ ( divide_divide_nat @ A5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( minus_minus_nat @ N4 @ one_one_nat ) ) ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3945_bit__rec,axiom,
% 9.17/5.38 ( bit_se8040316288895769887atural
% 9.17/5.38 = ( ^ [A5: code_natural,N4: nat] :
% 9.17/5.38 ( ( ( N4 = zero_zero_nat )
% 9.17/5.38 => ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A5 ) )
% 9.17/5.38 & ( ( N4 != zero_zero_nat )
% 9.17/5.38 => ( bit_se8040316288895769887atural @ ( divide5121882707175180666atural @ A5 @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) @ ( minus_minus_nat @ N4 @ one_one_nat ) ) ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3946_and__nat__unfold,axiom,
% 9.17/5.38 ( bit_se727722235901077358nd_nat
% 9.17/5.38 = ( ^ [M: nat,N4: nat] :
% 9.17/5.38 ( if_nat
% 9.17/5.38 @ ( ( M = zero_zero_nat )
% 9.17/5.38 | ( N4 = zero_zero_nat ) )
% 9.17/5.38 @ zero_zero_nat
% 9.17/5.38 @ ( plus_plus_nat @ ( times_times_nat @ ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( divide_divide_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3947_and__nat__rec,axiom,
% 9.17/5.38 ( bit_se727722235901077358nd_nat
% 9.17/5.38 = ( ^ [M: nat,N4: nat] :
% 9.17/5.38 ( plus_plus_nat
% 9.17/5.38 @ ( zero_n2687167440665602831ol_nat
% 9.17/5.38 @ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
% 9.17/5.38 & ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) )
% 9.17/5.38 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( divide_divide_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3948_set__bit__eq,axiom,
% 9.17/5.38 ( bit_se7879613467334960850it_int
% 9.17/5.38 = ( ^ [N4: nat,K4: int] :
% 9.17/5.38 ( plus_plus_int @ K4
% 9.17/5.38 @ ( times_times_int
% 9.17/5.38 @ ( zero_n2684676970156552555ol_int
% 9.17/5.38 @ ~ ( bit_se1146084159140164899it_int @ K4 @ N4 ) )
% 9.17/5.38 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N4 ) ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3949_and__not__num_Oelims,axiom,
% 9.17/5.38 ! [X: num,Xa: num,Y: option_num] :
% 9.17/5.38 ( ( ( bit_and_not_num @ X @ Xa )
% 9.17/5.38 = Y )
% 9.17/5.38 => ( ( ( X = one )
% 9.17/5.38 => ( ( Xa = one )
% 9.17/5.38 => ( Y != none_num ) ) )
% 9.17/5.38 => ( ( ( X = one )
% 9.17/5.38 => ( ? [N: num] :
% 9.17/5.38 ( Xa
% 9.17/5.38 = ( bit0 @ N ) )
% 9.17/5.38 => ( Y
% 9.17/5.38 != ( some_num @ one ) ) ) )
% 9.17/5.38 => ( ( ( X = one )
% 9.17/5.38 => ( ? [N: num] :
% 9.17/5.38 ( Xa
% 9.17/5.38 = ( bit1 @ N ) )
% 9.17/5.38 => ( Y != none_num ) ) )
% 9.17/5.38 => ( ! [M5: num] :
% 9.17/5.38 ( ( X
% 9.17/5.38 = ( bit0 @ M5 ) )
% 9.17/5.38 => ( ( Xa = one )
% 9.17/5.38 => ( Y
% 9.17/5.38 != ( some_num @ ( bit0 @ M5 ) ) ) ) )
% 9.17/5.38 => ( ! [M5: num] :
% 9.17/5.38 ( ( X
% 9.17/5.38 = ( bit0 @ M5 ) )
% 9.17/5.38 => ! [N: num] :
% 9.17/5.38 ( ( Xa
% 9.17/5.38 = ( bit0 @ N ) )
% 9.17/5.38 => ( Y
% 9.17/5.38 != ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M5 @ N ) ) ) ) )
% 9.17/5.38 => ( ! [M5: num] :
% 9.17/5.38 ( ( X
% 9.17/5.38 = ( bit0 @ M5 ) )
% 9.17/5.38 => ! [N: num] :
% 9.17/5.38 ( ( Xa
% 9.17/5.38 = ( bit1 @ N ) )
% 9.17/5.38 => ( Y
% 9.17/5.38 != ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M5 @ N ) ) ) ) )
% 9.17/5.38 => ( ! [M5: num] :
% 9.17/5.38 ( ( X
% 9.17/5.38 = ( bit1 @ M5 ) )
% 9.17/5.38 => ( ( Xa = one )
% 9.17/5.38 => ( Y
% 9.17/5.38 != ( some_num @ ( bit0 @ M5 ) ) ) ) )
% 9.17/5.38 => ( ! [M5: num] :
% 9.17/5.38 ( ( X
% 9.17/5.38 = ( bit1 @ M5 ) )
% 9.17/5.38 => ! [N: num] :
% 9.17/5.38 ( ( Xa
% 9.17/5.38 = ( bit0 @ N ) )
% 9.17/5.38 => ( Y
% 9.17/5.38 != ( case_o6005452278849405969um_num @ ( some_num @ one )
% 9.17/5.38 @ ^ [N8: num] : ( some_num @ ( bit1 @ N8 ) )
% 9.17/5.38 @ ( bit_and_not_num @ M5 @ N ) ) ) ) )
% 9.17/5.38 => ~ ! [M5: num] :
% 9.17/5.38 ( ( X
% 9.17/5.38 = ( bit1 @ M5 ) )
% 9.17/5.38 => ! [N: num] :
% 9.17/5.38 ( ( Xa
% 9.17/5.38 = ( bit1 @ N ) )
% 9.17/5.38 => ( Y
% 9.17/5.38 != ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M5 @ N ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3950_and__not__num_Opelims,axiom,
% 9.17/5.38 ! [X: num,Xa: num,Y: option_num] :
% 9.17/5.38 ( ( ( bit_and_not_num @ X @ Xa )
% 9.17/5.38 = Y )
% 9.17/5.38 => ( ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ X @ Xa ) )
% 9.17/5.38 => ( ( ( X = one )
% 9.17/5.38 => ( ( Xa = one )
% 9.17/5.38 => ( ( Y = none_num )
% 9.17/5.38 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 9.17/5.38 => ( ( ( X = one )
% 9.17/5.38 => ! [N: num] :
% 9.17/5.38 ( ( Xa
% 9.17/5.38 = ( bit0 @ N ) )
% 9.17/5.38 => ( ( Y
% 9.17/5.38 = ( some_num @ one ) )
% 9.17/5.38 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ one @ ( bit0 @ N ) ) ) ) ) )
% 9.17/5.38 => ( ( ( X = one )
% 9.17/5.38 => ! [N: num] :
% 9.17/5.38 ( ( Xa
% 9.17/5.38 = ( bit1 @ N ) )
% 9.17/5.38 => ( ( Y = none_num )
% 9.17/5.38 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ one @ ( bit1 @ N ) ) ) ) ) )
% 9.17/5.38 => ( ! [M5: num] :
% 9.17/5.38 ( ( X
% 9.17/5.38 = ( bit0 @ M5 ) )
% 9.17/5.38 => ( ( Xa = one )
% 9.17/5.38 => ( ( Y
% 9.17/5.38 = ( some_num @ ( bit0 @ M5 ) ) )
% 9.17/5.38 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ one ) ) ) ) )
% 9.17/5.38 => ( ! [M5: num] :
% 9.17/5.38 ( ( X
% 9.17/5.38 = ( bit0 @ M5 ) )
% 9.17/5.38 => ! [N: num] :
% 9.17/5.38 ( ( Xa
% 9.17/5.38 = ( bit0 @ N ) )
% 9.17/5.38 => ( ( Y
% 9.17/5.38 = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M5 @ N ) ) )
% 9.17/5.38 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ ( bit0 @ N ) ) ) ) ) )
% 9.17/5.38 => ( ! [M5: num] :
% 9.17/5.38 ( ( X
% 9.17/5.38 = ( bit0 @ M5 ) )
% 9.17/5.38 => ! [N: num] :
% 9.17/5.38 ( ( Xa
% 9.17/5.38 = ( bit1 @ N ) )
% 9.17/5.38 => ( ( Y
% 9.17/5.38 = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M5 @ N ) ) )
% 9.17/5.38 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ ( bit1 @ N ) ) ) ) ) )
% 9.17/5.38 => ( ! [M5: num] :
% 9.17/5.38 ( ( X
% 9.17/5.38 = ( bit1 @ M5 ) )
% 9.17/5.38 => ( ( Xa = one )
% 9.17/5.38 => ( ( Y
% 9.17/5.38 = ( some_num @ ( bit0 @ M5 ) ) )
% 9.17/5.38 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ one ) ) ) ) )
% 9.17/5.38 => ( ! [M5: num] :
% 9.17/5.38 ( ( X
% 9.17/5.38 = ( bit1 @ M5 ) )
% 9.17/5.38 => ! [N: num] :
% 9.17/5.38 ( ( Xa
% 9.17/5.38 = ( bit0 @ N ) )
% 9.17/5.38 => ( ( Y
% 9.17/5.38 = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 9.17/5.38 @ ^ [N8: num] : ( some_num @ ( bit1 @ N8 ) )
% 9.17/5.38 @ ( bit_and_not_num @ M5 @ N ) ) )
% 9.17/5.38 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ ( bit0 @ N ) ) ) ) ) )
% 9.17/5.38 => ~ ! [M5: num] :
% 9.17/5.38 ( ( X
% 9.17/5.38 = ( bit1 @ M5 ) )
% 9.17/5.38 => ! [N: num] :
% 9.17/5.38 ( ( Xa
% 9.17/5.38 = ( bit1 @ N ) )
% 9.17/5.38 => ( ( Y
% 9.17/5.38 = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M5 @ N ) ) )
% 9.17/5.38 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ ( bit1 @ N ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3951_and__num_Opelims,axiom,
% 9.17/5.38 ! [X: num,Xa: num,Y: option_num] :
% 9.17/5.38 ( ( ( bit_un7362597486090784418nd_num @ X @ Xa )
% 9.17/5.38 = Y )
% 9.17/5.38 => ( ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ X @ Xa ) )
% 9.17/5.38 => ( ( ( X = one )
% 9.17/5.38 => ( ( Xa = one )
% 9.17/5.38 => ( ( Y
% 9.17/5.38 = ( some_num @ one ) )
% 9.17/5.38 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 9.17/5.38 => ( ( ( X = one )
% 9.17/5.38 => ! [N: num] :
% 9.17/5.38 ( ( Xa
% 9.17/5.38 = ( bit0 @ N ) )
% 9.17/5.38 => ( ( Y = none_num )
% 9.17/5.38 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ one @ ( bit0 @ N ) ) ) ) ) )
% 9.17/5.38 => ( ( ( X = one )
% 9.17/5.38 => ! [N: num] :
% 9.17/5.38 ( ( Xa
% 9.17/5.38 = ( bit1 @ N ) )
% 9.17/5.38 => ( ( Y
% 9.17/5.38 = ( some_num @ one ) )
% 9.17/5.38 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ one @ ( bit1 @ N ) ) ) ) ) )
% 9.17/5.38 => ( ! [M5: num] :
% 9.17/5.38 ( ( X
% 9.17/5.38 = ( bit0 @ M5 ) )
% 9.17/5.38 => ( ( Xa = one )
% 9.17/5.38 => ( ( Y = none_num )
% 9.17/5.38 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ one ) ) ) ) )
% 9.17/5.38 => ( ! [M5: num] :
% 9.17/5.38 ( ( X
% 9.17/5.38 = ( bit0 @ M5 ) )
% 9.17/5.38 => ! [N: num] :
% 9.17/5.38 ( ( Xa
% 9.17/5.38 = ( bit0 @ N ) )
% 9.17/5.38 => ( ( Y
% 9.17/5.38 = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M5 @ N ) ) )
% 9.17/5.38 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ ( bit0 @ N ) ) ) ) ) )
% 9.17/5.38 => ( ! [M5: num] :
% 9.17/5.38 ( ( X
% 9.17/5.38 = ( bit0 @ M5 ) )
% 9.17/5.38 => ! [N: num] :
% 9.17/5.38 ( ( Xa
% 9.17/5.38 = ( bit1 @ N ) )
% 9.17/5.38 => ( ( Y
% 9.17/5.38 = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M5 @ N ) ) )
% 9.17/5.38 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ ( bit1 @ N ) ) ) ) ) )
% 9.17/5.38 => ( ! [M5: num] :
% 9.17/5.38 ( ( X
% 9.17/5.38 = ( bit1 @ M5 ) )
% 9.17/5.38 => ( ( Xa = one )
% 9.17/5.38 => ( ( Y
% 9.17/5.38 = ( some_num @ one ) )
% 9.17/5.38 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ one ) ) ) ) )
% 9.17/5.38 => ( ! [M5: num] :
% 9.17/5.38 ( ( X
% 9.17/5.38 = ( bit1 @ M5 ) )
% 9.17/5.38 => ! [N: num] :
% 9.17/5.38 ( ( Xa
% 9.17/5.38 = ( bit0 @ N ) )
% 9.17/5.38 => ( ( Y
% 9.17/5.38 = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M5 @ N ) ) )
% 9.17/5.38 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ ( bit0 @ N ) ) ) ) ) )
% 9.17/5.38 => ~ ! [M5: num] :
% 9.17/5.38 ( ( X
% 9.17/5.38 = ( bit1 @ M5 ) )
% 9.17/5.38 => ! [N: num] :
% 9.17/5.38 ( ( Xa
% 9.17/5.38 = ( bit1 @ N ) )
% 9.17/5.38 => ( ( Y
% 9.17/5.38 = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 9.17/5.38 @ ^ [N8: num] : ( some_num @ ( bit1 @ N8 ) )
% 9.17/5.38 @ ( bit_un7362597486090784418nd_num @ M5 @ N ) ) )
% 9.17/5.38 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ ( bit1 @ N ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3952_gbinomial__code,axiom,
% 9.17/5.38 ( gbinomial_rat
% 9.17/5.38 = ( ^ [A5: rat,K4: nat] :
% 9.17/5.38 ( if_rat @ ( K4 = zero_zero_nat ) @ one_one_rat
% 9.17/5.38 @ ( divide_divide_rat
% 9.17/5.38 @ ( set_fo1949268297981939178at_rat
% 9.17/5.38 @ ^ [L3: nat] : ( times_times_rat @ ( minus_minus_rat @ A5 @ ( semiri681578069525770553at_rat @ L3 ) ) )
% 9.17/5.38 @ zero_zero_nat
% 9.17/5.38 @ ( minus_minus_nat @ K4 @ one_one_nat )
% 9.17/5.38 @ one_one_rat )
% 9.17/5.38 @ ( semiri773545260158071498ct_rat @ K4 ) ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3953_xor__num_Oelims,axiom,
% 9.17/5.38 ! [X: num,Xa: num,Y: option_num] :
% 9.17/5.38 ( ( ( bit_un2480387367778600638or_num @ X @ Xa )
% 9.17/5.38 = Y )
% 9.17/5.38 => ( ( ( X = one )
% 9.17/5.38 => ( ( Xa = one )
% 9.17/5.38 => ( Y != none_num ) ) )
% 9.17/5.38 => ( ( ( X = one )
% 9.17/5.38 => ! [N: num] :
% 9.17/5.38 ( ( Xa
% 9.17/5.38 = ( bit0 @ N ) )
% 9.17/5.38 => ( Y
% 9.17/5.38 != ( some_num @ ( bit1 @ N ) ) ) ) )
% 9.17/5.38 => ( ( ( X = one )
% 9.17/5.38 => ! [N: num] :
% 9.17/5.38 ( ( Xa
% 9.17/5.38 = ( bit1 @ N ) )
% 9.17/5.38 => ( Y
% 9.17/5.38 != ( some_num @ ( bit0 @ N ) ) ) ) )
% 9.17/5.38 => ( ! [M5: num] :
% 9.17/5.38 ( ( X
% 9.17/5.38 = ( bit0 @ M5 ) )
% 9.17/5.38 => ( ( Xa = one )
% 9.17/5.38 => ( Y
% 9.17/5.38 != ( some_num @ ( bit1 @ M5 ) ) ) ) )
% 9.17/5.38 => ( ! [M5: num] :
% 9.17/5.38 ( ( X
% 9.17/5.38 = ( bit0 @ M5 ) )
% 9.17/5.38 => ! [N: num] :
% 9.17/5.38 ( ( Xa
% 9.17/5.38 = ( bit0 @ N ) )
% 9.17/5.38 => ( Y
% 9.17/5.38 != ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M5 @ N ) ) ) ) )
% 9.17/5.38 => ( ! [M5: num] :
% 9.17/5.38 ( ( X
% 9.17/5.38 = ( bit0 @ M5 ) )
% 9.17/5.38 => ! [N: num] :
% 9.17/5.38 ( ( Xa
% 9.17/5.38 = ( bit1 @ N ) )
% 9.17/5.38 => ( Y
% 9.17/5.38 != ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M5 @ N ) ) ) ) ) )
% 9.17/5.38 => ( ! [M5: num] :
% 9.17/5.38 ( ( X
% 9.17/5.38 = ( bit1 @ M5 ) )
% 9.17/5.38 => ( ( Xa = one )
% 9.17/5.38 => ( Y
% 9.17/5.38 != ( some_num @ ( bit0 @ M5 ) ) ) ) )
% 9.17/5.38 => ( ! [M5: num] :
% 9.17/5.38 ( ( X
% 9.17/5.38 = ( bit1 @ M5 ) )
% 9.17/5.38 => ! [N: num] :
% 9.17/5.38 ( ( Xa
% 9.17/5.38 = ( bit0 @ N ) )
% 9.17/5.38 => ( Y
% 9.17/5.38 != ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M5 @ N ) ) ) ) ) )
% 9.17/5.38 => ~ ! [M5: num] :
% 9.17/5.38 ( ( X
% 9.17/5.38 = ( bit1 @ M5 ) )
% 9.17/5.38 => ! [N: num] :
% 9.17/5.38 ( ( Xa
% 9.17/5.38 = ( bit1 @ N ) )
% 9.17/5.38 => ( Y
% 9.17/5.38 != ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M5 @ N ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3954_choose__alternating__sum,axiom,
% 9.17/5.38 ! [N2: nat] :
% 9.17/5.38 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 9.17/5.38 => ( ( groups2906978787729119204at_rat
% 9.17/5.38 @ ^ [I3: nat] : ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ I3 ) @ ( semiri681578069525770553at_rat @ ( binomial @ N2 @ I3 ) ) )
% 9.17/5.38 @ ( set_ord_atMost_nat @ N2 ) )
% 9.17/5.38 = zero_zero_rat ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3955_choose__alternating__sum,axiom,
% 9.17/5.38 ! [N2: nat] :
% 9.17/5.38 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 9.17/5.38 => ( ( groups3539618377306564664at_int
% 9.17/5.38 @ ^ [I3: nat] : ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ I3 ) @ ( semiri1314217659103216013at_int @ ( binomial @ N2 @ I3 ) ) )
% 9.17/5.38 @ ( set_ord_atMost_nat @ N2 ) )
% 9.17/5.38 = zero_zero_int ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3956_choose__alternating__sum,axiom,
% 9.17/5.38 ! [N2: nat] :
% 9.17/5.38 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 9.17/5.38 => ( ( groups7501900531339628137nteger
% 9.17/5.38 @ ^ [I3: nat] : ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ I3 ) @ ( semiri4939895301339042750nteger @ ( binomial @ N2 @ I3 ) ) )
% 9.17/5.38 @ ( set_ord_atMost_nat @ N2 ) )
% 9.17/5.38 = zero_z3403309356797280102nteger ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3957_choose__linear__sum,axiom,
% 9.17/5.38 ! [N2: nat] :
% 9.17/5.38 ( ( groups3542108847815614940at_nat
% 9.17/5.38 @ ^ [I3: nat] : ( times_times_nat @ I3 @ ( binomial @ N2 @ I3 ) )
% 9.17/5.38 @ ( set_ord_atMost_nat @ N2 ) )
% 9.17/5.38 = ( times_times_nat @ N2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3958_binomial__r__part__sum,axiom,
% 9.17/5.38 ! [M2: nat] :
% 9.17/5.38 ( ( groups3542108847815614940at_nat @ ( binomial @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ one_one_nat ) ) @ ( set_ord_atMost_nat @ M2 ) )
% 9.17/5.38 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3959_sum_Otriangle__reindex,axiom,
% 9.17/5.38 ! [G: nat > nat > nat,N2: nat] :
% 9.17/5.38 ( ( groups977919841031483927at_nat @ ( produc6842872674320459806at_nat @ G )
% 9.17/5.38 @ ( collec3392354462482085612at_nat
% 9.17/5.38 @ ( produc6081775807080527818_nat_o
% 9.17/5.38 @ ^ [I3: nat,J2: nat] : ( ord_less_nat @ ( plus_plus_nat @ I3 @ J2 ) @ N2 ) ) ) )
% 9.17/5.38 = ( groups3542108847815614940at_nat
% 9.17/5.38 @ ^ [K4: nat] :
% 9.17/5.38 ( groups3542108847815614940at_nat
% 9.17/5.38 @ ^ [I3: nat] : ( G @ I3 @ ( minus_minus_nat @ K4 @ I3 ) )
% 9.17/5.38 @ ( set_ord_atMost_nat @ K4 ) )
% 9.17/5.38 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3960_lessThan__eq__iff,axiom,
% 9.17/5.38 ! [X: nat,Y: nat] :
% 9.17/5.38 ( ( ( set_ord_lessThan_nat @ X )
% 9.17/5.38 = ( set_ord_lessThan_nat @ Y ) )
% 9.17/5.38 = ( X = Y ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3961_lessThan__iff,axiom,
% 9.17/5.38 ! [I: $o,K: $o] :
% 9.17/5.38 ( ( member_o @ I @ ( set_ord_lessThan_o @ K ) )
% 9.17/5.38 = ( ord_less_o @ I @ K ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3962_lessThan__iff,axiom,
% 9.17/5.38 ! [I: code_integer,K: code_integer] :
% 9.17/5.38 ( ( member_Code_integer @ I @ ( set_or5754767410780653050nteger @ K ) )
% 9.17/5.38 = ( ord_le6747313008572928689nteger @ I @ K ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3963_lessThan__iff,axiom,
% 9.17/5.38 ! [I: rat,K: rat] :
% 9.17/5.38 ( ( member_rat @ I @ ( set_ord_lessThan_rat @ K ) )
% 9.17/5.38 = ( ord_less_rat @ I @ K ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3964_lessThan__iff,axiom,
% 9.17/5.38 ! [I: num,K: num] :
% 9.17/5.38 ( ( member_num @ I @ ( set_ord_lessThan_num @ K ) )
% 9.17/5.38 = ( ord_less_num @ I @ K ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3965_lessThan__iff,axiom,
% 9.17/5.38 ! [I: int,K: int] :
% 9.17/5.38 ( ( member_int @ I @ ( set_ord_lessThan_int @ K ) )
% 9.17/5.38 = ( ord_less_int @ I @ K ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3966_lessThan__iff,axiom,
% 9.17/5.38 ! [I: nat,K: nat] :
% 9.17/5.38 ( ( member_nat @ I @ ( set_ord_lessThan_nat @ K ) )
% 9.17/5.38 = ( ord_less_nat @ I @ K ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3967_binomial__n__n,axiom,
% 9.17/5.38 ! [N2: nat] :
% 9.17/5.38 ( ( binomial @ N2 @ N2 )
% 9.17/5.38 = one_one_nat ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3968_lessThan__subset__iff,axiom,
% 9.17/5.38 ! [X: rat,Y: rat] :
% 9.17/5.38 ( ( ord_less_eq_set_rat @ ( set_ord_lessThan_rat @ X ) @ ( set_ord_lessThan_rat @ Y ) )
% 9.17/5.38 = ( ord_less_eq_rat @ X @ Y ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3969_lessThan__subset__iff,axiom,
% 9.17/5.38 ! [X: num,Y: num] :
% 9.17/5.38 ( ( ord_less_eq_set_num @ ( set_ord_lessThan_num @ X ) @ ( set_ord_lessThan_num @ Y ) )
% 9.17/5.38 = ( ord_less_eq_num @ X @ Y ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3970_lessThan__subset__iff,axiom,
% 9.17/5.38 ! [X: int,Y: int] :
% 9.17/5.38 ( ( ord_less_eq_set_int @ ( set_ord_lessThan_int @ X ) @ ( set_ord_lessThan_int @ Y ) )
% 9.17/5.38 = ( ord_less_eq_int @ X @ Y ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3971_lessThan__subset__iff,axiom,
% 9.17/5.38 ! [X: nat,Y: nat] :
% 9.17/5.38 ( ( ord_less_eq_set_nat @ ( set_ord_lessThan_nat @ X ) @ ( set_ord_lessThan_nat @ Y ) )
% 9.17/5.38 = ( ord_less_eq_nat @ X @ Y ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3972_binomial__Suc__Suc,axiom,
% 9.17/5.38 ! [N2: nat,K: nat] :
% 9.17/5.38 ( ( binomial @ ( suc @ N2 ) @ ( suc @ K ) )
% 9.17/5.38 = ( plus_plus_nat @ ( binomial @ N2 @ K ) @ ( binomial @ N2 @ ( suc @ K ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3973_binomial__n__0,axiom,
% 9.17/5.38 ! [N2: nat] :
% 9.17/5.38 ( ( binomial @ N2 @ zero_zero_nat )
% 9.17/5.38 = one_one_nat ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3974_sum_OlessThan__Suc,axiom,
% 9.17/5.38 ! [G: nat > multis2468970476368604999at_nat,N2: nat] :
% 9.17/5.38 ( ( groups6857163185585827899at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 9.17/5.38 = ( plus_p7104986032573967614at_nat @ ( groups6857163185585827899at_nat @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3975_sum_OlessThan__Suc,axiom,
% 9.17/5.38 ! [G: nat > rat,N2: nat] :
% 9.17/5.38 ( ( groups2906978787729119204at_rat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 9.17/5.38 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3976_sum_OlessThan__Suc,axiom,
% 9.17/5.38 ! [G: nat > int,N2: nat] :
% 9.17/5.38 ( ( groups3539618377306564664at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 9.17/5.38 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3977_sum_OlessThan__Suc,axiom,
% 9.17/5.38 ! [G: nat > nat,N2: nat] :
% 9.17/5.38 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 9.17/5.38 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3978_choose__one,axiom,
% 9.17/5.38 ! [N2: nat] :
% 9.17/5.38 ( ( binomial @ N2 @ one_one_nat )
% 9.17/5.38 = N2 ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3979_lessThan__def,axiom,
% 9.17/5.38 ( set_or5754767410780653050nteger
% 9.17/5.38 = ( ^ [U2: code_integer] :
% 9.17/5.38 ( collect_Code_integer
% 9.17/5.38 @ ^ [X3: code_integer] : ( ord_le6747313008572928689nteger @ X3 @ U2 ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3980_lessThan__def,axiom,
% 9.17/5.38 ( set_ord_lessThan_rat
% 9.17/5.38 = ( ^ [U2: rat] :
% 9.17/5.38 ( collect_rat
% 9.17/5.38 @ ^ [X3: rat] : ( ord_less_rat @ X3 @ U2 ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3981_lessThan__def,axiom,
% 9.17/5.38 ( set_ord_lessThan_num
% 9.17/5.38 = ( ^ [U2: num] :
% 9.17/5.38 ( collect_num
% 9.17/5.38 @ ^ [X3: num] : ( ord_less_num @ X3 @ U2 ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3982_lessThan__def,axiom,
% 9.17/5.38 ( set_ord_lessThan_int
% 9.17/5.38 = ( ^ [U2: int] :
% 9.17/5.38 ( collect_int
% 9.17/5.38 @ ^ [X3: int] : ( ord_less_int @ X3 @ U2 ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3983_lessThan__def,axiom,
% 9.17/5.38 ( set_ord_lessThan_nat
% 9.17/5.38 = ( ^ [U2: nat] :
% 9.17/5.38 ( collect_nat
% 9.17/5.38 @ ^ [X3: nat] : ( ord_less_nat @ X3 @ U2 ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3984_choose__mult__lemma,axiom,
% 9.17/5.38 ! [M2: nat,R2: nat,K: nat] :
% 9.17/5.38 ( ( times_times_nat @ ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ M2 @ R2 ) @ K ) @ ( plus_plus_nat @ M2 @ K ) ) @ ( binomial @ ( plus_plus_nat @ M2 @ K ) @ K ) )
% 9.17/5.38 = ( times_times_nat @ ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ M2 @ R2 ) @ K ) @ K ) @ ( binomial @ ( plus_plus_nat @ M2 @ R2 ) @ M2 ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3985_lessThan__Suc__atMost,axiom,
% 9.17/5.38 ! [K: nat] :
% 9.17/5.38 ( ( set_ord_lessThan_nat @ ( suc @ K ) )
% 9.17/5.38 = ( set_ord_atMost_nat @ K ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3986_bit__integer_Oabs__eq,axiom,
% 9.17/5.38 ! [X: int] :
% 9.17/5.38 ( ( bit_se9216721137139052372nteger @ ( code_integer_of_int @ X ) )
% 9.17/5.38 = ( bit_se1146084159140164899it_int @ X ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3987_lessThan__strict__subset__iff,axiom,
% 9.17/5.38 ! [M2: code_integer,N2: code_integer] :
% 9.17/5.38 ( ( ord_le1307284697595431911nteger @ ( set_or5754767410780653050nteger @ M2 ) @ ( set_or5754767410780653050nteger @ N2 ) )
% 9.17/5.38 = ( ord_le6747313008572928689nteger @ M2 @ N2 ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3988_lessThan__strict__subset__iff,axiom,
% 9.17/5.38 ! [M2: rat,N2: rat] :
% 9.17/5.38 ( ( ord_less_set_rat @ ( set_ord_lessThan_rat @ M2 ) @ ( set_ord_lessThan_rat @ N2 ) )
% 9.17/5.38 = ( ord_less_rat @ M2 @ N2 ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3989_lessThan__strict__subset__iff,axiom,
% 9.17/5.38 ! [M2: num,N2: num] :
% 9.17/5.38 ( ( ord_less_set_num @ ( set_ord_lessThan_num @ M2 ) @ ( set_ord_lessThan_num @ N2 ) )
% 9.17/5.38 = ( ord_less_num @ M2 @ N2 ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3990_lessThan__strict__subset__iff,axiom,
% 9.17/5.38 ! [M2: int,N2: int] :
% 9.17/5.38 ( ( ord_less_set_int @ ( set_ord_lessThan_int @ M2 ) @ ( set_ord_lessThan_int @ N2 ) )
% 9.17/5.38 = ( ord_less_int @ M2 @ N2 ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3991_lessThan__strict__subset__iff,axiom,
% 9.17/5.38 ! [M2: nat,N2: nat] :
% 9.17/5.38 ( ( ord_less_set_nat @ ( set_ord_lessThan_nat @ M2 ) @ ( set_ord_lessThan_nat @ N2 ) )
% 9.17/5.38 = ( ord_less_nat @ M2 @ N2 ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3992_Suc__times__binomial__add,axiom,
% 9.17/5.38 ! [A: nat,B: nat] :
% 9.17/5.38 ( ( times_times_nat @ ( suc @ A ) @ ( binomial @ ( suc @ ( plus_plus_nat @ A @ B ) ) @ ( suc @ A ) ) )
% 9.17/5.38 = ( times_times_nat @ ( suc @ B ) @ ( binomial @ ( suc @ ( plus_plus_nat @ A @ B ) ) @ A ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3993_binomial__absorb__comp,axiom,
% 9.17/5.38 ! [N2: nat,K: nat] :
% 9.17/5.38 ( ( times_times_nat @ ( minus_minus_nat @ N2 @ K ) @ ( binomial @ N2 @ K ) )
% 9.17/5.38 = ( times_times_nat @ N2 @ ( binomial @ ( minus_minus_nat @ N2 @ one_one_nat ) @ K ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3994_fact__fact__dvd__fact,axiom,
% 9.17/5.38 ! [K: nat,N2: nat] : ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ ( semiri3624122377584611663nteger @ K ) @ ( semiri3624122377584611663nteger @ N2 ) ) @ ( semiri3624122377584611663nteger @ ( plus_plus_nat @ K @ N2 ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3995_fact__fact__dvd__fact,axiom,
% 9.17/5.38 ! [K: nat,N2: nat] : ( dvd_dvd_rat @ ( times_times_rat @ ( semiri773545260158071498ct_rat @ K ) @ ( semiri773545260158071498ct_rat @ N2 ) ) @ ( semiri773545260158071498ct_rat @ ( plus_plus_nat @ K @ N2 ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3996_fact__fact__dvd__fact,axiom,
% 9.17/5.38 ! [K: nat,N2: nat] : ( dvd_dvd_int @ ( times_times_int @ ( semiri1406184849735516958ct_int @ K ) @ ( semiri1406184849735516958ct_int @ N2 ) ) @ ( semiri1406184849735516958ct_int @ ( plus_plus_nat @ K @ N2 ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3997_fact__fact__dvd__fact,axiom,
% 9.17/5.38 ! [K: nat,N2: nat] : ( dvd_dvd_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ N2 ) ) @ ( semiri1408675320244567234ct_nat @ ( plus_plus_nat @ K @ N2 ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3998_sum_Onat__diff__reindex,axiom,
% 9.17/5.38 ! [G: nat > nat,N2: nat] :
% 9.17/5.38 ( ( groups3542108847815614940at_nat
% 9.17/5.38 @ ^ [I3: nat] : ( G @ ( minus_minus_nat @ N2 @ ( suc @ I3 ) ) )
% 9.17/5.38 @ ( set_ord_lessThan_nat @ N2 ) )
% 9.17/5.38 = ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_3999_Iic__subset__Iio__iff,axiom,
% 9.17/5.38 ! [A: code_integer,B: code_integer] :
% 9.17/5.38 ( ( ord_le7084787975880047091nteger @ ( set_or9101266186257409494nteger @ A ) @ ( set_or5754767410780653050nteger @ B ) )
% 9.17/5.38 = ( ord_le6747313008572928689nteger @ A @ B ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4000_Iic__subset__Iio__iff,axiom,
% 9.17/5.38 ! [A: rat,B: rat] :
% 9.17/5.38 ( ( ord_less_eq_set_rat @ ( set_ord_atMost_rat @ A ) @ ( set_ord_lessThan_rat @ B ) )
% 9.17/5.38 = ( ord_less_rat @ A @ B ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4001_Iic__subset__Iio__iff,axiom,
% 9.17/5.38 ! [A: num,B: num] :
% 9.17/5.38 ( ( ord_less_eq_set_num @ ( set_ord_atMost_num @ A ) @ ( set_ord_lessThan_num @ B ) )
% 9.17/5.38 = ( ord_less_num @ A @ B ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4002_Iic__subset__Iio__iff,axiom,
% 9.17/5.38 ! [A: int,B: int] :
% 9.17/5.38 ( ( ord_less_eq_set_int @ ( set_ord_atMost_int @ A ) @ ( set_ord_lessThan_int @ B ) )
% 9.17/5.38 = ( ord_less_int @ A @ B ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4003_Iic__subset__Iio__iff,axiom,
% 9.17/5.38 ! [A: nat,B: nat] :
% 9.17/5.38 ( ( ord_less_eq_set_nat @ ( set_ord_atMost_nat @ A ) @ ( set_ord_lessThan_nat @ B ) )
% 9.17/5.38 = ( ord_less_nat @ A @ B ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4004_binomial__absorption,axiom,
% 9.17/5.38 ! [K: nat,N2: nat] :
% 9.17/5.38 ( ( times_times_nat @ ( suc @ K ) @ ( binomial @ N2 @ ( suc @ K ) ) )
% 9.17/5.38 = ( times_times_nat @ N2 @ ( binomial @ ( minus_minus_nat @ N2 @ one_one_nat ) @ K ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4005_sum__diff__distrib,axiom,
% 9.17/5.38 ! [Q: nat > nat,P: nat > nat,N2: nat] :
% 9.17/5.38 ( ! [X4: nat] : ( ord_less_eq_nat @ ( Q @ X4 ) @ ( P @ X4 ) )
% 9.17/5.38 => ( ( minus_minus_nat @ ( groups3542108847815614940at_nat @ P @ ( set_ord_lessThan_nat @ N2 ) ) @ ( groups3542108847815614940at_nat @ Q @ ( set_ord_lessThan_nat @ N2 ) ) )
% 9.17/5.38 = ( groups3542108847815614940at_nat
% 9.17/5.38 @ ^ [X3: nat] : ( minus_minus_nat @ ( P @ X3 ) @ ( Q @ X3 ) )
% 9.17/5.38 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4006_sum_OlessThan__Suc__shift,axiom,
% 9.17/5.38 ! [G: nat > multis2468970476368604999at_nat,N2: nat] :
% 9.17/5.38 ( ( groups6857163185585827899at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 9.17/5.38 = ( plus_p7104986032573967614at_nat @ ( G @ zero_zero_nat )
% 9.17/5.38 @ ( groups6857163185585827899at_nat
% 9.17/5.38 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 9.17/5.38 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4007_sum_OlessThan__Suc__shift,axiom,
% 9.17/5.38 ! [G: nat > rat,N2: nat] :
% 9.17/5.38 ( ( groups2906978787729119204at_rat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 9.17/5.38 = ( plus_plus_rat @ ( G @ zero_zero_nat )
% 9.17/5.38 @ ( groups2906978787729119204at_rat
% 9.17/5.38 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 9.17/5.38 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4008_sum_OlessThan__Suc__shift,axiom,
% 9.17/5.38 ! [G: nat > int,N2: nat] :
% 9.17/5.38 ( ( groups3539618377306564664at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 9.17/5.38 = ( plus_plus_int @ ( G @ zero_zero_nat )
% 9.17/5.38 @ ( groups3539618377306564664at_int
% 9.17/5.38 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 9.17/5.38 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4009_sum_OlessThan__Suc__shift,axiom,
% 9.17/5.38 ! [G: nat > nat,N2: nat] :
% 9.17/5.38 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 9.17/5.38 = ( plus_plus_nat @ ( G @ zero_zero_nat )
% 9.17/5.38 @ ( groups3542108847815614940at_nat
% 9.17/5.38 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 9.17/5.38 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4010_sum__lessThan__telescope,axiom,
% 9.17/5.38 ! [F: nat > code_integer,M2: nat] :
% 9.17/5.38 ( ( groups7501900531339628137nteger
% 9.17/5.38 @ ^ [N4: nat] : ( minus_8373710615458151222nteger @ ( F @ ( suc @ N4 ) ) @ ( F @ N4 ) )
% 9.17/5.38 @ ( set_ord_lessThan_nat @ M2 ) )
% 9.17/5.38 = ( minus_8373710615458151222nteger @ ( F @ M2 ) @ ( F @ zero_zero_nat ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4011_sum__lessThan__telescope,axiom,
% 9.17/5.38 ! [F: nat > rat,M2: nat] :
% 9.17/5.38 ( ( groups2906978787729119204at_rat
% 9.17/5.38 @ ^ [N4: nat] : ( minus_minus_rat @ ( F @ ( suc @ N4 ) ) @ ( F @ N4 ) )
% 9.17/5.38 @ ( set_ord_lessThan_nat @ M2 ) )
% 9.17/5.38 = ( minus_minus_rat @ ( F @ M2 ) @ ( F @ zero_zero_nat ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4012_sum__lessThan__telescope,axiom,
% 9.17/5.38 ! [F: nat > int,M2: nat] :
% 9.17/5.38 ( ( groups3539618377306564664at_int
% 9.17/5.38 @ ^ [N4: nat] : ( minus_minus_int @ ( F @ ( suc @ N4 ) ) @ ( F @ N4 ) )
% 9.17/5.38 @ ( set_ord_lessThan_nat @ M2 ) )
% 9.17/5.38 = ( minus_minus_int @ ( F @ M2 ) @ ( F @ zero_zero_nat ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4013_sum__lessThan__telescope_H,axiom,
% 9.17/5.38 ! [F: nat > code_integer,M2: nat] :
% 9.17/5.38 ( ( groups7501900531339628137nteger
% 9.17/5.38 @ ^ [N4: nat] : ( minus_8373710615458151222nteger @ ( F @ N4 ) @ ( F @ ( suc @ N4 ) ) )
% 9.17/5.38 @ ( set_ord_lessThan_nat @ M2 ) )
% 9.17/5.38 = ( minus_8373710615458151222nteger @ ( F @ zero_zero_nat ) @ ( F @ M2 ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4014_sum__lessThan__telescope_H,axiom,
% 9.17/5.38 ! [F: nat > rat,M2: nat] :
% 9.17/5.38 ( ( groups2906978787729119204at_rat
% 9.17/5.38 @ ^ [N4: nat] : ( minus_minus_rat @ ( F @ N4 ) @ ( F @ ( suc @ N4 ) ) )
% 9.17/5.38 @ ( set_ord_lessThan_nat @ M2 ) )
% 9.17/5.38 = ( minus_minus_rat @ ( F @ zero_zero_nat ) @ ( F @ M2 ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4015_sum__lessThan__telescope_H,axiom,
% 9.17/5.38 ! [F: nat > int,M2: nat] :
% 9.17/5.38 ( ( groups3539618377306564664at_int
% 9.17/5.38 @ ^ [N4: nat] : ( minus_minus_int @ ( F @ N4 ) @ ( F @ ( suc @ N4 ) ) )
% 9.17/5.38 @ ( set_ord_lessThan_nat @ M2 ) )
% 9.17/5.38 = ( minus_minus_int @ ( F @ zero_zero_nat ) @ ( F @ M2 ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4016_sum_OatLeast1__atMost__eq,axiom,
% 9.17/5.38 ! [G: nat > nat,N2: nat] :
% 9.17/5.38 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 9.17/5.38 = ( groups3542108847815614940at_nat
% 9.17/5.38 @ ^ [K4: nat] : ( G @ ( suc @ K4 ) )
% 9.17/5.38 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4017_sum__bounds__lt__plus1,axiom,
% 9.17/5.38 ! [F: nat > nat,Mm: nat] :
% 9.17/5.38 ( ( groups3542108847815614940at_nat
% 9.17/5.38 @ ^ [K4: nat] : ( F @ ( suc @ K4 ) )
% 9.17/5.38 @ ( set_ord_lessThan_nat @ Mm ) )
% 9.17/5.38 = ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ one_one_nat @ Mm ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4018_sum_Onested__swap_H,axiom,
% 9.17/5.38 ! [A: nat > nat > nat,N2: nat] :
% 9.17/5.38 ( ( groups3542108847815614940at_nat
% 9.17/5.38 @ ^ [I3: nat] : ( groups3542108847815614940at_nat @ ( A @ I3 ) @ ( set_ord_lessThan_nat @ I3 ) )
% 9.17/5.38 @ ( set_ord_atMost_nat @ N2 ) )
% 9.17/5.38 = ( groups3542108847815614940at_nat
% 9.17/5.38 @ ^ [J2: nat] :
% 9.17/5.38 ( groups3542108847815614940at_nat
% 9.17/5.38 @ ^ [I3: nat] : ( A @ I3 @ J2 )
% 9.17/5.38 @ ( set_or1269000886237332187st_nat @ ( suc @ J2 ) @ N2 ) )
% 9.17/5.38 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4019_sum__choose__lower,axiom,
% 9.17/5.38 ! [R2: nat,N2: nat] :
% 9.17/5.38 ( ( groups3542108847815614940at_nat
% 9.17/5.38 @ ^ [K4: nat] : ( binomial @ ( plus_plus_nat @ R2 @ K4 ) @ K4 )
% 9.17/5.38 @ ( set_ord_atMost_nat @ N2 ) )
% 9.17/5.38 = ( binomial @ ( suc @ ( plus_plus_nat @ R2 @ N2 ) ) @ N2 ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4020_choose__rising__sum_I2_J,axiom,
% 9.17/5.38 ! [N2: nat,M2: nat] :
% 9.17/5.38 ( ( groups3542108847815614940at_nat
% 9.17/5.38 @ ^ [J2: nat] : ( binomial @ ( plus_plus_nat @ N2 @ J2 ) @ N2 )
% 9.17/5.38 @ ( set_ord_atMost_nat @ M2 ) )
% 9.17/5.38 = ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ N2 @ M2 ) @ one_one_nat ) @ M2 ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4021_choose__rising__sum_I1_J,axiom,
% 9.17/5.38 ! [N2: nat,M2: nat] :
% 9.17/5.38 ( ( groups3542108847815614940at_nat
% 9.17/5.38 @ ^ [J2: nat] : ( binomial @ ( plus_plus_nat @ N2 @ J2 ) @ N2 )
% 9.17/5.38 @ ( set_ord_atMost_nat @ M2 ) )
% 9.17/5.38 = ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ N2 @ M2 ) @ one_one_nat ) @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4022_binomial__code,axiom,
% 9.17/5.38 ( binomial
% 9.17/5.38 = ( ^ [N4: nat,K4: nat] : ( if_nat @ ( ord_less_nat @ N4 @ K4 ) @ zero_zero_nat @ ( if_nat @ ( ord_less_nat @ N4 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K4 ) ) @ ( binomial @ N4 @ ( minus_minus_nat @ N4 @ K4 ) ) @ ( divide_divide_nat @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( plus_plus_nat @ ( minus_minus_nat @ N4 @ K4 ) @ one_one_nat ) @ N4 @ one_one_nat ) @ ( semiri1408675320244567234ct_nat @ K4 ) ) ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4023_choose__reduce__nat,axiom,
% 9.17/5.38 ! [N2: nat,K: nat] :
% 9.17/5.38 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 9.17/5.38 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 9.17/5.38 => ( ( binomial @ N2 @ K )
% 9.17/5.38 = ( plus_plus_nat @ ( binomial @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) @ ( binomial @ ( minus_minus_nat @ N2 @ one_one_nat ) @ K ) ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4024_times__binomial__minus1__eq,axiom,
% 9.17/5.38 ! [K: nat,N2: nat] :
% 9.17/5.38 ( ( ord_less_nat @ zero_zero_nat @ K )
% 9.17/5.38 => ( ( times_times_nat @ K @ ( binomial @ N2 @ K ) )
% 9.17/5.38 = ( times_times_nat @ N2 @ ( binomial @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4025_one__diff__power__eq,axiom,
% 9.17/5.38 ! [X: code_integer,N2: nat] :
% 9.17/5.38 ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ X @ N2 ) )
% 9.17/5.38 = ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ one_one_Code_integer @ X ) @ ( groups7501900531339628137nteger @ ( power_8256067586552552935nteger @ X ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4026_one__diff__power__eq,axiom,
% 9.17/5.38 ! [X: rat,N2: nat] :
% 9.17/5.38 ( ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ N2 ) )
% 9.17/5.38 = ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4027_one__diff__power__eq,axiom,
% 9.17/5.38 ! [X: int,N2: nat] :
% 9.17/5.38 ( ( minus_minus_int @ one_one_int @ ( power_power_int @ X @ N2 ) )
% 9.17/5.38 = ( times_times_int @ ( minus_minus_int @ one_one_int @ X ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4028_power__diff__1__eq,axiom,
% 9.17/5.38 ! [X: code_integer,N2: nat] :
% 9.17/5.38 ( ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ X @ N2 ) @ one_one_Code_integer )
% 9.17/5.38 = ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ X @ one_one_Code_integer ) @ ( groups7501900531339628137nteger @ ( power_8256067586552552935nteger @ X ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4029_power__diff__1__eq,axiom,
% 9.17/5.38 ! [X: rat,N2: nat] :
% 9.17/5.38 ( ( minus_minus_rat @ ( power_power_rat @ X @ N2 ) @ one_one_rat )
% 9.17/5.38 = ( times_times_rat @ ( minus_minus_rat @ X @ one_one_rat ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4030_power__diff__1__eq,axiom,
% 9.17/5.38 ! [X: int,N2: nat] :
% 9.17/5.38 ( ( minus_minus_int @ ( power_power_int @ X @ N2 ) @ one_one_int )
% 9.17/5.38 = ( times_times_int @ ( minus_minus_int @ X @ one_one_int ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4031_geometric__sum,axiom,
% 9.17/5.38 ! [X: rat,N2: nat] :
% 9.17/5.38 ( ( X != one_one_rat )
% 9.17/5.38 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_lessThan_nat @ N2 ) )
% 9.17/5.38 = ( divide_divide_rat @ ( minus_minus_rat @ ( power_power_rat @ X @ N2 ) @ one_one_rat ) @ ( minus_minus_rat @ X @ one_one_rat ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4032_sum_OatMost__shift,axiom,
% 9.17/5.38 ! [G: nat > multis2468970476368604999at_nat,N2: nat] :
% 9.17/5.38 ( ( groups6857163185585827899at_nat @ G @ ( set_ord_atMost_nat @ N2 ) )
% 9.17/5.38 = ( plus_p7104986032573967614at_nat @ ( G @ zero_zero_nat )
% 9.17/5.38 @ ( groups6857163185585827899at_nat
% 9.17/5.38 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 9.17/5.38 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4033_sum_OatMost__shift,axiom,
% 9.17/5.38 ! [G: nat > rat,N2: nat] :
% 9.17/5.38 ( ( groups2906978787729119204at_rat @ G @ ( set_ord_atMost_nat @ N2 ) )
% 9.17/5.38 = ( plus_plus_rat @ ( G @ zero_zero_nat )
% 9.17/5.38 @ ( groups2906978787729119204at_rat
% 9.17/5.38 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 9.17/5.38 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4034_sum_OatMost__shift,axiom,
% 9.17/5.38 ! [G: nat > int,N2: nat] :
% 9.17/5.38 ( ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ N2 ) )
% 9.17/5.38 = ( plus_plus_int @ ( G @ zero_zero_nat )
% 9.17/5.38 @ ( groups3539618377306564664at_int
% 9.17/5.38 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 9.17/5.38 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4035_sum_OatMost__shift,axiom,
% 9.17/5.38 ! [G: nat > nat,N2: nat] :
% 9.17/5.38 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ N2 ) )
% 9.17/5.38 = ( plus_plus_nat @ ( G @ zero_zero_nat )
% 9.17/5.38 @ ( groups3542108847815614940at_nat
% 9.17/5.38 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 9.17/5.38 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4036_vandermonde,axiom,
% 9.17/5.38 ! [M2: nat,N2: nat,R2: nat] :
% 9.17/5.38 ( ( groups3542108847815614940at_nat
% 9.17/5.38 @ ^ [K4: nat] : ( times_times_nat @ ( binomial @ M2 @ K4 ) @ ( binomial @ N2 @ ( minus_minus_nat @ R2 @ K4 ) ) )
% 9.17/5.38 @ ( set_ord_atMost_nat @ R2 ) )
% 9.17/5.38 = ( binomial @ ( plus_plus_nat @ M2 @ N2 ) @ R2 ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4037_binomial__addition__formula,axiom,
% 9.17/5.38 ! [N2: nat,K: nat] :
% 9.17/5.38 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 9.17/5.38 => ( ( binomial @ N2 @ ( suc @ K ) )
% 9.17/5.38 = ( plus_plus_nat @ ( binomial @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( suc @ K ) ) @ ( binomial @ ( minus_minus_nat @ N2 @ one_one_nat ) @ K ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4038_power__diff__sumr2,axiom,
% 9.17/5.38 ! [X: code_integer,N2: nat,Y: code_integer] :
% 9.17/5.38 ( ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ X @ N2 ) @ ( power_8256067586552552935nteger @ Y @ N2 ) )
% 9.17/5.38 = ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ X @ Y )
% 9.17/5.38 @ ( groups7501900531339628137nteger
% 9.17/5.38 @ ^ [I3: nat] : ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ Y @ ( minus_minus_nat @ N2 @ ( suc @ I3 ) ) ) @ ( power_8256067586552552935nteger @ X @ I3 ) )
% 9.17/5.38 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4039_power__diff__sumr2,axiom,
% 9.17/5.38 ! [X: rat,N2: nat,Y: rat] :
% 9.17/5.38 ( ( minus_minus_rat @ ( power_power_rat @ X @ N2 ) @ ( power_power_rat @ Y @ N2 ) )
% 9.17/5.38 = ( times_times_rat @ ( minus_minus_rat @ X @ Y )
% 9.17/5.38 @ ( groups2906978787729119204at_rat
% 9.17/5.38 @ ^ [I3: nat] : ( times_times_rat @ ( power_power_rat @ Y @ ( minus_minus_nat @ N2 @ ( suc @ I3 ) ) ) @ ( power_power_rat @ X @ I3 ) )
% 9.17/5.38 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4040_power__diff__sumr2,axiom,
% 9.17/5.38 ! [X: int,N2: nat,Y: int] :
% 9.17/5.38 ( ( minus_minus_int @ ( power_power_int @ X @ N2 ) @ ( power_power_int @ Y @ N2 ) )
% 9.17/5.38 = ( times_times_int @ ( minus_minus_int @ X @ Y )
% 9.17/5.38 @ ( groups3539618377306564664at_int
% 9.17/5.38 @ ^ [I3: nat] : ( times_times_int @ ( power_power_int @ Y @ ( minus_minus_nat @ N2 @ ( suc @ I3 ) ) ) @ ( power_power_int @ X @ I3 ) )
% 9.17/5.38 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4041_diff__power__eq__sum,axiom,
% 9.17/5.38 ! [X: code_integer,N2: nat,Y: code_integer] :
% 9.17/5.38 ( ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ X @ ( suc @ N2 ) ) @ ( power_8256067586552552935nteger @ Y @ ( suc @ N2 ) ) )
% 9.17/5.38 = ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ X @ Y )
% 9.17/5.38 @ ( groups7501900531339628137nteger
% 9.17/5.38 @ ^ [P6: nat] : ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ X @ P6 ) @ ( power_8256067586552552935nteger @ Y @ ( minus_minus_nat @ N2 @ P6 ) ) )
% 9.17/5.38 @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4042_diff__power__eq__sum,axiom,
% 9.17/5.38 ! [X: rat,N2: nat,Y: rat] :
% 9.17/5.38 ( ( minus_minus_rat @ ( power_power_rat @ X @ ( suc @ N2 ) ) @ ( power_power_rat @ Y @ ( suc @ N2 ) ) )
% 9.17/5.38 = ( times_times_rat @ ( minus_minus_rat @ X @ Y )
% 9.17/5.38 @ ( groups2906978787729119204at_rat
% 9.17/5.38 @ ^ [P6: nat] : ( times_times_rat @ ( power_power_rat @ X @ P6 ) @ ( power_power_rat @ Y @ ( minus_minus_nat @ N2 @ P6 ) ) )
% 9.17/5.38 @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4043_diff__power__eq__sum,axiom,
% 9.17/5.38 ! [X: int,N2: nat,Y: int] :
% 9.17/5.38 ( ( minus_minus_int @ ( power_power_int @ X @ ( suc @ N2 ) ) @ ( power_power_int @ Y @ ( suc @ N2 ) ) )
% 9.17/5.38 = ( times_times_int @ ( minus_minus_int @ X @ Y )
% 9.17/5.38 @ ( groups3539618377306564664at_int
% 9.17/5.38 @ ^ [P6: nat] : ( times_times_int @ ( power_power_int @ X @ P6 ) @ ( power_power_int @ Y @ ( minus_minus_nat @ N2 @ P6 ) ) )
% 9.17/5.38 @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4044_sum__gp__strict,axiom,
% 9.17/5.38 ! [X: rat,N2: nat] :
% 9.17/5.38 ( ( ( X = one_one_rat )
% 9.17/5.38 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_lessThan_nat @ N2 ) )
% 9.17/5.38 = ( semiri681578069525770553at_rat @ N2 ) ) )
% 9.17/5.38 & ( ( X != one_one_rat )
% 9.17/5.38 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_lessThan_nat @ N2 ) )
% 9.17/5.38 = ( divide_divide_rat @ ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ N2 ) ) @ ( minus_minus_rat @ one_one_rat @ X ) ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4045_binomial,axiom,
% 9.17/5.38 ! [A: nat,B: nat,N2: nat] :
% 9.17/5.38 ( ( power_power_nat @ ( plus_plus_nat @ A @ B ) @ N2 )
% 9.17/5.38 = ( groups3542108847815614940at_nat
% 9.17/5.38 @ ^ [K4: nat] : ( times_times_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( binomial @ N2 @ K4 ) ) @ ( power_power_nat @ A @ K4 ) ) @ ( power_power_nat @ B @ ( minus_minus_nat @ N2 @ K4 ) ) )
% 9.17/5.38 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4046_choose__two,axiom,
% 9.17/5.38 ! [N2: nat] :
% 9.17/5.38 ( ( binomial @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.17/5.38 = ( divide_divide_nat @ ( times_times_nat @ N2 @ ( minus_minus_nat @ N2 @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4047_one__diff__power__eq_H,axiom,
% 9.17/5.38 ! [X: code_integer,N2: nat] :
% 9.17/5.38 ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ X @ N2 ) )
% 9.17/5.38 = ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ one_one_Code_integer @ X )
% 9.17/5.38 @ ( groups7501900531339628137nteger
% 9.17/5.38 @ ^ [I3: nat] : ( power_8256067586552552935nteger @ X @ ( minus_minus_nat @ N2 @ ( suc @ I3 ) ) )
% 9.17/5.38 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4048_one__diff__power__eq_H,axiom,
% 9.17/5.38 ! [X: rat,N2: nat] :
% 9.17/5.38 ( ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ N2 ) )
% 9.17/5.38 = ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X )
% 9.17/5.38 @ ( groups2906978787729119204at_rat
% 9.17/5.38 @ ^ [I3: nat] : ( power_power_rat @ X @ ( minus_minus_nat @ N2 @ ( suc @ I3 ) ) )
% 9.17/5.38 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4049_one__diff__power__eq_H,axiom,
% 9.17/5.38 ! [X: int,N2: nat] :
% 9.17/5.38 ( ( minus_minus_int @ one_one_int @ ( power_power_int @ X @ N2 ) )
% 9.17/5.38 = ( times_times_int @ ( minus_minus_int @ one_one_int @ X )
% 9.17/5.38 @ ( groups3539618377306564664at_int
% 9.17/5.38 @ ^ [I3: nat] : ( power_power_int @ X @ ( minus_minus_nat @ N2 @ ( suc @ I3 ) ) )
% 9.17/5.38 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4050_binomial__ring,axiom,
% 9.17/5.38 ! [A: rat,B: rat,N2: nat] :
% 9.17/5.38 ( ( power_power_rat @ ( plus_plus_rat @ A @ B ) @ N2 )
% 9.17/5.38 = ( groups2906978787729119204at_rat
% 9.17/5.38 @ ^ [K4: nat] : ( times_times_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( binomial @ N2 @ K4 ) ) @ ( power_power_rat @ A @ K4 ) ) @ ( power_power_rat @ B @ ( minus_minus_nat @ N2 @ K4 ) ) )
% 9.17/5.38 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4051_binomial__ring,axiom,
% 9.17/5.38 ! [A: int,B: int,N2: nat] :
% 9.17/5.38 ( ( power_power_int @ ( plus_plus_int @ A @ B ) @ N2 )
% 9.17/5.38 = ( groups3539618377306564664at_int
% 9.17/5.38 @ ^ [K4: nat] : ( times_times_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ ( binomial @ N2 @ K4 ) ) @ ( power_power_int @ A @ K4 ) ) @ ( power_power_int @ B @ ( minus_minus_nat @ N2 @ K4 ) ) )
% 9.17/5.38 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4052_binomial__ring,axiom,
% 9.17/5.38 ! [A: code_integer,B: code_integer,N2: nat] :
% 9.17/5.38 ( ( power_8256067586552552935nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ N2 )
% 9.17/5.38 = ( groups7501900531339628137nteger
% 9.17/5.38 @ ^ [K4: nat] : ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ ( binomial @ N2 @ K4 ) ) @ ( power_8256067586552552935nteger @ A @ K4 ) ) @ ( power_8256067586552552935nteger @ B @ ( minus_minus_nat @ N2 @ K4 ) ) )
% 9.17/5.38 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4053_binomial__ring,axiom,
% 9.17/5.38 ! [A: code_natural,B: code_natural,N2: nat] :
% 9.17/5.38 ( ( power_7079662738309270450atural @ ( plus_p4538020629002901425atural @ A @ B ) @ N2 )
% 9.17/5.38 = ( groups6325495683096345652atural
% 9.17/5.38 @ ^ [K4: nat] : ( times_2397367101498566445atural @ ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ ( binomial @ N2 @ K4 ) ) @ ( power_7079662738309270450atural @ A @ K4 ) ) @ ( power_7079662738309270450atural @ B @ ( minus_minus_nat @ N2 @ K4 ) ) )
% 9.17/5.38 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4054_binomial__ring,axiom,
% 9.17/5.38 ! [A: nat,B: nat,N2: nat] :
% 9.17/5.38 ( ( power_power_nat @ ( plus_plus_nat @ A @ B ) @ N2 )
% 9.17/5.38 = ( groups3542108847815614940at_nat
% 9.17/5.38 @ ^ [K4: nat] : ( times_times_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( binomial @ N2 @ K4 ) ) @ ( power_power_nat @ A @ K4 ) ) @ ( power_power_nat @ B @ ( minus_minus_nat @ N2 @ K4 ) ) )
% 9.17/5.38 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4055_xor__num_Osimps_I6_J,axiom,
% 9.17/5.38 ! [M2: num,N2: num] :
% 9.17/5.38 ( ( bit_un2480387367778600638or_num @ ( bit0 @ M2 ) @ ( bit1 @ N2 ) )
% 9.17/5.38 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M2 @ N2 ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4056_xor__num_Osimps_I8_J,axiom,
% 9.17/5.38 ! [M2: num,N2: num] :
% 9.17/5.38 ( ( bit_un2480387367778600638or_num @ ( bit1 @ M2 ) @ ( bit0 @ N2 ) )
% 9.17/5.38 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M2 @ N2 ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4057_choose__alternating__linear__sum,axiom,
% 9.17/5.38 ! [N2: nat] :
% 9.17/5.38 ( ( N2 != one_one_nat )
% 9.17/5.38 => ( ( groups2906978787729119204at_rat
% 9.17/5.38 @ ^ [I3: nat] : ( times_times_rat @ ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ I3 ) @ ( semiri681578069525770553at_rat @ I3 ) ) @ ( semiri681578069525770553at_rat @ ( binomial @ N2 @ I3 ) ) )
% 9.17/5.38 @ ( set_ord_atMost_nat @ N2 ) )
% 9.17/5.38 = zero_zero_rat ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4058_choose__alternating__linear__sum,axiom,
% 9.17/5.38 ! [N2: nat] :
% 9.17/5.38 ( ( N2 != one_one_nat )
% 9.17/5.38 => ( ( groups3539618377306564664at_int
% 9.17/5.38 @ ^ [I3: nat] : ( times_times_int @ ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ I3 ) @ ( semiri1314217659103216013at_int @ I3 ) ) @ ( semiri1314217659103216013at_int @ ( binomial @ N2 @ I3 ) ) )
% 9.17/5.38 @ ( set_ord_atMost_nat @ N2 ) )
% 9.17/5.38 = zero_zero_int ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4059_choose__alternating__linear__sum,axiom,
% 9.17/5.38 ! [N2: nat] :
% 9.17/5.38 ( ( N2 != one_one_nat )
% 9.17/5.38 => ( ( groups7501900531339628137nteger
% 9.17/5.38 @ ^ [I3: nat] : ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ I3 ) @ ( semiri4939895301339042750nteger @ I3 ) ) @ ( semiri4939895301339042750nteger @ ( binomial @ N2 @ I3 ) ) )
% 9.17/5.38 @ ( set_ord_atMost_nat @ N2 ) )
% 9.17/5.38 = zero_z3403309356797280102nteger ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4060_fact__Suc__0,axiom,
% 9.17/5.38 ( ( semiri3624122377584611663nteger @ ( suc @ zero_zero_nat ) )
% 9.17/5.38 = one_one_Code_integer ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4061_fact__Suc__0,axiom,
% 9.17/5.38 ( ( semiri773545260158071498ct_rat @ ( suc @ zero_zero_nat ) )
% 9.17/5.38 = one_one_rat ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4062_fact__Suc__0,axiom,
% 9.17/5.38 ( ( semiri1406184849735516958ct_int @ ( suc @ zero_zero_nat ) )
% 9.17/5.38 = one_one_int ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4063_fact__Suc__0,axiom,
% 9.17/5.38 ( ( semiri1408675320244567234ct_nat @ ( suc @ zero_zero_nat ) )
% 9.17/5.38 = one_one_nat ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4064_fact__1,axiom,
% 9.17/5.38 ( ( semiri3624122377584611663nteger @ one_one_nat )
% 9.17/5.38 = one_one_Code_integer ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4065_fact__1,axiom,
% 9.17/5.38 ( ( semiri773545260158071498ct_rat @ one_one_nat )
% 9.17/5.38 = one_one_rat ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4066_fact__1,axiom,
% 9.17/5.38 ( ( semiri1406184849735516958ct_int @ one_one_nat )
% 9.17/5.38 = one_one_int ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4067_fact__1,axiom,
% 9.17/5.38 ( ( semiri1408675320244567234ct_nat @ one_one_nat )
% 9.17/5.38 = one_one_nat ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4068_fact__0,axiom,
% 9.17/5.38 ( ( semiri3624122377584611663nteger @ zero_zero_nat )
% 9.17/5.38 = one_one_Code_integer ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4069_fact__0,axiom,
% 9.17/5.38 ( ( semiri773545260158071498ct_rat @ zero_zero_nat )
% 9.17/5.38 = one_one_rat ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4070_fact__0,axiom,
% 9.17/5.38 ( ( semiri1406184849735516958ct_int @ zero_zero_nat )
% 9.17/5.38 = one_one_int ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4071_fact__0,axiom,
% 9.17/5.38 ( ( semiri1408675320244567234ct_nat @ zero_zero_nat )
% 9.17/5.38 = one_one_nat ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4072_fact__code,axiom,
% 9.17/5.38 ( semiri1406184849735516958ct_int
% 9.17/5.38 = ( ^ [N4: nat] : ( semiri1314217659103216013at_int @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 @ one_one_nat ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4073_fact__code,axiom,
% 9.17/5.38 ( semiri3624122377584611663nteger
% 9.17/5.38 = ( ^ [N4: nat] : ( semiri4939895301339042750nteger @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 @ one_one_nat ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4074_fact__code,axiom,
% 9.17/5.38 ( semiri2447717529341329178atural
% 9.17/5.38 = ( ^ [N4: nat] : ( semiri3763490453095760265atural @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 @ one_one_nat ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4075_fact__code,axiom,
% 9.17/5.38 ( semiri1408675320244567234ct_nat
% 9.17/5.38 = ( ^ [N4: nat] : ( semiri1316708129612266289at_nat @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 @ one_one_nat ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4076_fact__reduce,axiom,
% 9.17/5.38 ! [N2: nat] :
% 9.17/5.38 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 9.17/5.38 => ( ( semiri773545260158071498ct_rat @ N2 )
% 9.17/5.38 = ( times_times_rat @ ( semiri681578069525770553at_rat @ N2 ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4077_fact__reduce,axiom,
% 9.17/5.38 ! [N2: nat] :
% 9.17/5.38 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 9.17/5.38 => ( ( semiri1406184849735516958ct_int @ N2 )
% 9.17/5.38 = ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( semiri1406184849735516958ct_int @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4078_fact__reduce,axiom,
% 9.17/5.38 ! [N2: nat] :
% 9.17/5.38 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 9.17/5.38 => ( ( semiri3624122377584611663nteger @ N2 )
% 9.17/5.38 = ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N2 ) @ ( semiri3624122377584611663nteger @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4079_fact__reduce,axiom,
% 9.17/5.38 ! [N2: nat] :
% 9.17/5.38 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 9.17/5.38 => ( ( semiri2447717529341329178atural @ N2 )
% 9.17/5.38 = ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ N2 ) @ ( semiri2447717529341329178atural @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4080_fact__reduce,axiom,
% 9.17/5.38 ! [N2: nat] :
% 9.17/5.38 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 9.17/5.38 => ( ( semiri1408675320244567234ct_nat @ N2 )
% 9.17/5.38 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4081_fact__num__eq__if,axiom,
% 9.17/5.38 ( semiri773545260158071498ct_rat
% 9.17/5.38 = ( ^ [M: nat] : ( if_rat @ ( M = zero_zero_nat ) @ one_one_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ M @ one_one_nat ) ) ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4082_fact__num__eq__if,axiom,
% 9.17/5.38 ( semiri1406184849735516958ct_int
% 9.17/5.38 = ( ^ [M: nat] : ( if_int @ ( M = zero_zero_nat ) @ one_one_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1406184849735516958ct_int @ ( minus_minus_nat @ M @ one_one_nat ) ) ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4083_fact__num__eq__if,axiom,
% 9.17/5.38 ( semiri3624122377584611663nteger
% 9.17/5.38 = ( ^ [M: nat] : ( if_Code_integer @ ( M = zero_zero_nat ) @ one_one_Code_integer @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri3624122377584611663nteger @ ( minus_minus_nat @ M @ one_one_nat ) ) ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4084_fact__num__eq__if,axiom,
% 9.17/5.38 ( semiri2447717529341329178atural
% 9.17/5.38 = ( ^ [M: nat] : ( if_Code_natural @ ( M = zero_zero_nat ) @ one_one_Code_natural @ ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ M ) @ ( semiri2447717529341329178atural @ ( minus_minus_nat @ M @ one_one_nat ) ) ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4085_fact__num__eq__if,axiom,
% 9.17/5.38 ( semiri1408675320244567234ct_nat
% 9.17/5.38 = ( ^ [M: nat] : ( if_nat @ ( M = zero_zero_nat ) @ one_one_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ M @ one_one_nat ) ) ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4086_xor__num_Opelims,axiom,
% 9.17/5.38 ! [X: num,Xa: num,Y: option_num] :
% 9.17/5.38 ( ( ( bit_un2480387367778600638or_num @ X @ Xa )
% 9.17/5.38 = Y )
% 9.17/5.38 => ( ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ X @ Xa ) )
% 9.17/5.38 => ( ( ( X = one )
% 9.17/5.38 => ( ( Xa = one )
% 9.17/5.38 => ( ( Y = none_num )
% 9.17/5.38 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 9.17/5.38 => ( ( ( X = one )
% 9.17/5.38 => ! [N: num] :
% 9.17/5.38 ( ( Xa
% 9.17/5.38 = ( bit0 @ N ) )
% 9.17/5.38 => ( ( Y
% 9.17/5.38 = ( some_num @ ( bit1 @ N ) ) )
% 9.17/5.38 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ one @ ( bit0 @ N ) ) ) ) ) )
% 9.17/5.38 => ( ( ( X = one )
% 9.17/5.38 => ! [N: num] :
% 9.17/5.38 ( ( Xa
% 9.17/5.38 = ( bit1 @ N ) )
% 9.17/5.38 => ( ( Y
% 9.17/5.38 = ( some_num @ ( bit0 @ N ) ) )
% 9.17/5.38 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ one @ ( bit1 @ N ) ) ) ) ) )
% 9.17/5.38 => ( ! [M5: num] :
% 9.17/5.38 ( ( X
% 9.17/5.38 = ( bit0 @ M5 ) )
% 9.17/5.38 => ( ( Xa = one )
% 9.17/5.38 => ( ( Y
% 9.17/5.38 = ( some_num @ ( bit1 @ M5 ) ) )
% 9.17/5.38 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ one ) ) ) ) )
% 9.17/5.38 => ( ! [M5: num] :
% 9.17/5.38 ( ( X
% 9.17/5.38 = ( bit0 @ M5 ) )
% 9.17/5.38 => ! [N: num] :
% 9.17/5.38 ( ( Xa
% 9.17/5.38 = ( bit0 @ N ) )
% 9.17/5.38 => ( ( Y
% 9.17/5.38 = ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M5 @ N ) ) )
% 9.17/5.38 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ ( bit0 @ N ) ) ) ) ) )
% 9.17/5.38 => ( ! [M5: num] :
% 9.17/5.38 ( ( X
% 9.17/5.38 = ( bit0 @ M5 ) )
% 9.17/5.38 => ! [N: num] :
% 9.17/5.38 ( ( Xa
% 9.17/5.38 = ( bit1 @ N ) )
% 9.17/5.38 => ( ( Y
% 9.17/5.38 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M5 @ N ) ) ) )
% 9.17/5.38 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ ( bit1 @ N ) ) ) ) ) )
% 9.17/5.38 => ( ! [M5: num] :
% 9.17/5.38 ( ( X
% 9.17/5.38 = ( bit1 @ M5 ) )
% 9.17/5.38 => ( ( Xa = one )
% 9.17/5.38 => ( ( Y
% 9.17/5.38 = ( some_num @ ( bit0 @ M5 ) ) )
% 9.17/5.38 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ one ) ) ) ) )
% 9.17/5.38 => ( ! [M5: num] :
% 9.17/5.38 ( ( X
% 9.17/5.38 = ( bit1 @ M5 ) )
% 9.17/5.38 => ! [N: num] :
% 9.17/5.38 ( ( Xa
% 9.17/5.38 = ( bit0 @ N ) )
% 9.17/5.38 => ( ( Y
% 9.17/5.38 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M5 @ N ) ) ) )
% 9.17/5.38 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ ( bit0 @ N ) ) ) ) ) )
% 9.17/5.38 => ~ ! [M5: num] :
% 9.17/5.38 ( ( X
% 9.17/5.38 = ( bit1 @ M5 ) )
% 9.17/5.38 => ! [N: num] :
% 9.17/5.38 ( ( Xa
% 9.17/5.38 = ( bit1 @ N ) )
% 9.17/5.38 => ( ( Y
% 9.17/5.38 = ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M5 @ N ) ) )
% 9.17/5.38 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ ( bit1 @ N ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4087_dvd__fact,axiom,
% 9.17/5.38 ! [M2: nat,N2: nat] :
% 9.17/5.38 ( ( ord_less_eq_nat @ one_one_nat @ M2 )
% 9.17/5.38 => ( ( ord_less_eq_nat @ M2 @ N2 )
% 9.17/5.38 => ( dvd_dvd_nat @ M2 @ ( semiri1408675320244567234ct_nat @ N2 ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4088_fact__ge__1,axiom,
% 9.17/5.38 ! [N2: nat] : ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( semiri3624122377584611663nteger @ N2 ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4089_fact__ge__1,axiom,
% 9.17/5.38 ! [N2: nat] : ( ord_less_eq_rat @ one_one_rat @ ( semiri773545260158071498ct_rat @ N2 ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4090_fact__ge__1,axiom,
% 9.17/5.38 ! [N2: nat] : ( ord_less_eq_int @ one_one_int @ ( semiri1406184849735516958ct_int @ N2 ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4091_fact__ge__1,axiom,
% 9.17/5.38 ! [N2: nat] : ( ord_less_eq_nat @ one_one_nat @ ( semiri1408675320244567234ct_nat @ N2 ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4092_pochhammer__double,axiom,
% 9.17/5.38 ! [Z: rat,N2: nat] :
% 9.17/5.38 ( ( comm_s4028243227959126397er_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ Z ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 9.17/5.38 = ( times_times_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) @ ( comm_s4028243227959126397er_rat @ Z @ N2 ) ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ N2 ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4093_fact__double,axiom,
% 9.17/5.38 ! [N2: nat] :
% 9.17/5.38 ( ( semiri773545260158071498ct_rat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 9.17/5.38 = ( times_times_rat @ ( times_times_rat @ ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) @ ( comm_s4028243227959126397er_rat @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ N2 ) ) @ ( semiri773545260158071498ct_rat @ N2 ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4094_pochhammer__code,axiom,
% 9.17/5.38 ( comm_s4028243227959126397er_rat
% 9.17/5.38 = ( ^ [A5: rat,N4: nat] :
% 9.17/5.38 ( if_rat @ ( N4 = zero_zero_nat ) @ one_one_rat
% 9.17/5.38 @ ( set_fo1949268297981939178at_rat
% 9.17/5.38 @ ^ [O: nat] : ( times_times_rat @ ( plus_plus_rat @ A5 @ ( semiri681578069525770553at_rat @ O ) ) )
% 9.17/5.38 @ zero_zero_nat
% 9.17/5.38 @ ( minus_minus_nat @ N4 @ one_one_nat )
% 9.17/5.38 @ one_one_rat ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4095_pochhammer__code,axiom,
% 9.17/5.38 ( comm_s4660882817536571857er_int
% 9.17/5.38 = ( ^ [A5: int,N4: nat] :
% 9.17/5.38 ( if_int @ ( N4 = zero_zero_nat ) @ one_one_int
% 9.17/5.38 @ ( set_fo2581907887559384638at_int
% 9.17/5.38 @ ^ [O: nat] : ( times_times_int @ ( plus_plus_int @ A5 @ ( semiri1314217659103216013at_int @ O ) ) )
% 9.17/5.38 @ zero_zero_nat
% 9.17/5.38 @ ( minus_minus_nat @ N4 @ one_one_nat )
% 9.17/5.38 @ one_one_int ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4096_pochhammer__code,axiom,
% 9.17/5.38 ( comm_s8582702949713902594nteger
% 9.17/5.38 = ( ^ [A5: code_integer,N4: nat] :
% 9.17/5.38 ( if_Code_integer @ ( N4 = zero_zero_nat ) @ one_one_Code_integer
% 9.17/5.38 @ ( set_fo1084959871951514735nteger
% 9.17/5.38 @ ^ [O: nat] : ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ A5 @ ( semiri4939895301339042750nteger @ O ) ) )
% 9.17/5.38 @ zero_zero_nat
% 9.17/5.38 @ ( minus_minus_nat @ N4 @ one_one_nat )
% 9.17/5.38 @ one_one_Code_integer ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4097_pochhammer__code,axiom,
% 9.17/5.38 ( comm_s7406298101470620109atural
% 9.17/5.38 = ( ^ [A5: code_natural,N4: nat] :
% 9.17/5.38 ( if_Code_natural @ ( N4 = zero_zero_nat ) @ one_one_Code_natural
% 9.17/5.38 @ ( set_fo9131927060563008058atural
% 9.17/5.38 @ ^ [O: nat] : ( times_2397367101498566445atural @ ( plus_p4538020629002901425atural @ A5 @ ( semiri3763490453095760265atural @ O ) ) )
% 9.17/5.38 @ zero_zero_nat
% 9.17/5.38 @ ( minus_minus_nat @ N4 @ one_one_nat )
% 9.17/5.38 @ one_one_Code_natural ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4098_pochhammer__code,axiom,
% 9.17/5.38 ( comm_s4663373288045622133er_nat
% 9.17/5.38 = ( ^ [A5: nat,N4: nat] :
% 9.17/5.38 ( if_nat @ ( N4 = zero_zero_nat ) @ one_one_nat
% 9.17/5.38 @ ( set_fo2584398358068434914at_nat
% 9.17/5.38 @ ^ [O: nat] : ( times_times_nat @ ( plus_plus_nat @ A5 @ ( semiri1316708129612266289at_nat @ O ) ) )
% 9.17/5.38 @ zero_zero_nat
% 9.17/5.38 @ ( minus_minus_nat @ N4 @ one_one_nat )
% 9.17/5.38 @ one_one_nat ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4099_xor__Suc__0__eq,axiom,
% 9.17/5.38 ! [N2: nat] :
% 9.17/5.38 ( ( bit_se6528837805403552850or_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 9.17/5.38 = ( minus_minus_nat @ ( plus_plus_nat @ N2 @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 9.17/5.38 @ ( zero_n2687167440665602831ol_nat
% 9.17/5.38 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4100_Suc__0__xor__eq,axiom,
% 9.17/5.38 ! [N2: nat] :
% 9.17/5.38 ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 9.17/5.38 = ( minus_minus_nat @ ( plus_plus_nat @ N2 @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 9.17/5.38 @ ( zero_n2687167440665602831ol_nat
% 9.17/5.38 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4101_push__bit__numeral__minus__1,axiom,
% 9.17/5.38 ! [N2: num] :
% 9.17/5.38 ( ( bit_se7788150548672797655nteger @ ( numeral_numeral_nat @ N2 ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.17/5.38 = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ N2 ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4102_push__bit__numeral__minus__1,axiom,
% 9.17/5.38 ! [N2: num] :
% 9.17/5.38 ( ( bit_se545348938243370406it_int @ ( numeral_numeral_nat @ N2 ) @ ( uminus_uminus_int @ one_one_int ) )
% 9.17/5.38 = ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ N2 ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4103_num__of__integer__code,axiom,
% 9.17/5.38 ( code_num_of_integer
% 9.17/5.38 = ( ^ [K4: code_integer] :
% 9.17/5.38 ( if_num @ ( ord_le3102999989581377725nteger @ K4 @ one_one_Code_integer ) @ one
% 9.17/5.38 @ ( produc7336495610019696514er_num
% 9.17/5.38 @ ^ [L3: code_integer,J2: code_integer] : ( if_num @ ( J2 = zero_z3403309356797280102nteger ) @ ( plus_plus_num @ ( code_num_of_integer @ L3 ) @ ( code_num_of_integer @ L3 ) ) @ ( plus_plus_num @ ( plus_plus_num @ ( code_num_of_integer @ L3 ) @ ( code_num_of_integer @ L3 ) ) @ one ) )
% 9.17/5.38 @ ( code_divmod_integer @ K4 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4104_Sum__Ico__nat,axiom,
% 9.17/5.38 ! [M2: nat,N2: nat] :
% 9.17/5.38 ( ( groups3542108847815614940at_nat
% 9.17/5.38 @ ^ [X3: nat] : X3
% 9.17/5.38 @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) )
% 9.17/5.38 = ( divide_divide_nat @ ( minus_minus_nat @ ( times_times_nat @ N2 @ ( minus_minus_nat @ N2 @ one_one_nat ) ) @ ( times_times_nat @ M2 @ ( minus_minus_nat @ M2 @ one_one_nat ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4105_ivl__diff,axiom,
% 9.17/5.38 ! [I: rat,N2: rat,M2: rat] :
% 9.17/5.38 ( ( ord_less_eq_rat @ I @ N2 )
% 9.17/5.38 => ( ( minus_minus_set_rat @ ( set_or4029947393144176647an_rat @ I @ M2 ) @ ( set_or4029947393144176647an_rat @ I @ N2 ) )
% 9.17/5.38 = ( set_or4029947393144176647an_rat @ N2 @ M2 ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4106_ivl__diff,axiom,
% 9.17/5.38 ! [I: num,N2: num,M2: num] :
% 9.17/5.38 ( ( ord_less_eq_num @ I @ N2 )
% 9.17/5.38 => ( ( minus_minus_set_num @ ( set_or1222409239386451017an_num @ I @ M2 ) @ ( set_or1222409239386451017an_num @ I @ N2 ) )
% 9.17/5.38 = ( set_or1222409239386451017an_num @ N2 @ M2 ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4107_ivl__diff,axiom,
% 9.17/5.38 ! [I: nat,N2: nat,M2: nat] :
% 9.17/5.38 ( ( ord_less_eq_nat @ I @ N2 )
% 9.17/5.38 => ( ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ I @ M2 ) @ ( set_or4665077453230672383an_nat @ I @ N2 ) )
% 9.17/5.38 = ( set_or4665077453230672383an_nat @ N2 @ M2 ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4108_ivl__diff,axiom,
% 9.17/5.38 ! [I: code_integer,N2: code_integer,M2: code_integer] :
% 9.17/5.38 ( ( ord_le3102999989581377725nteger @ I @ N2 )
% 9.17/5.38 => ( ( minus_2355218937544613996nteger @ ( set_or8404916559141939852nteger @ I @ M2 ) @ ( set_or8404916559141939852nteger @ I @ N2 ) )
% 9.17/5.38 = ( set_or8404916559141939852nteger @ N2 @ M2 ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4109_ivl__diff,axiom,
% 9.17/5.38 ! [I: int,N2: int,M2: int] :
% 9.17/5.38 ( ( ord_less_eq_int @ I @ N2 )
% 9.17/5.38 => ( ( minus_minus_set_int @ ( set_or4662586982721622107an_int @ I @ M2 ) @ ( set_or4662586982721622107an_int @ I @ N2 ) )
% 9.17/5.38 = ( set_or4662586982721622107an_int @ N2 @ M2 ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4110_push__bit__push__bit,axiom,
% 9.17/5.38 ! [M2: nat,N2: nat,A: nat] :
% 9.17/5.38 ( ( bit_se547839408752420682it_nat @ M2 @ ( bit_se547839408752420682it_nat @ N2 @ A ) )
% 9.17/5.38 = ( bit_se547839408752420682it_nat @ ( plus_plus_nat @ M2 @ N2 ) @ A ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4111_push__bit__push__bit,axiom,
% 9.17/5.38 ! [M2: nat,N2: nat,A: code_integer] :
% 9.17/5.38 ( ( bit_se7788150548672797655nteger @ M2 @ ( bit_se7788150548672797655nteger @ N2 @ A ) )
% 9.17/5.38 = ( bit_se7788150548672797655nteger @ ( plus_plus_nat @ M2 @ N2 ) @ A ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4112_push__bit__push__bit,axiom,
% 9.17/5.38 ! [M2: nat,N2: nat,A: int] :
% 9.17/5.38 ( ( bit_se545348938243370406it_int @ M2 @ ( bit_se545348938243370406it_int @ N2 @ A ) )
% 9.17/5.38 = ( bit_se545348938243370406it_int @ ( plus_plus_nat @ M2 @ N2 ) @ A ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4113_push__bit__push__bit,axiom,
% 9.17/5.38 ! [M2: nat,N2: nat,A: code_natural] :
% 9.17/5.38 ( ( bit_se6611745700429515170atural @ M2 @ ( bit_se6611745700429515170atural @ N2 @ A ) )
% 9.17/5.38 = ( bit_se6611745700429515170atural @ ( plus_plus_nat @ M2 @ N2 ) @ A ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4114_lessThan__minus__lessThan,axiom,
% 9.17/5.38 ! [N2: nat,M2: nat] :
% 9.17/5.38 ( ( minus_minus_set_nat @ ( set_ord_lessThan_nat @ N2 ) @ ( set_ord_lessThan_nat @ M2 ) )
% 9.17/5.38 = ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4115_lessThan__minus__lessThan,axiom,
% 9.17/5.38 ! [N2: code_integer,M2: code_integer] :
% 9.17/5.38 ( ( minus_2355218937544613996nteger @ ( set_or5754767410780653050nteger @ N2 ) @ ( set_or5754767410780653050nteger @ M2 ) )
% 9.17/5.38 = ( set_or8404916559141939852nteger @ M2 @ N2 ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4116_lessThan__minus__lessThan,axiom,
% 9.17/5.38 ! [N2: int,M2: int] :
% 9.17/5.38 ( ( minus_minus_set_int @ ( set_ord_lessThan_int @ N2 ) @ ( set_ord_lessThan_int @ M2 ) )
% 9.17/5.38 = ( set_or4662586982721622107an_int @ M2 @ N2 ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4117_atLeastLessThan__iff,axiom,
% 9.17/5.38 ! [I: $o,L: $o,U: $o] :
% 9.17/5.38 ( ( member_o @ I @ ( set_or7139685690850216873Than_o @ L @ U ) )
% 9.17/5.38 = ( ( ord_less_eq_o @ L @ I )
% 9.17/5.38 & ( ord_less_o @ I @ U ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4118_atLeastLessThan__iff,axiom,
% 9.17/5.38 ! [I: set_nat,L: set_nat,U: set_nat] :
% 9.17/5.38 ( ( member_set_nat @ I @ ( set_or3540276404033026485et_nat @ L @ U ) )
% 9.17/5.38 = ( ( ord_less_eq_set_nat @ L @ I )
% 9.17/5.38 & ( ord_less_set_nat @ I @ U ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4119_atLeastLessThan__iff,axiom,
% 9.17/5.38 ! [I: rat,L: rat,U: rat] :
% 9.17/5.38 ( ( member_rat @ I @ ( set_or4029947393144176647an_rat @ L @ U ) )
% 9.17/5.38 = ( ( ord_less_eq_rat @ L @ I )
% 9.17/5.38 & ( ord_less_rat @ I @ U ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4120_atLeastLessThan__iff,axiom,
% 9.17/5.38 ! [I: num,L: num,U: num] :
% 9.17/5.38 ( ( member_num @ I @ ( set_or1222409239386451017an_num @ L @ U ) )
% 9.17/5.38 = ( ( ord_less_eq_num @ L @ I )
% 9.17/5.38 & ( ord_less_num @ I @ U ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4121_atLeastLessThan__iff,axiom,
% 9.17/5.38 ! [I: nat,L: nat,U: nat] :
% 9.17/5.38 ( ( member_nat @ I @ ( set_or4665077453230672383an_nat @ L @ U ) )
% 9.17/5.38 = ( ( ord_less_eq_nat @ L @ I )
% 9.17/5.38 & ( ord_less_nat @ I @ U ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4122_atLeastLessThan__iff,axiom,
% 9.17/5.38 ! [I: code_integer,L: code_integer,U: code_integer] :
% 9.17/5.38 ( ( member_Code_integer @ I @ ( set_or8404916559141939852nteger @ L @ U ) )
% 9.17/5.38 = ( ( ord_le3102999989581377725nteger @ L @ I )
% 9.17/5.38 & ( ord_le6747313008572928689nteger @ I @ U ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4123_atLeastLessThan__iff,axiom,
% 9.17/5.38 ! [I: int,L: int,U: int] :
% 9.17/5.38 ( ( member_int @ I @ ( set_or4662586982721622107an_int @ L @ U ) )
% 9.17/5.38 = ( ( ord_less_eq_int @ L @ I )
% 9.17/5.38 & ( ord_less_int @ I @ U ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4124_ivl__subset,axiom,
% 9.17/5.38 ! [I: rat,J: rat,M2: rat,N2: rat] :
% 9.17/5.38 ( ( ord_less_eq_set_rat @ ( set_or4029947393144176647an_rat @ I @ J ) @ ( set_or4029947393144176647an_rat @ M2 @ N2 ) )
% 9.17/5.38 = ( ( ord_less_eq_rat @ J @ I )
% 9.17/5.38 | ( ( ord_less_eq_rat @ M2 @ I )
% 9.17/5.38 & ( ord_less_eq_rat @ J @ N2 ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4125_ivl__subset,axiom,
% 9.17/5.38 ! [I: num,J: num,M2: num,N2: num] :
% 9.17/5.38 ( ( ord_less_eq_set_num @ ( set_or1222409239386451017an_num @ I @ J ) @ ( set_or1222409239386451017an_num @ M2 @ N2 ) )
% 9.17/5.38 = ( ( ord_less_eq_num @ J @ I )
% 9.17/5.38 | ( ( ord_less_eq_num @ M2 @ I )
% 9.17/5.38 & ( ord_less_eq_num @ J @ N2 ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4126_ivl__subset,axiom,
% 9.17/5.38 ! [I: nat,J: nat,M2: nat,N2: nat] :
% 9.17/5.38 ( ( ord_less_eq_set_nat @ ( set_or4665077453230672383an_nat @ I @ J ) @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) )
% 9.17/5.38 = ( ( ord_less_eq_nat @ J @ I )
% 9.17/5.38 | ( ( ord_less_eq_nat @ M2 @ I )
% 9.17/5.38 & ( ord_less_eq_nat @ J @ N2 ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4127_ivl__subset,axiom,
% 9.17/5.38 ! [I: code_integer,J: code_integer,M2: code_integer,N2: code_integer] :
% 9.17/5.38 ( ( ord_le7084787975880047091nteger @ ( set_or8404916559141939852nteger @ I @ J ) @ ( set_or8404916559141939852nteger @ M2 @ N2 ) )
% 9.17/5.38 = ( ( ord_le3102999989581377725nteger @ J @ I )
% 9.17/5.38 | ( ( ord_le3102999989581377725nteger @ M2 @ I )
% 9.17/5.38 & ( ord_le3102999989581377725nteger @ J @ N2 ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4128_ivl__subset,axiom,
% 9.17/5.38 ! [I: int,J: int,M2: int,N2: int] :
% 9.17/5.38 ( ( ord_less_eq_set_int @ ( set_or4662586982721622107an_int @ I @ J ) @ ( set_or4662586982721622107an_int @ M2 @ N2 ) )
% 9.17/5.38 = ( ( ord_less_eq_int @ J @ I )
% 9.17/5.38 | ( ( ord_less_eq_int @ M2 @ I )
% 9.17/5.38 & ( ord_less_eq_int @ J @ N2 ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4129_pochhammer__0,axiom,
% 9.17/5.38 ! [A: code_integer] :
% 9.17/5.38 ( ( comm_s8582702949713902594nteger @ A @ zero_zero_nat )
% 9.17/5.38 = one_one_Code_integer ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4130_pochhammer__0,axiom,
% 9.17/5.38 ! [A: rat] :
% 9.17/5.38 ( ( comm_s4028243227959126397er_rat @ A @ zero_zero_nat )
% 9.17/5.38 = one_one_rat ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4131_pochhammer__0,axiom,
% 9.17/5.38 ! [A: nat] :
% 9.17/5.38 ( ( comm_s4663373288045622133er_nat @ A @ zero_zero_nat )
% 9.17/5.38 = one_one_nat ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4132_pochhammer__0,axiom,
% 9.17/5.38 ! [A: int] :
% 9.17/5.38 ( ( comm_s4660882817536571857er_int @ A @ zero_zero_nat )
% 9.17/5.38 = one_one_int ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4133_xor__numerals_I1_J,axiom,
% 9.17/5.38 ! [Y: num] :
% 9.17/5.38 ( ( bit_se6528837805403552850or_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 9.17/5.38 = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4134_xor__numerals_I1_J,axiom,
% 9.17/5.38 ! [Y: num] :
% 9.17/5.38 ( ( bit_se3222712562003087583nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ Y ) ) )
% 9.17/5.38 = ( numera6620942414471956472nteger @ ( bit1 @ Y ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4135_xor__numerals_I1_J,axiom,
% 9.17/5.38 ! [Y: num] :
% 9.17/5.38 ( ( bit_se6526347334894502574or_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 9.17/5.38 = ( numeral_numeral_int @ ( bit1 @ Y ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4136_xor__numerals_I1_J,axiom,
% 9.17/5.38 ! [Y: num] :
% 9.17/5.38 ( ( bit_se2046307713759805098atural @ one_one_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ Y ) ) )
% 9.17/5.38 = ( numera5444537566228673987atural @ ( bit1 @ Y ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4137_xor__numerals_I2_J,axiom,
% 9.17/5.38 ! [Y: num] :
% 9.17/5.38 ( ( bit_se6528837805403552850or_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 9.17/5.38 = ( numeral_numeral_nat @ ( bit0 @ Y ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4138_xor__numerals_I2_J,axiom,
% 9.17/5.38 ! [Y: num] :
% 9.17/5.38 ( ( bit_se3222712562003087583nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit1 @ Y ) ) )
% 9.17/5.38 = ( numera6620942414471956472nteger @ ( bit0 @ Y ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4139_xor__numerals_I2_J,axiom,
% 9.17/5.38 ! [Y: num] :
% 9.17/5.38 ( ( bit_se6526347334894502574or_int @ one_one_int @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 9.17/5.38 = ( numeral_numeral_int @ ( bit0 @ Y ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4140_xor__numerals_I2_J,axiom,
% 9.17/5.38 ! [Y: num] :
% 9.17/5.38 ( ( bit_se2046307713759805098atural @ one_one_Code_natural @ ( numera5444537566228673987atural @ ( bit1 @ Y ) ) )
% 9.17/5.38 = ( numera5444537566228673987atural @ ( bit0 @ Y ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4141_xor__numerals_I5_J,axiom,
% 9.17/5.38 ! [X: num] :
% 9.17/5.38 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ one_one_nat )
% 9.17/5.38 = ( numeral_numeral_nat @ ( bit1 @ X ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4142_xor__numerals_I5_J,axiom,
% 9.17/5.38 ! [X: num] :
% 9.17/5.38 ( ( bit_se3222712562003087583nteger @ ( numera6620942414471956472nteger @ ( bit0 @ X ) ) @ one_one_Code_integer )
% 9.17/5.38 = ( numera6620942414471956472nteger @ ( bit1 @ X ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4143_xor__numerals_I5_J,axiom,
% 9.17/5.38 ! [X: num] :
% 9.17/5.38 ( ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ one_one_int )
% 9.17/5.38 = ( numeral_numeral_int @ ( bit1 @ X ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4144_xor__numerals_I5_J,axiom,
% 9.17/5.38 ! [X: num] :
% 9.17/5.38 ( ( bit_se2046307713759805098atural @ ( numera5444537566228673987atural @ ( bit0 @ X ) ) @ one_one_Code_natural )
% 9.17/5.38 = ( numera5444537566228673987atural @ ( bit1 @ X ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4145_xor__numerals_I8_J,axiom,
% 9.17/5.38 ! [X: num] :
% 9.17/5.38 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ one_one_nat )
% 9.17/5.38 = ( numeral_numeral_nat @ ( bit0 @ X ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4146_xor__numerals_I8_J,axiom,
% 9.17/5.38 ! [X: num] :
% 9.17/5.38 ( ( bit_se3222712562003087583nteger @ ( numera6620942414471956472nteger @ ( bit1 @ X ) ) @ one_one_Code_integer )
% 9.17/5.38 = ( numera6620942414471956472nteger @ ( bit0 @ X ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4147_xor__numerals_I8_J,axiom,
% 9.17/5.38 ! [X: num] :
% 9.17/5.38 ( ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ one_one_int )
% 9.17/5.38 = ( numeral_numeral_int @ ( bit0 @ X ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4148_xor__numerals_I8_J,axiom,
% 9.17/5.38 ! [X: num] :
% 9.17/5.38 ( ( bit_se2046307713759805098atural @ ( numera5444537566228673987atural @ ( bit1 @ X ) ) @ one_one_Code_natural )
% 9.17/5.38 = ( numera5444537566228673987atural @ ( bit0 @ X ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4149_push__bit__of__1,axiom,
% 9.17/5.38 ! [N2: nat] :
% 9.17/5.38 ( ( bit_se547839408752420682it_nat @ N2 @ one_one_nat )
% 9.17/5.38 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4150_push__bit__of__1,axiom,
% 9.17/5.38 ! [N2: nat] :
% 9.17/5.38 ( ( bit_se7788150548672797655nteger @ N2 @ one_one_Code_integer )
% 9.17/5.38 = ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4151_push__bit__of__1,axiom,
% 9.17/5.38 ! [N2: nat] :
% 9.17/5.38 ( ( bit_se545348938243370406it_int @ N2 @ one_one_int )
% 9.17/5.38 = ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4152_push__bit__of__1,axiom,
% 9.17/5.38 ! [N2: nat] :
% 9.17/5.38 ( ( bit_se6611745700429515170atural @ N2 @ one_one_Code_natural )
% 9.17/5.38 = ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N2 ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4153_sum_Oop__ivl__Suc,axiom,
% 9.17/5.38 ! [N2: nat,M2: nat,G: nat > code_integer] :
% 9.17/5.38 ( ( ( ord_less_nat @ N2 @ M2 )
% 9.17/5.38 => ( ( groups7501900531339628137nteger @ G @ ( set_or4665077453230672383an_nat @ M2 @ ( suc @ N2 ) ) )
% 9.17/5.38 = zero_z3403309356797280102nteger ) )
% 9.17/5.38 & ( ~ ( ord_less_nat @ N2 @ M2 )
% 9.17/5.38 => ( ( groups7501900531339628137nteger @ G @ ( set_or4665077453230672383an_nat @ M2 @ ( suc @ N2 ) ) )
% 9.17/5.38 = ( plus_p5714425477246183910nteger @ ( groups7501900531339628137nteger @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) @ ( G @ N2 ) ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4154_sum_Oop__ivl__Suc,axiom,
% 9.17/5.38 ! [N2: nat,M2: nat,G: nat > multis2468970476368604999at_nat] :
% 9.17/5.38 ( ( ( ord_less_nat @ N2 @ M2 )
% 9.17/5.38 => ( ( groups6857163185585827899at_nat @ G @ ( set_or4665077453230672383an_nat @ M2 @ ( suc @ N2 ) ) )
% 9.17/5.38 = zero_z1048942125864253310at_nat ) )
% 9.17/5.38 & ( ~ ( ord_less_nat @ N2 @ M2 )
% 9.17/5.38 => ( ( groups6857163185585827899at_nat @ G @ ( set_or4665077453230672383an_nat @ M2 @ ( suc @ N2 ) ) )
% 9.17/5.38 = ( plus_p7104986032573967614at_nat @ ( groups6857163185585827899at_nat @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) @ ( G @ N2 ) ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4155_sum_Oop__ivl__Suc,axiom,
% 9.17/5.38 ! [N2: nat,M2: nat,G: nat > rat] :
% 9.17/5.38 ( ( ( ord_less_nat @ N2 @ M2 )
% 9.17/5.38 => ( ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ M2 @ ( suc @ N2 ) ) )
% 9.17/5.38 = zero_zero_rat ) )
% 9.17/5.38 & ( ~ ( ord_less_nat @ N2 @ M2 )
% 9.17/5.38 => ( ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ M2 @ ( suc @ N2 ) ) )
% 9.17/5.38 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) @ ( G @ N2 ) ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4156_sum_Oop__ivl__Suc,axiom,
% 9.17/5.38 ! [N2: nat,M2: nat,G: nat > int] :
% 9.17/5.38 ( ( ( ord_less_nat @ N2 @ M2 )
% 9.17/5.38 => ( ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ M2 @ ( suc @ N2 ) ) )
% 9.17/5.38 = zero_zero_int ) )
% 9.17/5.38 & ( ~ ( ord_less_nat @ N2 @ M2 )
% 9.17/5.38 => ( ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ M2 @ ( suc @ N2 ) ) )
% 9.17/5.38 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) @ ( G @ N2 ) ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4157_sum_Oop__ivl__Suc,axiom,
% 9.17/5.38 ! [N2: nat,M2: nat,G: nat > nat] :
% 9.17/5.38 ( ( ( ord_less_nat @ N2 @ M2 )
% 9.17/5.38 => ( ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ M2 @ ( suc @ N2 ) ) )
% 9.17/5.38 = zero_zero_nat ) )
% 9.17/5.38 & ( ~ ( ord_less_nat @ N2 @ M2 )
% 9.17/5.38 => ( ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ M2 @ ( suc @ N2 ) ) )
% 9.17/5.38 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) @ ( G @ N2 ) ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4158_xor__numerals_I4_J,axiom,
% 9.17/5.38 ! [X: num,Y: num] :
% 9.17/5.38 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 9.17/5.38 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4159_xor__numerals_I4_J,axiom,
% 9.17/5.38 ! [X: num,Y: num] :
% 9.17/5.38 ( ( bit_se3222712562003087583nteger @ ( numera6620942414471956472nteger @ ( bit0 @ X ) ) @ ( numera6620942414471956472nteger @ ( bit1 @ Y ) ) )
% 9.17/5.38 = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se3222712562003087583nteger @ ( numera6620942414471956472nteger @ X ) @ ( numera6620942414471956472nteger @ Y ) ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4160_xor__numerals_I4_J,axiom,
% 9.17/5.38 ! [X: num,Y: num] :
% 9.17/5.38 ( ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 9.17/5.38 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4161_xor__numerals_I4_J,axiom,
% 9.17/5.38 ! [X: num,Y: num] :
% 9.17/5.38 ( ( bit_se2046307713759805098atural @ ( numera5444537566228673987atural @ ( bit0 @ X ) ) @ ( numera5444537566228673987atural @ ( bit1 @ Y ) ) )
% 9.17/5.38 = ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se2046307713759805098atural @ ( numera5444537566228673987atural @ X ) @ ( numera5444537566228673987atural @ Y ) ) ) ) ) ).
% 9.17/5.38
% 9.17/5.38 thf(fact_4162_xor__numerals_I6_J,axiom,
% 9.17/5.38 ! [X: num,Y: num] :
% 9.17/5.38 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 9.17/5.38 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4163_xor__numerals_I6_J,axiom,
% 9.17/5.39 ! [X: num,Y: num] :
% 9.17/5.39 ( ( bit_se3222712562003087583nteger @ ( numera6620942414471956472nteger @ ( bit1 @ X ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Y ) ) )
% 9.17/5.39 = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se3222712562003087583nteger @ ( numera6620942414471956472nteger @ X ) @ ( numera6620942414471956472nteger @ Y ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4164_xor__numerals_I6_J,axiom,
% 9.17/5.39 ! [X: num,Y: num] :
% 9.17/5.39 ( ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 9.17/5.39 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4165_xor__numerals_I6_J,axiom,
% 9.17/5.39 ! [X: num,Y: num] :
% 9.17/5.39 ( ( bit_se2046307713759805098atural @ ( numera5444537566228673987atural @ ( bit1 @ X ) ) @ ( numera5444537566228673987atural @ ( bit0 @ Y ) ) )
% 9.17/5.39 = ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se2046307713759805098atural @ ( numera5444537566228673987atural @ X ) @ ( numera5444537566228673987atural @ Y ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4166_flip__bit__nat__def,axiom,
% 9.17/5.39 ( bit_se2161824704523386999it_nat
% 9.17/5.39 = ( ^ [M: nat,N4: nat] : ( bit_se6528837805403552850or_nat @ N4 @ ( bit_se547839408752420682it_nat @ M @ one_one_nat ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4167_push__bit__integer_Oabs__eq,axiom,
% 9.17/5.39 ! [Xa: nat,X: int] :
% 9.17/5.39 ( ( bit_se7788150548672797655nteger @ Xa @ ( code_integer_of_int @ X ) )
% 9.17/5.39 = ( code_integer_of_int @ ( bit_se545348938243370406it_int @ Xa @ X ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4168_atLeastLessThan__inj_I2_J,axiom,
% 9.17/5.39 ! [A: rat,B: rat,C: rat,D2: rat] :
% 9.17/5.39 ( ( ( set_or4029947393144176647an_rat @ A @ B )
% 9.17/5.39 = ( set_or4029947393144176647an_rat @ C @ D2 ) )
% 9.17/5.39 => ( ( ord_less_rat @ A @ B )
% 9.17/5.39 => ( ( ord_less_rat @ C @ D2 )
% 9.17/5.39 => ( B = D2 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4169_atLeastLessThan__inj_I2_J,axiom,
% 9.17/5.39 ! [A: num,B: num,C: num,D2: num] :
% 9.17/5.39 ( ( ( set_or1222409239386451017an_num @ A @ B )
% 9.17/5.39 = ( set_or1222409239386451017an_num @ C @ D2 ) )
% 9.17/5.39 => ( ( ord_less_num @ A @ B )
% 9.17/5.39 => ( ( ord_less_num @ C @ D2 )
% 9.17/5.39 => ( B = D2 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4170_atLeastLessThan__inj_I2_J,axiom,
% 9.17/5.39 ! [A: nat,B: nat,C: nat,D2: nat] :
% 9.17/5.39 ( ( ( set_or4665077453230672383an_nat @ A @ B )
% 9.17/5.39 = ( set_or4665077453230672383an_nat @ C @ D2 ) )
% 9.17/5.39 => ( ( ord_less_nat @ A @ B )
% 9.17/5.39 => ( ( ord_less_nat @ C @ D2 )
% 9.17/5.39 => ( B = D2 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4171_atLeastLessThan__inj_I2_J,axiom,
% 9.17/5.39 ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 9.17/5.39 ( ( ( set_or8404916559141939852nteger @ A @ B )
% 9.17/5.39 = ( set_or8404916559141939852nteger @ C @ D2 ) )
% 9.17/5.39 => ( ( ord_le6747313008572928689nteger @ A @ B )
% 9.17/5.39 => ( ( ord_le6747313008572928689nteger @ C @ D2 )
% 9.17/5.39 => ( B = D2 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4172_atLeastLessThan__inj_I2_J,axiom,
% 9.17/5.39 ! [A: int,B: int,C: int,D2: int] :
% 9.17/5.39 ( ( ( set_or4662586982721622107an_int @ A @ B )
% 9.17/5.39 = ( set_or4662586982721622107an_int @ C @ D2 ) )
% 9.17/5.39 => ( ( ord_less_int @ A @ B )
% 9.17/5.39 => ( ( ord_less_int @ C @ D2 )
% 9.17/5.39 => ( B = D2 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4173_atLeastLessThan__inj_I1_J,axiom,
% 9.17/5.39 ! [A: rat,B: rat,C: rat,D2: rat] :
% 9.17/5.39 ( ( ( set_or4029947393144176647an_rat @ A @ B )
% 9.17/5.39 = ( set_or4029947393144176647an_rat @ C @ D2 ) )
% 9.17/5.39 => ( ( ord_less_rat @ A @ B )
% 9.17/5.39 => ( ( ord_less_rat @ C @ D2 )
% 9.17/5.39 => ( A = C ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4174_atLeastLessThan__inj_I1_J,axiom,
% 9.17/5.39 ! [A: num,B: num,C: num,D2: num] :
% 9.17/5.39 ( ( ( set_or1222409239386451017an_num @ A @ B )
% 9.17/5.39 = ( set_or1222409239386451017an_num @ C @ D2 ) )
% 9.17/5.39 => ( ( ord_less_num @ A @ B )
% 9.17/5.39 => ( ( ord_less_num @ C @ D2 )
% 9.17/5.39 => ( A = C ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4175_atLeastLessThan__inj_I1_J,axiom,
% 9.17/5.39 ! [A: nat,B: nat,C: nat,D2: nat] :
% 9.17/5.39 ( ( ( set_or4665077453230672383an_nat @ A @ B )
% 9.17/5.39 = ( set_or4665077453230672383an_nat @ C @ D2 ) )
% 9.17/5.39 => ( ( ord_less_nat @ A @ B )
% 9.17/5.39 => ( ( ord_less_nat @ C @ D2 )
% 9.17/5.39 => ( A = C ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4176_atLeastLessThan__inj_I1_J,axiom,
% 9.17/5.39 ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 9.17/5.39 ( ( ( set_or8404916559141939852nteger @ A @ B )
% 9.17/5.39 = ( set_or8404916559141939852nteger @ C @ D2 ) )
% 9.17/5.39 => ( ( ord_le6747313008572928689nteger @ A @ B )
% 9.17/5.39 => ( ( ord_le6747313008572928689nteger @ C @ D2 )
% 9.17/5.39 => ( A = C ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4177_atLeastLessThan__inj_I1_J,axiom,
% 9.17/5.39 ! [A: int,B: int,C: int,D2: int] :
% 9.17/5.39 ( ( ( set_or4662586982721622107an_int @ A @ B )
% 9.17/5.39 = ( set_or4662586982721622107an_int @ C @ D2 ) )
% 9.17/5.39 => ( ( ord_less_int @ A @ B )
% 9.17/5.39 => ( ( ord_less_int @ C @ D2 )
% 9.17/5.39 => ( A = C ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4178_atLeastLessThan__eq__iff,axiom,
% 9.17/5.39 ! [A: rat,B: rat,C: rat,D2: rat] :
% 9.17/5.39 ( ( ord_less_rat @ A @ B )
% 9.17/5.39 => ( ( ord_less_rat @ C @ D2 )
% 9.17/5.39 => ( ( ( set_or4029947393144176647an_rat @ A @ B )
% 9.17/5.39 = ( set_or4029947393144176647an_rat @ C @ D2 ) )
% 9.17/5.39 = ( ( A = C )
% 9.17/5.39 & ( B = D2 ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4179_atLeastLessThan__eq__iff,axiom,
% 9.17/5.39 ! [A: num,B: num,C: num,D2: num] :
% 9.17/5.39 ( ( ord_less_num @ A @ B )
% 9.17/5.39 => ( ( ord_less_num @ C @ D2 )
% 9.17/5.39 => ( ( ( set_or1222409239386451017an_num @ A @ B )
% 9.17/5.39 = ( set_or1222409239386451017an_num @ C @ D2 ) )
% 9.17/5.39 = ( ( A = C )
% 9.17/5.39 & ( B = D2 ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4180_atLeastLessThan__eq__iff,axiom,
% 9.17/5.39 ! [A: nat,B: nat,C: nat,D2: nat] :
% 9.17/5.39 ( ( ord_less_nat @ A @ B )
% 9.17/5.39 => ( ( ord_less_nat @ C @ D2 )
% 9.17/5.39 => ( ( ( set_or4665077453230672383an_nat @ A @ B )
% 9.17/5.39 = ( set_or4665077453230672383an_nat @ C @ D2 ) )
% 9.17/5.39 = ( ( A = C )
% 9.17/5.39 & ( B = D2 ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4181_atLeastLessThan__eq__iff,axiom,
% 9.17/5.39 ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 9.17/5.39 ( ( ord_le6747313008572928689nteger @ A @ B )
% 9.17/5.39 => ( ( ord_le6747313008572928689nteger @ C @ D2 )
% 9.17/5.39 => ( ( ( set_or8404916559141939852nteger @ A @ B )
% 9.17/5.39 = ( set_or8404916559141939852nteger @ C @ D2 ) )
% 9.17/5.39 = ( ( A = C )
% 9.17/5.39 & ( B = D2 ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4182_atLeastLessThan__eq__iff,axiom,
% 9.17/5.39 ! [A: int,B: int,C: int,D2: int] :
% 9.17/5.39 ( ( ord_less_int @ A @ B )
% 9.17/5.39 => ( ( ord_less_int @ C @ D2 )
% 9.17/5.39 => ( ( ( set_or4662586982721622107an_int @ A @ B )
% 9.17/5.39 = ( set_or4662586982721622107an_int @ C @ D2 ) )
% 9.17/5.39 = ( ( A = C )
% 9.17/5.39 & ( B = D2 ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4183_flip__bit__eq__xor,axiom,
% 9.17/5.39 ( bit_se2161824704523386999it_nat
% 9.17/5.39 = ( ^ [N4: nat,A5: nat] : ( bit_se6528837805403552850or_nat @ A5 @ ( bit_se547839408752420682it_nat @ N4 @ one_one_nat ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4184_flip__bit__eq__xor,axiom,
% 9.17/5.39 ( bit_se1345352211410354436nteger
% 9.17/5.39 = ( ^ [N4: nat,A5: code_integer] : ( bit_se3222712562003087583nteger @ A5 @ ( bit_se7788150548672797655nteger @ N4 @ one_one_Code_integer ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4185_flip__bit__eq__xor,axiom,
% 9.17/5.39 ( bit_se2159334234014336723it_int
% 9.17/5.39 = ( ^ [N4: nat,A5: int] : ( bit_se6526347334894502574or_int @ A5 @ ( bit_se545348938243370406it_int @ N4 @ one_one_int ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4186_flip__bit__eq__xor,axiom,
% 9.17/5.39 ( bit_se168947363167071951atural
% 9.17/5.39 = ( ^ [N4: nat,A5: code_natural] : ( bit_se2046307713759805098atural @ A5 @ ( bit_se6611745700429515170atural @ N4 @ one_one_Code_natural ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4187_push__bit__add,axiom,
% 9.17/5.39 ! [N2: nat,A: nat,B: nat] :
% 9.17/5.39 ( ( bit_se547839408752420682it_nat @ N2 @ ( plus_plus_nat @ A @ B ) )
% 9.17/5.39 = ( plus_plus_nat @ ( bit_se547839408752420682it_nat @ N2 @ A ) @ ( bit_se547839408752420682it_nat @ N2 @ B ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4188_push__bit__add,axiom,
% 9.17/5.39 ! [N2: nat,A: code_integer,B: code_integer] :
% 9.17/5.39 ( ( bit_se7788150548672797655nteger @ N2 @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 9.17/5.39 = ( plus_p5714425477246183910nteger @ ( bit_se7788150548672797655nteger @ N2 @ A ) @ ( bit_se7788150548672797655nteger @ N2 @ B ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4189_push__bit__add,axiom,
% 9.17/5.39 ! [N2: nat,A: int,B: int] :
% 9.17/5.39 ( ( bit_se545348938243370406it_int @ N2 @ ( plus_plus_int @ A @ B ) )
% 9.17/5.39 = ( plus_plus_int @ ( bit_se545348938243370406it_int @ N2 @ A ) @ ( bit_se545348938243370406it_int @ N2 @ B ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4190_push__bit__add,axiom,
% 9.17/5.39 ! [N2: nat,A: code_natural,B: code_natural] :
% 9.17/5.39 ( ( bit_se6611745700429515170atural @ N2 @ ( plus_p4538020629002901425atural @ A @ B ) )
% 9.17/5.39 = ( plus_p4538020629002901425atural @ ( bit_se6611745700429515170atural @ N2 @ A ) @ ( bit_se6611745700429515170atural @ N2 @ B ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4191_atLeastLessThan__subset__iff,axiom,
% 9.17/5.39 ! [A: rat,B: rat,C: rat,D2: rat] :
% 9.17/5.39 ( ( ord_less_eq_set_rat @ ( set_or4029947393144176647an_rat @ A @ B ) @ ( set_or4029947393144176647an_rat @ C @ D2 ) )
% 9.17/5.39 => ( ( ord_less_eq_rat @ B @ A )
% 9.17/5.39 | ( ( ord_less_eq_rat @ C @ A )
% 9.17/5.39 & ( ord_less_eq_rat @ B @ D2 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4192_atLeastLessThan__subset__iff,axiom,
% 9.17/5.39 ! [A: num,B: num,C: num,D2: num] :
% 9.17/5.39 ( ( ord_less_eq_set_num @ ( set_or1222409239386451017an_num @ A @ B ) @ ( set_or1222409239386451017an_num @ C @ D2 ) )
% 9.17/5.39 => ( ( ord_less_eq_num @ B @ A )
% 9.17/5.39 | ( ( ord_less_eq_num @ C @ A )
% 9.17/5.39 & ( ord_less_eq_num @ B @ D2 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4193_atLeastLessThan__subset__iff,axiom,
% 9.17/5.39 ! [A: nat,B: nat,C: nat,D2: nat] :
% 9.17/5.39 ( ( ord_less_eq_set_nat @ ( set_or4665077453230672383an_nat @ A @ B ) @ ( set_or4665077453230672383an_nat @ C @ D2 ) )
% 9.17/5.39 => ( ( ord_less_eq_nat @ B @ A )
% 9.17/5.39 | ( ( ord_less_eq_nat @ C @ A )
% 9.17/5.39 & ( ord_less_eq_nat @ B @ D2 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4194_atLeastLessThan__subset__iff,axiom,
% 9.17/5.39 ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 9.17/5.39 ( ( ord_le7084787975880047091nteger @ ( set_or8404916559141939852nteger @ A @ B ) @ ( set_or8404916559141939852nteger @ C @ D2 ) )
% 9.17/5.39 => ( ( ord_le3102999989581377725nteger @ B @ A )
% 9.17/5.39 | ( ( ord_le3102999989581377725nteger @ C @ A )
% 9.17/5.39 & ( ord_le3102999989581377725nteger @ B @ D2 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4195_atLeastLessThan__subset__iff,axiom,
% 9.17/5.39 ! [A: int,B: int,C: int,D2: int] :
% 9.17/5.39 ( ( ord_less_eq_set_int @ ( set_or4662586982721622107an_int @ A @ B ) @ ( set_or4662586982721622107an_int @ C @ D2 ) )
% 9.17/5.39 => ( ( ord_less_eq_int @ B @ A )
% 9.17/5.39 | ( ( ord_less_eq_int @ C @ A )
% 9.17/5.39 & ( ord_less_eq_int @ B @ D2 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4196_atLeastLessThanSuc__atLeastAtMost,axiom,
% 9.17/5.39 ! [L: nat,U: nat] :
% 9.17/5.39 ( ( set_or4665077453230672383an_nat @ L @ ( suc @ U ) )
% 9.17/5.39 = ( set_or1269000886237332187st_nat @ L @ U ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4197_lessThan__atLeast0,axiom,
% 9.17/5.39 ( set_ord_lessThan_nat
% 9.17/5.39 = ( set_or4665077453230672383an_nat @ zero_zero_nat ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4198_push__bit__take__bit,axiom,
% 9.17/5.39 ! [M2: nat,N2: nat,A: code_integer] :
% 9.17/5.39 ( ( bit_se7788150548672797655nteger @ M2 @ ( bit_se1745604003318907178nteger @ N2 @ A ) )
% 9.17/5.39 = ( bit_se1745604003318907178nteger @ ( plus_plus_nat @ M2 @ N2 ) @ ( bit_se7788150548672797655nteger @ M2 @ A ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4199_push__bit__take__bit,axiom,
% 9.17/5.39 ! [M2: nat,N2: nat,A: int] :
% 9.17/5.39 ( ( bit_se545348938243370406it_int @ M2 @ ( bit_se2923211474154528505it_int @ N2 @ A ) )
% 9.17/5.39 = ( bit_se2923211474154528505it_int @ ( plus_plus_nat @ M2 @ N2 ) @ ( bit_se545348938243370406it_int @ M2 @ A ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4200_push__bit__take__bit,axiom,
% 9.17/5.39 ! [M2: nat,N2: nat,A: nat] :
% 9.17/5.39 ( ( bit_se547839408752420682it_nat @ M2 @ ( bit_se2925701944663578781it_nat @ N2 @ A ) )
% 9.17/5.39 = ( bit_se2925701944663578781it_nat @ ( plus_plus_nat @ M2 @ N2 ) @ ( bit_se547839408752420682it_nat @ M2 @ A ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4201_push__bit__take__bit,axiom,
% 9.17/5.39 ! [M2: nat,N2: nat,A: code_natural] :
% 9.17/5.39 ( ( bit_se6611745700429515170atural @ M2 @ ( bit_se569199155075624693atural @ N2 @ A ) )
% 9.17/5.39 = ( bit_se569199155075624693atural @ ( plus_plus_nat @ M2 @ N2 ) @ ( bit_se6611745700429515170atural @ M2 @ A ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4202_pochhammer__fact,axiom,
% 9.17/5.39 ( semiri3624122377584611663nteger
% 9.17/5.39 = ( comm_s8582702949713902594nteger @ one_one_Code_integer ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4203_pochhammer__fact,axiom,
% 9.17/5.39 ( semiri773545260158071498ct_rat
% 9.17/5.39 = ( comm_s4028243227959126397er_rat @ one_one_rat ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4204_pochhammer__fact,axiom,
% 9.17/5.39 ( semiri1406184849735516958ct_int
% 9.17/5.39 = ( comm_s4660882817536571857er_int @ one_one_int ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4205_pochhammer__fact,axiom,
% 9.17/5.39 ( semiri1408675320244567234ct_nat
% 9.17/5.39 = ( comm_s4663373288045622133er_nat @ one_one_nat ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4206_sum_Oshift__bounds__Suc__ivl,axiom,
% 9.17/5.39 ! [G: nat > nat,M2: nat,N2: nat] :
% 9.17/5.39 ( ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ ( suc @ M2 ) @ ( suc @ N2 ) ) )
% 9.17/5.39 = ( groups3542108847815614940at_nat
% 9.17/5.39 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 9.17/5.39 @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4207_sum_Oshift__bounds__nat__ivl,axiom,
% 9.17/5.39 ! [G: nat > nat,M2: nat,K: nat,N2: nat] :
% 9.17/5.39 ( ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ ( plus_plus_nat @ M2 @ K ) @ ( plus_plus_nat @ N2 @ K ) ) )
% 9.17/5.39 = ( groups3542108847815614940at_nat
% 9.17/5.39 @ ^ [I3: nat] : ( G @ ( plus_plus_nat @ I3 @ K ) )
% 9.17/5.39 @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4208_sum_Oivl__cong,axiom,
% 9.17/5.39 ! [A: nat,C: nat,B: nat,D2: nat,G: nat > nat,H3: nat > nat] :
% 9.17/5.39 ( ( A = C )
% 9.17/5.39 => ( ( B = D2 )
% 9.17/5.39 => ( ! [X4: nat] :
% 9.17/5.39 ( ( ord_less_eq_nat @ C @ X4 )
% 9.17/5.39 => ( ( ord_less_nat @ X4 @ D2 )
% 9.17/5.39 => ( ( G @ X4 )
% 9.17/5.39 = ( H3 @ X4 ) ) ) )
% 9.17/5.39 => ( ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ A @ B ) )
% 9.17/5.39 = ( groups3542108847815614940at_nat @ H3 @ ( set_or4665077453230672383an_nat @ C @ D2 ) ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4209_sum_Oivl__cong,axiom,
% 9.17/5.39 ! [A: int,C: int,B: int,D2: int,G: int > int,H3: int > int] :
% 9.17/5.39 ( ( A = C )
% 9.17/5.39 => ( ( B = D2 )
% 9.17/5.39 => ( ! [X4: int] :
% 9.17/5.39 ( ( ord_less_eq_int @ C @ X4 )
% 9.17/5.39 => ( ( ord_less_int @ X4 @ D2 )
% 9.17/5.39 => ( ( G @ X4 )
% 9.17/5.39 = ( H3 @ X4 ) ) ) )
% 9.17/5.39 => ( ( groups4538972089207619220nt_int @ G @ ( set_or4662586982721622107an_int @ A @ B ) )
% 9.17/5.39 = ( groups4538972089207619220nt_int @ H3 @ ( set_or4662586982721622107an_int @ C @ D2 ) ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4210_sum_OatLeastLessThan__concat,axiom,
% 9.17/5.39 ! [M2: nat,N2: nat,P4: nat,G: nat > multis2468970476368604999at_nat] :
% 9.17/5.39 ( ( ord_less_eq_nat @ M2 @ N2 )
% 9.17/5.39 => ( ( ord_less_eq_nat @ N2 @ P4 )
% 9.17/5.39 => ( ( plus_p7104986032573967614at_nat @ ( groups6857163185585827899at_nat @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) @ ( groups6857163185585827899at_nat @ G @ ( set_or4665077453230672383an_nat @ N2 @ P4 ) ) )
% 9.17/5.39 = ( groups6857163185585827899at_nat @ G @ ( set_or4665077453230672383an_nat @ M2 @ P4 ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4211_sum_OatLeastLessThan__concat,axiom,
% 9.17/5.39 ! [M2: nat,N2: nat,P4: nat,G: nat > rat] :
% 9.17/5.39 ( ( ord_less_eq_nat @ M2 @ N2 )
% 9.17/5.39 => ( ( ord_less_eq_nat @ N2 @ P4 )
% 9.17/5.39 => ( ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) @ ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ N2 @ P4 ) ) )
% 9.17/5.39 = ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ M2 @ P4 ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4212_sum_OatLeastLessThan__concat,axiom,
% 9.17/5.39 ! [M2: nat,N2: nat,P4: nat,G: nat > int] :
% 9.17/5.39 ( ( ord_less_eq_nat @ M2 @ N2 )
% 9.17/5.39 => ( ( ord_less_eq_nat @ N2 @ P4 )
% 9.17/5.39 => ( ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) @ ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ N2 @ P4 ) ) )
% 9.17/5.39 = ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ M2 @ P4 ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4213_sum_OatLeastLessThan__concat,axiom,
% 9.17/5.39 ! [M2: nat,N2: nat,P4: nat,G: nat > nat] :
% 9.17/5.39 ( ( ord_less_eq_nat @ M2 @ N2 )
% 9.17/5.39 => ( ( ord_less_eq_nat @ N2 @ P4 )
% 9.17/5.39 => ( ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) @ ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ N2 @ P4 ) ) )
% 9.17/5.39 = ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ M2 @ P4 ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4214_sum__diff__nat__ivl,axiom,
% 9.17/5.39 ! [M2: nat,N2: nat,P4: nat,F: nat > code_integer] :
% 9.17/5.39 ( ( ord_less_eq_nat @ M2 @ N2 )
% 9.17/5.39 => ( ( ord_less_eq_nat @ N2 @ P4 )
% 9.17/5.39 => ( ( minus_8373710615458151222nteger @ ( groups7501900531339628137nteger @ F @ ( set_or4665077453230672383an_nat @ M2 @ P4 ) ) @ ( groups7501900531339628137nteger @ F @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) )
% 9.17/5.39 = ( groups7501900531339628137nteger @ F @ ( set_or4665077453230672383an_nat @ N2 @ P4 ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4215_sum__diff__nat__ivl,axiom,
% 9.17/5.39 ! [M2: nat,N2: nat,P4: nat,F: nat > rat] :
% 9.17/5.39 ( ( ord_less_eq_nat @ M2 @ N2 )
% 9.17/5.39 => ( ( ord_less_eq_nat @ N2 @ P4 )
% 9.17/5.39 => ( ( minus_minus_rat @ ( groups2906978787729119204at_rat @ F @ ( set_or4665077453230672383an_nat @ M2 @ P4 ) ) @ ( groups2906978787729119204at_rat @ F @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) )
% 9.17/5.39 = ( groups2906978787729119204at_rat @ F @ ( set_or4665077453230672383an_nat @ N2 @ P4 ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4216_sum__diff__nat__ivl,axiom,
% 9.17/5.39 ! [M2: nat,N2: nat,P4: nat,F: nat > int] :
% 9.17/5.39 ( ( ord_less_eq_nat @ M2 @ N2 )
% 9.17/5.39 => ( ( ord_less_eq_nat @ N2 @ P4 )
% 9.17/5.39 => ( ( minus_minus_int @ ( groups3539618377306564664at_int @ F @ ( set_or4665077453230672383an_nat @ M2 @ P4 ) ) @ ( groups3539618377306564664at_int @ F @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) )
% 9.17/5.39 = ( groups3539618377306564664at_int @ F @ ( set_or4665077453230672383an_nat @ N2 @ P4 ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4217_pochhammer__0__left,axiom,
% 9.17/5.39 ! [N2: nat] :
% 9.17/5.39 ( ( ( N2 = zero_zero_nat )
% 9.17/5.39 => ( ( comm_s8582702949713902594nteger @ zero_z3403309356797280102nteger @ N2 )
% 9.17/5.39 = one_one_Code_integer ) )
% 9.17/5.39 & ( ( N2 != zero_zero_nat )
% 9.17/5.39 => ( ( comm_s8582702949713902594nteger @ zero_z3403309356797280102nteger @ N2 )
% 9.17/5.39 = zero_z3403309356797280102nteger ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4218_pochhammer__0__left,axiom,
% 9.17/5.39 ! [N2: nat] :
% 9.17/5.39 ( ( ( N2 = zero_zero_nat )
% 9.17/5.39 => ( ( comm_s4028243227959126397er_rat @ zero_zero_rat @ N2 )
% 9.17/5.39 = one_one_rat ) )
% 9.17/5.39 & ( ( N2 != zero_zero_nat )
% 9.17/5.39 => ( ( comm_s4028243227959126397er_rat @ zero_zero_rat @ N2 )
% 9.17/5.39 = zero_zero_rat ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4219_pochhammer__0__left,axiom,
% 9.17/5.39 ! [N2: nat] :
% 9.17/5.39 ( ( ( N2 = zero_zero_nat )
% 9.17/5.39 => ( ( comm_s4663373288045622133er_nat @ zero_zero_nat @ N2 )
% 9.17/5.39 = one_one_nat ) )
% 9.17/5.39 & ( ( N2 != zero_zero_nat )
% 9.17/5.39 => ( ( comm_s4663373288045622133er_nat @ zero_zero_nat @ N2 )
% 9.17/5.39 = zero_zero_nat ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4220_pochhammer__0__left,axiom,
% 9.17/5.39 ! [N2: nat] :
% 9.17/5.39 ( ( ( N2 = zero_zero_nat )
% 9.17/5.39 => ( ( comm_s4660882817536571857er_int @ zero_zero_int @ N2 )
% 9.17/5.39 = one_one_int ) )
% 9.17/5.39 & ( ( N2 != zero_zero_nat )
% 9.17/5.39 => ( ( comm_s4660882817536571857er_int @ zero_zero_int @ N2 )
% 9.17/5.39 = zero_zero_int ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4221_sum_OatLeast__Suc__lessThan__Suc__shift,axiom,
% 9.17/5.39 ! [G: nat > nat,M2: nat,N2: nat] :
% 9.17/5.39 ( ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ ( suc @ M2 ) @ ( suc @ N2 ) ) )
% 9.17/5.39 = ( groups3542108847815614940at_nat @ ( comp_nat_nat_nat @ G @ suc ) @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4222_sum_OatLeastLessThan__shift__bounds,axiom,
% 9.17/5.39 ! [G: nat > nat,M2: nat,K: nat,N2: nat] :
% 9.17/5.39 ( ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ ( plus_plus_nat @ M2 @ K ) @ ( plus_plus_nat @ N2 @ K ) ) )
% 9.17/5.39 = ( groups3542108847815614940at_nat @ ( comp_nat_nat_nat @ G @ ( plus_plus_nat @ K ) ) @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4223_concat__bit__eq,axiom,
% 9.17/5.39 ( bit_concat_bit
% 9.17/5.39 = ( ^ [N4: nat,K4: int,L3: int] : ( plus_plus_int @ ( bit_se2923211474154528505it_int @ N4 @ K4 ) @ ( bit_se545348938243370406it_int @ N4 @ L3 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4224_atLeastAtMost__subseteq__atLeastLessThan__iff,axiom,
% 9.17/5.39 ! [A: set_nat,B: set_nat,C: set_nat,D2: set_nat] :
% 9.17/5.39 ( ( ord_le6893508408891458716et_nat @ ( set_or4548717258645045905et_nat @ A @ B ) @ ( set_or3540276404033026485et_nat @ C @ D2 ) )
% 9.17/5.39 = ( ( ord_less_eq_set_nat @ A @ B )
% 9.17/5.39 => ( ( ord_less_eq_set_nat @ C @ A )
% 9.17/5.39 & ( ord_less_set_nat @ B @ D2 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4225_atLeastAtMost__subseteq__atLeastLessThan__iff,axiom,
% 9.17/5.39 ! [A: rat,B: rat,C: rat,D2: rat] :
% 9.17/5.39 ( ( ord_less_eq_set_rat @ ( set_or633870826150836451st_rat @ A @ B ) @ ( set_or4029947393144176647an_rat @ C @ D2 ) )
% 9.17/5.39 = ( ( ord_less_eq_rat @ A @ B )
% 9.17/5.39 => ( ( ord_less_eq_rat @ C @ A )
% 9.17/5.39 & ( ord_less_rat @ B @ D2 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4226_atLeastAtMost__subseteq__atLeastLessThan__iff,axiom,
% 9.17/5.39 ! [A: num,B: num,C: num,D2: num] :
% 9.17/5.39 ( ( ord_less_eq_set_num @ ( set_or7049704709247886629st_num @ A @ B ) @ ( set_or1222409239386451017an_num @ C @ D2 ) )
% 9.17/5.39 = ( ( ord_less_eq_num @ A @ B )
% 9.17/5.39 => ( ( ord_less_eq_num @ C @ A )
% 9.17/5.39 & ( ord_less_num @ B @ D2 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4227_atLeastAtMost__subseteq__atLeastLessThan__iff,axiom,
% 9.17/5.39 ! [A: nat,B: nat,C: nat,D2: nat] :
% 9.17/5.39 ( ( ord_less_eq_set_nat @ ( set_or1269000886237332187st_nat @ A @ B ) @ ( set_or4665077453230672383an_nat @ C @ D2 ) )
% 9.17/5.39 = ( ( ord_less_eq_nat @ A @ B )
% 9.17/5.39 => ( ( ord_less_eq_nat @ C @ A )
% 9.17/5.39 & ( ord_less_nat @ B @ D2 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4228_atLeastAtMost__subseteq__atLeastLessThan__iff,axiom,
% 9.17/5.39 ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 9.17/5.39 ( ( ord_le7084787975880047091nteger @ ( set_or189985376899183464nteger @ A @ B ) @ ( set_or8404916559141939852nteger @ C @ D2 ) )
% 9.17/5.39 = ( ( ord_le3102999989581377725nteger @ A @ B )
% 9.17/5.39 => ( ( ord_le3102999989581377725nteger @ C @ A )
% 9.17/5.39 & ( ord_le6747313008572928689nteger @ B @ D2 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4229_atLeastAtMost__subseteq__atLeastLessThan__iff,axiom,
% 9.17/5.39 ! [A: int,B: int,C: int,D2: int] :
% 9.17/5.39 ( ( ord_less_eq_set_int @ ( set_or1266510415728281911st_int @ A @ B ) @ ( set_or4662586982721622107an_int @ C @ D2 ) )
% 9.17/5.39 = ( ( ord_less_eq_int @ A @ B )
% 9.17/5.39 => ( ( ord_less_eq_int @ C @ A )
% 9.17/5.39 & ( ord_less_int @ B @ D2 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4230_atLeastLessThan__subseteq__atLeastAtMost__iff,axiom,
% 9.17/5.39 ! [A: rat,B: rat,C: rat,D2: rat] :
% 9.17/5.39 ( ( ord_less_eq_set_rat @ ( set_or4029947393144176647an_rat @ A @ B ) @ ( set_or633870826150836451st_rat @ C @ D2 ) )
% 9.17/5.39 = ( ( ord_less_rat @ A @ B )
% 9.17/5.39 => ( ( ord_less_eq_rat @ C @ A )
% 9.17/5.39 & ( ord_less_eq_rat @ B @ D2 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4231_sum__shift__lb__Suc0__0__upt,axiom,
% 9.17/5.39 ! [F: nat > code_integer,K: nat] :
% 9.17/5.39 ( ( ( F @ zero_zero_nat )
% 9.17/5.39 = zero_z3403309356797280102nteger )
% 9.17/5.39 => ( ( groups7501900531339628137nteger @ F @ ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 9.17/5.39 = ( groups7501900531339628137nteger @ F @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4232_sum__shift__lb__Suc0__0__upt,axiom,
% 9.17/5.39 ! [F: nat > multis2468970476368604999at_nat,K: nat] :
% 9.17/5.39 ( ( ( F @ zero_zero_nat )
% 9.17/5.39 = zero_z1048942125864253310at_nat )
% 9.17/5.39 => ( ( groups6857163185585827899at_nat @ F @ ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 9.17/5.39 = ( groups6857163185585827899at_nat @ F @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4233_sum__shift__lb__Suc0__0__upt,axiom,
% 9.17/5.39 ! [F: nat > rat,K: nat] :
% 9.17/5.39 ( ( ( F @ zero_zero_nat )
% 9.17/5.39 = zero_zero_rat )
% 9.17/5.39 => ( ( groups2906978787729119204at_rat @ F @ ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 9.17/5.39 = ( groups2906978787729119204at_rat @ F @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4234_sum__shift__lb__Suc0__0__upt,axiom,
% 9.17/5.39 ! [F: nat > int,K: nat] :
% 9.17/5.39 ( ( ( F @ zero_zero_nat )
% 9.17/5.39 = zero_zero_int )
% 9.17/5.39 => ( ( groups3539618377306564664at_int @ F @ ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 9.17/5.39 = ( groups3539618377306564664at_int @ F @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4235_sum__shift__lb__Suc0__0__upt,axiom,
% 9.17/5.39 ! [F: nat > nat,K: nat] :
% 9.17/5.39 ( ( ( F @ zero_zero_nat )
% 9.17/5.39 = zero_zero_nat )
% 9.17/5.39 => ( ( groups3542108847815614940at_nat @ F @ ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 9.17/5.39 = ( groups3542108847815614940at_nat @ F @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4236_sum_OatLeast0__lessThan__Suc,axiom,
% 9.17/5.39 ! [G: nat > multis2468970476368604999at_nat,N2: nat] :
% 9.17/5.39 ( ( groups6857163185585827899at_nat @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 9.17/5.39 = ( plus_p7104986032573967614at_nat @ ( groups6857163185585827899at_nat @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4237_sum_OatLeast0__lessThan__Suc,axiom,
% 9.17/5.39 ! [G: nat > rat,N2: nat] :
% 9.17/5.39 ( ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 9.17/5.39 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4238_sum_OatLeast0__lessThan__Suc,axiom,
% 9.17/5.39 ! [G: nat > int,N2: nat] :
% 9.17/5.39 ( ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 9.17/5.39 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4239_sum_OatLeast0__lessThan__Suc,axiom,
% 9.17/5.39 ! [G: nat > nat,N2: nat] :
% 9.17/5.39 ( ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 9.17/5.39 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4240_sum_OatLeast__Suc__lessThan,axiom,
% 9.17/5.39 ! [M2: nat,N2: nat,G: nat > multis2468970476368604999at_nat] :
% 9.17/5.39 ( ( ord_less_nat @ M2 @ N2 )
% 9.17/5.39 => ( ( groups6857163185585827899at_nat @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) )
% 9.17/5.39 = ( plus_p7104986032573967614at_nat @ ( G @ M2 ) @ ( groups6857163185585827899at_nat @ G @ ( set_or4665077453230672383an_nat @ ( suc @ M2 ) @ N2 ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4241_sum_OatLeast__Suc__lessThan,axiom,
% 9.17/5.39 ! [M2: nat,N2: nat,G: nat > rat] :
% 9.17/5.39 ( ( ord_less_nat @ M2 @ N2 )
% 9.17/5.39 => ( ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) )
% 9.17/5.39 = ( plus_plus_rat @ ( G @ M2 ) @ ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ ( suc @ M2 ) @ N2 ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4242_sum_OatLeast__Suc__lessThan,axiom,
% 9.17/5.39 ! [M2: nat,N2: nat,G: nat > int] :
% 9.17/5.39 ( ( ord_less_nat @ M2 @ N2 )
% 9.17/5.39 => ( ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) )
% 9.17/5.39 = ( plus_plus_int @ ( G @ M2 ) @ ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ ( suc @ M2 ) @ N2 ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4243_sum_OatLeast__Suc__lessThan,axiom,
% 9.17/5.39 ! [M2: nat,N2: nat,G: nat > nat] :
% 9.17/5.39 ( ( ord_less_nat @ M2 @ N2 )
% 9.17/5.39 => ( ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) )
% 9.17/5.39 = ( plus_plus_nat @ ( G @ M2 ) @ ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ ( suc @ M2 ) @ N2 ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4244_sum_OatLeastLessThan__Suc,axiom,
% 9.17/5.39 ! [A: nat,B: nat,G: nat > multis2468970476368604999at_nat] :
% 9.17/5.39 ( ( ord_less_eq_nat @ A @ B )
% 9.17/5.39 => ( ( groups6857163185585827899at_nat @ G @ ( set_or4665077453230672383an_nat @ A @ ( suc @ B ) ) )
% 9.17/5.39 = ( plus_p7104986032573967614at_nat @ ( groups6857163185585827899at_nat @ G @ ( set_or4665077453230672383an_nat @ A @ B ) ) @ ( G @ B ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4245_sum_OatLeastLessThan__Suc,axiom,
% 9.17/5.39 ! [A: nat,B: nat,G: nat > rat] :
% 9.17/5.39 ( ( ord_less_eq_nat @ A @ B )
% 9.17/5.39 => ( ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ A @ ( suc @ B ) ) )
% 9.17/5.39 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ A @ B ) ) @ ( G @ B ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4246_sum_OatLeastLessThan__Suc,axiom,
% 9.17/5.39 ! [A: nat,B: nat,G: nat > int] :
% 9.17/5.39 ( ( ord_less_eq_nat @ A @ B )
% 9.17/5.39 => ( ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ A @ ( suc @ B ) ) )
% 9.17/5.39 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ A @ B ) ) @ ( G @ B ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4247_sum_OatLeastLessThan__Suc,axiom,
% 9.17/5.39 ! [A: nat,B: nat,G: nat > nat] :
% 9.17/5.39 ( ( ord_less_eq_nat @ A @ B )
% 9.17/5.39 => ( ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ A @ ( suc @ B ) ) )
% 9.17/5.39 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ A @ B ) ) @ ( G @ B ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4248_sum_Olast__plus,axiom,
% 9.17/5.39 ! [M2: nat,N2: nat,G: nat > multis2468970476368604999at_nat] :
% 9.17/5.39 ( ( ord_less_eq_nat @ M2 @ N2 )
% 9.17/5.39 => ( ( groups6857163185585827899at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 9.17/5.39 = ( plus_p7104986032573967614at_nat @ ( G @ N2 ) @ ( groups6857163185585827899at_nat @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4249_sum_Olast__plus,axiom,
% 9.17/5.39 ! [M2: nat,N2: nat,G: nat > rat] :
% 9.17/5.39 ( ( ord_less_eq_nat @ M2 @ N2 )
% 9.17/5.39 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 9.17/5.39 = ( plus_plus_rat @ ( G @ N2 ) @ ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4250_sum_Olast__plus,axiom,
% 9.17/5.39 ! [M2: nat,N2: nat,G: nat > int] :
% 9.17/5.39 ( ( ord_less_eq_nat @ M2 @ N2 )
% 9.17/5.39 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 9.17/5.39 = ( plus_plus_int @ ( G @ N2 ) @ ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4251_sum_Olast__plus,axiom,
% 9.17/5.39 ! [M2: nat,N2: nat,G: nat > nat] :
% 9.17/5.39 ( ( ord_less_eq_nat @ M2 @ N2 )
% 9.17/5.39 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 9.17/5.39 = ( plus_plus_nat @ ( G @ N2 ) @ ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4252_pochhammer__rec,axiom,
% 9.17/5.39 ! [A: code_integer,N2: nat] :
% 9.17/5.39 ( ( comm_s8582702949713902594nteger @ A @ ( suc @ N2 ) )
% 9.17/5.39 = ( times_3573771949741848930nteger @ A @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4253_pochhammer__rec,axiom,
% 9.17/5.39 ! [A: rat,N2: nat] :
% 9.17/5.39 ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N2 ) )
% 9.17/5.39 = ( times_times_rat @ A @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4254_pochhammer__rec,axiom,
% 9.17/5.39 ! [A: nat,N2: nat] :
% 9.17/5.39 ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N2 ) )
% 9.17/5.39 = ( times_times_nat @ A @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4255_pochhammer__rec,axiom,
% 9.17/5.39 ! [A: int,N2: nat] :
% 9.17/5.39 ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N2 ) )
% 9.17/5.39 = ( times_times_int @ A @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ A @ one_one_int ) @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4256_pochhammer__Suc,axiom,
% 9.17/5.39 ! [A: rat,N2: nat] :
% 9.17/5.39 ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N2 ) )
% 9.17/5.39 = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ A @ N2 ) @ ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ N2 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4257_pochhammer__Suc,axiom,
% 9.17/5.39 ! [A: int,N2: nat] :
% 9.17/5.39 ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N2 ) )
% 9.17/5.39 = ( times_times_int @ ( comm_s4660882817536571857er_int @ A @ N2 ) @ ( plus_plus_int @ A @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4258_pochhammer__Suc,axiom,
% 9.17/5.39 ! [A: nat,N2: nat] :
% 9.17/5.39 ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N2 ) )
% 9.17/5.39 = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ A @ N2 ) @ ( plus_plus_nat @ A @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4259_pochhammer__Suc,axiom,
% 9.17/5.39 ! [A: code_integer,N2: nat] :
% 9.17/5.39 ( ( comm_s8582702949713902594nteger @ A @ ( suc @ N2 ) )
% 9.17/5.39 = ( times_3573771949741848930nteger @ ( comm_s8582702949713902594nteger @ A @ N2 ) @ ( plus_p5714425477246183910nteger @ A @ ( semiri4939895301339042750nteger @ N2 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4260_pochhammer__Suc,axiom,
% 9.17/5.39 ! [A: code_natural,N2: nat] :
% 9.17/5.39 ( ( comm_s7406298101470620109atural @ A @ ( suc @ N2 ) )
% 9.17/5.39 = ( times_2397367101498566445atural @ ( comm_s7406298101470620109atural @ A @ N2 ) @ ( plus_p4538020629002901425atural @ A @ ( semiri3763490453095760265atural @ N2 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4261_pochhammer__rec_H,axiom,
% 9.17/5.39 ! [Z: rat,N2: nat] :
% 9.17/5.39 ( ( comm_s4028243227959126397er_rat @ Z @ ( suc @ N2 ) )
% 9.17/5.39 = ( times_times_rat @ ( plus_plus_rat @ Z @ ( semiri681578069525770553at_rat @ N2 ) ) @ ( comm_s4028243227959126397er_rat @ Z @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4262_pochhammer__rec_H,axiom,
% 9.17/5.39 ! [Z: int,N2: nat] :
% 9.17/5.39 ( ( comm_s4660882817536571857er_int @ Z @ ( suc @ N2 ) )
% 9.17/5.39 = ( times_times_int @ ( plus_plus_int @ Z @ ( semiri1314217659103216013at_int @ N2 ) ) @ ( comm_s4660882817536571857er_int @ Z @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4263_pochhammer__rec_H,axiom,
% 9.17/5.39 ! [Z: nat,N2: nat] :
% 9.17/5.39 ( ( comm_s4663373288045622133er_nat @ Z @ ( suc @ N2 ) )
% 9.17/5.39 = ( times_times_nat @ ( plus_plus_nat @ Z @ ( semiri1316708129612266289at_nat @ N2 ) ) @ ( comm_s4663373288045622133er_nat @ Z @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4264_pochhammer__rec_H,axiom,
% 9.17/5.39 ! [Z: code_integer,N2: nat] :
% 9.17/5.39 ( ( comm_s8582702949713902594nteger @ Z @ ( suc @ N2 ) )
% 9.17/5.39 = ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ Z @ ( semiri4939895301339042750nteger @ N2 ) ) @ ( comm_s8582702949713902594nteger @ Z @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4265_pochhammer__rec_H,axiom,
% 9.17/5.39 ! [Z: code_natural,N2: nat] :
% 9.17/5.39 ( ( comm_s7406298101470620109atural @ Z @ ( suc @ N2 ) )
% 9.17/5.39 = ( times_2397367101498566445atural @ ( plus_p4538020629002901425atural @ Z @ ( semiri3763490453095760265atural @ N2 ) ) @ ( comm_s7406298101470620109atural @ Z @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4266_pochhammer__product_H,axiom,
% 9.17/5.39 ! [Z: rat,N2: nat,M2: nat] :
% 9.17/5.39 ( ( comm_s4028243227959126397er_rat @ Z @ ( plus_plus_nat @ N2 @ M2 ) )
% 9.17/5.39 = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z @ N2 ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( semiri681578069525770553at_rat @ N2 ) ) @ M2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4267_pochhammer__product_H,axiom,
% 9.17/5.39 ! [Z: int,N2: nat,M2: nat] :
% 9.17/5.39 ( ( comm_s4660882817536571857er_int @ Z @ ( plus_plus_nat @ N2 @ M2 ) )
% 9.17/5.39 = ( times_times_int @ ( comm_s4660882817536571857er_int @ Z @ N2 ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ Z @ ( semiri1314217659103216013at_int @ N2 ) ) @ M2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4268_pochhammer__product_H,axiom,
% 9.17/5.39 ! [Z: nat,N2: nat,M2: nat] :
% 9.17/5.39 ( ( comm_s4663373288045622133er_nat @ Z @ ( plus_plus_nat @ N2 @ M2 ) )
% 9.17/5.39 = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ Z @ N2 ) @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ Z @ ( semiri1316708129612266289at_nat @ N2 ) ) @ M2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4269_pochhammer__product_H,axiom,
% 9.17/5.39 ! [Z: code_integer,N2: nat,M2: nat] :
% 9.17/5.39 ( ( comm_s8582702949713902594nteger @ Z @ ( plus_plus_nat @ N2 @ M2 ) )
% 9.17/5.39 = ( times_3573771949741848930nteger @ ( comm_s8582702949713902594nteger @ Z @ N2 ) @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ Z @ ( semiri4939895301339042750nteger @ N2 ) ) @ M2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4270_pochhammer__product_H,axiom,
% 9.17/5.39 ! [Z: code_natural,N2: nat,M2: nat] :
% 9.17/5.39 ( ( comm_s7406298101470620109atural @ Z @ ( plus_plus_nat @ N2 @ M2 ) )
% 9.17/5.39 = ( times_2397367101498566445atural @ ( comm_s7406298101470620109atural @ Z @ N2 ) @ ( comm_s7406298101470620109atural @ ( plus_p4538020629002901425atural @ Z @ ( semiri3763490453095760265atural @ N2 ) ) @ M2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4271_bit__iff__and__push__bit__not__eq__0,axiom,
% 9.17/5.39 ( bit_se1148574629649215175it_nat
% 9.17/5.39 = ( ^ [A5: nat,N4: nat] :
% 9.17/5.39 ( ( bit_se727722235901077358nd_nat @ A5 @ ( bit_se547839408752420682it_nat @ N4 @ one_one_nat ) )
% 9.17/5.39 != zero_zero_nat ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4272_bit__iff__and__push__bit__not__eq__0,axiom,
% 9.17/5.39 ( bit_se9216721137139052372nteger
% 9.17/5.39 = ( ^ [A5: code_integer,N4: nat] :
% 9.17/5.39 ( ( bit_se3949692690581998587nteger @ A5 @ ( bit_se7788150548672797655nteger @ N4 @ one_one_Code_integer ) )
% 9.17/5.39 != zero_z3403309356797280102nteger ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4273_bit__iff__and__push__bit__not__eq__0,axiom,
% 9.17/5.39 ( bit_se1146084159140164899it_int
% 9.17/5.39 = ( ^ [A5: int,N4: nat] :
% 9.17/5.39 ( ( bit_se725231765392027082nd_int @ A5 @ ( bit_se545348938243370406it_int @ N4 @ one_one_int ) )
% 9.17/5.39 != zero_zero_int ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4274_bit__iff__and__push__bit__not__eq__0,axiom,
% 9.17/5.39 ( bit_se8040316288895769887atural
% 9.17/5.39 = ( ^ [A5: code_natural,N4: nat] :
% 9.17/5.39 ( ( bit_se2773287842338716102atural @ A5 @ ( bit_se6611745700429515170atural @ N4 @ one_one_Code_natural ) )
% 9.17/5.39 != zero_z2226904508553997617atural ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4275_sum__Suc__diff_H,axiom,
% 9.17/5.39 ! [M2: nat,N2: nat,F: nat > code_integer] :
% 9.17/5.39 ( ( ord_less_eq_nat @ M2 @ N2 )
% 9.17/5.39 => ( ( groups7501900531339628137nteger
% 9.17/5.39 @ ^ [I3: nat] : ( minus_8373710615458151222nteger @ ( F @ ( suc @ I3 ) ) @ ( F @ I3 ) )
% 9.17/5.39 @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) )
% 9.17/5.39 = ( minus_8373710615458151222nteger @ ( F @ N2 ) @ ( F @ M2 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4276_sum__Suc__diff_H,axiom,
% 9.17/5.39 ! [M2: nat,N2: nat,F: nat > rat] :
% 9.17/5.39 ( ( ord_less_eq_nat @ M2 @ N2 )
% 9.17/5.39 => ( ( groups2906978787729119204at_rat
% 9.17/5.39 @ ^ [I3: nat] : ( minus_minus_rat @ ( F @ ( suc @ I3 ) ) @ ( F @ I3 ) )
% 9.17/5.39 @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) )
% 9.17/5.39 = ( minus_minus_rat @ ( F @ N2 ) @ ( F @ M2 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4277_sum__Suc__diff_H,axiom,
% 9.17/5.39 ! [M2: nat,N2: nat,F: nat > int] :
% 9.17/5.39 ( ( ord_less_eq_nat @ M2 @ N2 )
% 9.17/5.39 => ( ( groups3539618377306564664at_int
% 9.17/5.39 @ ^ [I3: nat] : ( minus_minus_int @ ( F @ ( suc @ I3 ) ) @ ( F @ I3 ) )
% 9.17/5.39 @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) )
% 9.17/5.39 = ( minus_minus_int @ ( F @ N2 ) @ ( F @ M2 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4278_sum_OatLeastLessThan__rev,axiom,
% 9.17/5.39 ! [G: nat > nat,N2: nat,M2: nat] :
% 9.17/5.39 ( ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ N2 @ M2 ) )
% 9.17/5.39 = ( groups3542108847815614940at_nat
% 9.17/5.39 @ ^ [I3: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M2 @ N2 ) @ ( suc @ I3 ) ) )
% 9.17/5.39 @ ( set_or4665077453230672383an_nat @ N2 @ M2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4279_sum_Onested__swap,axiom,
% 9.17/5.39 ! [A: nat > nat > nat,N2: nat] :
% 9.17/5.39 ( ( groups3542108847815614940at_nat
% 9.17/5.39 @ ^ [I3: nat] : ( groups3542108847815614940at_nat @ ( A @ I3 ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ I3 ) )
% 9.17/5.39 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 9.17/5.39 = ( groups3542108847815614940at_nat
% 9.17/5.39 @ ^ [J2: nat] :
% 9.17/5.39 ( groups3542108847815614940at_nat
% 9.17/5.39 @ ^ [I3: nat] : ( A @ I3 @ J2 )
% 9.17/5.39 @ ( set_or1269000886237332187st_nat @ ( suc @ J2 ) @ N2 ) )
% 9.17/5.39 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4280_sum_Onat__group,axiom,
% 9.17/5.39 ! [G: nat > nat,K: nat,N2: nat] :
% 9.17/5.39 ( ( groups3542108847815614940at_nat
% 9.17/5.39 @ ^ [M: nat] : ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ ( times_times_nat @ M @ K ) @ ( plus_plus_nat @ ( times_times_nat @ M @ K ) @ K ) ) )
% 9.17/5.39 @ ( set_ord_lessThan_nat @ N2 ) )
% 9.17/5.39 = ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ ( times_times_nat @ N2 @ K ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4281_numeral__xor__num,axiom,
% 9.17/5.39 ! [M2: num,N2: num] :
% 9.17/5.39 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ N2 ) )
% 9.17/5.39 = ( case_option_nat_num @ zero_zero_nat @ numeral_numeral_nat @ ( bit_un2480387367778600638or_num @ M2 @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4282_numeral__xor__num,axiom,
% 9.17/5.39 ! [M2: num,N2: num] :
% 9.17/5.39 ( ( bit_se3222712562003087583nteger @ ( numera6620942414471956472nteger @ M2 ) @ ( numera6620942414471956472nteger @ N2 ) )
% 9.17/5.39 = ( case_o356765784539232260er_num @ zero_z3403309356797280102nteger @ numera6620942414471956472nteger @ ( bit_un2480387367778600638or_num @ M2 @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4283_numeral__xor__num,axiom,
% 9.17/5.39 ! [M2: num,N2: num] :
% 9.17/5.39 ( ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N2 ) )
% 9.17/5.39 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_un2480387367778600638or_num @ M2 @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4284_numeral__xor__num,axiom,
% 9.17/5.39 ! [M2: num,N2: num] :
% 9.17/5.39 ( ( bit_se2046307713759805098atural @ ( numera5444537566228673987atural @ M2 ) @ ( numera5444537566228673987atural @ N2 ) )
% 9.17/5.39 = ( case_o5621594795226839503al_num @ zero_z2226904508553997617atural @ numera5444537566228673987atural @ ( bit_un2480387367778600638or_num @ M2 @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4285_sum_Ohead__if,axiom,
% 9.17/5.39 ! [N2: nat,M2: nat,G: nat > code_integer] :
% 9.17/5.39 ( ( ( ord_less_nat @ N2 @ M2 )
% 9.17/5.39 => ( ( groups7501900531339628137nteger @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 9.17/5.39 = zero_z3403309356797280102nteger ) )
% 9.17/5.39 & ( ~ ( ord_less_nat @ N2 @ M2 )
% 9.17/5.39 => ( ( groups7501900531339628137nteger @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 9.17/5.39 = ( plus_p5714425477246183910nteger @ ( groups7501900531339628137nteger @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) @ ( G @ N2 ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4286_sum_Ohead__if,axiom,
% 9.17/5.39 ! [N2: nat,M2: nat,G: nat > multis2468970476368604999at_nat] :
% 9.17/5.39 ( ( ( ord_less_nat @ N2 @ M2 )
% 9.17/5.39 => ( ( groups6857163185585827899at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 9.17/5.39 = zero_z1048942125864253310at_nat ) )
% 9.17/5.39 & ( ~ ( ord_less_nat @ N2 @ M2 )
% 9.17/5.39 => ( ( groups6857163185585827899at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 9.17/5.39 = ( plus_p7104986032573967614at_nat @ ( groups6857163185585827899at_nat @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) @ ( G @ N2 ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4287_sum_Ohead__if,axiom,
% 9.17/5.39 ! [N2: nat,M2: nat,G: nat > rat] :
% 9.17/5.39 ( ( ( ord_less_nat @ N2 @ M2 )
% 9.17/5.39 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 9.17/5.39 = zero_zero_rat ) )
% 9.17/5.39 & ( ~ ( ord_less_nat @ N2 @ M2 )
% 9.17/5.39 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 9.17/5.39 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) @ ( G @ N2 ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4288_sum_Ohead__if,axiom,
% 9.17/5.39 ! [N2: nat,M2: nat,G: nat > int] :
% 9.17/5.39 ( ( ( ord_less_nat @ N2 @ M2 )
% 9.17/5.39 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 9.17/5.39 = zero_zero_int ) )
% 9.17/5.39 & ( ~ ( ord_less_nat @ N2 @ M2 )
% 9.17/5.39 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 9.17/5.39 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) @ ( G @ N2 ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4289_sum_Ohead__if,axiom,
% 9.17/5.39 ! [N2: nat,M2: nat,G: nat > nat] :
% 9.17/5.39 ( ( ( ord_less_nat @ N2 @ M2 )
% 9.17/5.39 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 9.17/5.39 = zero_zero_nat ) )
% 9.17/5.39 & ( ~ ( ord_less_nat @ N2 @ M2 )
% 9.17/5.39 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 9.17/5.39 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) @ ( G @ N2 ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4290_sum_OatLeast0__lessThan__Suc__shift,axiom,
% 9.17/5.39 ! [G: nat > multis2468970476368604999at_nat,N2: nat] :
% 9.17/5.39 ( ( groups6857163185585827899at_nat @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 9.17/5.39 = ( plus_p7104986032573967614at_nat @ ( G @ zero_zero_nat ) @ ( groups6857163185585827899at_nat @ ( comp_n8698576032424989604at_nat @ G @ suc ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4291_sum_OatLeast0__lessThan__Suc__shift,axiom,
% 9.17/5.39 ! [G: nat > rat,N2: nat] :
% 9.17/5.39 ( ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 9.17/5.39 = ( plus_plus_rat @ ( G @ zero_zero_nat ) @ ( groups2906978787729119204at_rat @ ( comp_nat_rat_nat @ G @ suc ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4292_sum_OatLeast0__lessThan__Suc__shift,axiom,
% 9.17/5.39 ! [G: nat > int,N2: nat] :
% 9.17/5.39 ( ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 9.17/5.39 = ( plus_plus_int @ ( G @ zero_zero_nat ) @ ( groups3539618377306564664at_int @ ( comp_nat_int_nat @ G @ suc ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4293_sum_OatLeast0__lessThan__Suc__shift,axiom,
% 9.17/5.39 ! [G: nat > nat,N2: nat] :
% 9.17/5.39 ( ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 9.17/5.39 = ( plus_plus_nat @ ( G @ zero_zero_nat ) @ ( groups3542108847815614940at_nat @ ( comp_nat_nat_nat @ G @ suc ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4294_sum_OatLeastLessThan__shift__0,axiom,
% 9.17/5.39 ! [G: nat > nat,M2: nat,N2: nat] :
% 9.17/5.39 ( ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) )
% 9.17/5.39 = ( groups3542108847815614940at_nat @ ( comp_nat_nat_nat @ G @ ( plus_plus_nat @ M2 ) ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( minus_minus_nat @ N2 @ M2 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4295_pochhammer__product,axiom,
% 9.17/5.39 ! [M2: nat,N2: nat,Z: rat] :
% 9.17/5.39 ( ( ord_less_eq_nat @ M2 @ N2 )
% 9.17/5.39 => ( ( comm_s4028243227959126397er_rat @ Z @ N2 )
% 9.17/5.39 = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z @ M2 ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( semiri681578069525770553at_rat @ M2 ) ) @ ( minus_minus_nat @ N2 @ M2 ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4296_pochhammer__product,axiom,
% 9.17/5.39 ! [M2: nat,N2: nat,Z: int] :
% 9.17/5.39 ( ( ord_less_eq_nat @ M2 @ N2 )
% 9.17/5.39 => ( ( comm_s4660882817536571857er_int @ Z @ N2 )
% 9.17/5.39 = ( times_times_int @ ( comm_s4660882817536571857er_int @ Z @ M2 ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ Z @ ( semiri1314217659103216013at_int @ M2 ) ) @ ( minus_minus_nat @ N2 @ M2 ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4297_pochhammer__product,axiom,
% 9.17/5.39 ! [M2: nat,N2: nat,Z: nat] :
% 9.17/5.39 ( ( ord_less_eq_nat @ M2 @ N2 )
% 9.17/5.39 => ( ( comm_s4663373288045622133er_nat @ Z @ N2 )
% 9.17/5.39 = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ Z @ M2 ) @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ Z @ ( semiri1316708129612266289at_nat @ M2 ) ) @ ( minus_minus_nat @ N2 @ M2 ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4298_pochhammer__product,axiom,
% 9.17/5.39 ! [M2: nat,N2: nat,Z: code_integer] :
% 9.17/5.39 ( ( ord_less_eq_nat @ M2 @ N2 )
% 9.17/5.39 => ( ( comm_s8582702949713902594nteger @ Z @ N2 )
% 9.17/5.39 = ( times_3573771949741848930nteger @ ( comm_s8582702949713902594nteger @ Z @ M2 ) @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ Z @ ( semiri4939895301339042750nteger @ M2 ) ) @ ( minus_minus_nat @ N2 @ M2 ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4299_pochhammer__product,axiom,
% 9.17/5.39 ! [M2: nat,N2: nat,Z: code_natural] :
% 9.17/5.39 ( ( ord_less_eq_nat @ M2 @ N2 )
% 9.17/5.39 => ( ( comm_s7406298101470620109atural @ Z @ N2 )
% 9.17/5.39 = ( times_2397367101498566445atural @ ( comm_s7406298101470620109atural @ Z @ M2 ) @ ( comm_s7406298101470620109atural @ ( plus_p4538020629002901425atural @ Z @ ( semiri3763490453095760265atural @ M2 ) ) @ ( minus_minus_nat @ N2 @ M2 ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4300_sum_OatLeastLessThan__rev__at__least__Suc__atMost,axiom,
% 9.17/5.39 ! [G: nat > nat,N2: nat,M2: nat] :
% 9.17/5.39 ( ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ N2 @ M2 ) )
% 9.17/5.39 = ( groups3542108847815614940at_nat
% 9.17/5.39 @ ^ [I3: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M2 @ N2 ) @ I3 ) )
% 9.17/5.39 @ ( set_or1269000886237332187st_nat @ ( suc @ N2 ) @ M2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4301_sum_OatLeast__lessThan__pred__shift,axiom,
% 9.17/5.39 ! [G: nat > nat,M2: nat,N2: nat] :
% 9.17/5.39 ( ( groups3542108847815614940at_nat
% 9.17/5.39 @ ( comp_nat_nat_nat @ G
% 9.17/5.39 @ ^ [N4: nat] : ( minus_minus_nat @ N4 @ ( suc @ zero_zero_nat ) ) )
% 9.17/5.39 @ ( set_or4665077453230672383an_nat @ ( suc @ M2 ) @ ( suc @ N2 ) ) )
% 9.17/5.39 = ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4302_pochhammer__absorb__comp,axiom,
% 9.17/5.39 ! [R2: rat,K: nat] :
% 9.17/5.39 ( ( times_times_rat @ ( minus_minus_rat @ R2 @ ( semiri681578069525770553at_rat @ K ) ) @ ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ R2 ) @ K ) )
% 9.17/5.39 = ( times_times_rat @ R2 @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ R2 ) @ one_one_rat ) @ K ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4303_pochhammer__absorb__comp,axiom,
% 9.17/5.39 ! [R2: int,K: nat] :
% 9.17/5.39 ( ( times_times_int @ ( minus_minus_int @ R2 @ ( semiri1314217659103216013at_int @ K ) ) @ ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ R2 ) @ K ) )
% 9.17/5.39 = ( times_times_int @ R2 @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( uminus_uminus_int @ R2 ) @ one_one_int ) @ K ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4304_pochhammer__absorb__comp,axiom,
% 9.17/5.39 ! [R2: code_integer,K: nat] :
% 9.17/5.39 ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ R2 @ ( semiri4939895301339042750nteger @ K ) ) @ ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ R2 ) @ K ) )
% 9.17/5.39 = ( times_3573771949741848930nteger @ R2 @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ R2 ) @ one_one_Code_integer ) @ K ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4305_pochhammer__same,axiom,
% 9.17/5.39 ! [N2: nat] :
% 9.17/5.39 ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N2 ) ) @ N2 )
% 9.17/5.39 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 ) @ ( semiri773545260158071498ct_rat @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4306_pochhammer__same,axiom,
% 9.17/5.39 ! [N2: nat] :
% 9.17/5.39 ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) @ N2 )
% 9.17/5.39 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 ) @ ( semiri1406184849735516958ct_int @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4307_pochhammer__same,axiom,
% 9.17/5.39 ! [N2: nat] :
% 9.17/5.39 ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N2 ) ) @ N2 )
% 9.17/5.39 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 ) @ ( semiri3624122377584611663nteger @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4308_pochhammer__minus,axiom,
% 9.17/5.39 ! [B: rat,K: nat] :
% 9.17/5.39 ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ B ) @ K )
% 9.17/5.39 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( minus_minus_rat @ B @ ( semiri681578069525770553at_rat @ K ) ) @ one_one_rat ) @ K ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4309_pochhammer__minus,axiom,
% 9.17/5.39 ! [B: int,K: nat] :
% 9.17/5.39 ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ B ) @ K )
% 9.17/5.39 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ K ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( minus_minus_int @ B @ ( semiri1314217659103216013at_int @ K ) ) @ one_one_int ) @ K ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4310_pochhammer__minus,axiom,
% 9.17/5.39 ! [B: code_integer,K: nat] :
% 9.17/5.39 ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ B ) @ K )
% 9.17/5.39 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ K ) @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ B @ ( semiri4939895301339042750nteger @ K ) ) @ one_one_Code_integer ) @ K ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4311_pochhammer__minus_H,axiom,
% 9.17/5.39 ! [B: rat,K: nat] :
% 9.17/5.39 ( ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( minus_minus_rat @ B @ ( semiri681578069525770553at_rat @ K ) ) @ one_one_rat ) @ K )
% 9.17/5.39 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K ) @ ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ B ) @ K ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4312_pochhammer__minus_H,axiom,
% 9.17/5.39 ! [B: int,K: nat] :
% 9.17/5.39 ( ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( minus_minus_int @ B @ ( semiri1314217659103216013at_int @ K ) ) @ one_one_int ) @ K )
% 9.17/5.39 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ K ) @ ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ B ) @ K ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4313_pochhammer__minus_H,axiom,
% 9.17/5.39 ! [B: code_integer,K: nat] :
% 9.17/5.39 ( ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ B @ ( semiri4939895301339042750nteger @ K ) ) @ one_one_Code_integer ) @ K )
% 9.17/5.39 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ K ) @ ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ B ) @ K ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4314_gbinomial__pochhammer_H,axiom,
% 9.17/5.39 ( gbinomial_rat
% 9.17/5.39 = ( ^ [A5: rat,K4: nat] : ( divide_divide_rat @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( minus_minus_rat @ A5 @ ( semiri681578069525770553at_rat @ K4 ) ) @ one_one_rat ) @ K4 ) @ ( semiri773545260158071498ct_rat @ K4 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4315_gbinomial__pochhammer,axiom,
% 9.17/5.39 ( gbinomial_rat
% 9.17/5.39 = ( ^ [A5: rat,K4: nat] : ( divide_divide_rat @ ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K4 ) @ ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ A5 ) @ K4 ) ) @ ( semiri773545260158071498ct_rat @ K4 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4316_xor__nat__unfold,axiom,
% 9.17/5.39 ( bit_se6528837805403552850or_nat
% 9.17/5.39 = ( ^ [M: nat,N4: nat] : ( if_nat @ ( M = zero_zero_nat ) @ N4 @ ( if_nat @ ( N4 = zero_zero_nat ) @ M @ ( plus_plus_nat @ ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( divide_divide_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4317_num__of__integer_Oabs__eq,axiom,
% 9.17/5.39 ! [X: int] :
% 9.17/5.39 ( ( code_num_of_integer @ ( code_integer_of_int @ X ) )
% 9.17/5.39 = ( num_of_nat @ ( nat2 @ X ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4318_signed__take__bit__code,axiom,
% 9.17/5.39 ( bit_ri6519982836138164636nteger
% 9.17/5.39 = ( ^ [N4: nat,A5: code_integer] : ( if_Code_integer @ ( bit_se9216721137139052372nteger @ ( bit_se1745604003318907178nteger @ ( suc @ N4 ) @ A5 ) @ N4 ) @ ( plus_p5714425477246183910nteger @ ( bit_se1745604003318907178nteger @ ( suc @ N4 ) @ A5 ) @ ( bit_se7788150548672797655nteger @ ( suc @ N4 ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) @ ( bit_se1745604003318907178nteger @ ( suc @ N4 ) @ A5 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4319_signed__take__bit__code,axiom,
% 9.17/5.39 ( bit_ri631733984087533419it_int
% 9.17/5.39 = ( ^ [N4: nat,A5: int] : ( if_int @ ( bit_se1146084159140164899it_int @ ( bit_se2923211474154528505it_int @ ( suc @ N4 ) @ A5 ) @ N4 ) @ ( plus_plus_int @ ( bit_se2923211474154528505it_int @ ( suc @ N4 ) @ A5 ) @ ( bit_se545348938243370406it_int @ ( suc @ N4 ) @ ( uminus_uminus_int @ one_one_int ) ) ) @ ( bit_se2923211474154528505it_int @ ( suc @ N4 ) @ A5 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4320_xor__nat__rec,axiom,
% 9.17/5.39 ( bit_se6528837805403552850or_nat
% 9.17/5.39 = ( ^ [M: nat,N4: nat] :
% 9.17/5.39 ( plus_plus_nat
% 9.17/5.39 @ ( zero_n2687167440665602831ol_nat
% 9.17/5.39 @ ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 9.17/5.39 != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) ) )
% 9.17/5.39 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( divide_divide_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4321_xor__one__eq,axiom,
% 9.17/5.39 ! [A: nat] :
% 9.17/5.39 ( ( bit_se6528837805403552850or_nat @ A @ one_one_nat )
% 9.17/5.39 = ( minus_minus_nat @ ( plus_plus_nat @ A @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) )
% 9.17/5.39 @ ( zero_n2687167440665602831ol_nat
% 9.17/5.39 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4322_xor__one__eq,axiom,
% 9.17/5.39 ! [A: code_integer] :
% 9.17/5.39 ( ( bit_se3222712562003087583nteger @ A @ one_one_Code_integer )
% 9.17/5.39 = ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A @ ( zero_n356916108424825756nteger @ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) )
% 9.17/5.39 @ ( zero_n356916108424825756nteger
% 9.17/5.39 @ ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4323_xor__one__eq,axiom,
% 9.17/5.39 ! [A: int] :
% 9.17/5.39 ( ( bit_se6526347334894502574or_int @ A @ one_one_int )
% 9.17/5.39 = ( minus_minus_int @ ( plus_plus_int @ A @ ( zero_n2684676970156552555ol_int @ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) )
% 9.17/5.39 @ ( zero_n2684676970156552555ol_int
% 9.17/5.39 @ ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4324_xor__one__eq,axiom,
% 9.17/5.39 ! [A: code_natural] :
% 9.17/5.39 ( ( bit_se2046307713759805098atural @ A @ one_one_Code_natural )
% 9.17/5.39 = ( minus_7197305767214868737atural @ ( plus_p4538020629002901425atural @ A @ ( zero_n8403883297036319079atural @ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A ) ) )
% 9.17/5.39 @ ( zero_n8403883297036319079atural
% 9.17/5.39 @ ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4325_one__xor__eq,axiom,
% 9.17/5.39 ! [A: nat] :
% 9.17/5.39 ( ( bit_se6528837805403552850or_nat @ one_one_nat @ A )
% 9.17/5.39 = ( minus_minus_nat @ ( plus_plus_nat @ A @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) )
% 9.17/5.39 @ ( zero_n2687167440665602831ol_nat
% 9.17/5.39 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4326_one__xor__eq,axiom,
% 9.17/5.39 ! [A: code_integer] :
% 9.17/5.39 ( ( bit_se3222712562003087583nteger @ one_one_Code_integer @ A )
% 9.17/5.39 = ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A @ ( zero_n356916108424825756nteger @ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) )
% 9.17/5.39 @ ( zero_n356916108424825756nteger
% 9.17/5.39 @ ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4327_one__xor__eq,axiom,
% 9.17/5.39 ! [A: int] :
% 9.17/5.39 ( ( bit_se6526347334894502574or_int @ one_one_int @ A )
% 9.17/5.39 = ( minus_minus_int @ ( plus_plus_int @ A @ ( zero_n2684676970156552555ol_int @ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) )
% 9.17/5.39 @ ( zero_n2684676970156552555ol_int
% 9.17/5.39 @ ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4328_one__xor__eq,axiom,
% 9.17/5.39 ! [A: code_natural] :
% 9.17/5.39 ( ( bit_se2046307713759805098atural @ one_one_Code_natural @ A )
% 9.17/5.39 = ( minus_7197305767214868737atural @ ( plus_p4538020629002901425atural @ A @ ( zero_n8403883297036319079atural @ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A ) ) )
% 9.17/5.39 @ ( zero_n8403883297036319079atural
% 9.17/5.39 @ ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4329_pochhammer__binomial__sum,axiom,
% 9.17/5.39 ! [A: rat,B: rat,N2: nat] :
% 9.17/5.39 ( ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ A @ B ) @ N2 )
% 9.17/5.39 = ( groups2906978787729119204at_rat
% 9.17/5.39 @ ^ [K4: nat] : ( times_times_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( binomial @ N2 @ K4 ) ) @ ( comm_s4028243227959126397er_rat @ A @ K4 ) ) @ ( comm_s4028243227959126397er_rat @ B @ ( minus_minus_nat @ N2 @ K4 ) ) )
% 9.17/5.39 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4330_pochhammer__binomial__sum,axiom,
% 9.17/5.39 ! [A: int,B: int,N2: nat] :
% 9.17/5.39 ( ( comm_s4660882817536571857er_int @ ( plus_plus_int @ A @ B ) @ N2 )
% 9.17/5.39 = ( groups3539618377306564664at_int
% 9.17/5.39 @ ^ [K4: nat] : ( times_times_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ ( binomial @ N2 @ K4 ) ) @ ( comm_s4660882817536571857er_int @ A @ K4 ) ) @ ( comm_s4660882817536571857er_int @ B @ ( minus_minus_nat @ N2 @ K4 ) ) )
% 9.17/5.39 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4331_pochhammer__binomial__sum,axiom,
% 9.17/5.39 ! [A: code_integer,B: code_integer,N2: nat] :
% 9.17/5.39 ( ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ N2 )
% 9.17/5.39 = ( groups7501900531339628137nteger
% 9.17/5.39 @ ^ [K4: nat] : ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ ( binomial @ N2 @ K4 ) ) @ ( comm_s8582702949713902594nteger @ A @ K4 ) ) @ ( comm_s8582702949713902594nteger @ B @ ( minus_minus_nat @ N2 @ K4 ) ) )
% 9.17/5.39 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4332_divmod__integer__def,axiom,
% 9.17/5.39 ( code_divmod_integer
% 9.17/5.39 = ( ^ [K4: code_integer,L3: code_integer] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ K4 @ L3 ) @ ( modulo364778990260209775nteger @ K4 @ L3 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4333_sum__power2,axiom,
% 9.17/5.39 ! [K: nat] :
% 9.17/5.39 ( ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K ) )
% 9.17/5.39 = ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K ) @ one_one_nat ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4334_nat__of__integer__code,axiom,
% 9.17/5.39 ( code_nat_of_integer
% 9.17/5.39 = ( ^ [K4: code_integer] :
% 9.17/5.39 ( if_nat @ ( ord_le3102999989581377725nteger @ K4 @ zero_z3403309356797280102nteger ) @ zero_zero_nat
% 9.17/5.39 @ ( produc1555791787009142072er_nat
% 9.17/5.39 @ ^ [L3: code_integer,J2: code_integer] : ( if_nat @ ( J2 = zero_z3403309356797280102nteger ) @ ( plus_plus_nat @ ( code_nat_of_integer @ L3 ) @ ( code_nat_of_integer @ L3 ) ) @ ( plus_plus_nat @ ( plus_plus_nat @ ( code_nat_of_integer @ L3 ) @ ( code_nat_of_integer @ L3 ) ) @ one_one_nat ) )
% 9.17/5.39 @ ( code_divmod_integer @ K4 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4335_pochhammer__times__pochhammer__half,axiom,
% 9.17/5.39 ! [Z: rat,N2: nat] :
% 9.17/5.39 ( ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z @ ( suc @ N2 ) ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( suc @ N2 ) ) )
% 9.17/5.39 = ( groups73079841787564623at_rat
% 9.17/5.39 @ ^ [K4: nat] : ( plus_plus_rat @ Z @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ K4 ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 9.17/5.39 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4336_int__of__integer__code,axiom,
% 9.17/5.39 ( code_int_of_integer
% 9.17/5.39 = ( ^ [K4: code_integer] :
% 9.17/5.39 ( if_int @ ( ord_le6747313008572928689nteger @ K4 @ zero_z3403309356797280102nteger ) @ ( uminus_uminus_int @ ( code_int_of_integer @ ( uminus1351360451143612070nteger @ K4 ) ) )
% 9.17/5.39 @ ( if_int @ ( K4 = zero_z3403309356797280102nteger ) @ zero_zero_int
% 9.17/5.39 @ ( produc1553301316500091796er_int
% 9.17/5.39 @ ^ [L3: code_integer,J2: code_integer] : ( if_int @ ( J2 = zero_z3403309356797280102nteger ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( code_int_of_integer @ L3 ) ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( code_int_of_integer @ L3 ) ) @ one_one_int ) )
% 9.17/5.39 @ ( code_divmod_integer @ K4 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4337_divmod__integer__eq__cases,axiom,
% 9.17/5.39 ( code_divmod_integer
% 9.17/5.39 = ( ^ [K4: code_integer,L3: code_integer] :
% 9.17/5.39 ( if_Pro6119634080678213985nteger @ ( K4 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 9.17/5.39 @ ( if_Pro6119634080678213985nteger @ ( L3 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ K4 )
% 9.17/5.39 @ ( comp_C1593894019821074884nteger @ ( comp_C8797469213163452608nteger @ produc6499014454317279255nteger @ times_3573771949741848930nteger ) @ sgn_sgn_Code_integer @ L3
% 9.17/5.39 @ ( if_Pro6119634080678213985nteger
% 9.17/5.39 @ ( ( sgn_sgn_Code_integer @ K4 )
% 9.17/5.39 = ( sgn_sgn_Code_integer @ L3 ) )
% 9.17/5.39 @ ( code_divmod_abs @ K4 @ L3 )
% 9.17/5.39 @ ( produc6916734918728496179nteger
% 9.17/5.39 @ ^ [R3: code_integer,S4: code_integer] : ( if_Pro6119634080678213985nteger @ ( S4 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R3 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R3 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ ( abs_abs_Code_integer @ L3 ) @ S4 ) ) )
% 9.17/5.39 @ ( code_divmod_abs @ K4 @ L3 ) ) ) ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4338_time__def,axiom,
% 9.17/5.39 ( time_time_array_a
% 9.17/5.39 = ( ^ [C2: heap_T6362127782908069795rray_a,H: heap_e7401611519738050253t_unit] :
% 9.17/5.39 ( case_o1134687144775446439it_nat @ zero_zero_nat
% 9.17/5.39 @ ( produc6028340861379781217at_nat
% 9.17/5.39 @ ^ [X3: array_a] :
% 9.17/5.39 ( produc4278983685114131267at_nat
% 9.17/5.39 @ ^ [Xa4: heap_e7401611519738050253t_unit,T2: nat] : T2 ) )
% 9.17/5.39 @ ( heap_T5591663578999710211rray_a @ C2 @ H ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4339_time__def,axiom,
% 9.17/5.39 ( time_t4224138285095624986t_unit
% 9.17/5.39 = ( ^ [C2: heap_T5738788834812785303t_unit,H: heap_e7401611519738050253t_unit] :
% 9.17/5.39 ( case_o5424514124273913701it_nat @ zero_zero_nat
% 9.17/5.39 @ ( produc5629734405777326591at_nat
% 9.17/5.39 @ ^ [X3: product_unit] :
% 9.17/5.39 ( produc4278983685114131267at_nat
% 9.17/5.39 @ ^ [Xa4: heap_e7401611519738050253t_unit,T2: nat] : T2 ) )
% 9.17/5.39 @ ( heap_T875086893843062177t_unit @ C2 @ H ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4340_bit__cut__integer__def,axiom,
% 9.17/5.39 ( code_bit_cut_integer
% 9.17/5.39 = ( ^ [K4: code_integer] :
% 9.17/5.39 ( produc6677183202524767010eger_o @ ( divide6298287555418463151nteger @ K4 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 9.17/5.39 @ ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ K4 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4341_integer__of__num_I3_J,axiom,
% 9.17/5.39 ! [N2: num] :
% 9.17/5.39 ( ( code_integer_of_num @ ( bit1 @ N2 ) )
% 9.17/5.39 = ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( code_integer_of_num @ N2 ) @ ( code_integer_of_num @ N2 ) ) @ one_one_Code_integer ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4342_less__eq__int_Orep__eq,axiom,
% 9.17/5.39 ( ord_less_eq_int
% 9.17/5.39 = ( ^ [X3: int,Xa4: int] :
% 9.17/5.39 ( produc8739625826339149834_nat_o
% 9.17/5.39 @ ^ [Y3: nat,Z4: nat] :
% 9.17/5.39 ( produc6081775807080527818_nat_o
% 9.17/5.39 @ ^ [U2: nat,V2: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ Y3 @ V2 ) @ ( plus_plus_nat @ U2 @ Z4 ) ) )
% 9.17/5.39 @ ( rep_Integ @ X3 )
% 9.17/5.39 @ ( rep_Integ @ Xa4 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4343_nat__of__integer__of__nat,axiom,
% 9.17/5.39 ! [N2: nat] :
% 9.17/5.39 ( ( code_nat_of_integer @ ( semiri4939895301339042750nteger @ N2 ) )
% 9.17/5.39 = N2 ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4344_int__of__integer__of__nat,axiom,
% 9.17/5.39 ! [N2: nat] :
% 9.17/5.39 ( ( code_int_of_integer @ ( semiri4939895301339042750nteger @ N2 ) )
% 9.17/5.39 = ( semiri1314217659103216013at_int @ N2 ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4345_integer__of__int__int__of__integer,axiom,
% 9.17/5.39 ! [K: code_integer] :
% 9.17/5.39 ( ( code_integer_of_int @ ( code_int_of_integer @ K ) )
% 9.17/5.39 = K ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4346_int__of__integer__integer__of__int,axiom,
% 9.17/5.39 ! [K: int] :
% 9.17/5.39 ( ( code_int_of_integer @ ( code_integer_of_int @ K ) )
% 9.17/5.39 = K ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4347_int__of__integer__inverse,axiom,
% 9.17/5.39 ! [X: code_integer] :
% 9.17/5.39 ( ( code_integer_of_int @ ( code_int_of_integer @ X ) )
% 9.17/5.39 = X ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4348_apsnd__conv,axiom,
% 9.17/5.39 ! [F: produc8923325533196201883nteger > produc8923325533196201883nteger,X: produc6241069584506657477e_term > option6357759511663192854e_term,Y: produc8923325533196201883nteger] :
% 9.17/5.39 ( ( produc717174245515237944e_term @ F @ ( produc8603105652947943368nteger @ X @ Y ) )
% 9.17/5.39 = ( produc8603105652947943368nteger @ X @ ( F @ Y ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4349_apsnd__conv,axiom,
% 9.17/5.39 ! [F: produc3658429121746597890et_nat > produc3658429121746597890et_nat,X: produc3658429121746597890et_nat > $o,Y: produc3658429121746597890et_nat] :
% 9.17/5.39 ( ( produc8750854537940449737_nat_o @ F @ ( produc5001842942810119800et_nat @ X @ Y ) )
% 9.17/5.39 = ( produc5001842942810119800et_nat @ X @ ( F @ Y ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4350_apsnd__conv,axiom,
% 9.17/5.39 ! [F: produc3658429121746597890et_nat > produc3925858234332021118et_nat,X: produc3658429121746597890et_nat > $o,Y: produc3658429121746597890et_nat] :
% 9.17/5.39 ( ( produc7714581247149323085_nat_o @ F @ ( produc5001842942810119800et_nat @ X @ Y ) )
% 9.17/5.39 = ( produc2245416461498447860et_nat @ X @ ( F @ Y ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4351_apsnd__conv,axiom,
% 9.17/5.39 ! [F: produc3925858234332021118et_nat > produc3658429121746597890et_nat,X: produc3658429121746597890et_nat > $o,Y: produc3925858234332021118et_nat] :
% 9.17/5.39 ( ( produc1515462096303866701_nat_o @ F @ ( produc2245416461498447860et_nat @ X @ Y ) )
% 9.17/5.39 = ( produc5001842942810119800et_nat @ X @ ( F @ Y ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4352_apsnd__conv,axiom,
% 9.17/5.39 ! [F: produc3925858234332021118et_nat > produc3925858234332021118et_nat,X: produc3658429121746597890et_nat > $o,Y: produc3925858234332021118et_nat] :
% 9.17/5.39 ( ( produc969530845752564945_nat_o @ F @ ( produc2245416461498447860et_nat @ X @ Y ) )
% 9.17/5.39 = ( produc2245416461498447860et_nat @ X @ ( F @ Y ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4353_apsnd__conv,axiom,
% 9.17/5.39 ! [F: product_prod_int_int > product_prod_int_int,X: produc8551481072490612790e_term > option6357759511663192854e_term,Y: product_prod_int_int] :
% 9.17/5.39 ( ( produc4973430039190721449e_term @ F @ ( produc5700946648718959541nt_int @ X @ Y ) )
% 9.17/5.39 = ( produc5700946648718959541nt_int @ X @ ( F @ Y ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4354_apsnd__conv,axiom,
% 9.17/5.39 ! [F: product_prod_int_int > product_prod_int_int,X: int > option6357759511663192854e_term,Y: product_prod_int_int] :
% 9.17/5.39 ( ( produc7011684061226097695e_term @ F @ ( produc4305682042979456191nt_int @ X @ Y ) )
% 9.17/5.39 = ( produc4305682042979456191nt_int @ X @ ( F @ Y ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4355_apsnd__conv,axiom,
% 9.17/5.39 ! [F: code_integer > code_integer,X: code_integer,Y: code_integer] :
% 9.17/5.39 ( ( produc6499014454317279255nteger @ F @ ( produc1086072967326762835nteger @ X @ Y ) )
% 9.17/5.39 = ( produc1086072967326762835nteger @ X @ ( F @ Y ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4356_prod_Oneutral__const,axiom,
% 9.17/5.39 ! [A2: set_nat] :
% 9.17/5.39 ( ( groups708209901874060359at_nat
% 9.17/5.39 @ ^ [Uu: nat] : one_one_nat
% 9.17/5.39 @ A2 )
% 9.17/5.39 = one_one_nat ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4357_prod_Oneutral__const,axiom,
% 9.17/5.39 ! [A2: set_nat] :
% 9.17/5.39 ( ( groups705719431365010083at_int
% 9.17/5.39 @ ^ [Uu: nat] : one_one_int
% 9.17/5.39 @ A2 )
% 9.17/5.39 = one_one_int ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4358_prod_Oneutral__const,axiom,
% 9.17/5.39 ! [A2: set_int] :
% 9.17/5.39 ( ( groups1705073143266064639nt_int
% 9.17/5.39 @ ^ [Uu: int] : one_one_int
% 9.17/5.39 @ A2 )
% 9.17/5.39 = one_one_int ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4359_of__int__integer__of,axiom,
% 9.17/5.39 ! [K: code_integer] :
% 9.17/5.39 ( ( ring_18347121197199848620nteger @ ( code_int_of_integer @ K ) )
% 9.17/5.39 = K ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4360_int__of__integer__of__int,axiom,
% 9.17/5.39 ! [K: int] :
% 9.17/5.39 ( ( code_int_of_integer @ ( ring_18347121197199848620nteger @ K ) )
% 9.17/5.39 = K ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4361_zero__integer_Orep__eq,axiom,
% 9.17/5.39 ( ( code_int_of_integer @ zero_z3403309356797280102nteger )
% 9.17/5.39 = zero_zero_int ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4362_int__of__integer__numeral,axiom,
% 9.17/5.39 ! [K: num] :
% 9.17/5.39 ( ( code_int_of_integer @ ( numera6620942414471956472nteger @ K ) )
% 9.17/5.39 = ( numeral_numeral_int @ K ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4363_plus__integer_Orep__eq,axiom,
% 9.17/5.39 ! [X: code_integer,Xa: code_integer] :
% 9.17/5.39 ( ( code_int_of_integer @ ( plus_p5714425477246183910nteger @ X @ Xa ) )
% 9.17/5.39 = ( plus_plus_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Xa ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4364_one__integer_Orep__eq,axiom,
% 9.17/5.39 ( ( code_int_of_integer @ one_one_Code_integer )
% 9.17/5.39 = one_one_int ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4365_uminus__integer_Orep__eq,axiom,
% 9.17/5.39 ! [X: code_integer] :
% 9.17/5.39 ( ( code_int_of_integer @ ( uminus1351360451143612070nteger @ X ) )
% 9.17/5.39 = ( uminus_uminus_int @ ( code_int_of_integer @ X ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4366_times__integer_Orep__eq,axiom,
% 9.17/5.39 ! [X: code_integer,Xa: code_integer] :
% 9.17/5.39 ( ( code_int_of_integer @ ( times_3573771949741848930nteger @ X @ Xa ) )
% 9.17/5.39 = ( times_times_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Xa ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4367_minus__integer_Orep__eq,axiom,
% 9.17/5.39 ! [X: code_integer,Xa: code_integer] :
% 9.17/5.39 ( ( code_int_of_integer @ ( minus_8373710615458151222nteger @ X @ Xa ) )
% 9.17/5.39 = ( minus_minus_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Xa ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4368_abs__integer_Orep__eq,axiom,
% 9.17/5.39 ! [X: code_integer] :
% 9.17/5.39 ( ( code_int_of_integer @ ( abs_abs_Code_integer @ X ) )
% 9.17/5.39 = ( abs_abs_int @ ( code_int_of_integer @ X ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4369_divide__integer_Orep__eq,axiom,
% 9.17/5.39 ! [X: code_integer,Xa: code_integer] :
% 9.17/5.39 ( ( code_int_of_integer @ ( divide6298287555418463151nteger @ X @ Xa ) )
% 9.17/5.39 = ( divide_divide_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Xa ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4370_modulo__integer_Orep__eq,axiom,
% 9.17/5.39 ! [X: code_integer,Xa: code_integer] :
% 9.17/5.39 ( ( code_int_of_integer @ ( modulo364778990260209775nteger @ X @ Xa ) )
% 9.17/5.39 = ( modulo_modulo_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Xa ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4371_sgn__integer_Orep__eq,axiom,
% 9.17/5.39 ! [X: code_integer] :
% 9.17/5.39 ( ( code_int_of_integer @ ( sgn_sgn_Code_integer @ X ) )
% 9.17/5.39 = ( sgn_sgn_int @ ( code_int_of_integer @ X ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4372_prod_OatMost__Suc,axiom,
% 9.17/5.39 ! [G: nat > assn,N2: nat] :
% 9.17/5.39 ( ( groups6906906614972039071t_assn @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 9.17/5.39 = ( times_times_assn @ ( groups6906906614972039071t_assn @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4373_prod_OatMost__Suc,axiom,
% 9.17/5.39 ! [G: nat > rat,N2: nat] :
% 9.17/5.39 ( ( groups73079841787564623at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 9.17/5.39 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4374_prod_OatMost__Suc,axiom,
% 9.17/5.39 ! [G: nat > nat,N2: nat] :
% 9.17/5.39 ( ( groups708209901874060359at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 9.17/5.39 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4375_prod_OatMost__Suc,axiom,
% 9.17/5.39 ! [G: nat > int,N2: nat] :
% 9.17/5.39 ( ( groups705719431365010083at_int @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 9.17/5.39 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4376_prod_OlessThan__Suc,axiom,
% 9.17/5.39 ! [G: nat > assn,N2: nat] :
% 9.17/5.39 ( ( groups6906906614972039071t_assn @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 9.17/5.39 = ( times_times_assn @ ( groups6906906614972039071t_assn @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4377_prod_OlessThan__Suc,axiom,
% 9.17/5.39 ! [G: nat > rat,N2: nat] :
% 9.17/5.39 ( ( groups73079841787564623at_rat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 9.17/5.39 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4378_prod_OlessThan__Suc,axiom,
% 9.17/5.39 ! [G: nat > nat,N2: nat] :
% 9.17/5.39 ( ( groups708209901874060359at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 9.17/5.39 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4379_prod_OlessThan__Suc,axiom,
% 9.17/5.39 ! [G: nat > int,N2: nat] :
% 9.17/5.39 ( ( groups705719431365010083at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 9.17/5.39 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4380_nat__of__integer__non__positive,axiom,
% 9.17/5.39 ! [K: code_integer] :
% 9.17/5.39 ( ( ord_le3102999989581377725nteger @ K @ zero_z3403309356797280102nteger )
% 9.17/5.39 => ( ( code_nat_of_integer @ K )
% 9.17/5.39 = zero_zero_nat ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4381_prod_Ocl__ivl__Suc,axiom,
% 9.17/5.39 ! [N2: nat,M2: nat,G: nat > code_integer] :
% 9.17/5.39 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M2 )
% 9.17/5.39 => ( ( groups3455450783089532116nteger @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N2 ) ) )
% 9.17/5.39 = one_one_Code_integer ) )
% 9.17/5.39 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M2 )
% 9.17/5.39 => ( ( groups3455450783089532116nteger @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N2 ) ) )
% 9.17/5.39 = ( times_3573771949741848930nteger @ ( groups3455450783089532116nteger @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4382_prod_Ocl__ivl__Suc,axiom,
% 9.17/5.39 ! [N2: nat,M2: nat,G: nat > assn] :
% 9.17/5.39 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M2 )
% 9.17/5.39 => ( ( groups6906906614972039071t_assn @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N2 ) ) )
% 9.17/5.39 = one_one_assn ) )
% 9.17/5.39 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M2 )
% 9.17/5.39 => ( ( groups6906906614972039071t_assn @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N2 ) ) )
% 9.17/5.39 = ( times_times_assn @ ( groups6906906614972039071t_assn @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4383_prod_Ocl__ivl__Suc,axiom,
% 9.17/5.39 ! [N2: nat,M2: nat,G: nat > rat] :
% 9.17/5.39 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M2 )
% 9.17/5.39 => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N2 ) ) )
% 9.17/5.39 = one_one_rat ) )
% 9.17/5.39 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M2 )
% 9.17/5.39 => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N2 ) ) )
% 9.17/5.39 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4384_prod_Ocl__ivl__Suc,axiom,
% 9.17/5.39 ! [N2: nat,M2: nat,G: nat > nat] :
% 9.17/5.39 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M2 )
% 9.17/5.39 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N2 ) ) )
% 9.17/5.39 = one_one_nat ) )
% 9.17/5.39 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M2 )
% 9.17/5.39 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N2 ) ) )
% 9.17/5.39 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4385_prod_Ocl__ivl__Suc,axiom,
% 9.17/5.39 ! [N2: nat,M2: nat,G: nat > int] :
% 9.17/5.39 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M2 )
% 9.17/5.39 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N2 ) ) )
% 9.17/5.39 = one_one_int ) )
% 9.17/5.39 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M2 )
% 9.17/5.39 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N2 ) ) )
% 9.17/5.39 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4386_prod_Oop__ivl__Suc,axiom,
% 9.17/5.39 ! [N2: nat,M2: nat,G: nat > code_integer] :
% 9.17/5.39 ( ( ( ord_less_nat @ N2 @ M2 )
% 9.17/5.39 => ( ( groups3455450783089532116nteger @ G @ ( set_or4665077453230672383an_nat @ M2 @ ( suc @ N2 ) ) )
% 9.17/5.39 = one_one_Code_integer ) )
% 9.17/5.39 & ( ~ ( ord_less_nat @ N2 @ M2 )
% 9.17/5.39 => ( ( groups3455450783089532116nteger @ G @ ( set_or4665077453230672383an_nat @ M2 @ ( suc @ N2 ) ) )
% 9.17/5.39 = ( times_3573771949741848930nteger @ ( groups3455450783089532116nteger @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) @ ( G @ N2 ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4387_prod_Oop__ivl__Suc,axiom,
% 9.17/5.39 ! [N2: nat,M2: nat,G: nat > assn] :
% 9.17/5.39 ( ( ( ord_less_nat @ N2 @ M2 )
% 9.17/5.39 => ( ( groups6906906614972039071t_assn @ G @ ( set_or4665077453230672383an_nat @ M2 @ ( suc @ N2 ) ) )
% 9.17/5.39 = one_one_assn ) )
% 9.17/5.39 & ( ~ ( ord_less_nat @ N2 @ M2 )
% 9.17/5.39 => ( ( groups6906906614972039071t_assn @ G @ ( set_or4665077453230672383an_nat @ M2 @ ( suc @ N2 ) ) )
% 9.17/5.39 = ( times_times_assn @ ( groups6906906614972039071t_assn @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) @ ( G @ N2 ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4388_prod_Oop__ivl__Suc,axiom,
% 9.17/5.39 ! [N2: nat,M2: nat,G: nat > rat] :
% 9.17/5.39 ( ( ( ord_less_nat @ N2 @ M2 )
% 9.17/5.39 => ( ( groups73079841787564623at_rat @ G @ ( set_or4665077453230672383an_nat @ M2 @ ( suc @ N2 ) ) )
% 9.17/5.39 = one_one_rat ) )
% 9.17/5.39 & ( ~ ( ord_less_nat @ N2 @ M2 )
% 9.17/5.39 => ( ( groups73079841787564623at_rat @ G @ ( set_or4665077453230672383an_nat @ M2 @ ( suc @ N2 ) ) )
% 9.17/5.39 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) @ ( G @ N2 ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4389_prod_Oop__ivl__Suc,axiom,
% 9.17/5.39 ! [N2: nat,M2: nat,G: nat > nat] :
% 9.17/5.39 ( ( ( ord_less_nat @ N2 @ M2 )
% 9.17/5.39 => ( ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ M2 @ ( suc @ N2 ) ) )
% 9.17/5.39 = one_one_nat ) )
% 9.17/5.39 & ( ~ ( ord_less_nat @ N2 @ M2 )
% 9.17/5.39 => ( ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ M2 @ ( suc @ N2 ) ) )
% 9.17/5.39 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) @ ( G @ N2 ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4390_prod_Oop__ivl__Suc,axiom,
% 9.17/5.39 ! [N2: nat,M2: nat,G: nat > int] :
% 9.17/5.39 ( ( ( ord_less_nat @ N2 @ M2 )
% 9.17/5.39 => ( ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ M2 @ ( suc @ N2 ) ) )
% 9.17/5.39 = one_one_int ) )
% 9.17/5.39 & ( ~ ( ord_less_nat @ N2 @ M2 )
% 9.17/5.39 => ( ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ M2 @ ( suc @ N2 ) ) )
% 9.17/5.39 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) @ ( G @ N2 ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4391_xor__integer_Orep__eq,axiom,
% 9.17/5.39 ! [X: code_integer,Xa: code_integer] :
% 9.17/5.39 ( ( code_int_of_integer @ ( bit_se3222712562003087583nteger @ X @ Xa ) )
% 9.17/5.39 = ( bit_se6526347334894502574or_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Xa ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4392_push__bit__integer_Orep__eq,axiom,
% 9.17/5.39 ! [X: nat,Xa: code_integer] :
% 9.17/5.39 ( ( code_int_of_integer @ ( bit_se7788150548672797655nteger @ X @ Xa ) )
% 9.17/5.39 = ( bit_se545348938243370406it_int @ X @ ( code_int_of_integer @ Xa ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4393_xor__integer_Oabs__eq,axiom,
% 9.17/5.39 ! [Xa: int,X: int] :
% 9.17/5.39 ( ( bit_se3222712562003087583nteger @ ( code_integer_of_int @ Xa ) @ ( code_integer_of_int @ X ) )
% 9.17/5.39 = ( code_integer_of_int @ ( bit_se6526347334894502574or_int @ Xa @ X ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4394_nat__of__integer_Orep__eq,axiom,
% 9.17/5.39 ( code_nat_of_integer
% 9.17/5.39 = ( ^ [X3: code_integer] : ( nat2 @ ( code_int_of_integer @ X3 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4395_integer__eq__iff,axiom,
% 9.17/5.39 ( ( ^ [Y4: code_integer,Z2: code_integer] : ( Y4 = Z2 ) )
% 9.17/5.39 = ( ^ [K4: code_integer,L3: code_integer] :
% 9.17/5.39 ( ( code_int_of_integer @ K4 )
% 9.17/5.39 = ( code_int_of_integer @ L3 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4396_integer__eqI,axiom,
% 9.17/5.39 ! [K: code_integer,L: code_integer] :
% 9.17/5.39 ( ( ( code_int_of_integer @ K )
% 9.17/5.39 = ( code_int_of_integer @ L ) )
% 9.17/5.39 => ( K = L ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4397_int__of__integer__inject,axiom,
% 9.17/5.39 ! [X: code_integer,Y: code_integer] :
% 9.17/5.39 ( ( ( code_int_of_integer @ X )
% 9.17/5.39 = ( code_int_of_integer @ Y ) )
% 9.17/5.39 = ( X = Y ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4398_prod_Onot__neutral__contains__not__neutral,axiom,
% 9.17/5.39 ! [G: $o > code_integer,A2: set_o] :
% 9.17/5.39 ( ( ( groups7694694392188491536nteger @ G @ A2 )
% 9.17/5.39 != one_one_Code_integer )
% 9.17/5.39 => ~ ! [A3: $o] :
% 9.17/5.39 ( ( member_o @ A3 @ A2 )
% 9.17/5.39 => ( ( G @ A3 )
% 9.17/5.39 = one_one_Code_integer ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4399_prod_Onot__neutral__contains__not__neutral,axiom,
% 9.17/5.39 ! [G: nat > code_integer,A2: set_nat] :
% 9.17/5.39 ( ( ( groups3455450783089532116nteger @ G @ A2 )
% 9.17/5.39 != one_one_Code_integer )
% 9.17/5.39 => ~ ! [A3: nat] :
% 9.17/5.39 ( ( member_nat @ A3 @ A2 )
% 9.17/5.39 => ( ( G @ A3 )
% 9.17/5.39 = one_one_Code_integer ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4400_prod_Onot__neutral__contains__not__neutral,axiom,
% 9.17/5.39 ! [G: int > code_integer,A2: set_int] :
% 9.17/5.39 ( ( ( groups3827104343326376752nteger @ G @ A2 )
% 9.17/5.39 != one_one_Code_integer )
% 9.17/5.39 => ~ ! [A3: int] :
% 9.17/5.39 ( ( member_int @ A3 @ A2 )
% 9.17/5.39 => ( ( G @ A3 )
% 9.17/5.39 = one_one_Code_integer ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4401_prod_Onot__neutral__contains__not__neutral,axiom,
% 9.17/5.39 ! [G: $o > assn,A2: set_o] :
% 9.17/5.39 ( ( ( groups5301882518646026715o_assn @ G @ A2 )
% 9.17/5.39 != one_one_assn )
% 9.17/5.39 => ~ ! [A3: $o] :
% 9.17/5.39 ( ( member_o @ A3 @ A2 )
% 9.17/5.39 => ( ( G @ A3 )
% 9.17/5.39 = one_one_assn ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4402_prod_Onot__neutral__contains__not__neutral,axiom,
% 9.17/5.39 ! [G: nat > assn,A2: set_nat] :
% 9.17/5.39 ( ( ( groups6906906614972039071t_assn @ G @ A2 )
% 9.17/5.39 != one_one_assn )
% 9.17/5.39 => ~ ! [A3: nat] :
% 9.17/5.39 ( ( member_nat @ A3 @ A2 )
% 9.17/5.39 => ( ( G @ A3 )
% 9.17/5.39 = one_one_assn ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4403_prod_Onot__neutral__contains__not__neutral,axiom,
% 9.17/5.39 ! [G: int > assn,A2: set_int] :
% 9.17/5.39 ( ( ( groups7882442080178216443t_assn @ G @ A2 )
% 9.17/5.39 != one_one_assn )
% 9.17/5.39 => ~ ! [A3: int] :
% 9.17/5.39 ( ( member_int @ A3 @ A2 )
% 9.17/5.39 => ( ( G @ A3 )
% 9.17/5.39 = one_one_assn ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4404_prod_Onot__neutral__contains__not__neutral,axiom,
% 9.17/5.39 ! [G: $o > rat,A2: set_o] :
% 9.17/5.39 ( ( ( groups2869687844427037835_o_rat @ G @ A2 )
% 9.17/5.39 != one_one_rat )
% 9.17/5.39 => ~ ! [A3: $o] :
% 9.17/5.39 ( ( member_o @ A3 @ A2 )
% 9.17/5.39 => ( ( G @ A3 )
% 9.17/5.39 = one_one_rat ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4405_prod_Onot__neutral__contains__not__neutral,axiom,
% 9.17/5.39 ! [G: nat > rat,A2: set_nat] :
% 9.17/5.39 ( ( ( groups73079841787564623at_rat @ G @ A2 )
% 9.17/5.39 != one_one_rat )
% 9.17/5.39 => ~ ! [A3: nat] :
% 9.17/5.39 ( ( member_nat @ A3 @ A2 )
% 9.17/5.39 => ( ( G @ A3 )
% 9.17/5.39 = one_one_rat ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4406_prod_Onot__neutral__contains__not__neutral,axiom,
% 9.17/5.39 ! [G: int > rat,A2: set_int] :
% 9.17/5.39 ( ( ( groups1072433553688619179nt_rat @ G @ A2 )
% 9.17/5.39 != one_one_rat )
% 9.17/5.39 => ~ ! [A3: int] :
% 9.17/5.39 ( ( member_int @ A3 @ A2 )
% 9.17/5.39 => ( ( G @ A3 )
% 9.17/5.39 = one_one_rat ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4407_prod_Onot__neutral__contains__not__neutral,axiom,
% 9.17/5.39 ! [G: $o > nat,A2: set_o] :
% 9.17/5.39 ( ( ( groups3504817904513533571_o_nat @ G @ A2 )
% 9.17/5.39 != one_one_nat )
% 9.17/5.39 => ~ ! [A3: $o] :
% 9.17/5.39 ( ( member_o @ A3 @ A2 )
% 9.17/5.39 => ( ( G @ A3 )
% 9.17/5.39 = one_one_nat ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4408_prod_Oneutral,axiom,
% 9.17/5.39 ! [A2: set_nat,G: nat > nat] :
% 9.17/5.39 ( ! [X4: nat] :
% 9.17/5.39 ( ( member_nat @ X4 @ A2 )
% 9.17/5.39 => ( ( G @ X4 )
% 9.17/5.39 = one_one_nat ) )
% 9.17/5.39 => ( ( groups708209901874060359at_nat @ G @ A2 )
% 9.17/5.39 = one_one_nat ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4409_prod_Oneutral,axiom,
% 9.17/5.39 ! [A2: set_nat,G: nat > int] :
% 9.17/5.39 ( ! [X4: nat] :
% 9.17/5.39 ( ( member_nat @ X4 @ A2 )
% 9.17/5.39 => ( ( G @ X4 )
% 9.17/5.39 = one_one_int ) )
% 9.17/5.39 => ( ( groups705719431365010083at_int @ G @ A2 )
% 9.17/5.39 = one_one_int ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4410_prod_Oneutral,axiom,
% 9.17/5.39 ! [A2: set_int,G: int > int] :
% 9.17/5.39 ( ! [X4: int] :
% 9.17/5.39 ( ( member_int @ X4 @ A2 )
% 9.17/5.39 => ( ( G @ X4 )
% 9.17/5.39 = one_one_int ) )
% 9.17/5.39 => ( ( groups1705073143266064639nt_int @ G @ A2 )
% 9.17/5.39 = one_one_int ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4411_apsnd__compose,axiom,
% 9.17/5.39 ! [F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer,X: produc8923325533196201883nteger] :
% 9.17/5.39 ( ( produc9020447175693601247nteger @ F @ ( produc6499014454317279255nteger @ G @ X ) )
% 9.17/5.39 = ( produc9020447175693601247nteger @ ( comp_C1593894019821074884nteger @ F @ G ) @ X ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4412_apsnd__compose,axiom,
% 9.17/5.39 ! [F: code_integer > code_integer,G: num > code_integer,X: produc7142191362829087448er_num] :
% 9.17/5.39 ( ( produc6499014454317279255nteger @ F @ ( produc7418200839687411156nteger @ G @ X ) )
% 9.17/5.39 = ( produc7418200839687411156nteger @ ( comp_C3531382070062128313er_num @ F @ G ) @ X ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4413_apsnd__compose,axiom,
% 9.17/5.39 ! [F: code_integer > code_integer,G: code_integer > code_integer,X: produc8923325533196201883nteger] :
% 9.17/5.39 ( ( produc6499014454317279255nteger @ F @ ( produc6499014454317279255nteger @ G @ X ) )
% 9.17/5.39 = ( produc6499014454317279255nteger @ ( comp_C7449957260575251196nteger @ F @ G ) @ X ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4414_prod__ge__1,axiom,
% 9.17/5.39 ! [A2: set_o,F: $o > code_integer] :
% 9.17/5.39 ( ! [X4: $o] :
% 9.17/5.39 ( ( member_o @ X4 @ A2 )
% 9.17/5.39 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F @ X4 ) ) )
% 9.17/5.39 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( groups7694694392188491536nteger @ F @ A2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4415_prod__ge__1,axiom,
% 9.17/5.39 ! [A2: set_nat,F: nat > code_integer] :
% 9.17/5.39 ( ! [X4: nat] :
% 9.17/5.39 ( ( member_nat @ X4 @ A2 )
% 9.17/5.39 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F @ X4 ) ) )
% 9.17/5.39 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( groups3455450783089532116nteger @ F @ A2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4416_prod__ge__1,axiom,
% 9.17/5.39 ! [A2: set_int,F: int > code_integer] :
% 9.17/5.39 ( ! [X4: int] :
% 9.17/5.39 ( ( member_int @ X4 @ A2 )
% 9.17/5.39 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F @ X4 ) ) )
% 9.17/5.39 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( groups3827104343326376752nteger @ F @ A2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4417_prod__ge__1,axiom,
% 9.17/5.39 ! [A2: set_o,F: $o > rat] :
% 9.17/5.39 ( ! [X4: $o] :
% 9.17/5.39 ( ( member_o @ X4 @ A2 )
% 9.17/5.39 => ( ord_less_eq_rat @ one_one_rat @ ( F @ X4 ) ) )
% 9.17/5.39 => ( ord_less_eq_rat @ one_one_rat @ ( groups2869687844427037835_o_rat @ F @ A2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4418_prod__ge__1,axiom,
% 9.17/5.39 ! [A2: set_nat,F: nat > rat] :
% 9.17/5.39 ( ! [X4: nat] :
% 9.17/5.39 ( ( member_nat @ X4 @ A2 )
% 9.17/5.39 => ( ord_less_eq_rat @ one_one_rat @ ( F @ X4 ) ) )
% 9.17/5.39 => ( ord_less_eq_rat @ one_one_rat @ ( groups73079841787564623at_rat @ F @ A2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4419_prod__ge__1,axiom,
% 9.17/5.39 ! [A2: set_int,F: int > rat] :
% 9.17/5.39 ( ! [X4: int] :
% 9.17/5.39 ( ( member_int @ X4 @ A2 )
% 9.17/5.39 => ( ord_less_eq_rat @ one_one_rat @ ( F @ X4 ) ) )
% 9.17/5.39 => ( ord_less_eq_rat @ one_one_rat @ ( groups1072433553688619179nt_rat @ F @ A2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4420_prod__ge__1,axiom,
% 9.17/5.39 ! [A2: set_o,F: $o > nat] :
% 9.17/5.39 ( ! [X4: $o] :
% 9.17/5.39 ( ( member_o @ X4 @ A2 )
% 9.17/5.39 => ( ord_less_eq_nat @ one_one_nat @ ( F @ X4 ) ) )
% 9.17/5.39 => ( ord_less_eq_nat @ one_one_nat @ ( groups3504817904513533571_o_nat @ F @ A2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4421_prod__ge__1,axiom,
% 9.17/5.39 ! [A2: set_int,F: int > nat] :
% 9.17/5.39 ( ! [X4: int] :
% 9.17/5.39 ( ( member_int @ X4 @ A2 )
% 9.17/5.39 => ( ord_less_eq_nat @ one_one_nat @ ( F @ X4 ) ) )
% 9.17/5.39 => ( ord_less_eq_nat @ one_one_nat @ ( groups1707563613775114915nt_nat @ F @ A2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4422_prod__ge__1,axiom,
% 9.17/5.39 ! [A2: set_o,F: $o > int] :
% 9.17/5.39 ( ! [X4: $o] :
% 9.17/5.39 ( ( member_o @ X4 @ A2 )
% 9.17/5.39 => ( ord_less_eq_int @ one_one_int @ ( F @ X4 ) ) )
% 9.17/5.39 => ( ord_less_eq_int @ one_one_int @ ( groups3502327434004483295_o_int @ F @ A2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4423_prod__ge__1,axiom,
% 9.17/5.39 ! [A2: set_nat,F: nat > nat] :
% 9.17/5.39 ( ! [X4: nat] :
% 9.17/5.39 ( ( member_nat @ X4 @ A2 )
% 9.17/5.39 => ( ord_less_eq_nat @ one_one_nat @ ( F @ X4 ) ) )
% 9.17/5.39 => ( ord_less_eq_nat @ one_one_nat @ ( groups708209901874060359at_nat @ F @ A2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4424_int__of__integer__less__iff,axiom,
% 9.17/5.39 ! [X: code_integer,Y: code_integer] :
% 9.17/5.39 ( ( ord_less_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Y ) )
% 9.17/5.39 = ( ord_le6747313008572928689nteger @ X @ Y ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4425_integer__less__iff,axiom,
% 9.17/5.39 ( ord_le6747313008572928689nteger
% 9.17/5.39 = ( ^ [K4: code_integer,L3: code_integer] : ( ord_less_int @ ( code_int_of_integer @ K4 ) @ ( code_int_of_integer @ L3 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4426_less__integer_Orep__eq,axiom,
% 9.17/5.39 ( ord_le6747313008572928689nteger
% 9.17/5.39 = ( ^ [X3: code_integer,Xa4: code_integer] : ( ord_less_int @ ( code_int_of_integer @ X3 ) @ ( code_int_of_integer @ Xa4 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4427_less__eq__integer_Orep__eq,axiom,
% 9.17/5.39 ( ord_le3102999989581377725nteger
% 9.17/5.39 = ( ^ [X3: code_integer,Xa4: code_integer] : ( ord_less_eq_int @ ( code_int_of_integer @ X3 ) @ ( code_int_of_integer @ Xa4 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4428_integer__less__eq__iff,axiom,
% 9.17/5.39 ( ord_le3102999989581377725nteger
% 9.17/5.39 = ( ^ [K4: code_integer,L3: code_integer] : ( ord_less_eq_int @ ( code_int_of_integer @ K4 ) @ ( code_int_of_integer @ L3 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4429_prod_Oshift__bounds__cl__Suc__ivl,axiom,
% 9.17/5.39 ! [G: nat > nat,M2: nat,N2: nat] :
% 9.17/5.39 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ ( suc @ N2 ) ) )
% 9.17/5.39 = ( groups708209901874060359at_nat
% 9.17/5.39 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 9.17/5.39 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4430_prod_Oshift__bounds__cl__Suc__ivl,axiom,
% 9.17/5.39 ! [G: nat > int,M2: nat,N2: nat] :
% 9.17/5.39 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ ( suc @ N2 ) ) )
% 9.17/5.39 = ( groups705719431365010083at_int
% 9.17/5.39 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 9.17/5.39 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4431_prod_Oshift__bounds__Suc__ivl,axiom,
% 9.17/5.39 ! [G: nat > nat,M2: nat,N2: nat] :
% 9.17/5.39 ( ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ ( suc @ M2 ) @ ( suc @ N2 ) ) )
% 9.17/5.39 = ( groups708209901874060359at_nat
% 9.17/5.39 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 9.17/5.39 @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4432_prod_Oshift__bounds__Suc__ivl,axiom,
% 9.17/5.39 ! [G: nat > int,M2: nat,N2: nat] :
% 9.17/5.39 ( ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ ( suc @ M2 ) @ ( suc @ N2 ) ) )
% 9.17/5.39 = ( groups705719431365010083at_int
% 9.17/5.39 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 9.17/5.39 @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4433_prod_Oshift__bounds__cl__nat__ivl,axiom,
% 9.17/5.39 ! [G: nat > nat,M2: nat,K: nat,N2: nat] :
% 9.17/5.39 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M2 @ K ) @ ( plus_plus_nat @ N2 @ K ) ) )
% 9.17/5.39 = ( groups708209901874060359at_nat
% 9.17/5.39 @ ^ [I3: nat] : ( G @ ( plus_plus_nat @ I3 @ K ) )
% 9.17/5.39 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4434_prod_Oshift__bounds__cl__nat__ivl,axiom,
% 9.17/5.39 ! [G: nat > int,M2: nat,K: nat,N2: nat] :
% 9.17/5.39 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M2 @ K ) @ ( plus_plus_nat @ N2 @ K ) ) )
% 9.17/5.39 = ( groups705719431365010083at_int
% 9.17/5.39 @ ^ [I3: nat] : ( G @ ( plus_plus_nat @ I3 @ K ) )
% 9.17/5.39 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4435_prod_Oshift__bounds__nat__ivl,axiom,
% 9.17/5.39 ! [G: nat > nat,M2: nat,K: nat,N2: nat] :
% 9.17/5.39 ( ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ ( plus_plus_nat @ M2 @ K ) @ ( plus_plus_nat @ N2 @ K ) ) )
% 9.17/5.39 = ( groups708209901874060359at_nat
% 9.17/5.39 @ ^ [I3: nat] : ( G @ ( plus_plus_nat @ I3 @ K ) )
% 9.17/5.39 @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4436_prod_Oshift__bounds__nat__ivl,axiom,
% 9.17/5.39 ! [G: nat > int,M2: nat,K: nat,N2: nat] :
% 9.17/5.39 ( ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ ( plus_plus_nat @ M2 @ K ) @ ( plus_plus_nat @ N2 @ K ) ) )
% 9.17/5.39 = ( groups705719431365010083at_int
% 9.17/5.39 @ ^ [I3: nat] : ( G @ ( plus_plus_nat @ I3 @ K ) )
% 9.17/5.39 @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4437_atLeastLessThanPlusOne__atLeastAtMost__integer,axiom,
% 9.17/5.39 ! [L: code_integer,U: code_integer] :
% 9.17/5.39 ( ( set_or8404916559141939852nteger @ L @ ( plus_p5714425477246183910nteger @ U @ one_one_Code_integer ) )
% 9.17/5.39 = ( set_or189985376899183464nteger @ L @ U ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4438_prod__le__1,axiom,
% 9.17/5.39 ! [A2: set_o,F: $o > code_integer] :
% 9.17/5.39 ( ! [X4: $o] :
% 9.17/5.39 ( ( member_o @ X4 @ A2 )
% 9.17/5.39 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ X4 ) )
% 9.17/5.39 & ( ord_le3102999989581377725nteger @ ( F @ X4 ) @ one_one_Code_integer ) ) )
% 9.17/5.39 => ( ord_le3102999989581377725nteger @ ( groups7694694392188491536nteger @ F @ A2 ) @ one_one_Code_integer ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4439_prod__le__1,axiom,
% 9.17/5.39 ! [A2: set_nat,F: nat > code_integer] :
% 9.17/5.39 ( ! [X4: nat] :
% 9.17/5.39 ( ( member_nat @ X4 @ A2 )
% 9.17/5.39 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ X4 ) )
% 9.17/5.39 & ( ord_le3102999989581377725nteger @ ( F @ X4 ) @ one_one_Code_integer ) ) )
% 9.17/5.39 => ( ord_le3102999989581377725nteger @ ( groups3455450783089532116nteger @ F @ A2 ) @ one_one_Code_integer ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4440_prod__le__1,axiom,
% 9.17/5.39 ! [A2: set_int,F: int > code_integer] :
% 9.17/5.39 ( ! [X4: int] :
% 9.17/5.39 ( ( member_int @ X4 @ A2 )
% 9.17/5.39 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ X4 ) )
% 9.17/5.39 & ( ord_le3102999989581377725nteger @ ( F @ X4 ) @ one_one_Code_integer ) ) )
% 9.17/5.39 => ( ord_le3102999989581377725nteger @ ( groups3827104343326376752nteger @ F @ A2 ) @ one_one_Code_integer ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4441_prod__le__1,axiom,
% 9.17/5.39 ! [A2: set_o,F: $o > rat] :
% 9.17/5.39 ( ! [X4: $o] :
% 9.17/5.39 ( ( member_o @ X4 @ A2 )
% 9.17/5.39 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) )
% 9.17/5.39 & ( ord_less_eq_rat @ ( F @ X4 ) @ one_one_rat ) ) )
% 9.17/5.39 => ( ord_less_eq_rat @ ( groups2869687844427037835_o_rat @ F @ A2 ) @ one_one_rat ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4442_prod__le__1,axiom,
% 9.17/5.39 ! [A2: set_nat,F: nat > rat] :
% 9.17/5.39 ( ! [X4: nat] :
% 9.17/5.39 ( ( member_nat @ X4 @ A2 )
% 9.17/5.39 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) )
% 9.17/5.39 & ( ord_less_eq_rat @ ( F @ X4 ) @ one_one_rat ) ) )
% 9.17/5.39 => ( ord_less_eq_rat @ ( groups73079841787564623at_rat @ F @ A2 ) @ one_one_rat ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4443_prod__le__1,axiom,
% 9.17/5.39 ! [A2: set_int,F: int > rat] :
% 9.17/5.39 ( ! [X4: int] :
% 9.17/5.39 ( ( member_int @ X4 @ A2 )
% 9.17/5.39 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) )
% 9.17/5.39 & ( ord_less_eq_rat @ ( F @ X4 ) @ one_one_rat ) ) )
% 9.17/5.39 => ( ord_less_eq_rat @ ( groups1072433553688619179nt_rat @ F @ A2 ) @ one_one_rat ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4444_prod__le__1,axiom,
% 9.17/5.39 ! [A2: set_o,F: $o > nat] :
% 9.17/5.39 ( ! [X4: $o] :
% 9.17/5.39 ( ( member_o @ X4 @ A2 )
% 9.17/5.39 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X4 ) )
% 9.17/5.39 & ( ord_less_eq_nat @ ( F @ X4 ) @ one_one_nat ) ) )
% 9.17/5.39 => ( ord_less_eq_nat @ ( groups3504817904513533571_o_nat @ F @ A2 ) @ one_one_nat ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4445_prod__le__1,axiom,
% 9.17/5.39 ! [A2: set_int,F: int > nat] :
% 9.17/5.39 ( ! [X4: int] :
% 9.17/5.39 ( ( member_int @ X4 @ A2 )
% 9.17/5.39 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X4 ) )
% 9.17/5.39 & ( ord_less_eq_nat @ ( F @ X4 ) @ one_one_nat ) ) )
% 9.17/5.39 => ( ord_less_eq_nat @ ( groups1707563613775114915nt_nat @ F @ A2 ) @ one_one_nat ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4446_prod__le__1,axiom,
% 9.17/5.39 ! [A2: set_o,F: $o > int] :
% 9.17/5.39 ( ! [X4: $o] :
% 9.17/5.39 ( ( member_o @ X4 @ A2 )
% 9.17/5.39 => ( ( ord_less_eq_int @ zero_zero_int @ ( F @ X4 ) )
% 9.17/5.39 & ( ord_less_eq_int @ ( F @ X4 ) @ one_one_int ) ) )
% 9.17/5.39 => ( ord_less_eq_int @ ( groups3502327434004483295_o_int @ F @ A2 ) @ one_one_int ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4447_prod__le__1,axiom,
% 9.17/5.39 ! [A2: set_nat,F: nat > nat] :
% 9.17/5.39 ( ! [X4: nat] :
% 9.17/5.39 ( ( member_nat @ X4 @ A2 )
% 9.17/5.39 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X4 ) )
% 9.17/5.39 & ( ord_less_eq_nat @ ( F @ X4 ) @ one_one_nat ) ) )
% 9.17/5.39 => ( ord_less_eq_nat @ ( groups708209901874060359at_nat @ F @ A2 ) @ one_one_nat ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4448_prod_Oivl__cong,axiom,
% 9.17/5.39 ! [A: nat,C: nat,B: nat,D2: nat,G: nat > nat,H3: nat > nat] :
% 9.17/5.39 ( ( A = C )
% 9.17/5.39 => ( ( B = D2 )
% 9.17/5.39 => ( ! [X4: nat] :
% 9.17/5.39 ( ( ord_less_eq_nat @ C @ X4 )
% 9.17/5.39 => ( ( ord_less_nat @ X4 @ D2 )
% 9.17/5.39 => ( ( G @ X4 )
% 9.17/5.39 = ( H3 @ X4 ) ) ) )
% 9.17/5.39 => ( ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ A @ B ) )
% 9.17/5.39 = ( groups708209901874060359at_nat @ H3 @ ( set_or4665077453230672383an_nat @ C @ D2 ) ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4449_prod_Oivl__cong,axiom,
% 9.17/5.39 ! [A: nat,C: nat,B: nat,D2: nat,G: nat > int,H3: nat > int] :
% 9.17/5.39 ( ( A = C )
% 9.17/5.39 => ( ( B = D2 )
% 9.17/5.39 => ( ! [X4: nat] :
% 9.17/5.39 ( ( ord_less_eq_nat @ C @ X4 )
% 9.17/5.39 => ( ( ord_less_nat @ X4 @ D2 )
% 9.17/5.39 => ( ( G @ X4 )
% 9.17/5.39 = ( H3 @ X4 ) ) ) )
% 9.17/5.39 => ( ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ A @ B ) )
% 9.17/5.39 = ( groups705719431365010083at_int @ H3 @ ( set_or4665077453230672383an_nat @ C @ D2 ) ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4450_prod_Oivl__cong,axiom,
% 9.17/5.39 ! [A: int,C: int,B: int,D2: int,G: int > int,H3: int > int] :
% 9.17/5.39 ( ( A = C )
% 9.17/5.39 => ( ( B = D2 )
% 9.17/5.39 => ( ! [X4: int] :
% 9.17/5.39 ( ( ord_less_eq_int @ C @ X4 )
% 9.17/5.39 => ( ( ord_less_int @ X4 @ D2 )
% 9.17/5.39 => ( ( G @ X4 )
% 9.17/5.39 = ( H3 @ X4 ) ) ) )
% 9.17/5.39 => ( ( groups1705073143266064639nt_int @ G @ ( set_or4662586982721622107an_int @ A @ B ) )
% 9.17/5.39 = ( groups1705073143266064639nt_int @ H3 @ ( set_or4662586982721622107an_int @ C @ D2 ) ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4451_take__bit__integer_Orep__eq,axiom,
% 9.17/5.39 ! [X: nat,Xa: code_integer] :
% 9.17/5.39 ( ( code_int_of_integer @ ( bit_se1745604003318907178nteger @ X @ Xa ) )
% 9.17/5.39 = ( bit_se2923211474154528505it_int @ X @ ( code_int_of_integer @ Xa ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4452_and__integer_Orep__eq,axiom,
% 9.17/5.39 ! [X: code_integer,Xa: code_integer] :
% 9.17/5.39 ( ( code_int_of_integer @ ( bit_se3949692690581998587nteger @ X @ Xa ) )
% 9.17/5.39 = ( bit_se725231765392027082nd_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Xa ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4453_bit__integer_Orep__eq,axiom,
% 9.17/5.39 ( bit_se9216721137139052372nteger
% 9.17/5.39 = ( ^ [X3: code_integer] : ( bit_se1146084159140164899it_int @ ( code_int_of_integer @ X3 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4454_prod_OatLeastLessThan__concat,axiom,
% 9.17/5.39 ! [M2: nat,N2: nat,P4: nat,G: nat > assn] :
% 9.17/5.39 ( ( ord_less_eq_nat @ M2 @ N2 )
% 9.17/5.39 => ( ( ord_less_eq_nat @ N2 @ P4 )
% 9.17/5.39 => ( ( times_times_assn @ ( groups6906906614972039071t_assn @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) @ ( groups6906906614972039071t_assn @ G @ ( set_or4665077453230672383an_nat @ N2 @ P4 ) ) )
% 9.17/5.39 = ( groups6906906614972039071t_assn @ G @ ( set_or4665077453230672383an_nat @ M2 @ P4 ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4455_prod_OatLeastLessThan__concat,axiom,
% 9.17/5.39 ! [M2: nat,N2: nat,P4: nat,G: nat > rat] :
% 9.17/5.39 ( ( ord_less_eq_nat @ M2 @ N2 )
% 9.17/5.39 => ( ( ord_less_eq_nat @ N2 @ P4 )
% 9.17/5.39 => ( ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) @ ( groups73079841787564623at_rat @ G @ ( set_or4665077453230672383an_nat @ N2 @ P4 ) ) )
% 9.17/5.39 = ( groups73079841787564623at_rat @ G @ ( set_or4665077453230672383an_nat @ M2 @ P4 ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4456_prod_OatLeastLessThan__concat,axiom,
% 9.17/5.39 ! [M2: nat,N2: nat,P4: nat,G: nat > nat] :
% 9.17/5.39 ( ( ord_less_eq_nat @ M2 @ N2 )
% 9.17/5.39 => ( ( ord_less_eq_nat @ N2 @ P4 )
% 9.17/5.39 => ( ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) @ ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ N2 @ P4 ) ) )
% 9.17/5.39 = ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ M2 @ P4 ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4457_prod_OatLeastLessThan__concat,axiom,
% 9.17/5.39 ! [M2: nat,N2: nat,P4: nat,G: nat > int] :
% 9.17/5.39 ( ( ord_less_eq_nat @ M2 @ N2 )
% 9.17/5.39 => ( ( ord_less_eq_nat @ N2 @ P4 )
% 9.17/5.39 => ( ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) @ ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ N2 @ P4 ) ) )
% 9.17/5.39 = ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ M2 @ P4 ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4458_mask__integer_Orep__eq,axiom,
% 9.17/5.39 ! [X: nat] :
% 9.17/5.39 ( ( code_int_of_integer @ ( bit_se2119862282449309892nteger @ X ) )
% 9.17/5.39 = ( bit_se2000444600071755411sk_int @ X ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4459_integer__of__num__def,axiom,
% 9.17/5.39 code_integer_of_num = numera6620942414471956472nteger ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4460_unset__bit__integer_Orep__eq,axiom,
% 9.17/5.39 ! [X: nat,Xa: code_integer] :
% 9.17/5.39 ( ( code_int_of_integer @ ( bit_se8260200283734997820nteger @ X @ Xa ) )
% 9.17/5.39 = ( bit_se4203085406695923979it_int @ X @ ( code_int_of_integer @ Xa ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4461_set__bit__integer_Orep__eq,axiom,
% 9.17/5.39 ! [X: nat,Xa: code_integer] :
% 9.17/5.39 ( ( code_int_of_integer @ ( bit_se2793503036327961859nteger @ X @ Xa ) )
% 9.17/5.39 = ( bit_se7879613467334960850it_int @ X @ ( code_int_of_integer @ Xa ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4462_flip__bit__integer_Orep__eq,axiom,
% 9.17/5.39 ! [X: nat,Xa: code_integer] :
% 9.17/5.39 ( ( code_int_of_integer @ ( bit_se1345352211410354436nteger @ X @ Xa ) )
% 9.17/5.39 = ( bit_se2159334234014336723it_int @ X @ ( code_int_of_integer @ Xa ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4463_prod_OatLeast__Suc__atMost__Suc__shift,axiom,
% 9.17/5.39 ! [G: nat > nat,M2: nat,N2: nat] :
% 9.17/5.39 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ ( suc @ N2 ) ) )
% 9.17/5.39 = ( groups708209901874060359at_nat @ ( comp_nat_nat_nat @ G @ suc ) @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4464_prod_OatLeast__Suc__atMost__Suc__shift,axiom,
% 9.17/5.39 ! [G: nat > int,M2: nat,N2: nat] :
% 9.17/5.39 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ ( suc @ N2 ) ) )
% 9.17/5.39 = ( groups705719431365010083at_int @ ( comp_nat_int_nat @ G @ suc ) @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4465_prod_OatLeast__Suc__lessThan__Suc__shift,axiom,
% 9.17/5.39 ! [G: nat > nat,M2: nat,N2: nat] :
% 9.17/5.39 ( ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ ( suc @ M2 ) @ ( suc @ N2 ) ) )
% 9.17/5.39 = ( groups708209901874060359at_nat @ ( comp_nat_nat_nat @ G @ suc ) @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4466_prod_OatLeast__Suc__lessThan__Suc__shift,axiom,
% 9.17/5.39 ! [G: nat > int,M2: nat,N2: nat] :
% 9.17/5.39 ( ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ ( suc @ M2 ) @ ( suc @ N2 ) ) )
% 9.17/5.39 = ( groups705719431365010083at_int @ ( comp_nat_int_nat @ G @ suc ) @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4467_atLeastLessThanPlusOne__atLeastAtMost__int,axiom,
% 9.17/5.39 ! [L: int,U: int] :
% 9.17/5.39 ( ( set_or4662586982721622107an_int @ L @ ( plus_plus_int @ U @ one_one_int ) )
% 9.17/5.39 = ( set_or1266510415728281911st_int @ L @ U ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4468_prod_OatLeastAtMost__shift__bounds,axiom,
% 9.17/5.39 ! [G: nat > nat,M2: nat,K: nat,N2: nat] :
% 9.17/5.39 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M2 @ K ) @ ( plus_plus_nat @ N2 @ K ) ) )
% 9.17/5.39 = ( groups708209901874060359at_nat @ ( comp_nat_nat_nat @ G @ ( plus_plus_nat @ K ) ) @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4469_prod_OatLeastAtMost__shift__bounds,axiom,
% 9.17/5.39 ! [G: nat > int,M2: nat,K: nat,N2: nat] :
% 9.17/5.39 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M2 @ K ) @ ( plus_plus_nat @ N2 @ K ) ) )
% 9.17/5.39 = ( groups705719431365010083at_int @ ( comp_nat_int_nat @ G @ ( plus_plus_nat @ K ) ) @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4470_prod_OatLeastLessThan__shift__bounds,axiom,
% 9.17/5.39 ! [G: nat > nat,M2: nat,K: nat,N2: nat] :
% 9.17/5.39 ( ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ ( plus_plus_nat @ M2 @ K ) @ ( plus_plus_nat @ N2 @ K ) ) )
% 9.17/5.39 = ( groups708209901874060359at_nat @ ( comp_nat_nat_nat @ G @ ( plus_plus_nat @ K ) ) @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4471_prod_OatLeastLessThan__shift__bounds,axiom,
% 9.17/5.39 ! [G: nat > int,M2: nat,K: nat,N2: nat] :
% 9.17/5.39 ( ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ ( plus_plus_nat @ M2 @ K ) @ ( plus_plus_nat @ N2 @ K ) ) )
% 9.17/5.39 = ( groups705719431365010083at_int @ ( comp_nat_int_nat @ G @ ( plus_plus_nat @ K ) ) @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4472_prod_OatLeastAtMost__rev,axiom,
% 9.17/5.39 ! [G: nat > nat,N2: nat,M2: nat] :
% 9.17/5.39 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ N2 @ M2 ) )
% 9.17/5.39 = ( groups708209901874060359at_nat
% 9.17/5.39 @ ^ [I3: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M2 @ N2 ) @ I3 ) )
% 9.17/5.39 @ ( set_or1269000886237332187st_nat @ N2 @ M2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4473_prod_OatLeastAtMost__rev,axiom,
% 9.17/5.39 ! [G: nat > int,N2: nat,M2: nat] :
% 9.17/5.39 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ N2 @ M2 ) )
% 9.17/5.39 = ( groups705719431365010083at_int
% 9.17/5.39 @ ^ [I3: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M2 @ N2 ) @ I3 ) )
% 9.17/5.39 @ ( set_or1269000886237332187st_nat @ N2 @ M2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4474_prod_Onat__diff__reindex,axiom,
% 9.17/5.39 ! [G: nat > nat,N2: nat] :
% 9.17/5.39 ( ( groups708209901874060359at_nat
% 9.17/5.39 @ ^ [I3: nat] : ( G @ ( minus_minus_nat @ N2 @ ( suc @ I3 ) ) )
% 9.17/5.39 @ ( set_ord_lessThan_nat @ N2 ) )
% 9.17/5.39 = ( groups708209901874060359at_nat @ G @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4475_prod_Onat__diff__reindex,axiom,
% 9.17/5.39 ! [G: nat > int,N2: nat] :
% 9.17/5.39 ( ( groups705719431365010083at_int
% 9.17/5.39 @ ^ [I3: nat] : ( G @ ( minus_minus_nat @ N2 @ ( suc @ I3 ) ) )
% 9.17/5.39 @ ( set_ord_lessThan_nat @ N2 ) )
% 9.17/5.39 = ( groups705719431365010083at_int @ G @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4476_nat__of__integer_Oabs__eq,axiom,
% 9.17/5.39 ! [X: int] :
% 9.17/5.39 ( ( code_nat_of_integer @ ( code_integer_of_int @ X ) )
% 9.17/5.39 = ( nat2 @ X ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4477_num__of__integer_Orep__eq,axiom,
% 9.17/5.39 ( code_num_of_integer
% 9.17/5.39 = ( ^ [X3: code_integer] : ( num_of_nat @ ( nat2 @ ( code_int_of_integer @ X3 ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4478_prod_OatLeast0__atMost__Suc,axiom,
% 9.17/5.39 ! [G: nat > assn,N2: nat] :
% 9.17/5.39 ( ( groups6906906614972039071t_assn @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 9.17/5.39 = ( times_times_assn @ ( groups6906906614972039071t_assn @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4479_prod_OatLeast0__atMost__Suc,axiom,
% 9.17/5.39 ! [G: nat > rat,N2: nat] :
% 9.17/5.39 ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 9.17/5.39 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4480_prod_OatLeast0__atMost__Suc,axiom,
% 9.17/5.39 ! [G: nat > nat,N2: nat] :
% 9.17/5.39 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 9.17/5.39 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4481_prod_OatLeast0__atMost__Suc,axiom,
% 9.17/5.39 ! [G: nat > int,N2: nat] :
% 9.17/5.39 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 9.17/5.39 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4482_prod_OatLeast0__lessThan__Suc,axiom,
% 9.17/5.39 ! [G: nat > assn,N2: nat] :
% 9.17/5.39 ( ( groups6906906614972039071t_assn @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 9.17/5.39 = ( times_times_assn @ ( groups6906906614972039071t_assn @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4483_prod_OatLeast0__lessThan__Suc,axiom,
% 9.17/5.39 ! [G: nat > rat,N2: nat] :
% 9.17/5.39 ( ( groups73079841787564623at_rat @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 9.17/5.39 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4484_prod_OatLeast0__lessThan__Suc,axiom,
% 9.17/5.39 ! [G: nat > nat,N2: nat] :
% 9.17/5.39 ( ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 9.17/5.39 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4485_prod_OatLeast0__lessThan__Suc,axiom,
% 9.17/5.39 ! [G: nat > int,N2: nat] :
% 9.17/5.39 ( ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 9.17/5.39 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4486_prod_OatLeast__Suc__lessThan,axiom,
% 9.17/5.39 ! [M2: nat,N2: nat,G: nat > assn] :
% 9.17/5.39 ( ( ord_less_nat @ M2 @ N2 )
% 9.17/5.39 => ( ( groups6906906614972039071t_assn @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) )
% 9.17/5.39 = ( times_times_assn @ ( G @ M2 ) @ ( groups6906906614972039071t_assn @ G @ ( set_or4665077453230672383an_nat @ ( suc @ M2 ) @ N2 ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4487_prod_OatLeast__Suc__lessThan,axiom,
% 9.17/5.39 ! [M2: nat,N2: nat,G: nat > rat] :
% 9.17/5.39 ( ( ord_less_nat @ M2 @ N2 )
% 9.17/5.39 => ( ( groups73079841787564623at_rat @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) )
% 9.17/5.39 = ( times_times_rat @ ( G @ M2 ) @ ( groups73079841787564623at_rat @ G @ ( set_or4665077453230672383an_nat @ ( suc @ M2 ) @ N2 ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4488_prod_OatLeast__Suc__lessThan,axiom,
% 9.17/5.39 ! [M2: nat,N2: nat,G: nat > nat] :
% 9.17/5.39 ( ( ord_less_nat @ M2 @ N2 )
% 9.17/5.39 => ( ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) )
% 9.17/5.39 = ( times_times_nat @ ( G @ M2 ) @ ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ ( suc @ M2 ) @ N2 ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4489_prod_OatLeast__Suc__lessThan,axiom,
% 9.17/5.39 ! [M2: nat,N2: nat,G: nat > int] :
% 9.17/5.39 ( ( ord_less_nat @ M2 @ N2 )
% 9.17/5.39 => ( ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) )
% 9.17/5.39 = ( times_times_int @ ( G @ M2 ) @ ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ ( suc @ M2 ) @ N2 ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4490_prod_Onat__ivl__Suc_H,axiom,
% 9.17/5.39 ! [M2: nat,N2: nat,G: nat > assn] :
% 9.17/5.39 ( ( ord_less_eq_nat @ M2 @ ( suc @ N2 ) )
% 9.17/5.39 => ( ( groups6906906614972039071t_assn @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N2 ) ) )
% 9.17/5.39 = ( times_times_assn @ ( G @ ( suc @ N2 ) ) @ ( groups6906906614972039071t_assn @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4491_prod_Onat__ivl__Suc_H,axiom,
% 9.17/5.39 ! [M2: nat,N2: nat,G: nat > rat] :
% 9.17/5.39 ( ( ord_less_eq_nat @ M2 @ ( suc @ N2 ) )
% 9.17/5.39 => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N2 ) ) )
% 9.17/5.39 = ( times_times_rat @ ( G @ ( suc @ N2 ) ) @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4492_prod_Onat__ivl__Suc_H,axiom,
% 9.17/5.39 ! [M2: nat,N2: nat,G: nat > nat] :
% 9.17/5.39 ( ( ord_less_eq_nat @ M2 @ ( suc @ N2 ) )
% 9.17/5.39 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N2 ) ) )
% 9.17/5.39 = ( times_times_nat @ ( G @ ( suc @ N2 ) ) @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4493_prod_Onat__ivl__Suc_H,axiom,
% 9.17/5.39 ! [M2: nat,N2: nat,G: nat > int] :
% 9.17/5.39 ( ( ord_less_eq_nat @ M2 @ ( suc @ N2 ) )
% 9.17/5.39 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N2 ) ) )
% 9.17/5.39 = ( times_times_int @ ( G @ ( suc @ N2 ) ) @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4494_prod_OatLeast__Suc__atMost,axiom,
% 9.17/5.39 ! [M2: nat,N2: nat,G: nat > assn] :
% 9.17/5.39 ( ( ord_less_eq_nat @ M2 @ N2 )
% 9.17/5.39 => ( ( groups6906906614972039071t_assn @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 9.17/5.39 = ( times_times_assn @ ( G @ M2 ) @ ( groups6906906614972039071t_assn @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N2 ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4495_prod_OatLeast__Suc__atMost,axiom,
% 9.17/5.39 ! [M2: nat,N2: nat,G: nat > rat] :
% 9.17/5.39 ( ( ord_less_eq_nat @ M2 @ N2 )
% 9.17/5.39 => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 9.17/5.39 = ( times_times_rat @ ( G @ M2 ) @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N2 ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4496_prod_OatLeast__Suc__atMost,axiom,
% 9.17/5.39 ! [M2: nat,N2: nat,G: nat > nat] :
% 9.17/5.39 ( ( ord_less_eq_nat @ M2 @ N2 )
% 9.17/5.39 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 9.17/5.39 = ( times_times_nat @ ( G @ M2 ) @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N2 ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4497_prod_OatLeast__Suc__atMost,axiom,
% 9.17/5.39 ! [M2: nat,N2: nat,G: nat > int] :
% 9.17/5.39 ( ( ord_less_eq_nat @ M2 @ N2 )
% 9.17/5.39 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 9.17/5.39 = ( times_times_int @ ( G @ M2 ) @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N2 ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4498_prod_OatLeastLessThan__Suc,axiom,
% 9.17/5.39 ! [A: nat,B: nat,G: nat > assn] :
% 9.17/5.39 ( ( ord_less_eq_nat @ A @ B )
% 9.17/5.39 => ( ( groups6906906614972039071t_assn @ G @ ( set_or4665077453230672383an_nat @ A @ ( suc @ B ) ) )
% 9.17/5.39 = ( times_times_assn @ ( groups6906906614972039071t_assn @ G @ ( set_or4665077453230672383an_nat @ A @ B ) ) @ ( G @ B ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4499_prod_OatLeastLessThan__Suc,axiom,
% 9.17/5.39 ! [A: nat,B: nat,G: nat > rat] :
% 9.17/5.39 ( ( ord_less_eq_nat @ A @ B )
% 9.17/5.39 => ( ( groups73079841787564623at_rat @ G @ ( set_or4665077453230672383an_nat @ A @ ( suc @ B ) ) )
% 9.17/5.39 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or4665077453230672383an_nat @ A @ B ) ) @ ( G @ B ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4500_prod_OatLeastLessThan__Suc,axiom,
% 9.17/5.39 ! [A: nat,B: nat,G: nat > nat] :
% 9.17/5.39 ( ( ord_less_eq_nat @ A @ B )
% 9.17/5.39 => ( ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ A @ ( suc @ B ) ) )
% 9.17/5.39 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ A @ B ) ) @ ( G @ B ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4501_prod_OatLeastLessThan__Suc,axiom,
% 9.17/5.39 ! [A: nat,B: nat,G: nat > int] :
% 9.17/5.39 ( ( ord_less_eq_nat @ A @ B )
% 9.17/5.39 => ( ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ A @ ( suc @ B ) ) )
% 9.17/5.39 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ A @ B ) ) @ ( G @ B ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4502_divmod__abs__code_I6_J,axiom,
% 9.17/5.39 ! [J: code_integer] :
% 9.17/5.39 ( ( code_divmod_abs @ zero_z3403309356797280102nteger @ J )
% 9.17/5.39 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4503_prod_Olast__plus,axiom,
% 9.17/5.39 ! [M2: nat,N2: nat,G: nat > assn] :
% 9.17/5.39 ( ( ord_less_eq_nat @ M2 @ N2 )
% 9.17/5.39 => ( ( groups6906906614972039071t_assn @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 9.17/5.39 = ( times_times_assn @ ( G @ N2 ) @ ( groups6906906614972039071t_assn @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4504_prod_Olast__plus,axiom,
% 9.17/5.39 ! [M2: nat,N2: nat,G: nat > rat] :
% 9.17/5.39 ( ( ord_less_eq_nat @ M2 @ N2 )
% 9.17/5.39 => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 9.17/5.39 = ( times_times_rat @ ( G @ N2 ) @ ( groups73079841787564623at_rat @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4505_prod_Olast__plus,axiom,
% 9.17/5.39 ! [M2: nat,N2: nat,G: nat > nat] :
% 9.17/5.39 ( ( ord_less_eq_nat @ M2 @ N2 )
% 9.17/5.39 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 9.17/5.39 = ( times_times_nat @ ( G @ N2 ) @ ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4506_prod_Olast__plus,axiom,
% 9.17/5.39 ! [M2: nat,N2: nat,G: nat > int] :
% 9.17/5.39 ( ( ord_less_eq_nat @ M2 @ N2 )
% 9.17/5.39 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 9.17/5.39 = ( times_times_int @ ( G @ N2 ) @ ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4507_prod_OSuc__reindex__ivl,axiom,
% 9.17/5.39 ! [M2: nat,N2: nat,G: nat > assn] :
% 9.17/5.39 ( ( ord_less_eq_nat @ M2 @ N2 )
% 9.17/5.39 => ( ( times_times_assn @ ( groups6906906614972039071t_assn @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 9.17/5.39 = ( times_times_assn @ ( G @ M2 )
% 9.17/5.39 @ ( groups6906906614972039071t_assn
% 9.17/5.39 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 9.17/5.39 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4508_prod_OSuc__reindex__ivl,axiom,
% 9.17/5.39 ! [M2: nat,N2: nat,G: nat > rat] :
% 9.17/5.39 ( ( ord_less_eq_nat @ M2 @ N2 )
% 9.17/5.39 => ( ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 9.17/5.39 = ( times_times_rat @ ( G @ M2 )
% 9.17/5.39 @ ( groups73079841787564623at_rat
% 9.17/5.39 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 9.17/5.39 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4509_prod_OSuc__reindex__ivl,axiom,
% 9.17/5.39 ! [M2: nat,N2: nat,G: nat > nat] :
% 9.17/5.39 ( ( ord_less_eq_nat @ M2 @ N2 )
% 9.17/5.39 => ( ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 9.17/5.39 = ( times_times_nat @ ( G @ M2 )
% 9.17/5.39 @ ( groups708209901874060359at_nat
% 9.17/5.39 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 9.17/5.39 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4510_prod_OSuc__reindex__ivl,axiom,
% 9.17/5.39 ! [M2: nat,N2: nat,G: nat > int] :
% 9.17/5.39 ( ( ord_less_eq_nat @ M2 @ N2 )
% 9.17/5.39 => ( ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 9.17/5.39 = ( times_times_int @ ( G @ M2 )
% 9.17/5.39 @ ( groups705719431365010083at_int
% 9.17/5.39 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 9.17/5.39 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4511_prod_OatMost__Suc__shift,axiom,
% 9.17/5.39 ! [G: nat > assn,N2: nat] :
% 9.17/5.39 ( ( groups6906906614972039071t_assn @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 9.17/5.39 = ( times_times_assn @ ( G @ zero_zero_nat )
% 9.17/5.39 @ ( groups6906906614972039071t_assn
% 9.17/5.39 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 9.17/5.39 @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4512_prod_OatMost__Suc__shift,axiom,
% 9.17/5.39 ! [G: nat > rat,N2: nat] :
% 9.17/5.39 ( ( groups73079841787564623at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 9.17/5.39 = ( times_times_rat @ ( G @ zero_zero_nat )
% 9.17/5.39 @ ( groups73079841787564623at_rat
% 9.17/5.39 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 9.17/5.39 @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4513_prod_OatMost__Suc__shift,axiom,
% 9.17/5.39 ! [G: nat > nat,N2: nat] :
% 9.17/5.39 ( ( groups708209901874060359at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 9.17/5.39 = ( times_times_nat @ ( G @ zero_zero_nat )
% 9.17/5.39 @ ( groups708209901874060359at_nat
% 9.17/5.39 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 9.17/5.39 @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4514_prod_OatMost__Suc__shift,axiom,
% 9.17/5.39 ! [G: nat > int,N2: nat] :
% 9.17/5.39 ( ( groups705719431365010083at_int @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 9.17/5.39 = ( times_times_int @ ( G @ zero_zero_nat )
% 9.17/5.39 @ ( groups705719431365010083at_int
% 9.17/5.39 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 9.17/5.39 @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4515_prod_OlessThan__Suc__shift,axiom,
% 9.17/5.39 ! [G: nat > assn,N2: nat] :
% 9.17/5.39 ( ( groups6906906614972039071t_assn @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 9.17/5.39 = ( times_times_assn @ ( G @ zero_zero_nat )
% 9.17/5.39 @ ( groups6906906614972039071t_assn
% 9.17/5.39 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 9.17/5.39 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4516_prod_OlessThan__Suc__shift,axiom,
% 9.17/5.39 ! [G: nat > rat,N2: nat] :
% 9.17/5.39 ( ( groups73079841787564623at_rat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 9.17/5.39 = ( times_times_rat @ ( G @ zero_zero_nat )
% 9.17/5.39 @ ( groups73079841787564623at_rat
% 9.17/5.39 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 9.17/5.39 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4517_prod_OlessThan__Suc__shift,axiom,
% 9.17/5.39 ! [G: nat > nat,N2: nat] :
% 9.17/5.39 ( ( groups708209901874060359at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 9.17/5.39 = ( times_times_nat @ ( G @ zero_zero_nat )
% 9.17/5.39 @ ( groups708209901874060359at_nat
% 9.17/5.39 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 9.17/5.39 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4518_prod_OlessThan__Suc__shift,axiom,
% 9.17/5.39 ! [G: nat > int,N2: nat] :
% 9.17/5.39 ( ( groups705719431365010083at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 9.17/5.39 = ( times_times_int @ ( G @ zero_zero_nat )
% 9.17/5.39 @ ( groups705719431365010083at_int
% 9.17/5.39 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 9.17/5.39 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4519_prod_OatLeastLessThan__rev,axiom,
% 9.17/5.39 ! [G: nat > nat,N2: nat,M2: nat] :
% 9.17/5.39 ( ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ N2 @ M2 ) )
% 9.17/5.39 = ( groups708209901874060359at_nat
% 9.17/5.39 @ ^ [I3: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M2 @ N2 ) @ ( suc @ I3 ) ) )
% 9.17/5.39 @ ( set_or4665077453230672383an_nat @ N2 @ M2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4520_prod_OatLeastLessThan__rev,axiom,
% 9.17/5.39 ! [G: nat > int,N2: nat,M2: nat] :
% 9.17/5.39 ( ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ N2 @ M2 ) )
% 9.17/5.39 = ( groups705719431365010083at_int
% 9.17/5.39 @ ^ [I3: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M2 @ N2 ) @ ( suc @ I3 ) ) )
% 9.17/5.39 @ ( set_or4665077453230672383an_nat @ N2 @ M2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4521_prod_Onested__swap,axiom,
% 9.17/5.39 ! [A: nat > nat > nat,N2: nat] :
% 9.17/5.39 ( ( groups708209901874060359at_nat
% 9.17/5.39 @ ^ [I3: nat] : ( groups708209901874060359at_nat @ ( A @ I3 ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ I3 ) )
% 9.17/5.39 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 9.17/5.39 = ( groups708209901874060359at_nat
% 9.17/5.39 @ ^ [J2: nat] :
% 9.17/5.39 ( groups708209901874060359at_nat
% 9.17/5.39 @ ^ [I3: nat] : ( A @ I3 @ J2 )
% 9.17/5.39 @ ( set_or1269000886237332187st_nat @ ( suc @ J2 ) @ N2 ) )
% 9.17/5.39 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4522_prod_Onested__swap,axiom,
% 9.17/5.39 ! [A: nat > nat > int,N2: nat] :
% 9.17/5.39 ( ( groups705719431365010083at_int
% 9.17/5.39 @ ^ [I3: nat] : ( groups705719431365010083at_int @ ( A @ I3 ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ I3 ) )
% 9.17/5.39 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 9.17/5.39 = ( groups705719431365010083at_int
% 9.17/5.39 @ ^ [J2: nat] :
% 9.17/5.39 ( groups705719431365010083at_int
% 9.17/5.39 @ ^ [I3: nat] : ( A @ I3 @ J2 )
% 9.17/5.39 @ ( set_or1269000886237332187st_nat @ ( suc @ J2 ) @ N2 ) )
% 9.17/5.39 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4523_prod_OatLeast1__atMost__eq,axiom,
% 9.17/5.39 ! [G: nat > nat,N2: nat] :
% 9.17/5.39 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 9.17/5.39 = ( groups708209901874060359at_nat
% 9.17/5.39 @ ^ [K4: nat] : ( G @ ( suc @ K4 ) )
% 9.17/5.39 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4524_prod_OatLeast1__atMost__eq,axiom,
% 9.17/5.39 ! [G: nat > int,N2: nat] :
% 9.17/5.39 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 9.17/5.39 = ( groups705719431365010083at_int
% 9.17/5.39 @ ^ [K4: nat] : ( G @ ( suc @ K4 ) )
% 9.17/5.39 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4525_prod_Onat__group,axiom,
% 9.17/5.39 ! [G: nat > nat,K: nat,N2: nat] :
% 9.17/5.39 ( ( groups708209901874060359at_nat
% 9.17/5.39 @ ^ [M: nat] : ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ ( times_times_nat @ M @ K ) @ ( plus_plus_nat @ ( times_times_nat @ M @ K ) @ K ) ) )
% 9.17/5.39 @ ( set_ord_lessThan_nat @ N2 ) )
% 9.17/5.39 = ( groups708209901874060359at_nat @ G @ ( set_ord_lessThan_nat @ ( times_times_nat @ N2 @ K ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4526_prod_Onat__group,axiom,
% 9.17/5.39 ! [G: nat > int,K: nat,N2: nat] :
% 9.17/5.39 ( ( groups705719431365010083at_int
% 9.17/5.39 @ ^ [M: nat] : ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ ( times_times_nat @ M @ K ) @ ( plus_plus_nat @ ( times_times_nat @ M @ K ) @ K ) ) )
% 9.17/5.39 @ ( set_ord_lessThan_nat @ N2 ) )
% 9.17/5.39 = ( groups705719431365010083at_int @ G @ ( set_ord_lessThan_nat @ ( times_times_nat @ N2 @ K ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4527_fact__prod,axiom,
% 9.17/5.39 ( semiri1406184849735516958ct_int
% 9.17/5.39 = ( ^ [N4: nat] :
% 9.17/5.39 ( semiri1314217659103216013at_int
% 9.17/5.39 @ ( groups708209901874060359at_nat
% 9.17/5.39 @ ^ [X3: nat] : X3
% 9.17/5.39 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N4 ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4528_fact__prod,axiom,
% 9.17/5.39 ( semiri3624122377584611663nteger
% 9.17/5.39 = ( ^ [N4: nat] :
% 9.17/5.39 ( semiri4939895301339042750nteger
% 9.17/5.39 @ ( groups708209901874060359at_nat
% 9.17/5.39 @ ^ [X3: nat] : X3
% 9.17/5.39 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N4 ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4529_fact__prod,axiom,
% 9.17/5.39 ( semiri2447717529341329178atural
% 9.17/5.39 = ( ^ [N4: nat] :
% 9.17/5.39 ( semiri3763490453095760265atural
% 9.17/5.39 @ ( groups708209901874060359at_nat
% 9.17/5.39 @ ^ [X3: nat] : X3
% 9.17/5.39 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N4 ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4530_fact__prod,axiom,
% 9.17/5.39 ( semiri1408675320244567234ct_nat
% 9.17/5.39 = ( ^ [N4: nat] :
% 9.17/5.39 ( semiri1316708129612266289at_nat
% 9.17/5.39 @ ( groups708209901874060359at_nat
% 9.17/5.39 @ ^ [X3: nat] : X3
% 9.17/5.39 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N4 ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4531_prod_Onested__swap_H,axiom,
% 9.17/5.39 ! [A: nat > nat > nat,N2: nat] :
% 9.17/5.39 ( ( groups708209901874060359at_nat
% 9.17/5.39 @ ^ [I3: nat] : ( groups708209901874060359at_nat @ ( A @ I3 ) @ ( set_ord_lessThan_nat @ I3 ) )
% 9.17/5.39 @ ( set_ord_atMost_nat @ N2 ) )
% 9.17/5.39 = ( groups708209901874060359at_nat
% 9.17/5.39 @ ^ [J2: nat] :
% 9.17/5.39 ( groups708209901874060359at_nat
% 9.17/5.39 @ ^ [I3: nat] : ( A @ I3 @ J2 )
% 9.17/5.39 @ ( set_or1269000886237332187st_nat @ ( suc @ J2 ) @ N2 ) )
% 9.17/5.39 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4532_prod_Onested__swap_H,axiom,
% 9.17/5.39 ! [A: nat > nat > int,N2: nat] :
% 9.17/5.39 ( ( groups705719431365010083at_int
% 9.17/5.39 @ ^ [I3: nat] : ( groups705719431365010083at_int @ ( A @ I3 ) @ ( set_ord_lessThan_nat @ I3 ) )
% 9.17/5.39 @ ( set_ord_atMost_nat @ N2 ) )
% 9.17/5.39 = ( groups705719431365010083at_int
% 9.17/5.39 @ ^ [J2: nat] :
% 9.17/5.39 ( groups705719431365010083at_int
% 9.17/5.39 @ ^ [I3: nat] : ( A @ I3 @ J2 )
% 9.17/5.39 @ ( set_or1269000886237332187st_nat @ ( suc @ J2 ) @ N2 ) )
% 9.17/5.39 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4533_prod__atLeastAtMost__code,axiom,
% 9.17/5.39 ! [F: nat > code_integer,A: nat,B: nat] :
% 9.17/5.39 ( ( groups3455450783089532116nteger @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 9.17/5.39 = ( set_fo1084959871951514735nteger
% 9.17/5.39 @ ^ [A5: nat] : ( times_3573771949741848930nteger @ ( F @ A5 ) )
% 9.17/5.39 @ A
% 9.17/5.39 @ B
% 9.17/5.39 @ one_one_Code_integer ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4534_prod__atLeastAtMost__code,axiom,
% 9.17/5.39 ! [F: nat > assn,A: nat,B: nat] :
% 9.17/5.39 ( ( groups6906906614972039071t_assn @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 9.17/5.39 = ( set_fo1959793692361082170t_assn
% 9.17/5.39 @ ^ [A5: nat] : ( times_times_assn @ ( F @ A5 ) )
% 9.17/5.39 @ A
% 9.17/5.39 @ B
% 9.17/5.39 @ one_one_assn ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4535_prod__atLeastAtMost__code,axiom,
% 9.17/5.39 ! [F: nat > rat,A: nat,B: nat] :
% 9.17/5.39 ( ( groups73079841787564623at_rat @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 9.17/5.39 = ( set_fo1949268297981939178at_rat
% 9.17/5.39 @ ^ [A5: nat] : ( times_times_rat @ ( F @ A5 ) )
% 9.17/5.39 @ A
% 9.17/5.39 @ B
% 9.17/5.39 @ one_one_rat ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4536_prod__atLeastAtMost__code,axiom,
% 9.17/5.39 ! [F: nat > nat,A: nat,B: nat] :
% 9.17/5.39 ( ( groups708209901874060359at_nat @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 9.17/5.39 = ( set_fo2584398358068434914at_nat
% 9.17/5.39 @ ^ [A5: nat] : ( times_times_nat @ ( F @ A5 ) )
% 9.17/5.39 @ A
% 9.17/5.39 @ B
% 9.17/5.39 @ one_one_nat ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4537_prod__atLeastAtMost__code,axiom,
% 9.17/5.39 ! [F: nat > int,A: nat,B: nat] :
% 9.17/5.39 ( ( groups705719431365010083at_int @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 9.17/5.39 = ( set_fo2581907887559384638at_int
% 9.17/5.39 @ ^ [A5: nat] : ( times_times_int @ ( F @ A5 ) )
% 9.17/5.39 @ A
% 9.17/5.39 @ B
% 9.17/5.39 @ one_one_int ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4538_prod_Ohead__if,axiom,
% 9.17/5.39 ! [N2: nat,M2: nat,G: nat > code_integer] :
% 9.17/5.39 ( ( ( ord_less_nat @ N2 @ M2 )
% 9.17/5.39 => ( ( groups3455450783089532116nteger @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 9.17/5.39 = one_one_Code_integer ) )
% 9.17/5.39 & ( ~ ( ord_less_nat @ N2 @ M2 )
% 9.17/5.39 => ( ( groups3455450783089532116nteger @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 9.17/5.39 = ( times_3573771949741848930nteger @ ( groups3455450783089532116nteger @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) @ ( G @ N2 ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4539_prod_Ohead__if,axiom,
% 9.17/5.39 ! [N2: nat,M2: nat,G: nat > assn] :
% 9.17/5.39 ( ( ( ord_less_nat @ N2 @ M2 )
% 9.17/5.39 => ( ( groups6906906614972039071t_assn @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 9.17/5.39 = one_one_assn ) )
% 9.17/5.39 & ( ~ ( ord_less_nat @ N2 @ M2 )
% 9.17/5.39 => ( ( groups6906906614972039071t_assn @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 9.17/5.39 = ( times_times_assn @ ( groups6906906614972039071t_assn @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) @ ( G @ N2 ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4540_prod_Ohead__if,axiom,
% 9.17/5.39 ! [N2: nat,M2: nat,G: nat > rat] :
% 9.17/5.39 ( ( ( ord_less_nat @ N2 @ M2 )
% 9.17/5.39 => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 9.17/5.39 = one_one_rat ) )
% 9.17/5.39 & ( ~ ( ord_less_nat @ N2 @ M2 )
% 9.17/5.39 => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 9.17/5.39 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) @ ( G @ N2 ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4541_prod_Ohead__if,axiom,
% 9.17/5.39 ! [N2: nat,M2: nat,G: nat > nat] :
% 9.17/5.39 ( ( ( ord_less_nat @ N2 @ M2 )
% 9.17/5.39 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 9.17/5.39 = one_one_nat ) )
% 9.17/5.39 & ( ~ ( ord_less_nat @ N2 @ M2 )
% 9.17/5.39 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 9.17/5.39 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) @ ( G @ N2 ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4542_prod_Ohead__if,axiom,
% 9.17/5.39 ! [N2: nat,M2: nat,G: nat > int] :
% 9.17/5.39 ( ( ( ord_less_nat @ N2 @ M2 )
% 9.17/5.39 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 9.17/5.39 = one_one_int ) )
% 9.17/5.39 & ( ~ ( ord_less_nat @ N2 @ M2 )
% 9.17/5.39 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 9.17/5.39 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) @ ( G @ N2 ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4543_prod_Oub__add__nat,axiom,
% 9.17/5.39 ! [M2: nat,N2: nat,G: nat > assn,P4: nat] :
% 9.17/5.39 ( ( ord_less_eq_nat @ M2 @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 9.17/5.39 => ( ( groups6906906614972039071t_assn @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ N2 @ P4 ) ) )
% 9.17/5.39 = ( times_times_assn @ ( groups6906906614972039071t_assn @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) @ ( groups6906906614972039071t_assn @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ ( plus_plus_nat @ N2 @ P4 ) ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4544_prod_Oub__add__nat,axiom,
% 9.17/5.39 ! [M2: nat,N2: nat,G: nat > rat,P4: nat] :
% 9.17/5.39 ( ( ord_less_eq_nat @ M2 @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 9.17/5.39 => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ N2 @ P4 ) ) )
% 9.17/5.39 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ ( plus_plus_nat @ N2 @ P4 ) ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4545_prod_Oub__add__nat,axiom,
% 9.17/5.39 ! [M2: nat,N2: nat,G: nat > nat,P4: nat] :
% 9.17/5.39 ( ( ord_less_eq_nat @ M2 @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 9.17/5.39 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ N2 @ P4 ) ) )
% 9.17/5.39 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ ( plus_plus_nat @ N2 @ P4 ) ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4546_prod_Oub__add__nat,axiom,
% 9.17/5.39 ! [M2: nat,N2: nat,G: nat > int,P4: nat] :
% 9.17/5.39 ( ( ord_less_eq_nat @ M2 @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 9.17/5.39 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ N2 @ P4 ) ) )
% 9.17/5.39 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ ( plus_plus_nat @ N2 @ P4 ) ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4547_prod_OatLeast0__atMost__Suc__shift,axiom,
% 9.17/5.39 ! [G: nat > assn,N2: nat] :
% 9.17/5.39 ( ( groups6906906614972039071t_assn @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 9.17/5.39 = ( times_times_assn @ ( G @ zero_zero_nat ) @ ( groups6906906614972039071t_assn @ ( comp_nat_assn_nat @ G @ suc ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4548_prod_OatLeast0__atMost__Suc__shift,axiom,
% 9.17/5.39 ! [G: nat > rat,N2: nat] :
% 9.17/5.39 ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 9.17/5.39 = ( times_times_rat @ ( G @ zero_zero_nat ) @ ( groups73079841787564623at_rat @ ( comp_nat_rat_nat @ G @ suc ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4549_prod_OatLeast0__atMost__Suc__shift,axiom,
% 9.17/5.39 ! [G: nat > nat,N2: nat] :
% 9.17/5.39 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 9.17/5.39 = ( times_times_nat @ ( G @ zero_zero_nat ) @ ( groups708209901874060359at_nat @ ( comp_nat_nat_nat @ G @ suc ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4550_prod_OatLeast0__atMost__Suc__shift,axiom,
% 9.17/5.39 ! [G: nat > int,N2: nat] :
% 9.17/5.39 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 9.17/5.39 = ( times_times_int @ ( G @ zero_zero_nat ) @ ( groups705719431365010083at_int @ ( comp_nat_int_nat @ G @ suc ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4551_prod_OatLeast0__lessThan__Suc__shift,axiom,
% 9.17/5.39 ! [G: nat > assn,N2: nat] :
% 9.17/5.39 ( ( groups6906906614972039071t_assn @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 9.17/5.39 = ( times_times_assn @ ( G @ zero_zero_nat ) @ ( groups6906906614972039071t_assn @ ( comp_nat_assn_nat @ G @ suc ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4552_prod_OatLeast0__lessThan__Suc__shift,axiom,
% 9.17/5.39 ! [G: nat > rat,N2: nat] :
% 9.17/5.39 ( ( groups73079841787564623at_rat @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 9.17/5.39 = ( times_times_rat @ ( G @ zero_zero_nat ) @ ( groups73079841787564623at_rat @ ( comp_nat_rat_nat @ G @ suc ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4553_prod_OatLeast0__lessThan__Suc__shift,axiom,
% 9.17/5.39 ! [G: nat > nat,N2: nat] :
% 9.17/5.39 ( ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 9.17/5.39 = ( times_times_nat @ ( G @ zero_zero_nat ) @ ( groups708209901874060359at_nat @ ( comp_nat_nat_nat @ G @ suc ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4554_prod_OatLeast0__lessThan__Suc__shift,axiom,
% 9.17/5.39 ! [G: nat > int,N2: nat] :
% 9.17/5.39 ( ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 9.17/5.39 = ( times_times_int @ ( G @ zero_zero_nat ) @ ( groups705719431365010083at_int @ ( comp_nat_int_nat @ G @ suc ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4555_prod_OatLeastLessThan__shift__0,axiom,
% 9.17/5.39 ! [G: nat > nat,M2: nat,N2: nat] :
% 9.17/5.39 ( ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) )
% 9.17/5.39 = ( groups708209901874060359at_nat @ ( comp_nat_nat_nat @ G @ ( plus_plus_nat @ M2 ) ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( minus_minus_nat @ N2 @ M2 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4556_prod_OatLeastLessThan__shift__0,axiom,
% 9.17/5.39 ! [G: nat > int,M2: nat,N2: nat] :
% 9.17/5.39 ( ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) )
% 9.17/5.39 = ( groups705719431365010083at_int @ ( comp_nat_int_nat @ G @ ( plus_plus_nat @ M2 ) ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( minus_minus_nat @ N2 @ M2 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4557_integer__of__num__triv_I1_J,axiom,
% 9.17/5.39 ( ( code_integer_of_num @ one )
% 9.17/5.39 = one_one_Code_integer ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4558_prod_OatLeastLessThan__rev__at__least__Suc__atMost,axiom,
% 9.17/5.39 ! [G: nat > nat,N2: nat,M2: nat] :
% 9.17/5.39 ( ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ N2 @ M2 ) )
% 9.17/5.39 = ( groups708209901874060359at_nat
% 9.17/5.39 @ ^ [I3: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M2 @ N2 ) @ I3 ) )
% 9.17/5.39 @ ( set_or1269000886237332187st_nat @ ( suc @ N2 ) @ M2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4559_prod_OatLeastLessThan__rev__at__least__Suc__atMost,axiom,
% 9.17/5.39 ! [G: nat > int,N2: nat,M2: nat] :
% 9.17/5.39 ( ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ N2 @ M2 ) )
% 9.17/5.39 = ( groups705719431365010083at_int
% 9.17/5.39 @ ^ [I3: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M2 @ N2 ) @ I3 ) )
% 9.17/5.39 @ ( set_or1269000886237332187st_nat @ ( suc @ N2 ) @ M2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4560_prod_OatMost__shift,axiom,
% 9.17/5.39 ! [G: nat > assn,N2: nat] :
% 9.17/5.39 ( ( groups6906906614972039071t_assn @ G @ ( set_ord_atMost_nat @ N2 ) )
% 9.17/5.39 = ( times_times_assn @ ( G @ zero_zero_nat )
% 9.17/5.39 @ ( groups6906906614972039071t_assn
% 9.17/5.39 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 9.17/5.39 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4561_prod_OatMost__shift,axiom,
% 9.17/5.39 ! [G: nat > rat,N2: nat] :
% 9.17/5.39 ( ( groups73079841787564623at_rat @ G @ ( set_ord_atMost_nat @ N2 ) )
% 9.17/5.39 = ( times_times_rat @ ( G @ zero_zero_nat )
% 9.17/5.39 @ ( groups73079841787564623at_rat
% 9.17/5.39 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 9.17/5.39 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4562_prod_OatMost__shift,axiom,
% 9.17/5.39 ! [G: nat > nat,N2: nat] :
% 9.17/5.39 ( ( groups708209901874060359at_nat @ G @ ( set_ord_atMost_nat @ N2 ) )
% 9.17/5.39 = ( times_times_nat @ ( G @ zero_zero_nat )
% 9.17/5.39 @ ( groups708209901874060359at_nat
% 9.17/5.39 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 9.17/5.39 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4563_prod_OatMost__shift,axiom,
% 9.17/5.39 ! [G: nat > int,N2: nat] :
% 9.17/5.39 ( ( groups705719431365010083at_int @ G @ ( set_ord_atMost_nat @ N2 ) )
% 9.17/5.39 = ( times_times_int @ ( G @ zero_zero_nat )
% 9.17/5.39 @ ( groups705719431365010083at_int
% 9.17/5.39 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 9.17/5.39 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4564_pochhammer__prod,axiom,
% 9.17/5.39 ( comm_s4028243227959126397er_rat
% 9.17/5.39 = ( ^ [A5: rat,N4: nat] :
% 9.17/5.39 ( groups73079841787564623at_rat
% 9.17/5.39 @ ^ [I3: nat] : ( plus_plus_rat @ A5 @ ( semiri681578069525770553at_rat @ I3 ) )
% 9.17/5.39 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N4 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4565_pochhammer__prod,axiom,
% 9.17/5.39 ( comm_s8582702949713902594nteger
% 9.17/5.39 = ( ^ [A5: code_integer,N4: nat] :
% 9.17/5.39 ( groups3455450783089532116nteger
% 9.17/5.39 @ ^ [I3: nat] : ( plus_p5714425477246183910nteger @ A5 @ ( semiri4939895301339042750nteger @ I3 ) )
% 9.17/5.39 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N4 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4566_pochhammer__prod,axiom,
% 9.17/5.39 ( comm_s7406298101470620109atural
% 9.17/5.39 = ( ^ [A5: code_natural,N4: nat] :
% 9.17/5.39 ( groups2279045934846249631atural
% 9.17/5.39 @ ^ [I3: nat] : ( plus_p4538020629002901425atural @ A5 @ ( semiri3763490453095760265atural @ I3 ) )
% 9.17/5.39 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N4 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4567_pochhammer__prod,axiom,
% 9.17/5.39 ( comm_s4663373288045622133er_nat
% 9.17/5.39 = ( ^ [A5: nat,N4: nat] :
% 9.17/5.39 ( groups708209901874060359at_nat
% 9.17/5.39 @ ^ [I3: nat] : ( plus_plus_nat @ A5 @ ( semiri1316708129612266289at_nat @ I3 ) )
% 9.17/5.39 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N4 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4568_pochhammer__prod,axiom,
% 9.17/5.39 ( comm_s4660882817536571857er_int
% 9.17/5.39 = ( ^ [A5: int,N4: nat] :
% 9.17/5.39 ( groups705719431365010083at_int
% 9.17/5.39 @ ^ [I3: nat] : ( plus_plus_int @ A5 @ ( semiri1314217659103216013at_int @ I3 ) )
% 9.17/5.39 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N4 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4569_prod_OatLeast__atMost__pred__shift,axiom,
% 9.17/5.39 ! [G: nat > nat,M2: nat,N2: nat] :
% 9.17/5.39 ( ( groups708209901874060359at_nat
% 9.17/5.39 @ ( comp_nat_nat_nat @ G
% 9.17/5.39 @ ^ [N4: nat] : ( minus_minus_nat @ N4 @ ( suc @ zero_zero_nat ) ) )
% 9.17/5.39 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ ( suc @ N2 ) ) )
% 9.17/5.39 = ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4570_prod_OatLeast__atMost__pred__shift,axiom,
% 9.17/5.39 ! [G: nat > int,M2: nat,N2: nat] :
% 9.17/5.39 ( ( groups705719431365010083at_int
% 9.17/5.39 @ ( comp_nat_int_nat @ G
% 9.17/5.39 @ ^ [N4: nat] : ( minus_minus_nat @ N4 @ ( suc @ zero_zero_nat ) ) )
% 9.17/5.39 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ ( suc @ N2 ) ) )
% 9.17/5.39 = ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4571_prod_OatLeast__lessThan__pred__shift,axiom,
% 9.17/5.39 ! [G: nat > nat,M2: nat,N2: nat] :
% 9.17/5.39 ( ( groups708209901874060359at_nat
% 9.17/5.39 @ ( comp_nat_nat_nat @ G
% 9.17/5.39 @ ^ [N4: nat] : ( minus_minus_nat @ N4 @ ( suc @ zero_zero_nat ) ) )
% 9.17/5.39 @ ( set_or4665077453230672383an_nat @ ( suc @ M2 ) @ ( suc @ N2 ) ) )
% 9.17/5.39 = ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4572_prod_OatLeast__lessThan__pred__shift,axiom,
% 9.17/5.39 ! [G: nat > int,M2: nat,N2: nat] :
% 9.17/5.39 ( ( groups705719431365010083at_int
% 9.17/5.39 @ ( comp_nat_int_nat @ G
% 9.17/5.39 @ ^ [N4: nat] : ( minus_minus_nat @ N4 @ ( suc @ zero_zero_nat ) ) )
% 9.17/5.39 @ ( set_or4665077453230672383an_nat @ ( suc @ M2 ) @ ( suc @ N2 ) ) )
% 9.17/5.39 = ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4573_integer__of__num_I2_J,axiom,
% 9.17/5.39 ! [N2: num] :
% 9.17/5.39 ( ( code_integer_of_num @ ( bit0 @ N2 ) )
% 9.17/5.39 = ( plus_p5714425477246183910nteger @ ( code_integer_of_num @ N2 ) @ ( code_integer_of_num @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4574_divmod__abs__code_I5_J,axiom,
% 9.17/5.39 ! [J: code_integer] :
% 9.17/5.39 ( ( code_divmod_abs @ J @ zero_z3403309356797280102nteger )
% 9.17/5.39 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ J ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4575_prod_OatLeastAtMost__shift__0,axiom,
% 9.17/5.39 ! [M2: nat,N2: nat,G: nat > nat] :
% 9.17/5.39 ( ( ord_less_eq_nat @ M2 @ N2 )
% 9.17/5.39 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 9.17/5.39 = ( groups708209901874060359at_nat @ ( comp_nat_nat_nat @ G @ ( plus_plus_nat @ M2 ) ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( minus_minus_nat @ N2 @ M2 ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4576_prod_OatLeastAtMost__shift__0,axiom,
% 9.17/5.39 ! [M2: nat,N2: nat,G: nat > int] :
% 9.17/5.39 ( ( ord_less_eq_nat @ M2 @ N2 )
% 9.17/5.39 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 9.17/5.39 = ( groups705719431365010083at_int @ ( comp_nat_int_nat @ G @ ( plus_plus_nat @ M2 ) ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( minus_minus_nat @ N2 @ M2 ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4577_sum_OatLeast__int__lessThan__int__shift,axiom,
% 9.17/5.39 ! [G: int > nat,M2: nat,N2: nat] :
% 9.17/5.39 ( ( groups4541462559716669496nt_nat @ G @ ( set_or4662586982721622107an_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 9.17/5.39 = ( groups3542108847815614940at_nat @ ( comp_int_nat_nat @ G @ semiri1314217659103216013at_int ) @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4578_sum_OatLeast__int__lessThan__int__shift,axiom,
% 9.17/5.39 ! [G: int > int,M2: nat,N2: nat] :
% 9.17/5.39 ( ( groups4538972089207619220nt_int @ G @ ( set_or4662586982721622107an_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 9.17/5.39 = ( groups3539618377306564664at_int @ ( comp_int_int_nat @ G @ semiri1314217659103216013at_int ) @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4579_pochhammer__Suc__prod,axiom,
% 9.17/5.39 ! [A: rat,N2: nat] :
% 9.17/5.39 ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N2 ) )
% 9.17/5.39 = ( groups73079841787564623at_rat
% 9.17/5.39 @ ^ [I3: nat] : ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ I3 ) )
% 9.17/5.39 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4580_pochhammer__Suc__prod,axiom,
% 9.17/5.39 ! [A: code_integer,N2: nat] :
% 9.17/5.39 ( ( comm_s8582702949713902594nteger @ A @ ( suc @ N2 ) )
% 9.17/5.39 = ( groups3455450783089532116nteger
% 9.17/5.39 @ ^ [I3: nat] : ( plus_p5714425477246183910nteger @ A @ ( semiri4939895301339042750nteger @ I3 ) )
% 9.17/5.39 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4581_pochhammer__Suc__prod,axiom,
% 9.17/5.39 ! [A: code_natural,N2: nat] :
% 9.17/5.39 ( ( comm_s7406298101470620109atural @ A @ ( suc @ N2 ) )
% 9.17/5.39 = ( groups2279045934846249631atural
% 9.17/5.39 @ ^ [I3: nat] : ( plus_p4538020629002901425atural @ A @ ( semiri3763490453095760265atural @ I3 ) )
% 9.17/5.39 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4582_pochhammer__Suc__prod,axiom,
% 9.17/5.39 ! [A: nat,N2: nat] :
% 9.17/5.39 ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N2 ) )
% 9.17/5.39 = ( groups708209901874060359at_nat
% 9.17/5.39 @ ^ [I3: nat] : ( plus_plus_nat @ A @ ( semiri1316708129612266289at_nat @ I3 ) )
% 9.17/5.39 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4583_pochhammer__Suc__prod,axiom,
% 9.17/5.39 ! [A: int,N2: nat] :
% 9.17/5.39 ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N2 ) )
% 9.17/5.39 = ( groups705719431365010083at_int
% 9.17/5.39 @ ^ [I3: nat] : ( plus_plus_int @ A @ ( semiri1314217659103216013at_int @ I3 ) )
% 9.17/5.39 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4584_pochhammer__prod__rev,axiom,
% 9.17/5.39 ( comm_s4028243227959126397er_rat
% 9.17/5.39 = ( ^ [A5: rat,N4: nat] :
% 9.17/5.39 ( groups73079841787564623at_rat
% 9.17/5.39 @ ^ [I3: nat] : ( plus_plus_rat @ A5 @ ( semiri681578069525770553at_rat @ ( minus_minus_nat @ N4 @ I3 ) ) )
% 9.17/5.39 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N4 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4585_pochhammer__prod__rev,axiom,
% 9.17/5.39 ( comm_s8582702949713902594nteger
% 9.17/5.39 = ( ^ [A5: code_integer,N4: nat] :
% 9.17/5.39 ( groups3455450783089532116nteger
% 9.17/5.39 @ ^ [I3: nat] : ( plus_p5714425477246183910nteger @ A5 @ ( semiri4939895301339042750nteger @ ( minus_minus_nat @ N4 @ I3 ) ) )
% 9.17/5.39 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N4 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4586_pochhammer__prod__rev,axiom,
% 9.17/5.39 ( comm_s7406298101470620109atural
% 9.17/5.39 = ( ^ [A5: code_natural,N4: nat] :
% 9.17/5.39 ( groups2279045934846249631atural
% 9.17/5.39 @ ^ [I3: nat] : ( plus_p4538020629002901425atural @ A5 @ ( semiri3763490453095760265atural @ ( minus_minus_nat @ N4 @ I3 ) ) )
% 9.17/5.39 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N4 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4587_pochhammer__prod__rev,axiom,
% 9.17/5.39 ( comm_s4663373288045622133er_nat
% 9.17/5.39 = ( ^ [A5: nat,N4: nat] :
% 9.17/5.39 ( groups708209901874060359at_nat
% 9.17/5.39 @ ^ [I3: nat] : ( plus_plus_nat @ A5 @ ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ N4 @ I3 ) ) )
% 9.17/5.39 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N4 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4588_pochhammer__prod__rev,axiom,
% 9.17/5.39 ( comm_s4660882817536571857er_int
% 9.17/5.39 = ( ^ [A5: int,N4: nat] :
% 9.17/5.39 ( groups705719431365010083at_int
% 9.17/5.39 @ ^ [I3: nat] : ( plus_plus_int @ A5 @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ N4 @ I3 ) ) )
% 9.17/5.39 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N4 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4589_fact__div__fact,axiom,
% 9.17/5.39 ! [N2: nat,M2: nat] :
% 9.17/5.39 ( ( ord_less_eq_nat @ N2 @ M2 )
% 9.17/5.39 => ( ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ M2 ) @ ( semiri1408675320244567234ct_nat @ N2 ) )
% 9.17/5.39 = ( groups708209901874060359at_nat
% 9.17/5.39 @ ^ [X3: nat] : X3
% 9.17/5.39 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ M2 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4590_integer__of__num__triv_I2_J,axiom,
% 9.17/5.39 ( ( code_integer_of_num @ ( bit0 @ one ) )
% 9.17/5.39 = ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4591_prod_Oin__pairs,axiom,
% 9.17/5.39 ! [G: nat > assn,M2: nat,N2: nat] :
% 9.17/5.39 ( ( groups6906906614972039071t_assn @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 9.17/5.39 = ( groups6906906614972039071t_assn
% 9.17/5.39 @ ^ [I3: nat] : ( times_times_assn @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 9.17/5.39 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4592_prod_Oin__pairs,axiom,
% 9.17/5.39 ! [G: nat > rat,M2: nat,N2: nat] :
% 9.17/5.39 ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 9.17/5.39 = ( groups73079841787564623at_rat
% 9.17/5.39 @ ^ [I3: nat] : ( times_times_rat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 9.17/5.39 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4593_prod_Oin__pairs,axiom,
% 9.17/5.39 ! [G: nat > nat,M2: nat,N2: nat] :
% 9.17/5.39 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 9.17/5.39 = ( groups708209901874060359at_nat
% 9.17/5.39 @ ^ [I3: nat] : ( times_times_nat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 9.17/5.39 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4594_prod_Oin__pairs,axiom,
% 9.17/5.39 ! [G: nat > int,M2: nat,N2: nat] :
% 9.17/5.39 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 9.17/5.39 = ( groups705719431365010083at_int
% 9.17/5.39 @ ^ [I3: nat] : ( times_times_int @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 9.17/5.39 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4595_prod_Oin__pairs__0,axiom,
% 9.17/5.39 ! [G: nat > assn,N2: nat] :
% 9.17/5.39 ( ( groups6906906614972039071t_assn @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 9.17/5.39 = ( groups6906906614972039071t_assn
% 9.17/5.39 @ ^ [I3: nat] : ( times_times_assn @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 9.17/5.39 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4596_prod_Oin__pairs__0,axiom,
% 9.17/5.39 ! [G: nat > rat,N2: nat] :
% 9.17/5.39 ( ( groups73079841787564623at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 9.17/5.39 = ( groups73079841787564623at_rat
% 9.17/5.39 @ ^ [I3: nat] : ( times_times_rat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 9.17/5.39 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4597_prod_Oin__pairs__0,axiom,
% 9.17/5.39 ! [G: nat > nat,N2: nat] :
% 9.17/5.39 ( ( groups708209901874060359at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 9.17/5.39 = ( groups708209901874060359at_nat
% 9.17/5.39 @ ^ [I3: nat] : ( times_times_nat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 9.17/5.39 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4598_prod_Oin__pairs__0,axiom,
% 9.17/5.39 ! [G: nat > int,N2: nat] :
% 9.17/5.39 ( ( groups705719431365010083at_int @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 9.17/5.39 = ( groups705719431365010083at_int
% 9.17/5.39 @ ^ [I3: nat] : ( times_times_int @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 9.17/5.39 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4599_nat__of__integer__less__iff,axiom,
% 9.17/5.39 ! [X: code_integer,Y: code_integer] :
% 9.17/5.39 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X )
% 9.17/5.39 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y )
% 9.17/5.39 => ( ( ord_less_nat @ ( code_nat_of_integer @ X ) @ ( code_nat_of_integer @ Y ) )
% 9.17/5.39 = ( ord_le6747313008572928689nteger @ X @ Y ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4600_pochhammer__Suc__prod__rev,axiom,
% 9.17/5.39 ! [A: rat,N2: nat] :
% 9.17/5.39 ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N2 ) )
% 9.17/5.39 = ( groups73079841787564623at_rat
% 9.17/5.39 @ ^ [I3: nat] : ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ ( minus_minus_nat @ N2 @ I3 ) ) )
% 9.17/5.39 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4601_pochhammer__Suc__prod__rev,axiom,
% 9.17/5.39 ! [A: code_integer,N2: nat] :
% 9.17/5.39 ( ( comm_s8582702949713902594nteger @ A @ ( suc @ N2 ) )
% 9.17/5.39 = ( groups3455450783089532116nteger
% 9.17/5.39 @ ^ [I3: nat] : ( plus_p5714425477246183910nteger @ A @ ( semiri4939895301339042750nteger @ ( minus_minus_nat @ N2 @ I3 ) ) )
% 9.17/5.39 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4602_pochhammer__Suc__prod__rev,axiom,
% 9.17/5.39 ! [A: code_natural,N2: nat] :
% 9.17/5.39 ( ( comm_s7406298101470620109atural @ A @ ( suc @ N2 ) )
% 9.17/5.39 = ( groups2279045934846249631atural
% 9.17/5.39 @ ^ [I3: nat] : ( plus_p4538020629002901425atural @ A @ ( semiri3763490453095760265atural @ ( minus_minus_nat @ N2 @ I3 ) ) )
% 9.17/5.39 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4603_pochhammer__Suc__prod__rev,axiom,
% 9.17/5.39 ! [A: nat,N2: nat] :
% 9.17/5.39 ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N2 ) )
% 9.17/5.39 = ( groups708209901874060359at_nat
% 9.17/5.39 @ ^ [I3: nat] : ( plus_plus_nat @ A @ ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ N2 @ I3 ) ) )
% 9.17/5.39 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4604_pochhammer__Suc__prod__rev,axiom,
% 9.17/5.39 ! [A: int,N2: nat] :
% 9.17/5.39 ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N2 ) )
% 9.17/5.39 = ( groups705719431365010083at_int
% 9.17/5.39 @ ^ [I3: nat] : ( plus_plus_int @ A @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ N2 @ I3 ) ) )
% 9.17/5.39 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4605_divmod__integer__code,axiom,
% 9.17/5.39 ( code_divmod_integer
% 9.17/5.39 = ( ^ [K4: code_integer,L3: code_integer] :
% 9.17/5.39 ( if_Pro6119634080678213985nteger @ ( K4 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 9.17/5.39 @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ L3 )
% 9.17/5.39 @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ K4 ) @ ( code_divmod_abs @ K4 @ L3 )
% 9.17/5.39 @ ( produc6916734918728496179nteger
% 9.17/5.39 @ ^ [R3: code_integer,S4: code_integer] : ( if_Pro6119634080678213985nteger @ ( S4 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R3 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R3 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ L3 @ S4 ) ) )
% 9.17/5.39 @ ( code_divmod_abs @ K4 @ L3 ) ) )
% 9.17/5.39 @ ( if_Pro6119634080678213985nteger @ ( L3 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ K4 )
% 9.17/5.39 @ ( produc6499014454317279255nteger @ uminus1351360451143612070nteger
% 9.17/5.39 @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ K4 @ zero_z3403309356797280102nteger ) @ ( code_divmod_abs @ K4 @ L3 )
% 9.17/5.39 @ ( produc6916734918728496179nteger
% 9.17/5.39 @ ^ [R3: code_integer,S4: code_integer] : ( if_Pro6119634080678213985nteger @ ( S4 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R3 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R3 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ L3 ) @ S4 ) ) )
% 9.17/5.39 @ ( code_divmod_abs @ K4 @ L3 ) ) ) ) ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4606_bit__cut__integer__code,axiom,
% 9.17/5.39 ( code_bit_cut_integer
% 9.17/5.39 = ( ^ [K4: code_integer] :
% 9.17/5.39 ( if_Pro5737122678794959658eger_o @ ( K4 = zero_z3403309356797280102nteger ) @ ( produc6677183202524767010eger_o @ zero_z3403309356797280102nteger @ $false )
% 9.17/5.39 @ ( produc9125791028180074456eger_o
% 9.17/5.39 @ ^ [R3: code_integer,S4: code_integer] : ( produc6677183202524767010eger_o @ ( if_Code_integer @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ K4 ) @ R3 @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R3 ) @ S4 ) ) @ ( S4 = one_one_Code_integer ) )
% 9.17/5.39 @ ( code_divmod_abs @ K4 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4607_prod_Ozero__middle,axiom,
% 9.17/5.39 ! [P4: nat,K: nat,G: nat > code_integer,H3: nat > code_integer] :
% 9.17/5.39 ( ( ord_less_eq_nat @ one_one_nat @ P4 )
% 9.17/5.39 => ( ( ord_less_eq_nat @ K @ P4 )
% 9.17/5.39 => ( ( groups3455450783089532116nteger
% 9.17/5.39 @ ^ [J2: nat] : ( if_Code_integer @ ( ord_less_nat @ J2 @ K ) @ ( G @ J2 ) @ ( if_Code_integer @ ( J2 = K ) @ one_one_Code_integer @ ( H3 @ ( minus_minus_nat @ J2 @ ( suc @ zero_zero_nat ) ) ) ) )
% 9.17/5.39 @ ( set_ord_atMost_nat @ P4 ) )
% 9.17/5.39 = ( groups3455450783089532116nteger
% 9.17/5.39 @ ^ [J2: nat] : ( if_Code_integer @ ( ord_less_nat @ J2 @ K ) @ ( G @ J2 ) @ ( H3 @ J2 ) )
% 9.17/5.39 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P4 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4608_prod_Ozero__middle,axiom,
% 9.17/5.39 ! [P4: nat,K: nat,G: nat > assn,H3: nat > assn] :
% 9.17/5.39 ( ( ord_less_eq_nat @ one_one_nat @ P4 )
% 9.17/5.39 => ( ( ord_less_eq_nat @ K @ P4 )
% 9.17/5.39 => ( ( groups6906906614972039071t_assn
% 9.17/5.39 @ ^ [J2: nat] : ( if_assn @ ( ord_less_nat @ J2 @ K ) @ ( G @ J2 ) @ ( if_assn @ ( J2 = K ) @ one_one_assn @ ( H3 @ ( minus_minus_nat @ J2 @ ( suc @ zero_zero_nat ) ) ) ) )
% 9.17/5.39 @ ( set_ord_atMost_nat @ P4 ) )
% 9.17/5.39 = ( groups6906906614972039071t_assn
% 9.17/5.39 @ ^ [J2: nat] : ( if_assn @ ( ord_less_nat @ J2 @ K ) @ ( G @ J2 ) @ ( H3 @ J2 ) )
% 9.17/5.39 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P4 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4609_prod_Ozero__middle,axiom,
% 9.17/5.39 ! [P4: nat,K: nat,G: nat > rat,H3: nat > rat] :
% 9.17/5.39 ( ( ord_less_eq_nat @ one_one_nat @ P4 )
% 9.17/5.39 => ( ( ord_less_eq_nat @ K @ P4 )
% 9.17/5.39 => ( ( groups73079841787564623at_rat
% 9.17/5.39 @ ^ [J2: nat] : ( if_rat @ ( ord_less_nat @ J2 @ K ) @ ( G @ J2 ) @ ( if_rat @ ( J2 = K ) @ one_one_rat @ ( H3 @ ( minus_minus_nat @ J2 @ ( suc @ zero_zero_nat ) ) ) ) )
% 9.17/5.39 @ ( set_ord_atMost_nat @ P4 ) )
% 9.17/5.39 = ( groups73079841787564623at_rat
% 9.17/5.39 @ ^ [J2: nat] : ( if_rat @ ( ord_less_nat @ J2 @ K ) @ ( G @ J2 ) @ ( H3 @ J2 ) )
% 9.17/5.39 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P4 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4610_prod_Ozero__middle,axiom,
% 9.17/5.39 ! [P4: nat,K: nat,G: nat > nat,H3: nat > nat] :
% 9.17/5.39 ( ( ord_less_eq_nat @ one_one_nat @ P4 )
% 9.17/5.39 => ( ( ord_less_eq_nat @ K @ P4 )
% 9.17/5.39 => ( ( groups708209901874060359at_nat
% 9.17/5.39 @ ^ [J2: nat] : ( if_nat @ ( ord_less_nat @ J2 @ K ) @ ( G @ J2 ) @ ( if_nat @ ( J2 = K ) @ one_one_nat @ ( H3 @ ( minus_minus_nat @ J2 @ ( suc @ zero_zero_nat ) ) ) ) )
% 9.17/5.39 @ ( set_ord_atMost_nat @ P4 ) )
% 9.17/5.39 = ( groups708209901874060359at_nat
% 9.17/5.39 @ ^ [J2: nat] : ( if_nat @ ( ord_less_nat @ J2 @ K ) @ ( G @ J2 ) @ ( H3 @ J2 ) )
% 9.17/5.39 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P4 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4611_prod_Ozero__middle,axiom,
% 9.17/5.39 ! [P4: nat,K: nat,G: nat > int,H3: nat > int] :
% 9.17/5.39 ( ( ord_less_eq_nat @ one_one_nat @ P4 )
% 9.17/5.39 => ( ( ord_less_eq_nat @ K @ P4 )
% 9.17/5.39 => ( ( groups705719431365010083at_int
% 9.17/5.39 @ ^ [J2: nat] : ( if_int @ ( ord_less_nat @ J2 @ K ) @ ( G @ J2 ) @ ( if_int @ ( J2 = K ) @ one_one_int @ ( H3 @ ( minus_minus_nat @ J2 @ ( suc @ zero_zero_nat ) ) ) ) )
% 9.17/5.39 @ ( set_ord_atMost_nat @ P4 ) )
% 9.17/5.39 = ( groups705719431365010083at_int
% 9.17/5.39 @ ^ [J2: nat] : ( if_int @ ( ord_less_nat @ J2 @ K ) @ ( G @ J2 ) @ ( H3 @ J2 ) )
% 9.17/5.39 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P4 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4612_xor__int__rec,axiom,
% 9.17/5.39 ( bit_se6526347334894502574or_int
% 9.17/5.39 = ( ^ [K4: int,L3: int] :
% 9.17/5.39 ( plus_plus_int
% 9.17/5.39 @ ( zero_n2684676970156552555ol_int
% 9.17/5.39 @ ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K4 ) )
% 9.17/5.39 != ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L3 ) ) ) )
% 9.17/5.39 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( divide_divide_int @ K4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4613_divmod__abs__def,axiom,
% 9.17/5.39 ( code_divmod_abs
% 9.17/5.39 = ( ^ [K4: code_integer,L3: code_integer] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ ( abs_abs_Code_integer @ K4 ) @ ( abs_abs_Code_integer @ L3 ) ) @ ( modulo364778990260209775nteger @ ( abs_abs_Code_integer @ K4 ) @ ( abs_abs_Code_integer @ L3 ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4614_less__int_Orep__eq,axiom,
% 9.17/5.39 ( ord_less_int
% 9.17/5.39 = ( ^ [X3: int,Xa4: int] :
% 9.17/5.39 ( produc8739625826339149834_nat_o
% 9.17/5.39 @ ^ [Y3: nat,Z4: nat] :
% 9.17/5.39 ( produc6081775807080527818_nat_o
% 9.17/5.39 @ ^ [U2: nat,V2: nat] : ( ord_less_nat @ ( plus_plus_nat @ Y3 @ V2 ) @ ( plus_plus_nat @ U2 @ Z4 ) ) )
% 9.17/5.39 @ ( rep_Integ @ X3 )
% 9.17/5.39 @ ( rep_Integ @ Xa4 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4615_xor__int__unfold,axiom,
% 9.17/5.39 ( bit_se6526347334894502574or_int
% 9.17/5.39 = ( ^ [K4: int,L3: int] :
% 9.17/5.39 ( if_int
% 9.17/5.39 @ ( K4
% 9.17/5.39 = ( uminus_uminus_int @ one_one_int ) )
% 9.17/5.39 @ ( bit_ri7919022796975470100ot_int @ L3 )
% 9.17/5.39 @ ( if_int
% 9.17/5.39 @ ( L3
% 9.17/5.39 = ( uminus_uminus_int @ one_one_int ) )
% 9.17/5.39 @ ( bit_ri7919022796975470100ot_int @ K4 )
% 9.17/5.39 @ ( if_int @ ( K4 = zero_zero_int ) @ L3 @ ( if_int @ ( L3 = zero_zero_int ) @ K4 @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ ( modulo_modulo_int @ K4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ L3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( divide_divide_int @ K4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4616_take__bit__num__code,axiom,
% 9.17/5.39 ( bit_take_bit_num
% 9.17/5.39 = ( ^ [N4: nat,M: num] :
% 9.17/5.39 ( produc478579273971653890on_num
% 9.17/5.39 @ ^ [A5: nat,X3: num] :
% 9.17/5.39 ( case_nat_option_num @ none_num
% 9.17/5.39 @ ^ [O: nat] :
% 9.17/5.39 ( case_num_option_num @ ( some_num @ one )
% 9.17/5.39 @ ^ [P6: num] :
% 9.17/5.39 ( case_o6005452278849405969um_num @ none_num
% 9.17/5.39 @ ^ [Q5: num] : ( some_num @ ( bit0 @ Q5 ) )
% 9.17/5.39 @ ( bit_take_bit_num @ O @ P6 ) )
% 9.17/5.39 @ ^ [P6: num] : ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ O @ P6 ) ) )
% 9.17/5.39 @ X3 )
% 9.17/5.39 @ A5 )
% 9.17/5.39 @ ( product_Pair_nat_num @ N4 @ M ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4617_prod_Otriangle__reindex,axiom,
% 9.17/5.39 ! [G: nat > nat > nat,N2: nat] :
% 9.17/5.39 ( ( groups4077766827762148844at_nat @ ( produc6842872674320459806at_nat @ G )
% 9.17/5.39 @ ( collec3392354462482085612at_nat
% 9.17/5.39 @ ( produc6081775807080527818_nat_o
% 9.17/5.39 @ ^ [I3: nat,J2: nat] : ( ord_less_nat @ ( plus_plus_nat @ I3 @ J2 ) @ N2 ) ) ) )
% 9.17/5.39 = ( groups708209901874060359at_nat
% 9.17/5.39 @ ^ [K4: nat] :
% 9.17/5.39 ( groups708209901874060359at_nat
% 9.17/5.39 @ ^ [I3: nat] : ( G @ I3 @ ( minus_minus_nat @ K4 @ I3 ) )
% 9.17/5.39 @ ( set_ord_atMost_nat @ K4 ) )
% 9.17/5.39 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4618_prod_Otriangle__reindex,axiom,
% 9.17/5.39 ! [G: nat > nat > int,N2: nat] :
% 9.17/5.39 ( ( groups4075276357253098568at_int @ ( produc6840382203811409530at_int @ G )
% 9.17/5.39 @ ( collec3392354462482085612at_nat
% 9.17/5.39 @ ( produc6081775807080527818_nat_o
% 9.17/5.39 @ ^ [I3: nat,J2: nat] : ( ord_less_nat @ ( plus_plus_nat @ I3 @ J2 ) @ N2 ) ) ) )
% 9.17/5.39 = ( groups705719431365010083at_int
% 9.17/5.39 @ ^ [K4: nat] :
% 9.17/5.39 ( groups705719431365010083at_int
% 9.17/5.39 @ ^ [I3: nat] : ( G @ I3 @ ( minus_minus_nat @ K4 @ I3 ) )
% 9.17/5.39 @ ( set_ord_atMost_nat @ K4 ) )
% 9.17/5.39 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4619_case__nat__add__eq__if,axiom,
% 9.17/5.39 ! [A: option_num,F: nat > option_num,V: num,N2: nat] :
% 9.17/5.39 ( ( case_nat_option_num @ A @ F @ ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ N2 ) )
% 9.17/5.39 = ( F @ ( plus_plus_nat @ ( pred_numeral @ V ) @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4620_bit_Ocompl__zero,axiom,
% 9.17/5.39 ( ( bit_ri7919022796975470100ot_int @ zero_zero_int )
% 9.17/5.39 = ( uminus_uminus_int @ one_one_int ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4621_bit_Ocompl__zero,axiom,
% 9.17/5.39 ( ( bit_ri7632146776885996613nteger @ zero_z3403309356797280102nteger )
% 9.17/5.39 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4622_bit_Ocompl__one,axiom,
% 9.17/5.39 ( ( bit_ri7919022796975470100ot_int @ ( uminus_uminus_int @ one_one_int ) )
% 9.17/5.39 = zero_zero_int ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4623_bit_Ocompl__one,axiom,
% 9.17/5.39 ( ( bit_ri7632146776885996613nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.17/5.39 = zero_z3403309356797280102nteger ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4624_bit_Oxor__cancel__right,axiom,
% 9.17/5.39 ! [X: code_integer] :
% 9.17/5.39 ( ( bit_se3222712562003087583nteger @ X @ ( bit_ri7632146776885996613nteger @ X ) )
% 9.17/5.39 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4625_bit_Oxor__cancel__right,axiom,
% 9.17/5.39 ! [X: int] :
% 9.17/5.39 ( ( bit_se6526347334894502574or_int @ X @ ( bit_ri7919022796975470100ot_int @ X ) )
% 9.17/5.39 = ( uminus_uminus_int @ one_one_int ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4626_bit_Oxor__cancel__left,axiom,
% 9.17/5.39 ! [X: code_integer] :
% 9.17/5.39 ( ( bit_se3222712562003087583nteger @ ( bit_ri7632146776885996613nteger @ X ) @ X )
% 9.17/5.39 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4627_bit_Oxor__cancel__left,axiom,
% 9.17/5.39 ! [X: int] :
% 9.17/5.39 ( ( bit_se6526347334894502574or_int @ ( bit_ri7919022796975470100ot_int @ X ) @ X )
% 9.17/5.39 = ( uminus_uminus_int @ one_one_int ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4628_bit_Oxor__one__right,axiom,
% 9.17/5.39 ! [X: code_integer] :
% 9.17/5.39 ( ( bit_se3222712562003087583nteger @ X @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.17/5.39 = ( bit_ri7632146776885996613nteger @ X ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4629_bit_Oxor__one__right,axiom,
% 9.17/5.39 ! [X: int] :
% 9.17/5.39 ( ( bit_se6526347334894502574or_int @ X @ ( uminus_uminus_int @ one_one_int ) )
% 9.17/5.39 = ( bit_ri7919022796975470100ot_int @ X ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4630_bit_Oxor__one__left,axiom,
% 9.17/5.39 ! [X: code_integer] :
% 9.17/5.39 ( ( bit_se3222712562003087583nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ X )
% 9.17/5.39 = ( bit_ri7632146776885996613nteger @ X ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4631_bit_Oxor__one__left,axiom,
% 9.17/5.39 ! [X: int] :
% 9.17/5.39 ( ( bit_se6526347334894502574or_int @ ( uminus_uminus_int @ one_one_int ) @ X )
% 9.17/5.39 = ( bit_ri7919022796975470100ot_int @ X ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4632_push__bit__minus__one__eq__not__mask,axiom,
% 9.17/5.39 ! [N2: nat] :
% 9.17/5.39 ( ( bit_se7788150548672797655nteger @ N2 @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.17/5.39 = ( bit_ri7632146776885996613nteger @ ( bit_se2119862282449309892nteger @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4633_push__bit__minus__one__eq__not__mask,axiom,
% 9.17/5.39 ! [N2: nat] :
% 9.17/5.39 ( ( bit_se545348938243370406it_int @ N2 @ ( uminus_uminus_int @ one_one_int ) )
% 9.17/5.39 = ( bit_ri7919022796975470100ot_int @ ( bit_se2000444600071755411sk_int @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4634_not__one__eq,axiom,
% 9.17/5.39 ( ( bit_ri7919022796975470100ot_int @ one_one_int )
% 9.17/5.39 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4635_not__one__eq,axiom,
% 9.17/5.39 ( ( bit_ri7632146776885996613nteger @ one_one_Code_integer )
% 9.17/5.39 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4636_not__add__distrib,axiom,
% 9.17/5.39 ! [A: int,B: int] :
% 9.17/5.39 ( ( bit_ri7919022796975470100ot_int @ ( plus_plus_int @ A @ B ) )
% 9.17/5.39 = ( minus_minus_int @ ( bit_ri7919022796975470100ot_int @ A ) @ B ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4637_not__add__distrib,axiom,
% 9.17/5.39 ! [A: code_integer,B: code_integer] :
% 9.17/5.39 ( ( bit_ri7632146776885996613nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 9.17/5.39 = ( minus_8373710615458151222nteger @ ( bit_ri7632146776885996613nteger @ A ) @ B ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4638_not__diff__distrib,axiom,
% 9.17/5.39 ! [A: int,B: int] :
% 9.17/5.39 ( ( bit_ri7919022796975470100ot_int @ ( minus_minus_int @ A @ B ) )
% 9.17/5.39 = ( plus_plus_int @ ( bit_ri7919022796975470100ot_int @ A ) @ B ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4639_not__diff__distrib,axiom,
% 9.17/5.39 ! [A: code_integer,B: code_integer] :
% 9.17/5.39 ( ( bit_ri7632146776885996613nteger @ ( minus_8373710615458151222nteger @ A @ B ) )
% 9.17/5.39 = ( plus_p5714425477246183910nteger @ ( bit_ri7632146776885996613nteger @ A ) @ B ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4640_minus__eq__not__plus__1,axiom,
% 9.17/5.39 ( uminus_uminus_int
% 9.17/5.39 = ( ^ [A5: int] : ( plus_plus_int @ ( bit_ri7919022796975470100ot_int @ A5 ) @ one_one_int ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4641_minus__eq__not__plus__1,axiom,
% 9.17/5.39 ( uminus1351360451143612070nteger
% 9.17/5.39 = ( ^ [A5: code_integer] : ( plus_p5714425477246183910nteger @ ( bit_ri7632146776885996613nteger @ A5 ) @ one_one_Code_integer ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4642_minus__eq__not__minus__1,axiom,
% 9.17/5.39 ( uminus_uminus_int
% 9.17/5.39 = ( ^ [A5: int] : ( bit_ri7919022796975470100ot_int @ ( minus_minus_int @ A5 @ one_one_int ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4643_minus__eq__not__minus__1,axiom,
% 9.17/5.39 ( uminus1351360451143612070nteger
% 9.17/5.39 = ( ^ [A5: code_integer] : ( bit_ri7632146776885996613nteger @ ( minus_8373710615458151222nteger @ A5 @ one_one_Code_integer ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4644_not__eq__complement,axiom,
% 9.17/5.39 ( bit_ri7919022796975470100ot_int
% 9.17/5.39 = ( ^ [A5: int] : ( minus_minus_int @ ( uminus_uminus_int @ A5 ) @ one_one_int ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4645_not__eq__complement,axiom,
% 9.17/5.39 ( bit_ri7632146776885996613nteger
% 9.17/5.39 = ( ^ [A5: code_integer] : ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ A5 ) @ one_one_Code_integer ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4646_prod__int__eq,axiom,
% 9.17/5.39 ! [I: nat,J: nat] :
% 9.17/5.39 ( ( groups705719431365010083at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ I @ J ) )
% 9.17/5.39 = ( groups1705073143266064639nt_int
% 9.17/5.39 @ ^ [X3: int] : X3
% 9.17/5.39 @ ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ I ) @ ( semiri1314217659103216013at_int @ J ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4647_prod__int__plus__eq,axiom,
% 9.17/5.39 ! [I: nat,J: nat] :
% 9.17/5.39 ( ( groups705719431365010083at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ I @ ( plus_plus_nat @ I @ J ) ) )
% 9.17/5.39 = ( groups1705073143266064639nt_int
% 9.17/5.39 @ ^ [X3: int] : X3
% 9.17/5.39 @ ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ I ) @ ( semiri1314217659103216013at_int @ ( plus_plus_nat @ I @ J ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4648_push__bit__mask__eq,axiom,
% 9.17/5.39 ! [M2: nat,N2: nat] :
% 9.17/5.39 ( ( bit_se7788150548672797655nteger @ M2 @ ( bit_se2119862282449309892nteger @ N2 ) )
% 9.17/5.39 = ( bit_se3949692690581998587nteger @ ( bit_se2119862282449309892nteger @ ( plus_plus_nat @ N2 @ M2 ) ) @ ( bit_ri7632146776885996613nteger @ ( bit_se2119862282449309892nteger @ M2 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4649_push__bit__mask__eq,axiom,
% 9.17/5.39 ! [M2: nat,N2: nat] :
% 9.17/5.39 ( ( bit_se545348938243370406it_int @ M2 @ ( bit_se2000444600071755411sk_int @ N2 ) )
% 9.17/5.39 = ( bit_se725231765392027082nd_int @ ( bit_se2000444600071755411sk_int @ ( plus_plus_nat @ N2 @ M2 ) ) @ ( bit_ri7919022796975470100ot_int @ ( bit_se2000444600071755411sk_int @ M2 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4650_prod_OatLeast__int__lessThan__int__shift,axiom,
% 9.17/5.39 ! [G: int > nat,M2: nat,N2: nat] :
% 9.17/5.39 ( ( groups1707563613775114915nt_nat @ G @ ( set_or4662586982721622107an_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 9.17/5.39 = ( groups708209901874060359at_nat @ ( comp_int_nat_nat @ G @ semiri1314217659103216013at_int ) @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4651_prod_OatLeast__int__lessThan__int__shift,axiom,
% 9.17/5.39 ! [G: int > int,M2: nat,N2: nat] :
% 9.17/5.39 ( ( groups1705073143266064639nt_int @ G @ ( set_or4662586982721622107an_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 9.17/5.39 = ( groups705719431365010083at_int @ ( comp_int_int_nat @ G @ semiri1314217659103216013at_int ) @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4652_unset__bit__eq__and__not,axiom,
% 9.17/5.39 ( bit_se8260200283734997820nteger
% 9.17/5.39 = ( ^ [N4: nat,A5: code_integer] : ( bit_se3949692690581998587nteger @ A5 @ ( bit_ri7632146776885996613nteger @ ( bit_se7788150548672797655nteger @ N4 @ one_one_Code_integer ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4653_unset__bit__eq__and__not,axiom,
% 9.17/5.39 ( bit_se4203085406695923979it_int
% 9.17/5.39 = ( ^ [N4: nat,A5: int] : ( bit_se725231765392027082nd_int @ A5 @ ( bit_ri7919022796975470100ot_int @ ( bit_se545348938243370406it_int @ N4 @ one_one_int ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4654_prod_OatLeast__int__atMost__int__shift,axiom,
% 9.17/5.39 ! [G: int > nat,M2: nat,N2: nat] :
% 9.17/5.39 ( ( groups1707563613775114915nt_nat @ G @ ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 9.17/5.39 = ( groups708209901874060359at_nat @ ( comp_int_nat_nat @ G @ semiri1314217659103216013at_int ) @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4655_prod_OatLeast__int__atMost__int__shift,axiom,
% 9.17/5.39 ! [G: int > int,M2: nat,N2: nat] :
% 9.17/5.39 ( ( groups1705073143266064639nt_int @ G @ ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 9.17/5.39 = ( groups705719431365010083at_int @ ( comp_int_int_nat @ G @ semiri1314217659103216013at_int ) @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4656_int__numeral__not__and__num,axiom,
% 9.17/5.39 ! [M2: num,N2: num] :
% 9.17/5.39 ( ( bit_se725231765392027082nd_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ M2 ) ) @ ( numeral_numeral_int @ N2 ) )
% 9.17/5.39 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ N2 @ M2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4657_int__numeral__and__not__num,axiom,
% 9.17/5.39 ! [M2: num,N2: num] :
% 9.17/5.39 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M2 ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) )
% 9.17/5.39 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M2 @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4658_prod_Otriangle__reindex__eq,axiom,
% 9.17/5.39 ! [G: nat > nat > nat,N2: nat] :
% 9.17/5.39 ( ( groups4077766827762148844at_nat @ ( produc6842872674320459806at_nat @ G )
% 9.17/5.39 @ ( collec3392354462482085612at_nat
% 9.17/5.39 @ ( produc6081775807080527818_nat_o
% 9.17/5.39 @ ^ [I3: nat,J2: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ I3 @ J2 ) @ N2 ) ) ) )
% 9.17/5.39 = ( groups708209901874060359at_nat
% 9.17/5.39 @ ^ [K4: nat] :
% 9.17/5.39 ( groups708209901874060359at_nat
% 9.17/5.39 @ ^ [I3: nat] : ( G @ I3 @ ( minus_minus_nat @ K4 @ I3 ) )
% 9.17/5.39 @ ( set_ord_atMost_nat @ K4 ) )
% 9.17/5.39 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4659_prod_Otriangle__reindex__eq,axiom,
% 9.17/5.39 ! [G: nat > nat > int,N2: nat] :
% 9.17/5.39 ( ( groups4075276357253098568at_int @ ( produc6840382203811409530at_int @ G )
% 9.17/5.39 @ ( collec3392354462482085612at_nat
% 9.17/5.39 @ ( produc6081775807080527818_nat_o
% 9.17/5.39 @ ^ [I3: nat,J2: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ I3 @ J2 ) @ N2 ) ) ) )
% 9.17/5.39 = ( groups705719431365010083at_int
% 9.17/5.39 @ ^ [K4: nat] :
% 9.17/5.39 ( groups705719431365010083at_int
% 9.17/5.39 @ ^ [I3: nat] : ( G @ I3 @ ( minus_minus_nat @ K4 @ I3 ) )
% 9.17/5.39 @ ( set_ord_atMost_nat @ K4 ) )
% 9.17/5.39 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4660_and__not__numerals_I8_J,axiom,
% 9.17/5.39 ! [M2: num,N2: num] :
% 9.17/5.39 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M2 ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) )
% 9.17/5.39 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M2 ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4661_not__int__rec,axiom,
% 9.17/5.39 ( bit_ri7919022796975470100ot_int
% 9.17/5.39 = ( ^ [K4: int] : ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K4 ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri7919022796975470100ot_int @ ( divide_divide_int @ K4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4662_Nitpick_Ocase__nat__unfold,axiom,
% 9.17/5.39 ( case_nat_option_num
% 9.17/5.39 = ( ^ [X3: option_num,F2: nat > option_num,N4: nat] : ( if_option_num @ ( N4 = zero_zero_nat ) @ X3 @ ( F2 @ ( minus_minus_nat @ N4 @ one_one_nat ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4663_or__int__rec,axiom,
% 9.17/5.39 ( bit_se1409905431419307370or_int
% 9.17/5.39 = ( ^ [K4: int,L3: int] :
% 9.17/5.39 ( plus_plus_int
% 9.17/5.39 @ ( zero_n2684676970156552555ol_int
% 9.17/5.39 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K4 )
% 9.17/5.39 | ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L3 ) ) )
% 9.17/5.39 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( divide_divide_int @ K4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4664_or__numerals_I4_J,axiom,
% 9.17/5.39 ! [X: num,Y: num] :
% 9.17/5.39 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 9.17/5.39 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4665_or__numerals_I4_J,axiom,
% 9.17/5.39 ! [X: num,Y: num] :
% 9.17/5.39 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 9.17/5.39 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4666_or__numerals_I4_J,axiom,
% 9.17/5.39 ! [X: num,Y: num] :
% 9.17/5.39 ( ( bit_se1080825931792720795nteger @ ( numera6620942414471956472nteger @ ( bit0 @ X ) ) @ ( numera6620942414471956472nteger @ ( bit1 @ Y ) ) )
% 9.17/5.39 = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1080825931792720795nteger @ ( numera6620942414471956472nteger @ X ) @ ( numera6620942414471956472nteger @ Y ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4667_or__numerals_I4_J,axiom,
% 9.17/5.39 ! [X: num,Y: num] :
% 9.17/5.39 ( ( bit_se9127793120404214118atural @ ( numera5444537566228673987atural @ ( bit0 @ X ) ) @ ( numera5444537566228673987atural @ ( bit1 @ Y ) ) )
% 9.17/5.39 = ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se9127793120404214118atural @ ( numera5444537566228673987atural @ X ) @ ( numera5444537566228673987atural @ Y ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4668_or__numerals_I6_J,axiom,
% 9.17/5.39 ! [X: num,Y: num] :
% 9.17/5.39 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 9.17/5.39 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4669_or__numerals_I6_J,axiom,
% 9.17/5.39 ! [X: num,Y: num] :
% 9.17/5.39 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 9.17/5.39 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4670_or__numerals_I6_J,axiom,
% 9.17/5.39 ! [X: num,Y: num] :
% 9.17/5.39 ( ( bit_se1080825931792720795nteger @ ( numera6620942414471956472nteger @ ( bit1 @ X ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Y ) ) )
% 9.17/5.39 = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1080825931792720795nteger @ ( numera6620942414471956472nteger @ X ) @ ( numera6620942414471956472nteger @ Y ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4671_or__numerals_I6_J,axiom,
% 9.17/5.39 ! [X: num,Y: num] :
% 9.17/5.39 ( ( bit_se9127793120404214118atural @ ( numera5444537566228673987atural @ ( bit1 @ X ) ) @ ( numera5444537566228673987atural @ ( bit0 @ Y ) ) )
% 9.17/5.39 = ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se9127793120404214118atural @ ( numera5444537566228673987atural @ X ) @ ( numera5444537566228673987atural @ Y ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4672_or__numerals_I7_J,axiom,
% 9.17/5.39 ! [X: num,Y: num] :
% 9.17/5.39 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 9.17/5.39 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4673_or__numerals_I7_J,axiom,
% 9.17/5.39 ! [X: num,Y: num] :
% 9.17/5.39 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 9.17/5.39 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4674_or__numerals_I7_J,axiom,
% 9.17/5.39 ! [X: num,Y: num] :
% 9.17/5.39 ( ( bit_se1080825931792720795nteger @ ( numera6620942414471956472nteger @ ( bit1 @ X ) ) @ ( numera6620942414471956472nteger @ ( bit1 @ Y ) ) )
% 9.17/5.39 = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1080825931792720795nteger @ ( numera6620942414471956472nteger @ X ) @ ( numera6620942414471956472nteger @ Y ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4675_or__numerals_I7_J,axiom,
% 9.17/5.39 ! [X: num,Y: num] :
% 9.17/5.39 ( ( bit_se9127793120404214118atural @ ( numera5444537566228673987atural @ ( bit1 @ X ) ) @ ( numera5444537566228673987atural @ ( bit1 @ Y ) ) )
% 9.17/5.39 = ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se9127793120404214118atural @ ( numera5444537566228673987atural @ X ) @ ( numera5444537566228673987atural @ Y ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4676_or__nat__rec,axiom,
% 9.17/5.39 ( bit_se1412395901928357646or_nat
% 9.17/5.39 = ( ^ [M: nat,N4: nat] :
% 9.17/5.39 ( plus_plus_nat
% 9.17/5.39 @ ( zero_n2687167440665602831ol_nat
% 9.17/5.39 @ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
% 9.17/5.39 | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) )
% 9.17/5.39 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( divide_divide_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4677_or__not__numerals_I9_J,axiom,
% 9.17/5.39 ! [M2: num,N2: num] :
% 9.17/5.39 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M2 ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) )
% 9.17/5.39 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M2 ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4678_bit_Odisj__one__left,axiom,
% 9.17/5.39 ! [X: int] :
% 9.17/5.39 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ one_one_int ) @ X )
% 9.17/5.39 = ( uminus_uminus_int @ one_one_int ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4679_bit_Odisj__one__left,axiom,
% 9.17/5.39 ! [X: code_integer] :
% 9.17/5.39 ( ( bit_se1080825931792720795nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ X )
% 9.17/5.39 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4680_bit_Odisj__one__right,axiom,
% 9.17/5.39 ! [X: int] :
% 9.17/5.39 ( ( bit_se1409905431419307370or_int @ X @ ( uminus_uminus_int @ one_one_int ) )
% 9.17/5.39 = ( uminus_uminus_int @ one_one_int ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4681_bit_Odisj__one__right,axiom,
% 9.17/5.39 ! [X: code_integer] :
% 9.17/5.39 ( ( bit_se1080825931792720795nteger @ X @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.17/5.39 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4682_or__numerals_I8_J,axiom,
% 9.17/5.39 ! [X: num] :
% 9.17/5.39 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ one_one_int )
% 9.17/5.39 = ( numeral_numeral_int @ ( bit1 @ X ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4683_or__numerals_I8_J,axiom,
% 9.17/5.39 ! [X: num] :
% 9.17/5.39 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ one_one_nat )
% 9.17/5.39 = ( numeral_numeral_nat @ ( bit1 @ X ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4684_or__numerals_I8_J,axiom,
% 9.17/5.39 ! [X: num] :
% 9.17/5.39 ( ( bit_se1080825931792720795nteger @ ( numera6620942414471956472nteger @ ( bit1 @ X ) ) @ one_one_Code_integer )
% 9.17/5.39 = ( numera6620942414471956472nteger @ ( bit1 @ X ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4685_or__numerals_I8_J,axiom,
% 9.17/5.39 ! [X: num] :
% 9.17/5.39 ( ( bit_se9127793120404214118atural @ ( numera5444537566228673987atural @ ( bit1 @ X ) ) @ one_one_Code_natural )
% 9.17/5.39 = ( numera5444537566228673987atural @ ( bit1 @ X ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4686_or__numerals_I2_J,axiom,
% 9.17/5.39 ! [Y: num] :
% 9.17/5.39 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 9.17/5.39 = ( numeral_numeral_int @ ( bit1 @ Y ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4687_or__numerals_I2_J,axiom,
% 9.17/5.39 ! [Y: num] :
% 9.17/5.39 ( ( bit_se1412395901928357646or_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 9.17/5.39 = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4688_or__numerals_I2_J,axiom,
% 9.17/5.39 ! [Y: num] :
% 9.17/5.39 ( ( bit_se1080825931792720795nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit1 @ Y ) ) )
% 9.17/5.39 = ( numera6620942414471956472nteger @ ( bit1 @ Y ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4689_or__numerals_I2_J,axiom,
% 9.17/5.39 ! [Y: num] :
% 9.17/5.39 ( ( bit_se9127793120404214118atural @ one_one_Code_natural @ ( numera5444537566228673987atural @ ( bit1 @ Y ) ) )
% 9.17/5.39 = ( numera5444537566228673987atural @ ( bit1 @ Y ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4690_bit_Odisj__cancel__left,axiom,
% 9.17/5.39 ! [X: int] :
% 9.17/5.39 ( ( bit_se1409905431419307370or_int @ ( bit_ri7919022796975470100ot_int @ X ) @ X )
% 9.17/5.39 = ( uminus_uminus_int @ one_one_int ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4691_bit_Odisj__cancel__left,axiom,
% 9.17/5.39 ! [X: code_integer] :
% 9.17/5.39 ( ( bit_se1080825931792720795nteger @ ( bit_ri7632146776885996613nteger @ X ) @ X )
% 9.17/5.39 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4692_bit_Odisj__cancel__right,axiom,
% 9.17/5.39 ! [X: int] :
% 9.17/5.39 ( ( bit_se1409905431419307370or_int @ X @ ( bit_ri7919022796975470100ot_int @ X ) )
% 9.17/5.39 = ( uminus_uminus_int @ one_one_int ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4693_bit_Odisj__cancel__right,axiom,
% 9.17/5.39 ! [X: code_integer] :
% 9.17/5.39 ( ( bit_se1080825931792720795nteger @ X @ ( bit_ri7632146776885996613nteger @ X ) )
% 9.17/5.39 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4694_or__numerals_I5_J,axiom,
% 9.17/5.39 ! [X: num] :
% 9.17/5.39 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ one_one_int )
% 9.17/5.39 = ( numeral_numeral_int @ ( bit1 @ X ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4695_or__numerals_I5_J,axiom,
% 9.17/5.39 ! [X: num] :
% 9.17/5.39 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ one_one_nat )
% 9.17/5.39 = ( numeral_numeral_nat @ ( bit1 @ X ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4696_or__numerals_I5_J,axiom,
% 9.17/5.39 ! [X: num] :
% 9.17/5.39 ( ( bit_se1080825931792720795nteger @ ( numera6620942414471956472nteger @ ( bit0 @ X ) ) @ one_one_Code_integer )
% 9.17/5.39 = ( numera6620942414471956472nteger @ ( bit1 @ X ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4697_or__numerals_I5_J,axiom,
% 9.17/5.39 ! [X: num] :
% 9.17/5.39 ( ( bit_se9127793120404214118atural @ ( numera5444537566228673987atural @ ( bit0 @ X ) ) @ one_one_Code_natural )
% 9.17/5.39 = ( numera5444537566228673987atural @ ( bit1 @ X ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4698_or__numerals_I1_J,axiom,
% 9.17/5.39 ! [Y: num] :
% 9.17/5.39 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 9.17/5.39 = ( numeral_numeral_int @ ( bit1 @ Y ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4699_or__numerals_I1_J,axiom,
% 9.17/5.39 ! [Y: num] :
% 9.17/5.39 ( ( bit_se1412395901928357646or_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 9.17/5.39 = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4700_or__numerals_I1_J,axiom,
% 9.17/5.39 ! [Y: num] :
% 9.17/5.39 ( ( bit_se1080825931792720795nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ Y ) ) )
% 9.17/5.39 = ( numera6620942414471956472nteger @ ( bit1 @ Y ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4701_or__numerals_I1_J,axiom,
% 9.17/5.39 ! [Y: num] :
% 9.17/5.39 ( ( bit_se9127793120404214118atural @ one_one_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ Y ) ) )
% 9.17/5.39 = ( numera5444537566228673987atural @ ( bit1 @ Y ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4702_or__integer_Oabs__eq,axiom,
% 9.17/5.39 ! [Xa: int,X: int] :
% 9.17/5.39 ( ( bit_se1080825931792720795nteger @ ( code_integer_of_int @ Xa ) @ ( code_integer_of_int @ X ) )
% 9.17/5.39 = ( code_integer_of_int @ ( bit_se1409905431419307370or_int @ Xa @ X ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4703_or__integer_Orep__eq,axiom,
% 9.17/5.39 ! [X: code_integer,Xa: code_integer] :
% 9.17/5.39 ( ( code_int_of_integer @ ( bit_se1080825931792720795nteger @ X @ Xa ) )
% 9.17/5.39 = ( bit_se1409905431419307370or_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Xa ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4704_disjunctive__add,axiom,
% 9.17/5.39 ! [A: int,B: int] :
% 9.17/5.39 ( ! [N: nat] :
% 9.17/5.39 ( ~ ( bit_se1146084159140164899it_int @ A @ N )
% 9.17/5.39 | ~ ( bit_se1146084159140164899it_int @ B @ N ) )
% 9.17/5.39 => ( ( plus_plus_int @ A @ B )
% 9.17/5.39 = ( bit_se1409905431419307370or_int @ A @ B ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4705_disjunctive__add,axiom,
% 9.17/5.39 ! [A: nat,B: nat] :
% 9.17/5.39 ( ! [N: nat] :
% 9.17/5.39 ( ~ ( bit_se1148574629649215175it_nat @ A @ N )
% 9.17/5.39 | ~ ( bit_se1148574629649215175it_nat @ B @ N ) )
% 9.17/5.39 => ( ( plus_plus_nat @ A @ B )
% 9.17/5.39 = ( bit_se1412395901928357646or_nat @ A @ B ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4706_disjunctive__add,axiom,
% 9.17/5.39 ! [A: code_integer,B: code_integer] :
% 9.17/5.39 ( ! [N: nat] :
% 9.17/5.39 ( ~ ( bit_se9216721137139052372nteger @ A @ N )
% 9.17/5.39 | ~ ( bit_se9216721137139052372nteger @ B @ N ) )
% 9.17/5.39 => ( ( plus_p5714425477246183910nteger @ A @ B )
% 9.17/5.39 = ( bit_se1080825931792720795nteger @ A @ B ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4707_disjunctive__add,axiom,
% 9.17/5.39 ! [A: code_natural,B: code_natural] :
% 9.17/5.39 ( ! [N: nat] :
% 9.17/5.39 ( ~ ( bit_se8040316288895769887atural @ A @ N )
% 9.17/5.39 | ~ ( bit_se8040316288895769887atural @ B @ N ) )
% 9.17/5.39 => ( ( plus_p4538020629002901425atural @ A @ B )
% 9.17/5.39 = ( bit_se9127793120404214118atural @ A @ B ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4708_plus__and__or,axiom,
% 9.17/5.39 ! [X: int,Y: int] :
% 9.17/5.39 ( ( plus_plus_int @ ( bit_se725231765392027082nd_int @ X @ Y ) @ ( bit_se1409905431419307370or_int @ X @ Y ) )
% 9.17/5.39 = ( plus_plus_int @ X @ Y ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4709_not__integer_Orep__eq,axiom,
% 9.17/5.39 ! [X: code_integer] :
% 9.17/5.39 ( ( code_int_of_integer @ ( bit_ri7632146776885996613nteger @ X ) )
% 9.17/5.39 = ( bit_ri7919022796975470100ot_int @ ( code_int_of_integer @ X ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4710_set__bit__nat__def,axiom,
% 9.17/5.39 ( bit_se7882103937844011126it_nat
% 9.17/5.39 = ( ^ [M: nat,N4: nat] : ( bit_se1412395901928357646or_nat @ N4 @ ( bit_se547839408752420682it_nat @ M @ one_one_nat ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4711_not__integer_Oabs__eq,axiom,
% 9.17/5.39 ! [X: int] :
% 9.17/5.39 ( ( bit_ri7632146776885996613nteger @ ( code_integer_of_int @ X ) )
% 9.17/5.39 = ( code_integer_of_int @ ( bit_ri7919022796975470100ot_int @ X ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4712_set__bit__eq__or,axiom,
% 9.17/5.39 ( bit_se7882103937844011126it_nat
% 9.17/5.39 = ( ^ [N4: nat,A5: nat] : ( bit_se1412395901928357646or_nat @ A5 @ ( bit_se547839408752420682it_nat @ N4 @ one_one_nat ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4713_set__bit__eq__or,axiom,
% 9.17/5.39 ( bit_se2793503036327961859nteger
% 9.17/5.39 = ( ^ [N4: nat,A5: code_integer] : ( bit_se1080825931792720795nteger @ A5 @ ( bit_se7788150548672797655nteger @ N4 @ one_one_Code_integer ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4714_set__bit__eq__or,axiom,
% 9.17/5.39 ( bit_se7879613467334960850it_int
% 9.17/5.39 = ( ^ [N4: nat,A5: int] : ( bit_se1409905431419307370or_int @ A5 @ ( bit_se545348938243370406it_int @ N4 @ one_one_int ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4715_set__bit__eq__or,axiom,
% 9.17/5.39 ( bit_se1617098188084679374atural
% 9.17/5.39 = ( ^ [N4: nat,A5: code_natural] : ( bit_se9127793120404214118atural @ A5 @ ( bit_se6611745700429515170atural @ N4 @ one_one_Code_natural ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4716_bit_Ocomplement__unique,axiom,
% 9.17/5.39 ! [A: int,X: int,Y: int] :
% 9.17/5.39 ( ( ( bit_se725231765392027082nd_int @ A @ X )
% 9.17/5.39 = zero_zero_int )
% 9.17/5.39 => ( ( ( bit_se1409905431419307370or_int @ A @ X )
% 9.17/5.39 = ( uminus_uminus_int @ one_one_int ) )
% 9.17/5.39 => ( ( ( bit_se725231765392027082nd_int @ A @ Y )
% 9.17/5.39 = zero_zero_int )
% 9.17/5.39 => ( ( ( bit_se1409905431419307370or_int @ A @ Y )
% 9.17/5.39 = ( uminus_uminus_int @ one_one_int ) )
% 9.17/5.39 => ( X = Y ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4717_bit_Ocomplement__unique,axiom,
% 9.17/5.39 ! [A: code_integer,X: code_integer,Y: code_integer] :
% 9.17/5.39 ( ( ( bit_se3949692690581998587nteger @ A @ X )
% 9.17/5.39 = zero_z3403309356797280102nteger )
% 9.17/5.39 => ( ( ( bit_se1080825931792720795nteger @ A @ X )
% 9.17/5.39 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.17/5.39 => ( ( ( bit_se3949692690581998587nteger @ A @ Y )
% 9.17/5.39 = zero_z3403309356797280102nteger )
% 9.17/5.39 => ( ( ( bit_se1080825931792720795nteger @ A @ Y )
% 9.17/5.39 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.17/5.39 => ( X = Y ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4718_bit_Ocompl__unique,axiom,
% 9.17/5.39 ! [X: int,Y: int] :
% 9.17/5.39 ( ( ( bit_se725231765392027082nd_int @ X @ Y )
% 9.17/5.39 = zero_zero_int )
% 9.17/5.39 => ( ( ( bit_se1409905431419307370or_int @ X @ Y )
% 9.17/5.39 = ( uminus_uminus_int @ one_one_int ) )
% 9.17/5.39 => ( ( bit_ri7919022796975470100ot_int @ X )
% 9.17/5.39 = Y ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4719_bit_Ocompl__unique,axiom,
% 9.17/5.39 ! [X: code_integer,Y: code_integer] :
% 9.17/5.39 ( ( ( bit_se3949692690581998587nteger @ X @ Y )
% 9.17/5.39 = zero_z3403309356797280102nteger )
% 9.17/5.39 => ( ( ( bit_se1080825931792720795nteger @ X @ Y )
% 9.17/5.39 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.17/5.39 => ( ( bit_ri7632146776885996613nteger @ X )
% 9.17/5.39 = Y ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4720_or__one__eq,axiom,
% 9.17/5.39 ! [A: int] :
% 9.17/5.39 ( ( bit_se1409905431419307370or_int @ A @ one_one_int )
% 9.17/5.39 = ( plus_plus_int @ A @ ( zero_n2684676970156552555ol_int @ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4721_or__one__eq,axiom,
% 9.17/5.39 ! [A: nat] :
% 9.17/5.39 ( ( bit_se1412395901928357646or_nat @ A @ one_one_nat )
% 9.17/5.39 = ( plus_plus_nat @ A @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4722_or__one__eq,axiom,
% 9.17/5.39 ! [A: code_integer] :
% 9.17/5.39 ( ( bit_se1080825931792720795nteger @ A @ one_one_Code_integer )
% 9.17/5.39 = ( plus_p5714425477246183910nteger @ A @ ( zero_n356916108424825756nteger @ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4723_or__one__eq,axiom,
% 9.17/5.39 ! [A: code_natural] :
% 9.17/5.39 ( ( bit_se9127793120404214118atural @ A @ one_one_Code_natural )
% 9.17/5.39 = ( plus_p4538020629002901425atural @ A @ ( zero_n8403883297036319079atural @ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4724_one__or__eq,axiom,
% 9.17/5.39 ! [A: int] :
% 9.17/5.39 ( ( bit_se1409905431419307370or_int @ one_one_int @ A )
% 9.17/5.39 = ( plus_plus_int @ A @ ( zero_n2684676970156552555ol_int @ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4725_one__or__eq,axiom,
% 9.17/5.39 ! [A: nat] :
% 9.17/5.39 ( ( bit_se1412395901928357646or_nat @ one_one_nat @ A )
% 9.17/5.39 = ( plus_plus_nat @ A @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4726_one__or__eq,axiom,
% 9.17/5.39 ! [A: code_integer] :
% 9.17/5.39 ( ( bit_se1080825931792720795nteger @ one_one_Code_integer @ A )
% 9.17/5.39 = ( plus_p5714425477246183910nteger @ A @ ( zero_n356916108424825756nteger @ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4727_one__or__eq,axiom,
% 9.17/5.39 ! [A: code_natural] :
% 9.17/5.39 ( ( bit_se9127793120404214118atural @ one_one_Code_natural @ A )
% 9.17/5.39 = ( plus_p4538020629002901425atural @ A @ ( zero_n8403883297036319079atural @ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4728_mask__Suc__double,axiom,
% 9.17/5.39 ! [N2: nat] :
% 9.17/5.39 ( ( bit_se2000444600071755411sk_int @ ( suc @ N2 ) )
% 9.17/5.39 = ( bit_se1409905431419307370or_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2000444600071755411sk_int @ N2 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4729_mask__Suc__double,axiom,
% 9.17/5.39 ! [N2: nat] :
% 9.17/5.39 ( ( bit_se2119862282449309892nteger @ ( suc @ N2 ) )
% 9.17/5.39 = ( bit_se1080825931792720795nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se2119862282449309892nteger @ N2 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4730_mask__Suc__double,axiom,
% 9.17/5.39 ! [N2: nat] :
% 9.17/5.39 ( ( bit_se2002935070580805687sk_nat @ ( suc @ N2 ) )
% 9.17/5.39 = ( bit_se1412395901928357646or_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2002935070580805687sk_nat @ N2 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4731_mask__Suc__double,axiom,
% 9.17/5.39 ! [N2: nat] :
% 9.17/5.39 ( ( bit_se943457434206027407atural @ ( suc @ N2 ) )
% 9.17/5.39 = ( bit_se9127793120404214118atural @ one_one_Code_natural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se943457434206027407atural @ N2 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4732_or__not__numerals_I5_J,axiom,
% 9.17/5.39 ! [M2: num,N2: num] :
% 9.17/5.39 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M2 ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) )
% 9.17/5.39 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M2 ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4733_Suc__0__or__eq,axiom,
% 9.17/5.39 ! [N2: nat] :
% 9.17/5.39 ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 9.17/5.39 = ( plus_plus_nat @ N2 @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4734_or__Suc__0__eq,axiom,
% 9.17/5.39 ! [N2: nat] :
% 9.17/5.39 ( ( bit_se1412395901928357646or_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 9.17/5.39 = ( plus_plus_nat @ N2 @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4735_or__not__numerals_I8_J,axiom,
% 9.17/5.39 ! [M2: num,N2: num] :
% 9.17/5.39 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M2 ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) )
% 9.17/5.39 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M2 ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4736_or__int__unfold,axiom,
% 9.17/5.39 ( bit_se1409905431419307370or_int
% 9.17/5.39 = ( ^ [K4: int,L3: int] :
% 9.17/5.39 ( if_int
% 9.17/5.39 @ ( ( K4
% 9.17/5.39 = ( uminus_uminus_int @ one_one_int ) )
% 9.17/5.39 | ( L3
% 9.17/5.39 = ( uminus_uminus_int @ one_one_int ) ) )
% 9.17/5.39 @ ( uminus_uminus_int @ one_one_int )
% 9.17/5.39 @ ( if_int @ ( K4 = zero_zero_int ) @ L3 @ ( if_int @ ( L3 = zero_zero_int ) @ K4 @ ( plus_plus_int @ ( ord_max_int @ ( modulo_modulo_int @ K4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ L3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( divide_divide_int @ K4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4737_bit_Oabstract__boolean__algebra__sym__diff__axioms,axiom,
% 9.17/5.39 boolea2445317508997433345nteger @ bit_se3949692690581998587nteger @ bit_se1080825931792720795nteger @ bit_ri7632146776885996613nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ bit_se3222712562003087583nteger ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4738_bit_Oabstract__boolean__algebra__sym__diff__axioms,axiom,
% 9.17/5.39 boolea8527374999097803216ff_int @ bit_se725231765392027082nd_int @ bit_se1409905431419307370or_int @ bit_ri7919022796975470100ot_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) @ bit_se6526347334894502574or_int ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4739_or__nat__unfold,axiom,
% 9.17/5.39 ( bit_se1412395901928357646or_nat
% 9.17/5.39 = ( ^ [M: nat,N4: nat] : ( if_nat @ ( M = zero_zero_nat ) @ N4 @ ( if_nat @ ( N4 = zero_zero_nat ) @ M @ ( plus_plus_nat @ ( ord_max_nat @ ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( divide_divide_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4740_drop__bit__rec,axiom,
% 9.17/5.39 ( bit_se3928097537394005634nteger
% 9.17/5.39 = ( ^ [N4: nat,A5: code_integer] : ( if_Code_integer @ ( N4 = zero_zero_nat ) @ A5 @ ( bit_se3928097537394005634nteger @ ( minus_minus_nat @ N4 @ one_one_nat ) @ ( divide6298287555418463151nteger @ A5 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4741_drop__bit__rec,axiom,
% 9.17/5.39 ( bit_se8568078237143864401it_int
% 9.17/5.39 = ( ^ [N4: nat,A5: int] : ( if_int @ ( N4 = zero_zero_nat ) @ A5 @ ( bit_se8568078237143864401it_int @ ( minus_minus_nat @ N4 @ one_one_nat ) @ ( divide_divide_int @ A5 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4742_drop__bit__rec,axiom,
% 9.17/5.39 ( bit_se8570568707652914677it_nat
% 9.17/5.39 = ( ^ [N4: nat,A5: nat] : ( if_nat @ ( N4 = zero_zero_nat ) @ A5 @ ( bit_se8570568707652914677it_nat @ ( minus_minus_nat @ N4 @ one_one_nat ) @ ( divide_divide_nat @ A5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4743_drop__bit__rec,axiom,
% 9.17/5.39 ( bit_se2751692689150723149atural
% 9.17/5.39 = ( ^ [N4: nat,A5: code_natural] : ( if_Code_natural @ ( N4 = zero_zero_nat ) @ A5 @ ( bit_se2751692689150723149atural @ ( minus_minus_nat @ N4 @ one_one_nat ) @ ( divide5121882707175180666atural @ A5 @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4744_image__atLeastZeroLessThan__integer,axiom,
% 9.17/5.39 ! [U: code_integer] :
% 9.17/5.39 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ U )
% 9.17/5.39 => ( ( set_or8404916559141939852nteger @ zero_z3403309356797280102nteger @ U )
% 9.17/5.39 = ( image_1215581382706833972nteger @ semiri4939895301339042750nteger @ ( set_ord_lessThan_nat @ ( code_nat_of_integer @ U ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4745_uminus__int__def,axiom,
% 9.17/5.39 ( uminus_uminus_int
% 9.17/5.39 = ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ
% 9.17/5.39 @ ( produc2626176000494625587at_nat
% 9.17/5.39 @ ^ [X3: nat,Y3: nat] : ( product_Pair_nat_nat @ Y3 @ X3 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4746_bit_Oabstract__boolean__algebra__axioms,axiom,
% 9.17/5.39 boolea5469654029284665142ra_int @ bit_se725231765392027082nd_int @ bit_se1409905431419307370or_int @ bit_ri7919022796975470100ot_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4747_bit_Oabstract__boolean__algebra__axioms,axiom,
% 9.17/5.39 boolea5643492148547655015nteger @ bit_se3949692690581998587nteger @ bit_se1080825931792720795nteger @ bit_ri7632146776885996613nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4748_map__fun__apply,axiom,
% 9.17/5.39 ( map_fu4826362097070443709at_o_o
% 9.17/5.39 = ( ^ [F2: int > product_prod_nat_nat,G2: $o > $o,H: product_prod_nat_nat > $o,X3: int] : ( G2 @ ( H @ ( F2 @ X3 ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4749_map__fun__apply,axiom,
% 9.17/5.39 ( map_fu4960017516451851995nt_int
% 9.17/5.39 = ( ^ [F2: int > product_prod_nat_nat,G2: ( product_prod_nat_nat > product_prod_nat_nat ) > int > int,H: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,X3: int] : ( G2 @ ( H @ ( F2 @ X3 ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4750_map__fun__apply,axiom,
% 9.17/5.39 ( map_fu434086159418415080_int_o
% 9.17/5.39 = ( ^ [F2: int > product_prod_nat_nat,G2: ( product_prod_nat_nat > $o ) > int > $o,H: product_prod_nat_nat > product_prod_nat_nat > $o,X3: int] : ( G2 @ ( H @ ( F2 @ X3 ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4751_map__fun__apply,axiom,
% 9.17/5.39 ( map_fu3424225382358772769nt_rat
% 9.17/5.39 = ( ^ [F2: int > int,G2: product_prod_int_int > rat,H: int > product_prod_int_int,X3: int] : ( G2 @ ( H @ ( F2 @ X3 ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4752_map__fun__apply,axiom,
% 9.17/5.39 ( map_fu7831380289885515383nt_rat
% 9.17/5.39 = ( ^ [F2: int > int,G2: ( int > product_prod_int_int ) > int > rat,H: int > int > product_prod_int_int,X3: int] : ( G2 @ ( H @ ( F2 @ X3 ) ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4753_drop__bit__drop__bit,axiom,
% 9.17/5.39 ! [M2: nat,N2: nat,A: code_integer] :
% 9.17/5.39 ( ( bit_se3928097537394005634nteger @ M2 @ ( bit_se3928097537394005634nteger @ N2 @ A ) )
% 9.17/5.39 = ( bit_se3928097537394005634nteger @ ( plus_plus_nat @ M2 @ N2 ) @ A ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4754_drop__bit__drop__bit,axiom,
% 9.17/5.39 ! [M2: nat,N2: nat,A: int] :
% 9.17/5.39 ( ( bit_se8568078237143864401it_int @ M2 @ ( bit_se8568078237143864401it_int @ N2 @ A ) )
% 9.17/5.39 = ( bit_se8568078237143864401it_int @ ( plus_plus_nat @ M2 @ N2 ) @ A ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4755_drop__bit__drop__bit,axiom,
% 9.17/5.39 ! [M2: nat,N2: nat,A: nat] :
% 9.17/5.39 ( ( bit_se8570568707652914677it_nat @ M2 @ ( bit_se8570568707652914677it_nat @ N2 @ A ) )
% 9.17/5.39 = ( bit_se8570568707652914677it_nat @ ( plus_plus_nat @ M2 @ N2 ) @ A ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4756_drop__bit__drop__bit,axiom,
% 9.17/5.39 ! [M2: nat,N2: nat,A: code_natural] :
% 9.17/5.39 ( ( bit_se2751692689150723149atural @ M2 @ ( bit_se2751692689150723149atural @ N2 @ A ) )
% 9.17/5.39 = ( bit_se2751692689150723149atural @ ( plus_plus_nat @ M2 @ N2 ) @ A ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4757_image__add__atLeastAtMost,axiom,
% 9.17/5.39 ! [K: rat,I: rat,J: rat] :
% 9.17/5.39 ( ( image_rat_rat @ ( plus_plus_rat @ K ) @ ( set_or633870826150836451st_rat @ I @ J ) )
% 9.17/5.39 = ( set_or633870826150836451st_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ K ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4758_image__add__atLeastAtMost,axiom,
% 9.17/5.39 ! [K: int,I: int,J: int] :
% 9.17/5.39 ( ( image_int_int @ ( plus_plus_int @ K ) @ ( set_or1266510415728281911st_int @ I @ J ) )
% 9.17/5.39 = ( set_or1266510415728281911st_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ K ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4759_image__add__atLeastAtMost,axiom,
% 9.17/5.39 ! [K: nat,I: nat,J: nat] :
% 9.17/5.39 ( ( image_nat_nat @ ( plus_plus_nat @ K ) @ ( set_or1269000886237332187st_nat @ I @ J ) )
% 9.17/5.39 = ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4760_image__add__atLeastAtMost,axiom,
% 9.17/5.39 ! [K: code_integer,I: code_integer,J: code_integer] :
% 9.17/5.39 ( ( image_4470545334726330049nteger @ ( plus_p5714425477246183910nteger @ K ) @ ( set_or189985376899183464nteger @ I @ J ) )
% 9.17/5.39 = ( set_or189985376899183464nteger @ ( plus_p5714425477246183910nteger @ I @ K ) @ ( plus_p5714425477246183910nteger @ J @ K ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4761_image__diff__atLeastAtMost,axiom,
% 9.17/5.39 ! [D2: rat,A: rat,B: rat] :
% 9.17/5.39 ( ( image_rat_rat @ ( minus_minus_rat @ D2 ) @ ( set_or633870826150836451st_rat @ A @ B ) )
% 9.17/5.39 = ( set_or633870826150836451st_rat @ ( minus_minus_rat @ D2 @ B ) @ ( minus_minus_rat @ D2 @ A ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4762_image__diff__atLeastAtMost,axiom,
% 9.17/5.39 ! [D2: int,A: int,B: int] :
% 9.17/5.39 ( ( image_int_int @ ( minus_minus_int @ D2 ) @ ( set_or1266510415728281911st_int @ A @ B ) )
% 9.17/5.39 = ( set_or1266510415728281911st_int @ ( minus_minus_int @ D2 @ B ) @ ( minus_minus_int @ D2 @ A ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4763_image__diff__atLeastAtMost,axiom,
% 9.17/5.39 ! [D2: code_integer,A: code_integer,B: code_integer] :
% 9.17/5.39 ( ( image_4470545334726330049nteger @ ( minus_8373710615458151222nteger @ D2 ) @ ( set_or189985376899183464nteger @ A @ B ) )
% 9.17/5.39 = ( set_or189985376899183464nteger @ ( minus_8373710615458151222nteger @ D2 @ B ) @ ( minus_8373710615458151222nteger @ D2 @ A ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4764_image__add__atLeastLessThan,axiom,
% 9.17/5.39 ! [K: rat,I: rat,J: rat] :
% 9.17/5.39 ( ( image_rat_rat @ ( plus_plus_rat @ K ) @ ( set_or4029947393144176647an_rat @ I @ J ) )
% 9.17/5.39 = ( set_or4029947393144176647an_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ K ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4765_image__add__atLeastLessThan,axiom,
% 9.17/5.39 ! [K: nat,I: nat,J: nat] :
% 9.17/5.39 ( ( image_nat_nat @ ( plus_plus_nat @ K ) @ ( set_or4665077453230672383an_nat @ I @ J ) )
% 9.17/5.39 = ( set_or4665077453230672383an_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4766_image__add__atLeastLessThan,axiom,
% 9.17/5.39 ! [K: code_integer,I: code_integer,J: code_integer] :
% 9.17/5.39 ( ( image_4470545334726330049nteger @ ( plus_p5714425477246183910nteger @ K ) @ ( set_or8404916559141939852nteger @ I @ J ) )
% 9.17/5.39 = ( set_or8404916559141939852nteger @ ( plus_p5714425477246183910nteger @ I @ K ) @ ( plus_p5714425477246183910nteger @ J @ K ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4767_image__add__atLeastLessThan,axiom,
% 9.17/5.39 ! [K: int,I: int,J: int] :
% 9.17/5.39 ( ( image_int_int @ ( plus_plus_int @ K ) @ ( set_or4662586982721622107an_int @ I @ J ) )
% 9.17/5.39 = ( set_or4662586982721622107an_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ K ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4768_max__0__1_I1_J,axiom,
% 9.17/5.39 ( ( ord_max_rat @ zero_zero_rat @ one_one_rat )
% 9.17/5.39 = one_one_rat ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4769_max__0__1_I1_J,axiom,
% 9.17/5.39 ( ( ord_max_int @ zero_zero_int @ one_one_int )
% 9.17/5.39 = one_one_int ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4770_max__0__1_I1_J,axiom,
% 9.17/5.39 ( ( ord_max_nat @ zero_zero_nat @ one_one_nat )
% 9.17/5.39 = one_one_nat ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4771_max__0__1_I1_J,axiom,
% 9.17/5.39 ( ( ord_max_Code_integer @ zero_z3403309356797280102nteger @ one_one_Code_integer )
% 9.17/5.39 = one_one_Code_integer ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4772_max__0__1_I1_J,axiom,
% 9.17/5.39 ( ( ord_max_Code_natural @ zero_z2226904508553997617atural @ one_one_Code_natural )
% 9.17/5.39 = one_one_Code_natural ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4773_max__0__1_I2_J,axiom,
% 9.17/5.39 ( ( ord_max_rat @ one_one_rat @ zero_zero_rat )
% 9.17/5.39 = one_one_rat ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4774_max__0__1_I2_J,axiom,
% 9.17/5.39 ( ( ord_max_int @ one_one_int @ zero_zero_int )
% 9.17/5.39 = one_one_int ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4775_max__0__1_I2_J,axiom,
% 9.17/5.39 ( ( ord_max_nat @ one_one_nat @ zero_zero_nat )
% 9.17/5.39 = one_one_nat ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4776_max__0__1_I2_J,axiom,
% 9.17/5.39 ( ( ord_max_Code_integer @ one_one_Code_integer @ zero_z3403309356797280102nteger )
% 9.17/5.39 = one_one_Code_integer ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4777_max__0__1_I2_J,axiom,
% 9.17/5.39 ( ( ord_max_Code_natural @ one_one_Code_natural @ zero_z2226904508553997617atural )
% 9.17/5.39 = one_one_Code_natural ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4778_image__uminus__atLeastAtMost,axiom,
% 9.17/5.39 ! [X: rat,Y: rat] :
% 9.17/5.39 ( ( image_rat_rat @ uminus_uminus_rat @ ( set_or633870826150836451st_rat @ X @ Y ) )
% 9.17/5.39 = ( set_or633870826150836451st_rat @ ( uminus_uminus_rat @ Y ) @ ( uminus_uminus_rat @ X ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4779_image__uminus__atLeastAtMost,axiom,
% 9.17/5.39 ! [X: int,Y: int] :
% 9.17/5.39 ( ( image_int_int @ uminus_uminus_int @ ( set_or1266510415728281911st_int @ X @ Y ) )
% 9.17/5.39 = ( set_or1266510415728281911st_int @ ( uminus_uminus_int @ Y ) @ ( uminus_uminus_int @ X ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4780_image__uminus__atLeastAtMost,axiom,
% 9.17/5.39 ! [X: code_integer,Y: code_integer] :
% 9.17/5.39 ( ( image_4470545334726330049nteger @ uminus1351360451143612070nteger @ ( set_or189985376899183464nteger @ X @ Y ) )
% 9.17/5.39 = ( set_or189985376899183464nteger @ ( uminus1351360451143612070nteger @ Y ) @ ( uminus1351360451143612070nteger @ X ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4781_max__0__1_I6_J,axiom,
% 9.17/5.39 ! [X: num] :
% 9.17/5.39 ( ( ord_max_nat @ ( numeral_numeral_nat @ X ) @ one_one_nat )
% 9.17/5.39 = ( numeral_numeral_nat @ X ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4782_max__0__1_I6_J,axiom,
% 9.17/5.39 ! [X: num] :
% 9.17/5.39 ( ( ord_max_int @ ( numeral_numeral_int @ X ) @ one_one_int )
% 9.17/5.39 = ( numeral_numeral_int @ X ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4783_max__0__1_I6_J,axiom,
% 9.17/5.39 ! [X: num] :
% 9.17/5.39 ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ X ) @ one_one_Code_integer )
% 9.17/5.39 = ( numera6620942414471956472nteger @ X ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4784_max__0__1_I6_J,axiom,
% 9.17/5.39 ! [X: num] :
% 9.17/5.39 ( ( ord_max_rat @ ( numeral_numeral_rat @ X ) @ one_one_rat )
% 9.17/5.39 = ( numeral_numeral_rat @ X ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4785_max__0__1_I6_J,axiom,
% 9.17/5.39 ! [X: num] :
% 9.17/5.39 ( ( ord_max_Code_natural @ ( numera5444537566228673987atural @ X ) @ one_one_Code_natural )
% 9.17/5.39 = ( numera5444537566228673987atural @ X ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4786_max__0__1_I5_J,axiom,
% 9.17/5.39 ! [X: num] :
% 9.17/5.39 ( ( ord_max_nat @ one_one_nat @ ( numeral_numeral_nat @ X ) )
% 9.17/5.39 = ( numeral_numeral_nat @ X ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4787_max__0__1_I5_J,axiom,
% 9.17/5.39 ! [X: num] :
% 9.17/5.39 ( ( ord_max_int @ one_one_int @ ( numeral_numeral_int @ X ) )
% 9.17/5.39 = ( numeral_numeral_int @ X ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4788_max__0__1_I5_J,axiom,
% 9.17/5.39 ! [X: num] :
% 9.17/5.39 ( ( ord_max_Code_integer @ one_one_Code_integer @ ( numera6620942414471956472nteger @ X ) )
% 9.17/5.39 = ( numera6620942414471956472nteger @ X ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4789_max__0__1_I5_J,axiom,
% 9.17/5.39 ! [X: num] :
% 9.17/5.39 ( ( ord_max_rat @ one_one_rat @ ( numeral_numeral_rat @ X ) )
% 9.17/5.39 = ( numeral_numeral_rat @ X ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4790_max__0__1_I5_J,axiom,
% 9.17/5.39 ! [X: num] :
% 9.17/5.39 ( ( ord_max_Code_natural @ one_one_Code_natural @ ( numera5444537566228673987atural @ X ) )
% 9.17/5.39 = ( numera5444537566228673987atural @ X ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4791_image__add__atMost,axiom,
% 9.17/5.39 ! [C: rat,A: rat] :
% 9.17/5.39 ( ( image_rat_rat @ ( plus_plus_rat @ C ) @ ( set_ord_atMost_rat @ A ) )
% 9.17/5.39 = ( set_ord_atMost_rat @ ( plus_plus_rat @ C @ A ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4792_image__add__atMost,axiom,
% 9.17/5.39 ! [C: int,A: int] :
% 9.17/5.39 ( ( image_int_int @ ( plus_plus_int @ C ) @ ( set_ord_atMost_int @ A ) )
% 9.17/5.39 = ( set_ord_atMost_int @ ( plus_plus_int @ C @ A ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4793_image__add__atLeastAtMost_H,axiom,
% 9.17/5.39 ! [K: rat,I: rat,J: rat] :
% 9.17/5.39 ( ( image_rat_rat
% 9.17/5.39 @ ^ [N4: rat] : ( plus_plus_rat @ N4 @ K )
% 9.17/5.39 @ ( set_or633870826150836451st_rat @ I @ J ) )
% 9.17/5.39 = ( set_or633870826150836451st_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ K ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4794_image__add__atLeastAtMost_H,axiom,
% 9.17/5.39 ! [K: int,I: int,J: int] :
% 9.17/5.39 ( ( image_int_int
% 9.17/5.39 @ ^ [N4: int] : ( plus_plus_int @ N4 @ K )
% 9.17/5.39 @ ( set_or1266510415728281911st_int @ I @ J ) )
% 9.17/5.39 = ( set_or1266510415728281911st_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ K ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4795_image__add__atLeastAtMost_H,axiom,
% 9.17/5.39 ! [K: nat,I: nat,J: nat] :
% 9.17/5.39 ( ( image_nat_nat
% 9.17/5.39 @ ^ [N4: nat] : ( plus_plus_nat @ N4 @ K )
% 9.17/5.39 @ ( set_or1269000886237332187st_nat @ I @ J ) )
% 9.17/5.39 = ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4796_image__add__atLeastAtMost_H,axiom,
% 9.17/5.39 ! [K: code_integer,I: code_integer,J: code_integer] :
% 9.17/5.39 ( ( image_4470545334726330049nteger
% 9.17/5.39 @ ^ [N4: code_integer] : ( plus_p5714425477246183910nteger @ N4 @ K )
% 9.17/5.39 @ ( set_or189985376899183464nteger @ I @ J ) )
% 9.17/5.39 = ( set_or189985376899183464nteger @ ( plus_p5714425477246183910nteger @ I @ K ) @ ( plus_p5714425477246183910nteger @ J @ K ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4797_image__minus__const__atLeastAtMost_H,axiom,
% 9.17/5.39 ! [D2: rat,A: rat,B: rat] :
% 9.17/5.39 ( ( image_rat_rat
% 9.17/5.39 @ ^ [T2: rat] : ( minus_minus_rat @ T2 @ D2 )
% 9.17/5.39 @ ( set_or633870826150836451st_rat @ A @ B ) )
% 9.17/5.39 = ( set_or633870826150836451st_rat @ ( minus_minus_rat @ A @ D2 ) @ ( minus_minus_rat @ B @ D2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4798_image__minus__const__atLeastAtMost_H,axiom,
% 9.17/5.39 ! [D2: int,A: int,B: int] :
% 9.17/5.39 ( ( image_int_int
% 9.17/5.39 @ ^ [T2: int] : ( minus_minus_int @ T2 @ D2 )
% 9.17/5.39 @ ( set_or1266510415728281911st_int @ A @ B ) )
% 9.17/5.39 = ( set_or1266510415728281911st_int @ ( minus_minus_int @ A @ D2 ) @ ( minus_minus_int @ B @ D2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4799_image__minus__const__atLeastAtMost_H,axiom,
% 9.17/5.39 ! [D2: code_integer,A: code_integer,B: code_integer] :
% 9.17/5.39 ( ( image_4470545334726330049nteger
% 9.17/5.39 @ ^ [T2: code_integer] : ( minus_8373710615458151222nteger @ T2 @ D2 )
% 9.17/5.39 @ ( set_or189985376899183464nteger @ A @ B ) )
% 9.17/5.39 = ( set_or189985376899183464nteger @ ( minus_8373710615458151222nteger @ A @ D2 ) @ ( minus_8373710615458151222nteger @ B @ D2 ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4800_image__add__atLeastLessThan_H,axiom,
% 9.17/5.39 ! [K: rat,I: rat,J: rat] :
% 9.17/5.39 ( ( image_rat_rat
% 9.17/5.39 @ ^ [N4: rat] : ( plus_plus_rat @ N4 @ K )
% 9.17/5.39 @ ( set_or4029947393144176647an_rat @ I @ J ) )
% 9.17/5.39 = ( set_or4029947393144176647an_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ K ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4801_image__add__atLeastLessThan_H,axiom,
% 9.17/5.39 ! [K: nat,I: nat,J: nat] :
% 9.17/5.39 ( ( image_nat_nat
% 9.17/5.39 @ ^ [N4: nat] : ( plus_plus_nat @ N4 @ K )
% 9.17/5.39 @ ( set_or4665077453230672383an_nat @ I @ J ) )
% 9.17/5.39 = ( set_or4665077453230672383an_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4802_image__add__atLeastLessThan_H,axiom,
% 9.17/5.39 ! [K: code_integer,I: code_integer,J: code_integer] :
% 9.17/5.39 ( ( image_4470545334726330049nteger
% 9.17/5.39 @ ^ [N4: code_integer] : ( plus_p5714425477246183910nteger @ N4 @ K )
% 9.17/5.39 @ ( set_or8404916559141939852nteger @ I @ J ) )
% 9.17/5.39 = ( set_or8404916559141939852nteger @ ( plus_p5714425477246183910nteger @ I @ K ) @ ( plus_p5714425477246183910nteger @ J @ K ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4803_image__add__atLeastLessThan_H,axiom,
% 9.17/5.39 ! [K: int,I: int,J: int] :
% 9.17/5.39 ( ( image_int_int
% 9.17/5.39 @ ^ [N4: int] : ( plus_plus_int @ N4 @ K )
% 9.17/5.39 @ ( set_or4662586982721622107an_int @ I @ J ) )
% 9.17/5.39 = ( set_or4662586982721622107an_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ K ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4804_drop__bit__of__1,axiom,
% 9.17/5.39 ! [N2: nat] :
% 9.17/5.39 ( ( bit_se3928097537394005634nteger @ N2 @ one_one_Code_integer )
% 9.17/5.39 = ( zero_n356916108424825756nteger @ ( N2 = zero_zero_nat ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4805_drop__bit__of__1,axiom,
% 9.17/5.39 ! [N2: nat] :
% 9.17/5.39 ( ( bit_se8568078237143864401it_int @ N2 @ one_one_int )
% 9.17/5.39 = ( zero_n2684676970156552555ol_int @ ( N2 = zero_zero_nat ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4806_drop__bit__of__1,axiom,
% 9.17/5.39 ! [N2: nat] :
% 9.17/5.39 ( ( bit_se8570568707652914677it_nat @ N2 @ one_one_nat )
% 9.17/5.39 = ( zero_n2687167440665602831ol_nat @ ( N2 = zero_zero_nat ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4807_drop__bit__of__1,axiom,
% 9.17/5.39 ! [N2: nat] :
% 9.17/5.39 ( ( bit_se2751692689150723149atural @ N2 @ one_one_Code_natural )
% 9.17/5.39 = ( zero_n8403883297036319079atural @ ( N2 = zero_zero_nat ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4808_image__mult__atLeastAtMost,axiom,
% 9.17/5.39 ! [D2: rat,A: rat,B: rat] :
% 9.17/5.39 ( ( ord_less_rat @ zero_zero_rat @ D2 )
% 9.17/5.39 => ( ( image_rat_rat @ ( times_times_rat @ D2 ) @ ( set_or633870826150836451st_rat @ A @ B ) )
% 9.17/5.39 = ( set_or633870826150836451st_rat @ ( times_times_rat @ D2 @ A ) @ ( times_times_rat @ D2 @ B ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4809_image__divide__atLeastAtMost,axiom,
% 9.17/5.39 ! [D2: rat,A: rat,B: rat] :
% 9.17/5.39 ( ( ord_less_rat @ zero_zero_rat @ D2 )
% 9.17/5.39 => ( ( image_rat_rat
% 9.17/5.39 @ ^ [C2: rat] : ( divide_divide_rat @ C2 @ D2 )
% 9.17/5.39 @ ( set_or633870826150836451st_rat @ A @ B ) )
% 9.17/5.39 = ( set_or633870826150836451st_rat @ ( divide_divide_rat @ A @ D2 ) @ ( divide_divide_rat @ B @ D2 ) ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4810_drop__bit__integer_Orep__eq,axiom,
% 9.17/5.39 ! [X: nat,Xa: code_integer] :
% 9.17/5.39 ( ( code_int_of_integer @ ( bit_se3928097537394005634nteger @ X @ Xa ) )
% 9.17/5.39 = ( bit_se8568078237143864401it_int @ X @ ( code_int_of_integer @ Xa ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4811_drop__bit__integer_Oabs__eq,axiom,
% 9.17/5.39 ! [Xa: nat,X: int] :
% 9.17/5.39 ( ( bit_se3928097537394005634nteger @ Xa @ ( code_integer_of_int @ X ) )
% 9.17/5.39 = ( code_integer_of_int @ ( bit_se8568078237143864401it_int @ Xa @ X ) ) ) ).
% 9.17/5.39
% 9.17/5.39 thf(fact_4812_max__add__distrib__left,axiom,
% 9.17/5.40 ! [X: rat,Y: rat,Z: rat] :
% 9.17/5.40 ( ( plus_plus_rat @ ( ord_max_rat @ X @ Y ) @ Z )
% 9.17/5.40 = ( ord_max_rat @ ( plus_plus_rat @ X @ Z ) @ ( plus_plus_rat @ Y @ Z ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4813_max__add__distrib__left,axiom,
% 9.17/5.40 ! [X: int,Y: int,Z: int] :
% 9.17/5.40 ( ( plus_plus_int @ ( ord_max_int @ X @ Y ) @ Z )
% 9.17/5.40 = ( ord_max_int @ ( plus_plus_int @ X @ Z ) @ ( plus_plus_int @ Y @ Z ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4814_max__add__distrib__left,axiom,
% 9.17/5.40 ! [X: nat,Y: nat,Z: nat] :
% 9.17/5.40 ( ( plus_plus_nat @ ( ord_max_nat @ X @ Y ) @ Z )
% 9.17/5.40 = ( ord_max_nat @ ( plus_plus_nat @ X @ Z ) @ ( plus_plus_nat @ Y @ Z ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4815_max__add__distrib__left,axiom,
% 9.17/5.40 ! [X: code_integer,Y: code_integer,Z: code_integer] :
% 9.17/5.40 ( ( plus_p5714425477246183910nteger @ ( ord_max_Code_integer @ X @ Y ) @ Z )
% 9.17/5.40 = ( ord_max_Code_integer @ ( plus_p5714425477246183910nteger @ X @ Z ) @ ( plus_p5714425477246183910nteger @ Y @ Z ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4816_max__add__distrib__left,axiom,
% 9.17/5.40 ! [X: code_natural,Y: code_natural,Z: code_natural] :
% 9.17/5.40 ( ( plus_p4538020629002901425atural @ ( ord_max_Code_natural @ X @ Y ) @ Z )
% 9.17/5.40 = ( ord_max_Code_natural @ ( plus_p4538020629002901425atural @ X @ Z ) @ ( plus_p4538020629002901425atural @ Y @ Z ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4817_max__add__distrib__right,axiom,
% 9.17/5.40 ! [X: rat,Y: rat,Z: rat] :
% 9.17/5.40 ( ( plus_plus_rat @ X @ ( ord_max_rat @ Y @ Z ) )
% 9.17/5.40 = ( ord_max_rat @ ( plus_plus_rat @ X @ Y ) @ ( plus_plus_rat @ X @ Z ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4818_max__add__distrib__right,axiom,
% 9.17/5.40 ! [X: int,Y: int,Z: int] :
% 9.17/5.40 ( ( plus_plus_int @ X @ ( ord_max_int @ Y @ Z ) )
% 9.17/5.40 = ( ord_max_int @ ( plus_plus_int @ X @ Y ) @ ( plus_plus_int @ X @ Z ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4819_max__add__distrib__right,axiom,
% 9.17/5.40 ! [X: nat,Y: nat,Z: nat] :
% 9.17/5.40 ( ( plus_plus_nat @ X @ ( ord_max_nat @ Y @ Z ) )
% 9.17/5.40 = ( ord_max_nat @ ( plus_plus_nat @ X @ Y ) @ ( plus_plus_nat @ X @ Z ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4820_max__add__distrib__right,axiom,
% 9.17/5.40 ! [X: code_integer,Y: code_integer,Z: code_integer] :
% 9.17/5.40 ( ( plus_p5714425477246183910nteger @ X @ ( ord_max_Code_integer @ Y @ Z ) )
% 9.17/5.40 = ( ord_max_Code_integer @ ( plus_p5714425477246183910nteger @ X @ Y ) @ ( plus_p5714425477246183910nteger @ X @ Z ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4821_max__add__distrib__right,axiom,
% 9.17/5.40 ! [X: code_natural,Y: code_natural,Z: code_natural] :
% 9.17/5.40 ( ( plus_p4538020629002901425atural @ X @ ( ord_max_Code_natural @ Y @ Z ) )
% 9.17/5.40 = ( ord_max_Code_natural @ ( plus_p4538020629002901425atural @ X @ Y ) @ ( plus_p4538020629002901425atural @ X @ Z ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4822_max__diff__distrib__left,axiom,
% 9.17/5.40 ! [X: code_integer,Y: code_integer,Z: code_integer] :
% 9.17/5.40 ( ( minus_8373710615458151222nteger @ ( ord_max_Code_integer @ X @ Y ) @ Z )
% 9.17/5.40 = ( ord_max_Code_integer @ ( minus_8373710615458151222nteger @ X @ Z ) @ ( minus_8373710615458151222nteger @ Y @ Z ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4823_max__diff__distrib__left,axiom,
% 9.17/5.40 ! [X: rat,Y: rat,Z: rat] :
% 9.17/5.40 ( ( minus_minus_rat @ ( ord_max_rat @ X @ Y ) @ Z )
% 9.17/5.40 = ( ord_max_rat @ ( minus_minus_rat @ X @ Z ) @ ( minus_minus_rat @ Y @ Z ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4824_max__diff__distrib__left,axiom,
% 9.17/5.40 ! [X: int,Y: int,Z: int] :
% 9.17/5.40 ( ( minus_minus_int @ ( ord_max_int @ X @ Y ) @ Z )
% 9.17/5.40 = ( ord_max_int @ ( minus_minus_int @ X @ Z ) @ ( minus_minus_int @ Y @ Z ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4825_translation__Compl,axiom,
% 9.17/5.40 ! [A: rat,T: set_rat] :
% 9.17/5.40 ( ( image_rat_rat @ ( plus_plus_rat @ A ) @ ( uminus2201863774496077783et_rat @ T ) )
% 9.17/5.40 = ( uminus2201863774496077783et_rat @ ( image_rat_rat @ ( plus_plus_rat @ A ) @ T ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4826_translation__Compl,axiom,
% 9.17/5.40 ! [A: int,T: set_int] :
% 9.17/5.40 ( ( image_int_int @ ( plus_plus_int @ A ) @ ( uminus1532241313380277803et_int @ T ) )
% 9.17/5.40 = ( uminus1532241313380277803et_int @ ( image_int_int @ ( plus_plus_int @ A ) @ T ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4827_nat__add__max__right,axiom,
% 9.17/5.40 ! [M2: nat,N2: nat,Q3: nat] :
% 9.17/5.40 ( ( plus_plus_nat @ M2 @ ( ord_max_nat @ N2 @ Q3 ) )
% 9.17/5.40 = ( ord_max_nat @ ( plus_plus_nat @ M2 @ N2 ) @ ( plus_plus_nat @ M2 @ Q3 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4828_nat__add__max__left,axiom,
% 9.17/5.40 ! [M2: nat,N2: nat,Q3: nat] :
% 9.17/5.40 ( ( plus_plus_nat @ ( ord_max_nat @ M2 @ N2 ) @ Q3 )
% 9.17/5.40 = ( ord_max_nat @ ( plus_plus_nat @ M2 @ Q3 ) @ ( plus_plus_nat @ N2 @ Q3 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4829_image__eq__imp__comp,axiom,
% 9.17/5.40 ! [F: num > code_integer,A2: set_num,G: num > code_integer,B5: set_num,H3: code_integer > code_integer] :
% 9.17/5.40 ( ( ( image_8379761247532268670nteger @ F @ A2 )
% 9.17/5.40 = ( image_8379761247532268670nteger @ G @ B5 ) )
% 9.17/5.40 => ( ( image_8379761247532268670nteger @ ( comp_C3531382070062128313er_num @ H3 @ F ) @ A2 )
% 9.17/5.40 = ( image_8379761247532268670nteger @ ( comp_C3531382070062128313er_num @ H3 @ G ) @ B5 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4830_image__eq__imp__comp,axiom,
% 9.17/5.40 ! [F: int > nat,A2: set_int,G: int > nat,B5: set_int,H3: nat > num] :
% 9.17/5.40 ( ( ( image_int_nat @ F @ A2 )
% 9.17/5.40 = ( image_int_nat @ G @ B5 ) )
% 9.17/5.40 => ( ( image_int_num @ ( comp_nat_num_int @ H3 @ F ) @ A2 )
% 9.17/5.40 = ( image_int_num @ ( comp_nat_num_int @ H3 @ G ) @ B5 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4831_image__eq__imp__comp,axiom,
% 9.17/5.40 ! [F: num > code_integer,A2: set_num,G: nat > code_integer,B5: set_nat,H3: code_integer > code_integer] :
% 9.17/5.40 ( ( ( image_8379761247532268670nteger @ F @ A2 )
% 9.17/5.40 = ( image_1215581382706833972nteger @ G @ B5 ) )
% 9.17/5.40 => ( ( image_8379761247532268670nteger @ ( comp_C3531382070062128313er_num @ H3 @ F ) @ A2 )
% 9.17/5.40 = ( image_1215581382706833972nteger @ ( comp_C6974050283906349679er_nat @ H3 @ G ) @ B5 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4832_image__eq__imp__comp,axiom,
% 9.17/5.40 ! [F: int > code_integer,A2: set_int,G: nat > code_integer,B5: set_nat,H3: code_integer > int] :
% 9.17/5.40 ( ( ( image_1587234942943678608nteger @ F @ A2 )
% 9.17/5.40 = ( image_1215581382706833972nteger @ G @ B5 ) )
% 9.17/5.40 => ( ( image_int_int @ ( comp_C5046419837055054490nt_int @ H3 @ F ) @ A2 )
% 9.17/5.40 = ( image_nat_int @ ( comp_C5048910307564104766nt_nat @ H3 @ G ) @ B5 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4833_image__eq__imp__comp,axiom,
% 9.17/5.40 ! [F: int > nat,A2: set_int,G: nat > nat,B5: set_nat,H3: nat > num] :
% 9.17/5.40 ( ( ( image_int_nat @ F @ A2 )
% 9.17/5.40 = ( image_nat_nat @ G @ B5 ) )
% 9.17/5.40 => ( ( image_int_num @ ( comp_nat_num_int @ H3 @ F ) @ A2 )
% 9.17/5.40 = ( image_nat_num @ ( comp_nat_num_nat @ H3 @ G ) @ B5 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4834_image__eq__imp__comp,axiom,
% 9.17/5.40 ! [F: int > nat,A2: set_int,G: nat > nat,B5: set_nat,H3: nat > int] :
% 9.17/5.40 ( ( ( image_int_nat @ F @ A2 )
% 9.17/5.40 = ( image_nat_nat @ G @ B5 ) )
% 9.17/5.40 => ( ( image_int_int @ ( comp_nat_int_int @ H3 @ F ) @ A2 )
% 9.17/5.40 = ( image_nat_int @ ( comp_nat_int_nat @ H3 @ G ) @ B5 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4835_image__eq__imp__comp,axiom,
% 9.17/5.40 ! [F: nat > code_integer,A2: set_nat,G: num > code_integer,B5: set_num,H3: code_integer > code_integer] :
% 9.17/5.40 ( ( ( image_1215581382706833972nteger @ F @ A2 )
% 9.17/5.40 = ( image_8379761247532268670nteger @ G @ B5 ) )
% 9.17/5.40 => ( ( image_1215581382706833972nteger @ ( comp_C6974050283906349679er_nat @ H3 @ F ) @ A2 )
% 9.17/5.40 = ( image_8379761247532268670nteger @ ( comp_C3531382070062128313er_num @ H3 @ G ) @ B5 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4836_image__eq__imp__comp,axiom,
% 9.17/5.40 ! [F: nat > code_integer,A2: set_nat,G: int > code_integer,B5: set_int,H3: code_integer > int] :
% 9.17/5.40 ( ( ( image_1215581382706833972nteger @ F @ A2 )
% 9.17/5.40 = ( image_1587234942943678608nteger @ G @ B5 ) )
% 9.17/5.40 => ( ( image_nat_int @ ( comp_C5048910307564104766nt_nat @ H3 @ F ) @ A2 )
% 9.17/5.40 = ( image_int_int @ ( comp_C5046419837055054490nt_int @ H3 @ G ) @ B5 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4837_image__eq__imp__comp,axiom,
% 9.17/5.40 ! [F: nat > code_integer,A2: set_nat,G: nat > code_integer,B5: set_nat,H3: code_integer > code_integer] :
% 9.17/5.40 ( ( ( image_1215581382706833972nteger @ F @ A2 )
% 9.17/5.40 = ( image_1215581382706833972nteger @ G @ B5 ) )
% 9.17/5.40 => ( ( image_1215581382706833972nteger @ ( comp_C6974050283906349679er_nat @ H3 @ F ) @ A2 )
% 9.17/5.40 = ( image_1215581382706833972nteger @ ( comp_C6974050283906349679er_nat @ H3 @ G ) @ B5 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4838_image__eq__imp__comp,axiom,
% 9.17/5.40 ! [F: nat > code_integer,A2: set_nat,G: nat > code_integer,B5: set_nat,H3: code_integer > nat] :
% 9.17/5.40 ( ( ( image_1215581382706833972nteger @ F @ A2 )
% 9.17/5.40 = ( image_1215581382706833972nteger @ G @ B5 ) )
% 9.17/5.40 => ( ( image_nat_nat @ ( comp_C4049556595663050210at_nat @ H3 @ F ) @ A2 )
% 9.17/5.40 = ( image_nat_nat @ ( comp_C4049556595663050210at_nat @ H3 @ G ) @ B5 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4839_image__comp,axiom,
% 9.17/5.40 ! [F: code_integer > code_integer,G: num > code_integer,R2: set_num] :
% 9.17/5.40 ( ( image_4470545334726330049nteger @ F @ ( image_8379761247532268670nteger @ G @ R2 ) )
% 9.17/5.40 = ( image_8379761247532268670nteger @ ( comp_C3531382070062128313er_num @ F @ G ) @ R2 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4840_image__comp,axiom,
% 9.17/5.40 ! [F: nat > num,G: int > nat,R2: set_int] :
% 9.17/5.40 ( ( image_nat_num @ F @ ( image_int_nat @ G @ R2 ) )
% 9.17/5.40 = ( image_int_num @ ( comp_nat_num_int @ F @ G ) @ R2 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4841_image__comp,axiom,
% 9.17/5.40 ! [F: code_integer > code_integer,G: nat > code_integer,R2: set_nat] :
% 9.17/5.40 ( ( image_4470545334726330049nteger @ F @ ( image_1215581382706833972nteger @ G @ R2 ) )
% 9.17/5.40 = ( image_1215581382706833972nteger @ ( comp_C6974050283906349679er_nat @ F @ G ) @ R2 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4842_image__comp,axiom,
% 9.17/5.40 ! [F: code_integer > nat,G: nat > code_integer,R2: set_nat] :
% 9.17/5.40 ( ( image_951025933927791156er_nat @ F @ ( image_1215581382706833972nteger @ G @ R2 ) )
% 9.17/5.40 = ( image_nat_nat @ ( comp_C4049556595663050210at_nat @ F @ G ) @ R2 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4843_image__comp,axiom,
% 9.17/5.40 ! [F: code_integer > int,G: nat > code_integer,R2: set_nat] :
% 9.17/5.40 ( ( image_948535463418740880er_int @ F @ ( image_1215581382706833972nteger @ G @ R2 ) )
% 9.17/5.40 = ( image_nat_int @ ( comp_C5048910307564104766nt_nat @ F @ G ) @ R2 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4844_image__comp,axiom,
% 9.17/5.40 ! [F: int > code_integer,G: nat > int,R2: set_nat] :
% 9.17/5.40 ( ( image_1587234942943678608nteger @ F @ ( image_nat_int @ G @ R2 ) )
% 9.17/5.40 = ( image_1215581382706833972nteger @ ( comp_i1588355021709917246er_nat @ F @ G ) @ R2 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4845_image__comp,axiom,
% 9.17/5.40 ! [F: int > nat,G: nat > int,R2: set_nat] :
% 9.17/5.40 ( ( image_int_nat @ F @ ( image_nat_int @ G @ R2 ) )
% 9.17/5.40 = ( image_nat_nat @ ( comp_int_nat_nat @ F @ G ) @ R2 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4846_image__comp,axiom,
% 9.17/5.40 ! [F: nat > code_integer,G: nat > nat,R2: set_nat] :
% 9.17/5.40 ( ( image_1215581382706833972nteger @ F @ ( image_nat_nat @ G @ R2 ) )
% 9.17/5.40 = ( image_1215581382706833972nteger @ ( comp_n3898172953802868194er_nat @ F @ G ) @ R2 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4847_image__comp,axiom,
% 9.17/5.40 ! [F: nat > nat,G: nat > nat,R2: set_nat] :
% 9.17/5.40 ( ( image_nat_nat @ F @ ( image_nat_nat @ G @ R2 ) )
% 9.17/5.40 = ( image_nat_nat @ ( comp_nat_nat_nat @ F @ G ) @ R2 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4848_image__comp,axiom,
% 9.17/5.40 ! [F: nat > int,G: int > nat,R2: set_int] :
% 9.17/5.40 ( ( image_nat_int @ F @ ( image_int_nat @ G @ R2 ) )
% 9.17/5.40 = ( image_int_int @ ( comp_nat_int_int @ F @ G ) @ R2 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4849_map__fun__def,axiom,
% 9.17/5.40 ( map_fu2576242048321985878nteger
% 9.17/5.40 = ( ^ [F2: code_integer > code_integer,G2: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,H: code_integer > code_integer] : ( comp_C1593894019821074884nteger @ ( comp_C1593894019821074884nteger @ G2 @ H ) @ F2 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4850_map__fun__def,axiom,
% 9.17/5.40 ( map_fu6423247683660063826nteger
% 9.17/5.40 = ( ^ [F2: code_integer > code_integer,G2: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,H: code_integer > code_integer > code_integer] : ( comp_C1593894019821074884nteger @ ( comp_C8797469213163452608nteger @ G2 @ H ) @ F2 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4851_map__fun__def,axiom,
% 9.17/5.40 ( map_fu4826362097070443709at_o_o
% 9.17/5.40 = ( ^ [F2: int > product_prod_nat_nat,G2: $o > $o,H: product_prod_nat_nat > $o] : ( comp_P1289042343629989734_o_int @ ( comp_o8022916681612831582at_nat @ G2 @ H ) @ F2 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4852_map__fun__def,axiom,
% 9.17/5.40 ( map_fu4960017516451851995nt_int
% 9.17/5.40 = ( ^ [F2: int > product_prod_nat_nat,G2: ( product_prod_nat_nat > product_prod_nat_nat ) > int > int,H: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat] : ( comp_P1029605119844863363nt_int @ ( comp_P1872448293794610368at_nat @ G2 @ H ) @ F2 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4853_map__fun__def,axiom,
% 9.17/5.40 ( map_fu434086159418415080_int_o
% 9.17/5.40 = ( ^ [F2: int > product_prod_nat_nat,G2: ( product_prod_nat_nat > $o ) > int > $o,H: product_prod_nat_nat > product_prod_nat_nat > $o] : ( comp_P7507668834397697393_o_int @ ( comp_P9039549498699531069at_nat @ G2 @ H ) @ F2 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4854_map__fun__def,axiom,
% 9.17/5.40 ( map_fu3424225382358772769nt_rat
% 9.17/5.40 = ( ^ [F2: int > int,G2: product_prod_int_int > rat,H: int > product_prod_int_int] : ( comp_int_rat_int @ ( comp_P5335556815845735580at_int @ G2 @ H ) @ F2 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4855_map__fun__def,axiom,
% 9.17/5.40 ( map_fu7831380289885515383nt_rat
% 9.17/5.40 = ( ^ [F2: int > int,G2: ( int > product_prod_int_int ) > int > rat,H: int > int > product_prod_int_int] : ( comp_int_int_rat_int @ ( comp_i1302866070986779890at_int @ G2 @ H ) @ F2 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4856_map__fun_Ocompositionality,axiom,
% 9.17/5.40 ! [F: num > code_integer,G: code_integer > code_integer,H3: code_integer > code_integer,I: num > code_integer,Fun: code_integer > num] :
% 9.17/5.40 ( ( map_fu5269526691104299083nteger @ F @ G @ ( map_fu603974984455542859nteger @ H3 @ I @ Fun ) )
% 9.17/5.40 = ( map_fu8223014087597717000nteger @ ( comp_C3531382070062128313er_num @ H3 @ F ) @ ( comp_C3531382070062128313er_num @ G @ I ) @ Fun ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4857_map__fun_Ocompositionality,axiom,
% 9.17/5.40 ! [F: num > code_integer,G: nat > num,H3: code_integer > code_integer,I: int > nat,Fun: code_integer > int] :
% 9.17/5.40 ( ( map_fu7479816331989151099at_num @ F @ G @ ( map_fu5423760287386111952nt_nat @ H3 @ I @ Fun ) )
% 9.17/5.40 = ( map_fu8479170043890205655nt_num @ ( comp_C3531382070062128313er_num @ H3 @ F ) @ ( comp_nat_num_int @ G @ I ) @ Fun ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4858_map__fun_Ocompositionality,axiom,
% 9.17/5.40 ! [F: int > nat,G: code_integer > code_integer,H3: nat > num,I: num > code_integer,Fun: num > num] :
% 9.17/5.40 ( ( map_fu1717202910479192016nteger @ F @ G @ ( map_fu1090464068875036027nteger @ H3 @ I @ Fun ) )
% 9.17/5.40 = ( map_fu229184005524548567nteger @ ( comp_nat_num_int @ H3 @ F ) @ ( comp_C3531382070062128313er_num @ G @ I ) @ Fun ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4859_map__fun_Ocompositionality,axiom,
% 9.17/5.40 ! [F: int > nat,G: nat > num,H3: nat > num,I: int > nat,Fun: num > int] :
% 9.17/5.40 ( ( map_fu3669222299741785344at_num @ F @ G @ ( map_fu8361869985550671104nt_nat @ H3 @ I @ Fun ) )
% 9.17/5.40 = ( map_fu2609383839613498790nt_num @ ( comp_nat_num_int @ H3 @ F ) @ ( comp_nat_num_int @ G @ I ) @ Fun ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4860_map__fun_Ocompositionality,axiom,
% 9.17/5.40 ! [F: int > int,G: $o > $o,H3: int > product_prod_nat_nat,I: $o > $o,Fun: product_prod_nat_nat > $o] :
% 9.17/5.40 ( ( map_fun_int_int_o_o @ F @ G @ ( map_fu4826362097070443709at_o_o @ H3 @ I @ Fun ) )
% 9.17/5.40 = ( map_fu4826362097070443709at_o_o @ ( comp_i1108739374719436894at_int @ H3 @ F ) @ ( comp_o_o_o @ G @ I ) @ Fun ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4861_map__fun_Ocompositionality,axiom,
% 9.17/5.40 ! [F: int > int,G: rat > rat,H3: int > int,I: product_prod_int_int > rat,Fun: int > product_prod_int_int] :
% 9.17/5.40 ( ( map_fu6531859369801489698at_rat @ F @ G @ ( map_fu3424225382358772769nt_rat @ H3 @ I @ Fun ) )
% 9.17/5.40 = ( map_fu3424225382358772769nt_rat @ ( comp_int_int_int @ H3 @ F ) @ ( comp_r4727614531642239972nt_int @ G @ I ) @ Fun ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4862_map__fun_Ocompositionality,axiom,
% 9.17/5.40 ! [F: int > product_prod_nat_nat,G: $o > $o,H3: product_prod_nat_nat > product_prod_nat_nat,I: $o > $o,Fun: product_prod_nat_nat > $o] :
% 9.17/5.40 ( ( map_fu4826362097070443709at_o_o @ F @ G @ ( map_fu1707080289169145046at_o_o @ H3 @ I @ Fun ) )
% 9.17/5.40 = ( map_fu4826362097070443709at_o_o @ ( comp_P7428279379633703887at_int @ H3 @ F ) @ ( comp_o_o_o @ G @ I ) @ Fun ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4863_map__fun_Ocompositionality,axiom,
% 9.17/5.40 ! [F: int > int,G: product_prod_int_int > rat,H3: int > int,I: product_prod_int_int > product_prod_int_int,Fun: int > product_prod_int_int] :
% 9.17/5.40 ( ( map_fu3424225382358772769nt_rat @ F @ G @ ( map_fu2180209013632630320nt_int @ H3 @ I @ Fun ) )
% 9.17/5.40 = ( map_fu3424225382358772769nt_rat @ ( comp_int_int_int @ H3 @ F ) @ ( comp_P5648219952011055433nt_int @ G @ I ) @ Fun ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4864_map__fun_Ocompositionality,axiom,
% 9.17/5.40 ! [F: num > code_integer,G: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,H3: code_integer > code_integer,I: code_integer > code_integer,Fun: code_integer > code_integer] :
% 9.17/5.40 ( ( map_fu1235460277957925907nteger @ F @ G @ ( map_fu5082455417554595470nteger @ H3 @ I @ Fun ) )
% 9.17/5.40 = ( map_fu1235460277957925907nteger @ ( comp_C3531382070062128313er_num @ H3 @ F ) @ ( comp_C1593894019821074884nteger @ G @ I ) @ Fun ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4865_map__fun_Ocompositionality,axiom,
% 9.17/5.40 ! [F: code_integer > code_integer,G: code_integer > code_integer,H3: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,I: num > code_integer,Fun: ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > num] :
% 9.17/5.40 ( ( map_fu5082455417554595470nteger @ F @ G @ ( map_fu1335501423231535891nteger @ H3 @ I @ Fun ) )
% 9.17/5.40 = ( map_fu1335501423231535891nteger @ ( comp_C1593894019821074884nteger @ H3 @ F ) @ ( comp_C3531382070062128313er_num @ G @ I ) @ Fun ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4866_map__fun_Ocomp,axiom,
% 9.17/5.40 ! [F: num > code_integer,G: code_integer > code_integer,H3: code_integer > code_integer,I: num > code_integer] :
% 9.17/5.40 ( ( comp_C9104104092898552938er_num @ ( map_fu5269526691104299083nteger @ F @ G ) @ ( map_fu603974984455542859nteger @ H3 @ I ) )
% 9.17/5.40 = ( map_fu8223014087597717000nteger @ ( comp_C3531382070062128313er_num @ H3 @ F ) @ ( comp_C3531382070062128313er_num @ G @ I ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4867_map__fun_Ocomp,axiom,
% 9.17/5.40 ! [F: num > code_integer,G: nat > num,H3: code_integer > code_integer,I: int > nat] :
% 9.17/5.40 ( ( comp_C8127656796141369388er_int @ ( map_fu7479816331989151099at_num @ F @ G ) @ ( map_fu5423760287386111952nt_nat @ H3 @ I ) )
% 9.17/5.40 = ( map_fu8479170043890205655nt_num @ ( comp_C3531382070062128313er_num @ H3 @ F ) @ ( comp_nat_num_int @ G @ I ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4868_map__fun_Ocomp,axiom,
% 9.17/5.40 ! [F: int > nat,G: code_integer > code_integer,H3: nat > num,I: num > code_integer] :
% 9.17/5.40 ( ( comp_n3323228797031117228um_num @ ( map_fu1717202910479192016nteger @ F @ G ) @ ( map_fu1090464068875036027nteger @ H3 @ I ) )
% 9.17/5.40 = ( map_fu229184005524548567nteger @ ( comp_nat_num_int @ H3 @ F ) @ ( comp_C3531382070062128313er_num @ G @ I ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4869_map__fun_Ocomp,axiom,
% 9.17/5.40 ! [F: int > nat,G: nat > num,H3: nat > num,I: int > nat] :
% 9.17/5.40 ( ( comp_n4765151935410462062um_int @ ( map_fu3669222299741785344at_num @ F @ G ) @ ( map_fu8361869985550671104nt_nat @ H3 @ I ) )
% 9.17/5.40 = ( map_fu2609383839613498790nt_num @ ( comp_nat_num_int @ H3 @ F ) @ ( comp_nat_num_int @ G @ I ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4870_map__fun_Ocomp,axiom,
% 9.17/5.40 ! [F: int > int,G: $o > $o,H3: int > product_prod_nat_nat,I: $o > $o] :
% 9.17/5.40 ( ( comp_i6226780894115828703_nat_o @ ( map_fun_int_int_o_o @ F @ G ) @ ( map_fu4826362097070443709at_o_o @ H3 @ I ) )
% 9.17/5.40 = ( map_fu4826362097070443709at_o_o @ ( comp_i1108739374719436894at_int @ H3 @ F ) @ ( comp_o_o_o @ G @ I ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4871_map__fun_Ocomp,axiom,
% 9.17/5.40 ! [F: int > int,G: rat > rat,H3: int > int,I: product_prod_int_int > rat] :
% 9.17/5.40 ( ( comp_i5271019637457297241nt_int @ ( map_fu6531859369801489698at_rat @ F @ G ) @ ( map_fu3424225382358772769nt_rat @ H3 @ I ) )
% 9.17/5.40 = ( map_fu3424225382358772769nt_rat @ ( comp_int_int_int @ H3 @ F ) @ ( comp_r4727614531642239972nt_int @ G @ I ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4872_map__fun_Ocomp,axiom,
% 9.17/5.40 ! [F: int > product_prod_nat_nat,G: $o > $o,H3: product_prod_nat_nat > product_prod_nat_nat,I: $o > $o] :
% 9.17/5.40 ( ( comp_P286844350285437056_nat_o @ ( map_fu4826362097070443709at_o_o @ F @ G ) @ ( map_fu1707080289169145046at_o_o @ H3 @ I ) )
% 9.17/5.40 = ( map_fu4826362097070443709at_o_o @ ( comp_P7428279379633703887at_int @ H3 @ F ) @ ( comp_o_o_o @ G @ I ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4873_map__fun_Ocomp,axiom,
% 9.17/5.40 ! [F: int > int,G: product_prod_int_int > rat,H3: int > int,I: product_prod_int_int > product_prod_int_int] :
% 9.17/5.40 ( ( comp_i118865614814752126nt_int @ ( map_fu3424225382358772769nt_rat @ F @ G ) @ ( map_fu2180209013632630320nt_int @ H3 @ I ) )
% 9.17/5.40 = ( map_fu3424225382358772769nt_rat @ ( comp_int_int_int @ H3 @ F ) @ ( comp_P5648219952011055433nt_int @ G @ I ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4874_map__fun_Ocomp,axiom,
% 9.17/5.40 ! [F: num > code_integer,G: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,H3: code_integer > code_integer,I: code_integer > code_integer] :
% 9.17/5.40 ( ( comp_C5301300457492916725nteger @ ( map_fu1235460277957925907nteger @ F @ G ) @ ( map_fu5082455417554595470nteger @ H3 @ I ) )
% 9.17/5.40 = ( map_fu1235460277957925907nteger @ ( comp_C3531382070062128313er_num @ H3 @ F ) @ ( comp_C1593894019821074884nteger @ G @ I ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4875_map__fun_Ocomp,axiom,
% 9.17/5.40 ! [F: code_integer > code_integer,G: code_integer > code_integer,H3: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,I: num > code_integer] :
% 9.17/5.40 ( ( comp_C3959375555751086581er_num @ ( map_fu5082455417554595470nteger @ F @ G ) @ ( map_fu1335501423231535891nteger @ H3 @ I ) )
% 9.17/5.40 = ( map_fu1335501423231535891nteger @ ( comp_C1593894019821074884nteger @ H3 @ F ) @ ( comp_C3531382070062128313er_num @ G @ I ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4876_translation__subtract__Compl,axiom,
% 9.17/5.40 ! [A: code_integer,T: set_Code_integer] :
% 9.17/5.40 ( ( image_4470545334726330049nteger
% 9.17/5.40 @ ^ [X3: code_integer] : ( minus_8373710615458151222nteger @ X3 @ A )
% 9.17/5.40 @ ( uminus804700908173204444nteger @ T ) )
% 9.17/5.40 = ( uminus804700908173204444nteger
% 9.17/5.40 @ ( image_4470545334726330049nteger
% 9.17/5.40 @ ^ [X3: code_integer] : ( minus_8373710615458151222nteger @ X3 @ A )
% 9.17/5.40 @ T ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4877_translation__subtract__Compl,axiom,
% 9.17/5.40 ! [A: rat,T: set_rat] :
% 9.17/5.40 ( ( image_rat_rat
% 9.17/5.40 @ ^ [X3: rat] : ( minus_minus_rat @ X3 @ A )
% 9.17/5.40 @ ( uminus2201863774496077783et_rat @ T ) )
% 9.17/5.40 = ( uminus2201863774496077783et_rat
% 9.17/5.40 @ ( image_rat_rat
% 9.17/5.40 @ ^ [X3: rat] : ( minus_minus_rat @ X3 @ A )
% 9.17/5.40 @ T ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4878_translation__subtract__Compl,axiom,
% 9.17/5.40 ! [A: int,T: set_int] :
% 9.17/5.40 ( ( image_int_int
% 9.17/5.40 @ ^ [X3: int] : ( minus_minus_int @ X3 @ A )
% 9.17/5.40 @ ( uminus1532241313380277803et_int @ T ) )
% 9.17/5.40 = ( uminus1532241313380277803et_int
% 9.17/5.40 @ ( image_int_int
% 9.17/5.40 @ ^ [X3: int] : ( minus_minus_int @ X3 @ A )
% 9.17/5.40 @ T ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4879_nat__minus__add__max,axiom,
% 9.17/5.40 ! [N2: nat,M2: nat] :
% 9.17/5.40 ( ( plus_plus_nat @ ( minus_minus_nat @ N2 @ M2 ) @ M2 )
% 9.17/5.40 = ( ord_max_nat @ N2 @ M2 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4880_translation__diff,axiom,
% 9.17/5.40 ! [A: rat,S: set_rat,T: set_rat] :
% 9.17/5.40 ( ( image_rat_rat @ ( plus_plus_rat @ A ) @ ( minus_minus_set_rat @ S @ T ) )
% 9.17/5.40 = ( minus_minus_set_rat @ ( image_rat_rat @ ( plus_plus_rat @ A ) @ S ) @ ( image_rat_rat @ ( plus_plus_rat @ A ) @ T ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4881_translation__diff,axiom,
% 9.17/5.40 ! [A: int,S: set_int,T: set_int] :
% 9.17/5.40 ( ( image_int_int @ ( plus_plus_int @ A ) @ ( minus_minus_set_int @ S @ T ) )
% 9.17/5.40 = ( minus_minus_set_int @ ( image_int_int @ ( plus_plus_int @ A ) @ S ) @ ( image_int_int @ ( plus_plus_int @ A ) @ T ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4882_translation__subtract__diff,axiom,
% 9.17/5.40 ! [A: code_integer,S: set_Code_integer,T: set_Code_integer] :
% 9.17/5.40 ( ( image_4470545334726330049nteger
% 9.17/5.40 @ ^ [X3: code_integer] : ( minus_8373710615458151222nteger @ X3 @ A )
% 9.17/5.40 @ ( minus_2355218937544613996nteger @ S @ T ) )
% 9.17/5.40 = ( minus_2355218937544613996nteger
% 9.17/5.40 @ ( image_4470545334726330049nteger
% 9.17/5.40 @ ^ [X3: code_integer] : ( minus_8373710615458151222nteger @ X3 @ A )
% 9.17/5.40 @ S )
% 9.17/5.40 @ ( image_4470545334726330049nteger
% 9.17/5.40 @ ^ [X3: code_integer] : ( minus_8373710615458151222nteger @ X3 @ A )
% 9.17/5.40 @ T ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4883_translation__subtract__diff,axiom,
% 9.17/5.40 ! [A: rat,S: set_rat,T: set_rat] :
% 9.17/5.40 ( ( image_rat_rat
% 9.17/5.40 @ ^ [X3: rat] : ( minus_minus_rat @ X3 @ A )
% 9.17/5.40 @ ( minus_minus_set_rat @ S @ T ) )
% 9.17/5.40 = ( minus_minus_set_rat
% 9.17/5.40 @ ( image_rat_rat
% 9.17/5.40 @ ^ [X3: rat] : ( minus_minus_rat @ X3 @ A )
% 9.17/5.40 @ S )
% 9.17/5.40 @ ( image_rat_rat
% 9.17/5.40 @ ^ [X3: rat] : ( minus_minus_rat @ X3 @ A )
% 9.17/5.40 @ T ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4884_translation__subtract__diff,axiom,
% 9.17/5.40 ! [A: int,S: set_int,T: set_int] :
% 9.17/5.40 ( ( image_int_int
% 9.17/5.40 @ ^ [X3: int] : ( minus_minus_int @ X3 @ A )
% 9.17/5.40 @ ( minus_minus_set_int @ S @ T ) )
% 9.17/5.40 = ( minus_minus_set_int
% 9.17/5.40 @ ( image_int_int
% 9.17/5.40 @ ^ [X3: int] : ( minus_minus_int @ X3 @ A )
% 9.17/5.40 @ S )
% 9.17/5.40 @ ( image_int_int
% 9.17/5.40 @ ^ [X3: int] : ( minus_minus_int @ X3 @ A )
% 9.17/5.40 @ T ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4885_take__bit__drop__bit,axiom,
% 9.17/5.40 ! [M2: nat,N2: nat,A: code_integer] :
% 9.17/5.40 ( ( bit_se1745604003318907178nteger @ M2 @ ( bit_se3928097537394005634nteger @ N2 @ A ) )
% 9.17/5.40 = ( bit_se3928097537394005634nteger @ N2 @ ( bit_se1745604003318907178nteger @ ( plus_plus_nat @ M2 @ N2 ) @ A ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4886_take__bit__drop__bit,axiom,
% 9.17/5.40 ! [M2: nat,N2: nat,A: int] :
% 9.17/5.40 ( ( bit_se2923211474154528505it_int @ M2 @ ( bit_se8568078237143864401it_int @ N2 @ A ) )
% 9.17/5.40 = ( bit_se8568078237143864401it_int @ N2 @ ( bit_se2923211474154528505it_int @ ( plus_plus_nat @ M2 @ N2 ) @ A ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4887_take__bit__drop__bit,axiom,
% 9.17/5.40 ! [M2: nat,N2: nat,A: nat] :
% 9.17/5.40 ( ( bit_se2925701944663578781it_nat @ M2 @ ( bit_se8570568707652914677it_nat @ N2 @ A ) )
% 9.17/5.40 = ( bit_se8570568707652914677it_nat @ N2 @ ( bit_se2925701944663578781it_nat @ ( plus_plus_nat @ M2 @ N2 ) @ A ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4888_take__bit__drop__bit,axiom,
% 9.17/5.40 ! [M2: nat,N2: nat,A: code_natural] :
% 9.17/5.40 ( ( bit_se569199155075624693atural @ M2 @ ( bit_se2751692689150723149atural @ N2 @ A ) )
% 9.17/5.40 = ( bit_se2751692689150723149atural @ N2 @ ( bit_se569199155075624693atural @ ( plus_plus_nat @ M2 @ N2 ) @ A ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4889_bit__drop__bit__eq,axiom,
% 9.17/5.40 ! [N2: nat,A: code_integer] :
% 9.17/5.40 ( ( bit_se9216721137139052372nteger @ ( bit_se3928097537394005634nteger @ N2 @ A ) )
% 9.17/5.40 = ( comp_nat_o_nat @ ( bit_se9216721137139052372nteger @ A ) @ ( plus_plus_nat @ N2 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4890_bit__drop__bit__eq,axiom,
% 9.17/5.40 ! [N2: nat,A: int] :
% 9.17/5.40 ( ( bit_se1146084159140164899it_int @ ( bit_se8568078237143864401it_int @ N2 @ A ) )
% 9.17/5.40 = ( comp_nat_o_nat @ ( bit_se1146084159140164899it_int @ A ) @ ( plus_plus_nat @ N2 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4891_bit__drop__bit__eq,axiom,
% 9.17/5.40 ! [N2: nat,A: nat] :
% 9.17/5.40 ( ( bit_se1148574629649215175it_nat @ ( bit_se8570568707652914677it_nat @ N2 @ A ) )
% 9.17/5.40 = ( comp_nat_o_nat @ ( bit_se1148574629649215175it_nat @ A ) @ ( plus_plus_nat @ N2 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4892_bit__drop__bit__eq,axiom,
% 9.17/5.40 ! [N2: nat,A: code_natural] :
% 9.17/5.40 ( ( bit_se8040316288895769887atural @ ( bit_se2751692689150723149atural @ N2 @ A ) )
% 9.17/5.40 = ( comp_nat_o_nat @ ( bit_se8040316288895769887atural @ A ) @ ( plus_plus_nat @ N2 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4893_div__push__bit__of__1__eq__drop__bit,axiom,
% 9.17/5.40 ! [A: nat,N2: nat] :
% 9.17/5.40 ( ( divide_divide_nat @ A @ ( bit_se547839408752420682it_nat @ N2 @ one_one_nat ) )
% 9.17/5.40 = ( bit_se8570568707652914677it_nat @ N2 @ A ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4894_div__push__bit__of__1__eq__drop__bit,axiom,
% 9.17/5.40 ! [A: code_integer,N2: nat] :
% 9.17/5.40 ( ( divide6298287555418463151nteger @ A @ ( bit_se7788150548672797655nteger @ N2 @ one_one_Code_integer ) )
% 9.17/5.40 = ( bit_se3928097537394005634nteger @ N2 @ A ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4895_div__push__bit__of__1__eq__drop__bit,axiom,
% 9.17/5.40 ! [A: int,N2: nat] :
% 9.17/5.40 ( ( divide_divide_int @ A @ ( bit_se545348938243370406it_int @ N2 @ one_one_int ) )
% 9.17/5.40 = ( bit_se8568078237143864401it_int @ N2 @ A ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4896_div__push__bit__of__1__eq__drop__bit,axiom,
% 9.17/5.40 ! [A: code_natural,N2: nat] :
% 9.17/5.40 ( ( divide5121882707175180666atural @ A @ ( bit_se6611745700429515170atural @ N2 @ one_one_Code_natural ) )
% 9.17/5.40 = ( bit_se2751692689150723149atural @ N2 @ A ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4897_bit__iff__and__drop__bit__eq__1,axiom,
% 9.17/5.40 ( bit_se9216721137139052372nteger
% 9.17/5.40 = ( ^ [A5: code_integer,N4: nat] :
% 9.17/5.40 ( ( bit_se3949692690581998587nteger @ ( bit_se3928097537394005634nteger @ N4 @ A5 ) @ one_one_Code_integer )
% 9.17/5.40 = one_one_Code_integer ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4898_bit__iff__and__drop__bit__eq__1,axiom,
% 9.17/5.40 ( bit_se1146084159140164899it_int
% 9.17/5.40 = ( ^ [A5: int,N4: nat] :
% 9.17/5.40 ( ( bit_se725231765392027082nd_int @ ( bit_se8568078237143864401it_int @ N4 @ A5 ) @ one_one_int )
% 9.17/5.40 = one_one_int ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4899_bit__iff__and__drop__bit__eq__1,axiom,
% 9.17/5.40 ( bit_se1148574629649215175it_nat
% 9.17/5.40 = ( ^ [A5: nat,N4: nat] :
% 9.17/5.40 ( ( bit_se727722235901077358nd_nat @ ( bit_se8570568707652914677it_nat @ N4 @ A5 ) @ one_one_nat )
% 9.17/5.40 = one_one_nat ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4900_bit__iff__and__drop__bit__eq__1,axiom,
% 9.17/5.40 ( bit_se8040316288895769887atural
% 9.17/5.40 = ( ^ [A5: code_natural,N4: nat] :
% 9.17/5.40 ( ( bit_se2773287842338716102atural @ ( bit_se2751692689150723149atural @ N4 @ A5 ) @ one_one_Code_natural )
% 9.17/5.40 = one_one_Code_natural ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4901_bits__ident,axiom,
% 9.17/5.40 ! [N2: nat,A: code_integer] :
% 9.17/5.40 ( ( plus_p5714425477246183910nteger @ ( bit_se7788150548672797655nteger @ N2 @ ( bit_se3928097537394005634nteger @ N2 @ A ) ) @ ( bit_se1745604003318907178nteger @ N2 @ A ) )
% 9.17/5.40 = A ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4902_bits__ident,axiom,
% 9.17/5.40 ! [N2: nat,A: int] :
% 9.17/5.40 ( ( plus_plus_int @ ( bit_se545348938243370406it_int @ N2 @ ( bit_se8568078237143864401it_int @ N2 @ A ) ) @ ( bit_se2923211474154528505it_int @ N2 @ A ) )
% 9.17/5.40 = A ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4903_bits__ident,axiom,
% 9.17/5.40 ! [N2: nat,A: nat] :
% 9.17/5.40 ( ( plus_plus_nat @ ( bit_se547839408752420682it_nat @ N2 @ ( bit_se8570568707652914677it_nat @ N2 @ A ) ) @ ( bit_se2925701944663578781it_nat @ N2 @ A ) )
% 9.17/5.40 = A ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4904_bits__ident,axiom,
% 9.17/5.40 ! [N2: nat,A: code_natural] :
% 9.17/5.40 ( ( plus_p4538020629002901425atural @ ( bit_se6611745700429515170atural @ N2 @ ( bit_se2751692689150723149atural @ N2 @ A ) ) @ ( bit_se569199155075624693atural @ N2 @ A ) )
% 9.17/5.40 = A ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4905_slice__eq__mask,axiom,
% 9.17/5.40 ! [N2: nat,M2: nat,A: code_integer] :
% 9.17/5.40 ( ( bit_se7788150548672797655nteger @ N2 @ ( bit_se1745604003318907178nteger @ M2 @ ( bit_se3928097537394005634nteger @ N2 @ A ) ) )
% 9.17/5.40 = ( bit_se3949692690581998587nteger @ A @ ( bit_se3949692690581998587nteger @ ( bit_se2119862282449309892nteger @ ( plus_plus_nat @ M2 @ N2 ) ) @ ( bit_ri7632146776885996613nteger @ ( bit_se2119862282449309892nteger @ N2 ) ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4906_slice__eq__mask,axiom,
% 9.17/5.40 ! [N2: nat,M2: nat,A: int] :
% 9.17/5.40 ( ( bit_se545348938243370406it_int @ N2 @ ( bit_se2923211474154528505it_int @ M2 @ ( bit_se8568078237143864401it_int @ N2 @ A ) ) )
% 9.17/5.40 = ( bit_se725231765392027082nd_int @ A @ ( bit_se725231765392027082nd_int @ ( bit_se2000444600071755411sk_int @ ( plus_plus_nat @ M2 @ N2 ) ) @ ( bit_ri7919022796975470100ot_int @ ( bit_se2000444600071755411sk_int @ N2 ) ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4907_image__add__0,axiom,
% 9.17/5.40 ! [S2: set_Code_integer] :
% 9.17/5.40 ( ( image_4470545334726330049nteger @ ( plus_p5714425477246183910nteger @ zero_z3403309356797280102nteger ) @ S2 )
% 9.17/5.40 = S2 ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4908_image__add__0,axiom,
% 9.17/5.40 ! [S2: set_mu2057375006010111271at_nat] :
% 9.17/5.40 ( ( image_2516384619306764229at_nat @ ( plus_p7104986032573967614at_nat @ zero_z1048942125864253310at_nat ) @ S2 )
% 9.17/5.40 = S2 ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4909_image__add__0,axiom,
% 9.17/5.40 ! [S2: set_rat] :
% 9.17/5.40 ( ( image_rat_rat @ ( plus_plus_rat @ zero_zero_rat ) @ S2 )
% 9.17/5.40 = S2 ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4910_image__add__0,axiom,
% 9.17/5.40 ! [S2: set_nat] :
% 9.17/5.40 ( ( image_nat_nat @ ( plus_plus_nat @ zero_zero_nat ) @ S2 )
% 9.17/5.40 = S2 ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4911_image__add__0,axiom,
% 9.17/5.40 ! [S2: set_int] :
% 9.17/5.40 ( ( image_int_int @ ( plus_plus_int @ zero_zero_int ) @ S2 )
% 9.17/5.40 = S2 ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4912_times__int__def,axiom,
% 9.17/5.40 ( times_times_int
% 9.17/5.40 = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 9.17/5.40 @ ( produc27273713700761075at_nat
% 9.17/5.40 @ ^ [X3: nat,Y3: nat] :
% 9.17/5.40 ( produc2626176000494625587at_nat
% 9.17/5.40 @ ^ [U2: nat,V2: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X3 @ U2 ) @ ( times_times_nat @ Y3 @ V2 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X3 @ V2 ) @ ( times_times_nat @ Y3 @ U2 ) ) ) ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4913_minus__int__def,axiom,
% 9.17/5.40 ( minus_minus_int
% 9.17/5.40 = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 9.17/5.40 @ ( produc27273713700761075at_nat
% 9.17/5.40 @ ^ [X3: nat,Y3: nat] :
% 9.17/5.40 ( produc2626176000494625587at_nat
% 9.17/5.40 @ ^ [U2: nat,V2: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X3 @ V2 ) @ ( plus_plus_nat @ Y3 @ U2 ) ) ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4914_plus__int__def,axiom,
% 9.17/5.40 ( plus_plus_int
% 9.17/5.40 = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 9.17/5.40 @ ( produc27273713700761075at_nat
% 9.17/5.40 @ ^ [X3: nat,Y3: nat] :
% 9.17/5.40 ( produc2626176000494625587at_nat
% 9.17/5.40 @ ^ [U2: nat,V2: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X3 @ U2 ) @ ( plus_plus_nat @ Y3 @ V2 ) ) ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4915_rat__minus__code,axiom,
% 9.17/5.40 ! [P4: rat,Q3: rat] :
% 9.17/5.40 ( ( quotient_of @ ( minus_minus_rat @ P4 @ Q3 ) )
% 9.17/5.40 = ( produc4245557441103728435nt_int
% 9.17/5.40 @ ^ [A5: int,C2: int] :
% 9.17/5.40 ( produc4245557441103728435nt_int
% 9.17/5.40 @ ^ [B4: int,D4: int] : ( normalize @ ( product_Pair_int_int @ ( minus_minus_int @ ( times_times_int @ A5 @ D4 ) @ ( times_times_int @ B4 @ C2 ) ) @ ( times_times_int @ C2 @ D4 ) ) )
% 9.17/5.40 @ ( quotient_of @ Q3 ) )
% 9.17/5.40 @ ( quotient_of @ P4 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4916_rat__plus__code,axiom,
% 9.17/5.40 ! [P4: rat,Q3: rat] :
% 9.17/5.40 ( ( quotient_of @ ( plus_plus_rat @ P4 @ Q3 ) )
% 9.17/5.40 = ( produc4245557441103728435nt_int
% 9.17/5.40 @ ^ [A5: int,C2: int] :
% 9.17/5.40 ( produc4245557441103728435nt_int
% 9.17/5.40 @ ^ [B4: int,D4: int] : ( normalize @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ A5 @ D4 ) @ ( times_times_int @ B4 @ C2 ) ) @ ( times_times_int @ C2 @ D4 ) ) )
% 9.17/5.40 @ ( quotient_of @ Q3 ) )
% 9.17/5.40 @ ( quotient_of @ P4 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4917_image__Suc__atLeastAtMost,axiom,
% 9.17/5.40 ! [I: nat,J: nat] :
% 9.17/5.40 ( ( image_nat_nat @ suc @ ( set_or1269000886237332187st_nat @ I @ J ) )
% 9.17/5.40 = ( set_or1269000886237332187st_nat @ ( suc @ I ) @ ( suc @ J ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4918_image__Suc__atLeastLessThan,axiom,
% 9.17/5.40 ! [I: nat,J: nat] :
% 9.17/5.40 ( ( image_nat_nat @ suc @ ( set_or4665077453230672383an_nat @ I @ J ) )
% 9.17/5.40 = ( set_or4665077453230672383an_nat @ ( suc @ I ) @ ( suc @ J ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4919_in__inv__image,axiom,
% 9.17/5.40 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,R2: set_Pr4329608150637261639at_nat,F: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat] :
% 9.17/5.40 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ ( inv_im7023619800666061458at_nat @ R2 @ F ) )
% 9.17/5.40 = ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( F @ X ) @ ( F @ Y ) ) @ R2 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4920_in__inv__image,axiom,
% 9.17/5.40 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,R2: set_Pr1261947904930325089at_nat,F: set_Pr1261947904930325089at_nat > nat] :
% 9.17/5.40 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ ( inv_im6750873321330482877at_nat @ R2 @ F ) )
% 9.17/5.40 = ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ ( F @ X ) @ ( F @ Y ) ) @ R2 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4921_in__inv__image,axiom,
% 9.17/5.40 ! [X: nat,Y: nat,R2: set_Pr4329608150637261639at_nat,F: nat > set_Pr1261947904930325089at_nat] :
% 9.17/5.40 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( inv_im4437241714082187487at_nat @ R2 @ F ) )
% 9.17/5.40 = ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( F @ X ) @ ( F @ Y ) ) @ R2 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4922_in__inv__image,axiom,
% 9.17/5.40 ! [X: nat,Y: nat,R2: set_Pr1261947904930325089at_nat,F: nat > nat] :
% 9.17/5.40 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( inv_image_nat_nat @ R2 @ F ) )
% 9.17/5.40 = ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ ( F @ X ) @ ( F @ Y ) ) @ R2 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4923_pair__imageI,axiom,
% 9.17/5.40 ! [A: nat,B: nat,A2: set_Pr1261947904930325089at_nat,F: nat > nat > $o] :
% 9.17/5.40 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ A2 )
% 9.17/5.40 => ( member_o @ ( F @ A @ B ) @ ( image_3693632289388996572_nat_o @ ( produc6081775807080527818_nat_o @ F ) @ A2 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4924_pair__imageI,axiom,
% 9.17/5.40 ! [A: nat,B: nat,A2: set_Pr1261947904930325089at_nat,F: nat > nat > int] :
% 9.17/5.40 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ A2 )
% 9.17/5.40 => ( member_int @ ( F @ A @ B ) @ ( image_2483585944268220136at_int @ ( produc6840382203811409530at_int @ F ) @ A2 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4925_pair__imageI,axiom,
% 9.17/5.40 ! [A: nat,B: nat,A2: set_Pr1261947904930325089at_nat,F: nat > nat > nat] :
% 9.17/5.40 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ A2 )
% 9.17/5.40 => ( member_nat @ ( F @ A @ B ) @ ( image_2486076414777270412at_nat @ ( produc6842872674320459806at_nat @ F ) @ A2 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4926_pair__imageI,axiom,
% 9.17/5.40 ! [A: int,B: int,A2: set_Pr958786334691620121nt_int,F: int > int > int] :
% 9.17/5.40 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ A2 )
% 9.17/5.40 => ( member_int @ ( F @ A @ B ) @ ( image_5042161079198086560nt_int @ ( produc8211389475949308722nt_int @ F ) @ A2 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4927_pair__imageI,axiom,
% 9.17/5.40 ! [A: nat,B: nat,A2: set_Pr1261947904930325089at_nat,F: nat > nat > product_prod_nat_nat] :
% 9.17/5.40 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ A2 )
% 9.17/5.40 => ( member8440522571783428010at_nat @ ( F @ A @ B ) @ ( image_5168914502847457605at_nat @ ( produc2626176000494625587at_nat @ F ) @ A2 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4928_pair__imageI,axiom,
% 9.17/5.40 ! [A: int,B: int,A2: set_Pr958786334691620121nt_int,F: int > int > product_prod_int_int] :
% 9.17/5.40 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ A2 )
% 9.17/5.40 => ( member5262025264175285858nt_int @ ( F @ A @ B ) @ ( image_2653370878348428101nt_int @ ( produc4245557441103728435nt_int @ F ) @ A2 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4929_pair__imageI,axiom,
% 9.17/5.40 ! [A: nat,B: nat,A2: set_Pr1261947904930325089at_nat,F: nat > nat > product_prod_nat_nat > $o] :
% 9.17/5.40 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ A2 )
% 9.17/5.40 => ( member2006080708140975699_nat_o @ ( F @ A @ B ) @ ( image_2972642778337070200_nat_o @ ( produc8739625826339149834_nat_o @ F ) @ A2 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4930_pair__imageI,axiom,
% 9.17/5.40 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,A2: set_Pr4329608150637261639at_nat,F: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o] :
% 9.17/5.40 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ B ) @ A2 )
% 9.17/5.40 => ( member_o @ ( F @ A @ B ) @ ( image_3500134854233901558_nat_o @ ( produc410239310623530412_nat_o @ F ) @ A2 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4931_pair__imageI,axiom,
% 9.17/5.40 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,A2: set_Pr4329608150637261639at_nat,F: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > nat] :
% 9.17/5.40 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ B ) @ A2 )
% 9.17/5.40 => ( member_nat @ ( F @ A @ B ) @ ( image_3198525501578754290at_nat @ ( produc4001655692221972156at_nat @ F ) @ A2 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4932_pair__imageI,axiom,
% 9.17/5.40 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,A2: set_Pr4329608150637261639at_nat,F: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > int] :
% 9.17/5.40 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ B ) @ A2 )
% 9.17/5.40 => ( member_int @ ( F @ A @ B ) @ ( image_3196035031069704014at_int @ ( produc3999165221712921880at_int @ F ) @ A2 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4933_int__of__integer__max,axiom,
% 9.17/5.40 ! [K: code_integer,L: code_integer] :
% 9.17/5.40 ( ( code_int_of_integer @ ( ord_max_Code_integer @ K @ L ) )
% 9.17/5.40 = ( ord_max_int @ ( code_int_of_integer @ K ) @ ( code_int_of_integer @ L ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4934_rat__one__code,axiom,
% 9.17/5.40 ( ( quotient_of @ one_one_rat )
% 9.17/5.40 = ( product_Pair_int_int @ one_one_int @ one_one_int ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4935_of__nat__of__integer,axiom,
% 9.17/5.40 ! [K: code_integer] :
% 9.17/5.40 ( ( semiri4939895301339042750nteger @ ( code_nat_of_integer @ K ) )
% 9.17/5.40 = ( ord_max_Code_integer @ zero_z3403309356797280102nteger @ K ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4936_rat__zero__code,axiom,
% 9.17/5.40 ( ( quotient_of @ zero_zero_rat )
% 9.17/5.40 = ( product_Pair_int_int @ zero_zero_int @ one_one_int ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4937_quotient__of__number_I3_J,axiom,
% 9.17/5.40 ! [K: num] :
% 9.17/5.40 ( ( quotient_of @ ( numeral_numeral_rat @ K ) )
% 9.17/5.40 = ( product_Pair_int_int @ ( numeral_numeral_int @ K ) @ one_one_int ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4938_quotient__of__number_I4_J,axiom,
% 9.17/5.40 ( ( quotient_of @ ( uminus_uminus_rat @ one_one_rat ) )
% 9.17/5.40 = ( product_Pair_int_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4939_quotient__of__number_I5_J,axiom,
% 9.17/5.40 ! [K: num] :
% 9.17/5.40 ( ( quotient_of @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 9.17/5.40 = ( product_Pair_int_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4940_diff__rat__def,axiom,
% 9.17/5.40 ( minus_minus_rat
% 9.17/5.40 = ( ^ [Q5: rat,R3: rat] : ( plus_plus_rat @ Q5 @ ( uminus_uminus_rat @ R3 ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4941_quotient__of__div,axiom,
% 9.17/5.40 ! [R2: rat,N2: int,D2: int] :
% 9.17/5.40 ( ( ( quotient_of @ R2 )
% 9.17/5.40 = ( product_Pair_int_int @ N2 @ D2 ) )
% 9.17/5.40 => ( R2
% 9.17/5.40 = ( divide_divide_rat @ ( ring_1_of_int_rat @ N2 ) @ ( ring_1_of_int_rat @ D2 ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4942_zero__notin__Suc__image,axiom,
% 9.17/5.40 ! [A2: set_nat] :
% 9.17/5.40 ~ ( member_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ A2 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4943_None__notin__image__Some,axiom,
% 9.17/5.40 ! [A2: set_Pr5142436192348053284it_nat] :
% 9.17/5.40 ~ ( member3517700364412436275it_nat @ none_P2587165478634041381it_nat @ ( image_4799632500972785611it_nat @ some_P6105628898608307625it_nat @ A2 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4944_None__notin__image__Some,axiom,
% 9.17/5.40 ! [A2: set_num] :
% 9.17/5.40 ~ ( member_option_num @ none_num @ ( image_num_option_num @ some_num @ A2 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4945_None__notin__image__Some,axiom,
% 9.17/5.40 ! [A2: set_Pr1354866905816374718it_nat] :
% 9.17/5.40 ~ ( member5596548051065438575it_nat @ none_P9117596204409417319it_nat @ ( image_3455408117458022631it_nat @ some_P1914260805536162275it_nat @ A2 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4946_plus__integer__def,axiom,
% 9.17/5.40 ( plus_p5714425477246183910nteger
% 9.17/5.40 = ( map_fu8272188784021352819nteger @ code_int_of_integer @ ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int ) @ plus_plus_int ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4947_times__integer__def,axiom,
% 9.17/5.40 ( times_3573771949741848930nteger
% 9.17/5.40 = ( map_fu8272188784021352819nteger @ code_int_of_integer @ ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int ) @ times_times_int ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4948_minus__integer__def,axiom,
% 9.17/5.40 ( minus_8373710615458151222nteger
% 9.17/5.40 = ( map_fu8272188784021352819nteger @ code_int_of_integer @ ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int ) @ minus_minus_int ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4949_divide__integer__def,axiom,
% 9.17/5.40 ( divide6298287555418463151nteger
% 9.17/5.40 = ( map_fu8272188784021352819nteger @ code_int_of_integer @ ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int ) @ divide_divide_int ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4950_modulo__integer__def,axiom,
% 9.17/5.40 ( modulo364778990260209775nteger
% 9.17/5.40 = ( map_fu8272188784021352819nteger @ code_int_of_integer @ ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int ) @ modulo_modulo_int ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4951_and__integer__def,axiom,
% 9.17/5.40 ( bit_se3949692690581998587nteger
% 9.17/5.40 = ( map_fu8272188784021352819nteger @ code_int_of_integer @ ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int ) @ bit_se725231765392027082nd_int ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4952_or__integer__def,axiom,
% 9.17/5.40 ( bit_se1080825931792720795nteger
% 9.17/5.40 = ( map_fu8272188784021352819nteger @ code_int_of_integer @ ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int ) @ bit_se1409905431419307370or_int ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4953_xor__integer__def,axiom,
% 9.17/5.40 ( bit_se3222712562003087583nteger
% 9.17/5.40 = ( map_fu8272188784021352819nteger @ code_int_of_integer @ ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int ) @ bit_se6526347334894502574or_int ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4954_image__int__atLeastAtMost,axiom,
% 9.17/5.40 ! [A: nat,B: nat] :
% 9.17/5.40 ( ( image_nat_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 9.17/5.40 = ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4955_image__int__atLeastLessThan,axiom,
% 9.17/5.40 ! [A: nat,B: nat] :
% 9.17/5.40 ( ( image_nat_int @ semiri1314217659103216013at_int @ ( set_or4665077453230672383an_nat @ A @ B ) )
% 9.17/5.40 = ( set_or4662586982721622107an_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4956_quotient__of__denom__pos,axiom,
% 9.17/5.40 ! [R2: rat,P4: int,Q3: int] :
% 9.17/5.40 ( ( ( quotient_of @ R2 )
% 9.17/5.40 = ( product_Pair_int_int @ P4 @ Q3 ) )
% 9.17/5.40 => ( ord_less_int @ zero_zero_int @ Q3 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4957_image__Suc__atMost,axiom,
% 9.17/5.40 ! [N2: nat] :
% 9.17/5.40 ( ( image_nat_nat @ suc @ ( set_ord_atMost_nat @ N2 ) )
% 9.17/5.40 = ( set_or1269000886237332187st_nat @ one_one_nat @ ( suc @ N2 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4958_image__Suc__lessThan,axiom,
% 9.17/5.40 ! [N2: nat] :
% 9.17/5.40 ( ( image_nat_nat @ suc @ ( set_ord_lessThan_nat @ N2 ) )
% 9.17/5.40 = ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4959_rat__uminus__code,axiom,
% 9.17/5.40 ! [P4: rat] :
% 9.17/5.40 ( ( quotient_of @ ( uminus_uminus_rat @ P4 ) )
% 9.17/5.40 = ( produc4245557441103728435nt_int
% 9.17/5.40 @ ^ [A5: int] : ( product_Pair_int_int @ ( uminus_uminus_int @ A5 ) )
% 9.17/5.40 @ ( quotient_of @ P4 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4960_rat__abs__code,axiom,
% 9.17/5.40 ! [P4: rat] :
% 9.17/5.40 ( ( quotient_of @ ( abs_abs_rat @ P4 ) )
% 9.17/5.40 = ( produc4245557441103728435nt_int
% 9.17/5.40 @ ^ [A5: int] : ( product_Pair_int_int @ ( abs_abs_int @ A5 ) )
% 9.17/5.40 @ ( quotient_of @ P4 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4961_uminus__integer__def,axiom,
% 9.17/5.40 ( uminus1351360451143612070nteger
% 9.17/5.40 = ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int @ uminus_uminus_int ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4962_abs__integer__def,axiom,
% 9.17/5.40 ( abs_abs_Code_integer
% 9.17/5.40 = ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int @ abs_abs_int ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4963_image__add__int__atLeastLessThan,axiom,
% 9.17/5.40 ! [L: int,U: int] :
% 9.17/5.40 ( ( image_int_int
% 9.17/5.40 @ ^ [X3: int] : ( plus_plus_int @ X3 @ L )
% 9.17/5.40 @ ( set_or4662586982721622107an_int @ zero_zero_int @ ( minus_minus_int @ U @ L ) ) )
% 9.17/5.40 = ( set_or4662586982721622107an_int @ L @ U ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4964_sgn__integer__def,axiom,
% 9.17/5.40 ( sgn_sgn_Code_integer
% 9.17/5.40 = ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int @ sgn_sgn_int ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4965_not__integer__def,axiom,
% 9.17/5.40 ( bit_ri7632146776885996613nteger
% 9.17/5.40 = ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int @ bit_ri7919022796975470100ot_int ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4966_image__add__integer__atLeastLessThan,axiom,
% 9.17/5.40 ! [L: code_integer,U: code_integer] :
% 9.17/5.40 ( ( image_4470545334726330049nteger
% 9.17/5.40 @ ^ [X3: code_integer] : ( plus_p5714425477246183910nteger @ X3 @ L )
% 9.17/5.40 @ ( set_or8404916559141939852nteger @ zero_z3403309356797280102nteger @ ( minus_8373710615458151222nteger @ U @ L ) ) )
% 9.17/5.40 = ( set_or8404916559141939852nteger @ L @ U ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4967_rat__times__code,axiom,
% 9.17/5.40 ! [P4: rat,Q3: rat] :
% 9.17/5.40 ( ( quotient_of @ ( times_times_rat @ P4 @ Q3 ) )
% 9.17/5.40 = ( produc4245557441103728435nt_int
% 9.17/5.40 @ ^ [A5: int,C2: int] :
% 9.17/5.40 ( produc4245557441103728435nt_int
% 9.17/5.40 @ ^ [B4: int,D4: int] : ( normalize @ ( product_Pair_int_int @ ( times_times_int @ A5 @ B4 ) @ ( times_times_int @ C2 @ D4 ) ) )
% 9.17/5.40 @ ( quotient_of @ Q3 ) )
% 9.17/5.40 @ ( quotient_of @ P4 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4968_rat__divide__code,axiom,
% 9.17/5.40 ! [P4: rat,Q3: rat] :
% 9.17/5.40 ( ( quotient_of @ ( divide_divide_rat @ P4 @ Q3 ) )
% 9.17/5.40 = ( produc4245557441103728435nt_int
% 9.17/5.40 @ ^ [A5: int,C2: int] :
% 9.17/5.40 ( produc4245557441103728435nt_int
% 9.17/5.40 @ ^ [B4: int,D4: int] : ( normalize @ ( product_Pair_int_int @ ( times_times_int @ A5 @ D4 ) @ ( times_times_int @ C2 @ B4 ) ) )
% 9.17/5.40 @ ( quotient_of @ Q3 ) )
% 9.17/5.40 @ ( quotient_of @ P4 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4969_image__atLeastZeroLessThan__int,axiom,
% 9.17/5.40 ! [U: int] :
% 9.17/5.40 ( ( ord_less_eq_int @ zero_zero_int @ U )
% 9.17/5.40 => ( ( set_or4662586982721622107an_int @ zero_zero_int @ U )
% 9.17/5.40 = ( image_nat_int @ semiri1314217659103216013at_int @ ( set_ord_lessThan_nat @ ( nat2 @ U ) ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4970_quotient__of__int,axiom,
% 9.17/5.40 ! [A: int] :
% 9.17/5.40 ( ( quotient_of @ ( of_int @ A ) )
% 9.17/5.40 = ( product_Pair_int_int @ A @ one_one_int ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4971_rat__inverse__code,axiom,
% 9.17/5.40 ! [P4: rat] :
% 9.17/5.40 ( ( quotient_of @ ( inverse_inverse_rat @ P4 ) )
% 9.17/5.40 = ( produc4245557441103728435nt_int
% 9.17/5.40 @ ^ [A5: int,B4: int] : ( if_Pro3027730157355071871nt_int @ ( A5 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ ( times_times_int @ ( sgn_sgn_int @ A5 ) @ B4 ) @ ( abs_abs_int @ A5 ) ) )
% 9.17/5.40 @ ( quotient_of @ P4 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4972_diff__numeral__special_I8_J,axiom,
% 9.17/5.40 ! [M2: num] :
% 9.17/5.40 ( ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( uminus_uminus_int @ one_one_int ) )
% 9.17/5.40 = ( neg_numeral_sub_int @ one @ M2 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4973_diff__numeral__special_I8_J,axiom,
% 9.17/5.40 ! [M2: num] :
% 9.17/5.40 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.17/5.40 = ( neg_nu5755505904847501662nteger @ one @ M2 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4974_diff__numeral__special_I8_J,axiom,
% 9.17/5.40 ! [M2: num] :
% 9.17/5.40 ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 9.17/5.40 = ( neg_numeral_sub_rat @ one @ M2 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4975_diff__numeral__special_I7_J,axiom,
% 9.17/5.40 ! [N2: num] :
% 9.17/5.40 ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 9.17/5.40 = ( neg_numeral_sub_int @ N2 @ one ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4976_diff__numeral__special_I7_J,axiom,
% 9.17/5.40 ! [N2: num] :
% 9.17/5.40 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 9.17/5.40 = ( neg_nu5755505904847501662nteger @ N2 @ one ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4977_diff__numeral__special_I7_J,axiom,
% 9.17/5.40 ! [N2: num] :
% 9.17/5.40 ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 9.17/5.40 = ( neg_numeral_sub_rat @ N2 @ one ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4978_minus__sub__one__diff__one,axiom,
% 9.17/5.40 ! [M2: num] :
% 9.17/5.40 ( ( minus_minus_int @ ( uminus_uminus_int @ ( neg_numeral_sub_int @ M2 @ one ) ) @ one_one_int )
% 9.17/5.40 = ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4979_minus__sub__one__diff__one,axiom,
% 9.17/5.40 ! [M2: num] :
% 9.17/5.40 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ ( neg_nu5755505904847501662nteger @ M2 @ one ) ) @ one_one_Code_integer )
% 9.17/5.40 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4980_minus__sub__one__diff__one,axiom,
% 9.17/5.40 ! [M2: num] :
% 9.17/5.40 ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( neg_numeral_sub_rat @ M2 @ one ) ) @ one_one_rat )
% 9.17/5.40 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4981_add__neg__numeral__special_I4_J,axiom,
% 9.17/5.40 ! [N2: num] :
% 9.17/5.40 ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N2 ) )
% 9.17/5.40 = ( neg_numeral_sub_int @ N2 @ one ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4982_add__neg__numeral__special_I4_J,axiom,
% 9.17/5.40 ! [N2: num] :
% 9.17/5.40 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ N2 ) )
% 9.17/5.40 = ( neg_nu5755505904847501662nteger @ N2 @ one ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4983_add__neg__numeral__special_I4_J,axiom,
% 9.17/5.40 ! [N2: num] :
% 9.17/5.40 ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ N2 ) )
% 9.17/5.40 = ( neg_numeral_sub_rat @ N2 @ one ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4984_int__of__integer__sub,axiom,
% 9.17/5.40 ! [K: num,L: num] :
% 9.17/5.40 ( ( code_int_of_integer @ ( neg_nu5755505904847501662nteger @ K @ L ) )
% 9.17/5.40 = ( neg_numeral_sub_int @ K @ L ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4985_inverse__1,axiom,
% 9.17/5.40 ( ( inverse_inverse_rat @ one_one_rat )
% 9.17/5.40 = one_one_rat ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4986_inverse__eq__1__iff,axiom,
% 9.17/5.40 ! [X: rat] :
% 9.17/5.40 ( ( ( inverse_inverse_rat @ X )
% 9.17/5.40 = one_one_rat )
% 9.17/5.40 = ( X = one_one_rat ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4987_right__inverse,axiom,
% 9.17/5.40 ! [A: rat] :
% 9.17/5.40 ( ( A != zero_zero_rat )
% 9.17/5.40 => ( ( times_times_rat @ A @ ( inverse_inverse_rat @ A ) )
% 9.17/5.40 = one_one_rat ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4988_left__inverse,axiom,
% 9.17/5.40 ! [A: rat] :
% 9.17/5.40 ( ( A != zero_zero_rat )
% 9.17/5.40 => ( ( times_times_rat @ ( inverse_inverse_rat @ A ) @ A )
% 9.17/5.40 = one_one_rat ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4989_inverse__eq__divide__numeral,axiom,
% 9.17/5.40 ! [W: num] :
% 9.17/5.40 ( ( inverse_inverse_rat @ ( numeral_numeral_rat @ W ) )
% 9.17/5.40 = ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ W ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4990_add__neg__numeral__simps_I2_J,axiom,
% 9.17/5.40 ! [M2: num,N2: num] :
% 9.17/5.40 ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( numeral_numeral_int @ N2 ) )
% 9.17/5.40 = ( neg_numeral_sub_int @ N2 @ M2 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4991_add__neg__numeral__simps_I2_J,axiom,
% 9.17/5.40 ! [M2: num,N2: num] :
% 9.17/5.40 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ ( numera6620942414471956472nteger @ N2 ) )
% 9.17/5.40 = ( neg_nu5755505904847501662nteger @ N2 @ M2 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4992_add__neg__numeral__simps_I2_J,axiom,
% 9.17/5.40 ! [M2: num,N2: num] :
% 9.17/5.40 ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ ( numeral_numeral_rat @ N2 ) )
% 9.17/5.40 = ( neg_numeral_sub_rat @ N2 @ M2 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4993_add__neg__numeral__simps_I1_J,axiom,
% 9.17/5.40 ! [M2: num,N2: num] :
% 9.17/5.40 ( ( plus_plus_int @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 9.17/5.40 = ( neg_numeral_sub_int @ M2 @ N2 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4994_add__neg__numeral__simps_I1_J,axiom,
% 9.17/5.40 ! [M2: num,N2: num] :
% 9.17/5.40 ( ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ M2 ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 9.17/5.40 = ( neg_nu5755505904847501662nteger @ M2 @ N2 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4995_add__neg__numeral__simps_I1_J,axiom,
% 9.17/5.40 ! [M2: num,N2: num] :
% 9.17/5.40 ( ( plus_plus_rat @ ( numeral_numeral_rat @ M2 ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 9.17/5.40 = ( neg_numeral_sub_rat @ M2 @ N2 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4996_semiring__norm_I166_J,axiom,
% 9.17/5.40 ! [V: num,W: num,Y: int] :
% 9.17/5.40 ( ( plus_plus_int @ ( numeral_numeral_int @ V ) @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ Y ) )
% 9.17/5.40 = ( plus_plus_int @ ( neg_numeral_sub_int @ V @ W ) @ Y ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4997_semiring__norm_I166_J,axiom,
% 9.17/5.40 ! [V: num,W: num,Y: code_integer] :
% 9.17/5.40 ( ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ V ) @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) @ Y ) )
% 9.17/5.40 = ( plus_p5714425477246183910nteger @ ( neg_nu5755505904847501662nteger @ V @ W ) @ Y ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4998_semiring__norm_I166_J,axiom,
% 9.17/5.40 ! [V: num,W: num,Y: rat] :
% 9.17/5.40 ( ( plus_plus_rat @ ( numeral_numeral_rat @ V ) @ ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ Y ) )
% 9.17/5.40 = ( plus_plus_rat @ ( neg_numeral_sub_rat @ V @ W ) @ Y ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_4999_semiring__norm_I167_J,axiom,
% 9.17/5.40 ! [V: num,W: num,Y: int] :
% 9.17/5.40 ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( plus_plus_int @ ( numeral_numeral_int @ W ) @ Y ) )
% 9.17/5.40 = ( plus_plus_int @ ( neg_numeral_sub_int @ W @ V ) @ Y ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5000_semiring__norm_I167_J,axiom,
% 9.17/5.40 ! [V: num,W: num,Y: code_integer] :
% 9.17/5.40 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ W ) @ Y ) )
% 9.17/5.40 = ( plus_p5714425477246183910nteger @ ( neg_nu5755505904847501662nteger @ W @ V ) @ Y ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5001_semiring__norm_I167_J,axiom,
% 9.17/5.40 ! [V: num,W: num,Y: rat] :
% 9.17/5.40 ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ ( plus_plus_rat @ ( numeral_numeral_rat @ W ) @ Y ) )
% 9.17/5.40 = ( plus_plus_rat @ ( neg_numeral_sub_rat @ W @ V ) @ Y ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5002_inverse__eq__divide__neg__numeral,axiom,
% 9.17/5.40 ! [W: num] :
% 9.17/5.40 ( ( inverse_inverse_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 9.17/5.40 = ( divide_divide_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5003_diff__numeral__special_I2_J,axiom,
% 9.17/5.40 ! [M2: num] :
% 9.17/5.40 ( ( minus_minus_int @ ( numeral_numeral_int @ M2 ) @ one_one_int )
% 9.17/5.40 = ( neg_numeral_sub_int @ M2 @ one ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5004_diff__numeral__special_I2_J,axiom,
% 9.17/5.40 ! [M2: num] :
% 9.17/5.40 ( ( minus_8373710615458151222nteger @ ( numera6620942414471956472nteger @ M2 ) @ one_one_Code_integer )
% 9.17/5.40 = ( neg_nu5755505904847501662nteger @ M2 @ one ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5005_diff__numeral__special_I2_J,axiom,
% 9.17/5.40 ! [M2: num] :
% 9.17/5.40 ( ( minus_minus_rat @ ( numeral_numeral_rat @ M2 ) @ one_one_rat )
% 9.17/5.40 = ( neg_numeral_sub_rat @ M2 @ one ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5006_diff__numeral__special_I1_J,axiom,
% 9.17/5.40 ! [N2: num] :
% 9.17/5.40 ( ( minus_minus_int @ one_one_int @ ( numeral_numeral_int @ N2 ) )
% 9.17/5.40 = ( neg_numeral_sub_int @ one @ N2 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5007_diff__numeral__special_I1_J,axiom,
% 9.17/5.40 ! [N2: num] :
% 9.17/5.40 ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ N2 ) )
% 9.17/5.40 = ( neg_nu5755505904847501662nteger @ one @ N2 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5008_diff__numeral__special_I1_J,axiom,
% 9.17/5.40 ! [N2: num] :
% 9.17/5.40 ( ( minus_minus_rat @ one_one_rat @ ( numeral_numeral_rat @ N2 ) )
% 9.17/5.40 = ( neg_numeral_sub_rat @ one @ N2 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5009_add__neg__numeral__special_I1_J,axiom,
% 9.17/5.40 ! [M2: num] :
% 9.17/5.40 ( ( plus_plus_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) )
% 9.17/5.40 = ( neg_numeral_sub_int @ one @ M2 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5010_add__neg__numeral__special_I1_J,axiom,
% 9.17/5.40 ! [M2: num] :
% 9.17/5.40 ( ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) )
% 9.17/5.40 = ( neg_nu5755505904847501662nteger @ one @ M2 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5011_add__neg__numeral__special_I1_J,axiom,
% 9.17/5.40 ! [M2: num] :
% 9.17/5.40 ( ( plus_plus_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) )
% 9.17/5.40 = ( neg_numeral_sub_rat @ one @ M2 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5012_add__neg__numeral__special_I2_J,axiom,
% 9.17/5.40 ! [M2: num] :
% 9.17/5.40 ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ one_one_int )
% 9.17/5.40 = ( neg_numeral_sub_int @ one @ M2 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5013_add__neg__numeral__special_I2_J,axiom,
% 9.17/5.40 ! [M2: num] :
% 9.17/5.40 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ one_one_Code_integer )
% 9.17/5.40 = ( neg_nu5755505904847501662nteger @ one @ M2 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5014_add__neg__numeral__special_I2_J,axiom,
% 9.17/5.40 ! [M2: num] :
% 9.17/5.40 ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ one_one_rat )
% 9.17/5.40 = ( neg_numeral_sub_rat @ one @ M2 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5015_add__neg__numeral__special_I3_J,axiom,
% 9.17/5.40 ! [M2: num] :
% 9.17/5.40 ( ( plus_plus_int @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ one_one_int ) )
% 9.17/5.40 = ( neg_numeral_sub_int @ M2 @ one ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5016_add__neg__numeral__special_I3_J,axiom,
% 9.17/5.40 ! [M2: num] :
% 9.17/5.40 ( ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ M2 ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.17/5.40 = ( neg_nu5755505904847501662nteger @ M2 @ one ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5017_add__neg__numeral__special_I3_J,axiom,
% 9.17/5.40 ! [M2: num] :
% 9.17/5.40 ( ( plus_plus_rat @ ( numeral_numeral_rat @ M2 ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 9.17/5.40 = ( neg_numeral_sub_rat @ M2 @ one ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5018_inverse__unique,axiom,
% 9.17/5.40 ! [A: rat,B: rat] :
% 9.17/5.40 ( ( ( times_times_rat @ A @ B )
% 9.17/5.40 = one_one_rat )
% 9.17/5.40 => ( ( inverse_inverse_rat @ A )
% 9.17/5.40 = B ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5019_inverse__eq__divide,axiom,
% 9.17/5.40 ( inverse_inverse_rat
% 9.17/5.40 = ( divide_divide_rat @ one_one_rat ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5020_inverse__le__1__iff,axiom,
% 9.17/5.40 ! [X: rat] :
% 9.17/5.40 ( ( ord_less_eq_rat @ ( inverse_inverse_rat @ X ) @ one_one_rat )
% 9.17/5.40 = ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 9.17/5.40 | ( ord_less_eq_rat @ one_one_rat @ X ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5021_one__less__inverse__iff,axiom,
% 9.17/5.40 ! [X: rat] :
% 9.17/5.40 ( ( ord_less_rat @ one_one_rat @ ( inverse_inverse_rat @ X ) )
% 9.17/5.40 = ( ( ord_less_rat @ zero_zero_rat @ X )
% 9.17/5.40 & ( ord_less_rat @ X @ one_one_rat ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5022_one__less__inverse,axiom,
% 9.17/5.40 ! [A: rat] :
% 9.17/5.40 ( ( ord_less_rat @ zero_zero_rat @ A )
% 9.17/5.40 => ( ( ord_less_rat @ A @ one_one_rat )
% 9.17/5.40 => ( ord_less_rat @ one_one_rat @ ( inverse_inverse_rat @ A ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5023_division__ring__inverse__add,axiom,
% 9.17/5.40 ! [A: rat,B: rat] :
% 9.17/5.40 ( ( A != zero_zero_rat )
% 9.17/5.40 => ( ( B != zero_zero_rat )
% 9.17/5.40 => ( ( plus_plus_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 9.17/5.40 = ( times_times_rat @ ( times_times_rat @ ( inverse_inverse_rat @ A ) @ ( plus_plus_rat @ A @ B ) ) @ ( inverse_inverse_rat @ B ) ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5024_inverse__add,axiom,
% 9.17/5.40 ! [A: rat,B: rat] :
% 9.17/5.40 ( ( A != zero_zero_rat )
% 9.17/5.40 => ( ( B != zero_zero_rat )
% 9.17/5.40 => ( ( plus_plus_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 9.17/5.40 = ( times_times_rat @ ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ ( inverse_inverse_rat @ A ) ) @ ( inverse_inverse_rat @ B ) ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5025_field__class_Ofield__inverse,axiom,
% 9.17/5.40 ! [A: rat] :
% 9.17/5.40 ( ( A != zero_zero_rat )
% 9.17/5.40 => ( ( times_times_rat @ ( inverse_inverse_rat @ A ) @ A )
% 9.17/5.40 = one_one_rat ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5026_nonzero__inverse__eq__divide,axiom,
% 9.17/5.40 ! [A: rat] :
% 9.17/5.40 ( ( A != zero_zero_rat )
% 9.17/5.40 => ( ( inverse_inverse_rat @ A )
% 9.17/5.40 = ( divide_divide_rat @ one_one_rat @ A ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5027_one__le__inverse__iff,axiom,
% 9.17/5.40 ! [X: rat] :
% 9.17/5.40 ( ( ord_less_eq_rat @ one_one_rat @ ( inverse_inverse_rat @ X ) )
% 9.17/5.40 = ( ( ord_less_rat @ zero_zero_rat @ X )
% 9.17/5.40 & ( ord_less_eq_rat @ X @ one_one_rat ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5028_inverse__less__1__iff,axiom,
% 9.17/5.40 ! [X: rat] :
% 9.17/5.40 ( ( ord_less_rat @ ( inverse_inverse_rat @ X ) @ one_one_rat )
% 9.17/5.40 = ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 9.17/5.40 | ( ord_less_rat @ one_one_rat @ X ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5029_one__le__inverse,axiom,
% 9.17/5.40 ! [A: rat] :
% 9.17/5.40 ( ( ord_less_rat @ zero_zero_rat @ A )
% 9.17/5.40 => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 9.17/5.40 => ( ord_less_eq_rat @ one_one_rat @ ( inverse_inverse_rat @ A ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5030_Frct__code__post_I5_J,axiom,
% 9.17/5.40 ! [K: num] :
% 9.17/5.40 ( ( frct @ ( product_Pair_int_int @ one_one_int @ ( numeral_numeral_int @ K ) ) )
% 9.17/5.40 = ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ K ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5031_Code__Numeral_Odup__def,axiom,
% 9.17/5.40 ( code_dup
% 9.17/5.40 = ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int
% 9.17/5.40 @ ^ [K4: int] : ( plus_plus_int @ K4 @ K4 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5032_Frct__code__post_I6_J,axiom,
% 9.17/5.40 ! [K: num,L: num] :
% 9.17/5.40 ( ( frct @ ( product_Pair_int_int @ ( numeral_numeral_int @ K ) @ ( numeral_numeral_int @ L ) ) )
% 9.17/5.40 = ( divide_divide_rat @ ( numeral_numeral_rat @ K ) @ ( numeral_numeral_rat @ L ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5033_Frct__code__post_I4_J,axiom,
% 9.17/5.40 ! [K: num] :
% 9.17/5.40 ( ( frct @ ( product_Pair_int_int @ ( numeral_numeral_int @ K ) @ one_one_int ) )
% 9.17/5.40 = ( numeral_numeral_rat @ K ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5034_eq__numeral__iff__iszero_I8_J,axiom,
% 9.17/5.40 ! [Y: num] :
% 9.17/5.40 ( ( one_one_int
% 9.17/5.40 = ( uminus_uminus_int @ ( numeral_numeral_int @ Y ) ) )
% 9.17/5.40 = ( ring_1_iszero_int @ ( numeral_numeral_int @ ( plus_plus_num @ one @ Y ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5035_eq__numeral__iff__iszero_I8_J,axiom,
% 9.17/5.40 ! [Y: num] :
% 9.17/5.40 ( ( one_one_Code_integer
% 9.17/5.40 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ Y ) ) )
% 9.17/5.40 = ( ring_16219924574208605041nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ one @ Y ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5036_eq__numeral__iff__iszero_I8_J,axiom,
% 9.17/5.40 ! [Y: num] :
% 9.17/5.40 ( ( one_one_rat
% 9.17/5.40 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ Y ) ) )
% 9.17/5.40 = ( ring_1_iszero_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ one @ Y ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5037_eq__numeral__iff__iszero_I7_J,axiom,
% 9.17/5.40 ! [X: num] :
% 9.17/5.40 ( ( ( uminus_uminus_int @ ( numeral_numeral_int @ X ) )
% 9.17/5.40 = one_one_int )
% 9.17/5.40 = ( ring_1_iszero_int @ ( numeral_numeral_int @ ( plus_plus_num @ X @ one ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5038_eq__numeral__iff__iszero_I7_J,axiom,
% 9.17/5.40 ! [X: num] :
% 9.17/5.40 ( ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) )
% 9.17/5.40 = one_one_Code_integer )
% 9.17/5.40 = ( ring_16219924574208605041nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ X @ one ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5039_eq__numeral__iff__iszero_I7_J,axiom,
% 9.17/5.40 ! [X: num] :
% 9.17/5.40 ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) )
% 9.17/5.40 = one_one_rat )
% 9.17/5.40 = ( ring_1_iszero_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ X @ one ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5040_Inf_OINF__image,axiom,
% 9.17/5.40 ! [Inf: set_Code_integer > code_integer,G: code_integer > code_integer,F: num > code_integer,A2: set_num] :
% 9.17/5.40 ( ( Inf @ ( image_4470545334726330049nteger @ G @ ( image_8379761247532268670nteger @ F @ A2 ) ) )
% 9.17/5.40 = ( Inf @ ( image_8379761247532268670nteger @ ( comp_C3531382070062128313er_num @ G @ F ) @ A2 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5041_Inf_OINF__image,axiom,
% 9.17/5.40 ! [Inf: set_num > num,G: nat > num,F: int > nat,A2: set_int] :
% 9.17/5.40 ( ( Inf @ ( image_nat_num @ G @ ( image_int_nat @ F @ A2 ) ) )
% 9.17/5.40 = ( Inf @ ( image_int_num @ ( comp_nat_num_int @ G @ F ) @ A2 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5042_Inf_OINF__image,axiom,
% 9.17/5.40 ! [Inf: set_Code_integer > code_integer,G: code_integer > code_integer,F: nat > code_integer,A2: set_nat] :
% 9.17/5.40 ( ( Inf @ ( image_4470545334726330049nteger @ G @ ( image_1215581382706833972nteger @ F @ A2 ) ) )
% 9.17/5.40 = ( Inf @ ( image_1215581382706833972nteger @ ( comp_C6974050283906349679er_nat @ G @ F ) @ A2 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5043_Inf_OINF__image,axiom,
% 9.17/5.40 ! [Inf: set_nat > nat,G: code_integer > nat,F: nat > code_integer,A2: set_nat] :
% 9.17/5.40 ( ( Inf @ ( image_951025933927791156er_nat @ G @ ( image_1215581382706833972nteger @ F @ A2 ) ) )
% 9.17/5.40 = ( Inf @ ( image_nat_nat @ ( comp_C4049556595663050210at_nat @ G @ F ) @ A2 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5044_Inf_OINF__image,axiom,
% 9.17/5.40 ! [Inf: set_int > int,G: code_integer > int,F: nat > code_integer,A2: set_nat] :
% 9.17/5.40 ( ( Inf @ ( image_948535463418740880er_int @ G @ ( image_1215581382706833972nteger @ F @ A2 ) ) )
% 9.17/5.40 = ( Inf @ ( image_nat_int @ ( comp_C5048910307564104766nt_nat @ G @ F ) @ A2 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5045_Inf_OINF__image,axiom,
% 9.17/5.40 ! [Inf: set_Code_integer > code_integer,G: int > code_integer,F: nat > int,A2: set_nat] :
% 9.17/5.40 ( ( Inf @ ( image_1587234942943678608nteger @ G @ ( image_nat_int @ F @ A2 ) ) )
% 9.17/5.40 = ( Inf @ ( image_1215581382706833972nteger @ ( comp_i1588355021709917246er_nat @ G @ F ) @ A2 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5046_Inf_OINF__image,axiom,
% 9.17/5.40 ! [Inf: set_nat > nat,G: int > nat,F: nat > int,A2: set_nat] :
% 9.17/5.40 ( ( Inf @ ( image_int_nat @ G @ ( image_nat_int @ F @ A2 ) ) )
% 9.17/5.40 = ( Inf @ ( image_nat_nat @ ( comp_int_nat_nat @ G @ F ) @ A2 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5047_Inf_OINF__image,axiom,
% 9.17/5.40 ! [Inf: set_Code_integer > code_integer,G: nat > code_integer,F: nat > nat,A2: set_nat] :
% 9.17/5.40 ( ( Inf @ ( image_1215581382706833972nteger @ G @ ( image_nat_nat @ F @ A2 ) ) )
% 9.17/5.40 = ( Inf @ ( image_1215581382706833972nteger @ ( comp_n3898172953802868194er_nat @ G @ F ) @ A2 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5048_Inf_OINF__image,axiom,
% 9.17/5.40 ! [Inf: set_nat > nat,G: nat > nat,F: nat > nat,A2: set_nat] :
% 9.17/5.40 ( ( Inf @ ( image_nat_nat @ G @ ( image_nat_nat @ F @ A2 ) ) )
% 9.17/5.40 = ( Inf @ ( image_nat_nat @ ( comp_nat_nat_nat @ G @ F ) @ A2 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5049_Inf_OINF__image,axiom,
% 9.17/5.40 ! [Inf: set_int > int,G: nat > int,F: int > nat,A2: set_int] :
% 9.17/5.40 ( ( Inf @ ( image_nat_int @ G @ ( image_int_nat @ F @ A2 ) ) )
% 9.17/5.40 = ( Inf @ ( image_int_int @ ( comp_nat_int_int @ G @ F ) @ A2 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5050_not__iszero__1,axiom,
% 9.17/5.40 ~ ( ring_16219924574208605041nteger @ one_one_Code_integer ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5051_not__iszero__1,axiom,
% 9.17/5.40 ~ ( ring_1_iszero_rat @ one_one_rat ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5052_not__iszero__1,axiom,
% 9.17/5.40 ~ ( ring_1_iszero_int @ one_one_int ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5053_Code__Numeral_Odup__code_I1_J,axiom,
% 9.17/5.40 ( ( code_dup @ zero_z3403309356797280102nteger )
% 9.17/5.40 = zero_z3403309356797280102nteger ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5054_not__iszero__neg__1,axiom,
% 9.17/5.40 ~ ( ring_1_iszero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5055_not__iszero__neg__1,axiom,
% 9.17/5.40 ~ ( ring_16219924574208605041nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5056_not__iszero__neg__1,axiom,
% 9.17/5.40 ~ ( ring_1_iszero_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5057_dup_Orep__eq,axiom,
% 9.17/5.40 ! [X: code_integer] :
% 9.17/5.40 ( ( code_int_of_integer @ ( code_dup @ X ) )
% 9.17/5.40 = ( plus_plus_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ X ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5058_dup_Oabs__eq,axiom,
% 9.17/5.40 ! [X: int] :
% 9.17/5.40 ( ( code_dup @ ( code_integer_of_int @ X ) )
% 9.17/5.40 = ( code_integer_of_int @ ( plus_plus_int @ X @ X ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5059_eq__numeral__iff__iszero_I2_J,axiom,
% 9.17/5.40 ! [X: num,Y: num] :
% 9.17/5.40 ( ( ( numeral_numeral_int @ X )
% 9.17/5.40 = ( uminus_uminus_int @ ( numeral_numeral_int @ Y ) ) )
% 9.17/5.40 = ( ring_1_iszero_int @ ( numeral_numeral_int @ ( plus_plus_num @ X @ Y ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5060_eq__numeral__iff__iszero_I2_J,axiom,
% 9.17/5.40 ! [X: num,Y: num] :
% 9.17/5.40 ( ( ( numera6620942414471956472nteger @ X )
% 9.17/5.40 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ Y ) ) )
% 9.17/5.40 = ( ring_16219924574208605041nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ X @ Y ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5061_eq__numeral__iff__iszero_I2_J,axiom,
% 9.17/5.40 ! [X: num,Y: num] :
% 9.17/5.40 ( ( ( numeral_numeral_rat @ X )
% 9.17/5.40 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ Y ) ) )
% 9.17/5.40 = ( ring_1_iszero_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ X @ Y ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5062_eq__numeral__iff__iszero_I3_J,axiom,
% 9.17/5.40 ! [X: num,Y: num] :
% 9.17/5.40 ( ( ( uminus_uminus_int @ ( numeral_numeral_int @ X ) )
% 9.17/5.40 = ( numeral_numeral_int @ Y ) )
% 9.17/5.40 = ( ring_1_iszero_int @ ( numeral_numeral_int @ ( plus_plus_num @ X @ Y ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5063_eq__numeral__iff__iszero_I3_J,axiom,
% 9.17/5.40 ! [X: num,Y: num] :
% 9.17/5.40 ( ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) )
% 9.17/5.40 = ( numera6620942414471956472nteger @ Y ) )
% 9.17/5.40 = ( ring_16219924574208605041nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ X @ Y ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5064_eq__numeral__iff__iszero_I3_J,axiom,
% 9.17/5.40 ! [X: num,Y: num] :
% 9.17/5.40 ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) )
% 9.17/5.40 = ( numeral_numeral_rat @ Y ) )
% 9.17/5.40 = ( ring_1_iszero_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ X @ Y ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5065_Frct__code__post_I2_J,axiom,
% 9.17/5.40 ! [A: int] :
% 9.17/5.40 ( ( frct @ ( product_Pair_int_int @ A @ zero_zero_int ) )
% 9.17/5.40 = zero_zero_rat ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5066_Frct__code__post_I1_J,axiom,
% 9.17/5.40 ! [A: int] :
% 9.17/5.40 ( ( frct @ ( product_Pair_int_int @ zero_zero_int @ A ) )
% 9.17/5.40 = zero_zero_rat ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5067_Frct__code__post_I3_J,axiom,
% 9.17/5.40 ( ( frct @ ( product_Pair_int_int @ one_one_int @ one_one_int ) )
% 9.17/5.40 = one_one_rat ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5068_eq__numeral__iff__iszero_I6_J,axiom,
% 9.17/5.40 ! [Y: num] :
% 9.17/5.40 ( ( one_one_int
% 9.17/5.40 = ( numeral_numeral_int @ Y ) )
% 9.17/5.40 = ( ring_1_iszero_int @ ( neg_numeral_sub_int @ one @ Y ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5069_eq__numeral__iff__iszero_I6_J,axiom,
% 9.17/5.40 ! [Y: num] :
% 9.17/5.40 ( ( one_one_Code_integer
% 9.17/5.40 = ( numera6620942414471956472nteger @ Y ) )
% 9.17/5.40 = ( ring_16219924574208605041nteger @ ( neg_nu5755505904847501662nteger @ one @ Y ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5070_eq__numeral__iff__iszero_I6_J,axiom,
% 9.17/5.40 ! [Y: num] :
% 9.17/5.40 ( ( one_one_rat
% 9.17/5.40 = ( numeral_numeral_rat @ Y ) )
% 9.17/5.40 = ( ring_1_iszero_rat @ ( neg_numeral_sub_rat @ one @ Y ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5071_eq__numeral__iff__iszero_I5_J,axiom,
% 9.17/5.40 ! [X: num] :
% 9.17/5.40 ( ( ( numeral_numeral_int @ X )
% 9.17/5.40 = one_one_int )
% 9.17/5.40 = ( ring_1_iszero_int @ ( neg_numeral_sub_int @ X @ one ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5072_eq__numeral__iff__iszero_I5_J,axiom,
% 9.17/5.40 ! [X: num] :
% 9.17/5.40 ( ( ( numera6620942414471956472nteger @ X )
% 9.17/5.40 = one_one_Code_integer )
% 9.17/5.40 = ( ring_16219924574208605041nteger @ ( neg_nu5755505904847501662nteger @ X @ one ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5073_eq__numeral__iff__iszero_I5_J,axiom,
% 9.17/5.40 ! [X: num] :
% 9.17/5.40 ( ( ( numeral_numeral_rat @ X )
% 9.17/5.40 = one_one_rat )
% 9.17/5.40 = ( ring_1_iszero_rat @ ( neg_numeral_sub_rat @ X @ one ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5074_Frct__code__post_I7_J,axiom,
% 9.17/5.40 ! [A: int,B: int] :
% 9.17/5.40 ( ( frct @ ( product_Pair_int_int @ ( uminus_uminus_int @ A ) @ B ) )
% 9.17/5.40 = ( uminus_uminus_rat @ ( frct @ ( product_Pair_int_int @ A @ B ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5075_Frct__code__post_I8_J,axiom,
% 9.17/5.40 ! [A: int,B: int] :
% 9.17/5.40 ( ( frct @ ( product_Pair_int_int @ A @ ( uminus_uminus_int @ B ) ) )
% 9.17/5.40 = ( uminus_uminus_rat @ ( frct @ ( product_Pair_int_int @ A @ B ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5076_Sup_OSUP__image,axiom,
% 9.17/5.40 ! [Sup: set_Code_integer > code_integer,G: code_integer > code_integer,F: num > code_integer,A2: set_num] :
% 9.17/5.40 ( ( Sup @ ( image_4470545334726330049nteger @ G @ ( image_8379761247532268670nteger @ F @ A2 ) ) )
% 9.17/5.40 = ( Sup @ ( image_8379761247532268670nteger @ ( comp_C3531382070062128313er_num @ G @ F ) @ A2 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5077_Sup_OSUP__image,axiom,
% 9.17/5.40 ! [Sup: set_num > num,G: nat > num,F: int > nat,A2: set_int] :
% 9.17/5.40 ( ( Sup @ ( image_nat_num @ G @ ( image_int_nat @ F @ A2 ) ) )
% 9.17/5.40 = ( Sup @ ( image_int_num @ ( comp_nat_num_int @ G @ F ) @ A2 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5078_Sup_OSUP__image,axiom,
% 9.17/5.40 ! [Sup: set_Code_integer > code_integer,G: code_integer > code_integer,F: nat > code_integer,A2: set_nat] :
% 9.17/5.40 ( ( Sup @ ( image_4470545334726330049nteger @ G @ ( image_1215581382706833972nteger @ F @ A2 ) ) )
% 9.17/5.40 = ( Sup @ ( image_1215581382706833972nteger @ ( comp_C6974050283906349679er_nat @ G @ F ) @ A2 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5079_Sup_OSUP__image,axiom,
% 9.17/5.40 ! [Sup: set_nat > nat,G: code_integer > nat,F: nat > code_integer,A2: set_nat] :
% 9.17/5.40 ( ( Sup @ ( image_951025933927791156er_nat @ G @ ( image_1215581382706833972nteger @ F @ A2 ) ) )
% 9.17/5.40 = ( Sup @ ( image_nat_nat @ ( comp_C4049556595663050210at_nat @ G @ F ) @ A2 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5080_Sup_OSUP__image,axiom,
% 9.17/5.40 ! [Sup: set_int > int,G: code_integer > int,F: nat > code_integer,A2: set_nat] :
% 9.17/5.40 ( ( Sup @ ( image_948535463418740880er_int @ G @ ( image_1215581382706833972nteger @ F @ A2 ) ) )
% 9.17/5.40 = ( Sup @ ( image_nat_int @ ( comp_C5048910307564104766nt_nat @ G @ F ) @ A2 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5081_Sup_OSUP__image,axiom,
% 9.17/5.40 ! [Sup: set_Code_integer > code_integer,G: int > code_integer,F: nat > int,A2: set_nat] :
% 9.17/5.40 ( ( Sup @ ( image_1587234942943678608nteger @ G @ ( image_nat_int @ F @ A2 ) ) )
% 9.17/5.40 = ( Sup @ ( image_1215581382706833972nteger @ ( comp_i1588355021709917246er_nat @ G @ F ) @ A2 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5082_Sup_OSUP__image,axiom,
% 9.17/5.40 ! [Sup: set_nat > nat,G: int > nat,F: nat > int,A2: set_nat] :
% 9.17/5.40 ( ( Sup @ ( image_int_nat @ G @ ( image_nat_int @ F @ A2 ) ) )
% 9.17/5.40 = ( Sup @ ( image_nat_nat @ ( comp_int_nat_nat @ G @ F ) @ A2 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5083_Sup_OSUP__image,axiom,
% 9.17/5.40 ! [Sup: set_Code_integer > code_integer,G: nat > code_integer,F: nat > nat,A2: set_nat] :
% 9.17/5.40 ( ( Sup @ ( image_1215581382706833972nteger @ G @ ( image_nat_nat @ F @ A2 ) ) )
% 9.17/5.40 = ( Sup @ ( image_1215581382706833972nteger @ ( comp_n3898172953802868194er_nat @ G @ F ) @ A2 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5084_Sup_OSUP__image,axiom,
% 9.17/5.40 ! [Sup: set_nat > nat,G: nat > nat,F: nat > nat,A2: set_nat] :
% 9.17/5.40 ( ( Sup @ ( image_nat_nat @ G @ ( image_nat_nat @ F @ A2 ) ) )
% 9.17/5.40 = ( Sup @ ( image_nat_nat @ ( comp_nat_nat_nat @ G @ F ) @ A2 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5085_Sup_OSUP__image,axiom,
% 9.17/5.40 ! [Sup: set_int > int,G: nat > int,F: int > nat,A2: set_int] :
% 9.17/5.40 ( ( Sup @ ( image_nat_int @ G @ ( image_int_nat @ F @ A2 ) ) )
% 9.17/5.40 = ( Sup @ ( image_int_int @ ( comp_nat_int_int @ G @ F ) @ A2 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5086_Code__Numeral_Osub__code_I9_J,axiom,
% 9.17/5.40 ! [M2: num,N2: num] :
% 9.17/5.40 ( ( code_sub @ ( bit0 @ M2 ) @ ( bit1 @ N2 ) )
% 9.17/5.40 = ( minus_8373710615458151222nteger @ ( code_dup @ ( code_sub @ M2 @ N2 ) ) @ one_one_Code_integer ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5087_Code__Numeral_Osub__code_I8_J,axiom,
% 9.17/5.40 ! [M2: num,N2: num] :
% 9.17/5.40 ( ( code_sub @ ( bit1 @ M2 ) @ ( bit0 @ N2 ) )
% 9.17/5.40 = ( plus_p5714425477246183910nteger @ ( code_dup @ ( code_sub @ M2 @ N2 ) ) @ one_one_Code_integer ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5088_less__eq__int__def,axiom,
% 9.17/5.40 ( ord_less_eq_int
% 9.17/5.40 = ( map_fu434086159418415080_int_o @ rep_Integ @ ( map_fu4826362097070443709at_o_o @ rep_Integ @ id_o )
% 9.17/5.40 @ ( produc8739625826339149834_nat_o
% 9.17/5.40 @ ^ [X3: nat,Y3: nat] :
% 9.17/5.40 ( produc6081775807080527818_nat_o
% 9.17/5.40 @ ^ [U2: nat,V2: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X3 @ V2 ) @ ( plus_plus_nat @ U2 @ Y3 ) ) ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5089_less__int__def,axiom,
% 9.17/5.40 ( ord_less_int
% 9.17/5.40 = ( map_fu434086159418415080_int_o @ rep_Integ @ ( map_fu4826362097070443709at_o_o @ rep_Integ @ id_o )
% 9.17/5.40 @ ( produc8739625826339149834_nat_o
% 9.17/5.40 @ ^ [X3: nat,Y3: nat] :
% 9.17/5.40 ( produc6081775807080527818_nat_o
% 9.17/5.40 @ ^ [U2: nat,V2: nat] : ( ord_less_nat @ ( plus_plus_nat @ X3 @ V2 ) @ ( plus_plus_nat @ U2 @ Y3 ) ) ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5090_image__affinity__atLeastAtMost__div__diff,axiom,
% 9.17/5.40 ! [A: rat,B: rat,M2: rat,C: rat] :
% 9.17/5.40 ( ( ( ( set_or633870826150836451st_rat @ A @ B )
% 9.17/5.40 = bot_bot_set_rat )
% 9.17/5.40 => ( ( image_rat_rat
% 9.17/5.40 @ ^ [X3: rat] : ( minus_minus_rat @ ( divide_divide_rat @ X3 @ M2 ) @ C )
% 9.17/5.40 @ ( set_or633870826150836451st_rat @ A @ B ) )
% 9.17/5.40 = bot_bot_set_rat ) )
% 9.17/5.40 & ( ( ( set_or633870826150836451st_rat @ A @ B )
% 9.17/5.40 != bot_bot_set_rat )
% 9.17/5.40 => ( ( ( ord_less_eq_rat @ zero_zero_rat @ M2 )
% 9.17/5.40 => ( ( image_rat_rat
% 9.17/5.40 @ ^ [X3: rat] : ( minus_minus_rat @ ( divide_divide_rat @ X3 @ M2 ) @ C )
% 9.17/5.40 @ ( set_or633870826150836451st_rat @ A @ B ) )
% 9.17/5.40 = ( set_or633870826150836451st_rat @ ( minus_minus_rat @ ( divide_divide_rat @ A @ M2 ) @ C ) @ ( minus_minus_rat @ ( divide_divide_rat @ B @ M2 ) @ C ) ) ) )
% 9.17/5.40 & ( ~ ( ord_less_eq_rat @ zero_zero_rat @ M2 )
% 9.17/5.40 => ( ( image_rat_rat
% 9.17/5.40 @ ^ [X3: rat] : ( minus_minus_rat @ ( divide_divide_rat @ X3 @ M2 ) @ C )
% 9.17/5.40 @ ( set_or633870826150836451st_rat @ A @ B ) )
% 9.17/5.40 = ( set_or633870826150836451st_rat @ ( minus_minus_rat @ ( divide_divide_rat @ B @ M2 ) @ C ) @ ( minus_minus_rat @ ( divide_divide_rat @ A @ M2 ) @ C ) ) ) ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5091_image__affinity__atLeastAtMost__div,axiom,
% 9.17/5.40 ! [A: rat,B: rat,M2: rat,C: rat] :
% 9.17/5.40 ( ( ( ( set_or633870826150836451st_rat @ A @ B )
% 9.17/5.40 = bot_bot_set_rat )
% 9.17/5.40 => ( ( image_rat_rat
% 9.17/5.40 @ ^ [X3: rat] : ( plus_plus_rat @ ( divide_divide_rat @ X3 @ M2 ) @ C )
% 9.17/5.40 @ ( set_or633870826150836451st_rat @ A @ B ) )
% 9.17/5.40 = bot_bot_set_rat ) )
% 9.17/5.40 & ( ( ( set_or633870826150836451st_rat @ A @ B )
% 9.17/5.40 != bot_bot_set_rat )
% 9.17/5.40 => ( ( ( ord_less_eq_rat @ zero_zero_rat @ M2 )
% 9.17/5.40 => ( ( image_rat_rat
% 9.17/5.40 @ ^ [X3: rat] : ( plus_plus_rat @ ( divide_divide_rat @ X3 @ M2 ) @ C )
% 9.17/5.40 @ ( set_or633870826150836451st_rat @ A @ B ) )
% 9.17/5.40 = ( set_or633870826150836451st_rat @ ( plus_plus_rat @ ( divide_divide_rat @ A @ M2 ) @ C ) @ ( plus_plus_rat @ ( divide_divide_rat @ B @ M2 ) @ C ) ) ) )
% 9.17/5.40 & ( ~ ( ord_less_eq_rat @ zero_zero_rat @ M2 )
% 9.17/5.40 => ( ( image_rat_rat
% 9.17/5.40 @ ^ [X3: rat] : ( plus_plus_rat @ ( divide_divide_rat @ X3 @ M2 ) @ C )
% 9.17/5.40 @ ( set_or633870826150836451st_rat @ A @ B ) )
% 9.17/5.40 = ( set_or633870826150836451st_rat @ ( plus_plus_rat @ ( divide_divide_rat @ B @ M2 ) @ C ) @ ( plus_plus_rat @ ( divide_divide_rat @ A @ M2 ) @ C ) ) ) ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5092_image__affinity__atLeastAtMost__diff,axiom,
% 9.17/5.40 ! [A: rat,B: rat,M2: rat,C: rat] :
% 9.17/5.40 ( ( ( ( set_or633870826150836451st_rat @ A @ B )
% 9.17/5.40 = bot_bot_set_rat )
% 9.17/5.40 => ( ( image_rat_rat
% 9.17/5.40 @ ^ [X3: rat] : ( minus_minus_rat @ ( times_times_rat @ M2 @ X3 ) @ C )
% 9.17/5.40 @ ( set_or633870826150836451st_rat @ A @ B ) )
% 9.17/5.40 = bot_bot_set_rat ) )
% 9.17/5.40 & ( ( ( set_or633870826150836451st_rat @ A @ B )
% 9.17/5.40 != bot_bot_set_rat )
% 9.17/5.40 => ( ( ( ord_less_eq_rat @ zero_zero_rat @ M2 )
% 9.17/5.40 => ( ( image_rat_rat
% 9.17/5.40 @ ^ [X3: rat] : ( minus_minus_rat @ ( times_times_rat @ M2 @ X3 ) @ C )
% 9.17/5.40 @ ( set_or633870826150836451st_rat @ A @ B ) )
% 9.17/5.40 = ( set_or633870826150836451st_rat @ ( minus_minus_rat @ ( times_times_rat @ M2 @ A ) @ C ) @ ( minus_minus_rat @ ( times_times_rat @ M2 @ B ) @ C ) ) ) )
% 9.17/5.40 & ( ~ ( ord_less_eq_rat @ zero_zero_rat @ M2 )
% 9.17/5.40 => ( ( image_rat_rat
% 9.17/5.40 @ ^ [X3: rat] : ( minus_minus_rat @ ( times_times_rat @ M2 @ X3 ) @ C )
% 9.17/5.40 @ ( set_or633870826150836451st_rat @ A @ B ) )
% 9.17/5.40 = ( set_or633870826150836451st_rat @ ( minus_minus_rat @ ( times_times_rat @ M2 @ B ) @ C ) @ ( minus_minus_rat @ ( times_times_rat @ M2 @ A ) @ C ) ) ) ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5093_id__apply,axiom,
% 9.17/5.40 ( id_o
% 9.17/5.40 = ( ^ [X3: $o] : X3 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5094_id__apply,axiom,
% 9.17/5.40 ( id_nat
% 9.17/5.40 = ( ^ [X3: nat] : X3 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5095_id__apply,axiom,
% 9.17/5.40 ( id_nat_o
% 9.17/5.40 = ( ^ [X3: nat > $o] : X3 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5096_id__apply,axiom,
% 9.17/5.40 ( id_num
% 9.17/5.40 = ( ^ [X3: num] : X3 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5097_id__apply,axiom,
% 9.17/5.40 ( id_int
% 9.17/5.40 = ( ^ [X3: int] : X3 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5098_bijective__Empty,axiom,
% 9.17/5.40 biject3388518990857851981at_nat @ bot_bo228742789529271731at_nat ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5099_bijective__Empty,axiom,
% 9.17/5.40 bijective_nat_nat @ bot_bo2099793752762293965at_nat ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5100_image__id,axiom,
% 9.17/5.40 ( ( image_o_o @ id_o )
% 9.17/5.40 = id_set_o ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5101_image__id,axiom,
% 9.17/5.40 ( ( image_nat_o_nat_o @ id_nat_o )
% 9.17/5.40 = id_set_nat_o ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5102_image__id,axiom,
% 9.17/5.40 ( ( image_num_num @ id_num )
% 9.17/5.40 = id_set_num ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5103_image__id,axiom,
% 9.17/5.40 ( ( image_nat_nat @ id_nat )
% 9.17/5.40 = id_set_nat ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5104_image__id,axiom,
% 9.17/5.40 ( ( image_int_int @ id_int )
% 9.17/5.40 = id_set_int ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5105_fun_Omap__id,axiom,
% 9.17/5.40 ! [T: num > code_integer] :
% 9.17/5.40 ( ( comp_C3531382070062128313er_num @ id_Code_integer @ T )
% 9.17/5.40 = T ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5106_id__comp,axiom,
% 9.17/5.40 ! [G: num > code_integer] :
% 9.17/5.40 ( ( comp_C3531382070062128313er_num @ id_Code_integer @ G )
% 9.17/5.40 = G ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5107_comp__id,axiom,
% 9.17/5.40 ! [F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 9.17/5.40 ( ( comp_C1593894019821074884nteger @ F @ id_Code_integer )
% 9.17/5.40 = F ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5108_lessThan__0,axiom,
% 9.17/5.40 ( ( set_ord_lessThan_nat @ zero_zero_nat )
% 9.17/5.40 = bot_bot_set_nat ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5109_apsnd__id,axiom,
% 9.17/5.40 ( ( produc6499014454317279255nteger @ id_Code_integer )
% 9.17/5.40 = id_Pro2309048762231606924nteger ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5110_set__to__map__empty,axiom,
% 9.17/5.40 ( ( set_to4447731662395764663at_nat @ bot_bo228742789529271731at_nat )
% 9.17/5.40 = ( ^ [X3: set_Pr1261947904930325089at_nat] : none_s625347054029921090at_nat ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5111_set__to__map__empty,axiom,
% 9.17/5.40 ( ( set_to_map_nat_nat @ bot_bo2099793752762293965at_nat )
% 9.17/5.40 = ( ^ [X3: nat] : none_nat ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5112_atLeastatMost__empty__iff2,axiom,
% 9.17/5.40 ! [A: $o,B: $o] :
% 9.17/5.40 ( ( bot_bot_set_o
% 9.17/5.40 = ( set_or8904488021354931149Most_o @ A @ B ) )
% 9.17/5.40 = ( ~ ( ord_less_eq_o @ A @ B ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5113_atLeastatMost__empty__iff2,axiom,
% 9.17/5.40 ! [A: set_nat,B: set_nat] :
% 9.17/5.40 ( ( bot_bot_set_set_nat
% 9.17/5.40 = ( set_or4548717258645045905et_nat @ A @ B ) )
% 9.17/5.40 = ( ~ ( ord_less_eq_set_nat @ A @ B ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5114_atLeastatMost__empty__iff2,axiom,
% 9.17/5.40 ! [A: rat,B: rat] :
% 9.17/5.40 ( ( bot_bot_set_rat
% 9.17/5.40 = ( set_or633870826150836451st_rat @ A @ B ) )
% 9.17/5.40 = ( ~ ( ord_less_eq_rat @ A @ B ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5115_atLeastatMost__empty__iff2,axiom,
% 9.17/5.40 ! [A: num,B: num] :
% 9.17/5.40 ( ( bot_bot_set_num
% 9.17/5.40 = ( set_or7049704709247886629st_num @ A @ B ) )
% 9.17/5.40 = ( ~ ( ord_less_eq_num @ A @ B ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5116_atLeastatMost__empty__iff2,axiom,
% 9.17/5.40 ! [A: int,B: int] :
% 9.17/5.40 ( ( bot_bot_set_int
% 9.17/5.40 = ( set_or1266510415728281911st_int @ A @ B ) )
% 9.17/5.40 = ( ~ ( ord_less_eq_int @ A @ B ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5117_atLeastatMost__empty__iff2,axiom,
% 9.17/5.40 ! [A: nat,B: nat] :
% 9.17/5.40 ( ( bot_bot_set_nat
% 9.17/5.40 = ( set_or1269000886237332187st_nat @ A @ B ) )
% 9.17/5.40 = ( ~ ( ord_less_eq_nat @ A @ B ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5118_atLeastatMost__empty__iff2,axiom,
% 9.17/5.40 ! [A: code_integer,B: code_integer] :
% 9.17/5.40 ( ( bot_bo3990330152332043303nteger
% 9.17/5.40 = ( set_or189985376899183464nteger @ A @ B ) )
% 9.17/5.40 = ( ~ ( ord_le3102999989581377725nteger @ A @ B ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5119_atLeastatMost__empty__iff,axiom,
% 9.17/5.40 ! [A: $o,B: $o] :
% 9.17/5.40 ( ( ( set_or8904488021354931149Most_o @ A @ B )
% 9.17/5.40 = bot_bot_set_o )
% 9.17/5.40 = ( ~ ( ord_less_eq_o @ A @ B ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5120_atLeastatMost__empty__iff,axiom,
% 9.17/5.40 ! [A: set_nat,B: set_nat] :
% 9.17/5.40 ( ( ( set_or4548717258645045905et_nat @ A @ B )
% 9.17/5.40 = bot_bot_set_set_nat )
% 9.17/5.40 = ( ~ ( ord_less_eq_set_nat @ A @ B ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5121_atLeastatMost__empty__iff,axiom,
% 9.17/5.40 ! [A: rat,B: rat] :
% 9.17/5.40 ( ( ( set_or633870826150836451st_rat @ A @ B )
% 9.17/5.40 = bot_bot_set_rat )
% 9.17/5.40 = ( ~ ( ord_less_eq_rat @ A @ B ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5122_atLeastatMost__empty__iff,axiom,
% 9.17/5.40 ! [A: num,B: num] :
% 9.17/5.40 ( ( ( set_or7049704709247886629st_num @ A @ B )
% 9.17/5.40 = bot_bot_set_num )
% 9.17/5.40 = ( ~ ( ord_less_eq_num @ A @ B ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5123_atLeastatMost__empty__iff,axiom,
% 9.17/5.40 ! [A: int,B: int] :
% 9.17/5.40 ( ( ( set_or1266510415728281911st_int @ A @ B )
% 9.17/5.40 = bot_bot_set_int )
% 9.17/5.40 = ( ~ ( ord_less_eq_int @ A @ B ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5124_atLeastatMost__empty__iff,axiom,
% 9.17/5.40 ! [A: nat,B: nat] :
% 9.17/5.40 ( ( ( set_or1269000886237332187st_nat @ A @ B )
% 9.17/5.40 = bot_bot_set_nat )
% 9.17/5.40 = ( ~ ( ord_less_eq_nat @ A @ B ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5125_atLeastatMost__empty__iff,axiom,
% 9.17/5.40 ! [A: code_integer,B: code_integer] :
% 9.17/5.40 ( ( ( set_or189985376899183464nteger @ A @ B )
% 9.17/5.40 = bot_bo3990330152332043303nteger )
% 9.17/5.40 = ( ~ ( ord_le3102999989581377725nteger @ A @ B ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5126_atLeastatMost__empty,axiom,
% 9.17/5.40 ! [B: $o,A: $o] :
% 9.17/5.40 ( ( ord_less_o @ B @ A )
% 9.17/5.40 => ( ( set_or8904488021354931149Most_o @ A @ B )
% 9.17/5.40 = bot_bot_set_o ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5127_atLeastatMost__empty,axiom,
% 9.17/5.40 ! [B: rat,A: rat] :
% 9.17/5.40 ( ( ord_less_rat @ B @ A )
% 9.17/5.40 => ( ( set_or633870826150836451st_rat @ A @ B )
% 9.17/5.40 = bot_bot_set_rat ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5128_atLeastatMost__empty,axiom,
% 9.17/5.40 ! [B: num,A: num] :
% 9.17/5.40 ( ( ord_less_num @ B @ A )
% 9.17/5.40 => ( ( set_or7049704709247886629st_num @ A @ B )
% 9.17/5.40 = bot_bot_set_num ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5129_atLeastatMost__empty,axiom,
% 9.17/5.40 ! [B: int,A: int] :
% 9.17/5.40 ( ( ord_less_int @ B @ A )
% 9.17/5.40 => ( ( set_or1266510415728281911st_int @ A @ B )
% 9.17/5.40 = bot_bot_set_int ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5130_atLeastatMost__empty,axiom,
% 9.17/5.40 ! [B: nat,A: nat] :
% 9.17/5.40 ( ( ord_less_nat @ B @ A )
% 9.17/5.40 => ( ( set_or1269000886237332187st_nat @ A @ B )
% 9.17/5.40 = bot_bot_set_nat ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5131_atLeastatMost__empty,axiom,
% 9.17/5.40 ! [B: code_integer,A: code_integer] :
% 9.17/5.40 ( ( ord_le6747313008572928689nteger @ B @ A )
% 9.17/5.40 => ( ( set_or189985376899183464nteger @ A @ B )
% 9.17/5.40 = bot_bo3990330152332043303nteger ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5132_atLeastLessThan__empty,axiom,
% 9.17/5.40 ! [B: $o,A: $o] :
% 9.17/5.40 ( ( ord_less_eq_o @ B @ A )
% 9.17/5.40 => ( ( set_or7139685690850216873Than_o @ A @ B )
% 9.17/5.40 = bot_bot_set_o ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5133_atLeastLessThan__empty,axiom,
% 9.17/5.40 ! [B: set_nat,A: set_nat] :
% 9.17/5.40 ( ( ord_less_eq_set_nat @ B @ A )
% 9.17/5.40 => ( ( set_or3540276404033026485et_nat @ A @ B )
% 9.17/5.40 = bot_bot_set_set_nat ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5134_atLeastLessThan__empty,axiom,
% 9.17/5.40 ! [B: rat,A: rat] :
% 9.17/5.40 ( ( ord_less_eq_rat @ B @ A )
% 9.17/5.40 => ( ( set_or4029947393144176647an_rat @ A @ B )
% 9.17/5.40 = bot_bot_set_rat ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5135_atLeastLessThan__empty,axiom,
% 9.17/5.40 ! [B: num,A: num] :
% 9.17/5.40 ( ( ord_less_eq_num @ B @ A )
% 9.17/5.40 => ( ( set_or1222409239386451017an_num @ A @ B )
% 9.17/5.40 = bot_bot_set_num ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5136_atLeastLessThan__empty,axiom,
% 9.17/5.40 ! [B: nat,A: nat] :
% 9.17/5.40 ( ( ord_less_eq_nat @ B @ A )
% 9.17/5.40 => ( ( set_or4665077453230672383an_nat @ A @ B )
% 9.17/5.40 = bot_bot_set_nat ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5137_atLeastLessThan__empty,axiom,
% 9.17/5.40 ! [B: code_integer,A: code_integer] :
% 9.17/5.40 ( ( ord_le3102999989581377725nteger @ B @ A )
% 9.17/5.40 => ( ( set_or8404916559141939852nteger @ A @ B )
% 9.17/5.40 = bot_bo3990330152332043303nteger ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5138_atLeastLessThan__empty,axiom,
% 9.17/5.40 ! [B: int,A: int] :
% 9.17/5.40 ( ( ord_less_eq_int @ B @ A )
% 9.17/5.40 => ( ( set_or4662586982721622107an_int @ A @ B )
% 9.17/5.40 = bot_bot_set_int ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5139_atLeastLessThan__empty__iff,axiom,
% 9.17/5.40 ! [A: $o,B: $o] :
% 9.17/5.40 ( ( ( set_or7139685690850216873Than_o @ A @ B )
% 9.17/5.40 = bot_bot_set_o )
% 9.17/5.40 = ( ~ ( ord_less_o @ A @ B ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5140_atLeastLessThan__empty__iff,axiom,
% 9.17/5.40 ! [A: rat,B: rat] :
% 9.17/5.40 ( ( ( set_or4029947393144176647an_rat @ A @ B )
% 9.17/5.40 = bot_bot_set_rat )
% 9.17/5.40 = ( ~ ( ord_less_rat @ A @ B ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5141_atLeastLessThan__empty__iff,axiom,
% 9.17/5.40 ! [A: num,B: num] :
% 9.17/5.40 ( ( ( set_or1222409239386451017an_num @ A @ B )
% 9.17/5.40 = bot_bot_set_num )
% 9.17/5.40 = ( ~ ( ord_less_num @ A @ B ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5142_atLeastLessThan__empty__iff,axiom,
% 9.17/5.40 ! [A: nat,B: nat] :
% 9.17/5.40 ( ( ( set_or4665077453230672383an_nat @ A @ B )
% 9.17/5.40 = bot_bot_set_nat )
% 9.17/5.40 = ( ~ ( ord_less_nat @ A @ B ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5143_atLeastLessThan__empty__iff,axiom,
% 9.17/5.40 ! [A: code_integer,B: code_integer] :
% 9.17/5.40 ( ( ( set_or8404916559141939852nteger @ A @ B )
% 9.17/5.40 = bot_bo3990330152332043303nteger )
% 9.17/5.40 = ( ~ ( ord_le6747313008572928689nteger @ A @ B ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5144_atLeastLessThan__empty__iff,axiom,
% 9.17/5.40 ! [A: int,B: int] :
% 9.17/5.40 ( ( ( set_or4662586982721622107an_int @ A @ B )
% 9.17/5.40 = bot_bot_set_int )
% 9.17/5.40 = ( ~ ( ord_less_int @ A @ B ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5145_atLeastLessThan__empty__iff2,axiom,
% 9.17/5.40 ! [A: $o,B: $o] :
% 9.17/5.40 ( ( bot_bot_set_o
% 9.17/5.40 = ( set_or7139685690850216873Than_o @ A @ B ) )
% 9.17/5.40 = ( ~ ( ord_less_o @ A @ B ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5146_atLeastLessThan__empty__iff2,axiom,
% 9.17/5.40 ! [A: rat,B: rat] :
% 9.17/5.40 ( ( bot_bot_set_rat
% 9.17/5.40 = ( set_or4029947393144176647an_rat @ A @ B ) )
% 9.17/5.40 = ( ~ ( ord_less_rat @ A @ B ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5147_atLeastLessThan__empty__iff2,axiom,
% 9.17/5.40 ! [A: num,B: num] :
% 9.17/5.40 ( ( bot_bot_set_num
% 9.17/5.40 = ( set_or1222409239386451017an_num @ A @ B ) )
% 9.17/5.40 = ( ~ ( ord_less_num @ A @ B ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5148_atLeastLessThan__empty__iff2,axiom,
% 9.17/5.40 ! [A: nat,B: nat] :
% 9.17/5.40 ( ( bot_bot_set_nat
% 9.17/5.40 = ( set_or4665077453230672383an_nat @ A @ B ) )
% 9.17/5.40 = ( ~ ( ord_less_nat @ A @ B ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5149_atLeastLessThan__empty__iff2,axiom,
% 9.17/5.40 ! [A: code_integer,B: code_integer] :
% 9.17/5.40 ( ( bot_bo3990330152332043303nteger
% 9.17/5.40 = ( set_or8404916559141939852nteger @ A @ B ) )
% 9.17/5.40 = ( ~ ( ord_le6747313008572928689nteger @ A @ B ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5150_atLeastLessThan__empty__iff2,axiom,
% 9.17/5.40 ! [A: int,B: int] :
% 9.17/5.40 ( ( bot_bot_set_int
% 9.17/5.40 = ( set_or4662586982721622107an_int @ A @ B ) )
% 9.17/5.40 = ( ~ ( ord_less_int @ A @ B ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5151_prod_Oempty,axiom,
% 9.17/5.40 ! [G: $o > code_integer] :
% 9.17/5.40 ( ( groups7694694392188491536nteger @ G @ bot_bot_set_o )
% 9.17/5.40 = one_one_Code_integer ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5152_prod_Oempty,axiom,
% 9.17/5.40 ! [G: $o > assn] :
% 9.17/5.40 ( ( groups5301882518646026715o_assn @ G @ bot_bot_set_o )
% 9.17/5.40 = one_one_assn ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5153_prod_Oempty,axiom,
% 9.17/5.40 ! [G: $o > rat] :
% 9.17/5.40 ( ( groups2869687844427037835_o_rat @ G @ bot_bot_set_o )
% 9.17/5.40 = one_one_rat ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5154_prod_Oempty,axiom,
% 9.17/5.40 ! [G: $o > nat] :
% 9.17/5.40 ( ( groups3504817904513533571_o_nat @ G @ bot_bot_set_o )
% 9.17/5.40 = one_one_nat ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5155_prod_Oempty,axiom,
% 9.17/5.40 ! [G: $o > int] :
% 9.17/5.40 ( ( groups3502327434004483295_o_int @ G @ bot_bot_set_o )
% 9.17/5.40 = one_one_int ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5156_prod_Oempty,axiom,
% 9.17/5.40 ! [G: nat > code_integer] :
% 9.17/5.40 ( ( groups3455450783089532116nteger @ G @ bot_bot_set_nat )
% 9.17/5.40 = one_one_Code_integer ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5157_prod_Oempty,axiom,
% 9.17/5.40 ! [G: nat > assn] :
% 9.17/5.40 ( ( groups6906906614972039071t_assn @ G @ bot_bot_set_nat )
% 9.17/5.40 = one_one_assn ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5158_prod_Oempty,axiom,
% 9.17/5.40 ! [G: nat > rat] :
% 9.17/5.40 ( ( groups73079841787564623at_rat @ G @ bot_bot_set_nat )
% 9.17/5.40 = one_one_rat ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5159_prod_Oempty,axiom,
% 9.17/5.40 ! [G: int > code_integer] :
% 9.17/5.40 ( ( groups3827104343326376752nteger @ G @ bot_bot_set_int )
% 9.17/5.40 = one_one_Code_integer ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5160_prod_Oempty,axiom,
% 9.17/5.40 ! [G: int > assn] :
% 9.17/5.40 ( ( groups7882442080178216443t_assn @ G @ bot_bot_set_int )
% 9.17/5.40 = one_one_assn ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5161_group__add__class_Ominus__comp__minus,axiom,
% 9.17/5.40 ( ( comp_int_int_int @ uminus_uminus_int @ uminus_uminus_int )
% 9.17/5.40 = id_int ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5162_group__add__class_Ominus__comp__minus,axiom,
% 9.17/5.40 ( ( comp_C7449957260575251196nteger @ uminus1351360451143612070nteger @ uminus1351360451143612070nteger )
% 9.17/5.40 = id_Code_integer ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5163_group__add__class_Ominus__comp__minus,axiom,
% 9.17/5.40 ( ( comp_rat_rat_rat @ uminus_uminus_rat @ uminus_uminus_rat )
% 9.17/5.40 = id_rat ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5164_boolean__algebra__class_Ominus__comp__minus,axiom,
% 9.17/5.40 ( ( comp_o_o_o @ uminus_uminus_o @ uminus_uminus_o )
% 9.17/5.40 = id_o ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5165_boolean__algebra__class_Ominus__comp__minus,axiom,
% 9.17/5.40 ( ( comp_n5656820349209612572_nat_o @ uminus_uminus_nat_o @ uminus_uminus_nat_o )
% 9.17/5.40 = id_nat_o ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5166_boolean__algebra__class_Ominus__comp__minus,axiom,
% 9.17/5.40 ( ( comp_P7645380973975430442t_unit @ uminus2952777764628376836t_unit @ uminus2952777764628376836t_unit )
% 9.17/5.40 = id_Product_unit ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5167_rel__of__empty,axiom,
% 9.17/5.40 ! [P: produc3843707927480180839at_nat > $o] :
% 9.17/5.40 ( ( rel_of6563097375766832824at_nat
% 9.17/5.40 @ ^ [X3: set_Pr1261947904930325089at_nat] : none_s625347054029921090at_nat
% 9.17/5.40 @ P )
% 9.17/5.40 = bot_bo228742789529271731at_nat ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5168_rel__of__empty,axiom,
% 9.17/5.40 ! [P: product_prod_nat_nat > $o] :
% 9.17/5.40 ( ( rel_of_nat_nat
% 9.17/5.40 @ ^ [X3: nat] : none_nat
% 9.17/5.40 @ P )
% 9.17/5.40 = bot_bo2099793752762293965at_nat ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5169_comp__the__Some,axiom,
% 9.17/5.40 ( ( comp_option_o_o_o @ the_o @ some_o )
% 9.17/5.40 = id_o ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5170_comp__the__Some,axiom,
% 9.17/5.40 ( ( comp_o4663963155070737957at_nat @ the_nat @ some_nat )
% 9.17/5.40 = id_nat ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5171_comp__the__Some,axiom,
% 9.17/5.40 ( ( comp_o8860755393669798242_nat_o @ the_nat_o @ some_nat_o )
% 9.17/5.40 = id_nat_o ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5172_comp__the__Some,axiom,
% 9.17/5.40 ( ( comp_o2446264010603541305nt_int @ the_int2 @ some_int )
% 9.17/5.40 = id_int ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5173_comp__the__Some,axiom,
% 9.17/5.40 ( ( comp_o6342398210560591875um_num @ the_num @ some_num )
% 9.17/5.40 = id_num ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5174_comp__the__Some,axiom,
% 9.17/5.40 ( ( comp_o279924169626513613it_nat @ the_Pr7776125533777466484it_nat @ some_P1914260805536162275it_nat )
% 9.17/5.40 = id_Pro1159712480615372887it_nat ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5175_fun_Omap__id0,axiom,
% 9.17/5.40 ( ( comp_o_o_nat @ id_o )
% 9.17/5.40 = id_nat_o ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5176_fun_Omap__id0,axiom,
% 9.17/5.40 ( ( comp_C3531382070062128313er_num @ id_Code_integer )
% 9.17/5.40 = id_num_Code_integer ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5177_Iio__eq__empty__iff,axiom,
% 9.17/5.40 ! [N2: $o] :
% 9.17/5.40 ( ( ( set_ord_lessThan_o @ N2 )
% 9.17/5.40 = bot_bot_set_o )
% 9.17/5.40 = ( N2 = bot_bot_o ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5178_Iio__eq__empty__iff,axiom,
% 9.17/5.40 ! [N2: nat] :
% 9.17/5.40 ( ( ( set_ord_lessThan_nat @ N2 )
% 9.17/5.40 = bot_bot_set_nat )
% 9.17/5.40 = ( N2 = bot_bot_nat ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5179_option_Omap__id0,axiom,
% 9.17/5.40 ( ( map_option_o_o @ id_o )
% 9.17/5.40 = id_option_o ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5180_option_Omap__id0,axiom,
% 9.17/5.40 ( ( map_option_nat_nat @ id_nat )
% 9.17/5.40 = id_option_nat ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5181_option_Omap__id0,axiom,
% 9.17/5.40 ( ( map_op6424164270877473355_nat_o @ id_nat_o )
% 9.17/5.40 = id_option_nat_o ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5182_option_Omap__id0,axiom,
% 9.17/5.40 ( ( map_option_int_int @ id_int )
% 9.17/5.40 = id_option_int ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5183_option_Omap__id0,axiom,
% 9.17/5.40 ( ( map_option_num_num @ id_num )
% 9.17/5.40 = id_option_num ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5184_set__notEmptyE,axiom,
% 9.17/5.40 ! [S2: set_Pr4329608150637261639at_nat] :
% 9.17/5.40 ( ( S2 != bot_bo228742789529271731at_nat )
% 9.17/5.40 => ~ ! [X4: produc3843707927480180839at_nat] :
% 9.17/5.40 ~ ( member8757157785044589968at_nat @ X4 @ S2 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5185_set__notEmptyE,axiom,
% 9.17/5.40 ! [S2: set_Pr1261947904930325089at_nat] :
% 9.17/5.40 ( ( S2 != bot_bo2099793752762293965at_nat )
% 9.17/5.40 => ~ ! [X4: product_prod_nat_nat] :
% 9.17/5.40 ~ ( member8440522571783428010at_nat @ X4 @ S2 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5186_set__notEmptyE,axiom,
% 9.17/5.40 ! [S2: set_o] :
% 9.17/5.40 ( ( S2 != bot_bot_set_o )
% 9.17/5.40 => ~ ! [X4: $o] :
% 9.17/5.40 ~ ( member_o @ X4 @ S2 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5187_set__notEmptyE,axiom,
% 9.17/5.40 ! [S2: set_nat] :
% 9.17/5.40 ( ( S2 != bot_bot_set_nat )
% 9.17/5.40 => ~ ! [X4: nat] :
% 9.17/5.40 ~ ( member_nat @ X4 @ S2 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5188_set__notEmptyE,axiom,
% 9.17/5.40 ! [S2: set_int] :
% 9.17/5.40 ( ( S2 != bot_bot_set_int )
% 9.17/5.40 => ~ ! [X4: int] :
% 9.17/5.40 ~ ( member_int @ X4 @ S2 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5189_memb__imp__not__empty,axiom,
% 9.17/5.40 ! [X: produc3843707927480180839at_nat,S2: set_Pr4329608150637261639at_nat] :
% 9.17/5.40 ( ( member8757157785044589968at_nat @ X @ S2 )
% 9.17/5.40 => ( S2 != bot_bo228742789529271731at_nat ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5190_memb__imp__not__empty,axiom,
% 9.17/5.40 ! [X: product_prod_nat_nat,S2: set_Pr1261947904930325089at_nat] :
% 9.17/5.40 ( ( member8440522571783428010at_nat @ X @ S2 )
% 9.17/5.40 => ( S2 != bot_bo2099793752762293965at_nat ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5191_memb__imp__not__empty,axiom,
% 9.17/5.40 ! [X: $o,S2: set_o] :
% 9.17/5.40 ( ( member_o @ X @ S2 )
% 9.17/5.40 => ( S2 != bot_bot_set_o ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5192_memb__imp__not__empty,axiom,
% 9.17/5.40 ! [X: nat,S2: set_nat] :
% 9.17/5.40 ( ( member_nat @ X @ S2 )
% 9.17/5.40 => ( S2 != bot_bot_set_nat ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5193_memb__imp__not__empty,axiom,
% 9.17/5.40 ! [X: int,S2: set_int] :
% 9.17/5.40 ( ( member_int @ X @ S2 )
% 9.17/5.40 => ( S2 != bot_bot_set_int ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5194_id__def,axiom,
% 9.17/5.40 ( id_o
% 9.17/5.40 = ( ^ [X3: $o] : X3 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5195_id__def,axiom,
% 9.17/5.40 ( id_nat
% 9.17/5.40 = ( ^ [X3: nat] : X3 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5196_id__def,axiom,
% 9.17/5.40 ( id_nat_o
% 9.17/5.40 = ( ^ [X3: nat > $o] : X3 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5197_id__def,axiom,
% 9.17/5.40 ( id_num
% 9.17/5.40 = ( ^ [X3: num] : X3 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5198_id__def,axiom,
% 9.17/5.40 ( id_int
% 9.17/5.40 = ( ^ [X3: int] : X3 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5199_eq__id__iff,axiom,
% 9.17/5.40 ! [F: $o > $o] :
% 9.17/5.40 ( ( ! [X3: $o] :
% 9.17/5.40 ( ( F @ X3 )
% 9.17/5.40 = X3 ) )
% 9.17/5.40 = ( F = id_o ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5200_eq__id__iff,axiom,
% 9.17/5.40 ! [F: nat > nat] :
% 9.17/5.40 ( ( ! [X3: nat] :
% 9.17/5.40 ( ( F @ X3 )
% 9.17/5.40 = X3 ) )
% 9.17/5.40 = ( F = id_nat ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5201_eq__id__iff,axiom,
% 9.17/5.40 ! [F: ( nat > $o ) > nat > $o] :
% 9.17/5.40 ( ( ! [X3: nat > $o] :
% 9.17/5.40 ( ( F @ X3 )
% 9.17/5.40 = X3 ) )
% 9.17/5.40 = ( F = id_nat_o ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5202_eq__id__iff,axiom,
% 9.17/5.40 ! [F: num > num] :
% 9.17/5.40 ( ( ! [X3: num] :
% 9.17/5.40 ( ( F @ X3 )
% 9.17/5.40 = X3 ) )
% 9.17/5.40 = ( F = id_num ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5203_eq__id__iff,axiom,
% 9.17/5.40 ! [F: int > int] :
% 9.17/5.40 ( ( ! [X3: int] :
% 9.17/5.40 ( ( F @ X3 )
% 9.17/5.40 = X3 ) )
% 9.17/5.40 = ( F = id_int ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5204_comp__eq__id__dest,axiom,
% 9.17/5.40 ! [A: code_integer > code_integer,B: num > code_integer,C: num > code_integer,V: num] :
% 9.17/5.40 ( ( ( comp_C3531382070062128313er_num @ A @ B )
% 9.17/5.40 = ( comp_C3531382070062128313er_num @ id_Code_integer @ C ) )
% 9.17/5.40 => ( ( A @ ( B @ V ) )
% 9.17/5.40 = ( C @ V ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5205_comp__eq__id__dest,axiom,
% 9.17/5.40 ! [A: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,B: code_integer > code_integer,C: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,V: code_integer] :
% 9.17/5.40 ( ( ( comp_C1593894019821074884nteger @ A @ B )
% 9.17/5.40 = ( comp_P3928908779438215820nteger @ id_Pro496765588584934260nteger @ C ) )
% 9.17/5.40 => ( ( A @ ( B @ V ) )
% 9.17/5.40 = ( C @ V ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5206_comp__eq__id__dest,axiom,
% 9.17/5.40 ! [A: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,B: code_integer > code_integer > code_integer,C: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,V: code_integer] :
% 9.17/5.40 ( ( ( comp_C8797469213163452608nteger @ A @ B )
% 9.17/5.40 = ( comp_P3928908779438215820nteger @ id_Pro496765588584934260nteger @ C ) )
% 9.17/5.40 => ( ( A @ ( B @ V ) )
% 9.17/5.40 = ( C @ V ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5207_comp__eq__id__dest,axiom,
% 9.17/5.40 ! [A: nat > num,B: int > nat,C: int > num,V: int] :
% 9.17/5.40 ( ( ( comp_nat_num_int @ A @ B )
% 9.17/5.40 = ( comp_num_num_int @ id_num @ C ) )
% 9.17/5.40 => ( ( A @ ( B @ V ) )
% 9.17/5.40 = ( C @ V ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5208_option_Omap__id,axiom,
% 9.17/5.40 ! [T: option_o] :
% 9.17/5.40 ( ( map_option_o_o @ id_o @ T )
% 9.17/5.40 = T ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5209_option_Omap__id,axiom,
% 9.17/5.40 ! [T: option_nat] :
% 9.17/5.40 ( ( map_option_nat_nat @ id_nat @ T )
% 9.17/5.40 = T ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5210_option_Omap__id,axiom,
% 9.17/5.40 ! [T: option_nat_o] :
% 9.17/5.40 ( ( map_op6424164270877473355_nat_o @ id_nat_o @ T )
% 9.17/5.40 = T ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5211_option_Omap__id,axiom,
% 9.17/5.40 ! [T: option_int] :
% 9.17/5.40 ( ( map_option_int_int @ id_int @ T )
% 9.17/5.40 = T ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5212_option_Omap__id,axiom,
% 9.17/5.40 ! [T: option_num] :
% 9.17/5.40 ( ( map_option_num_num @ id_num @ T )
% 9.17/5.40 = T ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5213_not__empty__eq__Iic__eq__empty,axiom,
% 9.17/5.40 ! [H3: $o] :
% 9.17/5.40 ( bot_bot_set_o
% 9.17/5.40 != ( set_ord_atMost_o @ H3 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5214_not__empty__eq__Iic__eq__empty,axiom,
% 9.17/5.40 ! [H3: int] :
% 9.17/5.40 ( bot_bot_set_int
% 9.17/5.40 != ( set_ord_atMost_int @ H3 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5215_not__empty__eq__Iic__eq__empty,axiom,
% 9.17/5.40 ! [H3: nat] :
% 9.17/5.40 ( bot_bot_set_nat
% 9.17/5.40 != ( set_ord_atMost_nat @ H3 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5216_lessThan__non__empty,axiom,
% 9.17/5.40 ! [X: int] :
% 9.17/5.40 ( ( set_ord_lessThan_int @ X )
% 9.17/5.40 != bot_bot_set_int ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5217_subset__minus__empty,axiom,
% 9.17/5.40 ! [A2: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat] :
% 9.17/5.40 ( ( ord_le1268244103169919719at_nat @ A2 @ B5 )
% 9.17/5.40 => ( ( minus_3314409938677909166at_nat @ A2 @ B5 )
% 9.17/5.40 = bot_bo228742789529271731at_nat ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5218_subset__minus__empty,axiom,
% 9.17/5.40 ! [A2: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 9.17/5.40 ( ( ord_le3146513528884898305at_nat @ A2 @ B5 )
% 9.17/5.40 => ( ( minus_1356011639430497352at_nat @ A2 @ B5 )
% 9.17/5.40 = bot_bo2099793752762293965at_nat ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5219_subset__minus__empty,axiom,
% 9.17/5.40 ! [A2: set_o,B5: set_o] :
% 9.17/5.40 ( ( ord_less_eq_set_o @ A2 @ B5 )
% 9.17/5.40 => ( ( minus_minus_set_o @ A2 @ B5 )
% 9.17/5.40 = bot_bot_set_o ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5220_subset__minus__empty,axiom,
% 9.17/5.40 ! [A2: set_int,B5: set_int] :
% 9.17/5.40 ( ( ord_less_eq_set_int @ A2 @ B5 )
% 9.17/5.40 => ( ( minus_minus_set_int @ A2 @ B5 )
% 9.17/5.40 = bot_bot_set_int ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5221_subset__minus__empty,axiom,
% 9.17/5.40 ! [A2: set_nat,B5: set_nat] :
% 9.17/5.40 ( ( ord_less_eq_set_nat @ A2 @ B5 )
% 9.17/5.40 => ( ( minus_minus_set_nat @ A2 @ B5 )
% 9.17/5.40 = bot_bot_set_nat ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5222_atLeastLessThan0,axiom,
% 9.17/5.40 ! [M2: nat] :
% 9.17/5.40 ( ( set_or4665077453230672383an_nat @ M2 @ zero_zero_nat )
% 9.17/5.40 = bot_bot_set_nat ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5223_lessThan__empty__iff,axiom,
% 9.17/5.40 ! [N2: nat] :
% 9.17/5.40 ( ( ( set_ord_lessThan_nat @ N2 )
% 9.17/5.40 = bot_bot_set_nat )
% 9.17/5.40 = ( N2 = zero_zero_nat ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5224_set__to__map__empty__iff_I1_J,axiom,
% 9.17/5.40 ! [S2: set_Pr4329608150637261639at_nat] :
% 9.17/5.40 ( ( ( set_to4447731662395764663at_nat @ S2 )
% 9.17/5.40 = ( ^ [X3: set_Pr1261947904930325089at_nat] : none_s625347054029921090at_nat ) )
% 9.17/5.40 = ( S2 = bot_bo228742789529271731at_nat ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5225_set__to__map__empty__iff_I1_J,axiom,
% 9.17/5.40 ! [S2: set_Pr1261947904930325089at_nat] :
% 9.17/5.40 ( ( ( set_to_map_nat_nat @ S2 )
% 9.17/5.40 = ( ^ [X3: nat] : none_nat ) )
% 9.17/5.40 = ( S2 = bot_bo2099793752762293965at_nat ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5226_Code__Numeral_Osub__code_I1_J,axiom,
% 9.17/5.40 ( ( code_sub @ one @ one )
% 9.17/5.40 = zero_z3403309356797280102nteger ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5227_set__to__map__empty__iff_I2_J,axiom,
% 9.17/5.40 ! [S2: set_Pr4329608150637261639at_nat] :
% 9.17/5.40 ( ( ( ^ [X3: set_Pr1261947904930325089at_nat] : none_s625347054029921090at_nat )
% 9.17/5.40 = ( set_to4447731662395764663at_nat @ S2 ) )
% 9.17/5.40 = ( S2 = bot_bo228742789529271731at_nat ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5228_set__to__map__empty__iff_I2_J,axiom,
% 9.17/5.40 ! [S2: set_Pr1261947904930325089at_nat] :
% 9.17/5.40 ( ( ( ^ [X3: nat] : none_nat )
% 9.17/5.40 = ( set_to_map_nat_nat @ S2 ) )
% 9.17/5.40 = ( S2 = bot_bo2099793752762293965at_nat ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5229_less__integer__def,axiom,
% 9.17/5.40 ( ord_le6747313008572928689nteger
% 9.17/5.40 = ( map_fu2496120808607739376eger_o @ code_int_of_integer @ ( map_fu6957801986076833569nt_o_o @ code_int_of_integer @ id_o ) @ ord_less_int ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5230_less__eq__integer__def,axiom,
% 9.17/5.40 ( ord_le3102999989581377725nteger
% 9.17/5.40 = ( map_fu2496120808607739376eger_o @ code_int_of_integer @ ( map_fu6957801986076833569nt_o_o @ code_int_of_integer @ id_o ) @ ord_less_eq_int ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5231_Code__Numeral_Osub__code_I6_J,axiom,
% 9.17/5.40 ! [M2: num,N2: num] :
% 9.17/5.40 ( ( code_sub @ ( bit0 @ M2 ) @ ( bit0 @ N2 ) )
% 9.17/5.40 = ( code_dup @ ( code_sub @ M2 @ N2 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5232_Code__Numeral_Osub__code_I7_J,axiom,
% 9.17/5.40 ! [M2: num,N2: num] :
% 9.17/5.40 ( ( code_sub @ ( bit1 @ M2 ) @ ( bit1 @ N2 ) )
% 9.17/5.40 = ( code_dup @ ( code_sub @ M2 @ N2 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5233_sub_Orep__eq,axiom,
% 9.17/5.40 ! [X: num,Xa: num] :
% 9.17/5.40 ( ( code_int_of_integer @ ( code_sub @ X @ Xa ) )
% 9.17/5.40 = ( minus_minus_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Xa ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5234_sub_Oabs__eq,axiom,
% 9.17/5.40 ( code_sub
% 9.17/5.40 = ( ^ [Xa4: num,X3: num] : ( code_integer_of_int @ ( minus_minus_int @ ( numeral_numeral_int @ Xa4 ) @ ( numeral_numeral_int @ X3 ) ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5235_image__mult__atLeastAtMost__if,axiom,
% 9.17/5.40 ! [C: rat,X: rat,Y: rat] :
% 9.17/5.40 ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 9.17/5.40 => ( ( image_rat_rat @ ( times_times_rat @ C ) @ ( set_or633870826150836451st_rat @ X @ Y ) )
% 9.17/5.40 = ( set_or633870826150836451st_rat @ ( times_times_rat @ C @ X ) @ ( times_times_rat @ C @ Y ) ) ) )
% 9.17/5.40 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 9.17/5.40 => ( ( ( ord_less_eq_rat @ X @ Y )
% 9.17/5.40 => ( ( image_rat_rat @ ( times_times_rat @ C ) @ ( set_or633870826150836451st_rat @ X @ Y ) )
% 9.17/5.40 = ( set_or633870826150836451st_rat @ ( times_times_rat @ C @ Y ) @ ( times_times_rat @ C @ X ) ) ) )
% 9.17/5.40 & ( ~ ( ord_less_eq_rat @ X @ Y )
% 9.17/5.40 => ( ( image_rat_rat @ ( times_times_rat @ C ) @ ( set_or633870826150836451st_rat @ X @ Y ) )
% 9.17/5.40 = bot_bot_set_rat ) ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5236_image__mult__atLeastAtMost__if_H,axiom,
% 9.17/5.40 ! [X: rat,Y: rat,C: rat] :
% 9.17/5.40 ( ( ( ord_less_eq_rat @ X @ Y )
% 9.17/5.40 => ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 9.17/5.40 => ( ( image_rat_rat
% 9.17/5.40 @ ^ [X3: rat] : ( times_times_rat @ X3 @ C )
% 9.17/5.40 @ ( set_or633870826150836451st_rat @ X @ Y ) )
% 9.17/5.40 = ( set_or633870826150836451st_rat @ ( times_times_rat @ X @ C ) @ ( times_times_rat @ Y @ C ) ) ) )
% 9.17/5.40 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 9.17/5.40 => ( ( image_rat_rat
% 9.17/5.40 @ ^ [X3: rat] : ( times_times_rat @ X3 @ C )
% 9.17/5.40 @ ( set_or633870826150836451st_rat @ X @ Y ) )
% 9.17/5.40 = ( set_or633870826150836451st_rat @ ( times_times_rat @ Y @ C ) @ ( times_times_rat @ X @ C ) ) ) ) ) )
% 9.17/5.40 & ( ~ ( ord_less_eq_rat @ X @ Y )
% 9.17/5.40 => ( ( image_rat_rat
% 9.17/5.40 @ ^ [X3: rat] : ( times_times_rat @ X3 @ C )
% 9.17/5.40 @ ( set_or633870826150836451st_rat @ X @ Y ) )
% 9.17/5.40 = bot_bot_set_rat ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5237_image__affinity__atLeastAtMost,axiom,
% 9.17/5.40 ! [A: rat,B: rat,M2: rat,C: rat] :
% 9.17/5.40 ( ( ( ( set_or633870826150836451st_rat @ A @ B )
% 9.17/5.40 = bot_bot_set_rat )
% 9.17/5.40 => ( ( image_rat_rat
% 9.17/5.40 @ ^ [X3: rat] : ( plus_plus_rat @ ( times_times_rat @ M2 @ X3 ) @ C )
% 9.17/5.40 @ ( set_or633870826150836451st_rat @ A @ B ) )
% 9.17/5.40 = bot_bot_set_rat ) )
% 9.17/5.40 & ( ( ( set_or633870826150836451st_rat @ A @ B )
% 9.17/5.40 != bot_bot_set_rat )
% 9.17/5.40 => ( ( ( ord_less_eq_rat @ zero_zero_rat @ M2 )
% 9.17/5.40 => ( ( image_rat_rat
% 9.17/5.40 @ ^ [X3: rat] : ( plus_plus_rat @ ( times_times_rat @ M2 @ X3 ) @ C )
% 9.17/5.40 @ ( set_or633870826150836451st_rat @ A @ B ) )
% 9.17/5.40 = ( set_or633870826150836451st_rat @ ( plus_plus_rat @ ( times_times_rat @ M2 @ A ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ M2 @ B ) @ C ) ) ) )
% 9.17/5.40 & ( ~ ( ord_less_eq_rat @ zero_zero_rat @ M2 )
% 9.17/5.40 => ( ( image_rat_rat
% 9.17/5.40 @ ^ [X3: rat] : ( plus_plus_rat @ ( times_times_rat @ M2 @ X3 ) @ C )
% 9.17/5.40 @ ( set_or633870826150836451st_rat @ A @ B ) )
% 9.17/5.40 = ( set_or633870826150836451st_rat @ ( plus_plus_rat @ ( times_times_rat @ M2 @ B ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ M2 @ A ) @ C ) ) ) ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5238_and__int_Osimps,axiom,
% 9.17/5.40 ( bit_se725231765392027082nd_int
% 9.17/5.40 = ( ^ [K4: int,L3: int] :
% 9.17/5.40 ( if_int
% 9.17/5.40 @ ( ( member_int @ K4 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 9.17/5.40 & ( member_int @ L3 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 9.17/5.40 @ ( uminus_uminus_int
% 9.17/5.40 @ ( zero_n2684676970156552555ol_int
% 9.17/5.40 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K4 )
% 9.17/5.40 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L3 ) ) ) )
% 9.17/5.40 @ ( plus_plus_int
% 9.17/5.40 @ ( zero_n2684676970156552555ol_int
% 9.17/5.40 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K4 )
% 9.17/5.40 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L3 ) ) )
% 9.17/5.40 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5239_and__int_Oelims,axiom,
% 9.17/5.40 ! [X: int,Xa: int,Y: int] :
% 9.17/5.40 ( ( ( bit_se725231765392027082nd_int @ X @ Xa )
% 9.17/5.40 = Y )
% 9.17/5.40 => ( ( ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 9.17/5.40 & ( member_int @ Xa @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 9.17/5.40 => ( Y
% 9.17/5.40 = ( uminus_uminus_int
% 9.17/5.40 @ ( zero_n2684676970156552555ol_int
% 9.17/5.40 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 9.17/5.40 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa ) ) ) ) ) )
% 9.17/5.40 & ( ~ ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 9.17/5.40 & ( member_int @ Xa @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 9.17/5.40 => ( Y
% 9.17/5.40 = ( plus_plus_int
% 9.17/5.40 @ ( zero_n2684676970156552555ol_int
% 9.17/5.40 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 9.17/5.40 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa ) ) )
% 9.17/5.40 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ X @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ Xa @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5240_and__int_Opelims,axiom,
% 9.17/5.40 ! [X: int,Xa: int,Y: int] :
% 9.17/5.40 ( ( ( bit_se725231765392027082nd_int @ X @ Xa )
% 9.17/5.40 = Y )
% 9.17/5.40 => ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X @ Xa ) )
% 9.17/5.40 => ~ ( ( ( ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 9.17/5.40 & ( member_int @ Xa @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 9.17/5.40 => ( Y
% 9.17/5.40 = ( uminus_uminus_int
% 9.17/5.40 @ ( zero_n2684676970156552555ol_int
% 9.17/5.40 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 9.17/5.40 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa ) ) ) ) ) )
% 9.17/5.40 & ( ~ ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 9.17/5.40 & ( member_int @ Xa @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 9.17/5.40 => ( Y
% 9.17/5.40 = ( plus_plus_int
% 9.17/5.40 @ ( zero_n2684676970156552555ol_int
% 9.17/5.40 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 9.17/5.40 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa ) ) )
% 9.17/5.40 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ X @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ Xa @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 9.17/5.40 => ~ ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X @ Xa ) ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5241_and__int_Opsimps,axiom,
% 9.17/5.40 ! [K: int,L: int] :
% 9.17/5.40 ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ K @ L ) )
% 9.17/5.40 => ( ( ( ( member_int @ K @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 9.17/5.40 & ( member_int @ L @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 9.17/5.40 => ( ( bit_se725231765392027082nd_int @ K @ L )
% 9.17/5.40 = ( uminus_uminus_int
% 9.17/5.40 @ ( zero_n2684676970156552555ol_int
% 9.17/5.40 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 9.17/5.40 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) ) ) ) )
% 9.17/5.40 & ( ~ ( ( member_int @ K @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 9.17/5.40 & ( member_int @ L @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 9.17/5.40 => ( ( bit_se725231765392027082nd_int @ K @ L )
% 9.17/5.40 = ( plus_plus_int
% 9.17/5.40 @ ( zero_n2684676970156552555ol_int
% 9.17/5.40 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 9.17/5.40 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) )
% 9.17/5.40 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5242_and__int_Opinduct,axiom,
% 9.17/5.40 ! [A0: int,A1: int,P: int > int > $o] :
% 9.17/5.40 ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ A0 @ A1 ) )
% 9.17/5.40 => ( ! [K5: int,L5: int] :
% 9.17/5.40 ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ K5 @ L5 ) )
% 9.17/5.40 => ( ( ~ ( ( member_int @ K5 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 9.17/5.40 & ( member_int @ L5 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 9.17/5.40 => ( P @ ( divide_divide_int @ K5 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L5 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 9.17/5.40 => ( P @ K5 @ L5 ) ) )
% 9.17/5.40 => ( P @ A0 @ A1 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5243_mask__mod__exp,axiom,
% 9.17/5.40 ! [N2: nat,M2: nat] :
% 9.17/5.40 ( ( modulo_modulo_int @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ one_one_int ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 ) )
% 9.17/5.40 = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( ord_min_nat @ M2 @ N2 ) ) @ one_one_int ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5244_mask__mod__exp,axiom,
% 9.17/5.40 ! [N2: nat,M2: nat] :
% 9.17/5.40 ( ( modulo_modulo_nat @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 9.17/5.40 = ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( ord_min_nat @ M2 @ N2 ) ) @ one_one_nat ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5245_mask__mod__exp,axiom,
% 9.17/5.40 ! [N2: nat,M2: nat] :
% 9.17/5.40 ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) @ one_one_Code_integer ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M2 ) )
% 9.17/5.40 = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( ord_min_nat @ M2 @ N2 ) ) @ one_one_Code_integer ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5246_mask__mod__exp,axiom,
% 9.17/5.40 ! [N2: nat,M2: nat] :
% 9.17/5.40 ( ( modulo8411746178871703098atural @ ( minus_7197305767214868737atural @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N2 ) @ one_one_Code_natural ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ M2 ) )
% 9.17/5.40 = ( minus_7197305767214868737atural @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( ord_min_nat @ M2 @ N2 ) ) @ one_one_Code_natural ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5247_pair__leqI2,axiom,
% 9.17/5.40 ! [A: nat,B: nat,S: nat,T: nat] :
% 9.17/5.40 ( ( ord_less_eq_nat @ A @ B )
% 9.17/5.40 => ( ( ord_less_eq_nat @ S @ T )
% 9.17/5.40 => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A @ S ) @ ( product_Pair_nat_nat @ B @ T ) ) @ fun_pair_leq ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5248_min__eq__arg_I1_J,axiom,
% 9.17/5.40 ! [M2: code_integer,N2: code_integer] :
% 9.17/5.40 ( ( ( ord_min_Code_integer @ M2 @ N2 )
% 9.17/5.40 = M2 )
% 9.17/5.40 = ( ord_le3102999989581377725nteger @ M2 @ N2 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5249_min__eq__arg_I1_J,axiom,
% 9.17/5.40 ! [M2: code_natural,N2: code_natural] :
% 9.17/5.40 ( ( ( ord_min_Code_natural @ M2 @ N2 )
% 9.17/5.40 = M2 )
% 9.17/5.40 = ( ord_le1926595141338095240atural @ M2 @ N2 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5250_min__eq__arg_I1_J,axiom,
% 9.17/5.40 ! [M2: rat,N2: rat] :
% 9.17/5.40 ( ( ( ord_min_rat @ M2 @ N2 )
% 9.17/5.40 = M2 )
% 9.17/5.40 = ( ord_less_eq_rat @ M2 @ N2 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5251_min__eq__arg_I1_J,axiom,
% 9.17/5.40 ! [M2: num,N2: num] :
% 9.17/5.40 ( ( ( ord_min_num @ M2 @ N2 )
% 9.17/5.40 = M2 )
% 9.17/5.40 = ( ord_less_eq_num @ M2 @ N2 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5252_min__eq__arg_I1_J,axiom,
% 9.17/5.40 ! [M2: nat,N2: nat] :
% 9.17/5.40 ( ( ( ord_min_nat @ M2 @ N2 )
% 9.17/5.40 = M2 )
% 9.17/5.40 = ( ord_less_eq_nat @ M2 @ N2 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5253_min__eq__arg_I1_J,axiom,
% 9.17/5.40 ! [M2: int,N2: int] :
% 9.17/5.40 ( ( ( ord_min_int @ M2 @ N2 )
% 9.17/5.40 = M2 )
% 9.17/5.40 = ( ord_less_eq_int @ M2 @ N2 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5254_min__eq__arg_I2_J,axiom,
% 9.17/5.40 ! [M2: code_integer,N2: code_integer] :
% 9.17/5.40 ( ( ( ord_min_Code_integer @ M2 @ N2 )
% 9.17/5.40 = N2 )
% 9.17/5.40 = ( ord_le3102999989581377725nteger @ N2 @ M2 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5255_min__eq__arg_I2_J,axiom,
% 9.17/5.40 ! [M2: code_natural,N2: code_natural] :
% 9.17/5.40 ( ( ( ord_min_Code_natural @ M2 @ N2 )
% 9.17/5.40 = N2 )
% 9.17/5.40 = ( ord_le1926595141338095240atural @ N2 @ M2 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5256_min__eq__arg_I2_J,axiom,
% 9.17/5.40 ! [M2: rat,N2: rat] :
% 9.17/5.40 ( ( ( ord_min_rat @ M2 @ N2 )
% 9.17/5.40 = N2 )
% 9.17/5.40 = ( ord_less_eq_rat @ N2 @ M2 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5257_min__eq__arg_I2_J,axiom,
% 9.17/5.40 ! [M2: num,N2: num] :
% 9.17/5.40 ( ( ( ord_min_num @ M2 @ N2 )
% 9.17/5.40 = N2 )
% 9.17/5.40 = ( ord_less_eq_num @ N2 @ M2 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5258_min__eq__arg_I2_J,axiom,
% 9.17/5.40 ! [M2: nat,N2: nat] :
% 9.17/5.40 ( ( ( ord_min_nat @ M2 @ N2 )
% 9.17/5.40 = N2 )
% 9.17/5.40 = ( ord_less_eq_nat @ N2 @ M2 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5259_min__eq__arg_I2_J,axiom,
% 9.17/5.40 ! [M2: int,N2: int] :
% 9.17/5.40 ( ( ( ord_min_int @ M2 @ N2 )
% 9.17/5.40 = N2 )
% 9.17/5.40 = ( ord_less_eq_int @ N2 @ M2 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5260_min__arg__le_I1_J,axiom,
% 9.17/5.40 ! [N2: code_integer,M2: code_integer] :
% 9.17/5.40 ( ( ord_le3102999989581377725nteger @ N2 @ ( ord_min_Code_integer @ M2 @ N2 ) )
% 9.17/5.40 = ( ( ord_min_Code_integer @ M2 @ N2 )
% 9.17/5.40 = N2 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5261_min__arg__le_I1_J,axiom,
% 9.17/5.40 ! [N2: code_natural,M2: code_natural] :
% 9.17/5.40 ( ( ord_le1926595141338095240atural @ N2 @ ( ord_min_Code_natural @ M2 @ N2 ) )
% 9.17/5.40 = ( ( ord_min_Code_natural @ M2 @ N2 )
% 9.17/5.40 = N2 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5262_min__arg__le_I1_J,axiom,
% 9.17/5.40 ! [N2: set_nat,M2: set_nat] :
% 9.17/5.40 ( ( ord_less_eq_set_nat @ N2 @ ( ord_min_set_nat @ M2 @ N2 ) )
% 9.17/5.40 = ( ( ord_min_set_nat @ M2 @ N2 )
% 9.17/5.40 = N2 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5263_min__arg__le_I1_J,axiom,
% 9.17/5.40 ! [N2: rat,M2: rat] :
% 9.17/5.40 ( ( ord_less_eq_rat @ N2 @ ( ord_min_rat @ M2 @ N2 ) )
% 9.17/5.40 = ( ( ord_min_rat @ M2 @ N2 )
% 9.17/5.40 = N2 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5264_min__arg__le_I1_J,axiom,
% 9.17/5.40 ! [N2: num,M2: num] :
% 9.17/5.40 ( ( ord_less_eq_num @ N2 @ ( ord_min_num @ M2 @ N2 ) )
% 9.17/5.40 = ( ( ord_min_num @ M2 @ N2 )
% 9.17/5.40 = N2 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5265_min__arg__le_I1_J,axiom,
% 9.17/5.40 ! [N2: nat,M2: nat] :
% 9.17/5.40 ( ( ord_less_eq_nat @ N2 @ ( ord_min_nat @ M2 @ N2 ) )
% 9.17/5.40 = ( ( ord_min_nat @ M2 @ N2 )
% 9.17/5.40 = N2 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5266_min__arg__le_I1_J,axiom,
% 9.17/5.40 ! [N2: int,M2: int] :
% 9.17/5.40 ( ( ord_less_eq_int @ N2 @ ( ord_min_int @ M2 @ N2 ) )
% 9.17/5.40 = ( ( ord_min_int @ M2 @ N2 )
% 9.17/5.40 = N2 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5267_min__arg__le_I2_J,axiom,
% 9.17/5.40 ! [M2: code_integer,N2: code_integer] :
% 9.17/5.40 ( ( ord_le3102999989581377725nteger @ M2 @ ( ord_min_Code_integer @ M2 @ N2 ) )
% 9.17/5.40 = ( ( ord_min_Code_integer @ M2 @ N2 )
% 9.17/5.40 = M2 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5268_min__arg__le_I2_J,axiom,
% 9.17/5.40 ! [M2: code_natural,N2: code_natural] :
% 9.17/5.40 ( ( ord_le1926595141338095240atural @ M2 @ ( ord_min_Code_natural @ M2 @ N2 ) )
% 9.17/5.40 = ( ( ord_min_Code_natural @ M2 @ N2 )
% 9.17/5.40 = M2 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5269_min__arg__le_I2_J,axiom,
% 9.17/5.40 ! [M2: set_nat,N2: set_nat] :
% 9.17/5.40 ( ( ord_less_eq_set_nat @ M2 @ ( ord_min_set_nat @ M2 @ N2 ) )
% 9.17/5.40 = ( ( ord_min_set_nat @ M2 @ N2 )
% 9.17/5.40 = M2 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5270_min__arg__le_I2_J,axiom,
% 9.17/5.40 ! [M2: rat,N2: rat] :
% 9.17/5.40 ( ( ord_less_eq_rat @ M2 @ ( ord_min_rat @ M2 @ N2 ) )
% 9.17/5.40 = ( ( ord_min_rat @ M2 @ N2 )
% 9.17/5.40 = M2 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5271_min__arg__le_I2_J,axiom,
% 9.17/5.40 ! [M2: num,N2: num] :
% 9.17/5.40 ( ( ord_less_eq_num @ M2 @ ( ord_min_num @ M2 @ N2 ) )
% 9.17/5.40 = ( ( ord_min_num @ M2 @ N2 )
% 9.17/5.40 = M2 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5272_min__arg__le_I2_J,axiom,
% 9.17/5.40 ! [M2: nat,N2: nat] :
% 9.17/5.40 ( ( ord_less_eq_nat @ M2 @ ( ord_min_nat @ M2 @ N2 ) )
% 9.17/5.40 = ( ( ord_min_nat @ M2 @ N2 )
% 9.17/5.40 = M2 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5273_min__arg__le_I2_J,axiom,
% 9.17/5.40 ! [M2: int,N2: int] :
% 9.17/5.40 ( ( ord_less_eq_int @ M2 @ ( ord_min_int @ M2 @ N2 ) )
% 9.17/5.40 = ( ( ord_min_int @ M2 @ N2 )
% 9.17/5.40 = M2 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5274_min__arg__not__ge_I1_J,axiom,
% 9.17/5.40 ! [M2: code_natural,N2: code_natural] :
% 9.17/5.40 ( ( ~ ( ord_le5570908160329646204atural @ ( ord_min_Code_natural @ M2 @ N2 ) @ M2 ) )
% 9.17/5.40 = ( ( ord_min_Code_natural @ M2 @ N2 )
% 9.17/5.40 = M2 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5275_min__arg__not__ge_I1_J,axiom,
% 9.17/5.40 ! [M2: code_integer,N2: code_integer] :
% 9.17/5.40 ( ( ~ ( ord_le6747313008572928689nteger @ ( ord_min_Code_integer @ M2 @ N2 ) @ M2 ) )
% 9.17/5.40 = ( ( ord_min_Code_integer @ M2 @ N2 )
% 9.17/5.40 = M2 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5276_min__arg__not__ge_I1_J,axiom,
% 9.17/5.40 ! [M2: rat,N2: rat] :
% 9.17/5.40 ( ( ~ ( ord_less_rat @ ( ord_min_rat @ M2 @ N2 ) @ M2 ) )
% 9.17/5.40 = ( ( ord_min_rat @ M2 @ N2 )
% 9.17/5.40 = M2 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5277_min__arg__not__ge_I1_J,axiom,
% 9.17/5.40 ! [M2: num,N2: num] :
% 9.17/5.40 ( ( ~ ( ord_less_num @ ( ord_min_num @ M2 @ N2 ) @ M2 ) )
% 9.17/5.40 = ( ( ord_min_num @ M2 @ N2 )
% 9.17/5.40 = M2 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5278_min__arg__not__ge_I1_J,axiom,
% 9.17/5.40 ! [M2: nat,N2: nat] :
% 9.17/5.40 ( ( ~ ( ord_less_nat @ ( ord_min_nat @ M2 @ N2 ) @ M2 ) )
% 9.17/5.40 = ( ( ord_min_nat @ M2 @ N2 )
% 9.17/5.40 = M2 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5279_min__arg__not__ge_I1_J,axiom,
% 9.17/5.40 ! [M2: int,N2: int] :
% 9.17/5.40 ( ( ~ ( ord_less_int @ ( ord_min_int @ M2 @ N2 ) @ M2 ) )
% 9.17/5.40 = ( ( ord_min_int @ M2 @ N2 )
% 9.17/5.40 = M2 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5280_min__arg__not__ge_I2_J,axiom,
% 9.17/5.40 ! [M2: code_natural,N2: code_natural] :
% 9.17/5.40 ( ( ~ ( ord_le5570908160329646204atural @ ( ord_min_Code_natural @ M2 @ N2 ) @ N2 ) )
% 9.17/5.40 = ( ( ord_min_Code_natural @ M2 @ N2 )
% 9.17/5.40 = N2 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5281_min__arg__not__ge_I2_J,axiom,
% 9.17/5.40 ! [M2: code_integer,N2: code_integer] :
% 9.17/5.40 ( ( ~ ( ord_le6747313008572928689nteger @ ( ord_min_Code_integer @ M2 @ N2 ) @ N2 ) )
% 9.17/5.40 = ( ( ord_min_Code_integer @ M2 @ N2 )
% 9.17/5.40 = N2 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5282_min__arg__not__ge_I2_J,axiom,
% 9.17/5.40 ! [M2: rat,N2: rat] :
% 9.17/5.40 ( ( ~ ( ord_less_rat @ ( ord_min_rat @ M2 @ N2 ) @ N2 ) )
% 9.17/5.40 = ( ( ord_min_rat @ M2 @ N2 )
% 9.17/5.40 = N2 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5283_min__arg__not__ge_I2_J,axiom,
% 9.17/5.40 ! [M2: num,N2: num] :
% 9.17/5.40 ( ( ~ ( ord_less_num @ ( ord_min_num @ M2 @ N2 ) @ N2 ) )
% 9.17/5.40 = ( ( ord_min_num @ M2 @ N2 )
% 9.17/5.40 = N2 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5284_min__arg__not__ge_I2_J,axiom,
% 9.17/5.40 ! [M2: nat,N2: nat] :
% 9.17/5.40 ( ( ~ ( ord_less_nat @ ( ord_min_nat @ M2 @ N2 ) @ N2 ) )
% 9.17/5.40 = ( ( ord_min_nat @ M2 @ N2 )
% 9.17/5.40 = N2 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5285_min__arg__not__ge_I2_J,axiom,
% 9.17/5.40 ! [M2: int,N2: int] :
% 9.17/5.40 ( ( ~ ( ord_less_int @ ( ord_min_int @ M2 @ N2 ) @ N2 ) )
% 9.17/5.40 = ( ( ord_min_int @ M2 @ N2 )
% 9.17/5.40 = N2 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5286_min__less__self__conv_I1_J,axiom,
% 9.17/5.40 ! [A: code_natural,B: code_natural] :
% 9.17/5.40 ( ( ord_le5570908160329646204atural @ ( ord_min_Code_natural @ A @ B ) @ A )
% 9.17/5.40 = ( ord_le5570908160329646204atural @ B @ A ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5287_min__less__self__conv_I1_J,axiom,
% 9.17/5.40 ! [A: code_integer,B: code_integer] :
% 9.17/5.40 ( ( ord_le6747313008572928689nteger @ ( ord_min_Code_integer @ A @ B ) @ A )
% 9.17/5.40 = ( ord_le6747313008572928689nteger @ B @ A ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5288_min__less__self__conv_I1_J,axiom,
% 9.17/5.40 ! [A: rat,B: rat] :
% 9.17/5.40 ( ( ord_less_rat @ ( ord_min_rat @ A @ B ) @ A )
% 9.17/5.40 = ( ord_less_rat @ B @ A ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5289_min__less__self__conv_I1_J,axiom,
% 9.17/5.40 ! [A: num,B: num] :
% 9.17/5.40 ( ( ord_less_num @ ( ord_min_num @ A @ B ) @ A )
% 9.17/5.40 = ( ord_less_num @ B @ A ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5290_min__less__self__conv_I1_J,axiom,
% 9.17/5.40 ! [A: nat,B: nat] :
% 9.17/5.40 ( ( ord_less_nat @ ( ord_min_nat @ A @ B ) @ A )
% 9.17/5.40 = ( ord_less_nat @ B @ A ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5291_min__less__self__conv_I1_J,axiom,
% 9.17/5.40 ! [A: int,B: int] :
% 9.17/5.40 ( ( ord_less_int @ ( ord_min_int @ A @ B ) @ A )
% 9.17/5.40 = ( ord_less_int @ B @ A ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5292_min__less__self__conv_I2_J,axiom,
% 9.17/5.40 ! [A: code_natural,B: code_natural] :
% 9.17/5.40 ( ( ord_le5570908160329646204atural @ ( ord_min_Code_natural @ A @ B ) @ B )
% 9.17/5.40 = ( ord_le5570908160329646204atural @ A @ B ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5293_min__less__self__conv_I2_J,axiom,
% 9.17/5.40 ! [A: code_integer,B: code_integer] :
% 9.17/5.40 ( ( ord_le6747313008572928689nteger @ ( ord_min_Code_integer @ A @ B ) @ B )
% 9.17/5.40 = ( ord_le6747313008572928689nteger @ A @ B ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5294_min__less__self__conv_I2_J,axiom,
% 9.17/5.40 ! [A: rat,B: rat] :
% 9.17/5.40 ( ( ord_less_rat @ ( ord_min_rat @ A @ B ) @ B )
% 9.17/5.40 = ( ord_less_rat @ A @ B ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5295_min__less__self__conv_I2_J,axiom,
% 9.17/5.40 ! [A: num,B: num] :
% 9.17/5.40 ( ( ord_less_num @ ( ord_min_num @ A @ B ) @ B )
% 9.17/5.40 = ( ord_less_num @ A @ B ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5296_min__less__self__conv_I2_J,axiom,
% 9.17/5.40 ! [A: nat,B: nat] :
% 9.17/5.40 ( ( ord_less_nat @ ( ord_min_nat @ A @ B ) @ B )
% 9.17/5.40 = ( ord_less_nat @ A @ B ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5297_min__less__self__conv_I2_J,axiom,
% 9.17/5.40 ! [A: int,B: int] :
% 9.17/5.40 ( ( ord_less_int @ ( ord_min_int @ A @ B ) @ B )
% 9.17/5.40 = ( ord_less_int @ A @ B ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5298_min__simps_I1_J,axiom,
% 9.17/5.40 ! [A: code_natural,B: code_natural] :
% 9.17/5.40 ( ( ord_le5570908160329646204atural @ A @ B )
% 9.17/5.40 => ( ( ord_min_Code_natural @ A @ B )
% 9.17/5.40 = A ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5299_min__simps_I1_J,axiom,
% 9.17/5.40 ! [A: code_integer,B: code_integer] :
% 9.17/5.40 ( ( ord_le6747313008572928689nteger @ A @ B )
% 9.17/5.40 => ( ( ord_min_Code_integer @ A @ B )
% 9.17/5.40 = A ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5300_min__simps_I1_J,axiom,
% 9.17/5.40 ! [A: rat,B: rat] :
% 9.17/5.40 ( ( ord_less_rat @ A @ B )
% 9.17/5.40 => ( ( ord_min_rat @ A @ B )
% 9.17/5.40 = A ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5301_min__simps_I1_J,axiom,
% 9.17/5.40 ! [A: num,B: num] :
% 9.17/5.40 ( ( ord_less_num @ A @ B )
% 9.17/5.40 => ( ( ord_min_num @ A @ B )
% 9.17/5.40 = A ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5302_min__simps_I1_J,axiom,
% 9.17/5.40 ! [A: nat,B: nat] :
% 9.17/5.40 ( ( ord_less_nat @ A @ B )
% 9.17/5.40 => ( ( ord_min_nat @ A @ B )
% 9.17/5.40 = A ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5303_min__simps_I1_J,axiom,
% 9.17/5.40 ! [A: int,B: int] :
% 9.17/5.40 ( ( ord_less_int @ A @ B )
% 9.17/5.40 => ( ( ord_min_int @ A @ B )
% 9.17/5.40 = A ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5304_min__simps_I2_J,axiom,
% 9.17/5.40 ! [B: code_natural,A: code_natural] :
% 9.17/5.40 ( ( ord_le5570908160329646204atural @ B @ A )
% 9.17/5.40 => ( ( ord_min_Code_natural @ A @ B )
% 9.17/5.40 = B ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5305_min__simps_I2_J,axiom,
% 9.17/5.40 ! [B: code_integer,A: code_integer] :
% 9.17/5.40 ( ( ord_le6747313008572928689nteger @ B @ A )
% 9.17/5.40 => ( ( ord_min_Code_integer @ A @ B )
% 9.17/5.40 = B ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5306_min__simps_I2_J,axiom,
% 9.17/5.40 ! [B: rat,A: rat] :
% 9.17/5.40 ( ( ord_less_rat @ B @ A )
% 9.17/5.40 => ( ( ord_min_rat @ A @ B )
% 9.17/5.40 = B ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5307_min__simps_I2_J,axiom,
% 9.17/5.40 ! [B: num,A: num] :
% 9.17/5.40 ( ( ord_less_num @ B @ A )
% 9.17/5.40 => ( ( ord_min_num @ A @ B )
% 9.17/5.40 = B ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5308_min__simps_I2_J,axiom,
% 9.17/5.40 ! [B: nat,A: nat] :
% 9.17/5.40 ( ( ord_less_nat @ B @ A )
% 9.17/5.40 => ( ( ord_min_nat @ A @ B )
% 9.17/5.40 = B ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5309_min__simps_I2_J,axiom,
% 9.17/5.40 ! [B: int,A: int] :
% 9.17/5.40 ( ( ord_less_int @ B @ A )
% 9.17/5.40 => ( ( ord_min_int @ A @ B )
% 9.17/5.40 = B ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5310_min__0__1_I2_J,axiom,
% 9.17/5.40 ( ( ord_min_rat @ one_one_rat @ zero_zero_rat )
% 9.17/5.40 = zero_zero_rat ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5311_min__0__1_I2_J,axiom,
% 9.17/5.40 ( ( ord_min_nat @ one_one_nat @ zero_zero_nat )
% 9.17/5.40 = zero_zero_nat ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5312_min__0__1_I2_J,axiom,
% 9.17/5.40 ( ( ord_min_Code_integer @ one_one_Code_integer @ zero_z3403309356797280102nteger )
% 9.17/5.40 = zero_z3403309356797280102nteger ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5313_min__0__1_I2_J,axiom,
% 9.17/5.40 ( ( ord_min_int @ one_one_int @ zero_zero_int )
% 9.17/5.40 = zero_zero_int ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5314_min__0__1_I2_J,axiom,
% 9.17/5.40 ( ( ord_min_Code_natural @ one_one_Code_natural @ zero_z2226904508553997617atural )
% 9.17/5.40 = zero_z2226904508553997617atural ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5315_min__0__1_I1_J,axiom,
% 9.17/5.40 ( ( ord_min_rat @ zero_zero_rat @ one_one_rat )
% 9.17/5.40 = zero_zero_rat ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5316_min__0__1_I1_J,axiom,
% 9.17/5.40 ( ( ord_min_nat @ zero_zero_nat @ one_one_nat )
% 9.17/5.40 = zero_zero_nat ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5317_min__0__1_I1_J,axiom,
% 9.17/5.40 ( ( ord_min_Code_integer @ zero_z3403309356797280102nteger @ one_one_Code_integer )
% 9.17/5.40 = zero_z3403309356797280102nteger ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5318_min__0__1_I1_J,axiom,
% 9.17/5.40 ( ( ord_min_int @ zero_zero_int @ one_one_int )
% 9.17/5.40 = zero_zero_int ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5319_min__0__1_I1_J,axiom,
% 9.17/5.40 ( ( ord_min_Code_natural @ zero_z2226904508553997617atural @ one_one_Code_natural )
% 9.17/5.40 = zero_z2226904508553997617atural ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5320_min__0__1_I5_J,axiom,
% 9.17/5.40 ! [X: num] :
% 9.17/5.40 ( ( ord_min_nat @ one_one_nat @ ( numeral_numeral_nat @ X ) )
% 9.17/5.40 = one_one_nat ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5321_min__0__1_I5_J,axiom,
% 9.17/5.40 ! [X: num] :
% 9.17/5.40 ( ( ord_min_int @ one_one_int @ ( numeral_numeral_int @ X ) )
% 9.17/5.40 = one_one_int ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5322_min__0__1_I5_J,axiom,
% 9.17/5.40 ! [X: num] :
% 9.17/5.40 ( ( ord_min_Code_integer @ one_one_Code_integer @ ( numera6620942414471956472nteger @ X ) )
% 9.17/5.40 = one_one_Code_integer ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5323_min__0__1_I5_J,axiom,
% 9.17/5.40 ! [X: num] :
% 9.17/5.40 ( ( ord_min_rat @ one_one_rat @ ( numeral_numeral_rat @ X ) )
% 9.17/5.40 = one_one_rat ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5324_min__0__1_I5_J,axiom,
% 9.17/5.40 ! [X: num] :
% 9.17/5.40 ( ( ord_min_Code_natural @ one_one_Code_natural @ ( numera5444537566228673987atural @ X ) )
% 9.17/5.40 = one_one_Code_natural ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5325_min__0__1_I6_J,axiom,
% 9.17/5.40 ! [X: num] :
% 9.17/5.40 ( ( ord_min_nat @ ( numeral_numeral_nat @ X ) @ one_one_nat )
% 9.17/5.40 = one_one_nat ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5326_min__0__1_I6_J,axiom,
% 9.17/5.40 ! [X: num] :
% 9.17/5.40 ( ( ord_min_int @ ( numeral_numeral_int @ X ) @ one_one_int )
% 9.17/5.40 = one_one_int ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5327_min__0__1_I6_J,axiom,
% 9.17/5.40 ! [X: num] :
% 9.17/5.40 ( ( ord_min_Code_integer @ ( numera6620942414471956472nteger @ X ) @ one_one_Code_integer )
% 9.17/5.40 = one_one_Code_integer ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5328_min__0__1_I6_J,axiom,
% 9.17/5.40 ! [X: num] :
% 9.17/5.40 ( ( ord_min_rat @ ( numeral_numeral_rat @ X ) @ one_one_rat )
% 9.17/5.40 = one_one_rat ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5329_min__0__1_I6_J,axiom,
% 9.17/5.40 ! [X: num] :
% 9.17/5.40 ( ( ord_min_Code_natural @ ( numera5444537566228673987atural @ X ) @ one_one_Code_natural )
% 9.17/5.40 = one_one_Code_natural ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5330_atLeastAtMost__singleton__iff,axiom,
% 9.17/5.40 ! [A: $o,B: $o,C: $o] :
% 9.17/5.40 ( ( ( set_or8904488021354931149Most_o @ A @ B )
% 9.17/5.40 = ( insert_o @ C @ bot_bot_set_o ) )
% 9.17/5.40 = ( ( A = B )
% 9.17/5.40 & ( B = C ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5331_atLeastAtMost__singleton__iff,axiom,
% 9.17/5.40 ! [A: int,B: int,C: int] :
% 9.17/5.40 ( ( ( set_or1266510415728281911st_int @ A @ B )
% 9.17/5.40 = ( insert_int @ C @ bot_bot_set_int ) )
% 9.17/5.40 = ( ( A = B )
% 9.17/5.40 & ( B = C ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5332_atLeastAtMost__singleton__iff,axiom,
% 9.17/5.40 ! [A: nat,B: nat,C: nat] :
% 9.17/5.40 ( ( ( set_or1269000886237332187st_nat @ A @ B )
% 9.17/5.40 = ( insert_nat @ C @ bot_bot_set_nat ) )
% 9.17/5.40 = ( ( A = B )
% 9.17/5.40 & ( B = C ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5333_atLeastAtMost__singleton__iff,axiom,
% 9.17/5.40 ! [A: code_integer,B: code_integer,C: code_integer] :
% 9.17/5.40 ( ( ( set_or189985376899183464nteger @ A @ B )
% 9.17/5.40 = ( insert_Code_integer @ C @ bot_bo3990330152332043303nteger ) )
% 9.17/5.40 = ( ( A = B )
% 9.17/5.40 & ( B = C ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5334_atLeastAtMost__singleton,axiom,
% 9.17/5.40 ! [A: $o] :
% 9.17/5.40 ( ( set_or8904488021354931149Most_o @ A @ A )
% 9.17/5.40 = ( insert_o @ A @ bot_bot_set_o ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5335_atLeastAtMost__singleton,axiom,
% 9.17/5.40 ! [A: int] :
% 9.17/5.40 ( ( set_or1266510415728281911st_int @ A @ A )
% 9.17/5.40 = ( insert_int @ A @ bot_bot_set_int ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5336_atLeastAtMost__singleton,axiom,
% 9.17/5.40 ! [A: nat] :
% 9.17/5.40 ( ( set_or1269000886237332187st_nat @ A @ A )
% 9.17/5.40 = ( insert_nat @ A @ bot_bot_set_nat ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5337_atLeastAtMost__singleton,axiom,
% 9.17/5.40 ! [A: code_integer] :
% 9.17/5.40 ( ( set_or189985376899183464nteger @ A @ A )
% 9.17/5.40 = ( insert_Code_integer @ A @ bot_bo3990330152332043303nteger ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5338_min__Suc__gt_I2_J,axiom,
% 9.17/5.40 ! [A: nat,B: nat] :
% 9.17/5.40 ( ( ord_less_nat @ A @ B )
% 9.17/5.40 => ( ( ord_min_nat @ B @ ( suc @ A ) )
% 9.17/5.40 = ( suc @ A ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5339_min__Suc__gt_I1_J,axiom,
% 9.17/5.40 ! [A: nat,B: nat] :
% 9.17/5.40 ( ( ord_less_nat @ A @ B )
% 9.17/5.40 => ( ( ord_min_nat @ ( suc @ A ) @ B )
% 9.17/5.40 = ( suc @ A ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5340_case__prod__Pair,axiom,
% 9.17/5.40 ( ( produc6512950862096126219nteger @ produc8603105652947943368nteger )
% 9.17/5.40 = id_Pro1379270990444177765nteger ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5341_case__prod__Pair,axiom,
% 9.17/5.40 ( ( produc4058941399401191971et_nat @ produc5001842942810119800et_nat )
% 9.17/5.40 = id_Pro1888964116897856973et_nat ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5342_case__prod__Pair,axiom,
% 9.17/5.40 ( ( produc2377985495875741467et_nat @ produc2245416461498447860et_nat )
% 9.17/5.40 = id_Pro1297863087923562825et_nat ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5343_case__prod__Pair,axiom,
% 9.17/5.40 ( ( produc8492565224438309093nt_int @ produc5700946648718959541nt_int )
% 9.17/5.40 = id_Pro5422067691592394322nt_int ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5344_case__prod__Pair,axiom,
% 9.17/5.40 ( ( produc5122537100556696953nt_int @ produc4305682042979456191nt_int )
% 9.17/5.40 = id_Pro3923183700162330716nt_int ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5345_case__prod__Pair,axiom,
% 9.17/5.40 ( ( produc4245557441103728435nt_int @ product_Pair_int_int )
% 9.17/5.40 = id_Pro4381231610383771306nt_int ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5346_single__Diff__lessThan,axiom,
% 9.17/5.40 ! [K: $o] :
% 9.17/5.40 ( ( minus_minus_set_o @ ( insert_o @ K @ bot_bot_set_o ) @ ( set_ord_lessThan_o @ K ) )
% 9.17/5.40 = ( insert_o @ K @ bot_bot_set_o ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5347_single__Diff__lessThan,axiom,
% 9.17/5.40 ! [K: int] :
% 9.17/5.40 ( ( minus_minus_set_int @ ( insert_int @ K @ bot_bot_set_int ) @ ( set_ord_lessThan_int @ K ) )
% 9.17/5.40 = ( insert_int @ K @ bot_bot_set_int ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5348_single__Diff__lessThan,axiom,
% 9.17/5.40 ! [K: nat] :
% 9.17/5.40 ( ( minus_minus_set_nat @ ( insert_nat @ K @ bot_bot_set_nat ) @ ( set_ord_lessThan_nat @ K ) )
% 9.17/5.40 = ( insert_nat @ K @ bot_bot_set_nat ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5349_min__add__distrib__right,axiom,
% 9.17/5.40 ! [X: rat,Y: rat,Z: rat] :
% 9.17/5.40 ( ( plus_plus_rat @ X @ ( ord_min_rat @ Y @ Z ) )
% 9.17/5.40 = ( ord_min_rat @ ( plus_plus_rat @ X @ Y ) @ ( plus_plus_rat @ X @ Z ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5350_min__add__distrib__right,axiom,
% 9.17/5.40 ! [X: nat,Y: nat,Z: nat] :
% 9.17/5.40 ( ( plus_plus_nat @ X @ ( ord_min_nat @ Y @ Z ) )
% 9.17/5.40 = ( ord_min_nat @ ( plus_plus_nat @ X @ Y ) @ ( plus_plus_nat @ X @ Z ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5351_min__add__distrib__right,axiom,
% 9.17/5.40 ! [X: code_integer,Y: code_integer,Z: code_integer] :
% 9.17/5.40 ( ( plus_p5714425477246183910nteger @ X @ ( ord_min_Code_integer @ Y @ Z ) )
% 9.17/5.40 = ( ord_min_Code_integer @ ( plus_p5714425477246183910nteger @ X @ Y ) @ ( plus_p5714425477246183910nteger @ X @ Z ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5352_min__add__distrib__right,axiom,
% 9.17/5.40 ! [X: int,Y: int,Z: int] :
% 9.17/5.40 ( ( plus_plus_int @ X @ ( ord_min_int @ Y @ Z ) )
% 9.17/5.40 = ( ord_min_int @ ( plus_plus_int @ X @ Y ) @ ( plus_plus_int @ X @ Z ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5353_min__add__distrib__right,axiom,
% 9.17/5.40 ! [X: code_natural,Y: code_natural,Z: code_natural] :
% 9.17/5.40 ( ( plus_p4538020629002901425atural @ X @ ( ord_min_Code_natural @ Y @ Z ) )
% 9.17/5.40 = ( ord_min_Code_natural @ ( plus_p4538020629002901425atural @ X @ Y ) @ ( plus_p4538020629002901425atural @ X @ Z ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5354_min__add__distrib__left,axiom,
% 9.17/5.40 ! [X: rat,Y: rat,Z: rat] :
% 9.17/5.40 ( ( plus_plus_rat @ ( ord_min_rat @ X @ Y ) @ Z )
% 9.17/5.40 = ( ord_min_rat @ ( plus_plus_rat @ X @ Z ) @ ( plus_plus_rat @ Y @ Z ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5355_min__add__distrib__left,axiom,
% 9.17/5.40 ! [X: nat,Y: nat,Z: nat] :
% 9.17/5.40 ( ( plus_plus_nat @ ( ord_min_nat @ X @ Y ) @ Z )
% 9.17/5.40 = ( ord_min_nat @ ( plus_plus_nat @ X @ Z ) @ ( plus_plus_nat @ Y @ Z ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5356_min__add__distrib__left,axiom,
% 9.17/5.40 ! [X: code_integer,Y: code_integer,Z: code_integer] :
% 9.17/5.40 ( ( plus_p5714425477246183910nteger @ ( ord_min_Code_integer @ X @ Y ) @ Z )
% 9.17/5.40 = ( ord_min_Code_integer @ ( plus_p5714425477246183910nteger @ X @ Z ) @ ( plus_p5714425477246183910nteger @ Y @ Z ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5357_min__add__distrib__left,axiom,
% 9.17/5.40 ! [X: int,Y: int,Z: int] :
% 9.17/5.40 ( ( plus_plus_int @ ( ord_min_int @ X @ Y ) @ Z )
% 9.17/5.40 = ( ord_min_int @ ( plus_plus_int @ X @ Z ) @ ( plus_plus_int @ Y @ Z ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5358_min__add__distrib__left,axiom,
% 9.17/5.40 ! [X: code_natural,Y: code_natural,Z: code_natural] :
% 9.17/5.40 ( ( plus_p4538020629002901425atural @ ( ord_min_Code_natural @ X @ Y ) @ Z )
% 9.17/5.40 = ( ord_min_Code_natural @ ( plus_p4538020629002901425atural @ X @ Z ) @ ( plus_p4538020629002901425atural @ Y @ Z ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5359_min__diff__distrib__left,axiom,
% 9.17/5.40 ! [X: code_integer,Y: code_integer,Z: code_integer] :
% 9.17/5.40 ( ( minus_8373710615458151222nteger @ ( ord_min_Code_integer @ X @ Y ) @ Z )
% 9.17/5.40 = ( ord_min_Code_integer @ ( minus_8373710615458151222nteger @ X @ Z ) @ ( minus_8373710615458151222nteger @ Y @ Z ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5360_min__diff__distrib__left,axiom,
% 9.17/5.40 ! [X: rat,Y: rat,Z: rat] :
% 9.17/5.40 ( ( minus_minus_rat @ ( ord_min_rat @ X @ Y ) @ Z )
% 9.17/5.40 = ( ord_min_rat @ ( minus_minus_rat @ X @ Z ) @ ( minus_minus_rat @ Y @ Z ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5361_min__diff__distrib__left,axiom,
% 9.17/5.40 ! [X: int,Y: int,Z: int] :
% 9.17/5.40 ( ( minus_minus_int @ ( ord_min_int @ X @ Y ) @ Z )
% 9.17/5.40 = ( ord_min_int @ ( minus_minus_int @ X @ Z ) @ ( minus_minus_int @ Y @ Z ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5362_bot__option__def,axiom,
% 9.17/5.40 bot_bot_option_num = none_num ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5363_bot__empty__eq2,axiom,
% 9.17/5.40 ( bot_bo3000040243691356879eger_o
% 9.17/5.40 = ( ^ [X3: produc6241069584506657477e_term > option6357759511663192854e_term,Y3: produc8923325533196201883nteger] : ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X3 @ Y3 ) @ bot_bo5443222936135328352nteger ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5364_bot__empty__eq2,axiom,
% 9.17/5.40 ( bot_bo5580076615179976505_nat_o
% 9.17/5.40 = ( ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3658429121746597890et_nat] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X3 @ Y3 ) @ bot_bo1481135142794719944et_nat ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5365_bot__empty__eq2,axiom,
% 9.17/5.40 ( bot_bo3790638025767943357_nat_o
% 9.17/5.40 = ( ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3925858234332021118et_nat] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X3 @ Y3 ) @ bot_bo5635537948650799172et_nat ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5366_bot__empty__eq2,axiom,
% 9.17/5.40 ( bot_bo8662317086119403298_int_o
% 9.17/5.40 = ( ^ [X3: produc8551481072490612790e_term > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X3 @ Y3 ) @ bot_bo572930865798478029nt_int ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5367_bot__empty__eq2,axiom,
% 9.17/5.40 ( bot_bo1403522918969695512_int_o
% 9.17/5.40 = ( ^ [X3: int > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X3 @ Y3 ) @ bot_bo4508923176915781079nt_int ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5368_bot__empty__eq2,axiom,
% 9.17/5.40 ( bot_bo394778441745866138_nat_o
% 9.17/5.40 = ( ^ [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ Y3 ) @ bot_bo228742789529271731at_nat ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5369_bot__empty__eq2,axiom,
% 9.17/5.40 ( bot_bot_nat_nat_o
% 9.17/5.40 = ( ^ [X3: nat,Y3: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y3 ) @ bot_bo2099793752762293965at_nat ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5370_map__fun_Oidentity,axiom,
% 9.17/5.40 ( ( map_fun_nat_nat_o_o
% 9.17/5.40 @ ^ [X3: nat] : X3
% 9.17/5.40 @ ^ [X3: $o] : X3 )
% 9.17/5.40 = id_nat_o ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5371_map__option_Oidentity,axiom,
% 9.17/5.40 ( ( map_option_num_num
% 9.17/5.40 @ ^ [X3: num] : X3 )
% 9.17/5.40 = id_option_num ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5372_minus__max__eq__min,axiom,
% 9.17/5.40 ! [X: int,Y: int] :
% 9.17/5.40 ( ( uminus_uminus_int @ ( ord_max_int @ X @ Y ) )
% 9.17/5.40 = ( ord_min_int @ ( uminus_uminus_int @ X ) @ ( uminus_uminus_int @ Y ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5373_minus__max__eq__min,axiom,
% 9.17/5.40 ! [X: code_integer,Y: code_integer] :
% 9.17/5.40 ( ( uminus1351360451143612070nteger @ ( ord_max_Code_integer @ X @ Y ) )
% 9.17/5.40 = ( ord_min_Code_integer @ ( uminus1351360451143612070nteger @ X ) @ ( uminus1351360451143612070nteger @ Y ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5374_minus__max__eq__min,axiom,
% 9.17/5.40 ! [X: rat,Y: rat] :
% 9.17/5.40 ( ( uminus_uminus_rat @ ( ord_max_rat @ X @ Y ) )
% 9.17/5.40 = ( ord_min_rat @ ( uminus_uminus_rat @ X ) @ ( uminus_uminus_rat @ Y ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5375_minus__min__eq__max,axiom,
% 9.17/5.40 ! [X: int,Y: int] :
% 9.17/5.40 ( ( uminus_uminus_int @ ( ord_min_int @ X @ Y ) )
% 9.17/5.40 = ( ord_max_int @ ( uminus_uminus_int @ X ) @ ( uminus_uminus_int @ Y ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5376_minus__min__eq__max,axiom,
% 9.17/5.40 ! [X: code_integer,Y: code_integer] :
% 9.17/5.40 ( ( uminus1351360451143612070nteger @ ( ord_min_Code_integer @ X @ Y ) )
% 9.17/5.40 = ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ X ) @ ( uminus1351360451143612070nteger @ Y ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5377_minus__min__eq__max,axiom,
% 9.17/5.40 ! [X: rat,Y: rat] :
% 9.17/5.40 ( ( uminus_uminus_rat @ ( ord_min_rat @ X @ Y ) )
% 9.17/5.40 = ( ord_max_rat @ ( uminus_uminus_rat @ X ) @ ( uminus_uminus_rat @ Y ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5378_insert__minus__eq,axiom,
% 9.17/5.40 ! [X: produc3843707927480180839at_nat,Y: produc3843707927480180839at_nat,A2: set_Pr4329608150637261639at_nat] :
% 9.17/5.40 ( ( X != Y )
% 9.17/5.40 => ( ( minus_3314409938677909166at_nat @ ( insert9069300056098147895at_nat @ X @ A2 ) @ ( insert9069300056098147895at_nat @ Y @ bot_bo228742789529271731at_nat ) )
% 9.17/5.40 = ( insert9069300056098147895at_nat @ X @ ( minus_3314409938677909166at_nat @ A2 @ ( insert9069300056098147895at_nat @ Y @ bot_bo228742789529271731at_nat ) ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5379_insert__minus__eq,axiom,
% 9.17/5.40 ! [X: product_prod_nat_nat,Y: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat] :
% 9.17/5.40 ( ( X != Y )
% 9.17/5.40 => ( ( minus_1356011639430497352at_nat @ ( insert8211810215607154385at_nat @ X @ A2 ) @ ( insert8211810215607154385at_nat @ Y @ bot_bo2099793752762293965at_nat ) )
% 9.17/5.40 = ( insert8211810215607154385at_nat @ X @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ Y @ bot_bo2099793752762293965at_nat ) ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5380_insert__minus__eq,axiom,
% 9.17/5.40 ! [X: $o,Y: $o,A2: set_o] :
% 9.17/5.40 ( ( X != Y )
% 9.17/5.40 => ( ( minus_minus_set_o @ ( insert_o @ X @ A2 ) @ ( insert_o @ Y @ bot_bot_set_o ) )
% 9.17/5.40 = ( insert_o @ X @ ( minus_minus_set_o @ A2 @ ( insert_o @ Y @ bot_bot_set_o ) ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5381_insert__minus__eq,axiom,
% 9.17/5.40 ! [X: int,Y: int,A2: set_int] :
% 9.17/5.40 ( ( X != Y )
% 9.17/5.40 => ( ( minus_minus_set_int @ ( insert_int @ X @ A2 ) @ ( insert_int @ Y @ bot_bot_set_int ) )
% 9.17/5.40 = ( insert_int @ X @ ( minus_minus_set_int @ A2 @ ( insert_int @ Y @ bot_bot_set_int ) ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5382_insert__minus__eq,axiom,
% 9.17/5.40 ! [X: nat,Y: nat,A2: set_nat] :
% 9.17/5.40 ( ( X != Y )
% 9.17/5.40 => ( ( minus_minus_set_nat @ ( insert_nat @ X @ A2 ) @ ( insert_nat @ Y @ bot_bot_set_nat ) )
% 9.17/5.40 = ( insert_nat @ X @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ Y @ bot_bot_set_nat ) ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5383_set__minus__singleton__eq,axiom,
% 9.17/5.40 ! [X: produc3843707927480180839at_nat,X11: set_Pr4329608150637261639at_nat] :
% 9.17/5.40 ( ~ ( member8757157785044589968at_nat @ X @ X11 )
% 9.17/5.40 => ( ( minus_3314409938677909166at_nat @ X11 @ ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) )
% 9.17/5.40 = X11 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5384_set__minus__singleton__eq,axiom,
% 9.17/5.40 ! [X: product_prod_nat_nat,X11: set_Pr1261947904930325089at_nat] :
% 9.17/5.40 ( ~ ( member8440522571783428010at_nat @ X @ X11 )
% 9.17/5.40 => ( ( minus_1356011639430497352at_nat @ X11 @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) )
% 9.17/5.40 = X11 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5385_set__minus__singleton__eq,axiom,
% 9.17/5.40 ! [X: $o,X11: set_o] :
% 9.17/5.40 ( ~ ( member_o @ X @ X11 )
% 9.17/5.40 => ( ( minus_minus_set_o @ X11 @ ( insert_o @ X @ bot_bot_set_o ) )
% 9.17/5.40 = X11 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5386_set__minus__singleton__eq,axiom,
% 9.17/5.40 ! [X: int,X11: set_int] :
% 9.17/5.40 ( ~ ( member_int @ X @ X11 )
% 9.17/5.40 => ( ( minus_minus_set_int @ X11 @ ( insert_int @ X @ bot_bot_set_int ) )
% 9.17/5.40 = X11 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5387_set__minus__singleton__eq,axiom,
% 9.17/5.40 ! [X: nat,X11: set_nat] :
% 9.17/5.40 ( ~ ( member_nat @ X @ X11 )
% 9.17/5.40 => ( ( minus_minus_set_nat @ X11 @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 9.17/5.40 = X11 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5388_atLeastAtMost__singleton_H,axiom,
% 9.17/5.40 ! [A: $o,B: $o] :
% 9.17/5.40 ( ( A = B )
% 9.17/5.40 => ( ( set_or8904488021354931149Most_o @ A @ B )
% 9.17/5.40 = ( insert_o @ A @ bot_bot_set_o ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5389_atLeastAtMost__singleton_H,axiom,
% 9.17/5.40 ! [A: int,B: int] :
% 9.17/5.40 ( ( A = B )
% 9.17/5.40 => ( ( set_or1266510415728281911st_int @ A @ B )
% 9.17/5.40 = ( insert_int @ A @ bot_bot_set_int ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5390_atLeastAtMost__singleton_H,axiom,
% 9.17/5.40 ! [A: nat,B: nat] :
% 9.17/5.40 ( ( A = B )
% 9.17/5.40 => ( ( set_or1269000886237332187st_nat @ A @ B )
% 9.17/5.40 = ( insert_nat @ A @ bot_bot_set_nat ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5391_atLeastAtMost__singleton_H,axiom,
% 9.17/5.40 ! [A: code_integer,B: code_integer] :
% 9.17/5.40 ( ( A = B )
% 9.17/5.40 => ( ( set_or189985376899183464nteger @ A @ B )
% 9.17/5.40 = ( insert_Code_integer @ A @ bot_bo3990330152332043303nteger ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5392_remove__subset,axiom,
% 9.17/5.40 ! [X: produc3843707927480180839at_nat,S2: set_Pr4329608150637261639at_nat] :
% 9.17/5.40 ( ( member8757157785044589968at_nat @ X @ S2 )
% 9.17/5.40 => ( ord_le2604355607129572851at_nat @ ( minus_3314409938677909166at_nat @ S2 @ ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) ) @ S2 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5393_remove__subset,axiom,
% 9.17/5.40 ! [X: product_prod_nat_nat,S2: set_Pr1261947904930325089at_nat] :
% 9.17/5.40 ( ( member8440522571783428010at_nat @ X @ S2 )
% 9.17/5.40 => ( ord_le7866589430770878221at_nat @ ( minus_1356011639430497352at_nat @ S2 @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) @ S2 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5394_remove__subset,axiom,
% 9.17/5.40 ! [X: $o,S2: set_o] :
% 9.17/5.40 ( ( member_o @ X @ S2 )
% 9.17/5.40 => ( ord_less_set_o @ ( minus_minus_set_o @ S2 @ ( insert_o @ X @ bot_bot_set_o ) ) @ S2 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5395_remove__subset,axiom,
% 9.17/5.40 ! [X: int,S2: set_int] :
% 9.17/5.40 ( ( member_int @ X @ S2 )
% 9.17/5.40 => ( ord_less_set_int @ ( minus_minus_set_int @ S2 @ ( insert_int @ X @ bot_bot_set_int ) ) @ S2 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5396_remove__subset,axiom,
% 9.17/5.40 ! [X: nat,S2: set_nat] :
% 9.17/5.40 ( ( member_nat @ X @ S2 )
% 9.17/5.40 => ( ord_less_set_nat @ ( minus_minus_set_nat @ S2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) @ S2 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5397_nat__of__integer__def,axiom,
% 9.17/5.40 ( code_nat_of_integer
% 9.17/5.40 = ( map_fu6539832666145259331at_nat @ code_int_of_integer @ id_nat @ nat2 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5398_bit__integer__def,axiom,
% 9.17/5.40 ( bit_se9216721137139052372nteger
% 9.17/5.40 = ( map_fu186220595405829473_nat_o @ code_int_of_integer @ id_nat_o @ bit_se1146084159140164899it_int ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5399_mask__integer__def,axiom,
% 9.17/5.40 ( bit_se2119862282449309892nteger
% 9.17/5.40 = ( map_fu6290471996055670595nteger @ id_nat @ code_integer_of_int @ bit_se2000444600071755411sk_int ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5400_atLeastLessThan__eq__atLeastAtMost__diff,axiom,
% 9.17/5.40 ( set_or7139685690850216873Than_o
% 9.17/5.40 = ( ^ [A5: $o,B4: $o] : ( minus_minus_set_o @ ( set_or8904488021354931149Most_o @ A5 @ B4 ) @ ( insert_o @ B4 @ bot_bot_set_o ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5401_atLeastLessThan__eq__atLeastAtMost__diff,axiom,
% 9.17/5.40 ( set_or4665077453230672383an_nat
% 9.17/5.40 = ( ^ [A5: nat,B4: nat] : ( minus_minus_set_nat @ ( set_or1269000886237332187st_nat @ A5 @ B4 ) @ ( insert_nat @ B4 @ bot_bot_set_nat ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5402_atLeastLessThan__eq__atLeastAtMost__diff,axiom,
% 9.17/5.40 ( set_or8404916559141939852nteger
% 9.17/5.40 = ( ^ [A5: code_integer,B4: code_integer] : ( minus_2355218937544613996nteger @ ( set_or189985376899183464nteger @ A5 @ B4 ) @ ( insert_Code_integer @ B4 @ bot_bo3990330152332043303nteger ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5403_atLeastLessThan__eq__atLeastAtMost__diff,axiom,
% 9.17/5.40 ( set_or4662586982721622107an_int
% 9.17/5.40 = ( ^ [A5: int,B4: int] : ( minus_minus_set_int @ ( set_or1266510415728281911st_int @ A5 @ B4 ) @ ( insert_int @ B4 @ bot_bot_set_int ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5404_atLeastAtMostPlus1__int__conv,axiom,
% 9.17/5.40 ! [M2: int,N2: int] :
% 9.17/5.40 ( ( ord_less_eq_int @ M2 @ ( plus_plus_int @ one_one_int @ N2 ) )
% 9.17/5.40 => ( ( set_or1266510415728281911st_int @ M2 @ ( plus_plus_int @ one_one_int @ N2 ) )
% 9.17/5.40 = ( insert_int @ ( plus_plus_int @ one_one_int @ N2 ) @ ( set_or1266510415728281911st_int @ M2 @ N2 ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5405_simp__from__to,axiom,
% 9.17/5.40 ( set_or1266510415728281911st_int
% 9.17/5.40 = ( ^ [I3: int,J2: int] : ( if_set_int @ ( ord_less_int @ J2 @ I3 ) @ bot_bot_set_int @ ( insert_int @ I3 @ ( set_or1266510415728281911st_int @ ( plus_plus_int @ I3 @ one_one_int ) @ J2 ) ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5406_Code__Numeral_Osub__def,axiom,
% 9.17/5.40 ( code_sub
% 9.17/5.40 = ( map_fu6891787308814931657nteger @ id_num @ ( map_fu8638147718074629079nteger @ id_num @ code_integer_of_int )
% 9.17/5.40 @ ^ [M: num,N4: num] : ( minus_minus_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N4 ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5407_num__of__integer__def,axiom,
% 9.17/5.40 ( code_num_of_integer
% 9.17/5.40 = ( map_fu1227494855608507351um_num @ code_int_of_integer @ id_num @ ( comp_nat_num_int @ num_of_nat @ nat2 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5408_take__bit__integer__def,axiom,
% 9.17/5.40 ( bit_se1745604003318907178nteger
% 9.17/5.40 = ( map_fu8224359078269604234nteger @ id_nat @ ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int ) @ bit_se2923211474154528505it_int ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5409_drop__bit__integer__def,axiom,
% 9.17/5.40 ( bit_se3928097537394005634nteger
% 9.17/5.40 = ( map_fu8224359078269604234nteger @ id_nat @ ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int ) @ bit_se8568078237143864401it_int ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5410_push__bit__integer__def,axiom,
% 9.17/5.40 ( bit_se7788150548672797655nteger
% 9.17/5.40 = ( map_fu8224359078269604234nteger @ id_nat @ ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int ) @ bit_se545348938243370406it_int ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5411_unset__bit__integer__def,axiom,
% 9.17/5.40 ( bit_se8260200283734997820nteger
% 9.17/5.40 = ( map_fu8224359078269604234nteger @ id_nat @ ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int ) @ bit_se4203085406695923979it_int ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5412_set__bit__integer__def,axiom,
% 9.17/5.40 ( bit_se2793503036327961859nteger
% 9.17/5.40 = ( map_fu8224359078269604234nteger @ id_nat @ ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int ) @ bit_se7879613467334960850it_int ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5413_flip__bit__integer__def,axiom,
% 9.17/5.40 ( bit_se1345352211410354436nteger
% 9.17/5.40 = ( map_fu8224359078269604234nteger @ id_nat @ ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int ) @ bit_se2159334234014336723it_int ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5414_pair__leqI1,axiom,
% 9.17/5.40 ! [A: nat,B: nat,S: nat,T: nat] :
% 9.17/5.40 ( ( ord_less_nat @ A @ B )
% 9.17/5.40 => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A @ S ) @ ( product_Pair_nat_nat @ B @ T ) ) @ fun_pair_leq ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5415_image__minus__const__atLeastLessThan__nat,axiom,
% 9.17/5.40 ! [C: nat,Y: nat,X: nat] :
% 9.17/5.40 ( ( ( ord_less_nat @ C @ Y )
% 9.17/5.40 => ( ( image_nat_nat
% 9.17/5.40 @ ^ [I3: nat] : ( minus_minus_nat @ I3 @ C )
% 9.17/5.40 @ ( set_or4665077453230672383an_nat @ X @ Y ) )
% 9.17/5.40 = ( set_or4665077453230672383an_nat @ ( minus_minus_nat @ X @ C ) @ ( minus_minus_nat @ Y @ C ) ) ) )
% 9.17/5.40 & ( ~ ( ord_less_nat @ C @ Y )
% 9.17/5.40 => ( ( ( ord_less_nat @ X @ Y )
% 9.17/5.40 => ( ( image_nat_nat
% 9.17/5.40 @ ^ [I3: nat] : ( minus_minus_nat @ I3 @ C )
% 9.17/5.40 @ ( set_or4665077453230672383an_nat @ X @ Y ) )
% 9.17/5.40 = ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) )
% 9.17/5.40 & ( ~ ( ord_less_nat @ X @ Y )
% 9.17/5.40 => ( ( image_nat_nat
% 9.17/5.40 @ ^ [I3: nat] : ( minus_minus_nat @ I3 @ C )
% 9.17/5.40 @ ( set_or4665077453230672383an_nat @ X @ Y ) )
% 9.17/5.40 = bot_bot_set_nat ) ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5416_card__atLeastAtMost__int,axiom,
% 9.17/5.40 ! [L: int,U: int] :
% 9.17/5.40 ( ( finite_card_int @ ( set_or1266510415728281911st_int @ L @ U ) )
% 9.17/5.40 = ( nat2 @ ( plus_plus_int @ ( minus_minus_int @ U @ L ) @ one_one_int ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5417_range__mod,axiom,
% 9.17/5.40 ! [N2: nat] :
% 9.17/5.40 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 9.17/5.40 => ( ( image_nat_nat
% 9.17/5.40 @ ^ [M: nat] : ( modulo_modulo_nat @ M @ N2 )
% 9.17/5.40 @ top_top_set_nat )
% 9.17/5.40 = ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5418_Some__image__these__eq,axiom,
% 9.17/5.40 ! [A2: set_op3940070208846178154it_nat] :
% 9.17/5.40 ( ( image_4799632500972785611it_nat @ some_P6105628898608307625it_nat @ ( these_6645423997822192641it_nat @ A2 ) )
% 9.17/5.40 = ( collec8141831914148684149it_nat
% 9.17/5.40 @ ^ [X3: option3216581401566546698it_nat] :
% 9.17/5.40 ( ( member3517700364412436275it_nat @ X3 @ A2 )
% 9.17/5.40 & ( X3 != none_P2587165478634041381it_nat ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5419_Some__image__these__eq,axiom,
% 9.17/5.40 ! [A2: set_option_num] :
% 9.17/5.40 ( ( image_num_option_num @ some_num @ ( these_num @ A2 ) )
% 9.17/5.40 = ( collect_option_num
% 9.17/5.40 @ ^ [X3: option_num] :
% 9.17/5.40 ( ( member_option_num @ X3 @ A2 )
% 9.17/5.40 & ( X3 != none_num ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5420_Some__image__these__eq,axiom,
% 9.17/5.40 ! [A2: set_op239864471688321678it_nat] :
% 9.17/5.40 ( ( image_3455408117458022631it_nat @ some_P1914260805536162275it_nat @ ( these_3407724651694999947it_nat @ A2 ) )
% 9.17/5.40 = ( collec5742531119322951597it_nat
% 9.17/5.40 @ ^ [X3: option8956607266484857688it_nat] :
% 9.17/5.40 ( ( member5596548051065438575it_nat @ X3 @ A2 )
% 9.17/5.40 & ( X3 != none_P9117596204409417319it_nat ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5421_prod__mono2,axiom,
% 9.17/5.40 ! [B5: set_o,A2: set_o,F: $o > code_integer] :
% 9.17/5.40 ( ( finite_finite_o @ B5 )
% 9.17/5.40 => ( ( ord_less_eq_set_o @ A2 @ B5 )
% 9.17/5.40 => ( ! [B2: $o] :
% 9.17/5.40 ( ( member_o @ B2 @ ( minus_minus_set_o @ B5 @ A2 ) )
% 9.17/5.40 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F @ B2 ) ) )
% 9.17/5.40 => ( ! [A3: $o] :
% 9.17/5.40 ( ( member_o @ A3 @ A2 )
% 9.17/5.40 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ A3 ) ) )
% 9.17/5.40 => ( ord_le3102999989581377725nteger @ ( groups7694694392188491536nteger @ F @ A2 ) @ ( groups7694694392188491536nteger @ F @ B5 ) ) ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5422_prod__mono2,axiom,
% 9.17/5.40 ! [B5: set_int,A2: set_int,F: int > code_integer] :
% 9.17/5.40 ( ( finite_finite_int @ B5 )
% 9.17/5.40 => ( ( ord_less_eq_set_int @ A2 @ B5 )
% 9.17/5.40 => ( ! [B2: int] :
% 9.17/5.40 ( ( member_int @ B2 @ ( minus_minus_set_int @ B5 @ A2 ) )
% 9.17/5.40 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F @ B2 ) ) )
% 9.17/5.40 => ( ! [A3: int] :
% 9.17/5.40 ( ( member_int @ A3 @ A2 )
% 9.17/5.40 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ A3 ) ) )
% 9.17/5.40 => ( ord_le3102999989581377725nteger @ ( groups3827104343326376752nteger @ F @ A2 ) @ ( groups3827104343326376752nteger @ F @ B5 ) ) ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5423_prod__mono2,axiom,
% 9.17/5.40 ! [B5: set_Code_integer,A2: set_Code_integer,F: code_integer > code_integer] :
% 9.17/5.40 ( ( finite6017078050557962740nteger @ B5 )
% 9.17/5.40 => ( ( ord_le7084787975880047091nteger @ A2 @ B5 )
% 9.17/5.40 => ( ! [B2: code_integer] :
% 9.17/5.40 ( ( member_Code_integer @ B2 @ ( minus_2355218937544613996nteger @ B5 @ A2 ) )
% 9.17/5.40 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F @ B2 ) ) )
% 9.17/5.40 => ( ! [A3: code_integer] :
% 9.17/5.40 ( ( member_Code_integer @ A3 @ A2 )
% 9.17/5.40 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ A3 ) ) )
% 9.17/5.40 => ( ord_le3102999989581377725nteger @ ( groups3674199335183972705nteger @ F @ A2 ) @ ( groups3674199335183972705nteger @ F @ B5 ) ) ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5424_prod__mono2,axiom,
% 9.17/5.40 ! [B5: set_o,A2: set_o,F: $o > rat] :
% 9.17/5.40 ( ( finite_finite_o @ B5 )
% 9.17/5.40 => ( ( ord_less_eq_set_o @ A2 @ B5 )
% 9.17/5.40 => ( ! [B2: $o] :
% 9.17/5.40 ( ( member_o @ B2 @ ( minus_minus_set_o @ B5 @ A2 ) )
% 9.17/5.40 => ( ord_less_eq_rat @ one_one_rat @ ( F @ B2 ) ) )
% 9.17/5.40 => ( ! [A3: $o] :
% 9.17/5.40 ( ( member_o @ A3 @ A2 )
% 9.17/5.40 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ A3 ) ) )
% 9.17/5.40 => ( ord_less_eq_rat @ ( groups2869687844427037835_o_rat @ F @ A2 ) @ ( groups2869687844427037835_o_rat @ F @ B5 ) ) ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5425_prod__mono2,axiom,
% 9.17/5.40 ! [B5: set_int,A2: set_int,F: int > rat] :
% 9.17/5.40 ( ( finite_finite_int @ B5 )
% 9.17/5.40 => ( ( ord_less_eq_set_int @ A2 @ B5 )
% 9.17/5.40 => ( ! [B2: int] :
% 9.17/5.40 ( ( member_int @ B2 @ ( minus_minus_set_int @ B5 @ A2 ) )
% 9.17/5.40 => ( ord_less_eq_rat @ one_one_rat @ ( F @ B2 ) ) )
% 9.17/5.40 => ( ! [A3: int] :
% 9.17/5.40 ( ( member_int @ A3 @ A2 )
% 9.17/5.40 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ A3 ) ) )
% 9.17/5.40 => ( ord_less_eq_rat @ ( groups1072433553688619179nt_rat @ F @ A2 ) @ ( groups1072433553688619179nt_rat @ F @ B5 ) ) ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5426_prod__mono2,axiom,
% 9.17/5.40 ! [B5: set_Code_integer,A2: set_Code_integer,F: code_integer > rat] :
% 9.17/5.40 ( ( finite6017078050557962740nteger @ B5 )
% 9.17/5.40 => ( ( ord_le7084787975880047091nteger @ A2 @ B5 )
% 9.17/5.40 => ( ! [B2: code_integer] :
% 9.17/5.40 ( ( member_Code_integer @ B2 @ ( minus_2355218937544613996nteger @ B5 @ A2 ) )
% 9.17/5.40 => ( ord_less_eq_rat @ one_one_rat @ ( F @ B2 ) ) )
% 9.17/5.40 => ( ! [A3: code_integer] :
% 9.17/5.40 ( ( member_Code_integer @ A3 @ A2 )
% 9.17/5.40 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ A3 ) ) )
% 9.17/5.40 => ( ord_less_eq_rat @ ( groups2555765274223993564er_rat @ F @ A2 ) @ ( groups2555765274223993564er_rat @ F @ B5 ) ) ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5427_prod__mono2,axiom,
% 9.17/5.40 ! [B5: set_o,A2: set_o,F: $o > int] :
% 9.17/5.40 ( ( finite_finite_o @ B5 )
% 9.17/5.40 => ( ( ord_less_eq_set_o @ A2 @ B5 )
% 9.17/5.40 => ( ! [B2: $o] :
% 9.17/5.40 ( ( member_o @ B2 @ ( minus_minus_set_o @ B5 @ A2 ) )
% 9.17/5.40 => ( ord_less_eq_int @ one_one_int @ ( F @ B2 ) ) )
% 9.17/5.40 => ( ! [A3: $o] :
% 9.17/5.40 ( ( member_o @ A3 @ A2 )
% 9.17/5.40 => ( ord_less_eq_int @ zero_zero_int @ ( F @ A3 ) ) )
% 9.17/5.40 => ( ord_less_eq_int @ ( groups3502327434004483295_o_int @ F @ A2 ) @ ( groups3502327434004483295_o_int @ F @ B5 ) ) ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5428_prod__mono2,axiom,
% 9.17/5.40 ! [B5: set_Code_integer,A2: set_Code_integer,F: code_integer > int] :
% 9.17/5.40 ( ( finite6017078050557962740nteger @ B5 )
% 9.17/5.40 => ( ( ord_le7084787975880047091nteger @ A2 @ B5 )
% 9.17/5.40 => ( ! [B2: code_integer] :
% 9.17/5.40 ( ( member_Code_integer @ B2 @ ( minus_2355218937544613996nteger @ B5 @ A2 ) )
% 9.17/5.40 => ( ord_less_eq_int @ one_one_int @ ( F @ B2 ) ) )
% 9.17/5.40 => ( ! [A3: code_integer] :
% 9.17/5.40 ( ( member_Code_integer @ A3 @ A2 )
% 9.17/5.40 => ( ord_less_eq_int @ zero_zero_int @ ( F @ A3 ) ) )
% 9.17/5.40 => ( ord_less_eq_int @ ( groups3188404863801439024er_int @ F @ A2 ) @ ( groups3188404863801439024er_int @ F @ B5 ) ) ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5429_prod__mono2,axiom,
% 9.17/5.40 ! [B5: set_nat,A2: set_nat,F: nat > code_integer] :
% 9.17/5.40 ( ( finite_finite_nat @ B5 )
% 9.17/5.40 => ( ( ord_less_eq_set_nat @ A2 @ B5 )
% 9.17/5.40 => ( ! [B2: nat] :
% 9.17/5.40 ( ( member_nat @ B2 @ ( minus_minus_set_nat @ B5 @ A2 ) )
% 9.17/5.40 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F @ B2 ) ) )
% 9.17/5.40 => ( ! [A3: nat] :
% 9.17/5.40 ( ( member_nat @ A3 @ A2 )
% 9.17/5.40 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ A3 ) ) )
% 9.17/5.40 => ( ord_le3102999989581377725nteger @ ( groups3455450783089532116nteger @ F @ A2 ) @ ( groups3455450783089532116nteger @ F @ B5 ) ) ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5430_prod__mono2,axiom,
% 9.17/5.40 ! [B5: set_nat,A2: set_nat,F: nat > rat] :
% 9.17/5.40 ( ( finite_finite_nat @ B5 )
% 9.17/5.40 => ( ( ord_less_eq_set_nat @ A2 @ B5 )
% 9.17/5.40 => ( ! [B2: nat] :
% 9.17/5.40 ( ( member_nat @ B2 @ ( minus_minus_set_nat @ B5 @ A2 ) )
% 9.17/5.40 => ( ord_less_eq_rat @ one_one_rat @ ( F @ B2 ) ) )
% 9.17/5.40 => ( ! [A3: nat] :
% 9.17/5.40 ( ( member_nat @ A3 @ A2 )
% 9.17/5.40 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ A3 ) ) )
% 9.17/5.40 => ( ord_less_eq_rat @ ( groups73079841787564623at_rat @ F @ A2 ) @ ( groups73079841787564623at_rat @ F @ B5 ) ) ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5431_the__dflt__None__nonempty,axiom,
% 9.17/5.40 ! [S2: set_Pr4329608150637261639at_nat] :
% 9.17/5.40 ( ( S2 != bot_bo228742789529271731at_nat )
% 9.17/5.40 => ( ( dflt_N3208751546879591902at_nat @ S2 )
% 9.17/5.40 = ( some_s5890477192898017836at_nat @ S2 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5432_the__dflt__None__nonempty,axiom,
% 9.17/5.40 ! [S2: set_Pr1261947904930325089at_nat] :
% 9.17/5.40 ( ( S2 != bot_bo2099793752762293965at_nat )
% 9.17/5.40 => ( ( dflt_N6592383573632408824at_nat @ S2 )
% 9.17/5.40 = ( some_s147305329494351046at_nat @ S2 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5433_the__dflt__None__nonempty,axiom,
% 9.17/5.40 ! [S2: set_o] :
% 9.17/5.40 ( ( S2 != bot_bot_set_o )
% 9.17/5.40 => ( ( dflt_None_set_o @ S2 )
% 9.17/5.40 = ( some_set_o @ S2 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5434_the__dflt__None__nonempty,axiom,
% 9.17/5.40 ! [S2: set_nat] :
% 9.17/5.40 ( ( S2 != bot_bot_set_nat )
% 9.17/5.40 => ( ( dflt_None_set_nat @ S2 )
% 9.17/5.40 = ( some_set_nat @ S2 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5435_the__dflt__None__nonempty,axiom,
% 9.17/5.40 ! [S2: set_int] :
% 9.17/5.40 ( ( S2 != bot_bot_set_int )
% 9.17/5.40 => ( ( dflt_None_set_int @ S2 )
% 9.17/5.40 = ( some_set_int @ S2 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5436_the__dflt__None__empty,axiom,
% 9.17/5.40 ( ( dflt_N3208751546879591902at_nat @ bot_bo228742789529271731at_nat )
% 9.17/5.40 = none_s6518873173954064040at_nat ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5437_the__dflt__None__empty,axiom,
% 9.17/5.40 ( ( dflt_N6592383573632408824at_nat @ bot_bo2099793752762293965at_nat )
% 9.17/5.40 = none_s625347054029921090at_nat ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5438_the__dflt__None__empty,axiom,
% 9.17/5.40 ( ( dflt_None_set_o @ bot_bot_set_o )
% 9.17/5.40 = none_set_o ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5439_the__dflt__None__empty,axiom,
% 9.17/5.40 ( ( dflt_None_set_nat @ bot_bot_set_nat )
% 9.17/5.40 = none_set_nat ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5440_the__dflt__None__empty,axiom,
% 9.17/5.40 ( ( dflt_None_set_int @ bot_bot_set_int )
% 9.17/5.40 = none_set_int ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5441_atMost__UNIV__triv,axiom,
% 9.17/5.40 ( ( set_or4236626031148496127et_nat @ top_top_set_nat )
% 9.17/5.40 = top_top_set_set_nat ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5442_atMost__UNIV__triv,axiom,
% 9.17/5.40 ( ( set_or2827140217781692084t_unit @ top_to1996260823553986621t_unit )
% 9.17/5.40 = top_to1767297665138865437t_unit ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5443_atMost__UNIV__triv,axiom,
% 9.17/5.40 ( ( set_or58775011639299419et_int @ top_top_set_int )
% 9.17/5.40 = top_top_set_set_int ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5444_finite__atLeastAtMost,axiom,
% 9.17/5.40 ! [L: nat,U: nat] : ( finite_finite_nat @ ( set_or1269000886237332187st_nat @ L @ U ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5445_finite__atLeastLessThan,axiom,
% 9.17/5.40 ! [L: nat,U: nat] : ( finite_finite_nat @ ( set_or4665077453230672383an_nat @ L @ U ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5446_int__of__integer__min,axiom,
% 9.17/5.40 ! [K: code_integer,L: code_integer] :
% 9.17/5.40 ( ( code_int_of_integer @ ( ord_min_Code_integer @ K @ L ) )
% 9.17/5.40 = ( ord_min_int @ ( code_int_of_integer @ K ) @ ( code_int_of_integer @ L ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5447_finite__atMost,axiom,
% 9.17/5.40 ! [K: nat] : ( finite_finite_nat @ ( set_ord_atMost_nat @ K ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5448_finite__lessThan,axiom,
% 9.17/5.40 ! [K: nat] : ( finite_finite_nat @ ( set_ord_lessThan_nat @ K ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5449_finite__atLeastAtMost__int,axiom,
% 9.17/5.40 ! [L: int,U: int] : ( finite_finite_int @ ( set_or1266510415728281911st_int @ L @ U ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5450_finite__atLeastLessThan__int,axiom,
% 9.17/5.40 ! [L: int,U: int] : ( finite_finite_int @ ( set_or4662586982721622107an_int @ L @ U ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5451_finite__atLeastLessThan__integer,axiom,
% 9.17/5.40 ! [L: code_integer,U: code_integer] : ( finite6017078050557962740nteger @ ( set_or8404916559141939852nteger @ L @ U ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5452_finite__atLeastAtMost__integer,axiom,
% 9.17/5.40 ! [L: code_integer,U: code_integer] : ( finite6017078050557962740nteger @ ( set_or189985376899183464nteger @ L @ U ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5453_finite__option__UNIV,axiom,
% 9.17/5.40 ( ( finite6785661671136154180nteger @ top_to5929521628599800467nteger )
% 9.17/5.40 = ( finite6017078050557962740nteger @ top_to4645266643341252675nteger ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5454_finite__option__UNIV,axiom,
% 9.17/5.40 ( ( finite6732403688824079472at_nat @ top_to3251141154256563319at_nat )
% 9.17/5.40 = ( finite6177210948735845034at_nat @ top_to4669805908274784177at_nat ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5455_finite__option__UNIV,axiom,
% 9.17/5.40 ( ( finite5523153139673422903on_nat @ top_to8920198386146353926on_nat )
% 9.17/5.40 = ( finite_finite_nat @ top_top_set_nat ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5456_finite__option__UNIV,axiom,
% 9.17/5.40 ( ( finite1445617369574913404t_unit @ top_to2690860209552263555t_unit )
% 9.17/5.40 = ( finite4290736615968046902t_unit @ top_to1996260823553986621t_unit ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5457_finite__option__UNIV,axiom,
% 9.17/5.40 ( ( finite1345302120164226195on_int @ top_to6430115241214627170on_int )
% 9.17/5.40 = ( finite_finite_int @ top_top_set_int ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5458_card__eq__UNIV,axiom,
% 9.17/5.40 ! [S2: set_Product_unit] :
% 9.17/5.40 ( ( ( finite410649719033368117t_unit @ S2 )
% 9.17/5.40 = ( finite410649719033368117t_unit @ top_to1996260823553986621t_unit ) )
% 9.17/5.40 = ( S2 = top_to1996260823553986621t_unit ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5459_card__eq__UNIV2,axiom,
% 9.17/5.40 ! [S2: set_Product_unit] :
% 9.17/5.40 ( ( ( finite410649719033368117t_unit @ top_to1996260823553986621t_unit )
% 9.17/5.40 = ( finite410649719033368117t_unit @ S2 ) )
% 9.17/5.40 = ( S2 = top_to1996260823553986621t_unit ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5460_these__empty,axiom,
% 9.17/5.40 ( ( these_1872268174106123684at_nat @ bot_bo1471150103859235065at_nat )
% 9.17/5.40 = bot_bo228742789529271731at_nat ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5461_these__empty,axiom,
% 9.17/5.40 ( ( these_8061402112538453438at_nat @ bot_bo3414888551220300179at_nat )
% 9.17/5.40 = bot_bo2099793752762293965at_nat ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5462_these__empty,axiom,
% 9.17/5.40 ( ( these_o @ bot_bot_set_option_o )
% 9.17/5.40 = bot_bot_set_o ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5463_these__empty,axiom,
% 9.17/5.40 ( ( these_nat @ bot_bo5009843511495006442on_nat )
% 9.17/5.40 = bot_bot_set_nat ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5464_these__empty,axiom,
% 9.17/5.40 ( ( these_int @ bot_bo2519760366563279686on_int )
% 9.17/5.40 = bot_bot_set_int ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5465_these__insert__None,axiom,
% 9.17/5.40 ! [A2: set_op3940070208846178154it_nat] :
% 9.17/5.40 ( ( these_6645423997822192641it_nat @ ( insert7468008629046257882it_nat @ none_P2587165478634041381it_nat @ A2 ) )
% 9.17/5.40 = ( these_6645423997822192641it_nat @ A2 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5466_these__insert__None,axiom,
% 9.17/5.40 ! [A2: set_option_num] :
% 9.17/5.40 ( ( these_num @ ( insert_option_num @ none_num @ A2 ) )
% 9.17/5.40 = ( these_num @ A2 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5467_these__insert__None,axiom,
% 9.17/5.40 ! [A2: set_op239864471688321678it_nat] :
% 9.17/5.40 ( ( these_3407724651694999947it_nat @ ( insert2007652293347934600it_nat @ none_P9117596204409417319it_nat @ A2 ) )
% 9.17/5.40 = ( these_3407724651694999947it_nat @ A2 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5468_the__dflt__None__set,axiom,
% 9.17/5.40 ! [X: set_Pr4329608150637261639at_nat] :
% 9.17/5.40 ( ( the_de6830073021511528542at_nat @ bot_bo228742789529271731at_nat @ ( dflt_N3208751546879591902at_nat @ X ) )
% 9.17/5.40 = X ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5469_the__dflt__None__set,axiom,
% 9.17/5.40 ! [X: set_Pr1261947904930325089at_nat] :
% 9.17/5.40 ( ( the_de3668382347305825784at_nat @ bot_bo2099793752762293965at_nat @ ( dflt_N6592383573632408824at_nat @ X ) )
% 9.17/5.40 = X ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5470_the__dflt__None__set,axiom,
% 9.17/5.40 ! [X: set_o] :
% 9.17/5.40 ( ( the_default_set_o @ bot_bot_set_o @ ( dflt_None_set_o @ X ) )
% 9.17/5.40 = X ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5471_the__dflt__None__set,axiom,
% 9.17/5.40 ! [X: set_nat] :
% 9.17/5.40 ( ( the_default_set_nat @ bot_bot_set_nat @ ( dflt_None_set_nat @ X ) )
% 9.17/5.40 = X ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5472_the__dflt__None__set,axiom,
% 9.17/5.40 ! [X: set_int] :
% 9.17/5.40 ( ( the_default_set_int @ bot_bot_set_int @ ( dflt_None_set_int @ X ) )
% 9.17/5.40 = X ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5473_surj__plus,axiom,
% 9.17/5.40 ! [A: rat] :
% 9.17/5.40 ( ( image_rat_rat @ ( plus_plus_rat @ A ) @ top_top_set_rat )
% 9.17/5.40 = top_top_set_rat ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5474_surj__plus,axiom,
% 9.17/5.40 ! [A: int] :
% 9.17/5.40 ( ( image_int_int @ ( plus_plus_int @ A ) @ top_top_set_int )
% 9.17/5.40 = top_top_set_int ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5475_infinite__Icc__iff,axiom,
% 9.17/5.40 ! [A: rat,B: rat] :
% 9.17/5.40 ( ( ~ ( finite_finite_rat @ ( set_or633870826150836451st_rat @ A @ B ) ) )
% 9.17/5.40 = ( ord_less_rat @ A @ B ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5476_infinite__Ico__iff,axiom,
% 9.17/5.40 ! [A: rat,B: rat] :
% 9.17/5.40 ( ( ~ ( finite_finite_rat @ ( set_or4029947393144176647an_rat @ A @ B ) ) )
% 9.17/5.40 = ( ord_less_rat @ A @ B ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5477_prod_Oinfinite,axiom,
% 9.17/5.40 ! [A2: set_nat,G: nat > code_integer] :
% 9.17/5.40 ( ~ ( finite_finite_nat @ A2 )
% 9.17/5.40 => ( ( groups3455450783089532116nteger @ G @ A2 )
% 9.17/5.40 = one_one_Code_integer ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5478_prod_Oinfinite,axiom,
% 9.17/5.40 ! [A2: set_int,G: int > code_integer] :
% 9.17/5.40 ( ~ ( finite_finite_int @ A2 )
% 9.17/5.40 => ( ( groups3827104343326376752nteger @ G @ A2 )
% 9.17/5.40 = one_one_Code_integer ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5479_prod_Oinfinite,axiom,
% 9.17/5.40 ! [A2: set_Code_integer,G: code_integer > code_integer] :
% 9.17/5.40 ( ~ ( finite6017078050557962740nteger @ A2 )
% 9.17/5.40 => ( ( groups3674199335183972705nteger @ G @ A2 )
% 9.17/5.40 = one_one_Code_integer ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5480_prod_Oinfinite,axiom,
% 9.17/5.40 ! [A2: set_nat,G: nat > assn] :
% 9.17/5.40 ( ~ ( finite_finite_nat @ A2 )
% 9.17/5.40 => ( ( groups6906906614972039071t_assn @ G @ A2 )
% 9.17/5.40 = one_one_assn ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5481_prod_Oinfinite,axiom,
% 9.17/5.40 ! [A2: set_int,G: int > assn] :
% 9.17/5.40 ( ~ ( finite_finite_int @ A2 )
% 9.17/5.40 => ( ( groups7882442080178216443t_assn @ G @ A2 )
% 9.17/5.40 = one_one_assn ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5482_prod_Oinfinite,axiom,
% 9.17/5.40 ! [A2: set_Code_integer,G: code_integer > assn] :
% 9.17/5.40 ( ~ ( finite6017078050557962740nteger @ A2 )
% 9.17/5.40 => ( ( groups1304777262505850412r_assn @ G @ A2 )
% 9.17/5.40 = one_one_assn ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5483_prod_Oinfinite,axiom,
% 9.17/5.40 ! [A2: set_nat,G: nat > rat] :
% 9.17/5.40 ( ~ ( finite_finite_nat @ A2 )
% 9.17/5.40 => ( ( groups73079841787564623at_rat @ G @ A2 )
% 9.17/5.40 = one_one_rat ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5484_prod_Oinfinite,axiom,
% 9.17/5.40 ! [A2: set_int,G: int > rat] :
% 9.17/5.40 ( ~ ( finite_finite_int @ A2 )
% 9.17/5.40 => ( ( groups1072433553688619179nt_rat @ G @ A2 )
% 9.17/5.40 = one_one_rat ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5485_prod_Oinfinite,axiom,
% 9.17/5.40 ! [A2: set_Code_integer,G: code_integer > rat] :
% 9.17/5.40 ( ~ ( finite6017078050557962740nteger @ A2 )
% 9.17/5.40 => ( ( groups2555765274223993564er_rat @ G @ A2 )
% 9.17/5.40 = one_one_rat ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5486_prod_Oinfinite,axiom,
% 9.17/5.40 ! [A2: set_int,G: int > nat] :
% 9.17/5.40 ( ~ ( finite_finite_int @ A2 )
% 9.17/5.40 => ( ( groups1707563613775114915nt_nat @ G @ A2 )
% 9.17/5.40 = one_one_nat ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5487_card__ge__UNIV,axiom,
% 9.17/5.40 ! [S2: set_Product_unit] :
% 9.17/5.40 ( ( ord_less_eq_nat @ ( finite410649719033368117t_unit @ top_to1996260823553986621t_unit ) @ ( finite410649719033368117t_unit @ S2 ) )
% 9.17/5.40 = ( S2 = top_to1996260823553986621t_unit ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5488_surj__diff__right,axiom,
% 9.17/5.40 ! [A: code_integer] :
% 9.17/5.40 ( ( image_4470545334726330049nteger
% 9.17/5.40 @ ^ [X3: code_integer] : ( minus_8373710615458151222nteger @ X3 @ A )
% 9.17/5.40 @ top_to4645266643341252675nteger )
% 9.17/5.40 = top_to4645266643341252675nteger ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5489_surj__diff__right,axiom,
% 9.17/5.40 ! [A: rat] :
% 9.17/5.40 ( ( image_rat_rat
% 9.17/5.40 @ ^ [X3: rat] : ( minus_minus_rat @ X3 @ A )
% 9.17/5.40 @ top_top_set_rat )
% 9.17/5.40 = top_top_set_rat ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5490_surj__diff__right,axiom,
% 9.17/5.40 ! [A: int] :
% 9.17/5.40 ( ( image_int_int
% 9.17/5.40 @ ^ [X3: int] : ( minus_minus_int @ X3 @ A )
% 9.17/5.40 @ top_top_set_int )
% 9.17/5.40 = top_top_set_int ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5491_prod__eq__1__iff,axiom,
% 9.17/5.40 ! [A2: set_int,F: int > nat] :
% 9.17/5.40 ( ( finite_finite_int @ A2 )
% 9.17/5.40 => ( ( ( groups1707563613775114915nt_nat @ F @ A2 )
% 9.17/5.40 = one_one_nat )
% 9.17/5.40 = ( ! [X3: int] :
% 9.17/5.40 ( ( member_int @ X3 @ A2 )
% 9.17/5.40 => ( ( F @ X3 )
% 9.17/5.40 = one_one_nat ) ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5492_prod__eq__1__iff,axiom,
% 9.17/5.40 ! [A2: set_Code_integer,F: code_integer > nat] :
% 9.17/5.40 ( ( finite6017078050557962740nteger @ A2 )
% 9.17/5.40 => ( ( ( groups3190895334310489300er_nat @ F @ A2 )
% 9.17/5.40 = one_one_nat )
% 9.17/5.40 = ( ! [X3: code_integer] :
% 9.17/5.40 ( ( member_Code_integer @ X3 @ A2 )
% 9.17/5.40 => ( ( F @ X3 )
% 9.17/5.40 = one_one_nat ) ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5493_prod__eq__1__iff,axiom,
% 9.17/5.40 ! [A2: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > nat] :
% 9.17/5.40 ( ( finite6177210948735845034at_nat @ A2 )
% 9.17/5.40 => ( ( ( groups4077766827762148844at_nat @ F @ A2 )
% 9.17/5.40 = one_one_nat )
% 9.17/5.40 = ( ! [X3: product_prod_nat_nat] :
% 9.17/5.40 ( ( member8440522571783428010at_nat @ X3 @ A2 )
% 9.17/5.40 => ( ( F @ X3 )
% 9.17/5.40 = one_one_nat ) ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5494_prod__eq__1__iff,axiom,
% 9.17/5.40 ! [A2: set_nat,F: nat > nat] :
% 9.17/5.40 ( ( finite_finite_nat @ A2 )
% 9.17/5.40 => ( ( ( groups708209901874060359at_nat @ F @ A2 )
% 9.17/5.40 = one_one_nat )
% 9.17/5.40 = ( ! [X3: nat] :
% 9.17/5.40 ( ( member_nat @ X3 @ A2 )
% 9.17/5.40 => ( ( F @ X3 )
% 9.17/5.40 = one_one_nat ) ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5495_prod_Odelta,axiom,
% 9.17/5.40 ! [S2: set_o,A: $o,B: $o > code_integer] :
% 9.17/5.40 ( ( finite_finite_o @ S2 )
% 9.17/5.40 => ( ( ( member_o @ A @ S2 )
% 9.17/5.40 => ( ( groups7694694392188491536nteger
% 9.17/5.40 @ ^ [K4: $o] : ( if_Code_integer @ ( K4 = A ) @ ( B @ K4 ) @ one_one_Code_integer )
% 9.17/5.40 @ S2 )
% 9.17/5.40 = ( B @ A ) ) )
% 9.17/5.40 & ( ~ ( member_o @ A @ S2 )
% 9.17/5.40 => ( ( groups7694694392188491536nteger
% 9.17/5.40 @ ^ [K4: $o] : ( if_Code_integer @ ( K4 = A ) @ ( B @ K4 ) @ one_one_Code_integer )
% 9.17/5.40 @ S2 )
% 9.17/5.40 = one_one_Code_integer ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5496_prod_Odelta,axiom,
% 9.17/5.40 ! [S2: set_nat,A: nat,B: nat > code_integer] :
% 9.17/5.40 ( ( finite_finite_nat @ S2 )
% 9.17/5.40 => ( ( ( member_nat @ A @ S2 )
% 9.17/5.40 => ( ( groups3455450783089532116nteger
% 9.17/5.40 @ ^ [K4: nat] : ( if_Code_integer @ ( K4 = A ) @ ( B @ K4 ) @ one_one_Code_integer )
% 9.17/5.40 @ S2 )
% 9.17/5.40 = ( B @ A ) ) )
% 9.17/5.40 & ( ~ ( member_nat @ A @ S2 )
% 9.17/5.40 => ( ( groups3455450783089532116nteger
% 9.17/5.40 @ ^ [K4: nat] : ( if_Code_integer @ ( K4 = A ) @ ( B @ K4 ) @ one_one_Code_integer )
% 9.17/5.40 @ S2 )
% 9.17/5.40 = one_one_Code_integer ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5497_prod_Odelta,axiom,
% 9.17/5.40 ! [S2: set_int,A: int,B: int > code_integer] :
% 9.17/5.40 ( ( finite_finite_int @ S2 )
% 9.17/5.40 => ( ( ( member_int @ A @ S2 )
% 9.17/5.40 => ( ( groups3827104343326376752nteger
% 9.17/5.40 @ ^ [K4: int] : ( if_Code_integer @ ( K4 = A ) @ ( B @ K4 ) @ one_one_Code_integer )
% 9.17/5.40 @ S2 )
% 9.17/5.40 = ( B @ A ) ) )
% 9.17/5.40 & ( ~ ( member_int @ A @ S2 )
% 9.17/5.40 => ( ( groups3827104343326376752nteger
% 9.17/5.40 @ ^ [K4: int] : ( if_Code_integer @ ( K4 = A ) @ ( B @ K4 ) @ one_one_Code_integer )
% 9.17/5.40 @ S2 )
% 9.17/5.40 = one_one_Code_integer ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5498_prod_Odelta,axiom,
% 9.17/5.40 ! [S2: set_Code_integer,A: code_integer,B: code_integer > code_integer] :
% 9.17/5.40 ( ( finite6017078050557962740nteger @ S2 )
% 9.17/5.40 => ( ( ( member_Code_integer @ A @ S2 )
% 9.17/5.40 => ( ( groups3674199335183972705nteger
% 9.17/5.40 @ ^ [K4: code_integer] : ( if_Code_integer @ ( K4 = A ) @ ( B @ K4 ) @ one_one_Code_integer )
% 9.17/5.40 @ S2 )
% 9.17/5.40 = ( B @ A ) ) )
% 9.17/5.40 & ( ~ ( member_Code_integer @ A @ S2 )
% 9.17/5.40 => ( ( groups3674199335183972705nteger
% 9.17/5.40 @ ^ [K4: code_integer] : ( if_Code_integer @ ( K4 = A ) @ ( B @ K4 ) @ one_one_Code_integer )
% 9.17/5.40 @ S2 )
% 9.17/5.40 = one_one_Code_integer ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5499_prod_Odelta,axiom,
% 9.17/5.40 ! [S2: set_o,A: $o,B: $o > assn] :
% 9.17/5.40 ( ( finite_finite_o @ S2 )
% 9.17/5.40 => ( ( ( member_o @ A @ S2 )
% 9.17/5.40 => ( ( groups5301882518646026715o_assn
% 9.17/5.40 @ ^ [K4: $o] : ( if_assn @ ( K4 = A ) @ ( B @ K4 ) @ one_one_assn )
% 9.17/5.40 @ S2 )
% 9.17/5.40 = ( B @ A ) ) )
% 9.17/5.40 & ( ~ ( member_o @ A @ S2 )
% 9.17/5.40 => ( ( groups5301882518646026715o_assn
% 9.17/5.40 @ ^ [K4: $o] : ( if_assn @ ( K4 = A ) @ ( B @ K4 ) @ one_one_assn )
% 9.17/5.40 @ S2 )
% 9.17/5.40 = one_one_assn ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5500_prod_Odelta,axiom,
% 9.17/5.40 ! [S2: set_nat,A: nat,B: nat > assn] :
% 9.17/5.40 ( ( finite_finite_nat @ S2 )
% 9.17/5.40 => ( ( ( member_nat @ A @ S2 )
% 9.17/5.40 => ( ( groups6906906614972039071t_assn
% 9.17/5.40 @ ^ [K4: nat] : ( if_assn @ ( K4 = A ) @ ( B @ K4 ) @ one_one_assn )
% 9.17/5.40 @ S2 )
% 9.17/5.40 = ( B @ A ) ) )
% 9.17/5.40 & ( ~ ( member_nat @ A @ S2 )
% 9.17/5.40 => ( ( groups6906906614972039071t_assn
% 9.17/5.40 @ ^ [K4: nat] : ( if_assn @ ( K4 = A ) @ ( B @ K4 ) @ one_one_assn )
% 9.17/5.40 @ S2 )
% 9.17/5.40 = one_one_assn ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5501_prod_Odelta,axiom,
% 9.17/5.40 ! [S2: set_int,A: int,B: int > assn] :
% 9.17/5.40 ( ( finite_finite_int @ S2 )
% 9.17/5.40 => ( ( ( member_int @ A @ S2 )
% 9.17/5.40 => ( ( groups7882442080178216443t_assn
% 9.17/5.40 @ ^ [K4: int] : ( if_assn @ ( K4 = A ) @ ( B @ K4 ) @ one_one_assn )
% 9.17/5.40 @ S2 )
% 9.17/5.40 = ( B @ A ) ) )
% 9.17/5.40 & ( ~ ( member_int @ A @ S2 )
% 9.17/5.40 => ( ( groups7882442080178216443t_assn
% 9.17/5.40 @ ^ [K4: int] : ( if_assn @ ( K4 = A ) @ ( B @ K4 ) @ one_one_assn )
% 9.17/5.40 @ S2 )
% 9.17/5.40 = one_one_assn ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5502_prod_Odelta,axiom,
% 9.17/5.40 ! [S2: set_Code_integer,A: code_integer,B: code_integer > assn] :
% 9.17/5.40 ( ( finite6017078050557962740nteger @ S2 )
% 9.17/5.40 => ( ( ( member_Code_integer @ A @ S2 )
% 9.17/5.40 => ( ( groups1304777262505850412r_assn
% 9.17/5.40 @ ^ [K4: code_integer] : ( if_assn @ ( K4 = A ) @ ( B @ K4 ) @ one_one_assn )
% 9.17/5.40 @ S2 )
% 9.17/5.40 = ( B @ A ) ) )
% 9.17/5.40 & ( ~ ( member_Code_integer @ A @ S2 )
% 9.17/5.40 => ( ( groups1304777262505850412r_assn
% 9.17/5.40 @ ^ [K4: code_integer] : ( if_assn @ ( K4 = A ) @ ( B @ K4 ) @ one_one_assn )
% 9.17/5.40 @ S2 )
% 9.17/5.40 = one_one_assn ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5503_prod_Odelta,axiom,
% 9.17/5.40 ! [S2: set_o,A: $o,B: $o > rat] :
% 9.17/5.40 ( ( finite_finite_o @ S2 )
% 9.17/5.40 => ( ( ( member_o @ A @ S2 )
% 9.17/5.40 => ( ( groups2869687844427037835_o_rat
% 9.17/5.40 @ ^ [K4: $o] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ one_one_rat )
% 9.17/5.40 @ S2 )
% 9.17/5.40 = ( B @ A ) ) )
% 9.17/5.40 & ( ~ ( member_o @ A @ S2 )
% 9.17/5.40 => ( ( groups2869687844427037835_o_rat
% 9.17/5.40 @ ^ [K4: $o] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ one_one_rat )
% 9.17/5.40 @ S2 )
% 9.17/5.40 = one_one_rat ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5504_prod_Odelta,axiom,
% 9.17/5.40 ! [S2: set_nat,A: nat,B: nat > rat] :
% 9.17/5.40 ( ( finite_finite_nat @ S2 )
% 9.17/5.40 => ( ( ( member_nat @ A @ S2 )
% 9.17/5.40 => ( ( groups73079841787564623at_rat
% 9.17/5.40 @ ^ [K4: nat] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ one_one_rat )
% 9.17/5.40 @ S2 )
% 9.17/5.40 = ( B @ A ) ) )
% 9.17/5.40 & ( ~ ( member_nat @ A @ S2 )
% 9.17/5.40 => ( ( groups73079841787564623at_rat
% 9.17/5.40 @ ^ [K4: nat] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ one_one_rat )
% 9.17/5.40 @ S2 )
% 9.17/5.40 = one_one_rat ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5505_prod_Odelta_H,axiom,
% 9.17/5.40 ! [S2: set_o,A: $o,B: $o > code_integer] :
% 9.17/5.40 ( ( finite_finite_o @ S2 )
% 9.17/5.40 => ( ( ( member_o @ A @ S2 )
% 9.17/5.40 => ( ( groups7694694392188491536nteger
% 9.17/5.40 @ ^ [K4: $o] : ( if_Code_integer @ ( A = K4 ) @ ( B @ K4 ) @ one_one_Code_integer )
% 9.17/5.40 @ S2 )
% 9.17/5.40 = ( B @ A ) ) )
% 9.17/5.40 & ( ~ ( member_o @ A @ S2 )
% 9.17/5.40 => ( ( groups7694694392188491536nteger
% 9.17/5.40 @ ^ [K4: $o] : ( if_Code_integer @ ( A = K4 ) @ ( B @ K4 ) @ one_one_Code_integer )
% 9.17/5.40 @ S2 )
% 9.17/5.40 = one_one_Code_integer ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5506_prod_Odelta_H,axiom,
% 9.17/5.40 ! [S2: set_nat,A: nat,B: nat > code_integer] :
% 9.17/5.40 ( ( finite_finite_nat @ S2 )
% 9.17/5.40 => ( ( ( member_nat @ A @ S2 )
% 9.17/5.40 => ( ( groups3455450783089532116nteger
% 9.17/5.40 @ ^ [K4: nat] : ( if_Code_integer @ ( A = K4 ) @ ( B @ K4 ) @ one_one_Code_integer )
% 9.17/5.40 @ S2 )
% 9.17/5.40 = ( B @ A ) ) )
% 9.17/5.40 & ( ~ ( member_nat @ A @ S2 )
% 9.17/5.40 => ( ( groups3455450783089532116nteger
% 9.17/5.40 @ ^ [K4: nat] : ( if_Code_integer @ ( A = K4 ) @ ( B @ K4 ) @ one_one_Code_integer )
% 9.17/5.40 @ S2 )
% 9.17/5.40 = one_one_Code_integer ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5507_prod_Odelta_H,axiom,
% 9.17/5.40 ! [S2: set_int,A: int,B: int > code_integer] :
% 9.17/5.40 ( ( finite_finite_int @ S2 )
% 9.17/5.40 => ( ( ( member_int @ A @ S2 )
% 9.17/5.40 => ( ( groups3827104343326376752nteger
% 9.17/5.40 @ ^ [K4: int] : ( if_Code_integer @ ( A = K4 ) @ ( B @ K4 ) @ one_one_Code_integer )
% 9.17/5.40 @ S2 )
% 9.17/5.40 = ( B @ A ) ) )
% 9.17/5.40 & ( ~ ( member_int @ A @ S2 )
% 9.17/5.40 => ( ( groups3827104343326376752nteger
% 9.17/5.40 @ ^ [K4: int] : ( if_Code_integer @ ( A = K4 ) @ ( B @ K4 ) @ one_one_Code_integer )
% 9.17/5.40 @ S2 )
% 9.17/5.40 = one_one_Code_integer ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5508_prod_Odelta_H,axiom,
% 9.17/5.40 ! [S2: set_Code_integer,A: code_integer,B: code_integer > code_integer] :
% 9.17/5.40 ( ( finite6017078050557962740nteger @ S2 )
% 9.17/5.40 => ( ( ( member_Code_integer @ A @ S2 )
% 9.17/5.40 => ( ( groups3674199335183972705nteger
% 9.17/5.40 @ ^ [K4: code_integer] : ( if_Code_integer @ ( A = K4 ) @ ( B @ K4 ) @ one_one_Code_integer )
% 9.17/5.40 @ S2 )
% 9.17/5.40 = ( B @ A ) ) )
% 9.17/5.40 & ( ~ ( member_Code_integer @ A @ S2 )
% 9.17/5.40 => ( ( groups3674199335183972705nteger
% 9.17/5.40 @ ^ [K4: code_integer] : ( if_Code_integer @ ( A = K4 ) @ ( B @ K4 ) @ one_one_Code_integer )
% 9.17/5.40 @ S2 )
% 9.17/5.40 = one_one_Code_integer ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5509_prod_Odelta_H,axiom,
% 9.17/5.40 ! [S2: set_o,A: $o,B: $o > assn] :
% 9.17/5.40 ( ( finite_finite_o @ S2 )
% 9.17/5.40 => ( ( ( member_o @ A @ S2 )
% 9.17/5.40 => ( ( groups5301882518646026715o_assn
% 9.17/5.40 @ ^ [K4: $o] : ( if_assn @ ( A = K4 ) @ ( B @ K4 ) @ one_one_assn )
% 9.17/5.40 @ S2 )
% 9.17/5.40 = ( B @ A ) ) )
% 9.17/5.40 & ( ~ ( member_o @ A @ S2 )
% 9.17/5.40 => ( ( groups5301882518646026715o_assn
% 9.17/5.40 @ ^ [K4: $o] : ( if_assn @ ( A = K4 ) @ ( B @ K4 ) @ one_one_assn )
% 9.17/5.40 @ S2 )
% 9.17/5.40 = one_one_assn ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5510_prod_Odelta_H,axiom,
% 9.17/5.40 ! [S2: set_nat,A: nat,B: nat > assn] :
% 9.17/5.40 ( ( finite_finite_nat @ S2 )
% 9.17/5.40 => ( ( ( member_nat @ A @ S2 )
% 9.17/5.40 => ( ( groups6906906614972039071t_assn
% 9.17/5.40 @ ^ [K4: nat] : ( if_assn @ ( A = K4 ) @ ( B @ K4 ) @ one_one_assn )
% 9.17/5.40 @ S2 )
% 9.17/5.40 = ( B @ A ) ) )
% 9.17/5.40 & ( ~ ( member_nat @ A @ S2 )
% 9.17/5.40 => ( ( groups6906906614972039071t_assn
% 9.17/5.40 @ ^ [K4: nat] : ( if_assn @ ( A = K4 ) @ ( B @ K4 ) @ one_one_assn )
% 9.17/5.40 @ S2 )
% 9.17/5.40 = one_one_assn ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5511_prod_Odelta_H,axiom,
% 9.17/5.40 ! [S2: set_int,A: int,B: int > assn] :
% 9.17/5.40 ( ( finite_finite_int @ S2 )
% 9.17/5.40 => ( ( ( member_int @ A @ S2 )
% 9.17/5.40 => ( ( groups7882442080178216443t_assn
% 9.17/5.40 @ ^ [K4: int] : ( if_assn @ ( A = K4 ) @ ( B @ K4 ) @ one_one_assn )
% 9.17/5.40 @ S2 )
% 9.17/5.40 = ( B @ A ) ) )
% 9.17/5.40 & ( ~ ( member_int @ A @ S2 )
% 9.17/5.40 => ( ( groups7882442080178216443t_assn
% 9.17/5.40 @ ^ [K4: int] : ( if_assn @ ( A = K4 ) @ ( B @ K4 ) @ one_one_assn )
% 9.17/5.40 @ S2 )
% 9.17/5.40 = one_one_assn ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5512_prod_Odelta_H,axiom,
% 9.17/5.40 ! [S2: set_Code_integer,A: code_integer,B: code_integer > assn] :
% 9.17/5.40 ( ( finite6017078050557962740nteger @ S2 )
% 9.17/5.40 => ( ( ( member_Code_integer @ A @ S2 )
% 9.17/5.40 => ( ( groups1304777262505850412r_assn
% 9.17/5.40 @ ^ [K4: code_integer] : ( if_assn @ ( A = K4 ) @ ( B @ K4 ) @ one_one_assn )
% 9.17/5.40 @ S2 )
% 9.17/5.40 = ( B @ A ) ) )
% 9.17/5.40 & ( ~ ( member_Code_integer @ A @ S2 )
% 9.17/5.40 => ( ( groups1304777262505850412r_assn
% 9.17/5.40 @ ^ [K4: code_integer] : ( if_assn @ ( A = K4 ) @ ( B @ K4 ) @ one_one_assn )
% 9.17/5.40 @ S2 )
% 9.17/5.40 = one_one_assn ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5513_prod_Odelta_H,axiom,
% 9.17/5.40 ! [S2: set_o,A: $o,B: $o > rat] :
% 9.17/5.40 ( ( finite_finite_o @ S2 )
% 9.17/5.40 => ( ( ( member_o @ A @ S2 )
% 9.17/5.40 => ( ( groups2869687844427037835_o_rat
% 9.17/5.40 @ ^ [K4: $o] : ( if_rat @ ( A = K4 ) @ ( B @ K4 ) @ one_one_rat )
% 9.17/5.40 @ S2 )
% 9.17/5.40 = ( B @ A ) ) )
% 9.17/5.40 & ( ~ ( member_o @ A @ S2 )
% 9.17/5.40 => ( ( groups2869687844427037835_o_rat
% 9.17/5.40 @ ^ [K4: $o] : ( if_rat @ ( A = K4 ) @ ( B @ K4 ) @ one_one_rat )
% 9.17/5.40 @ S2 )
% 9.17/5.40 = one_one_rat ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5514_prod_Odelta_H,axiom,
% 9.17/5.40 ! [S2: set_nat,A: nat,B: nat > rat] :
% 9.17/5.40 ( ( finite_finite_nat @ S2 )
% 9.17/5.40 => ( ( ( member_nat @ A @ S2 )
% 9.17/5.40 => ( ( groups73079841787564623at_rat
% 9.17/5.40 @ ^ [K4: nat] : ( if_rat @ ( A = K4 ) @ ( B @ K4 ) @ one_one_rat )
% 9.17/5.40 @ S2 )
% 9.17/5.40 = ( B @ A ) ) )
% 9.17/5.40 & ( ~ ( member_nat @ A @ S2 )
% 9.17/5.40 => ( ( groups73079841787564623at_rat
% 9.17/5.40 @ ^ [K4: nat] : ( if_rat @ ( A = K4 ) @ ( B @ K4 ) @ one_one_rat )
% 9.17/5.40 @ S2 )
% 9.17/5.40 = one_one_rat ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5515_these__insert__Some,axiom,
% 9.17/5.40 ! [X: produc3843707927480180839at_nat,A2: set_op989438649584373901at_nat] :
% 9.17/5.40 ( ( these_1872268174106123684at_nat @ ( insert6833468608972679677at_nat @ ( some_P131194445498448716at_nat @ X ) @ A2 ) )
% 9.17/5.40 = ( insert9069300056098147895at_nat @ X @ ( these_1872268174106123684at_nat @ A2 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5516_these__insert__Some,axiom,
% 9.17/5.40 ! [X: product_prod_nat_nat,A2: set_op4508134149509766951at_nat] :
% 9.17/5.40 ( ( these_8061402112538453438at_nat @ ( insert6842972033726296599at_nat @ ( some_P7363390416028606310at_nat @ X ) @ A2 ) )
% 9.17/5.40 = ( insert8211810215607154385at_nat @ X @ ( these_8061402112538453438at_nat @ A2 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5517_these__insert__Some,axiom,
% 9.17/5.40 ! [X: $o,A2: set_option_o] :
% 9.17/5.40 ( ( these_o @ ( insert_option_o @ ( some_o @ X ) @ A2 ) )
% 9.17/5.40 = ( insert_o @ X @ ( these_o @ A2 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5518_these__insert__Some,axiom,
% 9.17/5.40 ! [X: nat,A2: set_option_nat] :
% 9.17/5.40 ( ( these_nat @ ( insert_option_nat @ ( some_nat @ X ) @ A2 ) )
% 9.17/5.40 = ( insert_nat @ X @ ( these_nat @ A2 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5519_these__insert__Some,axiom,
% 9.17/5.40 ! [X: int,A2: set_option_int] :
% 9.17/5.40 ( ( these_int @ ( insert_option_int @ ( some_int @ X ) @ A2 ) )
% 9.17/5.40 = ( insert_int @ X @ ( these_int @ A2 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5520_these__insert__Some,axiom,
% 9.17/5.40 ! [X: num,A2: set_option_num] :
% 9.17/5.40 ( ( these_num @ ( insert_option_num @ ( some_num @ X ) @ A2 ) )
% 9.17/5.40 = ( insert_num @ X @ ( these_num @ A2 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5521_these__insert__Some,axiom,
% 9.17/5.40 ! [X: produc8664842809031399944it_nat,A2: set_op239864471688321678it_nat] :
% 9.17/5.40 ( ( these_3407724651694999947it_nat @ ( insert2007652293347934600it_nat @ ( some_P1914260805536162275it_nat @ X ) @ A2 ) )
% 9.17/5.40 = ( insert5940566491043231800it_nat @ X @ ( these_3407724651694999947it_nat @ A2 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5522_these__image__Some__eq,axiom,
% 9.17/5.40 ! [A2: set_num] :
% 9.17/5.40 ( ( these_num @ ( image_num_option_num @ some_num @ A2 ) )
% 9.17/5.40 = A2 ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5523_these__image__Some__eq,axiom,
% 9.17/5.40 ! [A2: set_Pr1354866905816374718it_nat] :
% 9.17/5.40 ( ( these_3407724651694999947it_nat @ ( image_3455408117458022631it_nat @ some_P1914260805536162275it_nat @ A2 ) )
% 9.17/5.40 = A2 ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5524_sum_Oinsert,axiom,
% 9.17/5.40 ! [A2: set_o,X: $o,G: $o > rat] :
% 9.17/5.40 ( ( finite_finite_o @ A2 )
% 9.17/5.40 => ( ~ ( member_o @ X @ A2 )
% 9.17/5.40 => ( ( groups7872700643590313910_o_rat @ G @ ( insert_o @ X @ A2 ) )
% 9.17/5.40 = ( plus_plus_rat @ ( G @ X ) @ ( groups7872700643590313910_o_rat @ G @ A2 ) ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5525_sum_Oinsert,axiom,
% 9.17/5.40 ! [A2: set_nat,X: nat,G: nat > rat] :
% 9.17/5.40 ( ( finite_finite_nat @ A2 )
% 9.17/5.40 => ( ~ ( member_nat @ X @ A2 )
% 9.17/5.40 => ( ( groups2906978787729119204at_rat @ G @ ( insert_nat @ X @ A2 ) )
% 9.17/5.40 = ( plus_plus_rat @ ( G @ X ) @ ( groups2906978787729119204at_rat @ G @ A2 ) ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5526_sum_Oinsert,axiom,
% 9.17/5.40 ! [A2: set_int,X: int,G: int > rat] :
% 9.17/5.40 ( ( finite_finite_int @ A2 )
% 9.17/5.40 => ( ~ ( member_int @ X @ A2 )
% 9.17/5.40 => ( ( groups3906332499630173760nt_rat @ G @ ( insert_int @ X @ A2 ) )
% 9.17/5.40 = ( plus_plus_rat @ ( G @ X ) @ ( groups3906332499630173760nt_rat @ G @ A2 ) ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5527_sum_Oinsert,axiom,
% 9.17/5.40 ! [A2: set_Code_integer,X: code_integer,G: code_integer > rat] :
% 9.17/5.40 ( ( finite6017078050557962740nteger @ A2 )
% 9.17/5.40 => ( ~ ( member_Code_integer @ X @ A2 )
% 9.17/5.40 => ( ( groups6602215022474089585er_rat @ G @ ( insert_Code_integer @ X @ A2 ) )
% 9.17/5.40 = ( plus_plus_rat @ ( G @ X ) @ ( groups6602215022474089585er_rat @ G @ A2 ) ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5528_sum_Oinsert,axiom,
% 9.17/5.40 ! [A2: set_o,X: $o,G: $o > nat] :
% 9.17/5.40 ( ( finite_finite_o @ A2 )
% 9.17/5.40 => ( ~ ( member_o @ X @ A2 )
% 9.17/5.40 => ( ( groups8507830703676809646_o_nat @ G @ ( insert_o @ X @ A2 ) )
% 9.17/5.40 = ( plus_plus_nat @ ( G @ X ) @ ( groups8507830703676809646_o_nat @ G @ A2 ) ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5529_sum_Oinsert,axiom,
% 9.17/5.40 ! [A2: set_int,X: int,G: int > nat] :
% 9.17/5.40 ( ( finite_finite_int @ A2 )
% 9.17/5.40 => ( ~ ( member_int @ X @ A2 )
% 9.17/5.40 => ( ( groups4541462559716669496nt_nat @ G @ ( insert_int @ X @ A2 ) )
% 9.17/5.40 = ( plus_plus_nat @ ( G @ X ) @ ( groups4541462559716669496nt_nat @ G @ A2 ) ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5530_sum_Oinsert,axiom,
% 9.17/5.40 ! [A2: set_Code_integer,X: code_integer,G: code_integer > nat] :
% 9.17/5.40 ( ( finite6017078050557962740nteger @ A2 )
% 9.17/5.40 => ( ~ ( member_Code_integer @ X @ A2 )
% 9.17/5.40 => ( ( groups7237345082560585321er_nat @ G @ ( insert_Code_integer @ X @ A2 ) )
% 9.17/5.40 = ( plus_plus_nat @ ( G @ X ) @ ( groups7237345082560585321er_nat @ G @ A2 ) ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5531_sum_Oinsert,axiom,
% 9.17/5.40 ! [A2: set_o,X: $o,G: $o > int] :
% 9.17/5.40 ( ( finite_finite_o @ A2 )
% 9.17/5.40 => ( ~ ( member_o @ X @ A2 )
% 9.17/5.40 => ( ( groups8505340233167759370_o_int @ G @ ( insert_o @ X @ A2 ) )
% 9.17/5.40 = ( plus_plus_int @ ( G @ X ) @ ( groups8505340233167759370_o_int @ G @ A2 ) ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5532_sum_Oinsert,axiom,
% 9.17/5.40 ! [A2: set_nat,X: nat,G: nat > int] :
% 9.17/5.40 ( ( finite_finite_nat @ A2 )
% 9.17/5.40 => ( ~ ( member_nat @ X @ A2 )
% 9.17/5.40 => ( ( groups3539618377306564664at_int @ G @ ( insert_nat @ X @ A2 ) )
% 9.17/5.40 = ( plus_plus_int @ ( G @ X ) @ ( groups3539618377306564664at_int @ G @ A2 ) ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5533_sum_Oinsert,axiom,
% 9.17/5.40 ! [A2: set_Code_integer,X: code_integer,G: code_integer > int] :
% 9.17/5.40 ( ( finite6017078050557962740nteger @ A2 )
% 9.17/5.40 => ( ~ ( member_Code_integer @ X @ A2 )
% 9.17/5.40 => ( ( groups7234854612051535045er_int @ G @ ( insert_Code_integer @ X @ A2 ) )
% 9.17/5.40 = ( plus_plus_int @ ( G @ X ) @ ( groups7234854612051535045er_int @ G @ A2 ) ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5534_atLeastLessThan__singleton,axiom,
% 9.17/5.40 ! [M2: nat] :
% 9.17/5.40 ( ( set_or4665077453230672383an_nat @ M2 @ ( suc @ M2 ) )
% 9.17/5.40 = ( insert_nat @ M2 @ bot_bot_set_nat ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5535_atMost__0,axiom,
% 9.17/5.40 ( ( set_ord_atMost_nat @ zero_zero_nat )
% 9.17/5.40 = ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5536_card__atLeastLessThan__int,axiom,
% 9.17/5.40 ! [L: int,U: int] :
% 9.17/5.40 ( ( finite_card_int @ ( set_or4662586982721622107an_int @ L @ U ) )
% 9.17/5.40 = ( nat2 @ ( minus_minus_int @ U @ L ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5537_card__doubleton__eq__2__iff,axiom,
% 9.17/5.40 ! [A: product_unit,B: product_unit] :
% 9.17/5.40 ( ( ( finite410649719033368117t_unit @ ( insert_Product_unit @ A @ ( insert_Product_unit @ B @ bot_bo3957492148770167129t_unit ) ) )
% 9.17/5.40 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.17/5.40 = ( A != B ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5538_card__doubleton__eq__2__iff,axiom,
% 9.17/5.40 ! [A: list_nat,B: list_nat] :
% 9.17/5.40 ( ( ( finite_card_list_nat @ ( insert_list_nat @ A @ ( insert_list_nat @ B @ bot_bot_set_list_nat ) ) )
% 9.17/5.40 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.17/5.40 = ( A != B ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5539_card__doubleton__eq__2__iff,axiom,
% 9.17/5.40 ! [A: produc3843707927480180839at_nat,B: produc3843707927480180839at_nat] :
% 9.17/5.40 ( ( ( finite3771342082235030671at_nat @ ( insert9069300056098147895at_nat @ A @ ( insert9069300056098147895at_nat @ B @ bot_bo228742789529271731at_nat ) ) )
% 9.17/5.40 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.17/5.40 = ( A != B ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5540_card__doubleton__eq__2__iff,axiom,
% 9.17/5.40 ! [A: product_prod_nat_nat,B: product_prod_nat_nat] :
% 9.17/5.40 ( ( ( finite711546835091564841at_nat @ ( insert8211810215607154385at_nat @ A @ ( insert8211810215607154385at_nat @ B @ bot_bo2099793752762293965at_nat ) ) )
% 9.17/5.40 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.17/5.40 = ( A != B ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5541_card__doubleton__eq__2__iff,axiom,
% 9.17/5.40 ! [A: $o,B: $o] :
% 9.17/5.40 ( ( ( finite_card_o @ ( insert_o @ A @ ( insert_o @ B @ bot_bot_set_o ) ) )
% 9.17/5.40 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.17/5.40 = ( A != B ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5542_card__doubleton__eq__2__iff,axiom,
% 9.17/5.40 ! [A: nat,B: nat] :
% 9.17/5.40 ( ( ( finite_card_nat @ ( insert_nat @ A @ ( insert_nat @ B @ bot_bot_set_nat ) ) )
% 9.17/5.40 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.17/5.40 = ( A != B ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5543_card__doubleton__eq__2__iff,axiom,
% 9.17/5.40 ! [A: int,B: int] :
% 9.17/5.40 ( ( ( finite_card_int @ ( insert_int @ A @ ( insert_int @ B @ bot_bot_set_int ) ) )
% 9.17/5.40 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.17/5.40 = ( A != B ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5544_atMost__eq__UNIV__iff,axiom,
% 9.17/5.40 ! [X: set_nat] :
% 9.17/5.40 ( ( ( set_or4236626031148496127et_nat @ X )
% 9.17/5.40 = top_top_set_set_nat )
% 9.17/5.40 = ( X = top_top_set_nat ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5545_atMost__eq__UNIV__iff,axiom,
% 9.17/5.40 ! [X: set_Product_unit] :
% 9.17/5.40 ( ( ( set_or2827140217781692084t_unit @ X )
% 9.17/5.40 = top_to1767297665138865437t_unit )
% 9.17/5.40 = ( X = top_to1996260823553986621t_unit ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5546_atMost__eq__UNIV__iff,axiom,
% 9.17/5.40 ! [X: set_int] :
% 9.17/5.40 ( ( ( set_or58775011639299419et_int @ X )
% 9.17/5.40 = top_top_set_set_int )
% 9.17/5.40 = ( X = top_top_set_int ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5547_atMost__eq__UNIV__iff,axiom,
% 9.17/5.40 ! [X: assn] :
% 9.17/5.40 ( ( ( set_ord_atMost_assn @ X )
% 9.17/5.40 = top_top_set_assn )
% 9.17/5.40 = ( X = top_top_assn ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5548_atMost__eq__UNIV__iff,axiom,
% 9.17/5.40 ! [X: product_unit] :
% 9.17/5.40 ( ( ( set_or8621721900777396692t_unit @ X )
% 9.17/5.40 = top_to1996260823553986621t_unit )
% 9.17/5.40 = ( X = top_top_Product_unit ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5549_card__le__if__inj__on__rel,axiom,
% 9.17/5.40 ! [B5: set_o,A2: set_o,R2: $o > $o > $o] :
% 9.17/5.40 ( ( finite_finite_o @ B5 )
% 9.17/5.40 => ( ! [A3: $o] :
% 9.17/5.40 ( ( member_o @ A3 @ A2 )
% 9.17/5.40 => ? [B7: $o] :
% 9.17/5.40 ( ( member_o @ B7 @ B5 )
% 9.17/5.40 & ( R2 @ A3 @ B7 ) ) )
% 9.17/5.40 => ( ! [A13: $o,A24: $o,B2: $o] :
% 9.17/5.40 ( ( member_o @ A13 @ A2 )
% 9.17/5.40 => ( ( member_o @ A24 @ A2 )
% 9.17/5.40 => ( ( member_o @ B2 @ B5 )
% 9.17/5.40 => ( ( R2 @ A13 @ B2 )
% 9.17/5.40 => ( ( R2 @ A24 @ B2 )
% 9.17/5.40 => ( A13 = A24 ) ) ) ) ) )
% 9.17/5.40 => ( ord_less_eq_nat @ ( finite_card_o @ A2 ) @ ( finite_card_o @ B5 ) ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5550_card__le__if__inj__on__rel,axiom,
% 9.17/5.40 ! [B5: set_Product_unit,A2: set_o,R2: $o > product_unit > $o] :
% 9.17/5.40 ( ( finite4290736615968046902t_unit @ B5 )
% 9.17/5.40 => ( ! [A3: $o] :
% 9.17/5.40 ( ( member_o @ A3 @ A2 )
% 9.17/5.40 => ? [B7: product_unit] :
% 9.17/5.40 ( ( member_Product_unit @ B7 @ B5 )
% 9.17/5.40 & ( R2 @ A3 @ B7 ) ) )
% 9.17/5.40 => ( ! [A13: $o,A24: $o,B2: product_unit] :
% 9.17/5.40 ( ( member_o @ A13 @ A2 )
% 9.17/5.40 => ( ( member_o @ A24 @ A2 )
% 9.17/5.40 => ( ( member_Product_unit @ B2 @ B5 )
% 9.17/5.40 => ( ( R2 @ A13 @ B2 )
% 9.17/5.40 => ( ( R2 @ A24 @ B2 )
% 9.17/5.40 => ( A13 = A24 ) ) ) ) ) )
% 9.17/5.40 => ( ord_less_eq_nat @ ( finite_card_o @ A2 ) @ ( finite410649719033368117t_unit @ B5 ) ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5551_card__le__if__inj__on__rel,axiom,
% 9.17/5.40 ! [B5: set_o,A2: set_int,R2: int > $o > $o] :
% 9.17/5.40 ( ( finite_finite_o @ B5 )
% 9.17/5.40 => ( ! [A3: int] :
% 9.17/5.40 ( ( member_int @ A3 @ A2 )
% 9.17/5.40 => ? [B7: $o] :
% 9.17/5.40 ( ( member_o @ B7 @ B5 )
% 9.17/5.40 & ( R2 @ A3 @ B7 ) ) )
% 9.17/5.40 => ( ! [A13: int,A24: int,B2: $o] :
% 9.17/5.40 ( ( member_int @ A13 @ A2 )
% 9.17/5.40 => ( ( member_int @ A24 @ A2 )
% 9.17/5.40 => ( ( member_o @ B2 @ B5 )
% 9.17/5.40 => ( ( R2 @ A13 @ B2 )
% 9.17/5.40 => ( ( R2 @ A24 @ B2 )
% 9.17/5.40 => ( A13 = A24 ) ) ) ) ) )
% 9.17/5.40 => ( ord_less_eq_nat @ ( finite_card_int @ A2 ) @ ( finite_card_o @ B5 ) ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5552_card__le__if__inj__on__rel,axiom,
% 9.17/5.40 ! [B5: set_Product_unit,A2: set_int,R2: int > product_unit > $o] :
% 9.17/5.40 ( ( finite4290736615968046902t_unit @ B5 )
% 9.17/5.40 => ( ! [A3: int] :
% 9.17/5.40 ( ( member_int @ A3 @ A2 )
% 9.17/5.40 => ? [B7: product_unit] :
% 9.17/5.40 ( ( member_Product_unit @ B7 @ B5 )
% 9.17/5.40 & ( R2 @ A3 @ B7 ) ) )
% 9.17/5.40 => ( ! [A13: int,A24: int,B2: product_unit] :
% 9.17/5.40 ( ( member_int @ A13 @ A2 )
% 9.17/5.40 => ( ( member_int @ A24 @ A2 )
% 9.17/5.40 => ( ( member_Product_unit @ B2 @ B5 )
% 9.17/5.40 => ( ( R2 @ A13 @ B2 )
% 9.17/5.40 => ( ( R2 @ A24 @ B2 )
% 9.17/5.40 => ( A13 = A24 ) ) ) ) ) )
% 9.17/5.40 => ( ord_less_eq_nat @ ( finite_card_int @ A2 ) @ ( finite410649719033368117t_unit @ B5 ) ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5553_card__le__if__inj__on__rel,axiom,
% 9.17/5.40 ! [B5: set_o,A2: set_Product_unit,R2: product_unit > $o > $o] :
% 9.17/5.40 ( ( finite_finite_o @ B5 )
% 9.17/5.40 => ( ! [A3: product_unit] :
% 9.17/5.40 ( ( member_Product_unit @ A3 @ A2 )
% 9.17/5.40 => ? [B7: $o] :
% 9.17/5.40 ( ( member_o @ B7 @ B5 )
% 9.17/5.40 & ( R2 @ A3 @ B7 ) ) )
% 9.17/5.40 => ( ! [A13: product_unit,A24: product_unit,B2: $o] :
% 9.17/5.40 ( ( member_Product_unit @ A13 @ A2 )
% 9.17/5.40 => ( ( member_Product_unit @ A24 @ A2 )
% 9.17/5.40 => ( ( member_o @ B2 @ B5 )
% 9.17/5.40 => ( ( R2 @ A13 @ B2 )
% 9.17/5.40 => ( ( R2 @ A24 @ B2 )
% 9.17/5.40 => ( A13 = A24 ) ) ) ) ) )
% 9.17/5.40 => ( ord_less_eq_nat @ ( finite410649719033368117t_unit @ A2 ) @ ( finite_card_o @ B5 ) ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5554_card__le__if__inj__on__rel,axiom,
% 9.17/5.40 ! [B5: set_Product_unit,A2: set_Product_unit,R2: product_unit > product_unit > $o] :
% 9.17/5.40 ( ( finite4290736615968046902t_unit @ B5 )
% 9.17/5.40 => ( ! [A3: product_unit] :
% 9.17/5.40 ( ( member_Product_unit @ A3 @ A2 )
% 9.17/5.40 => ? [B7: product_unit] :
% 9.17/5.40 ( ( member_Product_unit @ B7 @ B5 )
% 9.17/5.40 & ( R2 @ A3 @ B7 ) ) )
% 9.17/5.40 => ( ! [A13: product_unit,A24: product_unit,B2: product_unit] :
% 9.17/5.40 ( ( member_Product_unit @ A13 @ A2 )
% 9.17/5.40 => ( ( member_Product_unit @ A24 @ A2 )
% 9.17/5.40 => ( ( member_Product_unit @ B2 @ B5 )
% 9.17/5.40 => ( ( R2 @ A13 @ B2 )
% 9.17/5.40 => ( ( R2 @ A24 @ B2 )
% 9.17/5.40 => ( A13 = A24 ) ) ) ) ) )
% 9.17/5.40 => ( ord_less_eq_nat @ ( finite410649719033368117t_unit @ A2 ) @ ( finite410649719033368117t_unit @ B5 ) ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5555_card__le__if__inj__on__rel,axiom,
% 9.17/5.40 ! [B5: set_o,A2: set_nat,R2: nat > $o > $o] :
% 9.17/5.40 ( ( finite_finite_o @ B5 )
% 9.17/5.40 => ( ! [A3: nat] :
% 9.17/5.40 ( ( member_nat @ A3 @ A2 )
% 9.17/5.40 => ? [B7: $o] :
% 9.17/5.40 ( ( member_o @ B7 @ B5 )
% 9.17/5.40 & ( R2 @ A3 @ B7 ) ) )
% 9.17/5.40 => ( ! [A13: nat,A24: nat,B2: $o] :
% 9.17/5.40 ( ( member_nat @ A13 @ A2 )
% 9.17/5.40 => ( ( member_nat @ A24 @ A2 )
% 9.17/5.40 => ( ( member_o @ B2 @ B5 )
% 9.17/5.40 => ( ( R2 @ A13 @ B2 )
% 9.17/5.40 => ( ( R2 @ A24 @ B2 )
% 9.17/5.40 => ( A13 = A24 ) ) ) ) ) )
% 9.17/5.40 => ( ord_less_eq_nat @ ( finite_card_nat @ A2 ) @ ( finite_card_o @ B5 ) ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5556_card__le__if__inj__on__rel,axiom,
% 9.17/5.40 ! [B5: set_Product_unit,A2: set_nat,R2: nat > product_unit > $o] :
% 9.17/5.40 ( ( finite4290736615968046902t_unit @ B5 )
% 9.17/5.40 => ( ! [A3: nat] :
% 9.17/5.40 ( ( member_nat @ A3 @ A2 )
% 9.17/5.40 => ? [B7: product_unit] :
% 9.17/5.40 ( ( member_Product_unit @ B7 @ B5 )
% 9.17/5.40 & ( R2 @ A3 @ B7 ) ) )
% 9.17/5.40 => ( ! [A13: nat,A24: nat,B2: product_unit] :
% 9.17/5.40 ( ( member_nat @ A13 @ A2 )
% 9.17/5.40 => ( ( member_nat @ A24 @ A2 )
% 9.17/5.40 => ( ( member_Product_unit @ B2 @ B5 )
% 9.17/5.40 => ( ( R2 @ A13 @ B2 )
% 9.17/5.40 => ( ( R2 @ A24 @ B2 )
% 9.17/5.40 => ( A13 = A24 ) ) ) ) ) )
% 9.17/5.40 => ( ord_less_eq_nat @ ( finite_card_nat @ A2 ) @ ( finite410649719033368117t_unit @ B5 ) ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5557_card__le__if__inj__on__rel,axiom,
% 9.17/5.40 ! [B5: set_nat,A2: set_o,R2: $o > nat > $o] :
% 9.17/5.40 ( ( finite_finite_nat @ B5 )
% 9.17/5.40 => ( ! [A3: $o] :
% 9.17/5.40 ( ( member_o @ A3 @ A2 )
% 9.17/5.40 => ? [B7: nat] :
% 9.17/5.40 ( ( member_nat @ B7 @ B5 )
% 9.17/5.40 & ( R2 @ A3 @ B7 ) ) )
% 9.17/5.40 => ( ! [A13: $o,A24: $o,B2: nat] :
% 9.17/5.40 ( ( member_o @ A13 @ A2 )
% 9.17/5.40 => ( ( member_o @ A24 @ A2 )
% 9.17/5.40 => ( ( member_nat @ B2 @ B5 )
% 9.17/5.40 => ( ( R2 @ A13 @ B2 )
% 9.17/5.40 => ( ( R2 @ A24 @ B2 )
% 9.17/5.40 => ( A13 = A24 ) ) ) ) ) )
% 9.17/5.40 => ( ord_less_eq_nat @ ( finite_card_o @ A2 ) @ ( finite_card_nat @ B5 ) ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5558_card__le__if__inj__on__rel,axiom,
% 9.17/5.40 ! [B5: set_nat,A2: set_int,R2: int > nat > $o] :
% 9.17/5.40 ( ( finite_finite_nat @ B5 )
% 9.17/5.40 => ( ! [A3: int] :
% 9.17/5.40 ( ( member_int @ A3 @ A2 )
% 9.17/5.40 => ? [B7: nat] :
% 9.17/5.40 ( ( member_nat @ B7 @ B5 )
% 9.17/5.40 & ( R2 @ A3 @ B7 ) ) )
% 9.17/5.40 => ( ! [A13: int,A24: int,B2: nat] :
% 9.17/5.40 ( ( member_int @ A13 @ A2 )
% 9.17/5.40 => ( ( member_int @ A24 @ A2 )
% 9.17/5.40 => ( ( member_nat @ B2 @ B5 )
% 9.17/5.40 => ( ( R2 @ A13 @ B2 )
% 9.17/5.40 => ( ( R2 @ A24 @ B2 )
% 9.17/5.40 => ( A13 = A24 ) ) ) ) ) )
% 9.17/5.40 => ( ord_less_eq_nat @ ( finite_card_int @ A2 ) @ ( finite_card_nat @ B5 ) ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5559_top__option__def,axiom,
% 9.17/5.40 ( top_to4826455019444611206et_nat
% 9.17/5.40 = ( some_set_nat @ top_top_set_nat ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5560_top__option__def,axiom,
% 9.17/5.40 ( top_to7662761140297458691t_unit
% 9.17/5.40 = ( some_s8043159101241848530t_unit @ top_to1996260823553986621t_unit ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5561_top__option__def,axiom,
% 9.17/5.40 ( top_to2336371874512884450et_int
% 9.17/5.40 = ( some_set_int @ top_top_set_int ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5562_top__option__def,axiom,
% 9.17/5.40 ( top_to4322782652514146083t_unit
% 9.17/5.40 = ( some_Product_unit @ top_top_Product_unit ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5563_top__option__def,axiom,
% 9.17/5.40 ( top_top_option_assn
% 9.17/5.40 = ( some_assn @ top_top_assn ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5564_finite__if__eq__beyond__finite,axiom,
% 9.17/5.40 ! [S2: set_int,S3: set_int] :
% 9.17/5.40 ( ( finite_finite_int @ S2 )
% 9.17/5.40 => ( finite6197958912794628473et_int
% 9.17/5.40 @ ( collect_set_int
% 9.17/5.40 @ ^ [S4: set_int] :
% 9.17/5.40 ( ( minus_minus_set_int @ S4 @ S2 )
% 9.17/5.40 = ( minus_minus_set_int @ S3 @ S2 ) ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5565_finite__if__eq__beyond__finite,axiom,
% 9.17/5.40 ! [S2: set_Code_integer,S3: set_Code_integer] :
% 9.17/5.40 ( ( finite6017078050557962740nteger @ S2 )
% 9.17/5.40 => ( finite6931041176100689706nteger
% 9.17/5.40 @ ( collec574505750873337192nteger
% 9.17/5.40 @ ^ [S4: set_Code_integer] :
% 9.17/5.40 ( ( minus_2355218937544613996nteger @ S4 @ S2 )
% 9.17/5.40 = ( minus_2355218937544613996nteger @ S3 @ S2 ) ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5566_finite__if__eq__beyond__finite,axiom,
% 9.17/5.40 ! [S2: set_Pr1261947904930325089at_nat,S3: set_Pr1261947904930325089at_nat] :
% 9.17/5.40 ( ( finite6177210948735845034at_nat @ S2 )
% 9.17/5.40 => ( finite9047747110432174090at_nat
% 9.17/5.40 @ ( collec5514110066124741708at_nat
% 9.17/5.40 @ ^ [S4: set_Pr1261947904930325089at_nat] :
% 9.17/5.40 ( ( minus_1356011639430497352at_nat @ S4 @ S2 )
% 9.17/5.40 = ( minus_1356011639430497352at_nat @ S3 @ S2 ) ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5567_finite__if__eq__beyond__finite,axiom,
% 9.17/5.40 ! [S2: set_nat,S3: set_nat] :
% 9.17/5.40 ( ( finite_finite_nat @ S2 )
% 9.17/5.40 => ( finite1152437895449049373et_nat
% 9.17/5.40 @ ( collect_set_nat
% 9.17/5.40 @ ^ [S4: set_nat] :
% 9.17/5.40 ( ( minus_minus_set_nat @ S4 @ S2 )
% 9.17/5.40 = ( minus_minus_set_nat @ S3 @ S2 ) ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5568_finite__range__Some,axiom,
% 9.17/5.40 ( ( finite6785661671136154180nteger @ ( image_8960079959263999889nteger @ some_Code_integer @ top_to4645266643341252675nteger ) )
% 9.17/5.40 = ( finite6017078050557962740nteger @ top_to4645266643341252675nteger ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5569_finite__range__Some,axiom,
% 9.17/5.40 ( ( finite6732403688824079472at_nat @ ( image_4198897800814241419at_nat @ some_P7363390416028606310at_nat @ top_to4669805908274784177at_nat ) )
% 9.17/5.40 = ( finite6177210948735845034at_nat @ top_to4669805908274784177at_nat ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5570_finite__range__Some,axiom,
% 9.17/5.40 ( ( finite6231397076622260609on_num @ ( image_num_option_num @ some_num @ top_top_set_num ) )
% 9.17/5.40 = ( finite_finite_num @ top_top_set_num ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5571_finite__range__Some,axiom,
% 9.17/5.40 ( ( finite6292238467249657455it_nat @ ( image_3455408117458022631it_nat @ some_P1914260805536162275it_nat @ top_to4082048134677576814it_nat ) )
% 9.17/5.40 = ( finite6446286893012251551it_nat @ top_to4082048134677576814it_nat ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5572_finite__range__Some,axiom,
% 9.17/5.40 ( ( finite5523153139673422903on_nat @ ( image_nat_option_nat @ some_nat @ top_top_set_nat ) )
% 9.17/5.40 = ( finite_finite_nat @ top_top_set_nat ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5573_finite__range__Some,axiom,
% 9.17/5.40 ( ( finite1445617369574913404t_unit @ ( image_7094380055901048587t_unit @ some_Product_unit @ top_to1996260823553986621t_unit ) )
% 9.17/5.40 = ( finite4290736615968046902t_unit @ top_to1996260823553986621t_unit ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5574_finite__range__Some,axiom,
% 9.17/5.40 ( ( finite1345302120164226195on_int @ ( image_int_option_int @ some_int @ top_top_set_int ) )
% 9.17/5.40 = ( finite_finite_int @ top_top_set_int ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5575_obtain__subset__with__card__n,axiom,
% 9.17/5.40 ! [N2: nat,S2: set_Product_unit] :
% 9.17/5.40 ( ( ord_less_eq_nat @ N2 @ ( finite410649719033368117t_unit @ S2 ) )
% 9.17/5.40 => ~ ! [T3: set_Product_unit] :
% 9.17/5.40 ( ( ord_le3507040750410214029t_unit @ T3 @ S2 )
% 9.17/5.40 => ( ( ( finite410649719033368117t_unit @ T3 )
% 9.17/5.40 = N2 )
% 9.17/5.40 => ~ ( finite4290736615968046902t_unit @ T3 ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5576_obtain__subset__with__card__n,axiom,
% 9.17/5.40 ! [N2: nat,S2: set_list_nat] :
% 9.17/5.40 ( ( ord_less_eq_nat @ N2 @ ( finite_card_list_nat @ S2 ) )
% 9.17/5.40 => ~ ! [T3: set_list_nat] :
% 9.17/5.40 ( ( ord_le6045566169113846134st_nat @ T3 @ S2 )
% 9.17/5.40 => ( ( ( finite_card_list_nat @ T3 )
% 9.17/5.40 = N2 )
% 9.17/5.40 => ~ ( finite8100373058378681591st_nat @ T3 ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5577_obtain__subset__with__card__n,axiom,
% 9.17/5.40 ! [N2: nat,S2: set_int] :
% 9.17/5.40 ( ( ord_less_eq_nat @ N2 @ ( finite_card_int @ S2 ) )
% 9.17/5.40 => ~ ! [T3: set_int] :
% 9.17/5.40 ( ( ord_less_eq_set_int @ T3 @ S2 )
% 9.17/5.40 => ( ( ( finite_card_int @ T3 )
% 9.17/5.40 = N2 )
% 9.17/5.40 => ~ ( finite_finite_int @ T3 ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5578_obtain__subset__with__card__n,axiom,
% 9.17/5.40 ! [N2: nat,S2: set_Code_integer] :
% 9.17/5.40 ( ( ord_less_eq_nat @ N2 @ ( finite4902975817058060853nteger @ S2 ) )
% 9.17/5.40 => ~ ! [T3: set_Code_integer] :
% 9.17/5.40 ( ( ord_le7084787975880047091nteger @ T3 @ S2 )
% 9.17/5.40 => ( ( ( finite4902975817058060853nteger @ T3 )
% 9.17/5.40 = N2 )
% 9.17/5.40 => ~ ( finite6017078050557962740nteger @ T3 ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5579_obtain__subset__with__card__n,axiom,
% 9.17/5.40 ! [N2: nat,S2: set_Pr1261947904930325089at_nat] :
% 9.17/5.40 ( ( ord_less_eq_nat @ N2 @ ( finite711546835091564841at_nat @ S2 ) )
% 9.17/5.40 => ~ ! [T3: set_Pr1261947904930325089at_nat] :
% 9.17/5.40 ( ( ord_le3146513528884898305at_nat @ T3 @ S2 )
% 9.17/5.40 => ( ( ( finite711546835091564841at_nat @ T3 )
% 9.17/5.40 = N2 )
% 9.17/5.40 => ~ ( finite6177210948735845034at_nat @ T3 ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5580_obtain__subset__with__card__n,axiom,
% 9.17/5.40 ! [N2: nat,S2: set_nat] :
% 9.17/5.40 ( ( ord_less_eq_nat @ N2 @ ( finite_card_nat @ S2 ) )
% 9.17/5.40 => ~ ! [T3: set_nat] :
% 9.17/5.40 ( ( ord_less_eq_set_nat @ T3 @ S2 )
% 9.17/5.40 => ( ( ( finite_card_nat @ T3 )
% 9.17/5.40 = N2 )
% 9.17/5.40 => ~ ( finite_finite_nat @ T3 ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5581_atLeastAtMost__eq__UNIV__iff,axiom,
% 9.17/5.40 ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat] :
% 9.17/5.40 ( ( ( set_or4049648398082403068at_nat @ X @ Y )
% 9.17/5.40 = top_to1754375979021635447at_nat )
% 9.17/5.40 = ( ( X = bot_bo228742789529271731at_nat )
% 9.17/5.40 & ( Y = top_to6833984726390702231at_nat ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5582_atLeastAtMost__eq__UNIV__iff,axiom,
% 9.17/5.40 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 9.17/5.40 ( ( ( set_or2784603332384507286at_nat @ X @ Y )
% 9.17/5.40 = top_to7629004291339433233at_nat )
% 9.17/5.40 = ( ( X = bot_bo2099793752762293965at_nat )
% 9.17/5.40 & ( Y = top_to4669805908274784177at_nat ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5583_atLeastAtMost__eq__UNIV__iff,axiom,
% 9.17/5.40 ! [X: set_o,Y: set_o] :
% 9.17/5.40 ( ( ( set_or266616469461849773_set_o @ X @ Y )
% 9.17/5.40 = top_top_set_set_o )
% 9.17/5.40 = ( ( X = bot_bot_set_o )
% 9.17/5.40 & ( Y = top_top_set_o ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5584_atLeastAtMost__eq__UNIV__iff,axiom,
% 9.17/5.40 ! [X: set_nat,Y: set_nat] :
% 9.17/5.40 ( ( ( set_or4548717258645045905et_nat @ X @ Y )
% 9.17/5.40 = top_top_set_set_nat )
% 9.17/5.40 = ( ( X = bot_bot_set_nat )
% 9.17/5.40 & ( Y = top_top_set_nat ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5585_atLeastAtMost__eq__UNIV__iff,axiom,
% 9.17/5.40 ! [X: set_Product_unit,Y: set_Product_unit] :
% 9.17/5.40 ( ( ( set_or269330187037242274t_unit @ X @ Y )
% 9.17/5.40 = top_to1767297665138865437t_unit )
% 9.17/5.40 = ( ( X = bot_bo3957492148770167129t_unit )
% 9.17/5.40 & ( Y = top_to1996260823553986621t_unit ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5586_atLeastAtMost__eq__UNIV__iff,axiom,
% 9.17/5.40 ! [X: set_int,Y: set_int] :
% 9.17/5.40 ( ( ( set_or370866239135849197et_int @ X @ Y )
% 9.17/5.40 = top_top_set_set_int )
% 9.17/5.40 = ( ( X = bot_bot_set_int )
% 9.17/5.40 & ( Y = top_top_set_int ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5587_atLeastAtMost__eq__UNIV__iff,axiom,
% 9.17/5.40 ! [X: assn,Y: assn] :
% 9.17/5.40 ( ( ( set_or7959216805967363635t_assn @ X @ Y )
% 9.17/5.40 = top_top_set_assn )
% 9.17/5.40 = ( ( X = bot_bot_assn )
% 9.17/5.40 & ( Y = top_top_assn ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5588_atLeastAtMost__eq__UNIV__iff,axiom,
% 9.17/5.40 ! [X: product_unit,Y: product_unit] :
% 9.17/5.40 ( ( ( set_or5692540242118139586t_unit @ X @ Y )
% 9.17/5.40 = top_to1996260823553986621t_unit )
% 9.17/5.40 = ( ( X = bot_bot_Product_unit )
% 9.17/5.40 & ( Y = top_top_Product_unit ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5589_UNIV__option__conv,axiom,
% 9.17/5.40 ( top_to7137183367772546234it_nat
% 9.17/5.40 = ( insert7468008629046257882it_nat @ none_P2587165478634041381it_nat @ ( image_4799632500972785611it_nat @ some_P6105628898608307625it_nat @ top_to3995162779041354868it_nat ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5590_UNIV__option__conv,axiom,
% 9.17/5.40 ( top_to4635417975585700688on_num
% 9.17/5.40 = ( insert_option_num @ none_num @ ( image_num_option_num @ some_num @ top_top_set_num ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5591_UNIV__option__conv,axiom,
% 9.17/5.40 ( top_to6632602878615679294it_nat
% 9.17/5.40 = ( insert2007652293347934600it_nat @ none_P9117596204409417319it_nat @ ( image_3455408117458022631it_nat @ some_P1914260805536162275it_nat @ top_to4082048134677576814it_nat ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5592_UNIV__option__conv,axiom,
% 9.17/5.40 ( top_to8920198386146353926on_nat
% 9.17/5.40 = ( insert_option_nat @ none_nat @ ( image_nat_option_nat @ some_nat @ top_top_set_nat ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5593_UNIV__option__conv,axiom,
% 9.17/5.40 ( top_to2690860209552263555t_unit
% 9.17/5.40 = ( insert2866144167138965411t_unit @ none_Product_unit @ ( image_7094380055901048587t_unit @ some_Product_unit @ top_to1996260823553986621t_unit ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5594_UNIV__option__conv,axiom,
% 9.17/5.40 ( top_to6430115241214627170on_int
% 9.17/5.40 = ( insert_option_int @ none_int @ ( image_int_option_int @ some_int @ top_top_set_int ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5595_bounded__nat__set__is__finite,axiom,
% 9.17/5.40 ! [N6: set_nat,N2: nat] :
% 9.17/5.40 ( ! [X4: nat] :
% 9.17/5.40 ( ( member_nat @ X4 @ N6 )
% 9.17/5.40 => ( ord_less_nat @ X4 @ N2 ) )
% 9.17/5.40 => ( finite_finite_nat @ N6 ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5596_finite__nat__set__iff__bounded,axiom,
% 9.17/5.40 ( finite_finite_nat
% 9.17/5.40 = ( ^ [N9: set_nat] :
% 9.17/5.40 ? [M: nat] :
% 9.17/5.40 ! [X3: nat] :
% 9.17/5.40 ( ( member_nat @ X3 @ N9 )
% 9.17/5.40 => ( ord_less_nat @ X3 @ M ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5597_finite__nat__set__iff__bounded__le,axiom,
% 9.17/5.40 ( finite_finite_nat
% 9.17/5.40 = ( ^ [N9: set_nat] :
% 9.17/5.40 ? [M: nat] :
% 9.17/5.40 ! [X3: nat] :
% 9.17/5.40 ( ( member_nat @ X3 @ N9 )
% 9.17/5.40 => ( ord_less_eq_nat @ X3 @ M ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5598_surjD,axiom,
% 9.17/5.40 ! [F: nat > code_integer,Y: code_integer] :
% 9.17/5.40 ( ( ( image_1215581382706833972nteger @ F @ top_top_set_nat )
% 9.17/5.40 = top_to4645266643341252675nteger )
% 9.17/5.40 => ? [X4: nat] :
% 9.17/5.40 ( Y
% 9.17/5.40 = ( F @ X4 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5599_surjD,axiom,
% 9.17/5.40 ! [F: nat > nat,Y: nat] :
% 9.17/5.40 ( ( ( image_nat_nat @ F @ top_top_set_nat )
% 9.17/5.40 = top_top_set_nat )
% 9.17/5.40 => ? [X4: nat] :
% 9.17/5.40 ( Y
% 9.17/5.40 = ( F @ X4 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5600_surjD,axiom,
% 9.17/5.40 ! [F: nat > product_unit,Y: product_unit] :
% 9.17/5.40 ( ( ( image_8730104196221521654t_unit @ F @ top_top_set_nat )
% 9.17/5.40 = top_to1996260823553986621t_unit )
% 9.17/5.40 => ? [X4: nat] :
% 9.17/5.40 ( Y
% 9.17/5.40 = ( F @ X4 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5601_surjD,axiom,
% 9.17/5.40 ! [F: nat > int,Y: int] :
% 9.17/5.40 ( ( ( image_nat_int @ F @ top_top_set_nat )
% 9.17/5.40 = top_top_set_int )
% 9.17/5.40 => ? [X4: nat] :
% 9.17/5.40 ( Y
% 9.17/5.40 = ( F @ X4 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5602_surjD,axiom,
% 9.17/5.40 ! [F: product_unit > nat,Y: nat] :
% 9.17/5.40 ( ( ( image_875570014554754200it_nat @ F @ top_to1996260823553986621t_unit )
% 9.17/5.40 = top_top_set_nat )
% 9.17/5.40 => ? [X4: product_unit] :
% 9.17/5.40 ( Y
% 9.17/5.40 = ( F @ X4 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5603_surjD,axiom,
% 9.17/5.40 ! [F: product_unit > product_unit,Y: product_unit] :
% 9.17/5.40 ( ( ( image_405062704495631173t_unit @ F @ top_to1996260823553986621t_unit )
% 9.17/5.40 = top_to1996260823553986621t_unit )
% 9.17/5.40 => ? [X4: product_unit] :
% 9.17/5.40 ( Y
% 9.17/5.40 = ( F @ X4 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5604_surjD,axiom,
% 9.17/5.40 ! [F: product_unit > int,Y: int] :
% 9.17/5.40 ( ( ( image_873079544045703924it_int @ F @ top_to1996260823553986621t_unit )
% 9.17/5.40 = top_top_set_int )
% 9.17/5.40 => ? [X4: product_unit] :
% 9.17/5.40 ( Y
% 9.17/5.40 = ( F @ X4 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5605_surjD,axiom,
% 9.17/5.40 ! [F: int > nat,Y: nat] :
% 9.17/5.40 ( ( ( image_int_nat @ F @ top_top_set_int )
% 9.17/5.40 = top_top_set_nat )
% 9.17/5.40 => ? [X4: int] :
% 9.17/5.40 ( Y
% 9.17/5.40 = ( F @ X4 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5606_surjD,axiom,
% 9.17/5.40 ! [F: int > product_unit,Y: product_unit] :
% 9.17/5.40 ( ( ( image_5846526143423701914t_unit @ F @ top_top_set_int )
% 9.17/5.40 = top_to1996260823553986621t_unit )
% 9.17/5.40 => ? [X4: int] :
% 9.17/5.40 ( Y
% 9.17/5.40 = ( F @ X4 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5607_surjD,axiom,
% 9.17/5.40 ! [F: int > int,Y: int] :
% 9.17/5.40 ( ( ( image_int_int @ F @ top_top_set_int )
% 9.17/5.40 = top_top_set_int )
% 9.17/5.40 => ? [X4: int] :
% 9.17/5.40 ( Y
% 9.17/5.40 = ( F @ X4 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5608_surjE,axiom,
% 9.17/5.40 ! [F: nat > code_integer,Y: code_integer] :
% 9.17/5.40 ( ( ( image_1215581382706833972nteger @ F @ top_top_set_nat )
% 9.17/5.40 = top_to4645266643341252675nteger )
% 9.17/5.40 => ~ ! [X4: nat] :
% 9.17/5.40 ( Y
% 9.17/5.40 != ( F @ X4 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5609_surjE,axiom,
% 9.17/5.40 ! [F: nat > nat,Y: nat] :
% 9.17/5.40 ( ( ( image_nat_nat @ F @ top_top_set_nat )
% 9.17/5.40 = top_top_set_nat )
% 9.17/5.40 => ~ ! [X4: nat] :
% 9.17/5.40 ( Y
% 9.17/5.40 != ( F @ X4 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5610_surjE,axiom,
% 9.17/5.40 ! [F: nat > product_unit,Y: product_unit] :
% 9.17/5.40 ( ( ( image_8730104196221521654t_unit @ F @ top_top_set_nat )
% 9.17/5.40 = top_to1996260823553986621t_unit )
% 9.17/5.40 => ~ ! [X4: nat] :
% 9.17/5.40 ( Y
% 9.17/5.40 != ( F @ X4 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5611_surjE,axiom,
% 9.17/5.40 ! [F: nat > int,Y: int] :
% 9.17/5.40 ( ( ( image_nat_int @ F @ top_top_set_nat )
% 9.17/5.40 = top_top_set_int )
% 9.17/5.40 => ~ ! [X4: nat] :
% 9.17/5.40 ( Y
% 9.17/5.40 != ( F @ X4 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5612_surjE,axiom,
% 9.17/5.40 ! [F: product_unit > nat,Y: nat] :
% 9.17/5.40 ( ( ( image_875570014554754200it_nat @ F @ top_to1996260823553986621t_unit )
% 9.17/5.40 = top_top_set_nat )
% 9.17/5.40 => ~ ! [X4: product_unit] :
% 9.17/5.40 ( Y
% 9.17/5.40 != ( F @ X4 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5613_surjE,axiom,
% 9.17/5.40 ! [F: product_unit > product_unit,Y: product_unit] :
% 9.17/5.40 ( ( ( image_405062704495631173t_unit @ F @ top_to1996260823553986621t_unit )
% 9.17/5.40 = top_to1996260823553986621t_unit )
% 9.17/5.40 => ~ ! [X4: product_unit] :
% 9.17/5.40 ( Y
% 9.17/5.40 != ( F @ X4 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5614_surjE,axiom,
% 9.17/5.40 ! [F: product_unit > int,Y: int] :
% 9.17/5.40 ( ( ( image_873079544045703924it_int @ F @ top_to1996260823553986621t_unit )
% 9.17/5.40 = top_top_set_int )
% 9.17/5.40 => ~ ! [X4: product_unit] :
% 9.17/5.40 ( Y
% 9.17/5.40 != ( F @ X4 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5615_surjE,axiom,
% 9.17/5.40 ! [F: int > nat,Y: nat] :
% 9.17/5.40 ( ( ( image_int_nat @ F @ top_top_set_int )
% 9.17/5.40 = top_top_set_nat )
% 9.17/5.40 => ~ ! [X4: int] :
% 9.17/5.40 ( Y
% 9.17/5.40 != ( F @ X4 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5616_surjE,axiom,
% 9.17/5.40 ! [F: int > product_unit,Y: product_unit] :
% 9.17/5.40 ( ( ( image_5846526143423701914t_unit @ F @ top_top_set_int )
% 9.17/5.40 = top_to1996260823553986621t_unit )
% 9.17/5.40 => ~ ! [X4: int] :
% 9.17/5.40 ( Y
% 9.17/5.40 != ( F @ X4 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5617_surjE,axiom,
% 9.17/5.40 ! [F: int > int,Y: int] :
% 9.17/5.40 ( ( ( image_int_int @ F @ top_top_set_int )
% 9.17/5.40 = top_top_set_int )
% 9.17/5.40 => ~ ! [X4: int] :
% 9.17/5.40 ( Y
% 9.17/5.40 != ( F @ X4 ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5618_surjI,axiom,
% 9.17/5.40 ! [G: nat > code_integer,F: code_integer > nat] :
% 9.17/5.40 ( ! [X4: code_integer] :
% 9.17/5.40 ( ( G @ ( F @ X4 ) )
% 9.17/5.40 = X4 )
% 9.17/5.40 => ( ( image_1215581382706833972nteger @ G @ top_top_set_nat )
% 9.17/5.40 = top_to4645266643341252675nteger ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5619_surjI,axiom,
% 9.17/5.40 ! [G: nat > nat,F: nat > nat] :
% 9.17/5.40 ( ! [X4: nat] :
% 9.17/5.40 ( ( G @ ( F @ X4 ) )
% 9.17/5.40 = X4 )
% 9.17/5.40 => ( ( image_nat_nat @ G @ top_top_set_nat )
% 9.17/5.40 = top_top_set_nat ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5620_surjI,axiom,
% 9.17/5.40 ! [G: nat > product_unit,F: product_unit > nat] :
% 9.17/5.40 ( ! [X4: product_unit] :
% 9.17/5.40 ( ( G @ ( F @ X4 ) )
% 9.17/5.40 = X4 )
% 9.17/5.40 => ( ( image_8730104196221521654t_unit @ G @ top_top_set_nat )
% 9.17/5.40 = top_to1996260823553986621t_unit ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5621_surjI,axiom,
% 9.17/5.40 ! [G: nat > int,F: int > nat] :
% 9.17/5.40 ( ! [X4: int] :
% 9.17/5.40 ( ( G @ ( F @ X4 ) )
% 9.17/5.40 = X4 )
% 9.17/5.40 => ( ( image_nat_int @ G @ top_top_set_nat )
% 9.17/5.40 = top_top_set_int ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5622_surjI,axiom,
% 9.17/5.40 ! [G: product_unit > nat,F: nat > product_unit] :
% 9.17/5.40 ( ! [X4: nat] :
% 9.17/5.40 ( ( G @ ( F @ X4 ) )
% 9.17/5.40 = X4 )
% 9.17/5.40 => ( ( image_875570014554754200it_nat @ G @ top_to1996260823553986621t_unit )
% 9.17/5.40 = top_top_set_nat ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5623_surjI,axiom,
% 9.17/5.40 ! [G: product_unit > product_unit,F: product_unit > product_unit] :
% 9.17/5.40 ( ! [X4: product_unit] :
% 9.17/5.40 ( ( G @ ( F @ X4 ) )
% 9.17/5.40 = X4 )
% 9.17/5.40 => ( ( image_405062704495631173t_unit @ G @ top_to1996260823553986621t_unit )
% 9.17/5.40 = top_to1996260823553986621t_unit ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5624_surjI,axiom,
% 9.17/5.40 ! [G: product_unit > int,F: int > product_unit] :
% 9.17/5.40 ( ! [X4: int] :
% 9.17/5.40 ( ( G @ ( F @ X4 ) )
% 9.17/5.40 = X4 )
% 9.17/5.40 => ( ( image_873079544045703924it_int @ G @ top_to1996260823553986621t_unit )
% 9.17/5.40 = top_top_set_int ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5625_surjI,axiom,
% 9.17/5.40 ! [G: int > nat,F: nat > int] :
% 9.17/5.40 ( ! [X4: nat] :
% 9.17/5.40 ( ( G @ ( F @ X4 ) )
% 9.17/5.40 = X4 )
% 9.17/5.40 => ( ( image_int_nat @ G @ top_top_set_int )
% 9.17/5.40 = top_top_set_nat ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5626_surjI,axiom,
% 9.17/5.40 ! [G: int > product_unit,F: product_unit > int] :
% 9.17/5.40 ( ! [X4: product_unit] :
% 9.17/5.40 ( ( G @ ( F @ X4 ) )
% 9.17/5.40 = X4 )
% 9.17/5.40 => ( ( image_5846526143423701914t_unit @ G @ top_top_set_int )
% 9.17/5.40 = top_to1996260823553986621t_unit ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5627_surjI,axiom,
% 9.17/5.40 ! [G: int > int,F: int > int] :
% 9.17/5.40 ( ! [X4: int] :
% 9.17/5.40 ( ( G @ ( F @ X4 ) )
% 9.17/5.40 = X4 )
% 9.17/5.40 => ( ( image_int_int @ G @ top_top_set_int )
% 9.17/5.40 = top_top_set_int ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5628_surj__def,axiom,
% 9.17/5.40 ! [F: nat > code_integer] :
% 9.17/5.40 ( ( ( image_1215581382706833972nteger @ F @ top_top_set_nat )
% 9.17/5.40 = top_to4645266643341252675nteger )
% 9.17/5.40 = ( ! [Y3: code_integer] :
% 9.17/5.40 ? [X3: nat] :
% 9.17/5.40 ( Y3
% 9.17/5.40 = ( F @ X3 ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5629_surj__def,axiom,
% 9.17/5.40 ! [F: nat > nat] :
% 9.17/5.40 ( ( ( image_nat_nat @ F @ top_top_set_nat )
% 9.17/5.40 = top_top_set_nat )
% 9.17/5.40 = ( ! [Y3: nat] :
% 9.17/5.40 ? [X3: nat] :
% 9.17/5.40 ( Y3
% 9.17/5.40 = ( F @ X3 ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5630_surj__def,axiom,
% 9.17/5.40 ! [F: nat > product_unit] :
% 9.17/5.40 ( ( ( image_8730104196221521654t_unit @ F @ top_top_set_nat )
% 9.17/5.40 = top_to1996260823553986621t_unit )
% 9.17/5.40 = ( ! [Y3: product_unit] :
% 9.17/5.40 ? [X3: nat] :
% 9.17/5.40 ( Y3
% 9.17/5.40 = ( F @ X3 ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5631_surj__def,axiom,
% 9.17/5.40 ! [F: nat > int] :
% 9.17/5.40 ( ( ( image_nat_int @ F @ top_top_set_nat )
% 9.17/5.40 = top_top_set_int )
% 9.17/5.40 = ( ! [Y3: int] :
% 9.17/5.40 ? [X3: nat] :
% 9.17/5.40 ( Y3
% 9.17/5.40 = ( F @ X3 ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5632_surj__def,axiom,
% 9.17/5.40 ! [F: product_unit > nat] :
% 9.17/5.40 ( ( ( image_875570014554754200it_nat @ F @ top_to1996260823553986621t_unit )
% 9.17/5.40 = top_top_set_nat )
% 9.17/5.40 = ( ! [Y3: nat] :
% 9.17/5.40 ? [X3: product_unit] :
% 9.17/5.40 ( Y3
% 9.17/5.40 = ( F @ X3 ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5633_surj__def,axiom,
% 9.17/5.40 ! [F: product_unit > product_unit] :
% 9.17/5.40 ( ( ( image_405062704495631173t_unit @ F @ top_to1996260823553986621t_unit )
% 9.17/5.40 = top_to1996260823553986621t_unit )
% 9.17/5.40 = ( ! [Y3: product_unit] :
% 9.17/5.40 ? [X3: product_unit] :
% 9.17/5.40 ( Y3
% 9.17/5.40 = ( F @ X3 ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5634_surj__def,axiom,
% 9.17/5.40 ! [F: product_unit > int] :
% 9.17/5.40 ( ( ( image_873079544045703924it_int @ F @ top_to1996260823553986621t_unit )
% 9.17/5.40 = top_top_set_int )
% 9.17/5.40 = ( ! [Y3: int] :
% 9.17/5.40 ? [X3: product_unit] :
% 9.17/5.40 ( Y3
% 9.17/5.40 = ( F @ X3 ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5635_surj__def,axiom,
% 9.17/5.40 ! [F: int > nat] :
% 9.17/5.40 ( ( ( image_int_nat @ F @ top_top_set_int )
% 9.17/5.40 = top_top_set_nat )
% 9.17/5.40 = ( ! [Y3: nat] :
% 9.17/5.40 ? [X3: int] :
% 9.17/5.40 ( Y3
% 9.17/5.40 = ( F @ X3 ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5636_surj__def,axiom,
% 9.17/5.40 ! [F: int > product_unit] :
% 9.17/5.40 ( ( ( image_5846526143423701914t_unit @ F @ top_top_set_int )
% 9.17/5.40 = top_to1996260823553986621t_unit )
% 9.17/5.40 = ( ! [Y3: product_unit] :
% 9.17/5.40 ? [X3: int] :
% 9.17/5.40 ( Y3
% 9.17/5.40 = ( F @ X3 ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5637_surj__def,axiom,
% 9.17/5.40 ! [F: int > int] :
% 9.17/5.40 ( ( ( image_int_int @ F @ top_top_set_int )
% 9.17/5.40 = top_top_set_int )
% 9.17/5.40 = ( ! [Y3: int] :
% 9.17/5.40 ? [X3: int] :
% 9.17/5.40 ( Y3
% 9.17/5.40 = ( F @ X3 ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5638_these__empty__eq,axiom,
% 9.17/5.40 ! [B5: set_op3940070208846178154it_nat] :
% 9.17/5.40 ( ( ( these_6645423997822192641it_nat @ B5 )
% 9.17/5.40 = bot_bo6361524548789211024it_nat )
% 9.17/5.40 = ( ( B5 = bot_bo8185009268211221974it_nat )
% 9.17/5.40 | ( B5
% 9.17/5.40 = ( insert7468008629046257882it_nat @ none_P2587165478634041381it_nat @ bot_bo8185009268211221974it_nat ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5639_these__empty__eq,axiom,
% 9.17/5.40 ! [B5: set_option_num] :
% 9.17/5.40 ( ( ( these_num @ B5 )
% 9.17/5.40 = bot_bot_set_num )
% 9.17/5.40 = ( ( B5 = bot_bo725063100934353204on_num )
% 9.17/5.40 | ( B5
% 9.17/5.40 = ( insert_option_num @ none_num @ bot_bo725063100934353204on_num ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5640_these__empty__eq,axiom,
% 9.17/5.40 ! [B5: set_op239864471688321678it_nat] :
% 9.17/5.40 ( ( ( these_3407724651694999947it_nat @ B5 )
% 9.17/5.40 = bot_bo5696401558416705618it_nat )
% 9.17/5.40 = ( ( B5 = bot_bo1172055076661450530it_nat )
% 9.17/5.40 | ( B5
% 9.17/5.40 = ( insert2007652293347934600it_nat @ none_P9117596204409417319it_nat @ bot_bo1172055076661450530it_nat ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5641_these__empty__eq,axiom,
% 9.17/5.40 ! [B5: set_op989438649584373901at_nat] :
% 9.17/5.40 ( ( ( these_1872268174106123684at_nat @ B5 )
% 9.17/5.40 = bot_bo228742789529271731at_nat )
% 9.17/5.40 = ( ( B5 = bot_bo1471150103859235065at_nat )
% 9.17/5.40 | ( B5
% 9.17/5.40 = ( insert6833468608972679677at_nat @ none_P5811896708078067656at_nat @ bot_bo1471150103859235065at_nat ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5642_these__empty__eq,axiom,
% 9.17/5.40 ! [B5: set_op4508134149509766951at_nat] :
% 9.17/5.40 ( ( ( these_8061402112538453438at_nat @ B5 )
% 9.17/5.40 = bot_bo2099793752762293965at_nat )
% 9.17/5.40 = ( ( B5 = bot_bo3414888551220300179at_nat )
% 9.17/5.40 | ( B5
% 9.17/5.40 = ( insert6842972033726296599at_nat @ none_P5556105721700978146at_nat @ bot_bo3414888551220300179at_nat ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5643_these__empty__eq,axiom,
% 9.17/5.40 ! [B5: set_option_o] :
% 9.17/5.40 ( ( ( these_o @ B5 )
% 9.17/5.40 = bot_bot_set_o )
% 9.17/5.40 = ( ( B5 = bot_bot_set_option_o )
% 9.17/5.40 | ( B5
% 9.17/5.40 = ( insert_option_o @ none_o @ bot_bot_set_option_o ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5644_these__empty__eq,axiom,
% 9.17/5.40 ! [B5: set_option_nat] :
% 9.17/5.40 ( ( ( these_nat @ B5 )
% 9.17/5.40 = bot_bot_set_nat )
% 9.17/5.40 = ( ( B5 = bot_bo5009843511495006442on_nat )
% 9.17/5.40 | ( B5
% 9.17/5.40 = ( insert_option_nat @ none_nat @ bot_bo5009843511495006442on_nat ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5645_these__empty__eq,axiom,
% 9.17/5.40 ! [B5: set_option_int] :
% 9.17/5.40 ( ( ( these_int @ B5 )
% 9.17/5.40 = bot_bot_set_int )
% 9.17/5.40 = ( ( B5 = bot_bo2519760366563279686on_int )
% 9.17/5.40 | ( B5
% 9.17/5.40 = ( insert_option_int @ none_int @ bot_bo2519760366563279686on_int ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5646_these__not__empty__eq,axiom,
% 9.17/5.40 ! [B5: set_op3940070208846178154it_nat] :
% 9.17/5.40 ( ( ( these_6645423997822192641it_nat @ B5 )
% 9.17/5.40 != bot_bo6361524548789211024it_nat )
% 9.17/5.40 = ( ( B5 != bot_bo8185009268211221974it_nat )
% 9.17/5.40 & ( B5
% 9.17/5.40 != ( insert7468008629046257882it_nat @ none_P2587165478634041381it_nat @ bot_bo8185009268211221974it_nat ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5647_these__not__empty__eq,axiom,
% 9.17/5.40 ! [B5: set_option_num] :
% 9.17/5.40 ( ( ( these_num @ B5 )
% 9.17/5.40 != bot_bot_set_num )
% 9.17/5.40 = ( ( B5 != bot_bo725063100934353204on_num )
% 9.17/5.40 & ( B5
% 9.17/5.40 != ( insert_option_num @ none_num @ bot_bo725063100934353204on_num ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5648_these__not__empty__eq,axiom,
% 9.17/5.40 ! [B5: set_op239864471688321678it_nat] :
% 9.17/5.40 ( ( ( these_3407724651694999947it_nat @ B5 )
% 9.17/5.40 != bot_bo5696401558416705618it_nat )
% 9.17/5.40 = ( ( B5 != bot_bo1172055076661450530it_nat )
% 9.17/5.40 & ( B5
% 9.17/5.40 != ( insert2007652293347934600it_nat @ none_P9117596204409417319it_nat @ bot_bo1172055076661450530it_nat ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5649_these__not__empty__eq,axiom,
% 9.17/5.40 ! [B5: set_op989438649584373901at_nat] :
% 9.17/5.40 ( ( ( these_1872268174106123684at_nat @ B5 )
% 9.17/5.40 != bot_bo228742789529271731at_nat )
% 9.17/5.40 = ( ( B5 != bot_bo1471150103859235065at_nat )
% 9.17/5.40 & ( B5
% 9.17/5.40 != ( insert6833468608972679677at_nat @ none_P5811896708078067656at_nat @ bot_bo1471150103859235065at_nat ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5650_these__not__empty__eq,axiom,
% 9.17/5.40 ! [B5: set_op4508134149509766951at_nat] :
% 9.17/5.40 ( ( ( these_8061402112538453438at_nat @ B5 )
% 9.17/5.40 != bot_bo2099793752762293965at_nat )
% 9.17/5.40 = ( ( B5 != bot_bo3414888551220300179at_nat )
% 9.17/5.40 & ( B5
% 9.17/5.40 != ( insert6842972033726296599at_nat @ none_P5556105721700978146at_nat @ bot_bo3414888551220300179at_nat ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5651_these__not__empty__eq,axiom,
% 9.17/5.40 ! [B5: set_option_o] :
% 9.17/5.40 ( ( ( these_o @ B5 )
% 9.17/5.40 != bot_bot_set_o )
% 9.17/5.40 = ( ( B5 != bot_bot_set_option_o )
% 9.17/5.40 & ( B5
% 9.17/5.40 != ( insert_option_o @ none_o @ bot_bot_set_option_o ) ) ) ) ).
% 9.17/5.40
% 9.17/5.40 thf(fact_5652_these__not__empty__eq,axiom,
% 9.17/5.41 ! [B5: set_option_nat] :
% 9.17/5.41 ( ( ( these_nat @ B5 )
% 9.17/5.41 != bot_bot_set_nat )
% 9.17/5.41 = ( ( B5 != bot_bo5009843511495006442on_nat )
% 9.17/5.41 & ( B5
% 9.17/5.41 != ( insert_option_nat @ none_nat @ bot_bo5009843511495006442on_nat ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5653_these__not__empty__eq,axiom,
% 9.17/5.41 ! [B5: set_option_int] :
% 9.17/5.41 ( ( ( these_int @ B5 )
% 9.17/5.41 != bot_bot_set_int )
% 9.17/5.41 = ( ( B5 != bot_bo2519760366563279686on_int )
% 9.17/5.41 & ( B5
% 9.17/5.41 != ( insert_option_int @ none_int @ bot_bo2519760366563279686on_int ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5654_not__UNIV__eq__Icc,axiom,
% 9.17/5.41 ! [L4: int,H5: int] :
% 9.17/5.41 ( top_top_set_int
% 9.17/5.41 != ( set_or1266510415728281911st_int @ L4 @ H5 ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5655_not__UNIV__eq__Icc,axiom,
% 9.17/5.41 ! [L4: nat,H5: nat] :
% 9.17/5.41 ( top_top_set_nat
% 9.17/5.41 != ( set_or1269000886237332187st_nat @ L4 @ H5 ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5656_infinite__Iic,axiom,
% 9.17/5.41 ! [A: int] :
% 9.17/5.41 ~ ( finite_finite_int @ ( set_ord_atMost_int @ A ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5657_infinite__Iio,axiom,
% 9.17/5.41 ! [A: int] :
% 9.17/5.41 ~ ( finite_finite_int @ ( set_ord_lessThan_int @ A ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5658_not__UNIV__eq__Iic,axiom,
% 9.17/5.41 ! [H5: int] :
% 9.17/5.41 ( top_top_set_int
% 9.17/5.41 != ( set_ord_atMost_int @ H5 ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5659_not__UNIV__eq__Iic,axiom,
% 9.17/5.41 ! [H5: nat] :
% 9.17/5.41 ( top_top_set_nat
% 9.17/5.41 != ( set_ord_atMost_nat @ H5 ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5660_card__1__singletonI,axiom,
% 9.17/5.41 ! [S2: set_Product_unit,X: product_unit] :
% 9.17/5.41 ( ( finite4290736615968046902t_unit @ S2 )
% 9.17/5.41 => ( ( ( finite410649719033368117t_unit @ S2 )
% 9.17/5.41 = one_one_nat )
% 9.17/5.41 => ( ( member_Product_unit @ X @ S2 )
% 9.17/5.41 => ( S2
% 9.17/5.41 = ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5661_card__1__singletonI,axiom,
% 9.17/5.41 ! [S2: set_list_nat,X: list_nat] :
% 9.17/5.41 ( ( finite8100373058378681591st_nat @ S2 )
% 9.17/5.41 => ( ( ( finite_card_list_nat @ S2 )
% 9.17/5.41 = one_one_nat )
% 9.17/5.41 => ( ( member_list_nat @ X @ S2 )
% 9.17/5.41 => ( S2
% 9.17/5.41 = ( insert_list_nat @ X @ bot_bot_set_list_nat ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5662_card__1__singletonI,axiom,
% 9.17/5.41 ! [S2: set_Code_integer,X: code_integer] :
% 9.17/5.41 ( ( finite6017078050557962740nteger @ S2 )
% 9.17/5.41 => ( ( ( finite4902975817058060853nteger @ S2 )
% 9.17/5.41 = one_one_nat )
% 9.17/5.41 => ( ( member_Code_integer @ X @ S2 )
% 9.17/5.41 => ( S2
% 9.17/5.41 = ( insert_Code_integer @ X @ bot_bo3990330152332043303nteger ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5663_card__1__singletonI,axiom,
% 9.17/5.41 ! [S2: set_Pr4329608150637261639at_nat,X: produc3843707927480180839at_nat] :
% 9.17/5.41 ( ( finite4343798906461161616at_nat @ S2 )
% 9.17/5.41 => ( ( ( finite3771342082235030671at_nat @ S2 )
% 9.17/5.41 = one_one_nat )
% 9.17/5.41 => ( ( member8757157785044589968at_nat @ X @ S2 )
% 9.17/5.41 => ( S2
% 9.17/5.41 = ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5664_card__1__singletonI,axiom,
% 9.17/5.41 ! [S2: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat] :
% 9.17/5.41 ( ( finite6177210948735845034at_nat @ S2 )
% 9.17/5.41 => ( ( ( finite711546835091564841at_nat @ S2 )
% 9.17/5.41 = one_one_nat )
% 9.17/5.41 => ( ( member8440522571783428010at_nat @ X @ S2 )
% 9.17/5.41 => ( S2
% 9.17/5.41 = ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5665_card__1__singletonI,axiom,
% 9.17/5.41 ! [S2: set_o,X: $o] :
% 9.17/5.41 ( ( finite_finite_o @ S2 )
% 9.17/5.41 => ( ( ( finite_card_o @ S2 )
% 9.17/5.41 = one_one_nat )
% 9.17/5.41 => ( ( member_o @ X @ S2 )
% 9.17/5.41 => ( S2
% 9.17/5.41 = ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5666_card__1__singletonI,axiom,
% 9.17/5.41 ! [S2: set_nat,X: nat] :
% 9.17/5.41 ( ( finite_finite_nat @ S2 )
% 9.17/5.41 => ( ( ( finite_card_nat @ S2 )
% 9.17/5.41 = one_one_nat )
% 9.17/5.41 => ( ( member_nat @ X @ S2 )
% 9.17/5.41 => ( S2
% 9.17/5.41 = ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5667_card__1__singletonI,axiom,
% 9.17/5.41 ! [S2: set_int,X: int] :
% 9.17/5.41 ( ( finite_finite_int @ S2 )
% 9.17/5.41 => ( ( ( finite_card_int @ S2 )
% 9.17/5.41 = one_one_nat )
% 9.17/5.41 => ( ( member_int @ X @ S2 )
% 9.17/5.41 => ( S2
% 9.17/5.41 = ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5668_finite__M__bounded__by__nat,axiom,
% 9.17/5.41 ! [P: nat > $o,I: nat] :
% 9.17/5.41 ( finite_finite_nat
% 9.17/5.41 @ ( collect_nat
% 9.17/5.41 @ ^ [K4: nat] :
% 9.17/5.41 ( ( P @ K4 )
% 9.17/5.41 & ( ord_less_nat @ K4 @ I ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5669_finite__less__ub,axiom,
% 9.17/5.41 ! [F: nat > nat,U: nat] :
% 9.17/5.41 ( ! [N: nat] : ( ord_less_eq_nat @ N @ ( F @ N ) )
% 9.17/5.41 => ( finite_finite_nat
% 9.17/5.41 @ ( collect_nat
% 9.17/5.41 @ ^ [N4: nat] : ( ord_less_eq_nat @ ( F @ N4 ) @ U ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5670_card__insert__disjoint_H,axiom,
% 9.17/5.41 ! [A2: set_Pr4329608150637261639at_nat,X: produc3843707927480180839at_nat] :
% 9.17/5.41 ( ( finite4343798906461161616at_nat @ A2 )
% 9.17/5.41 => ( ~ ( member8757157785044589968at_nat @ X @ A2 )
% 9.17/5.41 => ( ( minus_minus_nat @ ( finite3771342082235030671at_nat @ ( insert9069300056098147895at_nat @ X @ A2 ) ) @ ( suc @ zero_zero_nat ) )
% 9.17/5.41 = ( finite3771342082235030671at_nat @ A2 ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5671_card__insert__disjoint_H,axiom,
% 9.17/5.41 ! [A2: set_o,X: $o] :
% 9.17/5.41 ( ( finite_finite_o @ A2 )
% 9.17/5.41 => ( ~ ( member_o @ X @ A2 )
% 9.17/5.41 => ( ( minus_minus_nat @ ( finite_card_o @ ( insert_o @ X @ A2 ) ) @ ( suc @ zero_zero_nat ) )
% 9.17/5.41 = ( finite_card_o @ A2 ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5672_card__insert__disjoint_H,axiom,
% 9.17/5.41 ! [A2: set_Product_unit,X: product_unit] :
% 9.17/5.41 ( ( finite4290736615968046902t_unit @ A2 )
% 9.17/5.41 => ( ~ ( member_Product_unit @ X @ A2 )
% 9.17/5.41 => ( ( minus_minus_nat @ ( finite410649719033368117t_unit @ ( insert_Product_unit @ X @ A2 ) ) @ ( suc @ zero_zero_nat ) )
% 9.17/5.41 = ( finite410649719033368117t_unit @ A2 ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5673_card__insert__disjoint_H,axiom,
% 9.17/5.41 ! [A2: set_list_nat,X: list_nat] :
% 9.17/5.41 ( ( finite8100373058378681591st_nat @ A2 )
% 9.17/5.41 => ( ~ ( member_list_nat @ X @ A2 )
% 9.17/5.41 => ( ( minus_minus_nat @ ( finite_card_list_nat @ ( insert_list_nat @ X @ A2 ) ) @ ( suc @ zero_zero_nat ) )
% 9.17/5.41 = ( finite_card_list_nat @ A2 ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5674_card__insert__disjoint_H,axiom,
% 9.17/5.41 ! [A2: set_nat,X: nat] :
% 9.17/5.41 ( ( finite_finite_nat @ A2 )
% 9.17/5.41 => ( ~ ( member_nat @ X @ A2 )
% 9.17/5.41 => ( ( minus_minus_nat @ ( finite_card_nat @ ( insert_nat @ X @ A2 ) ) @ ( suc @ zero_zero_nat ) )
% 9.17/5.41 = ( finite_card_nat @ A2 ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5675_card__insert__disjoint_H,axiom,
% 9.17/5.41 ! [A2: set_int,X: int] :
% 9.17/5.41 ( ( finite_finite_int @ A2 )
% 9.17/5.41 => ( ~ ( member_int @ X @ A2 )
% 9.17/5.41 => ( ( minus_minus_nat @ ( finite_card_int @ ( insert_int @ X @ A2 ) ) @ ( suc @ zero_zero_nat ) )
% 9.17/5.41 = ( finite_card_int @ A2 ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5676_card__insert__disjoint_H,axiom,
% 9.17/5.41 ! [A2: set_Code_integer,X: code_integer] :
% 9.17/5.41 ( ( finite6017078050557962740nteger @ A2 )
% 9.17/5.41 => ( ~ ( member_Code_integer @ X @ A2 )
% 9.17/5.41 => ( ( minus_minus_nat @ ( finite4902975817058060853nteger @ ( insert_Code_integer @ X @ A2 ) ) @ ( suc @ zero_zero_nat ) )
% 9.17/5.41 = ( finite4902975817058060853nteger @ A2 ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5677_card__insert__disjoint_H,axiom,
% 9.17/5.41 ! [A2: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat] :
% 9.17/5.41 ( ( finite6177210948735845034at_nat @ A2 )
% 9.17/5.41 => ( ~ ( member8440522571783428010at_nat @ X @ A2 )
% 9.17/5.41 => ( ( minus_minus_nat @ ( finite711546835091564841at_nat @ ( insert8211810215607154385at_nat @ X @ A2 ) ) @ ( suc @ zero_zero_nat ) )
% 9.17/5.41 = ( finite711546835091564841at_nat @ A2 ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5678_in__these__eq,axiom,
% 9.17/5.41 ! [X: produc3843707927480180839at_nat,A2: set_op989438649584373901at_nat] :
% 9.17/5.41 ( ( member8757157785044589968at_nat @ X @ ( these_1872268174106123684at_nat @ A2 ) )
% 9.17/5.41 = ( member4288423094740844502at_nat @ ( some_P131194445498448716at_nat @ X ) @ A2 ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5679_in__these__eq,axiom,
% 9.17/5.41 ! [X: product_prod_nat_nat,A2: set_op4508134149509766951at_nat] :
% 9.17/5.41 ( ( member8440522571783428010at_nat @ X @ ( these_8061402112538453438at_nat @ A2 ) )
% 9.17/5.41 = ( member3954567711264315760at_nat @ ( some_P7363390416028606310at_nat @ X ) @ A2 ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5680_in__these__eq,axiom,
% 9.17/5.41 ! [X: $o,A2: set_option_o] :
% 9.17/5.41 ( ( member_o @ X @ ( these_o @ A2 ) )
% 9.17/5.41 = ( member_option_o @ ( some_o @ X ) @ A2 ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5681_in__these__eq,axiom,
% 9.17/5.41 ! [X: nat,A2: set_option_nat] :
% 9.17/5.41 ( ( member_nat @ X @ ( these_nat @ A2 ) )
% 9.17/5.41 = ( member_option_nat @ ( some_nat @ X ) @ A2 ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5682_in__these__eq,axiom,
% 9.17/5.41 ! [X: int,A2: set_option_int] :
% 9.17/5.41 ( ( member_int @ X @ ( these_int @ A2 ) )
% 9.17/5.41 = ( member_option_int @ ( some_int @ X ) @ A2 ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5683_in__these__eq,axiom,
% 9.17/5.41 ! [X: num,A2: set_option_num] :
% 9.17/5.41 ( ( member_num @ X @ ( these_num @ A2 ) )
% 9.17/5.41 = ( member_option_num @ ( some_num @ X ) @ A2 ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5684_in__these__eq,axiom,
% 9.17/5.41 ! [X: produc8664842809031399944it_nat,A2: set_op239864471688321678it_nat] :
% 9.17/5.41 ( ( member3421417852355157663it_nat @ X @ ( these_3407724651694999947it_nat @ A2 ) )
% 9.17/5.41 = ( member5596548051065438575it_nat @ ( some_P1914260805536162275it_nat @ X ) @ A2 ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5685_infinite__Icc,axiom,
% 9.17/5.41 ! [A: rat,B: rat] :
% 9.17/5.41 ( ( ord_less_rat @ A @ B )
% 9.17/5.41 => ~ ( finite_finite_rat @ ( set_or633870826150836451st_rat @ A @ B ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5686_infinite__Ico,axiom,
% 9.17/5.41 ! [A: rat,B: rat] :
% 9.17/5.41 ( ( ord_less_rat @ A @ B )
% 9.17/5.41 => ~ ( finite_finite_rat @ ( set_or4029947393144176647an_rat @ A @ B ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5687_subset__eq__atLeast0__atMost__finite,axiom,
% 9.17/5.41 ! [N6: set_nat,N2: nat] :
% 9.17/5.41 ( ( ord_less_eq_set_nat @ N6 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 9.17/5.41 => ( finite_finite_nat @ N6 ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5688_subset__eq__atLeast0__lessThan__finite,axiom,
% 9.17/5.41 ! [N6: set_nat,N2: nat] :
% 9.17/5.41 ( ( ord_less_eq_set_nat @ N6 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) )
% 9.17/5.41 => ( finite_finite_nat @ N6 ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5689_atMost__Suc,axiom,
% 9.17/5.41 ! [K: nat] :
% 9.17/5.41 ( ( set_ord_atMost_nat @ ( suc @ K ) )
% 9.17/5.41 = ( insert_nat @ ( suc @ K ) @ ( set_ord_atMost_nat @ K ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5690_surj__fun__eq,axiom,
% 9.17/5.41 ! [F: num > code_integer,X11: set_num,G1: code_integer > code_integer,G22: code_integer > code_integer] :
% 9.17/5.41 ( ( ( image_8379761247532268670nteger @ F @ X11 )
% 9.17/5.41 = top_to4645266643341252675nteger )
% 9.17/5.41 => ( ! [X4: num] :
% 9.17/5.41 ( ( member_num @ X4 @ X11 )
% 9.17/5.41 => ( ( comp_C3531382070062128313er_num @ G1 @ F @ X4 )
% 9.17/5.41 = ( comp_C3531382070062128313er_num @ G22 @ F @ X4 ) ) )
% 9.17/5.41 => ( G1 = G22 ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5691_surj__fun__eq,axiom,
% 9.17/5.41 ! [F: code_integer > code_integer,X11: set_Code_integer,G1: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,G22: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 9.17/5.41 ( ( ( image_4470545334726330049nteger @ F @ X11 )
% 9.17/5.41 = top_to4645266643341252675nteger )
% 9.17/5.41 => ( ! [X4: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ X4 @ X11 )
% 9.17/5.41 => ( ( comp_C1593894019821074884nteger @ G1 @ F @ X4 )
% 9.17/5.41 = ( comp_C1593894019821074884nteger @ G22 @ F @ X4 ) ) )
% 9.17/5.41 => ( G1 = G22 ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5692_surj__fun__eq,axiom,
% 9.17/5.41 ! [F: code_integer > code_integer > code_integer,X11: set_Code_integer,G1: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G22: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 9.17/5.41 ( ( ( image_2177946750938214461nteger @ F @ X11 )
% 9.17/5.41 = top_to3804862627464599871nteger )
% 9.17/5.41 => ( ! [X4: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ X4 @ X11 )
% 9.17/5.41 => ( ( comp_C8797469213163452608nteger @ G1 @ F @ X4 )
% 9.17/5.41 = ( comp_C8797469213163452608nteger @ G22 @ F @ X4 ) ) )
% 9.17/5.41 => ( G1 = G22 ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5693_surj__fun__eq,axiom,
% 9.17/5.41 ! [F: int > nat,X11: set_int,G1: nat > num,G22: nat > num] :
% 9.17/5.41 ( ( ( image_int_nat @ F @ X11 )
% 9.17/5.41 = top_top_set_nat )
% 9.17/5.41 => ( ! [X4: int] :
% 9.17/5.41 ( ( member_int @ X4 @ X11 )
% 9.17/5.41 => ( ( comp_nat_num_int @ G1 @ F @ X4 )
% 9.17/5.41 = ( comp_nat_num_int @ G22 @ F @ X4 ) ) )
% 9.17/5.41 => ( G1 = G22 ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5694_comp__surj,axiom,
% 9.17/5.41 ! [F: num > code_integer,G: code_integer > code_integer] :
% 9.17/5.41 ( ( ( image_8379761247532268670nteger @ F @ top_top_set_num )
% 9.17/5.41 = top_to4645266643341252675nteger )
% 9.17/5.41 => ( ( ( image_4470545334726330049nteger @ G @ top_to4645266643341252675nteger )
% 9.17/5.41 = top_to4645266643341252675nteger )
% 9.17/5.41 => ( ( image_8379761247532268670nteger @ ( comp_C3531382070062128313er_num @ G @ F ) @ top_top_set_num )
% 9.17/5.41 = top_to4645266643341252675nteger ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5695_comp__surj,axiom,
% 9.17/5.41 ! [F: nat > code_integer,G: code_integer > code_integer] :
% 9.17/5.41 ( ( ( image_1215581382706833972nteger @ F @ top_top_set_nat )
% 9.17/5.41 = top_to4645266643341252675nteger )
% 9.17/5.41 => ( ( ( image_4470545334726330049nteger @ G @ top_to4645266643341252675nteger )
% 9.17/5.41 = top_to4645266643341252675nteger )
% 9.17/5.41 => ( ( image_1215581382706833972nteger @ ( comp_C6974050283906349679er_nat @ G @ F ) @ top_top_set_nat )
% 9.17/5.41 = top_to4645266643341252675nteger ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5696_comp__surj,axiom,
% 9.17/5.41 ! [F: nat > code_integer,G: code_integer > nat] :
% 9.17/5.41 ( ( ( image_1215581382706833972nteger @ F @ top_top_set_nat )
% 9.17/5.41 = top_to4645266643341252675nteger )
% 9.17/5.41 => ( ( ( image_951025933927791156er_nat @ G @ top_to4645266643341252675nteger )
% 9.17/5.41 = top_top_set_nat )
% 9.17/5.41 => ( ( image_nat_nat @ ( comp_C4049556595663050210at_nat @ G @ F ) @ top_top_set_nat )
% 9.17/5.41 = top_top_set_nat ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5697_comp__surj,axiom,
% 9.17/5.41 ! [F: nat > code_integer,G: code_integer > product_unit] :
% 9.17/5.41 ( ( ( image_1215581382706833972nteger @ F @ top_top_set_nat )
% 9.17/5.41 = top_to4645266643341252675nteger )
% 9.17/5.41 => ( ( ( image_7182656606676592809t_unit @ G @ top_to4645266643341252675nteger )
% 9.17/5.41 = top_to1996260823553986621t_unit )
% 9.17/5.41 => ( ( image_8730104196221521654t_unit @ ( comp_C8086623346886033437it_nat @ G @ F ) @ top_top_set_nat )
% 9.17/5.41 = top_to1996260823553986621t_unit ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5698_comp__surj,axiom,
% 9.17/5.41 ! [F: nat > code_integer,G: code_integer > int] :
% 9.17/5.41 ( ( ( image_1215581382706833972nteger @ F @ top_top_set_nat )
% 9.17/5.41 = top_to4645266643341252675nteger )
% 9.17/5.41 => ( ( ( image_948535463418740880er_int @ G @ top_to4645266643341252675nteger )
% 9.17/5.41 = top_top_set_int )
% 9.17/5.41 => ( ( image_nat_int @ ( comp_C5048910307564104766nt_nat @ G @ F ) @ top_top_set_nat )
% 9.17/5.41 = top_top_set_int ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5699_comp__surj,axiom,
% 9.17/5.41 ! [F: nat > nat,G: nat > code_integer] :
% 9.17/5.41 ( ( ( image_nat_nat @ F @ top_top_set_nat )
% 9.17/5.41 = top_top_set_nat )
% 9.17/5.41 => ( ( ( image_1215581382706833972nteger @ G @ top_top_set_nat )
% 9.17/5.41 = top_to4645266643341252675nteger )
% 9.17/5.41 => ( ( image_1215581382706833972nteger @ ( comp_n3898172953802868194er_nat @ G @ F ) @ top_top_set_nat )
% 9.17/5.41 = top_to4645266643341252675nteger ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5700_comp__surj,axiom,
% 9.17/5.41 ! [F: nat > nat,G: nat > nat] :
% 9.17/5.41 ( ( ( image_nat_nat @ F @ top_top_set_nat )
% 9.17/5.41 = top_top_set_nat )
% 9.17/5.41 => ( ( ( image_nat_nat @ G @ top_top_set_nat )
% 9.17/5.41 = top_top_set_nat )
% 9.17/5.41 => ( ( image_nat_nat @ ( comp_nat_nat_nat @ G @ F ) @ top_top_set_nat )
% 9.17/5.41 = top_top_set_nat ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5701_comp__surj,axiom,
% 9.17/5.41 ! [F: nat > nat,G: nat > product_unit] :
% 9.17/5.41 ( ( ( image_nat_nat @ F @ top_top_set_nat )
% 9.17/5.41 = top_top_set_nat )
% 9.17/5.41 => ( ( ( image_8730104196221521654t_unit @ G @ top_top_set_nat )
% 9.17/5.41 = top_to1996260823553986621t_unit )
% 9.17/5.41 => ( ( image_8730104196221521654t_unit @ ( comp_n9025697279074352746it_nat @ G @ F ) @ top_top_set_nat )
% 9.17/5.41 = top_to1996260823553986621t_unit ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5702_comp__surj,axiom,
% 9.17/5.41 ! [F: nat > nat,G: nat > int] :
% 9.17/5.41 ( ( ( image_nat_nat @ F @ top_top_set_nat )
% 9.17/5.41 = top_top_set_nat )
% 9.17/5.41 => ( ( ( image_nat_int @ G @ top_top_set_nat )
% 9.17/5.41 = top_top_set_int )
% 9.17/5.41 => ( ( image_nat_int @ ( comp_nat_int_nat @ G @ F ) @ top_top_set_nat )
% 9.17/5.41 = top_top_set_int ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5703_comp__surj,axiom,
% 9.17/5.41 ! [F: nat > product_unit,G: product_unit > code_integer] :
% 9.17/5.41 ( ( ( image_8730104196221521654t_unit @ F @ top_top_set_nat )
% 9.17/5.41 = top_to1996260823553986621t_unit )
% 9.17/5.41 => ( ( ( image_3815118110082124069nteger @ G @ top_to1996260823553986621t_unit )
% 9.17/5.41 = top_to4645266643341252675nteger )
% 9.17/5.41 => ( ( image_1215581382706833972nteger @ ( comp_P756492639069434009er_nat @ G @ F ) @ top_top_set_nat )
% 9.17/5.41 = top_to4645266643341252675nteger ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5704_fun_Oset__map,axiom,
% 9.17/5.41 ! [F: code_integer > code_integer,V: num > code_integer] :
% 9.17/5.41 ( ( image_8379761247532268670nteger @ ( comp_C3531382070062128313er_num @ F @ V ) @ top_top_set_num )
% 9.17/5.41 = ( image_4470545334726330049nteger @ F @ ( image_8379761247532268670nteger @ V @ top_top_set_num ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5705_fun_Oset__map,axiom,
% 9.17/5.41 ! [F: code_integer > code_integer,V: nat > code_integer] :
% 9.17/5.41 ( ( image_1215581382706833972nteger @ ( comp_C6974050283906349679er_nat @ F @ V ) @ top_top_set_nat )
% 9.17/5.41 = ( image_4470545334726330049nteger @ F @ ( image_1215581382706833972nteger @ V @ top_top_set_nat ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5706_fun_Oset__map,axiom,
% 9.17/5.41 ! [F: int > code_integer,V: nat > int] :
% 9.17/5.41 ( ( image_1215581382706833972nteger @ ( comp_i1588355021709917246er_nat @ F @ V ) @ top_top_set_nat )
% 9.17/5.41 = ( image_1587234942943678608nteger @ F @ ( image_nat_int @ V @ top_top_set_nat ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5707_fun_Oset__map,axiom,
% 9.17/5.41 ! [F: nat > code_integer,V: nat > nat] :
% 9.17/5.41 ( ( image_1215581382706833972nteger @ ( comp_n3898172953802868194er_nat @ F @ V ) @ top_top_set_nat )
% 9.17/5.41 = ( image_1215581382706833972nteger @ F @ ( image_nat_nat @ V @ top_top_set_nat ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5708_fun_Oset__map,axiom,
% 9.17/5.41 ! [F: code_integer > nat,V: nat > code_integer] :
% 9.17/5.41 ( ( image_nat_nat @ ( comp_C4049556595663050210at_nat @ F @ V ) @ top_top_set_nat )
% 9.17/5.41 = ( image_951025933927791156er_nat @ F @ ( image_1215581382706833972nteger @ V @ top_top_set_nat ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5709_fun_Oset__map,axiom,
% 9.17/5.41 ! [F: int > nat,V: nat > int] :
% 9.17/5.41 ( ( image_nat_nat @ ( comp_int_nat_nat @ F @ V ) @ top_top_set_nat )
% 9.17/5.41 = ( image_int_nat @ F @ ( image_nat_int @ V @ top_top_set_nat ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5710_fun_Oset__map,axiom,
% 9.17/5.41 ! [F: nat > nat,V: nat > nat] :
% 9.17/5.41 ( ( image_nat_nat @ ( comp_nat_nat_nat @ F @ V ) @ top_top_set_nat )
% 9.17/5.41 = ( image_nat_nat @ F @ ( image_nat_nat @ V @ top_top_set_nat ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5711_fun_Oset__map,axiom,
% 9.17/5.41 ! [F: code_integer > int,V: nat > code_integer] :
% 9.17/5.41 ( ( image_nat_int @ ( comp_C5048910307564104766nt_nat @ F @ V ) @ top_top_set_nat )
% 9.17/5.41 = ( image_948535463418740880er_int @ F @ ( image_1215581382706833972nteger @ V @ top_top_set_nat ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5712_fun_Oset__map,axiom,
% 9.17/5.41 ! [F: nat > int,V: nat > nat] :
% 9.17/5.41 ( ( image_nat_int @ ( comp_nat_int_nat @ F @ V ) @ top_top_set_nat )
% 9.17/5.41 = ( image_nat_int @ F @ ( image_nat_nat @ V @ top_top_set_nat ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5713_fun_Oset__map,axiom,
% 9.17/5.41 ! [F: int > int,V: nat > int] :
% 9.17/5.41 ( ( image_nat_int @ ( comp_int_int_nat @ F @ V ) @ top_top_set_nat )
% 9.17/5.41 = ( image_int_int @ F @ ( image_nat_int @ V @ top_top_set_nat ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5714_fun_Omap__cong,axiom,
% 9.17/5.41 ! [X: num > code_integer,Ya: num > code_integer,F: code_integer > code_integer,G: code_integer > code_integer] :
% 9.17/5.41 ( ( X = Ya )
% 9.17/5.41 => ( ! [Z3: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ Z3 @ ( image_8379761247532268670nteger @ Ya @ top_top_set_num ) )
% 9.17/5.41 => ( ( F @ Z3 )
% 9.17/5.41 = ( G @ Z3 ) ) )
% 9.17/5.41 => ( ( comp_C3531382070062128313er_num @ F @ X )
% 9.17/5.41 = ( comp_C3531382070062128313er_num @ G @ Ya ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5715_fun_Omap__cong,axiom,
% 9.17/5.41 ! [X: code_integer > code_integer,Ya: code_integer > code_integer,F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 9.17/5.41 ( ( X = Ya )
% 9.17/5.41 => ( ! [Z3: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ Z3 @ ( image_4470545334726330049nteger @ Ya @ top_to4645266643341252675nteger ) )
% 9.17/5.41 => ( ( F @ Z3 )
% 9.17/5.41 = ( G @ Z3 ) ) )
% 9.17/5.41 => ( ( comp_C1593894019821074884nteger @ F @ X )
% 9.17/5.41 = ( comp_C1593894019821074884nteger @ G @ Ya ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5716_fun_Omap__cong,axiom,
% 9.17/5.41 ! [X: code_integer > code_integer > code_integer,Ya: code_integer > code_integer > code_integer,F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 9.17/5.41 ( ( X = Ya )
% 9.17/5.41 => ( ! [Z3: code_integer > code_integer] :
% 9.17/5.41 ( ( member2790140394383616496nteger @ Z3 @ ( image_2177946750938214461nteger @ Ya @ top_to4645266643341252675nteger ) )
% 9.17/5.41 => ( ( F @ Z3 )
% 9.17/5.41 = ( G @ Z3 ) ) )
% 9.17/5.41 => ( ( comp_C8797469213163452608nteger @ F @ X )
% 9.17/5.41 = ( comp_C8797469213163452608nteger @ G @ Ya ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5717_fun_Omap__cong,axiom,
% 9.17/5.41 ! [X: int > nat,Ya: int > nat,F: nat > num,G: nat > num] :
% 9.17/5.41 ( ( X = Ya )
% 9.17/5.41 => ( ! [Z3: nat] :
% 9.17/5.41 ( ( member_nat @ Z3 @ ( image_int_nat @ Ya @ top_top_set_int ) )
% 9.17/5.41 => ( ( F @ Z3 )
% 9.17/5.41 = ( G @ Z3 ) ) )
% 9.17/5.41 => ( ( comp_nat_num_int @ F @ X )
% 9.17/5.41 = ( comp_nat_num_int @ G @ Ya ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5718_fun_Omap__cong0,axiom,
% 9.17/5.41 ! [X: num > code_integer,F: code_integer > code_integer,G: code_integer > code_integer] :
% 9.17/5.41 ( ! [Z3: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ Z3 @ ( image_8379761247532268670nteger @ X @ top_top_set_num ) )
% 9.17/5.41 => ( ( F @ Z3 )
% 9.17/5.41 = ( G @ Z3 ) ) )
% 9.17/5.41 => ( ( comp_C3531382070062128313er_num @ F @ X )
% 9.17/5.41 = ( comp_C3531382070062128313er_num @ G @ X ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5719_fun_Omap__cong0,axiom,
% 9.17/5.41 ! [X: code_integer > code_integer,F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 9.17/5.41 ( ! [Z3: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ Z3 @ ( image_4470545334726330049nteger @ X @ top_to4645266643341252675nteger ) )
% 9.17/5.41 => ( ( F @ Z3 )
% 9.17/5.41 = ( G @ Z3 ) ) )
% 9.17/5.41 => ( ( comp_C1593894019821074884nteger @ F @ X )
% 9.17/5.41 = ( comp_C1593894019821074884nteger @ G @ X ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5720_fun_Omap__cong0,axiom,
% 9.17/5.41 ! [X: code_integer > code_integer > code_integer,F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 9.17/5.41 ( ! [Z3: code_integer > code_integer] :
% 9.17/5.41 ( ( member2790140394383616496nteger @ Z3 @ ( image_2177946750938214461nteger @ X @ top_to4645266643341252675nteger ) )
% 9.17/5.41 => ( ( F @ Z3 )
% 9.17/5.41 = ( G @ Z3 ) ) )
% 9.17/5.41 => ( ( comp_C8797469213163452608nteger @ F @ X )
% 9.17/5.41 = ( comp_C8797469213163452608nteger @ G @ X ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5721_fun_Omap__cong0,axiom,
% 9.17/5.41 ! [X: int > nat,F: nat > num,G: nat > num] :
% 9.17/5.41 ( ! [Z3: nat] :
% 9.17/5.41 ( ( member_nat @ Z3 @ ( image_int_nat @ X @ top_top_set_int ) )
% 9.17/5.41 => ( ( F @ Z3 )
% 9.17/5.41 = ( G @ Z3 ) ) )
% 9.17/5.41 => ( ( comp_nat_num_int @ F @ X )
% 9.17/5.41 = ( comp_nat_num_int @ G @ X ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5722_fun_Oinj__map__strong,axiom,
% 9.17/5.41 ! [X: num > code_integer,Xa: num > code_integer,F: code_integer > code_integer,Fa: code_integer > code_integer] :
% 9.17/5.41 ( ! [Z3: code_integer,Za: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ Z3 @ ( image_8379761247532268670nteger @ X @ top_top_set_num ) )
% 9.17/5.41 => ( ( member_Code_integer @ Za @ ( image_8379761247532268670nteger @ Xa @ top_top_set_num ) )
% 9.17/5.41 => ( ( ( F @ Z3 )
% 9.17/5.41 = ( Fa @ Za ) )
% 9.17/5.41 => ( Z3 = Za ) ) ) )
% 9.17/5.41 => ( ( ( comp_C3531382070062128313er_num @ F @ X )
% 9.17/5.41 = ( comp_C3531382070062128313er_num @ Fa @ Xa ) )
% 9.17/5.41 => ( X = Xa ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5723_fun_Oinj__map__strong,axiom,
% 9.17/5.41 ! [X: code_integer > code_integer,Xa: code_integer > code_integer,F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,Fa: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 9.17/5.41 ( ! [Z3: code_integer,Za: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ Z3 @ ( image_4470545334726330049nteger @ X @ top_to4645266643341252675nteger ) )
% 9.17/5.41 => ( ( member_Code_integer @ Za @ ( image_4470545334726330049nteger @ Xa @ top_to4645266643341252675nteger ) )
% 9.17/5.41 => ( ( ( F @ Z3 )
% 9.17/5.41 = ( Fa @ Za ) )
% 9.17/5.41 => ( Z3 = Za ) ) ) )
% 9.17/5.41 => ( ( ( comp_C1593894019821074884nteger @ F @ X )
% 9.17/5.41 = ( comp_C1593894019821074884nteger @ Fa @ Xa ) )
% 9.17/5.41 => ( X = Xa ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5724_fun_Oinj__map__strong,axiom,
% 9.17/5.41 ! [X: code_integer > code_integer > code_integer,Xa: code_integer > code_integer > code_integer,F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,Fa: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 9.17/5.41 ( ! [Z3: code_integer > code_integer,Za: code_integer > code_integer] :
% 9.17/5.41 ( ( member2790140394383616496nteger @ Z3 @ ( image_2177946750938214461nteger @ X @ top_to4645266643341252675nteger ) )
% 9.17/5.41 => ( ( member2790140394383616496nteger @ Za @ ( image_2177946750938214461nteger @ Xa @ top_to4645266643341252675nteger ) )
% 9.17/5.41 => ( ( ( F @ Z3 )
% 9.17/5.41 = ( Fa @ Za ) )
% 9.17/5.41 => ( Z3 = Za ) ) ) )
% 9.17/5.41 => ( ( ( comp_C8797469213163452608nteger @ F @ X )
% 9.17/5.41 = ( comp_C8797469213163452608nteger @ Fa @ Xa ) )
% 9.17/5.41 => ( X = Xa ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5725_fun_Oinj__map__strong,axiom,
% 9.17/5.41 ! [X: int > nat,Xa: int > nat,F: nat > num,Fa: nat > num] :
% 9.17/5.41 ( ! [Z3: nat,Za: nat] :
% 9.17/5.41 ( ( member_nat @ Z3 @ ( image_int_nat @ X @ top_top_set_int ) )
% 9.17/5.41 => ( ( member_nat @ Za @ ( image_int_nat @ Xa @ top_top_set_int ) )
% 9.17/5.41 => ( ( ( F @ Z3 )
% 9.17/5.41 = ( Fa @ Za ) )
% 9.17/5.41 => ( Z3 = Za ) ) ) )
% 9.17/5.41 => ( ( ( comp_nat_num_int @ F @ X )
% 9.17/5.41 = ( comp_nat_num_int @ Fa @ Xa ) )
% 9.17/5.41 => ( X = Xa ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5726_lessThan__Suc,axiom,
% 9.17/5.41 ! [K: nat] :
% 9.17/5.41 ( ( set_ord_lessThan_nat @ ( suc @ K ) )
% 9.17/5.41 = ( insert_nat @ K @ ( set_ord_lessThan_nat @ K ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5727_not__UNIV__le__Icc,axiom,
% 9.17/5.41 ! [L: int,H3: int] :
% 9.17/5.41 ~ ( ord_less_eq_set_int @ top_top_set_int @ ( set_or1266510415728281911st_int @ L @ H3 ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5728_not__UNIV__le__Icc,axiom,
% 9.17/5.41 ! [L: nat,H3: nat] :
% 9.17/5.41 ~ ( ord_less_eq_set_nat @ top_top_set_nat @ ( set_or1269000886237332187st_nat @ L @ H3 ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5729_surj__id,axiom,
% 9.17/5.41 ( ( image_o_o @ id_o @ top_top_set_o )
% 9.17/5.41 = top_top_set_o ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5730_surj__id,axiom,
% 9.17/5.41 ( ( image_nat_o_nat_o @ id_nat_o @ top_top_set_nat_o )
% 9.17/5.41 = top_top_set_nat_o ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5731_surj__id,axiom,
% 9.17/5.41 ( ( image_num_num @ id_num @ top_top_set_num )
% 9.17/5.41 = top_top_set_num ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5732_surj__id,axiom,
% 9.17/5.41 ( ( image_nat_nat @ id_nat @ top_top_set_nat )
% 9.17/5.41 = top_top_set_nat ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5733_surj__id,axiom,
% 9.17/5.41 ( ( image_405062704495631173t_unit @ id_Product_unit @ top_to1996260823553986621t_unit )
% 9.17/5.41 = top_to1996260823553986621t_unit ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5734_surj__id,axiom,
% 9.17/5.41 ( ( image_int_int @ id_int @ top_top_set_int )
% 9.17/5.41 = top_top_set_int ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5735_not__UNIV__le__Iic,axiom,
% 9.17/5.41 ! [H3: int] :
% 9.17/5.41 ~ ( ord_less_eq_set_int @ top_top_set_int @ ( set_ord_atMost_int @ H3 ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5736_not__UNIV__le__Iic,axiom,
% 9.17/5.41 ! [H3: nat] :
% 9.17/5.41 ~ ( ord_less_eq_set_nat @ top_top_set_nat @ ( set_ord_atMost_nat @ H3 ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5737_sum_Ofinite__Collect__op,axiom,
% 9.17/5.41 ! [I4: set_o,X: $o > code_integer,Y: $o > code_integer] :
% 9.17/5.41 ( ( finite_finite_o
% 9.17/5.41 @ ( collect_o
% 9.17/5.41 @ ^ [I3: $o] :
% 9.17/5.41 ( ( member_o @ I3 @ I4 )
% 9.17/5.41 & ( ( X @ I3 )
% 9.17/5.41 != zero_z3403309356797280102nteger ) ) ) )
% 9.17/5.41 => ( ( finite_finite_o
% 9.17/5.41 @ ( collect_o
% 9.17/5.41 @ ^ [I3: $o] :
% 9.17/5.41 ( ( member_o @ I3 @ I4 )
% 9.17/5.41 & ( ( Y @ I3 )
% 9.17/5.41 != zero_z3403309356797280102nteger ) ) ) )
% 9.17/5.41 => ( finite_finite_o
% 9.17/5.41 @ ( collect_o
% 9.17/5.41 @ ^ [I3: $o] :
% 9.17/5.41 ( ( member_o @ I3 @ I4 )
% 9.17/5.41 & ( ( plus_p5714425477246183910nteger @ ( X @ I3 ) @ ( Y @ I3 ) )
% 9.17/5.41 != zero_z3403309356797280102nteger ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5738_sum_Ofinite__Collect__op,axiom,
% 9.17/5.41 ! [I4: set_nat,X: nat > code_integer,Y: nat > code_integer] :
% 9.17/5.41 ( ( finite_finite_nat
% 9.17/5.41 @ ( collect_nat
% 9.17/5.41 @ ^ [I3: nat] :
% 9.17/5.41 ( ( member_nat @ I3 @ I4 )
% 9.17/5.41 & ( ( X @ I3 )
% 9.17/5.41 != zero_z3403309356797280102nteger ) ) ) )
% 9.17/5.41 => ( ( finite_finite_nat
% 9.17/5.41 @ ( collect_nat
% 9.17/5.41 @ ^ [I3: nat] :
% 9.17/5.41 ( ( member_nat @ I3 @ I4 )
% 9.17/5.41 & ( ( Y @ I3 )
% 9.17/5.41 != zero_z3403309356797280102nteger ) ) ) )
% 9.17/5.41 => ( finite_finite_nat
% 9.17/5.41 @ ( collect_nat
% 9.17/5.41 @ ^ [I3: nat] :
% 9.17/5.41 ( ( member_nat @ I3 @ I4 )
% 9.17/5.41 & ( ( plus_p5714425477246183910nteger @ ( X @ I3 ) @ ( Y @ I3 ) )
% 9.17/5.41 != zero_z3403309356797280102nteger ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5739_sum_Ofinite__Collect__op,axiom,
% 9.17/5.41 ! [I4: set_int,X: int > code_integer,Y: int > code_integer] :
% 9.17/5.41 ( ( finite_finite_int
% 9.17/5.41 @ ( collect_int
% 9.17/5.41 @ ^ [I3: int] :
% 9.17/5.41 ( ( member_int @ I3 @ I4 )
% 9.17/5.41 & ( ( X @ I3 )
% 9.17/5.41 != zero_z3403309356797280102nteger ) ) ) )
% 9.17/5.41 => ( ( finite_finite_int
% 9.17/5.41 @ ( collect_int
% 9.17/5.41 @ ^ [I3: int] :
% 9.17/5.41 ( ( member_int @ I3 @ I4 )
% 9.17/5.41 & ( ( Y @ I3 )
% 9.17/5.41 != zero_z3403309356797280102nteger ) ) ) )
% 9.17/5.41 => ( finite_finite_int
% 9.17/5.41 @ ( collect_int
% 9.17/5.41 @ ^ [I3: int] :
% 9.17/5.41 ( ( member_int @ I3 @ I4 )
% 9.17/5.41 & ( ( plus_p5714425477246183910nteger @ ( X @ I3 ) @ ( Y @ I3 ) )
% 9.17/5.41 != zero_z3403309356797280102nteger ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5740_sum_Ofinite__Collect__op,axiom,
% 9.17/5.41 ! [I4: set_Code_integer,X: code_integer > code_integer,Y: code_integer > code_integer] :
% 9.17/5.41 ( ( finite6017078050557962740nteger
% 9.17/5.41 @ ( collect_Code_integer
% 9.17/5.41 @ ^ [I3: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ I3 @ I4 )
% 9.17/5.41 & ( ( X @ I3 )
% 9.17/5.41 != zero_z3403309356797280102nteger ) ) ) )
% 9.17/5.41 => ( ( finite6017078050557962740nteger
% 9.17/5.41 @ ( collect_Code_integer
% 9.17/5.41 @ ^ [I3: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ I3 @ I4 )
% 9.17/5.41 & ( ( Y @ I3 )
% 9.17/5.41 != zero_z3403309356797280102nteger ) ) ) )
% 9.17/5.41 => ( finite6017078050557962740nteger
% 9.17/5.41 @ ( collect_Code_integer
% 9.17/5.41 @ ^ [I3: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ I3 @ I4 )
% 9.17/5.41 & ( ( plus_p5714425477246183910nteger @ ( X @ I3 ) @ ( Y @ I3 ) )
% 9.17/5.41 != zero_z3403309356797280102nteger ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5741_sum_Ofinite__Collect__op,axiom,
% 9.17/5.41 ! [I4: set_o,X: $o > rat,Y: $o > rat] :
% 9.17/5.41 ( ( finite_finite_o
% 9.17/5.41 @ ( collect_o
% 9.17/5.41 @ ^ [I3: $o] :
% 9.17/5.41 ( ( member_o @ I3 @ I4 )
% 9.17/5.41 & ( ( X @ I3 )
% 9.17/5.41 != zero_zero_rat ) ) ) )
% 9.17/5.41 => ( ( finite_finite_o
% 9.17/5.41 @ ( collect_o
% 9.17/5.41 @ ^ [I3: $o] :
% 9.17/5.41 ( ( member_o @ I3 @ I4 )
% 9.17/5.41 & ( ( Y @ I3 )
% 9.17/5.41 != zero_zero_rat ) ) ) )
% 9.17/5.41 => ( finite_finite_o
% 9.17/5.41 @ ( collect_o
% 9.17/5.41 @ ^ [I3: $o] :
% 9.17/5.41 ( ( member_o @ I3 @ I4 )
% 9.17/5.41 & ( ( plus_plus_rat @ ( X @ I3 ) @ ( Y @ I3 ) )
% 9.17/5.41 != zero_zero_rat ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5742_sum_Ofinite__Collect__op,axiom,
% 9.17/5.41 ! [I4: set_nat,X: nat > rat,Y: nat > rat] :
% 9.17/5.41 ( ( finite_finite_nat
% 9.17/5.41 @ ( collect_nat
% 9.17/5.41 @ ^ [I3: nat] :
% 9.17/5.41 ( ( member_nat @ I3 @ I4 )
% 9.17/5.41 & ( ( X @ I3 )
% 9.17/5.41 != zero_zero_rat ) ) ) )
% 9.17/5.41 => ( ( finite_finite_nat
% 9.17/5.41 @ ( collect_nat
% 9.17/5.41 @ ^ [I3: nat] :
% 9.17/5.41 ( ( member_nat @ I3 @ I4 )
% 9.17/5.41 & ( ( Y @ I3 )
% 9.17/5.41 != zero_zero_rat ) ) ) )
% 9.17/5.41 => ( finite_finite_nat
% 9.17/5.41 @ ( collect_nat
% 9.17/5.41 @ ^ [I3: nat] :
% 9.17/5.41 ( ( member_nat @ I3 @ I4 )
% 9.17/5.41 & ( ( plus_plus_rat @ ( X @ I3 ) @ ( Y @ I3 ) )
% 9.17/5.41 != zero_zero_rat ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5743_sum_Ofinite__Collect__op,axiom,
% 9.17/5.41 ! [I4: set_int,X: int > rat,Y: int > rat] :
% 9.17/5.41 ( ( finite_finite_int
% 9.17/5.41 @ ( collect_int
% 9.17/5.41 @ ^ [I3: int] :
% 9.17/5.41 ( ( member_int @ I3 @ I4 )
% 9.17/5.41 & ( ( X @ I3 )
% 9.17/5.41 != zero_zero_rat ) ) ) )
% 9.17/5.41 => ( ( finite_finite_int
% 9.17/5.41 @ ( collect_int
% 9.17/5.41 @ ^ [I3: int] :
% 9.17/5.41 ( ( member_int @ I3 @ I4 )
% 9.17/5.41 & ( ( Y @ I3 )
% 9.17/5.41 != zero_zero_rat ) ) ) )
% 9.17/5.41 => ( finite_finite_int
% 9.17/5.41 @ ( collect_int
% 9.17/5.41 @ ^ [I3: int] :
% 9.17/5.41 ( ( member_int @ I3 @ I4 )
% 9.17/5.41 & ( ( plus_plus_rat @ ( X @ I3 ) @ ( Y @ I3 ) )
% 9.17/5.41 != zero_zero_rat ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5744_sum_Ofinite__Collect__op,axiom,
% 9.17/5.41 ! [I4: set_Code_integer,X: code_integer > rat,Y: code_integer > rat] :
% 9.17/5.41 ( ( finite6017078050557962740nteger
% 9.17/5.41 @ ( collect_Code_integer
% 9.17/5.41 @ ^ [I3: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ I3 @ I4 )
% 9.17/5.41 & ( ( X @ I3 )
% 9.17/5.41 != zero_zero_rat ) ) ) )
% 9.17/5.41 => ( ( finite6017078050557962740nteger
% 9.17/5.41 @ ( collect_Code_integer
% 9.17/5.41 @ ^ [I3: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ I3 @ I4 )
% 9.17/5.41 & ( ( Y @ I3 )
% 9.17/5.41 != zero_zero_rat ) ) ) )
% 9.17/5.41 => ( finite6017078050557962740nteger
% 9.17/5.41 @ ( collect_Code_integer
% 9.17/5.41 @ ^ [I3: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ I3 @ I4 )
% 9.17/5.41 & ( ( plus_plus_rat @ ( X @ I3 ) @ ( Y @ I3 ) )
% 9.17/5.41 != zero_zero_rat ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5745_sum_Ofinite__Collect__op,axiom,
% 9.17/5.41 ! [I4: set_o,X: $o > nat,Y: $o > nat] :
% 9.17/5.41 ( ( finite_finite_o
% 9.17/5.41 @ ( collect_o
% 9.17/5.41 @ ^ [I3: $o] :
% 9.17/5.41 ( ( member_o @ I3 @ I4 )
% 9.17/5.41 & ( ( X @ I3 )
% 9.17/5.41 != zero_zero_nat ) ) ) )
% 9.17/5.41 => ( ( finite_finite_o
% 9.17/5.41 @ ( collect_o
% 9.17/5.41 @ ^ [I3: $o] :
% 9.17/5.41 ( ( member_o @ I3 @ I4 )
% 9.17/5.41 & ( ( Y @ I3 )
% 9.17/5.41 != zero_zero_nat ) ) ) )
% 9.17/5.41 => ( finite_finite_o
% 9.17/5.41 @ ( collect_o
% 9.17/5.41 @ ^ [I3: $o] :
% 9.17/5.41 ( ( member_o @ I3 @ I4 )
% 9.17/5.41 & ( ( plus_plus_nat @ ( X @ I3 ) @ ( Y @ I3 ) )
% 9.17/5.41 != zero_zero_nat ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5746_sum_Ofinite__Collect__op,axiom,
% 9.17/5.41 ! [I4: set_nat,X: nat > nat,Y: nat > nat] :
% 9.17/5.41 ( ( finite_finite_nat
% 9.17/5.41 @ ( collect_nat
% 9.17/5.41 @ ^ [I3: nat] :
% 9.17/5.41 ( ( member_nat @ I3 @ I4 )
% 9.17/5.41 & ( ( X @ I3 )
% 9.17/5.41 != zero_zero_nat ) ) ) )
% 9.17/5.41 => ( ( finite_finite_nat
% 9.17/5.41 @ ( collect_nat
% 9.17/5.41 @ ^ [I3: nat] :
% 9.17/5.41 ( ( member_nat @ I3 @ I4 )
% 9.17/5.41 & ( ( Y @ I3 )
% 9.17/5.41 != zero_zero_nat ) ) ) )
% 9.17/5.41 => ( finite_finite_nat
% 9.17/5.41 @ ( collect_nat
% 9.17/5.41 @ ^ [I3: nat] :
% 9.17/5.41 ( ( member_nat @ I3 @ I4 )
% 9.17/5.41 & ( ( plus_plus_nat @ ( X @ I3 ) @ ( Y @ I3 ) )
% 9.17/5.41 != zero_zero_nat ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5747_prod_Ofinite__Collect__op,axiom,
% 9.17/5.41 ! [I4: set_o,X: $o > code_integer,Y: $o > code_integer] :
% 9.17/5.41 ( ( finite_finite_o
% 9.17/5.41 @ ( collect_o
% 9.17/5.41 @ ^ [I3: $o] :
% 9.17/5.41 ( ( member_o @ I3 @ I4 )
% 9.17/5.41 & ( ( X @ I3 )
% 9.17/5.41 != one_one_Code_integer ) ) ) )
% 9.17/5.41 => ( ( finite_finite_o
% 9.17/5.41 @ ( collect_o
% 9.17/5.41 @ ^ [I3: $o] :
% 9.17/5.41 ( ( member_o @ I3 @ I4 )
% 9.17/5.41 & ( ( Y @ I3 )
% 9.17/5.41 != one_one_Code_integer ) ) ) )
% 9.17/5.41 => ( finite_finite_o
% 9.17/5.41 @ ( collect_o
% 9.17/5.41 @ ^ [I3: $o] :
% 9.17/5.41 ( ( member_o @ I3 @ I4 )
% 9.17/5.41 & ( ( times_3573771949741848930nteger @ ( X @ I3 ) @ ( Y @ I3 ) )
% 9.17/5.41 != one_one_Code_integer ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5748_prod_Ofinite__Collect__op,axiom,
% 9.17/5.41 ! [I4: set_nat,X: nat > code_integer,Y: nat > code_integer] :
% 9.17/5.41 ( ( finite_finite_nat
% 9.17/5.41 @ ( collect_nat
% 9.17/5.41 @ ^ [I3: nat] :
% 9.17/5.41 ( ( member_nat @ I3 @ I4 )
% 9.17/5.41 & ( ( X @ I3 )
% 9.17/5.41 != one_one_Code_integer ) ) ) )
% 9.17/5.41 => ( ( finite_finite_nat
% 9.17/5.41 @ ( collect_nat
% 9.17/5.41 @ ^ [I3: nat] :
% 9.17/5.41 ( ( member_nat @ I3 @ I4 )
% 9.17/5.41 & ( ( Y @ I3 )
% 9.17/5.41 != one_one_Code_integer ) ) ) )
% 9.17/5.41 => ( finite_finite_nat
% 9.17/5.41 @ ( collect_nat
% 9.17/5.41 @ ^ [I3: nat] :
% 9.17/5.41 ( ( member_nat @ I3 @ I4 )
% 9.17/5.41 & ( ( times_3573771949741848930nteger @ ( X @ I3 ) @ ( Y @ I3 ) )
% 9.17/5.41 != one_one_Code_integer ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5749_prod_Ofinite__Collect__op,axiom,
% 9.17/5.41 ! [I4: set_int,X: int > code_integer,Y: int > code_integer] :
% 9.17/5.41 ( ( finite_finite_int
% 9.17/5.41 @ ( collect_int
% 9.17/5.41 @ ^ [I3: int] :
% 9.17/5.41 ( ( member_int @ I3 @ I4 )
% 9.17/5.41 & ( ( X @ I3 )
% 9.17/5.41 != one_one_Code_integer ) ) ) )
% 9.17/5.41 => ( ( finite_finite_int
% 9.17/5.41 @ ( collect_int
% 9.17/5.41 @ ^ [I3: int] :
% 9.17/5.41 ( ( member_int @ I3 @ I4 )
% 9.17/5.41 & ( ( Y @ I3 )
% 9.17/5.41 != one_one_Code_integer ) ) ) )
% 9.17/5.41 => ( finite_finite_int
% 9.17/5.41 @ ( collect_int
% 9.17/5.41 @ ^ [I3: int] :
% 9.17/5.41 ( ( member_int @ I3 @ I4 )
% 9.17/5.41 & ( ( times_3573771949741848930nteger @ ( X @ I3 ) @ ( Y @ I3 ) )
% 9.17/5.41 != one_one_Code_integer ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5750_prod_Ofinite__Collect__op,axiom,
% 9.17/5.41 ! [I4: set_Code_integer,X: code_integer > code_integer,Y: code_integer > code_integer] :
% 9.17/5.41 ( ( finite6017078050557962740nteger
% 9.17/5.41 @ ( collect_Code_integer
% 9.17/5.41 @ ^ [I3: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ I3 @ I4 )
% 9.17/5.41 & ( ( X @ I3 )
% 9.17/5.41 != one_one_Code_integer ) ) ) )
% 9.17/5.41 => ( ( finite6017078050557962740nteger
% 9.17/5.41 @ ( collect_Code_integer
% 9.17/5.41 @ ^ [I3: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ I3 @ I4 )
% 9.17/5.41 & ( ( Y @ I3 )
% 9.17/5.41 != one_one_Code_integer ) ) ) )
% 9.17/5.41 => ( finite6017078050557962740nteger
% 9.17/5.41 @ ( collect_Code_integer
% 9.17/5.41 @ ^ [I3: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ I3 @ I4 )
% 9.17/5.41 & ( ( times_3573771949741848930nteger @ ( X @ I3 ) @ ( Y @ I3 ) )
% 9.17/5.41 != one_one_Code_integer ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5751_prod_Ofinite__Collect__op,axiom,
% 9.17/5.41 ! [I4: set_o,X: $o > assn,Y: $o > assn] :
% 9.17/5.41 ( ( finite_finite_o
% 9.17/5.41 @ ( collect_o
% 9.17/5.41 @ ^ [I3: $o] :
% 9.17/5.41 ( ( member_o @ I3 @ I4 )
% 9.17/5.41 & ( ( X @ I3 )
% 9.17/5.41 != one_one_assn ) ) ) )
% 9.17/5.41 => ( ( finite_finite_o
% 9.17/5.41 @ ( collect_o
% 9.17/5.41 @ ^ [I3: $o] :
% 9.17/5.41 ( ( member_o @ I3 @ I4 )
% 9.17/5.41 & ( ( Y @ I3 )
% 9.17/5.41 != one_one_assn ) ) ) )
% 9.17/5.41 => ( finite_finite_o
% 9.17/5.41 @ ( collect_o
% 9.17/5.41 @ ^ [I3: $o] :
% 9.17/5.41 ( ( member_o @ I3 @ I4 )
% 9.17/5.41 & ( ( times_times_assn @ ( X @ I3 ) @ ( Y @ I3 ) )
% 9.17/5.41 != one_one_assn ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5752_prod_Ofinite__Collect__op,axiom,
% 9.17/5.41 ! [I4: set_nat,X: nat > assn,Y: nat > assn] :
% 9.17/5.41 ( ( finite_finite_nat
% 9.17/5.41 @ ( collect_nat
% 9.17/5.41 @ ^ [I3: nat] :
% 9.17/5.41 ( ( member_nat @ I3 @ I4 )
% 9.17/5.41 & ( ( X @ I3 )
% 9.17/5.41 != one_one_assn ) ) ) )
% 9.17/5.41 => ( ( finite_finite_nat
% 9.17/5.41 @ ( collect_nat
% 9.17/5.41 @ ^ [I3: nat] :
% 9.17/5.41 ( ( member_nat @ I3 @ I4 )
% 9.17/5.41 & ( ( Y @ I3 )
% 9.17/5.41 != one_one_assn ) ) ) )
% 9.17/5.41 => ( finite_finite_nat
% 9.17/5.41 @ ( collect_nat
% 9.17/5.41 @ ^ [I3: nat] :
% 9.17/5.41 ( ( member_nat @ I3 @ I4 )
% 9.17/5.41 & ( ( times_times_assn @ ( X @ I3 ) @ ( Y @ I3 ) )
% 9.17/5.41 != one_one_assn ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5753_prod_Ofinite__Collect__op,axiom,
% 9.17/5.41 ! [I4: set_int,X: int > assn,Y: int > assn] :
% 9.17/5.41 ( ( finite_finite_int
% 9.17/5.41 @ ( collect_int
% 9.17/5.41 @ ^ [I3: int] :
% 9.17/5.41 ( ( member_int @ I3 @ I4 )
% 9.17/5.41 & ( ( X @ I3 )
% 9.17/5.41 != one_one_assn ) ) ) )
% 9.17/5.41 => ( ( finite_finite_int
% 9.17/5.41 @ ( collect_int
% 9.17/5.41 @ ^ [I3: int] :
% 9.17/5.41 ( ( member_int @ I3 @ I4 )
% 9.17/5.41 & ( ( Y @ I3 )
% 9.17/5.41 != one_one_assn ) ) ) )
% 9.17/5.41 => ( finite_finite_int
% 9.17/5.41 @ ( collect_int
% 9.17/5.41 @ ^ [I3: int] :
% 9.17/5.41 ( ( member_int @ I3 @ I4 )
% 9.17/5.41 & ( ( times_times_assn @ ( X @ I3 ) @ ( Y @ I3 ) )
% 9.17/5.41 != one_one_assn ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5754_prod_Ofinite__Collect__op,axiom,
% 9.17/5.41 ! [I4: set_Code_integer,X: code_integer > assn,Y: code_integer > assn] :
% 9.17/5.41 ( ( finite6017078050557962740nteger
% 9.17/5.41 @ ( collect_Code_integer
% 9.17/5.41 @ ^ [I3: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ I3 @ I4 )
% 9.17/5.41 & ( ( X @ I3 )
% 9.17/5.41 != one_one_assn ) ) ) )
% 9.17/5.41 => ( ( finite6017078050557962740nteger
% 9.17/5.41 @ ( collect_Code_integer
% 9.17/5.41 @ ^ [I3: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ I3 @ I4 )
% 9.17/5.41 & ( ( Y @ I3 )
% 9.17/5.41 != one_one_assn ) ) ) )
% 9.17/5.41 => ( finite6017078050557962740nteger
% 9.17/5.41 @ ( collect_Code_integer
% 9.17/5.41 @ ^ [I3: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ I3 @ I4 )
% 9.17/5.41 & ( ( times_times_assn @ ( X @ I3 ) @ ( Y @ I3 ) )
% 9.17/5.41 != one_one_assn ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5755_prod_Ofinite__Collect__op,axiom,
% 9.17/5.41 ! [I4: set_o,X: $o > rat,Y: $o > rat] :
% 9.17/5.41 ( ( finite_finite_o
% 9.17/5.41 @ ( collect_o
% 9.17/5.41 @ ^ [I3: $o] :
% 9.17/5.41 ( ( member_o @ I3 @ I4 )
% 9.17/5.41 & ( ( X @ I3 )
% 9.17/5.41 != one_one_rat ) ) ) )
% 9.17/5.41 => ( ( finite_finite_o
% 9.17/5.41 @ ( collect_o
% 9.17/5.41 @ ^ [I3: $o] :
% 9.17/5.41 ( ( member_o @ I3 @ I4 )
% 9.17/5.41 & ( ( Y @ I3 )
% 9.17/5.41 != one_one_rat ) ) ) )
% 9.17/5.41 => ( finite_finite_o
% 9.17/5.41 @ ( collect_o
% 9.17/5.41 @ ^ [I3: $o] :
% 9.17/5.41 ( ( member_o @ I3 @ I4 )
% 9.17/5.41 & ( ( times_times_rat @ ( X @ I3 ) @ ( Y @ I3 ) )
% 9.17/5.41 != one_one_rat ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5756_prod_Ofinite__Collect__op,axiom,
% 9.17/5.41 ! [I4: set_nat,X: nat > rat,Y: nat > rat] :
% 9.17/5.41 ( ( finite_finite_nat
% 9.17/5.41 @ ( collect_nat
% 9.17/5.41 @ ^ [I3: nat] :
% 9.17/5.41 ( ( member_nat @ I3 @ I4 )
% 9.17/5.41 & ( ( X @ I3 )
% 9.17/5.41 != one_one_rat ) ) ) )
% 9.17/5.41 => ( ( finite_finite_nat
% 9.17/5.41 @ ( collect_nat
% 9.17/5.41 @ ^ [I3: nat] :
% 9.17/5.41 ( ( member_nat @ I3 @ I4 )
% 9.17/5.41 & ( ( Y @ I3 )
% 9.17/5.41 != one_one_rat ) ) ) )
% 9.17/5.41 => ( finite_finite_nat
% 9.17/5.41 @ ( collect_nat
% 9.17/5.41 @ ^ [I3: nat] :
% 9.17/5.41 ( ( member_nat @ I3 @ I4 )
% 9.17/5.41 & ( ( times_times_rat @ ( X @ I3 ) @ ( Y @ I3 ) )
% 9.17/5.41 != one_one_rat ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5757_finite__atLeastZeroLessThan__int,axiom,
% 9.17/5.41 ! [U: int] : ( finite_finite_int @ ( set_or4662586982721622107an_int @ zero_zero_int @ U ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5758_card__eq__sum,axiom,
% 9.17/5.41 ( finite_card_int
% 9.17/5.41 = ( groups4541462559716669496nt_nat
% 9.17/5.41 @ ^ [X3: int] : one_one_nat ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5759_card__eq__sum,axiom,
% 9.17/5.41 ( finite410649719033368117t_unit
% 9.17/5.41 = ( groups8766797177574957219it_nat
% 9.17/5.41 @ ^ [X3: product_unit] : one_one_nat ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5760_card__eq__sum,axiom,
% 9.17/5.41 ( finite_card_list_nat
% 9.17/5.41 = ( groups4396056296759096172at_nat
% 9.17/5.41 @ ^ [X3: list_nat] : one_one_nat ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5761_card__eq__sum,axiom,
% 9.17/5.41 ( finite_card_nat
% 9.17/5.41 = ( groups3542108847815614940at_nat
% 9.17/5.41 @ ^ [X3: nat] : one_one_nat ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5762_prod_Ointer__filter,axiom,
% 9.17/5.41 ! [A2: set_o,G: $o > code_integer,P: $o > $o] :
% 9.17/5.41 ( ( finite_finite_o @ A2 )
% 9.17/5.41 => ( ( groups7694694392188491536nteger @ G
% 9.17/5.41 @ ( collect_o
% 9.17/5.41 @ ^ [X3: $o] :
% 9.17/5.41 ( ( member_o @ X3 @ A2 )
% 9.17/5.41 & ( P @ X3 ) ) ) )
% 9.17/5.41 = ( groups7694694392188491536nteger
% 9.17/5.41 @ ^ [X3: $o] : ( if_Code_integer @ ( P @ X3 ) @ ( G @ X3 ) @ one_one_Code_integer )
% 9.17/5.41 @ A2 ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5763_prod_Ointer__filter,axiom,
% 9.17/5.41 ! [A2: set_nat,G: nat > code_integer,P: nat > $o] :
% 9.17/5.41 ( ( finite_finite_nat @ A2 )
% 9.17/5.41 => ( ( groups3455450783089532116nteger @ G
% 9.17/5.41 @ ( collect_nat
% 9.17/5.41 @ ^ [X3: nat] :
% 9.17/5.41 ( ( member_nat @ X3 @ A2 )
% 9.17/5.41 & ( P @ X3 ) ) ) )
% 9.17/5.41 = ( groups3455450783089532116nteger
% 9.17/5.41 @ ^ [X3: nat] : ( if_Code_integer @ ( P @ X3 ) @ ( G @ X3 ) @ one_one_Code_integer )
% 9.17/5.41 @ A2 ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5764_prod_Ointer__filter,axiom,
% 9.17/5.41 ! [A2: set_int,G: int > code_integer,P: int > $o] :
% 9.17/5.41 ( ( finite_finite_int @ A2 )
% 9.17/5.41 => ( ( groups3827104343326376752nteger @ G
% 9.17/5.41 @ ( collect_int
% 9.17/5.41 @ ^ [X3: int] :
% 9.17/5.41 ( ( member_int @ X3 @ A2 )
% 9.17/5.41 & ( P @ X3 ) ) ) )
% 9.17/5.41 = ( groups3827104343326376752nteger
% 9.17/5.41 @ ^ [X3: int] : ( if_Code_integer @ ( P @ X3 ) @ ( G @ X3 ) @ one_one_Code_integer )
% 9.17/5.41 @ A2 ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5765_prod_Ointer__filter,axiom,
% 9.17/5.41 ! [A2: set_Code_integer,G: code_integer > code_integer,P: code_integer > $o] :
% 9.17/5.41 ( ( finite6017078050557962740nteger @ A2 )
% 9.17/5.41 => ( ( groups3674199335183972705nteger @ G
% 9.17/5.41 @ ( collect_Code_integer
% 9.17/5.41 @ ^ [X3: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ X3 @ A2 )
% 9.17/5.41 & ( P @ X3 ) ) ) )
% 9.17/5.41 = ( groups3674199335183972705nteger
% 9.17/5.41 @ ^ [X3: code_integer] : ( if_Code_integer @ ( P @ X3 ) @ ( G @ X3 ) @ one_one_Code_integer )
% 9.17/5.41 @ A2 ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5766_prod_Ointer__filter,axiom,
% 9.17/5.41 ! [A2: set_o,G: $o > assn,P: $o > $o] :
% 9.17/5.41 ( ( finite_finite_o @ A2 )
% 9.17/5.41 => ( ( groups5301882518646026715o_assn @ G
% 9.17/5.41 @ ( collect_o
% 9.17/5.41 @ ^ [X3: $o] :
% 9.17/5.41 ( ( member_o @ X3 @ A2 )
% 9.17/5.41 & ( P @ X3 ) ) ) )
% 9.17/5.41 = ( groups5301882518646026715o_assn
% 9.17/5.41 @ ^ [X3: $o] : ( if_assn @ ( P @ X3 ) @ ( G @ X3 ) @ one_one_assn )
% 9.17/5.41 @ A2 ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5767_prod_Ointer__filter,axiom,
% 9.17/5.41 ! [A2: set_nat,G: nat > assn,P: nat > $o] :
% 9.17/5.41 ( ( finite_finite_nat @ A2 )
% 9.17/5.41 => ( ( groups6906906614972039071t_assn @ G
% 9.17/5.41 @ ( collect_nat
% 9.17/5.41 @ ^ [X3: nat] :
% 9.17/5.41 ( ( member_nat @ X3 @ A2 )
% 9.17/5.41 & ( P @ X3 ) ) ) )
% 9.17/5.41 = ( groups6906906614972039071t_assn
% 9.17/5.41 @ ^ [X3: nat] : ( if_assn @ ( P @ X3 ) @ ( G @ X3 ) @ one_one_assn )
% 9.17/5.41 @ A2 ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5768_prod_Ointer__filter,axiom,
% 9.17/5.41 ! [A2: set_int,G: int > assn,P: int > $o] :
% 9.17/5.41 ( ( finite_finite_int @ A2 )
% 9.17/5.41 => ( ( groups7882442080178216443t_assn @ G
% 9.17/5.41 @ ( collect_int
% 9.17/5.41 @ ^ [X3: int] :
% 9.17/5.41 ( ( member_int @ X3 @ A2 )
% 9.17/5.41 & ( P @ X3 ) ) ) )
% 9.17/5.41 = ( groups7882442080178216443t_assn
% 9.17/5.41 @ ^ [X3: int] : ( if_assn @ ( P @ X3 ) @ ( G @ X3 ) @ one_one_assn )
% 9.17/5.41 @ A2 ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5769_prod_Ointer__filter,axiom,
% 9.17/5.41 ! [A2: set_Code_integer,G: code_integer > assn,P: code_integer > $o] :
% 9.17/5.41 ( ( finite6017078050557962740nteger @ A2 )
% 9.17/5.41 => ( ( groups1304777262505850412r_assn @ G
% 9.17/5.41 @ ( collect_Code_integer
% 9.17/5.41 @ ^ [X3: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ X3 @ A2 )
% 9.17/5.41 & ( P @ X3 ) ) ) )
% 9.17/5.41 = ( groups1304777262505850412r_assn
% 9.17/5.41 @ ^ [X3: code_integer] : ( if_assn @ ( P @ X3 ) @ ( G @ X3 ) @ one_one_assn )
% 9.17/5.41 @ A2 ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5770_prod_Ointer__filter,axiom,
% 9.17/5.41 ! [A2: set_o,G: $o > rat,P: $o > $o] :
% 9.17/5.41 ( ( finite_finite_o @ A2 )
% 9.17/5.41 => ( ( groups2869687844427037835_o_rat @ G
% 9.17/5.41 @ ( collect_o
% 9.17/5.41 @ ^ [X3: $o] :
% 9.17/5.41 ( ( member_o @ X3 @ A2 )
% 9.17/5.41 & ( P @ X3 ) ) ) )
% 9.17/5.41 = ( groups2869687844427037835_o_rat
% 9.17/5.41 @ ^ [X3: $o] : ( if_rat @ ( P @ X3 ) @ ( G @ X3 ) @ one_one_rat )
% 9.17/5.41 @ A2 ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5771_prod_Ointer__filter,axiom,
% 9.17/5.41 ! [A2: set_nat,G: nat > rat,P: nat > $o] :
% 9.17/5.41 ( ( finite_finite_nat @ A2 )
% 9.17/5.41 => ( ( groups73079841787564623at_rat @ G
% 9.17/5.41 @ ( collect_nat
% 9.17/5.41 @ ^ [X3: nat] :
% 9.17/5.41 ( ( member_nat @ X3 @ A2 )
% 9.17/5.41 & ( P @ X3 ) ) ) )
% 9.17/5.41 = ( groups73079841787564623at_rat
% 9.17/5.41 @ ^ [X3: nat] : ( if_rat @ ( P @ X3 ) @ ( G @ X3 ) @ one_one_rat )
% 9.17/5.41 @ A2 ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5772_prod__gen__delta,axiom,
% 9.17/5.41 ! [S2: set_o,A: $o,B: $o > assn,C: assn] :
% 9.17/5.41 ( ( finite_finite_o @ S2 )
% 9.17/5.41 => ( ( ( member_o @ A @ S2 )
% 9.17/5.41 => ( ( groups5301882518646026715o_assn
% 9.17/5.41 @ ^ [K4: $o] : ( if_assn @ ( K4 = A ) @ ( B @ K4 ) @ C )
% 9.17/5.41 @ S2 )
% 9.17/5.41 = ( times_times_assn @ ( B @ A ) @ ( power_power_assn @ C @ ( minus_minus_nat @ ( finite_card_o @ S2 ) @ one_one_nat ) ) ) ) )
% 9.17/5.41 & ( ~ ( member_o @ A @ S2 )
% 9.17/5.41 => ( ( groups5301882518646026715o_assn
% 9.17/5.41 @ ^ [K4: $o] : ( if_assn @ ( K4 = A ) @ ( B @ K4 ) @ C )
% 9.17/5.41 @ S2 )
% 9.17/5.41 = ( power_power_assn @ C @ ( finite_card_o @ S2 ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5773_prod__gen__delta,axiom,
% 9.17/5.41 ! [S2: set_Product_unit,A: product_unit,B: product_unit > assn,C: assn] :
% 9.17/5.41 ( ( finite4290736615968046902t_unit @ S2 )
% 9.17/5.41 => ( ( ( member_Product_unit @ A @ S2 )
% 9.17/5.41 => ( ( groups5360233303959380816t_assn
% 9.17/5.41 @ ^ [K4: product_unit] : ( if_assn @ ( K4 = A ) @ ( B @ K4 ) @ C )
% 9.17/5.41 @ S2 )
% 9.17/5.41 = ( times_times_assn @ ( B @ A ) @ ( power_power_assn @ C @ ( minus_minus_nat @ ( finite410649719033368117t_unit @ S2 ) @ one_one_nat ) ) ) ) )
% 9.17/5.41 & ( ~ ( member_Product_unit @ A @ S2 )
% 9.17/5.41 => ( ( groups5360233303959380816t_assn
% 9.17/5.41 @ ^ [K4: product_unit] : ( if_assn @ ( K4 = A ) @ ( B @ K4 ) @ C )
% 9.17/5.41 @ S2 )
% 9.17/5.41 = ( power_power_assn @ C @ ( finite410649719033368117t_unit @ S2 ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5774_prod__gen__delta,axiom,
% 9.17/5.41 ! [S2: set_nat,A: nat,B: nat > assn,C: assn] :
% 9.17/5.41 ( ( finite_finite_nat @ S2 )
% 9.17/5.41 => ( ( ( member_nat @ A @ S2 )
% 9.17/5.41 => ( ( groups6906906614972039071t_assn
% 9.17/5.41 @ ^ [K4: nat] : ( if_assn @ ( K4 = A ) @ ( B @ K4 ) @ C )
% 9.17/5.41 @ S2 )
% 9.17/5.41 = ( times_times_assn @ ( B @ A ) @ ( power_power_assn @ C @ ( minus_minus_nat @ ( finite_card_nat @ S2 ) @ one_one_nat ) ) ) ) )
% 9.17/5.41 & ( ~ ( member_nat @ A @ S2 )
% 9.17/5.41 => ( ( groups6906906614972039071t_assn
% 9.17/5.41 @ ^ [K4: nat] : ( if_assn @ ( K4 = A ) @ ( B @ K4 ) @ C )
% 9.17/5.41 @ S2 )
% 9.17/5.41 = ( power_power_assn @ C @ ( finite_card_nat @ S2 ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5775_prod__gen__delta,axiom,
% 9.17/5.41 ! [S2: set_int,A: int,B: int > assn,C: assn] :
% 9.17/5.41 ( ( finite_finite_int @ S2 )
% 9.17/5.41 => ( ( ( member_int @ A @ S2 )
% 9.17/5.41 => ( ( groups7882442080178216443t_assn
% 9.17/5.41 @ ^ [K4: int] : ( if_assn @ ( K4 = A ) @ ( B @ K4 ) @ C )
% 9.17/5.41 @ S2 )
% 9.17/5.41 = ( times_times_assn @ ( B @ A ) @ ( power_power_assn @ C @ ( minus_minus_nat @ ( finite_card_int @ S2 ) @ one_one_nat ) ) ) ) )
% 9.17/5.41 & ( ~ ( member_int @ A @ S2 )
% 9.17/5.41 => ( ( groups7882442080178216443t_assn
% 9.17/5.41 @ ^ [K4: int] : ( if_assn @ ( K4 = A ) @ ( B @ K4 ) @ C )
% 9.17/5.41 @ S2 )
% 9.17/5.41 = ( power_power_assn @ C @ ( finite_card_int @ S2 ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5776_prod__gen__delta,axiom,
% 9.17/5.41 ! [S2: set_Code_integer,A: code_integer,B: code_integer > assn,C: assn] :
% 9.17/5.41 ( ( finite6017078050557962740nteger @ S2 )
% 9.17/5.41 => ( ( ( member_Code_integer @ A @ S2 )
% 9.17/5.41 => ( ( groups1304777262505850412r_assn
% 9.17/5.41 @ ^ [K4: code_integer] : ( if_assn @ ( K4 = A ) @ ( B @ K4 ) @ C )
% 9.17/5.41 @ S2 )
% 9.17/5.41 = ( times_times_assn @ ( B @ A ) @ ( power_power_assn @ C @ ( minus_minus_nat @ ( finite4902975817058060853nteger @ S2 ) @ one_one_nat ) ) ) ) )
% 9.17/5.41 & ( ~ ( member_Code_integer @ A @ S2 )
% 9.17/5.41 => ( ( groups1304777262505850412r_assn
% 9.17/5.41 @ ^ [K4: code_integer] : ( if_assn @ ( K4 = A ) @ ( B @ K4 ) @ C )
% 9.17/5.41 @ S2 )
% 9.17/5.41 = ( power_power_assn @ C @ ( finite4902975817058060853nteger @ S2 ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5777_prod__gen__delta,axiom,
% 9.17/5.41 ! [S2: set_o,A: $o,B: $o > rat,C: rat] :
% 9.17/5.41 ( ( finite_finite_o @ S2 )
% 9.17/5.41 => ( ( ( member_o @ A @ S2 )
% 9.17/5.41 => ( ( groups2869687844427037835_o_rat
% 9.17/5.41 @ ^ [K4: $o] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ C )
% 9.17/5.41 @ S2 )
% 9.17/5.41 = ( times_times_rat @ ( B @ A ) @ ( power_power_rat @ C @ ( minus_minus_nat @ ( finite_card_o @ S2 ) @ one_one_nat ) ) ) ) )
% 9.17/5.41 & ( ~ ( member_o @ A @ S2 )
% 9.17/5.41 => ( ( groups2869687844427037835_o_rat
% 9.17/5.41 @ ^ [K4: $o] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ C )
% 9.17/5.41 @ S2 )
% 9.17/5.41 = ( power_power_rat @ C @ ( finite_card_o @ S2 ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5778_prod__gen__delta,axiom,
% 9.17/5.41 ! [S2: set_Product_unit,A: product_unit,B: product_unit > rat,C: rat] :
% 9.17/5.41 ( ( finite4290736615968046902t_unit @ S2 )
% 9.17/5.41 => ( ( ( member_Product_unit @ A @ S2 )
% 9.17/5.41 => ( ( groups8984663225794451456it_rat
% 9.17/5.41 @ ^ [K4: product_unit] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ C )
% 9.17/5.41 @ S2 )
% 9.17/5.41 = ( times_times_rat @ ( B @ A ) @ ( power_power_rat @ C @ ( minus_minus_nat @ ( finite410649719033368117t_unit @ S2 ) @ one_one_nat ) ) ) ) )
% 9.17/5.41 & ( ~ ( member_Product_unit @ A @ S2 )
% 9.17/5.41 => ( ( groups8984663225794451456it_rat
% 9.17/5.41 @ ^ [K4: product_unit] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ C )
% 9.17/5.41 @ S2 )
% 9.17/5.41 = ( power_power_rat @ C @ ( finite410649719033368117t_unit @ S2 ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5779_prod__gen__delta,axiom,
% 9.17/5.41 ! [S2: set_nat,A: nat,B: nat > rat,C: rat] :
% 9.17/5.41 ( ( finite_finite_nat @ S2 )
% 9.17/5.41 => ( ( ( member_nat @ A @ S2 )
% 9.17/5.41 => ( ( groups73079841787564623at_rat
% 9.17/5.41 @ ^ [K4: nat] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ C )
% 9.17/5.41 @ S2 )
% 9.17/5.41 = ( times_times_rat @ ( B @ A ) @ ( power_power_rat @ C @ ( minus_minus_nat @ ( finite_card_nat @ S2 ) @ one_one_nat ) ) ) ) )
% 9.17/5.41 & ( ~ ( member_nat @ A @ S2 )
% 9.17/5.41 => ( ( groups73079841787564623at_rat
% 9.17/5.41 @ ^ [K4: nat] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ C )
% 9.17/5.41 @ S2 )
% 9.17/5.41 = ( power_power_rat @ C @ ( finite_card_nat @ S2 ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5780_prod__gen__delta,axiom,
% 9.17/5.41 ! [S2: set_int,A: int,B: int > rat,C: rat] :
% 9.17/5.41 ( ( finite_finite_int @ S2 )
% 9.17/5.41 => ( ( ( member_int @ A @ S2 )
% 9.17/5.41 => ( ( groups1072433553688619179nt_rat
% 9.17/5.41 @ ^ [K4: int] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ C )
% 9.17/5.41 @ S2 )
% 9.17/5.41 = ( times_times_rat @ ( B @ A ) @ ( power_power_rat @ C @ ( minus_minus_nat @ ( finite_card_int @ S2 ) @ one_one_nat ) ) ) ) )
% 9.17/5.41 & ( ~ ( member_int @ A @ S2 )
% 9.17/5.41 => ( ( groups1072433553688619179nt_rat
% 9.17/5.41 @ ^ [K4: int] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ C )
% 9.17/5.41 @ S2 )
% 9.17/5.41 = ( power_power_rat @ C @ ( finite_card_int @ S2 ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5781_prod__gen__delta,axiom,
% 9.17/5.41 ! [S2: set_Code_integer,A: code_integer,B: code_integer > rat,C: rat] :
% 9.17/5.41 ( ( finite6017078050557962740nteger @ S2 )
% 9.17/5.41 => ( ( ( member_Code_integer @ A @ S2 )
% 9.17/5.41 => ( ( groups2555765274223993564er_rat
% 9.17/5.41 @ ^ [K4: code_integer] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ C )
% 9.17/5.41 @ S2 )
% 9.17/5.41 = ( times_times_rat @ ( B @ A ) @ ( power_power_rat @ C @ ( minus_minus_nat @ ( finite4902975817058060853nteger @ S2 ) @ one_one_nat ) ) ) ) )
% 9.17/5.41 & ( ~ ( member_Code_integer @ A @ S2 )
% 9.17/5.41 => ( ( groups2555765274223993564er_rat
% 9.17/5.41 @ ^ [K4: code_integer] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ C )
% 9.17/5.41 @ S2 )
% 9.17/5.41 = ( power_power_rat @ C @ ( finite4902975817058060853nteger @ S2 ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5782_finite__atLeastZeroLessThan__integer,axiom,
% 9.17/5.41 ! [U: code_integer] : ( finite6017078050557962740nteger @ ( set_or8404916559141939852nteger @ zero_z3403309356797280102nteger @ U ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5783_card__2__iff_H,axiom,
% 9.17/5.41 ! [S2: set_int] :
% 9.17/5.41 ( ( ( finite_card_int @ S2 )
% 9.17/5.41 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.17/5.41 = ( ? [X3: int] :
% 9.17/5.41 ( ( member_int @ X3 @ S2 )
% 9.17/5.41 & ? [Y3: int] :
% 9.17/5.41 ( ( member_int @ Y3 @ S2 )
% 9.17/5.41 & ( X3 != Y3 )
% 9.17/5.41 & ! [Z4: int] :
% 9.17/5.41 ( ( member_int @ Z4 @ S2 )
% 9.17/5.41 => ( ( Z4 = X3 )
% 9.17/5.41 | ( Z4 = Y3 ) ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5784_card__2__iff_H,axiom,
% 9.17/5.41 ! [S2: set_Product_unit] :
% 9.17/5.41 ( ( ( finite410649719033368117t_unit @ S2 )
% 9.17/5.41 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.17/5.41 = ( ? [X3: product_unit] :
% 9.17/5.41 ( ( member_Product_unit @ X3 @ S2 )
% 9.17/5.41 & ? [Y3: product_unit] :
% 9.17/5.41 ( ( member_Product_unit @ Y3 @ S2 )
% 9.17/5.41 & ( X3 != Y3 )
% 9.17/5.41 & ! [Z4: product_unit] :
% 9.17/5.41 ( ( member_Product_unit @ Z4 @ S2 )
% 9.17/5.41 => ( ( Z4 = X3 )
% 9.17/5.41 | ( Z4 = Y3 ) ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5785_card__2__iff_H,axiom,
% 9.17/5.41 ! [S2: set_nat] :
% 9.17/5.41 ( ( ( finite_card_nat @ S2 )
% 9.17/5.41 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.17/5.41 = ( ? [X3: nat] :
% 9.17/5.41 ( ( member_nat @ X3 @ S2 )
% 9.17/5.41 & ? [Y3: nat] :
% 9.17/5.41 ( ( member_nat @ Y3 @ S2 )
% 9.17/5.41 & ( X3 != Y3 )
% 9.17/5.41 & ! [Z4: nat] :
% 9.17/5.41 ( ( member_nat @ Z4 @ S2 )
% 9.17/5.41 => ( ( Z4 = X3 )
% 9.17/5.41 | ( Z4 = Y3 ) ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5786_card__2__iff_H,axiom,
% 9.17/5.41 ! [S2: set_list_nat] :
% 9.17/5.41 ( ( ( finite_card_list_nat @ S2 )
% 9.17/5.41 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.17/5.41 = ( ? [X3: list_nat] :
% 9.17/5.41 ( ( member_list_nat @ X3 @ S2 )
% 9.17/5.41 & ? [Y3: list_nat] :
% 9.17/5.41 ( ( member_list_nat @ Y3 @ S2 )
% 9.17/5.41 & ( X3 != Y3 )
% 9.17/5.41 & ! [Z4: list_nat] :
% 9.17/5.41 ( ( member_list_nat @ Z4 @ S2 )
% 9.17/5.41 => ( ( Z4 = X3 )
% 9.17/5.41 | ( Z4 = Y3 ) ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5787_sum_Orelated,axiom,
% 9.17/5.41 ! [R4: code_integer > code_integer > $o,S2: set_nat,H3: nat > code_integer,G: nat > code_integer] :
% 9.17/5.41 ( ( R4 @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 9.17/5.41 => ( ! [X13: code_integer,Y12: code_integer,X22: code_integer,Y22: code_integer] :
% 9.17/5.41 ( ( ( R4 @ X13 @ X22 )
% 9.17/5.41 & ( R4 @ Y12 @ Y22 ) )
% 9.17/5.41 => ( R4 @ ( plus_p5714425477246183910nteger @ X13 @ Y12 ) @ ( plus_p5714425477246183910nteger @ X22 @ Y22 ) ) )
% 9.17/5.41 => ( ( finite_finite_nat @ S2 )
% 9.17/5.41 => ( ! [X4: nat] :
% 9.17/5.41 ( ( member_nat @ X4 @ S2 )
% 9.17/5.41 => ( R4 @ ( H3 @ X4 ) @ ( G @ X4 ) ) )
% 9.17/5.41 => ( R4 @ ( groups7501900531339628137nteger @ H3 @ S2 ) @ ( groups7501900531339628137nteger @ G @ S2 ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5788_sum_Orelated,axiom,
% 9.17/5.41 ! [R4: code_integer > code_integer > $o,S2: set_int,H3: int > code_integer,G: int > code_integer] :
% 9.17/5.41 ( ( R4 @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 9.17/5.41 => ( ! [X13: code_integer,Y12: code_integer,X22: code_integer,Y22: code_integer] :
% 9.17/5.41 ( ( ( R4 @ X13 @ X22 )
% 9.17/5.41 & ( R4 @ Y12 @ Y22 ) )
% 9.17/5.41 => ( R4 @ ( plus_p5714425477246183910nteger @ X13 @ Y12 ) @ ( plus_p5714425477246183910nteger @ X22 @ Y22 ) ) )
% 9.17/5.41 => ( ( finite_finite_int @ S2 )
% 9.17/5.41 => ( ! [X4: int] :
% 9.17/5.41 ( ( member_int @ X4 @ S2 )
% 9.17/5.41 => ( R4 @ ( H3 @ X4 ) @ ( G @ X4 ) ) )
% 9.17/5.41 => ( R4 @ ( groups7873554091576472773nteger @ H3 @ S2 ) @ ( groups7873554091576472773nteger @ G @ S2 ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5789_sum_Orelated,axiom,
% 9.17/5.41 ! [R4: code_integer > code_integer > $o,S2: set_Code_integer,H3: code_integer > code_integer,G: code_integer > code_integer] :
% 9.17/5.41 ( ( R4 @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 9.17/5.41 => ( ! [X13: code_integer,Y12: code_integer,X22: code_integer,Y22: code_integer] :
% 9.17/5.41 ( ( ( R4 @ X13 @ X22 )
% 9.17/5.41 & ( R4 @ Y12 @ Y22 ) )
% 9.17/5.41 => ( R4 @ ( plus_p5714425477246183910nteger @ X13 @ Y12 ) @ ( plus_p5714425477246183910nteger @ X22 @ Y22 ) ) )
% 9.17/5.41 => ( ( finite6017078050557962740nteger @ S2 )
% 9.17/5.41 => ( ! [X4: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ X4 @ S2 )
% 9.17/5.41 => ( R4 @ ( H3 @ X4 ) @ ( G @ X4 ) ) )
% 9.17/5.41 => ( R4 @ ( groups879477027807139574nteger @ H3 @ S2 ) @ ( groups879477027807139574nteger @ G @ S2 ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5790_sum_Orelated,axiom,
% 9.17/5.41 ! [R4: rat > rat > $o,S2: set_nat,H3: nat > rat,G: nat > rat] :
% 9.17/5.41 ( ( R4 @ zero_zero_rat @ zero_zero_rat )
% 9.17/5.41 => ( ! [X13: rat,Y12: rat,X22: rat,Y22: rat] :
% 9.17/5.41 ( ( ( R4 @ X13 @ X22 )
% 9.17/5.41 & ( R4 @ Y12 @ Y22 ) )
% 9.17/5.41 => ( R4 @ ( plus_plus_rat @ X13 @ Y12 ) @ ( plus_plus_rat @ X22 @ Y22 ) ) )
% 9.17/5.41 => ( ( finite_finite_nat @ S2 )
% 9.17/5.41 => ( ! [X4: nat] :
% 9.17/5.41 ( ( member_nat @ X4 @ S2 )
% 9.17/5.41 => ( R4 @ ( H3 @ X4 ) @ ( G @ X4 ) ) )
% 9.17/5.41 => ( R4 @ ( groups2906978787729119204at_rat @ H3 @ S2 ) @ ( groups2906978787729119204at_rat @ G @ S2 ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5791_sum_Orelated,axiom,
% 9.17/5.41 ! [R4: rat > rat > $o,S2: set_int,H3: int > rat,G: int > rat] :
% 9.17/5.41 ( ( R4 @ zero_zero_rat @ zero_zero_rat )
% 9.17/5.41 => ( ! [X13: rat,Y12: rat,X22: rat,Y22: rat] :
% 9.17/5.41 ( ( ( R4 @ X13 @ X22 )
% 9.17/5.41 & ( R4 @ Y12 @ Y22 ) )
% 9.17/5.41 => ( R4 @ ( plus_plus_rat @ X13 @ Y12 ) @ ( plus_plus_rat @ X22 @ Y22 ) ) )
% 9.17/5.41 => ( ( finite_finite_int @ S2 )
% 9.17/5.41 => ( ! [X4: int] :
% 9.17/5.41 ( ( member_int @ X4 @ S2 )
% 9.17/5.41 => ( R4 @ ( H3 @ X4 ) @ ( G @ X4 ) ) )
% 9.17/5.41 => ( R4 @ ( groups3906332499630173760nt_rat @ H3 @ S2 ) @ ( groups3906332499630173760nt_rat @ G @ S2 ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5792_sum_Orelated,axiom,
% 9.17/5.41 ! [R4: rat > rat > $o,S2: set_Code_integer,H3: code_integer > rat,G: code_integer > rat] :
% 9.17/5.41 ( ( R4 @ zero_zero_rat @ zero_zero_rat )
% 9.17/5.41 => ( ! [X13: rat,Y12: rat,X22: rat,Y22: rat] :
% 9.17/5.41 ( ( ( R4 @ X13 @ X22 )
% 9.17/5.41 & ( R4 @ Y12 @ Y22 ) )
% 9.17/5.41 => ( R4 @ ( plus_plus_rat @ X13 @ Y12 ) @ ( plus_plus_rat @ X22 @ Y22 ) ) )
% 9.17/5.41 => ( ( finite6017078050557962740nteger @ S2 )
% 9.17/5.41 => ( ! [X4: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ X4 @ S2 )
% 9.17/5.41 => ( R4 @ ( H3 @ X4 ) @ ( G @ X4 ) ) )
% 9.17/5.41 => ( R4 @ ( groups6602215022474089585er_rat @ H3 @ S2 ) @ ( groups6602215022474089585er_rat @ G @ S2 ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5793_sum_Orelated,axiom,
% 9.17/5.41 ! [R4: nat > nat > $o,S2: set_int,H3: int > nat,G: int > nat] :
% 9.17/5.41 ( ( R4 @ zero_zero_nat @ zero_zero_nat )
% 9.17/5.41 => ( ! [X13: nat,Y12: nat,X22: nat,Y22: nat] :
% 9.17/5.41 ( ( ( R4 @ X13 @ X22 )
% 9.17/5.41 & ( R4 @ Y12 @ Y22 ) )
% 9.17/5.41 => ( R4 @ ( plus_plus_nat @ X13 @ Y12 ) @ ( plus_plus_nat @ X22 @ Y22 ) ) )
% 9.17/5.41 => ( ( finite_finite_int @ S2 )
% 9.17/5.41 => ( ! [X4: int] :
% 9.17/5.41 ( ( member_int @ X4 @ S2 )
% 9.17/5.41 => ( R4 @ ( H3 @ X4 ) @ ( G @ X4 ) ) )
% 9.17/5.41 => ( R4 @ ( groups4541462559716669496nt_nat @ H3 @ S2 ) @ ( groups4541462559716669496nt_nat @ G @ S2 ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5794_sum_Orelated,axiom,
% 9.17/5.41 ! [R4: nat > nat > $o,S2: set_Code_integer,H3: code_integer > nat,G: code_integer > nat] :
% 9.17/5.41 ( ( R4 @ zero_zero_nat @ zero_zero_nat )
% 9.17/5.41 => ( ! [X13: nat,Y12: nat,X22: nat,Y22: nat] :
% 9.17/5.41 ( ( ( R4 @ X13 @ X22 )
% 9.17/5.41 & ( R4 @ Y12 @ Y22 ) )
% 9.17/5.41 => ( R4 @ ( plus_plus_nat @ X13 @ Y12 ) @ ( plus_plus_nat @ X22 @ Y22 ) ) )
% 9.17/5.41 => ( ( finite6017078050557962740nteger @ S2 )
% 9.17/5.41 => ( ! [X4: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ X4 @ S2 )
% 9.17/5.41 => ( R4 @ ( H3 @ X4 ) @ ( G @ X4 ) ) )
% 9.17/5.41 => ( R4 @ ( groups7237345082560585321er_nat @ H3 @ S2 ) @ ( groups7237345082560585321er_nat @ G @ S2 ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5795_sum_Orelated,axiom,
% 9.17/5.41 ! [R4: int > int > $o,S2: set_nat,H3: nat > int,G: nat > int] :
% 9.17/5.41 ( ( R4 @ zero_zero_int @ zero_zero_int )
% 9.17/5.41 => ( ! [X13: int,Y12: int,X22: int,Y22: int] :
% 9.17/5.41 ( ( ( R4 @ X13 @ X22 )
% 9.17/5.41 & ( R4 @ Y12 @ Y22 ) )
% 9.17/5.41 => ( R4 @ ( plus_plus_int @ X13 @ Y12 ) @ ( plus_plus_int @ X22 @ Y22 ) ) )
% 9.17/5.41 => ( ( finite_finite_nat @ S2 )
% 9.17/5.41 => ( ! [X4: nat] :
% 9.17/5.41 ( ( member_nat @ X4 @ S2 )
% 9.17/5.41 => ( R4 @ ( H3 @ X4 ) @ ( G @ X4 ) ) )
% 9.17/5.41 => ( R4 @ ( groups3539618377306564664at_int @ H3 @ S2 ) @ ( groups3539618377306564664at_int @ G @ S2 ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5796_sum_Orelated,axiom,
% 9.17/5.41 ! [R4: int > int > $o,S2: set_Code_integer,H3: code_integer > int,G: code_integer > int] :
% 9.17/5.41 ( ( R4 @ zero_zero_int @ zero_zero_int )
% 9.17/5.41 => ( ! [X13: int,Y12: int,X22: int,Y22: int] :
% 9.17/5.41 ( ( ( R4 @ X13 @ X22 )
% 9.17/5.41 & ( R4 @ Y12 @ Y22 ) )
% 9.17/5.41 => ( R4 @ ( plus_plus_int @ X13 @ Y12 ) @ ( plus_plus_int @ X22 @ Y22 ) ) )
% 9.17/5.41 => ( ( finite6017078050557962740nteger @ S2 )
% 9.17/5.41 => ( ! [X4: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ X4 @ S2 )
% 9.17/5.41 => ( R4 @ ( H3 @ X4 ) @ ( G @ X4 ) ) )
% 9.17/5.41 => ( R4 @ ( groups7234854612051535045er_int @ H3 @ S2 ) @ ( groups7234854612051535045er_int @ G @ S2 ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5797_prod_Orelated,axiom,
% 9.17/5.41 ! [R4: code_integer > code_integer > $o,S2: set_nat,H3: nat > code_integer,G: nat > code_integer] :
% 9.17/5.41 ( ( R4 @ one_one_Code_integer @ one_one_Code_integer )
% 9.17/5.41 => ( ! [X13: code_integer,Y12: code_integer,X22: code_integer,Y22: code_integer] :
% 9.17/5.41 ( ( ( R4 @ X13 @ X22 )
% 9.17/5.41 & ( R4 @ Y12 @ Y22 ) )
% 9.17/5.41 => ( R4 @ ( times_3573771949741848930nteger @ X13 @ Y12 ) @ ( times_3573771949741848930nteger @ X22 @ Y22 ) ) )
% 9.17/5.41 => ( ( finite_finite_nat @ S2 )
% 9.17/5.41 => ( ! [X4: nat] :
% 9.17/5.41 ( ( member_nat @ X4 @ S2 )
% 9.17/5.41 => ( R4 @ ( H3 @ X4 ) @ ( G @ X4 ) ) )
% 9.17/5.41 => ( R4 @ ( groups3455450783089532116nteger @ H3 @ S2 ) @ ( groups3455450783089532116nteger @ G @ S2 ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5798_prod_Orelated,axiom,
% 9.17/5.41 ! [R4: code_integer > code_integer > $o,S2: set_int,H3: int > code_integer,G: int > code_integer] :
% 9.17/5.41 ( ( R4 @ one_one_Code_integer @ one_one_Code_integer )
% 9.17/5.41 => ( ! [X13: code_integer,Y12: code_integer,X22: code_integer,Y22: code_integer] :
% 9.17/5.41 ( ( ( R4 @ X13 @ X22 )
% 9.17/5.41 & ( R4 @ Y12 @ Y22 ) )
% 9.17/5.41 => ( R4 @ ( times_3573771949741848930nteger @ X13 @ Y12 ) @ ( times_3573771949741848930nteger @ X22 @ Y22 ) ) )
% 9.17/5.41 => ( ( finite_finite_int @ S2 )
% 9.17/5.41 => ( ! [X4: int] :
% 9.17/5.41 ( ( member_int @ X4 @ S2 )
% 9.17/5.41 => ( R4 @ ( H3 @ X4 ) @ ( G @ X4 ) ) )
% 9.17/5.41 => ( R4 @ ( groups3827104343326376752nteger @ H3 @ S2 ) @ ( groups3827104343326376752nteger @ G @ S2 ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5799_prod_Orelated,axiom,
% 9.17/5.41 ! [R4: code_integer > code_integer > $o,S2: set_Code_integer,H3: code_integer > code_integer,G: code_integer > code_integer] :
% 9.17/5.41 ( ( R4 @ one_one_Code_integer @ one_one_Code_integer )
% 9.17/5.41 => ( ! [X13: code_integer,Y12: code_integer,X22: code_integer,Y22: code_integer] :
% 9.17/5.41 ( ( ( R4 @ X13 @ X22 )
% 9.17/5.41 & ( R4 @ Y12 @ Y22 ) )
% 9.17/5.41 => ( R4 @ ( times_3573771949741848930nteger @ X13 @ Y12 ) @ ( times_3573771949741848930nteger @ X22 @ Y22 ) ) )
% 9.17/5.41 => ( ( finite6017078050557962740nteger @ S2 )
% 9.17/5.41 => ( ! [X4: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ X4 @ S2 )
% 9.17/5.41 => ( R4 @ ( H3 @ X4 ) @ ( G @ X4 ) ) )
% 9.17/5.41 => ( R4 @ ( groups3674199335183972705nteger @ H3 @ S2 ) @ ( groups3674199335183972705nteger @ G @ S2 ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5800_prod_Orelated,axiom,
% 9.17/5.41 ! [R4: assn > assn > $o,S2: set_nat,H3: nat > assn,G: nat > assn] :
% 9.17/5.41 ( ( R4 @ one_one_assn @ one_one_assn )
% 9.17/5.41 => ( ! [X13: assn,Y12: assn,X22: assn,Y22: assn] :
% 9.17/5.41 ( ( ( R4 @ X13 @ X22 )
% 9.17/5.41 & ( R4 @ Y12 @ Y22 ) )
% 9.17/5.41 => ( R4 @ ( times_times_assn @ X13 @ Y12 ) @ ( times_times_assn @ X22 @ Y22 ) ) )
% 9.17/5.41 => ( ( finite_finite_nat @ S2 )
% 9.17/5.41 => ( ! [X4: nat] :
% 9.17/5.41 ( ( member_nat @ X4 @ S2 )
% 9.17/5.41 => ( R4 @ ( H3 @ X4 ) @ ( G @ X4 ) ) )
% 9.17/5.41 => ( R4 @ ( groups6906906614972039071t_assn @ H3 @ S2 ) @ ( groups6906906614972039071t_assn @ G @ S2 ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5801_prod_Orelated,axiom,
% 9.17/5.41 ! [R4: assn > assn > $o,S2: set_int,H3: int > assn,G: int > assn] :
% 9.17/5.41 ( ( R4 @ one_one_assn @ one_one_assn )
% 9.17/5.41 => ( ! [X13: assn,Y12: assn,X22: assn,Y22: assn] :
% 9.17/5.41 ( ( ( R4 @ X13 @ X22 )
% 9.17/5.41 & ( R4 @ Y12 @ Y22 ) )
% 9.17/5.41 => ( R4 @ ( times_times_assn @ X13 @ Y12 ) @ ( times_times_assn @ X22 @ Y22 ) ) )
% 9.17/5.41 => ( ( finite_finite_int @ S2 )
% 9.17/5.41 => ( ! [X4: int] :
% 9.17/5.41 ( ( member_int @ X4 @ S2 )
% 9.17/5.41 => ( R4 @ ( H3 @ X4 ) @ ( G @ X4 ) ) )
% 9.17/5.41 => ( R4 @ ( groups7882442080178216443t_assn @ H3 @ S2 ) @ ( groups7882442080178216443t_assn @ G @ S2 ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5802_prod_Orelated,axiom,
% 9.17/5.41 ! [R4: assn > assn > $o,S2: set_Code_integer,H3: code_integer > assn,G: code_integer > assn] :
% 9.17/5.41 ( ( R4 @ one_one_assn @ one_one_assn )
% 9.17/5.41 => ( ! [X13: assn,Y12: assn,X22: assn,Y22: assn] :
% 9.17/5.41 ( ( ( R4 @ X13 @ X22 )
% 9.17/5.41 & ( R4 @ Y12 @ Y22 ) )
% 9.17/5.41 => ( R4 @ ( times_times_assn @ X13 @ Y12 ) @ ( times_times_assn @ X22 @ Y22 ) ) )
% 9.17/5.41 => ( ( finite6017078050557962740nteger @ S2 )
% 9.17/5.41 => ( ! [X4: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ X4 @ S2 )
% 9.17/5.41 => ( R4 @ ( H3 @ X4 ) @ ( G @ X4 ) ) )
% 9.17/5.41 => ( R4 @ ( groups1304777262505850412r_assn @ H3 @ S2 ) @ ( groups1304777262505850412r_assn @ G @ S2 ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5803_prod_Orelated,axiom,
% 9.17/5.41 ! [R4: rat > rat > $o,S2: set_nat,H3: nat > rat,G: nat > rat] :
% 9.17/5.41 ( ( R4 @ one_one_rat @ one_one_rat )
% 9.17/5.41 => ( ! [X13: rat,Y12: rat,X22: rat,Y22: rat] :
% 9.17/5.41 ( ( ( R4 @ X13 @ X22 )
% 9.17/5.41 & ( R4 @ Y12 @ Y22 ) )
% 9.17/5.41 => ( R4 @ ( times_times_rat @ X13 @ Y12 ) @ ( times_times_rat @ X22 @ Y22 ) ) )
% 9.17/5.41 => ( ( finite_finite_nat @ S2 )
% 9.17/5.41 => ( ! [X4: nat] :
% 9.17/5.41 ( ( member_nat @ X4 @ S2 )
% 9.17/5.41 => ( R4 @ ( H3 @ X4 ) @ ( G @ X4 ) ) )
% 9.17/5.41 => ( R4 @ ( groups73079841787564623at_rat @ H3 @ S2 ) @ ( groups73079841787564623at_rat @ G @ S2 ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5804_prod_Orelated,axiom,
% 9.17/5.41 ! [R4: rat > rat > $o,S2: set_int,H3: int > rat,G: int > rat] :
% 9.17/5.41 ( ( R4 @ one_one_rat @ one_one_rat )
% 9.17/5.41 => ( ! [X13: rat,Y12: rat,X22: rat,Y22: rat] :
% 9.17/5.41 ( ( ( R4 @ X13 @ X22 )
% 9.17/5.41 & ( R4 @ Y12 @ Y22 ) )
% 9.17/5.41 => ( R4 @ ( times_times_rat @ X13 @ Y12 ) @ ( times_times_rat @ X22 @ Y22 ) ) )
% 9.17/5.41 => ( ( finite_finite_int @ S2 )
% 9.17/5.41 => ( ! [X4: int] :
% 9.17/5.41 ( ( member_int @ X4 @ S2 )
% 9.17/5.41 => ( R4 @ ( H3 @ X4 ) @ ( G @ X4 ) ) )
% 9.17/5.41 => ( R4 @ ( groups1072433553688619179nt_rat @ H3 @ S2 ) @ ( groups1072433553688619179nt_rat @ G @ S2 ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5805_prod_Orelated,axiom,
% 9.17/5.41 ! [R4: rat > rat > $o,S2: set_Code_integer,H3: code_integer > rat,G: code_integer > rat] :
% 9.17/5.41 ( ( R4 @ one_one_rat @ one_one_rat )
% 9.17/5.41 => ( ! [X13: rat,Y12: rat,X22: rat,Y22: rat] :
% 9.17/5.41 ( ( ( R4 @ X13 @ X22 )
% 9.17/5.41 & ( R4 @ Y12 @ Y22 ) )
% 9.17/5.41 => ( R4 @ ( times_times_rat @ X13 @ Y12 ) @ ( times_times_rat @ X22 @ Y22 ) ) )
% 9.17/5.41 => ( ( finite6017078050557962740nteger @ S2 )
% 9.17/5.41 => ( ! [X4: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ X4 @ S2 )
% 9.17/5.41 => ( R4 @ ( H3 @ X4 ) @ ( G @ X4 ) ) )
% 9.17/5.41 => ( R4 @ ( groups2555765274223993564er_rat @ H3 @ S2 ) @ ( groups2555765274223993564er_rat @ G @ S2 ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5806_prod_Orelated,axiom,
% 9.17/5.41 ! [R4: nat > nat > $o,S2: set_int,H3: int > nat,G: int > nat] :
% 9.17/5.41 ( ( R4 @ one_one_nat @ one_one_nat )
% 9.17/5.41 => ( ! [X13: nat,Y12: nat,X22: nat,Y22: nat] :
% 9.17/5.41 ( ( ( R4 @ X13 @ X22 )
% 9.17/5.41 & ( R4 @ Y12 @ Y22 ) )
% 9.17/5.41 => ( R4 @ ( times_times_nat @ X13 @ Y12 ) @ ( times_times_nat @ X22 @ Y22 ) ) )
% 9.17/5.41 => ( ( finite_finite_int @ S2 )
% 9.17/5.41 => ( ! [X4: int] :
% 9.17/5.41 ( ( member_int @ X4 @ S2 )
% 9.17/5.41 => ( R4 @ ( H3 @ X4 ) @ ( G @ X4 ) ) )
% 9.17/5.41 => ( R4 @ ( groups1707563613775114915nt_nat @ H3 @ S2 ) @ ( groups1707563613775114915nt_nat @ G @ S2 ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5807_sum_Oinsert__if,axiom,
% 9.17/5.41 ! [A2: set_o,X: $o,G: $o > rat] :
% 9.17/5.41 ( ( finite_finite_o @ A2 )
% 9.17/5.41 => ( ( ( member_o @ X @ A2 )
% 9.17/5.41 => ( ( groups7872700643590313910_o_rat @ G @ ( insert_o @ X @ A2 ) )
% 9.17/5.41 = ( groups7872700643590313910_o_rat @ G @ A2 ) ) )
% 9.17/5.41 & ( ~ ( member_o @ X @ A2 )
% 9.17/5.41 => ( ( groups7872700643590313910_o_rat @ G @ ( insert_o @ X @ A2 ) )
% 9.17/5.41 = ( plus_plus_rat @ ( G @ X ) @ ( groups7872700643590313910_o_rat @ G @ A2 ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5808_sum_Oinsert__if,axiom,
% 9.17/5.41 ! [A2: set_nat,X: nat,G: nat > rat] :
% 9.17/5.41 ( ( finite_finite_nat @ A2 )
% 9.17/5.41 => ( ( ( member_nat @ X @ A2 )
% 9.17/5.41 => ( ( groups2906978787729119204at_rat @ G @ ( insert_nat @ X @ A2 ) )
% 9.17/5.41 = ( groups2906978787729119204at_rat @ G @ A2 ) ) )
% 9.17/5.41 & ( ~ ( member_nat @ X @ A2 )
% 9.17/5.41 => ( ( groups2906978787729119204at_rat @ G @ ( insert_nat @ X @ A2 ) )
% 9.17/5.41 = ( plus_plus_rat @ ( G @ X ) @ ( groups2906978787729119204at_rat @ G @ A2 ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5809_sum_Oinsert__if,axiom,
% 9.17/5.41 ! [A2: set_int,X: int,G: int > rat] :
% 9.17/5.41 ( ( finite_finite_int @ A2 )
% 9.17/5.41 => ( ( ( member_int @ X @ A2 )
% 9.17/5.41 => ( ( groups3906332499630173760nt_rat @ G @ ( insert_int @ X @ A2 ) )
% 9.17/5.41 = ( groups3906332499630173760nt_rat @ G @ A2 ) ) )
% 9.17/5.41 & ( ~ ( member_int @ X @ A2 )
% 9.17/5.41 => ( ( groups3906332499630173760nt_rat @ G @ ( insert_int @ X @ A2 ) )
% 9.17/5.41 = ( plus_plus_rat @ ( G @ X ) @ ( groups3906332499630173760nt_rat @ G @ A2 ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5810_sum_Oinsert__if,axiom,
% 9.17/5.41 ! [A2: set_Code_integer,X: code_integer,G: code_integer > rat] :
% 9.17/5.41 ( ( finite6017078050557962740nteger @ A2 )
% 9.17/5.41 => ( ( ( member_Code_integer @ X @ A2 )
% 9.17/5.41 => ( ( groups6602215022474089585er_rat @ G @ ( insert_Code_integer @ X @ A2 ) )
% 9.17/5.41 = ( groups6602215022474089585er_rat @ G @ A2 ) ) )
% 9.17/5.41 & ( ~ ( member_Code_integer @ X @ A2 )
% 9.17/5.41 => ( ( groups6602215022474089585er_rat @ G @ ( insert_Code_integer @ X @ A2 ) )
% 9.17/5.41 = ( plus_plus_rat @ ( G @ X ) @ ( groups6602215022474089585er_rat @ G @ A2 ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5811_sum_Oinsert__if,axiom,
% 9.17/5.41 ! [A2: set_o,X: $o,G: $o > nat] :
% 9.17/5.41 ( ( finite_finite_o @ A2 )
% 9.17/5.41 => ( ( ( member_o @ X @ A2 )
% 9.17/5.41 => ( ( groups8507830703676809646_o_nat @ G @ ( insert_o @ X @ A2 ) )
% 9.17/5.41 = ( groups8507830703676809646_o_nat @ G @ A2 ) ) )
% 9.17/5.41 & ( ~ ( member_o @ X @ A2 )
% 9.17/5.41 => ( ( groups8507830703676809646_o_nat @ G @ ( insert_o @ X @ A2 ) )
% 9.17/5.41 = ( plus_plus_nat @ ( G @ X ) @ ( groups8507830703676809646_o_nat @ G @ A2 ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5812_sum_Oinsert__if,axiom,
% 9.17/5.41 ! [A2: set_int,X: int,G: int > nat] :
% 9.17/5.41 ( ( finite_finite_int @ A2 )
% 9.17/5.41 => ( ( ( member_int @ X @ A2 )
% 9.17/5.41 => ( ( groups4541462559716669496nt_nat @ G @ ( insert_int @ X @ A2 ) )
% 9.17/5.41 = ( groups4541462559716669496nt_nat @ G @ A2 ) ) )
% 9.17/5.41 & ( ~ ( member_int @ X @ A2 )
% 9.17/5.41 => ( ( groups4541462559716669496nt_nat @ G @ ( insert_int @ X @ A2 ) )
% 9.17/5.41 = ( plus_plus_nat @ ( G @ X ) @ ( groups4541462559716669496nt_nat @ G @ A2 ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5813_sum_Oinsert__if,axiom,
% 9.17/5.41 ! [A2: set_Code_integer,X: code_integer,G: code_integer > nat] :
% 9.17/5.41 ( ( finite6017078050557962740nteger @ A2 )
% 9.17/5.41 => ( ( ( member_Code_integer @ X @ A2 )
% 9.17/5.41 => ( ( groups7237345082560585321er_nat @ G @ ( insert_Code_integer @ X @ A2 ) )
% 9.17/5.41 = ( groups7237345082560585321er_nat @ G @ A2 ) ) )
% 9.17/5.41 & ( ~ ( member_Code_integer @ X @ A2 )
% 9.17/5.41 => ( ( groups7237345082560585321er_nat @ G @ ( insert_Code_integer @ X @ A2 ) )
% 9.17/5.41 = ( plus_plus_nat @ ( G @ X ) @ ( groups7237345082560585321er_nat @ G @ A2 ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5814_sum_Oinsert__if,axiom,
% 9.17/5.41 ! [A2: set_o,X: $o,G: $o > int] :
% 9.17/5.41 ( ( finite_finite_o @ A2 )
% 9.17/5.41 => ( ( ( member_o @ X @ A2 )
% 9.17/5.41 => ( ( groups8505340233167759370_o_int @ G @ ( insert_o @ X @ A2 ) )
% 9.17/5.41 = ( groups8505340233167759370_o_int @ G @ A2 ) ) )
% 9.17/5.41 & ( ~ ( member_o @ X @ A2 )
% 9.17/5.41 => ( ( groups8505340233167759370_o_int @ G @ ( insert_o @ X @ A2 ) )
% 9.17/5.41 = ( plus_plus_int @ ( G @ X ) @ ( groups8505340233167759370_o_int @ G @ A2 ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5815_sum_Oinsert__if,axiom,
% 9.17/5.41 ! [A2: set_nat,X: nat,G: nat > int] :
% 9.17/5.41 ( ( finite_finite_nat @ A2 )
% 9.17/5.41 => ( ( ( member_nat @ X @ A2 )
% 9.17/5.41 => ( ( groups3539618377306564664at_int @ G @ ( insert_nat @ X @ A2 ) )
% 9.17/5.41 = ( groups3539618377306564664at_int @ G @ A2 ) ) )
% 9.17/5.41 & ( ~ ( member_nat @ X @ A2 )
% 9.17/5.41 => ( ( groups3539618377306564664at_int @ G @ ( insert_nat @ X @ A2 ) )
% 9.17/5.41 = ( plus_plus_int @ ( G @ X ) @ ( groups3539618377306564664at_int @ G @ A2 ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5816_sum_Oinsert__if,axiom,
% 9.17/5.41 ! [A2: set_Code_integer,X: code_integer,G: code_integer > int] :
% 9.17/5.41 ( ( finite6017078050557962740nteger @ A2 )
% 9.17/5.41 => ( ( ( member_Code_integer @ X @ A2 )
% 9.17/5.41 => ( ( groups7234854612051535045er_int @ G @ ( insert_Code_integer @ X @ A2 ) )
% 9.17/5.41 = ( groups7234854612051535045er_int @ G @ A2 ) ) )
% 9.17/5.41 & ( ~ ( member_Code_integer @ X @ A2 )
% 9.17/5.41 => ( ( groups7234854612051535045er_int @ G @ ( insert_Code_integer @ X @ A2 ) )
% 9.17/5.41 = ( plus_plus_int @ ( G @ X ) @ ( groups7234854612051535045er_int @ G @ A2 ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5817_atLeast0__atMost__Suc,axiom,
% 9.17/5.41 ! [N2: nat] :
% 9.17/5.41 ( ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) )
% 9.17/5.41 = ( insert_nat @ ( suc @ N2 ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5818_atLeast0__lessThan__Suc,axiom,
% 9.17/5.41 ! [N2: nat] :
% 9.17/5.41 ( ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N2 ) )
% 9.17/5.41 = ( insert_nat @ N2 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5819_Icc__eq__insert__lb__nat,axiom,
% 9.17/5.41 ! [M2: nat,N2: nat] :
% 9.17/5.41 ( ( ord_less_eq_nat @ M2 @ N2 )
% 9.17/5.41 => ( ( set_or1269000886237332187st_nat @ M2 @ N2 )
% 9.17/5.41 = ( insert_nat @ M2 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N2 ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5820_atLeastAtMostSuc__conv,axiom,
% 9.17/5.41 ! [M2: nat,N2: nat] :
% 9.17/5.41 ( ( ord_less_eq_nat @ M2 @ ( suc @ N2 ) )
% 9.17/5.41 => ( ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N2 ) )
% 9.17/5.41 = ( insert_nat @ ( suc @ N2 ) @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5821_atLeastAtMost__insertL,axiom,
% 9.17/5.41 ! [M2: nat,N2: nat] :
% 9.17/5.41 ( ( ord_less_eq_nat @ M2 @ N2 )
% 9.17/5.41 => ( ( insert_nat @ M2 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N2 ) )
% 9.17/5.41 = ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5822_prod_Oreindex__bij__witness__not__neutral,axiom,
% 9.17/5.41 ! [S7: set_o,T4: set_o,S2: set_o,I: $o > $o,J: $o > $o,T5: set_o,G: $o > code_integer,H3: $o > code_integer] :
% 9.17/5.41 ( ( finite_finite_o @ S7 )
% 9.17/5.41 => ( ( finite_finite_o @ T4 )
% 9.17/5.41 => ( ! [A3: $o] :
% 9.17/5.41 ( ( member_o @ A3 @ ( minus_minus_set_o @ S2 @ S7 ) )
% 9.17/5.41 => ( ( I @ ( J @ A3 ) )
% 9.17/5.41 = A3 ) )
% 9.17/5.41 => ( ! [A3: $o] :
% 9.17/5.41 ( ( member_o @ A3 @ ( minus_minus_set_o @ S2 @ S7 ) )
% 9.17/5.41 => ( member_o @ ( J @ A3 ) @ ( minus_minus_set_o @ T5 @ T4 ) ) )
% 9.17/5.41 => ( ! [B2: $o] :
% 9.17/5.41 ( ( member_o @ B2 @ ( minus_minus_set_o @ T5 @ T4 ) )
% 9.17/5.41 => ( ( J @ ( I @ B2 ) )
% 9.17/5.41 = B2 ) )
% 9.17/5.41 => ( ! [B2: $o] :
% 9.17/5.41 ( ( member_o @ B2 @ ( minus_minus_set_o @ T5 @ T4 ) )
% 9.17/5.41 => ( member_o @ ( I @ B2 ) @ ( minus_minus_set_o @ S2 @ S7 ) ) )
% 9.17/5.41 => ( ! [A3: $o] :
% 9.17/5.41 ( ( member_o @ A3 @ S7 )
% 9.17/5.41 => ( ( G @ A3 )
% 9.17/5.41 = one_one_Code_integer ) )
% 9.17/5.41 => ( ! [B2: $o] :
% 9.17/5.41 ( ( member_o @ B2 @ T4 )
% 9.17/5.41 => ( ( H3 @ B2 )
% 9.17/5.41 = one_one_Code_integer ) )
% 9.17/5.41 => ( ! [A3: $o] :
% 9.17/5.41 ( ( member_o @ A3 @ S2 )
% 9.17/5.41 => ( ( H3 @ ( J @ A3 ) )
% 9.17/5.41 = ( G @ A3 ) ) )
% 9.17/5.41 => ( ( groups7694694392188491536nteger @ G @ S2 )
% 9.17/5.41 = ( groups7694694392188491536nteger @ H3 @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5823_prod_Oreindex__bij__witness__not__neutral,axiom,
% 9.17/5.41 ! [S7: set_o,T4: set_int,S2: set_o,I: int > $o,J: $o > int,T5: set_int,G: $o > code_integer,H3: int > code_integer] :
% 9.17/5.41 ( ( finite_finite_o @ S7 )
% 9.17/5.41 => ( ( finite_finite_int @ T4 )
% 9.17/5.41 => ( ! [A3: $o] :
% 9.17/5.41 ( ( member_o @ A3 @ ( minus_minus_set_o @ S2 @ S7 ) )
% 9.17/5.41 => ( ( I @ ( J @ A3 ) )
% 9.17/5.41 = A3 ) )
% 9.17/5.41 => ( ! [A3: $o] :
% 9.17/5.41 ( ( member_o @ A3 @ ( minus_minus_set_o @ S2 @ S7 ) )
% 9.17/5.41 => ( member_int @ ( J @ A3 ) @ ( minus_minus_set_int @ T5 @ T4 ) ) )
% 9.17/5.41 => ( ! [B2: int] :
% 9.17/5.41 ( ( member_int @ B2 @ ( minus_minus_set_int @ T5 @ T4 ) )
% 9.17/5.41 => ( ( J @ ( I @ B2 ) )
% 9.17/5.41 = B2 ) )
% 9.17/5.41 => ( ! [B2: int] :
% 9.17/5.41 ( ( member_int @ B2 @ ( minus_minus_set_int @ T5 @ T4 ) )
% 9.17/5.41 => ( member_o @ ( I @ B2 ) @ ( minus_minus_set_o @ S2 @ S7 ) ) )
% 9.17/5.41 => ( ! [A3: $o] :
% 9.17/5.41 ( ( member_o @ A3 @ S7 )
% 9.17/5.41 => ( ( G @ A3 )
% 9.17/5.41 = one_one_Code_integer ) )
% 9.17/5.41 => ( ! [B2: int] :
% 9.17/5.41 ( ( member_int @ B2 @ T4 )
% 9.17/5.41 => ( ( H3 @ B2 )
% 9.17/5.41 = one_one_Code_integer ) )
% 9.17/5.41 => ( ! [A3: $o] :
% 9.17/5.41 ( ( member_o @ A3 @ S2 )
% 9.17/5.41 => ( ( H3 @ ( J @ A3 ) )
% 9.17/5.41 = ( G @ A3 ) ) )
% 9.17/5.41 => ( ( groups7694694392188491536nteger @ G @ S2 )
% 9.17/5.41 = ( groups3827104343326376752nteger @ H3 @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5824_prod_Oreindex__bij__witness__not__neutral,axiom,
% 9.17/5.41 ! [S7: set_o,T4: set_Code_integer,S2: set_o,I: code_integer > $o,J: $o > code_integer,T5: set_Code_integer,G: $o > code_integer,H3: code_integer > code_integer] :
% 9.17/5.41 ( ( finite_finite_o @ S7 )
% 9.17/5.41 => ( ( finite6017078050557962740nteger @ T4 )
% 9.17/5.41 => ( ! [A3: $o] :
% 9.17/5.41 ( ( member_o @ A3 @ ( minus_minus_set_o @ S2 @ S7 ) )
% 9.17/5.41 => ( ( I @ ( J @ A3 ) )
% 9.17/5.41 = A3 ) )
% 9.17/5.41 => ( ! [A3: $o] :
% 9.17/5.41 ( ( member_o @ A3 @ ( minus_minus_set_o @ S2 @ S7 ) )
% 9.17/5.41 => ( member_Code_integer @ ( J @ A3 ) @ ( minus_2355218937544613996nteger @ T5 @ T4 ) ) )
% 9.17/5.41 => ( ! [B2: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ B2 @ ( minus_2355218937544613996nteger @ T5 @ T4 ) )
% 9.17/5.41 => ( ( J @ ( I @ B2 ) )
% 9.17/5.41 = B2 ) )
% 9.17/5.41 => ( ! [B2: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ B2 @ ( minus_2355218937544613996nteger @ T5 @ T4 ) )
% 9.17/5.41 => ( member_o @ ( I @ B2 ) @ ( minus_minus_set_o @ S2 @ S7 ) ) )
% 9.17/5.41 => ( ! [A3: $o] :
% 9.17/5.41 ( ( member_o @ A3 @ S7 )
% 9.17/5.41 => ( ( G @ A3 )
% 9.17/5.41 = one_one_Code_integer ) )
% 9.17/5.41 => ( ! [B2: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ B2 @ T4 )
% 9.17/5.41 => ( ( H3 @ B2 )
% 9.17/5.41 = one_one_Code_integer ) )
% 9.17/5.41 => ( ! [A3: $o] :
% 9.17/5.41 ( ( member_o @ A3 @ S2 )
% 9.17/5.41 => ( ( H3 @ ( J @ A3 ) )
% 9.17/5.41 = ( G @ A3 ) ) )
% 9.17/5.41 => ( ( groups7694694392188491536nteger @ G @ S2 )
% 9.17/5.41 = ( groups3674199335183972705nteger @ H3 @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5825_prod_Oreindex__bij__witness__not__neutral,axiom,
% 9.17/5.41 ! [S7: set_int,T4: set_o,S2: set_int,I: $o > int,J: int > $o,T5: set_o,G: int > code_integer,H3: $o > code_integer] :
% 9.17/5.41 ( ( finite_finite_int @ S7 )
% 9.17/5.41 => ( ( finite_finite_o @ T4 )
% 9.17/5.41 => ( ! [A3: int] :
% 9.17/5.41 ( ( member_int @ A3 @ ( minus_minus_set_int @ S2 @ S7 ) )
% 9.17/5.41 => ( ( I @ ( J @ A3 ) )
% 9.17/5.41 = A3 ) )
% 9.17/5.41 => ( ! [A3: int] :
% 9.17/5.41 ( ( member_int @ A3 @ ( minus_minus_set_int @ S2 @ S7 ) )
% 9.17/5.41 => ( member_o @ ( J @ A3 ) @ ( minus_minus_set_o @ T5 @ T4 ) ) )
% 9.17/5.41 => ( ! [B2: $o] :
% 9.17/5.41 ( ( member_o @ B2 @ ( minus_minus_set_o @ T5 @ T4 ) )
% 9.17/5.41 => ( ( J @ ( I @ B2 ) )
% 9.17/5.41 = B2 ) )
% 9.17/5.41 => ( ! [B2: $o] :
% 9.17/5.41 ( ( member_o @ B2 @ ( minus_minus_set_o @ T5 @ T4 ) )
% 9.17/5.41 => ( member_int @ ( I @ B2 ) @ ( minus_minus_set_int @ S2 @ S7 ) ) )
% 9.17/5.41 => ( ! [A3: int] :
% 9.17/5.41 ( ( member_int @ A3 @ S7 )
% 9.17/5.41 => ( ( G @ A3 )
% 9.17/5.41 = one_one_Code_integer ) )
% 9.17/5.41 => ( ! [B2: $o] :
% 9.17/5.41 ( ( member_o @ B2 @ T4 )
% 9.17/5.41 => ( ( H3 @ B2 )
% 9.17/5.41 = one_one_Code_integer ) )
% 9.17/5.41 => ( ! [A3: int] :
% 9.17/5.41 ( ( member_int @ A3 @ S2 )
% 9.17/5.41 => ( ( H3 @ ( J @ A3 ) )
% 9.17/5.41 = ( G @ A3 ) ) )
% 9.17/5.41 => ( ( groups3827104343326376752nteger @ G @ S2 )
% 9.17/5.41 = ( groups7694694392188491536nteger @ H3 @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5826_prod_Oreindex__bij__witness__not__neutral,axiom,
% 9.17/5.41 ! [S7: set_int,T4: set_int,S2: set_int,I: int > int,J: int > int,T5: set_int,G: int > code_integer,H3: int > code_integer] :
% 9.17/5.41 ( ( finite_finite_int @ S7 )
% 9.17/5.41 => ( ( finite_finite_int @ T4 )
% 9.17/5.41 => ( ! [A3: int] :
% 9.17/5.41 ( ( member_int @ A3 @ ( minus_minus_set_int @ S2 @ S7 ) )
% 9.17/5.41 => ( ( I @ ( J @ A3 ) )
% 9.17/5.41 = A3 ) )
% 9.17/5.41 => ( ! [A3: int] :
% 9.17/5.41 ( ( member_int @ A3 @ ( minus_minus_set_int @ S2 @ S7 ) )
% 9.17/5.41 => ( member_int @ ( J @ A3 ) @ ( minus_minus_set_int @ T5 @ T4 ) ) )
% 9.17/5.41 => ( ! [B2: int] :
% 9.17/5.41 ( ( member_int @ B2 @ ( minus_minus_set_int @ T5 @ T4 ) )
% 9.17/5.41 => ( ( J @ ( I @ B2 ) )
% 9.17/5.41 = B2 ) )
% 9.17/5.41 => ( ! [B2: int] :
% 9.17/5.41 ( ( member_int @ B2 @ ( minus_minus_set_int @ T5 @ T4 ) )
% 9.17/5.41 => ( member_int @ ( I @ B2 ) @ ( minus_minus_set_int @ S2 @ S7 ) ) )
% 9.17/5.41 => ( ! [A3: int] :
% 9.17/5.41 ( ( member_int @ A3 @ S7 )
% 9.17/5.41 => ( ( G @ A3 )
% 9.17/5.41 = one_one_Code_integer ) )
% 9.17/5.41 => ( ! [B2: int] :
% 9.17/5.41 ( ( member_int @ B2 @ T4 )
% 9.17/5.41 => ( ( H3 @ B2 )
% 9.17/5.41 = one_one_Code_integer ) )
% 9.17/5.41 => ( ! [A3: int] :
% 9.17/5.41 ( ( member_int @ A3 @ S2 )
% 9.17/5.41 => ( ( H3 @ ( J @ A3 ) )
% 9.17/5.41 = ( G @ A3 ) ) )
% 9.17/5.41 => ( ( groups3827104343326376752nteger @ G @ S2 )
% 9.17/5.41 = ( groups3827104343326376752nteger @ H3 @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5827_prod_Oreindex__bij__witness__not__neutral,axiom,
% 9.17/5.41 ! [S7: set_int,T4: set_Code_integer,S2: set_int,I: code_integer > int,J: int > code_integer,T5: set_Code_integer,G: int > code_integer,H3: code_integer > code_integer] :
% 9.17/5.41 ( ( finite_finite_int @ S7 )
% 9.17/5.41 => ( ( finite6017078050557962740nteger @ T4 )
% 9.17/5.41 => ( ! [A3: int] :
% 9.17/5.41 ( ( member_int @ A3 @ ( minus_minus_set_int @ S2 @ S7 ) )
% 9.17/5.41 => ( ( I @ ( J @ A3 ) )
% 9.17/5.41 = A3 ) )
% 9.17/5.41 => ( ! [A3: int] :
% 9.17/5.41 ( ( member_int @ A3 @ ( minus_minus_set_int @ S2 @ S7 ) )
% 9.17/5.41 => ( member_Code_integer @ ( J @ A3 ) @ ( minus_2355218937544613996nteger @ T5 @ T4 ) ) )
% 9.17/5.41 => ( ! [B2: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ B2 @ ( minus_2355218937544613996nteger @ T5 @ T4 ) )
% 9.17/5.41 => ( ( J @ ( I @ B2 ) )
% 9.17/5.41 = B2 ) )
% 9.17/5.41 => ( ! [B2: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ B2 @ ( minus_2355218937544613996nteger @ T5 @ T4 ) )
% 9.17/5.41 => ( member_int @ ( I @ B2 ) @ ( minus_minus_set_int @ S2 @ S7 ) ) )
% 9.17/5.41 => ( ! [A3: int] :
% 9.17/5.41 ( ( member_int @ A3 @ S7 )
% 9.17/5.41 => ( ( G @ A3 )
% 9.17/5.41 = one_one_Code_integer ) )
% 9.17/5.41 => ( ! [B2: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ B2 @ T4 )
% 9.17/5.41 => ( ( H3 @ B2 )
% 9.17/5.41 = one_one_Code_integer ) )
% 9.17/5.41 => ( ! [A3: int] :
% 9.17/5.41 ( ( member_int @ A3 @ S2 )
% 9.17/5.41 => ( ( H3 @ ( J @ A3 ) )
% 9.17/5.41 = ( G @ A3 ) ) )
% 9.17/5.41 => ( ( groups3827104343326376752nteger @ G @ S2 )
% 9.17/5.41 = ( groups3674199335183972705nteger @ H3 @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5828_prod_Oreindex__bij__witness__not__neutral,axiom,
% 9.17/5.41 ! [S7: set_Code_integer,T4: set_o,S2: set_Code_integer,I: $o > code_integer,J: code_integer > $o,T5: set_o,G: code_integer > code_integer,H3: $o > code_integer] :
% 9.17/5.41 ( ( finite6017078050557962740nteger @ S7 )
% 9.17/5.41 => ( ( finite_finite_o @ T4 )
% 9.17/5.41 => ( ! [A3: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ A3 @ ( minus_2355218937544613996nteger @ S2 @ S7 ) )
% 9.17/5.41 => ( ( I @ ( J @ A3 ) )
% 9.17/5.41 = A3 ) )
% 9.17/5.41 => ( ! [A3: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ A3 @ ( minus_2355218937544613996nteger @ S2 @ S7 ) )
% 9.17/5.41 => ( member_o @ ( J @ A3 ) @ ( minus_minus_set_o @ T5 @ T4 ) ) )
% 9.17/5.41 => ( ! [B2: $o] :
% 9.17/5.41 ( ( member_o @ B2 @ ( minus_minus_set_o @ T5 @ T4 ) )
% 9.17/5.41 => ( ( J @ ( I @ B2 ) )
% 9.17/5.41 = B2 ) )
% 9.17/5.41 => ( ! [B2: $o] :
% 9.17/5.41 ( ( member_o @ B2 @ ( minus_minus_set_o @ T5 @ T4 ) )
% 9.17/5.41 => ( member_Code_integer @ ( I @ B2 ) @ ( minus_2355218937544613996nteger @ S2 @ S7 ) ) )
% 9.17/5.41 => ( ! [A3: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ A3 @ S7 )
% 9.17/5.41 => ( ( G @ A3 )
% 9.17/5.41 = one_one_Code_integer ) )
% 9.17/5.41 => ( ! [B2: $o] :
% 9.17/5.41 ( ( member_o @ B2 @ T4 )
% 9.17/5.41 => ( ( H3 @ B2 )
% 9.17/5.41 = one_one_Code_integer ) )
% 9.17/5.41 => ( ! [A3: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ A3 @ S2 )
% 9.17/5.41 => ( ( H3 @ ( J @ A3 ) )
% 9.17/5.41 = ( G @ A3 ) ) )
% 9.17/5.41 => ( ( groups3674199335183972705nteger @ G @ S2 )
% 9.17/5.41 = ( groups7694694392188491536nteger @ H3 @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5829_prod_Oreindex__bij__witness__not__neutral,axiom,
% 9.17/5.41 ! [S7: set_Code_integer,T4: set_int,S2: set_Code_integer,I: int > code_integer,J: code_integer > int,T5: set_int,G: code_integer > code_integer,H3: int > code_integer] :
% 9.17/5.41 ( ( finite6017078050557962740nteger @ S7 )
% 9.17/5.41 => ( ( finite_finite_int @ T4 )
% 9.17/5.41 => ( ! [A3: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ A3 @ ( minus_2355218937544613996nteger @ S2 @ S7 ) )
% 9.17/5.41 => ( ( I @ ( J @ A3 ) )
% 9.17/5.41 = A3 ) )
% 9.17/5.41 => ( ! [A3: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ A3 @ ( minus_2355218937544613996nteger @ S2 @ S7 ) )
% 9.17/5.41 => ( member_int @ ( J @ A3 ) @ ( minus_minus_set_int @ T5 @ T4 ) ) )
% 9.17/5.41 => ( ! [B2: int] :
% 9.17/5.41 ( ( member_int @ B2 @ ( minus_minus_set_int @ T5 @ T4 ) )
% 9.17/5.41 => ( ( J @ ( I @ B2 ) )
% 9.17/5.41 = B2 ) )
% 9.17/5.41 => ( ! [B2: int] :
% 9.17/5.41 ( ( member_int @ B2 @ ( minus_minus_set_int @ T5 @ T4 ) )
% 9.17/5.41 => ( member_Code_integer @ ( I @ B2 ) @ ( minus_2355218937544613996nteger @ S2 @ S7 ) ) )
% 9.17/5.41 => ( ! [A3: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ A3 @ S7 )
% 9.17/5.41 => ( ( G @ A3 )
% 9.17/5.41 = one_one_Code_integer ) )
% 9.17/5.41 => ( ! [B2: int] :
% 9.17/5.41 ( ( member_int @ B2 @ T4 )
% 9.17/5.41 => ( ( H3 @ B2 )
% 9.17/5.41 = one_one_Code_integer ) )
% 9.17/5.41 => ( ! [A3: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ A3 @ S2 )
% 9.17/5.41 => ( ( H3 @ ( J @ A3 ) )
% 9.17/5.41 = ( G @ A3 ) ) )
% 9.17/5.41 => ( ( groups3674199335183972705nteger @ G @ S2 )
% 9.17/5.41 = ( groups3827104343326376752nteger @ H3 @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5830_prod_Oreindex__bij__witness__not__neutral,axiom,
% 9.17/5.41 ! [S7: set_Code_integer,T4: set_Code_integer,S2: set_Code_integer,I: code_integer > code_integer,J: code_integer > code_integer,T5: set_Code_integer,G: code_integer > code_integer,H3: code_integer > code_integer] :
% 9.17/5.41 ( ( finite6017078050557962740nteger @ S7 )
% 9.17/5.41 => ( ( finite6017078050557962740nteger @ T4 )
% 9.17/5.41 => ( ! [A3: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ A3 @ ( minus_2355218937544613996nteger @ S2 @ S7 ) )
% 9.17/5.41 => ( ( I @ ( J @ A3 ) )
% 9.17/5.41 = A3 ) )
% 9.17/5.41 => ( ! [A3: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ A3 @ ( minus_2355218937544613996nteger @ S2 @ S7 ) )
% 9.17/5.41 => ( member_Code_integer @ ( J @ A3 ) @ ( minus_2355218937544613996nteger @ T5 @ T4 ) ) )
% 9.17/5.41 => ( ! [B2: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ B2 @ ( minus_2355218937544613996nteger @ T5 @ T4 ) )
% 9.17/5.41 => ( ( J @ ( I @ B2 ) )
% 9.17/5.41 = B2 ) )
% 9.17/5.41 => ( ! [B2: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ B2 @ ( minus_2355218937544613996nteger @ T5 @ T4 ) )
% 9.17/5.41 => ( member_Code_integer @ ( I @ B2 ) @ ( minus_2355218937544613996nteger @ S2 @ S7 ) ) )
% 9.17/5.41 => ( ! [A3: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ A3 @ S7 )
% 9.17/5.41 => ( ( G @ A3 )
% 9.17/5.41 = one_one_Code_integer ) )
% 9.17/5.41 => ( ! [B2: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ B2 @ T4 )
% 9.17/5.41 => ( ( H3 @ B2 )
% 9.17/5.41 = one_one_Code_integer ) )
% 9.17/5.41 => ( ! [A3: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ A3 @ S2 )
% 9.17/5.41 => ( ( H3 @ ( J @ A3 ) )
% 9.17/5.41 = ( G @ A3 ) ) )
% 9.17/5.41 => ( ( groups3674199335183972705nteger @ G @ S2 )
% 9.17/5.41 = ( groups3674199335183972705nteger @ H3 @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5831_prod_Oreindex__bij__witness__not__neutral,axiom,
% 9.17/5.41 ! [S7: set_o,T4: set_o,S2: set_o,I: $o > $o,J: $o > $o,T5: set_o,G: $o > assn,H3: $o > assn] :
% 9.17/5.41 ( ( finite_finite_o @ S7 )
% 9.17/5.41 => ( ( finite_finite_o @ T4 )
% 9.17/5.41 => ( ! [A3: $o] :
% 9.17/5.41 ( ( member_o @ A3 @ ( minus_minus_set_o @ S2 @ S7 ) )
% 9.17/5.41 => ( ( I @ ( J @ A3 ) )
% 9.17/5.41 = A3 ) )
% 9.17/5.41 => ( ! [A3: $o] :
% 9.17/5.41 ( ( member_o @ A3 @ ( minus_minus_set_o @ S2 @ S7 ) )
% 9.17/5.41 => ( member_o @ ( J @ A3 ) @ ( minus_minus_set_o @ T5 @ T4 ) ) )
% 9.17/5.41 => ( ! [B2: $o] :
% 9.17/5.41 ( ( member_o @ B2 @ ( minus_minus_set_o @ T5 @ T4 ) )
% 9.17/5.41 => ( ( J @ ( I @ B2 ) )
% 9.17/5.41 = B2 ) )
% 9.17/5.41 => ( ! [B2: $o] :
% 9.17/5.41 ( ( member_o @ B2 @ ( minus_minus_set_o @ T5 @ T4 ) )
% 9.17/5.41 => ( member_o @ ( I @ B2 ) @ ( minus_minus_set_o @ S2 @ S7 ) ) )
% 9.17/5.41 => ( ! [A3: $o] :
% 9.17/5.41 ( ( member_o @ A3 @ S7 )
% 9.17/5.41 => ( ( G @ A3 )
% 9.17/5.41 = one_one_assn ) )
% 9.17/5.41 => ( ! [B2: $o] :
% 9.17/5.41 ( ( member_o @ B2 @ T4 )
% 9.17/5.41 => ( ( H3 @ B2 )
% 9.17/5.41 = one_one_assn ) )
% 9.17/5.41 => ( ! [A3: $o] :
% 9.17/5.41 ( ( member_o @ A3 @ S2 )
% 9.17/5.41 => ( ( H3 @ ( J @ A3 ) )
% 9.17/5.41 = ( G @ A3 ) ) )
% 9.17/5.41 => ( ( groups5301882518646026715o_assn @ G @ S2 )
% 9.17/5.41 = ( groups5301882518646026715o_assn @ H3 @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5832_dflt__None__set__def,axiom,
% 9.17/5.41 ( dflt_N3208751546879591902at_nat
% 9.17/5.41 = ( ^ [S5: set_Pr4329608150637261639at_nat] : ( if_opt5121585740920863443at_nat @ ( S5 = bot_bo228742789529271731at_nat ) @ none_s6518873173954064040at_nat @ ( some_s5890477192898017836at_nat @ S5 ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5833_dflt__None__set__def,axiom,
% 9.17/5.41 ( dflt_N6592383573632408824at_nat
% 9.17/5.41 = ( ^ [S5: set_Pr1261947904930325089at_nat] : ( if_opt7704869406773131885at_nat @ ( S5 = bot_bo2099793752762293965at_nat ) @ none_s625347054029921090at_nat @ ( some_s147305329494351046at_nat @ S5 ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5834_dflt__None__set__def,axiom,
% 9.17/5.41 ( dflt_None_set_o
% 9.17/5.41 = ( ^ [S5: set_o] : ( if_option_set_o @ ( S5 = bot_bot_set_o ) @ none_set_o @ ( some_set_o @ S5 ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5835_dflt__None__set__def,axiom,
% 9.17/5.41 ( dflt_None_set_nat
% 9.17/5.41 = ( ^ [S5: set_nat] : ( if_option_set_nat @ ( S5 = bot_bot_set_nat ) @ none_set_nat @ ( some_set_nat @ S5 ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5836_dflt__None__set__def,axiom,
% 9.17/5.41 ( dflt_None_set_int
% 9.17/5.41 = ( ^ [S5: set_int] : ( if_option_set_int @ ( S5 = bot_bot_set_int ) @ none_set_int @ ( some_set_int @ S5 ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5837_sum__eq__1__iff,axiom,
% 9.17/5.41 ! [A2: set_int,F: int > nat] :
% 9.17/5.41 ( ( finite_finite_int @ A2 )
% 9.17/5.41 => ( ( ( groups4541462559716669496nt_nat @ F @ A2 )
% 9.17/5.41 = one_one_nat )
% 9.17/5.41 = ( ? [X3: int] :
% 9.17/5.41 ( ( member_int @ X3 @ A2 )
% 9.17/5.41 & ( ( F @ X3 )
% 9.17/5.41 = one_one_nat )
% 9.17/5.41 & ! [Y3: int] :
% 9.17/5.41 ( ( member_int @ Y3 @ A2 )
% 9.17/5.41 => ( ( X3 != Y3 )
% 9.17/5.41 => ( ( F @ Y3 )
% 9.17/5.41 = zero_zero_nat ) ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5838_sum__eq__1__iff,axiom,
% 9.17/5.41 ! [A2: set_Code_integer,F: code_integer > nat] :
% 9.17/5.41 ( ( finite6017078050557962740nteger @ A2 )
% 9.17/5.41 => ( ( ( groups7237345082560585321er_nat @ F @ A2 )
% 9.17/5.41 = one_one_nat )
% 9.17/5.41 = ( ? [X3: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ X3 @ A2 )
% 9.17/5.41 & ( ( F @ X3 )
% 9.17/5.41 = one_one_nat )
% 9.17/5.41 & ! [Y3: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ Y3 @ A2 )
% 9.17/5.41 => ( ( X3 != Y3 )
% 9.17/5.41 => ( ( F @ Y3 )
% 9.17/5.41 = zero_zero_nat ) ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5839_sum__eq__1__iff,axiom,
% 9.17/5.41 ! [A2: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > nat] :
% 9.17/5.41 ( ( finite6177210948735845034at_nat @ A2 )
% 9.17/5.41 => ( ( ( groups977919841031483927at_nat @ F @ A2 )
% 9.17/5.41 = one_one_nat )
% 9.17/5.41 = ( ? [X3: product_prod_nat_nat] :
% 9.17/5.41 ( ( member8440522571783428010at_nat @ X3 @ A2 )
% 9.17/5.41 & ( ( F @ X3 )
% 9.17/5.41 = one_one_nat )
% 9.17/5.41 & ! [Y3: product_prod_nat_nat] :
% 9.17/5.41 ( ( member8440522571783428010at_nat @ Y3 @ A2 )
% 9.17/5.41 => ( ( X3 != Y3 )
% 9.17/5.41 => ( ( F @ Y3 )
% 9.17/5.41 = zero_zero_nat ) ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5840_sum__eq__1__iff,axiom,
% 9.17/5.41 ! [A2: set_nat,F: nat > nat] :
% 9.17/5.41 ( ( finite_finite_nat @ A2 )
% 9.17/5.41 => ( ( ( groups3542108847815614940at_nat @ F @ A2 )
% 9.17/5.41 = one_one_nat )
% 9.17/5.41 = ( ? [X3: nat] :
% 9.17/5.41 ( ( member_nat @ X3 @ A2 )
% 9.17/5.41 & ( ( F @ X3 )
% 9.17/5.41 = one_one_nat )
% 9.17/5.41 & ! [Y3: nat] :
% 9.17/5.41 ( ( member_nat @ Y3 @ A2 )
% 9.17/5.41 => ( ( X3 != Y3 )
% 9.17/5.41 => ( ( F @ Y3 )
% 9.17/5.41 = zero_zero_nat ) ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5841_surj__Compl__image__subset,axiom,
% 9.17/5.41 ! [F: nat > code_integer,A2: set_nat] :
% 9.17/5.41 ( ( ( image_1215581382706833972nteger @ F @ top_top_set_nat )
% 9.17/5.41 = top_to4645266643341252675nteger )
% 9.17/5.41 => ( ord_le7084787975880047091nteger @ ( uminus804700908173204444nteger @ ( image_1215581382706833972nteger @ F @ A2 ) ) @ ( image_1215581382706833972nteger @ F @ ( uminus5710092332889474511et_nat @ A2 ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5842_surj__Compl__image__subset,axiom,
% 9.17/5.41 ! [F: nat > product_unit,A2: set_nat] :
% 9.17/5.41 ( ( ( image_8730104196221521654t_unit @ F @ top_top_set_nat )
% 9.17/5.41 = top_to1996260823553986621t_unit )
% 9.17/5.41 => ( ord_le3507040750410214029t_unit @ ( uminus5944136376168626660t_unit @ ( image_8730104196221521654t_unit @ F @ A2 ) ) @ ( image_8730104196221521654t_unit @ F @ ( uminus5710092332889474511et_nat @ A2 ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5843_surj__Compl__image__subset,axiom,
% 9.17/5.41 ! [F: nat > int,A2: set_nat] :
% 9.17/5.41 ( ( ( image_nat_int @ F @ top_top_set_nat )
% 9.17/5.41 = top_top_set_int )
% 9.17/5.41 => ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ ( image_nat_int @ F @ A2 ) ) @ ( image_nat_int @ F @ ( uminus5710092332889474511et_nat @ A2 ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5844_surj__Compl__image__subset,axiom,
% 9.17/5.41 ! [F: product_unit > product_unit,A2: set_Product_unit] :
% 9.17/5.41 ( ( ( image_405062704495631173t_unit @ F @ top_to1996260823553986621t_unit )
% 9.17/5.41 = top_to1996260823553986621t_unit )
% 9.17/5.41 => ( ord_le3507040750410214029t_unit @ ( uminus5944136376168626660t_unit @ ( image_405062704495631173t_unit @ F @ A2 ) ) @ ( image_405062704495631173t_unit @ F @ ( uminus5944136376168626660t_unit @ A2 ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5845_surj__Compl__image__subset,axiom,
% 9.17/5.41 ! [F: product_unit > int,A2: set_Product_unit] :
% 9.17/5.41 ( ( ( image_873079544045703924it_int @ F @ top_to1996260823553986621t_unit )
% 9.17/5.41 = top_top_set_int )
% 9.17/5.41 => ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ ( image_873079544045703924it_int @ F @ A2 ) ) @ ( image_873079544045703924it_int @ F @ ( uminus5944136376168626660t_unit @ A2 ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5846_surj__Compl__image__subset,axiom,
% 9.17/5.41 ! [F: int > product_unit,A2: set_int] :
% 9.17/5.41 ( ( ( image_5846526143423701914t_unit @ F @ top_top_set_int )
% 9.17/5.41 = top_to1996260823553986621t_unit )
% 9.17/5.41 => ( ord_le3507040750410214029t_unit @ ( uminus5944136376168626660t_unit @ ( image_5846526143423701914t_unit @ F @ A2 ) ) @ ( image_5846526143423701914t_unit @ F @ ( uminus1532241313380277803et_int @ A2 ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5847_surj__Compl__image__subset,axiom,
% 9.17/5.41 ! [F: int > int,A2: set_int] :
% 9.17/5.41 ( ( ( image_int_int @ F @ top_top_set_int )
% 9.17/5.41 = top_top_set_int )
% 9.17/5.41 => ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ ( image_int_int @ F @ A2 ) ) @ ( image_int_int @ F @ ( uminus1532241313380277803et_int @ A2 ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5848_surj__Compl__image__subset,axiom,
% 9.17/5.41 ! [F: nat > nat,A2: set_nat] :
% 9.17/5.41 ( ( ( image_nat_nat @ F @ top_top_set_nat )
% 9.17/5.41 = top_top_set_nat )
% 9.17/5.41 => ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ ( image_nat_nat @ F @ A2 ) ) @ ( image_nat_nat @ F @ ( uminus5710092332889474511et_nat @ A2 ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5849_surj__Compl__image__subset,axiom,
% 9.17/5.41 ! [F: product_unit > nat,A2: set_Product_unit] :
% 9.17/5.41 ( ( ( image_875570014554754200it_nat @ F @ top_to1996260823553986621t_unit )
% 9.17/5.41 = top_top_set_nat )
% 9.17/5.41 => ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ ( image_875570014554754200it_nat @ F @ A2 ) ) @ ( image_875570014554754200it_nat @ F @ ( uminus5944136376168626660t_unit @ A2 ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5850_surj__Compl__image__subset,axiom,
% 9.17/5.41 ! [F: int > nat,A2: set_int] :
% 9.17/5.41 ( ( ( image_int_nat @ F @ top_top_set_int )
% 9.17/5.41 = top_top_set_nat )
% 9.17/5.41 => ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ ( image_int_nat @ F @ A2 ) ) @ ( image_int_nat @ F @ ( uminus1532241313380277803et_int @ A2 ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5851_card__atLeastZeroLessThan__int,axiom,
% 9.17/5.41 ! [U: int] :
% 9.17/5.41 ( ( finite_card_int @ ( set_or4662586982721622107an_int @ zero_zero_int @ U ) )
% 9.17/5.41 = ( nat2 @ U ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5852_atMost__nat__numeral,axiom,
% 9.17/5.41 ! [K: num] :
% 9.17/5.41 ( ( set_ord_atMost_nat @ ( numeral_numeral_nat @ K ) )
% 9.17/5.41 = ( insert_nat @ ( numeral_numeral_nat @ K ) @ ( set_ord_atMost_nat @ ( pred_numeral @ K ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5853_lessThan__nat__numeral,axiom,
% 9.17/5.41 ! [K: num] :
% 9.17/5.41 ( ( set_ord_lessThan_nat @ ( numeral_numeral_nat @ K ) )
% 9.17/5.41 = ( insert_nat @ ( pred_numeral @ K ) @ ( set_ord_lessThan_nat @ ( pred_numeral @ K ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5854_sum__Suc,axiom,
% 9.17/5.41 ! [F: int > nat,A2: set_int] :
% 9.17/5.41 ( ( groups4541462559716669496nt_nat
% 9.17/5.41 @ ^ [X3: int] : ( suc @ ( F @ X3 ) )
% 9.17/5.41 @ A2 )
% 9.17/5.41 = ( plus_plus_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ ( finite_card_int @ A2 ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5855_sum__Suc,axiom,
% 9.17/5.41 ! [F: product_unit > nat,A2: set_Product_unit] :
% 9.17/5.41 ( ( groups8766797177574957219it_nat
% 9.17/5.41 @ ^ [X3: product_unit] : ( suc @ ( F @ X3 ) )
% 9.17/5.41 @ A2 )
% 9.17/5.41 = ( plus_plus_nat @ ( groups8766797177574957219it_nat @ F @ A2 ) @ ( finite410649719033368117t_unit @ A2 ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5856_sum__Suc,axiom,
% 9.17/5.41 ! [F: list_nat > nat,A2: set_list_nat] :
% 9.17/5.41 ( ( groups4396056296759096172at_nat
% 9.17/5.41 @ ^ [X3: list_nat] : ( suc @ ( F @ X3 ) )
% 9.17/5.41 @ A2 )
% 9.17/5.41 = ( plus_plus_nat @ ( groups4396056296759096172at_nat @ F @ A2 ) @ ( finite_card_list_nat @ A2 ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5857_sum__Suc,axiom,
% 9.17/5.41 ! [F: nat > nat,A2: set_nat] :
% 9.17/5.41 ( ( groups3542108847815614940at_nat
% 9.17/5.41 @ ^ [X3: nat] : ( suc @ ( F @ X3 ) )
% 9.17/5.41 @ A2 )
% 9.17/5.41 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ ( finite_card_nat @ A2 ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5858_prod_Osetdiff__irrelevant,axiom,
% 9.17/5.41 ! [A2: set_int,G: int > code_integer] :
% 9.17/5.41 ( ( finite_finite_int @ A2 )
% 9.17/5.41 => ( ( groups3827104343326376752nteger @ G
% 9.17/5.41 @ ( minus_minus_set_int @ A2
% 9.17/5.41 @ ( collect_int
% 9.17/5.41 @ ^ [X3: int] :
% 9.17/5.41 ( ( G @ X3 )
% 9.17/5.41 = one_one_Code_integer ) ) ) )
% 9.17/5.41 = ( groups3827104343326376752nteger @ G @ A2 ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5859_prod_Osetdiff__irrelevant,axiom,
% 9.17/5.41 ! [A2: set_Code_integer,G: code_integer > code_integer] :
% 9.17/5.41 ( ( finite6017078050557962740nteger @ A2 )
% 9.17/5.41 => ( ( groups3674199335183972705nteger @ G
% 9.17/5.41 @ ( minus_2355218937544613996nteger @ A2
% 9.17/5.41 @ ( collect_Code_integer
% 9.17/5.41 @ ^ [X3: code_integer] :
% 9.17/5.41 ( ( G @ X3 )
% 9.17/5.41 = one_one_Code_integer ) ) ) )
% 9.17/5.41 = ( groups3674199335183972705nteger @ G @ A2 ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5860_prod_Osetdiff__irrelevant,axiom,
% 9.17/5.41 ! [A2: set_int,G: int > assn] :
% 9.17/5.41 ( ( finite_finite_int @ A2 )
% 9.17/5.41 => ( ( groups7882442080178216443t_assn @ G
% 9.17/5.41 @ ( minus_minus_set_int @ A2
% 9.17/5.41 @ ( collect_int
% 9.17/5.41 @ ^ [X3: int] :
% 9.17/5.41 ( ( G @ X3 )
% 9.17/5.41 = one_one_assn ) ) ) )
% 9.17/5.41 = ( groups7882442080178216443t_assn @ G @ A2 ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5861_prod_Osetdiff__irrelevant,axiom,
% 9.17/5.41 ! [A2: set_Code_integer,G: code_integer > assn] :
% 9.17/5.41 ( ( finite6017078050557962740nteger @ A2 )
% 9.17/5.41 => ( ( groups1304777262505850412r_assn @ G
% 9.17/5.41 @ ( minus_2355218937544613996nteger @ A2
% 9.17/5.41 @ ( collect_Code_integer
% 9.17/5.41 @ ^ [X3: code_integer] :
% 9.17/5.41 ( ( G @ X3 )
% 9.17/5.41 = one_one_assn ) ) ) )
% 9.17/5.41 = ( groups1304777262505850412r_assn @ G @ A2 ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5862_prod_Osetdiff__irrelevant,axiom,
% 9.17/5.41 ! [A2: set_int,G: int > rat] :
% 9.17/5.41 ( ( finite_finite_int @ A2 )
% 9.17/5.41 => ( ( groups1072433553688619179nt_rat @ G
% 9.17/5.41 @ ( minus_minus_set_int @ A2
% 9.17/5.41 @ ( collect_int
% 9.17/5.41 @ ^ [X3: int] :
% 9.17/5.41 ( ( G @ X3 )
% 9.17/5.41 = one_one_rat ) ) ) )
% 9.17/5.41 = ( groups1072433553688619179nt_rat @ G @ A2 ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5863_prod_Osetdiff__irrelevant,axiom,
% 9.17/5.41 ! [A2: set_Code_integer,G: code_integer > rat] :
% 9.17/5.41 ( ( finite6017078050557962740nteger @ A2 )
% 9.17/5.41 => ( ( groups2555765274223993564er_rat @ G
% 9.17/5.41 @ ( minus_2355218937544613996nteger @ A2
% 9.17/5.41 @ ( collect_Code_integer
% 9.17/5.41 @ ^ [X3: code_integer] :
% 9.17/5.41 ( ( G @ X3 )
% 9.17/5.41 = one_one_rat ) ) ) )
% 9.17/5.41 = ( groups2555765274223993564er_rat @ G @ A2 ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5864_prod_Osetdiff__irrelevant,axiom,
% 9.17/5.41 ! [A2: set_int,G: int > nat] :
% 9.17/5.41 ( ( finite_finite_int @ A2 )
% 9.17/5.41 => ( ( groups1707563613775114915nt_nat @ G
% 9.17/5.41 @ ( minus_minus_set_int @ A2
% 9.17/5.41 @ ( collect_int
% 9.17/5.41 @ ^ [X3: int] :
% 9.17/5.41 ( ( G @ X3 )
% 9.17/5.41 = one_one_nat ) ) ) )
% 9.17/5.41 = ( groups1707563613775114915nt_nat @ G @ A2 ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5865_prod_Osetdiff__irrelevant,axiom,
% 9.17/5.41 ! [A2: set_Code_integer,G: code_integer > nat] :
% 9.17/5.41 ( ( finite6017078050557962740nteger @ A2 )
% 9.17/5.41 => ( ( groups3190895334310489300er_nat @ G
% 9.17/5.41 @ ( minus_2355218937544613996nteger @ A2
% 9.17/5.41 @ ( collect_Code_integer
% 9.17/5.41 @ ^ [X3: code_integer] :
% 9.17/5.41 ( ( G @ X3 )
% 9.17/5.41 = one_one_nat ) ) ) )
% 9.17/5.41 = ( groups3190895334310489300er_nat @ G @ A2 ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5866_prod_Osetdiff__irrelevant,axiom,
% 9.17/5.41 ! [A2: set_Code_integer,G: code_integer > int] :
% 9.17/5.41 ( ( finite6017078050557962740nteger @ A2 )
% 9.17/5.41 => ( ( groups3188404863801439024er_int @ G
% 9.17/5.41 @ ( minus_2355218937544613996nteger @ A2
% 9.17/5.41 @ ( collect_Code_integer
% 9.17/5.41 @ ^ [X3: code_integer] :
% 9.17/5.41 ( ( G @ X3 )
% 9.17/5.41 = one_one_int ) ) ) )
% 9.17/5.41 = ( groups3188404863801439024er_int @ G @ A2 ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5867_prod_Osetdiff__irrelevant,axiom,
% 9.17/5.41 ! [A2: set_nat,G: nat > code_integer] :
% 9.17/5.41 ( ( finite_finite_nat @ A2 )
% 9.17/5.41 => ( ( groups3455450783089532116nteger @ G
% 9.17/5.41 @ ( minus_minus_set_nat @ A2
% 9.17/5.41 @ ( collect_nat
% 9.17/5.41 @ ^ [X3: nat] :
% 9.17/5.41 ( ( G @ X3 )
% 9.17/5.41 = one_one_Code_integer ) ) ) )
% 9.17/5.41 = ( groups3455450783089532116nteger @ G @ A2 ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5868_notin__range__Some,axiom,
% 9.17/5.41 ! [X: option3216581401566546698it_nat] :
% 9.17/5.41 ( ( ~ ( member3517700364412436275it_nat @ X @ ( image_4799632500972785611it_nat @ some_P6105628898608307625it_nat @ top_to3995162779041354868it_nat ) ) )
% 9.17/5.41 = ( X = none_P2587165478634041381it_nat ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5869_notin__range__Some,axiom,
% 9.17/5.41 ! [X: option_num] :
% 9.17/5.41 ( ( ~ ( member_option_num @ X @ ( image_num_option_num @ some_num @ top_top_set_num ) ) )
% 9.17/5.41 = ( X = none_num ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5870_notin__range__Some,axiom,
% 9.17/5.41 ! [X: option8956607266484857688it_nat] :
% 9.17/5.41 ( ( ~ ( member5596548051065438575it_nat @ X @ ( image_3455408117458022631it_nat @ some_P1914260805536162275it_nat @ top_to4082048134677576814it_nat ) ) )
% 9.17/5.41 = ( X = none_P9117596204409417319it_nat ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5871_notin__range__Some,axiom,
% 9.17/5.41 ! [X: option_nat] :
% 9.17/5.41 ( ( ~ ( member_option_nat @ X @ ( image_nat_option_nat @ some_nat @ top_top_set_nat ) ) )
% 9.17/5.41 = ( X = none_nat ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5872_notin__range__Some,axiom,
% 9.17/5.41 ! [X: option_Product_unit] :
% 9.17/5.41 ( ( ~ ( member1378114217278917244t_unit @ X @ ( image_7094380055901048587t_unit @ some_Product_unit @ top_to1996260823553986621t_unit ) ) )
% 9.17/5.41 = ( X = none_Product_unit ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5873_notin__range__Some,axiom,
% 9.17/5.41 ! [X: option_int] :
% 9.17/5.41 ( ( ~ ( member_option_int @ X @ ( image_int_option_int @ some_int @ top_top_set_int ) ) )
% 9.17/5.41 = ( X = none_int ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5874_less__1__prod2,axiom,
% 9.17/5.41 ! [I4: set_o,I: $o,F: $o > code_integer] :
% 9.17/5.41 ( ( finite_finite_o @ I4 )
% 9.17/5.41 => ( ( member_o @ I @ I4 )
% 9.17/5.41 => ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( F @ I ) )
% 9.17/5.41 => ( ! [I2: $o] :
% 9.17/5.41 ( ( member_o @ I2 @ I4 )
% 9.17/5.41 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F @ I2 ) ) )
% 9.17/5.41 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( groups7694694392188491536nteger @ F @ I4 ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5875_less__1__prod2,axiom,
% 9.17/5.41 ! [I4: set_nat,I: nat,F: nat > code_integer] :
% 9.17/5.41 ( ( finite_finite_nat @ I4 )
% 9.17/5.41 => ( ( member_nat @ I @ I4 )
% 9.17/5.41 => ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( F @ I ) )
% 9.17/5.41 => ( ! [I2: nat] :
% 9.17/5.41 ( ( member_nat @ I2 @ I4 )
% 9.17/5.41 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F @ I2 ) ) )
% 9.17/5.41 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( groups3455450783089532116nteger @ F @ I4 ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5876_less__1__prod2,axiom,
% 9.17/5.41 ! [I4: set_int,I: int,F: int > code_integer] :
% 9.17/5.41 ( ( finite_finite_int @ I4 )
% 9.17/5.41 => ( ( member_int @ I @ I4 )
% 9.17/5.41 => ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( F @ I ) )
% 9.17/5.41 => ( ! [I2: int] :
% 9.17/5.41 ( ( member_int @ I2 @ I4 )
% 9.17/5.41 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F @ I2 ) ) )
% 9.17/5.41 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( groups3827104343326376752nteger @ F @ I4 ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5877_less__1__prod2,axiom,
% 9.17/5.41 ! [I4: set_Code_integer,I: code_integer,F: code_integer > code_integer] :
% 9.17/5.41 ( ( finite6017078050557962740nteger @ I4 )
% 9.17/5.41 => ( ( member_Code_integer @ I @ I4 )
% 9.17/5.41 => ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( F @ I ) )
% 9.17/5.41 => ( ! [I2: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ I2 @ I4 )
% 9.17/5.41 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F @ I2 ) ) )
% 9.17/5.41 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( groups3674199335183972705nteger @ F @ I4 ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5878_less__1__prod2,axiom,
% 9.17/5.41 ! [I4: set_o,I: $o,F: $o > rat] :
% 9.17/5.41 ( ( finite_finite_o @ I4 )
% 9.17/5.41 => ( ( member_o @ I @ I4 )
% 9.17/5.41 => ( ( ord_less_rat @ one_one_rat @ ( F @ I ) )
% 9.17/5.41 => ( ! [I2: $o] :
% 9.17/5.41 ( ( member_o @ I2 @ I4 )
% 9.17/5.41 => ( ord_less_eq_rat @ one_one_rat @ ( F @ I2 ) ) )
% 9.17/5.41 => ( ord_less_rat @ one_one_rat @ ( groups2869687844427037835_o_rat @ F @ I4 ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5879_less__1__prod2,axiom,
% 9.17/5.41 ! [I4: set_nat,I: nat,F: nat > rat] :
% 9.17/5.41 ( ( finite_finite_nat @ I4 )
% 9.17/5.41 => ( ( member_nat @ I @ I4 )
% 9.17/5.41 => ( ( ord_less_rat @ one_one_rat @ ( F @ I ) )
% 9.17/5.41 => ( ! [I2: nat] :
% 9.17/5.41 ( ( member_nat @ I2 @ I4 )
% 9.17/5.41 => ( ord_less_eq_rat @ one_one_rat @ ( F @ I2 ) ) )
% 9.17/5.41 => ( ord_less_rat @ one_one_rat @ ( groups73079841787564623at_rat @ F @ I4 ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5880_less__1__prod2,axiom,
% 9.17/5.41 ! [I4: set_int,I: int,F: int > rat] :
% 9.17/5.41 ( ( finite_finite_int @ I4 )
% 9.17/5.41 => ( ( member_int @ I @ I4 )
% 9.17/5.41 => ( ( ord_less_rat @ one_one_rat @ ( F @ I ) )
% 9.17/5.41 => ( ! [I2: int] :
% 9.17/5.41 ( ( member_int @ I2 @ I4 )
% 9.17/5.41 => ( ord_less_eq_rat @ one_one_rat @ ( F @ I2 ) ) )
% 9.17/5.41 => ( ord_less_rat @ one_one_rat @ ( groups1072433553688619179nt_rat @ F @ I4 ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5881_less__1__prod2,axiom,
% 9.17/5.41 ! [I4: set_Code_integer,I: code_integer,F: code_integer > rat] :
% 9.17/5.41 ( ( finite6017078050557962740nteger @ I4 )
% 9.17/5.41 => ( ( member_Code_integer @ I @ I4 )
% 9.17/5.41 => ( ( ord_less_rat @ one_one_rat @ ( F @ I ) )
% 9.17/5.41 => ( ! [I2: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ I2 @ I4 )
% 9.17/5.41 => ( ord_less_eq_rat @ one_one_rat @ ( F @ I2 ) ) )
% 9.17/5.41 => ( ord_less_rat @ one_one_rat @ ( groups2555765274223993564er_rat @ F @ I4 ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5882_less__1__prod2,axiom,
% 9.17/5.41 ! [I4: set_o,I: $o,F: $o > int] :
% 9.17/5.41 ( ( finite_finite_o @ I4 )
% 9.17/5.41 => ( ( member_o @ I @ I4 )
% 9.17/5.41 => ( ( ord_less_int @ one_one_int @ ( F @ I ) )
% 9.17/5.41 => ( ! [I2: $o] :
% 9.17/5.41 ( ( member_o @ I2 @ I4 )
% 9.17/5.41 => ( ord_less_eq_int @ one_one_int @ ( F @ I2 ) ) )
% 9.17/5.41 => ( ord_less_int @ one_one_int @ ( groups3502327434004483295_o_int @ F @ I4 ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5883_less__1__prod2,axiom,
% 9.17/5.41 ! [I4: set_Code_integer,I: code_integer,F: code_integer > int] :
% 9.17/5.41 ( ( finite6017078050557962740nteger @ I4 )
% 9.17/5.41 => ( ( member_Code_integer @ I @ I4 )
% 9.17/5.41 => ( ( ord_less_int @ one_one_int @ ( F @ I ) )
% 9.17/5.41 => ( ! [I2: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ I2 @ I4 )
% 9.17/5.41 => ( ord_less_eq_int @ one_one_int @ ( F @ I2 ) ) )
% 9.17/5.41 => ( ord_less_int @ one_one_int @ ( groups3188404863801439024er_int @ F @ I4 ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5884_less__1__prod,axiom,
% 9.17/5.41 ! [I4: set_Code_integer,F: code_integer > code_integer] :
% 9.17/5.41 ( ( finite6017078050557962740nteger @ I4 )
% 9.17/5.41 => ( ( I4 != bot_bo3990330152332043303nteger )
% 9.17/5.41 => ( ! [I2: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ I2 @ I4 )
% 9.17/5.41 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( F @ I2 ) ) )
% 9.17/5.41 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( groups3674199335183972705nteger @ F @ I4 ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5885_less__1__prod,axiom,
% 9.17/5.41 ! [I4: set_o,F: $o > code_integer] :
% 9.17/5.41 ( ( finite_finite_o @ I4 )
% 9.17/5.41 => ( ( I4 != bot_bot_set_o )
% 9.17/5.41 => ( ! [I2: $o] :
% 9.17/5.41 ( ( member_o @ I2 @ I4 )
% 9.17/5.41 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( F @ I2 ) ) )
% 9.17/5.41 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( groups7694694392188491536nteger @ F @ I4 ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5886_less__1__prod,axiom,
% 9.17/5.41 ! [I4: set_nat,F: nat > code_integer] :
% 9.17/5.41 ( ( finite_finite_nat @ I4 )
% 9.17/5.41 => ( ( I4 != bot_bot_set_nat )
% 9.17/5.41 => ( ! [I2: nat] :
% 9.17/5.41 ( ( member_nat @ I2 @ I4 )
% 9.17/5.41 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( F @ I2 ) ) )
% 9.17/5.41 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( groups3455450783089532116nteger @ F @ I4 ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5887_less__1__prod,axiom,
% 9.17/5.41 ! [I4: set_int,F: int > code_integer] :
% 9.17/5.41 ( ( finite_finite_int @ I4 )
% 9.17/5.41 => ( ( I4 != bot_bot_set_int )
% 9.17/5.41 => ( ! [I2: int] :
% 9.17/5.41 ( ( member_int @ I2 @ I4 )
% 9.17/5.41 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( F @ I2 ) ) )
% 9.17/5.41 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( groups3827104343326376752nteger @ F @ I4 ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5888_less__1__prod,axiom,
% 9.17/5.41 ! [I4: set_Code_integer,F: code_integer > rat] :
% 9.17/5.41 ( ( finite6017078050557962740nteger @ I4 )
% 9.17/5.41 => ( ( I4 != bot_bo3990330152332043303nteger )
% 9.17/5.41 => ( ! [I2: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ I2 @ I4 )
% 9.17/5.41 => ( ord_less_rat @ one_one_rat @ ( F @ I2 ) ) )
% 9.17/5.41 => ( ord_less_rat @ one_one_rat @ ( groups2555765274223993564er_rat @ F @ I4 ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5889_less__1__prod,axiom,
% 9.17/5.41 ! [I4: set_o,F: $o > rat] :
% 9.17/5.41 ( ( finite_finite_o @ I4 )
% 9.17/5.41 => ( ( I4 != bot_bot_set_o )
% 9.17/5.41 => ( ! [I2: $o] :
% 9.17/5.41 ( ( member_o @ I2 @ I4 )
% 9.17/5.41 => ( ord_less_rat @ one_one_rat @ ( F @ I2 ) ) )
% 9.17/5.41 => ( ord_less_rat @ one_one_rat @ ( groups2869687844427037835_o_rat @ F @ I4 ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5890_less__1__prod,axiom,
% 9.17/5.41 ! [I4: set_nat,F: nat > rat] :
% 9.17/5.41 ( ( finite_finite_nat @ I4 )
% 9.17/5.41 => ( ( I4 != bot_bot_set_nat )
% 9.17/5.41 => ( ! [I2: nat] :
% 9.17/5.41 ( ( member_nat @ I2 @ I4 )
% 9.17/5.41 => ( ord_less_rat @ one_one_rat @ ( F @ I2 ) ) )
% 9.17/5.41 => ( ord_less_rat @ one_one_rat @ ( groups73079841787564623at_rat @ F @ I4 ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5891_less__1__prod,axiom,
% 9.17/5.41 ! [I4: set_int,F: int > rat] :
% 9.17/5.41 ( ( finite_finite_int @ I4 )
% 9.17/5.41 => ( ( I4 != bot_bot_set_int )
% 9.17/5.41 => ( ! [I2: int] :
% 9.17/5.41 ( ( member_int @ I2 @ I4 )
% 9.17/5.41 => ( ord_less_rat @ one_one_rat @ ( F @ I2 ) ) )
% 9.17/5.41 => ( ord_less_rat @ one_one_rat @ ( groups1072433553688619179nt_rat @ F @ I4 ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5892_less__1__prod,axiom,
% 9.17/5.41 ! [I4: set_Code_integer,F: code_integer > int] :
% 9.17/5.41 ( ( finite6017078050557962740nteger @ I4 )
% 9.17/5.41 => ( ( I4 != bot_bo3990330152332043303nteger )
% 9.17/5.41 => ( ! [I2: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ I2 @ I4 )
% 9.17/5.41 => ( ord_less_int @ one_one_int @ ( F @ I2 ) ) )
% 9.17/5.41 => ( ord_less_int @ one_one_int @ ( groups3188404863801439024er_int @ F @ I4 ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5893_less__1__prod,axiom,
% 9.17/5.41 ! [I4: set_o,F: $o > int] :
% 9.17/5.41 ( ( finite_finite_o @ I4 )
% 9.17/5.41 => ( ( I4 != bot_bot_set_o )
% 9.17/5.41 => ( ! [I2: $o] :
% 9.17/5.41 ( ( member_o @ I2 @ I4 )
% 9.17/5.41 => ( ord_less_int @ one_one_int @ ( F @ I2 ) ) )
% 9.17/5.41 => ( ord_less_int @ one_one_int @ ( groups3502327434004483295_o_int @ F @ I4 ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5894_sum_Oreindex__nontrivial,axiom,
% 9.17/5.41 ! [A2: set_num,H3: num > code_integer,G: code_integer > code_integer] :
% 9.17/5.41 ( ( finite_finite_num @ A2 )
% 9.17/5.41 => ( ! [X4: num,Y5: num] :
% 9.17/5.41 ( ( member_num @ X4 @ A2 )
% 9.17/5.41 => ( ( member_num @ Y5 @ A2 )
% 9.17/5.41 => ( ( X4 != Y5 )
% 9.17/5.41 => ( ( ( H3 @ X4 )
% 9.17/5.41 = ( H3 @ Y5 ) )
% 9.17/5.41 => ( ( G @ ( H3 @ X4 ) )
% 9.17/5.41 = zero_z3403309356797280102nteger ) ) ) ) )
% 9.17/5.41 => ( ( groups879477027807139574nteger @ G @ ( image_8379761247532268670nteger @ H3 @ A2 ) )
% 9.17/5.41 = ( groups5442708359310287027nteger @ ( comp_C3531382070062128313er_num @ G @ H3 ) @ A2 ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5895_sum_Oreindex__nontrivial,axiom,
% 9.17/5.41 ! [A2: set_nat,H3: nat > code_integer,G: code_integer > code_integer] :
% 9.17/5.41 ( ( finite_finite_nat @ A2 )
% 9.17/5.41 => ( ! [X4: nat,Y5: nat] :
% 9.17/5.41 ( ( member_nat @ X4 @ A2 )
% 9.17/5.41 => ( ( member_nat @ Y5 @ A2 )
% 9.17/5.41 => ( ( X4 != Y5 )
% 9.17/5.41 => ( ( ( H3 @ X4 )
% 9.17/5.41 = ( H3 @ Y5 ) )
% 9.17/5.41 => ( ( G @ ( H3 @ X4 ) )
% 9.17/5.41 = zero_z3403309356797280102nteger ) ) ) ) )
% 9.17/5.41 => ( ( groups879477027807139574nteger @ G @ ( image_1215581382706833972nteger @ H3 @ A2 ) )
% 9.17/5.41 = ( groups7501900531339628137nteger @ ( comp_C6974050283906349679er_nat @ G @ H3 ) @ A2 ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5896_sum_Oreindex__nontrivial,axiom,
% 9.17/5.41 ! [A2: set_nat,H3: nat > nat,G: nat > code_integer] :
% 9.17/5.41 ( ( finite_finite_nat @ A2 )
% 9.17/5.41 => ( ! [X4: nat,Y5: nat] :
% 9.17/5.41 ( ( member_nat @ X4 @ A2 )
% 9.17/5.41 => ( ( member_nat @ Y5 @ A2 )
% 9.17/5.41 => ( ( X4 != Y5 )
% 9.17/5.41 => ( ( ( H3 @ X4 )
% 9.17/5.41 = ( H3 @ Y5 ) )
% 9.17/5.41 => ( ( G @ ( H3 @ X4 ) )
% 9.17/5.41 = zero_z3403309356797280102nteger ) ) ) ) )
% 9.17/5.41 => ( ( groups7501900531339628137nteger @ G @ ( image_nat_nat @ H3 @ A2 ) )
% 9.17/5.41 = ( groups7501900531339628137nteger @ ( comp_n3898172953802868194er_nat @ G @ H3 ) @ A2 ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5897_sum_Oreindex__nontrivial,axiom,
% 9.17/5.41 ! [A2: set_nat,H3: nat > int,G: int > code_integer] :
% 9.17/5.41 ( ( finite_finite_nat @ A2 )
% 9.17/5.41 => ( ! [X4: nat,Y5: nat] :
% 9.17/5.41 ( ( member_nat @ X4 @ A2 )
% 9.17/5.41 => ( ( member_nat @ Y5 @ A2 )
% 9.17/5.41 => ( ( X4 != Y5 )
% 9.17/5.41 => ( ( ( H3 @ X4 )
% 9.17/5.41 = ( H3 @ Y5 ) )
% 9.17/5.41 => ( ( G @ ( H3 @ X4 ) )
% 9.17/5.41 = zero_z3403309356797280102nteger ) ) ) ) )
% 9.17/5.41 => ( ( groups7873554091576472773nteger @ G @ ( image_nat_int @ H3 @ A2 ) )
% 9.17/5.41 = ( groups7501900531339628137nteger @ ( comp_i1588355021709917246er_nat @ G @ H3 ) @ A2 ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5898_sum_Oreindex__nontrivial,axiom,
% 9.17/5.41 ! [A2: set_int,H3: int > int,G: int > code_integer] :
% 9.17/5.41 ( ( finite_finite_int @ A2 )
% 9.17/5.41 => ( ! [X4: int,Y5: int] :
% 9.17/5.41 ( ( member_int @ X4 @ A2 )
% 9.17/5.41 => ( ( member_int @ Y5 @ A2 )
% 9.17/5.41 => ( ( X4 != Y5 )
% 9.17/5.41 => ( ( ( H3 @ X4 )
% 9.17/5.41 = ( H3 @ Y5 ) )
% 9.17/5.41 => ( ( G @ ( H3 @ X4 ) )
% 9.17/5.41 = zero_z3403309356797280102nteger ) ) ) ) )
% 9.17/5.41 => ( ( groups7873554091576472773nteger @ G @ ( image_int_int @ H3 @ A2 ) )
% 9.17/5.41 = ( groups7873554091576472773nteger @ ( comp_i1585864551200866970er_int @ G @ H3 ) @ A2 ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5899_sum_Oreindex__nontrivial,axiom,
% 9.17/5.41 ! [A2: set_nat,H3: nat > code_integer,G: code_integer > rat] :
% 9.17/5.41 ( ( finite_finite_nat @ A2 )
% 9.17/5.41 => ( ! [X4: nat,Y5: nat] :
% 9.17/5.41 ( ( member_nat @ X4 @ A2 )
% 9.17/5.41 => ( ( member_nat @ Y5 @ A2 )
% 9.17/5.41 => ( ( X4 != Y5 )
% 9.17/5.41 => ( ( ( H3 @ X4 )
% 9.17/5.41 = ( H3 @ Y5 ) )
% 9.17/5.41 => ( ( G @ ( H3 @ X4 ) )
% 9.17/5.41 = zero_zero_rat ) ) ) ) )
% 9.17/5.41 => ( ( groups6602215022474089585er_rat @ G @ ( image_1215581382706833972nteger @ H3 @ A2 ) )
% 9.17/5.41 = ( groups2906978787729119204at_rat @ ( comp_C3733001951728184298at_nat @ G @ H3 ) @ A2 ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5900_sum_Oreindex__nontrivial,axiom,
% 9.17/5.41 ! [A2: set_nat,H3: nat > nat,G: nat > rat] :
% 9.17/5.41 ( ( finite_finite_nat @ A2 )
% 9.17/5.41 => ( ! [X4: nat,Y5: nat] :
% 9.17/5.41 ( ( member_nat @ X4 @ A2 )
% 9.17/5.41 => ( ( member_nat @ Y5 @ A2 )
% 9.17/5.41 => ( ( X4 != Y5 )
% 9.17/5.41 => ( ( ( H3 @ X4 )
% 9.17/5.41 = ( H3 @ Y5 ) )
% 9.17/5.41 => ( ( G @ ( H3 @ X4 ) )
% 9.17/5.41 = zero_zero_rat ) ) ) ) )
% 9.17/5.41 => ( ( groups2906978787729119204at_rat @ G @ ( image_nat_nat @ H3 @ A2 ) )
% 9.17/5.41 = ( groups2906978787729119204at_rat @ ( comp_nat_rat_nat @ G @ H3 ) @ A2 ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5901_sum_Oreindex__nontrivial,axiom,
% 9.17/5.41 ! [A2: set_nat,H3: nat > int,G: int > rat] :
% 9.17/5.41 ( ( finite_finite_nat @ A2 )
% 9.17/5.41 => ( ! [X4: nat,Y5: nat] :
% 9.17/5.41 ( ( member_nat @ X4 @ A2 )
% 9.17/5.41 => ( ( member_nat @ Y5 @ A2 )
% 9.17/5.41 => ( ( X4 != Y5 )
% 9.17/5.41 => ( ( ( H3 @ X4 )
% 9.17/5.41 = ( H3 @ Y5 ) )
% 9.17/5.41 => ( ( G @ ( H3 @ X4 ) )
% 9.17/5.41 = zero_zero_rat ) ) ) ) )
% 9.17/5.41 => ( ( groups3906332499630173760nt_rat @ G @ ( image_nat_int @ H3 @ A2 ) )
% 9.17/5.41 = ( groups2906978787729119204at_rat @ ( comp_int_rat_nat @ G @ H3 ) @ A2 ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5902_sum_Oreindex__nontrivial,axiom,
% 9.17/5.41 ! [A2: set_int,H3: int > int,G: int > rat] :
% 9.17/5.41 ( ( finite_finite_int @ A2 )
% 9.17/5.41 => ( ! [X4: int,Y5: int] :
% 9.17/5.41 ( ( member_int @ X4 @ A2 )
% 9.17/5.41 => ( ( member_int @ Y5 @ A2 )
% 9.17/5.41 => ( ( X4 != Y5 )
% 9.17/5.41 => ( ( ( H3 @ X4 )
% 9.17/5.41 = ( H3 @ Y5 ) )
% 9.17/5.41 => ( ( G @ ( H3 @ X4 ) )
% 9.17/5.41 = zero_zero_rat ) ) ) ) )
% 9.17/5.41 => ( ( groups3906332499630173760nt_rat @ G @ ( image_int_int @ H3 @ A2 ) )
% 9.17/5.41 = ( groups3906332499630173760nt_rat @ ( comp_int_rat_int @ G @ H3 ) @ A2 ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5903_sum_Oreindex__nontrivial,axiom,
% 9.17/5.41 ! [A2: set_int,H3: int > int,G: int > nat] :
% 9.17/5.41 ( ( finite_finite_int @ A2 )
% 9.17/5.41 => ( ! [X4: int,Y5: int] :
% 9.17/5.41 ( ( member_int @ X4 @ A2 )
% 9.17/5.41 => ( ( member_int @ Y5 @ A2 )
% 9.17/5.41 => ( ( X4 != Y5 )
% 9.17/5.41 => ( ( ( H3 @ X4 )
% 9.17/5.41 = ( H3 @ Y5 ) )
% 9.17/5.41 => ( ( G @ ( H3 @ X4 ) )
% 9.17/5.41 = zero_zero_nat ) ) ) ) )
% 9.17/5.41 => ( ( groups4541462559716669496nt_nat @ G @ ( image_int_int @ H3 @ A2 ) )
% 9.17/5.41 = ( groups4541462559716669496nt_nat @ ( comp_int_nat_int @ G @ H3 ) @ A2 ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5904_prod_Oreindex__nontrivial,axiom,
% 9.17/5.41 ! [A2: set_num,H3: num > code_integer,G: code_integer > code_integer] :
% 9.17/5.41 ( ( finite_finite_num @ A2 )
% 9.17/5.41 => ( ! [X4: num,Y5: num] :
% 9.17/5.41 ( ( member_num @ X4 @ A2 )
% 9.17/5.41 => ( ( member_num @ Y5 @ A2 )
% 9.17/5.41 => ( ( X4 != Y5 )
% 9.17/5.41 => ( ( ( H3 @ X4 )
% 9.17/5.41 = ( H3 @ Y5 ) )
% 9.17/5.41 => ( ( G @ ( H3 @ X4 ) )
% 9.17/5.41 = one_one_Code_integer ) ) ) ) )
% 9.17/5.41 => ( ( groups3674199335183972705nteger @ G @ ( image_8379761247532268670nteger @ H3 @ A2 ) )
% 9.17/5.41 = ( groups1396258611060191006nteger @ ( comp_C3531382070062128313er_num @ G @ H3 ) @ A2 ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5905_prod_Oreindex__nontrivial,axiom,
% 9.17/5.41 ! [A2: set_nat,H3: nat > code_integer,G: code_integer > code_integer] :
% 9.17/5.41 ( ( finite_finite_nat @ A2 )
% 9.17/5.41 => ( ! [X4: nat,Y5: nat] :
% 9.17/5.41 ( ( member_nat @ X4 @ A2 )
% 9.17/5.41 => ( ( member_nat @ Y5 @ A2 )
% 9.17/5.41 => ( ( X4 != Y5 )
% 9.17/5.41 => ( ( ( H3 @ X4 )
% 9.17/5.41 = ( H3 @ Y5 ) )
% 9.17/5.41 => ( ( G @ ( H3 @ X4 ) )
% 9.17/5.41 = one_one_Code_integer ) ) ) ) )
% 9.17/5.41 => ( ( groups3674199335183972705nteger @ G @ ( image_1215581382706833972nteger @ H3 @ A2 ) )
% 9.17/5.41 = ( groups3455450783089532116nteger @ ( comp_C6974050283906349679er_nat @ G @ H3 ) @ A2 ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5906_prod_Oreindex__nontrivial,axiom,
% 9.17/5.41 ! [A2: set_nat,H3: nat > nat,G: nat > code_integer] :
% 9.17/5.41 ( ( finite_finite_nat @ A2 )
% 9.17/5.41 => ( ! [X4: nat,Y5: nat] :
% 9.17/5.41 ( ( member_nat @ X4 @ A2 )
% 9.17/5.41 => ( ( member_nat @ Y5 @ A2 )
% 9.17/5.41 => ( ( X4 != Y5 )
% 9.17/5.41 => ( ( ( H3 @ X4 )
% 9.17/5.41 = ( H3 @ Y5 ) )
% 9.17/5.41 => ( ( G @ ( H3 @ X4 ) )
% 9.17/5.41 = one_one_Code_integer ) ) ) ) )
% 9.17/5.41 => ( ( groups3455450783089532116nteger @ G @ ( image_nat_nat @ H3 @ A2 ) )
% 9.17/5.41 = ( groups3455450783089532116nteger @ ( comp_n3898172953802868194er_nat @ G @ H3 ) @ A2 ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5907_prod_Oreindex__nontrivial,axiom,
% 9.17/5.41 ! [A2: set_nat,H3: nat > int,G: int > code_integer] :
% 9.17/5.41 ( ( finite_finite_nat @ A2 )
% 9.17/5.41 => ( ! [X4: nat,Y5: nat] :
% 9.17/5.41 ( ( member_nat @ X4 @ A2 )
% 9.17/5.41 => ( ( member_nat @ Y5 @ A2 )
% 9.17/5.41 => ( ( X4 != Y5 )
% 9.17/5.41 => ( ( ( H3 @ X4 )
% 9.17/5.41 = ( H3 @ Y5 ) )
% 9.17/5.41 => ( ( G @ ( H3 @ X4 ) )
% 9.17/5.41 = one_one_Code_integer ) ) ) ) )
% 9.17/5.41 => ( ( groups3827104343326376752nteger @ G @ ( image_nat_int @ H3 @ A2 ) )
% 9.17/5.41 = ( groups3455450783089532116nteger @ ( comp_i1588355021709917246er_nat @ G @ H3 ) @ A2 ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5908_prod_Oreindex__nontrivial,axiom,
% 9.17/5.41 ! [A2: set_int,H3: int > int,G: int > code_integer] :
% 9.17/5.41 ( ( finite_finite_int @ A2 )
% 9.17/5.41 => ( ! [X4: int,Y5: int] :
% 9.17/5.41 ( ( member_int @ X4 @ A2 )
% 9.17/5.41 => ( ( member_int @ Y5 @ A2 )
% 9.17/5.41 => ( ( X4 != Y5 )
% 9.17/5.41 => ( ( ( H3 @ X4 )
% 9.17/5.41 = ( H3 @ Y5 ) )
% 9.17/5.41 => ( ( G @ ( H3 @ X4 ) )
% 9.17/5.41 = one_one_Code_integer ) ) ) ) )
% 9.17/5.41 => ( ( groups3827104343326376752nteger @ G @ ( image_int_int @ H3 @ A2 ) )
% 9.17/5.41 = ( groups3827104343326376752nteger @ ( comp_i1585864551200866970er_int @ G @ H3 ) @ A2 ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5909_prod_Oreindex__nontrivial,axiom,
% 9.17/5.41 ! [A2: set_nat,H3: nat > code_integer,G: code_integer > assn] :
% 9.17/5.41 ( ( finite_finite_nat @ A2 )
% 9.17/5.41 => ( ! [X4: nat,Y5: nat] :
% 9.17/5.41 ( ( member_nat @ X4 @ A2 )
% 9.17/5.41 => ( ( member_nat @ Y5 @ A2 )
% 9.17/5.41 => ( ( X4 != Y5 )
% 9.17/5.41 => ( ( ( H3 @ X4 )
% 9.17/5.41 = ( H3 @ Y5 ) )
% 9.17/5.41 => ( ( G @ ( H3 @ X4 ) )
% 9.17/5.41 = one_one_assn ) ) ) ) )
% 9.17/5.41 => ( ( groups1304777262505850412r_assn @ G @ ( image_1215581382706833972nteger @ H3 @ A2 ) )
% 9.17/5.41 = ( groups6906906614972039071t_assn @ ( comp_C8462447471145125178sn_nat @ G @ H3 ) @ A2 ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5910_prod_Oreindex__nontrivial,axiom,
% 9.17/5.41 ! [A2: set_nat,H3: nat > nat,G: nat > assn] :
% 9.17/5.41 ( ( finite_finite_nat @ A2 )
% 9.17/5.41 => ( ! [X4: nat,Y5: nat] :
% 9.17/5.41 ( ( member_nat @ X4 @ A2 )
% 9.17/5.41 => ( ( member_nat @ Y5 @ A2 )
% 9.17/5.41 => ( ( X4 != Y5 )
% 9.17/5.41 => ( ( ( H3 @ X4 )
% 9.17/5.41 = ( H3 @ Y5 ) )
% 9.17/5.41 => ( ( G @ ( H3 @ X4 ) )
% 9.17/5.41 = one_one_assn ) ) ) ) )
% 9.17/5.41 => ( ( groups6906906614972039071t_assn @ G @ ( image_nat_nat @ H3 @ A2 ) )
% 9.17/5.41 = ( groups6906906614972039071t_assn @ ( comp_nat_assn_nat @ G @ H3 ) @ A2 ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5911_prod_Oreindex__nontrivial,axiom,
% 9.17/5.41 ! [A2: set_nat,H3: nat > int,G: int > assn] :
% 9.17/5.41 ( ( finite_finite_nat @ A2 )
% 9.17/5.41 => ( ! [X4: nat,Y5: nat] :
% 9.17/5.41 ( ( member_nat @ X4 @ A2 )
% 9.17/5.41 => ( ( member_nat @ Y5 @ A2 )
% 9.17/5.41 => ( ( X4 != Y5 )
% 9.17/5.41 => ( ( ( H3 @ X4 )
% 9.17/5.41 = ( H3 @ Y5 ) )
% 9.17/5.41 => ( ( G @ ( H3 @ X4 ) )
% 9.17/5.41 = one_one_assn ) ) ) ) )
% 9.17/5.41 => ( ( groups7882442080178216443t_assn @ G @ ( image_nat_int @ H3 @ A2 ) )
% 9.17/5.41 = ( groups6906906614972039071t_assn @ ( comp_int_assn_nat @ G @ H3 ) @ A2 ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5912_prod_Oreindex__nontrivial,axiom,
% 9.17/5.41 ! [A2: set_int,H3: int > int,G: int > assn] :
% 9.17/5.41 ( ( finite_finite_int @ A2 )
% 9.17/5.41 => ( ! [X4: int,Y5: int] :
% 9.17/5.41 ( ( member_int @ X4 @ A2 )
% 9.17/5.41 => ( ( member_int @ Y5 @ A2 )
% 9.17/5.41 => ( ( X4 != Y5 )
% 9.17/5.41 => ( ( ( H3 @ X4 )
% 9.17/5.41 = ( H3 @ Y5 ) )
% 9.17/5.41 => ( ( G @ ( H3 @ X4 ) )
% 9.17/5.41 = one_one_assn ) ) ) ) )
% 9.17/5.41 => ( ( groups7882442080178216443t_assn @ G @ ( image_int_int @ H3 @ A2 ) )
% 9.17/5.41 = ( groups7882442080178216443t_assn @ ( comp_int_assn_int @ G @ H3 ) @ A2 ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5913_prod_Oreindex__nontrivial,axiom,
% 9.17/5.41 ! [A2: set_nat,H3: nat > code_integer,G: code_integer > rat] :
% 9.17/5.41 ( ( finite_finite_nat @ A2 )
% 9.17/5.41 => ( ! [X4: nat,Y5: nat] :
% 9.17/5.41 ( ( member_nat @ X4 @ A2 )
% 9.17/5.41 => ( ( member_nat @ Y5 @ A2 )
% 9.17/5.41 => ( ( X4 != Y5 )
% 9.17/5.41 => ( ( ( H3 @ X4 )
% 9.17/5.41 = ( H3 @ Y5 ) )
% 9.17/5.41 => ( ( G @ ( H3 @ X4 ) )
% 9.17/5.41 = one_one_rat ) ) ) ) )
% 9.17/5.41 => ( ( groups2555765274223993564er_rat @ G @ ( image_1215581382706833972nteger @ H3 @ A2 ) )
% 9.17/5.41 = ( groups73079841787564623at_rat @ ( comp_C3733001951728184298at_nat @ G @ H3 ) @ A2 ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5914_sum_Osubset__diff,axiom,
% 9.17/5.41 ! [B5: set_int,A2: set_int,G: int > rat] :
% 9.17/5.41 ( ( ord_less_eq_set_int @ B5 @ A2 )
% 9.17/5.41 => ( ( finite_finite_int @ A2 )
% 9.17/5.41 => ( ( groups3906332499630173760nt_rat @ G @ A2 )
% 9.17/5.41 = ( plus_plus_rat @ ( groups3906332499630173760nt_rat @ G @ ( minus_minus_set_int @ A2 @ B5 ) ) @ ( groups3906332499630173760nt_rat @ G @ B5 ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5915_sum_Osubset__diff,axiom,
% 9.17/5.41 ! [B5: set_Code_integer,A2: set_Code_integer,G: code_integer > rat] :
% 9.17/5.41 ( ( ord_le7084787975880047091nteger @ B5 @ A2 )
% 9.17/5.41 => ( ( finite6017078050557962740nteger @ A2 )
% 9.17/5.41 => ( ( groups6602215022474089585er_rat @ G @ A2 )
% 9.17/5.41 = ( plus_plus_rat @ ( groups6602215022474089585er_rat @ G @ ( minus_2355218937544613996nteger @ A2 @ B5 ) ) @ ( groups6602215022474089585er_rat @ G @ B5 ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5916_sum_Osubset__diff,axiom,
% 9.17/5.41 ! [B5: set_int,A2: set_int,G: int > nat] :
% 9.17/5.41 ( ( ord_less_eq_set_int @ B5 @ A2 )
% 9.17/5.41 => ( ( finite_finite_int @ A2 )
% 9.17/5.41 => ( ( groups4541462559716669496nt_nat @ G @ A2 )
% 9.17/5.41 = ( plus_plus_nat @ ( groups4541462559716669496nt_nat @ G @ ( minus_minus_set_int @ A2 @ B5 ) ) @ ( groups4541462559716669496nt_nat @ G @ B5 ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5917_sum_Osubset__diff,axiom,
% 9.17/5.41 ! [B5: set_Code_integer,A2: set_Code_integer,G: code_integer > nat] :
% 9.17/5.41 ( ( ord_le7084787975880047091nteger @ B5 @ A2 )
% 9.17/5.41 => ( ( finite6017078050557962740nteger @ A2 )
% 9.17/5.41 => ( ( groups7237345082560585321er_nat @ G @ A2 )
% 9.17/5.41 = ( plus_plus_nat @ ( groups7237345082560585321er_nat @ G @ ( minus_2355218937544613996nteger @ A2 @ B5 ) ) @ ( groups7237345082560585321er_nat @ G @ B5 ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5918_sum_Osubset__diff,axiom,
% 9.17/5.41 ! [B5: set_Code_integer,A2: set_Code_integer,G: code_integer > int] :
% 9.17/5.41 ( ( ord_le7084787975880047091nteger @ B5 @ A2 )
% 9.17/5.41 => ( ( finite6017078050557962740nteger @ A2 )
% 9.17/5.41 => ( ( groups7234854612051535045er_int @ G @ A2 )
% 9.17/5.41 = ( plus_plus_int @ ( groups7234854612051535045er_int @ G @ ( minus_2355218937544613996nteger @ A2 @ B5 ) ) @ ( groups7234854612051535045er_int @ G @ B5 ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5919_sum_Osubset__diff,axiom,
% 9.17/5.41 ! [B5: set_nat,A2: set_nat,G: nat > rat] :
% 9.17/5.41 ( ( ord_less_eq_set_nat @ B5 @ A2 )
% 9.17/5.41 => ( ( finite_finite_nat @ A2 )
% 9.17/5.41 => ( ( groups2906978787729119204at_rat @ G @ A2 )
% 9.17/5.41 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( minus_minus_set_nat @ A2 @ B5 ) ) @ ( groups2906978787729119204at_rat @ G @ B5 ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5920_sum_Osubset__diff,axiom,
% 9.17/5.41 ! [B5: set_nat,A2: set_nat,G: nat > int] :
% 9.17/5.41 ( ( ord_less_eq_set_nat @ B5 @ A2 )
% 9.17/5.41 => ( ( finite_finite_nat @ A2 )
% 9.17/5.41 => ( ( groups3539618377306564664at_int @ G @ A2 )
% 9.17/5.41 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( minus_minus_set_nat @ A2 @ B5 ) ) @ ( groups3539618377306564664at_int @ G @ B5 ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5921_sum_Osubset__diff,axiom,
% 9.17/5.41 ! [B5: set_nat,A2: set_nat,G: nat > nat] :
% 9.17/5.41 ( ( ord_less_eq_set_nat @ B5 @ A2 )
% 9.17/5.41 => ( ( finite_finite_nat @ A2 )
% 9.17/5.41 => ( ( groups3542108847815614940at_nat @ G @ A2 )
% 9.17/5.41 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( minus_minus_set_nat @ A2 @ B5 ) ) @ ( groups3542108847815614940at_nat @ G @ B5 ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5922_sum_Osubset__diff,axiom,
% 9.17/5.41 ! [B5: set_int,A2: set_int,G: int > int] :
% 9.17/5.41 ( ( ord_less_eq_set_int @ B5 @ A2 )
% 9.17/5.41 => ( ( finite_finite_int @ A2 )
% 9.17/5.41 => ( ( groups4538972089207619220nt_int @ G @ A2 )
% 9.17/5.41 = ( plus_plus_int @ ( groups4538972089207619220nt_int @ G @ ( minus_minus_set_int @ A2 @ B5 ) ) @ ( groups4538972089207619220nt_int @ G @ B5 ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5923_sum_Osubset__diff,axiom,
% 9.17/5.41 ! [B5: set_Pr1261947904930325089at_nat,A2: set_Pr1261947904930325089at_nat,G: product_prod_nat_nat > rat] :
% 9.17/5.41 ( ( ord_le3146513528884898305at_nat @ B5 @ A2 )
% 9.17/5.41 => ( ( finite6177210948735845034at_nat @ A2 )
% 9.17/5.41 => ( ( groups342789780944988191at_rat @ G @ A2 )
% 9.17/5.41 = ( plus_plus_rat @ ( groups342789780944988191at_rat @ G @ ( minus_1356011639430497352at_nat @ A2 @ B5 ) ) @ ( groups342789780944988191at_rat @ G @ B5 ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5924_prod_Osame__carrier,axiom,
% 9.17/5.41 ! [C4: set_o,A2: set_o,B5: set_o,G: $o > code_integer,H3: $o > code_integer] :
% 9.17/5.41 ( ( finite_finite_o @ C4 )
% 9.17/5.41 => ( ( ord_less_eq_set_o @ A2 @ C4 )
% 9.17/5.41 => ( ( ord_less_eq_set_o @ B5 @ C4 )
% 9.17/5.41 => ( ! [A3: $o] :
% 9.17/5.41 ( ( member_o @ A3 @ ( minus_minus_set_o @ C4 @ A2 ) )
% 9.17/5.41 => ( ( G @ A3 )
% 9.17/5.41 = one_one_Code_integer ) )
% 9.17/5.41 => ( ! [B2: $o] :
% 9.17/5.41 ( ( member_o @ B2 @ ( minus_minus_set_o @ C4 @ B5 ) )
% 9.17/5.41 => ( ( H3 @ B2 )
% 9.17/5.41 = one_one_Code_integer ) )
% 9.17/5.41 => ( ( ( groups7694694392188491536nteger @ G @ A2 )
% 9.17/5.41 = ( groups7694694392188491536nteger @ H3 @ B5 ) )
% 9.17/5.41 = ( ( groups7694694392188491536nteger @ G @ C4 )
% 9.17/5.41 = ( groups7694694392188491536nteger @ H3 @ C4 ) ) ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5925_prod_Osame__carrier,axiom,
% 9.17/5.41 ! [C4: set_int,A2: set_int,B5: set_int,G: int > code_integer,H3: int > code_integer] :
% 9.17/5.41 ( ( finite_finite_int @ C4 )
% 9.17/5.41 => ( ( ord_less_eq_set_int @ A2 @ C4 )
% 9.17/5.41 => ( ( ord_less_eq_set_int @ B5 @ C4 )
% 9.17/5.41 => ( ! [A3: int] :
% 9.17/5.41 ( ( member_int @ A3 @ ( minus_minus_set_int @ C4 @ A2 ) )
% 9.17/5.41 => ( ( G @ A3 )
% 9.17/5.41 = one_one_Code_integer ) )
% 9.17/5.41 => ( ! [B2: int] :
% 9.17/5.41 ( ( member_int @ B2 @ ( minus_minus_set_int @ C4 @ B5 ) )
% 9.17/5.41 => ( ( H3 @ B2 )
% 9.17/5.41 = one_one_Code_integer ) )
% 9.17/5.41 => ( ( ( groups3827104343326376752nteger @ G @ A2 )
% 9.17/5.41 = ( groups3827104343326376752nteger @ H3 @ B5 ) )
% 9.17/5.41 = ( ( groups3827104343326376752nteger @ G @ C4 )
% 9.17/5.41 = ( groups3827104343326376752nteger @ H3 @ C4 ) ) ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5926_prod_Osame__carrier,axiom,
% 9.17/5.41 ! [C4: set_Code_integer,A2: set_Code_integer,B5: set_Code_integer,G: code_integer > code_integer,H3: code_integer > code_integer] :
% 9.17/5.41 ( ( finite6017078050557962740nteger @ C4 )
% 9.17/5.41 => ( ( ord_le7084787975880047091nteger @ A2 @ C4 )
% 9.17/5.41 => ( ( ord_le7084787975880047091nteger @ B5 @ C4 )
% 9.17/5.41 => ( ! [A3: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ A3 @ ( minus_2355218937544613996nteger @ C4 @ A2 ) )
% 9.17/5.41 => ( ( G @ A3 )
% 9.17/5.41 = one_one_Code_integer ) )
% 9.17/5.41 => ( ! [B2: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ B2 @ ( minus_2355218937544613996nteger @ C4 @ B5 ) )
% 9.17/5.41 => ( ( H3 @ B2 )
% 9.17/5.41 = one_one_Code_integer ) )
% 9.17/5.41 => ( ( ( groups3674199335183972705nteger @ G @ A2 )
% 9.17/5.41 = ( groups3674199335183972705nteger @ H3 @ B5 ) )
% 9.17/5.41 = ( ( groups3674199335183972705nteger @ G @ C4 )
% 9.17/5.41 = ( groups3674199335183972705nteger @ H3 @ C4 ) ) ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5927_prod_Osame__carrier,axiom,
% 9.17/5.41 ! [C4: set_o,A2: set_o,B5: set_o,G: $o > assn,H3: $o > assn] :
% 9.17/5.41 ( ( finite_finite_o @ C4 )
% 9.17/5.41 => ( ( ord_less_eq_set_o @ A2 @ C4 )
% 9.17/5.41 => ( ( ord_less_eq_set_o @ B5 @ C4 )
% 9.17/5.41 => ( ! [A3: $o] :
% 9.17/5.41 ( ( member_o @ A3 @ ( minus_minus_set_o @ C4 @ A2 ) )
% 9.17/5.41 => ( ( G @ A3 )
% 9.17/5.41 = one_one_assn ) )
% 9.17/5.41 => ( ! [B2: $o] :
% 9.17/5.41 ( ( member_o @ B2 @ ( minus_minus_set_o @ C4 @ B5 ) )
% 9.17/5.41 => ( ( H3 @ B2 )
% 9.17/5.41 = one_one_assn ) )
% 9.17/5.41 => ( ( ( groups5301882518646026715o_assn @ G @ A2 )
% 9.17/5.41 = ( groups5301882518646026715o_assn @ H3 @ B5 ) )
% 9.17/5.41 = ( ( groups5301882518646026715o_assn @ G @ C4 )
% 9.17/5.41 = ( groups5301882518646026715o_assn @ H3 @ C4 ) ) ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5928_prod_Osame__carrier,axiom,
% 9.17/5.41 ! [C4: set_int,A2: set_int,B5: set_int,G: int > assn,H3: int > assn] :
% 9.17/5.41 ( ( finite_finite_int @ C4 )
% 9.17/5.41 => ( ( ord_less_eq_set_int @ A2 @ C4 )
% 9.17/5.41 => ( ( ord_less_eq_set_int @ B5 @ C4 )
% 9.17/5.41 => ( ! [A3: int] :
% 9.17/5.41 ( ( member_int @ A3 @ ( minus_minus_set_int @ C4 @ A2 ) )
% 9.17/5.41 => ( ( G @ A3 )
% 9.17/5.41 = one_one_assn ) )
% 9.17/5.41 => ( ! [B2: int] :
% 9.17/5.41 ( ( member_int @ B2 @ ( minus_minus_set_int @ C4 @ B5 ) )
% 9.17/5.41 => ( ( H3 @ B2 )
% 9.17/5.41 = one_one_assn ) )
% 9.17/5.41 => ( ( ( groups7882442080178216443t_assn @ G @ A2 )
% 9.17/5.41 = ( groups7882442080178216443t_assn @ H3 @ B5 ) )
% 9.17/5.41 = ( ( groups7882442080178216443t_assn @ G @ C4 )
% 9.17/5.41 = ( groups7882442080178216443t_assn @ H3 @ C4 ) ) ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5929_prod_Osame__carrier,axiom,
% 9.17/5.41 ! [C4: set_Code_integer,A2: set_Code_integer,B5: set_Code_integer,G: code_integer > assn,H3: code_integer > assn] :
% 9.17/5.41 ( ( finite6017078050557962740nteger @ C4 )
% 9.17/5.41 => ( ( ord_le7084787975880047091nteger @ A2 @ C4 )
% 9.17/5.41 => ( ( ord_le7084787975880047091nteger @ B5 @ C4 )
% 9.17/5.41 => ( ! [A3: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ A3 @ ( minus_2355218937544613996nteger @ C4 @ A2 ) )
% 9.17/5.41 => ( ( G @ A3 )
% 9.17/5.41 = one_one_assn ) )
% 9.17/5.41 => ( ! [B2: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ B2 @ ( minus_2355218937544613996nteger @ C4 @ B5 ) )
% 9.17/5.41 => ( ( H3 @ B2 )
% 9.17/5.41 = one_one_assn ) )
% 9.17/5.41 => ( ( ( groups1304777262505850412r_assn @ G @ A2 )
% 9.17/5.41 = ( groups1304777262505850412r_assn @ H3 @ B5 ) )
% 9.17/5.41 = ( ( groups1304777262505850412r_assn @ G @ C4 )
% 9.17/5.41 = ( groups1304777262505850412r_assn @ H3 @ C4 ) ) ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5930_prod_Osame__carrier,axiom,
% 9.17/5.41 ! [C4: set_o,A2: set_o,B5: set_o,G: $o > rat,H3: $o > rat] :
% 9.17/5.41 ( ( finite_finite_o @ C4 )
% 9.17/5.41 => ( ( ord_less_eq_set_o @ A2 @ C4 )
% 9.17/5.41 => ( ( ord_less_eq_set_o @ B5 @ C4 )
% 9.17/5.41 => ( ! [A3: $o] :
% 9.17/5.41 ( ( member_o @ A3 @ ( minus_minus_set_o @ C4 @ A2 ) )
% 9.17/5.41 => ( ( G @ A3 )
% 9.17/5.41 = one_one_rat ) )
% 9.17/5.41 => ( ! [B2: $o] :
% 9.17/5.41 ( ( member_o @ B2 @ ( minus_minus_set_o @ C4 @ B5 ) )
% 9.17/5.41 => ( ( H3 @ B2 )
% 9.17/5.41 = one_one_rat ) )
% 9.17/5.41 => ( ( ( groups2869687844427037835_o_rat @ G @ A2 )
% 9.17/5.41 = ( groups2869687844427037835_o_rat @ H3 @ B5 ) )
% 9.17/5.41 = ( ( groups2869687844427037835_o_rat @ G @ C4 )
% 9.17/5.41 = ( groups2869687844427037835_o_rat @ H3 @ C4 ) ) ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5931_prod_Osame__carrier,axiom,
% 9.17/5.41 ! [C4: set_int,A2: set_int,B5: set_int,G: int > rat,H3: int > rat] :
% 9.17/5.41 ( ( finite_finite_int @ C4 )
% 9.17/5.41 => ( ( ord_less_eq_set_int @ A2 @ C4 )
% 9.17/5.41 => ( ( ord_less_eq_set_int @ B5 @ C4 )
% 9.17/5.41 => ( ! [A3: int] :
% 9.17/5.41 ( ( member_int @ A3 @ ( minus_minus_set_int @ C4 @ A2 ) )
% 9.17/5.41 => ( ( G @ A3 )
% 9.17/5.41 = one_one_rat ) )
% 9.17/5.41 => ( ! [B2: int] :
% 9.17/5.41 ( ( member_int @ B2 @ ( minus_minus_set_int @ C4 @ B5 ) )
% 9.17/5.41 => ( ( H3 @ B2 )
% 9.17/5.41 = one_one_rat ) )
% 9.17/5.41 => ( ( ( groups1072433553688619179nt_rat @ G @ A2 )
% 9.17/5.41 = ( groups1072433553688619179nt_rat @ H3 @ B5 ) )
% 9.17/5.41 = ( ( groups1072433553688619179nt_rat @ G @ C4 )
% 9.17/5.41 = ( groups1072433553688619179nt_rat @ H3 @ C4 ) ) ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5932_prod_Osame__carrier,axiom,
% 9.17/5.41 ! [C4: set_Code_integer,A2: set_Code_integer,B5: set_Code_integer,G: code_integer > rat,H3: code_integer > rat] :
% 9.17/5.41 ( ( finite6017078050557962740nteger @ C4 )
% 9.17/5.41 => ( ( ord_le7084787975880047091nteger @ A2 @ C4 )
% 9.17/5.41 => ( ( ord_le7084787975880047091nteger @ B5 @ C4 )
% 9.17/5.41 => ( ! [A3: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ A3 @ ( minus_2355218937544613996nteger @ C4 @ A2 ) )
% 9.17/5.41 => ( ( G @ A3 )
% 9.17/5.41 = one_one_rat ) )
% 9.17/5.41 => ( ! [B2: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ B2 @ ( minus_2355218937544613996nteger @ C4 @ B5 ) )
% 9.17/5.41 => ( ( H3 @ B2 )
% 9.17/5.41 = one_one_rat ) )
% 9.17/5.41 => ( ( ( groups2555765274223993564er_rat @ G @ A2 )
% 9.17/5.41 = ( groups2555765274223993564er_rat @ H3 @ B5 ) )
% 9.17/5.41 = ( ( groups2555765274223993564er_rat @ G @ C4 )
% 9.17/5.41 = ( groups2555765274223993564er_rat @ H3 @ C4 ) ) ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5933_prod_Osame__carrier,axiom,
% 9.17/5.41 ! [C4: set_o,A2: set_o,B5: set_o,G: $o > nat,H3: $o > nat] :
% 9.17/5.41 ( ( finite_finite_o @ C4 )
% 9.17/5.41 => ( ( ord_less_eq_set_o @ A2 @ C4 )
% 9.17/5.41 => ( ( ord_less_eq_set_o @ B5 @ C4 )
% 9.17/5.41 => ( ! [A3: $o] :
% 9.17/5.41 ( ( member_o @ A3 @ ( minus_minus_set_o @ C4 @ A2 ) )
% 9.17/5.41 => ( ( G @ A3 )
% 9.17/5.41 = one_one_nat ) )
% 9.17/5.41 => ( ! [B2: $o] :
% 9.17/5.41 ( ( member_o @ B2 @ ( minus_minus_set_o @ C4 @ B5 ) )
% 9.17/5.41 => ( ( H3 @ B2 )
% 9.17/5.41 = one_one_nat ) )
% 9.17/5.41 => ( ( ( groups3504817904513533571_o_nat @ G @ A2 )
% 9.17/5.41 = ( groups3504817904513533571_o_nat @ H3 @ B5 ) )
% 9.17/5.41 = ( ( groups3504817904513533571_o_nat @ G @ C4 )
% 9.17/5.41 = ( groups3504817904513533571_o_nat @ H3 @ C4 ) ) ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5934_prod_Osame__carrierI,axiom,
% 9.17/5.41 ! [C4: set_o,A2: set_o,B5: set_o,G: $o > code_integer,H3: $o > code_integer] :
% 9.17/5.41 ( ( finite_finite_o @ C4 )
% 9.17/5.41 => ( ( ord_less_eq_set_o @ A2 @ C4 )
% 9.17/5.41 => ( ( ord_less_eq_set_o @ B5 @ C4 )
% 9.17/5.41 => ( ! [A3: $o] :
% 9.17/5.41 ( ( member_o @ A3 @ ( minus_minus_set_o @ C4 @ A2 ) )
% 9.17/5.41 => ( ( G @ A3 )
% 9.17/5.41 = one_one_Code_integer ) )
% 9.17/5.41 => ( ! [B2: $o] :
% 9.17/5.41 ( ( member_o @ B2 @ ( minus_minus_set_o @ C4 @ B5 ) )
% 9.17/5.41 => ( ( H3 @ B2 )
% 9.17/5.41 = one_one_Code_integer ) )
% 9.17/5.41 => ( ( ( groups7694694392188491536nteger @ G @ C4 )
% 9.17/5.41 = ( groups7694694392188491536nteger @ H3 @ C4 ) )
% 9.17/5.41 => ( ( groups7694694392188491536nteger @ G @ A2 )
% 9.17/5.41 = ( groups7694694392188491536nteger @ H3 @ B5 ) ) ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5935_prod_Osame__carrierI,axiom,
% 9.17/5.41 ! [C4: set_int,A2: set_int,B5: set_int,G: int > code_integer,H3: int > code_integer] :
% 9.17/5.41 ( ( finite_finite_int @ C4 )
% 9.17/5.41 => ( ( ord_less_eq_set_int @ A2 @ C4 )
% 9.17/5.41 => ( ( ord_less_eq_set_int @ B5 @ C4 )
% 9.17/5.41 => ( ! [A3: int] :
% 9.17/5.41 ( ( member_int @ A3 @ ( minus_minus_set_int @ C4 @ A2 ) )
% 9.17/5.41 => ( ( G @ A3 )
% 9.17/5.41 = one_one_Code_integer ) )
% 9.17/5.41 => ( ! [B2: int] :
% 9.17/5.41 ( ( member_int @ B2 @ ( minus_minus_set_int @ C4 @ B5 ) )
% 9.17/5.41 => ( ( H3 @ B2 )
% 9.17/5.41 = one_one_Code_integer ) )
% 9.17/5.41 => ( ( ( groups3827104343326376752nteger @ G @ C4 )
% 9.17/5.41 = ( groups3827104343326376752nteger @ H3 @ C4 ) )
% 9.17/5.41 => ( ( groups3827104343326376752nteger @ G @ A2 )
% 9.17/5.41 = ( groups3827104343326376752nteger @ H3 @ B5 ) ) ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5936_prod_Osame__carrierI,axiom,
% 9.17/5.41 ! [C4: set_Code_integer,A2: set_Code_integer,B5: set_Code_integer,G: code_integer > code_integer,H3: code_integer > code_integer] :
% 9.17/5.41 ( ( finite6017078050557962740nteger @ C4 )
% 9.17/5.41 => ( ( ord_le7084787975880047091nteger @ A2 @ C4 )
% 9.17/5.41 => ( ( ord_le7084787975880047091nteger @ B5 @ C4 )
% 9.17/5.41 => ( ! [A3: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ A3 @ ( minus_2355218937544613996nteger @ C4 @ A2 ) )
% 9.17/5.41 => ( ( G @ A3 )
% 9.17/5.41 = one_one_Code_integer ) )
% 9.17/5.41 => ( ! [B2: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ B2 @ ( minus_2355218937544613996nteger @ C4 @ B5 ) )
% 9.17/5.41 => ( ( H3 @ B2 )
% 9.17/5.41 = one_one_Code_integer ) )
% 9.17/5.41 => ( ( ( groups3674199335183972705nteger @ G @ C4 )
% 9.17/5.41 = ( groups3674199335183972705nteger @ H3 @ C4 ) )
% 9.17/5.41 => ( ( groups3674199335183972705nteger @ G @ A2 )
% 9.17/5.41 = ( groups3674199335183972705nteger @ H3 @ B5 ) ) ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5937_prod_Osame__carrierI,axiom,
% 9.17/5.41 ! [C4: set_o,A2: set_o,B5: set_o,G: $o > assn,H3: $o > assn] :
% 9.17/5.41 ( ( finite_finite_o @ C4 )
% 9.17/5.41 => ( ( ord_less_eq_set_o @ A2 @ C4 )
% 9.17/5.41 => ( ( ord_less_eq_set_o @ B5 @ C4 )
% 9.17/5.41 => ( ! [A3: $o] :
% 9.17/5.41 ( ( member_o @ A3 @ ( minus_minus_set_o @ C4 @ A2 ) )
% 9.17/5.41 => ( ( G @ A3 )
% 9.17/5.41 = one_one_assn ) )
% 9.17/5.41 => ( ! [B2: $o] :
% 9.17/5.41 ( ( member_o @ B2 @ ( minus_minus_set_o @ C4 @ B5 ) )
% 9.17/5.41 => ( ( H3 @ B2 )
% 9.17/5.41 = one_one_assn ) )
% 9.17/5.41 => ( ( ( groups5301882518646026715o_assn @ G @ C4 )
% 9.17/5.41 = ( groups5301882518646026715o_assn @ H3 @ C4 ) )
% 9.17/5.41 => ( ( groups5301882518646026715o_assn @ G @ A2 )
% 9.17/5.41 = ( groups5301882518646026715o_assn @ H3 @ B5 ) ) ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5938_prod_Osame__carrierI,axiom,
% 9.17/5.41 ! [C4: set_int,A2: set_int,B5: set_int,G: int > assn,H3: int > assn] :
% 9.17/5.41 ( ( finite_finite_int @ C4 )
% 9.17/5.41 => ( ( ord_less_eq_set_int @ A2 @ C4 )
% 9.17/5.41 => ( ( ord_less_eq_set_int @ B5 @ C4 )
% 9.17/5.41 => ( ! [A3: int] :
% 9.17/5.41 ( ( member_int @ A3 @ ( minus_minus_set_int @ C4 @ A2 ) )
% 9.17/5.41 => ( ( G @ A3 )
% 9.17/5.41 = one_one_assn ) )
% 9.17/5.41 => ( ! [B2: int] :
% 9.17/5.41 ( ( member_int @ B2 @ ( minus_minus_set_int @ C4 @ B5 ) )
% 9.17/5.41 => ( ( H3 @ B2 )
% 9.17/5.41 = one_one_assn ) )
% 9.17/5.41 => ( ( ( groups7882442080178216443t_assn @ G @ C4 )
% 9.17/5.41 = ( groups7882442080178216443t_assn @ H3 @ C4 ) )
% 9.17/5.41 => ( ( groups7882442080178216443t_assn @ G @ A2 )
% 9.17/5.41 = ( groups7882442080178216443t_assn @ H3 @ B5 ) ) ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5939_prod_Osame__carrierI,axiom,
% 9.17/5.41 ! [C4: set_Code_integer,A2: set_Code_integer,B5: set_Code_integer,G: code_integer > assn,H3: code_integer > assn] :
% 9.17/5.41 ( ( finite6017078050557962740nteger @ C4 )
% 9.17/5.41 => ( ( ord_le7084787975880047091nteger @ A2 @ C4 )
% 9.17/5.41 => ( ( ord_le7084787975880047091nteger @ B5 @ C4 )
% 9.17/5.41 => ( ! [A3: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ A3 @ ( minus_2355218937544613996nteger @ C4 @ A2 ) )
% 9.17/5.41 => ( ( G @ A3 )
% 9.17/5.41 = one_one_assn ) )
% 9.17/5.41 => ( ! [B2: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ B2 @ ( minus_2355218937544613996nteger @ C4 @ B5 ) )
% 9.17/5.41 => ( ( H3 @ B2 )
% 9.17/5.41 = one_one_assn ) )
% 9.17/5.41 => ( ( ( groups1304777262505850412r_assn @ G @ C4 )
% 9.17/5.41 = ( groups1304777262505850412r_assn @ H3 @ C4 ) )
% 9.17/5.41 => ( ( groups1304777262505850412r_assn @ G @ A2 )
% 9.17/5.41 = ( groups1304777262505850412r_assn @ H3 @ B5 ) ) ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5940_prod_Osame__carrierI,axiom,
% 9.17/5.41 ! [C4: set_o,A2: set_o,B5: set_o,G: $o > rat,H3: $o > rat] :
% 9.17/5.41 ( ( finite_finite_o @ C4 )
% 9.17/5.41 => ( ( ord_less_eq_set_o @ A2 @ C4 )
% 9.17/5.41 => ( ( ord_less_eq_set_o @ B5 @ C4 )
% 9.17/5.41 => ( ! [A3: $o] :
% 9.17/5.41 ( ( member_o @ A3 @ ( minus_minus_set_o @ C4 @ A2 ) )
% 9.17/5.41 => ( ( G @ A3 )
% 9.17/5.41 = one_one_rat ) )
% 9.17/5.41 => ( ! [B2: $o] :
% 9.17/5.41 ( ( member_o @ B2 @ ( minus_minus_set_o @ C4 @ B5 ) )
% 9.17/5.41 => ( ( H3 @ B2 )
% 9.17/5.41 = one_one_rat ) )
% 9.17/5.41 => ( ( ( groups2869687844427037835_o_rat @ G @ C4 )
% 9.17/5.41 = ( groups2869687844427037835_o_rat @ H3 @ C4 ) )
% 9.17/5.41 => ( ( groups2869687844427037835_o_rat @ G @ A2 )
% 9.17/5.41 = ( groups2869687844427037835_o_rat @ H3 @ B5 ) ) ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5941_prod_Osame__carrierI,axiom,
% 9.17/5.41 ! [C4: set_int,A2: set_int,B5: set_int,G: int > rat,H3: int > rat] :
% 9.17/5.41 ( ( finite_finite_int @ C4 )
% 9.17/5.41 => ( ( ord_less_eq_set_int @ A2 @ C4 )
% 9.17/5.41 => ( ( ord_less_eq_set_int @ B5 @ C4 )
% 9.17/5.41 => ( ! [A3: int] :
% 9.17/5.41 ( ( member_int @ A3 @ ( minus_minus_set_int @ C4 @ A2 ) )
% 9.17/5.41 => ( ( G @ A3 )
% 9.17/5.41 = one_one_rat ) )
% 9.17/5.41 => ( ! [B2: int] :
% 9.17/5.41 ( ( member_int @ B2 @ ( minus_minus_set_int @ C4 @ B5 ) )
% 9.17/5.41 => ( ( H3 @ B2 )
% 9.17/5.41 = one_one_rat ) )
% 9.17/5.41 => ( ( ( groups1072433553688619179nt_rat @ G @ C4 )
% 9.17/5.41 = ( groups1072433553688619179nt_rat @ H3 @ C4 ) )
% 9.17/5.41 => ( ( groups1072433553688619179nt_rat @ G @ A2 )
% 9.17/5.41 = ( groups1072433553688619179nt_rat @ H3 @ B5 ) ) ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5942_prod_Osame__carrierI,axiom,
% 9.17/5.41 ! [C4: set_Code_integer,A2: set_Code_integer,B5: set_Code_integer,G: code_integer > rat,H3: code_integer > rat] :
% 9.17/5.41 ( ( finite6017078050557962740nteger @ C4 )
% 9.17/5.41 => ( ( ord_le7084787975880047091nteger @ A2 @ C4 )
% 9.17/5.41 => ( ( ord_le7084787975880047091nteger @ B5 @ C4 )
% 9.17/5.41 => ( ! [A3: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ A3 @ ( minus_2355218937544613996nteger @ C4 @ A2 ) )
% 9.17/5.41 => ( ( G @ A3 )
% 9.17/5.41 = one_one_rat ) )
% 9.17/5.41 => ( ! [B2: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ B2 @ ( minus_2355218937544613996nteger @ C4 @ B5 ) )
% 9.17/5.41 => ( ( H3 @ B2 )
% 9.17/5.41 = one_one_rat ) )
% 9.17/5.41 => ( ( ( groups2555765274223993564er_rat @ G @ C4 )
% 9.17/5.41 = ( groups2555765274223993564er_rat @ H3 @ C4 ) )
% 9.17/5.41 => ( ( groups2555765274223993564er_rat @ G @ A2 )
% 9.17/5.41 = ( groups2555765274223993564er_rat @ H3 @ B5 ) ) ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5943_prod_Osame__carrierI,axiom,
% 9.17/5.41 ! [C4: set_o,A2: set_o,B5: set_o,G: $o > nat,H3: $o > nat] :
% 9.17/5.41 ( ( finite_finite_o @ C4 )
% 9.17/5.41 => ( ( ord_less_eq_set_o @ A2 @ C4 )
% 9.17/5.41 => ( ( ord_less_eq_set_o @ B5 @ C4 )
% 9.17/5.41 => ( ! [A3: $o] :
% 9.17/5.41 ( ( member_o @ A3 @ ( minus_minus_set_o @ C4 @ A2 ) )
% 9.17/5.41 => ( ( G @ A3 )
% 9.17/5.41 = one_one_nat ) )
% 9.17/5.41 => ( ! [B2: $o] :
% 9.17/5.41 ( ( member_o @ B2 @ ( minus_minus_set_o @ C4 @ B5 ) )
% 9.17/5.41 => ( ( H3 @ B2 )
% 9.17/5.41 = one_one_nat ) )
% 9.17/5.41 => ( ( ( groups3504817904513533571_o_nat @ G @ C4 )
% 9.17/5.41 = ( groups3504817904513533571_o_nat @ H3 @ C4 ) )
% 9.17/5.41 => ( ( groups3504817904513533571_o_nat @ G @ A2 )
% 9.17/5.41 = ( groups3504817904513533571_o_nat @ H3 @ B5 ) ) ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5944_prod_Omono__neutral__left,axiom,
% 9.17/5.41 ! [T5: set_int,S2: set_int,G: int > code_integer] :
% 9.17/5.41 ( ( finite_finite_int @ T5 )
% 9.17/5.41 => ( ( ord_less_eq_set_int @ S2 @ T5 )
% 9.17/5.41 => ( ! [X4: int] :
% 9.17/5.41 ( ( member_int @ X4 @ ( minus_minus_set_int @ T5 @ S2 ) )
% 9.17/5.41 => ( ( G @ X4 )
% 9.17/5.41 = one_one_Code_integer ) )
% 9.17/5.41 => ( ( groups3827104343326376752nteger @ G @ S2 )
% 9.17/5.41 = ( groups3827104343326376752nteger @ G @ T5 ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5945_prod_Omono__neutral__left,axiom,
% 9.17/5.41 ! [T5: set_Code_integer,S2: set_Code_integer,G: code_integer > code_integer] :
% 9.17/5.41 ( ( finite6017078050557962740nteger @ T5 )
% 9.17/5.41 => ( ( ord_le7084787975880047091nteger @ S2 @ T5 )
% 9.17/5.41 => ( ! [X4: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ X4 @ ( minus_2355218937544613996nteger @ T5 @ S2 ) )
% 9.17/5.41 => ( ( G @ X4 )
% 9.17/5.41 = one_one_Code_integer ) )
% 9.17/5.41 => ( ( groups3674199335183972705nteger @ G @ S2 )
% 9.17/5.41 = ( groups3674199335183972705nteger @ G @ T5 ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5946_prod_Omono__neutral__left,axiom,
% 9.17/5.41 ! [T5: set_int,S2: set_int,G: int > assn] :
% 9.17/5.41 ( ( finite_finite_int @ T5 )
% 9.17/5.41 => ( ( ord_less_eq_set_int @ S2 @ T5 )
% 9.17/5.41 => ( ! [X4: int] :
% 9.17/5.41 ( ( member_int @ X4 @ ( minus_minus_set_int @ T5 @ S2 ) )
% 9.17/5.41 => ( ( G @ X4 )
% 9.17/5.41 = one_one_assn ) )
% 9.17/5.41 => ( ( groups7882442080178216443t_assn @ G @ S2 )
% 9.17/5.41 = ( groups7882442080178216443t_assn @ G @ T5 ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5947_prod_Omono__neutral__left,axiom,
% 9.17/5.41 ! [T5: set_Code_integer,S2: set_Code_integer,G: code_integer > assn] :
% 9.17/5.41 ( ( finite6017078050557962740nteger @ T5 )
% 9.17/5.41 => ( ( ord_le7084787975880047091nteger @ S2 @ T5 )
% 9.17/5.41 => ( ! [X4: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ X4 @ ( minus_2355218937544613996nteger @ T5 @ S2 ) )
% 9.17/5.41 => ( ( G @ X4 )
% 9.17/5.41 = one_one_assn ) )
% 9.17/5.41 => ( ( groups1304777262505850412r_assn @ G @ S2 )
% 9.17/5.41 = ( groups1304777262505850412r_assn @ G @ T5 ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5948_prod_Omono__neutral__left,axiom,
% 9.17/5.41 ! [T5: set_int,S2: set_int,G: int > rat] :
% 9.17/5.41 ( ( finite_finite_int @ T5 )
% 9.17/5.41 => ( ( ord_less_eq_set_int @ S2 @ T5 )
% 9.17/5.41 => ( ! [X4: int] :
% 9.17/5.41 ( ( member_int @ X4 @ ( minus_minus_set_int @ T5 @ S2 ) )
% 9.17/5.41 => ( ( G @ X4 )
% 9.17/5.41 = one_one_rat ) )
% 9.17/5.41 => ( ( groups1072433553688619179nt_rat @ G @ S2 )
% 9.17/5.41 = ( groups1072433553688619179nt_rat @ G @ T5 ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5949_prod_Omono__neutral__left,axiom,
% 9.17/5.41 ! [T5: set_Code_integer,S2: set_Code_integer,G: code_integer > rat] :
% 9.17/5.41 ( ( finite6017078050557962740nteger @ T5 )
% 9.17/5.41 => ( ( ord_le7084787975880047091nteger @ S2 @ T5 )
% 9.17/5.41 => ( ! [X4: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ X4 @ ( minus_2355218937544613996nteger @ T5 @ S2 ) )
% 9.17/5.41 => ( ( G @ X4 )
% 9.17/5.41 = one_one_rat ) )
% 9.17/5.41 => ( ( groups2555765274223993564er_rat @ G @ S2 )
% 9.17/5.41 = ( groups2555765274223993564er_rat @ G @ T5 ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5950_prod_Omono__neutral__left,axiom,
% 9.17/5.41 ! [T5: set_int,S2: set_int,G: int > nat] :
% 9.17/5.41 ( ( finite_finite_int @ T5 )
% 9.17/5.41 => ( ( ord_less_eq_set_int @ S2 @ T5 )
% 9.17/5.41 => ( ! [X4: int] :
% 9.17/5.41 ( ( member_int @ X4 @ ( minus_minus_set_int @ T5 @ S2 ) )
% 9.17/5.41 => ( ( G @ X4 )
% 9.17/5.41 = one_one_nat ) )
% 9.17/5.41 => ( ( groups1707563613775114915nt_nat @ G @ S2 )
% 9.17/5.41 = ( groups1707563613775114915nt_nat @ G @ T5 ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5951_prod_Omono__neutral__left,axiom,
% 9.17/5.41 ! [T5: set_Code_integer,S2: set_Code_integer,G: code_integer > nat] :
% 9.17/5.41 ( ( finite6017078050557962740nteger @ T5 )
% 9.17/5.41 => ( ( ord_le7084787975880047091nteger @ S2 @ T5 )
% 9.17/5.41 => ( ! [X4: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ X4 @ ( minus_2355218937544613996nteger @ T5 @ S2 ) )
% 9.17/5.41 => ( ( G @ X4 )
% 9.17/5.41 = one_one_nat ) )
% 9.17/5.41 => ( ( groups3190895334310489300er_nat @ G @ S2 )
% 9.17/5.41 = ( groups3190895334310489300er_nat @ G @ T5 ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5952_prod_Omono__neutral__left,axiom,
% 9.17/5.41 ! [T5: set_Code_integer,S2: set_Code_integer,G: code_integer > int] :
% 9.17/5.41 ( ( finite6017078050557962740nteger @ T5 )
% 9.17/5.41 => ( ( ord_le7084787975880047091nteger @ S2 @ T5 )
% 9.17/5.41 => ( ! [X4: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ X4 @ ( minus_2355218937544613996nteger @ T5 @ S2 ) )
% 9.17/5.41 => ( ( G @ X4 )
% 9.17/5.41 = one_one_int ) )
% 9.17/5.41 => ( ( groups3188404863801439024er_int @ G @ S2 )
% 9.17/5.41 = ( groups3188404863801439024er_int @ G @ T5 ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5953_prod_Omono__neutral__left,axiom,
% 9.17/5.41 ! [T5: set_nat,S2: set_nat,G: nat > code_integer] :
% 9.17/5.41 ( ( finite_finite_nat @ T5 )
% 9.17/5.41 => ( ( ord_less_eq_set_nat @ S2 @ T5 )
% 9.17/5.41 => ( ! [X4: nat] :
% 9.17/5.41 ( ( member_nat @ X4 @ ( minus_minus_set_nat @ T5 @ S2 ) )
% 9.17/5.41 => ( ( G @ X4 )
% 9.17/5.41 = one_one_Code_integer ) )
% 9.17/5.41 => ( ( groups3455450783089532116nteger @ G @ S2 )
% 9.17/5.41 = ( groups3455450783089532116nteger @ G @ T5 ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5954_prod_Omono__neutral__right,axiom,
% 9.17/5.41 ! [T5: set_int,S2: set_int,G: int > code_integer] :
% 9.17/5.41 ( ( finite_finite_int @ T5 )
% 9.17/5.41 => ( ( ord_less_eq_set_int @ S2 @ T5 )
% 9.17/5.41 => ( ! [X4: int] :
% 9.17/5.41 ( ( member_int @ X4 @ ( minus_minus_set_int @ T5 @ S2 ) )
% 9.17/5.41 => ( ( G @ X4 )
% 9.17/5.41 = one_one_Code_integer ) )
% 9.17/5.41 => ( ( groups3827104343326376752nteger @ G @ T5 )
% 9.17/5.41 = ( groups3827104343326376752nteger @ G @ S2 ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5955_prod_Omono__neutral__right,axiom,
% 9.17/5.41 ! [T5: set_Code_integer,S2: set_Code_integer,G: code_integer > code_integer] :
% 9.17/5.41 ( ( finite6017078050557962740nteger @ T5 )
% 9.17/5.41 => ( ( ord_le7084787975880047091nteger @ S2 @ T5 )
% 9.17/5.41 => ( ! [X4: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ X4 @ ( minus_2355218937544613996nteger @ T5 @ S2 ) )
% 9.17/5.41 => ( ( G @ X4 )
% 9.17/5.41 = one_one_Code_integer ) )
% 9.17/5.41 => ( ( groups3674199335183972705nteger @ G @ T5 )
% 9.17/5.41 = ( groups3674199335183972705nteger @ G @ S2 ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5956_prod_Omono__neutral__right,axiom,
% 9.17/5.41 ! [T5: set_int,S2: set_int,G: int > assn] :
% 9.17/5.41 ( ( finite_finite_int @ T5 )
% 9.17/5.41 => ( ( ord_less_eq_set_int @ S2 @ T5 )
% 9.17/5.41 => ( ! [X4: int] :
% 9.17/5.41 ( ( member_int @ X4 @ ( minus_minus_set_int @ T5 @ S2 ) )
% 9.17/5.41 => ( ( G @ X4 )
% 9.17/5.41 = one_one_assn ) )
% 9.17/5.41 => ( ( groups7882442080178216443t_assn @ G @ T5 )
% 9.17/5.41 = ( groups7882442080178216443t_assn @ G @ S2 ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5957_prod_Omono__neutral__right,axiom,
% 9.17/5.41 ! [T5: set_Code_integer,S2: set_Code_integer,G: code_integer > assn] :
% 9.17/5.41 ( ( finite6017078050557962740nteger @ T5 )
% 9.17/5.41 => ( ( ord_le7084787975880047091nteger @ S2 @ T5 )
% 9.17/5.41 => ( ! [X4: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ X4 @ ( minus_2355218937544613996nteger @ T5 @ S2 ) )
% 9.17/5.41 => ( ( G @ X4 )
% 9.17/5.41 = one_one_assn ) )
% 9.17/5.41 => ( ( groups1304777262505850412r_assn @ G @ T5 )
% 9.17/5.41 = ( groups1304777262505850412r_assn @ G @ S2 ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5958_prod_Omono__neutral__right,axiom,
% 9.17/5.41 ! [T5: set_int,S2: set_int,G: int > rat] :
% 9.17/5.41 ( ( finite_finite_int @ T5 )
% 9.17/5.41 => ( ( ord_less_eq_set_int @ S2 @ T5 )
% 9.17/5.41 => ( ! [X4: int] :
% 9.17/5.41 ( ( member_int @ X4 @ ( minus_minus_set_int @ T5 @ S2 ) )
% 9.17/5.41 => ( ( G @ X4 )
% 9.17/5.41 = one_one_rat ) )
% 9.17/5.41 => ( ( groups1072433553688619179nt_rat @ G @ T5 )
% 9.17/5.41 = ( groups1072433553688619179nt_rat @ G @ S2 ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5959_prod_Omono__neutral__right,axiom,
% 9.17/5.41 ! [T5: set_Code_integer,S2: set_Code_integer,G: code_integer > rat] :
% 9.17/5.41 ( ( finite6017078050557962740nteger @ T5 )
% 9.17/5.41 => ( ( ord_le7084787975880047091nteger @ S2 @ T5 )
% 9.17/5.41 => ( ! [X4: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ X4 @ ( minus_2355218937544613996nteger @ T5 @ S2 ) )
% 9.17/5.41 => ( ( G @ X4 )
% 9.17/5.41 = one_one_rat ) )
% 9.17/5.41 => ( ( groups2555765274223993564er_rat @ G @ T5 )
% 9.17/5.41 = ( groups2555765274223993564er_rat @ G @ S2 ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5960_prod_Omono__neutral__right,axiom,
% 9.17/5.41 ! [T5: set_int,S2: set_int,G: int > nat] :
% 9.17/5.41 ( ( finite_finite_int @ T5 )
% 9.17/5.41 => ( ( ord_less_eq_set_int @ S2 @ T5 )
% 9.17/5.41 => ( ! [X4: int] :
% 9.17/5.41 ( ( member_int @ X4 @ ( minus_minus_set_int @ T5 @ S2 ) )
% 9.17/5.41 => ( ( G @ X4 )
% 9.17/5.41 = one_one_nat ) )
% 9.17/5.41 => ( ( groups1707563613775114915nt_nat @ G @ T5 )
% 9.17/5.41 = ( groups1707563613775114915nt_nat @ G @ S2 ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5961_prod_Omono__neutral__right,axiom,
% 9.17/5.41 ! [T5: set_Code_integer,S2: set_Code_integer,G: code_integer > nat] :
% 9.17/5.41 ( ( finite6017078050557962740nteger @ T5 )
% 9.17/5.41 => ( ( ord_le7084787975880047091nteger @ S2 @ T5 )
% 9.17/5.41 => ( ! [X4: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ X4 @ ( minus_2355218937544613996nteger @ T5 @ S2 ) )
% 9.17/5.41 => ( ( G @ X4 )
% 9.17/5.41 = one_one_nat ) )
% 9.17/5.41 => ( ( groups3190895334310489300er_nat @ G @ T5 )
% 9.17/5.41 = ( groups3190895334310489300er_nat @ G @ S2 ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5962_prod_Omono__neutral__right,axiom,
% 9.17/5.41 ! [T5: set_Code_integer,S2: set_Code_integer,G: code_integer > int] :
% 9.17/5.41 ( ( finite6017078050557962740nteger @ T5 )
% 9.17/5.41 => ( ( ord_le7084787975880047091nteger @ S2 @ T5 )
% 9.17/5.41 => ( ! [X4: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ X4 @ ( minus_2355218937544613996nteger @ T5 @ S2 ) )
% 9.17/5.41 => ( ( G @ X4 )
% 9.17/5.41 = one_one_int ) )
% 9.17/5.41 => ( ( groups3188404863801439024er_int @ G @ T5 )
% 9.17/5.41 = ( groups3188404863801439024er_int @ G @ S2 ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5963_prod_Omono__neutral__right,axiom,
% 9.17/5.41 ! [T5: set_nat,S2: set_nat,G: nat > code_integer] :
% 9.17/5.41 ( ( finite_finite_nat @ T5 )
% 9.17/5.41 => ( ( ord_less_eq_set_nat @ S2 @ T5 )
% 9.17/5.41 => ( ! [X4: nat] :
% 9.17/5.41 ( ( member_nat @ X4 @ ( minus_minus_set_nat @ T5 @ S2 ) )
% 9.17/5.41 => ( ( G @ X4 )
% 9.17/5.41 = one_one_Code_integer ) )
% 9.17/5.41 => ( ( groups3455450783089532116nteger @ G @ T5 )
% 9.17/5.41 = ( groups3455450783089532116nteger @ G @ S2 ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5964_prod_Omono__neutral__cong__left,axiom,
% 9.17/5.41 ! [T5: set_o,S2: set_o,H3: $o > code_integer,G: $o > code_integer] :
% 9.17/5.41 ( ( finite_finite_o @ T5 )
% 9.17/5.41 => ( ( ord_less_eq_set_o @ S2 @ T5 )
% 9.17/5.41 => ( ! [X4: $o] :
% 9.17/5.41 ( ( member_o @ X4 @ ( minus_minus_set_o @ T5 @ S2 ) )
% 9.17/5.41 => ( ( H3 @ X4 )
% 9.17/5.41 = one_one_Code_integer ) )
% 9.17/5.41 => ( ! [X4: $o] :
% 9.17/5.41 ( ( member_o @ X4 @ S2 )
% 9.17/5.41 => ( ( G @ X4 )
% 9.17/5.41 = ( H3 @ X4 ) ) )
% 9.17/5.41 => ( ( groups7694694392188491536nteger @ G @ S2 )
% 9.17/5.41 = ( groups7694694392188491536nteger @ H3 @ T5 ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5965_prod_Omono__neutral__cong__left,axiom,
% 9.17/5.41 ! [T5: set_int,S2: set_int,H3: int > code_integer,G: int > code_integer] :
% 9.17/5.41 ( ( finite_finite_int @ T5 )
% 9.17/5.41 => ( ( ord_less_eq_set_int @ S2 @ T5 )
% 9.17/5.41 => ( ! [X4: int] :
% 9.17/5.41 ( ( member_int @ X4 @ ( minus_minus_set_int @ T5 @ S2 ) )
% 9.17/5.41 => ( ( H3 @ X4 )
% 9.17/5.41 = one_one_Code_integer ) )
% 9.17/5.41 => ( ! [X4: int] :
% 9.17/5.41 ( ( member_int @ X4 @ S2 )
% 9.17/5.41 => ( ( G @ X4 )
% 9.17/5.41 = ( H3 @ X4 ) ) )
% 9.17/5.41 => ( ( groups3827104343326376752nteger @ G @ S2 )
% 9.17/5.41 = ( groups3827104343326376752nteger @ H3 @ T5 ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5966_prod_Omono__neutral__cong__left,axiom,
% 9.17/5.41 ! [T5: set_Code_integer,S2: set_Code_integer,H3: code_integer > code_integer,G: code_integer > code_integer] :
% 9.17/5.41 ( ( finite6017078050557962740nteger @ T5 )
% 9.17/5.41 => ( ( ord_le7084787975880047091nteger @ S2 @ T5 )
% 9.17/5.41 => ( ! [X4: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ X4 @ ( minus_2355218937544613996nteger @ T5 @ S2 ) )
% 9.17/5.41 => ( ( H3 @ X4 )
% 9.17/5.41 = one_one_Code_integer ) )
% 9.17/5.41 => ( ! [X4: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ X4 @ S2 )
% 9.17/5.41 => ( ( G @ X4 )
% 9.17/5.41 = ( H3 @ X4 ) ) )
% 9.17/5.41 => ( ( groups3674199335183972705nteger @ G @ S2 )
% 9.17/5.41 = ( groups3674199335183972705nteger @ H3 @ T5 ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5967_prod_Omono__neutral__cong__left,axiom,
% 9.17/5.41 ! [T5: set_o,S2: set_o,H3: $o > assn,G: $o > assn] :
% 9.17/5.41 ( ( finite_finite_o @ T5 )
% 9.17/5.41 => ( ( ord_less_eq_set_o @ S2 @ T5 )
% 9.17/5.41 => ( ! [X4: $o] :
% 9.17/5.41 ( ( member_o @ X4 @ ( minus_minus_set_o @ T5 @ S2 ) )
% 9.17/5.41 => ( ( H3 @ X4 )
% 9.17/5.41 = one_one_assn ) )
% 9.17/5.41 => ( ! [X4: $o] :
% 9.17/5.41 ( ( member_o @ X4 @ S2 )
% 9.17/5.41 => ( ( G @ X4 )
% 9.17/5.41 = ( H3 @ X4 ) ) )
% 9.17/5.41 => ( ( groups5301882518646026715o_assn @ G @ S2 )
% 9.17/5.41 = ( groups5301882518646026715o_assn @ H3 @ T5 ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5968_prod_Omono__neutral__cong__left,axiom,
% 9.17/5.41 ! [T5: set_int,S2: set_int,H3: int > assn,G: int > assn] :
% 9.17/5.41 ( ( finite_finite_int @ T5 )
% 9.17/5.41 => ( ( ord_less_eq_set_int @ S2 @ T5 )
% 9.17/5.41 => ( ! [X4: int] :
% 9.17/5.41 ( ( member_int @ X4 @ ( minus_minus_set_int @ T5 @ S2 ) )
% 9.17/5.41 => ( ( H3 @ X4 )
% 9.17/5.41 = one_one_assn ) )
% 9.17/5.41 => ( ! [X4: int] :
% 9.17/5.41 ( ( member_int @ X4 @ S2 )
% 9.17/5.41 => ( ( G @ X4 )
% 9.17/5.41 = ( H3 @ X4 ) ) )
% 9.17/5.41 => ( ( groups7882442080178216443t_assn @ G @ S2 )
% 9.17/5.41 = ( groups7882442080178216443t_assn @ H3 @ T5 ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5969_prod_Omono__neutral__cong__left,axiom,
% 9.17/5.41 ! [T5: set_Code_integer,S2: set_Code_integer,H3: code_integer > assn,G: code_integer > assn] :
% 9.17/5.41 ( ( finite6017078050557962740nteger @ T5 )
% 9.17/5.41 => ( ( ord_le7084787975880047091nteger @ S2 @ T5 )
% 9.17/5.41 => ( ! [X4: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ X4 @ ( minus_2355218937544613996nteger @ T5 @ S2 ) )
% 9.17/5.41 => ( ( H3 @ X4 )
% 9.17/5.41 = one_one_assn ) )
% 9.17/5.41 => ( ! [X4: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ X4 @ S2 )
% 9.17/5.41 => ( ( G @ X4 )
% 9.17/5.41 = ( H3 @ X4 ) ) )
% 9.17/5.41 => ( ( groups1304777262505850412r_assn @ G @ S2 )
% 9.17/5.41 = ( groups1304777262505850412r_assn @ H3 @ T5 ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5970_prod_Omono__neutral__cong__left,axiom,
% 9.17/5.41 ! [T5: set_o,S2: set_o,H3: $o > rat,G: $o > rat] :
% 9.17/5.41 ( ( finite_finite_o @ T5 )
% 9.17/5.41 => ( ( ord_less_eq_set_o @ S2 @ T5 )
% 9.17/5.41 => ( ! [X4: $o] :
% 9.17/5.41 ( ( member_o @ X4 @ ( minus_minus_set_o @ T5 @ S2 ) )
% 9.17/5.41 => ( ( H3 @ X4 )
% 9.17/5.41 = one_one_rat ) )
% 9.17/5.41 => ( ! [X4: $o] :
% 9.17/5.41 ( ( member_o @ X4 @ S2 )
% 9.17/5.41 => ( ( G @ X4 )
% 9.17/5.41 = ( H3 @ X4 ) ) )
% 9.17/5.41 => ( ( groups2869687844427037835_o_rat @ G @ S2 )
% 9.17/5.41 = ( groups2869687844427037835_o_rat @ H3 @ T5 ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5971_prod_Omono__neutral__cong__left,axiom,
% 9.17/5.41 ! [T5: set_int,S2: set_int,H3: int > rat,G: int > rat] :
% 9.17/5.41 ( ( finite_finite_int @ T5 )
% 9.17/5.41 => ( ( ord_less_eq_set_int @ S2 @ T5 )
% 9.17/5.41 => ( ! [X4: int] :
% 9.17/5.41 ( ( member_int @ X4 @ ( minus_minus_set_int @ T5 @ S2 ) )
% 9.17/5.41 => ( ( H3 @ X4 )
% 9.17/5.41 = one_one_rat ) )
% 9.17/5.41 => ( ! [X4: int] :
% 9.17/5.41 ( ( member_int @ X4 @ S2 )
% 9.17/5.41 => ( ( G @ X4 )
% 9.17/5.41 = ( H3 @ X4 ) ) )
% 9.17/5.41 => ( ( groups1072433553688619179nt_rat @ G @ S2 )
% 9.17/5.41 = ( groups1072433553688619179nt_rat @ H3 @ T5 ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5972_prod_Omono__neutral__cong__left,axiom,
% 9.17/5.41 ! [T5: set_Code_integer,S2: set_Code_integer,H3: code_integer > rat,G: code_integer > rat] :
% 9.17/5.41 ( ( finite6017078050557962740nteger @ T5 )
% 9.17/5.41 => ( ( ord_le7084787975880047091nteger @ S2 @ T5 )
% 9.17/5.41 => ( ! [X4: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ X4 @ ( minus_2355218937544613996nteger @ T5 @ S2 ) )
% 9.17/5.41 => ( ( H3 @ X4 )
% 9.17/5.41 = one_one_rat ) )
% 9.17/5.41 => ( ! [X4: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ X4 @ S2 )
% 9.17/5.41 => ( ( G @ X4 )
% 9.17/5.41 = ( H3 @ X4 ) ) )
% 9.17/5.41 => ( ( groups2555765274223993564er_rat @ G @ S2 )
% 9.17/5.41 = ( groups2555765274223993564er_rat @ H3 @ T5 ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5973_prod_Omono__neutral__cong__left,axiom,
% 9.17/5.41 ! [T5: set_o,S2: set_o,H3: $o > nat,G: $o > nat] :
% 9.17/5.41 ( ( finite_finite_o @ T5 )
% 9.17/5.41 => ( ( ord_less_eq_set_o @ S2 @ T5 )
% 9.17/5.41 => ( ! [X4: $o] :
% 9.17/5.41 ( ( member_o @ X4 @ ( minus_minus_set_o @ T5 @ S2 ) )
% 9.17/5.41 => ( ( H3 @ X4 )
% 9.17/5.41 = one_one_nat ) )
% 9.17/5.41 => ( ! [X4: $o] :
% 9.17/5.41 ( ( member_o @ X4 @ S2 )
% 9.17/5.41 => ( ( G @ X4 )
% 9.17/5.41 = ( H3 @ X4 ) ) )
% 9.17/5.41 => ( ( groups3504817904513533571_o_nat @ G @ S2 )
% 9.17/5.41 = ( groups3504817904513533571_o_nat @ H3 @ T5 ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5974_prod_Omono__neutral__cong__right,axiom,
% 9.17/5.41 ! [T5: set_o,S2: set_o,G: $o > code_integer,H3: $o > code_integer] :
% 9.17/5.41 ( ( finite_finite_o @ T5 )
% 9.17/5.41 => ( ( ord_less_eq_set_o @ S2 @ T5 )
% 9.17/5.41 => ( ! [X4: $o] :
% 9.17/5.41 ( ( member_o @ X4 @ ( minus_minus_set_o @ T5 @ S2 ) )
% 9.17/5.41 => ( ( G @ X4 )
% 9.17/5.41 = one_one_Code_integer ) )
% 9.17/5.41 => ( ! [X4: $o] :
% 9.17/5.41 ( ( member_o @ X4 @ S2 )
% 9.17/5.41 => ( ( G @ X4 )
% 9.17/5.41 = ( H3 @ X4 ) ) )
% 9.17/5.41 => ( ( groups7694694392188491536nteger @ G @ T5 )
% 9.17/5.41 = ( groups7694694392188491536nteger @ H3 @ S2 ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5975_prod_Omono__neutral__cong__right,axiom,
% 9.17/5.41 ! [T5: set_int,S2: set_int,G: int > code_integer,H3: int > code_integer] :
% 9.17/5.41 ( ( finite_finite_int @ T5 )
% 9.17/5.41 => ( ( ord_less_eq_set_int @ S2 @ T5 )
% 9.17/5.41 => ( ! [X4: int] :
% 9.17/5.41 ( ( member_int @ X4 @ ( minus_minus_set_int @ T5 @ S2 ) )
% 9.17/5.41 => ( ( G @ X4 )
% 9.17/5.41 = one_one_Code_integer ) )
% 9.17/5.41 => ( ! [X4: int] :
% 9.17/5.41 ( ( member_int @ X4 @ S2 )
% 9.17/5.41 => ( ( G @ X4 )
% 9.17/5.41 = ( H3 @ X4 ) ) )
% 9.17/5.41 => ( ( groups3827104343326376752nteger @ G @ T5 )
% 9.17/5.41 = ( groups3827104343326376752nteger @ H3 @ S2 ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5976_prod_Omono__neutral__cong__right,axiom,
% 9.17/5.41 ! [T5: set_Code_integer,S2: set_Code_integer,G: code_integer > code_integer,H3: code_integer > code_integer] :
% 9.17/5.41 ( ( finite6017078050557962740nteger @ T5 )
% 9.17/5.41 => ( ( ord_le7084787975880047091nteger @ S2 @ T5 )
% 9.17/5.41 => ( ! [X4: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ X4 @ ( minus_2355218937544613996nteger @ T5 @ S2 ) )
% 9.17/5.41 => ( ( G @ X4 )
% 9.17/5.41 = one_one_Code_integer ) )
% 9.17/5.41 => ( ! [X4: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ X4 @ S2 )
% 9.17/5.41 => ( ( G @ X4 )
% 9.17/5.41 = ( H3 @ X4 ) ) )
% 9.17/5.41 => ( ( groups3674199335183972705nteger @ G @ T5 )
% 9.17/5.41 = ( groups3674199335183972705nteger @ H3 @ S2 ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5977_prod_Omono__neutral__cong__right,axiom,
% 9.17/5.41 ! [T5: set_o,S2: set_o,G: $o > assn,H3: $o > assn] :
% 9.17/5.41 ( ( finite_finite_o @ T5 )
% 9.17/5.41 => ( ( ord_less_eq_set_o @ S2 @ T5 )
% 9.17/5.41 => ( ! [X4: $o] :
% 9.17/5.41 ( ( member_o @ X4 @ ( minus_minus_set_o @ T5 @ S2 ) )
% 9.17/5.41 => ( ( G @ X4 )
% 9.17/5.41 = one_one_assn ) )
% 9.17/5.41 => ( ! [X4: $o] :
% 9.17/5.41 ( ( member_o @ X4 @ S2 )
% 9.17/5.41 => ( ( G @ X4 )
% 9.17/5.41 = ( H3 @ X4 ) ) )
% 9.17/5.41 => ( ( groups5301882518646026715o_assn @ G @ T5 )
% 9.17/5.41 = ( groups5301882518646026715o_assn @ H3 @ S2 ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5978_prod_Omono__neutral__cong__right,axiom,
% 9.17/5.41 ! [T5: set_int,S2: set_int,G: int > assn,H3: int > assn] :
% 9.17/5.41 ( ( finite_finite_int @ T5 )
% 9.17/5.41 => ( ( ord_less_eq_set_int @ S2 @ T5 )
% 9.17/5.41 => ( ! [X4: int] :
% 9.17/5.41 ( ( member_int @ X4 @ ( minus_minus_set_int @ T5 @ S2 ) )
% 9.17/5.41 => ( ( G @ X4 )
% 9.17/5.41 = one_one_assn ) )
% 9.17/5.41 => ( ! [X4: int] :
% 9.17/5.41 ( ( member_int @ X4 @ S2 )
% 9.17/5.41 => ( ( G @ X4 )
% 9.17/5.41 = ( H3 @ X4 ) ) )
% 9.17/5.41 => ( ( groups7882442080178216443t_assn @ G @ T5 )
% 9.17/5.41 = ( groups7882442080178216443t_assn @ H3 @ S2 ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5979_prod_Omono__neutral__cong__right,axiom,
% 9.17/5.41 ! [T5: set_Code_integer,S2: set_Code_integer,G: code_integer > assn,H3: code_integer > assn] :
% 9.17/5.41 ( ( finite6017078050557962740nteger @ T5 )
% 9.17/5.41 => ( ( ord_le7084787975880047091nteger @ S2 @ T5 )
% 9.17/5.41 => ( ! [X4: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ X4 @ ( minus_2355218937544613996nteger @ T5 @ S2 ) )
% 9.17/5.41 => ( ( G @ X4 )
% 9.17/5.41 = one_one_assn ) )
% 9.17/5.41 => ( ! [X4: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ X4 @ S2 )
% 9.17/5.41 => ( ( G @ X4 )
% 9.17/5.41 = ( H3 @ X4 ) ) )
% 9.17/5.41 => ( ( groups1304777262505850412r_assn @ G @ T5 )
% 9.17/5.41 = ( groups1304777262505850412r_assn @ H3 @ S2 ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5980_prod_Omono__neutral__cong__right,axiom,
% 9.17/5.41 ! [T5: set_o,S2: set_o,G: $o > rat,H3: $o > rat] :
% 9.17/5.41 ( ( finite_finite_o @ T5 )
% 9.17/5.41 => ( ( ord_less_eq_set_o @ S2 @ T5 )
% 9.17/5.41 => ( ! [X4: $o] :
% 9.17/5.41 ( ( member_o @ X4 @ ( minus_minus_set_o @ T5 @ S2 ) )
% 9.17/5.41 => ( ( G @ X4 )
% 9.17/5.41 = one_one_rat ) )
% 9.17/5.41 => ( ! [X4: $o] :
% 9.17/5.41 ( ( member_o @ X4 @ S2 )
% 9.17/5.41 => ( ( G @ X4 )
% 9.17/5.41 = ( H3 @ X4 ) ) )
% 9.17/5.41 => ( ( groups2869687844427037835_o_rat @ G @ T5 )
% 9.17/5.41 = ( groups2869687844427037835_o_rat @ H3 @ S2 ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5981_prod_Omono__neutral__cong__right,axiom,
% 9.17/5.41 ! [T5: set_int,S2: set_int,G: int > rat,H3: int > rat] :
% 9.17/5.41 ( ( finite_finite_int @ T5 )
% 9.17/5.41 => ( ( ord_less_eq_set_int @ S2 @ T5 )
% 9.17/5.41 => ( ! [X4: int] :
% 9.17/5.41 ( ( member_int @ X4 @ ( minus_minus_set_int @ T5 @ S2 ) )
% 9.17/5.41 => ( ( G @ X4 )
% 9.17/5.41 = one_one_rat ) )
% 9.17/5.41 => ( ! [X4: int] :
% 9.17/5.41 ( ( member_int @ X4 @ S2 )
% 9.17/5.41 => ( ( G @ X4 )
% 9.17/5.41 = ( H3 @ X4 ) ) )
% 9.17/5.41 => ( ( groups1072433553688619179nt_rat @ G @ T5 )
% 9.17/5.41 = ( groups1072433553688619179nt_rat @ H3 @ S2 ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5982_prod_Omono__neutral__cong__right,axiom,
% 9.17/5.41 ! [T5: set_Code_integer,S2: set_Code_integer,G: code_integer > rat,H3: code_integer > rat] :
% 9.17/5.41 ( ( finite6017078050557962740nteger @ T5 )
% 9.17/5.41 => ( ( ord_le7084787975880047091nteger @ S2 @ T5 )
% 9.17/5.41 => ( ! [X4: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ X4 @ ( minus_2355218937544613996nteger @ T5 @ S2 ) )
% 9.17/5.41 => ( ( G @ X4 )
% 9.17/5.41 = one_one_rat ) )
% 9.17/5.41 => ( ! [X4: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ X4 @ S2 )
% 9.17/5.41 => ( ( G @ X4 )
% 9.17/5.41 = ( H3 @ X4 ) ) )
% 9.17/5.41 => ( ( groups2555765274223993564er_rat @ G @ T5 )
% 9.17/5.41 = ( groups2555765274223993564er_rat @ H3 @ S2 ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5983_prod_Omono__neutral__cong__right,axiom,
% 9.17/5.41 ! [T5: set_o,S2: set_o,G: $o > nat,H3: $o > nat] :
% 9.17/5.41 ( ( finite_finite_o @ T5 )
% 9.17/5.41 => ( ( ord_less_eq_set_o @ S2 @ T5 )
% 9.17/5.41 => ( ! [X4: $o] :
% 9.17/5.41 ( ( member_o @ X4 @ ( minus_minus_set_o @ T5 @ S2 ) )
% 9.17/5.41 => ( ( G @ X4 )
% 9.17/5.41 = one_one_nat ) )
% 9.17/5.41 => ( ! [X4: $o] :
% 9.17/5.41 ( ( member_o @ X4 @ S2 )
% 9.17/5.41 => ( ( G @ X4 )
% 9.17/5.41 = ( H3 @ X4 ) ) )
% 9.17/5.41 => ( ( groups3504817904513533571_o_nat @ G @ T5 )
% 9.17/5.41 = ( groups3504817904513533571_o_nat @ H3 @ S2 ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5984_atLeastLessThanSuc,axiom,
% 9.17/5.41 ! [M2: nat,N2: nat] :
% 9.17/5.41 ( ( ( ord_less_eq_nat @ M2 @ N2 )
% 9.17/5.41 => ( ( set_or4665077453230672383an_nat @ M2 @ ( suc @ N2 ) )
% 9.17/5.41 = ( insert_nat @ N2 @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) ) )
% 9.17/5.41 & ( ~ ( ord_less_eq_nat @ M2 @ N2 )
% 9.17/5.41 => ( ( set_or4665077453230672383an_nat @ M2 @ ( suc @ N2 ) )
% 9.17/5.41 = bot_bot_set_nat ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5985_Option_Othese__def,axiom,
% 9.17/5.41 ( these_6645423997822192641it_nat
% 9.17/5.41 = ( ^ [A7: set_op3940070208846178154it_nat] :
% 9.17/5.41 ( image_5549452628634654015it_nat @ the_Pr5856008525237892824it_nat
% 9.17/5.41 @ ( collec8141831914148684149it_nat
% 9.17/5.41 @ ^ [X3: option3216581401566546698it_nat] :
% 9.17/5.41 ( ( member3517700364412436275it_nat @ X3 @ A7 )
% 9.17/5.41 & ( X3 != none_P2587165478634041381it_nat ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5986_Option_Othese__def,axiom,
% 9.17/5.41 ( these_num
% 9.17/5.41 = ( ^ [A7: set_option_num] :
% 9.17/5.41 ( image_option_num_num @ the_num
% 9.17/5.41 @ ( collect_option_num
% 9.17/5.41 @ ^ [X3: option_num] :
% 9.17/5.41 ( ( member_option_num @ X3 @ A7 )
% 9.17/5.41 & ( X3 != none_num ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5987_Option_Othese__def,axiom,
% 9.17/5.41 ( these_3407724651694999947it_nat
% 9.17/5.41 = ( ^ [A7: set_op239864471688321678it_nat] :
% 9.17/5.41 ( image_1237920015125996135it_nat @ the_Pr7776125533777466484it_nat
% 9.17/5.41 @ ( collec5742531119322951597it_nat
% 9.17/5.41 @ ^ [X3: option8956607266484857688it_nat] :
% 9.17/5.41 ( ( member5596548051065438575it_nat @ X3 @ A7 )
% 9.17/5.41 & ( X3 != none_P9117596204409417319it_nat ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5988_atLeast0__atMost__Suc__eq__insert__0,axiom,
% 9.17/5.41 ! [N2: nat] :
% 9.17/5.41 ( ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) )
% 9.17/5.41 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5989_atLeast0__lessThan__Suc__eq__insert__0,axiom,
% 9.17/5.41 ! [N2: nat] :
% 9.17/5.41 ( ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N2 ) )
% 9.17/5.41 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5990_atMost__Suc__eq__insert__0,axiom,
% 9.17/5.41 ! [N2: nat] :
% 9.17/5.41 ( ( set_ord_atMost_nat @ ( suc @ N2 ) )
% 9.17/5.41 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5991_lessThan__Suc__eq__insert__0,axiom,
% 9.17/5.41 ! [N2: nat] :
% 9.17/5.41 ( ( set_ord_lessThan_nat @ ( suc @ N2 ) )
% 9.17/5.41 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5992_card__2__iff,axiom,
% 9.17/5.41 ! [S2: set_Product_unit] :
% 9.17/5.41 ( ( ( finite410649719033368117t_unit @ S2 )
% 9.17/5.41 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.17/5.41 = ( ? [X3: product_unit,Y3: product_unit] :
% 9.17/5.41 ( ( S2
% 9.17/5.41 = ( insert_Product_unit @ X3 @ ( insert_Product_unit @ Y3 @ bot_bo3957492148770167129t_unit ) ) )
% 9.17/5.41 & ( X3 != Y3 ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5993_card__2__iff,axiom,
% 9.17/5.41 ! [S2: set_list_nat] :
% 9.17/5.41 ( ( ( finite_card_list_nat @ S2 )
% 9.17/5.41 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.17/5.41 = ( ? [X3: list_nat,Y3: list_nat] :
% 9.17/5.41 ( ( S2
% 9.17/5.41 = ( insert_list_nat @ X3 @ ( insert_list_nat @ Y3 @ bot_bot_set_list_nat ) ) )
% 9.17/5.41 & ( X3 != Y3 ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5994_card__2__iff,axiom,
% 9.17/5.41 ! [S2: set_Pr4329608150637261639at_nat] :
% 9.17/5.41 ( ( ( finite3771342082235030671at_nat @ S2 )
% 9.17/5.41 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.17/5.41 = ( ? [X3: produc3843707927480180839at_nat,Y3: produc3843707927480180839at_nat] :
% 9.17/5.41 ( ( S2
% 9.17/5.41 = ( insert9069300056098147895at_nat @ X3 @ ( insert9069300056098147895at_nat @ Y3 @ bot_bo228742789529271731at_nat ) ) )
% 9.17/5.41 & ( X3 != Y3 ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5995_card__2__iff,axiom,
% 9.17/5.41 ! [S2: set_Pr1261947904930325089at_nat] :
% 9.17/5.41 ( ( ( finite711546835091564841at_nat @ S2 )
% 9.17/5.41 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.17/5.41 = ( ? [X3: product_prod_nat_nat,Y3: product_prod_nat_nat] :
% 9.17/5.41 ( ( S2
% 9.17/5.41 = ( insert8211810215607154385at_nat @ X3 @ ( insert8211810215607154385at_nat @ Y3 @ bot_bo2099793752762293965at_nat ) ) )
% 9.17/5.41 & ( X3 != Y3 ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5996_card__2__iff,axiom,
% 9.17/5.41 ! [S2: set_o] :
% 9.17/5.41 ( ( ( finite_card_o @ S2 )
% 9.17/5.41 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.17/5.41 = ( ? [X3: $o,Y3: $o] :
% 9.17/5.41 ( ( S2
% 9.17/5.41 = ( insert_o @ X3 @ ( insert_o @ Y3 @ bot_bot_set_o ) ) )
% 9.17/5.41 & ( X3 != Y3 ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5997_card__2__iff,axiom,
% 9.17/5.41 ! [S2: set_nat] :
% 9.17/5.41 ( ( ( finite_card_nat @ S2 )
% 9.17/5.41 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.17/5.41 = ( ? [X3: nat,Y3: nat] :
% 9.17/5.41 ( ( S2
% 9.17/5.41 = ( insert_nat @ X3 @ ( insert_nat @ Y3 @ bot_bot_set_nat ) ) )
% 9.17/5.41 & ( X3 != Y3 ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5998_card__2__iff,axiom,
% 9.17/5.41 ! [S2: set_int] :
% 9.17/5.41 ( ( ( finite_card_int @ S2 )
% 9.17/5.41 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.17/5.41 = ( ? [X3: int,Y3: int] :
% 9.17/5.41 ( ( S2
% 9.17/5.41 = ( insert_int @ X3 @ ( insert_int @ Y3 @ bot_bot_set_int ) ) )
% 9.17/5.41 & ( X3 != Y3 ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_5999_card__3__iff,axiom,
% 9.17/5.41 ! [S2: set_Product_unit] :
% 9.17/5.41 ( ( ( finite410649719033368117t_unit @ S2 )
% 9.17/5.41 = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 9.17/5.41 = ( ? [X3: product_unit,Y3: product_unit,Z4: product_unit] :
% 9.17/5.41 ( ( S2
% 9.17/5.41 = ( insert_Product_unit @ X3 @ ( insert_Product_unit @ Y3 @ ( insert_Product_unit @ Z4 @ bot_bo3957492148770167129t_unit ) ) ) )
% 9.17/5.41 & ( X3 != Y3 )
% 9.17/5.41 & ( Y3 != Z4 )
% 9.17/5.41 & ( X3 != Z4 ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6000_card__3__iff,axiom,
% 9.17/5.41 ! [S2: set_list_nat] :
% 9.17/5.41 ( ( ( finite_card_list_nat @ S2 )
% 9.17/5.41 = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 9.17/5.41 = ( ? [X3: list_nat,Y3: list_nat,Z4: list_nat] :
% 9.17/5.41 ( ( S2
% 9.17/5.41 = ( insert_list_nat @ X3 @ ( insert_list_nat @ Y3 @ ( insert_list_nat @ Z4 @ bot_bot_set_list_nat ) ) ) )
% 9.17/5.41 & ( X3 != Y3 )
% 9.17/5.41 & ( Y3 != Z4 )
% 9.17/5.41 & ( X3 != Z4 ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6001_card__3__iff,axiom,
% 9.17/5.41 ! [S2: set_Pr4329608150637261639at_nat] :
% 9.17/5.41 ( ( ( finite3771342082235030671at_nat @ S2 )
% 9.17/5.41 = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 9.17/5.41 = ( ? [X3: produc3843707927480180839at_nat,Y3: produc3843707927480180839at_nat,Z4: produc3843707927480180839at_nat] :
% 9.17/5.41 ( ( S2
% 9.17/5.41 = ( insert9069300056098147895at_nat @ X3 @ ( insert9069300056098147895at_nat @ Y3 @ ( insert9069300056098147895at_nat @ Z4 @ bot_bo228742789529271731at_nat ) ) ) )
% 9.17/5.41 & ( X3 != Y3 )
% 9.17/5.41 & ( Y3 != Z4 )
% 9.17/5.41 & ( X3 != Z4 ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6002_card__3__iff,axiom,
% 9.17/5.41 ! [S2: set_Pr1261947904930325089at_nat] :
% 9.17/5.41 ( ( ( finite711546835091564841at_nat @ S2 )
% 9.17/5.41 = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 9.17/5.41 = ( ? [X3: product_prod_nat_nat,Y3: product_prod_nat_nat,Z4: product_prod_nat_nat] :
% 9.17/5.41 ( ( S2
% 9.17/5.41 = ( insert8211810215607154385at_nat @ X3 @ ( insert8211810215607154385at_nat @ Y3 @ ( insert8211810215607154385at_nat @ Z4 @ bot_bo2099793752762293965at_nat ) ) ) )
% 9.17/5.41 & ( X3 != Y3 )
% 9.17/5.41 & ( Y3 != Z4 )
% 9.17/5.41 & ( X3 != Z4 ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6003_card__3__iff,axiom,
% 9.17/5.41 ! [S2: set_o] :
% 9.17/5.41 ( ( ( finite_card_o @ S2 )
% 9.17/5.41 = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 9.17/5.41 = ( ? [X3: $o,Y3: $o,Z4: $o] :
% 9.17/5.41 ( ( S2
% 9.17/5.41 = ( insert_o @ X3 @ ( insert_o @ Y3 @ ( insert_o @ Z4 @ bot_bot_set_o ) ) ) )
% 9.17/5.41 & ( X3 != Y3 )
% 9.17/5.41 & ( Y3 != Z4 )
% 9.17/5.41 & ( X3 != Z4 ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6004_card__3__iff,axiom,
% 9.17/5.41 ! [S2: set_nat] :
% 9.17/5.41 ( ( ( finite_card_nat @ S2 )
% 9.17/5.41 = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 9.17/5.41 = ( ? [X3: nat,Y3: nat,Z4: nat] :
% 9.17/5.41 ( ( S2
% 9.17/5.41 = ( insert_nat @ X3 @ ( insert_nat @ Y3 @ ( insert_nat @ Z4 @ bot_bot_set_nat ) ) ) )
% 9.17/5.41 & ( X3 != Y3 )
% 9.17/5.41 & ( Y3 != Z4 )
% 9.17/5.41 & ( X3 != Z4 ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6005_card__3__iff,axiom,
% 9.17/5.41 ! [S2: set_int] :
% 9.17/5.41 ( ( ( finite_card_int @ S2 )
% 9.17/5.41 = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 9.17/5.41 = ( ? [X3: int,Y3: int,Z4: int] :
% 9.17/5.41 ( ( S2
% 9.17/5.41 = ( insert_int @ X3 @ ( insert_int @ Y3 @ ( insert_int @ Z4 @ bot_bot_set_int ) ) ) )
% 9.17/5.41 & ( X3 != Y3 )
% 9.17/5.41 & ( Y3 != Z4 )
% 9.17/5.41 & ( X3 != Z4 ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6006_sum__image__le,axiom,
% 9.17/5.41 ! [I4: set_num,G: code_integer > code_integer,F: num > code_integer] :
% 9.17/5.41 ( ( finite_finite_num @ I4 )
% 9.17/5.41 => ( ! [I2: num] :
% 9.17/5.41 ( ( member_num @ I2 @ I4 )
% 9.17/5.41 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( G @ ( F @ I2 ) ) ) )
% 9.17/5.41 => ( ord_le3102999989581377725nteger @ ( groups879477027807139574nteger @ G @ ( image_8379761247532268670nteger @ F @ I4 ) ) @ ( groups5442708359310287027nteger @ ( comp_C3531382070062128313er_num @ G @ F ) @ I4 ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6007_sum__image__le,axiom,
% 9.17/5.41 ! [I4: set_nat,G: code_integer > code_integer,F: nat > code_integer] :
% 9.17/5.41 ( ( finite_finite_nat @ I4 )
% 9.17/5.41 => ( ! [I2: nat] :
% 9.17/5.41 ( ( member_nat @ I2 @ I4 )
% 9.17/5.41 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( G @ ( F @ I2 ) ) ) )
% 9.17/5.41 => ( ord_le3102999989581377725nteger @ ( groups879477027807139574nteger @ G @ ( image_1215581382706833972nteger @ F @ I4 ) ) @ ( groups7501900531339628137nteger @ ( comp_C6974050283906349679er_nat @ G @ F ) @ I4 ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6008_sum__image__le,axiom,
% 9.17/5.41 ! [I4: set_nat,G: nat > code_integer,F: nat > nat] :
% 9.17/5.41 ( ( finite_finite_nat @ I4 )
% 9.17/5.41 => ( ! [I2: nat] :
% 9.17/5.41 ( ( member_nat @ I2 @ I4 )
% 9.17/5.41 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( G @ ( F @ I2 ) ) ) )
% 9.17/5.41 => ( ord_le3102999989581377725nteger @ ( groups7501900531339628137nteger @ G @ ( image_nat_nat @ F @ I4 ) ) @ ( groups7501900531339628137nteger @ ( comp_n3898172953802868194er_nat @ G @ F ) @ I4 ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6009_sum__image__le,axiom,
% 9.17/5.41 ! [I4: set_nat,G: int > code_integer,F: nat > int] :
% 9.17/5.41 ( ( finite_finite_nat @ I4 )
% 9.17/5.41 => ( ! [I2: nat] :
% 9.17/5.41 ( ( member_nat @ I2 @ I4 )
% 9.17/5.41 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( G @ ( F @ I2 ) ) ) )
% 9.17/5.41 => ( ord_le3102999989581377725nteger @ ( groups7873554091576472773nteger @ G @ ( image_nat_int @ F @ I4 ) ) @ ( groups7501900531339628137nteger @ ( comp_i1588355021709917246er_nat @ G @ F ) @ I4 ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6010_sum__image__le,axiom,
% 9.17/5.41 ! [I4: set_int,G: int > code_integer,F: int > int] :
% 9.17/5.41 ( ( finite_finite_int @ I4 )
% 9.17/5.41 => ( ! [I2: int] :
% 9.17/5.41 ( ( member_int @ I2 @ I4 )
% 9.17/5.41 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( G @ ( F @ I2 ) ) ) )
% 9.17/5.41 => ( ord_le3102999989581377725nteger @ ( groups7873554091576472773nteger @ G @ ( image_int_int @ F @ I4 ) ) @ ( groups7873554091576472773nteger @ ( comp_i1585864551200866970er_int @ G @ F ) @ I4 ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6011_sum__image__le,axiom,
% 9.17/5.41 ! [I4: set_nat,G: code_integer > rat,F: nat > code_integer] :
% 9.17/5.41 ( ( finite_finite_nat @ I4 )
% 9.17/5.41 => ( ! [I2: nat] :
% 9.17/5.41 ( ( member_nat @ I2 @ I4 )
% 9.17/5.41 => ( ord_less_eq_rat @ zero_zero_rat @ ( G @ ( F @ I2 ) ) ) )
% 9.17/5.41 => ( ord_less_eq_rat @ ( groups6602215022474089585er_rat @ G @ ( image_1215581382706833972nteger @ F @ I4 ) ) @ ( groups2906978787729119204at_rat @ ( comp_C3733001951728184298at_nat @ G @ F ) @ I4 ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6012_sum__image__le,axiom,
% 9.17/5.41 ! [I4: set_nat,G: nat > rat,F: nat > nat] :
% 9.17/5.41 ( ( finite_finite_nat @ I4 )
% 9.17/5.41 => ( ! [I2: nat] :
% 9.17/5.41 ( ( member_nat @ I2 @ I4 )
% 9.17/5.41 => ( ord_less_eq_rat @ zero_zero_rat @ ( G @ ( F @ I2 ) ) ) )
% 9.17/5.41 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ G @ ( image_nat_nat @ F @ I4 ) ) @ ( groups2906978787729119204at_rat @ ( comp_nat_rat_nat @ G @ F ) @ I4 ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6013_sum__image__le,axiom,
% 9.17/5.41 ! [I4: set_nat,G: int > rat,F: nat > int] :
% 9.17/5.41 ( ( finite_finite_nat @ I4 )
% 9.17/5.41 => ( ! [I2: nat] :
% 9.17/5.41 ( ( member_nat @ I2 @ I4 )
% 9.17/5.41 => ( ord_less_eq_rat @ zero_zero_rat @ ( G @ ( F @ I2 ) ) ) )
% 9.17/5.41 => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ G @ ( image_nat_int @ F @ I4 ) ) @ ( groups2906978787729119204at_rat @ ( comp_int_rat_nat @ G @ F ) @ I4 ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6014_sum__image__le,axiom,
% 9.17/5.41 ! [I4: set_int,G: int > rat,F: int > int] :
% 9.17/5.41 ( ( finite_finite_int @ I4 )
% 9.17/5.41 => ( ! [I2: int] :
% 9.17/5.41 ( ( member_int @ I2 @ I4 )
% 9.17/5.41 => ( ord_less_eq_rat @ zero_zero_rat @ ( G @ ( F @ I2 ) ) ) )
% 9.17/5.41 => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ G @ ( image_int_int @ F @ I4 ) ) @ ( groups3906332499630173760nt_rat @ ( comp_int_rat_int @ G @ F ) @ I4 ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6015_sum__image__le,axiom,
% 9.17/5.41 ! [I4: set_int,G: int > nat,F: int > int] :
% 9.17/5.41 ( ( finite_finite_int @ I4 )
% 9.17/5.41 => ( ! [I2: int] :
% 9.17/5.41 ( ( member_int @ I2 @ I4 )
% 9.17/5.41 => ( ord_less_eq_nat @ zero_zero_nat @ ( G @ ( F @ I2 ) ) ) )
% 9.17/5.41 => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ G @ ( image_int_int @ F @ I4 ) ) @ ( groups4541462559716669496nt_nat @ ( comp_int_nat_int @ G @ F ) @ I4 ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6016_sum_Oremove,axiom,
% 9.17/5.41 ! [A2: set_Code_integer,X: code_integer,G: code_integer > rat] :
% 9.17/5.41 ( ( finite6017078050557962740nteger @ A2 )
% 9.17/5.41 => ( ( member_Code_integer @ X @ A2 )
% 9.17/5.41 => ( ( groups6602215022474089585er_rat @ G @ A2 )
% 9.17/5.41 = ( plus_plus_rat @ ( G @ X ) @ ( groups6602215022474089585er_rat @ G @ ( minus_2355218937544613996nteger @ A2 @ ( insert_Code_integer @ X @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6017_sum_Oremove,axiom,
% 9.17/5.41 ! [A2: set_Code_integer,X: code_integer,G: code_integer > nat] :
% 9.17/5.41 ( ( finite6017078050557962740nteger @ A2 )
% 9.17/5.41 => ( ( member_Code_integer @ X @ A2 )
% 9.17/5.41 => ( ( groups7237345082560585321er_nat @ G @ A2 )
% 9.17/5.41 = ( plus_plus_nat @ ( G @ X ) @ ( groups7237345082560585321er_nat @ G @ ( minus_2355218937544613996nteger @ A2 @ ( insert_Code_integer @ X @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6018_sum_Oremove,axiom,
% 9.17/5.41 ! [A2: set_Code_integer,X: code_integer,G: code_integer > int] :
% 9.17/5.41 ( ( finite6017078050557962740nteger @ A2 )
% 9.17/5.41 => ( ( member_Code_integer @ X @ A2 )
% 9.17/5.41 => ( ( groups7234854612051535045er_int @ G @ A2 )
% 9.17/5.41 = ( plus_plus_int @ ( G @ X ) @ ( groups7234854612051535045er_int @ G @ ( minus_2355218937544613996nteger @ A2 @ ( insert_Code_integer @ X @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6019_sum_Oremove,axiom,
% 9.17/5.41 ! [A2: set_o,X: $o,G: $o > rat] :
% 9.17/5.41 ( ( finite_finite_o @ A2 )
% 9.17/5.41 => ( ( member_o @ X @ A2 )
% 9.17/5.41 => ( ( groups7872700643590313910_o_rat @ G @ A2 )
% 9.17/5.41 = ( plus_plus_rat @ ( G @ X ) @ ( groups7872700643590313910_o_rat @ G @ ( minus_minus_set_o @ A2 @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6020_sum_Oremove,axiom,
% 9.17/5.41 ! [A2: set_o,X: $o,G: $o > nat] :
% 9.17/5.41 ( ( finite_finite_o @ A2 )
% 9.17/5.41 => ( ( member_o @ X @ A2 )
% 9.17/5.41 => ( ( groups8507830703676809646_o_nat @ G @ A2 )
% 9.17/5.41 = ( plus_plus_nat @ ( G @ X ) @ ( groups8507830703676809646_o_nat @ G @ ( minus_minus_set_o @ A2 @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6021_sum_Oremove,axiom,
% 9.17/5.41 ! [A2: set_o,X: $o,G: $o > int] :
% 9.17/5.41 ( ( finite_finite_o @ A2 )
% 9.17/5.41 => ( ( member_o @ X @ A2 )
% 9.17/5.41 => ( ( groups8505340233167759370_o_int @ G @ A2 )
% 9.17/5.41 = ( plus_plus_int @ ( G @ X ) @ ( groups8505340233167759370_o_int @ G @ ( minus_minus_set_o @ A2 @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6022_sum_Oremove,axiom,
% 9.17/5.41 ! [A2: set_int,X: int,G: int > rat] :
% 9.17/5.41 ( ( finite_finite_int @ A2 )
% 9.17/5.41 => ( ( member_int @ X @ A2 )
% 9.17/5.41 => ( ( groups3906332499630173760nt_rat @ G @ A2 )
% 9.17/5.41 = ( plus_plus_rat @ ( G @ X ) @ ( groups3906332499630173760nt_rat @ G @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6023_sum_Oremove,axiom,
% 9.17/5.41 ! [A2: set_int,X: int,G: int > nat] :
% 9.17/5.41 ( ( finite_finite_int @ A2 )
% 9.17/5.41 => ( ( member_int @ X @ A2 )
% 9.17/5.41 => ( ( groups4541462559716669496nt_nat @ G @ A2 )
% 9.17/5.41 = ( plus_plus_nat @ ( G @ X ) @ ( groups4541462559716669496nt_nat @ G @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6024_sum_Oremove,axiom,
% 9.17/5.41 ! [A2: set_nat,X: nat,G: nat > rat] :
% 9.17/5.41 ( ( finite_finite_nat @ A2 )
% 9.17/5.41 => ( ( member_nat @ X @ A2 )
% 9.17/5.41 => ( ( groups2906978787729119204at_rat @ G @ A2 )
% 9.17/5.41 = ( plus_plus_rat @ ( G @ X ) @ ( groups2906978787729119204at_rat @ G @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6025_sum_Oremove,axiom,
% 9.17/5.41 ! [A2: set_nat,X: nat,G: nat > int] :
% 9.17/5.41 ( ( finite_finite_nat @ A2 )
% 9.17/5.41 => ( ( member_nat @ X @ A2 )
% 9.17/5.41 => ( ( groups3539618377306564664at_int @ G @ A2 )
% 9.17/5.41 = ( plus_plus_int @ ( G @ X ) @ ( groups3539618377306564664at_int @ G @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6026_sum_Oinsert__remove,axiom,
% 9.17/5.41 ! [A2: set_Code_integer,G: code_integer > rat,X: code_integer] :
% 9.17/5.41 ( ( finite6017078050557962740nteger @ A2 )
% 9.17/5.41 => ( ( groups6602215022474089585er_rat @ G @ ( insert_Code_integer @ X @ A2 ) )
% 9.17/5.41 = ( plus_plus_rat @ ( G @ X ) @ ( groups6602215022474089585er_rat @ G @ ( minus_2355218937544613996nteger @ A2 @ ( insert_Code_integer @ X @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6027_sum_Oinsert__remove,axiom,
% 9.17/5.41 ! [A2: set_Code_integer,G: code_integer > nat,X: code_integer] :
% 9.17/5.41 ( ( finite6017078050557962740nteger @ A2 )
% 9.17/5.41 => ( ( groups7237345082560585321er_nat @ G @ ( insert_Code_integer @ X @ A2 ) )
% 9.17/5.41 = ( plus_plus_nat @ ( G @ X ) @ ( groups7237345082560585321er_nat @ G @ ( minus_2355218937544613996nteger @ A2 @ ( insert_Code_integer @ X @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6028_sum_Oinsert__remove,axiom,
% 9.17/5.41 ! [A2: set_Code_integer,G: code_integer > int,X: code_integer] :
% 9.17/5.41 ( ( finite6017078050557962740nteger @ A2 )
% 9.17/5.41 => ( ( groups7234854612051535045er_int @ G @ ( insert_Code_integer @ X @ A2 ) )
% 9.17/5.41 = ( plus_plus_int @ ( G @ X ) @ ( groups7234854612051535045er_int @ G @ ( minus_2355218937544613996nteger @ A2 @ ( insert_Code_integer @ X @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6029_sum_Oinsert__remove,axiom,
% 9.17/5.41 ! [A2: set_o,G: $o > rat,X: $o] :
% 9.17/5.41 ( ( finite_finite_o @ A2 )
% 9.17/5.41 => ( ( groups7872700643590313910_o_rat @ G @ ( insert_o @ X @ A2 ) )
% 9.17/5.41 = ( plus_plus_rat @ ( G @ X ) @ ( groups7872700643590313910_o_rat @ G @ ( minus_minus_set_o @ A2 @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6030_sum_Oinsert__remove,axiom,
% 9.17/5.41 ! [A2: set_o,G: $o > nat,X: $o] :
% 9.17/5.41 ( ( finite_finite_o @ A2 )
% 9.17/5.41 => ( ( groups8507830703676809646_o_nat @ G @ ( insert_o @ X @ A2 ) )
% 9.17/5.41 = ( plus_plus_nat @ ( G @ X ) @ ( groups8507830703676809646_o_nat @ G @ ( minus_minus_set_o @ A2 @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6031_sum_Oinsert__remove,axiom,
% 9.17/5.41 ! [A2: set_o,G: $o > int,X: $o] :
% 9.17/5.41 ( ( finite_finite_o @ A2 )
% 9.17/5.41 => ( ( groups8505340233167759370_o_int @ G @ ( insert_o @ X @ A2 ) )
% 9.17/5.41 = ( plus_plus_int @ ( G @ X ) @ ( groups8505340233167759370_o_int @ G @ ( minus_minus_set_o @ A2 @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6032_sum_Oinsert__remove,axiom,
% 9.17/5.41 ! [A2: set_int,G: int > rat,X: int] :
% 9.17/5.41 ( ( finite_finite_int @ A2 )
% 9.17/5.41 => ( ( groups3906332499630173760nt_rat @ G @ ( insert_int @ X @ A2 ) )
% 9.17/5.41 = ( plus_plus_rat @ ( G @ X ) @ ( groups3906332499630173760nt_rat @ G @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6033_sum_Oinsert__remove,axiom,
% 9.17/5.41 ! [A2: set_int,G: int > nat,X: int] :
% 9.17/5.41 ( ( finite_finite_int @ A2 )
% 9.17/5.41 => ( ( groups4541462559716669496nt_nat @ G @ ( insert_int @ X @ A2 ) )
% 9.17/5.41 = ( plus_plus_nat @ ( G @ X ) @ ( groups4541462559716669496nt_nat @ G @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6034_sum_Oinsert__remove,axiom,
% 9.17/5.41 ! [A2: set_nat,G: nat > rat,X: nat] :
% 9.17/5.41 ( ( finite_finite_nat @ A2 )
% 9.17/5.41 => ( ( groups2906978787729119204at_rat @ G @ ( insert_nat @ X @ A2 ) )
% 9.17/5.41 = ( plus_plus_rat @ ( G @ X ) @ ( groups2906978787729119204at_rat @ G @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6035_sum_Oinsert__remove,axiom,
% 9.17/5.41 ! [A2: set_nat,G: nat > int,X: nat] :
% 9.17/5.41 ( ( finite_finite_nat @ A2 )
% 9.17/5.41 => ( ( groups3539618377306564664at_int @ G @ ( insert_nat @ X @ A2 ) )
% 9.17/5.41 = ( plus_plus_int @ ( G @ X ) @ ( groups3539618377306564664at_int @ G @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6036_atLeast1__atMost__eq__remove0,axiom,
% 9.17/5.41 ! [N2: nat] :
% 9.17/5.41 ( ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 9.17/5.41 = ( minus_minus_set_nat @ ( set_ord_atMost_nat @ N2 ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6037_atLeast1__lessThan__eq__remove0,axiom,
% 9.17/5.41 ! [N2: nat] :
% 9.17/5.41 ( ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 9.17/5.41 = ( minus_minus_set_nat @ ( set_ord_lessThan_nat @ N2 ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6038_atLeastLessThan__nat__numeral,axiom,
% 9.17/5.41 ! [M2: nat,K: num] :
% 9.17/5.41 ( ( ( ord_less_eq_nat @ M2 @ ( pred_numeral @ K ) )
% 9.17/5.41 => ( ( set_or4665077453230672383an_nat @ M2 @ ( numeral_numeral_nat @ K ) )
% 9.17/5.41 = ( insert_nat @ ( pred_numeral @ K ) @ ( set_or4665077453230672383an_nat @ M2 @ ( pred_numeral @ K ) ) ) ) )
% 9.17/5.41 & ( ~ ( ord_less_eq_nat @ M2 @ ( pred_numeral @ K ) )
% 9.17/5.41 => ( ( set_or4665077453230672383an_nat @ M2 @ ( numeral_numeral_nat @ K ) )
% 9.17/5.41 = bot_bot_set_nat ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6039_sum_Odelta__remove,axiom,
% 9.17/5.41 ! [S2: set_Code_integer,A: code_integer,B: code_integer > rat,C: code_integer > rat] :
% 9.17/5.41 ( ( finite6017078050557962740nteger @ S2 )
% 9.17/5.41 => ( ( ( member_Code_integer @ A @ S2 )
% 9.17/5.41 => ( ( groups6602215022474089585er_rat
% 9.17/5.41 @ ^ [K4: code_integer] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 9.17/5.41 @ S2 )
% 9.17/5.41 = ( plus_plus_rat @ ( B @ A ) @ ( groups6602215022474089585er_rat @ C @ ( minus_2355218937544613996nteger @ S2 @ ( insert_Code_integer @ A @ bot_bo3990330152332043303nteger ) ) ) ) ) )
% 9.17/5.41 & ( ~ ( member_Code_integer @ A @ S2 )
% 9.17/5.41 => ( ( groups6602215022474089585er_rat
% 9.17/5.41 @ ^ [K4: code_integer] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 9.17/5.41 @ S2 )
% 9.17/5.41 = ( groups6602215022474089585er_rat @ C @ ( minus_2355218937544613996nteger @ S2 @ ( insert_Code_integer @ A @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6040_sum_Odelta__remove,axiom,
% 9.17/5.41 ! [S2: set_Code_integer,A: code_integer,B: code_integer > nat,C: code_integer > nat] :
% 9.17/5.41 ( ( finite6017078050557962740nteger @ S2 )
% 9.17/5.41 => ( ( ( member_Code_integer @ A @ S2 )
% 9.17/5.41 => ( ( groups7237345082560585321er_nat
% 9.17/5.41 @ ^ [K4: code_integer] : ( if_nat @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 9.17/5.41 @ S2 )
% 9.17/5.41 = ( plus_plus_nat @ ( B @ A ) @ ( groups7237345082560585321er_nat @ C @ ( minus_2355218937544613996nteger @ S2 @ ( insert_Code_integer @ A @ bot_bo3990330152332043303nteger ) ) ) ) ) )
% 9.17/5.41 & ( ~ ( member_Code_integer @ A @ S2 )
% 9.17/5.41 => ( ( groups7237345082560585321er_nat
% 9.17/5.41 @ ^ [K4: code_integer] : ( if_nat @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 9.17/5.41 @ S2 )
% 9.17/5.41 = ( groups7237345082560585321er_nat @ C @ ( minus_2355218937544613996nteger @ S2 @ ( insert_Code_integer @ A @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6041_sum_Odelta__remove,axiom,
% 9.17/5.41 ! [S2: set_Code_integer,A: code_integer,B: code_integer > int,C: code_integer > int] :
% 9.17/5.41 ( ( finite6017078050557962740nteger @ S2 )
% 9.17/5.41 => ( ( ( member_Code_integer @ A @ S2 )
% 9.17/5.41 => ( ( groups7234854612051535045er_int
% 9.17/5.41 @ ^ [K4: code_integer] : ( if_int @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 9.17/5.41 @ S2 )
% 9.17/5.41 = ( plus_plus_int @ ( B @ A ) @ ( groups7234854612051535045er_int @ C @ ( minus_2355218937544613996nteger @ S2 @ ( insert_Code_integer @ A @ bot_bo3990330152332043303nteger ) ) ) ) ) )
% 9.17/5.41 & ( ~ ( member_Code_integer @ A @ S2 )
% 9.17/5.41 => ( ( groups7234854612051535045er_int
% 9.17/5.41 @ ^ [K4: code_integer] : ( if_int @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 9.17/5.41 @ S2 )
% 9.17/5.41 = ( groups7234854612051535045er_int @ C @ ( minus_2355218937544613996nteger @ S2 @ ( insert_Code_integer @ A @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6042_sum_Odelta__remove,axiom,
% 9.17/5.41 ! [S2: set_o,A: $o,B: $o > rat,C: $o > rat] :
% 9.17/5.41 ( ( finite_finite_o @ S2 )
% 9.17/5.41 => ( ( ( member_o @ A @ S2 )
% 9.17/5.41 => ( ( groups7872700643590313910_o_rat
% 9.17/5.41 @ ^ [K4: $o] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 9.17/5.41 @ S2 )
% 9.17/5.41 = ( plus_plus_rat @ ( B @ A ) @ ( groups7872700643590313910_o_rat @ C @ ( minus_minus_set_o @ S2 @ ( insert_o @ A @ bot_bot_set_o ) ) ) ) ) )
% 9.17/5.41 & ( ~ ( member_o @ A @ S2 )
% 9.17/5.41 => ( ( groups7872700643590313910_o_rat
% 9.17/5.41 @ ^ [K4: $o] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 9.17/5.41 @ S2 )
% 9.17/5.41 = ( groups7872700643590313910_o_rat @ C @ ( minus_minus_set_o @ S2 @ ( insert_o @ A @ bot_bot_set_o ) ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6043_sum_Odelta__remove,axiom,
% 9.17/5.41 ! [S2: set_o,A: $o,B: $o > nat,C: $o > nat] :
% 9.17/5.41 ( ( finite_finite_o @ S2 )
% 9.17/5.41 => ( ( ( member_o @ A @ S2 )
% 9.17/5.41 => ( ( groups8507830703676809646_o_nat
% 9.17/5.41 @ ^ [K4: $o] : ( if_nat @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 9.17/5.41 @ S2 )
% 9.17/5.41 = ( plus_plus_nat @ ( B @ A ) @ ( groups8507830703676809646_o_nat @ C @ ( minus_minus_set_o @ S2 @ ( insert_o @ A @ bot_bot_set_o ) ) ) ) ) )
% 9.17/5.41 & ( ~ ( member_o @ A @ S2 )
% 9.17/5.41 => ( ( groups8507830703676809646_o_nat
% 9.17/5.41 @ ^ [K4: $o] : ( if_nat @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 9.17/5.41 @ S2 )
% 9.17/5.41 = ( groups8507830703676809646_o_nat @ C @ ( minus_minus_set_o @ S2 @ ( insert_o @ A @ bot_bot_set_o ) ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6044_sum_Odelta__remove,axiom,
% 9.17/5.41 ! [S2: set_o,A: $o,B: $o > int,C: $o > int] :
% 9.17/5.41 ( ( finite_finite_o @ S2 )
% 9.17/5.41 => ( ( ( member_o @ A @ S2 )
% 9.17/5.41 => ( ( groups8505340233167759370_o_int
% 9.17/5.41 @ ^ [K4: $o] : ( if_int @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 9.17/5.41 @ S2 )
% 9.17/5.41 = ( plus_plus_int @ ( B @ A ) @ ( groups8505340233167759370_o_int @ C @ ( minus_minus_set_o @ S2 @ ( insert_o @ A @ bot_bot_set_o ) ) ) ) ) )
% 9.17/5.41 & ( ~ ( member_o @ A @ S2 )
% 9.17/5.41 => ( ( groups8505340233167759370_o_int
% 9.17/5.41 @ ^ [K4: $o] : ( if_int @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 9.17/5.41 @ S2 )
% 9.17/5.41 = ( groups8505340233167759370_o_int @ C @ ( minus_minus_set_o @ S2 @ ( insert_o @ A @ bot_bot_set_o ) ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6045_sum_Odelta__remove,axiom,
% 9.17/5.41 ! [S2: set_int,A: int,B: int > rat,C: int > rat] :
% 9.17/5.41 ( ( finite_finite_int @ S2 )
% 9.17/5.41 => ( ( ( member_int @ A @ S2 )
% 9.17/5.41 => ( ( groups3906332499630173760nt_rat
% 9.17/5.41 @ ^ [K4: int] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 9.17/5.41 @ S2 )
% 9.17/5.41 = ( plus_plus_rat @ ( B @ A ) @ ( groups3906332499630173760nt_rat @ C @ ( minus_minus_set_int @ S2 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) )
% 9.17/5.41 & ( ~ ( member_int @ A @ S2 )
% 9.17/5.41 => ( ( groups3906332499630173760nt_rat
% 9.17/5.41 @ ^ [K4: int] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 9.17/5.41 @ S2 )
% 9.17/5.41 = ( groups3906332499630173760nt_rat @ C @ ( minus_minus_set_int @ S2 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6046_sum_Odelta__remove,axiom,
% 9.17/5.41 ! [S2: set_int,A: int,B: int > nat,C: int > nat] :
% 9.17/5.41 ( ( finite_finite_int @ S2 )
% 9.17/5.41 => ( ( ( member_int @ A @ S2 )
% 9.17/5.41 => ( ( groups4541462559716669496nt_nat
% 9.17/5.41 @ ^ [K4: int] : ( if_nat @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 9.17/5.41 @ S2 )
% 9.17/5.41 = ( plus_plus_nat @ ( B @ A ) @ ( groups4541462559716669496nt_nat @ C @ ( minus_minus_set_int @ S2 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) )
% 9.17/5.41 & ( ~ ( member_int @ A @ S2 )
% 9.17/5.41 => ( ( groups4541462559716669496nt_nat
% 9.17/5.41 @ ^ [K4: int] : ( if_nat @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 9.17/5.41 @ S2 )
% 9.17/5.41 = ( groups4541462559716669496nt_nat @ C @ ( minus_minus_set_int @ S2 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6047_sum_Odelta__remove,axiom,
% 9.17/5.41 ! [S2: set_nat,A: nat,B: nat > rat,C: nat > rat] :
% 9.17/5.41 ( ( finite_finite_nat @ S2 )
% 9.17/5.41 => ( ( ( member_nat @ A @ S2 )
% 9.17/5.41 => ( ( groups2906978787729119204at_rat
% 9.17/5.41 @ ^ [K4: nat] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 9.17/5.41 @ S2 )
% 9.17/5.41 = ( plus_plus_rat @ ( B @ A ) @ ( groups2906978787729119204at_rat @ C @ ( minus_minus_set_nat @ S2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ) )
% 9.17/5.41 & ( ~ ( member_nat @ A @ S2 )
% 9.17/5.41 => ( ( groups2906978787729119204at_rat
% 9.17/5.41 @ ^ [K4: nat] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 9.17/5.41 @ S2 )
% 9.17/5.41 = ( groups2906978787729119204at_rat @ C @ ( minus_minus_set_nat @ S2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6048_sum_Odelta__remove,axiom,
% 9.17/5.41 ! [S2: set_nat,A: nat,B: nat > int,C: nat > int] :
% 9.17/5.41 ( ( finite_finite_nat @ S2 )
% 9.17/5.41 => ( ( ( member_nat @ A @ S2 )
% 9.17/5.41 => ( ( groups3539618377306564664at_int
% 9.17/5.41 @ ^ [K4: nat] : ( if_int @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 9.17/5.41 @ S2 )
% 9.17/5.41 = ( plus_plus_int @ ( B @ A ) @ ( groups3539618377306564664at_int @ C @ ( minus_minus_set_nat @ S2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ) )
% 9.17/5.41 & ( ~ ( member_nat @ A @ S2 )
% 9.17/5.41 => ( ( groups3539618377306564664at_int
% 9.17/5.41 @ ^ [K4: nat] : ( if_int @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 9.17/5.41 @ S2 )
% 9.17/5.41 = ( groups3539618377306564664at_int @ C @ ( minus_minus_set_nat @ S2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6049_prod__le__power,axiom,
% 9.17/5.41 ! [A2: set_o,F: $o > code_integer,N2: code_integer,K: nat] :
% 9.17/5.41 ( ! [I2: $o] :
% 9.17/5.41 ( ( member_o @ I2 @ A2 )
% 9.17/5.41 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ I2 ) )
% 9.17/5.41 & ( ord_le3102999989581377725nteger @ ( F @ I2 ) @ N2 ) ) )
% 9.17/5.41 => ( ( ord_less_eq_nat @ ( finite_card_o @ A2 ) @ K )
% 9.17/5.41 => ( ( ord_le3102999989581377725nteger @ one_one_Code_integer @ N2 )
% 9.17/5.41 => ( ord_le3102999989581377725nteger @ ( groups7694694392188491536nteger @ F @ A2 ) @ ( power_8256067586552552935nteger @ N2 @ K ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6050_prod__le__power,axiom,
% 9.17/5.41 ! [A2: set_int,F: int > code_integer,N2: code_integer,K: nat] :
% 9.17/5.41 ( ! [I2: int] :
% 9.17/5.41 ( ( member_int @ I2 @ A2 )
% 9.17/5.41 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ I2 ) )
% 9.17/5.41 & ( ord_le3102999989581377725nteger @ ( F @ I2 ) @ N2 ) ) )
% 9.17/5.41 => ( ( ord_less_eq_nat @ ( finite_card_int @ A2 ) @ K )
% 9.17/5.41 => ( ( ord_le3102999989581377725nteger @ one_one_Code_integer @ N2 )
% 9.17/5.41 => ( ord_le3102999989581377725nteger @ ( groups3827104343326376752nteger @ F @ A2 ) @ ( power_8256067586552552935nteger @ N2 @ K ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6051_prod__le__power,axiom,
% 9.17/5.41 ! [A2: set_Product_unit,F: product_unit > code_integer,N2: code_integer,K: nat] :
% 9.17/5.41 ( ! [I2: product_unit] :
% 9.17/5.41 ( ( member_Product_unit @ I2 @ A2 )
% 9.17/5.41 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ I2 ) )
% 9.17/5.41 & ( ord_le3102999989581377725nteger @ ( F @ I2 ) @ N2 ) ) )
% 9.17/5.41 => ( ( ord_less_eq_nat @ ( finite410649719033368117t_unit @ A2 ) @ K )
% 9.17/5.41 => ( ( ord_le3102999989581377725nteger @ one_one_Code_integer @ N2 )
% 9.17/5.41 => ( ord_le3102999989581377725nteger @ ( groups8185359811944078981nteger @ F @ A2 ) @ ( power_8256067586552552935nteger @ N2 @ K ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6052_prod__le__power,axiom,
% 9.17/5.41 ! [A2: set_nat,F: nat > code_integer,N2: code_integer,K: nat] :
% 9.17/5.41 ( ! [I2: nat] :
% 9.17/5.41 ( ( member_nat @ I2 @ A2 )
% 9.17/5.41 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ I2 ) )
% 9.17/5.41 & ( ord_le3102999989581377725nteger @ ( F @ I2 ) @ N2 ) ) )
% 9.17/5.41 => ( ( ord_less_eq_nat @ ( finite_card_nat @ A2 ) @ K )
% 9.17/5.41 => ( ( ord_le3102999989581377725nteger @ one_one_Code_integer @ N2 )
% 9.17/5.41 => ( ord_le3102999989581377725nteger @ ( groups3455450783089532116nteger @ F @ A2 ) @ ( power_8256067586552552935nteger @ N2 @ K ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6053_prod__le__power,axiom,
% 9.17/5.41 ! [A2: set_o,F: $o > rat,N2: rat,K: nat] :
% 9.17/5.41 ( ! [I2: $o] :
% 9.17/5.41 ( ( member_o @ I2 @ A2 )
% 9.17/5.41 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) )
% 9.17/5.41 & ( ord_less_eq_rat @ ( F @ I2 ) @ N2 ) ) )
% 9.17/5.41 => ( ( ord_less_eq_nat @ ( finite_card_o @ A2 ) @ K )
% 9.17/5.41 => ( ( ord_less_eq_rat @ one_one_rat @ N2 )
% 9.17/5.41 => ( ord_less_eq_rat @ ( groups2869687844427037835_o_rat @ F @ A2 ) @ ( power_power_rat @ N2 @ K ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6054_prod__le__power,axiom,
% 9.17/5.41 ! [A2: set_int,F: int > rat,N2: rat,K: nat] :
% 9.17/5.41 ( ! [I2: int] :
% 9.17/5.41 ( ( member_int @ I2 @ A2 )
% 9.17/5.41 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) )
% 9.17/5.41 & ( ord_less_eq_rat @ ( F @ I2 ) @ N2 ) ) )
% 9.17/5.41 => ( ( ord_less_eq_nat @ ( finite_card_int @ A2 ) @ K )
% 9.17/5.41 => ( ( ord_less_eq_rat @ one_one_rat @ N2 )
% 9.17/5.41 => ( ord_less_eq_rat @ ( groups1072433553688619179nt_rat @ F @ A2 ) @ ( power_power_rat @ N2 @ K ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6055_prod__le__power,axiom,
% 9.17/5.41 ! [A2: set_Product_unit,F: product_unit > rat,N2: rat,K: nat] :
% 9.17/5.41 ( ! [I2: product_unit] :
% 9.17/5.41 ( ( member_Product_unit @ I2 @ A2 )
% 9.17/5.41 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) )
% 9.17/5.41 & ( ord_less_eq_rat @ ( F @ I2 ) @ N2 ) ) )
% 9.17/5.41 => ( ( ord_less_eq_nat @ ( finite410649719033368117t_unit @ A2 ) @ K )
% 9.17/5.41 => ( ( ord_less_eq_rat @ one_one_rat @ N2 )
% 9.17/5.41 => ( ord_less_eq_rat @ ( groups8984663225794451456it_rat @ F @ A2 ) @ ( power_power_rat @ N2 @ K ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6056_prod__le__power,axiom,
% 9.17/5.41 ! [A2: set_nat,F: nat > rat,N2: rat,K: nat] :
% 9.17/5.41 ( ! [I2: nat] :
% 9.17/5.41 ( ( member_nat @ I2 @ A2 )
% 9.17/5.41 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) )
% 9.17/5.41 & ( ord_less_eq_rat @ ( F @ I2 ) @ N2 ) ) )
% 9.17/5.41 => ( ( ord_less_eq_nat @ ( finite_card_nat @ A2 ) @ K )
% 9.17/5.41 => ( ( ord_less_eq_rat @ one_one_rat @ N2 )
% 9.17/5.41 => ( ord_less_eq_rat @ ( groups73079841787564623at_rat @ F @ A2 ) @ ( power_power_rat @ N2 @ K ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6057_prod__le__power,axiom,
% 9.17/5.41 ! [A2: set_o,F: $o > nat,N2: nat,K: nat] :
% 9.17/5.41 ( ! [I2: $o] :
% 9.17/5.41 ( ( member_o @ I2 @ A2 )
% 9.17/5.41 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I2 ) )
% 9.17/5.41 & ( ord_less_eq_nat @ ( F @ I2 ) @ N2 ) ) )
% 9.17/5.41 => ( ( ord_less_eq_nat @ ( finite_card_o @ A2 ) @ K )
% 9.17/5.41 => ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 9.17/5.41 => ( ord_less_eq_nat @ ( groups3504817904513533571_o_nat @ F @ A2 ) @ ( power_power_nat @ N2 @ K ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6058_prod__le__power,axiom,
% 9.17/5.41 ! [A2: set_int,F: int > nat,N2: nat,K: nat] :
% 9.17/5.41 ( ! [I2: int] :
% 9.17/5.41 ( ( member_int @ I2 @ A2 )
% 9.17/5.41 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I2 ) )
% 9.17/5.41 & ( ord_less_eq_nat @ ( F @ I2 ) @ N2 ) ) )
% 9.17/5.41 => ( ( ord_less_eq_nat @ ( finite_card_int @ A2 ) @ K )
% 9.17/5.41 => ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 9.17/5.41 => ( ord_less_eq_nat @ ( groups1707563613775114915nt_nat @ F @ A2 ) @ ( power_power_nat @ N2 @ K ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6059_card__Diff__insert,axiom,
% 9.17/5.41 ! [A: produc3843707927480180839at_nat,A2: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat] :
% 9.17/5.41 ( ( member8757157785044589968at_nat @ A @ A2 )
% 9.17/5.41 => ( ~ ( member8757157785044589968at_nat @ A @ B5 )
% 9.17/5.41 => ( ( finite3771342082235030671at_nat @ ( minus_3314409938677909166at_nat @ A2 @ ( insert9069300056098147895at_nat @ A @ B5 ) ) )
% 9.17/5.41 = ( minus_minus_nat @ ( finite3771342082235030671at_nat @ ( minus_3314409938677909166at_nat @ A2 @ B5 ) ) @ one_one_nat ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6060_card__Diff__insert,axiom,
% 9.17/5.41 ! [A: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 9.17/5.41 ( ( member8440522571783428010at_nat @ A @ A2 )
% 9.17/5.41 => ( ~ ( member8440522571783428010at_nat @ A @ B5 )
% 9.17/5.41 => ( ( finite711546835091564841at_nat @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ A @ B5 ) ) )
% 9.17/5.41 = ( minus_minus_nat @ ( finite711546835091564841at_nat @ ( minus_1356011639430497352at_nat @ A2 @ B5 ) ) @ one_one_nat ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6061_card__Diff__insert,axiom,
% 9.17/5.41 ! [A: $o,A2: set_o,B5: set_o] :
% 9.17/5.41 ( ( member_o @ A @ A2 )
% 9.17/5.41 => ( ~ ( member_o @ A @ B5 )
% 9.17/5.41 => ( ( finite_card_o @ ( minus_minus_set_o @ A2 @ ( insert_o @ A @ B5 ) ) )
% 9.17/5.41 = ( minus_minus_nat @ ( finite_card_o @ ( minus_minus_set_o @ A2 @ B5 ) ) @ one_one_nat ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6062_card__Diff__insert,axiom,
% 9.17/5.41 ! [A: int,A2: set_int,B5: set_int] :
% 9.17/5.41 ( ( member_int @ A @ A2 )
% 9.17/5.41 => ( ~ ( member_int @ A @ B5 )
% 9.17/5.41 => ( ( finite_card_int @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ B5 ) ) )
% 9.17/5.41 = ( minus_minus_nat @ ( finite_card_int @ ( minus_minus_set_int @ A2 @ B5 ) ) @ one_one_nat ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6063_card__Diff__insert,axiom,
% 9.17/5.41 ! [A: product_unit,A2: set_Product_unit,B5: set_Product_unit] :
% 9.17/5.41 ( ( member_Product_unit @ A @ A2 )
% 9.17/5.41 => ( ~ ( member_Product_unit @ A @ B5 )
% 9.17/5.41 => ( ( finite410649719033368117t_unit @ ( minus_6452836326544984404t_unit @ A2 @ ( insert_Product_unit @ A @ B5 ) ) )
% 9.17/5.41 = ( minus_minus_nat @ ( finite410649719033368117t_unit @ ( minus_6452836326544984404t_unit @ A2 @ B5 ) ) @ one_one_nat ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6064_card__Diff__insert,axiom,
% 9.17/5.41 ! [A: list_nat,A2: set_list_nat,B5: set_list_nat] :
% 9.17/5.41 ( ( member_list_nat @ A @ A2 )
% 9.17/5.41 => ( ~ ( member_list_nat @ A @ B5 )
% 9.17/5.41 => ( ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A2 @ ( insert_list_nat @ A @ B5 ) ) )
% 9.17/5.41 = ( minus_minus_nat @ ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A2 @ B5 ) ) @ one_one_nat ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6065_card__Diff__insert,axiom,
% 9.17/5.41 ! [A: nat,A2: set_nat,B5: set_nat] :
% 9.17/5.41 ( ( member_nat @ A @ A2 )
% 9.17/5.41 => ( ~ ( member_nat @ A @ B5 )
% 9.17/5.41 => ( ( finite_card_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ B5 ) ) )
% 9.17/5.41 = ( minus_minus_nat @ ( finite_card_nat @ ( minus_minus_set_nat @ A2 @ B5 ) ) @ one_one_nat ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6066_card__insert__le__m1,axiom,
% 9.17/5.41 ! [N2: nat,Y: set_Pr4329608150637261639at_nat,X: produc3843707927480180839at_nat] :
% 9.17/5.41 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 9.17/5.41 => ( ( ord_less_eq_nat @ ( finite3771342082235030671at_nat @ Y ) @ ( minus_minus_nat @ N2 @ one_one_nat ) )
% 9.17/5.41 => ( ord_less_eq_nat @ ( finite3771342082235030671at_nat @ ( insert9069300056098147895at_nat @ X @ Y ) ) @ N2 ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6067_card__insert__le__m1,axiom,
% 9.17/5.41 ! [N2: nat,Y: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat] :
% 9.17/5.41 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 9.17/5.41 => ( ( ord_less_eq_nat @ ( finite711546835091564841at_nat @ Y ) @ ( minus_minus_nat @ N2 @ one_one_nat ) )
% 9.17/5.41 => ( ord_less_eq_nat @ ( finite711546835091564841at_nat @ ( insert8211810215607154385at_nat @ X @ Y ) ) @ N2 ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6068_card__insert__le__m1,axiom,
% 9.17/5.41 ! [N2: nat,Y: set_o,X: $o] :
% 9.17/5.41 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 9.17/5.41 => ( ( ord_less_eq_nat @ ( finite_card_o @ Y ) @ ( minus_minus_nat @ N2 @ one_one_nat ) )
% 9.17/5.41 => ( ord_less_eq_nat @ ( finite_card_o @ ( insert_o @ X @ Y ) ) @ N2 ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6069_card__insert__le__m1,axiom,
% 9.17/5.41 ! [N2: nat,Y: set_int,X: int] :
% 9.17/5.41 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 9.17/5.41 => ( ( ord_less_eq_nat @ ( finite_card_int @ Y ) @ ( minus_minus_nat @ N2 @ one_one_nat ) )
% 9.17/5.41 => ( ord_less_eq_nat @ ( finite_card_int @ ( insert_int @ X @ Y ) ) @ N2 ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6070_card__insert__le__m1,axiom,
% 9.17/5.41 ! [N2: nat,Y: set_Product_unit,X: product_unit] :
% 9.17/5.41 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 9.17/5.41 => ( ( ord_less_eq_nat @ ( finite410649719033368117t_unit @ Y ) @ ( minus_minus_nat @ N2 @ one_one_nat ) )
% 9.17/5.41 => ( ord_less_eq_nat @ ( finite410649719033368117t_unit @ ( insert_Product_unit @ X @ Y ) ) @ N2 ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6071_card__insert__le__m1,axiom,
% 9.17/5.41 ! [N2: nat,Y: set_nat,X: nat] :
% 9.17/5.41 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 9.17/5.41 => ( ( ord_less_eq_nat @ ( finite_card_nat @ Y ) @ ( minus_minus_nat @ N2 @ one_one_nat ) )
% 9.17/5.41 => ( ord_less_eq_nat @ ( finite_card_nat @ ( insert_nat @ X @ Y ) ) @ N2 ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6072_card__insert__le__m1,axiom,
% 9.17/5.41 ! [N2: nat,Y: set_list_nat,X: list_nat] :
% 9.17/5.41 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 9.17/5.41 => ( ( ord_less_eq_nat @ ( finite_card_list_nat @ Y ) @ ( minus_minus_nat @ N2 @ one_one_nat ) )
% 9.17/5.41 => ( ord_less_eq_nat @ ( finite_card_list_nat @ ( insert_list_nat @ X @ Y ) ) @ N2 ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6073_card__Diff__singleton__if,axiom,
% 9.17/5.41 ! [X: product_unit,A2: set_Product_unit] :
% 9.17/5.41 ( ( ( member_Product_unit @ X @ A2 )
% 9.17/5.41 => ( ( finite410649719033368117t_unit @ ( minus_6452836326544984404t_unit @ A2 @ ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) ) )
% 9.17/5.41 = ( minus_minus_nat @ ( finite410649719033368117t_unit @ A2 ) @ one_one_nat ) ) )
% 9.17/5.41 & ( ~ ( member_Product_unit @ X @ A2 )
% 9.17/5.41 => ( ( finite410649719033368117t_unit @ ( minus_6452836326544984404t_unit @ A2 @ ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) ) )
% 9.17/5.41 = ( finite410649719033368117t_unit @ A2 ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6074_card__Diff__singleton__if,axiom,
% 9.17/5.41 ! [X: list_nat,A2: set_list_nat] :
% 9.17/5.41 ( ( ( member_list_nat @ X @ A2 )
% 9.17/5.41 => ( ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A2 @ ( insert_list_nat @ X @ bot_bot_set_list_nat ) ) )
% 9.17/5.41 = ( minus_minus_nat @ ( finite_card_list_nat @ A2 ) @ one_one_nat ) ) )
% 9.17/5.41 & ( ~ ( member_list_nat @ X @ A2 )
% 9.17/5.41 => ( ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A2 @ ( insert_list_nat @ X @ bot_bot_set_list_nat ) ) )
% 9.17/5.41 = ( finite_card_list_nat @ A2 ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6075_card__Diff__singleton__if,axiom,
% 9.17/5.41 ! [X: produc3843707927480180839at_nat,A2: set_Pr4329608150637261639at_nat] :
% 9.17/5.41 ( ( ( member8757157785044589968at_nat @ X @ A2 )
% 9.17/5.41 => ( ( finite3771342082235030671at_nat @ ( minus_3314409938677909166at_nat @ A2 @ ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) ) )
% 9.17/5.41 = ( minus_minus_nat @ ( finite3771342082235030671at_nat @ A2 ) @ one_one_nat ) ) )
% 9.17/5.41 & ( ~ ( member8757157785044589968at_nat @ X @ A2 )
% 9.17/5.41 => ( ( finite3771342082235030671at_nat @ ( minus_3314409938677909166at_nat @ A2 @ ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) ) )
% 9.17/5.41 = ( finite3771342082235030671at_nat @ A2 ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6076_card__Diff__singleton__if,axiom,
% 9.17/5.41 ! [X: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat] :
% 9.17/5.41 ( ( ( member8440522571783428010at_nat @ X @ A2 )
% 9.17/5.41 => ( ( finite711546835091564841at_nat @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) )
% 9.17/5.41 = ( minus_minus_nat @ ( finite711546835091564841at_nat @ A2 ) @ one_one_nat ) ) )
% 9.17/5.41 & ( ~ ( member8440522571783428010at_nat @ X @ A2 )
% 9.17/5.41 => ( ( finite711546835091564841at_nat @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) )
% 9.17/5.41 = ( finite711546835091564841at_nat @ A2 ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6077_card__Diff__singleton__if,axiom,
% 9.17/5.41 ! [X: $o,A2: set_o] :
% 9.17/5.41 ( ( ( member_o @ X @ A2 )
% 9.17/5.41 => ( ( finite_card_o @ ( minus_minus_set_o @ A2 @ ( insert_o @ X @ bot_bot_set_o ) ) )
% 9.17/5.41 = ( minus_minus_nat @ ( finite_card_o @ A2 ) @ one_one_nat ) ) )
% 9.17/5.41 & ( ~ ( member_o @ X @ A2 )
% 9.17/5.41 => ( ( finite_card_o @ ( minus_minus_set_o @ A2 @ ( insert_o @ X @ bot_bot_set_o ) ) )
% 9.17/5.41 = ( finite_card_o @ A2 ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6078_card__Diff__singleton__if,axiom,
% 9.17/5.41 ! [X: int,A2: set_int] :
% 9.17/5.41 ( ( ( member_int @ X @ A2 )
% 9.17/5.41 => ( ( finite_card_int @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) )
% 9.17/5.41 = ( minus_minus_nat @ ( finite_card_int @ A2 ) @ one_one_nat ) ) )
% 9.17/5.41 & ( ~ ( member_int @ X @ A2 )
% 9.17/5.41 => ( ( finite_card_int @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) )
% 9.17/5.41 = ( finite_card_int @ A2 ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6079_card__Diff__singleton__if,axiom,
% 9.17/5.41 ! [X: nat,A2: set_nat] :
% 9.17/5.41 ( ( ( member_nat @ X @ A2 )
% 9.17/5.41 => ( ( finite_card_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) )
% 9.17/5.41 = ( minus_minus_nat @ ( finite_card_nat @ A2 ) @ one_one_nat ) ) )
% 9.17/5.41 & ( ~ ( member_nat @ X @ A2 )
% 9.17/5.41 => ( ( finite_card_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) )
% 9.17/5.41 = ( finite_card_nat @ A2 ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6080_card__Diff__singleton,axiom,
% 9.17/5.41 ! [X: product_unit,A2: set_Product_unit] :
% 9.17/5.41 ( ( member_Product_unit @ X @ A2 )
% 9.17/5.41 => ( ( finite410649719033368117t_unit @ ( minus_6452836326544984404t_unit @ A2 @ ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) ) )
% 9.17/5.41 = ( minus_minus_nat @ ( finite410649719033368117t_unit @ A2 ) @ one_one_nat ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6081_card__Diff__singleton,axiom,
% 9.17/5.41 ! [X: list_nat,A2: set_list_nat] :
% 9.17/5.41 ( ( member_list_nat @ X @ A2 )
% 9.17/5.41 => ( ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A2 @ ( insert_list_nat @ X @ bot_bot_set_list_nat ) ) )
% 9.17/5.41 = ( minus_minus_nat @ ( finite_card_list_nat @ A2 ) @ one_one_nat ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6082_card__Diff__singleton,axiom,
% 9.17/5.41 ! [X: produc3843707927480180839at_nat,A2: set_Pr4329608150637261639at_nat] :
% 9.17/5.41 ( ( member8757157785044589968at_nat @ X @ A2 )
% 9.17/5.41 => ( ( finite3771342082235030671at_nat @ ( minus_3314409938677909166at_nat @ A2 @ ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) ) )
% 9.17/5.41 = ( minus_minus_nat @ ( finite3771342082235030671at_nat @ A2 ) @ one_one_nat ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6083_card__Diff__singleton,axiom,
% 9.17/5.41 ! [X: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat] :
% 9.17/5.41 ( ( member8440522571783428010at_nat @ X @ A2 )
% 9.17/5.41 => ( ( finite711546835091564841at_nat @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) )
% 9.17/5.41 = ( minus_minus_nat @ ( finite711546835091564841at_nat @ A2 ) @ one_one_nat ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6084_card__Diff__singleton,axiom,
% 9.17/5.41 ! [X: $o,A2: set_o] :
% 9.17/5.41 ( ( member_o @ X @ A2 )
% 9.17/5.41 => ( ( finite_card_o @ ( minus_minus_set_o @ A2 @ ( insert_o @ X @ bot_bot_set_o ) ) )
% 9.17/5.41 = ( minus_minus_nat @ ( finite_card_o @ A2 ) @ one_one_nat ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6085_card__Diff__singleton,axiom,
% 9.17/5.41 ! [X: int,A2: set_int] :
% 9.17/5.41 ( ( member_int @ X @ A2 )
% 9.17/5.41 => ( ( finite_card_int @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) )
% 9.17/5.41 = ( minus_minus_nat @ ( finite_card_int @ A2 ) @ one_one_nat ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6086_card__Diff__singleton,axiom,
% 9.17/5.41 ! [X: nat,A2: set_nat] :
% 9.17/5.41 ( ( member_nat @ X @ A2 )
% 9.17/5.41 => ( ( finite_card_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) )
% 9.17/5.41 = ( minus_minus_nat @ ( finite_card_nat @ A2 ) @ one_one_nat ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6087_in__finite__psubset,axiom,
% 9.17/5.41 ! [A2: set_nat,B5: set_nat] :
% 9.17/5.41 ( ( member8277197624267554838et_nat @ ( produc4532415448927165861et_nat @ A2 @ B5 ) @ finite_psubset_nat )
% 9.17/5.41 = ( ( ord_less_set_nat @ A2 @ B5 )
% 9.17/5.41 & ( finite_finite_nat @ B5 ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6088_in__finite__psubset,axiom,
% 9.17/5.41 ! [A2: set_int,B5: set_int] :
% 9.17/5.41 ( ( member2572552093476627150et_int @ ( produc6363374080413544029et_int @ A2 @ B5 ) @ finite_psubset_int )
% 9.17/5.41 = ( ( ord_less_set_int @ A2 @ B5 )
% 9.17/5.41 & ( finite_finite_int @ B5 ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6089_in__finite__psubset,axiom,
% 9.17/5.41 ! [A2: set_Code_integer,B5: set_Code_integer] :
% 9.17/5.41 ( ( member4307123515891402160nteger @ ( produc7443773368509356479nteger @ A2 @ B5 ) @ finite2416775604798480986nteger )
% 9.17/5.41 = ( ( ord_le1307284697595431911nteger @ A2 @ B5 )
% 9.17/5.41 & ( finite6017078050557962740nteger @ B5 ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6090_in__finite__psubset,axiom,
% 9.17/5.41 ! [A2: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 9.17/5.41 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A2 @ B5 ) @ finite469560695537375940at_nat )
% 9.17/5.41 = ( ( ord_le7866589430770878221at_nat @ A2 @ B5 )
% 9.17/5.41 & ( finite6177210948735845034at_nat @ B5 ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6091_card__1__singletonE,axiom,
% 9.17/5.41 ! [A2: set_Product_unit] :
% 9.17/5.41 ( ( ( finite410649719033368117t_unit @ A2 )
% 9.17/5.41 = one_one_nat )
% 9.17/5.41 => ~ ! [X4: product_unit] :
% 9.17/5.41 ( A2
% 9.17/5.41 != ( insert_Product_unit @ X4 @ bot_bo3957492148770167129t_unit ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6092_card__1__singletonE,axiom,
% 9.17/5.41 ! [A2: set_list_nat] :
% 9.17/5.41 ( ( ( finite_card_list_nat @ A2 )
% 9.17/5.41 = one_one_nat )
% 9.17/5.41 => ~ ! [X4: list_nat] :
% 9.17/5.41 ( A2
% 9.17/5.41 != ( insert_list_nat @ X4 @ bot_bot_set_list_nat ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6093_card__1__singletonE,axiom,
% 9.17/5.41 ! [A2: set_Pr4329608150637261639at_nat] :
% 9.17/5.41 ( ( ( finite3771342082235030671at_nat @ A2 )
% 9.17/5.41 = one_one_nat )
% 9.17/5.41 => ~ ! [X4: produc3843707927480180839at_nat] :
% 9.17/5.41 ( A2
% 9.17/5.41 != ( insert9069300056098147895at_nat @ X4 @ bot_bo228742789529271731at_nat ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6094_card__1__singletonE,axiom,
% 9.17/5.41 ! [A2: set_Pr1261947904930325089at_nat] :
% 9.17/5.41 ( ( ( finite711546835091564841at_nat @ A2 )
% 9.17/5.41 = one_one_nat )
% 9.17/5.41 => ~ ! [X4: product_prod_nat_nat] :
% 9.17/5.41 ( A2
% 9.17/5.41 != ( insert8211810215607154385at_nat @ X4 @ bot_bo2099793752762293965at_nat ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6095_card__1__singletonE,axiom,
% 9.17/5.41 ! [A2: set_o] :
% 9.17/5.41 ( ( ( finite_card_o @ A2 )
% 9.17/5.41 = one_one_nat )
% 9.17/5.41 => ~ ! [X4: $o] :
% 9.17/5.41 ( A2
% 9.17/5.41 != ( insert_o @ X4 @ bot_bot_set_o ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6096_card__1__singletonE,axiom,
% 9.17/5.41 ! [A2: set_nat] :
% 9.17/5.41 ( ( ( finite_card_nat @ A2 )
% 9.17/5.41 = one_one_nat )
% 9.17/5.41 => ~ ! [X4: nat] :
% 9.17/5.41 ( A2
% 9.17/5.41 != ( insert_nat @ X4 @ bot_bot_set_nat ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6097_card__1__singletonE,axiom,
% 9.17/5.41 ! [A2: set_int] :
% 9.17/5.41 ( ( ( finite_card_int @ A2 )
% 9.17/5.41 = one_one_nat )
% 9.17/5.41 => ~ ! [X4: int] :
% 9.17/5.41 ( A2
% 9.17/5.41 != ( insert_int @ X4 @ bot_bot_set_int ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6098_integer__of__nat__def,axiom,
% 9.17/5.41 ( code_integer_of_nat
% 9.17/5.41 = ( map_fu6290471996055670595nteger @ id_nat @ code_integer_of_int @ semiri1314217659103216013at_int ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6099_card__UNIV__unit,axiom,
% 9.17/5.41 ( ( finite410649719033368117t_unit @ top_to1996260823553986621t_unit )
% 9.17/5.41 = one_one_nat ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6100_card__lessThan,axiom,
% 9.17/5.41 ! [U: nat] :
% 9.17/5.41 ( ( finite_card_nat @ ( set_ord_lessThan_nat @ U ) )
% 9.17/5.41 = U ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6101_card__atLeastLessThan,axiom,
% 9.17/5.41 ! [L: nat,U: nat] :
% 9.17/5.41 ( ( finite_card_nat @ ( set_or4665077453230672383an_nat @ L @ U ) )
% 9.17/5.41 = ( minus_minus_nat @ U @ L ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6102_card__atMost,axiom,
% 9.17/5.41 ! [U: nat] :
% 9.17/5.41 ( ( finite_card_nat @ ( set_ord_atMost_nat @ U ) )
% 9.17/5.41 = ( suc @ U ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6103_Collect__const__case__prod,axiom,
% 9.17/5.41 ! [P: $o] :
% 9.17/5.41 ( ( P
% 9.17/5.41 => ( ( collec6321179662152712658at_nat
% 9.17/5.41 @ ( produc410239310623530412_nat_o
% 9.17/5.41 @ ^ [A5: set_Pr1261947904930325089at_nat,B4: set_Pr1261947904930325089at_nat] : P ) )
% 9.17/5.41 = top_to6833984726390702231at_nat ) )
% 9.17/5.41 & ( ~ P
% 9.17/5.41 => ( ( collec6321179662152712658at_nat
% 9.17/5.41 @ ( produc410239310623530412_nat_o
% 9.17/5.41 @ ^ [A5: set_Pr1261947904930325089at_nat,B4: set_Pr1261947904930325089at_nat] : P ) )
% 9.17/5.41 = bot_bo228742789529271731at_nat ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6104_Collect__const__case__prod,axiom,
% 9.17/5.41 ! [P: $o] :
% 9.17/5.41 ( ( P
% 9.17/5.41 => ( ( collec3392354462482085612at_nat
% 9.17/5.41 @ ( produc6081775807080527818_nat_o
% 9.17/5.41 @ ^ [A5: nat,B4: nat] : P ) )
% 9.17/5.41 = top_to4669805908274784177at_nat ) )
% 9.17/5.41 & ( ~ P
% 9.17/5.41 => ( ( collec3392354462482085612at_nat
% 9.17/5.41 @ ( produc6081775807080527818_nat_o
% 9.17/5.41 @ ^ [A5: nat,B4: nat] : P ) )
% 9.17/5.41 = bot_bo2099793752762293965at_nat ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6105_nat__of__integer__integer__of__nat,axiom,
% 9.17/5.41 ! [N2: nat] :
% 9.17/5.41 ( ( code_nat_of_integer @ ( code_integer_of_nat @ N2 ) )
% 9.17/5.41 = N2 ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6106_card__atLeastAtMost,axiom,
% 9.17/5.41 ! [L: nat,U: nat] :
% 9.17/5.41 ( ( finite_card_nat @ ( set_or1269000886237332187st_nat @ L @ U ) )
% 9.17/5.41 = ( minus_minus_nat @ ( suc @ U ) @ L ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6107_integer__of__nat_Orep__eq,axiom,
% 9.17/5.41 ! [X: nat] :
% 9.17/5.41 ( ( code_int_of_integer @ ( code_integer_of_nat @ X ) )
% 9.17/5.41 = ( semiri1314217659103216013at_int @ X ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6108_int__of__integer__integer__of__nat,axiom,
% 9.17/5.41 ! [N2: nat] :
% 9.17/5.41 ( ( code_int_of_integer @ ( code_integer_of_nat @ N2 ) )
% 9.17/5.41 = ( semiri1314217659103216013at_int @ N2 ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6109_top__empty__eq2,axiom,
% 9.17/5.41 ( top_to8903224817164384382_nat_o
% 9.17/5.41 = ( ^ [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ Y3 ) @ top_to6833984726390702231at_nat ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6110_top__empty__eq2,axiom,
% 9.17/5.41 ( top_top_nat_nat_o
% 9.17/5.41 = ( ^ [X3: nat,Y3: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y3 ) @ top_to4669805908274784177at_nat ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6111_top__empty__eq2,axiom,
% 9.17/5.41 ( top_to8112647782992986859eger_o
% 9.17/5.41 = ( ^ [X3: produc6241069584506657477e_term > option6357759511663192854e_term,Y3: produc8923325533196201883nteger] : ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X3 @ Y3 ) @ top_to7512759353274530428nteger ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6112_top__empty__eq2,axiom,
% 9.17/5.41 ( top_to2428096842796733269_nat_o
% 9.17/5.41 = ( ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3658429121746597890et_nat] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X3 @ Y3 ) @ top_to8753217654552796900et_nat ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6113_top__empty__eq2,axiom,
% 9.17/5.41 ( top_to7190503160269336793_nat_o
% 9.17/5.41 = ( ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3925858234332021118et_nat] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X3 @ Y3 ) @ top_to1599102959340997728et_nat ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6114_top__empty__eq2,axiom,
% 9.17/5.41 ( top_to6261655714344447806_int_o
% 9.17/5.41 = ( ^ [X3: produc8551481072490612790e_term > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X3 @ Y3 ) @ top_to3181862456159035625nt_int ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6115_top__empty__eq2,axiom,
% 9.17/5.41 ( top_to6513043852502318900_int_o
% 9.17/5.41 = ( ^ [X3: int > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X3 @ Y3 ) @ top_to2069137843433766899nt_int ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6116_int__of__integer__induct,axiom,
% 9.17/5.41 ! [Y: int,P: int > $o] :
% 9.17/5.41 ( ( member_int @ Y @ top_top_set_int )
% 9.17/5.41 => ( ! [X4: code_integer] : ( P @ ( code_int_of_integer @ X4 ) )
% 9.17/5.41 => ( P @ Y ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6117_int__of__integer__cases,axiom,
% 9.17/5.41 ! [Y: int] :
% 9.17/5.41 ( ( member_int @ Y @ top_top_set_int )
% 9.17/5.41 => ~ ! [X4: code_integer] :
% 9.17/5.41 ( Y
% 9.17/5.41 != ( code_int_of_integer @ X4 ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6118_int__of__integer,axiom,
% 9.17/5.41 ! [X: code_integer] : ( member_int @ ( code_int_of_integer @ X ) @ top_top_set_int ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6119_integer__of__int__inject,axiom,
% 9.17/5.41 ! [X: int,Y: int] :
% 9.17/5.41 ( ( member_int @ X @ top_top_set_int )
% 9.17/5.41 => ( ( member_int @ Y @ top_top_set_int )
% 9.17/5.41 => ( ( ( code_integer_of_int @ X )
% 9.17/5.41 = ( code_integer_of_int @ Y ) )
% 9.17/5.41 = ( X = Y ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6120_integer__of__int__induct,axiom,
% 9.17/5.41 ! [P: code_integer > $o,X: code_integer] :
% 9.17/5.41 ( ! [Y5: int] :
% 9.17/5.41 ( ( member_int @ Y5 @ top_top_set_int )
% 9.17/5.41 => ( P @ ( code_integer_of_int @ Y5 ) ) )
% 9.17/5.41 => ( P @ X ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6121_integer__of__int__cases,axiom,
% 9.17/5.41 ! [X: code_integer] :
% 9.17/5.41 ~ ! [Y5: int] :
% 9.17/5.41 ( ( X
% 9.17/5.41 = ( code_integer_of_int @ Y5 ) )
% 9.17/5.41 => ~ ( member_int @ Y5 @ top_top_set_int ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6122_subset__card__intvl__is__intvl,axiom,
% 9.17/5.41 ! [A2: set_nat,K: nat] :
% 9.17/5.41 ( ( ord_less_eq_set_nat @ A2 @ ( set_or4665077453230672383an_nat @ K @ ( plus_plus_nat @ K @ ( finite_card_nat @ A2 ) ) ) )
% 9.17/5.41 => ( A2
% 9.17/5.41 = ( set_or4665077453230672383an_nat @ K @ ( plus_plus_nat @ K @ ( finite_card_nat @ A2 ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6123_integer__of__int__inverse,axiom,
% 9.17/5.41 ! [Y: int] :
% 9.17/5.41 ( ( member_int @ Y @ top_top_set_int )
% 9.17/5.41 => ( ( code_int_of_integer @ ( code_integer_of_int @ Y ) )
% 9.17/5.41 = Y ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6124_subset__eq__atLeast0__lessThan__card,axiom,
% 9.17/5.41 ! [N6: set_nat,N2: nat] :
% 9.17/5.41 ( ( ord_less_eq_set_nat @ N6 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) )
% 9.17/5.41 => ( ord_less_eq_nat @ ( finite_card_nat @ N6 ) @ N2 ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6125_integer__of__nat__eq__of__nat,axiom,
% 9.17/5.41 code_integer_of_nat = semiri4939895301339042750nteger ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6126_card__less__Suc2,axiom,
% 9.17/5.41 ! [M3: set_nat,I: nat] :
% 9.17/5.41 ( ~ ( member_nat @ zero_zero_nat @ M3 )
% 9.17/5.41 => ( ( finite_card_nat
% 9.17/5.41 @ ( collect_nat
% 9.17/5.41 @ ^ [K4: nat] :
% 9.17/5.41 ( ( member_nat @ ( suc @ K4 ) @ M3 )
% 9.17/5.41 & ( ord_less_nat @ K4 @ I ) ) ) )
% 9.17/5.41 = ( finite_card_nat
% 9.17/5.41 @ ( collect_nat
% 9.17/5.41 @ ^ [K4: nat] :
% 9.17/5.41 ( ( member_nat @ K4 @ M3 )
% 9.17/5.41 & ( ord_less_nat @ K4 @ ( suc @ I ) ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6127_card__less__Suc,axiom,
% 9.17/5.41 ! [M3: set_nat,I: nat] :
% 9.17/5.41 ( ( member_nat @ zero_zero_nat @ M3 )
% 9.17/5.41 => ( ( suc
% 9.17/5.41 @ ( finite_card_nat
% 9.17/5.41 @ ( collect_nat
% 9.17/5.41 @ ^ [K4: nat] :
% 9.17/5.41 ( ( member_nat @ ( suc @ K4 ) @ M3 )
% 9.17/5.41 & ( ord_less_nat @ K4 @ I ) ) ) ) )
% 9.17/5.41 = ( finite_card_nat
% 9.17/5.41 @ ( collect_nat
% 9.17/5.41 @ ^ [K4: nat] :
% 9.17/5.41 ( ( member_nat @ K4 @ M3 )
% 9.17/5.41 & ( ord_less_nat @ K4 @ ( suc @ I ) ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6128_card__less,axiom,
% 9.17/5.41 ! [M3: set_nat,I: nat] :
% 9.17/5.41 ( ( member_nat @ zero_zero_nat @ M3 )
% 9.17/5.41 => ( ( finite_card_nat
% 9.17/5.41 @ ( collect_nat
% 9.17/5.41 @ ^ [K4: nat] :
% 9.17/5.41 ( ( member_nat @ K4 @ M3 )
% 9.17/5.41 & ( ord_less_nat @ K4 @ ( suc @ I ) ) ) ) )
% 9.17/5.41 != zero_zero_nat ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6129_integer__of__nat__0,axiom,
% 9.17/5.41 ( ( code_integer_of_nat @ zero_zero_nat )
% 9.17/5.41 = zero_z3403309356797280102nteger ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6130_integer__of__nat_Oabs__eq,axiom,
% 9.17/5.41 ( code_integer_of_nat
% 9.17/5.41 = ( ^ [X3: nat] : ( code_integer_of_int @ ( semiri1314217659103216013at_int @ X3 ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6131_integer__of__nat__numeral,axiom,
% 9.17/5.41 ! [N2: num] :
% 9.17/5.41 ( ( code_integer_of_nat @ ( numeral_numeral_nat @ N2 ) )
% 9.17/5.41 = ( numera6620942414471956472nteger @ N2 ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6132_integer__of__nat__1,axiom,
% 9.17/5.41 ( ( code_integer_of_nat @ one_one_nat )
% 9.17/5.41 = one_one_Code_integer ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6133_card__sum__le__nat__sum,axiom,
% 9.17/5.41 ! [S2: set_nat] :
% 9.17/5.41 ( ord_less_eq_nat
% 9.17/5.41 @ ( groups3542108847815614940at_nat
% 9.17/5.41 @ ^ [X3: nat] : X3
% 9.17/5.41 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( finite_card_nat @ S2 ) ) )
% 9.17/5.41 @ ( groups3542108847815614940at_nat
% 9.17/5.41 @ ^ [X3: nat] : X3
% 9.17/5.41 @ S2 ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6134_set__encode__insert,axiom,
% 9.17/5.41 ! [A2: set_nat,N2: nat] :
% 9.17/5.41 ( ( finite_finite_nat @ A2 )
% 9.17/5.41 => ( ~ ( member_nat @ N2 @ A2 )
% 9.17/5.41 => ( ( nat_set_encode @ ( insert_nat @ N2 @ A2 ) )
% 9.17/5.41 = ( plus_plus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ ( nat_set_encode @ A2 ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6135_card__greaterThanLessThan__int,axiom,
% 9.17/5.41 ! [L: int,U: int] :
% 9.17/5.41 ( ( finite_card_int @ ( set_or5832277885323065728an_int @ L @ U ) )
% 9.17/5.41 = ( nat2 @ ( minus_minus_int @ U @ ( plus_plus_int @ L @ one_one_int ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6136_wmax__insertI,axiom,
% 9.17/5.41 ! [Y: product_prod_nat_nat,YS: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat,XS: set_Pr1261947904930325089at_nat] :
% 9.17/5.41 ( ( member8440522571783428010at_nat @ Y @ YS )
% 9.17/5.41 => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X @ Y ) @ fun_pair_leq )
% 9.17/5.41 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ XS @ YS ) @ fun_max_weak )
% 9.17/5.41 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( insert8211810215607154385at_nat @ X @ XS ) @ YS ) @ fun_max_weak ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6137_wmin__insertI,axiom,
% 9.17/5.41 ! [X: product_prod_nat_nat,XS: set_Pr1261947904930325089at_nat,Y: product_prod_nat_nat,YS: set_Pr1261947904930325089at_nat] :
% 9.17/5.41 ( ( member8440522571783428010at_nat @ X @ XS )
% 9.17/5.41 => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X @ Y ) @ fun_pair_leq )
% 9.17/5.41 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ XS @ YS ) @ fun_min_weak )
% 9.17/5.41 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ XS @ ( insert8211810215607154385at_nat @ Y @ YS ) ) @ fun_min_weak ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6138_smin__insertI,axiom,
% 9.17/5.41 ! [X: product_prod_nat_nat,XS: set_Pr1261947904930325089at_nat,Y: product_prod_nat_nat,YS: set_Pr1261947904930325089at_nat] :
% 9.17/5.41 ( ( member8440522571783428010at_nat @ X @ XS )
% 9.17/5.41 => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X @ Y ) @ fun_pair_less )
% 9.17/5.41 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ XS @ YS ) @ fun_min_strict )
% 9.17/5.41 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ XS @ ( insert8211810215607154385at_nat @ Y @ YS ) ) @ fun_min_strict ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6139_prod_Oinsert_H,axiom,
% 9.17/5.41 ! [I4: set_o,P4: $o > code_integer,I: $o] :
% 9.17/5.41 ( ( finite_finite_o
% 9.17/5.41 @ ( collect_o
% 9.17/5.41 @ ^ [X3: $o] :
% 9.17/5.41 ( ( member_o @ X3 @ I4 )
% 9.17/5.41 & ( ( P4 @ X3 )
% 9.17/5.41 != one_one_Code_integer ) ) ) )
% 9.17/5.41 => ( ( ( member_o @ I @ I4 )
% 9.17/5.41 => ( ( groups2836416601086271911nteger @ P4 @ ( insert_o @ I @ I4 ) )
% 9.17/5.41 = ( groups2836416601086271911nteger @ P4 @ I4 ) ) )
% 9.17/5.41 & ( ~ ( member_o @ I @ I4 )
% 9.17/5.41 => ( ( groups2836416601086271911nteger @ P4 @ ( insert_o @ I @ I4 ) )
% 9.17/5.41 = ( times_3573771949741848930nteger @ ( P4 @ I ) @ ( groups2836416601086271911nteger @ P4 @ I4 ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6140_prod_Oinsert_H,axiom,
% 9.17/5.41 ! [I4: set_nat,P4: nat > code_integer,I: nat] :
% 9.17/5.41 ( ( finite_finite_nat
% 9.17/5.41 @ ( collect_nat
% 9.17/5.41 @ ^ [X3: nat] :
% 9.17/5.41 ( ( member_nat @ X3 @ I4 )
% 9.17/5.41 & ( ( P4 @ X3 )
% 9.17/5.41 != one_one_Code_integer ) ) ) )
% 9.17/5.41 => ( ( ( member_nat @ I @ I4 )
% 9.17/5.41 => ( ( groups8290090294887179773nteger @ P4 @ ( insert_nat @ I @ I4 ) )
% 9.17/5.41 = ( groups8290090294887179773nteger @ P4 @ I4 ) ) )
% 9.17/5.41 & ( ~ ( member_nat @ I @ I4 )
% 9.17/5.41 => ( ( groups8290090294887179773nteger @ P4 @ ( insert_nat @ I @ I4 ) )
% 9.17/5.41 = ( times_3573771949741848930nteger @ ( P4 @ I ) @ ( groups8290090294887179773nteger @ P4 @ I4 ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6141_prod_Oinsert_H,axiom,
% 9.17/5.41 ! [I4: set_int,P4: int > code_integer,I: int] :
% 9.17/5.41 ( ( finite_finite_int
% 9.17/5.41 @ ( collect_int
% 9.17/5.41 @ ^ [X3: int] :
% 9.17/5.41 ( ( member_int @ X3 @ I4 )
% 9.17/5.41 & ( ( P4 @ X3 )
% 9.17/5.41 != one_one_Code_integer ) ) ) )
% 9.17/5.41 => ( ( ( member_int @ I @ I4 )
% 9.17/5.41 => ( ( groups8661743855124024409nteger @ P4 @ ( insert_int @ I @ I4 ) )
% 9.17/5.41 = ( groups8661743855124024409nteger @ P4 @ I4 ) ) )
% 9.17/5.41 & ( ~ ( member_int @ I @ I4 )
% 9.17/5.41 => ( ( groups8661743855124024409nteger @ P4 @ ( insert_int @ I @ I4 ) )
% 9.17/5.41 = ( times_3573771949741848930nteger @ ( P4 @ I ) @ ( groups8661743855124024409nteger @ P4 @ I4 ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6142_prod_Oinsert_H,axiom,
% 9.17/5.41 ! [I4: set_Code_integer,P4: code_integer > code_integer,I: code_integer] :
% 9.17/5.41 ( ( finite6017078050557962740nteger
% 9.17/5.41 @ ( collect_Code_integer
% 9.17/5.41 @ ^ [X3: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ X3 @ I4 )
% 9.17/5.41 & ( ( P4 @ X3 )
% 9.17/5.41 != one_one_Code_integer ) ) ) )
% 9.17/5.41 => ( ( ( member_Code_integer @ I @ I4 )
% 9.17/5.41 => ( ( groups7219916603568234122nteger @ P4 @ ( insert_Code_integer @ I @ I4 ) )
% 9.17/5.41 = ( groups7219916603568234122nteger @ P4 @ I4 ) ) )
% 9.17/5.41 & ( ~ ( member_Code_integer @ I @ I4 )
% 9.17/5.41 => ( ( groups7219916603568234122nteger @ P4 @ ( insert_Code_integer @ I @ I4 ) )
% 9.17/5.41 = ( times_3573771949741848930nteger @ ( P4 @ I ) @ ( groups7219916603568234122nteger @ P4 @ I4 ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6143_prod_Oinsert_H,axiom,
% 9.17/5.41 ! [I4: set_o,P4: $o > assn,I: $o] :
% 9.17/5.41 ( ( finite_finite_o
% 9.17/5.41 @ ( collect_o
% 9.17/5.41 @ ^ [X3: $o] :
% 9.17/5.41 ( ( member_o @ X3 @ I4 )
% 9.17/5.41 & ( ( P4 @ X3 )
% 9.17/5.41 != one_one_assn ) ) ) )
% 9.17/5.41 => ( ( ( member_o @ I @ I4 )
% 9.17/5.41 => ( ( groups12625163056032370o_assn @ P4 @ ( insert_o @ I @ I4 ) )
% 9.17/5.41 = ( groups12625163056032370o_assn @ P4 @ I4 ) ) )
% 9.17/5.41 & ( ~ ( member_o @ I @ I4 )
% 9.17/5.41 => ( ( groups12625163056032370o_assn @ P4 @ ( insert_o @ I @ I4 ) )
% 9.17/5.41 = ( times_times_assn @ ( P4 @ I ) @ ( groups12625163056032370o_assn @ P4 @ I4 ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6144_prod_Oinsert_H,axiom,
% 9.17/5.41 ! [I4: set_nat,P4: nat > assn,I: nat] :
% 9.17/5.41 ( ( finite_finite_nat
% 9.17/5.41 @ ( collect_nat
% 9.17/5.41 @ ^ [X3: nat] :
% 9.17/5.41 ( ( member_nat @ X3 @ I4 )
% 9.17/5.41 & ( ( P4 @ X3 )
% 9.17/5.41 != one_one_assn ) ) ) )
% 9.17/5.41 => ( ( ( member_nat @ I @ I4 )
% 9.17/5.41 => ( ( groups3916077543535352520t_assn @ P4 @ ( insert_nat @ I @ I4 ) )
% 9.17/5.41 = ( groups3916077543535352520t_assn @ P4 @ I4 ) ) )
% 9.17/5.41 & ( ~ ( member_nat @ I @ I4 )
% 9.17/5.41 => ( ( groups3916077543535352520t_assn @ P4 @ ( insert_nat @ I @ I4 ) )
% 9.17/5.41 = ( times_times_assn @ ( P4 @ I ) @ ( groups3916077543535352520t_assn @ P4 @ I4 ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6145_prod_Oinsert_H,axiom,
% 9.17/5.41 ! [I4: set_int,P4: int > assn,I: int] :
% 9.17/5.41 ( ( finite_finite_int
% 9.17/5.41 @ ( collect_int
% 9.17/5.41 @ ^ [X3: int] :
% 9.17/5.41 ( ( member_int @ X3 @ I4 )
% 9.17/5.41 & ( ( P4 @ X3 )
% 9.17/5.41 != one_one_assn ) ) ) )
% 9.17/5.41 => ( ( ( member_int @ I @ I4 )
% 9.17/5.41 => ( ( groups4891613008741529892t_assn @ P4 @ ( insert_int @ I @ I4 ) )
% 9.17/5.41 = ( groups4891613008741529892t_assn @ P4 @ I4 ) ) )
% 9.17/5.41 & ( ~ ( member_int @ I @ I4 )
% 9.17/5.41 => ( ( groups4891613008741529892t_assn @ P4 @ ( insert_int @ I @ I4 ) )
% 9.17/5.41 = ( times_times_assn @ ( P4 @ I ) @ ( groups4891613008741529892t_assn @ P4 @ I4 ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6146_prod_Oinsert_H,axiom,
% 9.17/5.41 ! [I4: set_Code_integer,P4: code_integer > assn,I: code_integer] :
% 9.17/5.41 ( ( finite6017078050557962740nteger
% 9.17/5.41 @ ( collect_Code_integer
% 9.17/5.41 @ ^ [X3: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ X3 @ I4 )
% 9.17/5.41 & ( ( P4 @ X3 )
% 9.17/5.41 != one_one_assn ) ) ) )
% 9.17/5.41 => ( ( ( member_Code_integer @ I @ I4 )
% 9.17/5.41 => ( ( groups980104329299799381r_assn @ P4 @ ( insert_Code_integer @ I @ I4 ) )
% 9.17/5.41 = ( groups980104329299799381r_assn @ P4 @ I4 ) ) )
% 9.17/5.41 & ( ~ ( member_Code_integer @ I @ I4 )
% 9.17/5.41 => ( ( groups980104329299799381r_assn @ P4 @ ( insert_Code_integer @ I @ I4 ) )
% 9.17/5.41 = ( times_times_assn @ ( P4 @ I ) @ ( groups980104329299799381r_assn @ P4 @ I4 ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6147_prod_Oinsert_H,axiom,
% 9.17/5.41 ! [I4: set_o,P4: $o > rat,I: $o] :
% 9.17/5.41 ( ( finite_finite_o
% 9.17/5.41 @ ( collect_o
% 9.17/5.41 @ ^ [X3: $o] :
% 9.17/5.41 ( ( member_o @ X3 @ I4 )
% 9.17/5.41 & ( ( P4 @ X3 )
% 9.17/5.41 != one_one_rat ) ) ) )
% 9.17/5.41 => ( ( ( member_o @ I @ I4 )
% 9.17/5.41 => ( ( groups4688112016125141794_o_rat @ P4 @ ( insert_o @ I @ I4 ) )
% 9.17/5.41 = ( groups4688112016125141794_o_rat @ P4 @ I4 ) ) )
% 9.17/5.41 & ( ~ ( member_o @ I @ I4 )
% 9.17/5.41 => ( ( groups4688112016125141794_o_rat @ P4 @ ( insert_o @ I @ I4 ) )
% 9.17/5.41 = ( times_times_rat @ ( P4 @ I ) @ ( groups4688112016125141794_o_rat @ P4 @ I4 ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6148_prod_Oinsert_H,axiom,
% 9.17/5.41 ! [I4: set_nat,P4: nat > rat,I: nat] :
% 9.17/5.41 ( ( finite_finite_nat
% 9.17/5.41 @ ( collect_nat
% 9.17/5.41 @ ^ [X3: nat] :
% 9.17/5.41 ( ( member_nat @ X3 @ I4 )
% 9.17/5.41 & ( ( P4 @ X3 )
% 9.17/5.41 != one_one_rat ) ) ) )
% 9.17/5.41 => ( ( ( member_nat @ I @ I4 )
% 9.17/5.41 => ( ( groups4112464933559648120at_rat @ P4 @ ( insert_nat @ I @ I4 ) )
% 9.17/5.41 = ( groups4112464933559648120at_rat @ P4 @ I4 ) ) )
% 9.17/5.41 & ( ~ ( member_nat @ I @ I4 )
% 9.17/5.41 => ( ( groups4112464933559648120at_rat @ P4 @ ( insert_nat @ I @ I4 ) )
% 9.17/5.41 = ( times_times_rat @ ( P4 @ I ) @ ( groups4112464933559648120at_rat @ P4 @ I4 ) ) ) ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6149_greaterThanLessThan__iff,axiom,
% 9.17/5.41 ! [I: $o,L: $o,U: $o] :
% 9.17/5.41 ( ( member_o @ I @ ( set_or1716231572884733764Than_o @ L @ U ) )
% 9.17/5.41 = ( ( ord_less_o @ L @ I )
% 9.17/5.41 & ( ord_less_o @ I @ U ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6150_greaterThanLessThan__iff,axiom,
% 9.17/5.41 ! [I: rat,L: rat,U: rat] :
% 9.17/5.41 ( ( member_rat @ I @ ( set_or5199638295745620268an_rat @ L @ U ) )
% 9.17/5.41 = ( ( ord_less_rat @ L @ I )
% 9.17/5.41 & ( ord_less_rat @ I @ U ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6151_greaterThanLessThan__iff,axiom,
% 9.17/5.41 ! [I: num,L: num,U: num] :
% 9.17/5.41 ( ( member_num @ I @ ( set_or2392100141987894638an_num @ L @ U ) )
% 9.17/5.41 = ( ( ord_less_num @ L @ I )
% 9.17/5.41 & ( ord_less_num @ I @ U ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6152_greaterThanLessThan__iff,axiom,
% 9.17/5.41 ! [I: int,L: int,U: int] :
% 9.17/5.41 ( ( member_int @ I @ ( set_or5832277885323065728an_int @ L @ U ) )
% 9.17/5.41 = ( ( ord_less_int @ L @ I )
% 9.17/5.41 & ( ord_less_int @ I @ U ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6153_greaterThanLessThan__iff,axiom,
% 9.17/5.41 ! [I: nat,L: nat,U: nat] :
% 9.17/5.41 ( ( member_nat @ I @ ( set_or5834768355832116004an_nat @ L @ U ) )
% 9.17/5.41 = ( ( ord_less_nat @ L @ I )
% 9.17/5.41 & ( ord_less_nat @ I @ U ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6154_greaterThanLessThan__iff,axiom,
% 9.17/5.41 ! [I: code_integer,L: code_integer,U: code_integer] :
% 9.17/5.41 ( ( member_Code_integer @ I @ ( set_or4266950643985792945nteger @ L @ U ) )
% 9.17/5.41 = ( ( ord_le6747313008572928689nteger @ L @ I )
% 9.17/5.41 & ( ord_le6747313008572928689nteger @ I @ U ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6155_finite__greaterThanLessThan__int,axiom,
% 9.17/5.41 ! [L: int,U: int] : ( finite_finite_int @ ( set_or5832277885323065728an_int @ L @ U ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6156_greaterThanLessThan__empty__iff2,axiom,
% 9.17/5.41 ! [A: rat,B: rat] :
% 9.17/5.41 ( ( bot_bot_set_rat
% 9.17/5.41 = ( set_or5199638295745620268an_rat @ A @ B ) )
% 9.17/5.41 = ( ord_less_eq_rat @ B @ A ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6157_greaterThanLessThan__empty__iff,axiom,
% 9.17/5.41 ! [A: rat,B: rat] :
% 9.17/5.41 ( ( ( set_or5199638295745620268an_rat @ A @ B )
% 9.17/5.41 = bot_bot_set_rat )
% 9.17/5.41 = ( ord_less_eq_rat @ B @ A ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6158_greaterThanLessThan__empty,axiom,
% 9.17/5.41 ! [L: $o,K: $o] :
% 9.17/5.41 ( ( ord_less_eq_o @ L @ K )
% 9.17/5.41 => ( ( set_or1716231572884733764Than_o @ K @ L )
% 9.17/5.41 = bot_bot_set_o ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6159_greaterThanLessThan__empty,axiom,
% 9.17/5.41 ! [L: set_nat,K: set_nat] :
% 9.17/5.41 ( ( ord_less_eq_set_nat @ L @ K )
% 9.17/5.41 => ( ( set_or8625682525731655386et_nat @ K @ L )
% 9.17/5.41 = bot_bot_set_set_nat ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6160_greaterThanLessThan__empty,axiom,
% 9.17/5.41 ! [L: rat,K: rat] :
% 9.17/5.41 ( ( ord_less_eq_rat @ L @ K )
% 9.17/5.41 => ( ( set_or5199638295745620268an_rat @ K @ L )
% 9.17/5.41 = bot_bot_set_rat ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6161_greaterThanLessThan__empty,axiom,
% 9.17/5.41 ! [L: num,K: num] :
% 9.17/5.41 ( ( ord_less_eq_num @ L @ K )
% 9.17/5.41 => ( ( set_or2392100141987894638an_num @ K @ L )
% 9.17/5.41 = bot_bot_set_num ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6162_greaterThanLessThan__empty,axiom,
% 9.17/5.41 ! [L: int,K: int] :
% 9.17/5.41 ( ( ord_less_eq_int @ L @ K )
% 9.17/5.41 => ( ( set_or5832277885323065728an_int @ K @ L )
% 9.17/5.41 = bot_bot_set_int ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6163_greaterThanLessThan__empty,axiom,
% 9.17/5.41 ! [L: nat,K: nat] :
% 9.17/5.41 ( ( ord_less_eq_nat @ L @ K )
% 9.17/5.41 => ( ( set_or5834768355832116004an_nat @ K @ L )
% 9.17/5.41 = bot_bot_set_nat ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6164_greaterThanLessThan__empty,axiom,
% 9.17/5.41 ! [L: code_integer,K: code_integer] :
% 9.17/5.41 ( ( ord_le3102999989581377725nteger @ L @ K )
% 9.17/5.41 => ( ( set_or4266950643985792945nteger @ K @ L )
% 9.17/5.41 = bot_bo3990330152332043303nteger ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6165_infinite__Ioo__iff,axiom,
% 9.17/5.41 ! [A: rat,B: rat] :
% 9.17/5.41 ( ( ~ ( finite_finite_rat @ ( set_or5199638295745620268an_rat @ A @ B ) ) )
% 9.17/5.41 = ( ord_less_rat @ A @ B ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6166_image__uminus__greaterThanLessThan,axiom,
% 9.17/5.41 ! [X: rat,Y: rat] :
% 9.17/5.41 ( ( image_rat_rat @ uminus_uminus_rat @ ( set_or5199638295745620268an_rat @ X @ Y ) )
% 9.17/5.41 = ( set_or5199638295745620268an_rat @ ( uminus_uminus_rat @ Y ) @ ( uminus_uminus_rat @ X ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6167_image__uminus__greaterThanLessThan,axiom,
% 9.17/5.41 ! [X: int,Y: int] :
% 9.17/5.41 ( ( image_int_int @ uminus_uminus_int @ ( set_or5832277885323065728an_int @ X @ Y ) )
% 9.17/5.41 = ( set_or5832277885323065728an_int @ ( uminus_uminus_int @ Y ) @ ( uminus_uminus_int @ X ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6168_image__uminus__greaterThanLessThan,axiom,
% 9.17/5.41 ! [X: code_integer,Y: code_integer] :
% 9.17/5.41 ( ( image_4470545334726330049nteger @ uminus1351360451143612070nteger @ ( set_or4266950643985792945nteger @ X @ Y ) )
% 9.17/5.41 = ( set_or4266950643985792945nteger @ ( uminus1351360451143612070nteger @ Y ) @ ( uminus1351360451143612070nteger @ X ) ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6169_prod_Oempty_H,axiom,
% 9.17/5.41 ! [P4: $o > code_integer] :
% 9.17/5.41 ( ( groups2836416601086271911nteger @ P4 @ bot_bot_set_o )
% 9.17/5.41 = one_one_Code_integer ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6170_prod_Oempty_H,axiom,
% 9.17/5.41 ! [P4: $o > assn] :
% 9.17/5.41 ( ( groups12625163056032370o_assn @ P4 @ bot_bot_set_o )
% 9.17/5.41 = one_one_assn ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6171_prod_Oempty_H,axiom,
% 9.17/5.41 ! [P4: $o > rat] :
% 9.17/5.41 ( ( groups4688112016125141794_o_rat @ P4 @ bot_bot_set_o )
% 9.17/5.41 = one_one_rat ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6172_prod_Oempty_H,axiom,
% 9.17/5.41 ! [P4: $o > nat] :
% 9.17/5.41 ( ( groups5323242076211637530_o_nat @ P4 @ bot_bot_set_o )
% 9.17/5.41 = one_one_nat ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6173_prod_Oempty_H,axiom,
% 9.17/5.41 ! [P4: $o > int] :
% 9.17/5.41 ( ( groups5320751605702587254_o_int @ P4 @ bot_bot_set_o )
% 9.17/5.41 = one_one_int ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6174_prod_Oempty_H,axiom,
% 9.17/5.41 ! [P4: nat > code_integer] :
% 9.17/5.41 ( ( groups8290090294887179773nteger @ P4 @ bot_bot_set_nat )
% 9.17/5.41 = one_one_Code_integer ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6175_prod_Oempty_H,axiom,
% 9.17/5.41 ! [P4: nat > assn] :
% 9.17/5.41 ( ( groups3916077543535352520t_assn @ P4 @ bot_bot_set_nat )
% 9.17/5.41 = one_one_assn ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6176_prod_Oempty_H,axiom,
% 9.17/5.41 ! [P4: nat > rat] :
% 9.17/5.41 ( ( groups4112464933559648120at_rat @ P4 @ bot_bot_set_nat )
% 9.17/5.41 = one_one_rat ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6177_prod_Oempty_H,axiom,
% 9.17/5.41 ! [P4: nat > nat] :
% 9.17/5.41 ( ( groups4747594993646143856at_nat @ P4 @ bot_bot_set_nat )
% 9.17/5.41 = one_one_nat ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6178_prod_Oempty_H,axiom,
% 9.17/5.41 ! [P4: nat > int] :
% 9.17/5.41 ( ( groups4745104523137093580at_int @ P4 @ bot_bot_set_nat )
% 9.17/5.41 = one_one_int ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6179_smin__emptyI,axiom,
% 9.17/5.41 ! [X11: set_Pr1261947904930325089at_nat] :
% 9.17/5.41 ( ( X11 != bot_bo2099793752762293965at_nat )
% 9.17/5.41 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X11 @ bot_bo2099793752762293965at_nat ) @ fun_min_strict ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6180_wmax__emptyI,axiom,
% 9.17/5.41 ! [X11: set_Pr1261947904930325089at_nat] :
% 9.17/5.41 ( ( finite6177210948735845034at_nat @ X11 )
% 9.17/5.41 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ bot_bo2099793752762293965at_nat @ X11 ) @ fun_max_weak ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6181_wmin__emptyI,axiom,
% 9.17/5.41 ! [X11: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X11 @ bot_bo2099793752762293965at_nat ) @ fun_min_weak ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6182_prod_Onon__neutral_H,axiom,
% 9.17/5.41 ! [G: $o > code_integer,I4: set_o] :
% 9.17/5.41 ( ( groups2836416601086271911nteger @ G
% 9.17/5.41 @ ( collect_o
% 9.17/5.41 @ ^ [X3: $o] :
% 9.17/5.41 ( ( member_o @ X3 @ I4 )
% 9.17/5.41 & ( ( G @ X3 )
% 9.17/5.41 != one_one_Code_integer ) ) ) )
% 9.17/5.41 = ( groups2836416601086271911nteger @ G @ I4 ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6183_prod_Onon__neutral_H,axiom,
% 9.17/5.41 ! [G: int > code_integer,I4: set_int] :
% 9.17/5.41 ( ( groups8661743855124024409nteger @ G
% 9.17/5.41 @ ( collect_int
% 9.17/5.41 @ ^ [X3: int] :
% 9.17/5.41 ( ( member_int @ X3 @ I4 )
% 9.17/5.41 & ( ( G @ X3 )
% 9.17/5.41 != one_one_Code_integer ) ) ) )
% 9.17/5.41 = ( groups8661743855124024409nteger @ G @ I4 ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6184_prod_Onon__neutral_H,axiom,
% 9.17/5.41 ! [G: nat > code_integer,I4: set_nat] :
% 9.17/5.41 ( ( groups8290090294887179773nteger @ G
% 9.17/5.41 @ ( collect_nat
% 9.17/5.41 @ ^ [X3: nat] :
% 9.17/5.41 ( ( member_nat @ X3 @ I4 )
% 9.17/5.41 & ( ( G @ X3 )
% 9.17/5.41 != one_one_Code_integer ) ) ) )
% 9.17/5.41 = ( groups8290090294887179773nteger @ G @ I4 ) ) ).
% 9.17/5.41
% 9.17/5.41 thf(fact_6185_prod_Onon__neutral_H,axiom,
% 9.17/5.41 ! [G: $o > assn,I4: set_o] :
% 9.17/5.41 ( ( groups12625163056032370o_assn @ G
% 9.17/5.41 @ ( collect_o
% 9.17/5.41 @ ^ [X3: $o] :
% 9.17/5.41 ( ( member_o @ X3 @ I4 )
% 9.17/5.41 & ( ( G @ X3 )
% 9.17/5.41 != one_one_assn ) ) ) )
% 9.17/5.42 = ( groups12625163056032370o_assn @ G @ I4 ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6186_prod_Onon__neutral_H,axiom,
% 9.17/5.42 ! [G: int > assn,I4: set_int] :
% 9.17/5.42 ( ( groups4891613008741529892t_assn @ G
% 9.17/5.42 @ ( collect_int
% 9.17/5.42 @ ^ [X3: int] :
% 9.17/5.42 ( ( member_int @ X3 @ I4 )
% 9.17/5.42 & ( ( G @ X3 )
% 9.17/5.42 != one_one_assn ) ) ) )
% 9.17/5.42 = ( groups4891613008741529892t_assn @ G @ I4 ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6187_prod_Onon__neutral_H,axiom,
% 9.17/5.42 ! [G: nat > assn,I4: set_nat] :
% 9.17/5.42 ( ( groups3916077543535352520t_assn @ G
% 9.17/5.42 @ ( collect_nat
% 9.17/5.42 @ ^ [X3: nat] :
% 9.17/5.42 ( ( member_nat @ X3 @ I4 )
% 9.17/5.42 & ( ( G @ X3 )
% 9.17/5.42 != one_one_assn ) ) ) )
% 9.17/5.42 = ( groups3916077543535352520t_assn @ G @ I4 ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6188_prod_Onon__neutral_H,axiom,
% 9.17/5.42 ! [G: $o > rat,I4: set_o] :
% 9.17/5.42 ( ( groups4688112016125141794_o_rat @ G
% 9.17/5.42 @ ( collect_o
% 9.17/5.42 @ ^ [X3: $o] :
% 9.17/5.42 ( ( member_o @ X3 @ I4 )
% 9.17/5.42 & ( ( G @ X3 )
% 9.17/5.42 != one_one_rat ) ) ) )
% 9.17/5.42 = ( groups4688112016125141794_o_rat @ G @ I4 ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6189_prod_Onon__neutral_H,axiom,
% 9.17/5.42 ! [G: int > rat,I4: set_int] :
% 9.17/5.42 ( ( groups5111818645460702676nt_rat @ G
% 9.17/5.42 @ ( collect_int
% 9.17/5.42 @ ^ [X3: int] :
% 9.17/5.42 ( ( member_int @ X3 @ I4 )
% 9.17/5.42 & ( ( G @ X3 )
% 9.17/5.42 != one_one_rat ) ) ) )
% 9.17/5.42 = ( groups5111818645460702676nt_rat @ G @ I4 ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6190_prod_Onon__neutral_H,axiom,
% 9.17/5.42 ! [G: nat > rat,I4: set_nat] :
% 9.17/5.42 ( ( groups4112464933559648120at_rat @ G
% 9.17/5.42 @ ( collect_nat
% 9.17/5.42 @ ^ [X3: nat] :
% 9.17/5.42 ( ( member_nat @ X3 @ I4 )
% 9.17/5.42 & ( ( G @ X3 )
% 9.17/5.42 != one_one_rat ) ) ) )
% 9.17/5.42 = ( groups4112464933559648120at_rat @ G @ I4 ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6191_prod_Onon__neutral_H,axiom,
% 9.17/5.42 ! [G: $o > nat,I4: set_o] :
% 9.17/5.42 ( ( groups5323242076211637530_o_nat @ G
% 9.17/5.42 @ ( collect_o
% 9.17/5.42 @ ^ [X3: $o] :
% 9.17/5.42 ( ( member_o @ X3 @ I4 )
% 9.17/5.42 & ( ( G @ X3 )
% 9.17/5.42 != one_one_nat ) ) ) )
% 9.17/5.42 = ( groups5323242076211637530_o_nat @ G @ I4 ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6192_infinite__Ioo,axiom,
% 9.17/5.42 ! [A: rat,B: rat] :
% 9.17/5.42 ( ( ord_less_rat @ A @ B )
% 9.17/5.42 => ~ ( finite_finite_rat @ ( set_or5199638295745620268an_rat @ A @ B ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6193_greaterThanLessThan__subseteq__greaterThanLessThan,axiom,
% 9.17/5.42 ! [A: rat,B: rat,C: rat,D2: rat] :
% 9.17/5.42 ( ( ord_less_eq_set_rat @ ( set_or5199638295745620268an_rat @ A @ B ) @ ( set_or5199638295745620268an_rat @ C @ D2 ) )
% 9.17/5.42 = ( ( ord_less_rat @ A @ B )
% 9.17/5.42 => ( ( ord_less_eq_rat @ C @ A )
% 9.17/5.42 & ( ord_less_eq_rat @ B @ D2 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6194_prod__decode__aux_Ocases,axiom,
% 9.17/5.42 ! [X: product_prod_nat_nat] :
% 9.17/5.42 ~ ! [K5: nat,M5: nat] :
% 9.17/5.42 ( X
% 9.17/5.42 != ( product_Pair_nat_nat @ K5 @ M5 ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6195_atLeastPlusOneLessThan__greaterThanLessThan__int,axiom,
% 9.17/5.42 ! [L: int,U: int] :
% 9.17/5.42 ( ( set_or4662586982721622107an_int @ ( plus_plus_int @ L @ one_one_int ) @ U )
% 9.17/5.42 = ( set_or5832277885323065728an_int @ L @ U ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6196_prod_Omono__neutral__left_H,axiom,
% 9.17/5.42 ! [S2: set_nat,T5: set_nat,G: nat > code_integer] :
% 9.17/5.42 ( ( ord_less_eq_set_nat @ S2 @ T5 )
% 9.17/5.42 => ( ! [X4: nat] :
% 9.17/5.42 ( ( member_nat @ X4 @ ( minus_minus_set_nat @ T5 @ S2 ) )
% 9.17/5.42 => ( ( G @ X4 )
% 9.17/5.42 = one_one_Code_integer ) )
% 9.17/5.42 => ( ( groups8290090294887179773nteger @ G @ S2 )
% 9.17/5.42 = ( groups8290090294887179773nteger @ G @ T5 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6197_prod_Omono__neutral__left_H,axiom,
% 9.17/5.42 ! [S2: set_nat,T5: set_nat,G: nat > assn] :
% 9.17/5.42 ( ( ord_less_eq_set_nat @ S2 @ T5 )
% 9.17/5.42 => ( ! [X4: nat] :
% 9.17/5.42 ( ( member_nat @ X4 @ ( minus_minus_set_nat @ T5 @ S2 ) )
% 9.17/5.42 => ( ( G @ X4 )
% 9.17/5.42 = one_one_assn ) )
% 9.17/5.42 => ( ( groups3916077543535352520t_assn @ G @ S2 )
% 9.17/5.42 = ( groups3916077543535352520t_assn @ G @ T5 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6198_prod_Omono__neutral__left_H,axiom,
% 9.17/5.42 ! [S2: set_nat,T5: set_nat,G: nat > rat] :
% 9.17/5.42 ( ( ord_less_eq_set_nat @ S2 @ T5 )
% 9.17/5.42 => ( ! [X4: nat] :
% 9.17/5.42 ( ( member_nat @ X4 @ ( minus_minus_set_nat @ T5 @ S2 ) )
% 9.17/5.42 => ( ( G @ X4 )
% 9.17/5.42 = one_one_rat ) )
% 9.17/5.42 => ( ( groups4112464933559648120at_rat @ G @ S2 )
% 9.17/5.42 = ( groups4112464933559648120at_rat @ G @ T5 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6199_prod_Omono__neutral__left_H,axiom,
% 9.17/5.42 ! [S2: set_nat,T5: set_nat,G: nat > nat] :
% 9.17/5.42 ( ( ord_less_eq_set_nat @ S2 @ T5 )
% 9.17/5.42 => ( ! [X4: nat] :
% 9.17/5.42 ( ( member_nat @ X4 @ ( minus_minus_set_nat @ T5 @ S2 ) )
% 9.17/5.42 => ( ( G @ X4 )
% 9.17/5.42 = one_one_nat ) )
% 9.17/5.42 => ( ( groups4747594993646143856at_nat @ G @ S2 )
% 9.17/5.42 = ( groups4747594993646143856at_nat @ G @ T5 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6200_prod_Omono__neutral__left_H,axiom,
% 9.17/5.42 ! [S2: set_nat,T5: set_nat,G: nat > int] :
% 9.17/5.42 ( ( ord_less_eq_set_nat @ S2 @ T5 )
% 9.17/5.42 => ( ! [X4: nat] :
% 9.17/5.42 ( ( member_nat @ X4 @ ( minus_minus_set_nat @ T5 @ S2 ) )
% 9.17/5.42 => ( ( G @ X4 )
% 9.17/5.42 = one_one_int ) )
% 9.17/5.42 => ( ( groups4745104523137093580at_int @ G @ S2 )
% 9.17/5.42 = ( groups4745104523137093580at_int @ G @ T5 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6201_prod_Omono__neutral__right_H,axiom,
% 9.17/5.42 ! [S2: set_nat,T5: set_nat,G: nat > code_integer] :
% 9.17/5.42 ( ( ord_less_eq_set_nat @ S2 @ T5 )
% 9.17/5.42 => ( ! [X4: nat] :
% 9.17/5.42 ( ( member_nat @ X4 @ ( minus_minus_set_nat @ T5 @ S2 ) )
% 9.17/5.42 => ( ( G @ X4 )
% 9.17/5.42 = one_one_Code_integer ) )
% 9.17/5.42 => ( ( groups8290090294887179773nteger @ G @ T5 )
% 9.17/5.42 = ( groups8290090294887179773nteger @ G @ S2 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6202_prod_Omono__neutral__right_H,axiom,
% 9.17/5.42 ! [S2: set_nat,T5: set_nat,G: nat > assn] :
% 9.17/5.42 ( ( ord_less_eq_set_nat @ S2 @ T5 )
% 9.17/5.42 => ( ! [X4: nat] :
% 9.17/5.42 ( ( member_nat @ X4 @ ( minus_minus_set_nat @ T5 @ S2 ) )
% 9.17/5.42 => ( ( G @ X4 )
% 9.17/5.42 = one_one_assn ) )
% 9.17/5.42 => ( ( groups3916077543535352520t_assn @ G @ T5 )
% 9.17/5.42 = ( groups3916077543535352520t_assn @ G @ S2 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6203_prod_Omono__neutral__right_H,axiom,
% 9.17/5.42 ! [S2: set_nat,T5: set_nat,G: nat > rat] :
% 9.17/5.42 ( ( ord_less_eq_set_nat @ S2 @ T5 )
% 9.17/5.42 => ( ! [X4: nat] :
% 9.17/5.42 ( ( member_nat @ X4 @ ( minus_minus_set_nat @ T5 @ S2 ) )
% 9.17/5.42 => ( ( G @ X4 )
% 9.17/5.42 = one_one_rat ) )
% 9.17/5.42 => ( ( groups4112464933559648120at_rat @ G @ T5 )
% 9.17/5.42 = ( groups4112464933559648120at_rat @ G @ S2 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6204_prod_Omono__neutral__right_H,axiom,
% 9.17/5.42 ! [S2: set_nat,T5: set_nat,G: nat > nat] :
% 9.17/5.42 ( ( ord_less_eq_set_nat @ S2 @ T5 )
% 9.17/5.42 => ( ! [X4: nat] :
% 9.17/5.42 ( ( member_nat @ X4 @ ( minus_minus_set_nat @ T5 @ S2 ) )
% 9.17/5.42 => ( ( G @ X4 )
% 9.17/5.42 = one_one_nat ) )
% 9.17/5.42 => ( ( groups4747594993646143856at_nat @ G @ T5 )
% 9.17/5.42 = ( groups4747594993646143856at_nat @ G @ S2 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6205_prod_Omono__neutral__right_H,axiom,
% 9.17/5.42 ! [S2: set_nat,T5: set_nat,G: nat > int] :
% 9.17/5.42 ( ( ord_less_eq_set_nat @ S2 @ T5 )
% 9.17/5.42 => ( ! [X4: nat] :
% 9.17/5.42 ( ( member_nat @ X4 @ ( minus_minus_set_nat @ T5 @ S2 ) )
% 9.17/5.42 => ( ( G @ X4 )
% 9.17/5.42 = one_one_int ) )
% 9.17/5.42 => ( ( groups4745104523137093580at_int @ G @ T5 )
% 9.17/5.42 = ( groups4745104523137093580at_int @ G @ S2 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6206_prod_Omono__neutral__cong__left_H,axiom,
% 9.17/5.42 ! [S2: set_o,T5: set_o,H3: $o > code_integer,G: $o > code_integer] :
% 9.17/5.42 ( ( ord_less_eq_set_o @ S2 @ T5 )
% 9.17/5.42 => ( ! [I2: $o] :
% 9.17/5.42 ( ( member_o @ I2 @ ( minus_minus_set_o @ T5 @ S2 ) )
% 9.17/5.42 => ( ( H3 @ I2 )
% 9.17/5.42 = one_one_Code_integer ) )
% 9.17/5.42 => ( ! [X4: $o] :
% 9.17/5.42 ( ( member_o @ X4 @ S2 )
% 9.17/5.42 => ( ( G @ X4 )
% 9.17/5.42 = ( H3 @ X4 ) ) )
% 9.17/5.42 => ( ( groups2836416601086271911nteger @ G @ S2 )
% 9.17/5.42 = ( groups2836416601086271911nteger @ H3 @ T5 ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6207_prod_Omono__neutral__cong__left_H,axiom,
% 9.17/5.42 ! [S2: set_int,T5: set_int,H3: int > code_integer,G: int > code_integer] :
% 9.17/5.42 ( ( ord_less_eq_set_int @ S2 @ T5 )
% 9.17/5.42 => ( ! [I2: int] :
% 9.17/5.42 ( ( member_int @ I2 @ ( minus_minus_set_int @ T5 @ S2 ) )
% 9.17/5.42 => ( ( H3 @ I2 )
% 9.17/5.42 = one_one_Code_integer ) )
% 9.17/5.42 => ( ! [X4: int] :
% 9.17/5.42 ( ( member_int @ X4 @ S2 )
% 9.17/5.42 => ( ( G @ X4 )
% 9.17/5.42 = ( H3 @ X4 ) ) )
% 9.17/5.42 => ( ( groups8661743855124024409nteger @ G @ S2 )
% 9.17/5.42 = ( groups8661743855124024409nteger @ H3 @ T5 ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6208_prod_Omono__neutral__cong__left_H,axiom,
% 9.17/5.42 ! [S2: set_o,T5: set_o,H3: $o > assn,G: $o > assn] :
% 9.17/5.42 ( ( ord_less_eq_set_o @ S2 @ T5 )
% 9.17/5.42 => ( ! [I2: $o] :
% 9.17/5.42 ( ( member_o @ I2 @ ( minus_minus_set_o @ T5 @ S2 ) )
% 9.17/5.42 => ( ( H3 @ I2 )
% 9.17/5.42 = one_one_assn ) )
% 9.17/5.42 => ( ! [X4: $o] :
% 9.17/5.42 ( ( member_o @ X4 @ S2 )
% 9.17/5.42 => ( ( G @ X4 )
% 9.17/5.42 = ( H3 @ X4 ) ) )
% 9.17/5.42 => ( ( groups12625163056032370o_assn @ G @ S2 )
% 9.17/5.42 = ( groups12625163056032370o_assn @ H3 @ T5 ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6209_prod_Omono__neutral__cong__left_H,axiom,
% 9.17/5.42 ! [S2: set_int,T5: set_int,H3: int > assn,G: int > assn] :
% 9.17/5.42 ( ( ord_less_eq_set_int @ S2 @ T5 )
% 9.17/5.42 => ( ! [I2: int] :
% 9.17/5.42 ( ( member_int @ I2 @ ( minus_minus_set_int @ T5 @ S2 ) )
% 9.17/5.42 => ( ( H3 @ I2 )
% 9.17/5.42 = one_one_assn ) )
% 9.17/5.42 => ( ! [X4: int] :
% 9.17/5.42 ( ( member_int @ X4 @ S2 )
% 9.17/5.42 => ( ( G @ X4 )
% 9.17/5.42 = ( H3 @ X4 ) ) )
% 9.17/5.42 => ( ( groups4891613008741529892t_assn @ G @ S2 )
% 9.17/5.42 = ( groups4891613008741529892t_assn @ H3 @ T5 ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6210_prod_Omono__neutral__cong__left_H,axiom,
% 9.17/5.42 ! [S2: set_o,T5: set_o,H3: $o > rat,G: $o > rat] :
% 9.17/5.42 ( ( ord_less_eq_set_o @ S2 @ T5 )
% 9.17/5.42 => ( ! [I2: $o] :
% 9.17/5.42 ( ( member_o @ I2 @ ( minus_minus_set_o @ T5 @ S2 ) )
% 9.17/5.42 => ( ( H3 @ I2 )
% 9.17/5.42 = one_one_rat ) )
% 9.17/5.42 => ( ! [X4: $o] :
% 9.17/5.42 ( ( member_o @ X4 @ S2 )
% 9.17/5.42 => ( ( G @ X4 )
% 9.17/5.42 = ( H3 @ X4 ) ) )
% 9.17/5.42 => ( ( groups4688112016125141794_o_rat @ G @ S2 )
% 9.17/5.42 = ( groups4688112016125141794_o_rat @ H3 @ T5 ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6211_prod_Omono__neutral__cong__left_H,axiom,
% 9.17/5.42 ! [S2: set_int,T5: set_int,H3: int > rat,G: int > rat] :
% 9.17/5.42 ( ( ord_less_eq_set_int @ S2 @ T5 )
% 9.17/5.42 => ( ! [I2: int] :
% 9.17/5.42 ( ( member_int @ I2 @ ( minus_minus_set_int @ T5 @ S2 ) )
% 9.17/5.42 => ( ( H3 @ I2 )
% 9.17/5.42 = one_one_rat ) )
% 9.17/5.42 => ( ! [X4: int] :
% 9.17/5.42 ( ( member_int @ X4 @ S2 )
% 9.17/5.42 => ( ( G @ X4 )
% 9.17/5.42 = ( H3 @ X4 ) ) )
% 9.17/5.42 => ( ( groups5111818645460702676nt_rat @ G @ S2 )
% 9.17/5.42 = ( groups5111818645460702676nt_rat @ H3 @ T5 ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6212_prod_Omono__neutral__cong__left_H,axiom,
% 9.17/5.42 ! [S2: set_o,T5: set_o,H3: $o > nat,G: $o > nat] :
% 9.17/5.42 ( ( ord_less_eq_set_o @ S2 @ T5 )
% 9.17/5.42 => ( ! [I2: $o] :
% 9.17/5.42 ( ( member_o @ I2 @ ( minus_minus_set_o @ T5 @ S2 ) )
% 9.17/5.42 => ( ( H3 @ I2 )
% 9.17/5.42 = one_one_nat ) )
% 9.17/5.42 => ( ! [X4: $o] :
% 9.17/5.42 ( ( member_o @ X4 @ S2 )
% 9.17/5.42 => ( ( G @ X4 )
% 9.17/5.42 = ( H3 @ X4 ) ) )
% 9.17/5.42 => ( ( groups5323242076211637530_o_nat @ G @ S2 )
% 9.17/5.42 = ( groups5323242076211637530_o_nat @ H3 @ T5 ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6213_prod_Omono__neutral__cong__left_H,axiom,
% 9.17/5.42 ! [S2: set_int,T5: set_int,H3: int > nat,G: int > nat] :
% 9.17/5.42 ( ( ord_less_eq_set_int @ S2 @ T5 )
% 9.17/5.42 => ( ! [I2: int] :
% 9.17/5.42 ( ( member_int @ I2 @ ( minus_minus_set_int @ T5 @ S2 ) )
% 9.17/5.42 => ( ( H3 @ I2 )
% 9.17/5.42 = one_one_nat ) )
% 9.17/5.42 => ( ! [X4: int] :
% 9.17/5.42 ( ( member_int @ X4 @ S2 )
% 9.17/5.42 => ( ( G @ X4 )
% 9.17/5.42 = ( H3 @ X4 ) ) )
% 9.17/5.42 => ( ( groups5746948705547198412nt_nat @ G @ S2 )
% 9.17/5.42 = ( groups5746948705547198412nt_nat @ H3 @ T5 ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6214_prod_Omono__neutral__cong__left_H,axiom,
% 9.17/5.42 ! [S2: set_o,T5: set_o,H3: $o > int,G: $o > int] :
% 9.17/5.42 ( ( ord_less_eq_set_o @ S2 @ T5 )
% 9.17/5.42 => ( ! [I2: $o] :
% 9.17/5.42 ( ( member_o @ I2 @ ( minus_minus_set_o @ T5 @ S2 ) )
% 9.17/5.42 => ( ( H3 @ I2 )
% 9.17/5.42 = one_one_int ) )
% 9.17/5.42 => ( ! [X4: $o] :
% 9.17/5.42 ( ( member_o @ X4 @ S2 )
% 9.17/5.42 => ( ( G @ X4 )
% 9.17/5.42 = ( H3 @ X4 ) ) )
% 9.17/5.42 => ( ( groups5320751605702587254_o_int @ G @ S2 )
% 9.17/5.42 = ( groups5320751605702587254_o_int @ H3 @ T5 ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6215_prod_Omono__neutral__cong__left_H,axiom,
% 9.17/5.42 ! [S2: set_int,T5: set_int,H3: int > int,G: int > int] :
% 9.17/5.42 ( ( ord_less_eq_set_int @ S2 @ T5 )
% 9.17/5.42 => ( ! [I2: int] :
% 9.17/5.42 ( ( member_int @ I2 @ ( minus_minus_set_int @ T5 @ S2 ) )
% 9.17/5.42 => ( ( H3 @ I2 )
% 9.17/5.42 = one_one_int ) )
% 9.17/5.42 => ( ! [X4: int] :
% 9.17/5.42 ( ( member_int @ X4 @ S2 )
% 9.17/5.42 => ( ( G @ X4 )
% 9.17/5.42 = ( H3 @ X4 ) ) )
% 9.17/5.42 => ( ( groups5744458235038148136nt_int @ G @ S2 )
% 9.17/5.42 = ( groups5744458235038148136nt_int @ H3 @ T5 ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6216_prod_Omono__neutral__cong__right_H,axiom,
% 9.17/5.42 ! [S2: set_o,T5: set_o,G: $o > code_integer,H3: $o > code_integer] :
% 9.17/5.42 ( ( ord_less_eq_set_o @ S2 @ T5 )
% 9.17/5.42 => ( ! [X4: $o] :
% 9.17/5.42 ( ( member_o @ X4 @ ( minus_minus_set_o @ T5 @ S2 ) )
% 9.17/5.42 => ( ( G @ X4 )
% 9.17/5.42 = one_one_Code_integer ) )
% 9.17/5.42 => ( ! [X4: $o] :
% 9.17/5.42 ( ( member_o @ X4 @ S2 )
% 9.17/5.42 => ( ( G @ X4 )
% 9.17/5.42 = ( H3 @ X4 ) ) )
% 9.17/5.42 => ( ( groups2836416601086271911nteger @ G @ T5 )
% 9.17/5.42 = ( groups2836416601086271911nteger @ H3 @ S2 ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6217_prod_Omono__neutral__cong__right_H,axiom,
% 9.17/5.42 ! [S2: set_int,T5: set_int,G: int > code_integer,H3: int > code_integer] :
% 9.17/5.42 ( ( ord_less_eq_set_int @ S2 @ T5 )
% 9.17/5.42 => ( ! [X4: int] :
% 9.17/5.42 ( ( member_int @ X4 @ ( minus_minus_set_int @ T5 @ S2 ) )
% 9.17/5.42 => ( ( G @ X4 )
% 9.17/5.42 = one_one_Code_integer ) )
% 9.17/5.42 => ( ! [X4: int] :
% 9.17/5.42 ( ( member_int @ X4 @ S2 )
% 9.17/5.42 => ( ( G @ X4 )
% 9.17/5.42 = ( H3 @ X4 ) ) )
% 9.17/5.42 => ( ( groups8661743855124024409nteger @ G @ T5 )
% 9.17/5.42 = ( groups8661743855124024409nteger @ H3 @ S2 ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6218_prod_Omono__neutral__cong__right_H,axiom,
% 9.17/5.42 ! [S2: set_o,T5: set_o,G: $o > assn,H3: $o > assn] :
% 9.17/5.42 ( ( ord_less_eq_set_o @ S2 @ T5 )
% 9.17/5.42 => ( ! [X4: $o] :
% 9.17/5.42 ( ( member_o @ X4 @ ( minus_minus_set_o @ T5 @ S2 ) )
% 9.17/5.42 => ( ( G @ X4 )
% 9.17/5.42 = one_one_assn ) )
% 9.17/5.42 => ( ! [X4: $o] :
% 9.17/5.42 ( ( member_o @ X4 @ S2 )
% 9.17/5.42 => ( ( G @ X4 )
% 9.17/5.42 = ( H3 @ X4 ) ) )
% 9.17/5.42 => ( ( groups12625163056032370o_assn @ G @ T5 )
% 9.17/5.42 = ( groups12625163056032370o_assn @ H3 @ S2 ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6219_prod_Omono__neutral__cong__right_H,axiom,
% 9.17/5.42 ! [S2: set_int,T5: set_int,G: int > assn,H3: int > assn] :
% 9.17/5.42 ( ( ord_less_eq_set_int @ S2 @ T5 )
% 9.17/5.42 => ( ! [X4: int] :
% 9.17/5.42 ( ( member_int @ X4 @ ( minus_minus_set_int @ T5 @ S2 ) )
% 9.17/5.42 => ( ( G @ X4 )
% 9.17/5.42 = one_one_assn ) )
% 9.17/5.42 => ( ! [X4: int] :
% 9.17/5.42 ( ( member_int @ X4 @ S2 )
% 9.17/5.42 => ( ( G @ X4 )
% 9.17/5.42 = ( H3 @ X4 ) ) )
% 9.17/5.42 => ( ( groups4891613008741529892t_assn @ G @ T5 )
% 9.17/5.42 = ( groups4891613008741529892t_assn @ H3 @ S2 ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6220_prod_Omono__neutral__cong__right_H,axiom,
% 9.17/5.42 ! [S2: set_o,T5: set_o,G: $o > rat,H3: $o > rat] :
% 9.17/5.42 ( ( ord_less_eq_set_o @ S2 @ T5 )
% 9.17/5.42 => ( ! [X4: $o] :
% 9.17/5.42 ( ( member_o @ X4 @ ( minus_minus_set_o @ T5 @ S2 ) )
% 9.17/5.42 => ( ( G @ X4 )
% 9.17/5.42 = one_one_rat ) )
% 9.17/5.42 => ( ! [X4: $o] :
% 9.17/5.42 ( ( member_o @ X4 @ S2 )
% 9.17/5.42 => ( ( G @ X4 )
% 9.17/5.42 = ( H3 @ X4 ) ) )
% 9.17/5.42 => ( ( groups4688112016125141794_o_rat @ G @ T5 )
% 9.17/5.42 = ( groups4688112016125141794_o_rat @ H3 @ S2 ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6221_prod_Omono__neutral__cong__right_H,axiom,
% 9.17/5.42 ! [S2: set_int,T5: set_int,G: int > rat,H3: int > rat] :
% 9.17/5.42 ( ( ord_less_eq_set_int @ S2 @ T5 )
% 9.17/5.42 => ( ! [X4: int] :
% 9.17/5.42 ( ( member_int @ X4 @ ( minus_minus_set_int @ T5 @ S2 ) )
% 9.17/5.42 => ( ( G @ X4 )
% 9.17/5.42 = one_one_rat ) )
% 9.17/5.42 => ( ! [X4: int] :
% 9.17/5.42 ( ( member_int @ X4 @ S2 )
% 9.17/5.42 => ( ( G @ X4 )
% 9.17/5.42 = ( H3 @ X4 ) ) )
% 9.17/5.42 => ( ( groups5111818645460702676nt_rat @ G @ T5 )
% 9.17/5.42 = ( groups5111818645460702676nt_rat @ H3 @ S2 ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6222_prod_Omono__neutral__cong__right_H,axiom,
% 9.17/5.42 ! [S2: set_o,T5: set_o,G: $o > nat,H3: $o > nat] :
% 9.17/5.42 ( ( ord_less_eq_set_o @ S2 @ T5 )
% 9.17/5.42 => ( ! [X4: $o] :
% 9.17/5.42 ( ( member_o @ X4 @ ( minus_minus_set_o @ T5 @ S2 ) )
% 9.17/5.42 => ( ( G @ X4 )
% 9.17/5.42 = one_one_nat ) )
% 9.17/5.42 => ( ! [X4: $o] :
% 9.17/5.42 ( ( member_o @ X4 @ S2 )
% 9.17/5.42 => ( ( G @ X4 )
% 9.17/5.42 = ( H3 @ X4 ) ) )
% 9.17/5.42 => ( ( groups5323242076211637530_o_nat @ G @ T5 )
% 9.17/5.42 = ( groups5323242076211637530_o_nat @ H3 @ S2 ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6223_prod_Omono__neutral__cong__right_H,axiom,
% 9.17/5.42 ! [S2: set_int,T5: set_int,G: int > nat,H3: int > nat] :
% 9.17/5.42 ( ( ord_less_eq_set_int @ S2 @ T5 )
% 9.17/5.42 => ( ! [X4: int] :
% 9.17/5.42 ( ( member_int @ X4 @ ( minus_minus_set_int @ T5 @ S2 ) )
% 9.17/5.42 => ( ( G @ X4 )
% 9.17/5.42 = one_one_nat ) )
% 9.17/5.42 => ( ! [X4: int] :
% 9.17/5.42 ( ( member_int @ X4 @ S2 )
% 9.17/5.42 => ( ( G @ X4 )
% 9.17/5.42 = ( H3 @ X4 ) ) )
% 9.17/5.42 => ( ( groups5746948705547198412nt_nat @ G @ T5 )
% 9.17/5.42 = ( groups5746948705547198412nt_nat @ H3 @ S2 ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6224_prod_Omono__neutral__cong__right_H,axiom,
% 9.17/5.42 ! [S2: set_o,T5: set_o,G: $o > int,H3: $o > int] :
% 9.17/5.42 ( ( ord_less_eq_set_o @ S2 @ T5 )
% 9.17/5.42 => ( ! [X4: $o] :
% 9.17/5.42 ( ( member_o @ X4 @ ( minus_minus_set_o @ T5 @ S2 ) )
% 9.17/5.42 => ( ( G @ X4 )
% 9.17/5.42 = one_one_int ) )
% 9.17/5.42 => ( ! [X4: $o] :
% 9.17/5.42 ( ( member_o @ X4 @ S2 )
% 9.17/5.42 => ( ( G @ X4 )
% 9.17/5.42 = ( H3 @ X4 ) ) )
% 9.17/5.42 => ( ( groups5320751605702587254_o_int @ G @ T5 )
% 9.17/5.42 = ( groups5320751605702587254_o_int @ H3 @ S2 ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6225_prod_Omono__neutral__cong__right_H,axiom,
% 9.17/5.42 ! [S2: set_int,T5: set_int,G: int > int,H3: int > int] :
% 9.17/5.42 ( ( ord_less_eq_set_int @ S2 @ T5 )
% 9.17/5.42 => ( ! [X4: int] :
% 9.17/5.42 ( ( member_int @ X4 @ ( minus_minus_set_int @ T5 @ S2 ) )
% 9.17/5.42 => ( ( G @ X4 )
% 9.17/5.42 = one_one_int ) )
% 9.17/5.42 => ( ! [X4: int] :
% 9.17/5.42 ( ( member_int @ X4 @ S2 )
% 9.17/5.42 => ( ( G @ X4 )
% 9.17/5.42 = ( H3 @ X4 ) ) )
% 9.17/5.42 => ( ( groups5744458235038148136nt_int @ G @ T5 )
% 9.17/5.42 = ( groups5744458235038148136nt_int @ H3 @ S2 ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6226_prod_Odistrib_H,axiom,
% 9.17/5.42 ! [I4: set_o,G: $o > code_integer,H3: $o > code_integer] :
% 9.17/5.42 ( ( finite_finite_o
% 9.17/5.42 @ ( collect_o
% 9.17/5.42 @ ^ [X3: $o] :
% 9.17/5.42 ( ( member_o @ X3 @ I4 )
% 9.17/5.42 & ( ( G @ X3 )
% 9.17/5.42 != one_one_Code_integer ) ) ) )
% 9.17/5.42 => ( ( finite_finite_o
% 9.17/5.42 @ ( collect_o
% 9.17/5.42 @ ^ [X3: $o] :
% 9.17/5.42 ( ( member_o @ X3 @ I4 )
% 9.17/5.42 & ( ( H3 @ X3 )
% 9.17/5.42 != one_one_Code_integer ) ) ) )
% 9.17/5.42 => ( ( groups2836416601086271911nteger
% 9.17/5.42 @ ^ [I3: $o] : ( times_3573771949741848930nteger @ ( G @ I3 ) @ ( H3 @ I3 ) )
% 9.17/5.42 @ I4 )
% 9.17/5.42 = ( times_3573771949741848930nteger @ ( groups2836416601086271911nteger @ G @ I4 ) @ ( groups2836416601086271911nteger @ H3 @ I4 ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6227_prod_Odistrib_H,axiom,
% 9.17/5.42 ! [I4: set_nat,G: nat > code_integer,H3: nat > code_integer] :
% 9.17/5.42 ( ( finite_finite_nat
% 9.17/5.42 @ ( collect_nat
% 9.17/5.42 @ ^ [X3: nat] :
% 9.17/5.42 ( ( member_nat @ X3 @ I4 )
% 9.17/5.42 & ( ( G @ X3 )
% 9.17/5.42 != one_one_Code_integer ) ) ) )
% 9.17/5.42 => ( ( finite_finite_nat
% 9.17/5.42 @ ( collect_nat
% 9.17/5.42 @ ^ [X3: nat] :
% 9.17/5.42 ( ( member_nat @ X3 @ I4 )
% 9.17/5.42 & ( ( H3 @ X3 )
% 9.17/5.42 != one_one_Code_integer ) ) ) )
% 9.17/5.42 => ( ( groups8290090294887179773nteger
% 9.17/5.42 @ ^ [I3: nat] : ( times_3573771949741848930nteger @ ( G @ I3 ) @ ( H3 @ I3 ) )
% 9.17/5.42 @ I4 )
% 9.17/5.42 = ( times_3573771949741848930nteger @ ( groups8290090294887179773nteger @ G @ I4 ) @ ( groups8290090294887179773nteger @ H3 @ I4 ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6228_prod_Odistrib_H,axiom,
% 9.17/5.42 ! [I4: set_int,G: int > code_integer,H3: int > code_integer] :
% 9.17/5.42 ( ( finite_finite_int
% 9.17/5.42 @ ( collect_int
% 9.17/5.42 @ ^ [X3: int] :
% 9.17/5.42 ( ( member_int @ X3 @ I4 )
% 9.17/5.42 & ( ( G @ X3 )
% 9.17/5.42 != one_one_Code_integer ) ) ) )
% 9.17/5.42 => ( ( finite_finite_int
% 9.17/5.42 @ ( collect_int
% 9.17/5.42 @ ^ [X3: int] :
% 9.17/5.42 ( ( member_int @ X3 @ I4 )
% 9.17/5.42 & ( ( H3 @ X3 )
% 9.17/5.42 != one_one_Code_integer ) ) ) )
% 9.17/5.42 => ( ( groups8661743855124024409nteger
% 9.17/5.42 @ ^ [I3: int] : ( times_3573771949741848930nteger @ ( G @ I3 ) @ ( H3 @ I3 ) )
% 9.17/5.42 @ I4 )
% 9.17/5.42 = ( times_3573771949741848930nteger @ ( groups8661743855124024409nteger @ G @ I4 ) @ ( groups8661743855124024409nteger @ H3 @ I4 ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6229_prod_Odistrib_H,axiom,
% 9.17/5.42 ! [I4: set_Code_integer,G: code_integer > code_integer,H3: code_integer > code_integer] :
% 9.17/5.42 ( ( finite6017078050557962740nteger
% 9.17/5.42 @ ( collect_Code_integer
% 9.17/5.42 @ ^ [X3: code_integer] :
% 9.17/5.42 ( ( member_Code_integer @ X3 @ I4 )
% 9.17/5.42 & ( ( G @ X3 )
% 9.17/5.42 != one_one_Code_integer ) ) ) )
% 9.17/5.42 => ( ( finite6017078050557962740nteger
% 9.17/5.42 @ ( collect_Code_integer
% 9.17/5.42 @ ^ [X3: code_integer] :
% 9.17/5.42 ( ( member_Code_integer @ X3 @ I4 )
% 9.17/5.42 & ( ( H3 @ X3 )
% 9.17/5.42 != one_one_Code_integer ) ) ) )
% 9.17/5.42 => ( ( groups7219916603568234122nteger
% 9.17/5.42 @ ^ [I3: code_integer] : ( times_3573771949741848930nteger @ ( G @ I3 ) @ ( H3 @ I3 ) )
% 9.17/5.42 @ I4 )
% 9.17/5.42 = ( times_3573771949741848930nteger @ ( groups7219916603568234122nteger @ G @ I4 ) @ ( groups7219916603568234122nteger @ H3 @ I4 ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6230_prod_Odistrib_H,axiom,
% 9.17/5.42 ! [I4: set_o,G: $o > assn,H3: $o > assn] :
% 9.17/5.42 ( ( finite_finite_o
% 9.17/5.42 @ ( collect_o
% 9.17/5.42 @ ^ [X3: $o] :
% 9.17/5.42 ( ( member_o @ X3 @ I4 )
% 9.17/5.42 & ( ( G @ X3 )
% 9.17/5.42 != one_one_assn ) ) ) )
% 9.17/5.42 => ( ( finite_finite_o
% 9.17/5.42 @ ( collect_o
% 9.17/5.42 @ ^ [X3: $o] :
% 9.17/5.42 ( ( member_o @ X3 @ I4 )
% 9.17/5.42 & ( ( H3 @ X3 )
% 9.17/5.42 != one_one_assn ) ) ) )
% 9.17/5.42 => ( ( groups12625163056032370o_assn
% 9.17/5.42 @ ^ [I3: $o] : ( times_times_assn @ ( G @ I3 ) @ ( H3 @ I3 ) )
% 9.17/5.42 @ I4 )
% 9.17/5.42 = ( times_times_assn @ ( groups12625163056032370o_assn @ G @ I4 ) @ ( groups12625163056032370o_assn @ H3 @ I4 ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6231_prod_Odistrib_H,axiom,
% 9.17/5.42 ! [I4: set_nat,G: nat > assn,H3: nat > assn] :
% 9.17/5.42 ( ( finite_finite_nat
% 9.17/5.42 @ ( collect_nat
% 9.17/5.42 @ ^ [X3: nat] :
% 9.17/5.42 ( ( member_nat @ X3 @ I4 )
% 9.17/5.42 & ( ( G @ X3 )
% 9.17/5.42 != one_one_assn ) ) ) )
% 9.17/5.42 => ( ( finite_finite_nat
% 9.17/5.42 @ ( collect_nat
% 9.17/5.42 @ ^ [X3: nat] :
% 9.17/5.42 ( ( member_nat @ X3 @ I4 )
% 9.17/5.42 & ( ( H3 @ X3 )
% 9.17/5.42 != one_one_assn ) ) ) )
% 9.17/5.42 => ( ( groups3916077543535352520t_assn
% 9.17/5.42 @ ^ [I3: nat] : ( times_times_assn @ ( G @ I3 ) @ ( H3 @ I3 ) )
% 9.17/5.42 @ I4 )
% 9.17/5.42 = ( times_times_assn @ ( groups3916077543535352520t_assn @ G @ I4 ) @ ( groups3916077543535352520t_assn @ H3 @ I4 ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6232_prod_Odistrib_H,axiom,
% 9.17/5.42 ! [I4: set_int,G: int > assn,H3: int > assn] :
% 9.17/5.42 ( ( finite_finite_int
% 9.17/5.42 @ ( collect_int
% 9.17/5.42 @ ^ [X3: int] :
% 9.17/5.42 ( ( member_int @ X3 @ I4 )
% 9.17/5.42 & ( ( G @ X3 )
% 9.17/5.42 != one_one_assn ) ) ) )
% 9.17/5.42 => ( ( finite_finite_int
% 9.17/5.42 @ ( collect_int
% 9.17/5.42 @ ^ [X3: int] :
% 9.17/5.42 ( ( member_int @ X3 @ I4 )
% 9.17/5.42 & ( ( H3 @ X3 )
% 9.17/5.42 != one_one_assn ) ) ) )
% 9.17/5.42 => ( ( groups4891613008741529892t_assn
% 9.17/5.42 @ ^ [I3: int] : ( times_times_assn @ ( G @ I3 ) @ ( H3 @ I3 ) )
% 9.17/5.42 @ I4 )
% 9.17/5.42 = ( times_times_assn @ ( groups4891613008741529892t_assn @ G @ I4 ) @ ( groups4891613008741529892t_assn @ H3 @ I4 ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6233_prod_Odistrib_H,axiom,
% 9.17/5.42 ! [I4: set_Code_integer,G: code_integer > assn,H3: code_integer > assn] :
% 9.17/5.42 ( ( finite6017078050557962740nteger
% 9.17/5.42 @ ( collect_Code_integer
% 9.17/5.42 @ ^ [X3: code_integer] :
% 9.17/5.42 ( ( member_Code_integer @ X3 @ I4 )
% 9.17/5.42 & ( ( G @ X3 )
% 9.17/5.42 != one_one_assn ) ) ) )
% 9.17/5.42 => ( ( finite6017078050557962740nteger
% 9.17/5.42 @ ( collect_Code_integer
% 9.17/5.42 @ ^ [X3: code_integer] :
% 9.17/5.42 ( ( member_Code_integer @ X3 @ I4 )
% 9.17/5.42 & ( ( H3 @ X3 )
% 9.17/5.42 != one_one_assn ) ) ) )
% 9.17/5.42 => ( ( groups980104329299799381r_assn
% 9.17/5.42 @ ^ [I3: code_integer] : ( times_times_assn @ ( G @ I3 ) @ ( H3 @ I3 ) )
% 9.17/5.42 @ I4 )
% 9.17/5.42 = ( times_times_assn @ ( groups980104329299799381r_assn @ G @ I4 ) @ ( groups980104329299799381r_assn @ H3 @ I4 ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6234_prod_Odistrib_H,axiom,
% 9.17/5.42 ! [I4: set_o,G: $o > rat,H3: $o > rat] :
% 9.17/5.42 ( ( finite_finite_o
% 9.17/5.42 @ ( collect_o
% 9.17/5.42 @ ^ [X3: $o] :
% 9.17/5.42 ( ( member_o @ X3 @ I4 )
% 9.17/5.42 & ( ( G @ X3 )
% 9.17/5.42 != one_one_rat ) ) ) )
% 9.17/5.42 => ( ( finite_finite_o
% 9.17/5.42 @ ( collect_o
% 9.17/5.42 @ ^ [X3: $o] :
% 9.17/5.42 ( ( member_o @ X3 @ I4 )
% 9.17/5.42 & ( ( H3 @ X3 )
% 9.17/5.42 != one_one_rat ) ) ) )
% 9.17/5.42 => ( ( groups4688112016125141794_o_rat
% 9.17/5.42 @ ^ [I3: $o] : ( times_times_rat @ ( G @ I3 ) @ ( H3 @ I3 ) )
% 9.17/5.42 @ I4 )
% 9.17/5.42 = ( times_times_rat @ ( groups4688112016125141794_o_rat @ G @ I4 ) @ ( groups4688112016125141794_o_rat @ H3 @ I4 ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6235_prod_Odistrib_H,axiom,
% 9.17/5.42 ! [I4: set_nat,G: nat > rat,H3: nat > rat] :
% 9.17/5.42 ( ( finite_finite_nat
% 9.17/5.42 @ ( collect_nat
% 9.17/5.42 @ ^ [X3: nat] :
% 9.17/5.42 ( ( member_nat @ X3 @ I4 )
% 9.17/5.42 & ( ( G @ X3 )
% 9.17/5.42 != one_one_rat ) ) ) )
% 9.17/5.42 => ( ( finite_finite_nat
% 9.17/5.42 @ ( collect_nat
% 9.17/5.42 @ ^ [X3: nat] :
% 9.17/5.42 ( ( member_nat @ X3 @ I4 )
% 9.17/5.42 & ( ( H3 @ X3 )
% 9.17/5.42 != one_one_rat ) ) ) )
% 9.17/5.42 => ( ( groups4112464933559648120at_rat
% 9.17/5.42 @ ^ [I3: nat] : ( times_times_rat @ ( G @ I3 ) @ ( H3 @ I3 ) )
% 9.17/5.42 @ I4 )
% 9.17/5.42 = ( times_times_rat @ ( groups4112464933559648120at_rat @ G @ I4 ) @ ( groups4112464933559648120at_rat @ H3 @ I4 ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6236_prod_OG__def,axiom,
% 9.17/5.42 ( groups2836416601086271911nteger
% 9.17/5.42 = ( ^ [P6: $o > code_integer,I5: set_o] :
% 9.17/5.42 ( if_Code_integer
% 9.17/5.42 @ ( finite_finite_o
% 9.17/5.42 @ ( collect_o
% 9.17/5.42 @ ^ [X3: $o] :
% 9.17/5.42 ( ( member_o @ X3 @ I5 )
% 9.17/5.42 & ( ( P6 @ X3 )
% 9.17/5.42 != one_one_Code_integer ) ) ) )
% 9.17/5.42 @ ( groups7694694392188491536nteger @ P6
% 9.17/5.42 @ ( collect_o
% 9.17/5.42 @ ^ [X3: $o] :
% 9.17/5.42 ( ( member_o @ X3 @ I5 )
% 9.17/5.42 & ( ( P6 @ X3 )
% 9.17/5.42 != one_one_Code_integer ) ) ) )
% 9.17/5.42 @ one_one_Code_integer ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6237_prod_OG__def,axiom,
% 9.17/5.42 ( groups8290090294887179773nteger
% 9.17/5.42 = ( ^ [P6: nat > code_integer,I5: set_nat] :
% 9.17/5.42 ( if_Code_integer
% 9.17/5.42 @ ( finite_finite_nat
% 9.17/5.42 @ ( collect_nat
% 9.17/5.42 @ ^ [X3: nat] :
% 9.17/5.42 ( ( member_nat @ X3 @ I5 )
% 9.17/5.42 & ( ( P6 @ X3 )
% 9.17/5.42 != one_one_Code_integer ) ) ) )
% 9.17/5.42 @ ( groups3455450783089532116nteger @ P6
% 9.17/5.42 @ ( collect_nat
% 9.17/5.42 @ ^ [X3: nat] :
% 9.17/5.42 ( ( member_nat @ X3 @ I5 )
% 9.17/5.42 & ( ( P6 @ X3 )
% 9.17/5.42 != one_one_Code_integer ) ) ) )
% 9.17/5.42 @ one_one_Code_integer ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6238_prod_OG__def,axiom,
% 9.17/5.42 ( groups8661743855124024409nteger
% 9.17/5.42 = ( ^ [P6: int > code_integer,I5: set_int] :
% 9.17/5.42 ( if_Code_integer
% 9.17/5.42 @ ( finite_finite_int
% 9.17/5.42 @ ( collect_int
% 9.17/5.42 @ ^ [X3: int] :
% 9.17/5.42 ( ( member_int @ X3 @ I5 )
% 9.17/5.42 & ( ( P6 @ X3 )
% 9.17/5.42 != one_one_Code_integer ) ) ) )
% 9.17/5.42 @ ( groups3827104343326376752nteger @ P6
% 9.17/5.42 @ ( collect_int
% 9.17/5.42 @ ^ [X3: int] :
% 9.17/5.42 ( ( member_int @ X3 @ I5 )
% 9.17/5.42 & ( ( P6 @ X3 )
% 9.17/5.42 != one_one_Code_integer ) ) ) )
% 9.17/5.42 @ one_one_Code_integer ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6239_prod_OG__def,axiom,
% 9.17/5.42 ( groups7219916603568234122nteger
% 9.17/5.42 = ( ^ [P6: code_integer > code_integer,I5: set_Code_integer] :
% 9.17/5.42 ( if_Code_integer
% 9.17/5.42 @ ( finite6017078050557962740nteger
% 9.17/5.42 @ ( collect_Code_integer
% 9.17/5.42 @ ^ [X3: code_integer] :
% 9.17/5.42 ( ( member_Code_integer @ X3 @ I5 )
% 9.17/5.42 & ( ( P6 @ X3 )
% 9.17/5.42 != one_one_Code_integer ) ) ) )
% 9.17/5.42 @ ( groups3674199335183972705nteger @ P6
% 9.17/5.42 @ ( collect_Code_integer
% 9.17/5.42 @ ^ [X3: code_integer] :
% 9.17/5.42 ( ( member_Code_integer @ X3 @ I5 )
% 9.17/5.42 & ( ( P6 @ X3 )
% 9.17/5.42 != one_one_Code_integer ) ) ) )
% 9.17/5.42 @ one_one_Code_integer ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6240_prod_OG__def,axiom,
% 9.17/5.42 ( groups12625163056032370o_assn
% 9.17/5.42 = ( ^ [P6: $o > assn,I5: set_o] :
% 9.17/5.42 ( if_assn
% 9.17/5.42 @ ( finite_finite_o
% 9.17/5.42 @ ( collect_o
% 9.17/5.42 @ ^ [X3: $o] :
% 9.17/5.42 ( ( member_o @ X3 @ I5 )
% 9.17/5.42 & ( ( P6 @ X3 )
% 9.17/5.42 != one_one_assn ) ) ) )
% 9.17/5.42 @ ( groups5301882518646026715o_assn @ P6
% 9.17/5.42 @ ( collect_o
% 9.17/5.42 @ ^ [X3: $o] :
% 9.17/5.42 ( ( member_o @ X3 @ I5 )
% 9.17/5.42 & ( ( P6 @ X3 )
% 9.17/5.42 != one_one_assn ) ) ) )
% 9.17/5.42 @ one_one_assn ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6241_prod_OG__def,axiom,
% 9.17/5.42 ( groups3916077543535352520t_assn
% 9.17/5.42 = ( ^ [P6: nat > assn,I5: set_nat] :
% 9.17/5.42 ( if_assn
% 9.17/5.42 @ ( finite_finite_nat
% 9.17/5.42 @ ( collect_nat
% 9.17/5.42 @ ^ [X3: nat] :
% 9.17/5.42 ( ( member_nat @ X3 @ I5 )
% 9.17/5.42 & ( ( P6 @ X3 )
% 9.17/5.42 != one_one_assn ) ) ) )
% 9.17/5.42 @ ( groups6906906614972039071t_assn @ P6
% 9.17/5.42 @ ( collect_nat
% 9.17/5.42 @ ^ [X3: nat] :
% 9.17/5.42 ( ( member_nat @ X3 @ I5 )
% 9.17/5.42 & ( ( P6 @ X3 )
% 9.17/5.42 != one_one_assn ) ) ) )
% 9.17/5.42 @ one_one_assn ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6242_prod_OG__def,axiom,
% 9.17/5.42 ( groups4891613008741529892t_assn
% 9.17/5.42 = ( ^ [P6: int > assn,I5: set_int] :
% 9.17/5.42 ( if_assn
% 9.17/5.42 @ ( finite_finite_int
% 9.17/5.42 @ ( collect_int
% 9.17/5.42 @ ^ [X3: int] :
% 9.17/5.42 ( ( member_int @ X3 @ I5 )
% 9.17/5.42 & ( ( P6 @ X3 )
% 9.17/5.42 != one_one_assn ) ) ) )
% 9.17/5.42 @ ( groups7882442080178216443t_assn @ P6
% 9.17/5.42 @ ( collect_int
% 9.17/5.42 @ ^ [X3: int] :
% 9.17/5.42 ( ( member_int @ X3 @ I5 )
% 9.17/5.42 & ( ( P6 @ X3 )
% 9.17/5.42 != one_one_assn ) ) ) )
% 9.17/5.42 @ one_one_assn ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6243_prod_OG__def,axiom,
% 9.17/5.42 ( groups980104329299799381r_assn
% 9.17/5.42 = ( ^ [P6: code_integer > assn,I5: set_Code_integer] :
% 9.17/5.42 ( if_assn
% 9.17/5.42 @ ( finite6017078050557962740nteger
% 9.17/5.42 @ ( collect_Code_integer
% 9.17/5.42 @ ^ [X3: code_integer] :
% 9.17/5.42 ( ( member_Code_integer @ X3 @ I5 )
% 9.17/5.42 & ( ( P6 @ X3 )
% 9.17/5.42 != one_one_assn ) ) ) )
% 9.17/5.42 @ ( groups1304777262505850412r_assn @ P6
% 9.17/5.42 @ ( collect_Code_integer
% 9.17/5.42 @ ^ [X3: code_integer] :
% 9.17/5.42 ( ( member_Code_integer @ X3 @ I5 )
% 9.17/5.42 & ( ( P6 @ X3 )
% 9.17/5.42 != one_one_assn ) ) ) )
% 9.17/5.42 @ one_one_assn ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6244_prod_OG__def,axiom,
% 9.17/5.42 ( groups4688112016125141794_o_rat
% 9.17/5.42 = ( ^ [P6: $o > rat,I5: set_o] :
% 9.17/5.42 ( if_rat
% 9.17/5.42 @ ( finite_finite_o
% 9.17/5.42 @ ( collect_o
% 9.17/5.42 @ ^ [X3: $o] :
% 9.17/5.42 ( ( member_o @ X3 @ I5 )
% 9.17/5.42 & ( ( P6 @ X3 )
% 9.17/5.42 != one_one_rat ) ) ) )
% 9.17/5.42 @ ( groups2869687844427037835_o_rat @ P6
% 9.17/5.42 @ ( collect_o
% 9.17/5.42 @ ^ [X3: $o] :
% 9.17/5.42 ( ( member_o @ X3 @ I5 )
% 9.17/5.42 & ( ( P6 @ X3 )
% 9.17/5.42 != one_one_rat ) ) ) )
% 9.17/5.42 @ one_one_rat ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6245_prod_OG__def,axiom,
% 9.17/5.42 ( groups4112464933559648120at_rat
% 9.17/5.42 = ( ^ [P6: nat > rat,I5: set_nat] :
% 9.17/5.42 ( if_rat
% 9.17/5.42 @ ( finite_finite_nat
% 9.17/5.42 @ ( collect_nat
% 9.17/5.42 @ ^ [X3: nat] :
% 9.17/5.42 ( ( member_nat @ X3 @ I5 )
% 9.17/5.42 & ( ( P6 @ X3 )
% 9.17/5.42 != one_one_rat ) ) ) )
% 9.17/5.42 @ ( groups73079841787564623at_rat @ P6
% 9.17/5.42 @ ( collect_nat
% 9.17/5.42 @ ^ [X3: nat] :
% 9.17/5.42 ( ( member_nat @ X3 @ I5 )
% 9.17/5.42 & ( ( P6 @ X3 )
% 9.17/5.42 != one_one_rat ) ) ) )
% 9.17/5.42 @ one_one_rat ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6246_greaterThanLessThan__subseteq__atLeastAtMost__iff,axiom,
% 9.17/5.42 ! [A: rat,B: rat,C: rat,D2: rat] :
% 9.17/5.42 ( ( ord_less_eq_set_rat @ ( set_or5199638295745620268an_rat @ A @ B ) @ ( set_or633870826150836451st_rat @ C @ D2 ) )
% 9.17/5.42 = ( ( ord_less_rat @ A @ B )
% 9.17/5.42 => ( ( ord_less_eq_rat @ C @ A )
% 9.17/5.42 & ( ord_less_eq_rat @ B @ D2 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6247_greaterThanLessThan__subseteq__atLeastLessThan__iff,axiom,
% 9.17/5.42 ! [A: rat,B: rat,C: rat,D2: rat] :
% 9.17/5.42 ( ( ord_less_eq_set_rat @ ( set_or5199638295745620268an_rat @ A @ B ) @ ( set_or4029947393144176647an_rat @ C @ D2 ) )
% 9.17/5.42 = ( ( ord_less_rat @ A @ B )
% 9.17/5.42 => ( ( ord_less_eq_rat @ C @ A )
% 9.17/5.42 & ( ord_less_eq_rat @ B @ D2 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6248_atLeastAtMost__diff__ends,axiom,
% 9.17/5.42 ! [A: $o,B: $o] :
% 9.17/5.42 ( ( minus_minus_set_o @ ( set_or8904488021354931149Most_o @ A @ B ) @ ( insert_o @ A @ ( insert_o @ B @ bot_bot_set_o ) ) )
% 9.17/5.42 = ( set_or1716231572884733764Than_o @ A @ B ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6249_atLeastAtMost__diff__ends,axiom,
% 9.17/5.42 ! [A: int,B: int] :
% 9.17/5.42 ( ( minus_minus_set_int @ ( set_or1266510415728281911st_int @ A @ B ) @ ( insert_int @ A @ ( insert_int @ B @ bot_bot_set_int ) ) )
% 9.17/5.42 = ( set_or5832277885323065728an_int @ A @ B ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6250_atLeastAtMost__diff__ends,axiom,
% 9.17/5.42 ! [A: nat,B: nat] :
% 9.17/5.42 ( ( minus_minus_set_nat @ ( set_or1269000886237332187st_nat @ A @ B ) @ ( insert_nat @ A @ ( insert_nat @ B @ bot_bot_set_nat ) ) )
% 9.17/5.42 = ( set_or5834768355832116004an_nat @ A @ B ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6251_atLeastAtMost__diff__ends,axiom,
% 9.17/5.42 ! [A: code_integer,B: code_integer] :
% 9.17/5.42 ( ( minus_2355218937544613996nteger @ ( set_or189985376899183464nteger @ A @ B ) @ ( insert_Code_integer @ A @ ( insert_Code_integer @ B @ bot_bo3990330152332043303nteger ) ) )
% 9.17/5.42 = ( set_or4266950643985792945nteger @ A @ B ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6252_smax__insertI,axiom,
% 9.17/5.42 ! [Y: product_prod_nat_nat,Y9: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat,X11: set_Pr1261947904930325089at_nat] :
% 9.17/5.42 ( ( member8440522571783428010at_nat @ Y @ Y9 )
% 9.17/5.42 => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X @ Y ) @ fun_pair_less )
% 9.17/5.42 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X11 @ Y9 ) @ fun_max_strict )
% 9.17/5.42 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( insert8211810215607154385at_nat @ X @ X11 ) @ Y9 ) @ fun_max_strict ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6253_set__decode__plus__power__2,axiom,
% 9.17/5.42 ! [N2: nat,Z: nat] :
% 9.17/5.42 ( ~ ( member_nat @ N2 @ ( nat_set_decode @ Z ) )
% 9.17/5.42 => ( ( nat_set_decode @ ( plus_plus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ Z ) )
% 9.17/5.42 = ( insert_nat @ N2 @ ( nat_set_decode @ Z ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6254_prod__decode__aux_Osimps,axiom,
% 9.17/5.42 ( nat_prod_decode_aux
% 9.17/5.42 = ( ^ [K4: nat,M: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ M @ K4 ) @ ( product_Pair_nat_nat @ M @ ( minus_minus_nat @ K4 @ M ) ) @ ( nat_prod_decode_aux @ ( suc @ K4 ) @ ( minus_minus_nat @ M @ ( suc @ K4 ) ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6255_prod__decode__aux_Oelims,axiom,
% 9.17/5.42 ! [X: nat,Xa: nat,Y: product_prod_nat_nat] :
% 9.17/5.42 ( ( ( nat_prod_decode_aux @ X @ Xa )
% 9.17/5.42 = Y )
% 9.17/5.42 => ( ( ( ord_less_eq_nat @ Xa @ X )
% 9.17/5.42 => ( Y
% 9.17/5.42 = ( product_Pair_nat_nat @ Xa @ ( minus_minus_nat @ X @ Xa ) ) ) )
% 9.17/5.42 & ( ~ ( ord_less_eq_nat @ Xa @ X )
% 9.17/5.42 => ( Y
% 9.17/5.42 = ( nat_prod_decode_aux @ ( suc @ X ) @ ( minus_minus_nat @ Xa @ ( suc @ X ) ) ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6256_min__rpair__set,axiom,
% 9.17/5.42 fun_re2478310338295953701at_nat @ ( produc9060074326276436823at_nat @ fun_min_strict @ fun_min_weak ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6257_triangle__Suc,axiom,
% 9.17/5.42 ! [N2: nat] :
% 9.17/5.42 ( ( nat_triangle @ ( suc @ N2 ) )
% 9.17/5.42 = ( plus_plus_nat @ ( nat_triangle @ N2 ) @ ( suc @ N2 ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6258_finite__greaterThanLessThan,axiom,
% 9.17/5.42 ! [L: nat,U: nat] : ( finite_finite_nat @ ( set_or5834768355832116004an_nat @ L @ U ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6259_finite__greaterThanLessThan__integer,axiom,
% 9.17/5.42 ! [L: code_integer,U: code_integer] : ( finite6017078050557962740nteger @ ( set_or4266950643985792945nteger @ L @ U ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6260_card__greaterThanLessThan,axiom,
% 9.17/5.42 ! [L: nat,U: nat] :
% 9.17/5.42 ( ( finite_card_nat @ ( set_or5834768355832116004an_nat @ L @ U ) )
% 9.17/5.42 = ( minus_minus_nat @ U @ ( suc @ L ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6261_max__rpair__set,axiom,
% 9.17/5.42 fun_re2478310338295953701at_nat @ ( produc9060074326276436823at_nat @ fun_max_strict @ fun_max_weak ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6262_atLeastSucLessThan__greaterThanLessThan,axiom,
% 9.17/5.42 ! [L: nat,U: nat] :
% 9.17/5.42 ( ( set_or4665077453230672383an_nat @ ( suc @ L ) @ U )
% 9.17/5.42 = ( set_or5834768355832116004an_nat @ L @ U ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6263_smax__emptyI,axiom,
% 9.17/5.42 ! [Y9: set_Pr1261947904930325089at_nat] :
% 9.17/5.42 ( ( finite6177210948735845034at_nat @ Y9 )
% 9.17/5.42 => ( ( Y9 != bot_bo2099793752762293965at_nat )
% 9.17/5.42 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ bot_bo2099793752762293965at_nat @ Y9 ) @ fun_max_strict ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6264_atLeastPlusOneLessThan__greaterThanLessThan__integer,axiom,
% 9.17/5.42 ! [L: code_integer,U: code_integer] :
% 9.17/5.42 ( ( set_or8404916559141939852nteger @ ( plus_p5714425477246183910nteger @ L @ one_one_Code_integer ) @ U )
% 9.17/5.42 = ( set_or4266950643985792945nteger @ L @ U ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6265_prod__decode__aux_Opelims,axiom,
% 9.17/5.42 ! [X: nat,Xa: nat,Y: product_prod_nat_nat] :
% 9.17/5.42 ( ( ( nat_prod_decode_aux @ X @ Xa )
% 9.17/5.42 = Y )
% 9.17/5.42 => ( ( accp_P4275260045618599050at_nat @ nat_pr5047031295181774490ux_rel @ ( product_Pair_nat_nat @ X @ Xa ) )
% 9.17/5.42 => ~ ( ( ( ( ord_less_eq_nat @ Xa @ X )
% 9.17/5.42 => ( Y
% 9.17/5.42 = ( product_Pair_nat_nat @ Xa @ ( minus_minus_nat @ X @ Xa ) ) ) )
% 9.17/5.42 & ( ~ ( ord_less_eq_nat @ Xa @ X )
% 9.17/5.42 => ( Y
% 9.17/5.42 = ( nat_prod_decode_aux @ ( suc @ X ) @ ( minus_minus_nat @ Xa @ ( suc @ X ) ) ) ) ) )
% 9.17/5.42 => ~ ( accp_P4275260045618599050at_nat @ nat_pr5047031295181774490ux_rel @ ( product_Pair_nat_nat @ X @ Xa ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6266_total__on__singleton,axiom,
% 9.17/5.42 ! [X: set_Pr1261947904930325089at_nat] : ( total_7212417256332265445at_nat @ ( insert9200635055090092081at_nat @ X @ bot_bo3083307316010499117at_nat ) @ ( insert9069300056098147895at_nat @ ( produc2922128104949294807at_nat @ X @ X ) @ bot_bo228742789529271731at_nat ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6267_total__on__singleton,axiom,
% 9.17/5.42 ! [X: produc3843707927480180839at_nat] : ( total_1513685709984341995at_nat @ ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) @ ( insert398606708087465655at_nat @ ( produc2335810615602371415at_nat @ X @ X ) @ bot_bo7193250159860175667at_nat ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6268_total__on__singleton,axiom,
% 9.17/5.42 ! [X: product_prod_nat_nat] : ( total_3592101749530773125at_nat @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) @ ( insert5050368324300391991at_nat @ ( produc6161850002892822231at_nat @ X @ X ) @ bot_bo5327735625951526323at_nat ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6269_total__on__singleton,axiom,
% 9.17/5.42 ! [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 ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6270_total__on__singleton,axiom,
% 9.17/5.42 ! [X: nat] : ( total_on_nat @ ( insert_nat @ X @ bot_bot_set_nat ) @ ( insert8211810215607154385at_nat @ ( product_Pair_nat_nat @ X @ X ) @ bot_bo2099793752762293965at_nat ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6271_total__on__singleton,axiom,
% 9.17/5.42 ! [X: int] : ( total_on_int @ ( insert_int @ X @ bot_bot_set_int ) @ ( insert5033312907999012233nt_int @ ( product_Pair_int_int @ X @ X ) @ bot_bo1796632182523588997nt_int ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6272_prod__encode__prod__decode__aux,axiom,
% 9.17/5.42 ! [K: nat,M2: nat] :
% 9.17/5.42 ( ( nat_prod_encode @ ( nat_prod_decode_aux @ K @ M2 ) )
% 9.17/5.42 = ( plus_plus_nat @ ( nat_triangle @ K ) @ M2 ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6273_sum_Oinsert_H,axiom,
% 9.17/5.42 ! [I4: set_o,P4: $o > code_integer,I: $o] :
% 9.17/5.42 ( ( finite_finite_o
% 9.17/5.42 @ ( collect_o
% 9.17/5.42 @ ^ [X3: $o] :
% 9.17/5.42 ( ( member_o @ X3 @ I4 )
% 9.17/5.42 & ( ( P4 @ X3 )
% 9.17/5.42 != zero_z3403309356797280102nteger ) ) ) )
% 9.17/5.42 => ( ( ( member_o @ I @ I4 )
% 9.17/5.42 => ( ( groups1402912129352969042nteger @ P4 @ ( insert_o @ I @ I4 ) )
% 9.17/5.42 = ( groups1402912129352969042nteger @ P4 @ I4 ) ) )
% 9.17/5.42 & ( ~ ( member_o @ I @ I4 )
% 9.17/5.42 => ( ( groups1402912129352969042nteger @ P4 @ ( insert_o @ I @ I4 ) )
% 9.17/5.42 = ( plus_p5714425477246183910nteger @ ( P4 @ I ) @ ( groups1402912129352969042nteger @ P4 @ I4 ) ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6274_sum_Oinsert_H,axiom,
% 9.17/5.42 ! [I4: set_nat,P4: nat > code_integer,I: nat] :
% 9.17/5.42 ( ( finite_finite_nat
% 9.17/5.42 @ ( collect_nat
% 9.17/5.42 @ ^ [X3: nat] :
% 9.17/5.42 ( ( member_nat @ X3 @ I4 )
% 9.17/5.42 & ( ( P4 @ X3 )
% 9.17/5.42 != zero_z3403309356797280102nteger ) ) ) )
% 9.17/5.42 => ( ( ( member_nat @ I @ I4 )
% 9.17/5.42 => ( ( groups555127423416065298nteger @ P4 @ ( insert_nat @ I @ I4 ) )
% 9.17/5.42 = ( groups555127423416065298nteger @ P4 @ I4 ) ) )
% 9.17/5.42 & ( ~ ( member_nat @ I @ I4 )
% 9.17/5.42 => ( ( groups555127423416065298nteger @ P4 @ ( insert_nat @ I @ I4 ) )
% 9.17/5.42 = ( plus_p5714425477246183910nteger @ ( P4 @ I ) @ ( groups555127423416065298nteger @ P4 @ I4 ) ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6275_sum_Oinsert_H,axiom,
% 9.17/5.42 ! [I4: set_int,P4: int > code_integer,I: int] :
% 9.17/5.42 ( ( finite_finite_int
% 9.17/5.42 @ ( collect_int
% 9.17/5.42 @ ^ [X3: int] :
% 9.17/5.42 ( ( member_int @ X3 @ I4 )
% 9.17/5.42 & ( ( P4 @ X3 )
% 9.17/5.42 != zero_z3403309356797280102nteger ) ) ) )
% 9.17/5.42 => ( ( ( member_int @ I @ I4 )
% 9.17/5.42 => ( ( groups926780983652909934nteger @ P4 @ ( insert_int @ I @ I4 ) )
% 9.17/5.42 = ( groups926780983652909934nteger @ P4 @ I4 ) ) )
% 9.17/5.42 & ( ~ ( member_int @ I @ I4 )
% 9.17/5.42 => ( ( groups926780983652909934nteger @ P4 @ ( insert_int @ I @ I4 ) )
% 9.17/5.42 = ( plus_p5714425477246183910nteger @ ( P4 @ I ) @ ( groups926780983652909934nteger @ P4 @ I4 ) ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6276_sum_Oinsert_H,axiom,
% 9.17/5.42 ! [I4: set_Code_integer,P4: code_integer > code_integer,I: code_integer] :
% 9.17/5.42 ( ( finite6017078050557962740nteger
% 9.17/5.42 @ ( collect_Code_integer
% 9.17/5.42 @ ^ [X3: code_integer] :
% 9.17/5.42 ( ( member_Code_integer @ X3 @ I4 )
% 9.17/5.42 & ( ( P4 @ X3 )
% 9.17/5.42 != zero_z3403309356797280102nteger ) ) ) )
% 9.17/5.42 => ( ( ( member_Code_integer @ I @ I4 )
% 9.17/5.42 => ( ( groups910942671188738463nteger @ P4 @ ( insert_Code_integer @ I @ I4 ) )
% 9.17/5.42 = ( groups910942671188738463nteger @ P4 @ I4 ) ) )
% 9.17/5.42 & ( ~ ( member_Code_integer @ I @ I4 )
% 9.17/5.42 => ( ( groups910942671188738463nteger @ P4 @ ( insert_Code_integer @ I @ I4 ) )
% 9.17/5.42 = ( plus_p5714425477246183910nteger @ ( P4 @ I ) @ ( groups910942671188738463nteger @ P4 @ I4 ) ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6277_sum_Oinsert_H,axiom,
% 9.17/5.42 ! [I4: set_o,P4: $o > rat,I: $o] :
% 9.17/5.42 ( ( finite_finite_o
% 9.17/5.42 @ ( collect_o
% 9.17/5.42 @ ^ [X3: $o] :
% 9.17/5.42 ( ( member_o @ X3 @ I4 )
% 9.17/5.42 & ( ( P4 @ X3 )
% 9.17/5.42 != zero_zero_rat ) ) ) )
% 9.17/5.42 => ( ( ( member_o @ I @ I4 )
% 9.17/5.42 => ( ( groups3921277224699582669_o_rat @ P4 @ ( insert_o @ I @ I4 ) )
% 9.17/5.42 = ( groups3921277224699582669_o_rat @ P4 @ I4 ) ) )
% 9.17/5.42 & ( ~ ( member_o @ I @ I4 )
% 9.17/5.42 => ( ( groups3921277224699582669_o_rat @ P4 @ ( insert_o @ I @ I4 ) )
% 9.17/5.42 = ( plus_plus_rat @ ( P4 @ I ) @ ( groups3921277224699582669_o_rat @ P4 @ I4 ) ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6278_sum_Oinsert_H,axiom,
% 9.17/5.42 ! [I4: set_nat,P4: nat > rat,I: nat] :
% 9.17/5.42 ( ( finite_finite_nat
% 9.17/5.42 @ ( collect_nat
% 9.17/5.42 @ ^ [X3: nat] :
% 9.17/5.42 ( ( member_nat @ X3 @ I4 )
% 9.17/5.42 & ( ( P4 @ X3 )
% 9.17/5.42 != zero_zero_rat ) ) ) )
% 9.17/5.42 => ( ( ( member_nat @ I @ I4 )
% 9.17/5.42 => ( ( groups1351286907653491341at_rat @ P4 @ ( insert_nat @ I @ I4 ) )
% 9.17/5.42 = ( groups1351286907653491341at_rat @ P4 @ I4 ) ) )
% 9.17/5.42 & ( ~ ( member_nat @ I @ I4 )
% 9.17/5.42 => ( ( groups1351286907653491341at_rat @ P4 @ ( insert_nat @ I @ I4 ) )
% 9.17/5.42 = ( plus_plus_rat @ ( P4 @ I ) @ ( groups1351286907653491341at_rat @ P4 @ I4 ) ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6279_sum_Oinsert_H,axiom,
% 9.17/5.42 ! [I4: set_int,P4: int > rat,I: int] :
% 9.17/5.42 ( ( finite_finite_int
% 9.17/5.42 @ ( collect_int
% 9.17/5.42 @ ^ [X3: int] :
% 9.17/5.42 ( ( member_int @ X3 @ I4 )
% 9.17/5.42 & ( ( P4 @ X3 )
% 9.17/5.42 != zero_zero_rat ) ) ) )
% 9.17/5.42 => ( ( ( member_int @ I @ I4 )
% 9.17/5.42 => ( ( groups2350640619554545897nt_rat @ P4 @ ( insert_int @ I @ I4 ) )
% 9.17/5.42 = ( groups2350640619554545897nt_rat @ P4 @ I4 ) ) )
% 9.17/5.42 & ( ~ ( member_int @ I @ I4 )
% 9.17/5.42 => ( ( groups2350640619554545897nt_rat @ P4 @ ( insert_int @ I @ I4 ) )
% 9.17/5.42 = ( plus_plus_rat @ ( P4 @ I ) @ ( groups2350640619554545897nt_rat @ P4 @ I4 ) ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6280_sum_Oinsert_H,axiom,
% 9.17/5.42 ! [I4: set_Code_integer,P4: code_integer > rat,I: code_integer] :
% 9.17/5.42 ( ( finite6017078050557962740nteger
% 9.17/5.42 @ ( collect_Code_integer
% 9.17/5.42 @ ^ [X3: code_integer] :
% 9.17/5.42 ( ( member_Code_integer @ X3 @ I4 )
% 9.17/5.42 & ( ( P4 @ X3 )
% 9.17/5.42 != zero_zero_rat ) ) ) )
% 9.17/5.42 => ( ( ( member_Code_integer @ I @ I4 )
% 9.17/5.42 => ( ( groups8878813951405302554er_rat @ P4 @ ( insert_Code_integer @ I @ I4 ) )
% 9.17/5.42 = ( groups8878813951405302554er_rat @ P4 @ I4 ) ) )
% 9.17/5.42 & ( ~ ( member_Code_integer @ I @ I4 )
% 9.17/5.42 => ( ( groups8878813951405302554er_rat @ P4 @ ( insert_Code_integer @ I @ I4 ) )
% 9.17/5.42 = ( plus_plus_rat @ ( P4 @ I ) @ ( groups8878813951405302554er_rat @ P4 @ I4 ) ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6281_sum_Oinsert_H,axiom,
% 9.17/5.42 ! [I4: set_o,P4: $o > nat,I: $o] :
% 9.17/5.42 ( ( finite_finite_o
% 9.17/5.42 @ ( collect_o
% 9.17/5.42 @ ^ [X3: $o] :
% 9.17/5.42 ( ( member_o @ X3 @ I4 )
% 9.17/5.42 & ( ( P4 @ X3 )
% 9.17/5.42 != zero_zero_nat ) ) ) )
% 9.17/5.42 => ( ( ( member_o @ I @ I4 )
% 9.17/5.42 => ( ( groups4556407284786078405_o_nat @ P4 @ ( insert_o @ I @ I4 ) )
% 9.17/5.42 = ( groups4556407284786078405_o_nat @ P4 @ I4 ) ) )
% 9.17/5.42 & ( ~ ( member_o @ I @ I4 )
% 9.17/5.42 => ( ( groups4556407284786078405_o_nat @ P4 @ ( insert_o @ I @ I4 ) )
% 9.17/5.42 = ( plus_plus_nat @ ( P4 @ I ) @ ( groups4556407284786078405_o_nat @ P4 @ I4 ) ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6282_sum_Oinsert_H,axiom,
% 9.17/5.42 ! [I4: set_nat,P4: nat > nat,I: nat] :
% 9.17/5.42 ( ( finite_finite_nat
% 9.17/5.42 @ ( collect_nat
% 9.17/5.42 @ ^ [X3: nat] :
% 9.17/5.42 ( ( member_nat @ X3 @ I4 )
% 9.17/5.42 & ( ( P4 @ X3 )
% 9.17/5.42 != zero_zero_nat ) ) ) )
% 9.17/5.42 => ( ( ( member_nat @ I @ I4 )
% 9.17/5.42 => ( ( groups1986416967739987077at_nat @ P4 @ ( insert_nat @ I @ I4 ) )
% 9.17/5.42 = ( groups1986416967739987077at_nat @ P4 @ I4 ) ) )
% 9.17/5.42 & ( ~ ( member_nat @ I @ I4 )
% 9.17/5.42 => ( ( groups1986416967739987077at_nat @ P4 @ ( insert_nat @ I @ I4 ) )
% 9.17/5.42 = ( plus_plus_nat @ ( P4 @ I ) @ ( groups1986416967739987077at_nat @ P4 @ I4 ) ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6283_max__ext_Omax__extI,axiom,
% 9.17/5.42 ! [X11: set_se7855581050983116737at_nat,Y9: set_se7855581050983116737at_nat,R4: set_Pr4329608150637261639at_nat] :
% 9.17/5.42 ( ( finite9047747110432174090at_nat @ X11 )
% 9.17/5.42 => ( ( finite9047747110432174090at_nat @ Y9 )
% 9.17/5.42 => ( ( Y9 != bot_bo3083307316010499117at_nat )
% 9.17/5.42 => ( ! [X4: set_Pr1261947904930325089at_nat] :
% 9.17/5.42 ( ( member2643936169264416010at_nat @ X4 @ X11 )
% 9.17/5.42 => ? [Xa2: set_Pr1261947904930325089at_nat] :
% 9.17/5.42 ( ( member2643936169264416010at_nat @ Xa2 @ Y9 )
% 9.17/5.42 & ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X4 @ Xa2 ) @ R4 ) ) )
% 9.17/5.42 => ( member4300370950623927696at_nat @ ( produc7462898802507495127at_nat @ X11 @ Y9 ) @ ( max_ex4535816423174879388at_nat @ R4 ) ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6284_max__ext_Omax__extI,axiom,
% 9.17/5.42 ! [X11: set_Code_integer,Y9: set_Code_integer,R4: set_Pr4811707699266497531nteger] :
% 9.17/5.42 ( ( finite6017078050557962740nteger @ X11 )
% 9.17/5.42 => ( ( finite6017078050557962740nteger @ Y9 )
% 9.17/5.42 => ( ( Y9 != bot_bo3990330152332043303nteger )
% 9.17/5.42 => ( ! [X4: code_integer] :
% 9.17/5.42 ( ( member_Code_integer @ X4 @ X11 )
% 9.17/5.42 => ? [Xa2: code_integer] :
% 9.17/5.42 ( ( member_Code_integer @ Xa2 @ Y9 )
% 9.17/5.42 & ( member157494554546826820nteger @ ( produc1086072967326762835nteger @ X4 @ Xa2 ) @ R4 ) ) )
% 9.17/5.42 => ( member4307123515891402160nteger @ ( produc7443773368509356479nteger @ X11 @ Y9 ) @ ( max_ext_Code_integer @ R4 ) ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6285_max__ext_Omax__extI,axiom,
% 9.17/5.42 ! [X11: set_Pr4329608150637261639at_nat,Y9: set_Pr4329608150637261639at_nat,R4: set_Pr5564308138774400199at_nat] :
% 9.17/5.42 ( ( finite4343798906461161616at_nat @ X11 )
% 9.17/5.42 => ( ( finite4343798906461161616at_nat @ Y9 )
% 9.17/5.42 => ( ( Y9 != bot_bo228742789529271731at_nat )
% 9.17/5.42 => ( ! [X4: produc3843707927480180839at_nat] :
% 9.17/5.42 ( ( member8757157785044589968at_nat @ X4 @ X11 )
% 9.17/5.42 => ? [Xa2: produc3843707927480180839at_nat] :
% 9.17/5.42 ( ( member8757157785044589968at_nat @ Xa2 @ Y9 )
% 9.17/5.42 & ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ X4 @ Xa2 ) @ R4 ) ) )
% 9.17/5.42 => ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ X11 @ Y9 ) @ ( max_ex8833738776070432290at_nat @ R4 ) ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6286_max__ext_Omax__extI,axiom,
% 9.17/5.42 ! [X11: set_Pr1261947904930325089at_nat,Y9: set_Pr1261947904930325089at_nat,R4: set_Pr8693737435421807431at_nat] :
% 9.17/5.42 ( ( finite6177210948735845034at_nat @ X11 )
% 9.17/5.42 => ( ( finite6177210948735845034at_nat @ Y9 )
% 9.17/5.42 => ( ( Y9 != bot_bo2099793752762293965at_nat )
% 9.17/5.42 => ( ! [X4: product_prod_nat_nat] :
% 9.17/5.42 ( ( member8440522571783428010at_nat @ X4 @ X11 )
% 9.17/5.42 => ? [Xa2: product_prod_nat_nat] :
% 9.17/5.42 ( ( member8440522571783428010at_nat @ Xa2 @ Y9 )
% 9.17/5.42 & ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X4 @ Xa2 ) @ R4 ) ) )
% 9.17/5.42 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X11 @ Y9 ) @ ( max_ex8135407076693332796at_nat @ R4 ) ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6287_max__ext_Omax__extI,axiom,
% 9.17/5.42 ! [X11: set_o,Y9: set_o,R4: set_Product_prod_o_o] :
% 9.17/5.42 ( ( finite_finite_o @ X11 )
% 9.17/5.42 => ( ( finite_finite_o @ Y9 )
% 9.17/5.42 => ( ( Y9 != bot_bot_set_o )
% 9.17/5.42 => ( ! [X4: $o] :
% 9.17/5.42 ( ( member_o @ X4 @ X11 )
% 9.17/5.42 => ? [Xa2: $o] :
% 9.17/5.42 ( ( member_o @ Xa2 @ Y9 )
% 9.17/5.42 & ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ X4 @ Xa2 ) @ R4 ) ) )
% 9.17/5.42 => ( member9116954335612470352_set_o @ ( produc5838405689764958487_set_o @ X11 @ Y9 ) @ ( max_ext_o @ R4 ) ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6288_max__ext_Omax__extI,axiom,
% 9.17/5.42 ! [X11: set_nat,Y9: set_nat,R4: set_Pr1261947904930325089at_nat] :
% 9.17/5.42 ( ( finite_finite_nat @ X11 )
% 9.17/5.42 => ( ( finite_finite_nat @ Y9 )
% 9.17/5.42 => ( ( Y9 != bot_bot_set_nat )
% 9.17/5.42 => ( ! [X4: nat] :
% 9.17/5.42 ( ( member_nat @ X4 @ X11 )
% 9.17/5.42 => ? [Xa2: nat] :
% 9.17/5.42 ( ( member_nat @ Xa2 @ Y9 )
% 9.17/5.42 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Xa2 ) @ R4 ) ) )
% 9.17/5.42 => ( member8277197624267554838et_nat @ ( produc4532415448927165861et_nat @ X11 @ Y9 ) @ ( max_ext_nat @ R4 ) ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6289_max__ext_Omax__extI,axiom,
% 9.17/5.42 ! [X11: set_int,Y9: set_int,R4: set_Pr958786334691620121nt_int] :
% 9.17/5.42 ( ( finite_finite_int @ X11 )
% 9.17/5.42 => ( ( finite_finite_int @ Y9 )
% 9.17/5.42 => ( ( Y9 != bot_bot_set_int )
% 9.17/5.42 => ( ! [X4: int] :
% 9.17/5.42 ( ( member_int @ X4 @ X11 )
% 9.17/5.42 => ? [Xa2: int] :
% 9.17/5.42 ( ( member_int @ Xa2 @ Y9 )
% 9.17/5.42 & ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Xa2 ) @ R4 ) ) )
% 9.17/5.42 => ( member2572552093476627150et_int @ ( produc6363374080413544029et_int @ X11 @ Y9 ) @ ( max_ext_int @ R4 ) ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6290_total__on__def,axiom,
% 9.17/5.42 ( total_7212417256332265445at_nat
% 9.17/5.42 = ( ^ [A7: set_se7855581050983116737at_nat,R3: set_Pr4329608150637261639at_nat] :
% 9.17/5.42 ! [X3: set_Pr1261947904930325089at_nat] :
% 9.17/5.42 ( ( member2643936169264416010at_nat @ X3 @ A7 )
% 9.17/5.42 => ! [Y3: set_Pr1261947904930325089at_nat] :
% 9.17/5.42 ( ( member2643936169264416010at_nat @ Y3 @ A7 )
% 9.17/5.42 => ( ( X3 != Y3 )
% 9.17/5.42 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ Y3 ) @ R3 )
% 9.17/5.42 | ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ Y3 @ X3 ) @ R3 ) ) ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6291_total__on__def,axiom,
% 9.17/5.42 ( total_on_nat
% 9.17/5.42 = ( ^ [A7: set_nat,R3: set_Pr1261947904930325089at_nat] :
% 9.17/5.42 ! [X3: nat] :
% 9.17/5.42 ( ( member_nat @ X3 @ A7 )
% 9.17/5.42 => ! [Y3: nat] :
% 9.17/5.42 ( ( member_nat @ Y3 @ A7 )
% 9.17/5.42 => ( ( X3 != Y3 )
% 9.17/5.42 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y3 ) @ R3 )
% 9.17/5.42 | ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y3 @ X3 ) @ R3 ) ) ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6292_total__onI,axiom,
% 9.17/5.42 ! [A2: set_se7855581050983116737at_nat,R2: set_Pr4329608150637261639at_nat] :
% 9.17/5.42 ( ! [X4: set_Pr1261947904930325089at_nat,Y5: set_Pr1261947904930325089at_nat] :
% 9.17/5.42 ( ( member2643936169264416010at_nat @ X4 @ A2 )
% 9.17/5.42 => ( ( member2643936169264416010at_nat @ Y5 @ A2 )
% 9.17/5.42 => ( ( X4 != Y5 )
% 9.17/5.42 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X4 @ Y5 ) @ R2 )
% 9.17/5.42 | ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ Y5 @ X4 ) @ R2 ) ) ) ) )
% 9.17/5.42 => ( total_7212417256332265445at_nat @ A2 @ R2 ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6293_total__onI,axiom,
% 9.17/5.42 ! [A2: set_Pr4329608150637261639at_nat,R2: set_Pr5564308138774400199at_nat] :
% 9.17/5.42 ( ! [X4: produc3843707927480180839at_nat,Y5: produc3843707927480180839at_nat] :
% 9.17/5.42 ( ( member8757157785044589968at_nat @ X4 @ A2 )
% 9.17/5.42 => ( ( member8757157785044589968at_nat @ Y5 @ A2 )
% 9.17/5.42 => ( ( X4 != Y5 )
% 9.17/5.42 => ( ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ X4 @ Y5 ) @ R2 )
% 9.17/5.42 | ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ Y5 @ X4 ) @ R2 ) ) ) ) )
% 9.17/5.42 => ( total_1513685709984341995at_nat @ A2 @ R2 ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6294_total__onI,axiom,
% 9.17/5.42 ! [A2: set_Pr1261947904930325089at_nat,R2: set_Pr8693737435421807431at_nat] :
% 9.17/5.42 ( ! [X4: product_prod_nat_nat,Y5: product_prod_nat_nat] :
% 9.17/5.42 ( ( member8440522571783428010at_nat @ X4 @ A2 )
% 9.17/5.42 => ( ( member8440522571783428010at_nat @ Y5 @ A2 )
% 9.17/5.42 => ( ( X4 != Y5 )
% 9.17/5.42 => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X4 @ Y5 ) @ R2 )
% 9.17/5.42 | ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ Y5 @ X4 ) @ R2 ) ) ) ) )
% 9.17/5.42 => ( total_3592101749530773125at_nat @ A2 @ R2 ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6295_total__onI,axiom,
% 9.17/5.42 ! [A2: set_o,R2: set_Product_prod_o_o] :
% 9.17/5.42 ( ! [X4: $o,Y5: $o] :
% 9.17/5.42 ( ( member_o @ X4 @ A2 )
% 9.17/5.42 => ( ( member_o @ Y5 @ A2 )
% 9.17/5.42 => ( ( X4 != Y5 )
% 9.17/5.42 => ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ X4 @ Y5 ) @ R2 )
% 9.17/5.42 | ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ Y5 @ X4 ) @ R2 ) ) ) ) )
% 9.17/5.42 => ( total_on_o @ A2 @ R2 ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6296_total__onI,axiom,
% 9.17/5.42 ! [A2: set_nat,R2: set_Pr1261947904930325089at_nat] :
% 9.17/5.42 ( ! [X4: nat,Y5: nat] :
% 9.17/5.42 ( ( member_nat @ X4 @ A2 )
% 9.17/5.42 => ( ( member_nat @ Y5 @ A2 )
% 9.17/5.42 => ( ( X4 != Y5 )
% 9.17/5.42 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Y5 ) @ R2 )
% 9.17/5.42 | ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y5 @ X4 ) @ R2 ) ) ) ) )
% 9.17/5.42 => ( total_on_nat @ A2 @ R2 ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6297_total__onI,axiom,
% 9.17/5.42 ! [A2: set_int,R2: set_Pr958786334691620121nt_int] :
% 9.17/5.42 ( ! [X4: int,Y5: int] :
% 9.17/5.42 ( ( member_int @ X4 @ A2 )
% 9.17/5.42 => ( ( member_int @ Y5 @ A2 )
% 9.17/5.42 => ( ( X4 != Y5 )
% 9.17/5.42 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Y5 ) @ R2 )
% 9.17/5.42 | ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Y5 @ X4 ) @ R2 ) ) ) ) )
% 9.17/5.42 => ( total_on_int @ A2 @ R2 ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6298_sum_Odistrib__triv_H,axiom,
% 9.17/5.42 ! [I4: set_nat,G: nat > rat,H3: nat > rat] :
% 9.17/5.42 ( ( finite_finite_nat @ I4 )
% 9.17/5.42 => ( ( groups1351286907653491341at_rat
% 9.17/5.42 @ ^ [I3: nat] : ( plus_plus_rat @ ( G @ I3 ) @ ( H3 @ I3 ) )
% 9.17/5.42 @ I4 )
% 9.17/5.42 = ( plus_plus_rat @ ( groups1351286907653491341at_rat @ G @ I4 ) @ ( groups1351286907653491341at_rat @ H3 @ I4 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6299_sum_Odistrib__triv_H,axiom,
% 9.17/5.42 ! [I4: set_int,G: int > rat,H3: int > rat] :
% 9.17/5.42 ( ( finite_finite_int @ I4 )
% 9.17/5.42 => ( ( groups2350640619554545897nt_rat
% 9.17/5.42 @ ^ [I3: int] : ( plus_plus_rat @ ( G @ I3 ) @ ( H3 @ I3 ) )
% 9.17/5.42 @ I4 )
% 9.17/5.42 = ( plus_plus_rat @ ( groups2350640619554545897nt_rat @ G @ I4 ) @ ( groups2350640619554545897nt_rat @ H3 @ I4 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6300_sum_Odistrib__triv_H,axiom,
% 9.17/5.42 ! [I4: set_Code_integer,G: code_integer > rat,H3: code_integer > rat] :
% 9.17/5.42 ( ( finite6017078050557962740nteger @ I4 )
% 9.17/5.42 => ( ( groups8878813951405302554er_rat
% 9.17/5.42 @ ^ [I3: code_integer] : ( plus_plus_rat @ ( G @ I3 ) @ ( H3 @ I3 ) )
% 9.17/5.42 @ I4 )
% 9.17/5.42 = ( plus_plus_rat @ ( groups8878813951405302554er_rat @ G @ I4 ) @ ( groups8878813951405302554er_rat @ H3 @ I4 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6301_sum_Odistrib__triv_H,axiom,
% 9.17/5.42 ! [I4: set_nat,G: nat > nat,H3: nat > nat] :
% 9.17/5.42 ( ( finite_finite_nat @ I4 )
% 9.17/5.42 => ( ( groups1986416967739987077at_nat
% 9.17/5.42 @ ^ [I3: nat] : ( plus_plus_nat @ ( G @ I3 ) @ ( H3 @ I3 ) )
% 9.17/5.42 @ I4 )
% 9.17/5.42 = ( plus_plus_nat @ ( groups1986416967739987077at_nat @ G @ I4 ) @ ( groups1986416967739987077at_nat @ H3 @ I4 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6302_sum_Odistrib__triv_H,axiom,
% 9.17/5.42 ! [I4: set_int,G: int > nat,H3: int > nat] :
% 9.17/5.42 ( ( finite_finite_int @ I4 )
% 9.17/5.42 => ( ( groups2985770679641041633nt_nat
% 9.17/5.42 @ ^ [I3: int] : ( plus_plus_nat @ ( G @ I3 ) @ ( H3 @ I3 ) )
% 9.17/5.42 @ I4 )
% 9.17/5.42 = ( plus_plus_nat @ ( groups2985770679641041633nt_nat @ G @ I4 ) @ ( groups2985770679641041633nt_nat @ H3 @ I4 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6303_sum_Odistrib__triv_H,axiom,
% 9.17/5.42 ! [I4: set_Code_integer,G: code_integer > nat,H3: code_integer > nat] :
% 9.17/5.42 ( ( finite6017078050557962740nteger @ I4 )
% 9.17/5.42 => ( ( groups290571974637022482er_nat
% 9.17/5.42 @ ^ [I3: code_integer] : ( plus_plus_nat @ ( G @ I3 ) @ ( H3 @ I3 ) )
% 9.17/5.42 @ I4 )
% 9.17/5.42 = ( plus_plus_nat @ ( groups290571974637022482er_nat @ G @ I4 ) @ ( groups290571974637022482er_nat @ H3 @ I4 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6304_sum_Odistrib__triv_H,axiom,
% 9.17/5.42 ! [I4: set_nat,G: nat > int,H3: nat > int] :
% 9.17/5.42 ( ( finite_finite_nat @ I4 )
% 9.17/5.42 => ( ( groups1983926497230936801at_int
% 9.17/5.42 @ ^ [I3: nat] : ( plus_plus_int @ ( G @ I3 ) @ ( H3 @ I3 ) )
% 9.17/5.42 @ I4 )
% 9.17/5.42 = ( plus_plus_int @ ( groups1983926497230936801at_int @ G @ I4 ) @ ( groups1983926497230936801at_int @ H3 @ I4 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6305_sum_Odistrib__triv_H,axiom,
% 9.17/5.42 ! [I4: set_int,G: int > int,H3: int > int] :
% 9.17/5.42 ( ( finite_finite_int @ I4 )
% 9.17/5.42 => ( ( groups2983280209131991357nt_int
% 9.17/5.42 @ ^ [I3: int] : ( plus_plus_int @ ( G @ I3 ) @ ( H3 @ I3 ) )
% 9.17/5.42 @ I4 )
% 9.17/5.42 = ( plus_plus_int @ ( groups2983280209131991357nt_int @ G @ I4 ) @ ( groups2983280209131991357nt_int @ H3 @ I4 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6306_sum_Odistrib__triv_H,axiom,
% 9.17/5.42 ! [I4: set_Code_integer,G: code_integer > int,H3: code_integer > int] :
% 9.17/5.42 ( ( finite6017078050557962740nteger @ I4 )
% 9.17/5.42 => ( ( groups288081504127972206er_int
% 9.17/5.42 @ ^ [I3: code_integer] : ( plus_plus_int @ ( G @ I3 ) @ ( H3 @ I3 ) )
% 9.17/5.42 @ I4 )
% 9.17/5.42 = ( plus_plus_int @ ( groups288081504127972206er_int @ G @ I4 ) @ ( groups288081504127972206er_int @ H3 @ I4 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6307_sum_Odistrib__triv_H,axiom,
% 9.17/5.42 ! [I4: set_Pr1261947904930325089at_nat,G: product_prod_nat_nat > rat,H3: product_prod_nat_nat > rat] :
% 9.17/5.42 ( ( finite6177210948735845034at_nat @ I4 )
% 9.17/5.42 => ( ( groups3328076802468863542at_rat
% 9.17/5.42 @ ^ [I3: product_prod_nat_nat] : ( plus_plus_rat @ ( G @ I3 ) @ ( H3 @ I3 ) )
% 9.17/5.42 @ I4 )
% 9.17/5.42 = ( plus_plus_rat @ ( groups3328076802468863542at_rat @ G @ I4 ) @ ( groups3328076802468863542at_rat @ H3 @ I4 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6308_le__prod__encode__1,axiom,
% 9.17/5.42 ! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( nat_prod_encode @ ( product_Pair_nat_nat @ A @ B ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6309_le__prod__encode__2,axiom,
% 9.17/5.42 ! [B: nat,A: nat] : ( ord_less_eq_nat @ B @ ( nat_prod_encode @ ( product_Pair_nat_nat @ A @ B ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6310_sum_Odistrib_H,axiom,
% 9.17/5.42 ! [I4: set_o,G: $o > code_integer,H3: $o > code_integer] :
% 9.17/5.42 ( ( finite_finite_o
% 9.17/5.42 @ ( collect_o
% 9.17/5.42 @ ^ [X3: $o] :
% 9.17/5.42 ( ( member_o @ X3 @ I4 )
% 9.17/5.42 & ( ( G @ X3 )
% 9.17/5.42 != zero_z3403309356797280102nteger ) ) ) )
% 9.17/5.42 => ( ( finite_finite_o
% 9.17/5.42 @ ( collect_o
% 9.17/5.42 @ ^ [X3: $o] :
% 9.17/5.42 ( ( member_o @ X3 @ I4 )
% 9.17/5.42 & ( ( H3 @ X3 )
% 9.17/5.42 != zero_z3403309356797280102nteger ) ) ) )
% 9.17/5.42 => ( ( groups1402912129352969042nteger
% 9.17/5.42 @ ^ [I3: $o] : ( plus_p5714425477246183910nteger @ ( G @ I3 ) @ ( H3 @ I3 ) )
% 9.17/5.42 @ I4 )
% 9.17/5.42 = ( plus_p5714425477246183910nteger @ ( groups1402912129352969042nteger @ G @ I4 ) @ ( groups1402912129352969042nteger @ H3 @ I4 ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6311_sum_Odistrib_H,axiom,
% 9.17/5.42 ! [I4: set_nat,G: nat > code_integer,H3: nat > code_integer] :
% 9.17/5.42 ( ( finite_finite_nat
% 9.17/5.42 @ ( collect_nat
% 9.17/5.42 @ ^ [X3: nat] :
% 9.17/5.42 ( ( member_nat @ X3 @ I4 )
% 9.17/5.42 & ( ( G @ X3 )
% 9.17/5.42 != zero_z3403309356797280102nteger ) ) ) )
% 9.17/5.42 => ( ( finite_finite_nat
% 9.17/5.42 @ ( collect_nat
% 9.17/5.42 @ ^ [X3: nat] :
% 9.17/5.42 ( ( member_nat @ X3 @ I4 )
% 9.17/5.42 & ( ( H3 @ X3 )
% 9.17/5.42 != zero_z3403309356797280102nteger ) ) ) )
% 9.17/5.42 => ( ( groups555127423416065298nteger
% 9.17/5.42 @ ^ [I3: nat] : ( plus_p5714425477246183910nteger @ ( G @ I3 ) @ ( H3 @ I3 ) )
% 9.17/5.42 @ I4 )
% 9.17/5.42 = ( plus_p5714425477246183910nteger @ ( groups555127423416065298nteger @ G @ I4 ) @ ( groups555127423416065298nteger @ H3 @ I4 ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6312_sum_Odistrib_H,axiom,
% 9.17/5.42 ! [I4: set_int,G: int > code_integer,H3: int > code_integer] :
% 9.17/5.42 ( ( finite_finite_int
% 9.17/5.42 @ ( collect_int
% 9.17/5.42 @ ^ [X3: int] :
% 9.17/5.42 ( ( member_int @ X3 @ I4 )
% 9.17/5.42 & ( ( G @ X3 )
% 9.17/5.42 != zero_z3403309356797280102nteger ) ) ) )
% 9.17/5.42 => ( ( finite_finite_int
% 9.17/5.42 @ ( collect_int
% 9.17/5.42 @ ^ [X3: int] :
% 9.17/5.42 ( ( member_int @ X3 @ I4 )
% 9.17/5.42 & ( ( H3 @ X3 )
% 9.17/5.42 != zero_z3403309356797280102nteger ) ) ) )
% 9.17/5.42 => ( ( groups926780983652909934nteger
% 9.17/5.42 @ ^ [I3: int] : ( plus_p5714425477246183910nteger @ ( G @ I3 ) @ ( H3 @ I3 ) )
% 9.17/5.42 @ I4 )
% 9.17/5.42 = ( plus_p5714425477246183910nteger @ ( groups926780983652909934nteger @ G @ I4 ) @ ( groups926780983652909934nteger @ H3 @ I4 ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6313_sum_Odistrib_H,axiom,
% 9.17/5.42 ! [I4: set_Code_integer,G: code_integer > code_integer,H3: code_integer > code_integer] :
% 9.17/5.42 ( ( finite6017078050557962740nteger
% 9.17/5.42 @ ( collect_Code_integer
% 9.17/5.42 @ ^ [X3: code_integer] :
% 9.17/5.42 ( ( member_Code_integer @ X3 @ I4 )
% 9.17/5.42 & ( ( G @ X3 )
% 9.17/5.42 != zero_z3403309356797280102nteger ) ) ) )
% 9.17/5.42 => ( ( finite6017078050557962740nteger
% 9.17/5.42 @ ( collect_Code_integer
% 9.17/5.42 @ ^ [X3: code_integer] :
% 9.17/5.42 ( ( member_Code_integer @ X3 @ I4 )
% 9.17/5.42 & ( ( H3 @ X3 )
% 9.17/5.42 != zero_z3403309356797280102nteger ) ) ) )
% 9.17/5.42 => ( ( groups910942671188738463nteger
% 9.17/5.42 @ ^ [I3: code_integer] : ( plus_p5714425477246183910nteger @ ( G @ I3 ) @ ( H3 @ I3 ) )
% 9.17/5.42 @ I4 )
% 9.17/5.42 = ( plus_p5714425477246183910nteger @ ( groups910942671188738463nteger @ G @ I4 ) @ ( groups910942671188738463nteger @ H3 @ I4 ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6314_sum_Odistrib_H,axiom,
% 9.17/5.42 ! [I4: set_o,G: $o > rat,H3: $o > rat] :
% 9.17/5.42 ( ( finite_finite_o
% 9.17/5.42 @ ( collect_o
% 9.17/5.42 @ ^ [X3: $o] :
% 9.17/5.42 ( ( member_o @ X3 @ I4 )
% 9.17/5.42 & ( ( G @ X3 )
% 9.17/5.42 != zero_zero_rat ) ) ) )
% 9.17/5.42 => ( ( finite_finite_o
% 9.17/5.42 @ ( collect_o
% 9.17/5.42 @ ^ [X3: $o] :
% 9.17/5.42 ( ( member_o @ X3 @ I4 )
% 9.17/5.42 & ( ( H3 @ X3 )
% 9.17/5.42 != zero_zero_rat ) ) ) )
% 9.17/5.42 => ( ( groups3921277224699582669_o_rat
% 9.17/5.42 @ ^ [I3: $o] : ( plus_plus_rat @ ( G @ I3 ) @ ( H3 @ I3 ) )
% 9.17/5.42 @ I4 )
% 9.17/5.42 = ( plus_plus_rat @ ( groups3921277224699582669_o_rat @ G @ I4 ) @ ( groups3921277224699582669_o_rat @ H3 @ I4 ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6315_sum_Odistrib_H,axiom,
% 9.17/5.42 ! [I4: set_nat,G: nat > rat,H3: nat > rat] :
% 9.17/5.42 ( ( finite_finite_nat
% 9.17/5.42 @ ( collect_nat
% 9.17/5.42 @ ^ [X3: nat] :
% 9.17/5.42 ( ( member_nat @ X3 @ I4 )
% 9.17/5.42 & ( ( G @ X3 )
% 9.17/5.42 != zero_zero_rat ) ) ) )
% 9.17/5.42 => ( ( finite_finite_nat
% 9.17/5.42 @ ( collect_nat
% 9.17/5.42 @ ^ [X3: nat] :
% 9.17/5.42 ( ( member_nat @ X3 @ I4 )
% 9.17/5.42 & ( ( H3 @ X3 )
% 9.17/5.42 != zero_zero_rat ) ) ) )
% 9.17/5.42 => ( ( groups1351286907653491341at_rat
% 9.17/5.42 @ ^ [I3: nat] : ( plus_plus_rat @ ( G @ I3 ) @ ( H3 @ I3 ) )
% 9.17/5.42 @ I4 )
% 9.17/5.42 = ( plus_plus_rat @ ( groups1351286907653491341at_rat @ G @ I4 ) @ ( groups1351286907653491341at_rat @ H3 @ I4 ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6316_sum_Odistrib_H,axiom,
% 9.17/5.42 ! [I4: set_int,G: int > rat,H3: int > rat] :
% 9.17/5.42 ( ( finite_finite_int
% 9.17/5.42 @ ( collect_int
% 9.17/5.42 @ ^ [X3: int] :
% 9.17/5.42 ( ( member_int @ X3 @ I4 )
% 9.17/5.42 & ( ( G @ X3 )
% 9.17/5.42 != zero_zero_rat ) ) ) )
% 9.17/5.42 => ( ( finite_finite_int
% 9.17/5.42 @ ( collect_int
% 9.17/5.42 @ ^ [X3: int] :
% 9.17/5.42 ( ( member_int @ X3 @ I4 )
% 9.17/5.42 & ( ( H3 @ X3 )
% 9.17/5.42 != zero_zero_rat ) ) ) )
% 9.17/5.42 => ( ( groups2350640619554545897nt_rat
% 9.17/5.42 @ ^ [I3: int] : ( plus_plus_rat @ ( G @ I3 ) @ ( H3 @ I3 ) )
% 9.17/5.42 @ I4 )
% 9.17/5.42 = ( plus_plus_rat @ ( groups2350640619554545897nt_rat @ G @ I4 ) @ ( groups2350640619554545897nt_rat @ H3 @ I4 ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6317_sum_Odistrib_H,axiom,
% 9.17/5.42 ! [I4: set_Code_integer,G: code_integer > rat,H3: code_integer > rat] :
% 9.17/5.42 ( ( finite6017078050557962740nteger
% 9.17/5.42 @ ( collect_Code_integer
% 9.17/5.42 @ ^ [X3: code_integer] :
% 9.17/5.42 ( ( member_Code_integer @ X3 @ I4 )
% 9.17/5.42 & ( ( G @ X3 )
% 9.17/5.42 != zero_zero_rat ) ) ) )
% 9.17/5.42 => ( ( finite6017078050557962740nteger
% 9.17/5.42 @ ( collect_Code_integer
% 9.17/5.42 @ ^ [X3: code_integer] :
% 9.17/5.42 ( ( member_Code_integer @ X3 @ I4 )
% 9.17/5.42 & ( ( H3 @ X3 )
% 9.17/5.42 != zero_zero_rat ) ) ) )
% 9.17/5.42 => ( ( groups8878813951405302554er_rat
% 9.17/5.42 @ ^ [I3: code_integer] : ( plus_plus_rat @ ( G @ I3 ) @ ( H3 @ I3 ) )
% 9.17/5.42 @ I4 )
% 9.17/5.42 = ( plus_plus_rat @ ( groups8878813951405302554er_rat @ G @ I4 ) @ ( groups8878813951405302554er_rat @ H3 @ I4 ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6318_sum_Odistrib_H,axiom,
% 9.17/5.42 ! [I4: set_o,G: $o > nat,H3: $o > nat] :
% 9.17/5.42 ( ( finite_finite_o
% 9.17/5.42 @ ( collect_o
% 9.17/5.42 @ ^ [X3: $o] :
% 9.17/5.42 ( ( member_o @ X3 @ I4 )
% 9.17/5.42 & ( ( G @ X3 )
% 9.17/5.42 != zero_zero_nat ) ) ) )
% 9.17/5.42 => ( ( finite_finite_o
% 9.17/5.42 @ ( collect_o
% 9.17/5.42 @ ^ [X3: $o] :
% 9.17/5.42 ( ( member_o @ X3 @ I4 )
% 9.17/5.42 & ( ( H3 @ X3 )
% 9.17/5.42 != zero_zero_nat ) ) ) )
% 9.17/5.42 => ( ( groups4556407284786078405_o_nat
% 9.17/5.42 @ ^ [I3: $o] : ( plus_plus_nat @ ( G @ I3 ) @ ( H3 @ I3 ) )
% 9.17/5.42 @ I4 )
% 9.17/5.42 = ( plus_plus_nat @ ( groups4556407284786078405_o_nat @ G @ I4 ) @ ( groups4556407284786078405_o_nat @ H3 @ I4 ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6319_sum_Odistrib_H,axiom,
% 9.17/5.42 ! [I4: set_nat,G: nat > nat,H3: nat > nat] :
% 9.17/5.42 ( ( finite_finite_nat
% 9.17/5.42 @ ( collect_nat
% 9.17/5.42 @ ^ [X3: nat] :
% 9.17/5.42 ( ( member_nat @ X3 @ I4 )
% 9.17/5.42 & ( ( G @ X3 )
% 9.17/5.42 != zero_zero_nat ) ) ) )
% 9.17/5.42 => ( ( finite_finite_nat
% 9.17/5.42 @ ( collect_nat
% 9.17/5.42 @ ^ [X3: nat] :
% 9.17/5.42 ( ( member_nat @ X3 @ I4 )
% 9.17/5.42 & ( ( H3 @ X3 )
% 9.17/5.42 != zero_zero_nat ) ) ) )
% 9.17/5.42 => ( ( groups1986416967739987077at_nat
% 9.17/5.42 @ ^ [I3: nat] : ( plus_plus_nat @ ( G @ I3 ) @ ( H3 @ I3 ) )
% 9.17/5.42 @ I4 )
% 9.17/5.42 = ( plus_plus_nat @ ( groups1986416967739987077at_nat @ G @ I4 ) @ ( groups1986416967739987077at_nat @ H3 @ I4 ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6320_prod__encode__def,axiom,
% 9.17/5.42 ( nat_prod_encode
% 9.17/5.42 = ( produc6842872674320459806at_nat
% 9.17/5.42 @ ^ [M: nat,N4: nat] : ( plus_plus_nat @ ( nat_triangle @ ( plus_plus_nat @ M @ N4 ) ) @ M ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6321_max__ext_Ocases,axiom,
% 9.17/5.42 ! [A1: set_se7855581050983116737at_nat,A23: set_se7855581050983116737at_nat,R4: set_Pr4329608150637261639at_nat] :
% 9.17/5.42 ( ( member4300370950623927696at_nat @ ( produc7462898802507495127at_nat @ A1 @ A23 ) @ ( max_ex4535816423174879388at_nat @ R4 ) )
% 9.17/5.42 => ~ ( ( finite9047747110432174090at_nat @ A1 )
% 9.17/5.42 => ( ( finite9047747110432174090at_nat @ A23 )
% 9.17/5.42 => ( ( A23 != bot_bo3083307316010499117at_nat )
% 9.17/5.42 => ~ ! [X8: set_Pr1261947904930325089at_nat] :
% 9.17/5.42 ( ( member2643936169264416010at_nat @ X8 @ A1 )
% 9.17/5.42 => ? [Xa3: set_Pr1261947904930325089at_nat] :
% 9.17/5.42 ( ( member2643936169264416010at_nat @ Xa3 @ A23 )
% 9.17/5.42 & ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X8 @ Xa3 ) @ R4 ) ) ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6322_max__ext_Ocases,axiom,
% 9.17/5.42 ! [A1: set_Code_integer,A23: set_Code_integer,R4: set_Pr4811707699266497531nteger] :
% 9.17/5.42 ( ( member4307123515891402160nteger @ ( produc7443773368509356479nteger @ A1 @ A23 ) @ ( max_ext_Code_integer @ R4 ) )
% 9.17/5.42 => ~ ( ( finite6017078050557962740nteger @ A1 )
% 9.17/5.42 => ( ( finite6017078050557962740nteger @ A23 )
% 9.17/5.42 => ( ( A23 != bot_bo3990330152332043303nteger )
% 9.17/5.42 => ~ ! [X8: code_integer] :
% 9.17/5.42 ( ( member_Code_integer @ X8 @ A1 )
% 9.17/5.42 => ? [Xa3: code_integer] :
% 9.17/5.42 ( ( member_Code_integer @ Xa3 @ A23 )
% 9.17/5.42 & ( member157494554546826820nteger @ ( produc1086072967326762835nteger @ X8 @ Xa3 ) @ R4 ) ) ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6323_max__ext_Ocases,axiom,
% 9.17/5.42 ! [A1: set_Pr4329608150637261639at_nat,A23: set_Pr4329608150637261639at_nat,R4: set_Pr5564308138774400199at_nat] :
% 9.17/5.42 ( ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ A1 @ A23 ) @ ( max_ex8833738776070432290at_nat @ R4 ) )
% 9.17/5.42 => ~ ( ( finite4343798906461161616at_nat @ A1 )
% 9.17/5.42 => ( ( finite4343798906461161616at_nat @ A23 )
% 9.17/5.42 => ( ( A23 != bot_bo228742789529271731at_nat )
% 9.17/5.42 => ~ ! [X8: produc3843707927480180839at_nat] :
% 9.17/5.42 ( ( member8757157785044589968at_nat @ X8 @ A1 )
% 9.17/5.42 => ? [Xa3: produc3843707927480180839at_nat] :
% 9.17/5.42 ( ( member8757157785044589968at_nat @ Xa3 @ A23 )
% 9.17/5.42 & ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ X8 @ Xa3 ) @ R4 ) ) ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6324_max__ext_Ocases,axiom,
% 9.17/5.42 ! [A1: set_Pr1261947904930325089at_nat,A23: set_Pr1261947904930325089at_nat,R4: set_Pr8693737435421807431at_nat] :
% 9.17/5.42 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A1 @ A23 ) @ ( max_ex8135407076693332796at_nat @ R4 ) )
% 9.17/5.42 => ~ ( ( finite6177210948735845034at_nat @ A1 )
% 9.17/5.42 => ( ( finite6177210948735845034at_nat @ A23 )
% 9.17/5.42 => ( ( A23 != bot_bo2099793752762293965at_nat )
% 9.17/5.42 => ~ ! [X8: product_prod_nat_nat] :
% 9.17/5.42 ( ( member8440522571783428010at_nat @ X8 @ A1 )
% 9.17/5.42 => ? [Xa3: product_prod_nat_nat] :
% 9.17/5.42 ( ( member8440522571783428010at_nat @ Xa3 @ A23 )
% 9.17/5.42 & ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X8 @ Xa3 ) @ R4 ) ) ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6325_max__ext_Ocases,axiom,
% 9.17/5.42 ! [A1: set_o,A23: set_o,R4: set_Product_prod_o_o] :
% 9.17/5.42 ( ( member9116954335612470352_set_o @ ( produc5838405689764958487_set_o @ A1 @ A23 ) @ ( max_ext_o @ R4 ) )
% 9.17/5.42 => ~ ( ( finite_finite_o @ A1 )
% 9.17/5.42 => ( ( finite_finite_o @ A23 )
% 9.17/5.42 => ( ( A23 != bot_bot_set_o )
% 9.17/5.42 => ~ ! [X8: $o] :
% 9.17/5.42 ( ( member_o @ X8 @ A1 )
% 9.17/5.42 => ? [Xa3: $o] :
% 9.17/5.42 ( ( member_o @ Xa3 @ A23 )
% 9.17/5.42 & ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ X8 @ Xa3 ) @ R4 ) ) ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6326_max__ext_Ocases,axiom,
% 9.17/5.42 ! [A1: set_nat,A23: set_nat,R4: set_Pr1261947904930325089at_nat] :
% 9.17/5.42 ( ( member8277197624267554838et_nat @ ( produc4532415448927165861et_nat @ A1 @ A23 ) @ ( max_ext_nat @ R4 ) )
% 9.17/5.42 => ~ ( ( finite_finite_nat @ A1 )
% 9.17/5.42 => ( ( finite_finite_nat @ A23 )
% 9.17/5.42 => ( ( A23 != bot_bot_set_nat )
% 9.17/5.42 => ~ ! [X8: nat] :
% 9.17/5.42 ( ( member_nat @ X8 @ A1 )
% 9.17/5.42 => ? [Xa3: nat] :
% 9.17/5.42 ( ( member_nat @ Xa3 @ A23 )
% 9.17/5.42 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X8 @ Xa3 ) @ R4 ) ) ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6327_max__ext_Ocases,axiom,
% 9.17/5.42 ! [A1: set_int,A23: set_int,R4: set_Pr958786334691620121nt_int] :
% 9.17/5.42 ( ( member2572552093476627150et_int @ ( produc6363374080413544029et_int @ A1 @ A23 ) @ ( max_ext_int @ R4 ) )
% 9.17/5.42 => ~ ( ( finite_finite_int @ A1 )
% 9.17/5.42 => ( ( finite_finite_int @ A23 )
% 9.17/5.42 => ( ( A23 != bot_bot_set_int )
% 9.17/5.42 => ~ ! [X8: int] :
% 9.17/5.42 ( ( member_int @ X8 @ A1 )
% 9.17/5.42 => ? [Xa3: int] :
% 9.17/5.42 ( ( member_int @ Xa3 @ A23 )
% 9.17/5.42 & ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X8 @ Xa3 ) @ R4 ) ) ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6328_max__ext_Osimps,axiom,
% 9.17/5.42 ! [A1: set_se7855581050983116737at_nat,A23: set_se7855581050983116737at_nat,R4: set_Pr4329608150637261639at_nat] :
% 9.17/5.42 ( ( member4300370950623927696at_nat @ ( produc7462898802507495127at_nat @ A1 @ A23 ) @ ( max_ex4535816423174879388at_nat @ R4 ) )
% 9.17/5.42 = ( ( finite9047747110432174090at_nat @ A1 )
% 9.17/5.42 & ( finite9047747110432174090at_nat @ A23 )
% 9.17/5.42 & ( A23 != bot_bo3083307316010499117at_nat )
% 9.17/5.42 & ! [X3: set_Pr1261947904930325089at_nat] :
% 9.17/5.42 ( ( member2643936169264416010at_nat @ X3 @ A1 )
% 9.17/5.42 => ? [Y3: set_Pr1261947904930325089at_nat] :
% 9.17/5.42 ( ( member2643936169264416010at_nat @ Y3 @ A23 )
% 9.17/5.42 & ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ Y3 ) @ R4 ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6329_max__ext_Osimps,axiom,
% 9.17/5.42 ! [A1: set_Code_integer,A23: set_Code_integer,R4: set_Pr4811707699266497531nteger] :
% 9.17/5.42 ( ( member4307123515891402160nteger @ ( produc7443773368509356479nteger @ A1 @ A23 ) @ ( max_ext_Code_integer @ R4 ) )
% 9.17/5.42 = ( ( finite6017078050557962740nteger @ A1 )
% 9.17/5.42 & ( finite6017078050557962740nteger @ A23 )
% 9.17/5.42 & ( A23 != bot_bo3990330152332043303nteger )
% 9.17/5.42 & ! [X3: code_integer] :
% 9.17/5.42 ( ( member_Code_integer @ X3 @ A1 )
% 9.17/5.42 => ? [Y3: code_integer] :
% 9.17/5.42 ( ( member_Code_integer @ Y3 @ A23 )
% 9.17/5.42 & ( member157494554546826820nteger @ ( produc1086072967326762835nteger @ X3 @ Y3 ) @ R4 ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6330_max__ext_Osimps,axiom,
% 9.17/5.42 ! [A1: set_Pr4329608150637261639at_nat,A23: set_Pr4329608150637261639at_nat,R4: set_Pr5564308138774400199at_nat] :
% 9.17/5.42 ( ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ A1 @ A23 ) @ ( max_ex8833738776070432290at_nat @ R4 ) )
% 9.17/5.42 = ( ( finite4343798906461161616at_nat @ A1 )
% 9.17/5.42 & ( finite4343798906461161616at_nat @ A23 )
% 9.17/5.42 & ( A23 != bot_bo228742789529271731at_nat )
% 9.17/5.42 & ! [X3: produc3843707927480180839at_nat] :
% 9.17/5.42 ( ( member8757157785044589968at_nat @ X3 @ A1 )
% 9.17/5.42 => ? [Y3: produc3843707927480180839at_nat] :
% 9.17/5.42 ( ( member8757157785044589968at_nat @ Y3 @ A23 )
% 9.17/5.42 & ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ X3 @ Y3 ) @ R4 ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6331_max__ext_Osimps,axiom,
% 9.17/5.42 ! [A1: set_Pr1261947904930325089at_nat,A23: set_Pr1261947904930325089at_nat,R4: set_Pr8693737435421807431at_nat] :
% 9.17/5.42 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A1 @ A23 ) @ ( max_ex8135407076693332796at_nat @ R4 ) )
% 9.17/5.42 = ( ( finite6177210948735845034at_nat @ A1 )
% 9.17/5.42 & ( finite6177210948735845034at_nat @ A23 )
% 9.17/5.42 & ( A23 != bot_bo2099793752762293965at_nat )
% 9.17/5.42 & ! [X3: product_prod_nat_nat] :
% 9.17/5.42 ( ( member8440522571783428010at_nat @ X3 @ A1 )
% 9.17/5.42 => ? [Y3: product_prod_nat_nat] :
% 9.17/5.42 ( ( member8440522571783428010at_nat @ Y3 @ A23 )
% 9.17/5.42 & ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X3 @ Y3 ) @ R4 ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6332_max__ext_Osimps,axiom,
% 9.17/5.42 ! [A1: set_o,A23: set_o,R4: set_Product_prod_o_o] :
% 9.17/5.42 ( ( member9116954335612470352_set_o @ ( produc5838405689764958487_set_o @ A1 @ A23 ) @ ( max_ext_o @ R4 ) )
% 9.17/5.42 = ( ( finite_finite_o @ A1 )
% 9.17/5.42 & ( finite_finite_o @ A23 )
% 9.17/5.42 & ( A23 != bot_bot_set_o )
% 9.17/5.42 & ! [X3: $o] :
% 9.17/5.42 ( ( member_o @ X3 @ A1 )
% 9.17/5.42 => ? [Y3: $o] :
% 9.17/5.42 ( ( member_o @ Y3 @ A23 )
% 9.17/5.42 & ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ X3 @ Y3 ) @ R4 ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6333_max__ext_Osimps,axiom,
% 9.17/5.42 ! [A1: set_nat,A23: set_nat,R4: set_Pr1261947904930325089at_nat] :
% 9.17/5.42 ( ( member8277197624267554838et_nat @ ( produc4532415448927165861et_nat @ A1 @ A23 ) @ ( max_ext_nat @ R4 ) )
% 9.17/5.42 = ( ( finite_finite_nat @ A1 )
% 9.17/5.42 & ( finite_finite_nat @ A23 )
% 9.17/5.42 & ( A23 != bot_bot_set_nat )
% 9.17/5.42 & ! [X3: nat] :
% 9.17/5.42 ( ( member_nat @ X3 @ A1 )
% 9.17/5.42 => ? [Y3: nat] :
% 9.17/5.42 ( ( member_nat @ Y3 @ A23 )
% 9.17/5.42 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y3 ) @ R4 ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6334_max__ext_Osimps,axiom,
% 9.17/5.42 ! [A1: set_int,A23: set_int,R4: set_Pr958786334691620121nt_int] :
% 9.17/5.42 ( ( member2572552093476627150et_int @ ( produc6363374080413544029et_int @ A1 @ A23 ) @ ( max_ext_int @ R4 ) )
% 9.17/5.42 = ( ( finite_finite_int @ A1 )
% 9.17/5.42 & ( finite_finite_int @ A23 )
% 9.17/5.42 & ( A23 != bot_bot_set_int )
% 9.17/5.42 & ! [X3: int] :
% 9.17/5.42 ( ( member_int @ X3 @ A1 )
% 9.17/5.42 => ? [Y3: int] :
% 9.17/5.42 ( ( member_int @ Y3 @ A23 )
% 9.17/5.42 & ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X3 @ Y3 ) @ R4 ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6335_max__extp__eq,axiom,
% 9.17/5.42 ( max_ex4864111882549613972at_nat
% 9.17/5.42 = ( ^ [R3: product_prod_nat_nat > product_prod_nat_nat > $o,X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ Y3 ) @ ( max_ex8135407076693332796at_nat @ ( collec7088162979684241874at_nat @ ( produc6590410687421337004_nat_o @ R3 ) ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6336_max__extp__max__ext__eq,axiom,
% 9.17/5.42 ! [R4: set_Pr4329608150637261639at_nat] :
% 9.17/5.42 ( ( max_ex4845989503969680116at_nat
% 9.17/5.42 @ ^ [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ Y3 ) @ R4 ) )
% 9.17/5.42 = ( ^ [X3: set_se7855581050983116737at_nat,Y3: set_se7855581050983116737at_nat] : ( member4300370950623927696at_nat @ ( produc7462898802507495127at_nat @ X3 @ Y3 ) @ ( max_ex4535816423174879388at_nat @ R4 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6337_max__extp__max__ext__eq,axiom,
% 9.17/5.42 ! [R4: set_Pr1261947904930325089at_nat] :
% 9.17/5.42 ( ( max_extp_nat
% 9.17/5.42 @ ^ [X3: nat,Y3: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y3 ) @ R4 ) )
% 9.17/5.42 = ( ^ [X3: set_nat,Y3: set_nat] : ( member8277197624267554838et_nat @ ( produc4532415448927165861et_nat @ X3 @ Y3 ) @ ( max_ext_nat @ R4 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6338_max__extp__max__ext__eq,axiom,
% 9.17/5.42 ! [R4: set_Pr8693737435421807431at_nat] :
% 9.17/5.42 ( ( max_ex4864111882549613972at_nat
% 9.17/5.42 @ ^ [X3: product_prod_nat_nat,Y3: product_prod_nat_nat] : ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X3 @ Y3 ) @ R4 ) )
% 9.17/5.42 = ( ^ [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ Y3 ) @ ( max_ex8135407076693332796at_nat @ R4 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6339_one__div__numeral,axiom,
% 9.17/5.42 ! [N2: num] :
% 9.17/5.42 ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ N2 ) )
% 9.17/5.42 = ( produc8508995932063986495nteger @ ( unique3479559517661332726nteger @ one @ N2 ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6340_one__div__numeral,axiom,
% 9.17/5.42 ! [N2: num] :
% 9.17/5.42 ( ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ N2 ) )
% 9.17/5.42 = ( product_fst_int_int @ ( unique5052692396658037445od_int @ one @ N2 ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6341_one__div__numeral,axiom,
% 9.17/5.42 ! [N2: num] :
% 9.17/5.42 ( ( divide_divide_nat @ one_one_nat @ ( numeral_numeral_nat @ N2 ) )
% 9.17/5.42 = ( product_fst_nat_nat @ ( unique5055182867167087721od_nat @ one @ N2 ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6342_sqr_Osimps_I3_J,axiom,
% 9.17/5.42 ! [N2: num] :
% 9.17/5.42 ( ( sqr @ ( bit1 @ N2 ) )
% 9.17/5.42 = ( bit1 @ ( bit0 @ ( plus_plus_num @ ( sqr @ N2 ) @ N2 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6343_one__mod__numeral,axiom,
% 9.17/5.42 ! [N2: num] :
% 9.17/5.42 ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ N2 ) )
% 9.17/5.42 = ( produc6174133586879617921nteger @ ( unique3479559517661332726nteger @ one @ N2 ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6344_one__mod__numeral,axiom,
% 9.17/5.42 ! [N2: num] :
% 9.17/5.42 ( ( modulo_modulo_int @ one_one_int @ ( numeral_numeral_int @ N2 ) )
% 9.17/5.42 = ( product_snd_int_int @ ( unique5052692396658037445od_int @ one @ N2 ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6345_one__mod__numeral,axiom,
% 9.17/5.42 ! [N2: num] :
% 9.17/5.42 ( ( modulo_modulo_nat @ one_one_nat @ ( numeral_numeral_nat @ N2 ) )
% 9.17/5.42 = ( product_snd_nat_nat @ ( unique5055182867167087721od_nat @ one @ N2 ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6346_card__UNION,axiom,
% 9.17/5.42 ! [A2: set_set_Product_unit] :
% 9.17/5.42 ( ( finite1772178364199683094t_unit @ A2 )
% 9.17/5.42 => ( ! [X4: set_Product_unit] :
% 9.17/5.42 ( ( member5877623283571906838t_unit @ X4 @ A2 )
% 9.17/5.42 => ( finite4290736615968046902t_unit @ X4 ) )
% 9.17/5.42 => ( ( finite410649719033368117t_unit @ ( comple3349607820504768346t_unit @ A2 ) )
% 9.17/5.42 = ( nat2
% 9.17/5.42 @ ( groups9212676010950626495it_int
% 9.17/5.42 @ ^ [I5: set_set_Product_unit] : ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( plus_plus_nat @ ( finite22775419188893461t_unit @ I5 ) @ one_one_nat ) ) @ ( semiri1314217659103216013at_int @ ( finite410649719033368117t_unit @ ( comple7216939928495492468t_unit @ I5 ) ) ) )
% 9.17/5.42 @ ( collec4600646233855244344t_unit
% 9.17/5.42 @ ^ [I5: set_set_Product_unit] :
% 9.17/5.42 ( ( ord_le3674001228145610605t_unit @ I5 @ A2 )
% 9.17/5.42 & ( I5 != bot_bo6284674557190688313t_unit ) ) ) ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6347_card__UNION,axiom,
% 9.17/5.42 ! [A2: set_set_list_nat] :
% 9.17/5.42 ( ( finite7047420756378620717st_nat @ A2 )
% 9.17/5.42 => ( ! [X4: set_list_nat] :
% 9.17/5.42 ( ( member_set_list_nat @ X4 @ A2 )
% 9.17/5.42 => ( finite8100373058378681591st_nat @ X4 ) )
% 9.17/5.42 => ( ( finite_card_list_nat @ ( comple8404747032580312297st_nat @ A2 ) )
% 9.17/5.42 = ( nat2
% 9.17/5.42 @ ( groups7004213669654646580at_int
% 9.17/5.42 @ ^ [I5: set_set_list_nat] : ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( plus_plus_nat @ ( finite2364142230527598318st_nat @ I5 ) @ one_one_nat ) ) @ ( semiri1314217659103216013at_int @ ( finite_card_list_nat @ ( comple184543376406953807st_nat @ I5 ) ) ) )
% 9.17/5.42 @ ( collec4691811733418234273st_nat
% 9.17/5.42 @ ^ [I5: set_set_list_nat] :
% 9.17/5.42 ( ( ord_le1068707526560357548st_nat @ I5 @ A2 )
% 9.17/5.42 & ( I5 != bot_bo3886227569956363488st_nat ) ) ) ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6348_card__UNION,axiom,
% 9.17/5.42 ! [A2: set_set_int] :
% 9.17/5.42 ( ( finite6197958912794628473et_int @ A2 )
% 9.17/5.42 => ( ! [X4: set_int] :
% 9.17/5.42 ( ( member_set_int @ X4 @ A2 )
% 9.17/5.42 => ( finite_finite_int @ X4 ) )
% 9.17/5.42 => ( ( finite_card_int @ ( comple3221217463730067765et_int @ A2 ) )
% 9.17/5.42 = ( nat2
% 9.17/5.42 @ ( groups1080061135233207040nt_int
% 9.17/5.42 @ ^ [I5: set_set_int] : ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( plus_plus_nat @ ( finite_card_set_int @ I5 ) @ one_one_nat ) ) @ ( semiri1314217659103216013at_int @ ( finite_card_int @ ( comple3628384868704368283et_int @ I5 ) ) ) )
% 9.17/5.42 @ ( collect_set_set_int
% 9.17/5.42 @ ^ [I5: set_set_int] :
% 9.17/5.42 ( ( ord_le4403425263959731960et_int @ I5 @ A2 )
% 9.17/5.42 & ( I5 != bot_bot_set_set_int ) ) ) ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6349_card__UNION,axiom,
% 9.17/5.42 ! [A2: set_set_Code_integer] :
% 9.17/5.42 ( ( finite6931041176100689706nteger @ A2 )
% 9.17/5.42 => ( ! [X4: set_Code_integer] :
% 9.17/5.42 ( ( member1834298987299537450nteger @ X4 @ A2 )
% 9.17/5.42 => ( finite6017078050557962740nteger @ X4 ) )
% 9.17/5.42 => ( ( finite4902975817058060853nteger @ ( comple739944243200306918nteger @ A2 ) )
% 9.17/5.42 = ( nat2
% 9.17/5.42 @ ( groups2416162284031854641er_int
% 9.17/5.42 @ ^ [I5: set_set_Code_integer] : ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( plus_plus_nat @ ( finite1340570857867686763nteger @ I5 ) @ one_one_nat ) ) @ ( semiri1314217659103216013at_int @ ( finite4902975817058060853nteger @ ( comple1256288197631046732nteger @ I5 ) ) ) )
% 9.17/5.42 @ ( collec9208119312383884190nteger
% 9.17/5.42 @ ^ [I5: set_set_Code_integer] :
% 9.17/5.42 ( ( ord_le1914454125413604393nteger @ I5 @ A2 )
% 9.17/5.42 & ( I5 != bot_bo9204850693367297629nteger ) ) ) ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6350_card__UNION,axiom,
% 9.17/5.42 ! [A2: set_se7855581050983116737at_nat] :
% 9.17/5.42 ( ( finite9047747110432174090at_nat @ A2 )
% 9.17/5.42 => ( ! [X4: set_Pr1261947904930325089at_nat] :
% 9.17/5.42 ( ( member2643936169264416010at_nat @ X4 @ A2 )
% 9.17/5.42 => ( finite6177210948735845034at_nat @ X4 ) )
% 9.17/5.42 => ( ( finite711546835091564841at_nat @ ( comple5685304695842803022at_nat @ A2 ) )
% 9.17/5.42 = ( nat2
% 9.17/5.42 @ ( groups1759609815103008563at_int
% 9.17/5.42 @ ^ [I5: set_se7855581050983116737at_nat] : ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( plus_plus_nat @ ( finite4356350796350151305at_nat @ I5 ) @ one_one_nat ) ) @ ( semiri1314217659103216013at_int @ ( finite711546835091564841at_nat @ ( comple1930127330929219688at_nat @ I5 ) ) ) )
% 9.17/5.42 @ ( collec6698286964019821996at_nat
% 9.17/5.42 @ ^ [I5: set_se7855581050983116737at_nat] :
% 9.17/5.42 ( ( ord_le2077887516847798113at_nat @ I5 @ A2 )
% 9.17/5.42 & ( I5 != bot_bo3083307316010499117at_nat ) ) ) ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6351_card__UNION,axiom,
% 9.17/5.42 ! [A2: set_set_nat] :
% 9.17/5.42 ( ( finite1152437895449049373et_nat @ A2 )
% 9.17/5.42 => ( ! [X4: set_nat] :
% 9.17/5.42 ( ( member_set_nat @ X4 @ A2 )
% 9.17/5.42 => ( finite_finite_nat @ X4 ) )
% 9.17/5.42 => ( ( finite_card_nat @ ( comple7399068483239264473et_nat @ A2 ) )
% 9.17/5.42 = ( nat2
% 9.17/5.42 @ ( groups7084729577923612836at_int
% 9.17/5.42 @ ^ [I5: set_set_nat] : ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( plus_plus_nat @ ( finite_card_set_nat @ I5 ) @ one_one_nat ) ) @ ( semiri1314217659103216013at_int @ ( finite_card_nat @ ( comple7806235888213564991et_nat @ I5 ) ) ) )
% 9.17/5.42 @ ( collect_set_set_nat
% 9.17/5.42 @ ^ [I5: set_set_nat] :
% 9.17/5.42 ( ( ord_le6893508408891458716et_nat @ I5 @ A2 )
% 9.17/5.42 & ( I5 != bot_bot_set_set_nat ) ) ) ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6352_Sup__atMost,axiom,
% 9.17/5.42 ! [Y: set_nat] :
% 9.17/5.42 ( ( comple7399068483239264473et_nat @ ( set_or4236626031148496127et_nat @ Y ) )
% 9.17/5.42 = Y ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6353_Sup__atMost,axiom,
% 9.17/5.42 ! [Y: product_unit] :
% 9.17/5.42 ( ( comple4687483117567863418t_unit @ ( set_or8621721900777396692t_unit @ Y ) )
% 9.17/5.42 = Y ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6354_fst__apsnd,axiom,
% 9.17/5.42 ! [F: code_integer > code_integer,X: produc8923325533196201883nteger] :
% 9.17/5.42 ( ( produc8508995932063986495nteger @ ( produc6499014454317279255nteger @ F @ X ) )
% 9.17/5.42 = ( produc8508995932063986495nteger @ X ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6355_fst__apsnd,axiom,
% 9.17/5.42 ! [F: int > int,X: product_prod_int_int] :
% 9.17/5.42 ( ( product_fst_int_int @ ( produc4463282112584876420nt_int @ F @ X ) )
% 9.17/5.42 = ( product_fst_int_int @ X ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6356_fst__comp__apsnd,axiom,
% 9.17/5.42 ! [F: code_integer > code_integer] :
% 9.17/5.42 ( ( comp_P3428181540658402820nteger @ produc8508995932063986495nteger @ ( produc6499014454317279255nteger @ F ) )
% 9.17/5.42 = produc8508995932063986495nteger ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6357_fst__comp__apsnd,axiom,
% 9.17/5.42 ! [F: int > int] :
% 9.17/5.42 ( ( comp_P5356232565778667509nt_int @ product_fst_int_int @ ( produc4463282112584876420nt_int @ F ) )
% 9.17/5.42 = product_fst_int_int ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6358_apsnd__eq__conv,axiom,
% 9.17/5.42 ! [F: code_integer > code_integer,X: produc8923325533196201883nteger,G: code_integer > code_integer] :
% 9.17/5.42 ( ( ( produc6499014454317279255nteger @ F @ X )
% 9.17/5.42 = ( produc6499014454317279255nteger @ G @ X ) )
% 9.17/5.42 = ( ( F @ ( produc6174133586879617921nteger @ X ) )
% 9.17/5.42 = ( G @ ( produc6174133586879617921nteger @ X ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6359_snd__apsnd,axiom,
% 9.17/5.42 ! [F: code_integer > code_integer,X: produc8923325533196201883nteger] :
% 9.17/5.42 ( ( produc6174133586879617921nteger @ ( produc6499014454317279255nteger @ F @ X ) )
% 9.17/5.42 = ( F @ ( produc6174133586879617921nteger @ X ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6360_snd__apsnd,axiom,
% 9.17/5.42 ! [F: int > int,X: product_prod_int_int] :
% 9.17/5.42 ( ( product_snd_int_int @ ( produc4463282112584876420nt_int @ F @ X ) )
% 9.17/5.42 = ( F @ ( product_snd_int_int @ X ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6361_snd__apsnd,axiom,
% 9.17/5.42 ! [F: produc7822875418678951345atural > produc7822875418678951345atural,X: produc5835291356934675326atural] :
% 9.17/5.42 ( ( produc6591912806276919810atural @ ( produc4464772112783624294atural @ F @ X ) )
% 9.17/5.42 = ( F @ ( produc6591912806276919810atural @ X ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6362_snd__comp__apsnd,axiom,
% 9.17/5.42 ! [F: code_integer > code_integer] :
% 9.17/5.42 ( ( comp_P3428181540658402820nteger @ produc6174133586879617921nteger @ ( produc6499014454317279255nteger @ F ) )
% 9.17/5.42 = ( comp_C1043215000170864188nteger @ F @ produc6174133586879617921nteger ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6363_snd__comp__apsnd,axiom,
% 9.17/5.42 ! [F: int > int] :
% 9.17/5.42 ( ( comp_P5356232565778667509nt_int @ product_snd_int_int @ ( produc4463282112584876420nt_int @ F ) )
% 9.17/5.42 = ( comp_i4330622015127193916nt_int @ F @ product_snd_int_int ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6364_snd__comp__apsnd,axiom,
% 9.17/5.42 ! [F: produc7822875418678951345atural > produc7822875418678951345atural] :
% 9.17/5.42 ( ( comp_P7610810914149544718atural @ produc6591912806276919810atural @ ( produc4464772112783624294atural @ F ) )
% 9.17/5.42 = ( comp_P3067963646784605345atural @ F @ produc6591912806276919810atural ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6365_fst__divmod__integer,axiom,
% 9.17/5.42 ! [K: code_integer,L: code_integer] :
% 9.17/5.42 ( ( produc8508995932063986495nteger @ ( code_divmod_integer @ K @ L ) )
% 9.17/5.42 = ( divide6298287555418463151nteger @ K @ L ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6366_snd__divmod__integer,axiom,
% 9.17/5.42 ! [K: code_integer,L: code_integer] :
% 9.17/5.42 ( ( produc6174133586879617921nteger @ ( code_divmod_integer @ K @ L ) )
% 9.17/5.42 = ( modulo364778990260209775nteger @ K @ L ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6367_Sup__atLeastAtMost,axiom,
% 9.17/5.42 ! [X: set_nat,Y: set_nat] :
% 9.17/5.42 ( ( ord_less_eq_set_nat @ X @ Y )
% 9.17/5.42 => ( ( comple7399068483239264473et_nat @ ( set_or4548717258645045905et_nat @ X @ Y ) )
% 9.17/5.42 = Y ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6368_Sup__atLeastAtMost,axiom,
% 9.17/5.42 ! [X: product_unit,Y: product_unit] :
% 9.17/5.42 ( ( ord_le3221252021190050221t_unit @ X @ Y )
% 9.17/5.42 => ( ( comple4687483117567863418t_unit @ ( set_or5692540242118139586t_unit @ X @ Y ) )
% 9.17/5.42 = Y ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6369_Inf__atLeastAtMost,axiom,
% 9.17/5.42 ! [X: set_nat,Y: set_nat] :
% 9.17/5.42 ( ( ord_less_eq_set_nat @ X @ Y )
% 9.17/5.42 => ( ( comple7806235888213564991et_nat @ ( set_or4548717258645045905et_nat @ X @ Y ) )
% 9.17/5.42 = X ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6370_Inf__atLeastAtMost,axiom,
% 9.17/5.42 ! [X: product_unit,Y: product_unit] :
% 9.17/5.42 ( ( ord_le3221252021190050221t_unit @ X @ Y )
% 9.17/5.42 => ( ( comple2584293577114468500t_unit @ ( set_or5692540242118139586t_unit @ X @ Y ) )
% 9.17/5.42 = X ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6371_Inf__atLeastLessThan,axiom,
% 9.17/5.42 ! [X: set_nat,Y: set_nat] :
% 9.17/5.42 ( ( ord_less_set_nat @ X @ Y )
% 9.17/5.42 => ( ( comple7806235888213564991et_nat @ ( set_or3540276404033026485et_nat @ X @ Y ) )
% 9.17/5.42 = X ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6372_Inf__atLeastLessThan,axiom,
% 9.17/5.42 ! [X: product_unit,Y: product_unit] :
% 9.17/5.42 ( ( ord_le361264281704409273t_unit @ X @ Y )
% 9.17/5.42 => ( ( comple2584293577114468500t_unit @ ( set_or4663484573592751262t_unit @ X @ Y ) )
% 9.17/5.42 = X ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6373_prod_Ocollapse,axiom,
% 9.17/5.42 ! [Prod: produc1908205239877642774nteger] :
% 9.17/5.42 ( ( produc8603105652947943368nteger @ ( produc7822682618958472924nteger @ Prod ) @ ( produc7856867400915047194nteger @ Prod ) )
% 9.17/5.42 = Prod ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6374_prod_Ocollapse,axiom,
% 9.17/5.42 ! [Prod: produc3925858234332021118et_nat] :
% 9.17/5.42 ( ( produc5001842942810119800et_nat @ ( produc995936583742144908et_nat @ Prod ) @ ( produc4011572625026189258et_nat @ Prod ) )
% 9.17/5.42 = Prod ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6375_prod_Ocollapse,axiom,
% 9.17/5.42 ! [Prod: produc2732055786443039994et_nat] :
% 9.17/5.42 ( ( produc2245416461498447860et_nat @ ( produc180342877477747464et_nat @ Prod ) @ ( produc5374455773327741254et_nat @ Prod ) )
% 9.17/5.42 = Prod ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6376_prod_Ocollapse,axiom,
% 9.17/5.42 ! [Prod: produc2285326912895808259nt_int] :
% 9.17/5.42 ( ( produc5700946648718959541nt_int @ ( produc6816164490631068361nt_int @ Prod ) @ ( produc7328097813583171335nt_int @ Prod ) )
% 9.17/5.42 = Prod ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6377_prod_Ocollapse,axiom,
% 9.17/5.42 ! [Prod: produc7773217078559923341nt_int] :
% 9.17/5.42 ( ( produc4305682042979456191nt_int @ ( produc6230002227079971283nt_int @ Prod ) @ ( produc3162348030201620241nt_int @ Prod ) )
% 9.17/5.42 = Prod ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6378_prod_Ocollapse,axiom,
% 9.17/5.42 ! [Prod: produc8923325533196201883nteger] :
% 9.17/5.42 ( ( produc1086072967326762835nteger @ ( produc8508995932063986495nteger @ Prod ) @ ( produc6174133586879617921nteger @ Prod ) )
% 9.17/5.42 = Prod ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6379_prod_Ocollapse,axiom,
% 9.17/5.42 ! [Prod: product_prod_int_int] :
% 9.17/5.42 ( ( product_Pair_int_int @ ( product_fst_int_int @ Prod ) @ ( product_snd_int_int @ Prod ) )
% 9.17/5.42 = Prod ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6380_prod_Ocollapse,axiom,
% 9.17/5.42 ! [Prod: produc5835291356934675326atural] :
% 9.17/5.42 ( ( produc6639722614265839536atural @ ( produc497848011034438852atural @ Prod ) @ ( produc6591912806276919810atural @ Prod ) )
% 9.17/5.42 = Prod ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6381_Inf__atMost,axiom,
% 9.17/5.42 ! [X: set_Pr4329608150637261639at_nat] :
% 9.17/5.42 ( ( comple6751905152567503566at_nat @ ( set_or4071486571221009422at_nat @ X ) )
% 9.17/5.42 = bot_bo228742789529271731at_nat ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6382_Inf__atMost,axiom,
% 9.17/5.42 ! [X: set_Pr1261947904930325089at_nat] :
% 9.17/5.42 ( ( comple1930127330929219688at_nat @ ( set_or2762583123196137896at_nat @ X ) )
% 9.17/5.42 = bot_bo2099793752762293965at_nat ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6383_Inf__atMost,axiom,
% 9.17/5.42 ! [X: set_o] :
% 9.17/5.42 ( ( comple3063163877087187839_set_o @ ( set_ord_atMost_set_o @ X ) )
% 9.17/5.42 = bot_bot_set_o ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6384_Inf__atMost,axiom,
% 9.17/5.42 ! [X: set_int] :
% 9.17/5.42 ( ( comple3628384868704368283et_int @ ( set_or58775011639299419et_int @ X ) )
% 9.17/5.42 = bot_bot_set_int ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6385_Inf__atMost,axiom,
% 9.17/5.42 ! [X: set_nat] :
% 9.17/5.42 ( ( comple7806235888213564991et_nat @ ( set_or4236626031148496127et_nat @ X ) )
% 9.17/5.42 = bot_bot_set_nat ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6386_Inf__atMost,axiom,
% 9.17/5.42 ! [X: product_unit] :
% 9.17/5.42 ( ( comple2584293577114468500t_unit @ ( set_or8621721900777396692t_unit @ X ) )
% 9.17/5.42 = bot_bot_Product_unit ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6387_img__fst,axiom,
% 9.17/5.42 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,S2: set_Pr4329608150637261639at_nat] :
% 9.17/5.42 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ B ) @ S2 )
% 9.17/5.42 => ( member2643936169264416010at_nat @ A @ ( image_7979982168039674559at_nat @ produc6011863565407846595at_nat @ S2 ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6388_img__fst,axiom,
% 9.17/5.42 ! [A: nat,B: nat,S2: set_Pr1261947904930325089at_nat] :
% 9.17/5.42 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ S2 )
% 9.17/5.42 => ( member_nat @ A @ ( image_2486076414777270412at_nat @ product_fst_nat_nat @ S2 ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6389_img__fst,axiom,
% 9.17/5.42 ! [A: produc6241069584506657477e_term > option6357759511663192854e_term,B: produc8923325533196201883nteger,S2: set_Pr1281608226676607948nteger] :
% 9.17/5.42 ( ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ A @ B ) @ S2 )
% 9.17/5.42 => ( member4242434998011752849e_term @ A @ ( image_4436781500471753239e_term @ produc7822682618958472924nteger @ S2 ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6390_img__fst,axiom,
% 9.17/5.42 ! [A: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat,S2: set_Pr3286484037609594932et_nat] :
% 9.17/5.42 ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ A @ B ) @ S2 )
% 9.17/5.42 => ( member6576561426505652726_nat_o @ A @ ( image_6802380912191114376_nat_o @ produc995936583742144908et_nat @ S2 ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6391_img__fst,axiom,
% 9.17/5.42 ! [A: produc3658429121746597890et_nat > $o,B: produc3925858234332021118et_nat,S2: set_Pr8536935166611901872et_nat] :
% 9.17/5.42 ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ A @ B ) @ S2 )
% 9.17/5.42 => ( member6576561426505652726_nat_o @ A @ ( image_2517677226577294348_nat_o @ produc180342877477747464et_nat @ S2 ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6392_img__fst,axiom,
% 9.17/5.42 ! [A: produc8551481072490612790e_term > option6357759511663192854e_term,B: product_prod_int_int,S2: set_Pr9222295170931077689nt_int] :
% 9.17/5.42 ( ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ A @ B ) @ S2 )
% 9.17/5.42 => ( member3222579708246209666e_term @ A @ ( image_142517975987106933e_term @ produc6816164490631068361nt_int @ S2 ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6393_img__fst,axiom,
% 9.17/5.42 ! [A: int > option6357759511663192854e_term,B: product_prod_int_int,S2: set_Pr1872883991513573699nt_int] :
% 9.17/5.42 ( ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ A @ B ) @ S2 )
% 9.17/5.42 => ( member8845023287901829240e_term @ A @ ( image_4217645046469565813e_term @ produc6230002227079971283nt_int @ S2 ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6394_img__fst,axiom,
% 9.17/5.42 ! [A: code_integer,B: code_integer,S2: set_Pr4811707699266497531nteger] :
% 9.17/5.42 ( ( member157494554546826820nteger @ ( produc1086072967326762835nteger @ A @ B ) @ S2 )
% 9.17/5.42 => ( member_Code_integer @ A @ ( image_6316824473203919795nteger @ produc8508995932063986495nteger @ S2 ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6395_img__fst,axiom,
% 9.17/5.42 ! [A: int,B: int,S2: set_Pr958786334691620121nt_int] :
% 9.17/5.42 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ S2 )
% 9.17/5.42 => ( member_int @ A @ ( image_5042161079198086560nt_int @ product_fst_int_int @ S2 ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6396_img__snd,axiom,
% 9.17/5.42 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,S2: set_Pr4329608150637261639at_nat] :
% 9.17/5.42 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ B ) @ S2 )
% 9.17/5.42 => ( member2643936169264416010at_nat @ B @ ( image_7979982168039674559at_nat @ produc2937545259423399429at_nat @ S2 ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6397_img__snd,axiom,
% 9.17/5.42 ! [A: nat,B: nat,S2: set_Pr1261947904930325089at_nat] :
% 9.17/5.42 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ S2 )
% 9.17/5.42 => ( member_nat @ B @ ( image_2486076414777270412at_nat @ product_snd_nat_nat @ S2 ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6398_img__snd,axiom,
% 9.17/5.42 ! [A: produc6241069584506657477e_term > option6357759511663192854e_term,B: produc8923325533196201883nteger,S2: set_Pr1281608226676607948nteger] :
% 9.17/5.42 ( ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ A @ B ) @ S2 )
% 9.17/5.42 => ( member157494554546826820nteger @ B @ ( image_3141030398089242942nteger @ produc7856867400915047194nteger @ S2 ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6399_img__snd,axiom,
% 9.17/5.42 ! [A: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat,S2: set_Pr3286484037609594932et_nat] :
% 9.17/5.42 ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ A @ B ) @ S2 )
% 9.17/5.42 => ( member6260224972018164377et_nat @ B @ ( image_4390311411407041927et_nat @ produc4011572625026189258et_nat @ S2 ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6400_img__snd,axiom,
% 9.17/5.42 ! [A: produc3658429121746597890et_nat > $o,B: produc3925858234332021118et_nat,S2: set_Pr8536935166611901872et_nat] :
% 9.17/5.42 ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ A @ B ) @ S2 )
% 9.17/5.42 => ( member1996754912294343701et_nat @ B @ ( image_4557310310409863807et_nat @ produc5374455773327741254et_nat @ S2 ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6401_img__snd,axiom,
% 9.17/5.42 ! [A: produc8551481072490612790e_term > option6357759511663192854e_term,B: product_prod_int_int,S2: set_Pr9222295170931077689nt_int] :
% 9.17/5.42 ( ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ A @ B ) @ S2 )
% 9.17/5.42 => ( member5262025264175285858nt_int @ B @ ( image_3915291023682402351nt_int @ produc7328097813583171335nt_int @ S2 ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6402_img__snd,axiom,
% 9.17/5.42 ! [A: int > option6357759511663192854e_term,B: product_prod_int_int,S2: set_Pr1872883991513573699nt_int] :
% 9.17/5.42 ( ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ A @ B ) @ S2 )
% 9.17/5.42 => ( member5262025264175285858nt_int @ B @ ( image_3108077152341812517nt_int @ produc3162348030201620241nt_int @ S2 ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6403_img__snd,axiom,
% 9.17/5.42 ! [A: code_integer,B: code_integer,S2: set_Pr4811707699266497531nteger] :
% 9.17/5.42 ( ( member157494554546826820nteger @ ( produc1086072967326762835nteger @ A @ B ) @ S2 )
% 9.17/5.42 => ( member_Code_integer @ B @ ( image_6316824473203919795nteger @ produc6174133586879617921nteger @ S2 ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6404_img__snd,axiom,
% 9.17/5.42 ! [A: int,B: int,S2: set_Pr958786334691620121nt_int] :
% 9.17/5.42 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ S2 )
% 9.17/5.42 => ( member_int @ B @ ( image_5042161079198086560nt_int @ product_snd_int_int @ S2 ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6405_img__snd,axiom,
% 9.17/5.42 ! [A: code_natural,B: produc7822875418678951345atural,S2: set_Pr2352657477744078772atural] :
% 9.17/5.42 ( ( member2108296798382401941atural @ ( produc6639722614265839536atural @ A @ B ) @ S2 )
% 9.17/5.42 => ( member8280416476884352090atural @ B @ ( image_3837677093542026988atural @ produc6591912806276919810atural @ S2 ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6406_fst__divmod__abs,axiom,
% 9.17/5.42 ! [K: code_integer,L: code_integer] :
% 9.17/5.42 ( ( produc8508995932063986495nteger @ ( code_divmod_abs @ K @ L ) )
% 9.17/5.42 = ( divide6298287555418463151nteger @ ( abs_abs_Code_integer @ K ) @ ( abs_abs_Code_integer @ L ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6407_snd__divmod__abs,axiom,
% 9.17/5.42 ! [K: code_integer,L: code_integer] :
% 9.17/5.42 ( ( produc6174133586879617921nteger @ ( code_divmod_abs @ K @ L ) )
% 9.17/5.42 = ( modulo364778990260209775nteger @ ( abs_abs_Code_integer @ K ) @ ( abs_abs_Code_integer @ L ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6408_Inf__atMostLessThan,axiom,
% 9.17/5.42 ! [X: set_Pr4329608150637261639at_nat] :
% 9.17/5.42 ( ( ord_le2604355607129572851at_nat @ top_to6833984726390702231at_nat @ X )
% 9.17/5.42 => ( ( comple6751905152567503566at_nat @ ( set_or2137699863726836970at_nat @ X ) )
% 9.17/5.42 = bot_bo228742789529271731at_nat ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6409_Inf__atMostLessThan,axiom,
% 9.17/5.42 ! [X: set_Pr1261947904930325089at_nat] :
% 9.17/5.42 ( ( ord_le7866589430770878221at_nat @ top_to4669805908274784177at_nat @ X )
% 9.17/5.42 => ( ( comple1930127330929219688at_nat @ ( set_or5243998310507771012at_nat @ X ) )
% 9.17/5.42 = bot_bo2099793752762293965at_nat ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6410_Inf__atMostLessThan,axiom,
% 9.17/5.42 ! [X: set_o] :
% 9.17/5.42 ( ( ord_less_set_o @ top_top_set_o @ X )
% 9.17/5.42 => ( ( comple3063163877087187839_set_o @ ( set_or3489638696441961371_set_o @ X ) )
% 9.17/5.42 = bot_bot_set_o ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6411_Inf__atMostLessThan,axiom,
% 9.17/5.42 ! [X: set_Product_unit] :
% 9.17/5.42 ( ( ord_le8056459307392131481t_unit @ top_to1996260823553986621t_unit @ X )
% 9.17/5.42 => ( ( comple7216939928495492468t_unit @ ( set_or3324826255835560848t_unit @ X ) )
% 9.17/5.42 = bot_bo3957492148770167129t_unit ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6412_Inf__atMostLessThan,axiom,
% 9.17/5.42 ! [X: set_int] :
% 9.17/5.42 ( ( ord_less_set_int @ top_top_set_int @ X )
% 9.17/5.42 => ( ( comple3628384868704368283et_int @ ( set_or5935648273017318783et_int @ X ) )
% 9.17/5.42 = bot_bot_set_int ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6413_Inf__atMostLessThan,axiom,
% 9.17/5.42 ! [X: set_nat] :
% 9.17/5.42 ( ( ord_less_set_nat @ top_top_set_nat @ X )
% 9.17/5.42 => ( ( comple7806235888213564991et_nat @ ( set_or890127255671739683et_nat @ X ) )
% 9.17/5.42 = bot_bot_set_nat ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6414_Inf__atMostLessThan,axiom,
% 9.17/5.42 ! [X: product_unit] :
% 9.17/5.42 ( ( ord_le361264281704409273t_unit @ top_top_Product_unit @ X )
% 9.17/5.42 => ( ( comple2584293577114468500t_unit @ ( set_or8708608758551125680t_unit @ X ) )
% 9.17/5.42 = bot_bot_Product_unit ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6415_case__prod__beta_H,axiom,
% 9.17/5.42 ( produc6842872674320459806at_nat
% 9.17/5.42 = ( ^ [F2: nat > nat > nat,X3: product_prod_nat_nat] : ( F2 @ ( product_fst_nat_nat @ X3 ) @ ( product_snd_nat_nat @ X3 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6416_case__prod__beta_H,axiom,
% 9.17/5.42 ( produc27273713700761075at_nat
% 9.17/5.42 = ( ^ [F2: nat > nat > product_prod_nat_nat > product_prod_nat_nat,X3: product_prod_nat_nat] : ( F2 @ ( product_fst_nat_nat @ X3 ) @ ( product_snd_nat_nat @ X3 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6417_case__prod__beta_H,axiom,
% 9.17/5.42 ( produc8739625826339149834_nat_o
% 9.17/5.42 = ( ^ [F2: nat > nat > product_prod_nat_nat > $o,X3: product_prod_nat_nat] : ( F2 @ ( product_fst_nat_nat @ X3 ) @ ( product_snd_nat_nat @ X3 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6418_case__prod__beta_H,axiom,
% 9.17/5.42 ( produc4245557441103728435nt_int
% 9.17/5.42 = ( ^ [F2: int > int > product_prod_int_int,X3: product_prod_int_int] : ( F2 @ ( product_fst_int_int @ X3 ) @ ( product_snd_int_int @ X3 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6419_case__prod__beta_H,axiom,
% 9.17/5.42 ( produc8211389475949308722nt_int
% 9.17/5.42 = ( ^ [F2: int > int > int,X3: product_prod_int_int] : ( F2 @ ( product_fst_int_int @ X3 ) @ ( product_snd_int_int @ X3 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6420_case__prod__unfold,axiom,
% 9.17/5.42 ( produc6842872674320459806at_nat
% 9.17/5.42 = ( ^ [C2: nat > nat > nat,P6: product_prod_nat_nat] : ( C2 @ ( product_fst_nat_nat @ P6 ) @ ( product_snd_nat_nat @ P6 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6421_case__prod__unfold,axiom,
% 9.17/5.42 ( produc27273713700761075at_nat
% 9.17/5.42 = ( ^ [C2: nat > nat > product_prod_nat_nat > product_prod_nat_nat,P6: product_prod_nat_nat] : ( C2 @ ( product_fst_nat_nat @ P6 ) @ ( product_snd_nat_nat @ P6 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6422_case__prod__unfold,axiom,
% 9.17/5.42 ( produc8739625826339149834_nat_o
% 9.17/5.42 = ( ^ [C2: nat > nat > product_prod_nat_nat > $o,P6: product_prod_nat_nat] : ( C2 @ ( product_fst_nat_nat @ P6 ) @ ( product_snd_nat_nat @ P6 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6423_case__prod__unfold,axiom,
% 9.17/5.42 ( produc4245557441103728435nt_int
% 9.17/5.42 = ( ^ [C2: int > int > product_prod_int_int,P6: product_prod_int_int] : ( C2 @ ( product_fst_int_int @ P6 ) @ ( product_snd_int_int @ P6 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6424_case__prod__unfold,axiom,
% 9.17/5.42 ( produc8211389475949308722nt_int
% 9.17/5.42 = ( ^ [C2: int > int > int,P6: product_prod_int_int] : ( C2 @ ( product_fst_int_int @ P6 ) @ ( product_snd_int_int @ P6 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6425_Product__Type_OCollect__case__prodD,axiom,
% 9.17/5.42 ! [X: produc3843707927480180839at_nat,A2: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o] :
% 9.17/5.42 ( ( member8757157785044589968at_nat @ X @ ( collec6321179662152712658at_nat @ ( produc410239310623530412_nat_o @ A2 ) ) )
% 9.17/5.42 => ( A2 @ ( produc6011863565407846595at_nat @ X ) @ ( produc2937545259423399429at_nat @ X ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6426_Product__Type_OCollect__case__prodD,axiom,
% 9.17/5.42 ! [X: product_prod_nat_nat,A2: nat > nat > $o] :
% 9.17/5.42 ( ( member8440522571783428010at_nat @ X @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ A2 ) ) )
% 9.17/5.42 => ( A2 @ ( product_fst_nat_nat @ X ) @ ( product_snd_nat_nat @ X ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6427_Product__Type_OCollect__case__prodD,axiom,
% 9.17/5.42 ! [X: produc8923325533196201883nteger,A2: code_integer > code_integer > $o] :
% 9.17/5.42 ( ( member157494554546826820nteger @ X @ ( collec7766031446232907142nteger @ ( produc2066375834425727024eger_o @ A2 ) ) )
% 9.17/5.42 => ( A2 @ ( produc8508995932063986495nteger @ X ) @ ( produc6174133586879617921nteger @ X ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6428_Product__Type_OCollect__case__prodD,axiom,
% 9.17/5.42 ! [X: product_prod_int_int,A2: int > int > $o] :
% 9.17/5.42 ( ( member5262025264175285858nt_int @ X @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ A2 ) ) )
% 9.17/5.42 => ( A2 @ ( product_fst_int_int @ X ) @ ( product_snd_int_int @ X ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6429_Product__Type_OCollect__case__prodD,axiom,
% 9.17/5.42 ! [X: produc5835291356934675326atural,A2: code_natural > produc7822875418678951345atural > $o] :
% 9.17/5.42 ( ( member2108296798382401941atural @ X @ ( collec1991479681304692691atural @ ( produc7358226366420480123ural_o @ A2 ) ) )
% 9.17/5.42 => ( A2 @ ( produc497848011034438852atural @ X ) @ ( produc6591912806276919810atural @ X ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6430_case__prod__beta,axiom,
% 9.17/5.42 ( produc6842872674320459806at_nat
% 9.17/5.42 = ( ^ [F2: nat > nat > nat,P6: product_prod_nat_nat] : ( F2 @ ( product_fst_nat_nat @ P6 ) @ ( product_snd_nat_nat @ P6 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6431_case__prod__beta,axiom,
% 9.17/5.42 ( produc27273713700761075at_nat
% 9.17/5.42 = ( ^ [F2: nat > nat > product_prod_nat_nat > product_prod_nat_nat,P6: product_prod_nat_nat] : ( F2 @ ( product_fst_nat_nat @ P6 ) @ ( product_snd_nat_nat @ P6 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6432_case__prod__beta,axiom,
% 9.17/5.42 ( produc8739625826339149834_nat_o
% 9.17/5.42 = ( ^ [F2: nat > nat > product_prod_nat_nat > $o,P6: product_prod_nat_nat] : ( F2 @ ( product_fst_nat_nat @ P6 ) @ ( product_snd_nat_nat @ P6 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6433_case__prod__beta,axiom,
% 9.17/5.42 ( produc4245557441103728435nt_int
% 9.17/5.42 = ( ^ [F2: int > int > product_prod_int_int,P6: product_prod_int_int] : ( F2 @ ( product_fst_int_int @ P6 ) @ ( product_snd_int_int @ P6 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6434_case__prod__beta,axiom,
% 9.17/5.42 ( produc8211389475949308722nt_int
% 9.17/5.42 = ( ^ [F2: int > int > int,P6: product_prod_int_int] : ( F2 @ ( product_fst_int_int @ P6 ) @ ( product_snd_int_int @ P6 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6435_split__beta,axiom,
% 9.17/5.42 ( produc6842872674320459806at_nat
% 9.17/5.42 = ( ^ [F2: nat > nat > nat,Prod2: product_prod_nat_nat] : ( F2 @ ( product_fst_nat_nat @ Prod2 ) @ ( product_snd_nat_nat @ Prod2 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6436_split__beta,axiom,
% 9.17/5.42 ( produc27273713700761075at_nat
% 9.17/5.42 = ( ^ [F2: nat > nat > product_prod_nat_nat > product_prod_nat_nat,Prod2: product_prod_nat_nat] : ( F2 @ ( product_fst_nat_nat @ Prod2 ) @ ( product_snd_nat_nat @ Prod2 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6437_split__beta,axiom,
% 9.17/5.42 ( produc8739625826339149834_nat_o
% 9.17/5.42 = ( ^ [F2: nat > nat > product_prod_nat_nat > $o,Prod2: product_prod_nat_nat] : ( F2 @ ( product_fst_nat_nat @ Prod2 ) @ ( product_snd_nat_nat @ Prod2 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6438_split__beta,axiom,
% 9.17/5.42 ( produc4245557441103728435nt_int
% 9.17/5.42 = ( ^ [F2: int > int > product_prod_int_int,Prod2: product_prod_int_int] : ( F2 @ ( product_fst_int_int @ Prod2 ) @ ( product_snd_int_int @ Prod2 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6439_split__beta,axiom,
% 9.17/5.42 ( produc8211389475949308722nt_int
% 9.17/5.42 = ( ^ [F2: int > int > int,Prod2: product_prod_int_int] : ( F2 @ ( product_fst_int_int @ Prod2 ) @ ( product_snd_int_int @ Prod2 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6440_effect__guardI,axiom,
% 9.17/5.42 ! [P: heap_e7401611519738050253t_unit > $o,H3: heap_e7401611519738050253t_unit,H5: heap_e7401611519738050253t_unit,F: heap_e7401611519738050253t_unit > produc8664842809031399944it_nat,N2: nat,R2: product_unit] :
% 9.17/5.42 ( ( P @ H3 )
% 9.17/5.42 => ( ( H5
% 9.17/5.42 = ( produc2838810277069100634it_nat @ ( produc8604850587836428116it_nat @ ( F @ H3 ) ) ) )
% 9.17/5.42 => ( ( N2
% 9.17/5.42 = ( produc2594868675584459928it_nat @ ( produc8604850587836428116it_nat @ ( F @ H3 ) ) ) )
% 9.17/5.42 => ( ( R2
% 9.17/5.42 = ( produc4530234641508181270it_nat @ ( F @ H3 ) ) )
% 9.17/5.42 => ( heap_T6553295506729943825t_unit @ ( heap_T8440541562793052209t_unit @ P @ F ) @ H3 @ H5 @ R2 @ N2 ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6441_effect__guardI,axiom,
% 9.17/5.42 ! [P: heap_e7401611519738050253t_unit > $o,H3: heap_e7401611519738050253t_unit,H5: heap_e7401611519738050253t_unit,F: heap_e7401611519738050253t_unit > produc6714399278180371524it_nat,N2: nat,R2: array_a] :
% 9.17/5.42 ( ( P @ H3 )
% 9.17/5.42 => ( ( H5
% 9.17/5.42 = ( produc2838810277069100634it_nat @ ( produc6991280839920081578it_nat @ ( F @ H3 ) ) ) )
% 9.17/5.42 => ( ( N2
% 9.17/5.42 = ( produc2594868675584459928it_nat @ ( produc6991280839920081578it_nat @ ( F @ H3 ) ) ) )
% 9.17/5.42 => ( ( R2
% 9.17/5.42 = ( produc491454361838572648it_nat @ ( F @ H3 ) ) )
% 9.17/5.42 => ( heap_T5830633491639066771rray_a @ ( heap_T7685628758766326643rray_a @ P @ F ) @ H3 @ H5 @ R2 @ N2 ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6442_effect__guardE,axiom,
% 9.17/5.42 ! [P: heap_e7401611519738050253t_unit > $o,F: heap_e7401611519738050253t_unit > produc8664842809031399944it_nat,H3: heap_e7401611519738050253t_unit,H5: heap_e7401611519738050253t_unit,R2: product_unit,N2: nat] :
% 9.17/5.42 ( ( heap_T6553295506729943825t_unit @ ( heap_T8440541562793052209t_unit @ P @ F ) @ H3 @ H5 @ R2 @ N2 )
% 9.17/5.42 => ~ ( ( H5
% 9.17/5.42 = ( produc2838810277069100634it_nat @ ( produc8604850587836428116it_nat @ ( F @ H3 ) ) ) )
% 9.17/5.42 => ( ( N2
% 9.17/5.42 = ( produc2594868675584459928it_nat @ ( produc8604850587836428116it_nat @ ( F @ H3 ) ) ) )
% 9.17/5.42 => ( ( R2
% 9.17/5.42 = ( produc4530234641508181270it_nat @ ( F @ H3 ) ) )
% 9.17/5.42 => ~ ( P @ H3 ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6443_effect__guardE,axiom,
% 9.17/5.42 ! [P: heap_e7401611519738050253t_unit > $o,F: heap_e7401611519738050253t_unit > produc6714399278180371524it_nat,H3: heap_e7401611519738050253t_unit,H5: heap_e7401611519738050253t_unit,R2: array_a,N2: nat] :
% 9.17/5.42 ( ( heap_T5830633491639066771rray_a @ ( heap_T7685628758766326643rray_a @ P @ F ) @ H3 @ H5 @ R2 @ N2 )
% 9.17/5.42 => ~ ( ( H5
% 9.17/5.42 = ( produc2838810277069100634it_nat @ ( produc6991280839920081578it_nat @ ( F @ H3 ) ) ) )
% 9.17/5.42 => ( ( N2
% 9.17/5.42 = ( produc2594868675584459928it_nat @ ( produc6991280839920081578it_nat @ ( F @ H3 ) ) ) )
% 9.17/5.42 => ( ( R2
% 9.17/5.42 = ( produc491454361838572648it_nat @ ( F @ H3 ) ) )
% 9.17/5.42 => ~ ( P @ H3 ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6444_effectE,axiom,
% 9.17/5.42 ! [C: heap_T5738788834812785303t_unit,H3: heap_e7401611519738050253t_unit,H5: heap_e7401611519738050253t_unit,R2: product_unit,N2: nat] :
% 9.17/5.42 ( ( heap_T6553295506729943825t_unit @ C @ H3 @ H5 @ R2 @ N2 )
% 9.17/5.42 => ~ ( ( R2
% 9.17/5.42 = ( produc4530234641508181270it_nat @ ( the_Pr7776125533777466484it_nat @ ( heap_T875086893843062177t_unit @ C @ H3 ) ) ) )
% 9.17/5.42 => ( ( H5
% 9.17/5.42 = ( produc2838810277069100634it_nat @ ( produc8604850587836428116it_nat @ ( the_Pr7776125533777466484it_nat @ ( heap_T875086893843062177t_unit @ C @ H3 ) ) ) ) )
% 9.17/5.42 => ( ( N2
% 9.17/5.42 = ( produc2594868675584459928it_nat @ ( produc8604850587836428116it_nat @ ( the_Pr7776125533777466484it_nat @ ( heap_T875086893843062177t_unit @ C @ H3 ) ) ) ) )
% 9.17/5.42 => ~ ( heap_T584514906347983379t_unit @ C @ H3 ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6445_effectE,axiom,
% 9.17/5.42 ! [C: heap_T6362127782908069795rray_a,H3: heap_e7401611519738050253t_unit,H5: heap_e7401611519738050253t_unit,R2: array_a,N2: nat] :
% 9.17/5.42 ( ( heap_T5830633491639066771rray_a @ C @ H3 @ H5 @ R2 @ N2 )
% 9.17/5.42 => ~ ( ( R2
% 9.17/5.42 = ( produc491454361838572648it_nat @ ( the_Pr5856008525237892824it_nat @ ( heap_T5591663578999710211rray_a @ C @ H3 ) ) ) )
% 9.17/5.42 => ( ( H5
% 9.17/5.42 = ( produc2838810277069100634it_nat @ ( produc6991280839920081578it_nat @ ( the_Pr5856008525237892824it_nat @ ( heap_T5591663578999710211rray_a @ C @ H3 ) ) ) ) )
% 9.17/5.42 => ( ( N2
% 9.17/5.42 = ( produc2594868675584459928it_nat @ ( produc6991280839920081578it_nat @ ( the_Pr5856008525237892824it_nat @ ( heap_T5591663578999710211rray_a @ C @ H3 ) ) ) ) )
% 9.17/5.42 => ~ ( heap_T6932021131025641745rray_a @ C @ H3 ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6446_prod__eq__iff,axiom,
% 9.17/5.42 ( ( ^ [Y4: produc8923325533196201883nteger,Z2: produc8923325533196201883nteger] : ( Y4 = Z2 ) )
% 9.17/5.42 = ( ^ [S4: produc8923325533196201883nteger,T2: produc8923325533196201883nteger] :
% 9.17/5.42 ( ( ( produc8508995932063986495nteger @ S4 )
% 9.17/5.42 = ( produc8508995932063986495nteger @ T2 ) )
% 9.17/5.42 & ( ( produc6174133586879617921nteger @ S4 )
% 9.17/5.42 = ( produc6174133586879617921nteger @ T2 ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6447_prod__eq__iff,axiom,
% 9.17/5.42 ( ( ^ [Y4: product_prod_int_int,Z2: product_prod_int_int] : ( Y4 = Z2 ) )
% 9.17/5.42 = ( ^ [S4: product_prod_int_int,T2: product_prod_int_int] :
% 9.17/5.42 ( ( ( product_fst_int_int @ S4 )
% 9.17/5.42 = ( product_fst_int_int @ T2 ) )
% 9.17/5.42 & ( ( product_snd_int_int @ S4 )
% 9.17/5.42 = ( product_snd_int_int @ T2 ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6448_prod__eq__iff,axiom,
% 9.17/5.42 ( ( ^ [Y4: produc5835291356934675326atural,Z2: produc5835291356934675326atural] : ( Y4 = Z2 ) )
% 9.17/5.42 = ( ^ [S4: produc5835291356934675326atural,T2: produc5835291356934675326atural] :
% 9.17/5.42 ( ( ( produc497848011034438852atural @ S4 )
% 9.17/5.42 = ( produc497848011034438852atural @ T2 ) )
% 9.17/5.42 & ( ( produc6591912806276919810atural @ S4 )
% 9.17/5.42 = ( produc6591912806276919810atural @ T2 ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6449_prod__eqI,axiom,
% 9.17/5.42 ! [P4: produc8923325533196201883nteger,Q3: produc8923325533196201883nteger] :
% 9.17/5.42 ( ( ( produc8508995932063986495nteger @ P4 )
% 9.17/5.42 = ( produc8508995932063986495nteger @ Q3 ) )
% 9.17/5.42 => ( ( ( produc6174133586879617921nteger @ P4 )
% 9.17/5.42 = ( produc6174133586879617921nteger @ Q3 ) )
% 9.17/5.42 => ( P4 = Q3 ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6450_prod__eqI,axiom,
% 9.17/5.42 ! [P4: product_prod_int_int,Q3: product_prod_int_int] :
% 9.17/5.42 ( ( ( product_fst_int_int @ P4 )
% 9.17/5.42 = ( product_fst_int_int @ Q3 ) )
% 9.17/5.42 => ( ( ( product_snd_int_int @ P4 )
% 9.17/5.42 = ( product_snd_int_int @ Q3 ) )
% 9.17/5.42 => ( P4 = Q3 ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6451_prod__eqI,axiom,
% 9.17/5.42 ! [P4: produc5835291356934675326atural,Q3: produc5835291356934675326atural] :
% 9.17/5.42 ( ( ( produc497848011034438852atural @ P4 )
% 9.17/5.42 = ( produc497848011034438852atural @ Q3 ) )
% 9.17/5.42 => ( ( ( produc6591912806276919810atural @ P4 )
% 9.17/5.42 = ( produc6591912806276919810atural @ Q3 ) )
% 9.17/5.42 => ( P4 = Q3 ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6452_prod_Oexpand,axiom,
% 9.17/5.42 ! [Prod: produc8923325533196201883nteger,Prod3: produc8923325533196201883nteger] :
% 9.17/5.42 ( ( ( ( produc8508995932063986495nteger @ Prod )
% 9.17/5.42 = ( produc8508995932063986495nteger @ Prod3 ) )
% 9.17/5.42 & ( ( produc6174133586879617921nteger @ Prod )
% 9.17/5.42 = ( produc6174133586879617921nteger @ Prod3 ) ) )
% 9.17/5.42 => ( Prod = Prod3 ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6453_prod_Oexpand,axiom,
% 9.17/5.42 ! [Prod: product_prod_int_int,Prod3: product_prod_int_int] :
% 9.17/5.42 ( ( ( ( product_fst_int_int @ Prod )
% 9.17/5.42 = ( product_fst_int_int @ Prod3 ) )
% 9.17/5.42 & ( ( product_snd_int_int @ Prod )
% 9.17/5.42 = ( product_snd_int_int @ Prod3 ) ) )
% 9.17/5.42 => ( Prod = Prod3 ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6454_prod_Oexpand,axiom,
% 9.17/5.42 ! [Prod: produc5835291356934675326atural,Prod3: produc5835291356934675326atural] :
% 9.17/5.42 ( ( ( ( produc497848011034438852atural @ Prod )
% 9.17/5.42 = ( produc497848011034438852atural @ Prod3 ) )
% 9.17/5.42 & ( ( produc6591912806276919810atural @ Prod )
% 9.17/5.42 = ( produc6591912806276919810atural @ Prod3 ) ) )
% 9.17/5.42 => ( Prod = Prod3 ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6455_All__prod__contract,axiom,
% 9.17/5.42 ! [P: code_integer > code_integer > $o] :
% 9.17/5.42 ( ( ! [A5: code_integer,X9: code_integer] : ( P @ A5 @ X9 ) )
% 9.17/5.42 = ( ! [Z4: produc8923325533196201883nteger] : ( P @ ( produc8508995932063986495nteger @ Z4 ) @ ( produc6174133586879617921nteger @ Z4 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6456_All__prod__contract,axiom,
% 9.17/5.42 ! [P: int > int > $o] :
% 9.17/5.42 ( ( ! [A5: int,X9: int] : ( P @ A5 @ X9 ) )
% 9.17/5.42 = ( ! [Z4: product_prod_int_int] : ( P @ ( product_fst_int_int @ Z4 ) @ ( product_snd_int_int @ Z4 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6457_All__prod__contract,axiom,
% 9.17/5.42 ! [P: code_natural > produc7822875418678951345atural > $o] :
% 9.17/5.42 ( ( ! [A5: code_natural,X9: produc7822875418678951345atural] : ( P @ A5 @ X9 ) )
% 9.17/5.42 = ( ! [Z4: produc5835291356934675326atural] : ( P @ ( produc497848011034438852atural @ Z4 ) @ ( produc6591912806276919810atural @ Z4 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6458_Ex__prod__contract,axiom,
% 9.17/5.42 ! [P: code_integer > code_integer > $o] :
% 9.17/5.42 ( ( ? [A5: code_integer,X9: code_integer] : ( P @ A5 @ X9 ) )
% 9.17/5.42 = ( ? [Z4: produc8923325533196201883nteger] : ( P @ ( produc8508995932063986495nteger @ Z4 ) @ ( produc6174133586879617921nteger @ Z4 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6459_Ex__prod__contract,axiom,
% 9.17/5.42 ! [P: int > int > $o] :
% 9.17/5.42 ( ( ? [A5: int,X9: int] : ( P @ A5 @ X9 ) )
% 9.17/5.42 = ( ? [Z4: product_prod_int_int] : ( P @ ( product_fst_int_int @ Z4 ) @ ( product_snd_int_int @ Z4 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6460_Ex__prod__contract,axiom,
% 9.17/5.42 ! [P: code_natural > produc7822875418678951345atural > $o] :
% 9.17/5.42 ( ( ? [A5: code_natural,X9: produc7822875418678951345atural] : ( P @ A5 @ X9 ) )
% 9.17/5.42 = ( ? [Z4: produc5835291356934675326atural] : ( P @ ( produc497848011034438852atural @ Z4 ) @ ( produc6591912806276919810atural @ Z4 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6461_prod_Osplit__sel,axiom,
% 9.17/5.42 ! [P: nat > $o,F: nat > nat > nat,Prod: product_prod_nat_nat] :
% 9.17/5.42 ( ( P @ ( produc6842872674320459806at_nat @ F @ Prod ) )
% 9.17/5.42 = ( ( Prod
% 9.17/5.42 = ( product_Pair_nat_nat @ ( product_fst_nat_nat @ Prod ) @ ( product_snd_nat_nat @ Prod ) ) )
% 9.17/5.42 => ( P @ ( F @ ( product_fst_nat_nat @ Prod ) @ ( product_snd_nat_nat @ Prod ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6462_prod_Osplit__sel,axiom,
% 9.17/5.42 ! [P: ( product_prod_nat_nat > product_prod_nat_nat ) > $o,F: nat > nat > product_prod_nat_nat > product_prod_nat_nat,Prod: product_prod_nat_nat] :
% 9.17/5.42 ( ( P @ ( produc27273713700761075at_nat @ F @ Prod ) )
% 9.17/5.42 = ( ( Prod
% 9.17/5.42 = ( product_Pair_nat_nat @ ( product_fst_nat_nat @ Prod ) @ ( product_snd_nat_nat @ Prod ) ) )
% 9.17/5.42 => ( P @ ( F @ ( product_fst_nat_nat @ Prod ) @ ( product_snd_nat_nat @ Prod ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6463_prod_Osplit__sel,axiom,
% 9.17/5.42 ! [P: ( product_prod_nat_nat > $o ) > $o,F: nat > nat > product_prod_nat_nat > $o,Prod: product_prod_nat_nat] :
% 9.17/5.42 ( ( P @ ( produc8739625826339149834_nat_o @ F @ Prod ) )
% 9.17/5.42 = ( ( Prod
% 9.17/5.42 = ( product_Pair_nat_nat @ ( product_fst_nat_nat @ Prod ) @ ( product_snd_nat_nat @ Prod ) ) )
% 9.17/5.42 => ( P @ ( F @ ( product_fst_nat_nat @ Prod ) @ ( product_snd_nat_nat @ Prod ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6464_prod_Osplit__sel,axiom,
% 9.17/5.42 ! [P: product_prod_int_int > $o,F: int > int > product_prod_int_int,Prod: product_prod_int_int] :
% 9.17/5.42 ( ( P @ ( produc4245557441103728435nt_int @ F @ Prod ) )
% 9.17/5.42 = ( ( Prod
% 9.17/5.42 = ( product_Pair_int_int @ ( product_fst_int_int @ Prod ) @ ( product_snd_int_int @ Prod ) ) )
% 9.17/5.42 => ( P @ ( F @ ( product_fst_int_int @ Prod ) @ ( product_snd_int_int @ Prod ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6465_prod_Osplit__sel,axiom,
% 9.17/5.42 ! [P: int > $o,F: int > int > int,Prod: product_prod_int_int] :
% 9.17/5.42 ( ( P @ ( produc8211389475949308722nt_int @ F @ Prod ) )
% 9.17/5.42 = ( ( Prod
% 9.17/5.42 = ( product_Pair_int_int @ ( product_fst_int_int @ Prod ) @ ( product_snd_int_int @ Prod ) ) )
% 9.17/5.42 => ( P @ ( F @ ( product_fst_int_int @ Prod ) @ ( product_snd_int_int @ Prod ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6466_prod_Osplit__sel__asm,axiom,
% 9.17/5.42 ! [P: nat > $o,F: nat > nat > nat,Prod: product_prod_nat_nat] :
% 9.17/5.42 ( ( P @ ( produc6842872674320459806at_nat @ F @ Prod ) )
% 9.17/5.42 = ( ~ ( ( Prod
% 9.17/5.42 = ( product_Pair_nat_nat @ ( product_fst_nat_nat @ Prod ) @ ( product_snd_nat_nat @ Prod ) ) )
% 9.17/5.42 & ~ ( P @ ( F @ ( product_fst_nat_nat @ Prod ) @ ( product_snd_nat_nat @ Prod ) ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6467_prod_Osplit__sel__asm,axiom,
% 9.17/5.42 ! [P: ( product_prod_nat_nat > product_prod_nat_nat ) > $o,F: nat > nat > product_prod_nat_nat > product_prod_nat_nat,Prod: product_prod_nat_nat] :
% 9.17/5.42 ( ( P @ ( produc27273713700761075at_nat @ F @ Prod ) )
% 9.17/5.42 = ( ~ ( ( Prod
% 9.17/5.42 = ( product_Pair_nat_nat @ ( product_fst_nat_nat @ Prod ) @ ( product_snd_nat_nat @ Prod ) ) )
% 9.17/5.42 & ~ ( P @ ( F @ ( product_fst_nat_nat @ Prod ) @ ( product_snd_nat_nat @ Prod ) ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6468_prod_Osplit__sel__asm,axiom,
% 9.17/5.42 ! [P: ( product_prod_nat_nat > $o ) > $o,F: nat > nat > product_prod_nat_nat > $o,Prod: product_prod_nat_nat] :
% 9.17/5.42 ( ( P @ ( produc8739625826339149834_nat_o @ F @ Prod ) )
% 9.17/5.42 = ( ~ ( ( Prod
% 9.17/5.42 = ( product_Pair_nat_nat @ ( product_fst_nat_nat @ Prod ) @ ( product_snd_nat_nat @ Prod ) ) )
% 9.17/5.42 & ~ ( P @ ( F @ ( product_fst_nat_nat @ Prod ) @ ( product_snd_nat_nat @ Prod ) ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6469_prod_Osplit__sel__asm,axiom,
% 9.17/5.42 ! [P: product_prod_int_int > $o,F: int > int > product_prod_int_int,Prod: product_prod_int_int] :
% 9.17/5.42 ( ( P @ ( produc4245557441103728435nt_int @ F @ Prod ) )
% 9.17/5.42 = ( ~ ( ( Prod
% 9.17/5.42 = ( product_Pair_int_int @ ( product_fst_int_int @ Prod ) @ ( product_snd_int_int @ Prod ) ) )
% 9.17/5.42 & ~ ( P @ ( F @ ( product_fst_int_int @ Prod ) @ ( product_snd_int_int @ Prod ) ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6470_prod_Osplit__sel__asm,axiom,
% 9.17/5.42 ! [P: int > $o,F: int > int > int,Prod: product_prod_int_int] :
% 9.17/5.42 ( ( P @ ( produc8211389475949308722nt_int @ F @ Prod ) )
% 9.17/5.42 = ( ~ ( ( Prod
% 9.17/5.42 = ( product_Pair_int_int @ ( product_fst_int_int @ Prod ) @ ( product_snd_int_int @ Prod ) ) )
% 9.17/5.42 & ~ ( P @ ( F @ ( product_fst_int_int @ Prod ) @ ( product_snd_int_int @ Prod ) ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6471_surjective__pairing,axiom,
% 9.17/5.42 ! [T: produc1908205239877642774nteger] :
% 9.17/5.42 ( T
% 9.17/5.42 = ( produc8603105652947943368nteger @ ( produc7822682618958472924nteger @ T ) @ ( produc7856867400915047194nteger @ T ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6472_surjective__pairing,axiom,
% 9.17/5.42 ! [T: produc3925858234332021118et_nat] :
% 9.17/5.42 ( T
% 9.17/5.42 = ( produc5001842942810119800et_nat @ ( produc995936583742144908et_nat @ T ) @ ( produc4011572625026189258et_nat @ T ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6473_surjective__pairing,axiom,
% 9.17/5.42 ! [T: produc2732055786443039994et_nat] :
% 9.17/5.42 ( T
% 9.17/5.42 = ( produc2245416461498447860et_nat @ ( produc180342877477747464et_nat @ T ) @ ( produc5374455773327741254et_nat @ T ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6474_surjective__pairing,axiom,
% 9.17/5.42 ! [T: produc2285326912895808259nt_int] :
% 9.17/5.42 ( T
% 9.17/5.42 = ( produc5700946648718959541nt_int @ ( produc6816164490631068361nt_int @ T ) @ ( produc7328097813583171335nt_int @ T ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6475_surjective__pairing,axiom,
% 9.17/5.42 ! [T: produc7773217078559923341nt_int] :
% 9.17/5.42 ( T
% 9.17/5.42 = ( produc4305682042979456191nt_int @ ( produc6230002227079971283nt_int @ T ) @ ( produc3162348030201620241nt_int @ T ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6476_surjective__pairing,axiom,
% 9.17/5.42 ! [T: produc8923325533196201883nteger] :
% 9.17/5.42 ( T
% 9.17/5.42 = ( produc1086072967326762835nteger @ ( produc8508995932063986495nteger @ T ) @ ( produc6174133586879617921nteger @ T ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6477_surjective__pairing,axiom,
% 9.17/5.42 ! [T: product_prod_int_int] :
% 9.17/5.42 ( T
% 9.17/5.42 = ( product_Pair_int_int @ ( product_fst_int_int @ T ) @ ( product_snd_int_int @ T ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6478_surjective__pairing,axiom,
% 9.17/5.42 ! [T: produc5835291356934675326atural] :
% 9.17/5.42 ( T
% 9.17/5.42 = ( produc6639722614265839536atural @ ( produc497848011034438852atural @ T ) @ ( produc6591912806276919810atural @ T ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6479_prod_Oexhaust__sel,axiom,
% 9.17/5.42 ! [Prod: produc1908205239877642774nteger] :
% 9.17/5.42 ( Prod
% 9.17/5.42 = ( produc8603105652947943368nteger @ ( produc7822682618958472924nteger @ Prod ) @ ( produc7856867400915047194nteger @ Prod ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6480_prod_Oexhaust__sel,axiom,
% 9.17/5.42 ! [Prod: produc3925858234332021118et_nat] :
% 9.17/5.42 ( Prod
% 9.17/5.42 = ( produc5001842942810119800et_nat @ ( produc995936583742144908et_nat @ Prod ) @ ( produc4011572625026189258et_nat @ Prod ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6481_prod_Oexhaust__sel,axiom,
% 9.17/5.42 ! [Prod: produc2732055786443039994et_nat] :
% 9.17/5.42 ( Prod
% 9.17/5.42 = ( produc2245416461498447860et_nat @ ( produc180342877477747464et_nat @ Prod ) @ ( produc5374455773327741254et_nat @ Prod ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6482_prod_Oexhaust__sel,axiom,
% 9.17/5.42 ! [Prod: produc2285326912895808259nt_int] :
% 9.17/5.42 ( Prod
% 9.17/5.42 = ( produc5700946648718959541nt_int @ ( produc6816164490631068361nt_int @ Prod ) @ ( produc7328097813583171335nt_int @ Prod ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6483_prod_Oexhaust__sel,axiom,
% 9.17/5.42 ! [Prod: produc7773217078559923341nt_int] :
% 9.17/5.42 ( Prod
% 9.17/5.42 = ( produc4305682042979456191nt_int @ ( produc6230002227079971283nt_int @ Prod ) @ ( produc3162348030201620241nt_int @ Prod ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6484_prod_Oexhaust__sel,axiom,
% 9.17/5.42 ! [Prod: produc8923325533196201883nteger] :
% 9.17/5.42 ( Prod
% 9.17/5.42 = ( produc1086072967326762835nteger @ ( produc8508995932063986495nteger @ Prod ) @ ( produc6174133586879617921nteger @ Prod ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6485_prod_Oexhaust__sel,axiom,
% 9.17/5.42 ! [Prod: product_prod_int_int] :
% 9.17/5.42 ( Prod
% 9.17/5.42 = ( product_Pair_int_int @ ( product_fst_int_int @ Prod ) @ ( product_snd_int_int @ Prod ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6486_prod_Oexhaust__sel,axiom,
% 9.17/5.42 ! [Prod: produc5835291356934675326atural] :
% 9.17/5.42 ( Prod
% 9.17/5.42 = ( produc6639722614265839536atural @ ( produc497848011034438852atural @ Prod ) @ ( produc6591912806276919810atural @ Prod ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6487_exI__realizer,axiom,
% 9.17/5.42 ! [P: produc8923325533196201883nteger > ( produc6241069584506657477e_term > option6357759511663192854e_term ) > $o,Y: produc8923325533196201883nteger,X: produc6241069584506657477e_term > option6357759511663192854e_term] :
% 9.17/5.42 ( ( P @ Y @ X )
% 9.17/5.42 => ( P @ ( produc7856867400915047194nteger @ ( produc8603105652947943368nteger @ X @ Y ) ) @ ( produc7822682618958472924nteger @ ( produc8603105652947943368nteger @ X @ Y ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6488_exI__realizer,axiom,
% 9.17/5.42 ! [P: produc3658429121746597890et_nat > ( produc3658429121746597890et_nat > $o ) > $o,Y: produc3658429121746597890et_nat,X: produc3658429121746597890et_nat > $o] :
% 9.17/5.42 ( ( P @ Y @ X )
% 9.17/5.42 => ( P @ ( produc4011572625026189258et_nat @ ( produc5001842942810119800et_nat @ X @ Y ) ) @ ( produc995936583742144908et_nat @ ( produc5001842942810119800et_nat @ X @ Y ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6489_exI__realizer,axiom,
% 9.17/5.42 ! [P: produc3925858234332021118et_nat > ( produc3658429121746597890et_nat > $o ) > $o,Y: produc3925858234332021118et_nat,X: produc3658429121746597890et_nat > $o] :
% 9.17/5.42 ( ( P @ Y @ X )
% 9.17/5.42 => ( P @ ( produc5374455773327741254et_nat @ ( produc2245416461498447860et_nat @ X @ Y ) ) @ ( produc180342877477747464et_nat @ ( produc2245416461498447860et_nat @ X @ Y ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6490_exI__realizer,axiom,
% 9.17/5.42 ! [P: product_prod_int_int > ( produc8551481072490612790e_term > option6357759511663192854e_term ) > $o,Y: product_prod_int_int,X: produc8551481072490612790e_term > option6357759511663192854e_term] :
% 9.17/5.42 ( ( P @ Y @ X )
% 9.17/5.42 => ( P @ ( produc7328097813583171335nt_int @ ( produc5700946648718959541nt_int @ X @ Y ) ) @ ( produc6816164490631068361nt_int @ ( produc5700946648718959541nt_int @ X @ Y ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6491_exI__realizer,axiom,
% 9.17/5.42 ! [P: product_prod_int_int > ( int > option6357759511663192854e_term ) > $o,Y: product_prod_int_int,X: int > option6357759511663192854e_term] :
% 9.17/5.42 ( ( P @ Y @ X )
% 9.17/5.42 => ( P @ ( produc3162348030201620241nt_int @ ( produc4305682042979456191nt_int @ X @ Y ) ) @ ( produc6230002227079971283nt_int @ ( produc4305682042979456191nt_int @ X @ Y ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6492_exI__realizer,axiom,
% 9.17/5.42 ! [P: code_integer > code_integer > $o,Y: code_integer,X: code_integer] :
% 9.17/5.42 ( ( P @ Y @ X )
% 9.17/5.42 => ( P @ ( produc6174133586879617921nteger @ ( produc1086072967326762835nteger @ X @ Y ) ) @ ( produc8508995932063986495nteger @ ( produc1086072967326762835nteger @ X @ Y ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6493_exI__realizer,axiom,
% 9.17/5.42 ! [P: int > int > $o,Y: int,X: int] :
% 9.17/5.42 ( ( P @ Y @ X )
% 9.17/5.42 => ( P @ ( product_snd_int_int @ ( product_Pair_int_int @ X @ Y ) ) @ ( product_fst_int_int @ ( product_Pair_int_int @ X @ Y ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6494_exI__realizer,axiom,
% 9.17/5.42 ! [P: produc7822875418678951345atural > code_natural > $o,Y: produc7822875418678951345atural,X: code_natural] :
% 9.17/5.42 ( ( P @ Y @ X )
% 9.17/5.42 => ( P @ ( produc6591912806276919810atural @ ( produc6639722614265839536atural @ X @ Y ) ) @ ( produc497848011034438852atural @ ( produc6639722614265839536atural @ X @ Y ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6495_conjI__realizer,axiom,
% 9.17/5.42 ! [P: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > $o,P4: produc6241069584506657477e_term > option6357759511663192854e_term,Q: produc8923325533196201883nteger > $o,Q3: produc8923325533196201883nteger] :
% 9.17/5.42 ( ( P @ P4 )
% 9.17/5.42 => ( ( Q @ Q3 )
% 9.17/5.42 => ( ( P @ ( produc7822682618958472924nteger @ ( produc8603105652947943368nteger @ P4 @ Q3 ) ) )
% 9.17/5.42 & ( Q @ ( produc7856867400915047194nteger @ ( produc8603105652947943368nteger @ P4 @ Q3 ) ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6496_conjI__realizer,axiom,
% 9.17/5.42 ! [P: ( produc3658429121746597890et_nat > $o ) > $o,P4: produc3658429121746597890et_nat > $o,Q: produc3658429121746597890et_nat > $o,Q3: produc3658429121746597890et_nat] :
% 9.17/5.42 ( ( P @ P4 )
% 9.17/5.42 => ( ( Q @ Q3 )
% 9.17/5.42 => ( ( P @ ( produc995936583742144908et_nat @ ( produc5001842942810119800et_nat @ P4 @ Q3 ) ) )
% 9.17/5.42 & ( Q @ ( produc4011572625026189258et_nat @ ( produc5001842942810119800et_nat @ P4 @ Q3 ) ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6497_conjI__realizer,axiom,
% 9.17/5.42 ! [P: ( produc3658429121746597890et_nat > $o ) > $o,P4: produc3658429121746597890et_nat > $o,Q: produc3925858234332021118et_nat > $o,Q3: produc3925858234332021118et_nat] :
% 9.17/5.42 ( ( P @ P4 )
% 9.17/5.42 => ( ( Q @ Q3 )
% 9.17/5.42 => ( ( P @ ( produc180342877477747464et_nat @ ( produc2245416461498447860et_nat @ P4 @ Q3 ) ) )
% 9.17/5.42 & ( Q @ ( produc5374455773327741254et_nat @ ( produc2245416461498447860et_nat @ P4 @ Q3 ) ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6498_conjI__realizer,axiom,
% 9.17/5.42 ! [P: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > $o,P4: produc8551481072490612790e_term > option6357759511663192854e_term,Q: product_prod_int_int > $o,Q3: product_prod_int_int] :
% 9.17/5.42 ( ( P @ P4 )
% 9.17/5.42 => ( ( Q @ Q3 )
% 9.17/5.42 => ( ( P @ ( produc6816164490631068361nt_int @ ( produc5700946648718959541nt_int @ P4 @ Q3 ) ) )
% 9.17/5.42 & ( Q @ ( produc7328097813583171335nt_int @ ( produc5700946648718959541nt_int @ P4 @ Q3 ) ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6499_conjI__realizer,axiom,
% 9.17/5.42 ! [P: ( int > option6357759511663192854e_term ) > $o,P4: int > option6357759511663192854e_term,Q: product_prod_int_int > $o,Q3: product_prod_int_int] :
% 9.17/5.42 ( ( P @ P4 )
% 9.17/5.42 => ( ( Q @ Q3 )
% 9.17/5.42 => ( ( P @ ( produc6230002227079971283nt_int @ ( produc4305682042979456191nt_int @ P4 @ Q3 ) ) )
% 9.17/5.42 & ( Q @ ( produc3162348030201620241nt_int @ ( produc4305682042979456191nt_int @ P4 @ Q3 ) ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6500_conjI__realizer,axiom,
% 9.17/5.42 ! [P: code_integer > $o,P4: code_integer,Q: code_integer > $o,Q3: code_integer] :
% 9.17/5.42 ( ( P @ P4 )
% 9.17/5.42 => ( ( Q @ Q3 )
% 9.17/5.42 => ( ( P @ ( produc8508995932063986495nteger @ ( produc1086072967326762835nteger @ P4 @ Q3 ) ) )
% 9.17/5.42 & ( Q @ ( produc6174133586879617921nteger @ ( produc1086072967326762835nteger @ P4 @ Q3 ) ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6501_conjI__realizer,axiom,
% 9.17/5.42 ! [P: int > $o,P4: int,Q: int > $o,Q3: int] :
% 9.17/5.42 ( ( P @ P4 )
% 9.17/5.42 => ( ( Q @ Q3 )
% 9.17/5.42 => ( ( P @ ( product_fst_int_int @ ( product_Pair_int_int @ P4 @ Q3 ) ) )
% 9.17/5.42 & ( Q @ ( product_snd_int_int @ ( product_Pair_int_int @ P4 @ Q3 ) ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6502_conjI__realizer,axiom,
% 9.17/5.42 ! [P: code_natural > $o,P4: code_natural,Q: produc7822875418678951345atural > $o,Q3: produc7822875418678951345atural] :
% 9.17/5.42 ( ( P @ P4 )
% 9.17/5.42 => ( ( Q @ Q3 )
% 9.17/5.42 => ( ( P @ ( produc497848011034438852atural @ ( produc6639722614265839536atural @ P4 @ Q3 ) ) )
% 9.17/5.42 & ( Q @ ( produc6591912806276919810atural @ ( produc6639722614265839536atural @ P4 @ Q3 ) ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6503_execute__bind__success,axiom,
% 9.17/5.42 ! [F: heap_T5738788834812785303t_unit,H3: heap_e7401611519738050253t_unit,G: product_unit > heap_T6362127782908069795rray_a] :
% 9.17/5.42 ( ( heap_T584514906347983379t_unit @ F @ H3 )
% 9.17/5.42 => ( ( heap_T5591663578999710211rray_a @ ( heap_T7158140910958840029rray_a @ F @ G ) @ H3 )
% 9.17/5.42 = ( heap_T531568236820715630rray_a @ ( produc2594868675584459928it_nat @ ( produc8604850587836428116it_nat @ ( the_Pr7776125533777466484it_nat @ ( heap_T875086893843062177t_unit @ F @ H3 ) ) ) ) @ ( heap_T5591663578999710211rray_a @ ( G @ ( produc4530234641508181270it_nat @ ( the_Pr7776125533777466484it_nat @ ( heap_T875086893843062177t_unit @ F @ H3 ) ) ) ) @ ( produc2838810277069100634it_nat @ ( produc8604850587836428116it_nat @ ( the_Pr7776125533777466484it_nat @ ( heap_T875086893843062177t_unit @ F @ H3 ) ) ) ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6504_execute__bind__success,axiom,
% 9.17/5.42 ! [F: heap_T5738788834812785303t_unit,H3: heap_e7401611519738050253t_unit,G: product_unit > heap_T5738788834812785303t_unit] :
% 9.17/5.42 ( ( heap_T584514906347983379t_unit @ F @ H3 )
% 9.17/5.42 => ( ( heap_T875086893843062177t_unit @ ( heap_T2633723481742716231t_unit @ F @ G ) @ H3 )
% 9.17/5.42 = ( heap_T3616969660504097270t_unit @ ( produc2594868675584459928it_nat @ ( produc8604850587836428116it_nat @ ( the_Pr7776125533777466484it_nat @ ( heap_T875086893843062177t_unit @ F @ H3 ) ) ) ) @ ( heap_T875086893843062177t_unit @ ( G @ ( produc4530234641508181270it_nat @ ( the_Pr7776125533777466484it_nat @ ( heap_T875086893843062177t_unit @ F @ H3 ) ) ) ) @ ( produc2838810277069100634it_nat @ ( produc8604850587836428116it_nat @ ( the_Pr7776125533777466484it_nat @ ( heap_T875086893843062177t_unit @ F @ H3 ) ) ) ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6505_execute__bind__success,axiom,
% 9.17/5.42 ! [F: heap_T6362127782908069795rray_a,H3: heap_e7401611519738050253t_unit,G: array_a > heap_T6362127782908069795rray_a] :
% 9.17/5.42 ( ( heap_T6932021131025641745rray_a @ F @ H3 )
% 9.17/5.42 => ( ( heap_T5591663578999710211rray_a @ ( heap_T2407400398799471159rray_a @ F @ G ) @ H3 )
% 9.17/5.42 = ( heap_T531568236820715630rray_a @ ( produc2594868675584459928it_nat @ ( produc6991280839920081578it_nat @ ( the_Pr5856008525237892824it_nat @ ( heap_T5591663578999710211rray_a @ F @ H3 ) ) ) ) @ ( heap_T5591663578999710211rray_a @ ( G @ ( produc491454361838572648it_nat @ ( the_Pr5856008525237892824it_nat @ ( heap_T5591663578999710211rray_a @ F @ H3 ) ) ) ) @ ( produc2838810277069100634it_nat @ ( produc6991280839920081578it_nat @ ( the_Pr5856008525237892824it_nat @ ( heap_T5591663578999710211rray_a @ F @ H3 ) ) ) ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6506_execute__bind__success,axiom,
% 9.17/5.42 ! [F: heap_T6362127782908069795rray_a,H3: heap_e7401611519738050253t_unit,G: array_a > heap_T5738788834812785303t_unit] :
% 9.17/5.42 ( ( heap_T6932021131025641745rray_a @ F @ H3 )
% 9.17/5.42 => ( ( heap_T875086893843062177t_unit @ ( heap_T7324619625323989613t_unit @ F @ G ) @ H3 )
% 9.17/5.42 = ( heap_T3616969660504097270t_unit @ ( produc2594868675584459928it_nat @ ( produc6991280839920081578it_nat @ ( the_Pr5856008525237892824it_nat @ ( heap_T5591663578999710211rray_a @ F @ H3 ) ) ) ) @ ( heap_T875086893843062177t_unit @ ( G @ ( produc491454361838572648it_nat @ ( the_Pr5856008525237892824it_nat @ ( heap_T5591663578999710211rray_a @ F @ H3 ) ) ) ) @ ( produc2838810277069100634it_nat @ ( produc6991280839920081578it_nat @ ( the_Pr5856008525237892824it_nat @ ( heap_T5591663578999710211rray_a @ F @ H3 ) ) ) ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6507_sndI,axiom,
% 9.17/5.42 ! [X: produc1908205239877642774nteger,Y: produc6241069584506657477e_term > option6357759511663192854e_term,Z: produc8923325533196201883nteger] :
% 9.17/5.42 ( ( X
% 9.17/5.42 = ( produc8603105652947943368nteger @ Y @ Z ) )
% 9.17/5.42 => ( ( produc7856867400915047194nteger @ X )
% 9.17/5.42 = Z ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6508_sndI,axiom,
% 9.17/5.42 ! [X: produc3925858234332021118et_nat,Y: produc3658429121746597890et_nat > $o,Z: produc3658429121746597890et_nat] :
% 9.17/5.42 ( ( X
% 9.17/5.42 = ( produc5001842942810119800et_nat @ Y @ Z ) )
% 9.17/5.42 => ( ( produc4011572625026189258et_nat @ X )
% 9.17/5.42 = Z ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6509_sndI,axiom,
% 9.17/5.42 ! [X: produc2732055786443039994et_nat,Y: produc3658429121746597890et_nat > $o,Z: produc3925858234332021118et_nat] :
% 9.17/5.42 ( ( X
% 9.17/5.42 = ( produc2245416461498447860et_nat @ Y @ Z ) )
% 9.17/5.42 => ( ( produc5374455773327741254et_nat @ X )
% 9.17/5.42 = Z ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6510_sndI,axiom,
% 9.17/5.42 ! [X: produc2285326912895808259nt_int,Y: produc8551481072490612790e_term > option6357759511663192854e_term,Z: product_prod_int_int] :
% 9.17/5.42 ( ( X
% 9.17/5.42 = ( produc5700946648718959541nt_int @ Y @ Z ) )
% 9.17/5.42 => ( ( produc7328097813583171335nt_int @ X )
% 9.17/5.42 = Z ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6511_sndI,axiom,
% 9.17/5.42 ! [X: produc7773217078559923341nt_int,Y: int > option6357759511663192854e_term,Z: product_prod_int_int] :
% 9.17/5.42 ( ( X
% 9.17/5.42 = ( produc4305682042979456191nt_int @ Y @ Z ) )
% 9.17/5.42 => ( ( produc3162348030201620241nt_int @ X )
% 9.17/5.42 = Z ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6512_sndI,axiom,
% 9.17/5.42 ! [X: produc8923325533196201883nteger,Y: code_integer,Z: code_integer] :
% 9.17/5.42 ( ( X
% 9.17/5.42 = ( produc1086072967326762835nteger @ Y @ Z ) )
% 9.17/5.42 => ( ( produc6174133586879617921nteger @ X )
% 9.17/5.42 = Z ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6513_sndI,axiom,
% 9.17/5.42 ! [X: product_prod_int_int,Y: int,Z: int] :
% 9.17/5.42 ( ( X
% 9.17/5.42 = ( product_Pair_int_int @ Y @ Z ) )
% 9.17/5.42 => ( ( product_snd_int_int @ X )
% 9.17/5.42 = Z ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6514_sndI,axiom,
% 9.17/5.42 ! [X: produc5835291356934675326atural,Y: code_natural,Z: produc7822875418678951345atural] :
% 9.17/5.42 ( ( X
% 9.17/5.42 = ( produc6639722614265839536atural @ Y @ Z ) )
% 9.17/5.42 => ( ( produc6591912806276919810atural @ X )
% 9.17/5.42 = Z ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6515_sndE,axiom,
% 9.17/5.42 ! [X: produc1908205239877642774nteger,A: produc6241069584506657477e_term > option6357759511663192854e_term,B: produc8923325533196201883nteger,P: produc8923325533196201883nteger > $o] :
% 9.17/5.42 ( ( X
% 9.17/5.42 = ( produc8603105652947943368nteger @ A @ B ) )
% 9.17/5.42 => ( ( P @ ( produc7856867400915047194nteger @ X ) )
% 9.17/5.42 => ( P @ B ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6516_sndE,axiom,
% 9.17/5.42 ! [X: produc3925858234332021118et_nat,A: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat,P: produc3658429121746597890et_nat > $o] :
% 9.17/5.42 ( ( X
% 9.17/5.42 = ( produc5001842942810119800et_nat @ A @ B ) )
% 9.17/5.42 => ( ( P @ ( produc4011572625026189258et_nat @ X ) )
% 9.17/5.42 => ( P @ B ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6517_sndE,axiom,
% 9.17/5.42 ! [X: produc2732055786443039994et_nat,A: produc3658429121746597890et_nat > $o,B: produc3925858234332021118et_nat,P: produc3925858234332021118et_nat > $o] :
% 9.17/5.42 ( ( X
% 9.17/5.42 = ( produc2245416461498447860et_nat @ A @ B ) )
% 9.17/5.42 => ( ( P @ ( produc5374455773327741254et_nat @ X ) )
% 9.17/5.42 => ( P @ B ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6518_sndE,axiom,
% 9.17/5.42 ! [X: produc2285326912895808259nt_int,A: produc8551481072490612790e_term > option6357759511663192854e_term,B: product_prod_int_int,P: product_prod_int_int > $o] :
% 9.17/5.42 ( ( X
% 9.17/5.42 = ( produc5700946648718959541nt_int @ A @ B ) )
% 9.17/5.42 => ( ( P @ ( produc7328097813583171335nt_int @ X ) )
% 9.17/5.42 => ( P @ B ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6519_sndE,axiom,
% 9.17/5.42 ! [X: produc7773217078559923341nt_int,A: int > option6357759511663192854e_term,B: product_prod_int_int,P: product_prod_int_int > $o] :
% 9.17/5.42 ( ( X
% 9.17/5.42 = ( produc4305682042979456191nt_int @ A @ B ) )
% 9.17/5.42 => ( ( P @ ( produc3162348030201620241nt_int @ X ) )
% 9.17/5.42 => ( P @ B ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6520_sndE,axiom,
% 9.17/5.42 ! [X: produc8923325533196201883nteger,A: code_integer,B: code_integer,P: code_integer > $o] :
% 9.17/5.42 ( ( X
% 9.17/5.42 = ( produc1086072967326762835nteger @ A @ B ) )
% 9.17/5.42 => ( ( P @ ( produc6174133586879617921nteger @ X ) )
% 9.17/5.42 => ( P @ B ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6521_sndE,axiom,
% 9.17/5.42 ! [X: product_prod_int_int,A: int,B: int,P: int > $o] :
% 9.17/5.42 ( ( X
% 9.17/5.42 = ( product_Pair_int_int @ A @ B ) )
% 9.17/5.42 => ( ( P @ ( product_snd_int_int @ X ) )
% 9.17/5.42 => ( P @ B ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6522_sndE,axiom,
% 9.17/5.42 ! [X: produc5835291356934675326atural,A: code_natural,B: produc7822875418678951345atural,P: produc7822875418678951345atural > $o] :
% 9.17/5.42 ( ( X
% 9.17/5.42 = ( produc6639722614265839536atural @ A @ B ) )
% 9.17/5.42 => ( ( P @ ( produc6591912806276919810atural @ X ) )
% 9.17/5.42 => ( P @ B ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6523_snd__eqD,axiom,
% 9.17/5.42 ! [X: produc6241069584506657477e_term > option6357759511663192854e_term,Y: produc8923325533196201883nteger,A: produc8923325533196201883nteger] :
% 9.17/5.42 ( ( ( produc7856867400915047194nteger @ ( produc8603105652947943368nteger @ X @ Y ) )
% 9.17/5.42 = A )
% 9.17/5.42 => ( Y = A ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6524_snd__eqD,axiom,
% 9.17/5.42 ! [X: produc3658429121746597890et_nat > $o,Y: produc3658429121746597890et_nat,A: produc3658429121746597890et_nat] :
% 9.17/5.42 ( ( ( produc4011572625026189258et_nat @ ( produc5001842942810119800et_nat @ X @ Y ) )
% 9.17/5.42 = A )
% 9.17/5.42 => ( Y = A ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6525_snd__eqD,axiom,
% 9.17/5.42 ! [X: produc3658429121746597890et_nat > $o,Y: produc3925858234332021118et_nat,A: produc3925858234332021118et_nat] :
% 9.17/5.42 ( ( ( produc5374455773327741254et_nat @ ( produc2245416461498447860et_nat @ X @ Y ) )
% 9.17/5.42 = A )
% 9.17/5.42 => ( Y = A ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6526_snd__eqD,axiom,
% 9.17/5.42 ! [X: produc8551481072490612790e_term > option6357759511663192854e_term,Y: product_prod_int_int,A: product_prod_int_int] :
% 9.17/5.42 ( ( ( produc7328097813583171335nt_int @ ( produc5700946648718959541nt_int @ X @ Y ) )
% 9.17/5.42 = A )
% 9.17/5.42 => ( Y = A ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6527_snd__eqD,axiom,
% 9.17/5.42 ! [X: int > option6357759511663192854e_term,Y: product_prod_int_int,A: product_prod_int_int] :
% 9.17/5.42 ( ( ( produc3162348030201620241nt_int @ ( produc4305682042979456191nt_int @ X @ Y ) )
% 9.17/5.42 = A )
% 9.17/5.42 => ( Y = A ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6528_snd__eqD,axiom,
% 9.17/5.42 ! [X: code_integer,Y: code_integer,A: code_integer] :
% 9.17/5.42 ( ( ( produc6174133586879617921nteger @ ( produc1086072967326762835nteger @ X @ Y ) )
% 9.17/5.42 = A )
% 9.17/5.42 => ( Y = A ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6529_snd__eqD,axiom,
% 9.17/5.42 ! [X: int,Y: int,A: int] :
% 9.17/5.42 ( ( ( product_snd_int_int @ ( product_Pair_int_int @ X @ Y ) )
% 9.17/5.42 = A )
% 9.17/5.42 => ( Y = A ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6530_snd__eqD,axiom,
% 9.17/5.42 ! [X: code_natural,Y: produc7822875418678951345atural,A: produc7822875418678951345atural] :
% 9.17/5.42 ( ( ( produc6591912806276919810atural @ ( produc6639722614265839536atural @ X @ Y ) )
% 9.17/5.42 = A )
% 9.17/5.42 => ( Y = A ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6531_snd__conv,axiom,
% 9.17/5.42 ! [X1: produc6241069584506657477e_term > option6357759511663192854e_term,X2: produc8923325533196201883nteger] :
% 9.17/5.42 ( ( produc7856867400915047194nteger @ ( produc8603105652947943368nteger @ X1 @ X2 ) )
% 9.17/5.42 = X2 ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6532_snd__conv,axiom,
% 9.17/5.42 ! [X1: produc3658429121746597890et_nat > $o,X2: produc3658429121746597890et_nat] :
% 9.17/5.42 ( ( produc4011572625026189258et_nat @ ( produc5001842942810119800et_nat @ X1 @ X2 ) )
% 9.17/5.42 = X2 ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6533_snd__conv,axiom,
% 9.17/5.42 ! [X1: produc3658429121746597890et_nat > $o,X2: produc3925858234332021118et_nat] :
% 9.17/5.42 ( ( produc5374455773327741254et_nat @ ( produc2245416461498447860et_nat @ X1 @ X2 ) )
% 9.17/5.42 = X2 ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6534_snd__conv,axiom,
% 9.17/5.42 ! [X1: produc8551481072490612790e_term > option6357759511663192854e_term,X2: product_prod_int_int] :
% 9.17/5.42 ( ( produc7328097813583171335nt_int @ ( produc5700946648718959541nt_int @ X1 @ X2 ) )
% 9.17/5.42 = X2 ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6535_snd__conv,axiom,
% 9.17/5.42 ! [X1: int > option6357759511663192854e_term,X2: product_prod_int_int] :
% 9.17/5.42 ( ( produc3162348030201620241nt_int @ ( produc4305682042979456191nt_int @ X1 @ X2 ) )
% 9.17/5.42 = X2 ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6536_snd__conv,axiom,
% 9.17/5.42 ! [X1: code_integer,X2: code_integer] :
% 9.17/5.42 ( ( produc6174133586879617921nteger @ ( produc1086072967326762835nteger @ X1 @ X2 ) )
% 9.17/5.42 = X2 ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6537_snd__conv,axiom,
% 9.17/5.42 ! [X1: int,X2: int] :
% 9.17/5.42 ( ( product_snd_int_int @ ( product_Pair_int_int @ X1 @ X2 ) )
% 9.17/5.42 = X2 ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6538_snd__conv,axiom,
% 9.17/5.42 ! [X1: code_natural,X2: produc7822875418678951345atural] :
% 9.17/5.42 ( ( produc6591912806276919810atural @ ( produc6639722614265839536atural @ X1 @ X2 ) )
% 9.17/5.42 = X2 ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6539_Some__Inf,axiom,
% 9.17/5.42 ! [A2: set_set_nat] :
% 9.17/5.42 ( ( some_set_nat @ ( comple7806235888213564991et_nat @ A2 ) )
% 9.17/5.42 = ( comple3446467376476514063et_nat @ ( image_838307146230912995et_nat @ some_set_nat @ A2 ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6540_Some__Inf,axiom,
% 9.17/5.42 ! [A2: set_Product_unit] :
% 9.17/5.42 ( ( some_Product_unit @ ( comple2584293577114468500t_unit @ A2 ) )
% 9.17/5.42 = ( comple5564859526659248602t_unit @ ( image_7094380055901048587t_unit @ some_Product_unit @ A2 ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6541_fstI,axiom,
% 9.17/5.42 ! [X: produc1908205239877642774nteger,Y: produc6241069584506657477e_term > option6357759511663192854e_term,Z: produc8923325533196201883nteger] :
% 9.17/5.42 ( ( X
% 9.17/5.42 = ( produc8603105652947943368nteger @ Y @ Z ) )
% 9.17/5.42 => ( ( produc7822682618958472924nteger @ X )
% 9.17/5.42 = Y ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6542_fstI,axiom,
% 9.17/5.42 ! [X: produc3925858234332021118et_nat,Y: produc3658429121746597890et_nat > $o,Z: produc3658429121746597890et_nat] :
% 9.17/5.42 ( ( X
% 9.17/5.42 = ( produc5001842942810119800et_nat @ Y @ Z ) )
% 9.17/5.42 => ( ( produc995936583742144908et_nat @ X )
% 9.17/5.42 = Y ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6543_fstI,axiom,
% 9.17/5.42 ! [X: produc2732055786443039994et_nat,Y: produc3658429121746597890et_nat > $o,Z: produc3925858234332021118et_nat] :
% 9.17/5.42 ( ( X
% 9.17/5.42 = ( produc2245416461498447860et_nat @ Y @ Z ) )
% 9.17/5.42 => ( ( produc180342877477747464et_nat @ X )
% 9.17/5.42 = Y ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6544_fstI,axiom,
% 9.17/5.42 ! [X: produc2285326912895808259nt_int,Y: produc8551481072490612790e_term > option6357759511663192854e_term,Z: product_prod_int_int] :
% 9.17/5.42 ( ( X
% 9.17/5.42 = ( produc5700946648718959541nt_int @ Y @ Z ) )
% 9.17/5.42 => ( ( produc6816164490631068361nt_int @ X )
% 9.17/5.42 = Y ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6545_fstI,axiom,
% 9.17/5.42 ! [X: produc7773217078559923341nt_int,Y: int > option6357759511663192854e_term,Z: product_prod_int_int] :
% 9.17/5.42 ( ( X
% 9.17/5.42 = ( produc4305682042979456191nt_int @ Y @ Z ) )
% 9.17/5.42 => ( ( produc6230002227079971283nt_int @ X )
% 9.17/5.42 = Y ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6546_fstI,axiom,
% 9.17/5.42 ! [X: produc8923325533196201883nteger,Y: code_integer,Z: code_integer] :
% 9.17/5.42 ( ( X
% 9.17/5.42 = ( produc1086072967326762835nteger @ Y @ Z ) )
% 9.17/5.42 => ( ( produc8508995932063986495nteger @ X )
% 9.17/5.42 = Y ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6547_fstI,axiom,
% 9.17/5.42 ! [X: product_prod_int_int,Y: int,Z: int] :
% 9.17/5.42 ( ( X
% 9.17/5.42 = ( product_Pair_int_int @ Y @ Z ) )
% 9.17/5.42 => ( ( product_fst_int_int @ X )
% 9.17/5.42 = Y ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6548_fstE,axiom,
% 9.17/5.42 ! [X: produc1908205239877642774nteger,A: produc6241069584506657477e_term > option6357759511663192854e_term,B: produc8923325533196201883nteger,P: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > $o] :
% 9.17/5.42 ( ( X
% 9.17/5.42 = ( produc8603105652947943368nteger @ A @ B ) )
% 9.17/5.42 => ( ( P @ ( produc7822682618958472924nteger @ X ) )
% 9.17/5.42 => ( P @ A ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6549_fstE,axiom,
% 9.17/5.42 ! [X: produc3925858234332021118et_nat,A: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat,P: ( produc3658429121746597890et_nat > $o ) > $o] :
% 9.17/5.42 ( ( X
% 9.17/5.42 = ( produc5001842942810119800et_nat @ A @ B ) )
% 9.17/5.42 => ( ( P @ ( produc995936583742144908et_nat @ X ) )
% 9.17/5.42 => ( P @ A ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6550_fstE,axiom,
% 9.17/5.42 ! [X: produc2732055786443039994et_nat,A: produc3658429121746597890et_nat > $o,B: produc3925858234332021118et_nat,P: ( produc3658429121746597890et_nat > $o ) > $o] :
% 9.17/5.42 ( ( X
% 9.17/5.42 = ( produc2245416461498447860et_nat @ A @ B ) )
% 9.17/5.42 => ( ( P @ ( produc180342877477747464et_nat @ X ) )
% 9.17/5.42 => ( P @ A ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6551_fstE,axiom,
% 9.17/5.42 ! [X: produc2285326912895808259nt_int,A: produc8551481072490612790e_term > option6357759511663192854e_term,B: product_prod_int_int,P: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > $o] :
% 9.17/5.42 ( ( X
% 9.17/5.42 = ( produc5700946648718959541nt_int @ A @ B ) )
% 9.17/5.42 => ( ( P @ ( produc6816164490631068361nt_int @ X ) )
% 9.17/5.42 => ( P @ A ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6552_fstE,axiom,
% 9.17/5.42 ! [X: produc7773217078559923341nt_int,A: int > option6357759511663192854e_term,B: product_prod_int_int,P: ( int > option6357759511663192854e_term ) > $o] :
% 9.17/5.42 ( ( X
% 9.17/5.42 = ( produc4305682042979456191nt_int @ A @ B ) )
% 9.17/5.42 => ( ( P @ ( produc6230002227079971283nt_int @ X ) )
% 9.17/5.42 => ( P @ A ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6553_fstE,axiom,
% 9.17/5.42 ! [X: produc8923325533196201883nteger,A: code_integer,B: code_integer,P: code_integer > $o] :
% 9.17/5.42 ( ( X
% 9.17/5.42 = ( produc1086072967326762835nteger @ A @ B ) )
% 9.17/5.42 => ( ( P @ ( produc8508995932063986495nteger @ X ) )
% 9.17/5.42 => ( P @ A ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6554_fstE,axiom,
% 9.17/5.42 ! [X: product_prod_int_int,A: int,B: int,P: int > $o] :
% 9.17/5.42 ( ( X
% 9.17/5.42 = ( product_Pair_int_int @ A @ B ) )
% 9.17/5.42 => ( ( P @ ( product_fst_int_int @ X ) )
% 9.17/5.42 => ( P @ A ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6555_fst__eqD,axiom,
% 9.17/5.42 ! [X: produc6241069584506657477e_term > option6357759511663192854e_term,Y: produc8923325533196201883nteger,A: produc6241069584506657477e_term > option6357759511663192854e_term] :
% 9.17/5.42 ( ( ( produc7822682618958472924nteger @ ( produc8603105652947943368nteger @ X @ Y ) )
% 9.17/5.42 = A )
% 9.17/5.42 => ( X = A ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6556_fst__eqD,axiom,
% 9.17/5.42 ! [X: produc3658429121746597890et_nat > $o,Y: produc3658429121746597890et_nat,A: produc3658429121746597890et_nat > $o] :
% 9.17/5.42 ( ( ( produc995936583742144908et_nat @ ( produc5001842942810119800et_nat @ X @ Y ) )
% 9.17/5.42 = A )
% 9.17/5.42 => ( X = A ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6557_fst__eqD,axiom,
% 9.17/5.42 ! [X: produc3658429121746597890et_nat > $o,Y: produc3925858234332021118et_nat,A: produc3658429121746597890et_nat > $o] :
% 9.17/5.42 ( ( ( produc180342877477747464et_nat @ ( produc2245416461498447860et_nat @ X @ Y ) )
% 9.17/5.42 = A )
% 9.17/5.42 => ( X = A ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6558_fst__eqD,axiom,
% 9.17/5.42 ! [X: produc8551481072490612790e_term > option6357759511663192854e_term,Y: product_prod_int_int,A: produc8551481072490612790e_term > option6357759511663192854e_term] :
% 9.17/5.42 ( ( ( produc6816164490631068361nt_int @ ( produc5700946648718959541nt_int @ X @ Y ) )
% 9.17/5.42 = A )
% 9.17/5.42 => ( X = A ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6559_fst__eqD,axiom,
% 9.17/5.42 ! [X: int > option6357759511663192854e_term,Y: product_prod_int_int,A: int > option6357759511663192854e_term] :
% 9.17/5.42 ( ( ( produc6230002227079971283nt_int @ ( produc4305682042979456191nt_int @ X @ Y ) )
% 9.17/5.42 = A )
% 9.17/5.42 => ( X = A ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6560_fst__eqD,axiom,
% 9.17/5.42 ! [X: code_integer,Y: code_integer,A: code_integer] :
% 9.17/5.42 ( ( ( produc8508995932063986495nteger @ ( produc1086072967326762835nteger @ X @ Y ) )
% 9.17/5.42 = A )
% 9.17/5.42 => ( X = A ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6561_fst__eqD,axiom,
% 9.17/5.42 ! [X: int,Y: int,A: int] :
% 9.17/5.42 ( ( ( product_fst_int_int @ ( product_Pair_int_int @ X @ Y ) )
% 9.17/5.42 = A )
% 9.17/5.42 => ( X = A ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6562_fst__conv,axiom,
% 9.17/5.42 ! [X1: produc6241069584506657477e_term > option6357759511663192854e_term,X2: produc8923325533196201883nteger] :
% 9.17/5.42 ( ( produc7822682618958472924nteger @ ( produc8603105652947943368nteger @ X1 @ X2 ) )
% 9.17/5.42 = X1 ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6563_fst__conv,axiom,
% 9.17/5.42 ! [X1: produc3658429121746597890et_nat > $o,X2: produc3658429121746597890et_nat] :
% 9.17/5.42 ( ( produc995936583742144908et_nat @ ( produc5001842942810119800et_nat @ X1 @ X2 ) )
% 9.17/5.42 = X1 ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6564_fst__conv,axiom,
% 9.17/5.42 ! [X1: produc3658429121746597890et_nat > $o,X2: produc3925858234332021118et_nat] :
% 9.17/5.42 ( ( produc180342877477747464et_nat @ ( produc2245416461498447860et_nat @ X1 @ X2 ) )
% 9.17/5.42 = X1 ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6565_fst__conv,axiom,
% 9.17/5.42 ! [X1: produc8551481072490612790e_term > option6357759511663192854e_term,X2: product_prod_int_int] :
% 9.17/5.42 ( ( produc6816164490631068361nt_int @ ( produc5700946648718959541nt_int @ X1 @ X2 ) )
% 9.17/5.42 = X1 ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6566_fst__conv,axiom,
% 9.17/5.42 ! [X1: int > option6357759511663192854e_term,X2: product_prod_int_int] :
% 9.17/5.42 ( ( produc6230002227079971283nt_int @ ( produc4305682042979456191nt_int @ X1 @ X2 ) )
% 9.17/5.42 = X1 ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6567_fst__conv,axiom,
% 9.17/5.42 ! [X1: code_integer,X2: code_integer] :
% 9.17/5.42 ( ( produc8508995932063986495nteger @ ( produc1086072967326762835nteger @ X1 @ X2 ) )
% 9.17/5.42 = X1 ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6568_fst__conv,axiom,
% 9.17/5.42 ! [X1: int,X2: int] :
% 9.17/5.42 ( ( product_fst_int_int @ ( product_Pair_int_int @ X1 @ X2 ) )
% 9.17/5.42 = X1 ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6569_snd__fst__flip,axiom,
% 9.17/5.42 ( produc1152141638515386128e_term
% 9.17/5.42 = ( comp_P8650103696410638905e_term @ produc7822682618958472924nteger
% 9.17/5.42 @ ( produc5068368601420144385nteger
% 9.17/5.42 @ ^ [X3: produc8923325533196201883nteger,Y3: produc6241069584506657477e_term > option6357759511663192854e_term] : ( produc8603105652947943368nteger @ Y3 @ X3 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6570_snd__fst__flip,axiom,
% 9.17/5.42 ( produc1838968430882301508_nat_o
% 9.17/5.42 = ( comp_P1110778729668777324_nat_o @ produc995936583742144908et_nat
% 9.17/5.42 @ ( produc5206072795621629085et_nat
% 9.17/5.42 @ ^ [X3: produc3658429121746597890et_nat,Y3: produc3658429121746597890et_nat > $o] : ( produc5001842942810119800et_nat @ Y3 @ X3 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6571_snd__fst__flip,axiom,
% 9.17/5.42 ( produc6803565743942592456_nat_o
% 9.17/5.42 = ( comp_P4355506512671352436_nat_o @ produc180342877477747464et_nat
% 9.17/5.42 @ ( produc9203276081649983901et_nat
% 9.17/5.42 @ ^ [X3: produc3925858234332021118et_nat,Y3: produc3658429121746597890et_nat > $o] : ( produc2245416461498447860et_nat @ Y3 @ X3 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6572_snd__fst__flip,axiom,
% 9.17/5.42 ( produc6847057335086834975e_term
% 9.17/5.42 = ( comp_P8577347034251779110e_term @ produc6816164490631068361nt_int
% 9.17/5.42 @ ( produc199769199162113789nt_int
% 9.17/5.42 @ ^ [X3: product_prod_int_int,Y3: produc8551481072490612790e_term > option6357759511663192854e_term] : ( produc5700946648718959541nt_int @ Y3 @ X3 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6573_snd__fst__flip,axiom,
% 9.17/5.42 ( produc6373639247523685013e_term
% 9.17/5.42 = ( comp_P1875353012086385820e_term @ produc6230002227079971283nt_int
% 9.17/5.42 @ ( produc3478612561300218621nt_int
% 9.17/5.42 @ ^ [X3: product_prod_int_int,Y3: int > option6357759511663192854e_term] : ( produc4305682042979456191nt_int @ Y3 @ X3 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6574_snd__fst__flip,axiom,
% 9.17/5.42 ( produc6174133586879617921nteger
% 9.17/5.42 = ( comp_P3428181540658402820nteger @ produc8508995932063986495nteger
% 9.17/5.42 @ ( produc6916734918728496179nteger
% 9.17/5.42 @ ^ [X3: code_integer,Y3: code_integer] : ( produc1086072967326762835nteger @ Y3 @ X3 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6575_snd__fst__flip,axiom,
% 9.17/5.42 ( produc6591912806276919810atural
% 9.17/5.42 = ( comp_P3887058762840424708atural @ produc4353917038236142998atural
% 9.17/5.42 @ ( produc6785097126449100389atural
% 9.17/5.42 @ ^ [X3: code_natural,Y3: produc7822875418678951345atural] : ( produc1272419604612767874atural @ Y3 @ X3 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6576_snd__fst__flip,axiom,
% 9.17/5.42 ( product_snd_int_int
% 9.17/5.42 = ( comp_P5356232565778667509nt_int @ product_fst_int_int
% 9.17/5.42 @ ( produc4245557441103728435nt_int
% 9.17/5.42 @ ^ [X3: int,Y3: int] : ( product_Pair_int_int @ Y3 @ X3 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6577_fst__snd__flip,axiom,
% 9.17/5.42 ( produc1117956856558811858e_term
% 9.17/5.42 = ( comp_P1663382703091044646e_term @ produc7856867400915047194nteger
% 9.17/5.42 @ ( produc5068368601420144385nteger
% 9.17/5.42 @ ^ [X3: produc8923325533196201883nteger,Y3: produc6241069584506657477e_term > option6357759511663192854e_term] : ( produc8603105652947943368nteger @ Y3 @ X3 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6578_fst__snd__flip,axiom,
% 9.17/5.42 ( produc8046704426453032966_nat_o
% 9.17/5.42 = ( comp_P5089495125153697957_nat_o @ produc4011572625026189258et_nat
% 9.17/5.42 @ ( produc5206072795621629085et_nat
% 9.17/5.42 @ ^ [X3: produc3658429121746597890et_nat,Y3: produc3658429121746597890et_nat > $o] : ( produc5001842942810119800et_nat @ Y3 @ X3 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6579_fst__snd__flip,axiom,
% 9.17/5.42 ( produc1609452848092598666_nat_o
% 9.17/5.42 = ( comp_P9183373265949749025_nat_o @ produc5374455773327741254et_nat
% 9.17/5.42 @ ( produc9203276081649983901et_nat
% 9.17/5.42 @ ^ [X3: produc3925858234332021118et_nat,Y3: produc3658429121746597890et_nat > $o] : ( produc2245416461498447860et_nat @ Y3 @ X3 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6580_fst__snd__flip,axiom,
% 9.17/5.42 ( produc6335124012134732001e_term
% 9.17/5.42 = ( comp_P4057098934159210662e_term @ produc7328097813583171335nt_int
% 9.17/5.42 @ ( produc199769199162113789nt_int
% 9.17/5.42 @ ^ [X3: product_prod_int_int,Y3: produc8551481072490612790e_term > option6357759511663192854e_term] : ( produc5700946648718959541nt_int @ Y3 @ X3 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6581_fst__snd__flip,axiom,
% 9.17/5.42 ( produc217921407547260247e_term
% 9.17/5.42 = ( comp_P5363713469694551954e_term @ produc3162348030201620241nt_int
% 9.17/5.42 @ ( produc3478612561300218621nt_int
% 9.17/5.42 @ ^ [X3: product_prod_int_int,Y3: int > option6357759511663192854e_term] : ( produc4305682042979456191nt_int @ Y3 @ X3 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6582_fst__snd__flip,axiom,
% 9.17/5.42 ( produc8508995932063986495nteger
% 9.17/5.42 = ( comp_P3428181540658402820nteger @ produc6174133586879617921nteger
% 9.17/5.42 @ ( produc6916734918728496179nteger
% 9.17/5.42 @ ^ [X3: code_integer,Y3: code_integer] : ( produc1086072967326762835nteger @ Y3 @ X3 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6583_fst__snd__flip,axiom,
% 9.17/5.42 ( produc4353917038236142998atural
% 9.17/5.42 = ( comp_P5756991293874479000atural @ produc6591912806276919810atural
% 9.17/5.42 @ ( produc1198152457851389869atural
% 9.17/5.42 @ ^ [X3: produc7822875418678951345atural,Y3: code_natural] : ( produc6639722614265839536atural @ Y3 @ X3 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6584_fst__snd__flip,axiom,
% 9.17/5.42 ( product_fst_int_int
% 9.17/5.42 = ( comp_P5356232565778667509nt_int @ product_snd_int_int
% 9.17/5.42 @ ( produc4245557441103728435nt_int
% 9.17/5.42 @ ^ [X3: int,Y3: int] : ( product_Pair_int_int @ Y3 @ X3 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6585_finite__UNION__then__finite,axiom,
% 9.17/5.42 ! [B5: $o > set_int,A2: set_o,A: $o] :
% 9.17/5.42 ( ( finite_finite_int @ ( comple3221217463730067765et_int @ ( image_o_set_int @ B5 @ A2 ) ) )
% 9.17/5.42 => ( ( member_o @ A @ A2 )
% 9.17/5.42 => ( finite_finite_int @ ( B5 @ A ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6586_finite__UNION__then__finite,axiom,
% 9.17/5.42 ! [B5: nat > set_int,A2: set_nat,A: nat] :
% 9.17/5.42 ( ( finite_finite_int @ ( comple3221217463730067765et_int @ ( image_nat_set_int @ B5 @ A2 ) ) )
% 9.17/5.42 => ( ( member_nat @ A @ A2 )
% 9.17/5.42 => ( finite_finite_int @ ( B5 @ A ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6587_finite__UNION__then__finite,axiom,
% 9.17/5.42 ! [B5: int > set_int,A2: set_int,A: int] :
% 9.17/5.42 ( ( finite_finite_int @ ( comple3221217463730067765et_int @ ( image_int_set_int @ B5 @ A2 ) ) )
% 9.17/5.42 => ( ( member_int @ A @ A2 )
% 9.17/5.42 => ( finite_finite_int @ ( B5 @ A ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6588_finite__UNION__then__finite,axiom,
% 9.17/5.42 ! [B5: $o > set_Code_integer,A2: set_o,A: $o] :
% 9.17/5.42 ( ( finite6017078050557962740nteger @ ( comple739944243200306918nteger @ ( image_6491638074533506790nteger @ B5 @ A2 ) ) )
% 9.17/5.42 => ( ( member_o @ A @ A2 )
% 9.17/5.42 => ( finite6017078050557962740nteger @ ( B5 @ A ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6589_finite__UNION__then__finite,axiom,
% 9.17/5.42 ! [B5: nat > set_Code_integer,A2: set_nat,A: nat] :
% 9.17/5.42 ( ( finite6017078050557962740nteger @ ( comple739944243200306918nteger @ ( image_2385391725447763818nteger @ B5 @ A2 ) ) )
% 9.17/5.42 => ( ( member_nat @ A @ A2 )
% 9.17/5.42 => ( finite6017078050557962740nteger @ ( B5 @ A ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6590_finite__UNION__then__finite,axiom,
% 9.17/5.42 ! [B5: int > set_Code_integer,A2: set_int,A: int] :
% 9.17/5.42 ( ( finite6017078050557962740nteger @ ( comple739944243200306918nteger @ ( image_75573793354812870nteger @ B5 @ A2 ) ) )
% 9.17/5.42 => ( ( member_int @ A @ A2 )
% 9.17/5.42 => ( finite6017078050557962740nteger @ ( B5 @ A ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6591_finite__UNION__then__finite,axiom,
% 9.17/5.42 ! [B5: $o > set_nat,A2: set_o,A: $o] :
% 9.17/5.42 ( ( finite_finite_nat @ ( comple7399068483239264473et_nat @ ( image_o_set_nat @ B5 @ A2 ) ) )
% 9.17/5.42 => ( ( member_o @ A @ A2 )
% 9.17/5.42 => ( finite_finite_nat @ ( B5 @ A ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6592_finite__UNION__then__finite,axiom,
% 9.17/5.42 ! [B5: nat > set_nat,A2: set_nat,A: nat] :
% 9.17/5.42 ( ( finite_finite_nat @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ B5 @ A2 ) ) )
% 9.17/5.42 => ( ( member_nat @ A @ A2 )
% 9.17/5.42 => ( finite_finite_nat @ ( B5 @ A ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6593_finite__UNION__then__finite,axiom,
% 9.17/5.42 ! [B5: int > set_nat,A2: set_int,A: int] :
% 9.17/5.42 ( ( finite_finite_nat @ ( comple7399068483239264473et_nat @ ( image_int_set_nat @ B5 @ A2 ) ) )
% 9.17/5.42 => ( ( member_int @ A @ A2 )
% 9.17/5.42 => ( finite_finite_nat @ ( B5 @ A ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6594_finite__UNION__then__finite,axiom,
% 9.17/5.42 ! [B5: product_prod_nat_nat > set_int,A2: set_Pr1261947904930325089at_nat,A: product_prod_nat_nat] :
% 9.17/5.42 ( ( finite_finite_int @ ( comple3221217463730067765et_int @ ( image_5061345727057949854et_int @ B5 @ A2 ) ) )
% 9.17/5.42 => ( ( member8440522571783428010at_nat @ A @ A2 )
% 9.17/5.42 => ( finite_finite_int @ ( B5 @ A ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6595_case__prod__comp,axiom,
% 9.17/5.42 ! [F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer,X: produc3346328345660746739nteger] :
% 9.17/5.42 ( ( produc4281629032016041417nteger @ ( comp_C1593894019821074884nteger @ F @ G ) @ X )
% 9.17/5.42 = ( F @ ( G @ ( produc1861665112190112313nteger @ X ) ) @ ( produc7955729907432593271nteger @ X ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6596_case__prod__comp,axiom,
% 9.17/5.42 ! [F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer > code_integer,X: produc3346328345660746739nteger] :
% 9.17/5.42 ( ( produc4281629032016041417nteger @ ( comp_C8797469213163452608nteger @ F @ G ) @ X )
% 9.17/5.42 = ( F @ ( G @ ( produc1861665112190112313nteger @ X ) ) @ ( produc7955729907432593271nteger @ X ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6597_fn__snd__conv,axiom,
% 9.17/5.42 ! [F: nat > nat] :
% 9.17/5.42 ( ( ^ [X3: product_prod_nat_nat] : ( F @ ( product_snd_nat_nat @ X3 ) ) )
% 9.17/5.42 = ( produc6842872674320459806at_nat
% 9.17/5.42 @ ^ [Uu: nat] : F ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6598_fn__snd__conv,axiom,
% 9.17/5.42 ! [F: nat > product_prod_nat_nat > product_prod_nat_nat] :
% 9.17/5.42 ( ( ^ [X3: product_prod_nat_nat] : ( F @ ( product_snd_nat_nat @ X3 ) ) )
% 9.17/5.42 = ( produc27273713700761075at_nat
% 9.17/5.42 @ ^ [Uu: nat] : F ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6599_fn__snd__conv,axiom,
% 9.17/5.42 ! [F: nat > product_prod_nat_nat > $o] :
% 9.17/5.42 ( ( ^ [X3: product_prod_nat_nat] : ( F @ ( product_snd_nat_nat @ X3 ) ) )
% 9.17/5.42 = ( produc8739625826339149834_nat_o
% 9.17/5.42 @ ^ [Uu: nat] : F ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6600_fn__snd__conv,axiom,
% 9.17/5.42 ! [F: int > product_prod_int_int] :
% 9.17/5.42 ( ( ^ [X3: product_prod_int_int] : ( F @ ( product_snd_int_int @ X3 ) ) )
% 9.17/5.42 = ( produc4245557441103728435nt_int
% 9.17/5.42 @ ^ [Uu: int] : F ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6601_fn__snd__conv,axiom,
% 9.17/5.42 ! [F: int > int] :
% 9.17/5.42 ( ( ^ [X3: product_prod_int_int] : ( F @ ( product_snd_int_int @ X3 ) ) )
% 9.17/5.42 = ( produc8211389475949308722nt_int
% 9.17/5.42 @ ^ [Uu: int] : F ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6602_snd__def,axiom,
% 9.17/5.42 ( produc6174133586879617921nteger
% 9.17/5.42 = ( produc7469247390737344965nteger
% 9.17/5.42 @ ^ [X12: code_integer,X23: code_integer] : X23 ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6603_snd__def,axiom,
% 9.17/5.42 ( produc6591912806276919810atural
% 9.17/5.42 = ( produc6302656368764539796atural
% 9.17/5.42 @ ^ [X12: code_natural,X23: produc7822875418678951345atural] : X23 ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6604_snd__def,axiom,
% 9.17/5.42 ( product_snd_nat_nat
% 9.17/5.42 = ( produc6842872674320459806at_nat
% 9.17/5.42 @ ^ [X12: nat,X23: nat] : X23 ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6605_snd__def,axiom,
% 9.17/5.42 ( product_snd_int_int
% 9.17/5.42 = ( produc8211389475949308722nt_int
% 9.17/5.42 @ ^ [X12: int,X23: int] : X23 ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6606_fn__fst__conv,axiom,
% 9.17/5.42 ! [F: nat > nat] :
% 9.17/5.42 ( ( ^ [X3: product_prod_nat_nat] : ( F @ ( product_fst_nat_nat @ X3 ) ) )
% 9.17/5.42 = ( produc6842872674320459806at_nat
% 9.17/5.42 @ ^ [A5: nat,Uu: nat] : ( F @ A5 ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6607_fn__fst__conv,axiom,
% 9.17/5.42 ! [F: nat > product_prod_nat_nat > product_prod_nat_nat] :
% 9.17/5.42 ( ( ^ [X3: product_prod_nat_nat] : ( F @ ( product_fst_nat_nat @ X3 ) ) )
% 9.17/5.42 = ( produc27273713700761075at_nat
% 9.17/5.42 @ ^ [A5: nat,Uu: nat] : ( F @ A5 ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6608_fn__fst__conv,axiom,
% 9.17/5.42 ! [F: nat > product_prod_nat_nat > $o] :
% 9.17/5.42 ( ( ^ [X3: product_prod_nat_nat] : ( F @ ( product_fst_nat_nat @ X3 ) ) )
% 9.17/5.42 = ( produc8739625826339149834_nat_o
% 9.17/5.42 @ ^ [A5: nat,Uu: nat] : ( F @ A5 ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6609_fn__fst__conv,axiom,
% 9.17/5.42 ! [F: int > product_prod_int_int] :
% 9.17/5.42 ( ( ^ [X3: product_prod_int_int] : ( F @ ( product_fst_int_int @ X3 ) ) )
% 9.17/5.42 = ( produc4245557441103728435nt_int
% 9.17/5.42 @ ^ [A5: int,Uu: int] : ( F @ A5 ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6610_fn__fst__conv,axiom,
% 9.17/5.42 ! [F: int > int] :
% 9.17/5.42 ( ( ^ [X3: product_prod_int_int] : ( F @ ( product_fst_int_int @ X3 ) ) )
% 9.17/5.42 = ( produc8211389475949308722nt_int
% 9.17/5.42 @ ^ [A5: int,Uu: int] : ( F @ A5 ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6611_fst__def,axiom,
% 9.17/5.42 ( produc8508995932063986495nteger
% 9.17/5.42 = ( produc7469247390737344965nteger
% 9.17/5.42 @ ^ [X12: code_integer,X23: code_integer] : X12 ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6612_fst__def,axiom,
% 9.17/5.42 ( product_fst_nat_nat
% 9.17/5.42 = ( produc6842872674320459806at_nat
% 9.17/5.42 @ ^ [X12: nat,X23: nat] : X12 ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6613_fst__def,axiom,
% 9.17/5.42 ( product_fst_int_int
% 9.17/5.42 = ( produc8211389475949308722nt_int
% 9.17/5.42 @ ^ [X12: int,X23: int] : X12 ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6614_Collect__split__mono__strong,axiom,
% 9.17/5.42 ! [X11: set_Code_integer,A2: set_Pr4811707699266497531nteger,Y9: set_Code_integer,P: code_integer > code_integer > $o,Q: code_integer > code_integer > $o] :
% 9.17/5.42 ( ( X11
% 9.17/5.42 = ( image_6316824473203919795nteger @ produc8508995932063986495nteger @ A2 ) )
% 9.17/5.42 => ( ( Y9
% 9.17/5.42 = ( image_6316824473203919795nteger @ produc6174133586879617921nteger @ A2 ) )
% 9.17/5.42 => ( ! [X4: code_integer] :
% 9.17/5.42 ( ( member_Code_integer @ X4 @ X11 )
% 9.17/5.42 => ! [Xa3: code_integer] :
% 9.17/5.42 ( ( member_Code_integer @ Xa3 @ Y9 )
% 9.17/5.42 => ( ( P @ X4 @ Xa3 )
% 9.17/5.42 => ( Q @ X4 @ Xa3 ) ) ) )
% 9.17/5.42 => ( ( ord_le3725938330318615451nteger @ A2 @ ( collec7766031446232907142nteger @ ( produc2066375834425727024eger_o @ P ) ) )
% 9.17/5.42 => ( ord_le3725938330318615451nteger @ A2 @ ( collec7766031446232907142nteger @ ( produc2066375834425727024eger_o @ Q ) ) ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6615_Collect__split__mono__strong,axiom,
% 9.17/5.42 ! [X11: set_int,A2: set_Pr958786334691620121nt_int,Y9: set_int,P: int > int > $o,Q: int > int > $o] :
% 9.17/5.42 ( ( X11
% 9.17/5.42 = ( image_5042161079198086560nt_int @ product_fst_int_int @ A2 ) )
% 9.17/5.42 => ( ( Y9
% 9.17/5.42 = ( image_5042161079198086560nt_int @ product_snd_int_int @ A2 ) )
% 9.17/5.42 => ( ! [X4: int] :
% 9.17/5.42 ( ( member_int @ X4 @ X11 )
% 9.17/5.42 => ! [Xa3: int] :
% 9.17/5.42 ( ( member_int @ Xa3 @ Y9 )
% 9.17/5.42 => ( ( P @ X4 @ Xa3 )
% 9.17/5.42 => ( Q @ X4 @ Xa3 ) ) ) )
% 9.17/5.42 => ( ( ord_le2843351958646193337nt_int @ A2 @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ P ) ) )
% 9.17/5.42 => ( ord_le2843351958646193337nt_int @ A2 @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ Q ) ) ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6616_Collect__split__mono__strong,axiom,
% 9.17/5.42 ! [X11: set_Code_natural,A2: set_Pr2352657477744078772atural,Y9: set_Pr7564037697178849041atural,P: code_natural > produc7822875418678951345atural > $o,Q: code_natural > produc7822875418678951345atural > $o] :
% 9.17/5.42 ( ( X11
% 9.17/5.42 = ( image_8194678751871465133atural @ produc497848011034438852atural @ A2 ) )
% 9.17/5.42 => ( ( Y9
% 9.17/5.42 = ( image_3837677093542026988atural @ produc6591912806276919810atural @ A2 ) )
% 9.17/5.42 => ( ! [X4: code_natural] :
% 9.17/5.42 ( ( member_Code_natural @ X4 @ X11 )
% 9.17/5.42 => ! [Xa3: produc7822875418678951345atural] :
% 9.17/5.42 ( ( member8280416476884352090atural @ Xa3 @ Y9 )
% 9.17/5.42 => ( ( P @ X4 @ Xa3 )
% 9.17/5.42 => ( Q @ X4 @ Xa3 ) ) ) )
% 9.17/5.42 => ( ( ord_le2202040463148982292atural @ A2 @ ( collec1991479681304692691atural @ ( produc7358226366420480123ural_o @ P ) ) )
% 9.17/5.42 => ( ord_le2202040463148982292atural @ A2 @ ( collec1991479681304692691atural @ ( produc7358226366420480123ural_o @ Q ) ) ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6617_Some__Sup,axiom,
% 9.17/5.42 ! [A2: set_o] :
% 9.17/5.42 ( ( A2 != bot_bot_set_o )
% 9.17/5.42 => ( ( some_o @ ( complete_Sup_Sup_o @ A2 ) )
% 9.17/5.42 = ( comple4490649148004324043tion_o @ ( image_o_option_o @ some_o @ A2 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6618_Some__Sup,axiom,
% 9.17/5.42 ! [A2: set_set_nat] :
% 9.17/5.42 ( ( A2 != bot_bot_set_set_nat )
% 9.17/5.42 => ( ( some_set_nat @ ( comple7399068483239264473et_nat @ A2 ) )
% 9.17/5.42 = ( comple8455683388168444585et_nat @ ( image_838307146230912995et_nat @ some_set_nat @ A2 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6619_Some__Sup,axiom,
% 9.17/5.42 ! [A2: set_Product_unit] :
% 9.17/5.42 ( ( A2 != bot_bo3957492148770167129t_unit )
% 9.17/5.42 => ( ( some_Product_unit @ ( comple4687483117567863418t_unit @ A2 ) )
% 9.17/5.42 = ( comple7481738165189995200t_unit @ ( image_7094380055901048587t_unit @ some_Product_unit @ A2 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6620_Inf__option__def,axiom,
% 9.17/5.42 ( comple3446467376476514063et_nat
% 9.17/5.42 = ( ^ [A7: set_option_set_nat] : ( if_option_set_nat @ ( member8989860449721436141et_nat @ none_set_nat @ A7 ) @ none_set_nat @ ( some_set_nat @ ( comple7806235888213564991et_nat @ ( these_set_nat @ A7 ) ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6621_Inf__option__def,axiom,
% 9.17/5.42 ( comple5564859526659248602t_unit
% 9.17/5.42 = ( ^ [A7: set_op3165557761946182707t_unit] : ( if_opt6227717841141446553t_unit @ ( member1378114217278917244t_unit @ none_Product_unit @ A7 ) @ none_Product_unit @ ( some_Product_unit @ ( comple2584293577114468500t_unit @ ( these_Product_unit @ A7 ) ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6622_Some__INF,axiom,
% 9.17/5.42 ! [F: nat > set_nat,A2: set_nat] :
% 9.17/5.42 ( ( some_set_nat @ ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ F @ A2 ) ) )
% 9.17/5.42 = ( comple3446467376476514063et_nat
% 9.17/5.42 @ ( image_1085372205585808685et_nat
% 9.17/5.42 @ ^ [X3: nat] : ( some_set_nat @ ( F @ X3 ) )
% 9.17/5.42 @ A2 ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6623_INF__image,axiom,
% 9.17/5.42 ! [G: code_integer > nat,F: nat > code_integer,A2: set_nat] :
% 9.17/5.42 ( ( complete_Inf_Inf_nat @ ( image_951025933927791156er_nat @ G @ ( image_1215581382706833972nteger @ F @ A2 ) ) )
% 9.17/5.42 = ( complete_Inf_Inf_nat @ ( image_nat_nat @ ( comp_C4049556595663050210at_nat @ G @ F ) @ A2 ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6624_INF__image,axiom,
% 9.17/5.42 ! [G: code_integer > int,F: nat > code_integer,A2: set_nat] :
% 9.17/5.42 ( ( complete_Inf_Inf_int @ ( image_948535463418740880er_int @ G @ ( image_1215581382706833972nteger @ F @ A2 ) ) )
% 9.17/5.42 = ( complete_Inf_Inf_int @ ( image_nat_int @ ( comp_C5048910307564104766nt_nat @ G @ F ) @ A2 ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6625_INF__image,axiom,
% 9.17/5.42 ! [G: int > nat,F: nat > int,A2: set_nat] :
% 9.17/5.42 ( ( complete_Inf_Inf_nat @ ( image_int_nat @ G @ ( image_nat_int @ F @ A2 ) ) )
% 9.17/5.42 = ( complete_Inf_Inf_nat @ ( image_nat_nat @ ( comp_int_nat_nat @ G @ F ) @ A2 ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6626_INF__image,axiom,
% 9.17/5.42 ! [G: nat > nat,F: nat > nat,A2: set_nat] :
% 9.17/5.42 ( ( complete_Inf_Inf_nat @ ( image_nat_nat @ G @ ( image_nat_nat @ F @ A2 ) ) )
% 9.17/5.42 = ( complete_Inf_Inf_nat @ ( image_nat_nat @ ( comp_nat_nat_nat @ G @ F ) @ A2 ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6627_INF__image,axiom,
% 9.17/5.42 ! [G: nat > int,F: int > nat,A2: set_int] :
% 9.17/5.42 ( ( complete_Inf_Inf_int @ ( image_nat_int @ G @ ( image_int_nat @ F @ A2 ) ) )
% 9.17/5.42 = ( complete_Inf_Inf_int @ ( image_int_int @ ( comp_nat_int_int @ G @ F ) @ A2 ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6628_INF__image,axiom,
% 9.17/5.42 ! [G: nat > int,F: nat > nat,A2: set_nat] :
% 9.17/5.42 ( ( complete_Inf_Inf_int @ ( image_nat_int @ G @ ( image_nat_nat @ F @ A2 ) ) )
% 9.17/5.42 = ( complete_Inf_Inf_int @ ( image_nat_int @ ( comp_nat_int_nat @ G @ F ) @ A2 ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6629_INF__image,axiom,
% 9.17/5.42 ! [G: int > int,F: nat > int,A2: set_nat] :
% 9.17/5.42 ( ( complete_Inf_Inf_int @ ( image_int_int @ G @ ( image_nat_int @ F @ A2 ) ) )
% 9.17/5.42 = ( complete_Inf_Inf_int @ ( image_nat_int @ ( comp_int_int_nat @ G @ F ) @ A2 ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6630_INF__image,axiom,
% 9.17/5.42 ! [G: int > int,F: int > int,A2: set_int] :
% 9.17/5.42 ( ( complete_Inf_Inf_int @ ( image_int_int @ G @ ( image_int_int @ F @ A2 ) ) )
% 9.17/5.42 = ( complete_Inf_Inf_int @ ( image_int_int @ ( comp_int_int_int @ G @ F ) @ A2 ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6631_INF__image,axiom,
% 9.17/5.42 ! [G: code_integer > product_unit,F: nat > code_integer,A2: set_nat] :
% 9.17/5.42 ( ( comple2584293577114468500t_unit @ ( image_7182656606676592809t_unit @ G @ ( image_1215581382706833972nteger @ F @ A2 ) ) )
% 9.17/5.42 = ( comple2584293577114468500t_unit @ ( image_8730104196221521654t_unit @ ( comp_C8086623346886033437it_nat @ G @ F ) @ A2 ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6632_INF__image,axiom,
% 9.17/5.42 ! [G: nat > product_unit,F: nat > nat,A2: set_nat] :
% 9.17/5.42 ( ( comple2584293577114468500t_unit @ ( image_8730104196221521654t_unit @ G @ ( image_nat_nat @ F @ A2 ) ) )
% 9.17/5.42 = ( comple2584293577114468500t_unit @ ( image_8730104196221521654t_unit @ ( comp_n9025697279074352746it_nat @ G @ F ) @ A2 ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6633_SUP__image,axiom,
% 9.17/5.42 ! [G: code_integer > nat,F: nat > code_integer,A2: set_nat] :
% 9.17/5.42 ( ( complete_Sup_Sup_nat @ ( image_951025933927791156er_nat @ G @ ( image_1215581382706833972nteger @ F @ A2 ) ) )
% 9.17/5.42 = ( complete_Sup_Sup_nat @ ( image_nat_nat @ ( comp_C4049556595663050210at_nat @ G @ F ) @ A2 ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6634_SUP__image,axiom,
% 9.17/5.42 ! [G: code_integer > int,F: nat > code_integer,A2: set_nat] :
% 9.17/5.42 ( ( complete_Sup_Sup_int @ ( image_948535463418740880er_int @ G @ ( image_1215581382706833972nteger @ F @ A2 ) ) )
% 9.17/5.42 = ( complete_Sup_Sup_int @ ( image_nat_int @ ( comp_C5048910307564104766nt_nat @ G @ F ) @ A2 ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6635_SUP__image,axiom,
% 9.17/5.42 ! [G: int > nat,F: nat > int,A2: set_nat] :
% 9.17/5.42 ( ( complete_Sup_Sup_nat @ ( image_int_nat @ G @ ( image_nat_int @ F @ A2 ) ) )
% 9.17/5.42 = ( complete_Sup_Sup_nat @ ( image_nat_nat @ ( comp_int_nat_nat @ G @ F ) @ A2 ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6636_SUP__image,axiom,
% 9.17/5.42 ! [G: nat > nat,F: nat > nat,A2: set_nat] :
% 9.17/5.42 ( ( complete_Sup_Sup_nat @ ( image_nat_nat @ G @ ( image_nat_nat @ F @ A2 ) ) )
% 9.17/5.42 = ( complete_Sup_Sup_nat @ ( image_nat_nat @ ( comp_nat_nat_nat @ G @ F ) @ A2 ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6637_SUP__image,axiom,
% 9.17/5.42 ! [G: nat > int,F: int > nat,A2: set_int] :
% 9.17/5.42 ( ( complete_Sup_Sup_int @ ( image_nat_int @ G @ ( image_int_nat @ F @ A2 ) ) )
% 9.17/5.42 = ( complete_Sup_Sup_int @ ( image_int_int @ ( comp_nat_int_int @ G @ F ) @ A2 ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6638_SUP__image,axiom,
% 9.17/5.42 ! [G: nat > int,F: nat > nat,A2: set_nat] :
% 9.17/5.42 ( ( complete_Sup_Sup_int @ ( image_nat_int @ G @ ( image_nat_nat @ F @ A2 ) ) )
% 9.17/5.42 = ( complete_Sup_Sup_int @ ( image_nat_int @ ( comp_nat_int_nat @ G @ F ) @ A2 ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6639_SUP__image,axiom,
% 9.17/5.42 ! [G: int > int,F: nat > int,A2: set_nat] :
% 9.17/5.42 ( ( complete_Sup_Sup_int @ ( image_int_int @ G @ ( image_nat_int @ F @ A2 ) ) )
% 9.17/5.42 = ( complete_Sup_Sup_int @ ( image_nat_int @ ( comp_int_int_nat @ G @ F ) @ A2 ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6640_SUP__image,axiom,
% 9.17/5.42 ! [G: int > int,F: int > int,A2: set_int] :
% 9.17/5.42 ( ( complete_Sup_Sup_int @ ( image_int_int @ G @ ( image_int_int @ F @ A2 ) ) )
% 9.17/5.42 = ( complete_Sup_Sup_int @ ( image_int_int @ ( comp_int_int_int @ G @ F ) @ A2 ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6641_SUP__image,axiom,
% 9.17/5.42 ! [G: code_integer > product_unit,F: nat > code_integer,A2: set_nat] :
% 9.17/5.42 ( ( comple4687483117567863418t_unit @ ( image_7182656606676592809t_unit @ G @ ( image_1215581382706833972nteger @ F @ A2 ) ) )
% 9.17/5.42 = ( comple4687483117567863418t_unit @ ( image_8730104196221521654t_unit @ ( comp_C8086623346886033437it_nat @ G @ F ) @ A2 ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6642_SUP__image,axiom,
% 9.17/5.42 ! [G: nat > product_unit,F: nat > nat,A2: set_nat] :
% 9.17/5.42 ( ( comple4687483117567863418t_unit @ ( image_8730104196221521654t_unit @ G @ ( image_nat_nat @ F @ A2 ) ) )
% 9.17/5.42 = ( comple4687483117567863418t_unit @ ( image_8730104196221521654t_unit @ ( comp_n9025697279074352746it_nat @ G @ F ) @ A2 ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6643_in__snd__imageE,axiom,
% 9.17/5.42 ! [Y: set_Pr1261947904930325089at_nat,S2: set_Pr4329608150637261639at_nat] :
% 9.17/5.42 ( ( member2643936169264416010at_nat @ Y @ ( image_7979982168039674559at_nat @ produc2937545259423399429at_nat @ S2 ) )
% 9.17/5.42 => ~ ! [X4: set_Pr1261947904930325089at_nat] :
% 9.17/5.42 ~ ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X4 @ Y ) @ S2 ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6644_in__snd__imageE,axiom,
% 9.17/5.42 ! [Y: nat,S2: set_Pr1261947904930325089at_nat] :
% 9.17/5.42 ( ( member_nat @ Y @ ( image_2486076414777270412at_nat @ product_snd_nat_nat @ S2 ) )
% 9.17/5.42 => ~ ! [X4: nat] :
% 9.17/5.42 ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Y ) @ S2 ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6645_in__snd__imageE,axiom,
% 9.17/5.42 ! [Y: produc8923325533196201883nteger,S2: set_Pr1281608226676607948nteger] :
% 9.17/5.42 ( ( member157494554546826820nteger @ Y @ ( image_3141030398089242942nteger @ produc7856867400915047194nteger @ S2 ) )
% 9.17/5.42 => ~ ! [X4: produc6241069584506657477e_term > option6357759511663192854e_term] :
% 9.17/5.42 ~ ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X4 @ Y ) @ S2 ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6646_in__snd__imageE,axiom,
% 9.17/5.42 ! [Y: produc3658429121746597890et_nat,S2: set_Pr3286484037609594932et_nat] :
% 9.17/5.42 ( ( member6260224972018164377et_nat @ Y @ ( image_4390311411407041927et_nat @ produc4011572625026189258et_nat @ S2 ) )
% 9.17/5.42 => ~ ! [X4: produc3658429121746597890et_nat > $o] :
% 9.17/5.42 ~ ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X4 @ Y ) @ S2 ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6647_in__snd__imageE,axiom,
% 9.17/5.42 ! [Y: produc3925858234332021118et_nat,S2: set_Pr8536935166611901872et_nat] :
% 9.17/5.42 ( ( member1996754912294343701et_nat @ Y @ ( image_4557310310409863807et_nat @ produc5374455773327741254et_nat @ S2 ) )
% 9.17/5.42 => ~ ! [X4: produc3658429121746597890et_nat > $o] :
% 9.17/5.42 ~ ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X4 @ Y ) @ S2 ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6648_in__snd__imageE,axiom,
% 9.17/5.42 ! [Y: product_prod_int_int,S2: set_Pr9222295170931077689nt_int] :
% 9.17/5.42 ( ( member5262025264175285858nt_int @ Y @ ( image_3915291023682402351nt_int @ produc7328097813583171335nt_int @ S2 ) )
% 9.17/5.42 => ~ ! [X4: produc8551481072490612790e_term > option6357759511663192854e_term] :
% 9.17/5.42 ~ ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X4 @ Y ) @ S2 ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6649_in__snd__imageE,axiom,
% 9.17/5.42 ! [Y: product_prod_int_int,S2: set_Pr1872883991513573699nt_int] :
% 9.17/5.42 ( ( member5262025264175285858nt_int @ Y @ ( image_3108077152341812517nt_int @ produc3162348030201620241nt_int @ S2 ) )
% 9.17/5.42 => ~ ! [X4: int > option6357759511663192854e_term] :
% 9.17/5.42 ~ ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X4 @ Y ) @ S2 ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6650_in__snd__imageE,axiom,
% 9.17/5.42 ! [Y: code_integer,S2: set_Pr4811707699266497531nteger] :
% 9.17/5.42 ( ( member_Code_integer @ Y @ ( image_6316824473203919795nteger @ produc6174133586879617921nteger @ S2 ) )
% 9.17/5.42 => ~ ! [X4: code_integer] :
% 9.17/5.42 ~ ( member157494554546826820nteger @ ( produc1086072967326762835nteger @ X4 @ Y ) @ S2 ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6651_in__snd__imageE,axiom,
% 9.17/5.42 ! [Y: int,S2: set_Pr958786334691620121nt_int] :
% 9.17/5.42 ( ( member_int @ Y @ ( image_5042161079198086560nt_int @ product_snd_int_int @ S2 ) )
% 9.17/5.42 => ~ ! [X4: int] :
% 9.17/5.42 ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Y ) @ S2 ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6652_in__snd__imageE,axiom,
% 9.17/5.42 ! [Y: produc7822875418678951345atural,S2: set_Pr2352657477744078772atural] :
% 9.17/5.42 ( ( member8280416476884352090atural @ Y @ ( image_3837677093542026988atural @ produc6591912806276919810atural @ S2 ) )
% 9.17/5.42 => ~ ! [X4: code_natural] :
% 9.17/5.42 ~ ( member2108296798382401941atural @ ( produc6639722614265839536atural @ X4 @ Y ) @ S2 ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6653_in__fst__imageE,axiom,
% 9.17/5.42 ! [X: set_Pr1261947904930325089at_nat,S2: set_Pr4329608150637261639at_nat] :
% 9.17/5.42 ( ( member2643936169264416010at_nat @ X @ ( image_7979982168039674559at_nat @ produc6011863565407846595at_nat @ S2 ) )
% 9.17/5.42 => ~ ! [Y5: set_Pr1261947904930325089at_nat] :
% 9.17/5.42 ~ ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y5 ) @ S2 ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6654_in__fst__imageE,axiom,
% 9.17/5.42 ! [X: nat,S2: set_Pr1261947904930325089at_nat] :
% 9.17/5.42 ( ( member_nat @ X @ ( image_2486076414777270412at_nat @ product_fst_nat_nat @ S2 ) )
% 9.17/5.42 => ~ ! [Y5: nat] :
% 9.17/5.42 ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y5 ) @ S2 ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6655_in__fst__imageE,axiom,
% 9.17/5.42 ! [X: produc6241069584506657477e_term > option6357759511663192854e_term,S2: set_Pr1281608226676607948nteger] :
% 9.17/5.42 ( ( member4242434998011752849e_term @ X @ ( image_4436781500471753239e_term @ produc7822682618958472924nteger @ S2 ) )
% 9.17/5.42 => ~ ! [Y5: produc8923325533196201883nteger] :
% 9.17/5.42 ~ ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X @ Y5 ) @ S2 ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6656_in__fst__imageE,axiom,
% 9.17/5.42 ! [X: produc3658429121746597890et_nat > $o,S2: set_Pr3286484037609594932et_nat] :
% 9.17/5.42 ( ( member6576561426505652726_nat_o @ X @ ( image_6802380912191114376_nat_o @ produc995936583742144908et_nat @ S2 ) )
% 9.17/5.42 => ~ ! [Y5: produc3658429121746597890et_nat] :
% 9.17/5.42 ~ ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X @ Y5 ) @ S2 ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6657_in__fst__imageE,axiom,
% 9.17/5.42 ! [X: produc3658429121746597890et_nat > $o,S2: set_Pr8536935166611901872et_nat] :
% 9.17/5.42 ( ( member6576561426505652726_nat_o @ X @ ( image_2517677226577294348_nat_o @ produc180342877477747464et_nat @ S2 ) )
% 9.17/5.42 => ~ ! [Y5: produc3925858234332021118et_nat] :
% 9.17/5.42 ~ ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X @ Y5 ) @ S2 ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6658_in__fst__imageE,axiom,
% 9.17/5.42 ! [X: produc8551481072490612790e_term > option6357759511663192854e_term,S2: set_Pr9222295170931077689nt_int] :
% 9.17/5.42 ( ( member3222579708246209666e_term @ X @ ( image_142517975987106933e_term @ produc6816164490631068361nt_int @ S2 ) )
% 9.17/5.42 => ~ ! [Y5: product_prod_int_int] :
% 9.17/5.42 ~ ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X @ Y5 ) @ S2 ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6659_in__fst__imageE,axiom,
% 9.17/5.42 ! [X: int > option6357759511663192854e_term,S2: set_Pr1872883991513573699nt_int] :
% 9.17/5.42 ( ( member8845023287901829240e_term @ X @ ( image_4217645046469565813e_term @ produc6230002227079971283nt_int @ S2 ) )
% 9.17/5.42 => ~ ! [Y5: product_prod_int_int] :
% 9.17/5.42 ~ ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X @ Y5 ) @ S2 ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6660_in__fst__imageE,axiom,
% 9.17/5.42 ! [X: code_integer,S2: set_Pr4811707699266497531nteger] :
% 9.17/5.42 ( ( member_Code_integer @ X @ ( image_6316824473203919795nteger @ produc8508995932063986495nteger @ S2 ) )
% 9.17/5.42 => ~ ! [Y5: code_integer] :
% 9.17/5.42 ~ ( member157494554546826820nteger @ ( produc1086072967326762835nteger @ X @ Y5 ) @ S2 ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6661_in__fst__imageE,axiom,
% 9.17/5.42 ! [X: int,S2: set_Pr958786334691620121nt_int] :
% 9.17/5.42 ( ( member_int @ X @ ( image_5042161079198086560nt_int @ product_fst_int_int @ S2 ) )
% 9.17/5.42 => ~ ! [Y5: int] :
% 9.17/5.42 ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y5 ) @ S2 ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6662_Some__SUP,axiom,
% 9.17/5.42 ! [A2: set_Pr4329608150637261639at_nat,F: produc3843707927480180839at_nat > set_nat] :
% 9.17/5.42 ( ( A2 != bot_bo228742789529271731at_nat )
% 9.17/5.42 => ( ( some_set_nat @ ( comple7399068483239264473et_nat @ ( image_3160451284896210088et_nat @ F @ A2 ) ) )
% 9.17/5.42 = ( comple8455683388168444585et_nat
% 9.17/5.42 @ ( image_934083234596377592et_nat
% 9.17/5.42 @ ^ [X3: produc3843707927480180839at_nat] : ( some_set_nat @ ( F @ X3 ) )
% 9.17/5.42 @ A2 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6663_Some__SUP,axiom,
% 9.17/5.42 ! [A2: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > set_nat] :
% 9.17/5.42 ( ( A2 != bot_bo2099793752762293965at_nat )
% 9.17/5.42 => ( ( some_set_nat @ ( comple7399068483239264473et_nat @ ( image_15824709712370754et_nat @ F @ A2 ) ) )
% 9.17/5.42 = ( comple8455683388168444585et_nat
% 9.17/5.42 @ ( image_7383884694314771602et_nat
% 9.17/5.42 @ ^ [X3: product_prod_nat_nat] : ( some_set_nat @ ( F @ X3 ) )
% 9.17/5.42 @ A2 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6664_Some__SUP,axiom,
% 9.17/5.42 ! [A2: set_o,F: $o > set_nat] :
% 9.17/5.42 ( ( A2 != bot_bot_set_o )
% 9.17/5.42 => ( ( some_set_nat @ ( comple7399068483239264473et_nat @ ( image_o_set_nat @ F @ A2 ) ) )
% 9.17/5.42 = ( comple8455683388168444585et_nat
% 9.17/5.42 @ ( image_966425688229763753et_nat
% 9.17/5.42 @ ^ [X3: $o] : ( some_set_nat @ ( F @ X3 ) )
% 9.17/5.42 @ A2 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6665_Some__SUP,axiom,
% 9.17/5.42 ! [A2: set_nat,F: nat > set_nat] :
% 9.17/5.42 ( ( A2 != bot_bot_set_nat )
% 9.17/5.42 => ( ( some_set_nat @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ F @ A2 ) ) )
% 9.17/5.42 = ( comple8455683388168444585et_nat
% 9.17/5.42 @ ( image_1085372205585808685et_nat
% 9.17/5.42 @ ^ [X3: nat] : ( some_set_nat @ ( F @ X3 ) )
% 9.17/5.42 @ A2 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6666_Some__SUP,axiom,
% 9.17/5.42 ! [A2: set_int,F: int > set_nat] :
% 9.17/5.42 ( ( A2 != bot_bot_set_int )
% 9.17/5.42 => ( ( some_set_nat @ ( comple7399068483239264473et_nat @ ( image_int_set_nat @ F @ A2 ) ) )
% 9.17/5.42 = ( comple8455683388168444585et_nat
% 9.17/5.42 @ ( image_2293489338514188681et_nat
% 9.17/5.42 @ ^ [X3: int] : ( some_set_nat @ ( F @ X3 ) )
% 9.17/5.42 @ A2 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6667_Some__SUP,axiom,
% 9.17/5.42 ! [A2: set_Pr4329608150637261639at_nat,F: produc3843707927480180839at_nat > product_unit] :
% 9.17/5.42 ( ( A2 != bot_bo228742789529271731at_nat )
% 9.17/5.42 => ( ( some_Product_unit @ ( comple4687483117567863418t_unit @ ( image_7082456443403096939t_unit @ F @ A2 ) ) )
% 9.17/5.42 = ( comple7481738165189995200t_unit
% 9.17/5.42 @ ( image_8585598761158579761t_unit
% 9.17/5.42 @ ^ [X3: produc3843707927480180839at_nat] : ( some_Product_unit @ ( F @ X3 ) )
% 9.17/5.42 @ A2 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6668_Some__SUP,axiom,
% 9.17/5.42 ! [A2: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > product_unit] :
% 9.17/5.42 ( ( A2 != bot_bo2099793752762293965at_nat )
% 9.17/5.42 => ( ( some_Product_unit @ ( comple4687483117567863418t_unit @ ( image_6169909464789311569t_unit @ F @ A2 ) ) )
% 9.17/5.42 = ( comple7481738165189995200t_unit
% 9.17/5.42 @ ( image_7548311901266006551t_unit
% 9.17/5.42 @ ^ [X3: product_prod_nat_nat] : ( some_Product_unit @ ( F @ X3 ) )
% 9.17/5.42 @ A2 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6669_Some__SUP,axiom,
% 9.17/5.42 ! [A2: set_o,F: $o > product_unit] :
% 9.17/5.42 ( ( A2 != bot_bot_set_o )
% 9.17/5.42 => ( ( some_Product_unit @ ( comple4687483117567863418t_unit @ ( image_o_Product_unit @ F @ A2 ) ) )
% 9.17/5.42 = ( comple7481738165189995200t_unit
% 9.17/5.42 @ ( image_4415570909310888640t_unit
% 9.17/5.42 @ ^ [X3: $o] : ( some_Product_unit @ ( F @ X3 ) )
% 9.17/5.42 @ A2 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6670_Some__SUP,axiom,
% 9.17/5.42 ! [A2: set_nat,F: nat > product_unit] :
% 9.17/5.42 ( ( A2 != bot_bot_set_nat )
% 9.17/5.42 => ( ( some_Product_unit @ ( comple4687483117567863418t_unit @ ( image_8730104196221521654t_unit @ F @ A2 ) ) )
% 9.17/5.42 = ( comple7481738165189995200t_unit
% 9.17/5.42 @ ( image_1497621718204147004t_unit
% 9.17/5.42 @ ^ [X3: nat] : ( some_Product_unit @ ( F @ X3 ) )
% 9.17/5.42 @ A2 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6671_Some__SUP,axiom,
% 9.17/5.42 ! [A2: set_int,F: int > product_unit] :
% 9.17/5.42 ( ( A2 != bot_bot_set_int )
% 9.17/5.42 => ( ( some_Product_unit @ ( comple4687483117567863418t_unit @ ( image_5846526143423701914t_unit @ F @ A2 ) ) )
% 9.17/5.42 = ( comple7481738165189995200t_unit
% 9.17/5.42 @ ( image_1735198859854722016t_unit
% 9.17/5.42 @ ^ [X3: int] : ( some_Product_unit @ ( F @ X3 ) )
% 9.17/5.42 @ A2 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6672_finite__range__prod,axiom,
% 9.17/5.42 ! [F: nat > product_prod_nat_nat] :
% 9.17/5.42 ( ( finite_finite_nat @ ( image_nat_nat @ ( comp_P1955610211387027840at_nat @ product_fst_nat_nat @ F ) @ top_top_set_nat ) )
% 9.17/5.42 => ( ( finite_finite_nat @ ( image_nat_nat @ ( comp_P1955610211387027840at_nat @ product_snd_nat_nat @ F ) @ top_top_set_nat ) )
% 9.17/5.42 => ( finite6177210948735845034at_nat @ ( image_5846123807819985514at_nat @ F @ top_top_set_nat ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6673_finite__range__prod,axiom,
% 9.17/5.42 ! [F: nat > product_prod_nat_int] :
% 9.17/5.42 ( ( finite_finite_nat @ ( image_nat_nat @ ( comp_P7964419862382602716at_nat @ product_fst_nat_int @ F ) @ top_top_set_nat ) )
% 9.17/5.42 => ( ( finite_finite_int @ ( image_nat_int @ ( comp_P8963773574283657272nt_nat @ product_snd_nat_int @ F ) @ top_top_set_nat ) )
% 9.17/5.42 => ( finite1999359929226648326at_int @ ( image_1668272788310788806at_int @ F @ top_top_set_nat ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6674_finite__range__prod,axiom,
% 9.17/5.42 ! [F: nat > produc2591615631378489102nteger] :
% 9.17/5.42 ( ( finite_finite_nat @ ( image_nat_nat @ ( comp_P9144323761349829517at_nat @ produc8897218493789310642nteger @ F ) @ top_top_set_nat ) )
% 9.17/5.42 => ( ( finite6017078050557962740nteger @ ( image_1215581382706833972nteger @ ( comp_P5461341465284484122er_nat @ produc1781891006948753140nteger @ F ) @ top_top_set_nat ) )
% 9.17/5.42 => ( finite1154042800025562295nteger @ ( image_8507997478476487799nteger @ F @ top_top_set_nat ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6675_finite__range__prod,axiom,
% 9.17/5.42 ! [F: nat > product_prod_int_nat] :
% 9.17/5.42 ( ( finite_finite_int @ ( image_nat_int @ ( comp_P645145991195131448nt_nat @ product_fst_int_nat @ F ) @ top_top_set_nat ) )
% 9.17/5.42 => ( ( finite_finite_nat @ ( image_nat_nat @ ( comp_P8869164316148852700at_nat @ product_snd_int_nat @ F ) @ top_top_set_nat ) )
% 9.17/5.42 => ( finite7176564660636899590nt_nat @ ( image_6845477519721040070nt_nat @ F @ top_top_set_nat ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6676_finite__range__prod,axiom,
% 9.17/5.42 ! [F: nat > produc2963269191615333738nteger] :
% 9.17/5.42 ( ( finite_finite_int @ ( image_nat_int @ ( comp_P59025373045620805nt_nat @ produc45500017171379470nteger @ F ) @ top_top_set_nat ) )
% 9.17/5.42 => ( ( finite6017078050557962740nteger @ ( image_1215581382706833972nteger @ ( comp_P6870028373966156406er_nat @ produc2153544567185597776nteger @ F ) @ top_top_set_nat ) )
% 9.17/5.42 => ( finite1525696360262406931nteger @ ( image_8879651038713332435nteger @ F @ top_top_set_nat ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6677_finite__range__prod,axiom,
% 9.17/5.42 ! [F: nat > produc6433947425880249742er_nat] :
% 9.17/5.42 ( ( finite6017078050557962740nteger @ ( image_1215581382706833972nteger @ ( comp_P5700178199414968986er_nat @ produc8632663045010267826er_nat @ F ) @ top_top_set_nat ) )
% 9.17/5.42 => ( ( finite_finite_nat @ ( image_nat_nat @ ( comp_P1337767177661389325at_nat @ produc1517335558169710324er_nat @ F ) @ top_top_set_nat ) )
% 9.17/5.42 => ( finite4996374594527322935er_nat @ ( image_3126957236123472631er_nat @ F @ top_top_set_nat ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6678_finite__range__prod,axiom,
% 9.17/5.42 ! [F: nat > produc2256096406371053034er_int] :
% 9.17/5.42 ( ( finite6017078050557962740nteger @ ( image_1215581382706833972nteger @ ( comp_P2475326853202991862er_nat @ produc8630172574501217550er_int @ F ) @ top_top_set_nat ) )
% 9.17/5.42 => ( ( finite_finite_int @ ( image_nat_int @ ( comp_P8345930540558018757nt_nat @ produc1514845087660660048er_int @ F ) @ top_top_set_nat ) )
% 9.17/5.42 => ( finite818523575018126227er_int @ ( image_8172478253469051731er_int @ F @ top_top_set_nat ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6679_finite__range__prod,axiom,
% 9.17/5.42 ! [F: nat > produc8923325533196201883nteger] :
% 9.17/5.42 ( ( finite6017078050557962740nteger @ ( image_1215581382706833972nteger @ ( comp_P3109732533133679783er_nat @ produc8508995932063986495nteger @ F ) @ top_top_set_nat ) )
% 9.17/5.42 => ( ( finite6017078050557962740nteger @ ( image_1215581382706833972nteger @ ( comp_P3109732533133679783er_nat @ produc6174133586879617921nteger @ F ) @ top_top_set_nat ) )
% 9.17/5.42 => ( finite2154694888287295812nteger @ ( image_4272405876590741764nteger @ F @ top_top_set_nat ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6680_finite__range__prod,axiom,
% 9.17/5.42 ! [F: nat > product_prod_int_int] :
% 9.17/5.42 ( ( finite_finite_int @ ( image_nat_int @ ( comp_P6653955642190706324nt_nat @ product_fst_int_int @ F ) @ top_top_set_nat ) )
% 9.17/5.42 => ( ( finite_finite_int @ ( image_nat_int @ ( comp_P6653955642190706324nt_nat @ product_snd_int_int @ F ) @ top_top_set_nat ) )
% 9.17/5.42 => ( finite2998713641127702882nt_int @ ( image_2667626500211843362nt_int @ F @ top_top_set_nat ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6681_finite__range__prod,axiom,
% 9.17/5.42 ! [F: product_unit > product_prod_nat_nat] :
% 9.17/5.42 ( ( finite_finite_nat @ ( image_875570014554754200it_nat @ ( comp_P2980510830910040157t_unit @ product_fst_nat_nat @ F ) @ top_to1996260823553986621t_unit ) )
% 9.17/5.42 => ( ( finite_finite_nat @ ( image_875570014554754200it_nat @ ( comp_P2980510830910040157t_unit @ product_snd_nat_nat @ F ) @ top_to1996260823553986621t_unit ) )
% 9.17/5.42 => ( finite6177210948735845034at_nat @ ( image_7281959405765017145at_nat @ F @ top_to1996260823553986621t_unit ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6682_UN__atMost__UNIV,axiom,
% 9.17/5.42 ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ set_ord_atMost_nat @ top_top_set_nat ) )
% 9.17/5.42 = top_top_set_nat ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6683_UN__lessThan__UNIV,axiom,
% 9.17/5.42 ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ set_ord_lessThan_nat @ top_top_set_nat ) )
% 9.17/5.42 = top_top_set_nat ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6684_Sup__option__def,axiom,
% 9.17/5.42 ( comple8455683388168444585et_nat
% 9.17/5.42 = ( ^ [A7: set_option_set_nat] :
% 9.17/5.42 ( if_option_set_nat
% 9.17/5.42 @ ( ( A7 = bot_bo5650944848895983264et_nat )
% 9.17/5.42 | ( A7
% 9.17/5.42 = ( insert6281397740311767046et_nat @ none_set_nat @ bot_bo5650944848895983264et_nat ) ) )
% 9.17/5.42 @ none_set_nat
% 9.17/5.42 @ ( some_set_nat @ ( comple7399068483239264473et_nat @ ( these_set_nat @ A7 ) ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6685_Sup__option__def,axiom,
% 9.17/5.42 ( comple7481738165189995200t_unit
% 9.17/5.42 = ( ^ [A7: set_op3165557761946182707t_unit] :
% 9.17/5.42 ( if_opt6227717841141446553t_unit
% 9.17/5.42 @ ( ( A7 = bot_bo2792743115866486943t_unit )
% 9.17/5.42 | ( A7
% 9.17/5.42 = ( insert2866144167138965411t_unit @ none_Product_unit @ bot_bo2792743115866486943t_unit ) ) )
% 9.17/5.42 @ none_Product_unit
% 9.17/5.42 @ ( some_Product_unit @ ( comple4687483117567863418t_unit @ ( these_Product_unit @ A7 ) ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6686_snd__image__mp,axiom,
% 9.17/5.42 ! [A2: set_Pr4329608150637261639at_nat,B5: set_se7855581050983116737at_nat,X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 9.17/5.42 ( ( ord_le2077887516847798113at_nat @ ( image_7979982168039674559at_nat @ produc2937545259423399429at_nat @ A2 ) @ B5 )
% 9.17/5.42 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ A2 )
% 9.17/5.42 => ( member2643936169264416010at_nat @ Y @ B5 ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6687_snd__image__mp,axiom,
% 9.17/5.42 ! [A2: set_Pr1281608226676607948nteger,B5: set_Pr4811707699266497531nteger,X: produc6241069584506657477e_term > option6357759511663192854e_term,Y: produc8923325533196201883nteger] :
% 9.17/5.42 ( ( ord_le3725938330318615451nteger @ ( image_3141030398089242942nteger @ produc7856867400915047194nteger @ A2 ) @ B5 )
% 9.17/5.42 => ( ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X @ Y ) @ A2 )
% 9.17/5.42 => ( member157494554546826820nteger @ Y @ B5 ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6688_snd__image__mp,axiom,
% 9.17/5.42 ! [A2: set_Pr3286484037609594932et_nat,B5: set_Pr3948176798113811640et_nat,X: produc3658429121746597890et_nat > $o,Y: produc3658429121746597890et_nat] :
% 9.17/5.42 ( ( ord_le8090042543978450200et_nat @ ( image_4390311411407041927et_nat @ produc4011572625026189258et_nat @ A2 ) @ B5 )
% 9.17/5.42 => ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X @ Y ) @ A2 )
% 9.17/5.42 => ( member6260224972018164377et_nat @ Y @ B5 ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6689_snd__image__mp,axiom,
% 9.17/5.42 ! [A2: set_Pr8536935166611901872et_nat,B5: set_Pr3286484037609594932et_nat,X: produc3658429121746597890et_nat > $o,Y: produc3925858234332021118et_nat] :
% 9.17/5.42 ( ( ord_le5966269811547037844et_nat @ ( image_4557310310409863807et_nat @ produc5374455773327741254et_nat @ A2 ) @ B5 )
% 9.17/5.42 => ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X @ Y ) @ A2 )
% 9.17/5.42 => ( member1996754912294343701et_nat @ Y @ B5 ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6690_snd__image__mp,axiom,
% 9.17/5.42 ! [A2: set_Pr9222295170931077689nt_int,B5: set_Pr958786334691620121nt_int,X: produc8551481072490612790e_term > option6357759511663192854e_term,Y: product_prod_int_int] :
% 9.17/5.42 ( ( ord_le2843351958646193337nt_int @ ( image_3915291023682402351nt_int @ produc7328097813583171335nt_int @ A2 ) @ B5 )
% 9.17/5.42 => ( ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X @ Y ) @ A2 )
% 9.17/5.42 => ( member5262025264175285858nt_int @ Y @ B5 ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6691_snd__image__mp,axiom,
% 9.17/5.42 ! [A2: set_Pr1872883991513573699nt_int,B5: set_Pr958786334691620121nt_int,X: int > option6357759511663192854e_term,Y: product_prod_int_int] :
% 9.17/5.42 ( ( ord_le2843351958646193337nt_int @ ( image_3108077152341812517nt_int @ produc3162348030201620241nt_int @ A2 ) @ B5 )
% 9.17/5.42 => ( ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X @ Y ) @ A2 )
% 9.17/5.42 => ( member5262025264175285858nt_int @ Y @ B5 ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6692_snd__image__mp,axiom,
% 9.17/5.42 ! [A2: set_Pr4811707699266497531nteger,B5: set_Code_integer,X: code_integer,Y: code_integer] :
% 9.17/5.42 ( ( ord_le7084787975880047091nteger @ ( image_6316824473203919795nteger @ produc6174133586879617921nteger @ A2 ) @ B5 )
% 9.17/5.42 => ( ( member157494554546826820nteger @ ( produc1086072967326762835nteger @ X @ Y ) @ A2 )
% 9.17/5.42 => ( member_Code_integer @ Y @ B5 ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6693_snd__image__mp,axiom,
% 9.17/5.42 ! [A2: set_Pr958786334691620121nt_int,B5: set_int,X: int,Y: int] :
% 9.17/5.42 ( ( ord_less_eq_set_int @ ( image_5042161079198086560nt_int @ product_snd_int_int @ A2 ) @ B5 )
% 9.17/5.42 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ A2 )
% 9.17/5.42 => ( member_int @ Y @ B5 ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6694_snd__image__mp,axiom,
% 9.17/5.42 ! [A2: set_Pr2352657477744078772atural,B5: set_Pr7564037697178849041atural,X: code_natural,Y: produc7822875418678951345atural] :
% 9.17/5.42 ( ( ord_le6478268328230966961atural @ ( image_3837677093542026988atural @ produc6591912806276919810atural @ A2 ) @ B5 )
% 9.17/5.42 => ( ( member2108296798382401941atural @ ( produc6639722614265839536atural @ X @ Y ) @ A2 )
% 9.17/5.42 => ( member8280416476884352090atural @ Y @ B5 ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6695_snd__image__mp,axiom,
% 9.17/5.42 ! [A2: set_Pr1261947904930325089at_nat,B5: set_nat,X: nat,Y: nat] :
% 9.17/5.42 ( ( ord_less_eq_set_nat @ ( image_2486076414777270412at_nat @ product_snd_nat_nat @ A2 ) @ B5 )
% 9.17/5.42 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ A2 )
% 9.17/5.42 => ( member_nat @ Y @ B5 ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6696_fst__image__mp,axiom,
% 9.17/5.42 ! [A2: set_Pr4329608150637261639at_nat,B5: set_se7855581050983116737at_nat,X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 9.17/5.42 ( ( ord_le2077887516847798113at_nat @ ( image_7979982168039674559at_nat @ produc6011863565407846595at_nat @ A2 ) @ B5 )
% 9.17/5.42 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ A2 )
% 9.17/5.42 => ( member2643936169264416010at_nat @ X @ B5 ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6697_fst__image__mp,axiom,
% 9.17/5.42 ! [A2: set_Pr1281608226676607948nteger,B5: set_Pr7604974323444597168e_term,X: produc6241069584506657477e_term > option6357759511663192854e_term,Y: produc8923325533196201883nteger] :
% 9.17/5.42 ( ( ord_le7106919388332126736e_term @ ( image_4436781500471753239e_term @ produc7822682618958472924nteger @ A2 ) @ B5 )
% 9.17/5.42 => ( ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X @ Y ) @ A2 )
% 9.17/5.42 => ( member4242434998011752849e_term @ X @ B5 ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6698_fst__image__mp,axiom,
% 9.17/5.42 ! [A2: set_Pr3286484037609594932et_nat,B5: set_Pr4532377907799695533_nat_o,X: produc3658429121746597890et_nat > $o,Y: produc3658429121746597890et_nat] :
% 9.17/5.42 ( ( ord_le2965882846123202637_nat_o @ ( image_6802380912191114376_nat_o @ produc995936583742144908et_nat @ A2 ) @ B5 )
% 9.17/5.42 => ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X @ Y ) @ A2 )
% 9.17/5.42 => ( member6576561426505652726_nat_o @ X @ B5 ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6699_fst__image__mp,axiom,
% 9.17/5.42 ! [A2: set_Pr8536935166611901872et_nat,B5: set_Pr4532377907799695533_nat_o,X: produc3658429121746597890et_nat > $o,Y: produc3925858234332021118et_nat] :
% 9.17/5.42 ( ( ord_le2965882846123202637_nat_o @ ( image_2517677226577294348_nat_o @ produc180342877477747464et_nat @ A2 ) @ B5 )
% 9.17/5.42 => ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X @ Y ) @ A2 )
% 9.17/5.42 => ( member6576561426505652726_nat_o @ X @ B5 ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6700_fst__image__mp,axiom,
% 9.17/5.42 ! [A2: set_Pr9222295170931077689nt_int,B5: set_Pr3642885161833720865e_term,X: produc8551481072490612790e_term > option6357759511663192854e_term,Y: product_prod_int_int] :
% 9.17/5.42 ( ( ord_le4129093240937979009e_term @ ( image_142517975987106933e_term @ produc6816164490631068361nt_int @ A2 ) @ B5 )
% 9.17/5.42 => ( ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X @ Y ) @ A2 )
% 9.17/5.42 => ( member3222579708246209666e_term @ X @ B5 ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6701_fst__image__mp,axiom,
% 9.17/5.42 ! [A2: set_Pr1872883991513573699nt_int,B5: set_in3461395444621081367e_term,X: int > option6357759511663192854e_term,Y: product_prod_int_int] :
% 9.17/5.42 ( ( ord_le567748327753481079e_term @ ( image_4217645046469565813e_term @ produc6230002227079971283nt_int @ A2 ) @ B5 )
% 9.17/5.42 => ( ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X @ Y ) @ A2 )
% 9.17/5.42 => ( member8845023287901829240e_term @ X @ B5 ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6702_fst__image__mp,axiom,
% 9.17/5.42 ! [A2: set_Pr4811707699266497531nteger,B5: set_Code_integer,X: code_integer,Y: code_integer] :
% 9.17/5.42 ( ( ord_le7084787975880047091nteger @ ( image_6316824473203919795nteger @ produc8508995932063986495nteger @ A2 ) @ B5 )
% 9.17/5.42 => ( ( member157494554546826820nteger @ ( produc1086072967326762835nteger @ X @ Y ) @ A2 )
% 9.17/5.42 => ( member_Code_integer @ X @ B5 ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6703_fst__image__mp,axiom,
% 9.17/5.42 ! [A2: set_Pr958786334691620121nt_int,B5: set_int,X: int,Y: int] :
% 9.17/5.42 ( ( ord_less_eq_set_int @ ( image_5042161079198086560nt_int @ product_fst_int_int @ A2 ) @ B5 )
% 9.17/5.42 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ A2 )
% 9.17/5.42 => ( member_int @ X @ B5 ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6704_fst__image__mp,axiom,
% 9.17/5.42 ! [A2: set_Pr1261947904930325089at_nat,B5: set_nat,X: nat,Y: nat] :
% 9.17/5.42 ( ( ord_less_eq_set_nat @ ( image_2486076414777270412at_nat @ product_fst_nat_nat @ A2 ) @ B5 )
% 9.17/5.42 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ A2 )
% 9.17/5.42 => ( member_nat @ X @ B5 ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6705_prod_OUnion__comp,axiom,
% 9.17/5.42 ! [B5: set_set_o,G: $o > code_integer] :
% 9.17/5.42 ( ! [X4: set_o] :
% 9.17/5.42 ( ( member_set_o @ X4 @ B5 )
% 9.17/5.42 => ( finite_finite_o @ X4 ) )
% 9.17/5.42 => ( ! [A14: set_o] :
% 9.17/5.42 ( ( member_set_o @ A14 @ B5 )
% 9.17/5.42 => ! [A25: set_o] :
% 9.17/5.42 ( ( member_set_o @ A25 @ B5 )
% 9.17/5.42 => ( ( A14 != A25 )
% 9.17/5.42 => ! [X4: $o] :
% 9.17/5.42 ( ( member_o @ X4 @ A14 )
% 9.17/5.42 => ( ( member_o @ X4 @ A25 )
% 9.17/5.42 => ( ( G @ X4 )
% 9.17/5.42 = one_one_Code_integer ) ) ) ) ) )
% 9.17/5.42 => ( ( groups7694694392188491536nteger @ G @ ( comple90263536869209701_set_o @ B5 ) )
% 9.17/5.42 = ( comp_s262121120021782499nteger @ groups8987389756002350576nteger @ groups7694694392188491536nteger @ G @ B5 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6706_prod_OUnion__comp,axiom,
% 9.17/5.42 ! [B5: set_set_int,G: int > code_integer] :
% 9.17/5.42 ( ! [X4: set_int] :
% 9.17/5.42 ( ( member_set_int @ X4 @ B5 )
% 9.17/5.42 => ( finite_finite_int @ X4 ) )
% 9.17/5.42 => ( ! [A14: set_int] :
% 9.17/5.42 ( ( member_set_int @ A14 @ B5 )
% 9.17/5.42 => ! [A25: set_int] :
% 9.17/5.42 ( ( member_set_int @ A25 @ B5 )
% 9.17/5.42 => ( ( A14 != A25 )
% 9.17/5.42 => ! [X4: int] :
% 9.17/5.42 ( ( member_int @ X4 @ A14 )
% 9.17/5.42 => ( ( member_int @ X4 @ A25 )
% 9.17/5.42 => ( ( G @ X4 )
% 9.17/5.42 = one_one_Code_integer ) ) ) ) ) )
% 9.17/5.42 => ( ( groups3827104343326376752nteger @ G @ ( comple3221217463730067765et_int @ B5 ) )
% 9.17/5.42 = ( comp_s7646638485285982975nteger @ groups8770619586034088166nteger @ groups3827104343326376752nteger @ G @ B5 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6707_prod_OUnion__comp,axiom,
% 9.17/5.42 ! [B5: set_set_Code_integer,G: code_integer > code_integer] :
% 9.17/5.42 ( ! [X4: set_Code_integer] :
% 9.17/5.42 ( ( member1834298987299537450nteger @ X4 @ B5 )
% 9.17/5.42 => ( finite6017078050557962740nteger @ X4 ) )
% 9.17/5.42 => ( ! [A14: set_Code_integer] :
% 9.17/5.42 ( ( member1834298987299537450nteger @ A14 @ B5 )
% 9.17/5.42 => ! [A25: set_Code_integer] :
% 9.17/5.42 ( ( member1834298987299537450nteger @ A25 @ B5 )
% 9.17/5.42 => ( ( A14 != A25 )
% 9.17/5.42 => ! [X4: code_integer] :
% 9.17/5.42 ( ( member_Code_integer @ X4 @ A14 )
% 9.17/5.42 => ( ( member_Code_integer @ X4 @ A25 )
% 9.17/5.42 => ( ( G @ X4 )
% 9.17/5.42 = one_one_Code_integer ) ) ) ) ) )
% 9.17/5.42 => ( ( groups3674199335183972705nteger @ G @ ( comple739944243200306918nteger @ B5 ) )
% 9.17/5.42 = ( comp_s8484400498494363538nteger @ groups1474571732273379991nteger @ groups3674199335183972705nteger @ G @ B5 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6708_prod_OUnion__comp,axiom,
% 9.17/5.42 ! [B5: set_set_o,G: $o > assn] :
% 9.17/5.42 ( ! [X4: set_o] :
% 9.17/5.42 ( ( member_set_o @ X4 @ B5 )
% 9.17/5.42 => ( finite_finite_o @ X4 ) )
% 9.17/5.42 => ( ! [A14: set_o] :
% 9.17/5.42 ( ( member_set_o @ A14 @ B5 )
% 9.17/5.42 => ! [A25: set_o] :
% 9.17/5.42 ( ( member_set_o @ A25 @ B5 )
% 9.17/5.42 => ( ( A14 != A25 )
% 9.17/5.42 => ! [X4: $o] :
% 9.17/5.42 ( ( member_o @ X4 @ A14 )
% 9.17/5.42 => ( ( member_o @ X4 @ A25 )
% 9.17/5.42 => ( ( G @ X4 )
% 9.17/5.42 = one_one_assn ) ) ) ) ) )
% 9.17/5.42 => ( ( groups5301882518646026715o_assn @ G @ ( comple90263536869209701_set_o @ B5 ) )
% 9.17/5.42 = ( comp_s518380907012905326o_assn @ groups6963733262650904763o_assn @ groups5301882518646026715o_assn @ G @ B5 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6709_prod_OUnion__comp,axiom,
% 9.17/5.42 ! [B5: set_set_int,G: int > assn] :
% 9.17/5.42 ( ! [X4: set_int] :
% 9.17/5.42 ( ( member_set_int @ X4 @ B5 )
% 9.17/5.42 => ( finite_finite_int @ X4 ) )
% 9.17/5.42 => ( ! [A14: set_int] :
% 9.17/5.42 ( ( member_set_int @ A14 @ B5 )
% 9.17/5.42 => ! [A25: set_int] :
% 9.17/5.42 ( ( member_set_int @ A25 @ B5 )
% 9.17/5.42 => ( ( A14 != A25 )
% 9.17/5.42 => ! [X4: int] :
% 9.17/5.42 ( ( member_int @ X4 @ A14 )
% 9.17/5.42 => ( ( member_int @ X4 @ A25 )
% 9.17/5.42 => ( ( G @ X4 )
% 9.17/5.42 = one_one_assn ) ) ) ) ) )
% 9.17/5.42 => ( ( groups7882442080178216443t_assn @ G @ ( comple3221217463730067765et_int @ B5 ) )
% 9.17/5.42 = ( comp_s4595925057662634336t_assn @ groups5950967880310095793t_assn @ groups7882442080178216443t_assn @ G @ B5 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6710_prod_OUnion__comp,axiom,
% 9.17/5.42 ! [B5: set_set_Code_integer,G: code_integer > assn] :
% 9.17/5.42 ( ! [X4: set_Code_integer] :
% 9.17/5.42 ( ( member1834298987299537450nteger @ X4 @ B5 )
% 9.17/5.42 => ( finite6017078050557962740nteger @ X4 ) )
% 9.17/5.42 => ( ! [A14: set_Code_integer] :
% 9.17/5.42 ( ( member1834298987299537450nteger @ A14 @ B5 )
% 9.17/5.42 => ! [A25: set_Code_integer] :
% 9.17/5.42 ( ( member1834298987299537450nteger @ A25 @ B5 )
% 9.17/5.42 => ( ( A14 != A25 )
% 9.17/5.42 => ! [X4: code_integer] :
% 9.17/5.42 ( ( member_Code_integer @ X4 @ A14 )
% 9.17/5.42 => ( ( member_Code_integer @ X4 @ A25 )
% 9.17/5.42 => ( ( G @ X4 )
% 9.17/5.42 = one_one_assn ) ) ) ) ) )
% 9.17/5.42 => ( ( groups1304777262505850412r_assn @ G @ ( comple739944243200306918nteger @ B5 ) )
% 9.17/5.42 = ( comp_s3531641609786562035r_assn @ groups4245288774754739042r_assn @ groups1304777262505850412r_assn @ G @ B5 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6711_prod_OUnion__comp,axiom,
% 9.17/5.42 ! [B5: set_set_o,G: $o > rat] :
% 9.17/5.42 ( ! [X4: set_o] :
% 9.17/5.42 ( ( member_set_o @ X4 @ B5 )
% 9.17/5.42 => ( finite_finite_o @ X4 ) )
% 9.17/5.42 => ( ! [A14: set_o] :
% 9.17/5.42 ( ( member_set_o @ A14 @ B5 )
% 9.17/5.42 => ! [A25: set_o] :
% 9.17/5.42 ( ( member_set_o @ A25 @ B5 )
% 9.17/5.42 => ( ( A14 != A25 )
% 9.17/5.42 => ! [X4: $o] :
% 9.17/5.42 ( ( member_o @ X4 @ A14 )
% 9.17/5.42 => ( ( member_o @ X4 @ A25 )
% 9.17/5.42 => ( ( G @ X4 )
% 9.17/5.42 = one_one_rat ) ) ) ) ) )
% 9.17/5.42 => ( ( groups2869687844427037835_o_rat @ G @ ( comple90263536869209701_set_o @ B5 ) )
% 9.17/5.42 = ( comp_s1265507639253661726_o_rat @ groups4233643617323539307_o_rat @ groups2869687844427037835_o_rat @ G @ B5 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6712_prod_OUnion__comp,axiom,
% 9.17/5.42 ! [B5: set_set_int,G: int > rat] :
% 9.17/5.42 ( ! [X4: set_int] :
% 9.17/5.42 ( ( member_set_int @ X4 @ B5 )
% 9.17/5.42 => ( finite_finite_int @ X4 ) )
% 9.17/5.42 => ( ! [A14: set_int] :
% 9.17/5.42 ( ( member_set_int @ A14 @ B5 )
% 9.17/5.42 => ! [A25: set_int] :
% 9.17/5.42 ( ( member_set_int @ A25 @ B5 )
% 9.17/5.42 => ( ( A14 != A25 )
% 9.17/5.42 => ! [X4: int] :
% 9.17/5.42 ( ( member_int @ X4 @ A14 )
% 9.17/5.42 => ( ( member_int @ X4 @ A25 )
% 9.17/5.42 => ( ( G @ X4 )
% 9.17/5.42 = one_one_rat ) ) ) ) ) )
% 9.17/5.42 => ( ( groups1072433553688619179nt_rat @ G @ ( comple3221217463730067765et_int @ B5 ) )
% 9.17/5.42 = ( comp_s4088261402702255472nt_rat @ groups5800339274786551393nt_rat @ groups1072433553688619179nt_rat @ G @ B5 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6713_prod_OUnion__comp,axiom,
% 9.17/5.42 ! [B5: set_set_Code_integer,G: code_integer > rat] :
% 9.17/5.42 ( ! [X4: set_Code_integer] :
% 9.17/5.42 ( ( member1834298987299537450nteger @ X4 @ B5 )
% 9.17/5.42 => ( finite6017078050557962740nteger @ X4 ) )
% 9.17/5.42 => ( ! [A14: set_Code_integer] :
% 9.17/5.42 ( ( member1834298987299537450nteger @ A14 @ B5 )
% 9.17/5.42 => ! [A25: set_Code_integer] :
% 9.17/5.42 ( ( member1834298987299537450nteger @ A25 @ B5 )
% 9.17/5.42 => ( ( A14 != A25 )
% 9.17/5.42 => ! [X4: code_integer] :
% 9.17/5.42 ( ( member_Code_integer @ X4 @ A14 )
% 9.17/5.42 => ( ( member_Code_integer @ X4 @ A25 )
% 9.17/5.42 => ( ( G @ X4 )
% 9.17/5.42 = one_one_rat ) ) ) ) ) )
% 9.17/5.42 => ( ( groups2555765274223993564er_rat @ G @ ( comple739944243200306918nteger @ B5 ) )
% 9.17/5.42 = ( comp_s9045439038509510147er_rat @ groups5409254039008640018er_rat @ groups2555765274223993564er_rat @ G @ B5 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6714_prod_OUnion__comp,axiom,
% 9.17/5.42 ! [B5: set_set_o,G: $o > nat] :
% 9.17/5.42 ( ! [X4: set_o] :
% 9.17/5.42 ( ( member_set_o @ X4 @ B5 )
% 9.17/5.42 => ( finite_finite_o @ X4 ) )
% 9.17/5.42 => ( ! [A14: set_o] :
% 9.17/5.42 ( ( member_set_o @ A14 @ B5 )
% 9.17/5.42 => ! [A25: set_o] :
% 9.17/5.42 ( ( member_set_o @ A25 @ B5 )
% 9.17/5.42 => ( ( A14 != A25 )
% 9.17/5.42 => ! [X4: $o] :
% 9.17/5.42 ( ( member_o @ X4 @ A14 )
% 9.17/5.42 => ( ( member_o @ X4 @ A25 )
% 9.17/5.42 => ( ( G @ X4 )
% 9.17/5.42 = one_one_nat ) ) ) ) ) )
% 9.17/5.42 => ( ( groups3504817904513533571_o_nat @ G @ ( comple90263536869209701_set_o @ B5 ) )
% 9.17/5.42 = ( comp_s6084864194472624150_o_nat @ groups4868773677410035043_o_nat @ groups3504817904513533571_o_nat @ G @ B5 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6715_UN__UN__finite__eq,axiom,
% 9.17/5.42 ! [A2: nat > set_nat] :
% 9.17/5.42 ( ( comple7399068483239264473et_nat
% 9.17/5.42 @ ( image_nat_set_nat
% 9.17/5.42 @ ^ [N4: nat] : ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ A2 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N4 ) ) )
% 9.17/5.42 @ top_top_set_nat ) )
% 9.17/5.42 = ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ A2 @ top_top_set_nat ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6716_UN__le__add__shift,axiom,
% 9.17/5.42 ! [M3: nat > set_nat,K: nat,N2: nat] :
% 9.17/5.42 ( ( comple7399068483239264473et_nat
% 9.17/5.42 @ ( image_nat_set_nat
% 9.17/5.42 @ ^ [I3: nat] : ( M3 @ ( plus_plus_nat @ I3 @ K ) )
% 9.17/5.42 @ ( set_ord_atMost_nat @ N2 ) ) )
% 9.17/5.42 = ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ M3 @ ( set_or1269000886237332187st_nat @ K @ ( plus_plus_nat @ N2 @ K ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6717_UN__le__add__shift__strict,axiom,
% 9.17/5.42 ! [M3: nat > set_nat,K: nat,N2: nat] :
% 9.17/5.42 ( ( comple7399068483239264473et_nat
% 9.17/5.42 @ ( image_nat_set_nat
% 9.17/5.42 @ ^ [I3: nat] : ( M3 @ ( plus_plus_nat @ I3 @ K ) )
% 9.17/5.42 @ ( set_ord_lessThan_nat @ N2 ) ) )
% 9.17/5.42 = ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ M3 @ ( set_or4665077453230672383an_nat @ K @ ( plus_plus_nat @ N2 @ K ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6718_rat__sgn__code,axiom,
% 9.17/5.42 ! [P4: rat] :
% 9.17/5.42 ( ( quotient_of @ ( sgn_sgn_rat @ P4 ) )
% 9.17/5.42 = ( product_Pair_int_int @ ( sgn_sgn_int @ ( product_fst_int_int @ ( quotient_of @ P4 ) ) ) @ one_one_int ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6719_bezw__non__0,axiom,
% 9.17/5.42 ! [Y: nat,X: nat] :
% 9.17/5.42 ( ( ord_less_nat @ zero_zero_nat @ Y )
% 9.17/5.42 => ( ( bezw @ X @ Y )
% 9.17/5.42 = ( 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 ) ) ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6720_UN__finite__subset,axiom,
% 9.17/5.42 ! [A2: nat > set_nat,C4: set_nat] :
% 9.17/5.42 ( ! [N: nat] : ( ord_less_eq_set_nat @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ A2 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) @ C4 )
% 9.17/5.42 => ( ord_less_eq_set_nat @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ A2 @ top_top_set_nat ) ) @ C4 ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6721_UN__finite2__eq,axiom,
% 9.17/5.42 ! [A2: nat > set_nat,B5: nat > set_nat,K: nat] :
% 9.17/5.42 ( ! [N: nat] :
% 9.17/5.42 ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ A2 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) )
% 9.17/5.42 = ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ B5 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( plus_plus_nat @ N @ K ) ) ) ) )
% 9.17/5.42 => ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ A2 @ top_top_set_nat ) )
% 9.17/5.42 = ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ B5 @ top_top_set_nat ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6722_bezw_Oelims,axiom,
% 9.17/5.42 ! [X: nat,Xa: nat,Y: product_prod_int_int] :
% 9.17/5.42 ( ( ( bezw @ X @ Xa )
% 9.17/5.42 = Y )
% 9.17/5.42 => ( ( ( Xa = zero_zero_nat )
% 9.17/5.42 => ( Y
% 9.17/5.42 = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) )
% 9.17/5.42 & ( ( Xa != zero_zero_nat )
% 9.17/5.42 => ( Y
% 9.17/5.42 = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X @ Xa ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X @ Xa ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X @ Xa ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X @ Xa ) ) ) ) ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6723_bezw_Osimps,axiom,
% 9.17/5.42 ( bezw
% 9.17/5.42 = ( ^ [X3: nat,Y3: nat] : ( if_Pro3027730157355071871nt_int @ ( Y3 = zero_zero_nat ) @ ( product_Pair_int_int @ one_one_int @ zero_zero_int ) @ ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Y3 @ ( modulo_modulo_nat @ X3 @ Y3 ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Y3 @ ( modulo_modulo_nat @ X3 @ Y3 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Y3 @ ( modulo_modulo_nat @ X3 @ Y3 ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X3 @ Y3 ) ) ) ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6724_max__ext__def,axiom,
% 9.17/5.42 ( max_ex4535816423174879388at_nat
% 9.17/5.42 = ( ^ [R5: set_Pr4329608150637261639at_nat] :
% 9.17/5.42 ( collec2601550354786890194at_nat
% 9.17/5.42 @ ( produc1491100424724016556_nat_o
% 9.17/5.42 @ ( max_ex4845989503969680116at_nat
% 9.17/5.42 @ ^ [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ Y3 ) @ R5 ) ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6725_max__ext__def,axiom,
% 9.17/5.42 ( max_ext_nat
% 9.17/5.42 = ( ^ [R5: set_Pr1261947904930325089at_nat] :
% 9.17/5.42 ( collec6662362479098859352et_nat
% 9.17/5.42 @ ( produc6247414631856714078_nat_o
% 9.17/5.42 @ ( max_extp_nat
% 9.17/5.42 @ ^ [X3: nat,Y3: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y3 ) @ R5 ) ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6726_max__ext__def,axiom,
% 9.17/5.42 ( max_ex8135407076693332796at_nat
% 9.17/5.42 = ( ^ [R5: set_Pr8693737435421807431at_nat] :
% 9.17/5.42 ( collec6321179662152712658at_nat
% 9.17/5.42 @ ( produc410239310623530412_nat_o
% 9.17/5.42 @ ( max_ex4864111882549613972at_nat
% 9.17/5.42 @ ^ [X3: product_prod_nat_nat,Y3: product_prod_nat_nat] : ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X3 @ Y3 ) @ R5 ) ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6727_UN__finite2__subset,axiom,
% 9.17/5.42 ! [A2: nat > set_nat,B5: nat > set_nat,K: nat] :
% 9.17/5.42 ( ! [N: nat] : ( ord_less_eq_set_nat @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ A2 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ B5 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( plus_plus_nat @ N @ K ) ) ) ) )
% 9.17/5.42 => ( ord_less_eq_set_nat @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ A2 @ top_top_set_nat ) ) @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ B5 @ top_top_set_nat ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6728_bezw_Opelims,axiom,
% 9.17/5.42 ! [X: nat,Xa: nat,Y: product_prod_int_int] :
% 9.17/5.42 ( ( ( bezw @ X @ Xa )
% 9.17/5.42 = Y )
% 9.17/5.42 => ( ( accp_P4275260045618599050at_nat @ bezw_rel @ ( product_Pair_nat_nat @ X @ Xa ) )
% 9.17/5.42 => ~ ( ( ( ( Xa = zero_zero_nat )
% 9.17/5.42 => ( Y
% 9.17/5.42 = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) )
% 9.17/5.42 & ( ( Xa != zero_zero_nat )
% 9.17/5.42 => ( Y
% 9.17/5.42 = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X @ Xa ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X @ Xa ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X @ Xa ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X @ Xa ) ) ) ) ) ) ) )
% 9.17/5.42 => ~ ( accp_P4275260045618599050at_nat @ bezw_rel @ ( product_Pair_nat_nat @ X @ Xa ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6729_snd__diag__id,axiom,
% 9.17/5.42 ! [Z: $o] :
% 9.17/5.42 ( ( comp_P2137996956111167876_o_o_o @ product_snd_o_o
% 9.17/5.42 @ ^ [X3: $o] : ( product_Pair_o_o @ X3 @ X3 )
% 9.17/5.42 @ Z )
% 9.17/5.42 = ( id_o @ Z ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6730_snd__diag__id,axiom,
% 9.17/5.42 ! [Z: nat] :
% 9.17/5.42 ( ( comp_P1955610211387027840at_nat @ product_snd_nat_nat
% 9.17/5.42 @ ^ [X3: nat] : ( product_Pair_nat_nat @ X3 @ X3 )
% 9.17/5.42 @ Z )
% 9.17/5.42 = ( id_nat @ Z ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6731_snd__diag__id,axiom,
% 9.17/5.42 ! [Z: nat > $o] :
% 9.17/5.42 ( ( comp_P8312345242777556868_nat_o @ produc6795044007072221829_nat_o
% 9.17/5.42 @ ^ [X3: nat > $o] : ( produc5701653931590357335_nat_o @ X3 @ X3 )
% 9.17/5.42 @ Z )
% 9.17/5.42 = ( id_nat_o @ Z ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6732_snd__diag__id,axiom,
% 9.17/5.42 ! [Z: num] :
% 9.17/5.42 ( ( comp_P864883071962432936um_num @ product_snd_num_num
% 9.17/5.42 @ ^ [X3: num] : ( product_Pair_num_num @ X3 @ X3 )
% 9.17/5.42 @ Z )
% 9.17/5.42 = ( id_num @ Z ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6733_snd__diag__id,axiom,
% 9.17/5.42 ! [Z: code_integer] :
% 9.17/5.42 ( ( comp_P7111796090210262324nteger @ produc6174133586879617921nteger
% 9.17/5.42 @ ^ [X3: code_integer] : ( produc1086072967326762835nteger @ X3 @ X3 )
% 9.17/5.42 @ Z )
% 9.17/5.42 = ( id_Code_integer @ Z ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6734_snd__diag__id,axiom,
% 9.17/5.42 ! [Z: int] :
% 9.17/5.42 ( ( comp_P6651465171681656048nt_int @ product_snd_int_int
% 9.17/5.42 @ ^ [X3: int] : ( product_Pair_int_int @ X3 @ X3 )
% 9.17/5.42 @ Z )
% 9.17/5.42 = ( id_int @ Z ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6735_fst__diag__id,axiom,
% 9.17/5.42 ! [Z: $o] :
% 9.17/5.42 ( ( comp_P2137996956111167876_o_o_o @ product_fst_o_o
% 9.17/5.42 @ ^ [X3: $o] : ( product_Pair_o_o @ X3 @ X3 )
% 9.17/5.42 @ Z )
% 9.17/5.42 = ( id_o @ Z ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6736_fst__diag__id,axiom,
% 9.17/5.42 ! [Z: nat] :
% 9.17/5.42 ( ( comp_P1955610211387027840at_nat @ product_fst_nat_nat
% 9.17/5.42 @ ^ [X3: nat] : ( product_Pair_nat_nat @ X3 @ X3 )
% 9.17/5.42 @ Z )
% 9.17/5.42 = ( id_nat @ Z ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6737_fst__diag__id,axiom,
% 9.17/5.42 ! [Z: nat > $o] :
% 9.17/5.42 ( ( comp_P8312345242777556868_nat_o @ produc6972895793295859523_nat_o
% 9.17/5.42 @ ^ [X3: nat > $o] : ( produc5701653931590357335_nat_o @ X3 @ X3 )
% 9.17/5.42 @ Z )
% 9.17/5.42 = ( id_nat_o @ Z ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6738_fst__diag__id,axiom,
% 9.17/5.42 ! [Z: num] :
% 9.17/5.42 ( ( comp_P864883071962432936um_num @ product_fst_num_num
% 9.17/5.42 @ ^ [X3: num] : ( product_Pair_num_num @ X3 @ X3 )
% 9.17/5.42 @ Z )
% 9.17/5.42 = ( id_num @ Z ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6739_fst__diag__id,axiom,
% 9.17/5.42 ! [Z: code_integer] :
% 9.17/5.42 ( ( comp_P7111796090210262324nteger @ produc8508995932063986495nteger
% 9.17/5.42 @ ^ [X3: code_integer] : ( produc1086072967326762835nteger @ X3 @ X3 )
% 9.17/5.42 @ Z )
% 9.17/5.42 = ( id_Code_integer @ Z ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6740_fst__diag__id,axiom,
% 9.17/5.42 ! [Z: int] :
% 9.17/5.42 ( ( comp_P6651465171681656048nt_int @ product_fst_int_int
% 9.17/5.42 @ ^ [X3: int] : ( product_Pair_int_int @ X3 @ X3 )
% 9.17/5.42 @ Z )
% 9.17/5.42 = ( id_int @ Z ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6741_size__prod__simp,axiom,
% 9.17/5.42 ( basic_7565498685090299632nteger
% 9.17/5.42 = ( ^ [F2: code_integer > nat,G2: code_integer > nat,P6: produc8923325533196201883nteger] : ( plus_plus_nat @ ( plus_plus_nat @ ( F2 @ ( produc8508995932063986495nteger @ P6 ) ) @ ( G2 @ ( produc6174133586879617921nteger @ P6 ) ) ) @ ( suc @ zero_zero_nat ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6742_size__prod__simp,axiom,
% 9.17/5.42 ( basic_1872990034501187214nt_int
% 9.17/5.42 = ( ^ [F2: int > nat,G2: int > nat,P6: product_prod_int_int] : ( plus_plus_nat @ ( plus_plus_nat @ ( F2 @ ( product_fst_int_int @ P6 ) ) @ ( G2 @ ( product_snd_int_int @ P6 ) ) ) @ ( suc @ zero_zero_nat ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6743_size__prod__simp,axiom,
% 9.17/5.42 ( basic_8185638495112405971atural
% 9.17/5.42 = ( ^ [F2: code_natural > nat,G2: produc7822875418678951345atural > nat,P6: produc5835291356934675326atural] : ( plus_plus_nat @ ( plus_plus_nat @ ( F2 @ ( produc497848011034438852atural @ P6 ) ) @ ( G2 @ ( produc6591912806276919810atural @ P6 ) ) ) @ ( suc @ zero_zero_nat ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6744_fst__diag__snd,axiom,
% 9.17/5.42 ( ( comp_P3428181540658402820nteger @ produc8508995932063986495nteger
% 9.17/5.42 @ ( comp_C2277306503614464128nteger
% 9.17/5.42 @ ^ [X3: code_integer] : ( produc1086072967326762835nteger @ X3 @ X3 )
% 9.17/5.42 @ produc6174133586879617921nteger ) )
% 9.17/5.42 = produc6174133586879617921nteger ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6745_fst__diag__snd,axiom,
% 9.17/5.42 ( ( comp_P5356232565778667509nt_int @ product_fst_int_int
% 9.17/5.42 @ ( comp_i5941103828406351439nt_int
% 9.17/5.42 @ ^ [X3: int] : ( product_Pair_int_int @ X3 @ X3 )
% 9.17/5.42 @ product_snd_int_int ) )
% 9.17/5.42 = product_snd_int_int ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6746_fst__diag__snd,axiom,
% 9.17/5.42 ( ( comp_P230220204662055659atural @ produc1537665297809786051atural
% 9.17/5.42 @ ( comp_P4943825737035310295atural
% 9.17/5.42 @ ^ [X3: produc7822875418678951345atural] : ( produc4480994950612372183atural @ X3 @ X3 )
% 9.17/5.42 @ produc6591912806276919810atural ) )
% 9.17/5.42 = produc6591912806276919810atural ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6747_snd__diag__fst,axiom,
% 9.17/5.42 ( ( comp_P3428181540658402820nteger @ produc6174133586879617921nteger
% 9.17/5.42 @ ( comp_C2277306503614464128nteger
% 9.17/5.42 @ ^ [X3: code_integer] : ( produc1086072967326762835nteger @ X3 @ X3 )
% 9.17/5.42 @ produc8508995932063986495nteger ) )
% 9.17/5.42 = produc8508995932063986495nteger ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6748_snd__diag__fst,axiom,
% 9.17/5.42 ( ( comp_P5356232565778667509nt_int @ product_snd_int_int
% 9.17/5.42 @ ( comp_i5941103828406351439nt_int
% 9.17/5.42 @ ^ [X3: int] : ( product_Pair_int_int @ X3 @ X3 )
% 9.17/5.42 @ product_fst_int_int ) )
% 9.17/5.42 = product_fst_int_int ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6749_INF__Int__eq2,axiom,
% 9.17/5.42 ! [S2: set_se5479201105039950375at_nat] :
% 9.17/5.42 ( ( comple8322679762649017525_nat_o
% 9.17/5.42 @ ( image_6595146019508340652_nat_o
% 9.17/5.42 @ ^ [I3: set_Pr4329608150637261639at_nat,X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ Y3 ) @ I3 )
% 9.17/5.42 @ S2 ) )
% 9.17/5.42 = ( ^ [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ Y3 ) @ ( comple6751905152567503566at_nat @ S2 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6750_INF__Int__eq2,axiom,
% 9.17/5.42 ! [S2: set_se7855581050983116737at_nat] :
% 9.17/5.42 ( ( comple1675732732025788397_nat_o
% 9.17/5.42 @ ( image_6923511907955291850_nat_o
% 9.17/5.42 @ ^ [I3: set_Pr1261947904930325089at_nat,X3: nat,Y3: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y3 ) @ I3 )
% 9.17/5.42 @ S2 ) )
% 9.17/5.42 = ( ^ [X3: nat,Y3: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y3 ) @ ( comple1930127330929219688at_nat @ S2 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6751_INF__Int__eq2,axiom,
% 9.17/5.42 ! [S2: set_se124295367203800706nteger] :
% 9.17/5.42 ( ( comple797978290332539892eger_o
% 9.17/5.42 @ ( image_3377504002992083726eger_o
% 9.17/5.42 @ ^ [I3: set_Pr1281608226676607948nteger,X3: produc6241069584506657477e_term > option6357759511663192854e_term,Y3: produc8923325533196201883nteger] : ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X3 @ Y3 ) @ I3 )
% 9.17/5.42 @ S2 ) )
% 9.17/5.42 = ( ^ [X3: produc6241069584506657477e_term > option6357759511663192854e_term,Y3: produc8923325533196201883nteger] : ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X3 @ Y3 ) @ ( comple141797230998674821nteger @ S2 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6752_INF__Int__eq2,axiom,
% 9.17/5.42 ! [S2: set_se8543413830569400298et_nat] :
% 9.17/5.42 ( ( comple4401490224799119198_nat_o
% 9.17/5.42 @ ( image_1071233342602175200_nat_o
% 9.17/5.42 @ ^ [I3: set_Pr3286484037609594932et_nat,X3: produc3658429121746597890et_nat > $o,Y3: produc3658429121746597890et_nat] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X3 @ Y3 ) @ I3 )
% 9.17/5.42 @ S2 ) )
% 9.17/5.42 = ( ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3658429121746597890et_nat] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X3 @ Y3 ) @ ( comple8712884055654468845et_nat @ S2 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6753_INF__Int__eq2,axiom,
% 9.17/5.42 ! [S2: set_se5120235452707311462et_nat] :
% 9.17/5.42 ( ( comple1647972170925272290_nat_o
% 9.17/5.42 @ ( image_6856364241397052896_nat_o
% 9.17/5.42 @ ^ [I3: set_Pr8536935166611901872et_nat,X3: produc3658429121746597890et_nat > $o,Y3: produc3925858234332021118et_nat] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X3 @ Y3 ) @ I3 )
% 9.17/5.42 @ S2 ) )
% 9.17/5.42 = ( ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3925858234332021118et_nat] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X3 @ Y3 ) @ ( comple8400030738448405097et_nat @ S2 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6754_INF__Int__eq2,axiom,
% 9.17/5.42 ! [S2: set_se2364587433798273647nt_int] :
% 9.17/5.42 ( ( comple2375672059646964807_int_o
% 9.17/5.42 @ ( image_5684251269295653582_int_o
% 9.17/5.42 @ ^ [I3: set_Pr9222295170931077689nt_int,X3: produc8551481072490612790e_term > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X3 @ Y3 ) @ I3 )
% 9.17/5.42 @ S2 ) )
% 9.17/5.42 = ( ^ [X3: produc8551481072490612790e_term > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X3 @ Y3 ) @ ( comple6065809805536145394nt_int @ S2 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6755_INF__Int__eq2,axiom,
% 9.17/5.42 ! [S2: set_se7394616247590735609nt_int] :
% 9.17/5.42 ( ( comple7280212863790966717_int_o
% 9.17/5.42 @ ( image_1744818337813142478_int_o
% 9.17/5.42 @ ^ [I3: set_Pr1872883991513573699nt_int,X3: int > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X3 @ Y3 ) @ I3 )
% 9.17/5.42 @ S2 ) )
% 9.17/5.42 = ( ^ [X3: int > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X3 @ Y3 ) @ ( comple2057271477292249724nt_int @ S2 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6756_SUP__Sup__eq2,axiom,
% 9.17/5.42 ! [S2: set_se5479201105039950375at_nat] :
% 9.17/5.42 ( ( comple493620192902636699_nat_o
% 9.17/5.42 @ ( image_6595146019508340652_nat_o
% 9.17/5.42 @ ^ [I3: set_Pr4329608150637261639at_nat,X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ Y3 ) @ I3 )
% 9.17/5.42 @ S2 ) )
% 9.17/5.42 = ( ^ [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ Y3 ) @ ( comple4364388969068068532at_nat @ S2 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6757_SUP__Sup__eq2,axiom,
% 9.17/5.42 ! [S2: set_se7855581050983116737at_nat] :
% 9.17/5.42 ( ( comple3592611370556534995_nat_o
% 9.17/5.42 @ ( image_6923511907955291850_nat_o
% 9.17/5.42 @ ^ [I3: set_Pr1261947904930325089at_nat,X3: nat,Y3: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y3 ) @ I3 )
% 9.17/5.42 @ S2 ) )
% 9.17/5.42 = ( ^ [X3: nat,Y3: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y3 ) @ ( comple5685304695842803022at_nat @ S2 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6758_SUP__Sup__eq2,axiom,
% 9.17/5.42 ! [S2: set_se124295367203800706nteger] :
% 9.17/5.42 ( ( comple6692557002573936782eger_o
% 9.17/5.42 @ ( image_3377504002992083726eger_o
% 9.17/5.42 @ ^ [I3: set_Pr1281608226676607948nteger,X3: produc6241069584506657477e_term > option6357759511663192854e_term,Y3: produc8923325533196201883nteger] : ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X3 @ Y3 ) @ I3 )
% 9.17/5.42 @ S2 ) )
% 9.17/5.42 = ( ^ [X3: produc6241069584506657477e_term > option6357759511663192854e_term,Y3: produc8923325533196201883nteger] : ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X3 @ Y3 ) @ ( comple1324685164916153887nteger @ S2 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6759_SUP__Sup__eq2,axiom,
% 9.17/5.42 ! [S2: set_se8543413830569400298et_nat] :
% 9.17/5.42 ( ( comple2736776311324672504_nat_o
% 9.17/5.42 @ ( image_1071233342602175200_nat_o
% 9.17/5.42 @ ^ [I3: set_Pr3286484037609594932et_nat,X3: produc3658429121746597890et_nat > $o,Y3: produc3658429121746597890et_nat] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X3 @ Y3 ) @ I3 )
% 9.17/5.42 @ S2 ) )
% 9.17/5.42 = ( ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3658429121746597890et_nat] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X3 @ Y3 ) @ ( comple4849024849677941639et_nat @ S2 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6760_SUP__Sup__eq2,axiom,
% 9.17/5.42 ! [S2: set_se5120235452707311462et_nat] :
% 9.17/5.42 ( ( comple5542144468884744060_nat_o
% 9.17/5.42 @ ( image_6856364241397052896_nat_o
% 9.17/5.42 @ ^ [I3: set_Pr8536935166611901872et_nat,X3: produc3658429121746597890et_nat > $o,Y3: produc3925858234332021118et_nat] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X3 @ Y3 ) @ I3 )
% 9.17/5.42 @ S2 ) )
% 9.17/5.42 = ( ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3925858234332021118et_nat] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X3 @ Y3 ) @ ( comple5063570841203093763et_nat @ S2 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6761_SUP__Sup__eq2,axiom,
% 9.17/5.42 ! [S2: set_se2364587433798273647nt_int] :
% 9.17/5.42 ( ( comple7735192718774405345_int_o
% 9.17/5.42 @ ( image_5684251269295653582_int_o
% 9.17/5.42 @ ^ [I3: set_Pr9222295170931077689nt_int,X3: produc8551481072490612790e_term > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X3 @ Y3 ) @ I3 )
% 9.17/5.42 @ S2 ) )
% 9.17/5.42 = ( ^ [X3: produc8551481072490612790e_term > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X3 @ Y3 ) @ ( comple6871990601243273356nt_int @ S2 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6762_SUP__Sup__eq2,axiom,
% 9.17/5.42 ! [S2: set_se7394616247590735609nt_int] :
% 9.17/5.42 ( ( comple8902563120744349527_int_o
% 9.17/5.42 @ ( image_1744818337813142478_int_o
% 9.17/5.42 @ ^ [I3: set_Pr1872883991513573699nt_int,X3: int > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X3 @ Y3 ) @ I3 )
% 9.17/5.42 @ S2 ) )
% 9.17/5.42 = ( ^ [X3: int > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X3 @ Y3 ) @ ( comple5772984051336441366nt_int @ S2 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6763_Inf__INT__eq2,axiom,
% 9.17/5.42 ( comple8322679762649017525_nat_o
% 9.17/5.42 = ( ^ [S5: set_se9180647916752606350_nat_o,X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ Y3 ) @ ( comple6751905152567503566at_nat @ ( image_4902389024228248874at_nat @ collec6321179662152712658at_nat @ ( image_6226802281960588479_nat_o @ produc410239310623530412_nat_o @ S5 ) ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6764_Inf__INT__eq2,axiom,
% 9.17/5.42 ( comple1675732732025788397_nat_o
% 9.17/5.42 = ( ^ [S5: set_nat_nat_o,X3: nat,Y3: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y3 ) @ ( comple1930127330929219688at_nat @ ( image_7124889717316225246at_nat @ collec3392354462482085612at_nat @ ( image_7429393840292777309_nat_o @ produc6081775807080527818_nat_o @ S5 ) ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6765_Inf__INT__eq2,axiom,
% 9.17/5.42 ( comple797978290332539892eger_o
% 9.17/5.42 = ( ^ [S5: set_Pr8914822823351560561eger_o,X3: produc6241069584506657477e_term > option6357759511663192854e_term,Y3: produc8923325533196201883nteger] : ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X3 @ Y3 ) @ ( comple141797230998674821nteger @ ( image_2691561895000378432nteger @ collec6950949345391930603nteger @ ( image_5214523798439755767eger_o @ produc6253627499356882019eger_o @ S5 ) ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6766_Inf__INT__eq2,axiom,
% 9.17/5.42 ( comple4401490224799119198_nat_o
% 9.17/5.42 = ( ^ [S5: set_Pr8208987589773510107_nat_o,X3: produc3658429121746597890et_nat > $o,Y3: produc3658429121746597890et_nat] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X3 @ Y3 ) @ ( comple8712884055654468845et_nat @ ( image_8138495846740763712et_nat @ collec1402215087704437587et_nat @ ( image_8189751627993580965_nat_o @ produc1437786849005270451_nat_o @ S5 ) ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6767_Inf__INT__eq2,axiom,
% 9.17/5.42 ( comple1647972170925272290_nat_o
% 9.17/5.42 = ( ^ [S5: set_Pr1457143144315775327_nat_o,X3: produc3658429121746597890et_nat > $o,Y3: produc3925858234332021118et_nat] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X3 @ Y3 ) @ ( comple8400030738448405097et_nat @ ( image_3321512208570918720et_nat @ collec5543584681430388431et_nat @ ( image_1033581555836824229_nat_o @ produc838355143741117751_nat_o @ S5 ) ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6768_Inf__INT__eq2,axiom,
% 9.17/5.42 ( comple2375672059646964807_int_o
% 9.17/5.42 = ( ^ [S5: set_Pr5050529186185961540_int_o,X3: produc8551481072490612790e_term > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X3 @ Y3 ) @ ( comple6065809805536145394nt_int @ ( image_7643917626522560896nt_int @ collec1790188477890212312nt_int @ ( image_7631425643974863415_int_o @ produc1573362020775583542_int_o @ S5 ) ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6769_Inf__INT__eq2,axiom,
% 9.17/5.42 ( comple7280212863790966717_int_o
% 9.17/5.42 = ( ^ [S5: set_in8474487674441654202_int_o,X3: int > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X3 @ Y3 ) @ ( comple2057271477292249724nt_int @ ( image_2770089787918713472nt_int @ collec506566255779805410nt_int @ ( image_7670822187664137143_int_o @ produc2558449545302689196_int_o @ S5 ) ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6770_Sup__SUP__eq2,axiom,
% 9.17/5.42 ( comple493620192902636699_nat_o
% 9.17/5.42 = ( ^ [S5: set_se9180647916752606350_nat_o,X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ Y3 ) @ ( comple4364388969068068532at_nat @ ( image_4902389024228248874at_nat @ collec6321179662152712658at_nat @ ( image_6226802281960588479_nat_o @ produc410239310623530412_nat_o @ S5 ) ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6771_Sup__SUP__eq2,axiom,
% 9.17/5.42 ( comple3592611370556534995_nat_o
% 9.17/5.42 = ( ^ [S5: set_nat_nat_o,X3: nat,Y3: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y3 ) @ ( comple5685304695842803022at_nat @ ( image_7124889717316225246at_nat @ collec3392354462482085612at_nat @ ( image_7429393840292777309_nat_o @ produc6081775807080527818_nat_o @ S5 ) ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6772_Sup__SUP__eq2,axiom,
% 9.17/5.42 ( comple6692557002573936782eger_o
% 9.17/5.42 = ( ^ [S5: set_Pr8914822823351560561eger_o,X3: produc6241069584506657477e_term > option6357759511663192854e_term,Y3: produc8923325533196201883nteger] : ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X3 @ Y3 ) @ ( comple1324685164916153887nteger @ ( image_2691561895000378432nteger @ collec6950949345391930603nteger @ ( image_5214523798439755767eger_o @ produc6253627499356882019eger_o @ S5 ) ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6773_Sup__SUP__eq2,axiom,
% 9.17/5.42 ( comple2736776311324672504_nat_o
% 9.17/5.42 = ( ^ [S5: set_Pr8208987589773510107_nat_o,X3: produc3658429121746597890et_nat > $o,Y3: produc3658429121746597890et_nat] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X3 @ Y3 ) @ ( comple4849024849677941639et_nat @ ( image_8138495846740763712et_nat @ collec1402215087704437587et_nat @ ( image_8189751627993580965_nat_o @ produc1437786849005270451_nat_o @ S5 ) ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6774_Sup__SUP__eq2,axiom,
% 9.17/5.42 ( comple5542144468884744060_nat_o
% 9.17/5.42 = ( ^ [S5: set_Pr1457143144315775327_nat_o,X3: produc3658429121746597890et_nat > $o,Y3: produc3925858234332021118et_nat] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X3 @ Y3 ) @ ( comple5063570841203093763et_nat @ ( image_3321512208570918720et_nat @ collec5543584681430388431et_nat @ ( image_1033581555836824229_nat_o @ produc838355143741117751_nat_o @ S5 ) ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6775_Sup__SUP__eq2,axiom,
% 9.17/5.42 ( comple7735192718774405345_int_o
% 9.17/5.42 = ( ^ [S5: set_Pr5050529186185961540_int_o,X3: produc8551481072490612790e_term > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X3 @ Y3 ) @ ( comple6871990601243273356nt_int @ ( image_7643917626522560896nt_int @ collec1790188477890212312nt_int @ ( image_7631425643974863415_int_o @ produc1573362020775583542_int_o @ S5 ) ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6776_Sup__SUP__eq2,axiom,
% 9.17/5.42 ( comple8902563120744349527_int_o
% 9.17/5.42 = ( ^ [S5: set_in8474487674441654202_int_o,X3: int > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X3 @ Y3 ) @ ( comple5772984051336441366nt_int @ ( image_2770089787918713472nt_int @ collec506566255779805410nt_int @ ( image_7670822187664137143_int_o @ produc2558449545302689196_int_o @ S5 ) ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6777_fst__diag__fst,axiom,
% 9.17/5.42 ( ( comp_P3428181540658402820nteger @ produc8508995932063986495nteger
% 9.17/5.42 @ ( comp_C2277306503614464128nteger
% 9.17/5.42 @ ^ [X3: code_integer] : ( produc1086072967326762835nteger @ X3 @ X3 )
% 9.17/5.42 @ produc8508995932063986495nteger ) )
% 9.17/5.42 = produc8508995932063986495nteger ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6778_fst__diag__fst,axiom,
% 9.17/5.42 ( ( comp_P5356232565778667509nt_int @ product_fst_int_int
% 9.17/5.42 @ ( comp_i5941103828406351439nt_int
% 9.17/5.42 @ ^ [X3: int] : ( product_Pair_int_int @ X3 @ X3 )
% 9.17/5.42 @ product_fst_int_int ) )
% 9.17/5.42 = product_fst_int_int ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6779_snd__diag__snd,axiom,
% 9.17/5.42 ( ( comp_P230220204662055659atural @ produc7455300194457530885atural
% 9.17/5.42 @ ( comp_P4943825737035310295atural
% 9.17/5.42 @ ^ [X3: produc7822875418678951345atural] : ( produc4480994950612372183atural @ X3 @ X3 )
% 9.17/5.42 @ produc6591912806276919810atural ) )
% 9.17/5.42 = produc6591912806276919810atural ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6780_snd__diag__snd,axiom,
% 9.17/5.42 ( ( comp_P3428181540658402820nteger @ produc6174133586879617921nteger
% 9.17/5.42 @ ( comp_C2277306503614464128nteger
% 9.17/5.42 @ ^ [X3: code_integer] : ( produc1086072967326762835nteger @ X3 @ X3 )
% 9.17/5.42 @ produc6174133586879617921nteger ) )
% 9.17/5.42 = produc6174133586879617921nteger ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6781_snd__diag__snd,axiom,
% 9.17/5.42 ( ( comp_P5356232565778667509nt_int @ product_snd_int_int
% 9.17/5.42 @ ( comp_i5941103828406351439nt_int
% 9.17/5.42 @ ^ [X3: int] : ( product_Pair_int_int @ X3 @ X3 )
% 9.17/5.42 @ product_snd_int_int ) )
% 9.17/5.42 = product_snd_int_int ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6782_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 9.17/5.42 ! [P: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o,X: produc6241069584506657477e_term > option6357759511663192854e_term,Y: produc8923325533196201883nteger,A: produc1908205239877642774nteger] :
% 9.17/5.42 ( ( P @ X @ Y )
% 9.17/5.42 => ( ( A
% 9.17/5.42 = ( produc8603105652947943368nteger @ X @ Y ) )
% 9.17/5.42 => ( P @ ( produc7822682618958472924nteger @ A ) @ ( produc7856867400915047194nteger @ A ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6783_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 9.17/5.42 ! [P: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o,X: produc3658429121746597890et_nat > $o,Y: produc3658429121746597890et_nat,A: produc3925858234332021118et_nat] :
% 9.17/5.42 ( ( P @ X @ Y )
% 9.17/5.42 => ( ( A
% 9.17/5.42 = ( produc5001842942810119800et_nat @ X @ Y ) )
% 9.17/5.42 => ( P @ ( produc995936583742144908et_nat @ A ) @ ( produc4011572625026189258et_nat @ A ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6784_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 9.17/5.42 ! [P: ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o,X: produc3658429121746597890et_nat > $o,Y: produc3925858234332021118et_nat,A: produc2732055786443039994et_nat] :
% 9.17/5.42 ( ( P @ X @ Y )
% 9.17/5.42 => ( ( A
% 9.17/5.42 = ( produc2245416461498447860et_nat @ X @ Y ) )
% 9.17/5.42 => ( P @ ( produc180342877477747464et_nat @ A ) @ ( produc5374455773327741254et_nat @ A ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6785_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 9.17/5.42 ! [P: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o,X: produc8551481072490612790e_term > option6357759511663192854e_term,Y: product_prod_int_int,A: produc2285326912895808259nt_int] :
% 9.17/5.42 ( ( P @ X @ Y )
% 9.17/5.42 => ( ( A
% 9.17/5.42 = ( produc5700946648718959541nt_int @ X @ Y ) )
% 9.17/5.42 => ( P @ ( produc6816164490631068361nt_int @ A ) @ ( produc7328097813583171335nt_int @ A ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6786_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 9.17/5.42 ! [P: ( int > option6357759511663192854e_term ) > product_prod_int_int > $o,X: int > option6357759511663192854e_term,Y: product_prod_int_int,A: produc7773217078559923341nt_int] :
% 9.17/5.42 ( ( P @ X @ Y )
% 9.17/5.42 => ( ( A
% 9.17/5.42 = ( produc4305682042979456191nt_int @ X @ Y ) )
% 9.17/5.42 => ( P @ ( produc6230002227079971283nt_int @ A ) @ ( produc3162348030201620241nt_int @ A ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6787_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 9.17/5.42 ! [P: code_integer > code_integer > $o,X: code_integer,Y: code_integer,A: produc8923325533196201883nteger] :
% 9.17/5.42 ( ( P @ X @ Y )
% 9.17/5.42 => ( ( A
% 9.17/5.42 = ( produc1086072967326762835nteger @ X @ Y ) )
% 9.17/5.42 => ( P @ ( produc8508995932063986495nteger @ A ) @ ( produc6174133586879617921nteger @ A ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6788_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 9.17/5.42 ! [P: int > int > $o,X: int,Y: int,A: product_prod_int_int] :
% 9.17/5.42 ( ( P @ X @ Y )
% 9.17/5.42 => ( ( A
% 9.17/5.42 = ( product_Pair_int_int @ X @ Y ) )
% 9.17/5.42 => ( P @ ( product_fst_int_int @ A ) @ ( product_snd_int_int @ A ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6789_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 9.17/5.42 ! [P: code_natural > produc7822875418678951345atural > $o,X: code_natural,Y: produc7822875418678951345atural,A: produc5835291356934675326atural] :
% 9.17/5.42 ( ( P @ X @ Y )
% 9.17/5.42 => ( ( A
% 9.17/5.42 = ( produc6639722614265839536atural @ X @ Y ) )
% 9.17/5.42 => ( P @ ( produc497848011034438852atural @ A ) @ ( produc6591912806276919810atural @ A ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6790_normalize__def,axiom,
% 9.17/5.42 ( normalize
% 9.17/5.42 = ( ^ [P6: product_prod_int_int] :
% 9.17/5.42 ( if_Pro3027730157355071871nt_int @ ( ord_less_int @ zero_zero_int @ ( product_snd_int_int @ P6 ) ) @ ( product_Pair_int_int @ ( divide_divide_int @ ( product_fst_int_int @ P6 ) @ ( gcd_gcd_int @ ( product_fst_int_int @ P6 ) @ ( product_snd_int_int @ P6 ) ) ) @ ( divide_divide_int @ ( product_snd_int_int @ P6 ) @ ( gcd_gcd_int @ ( product_fst_int_int @ P6 ) @ ( product_snd_int_int @ P6 ) ) ) )
% 9.17/5.42 @ ( if_Pro3027730157355071871nt_int
% 9.17/5.42 @ ( ( product_snd_int_int @ P6 )
% 9.17/5.42 = zero_zero_int )
% 9.17/5.42 @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 9.17/5.42 @ ( product_Pair_int_int @ ( divide_divide_int @ ( product_fst_int_int @ P6 ) @ ( uminus_uminus_int @ ( gcd_gcd_int @ ( product_fst_int_int @ P6 ) @ ( product_snd_int_int @ P6 ) ) ) ) @ ( divide_divide_int @ ( product_snd_int_int @ P6 ) @ ( uminus_uminus_int @ ( gcd_gcd_int @ ( product_fst_int_int @ P6 ) @ ( product_snd_int_int @ P6 ) ) ) ) ) ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6791_range__prod,axiom,
% 9.17/5.42 ! [F: nat > produc6433947425880249742er_nat] :
% 9.17/5.42 ( ord_le3209295114279298062er_nat @ ( image_3126957236123472631er_nat @ F @ top_top_set_nat )
% 9.17/5.42 @ ( produc4260658192689636599er_nat @ ( image_1215581382706833972nteger @ ( comp_P5700178199414968986er_nat @ produc8632663045010267826er_nat @ F ) @ top_top_set_nat )
% 9.17/5.42 @ ^ [Uu: code_integer] : ( image_nat_nat @ ( comp_P1337767177661389325at_nat @ produc1517335558169710324er_nat @ F ) @ top_top_set_nat ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6792_range__prod,axiom,
% 9.17/5.42 ! [F: nat > produc2256096406371053034er_int] :
% 9.17/5.42 ( ord_le719211969347571306er_int @ ( image_8172478253469051731er_int @ F @ top_top_set_nat )
% 9.17/5.42 @ ( produc4258167722180586323er_int @ ( image_1215581382706833972nteger @ ( comp_P2475326853202991862er_nat @ produc8630172574501217550er_int @ F ) @ top_top_set_nat )
% 9.17/5.42 @ ^ [Uu: code_integer] : ( image_nat_int @ ( comp_P8345930540558018757nt_nat @ produc1514845087660660048er_int @ F ) @ top_top_set_nat ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6793_range__prod,axiom,
% 9.17/5.42 ! [F: nat > produc2591615631378489102nteger] :
% 9.17/5.42 ( ord_le5852610332322655630nteger @ ( image_8507997478476487799nteger @ F @ top_top_set_nat )
% 9.17/5.42 @ ( produc4525213641468679415nteger @ ( image_nat_nat @ ( comp_P9144323761349829517at_nat @ produc8897218493789310642nteger @ F ) @ top_top_set_nat )
% 9.17/5.42 @ ^ [Uu: nat] : ( image_1215581382706833972nteger @ ( comp_P5461341465284484122er_nat @ produc1781891006948753140nteger @ F ) @ top_top_set_nat ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6794_range__prod,axiom,
% 9.17/5.42 ! [F: nat > product_prod_nat_nat] :
% 9.17/5.42 ( ord_le3146513528884898305at_nat @ ( image_5846123807819985514at_nat @ F @ top_top_set_nat )
% 9.17/5.42 @ ( produc457027306803732586at_nat @ ( image_nat_nat @ ( comp_P1955610211387027840at_nat @ product_fst_nat_nat @ F ) @ top_top_set_nat )
% 9.17/5.42 @ ^ [Uu: nat] : ( image_nat_nat @ ( comp_P1955610211387027840at_nat @ product_snd_nat_nat @ F ) @ top_top_set_nat ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6795_range__prod,axiom,
% 9.17/5.42 ! [F: nat > product_prod_nat_int] :
% 9.17/5.42 ( ord_le656430383953171549at_int @ ( image_1668272788310788806at_int @ F @ top_top_set_nat )
% 9.17/5.42 @ ( produc454536836294682310at_int @ ( image_nat_nat @ ( comp_P7964419862382602716at_nat @ product_fst_nat_int @ F ) @ top_top_set_nat )
% 9.17/5.42 @ ^ [Uu: nat] : ( image_nat_int @ ( comp_P8963773574283657272nt_nat @ product_snd_nat_int @ F ) @ top_top_set_nat ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6796_range__prod,axiom,
% 9.17/5.42 ! [F: nat > produc2963269191615333738nteger] :
% 9.17/5.42 ( ord_le2638047946463454698nteger @ ( image_8879651038713332435nteger @ F @ top_top_set_nat )
% 9.17/5.42 @ ( produc4896867201705524051nteger @ ( image_nat_int @ ( comp_P59025373045620805nt_nat @ produc45500017171379470nteger @ F ) @ top_top_set_nat )
% 9.17/5.42 @ ^ [Uu: int] : ( image_1215581382706833972nteger @ ( comp_P6870028373966156406er_nat @ produc2153544567185597776nteger @ F ) @ top_top_set_nat ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6797_range__prod,axiom,
% 9.17/5.42 ! [F: nat > product_prod_int_nat] :
% 9.17/5.42 ( ord_le5333435103577920093nt_nat @ ( image_6845477519721040070nt_nat @ F @ top_top_set_nat )
% 9.17/5.42 @ ( produc1456381018704787142nt_nat @ ( image_nat_int @ ( comp_P645145991195131448nt_nat @ product_fst_int_nat @ F ) @ top_top_set_nat )
% 9.17/5.42 @ ^ [Uu: int] : ( image_nat_nat @ ( comp_P8869164316148852700at_nat @ product_snd_int_nat @ F ) @ top_top_set_nat ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6798_range__prod,axiom,
% 9.17/5.42 ! [F: nat > produc8923325533196201883nteger] :
% 9.17/5.42 ( ord_le3725938330318615451nteger @ ( image_4272405876590741764nteger @ F @ top_top_set_nat )
% 9.17/5.42 @ ( produc5882431272649516420nteger @ ( image_1215581382706833972nteger @ ( comp_P3109732533133679783er_nat @ produc8508995932063986495nteger @ F ) @ top_top_set_nat )
% 9.17/5.42 @ ^ [Uu: code_integer] : ( image_1215581382706833972nteger @ ( comp_P3109732533133679783er_nat @ produc6174133586879617921nteger @ F ) @ top_top_set_nat ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6799_range__prod,axiom,
% 9.17/5.42 ! [F: nat > product_prod_int_int] :
% 9.17/5.42 ( ord_le2843351958646193337nt_int @ ( image_2667626500211843362nt_int @ F @ top_top_set_nat )
% 9.17/5.42 @ ( produc1453890548195736866nt_int @ ( image_nat_int @ ( comp_P6653955642190706324nt_nat @ product_fst_int_int @ F ) @ top_top_set_nat )
% 9.17/5.42 @ ^ [Uu: int] : ( image_nat_int @ ( comp_P6653955642190706324nt_nat @ product_snd_int_int @ F ) @ top_top_set_nat ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6800_range__prod,axiom,
% 9.17/5.42 ! [F: product_unit > produc8923325533196201883nteger] :
% 9.17/5.42 ( ord_le3725938330318615451nteger @ ( image_8089323762101378259nteger @ F @ top_to1996260823553986621t_unit )
% 9.17/5.42 @ ( produc5882431272649516420nteger @ ( image_3815118110082124069nteger @ ( comp_P659088277599099894t_unit @ produc8508995932063986495nteger @ F ) @ top_to1996260823553986621t_unit )
% 9.17/5.42 @ ^ [Uu: code_integer] : ( image_3815118110082124069nteger @ ( comp_P659088277599099894t_unit @ produc6174133586879617921nteger @ F ) @ top_to1996260823553986621t_unit ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6801_fun_Oin__rel,axiom,
% 9.17/5.42 ! [R4: code_integer > code_integer > $o,A: nat > code_integer,B: nat > code_integer] :
% 9.17/5.42 ( ( bNF_re1236659899165691067nteger
% 9.17/5.42 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.42 @ R4
% 9.17/5.42 @ A
% 9.17/5.42 @ B )
% 9.17/5.42 = ( ? [Z4: nat > produc8923325533196201883nteger] :
% 9.17/5.42 ( ( member1326526067935671339nteger @ Z4
% 9.17/5.42 @ ( collec7299664631084759149nteger
% 9.17/5.42 @ ^ [X3: nat > produc8923325533196201883nteger] : ( ord_le3725938330318615451nteger @ ( image_4272405876590741764nteger @ X3 @ top_top_set_nat ) @ ( collec7766031446232907142nteger @ ( produc2066375834425727024eger_o @ R4 ) ) ) ) )
% 9.17/5.42 & ( ( comp_P3109732533133679783er_nat @ produc8508995932063986495nteger @ Z4 )
% 9.17/5.42 = A )
% 9.17/5.42 & ( ( comp_P3109732533133679783er_nat @ produc6174133586879617921nteger @ Z4 )
% 9.17/5.42 = B ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6802_fun_Oin__rel,axiom,
% 9.17/5.42 ! [R4: int > int > $o,A: nat > int,B: nat > int] :
% 9.17/5.42 ( ( bNF_re6650684261131312217nt_int
% 9.17/5.42 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.42 @ R4
% 9.17/5.42 @ A
% 9.17/5.42 @ B )
% 9.17/5.42 = ( ? [Z4: nat > product_prod_int_int] :
% 9.17/5.42 ( ( member6440191985751670089nt_int @ Z4
% 9.17/5.42 @ ( collec8414850927317488011nt_int
% 9.17/5.42 @ ^ [X3: nat > product_prod_int_int] : ( ord_le2843351958646193337nt_int @ ( image_2667626500211843362nt_int @ X3 @ top_top_set_nat ) @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ R4 ) ) ) ) )
% 9.17/5.42 & ( ( comp_P6653955642190706324nt_nat @ product_fst_int_int @ Z4 )
% 9.17/5.42 = A )
% 9.17/5.42 & ( ( comp_P6653955642190706324nt_nat @ product_snd_int_int @ Z4 )
% 9.17/5.42 = B ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6803_fun_Oin__rel,axiom,
% 9.17/5.42 ! [R4: code_integer > code_integer > $o,A: product_unit > code_integer,B: product_unit > code_integer] :
% 9.17/5.42 ( ( bNF_re8417623677625516633nteger
% 9.17/5.42 @ ^ [Y4: product_unit,Z2: product_unit] : ( Y4 = Z2 )
% 9.17/5.42 @ R4
% 9.17/5.42 @ A
% 9.17/5.42 @ B )
% 9.17/5.42 = ( ? [Z4: product_unit > produc8923325533196201883nteger] :
% 9.17/5.42 ( ( member2837767709637065162nteger @ Z4
% 9.17/5.42 @ ( collec492036462967229448nteger
% 9.17/5.42 @ ^ [X3: product_unit > produc8923325533196201883nteger] : ( ord_le3725938330318615451nteger @ ( image_8089323762101378259nteger @ X3 @ top_to1996260823553986621t_unit ) @ ( collec7766031446232907142nteger @ ( produc2066375834425727024eger_o @ R4 ) ) ) ) )
% 9.17/5.42 & ( ( comp_P659088277599099894t_unit @ produc8508995932063986495nteger @ Z4 )
% 9.17/5.42 = A )
% 9.17/5.42 & ( ( comp_P659088277599099894t_unit @ produc6174133586879617921nteger @ Z4 )
% 9.17/5.42 = B ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6804_fun_Oin__rel,axiom,
% 9.17/5.42 ! [R4: int > int > $o,A: product_unit > int,B: product_unit > int] :
% 9.17/5.42 ( ( bNF_re8422471777688076791nt_int
% 9.17/5.42 @ ^ [Y4: product_unit,Z2: product_unit] : ( Y4 = Z2 )
% 9.17/5.42 @ R4
% 9.17/5.42 @ A
% 9.17/5.42 @ B )
% 9.17/5.42 = ( ? [Z4: product_unit > product_prod_int_int] :
% 9.17/5.42 ( ( member5541948317052402408nt_int @ Z4
% 9.17/5.42 @ ( collec2513708037538135334nt_int
% 9.17/5.42 @ ^ [X3: product_unit > product_prod_int_int] : ( ord_le2843351958646193337nt_int @ ( image_4103462098156874993nt_int @ X3 @ top_to1996260823553986621t_unit ) @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ R4 ) ) ) ) )
% 9.17/5.42 & ( ( comp_P6796073005956588617t_unit @ product_fst_int_int @ Z4 )
% 9.17/5.42 = A )
% 9.17/5.42 & ( ( comp_P6796073005956588617t_unit @ product_snd_int_int @ Z4 )
% 9.17/5.42 = B ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6805_fun_Oin__rel,axiom,
% 9.17/5.42 ! [R4: code_integer > code_integer > $o,A: int > code_integer,B: int > code_integer] :
% 9.17/5.42 ( ( bNF_re1784066744496875891nteger
% 9.17/5.42 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.42 @ R4
% 9.17/5.42 @ A
% 9.17/5.42 @ B )
% 9.17/5.42 = ( ? [Z4: int > produc8923325533196201883nteger] :
% 9.17/5.42 ( ( member2248416676132969167nteger @ Z4
% 9.17/5.42 @ ( collec8221555239282056977nteger
% 9.17/5.42 @ ^ [X3: int > produc8923325533196201883nteger] : ( ord_le3725938330318615451nteger @ ( image_5194296484788039592nteger @ X3 @ top_top_set_int ) @ ( collec7766031446232907142nteger @ ( produc2066375834425727024eger_o @ R4 ) ) ) ) )
% 9.17/5.42 & ( ( comp_P3107242062624629507er_int @ produc8508995932063986495nteger @ Z4 )
% 9.17/5.42 = A )
% 9.17/5.42 & ( ( comp_P3107242062624629507er_int @ produc6174133586879617921nteger @ Z4 )
% 9.17/5.42 = B ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6806_fun_Oin__rel,axiom,
% 9.17/5.42 ! [R4: int > int > $o,A: int > int,B: int > int] :
% 9.17/5.42 ( ( bNF_re4712519889275205905nt_int
% 9.17/5.42 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.42 @ R4
% 9.17/5.42 @ A
% 9.17/5.42 @ B )
% 9.17/5.42 = ( ? [Z4: int > product_prod_int_int] :
% 9.17/5.42 ( ( member254662033361028077nt_int @ Z4
% 9.17/5.42 @ ( collec2229320974926845999nt_int
% 9.17/5.42 @ ^ [X3: int > product_prod_int_int] : ( ord_le2843351958646193337nt_int @ ( image_5705468584675977158nt_int @ X3 @ top_top_set_int ) @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ R4 ) ) ) ) )
% 9.17/5.42 & ( ( comp_P6651465171681656048nt_int @ product_fst_int_int @ Z4 )
% 9.17/5.42 = A )
% 9.17/5.42 & ( ( comp_P6651465171681656048nt_int @ product_snd_int_int @ Z4 )
% 9.17/5.42 = B ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6807_fun_Oin__rel,axiom,
% 9.17/5.42 ! [R4: code_natural > produc7822875418678951345atural > $o,A: nat > code_natural,B: nat > produc7822875418678951345atural] :
% 9.17/5.42 ( ( bNF_re6101645755646507080atural
% 9.17/5.42 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.42 @ R4
% 9.17/5.42 @ A
% 9.17/5.42 @ B )
% 9.17/5.42 = ( ? [Z4: nat > produc5835291356934675326atural] :
% 9.17/5.42 ( ( member528921174545443716atural @ Z4
% 9.17/5.42 @ ( collec3197714919839585474atural
% 9.17/5.42 @ ^ [X3: nat > produc5835291356934675326atural] : ( ord_le2202040463148982292atural @ ( image_4072043198136622805atural @ X3 @ top_top_set_nat ) @ ( collec1991479681304692691atural @ ( produc7358226366420480123ural_o @ R4 ) ) ) ) )
% 9.17/5.42 & ( ( comp_P5592315970379621083al_nat @ produc497848011034438852atural @ Z4 )
% 9.17/5.42 = A )
% 9.17/5.42 & ( ( comp_P8477885140431536992al_nat @ produc6591912806276919810atural @ Z4 )
% 9.17/5.42 = B ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6808_fun_Oin__rel,axiom,
% 9.17/5.42 ! [R4: code_natural > produc7822875418678951345atural > $o,A: product_unit > code_natural,B: product_unit > produc7822875418678951345atural] :
% 9.17/5.42 ( ( bNF_re5641277236161133866atural
% 9.17/5.42 @ ^ [Y4: product_unit,Z2: product_unit] : ( Y4 = Z2 )
% 9.17/5.42 @ R4
% 9.17/5.42 @ A
% 9.17/5.42 @ B )
% 9.17/5.42 = ( ? [Z4: product_unit > produc5835291356934675326atural] :
% 9.17/5.42 ( ( member4946248492122881829atural @ Z4
% 9.17/5.42 @ ( collec3282430933710331751atural
% 9.17/5.42 @ ^ [X3: product_unit > produc5835291356934675326atural] : ( ord_le2202040463148982292atural @ ( image_220848230107539526atural @ X3 @ top_to1996260823553986621t_unit ) @ ( collec1991479681304692691atural @ ( produc7358226366420480123ural_o @ R4 ) ) ) ) )
% 9.17/5.42 & ( ( comp_P210409258367696578t_unit @ produc497848011034438852atural @ Z4 )
% 9.17/5.42 = A )
% 9.17/5.42 & ( ( comp_P1945487127105810045t_unit @ produc6591912806276919810atural @ Z4 )
% 9.17/5.42 = B ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6809_fun_Oin__rel,axiom,
% 9.17/5.42 ! [R4: code_natural > produc7822875418678951345atural > $o,A: int > code_natural,B: int > produc7822875418678951345atural] :
% 9.17/5.42 ( ( bNF_re6290619412732081552atural
% 9.17/5.42 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.42 @ R4
% 9.17/5.42 @ A
% 9.17/5.42 @ B )
% 9.17/5.42 = ( ? [Z4: int > produc5835291356934675326atural] :
% 9.17/5.42 ( ( member3292482584629245920atural @ Z4
% 9.17/5.42 @ ( collec5961276329923387678atural
% 9.17/5.42 @ ^ [X3: int > produc5835291356934675326atural] : ( ord_le2202040463148982292atural @ ( image_6835604608220425009atural @ X3 @ top_top_set_int ) @ ( collec1991479681304692691atural @ ( produc7358226366420480123ural_o @ R4 ) ) ) ) )
% 9.17/5.42 & ( ( comp_P5589825499870570807al_int @ produc497848011034438852atural @ Z4 )
% 9.17/5.42 = A )
% 9.17/5.42 & ( ( comp_P8475394669922486716al_int @ produc6591912806276919810atural @ Z4 )
% 9.17/5.42 = B ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6810_fun_Oin__rel,axiom,
% 9.17/5.42 ! [R4: ( nat > $o ) > ( nat > $o ) > $o,A: int > nat > $o,B: int > nat > $o] :
% 9.17/5.42 ( ( bNF_re3376528473927230327_nat_o
% 9.17/5.42 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.42 @ R4
% 9.17/5.42 @ A
% 9.17/5.42 @ B )
% 9.17/5.42 = ( ? [Z4: int > produc7360885484439884007_nat_o] :
% 9.17/5.42 ( ( member7306185171444233115_nat_o @ Z4
% 9.17/5.42 @ ( collec2839945811840875229_nat_o
% 9.17/5.42 @ ^ [X3: int > produc7360885484439884007_nat_o] : ( ord_le3745675095661657703_nat_o @ ( image_259982842891744372_nat_o @ X3 @ top_top_set_int ) @ ( collec5110290359514967890_nat_o @ ( produc2845945524848125740at_o_o @ R4 ) ) ) ) )
% 9.17/5.42 & ( ( comp_P1075760313067033319_o_int @ produc6972895793295859523_nat_o @ Z4 )
% 9.17/5.42 = A )
% 9.17/5.42 & ( ( comp_P1075760313067033319_o_int @ produc6795044007072221829_nat_o @ Z4 )
% 9.17/5.42 = B ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6811_apfst__apsnd,axiom,
% 9.17/5.42 ! [F: code_integer > int > option6357759511663192854e_term,G: code_integer > product_prod_int_int,X: produc8923325533196201883nteger] :
% 9.17/5.42 ( ( produc5167107986097539517nt_int @ F @ ( produc3535056655957556987nteger @ G @ X ) )
% 9.17/5.42 = ( produc4305682042979456191nt_int @ ( F @ ( produc8508995932063986495nteger @ X ) ) @ ( G @ ( produc6174133586879617921nteger @ X ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6812_apfst__apsnd,axiom,
% 9.17/5.42 ! [F: int > int > option6357759511663192854e_term,G: int > product_prod_int_int,X: product_prod_int_int] :
% 9.17/5.42 ( ( produc7862092043137183022nt_int @ F @ ( produc6100211334659168315nt_int @ G @ X ) )
% 9.17/5.42 = ( produc4305682042979456191nt_int @ ( F @ ( product_fst_int_int @ X ) ) @ ( G @ ( product_snd_int_int @ X ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6813_apfst__apsnd,axiom,
% 9.17/5.42 ! [F: code_integer > produc3658429121746597890et_nat > $o,G: code_integer > produc3658429121746597890et_nat,X: produc8923325533196201883nteger] :
% 9.17/5.42 ( ( produc4644964300586701942et_nat @ F @ ( produc7246245855585345468nteger @ G @ X ) )
% 9.17/5.42 = ( produc5001842942810119800et_nat @ ( F @ ( produc8508995932063986495nteger @ X ) ) @ ( G @ ( produc6174133586879617921nteger @ X ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6814_apfst__apsnd,axiom,
% 9.17/5.42 ! [F: int > produc3658429121746597890et_nat > $o,G: int > produc3658429121746597890et_nat,X: product_prod_int_int] :
% 9.17/5.42 ( ( produc5259063908904861543et_nat @ F @ ( produc9121118195053341018at_int @ G @ X ) )
% 9.17/5.42 = ( produc5001842942810119800et_nat @ ( F @ ( product_fst_int_int @ X ) ) @ ( G @ ( product_snd_int_int @ X ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6815_apfst__apsnd,axiom,
% 9.17/5.42 ! [F: code_natural > int > option6357759511663192854e_term,G: produc7822875418678951345atural > product_prod_int_int,X: produc5835291356934675326atural] :
% 9.17/5.42 ( ( produc7347430915296828978nt_int @ F @ ( produc5167862320620071534atural @ G @ X ) )
% 9.17/5.42 = ( produc4305682042979456191nt_int @ ( F @ ( produc497848011034438852atural @ X ) ) @ ( G @ ( produc6591912806276919810atural @ X ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6816_apfst__apsnd,axiom,
% 9.17/5.42 ! [F: code_integer > produc6241069584506657477e_term > option6357759511663192854e_term,G: code_integer > produc8923325533196201883nteger,X: produc8923325533196201883nteger] :
% 9.17/5.42 ( ( produc5215714788235631558nteger @ F @ ( produc7166930624044334813nteger @ G @ X ) )
% 9.17/5.42 = ( produc8603105652947943368nteger @ ( F @ ( produc8508995932063986495nteger @ X ) ) @ ( G @ ( produc6174133586879617921nteger @ X ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6817_apfst__apsnd,axiom,
% 9.17/5.42 ! [F: code_integer > produc8551481072490612790e_term > option6357759511663192854e_term,G: code_integer > product_prod_int_int,X: produc8923325533196201883nteger] :
% 9.17/5.42 ( ( produc7725767832589379507nt_int @ F @ ( produc3535056655957556987nteger @ G @ X ) )
% 9.17/5.42 = ( produc5700946648718959541nt_int @ ( F @ ( produc8508995932063986495nteger @ X ) ) @ ( G @ ( produc6174133586879617921nteger @ X ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6818_apfst__apsnd,axiom,
% 9.17/5.42 ! [F: int > produc6241069584506657477e_term > option6357759511663192854e_term,G: int > produc8923325533196201883nteger,X: product_prod_int_int] :
% 9.17/5.42 ( ( produc5502177047915545527nteger @ F @ ( produc2935421404040714269er_int @ G @ X ) )
% 9.17/5.42 = ( produc8603105652947943368nteger @ ( F @ ( product_fst_int_int @ X ) ) @ ( G @ ( product_snd_int_int @ X ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6819_apfst__apsnd,axiom,
% 9.17/5.42 ! [F: int > produc8551481072490612790e_term > option6357759511663192854e_term,G: int > product_prod_int_int,X: product_prod_int_int] :
% 9.17/5.42 ( ( produc9204274687749184420nt_int @ F @ ( produc6100211334659168315nt_int @ G @ X ) )
% 9.17/5.42 = ( produc5700946648718959541nt_int @ ( F @ ( product_fst_int_int @ X ) ) @ ( G @ ( product_snd_int_int @ X ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6820_apfst__apsnd,axiom,
% 9.17/5.42 ! [F: code_natural > produc3658429121746597890et_nat > $o,G: produc7822875418678951345atural > produc3658429121746597890et_nat,X: produc5835291356934675326atural] :
% 9.17/5.42 ( ( produc7618241212158389867et_nat @ F @ ( produc1304257963789341151atural @ G @ X ) )
% 9.17/5.42 = ( produc5001842942810119800et_nat @ ( F @ ( produc497848011034438852atural @ X ) ) @ ( G @ ( produc6591912806276919810atural @ X ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6821_apsnd__apfst,axiom,
% 9.17/5.42 ! [F: code_integer > code_integer,G: code_integer > code_integer,X: produc8923325533196201883nteger] :
% 9.17/5.42 ( ( produc6499014454317279255nteger @ F @ ( produc3195571438000033749nteger @ G @ X ) )
% 9.17/5.42 = ( produc1086072967326762835nteger @ ( G @ ( produc8508995932063986495nteger @ X ) ) @ ( F @ ( produc6174133586879617921nteger @ X ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6822_apsnd__apfst,axiom,
% 9.17/5.42 ! [F: code_integer > product_prod_int_int,G: code_integer > int > option6357759511663192854e_term,X: produc8923325533196201883nteger] :
% 9.17/5.42 ( ( produc8992176017387436671e_term @ F @ ( produc3207347198985423705nteger @ G @ X ) )
% 9.17/5.42 = ( produc4305682042979456191nt_int @ ( G @ ( produc8508995932063986495nteger @ X ) ) @ ( F @ ( produc6174133586879617921nteger @ X ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6823_apsnd__apfst,axiom,
% 9.17/5.42 ! [F: int > product_prod_int_int,G: int > int > option6357759511663192854e_term,X: product_prod_int_int] :
% 9.17/5.42 ( ( produc3260485439724623344e_term @ F @ ( produc2895628470685950711rm_int @ G @ X ) )
% 9.17/5.42 = ( produc4305682042979456191nt_int @ ( G @ ( product_fst_int_int @ X ) ) @ ( F @ ( product_snd_int_int @ X ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6824_apsnd__apfst,axiom,
% 9.17/5.42 ! [F: code_integer > produc3658429121746597890et_nat,G: code_integer > produc3658429121746597890et_nat > $o,X: produc8923325533196201883nteger] :
% 9.17/5.42 ( ( produc898583841617791278_nat_o @ F @ ( produc7528800376889492689nteger @ G @ X ) )
% 9.17/5.42 = ( produc5001842942810119800et_nat @ ( G @ ( produc8508995932063986495nteger @ X ) ) @ ( F @ ( produc6174133586879617921nteger @ X ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6825_apsnd__apfst,axiom,
% 9.17/5.42 ! [F: int > produc3658429121746597890et_nat,G: int > produc3658429121746597890et_nat > $o,X: product_prod_int_int] :
% 9.17/5.42 ( ( produc3447581998352395295_nat_o @ F @ ( produc1933289243015553937_o_int @ G @ X ) )
% 9.17/5.42 = ( produc5001842942810119800et_nat @ ( G @ ( product_fst_int_int @ X ) ) @ ( F @ ( product_snd_int_int @ X ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6826_apsnd__apfst,axiom,
% 9.17/5.42 ! [F: produc7822875418678951345atural > product_prod_int_int,G: code_natural > int > option6357759511663192854e_term,X: produc5835291356934675326atural] :
% 9.17/5.42 ( ( produc7977970570655791143e_term @ F @ ( produc8323928115967317034atural @ G @ X ) )
% 9.17/5.42 = ( produc4305682042979456191nt_int @ ( G @ ( produc497848011034438852atural @ X ) ) @ ( F @ ( produc6591912806276919810atural @ X ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6827_apsnd__apfst,axiom,
% 9.17/5.42 ! [F: code_integer > produc8923325533196201883nteger,G: code_integer > produc6241069584506657477e_term > option6357759511663192854e_term,X: produc8923325533196201883nteger] :
% 9.17/5.42 ( ( produc4047920161794714618e_term @ F @ ( produc7628915689858001394nteger @ G @ X ) )
% 9.17/5.42 = ( produc8603105652947943368nteger @ ( G @ ( produc8508995932063986495nteger @ X ) ) @ ( F @ ( produc6174133586879617921nteger @ X ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6828_apsnd__apfst,axiom,
% 9.17/5.42 ! [F: code_integer > product_prod_int_int,G: code_integer > produc8551481072490612790e_term > option6357759511663192854e_term,X: produc8923325533196201883nteger] :
% 9.17/5.42 ( ( produc6067092816631456265e_term @ F @ ( produc7602971101079744739nteger @ G @ X ) )
% 9.17/5.42 = ( produc5700946648718959541nt_int @ ( G @ ( produc8508995932063986495nteger @ X ) ) @ ( F @ ( produc6174133586879617921nteger @ X ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6829_apsnd__apfst,axiom,
% 9.17/5.42 ! [F: int > produc8923325533196201883nteger,G: int > produc6241069584506657477e_term > option6357759511663192854e_term,X: product_prod_int_int] :
% 9.17/5.42 ( ( produc552091674517523435e_term @ F @ ( produc7344697412356995344rm_int @ G @ X ) )
% 9.17/5.42 = ( produc8603105652947943368nteger @ ( G @ ( product_fst_int_int @ X ) ) @ ( F @ ( product_snd_int_int @ X ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6830_apsnd__apfst,axiom,
% 9.17/5.42 ! [F: int > product_prod_int_int,G: int > produc8551481072490612790e_term > option6357759511663192854e_term,X: product_prod_int_int] :
% 9.17/5.42 ( ( produc189803804368834042e_term @ F @ ( produc212012705979908097rm_int @ G @ X ) )
% 9.17/5.42 = ( produc5700946648718959541nt_int @ ( G @ ( product_fst_int_int @ X ) ) @ ( F @ ( product_snd_int_int @ X ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6831_eq__snd__iff,axiom,
% 9.17/5.42 ! [B: produc8923325533196201883nteger,P4: produc1908205239877642774nteger] :
% 9.17/5.42 ( ( B
% 9.17/5.42 = ( produc7856867400915047194nteger @ P4 ) )
% 9.17/5.42 = ( ? [A5: produc6241069584506657477e_term > option6357759511663192854e_term] :
% 9.17/5.42 ( P4
% 9.17/5.42 = ( produc8603105652947943368nteger @ A5 @ B ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6832_eq__snd__iff,axiom,
% 9.17/5.42 ! [B: produc3658429121746597890et_nat,P4: produc3925858234332021118et_nat] :
% 9.17/5.42 ( ( B
% 9.17/5.42 = ( produc4011572625026189258et_nat @ P4 ) )
% 9.17/5.42 = ( ? [A5: produc3658429121746597890et_nat > $o] :
% 9.17/5.42 ( P4
% 9.17/5.42 = ( produc5001842942810119800et_nat @ A5 @ B ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6833_eq__snd__iff,axiom,
% 9.17/5.42 ! [B: produc3925858234332021118et_nat,P4: produc2732055786443039994et_nat] :
% 9.17/5.42 ( ( B
% 9.17/5.42 = ( produc5374455773327741254et_nat @ P4 ) )
% 9.17/5.42 = ( ? [A5: produc3658429121746597890et_nat > $o] :
% 9.17/5.42 ( P4
% 9.17/5.42 = ( produc2245416461498447860et_nat @ A5 @ B ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6834_eq__snd__iff,axiom,
% 9.17/5.42 ! [B: product_prod_int_int,P4: produc2285326912895808259nt_int] :
% 9.17/5.42 ( ( B
% 9.17/5.42 = ( produc7328097813583171335nt_int @ P4 ) )
% 9.17/5.42 = ( ? [A5: produc8551481072490612790e_term > option6357759511663192854e_term] :
% 9.17/5.42 ( P4
% 9.17/5.42 = ( produc5700946648718959541nt_int @ A5 @ B ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6835_eq__snd__iff,axiom,
% 9.17/5.42 ! [B: product_prod_int_int,P4: produc7773217078559923341nt_int] :
% 9.17/5.42 ( ( B
% 9.17/5.42 = ( produc3162348030201620241nt_int @ P4 ) )
% 9.17/5.42 = ( ? [A5: int > option6357759511663192854e_term] :
% 9.17/5.42 ( P4
% 9.17/5.42 = ( produc4305682042979456191nt_int @ A5 @ B ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6836_eq__snd__iff,axiom,
% 9.17/5.42 ! [B: code_integer,P4: produc8923325533196201883nteger] :
% 9.17/5.42 ( ( B
% 9.17/5.42 = ( produc6174133586879617921nteger @ P4 ) )
% 9.17/5.42 = ( ? [A5: code_integer] :
% 9.17/5.42 ( P4
% 9.17/5.42 = ( produc1086072967326762835nteger @ A5 @ B ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6837_eq__snd__iff,axiom,
% 9.17/5.42 ! [B: int,P4: product_prod_int_int] :
% 9.17/5.42 ( ( B
% 9.17/5.42 = ( product_snd_int_int @ P4 ) )
% 9.17/5.42 = ( ? [A5: int] :
% 9.17/5.42 ( P4
% 9.17/5.42 = ( product_Pair_int_int @ A5 @ B ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6838_eq__snd__iff,axiom,
% 9.17/5.42 ! [B: produc7822875418678951345atural,P4: produc5835291356934675326atural] :
% 9.17/5.42 ( ( B
% 9.17/5.42 = ( produc6591912806276919810atural @ P4 ) )
% 9.17/5.42 = ( ? [A5: code_natural] :
% 9.17/5.42 ( P4
% 9.17/5.42 = ( produc6639722614265839536atural @ A5 @ B ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6839_SigmaI,axiom,
% 9.17/5.42 ! [A: $o,A2: set_o,B: $o,B5: $o > set_o] :
% 9.17/5.42 ( ( member_o @ A @ A2 )
% 9.17/5.42 => ( ( member_o @ B @ ( B5 @ A ) )
% 9.17/5.42 => ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ A @ B ) @ ( product_Sigma_o_o @ A2 @ B5 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6840_SigmaI,axiom,
% 9.17/5.42 ! [A: $o,A2: set_o,B: nat,B5: $o > set_nat] :
% 9.17/5.42 ( ( member_o @ A @ A2 )
% 9.17/5.42 => ( ( member_nat @ B @ ( B5 @ A ) )
% 9.17/5.42 => ( member2802428098988154798_o_nat @ ( product_Pair_o_nat @ A @ B ) @ ( product_Sigma_o_nat @ A2 @ B5 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6841_SigmaI,axiom,
% 9.17/5.42 ! [A: $o,A2: set_o,B: int,B5: $o > set_int] :
% 9.17/5.42 ( ( member_o @ A @ A2 )
% 9.17/5.42 => ( ( member_int @ B @ ( B5 @ A ) )
% 9.17/5.42 => ( member7847949116333733898_o_int @ ( product_Pair_o_int @ A @ B ) @ ( product_Sigma_o_int @ A2 @ B5 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6842_SigmaI,axiom,
% 9.17/5.42 ! [A: nat,A2: set_nat,B: $o,B5: nat > set_o] :
% 9.17/5.42 ( ( member_nat @ A @ A2 )
% 9.17/5.42 => ( ( member_o @ B @ ( B5 @ A ) )
% 9.17/5.42 => ( member6310962623043647828_nat_o @ ( product_Pair_nat_o @ A @ B ) @ ( product_Sigma_nat_o @ A2 @ B5 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6843_SigmaI,axiom,
% 9.17/5.42 ! [A: nat,A2: set_nat,B: nat,B5: nat > set_nat] :
% 9.17/5.42 ( ( member_nat @ A @ A2 )
% 9.17/5.42 => ( ( member_nat @ B @ ( B5 @ A ) )
% 9.17/5.42 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ ( produc457027306803732586at_nat @ A2 @ B5 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6844_SigmaI,axiom,
% 9.17/5.42 ! [A: nat,A2: set_nat,B: int,B5: nat > set_int] :
% 9.17/5.42 ( ( member_nat @ A @ A2 )
% 9.17/5.42 => ( ( member_int @ B @ ( B5 @ A ) )
% 9.17/5.42 => ( member4262671552274231302at_int @ ( product_Pair_nat_int @ A @ B ) @ ( produc454536836294682310at_int @ A2 @ B5 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6845_SigmaI,axiom,
% 9.17/5.42 ! [A: int,A2: set_int,B: $o,B5: int > set_o] :
% 9.17/5.42 ( ( member_int @ A @ A2 )
% 9.17/5.42 => ( ( member_o @ B @ ( B5 @ A ) )
% 9.17/5.42 => ( member4489920277610959864_int_o @ ( product_Pair_int_o @ A @ B ) @ ( product_Sigma_int_o @ A2 @ B5 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6846_SigmaI,axiom,
% 9.17/5.42 ! [A: int,A2: set_int,B: nat,B5: int > set_nat] :
% 9.17/5.42 ( ( member_int @ A @ A2 )
% 9.17/5.42 => ( ( member_nat @ B @ ( B5 @ A ) )
% 9.17/5.42 => ( member216504246829706758nt_nat @ ( product_Pair_int_nat @ A @ B ) @ ( produc1456381018704787142nt_nat @ A2 @ B5 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6847_SigmaI,axiom,
% 9.17/5.42 ! [A: int,A2: set_int,B: int,B5: int > set_int] :
% 9.17/5.42 ( ( member_int @ A @ A2 )
% 9.17/5.42 => ( ( member_int @ B @ ( B5 @ A ) )
% 9.17/5.42 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ ( produc1453890548195736866nt_int @ A2 @ B5 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6848_SigmaI,axiom,
% 9.17/5.42 ! [A: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,B: $o,B5: product_prod_nat_nat > set_o] :
% 9.17/5.42 ( ( member8440522571783428010at_nat @ A @ A2 )
% 9.17/5.42 => ( ( member_o @ B @ ( B5 @ A ) )
% 9.17/5.42 => ( member2200362271989506215_nat_o @ ( produc855456346497908590_nat_o @ A @ B ) @ ( produc203973861852599583_nat_o @ A2 @ B5 ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6849_mem__Sigma__iff,axiom,
% 9.17/5.42 ! [A: $o,B: $o,A2: set_o,B5: $o > set_o] :
% 9.17/5.42 ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ A @ B ) @ ( product_Sigma_o_o @ A2 @ B5 ) )
% 9.17/5.42 = ( ( member_o @ A @ A2 )
% 9.17/5.42 & ( member_o @ B @ ( B5 @ A ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6850_mem__Sigma__iff,axiom,
% 9.17/5.42 ! [A: $o,B: nat,A2: set_o,B5: $o > set_nat] :
% 9.17/5.42 ( ( member2802428098988154798_o_nat @ ( product_Pair_o_nat @ A @ B ) @ ( product_Sigma_o_nat @ A2 @ B5 ) )
% 9.17/5.42 = ( ( member_o @ A @ A2 )
% 9.17/5.42 & ( member_nat @ B @ ( B5 @ A ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6851_mem__Sigma__iff,axiom,
% 9.17/5.42 ! [A: $o,B: int,A2: set_o,B5: $o > set_int] :
% 9.17/5.42 ( ( member7847949116333733898_o_int @ ( product_Pair_o_int @ A @ B ) @ ( product_Sigma_o_int @ A2 @ B5 ) )
% 9.17/5.42 = ( ( member_o @ A @ A2 )
% 9.17/5.42 & ( member_int @ B @ ( B5 @ A ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6852_mem__Sigma__iff,axiom,
% 9.17/5.42 ! [A: nat,B: $o,A2: set_nat,B5: nat > set_o] :
% 9.17/5.42 ( ( member6310962623043647828_nat_o @ ( product_Pair_nat_o @ A @ B ) @ ( product_Sigma_nat_o @ A2 @ B5 ) )
% 9.17/5.42 = ( ( member_nat @ A @ A2 )
% 9.17/5.42 & ( member_o @ B @ ( B5 @ A ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6853_mem__Sigma__iff,axiom,
% 9.17/5.42 ! [A: nat,B: int,A2: set_nat,B5: nat > set_int] :
% 9.17/5.42 ( ( member4262671552274231302at_int @ ( product_Pair_nat_int @ A @ B ) @ ( produc454536836294682310at_int @ A2 @ B5 ) )
% 9.17/5.42 = ( ( member_nat @ A @ A2 )
% 9.17/5.42 & ( member_int @ B @ ( B5 @ A ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6854_mem__Sigma__iff,axiom,
% 9.17/5.42 ! [A: int,B: $o,A2: set_int,B5: int > set_o] :
% 9.17/5.42 ( ( member4489920277610959864_int_o @ ( product_Pair_int_o @ A @ B ) @ ( product_Sigma_int_o @ A2 @ B5 ) )
% 9.17/5.42 = ( ( member_int @ A @ A2 )
% 9.17/5.42 & ( member_o @ B @ ( B5 @ A ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6855_mem__Sigma__iff,axiom,
% 9.17/5.42 ! [A: int,B: nat,A2: set_int,B5: int > set_nat] :
% 9.17/5.42 ( ( member216504246829706758nt_nat @ ( product_Pair_int_nat @ A @ B ) @ ( produc1456381018704787142nt_nat @ A2 @ B5 ) )
% 9.17/5.42 = ( ( member_int @ A @ A2 )
% 9.17/5.42 & ( member_nat @ B @ ( B5 @ A ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6856_mem__Sigma__iff,axiom,
% 9.17/5.42 ! [A: int,B: int,A2: set_int,B5: int > set_int] :
% 9.17/5.42 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ ( produc1453890548195736866nt_int @ A2 @ B5 ) )
% 9.17/5.42 = ( ( member_int @ A @ A2 )
% 9.17/5.42 & ( member_int @ B @ ( B5 @ A ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6857_mem__Sigma__iff,axiom,
% 9.17/5.42 ! [A: nat,B: nat,A2: set_nat,B5: nat > set_nat] :
% 9.17/5.42 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ ( produc457027306803732586at_nat @ A2 @ B5 ) )
% 9.17/5.42 = ( ( member_nat @ A @ A2 )
% 9.17/5.42 & ( member_nat @ B @ ( B5 @ A ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6858_mem__Sigma__iff,axiom,
% 9.17/5.42 ! [A: product_prod_nat_nat,B: $o,A2: set_Pr1261947904930325089at_nat,B5: product_prod_nat_nat > set_o] :
% 9.17/5.42 ( ( member2200362271989506215_nat_o @ ( produc855456346497908590_nat_o @ A @ B ) @ ( produc203973861852599583_nat_o @ A2 @ B5 ) )
% 9.17/5.42 = ( ( member8440522571783428010at_nat @ A @ A2 )
% 9.17/5.42 & ( member_o @ B @ ( B5 @ A ) ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6859_gcd__add1,axiom,
% 9.17/5.42 ! [M2: nat,N2: nat] :
% 9.17/5.42 ( ( gcd_gcd_nat @ ( plus_plus_nat @ M2 @ N2 ) @ N2 )
% 9.17/5.42 = ( gcd_gcd_nat @ M2 @ N2 ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6860_gcd__add1,axiom,
% 9.17/5.42 ! [M2: int,N2: int] :
% 9.17/5.42 ( ( gcd_gcd_int @ ( plus_plus_int @ M2 @ N2 ) @ N2 )
% 9.17/5.42 = ( gcd_gcd_int @ M2 @ N2 ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6861_gcd__add2,axiom,
% 9.17/5.42 ! [M2: nat,N2: nat] :
% 9.17/5.42 ( ( gcd_gcd_nat @ M2 @ ( plus_plus_nat @ M2 @ N2 ) )
% 9.17/5.42 = ( gcd_gcd_nat @ M2 @ N2 ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6862_gcd__add2,axiom,
% 9.17/5.42 ! [M2: int,N2: int] :
% 9.17/5.42 ( ( gcd_gcd_int @ M2 @ ( plus_plus_int @ M2 @ N2 ) )
% 9.17/5.42 = ( gcd_gcd_int @ M2 @ N2 ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6863_gcd_Obottom__left__bottom,axiom,
% 9.17/5.42 ! [A: nat] :
% 9.17/5.42 ( ( gcd_gcd_nat @ one_one_nat @ A )
% 9.17/5.42 = one_one_nat ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6864_gcd_Obottom__left__bottom,axiom,
% 9.17/5.42 ! [A: int] :
% 9.17/5.42 ( ( gcd_gcd_int @ one_one_int @ A )
% 9.17/5.42 = one_one_int ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6865_gcd_Obottom__right__bottom,axiom,
% 9.17/5.42 ! [A: nat] :
% 9.17/5.42 ( ( gcd_gcd_nat @ A @ one_one_nat )
% 9.17/5.42 = one_one_nat ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6866_gcd_Obottom__right__bottom,axiom,
% 9.17/5.42 ! [A: int] :
% 9.17/5.42 ( ( gcd_gcd_int @ A @ one_one_int )
% 9.17/5.42 = one_one_int ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6867_apfst__conv,axiom,
% 9.17/5.42 ! [F: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc6241069584506657477e_term > option6357759511663192854e_term,X: produc6241069584506657477e_term > option6357759511663192854e_term,Y: produc8923325533196201883nteger] :
% 9.17/5.42 ( ( produc2515316116081422825nteger @ F @ ( produc8603105652947943368nteger @ X @ Y ) )
% 9.17/5.42 = ( produc8603105652947943368nteger @ ( F @ X ) @ Y ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6868_apfst__conv,axiom,
% 9.17/5.42 ! [F: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o,X: produc3658429121746597890et_nat > $o,Y: produc3658429121746597890et_nat] :
% 9.17/5.42 ( ( produc3198230245617193214et_nat @ F @ ( produc5001842942810119800et_nat @ X @ Y ) )
% 9.17/5.42 = ( produc5001842942810119800et_nat @ ( F @ X ) @ Y ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6869_apfst__conv,axiom,
% 9.17/5.42 ! [F: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o,X: produc3658429121746597890et_nat > $o,Y: produc3925858234332021118et_nat] :
% 9.17/5.42 ( ( produc1442628905706551930et_nat @ F @ ( produc2245416461498447860et_nat @ X @ Y ) )
% 9.17/5.42 = ( produc2245416461498447860et_nat @ ( F @ X ) @ Y ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6870_apfst__conv,axiom,
% 9.17/5.42 ! [F: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > produc8551481072490612790e_term > option6357759511663192854e_term,X: produc8551481072490612790e_term > option6357759511663192854e_term,Y: product_prod_int_int] :
% 9.17/5.42 ( ( produc7277921532047535397nt_int @ F @ ( produc5700946648718959541nt_int @ X @ Y ) )
% 9.17/5.42 = ( produc5700946648718959541nt_int @ ( F @ X ) @ Y ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6871_apfst__conv,axiom,
% 9.17/5.42 ! [F: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > int > option6357759511663192854e_term,X: produc8551481072490612790e_term > option6357759511663192854e_term,Y: product_prod_int_int] :
% 9.17/5.42 ( ( produc6919319362177967663nt_int @ F @ ( produc5700946648718959541nt_int @ X @ Y ) )
% 9.17/5.42 = ( produc4305682042979456191nt_int @ ( F @ X ) @ Y ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6872_apfst__conv,axiom,
% 9.17/5.42 ! [F: ( int > option6357759511663192854e_term ) > produc8551481072490612790e_term > option6357759511663192854e_term,X: int > option6357759511663192854e_term,Y: product_prod_int_int] :
% 9.17/5.42 ( ( produc6067946493426971951nt_int @ F @ ( produc4305682042979456191nt_int @ X @ Y ) )
% 9.17/5.42 = ( produc5700946648718959541nt_int @ ( F @ X ) @ Y ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6873_apfst__conv,axiom,
% 9.17/5.42 ! [F: ( int > option6357759511663192854e_term ) > int > option6357759511663192854e_term,X: int > option6357759511663192854e_term,Y: product_prod_int_int] :
% 9.17/5.42 ( ( produc7131893314732144953nt_int @ F @ ( produc4305682042979456191nt_int @ X @ Y ) )
% 9.17/5.42 = ( produc4305682042979456191nt_int @ ( F @ X ) @ Y ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6874_fst__apfst,axiom,
% 9.17/5.42 ! [F: code_integer > code_integer,X: produc8923325533196201883nteger] :
% 9.17/5.42 ( ( produc8508995932063986495nteger @ ( produc3195571438000033749nteger @ F @ X ) )
% 9.17/5.42 = ( F @ ( produc8508995932063986495nteger @ X ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6875_fst__apfst,axiom,
% 9.17/5.42 ! [F: int > int,X: product_prod_int_int] :
% 9.17/5.42 ( ( product_fst_int_int @ ( produc2355237562570658114nt_int @ F @ X ) )
% 9.17/5.42 = ( F @ ( product_fst_int_int @ X ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6876_snd__apfst,axiom,
% 9.17/5.42 ! [F: code_integer > code_integer,X: produc8923325533196201883nteger] :
% 9.17/5.42 ( ( produc6174133586879617921nteger @ ( produc3195571438000033749nteger @ F @ X ) )
% 9.17/5.42 = ( produc6174133586879617921nteger @ X ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6877_snd__apfst,axiom,
% 9.17/5.42 ! [F: int > int,X: product_prod_int_int] :
% 9.17/5.42 ( ( product_snd_int_int @ ( produc2355237562570658114nt_int @ F @ X ) )
% 9.17/5.42 = ( product_snd_int_int @ X ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6878_snd__apfst,axiom,
% 9.17/5.42 ! [F: code_natural > code_natural,X: produc5835291356934675326atural] :
% 9.17/5.42 ( ( produc6591912806276919810atural @ ( produc4623092060929046819atural @ F @ X ) )
% 9.17/5.42 = ( produc6591912806276919810atural @ X ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6879_Collect__case__prod,axiom,
% 9.17/5.42 ! [P: nat > $o,Q: nat > $o] :
% 9.17/5.42 ( ( collec3392354462482085612at_nat
% 9.17/5.42 @ ( produc6081775807080527818_nat_o
% 9.17/5.42 @ ^ [A5: nat,B4: nat] :
% 9.17/5.42 ( ( P @ A5 )
% 9.17/5.42 & ( Q @ B4 ) ) ) )
% 9.17/5.42 = ( produc457027306803732586at_nat @ ( collect_nat @ P )
% 9.17/5.42 @ ^ [Uu: nat] : ( collect_nat @ Q ) ) ) ).
% 9.17/5.42
% 9.17/5.42 thf(fact_6880_Collect__case__prod,axiom,
% 9.17/5.42 ! [P: nat > $o,Q: list_nat > $o] :
% 9.17/5.42 ( ( collec1907656820224499068st_nat
% 9.17/5.42 @ ( produc5265810065896090426_nat_o
% 9.17/5.42 @ ^ [A5: nat,B4: list_nat] :
% 9.17/5.42 ( ( P @ A5 )
% 9.17/5.43 & ( Q @ B4 ) ) ) )
% 9.17/5.43 = ( produc5227933103413159546st_nat @ ( collect_nat @ P )
% 9.17/5.43 @ ^ [Uu: nat] : ( collect_list_nat @ Q ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6881_Collect__case__prod,axiom,
% 9.17/5.43 ! [P: list_nat > $o,Q: nat > $o] :
% 9.17/5.43 ( ( collec8096645339561496572at_nat
% 9.17/5.43 @ ( produc7308574044827705018_nat_o
% 9.17/5.43 @ ^ [A5: list_nat,B4: nat] :
% 9.17/5.43 ( ( P @ A5 )
% 9.17/5.43 & ( Q @ B4 ) ) ) )
% 9.17/5.43 = ( produc7466890150575444730at_nat @ ( collect_list_nat @ P )
% 9.17/5.43 @ ^ [Uu: list_nat] : ( collect_nat @ Q ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6882_Collect__case__prod,axiom,
% 9.17/5.43 ! [P: list_nat > $o,Q: list_nat > $o] :
% 9.17/5.43 ( ( collec1570431334306492044st_nat
% 9.17/5.43 @ ( produc6382697403170970154_nat_o
% 9.17/5.43 @ ^ [A5: list_nat,B4: list_nat] :
% 9.17/5.43 ( ( P @ A5 )
% 9.17/5.43 & ( Q @ B4 ) ) ) )
% 9.17/5.43 = ( produc6850429418872557834st_nat @ ( collect_list_nat @ P )
% 9.17/5.43 @ ^ [Uu: list_nat] : ( collect_list_nat @ Q ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6883_is__unit__gcd__iff,axiom,
% 9.17/5.43 ! [A: nat,B: nat] :
% 9.17/5.43 ( ( dvd_dvd_nat @ ( gcd_gcd_nat @ A @ B ) @ one_one_nat )
% 9.17/5.43 = ( ( gcd_gcd_nat @ A @ B )
% 9.17/5.43 = one_one_nat ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6884_is__unit__gcd__iff,axiom,
% 9.17/5.43 ! [A: int,B: int] :
% 9.17/5.43 ( ( dvd_dvd_int @ ( gcd_gcd_int @ A @ B ) @ one_one_int )
% 9.17/5.43 = ( ( gcd_gcd_int @ A @ B )
% 9.17/5.43 = one_one_int ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6885_Sigma__empty1,axiom,
% 9.17/5.43 ! [B5: set_Pr1261947904930325089at_nat > set_se7855581050983116737at_nat] :
% 9.17/5.43 ( ( produc7726050920695093128at_nat @ bot_bo3083307316010499117at_nat @ B5 )
% 9.17/5.43 = bot_bo228742789529271731at_nat ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6886_Sigma__empty1,axiom,
% 9.17/5.43 ! [B5: nat > set_nat] :
% 9.17/5.43 ( ( produc457027306803732586at_nat @ bot_bot_set_nat @ B5 )
% 9.17/5.43 = bot_bo2099793752762293965at_nat ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6887_Sigma__empty2,axiom,
% 9.17/5.43 ! [A2: set_se7855581050983116737at_nat] :
% 9.17/5.43 ( ( produc7726050920695093128at_nat @ A2
% 9.17/5.43 @ ^ [Uu: set_Pr1261947904930325089at_nat] : bot_bo3083307316010499117at_nat )
% 9.17/5.43 = bot_bo228742789529271731at_nat ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6888_Sigma__empty2,axiom,
% 9.17/5.43 ! [A2: set_nat] :
% 9.17/5.43 ( ( produc457027306803732586at_nat @ A2
% 9.17/5.43 @ ^ [Uu: nat] : bot_bot_set_nat )
% 9.17/5.43 = bot_bo2099793752762293965at_nat ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6889_Times__empty,axiom,
% 9.17/5.43 ! [A2: set_o,B5: set_o] :
% 9.17/5.43 ( ( ( product_Sigma_o_o @ A2
% 9.17/5.43 @ ^ [Uu: $o] : B5 )
% 9.17/5.43 = bot_bo7073875226086086771od_o_o )
% 9.17/5.43 = ( ( A2 = bot_bot_set_o )
% 9.17/5.43 | ( B5 = bot_bot_set_o ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6890_Times__empty,axiom,
% 9.17/5.43 ! [A2: set_o,B5: set_nat] :
% 9.17/5.43 ( ( ( product_Sigma_o_nat @ A2
% 9.17/5.43 @ ^ [Uu: $o] : B5 )
% 9.17/5.43 = bot_bo66526543525301729_o_nat )
% 9.17/5.43 = ( ( A2 = bot_bot_set_o )
% 9.17/5.43 | ( B5 = bot_bot_set_nat ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6891_Times__empty,axiom,
% 9.17/5.43 ! [A2: set_o,B5: set_int] :
% 9.17/5.43 ( ( ( product_Sigma_o_int @ A2
% 9.17/5.43 @ ^ [Uu: $o] : B5 )
% 9.17/5.43 = bot_bo6799815435448350781_o_int )
% 9.17/5.43 = ( ( A2 = bot_bot_set_o )
% 9.17/5.43 | ( B5 = bot_bot_set_int ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6892_Times__empty,axiom,
% 9.17/5.43 ! [A2: set_nat,B5: set_o] :
% 9.17/5.43 ( ( ( product_Sigma_nat_o @ A2
% 9.17/5.43 @ ^ [Uu: nat] : B5 )
% 9.17/5.43 = bot_bo1114129665703605383_nat_o )
% 9.17/5.43 = ( ( A2 = bot_bot_set_nat )
% 9.17/5.43 | ( B5 = bot_bot_set_o ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6893_Times__empty,axiom,
% 9.17/5.43 ! [A2: set_nat,B5: set_int] :
% 9.17/5.43 ( ( ( produc454536836294682310at_int @ A2
% 9.17/5.43 @ ^ [Uu: nat] : B5 )
% 9.17/5.43 = bot_bo8833082644685343017at_int )
% 9.17/5.43 = ( ( A2 = bot_bot_set_nat )
% 9.17/5.43 | ( B5 = bot_bot_set_int ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6894_Times__empty,axiom,
% 9.17/5.43 ! [A2: set_int,B5: set_o] :
% 9.17/5.43 ( ( ( product_Sigma_int_o @ A2
% 9.17/5.43 @ ^ [Uu: int] : B5 )
% 9.17/5.43 = bot_bo8092356734887935275_int_o )
% 9.17/5.43 = ( ( A2 = bot_bot_set_int )
% 9.17/5.43 | ( B5 = bot_bot_set_o ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6895_Times__empty,axiom,
% 9.17/5.43 ! [A2: set_int,B5: set_nat] :
% 9.17/5.43 ( ( ( produc1456381018704787142nt_nat @ A2
% 9.17/5.43 @ ^ [Uu: int] : B5 )
% 9.17/5.43 = bot_bo4286715327455315753nt_nat )
% 9.17/5.43 = ( ( A2 = bot_bot_set_int )
% 9.17/5.43 | ( B5 = bot_bot_set_nat ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6896_Times__empty,axiom,
% 9.17/5.43 ! [A2: set_int,B5: set_int] :
% 9.17/5.43 ( ( ( produc1453890548195736866nt_int @ A2
% 9.17/5.43 @ ^ [Uu: int] : B5 )
% 9.17/5.43 = bot_bo1796632182523588997nt_int )
% 9.17/5.43 = ( ( A2 = bot_bot_set_int )
% 9.17/5.43 | ( B5 = bot_bot_set_int ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6897_Times__empty,axiom,
% 9.17/5.43 ! [A2: set_nat,B5: set_nat] :
% 9.17/5.43 ( ( ( produc457027306803732586at_nat @ A2
% 9.17/5.43 @ ^ [Uu: nat] : B5 )
% 9.17/5.43 = bot_bo2099793752762293965at_nat )
% 9.17/5.43 = ( ( A2 = bot_bot_set_nat )
% 9.17/5.43 | ( B5 = bot_bot_set_nat ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6898_Times__empty,axiom,
% 9.17/5.43 ! [A2: set_Pr1261947904930325089at_nat,B5: set_o] :
% 9.17/5.43 ( ( ( produc203973861852599583_nat_o @ A2
% 9.17/5.43 @ ^ [Uu: product_prod_nat_nat] : B5 )
% 9.17/5.43 = bot_bo5454027612061941066_nat_o )
% 9.17/5.43 = ( ( A2 = bot_bo2099793752762293965at_nat )
% 9.17/5.43 | ( B5 = bot_bot_set_o ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6899_Sigma__UNIV__cancel,axiom,
% 9.17/5.43 ! [A2: set_se7855581050983116737at_nat,X11: set_se7855581050983116737at_nat] :
% 9.17/5.43 ( ( minus_3314409938677909166at_nat
% 9.17/5.43 @ ( produc7726050920695093128at_nat @ A2
% 9.17/5.43 @ ^ [Uu: set_Pr1261947904930325089at_nat] : X11 )
% 9.17/5.43 @ ( produc7726050920695093128at_nat @ A2
% 9.17/5.43 @ ^ [Uu: set_Pr1261947904930325089at_nat] : top_to7629004291339433233at_nat ) )
% 9.17/5.43 = bot_bo228742789529271731at_nat ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6900_Sigma__UNIV__cancel,axiom,
% 9.17/5.43 ! [A2: set_nat,X11: set_nat] :
% 9.17/5.43 ( ( minus_1356011639430497352at_nat
% 9.17/5.43 @ ( produc457027306803732586at_nat @ A2
% 9.17/5.43 @ ^ [Uu: nat] : X11 )
% 9.17/5.43 @ ( produc457027306803732586at_nat @ A2
% 9.17/5.43 @ ^ [Uu: nat] : top_top_set_nat ) )
% 9.17/5.43 = bot_bo2099793752762293965at_nat ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6901_snd__comp__apfst,axiom,
% 9.17/5.43 ! [F: code_integer > code_integer] :
% 9.17/5.43 ( ( comp_P3428181540658402820nteger @ produc6174133586879617921nteger @ ( produc3195571438000033749nteger @ F ) )
% 9.17/5.43 = produc6174133586879617921nteger ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6902_snd__comp__apfst,axiom,
% 9.17/5.43 ! [F: int > int] :
% 9.17/5.43 ( ( comp_P5356232565778667509nt_int @ product_snd_int_int @ ( produc2355237562570658114nt_int @ F ) )
% 9.17/5.43 = product_snd_int_int ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6903_snd__comp__apfst,axiom,
% 9.17/5.43 ! [F: code_natural > code_natural] :
% 9.17/5.43 ( ( comp_P7610810914149544718atural @ produc6591912806276919810atural @ ( produc4623092060929046819atural @ F ) )
% 9.17/5.43 = produc6591912806276919810atural ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6904_UNIV__Times__UNIV,axiom,
% 9.17/5.43 ( ( produc457027306803732586at_nat @ top_top_set_nat
% 9.17/5.43 @ ^ [Uu: nat] : top_top_set_nat )
% 9.17/5.43 = top_to4669805908274784177at_nat ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6905_UNIV__Times__UNIV,axiom,
% 9.17/5.43 ( ( produc5506539147108004339t_unit @ top_top_set_nat
% 9.17/5.43 @ ^ [Uu: nat] : top_to1996260823553986621t_unit )
% 9.17/5.43 = top_to8544742955230171288t_unit ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6906_UNIV__Times__UNIV,axiom,
% 9.17/5.43 ( ( produc454536836294682310at_int @ top_top_set_nat
% 9.17/5.43 @ ^ [Uu: nat] : top_top_set_int )
% 9.17/5.43 = top_to2179722763343057421at_int ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6907_UNIV__Times__UNIV,axiom,
% 9.17/5.43 ( ( produc6875377002296012693it_nat @ top_to1996260823553986621t_unit
% 9.17/5.43 @ ^ [Uu: product_unit] : top_top_set_nat )
% 9.17/5.43 = top_to5974110478112770290it_nat ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6908_UNIV__Times__UNIV,axiom,
% 9.17/5.43 ( ( produc6121607364029222536t_unit @ top_to1996260823553986621t_unit
% 9.17/5.43 @ ^ [Uu: product_unit] : top_to1996260823553986621t_unit )
% 9.17/5.43 = top_to1835807148980544151t_unit ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6909_UNIV__Times__UNIV,axiom,
% 9.17/5.43 ( ( produc6872886531786962417it_int @ top_to1996260823553986621t_unit
% 9.17/5.43 @ ^ [Uu: product_unit] : top_top_set_int )
% 9.17/5.43 = top_to3484027333181043534it_int ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6910_UNIV__Times__UNIV,axiom,
% 9.17/5.43 ( ( produc1456381018704787142nt_nat @ top_top_set_int
% 9.17/5.43 @ ^ [Uu: int] : top_top_set_nat )
% 9.17/5.43 = top_to6856727482967805965nt_nat ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6911_UNIV__Times__UNIV,axiom,
% 9.17/5.43 ( ( produc2622961094310184599t_unit @ top_top_set_int
% 9.17/5.43 @ ^ [Uu: int] : top_to1996260823553986621t_unit )
% 9.17/5.43 = top_to876157113852465980t_unit ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6912_UNIV__Times__UNIV,axiom,
% 9.17/5.43 ( ( produc1453890548195736866nt_int @ top_top_set_int
% 9.17/5.43 @ ^ [Uu: int] : top_top_set_int )
% 9.17/5.43 = top_to4366644338036079209nt_int ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6913_pairself__image__cart,axiom,
% 9.17/5.43 ! [F: nat > code_integer,A2: set_nat,B5: set_nat] :
% 9.17/5.43 ( ( image_5669961043262023647nteger @ ( pairse4825235148789309005nteger @ F )
% 9.17/5.43 @ ( produc457027306803732586at_nat @ A2
% 9.17/5.43 @ ^ [Uu: nat] : B5 ) )
% 9.17/5.43 = ( produc5882431272649516420nteger @ ( image_1215581382706833972nteger @ F @ A2 )
% 9.17/5.43 @ ^ [Uu: code_integer] : ( image_1215581382706833972nteger @ F @ B5 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6914_pairself__image__cart,axiom,
% 9.17/5.43 ! [F: nat > set_nat,A2: set_nat,B5: set_nat] :
% 9.17/5.43 ( ( image_4566292076127975857et_nat @ ( pairself_nat_set_nat @ F )
% 9.17/5.43 @ ( produc457027306803732586at_nat @ A2
% 9.17/5.43 @ ^ [Uu: nat] : B5 ) )
% 9.17/5.43 = ( produc105401717395143638et_nat @ ( image_nat_set_nat @ F @ A2 )
% 9.17/5.43 @ ^ [Uu: set_nat] : ( image_nat_set_nat @ F @ B5 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6915_pairself__image__cart,axiom,
% 9.17/5.43 ! [F: nat > nat,A2: set_nat,B5: set_nat] :
% 9.17/5.43 ( ( image_5168914502847457605at_nat @ ( pairself_nat_nat @ F )
% 9.17/5.43 @ ( produc457027306803732586at_nat @ A2
% 9.17/5.43 @ ^ [Uu: nat] : B5 ) )
% 9.17/5.43 = ( produc457027306803732586at_nat @ ( image_nat_nat @ F @ A2 )
% 9.17/5.43 @ ^ [Uu: nat] : ( image_nat_nat @ F @ B5 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6916_pairself__image__cart,axiom,
% 9.17/5.43 ! [F: nat > int,A2: set_nat,B5: set_nat] :
% 9.17/5.43 ( ( image_1990417195239315453nt_int @ ( pairself_nat_int @ F )
% 9.17/5.43 @ ( produc457027306803732586at_nat @ A2
% 9.17/5.43 @ ^ [Uu: nat] : B5 ) )
% 9.17/5.43 = ( produc1453890548195736866nt_int @ ( image_nat_int @ F @ A2 )
% 9.17/5.43 @ ^ [Uu: int] : ( image_nat_int @ F @ B5 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6917_pairself__image__cart,axiom,
% 9.17/5.43 ! [F: int > int,A2: set_int,B5: set_int] :
% 9.17/5.43 ( ( image_2653370878348428101nt_int @ ( pairself_int_int @ F )
% 9.17/5.43 @ ( produc1453890548195736866nt_int @ A2
% 9.17/5.43 @ ^ [Uu: int] : B5 ) )
% 9.17/5.43 = ( produc1453890548195736866nt_int @ ( image_int_int @ F @ A2 )
% 9.17/5.43 @ ^ [Uu: int] : ( image_int_int @ F @ B5 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6918_fst__image__times,axiom,
% 9.17/5.43 ! [B5: set_Code_integer,A2: set_Code_integer] :
% 9.17/5.43 ( ( ( B5 = bot_bo3990330152332043303nteger )
% 9.17/5.43 => ( ( image_6316824473203919795nteger @ produc8508995932063986495nteger
% 9.17/5.43 @ ( produc5882431272649516420nteger @ A2
% 9.17/5.43 @ ^ [Uu: code_integer] : B5 ) )
% 9.17/5.43 = bot_bo3990330152332043303nteger ) )
% 9.17/5.43 & ( ( B5 != bot_bo3990330152332043303nteger )
% 9.17/5.43 => ( ( image_6316824473203919795nteger @ produc8508995932063986495nteger
% 9.17/5.43 @ ( produc5882431272649516420nteger @ A2
% 9.17/5.43 @ ^ [Uu: code_integer] : B5 ) )
% 9.17/5.43 = A2 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6919_fst__image__times,axiom,
% 9.17/5.43 ! [B5: set_o,A2: set_o] :
% 9.17/5.43 ( ( ( B5 = bot_bot_set_o )
% 9.17/5.43 => ( ( image_7896445794123959606_o_o_o @ product_fst_o_o
% 9.17/5.43 @ ( product_Sigma_o_o @ A2
% 9.17/5.43 @ ^ [Uu: $o] : B5 ) )
% 9.17/5.43 = bot_bot_set_o ) )
% 9.17/5.43 & ( ( B5 != bot_bot_set_o )
% 9.17/5.43 => ( ( image_7896445794123959606_o_o_o @ product_fst_o_o
% 9.17/5.43 @ ( product_Sigma_o_o @ A2
% 9.17/5.43 @ ^ [Uu: $o] : B5 ) )
% 9.17/5.43 = A2 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6920_fst__image__times,axiom,
% 9.17/5.43 ! [B5: set_o,A2: set_nat] :
% 9.17/5.43 ( ( ( B5 = bot_bot_set_o )
% 9.17/5.43 => ( ( image_8629803608462650132_o_nat @ product_fst_nat_o
% 9.17/5.43 @ ( product_Sigma_nat_o @ A2
% 9.17/5.43 @ ^ [Uu: nat] : B5 ) )
% 9.17/5.43 = bot_bot_set_nat ) )
% 9.17/5.43 & ( ( B5 != bot_bot_set_o )
% 9.17/5.43 => ( ( image_8629803608462650132_o_nat @ product_fst_nat_o
% 9.17/5.43 @ ( product_Sigma_nat_o @ A2
% 9.17/5.43 @ ^ [Uu: nat] : B5 ) )
% 9.17/5.43 = A2 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6921_fst__image__times,axiom,
% 9.17/5.43 ! [B5: set_o,A2: set_int] :
% 9.17/5.43 ( ( ( B5 = bot_bot_set_o )
% 9.17/5.43 => ( ( image_90517134139374612_o_int @ product_fst_int_o
% 9.17/5.43 @ ( product_Sigma_int_o @ A2
% 9.17/5.43 @ ^ [Uu: int] : B5 ) )
% 9.17/5.43 = bot_bot_set_int ) )
% 9.17/5.43 & ( ( B5 != bot_bot_set_o )
% 9.17/5.43 => ( ( image_90517134139374612_o_int @ product_fst_int_o
% 9.17/5.43 @ ( product_Sigma_int_o @ A2
% 9.17/5.43 @ ^ [Uu: int] : B5 ) )
% 9.17/5.43 = A2 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6922_fst__image__times,axiom,
% 9.17/5.43 ! [B5: set_nat,A2: set_o] :
% 9.17/5.43 ( ( ( B5 = bot_bot_set_nat )
% 9.17/5.43 => ( ( image_8105710389281276538_nat_o @ product_fst_o_nat
% 9.17/5.43 @ ( product_Sigma_o_nat @ A2
% 9.17/5.43 @ ^ [Uu: $o] : B5 ) )
% 9.17/5.43 = bot_bot_set_o ) )
% 9.17/5.43 & ( ( B5 != bot_bot_set_nat )
% 9.17/5.43 => ( ( image_8105710389281276538_nat_o @ product_fst_o_nat
% 9.17/5.43 @ ( product_Sigma_o_nat @ A2
% 9.17/5.43 @ ^ [Uu: $o] : B5 ) )
% 9.17/5.43 = A2 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6923_fst__image__times,axiom,
% 9.17/5.43 ! [B5: set_nat,A2: set_nat] :
% 9.17/5.43 ( ( ( B5 = bot_bot_set_nat )
% 9.17/5.43 => ( ( image_2486076414777270412at_nat @ product_fst_nat_nat
% 9.17/5.43 @ ( produc457027306803732586at_nat @ A2
% 9.17/5.43 @ ^ [Uu: nat] : B5 ) )
% 9.17/5.43 = bot_bot_set_nat ) )
% 9.17/5.43 & ( ( B5 != bot_bot_set_nat )
% 9.17/5.43 => ( ( image_2486076414777270412at_nat @ product_fst_nat_nat
% 9.17/5.43 @ ( produc457027306803732586at_nat @ A2
% 9.17/5.43 @ ^ [Uu: nat] : B5 ) )
% 9.17/5.43 = A2 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6924_fst__image__times,axiom,
% 9.17/5.43 ! [B5: set_nat,A2: set_int] :
% 9.17/5.43 ( ( ( B5 = bot_bot_set_nat )
% 9.17/5.43 => ( ( image_2855239504505064772at_int @ product_fst_int_nat
% 9.17/5.43 @ ( produc1456381018704787142nt_nat @ A2
% 9.17/5.43 @ ^ [Uu: int] : B5 ) )
% 9.17/5.43 = bot_bot_set_int ) )
% 9.17/5.43 & ( ( B5 != bot_bot_set_nat )
% 9.17/5.43 => ( ( image_2855239504505064772at_int @ product_fst_int_nat
% 9.17/5.43 @ ( produc1456381018704787142nt_nat @ A2
% 9.17/5.43 @ ^ [Uu: int] : B5 ) )
% 9.17/5.43 = A2 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6925_fst__image__times,axiom,
% 9.17/5.43 ! [B5: set_int,A2: set_o] :
% 9.17/5.43 ( ( ( B5 = bot_bot_set_int )
% 9.17/5.43 => ( ( image_5860565421610830622_int_o @ product_fst_o_int
% 9.17/5.43 @ ( product_Sigma_o_int @ A2
% 9.17/5.43 @ ^ [Uu: $o] : B5 ) )
% 9.17/5.43 = bot_bot_set_o ) )
% 9.17/5.43 & ( ( B5 != bot_bot_set_int )
% 9.17/5.43 => ( ( image_5860565421610830622_int_o @ product_fst_o_int
% 9.17/5.43 @ ( product_Sigma_o_int @ A2
% 9.17/5.43 @ ^ [Uu: $o] : B5 ) )
% 9.17/5.43 = A2 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6926_fst__image__times,axiom,
% 9.17/5.43 ! [B5: set_int,A2: set_nat] :
% 9.17/5.43 ( ( ( B5 = bot_bot_set_int )
% 9.17/5.43 => ( ( image_4672997989470292200nt_nat @ product_fst_nat_int
% 9.17/5.43 @ ( produc454536836294682310at_int @ A2
% 9.17/5.43 @ ^ [Uu: nat] : B5 ) )
% 9.17/5.43 = bot_bot_set_nat ) )
% 9.17/5.43 & ( ( B5 != bot_bot_set_int )
% 9.17/5.43 => ( ( image_4672997989470292200nt_nat @ product_fst_nat_int
% 9.17/5.43 @ ( produc454536836294682310at_int @ A2
% 9.17/5.43 @ ^ [Uu: nat] : B5 ) )
% 9.17/5.43 = A2 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6927_fst__image__times,axiom,
% 9.17/5.43 ! [B5: set_int,A2: set_int] :
% 9.17/5.43 ( ( ( B5 = bot_bot_set_int )
% 9.17/5.43 => ( ( image_5042161079198086560nt_int @ product_fst_int_int
% 9.17/5.43 @ ( produc1453890548195736866nt_int @ A2
% 9.17/5.43 @ ^ [Uu: int] : B5 ) )
% 9.17/5.43 = bot_bot_set_int ) )
% 9.17/5.43 & ( ( B5 != bot_bot_set_int )
% 9.17/5.43 => ( ( image_5042161079198086560nt_int @ product_fst_int_int
% 9.17/5.43 @ ( produc1453890548195736866nt_int @ A2
% 9.17/5.43 @ ^ [Uu: int] : B5 ) )
% 9.17/5.43 = A2 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6928_snd__image__times,axiom,
% 9.17/5.43 ! [A2: set_Code_integer,B5: set_Code_integer] :
% 9.17/5.43 ( ( ( A2 = bot_bo3990330152332043303nteger )
% 9.17/5.43 => ( ( image_6316824473203919795nteger @ produc6174133586879617921nteger
% 9.17/5.43 @ ( produc5882431272649516420nteger @ A2
% 9.17/5.43 @ ^ [Uu: code_integer] : B5 ) )
% 9.17/5.43 = bot_bo3990330152332043303nteger ) )
% 9.17/5.43 & ( ( A2 != bot_bo3990330152332043303nteger )
% 9.17/5.43 => ( ( image_6316824473203919795nteger @ produc6174133586879617921nteger
% 9.17/5.43 @ ( produc5882431272649516420nteger @ A2
% 9.17/5.43 @ ^ [Uu: code_integer] : B5 ) )
% 9.17/5.43 = B5 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6929_snd__image__times,axiom,
% 9.17/5.43 ! [A2: set_o,B5: set_o] :
% 9.17/5.43 ( ( ( A2 = bot_bot_set_o )
% 9.17/5.43 => ( ( image_7896445794123959606_o_o_o @ product_snd_o_o
% 9.17/5.43 @ ( product_Sigma_o_o @ A2
% 9.17/5.43 @ ^ [Uu: $o] : B5 ) )
% 9.17/5.43 = bot_bot_set_o ) )
% 9.17/5.43 & ( ( A2 != bot_bot_set_o )
% 9.17/5.43 => ( ( image_7896445794123959606_o_o_o @ product_snd_o_o
% 9.17/5.43 @ ( product_Sigma_o_o @ A2
% 9.17/5.43 @ ^ [Uu: $o] : B5 ) )
% 9.17/5.43 = B5 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6930_snd__image__times,axiom,
% 9.17/5.43 ! [A2: set_o,B5: set_nat] :
% 9.17/5.43 ( ( ( A2 = bot_bot_set_o )
% 9.17/5.43 => ( ( image_4888532181312399726at_nat @ product_snd_o_nat
% 9.17/5.43 @ ( product_Sigma_o_nat @ A2
% 9.17/5.43 @ ^ [Uu: $o] : B5 ) )
% 9.17/5.43 = bot_bot_set_nat ) )
% 9.17/5.43 & ( ( A2 != bot_bot_set_o )
% 9.17/5.43 => ( ( image_4888532181312399726at_nat @ product_snd_o_nat
% 9.17/5.43 @ ( product_Sigma_o_nat @ A2
% 9.17/5.43 @ ^ [Uu: $o] : B5 ) )
% 9.17/5.43 = B5 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6931_snd__image__times,axiom,
% 9.17/5.43 ! [A2: set_o,B5: set_int] :
% 9.17/5.43 ( ( ( A2 = bot_bot_set_o )
% 9.17/5.43 => ( ( image_7072963285496371238nt_int @ product_snd_o_int
% 9.17/5.43 @ ( product_Sigma_o_int @ A2
% 9.17/5.43 @ ^ [Uu: $o] : B5 ) )
% 9.17/5.43 = bot_bot_set_int ) )
% 9.17/5.43 & ( ( A2 != bot_bot_set_o )
% 9.17/5.43 => ( ( image_7072963285496371238nt_int @ product_snd_o_int
% 9.17/5.43 @ ( product_Sigma_o_int @ A2
% 9.17/5.43 @ ^ [Uu: $o] : B5 ) )
% 9.17/5.43 = B5 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6932_snd__image__times,axiom,
% 9.17/5.43 ! [A2: set_nat,B5: set_o] :
% 9.17/5.43 ( ( ( A2 = bot_bot_set_nat )
% 9.17/5.43 => ( ( image_7478392465989118804at_o_o @ product_snd_nat_o
% 9.17/5.43 @ ( product_Sigma_nat_o @ A2
% 9.17/5.43 @ ^ [Uu: nat] : B5 ) )
% 9.17/5.43 = bot_bot_set_o ) )
% 9.17/5.43 & ( ( A2 != bot_bot_set_nat )
% 9.17/5.43 => ( ( image_7478392465989118804at_o_o @ product_snd_nat_o
% 9.17/5.43 @ ( product_Sigma_nat_o @ A2
% 9.17/5.43 @ ^ [Uu: nat] : B5 ) )
% 9.17/5.43 = B5 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6933_snd__image__times,axiom,
% 9.17/5.43 ! [A2: set_nat,B5: set_nat] :
% 9.17/5.43 ( ( ( A2 = bot_bot_set_nat )
% 9.17/5.43 => ( ( image_2486076414777270412at_nat @ product_snd_nat_nat
% 9.17/5.43 @ ( produc457027306803732586at_nat @ A2
% 9.17/5.43 @ ^ [Uu: nat] : B5 ) )
% 9.17/5.43 = bot_bot_set_nat ) )
% 9.17/5.43 & ( ( A2 != bot_bot_set_nat )
% 9.17/5.43 => ( ( image_2486076414777270412at_nat @ product_snd_nat_nat
% 9.17/5.43 @ ( produc457027306803732586at_nat @ A2
% 9.17/5.43 @ ^ [Uu: nat] : B5 ) )
% 9.17/5.43 = B5 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6934_snd__image__times,axiom,
% 9.17/5.43 ! [A2: set_nat,B5: set_int] :
% 9.17/5.43 ( ( ( A2 = bot_bot_set_nat )
% 9.17/5.43 => ( ( image_4670507518961241924nt_int @ product_snd_nat_int
% 9.17/5.43 @ ( produc454536836294682310at_int @ A2
% 9.17/5.43 @ ^ [Uu: nat] : B5 ) )
% 9.17/5.43 = bot_bot_set_int ) )
% 9.17/5.43 & ( ( A2 != bot_bot_set_nat )
% 9.17/5.43 => ( ( image_4670507518961241924nt_int @ product_snd_nat_int
% 9.17/5.43 @ ( produc454536836294682310at_int @ A2
% 9.17/5.43 @ ^ [Uu: nat] : B5 ) )
% 9.17/5.43 = B5 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6935_snd__image__times,axiom,
% 9.17/5.43 ! [A2: set_int,B5: set_o] :
% 9.17/5.43 ( ( ( A2 = bot_bot_set_int )
% 9.17/5.43 => ( ( image_5561579847027142576nt_o_o @ product_snd_int_o
% 9.17/5.43 @ ( product_Sigma_int_o @ A2
% 9.17/5.43 @ ^ [Uu: int] : B5 ) )
% 9.17/5.43 = bot_bot_set_o ) )
% 9.17/5.43 & ( ( A2 != bot_bot_set_int )
% 9.17/5.43 => ( ( image_5561579847027142576nt_o_o @ product_snd_int_o
% 9.17/5.43 @ ( product_Sigma_int_o @ A2
% 9.17/5.43 @ ^ [Uu: int] : B5 ) )
% 9.17/5.43 = B5 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6936_snd__image__times,axiom,
% 9.17/5.43 ! [A2: set_int,B5: set_nat] :
% 9.17/5.43 ( ( ( A2 = bot_bot_set_int )
% 9.17/5.43 => ( ( image_2857729975014115048at_nat @ product_snd_int_nat
% 9.17/5.43 @ ( produc1456381018704787142nt_nat @ A2
% 9.17/5.43 @ ^ [Uu: int] : B5 ) )
% 9.17/5.43 = bot_bot_set_nat ) )
% 9.17/5.43 & ( ( A2 != bot_bot_set_int )
% 9.17/5.43 => ( ( image_2857729975014115048at_nat @ product_snd_int_nat
% 9.17/5.43 @ ( produc1456381018704787142nt_nat @ A2
% 9.17/5.43 @ ^ [Uu: int] : B5 ) )
% 9.17/5.43 = B5 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6937_snd__image__times,axiom,
% 9.17/5.43 ! [A2: set_int,B5: set_int] :
% 9.17/5.43 ( ( ( A2 = bot_bot_set_int )
% 9.17/5.43 => ( ( image_5042161079198086560nt_int @ product_snd_int_int
% 9.17/5.43 @ ( produc1453890548195736866nt_int @ A2
% 9.17/5.43 @ ^ [Uu: int] : B5 ) )
% 9.17/5.43 = bot_bot_set_int ) )
% 9.17/5.43 & ( ( A2 != bot_bot_set_int )
% 9.17/5.43 => ( ( image_5042161079198086560nt_int @ product_snd_int_int
% 9.17/5.43 @ ( produc1453890548195736866nt_int @ A2
% 9.17/5.43 @ ^ [Uu: int] : B5 ) )
% 9.17/5.43 = B5 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6938_fst__comp__apfst,axiom,
% 9.17/5.43 ! [F: code_integer > code_integer] :
% 9.17/5.43 ( ( comp_P3428181540658402820nteger @ produc8508995932063986495nteger @ ( produc3195571438000033749nteger @ F ) )
% 9.17/5.43 = ( comp_C1043215000170864188nteger @ F @ produc8508995932063986495nteger ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6939_fst__comp__apfst,axiom,
% 9.17/5.43 ! [F: int > int] :
% 9.17/5.43 ( ( comp_P5356232565778667509nt_int @ product_fst_int_int @ ( produc2355237562570658114nt_int @ F ) )
% 9.17/5.43 = ( comp_i4330622015127193916nt_int @ F @ product_fst_int_int ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6940_fun_Omap__transfer,axiom,
% 9.17/5.43 ! [Rb2: code_integer > code_integer > $o,Sd: code_integer > code_integer > $o] :
% 9.17/5.43 ( bNF_re5979881370344185769nteger @ ( bNF_re1062419521925302741nteger @ Rb2 @ Sd )
% 9.17/5.43 @ ( bNF_re6097285183634142137nteger
% 9.17/5.43 @ ( bNF_re6741283560065411407nteger
% 9.17/5.43 @ ^ [Y4: num,Z2: num] : ( Y4 = Z2 )
% 9.17/5.43 @ Rb2 )
% 9.17/5.43 @ ( bNF_re6741283560065411407nteger
% 9.17/5.43 @ ^ [Y4: num,Z2: num] : ( Y4 = Z2 )
% 9.17/5.43 @ Sd ) )
% 9.17/5.43 @ comp_C3531382070062128313er_num
% 9.17/5.43 @ comp_C3531382070062128313er_num ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6941_fun_Omap__transfer,axiom,
% 9.17/5.43 ! [Rb2: nat > nat > $o,Sd: num > num > $o] :
% 9.17/5.43 ( bNF_re3846787885862361009nt_num @ ( bNF_re341483209202555957um_num @ Rb2 @ Sd )
% 9.17/5.43 @ ( bNF_re9099949428469764705nt_num
% 9.17/5.43 @ ( bNF_re3715656647883201625at_nat
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ Rb2 )
% 9.17/5.43 @ ( bNF_re7626690874201225453um_num
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ Sd ) )
% 9.17/5.43 @ comp_nat_num_int
% 9.17/5.43 @ comp_nat_num_int ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6942_fun_Omap__transfer,axiom,
% 9.17/5.43 ! [Rb2: int > int > $o,Sd: ( nat > $o ) > ( nat > $o ) > $o] :
% 9.17/5.43 ( bNF_re7908124382625962333_nat_o @ ( bNF_re3376528473927230327_nat_o @ Rb2 @ Sd )
% 9.17/5.43 @ ( bNF_re6033114333830760525_nat_o
% 9.17/5.43 @ ( bNF_re4712519889275205905nt_int
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ Rb2 )
% 9.17/5.43 @ ( bNF_re3376528473927230327_nat_o
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ Sd ) )
% 9.17/5.43 @ comp_int_nat_o_int
% 9.17/5.43 @ comp_int_nat_o_int ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6943_fun_Omap__transfer,axiom,
% 9.17/5.43 ! [Rb2: int > int > $o,Sd: ( int > $o ) > ( int > $o ) > $o] :
% 9.17/5.43 ( bNF_re1900612664124570461_int_o @ ( bNF_re3403563459893282935_int_o @ Rb2 @ Sd )
% 9.17/5.43 @ ( bNF_re3014639844587090765_int_o
% 9.17/5.43 @ ( bNF_re4712519889275205905nt_int
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ Rb2 )
% 9.17/5.43 @ ( bNF_re3403563459893282935_int_o
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ Sd ) )
% 9.17/5.43 @ comp_int_int_o_int
% 9.17/5.43 @ comp_int_int_o_int ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6944_fun_Omap__transfer,axiom,
% 9.17/5.43 ! [Rb2: int > int > $o,Sd: ( int > int ) > ( int > int ) > $o] :
% 9.17/5.43 ( bNF_re4984751527058004117nt_int @ ( bNF_re711492959462206631nt_int @ Rb2 @ Sd )
% 9.17/5.43 @ ( bNF_re724639330072410579nt_int
% 9.17/5.43 @ ( bNF_re4712519889275205905nt_int
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ Rb2 )
% 9.17/5.43 @ ( bNF_re711492959462206631nt_int
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ Sd ) )
% 9.17/5.43 @ comp_int_int_int_int
% 9.17/5.43 @ comp_int_int_int_int ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6945_fun_Omap__transfer,axiom,
% 9.17/5.43 ! [Rb2: int > int > $o,Sd: ( int > product_prod_int_int ) > ( int > rat ) > $o] :
% 9.17/5.43 ( bNF_re62019127700022579nt_rat @ ( bNF_re3461391660133120880nt_rat @ Rb2 @ Sd )
% 9.17/5.43 @ ( bNF_re949775918795716016nt_rat
% 9.17/5.43 @ ( bNF_re4712519889275205905nt_int
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ Rb2 )
% 9.17/5.43 @ ( bNF_re3461391660133120880nt_rat
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ Sd ) )
% 9.17/5.43 @ comp_i87437609017934369nt_int
% 9.17/5.43 @ comp_int_int_rat_int ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6946_fun_Omap__transfer,axiom,
% 9.17/5.43 ! [Rb2: ( nat > $o ) > ( nat > $o ) > $o,Sd: ( nat > $o ) > ( nat > $o ) > $o] :
% 9.17/5.43 ( bNF_re1550856938216548981_nat_o @ ( bNF_re2697311982885662685_nat_o @ Rb2 @ Sd )
% 9.17/5.43 @ ( bNF_re5673586069474677853_nat_o
% 9.17/5.43 @ ( bNF_re3376528473927230327_nat_o
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ Rb2 )
% 9.17/5.43 @ ( bNF_re3376528473927230327_nat_o
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ Sd ) )
% 9.17/5.43 @ comp_nat_o_nat_o_int
% 9.17/5.43 @ comp_nat_o_nat_o_int ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6947_fun_Omap__transfer,axiom,
% 9.17/5.43 ! [Rb2: ( nat > $o ) > ( nat > $o ) > $o,Sd: ( int > $o ) > ( int > $o ) > $o] :
% 9.17/5.43 ( bNF_re3491090157995142405_int_o @ ( bNF_re2724346968851715293_int_o @ Rb2 @ Sd )
% 9.17/5.43 @ ( bNF_re2655111580231008093_int_o
% 9.17/5.43 @ ( bNF_re3376528473927230327_nat_o
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ Rb2 )
% 9.17/5.43 @ ( bNF_re3403563459893282935_int_o
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ Sd ) )
% 9.17/5.43 @ comp_nat_o_int_o_int
% 9.17/5.43 @ comp_nat_o_int_o_int ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6948_fun_Omap__transfer,axiom,
% 9.17/5.43 ! [Rb2: ( nat > $o ) > ( nat > $o ) > $o,Sd: ( int > int ) > ( int > int ) > $o] :
% 9.17/5.43 ( bNF_re5539255234643219293nt_int @ ( bNF_re7183634743573646861nt_int @ Rb2 @ Sd )
% 9.17/5.43 @ ( bNF_re7395152722673581539nt_int
% 9.17/5.43 @ ( bNF_re3376528473927230327_nat_o
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ Rb2 )
% 9.17/5.43 @ ( bNF_re711492959462206631nt_int
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ Sd ) )
% 9.17/5.43 @ comp_n3090169619561918849nt_int
% 9.17/5.43 @ comp_n3090169619561918849nt_int ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6949_fun_Omap__transfer,axiom,
% 9.17/5.43 ! [Rb2: ( int > $o ) > ( int > $o ) > $o,Sd: ( nat > $o ) > ( nat > $o ) > $o] :
% 9.17/5.43 ( bNF_re615132412071444453_nat_o @ ( bNF_re2535741173671728349_nat_o @ Rb2 @ Sd )
% 9.17/5.43 @ ( bNF_re2446162618891206493_nat_o
% 9.17/5.43 @ ( bNF_re3403563459893282935_int_o
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ Rb2 )
% 9.17/5.43 @ ( bNF_re3376528473927230327_nat_o
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ Sd ) )
% 9.17/5.43 @ comp_int_o_nat_o_int
% 9.17/5.43 @ comp_int_o_nat_o_int ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6950_comp__transfer,axiom,
% 9.17/5.43 ! [B5: code_integer > code_integer > $o,C4: code_integer > code_integer > $o,A2: num > num > $o] : ( bNF_re5979881370344185769nteger @ ( bNF_re1062419521925302741nteger @ B5 @ C4 ) @ ( bNF_re6097285183634142137nteger @ ( bNF_re6741283560065411407nteger @ A2 @ B5 ) @ ( bNF_re6741283560065411407nteger @ A2 @ C4 ) ) @ comp_C3531382070062128313er_num @ comp_C3531382070062128313er_num ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6951_comp__transfer,axiom,
% 9.17/5.43 ! [B5: code_integer > nat > $o,C4: code_integer > num > $o,A2: num > int > $o] : ( bNF_re5469402333911078061nt_num @ ( bNF_re1758498617148825349er_num @ B5 @ C4 ) @ ( bNF_re1151383970801924621nt_num @ ( bNF_re6324211044263125204er_nat @ A2 @ B5 ) @ ( bNF_re2881542830418903838er_num @ A2 @ C4 ) ) @ comp_C3531382070062128313er_num @ comp_nat_num_int ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6952_comp__transfer,axiom,
% 9.17/5.43 ! [B5: nat > code_integer > $o,C4: num > code_integer > $o,A2: int > num > $o] : ( bNF_re2163612987331707565nteger @ ( bNF_re8763372240999575301nteger @ B5 @ C4 ) @ ( bNF_re8894579221946749965nteger @ ( bNF_re151304249936775380nteger @ A2 @ B5 ) @ ( bNF_re7315484114762210078nteger @ A2 @ C4 ) ) @ comp_nat_num_int @ comp_C3531382070062128313er_num ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6953_comp__transfer,axiom,
% 9.17/5.43 ! [B5: nat > nat > $o,C4: num > num > $o,A2: int > int > $o] : ( bNF_re3846787885862361009nt_num @ ( bNF_re341483209202555957um_num @ B5 @ C4 ) @ ( bNF_re9099949428469764705nt_num @ ( bNF_re3715656647883201625at_nat @ A2 @ B5 ) @ ( bNF_re7626690874201225453um_num @ A2 @ C4 ) ) @ comp_nat_num_int @ comp_nat_num_int ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6954_comp__transfer,axiom,
% 9.17/5.43 ! [B5: int > int > $o,C4: ( nat > $o ) > ( nat > $o ) > $o,A2: int > int > $o] : ( bNF_re7908124382625962333_nat_o @ ( bNF_re3376528473927230327_nat_o @ B5 @ C4 ) @ ( bNF_re6033114333830760525_nat_o @ ( bNF_re4712519889275205905nt_int @ A2 @ B5 ) @ ( bNF_re3376528473927230327_nat_o @ A2 @ C4 ) ) @ comp_int_nat_o_int @ comp_int_nat_o_int ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6955_comp__transfer,axiom,
% 9.17/5.43 ! [B5: int > int > $o,C4: ( int > $o ) > ( int > $o ) > $o,A2: int > int > $o] : ( bNF_re1900612664124570461_int_o @ ( bNF_re3403563459893282935_int_o @ B5 @ C4 ) @ ( bNF_re3014639844587090765_int_o @ ( bNF_re4712519889275205905nt_int @ A2 @ B5 ) @ ( bNF_re3403563459893282935_int_o @ A2 @ C4 ) ) @ comp_int_int_o_int @ comp_int_int_o_int ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6956_comp__transfer,axiom,
% 9.17/5.43 ! [B5: int > int > $o,C4: ( int > int ) > ( int > int ) > $o,A2: int > int > $o] : ( bNF_re4984751527058004117nt_int @ ( bNF_re711492959462206631nt_int @ B5 @ C4 ) @ ( bNF_re724639330072410579nt_int @ ( bNF_re4712519889275205905nt_int @ A2 @ B5 ) @ ( bNF_re711492959462206631nt_int @ A2 @ C4 ) ) @ comp_int_int_int_int @ comp_int_int_int_int ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6957_comp__transfer,axiom,
% 9.17/5.43 ! [B5: code_integer > code_integer > $o,C4: code_integer > ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > $o,A2: num > code_integer > $o] : ( bNF_re8134695817916415679nteger @ ( bNF_re3370092614548195229nteger @ B5 @ C4 ) @ ( bNF_re2439920061672227847nteger @ ( bNF_re5202476307641864082nteger @ A2 @ B5 ) @ ( bNF_re5031869190687302234nteger @ A2 @ C4 ) ) @ comp_C3531382070062128313er_num @ comp_C1593894019821074884nteger ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6958_comp__transfer,axiom,
% 9.17/5.43 ! [B5: code_integer > code_integer > $o,C4: ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > code_integer > $o,A2: code_integer > num > $o] : ( bNF_re4919612610145136063nteger @ ( bNF_re4341081746073172381nteger @ B5 @ C4 ) @ ( bNF_re6724329528997265415nteger @ ( bNF_re7350422212947406738nteger @ A2 @ B5 ) @ ( bNF_re166502229267952730nteger @ A2 @ C4 ) ) @ comp_C1593894019821074884nteger @ comp_C3531382070062128313er_num ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6959_comp__transfer,axiom,
% 9.17/5.43 ! [B5: code_integer > nat > $o,C4: ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > num > $o,A2: code_integer > int > $o] : ( bNF_re1890273300020150979nt_num @ ( bNF_re7119966052990372301er_num @ B5 @ C4 ) @ ( bNF_re5190287125156074331nt_num @ ( bNF_re2891348898900095767er_nat @ A2 @ B5 ) @ ( bNF_re8127238762813979689er_num @ A2 @ C4 ) ) @ comp_C1593894019821074884nteger @ comp_nat_num_int ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6960_power__transfer,axiom,
% 9.17/5.43 ! [R4: code_integer > code_integer > $o] :
% 9.17/5.43 ( ( R4 @ one_one_Code_integer @ one_one_Code_integer )
% 9.17/5.43 => ( ( bNF_re122555440370955213nteger @ R4 @ ( bNF_re1062419521925302741nteger @ R4 @ R4 ) @ times_3573771949741848930nteger @ times_3573771949741848930nteger )
% 9.17/5.43 => ( bNF_re5462749793222359603nteger @ R4
% 9.17/5.43 @ ( bNF_re1236659899165691067nteger
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.43 @ R4 )
% 9.17/5.43 @ power_8256067586552552935nteger
% 9.17/5.43 @ power_8256067586552552935nteger ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6961_power__transfer,axiom,
% 9.17/5.43 ! [R4: code_integer > assn > $o] :
% 9.17/5.43 ( ( R4 @ one_one_Code_integer @ one_one_assn )
% 9.17/5.43 => ( ( bNF_re7789648203153440174n_assn @ R4 @ ( bNF_re1475883931861434731r_assn @ R4 @ R4 ) @ times_3573771949741848930nteger @ times_times_assn )
% 9.17/5.43 => ( bNF_re2546461910754330953t_assn @ R4
% 9.17/5.43 @ ( bNF_re2692373401909853574r_assn
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.43 @ R4 )
% 9.17/5.43 @ power_8256067586552552935nteger
% 9.17/5.43 @ power_power_assn ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6962_power__transfer,axiom,
% 9.17/5.43 ! [R4: code_integer > rat > $o] :
% 9.17/5.43 ( ( R4 @ one_one_Code_integer @ one_one_rat )
% 9.17/5.43 => ( ( bNF_re2976496150901874110at_rat @ R4 @ ( bNF_re4698098036185532619er_rat @ R4 @ R4 ) @ times_3573771949741848930nteger @ times_times_rat )
% 9.17/5.43 => ( bNF_re1167376069379428009at_rat @ R4
% 9.17/5.43 @ ( bNF_re2882060999336173110er_rat
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.43 @ R4 )
% 9.17/5.43 @ power_8256067586552552935nteger
% 9.17/5.43 @ power_power_rat ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6963_power__transfer,axiom,
% 9.17/5.43 ! [R4: code_integer > nat > $o] :
% 9.17/5.43 ( ( R4 @ one_one_Code_integer @ one_one_nat )
% 9.17/5.43 => ( ( bNF_re3981674901896804262at_nat @ R4 @ ( bNF_re5201166830993046715er_nat @ R4 @ R4 ) @ times_3573771949741848930nteger @ times_times_nat )
% 9.17/5.43 => ( bNF_re4269568176766901913at_nat @ R4
% 9.17/5.43 @ ( bNF_re3517191059422668846er_nat
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.43 @ R4 )
% 9.17/5.43 @ power_8256067586552552935nteger
% 9.17/5.43 @ power_power_nat ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6964_power__transfer,axiom,
% 9.17/5.43 ! [R4: code_integer > int > $o] :
% 9.17/5.43 ( ( R4 @ one_one_Code_integer @ one_one_int )
% 9.17/5.43 => ( ( bNF_re8304916493157054650nt_int @ R4 @ ( bNF_re2888858428391045491er_int @ R4 @ R4 ) @ times_3573771949741848930nteger @ times_times_int )
% 9.17/5.43 => ( bNF_re6766650671887726929at_int @ R4
% 9.17/5.43 @ ( bNF_re3514700588913618570er_int
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.43 @ R4 )
% 9.17/5.43 @ power_8256067586552552935nteger
% 9.17/5.43 @ power_power_int ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6965_power__transfer,axiom,
% 9.17/5.43 ! [R4: assn > code_integer > $o] :
% 9.17/5.43 ( ( R4 @ one_one_assn @ one_one_Code_integer )
% 9.17/5.43 => ( ( bNF_re5822757241383739566nteger @ R4 @ ( bNF_re4134162077946812779nteger @ R4 @ R4 ) @ times_times_assn @ times_3573771949741848930nteger )
% 9.17/5.43 => ( bNF_re2102180915162216137nteger @ R4
% 9.17/5.43 @ ( bNF_re1831131418152741254nteger
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.43 @ R4 )
% 9.17/5.43 @ power_power_assn
% 9.17/5.43 @ power_8256067586552552935nteger ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6966_power__transfer,axiom,
% 9.17/5.43 ! [R4: assn > assn > $o] :
% 9.17/5.43 ( ( R4 @ one_one_assn @ one_one_assn )
% 9.17/5.43 => ( ( bNF_re9137223911888007311n_assn @ R4 @ ( bNF_re1143782165119297793n_assn @ R4 @ R4 ) @ times_times_assn @ times_times_assn )
% 9.17/5.43 => ( bNF_re3650450707543776735t_assn @ R4
% 9.17/5.43 @ ( bNF_re4051817429369991249n_assn
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.43 @ R4 )
% 9.17/5.43 @ power_power_assn
% 9.17/5.43 @ power_power_assn ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6967_power__transfer,axiom,
% 9.17/5.43 ! [R4: assn > rat > $o] :
% 9.17/5.43 ( ( R4 @ one_one_assn @ one_one_rat )
% 9.17/5.43 => ( ( bNF_re967558844708792991at_rat @ R4 @ ( bNF_re9003240792272343649sn_rat @ R4 @ R4 ) @ times_times_assn @ times_times_rat )
% 9.17/5.43 => ( bNF_re6138836914430330175at_rat @ R4
% 9.17/5.43 @ ( bNF_re4159627890580825857sn_rat
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.43 @ R4 )
% 9.17/5.43 @ power_power_assn
% 9.17/5.43 @ power_power_rat ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6968_power__transfer,axiom,
% 9.17/5.43 ! [R4: assn > nat > $o] :
% 9.17/5.43 ( ( R4 @ one_one_assn @ one_one_nat )
% 9.17/5.43 => ( ( bNF_re4386305596031132807at_nat @ R4 @ ( bNF_re6742580585434904145sn_nat @ R4 @ R4 ) @ times_times_assn @ times_times_nat )
% 9.17/5.43 => ( bNF_re8560028565313717551at_nat @ R4
% 9.17/5.43 @ ( bNF_re4794757950667321593sn_nat
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.43 @ R4 )
% 9.17/5.43 @ power_power_assn
% 9.17/5.43 @ power_power_nat ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6969_power__transfer,axiom,
% 9.17/5.43 ! [R4: assn > int > $o] :
% 9.17/5.43 ( ( R4 @ one_one_assn @ one_one_int )
% 9.17/5.43 => ( ( bNF_re7882741803053012379nt_int @ R4 @ ( bNF_re2927800259774540553sn_int @ R4 @ R4 ) @ times_times_assn @ times_times_int )
% 9.17/5.43 => ( bNF_re185025794348816359at_int @ R4
% 9.17/5.43 @ ( bNF_re4792267480158271317sn_int
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.43 @ R4 )
% 9.17/5.43 @ power_power_assn
% 9.17/5.43 @ power_power_int ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6970_times__integer_Orsp,axiom,
% 9.17/5.43 ( bNF_re711492959462206631nt_int
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ ( bNF_re4712519889275205905nt_int
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 ) )
% 9.17/5.43 @ times_times_int
% 9.17/5.43 @ times_times_int ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6971_times__natural_Orsp,axiom,
% 9.17/5.43 ( bNF_re1345281282404953727at_nat
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.43 @ ( bNF_re5653821019739307937at_nat
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 ) )
% 9.17/5.43 @ times_times_nat
% 9.17/5.43 @ times_times_nat ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6972_divide__natural_Orsp,axiom,
% 9.17/5.43 ( bNF_re1345281282404953727at_nat
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.43 @ ( bNF_re5653821019739307937at_nat
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 ) )
% 9.17/5.43 @ divide_divide_nat
% 9.17/5.43 @ divide_divide_nat ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6973_divide__integer_Orsp,axiom,
% 9.17/5.43 ( bNF_re711492959462206631nt_int
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ ( bNF_re4712519889275205905nt_int
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 ) )
% 9.17/5.43 @ divide_divide_int
% 9.17/5.43 @ divide_divide_int ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6974_or__natural_Orsp,axiom,
% 9.17/5.43 ( bNF_re1345281282404953727at_nat
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.43 @ ( bNF_re5653821019739307937at_nat
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 ) )
% 9.17/5.43 @ bit_se1412395901928357646or_nat
% 9.17/5.43 @ bit_se1412395901928357646or_nat ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6975_or__integer_Orsp,axiom,
% 9.17/5.43 ( bNF_re711492959462206631nt_int
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ ( bNF_re4712519889275205905nt_int
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 ) )
% 9.17/5.43 @ bit_se1409905431419307370or_int
% 9.17/5.43 @ bit_se1409905431419307370or_int ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6976_set__bit__integer_Orsp,axiom,
% 9.17/5.43 ( bNF_re4785983289428654063nt_int
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.43 @ ( bNF_re4712519889275205905nt_int
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 ) )
% 9.17/5.43 @ bit_se7879613467334960850it_int
% 9.17/5.43 @ bit_se7879613467334960850it_int ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6977_set__bit__natural_Orsp,axiom,
% 9.17/5.43 ( bNF_re1345281282404953727at_nat
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.43 @ ( bNF_re5653821019739307937at_nat
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 ) )
% 9.17/5.43 @ bit_se7882103937844011126it_nat
% 9.17/5.43 @ bit_se7882103937844011126it_nat ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6978_xor__integer_Orsp,axiom,
% 9.17/5.43 ( bNF_re711492959462206631nt_int
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ ( bNF_re4712519889275205905nt_int
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 ) )
% 9.17/5.43 @ bit_se6526347334894502574or_int
% 9.17/5.43 @ bit_se6526347334894502574or_int ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6979_xor__natural_Orsp,axiom,
% 9.17/5.43 ( bNF_re1345281282404953727at_nat
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.43 @ ( bNF_re5653821019739307937at_nat
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 ) )
% 9.17/5.43 @ bit_se6528837805403552850or_nat
% 9.17/5.43 @ bit_se6528837805403552850or_nat ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6980_and__integer_Orsp,axiom,
% 9.17/5.43 ( bNF_re711492959462206631nt_int
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ ( bNF_re4712519889275205905nt_int
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 ) )
% 9.17/5.43 @ bit_se725231765392027082nd_int
% 9.17/5.43 @ bit_se725231765392027082nd_int ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6981_and__natural_Orsp,axiom,
% 9.17/5.43 ( bNF_re1345281282404953727at_nat
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.43 @ ( bNF_re5653821019739307937at_nat
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 ) )
% 9.17/5.43 @ bit_se727722235901077358nd_nat
% 9.17/5.43 @ bit_se727722235901077358nd_nat ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6982_modulo__integer_Orsp,axiom,
% 9.17/5.43 ( bNF_re711492959462206631nt_int
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ ( bNF_re4712519889275205905nt_int
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 ) )
% 9.17/5.43 @ modulo_modulo_int
% 9.17/5.43 @ modulo_modulo_int ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6983_modulo__natural_Orsp,axiom,
% 9.17/5.43 ( bNF_re1345281282404953727at_nat
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.43 @ ( bNF_re5653821019739307937at_nat
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 ) )
% 9.17/5.43 @ modulo_modulo_nat
% 9.17/5.43 @ modulo_modulo_nat ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6984_less__integer_Orsp,axiom,
% 9.17/5.43 ( bNF_re3403563459893282935_int_o
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ ( bNF_re5089333283451836215nt_o_o
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ ^ [Y4: $o,Z2: $o] : ( Y4 = Z2 ) )
% 9.17/5.43 @ ord_less_int
% 9.17/5.43 @ ord_less_int ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6985_less__natural_Orsp,axiom,
% 9.17/5.43 ( bNF_re578469030762574527_nat_o
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.43 @ ( bNF_re4705727531993890431at_o_o
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.43 @ ^ [Y4: $o,Z2: $o] : ( Y4 = Z2 ) )
% 9.17/5.43 @ ord_less_nat
% 9.17/5.43 @ ord_less_nat ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6986_unset__bit__integer_Orsp,axiom,
% 9.17/5.43 ( bNF_re4785983289428654063nt_int
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.43 @ ( bNF_re4712519889275205905nt_int
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 ) )
% 9.17/5.43 @ bit_se4203085406695923979it_int
% 9.17/5.43 @ bit_se4203085406695923979it_int ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6987_take__bit__integer_Orsp,axiom,
% 9.17/5.43 ( bNF_re4785983289428654063nt_int
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.43 @ ( bNF_re4712519889275205905nt_int
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 ) )
% 9.17/5.43 @ bit_se2923211474154528505it_int
% 9.17/5.43 @ bit_se2923211474154528505it_int ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6988_flip__bit__integer_Orsp,axiom,
% 9.17/5.43 ( bNF_re4785983289428654063nt_int
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.43 @ ( bNF_re4712519889275205905nt_int
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 ) )
% 9.17/5.43 @ bit_se2159334234014336723it_int
% 9.17/5.43 @ bit_se2159334234014336723it_int ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6989_flip__bit__natural_Orsp,axiom,
% 9.17/5.43 ( bNF_re1345281282404953727at_nat
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.43 @ ( bNF_re5653821019739307937at_nat
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 ) )
% 9.17/5.43 @ bit_se2161824704523386999it_nat
% 9.17/5.43 @ bit_se2161824704523386999it_nat ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6990_push__bit__natural_Orsp,axiom,
% 9.17/5.43 ( bNF_re1345281282404953727at_nat
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.43 @ ( bNF_re5653821019739307937at_nat
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 ) )
% 9.17/5.43 @ bit_se547839408752420682it_nat
% 9.17/5.43 @ bit_se547839408752420682it_nat ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6991_push__bit__integer_Orsp,axiom,
% 9.17/5.43 ( bNF_re4785983289428654063nt_int
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.43 @ ( bNF_re4712519889275205905nt_int
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 ) )
% 9.17/5.43 @ bit_se545348938243370406it_int
% 9.17/5.43 @ bit_se545348938243370406it_int ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6992_plus__integer_Orsp,axiom,
% 9.17/5.43 ( bNF_re711492959462206631nt_int
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ ( bNF_re4712519889275205905nt_int
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 ) )
% 9.17/5.43 @ plus_plus_int
% 9.17/5.43 @ plus_plus_int ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6993_plus__natural_Orsp,axiom,
% 9.17/5.43 ( bNF_re1345281282404953727at_nat
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.43 @ ( bNF_re5653821019739307937at_nat
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 ) )
% 9.17/5.43 @ plus_plus_nat
% 9.17/5.43 @ plus_plus_nat ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6994_drop__bit__integer_Orsp,axiom,
% 9.17/5.43 ( bNF_re4785983289428654063nt_int
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.43 @ ( bNF_re4712519889275205905nt_int
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 ) )
% 9.17/5.43 @ bit_se8568078237143864401it_int
% 9.17/5.43 @ bit_se8568078237143864401it_int ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6995_minus__natural_Orsp,axiom,
% 9.17/5.43 ( bNF_re1345281282404953727at_nat
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.43 @ ( bNF_re5653821019739307937at_nat
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 ) )
% 9.17/5.43 @ minus_minus_nat
% 9.17/5.43 @ minus_minus_nat ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6996_minus__integer_Orsp,axiom,
% 9.17/5.43 ( bNF_re711492959462206631nt_int
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ ( bNF_re4712519889275205905nt_int
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 ) )
% 9.17/5.43 @ minus_minus_int
% 9.17/5.43 @ minus_minus_int ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6997_less__eq__integer_Orsp,axiom,
% 9.17/5.43 ( bNF_re3403563459893282935_int_o
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ ( bNF_re5089333283451836215nt_o_o
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ ^ [Y4: $o,Z2: $o] : ( Y4 = Z2 ) )
% 9.17/5.43 @ ord_less_eq_int
% 9.17/5.43 @ ord_less_eq_int ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6998_less__eq__natural_Orsp,axiom,
% 9.17/5.43 ( bNF_re578469030762574527_nat_o
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.43 @ ( bNF_re4705727531993890431at_o_o
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.43 @ ^ [Y4: $o,Z2: $o] : ( Y4 = Z2 ) )
% 9.17/5.43 @ ord_less_eq_nat
% 9.17/5.43 @ ord_less_eq_nat ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_6999_SigmaE,axiom,
% 9.17/5.43 ! [C: product_prod_o_o,A2: set_o,B5: $o > set_o] :
% 9.17/5.43 ( ( member7466972457876170832od_o_o @ C @ ( product_Sigma_o_o @ A2 @ B5 ) )
% 9.17/5.43 => ~ ! [X4: $o] :
% 9.17/5.43 ( ( member_o @ X4 @ A2 )
% 9.17/5.43 => ! [Y5: $o] :
% 9.17/5.43 ( ( member_o @ Y5 @ ( B5 @ X4 ) )
% 9.17/5.43 => ( C
% 9.17/5.43 != ( product_Pair_o_o @ X4 @ Y5 ) ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7000_SigmaE,axiom,
% 9.17/5.43 ! [C: product_prod_o_nat,A2: set_o,B5: $o > set_nat] :
% 9.17/5.43 ( ( member2802428098988154798_o_nat @ C @ ( product_Sigma_o_nat @ A2 @ B5 ) )
% 9.17/5.43 => ~ ! [X4: $o] :
% 9.17/5.43 ( ( member_o @ X4 @ A2 )
% 9.17/5.43 => ! [Y5: nat] :
% 9.17/5.43 ( ( member_nat @ Y5 @ ( B5 @ X4 ) )
% 9.17/5.43 => ( C
% 9.17/5.43 != ( product_Pair_o_nat @ X4 @ Y5 ) ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7001_SigmaE,axiom,
% 9.17/5.43 ! [C: product_prod_o_int,A2: set_o,B5: $o > set_int] :
% 9.17/5.43 ( ( member7847949116333733898_o_int @ C @ ( product_Sigma_o_int @ A2 @ B5 ) )
% 9.17/5.43 => ~ ! [X4: $o] :
% 9.17/5.43 ( ( member_o @ X4 @ A2 )
% 9.17/5.43 => ! [Y5: int] :
% 9.17/5.43 ( ( member_int @ Y5 @ ( B5 @ X4 ) )
% 9.17/5.43 => ( C
% 9.17/5.43 != ( product_Pair_o_int @ X4 @ Y5 ) ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7002_SigmaE,axiom,
% 9.17/5.43 ! [C: product_prod_nat_o,A2: set_nat,B5: nat > set_o] :
% 9.17/5.43 ( ( member6310962623043647828_nat_o @ C @ ( product_Sigma_nat_o @ A2 @ B5 ) )
% 9.17/5.43 => ~ ! [X4: nat] :
% 9.17/5.43 ( ( member_nat @ X4 @ A2 )
% 9.17/5.43 => ! [Y5: $o] :
% 9.17/5.43 ( ( member_o @ Y5 @ ( B5 @ X4 ) )
% 9.17/5.43 => ( C
% 9.17/5.43 != ( product_Pair_nat_o @ X4 @ Y5 ) ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7003_SigmaE,axiom,
% 9.17/5.43 ! [C: product_prod_nat_int,A2: set_nat,B5: nat > set_int] :
% 9.17/5.43 ( ( member4262671552274231302at_int @ C @ ( produc454536836294682310at_int @ A2 @ B5 ) )
% 9.17/5.43 => ~ ! [X4: nat] :
% 9.17/5.43 ( ( member_nat @ X4 @ A2 )
% 9.17/5.43 => ! [Y5: int] :
% 9.17/5.43 ( ( member_int @ Y5 @ ( B5 @ X4 ) )
% 9.17/5.43 => ( C
% 9.17/5.43 != ( product_Pair_nat_int @ X4 @ Y5 ) ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7004_SigmaE,axiom,
% 9.17/5.43 ! [C: product_prod_int_o,A2: set_int,B5: int > set_o] :
% 9.17/5.43 ( ( member4489920277610959864_int_o @ C @ ( product_Sigma_int_o @ A2 @ B5 ) )
% 9.17/5.43 => ~ ! [X4: int] :
% 9.17/5.43 ( ( member_int @ X4 @ A2 )
% 9.17/5.43 => ! [Y5: $o] :
% 9.17/5.43 ( ( member_o @ Y5 @ ( B5 @ X4 ) )
% 9.17/5.43 => ( C
% 9.17/5.43 != ( product_Pair_int_o @ X4 @ Y5 ) ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7005_SigmaE,axiom,
% 9.17/5.43 ! [C: product_prod_int_nat,A2: set_int,B5: int > set_nat] :
% 9.17/5.43 ( ( member216504246829706758nt_nat @ C @ ( produc1456381018704787142nt_nat @ A2 @ B5 ) )
% 9.17/5.43 => ~ ! [X4: int] :
% 9.17/5.43 ( ( member_int @ X4 @ A2 )
% 9.17/5.43 => ! [Y5: nat] :
% 9.17/5.43 ( ( member_nat @ Y5 @ ( B5 @ X4 ) )
% 9.17/5.43 => ( C
% 9.17/5.43 != ( product_Pair_int_nat @ X4 @ Y5 ) ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7006_SigmaE,axiom,
% 9.17/5.43 ! [C: product_prod_int_int,A2: set_int,B5: int > set_int] :
% 9.17/5.43 ( ( member5262025264175285858nt_int @ C @ ( produc1453890548195736866nt_int @ A2 @ B5 ) )
% 9.17/5.43 => ~ ! [X4: int] :
% 9.17/5.43 ( ( member_int @ X4 @ A2 )
% 9.17/5.43 => ! [Y5: int] :
% 9.17/5.43 ( ( member_int @ Y5 @ ( B5 @ X4 ) )
% 9.17/5.43 => ( C
% 9.17/5.43 != ( product_Pair_int_int @ X4 @ Y5 ) ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7007_SigmaE,axiom,
% 9.17/5.43 ! [C: product_prod_nat_nat,A2: set_nat,B5: nat > set_nat] :
% 9.17/5.43 ( ( member8440522571783428010at_nat @ C @ ( produc457027306803732586at_nat @ A2 @ B5 ) )
% 9.17/5.43 => ~ ! [X4: nat] :
% 9.17/5.43 ( ( member_nat @ X4 @ A2 )
% 9.17/5.43 => ! [Y5: nat] :
% 9.17/5.43 ( ( member_nat @ Y5 @ ( B5 @ X4 ) )
% 9.17/5.43 => ( C
% 9.17/5.43 != ( product_Pair_nat_nat @ X4 @ Y5 ) ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7008_SigmaE,axiom,
% 9.17/5.43 ! [C: produc652263959640188542_nat_o,A2: set_Pr1261947904930325089at_nat,B5: product_prod_nat_nat > set_o] :
% 9.17/5.43 ( ( member2200362271989506215_nat_o @ C @ ( produc203973861852599583_nat_o @ A2 @ B5 ) )
% 9.17/5.43 => ~ ! [X4: product_prod_nat_nat] :
% 9.17/5.43 ( ( member8440522571783428010at_nat @ X4 @ A2 )
% 9.17/5.43 => ! [Y5: $o] :
% 9.17/5.43 ( ( member_o @ Y5 @ ( B5 @ X4 ) )
% 9.17/5.43 => ( C
% 9.17/5.43 != ( produc855456346497908590_nat_o @ X4 @ Y5 ) ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7009_SigmaD1,axiom,
% 9.17/5.43 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,A2: set_se7855581050983116737at_nat,B5: set_Pr1261947904930325089at_nat > set_se7855581050983116737at_nat] :
% 9.17/5.43 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ B ) @ ( produc7726050920695093128at_nat @ A2 @ B5 ) )
% 9.17/5.43 => ( member2643936169264416010at_nat @ A @ A2 ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7010_SigmaD1,axiom,
% 9.17/5.43 ! [A: nat,B: nat,A2: set_nat,B5: nat > set_nat] :
% 9.17/5.43 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ ( produc457027306803732586at_nat @ A2 @ B5 ) )
% 9.17/5.43 => ( member_nat @ A @ A2 ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7011_SigmaD1,axiom,
% 9.17/5.43 ! [A: produc6241069584506657477e_term > option6357759511663192854e_term,B: produc8923325533196201883nteger,A2: set_Pr7604974323444597168e_term,B5: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > set_Pr4811707699266497531nteger] :
% 9.17/5.43 ( ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ A @ B ) @ ( produc7256824055837167575nteger @ A2 @ B5 ) )
% 9.17/5.43 => ( member4242434998011752849e_term @ A @ A2 ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7012_SigmaD1,axiom,
% 9.17/5.43 ! [A: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat,A2: set_Pr4532377907799695533_nat_o,B5: ( produc3658429121746597890et_nat > $o ) > set_Pr3948176798113811640et_nat] :
% 9.17/5.43 ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ A @ B ) @ ( produc8052021730408606599et_nat @ A2 @ B5 ) )
% 9.17/5.43 => ( member6576561426505652726_nat_o @ A @ A2 ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7013_SigmaD1,axiom,
% 9.17/5.43 ! [A: produc3658429121746597890et_nat > $o,B: produc3925858234332021118et_nat,A2: set_Pr4532377907799695533_nat_o,B5: ( produc3658429121746597890et_nat > $o ) > set_Pr3286484037609594932et_nat] :
% 9.17/5.43 ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ A @ B ) @ ( produc7016705354093686019et_nat @ A2 @ B5 ) )
% 9.17/5.43 => ( member6576561426505652726_nat_o @ A @ A2 ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7014_SigmaD1,axiom,
% 9.17/5.43 ! [A: produc8551481072490612790e_term > option6357759511663192854e_term,B: product_prod_int_int,A2: set_Pr3642885161833720865e_term,B5: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > set_Pr958786334691620121nt_int] :
% 9.17/5.43 ( ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ A @ B ) @ ( produc5808185664642557892nt_int @ A2 @ B5 ) )
% 9.17/5.43 => ( member3222579708246209666e_term @ A @ A2 ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7015_SigmaD1,axiom,
% 9.17/5.43 ! [A: int > option6357759511663192854e_term,B: product_prod_int_int,A2: set_in3461395444621081367e_term,B5: ( int > option6357759511663192854e_term ) > set_Pr958786334691620121nt_int] :
% 9.17/5.43 ( ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ A @ B ) @ ( produc1318478031590598990nt_int @ A2 @ B5 ) )
% 9.17/5.43 => ( member8845023287901829240e_term @ A @ A2 ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7016_SigmaD2,axiom,
% 9.17/5.43 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,A2: set_se7855581050983116737at_nat,B5: set_Pr1261947904930325089at_nat > set_se7855581050983116737at_nat] :
% 9.17/5.43 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ B ) @ ( produc7726050920695093128at_nat @ A2 @ B5 ) )
% 9.17/5.43 => ( member2643936169264416010at_nat @ B @ ( B5 @ A ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7017_SigmaD2,axiom,
% 9.17/5.43 ! [A: nat,B: nat,A2: set_nat,B5: nat > set_nat] :
% 9.17/5.43 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ ( produc457027306803732586at_nat @ A2 @ B5 ) )
% 9.17/5.43 => ( member_nat @ B @ ( B5 @ A ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7018_SigmaD2,axiom,
% 9.17/5.43 ! [A: produc6241069584506657477e_term > option6357759511663192854e_term,B: produc8923325533196201883nteger,A2: set_Pr7604974323444597168e_term,B5: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > set_Pr4811707699266497531nteger] :
% 9.17/5.43 ( ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ A @ B ) @ ( produc7256824055837167575nteger @ A2 @ B5 ) )
% 9.17/5.43 => ( member157494554546826820nteger @ B @ ( B5 @ A ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7019_SigmaD2,axiom,
% 9.17/5.43 ! [A: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat,A2: set_Pr4532377907799695533_nat_o,B5: ( produc3658429121746597890et_nat > $o ) > set_Pr3948176798113811640et_nat] :
% 9.17/5.43 ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ A @ B ) @ ( produc8052021730408606599et_nat @ A2 @ B5 ) )
% 9.17/5.43 => ( member6260224972018164377et_nat @ B @ ( B5 @ A ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7020_SigmaD2,axiom,
% 9.17/5.43 ! [A: produc3658429121746597890et_nat > $o,B: produc3925858234332021118et_nat,A2: set_Pr4532377907799695533_nat_o,B5: ( produc3658429121746597890et_nat > $o ) > set_Pr3286484037609594932et_nat] :
% 9.17/5.43 ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ A @ B ) @ ( produc7016705354093686019et_nat @ A2 @ B5 ) )
% 9.17/5.43 => ( member1996754912294343701et_nat @ B @ ( B5 @ A ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7021_SigmaD2,axiom,
% 9.17/5.43 ! [A: produc8551481072490612790e_term > option6357759511663192854e_term,B: product_prod_int_int,A2: set_Pr3642885161833720865e_term,B5: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > set_Pr958786334691620121nt_int] :
% 9.17/5.43 ( ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ A @ B ) @ ( produc5808185664642557892nt_int @ A2 @ B5 ) )
% 9.17/5.43 => ( member5262025264175285858nt_int @ B @ ( B5 @ A ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7022_SigmaD2,axiom,
% 9.17/5.43 ! [A: int > option6357759511663192854e_term,B: product_prod_int_int,A2: set_in3461395444621081367e_term,B5: ( int > option6357759511663192854e_term ) > set_Pr958786334691620121nt_int] :
% 9.17/5.43 ( ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ A @ B ) @ ( produc1318478031590598990nt_int @ A2 @ B5 ) )
% 9.17/5.43 => ( member5262025264175285858nt_int @ B @ ( B5 @ A ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7023_SigmaE2,axiom,
% 9.17/5.43 ! [A: $o,B: $o,A2: set_o,B5: $o > set_o] :
% 9.17/5.43 ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ A @ B ) @ ( product_Sigma_o_o @ A2 @ B5 ) )
% 9.17/5.43 => ~ ( ( member_o @ A @ A2 )
% 9.17/5.43 => ~ ( member_o @ B @ ( B5 @ A ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7024_SigmaE2,axiom,
% 9.17/5.43 ! [A: $o,B: nat,A2: set_o,B5: $o > set_nat] :
% 9.17/5.43 ( ( member2802428098988154798_o_nat @ ( product_Pair_o_nat @ A @ B ) @ ( product_Sigma_o_nat @ A2 @ B5 ) )
% 9.17/5.43 => ~ ( ( member_o @ A @ A2 )
% 9.17/5.43 => ~ ( member_nat @ B @ ( B5 @ A ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7025_SigmaE2,axiom,
% 9.17/5.43 ! [A: $o,B: int,A2: set_o,B5: $o > set_int] :
% 9.17/5.43 ( ( member7847949116333733898_o_int @ ( product_Pair_o_int @ A @ B ) @ ( product_Sigma_o_int @ A2 @ B5 ) )
% 9.17/5.43 => ~ ( ( member_o @ A @ A2 )
% 9.17/5.43 => ~ ( member_int @ B @ ( B5 @ A ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7026_SigmaE2,axiom,
% 9.17/5.43 ! [A: nat,B: $o,A2: set_nat,B5: nat > set_o] :
% 9.17/5.43 ( ( member6310962623043647828_nat_o @ ( product_Pair_nat_o @ A @ B ) @ ( product_Sigma_nat_o @ A2 @ B5 ) )
% 9.17/5.43 => ~ ( ( member_nat @ A @ A2 )
% 9.17/5.43 => ~ ( member_o @ B @ ( B5 @ A ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7027_SigmaE2,axiom,
% 9.17/5.43 ! [A: nat,B: int,A2: set_nat,B5: nat > set_int] :
% 9.17/5.43 ( ( member4262671552274231302at_int @ ( product_Pair_nat_int @ A @ B ) @ ( produc454536836294682310at_int @ A2 @ B5 ) )
% 9.17/5.43 => ~ ( ( member_nat @ A @ A2 )
% 9.17/5.43 => ~ ( member_int @ B @ ( B5 @ A ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7028_SigmaE2,axiom,
% 9.17/5.43 ! [A: int,B: $o,A2: set_int,B5: int > set_o] :
% 9.17/5.43 ( ( member4489920277610959864_int_o @ ( product_Pair_int_o @ A @ B ) @ ( product_Sigma_int_o @ A2 @ B5 ) )
% 9.17/5.43 => ~ ( ( member_int @ A @ A2 )
% 9.17/5.43 => ~ ( member_o @ B @ ( B5 @ A ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7029_SigmaE2,axiom,
% 9.17/5.43 ! [A: int,B: nat,A2: set_int,B5: int > set_nat] :
% 9.17/5.43 ( ( member216504246829706758nt_nat @ ( product_Pair_int_nat @ A @ B ) @ ( produc1456381018704787142nt_nat @ A2 @ B5 ) )
% 9.17/5.43 => ~ ( ( member_int @ A @ A2 )
% 9.17/5.43 => ~ ( member_nat @ B @ ( B5 @ A ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7030_SigmaE2,axiom,
% 9.17/5.43 ! [A: int,B: int,A2: set_int,B5: int > set_int] :
% 9.17/5.43 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ ( produc1453890548195736866nt_int @ A2 @ B5 ) )
% 9.17/5.43 => ~ ( ( member_int @ A @ A2 )
% 9.17/5.43 => ~ ( member_int @ B @ ( B5 @ A ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7031_SigmaE2,axiom,
% 9.17/5.43 ! [A: nat,B: nat,A2: set_nat,B5: nat > set_nat] :
% 9.17/5.43 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ ( produc457027306803732586at_nat @ A2 @ B5 ) )
% 9.17/5.43 => ~ ( ( member_nat @ A @ A2 )
% 9.17/5.43 => ~ ( member_nat @ B @ ( B5 @ A ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7032_SigmaE2,axiom,
% 9.17/5.43 ! [A: product_prod_nat_nat,B: $o,A2: set_Pr1261947904930325089at_nat,B5: product_prod_nat_nat > set_o] :
% 9.17/5.43 ( ( member2200362271989506215_nat_o @ ( produc855456346497908590_nat_o @ A @ B ) @ ( produc203973861852599583_nat_o @ A2 @ B5 ) )
% 9.17/5.43 => ~ ( ( member8440522571783428010at_nat @ A @ A2 )
% 9.17/5.43 => ~ ( member_o @ B @ ( B5 @ A ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7033_Suc_Orsp,axiom,
% 9.17/5.43 ( bNF_re5653821019739307937at_nat
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.43 @ suc
% 9.17/5.43 @ suc ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7034_sub_Orsp,axiom,
% 9.17/5.43 ( bNF_re8402795839162346335um_int
% 9.17/5.43 @ ^ [Y4: num,Z2: num] : ( Y4 = Z2 )
% 9.17/5.43 @ ( bNF_re1822329894187522285nt_int
% 9.17/5.43 @ ^ [Y4: num,Z2: num] : ( Y4 = Z2 )
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 ) )
% 9.17/5.43 @ ^ [M: num,N4: num] : ( minus_minus_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N4 ) )
% 9.17/5.43 @ ^ [M: num,N4: num] : ( minus_minus_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N4 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7035_transfer__rule__numeral,axiom,
% 9.17/5.43 ! [R4: nat > nat > $o] :
% 9.17/5.43 ( ( R4 @ zero_zero_nat @ zero_zero_nat )
% 9.17/5.43 => ( ( R4 @ one_one_nat @ one_one_nat )
% 9.17/5.43 => ( ( bNF_re1345281282404953727at_nat @ R4 @ ( bNF_re5653821019739307937at_nat @ R4 @ R4 ) @ plus_plus_nat @ plus_plus_nat )
% 9.17/5.43 => ( bNF_re825466652795518005at_nat
% 9.17/5.43 @ ^ [Y4: num,Z2: num] : ( Y4 = Z2 )
% 9.17/5.43 @ R4
% 9.17/5.43 @ numeral_numeral_nat
% 9.17/5.43 @ numeral_numeral_nat ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7036_transfer__rule__numeral,axiom,
% 9.17/5.43 ! [R4: nat > int > $o] :
% 9.17/5.43 ( ( R4 @ zero_zero_nat @ zero_zero_int )
% 9.17/5.43 => ( ( R4 @ one_one_nat @ one_one_int )
% 9.17/5.43 => ( ( bNF_re5864104203909894035nt_int @ R4 @ ( bNF_re6022984109467102297at_int @ R4 @ R4 ) @ plus_plus_nat @ plus_plus_int )
% 9.17/5.43 => ( bNF_re822976182286467729at_int
% 9.17/5.43 @ ^ [Y4: num,Z2: num] : ( Y4 = Z2 )
% 9.17/5.43 @ R4
% 9.17/5.43 @ numeral_numeral_nat
% 9.17/5.43 @ numeral_numeral_int ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7037_transfer__rule__numeral,axiom,
% 9.17/5.43 ! [R4: nat > code_integer > $o] :
% 9.17/5.43 ( ( R4 @ zero_zero_nat @ zero_z3403309356797280102nteger )
% 9.17/5.43 => ( ( R4 @ one_one_nat @ one_one_Code_integer )
% 9.17/5.43 => ( ( bNF_re7367609096550055590nteger @ R4 @ ( bNF_re1599192376174140603nteger @ R4 @ R4 ) @ plus_plus_nat @ plus_p5714425477246183910nteger )
% 9.17/5.43 => ( bNF_re6129422230220670146nteger
% 9.17/5.43 @ ^ [Y4: num,Z2: num] : ( Y4 = Z2 )
% 9.17/5.43 @ R4
% 9.17/5.43 @ numeral_numeral_nat
% 9.17/5.43 @ numera6620942414471956472nteger ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7038_transfer__rule__numeral,axiom,
% 9.17/5.43 ! [R4: nat > rat > $o] :
% 9.17/5.43 ( ( R4 @ zero_zero_nat @ zero_zero_rat )
% 9.17/5.43 => ( ( R4 @ one_one_nat @ one_one_rat )
% 9.17/5.43 => ( ( bNF_re3590448190763046039at_rat @ R4 @ ( bNF_re5790763769214331825at_rat @ R4 @ R4 ) @ plus_plus_nat @ plus_plus_rat )
% 9.17/5.43 => ( bNF_re190336592709022269at_rat
% 9.17/5.43 @ ^ [Y4: num,Z2: num] : ( Y4 = Z2 )
% 9.17/5.43 @ R4
% 9.17/5.43 @ numeral_numeral_nat
% 9.17/5.43 @ numeral_numeral_rat ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7039_transfer__rule__numeral,axiom,
% 9.17/5.43 ! [R4: nat > code_natural > $o] :
% 9.17/5.43 ( ( R4 @ zero_zero_nat @ zero_z2226904508553997617atural )
% 9.17/5.43 => ( ( R4 @ one_one_nat @ one_one_Code_natural )
% 9.17/5.43 => ( ( bNF_re88643428490162567atural @ R4 @ ( bNF_re3704215830270325841atural @ R4 @ R4 ) @ plus_plus_nat @ plus_p4538020629002901425atural )
% 9.17/5.43 => ( bNF_re4953017381977387661atural
% 9.17/5.43 @ ^ [Y4: num,Z2: num] : ( Y4 = Z2 )
% 9.17/5.43 @ R4
% 9.17/5.43 @ numeral_numeral_nat
% 9.17/5.43 @ numera5444537566228673987atural ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7040_transfer__rule__numeral,axiom,
% 9.17/5.43 ! [R4: int > nat > $o] :
% 9.17/5.43 ( ( R4 @ zero_zero_int @ zero_zero_nat )
% 9.17/5.43 => ( ( R4 @ one_one_int @ one_one_nat )
% 9.17/5.43 => ( ( bNF_re5416042074812042131at_nat @ R4 @ ( bNF_re4343356799547411545nt_nat @ R4 @ R4 ) @ plus_plus_int @ plus_plus_nat )
% 9.17/5.43 => ( bNF_re1824820364696572561nt_nat
% 9.17/5.43 @ ^ [Y4: num,Z2: num] : ( Y4 = Z2 )
% 9.17/5.43 @ R4
% 9.17/5.43 @ numeral_numeral_int
% 9.17/5.43 @ numeral_numeral_nat ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7041_transfer__rule__numeral,axiom,
% 9.17/5.43 ! [R4: int > int > $o] :
% 9.17/5.43 ( ( R4 @ zero_zero_int @ zero_zero_int )
% 9.17/5.43 => ( ( R4 @ one_one_int @ one_one_int )
% 9.17/5.43 => ( ( bNF_re711492959462206631nt_int @ R4 @ ( bNF_re4712519889275205905nt_int @ R4 @ R4 ) @ plus_plus_int @ plus_plus_int )
% 9.17/5.43 => ( bNF_re1822329894187522285nt_int
% 9.17/5.43 @ ^ [Y4: num,Z2: num] : ( Y4 = Z2 )
% 9.17/5.43 @ R4
% 9.17/5.43 @ numeral_numeral_int
% 9.17/5.43 @ numeral_numeral_int ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7042_transfer__rule__numeral,axiom,
% 9.17/5.43 ! [R4: int > code_integer > $o] :
% 9.17/5.43 ( ( R4 @ zero_zero_int @ zero_z3403309356797280102nteger )
% 9.17/5.43 => ( ( R4 @ one_one_int @ one_one_Code_integer )
% 9.17/5.43 => ( ( bNF_re398004352372739002nteger @ R4 @ ( bNF_re3379532845092657523nteger @ R4 @ R4 ) @ plus_plus_int @ plus_p5714425477246183910nteger )
% 9.17/5.43 => ( bNF_re6501075790457514782nteger
% 9.17/5.43 @ ^ [Y4: num,Z2: num] : ( Y4 = Z2 )
% 9.17/5.43 @ R4
% 9.17/5.43 @ numeral_numeral_int
% 9.17/5.43 @ numera6620942414471956472nteger ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7043_transfer__rule__numeral,axiom,
% 9.17/5.43 ! [R4: int > rat > $o] :
% 9.17/5.43 ( ( R4 @ zero_zero_int @ zero_zero_rat )
% 9.17/5.43 => ( ( R4 @ one_one_int @ one_one_rat )
% 9.17/5.43 => ( ( bNF_re7661208983170134443at_rat @ R4 @ ( bNF_re4480299549022435433nt_rat @ R4 @ R4 ) @ plus_plus_int @ plus_plus_rat )
% 9.17/5.43 => ( bNF_re1189690304610076825nt_rat
% 9.17/5.43 @ ^ [Y4: num,Z2: num] : ( Y4 = Z2 )
% 9.17/5.43 @ R4
% 9.17/5.43 @ numeral_numeral_int
% 9.17/5.43 @ numeral_numeral_rat ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7044_transfer__rule__numeral,axiom,
% 9.17/5.43 ! [R4: int > code_natural > $o] :
% 9.17/5.43 ( ( R4 @ zero_zero_int @ zero_z2226904508553997617atural )
% 9.17/5.43 => ( ( R4 @ one_one_int @ one_one_Code_natural )
% 9.17/5.43 => ( ( bNF_re2342410721167621787atural @ R4 @ ( bNF_re5484556299188842761atural @ R4 @ R4 ) @ plus_plus_int @ plus_p4538020629002901425atural )
% 9.17/5.43 => ( bNF_re5324670942214232297atural
% 9.17/5.43 @ ^ [Y4: num,Z2: num] : ( Y4 = Z2 )
% 9.17/5.43 @ R4
% 9.17/5.43 @ numeral_numeral_int
% 9.17/5.43 @ numera5444537566228673987atural ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7045_uminus__integer_Orsp,axiom,
% 9.17/5.43 ( bNF_re4712519889275205905nt_int
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ uminus_uminus_int
% 9.17/5.43 @ uminus_uminus_int ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7046_integer__of__natural_Orsp,axiom,
% 9.17/5.43 ( bNF_re6650684261131312217nt_int
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ semiri1314217659103216013at_int
% 9.17/5.43 @ semiri1314217659103216013at_int ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7047_natural__of__integer_Orsp,axiom,
% 9.17/5.43 ( bNF_re3715656647883201625at_nat
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.43 @ nat2
% 9.17/5.43 @ nat2 ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7048_abs__integer_Orsp,axiom,
% 9.17/5.43 ( bNF_re4712519889275205905nt_int
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ abs_abs_int
% 9.17/5.43 @ abs_abs_int ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7049_bit__integer_Orsp,axiom,
% 9.17/5.43 ( bNF_re3376528473927230327_nat_o
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ ^ [Y4: nat > $o,Z2: nat > $o] : ( Y4 = Z2 )
% 9.17/5.43 @ bit_se1146084159140164899it_int
% 9.17/5.43 @ bit_se1146084159140164899it_int ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7050_not__integer_Orsp,axiom,
% 9.17/5.43 ( bNF_re4712519889275205905nt_int
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ bit_ri7919022796975470100ot_int
% 9.17/5.43 @ bit_ri7919022796975470100ot_int ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7051_sgn__integer_Orsp,axiom,
% 9.17/5.43 ( bNF_re4712519889275205905nt_int
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ sgn_sgn_int
% 9.17/5.43 @ sgn_sgn_int ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7052_mask__integer_Orsp,axiom,
% 9.17/5.43 ( bNF_re6650684261131312217nt_int
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ bit_se2000444600071755411sk_int
% 9.17/5.43 @ bit_se2000444600071755411sk_int ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7053_mask__natural_Orsp,axiom,
% 9.17/5.43 ( bNF_re5653821019739307937at_nat
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.43 @ bit_se2002935070580805687sk_nat
% 9.17/5.43 @ bit_se2002935070580805687sk_nat ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7054_transfer__rule__of__int,axiom,
% 9.17/5.43 ! [R4: int > int > $o] :
% 9.17/5.43 ( ( R4 @ zero_zero_int @ zero_zero_int )
% 9.17/5.43 => ( ( R4 @ one_one_int @ one_one_int )
% 9.17/5.43 => ( ( bNF_re711492959462206631nt_int @ R4 @ ( bNF_re4712519889275205905nt_int @ R4 @ R4 ) @ plus_plus_int @ plus_plus_int )
% 9.17/5.43 => ( ( bNF_re4712519889275205905nt_int @ R4 @ R4 @ uminus_uminus_int @ uminus_uminus_int )
% 9.17/5.43 => ( bNF_re4712519889275205905nt_int
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ R4
% 9.17/5.43 @ ring_1_of_int_int
% 9.17/5.43 @ ring_1_of_int_int ) ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7055_transfer__rule__of__int,axiom,
% 9.17/5.43 ! [R4: int > code_integer > $o] :
% 9.17/5.43 ( ( R4 @ zero_zero_int @ zero_z3403309356797280102nteger )
% 9.17/5.43 => ( ( R4 @ one_one_int @ one_one_Code_integer )
% 9.17/5.43 => ( ( bNF_re398004352372739002nteger @ R4 @ ( bNF_re3379532845092657523nteger @ R4 @ R4 ) @ plus_plus_int @ plus_p5714425477246183910nteger )
% 9.17/5.43 => ( ( bNF_re3379532845092657523nteger @ R4 @ R4 @ uminus_uminus_int @ uminus1351360451143612070nteger )
% 9.17/5.43 => ( bNF_re982302072995117890nteger
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ R4
% 9.17/5.43 @ ring_1_of_int_int
% 9.17/5.43 @ ring_18347121197199848620nteger ) ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7056_transfer__rule__of__int,axiom,
% 9.17/5.43 ! [R4: int > rat > $o] :
% 9.17/5.43 ( ( R4 @ zero_zero_int @ zero_zero_rat )
% 9.17/5.43 => ( ( R4 @ one_one_int @ one_one_rat )
% 9.17/5.43 => ( ( bNF_re7661208983170134443at_rat @ R4 @ ( bNF_re4480299549022435433nt_rat @ R4 @ R4 ) @ plus_plus_int @ plus_plus_rat )
% 9.17/5.43 => ( ( bNF_re4480299549022435433nt_rat @ R4 @ R4 @ uminus_uminus_int @ uminus_uminus_rat )
% 9.17/5.43 => ( bNF_re4079880299697760445nt_rat
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ R4
% 9.17/5.43 @ ring_1_of_int_int
% 9.17/5.43 @ ring_1_of_int_rat ) ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7057_transfer__rule__of__int,axiom,
% 9.17/5.43 ! [R4: code_integer > int > $o] :
% 9.17/5.43 ( ( R4 @ zero_z3403309356797280102nteger @ zero_zero_int )
% 9.17/5.43 => ( ( R4 @ one_one_Code_integer @ one_one_int )
% 9.17/5.43 => ( ( bNF_re8304916493157054650nt_int @ R4 @ ( bNF_re2888858428391045491er_int @ R4 @ R4 ) @ plus_p5714425477246183910nteger @ plus_plus_int )
% 9.17/5.43 => ( ( bNF_re2888858428391045491er_int @ R4 @ R4 @ uminus1351360451143612070nteger @ uminus_uminus_int )
% 9.17/5.43 => ( bNF_re343602593470180162er_int
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ R4
% 9.17/5.43 @ ring_18347121197199848620nteger
% 9.17/5.43 @ ring_1_of_int_int ) ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7058_transfer__rule__of__int,axiom,
% 9.17/5.43 ! [R4: code_integer > code_integer > $o] :
% 9.17/5.43 ( ( R4 @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 9.17/5.43 => ( ( R4 @ one_one_Code_integer @ one_one_Code_integer )
% 9.17/5.43 => ( ( bNF_re122555440370955213nteger @ R4 @ ( bNF_re1062419521925302741nteger @ R4 @ R4 ) @ plus_p5714425477246183910nteger @ plus_p5714425477246183910nteger )
% 9.17/5.43 => ( ( bNF_re1062419521925302741nteger @ R4 @ R4 @ uminus1351360451143612070nteger @ uminus1351360451143612070nteger )
% 9.17/5.43 => ( bNF_re1784066744496875891nteger
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ R4
% 9.17/5.43 @ ring_18347121197199848620nteger
% 9.17/5.43 @ ring_18347121197199848620nteger ) ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7059_transfer__rule__of__int,axiom,
% 9.17/5.43 ! [R4: code_integer > rat > $o] :
% 9.17/5.43 ( ( R4 @ zero_z3403309356797280102nteger @ zero_zero_rat )
% 9.17/5.43 => ( ( R4 @ one_one_Code_integer @ one_one_rat )
% 9.17/5.43 => ( ( bNF_re2976496150901874110at_rat @ R4 @ ( bNF_re4698098036185532619er_rat @ R4 @ R4 ) @ plus_p5714425477246183910nteger @ plus_plus_rat )
% 9.17/5.43 => ( ( bNF_re4698098036185532619er_rat @ R4 @ R4 @ uminus1351360451143612070nteger @ uminus_uminus_rat )
% 9.17/5.43 => ( bNF_re8934335040747510510er_rat
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ R4
% 9.17/5.43 @ ring_18347121197199848620nteger
% 9.17/5.43 @ ring_1_of_int_rat ) ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7060_transfer__rule__of__int,axiom,
% 9.17/5.43 ! [R4: rat > int > $o] :
% 9.17/5.43 ( ( R4 @ zero_zero_rat @ zero_zero_int )
% 9.17/5.43 => ( ( R4 @ one_one_rat @ one_one_int )
% 9.17/5.43 => ( ( bNF_re8876735282041863595nt_int @ R4 @ ( bNF_re5838490730811218025at_int @ R4 @ R4 ) @ plus_plus_rat @ plus_plus_int )
% 9.17/5.43 => ( ( bNF_re5838490730811218025at_int @ R4 @ R4 @ uminus_uminus_rat @ uminus_uminus_int )
% 9.17/5.43 => ( bNF_re3396611533439285437at_int
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ R4
% 9.17/5.43 @ ring_1_of_int_rat
% 9.17/5.43 @ ring_1_of_int_int ) ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7061_transfer__rule__of__int,axiom,
% 9.17/5.43 ! [R4: rat > code_integer > $o] :
% 9.17/5.43 ( ( R4 @ zero_zero_rat @ zero_z3403309356797280102nteger )
% 9.17/5.43 => ( ( R4 @ one_one_rat @ one_one_Code_integer )
% 9.17/5.43 => ( ( bNF_re4307939118855507134nteger @ R4 @ ( bNF_re2328245411608324299nteger @ R4 @ R4 ) @ plus_plus_rat @ plus_p5714425477246183910nteger )
% 9.17/5.43 => ( ( bNF_re2328245411608324299nteger @ R4 @ R4 @ uminus_uminus_rat @ uminus1351360451143612070nteger )
% 9.17/5.43 => ( bNF_re1382721322319792878nteger
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ R4
% 9.17/5.43 @ ring_1_of_int_rat
% 9.17/5.43 @ ring_18347121197199848620nteger ) ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7062_transfer__rule__of__int,axiom,
% 9.17/5.43 ! [R4: rat > rat > $o] :
% 9.17/5.43 ( ( R4 @ zero_zero_rat @ zero_zero_rat )
% 9.17/5.43 => ( ( R4 @ one_one_rat @ one_one_rat )
% 9.17/5.43 => ( ( bNF_re6603079268895015599at_rat @ R4 @ ( bNF_re5606270390558447553at_rat @ R4 @ R4 ) @ plus_plus_rat @ plus_plus_rat )
% 9.17/5.43 => ( ( bNF_re5606270390558447553at_rat @ R4 @ R4 @ uminus_uminus_rat @ uminus_uminus_rat )
% 9.17/5.43 => ( bNF_re2763971943861839977at_rat
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ R4
% 9.17/5.43 @ ring_1_of_int_rat
% 9.17/5.43 @ ring_1_of_int_rat ) ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7063_fun_Orel__map_I1_J,axiom,
% 9.17/5.43 ! [Sb: ( nat > $o ) > ( nat > $o ) > $o,I: ( nat > $o ) > nat > $o,X: int > nat > $o,Y: int > nat > $o] :
% 9.17/5.43 ( ( bNF_re3376528473927230327_nat_o
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ Sb
% 9.17/5.43 @ ( comp_nat_o_nat_o_int @ I @ X )
% 9.17/5.43 @ Y )
% 9.17/5.43 = ( bNF_re3376528473927230327_nat_o
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ ^ [X3: nat > $o] : ( Sb @ ( I @ X3 ) )
% 9.17/5.43 @ X
% 9.17/5.43 @ Y ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7064_fun_Orel__map_I1_J,axiom,
% 9.17/5.43 ! [Sb: ( int > product_prod_int_int ) > ( int > product_prod_int_int ) > $o,I: ( int > product_prod_int_int ) > int > product_prod_int_int,X: int > int > product_prod_int_int,Y: int > int > product_prod_int_int] :
% 9.17/5.43 ( ( bNF_re157797125943740599nt_int
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ Sb
% 9.17/5.43 @ ( comp_i1790862786758963855nt_int @ I @ X )
% 9.17/5.43 @ Y )
% 9.17/5.43 = ( bNF_re157797125943740599nt_int
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ ^ [X3: int > product_prod_int_int] : ( Sb @ ( I @ X3 ) )
% 9.17/5.43 @ X
% 9.17/5.43 @ Y ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7065_fun_Orel__map_I1_J,axiom,
% 9.17/5.43 ! [Sb: ( int > product_prod_int_int ) > ( int > rat ) > $o,I: ( int > product_prod_int_int ) > int > product_prod_int_int,X: int > int > product_prod_int_int,Y: int > int > rat] :
% 9.17/5.43 ( ( bNF_re3461391660133120880nt_rat
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ Sb
% 9.17/5.43 @ ( comp_i1790862786758963855nt_int @ I @ X )
% 9.17/5.43 @ Y )
% 9.17/5.43 = ( bNF_re3461391660133120880nt_rat
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ ^ [X3: int > product_prod_int_int] : ( Sb @ ( I @ X3 ) )
% 9.17/5.43 @ X
% 9.17/5.43 @ Y ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7066_fun_Orel__map_I1_J,axiom,
% 9.17/5.43 ! [Sb: ( int > $o ) > ( int > $o ) > $o,I: ( int > $o ) > int > $o,X: int > int > $o,Y: int > int > $o] :
% 9.17/5.43 ( ( bNF_re3403563459893282935_int_o
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ Sb
% 9.17/5.43 @ ( comp_int_o_int_o_int @ I @ X )
% 9.17/5.43 @ Y )
% 9.17/5.43 = ( bNF_re3403563459893282935_int_o
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ ^ [X3: int > $o] : ( Sb @ ( I @ X3 ) )
% 9.17/5.43 @ X
% 9.17/5.43 @ Y ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7067_fun_Orel__map_I1_J,axiom,
% 9.17/5.43 ! [Sb: ( int > int ) > ( int > int ) > $o,I: ( int > int ) > int > int,X: int > int > int,Y: int > int > int] :
% 9.17/5.43 ( ( bNF_re711492959462206631nt_int
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ Sb
% 9.17/5.43 @ ( comp_i1129928922100200191nt_int @ I @ X )
% 9.17/5.43 @ Y )
% 9.17/5.43 = ( bNF_re711492959462206631nt_int
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ ^ [X3: int > int] : ( Sb @ ( I @ X3 ) )
% 9.17/5.43 @ X
% 9.17/5.43 @ Y ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7068_fun_Orel__map_I2_J,axiom,
% 9.17/5.43 ! [Sa: ( nat > $o ) > ( nat > $o ) > $o,X: int > nat > $o,G: ( nat > $o ) > nat > $o,Y: int > nat > $o] :
% 9.17/5.43 ( ( bNF_re3376528473927230327_nat_o
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ Sa
% 9.17/5.43 @ X
% 9.17/5.43 @ ( comp_nat_o_nat_o_int @ G @ Y ) )
% 9.17/5.43 = ( bNF_re3376528473927230327_nat_o
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ ^ [X3: nat > $o,Y3: nat > $o] : ( Sa @ X3 @ ( G @ Y3 ) )
% 9.17/5.43 @ X
% 9.17/5.43 @ Y ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7069_fun_Orel__map_I2_J,axiom,
% 9.17/5.43 ! [Sa: ( int > product_prod_int_int ) > ( int > product_prod_int_int ) > $o,X: int > int > product_prod_int_int,G: ( int > product_prod_int_int ) > int > product_prod_int_int,Y: int > int > product_prod_int_int] :
% 9.17/5.43 ( ( bNF_re157797125943740599nt_int
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ Sa
% 9.17/5.43 @ X
% 9.17/5.43 @ ( comp_i1790862786758963855nt_int @ G @ Y ) )
% 9.17/5.43 = ( bNF_re157797125943740599nt_int
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ ^ [X3: int > product_prod_int_int,Y3: int > product_prod_int_int] : ( Sa @ X3 @ ( G @ Y3 ) )
% 9.17/5.43 @ X
% 9.17/5.43 @ Y ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7070_fun_Orel__map_I2_J,axiom,
% 9.17/5.43 ! [Sa: ( int > product_prod_int_int ) > ( int > product_prod_int_int ) > $o,X: int > int > product_prod_int_int,G: ( int > rat ) > int > product_prod_int_int,Y: int > int > rat] :
% 9.17/5.43 ( ( bNF_re157797125943740599nt_int
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ Sa
% 9.17/5.43 @ X
% 9.17/5.43 @ ( comp_i929186717396404458nt_int @ G @ Y ) )
% 9.17/5.43 = ( bNF_re3461391660133120880nt_rat
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ ^ [X3: int > product_prod_int_int,Y3: int > rat] : ( Sa @ X3 @ ( G @ Y3 ) )
% 9.17/5.43 @ X
% 9.17/5.43 @ Y ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7071_fun_Orel__map_I2_J,axiom,
% 9.17/5.43 ! [Sa: ( int > product_prod_int_int ) > ( int > rat ) > $o,X: int > int > product_prod_int_int,G: ( int > product_prod_int_int ) > int > rat,Y: int > int > product_prod_int_int] :
% 9.17/5.43 ( ( bNF_re3461391660133120880nt_rat
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ Sa
% 9.17/5.43 @ X
% 9.17/5.43 @ ( comp_i1302866070986779890at_int @ G @ Y ) )
% 9.17/5.43 = ( bNF_re157797125943740599nt_int
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ ^ [X3: int > product_prod_int_int,Y3: int > product_prod_int_int] : ( Sa @ X3 @ ( G @ Y3 ) )
% 9.17/5.43 @ X
% 9.17/5.43 @ Y ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7072_fun_Orel__map_I2_J,axiom,
% 9.17/5.43 ! [Sa: ( int > product_prod_int_int ) > ( int > rat ) > $o,X: int > int > product_prod_int_int,G: ( int > rat ) > int > rat,Y: int > int > rat] :
% 9.17/5.43 ( ( bNF_re3461391660133120880nt_rat
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ Sa
% 9.17/5.43 @ X
% 9.17/5.43 @ ( comp_i8258899369942393943at_int @ G @ Y ) )
% 9.17/5.43 = ( bNF_re3461391660133120880nt_rat
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ ^ [X3: int > product_prod_int_int,Y3: int > rat] : ( Sa @ X3 @ ( G @ Y3 ) )
% 9.17/5.43 @ X
% 9.17/5.43 @ Y ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7073_fun_Orel__map_I2_J,axiom,
% 9.17/5.43 ! [Sa: ( int > $o ) > ( int > $o ) > $o,X: int > int > $o,G: ( int > $o ) > int > $o,Y: int > int > $o] :
% 9.17/5.43 ( ( bNF_re3403563459893282935_int_o
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ Sa
% 9.17/5.43 @ X
% 9.17/5.43 @ ( comp_int_o_int_o_int @ G @ Y ) )
% 9.17/5.43 = ( bNF_re3403563459893282935_int_o
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ ^ [X3: int > $o,Y3: int > $o] : ( Sa @ X3 @ ( G @ Y3 ) )
% 9.17/5.43 @ X
% 9.17/5.43 @ Y ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7074_fun_Orel__map_I2_J,axiom,
% 9.17/5.43 ! [Sa: ( int > int ) > ( int > int ) > $o,X: int > int > int,G: ( int > int ) > int > int,Y: int > int > int] :
% 9.17/5.43 ( ( bNF_re711492959462206631nt_int
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ Sa
% 9.17/5.43 @ X
% 9.17/5.43 @ ( comp_i1129928922100200191nt_int @ G @ Y ) )
% 9.17/5.43 = ( bNF_re711492959462206631nt_int
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ ^ [X3: int > int,Y3: int > int] : ( Sa @ X3 @ ( G @ Y3 ) )
% 9.17/5.43 @ X
% 9.17/5.43 @ Y ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7075_times__eq__iff,axiom,
% 9.17/5.43 ! [A2: set_o,B5: set_o,C4: set_o,D3: set_o] :
% 9.17/5.43 ( ( ( product_Sigma_o_o @ A2
% 9.17/5.43 @ ^ [Uu: $o] : B5 )
% 9.17/5.43 = ( product_Sigma_o_o @ C4
% 9.17/5.43 @ ^ [Uu: $o] : D3 ) )
% 9.17/5.43 = ( ( ( A2 = C4 )
% 9.17/5.43 & ( B5 = D3 ) )
% 9.17/5.43 | ( ( ( A2 = bot_bot_set_o )
% 9.17/5.43 | ( B5 = bot_bot_set_o ) )
% 9.17/5.43 & ( ( C4 = bot_bot_set_o )
% 9.17/5.43 | ( D3 = bot_bot_set_o ) ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7076_times__eq__iff,axiom,
% 9.17/5.43 ! [A2: set_o,B5: set_nat,C4: set_o,D3: set_nat] :
% 9.17/5.43 ( ( ( product_Sigma_o_nat @ A2
% 9.17/5.43 @ ^ [Uu: $o] : B5 )
% 9.17/5.43 = ( product_Sigma_o_nat @ C4
% 9.17/5.43 @ ^ [Uu: $o] : D3 ) )
% 9.17/5.43 = ( ( ( A2 = C4 )
% 9.17/5.43 & ( B5 = D3 ) )
% 9.17/5.43 | ( ( ( A2 = bot_bot_set_o )
% 9.17/5.43 | ( B5 = bot_bot_set_nat ) )
% 9.17/5.43 & ( ( C4 = bot_bot_set_o )
% 9.17/5.43 | ( D3 = bot_bot_set_nat ) ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7077_times__eq__iff,axiom,
% 9.17/5.43 ! [A2: set_o,B5: set_int,C4: set_o,D3: set_int] :
% 9.17/5.43 ( ( ( product_Sigma_o_int @ A2
% 9.17/5.43 @ ^ [Uu: $o] : B5 )
% 9.17/5.43 = ( product_Sigma_o_int @ C4
% 9.17/5.43 @ ^ [Uu: $o] : D3 ) )
% 9.17/5.43 = ( ( ( A2 = C4 )
% 9.17/5.43 & ( B5 = D3 ) )
% 9.17/5.43 | ( ( ( A2 = bot_bot_set_o )
% 9.17/5.43 | ( B5 = bot_bot_set_int ) )
% 9.17/5.43 & ( ( C4 = bot_bot_set_o )
% 9.17/5.43 | ( D3 = bot_bot_set_int ) ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7078_times__eq__iff,axiom,
% 9.17/5.43 ! [A2: set_nat,B5: set_o,C4: set_nat,D3: set_o] :
% 9.17/5.43 ( ( ( product_Sigma_nat_o @ A2
% 9.17/5.43 @ ^ [Uu: nat] : B5 )
% 9.17/5.43 = ( product_Sigma_nat_o @ C4
% 9.17/5.43 @ ^ [Uu: nat] : D3 ) )
% 9.17/5.43 = ( ( ( A2 = C4 )
% 9.17/5.43 & ( B5 = D3 ) )
% 9.17/5.43 | ( ( ( A2 = bot_bot_set_nat )
% 9.17/5.43 | ( B5 = bot_bot_set_o ) )
% 9.17/5.43 & ( ( C4 = bot_bot_set_nat )
% 9.17/5.43 | ( D3 = bot_bot_set_o ) ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7079_times__eq__iff,axiom,
% 9.17/5.43 ! [A2: set_nat,B5: set_nat,C4: set_nat,D3: set_nat] :
% 9.17/5.43 ( ( ( produc457027306803732586at_nat @ A2
% 9.17/5.43 @ ^ [Uu: nat] : B5 )
% 9.17/5.43 = ( produc457027306803732586at_nat @ C4
% 9.17/5.43 @ ^ [Uu: nat] : D3 ) )
% 9.17/5.43 = ( ( ( A2 = C4 )
% 9.17/5.43 & ( B5 = D3 ) )
% 9.17/5.43 | ( ( ( A2 = bot_bot_set_nat )
% 9.17/5.43 | ( B5 = bot_bot_set_nat ) )
% 9.17/5.43 & ( ( C4 = bot_bot_set_nat )
% 9.17/5.43 | ( D3 = bot_bot_set_nat ) ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7080_times__eq__iff,axiom,
% 9.17/5.43 ! [A2: set_nat,B5: set_int,C4: set_nat,D3: set_int] :
% 9.17/5.43 ( ( ( produc454536836294682310at_int @ A2
% 9.17/5.43 @ ^ [Uu: nat] : B5 )
% 9.17/5.43 = ( produc454536836294682310at_int @ C4
% 9.17/5.43 @ ^ [Uu: nat] : D3 ) )
% 9.17/5.43 = ( ( ( A2 = C4 )
% 9.17/5.43 & ( B5 = D3 ) )
% 9.17/5.43 | ( ( ( A2 = bot_bot_set_nat )
% 9.17/5.43 | ( B5 = bot_bot_set_int ) )
% 9.17/5.43 & ( ( C4 = bot_bot_set_nat )
% 9.17/5.43 | ( D3 = bot_bot_set_int ) ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7081_times__eq__iff,axiom,
% 9.17/5.43 ! [A2: set_int,B5: set_o,C4: set_int,D3: set_o] :
% 9.17/5.43 ( ( ( product_Sigma_int_o @ A2
% 9.17/5.43 @ ^ [Uu: int] : B5 )
% 9.17/5.43 = ( product_Sigma_int_o @ C4
% 9.17/5.43 @ ^ [Uu: int] : D3 ) )
% 9.17/5.43 = ( ( ( A2 = C4 )
% 9.17/5.43 & ( B5 = D3 ) )
% 9.17/5.43 | ( ( ( A2 = bot_bot_set_int )
% 9.17/5.43 | ( B5 = bot_bot_set_o ) )
% 9.17/5.43 & ( ( C4 = bot_bot_set_int )
% 9.17/5.43 | ( D3 = bot_bot_set_o ) ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7082_times__eq__iff,axiom,
% 9.17/5.43 ! [A2: set_int,B5: set_nat,C4: set_int,D3: set_nat] :
% 9.17/5.43 ( ( ( produc1456381018704787142nt_nat @ A2
% 9.17/5.43 @ ^ [Uu: int] : B5 )
% 9.17/5.43 = ( produc1456381018704787142nt_nat @ C4
% 9.17/5.43 @ ^ [Uu: int] : D3 ) )
% 9.17/5.43 = ( ( ( A2 = C4 )
% 9.17/5.43 & ( B5 = D3 ) )
% 9.17/5.43 | ( ( ( A2 = bot_bot_set_int )
% 9.17/5.43 | ( B5 = bot_bot_set_nat ) )
% 9.17/5.43 & ( ( C4 = bot_bot_set_int )
% 9.17/5.43 | ( D3 = bot_bot_set_nat ) ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7083_times__eq__iff,axiom,
% 9.17/5.43 ! [A2: set_int,B5: set_int,C4: set_int,D3: set_int] :
% 9.17/5.43 ( ( ( produc1453890548195736866nt_int @ A2
% 9.17/5.43 @ ^ [Uu: int] : B5 )
% 9.17/5.43 = ( produc1453890548195736866nt_int @ C4
% 9.17/5.43 @ ^ [Uu: int] : D3 ) )
% 9.17/5.43 = ( ( ( A2 = C4 )
% 9.17/5.43 & ( B5 = D3 ) )
% 9.17/5.43 | ( ( ( A2 = bot_bot_set_int )
% 9.17/5.43 | ( B5 = bot_bot_set_int ) )
% 9.17/5.43 & ( ( C4 = bot_bot_set_int )
% 9.17/5.43 | ( D3 = bot_bot_set_int ) ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7084_times__eq__iff,axiom,
% 9.17/5.43 ! [A2: set_Pr1261947904930325089at_nat,B5: set_o,C4: set_Pr1261947904930325089at_nat,D3: set_o] :
% 9.17/5.43 ( ( ( produc203973861852599583_nat_o @ A2
% 9.17/5.43 @ ^ [Uu: product_prod_nat_nat] : B5 )
% 9.17/5.43 = ( produc203973861852599583_nat_o @ C4
% 9.17/5.43 @ ^ [Uu: product_prod_nat_nat] : D3 ) )
% 9.17/5.43 = ( ( ( A2 = C4 )
% 9.17/5.43 & ( B5 = D3 ) )
% 9.17/5.43 | ( ( ( A2 = bot_bo2099793752762293965at_nat )
% 9.17/5.43 | ( B5 = bot_bot_set_o ) )
% 9.17/5.43 & ( ( C4 = bot_bo2099793752762293965at_nat )
% 9.17/5.43 | ( D3 = bot_bot_set_o ) ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7085_dup_Orsp,axiom,
% 9.17/5.43 ( bNF_re4712519889275205905nt_int
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ ^ [K4: int] : ( plus_plus_int @ K4 @ K4 )
% 9.17/5.43 @ ^ [K4: int] : ( plus_plus_int @ K4 @ K4 ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7086_Collect__case__prod__Sigma,axiom,
% 9.17/5.43 ! [P: nat > $o,Q: nat > nat > $o] :
% 9.17/5.43 ( ( collec3392354462482085612at_nat
% 9.17/5.43 @ ( produc6081775807080527818_nat_o
% 9.17/5.43 @ ^ [X3: nat,Y3: nat] :
% 9.17/5.43 ( ( P @ X3 )
% 9.17/5.43 & ( Q @ X3 @ Y3 ) ) ) )
% 9.17/5.43 = ( produc457027306803732586at_nat @ ( collect_nat @ P )
% 9.17/5.43 @ ^ [X3: nat] : ( collect_nat @ ( Q @ X3 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7087_Collect__case__prod__Sigma,axiom,
% 9.17/5.43 ! [P: nat > $o,Q: nat > list_nat > $o] :
% 9.17/5.43 ( ( collec1907656820224499068st_nat
% 9.17/5.43 @ ( produc5265810065896090426_nat_o
% 9.17/5.43 @ ^ [X3: nat,Y3: list_nat] :
% 9.17/5.43 ( ( P @ X3 )
% 9.17/5.43 & ( Q @ X3 @ Y3 ) ) ) )
% 9.17/5.43 = ( produc5227933103413159546st_nat @ ( collect_nat @ P )
% 9.17/5.43 @ ^ [X3: nat] : ( collect_list_nat @ ( Q @ X3 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7088_Collect__case__prod__Sigma,axiom,
% 9.17/5.43 ! [P: list_nat > $o,Q: list_nat > nat > $o] :
% 9.17/5.43 ( ( collec8096645339561496572at_nat
% 9.17/5.43 @ ( produc7308574044827705018_nat_o
% 9.17/5.43 @ ^ [X3: list_nat,Y3: nat] :
% 9.17/5.43 ( ( P @ X3 )
% 9.17/5.43 & ( Q @ X3 @ Y3 ) ) ) )
% 9.17/5.43 = ( produc7466890150575444730at_nat @ ( collect_list_nat @ P )
% 9.17/5.43 @ ^ [X3: list_nat] : ( collect_nat @ ( Q @ X3 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7089_Collect__case__prod__Sigma,axiom,
% 9.17/5.43 ! [P: list_nat > $o,Q: list_nat > list_nat > $o] :
% 9.17/5.43 ( ( collec1570431334306492044st_nat
% 9.17/5.43 @ ( produc6382697403170970154_nat_o
% 9.17/5.43 @ ^ [X3: list_nat,Y3: list_nat] :
% 9.17/5.43 ( ( P @ X3 )
% 9.17/5.43 & ( Q @ X3 @ Y3 ) ) ) )
% 9.17/5.43 = ( produc6850429418872557834st_nat @ ( collect_list_nat @ P )
% 9.17/5.43 @ ^ [X3: list_nat] : ( collect_list_nat @ ( Q @ X3 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7090_apsnd__apfst__commute,axiom,
% 9.17/5.43 ! [F: code_integer > code_integer,G: code_integer > code_integer,P4: produc8923325533196201883nteger] :
% 9.17/5.43 ( ( produc6499014454317279255nteger @ F @ ( produc3195571438000033749nteger @ G @ P4 ) )
% 9.17/5.43 = ( produc3195571438000033749nteger @ G @ ( produc6499014454317279255nteger @ F @ P4 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7091_gcd__add__mult,axiom,
% 9.17/5.43 ! [M2: nat,K: nat,N2: nat] :
% 9.17/5.43 ( ( gcd_gcd_nat @ M2 @ ( plus_plus_nat @ ( times_times_nat @ K @ M2 ) @ N2 ) )
% 9.17/5.43 = ( gcd_gcd_nat @ M2 @ N2 ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7092_gcd__add__mult,axiom,
% 9.17/5.43 ! [M2: int,K: int,N2: int] :
% 9.17/5.43 ( ( gcd_gcd_int @ M2 @ ( plus_plus_int @ ( times_times_int @ K @ M2 ) @ N2 ) )
% 9.17/5.43 = ( gcd_gcd_int @ M2 @ N2 ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7093_Sigma__mono,axiom,
% 9.17/5.43 ! [A2: set_Pr4329608150637261639at_nat,C4: set_Pr4329608150637261639at_nat,B5: produc3843707927480180839at_nat > set_nat,D3: produc3843707927480180839at_nat > set_nat] :
% 9.17/5.43 ( ( ord_le1268244103169919719at_nat @ A2 @ C4 )
% 9.17/5.43 => ( ! [X4: produc3843707927480180839at_nat] :
% 9.17/5.43 ( ( member8757157785044589968at_nat @ X4 @ A2 )
% 9.17/5.43 => ( ord_less_eq_set_nat @ ( B5 @ X4 ) @ ( D3 @ X4 ) ) )
% 9.17/5.43 => ( ord_le2145644191787020796at_nat @ ( produc1095920968030776047at_nat @ A2 @ B5 ) @ ( produc1095920968030776047at_nat @ C4 @ D3 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7094_Sigma__mono,axiom,
% 9.17/5.43 ! [A2: set_Pr1261947904930325089at_nat,C4: set_Pr1261947904930325089at_nat,B5: product_prod_nat_nat > set_nat,D3: product_prod_nat_nat > set_nat] :
% 9.17/5.43 ( ( ord_le3146513528884898305at_nat @ A2 @ C4 )
% 9.17/5.43 => ( ! [X4: product_prod_nat_nat] :
% 9.17/5.43 ( ( member8440522571783428010at_nat @ X4 @ A2 )
% 9.17/5.43 => ( ord_less_eq_set_nat @ ( B5 @ X4 ) @ ( D3 @ X4 ) ) )
% 9.17/5.43 => ( ord_le7094820750414311574at_nat @ ( produc7672662199629908489at_nat @ A2 @ B5 ) @ ( produc7672662199629908489at_nat @ C4 @ D3 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7095_Sigma__mono,axiom,
% 9.17/5.43 ! [A2: set_o,C4: set_o,B5: $o > set_nat,D3: $o > set_nat] :
% 9.17/5.43 ( ( ord_less_eq_set_o @ A2 @ C4 )
% 9.17/5.43 => ( ! [X4: $o] :
% 9.17/5.43 ( ( member_o @ X4 @ A2 )
% 9.17/5.43 => ( ord_less_eq_set_nat @ ( B5 @ X4 ) @ ( D3 @ X4 ) ) )
% 9.17/5.43 => ( ord_le6472378536984071597_o_nat @ ( product_Sigma_o_nat @ A2 @ B5 ) @ ( product_Sigma_o_nat @ C4 @ D3 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7096_Sigma__mono,axiom,
% 9.17/5.43 ! [A2: set_int,C4: set_int,B5: int > set_nat,D3: int > set_nat] :
% 9.17/5.43 ( ( ord_less_eq_set_int @ A2 @ C4 )
% 9.17/5.43 => ( ! [X4: int] :
% 9.17/5.43 ( ( member_int @ X4 @ A2 )
% 9.17/5.43 => ( ord_less_eq_set_nat @ ( B5 @ X4 ) @ ( D3 @ X4 ) ) )
% 9.17/5.43 => ( ord_le5333435103577920093nt_nat @ ( produc1456381018704787142nt_nat @ A2 @ B5 ) @ ( produc1456381018704787142nt_nat @ C4 @ D3 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7097_Sigma__mono,axiom,
% 9.17/5.43 ! [A2: set_nat,C4: set_nat,B5: nat > set_nat,D3: nat > set_nat] :
% 9.17/5.43 ( ( ord_less_eq_set_nat @ A2 @ C4 )
% 9.17/5.43 => ( ! [X4: nat] :
% 9.17/5.43 ( ( member_nat @ X4 @ A2 )
% 9.17/5.43 => ( ord_less_eq_set_nat @ ( B5 @ X4 ) @ ( D3 @ X4 ) ) )
% 9.17/5.43 => ( ord_le3146513528884898305at_nat @ ( produc457027306803732586at_nat @ A2 @ B5 ) @ ( produc457027306803732586at_nat @ C4 @ D3 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7098_bezout__int,axiom,
% 9.17/5.43 ! [X: int,Y: int] :
% 9.17/5.43 ? [U3: int,V4: int] :
% 9.17/5.43 ( ( plus_plus_int @ ( times_times_int @ U3 @ X ) @ ( times_times_int @ V4 @ Y ) )
% 9.17/5.43 = ( gcd_gcd_int @ X @ Y ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7099_Times__subset__cancel2,axiom,
% 9.17/5.43 ! [X: produc3843707927480180839at_nat,C4: set_Pr4329608150637261639at_nat,A2: set_nat,B5: set_nat] :
% 9.17/5.43 ( ( member8757157785044589968at_nat @ X @ C4 )
% 9.17/5.43 => ( ( ord_le3218026494883419554at_nat
% 9.17/5.43 @ ( produc396409126344608333at_nat @ A2
% 9.17/5.43 @ ^ [Uu: nat] : C4 )
% 9.17/5.43 @ ( produc396409126344608333at_nat @ B5
% 9.17/5.43 @ ^ [Uu: nat] : C4 ) )
% 9.17/5.43 = ( ord_less_eq_set_nat @ A2 @ B5 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7100_Times__subset__cancel2,axiom,
% 9.17/5.43 ! [X: product_prod_nat_nat,C4: set_Pr1261947904930325089at_nat,A2: set_nat,B5: set_nat] :
% 9.17/5.43 ( ( member8440522571783428010at_nat @ X @ C4 )
% 9.17/5.43 => ( ( ord_le3050193496395145148at_nat
% 9.17/5.43 @ ( produc1809337555817847783at_nat @ A2
% 9.17/5.43 @ ^ [Uu: nat] : C4 )
% 9.17/5.43 @ ( produc1809337555817847783at_nat @ B5
% 9.17/5.43 @ ^ [Uu: nat] : C4 ) )
% 9.17/5.43 = ( ord_less_eq_set_nat @ A2 @ B5 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7101_Times__subset__cancel2,axiom,
% 9.17/5.43 ! [X: $o,C4: set_o,A2: set_nat,B5: set_nat] :
% 9.17/5.43 ( ( member_o @ X @ C4 )
% 9.17/5.43 => ( ( ord_le7519981659162375251_nat_o
% 9.17/5.43 @ ( product_Sigma_nat_o @ A2
% 9.17/5.43 @ ^ [Uu: nat] : C4 )
% 9.17/5.43 @ ( product_Sigma_nat_o @ B5
% 9.17/5.43 @ ^ [Uu: nat] : C4 ) )
% 9.17/5.43 = ( ord_less_eq_set_nat @ A2 @ B5 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7102_Times__subset__cancel2,axiom,
% 9.17/5.43 ! [X: nat,C4: set_nat,A2: set_nat,B5: set_nat] :
% 9.17/5.43 ( ( member_nat @ X @ C4 )
% 9.17/5.43 => ( ( ord_le3146513528884898305at_nat
% 9.17/5.43 @ ( produc457027306803732586at_nat @ A2
% 9.17/5.43 @ ^ [Uu: nat] : C4 )
% 9.17/5.43 @ ( produc457027306803732586at_nat @ B5
% 9.17/5.43 @ ^ [Uu: nat] : C4 ) )
% 9.17/5.43 = ( ord_less_eq_set_nat @ A2 @ B5 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7103_Times__subset__cancel2,axiom,
% 9.17/5.43 ! [X: int,C4: set_int,A2: set_nat,B5: set_nat] :
% 9.17/5.43 ( ( member_int @ X @ C4 )
% 9.17/5.43 => ( ( ord_le656430383953171549at_int
% 9.17/5.43 @ ( produc454536836294682310at_int @ A2
% 9.17/5.43 @ ^ [Uu: nat] : C4 )
% 9.17/5.43 @ ( produc454536836294682310at_int @ B5
% 9.17/5.43 @ ^ [Uu: nat] : C4 ) )
% 9.17/5.43 = ( ord_less_eq_set_nat @ A2 @ B5 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7104_UN__Times__distrib,axiom,
% 9.17/5.43 ! [E3: nat > set_nat,F5: nat > set_nat,A2: set_nat,B5: set_nat] :
% 9.17/5.43 ( ( comple5685304695842803022at_nat
% 9.17/5.43 @ ( image_5423882813909314213at_nat
% 9.17/5.43 @ ( produc8197505143624133779at_nat
% 9.17/5.43 @ ^ [A5: nat,B4: nat] :
% 9.17/5.43 ( produc457027306803732586at_nat @ ( E3 @ A5 )
% 9.17/5.43 @ ^ [Uu: nat] : ( F5 @ B4 ) ) )
% 9.17/5.43 @ ( produc457027306803732586at_nat @ A2
% 9.17/5.43 @ ^ [Uu: nat] : B5 ) ) )
% 9.17/5.43 = ( produc457027306803732586at_nat @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ E3 @ A2 ) )
% 9.17/5.43 @ ^ [Uu: nat] : ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ F5 @ B5 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7105_mem__Times__iff,axiom,
% 9.17/5.43 ! [X: product_prod_o_o,A2: set_o,B5: set_o] :
% 9.17/5.43 ( ( member7466972457876170832od_o_o @ X
% 9.17/5.43 @ ( product_Sigma_o_o @ A2
% 9.17/5.43 @ ^ [Uu: $o] : B5 ) )
% 9.17/5.43 = ( ( member_o @ ( product_fst_o_o @ X ) @ A2 )
% 9.17/5.43 & ( member_o @ ( product_snd_o_o @ X ) @ B5 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7106_mem__Times__iff,axiom,
% 9.17/5.43 ! [X: product_prod_o_nat,A2: set_o,B5: set_nat] :
% 9.17/5.43 ( ( member2802428098988154798_o_nat @ X
% 9.17/5.43 @ ( product_Sigma_o_nat @ A2
% 9.17/5.43 @ ^ [Uu: $o] : B5 ) )
% 9.17/5.43 = ( ( member_o @ ( product_fst_o_nat @ X ) @ A2 )
% 9.17/5.43 & ( member_nat @ ( product_snd_o_nat @ X ) @ B5 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7107_mem__Times__iff,axiom,
% 9.17/5.43 ! [X: product_prod_o_int,A2: set_o,B5: set_int] :
% 9.17/5.43 ( ( member7847949116333733898_o_int @ X
% 9.17/5.43 @ ( product_Sigma_o_int @ A2
% 9.17/5.43 @ ^ [Uu: $o] : B5 ) )
% 9.17/5.43 = ( ( member_o @ ( product_fst_o_int @ X ) @ A2 )
% 9.17/5.43 & ( member_int @ ( product_snd_o_int @ X ) @ B5 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7108_mem__Times__iff,axiom,
% 9.17/5.43 ! [X: product_prod_nat_o,A2: set_nat,B5: set_o] :
% 9.17/5.43 ( ( member6310962623043647828_nat_o @ X
% 9.17/5.43 @ ( product_Sigma_nat_o @ A2
% 9.17/5.43 @ ^ [Uu: nat] : B5 ) )
% 9.17/5.43 = ( ( member_nat @ ( product_fst_nat_o @ X ) @ A2 )
% 9.17/5.43 & ( member_o @ ( product_snd_nat_o @ X ) @ B5 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7109_mem__Times__iff,axiom,
% 9.17/5.43 ! [X: product_prod_nat_int,A2: set_nat,B5: set_int] :
% 9.17/5.43 ( ( member4262671552274231302at_int @ X
% 9.17/5.43 @ ( produc454536836294682310at_int @ A2
% 9.17/5.43 @ ^ [Uu: nat] : B5 ) )
% 9.17/5.43 = ( ( member_nat @ ( product_fst_nat_int @ X ) @ A2 )
% 9.17/5.43 & ( member_int @ ( product_snd_nat_int @ X ) @ B5 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7110_mem__Times__iff,axiom,
% 9.17/5.43 ! [X: product_prod_int_o,A2: set_int,B5: set_o] :
% 9.17/5.43 ( ( member4489920277610959864_int_o @ X
% 9.17/5.43 @ ( product_Sigma_int_o @ A2
% 9.17/5.43 @ ^ [Uu: int] : B5 ) )
% 9.17/5.43 = ( ( member_int @ ( product_fst_int_o @ X ) @ A2 )
% 9.17/5.43 & ( member_o @ ( product_snd_int_o @ X ) @ B5 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7111_mem__Times__iff,axiom,
% 9.17/5.43 ! [X: product_prod_int_nat,A2: set_int,B5: set_nat] :
% 9.17/5.43 ( ( member216504246829706758nt_nat @ X
% 9.17/5.43 @ ( produc1456381018704787142nt_nat @ A2
% 9.17/5.43 @ ^ [Uu: int] : B5 ) )
% 9.17/5.43 = ( ( member_int @ ( product_fst_int_nat @ X ) @ A2 )
% 9.17/5.43 & ( member_nat @ ( product_snd_int_nat @ X ) @ B5 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7112_mem__Times__iff,axiom,
% 9.17/5.43 ! [X: product_prod_nat_nat,A2: set_nat,B5: set_nat] :
% 9.17/5.43 ( ( member8440522571783428010at_nat @ X
% 9.17/5.43 @ ( produc457027306803732586at_nat @ A2
% 9.17/5.43 @ ^ [Uu: nat] : B5 ) )
% 9.17/5.43 = ( ( member_nat @ ( product_fst_nat_nat @ X ) @ A2 )
% 9.17/5.43 & ( member_nat @ ( product_snd_nat_nat @ X ) @ B5 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7113_mem__Times__iff,axiom,
% 9.17/5.43 ! [X: produc8923325533196201883nteger,A2: set_Code_integer,B5: set_Code_integer] :
% 9.17/5.43 ( ( member157494554546826820nteger @ X
% 9.17/5.43 @ ( produc5882431272649516420nteger @ A2
% 9.17/5.43 @ ^ [Uu: code_integer] : B5 ) )
% 9.17/5.43 = ( ( member_Code_integer @ ( produc8508995932063986495nteger @ X ) @ A2 )
% 9.17/5.43 & ( member_Code_integer @ ( produc6174133586879617921nteger @ X ) @ B5 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7114_mem__Times__iff,axiom,
% 9.17/5.43 ! [X: product_prod_int_int,A2: set_int,B5: set_int] :
% 9.17/5.43 ( ( member5262025264175285858nt_int @ X
% 9.17/5.43 @ ( produc1453890548195736866nt_int @ A2
% 9.17/5.43 @ ^ [Uu: int] : B5 ) )
% 9.17/5.43 = ( ( member_int @ ( product_fst_int_int @ X ) @ A2 )
% 9.17/5.43 & ( member_int @ ( product_snd_int_int @ X ) @ B5 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7115_in__prod__fst__sndI,axiom,
% 9.17/5.43 ! [X: product_prod_o_o,A2: set_o,B5: set_o] :
% 9.17/5.43 ( ( member_o @ ( product_fst_o_o @ X ) @ A2 )
% 9.17/5.43 => ( ( member_o @ ( product_snd_o_o @ X ) @ B5 )
% 9.17/5.43 => ( member7466972457876170832od_o_o @ X
% 9.17/5.43 @ ( product_Sigma_o_o @ A2
% 9.17/5.43 @ ^ [Uu: $o] : B5 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7116_in__prod__fst__sndI,axiom,
% 9.17/5.43 ! [X: product_prod_o_nat,A2: set_o,B5: set_nat] :
% 9.17/5.43 ( ( member_o @ ( product_fst_o_nat @ X ) @ A2 )
% 9.17/5.43 => ( ( member_nat @ ( product_snd_o_nat @ X ) @ B5 )
% 9.17/5.43 => ( member2802428098988154798_o_nat @ X
% 9.17/5.43 @ ( product_Sigma_o_nat @ A2
% 9.17/5.43 @ ^ [Uu: $o] : B5 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7117_in__prod__fst__sndI,axiom,
% 9.17/5.43 ! [X: product_prod_o_int,A2: set_o,B5: set_int] :
% 9.17/5.43 ( ( member_o @ ( product_fst_o_int @ X ) @ A2 )
% 9.17/5.43 => ( ( member_int @ ( product_snd_o_int @ X ) @ B5 )
% 9.17/5.43 => ( member7847949116333733898_o_int @ X
% 9.17/5.43 @ ( product_Sigma_o_int @ A2
% 9.17/5.43 @ ^ [Uu: $o] : B5 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7118_in__prod__fst__sndI,axiom,
% 9.17/5.43 ! [X: product_prod_nat_o,A2: set_nat,B5: set_o] :
% 9.17/5.43 ( ( member_nat @ ( product_fst_nat_o @ X ) @ A2 )
% 9.17/5.43 => ( ( member_o @ ( product_snd_nat_o @ X ) @ B5 )
% 9.17/5.43 => ( member6310962623043647828_nat_o @ X
% 9.17/5.43 @ ( product_Sigma_nat_o @ A2
% 9.17/5.43 @ ^ [Uu: nat] : B5 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7119_in__prod__fst__sndI,axiom,
% 9.17/5.43 ! [X: product_prod_nat_nat,A2: set_nat,B5: set_nat] :
% 9.17/5.43 ( ( member_nat @ ( product_fst_nat_nat @ X ) @ A2 )
% 9.17/5.43 => ( ( member_nat @ ( product_snd_nat_nat @ X ) @ B5 )
% 9.17/5.43 => ( member8440522571783428010at_nat @ X
% 9.17/5.43 @ ( produc457027306803732586at_nat @ A2
% 9.17/5.43 @ ^ [Uu: nat] : B5 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7120_in__prod__fst__sndI,axiom,
% 9.17/5.43 ! [X: product_prod_nat_int,A2: set_nat,B5: set_int] :
% 9.17/5.43 ( ( member_nat @ ( product_fst_nat_int @ X ) @ A2 )
% 9.17/5.43 => ( ( member_int @ ( product_snd_nat_int @ X ) @ B5 )
% 9.17/5.43 => ( member4262671552274231302at_int @ X
% 9.17/5.43 @ ( produc454536836294682310at_int @ A2
% 9.17/5.43 @ ^ [Uu: nat] : B5 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7121_in__prod__fst__sndI,axiom,
% 9.17/5.43 ! [X: product_prod_int_o,A2: set_int,B5: set_o] :
% 9.17/5.43 ( ( member_int @ ( product_fst_int_o @ X ) @ A2 )
% 9.17/5.43 => ( ( member_o @ ( product_snd_int_o @ X ) @ B5 )
% 9.17/5.43 => ( member4489920277610959864_int_o @ X
% 9.17/5.43 @ ( product_Sigma_int_o @ A2
% 9.17/5.43 @ ^ [Uu: int] : B5 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7122_in__prod__fst__sndI,axiom,
% 9.17/5.43 ! [X: product_prod_int_nat,A2: set_int,B5: set_nat] :
% 9.17/5.43 ( ( member_int @ ( product_fst_int_nat @ X ) @ A2 )
% 9.17/5.43 => ( ( member_nat @ ( product_snd_int_nat @ X ) @ B5 )
% 9.17/5.43 => ( member216504246829706758nt_nat @ X
% 9.17/5.43 @ ( produc1456381018704787142nt_nat @ A2
% 9.17/5.43 @ ^ [Uu: int] : B5 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7123_in__prod__fst__sndI,axiom,
% 9.17/5.43 ! [X: produc8923325533196201883nteger,A2: set_Code_integer,B5: set_Code_integer] :
% 9.17/5.43 ( ( member_Code_integer @ ( produc8508995932063986495nteger @ X ) @ A2 )
% 9.17/5.43 => ( ( member_Code_integer @ ( produc6174133586879617921nteger @ X ) @ B5 )
% 9.17/5.43 => ( member157494554546826820nteger @ X
% 9.17/5.43 @ ( produc5882431272649516420nteger @ A2
% 9.17/5.43 @ ^ [Uu: code_integer] : B5 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7124_in__prod__fst__sndI,axiom,
% 9.17/5.43 ! [X: product_prod_int_int,A2: set_int,B5: set_int] :
% 9.17/5.43 ( ( member_int @ ( product_fst_int_int @ X ) @ A2 )
% 9.17/5.43 => ( ( member_int @ ( product_snd_int_int @ X ) @ B5 )
% 9.17/5.43 => ( member5262025264175285858nt_int @ X
% 9.17/5.43 @ ( produc1453890548195736866nt_int @ A2
% 9.17/5.43 @ ^ [Uu: int] : B5 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7125_swap__product,axiom,
% 9.17/5.43 ! [A2: set_Pr4811707699266497531nteger,B5: set_Pr7604974323444597168e_term] :
% 9.17/5.43 ( ( image_8159590125932948193nteger
% 9.17/5.43 @ ( produc5068368601420144385nteger
% 9.17/5.43 @ ^ [I3: produc8923325533196201883nteger,J2: produc6241069584506657477e_term > option6357759511663192854e_term] : ( produc8603105652947943368nteger @ J2 @ I3 ) )
% 9.17/5.43 @ ( produc552098293437506509e_term @ A2
% 9.17/5.43 @ ^ [Uu: produc8923325533196201883nteger] : B5 ) )
% 9.17/5.43 = ( produc7256824055837167575nteger @ B5
% 9.17/5.43 @ ^ [Uu: produc6241069584506657477e_term > option6357759511663192854e_term] : A2 ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7126_swap__product,axiom,
% 9.17/5.43 ! [A2: set_Pr3948176798113811640et_nat,B5: set_Pr4532377907799695533_nat_o] :
% 9.17/5.43 ( ( image_4501728140019976901et_nat
% 9.17/5.43 @ ( produc5206072795621629085et_nat
% 9.17/5.43 @ ^ [I3: produc3658429121746597890et_nat,J2: produc3658429121746597890et_nat > $o] : ( produc5001842942810119800et_nat @ J2 @ I3 ) )
% 9.17/5.43 @ ( produc5879417536264718849_nat_o @ A2
% 9.17/5.43 @ ^ [Uu: produc3658429121746597890et_nat] : B5 ) )
% 9.17/5.43 = ( produc8052021730408606599et_nat @ B5
% 9.17/5.43 @ ^ [Uu: produc3658429121746597890et_nat > $o] : A2 ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7127_swap__product,axiom,
% 9.17/5.43 ! [A2: set_Pr3286484037609594932et_nat,B5: set_Pr4532377907799695533_nat_o] :
% 9.17/5.43 ( ( image_7255662321850427333et_nat
% 9.17/5.43 @ ( produc9203276081649983901et_nat
% 9.17/5.43 @ ^ [I3: produc3925858234332021118et_nat,J2: produc3658429121746597890et_nat > $o] : ( produc2245416461498447860et_nat @ J2 @ I3 ) )
% 9.17/5.43 @ ( produc8445815324708537221_nat_o @ A2
% 9.17/5.43 @ ^ [Uu: produc3925858234332021118et_nat] : B5 ) )
% 9.17/5.43 = ( produc7016705354093686019et_nat @ B5
% 9.17/5.43 @ ^ [Uu: produc3658429121746597890et_nat > $o] : A2 ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7128_swap__product,axiom,
% 9.17/5.43 ! [A2: set_Pr958786334691620121nt_int,B5: set_Pr3642885161833720865e_term] :
% 9.17/5.43 ( ( image_1640129903684976221nt_int
% 9.17/5.43 @ ( produc199769199162113789nt_int
% 9.17/5.43 @ ^ [I3: product_prod_int_int,J2: produc8551481072490612790e_term > option6357759511663192854e_term] : ( produc5700946648718959541nt_int @ J2 @ I3 ) )
% 9.17/5.43 @ ( produc5327145186146221532e_term @ A2
% 9.17/5.43 @ ^ [Uu: product_prod_int_int] : B5 ) )
% 9.17/5.43 = ( produc5808185664642557892nt_int @ B5
% 9.17/5.43 @ ^ [Uu: produc8551481072490612790e_term > option6357759511663192854e_term] : A2 ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7129_swap__product,axiom,
% 9.17/5.43 ! [A2: set_Pr958786334691620121nt_int,B5: set_in3461395444621081367e_term] :
% 9.17/5.43 ( ( image_1292712855239066845nt_int
% 9.17/5.43 @ ( produc3478612561300218621nt_int
% 9.17/5.43 @ ^ [I3: product_prod_int_int,J2: int > option6357759511663192854e_term] : ( produc4305682042979456191nt_int @ J2 @ I3 ) )
% 9.17/5.43 @ ( produc4529769248912663762e_term @ A2
% 9.17/5.43 @ ^ [Uu: product_prod_int_int] : B5 ) )
% 9.17/5.43 = ( produc1318478031590598990nt_int @ B5
% 9.17/5.43 @ ^ [Uu: int > option6357759511663192854e_term] : A2 ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7130_swap__product,axiom,
% 9.17/5.43 ! [A2: set_int,B5: set_int] :
% 9.17/5.43 ( ( image_2653370878348428101nt_int
% 9.17/5.43 @ ( produc4245557441103728435nt_int
% 9.17/5.43 @ ^ [I3: int,J2: int] : ( product_Pair_int_int @ J2 @ I3 ) )
% 9.17/5.43 @ ( produc1453890548195736866nt_int @ A2
% 9.17/5.43 @ ^ [Uu: int] : B5 ) )
% 9.17/5.43 = ( produc1453890548195736866nt_int @ B5
% 9.17/5.43 @ ^ [Uu: int] : A2 ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7131_Sigma__empty__iff,axiom,
% 9.17/5.43 ! [I4: set_se7855581050983116737at_nat,X11: set_Pr1261947904930325089at_nat > set_se7855581050983116737at_nat] :
% 9.17/5.43 ( ( ( produc7726050920695093128at_nat @ I4 @ X11 )
% 9.17/5.43 = bot_bo228742789529271731at_nat )
% 9.17/5.43 = ( ! [X3: set_Pr1261947904930325089at_nat] :
% 9.17/5.43 ( ( member2643936169264416010at_nat @ X3 @ I4 )
% 9.17/5.43 => ( ( X11 @ X3 )
% 9.17/5.43 = bot_bo3083307316010499117at_nat ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7132_Sigma__empty__iff,axiom,
% 9.17/5.43 ! [I4: set_nat,X11: nat > set_nat] :
% 9.17/5.43 ( ( ( produc457027306803732586at_nat @ I4 @ X11 )
% 9.17/5.43 = bot_bo2099793752762293965at_nat )
% 9.17/5.43 = ( ! [X3: nat] :
% 9.17/5.43 ( ( member_nat @ X3 @ I4 )
% 9.17/5.43 => ( ( X11 @ X3 )
% 9.17/5.43 = bot_bot_set_nat ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7133_gcd__mult__unit2,axiom,
% 9.17/5.43 ! [A: nat,B: nat,C: nat] :
% 9.17/5.43 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 9.17/5.43 => ( ( gcd_gcd_nat @ B @ ( times_times_nat @ C @ A ) )
% 9.17/5.43 = ( gcd_gcd_nat @ B @ C ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7134_gcd__mult__unit2,axiom,
% 9.17/5.43 ! [A: int,B: int,C: int] :
% 9.17/5.43 ( ( dvd_dvd_int @ A @ one_one_int )
% 9.17/5.43 => ( ( gcd_gcd_int @ B @ ( times_times_int @ C @ A ) )
% 9.17/5.43 = ( gcd_gcd_int @ B @ C ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7135_gcd__mult__unit1,axiom,
% 9.17/5.43 ! [A: nat,B: nat,C: nat] :
% 9.17/5.43 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 9.17/5.43 => ( ( gcd_gcd_nat @ ( times_times_nat @ B @ A ) @ C )
% 9.17/5.43 = ( gcd_gcd_nat @ B @ C ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7136_gcd__mult__unit1,axiom,
% 9.17/5.43 ! [A: int,B: int,C: int] :
% 9.17/5.43 ( ( dvd_dvd_int @ A @ one_one_int )
% 9.17/5.43 => ( ( gcd_gcd_int @ ( times_times_int @ B @ A ) @ C )
% 9.17/5.43 = ( gcd_gcd_int @ B @ C ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7137_gcd__div__unit1,axiom,
% 9.17/5.43 ! [A: int,B: int,C: int] :
% 9.17/5.43 ( ( dvd_dvd_int @ A @ one_one_int )
% 9.17/5.43 => ( ( gcd_gcd_int @ ( divide_divide_int @ B @ A ) @ C )
% 9.17/5.43 = ( gcd_gcd_int @ B @ C ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7138_gcd__div__unit1,axiom,
% 9.17/5.43 ! [A: nat,B: nat,C: nat] :
% 9.17/5.43 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 9.17/5.43 => ( ( gcd_gcd_nat @ ( divide_divide_nat @ B @ A ) @ C )
% 9.17/5.43 = ( gcd_gcd_nat @ B @ C ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7139_gcd__div__unit2,axiom,
% 9.17/5.43 ! [A: int,B: int,C: int] :
% 9.17/5.43 ( ( dvd_dvd_int @ A @ one_one_int )
% 9.17/5.43 => ( ( gcd_gcd_int @ B @ ( divide_divide_int @ C @ A ) )
% 9.17/5.43 = ( gcd_gcd_int @ B @ C ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7140_gcd__div__unit2,axiom,
% 9.17/5.43 ! [A: nat,B: nat,C: nat] :
% 9.17/5.43 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 9.17/5.43 => ( ( gcd_gcd_nat @ B @ ( divide_divide_nat @ C @ A ) )
% 9.17/5.43 = ( gcd_gcd_nat @ B @ C ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7141_less__int_Otransfer,axiom,
% 9.17/5.43 ( bNF_re717283939379294677_int_o @ pcr_int
% 9.17/5.43 @ ( bNF_re6644619430987730960nt_o_o @ pcr_int
% 9.17/5.43 @ ^ [Y4: $o,Z2: $o] : ( Y4 = Z2 ) )
% 9.17/5.43 @ ( produc8739625826339149834_nat_o
% 9.17/5.43 @ ^ [X3: nat,Y3: nat] :
% 9.17/5.43 ( produc6081775807080527818_nat_o
% 9.17/5.43 @ ^ [U2: nat,V2: nat] : ( ord_less_nat @ ( plus_plus_nat @ X3 @ V2 ) @ ( plus_plus_nat @ U2 @ Y3 ) ) ) )
% 9.17/5.43 @ ord_less_int ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7142_less__eq__int_Otransfer,axiom,
% 9.17/5.43 ( bNF_re717283939379294677_int_o @ pcr_int
% 9.17/5.43 @ ( bNF_re6644619430987730960nt_o_o @ pcr_int
% 9.17/5.43 @ ^ [Y4: $o,Z2: $o] : ( Y4 = Z2 ) )
% 9.17/5.43 @ ( produc8739625826339149834_nat_o
% 9.17/5.43 @ ^ [X3: nat,Y3: nat] :
% 9.17/5.43 ( produc6081775807080527818_nat_o
% 9.17/5.43 @ ^ [U2: nat,V2: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X3 @ V2 ) @ ( plus_plus_nat @ U2 @ Y3 ) ) ) )
% 9.17/5.43 @ ord_less_eq_int ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7143_plus__int_Otransfer,axiom,
% 9.17/5.43 ( bNF_re7408651293131936558nt_int @ pcr_int @ ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int )
% 9.17/5.43 @ ( produc27273713700761075at_nat
% 9.17/5.43 @ ^ [X3: nat,Y3: nat] :
% 9.17/5.43 ( produc2626176000494625587at_nat
% 9.17/5.43 @ ^ [U2: nat,V2: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X3 @ U2 ) @ ( plus_plus_nat @ Y3 @ V2 ) ) ) )
% 9.17/5.43 @ plus_plus_int ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7144_minus__int_Otransfer,axiom,
% 9.17/5.43 ( bNF_re7408651293131936558nt_int @ pcr_int @ ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int )
% 9.17/5.43 @ ( produc27273713700761075at_nat
% 9.17/5.43 @ ^ [X3: nat,Y3: nat] :
% 9.17/5.43 ( produc2626176000494625587at_nat
% 9.17/5.43 @ ^ [U2: nat,V2: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X3 @ V2 ) @ ( plus_plus_nat @ Y3 @ U2 ) ) ) )
% 9.17/5.43 @ minus_minus_int ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7145_times__subset__iff,axiom,
% 9.17/5.43 ! [A2: set_o,C4: set_o,B5: set_o,D3: set_o] :
% 9.17/5.43 ( ( ord_le192195778054999463od_o_o
% 9.17/5.43 @ ( product_Sigma_o_o @ A2
% 9.17/5.43 @ ^ [Uu: $o] : C4 )
% 9.17/5.43 @ ( product_Sigma_o_o @ B5
% 9.17/5.43 @ ^ [Uu: $o] : D3 ) )
% 9.17/5.43 = ( ( A2 = bot_bot_set_o )
% 9.17/5.43 | ( C4 = bot_bot_set_o )
% 9.17/5.43 | ( ( ord_less_eq_set_o @ A2 @ B5 )
% 9.17/5.43 & ( ord_less_eq_set_o @ C4 @ D3 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7146_times__subset__iff,axiom,
% 9.17/5.43 ! [A2: set_o,C4: set_int,B5: set_o,D3: set_int] :
% 9.17/5.43 ( ( ord_le3982295392052344841_o_int
% 9.17/5.43 @ ( product_Sigma_o_int @ A2
% 9.17/5.43 @ ^ [Uu: $o] : C4 )
% 9.17/5.43 @ ( product_Sigma_o_int @ B5
% 9.17/5.43 @ ^ [Uu: $o] : D3 ) )
% 9.17/5.43 = ( ( A2 = bot_bot_set_o )
% 9.17/5.43 | ( C4 = bot_bot_set_int )
% 9.17/5.43 | ( ( ord_less_eq_set_o @ A2 @ B5 )
% 9.17/5.43 & ( ord_less_eq_set_int @ C4 @ D3 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7147_times__subset__iff,axiom,
% 9.17/5.43 ! [A2: set_int,C4: set_o,B5: set_int,D3: set_o] :
% 9.17/5.43 ( ( ord_le5274836691491929335_int_o
% 9.17/5.43 @ ( product_Sigma_int_o @ A2
% 9.17/5.43 @ ^ [Uu: int] : C4 )
% 9.17/5.43 @ ( product_Sigma_int_o @ B5
% 9.17/5.43 @ ^ [Uu: int] : D3 ) )
% 9.17/5.43 = ( ( A2 = bot_bot_set_int )
% 9.17/5.43 | ( C4 = bot_bot_set_o )
% 9.17/5.43 | ( ( ord_less_eq_set_int @ A2 @ B5 )
% 9.17/5.43 & ( ord_less_eq_set_o @ C4 @ D3 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7148_times__subset__iff,axiom,
% 9.17/5.43 ! [A2: set_int,C4: set_int,B5: set_int,D3: set_int] :
% 9.17/5.43 ( ( ord_le2843351958646193337nt_int
% 9.17/5.43 @ ( produc1453890548195736866nt_int @ A2
% 9.17/5.43 @ ^ [Uu: int] : C4 )
% 9.17/5.43 @ ( produc1453890548195736866nt_int @ B5
% 9.17/5.43 @ ^ [Uu: int] : D3 ) )
% 9.17/5.43 = ( ( A2 = bot_bot_set_int )
% 9.17/5.43 | ( C4 = bot_bot_set_int )
% 9.17/5.43 | ( ( ord_less_eq_set_int @ A2 @ B5 )
% 9.17/5.43 & ( ord_less_eq_set_int @ C4 @ D3 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7149_times__subset__iff,axiom,
% 9.17/5.43 ! [A2: set_o,C4: set_nat,B5: set_o,D3: set_nat] :
% 9.17/5.43 ( ( ord_le6472378536984071597_o_nat
% 9.17/5.43 @ ( product_Sigma_o_nat @ A2
% 9.17/5.43 @ ^ [Uu: $o] : C4 )
% 9.17/5.43 @ ( product_Sigma_o_nat @ B5
% 9.17/5.43 @ ^ [Uu: $o] : D3 ) )
% 9.17/5.43 = ( ( A2 = bot_bot_set_o )
% 9.17/5.43 | ( C4 = bot_bot_set_nat )
% 9.17/5.43 | ( ( ord_less_eq_set_o @ A2 @ B5 )
% 9.17/5.43 & ( ord_less_eq_set_nat @ C4 @ D3 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7150_times__subset__iff,axiom,
% 9.17/5.43 ! [A2: set_int,C4: set_nat,B5: set_int,D3: set_nat] :
% 9.17/5.43 ( ( ord_le5333435103577920093nt_nat
% 9.17/5.43 @ ( produc1456381018704787142nt_nat @ A2
% 9.17/5.43 @ ^ [Uu: int] : C4 )
% 9.17/5.43 @ ( produc1456381018704787142nt_nat @ B5
% 9.17/5.43 @ ^ [Uu: int] : D3 ) )
% 9.17/5.43 = ( ( A2 = bot_bot_set_int )
% 9.17/5.43 | ( C4 = bot_bot_set_nat )
% 9.17/5.43 | ( ( ord_less_eq_set_int @ A2 @ B5 )
% 9.17/5.43 & ( ord_less_eq_set_nat @ C4 @ D3 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7151_times__subset__iff,axiom,
% 9.17/5.43 ! [A2: set_nat,C4: set_o,B5: set_nat,D3: set_o] :
% 9.17/5.43 ( ( ord_le7519981659162375251_nat_o
% 9.17/5.43 @ ( product_Sigma_nat_o @ A2
% 9.17/5.43 @ ^ [Uu: nat] : C4 )
% 9.17/5.43 @ ( product_Sigma_nat_o @ B5
% 9.17/5.43 @ ^ [Uu: nat] : D3 ) )
% 9.17/5.43 = ( ( A2 = bot_bot_set_nat )
% 9.17/5.43 | ( C4 = bot_bot_set_o )
% 9.17/5.43 | ( ( ord_less_eq_set_nat @ A2 @ B5 )
% 9.17/5.43 & ( ord_less_eq_set_o @ C4 @ D3 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7152_times__subset__iff,axiom,
% 9.17/5.43 ! [A2: set_nat,C4: set_int,B5: set_nat,D3: set_int] :
% 9.17/5.43 ( ( ord_le656430383953171549at_int
% 9.17/5.43 @ ( produc454536836294682310at_int @ A2
% 9.17/5.43 @ ^ [Uu: nat] : C4 )
% 9.17/5.43 @ ( produc454536836294682310at_int @ B5
% 9.17/5.43 @ ^ [Uu: nat] : D3 ) )
% 9.17/5.43 = ( ( A2 = bot_bot_set_nat )
% 9.17/5.43 | ( C4 = bot_bot_set_int )
% 9.17/5.43 | ( ( ord_less_eq_set_nat @ A2 @ B5 )
% 9.17/5.43 & ( ord_less_eq_set_int @ C4 @ D3 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7153_times__subset__iff,axiom,
% 9.17/5.43 ! [A2: set_nat,C4: set_nat,B5: set_nat,D3: set_nat] :
% 9.17/5.43 ( ( ord_le3146513528884898305at_nat
% 9.17/5.43 @ ( produc457027306803732586at_nat @ A2
% 9.17/5.43 @ ^ [Uu: nat] : C4 )
% 9.17/5.43 @ ( produc457027306803732586at_nat @ B5
% 9.17/5.43 @ ^ [Uu: nat] : D3 ) )
% 9.17/5.43 = ( ( A2 = bot_bot_set_nat )
% 9.17/5.43 | ( C4 = bot_bot_set_nat )
% 9.17/5.43 | ( ( ord_less_eq_set_nat @ A2 @ B5 )
% 9.17/5.43 & ( ord_less_eq_set_nat @ C4 @ D3 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7154_times__subset__iff,axiom,
% 9.17/5.43 ! [A2: set_Pr1261947904930325089at_nat,C4: set_o,B5: set_Pr1261947904930325089at_nat,D3: set_o] :
% 9.17/5.43 ( ( ord_le5919393503700438654_nat_o
% 9.17/5.43 @ ( produc203973861852599583_nat_o @ A2
% 9.17/5.43 @ ^ [Uu: product_prod_nat_nat] : C4 )
% 9.17/5.43 @ ( produc203973861852599583_nat_o @ B5
% 9.17/5.43 @ ^ [Uu: product_prod_nat_nat] : D3 ) )
% 9.17/5.43 = ( ( A2 = bot_bo2099793752762293965at_nat )
% 9.17/5.43 | ( C4 = bot_bot_set_o )
% 9.17/5.43 | ( ( ord_le3146513528884898305at_nat @ A2 @ B5 )
% 9.17/5.43 & ( ord_less_eq_set_o @ C4 @ D3 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7155_image__paired__Times,axiom,
% 9.17/5.43 ! [F: nat > code_integer,G: nat > code_integer,A2: set_nat,B5: set_nat] :
% 9.17/5.43 ( ( image_5669961043262023647nteger
% 9.17/5.43 @ ( produc39701218431283661nteger
% 9.17/5.43 @ ^ [X3: nat,Y3: nat] : ( produc1086072967326762835nteger @ ( F @ X3 ) @ ( G @ Y3 ) ) )
% 9.17/5.43 @ ( produc457027306803732586at_nat @ A2
% 9.17/5.43 @ ^ [Uu: nat] : B5 ) )
% 9.17/5.43 = ( produc5882431272649516420nteger @ ( image_1215581382706833972nteger @ F @ A2 )
% 9.17/5.43 @ ^ [Uu: code_integer] : ( image_1215581382706833972nteger @ G @ B5 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7156_image__paired__Times,axiom,
% 9.17/5.43 ! [F: nat > code_integer,G: nat > nat,A2: set_nat,B5: set_nat] :
% 9.17/5.43 ( ( image_1372510298004463058er_nat
% 9.17/5.43 @ ( produc4146132627719282624er_nat
% 9.17/5.43 @ ^ [X3: nat,Y3: nat] : ( produc8807591364040884934er_nat @ ( F @ X3 ) @ ( G @ Y3 ) ) )
% 9.17/5.43 @ ( produc457027306803732586at_nat @ A2
% 9.17/5.43 @ ^ [Uu: nat] : B5 ) )
% 9.17/5.43 = ( produc4260658192689636599er_nat @ ( image_1215581382706833972nteger @ F @ A2 )
% 9.17/5.43 @ ^ [Uu: code_integer] : ( image_nat_nat @ G @ B5 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7157_image__paired__Times,axiom,
% 9.17/5.43 ! [F: nat > code_integer,G: nat > int,A2: set_nat,B5: set_nat] :
% 9.17/5.43 ( ( image_6418031315350042158er_int
% 9.17/5.43 @ ( produc9191653645064861724er_int
% 9.17/5.43 @ ^ [X3: nat,Y3: nat] : ( produc8805100893531834658er_int @ ( F @ X3 ) @ ( G @ Y3 ) ) )
% 9.17/5.43 @ ( produc457027306803732586at_nat @ A2
% 9.17/5.43 @ ^ [Uu: nat] : B5 ) )
% 9.17/5.43 = ( produc4258167722180586323er_int @ ( image_1215581382706833972nteger @ F @ A2 )
% 9.17/5.43 @ ^ [Uu: code_integer] : ( image_nat_int @ G @ B5 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7158_image__paired__Times,axiom,
% 9.17/5.43 ! [F: nat > code_integer,G: int > int,A2: set_nat,B5: set_int] :
% 9.17/5.43 ( ( image_202211252889950930er_int
% 9.17/5.43 @ ( produc1728318271963197120er_int
% 9.17/5.43 @ ^ [X3: nat,Y3: int] : ( produc8805100893531834658er_int @ ( F @ X3 ) @ ( G @ Y3 ) ) )
% 9.17/5.43 @ ( produc454536836294682310at_int @ A2
% 9.17/5.43 @ ^ [Uu: nat] : B5 ) )
% 9.17/5.43 = ( produc4258167722180586323er_int @ ( image_1215581382706833972nteger @ F @ A2 )
% 9.17/5.43 @ ^ [Uu: code_integer] : ( image_int_int @ G @ B5 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7159_image__paired__Times,axiom,
% 9.17/5.43 ! [F: nat > nat,G: nat > code_integer,A2: set_nat,B5: set_nat] :
% 9.17/5.43 ( ( image_6753550540357478226nteger
% 9.17/5.43 @ ( produc303800833217521984nteger
% 9.17/5.43 @ ^ [X3: nat,Y3: nat] : ( produc9072146812819927750nteger @ ( F @ X3 ) @ ( G @ Y3 ) ) )
% 9.17/5.43 @ ( produc457027306803732586at_nat @ A2
% 9.17/5.43 @ ^ [Uu: nat] : B5 ) )
% 9.17/5.43 = ( produc4525213641468679415nteger @ ( image_nat_nat @ F @ A2 )
% 9.17/5.43 @ ^ [Uu: nat] : ( image_1215581382706833972nteger @ G @ B5 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7160_image__paired__Times,axiom,
% 9.17/5.43 ! [F: nat > nat,G: nat > nat,A2: set_nat,B5: set_nat] :
% 9.17/5.43 ( ( image_5168914502847457605at_nat
% 9.17/5.43 @ ( produc2626176000494625587at_nat
% 9.17/5.43 @ ^ [X3: nat,Y3: nat] : ( product_Pair_nat_nat @ ( F @ X3 ) @ ( G @ Y3 ) ) )
% 9.17/5.43 @ ( produc457027306803732586at_nat @ A2
% 9.17/5.43 @ ^ [Uu: nat] : B5 ) )
% 9.17/5.43 = ( produc457027306803732586at_nat @ ( image_nat_nat @ F @ A2 )
% 9.17/5.43 @ ^ [Uu: nat] : ( image_nat_nat @ G @ B5 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7161_image__paired__Times,axiom,
% 9.17/5.43 ! [F: nat > nat,G: nat > int,A2: set_nat,B5: set_nat] :
% 9.17/5.43 ( ( image_991063483338260897at_int
% 9.17/5.43 @ ( produc7671697017840204687at_int
% 9.17/5.43 @ ^ [X3: nat,Y3: nat] : ( product_Pair_nat_int @ ( F @ X3 ) @ ( G @ Y3 ) ) )
% 9.17/5.43 @ ( produc457027306803732586at_nat @ A2
% 9.17/5.43 @ ^ [Uu: nat] : B5 ) )
% 9.17/5.43 = ( produc454536836294682310at_int @ ( image_nat_nat @ F @ A2 )
% 9.17/5.43 @ ^ [Uu: nat] : ( image_nat_int @ G @ B5 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7162_image__paired__Times,axiom,
% 9.17/5.43 ! [F: nat > nat,G: int > int,A2: set_nat,B5: set_int] :
% 9.17/5.43 ( ( image_9117352539549038149at_int
% 9.17/5.43 @ ( produc1486167065449562675at_int
% 9.17/5.43 @ ^ [X3: nat,Y3: int] : ( product_Pair_nat_int @ ( F @ X3 ) @ ( G @ Y3 ) ) )
% 9.17/5.43 @ ( produc454536836294682310at_int @ A2
% 9.17/5.43 @ ^ [Uu: nat] : B5 ) )
% 9.17/5.43 = ( produc454536836294682310at_int @ ( image_nat_nat @ F @ A2 )
% 9.17/5.43 @ ^ [Uu: nat] : ( image_int_int @ G @ B5 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7163_image__paired__Times,axiom,
% 9.17/5.43 ! [F: nat > int,G: nat > code_integer,A2: set_nat,B5: set_nat] :
% 9.17/5.43 ( ( image_7125204100594322862nteger
% 9.17/5.43 @ ( produc675454393454366620nteger
% 9.17/5.43 @ ^ [X3: nat,Y3: nat] : ( produc220428336201996578nteger @ ( F @ X3 ) @ ( G @ Y3 ) ) )
% 9.17/5.43 @ ( produc457027306803732586at_nat @ A2
% 9.17/5.43 @ ^ [Uu: nat] : B5 ) )
% 9.17/5.43 = ( produc4896867201705524051nteger @ ( image_nat_int @ F @ A2 )
% 9.17/5.43 @ ^ [Uu: int] : ( image_1215581382706833972nteger @ G @ B5 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7164_image__paired__Times,axiom,
% 9.17/5.43 ! [F: nat > int,G: nat > nat,A2: set_nat,B5: set_nat] :
% 9.17/5.43 ( ( image_6168268214748512161nt_nat
% 9.17/5.43 @ ( produc3625529712395680143nt_nat
% 9.17/5.43 @ ^ [X3: nat,Y3: nat] : ( product_Pair_int_nat @ ( F @ X3 ) @ ( G @ Y3 ) ) )
% 9.17/5.43 @ ( produc457027306803732586at_nat @ A2
% 9.17/5.43 @ ^ [Uu: nat] : B5 ) )
% 9.17/5.43 = ( produc1456381018704787142nt_nat @ ( image_nat_int @ F @ A2 )
% 9.17/5.43 @ ^ [Uu: int] : ( image_nat_nat @ G @ B5 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7165_fst__image__Sigma,axiom,
% 9.17/5.43 ! [A2: set_Code_integer,B5: code_integer > set_Code_integer] :
% 9.17/5.43 ( ( image_6316824473203919795nteger @ produc8508995932063986495nteger @ ( produc5882431272649516420nteger @ A2 @ B5 ) )
% 9.17/5.43 = ( collect_Code_integer
% 9.17/5.43 @ ^ [X3: code_integer] :
% 9.17/5.43 ( ( member_Code_integer @ X3 @ A2 )
% 9.17/5.43 & ( ( B5 @ X3 )
% 9.17/5.43 != bot_bo3990330152332043303nteger ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7166_fst__image__Sigma,axiom,
% 9.17/5.43 ! [A2: set_o,B5: $o > set_o] :
% 9.17/5.43 ( ( image_7896445794123959606_o_o_o @ product_fst_o_o @ ( product_Sigma_o_o @ A2 @ B5 ) )
% 9.17/5.43 = ( collect_o
% 9.17/5.43 @ ^ [X3: $o] :
% 9.17/5.43 ( ( member_o @ X3 @ A2 )
% 9.17/5.43 & ( ( B5 @ X3 )
% 9.17/5.43 != bot_bot_set_o ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7167_fst__image__Sigma,axiom,
% 9.17/5.43 ! [A2: set_int,B5: int > set_o] :
% 9.17/5.43 ( ( image_90517134139374612_o_int @ product_fst_int_o @ ( product_Sigma_int_o @ A2 @ B5 ) )
% 9.17/5.43 = ( collect_int
% 9.17/5.43 @ ^ [X3: int] :
% 9.17/5.43 ( ( member_int @ X3 @ A2 )
% 9.17/5.43 & ( ( B5 @ X3 )
% 9.17/5.43 != bot_bot_set_o ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7168_fst__image__Sigma,axiom,
% 9.17/5.43 ! [A2: set_nat,B5: nat > set_o] :
% 9.17/5.43 ( ( image_8629803608462650132_o_nat @ product_fst_nat_o @ ( product_Sigma_nat_o @ A2 @ B5 ) )
% 9.17/5.43 = ( collect_nat
% 9.17/5.43 @ ^ [X3: nat] :
% 9.17/5.43 ( ( member_nat @ X3 @ A2 )
% 9.17/5.43 & ( ( B5 @ X3 )
% 9.17/5.43 != bot_bot_set_o ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7169_fst__image__Sigma,axiom,
% 9.17/5.43 ! [A2: set_o,B5: $o > set_nat] :
% 9.17/5.43 ( ( image_8105710389281276538_nat_o @ product_fst_o_nat @ ( product_Sigma_o_nat @ A2 @ B5 ) )
% 9.17/5.43 = ( collect_o
% 9.17/5.43 @ ^ [X3: $o] :
% 9.17/5.43 ( ( member_o @ X3 @ A2 )
% 9.17/5.43 & ( ( B5 @ X3 )
% 9.17/5.43 != bot_bot_set_nat ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7170_fst__image__Sigma,axiom,
% 9.17/5.43 ! [A2: set_int,B5: int > set_nat] :
% 9.17/5.43 ( ( image_2855239504505064772at_int @ product_fst_int_nat @ ( produc1456381018704787142nt_nat @ A2 @ B5 ) )
% 9.17/5.43 = ( collect_int
% 9.17/5.43 @ ^ [X3: int] :
% 9.17/5.43 ( ( member_int @ X3 @ A2 )
% 9.17/5.43 & ( ( B5 @ X3 )
% 9.17/5.43 != bot_bot_set_nat ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7171_fst__image__Sigma,axiom,
% 9.17/5.43 ! [A2: set_nat,B5: nat > set_nat] :
% 9.17/5.43 ( ( image_2486076414777270412at_nat @ product_fst_nat_nat @ ( produc457027306803732586at_nat @ A2 @ B5 ) )
% 9.17/5.43 = ( collect_nat
% 9.17/5.43 @ ^ [X3: nat] :
% 9.17/5.43 ( ( member_nat @ X3 @ A2 )
% 9.17/5.43 & ( ( B5 @ X3 )
% 9.17/5.43 != bot_bot_set_nat ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7172_fst__image__Sigma,axiom,
% 9.17/5.43 ! [A2: set_o,B5: $o > set_int] :
% 9.17/5.43 ( ( image_5860565421610830622_int_o @ product_fst_o_int @ ( product_Sigma_o_int @ A2 @ B5 ) )
% 9.17/5.43 = ( collect_o
% 9.17/5.43 @ ^ [X3: $o] :
% 9.17/5.43 ( ( member_o @ X3 @ A2 )
% 9.17/5.43 & ( ( B5 @ X3 )
% 9.17/5.43 != bot_bot_set_int ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7173_fst__image__Sigma,axiom,
% 9.17/5.43 ! [A2: set_nat,B5: nat > set_int] :
% 9.17/5.43 ( ( image_4672997989470292200nt_nat @ product_fst_nat_int @ ( produc454536836294682310at_int @ A2 @ B5 ) )
% 9.17/5.43 = ( collect_nat
% 9.17/5.43 @ ^ [X3: nat] :
% 9.17/5.43 ( ( member_nat @ X3 @ A2 )
% 9.17/5.43 & ( ( B5 @ X3 )
% 9.17/5.43 != bot_bot_set_int ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7174_fst__image__Sigma,axiom,
% 9.17/5.43 ! [A2: set_int,B5: int > set_int] :
% 9.17/5.43 ( ( image_5042161079198086560nt_int @ product_fst_int_int @ ( produc1453890548195736866nt_int @ A2 @ B5 ) )
% 9.17/5.43 = ( collect_int
% 9.17/5.43 @ ^ [X3: int] :
% 9.17/5.43 ( ( member_int @ X3 @ A2 )
% 9.17/5.43 & ( ( B5 @ X3 )
% 9.17/5.43 != bot_bot_set_int ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7175_Sigma__def,axiom,
% 9.17/5.43 ( produc7256824055837167575nteger
% 9.17/5.43 = ( ^ [A7: set_Pr7604974323444597168e_term,B8: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > set_Pr4811707699266497531nteger] :
% 9.17/5.43 ( comple1324685164916153887nteger
% 9.17/5.43 @ ( image_3218922492622835021nteger
% 9.17/5.43 @ ^ [X3: produc6241069584506657477e_term > option6357759511663192854e_term] :
% 9.17/5.43 ( comple1324685164916153887nteger
% 9.17/5.43 @ ( image_5715966689554962722nteger
% 9.17/5.43 @ ^ [Y3: produc8923325533196201883nteger] : ( insert4245756632806152262nteger @ ( produc8603105652947943368nteger @ X3 @ Y3 ) @ bot_bo5443222936135328352nteger )
% 9.17/5.43 @ ( B8 @ X3 ) ) )
% 9.17/5.43 @ A7 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7176_Sigma__def,axiom,
% 9.17/5.43 ( produc8052021730408606599et_nat
% 9.17/5.43 = ( ^ [A7: set_Pr4532377907799695533_nat_o,B8: ( produc3658429121746597890et_nat > $o ) > set_Pr3948176798113811640et_nat] :
% 9.17/5.43 ( comple4849024849677941639et_nat
% 9.17/5.43 @ ( image_1916054815030244540et_nat
% 9.17/5.43 @ ^ [X3: produc3658429121746597890et_nat > $o] :
% 9.17/5.43 ( comple4849024849677941639et_nat
% 9.17/5.43 @ ( image_15228131989405757et_nat
% 9.17/5.43 @ ^ [Y3: produc3658429121746597890et_nat] : ( insert3111075074545270702et_nat @ ( produc5001842942810119800et_nat @ X3 @ Y3 ) @ bot_bo1481135142794719944et_nat )
% 9.17/5.43 @ ( B8 @ X3 ) ) )
% 9.17/5.43 @ A7 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7177_Sigma__def,axiom,
% 9.17/5.43 ( produc7016705354093686019et_nat
% 9.17/5.43 = ( ^ [A7: set_Pr4532377907799695533_nat_o,B8: ( produc3658429121746597890et_nat > $o ) > set_Pr3286484037609594932et_nat] :
% 9.17/5.43 ( comple5063570841203093763et_nat
% 9.17/5.43 @ ( image_4127253568139551288et_nat
% 9.17/5.43 @ ^ [X3: produc3658429121746597890et_nat > $o] :
% 9.17/5.43 ( comple5063570841203093763et_nat
% 9.17/5.43 @ ( image_8189767104526903093et_nat
% 9.17/5.43 @ ^ [Y3: produc3925858234332021118et_nat] : ( insert8297122186708525866et_nat @ ( produc2245416461498447860et_nat @ X3 @ Y3 ) @ bot_bo5635537948650799172et_nat )
% 9.17/5.43 @ ( B8 @ X3 ) ) )
% 9.17/5.43 @ A7 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7178_Sigma__def,axiom,
% 9.17/5.43 ( produc5808185664642557892nt_int
% 9.17/5.43 = ( ^ [A7: set_Pr3642885161833720865e_term,B8: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > set_Pr958786334691620121nt_int] :
% 9.17/5.43 ( comple6871990601243273356nt_int
% 9.17/5.43 @ ( image_5111841350319496619nt_int
% 9.17/5.43 @ ^ [X3: produc8551481072490612790e_term > option6357759511663192854e_term] :
% 9.17/5.43 ( comple6871990601243273356nt_int
% 9.17/5.43 @ ( image_815654828163180973nt_int
% 9.17/5.43 @ ^ [Y3: product_prod_int_int] : ( insert984290209421517107nt_int @ ( produc5700946648718959541nt_int @ X3 @ Y3 ) @ bot_bo572930865798478029nt_int )
% 9.17/5.43 @ ( B8 @ X3 ) ) )
% 9.17/5.43 @ A7 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7179_Sigma__def,axiom,
% 9.17/5.43 ( produc1318478031590598990nt_int
% 9.17/5.43 = ( ^ [A7: set_in3461395444621081367e_term,B8: ( int > option6357759511663192854e_term ) > set_Pr958786334691620121nt_int] :
% 9.17/5.43 ( comple5772984051336441366nt_int
% 9.17/5.43 @ ( image_7708985414016646955nt_int
% 9.17/5.43 @ ^ [X3: int > option6357759511663192854e_term] :
% 9.17/5.43 ( comple5772984051336441366nt_int
% 9.17/5.43 @ ( image_5963362749323609783nt_int
% 9.17/5.43 @ ^ [Y3: product_prod_int_int] : ( insert750232675644355261nt_int @ ( produc4305682042979456191nt_int @ X3 @ Y3 ) @ bot_bo4508923176915781079nt_int )
% 9.17/5.43 @ ( B8 @ X3 ) ) )
% 9.17/5.43 @ A7 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7180_Sigma__def,axiom,
% 9.17/5.43 ( produc7726050920695093128at_nat
% 9.17/5.43 = ( ^ [A7: set_se7855581050983116737at_nat,B8: set_Pr1261947904930325089at_nat > set_se7855581050983116737at_nat] :
% 9.17/5.43 ( comple4364388969068068532at_nat
% 9.17/5.43 @ ( image_6898982319499645995at_nat
% 9.17/5.43 @ ^ [X3: set_Pr1261947904930325089at_nat] :
% 9.17/5.43 ( comple4364388969068068532at_nat
% 9.17/5.43 @ ( image_6898982319499645995at_nat
% 9.17/5.43 @ ^ [Y3: set_Pr1261947904930325089at_nat] : ( insert9069300056098147895at_nat @ ( produc2922128104949294807at_nat @ X3 @ Y3 ) @ bot_bo228742789529271731at_nat )
% 9.17/5.43 @ ( B8 @ X3 ) ) )
% 9.17/5.43 @ A7 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7181_Sigma__def,axiom,
% 9.17/5.43 ( produc457027306803732586at_nat
% 9.17/5.43 = ( ^ [A7: set_nat,B8: nat > set_nat] :
% 9.17/5.43 ( comple5685304695842803022at_nat
% 9.17/5.43 @ ( image_7178329752028323786at_nat
% 9.17/5.43 @ ^ [X3: nat] :
% 9.17/5.43 ( comple5685304695842803022at_nat
% 9.17/5.43 @ ( image_7178329752028323786at_nat
% 9.17/5.43 @ ^ [Y3: nat] : ( insert8211810215607154385at_nat @ ( product_Pair_nat_nat @ X3 @ Y3 ) @ bot_bo2099793752762293965at_nat )
% 9.17/5.43 @ ( B8 @ X3 ) ) )
% 9.17/5.43 @ A7 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7182_times__int_Otransfer,axiom,
% 9.17/5.43 ( bNF_re7408651293131936558nt_int @ pcr_int @ ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int )
% 9.17/5.43 @ ( produc27273713700761075at_nat
% 9.17/5.43 @ ^ [X3: nat,Y3: nat] :
% 9.17/5.43 ( produc2626176000494625587at_nat
% 9.17/5.43 @ ^ [U2: nat,V2: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X3 @ U2 ) @ ( times_times_nat @ Y3 @ V2 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X3 @ V2 ) @ ( times_times_nat @ Y3 @ U2 ) ) ) ) )
% 9.17/5.43 @ times_times_int ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7183_num__of__integer_Orsp,axiom,
% 9.17/5.43 ( bNF_re7626690874201225453um_num
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ ^ [Y4: num,Z2: num] : ( Y4 = Z2 )
% 9.17/5.43 @ ( comp_nat_num_int @ num_of_nat @ nat2 )
% 9.17/5.43 @ ( comp_nat_num_int @ num_of_nat @ nat2 ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7184_snd__image__Sigma,axiom,
% 9.17/5.43 ! [A2: set_Code_integer,B5: code_integer > set_Code_integer] :
% 9.17/5.43 ( ( image_6316824473203919795nteger @ produc6174133586879617921nteger @ ( produc5882431272649516420nteger @ A2 @ B5 ) )
% 9.17/5.43 = ( comple739944243200306918nteger @ ( image_2291390168754192375nteger @ B5 @ A2 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7185_snd__image__Sigma,axiom,
% 9.17/5.43 ! [A2: set_int,B5: int > set_int] :
% 9.17/5.43 ( ( image_5042161079198086560nt_int @ product_snd_int_int @ ( produc1453890548195736866nt_int @ A2 @ B5 ) )
% 9.17/5.43 = ( comple3221217463730067765et_int @ ( image_int_set_int @ B5 @ A2 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7186_snd__image__Sigma,axiom,
% 9.17/5.43 ! [A2: set_Code_natural,B5: code_natural > set_Pr7564037697178849041atural] :
% 9.17/5.43 ( ( image_3837677093542026988atural @ produc6591912806276919810atural @ ( produc6231535905537262655atural @ A2 @ B5 ) )
% 9.17/5.43 = ( comple4956303571586142718atural @ ( image_3530315724569248802atural @ B5 @ A2 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7187_snd__image__Sigma,axiom,
% 9.17/5.43 ! [A2: set_nat,B5: nat > set_nat] :
% 9.17/5.43 ( ( image_2486076414777270412at_nat @ product_snd_nat_nat @ ( produc457027306803732586at_nat @ A2 @ B5 ) )
% 9.17/5.43 = ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ B5 @ A2 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7188_subset__fst__snd,axiom,
% 9.17/5.43 ! [A2: set_Pr4811707699266497531nteger] :
% 9.17/5.43 ( ord_le3725938330318615451nteger @ A2
% 9.17/5.43 @ ( produc5882431272649516420nteger @ ( image_6316824473203919795nteger @ produc8508995932063986495nteger @ A2 )
% 9.17/5.43 @ ^ [Uu: code_integer] : ( image_6316824473203919795nteger @ produc6174133586879617921nteger @ A2 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7189_subset__fst__snd,axiom,
% 9.17/5.43 ! [A2: set_Pr958786334691620121nt_int] :
% 9.17/5.43 ( ord_le2843351958646193337nt_int @ A2
% 9.17/5.43 @ ( produc1453890548195736866nt_int @ ( image_5042161079198086560nt_int @ product_fst_int_int @ A2 )
% 9.17/5.43 @ ^ [Uu: int] : ( image_5042161079198086560nt_int @ product_snd_int_int @ A2 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7190_subset__fst__snd,axiom,
% 9.17/5.43 ! [A2: set_Pr2352657477744078772atural] :
% 9.17/5.43 ( ord_le2202040463148982292atural @ A2
% 9.17/5.43 @ ( produc6231535905537262655atural @ ( image_8194678751871465133atural @ produc497848011034438852atural @ A2 )
% 9.17/5.43 @ ^ [Uu: code_natural] : ( image_3837677093542026988atural @ produc6591912806276919810atural @ A2 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7191_int__transfer,axiom,
% 9.17/5.43 ( bNF_re6830278522597306478at_int
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.43 @ pcr_int
% 9.17/5.43 @ ^ [N4: nat] : ( product_Pair_nat_nat @ N4 @ zero_zero_nat )
% 9.17/5.43 @ semiri1314217659103216013at_int ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7192_uminus__int_Otransfer,axiom,
% 9.17/5.43 ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int
% 9.17/5.43 @ ( produc2626176000494625587at_nat
% 9.17/5.43 @ ^ [X3: nat,Y3: nat] : ( product_Pair_nat_nat @ Y3 @ X3 ) )
% 9.17/5.43 @ uminus_uminus_int ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7193_eq__fst__iff,axiom,
% 9.17/5.43 ! [A: produc6241069584506657477e_term > option6357759511663192854e_term,P4: produc1908205239877642774nteger] :
% 9.17/5.43 ( ( A
% 9.17/5.43 = ( produc7822682618958472924nteger @ P4 ) )
% 9.17/5.43 = ( ? [B4: produc8923325533196201883nteger] :
% 9.17/5.43 ( P4
% 9.17/5.43 = ( produc8603105652947943368nteger @ A @ B4 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7194_eq__fst__iff,axiom,
% 9.17/5.43 ! [A: produc3658429121746597890et_nat > $o,P4: produc3925858234332021118et_nat] :
% 9.17/5.43 ( ( A
% 9.17/5.43 = ( produc995936583742144908et_nat @ P4 ) )
% 9.17/5.43 = ( ? [B4: produc3658429121746597890et_nat] :
% 9.17/5.43 ( P4
% 9.17/5.43 = ( produc5001842942810119800et_nat @ A @ B4 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7195_eq__fst__iff,axiom,
% 9.17/5.43 ! [A: produc3658429121746597890et_nat > $o,P4: produc2732055786443039994et_nat] :
% 9.17/5.43 ( ( A
% 9.17/5.43 = ( produc180342877477747464et_nat @ P4 ) )
% 9.17/5.43 = ( ? [B4: produc3925858234332021118et_nat] :
% 9.17/5.43 ( P4
% 9.17/5.43 = ( produc2245416461498447860et_nat @ A @ B4 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7196_eq__fst__iff,axiom,
% 9.17/5.43 ! [A: produc8551481072490612790e_term > option6357759511663192854e_term,P4: produc2285326912895808259nt_int] :
% 9.17/5.43 ( ( A
% 9.17/5.43 = ( produc6816164490631068361nt_int @ P4 ) )
% 9.17/5.43 = ( ? [B4: product_prod_int_int] :
% 9.17/5.43 ( P4
% 9.17/5.43 = ( produc5700946648718959541nt_int @ A @ B4 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7197_eq__fst__iff,axiom,
% 9.17/5.43 ! [A: int > option6357759511663192854e_term,P4: produc7773217078559923341nt_int] :
% 9.17/5.43 ( ( A
% 9.17/5.43 = ( produc6230002227079971283nt_int @ P4 ) )
% 9.17/5.43 = ( ? [B4: product_prod_int_int] :
% 9.17/5.43 ( P4
% 9.17/5.43 = ( produc4305682042979456191nt_int @ A @ B4 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7198_eq__fst__iff,axiom,
% 9.17/5.43 ! [A: code_integer,P4: produc8923325533196201883nteger] :
% 9.17/5.43 ( ( A
% 9.17/5.43 = ( produc8508995932063986495nteger @ P4 ) )
% 9.17/5.43 = ( ? [B4: code_integer] :
% 9.17/5.43 ( P4
% 9.17/5.43 = ( produc1086072967326762835nteger @ A @ B4 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7199_eq__fst__iff,axiom,
% 9.17/5.43 ! [A: int,P4: product_prod_int_int] :
% 9.17/5.43 ( ( A
% 9.17/5.43 = ( product_fst_int_int @ P4 ) )
% 9.17/5.43 = ( ? [B4: int] :
% 9.17/5.43 ( P4
% 9.17/5.43 = ( product_Pair_int_int @ A @ B4 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7200_transfer__rule__of__nat,axiom,
% 9.17/5.43 ! [R4: rat > rat > $o] :
% 9.17/5.43 ( ( R4 @ zero_zero_rat @ zero_zero_rat )
% 9.17/5.43 => ( ( R4 @ one_one_rat @ one_one_rat )
% 9.17/5.43 => ( ( bNF_re6603079268895015599at_rat @ R4 @ ( bNF_re5606270390558447553at_rat @ R4 @ R4 ) @ plus_plus_rat @ plus_plus_rat )
% 9.17/5.43 => ( bNF_re4702136315717946289at_rat
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.43 @ R4
% 9.17/5.43 @ semiri681578069525770553at_rat
% 9.17/5.43 @ semiri681578069525770553at_rat ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7201_transfer__rule__of__nat,axiom,
% 9.17/5.43 ! [R4: rat > int > $o] :
% 9.17/5.43 ( ( R4 @ zero_zero_rat @ zero_zero_int )
% 9.17/5.43 => ( ( R4 @ one_one_rat @ one_one_int )
% 9.17/5.43 => ( ( bNF_re8876735282041863595nt_int @ R4 @ ( bNF_re5838490730811218025at_int @ R4 @ R4 ) @ plus_plus_rat @ plus_plus_int )
% 9.17/5.43 => ( bNF_re5334775905295391749at_int
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.43 @ R4
% 9.17/5.43 @ semiri681578069525770553at_rat
% 9.17/5.43 @ semiri1314217659103216013at_int ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7202_transfer__rule__of__nat,axiom,
% 9.17/5.43 ! [R4: rat > nat > $o] :
% 9.17/5.43 ( ( R4 @ zero_zero_rat @ zero_zero_nat )
% 9.17/5.43 => ( ( R4 @ one_one_rat @ one_one_nat )
% 9.17/5.43 => ( ( bNF_re4357912360536923287at_nat @ R4 @ ( bNF_re5469327641083423665at_nat @ R4 @ R4 ) @ plus_plus_rat @ plus_plus_nat )
% 9.17/5.43 => ( bNF_re5337266375804442025at_nat
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.43 @ R4
% 9.17/5.43 @ semiri681578069525770553at_rat
% 9.17/5.43 @ semiri1316708129612266289at_nat ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7203_transfer__rule__of__nat,axiom,
% 9.17/5.43 ! [R4: rat > code_integer > $o] :
% 9.17/5.43 ( ( R4 @ zero_zero_rat @ zero_z3403309356797280102nteger )
% 9.17/5.43 => ( ( R4 @ one_one_rat @ one_one_Code_integer )
% 9.17/5.43 => ( ( bNF_re4307939118855507134nteger @ R4 @ ( bNF_re2328245411608324299nteger @ R4 @ R4 ) @ plus_plus_rat @ plus_p5714425477246183910nteger )
% 9.17/5.43 => ( bNF_re4553819317763231286nteger
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.43 @ R4
% 9.17/5.43 @ semiri681578069525770553at_rat
% 9.17/5.43 @ semiri4939895301339042750nteger ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7204_transfer__rule__of__nat,axiom,
% 9.17/5.43 ! [R4: rat > code_natural > $o] :
% 9.17/5.43 ( ( R4 @ zero_zero_rat @ zero_z2226904508553997617atural )
% 9.17/5.43 => ( ( R4 @ one_one_rat @ one_one_Code_natural )
% 9.17/5.43 => ( ( bNF_re6252345487650389919atural @ R4 @ ( bNF_re4433268865704509537atural @ R4 @ R4 ) @ plus_plus_rat @ plus_p4538020629002901425atural )
% 9.17/5.43 => ( bNF_re3377414469519948801atural
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.43 @ R4
% 9.17/5.43 @ semiri681578069525770553at_rat
% 9.17/5.43 @ semiri3763490453095760265atural ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7205_transfer__rule__of__nat,axiom,
% 9.17/5.43 ! [R4: int > rat > $o] :
% 9.17/5.43 ( ( R4 @ zero_zero_int @ zero_zero_rat )
% 9.17/5.43 => ( ( R4 @ one_one_int @ one_one_rat )
% 9.17/5.43 => ( ( bNF_re7661208983170134443at_rat @ R4 @ ( bNF_re4480299549022435433nt_rat @ R4 @ R4 ) @ plus_plus_int @ plus_plus_rat )
% 9.17/5.43 => ( bNF_re6018044671553866757nt_rat
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.43 @ R4
% 9.17/5.43 @ semiri1314217659103216013at_int
% 9.17/5.43 @ semiri681578069525770553at_rat ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7206_transfer__rule__of__nat,axiom,
% 9.17/5.43 ! [R4: int > int > $o] :
% 9.17/5.43 ( ( R4 @ zero_zero_int @ zero_zero_int )
% 9.17/5.43 => ( ( R4 @ one_one_int @ one_one_int )
% 9.17/5.43 => ( ( bNF_re711492959462206631nt_int @ R4 @ ( bNF_re4712519889275205905nt_int @ R4 @ R4 ) @ plus_plus_int @ plus_plus_int )
% 9.17/5.43 => ( bNF_re6650684261131312217nt_int
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.43 @ R4
% 9.17/5.43 @ semiri1314217659103216013at_int
% 9.17/5.43 @ semiri1314217659103216013at_int ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7207_transfer__rule__of__nat,axiom,
% 9.17/5.43 ! [R4: int > nat > $o] :
% 9.17/5.43 ( ( R4 @ zero_zero_int @ zero_zero_nat )
% 9.17/5.43 => ( ( R4 @ one_one_int @ one_one_nat )
% 9.17/5.43 => ( ( bNF_re5416042074812042131at_nat @ R4 @ ( bNF_re4343356799547411545nt_nat @ R4 @ R4 ) @ plus_plus_int @ plus_plus_nat )
% 9.17/5.43 => ( bNF_re6653174731640362493nt_nat
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.43 @ R4
% 9.17/5.43 @ semiri1314217659103216013at_int
% 9.17/5.43 @ semiri1316708129612266289at_nat ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7208_transfer__rule__of__nat,axiom,
% 9.17/5.43 ! [R4: int > code_integer > $o] :
% 9.17/5.43 ( ( R4 @ zero_zero_int @ zero_z3403309356797280102nteger )
% 9.17/5.43 => ( ( R4 @ one_one_int @ one_one_Code_integer )
% 9.17/5.43 => ( ( bNF_re398004352372739002nteger @ R4 @ ( bNF_re3379532845092657523nteger @ R4 @ R4 ) @ plus_plus_int @ plus_p5714425477246183910nteger )
% 9.17/5.43 => ( bNF_re4153400068438556298nteger
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.43 @ R4
% 9.17/5.43 @ semiri1314217659103216013at_int
% 9.17/5.43 @ semiri4939895301339042750nteger ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7209_transfer__rule__of__nat,axiom,
% 9.17/5.43 ! [R4: int > code_natural > $o] :
% 9.17/5.43 ( ( R4 @ zero_zero_int @ zero_z2226904508553997617atural )
% 9.17/5.43 => ( ( R4 @ one_one_int @ one_one_Code_natural )
% 9.17/5.43 => ( ( bNF_re2342410721167621787atural @ R4 @ ( bNF_re5484556299188842761atural @ R4 @ R4 ) @ plus_plus_int @ plus_p4538020629002901425atural )
% 9.17/5.43 => ( bNF_re2976995220195273813atural
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.43 @ R4
% 9.17/5.43 @ semiri1314217659103216013at_int
% 9.17/5.43 @ semiri3763490453095760265atural ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7210_transfer__rule__of__bool,axiom,
% 9.17/5.43 ! [R4: rat > rat > $o] :
% 9.17/5.43 ( ( R4 @ zero_zero_rat @ zero_zero_rat )
% 9.17/5.43 => ( ( R4 @ one_one_rat @ one_one_rat )
% 9.17/5.43 => ( bNF_re8824113547921424783at_rat
% 9.17/5.43 @ ^ [Y4: $o,Z2: $o] : ( Y4 = Z2 )
% 9.17/5.43 @ R4
% 9.17/5.43 @ zero_n2052037380579107095ol_rat
% 9.17/5.43 @ zero_n2052037380579107095ol_rat ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7211_transfer__rule__of__bool,axiom,
% 9.17/5.43 ! [R4: rat > nat > $o] :
% 9.17/5.43 ( ( R4 @ zero_zero_rat @ zero_zero_nat )
% 9.17/5.43 => ( ( R4 @ one_one_rat @ one_one_nat )
% 9.17/5.43 => ( bNF_re235871571153144711at_nat
% 9.17/5.43 @ ^ [Y4: $o,Z2: $o] : ( Y4 = Z2 )
% 9.17/5.43 @ R4
% 9.17/5.43 @ zero_n2052037380579107095ol_rat
% 9.17/5.43 @ zero_n2687167440665602831ol_nat ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7212_transfer__rule__of__bool,axiom,
% 9.17/5.43 ! [R4: rat > int > $o] :
% 9.17/5.43 ( ( R4 @ zero_zero_rat @ zero_zero_int )
% 9.17/5.43 => ( ( R4 @ one_one_rat @ one_one_int )
% 9.17/5.43 => ( bNF_re233381100644094435at_int
% 9.17/5.43 @ ^ [Y4: $o,Z2: $o] : ( Y4 = Z2 )
% 9.17/5.43 @ R4
% 9.17/5.43 @ zero_n2052037380579107095ol_rat
% 9.17/5.43 @ zero_n2684676970156552555ol_int ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7213_transfer__rule__of__bool,axiom,
% 9.17/5.43 ! [R4: rat > code_integer > $o] :
% 9.17/5.43 ( ( R4 @ zero_zero_rat @ zero_z3403309356797280102nteger )
% 9.17/5.43 => ( ( R4 @ one_one_rat @ one_one_Code_integer )
% 9.17/5.43 => ( bNF_re5635613845597506580nteger
% 9.17/5.43 @ ^ [Y4: $o,Z2: $o] : ( Y4 = Z2 )
% 9.17/5.43 @ R4
% 9.17/5.43 @ zero_n2052037380579107095ol_rat
% 9.17/5.43 @ zero_n356916108424825756nteger ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7214_transfer__rule__of__bool,axiom,
% 9.17/5.43 ! [R4: nat > rat > $o] :
% 9.17/5.43 ( ( R4 @ zero_zero_nat @ zero_zero_rat )
% 9.17/5.43 => ( ( R4 @ one_one_nat @ one_one_rat )
% 9.17/5.43 => ( bNF_re9140668191856290695at_rat
% 9.17/5.43 @ ^ [Y4: $o,Z2: $o] : ( Y4 = Z2 )
% 9.17/5.43 @ R4
% 9.17/5.43 @ zero_n2687167440665602831ol_nat
% 9.17/5.43 @ zero_n2052037380579107095ol_rat ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7215_transfer__rule__of__bool,axiom,
% 9.17/5.43 ! [R4: nat > nat > $o] :
% 9.17/5.43 ( ( R4 @ zero_zero_nat @ zero_zero_nat )
% 9.17/5.43 => ( ( R4 @ one_one_nat @ one_one_nat )
% 9.17/5.43 => ( bNF_re552426215088010623at_nat
% 9.17/5.43 @ ^ [Y4: $o,Z2: $o] : ( Y4 = Z2 )
% 9.17/5.43 @ R4
% 9.17/5.43 @ zero_n2687167440665602831ol_nat
% 9.17/5.43 @ zero_n2687167440665602831ol_nat ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7216_transfer__rule__of__bool,axiom,
% 9.17/5.43 ! [R4: nat > int > $o] :
% 9.17/5.43 ( ( R4 @ zero_zero_nat @ zero_zero_int )
% 9.17/5.43 => ( ( R4 @ one_one_nat @ one_one_int )
% 9.17/5.43 => ( bNF_re549935744578960347at_int
% 9.17/5.43 @ ^ [Y4: $o,Z2: $o] : ( Y4 = Z2 )
% 9.17/5.43 @ R4
% 9.17/5.43 @ zero_n2687167440665602831ol_nat
% 9.17/5.43 @ zero_n2684676970156552555ol_int ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7217_transfer__rule__of__bool,axiom,
% 9.17/5.43 ! [R4: nat > code_integer > $o] :
% 9.17/5.43 ( ( R4 @ zero_zero_nat @ zero_z3403309356797280102nteger )
% 9.17/5.43 => ( ( R4 @ one_one_nat @ one_one_Code_integer )
% 9.17/5.43 => ( bNF_re4863541036035986956nteger
% 9.17/5.43 @ ^ [Y4: $o,Z2: $o] : ( Y4 = Z2 )
% 9.17/5.43 @ R4
% 9.17/5.43 @ zero_n2687167440665602831ol_nat
% 9.17/5.43 @ zero_n356916108424825756nteger ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7218_transfer__rule__of__bool,axiom,
% 9.17/5.43 ! [R4: int > rat > $o] :
% 9.17/5.43 ( ( R4 @ zero_zero_int @ zero_zero_rat )
% 9.17/5.43 => ( ( R4 @ one_one_int @ one_one_rat )
% 9.17/5.43 => ( bNF_re916649866902569443nt_rat
% 9.17/5.43 @ ^ [Y4: $o,Z2: $o] : ( Y4 = Z2 )
% 9.17/5.43 @ R4
% 9.17/5.43 @ zero_n2684676970156552555ol_int
% 9.17/5.43 @ zero_n2052037380579107095ol_rat ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7219_transfer__rule__of__bool,axiom,
% 9.17/5.43 ! [R4: int > nat > $o] :
% 9.17/5.43 ( ( R4 @ zero_zero_int @ zero_zero_nat )
% 9.17/5.43 => ( ( R4 @ one_one_int @ one_one_nat )
% 9.17/5.43 => ( bNF_re1551779926989065179nt_nat
% 9.17/5.43 @ ^ [Y4: $o,Z2: $o] : ( Y4 = Z2 )
% 9.17/5.43 @ R4
% 9.17/5.43 @ zero_n2684676970156552555ol_int
% 9.17/5.43 @ zero_n2687167440665602831ol_nat ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7220_plus__rat_Otransfer,axiom,
% 9.17/5.43 ( bNF_re7627151682743391978at_rat @ pcr_rat @ ( bNF_re8279943556446156061nt_rat @ pcr_rat @ pcr_rat )
% 9.17/5.43 @ ^ [X3: product_prod_int_int,Y3: product_prod_int_int] : ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ X3 ) @ ( product_snd_int_int @ Y3 ) ) @ ( times_times_int @ ( product_fst_int_int @ Y3 ) @ ( product_snd_int_int @ X3 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ X3 ) @ ( product_snd_int_int @ Y3 ) ) )
% 9.17/5.43 @ plus_plus_rat ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7221_inverse__rat_Otransfer,axiom,
% 9.17/5.43 ( bNF_re8279943556446156061nt_rat @ pcr_rat @ pcr_rat
% 9.17/5.43 @ ^ [X3: product_prod_int_int] :
% 9.17/5.43 ( if_Pro3027730157355071871nt_int
% 9.17/5.43 @ ( ( product_fst_int_int @ X3 )
% 9.17/5.43 = zero_zero_int )
% 9.17/5.43 @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 9.17/5.43 @ ( product_Pair_int_int @ ( product_snd_int_int @ X3 ) @ ( product_fst_int_int @ X3 ) ) )
% 9.17/5.43 @ inverse_inverse_rat ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7222_Id__on__def,axiom,
% 9.17/5.43 ( id_on_6713504163309144702at_nat
% 9.17/5.43 = ( ^ [A7: set_se7855581050983116737at_nat] :
% 9.17/5.43 ( comple4364388969068068532at_nat
% 9.17/5.43 @ ( image_6898982319499645995at_nat
% 9.17/5.43 @ ^ [X3: set_Pr1261947904930325089at_nat] : ( insert9069300056098147895at_nat @ ( produc2922128104949294807at_nat @ X3 @ X3 ) @ bot_bo228742789529271731at_nat )
% 9.17/5.43 @ A7 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7223_Id__on__def,axiom,
% 9.17/5.43 ( id_on_nat
% 9.17/5.43 = ( ^ [A7: set_nat] :
% 9.17/5.43 ( comple5685304695842803022at_nat
% 9.17/5.43 @ ( image_7178329752028323786at_nat
% 9.17/5.43 @ ^ [X3: nat] : ( insert8211810215607154385at_nat @ ( product_Pair_nat_nat @ X3 @ X3 ) @ bot_bo2099793752762293965at_nat )
% 9.17/5.43 @ A7 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7224_times__rat_Otransfer,axiom,
% 9.17/5.43 ( bNF_re7627151682743391978at_rat @ pcr_rat @ ( bNF_re8279943556446156061nt_rat @ pcr_rat @ pcr_rat )
% 9.17/5.43 @ ^ [X3: product_prod_int_int,Y3: product_prod_int_int] : ( product_Pair_int_int @ ( times_times_int @ ( product_fst_int_int @ X3 ) @ ( product_fst_int_int @ Y3 ) ) @ ( times_times_int @ ( product_snd_int_int @ X3 ) @ ( product_snd_int_int @ Y3 ) ) )
% 9.17/5.43 @ times_times_rat ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7225_gcd__1__nat,axiom,
% 9.17/5.43 ! [M2: nat] :
% 9.17/5.43 ( ( gcd_gcd_nat @ M2 @ one_one_nat )
% 9.17/5.43 = one_one_nat ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7226_Id__onI,axiom,
% 9.17/5.43 ! [A: set_Pr1261947904930325089at_nat,A2: set_se7855581050983116737at_nat] :
% 9.17/5.43 ( ( member2643936169264416010at_nat @ A @ A2 )
% 9.17/5.43 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ A ) @ ( id_on_6713504163309144702at_nat @ A2 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7227_Id__onI,axiom,
% 9.17/5.43 ! [A: produc3843707927480180839at_nat,A2: set_Pr4329608150637261639at_nat] :
% 9.17/5.43 ( ( member8757157785044589968at_nat @ A @ A2 )
% 9.17/5.43 => ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ A @ A ) @ ( id_on_7869290023980668164at_nat @ A2 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7228_Id__onI,axiom,
% 9.17/5.43 ! [A: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat] :
% 9.17/5.43 ( ( member8440522571783428010at_nat @ A @ A2 )
% 9.17/5.43 => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ A @ A ) @ ( id_on_2554058798563519774at_nat @ A2 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7229_Id__onI,axiom,
% 9.17/5.43 ! [A: $o,A2: set_o] :
% 9.17/5.43 ( ( member_o @ A @ A2 )
% 9.17/5.43 => ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ A @ A ) @ ( id_on_o @ A2 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7230_Id__onI,axiom,
% 9.17/5.43 ! [A: nat,A2: set_nat] :
% 9.17/5.43 ( ( member_nat @ A @ A2 )
% 9.17/5.43 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ A ) @ ( id_on_nat @ A2 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7231_Id__onI,axiom,
% 9.17/5.43 ! [A: int,A2: set_int] :
% 9.17/5.43 ( ( member_int @ A @ A2 )
% 9.17/5.43 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ A ) @ ( id_on_int @ A2 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7232_unset__bit__natural_Orsp,axiom,
% 9.17/5.43 ( bNF_re1345281282404953727at_nat
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.43 @ ( bNF_re5653821019739307937at_nat
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 ) )
% 9.17/5.43 @ bit_se4205575877204974255it_nat
% 9.17/5.43 @ bit_se4205575877204974255it_nat ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7233_take__bit__natural_Orsp,axiom,
% 9.17/5.43 ( bNF_re1345281282404953727at_nat
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.43 @ ( bNF_re5653821019739307937at_nat
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 ) )
% 9.17/5.43 @ bit_se2925701944663578781it_nat
% 9.17/5.43 @ bit_se2925701944663578781it_nat ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7234_bit__natural_Orsp,axiom,
% 9.17/5.43 ( bNF_re578469030762574527_nat_o
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.43 @ ^ [Y4: nat > $o,Z2: nat > $o] : ( Y4 = Z2 )
% 9.17/5.43 @ bit_se1148574629649215175it_nat
% 9.17/5.43 @ bit_se1148574629649215175it_nat ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7235_drop__bit__natural_Orsp,axiom,
% 9.17/5.43 ( bNF_re1345281282404953727at_nat
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.43 @ ( bNF_re5653821019739307937at_nat
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 ) )
% 9.17/5.43 @ bit_se8570568707652914677it_nat
% 9.17/5.43 @ bit_se8570568707652914677it_nat ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7236_Id__on__iff,axiom,
% 9.17/5.43 ! [X: produc3843707927480180839at_nat,Y: produc3843707927480180839at_nat,A2: set_Pr4329608150637261639at_nat] :
% 9.17/5.43 ( ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ X @ Y ) @ ( id_on_7869290023980668164at_nat @ A2 ) )
% 9.17/5.43 = ( ( X = Y )
% 9.17/5.43 & ( member8757157785044589968at_nat @ X @ A2 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7237_Id__on__iff,axiom,
% 9.17/5.43 ! [X: product_prod_nat_nat,Y: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat] :
% 9.17/5.43 ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X @ Y ) @ ( id_on_2554058798563519774at_nat @ A2 ) )
% 9.17/5.43 = ( ( X = Y )
% 9.17/5.43 & ( member8440522571783428010at_nat @ X @ A2 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7238_Id__on__iff,axiom,
% 9.17/5.43 ! [X: $o,Y: $o,A2: set_o] :
% 9.17/5.43 ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ X @ Y ) @ ( id_on_o @ A2 ) )
% 9.17/5.43 = ( ( X = Y )
% 9.17/5.43 & ( member_o @ X @ A2 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7239_Id__on__iff,axiom,
% 9.17/5.43 ! [X: int,Y: int,A2: set_int] :
% 9.17/5.43 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( id_on_int @ A2 ) )
% 9.17/5.43 = ( ( X = Y )
% 9.17/5.43 & ( member_int @ X @ A2 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7240_Id__on__iff,axiom,
% 9.17/5.43 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,A2: set_se7855581050983116737at_nat] :
% 9.17/5.43 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ ( id_on_6713504163309144702at_nat @ A2 ) )
% 9.17/5.43 = ( ( X = Y )
% 9.17/5.43 & ( member2643936169264416010at_nat @ X @ A2 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7241_Id__on__iff,axiom,
% 9.17/5.43 ! [X: nat,Y: nat,A2: set_nat] :
% 9.17/5.43 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( id_on_nat @ A2 ) )
% 9.17/5.43 = ( ( X = Y )
% 9.17/5.43 & ( member_nat @ X @ A2 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7242_Id__on__eqI,axiom,
% 9.17/5.43 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,A2: set_se7855581050983116737at_nat] :
% 9.17/5.43 ( ( A = B )
% 9.17/5.43 => ( ( member2643936169264416010at_nat @ A @ A2 )
% 9.17/5.43 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ B ) @ ( id_on_6713504163309144702at_nat @ A2 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7243_Id__on__eqI,axiom,
% 9.17/5.43 ! [A: produc3843707927480180839at_nat,B: produc3843707927480180839at_nat,A2: set_Pr4329608150637261639at_nat] :
% 9.17/5.43 ( ( A = B )
% 9.17/5.43 => ( ( member8757157785044589968at_nat @ A @ A2 )
% 9.17/5.43 => ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ A @ B ) @ ( id_on_7869290023980668164at_nat @ A2 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7244_Id__on__eqI,axiom,
% 9.17/5.43 ! [A: product_prod_nat_nat,B: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat] :
% 9.17/5.43 ( ( A = B )
% 9.17/5.43 => ( ( member8440522571783428010at_nat @ A @ A2 )
% 9.17/5.43 => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ A @ B ) @ ( id_on_2554058798563519774at_nat @ A2 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7245_Id__on__eqI,axiom,
% 9.17/5.43 ! [A: $o,B: $o,A2: set_o] :
% 9.17/5.43 ( ( A = B )
% 9.17/5.43 => ( ( member_o @ A @ A2 )
% 9.17/5.43 => ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ A @ B ) @ ( id_on_o @ A2 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7246_Id__on__eqI,axiom,
% 9.17/5.43 ! [A: nat,B: nat,A2: set_nat] :
% 9.17/5.43 ( ( A = B )
% 9.17/5.43 => ( ( member_nat @ A @ A2 )
% 9.17/5.43 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ ( id_on_nat @ A2 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7247_Id__on__eqI,axiom,
% 9.17/5.43 ! [A: int,B: int,A2: set_int] :
% 9.17/5.43 ( ( A = B )
% 9.17/5.43 => ( ( member_int @ A @ A2 )
% 9.17/5.43 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ ( id_on_int @ A2 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7248_Id__onE,axiom,
% 9.17/5.43 ! [C: produc1906917888121415911at_nat,A2: set_Pr4329608150637261639at_nat] :
% 9.17/5.43 ( ( member6009668390874684176at_nat @ C @ ( id_on_7869290023980668164at_nat @ A2 ) )
% 9.17/5.43 => ~ ! [X4: produc3843707927480180839at_nat] :
% 9.17/5.43 ( ( member8757157785044589968at_nat @ X4 @ A2 )
% 9.17/5.43 => ( C
% 9.17/5.43 != ( produc2335810615602371415at_nat @ X4 @ X4 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7249_Id__onE,axiom,
% 9.17/5.43 ! [C: produc859450856879609959at_nat,A2: set_Pr1261947904930325089at_nat] :
% 9.17/5.43 ( ( member8206827879206165904at_nat @ C @ ( id_on_2554058798563519774at_nat @ A2 ) )
% 9.17/5.43 => ~ ! [X4: product_prod_nat_nat] :
% 9.17/5.43 ( ( member8440522571783428010at_nat @ X4 @ A2 )
% 9.17/5.43 => ( C
% 9.17/5.43 != ( produc6161850002892822231at_nat @ X4 @ X4 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7250_Id__onE,axiom,
% 9.17/5.43 ! [C: product_prod_o_o,A2: set_o] :
% 9.17/5.43 ( ( member7466972457876170832od_o_o @ C @ ( id_on_o @ A2 ) )
% 9.17/5.43 => ~ ! [X4: $o] :
% 9.17/5.43 ( ( member_o @ X4 @ A2 )
% 9.17/5.43 => ( C
% 9.17/5.43 != ( product_Pair_o_o @ X4 @ X4 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7251_Id__onE,axiom,
% 9.17/5.43 ! [C: product_prod_int_int,A2: set_int] :
% 9.17/5.43 ( ( member5262025264175285858nt_int @ C @ ( id_on_int @ A2 ) )
% 9.17/5.43 => ~ ! [X4: int] :
% 9.17/5.43 ( ( member_int @ X4 @ A2 )
% 9.17/5.43 => ( C
% 9.17/5.43 != ( product_Pair_int_int @ X4 @ X4 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7252_Id__onE,axiom,
% 9.17/5.43 ! [C: produc3843707927480180839at_nat,A2: set_se7855581050983116737at_nat] :
% 9.17/5.43 ( ( member8757157785044589968at_nat @ C @ ( id_on_6713504163309144702at_nat @ A2 ) )
% 9.17/5.43 => ~ ! [X4: set_Pr1261947904930325089at_nat] :
% 9.17/5.43 ( ( member2643936169264416010at_nat @ X4 @ A2 )
% 9.17/5.43 => ( C
% 9.17/5.43 != ( produc2922128104949294807at_nat @ X4 @ X4 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7253_Id__onE,axiom,
% 9.17/5.43 ! [C: product_prod_nat_nat,A2: set_nat] :
% 9.17/5.43 ( ( member8440522571783428010at_nat @ C @ ( id_on_nat @ A2 ) )
% 9.17/5.43 => ~ ! [X4: nat] :
% 9.17/5.43 ( ( member_nat @ X4 @ A2 )
% 9.17/5.43 => ( C
% 9.17/5.43 != ( product_Pair_nat_nat @ X4 @ X4 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7254_bezout__nat,axiom,
% 9.17/5.43 ! [A: nat,B: nat] :
% 9.17/5.43 ( ( A != zero_zero_nat )
% 9.17/5.43 => ? [X4: nat,Y5: nat] :
% 9.17/5.43 ( ( times_times_nat @ A @ X4 )
% 9.17/5.43 = ( plus_plus_nat @ ( times_times_nat @ B @ Y5 ) @ ( gcd_gcd_nat @ A @ B ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7255_one__rat_Otransfer,axiom,
% 9.17/5.43 pcr_rat @ ( product_Pair_int_int @ one_one_int @ one_one_int ) @ one_one_rat ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7256_zero__rat_Otransfer,axiom,
% 9.17/5.43 pcr_rat @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ zero_zero_rat ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7257_bezw__aux,axiom,
% 9.17/5.43 ! [X: nat,Y: nat] :
% 9.17/5.43 ( ( semiri1314217659103216013at_int @ ( gcd_gcd_nat @ X @ Y ) )
% 9.17/5.43 = ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ ( bezw @ X @ Y ) ) @ ( semiri1314217659103216013at_int @ X ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ X @ Y ) ) @ ( semiri1314217659103216013at_int @ Y ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7258_uminus__rat_Otransfer,axiom,
% 9.17/5.43 ( bNF_re8279943556446156061nt_rat @ pcr_rat @ pcr_rat
% 9.17/5.43 @ ^ [X3: product_prod_int_int] : ( product_Pair_int_int @ ( uminus_uminus_int @ ( product_fst_int_int @ X3 ) ) @ ( product_snd_int_int @ X3 ) )
% 9.17/5.43 @ uminus_uminus_rat ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7259_gcd__nat_Opelims,axiom,
% 9.17/5.43 ! [X: nat,Xa: nat,Y: nat] :
% 9.17/5.43 ( ( ( gcd_gcd_nat @ X @ Xa )
% 9.17/5.43 = Y )
% 9.17/5.43 => ( ( accp_P4275260045618599050at_nat @ gcd_nat_rel @ ( product_Pair_nat_nat @ X @ Xa ) )
% 9.17/5.43 => ~ ( ( ( ( Xa = zero_zero_nat )
% 9.17/5.43 => ( Y = X ) )
% 9.17/5.43 & ( ( Xa != zero_zero_nat )
% 9.17/5.43 => ( Y
% 9.17/5.43 = ( gcd_gcd_nat @ Xa @ ( modulo_modulo_nat @ X @ Xa ) ) ) ) )
% 9.17/5.43 => ~ ( accp_P4275260045618599050at_nat @ gcd_nat_rel @ ( product_Pair_nat_nat @ X @ Xa ) ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7260_o__rsp_I1_J,axiom,
% 9.17/5.43 ! [R23: code_integer > code_integer > $o,R32: code_integer > code_integer > $o,R12: num > num > $o] : ( bNF_re5979881370344185769nteger @ ( bNF_re1062419521925302741nteger @ R23 @ R32 ) @ ( bNF_re6097285183634142137nteger @ ( bNF_re6741283560065411407nteger @ R12 @ R23 ) @ ( bNF_re6741283560065411407nteger @ R12 @ R32 ) ) @ comp_C3531382070062128313er_num @ comp_C3531382070062128313er_num ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7261_o__rsp_I1_J,axiom,
% 9.17/5.43 ! [R23: code_integer > nat > $o,R32: code_integer > num > $o,R12: num > int > $o] : ( bNF_re5469402333911078061nt_num @ ( bNF_re1758498617148825349er_num @ R23 @ R32 ) @ ( bNF_re1151383970801924621nt_num @ ( bNF_re6324211044263125204er_nat @ R12 @ R23 ) @ ( bNF_re2881542830418903838er_num @ R12 @ R32 ) ) @ comp_C3531382070062128313er_num @ comp_nat_num_int ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7262_o__rsp_I1_J,axiom,
% 9.17/5.43 ! [R23: nat > code_integer > $o,R32: num > code_integer > $o,R12: int > num > $o] : ( bNF_re2163612987331707565nteger @ ( bNF_re8763372240999575301nteger @ R23 @ R32 ) @ ( bNF_re8894579221946749965nteger @ ( bNF_re151304249936775380nteger @ R12 @ R23 ) @ ( bNF_re7315484114762210078nteger @ R12 @ R32 ) ) @ comp_nat_num_int @ comp_C3531382070062128313er_num ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7263_o__rsp_I1_J,axiom,
% 9.17/5.43 ! [R23: nat > nat > $o,R32: num > num > $o,R12: int > int > $o] : ( bNF_re3846787885862361009nt_num @ ( bNF_re341483209202555957um_num @ R23 @ R32 ) @ ( bNF_re9099949428469764705nt_num @ ( bNF_re3715656647883201625at_nat @ R12 @ R23 ) @ ( bNF_re7626690874201225453um_num @ R12 @ R32 ) ) @ comp_nat_num_int @ comp_nat_num_int ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7264_o__rsp_I1_J,axiom,
% 9.17/5.43 ! [R23: int > int > $o,R32: ( nat > $o ) > ( nat > $o ) > $o,R12: int > int > $o] : ( bNF_re7908124382625962333_nat_o @ ( bNF_re3376528473927230327_nat_o @ R23 @ R32 ) @ ( bNF_re6033114333830760525_nat_o @ ( bNF_re4712519889275205905nt_int @ R12 @ R23 ) @ ( bNF_re3376528473927230327_nat_o @ R12 @ R32 ) ) @ comp_int_nat_o_int @ comp_int_nat_o_int ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7265_o__rsp_I1_J,axiom,
% 9.17/5.43 ! [R23: int > int > $o,R32: ( int > $o ) > ( int > $o ) > $o,R12: int > int > $o] : ( bNF_re1900612664124570461_int_o @ ( bNF_re3403563459893282935_int_o @ R23 @ R32 ) @ ( bNF_re3014639844587090765_int_o @ ( bNF_re4712519889275205905nt_int @ R12 @ R23 ) @ ( bNF_re3403563459893282935_int_o @ R12 @ R32 ) ) @ comp_int_int_o_int @ comp_int_int_o_int ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7266_o__rsp_I1_J,axiom,
% 9.17/5.43 ! [R23: int > int > $o,R32: ( int > int ) > ( int > int ) > $o,R12: int > int > $o] : ( bNF_re4984751527058004117nt_int @ ( bNF_re711492959462206631nt_int @ R23 @ R32 ) @ ( bNF_re724639330072410579nt_int @ ( bNF_re4712519889275205905nt_int @ R12 @ R23 ) @ ( bNF_re711492959462206631nt_int @ R12 @ R32 ) ) @ comp_int_int_int_int @ comp_int_int_int_int ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7267_o__rsp_I1_J,axiom,
% 9.17/5.43 ! [R23: code_integer > code_integer > $o,R32: code_integer > ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > $o,R12: num > code_integer > $o] : ( bNF_re8134695817916415679nteger @ ( bNF_re3370092614548195229nteger @ R23 @ R32 ) @ ( bNF_re2439920061672227847nteger @ ( bNF_re5202476307641864082nteger @ R12 @ R23 ) @ ( bNF_re5031869190687302234nteger @ R12 @ R32 ) ) @ comp_C3531382070062128313er_num @ comp_C1593894019821074884nteger ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7268_o__rsp_I1_J,axiom,
% 9.17/5.43 ! [R23: code_integer > code_integer > $o,R32: ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > code_integer > $o,R12: code_integer > num > $o] : ( bNF_re4919612610145136063nteger @ ( bNF_re4341081746073172381nteger @ R23 @ R32 ) @ ( bNF_re6724329528997265415nteger @ ( bNF_re7350422212947406738nteger @ R12 @ R23 ) @ ( bNF_re166502229267952730nteger @ R12 @ R32 ) ) @ comp_C1593894019821074884nteger @ comp_C3531382070062128313er_num ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7269_o__rsp_I1_J,axiom,
% 9.17/5.43 ! [R23: code_integer > nat > $o,R32: ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > num > $o,R12: code_integer > int > $o] : ( bNF_re1890273300020150979nt_num @ ( bNF_re7119966052990372301er_num @ R23 @ R32 ) @ ( bNF_re5190287125156074331nt_num @ ( bNF_re2891348898900095767er_nat @ R12 @ R23 ) @ ( bNF_re8127238762813979689er_num @ R12 @ R32 ) ) @ comp_C1593894019821074884nteger @ comp_nat_num_int ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7270_o__rsp_I2_J,axiom,
% 9.17/5.43 ! [R12: num > num > $o] :
% 9.17/5.43 ( bNF_re5979881370344185769nteger
% 9.17/5.43 @ ^ [Y4: code_integer > code_integer,Z2: code_integer > code_integer] : ( Y4 = Z2 )
% 9.17/5.43 @ ( bNF_re6097285183634142137nteger
% 9.17/5.43 @ ( bNF_re6741283560065411407nteger @ R12
% 9.17/5.43 @ ^ [Y4: code_integer,Z2: code_integer] : ( Y4 = Z2 ) )
% 9.17/5.43 @ ( bNF_re6741283560065411407nteger @ R12
% 9.17/5.43 @ ^ [Y4: code_integer,Z2: code_integer] : ( Y4 = Z2 ) ) )
% 9.17/5.43 @ comp_C3531382070062128313er_num
% 9.17/5.43 @ comp_C3531382070062128313er_num ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7271_o__rsp_I2_J,axiom,
% 9.17/5.43 ! [R12: int > int > $o] :
% 9.17/5.43 ( bNF_re3846787885862361009nt_num
% 9.17/5.43 @ ^ [Y4: nat > num,Z2: nat > num] : ( Y4 = Z2 )
% 9.17/5.43 @ ( bNF_re9099949428469764705nt_num
% 9.17/5.43 @ ( bNF_re3715656647883201625at_nat @ R12
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 ) )
% 9.17/5.43 @ ( bNF_re7626690874201225453um_num @ R12
% 9.17/5.43 @ ^ [Y4: num,Z2: num] : ( Y4 = Z2 ) ) )
% 9.17/5.43 @ comp_nat_num_int
% 9.17/5.43 @ comp_nat_num_int ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7272_o__rsp_I2_J,axiom,
% 9.17/5.43 ! [R12: int > int > $o] :
% 9.17/5.43 ( bNF_re1550856938216548981_nat_o
% 9.17/5.43 @ ^ [Y4: ( nat > $o ) > nat > $o,Z2: ( nat > $o ) > nat > $o] : ( Y4 = Z2 )
% 9.17/5.43 @ ( bNF_re5673586069474677853_nat_o
% 9.17/5.43 @ ( bNF_re3376528473927230327_nat_o @ R12
% 9.17/5.43 @ ^ [Y4: nat > $o,Z2: nat > $o] : ( Y4 = Z2 ) )
% 9.17/5.43 @ ( bNF_re3376528473927230327_nat_o @ R12
% 9.17/5.43 @ ^ [Y4: nat > $o,Z2: nat > $o] : ( Y4 = Z2 ) ) )
% 9.17/5.43 @ comp_nat_o_nat_o_int
% 9.17/5.43 @ comp_nat_o_nat_o_int ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7273_o__rsp_I2_J,axiom,
% 9.17/5.43 ! [R12: int > int > $o] :
% 9.17/5.43 ( bNF_re3491090157995142405_int_o
% 9.17/5.43 @ ^ [Y4: ( nat > $o ) > int > $o,Z2: ( nat > $o ) > int > $o] : ( Y4 = Z2 )
% 9.17/5.43 @ ( bNF_re2655111580231008093_int_o
% 9.17/5.43 @ ( bNF_re3376528473927230327_nat_o @ R12
% 9.17/5.43 @ ^ [Y4: nat > $o,Z2: nat > $o] : ( Y4 = Z2 ) )
% 9.17/5.43 @ ( bNF_re3403563459893282935_int_o @ R12
% 9.17/5.43 @ ^ [Y4: int > $o,Z2: int > $o] : ( Y4 = Z2 ) ) )
% 9.17/5.43 @ comp_nat_o_int_o_int
% 9.17/5.43 @ comp_nat_o_int_o_int ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7274_o__rsp_I2_J,axiom,
% 9.17/5.43 ! [R12: int > int > $o] :
% 9.17/5.43 ( bNF_re5539255234643219293nt_int
% 9.17/5.43 @ ^ [Y4: ( nat > $o ) > int > int,Z2: ( nat > $o ) > int > int] : ( Y4 = Z2 )
% 9.17/5.43 @ ( bNF_re7395152722673581539nt_int
% 9.17/5.43 @ ( bNF_re3376528473927230327_nat_o @ R12
% 9.17/5.43 @ ^ [Y4: nat > $o,Z2: nat > $o] : ( Y4 = Z2 ) )
% 9.17/5.43 @ ( bNF_re711492959462206631nt_int @ R12
% 9.17/5.43 @ ^ [Y4: int > int,Z2: int > int] : ( Y4 = Z2 ) ) )
% 9.17/5.43 @ comp_n3090169619561918849nt_int
% 9.17/5.43 @ comp_n3090169619561918849nt_int ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7275_o__rsp_I2_J,axiom,
% 9.17/5.43 ! [R12: int > int > $o] :
% 9.17/5.43 ( bNF_re615132412071444453_nat_o
% 9.17/5.43 @ ^ [Y4: ( int > $o ) > nat > $o,Z2: ( int > $o ) > nat > $o] : ( Y4 = Z2 )
% 9.17/5.43 @ ( bNF_re2446162618891206493_nat_o
% 9.17/5.43 @ ( bNF_re3403563459893282935_int_o @ R12
% 9.17/5.43 @ ^ [Y4: int > $o,Z2: int > $o] : ( Y4 = Z2 ) )
% 9.17/5.43 @ ( bNF_re3376528473927230327_nat_o @ R12
% 9.17/5.43 @ ^ [Y4: nat > $o,Z2: nat > $o] : ( Y4 = Z2 ) ) )
% 9.17/5.43 @ comp_int_o_nat_o_int
% 9.17/5.43 @ comp_int_o_nat_o_int ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7276_o__rsp_I2_J,axiom,
% 9.17/5.43 ! [R12: int > int > $o] :
% 9.17/5.43 ( bNF_re2555365631850037877_int_o
% 9.17/5.43 @ ^ [Y4: ( int > $o ) > int > $o,Z2: ( int > $o ) > int > $o] : ( Y4 = Z2 )
% 9.17/5.43 @ ( bNF_re8651060166502312541_int_o
% 9.17/5.43 @ ( bNF_re3403563459893282935_int_o @ R12
% 9.17/5.43 @ ^ [Y4: int > $o,Z2: int > $o] : ( Y4 = Z2 ) )
% 9.17/5.43 @ ( bNF_re3403563459893282935_int_o @ R12
% 9.17/5.43 @ ^ [Y4: int > $o,Z2: int > $o] : ( Y4 = Z2 ) ) )
% 9.17/5.43 @ comp_int_o_int_o_int
% 9.17/5.43 @ comp_int_o_int_o_int ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7277_o__rsp_I2_J,axiom,
% 9.17/5.43 ! [R12: int > int > $o] :
% 9.17/5.43 ( bNF_re5051145820034318685nt_int
% 9.17/5.43 @ ^ [Y4: ( int > $o ) > int > int,Z2: ( int > $o ) > int > int] : ( Y4 = Z2 )
% 9.17/5.43 @ ( bNF_re7462748251485907171nt_int
% 9.17/5.43 @ ( bNF_re3403563459893282935_int_o @ R12
% 9.17/5.43 @ ^ [Y4: int > $o,Z2: int > $o] : ( Y4 = Z2 ) )
% 9.17/5.43 @ ( bNF_re711492959462206631nt_int @ R12
% 9.17/5.43 @ ^ [Y4: int > int,Z2: int > int] : ( Y4 = Z2 ) ) )
% 9.17/5.43 @ comp_i1993086638917920293nt_int
% 9.17/5.43 @ comp_i1993086638917920293nt_int ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7278_o__rsp_I2_J,axiom,
% 9.17/5.43 ! [R12: int > int > $o] :
% 9.17/5.43 ( bNF_re4659646225794970589_nat_o
% 9.17/5.43 @ ^ [Y4: ( int > int ) > nat > $o,Z2: ( int > int ) > nat > $o] : ( Y4 = Z2 )
% 9.17/5.43 @ ( bNF_re4332408551980016867_nat_o
% 9.17/5.43 @ ( bNF_re711492959462206631nt_int @ R12
% 9.17/5.43 @ ^ [Y4: int > int,Z2: int > int] : ( Y4 = Z2 ) )
% 9.17/5.43 @ ( bNF_re3376528473927230327_nat_o @ R12
% 9.17/5.43 @ ^ [Y4: nat > $o,Z2: nat > $o] : ( Y4 = Z2 ) ) )
% 9.17/5.43 @ comp_i4411980392712547921_o_int
% 9.17/5.43 @ comp_i4411980392712547921_o_int ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7279_o__rsp_I2_J,axiom,
% 9.17/5.43 ! [R12: int > int > $o] :
% 9.17/5.43 ( bNF_re3161894838932316637_int_o
% 9.17/5.43 @ ^ [Y4: ( int > int ) > int > $o,Z2: ( int > int ) > int > $o] : ( Y4 = Z2 )
% 9.17/5.43 @ ( bNF_re1313934062736347107_int_o
% 9.17/5.43 @ ( bNF_re711492959462206631nt_int @ R12
% 9.17/5.43 @ ^ [Y4: int > int,Z2: int > int] : ( Y4 = Z2 ) )
% 9.17/5.43 @ ( bNF_re3403563459893282935_int_o @ R12
% 9.17/5.43 @ ^ [Y4: int > $o,Z2: int > $o] : ( Y4 = Z2 ) ) )
% 9.17/5.43 @ comp_i5098556425753098485_o_int
% 9.17/5.43 @ comp_i5098556425753098485_o_int ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7280_apfst__convE,axiom,
% 9.17/5.43 ! [Q3: produc1908205239877642774nteger,F: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc6241069584506657477e_term > option6357759511663192854e_term,P4: produc1908205239877642774nteger] :
% 9.17/5.43 ( ( Q3
% 9.17/5.43 = ( produc2515316116081422825nteger @ F @ P4 ) )
% 9.17/5.43 => ~ ! [X4: produc6241069584506657477e_term > option6357759511663192854e_term,Y5: produc8923325533196201883nteger] :
% 9.17/5.43 ( ( P4
% 9.17/5.43 = ( produc8603105652947943368nteger @ X4 @ Y5 ) )
% 9.17/5.43 => ( Q3
% 9.17/5.43 != ( produc8603105652947943368nteger @ ( F @ X4 ) @ Y5 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7281_apfst__convE,axiom,
% 9.17/5.43 ! [Q3: produc3925858234332021118et_nat,F: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o,P4: produc3925858234332021118et_nat] :
% 9.17/5.43 ( ( Q3
% 9.17/5.43 = ( produc3198230245617193214et_nat @ F @ P4 ) )
% 9.17/5.43 => ~ ! [X4: produc3658429121746597890et_nat > $o,Y5: produc3658429121746597890et_nat] :
% 9.17/5.43 ( ( P4
% 9.17/5.43 = ( produc5001842942810119800et_nat @ X4 @ Y5 ) )
% 9.17/5.43 => ( Q3
% 9.17/5.43 != ( produc5001842942810119800et_nat @ ( F @ X4 ) @ Y5 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7282_apfst__convE,axiom,
% 9.17/5.43 ! [Q3: produc2732055786443039994et_nat,F: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o,P4: produc2732055786443039994et_nat] :
% 9.17/5.43 ( ( Q3
% 9.17/5.43 = ( produc1442628905706551930et_nat @ F @ P4 ) )
% 9.17/5.43 => ~ ! [X4: produc3658429121746597890et_nat > $o,Y5: produc3925858234332021118et_nat] :
% 9.17/5.43 ( ( P4
% 9.17/5.43 = ( produc2245416461498447860et_nat @ X4 @ Y5 ) )
% 9.17/5.43 => ( Q3
% 9.17/5.43 != ( produc2245416461498447860et_nat @ ( F @ X4 ) @ Y5 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7283_apfst__convE,axiom,
% 9.17/5.43 ! [Q3: produc2285326912895808259nt_int,F: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > produc8551481072490612790e_term > option6357759511663192854e_term,P4: produc2285326912895808259nt_int] :
% 9.17/5.43 ( ( Q3
% 9.17/5.43 = ( produc7277921532047535397nt_int @ F @ P4 ) )
% 9.17/5.43 => ~ ! [X4: produc8551481072490612790e_term > option6357759511663192854e_term,Y5: product_prod_int_int] :
% 9.17/5.43 ( ( P4
% 9.17/5.43 = ( produc5700946648718959541nt_int @ X4 @ Y5 ) )
% 9.17/5.43 => ( Q3
% 9.17/5.43 != ( produc5700946648718959541nt_int @ ( F @ X4 ) @ Y5 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7284_apfst__convE,axiom,
% 9.17/5.43 ! [Q3: produc7773217078559923341nt_int,F: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > int > option6357759511663192854e_term,P4: produc2285326912895808259nt_int] :
% 9.17/5.43 ( ( Q3
% 9.17/5.43 = ( produc6919319362177967663nt_int @ F @ P4 ) )
% 9.17/5.43 => ~ ! [X4: produc8551481072490612790e_term > option6357759511663192854e_term,Y5: product_prod_int_int] :
% 9.17/5.43 ( ( P4
% 9.17/5.43 = ( produc5700946648718959541nt_int @ X4 @ Y5 ) )
% 9.17/5.43 => ( Q3
% 9.17/5.43 != ( produc4305682042979456191nt_int @ ( F @ X4 ) @ Y5 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7285_apfst__convE,axiom,
% 9.17/5.43 ! [Q3: produc2285326912895808259nt_int,F: ( int > option6357759511663192854e_term ) > produc8551481072490612790e_term > option6357759511663192854e_term,P4: produc7773217078559923341nt_int] :
% 9.17/5.43 ( ( Q3
% 9.17/5.43 = ( produc6067946493426971951nt_int @ F @ P4 ) )
% 9.17/5.43 => ~ ! [X4: int > option6357759511663192854e_term,Y5: product_prod_int_int] :
% 9.17/5.43 ( ( P4
% 9.17/5.43 = ( produc4305682042979456191nt_int @ X4 @ Y5 ) )
% 9.17/5.43 => ( Q3
% 9.17/5.43 != ( produc5700946648718959541nt_int @ ( F @ X4 ) @ Y5 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7286_apfst__convE,axiom,
% 9.17/5.43 ! [Q3: produc7773217078559923341nt_int,F: ( int > option6357759511663192854e_term ) > int > option6357759511663192854e_term,P4: produc7773217078559923341nt_int] :
% 9.17/5.43 ( ( Q3
% 9.17/5.43 = ( produc7131893314732144953nt_int @ F @ P4 ) )
% 9.17/5.43 => ~ ! [X4: int > option6357759511663192854e_term,Y5: product_prod_int_int] :
% 9.17/5.43 ( ( P4
% 9.17/5.43 = ( produc4305682042979456191nt_int @ X4 @ Y5 ) )
% 9.17/5.43 => ( Q3
% 9.17/5.43 != ( produc4305682042979456191nt_int @ ( F @ X4 ) @ Y5 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7287_UN__le__eq__Un0,axiom,
% 9.17/5.43 ! [M3: nat > set_Pr4329608150637261639at_nat,N2: nat] :
% 9.17/5.43 ( ( comple4364388969068068532at_nat @ ( image_1087905878993176368at_nat @ M3 @ ( set_ord_atMost_nat @ N2 ) ) )
% 9.17/5.43 = ( sup_su5525570899277871387at_nat @ ( comple4364388969068068532at_nat @ ( image_1087905878993176368at_nat @ M3 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) ) ) @ ( M3 @ zero_zero_nat ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7288_UN__le__eq__Un0,axiom,
% 9.17/5.43 ! [M3: nat > set_nat,N2: nat] :
% 9.17/5.43 ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ M3 @ ( set_ord_atMost_nat @ N2 ) ) )
% 9.17/5.43 = ( sup_sup_set_nat @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ M3 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) ) ) @ ( M3 @ zero_zero_nat ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7289_times__int_Orsp,axiom,
% 9.17/5.43 ( bNF_re3099431351363272937at_nat @ intrel @ ( bNF_re2241393799969408733at_nat @ intrel @ intrel )
% 9.17/5.43 @ ( produc27273713700761075at_nat
% 9.17/5.43 @ ^ [X3: nat,Y3: nat] :
% 9.17/5.43 ( produc2626176000494625587at_nat
% 9.17/5.43 @ ^ [U2: nat,V2: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X3 @ U2 ) @ ( times_times_nat @ Y3 @ V2 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X3 @ V2 ) @ ( times_times_nat @ Y3 @ U2 ) ) ) ) )
% 9.17/5.43 @ ( produc27273713700761075at_nat
% 9.17/5.43 @ ^ [X3: nat,Y3: nat] :
% 9.17/5.43 ( produc2626176000494625587at_nat
% 9.17/5.43 @ ^ [U2: nat,V2: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X3 @ U2 ) @ ( times_times_nat @ Y3 @ V2 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X3 @ V2 ) @ ( times_times_nat @ Y3 @ U2 ) ) ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7290_sup__Some,axiom,
% 9.17/5.43 ! [X: set_nat,Y: set_nat] :
% 9.17/5.43 ( ( sup_su3598758113090618626et_nat @ ( some_set_nat @ X ) @ ( some_set_nat @ Y ) )
% 9.17/5.43 = ( some_set_nat @ ( sup_sup_set_nat @ X @ Y ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7291_sup__Some,axiom,
% 9.17/5.43 ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat] :
% 9.17/5.43 ( ( sup_su2273273666271716065at_nat @ ( some_s5890477192898017836at_nat @ X ) @ ( some_s5890477192898017836at_nat @ Y ) )
% 9.17/5.43 = ( some_s5890477192898017836at_nat @ ( sup_su5525570899277871387at_nat @ X @ Y ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7292_sup__Some,axiom,
% 9.17/5.43 ! [X: product_unit,Y: product_unit] :
% 9.17/5.43 ( ( sup_su7717485023253700007t_unit @ ( some_Product_unit @ X ) @ ( some_Product_unit @ Y ) )
% 9.17/5.43 = ( some_Product_unit @ ( sup_sup_Product_unit @ X @ Y ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7293_sup__Some,axiom,
% 9.17/5.43 ! [X: assn,Y: assn] :
% 9.17/5.43 ( ( sup_sup_option_assn @ ( some_assn @ X ) @ ( some_assn @ Y ) )
% 9.17/5.43 = ( some_assn @ ( sup_sup_assn @ X @ Y ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7294_intrel__iff,axiom,
% 9.17/5.43 ! [X: nat,Y: nat,U: nat,V: nat] :
% 9.17/5.43 ( ( intrel @ ( product_Pair_nat_nat @ X @ Y ) @ ( product_Pair_nat_nat @ U @ V ) )
% 9.17/5.43 = ( ( plus_plus_nat @ X @ V )
% 9.17/5.43 = ( plus_plus_nat @ U @ Y ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7295_insert__Times__insert,axiom,
% 9.17/5.43 ! [A: $o,A2: set_o,B: $o,B5: set_o] :
% 9.17/5.43 ( ( product_Sigma_o_o @ ( insert_o @ A @ A2 )
% 9.17/5.43 @ ^ [Uu: $o] : ( insert_o @ B @ B5 ) )
% 9.17/5.43 = ( insert6201435330877294327od_o_o @ ( product_Pair_o_o @ A @ B )
% 9.17/5.43 @ ( sup_su5769328420594410459od_o_o
% 9.17/5.43 @ ( product_Sigma_o_o @ A2
% 9.17/5.43 @ ^ [Uu: $o] : ( insert_o @ B @ B5 ) )
% 9.17/5.43 @ ( product_Sigma_o_o @ ( insert_o @ A @ A2 )
% 9.17/5.43 @ ^ [Uu: $o] : B5 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7296_insert__Times__insert,axiom,
% 9.17/5.43 ! [A: $o,A2: set_o,B: nat,B5: set_nat] :
% 9.17/5.43 ( ( product_Sigma_o_nat @ ( insert_o @ A @ A2 )
% 9.17/5.43 @ ^ [Uu: $o] : ( insert_nat @ B @ B5 ) )
% 9.17/5.43 = ( insert7948214739558299847_o_nat @ ( product_Pair_o_nat @ A @ B )
% 9.17/5.43 @ ( sup_su8679140417860611193_o_nat
% 9.17/5.43 @ ( product_Sigma_o_nat @ A2
% 9.17/5.43 @ ^ [Uu: $o] : ( insert_nat @ B @ B5 ) )
% 9.17/5.43 @ ( product_Sigma_o_nat @ ( insert_o @ A @ A2 )
% 9.17/5.43 @ ^ [Uu: $o] : B5 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7297_insert__Times__insert,axiom,
% 9.17/5.43 ! [A: $o,A2: set_o,B: int,B5: set_int] :
% 9.17/5.43 ( ( product_Sigma_o_int @ ( insert_o @ A @ A2 )
% 9.17/5.43 @ ^ [Uu: $o] : ( insert_int @ B @ B5 ) )
% 9.17/5.43 = ( insert3770363720049103139_o_int @ ( product_Pair_o_int @ A @ B )
% 9.17/5.43 @ ( sup_su6189057272928884437_o_int
% 9.17/5.43 @ ( product_Sigma_o_int @ A2
% 9.17/5.43 @ ^ [Uu: $o] : ( insert_int @ B @ B5 ) )
% 9.17/5.43 @ ( product_Sigma_o_int @ ( insert_o @ A @ A2 )
% 9.17/5.43 @ ^ [Uu: $o] : B5 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7298_insert__Times__insert,axiom,
% 9.17/5.43 ! [A: nat,A2: set_nat,B: $o,B5: set_o] :
% 9.17/5.43 ( ( product_Sigma_nat_o @ ( insert_nat @ A @ A2 )
% 9.17/5.43 @ ^ [Uu: nat] : ( insert_o @ B @ B5 ) )
% 9.17/5.43 = ( insert2233377226759017069_nat_o @ ( product_Pair_nat_o @ A @ B )
% 9.17/5.43 @ ( sup_su503371503184139039_nat_o
% 9.17/5.43 @ ( product_Sigma_nat_o @ A2
% 9.17/5.43 @ ^ [Uu: nat] : ( insert_o @ B @ B5 ) )
% 9.17/5.43 @ ( product_Sigma_nat_o @ ( insert_nat @ A @ A2 )
% 9.17/5.43 @ ^ [Uu: nat] : B5 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7299_insert__Times__insert,axiom,
% 9.17/5.43 ! [A: nat,A2: set_nat,B: nat,B5: set_nat] :
% 9.17/5.43 ( ( produc457027306803732586at_nat @ ( insert_nat @ A @ A2 )
% 9.17/5.43 @ ^ [Uu: nat] : ( insert_nat @ B @ B5 ) )
% 9.17/5.43 = ( insert8211810215607154385at_nat @ ( product_Pair_nat_nat @ A @ B )
% 9.17/5.43 @ ( sup_su6327502436637775413at_nat
% 9.17/5.43 @ ( produc457027306803732586at_nat @ A2
% 9.17/5.43 @ ^ [Uu: nat] : ( insert_nat @ B @ B5 ) )
% 9.17/5.43 @ ( produc457027306803732586at_nat @ ( insert_nat @ A @ A2 )
% 9.17/5.43 @ ^ [Uu: nat] : B5 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7300_insert__Times__insert,axiom,
% 9.17/5.43 ! [A: nat,A2: set_nat,B: int,B5: set_int] :
% 9.17/5.43 ( ( produc454536836294682310at_int @ ( insert_nat @ A @ A2 )
% 9.17/5.43 @ ^ [Uu: nat] : ( insert_int @ B @ B5 ) )
% 9.17/5.43 = ( insert4033959196097957677at_int @ ( product_Pair_nat_int @ A @ B )
% 9.17/5.43 @ ( sup_su3837419291706048657at_int
% 9.17/5.43 @ ( produc454536836294682310at_int @ A2
% 9.17/5.43 @ ^ [Uu: nat] : ( insert_int @ B @ B5 ) )
% 9.17/5.43 @ ( produc454536836294682310at_int @ ( insert_nat @ A @ A2 )
% 9.17/5.43 @ ^ [Uu: nat] : B5 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7301_insert__Times__insert,axiom,
% 9.17/5.43 ! [A: int,A2: set_int,B: $o,B5: set_o] :
% 9.17/5.43 ( ( product_Sigma_int_o @ ( insert_int @ A @ A2 )
% 9.17/5.43 @ ^ [Uu: int] : ( insert_o @ B @ B5 ) )
% 9.17/5.43 = ( insert412334881326329105_int_o @ ( product_Pair_int_o @ A @ B )
% 9.17/5.43 @ ( sup_su7481598572368468931_int_o
% 9.17/5.43 @ ( product_Sigma_int_o @ A2
% 9.17/5.43 @ ^ [Uu: int] : ( insert_o @ B @ B5 ) )
% 9.17/5.43 @ ( product_Sigma_int_o @ ( insert_int @ A @ A2 )
% 9.17/5.43 @ ^ [Uu: int] : B5 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7302_insert__Times__insert,axiom,
% 9.17/5.43 ! [A: int,A2: set_int,B: nat,B5: set_nat] :
% 9.17/5.43 ( ( produc1456381018704787142nt_nat @ ( insert_int @ A @ A2 )
% 9.17/5.43 @ ^ [Uu: int] : ( insert_nat @ B @ B5 ) )
% 9.17/5.43 = ( insert9211163927508208941nt_nat @ ( product_Pair_int_nat @ A @ B )
% 9.17/5.43 @ ( sup_su8514424011330797201nt_nat
% 9.17/5.43 @ ( produc1456381018704787142nt_nat @ A2
% 9.17/5.43 @ ^ [Uu: int] : ( insert_nat @ B @ B5 ) )
% 9.17/5.43 @ ( produc1456381018704787142nt_nat @ ( insert_int @ A @ A2 )
% 9.17/5.43 @ ^ [Uu: int] : B5 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7303_insert__Times__insert,axiom,
% 9.17/5.43 ! [A: int,A2: set_int,B: int,B5: set_int] :
% 9.17/5.43 ( ( produc1453890548195736866nt_int @ ( insert_int @ A @ A2 )
% 9.17/5.43 @ ^ [Uu: int] : ( insert_int @ B @ B5 ) )
% 9.17/5.43 = ( insert5033312907999012233nt_int @ ( product_Pair_int_int @ A @ B )
% 9.17/5.43 @ ( sup_su6024340866399070445nt_int
% 9.17/5.43 @ ( produc1453890548195736866nt_int @ A2
% 9.17/5.43 @ ^ [Uu: int] : ( insert_int @ B @ B5 ) )
% 9.17/5.43 @ ( produc1453890548195736866nt_int @ ( insert_int @ A @ A2 )
% 9.17/5.43 @ ^ [Uu: int] : B5 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7304_insert__Times__insert,axiom,
% 9.17/5.43 ! [A: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,B: $o,B5: set_o] :
% 9.17/5.43 ( ( produc203973861852599583_nat_o @ ( insert8211810215607154385at_nat @ A @ A2 )
% 9.17/5.43 @ ^ [Uu: product_prod_nat_nat] : ( insert_o @ B @ B5 ) )
% 9.17/5.43 = ( insert2126339615020983374_nat_o @ ( produc855456346497908590_nat_o @ A @ B )
% 9.17/5.43 @ ( sup_su5921324857680904370_nat_o
% 9.17/5.43 @ ( produc203973861852599583_nat_o @ A2
% 9.17/5.43 @ ^ [Uu: product_prod_nat_nat] : ( insert_o @ B @ B5 ) )
% 9.17/5.43 @ ( produc203973861852599583_nat_o @ ( insert8211810215607154385at_nat @ A @ A2 )
% 9.17/5.43 @ ^ [Uu: product_prod_nat_nat] : B5 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7305_Sigma__Un__distrib1,axiom,
% 9.17/5.43 ! [I4: set_se7855581050983116737at_nat,J4: set_se7855581050983116737at_nat,C4: set_Pr1261947904930325089at_nat > set_se7855581050983116737at_nat] :
% 9.17/5.43 ( ( produc7726050920695093128at_nat @ ( sup_su3642409539654194069at_nat @ I4 @ J4 ) @ C4 )
% 9.17/5.43 = ( sup_su5525570899277871387at_nat @ ( produc7726050920695093128at_nat @ I4 @ C4 ) @ ( produc7726050920695093128at_nat @ J4 @ C4 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7306_Sigma__Un__distrib2,axiom,
% 9.17/5.43 ! [I4: set_se7855581050983116737at_nat,A2: set_Pr1261947904930325089at_nat > set_se7855581050983116737at_nat,B5: set_Pr1261947904930325089at_nat > set_se7855581050983116737at_nat] :
% 9.17/5.43 ( ( produc7726050920695093128at_nat @ I4
% 9.17/5.43 @ ^ [I3: set_Pr1261947904930325089at_nat] : ( sup_su3642409539654194069at_nat @ ( A2 @ I3 ) @ ( B5 @ I3 ) ) )
% 9.17/5.43 = ( sup_su5525570899277871387at_nat @ ( produc7726050920695093128at_nat @ I4 @ A2 ) @ ( produc7726050920695093128at_nat @ I4 @ B5 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7307_Times__Un__distrib1,axiom,
% 9.17/5.43 ! [A2: set_se7855581050983116737at_nat,B5: set_se7855581050983116737at_nat,C4: set_se7855581050983116737at_nat] :
% 9.17/5.43 ( ( produc7726050920695093128at_nat @ ( sup_su3642409539654194069at_nat @ A2 @ B5 )
% 9.17/5.43 @ ^ [Uu: set_Pr1261947904930325089at_nat] : C4 )
% 9.17/5.43 = ( sup_su5525570899277871387at_nat
% 9.17/5.43 @ ( produc7726050920695093128at_nat @ A2
% 9.17/5.43 @ ^ [Uu: set_Pr1261947904930325089at_nat] : C4 )
% 9.17/5.43 @ ( produc7726050920695093128at_nat @ B5
% 9.17/5.43 @ ^ [Uu: set_Pr1261947904930325089at_nat] : C4 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7308_set__diff__diff__left,axiom,
% 9.17/5.43 ! [A2: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat,C4: set_Pr4329608150637261639at_nat] :
% 9.17/5.43 ( ( minus_3314409938677909166at_nat @ ( minus_3314409938677909166at_nat @ A2 @ B5 ) @ C4 )
% 9.17/5.43 = ( minus_3314409938677909166at_nat @ A2 @ ( sup_su5525570899277871387at_nat @ B5 @ C4 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7309_set__diff__diff__left,axiom,
% 9.17/5.43 ! [A2: set_nat,B5: set_nat,C4: set_nat] :
% 9.17/5.43 ( ( minus_minus_set_nat @ ( minus_minus_set_nat @ A2 @ B5 ) @ C4 )
% 9.17/5.43 = ( minus_minus_set_nat @ A2 @ ( sup_sup_set_nat @ B5 @ C4 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7310_sup__option__def,axiom,
% 9.17/5.43 ( sup_su3598758113090618626et_nat
% 9.17/5.43 = ( ^ [X3: option_set_nat,Y3: option_set_nat] :
% 9.17/5.43 ( case_o4054078431260844265et_nat @ Y3
% 9.17/5.43 @ ^ [X10: set_nat] :
% 9.17/5.43 ( case_o4054078431260844265et_nat @ X3
% 9.17/5.43 @ ^ [Z4: set_nat] : ( some_set_nat @ ( sup_sup_set_nat @ X10 @ Z4 ) )
% 9.17/5.43 @ Y3 )
% 9.17/5.43 @ X3 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7311_sup__option__def,axiom,
% 9.17/5.43 ( sup_su2273273666271716065at_nat
% 9.17/5.43 = ( ^ [X3: option1583680563626158861at_nat,Y3: option1583680563626158861at_nat] :
% 9.17/5.43 ( case_o9080059180780454917at_nat @ Y3
% 9.17/5.43 @ ^ [X10: set_Pr4329608150637261639at_nat] :
% 9.17/5.43 ( case_o9080059180780454917at_nat @ X3
% 9.17/5.43 @ ^ [Z4: set_Pr4329608150637261639at_nat] : ( some_s5890477192898017836at_nat @ ( sup_su5525570899277871387at_nat @ X10 @ Z4 ) )
% 9.17/5.43 @ Y3 )
% 9.17/5.43 @ X3 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7312_sup__option__def,axiom,
% 9.17/5.43 ( sup_su7717485023253700007t_unit
% 9.17/5.43 = ( ^ [X3: option_Product_unit,Y3: option_Product_unit] :
% 9.17/5.43 ( case_o2985186191577459077t_unit @ Y3
% 9.17/5.43 @ ^ [X10: product_unit] :
% 9.17/5.43 ( case_o2985186191577459077t_unit @ X3
% 9.17/5.43 @ ^ [Z4: product_unit] : ( some_Product_unit @ ( sup_sup_Product_unit @ X10 @ Z4 ) )
% 9.17/5.43 @ Y3 )
% 9.17/5.43 @ X3 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7313_sup__option__def,axiom,
% 9.17/5.43 ( sup_sup_option_assn
% 9.17/5.43 = ( ^ [X3: option_assn,Y3: option_assn] :
% 9.17/5.43 ( case_o4484465799723439917n_assn @ Y3
% 9.17/5.43 @ ^ [X10: assn] :
% 9.17/5.43 ( case_o4484465799723439917n_assn @ X3
% 9.17/5.43 @ ^ [Z4: assn] : ( some_assn @ ( sup_sup_assn @ X10 @ Z4 ) )
% 9.17/5.43 @ Y3 )
% 9.17/5.43 @ X3 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7314_ivl__disj__un__two__touch_I4_J,axiom,
% 9.17/5.43 ! [L: rat,M2: rat,U: rat] :
% 9.17/5.43 ( ( ord_less_eq_rat @ L @ M2 )
% 9.17/5.43 => ( ( ord_less_eq_rat @ M2 @ U )
% 9.17/5.43 => ( ( sup_sup_set_rat @ ( set_or633870826150836451st_rat @ L @ M2 ) @ ( set_or633870826150836451st_rat @ M2 @ U ) )
% 9.17/5.43 = ( set_or633870826150836451st_rat @ L @ U ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7315_ivl__disj__un__two__touch_I4_J,axiom,
% 9.17/5.43 ! [L: num,M2: num,U: num] :
% 9.17/5.43 ( ( ord_less_eq_num @ L @ M2 )
% 9.17/5.43 => ( ( ord_less_eq_num @ M2 @ U )
% 9.17/5.43 => ( ( sup_sup_set_num @ ( set_or7049704709247886629st_num @ L @ M2 ) @ ( set_or7049704709247886629st_num @ M2 @ U ) )
% 9.17/5.43 = ( set_or7049704709247886629st_num @ L @ U ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7316_ivl__disj__un__two__touch_I4_J,axiom,
% 9.17/5.43 ! [L: int,M2: int,U: int] :
% 9.17/5.43 ( ( ord_less_eq_int @ L @ M2 )
% 9.17/5.43 => ( ( ord_less_eq_int @ M2 @ U )
% 9.17/5.43 => ( ( sup_sup_set_int @ ( set_or1266510415728281911st_int @ L @ M2 ) @ ( set_or1266510415728281911st_int @ M2 @ U ) )
% 9.17/5.43 = ( set_or1266510415728281911st_int @ L @ U ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7317_ivl__disj__un__two__touch_I4_J,axiom,
% 9.17/5.43 ! [L: nat,M2: nat,U: nat] :
% 9.17/5.43 ( ( ord_less_eq_nat @ L @ M2 )
% 9.17/5.43 => ( ( ord_less_eq_nat @ M2 @ U )
% 9.17/5.43 => ( ( sup_sup_set_nat @ ( set_or1269000886237332187st_nat @ L @ M2 ) @ ( set_or1269000886237332187st_nat @ M2 @ U ) )
% 9.17/5.43 = ( set_or1269000886237332187st_nat @ L @ U ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7318_ivl__disj__un__two__touch_I4_J,axiom,
% 9.17/5.43 ! [L: code_integer,M2: code_integer,U: code_integer] :
% 9.17/5.43 ( ( ord_le3102999989581377725nteger @ L @ M2 )
% 9.17/5.43 => ( ( ord_le3102999989581377725nteger @ M2 @ U )
% 9.17/5.43 => ( ( sup_su848401254843788991nteger @ ( set_or189985376899183464nteger @ L @ M2 ) @ ( set_or189985376899183464nteger @ M2 @ U ) )
% 9.17/5.43 = ( set_or189985376899183464nteger @ L @ U ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7319_ivl__disj__un__two_I3_J,axiom,
% 9.17/5.43 ! [L: rat,M2: rat,U: rat] :
% 9.17/5.43 ( ( ord_less_eq_rat @ L @ M2 )
% 9.17/5.43 => ( ( ord_less_eq_rat @ M2 @ U )
% 9.17/5.43 => ( ( sup_sup_set_rat @ ( set_or4029947393144176647an_rat @ L @ M2 ) @ ( set_or4029947393144176647an_rat @ M2 @ U ) )
% 9.17/5.43 = ( set_or4029947393144176647an_rat @ L @ U ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7320_ivl__disj__un__two_I3_J,axiom,
% 9.17/5.43 ! [L: num,M2: num,U: num] :
% 9.17/5.43 ( ( ord_less_eq_num @ L @ M2 )
% 9.17/5.43 => ( ( ord_less_eq_num @ M2 @ U )
% 9.17/5.43 => ( ( sup_sup_set_num @ ( set_or1222409239386451017an_num @ L @ M2 ) @ ( set_or1222409239386451017an_num @ M2 @ U ) )
% 9.17/5.43 = ( set_or1222409239386451017an_num @ L @ U ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7321_ivl__disj__un__two_I3_J,axiom,
% 9.17/5.43 ! [L: nat,M2: nat,U: nat] :
% 9.17/5.43 ( ( ord_less_eq_nat @ L @ M2 )
% 9.17/5.43 => ( ( ord_less_eq_nat @ M2 @ U )
% 9.17/5.43 => ( ( sup_sup_set_nat @ ( set_or4665077453230672383an_nat @ L @ M2 ) @ ( set_or4665077453230672383an_nat @ M2 @ U ) )
% 9.17/5.43 = ( set_or4665077453230672383an_nat @ L @ U ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7322_ivl__disj__un__two_I3_J,axiom,
% 9.17/5.43 ! [L: code_integer,M2: code_integer,U: code_integer] :
% 9.17/5.43 ( ( ord_le3102999989581377725nteger @ L @ M2 )
% 9.17/5.43 => ( ( ord_le3102999989581377725nteger @ M2 @ U )
% 9.17/5.43 => ( ( sup_su848401254843788991nteger @ ( set_or8404916559141939852nteger @ L @ M2 ) @ ( set_or8404916559141939852nteger @ M2 @ U ) )
% 9.17/5.43 = ( set_or8404916559141939852nteger @ L @ U ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7323_ivl__disj__un__two_I3_J,axiom,
% 9.17/5.43 ! [L: int,M2: int,U: int] :
% 9.17/5.43 ( ( ord_less_eq_int @ L @ M2 )
% 9.17/5.43 => ( ( ord_less_eq_int @ M2 @ U )
% 9.17/5.43 => ( ( sup_sup_set_int @ ( set_or4662586982721622107an_int @ L @ M2 ) @ ( set_or4662586982721622107an_int @ M2 @ U ) )
% 9.17/5.43 = ( set_or4662586982721622107an_int @ L @ U ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7324_max__ext__additive,axiom,
% 9.17/5.43 ! [A2: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat,R4: set_Pr8693737435421807431at_nat,C4: set_Pr1261947904930325089at_nat,D3: set_Pr1261947904930325089at_nat] :
% 9.17/5.43 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A2 @ B5 ) @ ( max_ex8135407076693332796at_nat @ R4 ) )
% 9.17/5.43 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ C4 @ D3 ) @ ( max_ex8135407076693332796at_nat @ R4 ) )
% 9.17/5.43 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( sup_su6327502436637775413at_nat @ A2 @ C4 ) @ ( sup_su6327502436637775413at_nat @ B5 @ D3 ) ) @ ( max_ex8135407076693332796at_nat @ R4 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7325_max__ext__additive,axiom,
% 9.17/5.43 ! [A2: set_nat,B5: set_nat,R4: set_Pr1261947904930325089at_nat,C4: set_nat,D3: set_nat] :
% 9.17/5.43 ( ( member8277197624267554838et_nat @ ( produc4532415448927165861et_nat @ A2 @ B5 ) @ ( max_ext_nat @ R4 ) )
% 9.17/5.43 => ( ( member8277197624267554838et_nat @ ( produc4532415448927165861et_nat @ C4 @ D3 ) @ ( max_ext_nat @ R4 ) )
% 9.17/5.43 => ( member8277197624267554838et_nat @ ( produc4532415448927165861et_nat @ ( sup_sup_set_nat @ A2 @ C4 ) @ ( sup_sup_set_nat @ B5 @ D3 ) ) @ ( max_ext_nat @ R4 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7326_max__ext__additive,axiom,
% 9.17/5.43 ! [A2: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat,R4: set_Pr5564308138774400199at_nat,C4: set_Pr4329608150637261639at_nat,D3: set_Pr4329608150637261639at_nat] :
% 9.17/5.43 ( ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ A2 @ B5 ) @ ( max_ex8833738776070432290at_nat @ R4 ) )
% 9.17/5.43 => ( ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ C4 @ D3 ) @ ( max_ex8833738776070432290at_nat @ R4 ) )
% 9.17/5.43 => ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ ( sup_su5525570899277871387at_nat @ A2 @ C4 ) @ ( sup_su5525570899277871387at_nat @ B5 @ D3 ) ) @ ( max_ex8833738776070432290at_nat @ R4 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7327_zero__int_Orsp,axiom,
% 9.17/5.43 intrel @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7328_ivl__disj__un__two_I7_J,axiom,
% 9.17/5.43 ! [L: rat,M2: rat,U: rat] :
% 9.17/5.43 ( ( ord_less_eq_rat @ L @ M2 )
% 9.17/5.43 => ( ( ord_less_eq_rat @ M2 @ U )
% 9.17/5.43 => ( ( sup_sup_set_rat @ ( set_or4029947393144176647an_rat @ L @ M2 ) @ ( set_or633870826150836451st_rat @ M2 @ U ) )
% 9.17/5.43 = ( set_or633870826150836451st_rat @ L @ U ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7329_ivl__disj__un__two_I7_J,axiom,
% 9.17/5.43 ! [L: num,M2: num,U: num] :
% 9.17/5.43 ( ( ord_less_eq_num @ L @ M2 )
% 9.17/5.43 => ( ( ord_less_eq_num @ M2 @ U )
% 9.17/5.43 => ( ( sup_sup_set_num @ ( set_or1222409239386451017an_num @ L @ M2 ) @ ( set_or7049704709247886629st_num @ M2 @ U ) )
% 9.17/5.43 = ( set_or7049704709247886629st_num @ L @ U ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7330_ivl__disj__un__two_I7_J,axiom,
% 9.17/5.43 ! [L: nat,M2: nat,U: nat] :
% 9.17/5.43 ( ( ord_less_eq_nat @ L @ M2 )
% 9.17/5.43 => ( ( ord_less_eq_nat @ M2 @ U )
% 9.17/5.43 => ( ( sup_sup_set_nat @ ( set_or4665077453230672383an_nat @ L @ M2 ) @ ( set_or1269000886237332187st_nat @ M2 @ U ) )
% 9.17/5.43 = ( set_or1269000886237332187st_nat @ L @ U ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7331_ivl__disj__un__two_I7_J,axiom,
% 9.17/5.43 ! [L: code_integer,M2: code_integer,U: code_integer] :
% 9.17/5.43 ( ( ord_le3102999989581377725nteger @ L @ M2 )
% 9.17/5.43 => ( ( ord_le3102999989581377725nteger @ M2 @ U )
% 9.17/5.43 => ( ( sup_su848401254843788991nteger @ ( set_or8404916559141939852nteger @ L @ M2 ) @ ( set_or189985376899183464nteger @ M2 @ U ) )
% 9.17/5.43 = ( set_or189985376899183464nteger @ L @ U ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7332_ivl__disj__un__two_I7_J,axiom,
% 9.17/5.43 ! [L: int,M2: int,U: int] :
% 9.17/5.43 ( ( ord_less_eq_int @ L @ M2 )
% 9.17/5.43 => ( ( ord_less_eq_int @ M2 @ U )
% 9.17/5.43 => ( ( sup_sup_set_int @ ( set_or4662586982721622107an_int @ L @ M2 ) @ ( set_or1266510415728281911st_int @ M2 @ U ) )
% 9.17/5.43 = ( set_or1266510415728281911st_int @ L @ U ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7333_card__Un__le,axiom,
% 9.17/5.43 ! [A2: set_int,B5: set_int] : ( ord_less_eq_nat @ ( finite_card_int @ ( sup_sup_set_int @ A2 @ B5 ) ) @ ( plus_plus_nat @ ( finite_card_int @ A2 ) @ ( finite_card_int @ B5 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7334_card__Un__le,axiom,
% 9.17/5.43 ! [A2: set_Product_unit,B5: set_Product_unit] : ( ord_less_eq_nat @ ( finite410649719033368117t_unit @ ( sup_su793286257634532545t_unit @ A2 @ B5 ) ) @ ( plus_plus_nat @ ( finite410649719033368117t_unit @ A2 ) @ ( finite410649719033368117t_unit @ B5 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7335_card__Un__le,axiom,
% 9.17/5.43 ! [A2: set_list_nat,B5: set_list_nat] : ( ord_less_eq_nat @ ( finite_card_list_nat @ ( sup_sup_set_list_nat @ A2 @ B5 ) ) @ ( plus_plus_nat @ ( finite_card_list_nat @ A2 ) @ ( finite_card_list_nat @ B5 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7336_card__Un__le,axiom,
% 9.17/5.43 ! [A2: set_nat,B5: set_nat] : ( ord_less_eq_nat @ ( finite_card_nat @ ( sup_sup_set_nat @ A2 @ B5 ) ) @ ( plus_plus_nat @ ( finite_card_nat @ A2 ) @ ( finite_card_nat @ B5 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7337_card__Un__le,axiom,
% 9.17/5.43 ! [A2: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat] : ( ord_less_eq_nat @ ( finite3771342082235030671at_nat @ ( sup_su5525570899277871387at_nat @ A2 @ B5 ) ) @ ( plus_plus_nat @ ( finite3771342082235030671at_nat @ A2 ) @ ( finite3771342082235030671at_nat @ B5 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7338_ivl__disj__un__one_I2_J,axiom,
% 9.17/5.43 ! [L: rat,U: rat] :
% 9.17/5.43 ( ( ord_less_eq_rat @ L @ U )
% 9.17/5.43 => ( ( sup_sup_set_rat @ ( set_ord_lessThan_rat @ L ) @ ( set_or4029947393144176647an_rat @ L @ U ) )
% 9.17/5.43 = ( set_ord_lessThan_rat @ U ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7339_ivl__disj__un__one_I2_J,axiom,
% 9.17/5.43 ! [L: num,U: num] :
% 9.17/5.43 ( ( ord_less_eq_num @ L @ U )
% 9.17/5.43 => ( ( sup_sup_set_num @ ( set_ord_lessThan_num @ L ) @ ( set_or1222409239386451017an_num @ L @ U ) )
% 9.17/5.43 = ( set_ord_lessThan_num @ U ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7340_ivl__disj__un__one_I2_J,axiom,
% 9.17/5.43 ! [L: nat,U: nat] :
% 9.17/5.43 ( ( ord_less_eq_nat @ L @ U )
% 9.17/5.43 => ( ( sup_sup_set_nat @ ( set_ord_lessThan_nat @ L ) @ ( set_or4665077453230672383an_nat @ L @ U ) )
% 9.17/5.43 = ( set_ord_lessThan_nat @ U ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7341_ivl__disj__un__one_I2_J,axiom,
% 9.17/5.43 ! [L: code_integer,U: code_integer] :
% 9.17/5.43 ( ( ord_le3102999989581377725nteger @ L @ U )
% 9.17/5.43 => ( ( sup_su848401254843788991nteger @ ( set_or5754767410780653050nteger @ L ) @ ( set_or8404916559141939852nteger @ L @ U ) )
% 9.17/5.43 = ( set_or5754767410780653050nteger @ U ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7342_ivl__disj__un__one_I2_J,axiom,
% 9.17/5.43 ! [L: int,U: int] :
% 9.17/5.43 ( ( ord_less_eq_int @ L @ U )
% 9.17/5.43 => ( ( sup_sup_set_int @ ( set_ord_lessThan_int @ L ) @ ( set_or4662586982721622107an_int @ L @ U ) )
% 9.17/5.43 = ( set_ord_lessThan_int @ U ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7343_atLeastLessThan__add__Un,axiom,
% 9.17/5.43 ! [I: nat,J: nat,K: nat] :
% 9.17/5.43 ( ( ord_less_eq_nat @ I @ J )
% 9.17/5.43 => ( ( set_or4665077453230672383an_nat @ I @ ( plus_plus_nat @ J @ K ) )
% 9.17/5.43 = ( sup_sup_set_nat @ ( set_or4665077453230672383an_nat @ I @ J ) @ ( set_or4665077453230672383an_nat @ J @ ( plus_plus_nat @ J @ K ) ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7344_uminus__int_Orsp,axiom,
% 9.17/5.43 ( bNF_re2241393799969408733at_nat @ intrel @ intrel
% 9.17/5.43 @ ( produc2626176000494625587at_nat
% 9.17/5.43 @ ^ [X3: nat,Y3: nat] : ( product_Pair_nat_nat @ Y3 @ X3 ) )
% 9.17/5.43 @ ( produc2626176000494625587at_nat
% 9.17/5.43 @ ^ [X3: nat,Y3: nat] : ( product_Pair_nat_nat @ Y3 @ X3 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7345_one__int_Orsp,axiom,
% 9.17/5.43 intrel @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7346_ivl__disj__un__two__touch_I2_J,axiom,
% 9.17/5.43 ! [L: rat,M2: rat,U: rat] :
% 9.17/5.43 ( ( ord_less_eq_rat @ L @ M2 )
% 9.17/5.43 => ( ( ord_less_rat @ M2 @ U )
% 9.17/5.43 => ( ( sup_sup_set_rat @ ( set_or633870826150836451st_rat @ L @ M2 ) @ ( set_or4029947393144176647an_rat @ M2 @ U ) )
% 9.17/5.43 = ( set_or4029947393144176647an_rat @ L @ U ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7347_ivl__disj__un__two__touch_I2_J,axiom,
% 9.17/5.43 ! [L: num,M2: num,U: num] :
% 9.17/5.43 ( ( ord_less_eq_num @ L @ M2 )
% 9.17/5.43 => ( ( ord_less_num @ M2 @ U )
% 9.17/5.43 => ( ( sup_sup_set_num @ ( set_or7049704709247886629st_num @ L @ M2 ) @ ( set_or1222409239386451017an_num @ M2 @ U ) )
% 9.17/5.43 = ( set_or1222409239386451017an_num @ L @ U ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7348_ivl__disj__un__two__touch_I2_J,axiom,
% 9.17/5.43 ! [L: nat,M2: nat,U: nat] :
% 9.17/5.43 ( ( ord_less_eq_nat @ L @ M2 )
% 9.17/5.43 => ( ( ord_less_nat @ M2 @ U )
% 9.17/5.43 => ( ( sup_sup_set_nat @ ( set_or1269000886237332187st_nat @ L @ M2 ) @ ( set_or4665077453230672383an_nat @ M2 @ U ) )
% 9.17/5.43 = ( set_or4665077453230672383an_nat @ L @ U ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7349_ivl__disj__un__two__touch_I2_J,axiom,
% 9.17/5.43 ! [L: code_integer,M2: code_integer,U: code_integer] :
% 9.17/5.43 ( ( ord_le3102999989581377725nteger @ L @ M2 )
% 9.17/5.43 => ( ( ord_le6747313008572928689nteger @ M2 @ U )
% 9.17/5.43 => ( ( sup_su848401254843788991nteger @ ( set_or189985376899183464nteger @ L @ M2 ) @ ( set_or8404916559141939852nteger @ M2 @ U ) )
% 9.17/5.43 = ( set_or8404916559141939852nteger @ L @ U ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7350_ivl__disj__un__two__touch_I2_J,axiom,
% 9.17/5.43 ! [L: int,M2: int,U: int] :
% 9.17/5.43 ( ( ord_less_eq_int @ L @ M2 )
% 9.17/5.43 => ( ( ord_less_int @ M2 @ U )
% 9.17/5.43 => ( ( sup_sup_set_int @ ( set_or1266510415728281911st_int @ L @ M2 ) @ ( set_or4662586982721622107an_int @ M2 @ U ) )
% 9.17/5.43 = ( set_or4662586982721622107an_int @ L @ U ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7351_ivl__disj__un__two_I1_J,axiom,
% 9.17/5.43 ! [L: rat,M2: rat,U: rat] :
% 9.17/5.43 ( ( ord_less_rat @ L @ M2 )
% 9.17/5.43 => ( ( ord_less_eq_rat @ M2 @ U )
% 9.17/5.43 => ( ( sup_sup_set_rat @ ( set_or5199638295745620268an_rat @ L @ M2 ) @ ( set_or4029947393144176647an_rat @ M2 @ U ) )
% 9.17/5.43 = ( set_or5199638295745620268an_rat @ L @ U ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7352_ivl__disj__un__two_I1_J,axiom,
% 9.17/5.43 ! [L: num,M2: num,U: num] :
% 9.17/5.43 ( ( ord_less_num @ L @ M2 )
% 9.17/5.43 => ( ( ord_less_eq_num @ M2 @ U )
% 9.17/5.43 => ( ( sup_sup_set_num @ ( set_or2392100141987894638an_num @ L @ M2 ) @ ( set_or1222409239386451017an_num @ M2 @ U ) )
% 9.17/5.43 = ( set_or2392100141987894638an_num @ L @ U ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7353_ivl__disj__un__two_I1_J,axiom,
% 9.17/5.43 ! [L: int,M2: int,U: int] :
% 9.17/5.43 ( ( ord_less_int @ L @ M2 )
% 9.17/5.43 => ( ( ord_less_eq_int @ M2 @ U )
% 9.17/5.43 => ( ( sup_sup_set_int @ ( set_or5832277885323065728an_int @ L @ M2 ) @ ( set_or4662586982721622107an_int @ M2 @ U ) )
% 9.17/5.43 = ( set_or5832277885323065728an_int @ L @ U ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7354_ivl__disj__un__two_I1_J,axiom,
% 9.17/5.43 ! [L: nat,M2: nat,U: nat] :
% 9.17/5.43 ( ( ord_less_nat @ L @ M2 )
% 9.17/5.43 => ( ( ord_less_eq_nat @ M2 @ U )
% 9.17/5.43 => ( ( sup_sup_set_nat @ ( set_or5834768355832116004an_nat @ L @ M2 ) @ ( set_or4665077453230672383an_nat @ M2 @ U ) )
% 9.17/5.43 = ( set_or5834768355832116004an_nat @ L @ U ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7355_ivl__disj__un__two_I1_J,axiom,
% 9.17/5.43 ! [L: code_integer,M2: code_integer,U: code_integer] :
% 9.17/5.43 ( ( ord_le6747313008572928689nteger @ L @ M2 )
% 9.17/5.43 => ( ( ord_le3102999989581377725nteger @ M2 @ U )
% 9.17/5.43 => ( ( sup_su848401254843788991nteger @ ( set_or4266950643985792945nteger @ L @ M2 ) @ ( set_or8404916559141939852nteger @ M2 @ U ) )
% 9.17/5.43 = ( set_or4266950643985792945nteger @ L @ U ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7356_ivl__disj__un__singleton_I2_J,axiom,
% 9.17/5.43 ! [U: $o] :
% 9.17/5.43 ( ( sup_sup_set_o @ ( set_ord_lessThan_o @ U ) @ ( insert_o @ U @ bot_bot_set_o ) )
% 9.17/5.43 = ( set_ord_atMost_o @ U ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7357_ivl__disj__un__singleton_I2_J,axiom,
% 9.17/5.43 ! [U: int] :
% 9.17/5.43 ( ( sup_sup_set_int @ ( set_ord_lessThan_int @ U ) @ ( insert_int @ U @ bot_bot_set_int ) )
% 9.17/5.43 = ( set_ord_atMost_int @ U ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7358_ivl__disj__un__singleton_I2_J,axiom,
% 9.17/5.43 ! [U: nat] :
% 9.17/5.43 ( ( sup_sup_set_nat @ ( set_ord_lessThan_nat @ U ) @ ( insert_nat @ U @ bot_bot_set_nat ) )
% 9.17/5.43 = ( set_ord_atMost_nat @ U ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7359_ivl__disj__un__one_I4_J,axiom,
% 9.17/5.43 ! [L: rat,U: rat] :
% 9.17/5.43 ( ( ord_less_eq_rat @ L @ U )
% 9.17/5.43 => ( ( sup_sup_set_rat @ ( set_ord_lessThan_rat @ L ) @ ( set_or633870826150836451st_rat @ L @ U ) )
% 9.17/5.43 = ( set_ord_atMost_rat @ U ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7360_ivl__disj__un__one_I4_J,axiom,
% 9.17/5.43 ! [L: num,U: num] :
% 9.17/5.43 ( ( ord_less_eq_num @ L @ U )
% 9.17/5.43 => ( ( sup_sup_set_num @ ( set_ord_lessThan_num @ L ) @ ( set_or7049704709247886629st_num @ L @ U ) )
% 9.17/5.43 = ( set_ord_atMost_num @ U ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7361_ivl__disj__un__one_I4_J,axiom,
% 9.17/5.43 ! [L: int,U: int] :
% 9.17/5.43 ( ( ord_less_eq_int @ L @ U )
% 9.17/5.43 => ( ( sup_sup_set_int @ ( set_ord_lessThan_int @ L ) @ ( set_or1266510415728281911st_int @ L @ U ) )
% 9.17/5.43 = ( set_ord_atMost_int @ U ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7362_ivl__disj__un__one_I4_J,axiom,
% 9.17/5.43 ! [L: nat,U: nat] :
% 9.17/5.43 ( ( ord_less_eq_nat @ L @ U )
% 9.17/5.43 => ( ( sup_sup_set_nat @ ( set_ord_lessThan_nat @ L ) @ ( set_or1269000886237332187st_nat @ L @ U ) )
% 9.17/5.43 = ( set_ord_atMost_nat @ U ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7363_ivl__disj__un__one_I4_J,axiom,
% 9.17/5.43 ! [L: code_integer,U: code_integer] :
% 9.17/5.43 ( ( ord_le3102999989581377725nteger @ L @ U )
% 9.17/5.43 => ( ( sup_su848401254843788991nteger @ ( set_or5754767410780653050nteger @ L ) @ ( set_or189985376899183464nteger @ L @ U ) )
% 9.17/5.43 = ( set_or9101266186257409494nteger @ U ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7364_ivl__disj__un__one_I1_J,axiom,
% 9.17/5.43 ! [L: rat,U: rat] :
% 9.17/5.43 ( ( ord_less_rat @ L @ U )
% 9.17/5.43 => ( ( sup_sup_set_rat @ ( set_ord_atMost_rat @ L ) @ ( set_or5199638295745620268an_rat @ L @ U ) )
% 9.17/5.43 = ( set_ord_lessThan_rat @ U ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7365_ivl__disj__un__one_I1_J,axiom,
% 9.17/5.43 ! [L: num,U: num] :
% 9.17/5.43 ( ( ord_less_num @ L @ U )
% 9.17/5.43 => ( ( sup_sup_set_num @ ( set_ord_atMost_num @ L ) @ ( set_or2392100141987894638an_num @ L @ U ) )
% 9.17/5.43 = ( set_ord_lessThan_num @ U ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7366_ivl__disj__un__one_I1_J,axiom,
% 9.17/5.43 ! [L: int,U: int] :
% 9.17/5.43 ( ( ord_less_int @ L @ U )
% 9.17/5.43 => ( ( sup_sup_set_int @ ( set_ord_atMost_int @ L ) @ ( set_or5832277885323065728an_int @ L @ U ) )
% 9.17/5.43 = ( set_ord_lessThan_int @ U ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7367_ivl__disj__un__one_I1_J,axiom,
% 9.17/5.43 ! [L: nat,U: nat] :
% 9.17/5.43 ( ( ord_less_nat @ L @ U )
% 9.17/5.43 => ( ( sup_sup_set_nat @ ( set_ord_atMost_nat @ L ) @ ( set_or5834768355832116004an_nat @ L @ U ) )
% 9.17/5.43 = ( set_ord_lessThan_nat @ U ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7368_ivl__disj__un__one_I1_J,axiom,
% 9.17/5.43 ! [L: code_integer,U: code_integer] :
% 9.17/5.43 ( ( ord_le6747313008572928689nteger @ L @ U )
% 9.17/5.43 => ( ( sup_su848401254843788991nteger @ ( set_or9101266186257409494nteger @ L ) @ ( set_or4266950643985792945nteger @ L @ U ) )
% 9.17/5.43 = ( set_or5754767410780653050nteger @ U ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7369_intrel__def,axiom,
% 9.17/5.43 ( intrel
% 9.17/5.43 = ( produc8739625826339149834_nat_o
% 9.17/5.43 @ ^ [X3: nat,Y3: nat] :
% 9.17/5.43 ( produc6081775807080527818_nat_o
% 9.17/5.43 @ ^ [U2: nat,V2: nat] :
% 9.17/5.43 ( ( plus_plus_nat @ X3 @ V2 )
% 9.17/5.43 = ( plus_plus_nat @ U2 @ Y3 ) ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7370_ivl__disj__un__singleton_I6_J,axiom,
% 9.17/5.43 ! [L: $o,U: $o] :
% 9.17/5.43 ( ( ord_less_eq_o @ L @ U )
% 9.17/5.43 => ( ( sup_sup_set_o @ ( set_or7139685690850216873Than_o @ L @ U ) @ ( insert_o @ U @ bot_bot_set_o ) )
% 9.17/5.43 = ( set_or8904488021354931149Most_o @ L @ U ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7371_ivl__disj__un__singleton_I6_J,axiom,
% 9.17/5.43 ! [L: rat,U: rat] :
% 9.17/5.43 ( ( ord_less_eq_rat @ L @ U )
% 9.17/5.43 => ( ( sup_sup_set_rat @ ( set_or4029947393144176647an_rat @ L @ U ) @ ( insert_rat @ U @ bot_bot_set_rat ) )
% 9.17/5.43 = ( set_or633870826150836451st_rat @ L @ U ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7372_ivl__disj__un__singleton_I6_J,axiom,
% 9.17/5.43 ! [L: num,U: num] :
% 9.17/5.43 ( ( ord_less_eq_num @ L @ U )
% 9.17/5.43 => ( ( sup_sup_set_num @ ( set_or1222409239386451017an_num @ L @ U ) @ ( insert_num @ U @ bot_bot_set_num ) )
% 9.17/5.43 = ( set_or7049704709247886629st_num @ L @ U ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7373_ivl__disj__un__singleton_I6_J,axiom,
% 9.17/5.43 ! [L: nat,U: nat] :
% 9.17/5.43 ( ( ord_less_eq_nat @ L @ U )
% 9.17/5.43 => ( ( sup_sup_set_nat @ ( set_or4665077453230672383an_nat @ L @ U ) @ ( insert_nat @ U @ bot_bot_set_nat ) )
% 9.17/5.43 = ( set_or1269000886237332187st_nat @ L @ U ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7374_ivl__disj__un__singleton_I6_J,axiom,
% 9.17/5.43 ! [L: code_integer,U: code_integer] :
% 9.17/5.43 ( ( ord_le3102999989581377725nteger @ L @ U )
% 9.17/5.43 => ( ( sup_su848401254843788991nteger @ ( set_or8404916559141939852nteger @ L @ U ) @ ( insert_Code_integer @ U @ bot_bo3990330152332043303nteger ) )
% 9.17/5.43 = ( set_or189985376899183464nteger @ L @ U ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7375_ivl__disj__un__singleton_I6_J,axiom,
% 9.17/5.43 ! [L: int,U: int] :
% 9.17/5.43 ( ( ord_less_eq_int @ L @ U )
% 9.17/5.43 => ( ( sup_sup_set_int @ ( set_or4662586982721622107an_int @ L @ U ) @ ( insert_int @ U @ bot_bot_set_int ) )
% 9.17/5.43 = ( set_or1266510415728281911st_int @ L @ U ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7376_ivl__disj__un__singleton_I3_J,axiom,
% 9.17/5.43 ! [L: $o,U: $o] :
% 9.17/5.43 ( ( ord_less_o @ L @ U )
% 9.17/5.43 => ( ( sup_sup_set_o @ ( insert_o @ L @ bot_bot_set_o ) @ ( set_or1716231572884733764Than_o @ L @ U ) )
% 9.17/5.43 = ( set_or7139685690850216873Than_o @ L @ U ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7377_ivl__disj__un__singleton_I3_J,axiom,
% 9.17/5.43 ! [L: rat,U: rat] :
% 9.17/5.43 ( ( ord_less_rat @ L @ U )
% 9.17/5.43 => ( ( sup_sup_set_rat @ ( insert_rat @ L @ bot_bot_set_rat ) @ ( set_or5199638295745620268an_rat @ L @ U ) )
% 9.17/5.43 = ( set_or4029947393144176647an_rat @ L @ U ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7378_ivl__disj__un__singleton_I3_J,axiom,
% 9.17/5.43 ! [L: num,U: num] :
% 9.17/5.43 ( ( ord_less_num @ L @ U )
% 9.17/5.43 => ( ( sup_sup_set_num @ ( insert_num @ L @ bot_bot_set_num ) @ ( set_or2392100141987894638an_num @ L @ U ) )
% 9.17/5.43 = ( set_or1222409239386451017an_num @ L @ U ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7379_ivl__disj__un__singleton_I3_J,axiom,
% 9.17/5.43 ! [L: int,U: int] :
% 9.17/5.43 ( ( ord_less_int @ L @ U )
% 9.17/5.43 => ( ( sup_sup_set_int @ ( insert_int @ L @ bot_bot_set_int ) @ ( set_or5832277885323065728an_int @ L @ U ) )
% 9.17/5.43 = ( set_or4662586982721622107an_int @ L @ U ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7380_ivl__disj__un__singleton_I3_J,axiom,
% 9.17/5.43 ! [L: nat,U: nat] :
% 9.17/5.43 ( ( ord_less_nat @ L @ U )
% 9.17/5.43 => ( ( sup_sup_set_nat @ ( insert_nat @ L @ bot_bot_set_nat ) @ ( set_or5834768355832116004an_nat @ L @ U ) )
% 9.17/5.43 = ( set_or4665077453230672383an_nat @ L @ U ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7381_ivl__disj__un__singleton_I3_J,axiom,
% 9.17/5.43 ! [L: code_integer,U: code_integer] :
% 9.17/5.43 ( ( ord_le6747313008572928689nteger @ L @ U )
% 9.17/5.43 => ( ( sup_su848401254843788991nteger @ ( insert_Code_integer @ L @ bot_bo3990330152332043303nteger ) @ ( set_or4266950643985792945nteger @ L @ U ) )
% 9.17/5.43 = ( set_or8404916559141939852nteger @ L @ U ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7382_ivl__disj__un__two_I4_J,axiom,
% 9.17/5.43 ! [L: rat,M2: rat,U: rat] :
% 9.17/5.43 ( ( ord_less_eq_rat @ L @ M2 )
% 9.17/5.43 => ( ( ord_less_rat @ M2 @ U )
% 9.17/5.43 => ( ( sup_sup_set_rat @ ( set_or633870826150836451st_rat @ L @ M2 ) @ ( set_or5199638295745620268an_rat @ M2 @ U ) )
% 9.17/5.43 = ( set_or4029947393144176647an_rat @ L @ U ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7383_ivl__disj__un__two_I4_J,axiom,
% 9.17/5.43 ! [L: num,M2: num,U: num] :
% 9.17/5.43 ( ( ord_less_eq_num @ L @ M2 )
% 9.17/5.43 => ( ( ord_less_num @ M2 @ U )
% 9.17/5.43 => ( ( sup_sup_set_num @ ( set_or7049704709247886629st_num @ L @ M2 ) @ ( set_or2392100141987894638an_num @ M2 @ U ) )
% 9.17/5.43 = ( set_or1222409239386451017an_num @ L @ U ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7384_ivl__disj__un__two_I4_J,axiom,
% 9.17/5.43 ! [L: int,M2: int,U: int] :
% 9.17/5.43 ( ( ord_less_eq_int @ L @ M2 )
% 9.17/5.43 => ( ( ord_less_int @ M2 @ U )
% 9.17/5.43 => ( ( sup_sup_set_int @ ( set_or1266510415728281911st_int @ L @ M2 ) @ ( set_or5832277885323065728an_int @ M2 @ U ) )
% 9.17/5.43 = ( set_or4662586982721622107an_int @ L @ U ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7385_ivl__disj__un__two_I4_J,axiom,
% 9.17/5.43 ! [L: nat,M2: nat,U: nat] :
% 9.17/5.43 ( ( ord_less_eq_nat @ L @ M2 )
% 9.17/5.43 => ( ( ord_less_nat @ M2 @ U )
% 9.17/5.43 => ( ( sup_sup_set_nat @ ( set_or1269000886237332187st_nat @ L @ M2 ) @ ( set_or5834768355832116004an_nat @ M2 @ U ) )
% 9.17/5.43 = ( set_or4665077453230672383an_nat @ L @ U ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7386_ivl__disj__un__two_I4_J,axiom,
% 9.17/5.43 ! [L: code_integer,M2: code_integer,U: code_integer] :
% 9.17/5.43 ( ( ord_le3102999989581377725nteger @ L @ M2 )
% 9.17/5.43 => ( ( ord_le6747313008572928689nteger @ M2 @ U )
% 9.17/5.43 => ( ( sup_su848401254843788991nteger @ ( set_or189985376899183464nteger @ L @ M2 ) @ ( set_or4266950643985792945nteger @ M2 @ U ) )
% 9.17/5.43 = ( set_or8404916559141939852nteger @ L @ U ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7387_less__int_Orsp,axiom,
% 9.17/5.43 ( bNF_re4202695980764964119_nat_o @ intrel
% 9.17/5.43 @ ( bNF_re3666534408544137501at_o_o @ intrel
% 9.17/5.43 @ ^ [Y4: $o,Z2: $o] : ( Y4 = Z2 ) )
% 9.17/5.43 @ ( produc8739625826339149834_nat_o
% 9.17/5.43 @ ^ [X3: nat,Y3: nat] :
% 9.17/5.43 ( produc6081775807080527818_nat_o
% 9.17/5.43 @ ^ [U2: nat,V2: nat] : ( ord_less_nat @ ( plus_plus_nat @ X3 @ V2 ) @ ( plus_plus_nat @ U2 @ Y3 ) ) ) )
% 9.17/5.43 @ ( produc8739625826339149834_nat_o
% 9.17/5.43 @ ^ [X3: nat,Y3: nat] :
% 9.17/5.43 ( produc6081775807080527818_nat_o
% 9.17/5.43 @ ^ [U2: nat,V2: nat] : ( ord_less_nat @ ( plus_plus_nat @ X3 @ V2 ) @ ( plus_plus_nat @ U2 @ Y3 ) ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7388_less__eq__int_Orsp,axiom,
% 9.17/5.43 ( bNF_re4202695980764964119_nat_o @ intrel
% 9.17/5.43 @ ( bNF_re3666534408544137501at_o_o @ intrel
% 9.17/5.43 @ ^ [Y4: $o,Z2: $o] : ( Y4 = Z2 ) )
% 9.17/5.43 @ ( produc8739625826339149834_nat_o
% 9.17/5.43 @ ^ [X3: nat,Y3: nat] :
% 9.17/5.43 ( produc6081775807080527818_nat_o
% 9.17/5.43 @ ^ [U2: nat,V2: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X3 @ V2 ) @ ( plus_plus_nat @ U2 @ Y3 ) ) ) )
% 9.17/5.43 @ ( produc8739625826339149834_nat_o
% 9.17/5.43 @ ^ [X3: nat,Y3: nat] :
% 9.17/5.43 ( produc6081775807080527818_nat_o
% 9.17/5.43 @ ^ [U2: nat,V2: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X3 @ V2 ) @ ( plus_plus_nat @ U2 @ Y3 ) ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7389_plus__int_Orsp,axiom,
% 9.17/5.43 ( bNF_re3099431351363272937at_nat @ intrel @ ( bNF_re2241393799969408733at_nat @ intrel @ intrel )
% 9.17/5.43 @ ( produc27273713700761075at_nat
% 9.17/5.43 @ ^ [X3: nat,Y3: nat] :
% 9.17/5.43 ( produc2626176000494625587at_nat
% 9.17/5.43 @ ^ [U2: nat,V2: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X3 @ U2 ) @ ( plus_plus_nat @ Y3 @ V2 ) ) ) )
% 9.17/5.43 @ ( produc27273713700761075at_nat
% 9.17/5.43 @ ^ [X3: nat,Y3: nat] :
% 9.17/5.43 ( produc2626176000494625587at_nat
% 9.17/5.43 @ ^ [U2: nat,V2: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X3 @ U2 ) @ ( plus_plus_nat @ Y3 @ V2 ) ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7390_minus__int_Orsp,axiom,
% 9.17/5.43 ( bNF_re3099431351363272937at_nat @ intrel @ ( bNF_re2241393799969408733at_nat @ intrel @ intrel )
% 9.17/5.43 @ ( produc27273713700761075at_nat
% 9.17/5.43 @ ^ [X3: nat,Y3: nat] :
% 9.17/5.43 ( produc2626176000494625587at_nat
% 9.17/5.43 @ ^ [U2: nat,V2: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X3 @ V2 ) @ ( plus_plus_nat @ Y3 @ U2 ) ) ) )
% 9.17/5.43 @ ( produc27273713700761075at_nat
% 9.17/5.43 @ ^ [X3: nat,Y3: nat] :
% 9.17/5.43 ( produc2626176000494625587at_nat
% 9.17/5.43 @ ^ [U2: nat,V2: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X3 @ V2 ) @ ( plus_plus_nat @ Y3 @ U2 ) ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7391_max__weak__def,axiom,
% 9.17/5.43 ( fun_max_weak
% 9.17/5.43 = ( sup_su5525570899277871387at_nat @ ( max_ex8135407076693332796at_nat @ fun_pair_leq ) @ ( insert9069300056098147895at_nat @ ( produc2922128104949294807at_nat @ bot_bo2099793752762293965at_nat @ bot_bo2099793752762293965at_nat ) @ bot_bo228742789529271731at_nat ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7392_min__weak__def,axiom,
% 9.17/5.43 ( fun_min_weak
% 9.17/5.43 = ( sup_su5525570899277871387at_nat @ ( min_ex6901939911449802026at_nat @ fun_pair_leq ) @ ( insert9069300056098147895at_nat @ ( produc2922128104949294807at_nat @ bot_bo2099793752762293965at_nat @ bot_bo2099793752762293965at_nat ) @ bot_bo228742789529271731at_nat ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7393_fold__union__pair,axiom,
% 9.17/5.43 ! [B5: set_Pr4811707699266497531nteger,X: produc6241069584506657477e_term > option6357759511663192854e_term,A2: set_Pr1281608226676607948nteger] :
% 9.17/5.43 ( ( finite2154694888287295812nteger @ B5 )
% 9.17/5.43 => ( ( sup_su4591284015454442744nteger
% 9.17/5.43 @ ( comple1324685164916153887nteger
% 9.17/5.43 @ ( image_5715966689554962722nteger
% 9.17/5.43 @ ^ [Y3: produc8923325533196201883nteger] : ( insert4245756632806152262nteger @ ( produc8603105652947943368nteger @ X @ Y3 ) @ bot_bo5443222936135328352nteger )
% 9.17/5.43 @ B5 ) )
% 9.17/5.43 @ A2 )
% 9.17/5.43 = ( finite7641027033760462367nteger
% 9.17/5.43 @ ^ [Y3: produc8923325533196201883nteger] : ( insert4245756632806152262nteger @ ( produc8603105652947943368nteger @ X @ Y3 ) )
% 9.17/5.43 @ A2
% 9.17/5.43 @ B5 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7394_fold__union__pair,axiom,
% 9.17/5.43 ! [B5: set_Pr3948176798113811640et_nat,X: produc3658429121746597890et_nat > $o,A2: set_Pr3286484037609594932et_nat] :
% 9.17/5.43 ( ( finite2970523954037356441et_nat @ B5 )
% 9.17/5.43 => ( ( sup_su7128418612487073120et_nat
% 9.17/5.43 @ ( comple4849024849677941639et_nat
% 9.17/5.43 @ ( image_15228131989405757et_nat
% 9.17/5.43 @ ^ [Y3: produc3658429121746597890et_nat] : ( insert3111075074545270702et_nat @ ( produc5001842942810119800et_nat @ X @ Y3 ) @ bot_bo1481135142794719944et_nat )
% 9.17/5.43 @ B5 ) )
% 9.17/5.43 @ A2 )
% 9.17/5.43 = ( finite2494574492299216512et_nat
% 9.17/5.43 @ ^ [Y3: produc3658429121746597890et_nat] : ( insert3111075074545270702et_nat @ ( produc5001842942810119800et_nat @ X @ Y3 ) )
% 9.17/5.43 @ A2
% 9.17/5.43 @ B5 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7395_fold__union__pair,axiom,
% 9.17/5.43 ! [B5: set_Pr3286484037609594932et_nat,X: produc3658429121746597890et_nat > $o,A2: set_Pr8536935166611901872et_nat] :
% 9.17/5.43 ( ( finite4151335170723375381et_nat @ B5 )
% 9.17/5.43 => ( ( sup_su8975264963432250076et_nat
% 9.17/5.43 @ ( comple5063570841203093763et_nat
% 9.17/5.43 @ ( image_8189767104526903093et_nat
% 9.17/5.43 @ ^ [Y3: produc3925858234332021118et_nat] : ( insert8297122186708525866et_nat @ ( produc2245416461498447860et_nat @ X @ Y3 ) @ bot_bo5635537948650799172et_nat )
% 9.17/5.43 @ B5 ) )
% 9.17/5.43 @ A2 )
% 9.17/5.43 = ( finite8124994865635982712et_nat
% 9.17/5.43 @ ^ [Y3: produc3925858234332021118et_nat] : ( insert8297122186708525866et_nat @ ( produc2245416461498447860et_nat @ X @ Y3 ) )
% 9.17/5.43 @ A2
% 9.17/5.43 @ B5 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7396_fold__union__pair,axiom,
% 9.17/5.43 ! [B5: set_Pr958786334691620121nt_int,X: produc8551481072490612790e_term > option6357759511663192854e_term,A2: set_Pr9222295170931077689nt_int] :
% 9.17/5.43 ( ( finite2998713641127702882nt_int @ B5 )
% 9.17/5.43 => ( ( sup_su3382966977382714213nt_int
% 9.17/5.43 @ ( comple6871990601243273356nt_int
% 9.17/5.43 @ ( image_815654828163180973nt_int
% 9.17/5.43 @ ^ [Y3: product_prod_int_int] : ( insert984290209421517107nt_int @ ( produc5700946648718959541nt_int @ X @ Y3 ) @ bot_bo572930865798478029nt_int )
% 9.17/5.43 @ B5 ) )
% 9.17/5.43 @ A2 )
% 9.17/5.43 = ( finite1318812335397358250nt_int
% 9.17/5.43 @ ^ [Y3: product_prod_int_int] : ( insert984290209421517107nt_int @ ( produc5700946648718959541nt_int @ X @ Y3 ) )
% 9.17/5.43 @ A2
% 9.17/5.43 @ B5 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7397_fold__union__pair,axiom,
% 9.17/5.43 ! [B5: set_Pr958786334691620121nt_int,X: int > option6357759511663192854e_term,A2: set_Pr1872883991513573699nt_int] :
% 9.17/5.43 ( ( finite2998713641127702882nt_int @ B5 )
% 9.17/5.43 => ( ( sup_su3298353300217089135nt_int
% 9.17/5.43 @ ( comple5772984051336441366nt_int
% 9.17/5.43 @ ( image_5963362749323609783nt_int
% 9.17/5.43 @ ^ [Y3: product_prod_int_int] : ( insert750232675644355261nt_int @ ( produc4305682042979456191nt_int @ X @ Y3 ) @ bot_bo4508923176915781079nt_int )
% 9.17/5.43 @ B5 ) )
% 9.17/5.43 @ A2 )
% 9.17/5.43 = ( finite5333674244414288180nt_int
% 9.17/5.43 @ ^ [Y3: product_prod_int_int] : ( insert750232675644355261nt_int @ ( produc4305682042979456191nt_int @ X @ Y3 ) )
% 9.17/5.43 @ A2
% 9.17/5.43 @ B5 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7398_fold__union__pair,axiom,
% 9.17/5.43 ! [B5: set_se7855581050983116737at_nat,X: set_Pr1261947904930325089at_nat,A2: set_Pr4329608150637261639at_nat] :
% 9.17/5.43 ( ( finite9047747110432174090at_nat @ B5 )
% 9.17/5.43 => ( ( sup_su5525570899277871387at_nat
% 9.17/5.43 @ ( comple4364388969068068532at_nat
% 9.17/5.43 @ ( image_6898982319499645995at_nat
% 9.17/5.43 @ ^ [Y3: set_Pr1261947904930325089at_nat] : ( insert9069300056098147895at_nat @ ( produc2922128104949294807at_nat @ X @ Y3 ) @ bot_bo228742789529271731at_nat )
% 9.17/5.43 @ B5 ) )
% 9.17/5.43 @ A2 )
% 9.17/5.43 = ( finite3179781904389220718at_nat
% 9.17/5.43 @ ^ [Y3: set_Pr1261947904930325089at_nat] : ( insert9069300056098147895at_nat @ ( produc2922128104949294807at_nat @ X @ Y3 ) )
% 9.17/5.43 @ A2
% 9.17/5.43 @ B5 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7399_fold__union__pair,axiom,
% 9.17/5.43 ! [B5: set_nat,X: nat,A2: set_Pr1261947904930325089at_nat] :
% 9.17/5.43 ( ( finite_finite_nat @ B5 )
% 9.17/5.43 => ( ( sup_su6327502436637775413at_nat
% 9.17/5.43 @ ( comple5685304695842803022at_nat
% 9.17/5.43 @ ( image_7178329752028323786at_nat
% 9.17/5.43 @ ^ [Y3: nat] : ( insert8211810215607154385at_nat @ ( product_Pair_nat_nat @ X @ Y3 ) @ bot_bo2099793752762293965at_nat )
% 9.17/5.43 @ B5 ) )
% 9.17/5.43 @ A2 )
% 9.17/5.43 = ( finite3745491028973389255at_nat
% 9.17/5.43 @ ^ [Y3: nat] : ( insert8211810215607154385at_nat @ ( product_Pair_nat_nat @ X @ Y3 ) )
% 9.17/5.43 @ A2
% 9.17/5.43 @ B5 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7400_Field__insert,axiom,
% 9.17/5.43 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,R2: set_Pr4329608150637261639at_nat] :
% 9.17/5.43 ( ( field_3145993188331922222at_nat @ ( insert9069300056098147895at_nat @ ( produc2922128104949294807at_nat @ A @ B ) @ R2 ) )
% 9.17/5.43 = ( sup_su3642409539654194069at_nat @ ( insert9200635055090092081at_nat @ A @ ( insert9200635055090092081at_nat @ B @ bot_bo3083307316010499117at_nat ) ) @ ( field_3145993188331922222at_nat @ R2 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7401_Field__insert,axiom,
% 9.17/5.43 ! [A: produc3843707927480180839at_nat,B: produc3843707927480180839at_nat,R2: set_Pr5564308138774400199at_nat] :
% 9.17/5.43 ( ( field_2862844103579723188at_nat @ ( insert398606708087465655at_nat @ ( produc2335810615602371415at_nat @ A @ B ) @ R2 ) )
% 9.17/5.43 = ( sup_su5525570899277871387at_nat @ ( insert9069300056098147895at_nat @ A @ ( insert9069300056098147895at_nat @ B @ bot_bo228742789529271731at_nat ) ) @ ( field_2862844103579723188at_nat @ R2 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7402_Field__insert,axiom,
% 9.17/5.43 ! [A: product_prod_nat_nat,B: product_prod_nat_nat,R2: set_Pr8693737435421807431at_nat] :
% 9.17/5.43 ( ( field_4706345496283612622at_nat @ ( insert5050368324300391991at_nat @ ( produc6161850002892822231at_nat @ A @ B ) @ R2 ) )
% 9.17/5.43 = ( sup_su6327502436637775413at_nat @ ( insert8211810215607154385at_nat @ A @ ( insert8211810215607154385at_nat @ B @ bot_bo2099793752762293965at_nat ) ) @ ( field_4706345496283612622at_nat @ R2 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7403_Field__insert,axiom,
% 9.17/5.43 ! [A: $o,B: $o,R2: set_Product_prod_o_o] :
% 9.17/5.43 ( ( field_o @ ( insert6201435330877294327od_o_o @ ( product_Pair_o_o @ A @ B ) @ R2 ) )
% 9.17/5.43 = ( sup_sup_set_o @ ( insert_o @ A @ ( insert_o @ B @ bot_bot_set_o ) ) @ ( field_o @ R2 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7404_Field__insert,axiom,
% 9.17/5.43 ! [A: nat,B: nat,R2: set_Pr1261947904930325089at_nat] :
% 9.17/5.43 ( ( field_nat @ ( insert8211810215607154385at_nat @ ( product_Pair_nat_nat @ A @ B ) @ R2 ) )
% 9.17/5.43 = ( sup_sup_set_nat @ ( insert_nat @ A @ ( insert_nat @ B @ bot_bot_set_nat ) ) @ ( field_nat @ R2 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7405_Field__insert,axiom,
% 9.17/5.43 ! [A: int,B: int,R2: set_Pr958786334691620121nt_int] :
% 9.17/5.43 ( ( field_int @ ( insert5033312907999012233nt_int @ ( product_Pair_int_int @ A @ B ) @ R2 ) )
% 9.17/5.43 = ( sup_sup_set_int @ ( insert_int @ A @ ( insert_int @ B @ bot_bot_set_int ) ) @ ( field_int @ R2 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7406_set__to__map__insert,axiom,
% 9.17/5.43 ! [Kv: product_prod_nat_nat,S2: set_Pr1261947904930325089at_nat] :
% 9.17/5.43 ( ~ ( member_nat @ ( product_fst_nat_nat @ Kv ) @ ( image_2486076414777270412at_nat @ product_fst_nat_nat @ S2 ) )
% 9.17/5.43 => ( ( set_to_map_nat_nat @ ( insert8211810215607154385at_nat @ Kv @ S2 ) )
% 9.17/5.43 = ( fun_up1493157387958331631on_nat @ ( set_to_map_nat_nat @ S2 ) @ ( product_fst_nat_nat @ Kv ) @ ( some_nat @ ( product_snd_nat_nat @ Kv ) ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7407_set__to__map__insert,axiom,
% 9.17/5.43 ! [Kv: product_prod_o_num,S2: set_Pr7040061329075590551_o_num] :
% 9.17/5.43 ( ~ ( member_o @ ( product_fst_o_num @ Kv ) @ ( image_8863890952250787504_num_o @ product_fst_o_num @ S2 ) )
% 9.17/5.43 => ( ( set_to_map_o_num @ ( insert8656458676507137553_o_num @ Kv @ S2 ) )
% 9.17/5.43 = ( fun_upd_o_option_num @ ( set_to_map_o_num @ S2 ) @ ( product_fst_o_num @ Kv ) @ ( some_num @ ( product_snd_o_num @ Kv ) ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7408_set__to__map__insert,axiom,
% 9.17/5.43 ! [Kv: product_prod_nat_num,S2: set_Pr6200539531224447659at_num] :
% 9.17/5.43 ( ~ ( member_nat @ ( product_fst_nat_num @ Kv ) @ ( image_4504471508743443926um_nat @ product_fst_nat_num @ S2 ) )
% 9.17/5.43 => ( ( set_to_map_nat_num @ ( insert8920054152555992091at_num @ Kv @ S2 ) )
% 9.17/5.43 = ( fun_up2201401324907169337on_num @ ( set_to_map_nat_num @ S2 ) @ ( product_fst_nat_num @ Kv ) @ ( some_num @ ( product_snd_nat_num @ Kv ) ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7409_set__to__map__insert,axiom,
% 9.17/5.43 ! [Kv: product_prod_int_num,S2: set_Pr8387461105917469447nt_num] :
% 9.17/5.43 ( ~ ( member_int @ ( product_fst_int_num @ Kv ) @ ( image_4873634598471238286um_int @ product_fst_int_num @ S2 ) )
% 9.17/5.43 => ( ( set_to_map_int_num @ ( insert696035827602270839nt_num @ Kv @ S2 ) )
% 9.17/5.43 = ( fun_up4328768054909231765on_num @ ( set_to_map_int_num @ S2 ) @ ( product_fst_int_num @ Kv ) @ ( some_num @ ( product_snd_int_num @ Kv ) ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7410_set__to__map__insert,axiom,
% 9.17/5.43 ! [Kv: produc8923325533196201883nteger,S2: set_Pr4811707699266497531nteger] :
% 9.17/5.43 ( ~ ( member_Code_integer @ ( produc8508995932063986495nteger @ Kv ) @ ( image_6316824473203919795nteger @ produc8508995932063986495nteger @ S2 ) )
% 9.17/5.43 => ( ( set_to6264436334439079987nteger @ ( insert4913895101485356395nteger @ Kv @ S2 ) )
% 9.17/5.43 = ( fun_up6566892301432185865nteger @ ( set_to6264436334439079987nteger @ S2 ) @ ( produc8508995932063986495nteger @ Kv ) @ ( some_Code_integer @ ( produc6174133586879617921nteger @ Kv ) ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7411_set__to__map__insert,axiom,
% 9.17/5.43 ! [Kv: product_prod_int_int,S2: set_Pr958786334691620121nt_int] :
% 9.17/5.43 ( ~ ( member_int @ ( product_fst_int_int @ Kv ) @ ( image_5042161079198086560nt_int @ product_fst_int_int @ S2 ) )
% 9.17/5.43 => ( ( set_to_map_int_int @ ( insert5033312907999012233nt_int @ Kv @ S2 ) )
% 9.17/5.43 = ( fun_up8666045135305973159on_int @ ( set_to_map_int_int @ S2 ) @ ( product_fst_int_int @ Kv ) @ ( some_int @ ( product_snd_int_int @ Kv ) ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7412_set__to__map__insert,axiom,
% 9.17/5.43 ! [Kv: produc9082142974458947146at_num,S2: set_Pr7477759153910077568at_num] :
% 9.17/5.43 ( ~ ( member8440522571783428010at_nat @ ( produc1179527155093393624at_num @ Kv ) @ ( image_7418169580930627696at_nat @ produc1179527155093393624at_num @ S2 ) )
% 9.17/5.43 => ( ( set_to5081529003106763492at_num @ ( insert2790150385885543546at_num @ Kv @ S2 ) )
% 9.17/5.43 = ( fun_up8025039454679724718on_num @ ( set_to5081529003106763492at_num @ S2 ) @ ( produc1179527155093393624at_num @ Kv ) @ ( some_num @ ( produc8847702614181477910at_num @ Kv ) ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7413_set__to__map__insert,axiom,
% 9.17/5.43 ! [Kv: produc5835291356934675326atural,S2: set_Pr2352657477744078772atural] :
% 9.17/5.43 ( ~ ( member_Code_natural @ ( produc497848011034438852atural @ Kv ) @ ( image_8194678751871465133atural @ produc497848011034438852atural @ S2 ) )
% 9.17/5.43 => ( ( set_to6039658477269176016atural @ ( insert6505218763252461998atural @ Kv @ S2 ) )
% 9.17/5.43 = ( fun_up2923169431403285008atural @ ( set_to6039658477269176016atural @ S2 ) @ ( produc497848011034438852atural @ Kv ) @ ( some_P5671840033927537686atural @ ( produc6591912806276919810atural @ Kv ) ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7414_set__to__map__insert,axiom,
% 9.17/5.43 ! [Kv: produc2900562427881843919it_nat,S2: set_Pr6777250647868329861it_nat] :
% 9.17/5.43 ( ~ ( member_o @ ( produc1440270732834495325it_nat @ Kv ) @ ( image_5849890305759347266_nat_o @ produc1440270732834495325it_nat @ S2 ) )
% 9.17/5.43 => ( ( set_to3023635543527487849it_nat @ ( insert6915099157023601407it_nat @ Kv @ S2 ) )
% 9.17/5.43 = ( fun_up1288979561775348147it_nat @ ( set_to3023635543527487849it_nat @ S2 ) @ ( produc1440270732834495325it_nat @ Kv ) @ ( some_P1914260805536162275it_nat @ ( produc5978051280710547099it_nat @ Kv ) ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7415_set__to__map__insert,axiom,
% 9.17/5.43 ! [Kv: produc3839731585411834681it_nat,S2: set_Pr633603713510679705it_nat] :
% 9.17/5.43 ( ~ ( member_nat @ ( produc5854401122675660893it_nat @ Kv ) @ ( image_5261730836495542980at_nat @ produc5854401122675660893it_nat @ S2 ) )
% 9.17/5.43 => ( ( set_to785951348762482001it_nat @ ( insert2528233410557839625it_nat @ Kv @ S2 ) )
% 9.17/5.43 = ( fun_up4116053422210368295it_nat @ ( set_to785951348762482001it_nat @ S2 ) @ ( produc5854401122675660893it_nat @ Kv ) @ ( some_P1914260805536162275it_nat @ ( produc8417671938598930591it_nat @ Kv ) ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7416_plus__rat_Orsp,axiom,
% 9.17/5.43 ( bNF_re5228765855967844073nt_int @ ratrel @ ( bNF_re7145576690424134365nt_int @ ratrel @ ratrel )
% 9.17/5.43 @ ^ [X3: product_prod_int_int,Y3: product_prod_int_int] : ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ X3 ) @ ( product_snd_int_int @ Y3 ) ) @ ( times_times_int @ ( product_fst_int_int @ Y3 ) @ ( product_snd_int_int @ X3 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ X3 ) @ ( product_snd_int_int @ Y3 ) ) )
% 9.17/5.43 @ ^ [X3: product_prod_int_int,Y3: product_prod_int_int] : ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ X3 ) @ ( product_snd_int_int @ Y3 ) ) @ ( times_times_int @ ( product_fst_int_int @ Y3 ) @ ( product_snd_int_int @ X3 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ X3 ) @ ( product_snd_int_int @ Y3 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7417_inverse__rat_Orsp,axiom,
% 9.17/5.43 ( bNF_re7145576690424134365nt_int @ ratrel @ ratrel
% 9.17/5.43 @ ^ [X3: product_prod_int_int] :
% 9.17/5.43 ( if_Pro3027730157355071871nt_int
% 9.17/5.43 @ ( ( product_fst_int_int @ X3 )
% 9.17/5.43 = zero_zero_int )
% 9.17/5.43 @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 9.17/5.43 @ ( product_Pair_int_int @ ( product_snd_int_int @ X3 ) @ ( product_fst_int_int @ X3 ) ) )
% 9.17/5.43 @ ^ [X3: product_prod_int_int] :
% 9.17/5.43 ( if_Pro3027730157355071871nt_int
% 9.17/5.43 @ ( ( product_fst_int_int @ X3 )
% 9.17/5.43 = zero_zero_int )
% 9.17/5.43 @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 9.17/5.43 @ ( product_Pair_int_int @ ( product_snd_int_int @ X3 ) @ ( product_fst_int_int @ X3 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7418_image__update,axiom,
% 9.17/5.43 ! [X: nat,A2: set_nat,F: nat > code_integer,N2: code_integer] :
% 9.17/5.43 ( ~ ( member_nat @ X @ A2 )
% 9.17/5.43 => ( ( image_1215581382706833972nteger @ ( fun_up3904115110581602988nteger @ F @ X @ N2 ) @ A2 )
% 9.17/5.43 = ( image_1215581382706833972nteger @ F @ A2 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7419_image__update,axiom,
% 9.17/5.43 ! [X: nat,A2: set_nat,F: nat > set_nat,N2: set_nat] :
% 9.17/5.43 ( ~ ( member_nat @ X @ A2 )
% 9.17/5.43 => ( ( image_nat_set_nat @ ( fun_upd_nat_set_nat @ F @ X @ N2 ) @ A2 )
% 9.17/5.43 = ( image_nat_set_nat @ F @ A2 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7420_image__update,axiom,
% 9.17/5.43 ! [X: nat,A2: set_nat,F: nat > nat,N2: nat] :
% 9.17/5.43 ( ~ ( member_nat @ X @ A2 )
% 9.17/5.43 => ( ( image_nat_nat @ ( fun_upd_nat_nat @ F @ X @ N2 ) @ A2 )
% 9.17/5.43 = ( image_nat_nat @ F @ A2 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7421_image__update,axiom,
% 9.17/5.43 ! [X: nat,A2: set_nat,F: nat > int,N2: int] :
% 9.17/5.43 ( ~ ( member_nat @ X @ A2 )
% 9.17/5.43 => ( ( image_nat_int @ ( fun_upd_nat_int @ F @ X @ N2 ) @ A2 )
% 9.17/5.43 = ( image_nat_int @ F @ A2 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7422_image__update,axiom,
% 9.17/5.43 ! [X: int,A2: set_int,F: int > int,N2: int] :
% 9.17/5.43 ( ~ ( member_int @ X @ A2 )
% 9.17/5.43 => ( ( image_int_int @ ( fun_upd_int_int @ F @ X @ N2 ) @ A2 )
% 9.17/5.43 = ( image_int_int @ F @ A2 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7423_finite__Field__eq__finite,axiom,
% 9.17/5.43 ! [R4: set_Product_prod_o_o] :
% 9.17/5.43 ( ( finite_finite_o @ ( field_o @ R4 ) )
% 9.17/5.43 = ( finite6120865539452801872od_o_o @ R4 ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7424_finite__Field__eq__finite,axiom,
% 9.17/5.43 ! [R4: set_Pr1261947904930325089at_nat] :
% 9.17/5.43 ( ( finite_finite_nat @ ( field_nat @ R4 ) )
% 9.17/5.43 = ( finite6177210948735845034at_nat @ R4 ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7425_finite__Field__eq__finite,axiom,
% 9.17/5.43 ! [R4: set_Pr958786334691620121nt_int] :
% 9.17/5.43 ( ( finite_finite_int @ ( field_int @ R4 ) )
% 9.17/5.43 = ( finite2998713641127702882nt_int @ R4 ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7426_finite__Field__eq__finite,axiom,
% 9.17/5.43 ! [R4: set_Pr4811707699266497531nteger] :
% 9.17/5.43 ( ( finite6017078050557962740nteger @ ( field_Code_integer @ R4 ) )
% 9.17/5.43 = ( finite2154694888287295812nteger @ R4 ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7427_finite__Field__eq__finite,axiom,
% 9.17/5.43 ! [R4: set_Pr8693737435421807431at_nat] :
% 9.17/5.43 ( ( finite6177210948735845034at_nat @ ( field_4706345496283612622at_nat @ R4 ) )
% 9.17/5.43 = ( finite4392333629123659920at_nat @ R4 ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7428_image__map__upd,axiom,
% 9.17/5.43 ! [X: produc3843707927480180839at_nat,A2: set_Pr4329608150637261639at_nat,M2: produc3843707927480180839at_nat > option_num,Y: num] :
% 9.17/5.43 ( ~ ( member8757157785044589968at_nat @ X @ A2 )
% 9.17/5.43 => ( ( image_8464016542990802060on_num @ ( fun_up3286109336741039636on_num @ M2 @ X @ ( some_num @ Y ) ) @ A2 )
% 9.17/5.43 = ( image_8464016542990802060on_num @ M2 @ A2 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7429_image__map__upd,axiom,
% 9.17/5.43 ! [X: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,M2: product_prod_nat_nat > option_num,Y: num] :
% 9.17/5.43 ( ~ ( member8440522571783428010at_nat @ X @ A2 )
% 9.17/5.43 => ( ( image_1023191801488348454on_num @ ( fun_up8025039454679724718on_num @ M2 @ X @ ( some_num @ Y ) ) @ A2 )
% 9.17/5.43 = ( image_1023191801488348454on_num @ M2 @ A2 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7430_image__map__upd,axiom,
% 9.17/5.43 ! [X: $o,A2: set_o,M2: $o > option_num,Y: num] :
% 9.17/5.43 ( ~ ( member_o @ X @ A2 )
% 9.17/5.43 => ( ( image_o_option_num @ ( fun_upd_o_option_num @ M2 @ X @ ( some_num @ Y ) ) @ A2 )
% 9.17/5.43 = ( image_o_option_num @ M2 @ A2 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7431_image__map__upd,axiom,
% 9.17/5.43 ! [X: nat,A2: set_nat,M2: nat > option_num,Y: num] :
% 9.17/5.43 ( ~ ( member_nat @ X @ A2 )
% 9.17/5.43 => ( ( image_nat_option_num @ ( fun_up2201401324907169337on_num @ M2 @ X @ ( some_num @ Y ) ) @ A2 )
% 9.17/5.43 = ( image_nat_option_num @ M2 @ A2 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7432_image__map__upd,axiom,
% 9.17/5.43 ! [X: int,A2: set_int,M2: int > option_num,Y: num] :
% 9.17/5.43 ( ~ ( member_int @ X @ A2 )
% 9.17/5.43 => ( ( image_int_option_num @ ( fun_up4328768054909231765on_num @ M2 @ X @ ( some_num @ Y ) ) @ A2 )
% 9.17/5.43 = ( image_int_option_num @ M2 @ A2 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7433_image__map__upd,axiom,
% 9.17/5.43 ! [X: produc3843707927480180839at_nat,A2: set_Pr4329608150637261639at_nat,M2: produc3843707927480180839at_nat > option8956607266484857688it_nat,Y: produc8664842809031399944it_nat] :
% 9.17/5.43 ( ~ ( member8757157785044589968at_nat @ X @ A2 )
% 9.17/5.43 => ( ( image_140351626946063738it_nat @ ( fun_up5549328659429834498it_nat @ M2 @ X @ ( some_P1914260805536162275it_nat @ Y ) ) @ A2 )
% 9.17/5.43 = ( image_140351626946063738it_nat @ M2 @ A2 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7434_image__map__upd,axiom,
% 9.17/5.43 ! [X: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,M2: product_prod_nat_nat > option8956607266484857688it_nat,Y: produc8664842809031399944it_nat] :
% 9.17/5.43 ( ~ ( member8440522571783428010at_nat @ X @ A2 )
% 9.17/5.43 => ( ( image_5755308894823448084it_nat @ ( fun_up3996838528606387100it_nat @ M2 @ X @ ( some_P1914260805536162275it_nat @ Y ) ) @ A2 )
% 9.17/5.43 = ( image_5755308894823448084it_nat @ M2 @ A2 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7435_image__map__upd,axiom,
% 9.17/5.43 ! [X: $o,A2: set_o,M2: $o > option8956607266484857688it_nat,Y: produc8664842809031399944it_nat] :
% 9.17/5.43 ( ~ ( member_o @ X @ A2 )
% 9.17/5.43 => ( ( image_5849929686412825643it_nat @ ( fun_up1288979561775348147it_nat @ M2 @ X @ ( some_P1914260805536162275it_nat @ Y ) ) @ A2 )
% 9.17/5.43 = ( image_5849929686412825643it_nat @ M2 @ A2 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7436_image__map__upd,axiom,
% 9.17/5.43 ! [X: nat,A2: set_nat,M2: nat > option8956607266484857688it_nat,Y: produc8664842809031399944it_nat] :
% 9.17/5.43 ( ~ ( member_nat @ X @ A2 )
% 9.17/5.43 => ( ( image_5028743614110135983it_nat @ ( fun_up4116053422210368295it_nat @ M2 @ X @ ( some_P1914260805536162275it_nat @ Y ) ) @ A2 )
% 9.17/5.43 = ( image_5028743614110135983it_nat @ M2 @ A2 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7437_image__map__upd,axiom,
% 9.17/5.43 ! [X: int,A2: set_int,M2: int > option8956607266484857688it_nat,Y: produc8664842809031399944it_nat] :
% 9.17/5.43 ( ~ ( member_int @ X @ A2 )
% 9.17/5.43 => ( ( image_7905038228067148555it_nat @ ( fun_up6992348036167380867it_nat @ M2 @ X @ ( some_P1914260805536162275it_nat @ Y ) ) @ A2 )
% 9.17/5.43 = ( image_7905038228067148555it_nat @ M2 @ A2 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7438_FieldI2,axiom,
% 9.17/5.43 ! [I: produc3843707927480180839at_nat,J: produc3843707927480180839at_nat,R4: set_Pr5564308138774400199at_nat] :
% 9.17/5.43 ( ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ I @ J ) @ R4 )
% 9.17/5.43 => ( member8757157785044589968at_nat @ J @ ( field_2862844103579723188at_nat @ R4 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7439_FieldI2,axiom,
% 9.17/5.43 ! [I: product_prod_nat_nat,J: product_prod_nat_nat,R4: set_Pr8693737435421807431at_nat] :
% 9.17/5.43 ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ I @ J ) @ R4 )
% 9.17/5.43 => ( member8440522571783428010at_nat @ J @ ( field_4706345496283612622at_nat @ R4 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7440_FieldI2,axiom,
% 9.17/5.43 ! [I: int,J: int,R4: set_Pr958786334691620121nt_int] :
% 9.17/5.43 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ I @ J ) @ R4 )
% 9.17/5.43 => ( member_int @ J @ ( field_int @ R4 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7441_FieldI2,axiom,
% 9.17/5.43 ! [I: set_Pr1261947904930325089at_nat,J: set_Pr1261947904930325089at_nat,R4: set_Pr4329608150637261639at_nat] :
% 9.17/5.43 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ I @ J ) @ R4 )
% 9.17/5.43 => ( member2643936169264416010at_nat @ J @ ( field_3145993188331922222at_nat @ R4 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7442_FieldI2,axiom,
% 9.17/5.43 ! [I: nat,J: nat,R4: set_Pr1261947904930325089at_nat] :
% 9.17/5.43 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ I @ J ) @ R4 )
% 9.17/5.43 => ( member_nat @ J @ ( field_nat @ R4 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7443_FieldI2,axiom,
% 9.17/5.43 ! [I: $o,J: $o,R4: set_Product_prod_o_o] :
% 9.17/5.43 ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ I @ J ) @ R4 )
% 9.17/5.43 => ( member_o @ J @ ( field_o @ R4 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7444_FieldI1,axiom,
% 9.17/5.43 ! [I: produc3843707927480180839at_nat,J: produc3843707927480180839at_nat,R4: set_Pr5564308138774400199at_nat] :
% 9.17/5.43 ( ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ I @ J ) @ R4 )
% 9.17/5.43 => ( member8757157785044589968at_nat @ I @ ( field_2862844103579723188at_nat @ R4 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7445_FieldI1,axiom,
% 9.17/5.43 ! [I: product_prod_nat_nat,J: product_prod_nat_nat,R4: set_Pr8693737435421807431at_nat] :
% 9.17/5.43 ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ I @ J ) @ R4 )
% 9.17/5.43 => ( member8440522571783428010at_nat @ I @ ( field_4706345496283612622at_nat @ R4 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7446_FieldI1,axiom,
% 9.17/5.43 ! [I: int,J: int,R4: set_Pr958786334691620121nt_int] :
% 9.17/5.43 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ I @ J ) @ R4 )
% 9.17/5.43 => ( member_int @ I @ ( field_int @ R4 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7447_FieldI1,axiom,
% 9.17/5.43 ! [I: set_Pr1261947904930325089at_nat,J: set_Pr1261947904930325089at_nat,R4: set_Pr4329608150637261639at_nat] :
% 9.17/5.43 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ I @ J ) @ R4 )
% 9.17/5.43 => ( member2643936169264416010at_nat @ I @ ( field_3145993188331922222at_nat @ R4 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7448_FieldI1,axiom,
% 9.17/5.43 ! [I: nat,J: nat,R4: set_Pr1261947904930325089at_nat] :
% 9.17/5.43 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ I @ J ) @ R4 )
% 9.17/5.43 => ( member_nat @ I @ ( field_nat @ R4 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7449_FieldI1,axiom,
% 9.17/5.43 ! [I: $o,J: $o,R4: set_Product_prod_o_o] :
% 9.17/5.43 ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ I @ J ) @ R4 )
% 9.17/5.43 => ( member_o @ I @ ( field_o @ R4 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7450_sup__Un__eq2,axiom,
% 9.17/5.43 ! [R4: set_Pr1261947904930325089at_nat,S2: set_Pr1261947904930325089at_nat] :
% 9.17/5.43 ( ( sup_sup_nat_nat_o
% 9.17/5.43 @ ^ [X3: nat,Y3: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y3 ) @ R4 )
% 9.17/5.43 @ ^ [X3: nat,Y3: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y3 ) @ S2 ) )
% 9.17/5.43 = ( ^ [X3: nat,Y3: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y3 ) @ ( sup_su6327502436637775413at_nat @ R4 @ S2 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7451_sup__Un__eq2,axiom,
% 9.17/5.43 ! [R4: set_Pr1281608226676607948nteger,S2: set_Pr1281608226676607948nteger] :
% 9.17/5.43 ( ( sup_su234547053653886311eger_o
% 9.17/5.43 @ ^ [X3: produc6241069584506657477e_term > option6357759511663192854e_term,Y3: produc8923325533196201883nteger] : ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X3 @ Y3 ) @ R4 )
% 9.17/5.43 @ ^ [X3: produc6241069584506657477e_term > option6357759511663192854e_term,Y3: produc8923325533196201883nteger] : ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X3 @ Y3 ) @ S2 ) )
% 9.17/5.43 = ( ^ [X3: produc6241069584506657477e_term > option6357759511663192854e_term,Y3: produc8923325533196201883nteger] : ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X3 @ Y3 ) @ ( sup_su4591284015454442744nteger @ R4 @ S2 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7452_sup__Un__eq2,axiom,
% 9.17/5.43 ! [R4: set_Pr3286484037609594932et_nat,S2: set_Pr3286484037609594932et_nat] :
% 9.17/5.43 ( ( sup_su1630790145277462993_nat_o
% 9.17/5.43 @ ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3658429121746597890et_nat] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X3 @ Y3 ) @ R4 )
% 9.17/5.43 @ ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3658429121746597890et_nat] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X3 @ Y3 ) @ S2 ) )
% 9.17/5.43 = ( ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3658429121746597890et_nat] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X3 @ Y3 ) @ ( sup_su7128418612487073120et_nat @ R4 @ S2 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7453_sup__Un__eq2,axiom,
% 9.17/5.43 ! [R4: set_Pr8536935166611901872et_nat,S2: set_Pr8536935166611901872et_nat] :
% 9.17/5.43 ( ( sup_su6535292691877529429_nat_o
% 9.17/5.43 @ ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3925858234332021118et_nat] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X3 @ Y3 ) @ R4 )
% 9.17/5.43 @ ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3925858234332021118et_nat] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X3 @ Y3 ) @ S2 ) )
% 9.17/5.43 = ( ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3925858234332021118et_nat] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X3 @ Y3 ) @ ( sup_su8975264963432250076et_nat @ R4 @ S2 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7454_sup__Un__eq2,axiom,
% 9.17/5.43 ! [R4: set_Pr9222295170931077689nt_int,S2: set_Pr9222295170931077689nt_int] :
% 9.17/5.43 ( ( sup_su4182031696650224058_int_o
% 9.17/5.43 @ ^ [X3: produc8551481072490612790e_term > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X3 @ Y3 ) @ R4 )
% 9.17/5.43 @ ^ [X3: produc8551481072490612790e_term > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X3 @ Y3 ) @ S2 ) )
% 9.17/5.43 = ( ^ [X3: produc8551481072490612790e_term > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X3 @ Y3 ) @ ( sup_su3382966977382714213nt_int @ R4 @ S2 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7455_sup__Un__eq2,axiom,
% 9.17/5.43 ! [R4: set_Pr1872883991513573699nt_int,S2: set_Pr1872883991513573699nt_int] :
% 9.17/5.43 ( ( sup_su600977994968626096_int_o
% 9.17/5.43 @ ^ [X3: int > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X3 @ Y3 ) @ R4 )
% 9.17/5.43 @ ^ [X3: int > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X3 @ Y3 ) @ S2 ) )
% 9.17/5.43 = ( ^ [X3: int > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X3 @ Y3 ) @ ( sup_su3298353300217089135nt_int @ R4 @ S2 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7456_sup__Un__eq2,axiom,
% 9.17/5.43 ! [R4: set_Pr4329608150637261639at_nat,S2: set_Pr4329608150637261639at_nat] :
% 9.17/5.43 ( ( sup_su7519161239522478338_nat_o
% 9.17/5.43 @ ^ [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ Y3 ) @ R4 )
% 9.17/5.43 @ ^ [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ Y3 ) @ S2 ) )
% 9.17/5.43 = ( ^ [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ Y3 ) @ ( sup_su5525570899277871387at_nat @ R4 @ S2 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7457_fun__upd__comp,axiom,
% 9.17/5.43 ! [F: code_integer > code_integer,G: num > code_integer,X: num,Y: code_integer] :
% 9.17/5.43 ( ( comp_C3531382070062128313er_num @ F @ ( fun_up1844922938552261878nteger @ G @ X @ Y ) )
% 9.17/5.43 = ( fun_up1844922938552261878nteger @ ( comp_C3531382070062128313er_num @ F @ G ) @ X @ ( F @ Y ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7458_fun__upd__comp,axiom,
% 9.17/5.43 ! [F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer,X: code_integer,Y: code_integer] :
% 9.17/5.43 ( ( comp_C1593894019821074884nteger @ F @ ( fun_up8355007323143964473nteger @ G @ X @ Y ) )
% 9.17/5.43 = ( fun_up8139772397987072257nteger @ ( comp_C1593894019821074884nteger @ F @ G ) @ X @ ( F @ Y ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7459_fun__upd__comp,axiom,
% 9.17/5.43 ! [F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer > code_integer,X: code_integer,Y: code_integer > code_integer] :
% 9.17/5.43 ( ( comp_C8797469213163452608nteger @ F @ ( fun_up8056716234270145717nteger @ G @ X @ Y ) )
% 9.17/5.43 = ( fun_up8139772397987072257nteger @ ( comp_C8797469213163452608nteger @ F @ G ) @ X @ ( F @ Y ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7460_fun__upd__comp,axiom,
% 9.17/5.43 ! [F: nat > num,G: int > nat,X: int,Y: nat] :
% 9.17/5.43 ( ( comp_nat_num_int @ F @ ( fun_upd_int_nat @ G @ X @ Y ) )
% 9.17/5.43 = ( fun_upd_int_num @ ( comp_nat_num_int @ F @ G ) @ X @ ( F @ Y ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7461_one__rat_Orsp,axiom,
% 9.17/5.43 ratrel @ ( product_Pair_int_int @ one_one_int @ one_one_int ) @ ( product_Pair_int_int @ one_one_int @ one_one_int ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7462_R__subset__Field,axiom,
% 9.17/5.43 ! [R4: set_Pr1261947904930325089at_nat] :
% 9.17/5.43 ( ord_le3146513528884898305at_nat @ R4
% 9.17/5.43 @ ( produc457027306803732586at_nat @ ( field_nat @ R4 )
% 9.17/5.43 @ ^ [Uu: nat] : ( field_nat @ R4 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7463_R__subset__Field,axiom,
% 9.17/5.43 ! [R4: set_Product_prod_o_o] :
% 9.17/5.43 ( ord_le192195778054999463od_o_o @ R4
% 9.17/5.43 @ ( product_Sigma_o_o @ ( field_o @ R4 )
% 9.17/5.43 @ ^ [Uu: $o] : ( field_o @ R4 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7464_fst__in__Field,axiom,
% 9.17/5.43 ! [R4: set_Product_prod_o_o] : ( ord_less_eq_set_o @ ( image_7896445794123959606_o_o_o @ product_fst_o_o @ R4 ) @ ( field_o @ R4 ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7465_fst__in__Field,axiom,
% 9.17/5.43 ! [R4: set_Pr4811707699266497531nteger] : ( ord_le7084787975880047091nteger @ ( image_6316824473203919795nteger @ produc8508995932063986495nteger @ R4 ) @ ( field_Code_integer @ R4 ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7466_fst__in__Field,axiom,
% 9.17/5.43 ! [R4: set_Pr958786334691620121nt_int] : ( ord_less_eq_set_int @ ( image_5042161079198086560nt_int @ product_fst_int_int @ R4 ) @ ( field_int @ R4 ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7467_fst__in__Field,axiom,
% 9.17/5.43 ! [R4: set_Pr1261947904930325089at_nat] : ( ord_less_eq_set_nat @ ( image_2486076414777270412at_nat @ product_fst_nat_nat @ R4 ) @ ( field_nat @ R4 ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7468_snd__in__Field,axiom,
% 9.17/5.43 ! [R4: set_Product_prod_o_o] : ( ord_less_eq_set_o @ ( image_7896445794123959606_o_o_o @ product_snd_o_o @ R4 ) @ ( field_o @ R4 ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7469_snd__in__Field,axiom,
% 9.17/5.43 ! [R4: set_Pr4811707699266497531nteger] : ( ord_le7084787975880047091nteger @ ( image_6316824473203919795nteger @ produc6174133586879617921nteger @ R4 ) @ ( field_Code_integer @ R4 ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7470_snd__in__Field,axiom,
% 9.17/5.43 ! [R4: set_Pr958786334691620121nt_int] : ( ord_less_eq_set_int @ ( image_5042161079198086560nt_int @ product_snd_int_int @ R4 ) @ ( field_int @ R4 ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7471_snd__in__Field,axiom,
% 9.17/5.43 ! [R4: set_Pr1261947904930325089at_nat] : ( ord_less_eq_set_nat @ ( image_2486076414777270412at_nat @ product_snd_nat_nat @ R4 ) @ ( field_nat @ R4 ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7472_zero__rat_Orsp,axiom,
% 9.17/5.43 ratrel @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7473_Fract_Orsp,axiom,
% 9.17/5.43 ( bNF_re157797125943740599nt_int
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ ( bNF_re6250860962936578807nt_int
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ ratrel )
% 9.17/5.43 @ ^ [A5: int,B4: int] : ( if_Pro3027730157355071871nt_int @ ( B4 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ A5 @ B4 ) )
% 9.17/5.43 @ ^ [A5: int,B4: int] : ( if_Pro3027730157355071871nt_int @ ( B4 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ A5 @ B4 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7474_sum_Oeq__fold,axiom,
% 9.17/5.43 ( groups3542108847815614940at_nat
% 9.17/5.43 = ( ^ [G2: nat > nat] : ( finite_fold_nat_nat @ ( comp_nat_nat_nat_nat @ plus_plus_nat @ G2 ) @ zero_zero_nat ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7475_sum_Oeq__fold,axiom,
% 9.17/5.43 ( groups4538972089207619220nt_int
% 9.17/5.43 = ( ^ [G2: int > int] : ( finite_fold_int_int @ ( comp_int_int_int_int @ plus_plus_int @ G2 ) @ zero_zero_int ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7476_prod_Oeq__fold,axiom,
% 9.17/5.43 ( groups708209901874060359at_nat
% 9.17/5.43 = ( ^ [G2: nat > nat] : ( finite_fold_nat_nat @ ( comp_nat_nat_nat_nat @ times_times_nat @ G2 ) @ one_one_nat ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7477_prod_Oeq__fold,axiom,
% 9.17/5.43 ( groups705719431365010083at_int
% 9.17/5.43 = ( ^ [G2: nat > int] : ( finite_fold_nat_int @ ( comp_int_int_int_nat @ times_times_int @ G2 ) @ one_one_int ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7478_prod_Oeq__fold,axiom,
% 9.17/5.43 ( groups1705073143266064639nt_int
% 9.17/5.43 = ( ^ [G2: int > int] : ( finite_fold_int_int @ ( comp_int_int_int_int @ times_times_int @ G2 ) @ one_one_int ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7479_finite__range__updI,axiom,
% 9.17/5.43 ! [F: nat > option_num,A: nat,B: num] :
% 9.17/5.43 ( ( finite6231397076622260609on_num @ ( image_nat_option_num @ F @ top_top_set_nat ) )
% 9.17/5.43 => ( finite6231397076622260609on_num @ ( image_nat_option_num @ ( fun_up2201401324907169337on_num @ F @ A @ ( some_num @ B ) ) @ top_top_set_nat ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7480_finite__range__updI,axiom,
% 9.17/5.43 ! [F: nat > option8956607266484857688it_nat,A: nat,B: produc8664842809031399944it_nat] :
% 9.17/5.43 ( ( finite6292238467249657455it_nat @ ( image_5028743614110135983it_nat @ F @ top_top_set_nat ) )
% 9.17/5.43 => ( finite6292238467249657455it_nat @ ( image_5028743614110135983it_nat @ ( fun_up4116053422210368295it_nat @ F @ A @ ( some_P1914260805536162275it_nat @ B ) ) @ top_top_set_nat ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7481_finite__range__updI,axiom,
% 9.17/5.43 ! [F: product_unit > option_num,A: product_unit,B: num] :
% 9.17/5.43 ( ( finite6231397076622260609on_num @ ( image_5965367930834091826on_num @ F @ top_to1996260823553986621t_unit ) )
% 9.17/5.43 => ( finite6231397076622260609on_num @ ( image_5965367930834091826on_num @ ( fun_up4695802795598371002on_num @ F @ A @ ( some_num @ B ) ) @ top_to1996260823553986621t_unit ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7482_finite__range__updI,axiom,
% 9.17/5.43 ! [F: product_unit > option8956607266484857688it_nat,A: product_unit,B: produc8664842809031399944it_nat] :
% 9.17/5.43 ( ( finite6292238467249657455it_nat @ ( image_5022536681399171104it_nat @ F @ top_to1996260823553986621t_unit ) )
% 9.17/5.43 => ( finite6292238467249657455it_nat @ ( image_5022536681399171104it_nat @ ( fun_up1973317344121680296it_nat @ F @ A @ ( some_P1914260805536162275it_nat @ B ) ) @ top_to1996260823553986621t_unit ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7483_finite__range__updI,axiom,
% 9.17/5.43 ! [F: int > option_num,A: int,B: num] :
% 9.17/5.43 ( ( finite6231397076622260609on_num @ ( image_int_option_num @ F @ top_top_set_int ) )
% 9.17/5.43 => ( finite6231397076622260609on_num @ ( image_int_option_num @ ( fun_up4328768054909231765on_num @ F @ A @ ( some_num @ B ) ) @ top_top_set_int ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7484_finite__range__updI,axiom,
% 9.17/5.43 ! [F: int > option8956607266484857688it_nat,A: int,B: produc8664842809031399944it_nat] :
% 9.17/5.43 ( ( finite6292238467249657455it_nat @ ( image_7905038228067148555it_nat @ F @ top_top_set_int ) )
% 9.17/5.43 => ( finite6292238467249657455it_nat @ ( image_7905038228067148555it_nat @ ( fun_up6992348036167380867it_nat @ F @ A @ ( some_P1914260805536162275it_nat @ B ) ) @ top_top_set_int ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7485_fun__upd__image,axiom,
% 9.17/5.43 ! [X: $o,A2: set_o,F: $o > $o,Y: $o] :
% 9.17/5.43 ( ( ( member_o @ X @ A2 )
% 9.17/5.43 => ( ( image_o_o @ ( fun_upd_o_o @ F @ X @ Y ) @ A2 )
% 9.17/5.43 = ( insert_o @ Y @ ( image_o_o @ F @ ( minus_minus_set_o @ A2 @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) )
% 9.17/5.43 & ( ~ ( member_o @ X @ A2 )
% 9.17/5.43 => ( ( image_o_o @ ( fun_upd_o_o @ F @ X @ Y ) @ A2 )
% 9.17/5.43 = ( image_o_o @ F @ A2 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7486_fun__upd__image,axiom,
% 9.17/5.43 ! [X: $o,A2: set_o,F: $o > nat,Y: nat] :
% 9.17/5.43 ( ( ( member_o @ X @ A2 )
% 9.17/5.43 => ( ( image_o_nat @ ( fun_upd_o_nat @ F @ X @ Y ) @ A2 )
% 9.17/5.43 = ( insert_nat @ Y @ ( image_o_nat @ F @ ( minus_minus_set_o @ A2 @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) )
% 9.17/5.43 & ( ~ ( member_o @ X @ A2 )
% 9.17/5.43 => ( ( image_o_nat @ ( fun_upd_o_nat @ F @ X @ Y ) @ A2 )
% 9.17/5.43 = ( image_o_nat @ F @ A2 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7487_fun__upd__image,axiom,
% 9.17/5.43 ! [X: $o,A2: set_o,F: $o > int,Y: int] :
% 9.17/5.43 ( ( ( member_o @ X @ A2 )
% 9.17/5.43 => ( ( image_o_int @ ( fun_upd_o_int @ F @ X @ Y ) @ A2 )
% 9.17/5.43 = ( insert_int @ Y @ ( image_o_int @ F @ ( minus_minus_set_o @ A2 @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) )
% 9.17/5.43 & ( ~ ( member_o @ X @ A2 )
% 9.17/5.43 => ( ( image_o_int @ ( fun_upd_o_int @ F @ X @ Y ) @ A2 )
% 9.17/5.43 = ( image_o_int @ F @ A2 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7488_fun__upd__image,axiom,
% 9.17/5.43 ! [X: int,A2: set_int,F: int > $o,Y: $o] :
% 9.17/5.43 ( ( ( member_int @ X @ A2 )
% 9.17/5.43 => ( ( image_int_o @ ( fun_upd_int_o @ F @ X @ Y ) @ A2 )
% 9.17/5.43 = ( insert_o @ Y @ ( image_int_o @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) )
% 9.17/5.43 & ( ~ ( member_int @ X @ A2 )
% 9.17/5.43 => ( ( image_int_o @ ( fun_upd_int_o @ F @ X @ Y ) @ A2 )
% 9.17/5.43 = ( image_int_o @ F @ A2 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7489_fun__upd__image,axiom,
% 9.17/5.43 ! [X: int,A2: set_int,F: int > nat,Y: nat] :
% 9.17/5.43 ( ( ( member_int @ X @ A2 )
% 9.17/5.43 => ( ( image_int_nat @ ( fun_upd_int_nat @ F @ X @ Y ) @ A2 )
% 9.17/5.43 = ( insert_nat @ Y @ ( image_int_nat @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) )
% 9.17/5.43 & ( ~ ( member_int @ X @ A2 )
% 9.17/5.43 => ( ( image_int_nat @ ( fun_upd_int_nat @ F @ X @ Y ) @ A2 )
% 9.17/5.43 = ( image_int_nat @ F @ A2 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7490_fun__upd__image,axiom,
% 9.17/5.43 ! [X: int,A2: set_int,F: int > int,Y: int] :
% 9.17/5.43 ( ( ( member_int @ X @ A2 )
% 9.17/5.43 => ( ( image_int_int @ ( fun_upd_int_int @ F @ X @ Y ) @ A2 )
% 9.17/5.43 = ( insert_int @ Y @ ( image_int_int @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) )
% 9.17/5.43 & ( ~ ( member_int @ X @ A2 )
% 9.17/5.43 => ( ( image_int_int @ ( fun_upd_int_int @ F @ X @ Y ) @ A2 )
% 9.17/5.43 = ( image_int_int @ F @ A2 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7491_fun__upd__image,axiom,
% 9.17/5.43 ! [X: nat,A2: set_nat,F: nat > code_integer,Y: code_integer] :
% 9.17/5.43 ( ( ( member_nat @ X @ A2 )
% 9.17/5.43 => ( ( image_1215581382706833972nteger @ ( fun_up3904115110581602988nteger @ F @ X @ Y ) @ A2 )
% 9.17/5.43 = ( insert_Code_integer @ Y @ ( image_1215581382706833972nteger @ F @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) )
% 9.17/5.43 & ( ~ ( member_nat @ X @ A2 )
% 9.17/5.43 => ( ( image_1215581382706833972nteger @ ( fun_up3904115110581602988nteger @ F @ X @ Y ) @ A2 )
% 9.17/5.43 = ( image_1215581382706833972nteger @ F @ A2 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7492_fun__upd__image,axiom,
% 9.17/5.43 ! [X: nat,A2: set_nat,F: nat > $o,Y: $o] :
% 9.17/5.43 ( ( ( member_nat @ X @ A2 )
% 9.17/5.43 => ( ( image_nat_o @ ( fun_upd_nat_o @ F @ X @ Y ) @ A2 )
% 9.17/5.43 = ( insert_o @ Y @ ( image_nat_o @ F @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) )
% 9.17/5.43 & ( ~ ( member_nat @ X @ A2 )
% 9.17/5.43 => ( ( image_nat_o @ ( fun_upd_nat_o @ F @ X @ Y ) @ A2 )
% 9.17/5.43 = ( image_nat_o @ F @ A2 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7493_fun__upd__image,axiom,
% 9.17/5.43 ! [X: nat,A2: set_nat,F: nat > nat,Y: nat] :
% 9.17/5.43 ( ( ( member_nat @ X @ A2 )
% 9.17/5.43 => ( ( image_nat_nat @ ( fun_upd_nat_nat @ F @ X @ Y ) @ A2 )
% 9.17/5.43 = ( insert_nat @ Y @ ( image_nat_nat @ F @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) )
% 9.17/5.43 & ( ~ ( member_nat @ X @ A2 )
% 9.17/5.43 => ( ( image_nat_nat @ ( fun_upd_nat_nat @ F @ X @ Y ) @ A2 )
% 9.17/5.43 = ( image_nat_nat @ F @ A2 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7494_fun__upd__image,axiom,
% 9.17/5.43 ! [X: nat,A2: set_nat,F: nat > int,Y: int] :
% 9.17/5.43 ( ( ( member_nat @ X @ A2 )
% 9.17/5.43 => ( ( image_nat_int @ ( fun_upd_nat_int @ F @ X @ Y ) @ A2 )
% 9.17/5.43 = ( insert_int @ Y @ ( image_nat_int @ F @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) )
% 9.17/5.43 & ( ~ ( member_nat @ X @ A2 )
% 9.17/5.43 => ( ( image_nat_int @ ( fun_upd_nat_int @ F @ X @ Y ) @ A2 )
% 9.17/5.43 = ( image_nat_int @ F @ A2 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7495_times__rat_Orsp,axiom,
% 9.17/5.43 ( bNF_re5228765855967844073nt_int @ ratrel @ ( bNF_re7145576690424134365nt_int @ ratrel @ ratrel )
% 9.17/5.43 @ ^ [X3: product_prod_int_int,Y3: product_prod_int_int] : ( product_Pair_int_int @ ( times_times_int @ ( product_fst_int_int @ X3 ) @ ( product_fst_int_int @ Y3 ) ) @ ( times_times_int @ ( product_snd_int_int @ X3 ) @ ( product_snd_int_int @ Y3 ) ) )
% 9.17/5.43 @ ^ [X3: product_prod_int_int,Y3: product_prod_int_int] : ( product_Pair_int_int @ ( times_times_int @ ( product_fst_int_int @ X3 ) @ ( product_fst_int_int @ Y3 ) ) @ ( times_times_int @ ( product_snd_int_int @ X3 ) @ ( product_snd_int_int @ Y3 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7496_uminus__rat_Orsp,axiom,
% 9.17/5.43 ( bNF_re7145576690424134365nt_int @ ratrel @ ratrel
% 9.17/5.43 @ ^ [X3: product_prod_int_int] : ( product_Pair_int_int @ ( uminus_uminus_int @ ( product_fst_int_int @ X3 ) ) @ ( product_snd_int_int @ X3 ) )
% 9.17/5.43 @ ^ [X3: product_prod_int_int] : ( product_Pair_int_int @ ( uminus_uminus_int @ ( product_fst_int_int @ X3 ) ) @ ( product_snd_int_int @ X3 ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7497_plus__rat_Oabs__eq,axiom,
% 9.17/5.43 ! [Xa: product_prod_int_int,X: product_prod_int_int] :
% 9.17/5.43 ( ( ratrel @ Xa @ Xa )
% 9.17/5.43 => ( ( ratrel @ X @ X )
% 9.17/5.43 => ( ( plus_plus_rat @ ( abs_Rat @ Xa ) @ ( abs_Rat @ X ) )
% 9.17/5.43 = ( abs_Rat @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ Xa ) @ ( product_snd_int_int @ X ) ) @ ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_snd_int_int @ Xa ) ) ) @ ( times_times_int @ ( product_snd_int_int @ Xa ) @ ( product_snd_int_int @ X ) ) ) ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7498_inverse__rat_Oabs__eq,axiom,
% 9.17/5.43 ! [X: product_prod_int_int] :
% 9.17/5.43 ( ( ratrel @ X @ X )
% 9.17/5.43 => ( ( inverse_inverse_rat @ ( abs_Rat @ X ) )
% 9.17/5.43 = ( abs_Rat
% 9.17/5.43 @ ( if_Pro3027730157355071871nt_int
% 9.17/5.43 @ ( ( product_fst_int_int @ X )
% 9.17/5.43 = zero_zero_int )
% 9.17/5.43 @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 9.17/5.43 @ ( product_Pair_int_int @ ( product_snd_int_int @ X ) @ ( product_fst_int_int @ X ) ) ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7499_times__rat_Oabs__eq,axiom,
% 9.17/5.43 ! [Xa: product_prod_int_int,X: product_prod_int_int] :
% 9.17/5.43 ( ( ratrel @ Xa @ Xa )
% 9.17/5.43 => ( ( ratrel @ X @ X )
% 9.17/5.43 => ( ( times_times_rat @ ( abs_Rat @ Xa ) @ ( abs_Rat @ X ) )
% 9.17/5.43 = ( abs_Rat @ ( product_Pair_int_int @ ( times_times_int @ ( product_fst_int_int @ Xa ) @ ( product_fst_int_int @ X ) ) @ ( times_times_int @ ( product_snd_int_int @ Xa ) @ ( product_snd_int_int @ X ) ) ) ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7500_uminus__rat_Oabs__eq,axiom,
% 9.17/5.43 ! [X: product_prod_int_int] :
% 9.17/5.43 ( ( ratrel @ X @ X )
% 9.17/5.43 => ( ( uminus_uminus_rat @ ( abs_Rat @ X ) )
% 9.17/5.43 = ( abs_Rat @ ( product_Pair_int_int @ ( uminus_uminus_int @ ( product_fst_int_int @ X ) ) @ ( product_snd_int_int @ X ) ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7501_one__rat__def,axiom,
% 9.17/5.43 ( one_one_rat
% 9.17/5.43 = ( abs_Rat @ ( product_Pair_int_int @ one_one_int @ one_one_int ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7502_zero__rat__def,axiom,
% 9.17/5.43 ( zero_zero_rat
% 9.17/5.43 = ( abs_Rat @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7503_plus__rat__def,axiom,
% 9.17/5.43 ( plus_plus_rat
% 9.17/5.43 = ( map_fu4333342158222067775at_rat @ rep_Rat @ ( map_fu5673905371560938248nt_rat @ rep_Rat @ abs_Rat )
% 9.17/5.43 @ ^ [X3: product_prod_int_int,Y3: product_prod_int_int] : ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ X3 ) @ ( product_snd_int_int @ Y3 ) ) @ ( times_times_int @ ( product_fst_int_int @ Y3 ) @ ( product_snd_int_int @ X3 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ X3 ) @ ( product_snd_int_int @ Y3 ) ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7504_inverse__rat__def,axiom,
% 9.17/5.43 ( inverse_inverse_rat
% 9.17/5.43 = ( map_fu5673905371560938248nt_rat @ rep_Rat @ abs_Rat
% 9.17/5.43 @ ^ [X3: product_prod_int_int] :
% 9.17/5.43 ( if_Pro3027730157355071871nt_int
% 9.17/5.43 @ ( ( product_fst_int_int @ X3 )
% 9.17/5.43 = zero_zero_int )
% 9.17/5.43 @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 9.17/5.43 @ ( product_Pair_int_int @ ( product_snd_int_int @ X3 ) @ ( product_fst_int_int @ X3 ) ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7505_times__rat__def,axiom,
% 9.17/5.43 ( times_times_rat
% 9.17/5.43 = ( map_fu4333342158222067775at_rat @ rep_Rat @ ( map_fu5673905371560938248nt_rat @ rep_Rat @ abs_Rat )
% 9.17/5.43 @ ^ [X3: product_prod_int_int,Y3: product_prod_int_int] : ( product_Pair_int_int @ ( times_times_int @ ( product_fst_int_int @ X3 ) @ ( product_fst_int_int @ Y3 ) ) @ ( times_times_int @ ( product_snd_int_int @ X3 ) @ ( product_snd_int_int @ Y3 ) ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7506_uminus__rat__def,axiom,
% 9.17/5.43 ( uminus_uminus_rat
% 9.17/5.43 = ( map_fu5673905371560938248nt_rat @ rep_Rat @ abs_Rat
% 9.17/5.43 @ ^ [X3: product_prod_int_int] : ( product_Pair_int_int @ ( uminus_uminus_int @ ( product_fst_int_int @ X3 ) ) @ ( product_snd_int_int @ X3 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7507_card__le__Suc__Max,axiom,
% 9.17/5.43 ! [S2: set_nat] :
% 9.17/5.43 ( ( finite_finite_nat @ S2 )
% 9.17/5.43 => ( ord_less_eq_nat @ ( finite_card_nat @ S2 ) @ ( suc @ ( lattic8265883725875713057ax_nat @ S2 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7508_greaterThan__Suc,axiom,
% 9.17/5.43 ! [K: nat] :
% 9.17/5.43 ( ( set_or1210151606488870762an_nat @ ( suc @ K ) )
% 9.17/5.43 = ( minus_minus_set_nat @ ( set_or1210151606488870762an_nat @ K ) @ ( insert_nat @ ( suc @ K ) @ bot_bot_set_nat ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7509_INT__greaterThan__UNIV,axiom,
% 9.17/5.43 ( ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ set_or1210151606488870762an_nat @ top_top_set_nat ) )
% 9.17/5.43 = bot_bot_set_nat ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7510_greaterThan__0,axiom,
% 9.17/5.43 ( ( set_or1210151606488870762an_nat @ zero_zero_nat )
% 9.17/5.43 = ( image_nat_nat @ suc @ top_top_set_nat ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7511_euclidean__size__integer_Orep__eq,axiom,
% 9.17/5.43 ( euclid6377331345833325938nteger
% 9.17/5.43 = ( ^ [X3: code_integer] : ( euclid4774559944035922753ze_int @ ( code_int_of_integer @ X3 ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7512_euclidean__size__integer_Oabs__eq,axiom,
% 9.17/5.43 ! [X: int] :
% 9.17/5.43 ( ( euclid6377331345833325938nteger @ ( code_integer_of_int @ X ) )
% 9.17/5.43 = ( euclid4774559944035922753ze_int @ X ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7513_euclidean__size__natural_Orsp,axiom,
% 9.17/5.43 ( bNF_re5653821019739307937at_nat
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.43 @ euclid4777050414544973029ze_nat
% 9.17/5.43 @ euclid4777050414544973029ze_nat ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7514_euclidean__size__integer__def,axiom,
% 9.17/5.43 ( euclid6377331345833325938nteger
% 9.17/5.43 = ( map_fu6539832666145259331at_nat @ code_int_of_integer @ id_nat @ euclid4774559944035922753ze_int ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7515_euclidean__size__integer_Orsp,axiom,
% 9.17/5.43 ( bNF_re3715656647883201625at_nat
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.43 @ euclid4774559944035922753ze_int
% 9.17/5.43 @ euclid4774559944035922753ze_int ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7516_division__segment__integer_Orep__eq,axiom,
% 9.17/5.43 ! [X: code_integer] :
% 9.17/5.43 ( ( code_int_of_integer @ ( euclid6289375185220004616nteger @ X ) )
% 9.17/5.43 = ( euclid3395696857347342551nt_int @ ( code_int_of_integer @ X ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7517_division__segment__integer_Oabs__eq,axiom,
% 9.17/5.43 ! [X: int] :
% 9.17/5.43 ( ( euclid6289375185220004616nteger @ ( code_integer_of_int @ X ) )
% 9.17/5.43 = ( code_integer_of_int @ ( euclid3395696857347342551nt_int @ X ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7518_division__segment__nat__def,axiom,
% 9.17/5.43 ( euclid3398187327856392827nt_nat
% 9.17/5.43 = ( ^ [N4: nat] : one_one_nat ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7519_division__segment__integer_Orsp,axiom,
% 9.17/5.43 ( bNF_re4712519889275205905nt_int
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ euclid3395696857347342551nt_int
% 9.17/5.43 @ euclid3395696857347342551nt_int ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7520_division__segment__natural_Orsp,axiom,
% 9.17/5.43 ( bNF_re5653821019739307937at_nat
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.43 @ euclid3398187327856392827nt_nat
% 9.17/5.43 @ euclid3398187327856392827nt_nat ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7521_division__segment__integer__def,axiom,
% 9.17/5.43 ( euclid6289375185220004616nteger
% 9.17/5.43 = ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int @ euclid3395696857347342551nt_int ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7522_finite__greaterThanAtMost,axiom,
% 9.17/5.43 ! [L: nat,U: nat] : ( finite_finite_nat @ ( set_or6659071591806873216st_nat @ L @ U ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7523_finite__greaterThanAtMost__int,axiom,
% 9.17/5.43 ! [L: int,U: int] : ( finite_finite_int @ ( set_or6656581121297822940st_int @ L @ U ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7524_finite__greaterThanAtMost__integer,axiom,
% 9.17/5.43 ! [L: code_integer,U: code_integer] : ( finite6017078050557962740nteger @ ( set_or2715278749043346189nteger @ L @ U ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7525_card__greaterThanAtMost,axiom,
% 9.17/5.43 ! [L: nat,U: nat] :
% 9.17/5.43 ( ( finite_card_nat @ ( set_or6659071591806873216st_nat @ L @ U ) )
% 9.17/5.43 = ( minus_minus_nat @ U @ L ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7526_card__greaterThanAtMost__int,axiom,
% 9.17/5.43 ! [L: int,U: int] :
% 9.17/5.43 ( ( finite_card_int @ ( set_or6656581121297822940st_int @ L @ U ) )
% 9.17/5.43 = ( nat2 @ ( minus_minus_int @ U @ L ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7527_atLeastSucAtMost__greaterThanAtMost,axiom,
% 9.17/5.43 ! [L: nat,U: nat] :
% 9.17/5.43 ( ( set_or1269000886237332187st_nat @ ( suc @ L ) @ U )
% 9.17/5.43 = ( set_or6659071591806873216st_nat @ L @ U ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7528_atLeastPlusOneAtMost__greaterThanAtMost__int,axiom,
% 9.17/5.43 ! [L: int,U: int] :
% 9.17/5.43 ( ( set_or1266510415728281911st_int @ ( plus_plus_int @ L @ one_one_int ) @ U )
% 9.17/5.43 = ( set_or6656581121297822940st_int @ L @ U ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7529_atLeastPlusOneAtMost__greaterThanAtMost__integer,axiom,
% 9.17/5.43 ! [L: code_integer,U: code_integer] :
% 9.17/5.43 ( ( set_or189985376899183464nteger @ ( plus_p5714425477246183910nteger @ L @ one_one_Code_integer ) @ U )
% 9.17/5.43 = ( set_or2715278749043346189nteger @ L @ U ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7530_UN__atLeast__UNIV,axiom,
% 9.17/5.43 ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ set_ord_atLeast_nat @ top_top_set_nat ) )
% 9.17/5.43 = top_top_set_nat ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7531_atLeast__0,axiom,
% 9.17/5.43 ( ( set_ord_atLeast_nat @ zero_zero_nat )
% 9.17/5.43 = top_top_set_nat ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7532_Inf__unit__def,axiom,
% 9.17/5.43 ( comple2584293577114468500t_unit
% 9.17/5.43 = ( ^ [Uu3: set_Product_unit] : product_Unity ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7533_Sup__unit__def,axiom,
% 9.17/5.43 ( comple4687483117567863418t_unit
% 9.17/5.43 = ( ^ [Uu3: set_Product_unit] : product_Unity ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7534_old_Ounit_Oexhaust,axiom,
% 9.17/5.43 ! [Y: product_unit] : ( Y = product_Unity ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7535_top__unit__def,axiom,
% 9.17/5.43 top_top_Product_unit = product_Unity ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7536_uminus__unit__def,axiom,
% 9.17/5.43 ( uminus2952777764628376836t_unit
% 9.17/5.43 = ( ^ [Uu3: product_unit] : product_Unity ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7537_bot__unit__def,axiom,
% 9.17/5.43 bot_bot_Product_unit = product_Unity ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7538_sup__unit__def,axiom,
% 9.17/5.43 ( sup_sup_Product_unit
% 9.17/5.43 = ( ^ [Uu3: product_unit,Uv: product_unit] : product_Unity ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7539_UNIV__unit,axiom,
% 9.17/5.43 ( top_to1996260823553986621t_unit
% 9.17/5.43 = ( insert_Product_unit @ product_Unity @ bot_bo3957492148770167129t_unit ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7540_atLeast__Suc__greaterThan,axiom,
% 9.17/5.43 ! [K: nat] :
% 9.17/5.43 ( ( set_ord_atLeast_nat @ ( suc @ K ) )
% 9.17/5.43 = ( set_or1210151606488870762an_nat @ K ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7541_wait__def,axiom,
% 9.17/5.43 ( heap_Time_wait
% 9.17/5.43 = ( ^ [N4: nat] :
% 9.17/5.43 ( heap_T6183433275982383450t_unit
% 9.17/5.43 @ ^ [H: heap_e7401611519738050253t_unit] : ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ product_Unity @ ( produc584006145561248582it_nat @ H @ N4 ) ) ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7542_execute__assert_H,axiom,
% 9.17/5.43 ! [P: $o,H3: heap_e7401611519738050253t_unit] :
% 9.17/5.43 ( ( P
% 9.17/5.43 => ( ( heap_T875086893843062177t_unit @ ( refine_Imp_assert @ P ) @ H3 )
% 9.17/5.43 = ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ product_Unity @ ( produc584006145561248582it_nat @ H3 @ zero_zero_nat ) ) ) ) )
% 9.17/5.43 & ( ~ P
% 9.17/5.43 => ( ( heap_T875086893843062177t_unit @ ( refine_Imp_assert @ P ) @ H3 )
% 9.17/5.43 = none_P9117596204409417319it_nat ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7543_atLeast__Suc,axiom,
% 9.17/5.43 ! [K: nat] :
% 9.17/5.43 ( ( set_ord_atLeast_nat @ ( suc @ K ) )
% 9.17/5.43 = ( minus_minus_set_nat @ ( set_ord_atLeast_nat @ K ) @ ( insert_nat @ K @ bot_bot_set_nat ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7544_default__unit__def,axiom,
% 9.17/5.43 defaul566961228789861419t_unit = product_Unity ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7545_inf__unit__def,axiom,
% 9.17/5.43 ( inf_inf_Product_unit
% 9.17/5.43 = ( ^ [Uu3: product_unit,Uv: product_unit] : product_Unity ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7546_floor__rat__def,axiom,
% 9.17/5.43 ( archim3151403230148437115or_rat
% 9.17/5.43 = ( ^ [X3: rat] :
% 9.17/5.43 ( the_int
% 9.17/5.43 @ ^ [Z4: int] :
% 9.17/5.43 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z4 ) @ X3 )
% 9.17/5.43 & ( ord_less_rat @ X3 @ ( ring_1_of_int_rat @ ( plus_plus_int @ Z4 @ one_one_int ) ) ) ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7547_rat__floor__lemma,axiom,
% 9.17/5.43 ! [A: int,B: int] :
% 9.17/5.43 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( divide_divide_int @ A @ B ) ) @ ( fract @ A @ B ) )
% 9.17/5.43 & ( ord_less_rat @ ( fract @ A @ B ) @ ( ring_1_of_int_rat @ ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7548_num__of__integer_Otransfer,axiom,
% 9.17/5.43 ( bNF_re6718328864250387230um_num @ code_pcr_integer
% 9.17/5.43 @ ^ [Y4: num,Z2: num] : ( Y4 = Z2 )
% 9.17/5.43 @ ( comp_nat_num_int @ num_of_nat @ nat2 )
% 9.17/5.43 @ code_num_of_integer ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7549_prod__decode__triangle__add,axiom,
% 9.17/5.43 ! [K: nat,M2: nat] :
% 9.17/5.43 ( ( nat_prod_decode @ ( plus_plus_nat @ ( nat_triangle @ K ) @ M2 ) )
% 9.17/5.43 = ( nat_prod_decode_aux @ K @ M2 ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7550_add__rat,axiom,
% 9.17/5.43 ! [B: int,D2: int,A: int,C: int] :
% 9.17/5.43 ( ( B != zero_zero_int )
% 9.17/5.43 => ( ( D2 != zero_zero_int )
% 9.17/5.43 => ( ( plus_plus_rat @ ( fract @ A @ B ) @ ( fract @ C @ D2 ) )
% 9.17/5.43 = ( fract @ ( plus_plus_int @ ( times_times_int @ A @ D2 ) @ ( times_times_int @ C @ B ) ) @ ( times_times_int @ B @ D2 ) ) ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7551_integer_Orep__transfer,axiom,
% 9.17/5.43 ( bNF_re3804157879324367682nt_int @ code_pcr_integer
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ ^ [X3: int] : X3
% 9.17/5.43 @ code_int_of_integer ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7552_integer_Oid__abs__transfer,axiom,
% 9.17/5.43 ( bNF_re982302072995117890nteger
% 9.17/5.43 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.43 @ code_pcr_integer
% 9.17/5.43 @ ^ [X3: int] : X3
% 9.17/5.43 @ code_integer_of_int ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7553_zero__integer_Otransfer,axiom,
% 9.17/5.43 code_pcr_integer @ zero_zero_int @ zero_z3403309356797280102nteger ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7554_plus__integer_Otransfer,axiom,
% 9.17/5.43 bNF_re398004352372739002nteger @ code_pcr_integer @ ( bNF_re3379532845092657523nteger @ code_pcr_integer @ code_pcr_integer ) @ plus_plus_int @ plus_p5714425477246183910nteger ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7555_quotient__of__eq,axiom,
% 9.17/5.43 ! [A: int,B: int,P4: int,Q3: int] :
% 9.17/5.43 ( ( ( quotient_of @ ( fract @ A @ B ) )
% 9.17/5.43 = ( product_Pair_int_int @ P4 @ Q3 ) )
% 9.17/5.43 => ( ( fract @ P4 @ Q3 )
% 9.17/5.43 = ( fract @ A @ B ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7556_less__integer_Otransfer,axiom,
% 9.17/5.43 ( bNF_re6321650412969554871eger_o @ code_pcr_integer
% 9.17/5.43 @ ( bNF_re6574881592172037608er_o_o @ code_pcr_integer
% 9.17/5.43 @ ^ [Y4: $o,Z2: $o] : ( Y4 = Z2 ) )
% 9.17/5.43 @ ord_less_int
% 9.17/5.43 @ ord_le6747313008572928689nteger ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7557_one__integer_Otransfer,axiom,
% 9.17/5.43 code_pcr_integer @ one_one_int @ one_one_Code_integer ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7558_less__eq__integer_Otransfer,axiom,
% 9.17/5.43 ( bNF_re6321650412969554871eger_o @ code_pcr_integer
% 9.17/5.43 @ ( bNF_re6574881592172037608er_o_o @ code_pcr_integer
% 9.17/5.43 @ ^ [Y4: $o,Z2: $o] : ( Y4 = Z2 ) )
% 9.17/5.43 @ ord_less_eq_int
% 9.17/5.43 @ ord_le3102999989581377725nteger ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7559_uminus__integer_Otransfer,axiom,
% 9.17/5.43 bNF_re3379532845092657523nteger @ code_pcr_integer @ code_pcr_integer @ uminus_uminus_int @ uminus1351360451143612070nteger ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7560_times__integer_Otransfer,axiom,
% 9.17/5.43 bNF_re398004352372739002nteger @ code_pcr_integer @ ( bNF_re3379532845092657523nteger @ code_pcr_integer @ code_pcr_integer ) @ times_times_int @ times_3573771949741848930nteger ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7561_minus__integer_Otransfer,axiom,
% 9.17/5.43 bNF_re398004352372739002nteger @ code_pcr_integer @ ( bNF_re3379532845092657523nteger @ code_pcr_integer @ code_pcr_integer ) @ minus_minus_int @ minus_8373710615458151222nteger ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7562_abs__integer_Otransfer,axiom,
% 9.17/5.43 bNF_re3379532845092657523nteger @ code_pcr_integer @ code_pcr_integer @ abs_abs_int @ abs_abs_Code_integer ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7563_nat__of__integer_Otransfer,axiom,
% 9.17/5.43 ( bNF_re2807294637932363402at_nat @ code_pcr_integer
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.43 @ nat2
% 9.17/5.43 @ code_nat_of_integer ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7564_normalize__eq,axiom,
% 9.17/5.43 ! [A: int,B: int,P4: int,Q3: int] :
% 9.17/5.43 ( ( ( normalize @ ( product_Pair_int_int @ A @ B ) )
% 9.17/5.43 = ( product_Pair_int_int @ P4 @ Q3 ) )
% 9.17/5.43 => ( ( fract @ P4 @ Q3 )
% 9.17/5.43 = ( fract @ A @ B ) ) ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7565_integer__of__nat_Otransfer,axiom,
% 9.17/5.43 ( bNF_re4153400068438556298nteger
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.43 @ code_pcr_integer
% 9.17/5.43 @ semiri1314217659103216013at_int
% 9.17/5.43 @ code_integer_of_nat ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7566_divide__integer_Otransfer,axiom,
% 9.17/5.43 bNF_re398004352372739002nteger @ code_pcr_integer @ ( bNF_re3379532845092657523nteger @ code_pcr_integer @ code_pcr_integer ) @ divide_divide_int @ divide6298287555418463151nteger ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7567_modulo__integer_Otransfer,axiom,
% 9.17/5.43 bNF_re398004352372739002nteger @ code_pcr_integer @ ( bNF_re3379532845092657523nteger @ code_pcr_integer @ code_pcr_integer ) @ modulo_modulo_int @ modulo364778990260209775nteger ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7568_sgn__integer_Otransfer,axiom,
% 9.17/5.43 bNF_re3379532845092657523nteger @ code_pcr_integer @ code_pcr_integer @ sgn_sgn_int @ sgn_sgn_Code_integer ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7569_dup_Otransfer,axiom,
% 9.17/5.43 ( bNF_re3379532845092657523nteger @ code_pcr_integer @ code_pcr_integer
% 9.17/5.43 @ ^ [K4: int] : ( plus_plus_int @ K4 @ K4 )
% 9.17/5.43 @ code_dup ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7570_take__bit__integer_Otransfer,axiom,
% 9.17/5.43 ( bNF_re4935368626670024657nteger
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.43 @ ( bNF_re3379532845092657523nteger @ code_pcr_integer @ code_pcr_integer )
% 9.17/5.43 @ bit_se2923211474154528505it_int
% 9.17/5.43 @ bit_se1745604003318907178nteger ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7571_not__integer_Otransfer,axiom,
% 9.17/5.43 bNF_re3379532845092657523nteger @ code_pcr_integer @ code_pcr_integer @ bit_ri7919022796975470100ot_int @ bit_ri7632146776885996613nteger ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7572_and__integer_Otransfer,axiom,
% 9.17/5.43 bNF_re398004352372739002nteger @ code_pcr_integer @ ( bNF_re3379532845092657523nteger @ code_pcr_integer @ code_pcr_integer ) @ bit_se725231765392027082nd_int @ bit_se3949692690581998587nteger ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7573_bit__integer_Otransfer,axiom,
% 9.17/5.43 ( bNF_re4711666741709854504_nat_o @ code_pcr_integer
% 9.17/5.43 @ ^ [Y4: nat > $o,Z2: nat > $o] : ( Y4 = Z2 )
% 9.17/5.43 @ bit_se1146084159140164899it_int
% 9.17/5.43 @ bit_se9216721137139052372nteger ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7574_or__integer_Otransfer,axiom,
% 9.17/5.43 bNF_re398004352372739002nteger @ code_pcr_integer @ ( bNF_re3379532845092657523nteger @ code_pcr_integer @ code_pcr_integer ) @ bit_se1409905431419307370or_int @ bit_se1080825931792720795nteger ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7575_xor__integer_Otransfer,axiom,
% 9.17/5.43 bNF_re398004352372739002nteger @ code_pcr_integer @ ( bNF_re3379532845092657523nteger @ code_pcr_integer @ code_pcr_integer ) @ bit_se6526347334894502574or_int @ bit_se3222712562003087583nteger ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7576_drop__bit__integer_Otransfer,axiom,
% 9.17/5.43 ( bNF_re4935368626670024657nteger
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.43 @ ( bNF_re3379532845092657523nteger @ code_pcr_integer @ code_pcr_integer )
% 9.17/5.43 @ bit_se8568078237143864401it_int
% 9.17/5.43 @ bit_se3928097537394005634nteger ) ).
% 9.17/5.43
% 9.17/5.43 thf(fact_7577_push__bit__integer_Otransfer,axiom,
% 9.17/5.43 ( bNF_re4935368626670024657nteger
% 9.17/5.43 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.43 @ ( bNF_re3379532845092657523nteger @ code_pcr_integer @ code_pcr_integer )
% 9.17/5.44 @ bit_se545348938243370406it_int
% 9.17/5.44 @ bit_se7788150548672797655nteger ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7578_mask__integer_Otransfer,axiom,
% 9.17/5.44 ( bNF_re4153400068438556298nteger
% 9.17/5.44 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.44 @ code_pcr_integer
% 9.17/5.44 @ bit_se2000444600071755411sk_int
% 9.17/5.44 @ bit_se2119862282449309892nteger ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7579_unset__bit__integer_Otransfer,axiom,
% 9.17/5.44 ( bNF_re4935368626670024657nteger
% 9.17/5.44 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.44 @ ( bNF_re3379532845092657523nteger @ code_pcr_integer @ code_pcr_integer )
% 9.17/5.44 @ bit_se4203085406695923979it_int
% 9.17/5.44 @ bit_se8260200283734997820nteger ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7580_set__bit__integer_Otransfer,axiom,
% 9.17/5.44 ( bNF_re4935368626670024657nteger
% 9.17/5.44 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.44 @ ( bNF_re3379532845092657523nteger @ code_pcr_integer @ code_pcr_integer )
% 9.17/5.44 @ bit_se7879613467334960850it_int
% 9.17/5.44 @ bit_se2793503036327961859nteger ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7581_division__segment__integer_Otransfer,axiom,
% 9.17/5.44 bNF_re3379532845092657523nteger @ code_pcr_integer @ code_pcr_integer @ euclid3395696857347342551nt_int @ euclid6289375185220004616nteger ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7582_flip__bit__integer_Otransfer,axiom,
% 9.17/5.44 ( bNF_re4935368626670024657nteger
% 9.17/5.44 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.44 @ ( bNF_re3379532845092657523nteger @ code_pcr_integer @ code_pcr_integer )
% 9.17/5.44 @ bit_se2159334234014336723it_int
% 9.17/5.44 @ bit_se1345352211410354436nteger ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7583_euclidean__size__integer_Otransfer,axiom,
% 9.17/5.44 ( bNF_re2807294637932363402at_nat @ code_pcr_integer
% 9.17/5.44 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.44 @ euclid4774559944035922753ze_int
% 9.17/5.44 @ euclid6377331345833325938nteger ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7584_quotient__of__Fract,axiom,
% 9.17/5.44 ! [A: int,B: int] :
% 9.17/5.44 ( ( quotient_of @ ( fract @ A @ B ) )
% 9.17/5.44 = ( normalize @ ( product_Pair_int_int @ A @ B ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7585_sub_Otransfer,axiom,
% 9.17/5.44 ( bNF_re7876454716742015248nteger
% 9.17/5.44 @ ^ [Y4: num,Z2: num] : ( Y4 = Z2 )
% 9.17/5.44 @ ( bNF_re6501075790457514782nteger
% 9.17/5.44 @ ^ [Y4: num,Z2: num] : ( Y4 = Z2 )
% 9.17/5.44 @ code_pcr_integer )
% 9.17/5.44 @ ^ [M: num,N4: num] : ( minus_minus_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N4 ) )
% 9.17/5.44 @ code_sub ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7586_Fract_Oabs__eq,axiom,
% 9.17/5.44 ( fract
% 9.17/5.44 = ( ^ [Xa4: int,X3: int] : ( abs_Rat @ ( if_Pro3027730157355071871nt_int @ ( X3 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ Xa4 @ X3 ) ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7587_Fract_Otransfer,axiom,
% 9.17/5.44 ( bNF_re3461391660133120880nt_rat
% 9.17/5.44 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.44 @ ( bNF_re2214769303045360666nt_rat
% 9.17/5.44 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.44 @ pcr_rat )
% 9.17/5.44 @ ^ [A5: int,B4: int] : ( if_Pro3027730157355071871nt_int @ ( B4 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ A5 @ B4 ) )
% 9.17/5.44 @ fract ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7588_Fract__add__one,axiom,
% 9.17/5.44 ! [N2: int,M2: int] :
% 9.17/5.44 ( ( N2 != zero_zero_int )
% 9.17/5.44 => ( ( fract @ ( plus_plus_int @ M2 @ N2 ) @ N2 )
% 9.17/5.44 = ( plus_plus_rat @ ( fract @ M2 @ N2 ) @ one_one_rat ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7589_Fract__def,axiom,
% 9.17/5.44 ( fract
% 9.17/5.44 = ( map_fu7831380289885515383nt_rat @ id_int @ ( map_fu3424225382358772769nt_rat @ id_int @ abs_Rat )
% 9.17/5.44 @ ^ [A5: int,B4: int] : ( if_Pro3027730157355071871nt_int @ ( B4 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ A5 @ B4 ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7590_list__decode_Opinduct,axiom,
% 9.17/5.44 ! [A0: nat,P: nat > $o] :
% 9.17/5.44 ( ( accp_nat @ nat_list_decode_rel @ A0 )
% 9.17/5.44 => ( ( ( accp_nat @ nat_list_decode_rel @ zero_zero_nat )
% 9.17/5.44 => ( P @ zero_zero_nat ) )
% 9.17/5.44 => ( ! [N: nat] :
% 9.17/5.44 ( ( accp_nat @ nat_list_decode_rel @ ( suc @ N ) )
% 9.17/5.44 => ( ! [X8: nat,Y6: nat] :
% 9.17/5.44 ( ( ( product_Pair_nat_nat @ X8 @ Y6 )
% 9.17/5.44 = ( nat_prod_decode @ N ) )
% 9.17/5.44 => ( P @ Y6 ) )
% 9.17/5.44 => ( P @ ( suc @ N ) ) ) )
% 9.17/5.44 => ( P @ A0 ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7591_type__definition__integer,axiom,
% 9.17/5.44 type_d8366093980585677751er_int @ code_int_of_integer @ code_integer_of_int @ top_top_set_int ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7592_pred__nat__trancl__eq__le,axiom,
% 9.17/5.44 ! [M2: nat,N2: nat] :
% 9.17/5.44 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ M2 @ N2 ) @ ( transi2905341329935302413cl_nat @ pred_nat ) )
% 9.17/5.44 = ( ord_less_eq_nat @ M2 @ N2 ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7593_less__eq,axiom,
% 9.17/5.44 ! [M2: nat,N2: nat] :
% 9.17/5.44 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ M2 @ N2 ) @ ( transi6264000038957366511cl_nat @ pred_nat ) )
% 9.17/5.44 = ( ord_less_nat @ M2 @ N2 ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7594_upt__0__eq__Nil__conv,axiom,
% 9.17/5.44 ! [J: nat] :
% 9.17/5.44 ( ( ( upt @ zero_zero_nat @ J )
% 9.17/5.44 = nil_nat )
% 9.17/5.44 = ( J = zero_zero_nat ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7595_map__add__upt_H,axiom,
% 9.17/5.44 ! [Ofs: nat,A: nat,B: nat] :
% 9.17/5.44 ( ( map_nat_nat
% 9.17/5.44 @ ^ [I3: nat] : ( plus_plus_nat @ I3 @ Ofs )
% 9.17/5.44 @ ( upt @ A @ B ) )
% 9.17/5.44 = ( upt @ ( plus_plus_nat @ A @ Ofs ) @ ( plus_plus_nat @ B @ Ofs ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7596_map__add__upt,axiom,
% 9.17/5.44 ! [N2: nat,M2: nat] :
% 9.17/5.44 ( ( map_nat_nat
% 9.17/5.44 @ ^ [I3: nat] : ( plus_plus_nat @ I3 @ N2 )
% 9.17/5.44 @ ( upt @ zero_zero_nat @ M2 ) )
% 9.17/5.44 = ( upt @ N2 @ ( plus_plus_nat @ M2 @ N2 ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7597_upt__filter__extend,axiom,
% 9.17/5.44 ! [U: nat,U4: nat,P: nat > $o] :
% 9.17/5.44 ( ( ord_less_eq_nat @ U @ U4 )
% 9.17/5.44 => ( ! [I2: nat] :
% 9.17/5.44 ( ( ( ord_less_eq_nat @ U @ I2 )
% 9.17/5.44 & ( ord_less_nat @ I2 @ U4 ) )
% 9.17/5.44 => ~ ( P @ I2 ) )
% 9.17/5.44 => ( ( filter_nat @ P @ ( upt @ zero_zero_nat @ U ) )
% 9.17/5.44 = ( filter_nat @ P @ ( upt @ zero_zero_nat @ U4 ) ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7598_nth__upt,axiom,
% 9.17/5.44 ! [I: nat,K: nat,J: nat] :
% 9.17/5.44 ( ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ J )
% 9.17/5.44 => ( ( nth_nat @ ( upt @ I @ J ) @ K )
% 9.17/5.44 = ( plus_plus_nat @ I @ K ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7599_upt__eq__Cons__conv,axiom,
% 9.17/5.44 ! [I: nat,J: nat,X: nat,Xs: list_nat] :
% 9.17/5.44 ( ( ( upt @ I @ J )
% 9.17/5.44 = ( cons_nat @ X @ Xs ) )
% 9.17/5.44 = ( ( ord_less_nat @ I @ J )
% 9.17/5.44 & ( I = X )
% 9.17/5.44 & ( ( upt @ ( plus_plus_nat @ I @ one_one_nat ) @ J )
% 9.17/5.44 = Xs ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7600_list__decode_Opelims,axiom,
% 9.17/5.44 ! [X: nat,Y: list_nat] :
% 9.17/5.44 ( ( ( nat_list_decode @ X )
% 9.17/5.44 = Y )
% 9.17/5.44 => ( ( accp_nat @ nat_list_decode_rel @ X )
% 9.17/5.44 => ( ( ( X = zero_zero_nat )
% 9.17/5.44 => ( ( Y = nil_nat )
% 9.17/5.44 => ~ ( accp_nat @ nat_list_decode_rel @ zero_zero_nat ) ) )
% 9.17/5.44 => ~ ! [N: nat] :
% 9.17/5.44 ( ( X
% 9.17/5.44 = ( suc @ N ) )
% 9.17/5.44 => ( ( Y
% 9.17/5.44 = ( produc2761476792215241774st_nat
% 9.17/5.44 @ ^ [X3: nat,Y3: nat] : ( cons_nat @ X3 @ ( nat_list_decode @ Y3 ) )
% 9.17/5.44 @ ( nat_prod_decode @ N ) ) )
% 9.17/5.44 => ~ ( accp_nat @ nat_list_decode_rel @ ( suc @ N ) ) ) ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7601_drop__upt,axiom,
% 9.17/5.44 ! [M2: nat,I: nat,J: nat] :
% 9.17/5.44 ( ( drop_nat @ M2 @ ( upt @ I @ J ) )
% 9.17/5.44 = ( upt @ ( plus_plus_nat @ I @ M2 ) @ J ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7602_natural__zero__minus__one,axiom,
% 9.17/5.44 ( ( minus_7197305767214868737atural @ zero_z2226904508553997617atural @ one_one_Code_natural )
% 9.17/5.44 = zero_z2226904508553997617atural ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7603_list__decode_Opsimps_I1_J,axiom,
% 9.17/5.44 ( ( accp_nat @ nat_list_decode_rel @ zero_zero_nat )
% 9.17/5.44 => ( ( nat_list_decode @ zero_zero_nat )
% 9.17/5.44 = nil_nat ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7604_list__decode_Opsimps_I2_J,axiom,
% 9.17/5.44 ! [N2: nat] :
% 9.17/5.44 ( ( accp_nat @ nat_list_decode_rel @ ( suc @ N2 ) )
% 9.17/5.44 => ( ( nat_list_decode @ ( suc @ N2 ) )
% 9.17/5.44 = ( produc2761476792215241774st_nat
% 9.17/5.44 @ ^ [X3: nat,Y3: nat] : ( cons_nat @ X3 @ ( nat_list_decode @ Y3 ) )
% 9.17/5.44 @ ( nat_prod_decode @ N2 ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7605_list__encode_Oelims,axiom,
% 9.17/5.44 ! [X: list_nat,Y: nat] :
% 9.17/5.44 ( ( ( nat_list_encode @ X )
% 9.17/5.44 = Y )
% 9.17/5.44 => ( ( ( X = nil_nat )
% 9.17/5.44 => ( Y != zero_zero_nat ) )
% 9.17/5.44 => ~ ! [X4: nat,Xs2: list_nat] :
% 9.17/5.44 ( ( X
% 9.17/5.44 = ( cons_nat @ X4 @ Xs2 ) )
% 9.17/5.44 => ( Y
% 9.17/5.44 != ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X4 @ ( nat_list_encode @ Xs2 ) ) ) ) ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7606_upt__merge,axiom,
% 9.17/5.44 ! [I: nat,J: nat,K: nat] :
% 9.17/5.44 ( ( ( ord_less_eq_nat @ I @ J )
% 9.17/5.44 & ( ord_less_eq_nat @ J @ K ) )
% 9.17/5.44 => ( ( append_nat @ ( upt @ I @ J ) @ ( upt @ J @ K ) )
% 9.17/5.44 = ( upt @ I @ K ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7607_upt__eq__append__conv,axiom,
% 9.17/5.44 ! [I: nat,J: nat,Xs: list_nat,Ys: list_nat] :
% 9.17/5.44 ( ( ord_less_eq_nat @ I @ J )
% 9.17/5.44 => ( ( ( upt @ I @ J )
% 9.17/5.44 = ( append_nat @ Xs @ Ys ) )
% 9.17/5.44 = ( ? [K4: nat] :
% 9.17/5.44 ( ( ord_less_eq_nat @ I @ K4 )
% 9.17/5.44 & ( ord_less_eq_nat @ K4 @ J )
% 9.17/5.44 & ( ( upt @ I @ K4 )
% 9.17/5.44 = Xs )
% 9.17/5.44 & ( ( upt @ K4 @ J )
% 9.17/5.44 = Ys ) ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7608_upt__append,axiom,
% 9.17/5.44 ! [I: nat,J: nat] :
% 9.17/5.44 ( ( ord_less_nat @ I @ J )
% 9.17/5.44 => ( ( append_nat @ ( upt @ zero_zero_nat @ I ) @ ( upt @ I @ J ) )
% 9.17/5.44 = ( upt @ zero_zero_nat @ J ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7609_upt__add__eq__append,axiom,
% 9.17/5.44 ! [I: nat,J: nat,K: nat] :
% 9.17/5.44 ( ( ord_less_eq_nat @ I @ J )
% 9.17/5.44 => ( ( upt @ I @ ( plus_plus_nat @ J @ K ) )
% 9.17/5.44 = ( append_nat @ ( upt @ I @ J ) @ ( upt @ J @ ( plus_plus_nat @ J @ K ) ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7610_upt__eq__lel__conv,axiom,
% 9.17/5.44 ! [L: nat,H3: nat,Is1: list_nat,I: nat,Is2: list_nat] :
% 9.17/5.44 ( ( ( upt @ L @ H3 )
% 9.17/5.44 = ( append_nat @ Is1 @ ( cons_nat @ I @ Is2 ) ) )
% 9.17/5.44 = ( ( Is1
% 9.17/5.44 = ( upt @ L @ I ) )
% 9.17/5.44 & ( Is2
% 9.17/5.44 = ( upt @ ( suc @ I ) @ H3 ) )
% 9.17/5.44 & ( ord_less_eq_nat @ L @ I )
% 9.17/5.44 & ( ord_less_nat @ I @ H3 ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7611_list__encode_Osimps_I2_J,axiom,
% 9.17/5.44 ! [X: nat,Xs: list_nat] :
% 9.17/5.44 ( ( nat_list_encode @ ( cons_nat @ X @ Xs ) )
% 9.17/5.44 = ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X @ ( nat_list_encode @ Xs ) ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7612_list__encode_Opelims,axiom,
% 9.17/5.44 ! [X: list_nat,Y: nat] :
% 9.17/5.44 ( ( ( nat_list_encode @ X )
% 9.17/5.44 = Y )
% 9.17/5.44 => ( ( accp_list_nat @ nat_list_encode_rel @ X )
% 9.17/5.44 => ( ( ( X = nil_nat )
% 9.17/5.44 => ( ( Y = zero_zero_nat )
% 9.17/5.44 => ~ ( accp_list_nat @ nat_list_encode_rel @ nil_nat ) ) )
% 9.17/5.44 => ~ ! [X4: nat,Xs2: list_nat] :
% 9.17/5.44 ( ( X
% 9.17/5.44 = ( cons_nat @ X4 @ Xs2 ) )
% 9.17/5.44 => ( ( Y
% 9.17/5.44 = ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X4 @ ( nat_list_encode @ Xs2 ) ) ) ) )
% 9.17/5.44 => ~ ( accp_list_nat @ nat_list_encode_rel @ ( cons_nat @ X4 @ Xs2 ) ) ) ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7613_last__upt,axiom,
% 9.17/5.44 ! [I: nat,J: nat] :
% 9.17/5.44 ( ( ord_less_nat @ I @ J )
% 9.17/5.44 => ( ( last_nat @ ( upt @ I @ J ) )
% 9.17/5.44 = ( minus_minus_nat @ J @ one_one_nat ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7614_nth__sorted__list__of__set__greaterThanLessThan,axiom,
% 9.17/5.44 ! [N2: nat,J: nat,I: nat] :
% 9.17/5.44 ( ( ord_less_nat @ N2 @ ( minus_minus_nat @ J @ ( suc @ I ) ) )
% 9.17/5.44 => ( ( nth_nat @ ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ I @ J ) ) @ N2 )
% 9.17/5.44 = ( suc @ ( plus_plus_nat @ I @ N2 ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7615_nth__sorted__list__of__set__greaterThanAtMost,axiom,
% 9.17/5.44 ! [N2: nat,J: nat,I: nat] :
% 9.17/5.44 ( ( ord_less_nat @ N2 @ ( minus_minus_nat @ J @ I ) )
% 9.17/5.44 => ( ( nth_nat @ ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ I @ J ) ) @ N2 )
% 9.17/5.44 = ( suc @ ( plus_plus_nat @ I @ N2 ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7616_upto_Opelims,axiom,
% 9.17/5.44 ! [X: int,Xa: int,Y: list_int] :
% 9.17/5.44 ( ( ( upto @ X @ Xa )
% 9.17/5.44 = Y )
% 9.17/5.44 => ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ X @ Xa ) )
% 9.17/5.44 => ~ ( ( ( ( ord_less_eq_int @ X @ Xa )
% 9.17/5.44 => ( Y
% 9.17/5.44 = ( cons_int @ X @ ( upto @ ( plus_plus_int @ X @ one_one_int ) @ Xa ) ) ) )
% 9.17/5.44 & ( ~ ( ord_less_eq_int @ X @ Xa )
% 9.17/5.44 => ( Y = nil_int ) ) )
% 9.17/5.44 => ~ ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ X @ Xa ) ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7617_upto_Opsimps,axiom,
% 9.17/5.44 ! [I: int,J: int] :
% 9.17/5.44 ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ I @ J ) )
% 9.17/5.44 => ( ( ( ord_less_eq_int @ I @ J )
% 9.17/5.44 => ( ( upto @ I @ J )
% 9.17/5.44 = ( cons_int @ I @ ( upto @ ( plus_plus_int @ I @ one_one_int ) @ J ) ) ) )
% 9.17/5.44 & ( ~ ( ord_less_eq_int @ I @ J )
% 9.17/5.44 => ( ( upto @ I @ J )
% 9.17/5.44 = nil_int ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7618_nth__upto,axiom,
% 9.17/5.44 ! [I: int,K: nat,J: int] :
% 9.17/5.44 ( ( ord_less_eq_int @ ( plus_plus_int @ I @ ( semiri1314217659103216013at_int @ K ) ) @ J )
% 9.17/5.44 => ( ( nth_int @ ( upto @ I @ J ) @ K )
% 9.17/5.44 = ( plus_plus_int @ I @ ( semiri1314217659103216013at_int @ K ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7619_length__upto,axiom,
% 9.17/5.44 ! [I: int,J: int] :
% 9.17/5.44 ( ( size_size_list_int @ ( upto @ I @ J ) )
% 9.17/5.44 = ( nat2 @ ( plus_plus_int @ ( minus_minus_int @ J @ I ) @ one_one_int ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7620_upto__rec__numeral_I1_J,axiom,
% 9.17/5.44 ! [M2: num,N2: num] :
% 9.17/5.44 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N2 ) )
% 9.17/5.44 => ( ( upto @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N2 ) )
% 9.17/5.44 = ( cons_int @ ( numeral_numeral_int @ M2 ) @ ( upto @ ( plus_plus_int @ ( numeral_numeral_int @ M2 ) @ one_one_int ) @ ( numeral_numeral_int @ N2 ) ) ) ) )
% 9.17/5.44 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N2 ) )
% 9.17/5.44 => ( ( upto @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N2 ) )
% 9.17/5.44 = nil_int ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7621_upto__rec__numeral_I2_J,axiom,
% 9.17/5.44 ! [M2: num,N2: num] :
% 9.17/5.44 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 9.17/5.44 => ( ( upto @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 9.17/5.44 = ( cons_int @ ( numeral_numeral_int @ M2 ) @ ( upto @ ( plus_plus_int @ ( numeral_numeral_int @ M2 ) @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ) ) )
% 9.17/5.44 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 9.17/5.44 => ( ( upto @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 9.17/5.44 = nil_int ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7622_upto__rec__numeral_I3_J,axiom,
% 9.17/5.44 ! [M2: num,N2: num] :
% 9.17/5.44 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( numeral_numeral_int @ N2 ) )
% 9.17/5.44 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( numeral_numeral_int @ N2 ) )
% 9.17/5.44 = ( cons_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( upto @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ one_one_int ) @ ( numeral_numeral_int @ N2 ) ) ) ) )
% 9.17/5.44 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( numeral_numeral_int @ N2 ) )
% 9.17/5.44 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( numeral_numeral_int @ N2 ) )
% 9.17/5.44 = nil_int ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7623_upto__rec__numeral_I4_J,axiom,
% 9.17/5.44 ! [M2: num,N2: num] :
% 9.17/5.44 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 9.17/5.44 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 9.17/5.44 = ( cons_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( upto @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ) ) )
% 9.17/5.44 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 9.17/5.44 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 9.17/5.44 = nil_int ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7624_upto__split2,axiom,
% 9.17/5.44 ! [I: int,J: int,K: int] :
% 9.17/5.44 ( ( ord_less_eq_int @ I @ J )
% 9.17/5.44 => ( ( ord_less_eq_int @ J @ K )
% 9.17/5.44 => ( ( upto @ I @ K )
% 9.17/5.44 = ( append_int @ ( upto @ I @ J ) @ ( upto @ ( plus_plus_int @ J @ one_one_int ) @ K ) ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7625_upto__rec1,axiom,
% 9.17/5.44 ! [I: int,J: int] :
% 9.17/5.44 ( ( ord_less_eq_int @ I @ J )
% 9.17/5.44 => ( ( upto @ I @ J )
% 9.17/5.44 = ( cons_int @ I @ ( upto @ ( plus_plus_int @ I @ one_one_int ) @ J ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7626_upto_Osimps,axiom,
% 9.17/5.44 ( upto
% 9.17/5.44 = ( ^ [I3: int,J2: int] : ( if_list_int @ ( ord_less_eq_int @ I3 @ J2 ) @ ( cons_int @ I3 @ ( upto @ ( plus_plus_int @ I3 @ one_one_int ) @ J2 ) ) @ nil_int ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7627_upto_Oelims,axiom,
% 9.17/5.44 ! [X: int,Xa: int,Y: list_int] :
% 9.17/5.44 ( ( ( upto @ X @ Xa )
% 9.17/5.44 = Y )
% 9.17/5.44 => ( ( ( ord_less_eq_int @ X @ Xa )
% 9.17/5.44 => ( Y
% 9.17/5.44 = ( cons_int @ X @ ( upto @ ( plus_plus_int @ X @ one_one_int ) @ Xa ) ) ) )
% 9.17/5.44 & ( ~ ( ord_less_eq_int @ X @ Xa )
% 9.17/5.44 => ( Y = nil_int ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7628_greaterThanAtMost__upto,axiom,
% 9.17/5.44 ( set_or6656581121297822940st_int
% 9.17/5.44 = ( ^ [I3: int,J2: int] : ( set_int2 @ ( upto @ ( plus_plus_int @ I3 @ one_one_int ) @ J2 ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7629_upto__split3,axiom,
% 9.17/5.44 ! [I: int,J: int,K: int] :
% 9.17/5.44 ( ( ord_less_eq_int @ I @ J )
% 9.17/5.44 => ( ( ord_less_eq_int @ J @ K )
% 9.17/5.44 => ( ( upto @ I @ K )
% 9.17/5.44 = ( append_int @ ( upto @ I @ ( minus_minus_int @ J @ one_one_int ) ) @ ( cons_int @ J @ ( upto @ ( plus_plus_int @ J @ one_one_int ) @ K ) ) ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7630_greaterThanLessThan__upto,axiom,
% 9.17/5.44 ( set_or5832277885323065728an_int
% 9.17/5.44 = ( ^ [I3: int,J2: int] : ( set_int2 @ ( upto @ ( plus_plus_int @ I3 @ one_one_int ) @ ( minus_minus_int @ J2 @ one_one_int ) ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7631_take__upt,axiom,
% 9.17/5.44 ! [I: nat,M2: nat,N2: nat] :
% 9.17/5.44 ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ M2 ) @ N2 )
% 9.17/5.44 => ( ( take_nat @ M2 @ ( upt @ I @ N2 ) )
% 9.17/5.44 = ( upt @ I @ ( plus_plus_nat @ I @ M2 ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7632_butlast__upt,axiom,
% 9.17/5.44 ! [M2: nat,N2: nat] :
% 9.17/5.44 ( ( butlast_nat @ ( upt @ M2 @ N2 ) )
% 9.17/5.44 = ( upt @ M2 @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7633_next_Osimps,axiom,
% 9.17/5.44 ! [V: code_natural,W: code_natural] :
% 9.17/5.44 ( ( next @ ( produc3574140220909816553atural @ V @ W ) )
% 9.17/5.44 = ( produc6639722614265839536atural @ ( plus_p4538020629002901425atural @ ( minus_shift @ ( numera5444537566228673987atural @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( minus_shift @ ( numera5444537566228673987atural @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( times_2397367101498566445atural @ ( modulo8411746178871703098atural @ V @ ( numera5444537566228673987atural @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( numera5444537566228673987atural @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ V @ ( numera5444537566228673987atural @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( numera5444537566228673987atural @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( plus_p4538020629002901425atural @ ( minus_shift @ ( numera5444537566228673987atural @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( times_2397367101498566445atural @ ( modulo8411746178871703098atural @ W @ ( numera5444537566228673987atural @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( numera5444537566228673987atural @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ W @ ( numera5444537566228673987atural @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( numera5444537566228673987atural @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ one_one_Code_natural ) ) @ one_one_Code_natural ) @ ( produc3574140220909816553atural @ ( minus_shift @ ( numera5444537566228673987atural @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( times_2397367101498566445atural @ ( modulo8411746178871703098atural @ V @ ( numera5444537566228673987atural @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( numera5444537566228673987atural @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ V @ ( numera5444537566228673987atural @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( numera5444537566228673987atural @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( minus_shift @ ( numera5444537566228673987atural @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( times_2397367101498566445atural @ ( modulo8411746178871703098atural @ W @ ( numera5444537566228673987atural @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( numera5444537566228673987atural @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ W @ ( numera5444537566228673987atural @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( numera5444537566228673987atural @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7634_full__exhaustive__natural_H_Ocases,axiom,
% 9.17/5.44 ! [X: produc989692990947075319atural] :
% 9.17/5.44 ~ ! [F3: produc4972180933644002618e_term > option6357759511663192854e_term,D: code_natural,I2: code_natural] :
% 9.17/5.44 ( X
% 9.17/5.44 != ( produc3831813291587773865atural @ F3 @ ( produc3574140220909816553atural @ D @ I2 ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7635_exhaustive__natural_H_Ocases,axiom,
% 9.17/5.44 ! [X: produc8731074985263844745atural] :
% 9.17/5.44 ~ ! [F3: code_natural > option6357759511663192854e_term,D: code_natural,I2: code_natural] :
% 9.17/5.44 ( X
% 9.17/5.44 != ( produc2252593628808123835atural @ F3 @ ( produc3574140220909816553atural @ D @ I2 ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7636_log_Ocases,axiom,
% 9.17/5.44 ! [X: produc7822875418678951345atural] :
% 9.17/5.44 ~ ! [B2: code_natural,I2: code_natural] :
% 9.17/5.44 ( X
% 9.17/5.44 != ( produc3574140220909816553atural @ B2 @ I2 ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7637_minus__shift__def,axiom,
% 9.17/5.44 ( minus_shift
% 9.17/5.44 = ( ^ [R3: code_natural,K4: code_natural,L3: code_natural] : ( if_Code_natural @ ( ord_le5570908160329646204atural @ K4 @ L3 ) @ ( minus_7197305767214868737atural @ ( plus_p4538020629002901425atural @ R3 @ K4 ) @ L3 ) @ ( minus_7197305767214868737atural @ K4 @ L3 ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7638_split__seed__def,axiom,
% 9.17/5.44 ( split_seed
% 9.17/5.44 = ( ^ [S4: produc7822875418678951345atural] :
% 9.17/5.44 ( produc8282080750456430313atural
% 9.17/5.44 @ ^ [V2: code_natural,W2: code_natural] :
% 9.17/5.44 ( produc8282080750456430313atural
% 9.17/5.44 @ ^ [V5: code_natural,W3: code_natural] : ( produc4480994950612372183atural @ ( produc3574140220909816553atural @ ( inc_shift @ ( numera5444537566228673987atural @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ V2 ) @ W3 ) @ ( produc3574140220909816553atural @ V5 @ ( inc_shift @ ( numera5444537566228673987atural @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ W2 ) ) )
% 9.17/5.44 @ ( produc6591912806276919810atural @ ( next @ S4 ) ) )
% 9.17/5.44 @ S4 ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7639_log_Osimps,axiom,
% 9.17/5.44 ( log
% 9.17/5.44 = ( ^ [B4: code_natural,I3: code_natural] :
% 9.17/5.44 ( if_Code_natural
% 9.17/5.44 @ ( ( ord_le1926595141338095240atural @ B4 @ one_one_Code_natural )
% 9.17/5.44 | ( ord_le5570908160329646204atural @ I3 @ B4 ) )
% 9.17/5.44 @ one_one_Code_natural
% 9.17/5.44 @ ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( log @ B4 @ ( divide5121882707175180666atural @ I3 @ B4 ) ) ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7640_log_Oelims,axiom,
% 9.17/5.44 ! [X: code_natural,Xa: code_natural,Y: code_natural] :
% 9.17/5.44 ( ( ( log @ X @ Xa )
% 9.17/5.44 = Y )
% 9.17/5.44 => ( ( ( ( ord_le1926595141338095240atural @ X @ one_one_Code_natural )
% 9.17/5.44 | ( ord_le5570908160329646204atural @ Xa @ X ) )
% 9.17/5.44 => ( Y = one_one_Code_natural ) )
% 9.17/5.44 & ( ~ ( ( ord_le1926595141338095240atural @ X @ one_one_Code_natural )
% 9.17/5.44 | ( ord_le5570908160329646204atural @ Xa @ X ) )
% 9.17/5.44 => ( Y
% 9.17/5.44 = ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( log @ X @ ( divide5121882707175180666atural @ Xa @ X ) ) ) ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7641_inc__shift__def,axiom,
% 9.17/5.44 ( inc_shift
% 9.17/5.44 = ( ^ [V2: code_natural,K4: code_natural] : ( if_Code_natural @ ( V2 = K4 ) @ one_one_Code_natural @ ( plus_p4538020629002901425atural @ K4 @ one_one_Code_natural ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7642_log_Opelims,axiom,
% 9.17/5.44 ! [X: code_natural,Xa: code_natural,Y: code_natural] :
% 9.17/5.44 ( ( ( log @ X @ Xa )
% 9.17/5.44 = Y )
% 9.17/5.44 => ( ( accp_P8126237942716283194atural @ log_rel @ ( produc3574140220909816553atural @ X @ Xa ) )
% 9.17/5.44 => ~ ( ( ( ( ( ord_le1926595141338095240atural @ X @ one_one_Code_natural )
% 9.17/5.44 | ( ord_le5570908160329646204atural @ Xa @ X ) )
% 9.17/5.44 => ( Y = one_one_Code_natural ) )
% 9.17/5.44 & ( ~ ( ( ord_le1926595141338095240atural @ X @ one_one_Code_natural )
% 9.17/5.44 | ( ord_le5570908160329646204atural @ Xa @ X ) )
% 9.17/5.44 => ( Y
% 9.17/5.44 = ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( log @ X @ ( divide5121882707175180666atural @ Xa @ X ) ) ) ) ) )
% 9.17/5.44 => ~ ( accp_P8126237942716283194atural @ log_rel @ ( produc3574140220909816553atural @ X @ Xa ) ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7643_Random_Orange__def,axiom,
% 9.17/5.44 ( range
% 9.17/5.44 = ( ^ [K4: code_natural] :
% 9.17/5.44 ( produc5538323210962509403atural
% 9.17/5.44 @ ( iterat8892046348760725948atural @ ( log @ ( numera5444537566228673987atural @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ K4 )
% 9.17/5.44 @ ^ [L3: code_natural] :
% 9.17/5.44 ( produc5538323210962509403atural @ next
% 9.17/5.44 @ ^ [V2: code_natural] : ( produc6639722614265839536atural @ ( plus_p4538020629002901425atural @ V2 @ ( times_2397367101498566445atural @ L3 @ ( numera5444537566228673987atural @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 9.17/5.44 @ one_one_Code_natural )
% 9.17/5.44 @ ^ [V2: code_natural] : ( produc6639722614265839536atural @ ( modulo8411746178871703098atural @ V2 @ K4 ) ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7644_wmsI,axiom,
% 9.17/5.44 ! [A2: multis2468970476368604999at_nat,B5: multis2468970476368604999at_nat,Z7: multis2468970476368604999at_nat] :
% 9.17/5.44 ( ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( set_ms8126754132646256062at_nat @ A2 ) @ ( set_ms8126754132646256062at_nat @ B5 ) ) @ fun_max_strict )
% 9.17/5.44 | ( ( A2 = zero_z1048942125864253310at_nat )
% 9.17/5.44 & ( B5 = zero_z1048942125864253310at_nat ) ) )
% 9.17/5.44 => ( member6689249552917799696at_nat @ ( produc4348348721325984599at_nat @ ( plus_p7104986032573967614at_nat @ Z7 @ A2 ) @ ( plus_p7104986032573967614at_nat @ Z7 @ B5 ) ) @ ms_weak ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7645_smsI,axiom,
% 9.17/5.44 ! [A2: multis2468970476368604999at_nat,B5: multis2468970476368604999at_nat,Z7: multis2468970476368604999at_nat] :
% 9.17/5.44 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( set_ms8126754132646256062at_nat @ A2 ) @ ( set_ms8126754132646256062at_nat @ B5 ) ) @ fun_max_strict )
% 9.17/5.44 => ( member6689249552917799696at_nat @ ( produc4348348721325984599at_nat @ ( plus_p7104986032573967614at_nat @ Z7 @ A2 ) @ ( plus_p7104986032573967614at_nat @ Z7 @ B5 ) ) @ ms_strict ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7646_ms__reduction__pair,axiom,
% 9.17/5.44 fun_re7357418987779152907at_nat @ ( produc5245064249948416855at_nat @ ms_strict @ ms_weak ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7647_ms__strictI,axiom,
% 9.17/5.44 ! [Z7: multis2468970476368604999at_nat,Z8: multis2468970476368604999at_nat,A2: multis2468970476368604999at_nat,B5: multis2468970476368604999at_nat] :
% 9.17/5.44 ( ( pw_leq @ Z7 @ Z8 )
% 9.17/5.44 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( set_ms8126754132646256062at_nat @ A2 ) @ ( set_ms8126754132646256062at_nat @ B5 ) ) @ fun_max_strict )
% 9.17/5.44 => ( member6689249552917799696at_nat @ ( produc4348348721325984599at_nat @ ( plus_p7104986032573967614at_nat @ Z7 @ A2 ) @ ( plus_p7104986032573967614at_nat @ Z8 @ B5 ) ) @ ms_strict ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7648_ms__weakI1,axiom,
% 9.17/5.44 ! [Z7: multis2468970476368604999at_nat,Z8: multis2468970476368604999at_nat,A2: multis2468970476368604999at_nat,B5: multis2468970476368604999at_nat] :
% 9.17/5.44 ( ( pw_leq @ Z7 @ Z8 )
% 9.17/5.44 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( set_ms8126754132646256062at_nat @ A2 ) @ ( set_ms8126754132646256062at_nat @ B5 ) ) @ fun_max_strict )
% 9.17/5.44 => ( member6689249552917799696at_nat @ ( produc4348348721325984599at_nat @ ( plus_p7104986032573967614at_nat @ Z7 @ A2 ) @ ( plus_p7104986032573967614at_nat @ Z8 @ B5 ) ) @ ms_weak ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7649_pw__leq__split,axiom,
% 9.17/5.44 ! [X11: multis2468970476368604999at_nat,Y9: multis2468970476368604999at_nat] :
% 9.17/5.44 ( ( pw_leq @ X11 @ Y9 )
% 9.17/5.44 => ? [A8: multis2468970476368604999at_nat,B9: multis2468970476368604999at_nat,Z9: multis2468970476368604999at_nat] :
% 9.17/5.44 ( ( X11
% 9.17/5.44 = ( plus_p7104986032573967614at_nat @ A8 @ Z9 ) )
% 9.17/5.44 & ( Y9
% 9.17/5.44 = ( plus_p7104986032573967614at_nat @ B9 @ Z9 ) )
% 9.17/5.44 & ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( set_ms8126754132646256062at_nat @ A8 ) @ ( set_ms8126754132646256062at_nat @ B9 ) ) @ fun_max_strict )
% 9.17/5.44 | ( ( B9 = zero_z1048942125864253310at_nat )
% 9.17/5.44 & ( A8 = zero_z1048942125864253310at_nat ) ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7650_ms__weakI2,axiom,
% 9.17/5.44 ! [Z7: multis2468970476368604999at_nat,Z8: multis2468970476368604999at_nat] :
% 9.17/5.44 ( ( pw_leq @ Z7 @ Z8 )
% 9.17/5.44 => ( member6689249552917799696at_nat @ ( produc4348348721325984599at_nat @ ( plus_p7104986032573967614at_nat @ Z7 @ zero_z1048942125864253310at_nat ) @ ( plus_p7104986032573967614at_nat @ Z8 @ zero_z1048942125864253310at_nat ) ) @ ms_weak ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7651_pw__leq__lstep,axiom,
% 9.17/5.44 ! [X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 9.17/5.44 ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X @ Y ) @ fun_pair_leq )
% 9.17/5.44 => ( pw_leq @ ( add_ms2612439473150266591at_nat @ X @ zero_z1048942125864253310at_nat ) @ ( add_ms2612439473150266591at_nat @ Y @ zero_z1048942125864253310at_nat ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7652_pw__leq__step,axiom,
% 9.17/5.44 ! [X: product_prod_nat_nat,Y: product_prod_nat_nat,X11: multis2468970476368604999at_nat,Y9: multis2468970476368604999at_nat] :
% 9.17/5.44 ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X @ Y ) @ fun_pair_leq )
% 9.17/5.44 => ( ( pw_leq @ X11 @ Y9 )
% 9.17/5.44 => ( pw_leq @ ( plus_p7104986032573967614at_nat @ ( add_ms2612439473150266591at_nat @ X @ zero_z1048942125864253310at_nat ) @ X11 ) @ ( plus_p7104986032573967614at_nat @ ( add_ms2612439473150266591at_nat @ Y @ zero_z1048942125864253310at_nat ) @ Y9 ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7653_pw__leq_Osimps,axiom,
% 9.17/5.44 ( pw_leq
% 9.17/5.44 = ( ^ [A12: multis2468970476368604999at_nat,A22: multis2468970476368604999at_nat] :
% 9.17/5.44 ( ( ( A12 = zero_z1048942125864253310at_nat )
% 9.17/5.44 & ( A22 = zero_z1048942125864253310at_nat ) )
% 9.17/5.44 | ? [X3: product_prod_nat_nat,Y3: product_prod_nat_nat,X9: multis2468970476368604999at_nat,Y10: multis2468970476368604999at_nat] :
% 9.17/5.44 ( ( A12
% 9.17/5.44 = ( plus_p7104986032573967614at_nat @ ( add_ms2612439473150266591at_nat @ X3 @ zero_z1048942125864253310at_nat ) @ X9 ) )
% 9.17/5.44 & ( A22
% 9.17/5.44 = ( plus_p7104986032573967614at_nat @ ( add_ms2612439473150266591at_nat @ Y3 @ zero_z1048942125864253310at_nat ) @ Y10 ) )
% 9.17/5.44 & ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X3 @ Y3 ) @ fun_pair_leq )
% 9.17/5.44 & ( pw_leq @ X9 @ Y10 ) ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7654_pw__leq_Ocases,axiom,
% 9.17/5.44 ! [A1: multis2468970476368604999at_nat,A23: multis2468970476368604999at_nat] :
% 9.17/5.44 ( ( pw_leq @ A1 @ A23 )
% 9.17/5.44 => ( ( ( A1 = zero_z1048942125864253310at_nat )
% 9.17/5.44 => ( A23 != zero_z1048942125864253310at_nat ) )
% 9.17/5.44 => ~ ! [X4: product_prod_nat_nat,Y5: product_prod_nat_nat,X14: multis2468970476368604999at_nat] :
% 9.17/5.44 ( ( A1
% 9.17/5.44 = ( plus_p7104986032573967614at_nat @ ( add_ms2612439473150266591at_nat @ X4 @ zero_z1048942125864253310at_nat ) @ X14 ) )
% 9.17/5.44 => ! [Y11: multis2468970476368604999at_nat] :
% 9.17/5.44 ( ( A23
% 9.17/5.44 = ( plus_p7104986032573967614at_nat @ ( add_ms2612439473150266591at_nat @ Y5 @ zero_z1048942125864253310at_nat ) @ Y11 ) )
% 9.17/5.44 => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X4 @ Y5 ) @ fun_pair_leq )
% 9.17/5.44 => ~ ( pw_leq @ X14 @ Y11 ) ) ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7655_Code__Numeral_Osub__code_I4_J,axiom,
% 9.17/5.44 ! [N2: num] :
% 9.17/5.44 ( ( code_sub @ one @ ( bit0 @ N2 ) )
% 9.17/5.44 = ( code_Neg @ ( bitM @ N2 ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7656_Code__Numeral_Odup__code_I3_J,axiom,
% 9.17/5.44 ! [N2: num] :
% 9.17/5.44 ( ( code_dup @ ( code_Neg @ N2 ) )
% 9.17/5.44 = ( code_Neg @ ( bit0 @ N2 ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7657_less__integer__code_I3_J,axiom,
% 9.17/5.44 ! [L: num] :
% 9.17/5.44 ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( code_Neg @ L ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7658_less__integer__code_I7_J,axiom,
% 9.17/5.44 ! [K: num] : ( ord_le6747313008572928689nteger @ ( code_Neg @ K ) @ zero_z3403309356797280102nteger ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7659_plus__integer__code_I6_J,axiom,
% 9.17/5.44 ! [M2: num,N2: num] :
% 9.17/5.44 ( ( plus_p5714425477246183910nteger @ ( code_Neg @ M2 ) @ ( code_Neg @ N2 ) )
% 9.17/5.44 = ( code_Neg @ ( plus_plus_num @ M2 @ N2 ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7660_less__eq__integer__code_I7_J,axiom,
% 9.17/5.44 ! [K: num] : ( ord_le3102999989581377725nteger @ ( code_Neg @ K ) @ zero_z3403309356797280102nteger ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7661_less__eq__integer__code_I3_J,axiom,
% 9.17/5.44 ! [L: num] :
% 9.17/5.44 ~ ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( code_Neg @ L ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7662_less__integer__code_I9_J,axiom,
% 9.17/5.44 ! [K: num,L: num] :
% 9.17/5.44 ( ( ord_le6747313008572928689nteger @ ( code_Neg @ K ) @ ( code_Neg @ L ) )
% 9.17/5.44 = ( ord_less_num @ L @ K ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7663_less__eq__integer__code_I9_J,axiom,
% 9.17/5.44 ! [K: num,L: num] :
% 9.17/5.44 ( ( ord_le3102999989581377725nteger @ ( code_Neg @ K ) @ ( code_Neg @ L ) )
% 9.17/5.44 = ( ord_less_eq_num @ L @ K ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7664_minus__integer__code_I6_J,axiom,
% 9.17/5.44 ! [M2: num,N2: num] :
% 9.17/5.44 ( ( minus_8373710615458151222nteger @ ( code_Neg @ M2 ) @ ( code_Neg @ N2 ) )
% 9.17/5.44 = ( code_sub @ N2 @ M2 ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7665_divmod__abs__code_I2_J,axiom,
% 9.17/5.44 ! [K: num,L: num] :
% 9.17/5.44 ( ( code_divmod_abs @ ( code_Neg @ K ) @ ( code_Neg @ L ) )
% 9.17/5.44 = ( unique3479559517661332726nteger @ K @ L ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7666_Code__Numeral_Osub__code_I5_J,axiom,
% 9.17/5.44 ! [N2: num] :
% 9.17/5.44 ( ( code_sub @ one @ ( bit1 @ N2 ) )
% 9.17/5.44 = ( code_Neg @ ( bit0 @ N2 ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7667_card__length__sum__list__rec,axiom,
% 9.17/5.44 ! [M2: nat,N6: nat] :
% 9.17/5.44 ( ( ord_less_eq_nat @ one_one_nat @ M2 )
% 9.17/5.44 => ( ( finite_card_list_nat
% 9.17/5.44 @ ( collect_list_nat
% 9.17/5.44 @ ^ [L3: list_nat] :
% 9.17/5.44 ( ( ( size_size_list_nat @ L3 )
% 9.17/5.44 = M2 )
% 9.17/5.44 & ( ( groups4561878855575611511st_nat @ L3 )
% 9.17/5.44 = N6 ) ) ) )
% 9.17/5.44 = ( plus_plus_nat
% 9.17/5.44 @ ( finite_card_list_nat
% 9.17/5.44 @ ( collect_list_nat
% 9.17/5.44 @ ^ [L3: list_nat] :
% 9.17/5.44 ( ( ( size_size_list_nat @ L3 )
% 9.17/5.44 = ( minus_minus_nat @ M2 @ one_one_nat ) )
% 9.17/5.44 & ( ( groups4561878855575611511st_nat @ L3 )
% 9.17/5.44 = N6 ) ) ) )
% 9.17/5.44 @ ( finite_card_list_nat
% 9.17/5.44 @ ( collect_list_nat
% 9.17/5.44 @ ^ [L3: list_nat] :
% 9.17/5.44 ( ( ( size_size_list_nat @ L3 )
% 9.17/5.44 = M2 )
% 9.17/5.44 & ( ( plus_plus_nat @ ( groups4561878855575611511st_nat @ L3 ) @ one_one_nat )
% 9.17/5.44 = N6 ) ) ) ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7668_card__length__sum__list,axiom,
% 9.17/5.44 ! [M2: nat,N6: nat] :
% 9.17/5.44 ( ( finite_card_list_nat
% 9.17/5.44 @ ( collect_list_nat
% 9.17/5.44 @ ^ [L3: list_nat] :
% 9.17/5.44 ( ( ( size_size_list_nat @ L3 )
% 9.17/5.44 = M2 )
% 9.17/5.44 & ( ( groups4561878855575611511st_nat @ L3 )
% 9.17/5.44 = N6 ) ) ) )
% 9.17/5.44 = ( binomial @ ( minus_minus_nat @ ( plus_plus_nat @ N6 @ M2 ) @ one_one_nat ) @ N6 ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7669_natural__of__nat__of__nat,axiom,
% 9.17/5.44 code_natural_of_nat = semiri3763490453095760265atural ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7670_division__segment__natural_Oabs__eq,axiom,
% 9.17/5.44 ! [X: nat] :
% 9.17/5.44 ( ( euclid5112970336976722131atural @ ( code_natural_of_nat @ X ) )
% 9.17/5.44 = ( code_natural_of_nat @ ( euclid3398187327856392827nt_nat @ X ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7671_set__bit__natural_Oabs__eq,axiom,
% 9.17/5.44 ! [Xa: nat,X: nat] :
% 9.17/5.44 ( ( bit_se1617098188084679374atural @ Xa @ ( code_natural_of_nat @ X ) )
% 9.17/5.44 = ( code_natural_of_nat @ ( bit_se7882103937844011126it_nat @ Xa @ X ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7672_flip__bit__natural_Oabs__eq,axiom,
% 9.17/5.44 ! [Xa: nat,X: nat] :
% 9.17/5.44 ( ( bit_se168947363167071951atural @ Xa @ ( code_natural_of_nat @ X ) )
% 9.17/5.44 = ( code_natural_of_nat @ ( bit_se2161824704523386999it_nat @ Xa @ X ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7673_unset__bit__natural_Oabs__eq,axiom,
% 9.17/5.44 ! [Xa: nat,X: nat] :
% 9.17/5.44 ( ( bit_se7083795435491715335atural @ Xa @ ( code_natural_of_nat @ X ) )
% 9.17/5.44 = ( code_natural_of_nat @ ( bit_se4205575877204974255it_nat @ Xa @ X ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7674_euclidean__size__natural_Oabs__eq,axiom,
% 9.17/5.44 ! [X: nat] :
% 9.17/5.44 ( ( euclid5200926497590043453atural @ ( code_natural_of_nat @ X ) )
% 9.17/5.44 = ( euclid4777050414544973029ze_nat @ X ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7675_bit__natural_Oabs__eq,axiom,
% 9.17/5.44 ! [X: nat] :
% 9.17/5.44 ( ( bit_se8040316288895769887atural @ ( code_natural_of_nat @ X ) )
% 9.17/5.44 = ( bit_se1148574629649215175it_nat @ X ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7676_natural__of__nat__cases,axiom,
% 9.17/5.44 ! [X: code_natural] :
% 9.17/5.44 ~ ! [Y5: nat] :
% 9.17/5.44 ( ( X
% 9.17/5.44 = ( code_natural_of_nat @ Y5 ) )
% 9.17/5.44 => ~ ( member_nat @ Y5 @ top_top_set_nat ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7677_natural__of__nat__induct,axiom,
% 9.17/5.44 ! [P: code_natural > $o,X: code_natural] :
% 9.17/5.44 ( ! [Y5: nat] :
% 9.17/5.44 ( ( member_nat @ Y5 @ top_top_set_nat )
% 9.17/5.44 => ( P @ ( code_natural_of_nat @ Y5 ) ) )
% 9.17/5.44 => ( P @ X ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7678_natural__of__nat__inject,axiom,
% 9.17/5.44 ! [X: nat,Y: nat] :
% 9.17/5.44 ( ( member_nat @ X @ top_top_set_nat )
% 9.17/5.44 => ( ( member_nat @ Y @ top_top_set_nat )
% 9.17/5.44 => ( ( ( code_natural_of_nat @ X )
% 9.17/5.44 = ( code_natural_of_nat @ Y ) )
% 9.17/5.44 = ( X = Y ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7679_take__bit__natural_Oabs__eq,axiom,
% 9.17/5.44 ! [Xa: nat,X: nat] :
% 9.17/5.44 ( ( bit_se569199155075624693atural @ Xa @ ( code_natural_of_nat @ X ) )
% 9.17/5.44 = ( code_natural_of_nat @ ( bit_se2925701944663578781it_nat @ Xa @ X ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7680_and__natural_Oabs__eq,axiom,
% 9.17/5.44 ! [Xa: nat,X: nat] :
% 9.17/5.44 ( ( bit_se2773287842338716102atural @ ( code_natural_of_nat @ Xa ) @ ( code_natural_of_nat @ X ) )
% 9.17/5.44 = ( code_natural_of_nat @ ( bit_se727722235901077358nd_nat @ Xa @ X ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7681_xor__natural_Oabs__eq,axiom,
% 9.17/5.44 ! [Xa: nat,X: nat] :
% 9.17/5.44 ( ( bit_se2046307713759805098atural @ ( code_natural_of_nat @ Xa ) @ ( code_natural_of_nat @ X ) )
% 9.17/5.44 = ( code_natural_of_nat @ ( bit_se6528837805403552850or_nat @ Xa @ X ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7682_or__natural_Oabs__eq,axiom,
% 9.17/5.44 ! [Xa: nat,X: nat] :
% 9.17/5.44 ( ( bit_se9127793120404214118atural @ ( code_natural_of_nat @ Xa ) @ ( code_natural_of_nat @ X ) )
% 9.17/5.44 = ( code_natural_of_nat @ ( bit_se1412395901928357646or_nat @ Xa @ X ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7683_mask__natural_Oabs__eq,axiom,
% 9.17/5.44 ( bit_se943457434206027407atural
% 9.17/5.44 = ( ^ [X3: nat] : ( code_natural_of_nat @ ( bit_se2002935070580805687sk_nat @ X3 ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7684_push__bit__natural_Oabs__eq,axiom,
% 9.17/5.44 ! [Xa: nat,X: nat] :
% 9.17/5.44 ( ( bit_se6611745700429515170atural @ Xa @ ( code_natural_of_nat @ X ) )
% 9.17/5.44 = ( code_natural_of_nat @ ( bit_se547839408752420682it_nat @ Xa @ X ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7685_drop__bit__natural_Oabs__eq,axiom,
% 9.17/5.44 ! [Xa: nat,X: nat] :
% 9.17/5.44 ( ( bit_se2751692689150723149atural @ Xa @ ( code_natural_of_nat @ X ) )
% 9.17/5.44 = ( code_natural_of_nat @ ( bit_se8570568707652914677it_nat @ Xa @ X ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7686_zero__natural__def,axiom,
% 9.17/5.44 ( zero_z2226904508553997617atural
% 9.17/5.44 = ( code_natural_of_nat @ zero_zero_nat ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7687_one__natural__def,axiom,
% 9.17/5.44 ( one_one_Code_natural
% 9.17/5.44 = ( code_natural_of_nat @ one_one_nat ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7688_less__natural_Oabs__eq,axiom,
% 9.17/5.44 ! [Xa: nat,X: nat] :
% 9.17/5.44 ( ( ord_le5570908160329646204atural @ ( code_natural_of_nat @ Xa ) @ ( code_natural_of_nat @ X ) )
% 9.17/5.44 = ( ord_less_nat @ Xa @ X ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7689_plus__natural_Oabs__eq,axiom,
% 9.17/5.44 ! [Xa: nat,X: nat] :
% 9.17/5.44 ( ( plus_p4538020629002901425atural @ ( code_natural_of_nat @ Xa ) @ ( code_natural_of_nat @ X ) )
% 9.17/5.44 = ( code_natural_of_nat @ ( plus_plus_nat @ Xa @ X ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7690_minus__natural_Oabs__eq,axiom,
% 9.17/5.44 ! [Xa: nat,X: nat] :
% 9.17/5.44 ( ( minus_7197305767214868737atural @ ( code_natural_of_nat @ Xa ) @ ( code_natural_of_nat @ X ) )
% 9.17/5.44 = ( code_natural_of_nat @ ( minus_minus_nat @ Xa @ X ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7691_less__eq__natural_Oabs__eq,axiom,
% 9.17/5.44 ! [Xa: nat,X: nat] :
% 9.17/5.44 ( ( ord_le1926595141338095240atural @ ( code_natural_of_nat @ Xa ) @ ( code_natural_of_nat @ X ) )
% 9.17/5.44 = ( ord_less_eq_nat @ Xa @ X ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7692_times__natural_Oabs__eq,axiom,
% 9.17/5.44 ! [Xa: nat,X: nat] :
% 9.17/5.44 ( ( times_2397367101498566445atural @ ( code_natural_of_nat @ Xa ) @ ( code_natural_of_nat @ X ) )
% 9.17/5.44 = ( code_natural_of_nat @ ( times_times_nat @ Xa @ X ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7693_divide__natural_Oabs__eq,axiom,
% 9.17/5.44 ! [Xa: nat,X: nat] :
% 9.17/5.44 ( ( divide5121882707175180666atural @ ( code_natural_of_nat @ Xa ) @ ( code_natural_of_nat @ X ) )
% 9.17/5.44 = ( code_natural_of_nat @ ( divide_divide_nat @ Xa @ X ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7694_mask__natural__def,axiom,
% 9.17/5.44 ( bit_se943457434206027407atural
% 9.17/5.44 = ( map_fu4742413587575543474atural @ id_nat @ code_natural_of_nat @ bit_se2002935070580805687sk_nat ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7695_modulo__natural_Oabs__eq,axiom,
% 9.17/5.44 ! [Xa: nat,X: nat] :
% 9.17/5.44 ( ( modulo8411746178871703098atural @ ( code_natural_of_nat @ Xa ) @ ( code_natural_of_nat @ X ) )
% 9.17/5.44 = ( code_natural_of_nat @ ( modulo_modulo_nat @ Xa @ X ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7696_Nat_Oabs__eq,axiom,
% 9.17/5.44 ! [X: int] :
% 9.17/5.44 ( ( code_Nat @ ( code_integer_of_int @ X ) )
% 9.17/5.44 = ( code_natural_of_nat @ ( nat2 @ X ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7697_Nat__def,axiom,
% 9.17/5.44 ( code_Nat
% 9.17/5.44 = ( map_fu1051355602067684763atural @ code_int_of_integer @ code_natural_of_nat @ nat2 ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7698_natural__of__integer_Oabs__eq,axiom,
% 9.17/5.44 ! [X: int] :
% 9.17/5.44 ( ( code_n4118661773612635043nteger @ ( code_integer_of_int @ X ) )
% 9.17/5.44 = ( code_natural_of_nat @ ( nat2 @ X ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7699_natural__of__nat__of__natural__inverse,axiom,
% 9.17/5.44 ! [N2: code_natural] :
% 9.17/5.44 ( ( code_natural_of_nat @ ( code_nat_of_natural @ N2 ) )
% 9.17/5.44 = N2 ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7700_nat__of__natural__of__nat__inverse,axiom,
% 9.17/5.44 ! [N2: nat] :
% 9.17/5.44 ( ( code_nat_of_natural @ ( code_natural_of_nat @ N2 ) )
% 9.17/5.44 = N2 ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7701_nat__of__natural__inverse,axiom,
% 9.17/5.44 ! [X: code_natural] :
% 9.17/5.44 ( ( code_natural_of_nat @ ( code_nat_of_natural @ X ) )
% 9.17/5.44 = X ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7702_nat__of__natural__min,axiom,
% 9.17/5.44 ! [K: code_natural,L: code_natural] :
% 9.17/5.44 ( ( code_nat_of_natural @ ( ord_min_Code_natural @ K @ L ) )
% 9.17/5.44 = ( ord_min_nat @ ( code_nat_of_natural @ K ) @ ( code_nat_of_natural @ L ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7703_nat__of__natural__max,axiom,
% 9.17/5.44 ! [K: code_natural,L: code_natural] :
% 9.17/5.44 ( ( code_nat_of_natural @ ( ord_max_Code_natural @ K @ L ) )
% 9.17/5.44 = ( ord_max_nat @ ( code_nat_of_natural @ K ) @ ( code_nat_of_natural @ L ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7704_of__nat__of__natural,axiom,
% 9.17/5.44 ! [N2: code_natural] :
% 9.17/5.44 ( ( semiri3763490453095760265atural @ ( code_nat_of_natural @ N2 ) )
% 9.17/5.44 = N2 ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7705_nat__of__natural__of__nat,axiom,
% 9.17/5.44 ! [N2: nat] :
% 9.17/5.44 ( ( code_nat_of_natural @ ( semiri3763490453095760265atural @ N2 ) )
% 9.17/5.44 = N2 ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7706_zero__natural_Orep__eq,axiom,
% 9.17/5.44 ( ( code_nat_of_natural @ zero_z2226904508553997617atural )
% 9.17/5.44 = zero_zero_nat ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7707_one__natural_Orep__eq,axiom,
% 9.17/5.44 ( ( code_nat_of_natural @ one_one_Code_natural )
% 9.17/5.44 = one_one_nat ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7708_plus__natural_Orep__eq,axiom,
% 9.17/5.44 ! [X: code_natural,Xa: code_natural] :
% 9.17/5.44 ( ( code_nat_of_natural @ ( plus_p4538020629002901425atural @ X @ Xa ) )
% 9.17/5.44 = ( plus_plus_nat @ ( code_nat_of_natural @ X ) @ ( code_nat_of_natural @ Xa ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7709_minus__natural_Orep__eq,axiom,
% 9.17/5.44 ! [X: code_natural,Xa: code_natural] :
% 9.17/5.44 ( ( code_nat_of_natural @ ( minus_7197305767214868737atural @ X @ Xa ) )
% 9.17/5.44 = ( minus_minus_nat @ ( code_nat_of_natural @ X ) @ ( code_nat_of_natural @ Xa ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7710_nat__of__natural__numeral,axiom,
% 9.17/5.44 ! [K: num] :
% 9.17/5.44 ( ( code_nat_of_natural @ ( numera5444537566228673987atural @ K ) )
% 9.17/5.44 = ( numeral_numeral_nat @ K ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7711_times__natural_Orep__eq,axiom,
% 9.17/5.44 ! [X: code_natural,Xa: code_natural] :
% 9.17/5.44 ( ( code_nat_of_natural @ ( times_2397367101498566445atural @ X @ Xa ) )
% 9.17/5.44 = ( times_times_nat @ ( code_nat_of_natural @ X ) @ ( code_nat_of_natural @ Xa ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7712_divide__natural_Orep__eq,axiom,
% 9.17/5.44 ! [X: code_natural,Xa: code_natural] :
% 9.17/5.44 ( ( code_nat_of_natural @ ( divide5121882707175180666atural @ X @ Xa ) )
% 9.17/5.44 = ( divide_divide_nat @ ( code_nat_of_natural @ X ) @ ( code_nat_of_natural @ Xa ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7713_modulo__natural_Orep__eq,axiom,
% 9.17/5.44 ! [X: code_natural,Xa: code_natural] :
% 9.17/5.44 ( ( code_nat_of_natural @ ( modulo8411746178871703098atural @ X @ Xa ) )
% 9.17/5.44 = ( modulo_modulo_nat @ ( code_nat_of_natural @ X ) @ ( code_nat_of_natural @ Xa ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7714_division__segment__natural_Orep__eq,axiom,
% 9.17/5.44 ! [X: code_natural] :
% 9.17/5.44 ( ( code_nat_of_natural @ ( euclid5112970336976722131atural @ X ) )
% 9.17/5.44 = ( euclid3398187327856392827nt_nat @ ( code_nat_of_natural @ X ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7715_euclidean__size__natural_Orep__eq,axiom,
% 9.17/5.44 ( euclid5200926497590043453atural
% 9.17/5.44 = ( ^ [X3: code_natural] : ( euclid4777050414544973029ze_nat @ ( code_nat_of_natural @ X3 ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7716_unset__bit__natural_Orep__eq,axiom,
% 9.17/5.44 ! [X: nat,Xa: code_natural] :
% 9.17/5.44 ( ( code_nat_of_natural @ ( bit_se7083795435491715335atural @ X @ Xa ) )
% 9.17/5.44 = ( bit_se4205575877204974255it_nat @ X @ ( code_nat_of_natural @ Xa ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7717_flip__bit__natural_Orep__eq,axiom,
% 9.17/5.44 ! [X: nat,Xa: code_natural] :
% 9.17/5.44 ( ( code_nat_of_natural @ ( bit_se168947363167071951atural @ X @ Xa ) )
% 9.17/5.44 = ( bit_se2161824704523386999it_nat @ X @ ( code_nat_of_natural @ Xa ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7718_set__bit__natural_Orep__eq,axiom,
% 9.17/5.44 ! [X: nat,Xa: code_natural] :
% 9.17/5.44 ( ( code_nat_of_natural @ ( bit_se1617098188084679374atural @ X @ Xa ) )
% 9.17/5.44 = ( bit_se7882103937844011126it_nat @ X @ ( code_nat_of_natural @ Xa ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7719_Nat_Orep__eq,axiom,
% 9.17/5.44 ! [X: code_integer] :
% 9.17/5.44 ( ( code_nat_of_natural @ ( code_Nat @ X ) )
% 9.17/5.44 = ( nat2 @ ( code_int_of_integer @ X ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7720_push__bit__natural_Orep__eq,axiom,
% 9.17/5.44 ! [X: nat,Xa: code_natural] :
% 9.17/5.44 ( ( code_nat_of_natural @ ( bit_se6611745700429515170atural @ X @ Xa ) )
% 9.17/5.44 = ( bit_se547839408752420682it_nat @ X @ ( code_nat_of_natural @ Xa ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7721_mask__natural_Orep__eq,axiom,
% 9.17/5.44 ! [X: nat] :
% 9.17/5.44 ( ( code_nat_of_natural @ ( bit_se943457434206027407atural @ X ) )
% 9.17/5.44 = ( bit_se2002935070580805687sk_nat @ X ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7722_and__natural_Orep__eq,axiom,
% 9.17/5.44 ! [X: code_natural,Xa: code_natural] :
% 9.17/5.44 ( ( code_nat_of_natural @ ( bit_se2773287842338716102atural @ X @ Xa ) )
% 9.17/5.44 = ( bit_se727722235901077358nd_nat @ ( code_nat_of_natural @ X ) @ ( code_nat_of_natural @ Xa ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7723_bit__natural_Orep__eq,axiom,
% 9.17/5.44 ( bit_se8040316288895769887atural
% 9.17/5.44 = ( ^ [X3: code_natural] : ( bit_se1148574629649215175it_nat @ ( code_nat_of_natural @ X3 ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7724_nat__of__natural__inject,axiom,
% 9.17/5.44 ! [X: code_natural,Y: code_natural] :
% 9.17/5.44 ( ( ( code_nat_of_natural @ X )
% 9.17/5.44 = ( code_nat_of_natural @ Y ) )
% 9.17/5.44 = ( X = Y ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7725_natural__eqI,axiom,
% 9.17/5.44 ! [M2: code_natural,N2: code_natural] :
% 9.17/5.44 ( ( ( code_nat_of_natural @ M2 )
% 9.17/5.44 = ( code_nat_of_natural @ N2 ) )
% 9.17/5.44 => ( M2 = N2 ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7726_natural__eq__iff,axiom,
% 9.17/5.44 ( ( ^ [Y4: code_natural,Z2: code_natural] : ( Y4 = Z2 ) )
% 9.17/5.44 = ( ^ [M: code_natural,N4: code_natural] :
% 9.17/5.44 ( ( code_nat_of_natural @ M )
% 9.17/5.44 = ( code_nat_of_natural @ N4 ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7727_natural__cases,axiom,
% 9.17/5.44 ! [M2: code_natural] :
% 9.17/5.44 ~ ! [N: nat] :
% 9.17/5.44 ( M2
% 9.17/5.44 != ( semiri3763490453095760265atural @ N ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7728_nat__of__natural,axiom,
% 9.17/5.44 ! [X: code_natural] : ( member_nat @ ( code_nat_of_natural @ X ) @ top_top_set_nat ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7729_nat__of__natural__cases,axiom,
% 9.17/5.44 ! [Y: nat] :
% 9.17/5.44 ( ( member_nat @ Y @ top_top_set_nat )
% 9.17/5.44 => ~ ! [X4: code_natural] :
% 9.17/5.44 ( Y
% 9.17/5.44 != ( code_nat_of_natural @ X4 ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7730_nat__of__natural__induct,axiom,
% 9.17/5.44 ! [Y: nat,P: nat > $o] :
% 9.17/5.44 ( ( member_nat @ Y @ top_top_set_nat )
% 9.17/5.44 => ( ! [X4: code_natural] : ( P @ ( code_nat_of_natural @ X4 ) )
% 9.17/5.44 => ( P @ Y ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7731_take__bit__natural_Orep__eq,axiom,
% 9.17/5.44 ! [X: nat,Xa: code_natural] :
% 9.17/5.44 ( ( code_nat_of_natural @ ( bit_se569199155075624693atural @ X @ Xa ) )
% 9.17/5.44 = ( bit_se2925701944663578781it_nat @ X @ ( code_nat_of_natural @ Xa ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7732_or__natural_Orep__eq,axiom,
% 9.17/5.44 ! [X: code_natural,Xa: code_natural] :
% 9.17/5.44 ( ( code_nat_of_natural @ ( bit_se9127793120404214118atural @ X @ Xa ) )
% 9.17/5.44 = ( bit_se1412395901928357646or_nat @ ( code_nat_of_natural @ X ) @ ( code_nat_of_natural @ Xa ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7733_xor__natural_Orep__eq,axiom,
% 9.17/5.44 ! [X: code_natural,Xa: code_natural] :
% 9.17/5.44 ( ( code_nat_of_natural @ ( bit_se2046307713759805098atural @ X @ Xa ) )
% 9.17/5.44 = ( bit_se6528837805403552850or_nat @ ( code_nat_of_natural @ X ) @ ( code_nat_of_natural @ Xa ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7734_drop__bit__natural_Orep__eq,axiom,
% 9.17/5.44 ! [X: nat,Xa: code_natural] :
% 9.17/5.44 ( ( code_nat_of_natural @ ( bit_se2751692689150723149atural @ X @ Xa ) )
% 9.17/5.44 = ( bit_se8570568707652914677it_nat @ X @ ( code_nat_of_natural @ Xa ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7735_natural__of__integer_Orep__eq,axiom,
% 9.17/5.44 ! [X: code_integer] :
% 9.17/5.44 ( ( code_nat_of_natural @ ( code_n4118661773612635043nteger @ X ) )
% 9.17/5.44 = ( nat2 @ ( code_int_of_integer @ X ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7736_less__natural_Orep__eq,axiom,
% 9.17/5.44 ( ord_le5570908160329646204atural
% 9.17/5.44 = ( ^ [X3: code_natural,Xa4: code_natural] : ( ord_less_nat @ ( code_nat_of_natural @ X3 ) @ ( code_nat_of_natural @ Xa4 ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7737_natural__of__nat__inverse,axiom,
% 9.17/5.44 ! [Y: nat] :
% 9.17/5.44 ( ( member_nat @ Y @ top_top_set_nat )
% 9.17/5.44 => ( ( code_nat_of_natural @ ( code_natural_of_nat @ Y ) )
% 9.17/5.44 = Y ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7738_type__definition__natural,axiom,
% 9.17/5.44 type_d4410041424927559462al_nat @ code_nat_of_natural @ code_natural_of_nat @ top_top_set_nat ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7739_or__natural__def,axiom,
% 9.17/5.44 ( bit_se9127793120404214118atural
% 9.17/5.44 = ( map_fu6549440983881763648atural @ code_nat_of_natural @ ( map_fu1239815594074539274atural @ code_nat_of_natural @ code_natural_of_nat ) @ bit_se1412395901928357646or_nat ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7740_xor__natural__def,axiom,
% 9.17/5.44 ( bit_se2046307713759805098atural
% 9.17/5.44 = ( map_fu6549440983881763648atural @ code_nat_of_natural @ ( map_fu1239815594074539274atural @ code_nat_of_natural @ code_natural_of_nat ) @ bit_se6528837805403552850or_nat ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7741_and__natural__def,axiom,
% 9.17/5.44 ( bit_se2773287842338716102atural
% 9.17/5.44 = ( map_fu6549440983881763648atural @ code_nat_of_natural @ ( map_fu1239815594074539274atural @ code_nat_of_natural @ code_natural_of_nat ) @ bit_se727722235901077358nd_nat ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7742_less__eq__natural_Orep__eq,axiom,
% 9.17/5.44 ( ord_le1926595141338095240atural
% 9.17/5.44 = ( ^ [X3: code_natural,Xa4: code_natural] : ( ord_less_eq_nat @ ( code_nat_of_natural @ X3 ) @ ( code_nat_of_natural @ Xa4 ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7743_division__segment__natural__def,axiom,
% 9.17/5.44 ( euclid5112970336976722131atural
% 9.17/5.44 = ( map_fu1239815594074539274atural @ code_nat_of_natural @ code_natural_of_nat @ euclid3398187327856392827nt_nat ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7744_euclidean__size__natural__def,axiom,
% 9.17/5.44 ( euclid5200926497590043453atural
% 9.17/5.44 = ( map_fu226235371393106610at_nat @ code_nat_of_natural @ id_nat @ euclid4777050414544973029ze_nat ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7745_plus__natural__def,axiom,
% 9.17/5.44 ( plus_p4538020629002901425atural
% 9.17/5.44 = ( map_fu6549440983881763648atural @ code_nat_of_natural @ ( map_fu1239815594074539274atural @ code_nat_of_natural @ code_natural_of_nat ) @ plus_plus_nat ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7746_minus__natural__def,axiom,
% 9.17/5.44 ( minus_7197305767214868737atural
% 9.17/5.44 = ( map_fu6549440983881763648atural @ code_nat_of_natural @ ( map_fu1239815594074539274atural @ code_nat_of_natural @ code_natural_of_nat ) @ minus_minus_nat ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7747_bit__natural__def,axiom,
% 9.17/5.44 ( bit_se8040316288895769887atural
% 9.17/5.44 = ( map_fu6244533035418998608_nat_o @ code_nat_of_natural @ id_nat_o @ bit_se1148574629649215175it_nat ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7748_less__natural__def,axiom,
% 9.17/5.44 ( ord_le5570908160329646204atural
% 9.17/5.44 = ( map_fu6256889081107267320ural_o @ code_nat_of_natural @ ( map_fu4892316939951275536at_o_o @ code_nat_of_natural @ id_o ) @ ord_less_nat ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7749_times__natural__def,axiom,
% 9.17/5.44 ( times_2397367101498566445atural
% 9.17/5.44 = ( map_fu6549440983881763648atural @ code_nat_of_natural @ ( map_fu1239815594074539274atural @ code_nat_of_natural @ code_natural_of_nat ) @ times_times_nat ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7750_divide__natural__def,axiom,
% 9.17/5.44 ( divide5121882707175180666atural
% 9.17/5.44 = ( map_fu6549440983881763648atural @ code_nat_of_natural @ ( map_fu1239815594074539274atural @ code_nat_of_natural @ code_natural_of_nat ) @ divide_divide_nat ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7751_take__bit__natural__def,axiom,
% 9.17/5.44 ( bit_se569199155075624693atural
% 9.17/5.44 = ( map_fu6981160461238011112atural @ id_nat @ ( map_fu1239815594074539274atural @ code_nat_of_natural @ code_natural_of_nat ) @ bit_se2925701944663578781it_nat ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7752_push__bit__natural__def,axiom,
% 9.17/5.44 ( bit_se6611745700429515170atural
% 9.17/5.44 = ( map_fu6981160461238011112atural @ id_nat @ ( map_fu1239815594074539274atural @ code_nat_of_natural @ code_natural_of_nat ) @ bit_se547839408752420682it_nat ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7753_less__eq__natural__def,axiom,
% 9.17/5.44 ( ord_le1926595141338095240atural
% 9.17/5.44 = ( map_fu6256889081107267320ural_o @ code_nat_of_natural @ ( map_fu4892316939951275536at_o_o @ code_nat_of_natural @ id_o ) @ ord_less_eq_nat ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7754_modulo__natural__def,axiom,
% 9.17/5.44 ( modulo8411746178871703098atural
% 9.17/5.44 = ( map_fu6549440983881763648atural @ code_nat_of_natural @ ( map_fu1239815594074539274atural @ code_nat_of_natural @ code_natural_of_nat ) @ modulo_modulo_nat ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7755_drop__bit__natural__def,axiom,
% 9.17/5.44 ( bit_se2751692689150723149atural
% 9.17/5.44 = ( map_fu6981160461238011112atural @ id_nat @ ( map_fu1239815594074539274atural @ code_nat_of_natural @ code_natural_of_nat ) @ bit_se8570568707652914677it_nat ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7756_unset__bit__natural__def,axiom,
% 9.17/5.44 ( bit_se7083795435491715335atural
% 9.17/5.44 = ( map_fu6981160461238011112atural @ id_nat @ ( map_fu1239815594074539274atural @ code_nat_of_natural @ code_natural_of_nat ) @ bit_se4205575877204974255it_nat ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7757_flip__bit__natural__def,axiom,
% 9.17/5.44 ( bit_se168947363167071951atural
% 9.17/5.44 = ( map_fu6981160461238011112atural @ id_nat @ ( map_fu1239815594074539274atural @ code_nat_of_natural @ code_natural_of_nat ) @ bit_se2161824704523386999it_nat ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7758_set__bit__natural__def,axiom,
% 9.17/5.44 ( bit_se1617098188084679374atural
% 9.17/5.44 = ( map_fu6981160461238011112atural @ id_nat @ ( map_fu1239815594074539274atural @ code_nat_of_natural @ code_natural_of_nat ) @ bit_se7882103937844011126it_nat ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7759_natural__decr,axiom,
% 9.17/5.44 ! [N2: code_natural] :
% 9.17/5.44 ( ( N2 != zero_z2226904508553997617atural )
% 9.17/5.44 => ( ord_less_nat @ ( minus_minus_nat @ ( code_nat_of_natural @ N2 ) @ ( suc @ zero_zero_nat ) ) @ ( code_nat_of_natural @ N2 ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7760_natural__of__integer__def,axiom,
% 9.17/5.44 ( code_n4118661773612635043nteger
% 9.17/5.44 = ( map_fu1051355602067684763atural @ code_int_of_integer @ code_natural_of_nat @ nat2 ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7761_integer__of__natural__of__integer,axiom,
% 9.17/5.44 ! [K: code_integer] :
% 9.17/5.44 ( ( code_i5400310926305786745atural @ ( code_n4118661773612635043nteger @ K ) )
% 9.17/5.44 = ( ord_max_Code_integer @ zero_z3403309356797280102nteger @ K ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7762_integer__of__natural_Orep__eq,axiom,
% 9.17/5.44 ! [X: code_natural] :
% 9.17/5.44 ( ( code_int_of_integer @ ( code_i5400310926305786745atural @ X ) )
% 9.17/5.44 = ( semiri1314217659103216013at_int @ ( code_nat_of_natural @ X ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7763_int__of__integer__of__natural,axiom,
% 9.17/5.44 ! [N2: code_natural] :
% 9.17/5.44 ( ( code_int_of_integer @ ( code_i5400310926305786745atural @ N2 ) )
% 9.17/5.44 = ( semiri1314217659103216013at_int @ ( code_nat_of_natural @ N2 ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7764_integer__of__natural__of__nat,axiom,
% 9.17/5.44 ! [N2: nat] :
% 9.17/5.44 ( ( code_i5400310926305786745atural @ ( semiri3763490453095760265atural @ N2 ) )
% 9.17/5.44 = ( semiri4939895301339042750nteger @ N2 ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7765_natural__of__integer__of__natural,axiom,
% 9.17/5.44 ! [N2: code_natural] :
% 9.17/5.44 ( ( code_n4118661773612635043nteger @ ( code_i5400310926305786745atural @ N2 ) )
% 9.17/5.44 = N2 ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7766_integer__of__natural__def,axiom,
% 9.17/5.44 ( code_i5400310926305786745atural
% 9.17/5.44 = ( map_fu2787874002554666395nteger @ code_nat_of_natural @ code_integer_of_int @ semiri1314217659103216013at_int ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7767_integer__of__natural_Oabs__eq,axiom,
% 9.17/5.44 ! [X: nat] :
% 9.17/5.44 ( ( code_i5400310926305786745atural @ ( code_natural_of_nat @ X ) )
% 9.17/5.44 = ( code_integer_of_int @ ( semiri1314217659103216013at_int @ X ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7768_Code__Numeral_Osize__nat__def,axiom,
% 9.17/5.44 code_size_nat = code_nat_of_natural ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7769_Code__Numeral_OSuc__def,axiom,
% 9.17/5.44 ( code_Suc
% 9.17/5.44 = ( map_fu1239815594074539274atural @ code_nat_of_natural @ code_natural_of_nat @ suc ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7770_natural_Oinject,axiom,
% 9.17/5.44 ! [Natural: code_natural,Natural2: code_natural] :
% 9.17/5.44 ( ( ( code_Suc @ Natural )
% 9.17/5.44 = ( code_Suc @ Natural2 ) )
% 9.17/5.44 = ( Natural = Natural2 ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7771_Suc_Orep__eq,axiom,
% 9.17/5.44 ! [X: code_natural] :
% 9.17/5.44 ( ( code_nat_of_natural @ ( code_Suc @ X ) )
% 9.17/5.44 = ( suc @ ( code_nat_of_natural @ X ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7772_natural_Oexhaust,axiom,
% 9.17/5.44 ! [Y: code_natural] :
% 9.17/5.44 ( ( Y != zero_z2226904508553997617atural )
% 9.17/5.44 => ~ ! [Natural3: code_natural] :
% 9.17/5.44 ( Y
% 9.17/5.44 != ( code_Suc @ Natural3 ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7773_natural_Odistinct_I1_J,axiom,
% 9.17/5.44 ! [Natural2: code_natural] :
% 9.17/5.44 ( zero_z2226904508553997617atural
% 9.17/5.44 != ( code_Suc @ Natural2 ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7774_natural_Odistinct_I2_J,axiom,
% 9.17/5.44 ! [Natural2: code_natural] :
% 9.17/5.44 ( ( code_Suc @ Natural2 )
% 9.17/5.44 != zero_z2226904508553997617atural ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7775_Suc_Oabs__eq,axiom,
% 9.17/5.44 ! [X: nat] :
% 9.17/5.44 ( ( code_Suc @ ( code_natural_of_nat @ X ) )
% 9.17/5.44 = ( code_natural_of_nat @ ( suc @ X ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7776_Suc__natural__minus__one,axiom,
% 9.17/5.44 ! [N2: code_natural] :
% 9.17/5.44 ( ( minus_7197305767214868737atural @ ( code_Suc @ N2 ) @ one_one_Code_natural )
% 9.17/5.44 = N2 ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7777_random__aux__set_Ocases,axiom,
% 9.17/5.44 ! [X: produc7822875418678951345atural] :
% 9.17/5.44 ( ! [J3: code_natural] :
% 9.17/5.44 ( X
% 9.17/5.44 != ( produc3574140220909816553atural @ zero_z2226904508553997617atural @ J3 ) )
% 9.17/5.44 => ~ ! [I2: code_natural,J3: code_natural] :
% 9.17/5.44 ( X
% 9.17/5.44 != ( produc3574140220909816553atural @ ( code_Suc @ I2 ) @ J3 ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7778_Code__Numeral_Osub__code_I2_J,axiom,
% 9.17/5.44 ! [M2: num] :
% 9.17/5.44 ( ( code_sub @ ( bit0 @ M2 ) @ one )
% 9.17/5.44 = ( code_Pos @ ( bitM @ M2 ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7779_Code__Numeral_OPos__def,axiom,
% 9.17/5.44 code_Pos = numera6620942414471956472nteger ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7780_Pos__fold_I2_J,axiom,
% 9.17/5.44 ! [K: num] :
% 9.17/5.44 ( ( numera6620942414471956472nteger @ ( bit0 @ K ) )
% 9.17/5.44 = ( code_Pos @ ( bit0 @ K ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7781_Pos__fold_I1_J,axiom,
% 9.17/5.44 ( ( numera6620942414471956472nteger @ one )
% 9.17/5.44 = ( code_Pos @ one ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7782_Pos__fold_I3_J,axiom,
% 9.17/5.44 ! [K: num] :
% 9.17/5.44 ( ( numera6620942414471956472nteger @ ( bit1 @ K ) )
% 9.17/5.44 = ( code_Pos @ ( bit1 @ K ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7783_one__integer__code,axiom,
% 9.17/5.44 ( one_one_Code_integer
% 9.17/5.44 = ( code_Pos @ one ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7784_Code__Numeral_Odup__code_I2_J,axiom,
% 9.17/5.44 ! [N2: num] :
% 9.17/5.44 ( ( code_dup @ ( code_Pos @ N2 ) )
% 9.17/5.44 = ( code_Pos @ ( bit0 @ N2 ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7785_less__integer__code_I4_J,axiom,
% 9.17/5.44 ! [K: num] :
% 9.17/5.44 ~ ( ord_le6747313008572928689nteger @ ( code_Pos @ K ) @ zero_z3403309356797280102nteger ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7786_less__integer__code_I2_J,axiom,
% 9.17/5.44 ! [L: num] : ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( code_Pos @ L ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7787_plus__integer__code_I3_J,axiom,
% 9.17/5.44 ! [M2: num,N2: num] :
% 9.17/5.44 ( ( plus_p5714425477246183910nteger @ ( code_Pos @ M2 ) @ ( code_Pos @ N2 ) )
% 9.17/5.44 = ( code_Pos @ ( plus_plus_num @ M2 @ N2 ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7788_less__eq__integer__code_I2_J,axiom,
% 9.17/5.44 ! [L: num] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( code_Pos @ L ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7789_less__eq__integer__code_I4_J,axiom,
% 9.17/5.44 ! [K: num] :
% 9.17/5.44 ~ ( ord_le3102999989581377725nteger @ ( code_Pos @ K ) @ zero_z3403309356797280102nteger ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7790_less__integer__code_I8_J,axiom,
% 9.17/5.44 ! [K: num,L: num] : ( ord_le6747313008572928689nteger @ ( code_Neg @ K ) @ ( code_Pos @ L ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7791_less__integer__code_I6_J,axiom,
% 9.17/5.44 ! [K: num,L: num] :
% 9.17/5.44 ~ ( ord_le6747313008572928689nteger @ ( code_Pos @ K ) @ ( code_Neg @ L ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7792_uminus__integer__code_I3_J,axiom,
% 9.17/5.44 ! [M2: num] :
% 9.17/5.44 ( ( uminus1351360451143612070nteger @ ( code_Neg @ M2 ) )
% 9.17/5.44 = ( code_Pos @ M2 ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7793_uminus__integer__code_I2_J,axiom,
% 9.17/5.44 ! [M2: num] :
% 9.17/5.44 ( ( uminus1351360451143612070nteger @ ( code_Pos @ M2 ) )
% 9.17/5.44 = ( code_Neg @ M2 ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7794_Code__Numeral_ONeg__def,axiom,
% 9.17/5.44 ( code_Neg
% 9.17/5.44 = ( ^ [N4: num] : ( uminus1351360451143612070nteger @ ( code_Pos @ N4 ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7795_less__eq__integer__code_I8_J,axiom,
% 9.17/5.44 ! [K: num,L: num] : ( ord_le3102999989581377725nteger @ ( code_Neg @ K ) @ ( code_Pos @ L ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7796_less__eq__integer__code_I6_J,axiom,
% 9.17/5.44 ! [K: num,L: num] :
% 9.17/5.44 ~ ( ord_le3102999989581377725nteger @ ( code_Pos @ K ) @ ( code_Neg @ L ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7797_times__integer__code_I3_J,axiom,
% 9.17/5.44 ! [M2: num,N2: num] :
% 9.17/5.44 ( ( times_3573771949741848930nteger @ ( code_Pos @ M2 ) @ ( code_Pos @ N2 ) )
% 9.17/5.44 = ( code_Pos @ ( times_times_num @ M2 @ N2 ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7798_less__integer__code_I5_J,axiom,
% 9.17/5.44 ! [K: num,L: num] :
% 9.17/5.44 ( ( ord_le6747313008572928689nteger @ ( code_Pos @ K ) @ ( code_Pos @ L ) )
% 9.17/5.44 = ( ord_less_num @ K @ L ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7799_less__eq__integer__code_I5_J,axiom,
% 9.17/5.44 ! [K: num,L: num] :
% 9.17/5.44 ( ( ord_le3102999989581377725nteger @ ( code_Pos @ K ) @ ( code_Pos @ L ) )
% 9.17/5.44 = ( ord_less_eq_num @ K @ L ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7800_minus__integer__code_I3_J,axiom,
% 9.17/5.44 ! [M2: num,N2: num] :
% 9.17/5.44 ( ( minus_8373710615458151222nteger @ ( code_Pos @ M2 ) @ ( code_Pos @ N2 ) )
% 9.17/5.44 = ( code_sub @ M2 @ N2 ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7801_divmod__abs__code_I1_J,axiom,
% 9.17/5.44 ! [K: num,L: num] :
% 9.17/5.44 ( ( code_divmod_abs @ ( code_Pos @ K ) @ ( code_Pos @ L ) )
% 9.17/5.44 = ( unique3479559517661332726nteger @ K @ L ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7802_minus__integer__code_I4_J,axiom,
% 9.17/5.44 ! [M2: num,N2: num] :
% 9.17/5.44 ( ( minus_8373710615458151222nteger @ ( code_Pos @ M2 ) @ ( code_Neg @ N2 ) )
% 9.17/5.44 = ( code_Pos @ ( plus_plus_num @ M2 @ N2 ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7803_minus__integer__code_I5_J,axiom,
% 9.17/5.44 ! [M2: num,N2: num] :
% 9.17/5.44 ( ( minus_8373710615458151222nteger @ ( code_Neg @ M2 ) @ ( code_Pos @ N2 ) )
% 9.17/5.44 = ( code_Neg @ ( plus_plus_num @ M2 @ N2 ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7804_times__integer__code_I4_J,axiom,
% 9.17/5.44 ! [M2: num,N2: num] :
% 9.17/5.44 ( ( times_3573771949741848930nteger @ ( code_Pos @ M2 ) @ ( code_Neg @ N2 ) )
% 9.17/5.44 = ( code_Neg @ ( times_times_num @ M2 @ N2 ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7805_times__integer__code_I5_J,axiom,
% 9.17/5.44 ! [M2: num,N2: num] :
% 9.17/5.44 ( ( times_3573771949741848930nteger @ ( code_Neg @ M2 ) @ ( code_Pos @ N2 ) )
% 9.17/5.44 = ( code_Neg @ ( times_times_num @ M2 @ N2 ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7806_times__integer__code_I6_J,axiom,
% 9.17/5.44 ! [M2: num,N2: num] :
% 9.17/5.44 ( ( times_3573771949741848930nteger @ ( code_Neg @ M2 ) @ ( code_Neg @ N2 ) )
% 9.17/5.44 = ( code_Pos @ ( times_times_num @ M2 @ N2 ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7807_plus__integer__code_I4_J,axiom,
% 9.17/5.44 ! [M2: num,N2: num] :
% 9.17/5.44 ( ( plus_p5714425477246183910nteger @ ( code_Pos @ M2 ) @ ( code_Neg @ N2 ) )
% 9.17/5.44 = ( code_sub @ M2 @ N2 ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7808_plus__integer__code_I5_J,axiom,
% 9.17/5.44 ! [M2: num,N2: num] :
% 9.17/5.44 ( ( plus_p5714425477246183910nteger @ ( code_Neg @ M2 ) @ ( code_Pos @ N2 ) )
% 9.17/5.44 = ( code_sub @ N2 @ M2 ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7809_divmod__abs__code_I3_J,axiom,
% 9.17/5.44 ! [K: num,L: num] :
% 9.17/5.44 ( ( code_divmod_abs @ ( code_Neg @ K ) @ ( code_Pos @ L ) )
% 9.17/5.44 = ( unique3479559517661332726nteger @ K @ L ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7810_divmod__abs__code_I4_J,axiom,
% 9.17/5.44 ! [K: num,L: num] :
% 9.17/5.44 ( ( code_divmod_abs @ ( code_Pos @ K ) @ ( code_Neg @ L ) )
% 9.17/5.44 = ( unique3479559517661332726nteger @ K @ L ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7811_Code__Numeral_Osub__code_I3_J,axiom,
% 9.17/5.44 ! [M2: num] :
% 9.17/5.44 ( ( code_sub @ ( bit1 @ M2 ) @ one )
% 9.17/5.44 = ( code_Pos @ ( bit0 @ M2 ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7812_normalize__stable,axiom,
% 9.17/5.44 ! [Q3: int,P4: int] :
% 9.17/5.44 ( ( ord_less_int @ zero_zero_int @ Q3 )
% 9.17/5.44 => ( ( algebr932160517623751201me_int @ P4 @ Q3 )
% 9.17/5.44 => ( ( normalize @ ( product_Pair_int_int @ P4 @ Q3 ) )
% 9.17/5.44 = ( product_Pair_int_int @ P4 @ Q3 ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7813_quotient__of__coprime,axiom,
% 9.17/5.44 ! [R2: rat,P4: int,Q3: int] :
% 9.17/5.44 ( ( ( quotient_of @ R2 )
% 9.17/5.44 = ( product_Pair_int_int @ P4 @ Q3 ) )
% 9.17/5.44 => ( algebr932160517623751201me_int @ P4 @ Q3 ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7814_normalize__coprime,axiom,
% 9.17/5.44 ! [R2: product_prod_int_int,P4: int,Q3: int] :
% 9.17/5.44 ( ( ( normalize @ R2 )
% 9.17/5.44 = ( product_Pair_int_int @ P4 @ Q3 ) )
% 9.17/5.44 => ( algebr932160517623751201me_int @ P4 @ Q3 ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7815_coprime__common__divisor__nat,axiom,
% 9.17/5.44 ! [A: nat,B: nat,X: nat] :
% 9.17/5.44 ( ( algebr934650988132801477me_nat @ A @ B )
% 9.17/5.44 => ( ( dvd_dvd_nat @ X @ A )
% 9.17/5.44 => ( ( dvd_dvd_nat @ X @ B )
% 9.17/5.44 => ( X = one_one_nat ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7816_coprime__diff__one__right__nat,axiom,
% 9.17/5.44 ! [N2: nat] :
% 9.17/5.44 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 9.17/5.44 => ( algebr934650988132801477me_nat @ N2 @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7817_coprime__diff__one__left__nat,axiom,
% 9.17/5.44 ! [N2: nat] :
% 9.17/5.44 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 9.17/5.44 => ( algebr934650988132801477me_nat @ ( minus_minus_nat @ N2 @ one_one_nat ) @ N2 ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7818_integer__of__char__code,axiom,
% 9.17/5.44 ! [B0: $o,B1: $o,B22: $o,B32: $o,B42: $o,B52: $o,B62: $o,B72: $o] :
% 9.17/5.44 ( ( integer_of_char @ ( char2 @ B0 @ B1 @ B22 @ B32 @ B42 @ B52 @ B62 @ B72 ) )
% 9.17/5.44 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ B72 ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B62 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B52 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B42 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B32 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B22 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B1 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B0 ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7819_Suc__funpow,axiom,
% 9.17/5.44 ! [N2: nat] :
% 9.17/5.44 ( ( compow_nat_nat @ N2 @ suc )
% 9.17/5.44 = ( plus_plus_nat @ N2 ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7820_or__not__num__neg_Opelims,axiom,
% 9.17/5.44 ! [X: num,Xa: num,Y: num] :
% 9.17/5.44 ( ( ( bit_or_not_num_neg @ X @ Xa )
% 9.17/5.44 = Y )
% 9.17/5.44 => ( ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ X @ Xa ) )
% 9.17/5.44 => ( ( ( X = one )
% 9.17/5.44 => ( ( Xa = one )
% 9.17/5.44 => ( ( Y = one )
% 9.17/5.44 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 9.17/5.44 => ( ( ( X = one )
% 9.17/5.44 => ! [M5: num] :
% 9.17/5.44 ( ( Xa
% 9.17/5.44 = ( bit0 @ M5 ) )
% 9.17/5.44 => ( ( Y
% 9.17/5.44 = ( bit1 @ M5 ) )
% 9.17/5.44 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ one @ ( bit0 @ M5 ) ) ) ) ) )
% 9.17/5.44 => ( ( ( X = one )
% 9.17/5.44 => ! [M5: num] :
% 9.17/5.44 ( ( Xa
% 9.17/5.44 = ( bit1 @ M5 ) )
% 9.17/5.44 => ( ( Y
% 9.17/5.44 = ( bit1 @ M5 ) )
% 9.17/5.44 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ one @ ( bit1 @ M5 ) ) ) ) ) )
% 9.17/5.44 => ( ! [N: num] :
% 9.17/5.44 ( ( X
% 9.17/5.44 = ( bit0 @ N ) )
% 9.17/5.44 => ( ( Xa = one )
% 9.17/5.44 => ( ( Y
% 9.17/5.44 = ( bit0 @ one ) )
% 9.17/5.44 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit0 @ N ) @ one ) ) ) ) )
% 9.17/5.44 => ( ! [N: num] :
% 9.17/5.44 ( ( X
% 9.17/5.44 = ( bit0 @ N ) )
% 9.17/5.44 => ! [M5: num] :
% 9.17/5.44 ( ( Xa
% 9.17/5.44 = ( bit0 @ M5 ) )
% 9.17/5.44 => ( ( Y
% 9.17/5.44 = ( bitM @ ( bit_or_not_num_neg @ N @ M5 ) ) )
% 9.17/5.44 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit0 @ N ) @ ( bit0 @ M5 ) ) ) ) ) )
% 9.17/5.44 => ( ! [N: num] :
% 9.17/5.44 ( ( X
% 9.17/5.44 = ( bit0 @ N ) )
% 9.17/5.44 => ! [M5: num] :
% 9.17/5.44 ( ( Xa
% 9.17/5.44 = ( bit1 @ M5 ) )
% 9.17/5.44 => ( ( Y
% 9.17/5.44 = ( bit0 @ ( bit_or_not_num_neg @ N @ M5 ) ) )
% 9.17/5.44 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit0 @ N ) @ ( bit1 @ M5 ) ) ) ) ) )
% 9.17/5.44 => ( ! [N: num] :
% 9.17/5.44 ( ( X
% 9.17/5.44 = ( bit1 @ N ) )
% 9.17/5.44 => ( ( Xa = one )
% 9.17/5.44 => ( ( Y = one )
% 9.17/5.44 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit1 @ N ) @ one ) ) ) ) )
% 9.17/5.44 => ( ! [N: num] :
% 9.17/5.44 ( ( X
% 9.17/5.44 = ( bit1 @ N ) )
% 9.17/5.44 => ! [M5: num] :
% 9.17/5.44 ( ( Xa
% 9.17/5.44 = ( bit0 @ M5 ) )
% 9.17/5.44 => ( ( Y
% 9.17/5.44 = ( bitM @ ( bit_or_not_num_neg @ N @ M5 ) ) )
% 9.17/5.44 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit1 @ N ) @ ( bit0 @ M5 ) ) ) ) ) )
% 9.17/5.44 => ~ ! [N: num] :
% 9.17/5.44 ( ( X
% 9.17/5.44 = ( bit1 @ N ) )
% 9.17/5.44 => ! [M5: num] :
% 9.17/5.44 ( ( Xa
% 9.17/5.44 = ( bit1 @ M5 ) )
% 9.17/5.44 => ( ( Y
% 9.17/5.44 = ( bitM @ ( bit_or_not_num_neg @ N @ M5 ) ) )
% 9.17/5.44 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit1 @ N ) @ ( bit1 @ M5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7821_cr__natural__def,axiom,
% 9.17/5.44 ( code_cr_natural
% 9.17/5.44 = ( ^ [X3: nat,Y3: code_natural] :
% 9.17/5.44 ( X3
% 9.17/5.44 = ( code_nat_of_natural @ Y3 ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7822_cr__integer__def,axiom,
% 9.17/5.44 ( code_cr_integer
% 9.17/5.44 = ( ^ [X3: int,Y3: code_integer] :
% 9.17/5.44 ( X3
% 9.17/5.44 = ( code_int_of_integer @ Y3 ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7823_integer_Opcr__cr__eq,axiom,
% 9.17/5.44 code_pcr_integer = code_cr_integer ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7824_unit__factor__simps_I2_J,axiom,
% 9.17/5.44 ! [N2: nat] :
% 9.17/5.44 ( ( unit_f2748546683901255202or_nat @ ( suc @ N2 ) )
% 9.17/5.44 = one_one_nat ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7825_unit__factor__nat__def,axiom,
% 9.17/5.44 ( unit_f2748546683901255202or_nat
% 9.17/5.44 = ( ^ [N4: nat] : ( if_nat @ ( N4 = zero_zero_nat ) @ zero_zero_nat @ one_one_nat ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7826_Nat_Otransfer,axiom,
% 9.17/5.44 bNF_re1831474436612530402atural @ code_pcr_integer @ code_pcr_natural @ nat2 @ code_Nat ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7827_pcr__natural__def,axiom,
% 9.17/5.44 ( code_pcr_natural
% 9.17/5.44 = ( relcom1729257228895983867atural
% 9.17/5.44 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.44 @ code_cr_natural ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7828_natural_Orep__transfer,axiom,
% 9.17/5.44 ( bNF_re7333046803109187065at_nat @ code_pcr_natural
% 9.17/5.44 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.44 @ ^ [X3: nat] : X3
% 9.17/5.44 @ code_nat_of_natural ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7829_natural_Oid__abs__transfer,axiom,
% 9.17/5.44 ( bNF_re2605341659958429177atural
% 9.17/5.44 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.44 @ code_pcr_natural
% 9.17/5.44 @ ^ [X3: nat] : X3
% 9.17/5.44 @ code_natural_of_nat ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7830_natural_Opcr__cr__eq,axiom,
% 9.17/5.44 code_pcr_natural = code_cr_natural ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7831_zero__natural_Otransfer,axiom,
% 9.17/5.44 code_pcr_natural @ zero_zero_nat @ zero_z2226904508553997617atural ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7832_one__natural_Otransfer,axiom,
% 9.17/5.44 code_pcr_natural @ one_one_nat @ one_one_Code_natural ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7833_less__natural_Otransfer,axiom,
% 9.17/5.44 ( bNF_re1639080489988575423ural_o @ code_pcr_natural
% 9.17/5.44 @ ( bNF_re2785088596696291543al_o_o @ code_pcr_natural
% 9.17/5.44 @ ^ [Y4: $o,Z2: $o] : ( Y4 = Z2 ) )
% 9.17/5.44 @ ord_less_nat
% 9.17/5.44 @ ord_le5570908160329646204atural ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7834_plus__natural_Otransfer,axiom,
% 9.17/5.44 bNF_re88643428490162567atural @ code_pcr_natural @ ( bNF_re3704215830270325841atural @ code_pcr_natural @ code_pcr_natural ) @ plus_plus_nat @ plus_p4538020629002901425atural ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7835_Suc_Otransfer,axiom,
% 9.17/5.44 bNF_re3704215830270325841atural @ code_pcr_natural @ code_pcr_natural @ suc @ code_Suc ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7836_minus__natural_Otransfer,axiom,
% 9.17/5.44 bNF_re88643428490162567atural @ code_pcr_natural @ ( bNF_re3704215830270325841atural @ code_pcr_natural @ code_pcr_natural ) @ minus_minus_nat @ minus_7197305767214868737atural ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7837_pcr__integer__def,axiom,
% 9.17/5.44 ( code_pcr_integer
% 9.17/5.44 = ( relcom967497705283160040nteger
% 9.17/5.44 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.44 @ code_cr_integer ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7838_less__eq__natural_Otransfer,axiom,
% 9.17/5.44 ( bNF_re1639080489988575423ural_o @ code_pcr_natural
% 9.17/5.44 @ ( bNF_re2785088596696291543al_o_o @ code_pcr_natural
% 9.17/5.44 @ ^ [Y4: $o,Z2: $o] : ( Y4 = Z2 ) )
% 9.17/5.44 @ ord_less_eq_nat
% 9.17/5.44 @ ord_le1926595141338095240atural ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7839_times__natural_Otransfer,axiom,
% 9.17/5.44 bNF_re88643428490162567atural @ code_pcr_natural @ ( bNF_re3704215830270325841atural @ code_pcr_natural @ code_pcr_natural ) @ times_times_nat @ times_2397367101498566445atural ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7840_divide__natural_Otransfer,axiom,
% 9.17/5.44 bNF_re88643428490162567atural @ code_pcr_natural @ ( bNF_re3704215830270325841atural @ code_pcr_natural @ code_pcr_natural ) @ divide_divide_nat @ divide5121882707175180666atural ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7841_modulo__natural_Otransfer,axiom,
% 9.17/5.44 bNF_re88643428490162567atural @ code_pcr_natural @ ( bNF_re3704215830270325841atural @ code_pcr_natural @ code_pcr_natural ) @ modulo_modulo_nat @ modulo8411746178871703098atural ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7842_take__bit__natural_Otransfer,axiom,
% 9.17/5.44 ( bNF_re3692170009638431535atural
% 9.17/5.44 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.44 @ ( bNF_re3704215830270325841atural @ code_pcr_natural @ code_pcr_natural )
% 9.17/5.44 @ bit_se2925701944663578781it_nat
% 9.17/5.44 @ bit_se569199155075624693atural ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7843_xor__natural_Otransfer,axiom,
% 9.17/5.44 bNF_re88643428490162567atural @ code_pcr_natural @ ( bNF_re3704215830270325841atural @ code_pcr_natural @ code_pcr_natural ) @ bit_se6528837805403552850or_nat @ bit_se2046307713759805098atural ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7844_or__natural_Otransfer,axiom,
% 9.17/5.44 bNF_re88643428490162567atural @ code_pcr_natural @ ( bNF_re3704215830270325841atural @ code_pcr_natural @ code_pcr_natural ) @ bit_se1412395901928357646or_nat @ bit_se9127793120404214118atural ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7845_and__natural_Otransfer,axiom,
% 9.17/5.44 bNF_re88643428490162567atural @ code_pcr_natural @ ( bNF_re3704215830270325841atural @ code_pcr_natural @ code_pcr_natural ) @ bit_se727722235901077358nd_nat @ bit_se2773287842338716102atural ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7846_bit__natural_Otransfer,axiom,
% 9.17/5.44 ( bNF_re2895713572246619415_nat_o @ code_pcr_natural
% 9.17/5.44 @ ^ [Y4: nat > $o,Z2: nat > $o] : ( Y4 = Z2 )
% 9.17/5.44 @ bit_se1148574629649215175it_nat
% 9.17/5.44 @ bit_se8040316288895769887atural ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7847_push__bit__natural_Otransfer,axiom,
% 9.17/5.44 ( bNF_re3692170009638431535atural
% 9.17/5.44 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.44 @ ( bNF_re3704215830270325841atural @ code_pcr_natural @ code_pcr_natural )
% 9.17/5.44 @ bit_se547839408752420682it_nat
% 9.17/5.44 @ bit_se6611745700429515170atural ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7848_mask__natural_Otransfer,axiom,
% 9.17/5.44 ( bNF_re2605341659958429177atural
% 9.17/5.44 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.44 @ code_pcr_natural
% 9.17/5.44 @ bit_se2002935070580805687sk_nat
% 9.17/5.44 @ bit_se943457434206027407atural ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7849_drop__bit__natural_Otransfer,axiom,
% 9.17/5.44 ( bNF_re3692170009638431535atural
% 9.17/5.44 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.44 @ ( bNF_re3704215830270325841atural @ code_pcr_natural @ code_pcr_natural )
% 9.17/5.44 @ bit_se8570568707652914677it_nat
% 9.17/5.44 @ bit_se2751692689150723149atural ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7850_division__segment__natural_Otransfer,axiom,
% 9.17/5.44 bNF_re3704215830270325841atural @ code_pcr_natural @ code_pcr_natural @ euclid3398187327856392827nt_nat @ euclid5112970336976722131atural ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7851_flip__bit__natural_Otransfer,axiom,
% 9.17/5.44 ( bNF_re3692170009638431535atural
% 9.17/5.44 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.44 @ ( bNF_re3704215830270325841atural @ code_pcr_natural @ code_pcr_natural )
% 9.17/5.44 @ bit_se2161824704523386999it_nat
% 9.17/5.44 @ bit_se168947363167071951atural ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7852_set__bit__natural_Otransfer,axiom,
% 9.17/5.44 ( bNF_re3692170009638431535atural
% 9.17/5.44 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.44 @ ( bNF_re3704215830270325841atural @ code_pcr_natural @ code_pcr_natural )
% 9.17/5.44 @ bit_se7882103937844011126it_nat
% 9.17/5.44 @ bit_se1617098188084679374atural ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7853_unset__bit__natural_Otransfer,axiom,
% 9.17/5.44 ( bNF_re3692170009638431535atural
% 9.17/5.44 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.44 @ ( bNF_re3704215830270325841atural @ code_pcr_natural @ code_pcr_natural )
% 9.17/5.44 @ bit_se4205575877204974255it_nat
% 9.17/5.44 @ bit_se7083795435491715335atural ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7854_euclidean__size__natural_Otransfer,axiom,
% 9.17/5.44 ( bNF_re7333046803109187065at_nat @ code_pcr_natural
% 9.17/5.44 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.44 @ euclid4777050414544973029ze_nat
% 9.17/5.44 @ euclid5200926497590043453atural ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7855_integer__of__natural_Otransfer,axiom,
% 9.17/5.44 bNF_re5252274238750452962nteger @ code_pcr_natural @ code_pcr_integer @ semiri1314217659103216013at_int @ code_i5400310926305786745atural ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7856_natural__of__integer_Otransfer,axiom,
% 9.17/5.44 bNF_re1831474436612530402atural @ code_pcr_integer @ code_pcr_natural @ nat2 @ code_n4118661773612635043nteger ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7857_plus__num__def,axiom,
% 9.17/5.44 ( plus_plus_num
% 9.17/5.44 = ( ^ [M: num,N4: num] : ( num_of_nat @ ( plus_plus_nat @ ( nat_of_num @ M ) @ ( nat_of_num @ N4 ) ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7858_Lcm__nat__empty,axiom,
% 9.17/5.44 ( ( gcd_Lcm_nat @ bot_bot_set_nat )
% 9.17/5.44 = one_one_nat ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7859_nat__of__num_Osimps_I2_J,axiom,
% 9.17/5.44 ! [X: num] :
% 9.17/5.44 ( ( nat_of_num @ ( bit0 @ X ) )
% 9.17/5.44 = ( plus_plus_nat @ ( nat_of_num @ X ) @ ( nat_of_num @ X ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7860_nat__of__num__code_I1_J,axiom,
% 9.17/5.44 ( ( nat_of_num @ one )
% 9.17/5.44 = one_one_nat ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7861_nat__of__num__add,axiom,
% 9.17/5.44 ! [X: num,Y: num] :
% 9.17/5.44 ( ( nat_of_num @ ( plus_plus_num @ X @ Y ) )
% 9.17/5.44 = ( plus_plus_nat @ ( nat_of_num @ X ) @ ( nat_of_num @ Y ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7862_nat__of__num__code_I2_J,axiom,
% 9.17/5.44 ! [N2: num] :
% 9.17/5.44 ( ( nat_of_num @ ( bit0 @ N2 ) )
% 9.17/5.44 = ( plus_plus_nat @ ( nat_of_num @ N2 ) @ ( nat_of_num @ N2 ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7863_nat__of__num_Osimps_I3_J,axiom,
% 9.17/5.44 ! [X: num] :
% 9.17/5.44 ( ( nat_of_num @ ( bit1 @ X ) )
% 9.17/5.44 = ( suc @ ( plus_plus_nat @ ( nat_of_num @ X ) @ ( nat_of_num @ X ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7864_nat__of__num__code_I3_J,axiom,
% 9.17/5.44 ! [N2: num] :
% 9.17/5.44 ( ( nat_of_num @ ( bit1 @ N2 ) )
% 9.17/5.44 = ( suc @ ( plus_plus_nat @ ( nat_of_num @ N2 ) @ ( nat_of_num @ N2 ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7865_Gcd__nat__eq__one,axiom,
% 9.17/5.44 ! [N6: set_nat] :
% 9.17/5.44 ( ( member_nat @ one_one_nat @ N6 )
% 9.17/5.44 => ( ( gcd_Gcd_nat @ N6 )
% 9.17/5.44 = one_one_nat ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7866_card__of__Field__natLeq,axiom,
% 9.17/5.44 member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( bNF_Ca3793111618940312692of_nat @ ( field_nat @ bNF_Ca8665028551170535155natLeq ) ) @ bNF_Ca8665028551170535155natLeq ) @ bNF_We5258908940166488438at_nat ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7867_card__of__nat,axiom,
% 9.17/5.44 member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( bNF_Ca3793111618940312692of_nat @ top_top_set_nat ) @ bNF_Ca8665028551170535155natLeq ) @ bNF_We5258908940166488438at_nat ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7868_ctwo__Cnotzero,axiom,
% 9.17/5.44 ( ~ ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ bNF_Cardinal_ctwo @ bNF_Cardinal_czero_o ) @ bNF_We2654380646378065620so_o_o )
% 9.17/5.44 & ( bNF_Ca8331644756375544342r_on_o @ ( field_o @ bNF_Cardinal_ctwo ) @ bNF_Cardinal_ctwo ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7869_ctwo__ordLess__natLeq,axiom,
% 9.17/5.44 member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ bNF_Cardinal_ctwo @ bNF_Ca8665028551170535155natLeq ) @ bNF_We8182288985678559134_o_nat ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7870_or__num_Opelims,axiom,
% 9.17/5.44 ! [X: num,Xa: num,Y: num] :
% 9.17/5.44 ( ( ( bit_un6697907153464112080or_num @ X @ Xa )
% 9.17/5.44 = Y )
% 9.17/5.44 => ( ( accp_P3113834385874906142um_num @ bit_un4773296044027857193um_rel @ ( product_Pair_num_num @ X @ Xa ) )
% 9.17/5.44 => ( ( ( X = one )
% 9.17/5.44 => ( ( Xa = one )
% 9.17/5.44 => ( ( Y = one )
% 9.17/5.44 => ~ ( accp_P3113834385874906142um_num @ bit_un4773296044027857193um_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 9.17/5.44 => ( ( ( X = one )
% 9.17/5.44 => ! [N: num] :
% 9.17/5.44 ( ( Xa
% 9.17/5.44 = ( bit0 @ N ) )
% 9.17/5.44 => ( ( Y
% 9.17/5.44 = ( bit1 @ N ) )
% 9.17/5.44 => ~ ( accp_P3113834385874906142um_num @ bit_un4773296044027857193um_rel @ ( product_Pair_num_num @ one @ ( bit0 @ N ) ) ) ) ) )
% 9.17/5.44 => ( ( ( X = one )
% 9.17/5.44 => ! [N: num] :
% 9.17/5.44 ( ( Xa
% 9.17/5.44 = ( bit1 @ N ) )
% 9.17/5.44 => ( ( Y
% 9.17/5.44 = ( bit1 @ N ) )
% 9.17/5.44 => ~ ( accp_P3113834385874906142um_num @ bit_un4773296044027857193um_rel @ ( product_Pair_num_num @ one @ ( bit1 @ N ) ) ) ) ) )
% 9.17/5.44 => ( ! [M5: num] :
% 9.17/5.44 ( ( X
% 9.17/5.44 = ( bit0 @ M5 ) )
% 9.17/5.44 => ( ( Xa = one )
% 9.17/5.44 => ( ( Y
% 9.17/5.44 = ( bit1 @ M5 ) )
% 9.17/5.44 => ~ ( accp_P3113834385874906142um_num @ bit_un4773296044027857193um_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ one ) ) ) ) )
% 9.17/5.44 => ( ! [M5: num] :
% 9.17/5.44 ( ( X
% 9.17/5.44 = ( bit0 @ M5 ) )
% 9.17/5.44 => ! [N: num] :
% 9.17/5.44 ( ( Xa
% 9.17/5.44 = ( bit0 @ N ) )
% 9.17/5.44 => ( ( Y
% 9.17/5.44 = ( bit0 @ ( bit_un6697907153464112080or_num @ M5 @ N ) ) )
% 9.17/5.44 => ~ ( accp_P3113834385874906142um_num @ bit_un4773296044027857193um_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ ( bit0 @ N ) ) ) ) ) )
% 9.17/5.44 => ( ! [M5: num] :
% 9.17/5.44 ( ( X
% 9.17/5.44 = ( bit0 @ M5 ) )
% 9.17/5.44 => ! [N: num] :
% 9.17/5.44 ( ( Xa
% 9.17/5.44 = ( bit1 @ N ) )
% 9.17/5.44 => ( ( Y
% 9.17/5.44 = ( bit1 @ ( bit_un6697907153464112080or_num @ M5 @ N ) ) )
% 9.17/5.44 => ~ ( accp_P3113834385874906142um_num @ bit_un4773296044027857193um_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ ( bit1 @ N ) ) ) ) ) )
% 9.17/5.44 => ( ! [M5: num] :
% 9.17/5.44 ( ( X
% 9.17/5.44 = ( bit1 @ M5 ) )
% 9.17/5.44 => ( ( Xa = one )
% 9.17/5.44 => ( ( Y
% 9.17/5.44 = ( bit1 @ M5 ) )
% 9.17/5.44 => ~ ( accp_P3113834385874906142um_num @ bit_un4773296044027857193um_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ one ) ) ) ) )
% 9.17/5.44 => ( ! [M5: num] :
% 9.17/5.44 ( ( X
% 9.17/5.44 = ( bit1 @ M5 ) )
% 9.17/5.44 => ! [N: num] :
% 9.17/5.44 ( ( Xa
% 9.17/5.44 = ( bit0 @ N ) )
% 9.17/5.44 => ( ( Y
% 9.17/5.44 = ( bit1 @ ( bit_un6697907153464112080or_num @ M5 @ N ) ) )
% 9.17/5.44 => ~ ( accp_P3113834385874906142um_num @ bit_un4773296044027857193um_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ ( bit0 @ N ) ) ) ) ) )
% 9.17/5.44 => ~ ! [M5: num] :
% 9.17/5.44 ( ( X
% 9.17/5.44 = ( bit1 @ M5 ) )
% 9.17/5.44 => ! [N: num] :
% 9.17/5.44 ( ( Xa
% 9.17/5.44 = ( bit1 @ N ) )
% 9.17/5.44 => ( ( Y
% 9.17/5.44 = ( bit1 @ ( bit_un6697907153464112080or_num @ M5 @ N ) ) )
% 9.17/5.44 => ~ ( accp_P3113834385874906142um_num @ bit_un4773296044027857193um_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ ( bit1 @ N ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7871_Quotient__natural,axiom,
% 9.17/5.44 ( quotie743640454666494480atural
% 9.17/5.44 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 9.17/5.44 @ code_natural_of_nat
% 9.17/5.44 @ code_nat_of_natural
% 9.17/5.44 @ code_cr_natural ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7872_Quotient__integer,axiom,
% 9.17/5.44 ( quotie2291698863146621601nteger
% 9.17/5.44 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 9.17/5.44 @ code_integer_of_int
% 9.17/5.44 @ code_int_of_integer
% 9.17/5.44 @ code_cr_integer ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7873_Lcm__nat__def,axiom,
% 9.17/5.44 ( gcd_Lcm_nat
% 9.17/5.44 = ( ^ [M7: set_nat] : ( if_nat @ ( finite_finite_nat @ M7 ) @ ( lattic7826324295020591184_F_nat @ gcd_lcm_nat @ one_one_nat @ M7 ) @ zero_zero_nat ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7874_Lcm__nat__set__eq__fold,axiom,
% 9.17/5.44 ! [Xs: list_nat] :
% 9.17/5.44 ( ( gcd_Lcm_nat @ ( set_nat2 @ Xs ) )
% 9.17/5.44 = ( fold_nat_nat @ gcd_lcm_nat @ Xs @ one_one_nat ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7875_mod__h__bot__iff_I7_J,axiom,
% 9.17/5.44 ! [P: assn,Q: assn,H3: heap_e7401611519738050253t_unit] :
% 9.17/5.44 ( ( rep_assn @ ( sup_sup_assn @ P @ Q ) @ ( produc7507926704131184380et_nat @ H3 @ bot_bot_set_nat ) )
% 9.17/5.44 = ( ( rep_assn @ P @ ( produc7507926704131184380et_nat @ H3 @ bot_bot_set_nat ) )
% 9.17/5.44 | ( rep_assn @ Q @ ( produc7507926704131184380et_nat @ H3 @ bot_bot_set_nat ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7876_mod__h__bot__iff_I5_J,axiom,
% 9.17/5.44 ! [P: assn,Q: assn,H3: heap_e7401611519738050253t_unit] :
% 9.17/5.44 ( ( rep_assn @ ( times_times_assn @ P @ Q ) @ ( produc7507926704131184380et_nat @ H3 @ bot_bot_set_nat ) )
% 9.17/5.44 = ( ( rep_assn @ P @ ( produc7507926704131184380et_nat @ H3 @ bot_bot_set_nat ) )
% 9.17/5.44 & ( rep_assn @ Q @ ( produc7507926704131184380et_nat @ H3 @ bot_bot_set_nat ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7877_mod__h__bot__iff_I6_J,axiom,
% 9.17/5.44 ! [P: assn,Q: assn,H3: heap_e7401611519738050253t_unit] :
% 9.17/5.44 ( ( rep_assn @ ( inf_inf_assn @ P @ Q ) @ ( produc7507926704131184380et_nat @ H3 @ bot_bot_set_nat ) )
% 9.17/5.44 = ( ( rep_assn @ P @ ( produc7507926704131184380et_nat @ H3 @ bot_bot_set_nat ) )
% 9.17/5.44 & ( rep_assn @ Q @ ( produc7507926704131184380et_nat @ H3 @ bot_bot_set_nat ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7878_mod__h__bot__iff_I2_J,axiom,
% 9.17/5.44 ! [H3: heap_e7401611519738050253t_unit] : ( rep_assn @ top_top_assn @ ( produc7507926704131184380et_nat @ H3 @ bot_bot_set_nat ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7879_times__assn__raw_Ocases,axiom,
% 9.17/5.44 ! [X: produc2732055786443039994et_nat] :
% 9.17/5.44 ~ ! [P7: produc3658429121746597890et_nat > $o,Q6: produc3658429121746597890et_nat > $o,H2: heap_e7401611519738050253t_unit,As: set_nat] :
% 9.17/5.44 ( X
% 9.17/5.44 != ( produc2245416461498447860et_nat @ P7 @ ( produc5001842942810119800et_nat @ Q6 @ ( produc7507926704131184380et_nat @ H2 @ As ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7880_one__assn__raw_Ocases,axiom,
% 9.17/5.44 ! [X: produc3658429121746597890et_nat] :
% 9.17/5.44 ~ ! [H2: heap_e7401611519738050253t_unit,As: set_nat] :
% 9.17/5.44 ( X
% 9.17/5.44 != ( produc7507926704131184380et_nat @ H2 @ As ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7881_mod__star__conv,axiom,
% 9.17/5.44 ! [A2: assn,B5: assn,H3: produc3658429121746597890et_nat] :
% 9.17/5.44 ( ( rep_assn @ ( times_times_assn @ A2 @ B5 ) @ H3 )
% 9.17/5.44 = ( ? [Hr: heap_e7401611519738050253t_unit,As1: set_nat,As2: set_nat] :
% 9.17/5.44 ( ( H3
% 9.17/5.44 = ( produc7507926704131184380et_nat @ Hr @ ( sup_sup_set_nat @ As1 @ As2 ) ) )
% 9.17/5.44 & ( ( inf_inf_set_nat @ As1 @ As2 )
% 9.17/5.44 = bot_bot_set_nat )
% 9.17/5.44 & ( rep_assn @ A2 @ ( produc7507926704131184380et_nat @ Hr @ As1 ) )
% 9.17/5.44 & ( rep_assn @ B5 @ ( produc7507926704131184380et_nat @ Hr @ As2 ) ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7882_star__assnI,axiom,
% 9.17/5.44 ! [P: assn,H3: heap_e7401611519738050253t_unit,As3: set_nat,Q: assn,As4: set_nat] :
% 9.17/5.44 ( ( rep_assn @ P @ ( produc7507926704131184380et_nat @ H3 @ As3 ) )
% 9.17/5.44 => ( ( rep_assn @ Q @ ( produc7507926704131184380et_nat @ H3 @ As4 ) )
% 9.17/5.44 => ( ( ( inf_inf_set_nat @ As3 @ As4 )
% 9.17/5.44 = bot_bot_set_nat )
% 9.17/5.44 => ( rep_assn @ ( times_times_assn @ P @ Q ) @ ( produc7507926704131184380et_nat @ H3 @ ( sup_sup_set_nat @ As3 @ As4 ) ) ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7883_mod__emp__simp,axiom,
% 9.17/5.44 ! [H3: heap_e7401611519738050253t_unit] : ( rep_assn @ one_one_assn @ ( produc7507926704131184380et_nat @ H3 @ bot_bot_set_nat ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7884_mod__h__bot__indep,axiom,
% 9.17/5.44 ! [P: assn,H3: heap_e7401611519738050253t_unit,H5: heap_e7401611519738050253t_unit] :
% 9.17/5.44 ( ( rep_assn @ P @ ( produc7507926704131184380et_nat @ H3 @ bot_bot_set_nat ) )
% 9.17/5.44 = ( rep_assn @ P @ ( produc7507926704131184380et_nat @ H5 @ bot_bot_set_nat ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7885_times__assn__raw_Osimps,axiom,
% 9.17/5.44 ! [P: produc3658429121746597890et_nat > $o,Q: produc3658429121746597890et_nat > $o,H3: heap_e7401611519738050253t_unit,As3: set_nat] :
% 9.17/5.44 ( ( times_assn_raw @ P @ Q @ ( produc7507926704131184380et_nat @ H3 @ As3 ) )
% 9.17/5.44 = ( ? [As1: set_nat,As2: set_nat] :
% 9.17/5.44 ( ( As3
% 9.17/5.44 = ( sup_sup_set_nat @ As1 @ As2 ) )
% 9.17/5.44 & ( ( inf_inf_set_nat @ As1 @ As2 )
% 9.17/5.44 = bot_bot_set_nat )
% 9.17/5.44 & ( P @ ( produc7507926704131184380et_nat @ H3 @ As1 ) )
% 9.17/5.44 & ( Q @ ( produc7507926704131184380et_nat @ H3 @ As2 ) ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7886_times__assn__raw_Oelims_I3_J,axiom,
% 9.17/5.44 ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat] :
% 9.17/5.44 ( ~ ( times_assn_raw @ X @ Xa @ Xb )
% 9.17/5.44 => ~ ! [H2: heap_e7401611519738050253t_unit,As: set_nat] :
% 9.17/5.44 ( ( Xb
% 9.17/5.44 = ( produc7507926704131184380et_nat @ H2 @ As ) )
% 9.17/5.44 => ? [As12: set_nat,As22: set_nat] :
% 9.17/5.44 ( ( As
% 9.17/5.44 = ( sup_sup_set_nat @ As12 @ As22 ) )
% 9.17/5.44 & ( ( inf_inf_set_nat @ As12 @ As22 )
% 9.17/5.44 = bot_bot_set_nat )
% 9.17/5.44 & ( X @ ( produc7507926704131184380et_nat @ H2 @ As12 ) )
% 9.17/5.44 & ( Xa @ ( produc7507926704131184380et_nat @ H2 @ As22 ) ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7887_times__assn__raw_Oelims_I2_J,axiom,
% 9.17/5.44 ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat] :
% 9.17/5.44 ( ( times_assn_raw @ X @ Xa @ Xb )
% 9.17/5.44 => ~ ! [H2: heap_e7401611519738050253t_unit,As: set_nat] :
% 9.17/5.44 ( ( Xb
% 9.17/5.44 = ( produc7507926704131184380et_nat @ H2 @ As ) )
% 9.17/5.44 => ~ ? [As13: set_nat,As23: set_nat] :
% 9.17/5.44 ( ( As
% 9.17/5.44 = ( sup_sup_set_nat @ As13 @ As23 ) )
% 9.17/5.44 & ( ( inf_inf_set_nat @ As13 @ As23 )
% 9.17/5.44 = bot_bot_set_nat )
% 9.17/5.44 & ( X @ ( produc7507926704131184380et_nat @ H2 @ As13 ) )
% 9.17/5.44 & ( Xa @ ( produc7507926704131184380et_nat @ H2 @ As23 ) ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7888_times__assn__raw_Oelims_I1_J,axiom,
% 9.17/5.44 ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat,Y: $o] :
% 9.17/5.44 ( ( ( times_assn_raw @ X @ Xa @ Xb )
% 9.17/5.44 = Y )
% 9.17/5.44 => ~ ! [H2: heap_e7401611519738050253t_unit,As: set_nat] :
% 9.17/5.44 ( ( Xb
% 9.17/5.44 = ( produc7507926704131184380et_nat @ H2 @ As ) )
% 9.17/5.44 => ( Y
% 9.17/5.44 = ( ~ ? [As1: set_nat,As2: set_nat] :
% 9.17/5.44 ( ( As
% 9.17/5.44 = ( sup_sup_set_nat @ As1 @ As2 ) )
% 9.17/5.44 & ( ( inf_inf_set_nat @ As1 @ As2 )
% 9.17/5.44 = bot_bot_set_nat )
% 9.17/5.44 & ( X @ ( produc7507926704131184380et_nat @ H2 @ As1 ) )
% 9.17/5.44 & ( Xa @ ( produc7507926704131184380et_nat @ H2 @ As2 ) ) ) ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7889_times__assn__raw_Opelims_I1_J,axiom,
% 9.17/5.44 ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat,Y: $o] :
% 9.17/5.44 ( ( ( times_assn_raw @ X @ Xa @ Xb )
% 9.17/5.44 = Y )
% 9.17/5.44 => ( ( accp_P1862375125659990705et_nat @ times_assn_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ Xb ) ) )
% 9.17/5.44 => ~ ! [H2: heap_e7401611519738050253t_unit,As: set_nat] :
% 9.17/5.44 ( ( Xb
% 9.17/5.44 = ( produc7507926704131184380et_nat @ H2 @ As ) )
% 9.17/5.44 => ( ( Y
% 9.17/5.44 = ( ? [As1: set_nat,As2: set_nat] :
% 9.17/5.44 ( ( As
% 9.17/5.44 = ( sup_sup_set_nat @ As1 @ As2 ) )
% 9.17/5.44 & ( ( inf_inf_set_nat @ As1 @ As2 )
% 9.17/5.44 = bot_bot_set_nat )
% 9.17/5.44 & ( X @ ( produc7507926704131184380et_nat @ H2 @ As1 ) )
% 9.17/5.44 & ( Xa @ ( produc7507926704131184380et_nat @ H2 @ As2 ) ) ) ) )
% 9.17/5.44 => ~ ( accp_P1862375125659990705et_nat @ times_assn_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ ( produc7507926704131184380et_nat @ H2 @ As ) ) ) ) ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7890_times__assn__raw_Opelims_I2_J,axiom,
% 9.17/5.44 ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat] :
% 9.17/5.44 ( ( times_assn_raw @ X @ Xa @ Xb )
% 9.17/5.44 => ( ( accp_P1862375125659990705et_nat @ times_assn_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ Xb ) ) )
% 9.17/5.44 => ~ ! [H2: heap_e7401611519738050253t_unit,As: set_nat] :
% 9.17/5.44 ( ( Xb
% 9.17/5.44 = ( produc7507926704131184380et_nat @ H2 @ As ) )
% 9.17/5.44 => ( ( accp_P1862375125659990705et_nat @ times_assn_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ ( produc7507926704131184380et_nat @ H2 @ As ) ) ) )
% 9.17/5.44 => ~ ? [As13: set_nat,As23: set_nat] :
% 9.17/5.44 ( ( As
% 9.17/5.44 = ( sup_sup_set_nat @ As13 @ As23 ) )
% 9.17/5.44 & ( ( inf_inf_set_nat @ As13 @ As23 )
% 9.17/5.44 = bot_bot_set_nat )
% 9.17/5.44 & ( X @ ( produc7507926704131184380et_nat @ H2 @ As13 ) )
% 9.17/5.44 & ( Xa @ ( produc7507926704131184380et_nat @ H2 @ As23 ) ) ) ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7891_times__assn__raw_Opelims_I3_J,axiom,
% 9.17/5.44 ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat] :
% 9.17/5.44 ( ~ ( times_assn_raw @ X @ Xa @ Xb )
% 9.17/5.44 => ( ( accp_P1862375125659990705et_nat @ times_assn_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ Xb ) ) )
% 9.17/5.44 => ~ ! [H2: heap_e7401611519738050253t_unit,As: set_nat] :
% 9.17/5.44 ( ( Xb
% 9.17/5.44 = ( produc7507926704131184380et_nat @ H2 @ As ) )
% 9.17/5.44 => ( ( accp_P1862375125659990705et_nat @ times_assn_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ ( produc7507926704131184380et_nat @ H2 @ As ) ) ) )
% 9.17/5.44 => ? [As12: set_nat,As22: set_nat] :
% 9.17/5.44 ( ( As
% 9.17/5.44 = ( sup_sup_set_nat @ As12 @ As22 ) )
% 9.17/5.44 & ( ( inf_inf_set_nat @ As12 @ As22 )
% 9.17/5.44 = bot_bot_set_nat )
% 9.17/5.44 & ( X @ ( produc7507926704131184380et_nat @ H2 @ As12 ) )
% 9.17/5.44 & ( Xa @ ( produc7507926704131184380et_nat @ H2 @ As22 ) ) ) ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7892_mod__h__bot__iff_I1_J,axiom,
% 9.17/5.44 ! [B: $o,H3: heap_e7401611519738050253t_unit] :
% 9.17/5.44 ( ( rep_assn @ ( pure_assn @ B ) @ ( produc7507926704131184380et_nat @ H3 @ bot_bot_set_nat ) )
% 9.17/5.44 = B ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7893_mod__relH,axiom,
% 9.17/5.44 ! [As3: set_nat,H3: heap_e7401611519738050253t_unit,H5: heap_e7401611519738050253t_unit,P: assn] :
% 9.17/5.44 ( ( relH @ As3 @ H3 @ H5 )
% 9.17/5.44 => ( ( rep_assn @ P @ ( produc7507926704131184380et_nat @ H3 @ As3 ) )
% 9.17/5.44 = ( rep_assn @ P @ ( produc7507926704131184380et_nat @ H5 @ As3 ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7894_in__range__empty,axiom,
% 9.17/5.44 ! [H3: heap_e7401611519738050253t_unit] : ( in_range @ ( produc7507926704131184380et_nat @ H3 @ bot_bot_set_nat ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7895_in__range__dist__union,axiom,
% 9.17/5.44 ! [H3: heap_e7401611519738050253t_unit,As3: set_nat,As4: set_nat] :
% 9.17/5.44 ( ( in_range @ ( produc7507926704131184380et_nat @ H3 @ ( sup_sup_set_nat @ As3 @ As4 ) ) )
% 9.17/5.44 = ( ( in_range @ ( produc7507926704131184380et_nat @ H3 @ As3 ) )
% 9.17/5.44 & ( in_range @ ( produc7507926704131184380et_nat @ H3 @ As4 ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7896_relH__refl,axiom,
% 9.17/5.44 ! [H3: heap_e7401611519738050253t_unit,As3: set_nat] :
% 9.17/5.44 ( ( in_range @ ( produc7507926704131184380et_nat @ H3 @ As3 ) )
% 9.17/5.44 => ( relH @ As3 @ H3 @ H3 ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7897_relH__in__rangeI_I1_J,axiom,
% 9.17/5.44 ! [As3: set_nat,H3: heap_e7401611519738050253t_unit,H5: heap_e7401611519738050253t_unit] :
% 9.17/5.44 ( ( relH @ As3 @ H3 @ H5 )
% 9.17/5.44 => ( in_range @ ( produc7507926704131184380et_nat @ H3 @ As3 ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7898_relH__in__rangeI_I2_J,axiom,
% 9.17/5.44 ! [As3: set_nat,H3: heap_e7401611519738050253t_unit,H5: heap_e7401611519738050253t_unit] :
% 9.17/5.44 ( ( relH @ As3 @ H3 @ H5 )
% 9.17/5.44 => ( in_range @ ( produc7507926704131184380et_nat @ H5 @ As3 ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7899_in__range__subset,axiom,
% 9.17/5.44 ! [As3: set_nat,As4: set_nat,H3: heap_e7401611519738050253t_unit] :
% 9.17/5.44 ( ( ord_less_eq_set_nat @ As3 @ As4 )
% 9.17/5.44 => ( ( in_range @ ( produc7507926704131184380et_nat @ H3 @ As4 ) )
% 9.17/5.44 => ( in_range @ ( produc7507926704131184380et_nat @ H3 @ As3 ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7900_in__range_Oelims_I3_J,axiom,
% 9.17/5.44 ! [X: produc3658429121746597890et_nat] :
% 9.17/5.44 ( ~ ( in_range @ X )
% 9.17/5.44 => ~ ! [H2: heap_e7401611519738050253t_unit,As: set_nat] :
% 9.17/5.44 ( ( X
% 9.17/5.44 = ( produc7507926704131184380et_nat @ H2 @ As ) )
% 9.17/5.44 => ! [X4: nat] :
% 9.17/5.44 ( ( member_nat @ X4 @ As )
% 9.17/5.44 => ( ord_less_nat @ X4 @ ( lim_Product_unit @ H2 ) ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7901_in__range_Oelims_I2_J,axiom,
% 9.17/5.44 ! [X: produc3658429121746597890et_nat] :
% 9.17/5.44 ( ( in_range @ X )
% 9.17/5.44 => ~ ! [H2: heap_e7401611519738050253t_unit,As: set_nat] :
% 9.17/5.44 ( ( X
% 9.17/5.44 = ( produc7507926704131184380et_nat @ H2 @ As ) )
% 9.17/5.44 => ~ ! [X8: nat] :
% 9.17/5.44 ( ( member_nat @ X8 @ As )
% 9.17/5.44 => ( ord_less_nat @ X8 @ ( lim_Product_unit @ H2 ) ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7902_in__range_Oelims_I1_J,axiom,
% 9.17/5.44 ! [X: produc3658429121746597890et_nat,Y: $o] :
% 9.17/5.44 ( ( ( in_range @ X )
% 9.17/5.44 = Y )
% 9.17/5.44 => ~ ! [H2: heap_e7401611519738050253t_unit,As: set_nat] :
% 9.17/5.44 ( ( X
% 9.17/5.44 = ( produc7507926704131184380et_nat @ H2 @ As ) )
% 9.17/5.44 => ( Y
% 9.17/5.44 = ( ~ ! [X3: nat] :
% 9.17/5.44 ( ( member_nat @ X3 @ As )
% 9.17/5.44 => ( ord_less_nat @ X3 @ ( lim_Product_unit @ H2 ) ) ) ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7903_in__range_Osimps,axiom,
% 9.17/5.44 ! [H3: heap_e7401611519738050253t_unit,As3: set_nat] :
% 9.17/5.44 ( ( in_range @ ( produc7507926704131184380et_nat @ H3 @ As3 ) )
% 9.17/5.44 = ( ! [X3: nat] :
% 9.17/5.44 ( ( member_nat @ X3 @ As3 )
% 9.17/5.44 => ( ord_less_nat @ X3 @ ( lim_Product_unit @ H3 ) ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7904_wand__assnI,axiom,
% 9.17/5.44 ! [H3: heap_e7401611519738050253t_unit,As3: set_nat,Q: assn,R4: assn] :
% 9.17/5.44 ( ( in_range @ ( produc7507926704131184380et_nat @ H3 @ As3 ) )
% 9.17/5.44 => ( ! [H4: heap_e7401611519738050253t_unit,As5: set_nat] :
% 9.17/5.44 ( ( ( inf_inf_set_nat @ As3 @ As5 )
% 9.17/5.44 = bot_bot_set_nat )
% 9.17/5.44 => ( ( relH @ As3 @ H3 @ H4 )
% 9.17/5.44 => ( ( in_range @ ( produc7507926704131184380et_nat @ H4 @ As3 ) )
% 9.17/5.44 => ( ( rep_assn @ Q @ ( produc7507926704131184380et_nat @ H4 @ As5 ) )
% 9.17/5.44 => ( rep_assn @ R4 @ ( produc7507926704131184380et_nat @ H4 @ ( sup_sup_set_nat @ As3 @ As5 ) ) ) ) ) ) )
% 9.17/5.44 => ( rep_assn @ ( wand_assn @ Q @ R4 ) @ ( produc7507926704131184380et_nat @ H3 @ As3 ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7905_wand__raw_Osimps,axiom,
% 9.17/5.44 ! [P: produc3658429121746597890et_nat > $o,Q: produc3658429121746597890et_nat > $o,H3: heap_e7401611519738050253t_unit,As3: set_nat] :
% 9.17/5.44 ( ( wand_raw @ P @ Q @ ( produc7507926704131184380et_nat @ H3 @ As3 ) )
% 9.17/5.44 = ( ( in_range @ ( produc7507926704131184380et_nat @ H3 @ As3 ) )
% 9.17/5.44 & ! [H6: heap_e7401611519738050253t_unit,As6: set_nat] :
% 9.17/5.44 ( ( ( ( inf_inf_set_nat @ As3 @ As6 )
% 9.17/5.44 = bot_bot_set_nat )
% 9.17/5.44 & ( relH @ As3 @ H3 @ H6 )
% 9.17/5.44 & ( in_range @ ( produc7507926704131184380et_nat @ H6 @ As3 ) )
% 9.17/5.44 & ( P @ ( produc7507926704131184380et_nat @ H6 @ As6 ) ) )
% 9.17/5.44 => ( Q @ ( produc7507926704131184380et_nat @ H6 @ ( sup_sup_set_nat @ As3 @ As6 ) ) ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7906_wand__raw_Oelims_I1_J,axiom,
% 9.17/5.44 ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat,Y: $o] :
% 9.17/5.44 ( ( ( wand_raw @ X @ Xa @ Xb )
% 9.17/5.44 = Y )
% 9.17/5.44 => ~ ! [H2: heap_e7401611519738050253t_unit,As: set_nat] :
% 9.17/5.44 ( ( Xb
% 9.17/5.44 = ( produc7507926704131184380et_nat @ H2 @ As ) )
% 9.17/5.44 => ( Y
% 9.17/5.44 = ( ~ ( ( in_range @ ( produc7507926704131184380et_nat @ H2 @ As ) )
% 9.17/5.44 & ! [H6: heap_e7401611519738050253t_unit,As6: set_nat] :
% 9.17/5.44 ( ( ( ( inf_inf_set_nat @ As @ As6 )
% 9.17/5.44 = bot_bot_set_nat )
% 9.17/5.44 & ( relH @ As @ H2 @ H6 )
% 9.17/5.44 & ( in_range @ ( produc7507926704131184380et_nat @ H6 @ As ) )
% 9.17/5.44 & ( X @ ( produc7507926704131184380et_nat @ H6 @ As6 ) ) )
% 9.17/5.44 => ( Xa @ ( produc7507926704131184380et_nat @ H6 @ ( sup_sup_set_nat @ As @ As6 ) ) ) ) ) ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7907_wand__raw_Oelims_I3_J,axiom,
% 9.17/5.44 ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat] :
% 9.17/5.44 ( ~ ( wand_raw @ X @ Xa @ Xb )
% 9.17/5.44 => ~ ! [H2: heap_e7401611519738050253t_unit,As: set_nat] :
% 9.17/5.44 ( ( Xb
% 9.17/5.44 = ( produc7507926704131184380et_nat @ H2 @ As ) )
% 9.17/5.44 => ( ( in_range @ ( produc7507926704131184380et_nat @ H2 @ As ) )
% 9.17/5.44 & ! [H4: heap_e7401611519738050253t_unit,As5: set_nat] :
% 9.17/5.44 ( ( ( ( inf_inf_set_nat @ As @ As5 )
% 9.17/5.44 = bot_bot_set_nat )
% 9.17/5.44 & ( relH @ As @ H2 @ H4 )
% 9.17/5.44 & ( in_range @ ( produc7507926704131184380et_nat @ H4 @ As ) )
% 9.17/5.44 & ( X @ ( produc7507926704131184380et_nat @ H4 @ As5 ) ) )
% 9.17/5.44 => ( Xa @ ( produc7507926704131184380et_nat @ H4 @ ( sup_sup_set_nat @ As @ As5 ) ) ) ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7908_wand__raw_Oelims_I2_J,axiom,
% 9.17/5.44 ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat] :
% 9.17/5.44 ( ( wand_raw @ X @ Xa @ Xb )
% 9.17/5.44 => ~ ! [H2: heap_e7401611519738050253t_unit,As: set_nat] :
% 9.17/5.44 ( ( Xb
% 9.17/5.44 = ( produc7507926704131184380et_nat @ H2 @ As ) )
% 9.17/5.44 => ~ ( ( in_range @ ( produc7507926704131184380et_nat @ H2 @ As ) )
% 9.17/5.44 & ! [H8: heap_e7401611519738050253t_unit,As7: set_nat] :
% 9.17/5.44 ( ( ( ( inf_inf_set_nat @ As @ As7 )
% 9.17/5.44 = bot_bot_set_nat )
% 9.17/5.44 & ( relH @ As @ H2 @ H8 )
% 9.17/5.44 & ( in_range @ ( produc7507926704131184380et_nat @ H8 @ As ) )
% 9.17/5.44 & ( X @ ( produc7507926704131184380et_nat @ H8 @ As7 ) ) )
% 9.17/5.44 => ( Xa @ ( produc7507926704131184380et_nat @ H8 @ ( sup_sup_set_nat @ As @ As7 ) ) ) ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7909_wand__raw_Opelims_I3_J,axiom,
% 9.17/5.44 ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat] :
% 9.17/5.44 ( ~ ( wand_raw @ X @ Xa @ Xb )
% 9.17/5.44 => ( ( accp_P1862375125659990705et_nat @ wand_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ Xb ) ) )
% 9.17/5.44 => ~ ! [H2: heap_e7401611519738050253t_unit,As: set_nat] :
% 9.17/5.44 ( ( Xb
% 9.17/5.44 = ( produc7507926704131184380et_nat @ H2 @ As ) )
% 9.17/5.44 => ( ( accp_P1862375125659990705et_nat @ wand_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ ( produc7507926704131184380et_nat @ H2 @ As ) ) ) )
% 9.17/5.44 => ( ( in_range @ ( produc7507926704131184380et_nat @ H2 @ As ) )
% 9.17/5.44 & ! [H4: heap_e7401611519738050253t_unit,As5: set_nat] :
% 9.17/5.44 ( ( ( ( inf_inf_set_nat @ As @ As5 )
% 9.17/5.44 = bot_bot_set_nat )
% 9.17/5.44 & ( relH @ As @ H2 @ H4 )
% 9.17/5.44 & ( in_range @ ( produc7507926704131184380et_nat @ H4 @ As ) )
% 9.17/5.44 & ( X @ ( produc7507926704131184380et_nat @ H4 @ As5 ) ) )
% 9.17/5.44 => ( Xa @ ( produc7507926704131184380et_nat @ H4 @ ( sup_sup_set_nat @ As @ As5 ) ) ) ) ) ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7910_wand__raw_Opelims_I2_J,axiom,
% 9.17/5.44 ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat] :
% 9.17/5.44 ( ( wand_raw @ X @ Xa @ Xb )
% 9.17/5.44 => ( ( accp_P1862375125659990705et_nat @ wand_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ Xb ) ) )
% 9.17/5.44 => ~ ! [H2: heap_e7401611519738050253t_unit,As: set_nat] :
% 9.17/5.44 ( ( Xb
% 9.17/5.44 = ( produc7507926704131184380et_nat @ H2 @ As ) )
% 9.17/5.44 => ( ( accp_P1862375125659990705et_nat @ wand_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ ( produc7507926704131184380et_nat @ H2 @ As ) ) ) )
% 9.17/5.44 => ~ ( ( in_range @ ( produc7507926704131184380et_nat @ H2 @ As ) )
% 9.17/5.44 & ! [H8: heap_e7401611519738050253t_unit,As7: set_nat] :
% 9.17/5.44 ( ( ( ( inf_inf_set_nat @ As @ As7 )
% 9.17/5.44 = bot_bot_set_nat )
% 9.17/5.44 & ( relH @ As @ H2 @ H8 )
% 9.17/5.44 & ( in_range @ ( produc7507926704131184380et_nat @ H8 @ As ) )
% 9.17/5.44 & ( X @ ( produc7507926704131184380et_nat @ H8 @ As7 ) ) )
% 9.17/5.44 => ( Xa @ ( produc7507926704131184380et_nat @ H8 @ ( sup_sup_set_nat @ As @ As7 ) ) ) ) ) ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7911_wand__raw_Opelims_I1_J,axiom,
% 9.17/5.44 ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat,Y: $o] :
% 9.17/5.44 ( ( ( wand_raw @ X @ Xa @ Xb )
% 9.17/5.44 = Y )
% 9.17/5.44 => ( ( accp_P1862375125659990705et_nat @ wand_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ Xb ) ) )
% 9.17/5.44 => ~ ! [H2: heap_e7401611519738050253t_unit,As: set_nat] :
% 9.17/5.44 ( ( Xb
% 9.17/5.44 = ( produc7507926704131184380et_nat @ H2 @ As ) )
% 9.17/5.44 => ( ( Y
% 9.17/5.44 = ( ( in_range @ ( produc7507926704131184380et_nat @ H2 @ As ) )
% 9.17/5.44 & ! [H6: heap_e7401611519738050253t_unit,As6: set_nat] :
% 9.17/5.44 ( ( ( ( inf_inf_set_nat @ As @ As6 )
% 9.17/5.44 = bot_bot_set_nat )
% 9.17/5.44 & ( relH @ As @ H2 @ H6 )
% 9.17/5.44 & ( in_range @ ( produc7507926704131184380et_nat @ H6 @ As ) )
% 9.17/5.44 & ( X @ ( produc7507926704131184380et_nat @ H6 @ As6 ) ) )
% 9.17/5.44 => ( Xa @ ( produc7507926704131184380et_nat @ H6 @ ( sup_sup_set_nat @ As @ As6 ) ) ) ) ) )
% 9.17/5.44 => ~ ( accp_P1862375125659990705et_nat @ wand_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ ( produc7507926704131184380et_nat @ H2 @ As ) ) ) ) ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7912_in__range_Opelims_I3_J,axiom,
% 9.17/5.44 ! [X: produc3658429121746597890et_nat] :
% 9.17/5.44 ( ~ ( in_range @ X )
% 9.17/5.44 => ( ( accp_P5801069581201407417et_nat @ in_range_rel @ X )
% 9.17/5.44 => ~ ! [H2: heap_e7401611519738050253t_unit,As: set_nat] :
% 9.17/5.44 ( ( X
% 9.17/5.44 = ( produc7507926704131184380et_nat @ H2 @ As ) )
% 9.17/5.44 => ( ( accp_P5801069581201407417et_nat @ in_range_rel @ ( produc7507926704131184380et_nat @ H2 @ As ) )
% 9.17/5.44 => ! [X4: nat] :
% 9.17/5.44 ( ( member_nat @ X4 @ As )
% 9.17/5.44 => ( ord_less_nat @ X4 @ ( lim_Product_unit @ H2 ) ) ) ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7913_in__range_Opelims_I2_J,axiom,
% 9.17/5.44 ! [X: produc3658429121746597890et_nat] :
% 9.17/5.44 ( ( in_range @ X )
% 9.17/5.44 => ( ( accp_P5801069581201407417et_nat @ in_range_rel @ X )
% 9.17/5.44 => ~ ! [H2: heap_e7401611519738050253t_unit,As: set_nat] :
% 9.17/5.44 ( ( X
% 9.17/5.44 = ( produc7507926704131184380et_nat @ H2 @ As ) )
% 9.17/5.44 => ( ( accp_P5801069581201407417et_nat @ in_range_rel @ ( produc7507926704131184380et_nat @ H2 @ As ) )
% 9.17/5.44 => ~ ! [X8: nat] :
% 9.17/5.44 ( ( member_nat @ X8 @ As )
% 9.17/5.44 => ( ord_less_nat @ X8 @ ( lim_Product_unit @ H2 ) ) ) ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7914_in__range_Opelims_I1_J,axiom,
% 9.17/5.44 ! [X: produc3658429121746597890et_nat,Y: $o] :
% 9.17/5.44 ( ( ( in_range @ X )
% 9.17/5.44 = Y )
% 9.17/5.44 => ( ( accp_P5801069581201407417et_nat @ in_range_rel @ X )
% 9.17/5.44 => ~ ! [H2: heap_e7401611519738050253t_unit,As: set_nat] :
% 9.17/5.44 ( ( X
% 9.17/5.44 = ( produc7507926704131184380et_nat @ H2 @ As ) )
% 9.17/5.44 => ( ( Y
% 9.17/5.44 = ( ! [X3: nat] :
% 9.17/5.44 ( ( member_nat @ X3 @ As )
% 9.17/5.44 => ( ord_less_nat @ X3 @ ( lim_Product_unit @ H2 ) ) ) ) )
% 9.17/5.44 => ~ ( accp_P5801069581201407417et_nat @ in_range_rel @ ( produc7507926704131184380et_nat @ H2 @ As ) ) ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7915_one__assn__raw_Oelims_I3_J,axiom,
% 9.17/5.44 ! [X: produc3658429121746597890et_nat] :
% 9.17/5.44 ( ~ ( one_assn_raw @ X )
% 9.17/5.44 => ~ ! [H2: heap_e7401611519738050253t_unit,As: set_nat] :
% 9.17/5.44 ( ( X
% 9.17/5.44 = ( produc7507926704131184380et_nat @ H2 @ As ) )
% 9.17/5.44 => ( As = bot_bot_set_nat ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7916_one__assn__raw_Oelims_I2_J,axiom,
% 9.17/5.44 ! [X: produc3658429121746597890et_nat] :
% 9.17/5.44 ( ( one_assn_raw @ X )
% 9.17/5.44 => ~ ! [H2: heap_e7401611519738050253t_unit,As: set_nat] :
% 9.17/5.44 ( ( X
% 9.17/5.44 = ( produc7507926704131184380et_nat @ H2 @ As ) )
% 9.17/5.44 => ( As != bot_bot_set_nat ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7917_one__assn__raw_Oelims_I1_J,axiom,
% 9.17/5.44 ! [X: produc3658429121746597890et_nat,Y: $o] :
% 9.17/5.44 ( ( ( one_assn_raw @ X )
% 9.17/5.44 = Y )
% 9.17/5.44 => ~ ! [H2: heap_e7401611519738050253t_unit,As: set_nat] :
% 9.17/5.44 ( ( X
% 9.17/5.44 = ( produc7507926704131184380et_nat @ H2 @ As ) )
% 9.17/5.44 => ( Y
% 9.17/5.44 = ( As != bot_bot_set_nat ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7918_one__assn__raw_Osimps,axiom,
% 9.17/5.44 ! [H3: heap_e7401611519738050253t_unit,As3: set_nat] :
% 9.17/5.44 ( ( one_assn_raw @ ( produc7507926704131184380et_nat @ H3 @ As3 ) )
% 9.17/5.44 = ( As3 = bot_bot_set_nat ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7919_one__assn__raw_Opelims_I3_J,axiom,
% 9.17/5.44 ! [X: produc3658429121746597890et_nat] :
% 9.17/5.44 ( ~ ( one_assn_raw @ X )
% 9.17/5.44 => ( ( accp_P5801069581201407417et_nat @ one_assn_raw_rel @ X )
% 9.17/5.44 => ~ ! [H2: heap_e7401611519738050253t_unit,As: set_nat] :
% 9.17/5.44 ( ( X
% 9.17/5.44 = ( produc7507926704131184380et_nat @ H2 @ As ) )
% 9.17/5.44 => ( ( accp_P5801069581201407417et_nat @ one_assn_raw_rel @ ( produc7507926704131184380et_nat @ H2 @ As ) )
% 9.17/5.44 => ( As = bot_bot_set_nat ) ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7920_one__assn__raw_Opelims_I2_J,axiom,
% 9.17/5.44 ! [X: produc3658429121746597890et_nat] :
% 9.17/5.44 ( ( one_assn_raw @ X )
% 9.17/5.44 => ( ( accp_P5801069581201407417et_nat @ one_assn_raw_rel @ X )
% 9.17/5.44 => ~ ! [H2: heap_e7401611519738050253t_unit,As: set_nat] :
% 9.17/5.44 ( ( X
% 9.17/5.44 = ( produc7507926704131184380et_nat @ H2 @ As ) )
% 9.17/5.44 => ( ( accp_P5801069581201407417et_nat @ one_assn_raw_rel @ ( produc7507926704131184380et_nat @ H2 @ As ) )
% 9.17/5.44 => ( As != bot_bot_set_nat ) ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7921_one__assn__raw_Opelims_I1_J,axiom,
% 9.17/5.44 ! [X: produc3658429121746597890et_nat,Y: $o] :
% 9.17/5.44 ( ( ( one_assn_raw @ X )
% 9.17/5.44 = Y )
% 9.17/5.44 => ( ( accp_P5801069581201407417et_nat @ one_assn_raw_rel @ X )
% 9.17/5.44 => ~ ! [H2: heap_e7401611519738050253t_unit,As: set_nat] :
% 9.17/5.44 ( ( X
% 9.17/5.44 = ( produc7507926704131184380et_nat @ H2 @ As ) )
% 9.17/5.44 => ( ( Y
% 9.17/5.44 = ( As = bot_bot_set_nat ) )
% 9.17/5.44 => ~ ( accp_P5801069581201407417et_nat @ one_assn_raw_rel @ ( produc7507926704131184380et_nat @ H2 @ As ) ) ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7922_proper__iff,axiom,
% 9.17/5.44 ! [P: produc3658429121746597890et_nat > $o,As3: set_nat,H3: heap_e7401611519738050253t_unit,H5: heap_e7401611519738050253t_unit] :
% 9.17/5.44 ( ( proper @ P )
% 9.17/5.44 => ( ( relH @ As3 @ H3 @ H5 )
% 9.17/5.44 => ( ( in_range @ ( produc7507926704131184380et_nat @ H5 @ As3 ) )
% 9.17/5.44 => ( ( P @ ( produc7507926704131184380et_nat @ H3 @ As3 ) )
% 9.17/5.44 = ( P @ ( produc7507926704131184380et_nat @ H5 @ As3 ) ) ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7923_proper__def,axiom,
% 9.17/5.44 ( proper
% 9.17/5.44 = ( ^ [P3: produc3658429121746597890et_nat > $o] :
% 9.17/5.44 ! [H: heap_e7401611519738050253t_unit,H6: heap_e7401611519738050253t_unit,As8: set_nat] :
% 9.17/5.44 ( ( ( P3 @ ( produc7507926704131184380et_nat @ H @ As8 ) )
% 9.17/5.44 => ( in_range @ ( produc7507926704131184380et_nat @ H @ As8 ) ) )
% 9.17/5.44 & ( ( ( P3 @ ( produc7507926704131184380et_nat @ H @ As8 ) )
% 9.17/5.44 & ( relH @ As8 @ H @ H6 )
% 9.17/5.44 & ( in_range @ ( produc7507926704131184380et_nat @ H6 @ As8 ) ) )
% 9.17/5.44 => ( P3 @ ( produc7507926704131184380et_nat @ H6 @ As8 ) ) ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7924_properD2,axiom,
% 9.17/5.44 ! [P: produc3658429121746597890et_nat > $o,H3: heap_e7401611519738050253t_unit,As3: set_nat,H5: heap_e7401611519738050253t_unit] :
% 9.17/5.44 ( ( proper @ P )
% 9.17/5.44 => ( ( P @ ( produc7507926704131184380et_nat @ H3 @ As3 ) )
% 9.17/5.44 => ( ( relH @ As3 @ H3 @ H5 )
% 9.17/5.44 => ( ( in_range @ ( produc7507926704131184380et_nat @ H5 @ As3 ) )
% 9.17/5.44 => ( P @ ( produc7507926704131184380et_nat @ H5 @ As3 ) ) ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7925_properD1,axiom,
% 9.17/5.44 ! [P: produc3658429121746597890et_nat > $o,H3: heap_e7401611519738050253t_unit,As3: set_nat] :
% 9.17/5.44 ( ( proper @ P )
% 9.17/5.44 => ( ( P @ ( produc7507926704131184380et_nat @ H3 @ As3 ) )
% 9.17/5.44 => ( in_range @ ( produc7507926704131184380et_nat @ H3 @ As3 ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7926_properI,axiom,
% 9.17/5.44 ! [P: produc3658429121746597890et_nat > $o] :
% 9.17/5.44 ( ! [As: set_nat,H2: heap_e7401611519738050253t_unit] :
% 9.17/5.44 ( ( P @ ( produc7507926704131184380et_nat @ H2 @ As ) )
% 9.17/5.44 => ( in_range @ ( produc7507926704131184380et_nat @ H2 @ As ) ) )
% 9.17/5.44 => ( ! [As: set_nat,H2: heap_e7401611519738050253t_unit,H4: heap_e7401611519738050253t_unit] :
% 9.17/5.44 ( ( P @ ( produc7507926704131184380et_nat @ H2 @ As ) )
% 9.17/5.44 => ( ( relH @ As @ H2 @ H4 )
% 9.17/5.44 => ( ( in_range @ ( produc7507926704131184380et_nat @ H4 @ As ) )
% 9.17/5.44 => ( P @ ( produc7507926704131184380et_nat @ H4 @ As ) ) ) ) )
% 9.17/5.44 => ( proper @ P ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7927_Int_Osub__code_I8_J,axiom,
% 9.17/5.44 ! [M2: num,N2: num] :
% 9.17/5.44 ( ( sub @ ( bit1 @ M2 ) @ ( bit0 @ N2 ) )
% 9.17/5.44 = ( plus_plus_int @ ( dup @ ( sub @ M2 @ N2 ) ) @ one_one_int ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7928_Int_Odup__def,axiom,
% 9.17/5.44 ( dup
% 9.17/5.44 = ( ^ [K4: int] : ( plus_plus_int @ K4 @ K4 ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7929_relH__def,axiom,
% 9.17/5.44 ( relH
% 9.17/5.44 = ( ^ [As8: set_nat,H: heap_e7401611519738050253t_unit,H6: heap_e7401611519738050253t_unit] :
% 9.17/5.44 ( ( in_range @ ( produc7507926704131184380et_nat @ H @ As8 ) )
% 9.17/5.44 & ( in_range @ ( produc7507926704131184380et_nat @ H6 @ As8 ) )
% 9.17/5.44 & ! [T2: typerep,X3: nat] :
% 9.17/5.44 ( ( member_nat @ X3 @ As8 )
% 9.17/5.44 => ( ( ( refs_Product_unit @ H @ T2 @ X3 )
% 9.17/5.44 = ( refs_Product_unit @ H6 @ T2 @ X3 ) )
% 9.17/5.44 & ( ( arrays_Product_unit @ H @ T2 @ X3 )
% 9.17/5.44 = ( arrays_Product_unit @ H6 @ T2 @ X3 ) ) ) ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7930_plus__int__code_I6_J,axiom,
% 9.17/5.44 ! [M2: num,N2: num] :
% 9.17/5.44 ( ( plus_plus_int @ ( neg @ M2 ) @ ( neg @ N2 ) )
% 9.17/5.44 = ( neg @ ( plus_plus_num @ M2 @ N2 ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7931_plus__int__code_I5_J,axiom,
% 9.17/5.44 ! [M2: num,N2: num] :
% 9.17/5.44 ( ( plus_plus_int @ ( neg @ M2 ) @ ( pos @ N2 ) )
% 9.17/5.44 = ( sub @ N2 @ M2 ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7932_plus__int__code_I4_J,axiom,
% 9.17/5.44 ! [M2: num,N2: num] :
% 9.17/5.44 ( ( plus_plus_int @ ( pos @ M2 ) @ ( neg @ N2 ) )
% 9.17/5.44 = ( sub @ M2 @ N2 ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7933_minus__int__code_I4_J,axiom,
% 9.17/5.44 ! [M2: num,N2: num] :
% 9.17/5.44 ( ( minus_minus_int @ ( pos @ M2 ) @ ( neg @ N2 ) )
% 9.17/5.44 = ( pos @ ( plus_plus_num @ M2 @ N2 ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7934_plus__int__code_I3_J,axiom,
% 9.17/5.44 ! [M2: num,N2: num] :
% 9.17/5.44 ( ( plus_plus_int @ ( pos @ M2 ) @ ( pos @ N2 ) )
% 9.17/5.44 = ( pos @ ( plus_plus_num @ M2 @ N2 ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7935_minus__int__code_I5_J,axiom,
% 9.17/5.44 ! [M2: num,N2: num] :
% 9.17/5.44 ( ( minus_minus_int @ ( neg @ M2 ) @ ( pos @ N2 ) )
% 9.17/5.44 = ( neg @ ( plus_plus_num @ M2 @ N2 ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7936_Unity__def,axiom,
% 9.17/5.44 ( product_Unity
% 9.17/5.44 = ( product_Abs_unit @ $true ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7937_Abs__unit__inject,axiom,
% 9.17/5.44 ! [X: $o,Y: $o] :
% 9.17/5.44 ( ( member_o @ X @ ( insert_o @ $true @ bot_bot_set_o ) )
% 9.17/5.44 => ( ( member_o @ Y @ ( insert_o @ $true @ bot_bot_set_o ) )
% 9.17/5.44 => ( ( ( product_Abs_unit @ X )
% 9.17/5.44 = ( product_Abs_unit @ Y ) )
% 9.17/5.44 = ( X = Y ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7938_Abs__unit__induct,axiom,
% 9.17/5.44 ! [P: product_unit > $o,X: product_unit] :
% 9.17/5.44 ( ! [Y5: $o] :
% 9.17/5.44 ( ( member_o @ Y5 @ ( insert_o @ $true @ bot_bot_set_o ) )
% 9.17/5.44 => ( P @ ( product_Abs_unit @ Y5 ) ) )
% 9.17/5.44 => ( P @ X ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7939_Abs__unit__cases,axiom,
% 9.17/5.44 ! [X: product_unit] :
% 9.17/5.44 ~ ! [Y5: $o] :
% 9.17/5.44 ( ( X
% 9.17/5.44 = ( product_Abs_unit @ Y5 ) )
% 9.17/5.44 => ~ ( member_o @ Y5 @ ( insert_o @ $true @ bot_bot_set_o ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7940_integer_Odomain,axiom,
% 9.17/5.44 ! [P: int > $o] :
% 9.17/5.44 ( ( ( domainp_int_int
% 9.17/5.44 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 ) )
% 9.17/5.44 = P )
% 9.17/5.44 => ( ( domain452967906960104687nteger @ code_pcr_integer )
% 9.17/5.44 = P ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7941_natural_Odomain,axiom,
% 9.17/5.44 ! [P: nat > $o] :
% 9.17/5.44 ( ( ( domainp_nat_nat
% 9.17/5.44 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 ) )
% 9.17/5.44 = P )
% 9.17/5.44 => ( ( domain8128281535334753374atural @ code_pcr_natural )
% 9.17/5.44 = P ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7942_Abs__unit__inverse,axiom,
% 9.17/5.44 ! [Y: $o] :
% 9.17/5.44 ( ( member_o @ Y @ ( insert_o @ $true @ bot_bot_set_o ) )
% 9.17/5.44 => ( ( product_Rep_unit @ ( product_Abs_unit @ Y ) )
% 9.17/5.44 = Y ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7943_type__definition__unit,axiom,
% 9.17/5.44 type_d6188575255521822967unit_o @ product_Rep_unit @ product_Abs_unit @ ( insert_o @ $true @ bot_bot_set_o ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7944_Rep__unit__inverse,axiom,
% 9.17/5.44 ! [X: product_unit] :
% 9.17/5.44 ( ( product_Abs_unit @ ( product_Rep_unit @ X ) )
% 9.17/5.44 = X ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7945_Rep__unit__inject,axiom,
% 9.17/5.44 ! [X: product_unit,Y: product_unit] :
% 9.17/5.44 ( ( ( product_Rep_unit @ X )
% 9.17/5.44 = ( product_Rep_unit @ Y ) )
% 9.17/5.44 = ( X = Y ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7946_Rep__unit,axiom,
% 9.17/5.44 ! [X: product_unit] : ( member_o @ ( product_Rep_unit @ X ) @ ( insert_o @ $true @ bot_bot_set_o ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7947_Rep__unit__cases,axiom,
% 9.17/5.44 ! [Y: $o] :
% 9.17/5.44 ( ( member_o @ Y @ ( insert_o @ $true @ bot_bot_set_o ) )
% 9.17/5.44 => ~ ! [X4: product_unit] :
% 9.17/5.44 ( Y
% 9.17/5.44 = ( ~ ( product_Rep_unit @ X4 ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7948_Rep__unit__induct,axiom,
% 9.17/5.44 ! [Y: $o,P: $o > $o] :
% 9.17/5.44 ( ( member_o @ Y @ ( insert_o @ $true @ bot_bot_set_o ) )
% 9.17/5.44 => ( ! [X4: product_unit] : ( P @ ( product_Rep_unit @ X4 ) )
% 9.17/5.44 => ( P @ Y ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7949_positive__add,axiom,
% 9.17/5.44 ! [X: rat,Y: rat] :
% 9.17/5.44 ( ( positive @ X )
% 9.17/5.44 => ( ( positive @ Y )
% 9.17/5.44 => ( positive @ ( plus_plus_rat @ X @ Y ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(fact_7950_nth__item_Opinduct,axiom,
% 9.17/5.44 ! [A0: nat,P: nat > $o] :
% 9.17/5.44 ( ( accp_nat @ nth_item_rel @ A0 )
% 9.17/5.44 => ( ( ( accp_nat @ nth_item_rel @ zero_zero_nat )
% 9.17/5.44 => ( P @ zero_zero_nat ) )
% 9.17/5.44 => ( ! [N: nat] :
% 9.17/5.44 ( ( accp_nat @ nth_item_rel @ ( suc @ N ) )
% 9.17/5.44 => ( ! [A9: nat,Aa2: nat] :
% 9.17/5.44 ( ( ( nat_sum_decode @ N )
% 9.17/5.44 = ( sum_Inl_nat_nat @ A9 ) )
% 9.17/5.44 => ( ( ( nat_sum_decode @ A9 )
% 9.17/5.44 = ( sum_Inl_nat_nat @ Aa2 ) )
% 9.17/5.44 => ( P @ Aa2 ) ) )
% 9.17/5.44 => ( ! [A9: nat,B7: nat] :
% 9.17/5.44 ( ( ( nat_sum_decode @ N )
% 9.17/5.44 = ( sum_Inl_nat_nat @ A9 ) )
% 9.17/5.44 => ( ( ( nat_sum_decode @ A9 )
% 9.17/5.44 = ( sum_Inr_nat_nat @ B7 ) )
% 9.17/5.44 => ( P @ B7 ) ) )
% 9.17/5.44 => ( ! [B7: nat,Ba: nat,X8: nat,Y6: nat] :
% 9.17/5.44 ( ( ( nat_sum_decode @ N )
% 9.17/5.44 = ( sum_Inr_nat_nat @ B7 ) )
% 9.17/5.44 => ( ( ( nat_sum_decode @ B7 )
% 9.17/5.44 = ( sum_Inr_nat_nat @ Ba ) )
% 9.17/5.44 => ( ( ( product_Pair_nat_nat @ X8 @ Y6 )
% 9.17/5.44 = ( nat_prod_decode @ Ba ) )
% 9.17/5.44 => ( P @ X8 ) ) ) )
% 9.17/5.44 => ( ! [B7: nat,Ba: nat,X8: nat,Y6: nat] :
% 9.17/5.44 ( ( ( nat_sum_decode @ N )
% 9.17/5.44 = ( sum_Inr_nat_nat @ B7 ) )
% 9.17/5.44 => ( ( ( nat_sum_decode @ B7 )
% 9.17/5.44 = ( sum_Inr_nat_nat @ Ba ) )
% 9.17/5.44 => ( ( ( product_Pair_nat_nat @ X8 @ Y6 )
% 9.17/5.44 = ( nat_prod_decode @ Ba ) )
% 9.17/5.44 => ( P @ Y6 ) ) ) )
% 9.17/5.44 => ( P @ ( suc @ N ) ) ) ) ) ) )
% 9.17/5.44 => ( P @ A0 ) ) ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(help_If_2_1_If_001t__Int__Oint_T,axiom,
% 9.17/5.44 ! [X: int,Y: int] :
% 9.17/5.44 ( ( if_int @ $false @ X @ Y )
% 9.17/5.44 = Y ) ).
% 9.17/5.44
% 9.17/5.44 thf(help_If_1_1_If_001t__Int__Oint_T,axiom,
% 9.17/5.44 ! [X: int,Y: int] :
% 9.17/5.44 ( ( if_int @ $true @ X @ Y )
% 9.17/5.44 = X ) ).
% 9.17/5.44
% 9.17/5.44 thf(help_If_2_1_If_001t__Nat__Onat_T,axiom,
% 9.17/5.44 ! [X: nat,Y: nat] :
% 9.17/5.44 ( ( if_nat @ $false @ X @ Y )
% 9.17/5.44 = Y ) ).
% 9.17/5.44
% 9.17/5.44 thf(help_If_1_1_If_001t__Nat__Onat_T,axiom,
% 9.17/5.44 ! [X: nat,Y: nat] :
% 9.17/5.44 ( ( if_nat @ $true @ X @ Y )
% 9.17/5.44 = X ) ).
% 9.17/5.44
% 9.17/5.44 thf(help_If_2_1_If_001t__Num__Onum_T,axiom,
% 9.17/5.44 ! [X: num,Y: num] :
% 9.17/5.44 ( ( if_num @ $false @ X @ Y )
% 9.17/5.44 = Y ) ).
% 9.17/5.44
% 9.17/5.44 thf(help_If_1_1_If_001t__Num__Onum_T,axiom,
% 9.17/5.44 ! [X: num,Y: num] :
% 9.17/5.44 ( ( if_num @ $true @ X @ Y )
% 9.17/5.44 = X ) ).
% 9.17/5.44
% 9.17/5.44 thf(help_If_2_1_If_001t__Rat__Orat_T,axiom,
% 9.17/5.44 ! [X: rat,Y: rat] :
% 9.17/5.44 ( ( if_rat @ $false @ X @ Y )
% 9.17/5.44 = Y ) ).
% 9.17/5.44
% 9.17/5.44 thf(help_If_1_1_If_001t__Rat__Orat_T,axiom,
% 9.17/5.44 ! [X: rat,Y: rat] :
% 9.17/5.44 ( ( if_rat @ $true @ X @ Y )
% 9.17/5.44 = X ) ).
% 9.17/5.44
% 9.17/5.44 thf(help_If_2_1_If_001t__Assertions__Oassn_T,axiom,
% 9.17/5.44 ! [X: assn,Y: assn] :
% 9.17/5.44 ( ( if_assn @ $false @ X @ Y )
% 9.17/5.44 = Y ) ).
% 9.17/5.44
% 9.17/5.44 thf(help_If_1_1_If_001t__Assertions__Oassn_T,axiom,
% 9.17/5.44 ! [X: assn,Y: assn] :
% 9.17/5.44 ( ( if_assn @ $true @ X @ Y )
% 9.17/5.44 = X ) ).
% 9.17/5.44
% 9.17/5.44 thf(help_If_2_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 9.17/5.44 ! [X: code_integer,Y: code_integer] :
% 9.17/5.44 ( ( if_Code_integer @ $false @ X @ Y )
% 9.17/5.44 = Y ) ).
% 9.17/5.44
% 9.17/5.44 thf(help_If_1_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 9.17/5.44 ! [X: code_integer,Y: code_integer] :
% 9.17/5.44 ( ( if_Code_integer @ $true @ X @ Y )
% 9.17/5.44 = X ) ).
% 9.17/5.44
% 9.17/5.44 thf(help_If_2_1_If_001t__Code____Numeral__Onatural_T,axiom,
% 9.17/5.44 ! [X: code_natural,Y: code_natural] :
% 9.17/5.44 ( ( if_Code_natural @ $false @ X @ Y )
% 9.17/5.44 = Y ) ).
% 9.17/5.44
% 9.17/5.44 thf(help_If_1_1_If_001t__Code____Numeral__Onatural_T,axiom,
% 9.17/5.44 ! [X: code_natural,Y: code_natural] :
% 9.17/5.44 ( ( if_Code_natural @ $true @ X @ Y )
% 9.17/5.44 = X ) ).
% 9.17/5.44
% 9.17/5.44 thf(help_If_2_1_If_001t__Set__Oset_It__Int__Oint_J_T,axiom,
% 9.17/5.44 ! [X: set_int,Y: set_int] :
% 9.17/5.44 ( ( if_set_int @ $false @ X @ Y )
% 9.17/5.44 = Y ) ).
% 9.17/5.44
% 9.17/5.44 thf(help_If_1_1_If_001t__Set__Oset_It__Int__Oint_J_T,axiom,
% 9.17/5.44 ! [X: set_int,Y: set_int] :
% 9.17/5.44 ( ( if_set_int @ $true @ X @ Y )
% 9.17/5.44 = X ) ).
% 9.17/5.44
% 9.17/5.44 thf(help_If_2_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
% 9.17/5.44 ! [X: list_int,Y: list_int] :
% 9.17/5.44 ( ( if_list_int @ $false @ X @ Y )
% 9.17/5.44 = Y ) ).
% 9.17/5.44
% 9.17/5.44 thf(help_If_1_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
% 9.17/5.44 ! [X: list_int,Y: list_int] :
% 9.17/5.44 ( ( if_list_int @ $true @ X @ Y )
% 9.17/5.44 = X ) ).
% 9.17/5.44
% 9.17/5.44 thf(help_If_2_1_If_001t__Option__Ooption_It__Num__Onum_J_T,axiom,
% 9.17/5.44 ! [X: option_num,Y: option_num] :
% 9.17/5.44 ( ( if_option_num @ $false @ X @ Y )
% 9.17/5.44 = Y ) ).
% 9.17/5.44
% 9.17/5.44 thf(help_If_1_1_If_001t__Option__Ooption_It__Num__Onum_J_T,axiom,
% 9.17/5.44 ! [X: option_num,Y: option_num] :
% 9.17/5.44 ( ( if_option_num @ $true @ X @ Y )
% 9.17/5.44 = X ) ).
% 9.17/5.44
% 9.17/5.44 thf(help_If_2_1_If_001t__Option__Ooption_It__Set__Oset_I_Eo_J_J_T,axiom,
% 9.17/5.44 ! [X: option_set_o,Y: option_set_o] :
% 9.17/5.44 ( ( if_option_set_o @ $false @ X @ Y )
% 9.17/5.44 = Y ) ).
% 9.17/5.44
% 9.17/5.44 thf(help_If_1_1_If_001t__Option__Ooption_It__Set__Oset_I_Eo_J_J_T,axiom,
% 9.17/5.44 ! [X: option_set_o,Y: option_set_o] :
% 9.17/5.44 ( ( if_option_set_o @ $true @ X @ Y )
% 9.17/5.44 = X ) ).
% 9.17/5.44
% 9.17/5.44 thf(help_If_2_1_If_001t__Option__Ooption_It__Product____Type__Ounit_J_T,axiom,
% 9.17/5.44 ! [X: option_Product_unit,Y: option_Product_unit] :
% 9.17/5.44 ( ( if_opt6227717841141446553t_unit @ $false @ X @ Y )
% 9.17/5.44 = Y ) ).
% 9.17/5.44
% 9.17/5.44 thf(help_If_1_1_If_001t__Option__Ooption_It__Product____Type__Ounit_J_T,axiom,
% 9.17/5.44 ! [X: option_Product_unit,Y: option_Product_unit] :
% 9.17/5.44 ( ( if_opt6227717841141446553t_unit @ $true @ X @ Y )
% 9.17/5.44 = X ) ).
% 9.17/5.44
% 9.17/5.44 thf(help_If_2_1_If_001t__Option__Ooption_It__Set__Oset_It__Int__Oint_J_J_T,axiom,
% 9.17/5.44 ! [X: option_set_int,Y: option_set_int] :
% 9.17/5.44 ( ( if_option_set_int @ $false @ X @ Y )
% 9.17/5.44 = Y ) ).
% 9.17/5.44
% 9.17/5.44 thf(help_If_1_1_If_001t__Option__Ooption_It__Set__Oset_It__Int__Oint_J_J_T,axiom,
% 9.17/5.44 ! [X: option_set_int,Y: option_set_int] :
% 9.17/5.44 ( ( if_option_set_int @ $true @ X @ Y )
% 9.17/5.44 = X ) ).
% 9.17/5.44
% 9.17/5.44 thf(help_If_2_1_If_001t__Option__Ooption_It__Set__Oset_It__Nat__Onat_J_J_T,axiom,
% 9.17/5.44 ! [X: option_set_nat,Y: option_set_nat] :
% 9.17/5.44 ( ( if_option_set_nat @ $false @ X @ Y )
% 9.17/5.44 = Y ) ).
% 9.17/5.44
% 9.17/5.44 thf(help_If_1_1_If_001t__Option__Ooption_It__Set__Oset_It__Nat__Onat_J_J_T,axiom,
% 9.17/5.44 ! [X: option_set_nat,Y: option_set_nat] :
% 9.17/5.44 ( ( if_option_set_nat @ $true @ X @ Y )
% 9.17/5.44 = X ) ).
% 9.17/5.44
% 9.17/5.44 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 9.17/5.44 ! [X: product_prod_int_int,Y: product_prod_int_int] :
% 9.17/5.44 ( ( if_Pro3027730157355071871nt_int @ $false @ X @ Y )
% 9.17/5.44 = Y ) ).
% 9.17/5.44
% 9.17/5.44 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 9.17/5.44 ! [X: product_prod_int_int,Y: product_prod_int_int] :
% 9.17/5.44 ( ( if_Pro3027730157355071871nt_int @ $true @ X @ Y )
% 9.17/5.44 = X ) ).
% 9.17/5.44
% 9.17/5.44 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 9.17/5.44 ! [X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 9.17/5.44 ( ( if_Pro6206227464963214023at_nat @ $false @ X @ Y )
% 9.17/5.44 = Y ) ).
% 9.17/5.44
% 9.17/5.44 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 9.17/5.44 ! [X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 9.17/5.44 ( ( if_Pro6206227464963214023at_nat @ $true @ X @ Y )
% 9.17/5.44 = X ) ).
% 9.17/5.44
% 9.17/5.44 thf(help_If_2_1_If_001t__Heap____Time____Monad__OHeap_It__Heap__Oarray_Itf__a_J_J_T,axiom,
% 9.17/5.44 ! [X: heap_T6362127782908069795rray_a,Y: heap_T6362127782908069795rray_a] :
% 9.17/5.44 ( ( if_Hea5896630067203373929rray_a @ $false @ X @ Y )
% 9.17/5.44 = Y ) ).
% 9.17/5.44
% 9.17/5.44 thf(help_If_1_1_If_001t__Heap____Time____Monad__OHeap_It__Heap__Oarray_Itf__a_J_J_T,axiom,
% 9.17/5.44 ! [X: heap_T6362127782908069795rray_a,Y: heap_T6362127782908069795rray_a] :
% 9.17/5.44 ( ( if_Hea5896630067203373929rray_a @ $true @ X @ Y )
% 9.17/5.44 = X ) ).
% 9.17/5.44
% 9.17/5.44 thf(help_If_2_1_If_001t__Heap____Time____Monad__OHeap_It__Product____Type__Ounit_J_T,axiom,
% 9.17/5.44 ! [X: heap_T5738788834812785303t_unit,Y: heap_T5738788834812785303t_unit] :
% 9.17/5.44 ( ( if_Hea8138950348631371857t_unit @ $false @ X @ Y )
% 9.17/5.44 = Y ) ).
% 9.17/5.44
% 9.17/5.44 thf(help_If_1_1_If_001t__Heap____Time____Monad__OHeap_It__Product____Type__Ounit_J_T,axiom,
% 9.17/5.44 ! [X: heap_T5738788834812785303t_unit,Y: heap_T5738788834812785303t_unit] :
% 9.17/5.44 ( ( if_Hea8138950348631371857t_unit @ $true @ X @ Y )
% 9.17/5.44 = X ) ).
% 9.17/5.44
% 9.17/5.44 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J_T,axiom,
% 9.17/5.44 ! [X: produc6271795597528267376eger_o,Y: produc6271795597528267376eger_o] :
% 9.17/5.44 ( ( if_Pro5737122678794959658eger_o @ $false @ X @ Y )
% 9.17/5.44 = Y ) ).
% 9.17/5.44
% 9.17/5.44 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J_T,axiom,
% 9.17/5.44 ! [X: produc6271795597528267376eger_o,Y: produc6271795597528267376eger_o] :
% 9.17/5.44 ( ( if_Pro5737122678794959658eger_o @ $true @ X @ Y )
% 9.17/5.44 = X ) ).
% 9.17/5.44
% 9.17/5.44 thf(help_If_2_1_If_001t__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_T,axiom,
% 9.17/5.44 ! [X: multis2468970476368604999at_nat,Y: multis2468970476368604999at_nat] :
% 9.17/5.44 ( ( if_mul8430962117462786573at_nat @ $false @ X @ Y )
% 9.17/5.44 = Y ) ).
% 9.17/5.44
% 9.17/5.44 thf(help_If_1_1_If_001t__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_T,axiom,
% 9.17/5.44 ! [X: multis2468970476368604999at_nat,Y: multis2468970476368604999at_nat] :
% 9.17/5.44 ( ( if_mul8430962117462786573at_nat @ $true @ X @ Y )
% 9.17/5.44 = X ) ).
% 9.17/5.44
% 9.17/5.44 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 9.17/5.44 ! [X: produc8923325533196201883nteger,Y: produc8923325533196201883nteger] :
% 9.17/5.44 ( ( if_Pro6119634080678213985nteger @ $false @ X @ Y )
% 9.17/5.44 = Y ) ).
% 9.17/5.44
% 9.17/5.44 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 9.17/5.44 ! [X: produc8923325533196201883nteger,Y: produc8923325533196201883nteger] :
% 9.17/5.44 ( ( if_Pro6119634080678213985nteger @ $true @ X @ Y )
% 9.17/5.44 = X ) ).
% 9.17/5.44
% 9.17/5.44 thf(help_If_2_1_If_001t__Option__Ooption_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_T,axiom,
% 9.17/5.44 ! [X: option8963830502488799655at_nat,Y: option8963830502488799655at_nat] :
% 9.17/5.44 ( ( if_opt7704869406773131885at_nat @ $false @ X @ Y )
% 9.17/5.44 = Y ) ).
% 9.17/5.44
% 9.17/5.44 thf(help_If_1_1_If_001t__Option__Ooption_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_T,axiom,
% 9.17/5.44 ! [X: option8963830502488799655at_nat,Y: option8963830502488799655at_nat] :
% 9.17/5.44 ( ( if_opt7704869406773131885at_nat @ $true @ X @ Y )
% 9.17/5.44 = X ) ).
% 9.17/5.44
% 9.17/5.44 thf(help_If_2_1_If_001t__Option__Ooption_It__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_T,axiom,
% 9.17/5.44 ! [X: option3216581401566546698it_nat,Y: option3216581401566546698it_nat] :
% 9.17/5.44 ( ( if_opt7017092727090204112it_nat @ $false @ X @ Y )
% 9.17/5.44 = Y ) ).
% 9.17/5.44
% 9.17/5.44 thf(help_If_1_1_If_001t__Option__Ooption_It__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_T,axiom,
% 9.17/5.44 ! [X: option3216581401566546698it_nat,Y: option3216581401566546698it_nat] :
% 9.17/5.44 ( ( if_opt7017092727090204112it_nat @ $true @ X @ Y )
% 9.17/5.44 = X ) ).
% 9.17/5.44
% 9.17/5.44 thf(help_If_2_1_If_001t__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_T,axiom,
% 9.17/5.44 ! [X: option8956607266484857688it_nat,Y: option8956607266484857688it_nat] :
% 9.17/5.44 ( ( if_opt1729522071442692626it_nat @ $false @ X @ Y )
% 9.17/5.44 = Y ) ).
% 9.17/5.44
% 9.17/5.44 thf(help_If_1_1_If_001t__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_T,axiom,
% 9.17/5.44 ! [X: option8956607266484857688it_nat,Y: option8956607266484857688it_nat] :
% 9.17/5.44 ( ( if_opt1729522071442692626it_nat @ $true @ X @ Y )
% 9.17/5.44 = X ) ).
% 9.17/5.44
% 9.17/5.44 thf(help_If_3_1_If_001t__Option__Ooption_It__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J_T,axiom,
% 9.17/5.44 ! [P: $o] :
% 9.17/5.44 ( ( P = $true )
% 9.17/5.44 | ( P = $false ) ) ).
% 9.17/5.44
% 9.17/5.44 thf(help_If_2_1_If_001t__Option__Ooption_It__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J_T,axiom,
% 9.17/5.44 ! [X: option1583680563626158861at_nat,Y: option1583680563626158861at_nat] :
% 9.17/5.44 ( ( if_opt5121585740920863443at_nat @ $false @ X @ Y )
% 9.17/5.44 = Y ) ).
% 9.17/5.44
% 9.17/5.44 thf(help_If_1_1_If_001t__Option__Ooption_It__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J_T,axiom,
% 9.17/5.44 ! [X: option1583680563626158861at_nat,Y: option1583680563626158861at_nat] :
% 9.17/5.44 ( ( if_opt5121585740920863443at_nat @ $true @ X @ Y )
% 9.17/5.44 = X ) ).
% 9.17/5.44
% 9.17/5.44 thf(conj_0,conjecture,
% 9.17/5.44 ( ( heap_T5591663578999710211rray_a @ ( array_of_list_a @ xs ) @ h )
% 9.17/5.44 != none_P2587165478634041381it_nat ) ).
% 9.17/5.44 ------------------------
% 9.18/5.91 % (32743)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_32404 for (2995ds/4Mi)
% 9.18/5.91 % (32742)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_32404 for (2995ds/183Mi)
% 9.18/5.91 % (32745)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_32404 for (2995ds/2Mi)
% 9.18/5.91 % (32744)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_32404 for (2995ds/27Mi)
% 9.18/5.91 % (32746)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_32404 for (2995ds/2Mi)
% 9.18/5.91 % (32747)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_32404 for (2995ds/275Mi)
% 9.18/5.91 % (32748)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_32404 for (2995ds/18Mi)
% 9.18/5.91 % (32745)Instruction limit reached!
% 9.18/5.91 % (32745)------------------------------
% 9.18/5.91 % (32745)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.18/5.91 % (32745)Termination reason: Unknown
% 9.18/5.91 % (32745)Termination phase: shuffling
% 9.18/5.91
% 9.18/5.91 % (32745)Memory used [KB]: 13432
% 9.18/5.91 % (32745)Time elapsed: 0.003 s
% 9.18/5.91 % (32745)Instructions burned: 2 (million)
% 9.18/5.91 % (32745)------------------------------
% 9.18/5.91 % (32745)------------------------------
% 9.18/5.92 % (32746)Instruction limit reached!
% 9.18/5.92 % (32746)------------------------------
% 9.18/5.92 % (32746)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.18/5.92 % (32746)Termination reason: Unknown
% 9.18/5.92 % (32746)Termination phase: shuffling
% 9.18/5.92
% 9.18/5.92 % (32746)Memory used [KB]: 13432
% 9.18/5.92 % (32746)Time elapsed: 0.004 s
% 9.18/5.92 % (32746)Instructions burned: 2 (million)
% 9.18/5.92 % (32746)------------------------------
% 9.18/5.92 % (32746)------------------------------
% 9.18/5.92 % (32743)Instruction limit reached!
% 9.18/5.92 % (32743)------------------------------
% 9.18/5.92 % (32743)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.18/5.92 % (32743)Termination reason: Unknown
% 9.18/5.92 % (32743)Termination phase: shuffling
% 9.18/5.92
% 9.18/5.92 % (32743)Memory used [KB]: 13560
% 9.18/5.92 % (32743)Time elapsed: 0.007 s
% 9.18/5.92 % (32743)Instructions burned: 4 (million)
% 9.18/5.92 % (32743)------------------------------
% 9.18/5.92 % (32743)------------------------------
% 9.18/5.93 % (32748)Instruction limit reached!
% 9.18/5.93 % (32748)------------------------------
% 9.18/5.93 % (32748)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.18/5.93 % (32748)Termination reason: Unknown
% 9.18/5.93 % (32748)Termination phase: shuffling
% 9.18/5.93
% 9.18/5.93 % (32748)Memory used [KB]: 14200
% 9.18/5.93 % (32748)Time elapsed: 0.023 s
% 9.18/5.93 % (32748)Instructions burned: 18 (million)
% 9.18/5.93 % (32748)------------------------------
% 9.18/5.93 % (32748)------------------------------
% 9.18/5.94 % (32749)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_32404 for (2995ds/3Mi)
% 9.18/5.94 % (32750)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_32404 for (2995ds/37Mi)
% 9.18/5.94 % (32749)Instruction limit reached!
% 9.18/5.94 % (32749)------------------------------
% 9.18/5.94 % (32749)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.18/5.94 % (32749)Termination reason: Unknown
% 9.18/5.94 % (32749)Termination phase: shuffling
% 9.18/5.94
% 9.18/5.94 % (32749)Memory used [KB]: 13560
% 9.18/5.94 % (32749)Time elapsed: 0.005 s
% 9.18/5.94 % (32749)Instructions burned: 3 (million)
% 9.18/5.94 % (32749)------------------------------
% 9.18/5.94 % (32749)------------------------------
% 9.18/5.94 % (32751)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_32404 for (2995ds/15Mi)
% 9.18/5.94 % (32744)Instruction limit reached!
% 9.18/5.94 % (32744)------------------------------
% 9.18/5.94 % (32744)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.18/5.94 % (32744)Termination reason: Unknown
% 9.18/5.94 % (32744)Termination phase: shuffling
% 9.18/5.94
% 9.18/5.94 % (32744)Memory used [KB]: 14328
% 9.18/5.94 % (32744)Time elapsed: 0.028 s
% 9.18/5.94 % (32744)Instructions burned: 27 (million)
% 9.18/5.94 % (32744)------------------------------
% 9.18/5.94 % (32744)------------------------------
% 9.18/5.96 % (32752)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_32404 for (2995ds/3Mi)
% 9.18/5.96 % (32751)Instruction limit reached!
% 9.18/5.96 % (32751)------------------------------
% 9.18/5.96 % (32751)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.18/5.96 % (32751)Termination reason: Unknown
% 9.18/5.96 % (32751)Termination phase: shuffling
% 9.18/5.96
% 9.18/5.96 % (32751)Memory used [KB]: 14200
% 9.18/5.96 % (32751)Time elapsed: 0.021 s
% 9.18/5.96 % (32751)Instructions burned: 15 (million)
% 9.18/5.96 % (32751)------------------------------
% 9.18/5.96 % (32751)------------------------------
% 9.18/5.96 % (32753)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_32404 for (2995ds/1041Mi)
% 9.18/5.96 % (32752)Instruction limit reached!
% 9.18/5.96 % (32752)------------------------------
% 9.18/5.96 % (32752)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.18/5.96 % (32752)Termination reason: Unknown
% 9.18/5.96 % (32752)Termination phase: shuffling
% 9.18/5.96
% 9.18/5.96 % (32752)Memory used [KB]: 13560
% 9.18/5.96 % (32752)Time elapsed: 0.006 s
% 9.18/5.96 % (32752)Instructions burned: 3 (million)
% 9.18/5.96 % (32752)------------------------------
% 9.18/5.96 % (32752)------------------------------
% 9.18/5.96 % (32754)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_32404 for (2995ds/7Mi)
% 9.18/5.97 % (32750)Instruction limit reached!
% 9.18/5.97 % (32750)------------------------------
% 9.18/5.97 % (32750)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.18/5.97 % (32750)Termination reason: Unknown
% 9.18/5.97 % (32750)Termination phase: shuffling
% 9.18/5.97
% 9.18/5.97 % (32750)Memory used [KB]: 14583
% 9.18/5.97 % (32750)Time elapsed: 0.033 s
% 9.18/5.97 % (32750)Instructions burned: 38 (million)
% 9.18/5.97 % (32750)------------------------------
% 9.18/5.97 % (32750)------------------------------
% 9.18/5.97 % (32754)Instruction limit reached!
% 9.18/5.97 % (32754)------------------------------
% 9.18/5.97 % (32754)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.18/5.97 % (32754)Termination reason: Unknown
% 9.18/5.97 % (32754)Termination phase: shuffling
% 9.18/5.97
% 9.18/5.97 % (32754)Memory used [KB]: 13816
% 9.18/5.97 % (32754)Time elapsed: 0.012 s
% 9.18/5.97 % (32754)Instructions burned: 7 (million)
% 9.18/5.97 % (32754)------------------------------
% 9.18/5.97 % (32754)------------------------------
% 9.18/5.98 % (32755)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_32404 for (2994ds/16Mi)
% 9.18/5.98 % (32756)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_32404 for (2994ds/3Mi)
% 9.18/5.98 % (32756)Instruction limit reached!
% 9.18/5.98 % (32756)------------------------------
% 9.18/5.98 % (32756)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.18/5.98 % (32756)Termination reason: Unknown
% 9.18/5.98 % (32756)Termination phase: shuffling
% 9.18/5.98
% 9.18/5.98 % (32756)Memory used [KB]: 13560
% 9.18/5.98 % (32756)Time elapsed: 0.005 s
% 9.18/5.98 % (32756)Instructions burned: 3 (million)
% 9.18/5.98 % (32756)------------------------------
% 9.18/5.98 % (32756)------------------------------
% 9.18/5.99 % (32757)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_32404 for (2994ds/3Mi)
% 9.18/5.99 % (32757)Instruction limit reached!
% 9.18/5.99 % (32757)------------------------------
% 9.18/5.99 % (32757)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.18/5.99 % (32757)Termination reason: Unknown
% 9.18/5.99 % (32757)Termination phase: shuffling
% 9.18/5.99
% 9.18/5.99 % (32757)Memory used [KB]: 13560
% 9.18/5.99 % (32757)Time elapsed: 0.006 s
% 9.18/5.99 % (32757)Instructions burned: 3 (million)
% 9.18/5.99 % (32757)------------------------------
% 9.18/5.99 % (32757)------------------------------
% 9.18/5.99 % (32758)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_32404 for (2994ds/7Mi)
% 9.18/6.00 % (32755)Instruction limit reached!
% 9.18/6.00 % (32755)------------------------------
% 9.18/6.00 % (32755)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.18/6.00 % (32755)Termination reason: Unknown
% 9.18/6.00 % (32755)Termination phase: shuffling
% 9.18/6.00
% 9.18/6.00 % (32755)Memory used [KB]: 14200
% 9.18/6.00 % (32755)Time elapsed: 0.021 s
% 9.18/6.00 % (32755)Instructions burned: 17 (million)
% 9.18/6.00 % (32755)------------------------------
% 9.18/6.00 % (32755)------------------------------
% 9.18/6.00 % (32758)Instruction limit reached!
% 9.18/6.00 % (32758)------------------------------
% 9.18/6.00 % (32758)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.18/6.00 % (32758)Termination reason: Unknown
% 9.18/6.00 % (32758)Termination phase: shuffling
% 9.18/6.00
% 9.18/6.00 % (32758)Memory used [KB]: 13816
% 9.18/6.00 % (32758)Time elapsed: 0.011 s
% 9.18/6.00 % (32758)Instructions burned: 7 (million)
% 9.18/6.00 % (32758)------------------------------
% 9.18/6.00 % (32758)------------------------------
% 9.18/6.00 % (32759)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_32404 for (2994ds/3Mi)
% 9.18/6.00 % (32759)Instruction limit reached!
% 9.18/6.00 % (32759)------------------------------
% 9.18/6.00 % (32759)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.18/6.00 % (32759)Termination reason: Unknown
% 9.18/6.00 % (32759)Termination phase: shuffling
% 9.18/6.00
% 9.18/6.00 % (32759)Memory used [KB]: 13560
% 9.18/6.00 % (32759)Time elapsed: 0.005 s
% 9.18/6.00 % (32759)Instructions burned: 3 (million)
% 9.18/6.00 % (32759)------------------------------
% 9.18/6.00 % (32759)------------------------------
% 9.18/6.01 % (32760)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_32404 for (2994ds/4Mi)
% 9.18/6.01 % (32761)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_32404 for (2994ds/18Mi)
% 9.18/6.01 % (32762)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_32404 for (2994ds/710Mi)
% 9.18/6.01 % (32760)Instruction limit reached!
% 9.18/6.01 % (32760)------------------------------
% 9.18/6.01 % (32760)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.18/6.01 % (32760)Termination reason: Unknown
% 9.18/6.01 % (32760)Termination phase: shuffling
% 9.18/6.01
% 9.18/6.01 % (32760)Memory used [KB]: 13560
% 9.18/6.01 % (32760)Time elapsed: 0.005 s
% 9.18/6.01 % (32760)Instructions burned: 4 (million)
% 9.18/6.01 % (32760)------------------------------
% 9.18/6.01 % (32760)------------------------------
% 10.40/6.02 % (32763)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_32404 for (2994ds/6Mi)
% 10.40/6.02 % (32763)Instruction limit reached!
% 10.40/6.02 % (32763)------------------------------
% 10.40/6.02 % (32763)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.40/6.02 % (32763)Termination reason: Unknown
% 10.40/6.02 % (32763)Termination phase: shuffling
% 10.40/6.02
% 10.40/6.02 % (32763)Memory used [KB]: 13688
% 10.40/6.02 % (32763)Time elapsed: 0.007 s
% 10.40/6.02 % (32763)Instructions burned: 6 (million)
% 10.40/6.02 % (32763)------------------------------
% 10.40/6.02 % (32763)------------------------------
% 10.40/6.02 % (32761)Instruction limit reached!
% 10.40/6.02 % (32761)------------------------------
% 10.40/6.02 % (32761)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.40/6.02 % (32761)Termination reason: Unknown
% 10.40/6.02 % (32761)Termination phase: shuffling
% 10.40/6.02
% 10.40/6.02 % (32761)Memory used [KB]: 14200
% 10.40/6.02 % (32761)Time elapsed: 0.014 s
% 10.40/6.02 % (32761)Instructions burned: 18 (million)
% 10.40/6.02 % (32761)------------------------------
% 10.40/6.02 % (32761)------------------------------
% 10.40/6.02 % (32742)Instruction limit reached!
% 10.40/6.02 % (32742)------------------------------
% 10.40/6.02 % (32742)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.40/6.02 % (32742)Termination reason: Unknown
% 10.40/6.02 % (32742)Termination phase: shuffling
% 10.40/6.02
% 10.40/6.02 % (32742)Memory used [KB]: 16375
% 10.40/6.02 % (32742)Time elapsed: 0.112 s
% 10.40/6.02 % (32742)Instructions burned: 183 (million)
% 10.40/6.02 % (32742)------------------------------
% 10.40/6.02 % (32742)------------------------------
% 10.40/6.02 % (32764)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_32404 for (2994ds/902Mi)
% 10.40/6.04 % (32766)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_32404 for (2994ds/5Mi)
% 10.40/6.04 % (32765)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_32404 for (2994ds/21Mi)
% 10.40/6.04 % (32767)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_32404 for (2994ds/6Mi)
% 10.40/6.04 % (32766)Instruction limit reached!
% 10.40/6.04 % (32766)------------------------------
% 10.40/6.04 % (32766)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.40/6.04 % (32766)Termination reason: Unknown
% 10.40/6.04 % (32766)Termination phase: shuffling
% 10.40/6.04
% 10.40/6.04 % (32766)Memory used [KB]: 13688
% 10.40/6.04 % (32766)Time elapsed: 0.006 s
% 10.40/6.04 % (32766)Instructions burned: 5 (million)
% 10.40/6.04 % (32766)------------------------------
% 10.40/6.04 % (32766)------------------------------
% 10.40/6.04 % (32767)Instruction limit reached!
% 10.40/6.04 % (32767)------------------------------
% 10.40/6.04 % (32767)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.40/6.04 % (32767)Termination reason: Unknown
% 10.40/6.04 % (32767)Termination phase: shuffling
% 10.40/6.04
% 10.40/6.04 % (32767)Memory used [KB]: 13816
% 10.40/6.04 % (32767)Time elapsed: 0.007 s
% 10.40/6.04 % (32767)Instructions burned: 6 (million)
% 10.40/6.04 % (32767)------------------------------
% 10.40/6.04 % (32767)------------------------------
% 10.40/6.05 % (32765)Instruction limit reached!
% 10.40/6.05 % (32765)------------------------------
% 10.40/6.05 % (32765)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.40/6.05 % (32765)Termination reason: Unknown
% 10.40/6.05 % (32765)Termination phase: shuffling
% 10.40/6.05
% 10.40/6.05 % (32765)Memory used [KB]: 14200
% 10.40/6.05 % (32765)Time elapsed: 0.016 s
% 10.40/6.05 % (32765)Instructions burned: 22 (million)
% 10.40/6.05 % (32765)------------------------------
% 10.40/6.05 % (32765)------------------------------
% 10.40/6.05 % (300)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_32404 for (2993ds/377Mi)
% 10.40/6.05 % (301)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_32404 for (2993ds/779Mi)
% 10.40/6.06 % (32747)Instruction limit reached!
% 10.40/6.06 % (32747)------------------------------
% 10.40/6.06 % (32747)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.40/6.06 % (32747)Termination reason: Unknown
% 10.40/6.06 % (32747)Termination phase: shuffling
% 10.40/6.06
% 10.40/6.06 % (32747)Memory used [KB]: 17654
% 10.40/6.06 % (32747)Time elapsed: 0.144 s
% 10.40/6.06 % (32747)Instructions burned: 276 (million)
% 10.40/6.06 % (32747)------------------------------
% 10.40/6.06 % (32747)------------------------------
% 10.40/6.06 % (302)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_32404 for (2993ds/19Mi)
% 10.40/6.07 % (303)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_32404 for (2993ds/879Mi)
% 10.40/6.08 % (302)Instruction limit reached!
% 10.40/6.08 % (302)------------------------------
% 10.40/6.08 % (302)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.40/6.08 % (302)Termination reason: Unknown
% 10.40/6.08 % (302)Termination phase: shuffling
% 10.40/6.08
% 10.40/6.08 % (302)Memory used [KB]: 14328
% 10.40/6.08 % (302)Time elapsed: 0.016 s
% 10.40/6.08 % (302)Instructions burned: 21 (million)
% 10.40/6.08 % (302)------------------------------
% 10.40/6.08 % (302)------------------------------
% 10.40/6.09 % (304)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_32404 for (2993ds/17Mi)
% 10.40/6.10 % (304)Instruction limit reached!
% 10.40/6.10 % (304)------------------------------
% 10.40/6.10 % (304)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.40/6.10 % (304)Termination reason: Unknown
% 10.40/6.10 % (304)Termination phase: shuffling
% 10.40/6.10
% 10.40/6.10 % (304)Memory used [KB]: 14200
% 10.40/6.10 % (304)Time elapsed: 0.015 s
% 10.40/6.10 % (304)Instructions burned: 18 (million)
% 10.40/6.10 % (304)------------------------------
% 10.40/6.10 % (304)------------------------------
% 10.40/6.12 % (305)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_32404 for (2993ds/3Mi)
% 10.72/6.12 % (305)Instruction limit reached!
% 10.72/6.12 % (305)------------------------------
% 10.72/6.12 % (305)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.72/6.12 % (305)Termination reason: Unknown
% 10.72/6.12 % (305)Termination phase: shuffling
% 10.72/6.12
% 10.72/6.12 % (305)Memory used [KB]: 13560
% 10.72/6.12 % (305)Time elapsed: 0.004 s
% 10.72/6.12 % (305)Instructions burned: 3 (million)
% 10.72/6.12 % (305)------------------------------
% 10.72/6.12 % (305)------------------------------
% 10.72/6.13 % (306)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_32404 for (2993ds/30Mi)
% 10.72/6.15 % (306)Instruction limit reached!
% 10.72/6.15 % (306)------------------------------
% 10.72/6.15 % (306)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.72/6.15 % (306)Termination reason: Unknown
% 10.72/6.15 % (306)Termination phase: shuffling
% 10.72/6.15
% 10.72/6.15 % (306)Memory used [KB]: 14456
% 10.72/6.15 % (306)Time elapsed: 0.019 s
% 10.72/6.15 % (306)Instructions burned: 30 (million)
% 10.72/6.15 % (306)------------------------------
% 10.72/6.15 % (306)------------------------------
% 10.72/6.16 % (307)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_32404 for (2992ds/127Mi)
% 10.72/6.19 % (300)Instruction limit reached!
% 10.72/6.19 % (300)------------------------------
% 10.72/6.19 % (300)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.72/6.19 % (300)Termination reason: Unknown
% 10.72/6.19 % (300)Termination phase: shuffling
% 10.72/6.19
% 10.72/6.19 % (300)Memory used [KB]: 18933
% 10.72/6.19 % (300)Time elapsed: 0.138 s
% 10.72/6.19 % (300)Instructions burned: 379 (million)
% 10.72/6.19 % (300)------------------------------
% 10.72/6.19 % (300)------------------------------
% 11.02/6.20 % (308)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_32404 for (2992ds/100Mi)
% 11.02/6.22 % (307)Instruction limit reached!
% 11.02/6.22 % (307)------------------------------
% 11.02/6.22 % (307)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.02/6.22 % (307)Termination reason: Unknown
% 11.02/6.22 % (307)Termination phase: shuffling
% 11.02/6.22
% 11.02/6.22 % (307)Memory used [KB]: 15607
% 11.02/6.22 % (307)Time elapsed: 0.054 s
% 11.02/6.22 % (307)Instructions burned: 127 (million)
% 11.02/6.22 % (307)------------------------------
% 11.02/6.22 % (307)------------------------------
% 11.02/6.23 % (309)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_32404 for (2992ds/3Mi)
% 11.02/6.23 % (309)Instruction limit reached!
% 11.02/6.23 % (309)------------------------------
% 11.02/6.23 % (309)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.02/6.23 % (309)Termination reason: Unknown
% 11.02/6.23 % (309)Termination phase: shuffling
% 11.02/6.23
% 11.02/6.23 % (309)Memory used [KB]: 13560
% 11.02/6.23 % (309)Time elapsed: 0.004 s
% 11.02/6.23 % (309)Instructions burned: 3 (million)
% 11.02/6.23 % (309)------------------------------
% 11.02/6.23 % (309)------------------------------
% 11.02/6.24 % (308)Instruction limit reached!
% 11.02/6.24 % (308)------------------------------
% 11.02/6.24 % (308)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.02/6.24 % (308)Termination reason: Unknown
% 11.02/6.24 % (308)Termination phase: shuffling
% 11.02/6.24
% 11.02/6.24 % (308)Memory used [KB]: 15351
% 11.02/6.24 % (308)Time elapsed: 0.036 s
% 11.02/6.24 % (308)Instructions burned: 100 (million)
% 11.02/6.24 % (308)------------------------------
% 11.02/6.24 % (308)------------------------------
% 11.02/6.24 % (310)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_32404 for (2992ds/20Mi)
% 11.02/6.25 % (311)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_32404 for (2992ds/86Mi)
% 11.02/6.26 % (310)Instruction limit reached!
% 11.02/6.26 % (310)------------------------------
% 11.02/6.26 % (310)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.02/6.26 % (310)Termination reason: Unknown
% 11.02/6.26 % (310)Termination phase: shuffling
% 11.02/6.26
% 11.02/6.26 % (310)Memory used [KB]: 14328
% 11.02/6.26 % (310)Time elapsed: 0.016 s
% 11.02/6.26 % (310)Instructions burned: 21 (million)
% 11.02/6.26 % (310)------------------------------
% 11.02/6.26 % (310)------------------------------
% 11.02/6.26 % (32762)Instruction limit reached!
% 11.02/6.26 % (32762)------------------------------
% 11.02/6.26 % (32762)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.02/6.26 % (32762)Termination reason: Unknown
% 11.02/6.26 % (32762)Termination phase: Property scanning
% 11.02/6.26
% 11.02/6.26 % (32762)Memory used [KB]: 24434
% 11.02/6.26 % (32762)Time elapsed: 0.254 s
% 11.02/6.26 % (32762)Instructions burned: 711 (million)
% 11.02/6.26 % (32762)------------------------------
% 11.02/6.26 % (32762)------------------------------
% 11.02/6.27 % (312)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_32404 for (2991ds/107Mi)
% 11.02/6.28 % (313)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_32404 for (2991ds/39Mi)
% 11.02/6.28 % (311)Instruction limit reached!
% 11.02/6.28 % (311)------------------------------
% 11.02/6.28 % (311)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.02/6.28 % (311)Termination reason: Unknown
% 11.02/6.28 % (311)Termination phase: shuffling
% 11.02/6.28
% 11.02/6.28 % (311)Memory used [KB]: 14967
% 11.02/6.28 % (311)Time elapsed: 0.036 s
% 11.02/6.28 % (311)Instructions burned: 86 (million)
% 11.02/6.28 % (311)------------------------------
% 11.02/6.28 % (311)------------------------------
% 11.02/6.29 % (313)Instruction limit reached!
% 11.02/6.29 % (313)------------------------------
% 11.02/6.29 % (313)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.02/6.29 % (313)Termination reason: Unknown
% 11.02/6.29 % (313)Termination phase: shuffling
% 11.02/6.29
% 11.02/6.29 % (313)Memory used [KB]: 14583
% 11.02/6.29 % (313)Time elapsed: 0.019 s
% 11.02/6.29 % (313)Instructions burned: 41 (million)
% 11.02/6.29 % (313)------------------------------
% 11.02/6.29 % (313)------------------------------
% 11.02/6.29 % (314)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_32404 for (2991ds/448Mi)
% 11.59/6.31 % (315)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_32404 for (2991ds/46Mi)
% 11.59/6.31 % (301)Instruction limit reached!
% 11.59/6.31 % (301)------------------------------
% 11.59/6.31 % (301)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.59/6.31 % (301)Termination reason: Unknown
% 11.59/6.31 % (301)Termination phase: shuffling
% 11.59/6.31
% 11.59/6.31 % (301)Memory used [KB]: 31086
% 11.59/6.31 % (301)Time elapsed: 0.261 s
% 11.59/6.31 % (301)Instructions burned: 780 (million)
% 11.59/6.31 % (301)------------------------------
% 11.59/6.31 % (301)------------------------------
% 11.59/6.32 % (312)Instruction limit reached!
% 11.59/6.32 % (312)------------------------------
% 11.59/6.32 % (312)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.59/6.32 % (312)Termination reason: Unknown
% 11.59/6.32 % (312)Termination phase: shuffling
% 11.59/6.32
% 11.59/6.32 % (312)Memory used [KB]: 15351
% 11.59/6.32 % (312)Time elapsed: 0.048 s
% 11.59/6.32 % (312)Instructions burned: 109 (million)
% 11.59/6.32 % (312)------------------------------
% 11.59/6.32 % (312)------------------------------
% 11.59/6.32 % (32753)Instruction limit reached!
% 11.59/6.32 % (32753)------------------------------
% 11.59/6.32 % (32753)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.59/6.32 % (32753)Termination reason: Unknown
% 11.59/6.32 % (32753)Termination phase: shuffling
% 11.59/6.32
% 11.59/6.32 % (32753)Memory used [KB]: 34668
% 11.59/6.32 % (32753)Time elapsed: 0.366 s
% 11.59/6.32 % (32753)Instructions burned: 1043 (million)
% 11.59/6.32 % (32753)------------------------------
% 11.59/6.32 % (32753)------------------------------
% 11.59/6.33 % (315)Instruction limit reached!
% 11.59/6.33 % (315)------------------------------
% 11.59/6.33 % (315)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.59/6.33 % (315)Termination reason: Unknown
% 11.59/6.33 % (315)Termination phase: shuffling
% 11.59/6.33
% 11.59/6.33 % (315)Memory used [KB]: 14456
% 11.59/6.33 % (315)Time elapsed: 0.024 s
% 11.59/6.33 % (315)Instructions burned: 47 (million)
% 11.59/6.33 % (315)------------------------------
% 11.59/6.33 % (315)------------------------------
% 11.59/6.33 % (316)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_32404 for (2991ds/98Mi)
% 11.59/6.33 % (317)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_32404 for (2991ds/507Mi)
% 11.59/6.34 % (318)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_32404 for (2991ds/149Mi)
% 11.59/6.34 % (319)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_32404 for (2991ds/39Mi)
% 11.59/6.35 % (32764)Instruction limit reached!
% 11.59/6.35 % (32764)------------------------------
% 11.59/6.35 % (32764)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.59/6.35 % (32764)Termination reason: Unknown
% 11.59/6.35 % (32764)Termination phase: Property scanning
% 11.59/6.35
% 11.59/6.35 % (32764)Memory used [KB]: 24562
% 11.59/6.35 % (32764)Time elapsed: 0.329 s
% 11.59/6.35 % (32764)Instructions burned: 902 (million)
% 11.59/6.35 % (32764)------------------------------
% 11.59/6.35 % (32764)------------------------------
% 11.59/6.36 % (319)Instruction limit reached!
% 11.59/6.36 % (319)------------------------------
% 11.59/6.36 % (319)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.59/6.36 % (319)Termination reason: Unknown
% 11.59/6.36 % (319)Termination phase: shuffling
% 11.59/6.36
% 11.59/6.36 % (319)Memory used [KB]: 14456
% 11.59/6.36 % (319)Time elapsed: 0.021 s
% 11.59/6.36 % (319)Instructions burned: 41 (million)
% 11.59/6.36 % (319)------------------------------
% 11.59/6.36 % (319)------------------------------
% 11.59/6.36 % (316)Instruction limit reached!
% 11.59/6.36 % (316)------------------------------
% 11.59/6.36 % (316)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.59/6.36 % (316)Termination reason: Unknown
% 11.59/6.36 % (316)Termination phase: shuffling
% 11.59/6.36
% 11.59/6.36 % (316)Memory used [KB]: 15351
% 11.59/6.36 % (316)Time elapsed: 0.037 s
% 11.59/6.36 % (316)Instructions burned: 100 (million)
% 11.59/6.36 % (316)------------------------------
% 11.59/6.36 % (316)------------------------------
% 11.59/6.36 % (320)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_32404 for (2991ds/6Mi)
% 11.59/6.37 % (320)Instruction limit reached!
% 11.59/6.37 % (320)------------------------------
% 11.59/6.37 % (320)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.59/6.37 % (320)Termination reason: Unknown
% 11.59/6.37 % (320)Termination phase: shuffling
% 11.59/6.37
% 11.59/6.37 % (320)Memory used [KB]: 13816
% 11.59/6.37 % (320)Time elapsed: 0.007 s
% 11.59/6.37 % (320)Instructions burned: 6 (million)
% 11.59/6.37 % (320)------------------------------
% 11.59/6.37 % (320)------------------------------
% 11.59/6.37 % (321)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_32404 for (2990ds/1087Mi)
% 11.59/6.38 % (322)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_32404 for (2990ds/47Mi)
% 11.59/6.38 % (323)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_32404 for (2990ds/44Mi)
% 11.59/6.38 % (303)Instruction limit reached!
% 11.59/6.38 % (303)------------------------------
% 11.59/6.38 % (303)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.59/6.38 % (303)Termination reason: Unknown
% 11.59/6.38 % (303)Termination phase: Property scanning
% 11.59/6.38
% 11.59/6.38 % (303)Memory used [KB]: 24562
% 11.59/6.38 % (303)Time elapsed: 0.316 s
% 11.59/6.38 % (303)Instructions burned: 882 (million)
% 11.59/6.38 % (303)------------------------------
% 11.59/6.38 % (303)------------------------------
% 11.59/6.39 % (318)Instruction limit reached!
% 11.59/6.39 % (318)------------------------------
% 11.59/6.39 % (318)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.59/6.39 % (318)Termination reason: Unknown
% 11.59/6.39 % (318)Termination phase: shuffling
% 11.59/6.39
% 11.59/6.39 % (318)Memory used [KB]: 15863
% 11.59/6.39 % (318)Time elapsed: 0.058 s
% 11.59/6.39 % (318)Instructions burned: 149 (million)
% 11.59/6.39 % (318)------------------------------
% 11.59/6.39 % (318)------------------------------
% 12.85/6.40 % (324)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_32404 for (2990ds/432Mi)
% 12.85/6.40 % (322)Instruction limit reached!
% 12.85/6.40 % (322)------------------------------
% 12.85/6.40 % (322)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.85/6.40 % (322)Termination reason: Unknown
% 12.85/6.40 % (322)Termination phase: shuffling
% 12.85/6.40
% 12.85/6.40 % (322)Memory used [KB]: 14583
% 12.85/6.40 % (322)Time elapsed: 0.024 s
% 12.85/6.40 % (322)Instructions burned: 49 (million)
% 12.85/6.40 % (322)------------------------------
% 12.85/6.40 % (322)------------------------------
% 12.85/6.40 % (323)Instruction limit reached!
% 12.85/6.40 % (323)------------------------------
% 12.85/6.40 % (323)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.85/6.40 % (323)Termination reason: Unknown
% 12.85/6.40 % (323)Termination phase: shuffling
% 12.85/6.40
% 12.85/6.40 % (323)Memory used [KB]: 14583
% 12.85/6.40 % (323)Time elapsed: 0.022 s
% 12.85/6.40 % (323)Instructions burned: 46 (million)
% 12.85/6.40 % (323)------------------------------
% 12.85/6.40 % (323)------------------------------
% 12.85/6.40 % (325)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_32404 for (2990ds/62Mi)
% 12.85/6.41 % (326)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_32404 for (2990ds/31Mi)
% 12.85/6.41 % (327)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_32404 for (2990ds/96Mi)
% 12.85/6.43 % (325)Instruction limit reached!
% 12.85/6.43 % (325)------------------------------
% 12.85/6.43 % (325)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.85/6.43 % (325)Termination reason: Unknown
% 12.85/6.43 % (325)Termination phase: shuffling
% 12.85/6.43
% 12.85/6.43 % (325)Memory used [KB]: 14839
% 12.85/6.43 % (325)Time elapsed: 0.027 s
% 12.85/6.43 % (325)Instructions burned: 63 (million)
% 12.85/6.43 % (325)------------------------------
% 12.85/6.43 % (325)------------------------------
% 12.85/6.43 % (326)Instruction limit reached!
% 12.85/6.43 % (326)------------------------------
% 12.85/6.43 % (326)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.85/6.43 % (326)Termination reason: Unknown
% 12.85/6.43 % (326)Termination phase: shuffling
% 12.85/6.43
% 12.85/6.43 % (326)Memory used [KB]: 14328
% 12.85/6.43 % (326)Time elapsed: 0.020 s
% 12.85/6.43 % (326)Instructions burned: 33 (million)
% 12.85/6.43 % (326)------------------------------
% 12.85/6.43 % (326)------------------------------
% 12.85/6.43 % (314)Instruction limit reached!
% 12.85/6.43 % (314)------------------------------
% 12.85/6.43 % (314)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.85/6.43 % (314)Termination reason: Unknown
% 12.85/6.43 % (314)Termination phase: shuffling
% 12.85/6.43
% 12.85/6.43 % (314)Memory used [KB]: 22387
% 12.85/6.43 % (314)Time elapsed: 0.142 s
% 12.85/6.43 % (314)Instructions burned: 450 (million)
% 12.85/6.43 % (314)------------------------------
% 12.85/6.43 % (314)------------------------------
% 12.85/6.44 % (328)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_32404 for (2990ds/453Mi)
% 12.85/6.44 % (329)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_32404 for (2990ds/71Mi)
% 12.85/6.45 % (330)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_32404 for (2990ds/83Mi)
% 12.85/6.45 % (327)Instruction limit reached!
% 12.85/6.45 % (327)------------------------------
% 12.85/6.45 % (327)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.85/6.45 % (327)Termination reason: Unknown
% 12.85/6.45 % (327)Termination phase: shuffling
% 12.85/6.45
% 12.85/6.45 % (327)Memory used [KB]: 15223
% 12.85/6.45 % (327)Time elapsed: 0.041 s
% 12.85/6.45 % (327)Instructions burned: 97 (million)
% 12.85/6.45 % (327)------------------------------
% 12.85/6.45 % (327)------------------------------
% 12.85/6.47 % (331)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_32404 for (2989ds/11Mi)
% 12.85/6.47 % (329)Instruction limit reached!
% 12.85/6.47 % (329)------------------------------
% 12.85/6.47 % (329)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.85/6.47 % (329)Termination reason: Unknown
% 12.85/6.47 % (329)Termination phase: shuffling
% 12.85/6.47
% 12.85/6.47 % (329)Memory used [KB]: 14839
% 12.85/6.47 % (329)Time elapsed: 0.032 s
% 12.85/6.47 % (329)Instructions burned: 71 (million)
% 12.85/6.47 % (329)------------------------------
% 12.85/6.47 % (329)------------------------------
% 12.85/6.48 % (331)Instruction limit reached!
% 12.85/6.48 % (331)------------------------------
% 12.85/6.48 % (331)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.85/6.48 % (331)Termination reason: Unknown
% 12.85/6.48 % (331)Termination phase: shuffling
% 12.85/6.48
% 12.85/6.48 % (331)Memory used [KB]: 14072
% 12.85/6.48 % (331)Time elapsed: 0.012 s
% 12.85/6.48 % (331)Instructions burned: 11 (million)
% 12.85/6.48 % (331)------------------------------
% 12.85/6.48 % (331)------------------------------
% 12.85/6.48 % (330)Instruction limit reached!
% 12.85/6.48 % (330)------------------------------
% 12.85/6.48 % (330)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.85/6.48 % (330)Termination reason: Unknown
% 12.85/6.48 % (330)Termination phase: shuffling
% 12.85/6.48
% 12.85/6.48 % (330)Memory used [KB]: 15095
% 12.85/6.48 % (330)Time elapsed: 0.036 s
% 12.85/6.48 % (330)Instructions burned: 84 (million)
% 12.85/6.48 % (330)------------------------------
% 12.85/6.48 % (330)------------------------------
% 12.85/6.49 % (332)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_32404 for (2989ds/41Mi)
% 12.85/6.49 % (333)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_32404 for (2989ds/6Mi)
% 12.85/6.49 % (333)Instruction limit reached!
% 12.85/6.49 % (333)------------------------------
% 12.85/6.49 % (333)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.85/6.49 % (333)Termination reason: Unknown
% 12.85/6.49 % (333)Termination phase: shuffling
% 12.85/6.49
% 12.85/6.49 % (333)Memory used [KB]: 13816
% 12.85/6.49 % (333)Time elapsed: 0.007 s
% 12.85/6.49 % (333)Instructions burned: 6 (million)
% 12.85/6.49 % (333)------------------------------
% 12.85/6.49 % (333)------------------------------
% 12.85/6.49 % (334)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_32404 for (2989ds/150Mi)
% 13.32/6.50 % (335)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_32404 for (2989ds/343Mi)
% 13.32/6.51 % (332)Instruction limit reached!
% 13.32/6.51 % (332)------------------------------
% 13.32/6.51 % (332)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.32/6.51 % (332)Termination reason: Unknown
% 13.32/6.51 % (332)Termination phase: shuffling
% 13.32/6.51
% 13.32/6.51 % (332)Memory used [KB]: 14583
% 13.32/6.51 % (332)Time elapsed: 0.021 s
% 13.32/6.51 % (332)Instructions burned: 43 (million)
% 13.32/6.51 % (332)------------------------------
% 13.32/6.51 % (332)------------------------------
% 13.32/6.51 % (317)Instruction limit reached!
% 13.32/6.51 % (317)------------------------------
% 13.32/6.51 % (317)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.32/6.51 % (317)Termination reason: Unknown
% 13.32/6.51 % (317)Termination phase: shuffling
% 13.32/6.51
% 13.32/6.51 % (317)Memory used [KB]: 22259
% 13.32/6.51 % (317)Time elapsed: 0.182 s
% 13.32/6.51 % (317)Instructions burned: 507 (million)
% 13.32/6.51 % (317)------------------------------
% 13.32/6.51 % (317)------------------------------
% 13.32/6.52 % (336)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_32404 for (2989ds/109Mi)
% 13.32/6.53 % (337)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_32404 for (2989ds/253Mi)
% 13.32/6.53 % (324)Instruction limit reached!
% 13.32/6.53 % (324)------------------------------
% 13.32/6.53 % (324)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.32/6.53 % (324)Termination reason: Unknown
% 13.32/6.53 % (324)Termination phase: shuffling
% 13.32/6.53
% 13.32/6.53 % (324)Memory used [KB]: 22259
% 13.32/6.53 % (324)Time elapsed: 0.138 s
% 13.32/6.53 % (324)Instructions burned: 434 (million)
% 13.32/6.53 % (324)------------------------------
% 13.32/6.53 % (324)------------------------------
% 13.32/6.55 % (338)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_32404 for (2989ds/140Mi)
% 13.32/6.55 % (334)Instruction limit reached!
% 13.32/6.55 % (334)------------------------------
% 13.32/6.55 % (334)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.32/6.55 % (334)Termination reason: Unknown
% 13.32/6.55 % (334)Termination phase: shuffling
% 13.32/6.55
% 13.32/6.55 % (334)Memory used [KB]: 15991
% 13.32/6.55 % (334)Time elapsed: 0.059 s
% 13.32/6.55 % (334)Instructions burned: 152 (million)
% 13.32/6.55 % (334)------------------------------
% 13.32/6.55 % (334)------------------------------
% 13.32/6.56 % (336)Instruction limit reached!
% 13.32/6.56 % (336)------------------------------
% 13.32/6.56 % (336)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.32/6.56 % (336)Termination reason: Unknown
% 13.32/6.56 % (336)Termination phase: shuffling
% 13.32/6.56
% 13.32/6.56 % (336)Memory used [KB]: 15351
% 13.32/6.56 % (336)Time elapsed: 0.045 s
% 13.32/6.56 % (336)Instructions burned: 109 (million)
% 13.32/6.56 % (336)------------------------------
% 13.32/6.56 % (336)------------------------------
% 13.32/6.56 % (339)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_32404 for (2988ds/614Mi)
% 13.32/6.57 % (340)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_32404 for (2988ds/202Mi)
% 13.32/6.58 % (328)Instruction limit reached!
% 13.32/6.58 % (328)------------------------------
% 13.32/6.58 % (328)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.32/6.58 % (328)Termination reason: Unknown
% 13.32/6.58 % (328)Termination phase: shuffling
% 13.32/6.58
% 13.32/6.58 % (328)Memory used [KB]: 22515
% 13.32/6.58 % (328)Time elapsed: 0.144 s
% 13.32/6.58 % (328)Instructions burned: 454 (million)
% 13.32/6.58 % (328)------------------------------
% 13.32/6.58 % (328)------------------------------
% 13.98/6.60 % (341)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_32404 for (2988ds/339Mi)
% 13.98/6.60 % (338)Instruction limit reached!
% 13.98/6.60 % (338)------------------------------
% 13.98/6.60 % (338)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.98/6.60 % (338)Termination reason: Unknown
% 13.98/6.60 % (338)Termination phase: shuffling
% 13.98/6.60
% 13.98/6.60 % (338)Memory used [KB]: 15735
% 13.98/6.60 % (338)Time elapsed: 0.054 s
% 13.98/6.60 % (338)Instructions burned: 140 (million)
% 13.98/6.60 % (338)------------------------------
% 13.98/6.60 % (338)------------------------------
% 13.98/6.61 % (342)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_32404 for (2988ds/283Mi)
% 13.98/6.62 % (337)Instruction limit reached!
% 13.98/6.62 % (337)------------------------------
% 13.98/6.62 % (337)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.98/6.62 % (337)Termination reason: Unknown
% 13.98/6.62 % (337)Termination phase: shuffling
% 13.98/6.62
% 13.98/6.62 % (337)Memory used [KB]: 17270
% 13.98/6.62 % (337)Time elapsed: 0.094 s
% 13.98/6.62 % (337)Instructions burned: 253 (million)
% 13.98/6.62 % (337)------------------------------
% 13.98/6.62 % (337)------------------------------
% 13.98/6.63 % (335)Instruction limit reached!
% 13.98/6.63 % (335)------------------------------
% 13.98/6.63 % (335)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.98/6.63 % (335)Termination reason: Unknown
% 13.98/6.63 % (335)Termination phase: shuffling
% 13.98/6.63
% 13.98/6.63 % (335)Memory used [KB]: 18421
% 13.98/6.63 % (335)Time elapsed: 0.126 s
% 13.98/6.63 % (335)Instructions burned: 345 (million)
% 13.98/6.63 % (335)------------------------------
% 13.98/6.63 % (335)------------------------------
% 13.98/6.63 % (343)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_32404 for (2988ds/134Mi)
% 13.98/6.64 % (344)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_32404 for (2988ds/298Mi)
% 13.98/6.65 % (340)Instruction limit reached!
% 13.98/6.65 % (340)------------------------------
% 13.98/6.65 % (340)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.98/6.65 % (340)Termination reason: Unknown
% 13.98/6.65 % (340)Termination phase: shuffling
% 13.98/6.65
% 13.98/6.65 % (340)Memory used [KB]: 16630
% 13.98/6.65 % (340)Time elapsed: 0.077 s
% 13.98/6.65 % (340)Instructions burned: 202 (million)
% 13.98/6.65 % (340)------------------------------
% 13.98/6.65 % (340)------------------------------
% 13.98/6.66 % (345)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_32404 for (2988ds/192Mi)
% 13.98/6.68 % (343)Instruction limit reached!
% 13.98/6.68 % (343)------------------------------
% 13.98/6.68 % (343)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.98/6.68 % (343)Termination reason: Unknown
% 13.98/6.68 % (343)Termination phase: shuffling
% 13.98/6.68
% 13.98/6.68 % (343)Memory used [KB]: 15735
% 13.98/6.68 % (343)Time elapsed: 0.053 s
% 13.98/6.68 % (343)Instructions burned: 134 (million)
% 13.98/6.68 % (343)------------------------------
% 13.98/6.68 % (343)------------------------------
% 13.98/6.69 % (346)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_32404 for (2987ds/258Mi)
% 14.43/6.70 % (342)Instruction limit reached!
% 14.43/6.70 % (342)------------------------------
% 14.43/6.70 % (342)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.43/6.70 % (342)Termination reason: Unknown
% 14.43/6.70 % (342)Termination phase: shuffling
% 14.43/6.70
% 14.43/6.70 % (342)Memory used [KB]: 20084
% 14.43/6.70 % (342)Time elapsed: 0.092 s
% 14.43/6.70 % (342)Instructions burned: 286 (million)
% 14.43/6.70 % (342)------------------------------
% 14.43/6.70 % (342)------------------------------
% 14.43/6.71 % (347)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_32404 for (2987ds/90Mi)
% 14.43/6.72 % (341)Instruction limit reached!
% 14.43/6.72 % (341)------------------------------
% 14.43/6.72 % (341)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.43/6.72 % (341)Termination reason: Unknown
% 14.43/6.72 % (341)Termination phase: shuffling
% 14.43/6.72
% 14.43/6.72 % (341)Memory used [KB]: 18293
% 14.43/6.72 % (341)Time elapsed: 0.123 s
% 14.43/6.72 % (341)Instructions burned: 340 (million)
% 14.43/6.72 % (341)------------------------------
% 14.43/6.72 % (341)------------------------------
% 14.43/6.73 % (321)Instruction limit reached!
% 14.43/6.73 % (321)------------------------------
% 14.43/6.73 % (321)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.43/6.73 % (321)Termination reason: Unknown
% 14.43/6.73 % (321)Termination phase: Property scanning
% 14.43/6.73
% 14.43/6.73 % (321)Memory used [KB]: 24562
% 14.43/6.73 % (321)Time elapsed: 0.357 s
% 14.43/6.73 % (321)Instructions burned: 1087 (million)
% 14.43/6.73 % (321)------------------------------
% 14.43/6.73 % (321)------------------------------
% 14.43/6.73 % (348)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_32404 for (2987ds/231Mi)
% 14.43/6.73 % (345)Instruction limit reached!
% 14.43/6.73 % (345)------------------------------
% 14.43/6.73 % (345)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.43/6.73 % (345)Termination reason: Unknown
% 14.43/6.73 % (345)Termination phase: shuffling
% 14.43/6.73
% 14.43/6.73 % (345)Memory used [KB]: 16502
% 14.43/6.73 % (345)Time elapsed: 0.073 s
% 14.43/6.73 % (345)Instructions burned: 192 (million)
% 14.43/6.73 % (345)------------------------------
% 14.43/6.73 % (345)------------------------------
% 14.43/6.74 % (344)Instruction limit reached!
% 14.43/6.74 % (344)------------------------------
% 14.43/6.74 % (344)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.43/6.74 % (344)Termination reason: Unknown
% 14.43/6.74 % (344)Termination phase: shuffling
% 14.43/6.74
% 14.43/6.74 % (344)Memory used [KB]: 20340
% 14.43/6.74 % (344)Time elapsed: 0.095 s
% 14.43/6.74 % (344)Instructions burned: 299 (million)
% 14.43/6.74 % (344)------------------------------
% 14.43/6.74 % (344)------------------------------
% 14.43/6.74 % (349)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_32404 for (2987ds/458Mi)
% 14.43/6.75 % (350)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_32404 for (2987ds/31Mi)
% 14.43/6.75 % (351)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_32404 for (2987ds/297Mi)
% 14.43/6.75 % (347)Instruction limit reached!
% 14.43/6.75 % (347)------------------------------
% 14.43/6.75 % (347)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.43/6.75 % (347)Termination reason: Unknown
% 14.43/6.75 % (347)Termination phase: shuffling
% 14.43/6.75
% 14.43/6.75 % (347)Memory used [KB]: 15223
% 14.43/6.75 % (347)Time elapsed: 0.038 s
% 14.43/6.75 % (347)Instructions burned: 92 (million)
% 14.43/6.75 % (347)------------------------------
% 14.43/6.75 % (347)------------------------------
% 14.43/6.76 % (350)Instruction limit reached!
% 14.43/6.76 % (350)------------------------------
% 14.43/6.76 % (350)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.43/6.76 % (350)Termination reason: Unknown
% 14.43/6.76 % (350)Termination phase: shuffling
% 14.43/6.76
% 14.43/6.76 % (350)Memory used [KB]: 14328
% 14.43/6.76 % (350)Time elapsed: 0.019 s
% 14.43/6.76 % (350)Instructions burned: 34 (million)
% 14.43/6.76 % (350)------------------------------
% 14.43/6.76 % (350)------------------------------
% 14.43/6.76 % (352)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_32404 for (2986ds/987Mi)
% 14.43/6.78 % (353)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_32404 for (2986ds/182Mi)
% 14.43/6.78 % (339)Instruction limit reached!
% 14.43/6.78 % (339)------------------------------
% 14.43/6.78 % (339)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.43/6.78 % (339)Termination reason: Unknown
% 14.43/6.78 % (339)Termination phase: shuffling
% 14.43/6.78
% 14.43/6.78 % (339)Memory used [KB]: 23794
% 14.43/6.78 % (339)Time elapsed: 0.218 s
% 14.43/6.78 % (339)Instructions burned: 615 (million)
% 14.43/6.78 % (339)------------------------------
% 14.43/6.78 % (339)------------------------------
% 14.43/6.79 % (346)Instruction limit reached!
% 14.43/6.79 % (346)------------------------------
% 14.43/6.79 % (346)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.43/6.79 % (346)Termination reason: Unknown
% 14.43/6.79 % (346)Termination phase: shuffling
% 14.43/6.79
% 14.43/6.79 % (346)Memory used [KB]: 17398
% 14.43/6.79 % (346)Time elapsed: 0.095 s
% 14.43/6.79 % (346)Instructions burned: 259 (million)
% 14.43/6.79 % (346)------------------------------
% 14.43/6.79 % (346)------------------------------
% 14.43/6.79 % (354)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_32404 for (2986ds/182Mi)
% 15.65/6.80 % (355)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_32404 for (2986ds/154Mi)
% 15.65/6.81 % (348)Instruction limit reached!
% 15.65/6.81 % (348)------------------------------
% 15.65/6.81 % (348)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.65/6.81 % (348)Termination reason: Unknown
% 15.65/6.81 % (348)Termination phase: shuffling
% 15.65/6.81
% 15.65/6.81 % (348)Memory used [KB]: 19317
% 15.65/6.81 % (348)Time elapsed: 0.076 s
% 15.65/6.81 % (348)Instructions burned: 232 (million)
% 15.65/6.81 % (348)------------------------------
% 15.65/6.81 % (348)------------------------------
% 15.65/6.82 % (356)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_32404 for (2986ds/79Mi)
% 15.65/6.84 % (351)Instruction limit reached!
% 15.65/6.84 % (351)------------------------------
% 15.65/6.84 % (351)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.65/6.84 % (351)Termination reason: Unknown
% 15.65/6.84 % (351)Termination phase: shuffling
% 15.65/6.84
% 15.65/6.84 % (351)Memory used [KB]: 20340
% 15.65/6.84 % (351)Time elapsed: 0.094 s
% 15.65/6.84 % (351)Instructions burned: 299 (million)
% 15.65/6.84 % (351)------------------------------
% 15.65/6.84 % (351)------------------------------
% 15.65/6.84 % (353)Instruction limit reached!
% 15.65/6.84 % (353)------------------------------
% 15.65/6.84 % (353)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.65/6.84 % (353)Termination reason: Unknown
% 15.65/6.84 % (353)Termination phase: shuffling
% 15.65/6.84
% 15.65/6.84 % (353)Memory used [KB]: 16375
% 15.65/6.84 % (353)Time elapsed: 0.069 s
% 15.65/6.84 % (353)Instructions burned: 184 (million)
% 15.65/6.84 % (353)------------------------------
% 15.65/6.84 % (353)------------------------------
% 15.65/6.85 % (355)Instruction limit reached!
% 15.65/6.85 % (355)------------------------------
% 15.65/6.85 % (355)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.65/6.85 % (355)Termination reason: Unknown
% 15.65/6.85 % (355)Termination phase: shuffling
% 15.65/6.85
% 15.65/6.85 % (355)Memory used [KB]: 16247
% 15.65/6.85 % (355)Time elapsed: 0.052 s
% 15.65/6.85 % (355)Instructions burned: 156 (million)
% 15.65/6.85 % (355)------------------------------
% 15.65/6.85 % (355)------------------------------
% 15.65/6.85 % (356)Instruction limit reached!
% 15.65/6.85 % (356)------------------------------
% 15.65/6.85 % (356)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.65/6.85 % (356)Termination reason: Unknown
% 15.65/6.85 % (356)Termination phase: shuffling
% 15.65/6.85
% 15.65/6.85 % (356)Memory used [KB]: 14967
% 15.65/6.85 % (356)Time elapsed: 0.034 s
% 15.65/6.85 % (356)Instructions burned: 81 (million)
% 15.65/6.85 % (356)------------------------------
% 15.65/6.85 % (356)------------------------------
% 15.65/6.85 % (357)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_32404 for (2986ds/216Mi)
% 15.65/6.85 % (358)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_32404 for (2985ds/114Mi)
% 15.65/6.86 % (359)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_32404 for (2985ds/922Mi)
% 15.65/6.86 % (354)Instruction limit reached!
% 15.65/6.86 % (354)------------------------------
% 15.65/6.86 % (354)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.65/6.86 % (354)Termination reason: Unknown
% 15.65/6.86 % (354)Termination phase: shuffling
% 15.65/6.86
% 15.65/6.86 % (354)Memory used [KB]: 16375
% 15.65/6.86 % (354)Time elapsed: 0.070 s
% 15.65/6.86 % (354)Instructions burned: 184 (million)
% 15.65/6.86 % (354)------------------------------
% 15.65/6.86 % (354)------------------------------
% 15.65/6.86 % (360)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_32404 for (2985ds/182Mi)
% 15.65/6.88 % (361)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_32404 for (2985ds/164Mi)
% 16.12/6.90 % (358)Instruction limit reached!
% 16.12/6.90 % (358)------------------------------
% 16.12/6.90 % (358)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.12/6.90 % (358)Termination reason: Unknown
% 16.12/6.90 % (358)Termination phase: shuffling
% 16.12/6.90
% 16.12/6.90 % (358)Memory used [KB]: 15479
% 16.12/6.90 % (358)Time elapsed: 0.046 s
% 16.12/6.90 % (358)Instructions burned: 115 (million)
% 16.12/6.90 % (358)------------------------------
% 16.12/6.90 % (358)------------------------------
% 16.12/6.91 % (349)Instruction limit reached!
% 16.12/6.91 % (349)------------------------------
% 16.12/6.91 % (349)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.12/6.91 % (349)Termination reason: Unknown
% 16.12/6.91 % (349)Termination phase: shuffling
% 16.12/6.91
% 16.12/6.91 % (349)Memory used [KB]: 21875
% 16.12/6.91 % (349)Time elapsed: 0.166 s
% 16.12/6.91 % (349)Instructions burned: 458 (million)
% 16.12/6.91 % (349)------------------------------
% 16.12/6.91 % (349)------------------------------
% 16.12/6.91 % (362)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_32404 for (2985ds/50Mi)
% 16.12/6.92 % (363)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_32404 for (2985ds/368Mi)
% 16.12/6.92 % (360)Instruction limit reached!
% 16.12/6.92 % (360)------------------------------
% 16.12/6.92 % (360)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.12/6.92 % (360)Termination reason: Unknown
% 16.12/6.92 % (360)Termination phase: shuffling
% 16.12/6.92
% 16.12/6.92 % (360)Memory used [KB]: 16630
% 16.12/6.92 % (360)Time elapsed: 0.060 s
% 16.12/6.92 % (360)Instructions burned: 183 (million)
% 16.12/6.92 % (360)------------------------------
% 16.12/6.92 % (360)------------------------------
% 16.12/6.92 % (357)Instruction limit reached!
% 16.12/6.92 % (357)------------------------------
% 16.12/6.92 % (357)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.12/6.92 % (357)Termination reason: Unknown
% 16.12/6.92 % (357)Termination phase: shuffling
% 16.12/6.92
% 16.12/6.92 % (357)Memory used [KB]: 19189
% 16.12/6.92 % (357)Time elapsed: 0.071 s
% 16.12/6.92 % (357)Instructions burned: 218 (million)
% 16.12/6.92 % (357)------------------------------
% 16.12/6.92 % (357)------------------------------
% 16.12/6.93 % (361)Instruction limit reached!
% 16.12/6.93 % (361)------------------------------
% 16.12/6.93 % (361)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.12/6.93 % (361)Termination reason: Unknown
% 16.12/6.93 % (361)Termination phase: shuffling
% 16.12/6.93
% 16.12/6.93 % (361)Memory used [KB]: 16375
% 16.12/6.93 % (361)Time elapsed: 0.056 s
% 16.12/6.93 % (361)Instructions burned: 166 (million)
% 16.12/6.93 % (361)------------------------------
% 16.12/6.93 % (361)------------------------------
% 16.12/6.93 % (362)Instruction limit reached!
% 16.12/6.93 % (362)------------------------------
% 16.12/6.93 % (362)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.12/6.93 % (362)Termination reason: Unknown
% 16.12/6.93 % (362)Termination phase: shuffling
% 16.12/6.93
% 16.12/6.93 % (362)Memory used [KB]: 14583
% 16.12/6.93 % (362)Time elapsed: 0.023 s
% 16.12/6.93 % (362)Instructions burned: 51 (million)
% 16.12/6.93 % (362)------------------------------
% 16.12/6.93 % (362)------------------------------
% 16.12/6.94 % (364)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_32404 for (2985ds/1021Mi)
% 16.12/6.94 % (365)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_32404 for (2985ds/267Mi)
% 16.12/6.94 % (366)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_32404 for (2985ds/204Mi)
% 16.12/6.95 % (367)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_32404 for (2985ds/26Mi)
% 16.12/6.96 % (367)Instruction limit reached!
% 16.12/6.96 % (367)------------------------------
% 16.12/6.96 % (367)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.12/6.96 % (367)Termination reason: Unknown
% 16.12/6.96 % (367)Termination phase: shuffling
% 16.12/6.96
% 16.12/6.96 % (367)Memory used [KB]: 14328
% 16.12/6.96 % (367)Time elapsed: 0.016 s
% 16.12/6.96 % (367)Instructions burned: 26 (million)
% 16.12/6.96 % (367)------------------------------
% 16.12/6.96 % (367)------------------------------
% 16.12/6.97 % (368)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_32404 for (2984ds/53Mi)
% 16.12/6.99 % (368)Instruction limit reached!
% 16.12/6.99 % (368)------------------------------
% 16.12/6.99 % (368)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.12/6.99 % (368)Termination reason: Unknown
% 16.12/6.99 % (368)Termination phase: shuffling
% 16.12/6.99
% 16.12/6.99 % (368)Memory used [KB]: 14711
% 16.12/6.99 % (368)Time elapsed: 0.023 s
% 16.12/6.99 % (368)Instructions burned: 54 (million)
% 16.12/6.99 % (368)------------------------------
% 16.12/6.99 % (368)------------------------------
% 16.12/7.01 % (369)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_32404 for (2984ds/4436Mi)
% 16.12/7.02 % (366)Instruction limit reached!
% 16.12/7.02 % (366)------------------------------
% 16.12/7.02 % (366)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.12/7.02 % (366)Termination reason: Unknown
% 16.12/7.02 % (366)Termination phase: shuffling
% 16.12/7.02
% 16.12/7.02 % (366)Memory used [KB]: 16630
% 16.12/7.02 % (366)Time elapsed: 0.076 s
% 16.12/7.02 % (366)Instructions burned: 204 (million)
% 16.12/7.02 % (366)------------------------------
% 16.12/7.02 % (366)------------------------------
% 16.12/7.02 % (365)Instruction limit reached!
% 16.12/7.02 % (365)------------------------------
% 16.12/7.02 % (365)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.12/7.02 % (365)Termination reason: Unknown
% 16.12/7.02 % (365)Termination phase: shuffling
% 16.12/7.02
% 16.12/7.02 % (365)Memory used [KB]: 19829
% 16.12/7.02 % (365)Time elapsed: 0.086 s
% 16.12/7.02 % (365)Instructions burned: 268 (million)
% 16.12/7.02 % (365)------------------------------
% 16.12/7.02 % (365)------------------------------
% 17.54/7.03 % (370)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_32404 for (2984ds/1539Mi)
% 17.54/7.03 % (371)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_32404 for (2984ds/408Mi)
% 17.54/7.05 % (363)Instruction limit reached!
% 17.54/7.05 % (363)------------------------------
% 17.54/7.05 % (363)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.54/7.05 % (363)Termination reason: Unknown
% 17.54/7.05 % (363)Termination phase: shuffling
% 17.54/7.05
% 17.54/7.05 % (363)Memory used [KB]: 18677
% 17.54/7.05 % (363)Time elapsed: 0.133 s
% 17.54/7.05 % (363)Instructions burned: 370 (million)
% 17.54/7.05 % (363)------------------------------
% 17.54/7.05 % (363)------------------------------
% 17.54/7.06 % (372)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_32404 for (2983ds/5205Mi)
% 17.54/7.06 % (352)Instruction limit reached!
% 17.54/7.06 % (352)------------------------------
% 17.54/7.06 % (352)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.54/7.06 % (352)Termination reason: Unknown
% 17.54/7.06 % (352)Termination phase: shuffling
% 17.54/7.06
% 17.54/7.06 % (352)Memory used [KB]: 33901
% 17.54/7.06 % (352)Time elapsed: 0.302 s
% 17.54/7.06 % (352)Instructions burned: 987 (million)
% 17.54/7.06 % (352)------------------------------
% 17.54/7.06 % (352)------------------------------
% 17.54/7.08 % (373)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_32404 for (2983ds/1913Mi)
% 17.89/7.17 % (359)Instruction limit reached!
% 17.89/7.17 % (359)------------------------------
% 17.89/7.17 % (359)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.89/7.17 % (359)Termination reason: Unknown
% 17.89/7.17 % (359)Termination phase: Property scanning
% 17.89/7.17
% 17.89/7.17 % (359)Memory used [KB]: 24562
% 17.89/7.17 % (359)Time elapsed: 0.308 s
% 17.89/7.17 % (359)Instructions burned: 924 (million)
% 17.89/7.17 % (359)------------------------------
% 17.89/7.17 % (359)------------------------------
% 17.89/7.18 % (371)Instruction limit reached!
% 17.89/7.18 % (371)------------------------------
% 17.89/7.18 % (371)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.89/7.18 % (371)Termination reason: Unknown
% 17.89/7.18 % (371)Termination phase: shuffling
% 17.89/7.18
% 17.89/7.18 % (371)Memory used [KB]: 19317
% 17.89/7.18 % (371)Time elapsed: 0.145 s
% 17.89/7.18 % (371)Instructions burned: 408 (million)
% 17.89/7.18 % (371)------------------------------
% 17.89/7.18 % (371)------------------------------
% 17.89/7.18 % (374)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_32404 for (2982ds/4350Mi)
% 17.89/7.19 % (375)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_32404 for (2982ds/68Mi)
% 18.24/7.22 % (375)Instruction limit reached!
% 18.24/7.22 % (375)------------------------------
% 18.24/7.22 % (375)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.24/7.22 % (375)Termination reason: Unknown
% 18.24/7.22 % (375)Termination phase: shuffling
% 18.24/7.22
% 18.24/7.22 % (375)Memory used [KB]: 14839
% 18.24/7.22 % (375)Time elapsed: 0.032 s
% 18.24/7.22 % (375)Instructions burned: 70 (million)
% 18.24/7.22 % (375)------------------------------
% 18.24/7.22 % (375)------------------------------
% 18.24/7.23 % (376)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_32404 for (2982ds/358Mi)
% 18.24/7.27 % (364)Instruction limit reached!
% 18.24/7.27 % (364)------------------------------
% 18.24/7.27 % (364)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.24/7.27 % (364)Termination reason: Unknown
% 18.24/7.27 % (364)Termination phase: Property scanning
% 18.24/7.27
% 18.24/7.27 % (364)Memory used [KB]: 24562
% 18.24/7.27 % (364)Time elapsed: 0.337 s
% 18.24/7.27 % (364)Instructions burned: 1024 (million)
% 18.24/7.27 % (364)------------------------------
% 18.24/7.27 % (364)------------------------------
% 18.24/7.28 % (377)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_32404 for (2981ds/31Mi)
% 18.48/7.30 % (377)Instruction limit reached!
% 18.48/7.30 % (377)------------------------------
% 18.48/7.30 % (377)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.48/7.30 % (377)Termination reason: Unknown
% 18.48/7.30 % (377)Termination phase: shuffling
% 18.48/7.30
% 18.48/7.30 % (377)Memory used [KB]: 14328
% 18.48/7.30 % (377)Time elapsed: 0.018 s
% 18.48/7.30 % (377)Instructions burned: 31 (million)
% 18.48/7.30 % (377)------------------------------
% 18.48/7.30 % (377)------------------------------
% 18.48/7.31 % (378)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_32404 for (2981ds/279Mi)
% 18.48/7.36 % (376)Instruction limit reached!
% 18.48/7.36 % (376)------------------------------
% 18.48/7.36 % (376)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.48/7.36 % (376)Termination reason: Unknown
% 18.48/7.36 % (376)Termination phase: shuffling
% 18.48/7.36
% 18.48/7.36 % (376)Memory used [KB]: 18677
% 18.48/7.36 % (376)Time elapsed: 0.128 s
% 18.48/7.36 % (376)Instructions burned: 359 (million)
% 18.48/7.36 % (376)------------------------------
% 18.48/7.36 % (376)------------------------------
% 18.48/7.37 % (379)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_32404 for (2980ds/258Mi)
% 18.75/7.40 % (378)Instruction limit reached!
% 18.75/7.40 % (378)------------------------------
% 18.75/7.40 % (378)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.75/7.40 % (378)Termination reason: Unknown
% 18.75/7.40 % (378)Termination phase: shuffling
% 18.75/7.40
% 18.75/7.40 % (378)Memory used [KB]: 19957
% 18.75/7.40 % (378)Time elapsed: 0.089 s
% 18.75/7.40 % (378)Instructions burned: 279 (million)
% 18.75/7.40 % (378)------------------------------
% 18.75/7.40 % (378)------------------------------
% 18.75/7.41 % (380)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_32404 for (2980ds/26Mi)
% 18.75/7.43 % (380)Instruction limit reached!
% 18.75/7.43 % (380)------------------------------
% 18.75/7.43 % (380)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.75/7.43 % (380)Termination reason: Unknown
% 18.75/7.43 % (380)Termination phase: shuffling
% 18.75/7.43
% 18.75/7.43 % (380)Memory used [KB]: 14456
% 18.75/7.43 % (380)Time elapsed: 0.016 s
% 18.75/7.43 % (380)Instructions burned: 28 (million)
% 18.75/7.43 % (380)------------------------------
% 18.75/7.43 % (380)------------------------------
% 18.75/7.44 % (369)First to succeed.
% 18.75/7.44 % (381)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_32404 for (2980ds/995Mi)
% 18.75/7.45 % (369)Refutation found. Thanks to Tanya!
% 18.75/7.45 % SZS status Theorem for DTF2THF_32404
% 18.75/7.45 % SZS output start Proof for DTF2THF_32404
% 18.75/7.45 thf(type_def_5, type, rat: $tType).
% 18.75/7.45 thf(type_def_6, type, int: $tType).
% 18.75/7.45 thf(type_def_8, type, nat: $tType).
% 18.75/7.45 thf(type_def_9, type, a: $tType).
% 18.75/7.45 thf(type_def_10, type, heap_T6362127782908069795rray_a: $tType).
% 18.75/7.45 thf(type_def_11, type, list_a: $tType).
% 18.75/7.45 thf(type_def_12, type, assn: $tType).
% 18.75/7.45 thf(type_def_13, type, produc3658429121746597890et_nat: $tType).
% 18.75/7.45 thf(type_def_14, type, set_nat: $tType).
% 18.75/7.45 thf(type_def_15, type, heap_e7401611519738050253t_unit: $tType).
% 18.75/7.45 thf(type_def_16, type, produc2732055786443039994et_nat: $tType).
% 18.75/7.45 thf(type_def_17, type, set_Product_prod_o_o: $tType).
% 18.75/7.45 thf(type_def_18, type, set_Pr1261947904930325089at_nat: $tType).
% 18.75/7.45 thf(type_def_19, type, set_o: $tType).
% 18.75/7.45 thf(type_def_20, type, code_integer: $tType).
% 18.75/7.45 thf(type_def_21, type, produc8923325533196201883nteger: $tType).
% 18.75/7.45 thf(type_def_22, type, num: $tType).
% 18.75/7.45 thf(type_def_23, type, product_prod_int_int: $tType).
% 18.75/7.45 thf(type_def_24, type, code_natural: $tType).
% 18.75/7.45 thf(type_def_25, type, produc7822875418678951345atural: $tType).
% 18.75/7.45 thf(type_def_26, type, product_prod_nat_nat: $tType).
% 18.75/7.45 thf(type_def_27, type, product_unit: $tType).
% 18.75/7.45 thf(type_def_28, type, set_Pr1932065953672099015od_o_o: $tType).
% 18.75/7.45 thf(type_def_29, type, set_Pr4329608150637261639at_nat: $tType).
% 18.75/7.45 thf(type_def_30, type, set_Pr457366540195662369at_nat: $tType).
% 18.75/7.45 thf(type_def_31, type, produc5835291356934675326atural: $tType).
% 18.75/7.45 thf(type_def_32, type, option_num: $tType).
% 18.75/7.45 thf(type_def_33, type, product_prod_num_num: $tType).
% 18.75/7.45 thf(type_def_34, type, produc6271795597528267376eger_o: $tType).
% 18.75/7.45 thf(type_def_35, type, set_in8474487674441654202_int_o: $tType).
% 18.75/7.45 thf(type_def_36, type, option6357759511663192854e_term: $tType).
% 18.75/7.45 thf(type_def_37, type, set_Pr8914822823351560561eger_o: $tType).
% 18.75/7.45 thf(type_def_38, type, produc6241069584506657477e_term: $tType).
% 18.75/7.45 thf(type_def_39, type, set_Pr1457143144315775327_nat_o: $tType).
% 18.75/7.45 thf(type_def_40, type, produc3925858234332021118et_nat: $tType).
% 18.75/7.45 thf(type_def_41, type, set_Pr8208987589773510107_nat_o: $tType).
% 18.75/7.45 thf(type_def_42, type, set_Pr5050529186185961540_int_o: $tType).
% 18.75/7.45 thf(type_def_43, type, produc8551481072490612790e_term: $tType).
% 18.75/7.45 thf(type_def_44, type, set_nat_nat_o: $tType).
% 18.75/7.45 thf(type_def_45, type, set_se9180647916752606350_nat_o: $tType).
% 18.75/7.45 thf(type_def_46, type, set_int: $tType).
% 18.75/7.45 thf(type_def_47, type, set_op3165557761946182707t_unit: $tType).
% 18.75/7.45 thf(type_def_48, type, option_Product_unit: $tType).
% 18.75/7.45 thf(type_def_49, type, set_option_set_nat: $tType).
% 18.75/7.45 thf(type_def_50, type, option_set_nat: $tType).
% 18.75/7.45 thf(type_def_51, type, set_Product_unit: $tType).
% 18.75/7.45 thf(type_def_52, type, set_set_o: $tType).
% 18.75/7.45 thf(type_def_53, type, set_set_Code_integer: $tType).
% 18.75/7.45 thf(type_def_54, type, set_Code_integer: $tType).
% 18.75/7.45 thf(type_def_55, type, set_set_int: $tType).
% 18.75/7.45 thf(type_def_56, type, set_set_list_nat: $tType).
% 18.75/7.45 thf(type_def_57, type, set_list_nat: $tType).
% 18.75/7.45 thf(type_def_58, type, set_set_nat: $tType).
% 18.75/7.45 thf(type_def_59, type, set_se7394616247590735609nt_int: $tType).
% 18.75/7.45 thf(type_def_60, type, set_Pr1872883991513573699nt_int: $tType).
% 18.75/7.45 thf(type_def_61, type, set_se124295367203800706nteger: $tType).
% 18.75/7.45 thf(type_def_62, type, set_Pr1281608226676607948nteger: $tType).
% 18.75/7.45 thf(type_def_63, type, set_se5120235452707311462et_nat: $tType).
% 18.75/7.45 thf(type_def_64, type, set_Pr8536935166611901872et_nat: $tType).
% 18.75/7.45 thf(type_def_65, type, set_se8543413830569400298et_nat: $tType).
% 18.75/7.45 thf(type_def_66, type, set_Pr3286484037609594932et_nat: $tType).
% 18.75/7.45 thf(type_def_67, type, set_se2364587433798273647nt_int: $tType).
% 18.75/7.45 thf(type_def_68, type, set_Pr9222295170931077689nt_int: $tType).
% 18.75/7.45 thf(type_def_69, type, set_se7855581050983116737at_nat: $tType).
% 18.75/7.45 thf(type_def_70, type, set_se5479201105039950375at_nat: $tType).
% 18.75/7.45 thf(type_def_71, type, set_set_Product_unit: $tType).
% 18.75/7.45 thf(type_def_72, type, set_option_o: $tType).
% 18.75/7.45 thf(type_def_73, type, option_o: $tType).
% 18.75/7.45 thf(type_def_74, type, set_se3372686590935047281atural: $tType).
% 18.75/7.45 thf(type_def_75, type, set_Pr7564037697178849041atural: $tType).
% 18.75/7.45 thf(type_def_76, type, set_num: $tType).
% 18.75/7.45 thf(type_def_77, type, set_op687863988967635939nteger: $tType).
% 18.75/7.45 thf(type_def_78, type, set_option_int: $tType).
% 18.75/7.45 thf(type_def_79, type, set_option_nat: $tType).
% 18.75/7.45 thf(type_def_80, type, set_option_num: $tType).
% 18.75/7.45 thf(type_def_81, type, set_op4508134149509766951at_nat: $tType).
% 18.75/7.45 thf(type_def_82, type, set_op239864471688321678it_nat: $tType).
% 18.75/7.45 thf(type_def_83, type, set_Pr4811707699266497531nteger: $tType).
% 18.75/7.45 thf(type_def_84, type, set_Pr6496905503482889930er_int: $tType).
% 18.75/7.45 thf(type_def_85, type, set_Pr8986988648414616686er_nat: $tType).
% 18.75/7.45 thf(type_def_86, type, set_Pr3948176798113811640et_nat: $tType).
% 18.75/7.45 thf(type_def_87, type, set_Pr8415741480598773322nteger: $tType).
% 18.75/7.45 thf(type_def_88, type, set_Pr958786334691620121nt_int: $tType).
% 18.75/7.45 thf(type_def_89, type, set_Pr3448869479623346877nt_nat: $tType).
% 18.75/7.45 thf(type_def_90, type, set_Pr2406931829603198446nteger: $tType).
% 18.75/7.45 thf(type_def_91, type, set_Pr7995236796853374141at_int: $tType).
% 18.75/7.45 thf(type_def_92, type, set_Pr8693737435421807431at_nat: $tType).
% 18.75/7.45 thf(type_def_93, type, set_Pr1354866905816374718it_nat: $tType).
% 18.75/7.45 thf(type_def_94, type, set_rat: $tType).
% 18.75/7.45 thf(type_def_95, type, multis2468970476368604999at_nat: $tType).
% 18.75/7.45 thf(type_def_96, type, option8057788054806935849nteger: $tType).
% 18.75/7.45 thf(type_def_97, type, option7428179582072448501nteger: $tType).
% 18.75/7.45 thf(type_def_98, type, option_Code_integer: $tType).
% 18.75/7.45 thf(type_def_99, type, option_nat_o: $tType).
% 18.75/7.45 thf(type_def_100, type, option_int: $tType).
% 18.75/7.45 thf(type_def_101, type, option_nat: $tType).
% 18.75/7.45 thf(type_def_102, type, option8956607266484857688it_nat: $tType).
% 18.75/7.45 thf(type_def_103, type, produc8664842809031399944it_nat: $tType).
% 18.75/7.45 thf(type_def_104, type, produc7773217078559923341nt_int: $tType).
% 18.75/7.45 thf(type_def_105, type, produc3832618445565238089e_term: $tType).
% 18.75/7.45 thf(type_def_106, type, produc7360885484439884007_nat_o: $tType).
% 18.75/7.45 thf(type_def_107, type, produc1908205239877642774nteger: $tType).
% 18.75/7.45 thf(type_def_108, type, produc998928222018024388e_term: $tType).
% 18.75/7.45 thf(type_def_109, type, produc4962441903510821572_nat_o: $tType).
% 18.75/7.45 thf(type_def_110, type, produc6907119039986491712_nat_o: $tType).
% 18.75/7.45 thf(type_def_111, type, produc2285326912895808259nt_int: $tType).
% 18.75/7.45 thf(type_def_112, type, produc1821397396195235155e_term: $tType).
% 18.75/7.45 thf(type_def_113, type, product_prod_o_o: $tType).
% 18.75/7.45 thf(type_def_114, type, produc2256096406371053034er_int: $tType).
% 18.75/7.45 thf(type_def_115, type, produc6433947425880249742er_nat: $tType).
% 18.75/7.45 thf(type_def_116, type, produc6756470014200349799atural: $tType).
% 18.75/7.45 thf(type_def_117, type, produc3981471736659609608atural: $tType).
% 18.75/7.45 thf(type_def_118, type, produc6714399278180371524it_nat: $tType).
% 18.75/7.45 thf(type_def_119, type, option3216581401566546698it_nat: $tType).
% 18.75/7.45 thf(type_def_120, type, produc2963269191615333738nteger: $tType).
% 18.75/7.45 thf(type_def_121, type, product_prod_int_nat: $tType).
% 18.75/7.45 thf(type_def_122, type, produc2591615631378489102nteger: $tType).
% 18.75/7.45 thf(type_def_123, type, product_prod_nat_int: $tType).
% 18.75/7.45 thf(type_def_124, type, option5403585828896915703atural: $tType).
% 18.75/7.45 thf(type_def_125, type, produc3843707927480180839at_nat: $tType).
% 18.75/7.45 thf(type_def_126, type, set_nat_o: $tType).
% 18.75/7.45 thf(type_def_127, type, produc4193628355235574503at_nat: $tType).
% 18.75/7.45 thf(type_def_128, type, produc1319942482725812455at_nat: $tType).
% 18.75/7.45 thf(type_def_129, type, list_nat: $tType).
% 18.75/7.45 thf(type_def_130, type, set_se8531188866349061887nteger: $tType).
% 18.75/7.45 thf(type_def_131, type, set_set_set_int: $tType).
% 18.75/7.45 thf(type_def_132, type, set_set_set_list_nat: $tType).
% 18.75/7.45 thf(type_def_133, type, set_set_set_nat: $tType).
% 18.75/7.45 thf(type_def_134, type, set_se5158245632345848097at_nat: $tType).
% 18.75/7.45 thf(type_def_135, type, set_se7118615804146677933t_unit: $tType).
% 18.75/7.45 thf(type_def_136, type, array_a: $tType).
% 18.75/7.45 thf(type_def_137, type, typerep: $tType).
% 18.75/7.45 thf(type_def_138, type, heap_T5738788834812785303t_unit: $tType).
% 18.75/7.45 thf(type_def_139, type, list_char: $tType).
% 18.75/7.45 thf(type_def_140, type, produc2867611627572283311it_nat: $tType).
% 18.75/7.45 thf(type_def_141, type, produc3911288613690379145it_nat: $tType).
% 18.75/7.45 thf(type_def_142, type, list_int: $tType).
% 18.75/7.45 thf(type_def_143, type, option_set_o: $tType).
% 18.75/7.45 thf(type_def_144, type, option_set_int: $tType).
% 18.75/7.45 thf(type_def_145, type, option8963830502488799655at_nat: $tType).
% 18.75/7.45 thf(type_def_146, type, option1583680563626158861at_nat: $tType).
% 18.75/7.45 thf(type_def_147, type, option_assn: $tType).
% 18.75/7.45 thf(type_def_148, type, set_Pr8834758594704517033_o_int: $tType).
% 18.75/7.45 thf(type_def_149, type, set_Pr2101469702781467981_o_nat: $tType).
% 18.75/7.45 thf(type_def_150, type, set_Pr903927857289325719_int_o: $tType).
% 18.75/7.45 thf(type_def_151, type, set_Pr3149072824959771635_nat_o: $tType).
% 18.75/7.45 thf(type_def_152, type, set_Pr6558897299634722526_nat_o: $tType).
% 18.75/7.45 thf(type_def_153, type, option5190343406534369742et_nat: $tType).
% 18.75/7.45 thf(type_def_154, type, option2651255830984564193nteger: $tType).
% 18.75/7.45 thf(type_def_155, type, option936205604648967762et_nat: $tType).
% 18.75/7.45 thf(type_def_156, type, option4624381673175914239nt_int: $tType).
% 18.75/7.45 thf(type_def_157, type, produc6576344331059438605e_term: $tType).
% 18.75/7.45 thf(type_def_158, type, produc7819656566062154093et_nat: $tType).
% 18.75/7.45 thf(type_def_159, type, set_Pr7040061329075590551_o_num: $tType).
% 18.75/7.45 thf(type_def_160, type, set_Pr6777250647868329861it_nat: $tType).
% 18.75/7.45 thf(type_def_161, type, set_Pr2352657477744078772atural: $tType).
% 18.75/7.45 thf(type_def_162, type, set_Pr8387461105917469447nt_num: $tType).
% 18.75/7.45 thf(type_def_163, type, set_Pr6200539531224447659at_num: $tType).
% 18.75/7.45 thf(type_def_164, type, set_Pr633603713510679705it_nat: $tType).
% 18.75/7.45 thf(type_def_165, type, set_Pr7477759153910077568at_num: $tType).
% 18.75/7.45 thf(type_def_166, type, set_Pr8551490117392284871at_nat: $tType).
% 18.75/7.45 thf(type_def_167, type, sum_sum_nat_nat: $tType).
% 18.75/7.45 thf(type_def_168, type, option4256020574406277085nt_int: $tType).
% 18.75/7.45 thf(type_def_169, type, option8051342751916580710nteger: $tType).
% 18.75/7.45 thf(type_def_170, type, option2860828798490689354et_nat: $tType).
% 18.75/7.45 thf(type_def_171, type, option7541221861074943443nt_int: $tType).
% 18.75/7.45 thf(type_def_172, type, option4927543243414619207at_nat: $tType).
% 18.75/7.45 thf(type_def_173, type, option8699557107911914541at_nat: $tType).
% 18.75/7.45 thf(type_def_174, type, option_rat: $tType).
% 18.75/7.45 thf(type_def_175, type, option8137458692691377843t_unit: $tType).
% 18.75/7.45 thf(type_def_176, type, set_op3940070208846178154it_nat: $tType).
% 18.75/7.45 thf(type_def_177, type, set_Pr5142436192348053284it_nat: $tType).
% 18.75/7.45 thf(type_def_178, type, set_op989438649584373901at_nat: $tType).
% 18.75/7.45 thf(type_def_179, type, set_Pr5564308138774400199at_nat: $tType).
% 18.75/7.45 thf(type_def_180, type, set_in3461395444621081367e_term: $tType).
% 18.75/7.45 thf(type_def_181, type, set_Pr7604974323444597168e_term: $tType).
% 18.75/7.45 thf(type_def_182, type, set_Pr4532377907799695533_nat_o: $tType).
% 18.75/7.45 thf(type_def_183, type, set_Pr3642885161833720865e_term: $tType).
% 18.75/7.45 thf(type_def_184, type, set_Pr7909803484932130503_nat_o: $tType).
% 18.75/7.45 thf(type_def_185, type, set_Pr7717912310451564380at_nat: $tType).
% 18.75/7.45 thf(type_def_186, type, set_Pr1625285437083415874at_nat: $tType).
% 18.75/7.45 thf(type_def_187, type, set_Pr2539167527615954998at_nat: $tType).
% 18.75/7.45 thf(type_def_188, type, set_Pr552903133987017116at_nat: $tType).
% 18.75/7.45 thf(type_def_189, type, set_Co726186806682698383nteger: $tType).
% 18.75/7.45 thf(type_def_190, type, set_assn: $tType).
% 18.75/7.45 thf(type_def_191, type, set_Pr5889264611543340172t_unit: $tType).
% 18.75/7.45 thf(type_def_192, type, set_Pr4334478416066269672t_unit: $tType).
% 18.75/7.45 thf(type_def_193, type, set_Pr8497134830871917726it_int: $tType).
% 18.75/7.45 thf(type_def_194, type, set_Pr1763845938948868674it_nat: $tType).
% 18.75/7.45 thf(type_def_195, type, set_Pr5094982260447487303t_unit: $tType).
% 18.75/7.45 thf(type_def_196, type, produc8763457246119570046nteger: $tType).
% 18.75/7.45 thf(type_def_197, type, produc8731074985263844745atural: $tType).
% 18.75/7.45 thf(type_def_198, type, produc1945540942535730339e_term: $tType).
% 18.75/7.45 thf(type_def_199, type, produc7248412053542808358at_nat: $tType).
% 18.75/7.45 thf(type_def_200, type, produc4471711990508489141at_nat: $tType).
% 18.75/7.45 thf(type_def_201, type, produc8187290932660736981e_term: $tType).
% 18.75/7.45 thf(type_def_202, type, produc4972180933644002618e_term: $tType).
% 18.75/7.45 thf(type_def_203, type, produc989692990947075319atural: $tType).
% 18.75/7.45 thf(type_def_204, type, produc4928098042776334183_nat_o: $tType).
% 18.75/7.45 thf(type_def_205, type, produc4499399687821757879e_term: $tType).
% 18.75/7.45 thf(type_def_206, type, product_prod_o_int: $tType).
% 18.75/7.45 thf(type_def_207, type, product_prod_o_nat: $tType).
% 18.75/7.45 thf(type_def_208, type, produc6653097349344004940it_nat: $tType).
% 18.75/7.45 thf(type_def_209, type, product_prod_int_o: $tType).
% 18.75/7.45 thf(type_def_210, type, produc4166570645942440679at_nat: $tType).
% 18.75/7.45 thf(type_def_211, type, product_prod_nat_o: $tType).
% 18.75/7.45 thf(type_def_212, type, product_prod_nat_num: $tType).
% 18.75/7.45 thf(type_def_213, type, produc3313772616054891654at_nat: $tType).
% 18.75/7.45 thf(type_def_214, type, produc2501202720802129403nt_int: $tType).
% 18.75/7.45 thf(type_def_215, type, produc824974754969098637nteger: $tType).
% 18.75/7.45 thf(type_def_216, type, produc5657529347773406293et_nat: $tType).
% 18.75/7.45 thf(type_def_217, type, produc6830853553727218525et_nat: $tType).
% 18.75/7.45 thf(type_def_218, type, produc2432570611225516007nt_int: $tType).
% 18.75/7.45 thf(type_def_219, type, produc3334582477557816039nteger: $tType).
% 18.75/7.45 thf(type_def_220, type, produc8111630337999740517et_nat: $tType).
% 18.75/7.45 thf(type_def_221, type, produc1219242969750017639nt_int: $tType).
% 18.75/7.45 thf(type_def_222, type, produc652263959640188542_nat_o: $tType).
% 18.75/7.45 thf(type_def_223, type, produc859450856879609959at_nat: $tType).
% 18.75/7.45 thf(type_def_224, type, produc2714363965264676845at_nat: $tType).
% 18.75/7.45 thf(type_def_225, type, produc366245978424229472at_nat: $tType).
% 18.75/7.45 thf(type_def_226, type, produc2087150632810049441at_nat: $tType).
% 18.75/7.45 thf(type_def_227, type, produc1906917888121415911at_nat: $tType).
% 18.75/7.45 thf(type_def_228, type, produc7369051934464679207_set_o: $tType).
% 18.75/7.45 thf(type_def_229, type, produc6491284506569428743nteger: $tType).
% 18.75/7.45 thf(type_def_230, type, produc2115011035271226405et_int: $tType).
% 18.75/7.45 thf(type_def_231, type, produc2934264451710624999od_o_o: $tType).
% 18.75/7.45 thf(type_def_232, type, produc732395585841259969at_nat: $tType).
% 18.75/7.45 thf(type_def_233, type, produc7299876168958306407at_nat: $tType).
% 18.75/7.45 thf(type_def_234, type, set_Code_natural: $tType).
% 18.75/7.45 thf(type_def_235, type, set_Pr3451248702717554689st_nat: $tType).
% 18.75/7.45 thf(type_def_236, type, set_Pr7549493975000385137at_nat: $tType).
% 18.75/7.45 thf(type_def_237, type, set_Pr698032948827214833st_nat: $tType).
% 18.75/7.45 thf(type_def_238, type, set_Pr7705059561495379578_nat_o: $tType).
% 18.75/7.45 thf(type_def_239, type, set_Pr1628540301243981434e_term: $tType).
% 18.75/7.45 thf(type_def_240, type, set_Pr4208978187861016310_nat_o: $tType).
% 18.75/7.45 thf(type_def_241, type, set_Pr9020418513037773311e_term: $tType).
% 18.75/7.45 thf(type_def_242, type, set_Pr7309386651551657097e_term: $tType).
% 18.75/7.45 thf(type_def_243, type, set_Pr5488025237498180813et_nat: $tType).
% 18.75/7.45 thf(type_def_244, type, produc6237349844158694175nteger: $tType).
% 18.75/7.45 thf(type_def_245, type, produc382792921321436433nt_int: $tType).
% 18.75/7.45 thf(type_def_246, type, produc3295550550304853304nteger: $tType).
% 18.75/7.45 thf(type_def_247, type, produc3346328345660746739nteger: $tType).
% 18.75/7.45 thf(type_def_248, type, produc6691574917238108761nteger: $tType).
% 18.75/7.45 thf(type_def_249, type, produc8299537390109905600et_nat: $tType).
% 18.75/7.45 thf(type_def_250, type, produc4130039061994950697nteger: $tType).
% 18.75/7.45 thf(type_def_251, type, produc5219672859094816389atural: $tType).
% 18.75/7.45 thf(type_def_252, type, produc5665947927044467078nt_int: $tType).
% 18.75/7.45 thf(type_def_253, type, produc5111566536631596683et_nat: $tType).
% 18.75/7.45 thf(type_def_254, type, produc6025053409261769070rm_int: $tType).
% 18.75/7.45 thf(type_def_255, type, produc759720530913461378nt_int: $tType).
% 18.75/7.45 thf(type_def_256, type, produc7172142986261921671rm_int: $tType).
% 18.75/7.45 thf(type_def_257, type, produc6162884466328367972nteger: $tType).
% 18.75/7.45 thf(type_def_258, type, produc3776562785724475560_o_int: $tType).
% 18.75/7.45 thf(type_def_259, type, produc8065447618272157327et_nat: $tType).
% 18.75/7.45 thf(type_def_260, type, produc5577056076408194680rm_int: $tType).
% 18.75/7.45 thf(type_def_261, type, produc5966032636589952099nteger: $tType).
% 18.75/7.45 thf(type_def_262, type, produc7142191362829087448er_num: $tType).
% 18.75/7.45 thf(type_def_263, type, produc1828647624359046049st_nat: $tType).
% 18.75/7.45 thf(type_def_264, type, produc1540777390238407569at_nat: $tType).
% 18.75/7.45 thf(type_def_265, type, produc4575160907756185873st_nat: $tType).
% 18.75/7.45 thf(type_def_266, type, product_prod_o_num: $tType).
% 18.75/7.45 thf(type_def_267, type, produc2900562427881843919it_nat: $tType).
% 18.75/7.45 thf(type_def_268, type, product_prod_int_num: $tType).
% 18.75/7.45 thf(type_def_269, type, produc3839731585411834681it_nat: $tType).
% 18.75/7.45 thf(type_def_270, type, produc9082142974458947146at_num: $tType).
% 18.75/7.45 thf(type_def_271, type, ref_array_a: $tType).
% 18.75/7.45 thf(type_def_272, type, ref_Product_unit: $tType).
% 18.75/7.45 thf(type_def_273, type, set_in2553536192574375378_nat_o: $tType).
% 18.75/7.45 thf(type_def_274, type, set_in2260935666578096390nteger: $tType).
% 18.75/7.45 thf(type_def_275, type, set_in1345054734626228863atural: $tType).
% 18.75/7.45 thf(type_def_276, type, set_in6154042108061588260nt_int: $tType).
% 18.75/7.45 thf(type_def_277, type, set_na3661387095409732706nteger: $tType).
% 18.75/7.45 thf(type_def_278, type, set_na2454399383705037859atural: $tType).
% 18.75/7.45 thf(type_def_279, type, set_na7251125088705586816nt_int: $tType).
% 18.75/7.45 thf(type_def_280, type, set_Pr9591959067864425nteger: $tType).
% 18.75/7.45 thf(type_def_281, type, set_Pr7322412474522714716atural: $tType).
% 18.75/7.45 thf(type_def_282, type, set_Pr3770298976803184519nt_int: $tType).
% 18.75/7.45 thf(type_def_283, type, set_Pr2072254264782222413at_nat: $tType).
% 18.75/7.45 thf(type_def_284, type, set_Pr5070339090747523585at_nat: $tType).
% 18.75/7.45 thf(type_def_285, type, set_Pr1604112560894399303at_nat: $tType).
% 18.75/7.45 thf(type_def_286, type, set_Pr1425283071195816930_int_o: $tType).
% 18.75/7.45 thf(type_def_287, type, set_Pr606876518868980121eger_o: $tType).
% 18.75/7.45 thf(type_def_288, type, set_Pr1230246726286442933_nat_o: $tType).
% 18.75/7.45 thf(type_def_289, type, set_Pr8959645425803247153_nat_o: $tType).
% 18.75/7.45 thf(type_def_290, type, set_Pr6358892174463501804_int_o: $tType).
% 18.75/7.45 thf(type_def_291, type, set_Pr5582243495563764594_nat_o: $tType).
% 18.75/7.45 thf(type_def_292, type, set_Pr7010166363911110284_nat_o: $tType).
% 18.75/7.45 thf(type_def_293, type, set_mu2057375006010111271at_nat: $tType).
% 18.75/7.45 thf(type_def_294, type, char: $tType).
% 18.75/7.45 thf(type_def_295, type, set_Pr7577011563204128103nteger: $tType).
% 18.75/7.45 thf(type_def_296, type, set_Pr2522554150109002629et_int: $tType).
% 18.75/7.45 thf(type_def_297, type, set_Pr7140365069852192003e_term: $tType).
% 18.75/7.45 thf(type_def_298, type, set_Pr2560585780119916871nt_int: $tType).
% 18.75/7.45 thf(type_def_299, type, set_Pr8634505666381077339nt_int: $tType).
% 18.75/7.45 thf(type_def_300, type, set_Pr6418322821503574069e_term: $tType).
% 18.75/7.45 thf(type_def_301, type, set_Pr5052581263052047815nteger: $tType).
% 18.75/7.45 thf(type_def_302, type, set_Pr1722956316086891245nteger: $tType).
% 18.75/7.45 thf(type_def_303, type, set_Pr2161125870931222855_nat_o: $tType).
% 18.75/7.45 thf(type_def_304, type, set_Pr7928877670098842301et_nat: $tType).
% 18.75/7.45 thf(type_def_305, type, set_Pr3444600963470892981et_nat: $tType).
% 18.75/7.45 thf(type_def_306, type, set_Pr719794911490849221et_nat: $tType).
% 18.75/7.45 thf(type_def_307, type, set_Pr4675205556198584599e_term: $tType).
% 18.75/7.45 thf(type_def_308, type, set_Pr4708930517165415495nt_int: $tType).
% 18.75/7.45 thf(type_def_309, type, set_Pr4577759397028426247_set_o: $tType).
% 18.75/7.45 thf(type_def_310, type, set_Pr7459493094073627847at_nat: $tType).
% 18.75/7.45 thf(func_def_0, type, set_Pr3444600963470892981et_nat: $tType).
% 18.75/7.45 thf(func_def_1, type, produc5657529347773406293et_nat: $tType).
% 18.75/7.45 thf(func_def_2, type, set_Pr1722956316086891245nteger: $tType).
% 18.75/7.45 thf(func_def_3, type, produc824974754969098637nteger: $tType).
% 18.75/7.45 thf(func_def_4, type, set_Pr4708930517165415495nt_int: $tType).
% 18.75/7.45 thf(func_def_5, type, produc2432570611225516007nt_int: $tType).
% 18.75/7.45 thf(func_def_6, type, set_Pr7928877670098842301et_nat: $tType).
% 18.75/7.45 thf(func_def_7, type, produc6830853553727218525et_nat: $tType).
% 18.75/7.45 thf(func_def_8, type, set_Pr6418322821503574069e_term: $tType).
% 18.75/7.45 thf(func_def_9, type, produc8187290932660736981e_term: $tType).
% 18.75/7.45 thf(func_def_10, type, set_Pr4675205556198584599e_term: $tType).
% 18.75/7.45 thf(func_def_11, type, set_se5120235452707311462et_nat: $tType).
% 18.75/7.45 thf(func_def_12, type, set_Pr8634505666381077339nt_int: $tType).
% 18.75/7.45 thf(func_def_13, type, produc4499399687821757879e_term: $tType).
% 18.75/7.45 thf(func_def_14, type, set_Pr1230246726286442933_nat_o: $tType).
% 18.75/7.45 thf(func_def_15, type, option2860828798490689354et_nat: $tType).
% 18.75/7.45 thf(func_def_16, type, set_Pr7705059561495379578_nat_o: $tType).
% 18.75/7.45 thf(func_def_17, type, set_Pr8536935166611901872et_nat: $tType).
% 18.75/7.45 thf(func_def_18, type, produc2501202720802129403nt_int: $tType).
% 18.75/7.45 thf(func_def_19, type, produc4193628355235574503at_nat: $tType).
% 18.75/7.45 thf(func_def_20, type, set_Pr1457143144315775327_nat_o: $tType).
% 18.75/7.45 thf(func_def_21, type, produc4962441903510821572_nat_o: $tType).
% 18.75/7.45 thf(func_def_22, type, produc2732055786443039994et_nat: $tType).
% 18.75/7.45 thf(func_def_23, type, set_Pr7459493094073627847at_nat: $tType).
% 18.75/7.45 thf(func_def_24, type, produc1319942482725812455at_nat: $tType).
% 18.75/7.45 thf(func_def_25, type, set_Pr5564308138774400199at_nat: $tType).
% 18.75/7.45 thf(func_def_26, type, set_se124295367203800706nteger: $tType).
% 18.75/7.45 thf(func_def_27, type, set_Pr606876518868980121eger_o: $tType).
% 18.75/7.45 thf(func_def_28, type, produc1906917888121415911at_nat: $tType).
% 18.75/7.45 thf(func_def_29, type, option8051342751916580710nteger: $tType).
% 18.75/7.45 thf(func_def_30, type, set_Pr1628540301243981434e_term: $tType).
% 18.75/7.45 thf(func_def_31, type, set_Pr1281608226676607948nteger: $tType).
% 18.75/7.45 thf(func_def_32, type, set_Pr8914822823351560561eger_o: $tType).
% 18.75/7.45 thf(func_def_33, type, produc998928222018024388e_term: $tType).
% 18.75/7.45 thf(func_def_34, type, produc989692990947075319atural: $tType).
% 18.75/7.45 thf(func_def_35, type, produc1908205239877642774nteger: $tType).
% 18.75/7.45 thf(func_def_36, type, set_se2364587433798273647nt_int: $tType).
% 18.75/7.45 thf(func_def_37, type, set_Pr6358892174463501804_int_o: $tType).
% 18.75/7.45 thf(func_def_38, type, option7541221861074943443nt_int: $tType).
% 18.75/7.45 thf(func_def_39, type, set_Pr7309386651551657097e_term: $tType).
% 18.75/7.45 thf(func_def_40, type, set_Pr9222295170931077689nt_int: $tType).
% 18.75/7.45 thf(func_def_41, type, set_Pr5050529186185961540_int_o: $tType).
% 18.75/7.45 thf(func_def_42, type, set_se8543413830569400298et_nat: $tType).
% 18.75/7.45 thf(func_def_43, type, set_Pr2161125870931222855_nat_o: $tType).
% 18.75/7.45 thf(func_def_44, type, set_Pr8959645425803247153_nat_o: $tType).
% 18.75/7.45 thf(func_def_45, type, produc1821397396195235155e_term: $tType).
% 18.75/7.45 thf(func_def_46, type, produc2285326912895808259nt_int: $tType).
% 18.75/7.45 thf(func_def_47, type, option5190343406534369742et_nat: $tType).
% 18.75/7.45 thf(func_def_48, type, set_Pr7140365069852192003e_term: $tType).
% 18.75/7.45 thf(func_def_49, type, produc3295550550304853304nteger: $tType).
% 18.75/7.45 thf(func_def_50, type, set_Pr4208978187861016310_nat_o: $tType).
% 18.75/7.45 thf(func_def_51, type, set_Pr3286484037609594932et_nat: $tType).
% 18.75/7.45 thf(func_def_52, type, produc4928098042776334183_nat_o: $tType).
% 18.75/7.45 thf(func_def_53, type, set_Pr8208987589773510107_nat_o: $tType).
% 18.75/7.45 thf(func_def_54, type, set_Pr719794911490849221et_nat: $tType).
% 18.75/7.45 thf(func_def_55, type, produc1945540942535730339e_term: $tType).
% 18.75/7.45 thf(func_def_56, type, produc4130039061994950697nteger: $tType).
% 18.75/7.45 thf(func_def_57, type, produc7172142986261921671rm_int: $tType).
% 18.75/7.45 thf(func_def_58, type, produc6907119039986491712_nat_o: $tType).
% 18.75/7.45 thf(func_def_59, type, produc3925858234332021118et_nat: $tType).
% 18.75/7.45 thf(func_def_60, type, set_Pr5070339090747523585at_nat: $tType).
% 18.75/7.45 thf(func_def_61, type, set_Pr2072254264782222413at_nat: $tType).
% 18.75/7.45 thf(func_def_62, type, produc8111630337999740517et_nat: $tType).
% 18.75/7.45 thf(func_def_63, type, produc5577056076408194680rm_int: $tType).
% 18.75/7.45 thf(func_def_64, type, produc2087150632810049441at_nat: $tType).
% 18.75/7.45 thf(func_def_65, type, produc2714363965264676845at_nat: $tType).
% 18.75/7.45 thf(func_def_66, type, produc8731074985263844745atural: $tType).
% 18.75/7.45 thf(func_def_67, type, produc8763457246119570046nteger: $tType).
% 18.75/7.45 thf(func_def_68, type, set_Pr7604974323444597168e_term: $tType).
% 18.75/7.45 thf(func_def_69, type, produc5966032636589952099nteger: $tType).
% 18.75/7.45 thf(func_def_70, type, set_se7394616247590735609nt_int: $tType).
% 18.75/7.45 thf(func_def_71, type, produc5219672859094816389atural: $tType).
% 18.75/7.45 thf(func_def_72, type, set_Pr1425283071195816930_int_o: $tType).
% 18.75/7.45 thf(func_def_73, type, produc6576344331059438605e_term: $tType).
% 18.75/7.45 thf(func_def_74, type, set_Pr3642885161833720865e_term: $tType).
% 18.75/7.45 thf(func_def_75, type, set_Pr552903133987017116at_nat: $tType).
% 18.75/7.45 thf(func_def_76, type, set_Pr1625285437083415874at_nat: $tType).
% 18.75/7.45 thf(func_def_77, type, option4256020574406277085nt_int: $tType).
% 18.75/7.45 thf(func_def_78, type, set_Pr9020418513037773311e_term: $tType).
% 18.75/7.45 thf(func_def_79, type, set_Pr1872883991513573699nt_int: $tType).
% 18.75/7.45 thf(func_def_80, type, set_Pr1604112560894399303at_nat: $tType).
% 18.75/7.45 thf(func_def_81, type, set_Pr5052581263052047815nteger: $tType).
% 18.75/7.45 thf(func_def_82, type, produc3911288613690379145it_nat: $tType).
% 18.75/7.45 thf(func_def_83, type, produc2867611627572283311it_nat: $tType).
% 18.75/7.45 thf(func_def_84, type, set_in8474487674441654202_int_o: $tType).
% 18.75/7.45 thf(func_def_85, type, set_Pr633603713510679705it_nat: $tType).
% 18.75/7.45 thf(func_def_86, type, set_op989438649584373901at_nat: $tType).
% 18.75/7.45 thf(func_def_87, type, option1583680563626158861at_nat: $tType).
% 18.75/7.45 thf(func_def_88, type, produc3832618445565238089e_term: $tType).
% 18.75/7.45 thf(func_def_89, type, produc7773217078559923341nt_int: $tType).
% 18.75/7.45 thf(func_def_90, type, set_Pr8551490117392284871at_nat: $tType).
% 18.75/7.45 thf(func_def_91, type, set_Pr6777250647868329861it_nat: $tType).
% 18.75/7.45 thf(func_def_92, type, option7428179582072448501nteger: $tType).
% 18.75/7.45 thf(func_def_93, type, set_se5479201105039950375at_nat: $tType).
% 18.75/7.45 thf(func_def_94, type, produc7299876168958306407at_nat: $tType).
% 18.75/7.45 thf(func_def_95, type, produc6756470014200349799atural: $tType).
% 18.75/7.45 thf(func_def_96, type, produc3334582477557816039nteger: $tType).
% 18.75/7.45 thf(func_def_97, type, set_Pr7010166363911110284_nat_o: $tType).
% 18.75/7.45 thf(func_def_98, type, produc3839731585411834681it_nat: $tType).
% 18.75/7.45 thf(func_def_99, type, set_Pr7322412474522714716atural: $tType).
% 18.75/7.45 thf(func_def_100, type, option8699557107911914541at_nat: $tType).
% 18.75/7.45 thf(func_def_101, type, set_op239864471688321678it_nat: $tType).
% 18.75/7.45 thf(func_def_102, type, set_op3940070208846178154it_nat: $tType).
% 18.75/7.45 thf(func_def_103, type, produc4166570645942440679at_nat: $tType).
% 18.75/7.45 thf(func_def_104, type, produc2900562427881843919it_nat: $tType).
% 18.75/7.45 thf(func_def_105, type, set_Pr4329608150637261639at_nat: $tType).
% 18.75/7.45 thf(func_def_106, type, produc6691574917238108761nteger: $tType).
% 18.75/7.45 thf(func_def_107, type, produc4471711990508489141at_nat: $tType).
% 18.75/7.45 thf(func_def_108, type, set_na2454399383705037859atural: $tType).
% 18.75/7.45 thf(func_def_109, type, set_in1345054734626228863atural: $tType).
% 18.75/7.45 thf(func_def_110, type, produc6237349844158694175nteger: $tType).
% 18.75/7.45 thf(func_def_111, type, set_se9180647916752606350_nat_o: $tType).
% 18.75/7.45 thf(func_def_112, type, option8956607266484857688it_nat: $tType).
% 18.75/7.45 thf(func_def_113, type, option3216581401566546698it_nat: $tType).
% 18.75/7.45 thf(func_def_114, type, produc5111566536631596683et_nat: $tType).
% 18.75/7.45 thf(func_def_115, type, produc8299537390109905600et_nat: $tType).
% 18.75/7.45 thf(func_def_116, type, produc3843707927480180839at_nat: $tType).
% 18.75/7.45 thf(func_def_117, type, set_Pr1354866905816374718it_nat: $tType).
% 18.75/7.45 thf(func_def_118, type, produc3776562785724475560_o_int: $tType).
% 18.75/7.45 thf(func_def_119, type, set_Pr457366540195662369at_nat: $tType).
% 18.75/7.45 thf(func_def_120, type, set_Pr5142436192348053284it_nat: $tType).
% 18.75/7.45 thf(func_def_121, type, produc6025053409261769070rm_int: $tType).
% 18.75/7.45 thf(func_def_122, type, set_Pr2352657477744078772atural: $tType).
% 18.75/7.45 thf(func_def_123, type, produc8065447618272157327et_nat: $tType).
% 18.75/7.45 thf(func_def_124, type, set_Pr8693737435421807431at_nat: $tType).
% 18.75/7.45 thf(func_def_125, type, set_Pr2560585780119916871nt_int: $tType).
% 18.75/7.45 thf(func_def_126, type, produc8664842809031399944it_nat: $tType).
% 18.75/7.45 thf(func_def_127, type, produc732395585841259969at_nat: $tType).
% 18.75/7.45 thf(func_def_128, type, produc6714399278180371524it_nat: $tType).
% 18.75/7.45 thf(func_def_129, type, set_Pr1932065953672099015od_o_o: $tType).
% 18.75/7.45 thf(func_def_130, type, produc3981471736659609608atural: $tType).
% 18.75/7.45 thf(func_def_131, type, produc5835291356934675326atural: $tType).
% 18.75/7.45 thf(func_def_132, type, produc3346328345660746739nteger: $tType).
% 18.75/7.45 thf(func_def_133, type, set_Pr4532377907799695533_nat_o: $tType).
% 18.75/7.45 thf(func_def_134, type, produc859450856879609959at_nat: $tType).
% 18.75/7.45 thf(func_def_135, type, produc1219242969750017639nt_int: $tType).
% 18.75/7.45 thf(func_def_136, type, set_in3461395444621081367e_term: $tType).
% 18.75/7.45 thf(func_def_137, type, set_Pr9591959067864425nteger: $tType).
% 18.75/7.45 thf(func_def_138, type, option936205604648967762et_nat: $tType).
% 18.75/7.45 thf(func_def_139, type, produc2934264451710624999od_o_o: $tType).
% 18.75/7.45 thf(func_def_140, type, set_Pr7577011563204128103nteger: $tType).
% 18.75/7.45 thf(func_def_141, type, set_Pr3948176798113811640et_nat: $tType).
% 18.75/7.45 thf(func_def_142, type, produc6162884466328367972nteger: $tType).
% 18.75/7.45 thf(func_def_143, type, set_na3661387095409732706nteger: $tType).
% 18.75/7.45 thf(func_def_144, type, set_in2260935666578096390nteger: $tType).
% 18.75/7.45 thf(func_def_145, type, produc4972180933644002618e_term: $tType).
% 18.75/7.45 thf(func_def_146, type, produc6241069584506657477e_term: $tType).
% 18.75/7.45 thf(func_def_147, type, set_se3372686590935047281atural: $tType).
% 18.75/7.45 thf(func_def_148, type, set_in2553536192574375378_nat_o: $tType).
% 18.75/7.45 thf(func_def_149, type, produc6491284506569428743nteger: $tType).
% 18.75/7.45 thf(func_def_150, type, produc3658429121746597890et_nat: $tType).
% 18.75/7.45 thf(func_def_151, type, set_Pr7477759153910077568at_num: $tType).
% 18.75/7.45 thf(func_def_152, type, set_Pr2539167527615954998at_nat: $tType).
% 18.75/7.45 thf(func_def_153, type, set_Pr7717912310451564380at_nat: $tType).
% 18.75/7.45 thf(func_def_154, type, produc366245978424229472at_nat: $tType).
% 18.75/7.45 thf(func_def_155, type, produc3313772616054891654at_nat: $tType).
% 18.75/7.45 thf(func_def_156, type, produc5665947927044467078nt_int: $tType).
% 18.75/7.45 thf(func_def_157, type, produc382792921321436433nt_int: $tType).
% 18.75/7.45 thf(func_def_158, type, option5403585828896915703atural: $tType).
% 18.75/7.45 thf(func_def_159, type, option2651255830984564193nteger: $tType).
% 18.75/7.45 thf(func_def_160, type, set_Pr3451248702717554689st_nat: $tType).
% 18.75/7.45 thf(func_def_161, type, set_Pr3770298976803184519nt_int: $tType).
% 18.75/7.45 thf(func_def_162, type, produc8551481072490612790e_term: $tType).
% 18.75/7.45 thf(func_def_163, type, set_Pr6558897299634722526_nat_o: $tType).
% 18.75/7.45 thf(func_def_164, type, set_se5158245632345848097at_nat: $tType).
% 18.75/7.45 thf(func_def_165, type, set_Pr5488025237498180813et_nat: $tType).
% 18.75/7.45 thf(func_def_166, type, set_Pr2522554150109002629et_int: $tType).
% 18.75/7.45 thf(func_def_167, type, set_Pr7564037697178849041atural: $tType).
% 18.75/7.45 thf(func_def_168, type, set_Pr4811707699266497531nteger: $tType).
% 18.75/7.45 thf(func_def_169, type, option6357759511663192854e_term: $tType).
% 18.75/7.45 thf(func_def_170, type, produc6653097349344004940it_nat: $tType).
% 18.75/7.45 thf(func_def_171, type, produc9082142974458947146at_num: $tType).
% 18.75/7.45 thf(func_def_172, type, produc7248412053542808358at_nat: $tType).
% 18.75/7.45 thf(func_def_173, type, produc759720530913461378nt_int: $tType).
% 18.75/7.45 thf(func_def_174, type, set_Pr5094982260447487303t_unit: $tType).
% 18.75/7.45 thf(func_def_175, type, set_Pr7909803484932130503_nat_o: $tType).
% 18.75/7.45 thf(func_def_176, type, set_mu2057375006010111271at_nat: $tType).
% 18.75/7.45 thf(func_def_177, type, set_op4508134149509766951at_nat: $tType).
% 18.75/7.45 thf(func_def_178, type, set_na7251125088705586816nt_int: $tType).
% 18.75/7.45 thf(func_def_179, type, set_in6154042108061588260nt_int: $tType).
% 18.75/7.45 thf(func_def_180, type, option8963830502488799655at_nat: $tType).
% 18.75/7.45 thf(func_def_181, type, produc1828647624359046049st_nat: $tType).
% 18.75/7.45 thf(func_def_182, type, set_Pr698032948827214833st_nat: $tType).
% 18.75/7.45 thf(func_def_183, type, set_Pr7549493975000385137at_nat: $tType).
% 18.75/7.45 thf(func_def_184, type, produc652263959640188542_nat_o: $tType).
% 18.75/7.45 thf(func_def_185, type, option8057788054806935849nteger: $tType).
% 18.75/7.45 thf(func_def_186, type, set_se7855581050983116737at_nat: $tType).
% 18.75/7.45 thf(func_def_187, type, set_Pr2406931829603198446nteger: $tType).
% 18.75/7.45 thf(func_def_188, type, set_Pr8415741480598773322nteger: $tType).
% 18.75/7.45 thf(func_def_189, type, set_Pr8986988648414616686er_nat: $tType).
% 18.75/7.45 thf(func_def_190, type, set_Pr6496905503482889930er_int: $tType).
% 18.75/7.45 thf(func_def_191, type, produc7819656566062154093et_nat: $tType).
% 18.75/7.45 thf(func_def_192, type, produc2115011035271226405et_int: $tType).
% 18.75/7.45 thf(func_def_193, type, produc7822875418678951345atural: $tType).
% 18.75/7.45 thf(func_def_194, type, produc8923325533196201883nteger: $tType).
% 18.75/7.45 thf(func_def_195, type, set_Pr4577759397028426247_set_o: $tType).
% 18.75/7.45 thf(func_def_196, type, set_Pr1763845938948868674it_nat: $tType).
% 18.75/7.45 thf(func_def_197, type, set_Pr8497134830871917726it_int: $tType).
% 18.75/7.45 thf(func_def_198, type, set_Pr4334478416066269672t_unit: $tType).
% 18.75/7.45 thf(func_def_199, type, set_Pr5889264611543340172t_unit: $tType).
% 18.75/7.45 thf(func_def_200, type, set_Pr5582243495563764594_nat_o: $tType).
% 18.75/7.45 thf(func_def_201, type, set_Co726186806682698383nteger: $tType).
% 18.75/7.45 thf(func_def_202, type, produc7360885484439884007_nat_o: $tType).
% 18.75/7.45 thf(func_def_203, type, multis2468970476368604999at_nat: $tType).
% 18.75/7.45 thf(func_def_204, type, set_set_set_list_nat: $tType).
% 18.75/7.45 thf(func_def_205, type, option4927543243414619207at_nat: $tType).
% 18.75/7.45 thf(func_def_206, type, option4624381673175914239nt_int: $tType).
% 18.75/7.45 thf(func_def_207, type, set_se8531188866349061887nteger: $tType).
% 18.75/7.45 thf(func_def_208, type, set_se7118615804146677933t_unit: $tType).
% 18.75/7.45 thf(func_def_209, type, produc4575160907756185873st_nat: $tType).
% 18.75/7.45 thf(func_def_210, type, produc1540777390238407569at_nat: $tType).
% 18.75/7.45 thf(func_def_211, type, set_Pr6200539531224447659at_num: $tType).
% 18.75/7.45 thf(func_def_212, type, set_Pr1261947904930325089at_nat: $tType).
% 18.75/7.45 thf(func_def_213, type, set_Pr7995236796853374141at_int: $tType).
% 18.75/7.45 thf(func_def_214, type, set_Pr8387461105917469447nt_num: $tType).
% 18.75/7.45 thf(func_def_215, type, set_Pr3448869479623346877nt_nat: $tType).
% 18.75/7.45 thf(func_def_216, type, set_Pr958786334691620121nt_int: $tType).
% 18.75/7.45 thf(func_def_217, type, produc2591615631378489102nteger: $tType).
% 18.75/7.45 thf(func_def_218, type, produc2963269191615333738nteger: $tType).
% 18.75/7.45 thf(func_def_219, type, produc7142191362829087448er_num: $tType).
% 18.75/7.45 thf(func_def_220, type, produc6433947425880249742er_nat: $tType).
% 18.75/7.45 thf(func_def_221, type, produc2256096406371053034er_int: $tType).
% 18.75/7.45 thf(func_def_222, type, produc7369051934464679207_set_o: $tType).
% 18.75/7.45 thf(func_def_223, type, set_option_set_nat: $tType).
% 18.75/7.45 thf(func_def_224, type, set_op687863988967635939nteger: $tType).
% 18.75/7.45 thf(func_def_225, type, set_op3165557761946182707t_unit: $tType).
% 18.75/7.45 thf(func_def_226, type, set_nat_nat_o: $tType).
% 18.75/7.45 thf(func_def_227, type, option8137458692691377843t_unit: $tType).
% 18.75/7.45 thf(func_def_228, type, set_set_list_nat: $tType).
% 18.75/7.45 thf(func_def_229, type, set_Pr3149072824959771635_nat_o: $tType).
% 18.75/7.45 thf(func_def_230, type, set_Pr903927857289325719_int_o: $tType).
% 18.75/7.45 thf(func_def_231, type, set_Pr7040061329075590551_o_num: $tType).
% 18.75/7.45 thf(func_def_232, type, set_Pr2101469702781467981_o_nat: $tType).
% 18.75/7.45 thf(func_def_233, type, set_Pr8834758594704517033_o_int: $tType).
% 18.75/7.45 thf(func_def_234, type, produc6271795597528267376eger_o: $tType).
% 18.75/7.45 thf(func_def_235, type, set_set_set_nat: $tType).
% 18.75/7.45 thf(func_def_236, type, set_set_set_int: $tType).
% 18.75/7.45 thf(func_def_237, type, set_set_Code_integer: $tType).
% 18.75/7.45 thf(func_def_238, type, heap_T5738788834812785303t_unit: $tType).
% 18.75/7.45 thf(func_def_239, type, heap_T6362127782908069795rray_a: $tType).
% 18.75/7.45 thf(func_def_240, type, set_set_Product_unit: $tType).
% 18.75/7.45 thf(func_def_241, type, heap_e7401611519738050253t_unit: $tType).
% 18.75/7.45 thf(func_def_242, type, product_prod_num_num: $tType).
% 18.75/7.45 thf(func_def_243, type, product_prod_nat_num: $tType).
% 18.75/7.45 thf(func_def_244, type, product_prod_nat_nat: $tType).
% 18.75/7.45 thf(func_def_245, type, product_prod_nat_int: $tType).
% 18.75/7.45 thf(func_def_246, type, product_prod_int_num: $tType).
% 18.75/7.45 thf(func_def_247, type, product_prod_int_nat: $tType).
% 18.75/7.45 thf(func_def_248, type, product_prod_int_int: $tType).
% 18.75/7.45 thf(func_def_249, type, set_Product_prod_o_o: $tType).
% 18.75/7.45 thf(func_def_250, type, sum_sum_nat_nat: $tType).
% 18.75/7.45 thf(func_def_251, type, set_option_num: $tType).
% 18.75/7.45 thf(func_def_252, type, set_option_nat: $tType).
% 18.75/7.45 thf(func_def_253, type, set_option_int: $tType).
% 18.75/7.45 thf(func_def_254, type, option_set_nat: $tType).
% 18.75/7.45 thf(func_def_255, type, option_set_int: $tType).
% 18.75/7.45 thf(func_def_256, type, option_Code_integer: $tType).
% 18.75/7.45 thf(func_def_257, type, option_Product_unit: $tType).
% 18.75/7.45 thf(func_def_258, type, option_nat_o: $tType).
% 18.75/7.45 thf(func_def_259, type, set_list_nat: $tType).
% 18.75/7.45 thf(func_def_260, type, product_prod_nat_o: $tType).
% 18.75/7.45 thf(func_def_261, type, product_prod_int_o: $tType).
% 18.75/7.45 thf(func_def_262, type, product_prod_o_num: $tType).
% 18.75/7.45 thf(func_def_263, type, product_prod_o_nat: $tType).
% 18.75/7.45 thf(func_def_264, type, product_prod_o_int: $tType).
% 18.75/7.45 thf(func_def_265, type, set_set_nat: $tType).
% 18.75/7.45 thf(func_def_266, type, set_set_int: $tType).
% 18.75/7.45 thf(func_def_267, type, set_Code_natural: $tType).
% 18.75/7.45 thf(func_def_268, type, set_Code_integer: $tType).
% 18.75/7.45 thf(func_def_269, type, option_assn: $tType).
% 18.75/7.45 thf(func_def_270, type, ref_Product_unit: $tType).
% 18.75/7.45 thf(func_def_271, type, set_Product_unit: $tType).
% 18.75/7.45 thf(func_def_272, type, set_option_o: $tType).
% 18.75/7.45 thf(func_def_273, type, set_nat_o: $tType).
% 18.75/7.45 thf(func_def_274, type, option_set_o: $tType).
% 18.75/7.45 thf(func_def_275, type, ref_array_a: $tType).
% 18.75/7.45 thf(func_def_276, type, product_prod_o_o: $tType).
% 18.75/7.45 thf(func_def_277, type, set_assn: $tType).
% 18.75/7.45 thf(func_def_278, type, set_set_o: $tType).
% 18.75/7.45 thf(func_def_279, type, option_rat: $tType).
% 18.75/7.45 thf(func_def_280, type, option_num: $tType).
% 18.75/7.45 thf(func_def_281, type, option_nat: $tType).
% 18.75/7.45 thf(func_def_282, type, option_int: $tType).
% 18.75/7.45 thf(func_def_283, type, list_char: $tType).
% 18.75/7.45 thf(func_def_284, type, list_nat: $tType).
% 18.75/7.45 thf(func_def_285, type, list_int: $tType).
% 18.75/7.45 thf(func_def_286, type, set_rat: $tType).
% 18.75/7.45 thf(func_def_287, type, set_num: $tType).
% 18.75/7.45 thf(func_def_288, type, set_nat: $tType).
% 18.75/7.45 thf(func_def_289, type, set_int: $tType).
% 18.75/7.45 thf(func_def_290, type, code_natural: $tType).
% 18.75/7.45 thf(func_def_291, type, code_integer: $tType).
% 18.75/7.45 thf(func_def_292, type, product_unit: $tType).
% 18.75/7.45 thf(func_def_293, type, option_o: $tType).
% 18.75/7.45 thf(func_def_294, type, array_a: $tType).
% 18.75/7.45 thf(func_def_295, type, list_a: $tType).
% 18.75/7.45 thf(func_def_296, type, typerep: $tType).
% 18.75/7.45 thf(func_def_297, type, assn: $tType).
% 18.75/7.45 thf(func_def_298, type, set_o: $tType).
% 18.75/7.45 thf(func_def_299, type, char: $tType).
% 18.75/7.45 thf(func_def_300, type, rat: $tType).
% 18.75/7.45 thf(func_def_301, type, num: $tType).
% 18.75/7.45 thf(func_def_302, type, nat: $tType).
% 18.75/7.45 thf(func_def_303, type, int: $tType).
% 18.75/7.45 thf(func_def_304, type, a: $tType).
% 18.75/7.45 thf(func_def_305, type, archim2889992004027027881ng_rat: rat > int).
% 18.75/7.45 thf(func_def_306, type, archim3151403230148437115or_rat: rat > int).
% 18.75/7.45 thf(func_def_307, type, archimedean_frac_rat: rat > rat).
% 18.75/7.45 thf(func_def_308, type, archim7778729529865785530nd_rat: rat > int).
% 18.75/7.45 thf(func_def_309, type, array_make_a: nat > (nat > a) > heap_T6362127782908069795rray_a).
% 18.75/7.45 thf(func_def_310, type, array_new_a: nat > a > heap_T6362127782908069795rray_a).
% 18.75/7.45 thf(func_def_311, type, array_of_list_a: list_a > heap_T6362127782908069795rray_a).
% 18.75/7.45 thf(func_def_312, type, rep_assn: assn > produc3658429121746597890et_nat > $o).
% 18.75/7.45 thf(func_def_313, type, in_range: produc3658429121746597890et_nat > $o).
% 18.75/7.45 thf(func_def_314, type, in_range_rel: produc3658429121746597890et_nat > produc3658429121746597890et_nat > $o).
% 18.75/7.45 thf(func_def_315, type, one_assn_raw: produc3658429121746597890et_nat > $o).
% 18.75/7.45 thf(func_def_316, type, one_assn_raw_rel: produc3658429121746597890et_nat > produc3658429121746597890et_nat > $o).
% 18.75/7.45 thf(func_def_317, type, proper: (produc3658429121746597890et_nat > $o) > $o).
% 18.75/7.45 thf(func_def_318, type, pure_assn: $o > assn).
% 18.75/7.45 thf(func_def_319, type, relH: set_nat > heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit > $o).
% 18.75/7.45 thf(func_def_320, type, times_assn_raw: (produc3658429121746597890et_nat > $o) > (produc3658429121746597890et_nat > $o) > produc3658429121746597890et_nat > $o).
% 18.75/7.45 thf(func_def_321, type, times_assn_raw_rel: produc2732055786443039994et_nat > produc2732055786443039994et_nat > $o).
% 18.75/7.45 thf(func_def_322, type, wand_assn: assn > assn > assn).
% 18.75/7.45 thf(func_def_323, type, wand_raw: (produc3658429121746597890et_nat > $o) > (produc3658429121746597890et_nat > $o) > produc3658429121746597890et_nat > $o).
% 18.75/7.45 thf(func_def_324, type, wand_raw_rel: produc2732055786443039994et_nat > produc2732055786443039994et_nat > $o).
% 18.75/7.45 thf(func_def_325, type, bNF_Cardinal_ctwo: set_Product_prod_o_o).
% 18.75/7.45 thf(func_def_326, type, bNF_Cardinal_czero_o: set_Product_prod_o_o).
% 18.75/7.45 thf(func_def_327, type, bNF_Ca3793111618940312692of_nat: set_nat > set_Pr1261947904930325089at_nat).
% 18.75/7.45 thf(func_def_328, type, bNF_Ca8331644756375544342r_on_o: set_o > set_Product_prod_o_o > $o).
% 18.75/7.45 thf(func_def_329, type, bNF_Ca8665028551170535155natLeq: set_Pr1261947904930325089at_nat).
% 18.75/7.45 thf(func_def_330, type, bNF_re2555365631850037877_int_o: (((int > $o) > int > $o) > ((int > $o) > int > $o) > $o) > (((int > int > $o) > int > int > $o) > ((int > int > $o) > int > int > $o) > $o) > (((int > $o) > int > $o) > (int > int > $o) > int > int > $o) > (((int > $o) > int > $o) > (int > int > $o) > int > int > $o) > $o).
% 18.75/7.45 thf(func_def_331, type, bNF_re5051145820034318685nt_int: (((int > $o) > int > int) > ((int > $o) > int > int) > $o) > (((int > int > $o) > int > int > int) > ((int > int > $o) > int > int > int) > $o) > (((int > $o) > int > int) > (int > int > $o) > int > int > int) > (((int > $o) > int > int) > (int > int > $o) > int > int > int) > $o).
% 18.75/7.45 thf(func_def_332, type, bNF_re615132412071444453_nat_o: (((int > $o) > nat > $o) > ((int > $o) > nat > $o) > $o) > (((int > int > $o) > int > nat > $o) > ((int > int > $o) > int > nat > $o) > $o) > (((int > $o) > nat > $o) > (int > int > $o) > int > nat > $o) > (((int > $o) > nat > $o) > (int > int > $o) > int > nat > $o) > $o).
% 18.75/7.45 thf(func_def_333, type, bNF_re3161894838932316637_int_o: (((int > int) > int > $o) > ((int > int) > int > $o) > $o) > (((int > int > int) > int > int > $o) > ((int > int > int) > int > int > $o) > $o) > (((int > int) > int > $o) > (int > int > int) > int > int > $o) > (((int > int) > int > $o) > (int > int > int) > int > int > $o) > $o).
% 18.75/7.45 thf(func_def_334, type, bNF_re4659646225794970589_nat_o: (((int > int) > nat > $o) > ((int > int) > nat > $o) > $o) > (((int > int > int) > int > nat > $o) > ((int > int > int) > int > nat > $o) > $o) > (((int > int) > nat > $o) > (int > int > int) > int > nat > $o) > (((int > int) > nat > $o) > (int > int > int) > int > nat > $o) > $o).
% 18.75/7.45 thf(func_def_335, type, bNF_re3491090157995142405_int_o: (((nat > $o) > int > $o) > ((nat > $o) > int > $o) > $o) > (((int > nat > $o) > int > int > $o) > ((int > nat > $o) > int > int > $o) > $o) > (((nat > $o) > int > $o) > (int > nat > $o) > int > int > $o) > (((nat > $o) > int > $o) > (int > nat > $o) > int > int > $o) > $o).
% 18.75/7.45 thf(func_def_336, type, bNF_re5539255234643219293nt_int: (((nat > $o) > int > int) > ((nat > $o) > int > int) > $o) > (((int > nat > $o) > int > int > int) > ((int > nat > $o) > int > int > int) > $o) > (((nat > $o) > int > int) > (int > nat > $o) > int > int > int) > (((nat > $o) > int > int) > (int > nat > $o) > int > int > int) > $o).
% 18.75/7.45 thf(func_def_337, type, bNF_re1550856938216548981_nat_o: (((nat > $o) > nat > $o) > ((nat > $o) > nat > $o) > $o) > (((int > nat > $o) > int > nat > $o) > ((int > nat > $o) > int > nat > $o) > $o) > (((nat > $o) > nat > $o) > (int > nat > $o) > int > nat > $o) > (((nat > $o) > nat > $o) > (int > nat > $o) > int > nat > $o) > $o).
% 18.75/7.45 thf(func_def_338, type, bNF_re4919612610145136063nteger: ((code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger) > (code_integer > code_integer) > $o) > (((code_integer > code_integer) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger) > ((num > code_integer) > num > code_integer) > $o) > ((code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger) > (code_integer > code_integer) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger) > ((code_integer > code_integer) > (num > code_integer) > num > code_integer) > $o).
% 18.75/7.45 thf(func_def_339, type, bNF_re1890273300020150979nt_num: ((code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger) > (nat > num) > $o) > (((code_integer > code_integer) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger) > ((int > nat) > int > num) > $o) > ((code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger) > (code_integer > code_integer) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger) > ((nat > num) > (int > nat) > int > num) > $o).
% 18.75/7.45 thf(func_def_340, type, bNF_re8134695817916415679nteger: ((code_integer > code_integer) > (code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger) > $o) > (((num > code_integer) > num > code_integer) > ((code_integer > code_integer) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger) > $o) > ((code_integer > code_integer) > (num > code_integer) > num > code_integer) > ((code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger) > (code_integer > code_integer) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger) > $o).
% 18.75/7.45 thf(func_def_341, type, bNF_re5979881370344185769nteger: ((code_integer > code_integer) > (code_integer > code_integer) > $o) > (((num > code_integer) > num > code_integer) > ((num > code_integer) > num > code_integer) > $o) > ((code_integer > code_integer) > (num > code_integer) > num > code_integer) > ((code_integer > code_integer) > (num > code_integer) > num > code_integer) > $o).
% 18.75/7.45 thf(func_def_342, type, bNF_re5190287125156074331nt_num: ((code_integer > code_integer) > (int > nat) > $o) > ((code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger) > (int > num) > $o) > ((code_integer > code_integer) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger) > ((int > nat) > int > num) > $o).
% 18.75/7.45 thf(func_def_343, type, bNF_re5469402333911078061nt_num: ((code_integer > code_integer) > (nat > num) > $o) > (((num > code_integer) > num > code_integer) > ((int > nat) > int > num) > $o) > ((code_integer > code_integer) > (num > code_integer) > num > code_integer) > ((nat > num) > (int > nat) > int > num) > $o).
% 18.75/7.45 thf(func_def_344, type, bNF_re6724329528997265415nteger: ((code_integer > code_integer) > (num > code_integer) > $o) > ((code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger) > (num > code_integer) > $o) > ((code_integer > code_integer) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger) > ((num > code_integer) > num > code_integer) > $o).
% 18.75/7.45 thf(func_def_345, type, bNF_re1900612664124570461_int_o: ((int > int > $o) > (int > int > $o) > $o) > (((int > int) > int > int > $o) > ((int > int) > int > int > $o) > $o) > ((int > int > $o) > (int > int) > int > int > $o) > ((int > int > $o) > (int > int) > int > int > $o) > $o).
% 18.75/7.45 thf(func_def_346, type, bNF_re8651060166502312541_int_o: ((int > int > $o) > (int > int > $o) > $o) > ((int > int > $o) > (int > int > $o) > $o) > ((int > int > $o) > int > int > $o) > ((int > int > $o) > int > int > $o) > $o).
% 18.75/7.45 thf(func_def_347, type, bNF_re7462748251485907171nt_int: ((int > int > $o) > (int > int > $o) > $o) > ((int > int > int) > (int > int > int) > $o) > ((int > int > $o) > int > int > int) > ((int > int > $o) > int > int > int) > $o).
% 18.75/7.45 thf(func_def_348, type, bNF_re2446162618891206493_nat_o: ((int > int > $o) > (int > int > $o) > $o) > ((int > nat > $o) > (int > nat > $o) > $o) > ((int > int > $o) > int > nat > $o) > ((int > int > $o) > int > nat > $o) > $o).
% 18.75/7.45 thf(func_def_349, type, bNF_re4984751527058004117nt_int: ((int > int > int) > (int > int > int) > $o) > (((int > int) > int > int > int) > ((int > int) > int > int > int) > $o) > ((int > int > int) > (int > int) > int > int > int) > ((int > int > int) > (int > int) > int > int > int) > $o).
% 18.75/7.45 thf(func_def_350, type, bNF_re1313934062736347107_int_o: ((int > int > int) > (int > int > int) > $o) > ((int > int > $o) > (int > int > $o) > $o) > ((int > int > int) > int > int > $o) > ((int > int > int) > int > int > $o) > $o).
% 18.75/7.45 thf(func_def_351, type, bNF_re4332408551980016867_nat_o: ((int > int > int) > (int > int > int) > $o) > ((int > nat > $o) > (int > nat > $o) > $o) > ((int > int > int) > int > nat > $o) > ((int > int > int) > int > nat > $o) > $o).
% 18.75/7.45 thf(func_def_352, type, bNF_re62019127700022579nt_rat: ((int > int > product_prod_int_int) > (int > int > rat) > $o) > (((int > int) > int > int > product_prod_int_int) > ((int > int) > int > int > rat) > $o) > ((int > int > product_prod_int_int) > (int > int) > int > int > product_prod_int_int) > ((int > int > rat) > (int > int) > int > int > rat) > $o).
% 18.75/7.45 thf(func_def_353, type, bNF_re7908124382625962333_nat_o: ((int > nat > $o) > (int > nat > $o) > $o) > (((int > int) > int > nat > $o) > ((int > int) > int > nat > $o) > $o) > ((int > nat > $o) > (int > int) > int > nat > $o) > ((int > nat > $o) > (int > int) > int > nat > $o) > $o).
% 18.75/7.45 thf(func_def_354, type, bNF_re2655111580231008093_int_o: ((int > nat > $o) > (int > nat > $o) > $o) > ((int > int > $o) > (int > int > $o) > $o) > ((int > nat > $o) > int > int > $o) > ((int > nat > $o) > int > int > $o) > $o).
% 18.75/7.45 thf(func_def_355, type, bNF_re7395152722673581539nt_int: ((int > nat > $o) > (int > nat > $o) > $o) > ((int > int > int) > (int > int > int) > $o) > ((int > nat > $o) > int > int > int) > ((int > nat > $o) > int > int > int) > $o).
% 18.75/7.45 thf(func_def_356, type, bNF_re5673586069474677853_nat_o: ((int > nat > $o) > (int > nat > $o) > $o) > ((int > nat > $o) > (int > nat > $o) > $o) > ((int > nat > $o) > int > nat > $o) > ((int > nat > $o) > int > nat > $o) > $o).
% 18.75/7.45 thf(func_def_357, type, bNF_re2535741173671728349_nat_o: ((int > $o) > (int > $o) > $o) > ((nat > $o) > (nat > $o) > $o) > ((int > $o) > nat > $o) > ((int > $o) > nat > $o) > $o).
% 18.75/7.45 thf(func_def_358, type, bNF_re3014639844587090765_int_o: ((int > int) > (int > int) > $o) > ((int > int > $o) > (int > int > $o) > $o) > ((int > int) > int > int > $o) > ((int > int) > int > int > $o) > $o).
% 18.75/7.45 thf(func_def_359, type, bNF_re724639330072410579nt_int: ((int > int) > (int > int) > $o) > ((int > int > int) > (int > int > int) > $o) > ((int > int) > int > int > int) > ((int > int) > int > int > int) > $o).
% 18.75/7.45 thf(func_def_360, type, bNF_re949775918795716016nt_rat: ((int > int) > (int > int) > $o) > ((int > int > product_prod_int_int) > (int > int > rat) > $o) > ((int > int) > int > int > product_prod_int_int) > ((int > int) > int > int > rat) > $o).
% 18.75/7.45 thf(func_def_361, type, bNF_re6033114333830760525_nat_o: ((int > int) > (int > int) > $o) > ((int > nat > $o) > (int > nat > $o) > $o) > ((int > int) > int > nat > $o) > ((int > int) > int > nat > $o) > $o).
% 18.75/7.45 thf(func_def_362, type, bNF_re9099949428469764705nt_num: ((int > nat) > (int > nat) > $o) > ((int > num) > (int > num) > $o) > ((int > nat) > int > num) > ((int > nat) > int > num) > $o).
% 18.75/7.45 thf(func_def_363, type, bNF_re8894579221946749965nteger: ((int > nat) > (num > code_integer) > $o) > ((int > num) > (num > code_integer) > $o) > ((int > nat) > int > num) > ((num > code_integer) > num > code_integer) > $o).
% 18.75/7.45 thf(func_def_364, type, bNF_re2724346968851715293_int_o: ((nat > $o) > (nat > $o) > $o) > ((int > $o) > (int > $o) > $o) > ((nat > $o) > int > $o) > ((nat > $o) > int > $o) > $o).
% 18.75/7.45 thf(func_def_365, type, bNF_re7183634743573646861nt_int: ((nat > $o) > (nat > $o) > $o) > ((int > int) > (int > int) > $o) > ((nat > $o) > int > int) > ((nat > $o) > int > int) > $o).
% 18.75/7.45 thf(func_def_366, type, bNF_re2697311982885662685_nat_o: ((nat > $o) > (nat > $o) > $o) > ((nat > $o) > (nat > $o) > $o) > ((nat > $o) > nat > $o) > ((nat > $o) > nat > $o) > $o).
% 18.75/7.45 thf(func_def_367, type, bNF_re2163612987331707565nteger: ((nat > num) > (code_integer > code_integer) > $o) > (((int > nat) > int > num) > ((num > code_integer) > num > code_integer) > $o) > ((nat > num) > (int > nat) > int > num) > ((code_integer > code_integer) > (num > code_integer) > num > code_integer) > $o).
% 18.75/7.45 thf(func_def_368, type, bNF_re3846787885862361009nt_num: ((nat > num) > (nat > num) > $o) > (((int > nat) > int > num) > ((int > nat) > int > num) > $o) > ((nat > num) > (int > nat) > int > num) > ((nat > num) > (int > nat) > int > num) > $o).
% 18.75/7.45 thf(func_def_369, type, bNF_re2439920061672227847nteger: ((num > code_integer) > (code_integer > code_integer) > $o) > ((num > code_integer) > (code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger) > $o) > ((num > code_integer) > num > code_integer) > ((code_integer > code_integer) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger) > $o).
% 18.75/7.45 thf(func_def_370, type, bNF_re1151383970801924621nt_num: ((num > code_integer) > (int > nat) > $o) > ((num > code_integer) > (int > num) > $o) > ((num > code_integer) > num > code_integer) > ((int > nat) > int > num) > $o).
% 18.75/7.45 thf(func_def_371, type, bNF_re6097285183634142137nteger: ((num > code_integer) > (num > code_integer) > $o) > ((num > code_integer) > (num > code_integer) > $o) > ((num > code_integer) > num > code_integer) > ((num > code_integer) > num > code_integer) > $o).
% 18.75/7.45 thf(func_def_372, type, bNF_re1551779926989065179nt_nat: ($o > $o > $o) > (int > nat > $o) > ($o > int) > ($o > nat) > $o).
% 18.75/7.45 thf(func_def_373, type, bNF_re916649866902569443nt_rat: ($o > $o > $o) > (int > rat > $o) > ($o > int) > ($o > rat) > $o).
% 18.75/7.45 thf(func_def_374, type, bNF_re4863541036035986956nteger: ($o > $o > $o) > (nat > code_integer > $o) > ($o > nat) > ($o > code_integer) > $o).
% 18.75/7.45 thf(func_def_375, type, bNF_re549935744578960347at_int: ($o > $o > $o) > (nat > int > $o) > ($o > nat) > ($o > int) > $o).
% 18.75/7.45 thf(func_def_376, type, bNF_re552426215088010623at_nat: ($o > $o > $o) > (nat > nat > $o) > ($o > nat) > ($o > nat) > $o).
% 18.75/7.45 thf(func_def_377, type, bNF_re9140668191856290695at_rat: ($o > $o > $o) > (nat > rat > $o) > ($o > nat) > ($o > rat) > $o).
% 18.75/7.45 thf(func_def_378, type, bNF_re5635613845597506580nteger: ($o > $o > $o) > (rat > code_integer > $o) > ($o > rat) > ($o > code_integer) > $o).
% 18.75/7.45 thf(func_def_379, type, bNF_re233381100644094435at_int: ($o > $o > $o) > (rat > int > $o) > ($o > rat) > ($o > int) > $o).
% 18.75/7.45 thf(func_def_380, type, bNF_re235871571153144711at_nat: ($o > $o > $o) > (rat > nat > $o) > ($o > rat) > ($o > nat) > $o).
% 18.75/7.45 thf(func_def_381, type, bNF_re8824113547921424783at_rat: ($o > $o > $o) > (rat > rat > $o) > ($o > rat) > ($o > rat) > $o).
% 18.75/7.45 thf(func_def_382, type, bNF_re9137223911888007311n_assn: (assn > assn > $o) > ((assn > assn) > (assn > assn) > $o) > (assn > assn > assn) > (assn > assn > assn) > $o).
% 18.75/7.45 thf(func_def_383, type, bNF_re3650450707543776735t_assn: (assn > assn > $o) > ((nat > assn) > (nat > assn) > $o) > (assn > nat > assn) > (assn > nat > assn) > $o).
% 18.75/7.45 thf(func_def_384, type, bNF_re1143782165119297793n_assn: (assn > assn > $o) > (assn > assn > $o) > (assn > assn) > (assn > assn) > $o).
% 18.75/7.45 thf(func_def_385, type, bNF_re5822757241383739566nteger: (assn > code_integer > $o) > ((assn > assn) > (code_integer > code_integer) > $o) > (assn > assn > assn) > (code_integer > code_integer > code_integer) > $o).
% 18.75/7.45 thf(func_def_386, type, bNF_re2102180915162216137nteger: (assn > code_integer > $o) > ((nat > assn) > (nat > code_integer) > $o) > (assn > nat > assn) > (code_integer > nat > code_integer) > $o).
% 18.75/7.45 thf(func_def_387, type, bNF_re4134162077946812779nteger: (assn > code_integer > $o) > (assn > code_integer > $o) > (assn > assn) > (code_integer > code_integer) > $o).
% 18.75/7.45 thf(func_def_388, type, bNF_re7882741803053012379nt_int: (assn > int > $o) > ((assn > assn) > (int > int) > $o) > (assn > assn > assn) > (int > int > int) > $o).
% 18.75/7.45 thf(func_def_389, type, bNF_re185025794348816359at_int: (assn > int > $o) > ((nat > assn) > (nat > int) > $o) > (assn > nat > assn) > (int > nat > int) > $o).
% 18.75/7.45 thf(func_def_390, type, bNF_re2927800259774540553sn_int: (assn > int > $o) > (assn > int > $o) > (assn > assn) > (int > int) > $o).
% 18.75/7.45 thf(func_def_391, type, bNF_re4386305596031132807at_nat: (assn > nat > $o) > ((assn > assn) > (nat > nat) > $o) > (assn > assn > assn) > (nat > nat > nat) > $o).
% 18.75/7.45 thf(func_def_392, type, bNF_re8560028565313717551at_nat: (assn > nat > $o) > ((nat > assn) > (nat > nat) > $o) > (assn > nat > assn) > (nat > nat > nat) > $o).
% 18.75/7.45 thf(func_def_393, type, bNF_re6742580585434904145sn_nat: (assn > nat > $o) > (assn > nat > $o) > (assn > assn) > (nat > nat) > $o).
% 18.75/7.45 thf(func_def_394, type, bNF_re967558844708792991at_rat: (assn > rat > $o) > ((assn > assn) > (rat > rat) > $o) > (assn > assn > assn) > (rat > rat > rat) > $o).
% 18.75/7.45 thf(func_def_395, type, bNF_re6138836914430330175at_rat: (assn > rat > $o) > ((nat > assn) > (nat > rat) > $o) > (assn > nat > assn) > (rat > nat > rat) > $o).
% 18.75/7.45 thf(func_def_396, type, bNF_re9003240792272343649sn_rat: (assn > rat > $o) > (assn > rat > $o) > (assn > assn) > (rat > rat) > $o).
% 18.75/7.45 thf(func_def_397, type, bNF_re7789648203153440174n_assn: (code_integer > assn > $o) > ((code_integer > code_integer) > (assn > assn) > $o) > (code_integer > code_integer > code_integer) > (assn > assn > assn) > $o).
% 18.75/7.45 thf(func_def_398, type, bNF_re2546461910754330953t_assn: (code_integer > assn > $o) > ((nat > code_integer) > (nat > assn) > $o) > (code_integer > nat > code_integer) > (assn > nat > assn) > $o).
% 18.75/7.45 thf(func_def_399, type, bNF_re1475883931861434731r_assn: (code_integer > assn > $o) > (code_integer > assn > $o) > (code_integer > code_integer) > (assn > assn) > $o).
% 18.75/7.45 thf(func_def_400, type, bNF_re122555440370955213nteger: (code_integer > code_integer > $o) > ((code_integer > code_integer) > (code_integer > code_integer) > $o) > (code_integer > code_integer > code_integer) > (code_integer > code_integer > code_integer) > $o).
% 18.75/7.45 thf(func_def_401, type, bNF_re5462749793222359603nteger: (code_integer > code_integer > $o) > ((nat > code_integer) > (nat > code_integer) > $o) > (code_integer > nat > code_integer) > (code_integer > nat > code_integer) > $o).
% 18.75/7.45 thf(func_def_402, type, bNF_re4341081746073172381nteger: (code_integer > code_integer > $o) > ((produc8923325533196201883nteger > produc8923325533196201883nteger) > code_integer > $o) > (code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger) > (code_integer > code_integer) > $o).
% 18.75/7.45 thf(func_def_403, type, bNF_re3370092614548195229nteger: (code_integer > code_integer > $o) > (code_integer > (produc8923325533196201883nteger > produc8923325533196201883nteger) > $o) > (code_integer > code_integer) > (code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger) > $o).
% 18.75/7.45 thf(func_def_404, type, bNF_re1062419521925302741nteger: (code_integer > code_integer > $o) > (code_integer > code_integer > $o) > (code_integer > code_integer) > (code_integer > code_integer) > $o).
% 18.75/7.45 thf(func_def_405, type, bNF_re8304916493157054650nt_int: (code_integer > int > $o) > ((code_integer > code_integer) > (int > int) > $o) > (code_integer > code_integer > code_integer) > (int > int > int) > $o).
% 18.75/7.45 thf(func_def_406, type, bNF_re6766650671887726929at_int: (code_integer > int > $o) > ((nat > code_integer) > (nat > int) > $o) > (code_integer > nat > code_integer) > (int > nat > int) > $o).
% 18.75/7.45 thf(func_def_407, type, bNF_re8127238762813979689er_num: (code_integer > int > $o) > ((produc8923325533196201883nteger > produc8923325533196201883nteger) > num > $o) > (code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger) > (int > num) > $o).
% 18.75/7.45 thf(func_def_408, type, bNF_re2888858428391045491er_int: (code_integer > int > $o) > (code_integer > int > $o) > (code_integer > code_integer) > (int > int) > $o).
% 18.75/7.45 thf(func_def_409, type, bNF_re2891348898900095767er_nat: (code_integer > int > $o) > (code_integer > nat > $o) > (code_integer > code_integer) > (int > nat) > $o).
% 18.75/7.45 thf(func_def_410, type, bNF_re3981674901896804262at_nat: (code_integer > nat > $o) > ((code_integer > code_integer) > (nat > nat) > $o) > (code_integer > code_integer > code_integer) > (nat > nat > nat) > $o).
% 18.75/7.45 thf(func_def_411, type, bNF_re4269568176766901913at_nat: (code_integer > nat > $o) > ((nat > code_integer) > (nat > nat) > $o) > (code_integer > nat > code_integer) > (nat > nat > nat) > $o).
% 18.75/7.45 thf(func_def_412, type, bNF_re7119966052990372301er_num: (code_integer > nat > $o) > ((produc8923325533196201883nteger > produc8923325533196201883nteger) > num > $o) > (code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger) > (nat > num) > $o).
% 18.75/7.45 thf(func_def_413, type, bNF_re5201166830993046715er_nat: (code_integer > nat > $o) > (code_integer > nat > $o) > (code_integer > code_integer) > (nat > nat) > $o).
% 18.75/7.45 thf(func_def_414, type, bNF_re1758498617148825349er_num: (code_integer > nat > $o) > (code_integer > num > $o) > (code_integer > code_integer) > (nat > num) > $o).
% 18.75/7.45 thf(func_def_415, type, bNF_re166502229267952730nteger: (code_integer > num > $o) > ((produc8923325533196201883nteger > produc8923325533196201883nteger) > code_integer > $o) > (code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger) > (num > code_integer) > $o).
% 18.75/7.45 thf(func_def_416, type, bNF_re7350422212947406738nteger: (code_integer > num > $o) > (code_integer > code_integer > $o) > (code_integer > code_integer) > (num > code_integer) > $o).
% 18.75/7.45 thf(func_def_417, type, bNF_re2976496150901874110at_rat: (code_integer > rat > $o) > ((code_integer > code_integer) > (rat > rat) > $o) > (code_integer > code_integer > code_integer) > (rat > rat > rat) > $o).
% 18.75/7.45 thf(func_def_418, type, bNF_re1167376069379428009at_rat: (code_integer > rat > $o) > ((nat > code_integer) > (nat > rat) > $o) > (code_integer > nat > code_integer) > (rat > nat > rat) > $o).
% 18.75/7.45 thf(func_def_419, type, bNF_re4698098036185532619er_rat: (code_integer > rat > $o) > (code_integer > rat > $o) > (code_integer > code_integer) > (rat > rat) > $o).
% 18.75/7.45 thf(func_def_420, type, bNF_re6321650412969554871eger_o: (int > code_integer > $o) > ((int > $o) > (code_integer > $o) > $o) > (int > int > $o) > (code_integer > code_integer > $o) > $o).
% 18.75/7.45 thf(func_def_421, type, bNF_re398004352372739002nteger: (int > code_integer > $o) > ((int > int) > (code_integer > code_integer) > $o) > (int > int > int) > (code_integer > code_integer > code_integer) > $o).
% 18.75/7.45 thf(func_def_422, type, bNF_re4711666741709854504_nat_o: (int > code_integer > $o) > ((nat > $o) > (nat > $o) > $o) > (int > nat > $o) > (code_integer > nat > $o) > $o).
% 18.75/7.45 thf(func_def_423, type, bNF_re6574881592172037608er_o_o: (int > code_integer > $o) > ($o > $o > $o) > (int > $o) > (code_integer > $o) > $o).
% 18.75/7.45 thf(func_def_424, type, bNF_re3379532845092657523nteger: (int > code_integer > $o) > (int > code_integer > $o) > (int > int) > (code_integer > code_integer) > $o).
% 18.75/7.45 thf(func_def_425, type, bNF_re3804157879324367682nt_int: (int > code_integer > $o) > (int > int > $o) > (int > int) > (code_integer > int) > $o).
% 18.75/7.45 thf(func_def_426, type, bNF_re1831474436612530402atural: (int > code_integer > $o) > (nat > code_natural > $o) > (int > nat) > (code_integer > code_natural) > $o).
% 18.75/7.45 thf(func_def_427, type, bNF_re2807294637932363402at_nat: (int > code_integer > $o) > (nat > nat > $o) > (int > nat) > (code_integer > nat) > $o).
% 18.75/7.45 thf(func_def_428, type, bNF_re6718328864250387230um_num: (int > code_integer > $o) > (num > num > $o) > (int > num) > (code_integer > num) > $o).
% 18.75/7.45 thf(func_def_429, type, bNF_re2342410721167621787atural: (int > code_natural > $o) > ((int > int) > (code_natural > code_natural) > $o) > (int > int > int) > (code_natural > code_natural > code_natural) > $o).
% 18.75/7.45 thf(func_def_430, type, bNF_re5484556299188842761atural: (int > code_natural > $o) > (int > code_natural > $o) > (int > int) > (code_natural > code_natural) > $o).
% 18.75/7.45 thf(func_def_431, type, bNF_re3403563459893282935_int_o: (int > int > $o) > ((int > $o) > (int > $o) > $o) > (int > int > $o) > (int > int > $o) > $o).
% 18.75/7.45 thf(func_def_432, type, bNF_re711492959462206631nt_int: (int > int > $o) > ((int > int) > (int > int) > $o) > (int > int > int) > (int > int > int) > $o).
% 18.75/7.45 thf(func_def_433, type, bNF_re157797125943740599nt_int: (int > int > $o) > ((int > product_prod_int_int) > (int > product_prod_int_int) > $o) > (int > int > product_prod_int_int) > (int > int > product_prod_int_int) > $o).
% 18.75/7.45 thf(func_def_434, type, bNF_re3461391660133120880nt_rat: (int > int > $o) > ((int > product_prod_int_int) > (int > rat) > $o) > (int > int > product_prod_int_int) > (int > int > rat) > $o).
% 18.75/7.45 thf(func_def_435, type, bNF_re3376528473927230327_nat_o: (int > int > $o) > ((nat > $o) > (nat > $o) > $o) > (int > nat > $o) > (int > nat > $o) > $o).
% 18.75/7.45 thf(func_def_436, type, bNF_re5089333283451836215nt_o_o: (int > int > $o) > ($o > $o > $o) > (int > $o) > (int > $o) > $o).
% 18.75/7.45 thf(func_def_437, type, bNF_re1784066744496875891nteger: (int > int > $o) > (code_integer > code_integer > $o) > (int > code_integer) > (int > code_integer) > $o).
% 18.75/7.45 thf(func_def_438, type, bNF_re343602593470180162er_int: (int > int > $o) > (code_integer > int > $o) > (int > code_integer) > (int > int) > $o).
% 18.75/7.45 thf(func_def_439, type, bNF_re8934335040747510510er_rat: (int > int > $o) > (code_integer > rat > $o) > (int > code_integer) > (int > rat) > $o).
% 18.75/7.45 thf(func_def_440, type, bNF_re6290619412732081552atural: (int > int > $o) > (code_natural > produc7822875418678951345atural > $o) > (int > code_natural) > (int > produc7822875418678951345atural) > $o).
% 18.75/7.45 thf(func_def_441, type, bNF_re982302072995117890nteger: (int > int > $o) > (int > code_integer > $o) > (int > int) > (int > code_integer) > $o).
% 18.75/7.45 thf(func_def_442, type, bNF_re4712519889275205905nt_int: (int > int > $o) > (int > int > $o) > (int > int) > (int > int) > $o).
% 18.75/7.45 thf(func_def_443, type, bNF_re4079880299697760445nt_rat: (int > int > $o) > (int > rat > $o) > (int > int) > (int > rat) > $o).
% 18.75/7.45 thf(func_def_444, type, bNF_re3715656647883201625at_nat: (int > int > $o) > (nat > nat > $o) > (int > nat) > (int > nat) > $o).
% 18.75/7.45 thf(func_def_445, type, bNF_re7626690874201225453um_num: (int > int > $o) > (num > num > $o) > (int > num) > (int > num) > $o).
% 18.75/7.45 thf(func_def_446, type, bNF_re6250860962936578807nt_int: (int > int > $o) > (product_prod_int_int > product_prod_int_int > $o) > (int > product_prod_int_int) > (int > product_prod_int_int) > $o).
% 18.75/7.45 thf(func_def_447, type, bNF_re2214769303045360666nt_rat: (int > int > $o) > (product_prod_int_int > rat > $o) > (int > product_prod_int_int) > (int > rat) > $o).
% 18.75/7.45 thf(func_def_448, type, bNF_re1382721322319792878nteger: (int > int > $o) > (rat > code_integer > $o) > (int > rat) > (int > code_integer) > $o).
% 18.75/7.45 thf(func_def_449, type, bNF_re3396611533439285437at_int: (int > int > $o) > (rat > int > $o) > (int > rat) > (int > int) > $o).
% 18.75/7.45 thf(func_def_450, type, bNF_re2763971943861839977at_rat: (int > int > $o) > (rat > rat > $o) > (int > rat) > (int > rat) > $o).
% 18.75/7.45 thf(func_def_451, type, bNF_re5416042074812042131at_nat: (int > nat > $o) > ((int > int) > (nat > nat) > $o) > (int > int > int) > (nat > nat > nat) > $o).
% 18.75/7.45 thf(func_def_452, type, bNF_re4343356799547411545nt_nat: (int > nat > $o) > (int > nat > $o) > (int > int) > (nat > nat) > $o).
% 18.75/7.45 thf(func_def_453, type, bNF_re151304249936775380nteger: (int > num > $o) > (nat > code_integer > $o) > (int > nat) > (num > code_integer) > $o).
% 18.75/7.45 thf(func_def_454, type, bNF_re7315484114762210078nteger: (int > num > $o) > (num > code_integer > $o) > (int > num) > (num > code_integer) > $o).
% 18.75/7.45 thf(func_def_455, type, bNF_re7661208983170134443at_rat: (int > rat > $o) > ((int > int) > (rat > rat) > $o) > (int > int > int) > (rat > rat > rat) > $o).
% 18.75/7.45 thf(func_def_456, type, bNF_re4480299549022435433nt_rat: (int > rat > $o) > (int > rat > $o) > (int > int) > (rat > rat) > $o).
% 18.75/7.45 thf(func_def_457, type, bNF_re7367609096550055590nteger: (nat > code_integer > $o) > ((nat > nat) > (code_integer > code_integer) > $o) > (nat > nat > nat) > (code_integer > code_integer > code_integer) > $o).
% 18.75/7.45 thf(func_def_458, type, bNF_re1599192376174140603nteger: (nat > code_integer > $o) > (nat > code_integer > $o) > (nat > nat) > (code_integer > code_integer) > $o).
% 18.75/7.45 thf(func_def_459, type, bNF_re8763372240999575301nteger: (nat > code_integer > $o) > (num > code_integer > $o) > (nat > num) > (code_integer > code_integer) > $o).
% 18.75/7.45 thf(func_def_460, type, bNF_re1639080489988575423ural_o: (nat > code_natural > $o) > ((nat > $o) > (code_natural > $o) > $o) > (nat > nat > $o) > (code_natural > code_natural > $o) > $o).
% 18.75/7.45 thf(func_def_461, type, bNF_re2895713572246619415_nat_o: (nat > code_natural > $o) > ((nat > $o) > (nat > $o) > $o) > (nat > nat > $o) > (code_natural > nat > $o) > $o).
% 18.75/7.45 thf(func_def_462, type, bNF_re88643428490162567atural: (nat > code_natural > $o) > ((nat > nat) > (code_natural > code_natural) > $o) > (nat > nat > nat) > (code_natural > code_natural > code_natural) > $o).
% 18.75/7.45 thf(func_def_463, type, bNF_re2785088596696291543al_o_o: (nat > code_natural > $o) > ($o > $o > $o) > (nat > $o) > (code_natural > $o) > $o).
% 18.75/7.45 thf(func_def_464, type, bNF_re5252274238750452962nteger: (nat > code_natural > $o) > (int > code_integer > $o) > (nat > int) > (code_natural > code_integer) > $o).
% 18.75/7.45 thf(func_def_465, type, bNF_re3704215830270325841atural: (nat > code_natural > $o) > (nat > code_natural > $o) > (nat > nat) > (code_natural > code_natural) > $o).
% 18.75/7.45 thf(func_def_466, type, bNF_re7333046803109187065at_nat: (nat > code_natural > $o) > (nat > nat > $o) > (nat > nat) > (code_natural > nat) > $o).
% 18.75/7.45 thf(func_def_467, type, bNF_re5864104203909894035nt_int: (nat > int > $o) > ((nat > nat) > (int > int) > $o) > (nat > nat > nat) > (int > int > int) > $o).
% 18.75/7.45 thf(func_def_468, type, bNF_re6022984109467102297at_int: (nat > int > $o) > (nat > int > $o) > (nat > nat) > (int > int) > $o).
% 18.75/7.45 thf(func_def_469, type, bNF_re4935368626670024657nteger: (nat > nat > $o) > ((int > int) > (code_integer > code_integer) > $o) > (nat > int > int) > (nat > code_integer > code_integer) > $o).
% 18.75/7.45 thf(func_def_470, type, bNF_re4785983289428654063nt_int: (nat > nat > $o) > ((int > int) > (int > int) > $o) > (nat > int > int) > (nat > int > int) > $o).
% 18.75/7.45 thf(func_def_471, type, bNF_re578469030762574527_nat_o: (nat > nat > $o) > ((nat > $o) > (nat > $o) > $o) > (nat > nat > $o) > (nat > nat > $o) > $o).
% 18.75/7.45 thf(func_def_472, type, bNF_re3692170009638431535atural: (nat > nat > $o) > ((nat > nat) > (code_natural > code_natural) > $o) > (nat > nat > nat) > (nat > code_natural > code_natural) > $o).
% 18.75/7.45 thf(func_def_473, type, bNF_re1345281282404953727at_nat: (nat > nat > $o) > ((nat > nat) > (nat > nat) > $o) > (nat > nat > nat) > (nat > nat > nat) > $o).
% 18.75/7.45 thf(func_def_474, type, bNF_re4705727531993890431at_o_o: (nat > nat > $o) > ($o > $o > $o) > (nat > $o) > (nat > $o) > $o).
% 18.75/7.45 thf(func_def_475, type, bNF_re4051817429369991249n_assn: (nat > nat > $o) > (assn > assn > $o) > (nat > assn) > (nat > assn) > $o).
% 18.75/7.45 thf(func_def_476, type, bNF_re1831131418152741254nteger: (nat > nat > $o) > (assn > code_integer > $o) > (nat > assn) > (nat > code_integer) > $o).
% 18.75/7.45 thf(func_def_477, type, bNF_re4792267480158271317sn_int: (nat > nat > $o) > (assn > int > $o) > (nat > assn) > (nat > int) > $o).
% 18.75/7.45 thf(func_def_478, type, bNF_re4794757950667321593sn_nat: (nat > nat > $o) > (assn > nat > $o) > (nat > assn) > (nat > nat) > $o).
% 18.75/7.45 thf(func_def_479, type, bNF_re4159627890580825857sn_rat: (nat > nat > $o) > (assn > rat > $o) > (nat > assn) > (nat > rat) > $o).
% 18.75/7.45 thf(func_def_480, type, bNF_re2692373401909853574r_assn: (nat > nat > $o) > (code_integer > assn > $o) > (nat > code_integer) > (nat > assn) > $o).
% 18.75/7.45 thf(func_def_481, type, bNF_re1236659899165691067nteger: (nat > nat > $o) > (code_integer > code_integer > $o) > (nat > code_integer) > (nat > code_integer) > $o).
% 18.75/7.45 thf(func_def_482, type, bNF_re3514700588913618570er_int: (nat > nat > $o) > (code_integer > int > $o) > (nat > code_integer) > (nat > int) > $o).
% 18.75/7.45 thf(func_def_483, type, bNF_re3517191059422668846er_nat: (nat > nat > $o) > (code_integer > nat > $o) > (nat > code_integer) > (nat > nat) > $o).
% 18.75/7.45 thf(func_def_484, type, bNF_re2882060999336173110er_rat: (nat > nat > $o) > (code_integer > rat > $o) > (nat > code_integer) > (nat > rat) > $o).
% 18.75/7.45 thf(func_def_485, type, bNF_re6101645755646507080atural: (nat > nat > $o) > (code_natural > produc7822875418678951345atural > $o) > (nat > code_natural) > (nat > produc7822875418678951345atural) > $o).
% 18.75/7.45 thf(func_def_486, type, bNF_re4153400068438556298nteger: (nat > nat > $o) > (int > code_integer > $o) > (nat > int) > (nat > code_integer) > $o).
% 18.75/7.45 thf(func_def_487, type, bNF_re2976995220195273813atural: (nat > nat > $o) > (int > code_natural > $o) > (nat > int) > (nat > code_natural) > $o).
% 18.75/7.45 thf(func_def_488, type, bNF_re6650684261131312217nt_int: (nat > nat > $o) > (int > int > $o) > (nat > int) > (nat > int) > $o).
% 18.75/7.45 thf(func_def_489, type, bNF_re6653174731640362493nt_nat: (nat > nat > $o) > (int > nat > $o) > (nat > int) > (nat > nat) > $o).
% 18.75/7.45 thf(func_def_490, type, bNF_re6018044671553866757nt_rat: (nat > nat > $o) > (int > rat > $o) > (nat > int) > (nat > rat) > $o).
% 18.75/7.45 thf(func_def_491, type, bNF_re2605341659958429177atural: (nat > nat > $o) > (nat > code_natural > $o) > (nat > nat) > (nat > code_natural) > $o).
% 18.75/7.45 thf(func_def_492, type, bNF_re5653821019739307937at_nat: (nat > nat > $o) > (nat > nat > $o) > (nat > nat) > (nat > nat) > $o).
% 18.75/7.45 thf(func_def_493, type, bNF_re341483209202555957um_num: (nat > nat > $o) > (num > num > $o) > (nat > num) > (nat > num) > $o).
% 18.75/7.45 thf(func_def_494, type, bNF_re6830278522597306478at_int: (nat > nat > $o) > (product_prod_nat_nat > int > $o) > (nat > product_prod_nat_nat) > (nat > int) > $o).
% 18.75/7.45 thf(func_def_495, type, bNF_re4553819317763231286nteger: (nat > nat > $o) > (rat > code_integer > $o) > (nat > rat) > (nat > code_integer) > $o).
% 18.75/7.45 thf(func_def_496, type, bNF_re3377414469519948801atural: (nat > nat > $o) > (rat > code_natural > $o) > (nat > rat) > (nat > code_natural) > $o).
% 18.75/7.45 thf(func_def_497, type, bNF_re5334775905295391749at_int: (nat > nat > $o) > (rat > int > $o) > (nat > rat) > (nat > int) > $o).
% 18.75/7.45 thf(func_def_498, type, bNF_re5337266375804442025at_nat: (nat > nat > $o) > (rat > nat > $o) > (nat > rat) > (nat > nat) > $o).
% 18.75/7.45 thf(func_def_499, type, bNF_re4702136315717946289at_rat: (nat > nat > $o) > (rat > rat > $o) > (nat > rat) > (nat > rat) > $o).
% 18.75/7.45 thf(func_def_500, type, bNF_re3590448190763046039at_rat: (nat > rat > $o) > ((nat > nat) > (rat > rat) > $o) > (nat > nat > nat) > (rat > rat > rat) > $o).
% 18.75/7.45 thf(func_def_501, type, bNF_re5790763769214331825at_rat: (nat > rat > $o) > (nat > rat > $o) > (nat > nat) > (rat > rat) > $o).
% 18.75/7.45 thf(func_def_502, type, bNF_re5031869190687302234nteger: (num > code_integer > $o) > (code_integer > (produc8923325533196201883nteger > produc8923325533196201883nteger) > $o) > (num > code_integer) > (code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger) > $o).
% 18.75/7.45 thf(func_def_503, type, bNF_re5202476307641864082nteger: (num > code_integer > $o) > (code_integer > code_integer > $o) > (num > code_integer) > (code_integer > code_integer) > $o).
% 18.75/7.45 thf(func_def_504, type, bNF_re6324211044263125204er_nat: (num > int > $o) > (code_integer > nat > $o) > (num > code_integer) > (int > nat) > $o).
% 18.75/7.45 thf(func_def_505, type, bNF_re2881542830418903838er_num: (num > int > $o) > (code_integer > num > $o) > (num > code_integer) > (int > num) > $o).
% 18.75/7.45 thf(func_def_506, type, bNF_re7876454716742015248nteger: (num > num > $o) > ((num > int) > (num > code_integer) > $o) > (num > num > int) > (num > num > code_integer) > $o).
% 18.75/7.45 thf(func_def_507, type, bNF_re8402795839162346335um_int: (num > num > $o) > ((num > int) > (num > int) > $o) > (num > num > int) > (num > num > int) > $o).
% 18.75/7.45 thf(func_def_508, type, bNF_re6741283560065411407nteger: (num > num > $o) > (code_integer > code_integer > $o) > (num > code_integer) > (num > code_integer) > $o).
% 18.75/7.45 thf(func_def_509, type, bNF_re6501075790457514782nteger: (num > num > $o) > (int > code_integer > $o) > (num > int) > (num > code_integer) > $o).
% 18.75/7.45 thf(func_def_510, type, bNF_re5324670942214232297atural: (num > num > $o) > (int > code_natural > $o) > (num > int) > (num > code_natural) > $o).
% 18.75/7.45 thf(func_def_511, type, bNF_re1822329894187522285nt_int: (num > num > $o) > (int > int > $o) > (num > int) > (num > int) > $o).
% 18.75/7.45 thf(func_def_512, type, bNF_re1824820364696572561nt_nat: (num > num > $o) > (int > nat > $o) > (num > int) > (num > nat) > $o).
% 18.75/7.45 thf(func_def_513, type, bNF_re1189690304610076825nt_rat: (num > num > $o) > (int > rat > $o) > (num > int) > (num > rat) > $o).
% 18.75/7.45 thf(func_def_514, type, bNF_re6129422230220670146nteger: (num > num > $o) > (nat > code_integer > $o) > (num > nat) > (num > code_integer) > $o).
% 18.75/7.45 thf(func_def_515, type, bNF_re4953017381977387661atural: (num > num > $o) > (nat > code_natural > $o) > (num > nat) > (num > code_natural) > $o).
% 18.75/7.45 thf(func_def_516, type, bNF_re822976182286467729at_int: (num > num > $o) > (nat > int > $o) > (num > nat) > (num > int) > $o).
% 18.75/7.45 thf(func_def_517, type, bNF_re825466652795518005at_nat: (num > num > $o) > (nat > nat > $o) > (num > nat) > (num > nat) > $o).
% 18.75/7.45 thf(func_def_518, type, bNF_re190336592709022269at_rat: (num > num > $o) > (nat > rat > $o) > (num > nat) > (num > rat) > $o).
% 18.75/7.45 thf(func_def_519, type, bNF_re5228765855967844073nt_int: (product_prod_int_int > product_prod_int_int > $o) > ((product_prod_int_int > product_prod_int_int) > (product_prod_int_int > product_prod_int_int) > $o) > (product_prod_int_int > product_prod_int_int > product_prod_int_int) > (product_prod_int_int > product_prod_int_int > product_prod_int_int) > $o).
% 18.75/7.45 thf(func_def_520, type, bNF_re7145576690424134365nt_int: (product_prod_int_int > product_prod_int_int > $o) > (product_prod_int_int > product_prod_int_int > $o) > (product_prod_int_int > product_prod_int_int) > (product_prod_int_int > product_prod_int_int) > $o).
% 18.75/7.45 thf(func_def_521, type, bNF_re7627151682743391978at_rat: (product_prod_int_int > rat > $o) > ((product_prod_int_int > product_prod_int_int) > (rat > rat) > $o) > (product_prod_int_int > product_prod_int_int > product_prod_int_int) > (rat > rat > rat) > $o).
% 18.75/7.45 thf(func_def_522, type, bNF_re8279943556446156061nt_rat: (product_prod_int_int > rat > $o) > (product_prod_int_int > rat > $o) > (product_prod_int_int > product_prod_int_int) > (rat > rat) > $o).
% 18.75/7.45 thf(func_def_523, type, bNF_re717283939379294677_int_o: (product_prod_nat_nat > int > $o) > ((product_prod_nat_nat > $o) > (int > $o) > $o) > (product_prod_nat_nat > product_prod_nat_nat > $o) > (int > int > $o) > $o).
% 18.75/7.45 thf(func_def_524, type, bNF_re7408651293131936558nt_int: (product_prod_nat_nat > int > $o) > ((product_prod_nat_nat > product_prod_nat_nat) > (int > int) > $o) > (product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat) > (int > int > int) > $o).
% 18.75/7.45 thf(func_def_525, type, bNF_re6644619430987730960nt_o_o: (product_prod_nat_nat > int > $o) > ($o > $o > $o) > (product_prod_nat_nat > $o) > (int > $o) > $o).
% 18.75/7.45 thf(func_def_526, type, bNF_re7400052026677387805at_int: (product_prod_nat_nat > int > $o) > (product_prod_nat_nat > int > $o) > (product_prod_nat_nat > product_prod_nat_nat) > (int > int) > $o).
% 18.75/7.45 thf(func_def_527, type, bNF_re4202695980764964119_nat_o: (product_prod_nat_nat > product_prod_nat_nat > $o) > ((product_prod_nat_nat > $o) > (product_prod_nat_nat > $o) > $o) > (product_prod_nat_nat > product_prod_nat_nat > $o) > (product_prod_nat_nat > product_prod_nat_nat > $o) > $o).
% 18.75/7.45 thf(func_def_528, type, bNF_re3099431351363272937at_nat: (product_prod_nat_nat > product_prod_nat_nat > $o) > ((product_prod_nat_nat > product_prod_nat_nat) > (product_prod_nat_nat > product_prod_nat_nat) > $o) > (product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat) > (product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat) > $o).
% 18.75/7.45 thf(func_def_529, type, bNF_re3666534408544137501at_o_o: (product_prod_nat_nat > product_prod_nat_nat > $o) > ($o > $o > $o) > (product_prod_nat_nat > $o) > (product_prod_nat_nat > $o) > $o).
% 18.75/7.45 thf(func_def_530, type, bNF_re2241393799969408733at_nat: (product_prod_nat_nat > product_prod_nat_nat > $o) > (product_prod_nat_nat > product_prod_nat_nat > $o) > (product_prod_nat_nat > product_prod_nat_nat) > (product_prod_nat_nat > product_prod_nat_nat) > $o).
% 18.75/7.45 thf(func_def_531, type, bNF_re8417623677625516633nteger: (product_unit > product_unit > $o) > (code_integer > code_integer > $o) > (product_unit > code_integer) > (product_unit > code_integer) > $o).
% 18.75/7.45 thf(func_def_532, type, bNF_re5641277236161133866atural: (product_unit > product_unit > $o) > (code_natural > produc7822875418678951345atural > $o) > (product_unit > code_natural) > (product_unit > produc7822875418678951345atural) > $o).
% 18.75/7.45 thf(func_def_533, type, bNF_re8422471777688076791nt_int: (product_unit > product_unit > $o) > (int > int > $o) > (product_unit > int) > (product_unit > int) > $o).
% 18.75/7.45 thf(func_def_534, type, bNF_re4307939118855507134nteger: (rat > code_integer > $o) > ((rat > rat) > (code_integer > code_integer) > $o) > (rat > rat > rat) > (code_integer > code_integer > code_integer) > $o).
% 18.75/7.45 thf(func_def_535, type, bNF_re2328245411608324299nteger: (rat > code_integer > $o) > (rat > code_integer > $o) > (rat > rat) > (code_integer > code_integer) > $o).
% 18.75/7.45 thf(func_def_536, type, bNF_re6252345487650389919atural: (rat > code_natural > $o) > ((rat > rat) > (code_natural > code_natural) > $o) > (rat > rat > rat) > (code_natural > code_natural > code_natural) > $o).
% 18.75/7.45 thf(func_def_537, type, bNF_re4433268865704509537atural: (rat > code_natural > $o) > (rat > code_natural > $o) > (rat > rat) > (code_natural > code_natural) > $o).
% 18.75/7.45 thf(func_def_538, type, bNF_re8876735282041863595nt_int: (rat > int > $o) > ((rat > rat) > (int > int) > $o) > (rat > rat > rat) > (int > int > int) > $o).
% 18.75/7.45 thf(func_def_539, type, bNF_re5838490730811218025at_int: (rat > int > $o) > (rat > int > $o) > (rat > rat) > (int > int) > $o).
% 18.75/7.45 thf(func_def_540, type, bNF_re4357912360536923287at_nat: (rat > nat > $o) > ((rat > rat) > (nat > nat) > $o) > (rat > rat > rat) > (nat > nat > nat) > $o).
% 18.75/7.45 thf(func_def_541, type, bNF_re5469327641083423665at_nat: (rat > nat > $o) > (rat > nat > $o) > (rat > rat) > (nat > nat) > $o).
% 18.75/7.45 thf(func_def_542, type, bNF_re6603079268895015599at_rat: (rat > rat > $o) > ((rat > rat) > (rat > rat) > $o) > (rat > rat > rat) > (rat > rat > rat) > $o).
% 18.75/7.45 thf(func_def_543, type, bNF_re5606270390558447553at_rat: (rat > rat > $o) > (rat > rat > $o) > (rat > rat) > (rat > rat) > $o).
% 18.75/7.45 thf(func_def_544, type, bNF_We2654380646378065620so_o_o: set_Pr1932065953672099015od_o_o).
% 18.75/7.45 thf(func_def_545, type, bNF_We5258908940166488438at_nat: set_Pr4329608150637261639at_nat).
% 18.75/7.45 thf(func_def_546, type, bNF_We8182288985678559134_o_nat: set_Pr457366540195662369at_nat).
% 18.75/7.45 thf(func_def_547, type, basic_7565498685090299632nteger: (code_integer > nat) > (code_integer > nat) > produc8923325533196201883nteger > nat).
% 18.75/7.45 thf(func_def_548, type, basic_8185638495112405971atural: (code_natural > nat) > (produc7822875418678951345atural > nat) > produc5835291356934675326atural > nat).
% 18.75/7.45 thf(func_def_549, type, basic_1872990034501187214nt_int: (int > nat) > (int > nat) > product_prod_int_int > nat).
% 18.75/7.45 thf(func_def_550, type, binomial: nat > nat > nat).
% 18.75/7.45 thf(func_def_551, type, gbinom8545251970709558553nteger: code_integer > nat > code_integer).
% 18.75/7.45 thf(func_def_552, type, gbinomial_int: int > nat > int).
% 18.75/7.45 thf(func_def_553, type, gbinomial_nat: nat > nat > nat).
% 18.75/7.45 thf(func_def_554, type, gbinomial_rat: rat > nat > rat).
% 18.75/7.45 thf(func_def_555, type, bit_and_int_rel: product_prod_int_int > product_prod_int_int > $o).
% 18.75/7.45 thf(func_def_556, type, bit_and_not_num: num > num > option_num).
% 18.75/7.45 thf(func_def_557, type, bit_and_not_num_rel: product_prod_num_num > product_prod_num_num > $o).
% 18.75/7.45 thf(func_def_558, type, bit_concat_bit: nat > int > int > int).
% 18.75/7.45 thf(func_def_559, type, bit_or_not_num_neg: num > num > num).
% 18.75/7.45 thf(func_def_560, type, bit_or3848514188828904588eg_rel: product_prod_num_num > product_prod_num_num > $o).
% 18.75/7.45 thf(func_def_561, type, bit_ri7632146776885996613nteger: code_integer > code_integer).
% 18.75/7.45 thf(func_def_562, type, bit_ri7919022796975470100ot_int: int > int).
% 18.75/7.45 thf(func_def_563, type, bit_ri6519982836138164636nteger: nat > code_integer > code_integer).
% 18.75/7.45 thf(func_def_564, type, bit_ri631733984087533419it_int: nat > int > int).
% 18.75/7.45 thf(func_def_565, type, bit_se3949692690581998587nteger: code_integer > code_integer > code_integer).
% 18.75/7.45 thf(func_def_566, type, bit_se2773287842338716102atural: code_natural > code_natural > code_natural).
% 18.75/7.45 thf(func_def_567, type, bit_se725231765392027082nd_int: int > int > int).
% 18.75/7.45 thf(func_def_568, type, bit_se727722235901077358nd_nat: nat > nat > nat).
% 18.75/7.45 thf(func_def_569, type, bit_se3928097537394005634nteger: nat > code_integer > code_integer).
% 18.75/7.45 thf(func_def_570, type, bit_se2751692689150723149atural: nat > code_natural > code_natural).
% 18.75/7.45 thf(func_def_571, type, bit_se8568078237143864401it_int: nat > int > int).
% 18.75/7.45 thf(func_def_572, type, bit_se8570568707652914677it_nat: nat > nat > nat).
% 18.75/7.45 thf(func_def_573, type, bit_se1345352211410354436nteger: nat > code_integer > code_integer).
% 18.75/7.45 thf(func_def_574, type, bit_se168947363167071951atural: nat > code_natural > code_natural).
% 18.75/7.45 thf(func_def_575, type, bit_se2159334234014336723it_int: nat > int > int).
% 18.75/7.45 thf(func_def_576, type, bit_se2161824704523386999it_nat: nat > nat > nat).
% 18.75/7.45 thf(func_def_577, type, bit_se2119862282449309892nteger: nat > code_integer).
% 18.75/7.45 thf(func_def_578, type, bit_se943457434206027407atural: nat > code_natural).
% 18.75/7.45 thf(func_def_579, type, bit_se2000444600071755411sk_int: nat > int).
% 18.75/7.45 thf(func_def_580, type, bit_se2002935070580805687sk_nat: nat > nat).
% 18.75/7.45 thf(func_def_581, type, bit_se1080825931792720795nteger: code_integer > code_integer > code_integer).
% 18.75/7.45 thf(func_def_582, type, bit_se9127793120404214118atural: code_natural > code_natural > code_natural).
% 18.75/7.45 thf(func_def_583, type, bit_se1409905431419307370or_int: int > int > int).
% 18.75/7.45 thf(func_def_584, type, bit_se1412395901928357646or_nat: nat > nat > nat).
% 18.75/7.45 thf(func_def_585, type, bit_se7788150548672797655nteger: nat > code_integer > code_integer).
% 18.75/7.45 thf(func_def_586, type, bit_se6611745700429515170atural: nat > code_natural > code_natural).
% 18.75/7.45 thf(func_def_587, type, bit_se545348938243370406it_int: nat > int > int).
% 18.75/7.45 thf(func_def_588, type, bit_se547839408752420682it_nat: nat > nat > nat).
% 18.75/7.45 thf(func_def_589, type, bit_se2793503036327961859nteger: nat > code_integer > code_integer).
% 18.75/7.45 thf(func_def_590, type, bit_se1617098188084679374atural: nat > code_natural > code_natural).
% 18.75/7.45 thf(func_def_591, type, bit_se7879613467334960850it_int: nat > int > int).
% 18.75/7.45 thf(func_def_592, type, bit_se7882103937844011126it_nat: nat > nat > nat).
% 18.75/7.45 thf(func_def_593, type, bit_se1745604003318907178nteger: nat > code_integer > code_integer).
% 18.75/7.45 thf(func_def_594, type, bit_se569199155075624693atural: nat > code_natural > code_natural).
% 18.75/7.45 thf(func_def_595, type, bit_se2923211474154528505it_int: nat > int > int).
% 18.75/7.45 thf(func_def_596, type, bit_se2925701944663578781it_nat: nat > nat > nat).
% 18.75/7.45 thf(func_def_597, type, bit_se8260200283734997820nteger: nat > code_integer > code_integer).
% 18.75/7.45 thf(func_def_598, type, bit_se7083795435491715335atural: nat > code_natural > code_natural).
% 18.75/7.45 thf(func_def_599, type, bit_se4203085406695923979it_int: nat > int > int).
% 18.75/7.45 thf(func_def_600, type, bit_se4205575877204974255it_nat: nat > nat > nat).
% 18.75/7.45 thf(func_def_601, type, bit_se3222712562003087583nteger: code_integer > code_integer > code_integer).
% 18.75/7.45 thf(func_def_602, type, bit_se2046307713759805098atural: code_natural > code_natural > code_natural).
% 18.75/7.45 thf(func_def_603, type, bit_se6526347334894502574or_int: int > int > int).
% 18.75/7.45 thf(func_def_604, type, bit_se6528837805403552850or_nat: nat > nat > nat).
% 18.75/7.45 thf(func_def_605, type, bit_se9216721137139052372nteger: code_integer > nat > $o).
% 18.75/7.45 thf(func_def_606, type, bit_se8040316288895769887atural: code_natural > nat > $o).
% 18.75/7.45 thf(func_def_607, type, bit_se1146084159140164899it_int: int > nat > $o).
% 18.75/7.45 thf(func_def_608, type, bit_se1148574629649215175it_nat: nat > nat > $o).
% 18.75/7.45 thf(func_def_609, type, bit_take_bit_num: nat > num > option_num).
% 18.75/7.45 thf(func_def_610, type, bit_un7362597486090784418nd_num: num > num > option_num).
% 18.75/7.45 thf(func_def_611, type, bit_un4731106466462545111um_rel: product_prod_num_num > product_prod_num_num > $o).
% 18.75/7.45 thf(func_def_612, type, bit_un6697907153464112080or_num: num > num > num).
% 18.75/7.45 thf(func_def_613, type, bit_un4773296044027857193um_rel: product_prod_num_num > product_prod_num_num > $o).
% 18.75/7.45 thf(func_def_614, type, bit_un2480387367778600638or_num: num > num > option_num).
% 18.75/7.45 thf(func_def_615, type, bit_un2901131394128224187um_rel: product_prod_num_num > product_prod_num_num > $o).
% 18.75/7.45 thf(func_def_616, type, boolea5643492148547655015nteger: (code_integer > code_integer > code_integer) > (code_integer > code_integer > code_integer) > (code_integer > code_integer) > code_integer > code_integer > $o).
% 18.75/7.45 thf(func_def_617, type, boolea5469654029284665142ra_int: (int > int > int) > (int > int > int) > (int > int) > int > int > $o).
% 18.75/7.45 thf(func_def_618, type, boolea2445317508997433345nteger: (code_integer > code_integer > code_integer) > (code_integer > code_integer > code_integer) > (code_integer > code_integer) > code_integer > code_integer > (code_integer > code_integer > code_integer) > $o).
% 18.75/7.45 thf(func_def_619, type, boolea8527374999097803216ff_int: (int > int > int) > (int > int > int) > (int > int) > int > int > (int > int > int) > $o).
% 18.75/7.45 thf(func_def_620, type, code_Nat: code_integer > code_natural).
% 18.75/7.45 thf(func_def_621, type, code_Neg: num > code_integer).
% 18.75/7.45 thf(func_def_622, type, code_Pos: num > code_integer).
% 18.75/7.45 thf(func_def_623, type, code_Suc: code_natural > code_natural).
% 18.75/7.45 thf(func_def_624, type, code_bit_cut_integer: code_integer > produc6271795597528267376eger_o).
% 18.75/7.45 thf(func_def_625, type, code_cr_integer: int > code_integer > $o).
% 18.75/7.45 thf(func_def_626, type, code_cr_natural: nat > code_natural > $o).
% 18.75/7.45 thf(func_def_627, type, code_divmod_abs: code_integer > code_integer > produc8923325533196201883nteger).
% 18.75/7.45 thf(func_def_628, type, code_divmod_integer: code_integer > code_integer > produc8923325533196201883nteger).
% 18.75/7.45 thf(func_def_629, type, code_dup: code_integer > code_integer).
% 18.75/7.45 thf(func_def_630, type, code_int_of_integer: code_integer > int).
% 18.75/7.45 thf(func_def_631, type, code_integer_of_int: int > code_integer).
% 18.75/7.45 thf(func_def_632, type, code_integer_of_nat: nat > code_integer).
% 18.75/7.45 thf(func_def_633, type, code_i5400310926305786745atural: code_natural > code_integer).
% 18.75/7.45 thf(func_def_634, type, code_integer_of_num: num > code_integer).
% 18.75/7.45 thf(func_def_635, type, code_nat_of_integer: code_integer > nat).
% 18.75/7.45 thf(func_def_636, type, code_nat_of_natural: code_natural > nat).
% 18.75/7.45 thf(func_def_637, type, code_natural_of_nat: nat > code_natural).
% 18.75/7.45 thf(func_def_638, type, code_n4118661773612635043nteger: code_integer > code_natural).
% 18.75/7.45 thf(func_def_639, type, code_negative: num > code_integer).
% 18.75/7.45 thf(func_def_640, type, code_num_of_integer: code_integer > num).
% 18.75/7.45 thf(func_def_641, type, code_pcr_integer: int > code_integer > $o).
% 18.75/7.45 thf(func_def_642, type, code_pcr_natural: nat > code_natural > $o).
% 18.75/7.45 thf(func_def_643, type, code_positive: num > code_integer).
% 18.75/7.45 thf(func_def_644, type, code_size_nat: code_natural > nat).
% 18.75/7.45 thf(func_def_645, type, code_sub: num > num > code_integer).
% 18.75/7.45 thf(func_def_646, type, comple7280212863790966717_int_o: set_in8474487674441654202_int_o > (int > option6357759511663192854e_term) > product_prod_int_int > $o).
% 18.75/7.45 thf(func_def_647, type, comple797978290332539892eger_o: set_Pr8914822823351560561eger_o > (produc6241069584506657477e_term > option6357759511663192854e_term) > produc8923325533196201883nteger > $o).
% 18.75/7.45 thf(func_def_648, type, comple1647972170925272290_nat_o: set_Pr1457143144315775327_nat_o > (produc3658429121746597890et_nat > $o) > produc3925858234332021118et_nat > $o).
% 18.75/7.45 thf(func_def_649, type, comple4401490224799119198_nat_o: set_Pr8208987589773510107_nat_o > (produc3658429121746597890et_nat > $o) > produc3658429121746597890et_nat > $o).
% 18.75/7.45 thf(func_def_650, type, comple2375672059646964807_int_o: set_Pr5050529186185961540_int_o > (produc8551481072490612790e_term > option6357759511663192854e_term) > product_prod_int_int > $o).
% 18.75/7.45 thf(func_def_651, type, comple1675732732025788397_nat_o: set_nat_nat_o > nat > nat > $o).
% 18.75/7.45 thf(func_def_652, type, comple8322679762649017525_nat_o: set_se9180647916752606350_nat_o > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o).
% 18.75/7.45 thf(func_def_653, type, complete_Inf_Inf_int: set_int > int).
% 18.75/7.45 thf(func_def_654, type, complete_Inf_Inf_nat: set_nat > nat).
% 18.75/7.45 thf(func_def_655, type, comple5564859526659248602t_unit: set_op3165557761946182707t_unit > option_Product_unit).
% 18.75/7.45 thf(func_def_656, type, comple3446467376476514063et_nat: set_option_set_nat > option_set_nat).
% 18.75/7.45 thf(func_def_657, type, comple2584293577114468500t_unit: set_Product_unit > product_unit).
% 18.75/7.45 thf(func_def_658, type, comple3063163877087187839_set_o: set_set_o > set_o).
% 18.75/7.45 thf(func_def_659, type, comple1256288197631046732nteger: set_set_Code_integer > set_Code_integer).
% 18.75/7.45 thf(func_def_660, type, comple3628384868704368283et_int: set_set_int > set_int).
% 18.75/7.45 thf(func_def_661, type, comple184543376406953807st_nat: set_set_list_nat > set_list_nat).
% 18.75/7.45 thf(func_def_662, type, comple7806235888213564991et_nat: set_set_nat > set_nat).
% 18.75/7.45 thf(func_def_663, type, comple2057271477292249724nt_int: set_se7394616247590735609nt_int > set_Pr1872883991513573699nt_int).
% 18.75/7.45 thf(func_def_664, type, comple141797230998674821nteger: set_se124295367203800706nteger > set_Pr1281608226676607948nteger).
% 18.75/7.45 thf(func_def_665, type, comple8400030738448405097et_nat: set_se5120235452707311462et_nat > set_Pr8536935166611901872et_nat).
% 18.75/7.45 thf(func_def_666, type, comple8712884055654468845et_nat: set_se8543413830569400298et_nat > set_Pr3286484037609594932et_nat).
% 18.75/7.45 thf(func_def_667, type, comple6065809805536145394nt_int: set_se2364587433798273647nt_int > set_Pr9222295170931077689nt_int).
% 18.75/7.45 thf(func_def_668, type, comple1930127330929219688at_nat: set_se7855581050983116737at_nat > set_Pr1261947904930325089at_nat).
% 18.75/7.45 thf(func_def_669, type, comple6751905152567503566at_nat: set_se5479201105039950375at_nat > set_Pr4329608150637261639at_nat).
% 18.75/7.45 thf(func_def_670, type, comple7216939928495492468t_unit: set_set_Product_unit > set_Product_unit).
% 18.75/7.45 thf(func_def_671, type, comple8902563120744349527_int_o: set_in8474487674441654202_int_o > (int > option6357759511663192854e_term) > product_prod_int_int > $o).
% 18.75/7.45 thf(func_def_672, type, comple6692557002573936782eger_o: set_Pr8914822823351560561eger_o > (produc6241069584506657477e_term > option6357759511663192854e_term) > produc8923325533196201883nteger > $o).
% 18.75/7.45 thf(func_def_673, type, comple5542144468884744060_nat_o: set_Pr1457143144315775327_nat_o > (produc3658429121746597890et_nat > $o) > produc3925858234332021118et_nat > $o).
% 18.75/7.45 thf(func_def_674, type, comple2736776311324672504_nat_o: set_Pr8208987589773510107_nat_o > (produc3658429121746597890et_nat > $o) > produc3658429121746597890et_nat > $o).
% 18.75/7.45 thf(func_def_675, type, comple7735192718774405345_int_o: set_Pr5050529186185961540_int_o > (produc8551481072490612790e_term > option6357759511663192854e_term) > product_prod_int_int > $o).
% 18.75/7.45 thf(func_def_676, type, comple3592611370556534995_nat_o: set_nat_nat_o > nat > nat > $o).
% 18.75/7.45 thf(func_def_677, type, comple493620192902636699_nat_o: set_se9180647916752606350_nat_o > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o).
% 18.75/7.45 thf(func_def_678, type, complete_Sup_Sup_o: set_o > $o).
% 18.75/7.45 thf(func_def_679, type, complete_Sup_Sup_int: set_int > int).
% 18.75/7.45 thf(func_def_680, type, complete_Sup_Sup_nat: set_nat > nat).
% 18.75/7.45 thf(func_def_681, type, comple4490649148004324043tion_o: set_option_o > option_o).
% 18.75/7.45 thf(func_def_682, type, comple7481738165189995200t_unit: set_op3165557761946182707t_unit > option_Product_unit).
% 18.75/7.45 thf(func_def_683, type, comple8455683388168444585et_nat: set_option_set_nat > option_set_nat).
% 18.75/7.45 thf(func_def_684, type, comple4687483117567863418t_unit: set_Product_unit > product_unit).
% 18.75/7.45 thf(func_def_685, type, comple90263536869209701_set_o: set_set_o > set_o).
% 18.75/7.45 thf(func_def_686, type, comple739944243200306918nteger: set_set_Code_integer > set_Code_integer).
% 18.75/7.45 thf(func_def_687, type, comple3221217463730067765et_int: set_set_int > set_int).
% 18.75/7.45 thf(func_def_688, type, comple8404747032580312297st_nat: set_set_list_nat > set_list_nat).
% 18.75/7.45 thf(func_def_689, type, comple7399068483239264473et_nat: set_set_nat > set_nat).
% 18.75/7.45 thf(func_def_690, type, comple5772984051336441366nt_int: set_se7394616247590735609nt_int > set_Pr1872883991513573699nt_int).
% 18.75/7.45 thf(func_def_691, type, comple1324685164916153887nteger: set_se124295367203800706nteger > set_Pr1281608226676607948nteger).
% 18.75/7.45 thf(func_def_692, type, comple5063570841203093763et_nat: set_se5120235452707311462et_nat > set_Pr8536935166611901872et_nat).
% 18.75/7.45 thf(func_def_693, type, comple4849024849677941639et_nat: set_se8543413830569400298et_nat > set_Pr3286484037609594932et_nat).
% 18.75/7.45 thf(func_def_694, type, comple6871990601243273356nt_int: set_se2364587433798273647nt_int > set_Pr9222295170931077689nt_int).
% 18.75/7.45 thf(func_def_695, type, comple4956303571586142718atural: set_se3372686590935047281atural > set_Pr7564037697178849041atural).
% 18.75/7.45 thf(func_def_696, type, comple5685304695842803022at_nat: set_se7855581050983116737at_nat > set_Pr1261947904930325089at_nat).
% 18.75/7.45 thf(func_def_697, type, comple4364388969068068532at_nat: set_se5479201105039950375at_nat > set_Pr4329608150637261639at_nat).
% 18.75/7.45 thf(func_def_698, type, comple3349607820504768346t_unit: set_set_Product_unit > set_Product_unit).
% 18.75/7.45 thf(func_def_699, type, nth_item_rel: nat > nat > $o).
% 18.75/7.45 thf(func_def_700, type, adjust_div: product_prod_int_int > int).
% 18.75/7.45 thf(func_def_701, type, divmod_nat: nat > nat > product_prod_nat_nat).
% 18.75/7.45 thf(func_def_702, type, eucl_rel_int: int > int > product_prod_int_int > $o).
% 18.75/7.45 thf(func_def_703, type, unique5706413561485394159nteger: produc8923325533196201883nteger > $o).
% 18.75/7.45 thf(func_def_704, type, unique6319869463603278526ux_int: product_prod_int_int > $o).
% 18.75/7.45 thf(func_def_705, type, unique6322359934112328802ux_nat: product_prod_nat_nat > $o).
% 18.75/7.45 thf(func_def_706, type, unique3479559517661332726nteger: num > num > produc8923325533196201883nteger).
% 18.75/7.45 thf(func_def_707, type, unique5052692396658037445od_int: num > num > product_prod_int_int).
% 18.75/7.45 thf(func_def_708, type, unique5055182867167087721od_nat: num > num > product_prod_nat_nat).
% 18.75/7.45 thf(func_def_709, type, unique4921790084139445826nteger: num > produc8923325533196201883nteger > produc8923325533196201883nteger).
% 18.75/7.45 thf(func_def_710, type, unique5024387138958732305ep_int: num > product_prod_int_int > product_prod_int_int).
% 18.75/7.45 thf(func_def_711, type, unique5026877609467782581ep_nat: num > product_prod_nat_nat > product_prod_nat_nat).
% 18.75/7.45 thf(func_def_712, type, euclid6377331345833325938nteger: code_integer > nat).
% 18.75/7.45 thf(func_def_713, type, euclid5200926497590043453atural: code_natural > nat).
% 18.75/7.45 thf(func_def_714, type, euclid4774559944035922753ze_int: int > nat).
% 18.75/7.45 thf(func_def_715, type, euclid4777050414544973029ze_nat: nat > nat).
% 18.75/7.45 thf(func_def_716, type, euclid6289375185220004616nteger: code_integer > code_integer).
% 18.75/7.45 thf(func_def_717, type, euclid5112970336976722131atural: code_natural > code_natural).
% 18.75/7.45 thf(func_def_718, type, euclid3395696857347342551nt_int: int > int).
% 18.75/7.45 thf(func_def_719, type, euclid3398187327856392827nt_nat: nat > nat).
% 18.75/7.45 thf(func_def_720, type, comm_s8582702949713902594nteger: code_integer > nat > code_integer).
% 18.75/7.45 thf(func_def_721, type, comm_s7406298101470620109atural: code_natural > nat > code_natural).
% 18.75/7.45 thf(func_def_722, type, comm_s4660882817536571857er_int: int > nat > int).
% 18.75/7.45 thf(func_def_723, type, comm_s4663373288045622133er_nat: nat > nat > nat).
% 18.75/7.45 thf(func_def_724, type, comm_s4028243227959126397er_rat: rat > nat > rat).
% 18.75/7.45 thf(func_def_725, type, semiri3624122377584611663nteger: nat > code_integer).
% 18.75/7.45 thf(func_def_726, type, semiri2447717529341329178atural: nat > code_natural).
% 18.75/7.45 thf(func_def_727, type, semiri1406184849735516958ct_int: nat > int).
% 18.75/7.45 thf(func_def_728, type, semiri1408675320244567234ct_nat: nat > nat).
% 18.75/7.45 thf(func_def_729, type, semiri773545260158071498ct_rat: nat > rat).
% 18.75/7.45 thf(func_def_730, type, inverse_inverse_rat: rat > rat).
% 18.75/7.45 thf(func_def_731, type, finite_card_o: set_o > nat).
% 18.75/7.45 thf(func_def_732, type, finite4902975817058060853nteger: set_Code_integer > nat).
% 18.75/7.45 thf(func_def_733, type, finite_card_int: set_int > nat).
% 18.75/7.45 thf(func_def_734, type, finite_card_list_nat: set_list_nat > nat).
% 18.75/7.45 thf(func_def_735, type, finite_card_nat: set_nat > nat).
% 18.75/7.45 thf(func_def_736, type, finite711546835091564841at_nat: set_Pr1261947904930325089at_nat > nat).
% 18.75/7.45 thf(func_def_737, type, finite3771342082235030671at_nat: set_Pr4329608150637261639at_nat > nat).
% 18.75/7.45 thf(func_def_738, type, finite410649719033368117t_unit: set_Product_unit > nat).
% 18.75/7.45 thf(func_def_739, type, finite1340570857867686763nteger: set_set_Code_integer > nat).
% 18.75/7.45 thf(func_def_740, type, finite_card_set_int: set_set_int > nat).
% 18.75/7.45 thf(func_def_741, type, finite2364142230527598318st_nat: set_set_list_nat > nat).
% 18.75/7.45 thf(func_def_742, type, finite_card_set_nat: set_set_nat > nat).
% 18.75/7.45 thf(func_def_743, type, finite4356350796350151305at_nat: set_se7855581050983116737at_nat > nat).
% 18.75/7.45 thf(func_def_744, type, finite22775419188893461t_unit: set_set_Product_unit > nat).
% 18.75/7.45 thf(func_def_745, type, finite_finite_o: set_o > $o).
% 18.75/7.45 thf(func_def_746, type, finite6017078050557962740nteger: set_Code_integer > $o).
% 18.75/7.45 thf(func_def_747, type, finite_finite_int: set_int > $o).
% 18.75/7.45 thf(func_def_748, type, finite8100373058378681591st_nat: set_list_nat > $o).
% 18.75/7.45 thf(func_def_749, type, finite_finite_nat: set_nat > $o).
% 18.75/7.45 thf(func_def_750, type, finite_finite_num: set_num > $o).
% 18.75/7.45 thf(func_def_751, type, finite6785661671136154180nteger: set_op687863988967635939nteger > $o).
% 18.75/7.45 thf(func_def_752, type, finite1345302120164226195on_int: set_option_int > $o).
% 18.75/7.45 thf(func_def_753, type, finite5523153139673422903on_nat: set_option_nat > $o).
% 18.75/7.45 thf(func_def_754, type, finite6231397076622260609on_num: set_option_num > $o).
% 18.75/7.45 thf(func_def_755, type, finite6732403688824079472at_nat: set_op4508134149509766951at_nat > $o).
% 18.75/7.45 thf(func_def_756, type, finite6292238467249657455it_nat: set_op239864471688321678it_nat > $o).
% 18.75/7.45 thf(func_def_757, type, finite1445617369574913404t_unit: set_op3165557761946182707t_unit > $o).
% 18.75/7.45 thf(func_def_758, type, finite4151335170723375381et_nat: set_Pr3286484037609594932et_nat > $o).
% 18.75/7.45 thf(func_def_759, type, finite6120865539452801872od_o_o: set_Product_prod_o_o > $o).
% 18.75/7.45 thf(func_def_760, type, finite2154694888287295812nteger: set_Pr4811707699266497531nteger > $o).
% 18.75/7.45 thf(func_def_761, type, finite818523575018126227er_int: set_Pr6496905503482889930er_int > $o).
% 18.75/7.45 thf(func_def_762, type, finite4996374594527322935er_nat: set_Pr8986988648414616686er_nat > $o).
% 18.75/7.45 thf(func_def_763, type, finite2970523954037356441et_nat: set_Pr3948176798113811640et_nat > $o).
% 18.75/7.45 thf(func_def_764, type, finite1525696360262406931nteger: set_Pr8415741480598773322nteger > $o).
% 18.75/7.45 thf(func_def_765, type, finite2998713641127702882nt_int: set_Pr958786334691620121nt_int > $o).
% 18.75/7.45 thf(func_def_766, type, finite7176564660636899590nt_nat: set_Pr3448869479623346877nt_nat > $o).
% 18.75/7.45 thf(func_def_767, type, finite1154042800025562295nteger: set_Pr2406931829603198446nteger > $o).
% 18.75/7.45 thf(func_def_768, type, finite1999359929226648326at_int: set_Pr7995236796853374141at_int > $o).
% 18.75/7.45 thf(func_def_769, type, finite6177210948735845034at_nat: set_Pr1261947904930325089at_nat > $o).
% 18.75/7.45 thf(func_def_770, type, finite4392333629123659920at_nat: set_Pr8693737435421807431at_nat > $o).
% 18.75/7.45 thf(func_def_771, type, finite6446286893012251551it_nat: set_Pr1354866905816374718it_nat > $o).
% 18.75/7.45 thf(func_def_772, type, finite4343798906461161616at_nat: set_Pr4329608150637261639at_nat > $o).
% 18.75/7.45 thf(func_def_773, type, finite4290736615968046902t_unit: set_Product_unit > $o).
% 18.75/7.45 thf(func_def_774, type, finite_finite_rat: set_rat > $o).
% 18.75/7.45 thf(func_def_775, type, finite6931041176100689706nteger: set_set_Code_integer > $o).
% 18.75/7.45 thf(func_def_776, type, finite6197958912794628473et_int: set_set_int > $o).
% 18.75/7.45 thf(func_def_777, type, finite7047420756378620717st_nat: set_set_list_nat > $o).
% 18.75/7.45 thf(func_def_778, type, finite1152437895449049373et_nat: set_set_nat > $o).
% 18.75/7.45 thf(func_def_779, type, finite9047747110432174090at_nat: set_se7855581050983116737at_nat > $o).
% 18.75/7.45 thf(func_def_780, type, finite1772178364199683094t_unit: set_set_Product_unit > $o).
% 18.75/7.45 thf(func_def_781, type, finite_fold_int_int: (int > int > int) > int > set_int > int).
% 18.75/7.45 thf(func_def_782, type, finite_fold_nat_int: (nat > int > int) > int > set_nat > int).
% 18.75/7.45 thf(func_def_783, type, finite_fold_nat_nat: (nat > nat > nat) > nat > set_nat > nat).
% 18.75/7.45 thf(func_def_784, type, finite3745491028973389255at_nat: (nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat) > set_Pr1261947904930325089at_nat > set_nat > set_Pr1261947904930325089at_nat).
% 18.75/7.45 thf(func_def_785, type, finite8124994865635982712et_nat: (produc3925858234332021118et_nat > set_Pr8536935166611901872et_nat > set_Pr8536935166611901872et_nat) > set_Pr8536935166611901872et_nat > set_Pr3286484037609594932et_nat > set_Pr8536935166611901872et_nat).
% 18.75/7.45 thf(func_def_786, type, finite7641027033760462367nteger: (produc8923325533196201883nteger > set_Pr1281608226676607948nteger > set_Pr1281608226676607948nteger) > set_Pr1281608226676607948nteger > set_Pr4811707699266497531nteger > set_Pr1281608226676607948nteger).
% 18.75/7.45 thf(func_def_787, type, finite2494574492299216512et_nat: (produc3658429121746597890et_nat > set_Pr3286484037609594932et_nat > set_Pr3286484037609594932et_nat) > set_Pr3286484037609594932et_nat > set_Pr3948176798113811640et_nat > set_Pr3286484037609594932et_nat).
% 18.75/7.45 thf(func_def_788, type, finite5333674244414288180nt_int: (product_prod_int_int > set_Pr1872883991513573699nt_int > set_Pr1872883991513573699nt_int) > set_Pr1872883991513573699nt_int > set_Pr958786334691620121nt_int > set_Pr1872883991513573699nt_int).
% 18.75/7.45 thf(func_def_789, type, finite1318812335397358250nt_int: (product_prod_int_int > set_Pr9222295170931077689nt_int > set_Pr9222295170931077689nt_int) > set_Pr9222295170931077689nt_int > set_Pr958786334691620121nt_int > set_Pr9222295170931077689nt_int).
% 18.75/7.45 thf(func_def_790, type, finite3179781904389220718at_nat: (set_Pr1261947904930325089at_nat > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat) > set_Pr4329608150637261639at_nat > set_se7855581050983116737at_nat > set_Pr4329608150637261639at_nat).
% 18.75/7.45 thf(func_def_791, type, comp_C3959375555751086581er_num: ((code_integer > code_integer) > code_integer > code_integer) > (((produc8923325533196201883nteger > produc8923325533196201883nteger) > num) > code_integer > code_integer) > ((produc8923325533196201883nteger > produc8923325533196201883nteger) > num) > code_integer > code_integer).
% 18.75/7.45 thf(func_def_792, type, comp_C2822359487432382964nteger: ((code_integer > code_integer) > code_integer > code_integer) > (code_integer > code_integer > code_integer) > code_integer > code_integer > code_integer).
% 18.75/7.45 thf(func_def_793, type, comp_C5301300457492916725nteger: ((code_integer > code_integer) > num > produc8923325533196201883nteger > produc8923325533196201883nteger) > ((code_integer > code_integer) > code_integer > code_integer) > (code_integer > code_integer) > num > produc8923325533196201883nteger > produc8923325533196201883nteger).
% 18.75/7.45 thf(func_def_794, type, comp_C9104104092898552938er_num: ((code_integer > code_integer) > num > code_integer) > ((code_integer > num) > code_integer > code_integer) > (code_integer > num) > num > code_integer).
% 18.75/7.45 thf(func_def_795, type, comp_C3983183376822107068nteger: ((code_integer > code_integer) > produc8923325533196201883nteger > produc8923325533196201883nteger) > ((code_integer > code_integer) > code_integer > code_integer) > (code_integer > code_integer) > produc8923325533196201883nteger > produc8923325533196201883nteger).
% 18.75/7.45 thf(func_def_796, type, comp_C8797469213163452608nteger: ((code_integer > code_integer) > produc8923325533196201883nteger > produc8923325533196201883nteger) > (code_integer > code_integer > code_integer) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger).
% 18.75/7.45 thf(func_def_797, type, comp_C8645541002826910333er_num: ((code_integer > code_integer) > produc8923325533196201883nteger > produc8923325533196201883nteger) > (num > code_integer > code_integer) > num > produc8923325533196201883nteger > produc8923325533196201883nteger).
% 18.75/7.45 thf(func_def_798, type, comp_C5076291335850163704nteger: ((code_integer > code_integer) > code_integer) > (code_integer > code_integer > code_integer) > code_integer > code_integer).
% 18.75/7.45 thf(func_def_799, type, comp_C8127656796141369388er_int: ((code_integer > nat) > num > num) > ((code_integer > int) > code_integer > nat) > (code_integer > int) > num > num).
% 18.75/7.45 thf(func_def_800, type, comp_i6226780894115828703_nat_o: ((int > $o) > int > $o) > ((product_prod_nat_nat > $o) > int > $o) > (product_prod_nat_nat > $o) > int > $o).
% 18.75/7.45 thf(func_def_801, type, comp_int_o_int_o_int: ((int > $o) > int > $o) > (int > int > $o) > int > int > $o).
% 18.75/7.45 thf(func_def_802, type, comp_i1993086638917920293nt_int: ((int > $o) > int > int) > (int > int > $o) > int > int > int).
% 18.75/7.45 thf(func_def_803, type, comp_int_o_nat_o_int: ((int > $o) > nat > $o) > (int > int > $o) > int > nat > $o).
% 18.75/7.45 thf(func_def_804, type, comp_i5098556425753098485_o_int: ((int > int) > int > $o) > (int > int > int) > int > int > $o).
% 18.75/7.45 thf(func_def_805, type, comp_i1129928922100200191nt_int: ((int > int) > int > int) > (int > int > int) > int > int > int).
% 18.75/7.45 thf(func_def_806, type, comp_i4411980392712547921_o_int: ((int > int) > nat > $o) > (int > int > int) > int > nat > $o).
% 18.75/7.45 thf(func_def_807, type, comp_i1790862786758963855nt_int: ((int > product_prod_int_int) > int > product_prod_int_int) > (int > int > product_prod_int_int) > int > int > product_prod_int_int).
% 18.75/7.45 thf(func_def_808, type, comp_i118865614814752126nt_int: ((int > product_prod_int_int) > int > rat) > ((int > product_prod_int_int) > int > product_prod_int_int) > (int > product_prod_int_int) > int > rat).
% 18.75/7.45 thf(func_def_809, type, comp_i1302866070986779890at_int: ((int > product_prod_int_int) > int > rat) > (int > int > product_prod_int_int) > int > int > rat).
% 18.75/7.45 thf(func_def_810, type, comp_i929186717396404458nt_int: ((int > rat) > int > product_prod_int_int) > (int > int > rat) > int > int > product_prod_int_int).
% 18.75/7.45 thf(func_def_811, type, comp_i5271019637457297241nt_int: ((int > rat) > int > rat) > ((int > product_prod_int_int) > int > rat) > (int > product_prod_int_int) > int > rat).
% 18.75/7.45 thf(func_def_812, type, comp_i8258899369942393943at_int: ((int > rat) > int > rat) > (int > int > rat) > int > int > rat).
% 18.75/7.45 thf(func_def_813, type, comp_nat_o_int_o_int: ((nat > $o) > int > $o) > (int > nat > $o) > int > int > $o).
% 18.75/7.45 thf(func_def_814, type, comp_n3090169619561918849nt_int: ((nat > $o) > int > int) > (int > nat > $o) > int > int > int).
% 18.75/7.45 thf(func_def_815, type, comp_n5656820349209612572_nat_o: ((nat > $o) > nat > $o) > ((nat > $o) > nat > $o) > (nat > $o) > nat > $o).
% 18.75/7.45 thf(func_def_816, type, comp_nat_o_nat_o_int: ((nat > $o) > nat > $o) > (int > nat > $o) > int > nat > $o).
% 18.75/7.45 thf(func_def_817, type, comp_n3323228797031117228um_num: ((nat > code_integer) > int > code_integer) > ((num > num) > nat > code_integer) > (num > num) > int > code_integer).
% 18.75/7.45 thf(func_def_818, type, comp_n4765151935410462062um_int: ((nat > nat) > int > num) > ((num > int) > nat > nat) > (num > int) > int > num).
% 18.75/7.45 thf(func_def_819, type, comp_P3928908779438215820nteger: ((produc8923325533196201883nteger > produc8923325533196201883nteger) > produc8923325533196201883nteger > produc8923325533196201883nteger) > (code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger).
% 18.75/7.45 thf(func_def_820, type, comp_P286844350285437056_nat_o: ((product_prod_nat_nat > $o) > int > $o) > ((product_prod_nat_nat > $o) > product_prod_nat_nat > $o) > (product_prod_nat_nat > $o) > int > $o).
% 18.75/7.45 thf(func_def_821, type, comp_P9039549498699531069at_nat: ((product_prod_nat_nat > $o) > int > $o) > (product_prod_nat_nat > product_prod_nat_nat > $o) > product_prod_nat_nat > int > $o).
% 18.75/7.45 thf(func_def_822, type, comp_P1872448293794610368at_nat: ((product_prod_nat_nat > product_prod_nat_nat) > int > int) > (product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat) > product_prod_nat_nat > int > int).
% 18.75/7.45 thf(func_def_823, type, comp_s518380907012905326o_assn: ((set_o > assn) > set_set_o > assn) > (($o > assn) > set_o > assn) > ($o > assn) > set_set_o > assn).
% 18.75/7.45 thf(func_def_824, type, comp_s262121120021782499nteger: ((set_o > code_integer) > set_set_o > code_integer) > (($o > code_integer) > set_o > code_integer) > ($o > code_integer) > set_set_o > code_integer).
% 18.75/7.45 thf(func_def_825, type, comp_s6084864194472624150_o_nat: ((set_o > nat) > set_set_o > nat) > (($o > nat) > set_o > nat) > ($o > nat) > set_set_o > nat).
% 18.75/7.45 thf(func_def_826, type, comp_s1265507639253661726_o_rat: ((set_o > rat) > set_set_o > rat) > (($o > rat) > set_o > rat) > ($o > rat) > set_set_o > rat).
% 18.75/7.45 thf(func_def_827, type, comp_s3531641609786562035r_assn: ((set_Code_integer > assn) > set_set_Code_integer > assn) > ((code_integer > assn) > set_Code_integer > assn) > (code_integer > assn) > set_set_Code_integer > assn).
% 18.75/7.45 thf(func_def_828, type, comp_s8484400498494363538nteger: ((set_Code_integer > code_integer) > set_set_Code_integer > code_integer) > ((code_integer > code_integer) > set_Code_integer > code_integer) > (code_integer > code_integer) > set_set_Code_integer > code_integer).
% 18.75/7.45 thf(func_def_829, type, comp_s9045439038509510147er_rat: ((set_Code_integer > rat) > set_set_Code_integer > rat) > ((code_integer > rat) > set_Code_integer > rat) > (code_integer > rat) > set_set_Code_integer > rat).
% 18.75/7.45 thf(func_def_830, type, comp_s4595925057662634336t_assn: ((set_int > assn) > set_set_int > assn) > ((int > assn) > set_int > assn) > (int > assn) > set_set_int > assn).
% 18.75/7.45 thf(func_def_831, type, comp_s7646638485285982975nteger: ((set_int > code_integer) > set_set_int > code_integer) > ((int > code_integer) > set_int > code_integer) > (int > code_integer) > set_set_int > code_integer).
% 18.75/7.45 thf(func_def_832, type, comp_s4088261402702255472nt_rat: ((set_int > rat) > set_set_int > rat) > ((int > rat) > set_int > rat) > (int > rat) > set_set_int > rat).
% 18.75/7.45 thf(func_def_833, type, comp_o_o_o: ($o > $o) > ($o > $o) > $o > $o).
% 18.75/7.45 thf(func_def_834, type, comp_o_o_nat: ($o > $o) > (nat > $o) > nat > $o).
% 18.75/7.45 thf(func_def_835, type, comp_o8022916681612831582at_nat: ($o > $o) > (product_prod_nat_nat > $o) > product_prod_nat_nat > $o).
% 18.75/7.45 thf(func_def_836, type, comp_C2931745410781319416nteger: (code_integer > code_integer > code_integer) > (code_integer > code_integer) > code_integer > code_integer > code_integer).
% 18.75/7.45 thf(func_def_837, type, comp_C3662112809048933045er_num: (code_integer > code_integer > code_integer) > (num > code_integer) > num > code_integer > code_integer).
% 18.75/7.45 thf(func_def_838, type, comp_C95226695241045696nteger: (code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger) > ((code_integer > code_integer) > code_integer) > (code_integer > code_integer) > produc8923325533196201883nteger > produc8923325533196201883nteger).
% 18.75/7.45 thf(func_def_839, type, comp_C1593894019821074884nteger: (code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger) > (code_integer > code_integer) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger).
% 18.75/7.45 thf(func_def_840, type, comp_C6617437204949736321er_num: (code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger) > (num > code_integer) > num > produc8923325533196201883nteger > produc8923325533196201883nteger).
% 18.75/7.45 thf(func_def_841, type, comp_C8462447471145125178sn_nat: (code_integer > assn) > (nat > code_integer) > nat > assn).
% 18.75/7.45 thf(func_def_842, type, comp_C7449957260575251196nteger: (code_integer > code_integer) > (code_integer > code_integer) > code_integer > code_integer).
% 18.75/7.45 thf(func_def_843, type, comp_C6974050283906349679er_nat: (code_integer > code_integer) > (nat > code_integer) > nat > code_integer).
% 18.75/7.45 thf(func_def_844, type, comp_C3531382070062128313er_num: (code_integer > code_integer) > (num > code_integer) > num > code_integer).
% 18.75/7.45 thf(func_def_845, type, comp_C1043215000170864188nteger: (code_integer > code_integer) > (produc8923325533196201883nteger > code_integer) > produc8923325533196201883nteger > code_integer).
% 18.75/7.45 thf(func_def_846, type, comp_C5046419837055054490nt_int: (code_integer > int) > (int > code_integer) > int > int).
% 18.75/7.45 thf(func_def_847, type, comp_C5048910307564104766nt_nat: (code_integer > int) > (nat > code_integer) > nat > int).
% 18.75/7.45 thf(func_def_848, type, comp_C4049556595663050210at_nat: (code_integer > nat) > (nat > code_integer) > nat > nat).
% 18.75/7.45 thf(func_def_849, type, comp_C2277306503614464128nteger: (code_integer > produc8923325533196201883nteger) > (produc8923325533196201883nteger > code_integer) > produc8923325533196201883nteger > produc8923325533196201883nteger).
% 18.75/7.45 thf(func_def_850, type, comp_C8086623346886033437it_nat: (code_integer > product_unit) > (nat > code_integer) > nat > product_unit).
% 18.75/7.45 thf(func_def_851, type, comp_C3733001951728184298at_nat: (code_integer > rat) > (nat > code_integer) > nat > rat).
% 18.75/7.45 thf(func_def_852, type, comp_int_int_o_int: (int > int > $o) > (int > int) > int > int > $o).
% 18.75/7.45 thf(func_def_853, type, comp_int_int_int_int: (int > int > int) > (int > int) > int > int > int).
% 18.75/7.45 thf(func_def_854, type, comp_int_int_int_nat: (int > int > int) > (nat > int) > nat > int > int).
% 18.75/7.45 thf(func_def_855, type, comp_i87437609017934369nt_int: (int > int > product_prod_int_int) > (int > int) > int > int > product_prod_int_int).
% 18.75/7.45 thf(func_def_856, type, comp_int_int_rat_int: (int > int > rat) > (int > int) > int > int > rat).
% 18.75/7.45 thf(func_def_857, type, comp_int_nat_o_int: (int > nat > $o) > (int > int) > int > nat > $o).
% 18.75/7.45 thf(func_def_858, type, comp_int_assn_int: (int > assn) > (int > int) > int > assn).
% 18.75/7.45 thf(func_def_859, type, comp_int_assn_nat: (int > assn) > (nat > int) > nat > assn).
% 18.75/7.45 thf(func_def_860, type, comp_i1585864551200866970er_int: (int > code_integer) > (int > int) > int > code_integer).
% 18.75/7.45 thf(func_def_861, type, comp_i1588355021709917246er_nat: (int > code_integer) > (nat > int) > nat > code_integer).
% 18.75/7.45 thf(func_def_862, type, comp_int_int_int: (int > int) > (int > int) > int > int).
% 18.75/7.45 thf(func_def_863, type, comp_int_int_nat: (int > int) > (nat > int) > nat > int).
% 18.75/7.45 thf(func_def_864, type, comp_i4330622015127193916nt_int: (int > int) > (product_prod_int_int > int) > product_prod_int_int > int).
% 18.75/7.45 thf(func_def_865, type, comp_int_nat_int: (int > nat) > (int > int) > int > nat).
% 18.75/7.45 thf(func_def_866, type, comp_int_nat_nat: (int > nat) > (nat > int) > nat > nat).
% 18.75/7.45 thf(func_def_867, type, comp_int_num_int: (int > num) > (int > int) > int > num).
% 18.75/7.45 thf(func_def_868, type, comp_i5941103828406351439nt_int: (int > product_prod_int_int) > (product_prod_int_int > int) > product_prod_int_int > product_prod_int_int).
% 18.75/7.45 thf(func_def_869, type, comp_i1108739374719436894at_int: (int > product_prod_nat_nat) > (int > int) > int > product_prod_nat_nat).
% 18.75/7.45 thf(func_def_870, type, comp_int_rat_int: (int > rat) > (int > int) > int > rat).
% 18.75/7.45 thf(func_def_871, type, comp_int_rat_nat: (int > rat) > (nat > int) > nat > rat).
% 18.75/7.45 thf(func_def_872, type, comp_nat_nat_nat_nat: (nat > nat > nat) > (nat > nat) > nat > nat > nat).
% 18.75/7.45 thf(func_def_873, type, comp_nat_o_nat: (nat > $o) > (nat > nat) > nat > $o).
% 18.75/7.45 thf(func_def_874, type, comp_nat_assn_nat: (nat > assn) > (nat > nat) > nat > assn).
% 18.75/7.45 thf(func_def_875, type, comp_n3898172953802868194er_nat: (nat > code_integer) > (nat > nat) > nat > code_integer).
% 18.75/7.45 thf(func_def_876, type, comp_nat_int_int: (nat > int) > (int > nat) > int > int).
% 18.75/7.45 thf(func_def_877, type, comp_nat_int_nat: (nat > int) > (nat > nat) > nat > int).
% 18.75/7.45 thf(func_def_878, type, comp_n8698576032424989604at_nat: (nat > multis2468970476368604999at_nat) > (nat > nat) > nat > multis2468970476368604999at_nat).
% 18.75/7.45 thf(func_def_879, type, comp_nat_nat_int: (nat > nat) > (int > nat) > int > nat).
% 18.75/7.45 thf(func_def_880, type, comp_nat_nat_nat: (nat > nat) > (nat > nat) > nat > nat).
% 18.75/7.45 thf(func_def_881, type, comp_nat_num_int: (nat > num) > (int > nat) > int > num).
% 18.75/7.45 thf(func_def_882, type, comp_nat_num_nat: (nat > num) > (nat > nat) > nat > num).
% 18.75/7.45 thf(func_def_883, type, comp_n9025697279074352746it_nat: (nat > product_unit) > (nat > nat) > nat > product_unit).
% 18.75/7.45 thf(func_def_884, type, comp_nat_rat_nat: (nat > rat) > (nat > nat) > nat > rat).
% 18.75/7.45 thf(func_def_885, type, comp_n6909714581898973814er_num: (num > code_integer) > (num > num) > num > code_integer).
% 18.75/7.45 thf(func_def_886, type, comp_num_int_num: (num > int) > (num > num) > num > int).
% 18.75/7.45 thf(func_def_887, type, comp_num_nat_num: (num > nat) > (num > num) > num > nat).
% 18.75/7.45 thf(func_def_888, type, comp_num_num_int: (num > num) > (int > num) > int > num).
% 18.75/7.45 thf(func_def_889, type, comp_num_num_nat: (num > num) > (nat > num) > nat > num).
% 18.75/7.45 thf(func_def_890, type, comp_num_num_num: (num > num) > (num > num) > num > num).
% 18.75/7.45 thf(func_def_891, type, comp_n6731957995704128387um_num: (num > option_num) > (num > num) > num > option_num).
% 18.75/7.45 thf(func_def_892, type, comp_o7188567781464924208nteger: (option8057788054806935849nteger > option7428179582072448501nteger) > (option_Code_integer > option8057788054806935849nteger) > option_Code_integer > option7428179582072448501nteger).
% 18.75/7.45 thf(func_def_893, type, comp_o8860755393669798242_nat_o: (option_nat_o > nat > $o) > ((nat > $o) > option_nat_o) > (nat > $o) > nat > $o).
% 18.75/7.45 thf(func_def_894, type, comp_option_o_o_o: (option_o > $o) > ($o > option_o) > $o > $o).
% 18.75/7.45 thf(func_def_895, type, comp_o9011007105448239796nteger: (option_Code_integer > option7428179582072448501nteger) > (option_Code_integer > option_Code_integer) > option_Code_integer > option7428179582072448501nteger).
% 18.75/7.45 thf(func_def_896, type, comp_o5321900959263616553on_num: (option_Code_integer > option_Code_integer) > (option_num > option_Code_integer) > option_num > option_Code_integer).
% 18.75/7.45 thf(func_def_897, type, comp_o2446264010603541305nt_int: (option_int > int) > (int > option_int) > int > int).
% 18.75/7.45 thf(func_def_898, type, comp_o4663963155070737957at_nat: (option_nat > nat) > (nat > option_nat) > nat > nat).
% 18.75/7.45 thf(func_def_899, type, comp_o3128663659858294251on_int: (option_nat > option_num) > (option_int > option_nat) > option_int > option_num).
% 18.75/7.45 thf(func_def_900, type, comp_o6878144249584144265on_num: (option_num > nat) > (option_num > option_num) > option_num > nat).
% 18.75/7.45 thf(func_def_901, type, comp_o6342398210560591875um_num: (option_num > num) > (num > option_num) > num > num).
% 18.75/7.45 thf(func_def_902, type, comp_o8931257242830428707on_num: (option_num > option_num) > (option_num > option_num) > option_num > option_num).
% 18.75/7.45 thf(func_def_903, type, comp_o279924169626513613it_nat: (option8956607266484857688it_nat > produc8664842809031399944it_nat) > (produc8664842809031399944it_nat > option8956607266484857688it_nat) > produc8664842809031399944it_nat > produc8664842809031399944it_nat).
% 18.75/7.45 thf(func_def_904, type, comp_P1875353012086385820e_term: (produc7773217078559923341nt_int > int > option6357759511663192854e_term) > (produc3832618445565238089e_term > produc7773217078559923341nt_int) > produc3832618445565238089e_term > int > option6357759511663192854e_term).
% 18.75/7.45 thf(func_def_905, type, comp_P5363713469694551954e_term: (produc7773217078559923341nt_int > product_prod_int_int) > (produc3832618445565238089e_term > produc7773217078559923341nt_int) > produc3832618445565238089e_term > product_prod_int_int).
% 18.75/7.45 thf(func_def_906, type, comp_P8312345242777556868_nat_o: (produc7360885484439884007_nat_o > nat > $o) > ((nat > $o) > produc7360885484439884007_nat_o) > (nat > $o) > nat > $o).
% 18.75/7.45 thf(func_def_907, type, comp_P1075760313067033319_o_int: (produc7360885484439884007_nat_o > nat > $o) > (int > produc7360885484439884007_nat_o) > int > nat > $o).
% 18.75/7.45 thf(func_def_908, type, comp_P8650103696410638905e_term: (produc1908205239877642774nteger > produc6241069584506657477e_term > option6357759511663192854e_term) > (produc998928222018024388e_term > produc1908205239877642774nteger) > produc998928222018024388e_term > produc6241069584506657477e_term > option6357759511663192854e_term).
% 18.75/7.45 thf(func_def_909, type, comp_P1663382703091044646e_term: (produc1908205239877642774nteger > produc8923325533196201883nteger) > (produc998928222018024388e_term > produc1908205239877642774nteger) > produc998928222018024388e_term > produc8923325533196201883nteger).
% 18.75/7.45 thf(func_def_910, type, comp_P4355506512671352436_nat_o: (produc2732055786443039994et_nat > produc3658429121746597890et_nat > $o) > (produc4962441903510821572_nat_o > produc2732055786443039994et_nat) > produc4962441903510821572_nat_o > produc3658429121746597890et_nat > $o).
% 18.75/7.45 thf(func_def_911, type, comp_P9183373265949749025_nat_o: (produc2732055786443039994et_nat > produc3925858234332021118et_nat) > (produc4962441903510821572_nat_o > produc2732055786443039994et_nat) > produc4962441903510821572_nat_o > produc3925858234332021118et_nat).
% 18.75/7.45 thf(func_def_912, type, comp_P1110778729668777324_nat_o: (produc3925858234332021118et_nat > produc3658429121746597890et_nat > $o) > (produc6907119039986491712_nat_o > produc3925858234332021118et_nat) > produc6907119039986491712_nat_o > produc3658429121746597890et_nat > $o).
% 18.75/7.45 thf(func_def_913, type, comp_P5089495125153697957_nat_o: (produc3925858234332021118et_nat > produc3658429121746597890et_nat) > (produc6907119039986491712_nat_o > produc3925858234332021118et_nat) > produc6907119039986491712_nat_o > produc3658429121746597890et_nat).
% 18.75/7.45 thf(func_def_914, type, comp_P8577347034251779110e_term: (produc2285326912895808259nt_int > produc8551481072490612790e_term > option6357759511663192854e_term) > (produc1821397396195235155e_term > produc2285326912895808259nt_int) > produc1821397396195235155e_term > produc8551481072490612790e_term > option6357759511663192854e_term).
% 18.75/7.45 thf(func_def_915, type, comp_P4057098934159210662e_term: (produc2285326912895808259nt_int > product_prod_int_int) > (produc1821397396195235155e_term > produc2285326912895808259nt_int) > produc1821397396195235155e_term > product_prod_int_int).
% 18.75/7.45 thf(func_def_916, type, comp_P2137996956111167876_o_o_o: (product_prod_o_o > $o) > ($o > product_prod_o_o) > $o > $o).
% 18.75/7.45 thf(func_def_917, type, comp_P7111796090210262324nteger: (produc8923325533196201883nteger > code_integer) > (code_integer > produc8923325533196201883nteger) > code_integer > code_integer).
% 18.75/7.45 thf(func_def_918, type, comp_P3107242062624629507er_int: (produc8923325533196201883nteger > code_integer) > (int > produc8923325533196201883nteger) > int > code_integer).
% 18.75/7.45 thf(func_def_919, type, comp_P3109732533133679783er_nat: (produc8923325533196201883nteger > code_integer) > (nat > produc8923325533196201883nteger) > nat > code_integer).
% 18.75/7.45 thf(func_def_920, type, comp_P3428181540658402820nteger: (produc8923325533196201883nteger > code_integer) > (produc8923325533196201883nteger > produc8923325533196201883nteger) > produc8923325533196201883nteger > code_integer).
% 18.75/7.45 thf(func_def_921, type, comp_P659088277599099894t_unit: (produc8923325533196201883nteger > code_integer) > (product_unit > produc8923325533196201883nteger) > product_unit > code_integer).
% 18.75/7.45 thf(func_def_922, type, comp_P2475326853202991862er_nat: (produc2256096406371053034er_int > code_integer) > (nat > produc2256096406371053034er_int) > nat > code_integer).
% 18.75/7.45 thf(func_def_923, type, comp_P8345930540558018757nt_nat: (produc2256096406371053034er_int > int) > (nat > produc2256096406371053034er_int) > nat > int).
% 18.75/7.45 thf(func_def_924, type, comp_P5700178199414968986er_nat: (produc6433947425880249742er_nat > code_integer) > (nat > produc6433947425880249742er_nat) > nat > code_integer).
% 18.75/7.45 thf(func_def_925, type, comp_P1337767177661389325at_nat: (produc6433947425880249742er_nat > nat) > (nat > produc6433947425880249742er_nat) > nat > nat).
% 18.75/7.45 thf(func_def_926, type, comp_P3067963646784605345atural: (produc7822875418678951345atural > produc7822875418678951345atural) > (produc5835291356934675326atural > produc7822875418678951345atural) > produc5835291356934675326atural > produc7822875418678951345atural).
% 18.75/7.45 thf(func_def_927, type, comp_P4943825737035310295atural: (produc7822875418678951345atural > produc6756470014200349799atural) > (produc5835291356934675326atural > produc7822875418678951345atural) > produc5835291356934675326atural > produc6756470014200349799atural).
% 18.75/7.45 thf(func_def_928, type, comp_P5589825499870570807al_int: (produc5835291356934675326atural > code_natural) > (int > produc5835291356934675326atural) > int > code_natural).
% 18.75/7.45 thf(func_def_929, type, comp_P5592315970379621083al_nat: (produc5835291356934675326atural > code_natural) > (nat > produc5835291356934675326atural) > nat > code_natural).
% 18.75/7.45 thf(func_def_930, type, comp_P210409258367696578t_unit: (produc5835291356934675326atural > code_natural) > (product_unit > produc5835291356934675326atural) > product_unit > code_natural).
% 18.75/7.45 thf(func_def_931, type, comp_P8475394669922486716al_int: (produc5835291356934675326atural > produc7822875418678951345atural) > (int > produc5835291356934675326atural) > int > produc7822875418678951345atural).
% 18.75/7.45 thf(func_def_932, type, comp_P8477885140431536992al_nat: (produc5835291356934675326atural > produc7822875418678951345atural) > (nat > produc5835291356934675326atural) > nat > produc7822875418678951345atural).
% 18.75/7.45 thf(func_def_933, type, comp_P7610810914149544718atural: (produc5835291356934675326atural > produc7822875418678951345atural) > (produc5835291356934675326atural > produc5835291356934675326atural) > produc5835291356934675326atural > produc7822875418678951345atural).
% 18.75/7.45 thf(func_def_934, type, comp_P5756991293874479000atural: (produc5835291356934675326atural > produc7822875418678951345atural) > (produc3981471736659609608atural > produc5835291356934675326atural) > produc3981471736659609608atural > produc7822875418678951345atural).
% 18.75/7.45 thf(func_def_935, type, comp_P1945487127105810045t_unit: (produc5835291356934675326atural > produc7822875418678951345atural) > (product_unit > produc5835291356934675326atural) > product_unit > produc7822875418678951345atural).
% 18.75/7.45 thf(func_def_936, type, comp_P2097125496263478628t_unit: (produc6714399278180371524it_nat > option3216581401566546698it_nat) > (heap_e7401611519738050253t_unit > produc6714399278180371524it_nat) > heap_e7401611519738050253t_unit > option3216581401566546698it_nat).
% 18.75/7.45 thf(func_def_937, type, comp_P6870028373966156406er_nat: (produc2963269191615333738nteger > code_integer) > (nat > produc2963269191615333738nteger) > nat > code_integer).
% 18.75/7.45 thf(func_def_938, type, comp_P59025373045620805nt_nat: (produc2963269191615333738nteger > int) > (nat > produc2963269191615333738nteger) > nat > int).
% 18.75/7.45 thf(func_def_939, type, comp_P6651465171681656048nt_int: (product_prod_int_int > int) > (int > product_prod_int_int) > int > int).
% 18.75/7.45 thf(func_def_940, type, comp_P6653955642190706324nt_nat: (product_prod_int_int > int) > (nat > product_prod_int_int) > nat > int).
% 18.75/7.45 thf(func_def_941, type, comp_P5356232565778667509nt_int: (product_prod_int_int > int) > (product_prod_int_int > product_prod_int_int) > product_prod_int_int > int).
% 18.75/7.45 thf(func_def_942, type, comp_P6796073005956588617t_unit: (product_prod_int_int > int) > (product_unit > product_prod_int_int) > product_unit > int).
% 18.75/7.45 thf(func_def_943, type, comp_P5335556815845735580at_int: (product_prod_int_int > rat) > (int > product_prod_int_int) > int > rat).
% 18.75/7.45 thf(func_def_944, type, comp_P5648219952011055433nt_int: (product_prod_int_int > rat) > (product_prod_int_int > product_prod_int_int) > product_prod_int_int > rat).
% 18.75/7.45 thf(func_def_945, type, comp_P645145991195131448nt_nat: (product_prod_int_nat > int) > (nat > product_prod_int_nat) > nat > int).
% 18.75/7.45 thf(func_def_946, type, comp_P8869164316148852700at_nat: (product_prod_int_nat > nat) > (nat > product_prod_int_nat) > nat > nat).
% 18.75/7.45 thf(func_def_947, type, comp_P5461341465284484122er_nat: (produc2591615631378489102nteger > code_integer) > (nat > produc2591615631378489102nteger) > nat > code_integer).
% 18.75/7.45 thf(func_def_948, type, comp_P9144323761349829517at_nat: (produc2591615631378489102nteger > nat) > (nat > produc2591615631378489102nteger) > nat > nat).
% 18.75/7.45 thf(func_def_949, type, comp_P8963773574283657272nt_nat: (product_prod_nat_int > int) > (nat > product_prod_nat_int) > nat > int).
% 18.75/7.45 thf(func_def_950, type, comp_P7964419862382602716at_nat: (product_prod_nat_int > nat) > (nat > product_prod_nat_int) > nat > nat).
% 18.75/7.45 thf(func_def_951, type, comp_P7507668834397697393_o_int: (product_prod_nat_nat > int > $o) > (int > product_prod_nat_nat) > int > int > $o).
% 18.75/7.45 thf(func_def_952, type, comp_P1029605119844863363nt_int: (product_prod_nat_nat > int > int) > (int > product_prod_nat_nat) > int > int > int).
% 18.75/7.45 thf(func_def_953, type, comp_P1289042343629989734_o_int: (product_prod_nat_nat > $o) > (int > product_prod_nat_nat) > int > $o).
% 18.75/7.45 thf(func_def_954, type, comp_P1955610211387027840at_nat: (product_prod_nat_nat > nat) > (nat > product_prod_nat_nat) > nat > nat).
% 18.75/7.45 thf(func_def_955, type, comp_P2980510830910040157t_unit: (product_prod_nat_nat > nat) > (product_unit > product_prod_nat_nat) > product_unit > nat).
% 18.75/7.45 thf(func_def_956, type, comp_P7428279379633703887at_int: (product_prod_nat_nat > product_prod_nat_nat) > (int > product_prod_nat_nat) > int > product_prod_nat_nat).
% 18.75/7.45 thf(func_def_957, type, comp_P864883071962432936um_num: (product_prod_num_num > num) > (num > product_prod_num_num) > num > num).
% 18.75/7.45 thf(func_def_958, type, comp_P3887058762840424708atural: (produc3981471736659609608atural > produc7822875418678951345atural) > (produc5835291356934675326atural > produc3981471736659609608atural) > produc5835291356934675326atural > produc7822875418678951345atural).
% 18.75/7.45 thf(func_def_959, type, comp_P230220204662055659atural: (produc6756470014200349799atural > produc7822875418678951345atural) > (produc5835291356934675326atural > produc6756470014200349799atural) > produc5835291356934675326atural > produc7822875418678951345atural).
% 18.75/7.45 thf(func_def_960, type, comp_P3118722334806803912t_unit: (produc8664842809031399944it_nat > option8956607266484857688it_nat) > (heap_e7401611519738050253t_unit > produc8664842809031399944it_nat) > heap_e7401611519738050253t_unit > option8956607266484857688it_nat).
% 18.75/7.45 thf(func_def_961, type, comp_P756492639069434009er_nat: (product_unit > code_integer) > (nat > product_unit) > nat > code_integer).
% 18.75/7.45 thf(func_def_962, type, comp_P7645380973975430442t_unit: (product_unit > product_unit) > (product_unit > product_unit) > product_unit > product_unit).
% 18.75/7.45 thf(func_def_963, type, comp_rat_nat_nat: (rat > nat) > (nat > rat) > nat > nat).
% 18.75/7.45 thf(func_def_964, type, comp_r4727614531642239972nt_int: (rat > rat) > (product_prod_int_int > rat) > product_prod_int_int > rat).
% 18.75/7.45 thf(func_def_965, type, comp_rat_rat_rat: (rat > rat) > (rat > rat) > rat > rat).
% 18.75/7.45 thf(func_def_966, type, fun_upd_o_o: ($o > $o) > $o > $o > $o > $o).
% 18.75/7.45 thf(func_def_967, type, fun_upd_o_int: ($o > int) > $o > int > $o > int).
% 18.75/7.45 thf(func_def_968, type, fun_upd_o_nat: ($o > nat) > $o > nat > $o > nat).
% 18.75/7.45 thf(func_def_969, type, fun_upd_o_option_num: ($o > option_num) > $o > option_num > $o > option_num).
% 18.75/7.45 thf(func_def_970, type, fun_up1288979561775348147it_nat: ($o > option8956607266484857688it_nat) > $o > option8956607266484857688it_nat > $o > option8956607266484857688it_nat).
% 18.75/7.45 thf(func_def_971, type, fun_up8056716234270145717nteger: (code_integer > code_integer > code_integer) > code_integer > (code_integer > code_integer) > code_integer > code_integer > code_integer).
% 18.75/7.45 thf(func_def_972, type, fun_up8139772397987072257nteger: (code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger) > code_integer > (produc8923325533196201883nteger > produc8923325533196201883nteger) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger).
% 18.75/7.45 thf(func_def_973, type, fun_up8355007323143964473nteger: (code_integer > code_integer) > code_integer > code_integer > code_integer > code_integer).
% 18.75/7.45 thf(func_def_974, type, fun_up6566892301432185865nteger: (code_integer > option_Code_integer) > code_integer > option_Code_integer > code_integer > option_Code_integer).
% 18.75/7.45 thf(func_def_975, type, fun_up2923169431403285008atural: (code_natural > option5403585828896915703atural) > code_natural > option5403585828896915703atural > code_natural > option5403585828896915703atural).
% 18.75/7.45 thf(func_def_976, type, fun_upd_int_o: (int > $o) > int > $o > int > $o).
% 18.75/7.45 thf(func_def_977, type, fun_upd_int_int: (int > int) > int > int > int > int).
% 18.75/7.45 thf(func_def_978, type, fun_upd_int_nat: (int > nat) > int > nat > int > nat).
% 18.75/7.45 thf(func_def_979, type, fun_upd_int_num: (int > num) > int > num > int > num).
% 18.75/7.45 thf(func_def_980, type, fun_up8666045135305973159on_int: (int > option_int) > int > option_int > int > option_int).
% 18.75/7.45 thf(func_def_981, type, fun_up4328768054909231765on_num: (int > option_num) > int > option_num > int > option_num).
% 18.75/7.45 thf(func_def_982, type, fun_up6992348036167380867it_nat: (int > option8956607266484857688it_nat) > int > option8956607266484857688it_nat > int > option8956607266484857688it_nat).
% 18.75/7.45 thf(func_def_983, type, fun_upd_nat_o: (nat > $o) > nat > $o > nat > $o).
% 18.75/7.45 thf(func_def_984, type, fun_up3904115110581602988nteger: (nat > code_integer) > nat > code_integer > nat > code_integer).
% 18.75/7.45 thf(func_def_985, type, fun_upd_nat_int: (nat > int) > nat > int > nat > int).
% 18.75/7.45 thf(func_def_986, type, fun_upd_nat_nat: (nat > nat) > nat > nat > nat > nat).
% 18.75/7.45 thf(func_def_987, type, fun_up1493157387958331631on_nat: (nat > option_nat) > nat > option_nat > nat > option_nat).
% 18.75/7.45 thf(func_def_988, type, fun_up2201401324907169337on_num: (nat > option_num) > nat > option_num > nat > option_num).
% 18.75/7.45 thf(func_def_989, type, fun_up4116053422210368295it_nat: (nat > option8956607266484857688it_nat) > nat > option8956607266484857688it_nat > nat > option8956607266484857688it_nat).
% 18.75/7.45 thf(func_def_990, type, fun_upd_nat_set_nat: (nat > set_nat) > nat > set_nat > nat > set_nat).
% 18.75/7.45 thf(func_def_991, type, fun_up1844922938552261878nteger: (num > code_integer) > num > code_integer > num > code_integer).
% 18.75/7.45 thf(func_def_992, type, fun_up8025039454679724718on_num: (product_prod_nat_nat > option_num) > product_prod_nat_nat > option_num > product_prod_nat_nat > option_num).
% 18.75/7.45 thf(func_def_993, type, fun_up3996838528606387100it_nat: (product_prod_nat_nat > option8956607266484857688it_nat) > product_prod_nat_nat > option8956607266484857688it_nat > product_prod_nat_nat > option8956607266484857688it_nat).
% 18.75/7.45 thf(func_def_994, type, fun_up3286109336741039636on_num: (produc3843707927480180839at_nat > option_num) > produc3843707927480180839at_nat > option_num > produc3843707927480180839at_nat > option_num).
% 18.75/7.45 thf(func_def_995, type, fun_up5549328659429834498it_nat: (produc3843707927480180839at_nat > option8956607266484857688it_nat) > produc3843707927480180839at_nat > option8956607266484857688it_nat > produc3843707927480180839at_nat > option8956607266484857688it_nat).
% 18.75/7.45 thf(func_def_996, type, fun_up4695802795598371002on_num: (product_unit > option_num) > product_unit > option_num > product_unit > option_num).
% 18.75/7.45 thf(func_def_997, type, fun_up1973317344121680296it_nat: (product_unit > option8956607266484857688it_nat) > product_unit > option8956607266484857688it_nat > product_unit > option8956607266484857688it_nat).
% 18.75/7.45 thf(func_def_998, type, id_nat_o: (nat > $o) > nat > $o).
% 18.75/7.45 thf(func_def_999, type, id_num_Code_integer: (num > code_integer) > num > code_integer).
% 18.75/7.45 thf(func_def_1000, type, id_Pro496765588584934260nteger: (produc8923325533196201883nteger > produc8923325533196201883nteger) > produc8923325533196201883nteger > produc8923325533196201883nteger).
% 18.75/7.45 thf(func_def_1001, type, id_o: $o > $o).
% 18.75/7.45 thf(func_def_1002, type, id_Code_integer: code_integer > code_integer).
% 18.75/7.45 thf(func_def_1003, type, id_int: int > int).
% 18.75/7.45 thf(func_def_1004, type, id_nat: nat > nat).
% 18.75/7.45 thf(func_def_1005, type, id_num: num > num).
% 18.75/7.45 thf(func_def_1006, type, id_option_nat_o: option_nat_o > option_nat_o).
% 18.75/7.45 thf(func_def_1007, type, id_option_o: option_o > option_o).
% 18.75/7.45 thf(func_def_1008, type, id_option_int: option_int > option_int).
% 18.75/7.45 thf(func_def_1009, type, id_option_nat: option_nat > option_nat).
% 18.75/7.45 thf(func_def_1010, type, id_option_num: option_num > option_num).
% 18.75/7.45 thf(func_def_1011, type, id_Pro3923183700162330716nt_int: produc7773217078559923341nt_int > produc7773217078559923341nt_int).
% 18.75/7.45 thf(func_def_1012, type, id_Pro1379270990444177765nteger: produc1908205239877642774nteger > produc1908205239877642774nteger).
% 18.75/7.45 thf(func_def_1013, type, id_Pro1297863087923562825et_nat: produc2732055786443039994et_nat > produc2732055786443039994et_nat).
% 18.75/7.45 thf(func_def_1014, type, id_Pro1888964116897856973et_nat: produc3925858234332021118et_nat > produc3925858234332021118et_nat).
% 18.75/7.45 thf(func_def_1015, type, id_Pro5422067691592394322nt_int: produc2285326912895808259nt_int > produc2285326912895808259nt_int).
% 18.75/7.45 thf(func_def_1016, type, id_Pro2309048762231606924nteger: produc8923325533196201883nteger > produc8923325533196201883nteger).
% 18.75/7.45 thf(func_def_1017, type, id_Pro4381231610383771306nt_int: product_prod_int_int > product_prod_int_int).
% 18.75/7.45 thf(func_def_1018, type, id_Pro1159712480615372887it_nat: produc8664842809031399944it_nat > produc8664842809031399944it_nat).
% 18.75/7.45 thf(func_def_1019, type, id_Product_unit: product_unit > product_unit).
% 18.75/7.45 thf(func_def_1020, type, id_rat: rat > rat).
% 18.75/7.45 thf(func_def_1021, type, id_set_nat_o: set_nat_o > set_nat_o).
% 18.75/7.45 thf(func_def_1022, type, id_set_o: set_o > set_o).
% 18.75/7.45 thf(func_def_1023, type, id_set_int: set_int > set_int).
% 18.75/7.45 thf(func_def_1024, type, id_set_nat: set_nat > set_nat).
% 18.75/7.45 thf(func_def_1025, type, id_set_num: set_num > set_num).
% 18.75/7.45 thf(func_def_1026, type, map_fu1335501423231535891nteger: (code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger) > (num > code_integer) > ((produc8923325533196201883nteger > produc8923325533196201883nteger) > num) > code_integer > code_integer).
% 18.75/7.45 thf(func_def_1027, type, map_fu6423247683660063826nteger: (code_integer > code_integer) > ((code_integer > code_integer) > produc8923325533196201883nteger > produc8923325533196201883nteger) > (code_integer > code_integer > code_integer) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger).
% 18.75/7.45 thf(func_def_1028, type, map_fu2576242048321985878nteger: (code_integer > code_integer) > (code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger) > (code_integer > code_integer) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger).
% 18.75/7.45 thf(func_def_1029, type, map_fu5082455417554595470nteger: (code_integer > code_integer) > (code_integer > code_integer) > (code_integer > code_integer) > code_integer > code_integer).
% 18.75/7.45 thf(func_def_1030, type, map_fu5423760287386111952nt_nat: (code_integer > code_integer) > (int > nat) > (code_integer > int) > code_integer > nat).
% 18.75/7.45 thf(func_def_1031, type, map_fu603974984455542859nteger: (code_integer > code_integer) > (num > code_integer) > (code_integer > num) > code_integer > code_integer).
% 18.75/7.45 thf(func_def_1032, type, map_fu2496120808607739376eger_o: (code_integer > int) > ((int > $o) > code_integer > $o) > (int > int > $o) > code_integer > code_integer > $o).
% 18.75/7.45 thf(func_def_1033, type, map_fu8272188784021352819nteger: (code_integer > int) > ((int > int) > code_integer > code_integer) > (int > int > int) > code_integer > code_integer > code_integer).
% 18.75/7.45 thf(func_def_1034, type, map_fu186220595405829473_nat_o: (code_integer > int) > ((nat > $o) > nat > $o) > (int > nat > $o) > code_integer > nat > $o).
% 18.75/7.45 thf(func_def_1035, type, map_fu6957801986076833569nt_o_o: (code_integer > int) > ($o > $o) > (int > $o) > code_integer > $o).
% 18.75/7.45 thf(func_def_1036, type, map_fu2599414010547811884nteger: (code_integer > int) > (int > code_integer) > (int > int) > code_integer > code_integer).
% 18.75/7.45 thf(func_def_1037, type, map_fu1051355602067684763atural: (code_integer > int) > (nat > code_natural) > (int > nat) > code_integer > code_natural).
% 18.75/7.45 thf(func_def_1038, type, map_fu6539832666145259331at_nat: (code_integer > int) > (nat > nat) > (int > nat) > code_integer > nat).
% 18.75/7.45 thf(func_def_1039, type, map_fu1227494855608507351um_num: (code_integer > int) > (num > num) > (int > num) > code_integer > num).
% 18.75/7.45 thf(func_def_1040, type, map_fu6256889081107267320ural_o: (code_natural > nat) > ((nat > $o) > code_natural > $o) > (nat > nat > $o) > code_natural > code_natural > $o).
% 18.75/7.45 thf(func_def_1041, type, map_fu6244533035418998608_nat_o: (code_natural > nat) > ((nat > $o) > nat > $o) > (nat > nat > $o) > code_natural > nat > $o).
% 18.75/7.45 thf(func_def_1042, type, map_fu6549440983881763648atural: (code_natural > nat) > ((nat > nat) > code_natural > code_natural) > (nat > nat > nat) > code_natural > code_natural > code_natural).
% 18.75/7.45 thf(func_def_1043, type, map_fu4892316939951275536at_o_o: (code_natural > nat) > ($o > $o) > (nat > $o) > code_natural > $o).
% 18.75/7.45 thf(func_def_1044, type, map_fu2787874002554666395nteger: (code_natural > nat) > (int > code_integer) > (nat > int) > code_natural > code_integer).
% 18.75/7.45 thf(func_def_1045, type, map_fu1239815594074539274atural: (code_natural > nat) > (nat > code_natural) > (nat > nat) > code_natural > code_natural).
% 18.75/7.45 thf(func_def_1046, type, map_fu226235371393106610at_nat: (code_natural > nat) > (nat > nat) > (nat > nat) > code_natural > nat).
% 18.75/7.45 thf(func_def_1047, type, map_fu7831380289885515383nt_rat: (int > int) > ((int > product_prod_int_int) > int > rat) > (int > int > product_prod_int_int) > int > int > rat).
% 18.75/7.45 thf(func_def_1048, type, map_fun_int_int_o_o: (int > int) > ($o > $o) > (int > $o) > int > $o).
% 18.75/7.45 thf(func_def_1049, type, map_fu2180209013632630320nt_int: (int > int) > (product_prod_int_int > product_prod_int_int) > (int > product_prod_int_int) > int > product_prod_int_int).
% 18.75/7.45 thf(func_def_1050, type, map_fu3424225382358772769nt_rat: (int > int) > (product_prod_int_int > rat) > (int > product_prod_int_int) > int > rat).
% 18.75/7.45 thf(func_def_1051, type, map_fu6531859369801489698at_rat: (int > int) > (rat > rat) > (int > rat) > int > rat).
% 18.75/7.45 thf(func_def_1052, type, map_fu1717202910479192016nteger: (int > nat) > (code_integer > code_integer) > (nat > code_integer) > int > code_integer).
% 18.75/7.45 thf(func_def_1053, type, map_fu3669222299741785344at_num: (int > nat) > (nat > num) > (nat > nat) > int > num).
% 18.75/7.45 thf(func_def_1054, type, map_fu2609383839613498790nt_num: (int > num) > (int > num) > (num > int) > int > num).
% 18.75/7.45 thf(func_def_1055, type, map_fu229184005524548567nteger: (int > num) > (num > code_integer) > (num > num) > int > code_integer).
% 18.75/7.45 thf(func_def_1056, type, map_fu434086159418415080_int_o: (int > product_prod_nat_nat) > ((product_prod_nat_nat > $o) > int > $o) > (product_prod_nat_nat > product_prod_nat_nat > $o) > int > int > $o).
% 18.75/7.45 thf(func_def_1057, type, map_fu4960017516451851995nt_int: (int > product_prod_nat_nat) > ((product_prod_nat_nat > product_prod_nat_nat) > int > int) > (product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat) > int > int > int).
% 18.75/7.45 thf(func_def_1058, type, map_fu4826362097070443709at_o_o: (int > product_prod_nat_nat) > ($o > $o) > (product_prod_nat_nat > $o) > int > $o).
% 18.75/7.45 thf(func_def_1059, type, map_fu3667384564859982768at_int: (int > product_prod_nat_nat) > (product_prod_nat_nat > int) > (product_prod_nat_nat > product_prod_nat_nat) > int > int).
% 18.75/7.45 thf(func_def_1060, type, map_fu8224359078269604234nteger: (nat > nat) > ((int > int) > code_integer > code_integer) > (nat > int > int) > nat > code_integer > code_integer).
% 18.75/7.45 thf(func_def_1061, type, map_fu6981160461238011112atural: (nat > nat) > ((nat > nat) > code_natural > code_natural) > (nat > nat > nat) > nat > code_natural > code_natural).
% 18.75/7.45 thf(func_def_1062, type, map_fun_nat_nat_o_o: (nat > nat) > ($o > $o) > (nat > $o) > nat > $o).
% 18.75/7.45 thf(func_def_1063, type, map_fu6290471996055670595nteger: (nat > nat) > (int > code_integer) > (nat > int) > nat > code_integer).
% 18.75/7.45 thf(func_def_1064, type, map_fu4742413587575543474atural: (nat > nat) > (nat > code_natural) > (nat > nat) > nat > code_natural).
% 18.75/7.45 thf(func_def_1065, type, map_fu8361869985550671104nt_nat: (nat > num) > (int > nat) > (num > int) > nat > nat).
% 18.75/7.45 thf(func_def_1066, type, map_fu1090464068875036027nteger: (nat > num) > (num > code_integer) > (num > num) > nat > code_integer).
% 18.75/7.45 thf(func_def_1067, type, map_fu1235460277957925907nteger: (num > code_integer) > (code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger) > (code_integer > code_integer) > num > produc8923325533196201883nteger > produc8923325533196201883nteger).
% 18.75/7.45 thf(func_def_1068, type, map_fu5269526691104299083nteger: (num > code_integer) > (code_integer > code_integer) > (code_integer > code_integer) > num > code_integer).
% 18.75/7.45 thf(func_def_1069, type, map_fu8479170043890205655nt_num: (num > code_integer) > (int > num) > (code_integer > int) > num > num).
% 18.75/7.45 thf(func_def_1070, type, map_fu7479816331989151099at_num: (num > code_integer) > (nat > num) > (code_integer > nat) > num > num).
% 18.75/7.45 thf(func_def_1071, type, map_fu8223014087597717000nteger: (num > code_integer) > (num > code_integer) > (code_integer > num) > num > code_integer).
% 18.75/7.45 thf(func_def_1072, type, map_fu6891787308814931657nteger: (num > num) > ((num > int) > num > code_integer) > (num > num > int) > num > num > code_integer).
% 18.75/7.45 thf(func_def_1073, type, map_fu8638147718074629079nteger: (num > num) > (int > code_integer) > (num > int) > num > code_integer).
% 18.75/7.45 thf(func_def_1074, type, map_fu1707080289169145046at_o_o: (product_prod_nat_nat > product_prod_nat_nat) > ($o > $o) > (product_prod_nat_nat > $o) > product_prod_nat_nat > $o).
% 18.75/7.45 thf(func_def_1075, type, map_fu4333342158222067775at_rat: (rat > product_prod_int_int) > ((product_prod_int_int > product_prod_int_int) > rat > rat) > (product_prod_int_int > product_prod_int_int > product_prod_int_int) > rat > rat > rat).
% 18.75/7.45 thf(func_def_1076, type, map_fu5673905371560938248nt_rat: (rat > product_prod_int_int) > (product_prod_int_int > rat) > (product_prod_int_int > product_prod_int_int) > rat > rat).
% 18.75/7.45 thf(func_def_1077, type, fun_max_strict: set_Pr4329608150637261639at_nat).
% 18.75/7.45 thf(func_def_1078, type, fun_max_weak: set_Pr4329608150637261639at_nat).
% 18.75/7.45 thf(func_def_1079, type, fun_min_strict: set_Pr4329608150637261639at_nat).
% 18.75/7.45 thf(func_def_1080, type, fun_min_weak: set_Pr4329608150637261639at_nat).
% 18.75/7.45 thf(func_def_1081, type, fun_pair_leq: set_Pr8693737435421807431at_nat).
% 18.75/7.45 thf(func_def_1082, type, fun_pair_less: set_Pr8693737435421807431at_nat).
% 18.75/7.45 thf(func_def_1083, type, fun_re7357418987779152907at_nat: produc4193628355235574503at_nat > $o).
% 18.75/7.45 thf(func_def_1084, type, fun_re2478310338295953701at_nat: produc1319942482725812455at_nat > $o).
% 18.75/7.45 thf(func_def_1085, type, gcd_Gcd_nat: set_nat > nat).
% 18.75/7.45 thf(func_def_1086, type, gcd_Lcm_nat: set_nat > nat).
% 18.75/7.45 thf(func_def_1087, type, bezw: nat > nat > product_prod_int_int).
% 18.75/7.45 thf(func_def_1088, type, bezw_rel: product_prod_nat_nat > product_prod_nat_nat > $o).
% 18.75/7.45 thf(func_def_1089, type, gcd_gcd_int: int > int > int).
% 18.75/7.45 thf(func_def_1090, type, gcd_gcd_nat: nat > nat > nat).
% 18.75/7.45 thf(func_def_1091, type, gcd_lcm_nat: nat > nat > nat).
% 18.75/7.45 thf(func_def_1092, type, gcd_nat_rel: product_prod_nat_nat > product_prod_nat_nat > $o).
% 18.75/7.45 thf(func_def_1093, type, abs_abs_Code_integer: code_integer > code_integer).
% 18.75/7.45 thf(func_def_1094, type, abs_abs_int: int > int).
% 18.75/7.45 thf(func_def_1095, type, abs_abs_rat: rat > rat).
% 18.75/7.45 thf(func_def_1096, type, group_Code_integer: (code_integer > code_integer > code_integer) > code_integer > (code_integer > code_integer) > $o).
% 18.75/7.45 thf(func_def_1097, type, group_int: (int > int > int) > int > (int > int) > $o).
% 18.75/7.45 thf(func_def_1098, type, group_rat: (rat > rat > rat) > rat > (rat > rat) > $o).
% 18.75/7.45 thf(func_def_1099, type, minus_8373710615458151222nteger: code_integer > code_integer > code_integer).
% 18.75/7.45 thf(func_def_1100, type, minus_7197305767214868737atural: code_natural > code_natural > code_natural).
% 18.75/7.45 thf(func_def_1101, type, minus_minus_int: int > int > int).
% 18.75/7.45 thf(func_def_1102, type, minus_4286766774447292334at_nat: multis2468970476368604999at_nat > multis2468970476368604999at_nat > multis2468970476368604999at_nat).
% 18.75/7.45 thf(func_def_1103, type, minus_minus_nat: nat > nat > nat).
% 18.75/7.45 thf(func_def_1104, type, minus_minus_rat: rat > rat > rat).
% 18.75/7.45 thf(func_def_1105, type, minus_minus_set_o: set_o > set_o > set_o).
% 18.75/7.45 thf(func_def_1106, type, minus_2355218937544613996nteger: set_Code_integer > set_Code_integer > set_Code_integer).
% 18.75/7.45 thf(func_def_1107, type, minus_minus_set_int: set_int > set_int > set_int).
% 18.75/7.45 thf(func_def_1108, type, minus_7954133019191499631st_nat: set_list_nat > set_list_nat > set_list_nat).
% 18.75/7.45 thf(func_def_1109, type, minus_minus_set_nat: set_nat > set_nat > set_nat).
% 18.75/7.45 thf(func_def_1110, type, minus_minus_set_num: set_num > set_num > set_num).
% 18.75/7.45 thf(func_def_1111, type, minus_1356011639430497352at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat).
% 18.75/7.45 thf(func_def_1112, type, minus_3314409938677909166at_nat: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat).
% 18.75/7.45 thf(func_def_1113, type, minus_6452836326544984404t_unit: set_Product_unit > set_Product_unit > set_Product_unit).
% 18.75/7.45 thf(func_def_1114, type, minus_minus_set_rat: set_rat > set_rat > set_rat).
% 18.75/7.45 thf(func_def_1115, type, one_one_assn: assn).
% 18.75/7.45 thf(func_def_1116, type, one_one_Code_integer: code_integer).
% 18.75/7.45 thf(func_def_1117, type, one_one_Code_natural: code_natural).
% 18.75/7.45 thf(func_def_1118, type, one_one_int: int).
% 18.75/7.45 thf(func_def_1119, type, one_one_nat: nat).
% 18.75/7.45 thf(func_def_1120, type, one_one_rat: rat).
% 18.75/7.45 thf(func_def_1121, type, plus_p5714425477246183910nteger: code_integer > code_integer > code_integer).
% 18.75/7.45 thf(func_def_1122, type, plus_p4538020629002901425atural: code_natural > code_natural > code_natural).
% 18.75/7.45 thf(func_def_1123, type, plus_plus_int: int > int > int).
% 18.75/7.45 thf(func_def_1124, type, plus_p7104986032573967614at_nat: multis2468970476368604999at_nat > multis2468970476368604999at_nat > multis2468970476368604999at_nat).
% 18.75/7.45 thf(func_def_1125, type, plus_plus_nat: nat > nat > nat).
% 18.75/7.45 thf(func_def_1126, type, plus_plus_num: num > num > num).
% 18.75/7.45 thf(func_def_1127, type, plus_plus_rat: rat > rat > rat).
% 18.75/7.45 thf(func_def_1128, type, sgn_sgn_Code_integer: code_integer > code_integer).
% 18.75/7.45 thf(func_def_1129, type, sgn_sgn_int: int > int).
% 18.75/7.45 thf(func_def_1130, type, sgn_sgn_rat: rat > rat).
% 18.75/7.45 thf(func_def_1131, type, times_times_assn: assn > assn > assn).
% 18.75/7.45 thf(func_def_1132, type, times_3573771949741848930nteger: code_integer > code_integer > code_integer).
% 18.75/7.45 thf(func_def_1133, type, times_2397367101498566445atural: code_natural > code_natural > code_natural).
% 18.75/7.45 thf(func_def_1134, type, times_times_int: int > int > int).
% 18.75/7.45 thf(func_def_1135, type, times_times_nat: nat > nat > nat).
% 18.75/7.45 thf(func_def_1136, type, times_times_num: num > num > num).
% 18.75/7.45 thf(func_def_1137, type, times_times_rat: rat > rat > rat).
% 18.75/7.45 thf(func_def_1138, type, uminus_uminus_nat_o: (nat > $o) > nat > $o).
% 18.75/7.45 thf(func_def_1139, type, uminus_uminus_o: $o > $o).
% 18.75/7.45 thf(func_def_1140, type, uminus1351360451143612070nteger: code_integer > code_integer).
% 18.75/7.45 thf(func_def_1141, type, uminus_uminus_int: int > int).
% 18.75/7.45 thf(func_def_1142, type, uminus2952777764628376836t_unit: product_unit > product_unit).
% 18.75/7.45 thf(func_def_1143, type, uminus_uminus_rat: rat > rat).
% 18.75/7.45 thf(func_def_1144, type, uminus804700908173204444nteger: set_Code_integer > set_Code_integer).
% 18.75/7.45 thf(func_def_1145, type, uminus1532241313380277803et_int: set_int > set_int).
% 18.75/7.45 thf(func_def_1146, type, uminus5710092332889474511et_nat: set_nat > set_nat).
% 18.75/7.45 thf(func_def_1147, type, uminus5944136376168626660t_unit: set_Product_unit > set_Product_unit).
% 18.75/7.45 thf(func_def_1148, type, uminus2201863774496077783et_rat: set_rat > set_rat).
% 18.75/7.45 thf(func_def_1149, type, zero_z3403309356797280102nteger: code_integer).
% 18.75/7.45 thf(func_def_1150, type, zero_z2226904508553997617atural: code_natural).
% 18.75/7.45 thf(func_def_1151, type, zero_zero_int: int).
% 18.75/7.45 thf(func_def_1152, type, zero_z1048942125864253310at_nat: multis2468970476368604999at_nat).
% 18.75/7.45 thf(func_def_1153, type, zero_zero_nat: nat).
% 18.75/7.45 thf(func_def_1154, type, zero_zero_rat: rat).
% 18.75/7.45 thf(func_def_1155, type, groups4406642042086082107nteger: ($o > code_integer) > set_o > code_integer).
% 18.75/7.45 thf(func_def_1156, type, groups8505340233167759370_o_int: ($o > int) > set_o > int).
% 18.75/7.45 thf(func_def_1157, type, groups8507830703676809646_o_nat: ($o > nat) > set_o > nat).
% 18.75/7.45 thf(func_def_1158, type, groups7872700643590313910_o_rat: ($o > rat) > set_o > rat).
% 18.75/7.45 thf(func_def_1159, type, groups879477027807139574nteger: (code_integer > code_integer) > set_Code_integer > code_integer).
% 18.75/7.45 thf(func_def_1160, type, groups7234854612051535045er_int: (code_integer > int) > set_Code_integer > int).
% 18.75/7.45 thf(func_def_1161, type, groups7237345082560585321er_nat: (code_integer > nat) > set_Code_integer > nat).
% 18.75/7.45 thf(func_def_1162, type, groups6602215022474089585er_rat: (code_integer > rat) > set_Code_integer > rat).
% 18.75/7.45 thf(func_def_1163, type, groups7873554091576472773nteger: (int > code_integer) > set_int > code_integer).
% 18.75/7.45 thf(func_def_1164, type, groups4538972089207619220nt_int: (int > int) > set_int > int).
% 18.75/7.45 thf(func_def_1165, type, groups4541462559716669496nt_nat: (int > nat) > set_int > nat).
% 18.75/7.45 thf(func_def_1166, type, groups3906332499630173760nt_rat: (int > rat) > set_int > rat).
% 18.75/7.45 thf(func_def_1167, type, groups4396056296759096172at_nat: (list_nat > nat) > set_list_nat > nat).
% 18.75/7.45 thf(func_def_1168, type, groups7501900531339628137nteger: (nat > code_integer) > set_nat > code_integer).
% 18.75/7.45 thf(func_def_1169, type, groups6325495683096345652atural: (nat > code_natural) > set_nat > code_natural).
% 18.75/7.45 thf(func_def_1170, type, groups3539618377306564664at_int: (nat > int) > set_nat > int).
% 18.75/7.45 thf(func_def_1171, type, groups6857163185585827899at_nat: (nat > multis2468970476368604999at_nat) > set_nat > multis2468970476368604999at_nat).
% 18.75/7.45 thf(func_def_1172, type, groups3542108847815614940at_nat: (nat > nat) > set_nat > nat).
% 18.75/7.45 thf(func_def_1173, type, groups2906978787729119204at_rat: (nat > rat) > set_nat > rat).
% 18.75/7.45 thf(func_def_1174, type, groups5442708359310287027nteger: (num > code_integer) > set_num > code_integer).
% 18.75/7.45 thf(func_def_1175, type, groups196832835297161892nteger: (product_prod_nat_nat > code_integer) > set_Pr1261947904930325089at_nat > code_integer).
% 18.75/7.45 thf(func_def_1176, type, groups977919841031483927at_nat: (product_prod_nat_nat > nat) > set_Pr1261947904930325089at_nat > nat).
% 18.75/7.45 thf(func_def_1177, type, groups342789780944988191at_rat: (product_prod_nat_nat > rat) > set_Pr1261947904930325089at_nat > rat).
% 18.75/7.45 thf(func_def_1178, type, groups8766797177574957219it_nat: (product_unit > nat) > set_Product_unit > nat).
% 18.75/7.45 thf(func_def_1179, type, groups2416162284031854641er_int: (set_set_Code_integer > int) > set_se8531188866349061887nteger > int).
% 18.75/7.45 thf(func_def_1180, type, groups1080061135233207040nt_int: (set_set_int > int) > set_set_set_int > int).
% 18.75/7.45 thf(func_def_1181, type, groups7004213669654646580at_int: (set_set_list_nat > int) > set_set_set_list_nat > int).
% 18.75/7.45 thf(func_def_1182, type, groups7084729577923612836at_int: (set_set_nat > int) > set_set_set_nat > int).
% 18.75/7.45 thf(func_def_1183, type, groups1759609815103008563at_int: (set_se7855581050983116737at_nat > int) > set_se5158245632345848097at_nat > int).
% 18.75/7.45 thf(func_def_1184, type, groups9212676010950626495it_int: (set_set_Product_unit > int) > set_se7118615804146677933t_unit > int).
% 18.75/7.45 thf(func_def_1185, type, groups1402912129352969042nteger: ($o > code_integer) > set_o > code_integer).
% 18.75/7.45 thf(func_def_1186, type, groups4556407284786078405_o_nat: ($o > nat) > set_o > nat).
% 18.75/7.45 thf(func_def_1187, type, groups3921277224699582669_o_rat: ($o > rat) > set_o > rat).
% 18.75/7.45 thf(func_def_1188, type, groups910942671188738463nteger: (code_integer > code_integer) > set_Code_integer > code_integer).
% 18.75/7.45 thf(func_def_1189, type, groups288081504127972206er_int: (code_integer > int) > set_Code_integer > int).
% 18.75/7.45 thf(func_def_1190, type, groups290571974637022482er_nat: (code_integer > nat) > set_Code_integer > nat).
% 18.75/7.45 thf(func_def_1191, type, groups8878813951405302554er_rat: (code_integer > rat) > set_Code_integer > rat).
% 18.75/7.45 thf(func_def_1192, type, groups926780983652909934nteger: (int > code_integer) > set_int > code_integer).
% 18.75/7.45 thf(func_def_1193, type, groups2983280209131991357nt_int: (int > int) > set_int > int).
% 18.75/7.45 thf(func_def_1194, type, groups2985770679641041633nt_nat: (int > nat) > set_int > nat).
% 18.75/7.45 thf(func_def_1195, type, groups2350640619554545897nt_rat: (int > rat) > set_int > rat).
% 18.75/7.45 thf(func_def_1196, type, groups555127423416065298nteger: (nat > code_integer) > set_nat > code_integer).
% 18.75/7.45 thf(func_def_1197, type, groups1983926497230936801at_int: (nat > int) > set_nat > int).
% 18.75/7.45 thf(func_def_1198, type, groups1986416967739987077at_nat: (nat > nat) > set_nat > nat).
% 18.75/7.45 thf(func_def_1199, type, groups1351286907653491341at_rat: (nat > rat) > set_nat > rat).
% 18.75/7.45 thf(func_def_1200, type, groups3328076802468863542at_rat: (product_prod_nat_nat > rat) > set_Pr1261947904930325089at_nat > rat).
% 18.75/7.45 thf(func_def_1201, type, groups5301882518646026715o_assn: ($o > assn) > set_o > assn).
% 18.75/7.45 thf(func_def_1202, type, groups7694694392188491536nteger: ($o > code_integer) > set_o > code_integer).
% 18.75/7.45 thf(func_def_1203, type, groups3502327434004483295_o_int: ($o > int) > set_o > int).
% 18.75/7.45 thf(func_def_1204, type, groups3504817904513533571_o_nat: ($o > nat) > set_o > nat).
% 18.75/7.45 thf(func_def_1205, type, groups2869687844427037835_o_rat: ($o > rat) > set_o > rat).
% 18.75/7.45 thf(func_def_1206, type, groups1304777262505850412r_assn: (code_integer > assn) > set_Code_integer > assn).
% 18.75/7.45 thf(func_def_1207, type, groups3674199335183972705nteger: (code_integer > code_integer) > set_Code_integer > code_integer).
% 18.75/7.45 thf(func_def_1208, type, groups3188404863801439024er_int: (code_integer > int) > set_Code_integer > int).
% 18.75/7.45 thf(func_def_1209, type, groups3190895334310489300er_nat: (code_integer > nat) > set_Code_integer > nat).
% 18.75/7.45 thf(func_def_1210, type, groups2555765274223993564er_rat: (code_integer > rat) > set_Code_integer > rat).
% 18.75/7.45 thf(func_def_1211, type, groups7882442080178216443t_assn: (int > assn) > set_int > assn).
% 18.75/7.45 thf(func_def_1212, type, groups3827104343326376752nteger: (int > code_integer) > set_int > code_integer).
% 18.75/7.45 thf(func_def_1213, type, groups1705073143266064639nt_int: (int > int) > set_int > int).
% 18.75/7.45 thf(func_def_1214, type, groups1707563613775114915nt_nat: (int > nat) > set_int > nat).
% 18.75/7.45 thf(func_def_1215, type, groups1072433553688619179nt_rat: (int > rat) > set_int > rat).
% 18.75/7.45 thf(func_def_1216, type, groups6906906614972039071t_assn: (nat > assn) > set_nat > assn).
% 18.75/7.45 thf(func_def_1217, type, groups3455450783089532116nteger: (nat > code_integer) > set_nat > code_integer).
% 18.75/7.45 thf(func_def_1218, type, groups2279045934846249631atural: (nat > code_natural) > set_nat > code_natural).
% 18.75/7.45 thf(func_def_1219, type, groups705719431365010083at_int: (nat > int) > set_nat > int).
% 18.75/7.45 thf(func_def_1220, type, groups708209901874060359at_nat: (nat > nat) > set_nat > nat).
% 18.75/7.45 thf(func_def_1221, type, groups73079841787564623at_rat: (nat > rat) > set_nat > rat).
% 18.75/7.45 thf(func_def_1222, type, groups1396258611060191006nteger: (num > code_integer) > set_num > code_integer).
% 18.75/7.45 thf(func_def_1223, type, groups4075276357253098568at_int: (product_prod_nat_nat > int) > set_Pr1261947904930325089at_nat > int).
% 18.75/7.45 thf(func_def_1224, type, groups4077766827762148844at_nat: (product_prod_nat_nat > nat) > set_Pr1261947904930325089at_nat > nat).
% 18.75/7.45 thf(func_def_1225, type, groups5360233303959380816t_assn: (product_unit > assn) > set_Product_unit > assn).
% 18.75/7.45 thf(func_def_1226, type, groups8185359811944078981nteger: (product_unit > code_integer) > set_Product_unit > code_integer).
% 18.75/7.45 thf(func_def_1227, type, groups8984663225794451456it_rat: (product_unit > rat) > set_Product_unit > rat).
% 18.75/7.45 thf(func_def_1228, type, groups6963733262650904763o_assn: (set_o > assn) > set_set_o > assn).
% 18.75/7.45 thf(func_def_1229, type, groups8987389756002350576nteger: (set_o > code_integer) > set_set_o > code_integer).
% 18.75/7.45 thf(func_def_1230, type, groups4868773677410035043_o_nat: (set_o > nat) > set_set_o > nat).
% 18.75/7.45 thf(func_def_1231, type, groups4233643617323539307_o_rat: (set_o > rat) > set_set_o > rat).
% 18.75/7.45 thf(func_def_1232, type, groups4245288774754739042r_assn: (set_Code_integer > assn) > set_set_Code_integer > assn).
% 18.75/7.45 thf(func_def_1233, type, groups1474571732273379991nteger: (set_Code_integer > code_integer) > set_set_Code_integer > code_integer).
% 18.75/7.45 thf(func_def_1234, type, groups5409254039008640018er_rat: (set_Code_integer > rat) > set_set_Code_integer > rat).
% 18.75/7.45 thf(func_def_1235, type, groups5950967880310095793t_assn: (set_int > assn) > set_set_int > assn).
% 18.75/7.45 thf(func_def_1236, type, groups8770619586034088166nteger: (set_int > code_integer) > set_set_int > code_integer).
% 18.75/7.45 thf(func_def_1237, type, groups5800339274786551393nt_rat: (set_int > rat) > set_set_int > rat).
% 18.75/7.45 thf(func_def_1238, type, groups12625163056032370o_assn: ($o > assn) > set_o > assn).
% 18.75/7.45 thf(func_def_1239, type, groups2836416601086271911nteger: ($o > code_integer) > set_o > code_integer).
% 18.75/7.45 thf(func_def_1240, type, groups5320751605702587254_o_int: ($o > int) > set_o > int).
% 18.75/7.45 thf(func_def_1241, type, groups5323242076211637530_o_nat: ($o > nat) > set_o > nat).
% 18.75/7.45 thf(func_def_1242, type, groups4688112016125141794_o_rat: ($o > rat) > set_o > rat).
% 18.75/7.45 thf(func_def_1243, type, groups980104329299799381r_assn: (code_integer > assn) > set_Code_integer > assn).
% 18.75/7.45 thf(func_def_1244, type, groups7219916603568234122nteger: (code_integer > code_integer) > set_Code_integer > code_integer).
% 18.75/7.45 thf(func_def_1245, type, groups4891613008741529892t_assn: (int > assn) > set_int > assn).
% 18.75/7.45 thf(func_def_1246, type, groups8661743855124024409nteger: (int > code_integer) > set_int > code_integer).
% 18.75/7.45 thf(func_def_1247, type, groups5744458235038148136nt_int: (int > int) > set_int > int).
% 18.75/7.45 thf(func_def_1248, type, groups5746948705547198412nt_nat: (int > nat) > set_int > nat).
% 18.75/7.45 thf(func_def_1249, type, groups5111818645460702676nt_rat: (int > rat) > set_int > rat).
% 18.75/7.45 thf(func_def_1250, type, groups3916077543535352520t_assn: (nat > assn) > set_nat > assn).
% 18.75/7.45 thf(func_def_1251, type, groups8290090294887179773nteger: (nat > code_integer) > set_nat > code_integer).
% 18.75/7.45 thf(func_def_1252, type, groups4745104523137093580at_int: (nat > int) > set_nat > int).
% 18.75/7.45 thf(func_def_1253, type, groups4747594993646143856at_nat: (nat > nat) > set_nat > nat).
% 18.75/7.45 thf(func_def_1254, type, groups4112464933559648120at_rat: (nat > rat) > set_nat > rat).
% 18.75/7.45 thf(func_def_1255, type, groups4561878855575611511st_nat: list_nat > nat).
% 18.75/7.45 thf(func_def_1256, type, nO_MAT8252062027627875367nteger: code_integer > code_integer > $o).
% 18.75/7.45 thf(func_def_1257, type, nO_MAT8427913294028938742er_int: code_integer > int > $o).
% 18.75/7.45 thf(func_def_1258, type, nO_MAT8430403764537989018er_nat: code_integer > nat > $o).
% 18.75/7.45 thf(func_def_1259, type, nO_MAT7795273704451493282er_rat: code_integer > rat > $o).
% 18.75/7.45 thf(func_def_1260, type, nO_MATCH_int_int: int > int > $o).
% 18.75/7.45 thf(func_def_1261, type, nO_MATCH_int_nat: int > nat > $o).
% 18.75/7.45 thf(func_def_1262, type, nO_MATCH_int_rat: int > rat > $o).
% 18.75/7.45 thf(func_def_1263, type, nO_MATCH_nat_int: nat > int > $o).
% 18.75/7.45 thf(func_def_1264, type, nO_MATCH_nat_nat: nat > nat > $o).
% 18.75/7.45 thf(func_def_1265, type, nO_MATCH_nat_rat: nat > rat > $o).
% 18.75/7.45 thf(func_def_1266, type, nO_MATCH_rat_rat: rat > rat > $o).
% 18.75/7.45 thf(func_def_1267, type, the_int: (int > $o) > int).
% 18.75/7.45 thf(func_def_1268, type, defaul566961228789861419t_unit: product_unit).
% 18.75/7.45 thf(func_def_1269, type, undefined_array_a: array_a).
% 18.75/7.45 thf(func_def_1270, type, undefi8805113437130903861t_unit: heap_e7401611519738050253t_unit).
% 18.75/7.45 thf(func_def_1271, type, undefined_num: num).
% 18.75/7.45 thf(func_def_1272, type, undefi2974082611360736373t_unit: product_unit).
% 18.75/7.45 thf(func_def_1273, type, arrays_Product_unit: heap_e7401611519738050253t_unit > typerep > nat > list_nat).
% 18.75/7.45 thf(func_def_1274, type, lim_Product_unit: heap_e7401611519738050253t_unit > nat).
% 18.75/7.45 thf(func_def_1275, type, refs_Product_unit: heap_e7401611519738050253t_unit > typerep > nat > nat).
% 18.75/7.45 thf(func_def_1276, type, heap_T1488828001306802186rray_a: (heap_e7401611519738050253t_unit > option3216581401566546698it_nat) > heap_T6362127782908069795rray_a).
% 18.75/7.45 thf(func_def_1277, type, heap_T6183433275982383450t_unit: (heap_e7401611519738050253t_unit > option8956607266484857688it_nat) > heap_T5738788834812785303t_unit).
% 18.75/7.45 thf(func_def_1278, type, heap_T4142866422068808505t_unit: (product_unit > nat) > heap_T5738788834812785303t_unit > nat).
% 18.75/7.45 thf(func_def_1279, type, heap_T3039585018531920163rray_a: heap_T6362127782908069795rray_a > heap_T6362127782908069795rray_a > $o).
% 18.75/7.45 thf(func_def_1280, type, heap_T499439718319394433t_unit: heap_T5738788834812785303t_unit > heap_T5738788834812785303t_unit > $o).
% 18.75/7.45 thf(func_def_1281, type, heap_T7971689983404357896rray_a: (array_a > $o) > array_a > heap_T6362127782908069795rray_a).
% 18.75/7.45 thf(func_def_1282, type, heap_T4208721593536448476t_unit: (product_unit > $o) > product_unit > heap_T5738788834812785303t_unit).
% 18.75/7.45 thf(func_def_1283, type, heap_T2407400398799471159rray_a: heap_T6362127782908069795rray_a > (array_a > heap_T6362127782908069795rray_a) > heap_T6362127782908069795rray_a).
% 18.75/7.45 thf(func_def_1284, type, heap_T7324619625323989613t_unit: heap_T6362127782908069795rray_a > (array_a > heap_T5738788834812785303t_unit) > heap_T5738788834812785303t_unit).
% 18.75/7.45 thf(func_def_1285, type, heap_T7158140910958840029rray_a: heap_T5738788834812785303t_unit > (product_unit > heap_T6362127782908069795rray_a) > heap_T6362127782908069795rray_a).
% 18.75/7.45 thf(func_def_1286, type, heap_T2633723481742716231t_unit: heap_T5738788834812785303t_unit > (product_unit > heap_T5738788834812785303t_unit) > heap_T5738788834812785303t_unit).
% 18.75/7.45 thf(func_def_1287, type, heap_T5830633491639066771rray_a: heap_T6362127782908069795rray_a > heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit > array_a > nat > $o).
% 18.75/7.45 thf(func_def_1288, type, heap_T6553295506729943825t_unit: heap_T5738788834812785303t_unit > heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit > product_unit > nat > $o).
% 18.75/7.45 thf(func_def_1289, type, heap_T5591663578999710211rray_a: heap_T6362127782908069795rray_a > heap_e7401611519738050253t_unit > option3216581401566546698it_nat).
% 18.75/7.45 thf(func_def_1290, type, heap_T875086893843062177t_unit: heap_T5738788834812785303t_unit > heap_e7401611519738050253t_unit > option8956607266484857688it_nat).
% 18.75/7.45 thf(func_def_1291, type, heap_T7685628758766326643rray_a: (heap_e7401611519738050253t_unit > $o) > (heap_e7401611519738050253t_unit > produc6714399278180371524it_nat) > heap_T6362127782908069795rray_a).
% 18.75/7.45 thf(func_def_1292, type, heap_T8440541562793052209t_unit: (heap_e7401611519738050253t_unit > $o) > (heap_e7401611519738050253t_unit > produc8664842809031399944it_nat) > heap_T5738788834812785303t_unit).
% 18.75/7.45 thf(func_def_1293, type, heap_T7473999186002612558rray_a: (heap_e7401611519738050253t_unit > produc6714399278180371524it_nat) > heap_T6362127782908069795rray_a).
% 18.75/7.45 thf(func_def_1294, type, heap_T6927113302350381334t_unit: (heap_e7401611519738050253t_unit > produc8664842809031399944it_nat) > heap_T5738788834812785303t_unit).
% 18.75/7.45 thf(func_def_1295, type, heap_T1552190017797416154rray_a: list_char > heap_T6362127782908069795rray_a).
% 18.75/7.45 thf(func_def_1296, type, heap_T2927564422264180874t_unit: list_char > heap_T5738788834812785303t_unit).
% 18.75/7.45 thf(func_def_1297, type, heap_T4896204969850773234rray_a: array_a > heap_T6362127782908069795rray_a).
% 18.75/7.45 thf(func_def_1298, type, heap_T7507251653302230130t_unit: product_unit > heap_T5738788834812785303t_unit).
% 18.75/7.45 thf(func_def_1299, type, heap_T6932021131025641745rray_a: heap_T6362127782908069795rray_a > heap_e7401611519738050253t_unit > $o).
% 18.75/7.45 thf(func_def_1300, type, heap_T584514906347983379t_unit: heap_T5738788834812785303t_unit > heap_e7401611519738050253t_unit > $o).
% 18.75/7.45 thf(func_def_1301, type, heap_T2055650868554030641rray_a: (heap_e7401611519738050253t_unit > array_a) > heap_T6362127782908069795rray_a).
% 18.75/7.45 thf(func_def_1302, type, heap_T560649228465745139t_unit: (heap_e7401611519738050253t_unit > product_unit) > heap_T5738788834812785303t_unit).
% 18.75/7.45 thf(func_def_1303, type, heap_T531568236820715630rray_a: nat > option3216581401566546698it_nat > option3216581401566546698it_nat).
% 18.75/7.45 thf(func_def_1304, type, heap_T3616969660504097270t_unit: nat > option8956607266484857688it_nat > option8956607266484857688it_nat).
% 18.75/7.45 thf(func_def_1305, type, heap_T6578553156929092987rray_a: produc2867611627572283311it_nat > produc2867611627572283311it_nat > $o).
% 18.75/7.45 thf(func_def_1306, type, heap_T996182799752388649t_unit: produc3911288613690379145it_nat > produc3911288613690379145it_nat > $o).
% 18.75/7.45 thf(func_def_1307, type, heap_T4328122439115681491rray_a: array_a > heap_T6362127782908069795rray_a).
% 18.75/7.45 thf(func_def_1308, type, heap_T4284346855313245393t_unit: product_unit > heap_T5738788834812785303t_unit).
% 18.75/7.45 thf(func_def_1309, type, heap_Time_wait: nat > heap_T5738788834812785303t_unit).
% 18.75/7.45 thf(func_def_1310, type, if_assn: $o > assn > assn > assn).
% 18.75/7.45 thf(func_def_1311, type, if_Code_integer: $o > code_integer > code_integer > code_integer).
% 18.75/7.45 thf(func_def_1312, type, if_Code_natural: $o > code_natural > code_natural > code_natural).
% 18.75/7.45 thf(func_def_1313, type, if_Hea5896630067203373929rray_a: $o > heap_T6362127782908069795rray_a > heap_T6362127782908069795rray_a > heap_T6362127782908069795rray_a).
% 18.75/7.45 thf(func_def_1314, type, if_Hea8138950348631371857t_unit: $o > heap_T5738788834812785303t_unit > heap_T5738788834812785303t_unit > heap_T5738788834812785303t_unit).
% 18.75/7.45 thf(func_def_1315, type, if_int: $o > int > int > int).
% 18.75/7.45 thf(func_def_1316, type, if_list_int: $o > list_int > list_int > list_int).
% 18.75/7.45 thf(func_def_1317, type, if_mul8430962117462786573at_nat: $o > multis2468970476368604999at_nat > multis2468970476368604999at_nat > multis2468970476368604999at_nat).
% 18.75/7.45 thf(func_def_1318, type, if_nat: $o > nat > nat > nat).
% 18.75/7.45 thf(func_def_1319, type, if_num: $o > num > num > num).
% 18.75/7.45 thf(func_def_1320, type, if_option_num: $o > option_num > option_num > option_num).
% 18.75/7.45 thf(func_def_1321, type, if_opt7017092727090204112it_nat: $o > option3216581401566546698it_nat > option3216581401566546698it_nat > option3216581401566546698it_nat).
% 18.75/7.45 thf(func_def_1322, type, if_opt1729522071442692626it_nat: $o > option8956607266484857688it_nat > option8956607266484857688it_nat > option8956607266484857688it_nat).
% 18.75/7.45 thf(func_def_1323, type, if_opt6227717841141446553t_unit: $o > option_Product_unit > option_Product_unit > option_Product_unit).
% 18.75/7.45 thf(func_def_1324, type, if_option_set_o: $o > option_set_o > option_set_o > option_set_o).
% 18.75/7.45 thf(func_def_1325, type, if_option_set_int: $o > option_set_int > option_set_int > option_set_int).
% 18.75/7.45 thf(func_def_1326, type, if_option_set_nat: $o > option_set_nat > option_set_nat > option_set_nat).
% 18.75/7.45 thf(func_def_1327, type, if_opt7704869406773131885at_nat: $o > option8963830502488799655at_nat > option8963830502488799655at_nat > option8963830502488799655at_nat).
% 18.75/7.45 thf(func_def_1328, type, if_opt5121585740920863443at_nat: $o > option1583680563626158861at_nat > option1583680563626158861at_nat > option1583680563626158861at_nat).
% 18.75/7.45 thf(func_def_1329, type, if_Pro5737122678794959658eger_o: $o > produc6271795597528267376eger_o > produc6271795597528267376eger_o > produc6271795597528267376eger_o).
% 18.75/7.45 thf(func_def_1330, type, if_Pro6119634080678213985nteger: $o > produc8923325533196201883nteger > produc8923325533196201883nteger > produc8923325533196201883nteger).
% 18.75/7.45 thf(func_def_1331, type, if_Pro3027730157355071871nt_int: $o > product_prod_int_int > product_prod_int_int > product_prod_int_int).
% 18.75/7.45 thf(func_def_1332, type, if_Pro6206227464963214023at_nat: $o > product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat).
% 18.75/7.45 thf(func_def_1333, type, if_rat: $o > rat > rat > rat).
% 18.75/7.45 thf(func_def_1334, type, if_set_int: $o > set_int > set_int > set_int).
% 18.75/7.45 thf(func_def_1335, type, abs_Integ: product_prod_nat_nat > int).
% 18.75/7.45 thf(func_def_1336, type, neg: num > int).
% 18.75/7.45 thf(func_def_1337, type, pos: num > int).
% 18.75/7.45 thf(func_def_1338, type, rep_Integ: int > product_prod_nat_nat).
% 18.75/7.45 thf(func_def_1339, type, dup: int > int).
% 18.75/7.45 thf(func_def_1340, type, intrel: product_prod_nat_nat > product_prod_nat_nat > $o).
% 18.75/7.45 thf(func_def_1341, type, nat2: int > nat).
% 18.75/7.45 thf(func_def_1342, type, pcr_int: product_prod_nat_nat > int > $o).
% 18.75/7.45 thf(func_def_1343, type, ring_11222124179247155820nteger: set_Code_integer).
% 18.75/7.45 thf(func_def_1344, type, ring_1_Ints_int: set_int).
% 18.75/7.45 thf(func_def_1345, type, ring_1_Ints_rat: set_rat).
% 18.75/7.45 thf(func_def_1346, type, ring_18347121197199848620nteger: int > code_integer).
% 18.75/7.45 thf(func_def_1347, type, ring_1_of_int_int: int > int).
% 18.75/7.45 thf(func_def_1348, type, ring_1_of_int_rat: int > rat).
% 18.75/7.45 thf(func_def_1349, type, sub: num > num > int).
% 18.75/7.45 thf(func_def_1350, type, inf_inf_assn: assn > assn > assn).
% 18.75/7.45 thf(func_def_1351, type, inf_inf_Product_unit: product_unit > product_unit > product_unit).
% 18.75/7.45 thf(func_def_1352, type, inf_inf_set_nat: set_nat > set_nat > set_nat).
% 18.75/7.45 thf(func_def_1353, type, sup_su600977994968626096_int_o: ((int > option6357759511663192854e_term) > product_prod_int_int > $o) > ((int > option6357759511663192854e_term) > product_prod_int_int > $o) > (int > option6357759511663192854e_term) > product_prod_int_int > $o).
% 18.75/7.45 thf(func_def_1354, type, sup_su234547053653886311eger_o: ((produc6241069584506657477e_term > option6357759511663192854e_term) > produc8923325533196201883nteger > $o) > ((produc6241069584506657477e_term > option6357759511663192854e_term) > produc8923325533196201883nteger > $o) > (produc6241069584506657477e_term > option6357759511663192854e_term) > produc8923325533196201883nteger > $o).
% 18.75/7.45 thf(func_def_1355, type, sup_su6535292691877529429_nat_o: ((produc3658429121746597890et_nat > $o) > produc3925858234332021118et_nat > $o) > ((produc3658429121746597890et_nat > $o) > produc3925858234332021118et_nat > $o) > (produc3658429121746597890et_nat > $o) > produc3925858234332021118et_nat > $o).
% 18.75/7.45 thf(func_def_1356, type, sup_su1630790145277462993_nat_o: ((produc3658429121746597890et_nat > $o) > produc3658429121746597890et_nat > $o) > ((produc3658429121746597890et_nat > $o) > produc3658429121746597890et_nat > $o) > (produc3658429121746597890et_nat > $o) > produc3658429121746597890et_nat > $o).
% 18.75/7.45 thf(func_def_1357, type, sup_su4182031696650224058_int_o: ((produc8551481072490612790e_term > option6357759511663192854e_term) > product_prod_int_int > $o) > ((produc8551481072490612790e_term > option6357759511663192854e_term) > product_prod_int_int > $o) > (produc8551481072490612790e_term > option6357759511663192854e_term) > product_prod_int_int > $o).
% 18.75/7.45 thf(func_def_1358, type, sup_sup_nat_nat_o: (nat > nat > $o) > (nat > nat > $o) > nat > nat > $o).
% 18.75/7.45 thf(func_def_1359, type, sup_su7519161239522478338_nat_o: (set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o) > (set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o) > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o).
% 18.75/7.45 thf(func_def_1360, type, sup_sup_assn: assn > assn > assn).
% 18.75/7.45 thf(func_def_1361, type, sup_sup_option_assn: option_assn > option_assn > option_assn).
% 18.75/7.45 thf(func_def_1362, type, sup_su7717485023253700007t_unit: option_Product_unit > option_Product_unit > option_Product_unit).
% 18.75/7.45 thf(func_def_1363, type, sup_su3598758113090618626et_nat: option_set_nat > option_set_nat > option_set_nat).
% 18.75/7.45 thf(func_def_1364, type, sup_su2273273666271716065at_nat: option1583680563626158861at_nat > option1583680563626158861at_nat > option1583680563626158861at_nat).
% 18.75/7.45 thf(func_def_1365, type, sup_sup_Product_unit: product_unit > product_unit > product_unit).
% 18.75/7.45 thf(func_def_1366, type, sup_sup_set_o: set_o > set_o > set_o).
% 18.75/7.45 thf(func_def_1367, type, sup_su848401254843788991nteger: set_Code_integer > set_Code_integer > set_Code_integer).
% 18.75/7.45 thf(func_def_1368, type, sup_sup_set_int: set_int > set_int > set_int).
% 18.75/7.45 thf(func_def_1369, type, sup_sup_set_list_nat: set_list_nat > set_list_nat > set_list_nat).
% 18.75/7.45 thf(func_def_1370, type, sup_sup_set_nat: set_nat > set_nat > set_nat).
% 18.75/7.45 thf(func_def_1371, type, sup_sup_set_num: set_num > set_num > set_num).
% 18.75/7.45 thf(func_def_1372, type, sup_su3298353300217089135nt_int: set_Pr1872883991513573699nt_int > set_Pr1872883991513573699nt_int > set_Pr1872883991513573699nt_int).
% 18.75/7.45 thf(func_def_1373, type, sup_su4591284015454442744nteger: set_Pr1281608226676607948nteger > set_Pr1281608226676607948nteger > set_Pr1281608226676607948nteger).
% 18.75/7.45 thf(func_def_1374, type, sup_su8975264963432250076et_nat: set_Pr8536935166611901872et_nat > set_Pr8536935166611901872et_nat > set_Pr8536935166611901872et_nat).
% 18.75/7.45 thf(func_def_1375, type, sup_su7128418612487073120et_nat: set_Pr3286484037609594932et_nat > set_Pr3286484037609594932et_nat > set_Pr3286484037609594932et_nat).
% 18.75/7.45 thf(func_def_1376, type, sup_su3382966977382714213nt_int: set_Pr9222295170931077689nt_int > set_Pr9222295170931077689nt_int > set_Pr9222295170931077689nt_int).
% 18.75/7.45 thf(func_def_1377, type, sup_su5769328420594410459od_o_o: set_Product_prod_o_o > set_Product_prod_o_o > set_Product_prod_o_o).
% 18.75/7.45 thf(func_def_1378, type, sup_su6189057272928884437_o_int: set_Pr8834758594704517033_o_int > set_Pr8834758594704517033_o_int > set_Pr8834758594704517033_o_int).
% 18.75/7.45 thf(func_def_1379, type, sup_su8679140417860611193_o_nat: set_Pr2101469702781467981_o_nat > set_Pr2101469702781467981_o_nat > set_Pr2101469702781467981_o_nat).
% 18.75/7.45 thf(func_def_1380, type, sup_su7481598572368468931_int_o: set_Pr903927857289325719_int_o > set_Pr903927857289325719_int_o > set_Pr903927857289325719_int_o).
% 18.75/7.45 thf(func_def_1381, type, sup_su6024340866399070445nt_int: set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int).
% 18.75/7.45 thf(func_def_1382, type, sup_su8514424011330797201nt_nat: set_Pr3448869479623346877nt_nat > set_Pr3448869479623346877nt_nat > set_Pr3448869479623346877nt_nat).
% 18.75/7.45 thf(func_def_1383, type, sup_su503371503184139039_nat_o: set_Pr3149072824959771635_nat_o > set_Pr3149072824959771635_nat_o > set_Pr3149072824959771635_nat_o).
% 18.75/7.45 thf(func_def_1384, type, sup_su3837419291706048657at_int: set_Pr7995236796853374141at_int > set_Pr7995236796853374141at_int > set_Pr7995236796853374141at_int).
% 18.75/7.45 thf(func_def_1385, type, sup_su6327502436637775413at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat).
% 18.75/7.45 thf(func_def_1386, type, sup_su5921324857680904370_nat_o: set_Pr6558897299634722526_nat_o > set_Pr6558897299634722526_nat_o > set_Pr6558897299634722526_nat_o).
% 18.75/7.45 thf(func_def_1387, type, sup_su5525570899277871387at_nat: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat).
% 18.75/7.45 thf(func_def_1388, type, sup_su793286257634532545t_unit: set_Product_unit > set_Product_unit > set_Product_unit).
% 18.75/7.45 thf(func_def_1389, type, sup_sup_set_rat: set_rat > set_rat > set_rat).
% 18.75/7.45 thf(func_def_1390, type, sup_su3642409539654194069at_nat: set_se7855581050983116737at_nat > set_se7855581050983116737at_nat > set_se7855581050983116737at_nat).
% 18.75/7.45 thf(func_def_1391, type, lattic8265883725875713057ax_nat: set_nat > nat).
% 18.75/7.45 thf(func_def_1392, type, lattic7826324295020591184_F_nat: (nat > nat > nat) > nat > set_nat > nat).
% 18.75/7.45 thf(func_def_1393, type, quotie2291698863146621601nteger: (int > int > $o) > (int > code_integer) > (code_integer > int) > (int > code_integer > $o) > $o).
% 18.75/7.45 thf(func_def_1394, type, quotie743640454666494480atural: (nat > nat > $o) > (nat > code_natural) > (code_natural > nat) > (nat > code_natural > $o) > $o).
% 18.75/7.45 thf(func_def_1395, type, append_int: list_int > list_int > list_int).
% 18.75/7.45 thf(func_def_1396, type, append_nat: list_nat > list_nat > list_nat).
% 18.75/7.45 thf(func_def_1397, type, butlast_nat: list_nat > list_nat).
% 18.75/7.45 thf(func_def_1398, type, drop_nat: nat > list_nat > list_nat).
% 18.75/7.45 thf(func_def_1399, type, filter_nat: (nat > $o) > list_nat > list_nat).
% 18.75/7.45 thf(func_def_1400, type, fold_nat_nat: (nat > nat > nat) > list_nat > nat > nat).
% 18.75/7.45 thf(func_def_1401, type, last_nat: list_nat > nat).
% 18.75/7.45 thf(func_def_1402, type, linord2614967742042102400et_nat: set_nat > list_nat).
% 18.75/7.45 thf(func_def_1403, type, cons_int: int > list_int > list_int).
% 18.75/7.45 thf(func_def_1404, type, cons_nat: nat > list_nat > list_nat).
% 18.75/7.45 thf(func_def_1405, type, nil_int: list_int).
% 18.75/7.45 thf(func_def_1406, type, nil_nat: list_nat).
% 18.75/7.45 thf(func_def_1407, type, map_nat_nat: (nat > nat) > list_nat > list_nat).
% 18.75/7.45 thf(func_def_1408, type, set_int2: list_int > set_int).
% 18.75/7.45 thf(func_def_1409, type, set_nat2: list_nat > set_nat).
% 18.75/7.45 thf(func_def_1410, type, nth_int: list_int > nat > int).
% 18.75/7.45 thf(func_def_1411, type, nth_nat: list_nat > nat > nat).
% 18.75/7.45 thf(func_def_1412, type, take_nat: nat > list_nat > list_nat).
% 18.75/7.45 thf(func_def_1413, type, upt: nat > nat > list_nat).
% 18.75/7.45 thf(func_def_1414, type, upto: int > int > list_int).
% 18.75/7.45 thf(func_def_1415, type, upto_rel: product_prod_int_int > product_prod_int_int > $o).
% 18.75/7.45 thf(func_def_1416, type, eps_Opt_nat: (nat > $o) > option_nat).
% 18.75/7.45 thf(func_def_1417, type, eps_Opt_num: (num > $o) > option_num).
% 18.75/7.45 thf(func_def_1418, type, eps_Op6423059015816587746et_nat: (produc3925858234332021118et_nat > $o) > option5190343406534369742et_nat).
% 18.75/7.45 thf(func_def_1419, type, eps_Op9034888937550303799nteger: (produc8923325533196201883nteger > $o) > option2651255830984564193nteger).
% 18.75/7.45 thf(func_def_1420, type, eps_Op1141264490366522080it_nat: (produc6714399278180371524it_nat > $o) > option3216581401566546698it_nat).
% 18.75/7.45 thf(func_def_1421, type, eps_Op2013419657081471078et_nat: (produc3658429121746597890et_nat > $o) > option936205604648967762et_nat).
% 18.75/7.45 thf(func_def_1422, type, eps_Op2446201859369042517nt_int: (product_prod_int_int > $o) > option4624381673175914239nt_int).
% 18.75/7.45 thf(func_def_1423, type, eps_Op3393321821070424684it_nat: (produc8664842809031399944it_nat > $o) > option8956607266484857688it_nat).
% 18.75/7.45 thf(func_def_1424, type, eps_Op994234036888646909at_nat: (set_Pr1261947904930325089at_nat > $o) > option8963830502488799655at_nat).
% 18.75/7.45 thf(func_def_1425, type, biject576505603616484041nt_int: set_Pr1872883991513573699nt_int > $o).
% 18.75/7.45 thf(func_def_1426, type, biject9051520373387432658nteger: set_Pr1281608226676607948nteger > $o).
% 18.75/7.45 thf(func_def_1427, type, biject1468766312547416318et_nat: set_Pr8536935166611901872et_nat > $o).
% 18.75/7.45 thf(func_def_1428, type, biject2615096655818420098et_nat: set_Pr3286484037609594932et_nat > $o).
% 18.75/7.45 thf(func_def_1429, type, biject383251550997737151nt_int: set_Pr9222295170931077689nt_int > $o).
% 18.75/7.45 thf(func_def_1430, type, bijective_nat_nat: set_Pr1261947904930325089at_nat > $o).
% 18.75/7.45 thf(func_def_1431, type, biject3388518990857851981at_nat: set_Pr4329608150637261639at_nat > $o).
% 18.75/7.45 thf(func_def_1432, type, dflt_None_set_o: set_o > option_set_o).
% 18.75/7.45 thf(func_def_1433, type, dflt_None_set_int: set_int > option_set_int).
% 18.75/7.45 thf(func_def_1434, type, dflt_None_set_nat: set_nat > option_set_nat).
% 18.75/7.45 thf(func_def_1435, type, dflt_N6592383573632408824at_nat: set_Pr1261947904930325089at_nat > option8963830502488799655at_nat).
% 18.75/7.45 thf(func_def_1436, type, dflt_N3208751546879591902at_nat: set_Pr4329608150637261639at_nat > option1583680563626158861at_nat).
% 18.75/7.45 thf(func_def_1437, type, map_mmupd_o_num: ($o > option_num) > set_o > num > $o > option_num).
% 18.75/7.45 thf(func_def_1438, type, map_mm4340940675810032635it_nat: ($o > option8956607266484857688it_nat) > set_o > produc8664842809031399944it_nat > $o > option8956607266484857688it_nat).
% 18.75/7.45 thf(func_def_1439, type, map_mmupd_int_num: (int > option_num) > set_int > num > int > option_num).
% 18.75/7.45 thf(func_def_1440, type, map_mm5942422175790858651it_nat: (int > option8956607266484857688it_nat) > set_int > produc8664842809031399944it_nat > int > option8956607266484857688it_nat).
% 18.75/7.45 thf(func_def_1441, type, map_mmupd_nat_num: (nat > option_num) > set_nat > num > nat > option_num).
% 18.75/7.45 thf(func_def_1442, type, map_mm4316137065318800191it_nat: (nat > option8956607266484857688it_nat) > set_nat > produc8664842809031399944it_nat > nat > option8956607266484857688it_nat).
% 18.75/7.45 thf(func_def_1443, type, map_mm6272435474268545910at_num: (product_prod_nat_nat > option_num) > set_Pr1261947904930325089at_nat > num > product_prod_nat_nat > option_num).
% 18.75/7.45 thf(func_def_1444, type, map_mm8925508573636269924it_nat: (product_prod_nat_nat > option8956607266484857688it_nat) > set_Pr1261947904930325089at_nat > produc8664842809031399944it_nat > product_prod_nat_nat > option8956607266484857688it_nat).
% 18.75/7.45 thf(func_def_1445, type, map_mm2124855372588256220at_num: (produc3843707927480180839at_nat > option_num) > set_Pr4329608150637261639at_nat > num > produc3843707927480180839at_nat > option_num).
% 18.75/7.45 thf(func_def_1446, type, map_mm6227321356191524810it_nat: (produc3843707927480180839at_nat > option8956607266484857688it_nat) > set_Pr4329608150637261639at_nat > produc8664842809031399944it_nat > produc3843707927480180839at_nat > option8956607266484857688it_nat).
% 18.75/7.45 thf(func_def_1447, type, pairself_int_int: (int > int) > product_prod_int_int > product_prod_int_int).
% 18.75/7.45 thf(func_def_1448, type, pairse3534876335208825186e_term: (int > option6357759511663192854e_term) > product_prod_int_int > produc6576344331059438605e_term).
% 18.75/7.45 thf(func_def_1449, type, pairse4825235148789309005nteger: (nat > code_integer) > product_prod_nat_nat > produc8923325533196201883nteger).
% 18.75/7.45 thf(func_def_1450, type, pairself_nat_int: (nat > int) > product_prod_nat_nat > product_prod_int_int).
% 18.75/7.45 thf(func_def_1451, type, pairself_nat_nat: (nat > nat) > product_prod_nat_nat > product_prod_nat_nat).
% 18.75/7.45 thf(func_def_1452, type, pairself_nat_set_nat: (nat > set_nat) > product_prod_nat_nat > produc7819656566062154093et_nat).
% 18.75/7.45 thf(func_def_1453, type, pairse6848479906795794847e_term: produc7773217078559923341nt_int > produc7773217078559923341nt_int > $o).
% 18.75/7.45 thf(func_def_1454, type, rel_of5543720577181062686nt_int: ((int > option6357759511663192854e_term) > option4624381673175914239nt_int) > (produc7773217078559923341nt_int > $o) > set_Pr1872883991513573699nt_int).
% 18.75/7.45 thf(func_def_1455, type, rel_of7835217753297429671nteger: ((produc6241069584506657477e_term > option6357759511663192854e_term) > option2651255830984564193nteger) > (produc1908205239877642774nteger > $o) > set_Pr1281608226676607948nteger).
% 18.75/7.45 thf(func_def_1456, type, rel_of7774016450764239315et_nat: ((produc3658429121746597890et_nat > $o) > option5190343406534369742et_nat) > (produc2732055786443039994et_nat > $o) > set_Pr8536935166611901872et_nat).
% 18.75/7.45 thf(func_def_1457, type, rel_of4838799251197538391et_nat: ((produc3658429121746597890et_nat > $o) > option936205604648967762et_nat) > (produc3925858234332021118et_nat > $o) > set_Pr3286484037609594932et_nat).
% 18.75/7.45 thf(func_def_1458, type, rel_of8306664904814525588nt_int: ((produc8551481072490612790e_term > option6357759511663192854e_term) > option4624381673175914239nt_int) > (produc2285326912895808259nt_int > $o) > set_Pr9222295170931077689nt_int).
% 18.75/7.45 thf(func_def_1459, type, rel_of_nat_nat: (nat > option_nat) > (product_prod_nat_nat > $o) > set_Pr1261947904930325089at_nat).
% 18.75/7.45 thf(func_def_1460, type, rel_of6563097375766832824at_nat: (set_Pr1261947904930325089at_nat > option8963830502488799655at_nat) > (produc3843707927480180839at_nat > $o) > set_Pr4329608150637261639at_nat).
% 18.75/7.45 thf(func_def_1461, type, set_to1653371902132773855nt_int: set_Pr1872883991513573699nt_int > (int > option6357759511663192854e_term) > option4624381673175914239nt_int).
% 18.75/7.45 thf(func_def_1462, type, set_to680829756418416360nteger: set_Pr1281608226676607948nteger > (produc6241069584506657477e_term > option6357759511663192854e_term) > option2651255830984564193nteger).
% 18.75/7.45 thf(func_def_1463, type, set_to2047380710992656148et_nat: set_Pr8536935166611901872et_nat > (produc3658429121746597890et_nat > $o) > option5190343406534369742et_nat).
% 18.75/7.45 thf(func_def_1464, type, set_to6040779677306527128et_nat: set_Pr3286484037609594932et_nat > (produc3658429121746597890et_nat > $o) > option936205604648967762et_nat).
% 18.75/7.45 thf(func_def_1465, type, set_to6585427216324510421nt_int: set_Pr9222295170931077689nt_int > (produc8551481072490612790e_term > option6357759511663192854e_term) > option4624381673175914239nt_int).
% 18.75/7.45 thf(func_def_1466, type, set_to_map_o_num: set_Pr7040061329075590551_o_num > $o > option_num).
% 18.75/7.45 thf(func_def_1467, type, set_to3023635543527487849it_nat: set_Pr6777250647868329861it_nat > $o > option8956607266484857688it_nat).
% 18.75/7.45 thf(func_def_1468, type, set_to6264436334439079987nteger: set_Pr4811707699266497531nteger > code_integer > option_Code_integer).
% 18.75/7.45 thf(func_def_1469, type, set_to6039658477269176016atural: set_Pr2352657477744078772atural > code_natural > option5403585828896915703atural).
% 18.75/7.45 thf(func_def_1470, type, set_to_map_int_int: set_Pr958786334691620121nt_int > int > option_int).
% 18.75/7.45 thf(func_def_1471, type, set_to_map_int_num: set_Pr8387461105917469447nt_num > int > option_num).
% 18.75/7.45 thf(func_def_1472, type, set_to_map_nat_nat: set_Pr1261947904930325089at_nat > nat > option_nat).
% 18.75/7.45 thf(func_def_1473, type, set_to_map_nat_num: set_Pr6200539531224447659at_num > nat > option_num).
% 18.75/7.45 thf(func_def_1474, type, set_to785951348762482001it_nat: set_Pr633603713510679705it_nat > nat > option8956607266484857688it_nat).
% 18.75/7.45 thf(func_def_1475, type, set_to5081529003106763492at_num: set_Pr7477759153910077568at_num > product_prod_nat_nat > option_num).
% 18.75/7.45 thf(func_def_1476, type, set_to4447731662395764663at_nat: set_Pr4329608150637261639at_nat > set_Pr1261947904930325089at_nat > option8963830502488799655at_nat).
% 18.75/7.45 thf(func_def_1477, type, the_default_num: num > option_num > num).
% 18.75/7.45 thf(func_def_1478, type, the_de8559148246674365659it_nat: produc6714399278180371524it_nat > option3216581401566546698it_nat > produc6714399278180371524it_nat).
% 18.75/7.45 thf(func_def_1479, type, the_de2487931475039285041it_nat: produc8664842809031399944it_nat > option8956607266484857688it_nat > produc8664842809031399944it_nat).
% 18.75/7.45 thf(func_def_1480, type, the_default_set_o: set_o > option_set_o > set_o).
% 18.75/7.45 thf(func_def_1481, type, the_default_set_int: set_int > option_set_int > set_int).
% 18.75/7.45 thf(func_def_1482, type, the_default_set_nat: set_nat > option_set_nat > set_nat).
% 18.75/7.45 thf(func_def_1483, type, the_de3668382347305825784at_nat: set_Pr1261947904930325089at_nat > option8963830502488799655at_nat > set_Pr1261947904930325089at_nat).
% 18.75/7.45 thf(func_def_1484, type, the_de6830073021511528542at_nat: set_Pr4329608150637261639at_nat > option1583680563626158861at_nat > set_Pr4329608150637261639at_nat).
% 18.75/7.45 thf(func_def_1485, type, uncurry_int_int_int: (int > int > int) > product_prod_int_int > int).
% 18.75/7.45 thf(func_def_1486, type, uncurr7650761721940715016nt_int: (int > int > product_prod_int_int) > product_prod_int_int > product_prod_int_int).
% 18.75/7.45 thf(func_def_1487, type, uncurr7511940902602773877_nat_o: (nat > nat > product_prod_nat_nat > $o) > product_prod_nat_nat > product_prod_nat_nat > $o).
% 18.75/7.45 thf(func_def_1488, type, uncurr8011562610307062878at_nat: (nat > nat > product_prod_nat_nat > product_prod_nat_nat) > product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat).
% 18.75/7.45 thf(func_def_1489, type, uncurry_nat_nat_nat: (nat > nat > nat) > product_prod_nat_nat > nat).
% 18.75/7.45 thf(func_def_1490, type, add_ms2612439473150266591at_nat: product_prod_nat_nat > multis2468970476368604999at_nat > multis2468970476368604999at_nat).
% 18.75/7.45 thf(func_def_1491, type, ms_strict: set_Pr8551490117392284871at_nat).
% 18.75/7.45 thf(func_def_1492, type, ms_weak: set_Pr8551490117392284871at_nat).
% 18.75/7.45 thf(func_def_1493, type, pw_leq: multis2468970476368604999at_nat > multis2468970476368604999at_nat > $o).
% 18.75/7.45 thf(func_def_1494, type, set_ms8126754132646256062at_nat: multis2468970476368604999at_nat > set_Pr1261947904930325089at_nat).
% 18.75/7.45 thf(func_def_1495, type, suc: nat > nat).
% 18.75/7.45 thf(func_def_1496, type, compow_nat_nat: nat > (nat > nat) > nat > nat).
% 18.75/7.45 thf(func_def_1497, type, case_nat_option_num: option_num > (nat > option_num) > nat > option_num).
% 18.75/7.45 thf(func_def_1498, type, semiri4939895301339042750nteger: nat > code_integer).
% 18.75/7.45 thf(func_def_1499, type, semiri3763490453095760265atural: nat > code_natural).
% 18.75/7.45 thf(func_def_1500, type, semiri1314217659103216013at_int: nat > int).
% 18.75/7.45 thf(func_def_1501, type, semiri1316708129612266289at_nat: nat > nat).
% 18.75/7.45 thf(func_def_1502, type, semiri681578069525770553at_rat: nat > rat).
% 18.75/7.45 thf(func_def_1503, type, semiri4055485073559036834nteger: (code_integer > code_integer) > nat > code_integer > code_integer).
% 18.75/7.45 thf(func_def_1504, type, semiri2879080225315754349atural: (code_natural > code_natural) > nat > code_natural > code_natural).
% 18.75/7.45 thf(func_def_1505, type, semiri8420488043553186161ux_int: (int > int) > nat > int > int).
% 18.75/7.45 thf(func_def_1506, type, semiri8422978514062236437ux_nat: (nat > nat) > nat > nat > nat).
% 18.75/7.45 thf(func_def_1507, type, semiri7787848453975740701ux_rat: (rat > rat) > nat > rat > rat).
% 18.75/7.45 thf(func_def_1508, type, size_s1564113455978345259t_unit: heap_T5738788834812785303t_unit > nat).
% 18.75/7.45 thf(func_def_1509, type, size_size_list_int: list_int > nat).
% 18.75/7.45 thf(func_def_1510, type, size_size_list_nat: list_nat > nat).
% 18.75/7.45 thf(func_def_1511, type, size_size_num: num > nat).
% 18.75/7.45 thf(func_def_1512, type, size_size_option_num: option_num > nat).
% 18.75/7.45 thf(func_def_1513, type, size_s6797157356856800118it_nat: option3216581401566546698it_nat > nat).
% 18.75/7.45 thf(func_def_1514, type, size_s8766407808098229740it_nat: option8956607266484857688it_nat > nat).
% 18.75/7.45 thf(func_def_1515, type, nat_list_decode: nat > list_nat).
% 18.75/7.45 thf(func_def_1516, type, nat_list_decode_rel: nat > nat > $o).
% 18.75/7.45 thf(func_def_1517, type, nat_list_encode: list_nat > nat).
% 18.75/7.45 thf(func_def_1518, type, nat_list_encode_rel: list_nat > list_nat > $o).
% 18.75/7.45 thf(func_def_1519, type, nat_prod_decode: nat > product_prod_nat_nat).
% 18.75/7.45 thf(func_def_1520, type, nat_prod_decode_aux: nat > nat > product_prod_nat_nat).
% 18.75/7.45 thf(func_def_1521, type, nat_pr5047031295181774490ux_rel: product_prod_nat_nat > product_prod_nat_nat > $o).
% 18.75/7.45 thf(func_def_1522, type, nat_prod_encode: product_prod_nat_nat > nat).
% 18.75/7.45 thf(func_def_1523, type, nat_set_decode: nat > set_nat).
% 18.75/7.45 thf(func_def_1524, type, nat_set_encode: set_nat > nat).
% 18.75/7.45 thf(func_def_1525, type, nat_sum_decode: nat > sum_sum_nat_nat).
% 18.75/7.45 thf(func_def_1526, type, nat_triangle: nat > nat).
% 18.75/7.45 thf(func_def_1527, type, bitM: num > num).
% 18.75/7.45 thf(func_def_1528, type, inc: num > num).
% 18.75/7.45 thf(func_def_1529, type, nat_of_num: num > nat).
% 18.75/7.45 thf(func_def_1530, type, neg_nu8804712462038260780nteger: code_integer > code_integer).
% 18.75/7.45 thf(func_def_1531, type, neg_numeral_dbl_int: int > int).
% 18.75/7.45 thf(func_def_1532, type, neg_numeral_dbl_rat: rat > rat).
% 18.75/7.45 thf(func_def_1533, type, neg_nu7757733837767384882nteger: code_integer > code_integer).
% 18.75/7.45 thf(func_def_1534, type, neg_nu3811975205180677377ec_int: int > int).
% 18.75/7.45 thf(func_def_1535, type, neg_nu3179335615603231917ec_rat: rat > rat).
% 18.75/7.45 thf(func_def_1536, type, neg_nu5831290666863070958nteger: code_integer > code_integer).
% 18.75/7.45 thf(func_def_1537, type, neg_nu5851722552734809277nc_int: int > int).
% 18.75/7.45 thf(func_def_1538, type, neg_nu5219082963157363817nc_rat: rat > rat).
% 18.75/7.45 thf(func_def_1539, type, neg_nu2435721316971906650nteger: code_integer > $o).
% 18.75/7.45 thf(func_def_1540, type, neg_nu7441568979088483369um_int: int > $o).
% 18.75/7.45 thf(func_def_1541, type, neg_nu6808929389511037909um_rat: rat > $o).
% 18.75/7.45 thf(func_def_1542, type, neg_nu5755505904847501662nteger: num > num > code_integer).
% 18.75/7.45 thf(func_def_1543, type, neg_numeral_sub_int: num > num > int).
% 18.75/7.45 thf(func_def_1544, type, neg_numeral_sub_rat: num > num > rat).
% 18.75/7.45 thf(func_def_1545, type, bit0: num > num).
% 18.75/7.45 thf(func_def_1546, type, bit1: num > num).
% 18.75/7.45 thf(func_def_1547, type, one: num).
% 18.75/7.45 thf(func_def_1548, type, case_num_option_num: option_num > (num > option_num) > (num > option_num) > num > option_num).
% 18.75/7.45 thf(func_def_1549, type, size_num: num > nat).
% 18.75/7.45 thf(func_def_1550, type, num_of_nat: nat > num).
% 18.75/7.45 thf(func_def_1551, type, numera6620942414471956472nteger: num > code_integer).
% 18.75/7.45 thf(func_def_1552, type, numera5444537566228673987atural: num > code_natural).
% 18.75/7.45 thf(func_def_1553, type, numeral_numeral_int: num > int).
% 18.75/7.45 thf(func_def_1554, type, numeral_numeral_nat: num > nat).
% 18.75/7.45 thf(func_def_1555, type, numeral_numeral_rat: num > rat).
% 18.75/7.45 thf(func_def_1556, type, pred_numeral: num > nat).
% 18.75/7.45 thf(func_def_1557, type, ring_16219924574208605041nteger: code_integer > $o).
% 18.75/7.45 thf(func_def_1558, type, ring_1_iszero_int: int > $o).
% 18.75/7.45 thf(func_def_1559, type, ring_1_iszero_rat: rat > $o).
% 18.75/7.45 thf(func_def_1560, type, sqr: num > num).
% 18.75/7.45 thf(func_def_1561, type, bind_num_num: option_num > (num > option_num) > option_num).
% 18.75/7.45 thf(func_def_1562, type, bind_n6186876254402743274it_nat: option_num > (num > option3216581401566546698it_nat) > option3216581401566546698it_nat).
% 18.75/7.45 thf(func_def_1563, type, bind_n550516262659884002it_nat: option_num > (num > option8956607266484857688it_nat) > option8956607266484857688it_nat).
% 18.75/7.45 thf(func_def_1564, type, bind_P7816469540982926368at_num: option3216581401566546698it_nat > (produc6714399278180371524it_nat > option_num) > option_num).
% 18.75/7.45 thf(func_def_1565, type, bind_P1787608729393679550it_nat: option3216581401566546698it_nat > (produc6714399278180371524it_nat > option3216581401566546698it_nat) > option3216581401566546698it_nat).
% 18.75/7.45 thf(func_def_1566, type, bind_P3087804342168909838it_nat: option3216581401566546698it_nat > (produc6714399278180371524it_nat > option8956607266484857688it_nat) > option8956607266484857688it_nat).
% 18.75/7.45 thf(func_def_1567, type, bind_P4387644102537648098at_num: option8956607266484857688it_nat > (produc8664842809031399944it_nat > option_num) > option_num).
% 18.75/7.45 thf(func_def_1568, type, bind_P1106314856888375420it_nat: option8956607266484857688it_nat > (produc8664842809031399944it_nat > option3216581401566546698it_nat) > option3216581401566546698it_nat).
% 18.75/7.45 thf(func_def_1569, type, bind_P7351952464966851536it_nat: option8956607266484857688it_nat > (produc8664842809031399944it_nat > option8956607266484857688it_nat) > option8956607266484857688it_nat).
% 18.75/7.45 thf(func_def_1570, type, combine_options_num: (num > num > num) > option_num > option_num > option_num).
% 18.75/7.45 thf(func_def_1571, type, combin3867838909898076099it_nat: (produc6714399278180371524it_nat > produc6714399278180371524it_nat > produc6714399278180371524it_nat) > option3216581401566546698it_nat > option3216581401566546698it_nat > option3216581401566546698it_nat).
% 18.75/7.45 thf(func_def_1572, type, combin4318129983670048329it_nat: (produc8664842809031399944it_nat > produc8664842809031399944it_nat > produc8664842809031399944it_nat) > option8956607266484857688it_nat > option8956607266484857688it_nat > option8956607266484857688it_nat).
% 18.75/7.45 thf(func_def_1573, type, none_o: option_o).
% 18.75/7.45 thf(func_def_1574, type, none_int: option_int).
% 18.75/7.45 thf(func_def_1575, type, none_nat: option_nat).
% 18.75/7.45 thf(func_def_1576, type, none_num: option_num).
% 18.75/7.45 thf(func_def_1577, type, none_P3773570700014501484nt_int: option4256020574406277085nt_int).
% 18.75/7.45 thf(func_def_1578, type, none_P4442379456014020469nteger: option8051342751916580710nteger).
% 18.75/7.45 thf(func_def_1579, type, none_P199884684680593241et_nat: option2860828798490689354et_nat).
% 18.75/7.45 thf(func_def_1580, type, none_P4972525538344268765et_nat: option5190343406534369742et_nat).
% 18.75/7.45 thf(func_def_1581, type, none_P1286213070022356066nt_int: option7541221861074943443nt_int).
% 18.75/7.45 thf(func_def_1582, type, none_P2587165478634041381it_nat: option3216581401566546698it_nat).
% 18.75/7.45 thf(func_def_1583, type, none_P5556105721700978146at_nat: option4927543243414619207at_nat).
% 18.75/7.45 thf(func_def_1584, type, none_P9117596204409417319it_nat: option8956607266484857688it_nat).
% 18.75/7.45 thf(func_def_1585, type, none_P5811896708078067656at_nat: option8699557107911914541at_nat).
% 18.75/7.45 thf(func_def_1586, type, none_Product_unit: option_Product_unit).
% 18.75/7.45 thf(func_def_1587, type, none_set_o: option_set_o).
% 18.75/7.45 thf(func_def_1588, type, none_set_int: option_set_int).
% 18.75/7.45 thf(func_def_1589, type, none_set_nat: option_set_nat).
% 18.75/7.45 thf(func_def_1590, type, none_s625347054029921090at_nat: option8963830502488799655at_nat).
% 18.75/7.45 thf(func_def_1591, type, none_s6518873173954064040at_nat: option1583680563626158861at_nat).
% 18.75/7.45 thf(func_def_1592, type, some_nat_o: (nat > $o) > option_nat_o).
% 18.75/7.45 thf(func_def_1593, type, some_o: $o > option_o).
% 18.75/7.45 thf(func_def_1594, type, some_assn: assn > option_assn).
% 18.75/7.45 thf(func_def_1595, type, some_Code_integer: code_integer > option_Code_integer).
% 18.75/7.45 thf(func_def_1596, type, some_int: int > option_int).
% 18.75/7.45 thf(func_def_1597, type, some_nat: nat > option_nat).
% 18.75/7.45 thf(func_def_1598, type, some_num: num > option_num).
% 18.75/7.45 thf(func_def_1599, type, some_P7455497367792166888nt_int: produc7773217078559923341nt_int > option4256020574406277085nt_int).
% 18.75/7.45 thf(func_def_1600, type, some_P1462369734362851057nteger: produc1908205239877642774nteger > option8051342751916580710nteger).
% 18.75/7.45 thf(func_def_1601, type, some_P1630309045189364437et_nat: produc2732055786443039994et_nat > option2860828798490689354et_nat).
% 18.75/7.45 thf(func_def_1602, type, some_P750831030444334937et_nat: produc3925858234332021118et_nat > option5190343406534369742et_nat).
% 18.75/7.45 thf(func_def_1603, type, some_P2355398578364412894nt_int: produc2285326912895808259nt_int > option7541221861074943443nt_int).
% 18.75/7.45 thf(func_def_1604, type, some_P6772290148444788224nteger: produc8923325533196201883nteger > option2651255830984564193nteger).
% 18.75/7.45 thf(func_def_1605, type, some_P5671840033927537686atural: produc7822875418678951345atural > option5403585828896915703atural).
% 18.75/7.45 thf(func_def_1606, type, some_P6105628898608307625it_nat: produc6714399278180371524it_nat > option3216581401566546698it_nat).
% 18.75/7.45 thf(func_def_1607, type, some_P624177172695371229et_nat: produc3658429121746597890et_nat > option936205604648967762et_nat).
% 18.75/7.45 thf(func_def_1608, type, some_P4184893108420464158nt_int: product_prod_int_int > option4624381673175914239nt_int).
% 18.75/7.45 thf(func_def_1609, type, some_P7363390416028606310at_nat: product_prod_nat_nat > option4927543243414619207at_nat).
% 18.75/7.45 thf(func_def_1610, type, some_P1914260805536162275it_nat: produc8664842809031399944it_nat > option8956607266484857688it_nat).
% 18.75/7.45 thf(func_def_1611, type, some_P131194445498448716at_nat: produc3843707927480180839at_nat > option8699557107911914541at_nat).
% 18.75/7.45 thf(func_def_1612, type, some_Product_unit: product_unit > option_Product_unit).
% 18.75/7.45 thf(func_def_1613, type, some_rat: rat > option_rat).
% 18.75/7.45 thf(func_def_1614, type, some_set_o: set_o > option_set_o).
% 18.75/7.45 thf(func_def_1615, type, some_set_int: set_int > option_set_int).
% 18.75/7.45 thf(func_def_1616, type, some_set_nat: set_nat > option_set_nat).
% 18.75/7.45 thf(func_def_1617, type, some_s147305329494351046at_nat: set_Pr1261947904930325089at_nat > option8963830502488799655at_nat).
% 18.75/7.45 thf(func_def_1618, type, some_s5890477192898017836at_nat: set_Pr4329608150637261639at_nat > option1583680563626158861at_nat).
% 18.75/7.45 thf(func_def_1619, type, some_s8043159101241848530t_unit: set_Product_unit > option8137458692691377843t_unit).
% 18.75/7.45 thf(func_def_1620, type, case_o1441893360019914891nteger: (produc8923325533196201883nteger > produc8923325533196201883nteger) > ((code_integer > code_integer) > produc8923325533196201883nteger > produc8923325533196201883nteger) > option8057788054806935849nteger > produc8923325533196201883nteger > produc8923325533196201883nteger).
% 18.75/7.45 thf(func_def_1621, type, case_o7134296353695833103nteger: (produc8923325533196201883nteger > produc8923325533196201883nteger) > (code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger) > option_Code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger).
% 18.75/7.45 thf(func_def_1622, type, case_o43118980978444458nteger: $o > (code_integer > $o) > option_Code_integer > $o).
% 18.75/7.45 thf(func_def_1623, type, case_option_o_int: $o > (int > $o) > option_int > $o).
% 18.75/7.45 thf(func_def_1624, type, case_option_o_nat: $o > (nat > $o) > option_nat > $o).
% 18.75/7.45 thf(func_def_1625, type, case_option_o_num: $o > (num > $o) > option_num > $o).
% 18.75/7.45 thf(func_def_1626, type, case_o2169478532838437047it_nat: $o > (produc6714399278180371524it_nat > $o) > option3216581401566546698it_nat > $o).
% 18.75/7.45 thf(func_def_1627, type, case_o2686588417244861013it_nat: $o > (produc8664842809031399944it_nat > $o) > option8956607266484857688it_nat > $o).
% 18.75/7.45 thf(func_def_1628, type, case_option_o_rat: $o > (rat > $o) > option_rat > $o).
% 18.75/7.45 thf(func_def_1629, type, case_o4401850862724306899et_nat: $o > (set_nat > $o) > option_set_nat > $o).
% 18.75/7.45 thf(func_def_1630, type, case_o9049918639272118855nteger: code_integer > (code_integer > code_integer) > option_Code_integer > code_integer).
% 18.75/7.45 thf(func_def_1631, type, case_o356765784539232260er_num: code_integer > (num > code_integer) > option_num > code_integer).
% 18.75/7.45 thf(func_def_1632, type, case_o5621594795226839503al_num: code_natural > (num > code_natural) > option_num > code_natural).
% 18.75/7.45 thf(func_def_1633, type, case_o8314599424437789472it_nat: array_a > (produc6714399278180371524it_nat > array_a) > option3216581401566546698it_nat > array_a).
% 18.75/7.45 thf(func_def_1634, type, case_o8180226181140434498it_nat: heap_e7401611519738050253t_unit > (produc6714399278180371524it_nat > heap_e7401611519738050253t_unit) > option3216581401566546698it_nat > heap_e7401611519738050253t_unit).
% 18.75/7.45 thf(func_def_1635, type, case_o2566993838309857162it_nat: heap_e7401611519738050253t_unit > (produc8664842809031399944it_nat > heap_e7401611519738050253t_unit) > option8956607266484857688it_nat > heap_e7401611519738050253t_unit).
% 18.75/7.45 thf(func_def_1636, type, case_option_int_num: int > (num > int) > option_num > int).
% 18.75/7.45 thf(func_def_1637, type, case_option_nat_num: nat > (num > nat) > option_num > nat).
% 18.75/7.45 thf(func_def_1638, type, case_o1134687144775446439it_nat: nat > (produc6714399278180371524it_nat > nat) > option3216581401566546698it_nat > nat).
% 18.75/7.45 thf(func_def_1639, type, case_o5424514124273913701it_nat: nat > (produc8664842809031399944it_nat > nat) > option8956607266484857688it_nat > nat).
% 18.75/7.45 thf(func_def_1640, type, case_option_num_int: num > (int > num) > option_int > num).
% 18.75/7.45 thf(func_def_1641, type, case_option_num_nat: num > (nat > num) > option_nat > num).
% 18.75/7.45 thf(func_def_1642, type, case_option_num_num: num > (num > num) > option_num > num).
% 18.75/7.45 thf(func_def_1643, type, case_o4484465799723439917n_assn: option_assn > (assn > option_assn) > option_assn > option_assn).
% 18.75/7.45 thf(func_def_1644, type, case_o6005452278849405969um_num: option_num > (num > option_num) > option_num > option_num).
% 18.75/7.45 thf(func_def_1645, type, case_o8555119740594961093it_nat: option3216581401566546698it_nat > (produc6714399278180371524it_nat > option3216581401566546698it_nat) > option3216581401566546698it_nat > option3216581401566546698it_nat).
% 18.75/7.45 thf(func_def_1646, type, case_o5699750240967658439it_nat: option3216581401566546698it_nat > (produc8664842809031399944it_nat > option3216581401566546698it_nat) > option8956607266484857688it_nat > option3216581401566546698it_nat).
% 18.75/7.45 thf(func_def_1647, type, case_o3886096569520666655it_nat: option8956607266484857688it_nat > (produc6714399278180371524it_nat > option8956607266484857688it_nat) > option3216581401566546698it_nat > option8956607266484857688it_nat).
% 18.75/7.45 thf(func_def_1648, type, case_o2963978774867076333it_nat: option8956607266484857688it_nat > (produc8664842809031399944it_nat > option8956607266484857688it_nat) > option8956607266484857688it_nat > option8956607266484857688it_nat).
% 18.75/7.45 thf(func_def_1649, type, case_o2985186191577459077t_unit: option_Product_unit > (product_unit > option_Product_unit) > option_Product_unit > option_Product_unit).
% 18.75/7.45 thf(func_def_1650, type, case_o4054078431260844265et_nat: option_set_nat > (set_nat > option_set_nat) > option_set_nat > option_set_nat).
% 18.75/7.45 thf(func_def_1651, type, case_o9080059180780454917at_nat: option1583680563626158861at_nat > (set_Pr4329608150637261639at_nat > option1583680563626158861at_nat) > option1583680563626158861at_nat > option1583680563626158861at_nat).
% 18.75/7.45 thf(func_def_1652, type, case_o9196786658626276042it_nat: product_unit > (produc8664842809031399944it_nat > product_unit) > option8956607266484857688it_nat > product_unit).
% 18.75/7.45 thf(func_def_1653, type, map_op3563471509957180299nteger: ((code_integer > code_integer) > produc8923325533196201883nteger > produc8923325533196201883nteger) > option8057788054806935849nteger > option7428179582072448501nteger).
% 18.75/7.45 thf(func_def_1654, type, map_op6424164270877473355_nat_o: ((nat > $o) > nat > $o) > option_nat_o > option_nat_o).
% 18.75/7.45 thf(func_def_1655, type, map_option_o_o: ($o > $o) > option_o > option_o).
% 18.75/7.45 thf(func_def_1656, type, map_op370346339404370627nteger: (code_integer > code_integer > code_integer) > option_Code_integer > option8057788054806935849nteger).
% 18.75/7.45 thf(func_def_1657, type, map_op9146685272036663823nteger: (code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger) > option_Code_integer > option7428179582072448501nteger).
% 18.75/7.45 thf(func_def_1658, type, map_op3669829223712506439nteger: (code_integer > code_integer) > option_Code_integer > option_Code_integer).
% 18.75/7.45 thf(func_def_1659, type, map_option_int_int: (int > int) > option_int > option_int).
% 18.75/7.45 thf(func_def_1660, type, map_option_int_nat: (int > nat) > option_int > option_nat).
% 18.75/7.45 thf(func_def_1661, type, map_option_int_num: (int > num) > option_int > option_num).
% 18.75/7.45 thf(func_def_1662, type, map_option_nat_nat: (nat > nat) > option_nat > option_nat).
% 18.75/7.45 thf(func_def_1663, type, map_option_nat_num: (nat > num) > option_nat > option_num).
% 18.75/7.45 thf(func_def_1664, type, map_op2849635639313731588nteger: (num > code_integer) > option_num > option_Code_integer).
% 18.75/7.45 thf(func_def_1665, type, map_option_num_num: (num > num) > option_num > option_num).
% 18.75/7.45 thf(func_def_1666, type, map_op6598675229099881181it_nat: (num > produc6714399278180371524it_nat) > option_num > option3216581401566546698it_nat).
% 18.75/7.45 thf(func_def_1667, type, map_op8118133509425879471it_nat: (num > produc8664842809031399944it_nat) > option_num > option8956607266484857688it_nat).
% 18.75/7.45 thf(func_def_1668, type, map_op8228268515680064275at_num: (produc6714399278180371524it_nat > num) > option3216581401566546698it_nat > option_num).
% 18.75/7.45 thf(func_def_1669, type, map_op6002829699023054091it_nat: (produc6714399278180371524it_nat > produc6714399278180371524it_nat) > option3216581401566546698it_nat > option3216581401566546698it_nat).
% 18.75/7.45 thf(func_def_1670, type, map_op674526153330701057it_nat: (produc6714399278180371524it_nat > produc8664842809031399944it_nat) > option3216581401566546698it_nat > option8956607266484857688it_nat).
% 18.75/7.45 thf(func_def_1671, type, map_op2731889312448867759at_num: (produc8664842809031399944it_nat > num) > option8956607266484857688it_nat > option_num).
% 18.75/7.45 thf(func_def_1672, type, map_op7916408704904942447it_nat: (produc8664842809031399944it_nat > produc6714399278180371524it_nat) > option8956607266484857688it_nat > option3216581401566546698it_nat).
% 18.75/7.45 thf(func_def_1673, type, map_op8673683442680995229it_nat: (produc8664842809031399944it_nat > produc8664842809031399944it_nat) > option8956607266484857688it_nat > option8956607266484857688it_nat).
% 18.75/7.45 thf(func_def_1674, type, size_option_num: (num > nat) > option_num > nat).
% 18.75/7.45 thf(func_def_1675, type, size_o5312321843473198183it_nat: (produc6714399278180371524it_nat > nat) > option3216581401566546698it_nat > nat).
% 18.75/7.45 thf(func_def_1676, type, size_o29782932136985253it_nat: (produc8664842809031399944it_nat > nat) > option8956607266484857688it_nat > nat).
% 18.75/7.45 thf(func_def_1677, type, the_nat_o: option_nat_o > nat > $o).
% 18.75/7.45 thf(func_def_1678, type, the_o: option_o > $o).
% 18.75/7.45 thf(func_def_1679, type, the_int2: option_int > int).
% 18.75/7.45 thf(func_def_1680, type, the_nat: option_nat > nat).
% 18.75/7.45 thf(func_def_1681, type, the_num: option_num > num).
% 18.75/7.45 thf(func_def_1682, type, the_Pr5856008525237892824it_nat: option3216581401566546698it_nat > produc6714399278180371524it_nat).
% 18.75/7.45 thf(func_def_1683, type, the_Pr7776125533777466484it_nat: option8956607266484857688it_nat > produc8664842809031399944it_nat).
% 18.75/7.45 thf(func_def_1684, type, these_o: set_option_o > set_o).
% 18.75/7.45 thf(func_def_1685, type, these_int: set_option_int > set_int).
% 18.75/7.45 thf(func_def_1686, type, these_nat: set_option_nat > set_nat).
% 18.75/7.45 thf(func_def_1687, type, these_num: set_option_num > set_num).
% 18.75/7.45 thf(func_def_1688, type, these_6645423997822192641it_nat: set_op3940070208846178154it_nat > set_Pr5142436192348053284it_nat).
% 18.75/7.45 thf(func_def_1689, type, these_8061402112538453438at_nat: set_op4508134149509766951at_nat > set_Pr1261947904930325089at_nat).
% 18.75/7.45 thf(func_def_1690, type, these_3407724651694999947it_nat: set_op239864471688321678it_nat > set_Pr1354866905816374718it_nat).
% 18.75/7.45 thf(func_def_1691, type, these_1872268174106123684at_nat: set_op989438649584373901at_nat > set_Pr4329608150637261639at_nat).
% 18.75/7.45 thf(func_def_1692, type, these_Product_unit: set_op3165557761946182707t_unit > set_Product_unit).
% 18.75/7.45 thf(func_def_1693, type, these_set_nat: set_option_set_nat > set_set_nat).
% 18.75/7.45 thf(func_def_1694, type, bot_bo1403522918969695512_int_o: (int > option6357759511663192854e_term) > product_prod_int_int > $o).
% 18.75/7.45 thf(func_def_1695, type, bot_bo3000040243691356879eger_o: (produc6241069584506657477e_term > option6357759511663192854e_term) > produc8923325533196201883nteger > $o).
% 18.75/7.45 thf(func_def_1696, type, bot_bo3790638025767943357_nat_o: (produc3658429121746597890et_nat > $o) > produc3925858234332021118et_nat > $o).
% 18.75/7.45 thf(func_def_1697, type, bot_bo5580076615179976505_nat_o: (produc3658429121746597890et_nat > $o) > produc3658429121746597890et_nat > $o).
% 18.75/7.45 thf(func_def_1698, type, bot_bo8662317086119403298_int_o: (produc8551481072490612790e_term > option6357759511663192854e_term) > product_prod_int_int > $o).
% 18.75/7.45 thf(func_def_1699, type, bot_bot_nat_nat_o: nat > nat > $o).
% 18.75/7.45 thf(func_def_1700, type, bot_bo394778441745866138_nat_o: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o).
% 18.75/7.45 thf(func_def_1702, type, bot_bot_assn: assn).
% 18.75/7.45 thf(func_def_1703, type, bot_bot_nat: nat).
% 18.75/7.45 thf(func_def_1704, type, bot_bot_option_num: option_num).
% 18.75/7.45 thf(func_def_1705, type, bot_bot_Product_unit: product_unit).
% 18.75/7.45 thf(func_def_1706, type, bot_bot_set_o: set_o).
% 18.75/7.45 thf(func_def_1707, type, bot_bo3990330152332043303nteger: set_Code_integer).
% 18.75/7.45 thf(func_def_1708, type, bot_bot_set_int: set_int).
% 18.75/7.45 thf(func_def_1709, type, bot_bot_set_list_nat: set_list_nat).
% 18.75/7.45 thf(func_def_1710, type, bot_bot_set_nat: set_nat).
% 18.75/7.45 thf(func_def_1711, type, bot_bot_set_num: set_num).
% 18.75/7.45 thf(func_def_1712, type, bot_bot_set_option_o: set_option_o).
% 18.75/7.45 thf(func_def_1713, type, bot_bo2519760366563279686on_int: set_option_int).
% 18.75/7.45 thf(func_def_1714, type, bot_bo5009843511495006442on_nat: set_option_nat).
% 18.75/7.45 thf(func_def_1715, type, bot_bo725063100934353204on_num: set_option_num).
% 18.75/7.45 thf(func_def_1716, type, bot_bo8185009268211221974it_nat: set_op3940070208846178154it_nat).
% 18.75/7.45 thf(func_def_1717, type, bot_bo3414888551220300179at_nat: set_op4508134149509766951at_nat).
% 18.75/7.45 thf(func_def_1718, type, bot_bo1172055076661450530it_nat: set_op239864471688321678it_nat).
% 18.75/7.45 thf(func_def_1719, type, bot_bo1471150103859235065at_nat: set_op989438649584373901at_nat).
% 18.75/7.45 thf(func_def_1720, type, bot_bo2792743115866486943t_unit: set_op3165557761946182707t_unit).
% 18.75/7.45 thf(func_def_1721, type, bot_bo5650944848895983264et_nat: set_option_set_nat).
% 18.75/7.45 thf(func_def_1722, type, bot_bo4508923176915781079nt_int: set_Pr1872883991513573699nt_int).
% 18.75/7.45 thf(func_def_1723, type, bot_bo5443222936135328352nteger: set_Pr1281608226676607948nteger).
% 18.75/7.45 thf(func_def_1724, type, bot_bo5635537948650799172et_nat: set_Pr8536935166611901872et_nat).
% 18.75/7.45 thf(func_def_1725, type, bot_bo1481135142794719944et_nat: set_Pr3286484037609594932et_nat).
% 18.75/7.45 thf(func_def_1726, type, bot_bo572930865798478029nt_int: set_Pr9222295170931077689nt_int).
% 18.75/7.45 thf(func_def_1727, type, bot_bo7073875226086086771od_o_o: set_Product_prod_o_o).
% 18.75/7.45 thf(func_def_1728, type, bot_bo6799815435448350781_o_int: set_Pr8834758594704517033_o_int).
% 18.75/7.45 thf(func_def_1729, type, bot_bo66526543525301729_o_nat: set_Pr2101469702781467981_o_nat).
% 18.75/7.45 thf(func_def_1730, type, bot_bo6361524548789211024it_nat: set_Pr5142436192348053284it_nat).
% 18.75/7.45 thf(func_def_1731, type, bot_bo8092356734887935275_int_o: set_Pr903927857289325719_int_o).
% 18.75/7.45 thf(func_def_1732, type, bot_bo1796632182523588997nt_int: set_Pr958786334691620121nt_int).
% 18.75/7.45 thf(func_def_1733, type, bot_bo4286715327455315753nt_nat: set_Pr3448869479623346877nt_nat).
% 18.75/7.45 thf(func_def_1734, type, bot_bo1114129665703605383_nat_o: set_Pr3149072824959771635_nat_o).
% 18.75/7.45 thf(func_def_1735, type, bot_bo8833082644685343017at_int: set_Pr7995236796853374141at_int).
% 18.75/7.45 thf(func_def_1736, type, bot_bo2099793752762293965at_nat: set_Pr1261947904930325089at_nat).
% 18.75/7.45 thf(func_def_1737, type, bot_bo5454027612061941066_nat_o: set_Pr6558897299634722526_nat_o).
% 18.75/7.45 thf(func_def_1738, type, bot_bo5327735625951526323at_nat: set_Pr8693737435421807431at_nat).
% 18.75/7.45 thf(func_def_1739, type, bot_bo7193250159860175667at_nat: set_Pr5564308138774400199at_nat).
% 18.75/7.45 thf(func_def_1740, type, bot_bo5696401558416705618it_nat: set_Pr1354866905816374718it_nat).
% 18.75/7.45 thf(func_def_1741, type, bot_bo228742789529271731at_nat: set_Pr4329608150637261639at_nat).
% 18.75/7.45 thf(func_def_1742, type, bot_bo3957492148770167129t_unit: set_Product_unit).
% 18.75/7.45 thf(func_def_1743, type, bot_bot_set_rat: set_rat).
% 18.75/7.45 thf(func_def_1744, type, bot_bo9204850693367297629nteger: set_set_Code_integer).
% 18.75/7.45 thf(func_def_1745, type, bot_bot_set_set_int: set_set_int).
% 18.75/7.45 thf(func_def_1746, type, bot_bo3886227569956363488st_nat: set_set_list_nat).
% 18.75/7.46 thf(func_def_1747, type, bot_bot_set_set_nat: set_set_nat).
% 18.75/7.46 thf(func_def_1748, type, bot_bo3083307316010499117at_nat: set_se7855581050983116737at_nat).
% 18.75/7.46 thf(func_def_1749, type, bot_bo6284674557190688313t_unit: set_set_Product_unit).
% 18.75/7.46 thf(func_def_1750, type, ord_less_o: $o > $o > $o).
% 18.75/7.46 thf(func_def_1751, type, ord_le6747313008572928689nteger: code_integer > code_integer > $o).
% 18.75/7.46 thf(func_def_1752, type, ord_le5570908160329646204atural: code_natural > code_natural > $o).
% 18.75/7.46 thf(func_def_1753, type, ord_less_int: int > int > $o).
% 18.75/7.46 thf(func_def_1754, type, ord_less_nat: nat > nat > $o).
% 18.75/7.46 thf(func_def_1755, type, ord_less_num: num > num > $o).
% 18.75/7.46 thf(func_def_1756, type, ord_le7113747843092208513nteger: option_Code_integer > option_Code_integer > $o).
% 18.75/7.46 thf(func_def_1757, type, ord_less_option_int: option_int > option_int > $o).
% 18.75/7.46 thf(func_def_1758, type, ord_less_option_nat: option_nat > option_nat > $o).
% 18.75/7.46 thf(func_def_1759, type, ord_less_option_num: option_num > option_num > $o).
% 18.75/7.46 thf(func_def_1760, type, ord_less_option_rat: option_rat > option_rat > $o).
% 18.75/7.46 thf(func_def_1761, type, ord_le361264281704409273t_unit: product_unit > product_unit > $o).
% 18.75/7.46 thf(func_def_1762, type, ord_less_rat: rat > rat > $o).
% 18.75/7.46 thf(func_def_1763, type, ord_less_set_o: set_o > set_o > $o).
% 18.75/7.46 thf(func_def_1764, type, ord_le1307284697595431911nteger: set_Code_integer > set_Code_integer > $o).
% 18.75/7.46 thf(func_def_1765, type, ord_less_set_int: set_int > set_int > $o).
% 18.75/7.46 thf(func_def_1766, type, ord_less_set_nat: set_nat > set_nat > $o).
% 18.75/7.46 thf(func_def_1767, type, ord_less_set_num: set_num > set_num > $o).
% 18.75/7.46 thf(func_def_1768, type, ord_le7866589430770878221at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o).
% 18.75/7.46 thf(func_def_1769, type, ord_le2604355607129572851at_nat: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o).
% 18.75/7.46 thf(func_def_1770, type, ord_le8056459307392131481t_unit: set_Product_unit > set_Product_unit > $o).
% 18.75/7.46 thf(func_def_1771, type, ord_less_set_rat: set_rat > set_rat > $o).
% 18.75/7.46 thf(func_def_1772, type, ord_less_set_set_nat: set_set_nat > set_set_nat > $o).
% 18.75/7.46 thf(func_def_1773, type, ord_le2124322318746777828_int_o: ((int > option6357759511663192854e_term) > product_prod_int_int > $o) > ((int > option6357759511663192854e_term) > product_prod_int_int > $o) > $o).
% 18.75/7.46 thf(func_def_1774, type, ord_le4340812435750786203eger_o: ((produc6241069584506657477e_term > option6357759511663192854e_term) > produc8923325533196201883nteger > $o) > ((produc6241069584506657477e_term > option6357759511663192854e_term) > produc8923325533196201883nteger > $o) > $o).
% 18.75/7.46 thf(func_def_1775, type, ord_le6753239538765779593_nat_o: ((produc3658429121746597890et_nat > $o) > produc3925858234332021118et_nat > $o) > ((produc3658429121746597890et_nat > $o) > produc3925858234332021118et_nat > $o) > $o).
% 18.75/7.46 thf(func_def_1776, type, ord_le8000401564054156549_nat_o: ((produc3658429121746597890et_nat > $o) > produc3658429121746597890et_nat > $o) > ((produc3658429121746597890et_nat > $o) > produc3658429121746597890et_nat > $o) > $o).
% 18.75/7.46 thf(func_def_1777, type, ord_le5643404153117327598_int_o: ((produc8551481072490612790e_term > option6357759511663192854e_term) > product_prod_int_int > $o) > ((produc8551481072490612790e_term > option6357759511663192854e_term) > product_prod_int_int > $o) > $o).
% 18.75/7.46 thf(func_def_1778, type, ord_le6558929396352911974_nat_o: (list_nat > list_nat > $o) > (list_nat > list_nat > $o) > $o).
% 18.75/7.46 thf(func_def_1779, type, ord_le1520216061033275535_nat_o: (list_nat > $o) > (list_nat > $o) > $o).
% 18.75/7.46 thf(func_def_1780, type, ord_le2646555220125990790_nat_o: (nat > nat > $o) > (nat > nat > $o) > $o).
% 18.75/7.46 thf(func_def_1781, type, ord_less_eq_nat_o: (nat > $o) > (nat > $o) > $o).
% 18.75/7.46 thf(func_def_1782, type, ord_le7226304311989208114_nat_o: (produc2732055786443039994et_nat > produc2732055786443039994et_nat > $o) > (produc2732055786443039994et_nat > produc2732055786443039994et_nat > $o) > $o).
% 18.75/7.46 thf(func_def_1783, type, ord_le1658592502415435381_nat_o: (produc2732055786443039994et_nat > $o) > (produc2732055786443039994et_nat > $o) > $o).
% 18.75/7.46 thf(func_def_1784, type, ord_le1598226405681992910_int_o: (product_prod_int_int > product_prod_int_int > $o) > (product_prod_int_int > product_prod_int_int > $o) > $o).
% 18.75/7.46 thf(func_def_1785, type, ord_le8369615600986905444_int_o: (product_prod_int_int > $o) > (product_prod_int_int > $o) > $o).
% 18.75/7.46 thf(func_def_1786, type, ord_le5604493270027003598_nat_o: (product_prod_nat_nat > product_prod_nat_nat > $o) > (product_prod_nat_nat > product_prod_nat_nat > $o) > $o).
% 18.75/7.46 thf(func_def_1787, type, ord_le704812498762024988_nat_o: (product_prod_nat_nat > $o) > (product_prod_nat_nat > $o) > $o).
% 18.75/7.46 thf(func_def_1788, type, ord_le3935385432712749774_nat_o: (set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o) > (set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o) > $o).
% 18.75/7.46 thf(func_def_1789, type, ord_less_eq_o: $o > $o > $o).
% 18.75/7.46 thf(func_def_1790, type, ord_le3102999989581377725nteger: code_integer > code_integer > $o).
% 18.75/7.46 thf(func_def_1791, type, ord_le1926595141338095240atural: code_natural > code_natural > $o).
% 18.75/7.46 thf(func_def_1792, type, ord_less_eq_int: int > int > $o).
% 18.75/7.46 thf(func_def_1793, type, ord_less_eq_nat: nat > nat > $o).
% 18.75/7.46 thf(func_def_1794, type, ord_less_eq_num: num > num > $o).
% 18.75/7.46 thf(func_def_1795, type, ord_le1736525451366464988on_int: option_int > option_int > $o).
% 18.75/7.46 thf(func_def_1796, type, ord_le5914376470875661696on_nat: option_nat > option_nat > $o).
% 18.75/7.46 thf(func_def_1797, type, ord_le6622620407824499402on_num: option_num > option_num > $o).
% 18.75/7.46 thf(func_def_1798, type, ord_le2406147912482264968on_rat: option_rat > option_rat > $o).
% 18.75/7.46 thf(func_def_1799, type, ord_le2843612097646854710et_nat: option_set_nat > option_set_nat > $o).
% 18.75/7.46 thf(func_def_1800, type, ord_le3221252021190050221t_unit: product_unit > product_unit > $o).
% 18.75/7.46 thf(func_def_1801, type, ord_less_eq_rat: rat > rat > $o).
% 18.75/7.46 thf(func_def_1802, type, ord_le567748327753481079e_term: set_in3461395444621081367e_term > set_in3461395444621081367e_term > $o).
% 18.75/7.46 thf(func_def_1803, type, ord_le7106919388332126736e_term: set_Pr7604974323444597168e_term > set_Pr7604974323444597168e_term > $o).
% 18.75/7.46 thf(func_def_1804, type, ord_le2965882846123202637_nat_o: set_Pr4532377907799695533_nat_o > set_Pr4532377907799695533_nat_o > $o).
% 18.75/7.46 thf(func_def_1805, type, ord_le4129093240937979009e_term: set_Pr3642885161833720865e_term > set_Pr3642885161833720865e_term > $o).
% 18.75/7.46 thf(func_def_1806, type, ord_less_eq_set_o: set_o > set_o > $o).
% 18.75/7.46 thf(func_def_1807, type, ord_le7084787975880047091nteger: set_Code_integer > set_Code_integer > $o).
% 18.75/7.46 thf(func_def_1808, type, ord_less_eq_set_int: set_int > set_int > $o).
% 18.75/7.46 thf(func_def_1809, type, ord_le6045566169113846134st_nat: set_list_nat > set_list_nat > $o).
% 18.75/7.46 thf(func_def_1810, type, ord_less_eq_set_nat: set_nat > set_nat > $o).
% 18.75/7.46 thf(func_def_1811, type, ord_less_eq_set_num: set_num > set_num > $o).
% 18.75/7.46 thf(func_def_1812, type, ord_le135402666524580259nt_int: set_Pr1872883991513573699nt_int > set_Pr1872883991513573699nt_int > $o).
% 18.75/7.46 thf(func_def_1813, type, ord_le3745675095661657703_nat_o: set_Pr7909803484932130503_nat_o > set_Pr7909803484932130503_nat_o > $o).
% 18.75/7.46 thf(func_def_1814, type, ord_le653643898420964396nteger: set_Pr1281608226676607948nteger > set_Pr1281608226676607948nteger > $o).
% 18.75/7.46 thf(func_def_1815, type, ord_le4763372923235995152et_nat: set_Pr8536935166611901872et_nat > set_Pr8536935166611901872et_nat > $o).
% 18.75/7.46 thf(func_def_1816, type, ord_le5966269811547037844et_nat: set_Pr3286484037609594932et_nat > set_Pr3286484037609594932et_nat > $o).
% 18.75/7.46 thf(func_def_1817, type, ord_le8725513860283290265nt_int: set_Pr9222295170931077689nt_int > set_Pr9222295170931077689nt_int > $o).
% 18.75/7.46 thf(func_def_1818, type, ord_le192195778054999463od_o_o: set_Product_prod_o_o > set_Product_prod_o_o > $o).
% 18.75/7.46 thf(func_def_1819, type, ord_le3982295392052344841_o_int: set_Pr8834758594704517033_o_int > set_Pr8834758594704517033_o_int > $o).
% 18.75/7.46 thf(func_def_1820, type, ord_le6472378536984071597_o_nat: set_Pr2101469702781467981_o_nat > set_Pr2101469702781467981_o_nat > $o).
% 18.75/7.46 thf(func_def_1821, type, ord_le3725938330318615451nteger: set_Pr4811707699266497531nteger > set_Pr4811707699266497531nteger > $o).
% 18.75/7.46 thf(func_def_1822, type, ord_le719211969347571306er_int: set_Pr6496905503482889930er_int > set_Pr6496905503482889930er_int > $o).
% 18.75/7.46 thf(func_def_1823, type, ord_le3209295114279298062er_nat: set_Pr8986988648414616686er_nat > set_Pr8986988648414616686er_nat > $o).
% 18.75/7.46 thf(func_def_1824, type, ord_le6478268328230966961atural: set_Pr7564037697178849041atural > set_Pr7564037697178849041atural > $o).
% 18.75/7.46 thf(func_def_1825, type, ord_le2202040463148982292atural: set_Pr2352657477744078772atural > set_Pr2352657477744078772atural > $o).
% 18.75/7.46 thf(func_def_1826, type, ord_le8090042543978450200et_nat: set_Pr3948176798113811640et_nat > set_Pr3948176798113811640et_nat > $o).
% 18.75/7.46 thf(func_def_1827, type, ord_le5274836691491929335_int_o: set_Pr903927857289325719_int_o > set_Pr903927857289325719_int_o > $o).
% 18.75/7.46 thf(func_def_1828, type, ord_le2638047946463454698nteger: set_Pr8415741480598773322nteger > set_Pr8415741480598773322nteger > $o).
% 18.75/7.46 thf(func_def_1829, type, ord_le2843351958646193337nt_int: set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int > $o).
% 18.75/7.46 thf(func_def_1830, type, ord_le5333435103577920093nt_nat: set_Pr3448869479623346877nt_nat > set_Pr3448869479623346877nt_nat > $o).
% 18.75/7.46 thf(func_def_1831, type, ord_le7519981659162375251_nat_o: set_Pr3149072824959771635_nat_o > set_Pr3149072824959771635_nat_o > $o).
% 18.75/7.46 thf(func_def_1832, type, ord_le5852610332322655630nteger: set_Pr2406931829603198446nteger > set_Pr2406931829603198446nteger > $o).
% 18.75/7.46 thf(func_def_1833, type, ord_le656430383953171549at_int: set_Pr7995236796853374141at_int > set_Pr7995236796853374141at_int > $o).
% 18.75/7.46 thf(func_def_1834, type, ord_le3146513528884898305at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o).
% 18.75/7.46 thf(func_def_1835, type, ord_le3050193496395145148at_nat: set_Pr7717912310451564380at_nat > set_Pr7717912310451564380at_nat > $o).
% 18.75/7.46 thf(func_def_1836, type, ord_le3218026494883419554at_nat: set_Pr1625285437083415874at_nat > set_Pr1625285437083415874at_nat > $o).
% 18.75/7.46 thf(func_def_1837, type, ord_le5919393503700438654_nat_o: set_Pr6558897299634722526_nat_o > set_Pr6558897299634722526_nat_o > $o).
% 18.75/7.46 thf(func_def_1838, type, ord_le7094820750414311574at_nat: set_Pr2539167527615954998at_nat > set_Pr2539167527615954998at_nat > $o).
% 18.75/7.46 thf(func_def_1839, type, ord_le2145644191787020796at_nat: set_Pr552903133987017116at_nat > set_Pr552903133987017116at_nat > $o).
% 18.75/7.46 thf(func_def_1840, type, ord_le1268244103169919719at_nat: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o).
% 18.75/7.46 thf(func_def_1841, type, ord_le3507040750410214029t_unit: set_Product_unit > set_Product_unit > $o).
% 18.75/7.46 thf(func_def_1842, type, ord_less_eq_set_rat: set_rat > set_rat > $o).
% 18.75/7.46 thf(func_def_1843, type, ord_le1914454125413604393nteger: set_set_Code_integer > set_set_Code_integer > $o).
% 18.75/7.46 thf(func_def_1844, type, ord_le4403425263959731960et_int: set_set_int > set_set_int > $o).
% 18.75/7.46 thf(func_def_1845, type, ord_le1068707526560357548st_nat: set_set_list_nat > set_set_list_nat > $o).
% 18.75/7.46 thf(func_def_1846, type, ord_le6893508408891458716et_nat: set_set_nat > set_set_nat > $o).
% 18.75/7.46 thf(func_def_1847, type, ord_le2077887516847798113at_nat: set_se7855581050983116737at_nat > set_se7855581050983116737at_nat > $o).
% 18.75/7.46 thf(func_def_1848, type, ord_le3674001228145610605t_unit: set_set_Product_unit > set_set_Product_unit > $o).
% 18.75/7.46 thf(func_def_1849, type, ord_max_Code_integer: code_integer > code_integer > code_integer).
% 18.75/7.46 thf(func_def_1850, type, ord_max_Code_natural: code_natural > code_natural > code_natural).
% 18.75/7.46 thf(func_def_1851, type, ord_max_int: int > int > int).
% 18.75/7.46 thf(func_def_1852, type, ord_max_nat: nat > nat > nat).
% 18.75/7.46 thf(func_def_1853, type, ord_max_rat: rat > rat > rat).
% 18.75/7.46 thf(func_def_1854, type, ord_min_Code_integer: code_integer > code_integer > code_integer).
% 18.75/7.46 thf(func_def_1855, type, ord_min_Code_natural: code_natural > code_natural > code_natural).
% 18.75/7.46 thf(func_def_1856, type, ord_min_int: int > int > int).
% 18.75/7.46 thf(func_def_1857, type, ord_min_nat: nat > nat > nat).
% 18.75/7.46 thf(func_def_1858, type, ord_min_num: num > num > num).
% 18.75/7.46 thf(func_def_1859, type, ord_min_rat: rat > rat > rat).
% 18.75/7.46 thf(func_def_1860, type, ord_min_set_nat: set_nat > set_nat > set_nat).
% 18.75/7.46 thf(func_def_1861, type, top_to6513043852502318900_int_o: (int > option6357759511663192854e_term) > product_prod_int_int > $o).
% 18.75/7.46 thf(func_def_1862, type, top_to8112647782992986859eger_o: (produc6241069584506657477e_term > option6357759511663192854e_term) > produc8923325533196201883nteger > $o).
% 18.75/7.46 thf(func_def_1863, type, top_to7190503160269336793_nat_o: (produc3658429121746597890et_nat > $o) > produc3925858234332021118et_nat > $o).
% 18.75/7.46 thf(func_def_1864, type, top_to2428096842796733269_nat_o: (produc3658429121746597890et_nat > $o) > produc3658429121746597890et_nat > $o).
% 18.75/7.46 thf(func_def_1865, type, top_to6261655714344447806_int_o: (produc8551481072490612790e_term > option6357759511663192854e_term) > product_prod_int_int > $o).
% 18.75/7.46 thf(func_def_1866, type, top_top_nat_nat_o: nat > nat > $o).
% 18.75/7.46 thf(func_def_1867, type, top_to8903224817164384382_nat_o: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o).
% 18.75/7.46 thf(func_def_1868, type, top_top_assn: assn).
% 18.75/7.46 thf(func_def_1869, type, top_top_option_assn: option_assn).
% 18.75/7.46 thf(func_def_1870, type, top_to4322782652514146083t_unit: option_Product_unit).
% 18.75/7.46 thf(func_def_1871, type, top_to2336371874512884450et_int: option_set_int).
% 18.75/7.46 thf(func_def_1872, type, top_to4826455019444611206et_nat: option_set_nat).
% 18.75/7.46 thf(func_def_1873, type, top_to7662761140297458691t_unit: option8137458692691377843t_unit).
% 18.75/7.46 thf(func_def_1874, type, top_top_Product_unit: product_unit).
% 18.75/7.46 thf(func_def_1875, type, top_to3804862627464599871nteger: set_Co726186806682698383nteger).
% 18.75/7.46 thf(func_def_1876, type, top_top_set_nat_o: set_nat_o).
% 18.75/7.46 thf(func_def_1877, type, top_top_set_o: set_o).
% 18.75/7.46 thf(func_def_1878, type, top_top_set_assn: set_assn).
% 18.75/7.46 thf(func_def_1879, type, top_to4645266643341252675nteger: set_Code_integer).
% 18.75/7.46 thf(func_def_1880, type, top_top_set_int: set_int).
% 18.75/7.46 thf(func_def_1881, type, top_top_set_nat: set_nat).
% 18.75/7.46 thf(func_def_1882, type, top_top_set_num: set_num).
% 18.75/7.46 thf(func_def_1883, type, top_to5929521628599800467nteger: set_op687863988967635939nteger).
% 18.75/7.46 thf(func_def_1884, type, top_to6430115241214627170on_int: set_option_int).
% 18.75/7.46 thf(func_def_1885, type, top_to8920198386146353926on_nat: set_option_nat).
% 18.75/7.46 thf(func_def_1886, type, top_to4635417975585700688on_num: set_option_num).
% 18.75/7.46 thf(func_def_1887, type, top_to7137183367772546234it_nat: set_op3940070208846178154it_nat).
% 18.75/7.46 thf(func_def_1888, type, top_to3251141154256563319at_nat: set_op4508134149509766951at_nat).
% 18.75/7.46 thf(func_def_1889, type, top_to6632602878615679294it_nat: set_op239864471688321678it_nat).
% 18.75/7.46 thf(func_def_1890, type, top_to2690860209552263555t_unit: set_op3165557761946182707t_unit).
% 18.75/7.46 thf(func_def_1891, type, top_to2069137843433766899nt_int: set_Pr1872883991513573699nt_int).
% 18.75/7.46 thf(func_def_1892, type, top_to7512759353274530428nteger: set_Pr1281608226676607948nteger).
% 18.75/7.46 thf(func_def_1893, type, top_to1599102959340997728et_nat: set_Pr8536935166611901872et_nat).
% 18.75/7.46 thf(func_def_1894, type, top_to8753217654552796900et_nat: set_Pr3286484037609594932et_nat).
% 18.75/7.46 thf(func_def_1895, type, top_to3181862456159035625nt_int: set_Pr9222295170931077689nt_int).
% 18.75/7.46 thf(func_def_1896, type, top_to3995162779041354868it_nat: set_Pr5142436192348053284it_nat).
% 18.75/7.46 thf(func_def_1897, type, top_to4366644338036079209nt_int: set_Pr958786334691620121nt_int).
% 18.75/7.46 thf(func_def_1898, type, top_to6856727482967805965nt_nat: set_Pr3448869479623346877nt_nat).
% 18.75/7.46 thf(func_def_1899, type, top_to876157113852465980t_unit: set_Pr5889264611543340172t_unit).
% 18.75/7.46 thf(func_def_1900, type, top_to2179722763343057421at_int: set_Pr7995236796853374141at_int).
% 18.75/7.46 thf(func_def_1901, type, top_to4669805908274784177at_nat: set_Pr1261947904930325089at_nat).
% 18.75/7.46 thf(func_def_1902, type, top_to8544742955230171288t_unit: set_Pr4334478416066269672t_unit).
% 18.75/7.46 thf(func_def_1903, type, top_to3484027333181043534it_int: set_Pr8497134830871917726it_int).
% 18.75/7.46 thf(func_def_1904, type, top_to5974110478112770290it_nat: set_Pr1763845938948868674it_nat).
% 18.75/7.46 thf(func_def_1905, type, top_to4082048134677576814it_nat: set_Pr1354866905816374718it_nat).
% 18.75/7.46 thf(func_def_1906, type, top_to1835807148980544151t_unit: set_Pr5094982260447487303t_unit).
% 18.75/7.46 thf(func_def_1907, type, top_to6833984726390702231at_nat: set_Pr4329608150637261639at_nat).
% 18.75/7.46 thf(func_def_1908, type, top_to1996260823553986621t_unit: set_Product_unit).
% 18.75/7.46 thf(func_def_1909, type, top_top_set_rat: set_rat).
% 18.75/7.46 thf(func_def_1910, type, top_top_set_set_o: set_set_o).
% 18.75/7.46 thf(func_def_1911, type, top_top_set_set_int: set_set_int).
% 18.75/7.46 thf(func_def_1912, type, top_top_set_set_nat: set_set_nat).
% 18.75/7.46 thf(func_def_1913, type, top_to7629004291339433233at_nat: set_se7855581050983116737at_nat).
% 18.75/7.46 thf(func_def_1914, type, top_to1754375979021635447at_nat: set_se5479201105039950375at_nat).
% 18.75/7.46 thf(func_def_1915, type, top_to1767297665138865437t_unit: set_set_Product_unit).
% 18.75/7.46 thf(func_def_1916, type, power_power_assn: assn > nat > assn).
% 18.75/7.46 thf(func_def_1917, type, power_8256067586552552935nteger: code_integer > nat > code_integer).
% 18.75/7.46 thf(func_def_1918, type, power_7079662738309270450atural: code_natural > nat > code_natural).
% 18.75/7.46 thf(func_def_1919, type, power_power_int: int > nat > int).
% 18.75/7.46 thf(func_def_1920, type, power_power_nat: nat > nat > nat).
% 18.75/7.46 thf(func_def_1921, type, power_power_rat: rat > nat > rat).
% 18.75/7.46 thf(func_def_1922, type, produc6137756002093451184nteger: (code_integer > option6357759511663192854e_term) > produc8923325533196201883nteger > produc8763457246119570046nteger).
% 18.75/7.46 thf(func_def_1923, type, produc2252593628808123835atural: (code_natural > option6357759511663192854e_term) > produc7822875418678951345atural > produc8731074985263844745atural).
% 18.75/7.46 thf(func_def_1924, type, produc4510790414113558107e_term: (int > option6357759511663192854e_term) > (int > option6357759511663192854e_term) > produc1945540942535730339e_term).
% 18.75/7.46 thf(func_def_1925, type, produc4305682042979456191nt_int: (int > option6357759511663192854e_term) > product_prod_int_int > produc7773217078559923341nt_int).
% 18.75/7.46 thf(func_def_1926, type, produc3209952032786966637at_nat: (nat > nat > nat) > produc7248412053542808358at_nat > produc4471711990508489141at_nat).
% 18.75/7.46 thf(func_def_1927, type, produc5701653931590357335_nat_o: (nat > $o) > (nat > $o) > produc7360885484439884007_nat_o).
% 18.75/7.46 thf(func_def_1928, type, produc6915061378690470669e_term: (produc6241069584506657477e_term > option6357759511663192854e_term) > (produc6241069584506657477e_term > option6357759511663192854e_term) > produc8187290932660736981e_term).
% 18.75/7.46 thf(func_def_1929, type, produc8603105652947943368nteger: (produc6241069584506657477e_term > option6357759511663192854e_term) > produc8923325533196201883nteger > produc1908205239877642774nteger).
% 18.75/7.46 thf(func_def_1930, type, produc3831813291587773865atural: (produc4972180933644002618e_term > option6357759511663192854e_term) > produc7822875418678951345atural > produc989692990947075319atural).
% 18.75/7.46 thf(func_def_1931, type, produc7368190662567826135_nat_o: (produc3658429121746597890et_nat > $o) > (produc3658429121746597890et_nat > $o) > produc4928098042776334183_nat_o).
% 18.75/7.46 thf(func_def_1932, type, produc2245416461498447860et_nat: (produc3658429121746597890et_nat > $o) > produc3925858234332021118et_nat > produc2732055786443039994et_nat).
% 18.75/7.46 thf(func_def_1933, type, produc5001842942810119800et_nat: (produc3658429121746597890et_nat > $o) > produc3658429121746597890et_nat > produc3925858234332021118et_nat).
% 18.75/7.46 thf(func_def_1934, type, produc8124735558134971759e_term: (produc8551481072490612790e_term > option6357759511663192854e_term) > (produc8551481072490612790e_term > option6357759511663192854e_term) > produc4499399687821757879e_term).
% 18.75/7.46 thf(func_def_1935, type, produc5700946648718959541nt_int: (produc8551481072490612790e_term > option6357759511663192854e_term) > product_prod_int_int > produc2285326912895808259nt_int).
% 18.75/7.46 thf(func_def_1936, type, product_Pair_o_o: $o > $o > product_prod_o_o).
% 18.75/7.46 thf(func_def_1937, type, product_Pair_o_int: $o > int > product_prod_o_int).
% 18.75/7.46 thf(func_def_1938, type, product_Pair_o_nat: $o > nat > product_prod_o_nat).
% 18.75/7.46 thf(func_def_1939, type, produc6677183202524767010eger_o: code_integer > $o > produc6271795597528267376eger_o).
% 18.75/7.46 thf(func_def_1940, type, produc1086072967326762835nteger: code_integer > code_integer > produc8923325533196201883nteger).
% 18.75/7.46 thf(func_def_1941, type, produc8805100893531834658er_int: code_integer > int > produc2256096406371053034er_int).
% 18.75/7.46 thf(func_def_1942, type, produc8807591364040884934er_nat: code_integer > nat > produc6433947425880249742er_nat).
% 18.75/7.46 thf(func_def_1943, type, produc3574140220909816553atural: code_natural > code_natural > produc7822875418678951345atural).
% 18.75/7.46 thf(func_def_1944, type, produc6639722614265839536atural: code_natural > produc7822875418678951345atural > produc5835291356934675326atural).
% 18.75/7.46 thf(func_def_1945, type, produc1733996804261680252it_nat: array_a > produc6653097349344004940it_nat > produc6714399278180371524it_nat).
% 18.75/7.46 thf(func_def_1946, type, produc584006145561248582it_nat: heap_e7401611519738050253t_unit > nat > produc6653097349344004940it_nat).
% 18.75/7.46 thf(func_def_1947, type, produc7507926704131184380et_nat: heap_e7401611519738050253t_unit > set_nat > produc3658429121746597890et_nat).
% 18.75/7.46 thf(func_def_1948, type, product_Pair_int_o: int > $o > product_prod_int_o).
% 18.75/7.46 thf(func_def_1949, type, produc220428336201996578nteger: int > code_integer > produc2963269191615333738nteger).
% 18.75/7.46 thf(func_def_1950, type, product_Pair_int_int: int > int > product_prod_int_int).
% 18.75/7.46 thf(func_def_1951, type, product_Pair_int_nat: int > nat > product_prod_int_nat).
% 18.75/7.46 thf(func_def_1952, type, produc4348348721325984599at_nat: multis2468970476368604999at_nat > multis2468970476368604999at_nat > produc4166570645942440679at_nat).
% 18.75/7.46 thf(func_def_1953, type, product_Pair_nat_o: nat > $o > product_prod_nat_o).
% 18.75/7.46 thf(func_def_1954, type, produc9072146812819927750nteger: nat > code_integer > produc2591615631378489102nteger).
% 18.75/7.46 thf(func_def_1955, type, product_Pair_nat_int: nat > int > product_prod_nat_int).
% 18.75/7.46 thf(func_def_1956, type, product_Pair_nat_nat: nat > nat > product_prod_nat_nat).
% 18.75/7.46 thf(func_def_1957, type, product_Pair_nat_num: nat > num > product_prod_nat_num).
% 18.75/7.46 thf(func_def_1958, type, produc3378006678175723489it_nat: nat > option3216581401566546698it_nat > produc2867611627572283311it_nat).
% 18.75/7.46 thf(func_def_1959, type, produc638857205735767105it_nat: nat > option8956607266484857688it_nat > produc3911288613690379145it_nat).
% 18.75/7.46 thf(func_def_1960, type, produc487386426758144856at_nat: nat > product_prod_nat_nat > produc7248412053542808358at_nat).
% 18.75/7.46 thf(func_def_1961, type, produc5463602008962177208at_nat: nat > set_Pr1261947904930325089at_nat > produc3313772616054891654at_nat).
% 18.75/7.46 thf(func_def_1962, type, product_Pair_num_num: num > num > product_prod_num_num).
% 18.75/7.46 thf(func_def_1963, type, produc5950683997804057413e_term: option6357759511663192854e_term > option6357759511663192854e_term > produc6576344331059438605e_term).
% 18.75/7.46 thf(func_def_1964, type, produc8406175334058502835nt_int: produc7773217078559923341nt_int > produc7773217078559923341nt_int > produc2501202720802129403nt_int).
% 18.75/7.46 thf(func_def_1965, type, produc7954516348491987909nteger: produc1908205239877642774nteger > produc1908205239877642774nteger > produc824974754969098637nteger).
% 18.75/7.46 thf(func_def_1966, type, produc1940133919992309389et_nat: produc2732055786443039994et_nat > produc2732055786443039994et_nat > produc5657529347773406293et_nat).
% 18.75/7.46 thf(func_def_1967, type, produc8599840265553166229et_nat: produc3925858234332021118et_nat > produc3925858234332021118et_nat > produc6830853553727218525et_nat).
% 18.75/7.46 thf(func_def_1968, type, produc7601053194514725023nt_int: produc2285326912895808259nt_int > produc2285326912895808259nt_int > produc2432570611225516007nt_int).
% 18.75/7.46 thf(func_def_1969, type, produc4911887526399440471nteger: produc8923325533196201883nteger > produc8923325533196201883nteger > produc3334582477557816039nteger).
% 18.75/7.46 thf(func_def_1970, type, produc1272419604612767874atural: produc7822875418678951345atural > code_natural > produc3981471736659609608atural).
% 18.75/7.46 thf(func_def_1971, type, produc4480994950612372183atural: produc7822875418678951345atural > produc7822875418678951345atural > produc6756470014200349799atural).
% 18.75/7.46 thf(func_def_1972, type, produc8199053930788261021et_nat: produc3658429121746597890et_nat > produc3658429121746597890et_nat > produc8111630337999740517et_nat).
% 18.75/7.46 thf(func_def_1973, type, produc3646306378393792727nt_int: product_prod_int_int > product_prod_int_int > produc1219242969750017639nt_int).
% 18.75/7.46 thf(func_def_1974, type, produc855456346497908590_nat_o: product_prod_nat_nat > $o > produc652263959640188542_nat_o).
% 18.75/7.46 thf(func_def_1975, type, produc6161850002892822231at_nat: product_prod_nat_nat > product_prod_nat_nat > produc859450856879609959at_nat).
% 18.75/7.46 thf(func_def_1976, type, produc8824474337961625893at_nat: produc3313772616054891654at_nat > produc3313772616054891654at_nat > produc2714363965264676845at_nat).
% 18.75/7.46 thf(func_def_1977, type, produc3585720979125124569at_nat: produc366245978424229472at_nat > produc366245978424229472at_nat > produc2087150632810049441at_nat).
% 18.75/7.46 thf(func_def_1978, type, produc2335810615602371415at_nat: produc3843707927480180839at_nat > produc3843707927480180839at_nat > produc1906917888121415911at_nat).
% 18.75/7.46 thf(func_def_1979, type, produc7133225469290080770it_nat: product_unit > produc6653097349344004940it_nat > produc8664842809031399944it_nat).
% 18.75/7.46 thf(func_def_1980, type, produc5838405689764958487_set_o: set_o > set_o > produc7369051934464679207_set_o).
% 18.75/7.46 thf(func_def_1981, type, produc7443773368509356479nteger: set_Code_integer > set_Code_integer > produc6491284506569428743nteger).
% 18.75/7.46 thf(func_def_1982, type, produc6363374080413544029et_int: set_int > set_int > produc2115011035271226405et_int).
% 18.75/7.46 thf(func_def_1983, type, produc4532415448927165861et_nat: set_nat > set_nat > produc7819656566062154093et_nat).
% 18.75/7.46 thf(func_def_1984, type, produc763777882069021527od_o_o: set_Product_prod_o_o > set_Product_prod_o_o > produc2934264451710624999od_o_o).
% 18.75/7.46 thf(func_def_1985, type, produc8517790099723286449at_nat: set_Product_prod_o_o > set_Pr1261947904930325089at_nat > produc732395585841259969at_nat).
% 18.75/7.46 thf(func_def_1986, type, produc5245064249948416855at_nat: set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat > produc4193628355235574503at_nat).
% 18.75/7.46 thf(func_def_1987, type, produc3149970401713881818at_nat: set_Pr1261947904930325089at_nat > nat > produc366245978424229472at_nat).
% 18.75/7.46 thf(func_def_1988, type, produc2922128104949294807at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > produc3843707927480180839at_nat).
% 18.75/7.46 thf(func_def_1989, type, produc9060074326276436823at_nat: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > produc1319942482725812455at_nat).
% 18.75/7.46 thf(func_def_1990, type, produc7462898802507495127at_nat: set_se7855581050983116737at_nat > set_se7855581050983116737at_nat > produc7299876168958306407at_nat).
% 18.75/7.46 thf(func_def_1991, type, produc1318478031590598990nt_int: set_in3461395444621081367e_term > ((int > option6357759511663192854e_term) > set_Pr958786334691620121nt_int) > set_Pr1872883991513573699nt_int).
% 18.75/7.46 thf(func_def_1992, type, produc7256824055837167575nteger: set_Pr7604974323444597168e_term > ((produc6241069584506657477e_term > option6357759511663192854e_term) > set_Pr4811707699266497531nteger) > set_Pr1281608226676607948nteger).
% 18.75/7.46 thf(func_def_1993, type, produc7016705354093686019et_nat: set_Pr4532377907799695533_nat_o > ((produc3658429121746597890et_nat > $o) > set_Pr3286484037609594932et_nat) > set_Pr8536935166611901872et_nat).
% 18.75/7.46 thf(func_def_1994, type, produc8052021730408606599et_nat: set_Pr4532377907799695533_nat_o > ((produc3658429121746597890et_nat > $o) > set_Pr3948176798113811640et_nat) > set_Pr3286484037609594932et_nat).
% 18.75/7.46 thf(func_def_1995, type, produc5808185664642557892nt_int: set_Pr3642885161833720865e_term > ((produc8551481072490612790e_term > option6357759511663192854e_term) > set_Pr958786334691620121nt_int) > set_Pr9222295170931077689nt_int).
% 18.75/7.46 thf(func_def_1996, type, product_Sigma_o_o: set_o > ($o > set_o) > set_Product_prod_o_o).
% 18.75/7.46 thf(func_def_1997, type, product_Sigma_o_int: set_o > ($o > set_int) > set_Pr8834758594704517033_o_int).
% 18.75/7.46 thf(func_def_1998, type, product_Sigma_o_nat: set_o > ($o > set_nat) > set_Pr2101469702781467981_o_nat).
% 18.75/7.46 thf(func_def_1999, type, produc5882431272649516420nteger: set_Code_integer > (code_integer > set_Code_integer) > set_Pr4811707699266497531nteger).
% 18.75/7.46 thf(func_def_2000, type, produc4258167722180586323er_int: set_Code_integer > (code_integer > set_int) > set_Pr6496905503482889930er_int).
% 18.75/7.46 thf(func_def_2001, type, produc4260658192689636599er_nat: set_Code_integer > (code_integer > set_nat) > set_Pr8986988648414616686er_nat).
% 18.75/7.46 thf(func_def_2002, type, produc6231535905537262655atural: set_Code_natural > (code_natural > set_Pr7564037697178849041atural) > set_Pr2352657477744078772atural).
% 18.75/7.46 thf(func_def_2003, type, product_Sigma_int_o: set_int > (int > set_o) > set_Pr903927857289325719_int_o).
% 18.75/7.46 thf(func_def_2004, type, produc4896867201705524051nteger: set_int > (int > set_Code_integer) > set_Pr8415741480598773322nteger).
% 18.75/7.46 thf(func_def_2005, type, produc1453890548195736866nt_int: set_int > (int > set_int) > set_Pr958786334691620121nt_int).
% 18.75/7.46 thf(func_def_2006, type, produc1456381018704787142nt_nat: set_int > (int > set_nat) > set_Pr3448869479623346877nt_nat).
% 18.75/7.46 thf(func_def_2007, type, produc2622961094310184599t_unit: set_int > (int > set_Product_unit) > set_Pr5889264611543340172t_unit).
% 18.75/7.46 thf(func_def_2008, type, produc6850429418872557834st_nat: set_list_nat > (list_nat > set_list_nat) > set_Pr3451248702717554689st_nat).
% 18.75/7.46 thf(func_def_2009, type, produc7466890150575444730at_nat: set_list_nat > (list_nat > set_nat) > set_Pr7549493975000385137at_nat).
% 18.75/7.46 thf(func_def_2010, type, product_Sigma_nat_o: set_nat > (nat > set_o) > set_Pr3149072824959771635_nat_o).
% 18.75/7.46 thf(func_def_2011, type, produc4525213641468679415nteger: set_nat > (nat > set_Code_integer) > set_Pr2406931829603198446nteger).
% 18.75/7.46 thf(func_def_2012, type, produc454536836294682310at_int: set_nat > (nat > set_int) > set_Pr7995236796853374141at_int).
% 18.75/7.46 thf(func_def_2013, type, produc5227933103413159546st_nat: set_nat > (nat > set_list_nat) > set_Pr698032948827214833st_nat).
% 18.75/7.46 thf(func_def_2014, type, produc457027306803732586at_nat: set_nat > (nat > set_nat) > set_Pr1261947904930325089at_nat).
% 18.75/7.46 thf(func_def_2015, type, produc1809337555817847783at_nat: set_nat > (nat > set_Pr1261947904930325089at_nat) > set_Pr7717912310451564380at_nat).
% 18.75/7.46 thf(func_def_2016, type, produc396409126344608333at_nat: set_nat > (nat > set_Pr4329608150637261639at_nat) > set_Pr1625285437083415874at_nat).
% 18.75/7.46 thf(func_def_2017, type, produc5506539147108004339t_unit: set_nat > (nat > set_Product_unit) > set_Pr4334478416066269672t_unit).
% 18.75/7.46 thf(func_def_2018, type, produc8445815324708537221_nat_o: set_Pr3286484037609594932et_nat > (produc3925858234332021118et_nat > set_Pr4532377907799695533_nat_o) > set_Pr7705059561495379578_nat_o).
% 18.75/7.46 thf(func_def_2019, type, produc552098293437506509e_term: set_Pr4811707699266497531nteger > (produc8923325533196201883nteger > set_Pr7604974323444597168e_term) > set_Pr1628540301243981434e_term).
% 18.75/7.46 thf(func_def_2020, type, produc5879417536264718849_nat_o: set_Pr3948176798113811640et_nat > (produc3658429121746597890et_nat > set_Pr4532377907799695533_nat_o) > set_Pr4208978187861016310_nat_o).
% 18.75/7.46 thf(func_def_2021, type, produc4529769248912663762e_term: set_Pr958786334691620121nt_int > (product_prod_int_int > set_in3461395444621081367e_term) > set_Pr9020418513037773311e_term).
% 18.75/7.46 thf(func_def_2022, type, produc5327145186146221532e_term: set_Pr958786334691620121nt_int > (product_prod_int_int > set_Pr3642885161833720865e_term) > set_Pr7309386651551657097e_term).
% 18.75/7.46 thf(func_def_2023, type, produc203973861852599583_nat_o: set_Pr1261947904930325089at_nat > (product_prod_nat_nat > set_o) > set_Pr6558897299634722526_nat_o).
% 18.75/7.46 thf(func_def_2024, type, produc7672662199629908489at_nat: set_Pr1261947904930325089at_nat > (product_prod_nat_nat > set_nat) > set_Pr2539167527615954998at_nat).
% 18.75/7.46 thf(func_def_2025, type, produc1095920968030776047at_nat: set_Pr4329608150637261639at_nat > (produc3843707927480180839at_nat > set_nat) > set_Pr552903133987017116at_nat).
% 18.75/7.46 thf(func_def_2026, type, produc6872886531786962417it_int: set_Product_unit > (product_unit > set_int) > set_Pr8497134830871917726it_int).
% 18.75/7.46 thf(func_def_2027, type, produc6875377002296012693it_nat: set_Product_unit > (product_unit > set_nat) > set_Pr1763845938948868674it_nat).
% 18.75/7.46 thf(func_def_2028, type, produc6121607364029222536t_unit: set_Product_unit > (product_unit > set_Product_unit) > set_Pr5094982260447487303t_unit).
% 18.75/7.46 thf(func_def_2029, type, produc105401717395143638et_nat: set_set_nat > (set_nat > set_set_nat) > set_Pr5488025237498180813et_nat).
% 18.75/7.46 thf(func_def_2030, type, produc7726050920695093128at_nat: set_se7855581050983116737at_nat > (set_Pr1261947904930325089at_nat > set_se7855581050983116737at_nat) > set_Pr4329608150637261639at_nat).
% 18.75/7.46 thf(func_def_2031, type, product_Unity: product_unit).
% 18.75/7.46 thf(func_def_2032, type, produc7131893314732144953nt_int: ((int > option6357759511663192854e_term) > int > option6357759511663192854e_term) > produc7773217078559923341nt_int > produc7773217078559923341nt_int).
% 18.75/7.46 thf(func_def_2033, type, produc6067946493426971951nt_int: ((int > option6357759511663192854e_term) > produc8551481072490612790e_term > option6357759511663192854e_term) > produc7773217078559923341nt_int > produc2285326912895808259nt_int).
% 18.75/7.46 thf(func_def_2034, type, produc2515316116081422825nteger: ((produc6241069584506657477e_term > option6357759511663192854e_term) > produc6241069584506657477e_term > option6357759511663192854e_term) > produc1908205239877642774nteger > produc1908205239877642774nteger).
% 18.75/7.46 thf(func_def_2035, type, produc1442628905706551930et_nat: ((produc3658429121746597890et_nat > $o) > produc3658429121746597890et_nat > $o) > produc2732055786443039994et_nat > produc2732055786443039994et_nat).
% 18.75/7.46 thf(func_def_2036, type, produc3198230245617193214et_nat: ((produc3658429121746597890et_nat > $o) > produc3658429121746597890et_nat > $o) > produc3925858234332021118et_nat > produc3925858234332021118et_nat).
% 18.75/7.46 thf(func_def_2037, type, produc6919319362177967663nt_int: ((produc8551481072490612790e_term > option6357759511663192854e_term) > int > option6357759511663192854e_term) > produc2285326912895808259nt_int > produc7773217078559923341nt_int).
% 18.75/7.46 thf(func_def_2038, type, produc7277921532047535397nt_int: ((produc8551481072490612790e_term > option6357759511663192854e_term) > produc8551481072490612790e_term > option6357759511663192854e_term) > produc2285326912895808259nt_int > produc2285326912895808259nt_int).
% 18.75/7.46 thf(func_def_2039, type, produc3207347198985423705nteger: (code_integer > int > option6357759511663192854e_term) > produc8923325533196201883nteger > produc6237349844158694175nteger).
% 18.75/7.46 thf(func_def_2040, type, produc5167107986097539517nt_int: (code_integer > int > option6357759511663192854e_term) > produc382792921321436433nt_int > produc7773217078559923341nt_int).
% 18.75/7.46 thf(func_def_2041, type, produc7628915689858001394nteger: (code_integer > produc6241069584506657477e_term > option6357759511663192854e_term) > produc8923325533196201883nteger > produc3295550550304853304nteger).
% 18.75/7.46 thf(func_def_2042, type, produc5215714788235631558nteger: (code_integer > produc6241069584506657477e_term > option6357759511663192854e_term) > produc3346328345660746739nteger > produc1908205239877642774nteger).
% 18.75/7.46 thf(func_def_2043, type, produc7528800376889492689nteger: (code_integer > produc3658429121746597890et_nat > $o) > produc8923325533196201883nteger > produc6691574917238108761nteger).
% 18.75/7.46 thf(func_def_2044, type, produc4644964300586701942et_nat: (code_integer > produc3658429121746597890et_nat > $o) > produc8299537390109905600et_nat > produc3925858234332021118et_nat).
% 18.75/7.46 thf(func_def_2045, type, produc7602971101079744739nteger: (code_integer > produc8551481072490612790e_term > option6357759511663192854e_term) > produc8923325533196201883nteger > produc4130039061994950697nteger).
% 18.75/7.46 thf(func_def_2046, type, produc7725767832589379507nt_int: (code_integer > produc8551481072490612790e_term > option6357759511663192854e_term) > produc382792921321436433nt_int > produc2285326912895808259nt_int).
% 18.75/7.46 thf(func_def_2047, type, produc3195571438000033749nteger: (code_integer > code_integer) > produc8923325533196201883nteger > produc8923325533196201883nteger).
% 18.75/7.46 thf(func_def_2048, type, produc8323928115967317034atural: (code_natural > int > option6357759511663192854e_term) > produc5835291356934675326atural > produc5219672859094816389atural).
% 18.75/7.46 thf(func_def_2049, type, produc7347430915296828978nt_int: (code_natural > int > option6357759511663192854e_term) > produc5665947927044467078nt_int > produc7773217078559923341nt_int).
% 18.75/7.46 thf(func_def_2050, type, produc7618241212158389867et_nat: (code_natural > produc3658429121746597890et_nat > $o) > produc5111566536631596683et_nat > produc3925858234332021118et_nat).
% 18.75/7.46 thf(func_def_2051, type, produc4623092060929046819atural: (code_natural > code_natural) > produc5835291356934675326atural > produc5835291356934675326atural).
% 18.75/7.46 thf(func_def_2052, type, produc2895628470685950711rm_int: (int > int > option6357759511663192854e_term) > product_prod_int_int > produc6025053409261769070rm_int).
% 18.75/7.46 thf(func_def_2053, type, produc7862092043137183022nt_int: (int > int > option6357759511663192854e_term) > produc759720530913461378nt_int > produc7773217078559923341nt_int).
% 18.75/7.46 thf(func_def_2054, type, produc7344697412356995344rm_int: (int > produc6241069584506657477e_term > option6357759511663192854e_term) > product_prod_int_int > produc7172142986261921671rm_int).
% 18.75/7.46 thf(func_def_2055, type, produc5502177047915545527nteger: (int > produc6241069584506657477e_term > option6357759511663192854e_term) > produc6162884466328367972nteger > produc1908205239877642774nteger).
% 18.75/7.46 thf(func_def_2056, type, produc1933289243015553937_o_int: (int > produc3658429121746597890et_nat > $o) > product_prod_int_int > produc3776562785724475560_o_int).
% 18.75/7.46 thf(func_def_2057, type, produc5259063908904861543et_nat: (int > produc3658429121746597890et_nat > $o) > produc8065447618272157327et_nat > produc3925858234332021118et_nat).
% 18.75/7.46 thf(func_def_2058, type, produc212012705979908097rm_int: (int > produc8551481072490612790e_term > option6357759511663192854e_term) > product_prod_int_int > produc5577056076408194680rm_int).
% 18.75/7.46 thf(func_def_2059, type, produc9204274687749184420nt_int: (int > produc8551481072490612790e_term > option6357759511663192854e_term) > produc759720530913461378nt_int > produc2285326912895808259nt_int).
% 18.75/7.46 thf(func_def_2060, type, produc2355237562570658114nt_int: (int > int) > product_prod_int_int > product_prod_int_int).
% 18.75/7.46 thf(func_def_2061, type, produc9020447175693601247nteger: (code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger) > produc8923325533196201883nteger > produc5966032636589952099nteger).
% 18.75/7.46 thf(func_def_2062, type, produc6499014454317279255nteger: (code_integer > code_integer) > produc8923325533196201883nteger > produc8923325533196201883nteger).
% 18.75/7.46 thf(func_def_2063, type, produc4047920161794714618e_term: (code_integer > produc8923325533196201883nteger) > produc3295550550304853304nteger > produc1908205239877642774nteger).
% 18.75/7.46 thf(func_def_2064, type, produc7166930624044334813nteger: (code_integer > produc8923325533196201883nteger) > produc8923325533196201883nteger > produc3346328345660746739nteger).
% 18.75/7.46 thf(func_def_2065, type, produc898583841617791278_nat_o: (code_integer > produc3658429121746597890et_nat) > produc6691574917238108761nteger > produc3925858234332021118et_nat).
% 18.75/7.46 thf(func_def_2066, type, produc7246245855585345468nteger: (code_integer > produc3658429121746597890et_nat) > produc8923325533196201883nteger > produc8299537390109905600et_nat).
% 18.75/7.46 thf(func_def_2067, type, produc8992176017387436671e_term: (code_integer > product_prod_int_int) > produc6237349844158694175nteger > produc7773217078559923341nt_int).
% 18.75/7.46 thf(func_def_2068, type, produc6067092816631456265e_term: (code_integer > product_prod_int_int) > produc4130039061994950697nteger > produc2285326912895808259nt_int).
% 18.75/7.46 thf(func_def_2069, type, produc3535056655957556987nteger: (code_integer > product_prod_int_int) > produc8923325533196201883nteger > produc382792921321436433nt_int).
% 18.75/7.46 thf(func_def_2070, type, produc4463282112584876420nt_int: (int > int) > product_prod_int_int > product_prod_int_int).
% 18.75/7.46 thf(func_def_2071, type, produc552091674517523435e_term: (int > produc8923325533196201883nteger) > produc7172142986261921671rm_int > produc1908205239877642774nteger).
% 18.75/7.46 thf(func_def_2072, type, produc2935421404040714269er_int: (int > produc8923325533196201883nteger) > product_prod_int_int > produc6162884466328367972nteger).
% 18.75/7.46 thf(func_def_2073, type, produc3447581998352395295_nat_o: (int > produc3658429121746597890et_nat) > produc3776562785724475560_o_int > produc3925858234332021118et_nat).
% 18.75/7.46 thf(func_def_2074, type, produc9121118195053341018at_int: (int > produc3658429121746597890et_nat) > product_prod_int_int > produc8065447618272157327et_nat).
% 18.75/7.46 thf(func_def_2075, type, produc3260485439724623344e_term: (int > product_prod_int_int) > produc6025053409261769070rm_int > produc7773217078559923341nt_int).
% 18.75/7.46 thf(func_def_2076, type, produc189803804368834042e_term: (int > product_prod_int_int) > produc5577056076408194680rm_int > produc2285326912895808259nt_int).
% 18.75/7.46 thf(func_def_2077, type, produc6100211334659168315nt_int: (int > product_prod_int_int) > product_prod_int_int > produc759720530913461378nt_int).
% 18.75/7.46 thf(func_def_2078, type, produc7418200839687411156nteger: (num > code_integer) > produc7142191362829087448er_num > produc8923325533196201883nteger).
% 18.75/7.46 thf(func_def_2079, type, produc969530845752564945_nat_o: (produc3925858234332021118et_nat > produc3925858234332021118et_nat) > produc2732055786443039994et_nat > produc2732055786443039994et_nat).
% 18.75/7.46 thf(func_def_2080, type, produc1515462096303866701_nat_o: (produc3925858234332021118et_nat > produc3658429121746597890et_nat) > produc2732055786443039994et_nat > produc3925858234332021118et_nat).
% 18.75/7.46 thf(func_def_2081, type, produc717174245515237944e_term: (produc8923325533196201883nteger > produc8923325533196201883nteger) > produc1908205239877642774nteger > produc1908205239877642774nteger).
% 18.75/7.46 thf(func_def_2082, type, produc4464772112783624294atural: (produc7822875418678951345atural > produc7822875418678951345atural) > produc5835291356934675326atural > produc5835291356934675326atural).
% 18.75/7.46 thf(func_def_2083, type, produc1304257963789341151atural: (produc7822875418678951345atural > produc3658429121746597890et_nat) > produc5835291356934675326atural > produc5111566536631596683et_nat).
% 18.75/7.46 thf(func_def_2084, type, produc7977970570655791143e_term: (produc7822875418678951345atural > product_prod_int_int) > produc5219672859094816389atural > produc7773217078559923341nt_int).
% 18.75/7.46 thf(func_def_2085, type, produc5167862320620071534atural: (produc7822875418678951345atural > product_prod_int_int) > produc5835291356934675326atural > produc5665947927044467078nt_int).
% 18.75/7.46 thf(func_def_2086, type, produc7714581247149323085_nat_o: (produc3658429121746597890et_nat > produc3925858234332021118et_nat) > produc3925858234332021118et_nat > produc2732055786443039994et_nat).
% 18.75/7.46 thf(func_def_2087, type, produc8750854537940449737_nat_o: (produc3658429121746597890et_nat > produc3658429121746597890et_nat) > produc3925858234332021118et_nat > produc3925858234332021118et_nat).
% 18.75/7.46 thf(func_def_2088, type, produc7011684061226097695e_term: (product_prod_int_int > product_prod_int_int) > produc7773217078559923341nt_int > produc7773217078559923341nt_int).
% 18.75/7.46 thf(func_def_2089, type, produc4973430039190721449e_term: (product_prod_int_int > product_prod_int_int) > produc2285326912895808259nt_int > produc2285326912895808259nt_int).
% 18.75/7.46 thf(func_def_2090, type, produc9098658269643458507_int_o: (produc7773217078559923341nt_int > $o) > (int > option6357759511663192854e_term) > product_prod_int_int > $o).
% 18.75/7.46 thf(func_def_2091, type, produc1217013493180205570eger_o: (produc1908205239877642774nteger > $o) > (produc6241069584506657477e_term > option6357759511663192854e_term) > produc8923325533196201883nteger > $o).
% 18.75/7.46 thf(func_def_2092, type, produc5101573711933517782_nat_o: (produc2732055786443039994et_nat > $o) > (produc3658429121746597890et_nat > $o) > produc3925858234332021118et_nat > $o).
% 18.75/7.46 thf(func_def_2093, type, produc6216949301066131538_nat_o: (produc3925858234332021118et_nat > $o) > (produc3658429121746597890et_nat > $o) > produc3658429121746597890et_nat > $o).
% 18.75/7.46 thf(func_def_2094, type, produc730925184835016917_int_o: (produc2285326912895808259nt_int > $o) > (produc8551481072490612790e_term > option6357759511663192854e_term) > product_prod_int_int > $o).
% 18.75/7.46 thf(func_def_2095, type, produc1016772743285680337nt_int: (product_prod_int_int > int) > int > int > int).
% 18.75/7.46 thf(func_def_2096, type, produc8249235968001453780nt_int: (product_prod_int_int > product_prod_int_int) > int > int > product_prod_int_int).
% 18.75/7.46 thf(func_def_2097, type, produc3704529784387675049_nat_o: (product_prod_nat_nat > product_prod_nat_nat > $o) > nat > nat > product_prod_nat_nat > $o).
% 18.75/7.46 thf(func_def_2098, type, produc3610074571335452306at_nat: (product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat) > nat > nat > product_prod_nat_nat > product_prod_nat_nat).
% 18.75/7.46 thf(func_def_2099, type, produc8871627978511607229at_nat: (product_prod_nat_nat > nat) > nat > nat > nat).
% 18.75/7.46 thf(func_def_2100, type, produc7926200574084438792nt_int: (int > int > int) > product_prod_int_int > int).
% 18.75/7.46 thf(func_def_2101, type, produc297006045350968285nt_int: (int > int > product_prod_int_int) > product_prod_int_int > product_prod_int_int).
% 18.75/7.46 thf(func_def_2102, type, produc4780622933104268256_nat_o: (nat > nat > product_prod_nat_nat > $o) > product_prod_nat_nat > product_prod_nat_nat > $o).
% 18.75/7.46 thf(func_def_2103, type, produc1854806715440696265at_nat: (nat > nat > product_prod_nat_nat > product_prod_nat_nat) > product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat).
% 18.75/7.46 thf(func_def_2104, type, produc6557683772455589876at_nat: (nat > nat > nat) > product_prod_nat_nat > nat).
% 18.75/7.46 thf(func_def_2105, type, produc2558449545302689196_int_o: ((int > option6357759511663192854e_term) > product_prod_int_int > $o) > produc7773217078559923341nt_int > $o).
% 18.75/7.46 thf(func_def_2106, type, produc5122537100556696953nt_int: ((int > option6357759511663192854e_term) > product_prod_int_int > produc7773217078559923341nt_int) > produc7773217078559923341nt_int > produc7773217078559923341nt_int).
% 18.75/7.46 thf(func_def_2107, type, produc8646739037753556108_set_o: ((int > option6357759511663192854e_term) > product_prod_int_int > set_o) > produc7773217078559923341nt_int > set_o).
% 18.75/7.46 thf(func_def_2108, type, produc4111701587417901774et_int: ((int > option6357759511663192854e_term) > product_prod_int_int > set_int) > produc7773217078559923341nt_int > set_int).
% 18.75/7.46 thf(func_def_2109, type, produc8289552606927098482et_nat: ((int > option6357759511663192854e_term) > product_prod_int_int > set_nat) > produc7773217078559923341nt_int > set_nat).
% 18.75/7.46 thf(func_def_2110, type, produc5154663461364529269at_nat: ((int > option6357759511663192854e_term) > product_prod_int_int > set_Pr1261947904930325089at_nat) > produc7773217078559923341nt_int > set_Pr1261947904930325089at_nat).
% 18.75/7.46 thf(func_def_2111, type, produc2845945524848125740at_o_o: ((nat > $o) > (nat > $o) > $o) > produc7360885484439884007_nat_o > $o).
% 18.75/7.46 thf(func_def_2112, type, produc6253627499356882019eger_o: ((produc6241069584506657477e_term > option6357759511663192854e_term) > produc8923325533196201883nteger > $o) > produc1908205239877642774nteger > $o).
% 18.75/7.46 thf(func_def_2113, type, produc6512950862096126219nteger: ((produc6241069584506657477e_term > option6357759511663192854e_term) > produc8923325533196201883nteger > produc1908205239877642774nteger) > produc1908205239877642774nteger > produc1908205239877642774nteger).
% 18.75/7.46 thf(func_def_2114, type, produc2373554395599118147_set_o: ((produc6241069584506657477e_term > option6357759511663192854e_term) > produc8923325533196201883nteger > set_o) > produc1908205239877642774nteger > set_o).
% 18.75/7.46 thf(func_def_2115, type, produc5700143819190870999et_int: ((produc6241069584506657477e_term > option6357759511663192854e_term) > produc8923325533196201883nteger > set_int) > produc1908205239877642774nteger > set_int).
% 18.75/7.46 thf(func_def_2116, type, produc654622801845291899et_nat: ((produc6241069584506657477e_term > option6357759511663192854e_term) > produc8923325533196201883nteger > set_nat) > produc1908205239877642774nteger > set_nat).
% 18.75/7.46 thf(func_def_2117, type, produc838355143741117751_nat_o: ((produc3658429121746597890et_nat > $o) > produc3925858234332021118et_nat > $o) > produc2732055786443039994et_nat > $o).
% 18.75/7.46 thf(func_def_2118, type, produc2377985495875741467et_nat: ((produc3658429121746597890et_nat > $o) > produc3925858234332021118et_nat > produc2732055786443039994et_nat) > produc2732055786443039994et_nat > produc2732055786443039994et_nat).
% 18.75/7.46 thf(func_def_2119, type, produc1437786849005270451_nat_o: ((produc3658429121746597890et_nat > $o) > produc3658429121746597890et_nat > $o) > produc3925858234332021118et_nat > $o).
% 18.75/7.46 thf(func_def_2120, type, produc4058941399401191971et_nat: ((produc3658429121746597890et_nat > $o) > produc3658429121746597890et_nat > produc3925858234332021118et_nat) > produc3925858234332021118et_nat > produc3925858234332021118et_nat).
% 18.75/7.46 thf(func_def_2121, type, produc7715693535893868691_set_o: ((produc3658429121746597890et_nat > $o) > produc3658429121746597890et_nat > set_o) > produc3925858234332021118et_nat > set_o).
% 18.75/7.46 thf(func_def_2122, type, produc4627640435386541703et_int: ((produc3658429121746597890et_nat > $o) > produc3658429121746597890et_nat > set_int) > produc3925858234332021118et_nat > set_int).
% 18.75/7.46 thf(func_def_2123, type, produc8805491454895738411et_nat: ((produc3658429121746597890et_nat > $o) > produc3658429121746597890et_nat > set_nat) > produc3925858234332021118et_nat > set_nat).
% 18.75/7.46 thf(func_def_2124, type, produc1573362020775583542_int_o: ((produc8551481072490612790e_term > option6357759511663192854e_term) > product_prod_int_int > $o) > produc2285326912895808259nt_int > $o).
% 18.75/7.46 thf(func_def_2125, type, produc8492565224438309093nt_int: ((produc8551481072490612790e_term > option6357759511663192854e_term) > product_prod_int_int > produc2285326912895808259nt_int) > produc2285326912895808259nt_int > produc2285326912895808259nt_int).
% 18.75/7.46 thf(func_def_2126, type, produc2066375834425727024eger_o: (code_integer > code_integer > $o) > produc8923325533196201883nteger > $o).
% 18.75/7.46 thf(func_def_2127, type, produc7469247390737344965nteger: (code_integer > code_integer > code_integer) > produc8923325533196201883nteger > code_integer).
% 18.75/7.46 thf(func_def_2128, type, produc1553301316500091796er_int: (code_integer > code_integer > int) > produc8923325533196201883nteger > int).
% 18.75/7.46 thf(func_def_2129, type, produc1555791787009142072er_nat: (code_integer > code_integer > nat) > produc8923325533196201883nteger > nat).
% 18.75/7.46 thf(func_def_2130, type, produc7336495610019696514er_num: (code_integer > code_integer > num) > produc8923325533196201883nteger > num).
% 18.75/7.46 thf(func_def_2131, type, produc9125791028180074456eger_o: (code_integer > code_integer > produc6271795597528267376eger_o) > produc8923325533196201883nteger > produc6271795597528267376eger_o).
% 18.75/7.46 thf(func_def_2132, type, produc6916734918728496179nteger: (code_integer > code_integer > produc8923325533196201883nteger) > produc8923325533196201883nteger > produc8923325533196201883nteger).
% 18.75/7.46 thf(func_def_2133, type, produc4281629032016041417nteger: (code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger) > produc3346328345660746739nteger > produc8923325533196201883nteger).
% 18.75/7.46 thf(func_def_2134, type, produc8282080750456430313atural: (code_natural > code_natural > produc6756470014200349799atural) > produc7822875418678951345atural > produc6756470014200349799atural).
% 18.75/7.46 thf(func_def_2135, type, produc7358226366420480123ural_o: (code_natural > produc7822875418678951345atural > $o) > produc5835291356934675326atural > $o).
% 18.75/7.46 thf(func_def_2136, type, produc6302656368764539796atural: (code_natural > produc7822875418678951345atural > produc7822875418678951345atural) > produc5835291356934675326atural > produc7822875418678951345atural).
% 18.75/7.46 thf(func_def_2137, type, produc6785097126449100389atural: (code_natural > produc7822875418678951345atural > produc3981471736659609608atural) > produc5835291356934675326atural > produc3981471736659609608atural).
% 18.75/7.46 thf(func_def_2138, type, produc8767961711439910440rray_a: (array_a > produc6653097349344004940it_nat > array_a) > produc6714399278180371524it_nat > array_a).
% 18.75/7.46 thf(func_def_2139, type, produc7016084256669755260t_unit: (array_a > produc6653097349344004940it_nat > heap_e7401611519738050253t_unit) > produc6714399278180371524it_nat > heap_e7401611519738050253t_unit).
% 18.75/7.46 thf(func_def_2140, type, produc6028340861379781217at_nat: (array_a > produc6653097349344004940it_nat > nat) > produc6714399278180371524it_nat > nat).
% 18.75/7.46 thf(func_def_2141, type, produc8915672860170107321it_nat: (array_a > produc6653097349344004940it_nat > option3216581401566546698it_nat) > produc6714399278180371524it_nat > option3216581401566546698it_nat).
% 18.75/7.46 thf(func_def_2142, type, produc3495058329975564393it_nat: (array_a > produc6653097349344004940it_nat > option8956607266484857688it_nat) > produc6714399278180371524it_nat > option8956607266484857688it_nat).
% 18.75/7.46 thf(func_def_2143, type, produc2025300630104146186rray_a: (heap_e7401611519738050253t_unit > nat > array_a) > produc6653097349344004940it_nat > array_a).
% 18.75/7.46 thf(func_def_2144, type, produc9092781844693468442t_unit: (heap_e7401611519738050253t_unit > nat > heap_e7401611519738050253t_unit) > produc6653097349344004940it_nat > heap_e7401611519738050253t_unit).
% 18.75/7.46 thf(func_def_2145, type, produc4278983685114131267at_nat: (heap_e7401611519738050253t_unit > nat > nat) > produc6653097349344004940it_nat > nat).
% 18.75/7.46 thf(func_def_2146, type, produc921929042997482327it_nat: (heap_e7401611519738050253t_unit > nat > option3216581401566546698it_nat) > produc6653097349344004940it_nat > option3216581401566546698it_nat).
% 18.75/7.46 thf(func_def_2147, type, produc7488178964372371019it_nat: (heap_e7401611519738050253t_unit > nat > option8956607266484857688it_nat) > produc6653097349344004940it_nat > option8956607266484857688it_nat).
% 18.75/7.46 thf(func_def_2148, type, produc1863717115126956122t_unit: (heap_e7401611519738050253t_unit > nat > product_unit) > produc6653097349344004940it_nat > product_unit).
% 18.75/7.46 thf(func_def_2149, type, produc4947309494688390418_int_o: (int > int > $o) > product_prod_int_int > $o).
% 18.75/7.46 thf(func_def_2150, type, produc8211389475949308722nt_int: (int > int > int) > product_prod_int_int > int).
% 18.75/7.46 thf(func_def_2151, type, produc4245557441103728435nt_int: (int > int > product_prod_int_int) > product_prod_int_int > product_prod_int_int).
% 18.75/7.46 thf(func_def_2152, type, produc6382697403170970154_nat_o: (list_nat > list_nat > $o) > produc1828647624359046049st_nat > $o).
% 18.75/7.46 thf(func_def_2153, type, produc7308574044827705018_nat_o: (list_nat > nat > $o) > produc1540777390238407569at_nat > $o).
% 18.75/7.46 thf(func_def_2154, type, produc1728318271963197120er_int: (nat > int > produc2256096406371053034er_int) > product_prod_nat_int > produc2256096406371053034er_int).
% 18.75/7.46 thf(func_def_2155, type, produc1486167065449562675at_int: (nat > int > product_prod_nat_int) > product_prod_nat_int > product_prod_nat_int).
% 18.75/7.46 thf(func_def_2156, type, produc5265810065896090426_nat_o: (nat > list_nat > $o) > produc4575160907756185873st_nat > $o).
% 18.75/7.46 thf(func_def_2157, type, produc8739625826339149834_nat_o: (nat > nat > product_prod_nat_nat > $o) > product_prod_nat_nat > product_prod_nat_nat > $o).
% 18.75/7.46 thf(func_def_2158, type, produc27273713700761075at_nat: (nat > nat > product_prod_nat_nat > product_prod_nat_nat) > product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat).
% 18.75/7.46 thf(func_def_2159, type, produc6081775807080527818_nat_o: (nat > nat > $o) > product_prod_nat_nat > $o).
% 18.75/7.46 thf(func_def_2160, type, produc6840382203811409530at_int: (nat > nat > int) > product_prod_nat_nat > int).
% 18.75/7.46 thf(func_def_2161, type, produc2761476792215241774st_nat: (nat > nat > list_nat) > product_prod_nat_nat > list_nat).
% 18.75/7.46 thf(func_def_2162, type, produc6842872674320459806at_nat: (nat > nat > nat) > product_prod_nat_nat > nat).
% 18.75/7.46 thf(func_def_2163, type, produc39701218431283661nteger: (nat > nat > produc8923325533196201883nteger) > product_prod_nat_nat > produc8923325533196201883nteger).
% 18.75/7.46 thf(func_def_2164, type, produc9191653645064861724er_int: (nat > nat > produc2256096406371053034er_int) > product_prod_nat_nat > produc2256096406371053034er_int).
% 18.75/7.46 thf(func_def_2165, type, produc4146132627719282624er_nat: (nat > nat > produc6433947425880249742er_nat) > product_prod_nat_nat > produc6433947425880249742er_nat).
% 18.75/7.46 thf(func_def_2166, type, produc675454393454366620nteger: (nat > nat > produc2963269191615333738nteger) > product_prod_nat_nat > produc2963269191615333738nteger).
% 18.75/7.46 thf(func_def_2167, type, produc3625529712395680143nt_nat: (nat > nat > product_prod_int_nat) > product_prod_nat_nat > product_prod_int_nat).
% 18.75/7.46 thf(func_def_2168, type, produc303800833217521984nteger: (nat > nat > produc2591615631378489102nteger) > product_prod_nat_nat > produc2591615631378489102nteger).
% 18.75/7.46 thf(func_def_2169, type, produc7671697017840204687at_int: (nat > nat > product_prod_nat_int) > product_prod_nat_nat > product_prod_nat_int).
% 18.75/7.46 thf(func_def_2170, type, produc2626176000494625587at_nat: (nat > nat > product_prod_nat_nat) > product_prod_nat_nat > product_prod_nat_nat).
% 18.75/7.46 thf(func_def_2171, type, produc8197505143624133779at_nat: (nat > nat > set_Pr1261947904930325089at_nat) > product_prod_nat_nat > set_Pr1261947904930325089at_nat).
% 18.75/7.46 thf(func_def_2172, type, produc478579273971653890on_num: (nat > num > option_num) > product_prod_nat_num > option_num).
% 18.75/7.46 thf(func_def_2173, type, produc1908958340173245860_nat_o: (nat > set_Pr1261947904930325089at_nat > produc3313772616054891654at_nat > $o) > produc3313772616054891654at_nat > produc3313772616054891654at_nat > $o).
% 18.75/7.46 thf(func_def_2174, type, produc7997411485876045171_nat_o: (nat > set_Pr1261947904930325089at_nat > $o) > produc3313772616054891654at_nat > $o).
% 18.75/7.46 thf(func_def_2175, type, produc9203276081649983901et_nat: (produc3925858234332021118et_nat > (produc3658429121746597890et_nat > $o) > produc2732055786443039994et_nat) > produc4962441903510821572_nat_o > produc2732055786443039994et_nat).
% 18.75/7.46 thf(func_def_2176, type, produc5068368601420144385nteger: (produc8923325533196201883nteger > (produc6241069584506657477e_term > option6357759511663192854e_term) > produc1908205239877642774nteger) > produc998928222018024388e_term > produc1908205239877642774nteger).
% 18.75/7.46 thf(func_def_2177, type, produc1198152457851389869atural: (produc7822875418678951345atural > code_natural > produc5835291356934675326atural) > produc3981471736659609608atural > produc5835291356934675326atural).
% 18.75/7.46 thf(func_def_2178, type, produc5206072795621629085et_nat: (produc3658429121746597890et_nat > (produc3658429121746597890et_nat > $o) > produc3925858234332021118et_nat) > produc6907119039986491712_nat_o > produc3925858234332021118et_nat).
% 18.75/7.46 thf(func_def_2179, type, produc3478612561300218621nt_int: (product_prod_int_int > (int > option6357759511663192854e_term) > produc7773217078559923341nt_int) > produc3832618445565238089e_term > produc7773217078559923341nt_int).
% 18.75/7.46 thf(func_def_2180, type, produc199769199162113789nt_int: (product_prod_int_int > (produc8551481072490612790e_term > option6357759511663192854e_term) > produc2285326912895808259nt_int) > produc1821397396195235155e_term > produc2285326912895808259nt_int).
% 18.75/7.46 thf(func_def_2181, type, produc6590410687421337004_nat_o: (product_prod_nat_nat > product_prod_nat_nat > $o) > produc859450856879609959at_nat > $o).
% 18.75/7.46 thf(func_def_2182, type, produc7830147906768200158_nat_o: (produc3313772616054891654at_nat > produc3313772616054891654at_nat > $o) > produc2714363965264676845at_nat > $o).
% 18.75/7.46 thf(func_def_2183, type, produc8701595406162815018_nat_o: (produc366245978424229472at_nat > produc366245978424229472at_nat > $o) > produc2087150632810049441at_nat > $o).
% 18.75/7.46 thf(func_def_2184, type, produc1561160019221259564_nat_o: (produc3843707927480180839at_nat > produc3843707927480180839at_nat > $o) > produc1906917888121415911at_nat > $o).
% 18.75/7.46 thf(func_def_2185, type, produc6568152436032731486t_unit: (product_unit > produc6653097349344004940it_nat > heap_e7401611519738050253t_unit) > produc8664842809031399944it_nat > heap_e7401611519738050253t_unit).
% 18.75/7.46 thf(func_def_2186, type, produc5629734405777326591at_nat: (product_unit > produc6653097349344004940it_nat > nat) > produc8664842809031399944it_nat > nat).
% 18.75/7.46 thf(func_def_2187, type, produc875294279294635931it_nat: (product_unit > produc6653097349344004940it_nat > option3216581401566546698it_nat) > produc8664842809031399944it_nat > option3216581401566546698it_nat).
% 18.75/7.46 thf(func_def_2188, type, produc1230459020282432263it_nat: (product_unit > produc6653097349344004940it_nat > option8956607266484857688it_nat) > produc8664842809031399944it_nat > option8956607266484857688it_nat).
% 18.75/7.46 thf(func_def_2189, type, produc5075907435489727646t_unit: (product_unit > produc6653097349344004940it_nat > product_unit) > produc8664842809031399944it_nat > product_unit).
% 18.75/7.46 thf(func_def_2190, type, produc6247414631856714078_nat_o: (set_nat > set_nat > $o) > produc7819656566062154093et_nat > $o).
% 18.75/7.46 thf(func_def_2191, type, produc7110675705651593384_nat_o: (set_Pr1261947904930325089at_nat > nat > produc366245978424229472at_nat > $o) > produc366245978424229472at_nat > produc366245978424229472at_nat > $o).
% 18.75/7.46 thf(func_def_2192, type, produc3595121349294487249_nat_o: (set_Pr1261947904930325089at_nat > nat > $o) > produc366245978424229472at_nat > $o).
% 18.75/7.46 thf(func_def_2193, type, produc1971064617671185730_nat_o: (set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > produc3843707927480180839at_nat > $o) > produc3843707927480180839at_nat > produc3843707927480180839at_nat > $o).
% 18.75/7.46 thf(func_def_2194, type, produc410239310623530412_nat_o: (set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o) > produc3843707927480180839at_nat > $o).
% 18.75/7.46 thf(func_def_2195, type, produc3999165221712921880at_int: (set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > int) > produc3843707927480180839at_nat > int).
% 18.75/7.46 thf(func_def_2196, type, produc4001655692221972156at_nat: (set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > nat) > produc3843707927480180839at_nat > nat).
% 18.75/7.46 thf(func_def_2197, type, produc1491100424724016556_nat_o: (set_se7855581050983116737at_nat > set_se7855581050983116737at_nat > $o) > produc7299876168958306407at_nat > $o).
% 18.75/7.46 thf(func_def_2198, type, produc6230002227079971283nt_int: produc7773217078559923341nt_int > int > option6357759511663192854e_term).
% 18.75/7.46 thf(func_def_2199, type, produc6972895793295859523_nat_o: produc7360885484439884007_nat_o > nat > $o).
% 18.75/7.46 thf(func_def_2200, type, produc7822682618958472924nteger: produc1908205239877642774nteger > produc6241069584506657477e_term > option6357759511663192854e_term).
% 18.75/7.46 thf(func_def_2201, type, produc180342877477747464et_nat: produc2732055786443039994et_nat > produc3658429121746597890et_nat > $o).
% 18.75/7.46 thf(func_def_2202, type, produc995936583742144908et_nat: produc3925858234332021118et_nat > produc3658429121746597890et_nat > $o).
% 18.75/7.46 thf(func_def_2203, type, produc6816164490631068361nt_int: produc2285326912895808259nt_int > produc8551481072490612790e_term > option6357759511663192854e_term).
% 18.75/7.46 thf(func_def_2204, type, product_fst_o_o: product_prod_o_o > $o).
% 18.75/7.46 thf(func_def_2205, type, product_fst_o_int: product_prod_o_int > $o).
% 18.75/7.46 thf(func_def_2206, type, product_fst_o_nat: product_prod_o_nat > $o).
% 18.75/7.46 thf(func_def_2207, type, product_fst_o_num: product_prod_o_num > $o).
% 18.75/7.46 thf(func_def_2208, type, produc1440270732834495325it_nat: produc2900562427881843919it_nat > $o).
% 18.75/7.46 thf(func_def_2209, type, produc8508995932063986495nteger: produc8923325533196201883nteger > code_integer).
% 18.75/7.46 thf(func_def_2210, type, produc8630172574501217550er_int: produc2256096406371053034er_int > code_integer).
% 18.75/7.46 thf(func_def_2211, type, produc8632663045010267826er_nat: produc6433947425880249742er_nat > code_integer).
% 18.75/7.46 thf(func_def_2212, type, produc1861665112190112313nteger: produc3346328345660746739nteger > code_integer).
% 18.75/7.46 thf(func_def_2213, type, produc497848011034438852atural: produc5835291356934675326atural > code_natural).
% 18.75/7.46 thf(func_def_2214, type, produc491454361838572648it_nat: produc6714399278180371524it_nat > array_a).
% 18.75/7.46 thf(func_def_2215, type, produc2838810277069100634it_nat: produc6653097349344004940it_nat > heap_e7401611519738050253t_unit).
% 18.75/7.46 thf(func_def_2216, type, product_fst_int_o: product_prod_int_o > int).
% 18.75/7.46 thf(func_def_2217, type, produc45500017171379470nteger: produc2963269191615333738nteger > int).
% 18.75/7.46 thf(func_def_2218, type, product_fst_int_int: product_prod_int_int > int).
% 18.75/7.46 thf(func_def_2219, type, product_fst_int_nat: product_prod_int_nat > int).
% 18.75/7.46 thf(func_def_2220, type, product_fst_int_num: product_prod_int_num > int).
% 18.75/7.46 thf(func_def_2221, type, product_fst_nat_o: product_prod_nat_o > nat).
% 18.75/7.46 thf(func_def_2222, type, produc8897218493789310642nteger: produc2591615631378489102nteger > nat).
% 18.75/7.46 thf(func_def_2223, type, product_fst_nat_int: product_prod_nat_int > nat).
% 18.75/7.46 thf(func_def_2224, type, product_fst_nat_nat: product_prod_nat_nat > nat).
% 18.75/7.46 thf(func_def_2225, type, product_fst_nat_num: product_prod_nat_num > nat).
% 18.75/7.46 thf(func_def_2226, type, produc5854401122675660893it_nat: produc3839731585411834681it_nat > nat).
% 18.75/7.46 thf(func_def_2227, type, product_fst_num_num: product_prod_num_num > num).
% 18.75/7.46 thf(func_def_2228, type, produc1609452848092598666_nat_o: produc4962441903510821572_nat_o > produc3925858234332021118et_nat).
% 18.75/7.46 thf(func_def_2229, type, produc1117956856558811858e_term: produc998928222018024388e_term > produc8923325533196201883nteger).
% 18.75/7.46 thf(func_def_2230, type, produc4353917038236142998atural: produc3981471736659609608atural > produc7822875418678951345atural).
% 18.75/7.46 thf(func_def_2231, type, produc1537665297809786051atural: produc6756470014200349799atural > produc7822875418678951345atural).
% 18.75/7.46 thf(func_def_2232, type, produc8046704426453032966_nat_o: produc6907119039986491712_nat_o > produc3658429121746597890et_nat).
% 18.75/7.46 thf(func_def_2233, type, produc217921407547260247e_term: produc3832618445565238089e_term > product_prod_int_int).
% 18.75/7.46 thf(func_def_2234, type, produc6335124012134732001e_term: produc1821397396195235155e_term > product_prod_int_int).
% 18.75/7.46 thf(func_def_2235, type, produc1179527155093393624at_num: produc9082142974458947146at_num > product_prod_nat_nat).
% 18.75/7.46 thf(func_def_2236, type, produc4530234641508181270it_nat: produc8664842809031399944it_nat > product_unit).
% 18.75/7.46 thf(func_def_2237, type, produc6011863565407846595at_nat: produc3843707927480180839at_nat > set_Pr1261947904930325089at_nat).
% 18.75/7.46 thf(func_def_2238, type, produc3162348030201620241nt_int: produc7773217078559923341nt_int > product_prod_int_int).
% 18.75/7.46 thf(func_def_2239, type, produc6795044007072221829_nat_o: produc7360885484439884007_nat_o > nat > $o).
% 18.75/7.46 thf(func_def_2240, type, produc7856867400915047194nteger: produc1908205239877642774nteger > produc8923325533196201883nteger).
% 18.75/7.46 thf(func_def_2241, type, produc5374455773327741254et_nat: produc2732055786443039994et_nat > produc3925858234332021118et_nat).
% 18.75/7.46 thf(func_def_2242, type, produc4011572625026189258et_nat: produc3925858234332021118et_nat > produc3658429121746597890et_nat).
% 18.75/7.46 thf(func_def_2243, type, produc7328097813583171335nt_int: produc2285326912895808259nt_int > product_prod_int_int).
% 18.75/7.46 thf(func_def_2244, type, product_snd_o_o: product_prod_o_o > $o).
% 18.75/7.46 thf(func_def_2245, type, product_snd_o_int: product_prod_o_int > int).
% 18.75/7.46 thf(func_def_2246, type, product_snd_o_nat: product_prod_o_nat > nat).
% 18.75/7.46 thf(func_def_2247, type, product_snd_o_num: product_prod_o_num > num).
% 18.75/7.46 thf(func_def_2248, type, produc5978051280710547099it_nat: produc2900562427881843919it_nat > produc8664842809031399944it_nat).
% 18.75/7.46 thf(func_def_2249, type, produc6174133586879617921nteger: produc8923325533196201883nteger > code_integer).
% 18.75/7.46 thf(func_def_2250, type, produc1514845087660660048er_int: produc2256096406371053034er_int > int).
% 18.75/7.46 thf(func_def_2251, type, produc1517335558169710324er_nat: produc6433947425880249742er_nat > nat).
% 18.75/7.46 thf(func_def_2252, type, produc7955729907432593271nteger: produc3346328345660746739nteger > produc8923325533196201883nteger).
% 18.75/7.46 thf(func_def_2253, type, produc6591912806276919810atural: produc5835291356934675326atural > produc7822875418678951345atural).
% 18.75/7.46 thf(func_def_2254, type, produc6991280839920081578it_nat: produc6714399278180371524it_nat > produc6653097349344004940it_nat).
% 18.75/7.46 thf(func_def_2255, type, produc2594868675584459928it_nat: produc6653097349344004940it_nat > nat).
% 18.75/7.46 thf(func_def_2256, type, product_snd_int_o: product_prod_int_o > $o).
% 18.75/7.46 thf(func_def_2257, type, produc2153544567185597776nteger: produc2963269191615333738nteger > code_integer).
% 18.75/7.46 thf(func_def_2258, type, product_snd_int_int: product_prod_int_int > int).
% 18.75/7.46 thf(func_def_2259, type, product_snd_int_nat: product_prod_int_nat > nat).
% 18.75/7.46 thf(func_def_2260, type, product_snd_int_num: product_prod_int_num > num).
% 18.75/7.46 thf(func_def_2261, type, product_snd_nat_o: product_prod_nat_o > $o).
% 18.75/7.46 thf(func_def_2262, type, produc1781891006948753140nteger: produc2591615631378489102nteger > code_integer).
% 18.75/7.46 thf(func_def_2263, type, product_snd_nat_int: product_prod_nat_int > int).
% 18.75/7.46 thf(func_def_2264, type, product_snd_nat_nat: product_prod_nat_nat > nat).
% 18.75/7.46 thf(func_def_2265, type, product_snd_nat_num: product_prod_nat_num > num).
% 18.75/7.46 thf(func_def_2266, type, produc8417671938598930591it_nat: produc3839731585411834681it_nat > produc8664842809031399944it_nat).
% 18.75/7.46 thf(func_def_2267, type, product_snd_num_num: product_prod_num_num > num).
% 18.75/7.46 thf(func_def_2268, type, produc6803565743942592456_nat_o: produc4962441903510821572_nat_o > produc3658429121746597890et_nat > $o).
% 18.75/7.46 thf(func_def_2269, type, produc1152141638515386128e_term: produc998928222018024388e_term > produc6241069584506657477e_term > option6357759511663192854e_term).
% 18.75/7.46 thf(func_def_2270, type, produc7455300194457530885atural: produc6756470014200349799atural > produc7822875418678951345atural).
% 18.75/7.46 thf(func_def_2271, type, produc1838968430882301508_nat_o: produc6907119039986491712_nat_o > produc3658429121746597890et_nat > $o).
% 18.75/7.46 thf(func_def_2272, type, produc6373639247523685013e_term: produc3832618445565238089e_term > int > option6357759511663192854e_term).
% 18.75/7.46 thf(func_def_2273, type, produc6847057335086834975e_term: produc1821397396195235155e_term > produc8551481072490612790e_term > option6357759511663192854e_term).
% 18.75/7.46 thf(func_def_2274, type, produc8847702614181477910at_num: produc9082142974458947146at_num > num).
% 18.75/7.46 thf(func_def_2275, type, produc8604850587836428116it_nat: produc8664842809031399944it_nat > produc6653097349344004940it_nat).
% 18.75/7.46 thf(func_def_2276, type, produc2937545259423399429at_nat: produc3843707927480180839at_nat > set_Pr1261947904930325089at_nat).
% 18.75/7.46 thf(func_def_2277, type, produc5538323210962509403atural: (produc7822875418678951345atural > produc5835291356934675326atural) > (code_natural > produc7822875418678951345atural > produc5835291356934675326atural) > produc7822875418678951345atural > produc5835291356934675326atural).
% 18.75/7.46 thf(func_def_2278, type, product_Abs_unit: $o > product_unit).
% 18.75/7.46 thf(func_def_2279, type, product_Rep_unit: product_unit > $o).
% 18.75/7.46 thf(func_def_2280, type, inc_shift: code_natural > code_natural > code_natural).
% 18.75/7.46 thf(func_def_2281, type, iterat8892046348760725948atural: code_natural > (code_natural > produc7822875418678951345atural > produc5835291356934675326atural) > code_natural > produc7822875418678951345atural > produc5835291356934675326atural).
% 18.75/7.46 thf(func_def_2282, type, log: code_natural > code_natural > code_natural).
% 18.75/7.46 thf(func_def_2283, type, log_rel: produc7822875418678951345atural > produc7822875418678951345atural > $o).
% 18.75/7.46 thf(func_def_2284, type, minus_shift: code_natural > code_natural > code_natural > code_natural).
% 18.75/7.46 thf(func_def_2285, type, next: produc7822875418678951345atural > produc5835291356934675326atural).
% 18.75/7.46 thf(func_def_2286, type, range: code_natural > produc7822875418678951345atural > produc5835291356934675326atural).
% 18.75/7.46 thf(func_def_2287, type, split_seed: produc7822875418678951345atural > produc6756470014200349799atural).
% 18.75/7.46 thf(func_def_2288, type, abs_Rat: product_prod_int_int > rat).
% 18.75/7.46 thf(func_def_2289, type, fract: int > int > rat).
% 18.75/7.46 thf(func_def_2290, type, frct: product_prod_int_int > rat).
% 18.75/7.46 thf(func_def_2291, type, rep_Rat: rat > product_prod_int_int).
% 18.75/7.46 thf(func_def_2292, type, normalize: product_prod_int_int > product_prod_int_int).
% 18.75/7.46 thf(func_def_2293, type, of_int: int > rat).
% 18.75/7.46 thf(func_def_2294, type, pcr_rat: product_prod_int_int > rat > $o).
% 18.75/7.46 thf(func_def_2295, type, positive: rat > $o).
% 18.75/7.46 thf(func_def_2296, type, quotient_of: rat > product_prod_int_int).
% 18.75/7.46 thf(func_def_2297, type, ratrel: product_prod_int_int > product_prod_int_int > $o).
% 18.75/7.46 thf(func_def_2298, type, ref_change_array_a: (array_a > array_a) > ref_array_a > heap_T6362127782908069795rray_a).
% 18.75/7.46 thf(func_def_2299, type, ref_ch7259622376331601608t_unit: (product_unit > product_unit) > ref_Product_unit > heap_T5738788834812785303t_unit).
% 18.75/7.46 thf(func_def_2300, type, ref_get_array_a: heap_e7401611519738050253t_unit > ref_array_a > array_a).
% 18.75/7.46 thf(func_def_2301, type, ref_get_Product_unit: heap_e7401611519738050253t_unit > ref_Product_unit > product_unit).
% 18.75/7.46 thf(func_def_2302, type, ref_lookup_array_a: ref_array_a > heap_T6362127782908069795rray_a).
% 18.75/7.46 thf(func_def_2303, type, ref_lo7930775386976318366t_unit: ref_Product_unit > heap_T5738788834812785303t_unit).
% 18.75/7.46 thf(func_def_2304, type, ref_set_array_a: ref_array_a > array_a > heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit).
% 18.75/7.46 thf(func_def_2305, type, ref_set_Product_unit: ref_Product_unit > product_unit > heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit).
% 18.75/7.46 thf(func_def_2306, type, refine_Imp_assert: $o > heap_T5738788834812785303t_unit).
% 18.75/7.46 thf(func_def_2307, type, domain452967906960104687nteger: (int > code_integer > $o) > int > $o).
% 18.75/7.46 thf(func_def_2308, type, domainp_int_int: (int > int > $o) > int > $o).
% 18.75/7.46 thf(func_def_2309, type, domain8128281535334753374atural: (nat > code_natural > $o) > nat > $o).
% 18.75/7.46 thf(func_def_2310, type, domainp_nat_nat: (nat > nat > $o) > nat > $o).
% 18.75/7.46 thf(func_def_2311, type, field_o: set_Product_prod_o_o > set_o).
% 18.75/7.46 thf(func_def_2312, type, field_Code_integer: set_Pr4811707699266497531nteger > set_Code_integer).
% 18.75/7.46 thf(func_def_2313, type, field_int: set_Pr958786334691620121nt_int > set_int).
% 18.75/7.46 thf(func_def_2314, type, field_nat: set_Pr1261947904930325089at_nat > set_nat).
% 18.75/7.46 thf(func_def_2315, type, field_4706345496283612622at_nat: set_Pr8693737435421807431at_nat > set_Pr1261947904930325089at_nat).
% 18.75/7.46 thf(func_def_2316, type, field_2862844103579723188at_nat: set_Pr5564308138774400199at_nat > set_Pr4329608150637261639at_nat).
% 18.75/7.46 thf(func_def_2317, type, field_3145993188331922222at_nat: set_Pr4329608150637261639at_nat > set_se7855581050983116737at_nat).
% 18.75/7.46 thf(func_def_2318, type, id_on_o: set_o > set_Product_prod_o_o).
% 18.75/7.46 thf(func_def_2319, type, id_on_int: set_int > set_Pr958786334691620121nt_int).
% 18.75/7.46 thf(func_def_2320, type, id_on_nat: set_nat > set_Pr1261947904930325089at_nat).
% 18.75/7.46 thf(func_def_2321, type, id_on_2554058798563519774at_nat: set_Pr1261947904930325089at_nat > set_Pr8693737435421807431at_nat).
% 18.75/7.46 thf(func_def_2322, type, id_on_7869290023980668164at_nat: set_Pr4329608150637261639at_nat > set_Pr5564308138774400199at_nat).
% 18.75/7.46 thf(func_def_2323, type, id_on_6713504163309144702at_nat: set_se7855581050983116737at_nat > set_Pr4329608150637261639at_nat).
% 18.75/7.46 thf(func_def_2324, type, inv_image_nat_nat: set_Pr1261947904930325089at_nat > (nat > nat) > set_Pr1261947904930325089at_nat).
% 18.75/7.46 thf(func_def_2325, type, inv_im6750873321330482877at_nat: set_Pr1261947904930325089at_nat > (set_Pr1261947904930325089at_nat > nat) > set_Pr4329608150637261639at_nat).
% 18.75/7.46 thf(func_def_2326, type, inv_im4437241714082187487at_nat: set_Pr4329608150637261639at_nat > (nat > set_Pr1261947904930325089at_nat) > set_Pr1261947904930325089at_nat).
% 18.75/7.46 thf(func_def_2327, type, inv_im7023619800666061458at_nat: set_Pr4329608150637261639at_nat > (set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat) > set_Pr4329608150637261639at_nat).
% 18.75/7.46 thf(func_def_2328, type, relcom967497705283160040nteger: (int > int > $o) > (int > code_integer > $o) > int > code_integer > $o).
% 18.75/7.46 thf(func_def_2329, type, relcom1729257228895983867atural: (nat > nat > $o) > (nat > code_natural > $o) > nat > code_natural > $o).
% 18.75/7.46 thf(func_def_2330, type, total_on_o: set_o > set_Product_prod_o_o > $o).
% 18.75/7.46 thf(func_def_2331, type, total_on_int: set_int > set_Pr958786334691620121nt_int > $o).
% 18.75/7.46 thf(func_def_2332, type, total_on_nat: set_nat > set_Pr1261947904930325089at_nat > $o).
% 18.75/7.46 thf(func_def_2333, type, total_3592101749530773125at_nat: set_Pr1261947904930325089at_nat > set_Pr8693737435421807431at_nat > $o).
% 18.75/7.46 thf(func_def_2334, type, total_1513685709984341995at_nat: set_Pr4329608150637261639at_nat > set_Pr5564308138774400199at_nat > $o).
% 18.75/7.46 thf(func_def_2335, type, total_7212417256332265445at_nat: set_se7855581050983116737at_nat > set_Pr4329608150637261639at_nat > $o).
% 18.75/7.46 thf(func_def_2336, type, algebr932160517623751201me_int: int > int > $o).
% 18.75/7.46 thf(func_def_2337, type, algebr934650988132801477me_nat: nat > nat > $o).
% 18.75/7.46 thf(func_def_2338, type, divide6298287555418463151nteger: code_integer > code_integer > code_integer).
% 18.75/7.46 thf(func_def_2339, type, divide5121882707175180666atural: code_natural > code_natural > code_natural).
% 18.75/7.46 thf(func_def_2340, type, divide_divide_int: int > int > int).
% 18.75/7.46 thf(func_def_2341, type, divide_divide_nat: nat > nat > nat).
% 18.75/7.46 thf(func_def_2342, type, divide_divide_rat: rat > rat > rat).
% 18.75/7.46 thf(func_def_2343, type, dvd_dvd_assn: assn > assn > $o).
% 18.75/7.46 thf(func_def_2344, type, dvd_dvd_Code_integer: code_integer > code_integer > $o).
% 18.75/7.46 thf(func_def_2345, type, dvd_dvd_Code_natural: code_natural > code_natural > $o).
% 18.75/7.46 thf(func_def_2346, type, dvd_dvd_int: int > int > $o).
% 18.75/7.46 thf(func_def_2347, type, dvd_dvd_nat: nat > nat > $o).
% 18.75/7.46 thf(func_def_2348, type, dvd_dvd_rat: rat > rat > $o).
% 18.75/7.46 thf(func_def_2349, type, modulo364778990260209775nteger: code_integer > code_integer > code_integer).
% 18.75/7.46 thf(func_def_2350, type, modulo8411746178871703098atural: code_natural > code_natural > code_natural).
% 18.75/7.46 thf(func_def_2351, type, modulo_modulo_int: int > int > int).
% 18.75/7.46 thf(func_def_2352, type, modulo_modulo_nat: nat > nat > nat).
% 18.75/7.46 thf(func_def_2353, type, unit_f2748546683901255202or_nat: nat > nat).
% 18.75/7.46 thf(func_def_2354, type, zero_n356916108424825756nteger: $o > code_integer).
% 18.75/7.46 thf(func_def_2355, type, zero_n8403883297036319079atural: $o > code_natural).
% 18.75/7.46 thf(func_def_2356, type, zero_n2684676970156552555ol_int: $o > int).
% 18.75/7.46 thf(func_def_2357, type, zero_n2687167440665602831ol_nat: $o > nat).
% 18.75/7.46 thf(func_def_2358, type, zero_n2052037380579107095ol_rat: $o > rat).
% 18.75/7.46 thf(func_def_2359, type, collec2839945811840875229_nat_o: ((int > produc7360885484439884007_nat_o) > $o) > set_in2553536192574375378_nat_o).
% 18.75/7.46 thf(func_def_2360, type, collec8221555239282056977nteger: ((int > produc8923325533196201883nteger) > $o) > set_in2260935666578096390nteger).
% 18.75/7.46 thf(func_def_2361, type, collec5961276329923387678atural: ((int > produc5835291356934675326atural) > $o) > set_in1345054734626228863atural).
% 18.75/7.46 thf(func_def_2362, type, collec2229320974926845999nt_int: ((int > product_prod_int_int) > $o) > set_in6154042108061588260nt_int).
% 18.75/7.46 thf(func_def_2363, type, collec7299664631084759149nteger: ((nat > produc8923325533196201883nteger) > $o) > set_na3661387095409732706nteger).
% 18.75/7.46 thf(func_def_2364, type, collec3197714919839585474atural: ((nat > produc5835291356934675326atural) > $o) > set_na2454399383705037859atural).
% 18.75/7.46 thf(func_def_2365, type, collec8414850927317488011nt_int: ((nat > product_prod_int_int) > $o) > set_na7251125088705586816nt_int).
% 18.75/7.46 thf(func_def_2366, type, collec492036462967229448nteger: ((product_unit > produc8923325533196201883nteger) > $o) > set_Pr9591959067864425nteger).
% 18.75/7.46 thf(func_def_2367, type, collec3282430933710331751atural: ((product_unit > produc5835291356934675326atural) > $o) > set_Pr7322412474522714716atural).
% 18.75/7.46 thf(func_def_2368, type, collec2513708037538135334nt_int: ((product_unit > product_prod_int_int) > $o) > set_Pr3770298976803184519nt_int).
% 18.75/7.46 thf(func_def_2369, type, collect_o: ($o > $o) > set_o).
% 18.75/7.46 thf(func_def_2370, type, collect_Code_integer: (code_integer > $o) > set_Code_integer).
% 18.75/7.46 thf(func_def_2371, type, collect_int: (int > $o) > set_int).
% 18.75/7.46 thf(func_def_2372, type, collect_list_nat: (list_nat > $o) > set_list_nat).
% 18.75/7.46 thf(func_def_2373, type, collect_nat: (nat > $o) > set_nat).
% 18.75/7.46 thf(func_def_2374, type, collect_num: (num > $o) > set_num).
% 18.75/7.46 thf(func_def_2375, type, collect_option_num: (option_num > $o) > set_option_num).
% 18.75/7.46 thf(func_def_2376, type, collec8141831914148684149it_nat: (option3216581401566546698it_nat > $o) > set_op3940070208846178154it_nat).
% 18.75/7.46 thf(func_def_2377, type, collec5742531119322951597it_nat: (option8956607266484857688it_nat > $o) > set_op239864471688321678it_nat).
% 18.75/7.46 thf(func_def_2378, type, collec506566255779805410nt_int: (produc7773217078559923341nt_int > $o) > set_Pr1872883991513573699nt_int).
% 18.75/7.46 thf(func_def_2379, type, collec5110290359514967890_nat_o: (produc7360885484439884007_nat_o > $o) > set_Pr7909803484932130503_nat_o).
% 18.75/7.46 thf(func_def_2380, type, collec6950949345391930603nteger: (produc1908205239877642774nteger > $o) > set_Pr1281608226676607948nteger).
% 18.75/7.46 thf(func_def_2381, type, collec5543584681430388431et_nat: (produc2732055786443039994et_nat > $o) > set_Pr8536935166611901872et_nat).
% 18.75/7.46 thf(func_def_2382, type, collec1402215087704437587et_nat: (produc3925858234332021118et_nat > $o) > set_Pr3286484037609594932et_nat).
% 18.75/7.46 thf(func_def_2383, type, collec1790188477890212312nt_int: (produc2285326912895808259nt_int > $o) > set_Pr9222295170931077689nt_int).
% 18.75/7.46 thf(func_def_2384, type, collec7766031446232907142nteger: (produc8923325533196201883nteger > $o) > set_Pr4811707699266497531nteger).
% 18.75/7.46 thf(func_def_2385, type, collec1991479681304692691atural: (produc5835291356934675326atural > $o) > set_Pr2352657477744078772atural).
% 18.75/7.46 thf(func_def_2386, type, collec213857154873943460nt_int: (product_prod_int_int > $o) > set_Pr958786334691620121nt_int).
% 18.75/7.46 thf(func_def_2387, type, collec1570431334306492044st_nat: (produc1828647624359046049st_nat > $o) > set_Pr3451248702717554689st_nat).
% 18.75/7.46 thf(func_def_2388, type, collec8096645339561496572at_nat: (produc1540777390238407569at_nat > $o) > set_Pr7549493975000385137at_nat).
% 18.75/7.46 thf(func_def_2389, type, collec1907656820224499068st_nat: (produc4575160907756185873st_nat > $o) > set_Pr698032948827214833st_nat).
% 18.75/7.46 thf(func_def_2390, type, collec3392354462482085612at_nat: (product_prod_nat_nat > $o) > set_Pr1261947904930325089at_nat).
% 18.75/7.46 thf(func_def_2391, type, collec7088162979684241874at_nat: (produc859450856879609959at_nat > $o) > set_Pr8693737435421807431at_nat).
% 18.75/7.46 thf(func_def_2392, type, collec2088441199205367000at_nat: (produc2714363965264676845at_nat > $o) > set_Pr2072254264782222413at_nat).
% 18.75/7.46 thf(func_def_2393, type, collec1461227866750739596at_nat: (produc2087150632810049441at_nat > $o) > set_Pr5070339090747523585at_nat).
% 18.75/7.46 thf(func_def_2394, type, collec223960383693904210at_nat: (produc1906917888121415911at_nat > $o) > set_Pr5564308138774400199at_nat).
% 18.75/7.46 thf(func_def_2395, type, collec6662362479098859352et_nat: (produc7819656566062154093et_nat > $o) > set_Pr5488025237498180813et_nat).
% 18.75/7.46 thf(func_def_2396, type, collec6321179662152712658at_nat: (produc3843707927480180839at_nat > $o) > set_Pr4329608150637261639at_nat).
% 18.75/7.46 thf(func_def_2397, type, collec2601550354786890194at_nat: (produc7299876168958306407at_nat > $o) > set_Pr1604112560894399303at_nat).
% 18.75/7.46 thf(func_def_2398, type, collect_rat: (rat > $o) > set_rat).
% 18.75/7.46 thf(func_def_2399, type, collec574505750873337192nteger: (set_Code_integer > $o) > set_set_Code_integer).
% 18.75/7.46 thf(func_def_2400, type, collect_set_int: (set_int > $o) > set_set_int).
% 18.75/7.46 thf(func_def_2401, type, collect_set_nat: (set_nat > $o) > set_set_nat).
% 18.75/7.46 thf(func_def_2402, type, collec5514110066124741708at_nat: (set_Pr1261947904930325089at_nat > $o) > set_se7855581050983116737at_nat).
% 18.75/7.46 thf(func_def_2403, type, collec9208119312383884190nteger: (set_set_Code_integer > $o) > set_se8531188866349061887nteger).
% 18.75/7.46 thf(func_def_2404, type, collect_set_set_int: (set_set_int > $o) > set_set_set_int).
% 18.75/7.46 thf(func_def_2405, type, collec4691811733418234273st_nat: (set_set_list_nat > $o) > set_set_set_list_nat).
% 18.75/7.46 thf(func_def_2406, type, collect_set_set_nat: (set_set_nat > $o) > set_set_set_nat).
% 18.75/7.46 thf(func_def_2407, type, collec6698286964019821996at_nat: (set_se7855581050983116737at_nat > $o) > set_se5158245632345848097at_nat).
% 18.75/7.46 thf(func_def_2408, type, collec4600646233855244344t_unit: (set_set_Product_unit > $o) > set_se7118615804146677933t_unit).
% 18.75/7.46 thf(func_def_2409, type, image_7670822187664137143_int_o: (((int > option6357759511663192854e_term) > product_prod_int_int > $o) > produc7773217078559923341nt_int > $o) > set_in8474487674441654202_int_o > set_Pr1425283071195816930_int_o).
% 18.75/7.46 thf(func_def_2410, type, image_5214523798439755767eger_o: (((produc6241069584506657477e_term > option6357759511663192854e_term) > produc8923325533196201883nteger > $o) > produc1908205239877642774nteger > $o) > set_Pr8914822823351560561eger_o > set_Pr606876518868980121eger_o).
% 18.75/7.46 thf(func_def_2411, type, image_1033581555836824229_nat_o: (((produc3658429121746597890et_nat > $o) > produc3925858234332021118et_nat > $o) > produc2732055786443039994et_nat > $o) > set_Pr1457143144315775327_nat_o > set_Pr1230246726286442933_nat_o).
% 18.75/7.46 thf(func_def_2412, type, image_8189751627993580965_nat_o: (((produc3658429121746597890et_nat > $o) > produc3658429121746597890et_nat > $o) > produc3925858234332021118et_nat > $o) > set_Pr8208987589773510107_nat_o > set_Pr8959645425803247153_nat_o).
% 18.75/7.46 thf(func_def_2413, type, image_7631425643974863415_int_o: (((produc8551481072490612790e_term > option6357759511663192854e_term) > product_prod_int_int > $o) > produc2285326912895808259nt_int > $o) > set_Pr5050529186185961540_int_o > set_Pr6358892174463501804_int_o).
% 18.75/7.46 thf(func_def_2414, type, image_7708985414016646955nt_int: ((int > option6357759511663192854e_term) > set_Pr1872883991513573699nt_int) > set_in3461395444621081367e_term > set_se7394616247590735609nt_int).
% 18.75/7.46 thf(func_def_2415, type, image_7429393840292777309_nat_o: ((nat > nat > $o) > product_prod_nat_nat > $o) > set_nat_nat_o > set_Pr5582243495563764594_nat_o).
% 18.75/7.46 thf(func_def_2416, type, image_nat_o_nat_o: ((nat > $o) > nat > $o) > set_nat_o > set_nat_o).
% 18.75/7.46 thf(func_def_2417, type, image_2770089787918713472nt_int: ((produc7773217078559923341nt_int > $o) > set_Pr1872883991513573699nt_int) > set_Pr1425283071195816930_int_o > set_se7394616247590735609nt_int).
% 18.75/7.46 thf(func_def_2418, type, image_2691561895000378432nteger: ((produc1908205239877642774nteger > $o) > set_Pr1281608226676607948nteger) > set_Pr606876518868980121eger_o > set_se124295367203800706nteger).
% 18.75/7.46 thf(func_def_2419, type, image_3321512208570918720et_nat: ((produc2732055786443039994et_nat > $o) > set_Pr8536935166611901872et_nat) > set_Pr1230246726286442933_nat_o > set_se5120235452707311462et_nat).
% 18.75/7.46 thf(func_def_2420, type, image_8138495846740763712et_nat: ((produc3925858234332021118et_nat > $o) > set_Pr3286484037609594932et_nat) > set_Pr8959645425803247153_nat_o > set_se8543413830569400298et_nat).
% 18.75/7.46 thf(func_def_2421, type, image_7643917626522560896nt_int: ((produc2285326912895808259nt_int > $o) > set_Pr9222295170931077689nt_int) > set_Pr6358892174463501804_int_o > set_se2364587433798273647nt_int).
% 18.75/7.46 thf(func_def_2422, type, image_3218922492622835021nteger: ((produc6241069584506657477e_term > option6357759511663192854e_term) > set_Pr1281608226676607948nteger) > set_Pr7604974323444597168e_term > set_se124295367203800706nteger).
% 18.75/7.46 thf(func_def_2423, type, image_4127253568139551288et_nat: ((produc3658429121746597890et_nat > $o) > set_Pr8536935166611901872et_nat) > set_Pr4532377907799695533_nat_o > set_se5120235452707311462et_nat).
% 18.75/7.46 thf(func_def_2424, type, image_1916054815030244540et_nat: ((produc3658429121746597890et_nat > $o) > set_Pr3286484037609594932et_nat) > set_Pr4532377907799695533_nat_o > set_se8543413830569400298et_nat).
% 18.75/7.46 thf(func_def_2425, type, image_5111841350319496619nt_int: ((produc8551481072490612790e_term > option6357759511663192854e_term) > set_Pr9222295170931077689nt_int) > set_Pr3642885161833720865e_term > set_se2364587433798273647nt_int).
% 18.75/7.46 thf(func_def_2426, type, image_7124889717316225246at_nat: ((product_prod_nat_nat > $o) > set_Pr1261947904930325089at_nat) > set_Pr5582243495563764594_nat_o > set_se7855581050983116737at_nat).
% 18.75/7.46 thf(func_def_2427, type, image_4902389024228248874at_nat: ((produc3843707927480180839at_nat > $o) > set_Pr4329608150637261639at_nat) > set_Pr7010166363911110284_nat_o > set_se5479201105039950375at_nat).
% 18.75/7.46 thf(func_def_2428, type, image_6226802281960588479_nat_o: ((set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o) > produc3843707927480180839at_nat > $o) > set_se9180647916752606350_nat_o > set_Pr7010166363911110284_nat_o).
% 18.75/7.46 thf(func_def_2429, type, image_o_o: ($o > $o) > set_o > set_o).
% 18.75/7.46 thf(func_def_2430, type, image_o_int: ($o > int) > set_o > set_int).
% 18.75/7.46 thf(func_def_2431, type, image_o_nat: ($o > nat) > set_o > set_nat).
% 18.75/7.46 thf(func_def_2432, type, image_o_option_o: ($o > option_o) > set_o > set_option_o).
% 18.75/7.46 thf(func_def_2433, type, image_o_option_num: ($o > option_num) > set_o > set_option_num).
% 18.75/7.46 thf(func_def_2434, type, image_5849929686412825643it_nat: ($o > option8956607266484857688it_nat) > set_o > set_op239864471688321678it_nat).
% 18.75/7.46 thf(func_def_2435, type, image_4415570909310888640t_unit: ($o > option_Product_unit) > set_o > set_op3165557761946182707t_unit).
% 18.75/7.46 thf(func_def_2436, type, image_966425688229763753et_nat: ($o > option_set_nat) > set_o > set_option_set_nat).
% 18.75/7.46 thf(func_def_2437, type, image_o_Product_unit: ($o > product_unit) > set_o > set_Product_unit).
% 18.75/7.46 thf(func_def_2438, type, image_6491638074533506790nteger: ($o > set_Code_integer) > set_o > set_set_Code_integer).
% 18.75/7.46 thf(func_def_2439, type, image_o_set_int: ($o > set_int) > set_o > set_set_int).
% 18.75/7.46 thf(func_def_2440, type, image_o_set_nat: ($o > set_nat) > set_o > set_set_nat).
% 18.75/7.46 thf(func_def_2441, type, image_2177946750938214461nteger: (code_integer > code_integer > code_integer) > set_Code_integer > set_Co726186806682698383nteger).
% 18.75/7.46 thf(func_def_2442, type, image_4470545334726330049nteger: (code_integer > code_integer) > set_Code_integer > set_Code_integer).
% 18.75/7.46 thf(func_def_2443, type, image_948535463418740880er_int: (code_integer > int) > set_Code_integer > set_int).
% 18.75/7.46 thf(func_def_2444, type, image_951025933927791156er_nat: (code_integer > nat) > set_Code_integer > set_nat).
% 18.75/7.46 thf(func_def_2445, type, image_8960079959263999889nteger: (code_integer > option_Code_integer) > set_Code_integer > set_op687863988967635939nteger).
% 18.75/7.46 thf(func_def_2446, type, image_7182656606676592809t_unit: (code_integer > product_unit) > set_Code_integer > set_Product_unit).
% 18.75/7.46 thf(func_def_2447, type, image_2291390168754192375nteger: (code_integer > set_Code_integer) > set_Code_integer > set_set_Code_integer).
% 18.75/7.46 thf(func_def_2448, type, image_3530315724569248802atural: (code_natural > set_Pr7564037697178849041atural) > set_Code_natural > set_se3372686590935047281atural).
% 18.75/7.46 thf(func_def_2449, type, image_int_o: (int > $o) > set_int > set_o).
% 18.75/7.46 thf(func_def_2450, type, image_1587234942943678608nteger: (int > code_integer) > set_int > set_Code_integer).
% 18.75/7.46 thf(func_def_2451, type, image_int_int: (int > int) > set_int > set_int).
% 18.75/7.46 thf(func_def_2452, type, image_int_nat: (int > nat) > set_int > set_nat).
% 18.75/7.46 thf(func_def_2453, type, image_int_num: (int > num) > set_int > set_num).
% 18.75/7.46 thf(func_def_2454, type, image_int_option_int: (int > option_int) > set_int > set_option_int).
% 18.75/7.46 thf(func_def_2455, type, image_int_option_num: (int > option_num) > set_int > set_option_num).
% 18.75/7.46 thf(func_def_2456, type, image_7905038228067148555it_nat: (int > option8956607266484857688it_nat) > set_int > set_op239864471688321678it_nat).
% 18.75/7.46 thf(func_def_2457, type, image_1735198859854722016t_unit: (int > option_Product_unit) > set_int > set_op3165557761946182707t_unit).
% 18.75/7.46 thf(func_def_2458, type, image_2293489338514188681et_nat: (int > option_set_nat) > set_int > set_option_set_nat).
% 18.75/7.46 thf(func_def_2459, type, image_259982842891744372_nat_o: (int > produc7360885484439884007_nat_o) > set_int > set_Pr7909803484932130503_nat_o).
% 18.75/7.46 thf(func_def_2460, type, image_5194296484788039592nteger: (int > produc8923325533196201883nteger) > set_int > set_Pr4811707699266497531nteger).
% 18.75/7.46 thf(func_def_2461, type, image_6835604608220425009atural: (int > produc5835291356934675326atural) > set_int > set_Pr2352657477744078772atural).
% 18.75/7.46 thf(func_def_2462, type, image_5705468584675977158nt_int: (int > product_prod_int_int) > set_int > set_Pr958786334691620121nt_int).
% 18.75/7.46 thf(func_def_2463, type, image_5846526143423701914t_unit: (int > product_unit) > set_int > set_Product_unit).
% 18.75/7.46 thf(func_def_2464, type, image_75573793354812870nteger: (int > set_Code_integer) > set_int > set_set_Code_integer).
% 18.75/7.46 thf(func_def_2465, type, image_int_set_int: (int > set_int) > set_int > set_set_int).
% 18.75/7.46 thf(func_def_2466, type, image_int_set_nat: (int > set_nat) > set_int > set_set_nat).
% 18.75/7.46 thf(func_def_2467, type, image_2516384619306764229at_nat: (multis2468970476368604999at_nat > multis2468970476368604999at_nat) > set_mu2057375006010111271at_nat > set_mu2057375006010111271at_nat).
% 18.75/7.46 thf(func_def_2468, type, image_nat_o: (nat > $o) > set_nat > set_o).
% 18.75/7.46 thf(func_def_2469, type, image_1215581382706833972nteger: (nat > code_integer) > set_nat > set_Code_integer).
% 18.75/7.46 thf(func_def_2470, type, image_nat_int: (nat > int) > set_nat > set_int).
% 18.75/7.46 thf(func_def_2471, type, image_nat_nat: (nat > nat) > set_nat > set_nat).
% 18.75/7.46 thf(func_def_2472, type, image_nat_num: (nat > num) > set_nat > set_num).
% 18.75/7.46 thf(func_def_2473, type, image_nat_option_nat: (nat > option_nat) > set_nat > set_option_nat).
% 18.75/7.46 thf(func_def_2474, type, image_nat_option_num: (nat > option_num) > set_nat > set_option_num).
% 18.75/7.46 thf(func_def_2475, type, image_5028743614110135983it_nat: (nat > option8956607266484857688it_nat) > set_nat > set_op239864471688321678it_nat).
% 18.75/7.46 thf(func_def_2476, type, image_1497621718204147004t_unit: (nat > option_Product_unit) > set_nat > set_op3165557761946182707t_unit).
% 18.75/7.46 thf(func_def_2477, type, image_1085372205585808685et_nat: (nat > option_set_nat) > set_nat > set_option_set_nat).
% 18.75/7.46 thf(func_def_2478, type, image_4272405876590741764nteger: (nat > produc8923325533196201883nteger) > set_nat > set_Pr4811707699266497531nteger).
% 18.75/7.46 thf(func_def_2479, type, image_8172478253469051731er_int: (nat > produc2256096406371053034er_int) > set_nat > set_Pr6496905503482889930er_int).
% 18.75/7.46 thf(func_def_2480, type, image_3126957236123472631er_nat: (nat > produc6433947425880249742er_nat) > set_nat > set_Pr8986988648414616686er_nat).
% 18.75/7.46 thf(func_def_2481, type, image_4072043198136622805atural: (nat > produc5835291356934675326atural) > set_nat > set_Pr2352657477744078772atural).
% 18.75/7.46 thf(func_def_2482, type, image_8879651038713332435nteger: (nat > produc2963269191615333738nteger) > set_nat > set_Pr8415741480598773322nteger).
% 18.75/7.46 thf(func_def_2483, type, image_2667626500211843362nt_int: (nat > product_prod_int_int) > set_nat > set_Pr958786334691620121nt_int).
% 18.75/7.46 thf(func_def_2484, type, image_6845477519721040070nt_nat: (nat > product_prod_int_nat) > set_nat > set_Pr3448869479623346877nt_nat).
% 18.75/7.46 thf(func_def_2485, type, image_8507997478476487799nteger: (nat > produc2591615631378489102nteger) > set_nat > set_Pr2406931829603198446nteger).
% 18.75/7.46 thf(func_def_2486, type, image_1668272788310788806at_int: (nat > product_prod_nat_int) > set_nat > set_Pr7995236796853374141at_int).
% 18.75/7.46 thf(func_def_2487, type, image_5846123807819985514at_nat: (nat > product_prod_nat_nat) > set_nat > set_Pr1261947904930325089at_nat).
% 18.75/7.46 thf(func_def_2488, type, image_8730104196221521654t_unit: (nat > product_unit) > set_nat > set_Product_unit).
% 18.75/7.46 thf(func_def_2489, type, image_2385391725447763818nteger: (nat > set_Code_integer) > set_nat > set_set_Code_integer).
% 18.75/7.46 thf(func_def_2490, type, image_nat_set_int: (nat > set_int) > set_nat > set_set_int).
% 18.75/7.46 thf(func_def_2491, type, image_nat_set_nat: (nat > set_nat) > set_nat > set_set_nat).
% 18.75/7.46 thf(func_def_2492, type, image_7178329752028323786at_nat: (nat > set_Pr1261947904930325089at_nat) > set_nat > set_se7855581050983116737at_nat).
% 18.75/7.46 thf(func_def_2493, type, image_1087905878993176368at_nat: (nat > set_Pr4329608150637261639at_nat) > set_nat > set_se5479201105039950375at_nat).
% 18.75/7.46 thf(func_def_2494, type, image_8379761247532268670nteger: (num > code_integer) > set_num > set_Code_integer).
% 18.75/7.46 thf(func_def_2495, type, image_num_num: (num > num) > set_num > set_num).
% 18.75/7.46 thf(func_def_2496, type, image_num_option_num: (num > option_num) > set_num > set_option_num).
% 18.75/7.46 thf(func_def_2497, type, image_option_num_num: (option_num > num) > set_option_num > set_num).
% 18.75/7.46 thf(func_def_2498, type, image_5549452628634654015it_nat: (option3216581401566546698it_nat > produc6714399278180371524it_nat) > set_op3940070208846178154it_nat > set_Pr5142436192348053284it_nat).
% 18.75/7.46 thf(func_def_2499, type, image_1237920015125996135it_nat: (option8956607266484857688it_nat > produc8664842809031399944it_nat) > set_op239864471688321678it_nat > set_Pr1354866905816374718it_nat).
% 18.75/7.46 thf(func_def_2500, type, image_4217645046469565813e_term: (produc7773217078559923341nt_int > int > option6357759511663192854e_term) > set_Pr1872883991513573699nt_int > set_in3461395444621081367e_term).
% 18.75/7.46 thf(func_def_2501, type, image_3108077152341812517nt_int: (produc7773217078559923341nt_int > product_prod_int_int) > set_Pr1872883991513573699nt_int > set_Pr958786334691620121nt_int).
% 18.75/7.46 thf(func_def_2502, type, image_4436781500471753239e_term: (produc1908205239877642774nteger > produc6241069584506657477e_term > option6357759511663192854e_term) > set_Pr1281608226676607948nteger > set_Pr7604974323444597168e_term).
% 18.75/7.46 thf(func_def_2503, type, image_3141030398089242942nteger: (produc1908205239877642774nteger > produc8923325533196201883nteger) > set_Pr1281608226676607948nteger > set_Pr4811707699266497531nteger).
% 18.75/7.46 thf(func_def_2504, type, image_2517677226577294348_nat_o: (produc2732055786443039994et_nat > produc3658429121746597890et_nat > $o) > set_Pr8536935166611901872et_nat > set_Pr4532377907799695533_nat_o).
% 18.75/7.46 thf(func_def_2505, type, image_4557310310409863807et_nat: (produc2732055786443039994et_nat > produc3925858234332021118et_nat) > set_Pr8536935166611901872et_nat > set_Pr3286484037609594932et_nat).
% 18.75/7.46 thf(func_def_2506, type, image_6802380912191114376_nat_o: (produc3925858234332021118et_nat > produc3658429121746597890et_nat > $o) > set_Pr3286484037609594932et_nat > set_Pr4532377907799695533_nat_o).
% 18.75/7.46 thf(func_def_2507, type, image_4390311411407041927et_nat: (produc3925858234332021118et_nat > produc3658429121746597890et_nat) > set_Pr3286484037609594932et_nat > set_Pr3948176798113811640et_nat).
% 18.75/7.46 thf(func_def_2508, type, image_8189767104526903093et_nat: (produc3925858234332021118et_nat > set_Pr8536935166611901872et_nat) > set_Pr3286484037609594932et_nat > set_se5120235452707311462et_nat).
% 18.75/7.46 thf(func_def_2509, type, image_142517975987106933e_term: (produc2285326912895808259nt_int > produc8551481072490612790e_term > option6357759511663192854e_term) > set_Pr9222295170931077689nt_int > set_Pr3642885161833720865e_term).
% 18.75/7.46 thf(func_def_2510, type, image_3915291023682402351nt_int: (produc2285326912895808259nt_int > product_prod_int_int) > set_Pr9222295170931077689nt_int > set_Pr958786334691620121nt_int).
% 18.75/7.46 thf(func_def_2511, type, image_7896445794123959606_o_o_o: (product_prod_o_o > $o) > set_Product_prod_o_o > set_o).
% 18.75/7.46 thf(func_def_2512, type, image_5860565421610830622_int_o: (product_prod_o_int > $o) > set_Pr8834758594704517033_o_int > set_o).
% 18.75/7.46 thf(func_def_2513, type, image_7072963285496371238nt_int: (product_prod_o_int > int) > set_Pr8834758594704517033_o_int > set_int).
% 18.75/7.46 thf(func_def_2514, type, image_8105710389281276538_nat_o: (product_prod_o_nat > $o) > set_Pr2101469702781467981_o_nat > set_o).
% 18.75/7.46 thf(func_def_2515, type, image_4888532181312399726at_nat: (product_prod_o_nat > nat) > set_Pr2101469702781467981_o_nat > set_nat).
% 18.75/7.46 thf(func_def_2516, type, image_8863890952250787504_num_o: (product_prod_o_num > $o) > set_Pr7040061329075590551_o_num > set_o).
% 18.75/7.46 thf(func_def_2517, type, image_5849890305759347266_nat_o: (produc2900562427881843919it_nat > $o) > set_Pr6777250647868329861it_nat > set_o).
% 18.75/7.46 thf(func_def_2518, type, image_6316824473203919795nteger: (produc8923325533196201883nteger > code_integer) > set_Pr4811707699266497531nteger > set_Code_integer).
% 18.75/7.46 thf(func_def_2519, type, image_5715966689554962722nteger: (produc8923325533196201883nteger > set_Pr1281608226676607948nteger) > set_Pr4811707699266497531nteger > set_se124295367203800706nteger).
% 18.75/7.46 thf(func_def_2520, type, image_8194678751871465133atural: (produc5835291356934675326atural > code_natural) > set_Pr2352657477744078772atural > set_Code_natural).
% 18.75/7.46 thf(func_def_2521, type, image_3837677093542026988atural: (produc5835291356934675326atural > produc7822875418678951345atural) > set_Pr2352657477744078772atural > set_Pr7564037697178849041atural).
% 18.75/7.46 thf(func_def_2522, type, image_4799632500972785611it_nat: (produc6714399278180371524it_nat > option3216581401566546698it_nat) > set_Pr5142436192348053284it_nat > set_op3940070208846178154it_nat).
% 18.75/7.46 thf(func_def_2523, type, image_15228131989405757et_nat: (produc3658429121746597890et_nat > set_Pr3286484037609594932et_nat) > set_Pr3948176798113811640et_nat > set_se8543413830569400298et_nat).
% 18.75/7.46 thf(func_def_2524, type, image_5561579847027142576nt_o_o: (product_prod_int_o > $o) > set_Pr903927857289325719_int_o > set_o).
% 18.75/7.46 thf(func_def_2525, type, image_90517134139374612_o_int: (product_prod_int_o > int) > set_Pr903927857289325719_int_o > set_int).
% 18.75/7.46 thf(func_def_2526, type, image_5042161079198086560nt_int: (product_prod_int_int > int) > set_Pr958786334691620121nt_int > set_int).
% 18.75/7.46 thf(func_def_2527, type, image_2653370878348428101nt_int: (product_prod_int_int > product_prod_int_int) > set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int).
% 18.75/7.46 thf(func_def_2528, type, image_5963362749323609783nt_int: (product_prod_int_int > set_Pr1872883991513573699nt_int) > set_Pr958786334691620121nt_int > set_se7394616247590735609nt_int).
% 18.75/7.46 thf(func_def_2529, type, image_815654828163180973nt_int: (product_prod_int_int > set_Pr9222295170931077689nt_int) > set_Pr958786334691620121nt_int > set_se2364587433798273647nt_int).
% 18.75/7.46 thf(func_def_2530, type, image_2855239504505064772at_int: (product_prod_int_nat > int) > set_Pr3448869479623346877nt_nat > set_int).
% 18.75/7.46 thf(func_def_2531, type, image_2857729975014115048at_nat: (product_prod_int_nat > nat) > set_Pr3448869479623346877nt_nat > set_nat).
% 18.75/7.46 thf(func_def_2532, type, image_4873634598471238286um_int: (product_prod_int_num > int) > set_Pr8387461105917469447nt_num > set_int).
% 18.75/7.46 thf(func_def_2533, type, image_7478392465989118804at_o_o: (product_prod_nat_o > $o) > set_Pr3149072824959771635_nat_o > set_o).
% 18.75/7.46 thf(func_def_2534, type, image_8629803608462650132_o_nat: (product_prod_nat_o > nat) > set_Pr3149072824959771635_nat_o > set_nat).
% 18.75/7.46 thf(func_def_2535, type, image_4670507518961241924nt_int: (product_prod_nat_int > int) > set_Pr7995236796853374141at_int > set_int).
% 18.75/7.46 thf(func_def_2536, type, image_4672997989470292200nt_nat: (product_prod_nat_int > nat) > set_Pr7995236796853374141at_int > set_nat).
% 18.75/7.46 thf(func_def_2537, type, image_202211252889950930er_int: (product_prod_nat_int > produc2256096406371053034er_int) > set_Pr7995236796853374141at_int > set_Pr6496905503482889930er_int).
% 18.75/7.46 thf(func_def_2538, type, image_9117352539549038149at_int: (product_prod_nat_int > product_prod_nat_int) > set_Pr7995236796853374141at_int > set_Pr7995236796853374141at_int).
% 18.75/7.46 thf(func_def_2539, type, image_2972642778337070200_nat_o: (product_prod_nat_nat > product_prod_nat_nat > $o) > set_Pr1261947904930325089at_nat > set_Pr5582243495563764594_nat_o).
% 18.75/7.46 thf(func_def_2540, type, image_3693632289388996572_nat_o: (product_prod_nat_nat > $o) > set_Pr1261947904930325089at_nat > set_o).
% 18.75/7.46 thf(func_def_2541, type, image_2483585944268220136at_int: (product_prod_nat_nat > int) > set_Pr1261947904930325089at_nat > set_int).
% 18.75/7.46 thf(func_def_2542, type, image_2486076414777270412at_nat: (product_prod_nat_nat > nat) > set_Pr1261947904930325089at_nat > set_nat).
% 18.75/7.46 thf(func_def_2543, type, image_1023191801488348454on_num: (product_prod_nat_nat > option_num) > set_Pr1261947904930325089at_nat > set_option_num).
% 18.75/7.46 thf(func_def_2544, type, image_4198897800814241419at_nat: (product_prod_nat_nat > option4927543243414619207at_nat) > set_Pr1261947904930325089at_nat > set_op4508134149509766951at_nat).
% 18.75/7.46 thf(func_def_2545, type, image_5755308894823448084it_nat: (product_prod_nat_nat > option8956607266484857688it_nat) > set_Pr1261947904930325089at_nat > set_op239864471688321678it_nat).
% 18.75/7.46 thf(func_def_2546, type, image_7548311901266006551t_unit: (product_prod_nat_nat > option_Product_unit) > set_Pr1261947904930325089at_nat > set_op3165557761946182707t_unit).
% 18.75/7.46 thf(func_def_2547, type, image_7383884694314771602et_nat: (product_prod_nat_nat > option_set_nat) > set_Pr1261947904930325089at_nat > set_option_set_nat).
% 18.75/7.46 thf(func_def_2548, type, image_5669961043262023647nteger: (product_prod_nat_nat > produc8923325533196201883nteger) > set_Pr1261947904930325089at_nat > set_Pr4811707699266497531nteger).
% 18.75/7.46 thf(func_def_2549, type, image_6418031315350042158er_int: (product_prod_nat_nat > produc2256096406371053034er_int) > set_Pr1261947904930325089at_nat > set_Pr6496905503482889930er_int).
% 18.75/7.46 thf(func_def_2550, type, image_1372510298004463058er_nat: (product_prod_nat_nat > produc6433947425880249742er_nat) > set_Pr1261947904930325089at_nat > set_Pr8986988648414616686er_nat).
% 18.75/7.46 thf(func_def_2551, type, image_7125204100594322862nteger: (product_prod_nat_nat > produc2963269191615333738nteger) > set_Pr1261947904930325089at_nat > set_Pr8415741480598773322nteger).
% 18.75/7.46 thf(func_def_2552, type, image_1990417195239315453nt_int: (product_prod_nat_nat > product_prod_int_int) > set_Pr1261947904930325089at_nat > set_Pr958786334691620121nt_int).
% 18.75/7.46 thf(func_def_2553, type, image_6168268214748512161nt_nat: (product_prod_nat_nat > product_prod_int_nat) > set_Pr1261947904930325089at_nat > set_Pr3448869479623346877nt_nat).
% 18.75/7.46 thf(func_def_2554, type, image_6753550540357478226nteger: (product_prod_nat_nat > produc2591615631378489102nteger) > set_Pr1261947904930325089at_nat > set_Pr2406931829603198446nteger).
% 18.75/7.46 thf(func_def_2555, type, image_991063483338260897at_int: (product_prod_nat_nat > product_prod_nat_int) > set_Pr1261947904930325089at_nat > set_Pr7995236796853374141at_int).
% 18.75/7.46 thf(func_def_2556, type, image_5168914502847457605at_nat: (product_prod_nat_nat > product_prod_nat_nat) > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat).
% 18.75/7.46 thf(func_def_2557, type, image_4566292076127975857et_nat: (product_prod_nat_nat > produc7819656566062154093et_nat) > set_Pr1261947904930325089at_nat > set_Pr5488025237498180813et_nat).
% 18.75/7.46 thf(func_def_2558, type, image_6169909464789311569t_unit: (product_prod_nat_nat > product_unit) > set_Pr1261947904930325089at_nat > set_Product_unit).
% 18.75/7.46 thf(func_def_2559, type, image_5061345727057949854et_int: (product_prod_nat_nat > set_int) > set_Pr1261947904930325089at_nat > set_set_int).
% 18.75/7.46 thf(func_def_2560, type, image_15824709712370754et_nat: (product_prod_nat_nat > set_nat) > set_Pr1261947904930325089at_nat > set_set_nat).
% 18.75/7.46 thf(func_def_2561, type, image_5423882813909314213at_nat: (product_prod_nat_nat > set_Pr1261947904930325089at_nat) > set_Pr1261947904930325089at_nat > set_se7855581050983116737at_nat).
% 18.75/7.46 thf(func_def_2562, type, image_4504471508743443926um_nat: (product_prod_nat_num > nat) > set_Pr6200539531224447659at_num > set_nat).
% 18.75/7.46 thf(func_def_2563, type, image_5261730836495542980at_nat: (produc3839731585411834681it_nat > nat) > set_Pr633603713510679705it_nat > set_nat).
% 18.75/7.46 thf(func_def_2564, type, image_7255662321850427333et_nat: (produc4962441903510821572_nat_o > produc2732055786443039994et_nat) > set_Pr7705059561495379578_nat_o > set_Pr8536935166611901872et_nat).
% 18.75/7.46 thf(func_def_2565, type, image_8159590125932948193nteger: (produc998928222018024388e_term > produc1908205239877642774nteger) > set_Pr1628540301243981434e_term > set_Pr1281608226676607948nteger).
% 18.75/7.46 thf(func_def_2566, type, image_4501728140019976901et_nat: (produc6907119039986491712_nat_o > produc3925858234332021118et_nat) > set_Pr4208978187861016310_nat_o > set_Pr3286484037609594932et_nat).
% 18.75/7.46 thf(func_def_2567, type, image_1292712855239066845nt_int: (produc3832618445565238089e_term > produc7773217078559923341nt_int) > set_Pr9020418513037773311e_term > set_Pr1872883991513573699nt_int).
% 18.75/7.46 thf(func_def_2568, type, image_1640129903684976221nt_int: (produc1821397396195235155e_term > produc2285326912895808259nt_int) > set_Pr7309386651551657097e_term > set_Pr9222295170931077689nt_int).
% 18.75/7.46 thf(func_def_2569, type, image_7418169580930627696at_nat: (produc9082142974458947146at_num > product_prod_nat_nat) > set_Pr7477759153910077568at_num > set_Pr1261947904930325089at_nat).
% 18.75/7.46 thf(func_def_2570, type, image_3455408117458022631it_nat: (produc8664842809031399944it_nat > option8956607266484857688it_nat) > set_Pr1354866905816374718it_nat > set_op239864471688321678it_nat).
% 18.75/7.46 thf(func_def_2571, type, image_3500134854233901558_nat_o: (produc3843707927480180839at_nat > $o) > set_Pr4329608150637261639at_nat > set_o).
% 18.75/7.46 thf(func_def_2572, type, image_3196035031069704014at_int: (produc3843707927480180839at_nat > int) > set_Pr4329608150637261639at_nat > set_int).
% 18.75/7.46 thf(func_def_2573, type, image_3198525501578754290at_nat: (produc3843707927480180839at_nat > nat) > set_Pr4329608150637261639at_nat > set_nat).
% 18.75/7.46 thf(func_def_2574, type, image_8464016542990802060on_num: (produc3843707927480180839at_nat > option_num) > set_Pr4329608150637261639at_nat > set_option_num).
% 18.75/7.46 thf(func_def_2575, type, image_140351626946063738it_nat: (produc3843707927480180839at_nat > option8956607266484857688it_nat) > set_Pr4329608150637261639at_nat > set_op239864471688321678it_nat).
% 18.75/7.46 thf(func_def_2576, type, image_8585598761158579761t_unit: (produc3843707927480180839at_nat > option_Product_unit) > set_Pr4329608150637261639at_nat > set_op3165557761946182707t_unit).
% 18.75/7.46 thf(func_def_2577, type, image_934083234596377592et_nat: (produc3843707927480180839at_nat > option_set_nat) > set_Pr4329608150637261639at_nat > set_option_set_nat).
% 18.75/7.46 thf(func_def_2578, type, image_7082456443403096939t_unit: (produc3843707927480180839at_nat > product_unit) > set_Pr4329608150637261639at_nat > set_Product_unit).
% 18.75/7.46 thf(func_def_2579, type, image_3160451284896210088et_nat: (produc3843707927480180839at_nat > set_nat) > set_Pr4329608150637261639at_nat > set_set_nat).
% 18.75/7.46 thf(func_def_2580, type, image_7979982168039674559at_nat: (produc3843707927480180839at_nat > set_Pr1261947904930325089at_nat) > set_Pr4329608150637261639at_nat > set_se7855581050983116737at_nat).
% 18.75/7.46 thf(func_def_2581, type, image_3815118110082124069nteger: (product_unit > code_integer) > set_Product_unit > set_Code_integer).
% 18.75/7.46 thf(func_def_2582, type, image_873079544045703924it_int: (product_unit > int) > set_Product_unit > set_int).
% 18.75/7.46 thf(func_def_2583, type, image_875570014554754200it_nat: (product_unit > nat) > set_Product_unit > set_nat).
% 18.75/7.46 thf(func_def_2584, type, image_5965367930834091826on_num: (product_unit > option_num) > set_Product_unit > set_option_num).
% 18.75/7.46 thf(func_def_2585, type, image_5022536681399171104it_nat: (product_unit > option8956607266484857688it_nat) > set_Product_unit > set_op239864471688321678it_nat).
% 18.75/7.46 thf(func_def_2586, type, image_7094380055901048587t_unit: (product_unit > option_Product_unit) > set_Product_unit > set_op3165557761946182707t_unit).
% 18.75/7.46 thf(func_def_2587, type, image_8089323762101378259nteger: (product_unit > produc8923325533196201883nteger) > set_Product_unit > set_Pr4811707699266497531nteger).
% 18.75/7.46 thf(func_def_2588, type, image_220848230107539526atural: (product_unit > produc5835291356934675326atural) > set_Product_unit > set_Pr2352657477744078772atural).
% 18.75/7.46 thf(func_def_2589, type, image_4103462098156874993nt_int: (product_unit > product_prod_int_int) > set_Product_unit > set_Pr958786334691620121nt_int).
% 18.75/7.46 thf(func_def_2590, type, image_7281959405765017145at_nat: (product_unit > product_prod_nat_nat) > set_Product_unit > set_Pr1261947904930325089at_nat).
% 18.75/7.46 thf(func_def_2591, type, image_405062704495631173t_unit: (product_unit > product_unit) > set_Product_unit > set_Product_unit).
% 18.75/7.46 thf(func_def_2592, type, image_rat_rat: (rat > rat) > set_rat > set_rat).
% 18.75/7.46 thf(func_def_2593, type, image_838307146230912995et_nat: (set_nat > option_set_nat) > set_set_nat > set_option_set_nat).
% 18.75/7.46 thf(func_def_2594, type, image_1744818337813142478_int_o: (set_Pr1872883991513573699nt_int > (int > option6357759511663192854e_term) > product_prod_int_int > $o) > set_se7394616247590735609nt_int > set_in8474487674441654202_int_o).
% 18.75/7.46 thf(func_def_2595, type, image_3377504002992083726eger_o: (set_Pr1281608226676607948nteger > (produc6241069584506657477e_term > option6357759511663192854e_term) > produc8923325533196201883nteger > $o) > set_se124295367203800706nteger > set_Pr8914822823351560561eger_o).
% 18.75/7.46 thf(func_def_2596, type, image_6856364241397052896_nat_o: (set_Pr8536935166611901872et_nat > (produc3658429121746597890et_nat > $o) > produc3925858234332021118et_nat > $o) > set_se5120235452707311462et_nat > set_Pr1457143144315775327_nat_o).
% 18.75/7.46 thf(func_def_2597, type, image_1071233342602175200_nat_o: (set_Pr3286484037609594932et_nat > (produc3658429121746597890et_nat > $o) > produc3658429121746597890et_nat > $o) > set_se8543413830569400298et_nat > set_Pr8208987589773510107_nat_o).
% 18.75/7.46 thf(func_def_2598, type, image_5684251269295653582_int_o: (set_Pr9222295170931077689nt_int > (produc8551481072490612790e_term > option6357759511663192854e_term) > product_prod_int_int > $o) > set_se2364587433798273647nt_int > set_Pr5050529186185961540_int_o).
% 18.75/7.46 thf(func_def_2599, type, image_6923511907955291850_nat_o: (set_Pr1261947904930325089at_nat > nat > nat > $o) > set_se7855581050983116737at_nat > set_nat_nat_o).
% 18.75/7.46 thf(func_def_2600, type, image_6898982319499645995at_nat: (set_Pr1261947904930325089at_nat > set_Pr4329608150637261639at_nat) > set_se7855581050983116737at_nat > set_se5479201105039950375at_nat).
% 18.75/7.46 thf(func_def_2601, type, image_6595146019508340652_nat_o: (set_Pr4329608150637261639at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o) > set_se5479201105039950375at_nat > set_se9180647916752606350_nat_o).
% 18.75/7.46 thf(func_def_2602, type, insert_o: $o > set_o > set_o).
% 18.75/7.46 thf(func_def_2603, type, insert_Code_integer: code_integer > set_Code_integer > set_Code_integer).
% 18.75/7.46 thf(func_def_2604, type, insert_int: int > set_int > set_int).
% 18.75/7.46 thf(func_def_2605, type, insert_list_nat: list_nat > set_list_nat > set_list_nat).
% 18.75/7.46 thf(func_def_2606, type, insert_nat: nat > set_nat > set_nat).
% 18.75/7.46 thf(func_def_2607, type, insert_num: num > set_num > set_num).
% 18.75/7.46 thf(func_def_2608, type, insert_option_o: option_o > set_option_o > set_option_o).
% 18.75/7.46 thf(func_def_2609, type, insert_option_int: option_int > set_option_int > set_option_int).
% 18.75/7.46 thf(func_def_2610, type, insert_option_nat: option_nat > set_option_nat > set_option_nat).
% 18.75/7.46 thf(func_def_2611, type, insert_option_num: option_num > set_option_num > set_option_num).
% 18.75/7.46 thf(func_def_2612, type, insert7468008629046257882it_nat: option3216581401566546698it_nat > set_op3940070208846178154it_nat > set_op3940070208846178154it_nat).
% 18.75/7.46 thf(func_def_2613, type, insert6842972033726296599at_nat: option4927543243414619207at_nat > set_op4508134149509766951at_nat > set_op4508134149509766951at_nat).
% 18.75/7.46 thf(func_def_2614, type, insert2007652293347934600it_nat: option8956607266484857688it_nat > set_op239864471688321678it_nat > set_op239864471688321678it_nat).
% 18.75/7.46 thf(func_def_2615, type, insert6833468608972679677at_nat: option8699557107911914541at_nat > set_op989438649584373901at_nat > set_op989438649584373901at_nat).
% 18.75/7.46 thf(func_def_2616, type, insert2866144167138965411t_unit: option_Product_unit > set_op3165557761946182707t_unit > set_op3165557761946182707t_unit).
% 18.75/7.46 thf(func_def_2617, type, insert6281397740311767046et_nat: option_set_nat > set_option_set_nat > set_option_set_nat).
% 18.75/7.46 thf(func_def_2618, type, insert750232675644355261nt_int: produc7773217078559923341nt_int > set_Pr1872883991513573699nt_int > set_Pr1872883991513573699nt_int).
% 18.75/7.46 thf(func_def_2619, type, insert4245756632806152262nteger: produc1908205239877642774nteger > set_Pr1281608226676607948nteger > set_Pr1281608226676607948nteger).
% 18.75/7.46 thf(func_def_2620, type, insert8297122186708525866et_nat: produc2732055786443039994et_nat > set_Pr8536935166611901872et_nat > set_Pr8536935166611901872et_nat).
% 18.75/7.46 thf(func_def_2621, type, insert3111075074545270702et_nat: produc3925858234332021118et_nat > set_Pr3286484037609594932et_nat > set_Pr3286484037609594932et_nat).
% 18.75/7.46 thf(func_def_2622, type, insert984290209421517107nt_int: produc2285326912895808259nt_int > set_Pr9222295170931077689nt_int > set_Pr9222295170931077689nt_int).
% 18.75/7.46 thf(func_def_2623, type, insert6201435330877294327od_o_o: product_prod_o_o > set_Product_prod_o_o > set_Product_prod_o_o).
% 18.75/7.46 thf(func_def_2624, type, insert3770363720049103139_o_int: product_prod_o_int > set_Pr8834758594704517033_o_int > set_Pr8834758594704517033_o_int).
% 18.75/7.46 thf(func_def_2625, type, insert7948214739558299847_o_nat: product_prod_o_nat > set_Pr2101469702781467981_o_nat > set_Pr2101469702781467981_o_nat).
% 18.75/7.46 thf(func_def_2626, type, insert8656458676507137553_o_num: product_prod_o_num > set_Pr7040061329075590551_o_num > set_Pr7040061329075590551_o_num).
% 18.75/7.46 thf(func_def_2627, type, insert6915099157023601407it_nat: produc2900562427881843919it_nat > set_Pr6777250647868329861it_nat > set_Pr6777250647868329861it_nat).
% 18.75/7.46 thf(func_def_2628, type, insert4913895101485356395nteger: produc8923325533196201883nteger > set_Pr4811707699266497531nteger > set_Pr4811707699266497531nteger).
% 18.75/7.46 thf(func_def_2629, type, insert6505218763252461998atural: produc5835291356934675326atural > set_Pr2352657477744078772atural > set_Pr2352657477744078772atural).
% 18.75/7.46 thf(func_def_2630, type, insert412334881326329105_int_o: product_prod_int_o > set_Pr903927857289325719_int_o > set_Pr903927857289325719_int_o).
% 18.75/7.46 thf(func_def_2631, type, insert5033312907999012233nt_int: product_prod_int_int > set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int).
% 18.75/7.46 thf(func_def_2632, type, insert9211163927508208941nt_nat: product_prod_int_nat > set_Pr3448869479623346877nt_nat > set_Pr3448869479623346877nt_nat).
% 18.75/7.46 thf(func_def_2633, type, insert696035827602270839nt_num: product_prod_int_num > set_Pr8387461105917469447nt_num > set_Pr8387461105917469447nt_num).
% 18.75/7.46 thf(func_def_2634, type, insert2233377226759017069_nat_o: product_prod_nat_o > set_Pr3149072824959771635_nat_o > set_Pr3149072824959771635_nat_o).
% 18.75/7.46 thf(func_def_2635, type, insert4033959196097957677at_int: product_prod_nat_int > set_Pr7995236796853374141at_int > set_Pr7995236796853374141at_int).
% 18.75/7.46 thf(func_def_2636, type, insert8211810215607154385at_nat: product_prod_nat_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat).
% 18.75/7.46 thf(func_def_2637, type, insert8920054152555992091at_num: product_prod_nat_num > set_Pr6200539531224447659at_num > set_Pr6200539531224447659at_num).
% 18.75/7.46 thf(func_def_2638, type, insert2528233410557839625it_nat: produc3839731585411834681it_nat > set_Pr633603713510679705it_nat > set_Pr633603713510679705it_nat).
% 18.75/7.46 thf(func_def_2639, type, insert2126339615020983374_nat_o: produc652263959640188542_nat_o > set_Pr6558897299634722526_nat_o > set_Pr6558897299634722526_nat_o).
% 18.75/7.46 thf(func_def_2640, type, insert2790150385885543546at_num: produc9082142974458947146at_num > set_Pr7477759153910077568at_num > set_Pr7477759153910077568at_num).
% 18.75/7.46 thf(func_def_2641, type, insert5050368324300391991at_nat: produc859450856879609959at_nat > set_Pr8693737435421807431at_nat > set_Pr8693737435421807431at_nat).
% 18.75/7.46 thf(func_def_2642, type, insert398606708087465655at_nat: produc1906917888121415911at_nat > set_Pr5564308138774400199at_nat > set_Pr5564308138774400199at_nat).
% 18.75/7.46 thf(func_def_2643, type, insert5940566491043231800it_nat: produc8664842809031399944it_nat > set_Pr1354866905816374718it_nat > set_Pr1354866905816374718it_nat).
% 18.75/7.46 thf(func_def_2644, type, insert9069300056098147895at_nat: produc3843707927480180839at_nat > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat).
% 18.75/7.46 thf(func_def_2645, type, insert_Product_unit: product_unit > set_Product_unit > set_Product_unit).
% 18.75/7.46 thf(func_def_2646, type, insert_rat: rat > set_rat > set_rat).
% 18.75/7.46 thf(func_def_2647, type, insert9200635055090092081at_nat: set_Pr1261947904930325089at_nat > set_se7855581050983116737at_nat > set_se7855581050983116737at_nat).
% 18.75/7.46 thf(func_def_2648, type, set_fo1959793692361082170t_assn: (nat > assn > assn) > nat > nat > assn > assn).
% 18.75/7.46 thf(func_def_2649, type, set_fo1084959871951514735nteger: (nat > code_integer > code_integer) > nat > nat > code_integer > code_integer).
% 18.75/7.46 thf(func_def_2650, type, set_fo9131927060563008058atural: (nat > code_natural > code_natural) > nat > nat > code_natural > code_natural).
% 18.75/7.46 thf(func_def_2651, type, set_fo2581907887559384638at_int: (nat > int > int) > nat > nat > int > int).
% 18.75/7.46 thf(func_def_2652, type, set_fo4497565046347964853at_nat: (nat > multis2468970476368604999at_nat > multis2468970476368604999at_nat) > nat > nat > multis2468970476368604999at_nat > multis2468970476368604999at_nat).
% 18.75/7.46 thf(func_def_2653, type, set_fo2584398358068434914at_nat: (nat > nat > nat) > nat > nat > nat > nat).
% 18.75/7.46 thf(func_def_2654, type, set_fo1949268297981939178at_rat: (nat > rat > rat) > nat > nat > rat > rat).
% 18.75/7.46 thf(func_def_2655, type, set_fo3699595496184130361el_nat: produc4471711990508489141at_nat > produc4471711990508489141at_nat > $o).
% 18.75/7.46 thf(func_def_2656, type, set_or8904488021354931149Most_o: $o > $o > set_o).
% 18.75/7.46 thf(func_def_2657, type, set_or7959216805967363635t_assn: assn > assn > set_assn).
% 18.75/7.46 thf(func_def_2658, type, set_or189985376899183464nteger: code_integer > code_integer > set_Code_integer).
% 18.75/7.46 thf(func_def_2659, type, set_or1266510415728281911st_int: int > int > set_int).
% 18.75/7.46 thf(func_def_2660, type, set_or1269000886237332187st_nat: nat > nat > set_nat).
% 18.75/7.46 thf(func_def_2661, type, set_or7049704709247886629st_num: num > num > set_num).
% 18.75/7.46 thf(func_def_2662, type, set_or5692540242118139586t_unit: product_unit > product_unit > set_Product_unit).
% 18.75/7.46 thf(func_def_2663, type, set_or633870826150836451st_rat: rat > rat > set_rat).
% 18.75/7.46 thf(func_def_2664, type, set_or266616469461849773_set_o: set_o > set_o > set_set_o).
% 18.75/7.46 thf(func_def_2665, type, set_or370866239135849197et_int: set_int > set_int > set_set_int).
% 18.75/7.46 thf(func_def_2666, type, set_or4548717258645045905et_nat: set_nat > set_nat > set_set_nat).
% 18.75/7.46 thf(func_def_2667, type, set_or2784603332384507286at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_se7855581050983116737at_nat).
% 18.75/7.46 thf(func_def_2668, type, set_or4049648398082403068at_nat: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > set_se5479201105039950375at_nat).
% 18.75/7.46 thf(func_def_2669, type, set_or269330187037242274t_unit: set_Product_unit > set_Product_unit > set_set_Product_unit).
% 18.75/7.46 thf(func_def_2670, type, set_or7139685690850216873Than_o: $o > $o > set_o).
% 18.75/7.46 thf(func_def_2671, type, set_or8404916559141939852nteger: code_integer > code_integer > set_Code_integer).
% 18.75/7.46 thf(func_def_2672, type, set_or4662586982721622107an_int: int > int > set_int).
% 18.75/7.46 thf(func_def_2673, type, set_or4665077453230672383an_nat: nat > nat > set_nat).
% 18.75/7.46 thf(func_def_2674, type, set_or1222409239386451017an_num: num > num > set_num).
% 18.75/7.46 thf(func_def_2675, type, set_or4663484573592751262t_unit: product_unit > product_unit > set_Product_unit).
% 18.75/7.46 thf(func_def_2676, type, set_or4029947393144176647an_rat: rat > rat > set_rat).
% 18.75/7.46 thf(func_def_2677, type, set_or3540276404033026485et_nat: set_nat > set_nat > set_set_nat).
% 18.75/7.46 thf(func_def_2678, type, set_ord_atLeast_nat: nat > set_nat).
% 18.75/7.46 thf(func_def_2679, type, set_ord_atMost_o: $o > set_o).
% 18.75/7.46 thf(func_def_2680, type, set_ord_atMost_assn: assn > set_assn).
% 18.75/7.46 thf(func_def_2681, type, set_or9101266186257409494nteger: code_integer > set_Code_integer).
% 18.75/7.46 thf(func_def_2682, type, set_ord_atMost_int: int > set_int).
% 18.75/7.46 thf(func_def_2683, type, set_ord_atMost_nat: nat > set_nat).
% 18.75/7.46 thf(func_def_2684, type, set_ord_atMost_num: num > set_num).
% 18.75/7.46 thf(func_def_2685, type, set_or8621721900777396692t_unit: product_unit > set_Product_unit).
% 18.75/7.46 thf(func_def_2686, type, set_ord_atMost_rat: rat > set_rat).
% 18.75/7.46 thf(func_def_2687, type, set_ord_atMost_set_o: set_o > set_set_o).
% 18.75/7.46 thf(func_def_2688, type, set_or58775011639299419et_int: set_int > set_set_int).
% 18.75/7.46 thf(func_def_2689, type, set_or4236626031148496127et_nat: set_nat > set_set_nat).
% 18.75/7.46 thf(func_def_2690, type, set_or2762583123196137896at_nat: set_Pr1261947904930325089at_nat > set_se7855581050983116737at_nat).
% 18.75/7.46 thf(func_def_2691, type, set_or4071486571221009422at_nat: set_Pr4329608150637261639at_nat > set_se5479201105039950375at_nat).
% 18.75/7.46 thf(func_def_2692, type, set_or2827140217781692084t_unit: set_Product_unit > set_set_Product_unit).
% 18.75/7.46 thf(func_def_2693, type, set_or2715278749043346189nteger: code_integer > code_integer > set_Code_integer).
% 18.75/7.46 thf(func_def_2694, type, set_or6656581121297822940st_int: int > int > set_int).
% 18.75/7.46 thf(func_def_2695, type, set_or6659071591806873216st_nat: nat > nat > set_nat).
% 18.75/7.46 thf(func_def_2696, type, set_or1716231572884733764Than_o: $o > $o > set_o).
% 18.75/7.46 thf(func_def_2697, type, set_or4266950643985792945nteger: code_integer > code_integer > set_Code_integer).
% 18.75/7.46 thf(func_def_2698, type, set_or5832277885323065728an_int: int > int > set_int).
% 18.75/7.46 thf(func_def_2699, type, set_or5834768355832116004an_nat: nat > nat > set_nat).
% 18.75/7.46 thf(func_def_2700, type, set_or2392100141987894638an_num: num > num > set_num).
% 18.75/7.46 thf(func_def_2701, type, set_or5199638295745620268an_rat: rat > rat > set_rat).
% 18.75/7.46 thf(func_def_2702, type, set_or8625682525731655386et_nat: set_nat > set_nat > set_set_nat).
% 18.75/7.46 thf(func_def_2703, type, set_or1210151606488870762an_nat: nat > set_nat).
% 18.75/7.46 thf(func_def_2704, type, set_ord_lessThan_o: $o > set_o).
% 18.75/7.46 thf(func_def_2705, type, set_or5754767410780653050nteger: code_integer > set_Code_integer).
% 18.75/7.46 thf(func_def_2706, type, set_ord_lessThan_int: int > set_int).
% 18.75/7.46 thf(func_def_2707, type, set_ord_lessThan_nat: nat > set_nat).
% 18.75/7.46 thf(func_def_2708, type, set_ord_lessThan_num: num > set_num).
% 18.75/7.46 thf(func_def_2709, type, set_or8708608758551125680t_unit: product_unit > set_Product_unit).
% 18.75/7.46 thf(func_def_2710, type, set_ord_lessThan_rat: rat > set_rat).
% 18.75/7.46 thf(func_def_2711, type, set_or3489638696441961371_set_o: set_o > set_set_o).
% 18.75/7.46 thf(func_def_2712, type, set_or5935648273017318783et_int: set_int > set_set_int).
% 18.75/7.46 thf(func_def_2713, type, set_or890127255671739683et_nat: set_nat > set_set_nat).
% 18.75/7.46 thf(func_def_2714, type, set_or5243998310507771012at_nat: set_Pr1261947904930325089at_nat > set_se7855581050983116737at_nat).
% 18.75/7.46 thf(func_def_2715, type, set_or2137699863726836970at_nat: set_Pr4329608150637261639at_nat > set_se5479201105039950375at_nat).
% 18.75/7.46 thf(func_def_2716, type, set_or3324826255835560848t_unit: set_Product_unit > set_set_Product_unit).
% 18.75/7.46 thf(func_def_2717, type, char2: $o > $o > $o > $o > $o > $o > $o > $o > char).
% 18.75/7.46 thf(func_def_2718, type, integer_of_char: char > code_integer).
% 18.75/7.46 thf(func_def_2719, type, sum_Inl_nat_nat: nat > sum_sum_nat_nat).
% 18.75/7.46 thf(func_def_2720, type, sum_Inr_nat_nat: nat > sum_sum_nat_nat).
% 18.75/7.46 thf(func_def_2721, type, syntax5678989248478167196nt_int: int > int > $o).
% 18.75/7.46 thf(func_def_2722, type, syntax5084084251851430274at_nat: multis2468970476368604999at_nat > multis2468970476368604999at_nat > $o).
% 18.75/7.46 thf(func_def_2723, type, syntax4682126007086162916at_nat: nat > nat > $o).
% 18.75/7.46 thf(func_def_2724, type, syntax3730441303064801268at_rat: rat > rat > $o).
% 18.75/7.46 thf(func_def_2725, type, time_fails_array_a: heap_T6362127782908069795rray_a > heap_e7401611519738050253t_unit > $o).
% 18.75/7.46 thf(func_def_2726, type, time_f8834461667527620124t_unit: heap_T5738788834812785303t_unit > heap_e7401611519738050253t_unit > $o).
% 18.75/7.46 thf(func_def_2727, type, time_t490086488869527696rray_a: heap_T6362127782908069795rray_a > heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit).
% 18.75/7.46 thf(func_def_2728, type, time_t3350536682685678164t_unit: heap_T5738788834812785303t_unit > heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit).
% 18.75/7.46 thf(func_def_2729, type, time_the_res_array_a: heap_T6362127782908069795rray_a > heap_e7401611519738050253t_unit > array_a).
% 18.75/7.46 thf(func_def_2730, type, time_t2745601220510131320t_unit: heap_T5738788834812785303t_unit > heap_e7401611519738050253t_unit > product_unit).
% 18.75/7.46 thf(func_def_2731, type, time_time_array_a: heap_T6362127782908069795rray_a > heap_e7401611519738050253t_unit > nat).
% 18.75/7.46 thf(func_def_2732, type, time_t4224138285095624986t_unit: heap_T5738788834812785303t_unit > heap_e7401611519738050253t_unit > nat).
% 18.75/7.46 thf(func_def_2733, type, transi2905341329935302413cl_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat).
% 18.75/7.46 thf(func_def_2734, type, transi6264000038957366511cl_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat).
% 18.75/7.46 thf(func_def_2735, type, type_d8366093980585677751er_int: (code_integer > int) > (int > code_integer) > set_int > $o).
% 18.75/7.46 thf(func_def_2736, type, type_d4410041424927559462al_nat: (code_natural > nat) > (nat > code_natural) > set_nat > $o).
% 18.75/7.46 thf(func_def_2737, type, type_d6188575255521822967unit_o: (product_unit > $o) > ($o > product_unit) > set_o > $o).
% 18.75/7.46 thf(func_def_2738, type, accp_list_nat: (list_nat > list_nat > $o) > list_nat > $o).
% 18.75/7.46 thf(func_def_2739, type, accp_nat: (nat > nat > $o) > nat > $o).
% 18.75/7.46 thf(func_def_2740, type, accp_P8928870874622223812nt_int: (produc7773217078559923341nt_int > produc7773217078559923341nt_int > $o) > produc7773217078559923341nt_int > $o).
% 18.75/7.46 thf(func_def_2741, type, accp_P6019419558468335806at_nat: (produc4471711990508489141at_nat > produc4471711990508489141at_nat > $o) > produc4471711990508489141at_nat > $o).
% 18.75/7.46 thf(func_def_2742, type, accp_P1862375125659990705et_nat: (produc2732055786443039994et_nat > produc2732055786443039994et_nat > $o) > produc2732055786443039994et_nat > $o).
% 18.75/7.46 thf(func_def_2743, type, accp_P8126237942716283194atural: (produc7822875418678951345atural > produc7822875418678951345atural > $o) > produc7822875418678951345atural > $o).
% 18.75/7.46 thf(func_def_2744, type, accp_P5801069581201407417et_nat: (produc3658429121746597890et_nat > produc3658429121746597890et_nat > $o) > produc3658429121746597890et_nat > $o).
% 18.75/7.46 thf(func_def_2745, type, accp_P1096762738010456898nt_int: (product_prod_int_int > product_prod_int_int > $o) > product_prod_int_int > $o).
% 18.75/7.46 thf(func_def_2746, type, accp_P4275260045618599050at_nat: (product_prod_nat_nat > product_prod_nat_nat > $o) > product_prod_nat_nat > $o).
% 18.75/7.46 thf(func_def_2747, type, accp_P8948468358075348838it_nat: (produc2867611627572283311it_nat > produc2867611627572283311it_nat > $o) > produc2867611627572283311it_nat > $o).
% 18.75/7.46 thf(func_def_2748, type, accp_P414730952086964626it_nat: (produc3911288613690379145it_nat > produc3911288613690379145it_nat > $o) > produc3911288613690379145it_nat > $o).
% 18.75/7.46 thf(func_def_2749, type, accp_P3113834385874906142um_num: (product_prod_num_num > product_prod_num_num > $o) > product_prod_num_num > $o).
% 18.75/7.46 thf(func_def_2750, type, finite2416775604798480986nteger: set_Pr7577011563204128103nteger).
% 18.75/7.46 thf(func_def_2751, type, finite_psubset_int: set_Pr2522554150109002629et_int).
% 18.75/7.46 thf(func_def_2752, type, finite_psubset_nat: set_Pr5488025237498180813et_nat).
% 18.75/7.46 thf(func_def_2753, type, finite469560695537375940at_nat: set_Pr4329608150637261639at_nat).
% 18.75/7.46 thf(func_def_2754, type, less_than: set_Pr1261947904930325089at_nat).
% 18.75/7.46 thf(func_def_2755, type, lex_pr7234932505866811047nt_int: set_Pr7140365069852192003e_term > set_Pr2560585780119916871nt_int > set_Pr8634505666381077339nt_int).
% 18.75/7.46 thf(func_def_2756, type, lex_pr3763927252266284464nteger: set_Pr6418322821503574069e_term > set_Pr5052581263052047815nteger > set_Pr1722956316086891245nteger).
% 18.75/7.46 thf(func_def_2757, type, lex_pr4722427456421979612et_nat: set_Pr2161125870931222855_nat_o > set_Pr7928877670098842301et_nat > set_Pr3444600963470892981et_nat).
% 18.75/7.46 thf(func_def_2758, type, lex_pr5340572901959109728et_nat: set_Pr2161125870931222855_nat_o > set_Pr719794911490849221et_nat > set_Pr7928877670098842301et_nat).
% 18.75/7.46 thf(func_def_2759, type, lex_pr4548132154224949661nt_int: set_Pr4675205556198584599e_term > set_Pr2560585780119916871nt_int > set_Pr4708930517165415495nt_int).
% 18.75/7.46 thf(func_def_2760, type, lex_prod_nat_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr8693737435421807431at_nat).
% 18.75/7.46 thf(func_def_2761, type, lex_pr4265550801952275104at_nat: set_Pr1261947904930325089at_nat > set_Pr4329608150637261639at_nat > set_Pr2072254264782222413at_nat).
% 18.75/7.46 thf(func_def_2762, type, lex_pr1951919194703979714at_nat: set_Pr4329608150637261639at_nat > set_Pr1261947904930325089at_nat > set_Pr5070339090747523585at_nat).
% 18.75/7.46 thf(func_def_2763, type, lex_pr8000699672184251119at_nat: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > set_Pr5564308138774400199at_nat).
% 18.75/7.46 thf(func_def_2764, type, max_ext_o: set_Product_prod_o_o > set_Pr4577759397028426247_set_o).
% 18.75/7.46 thf(func_def_2765, type, max_ext_Code_integer: set_Pr4811707699266497531nteger > set_Pr7577011563204128103nteger).
% 18.75/7.46 thf(func_def_2766, type, max_ext_int: set_Pr958786334691620121nt_int > set_Pr2522554150109002629et_int).
% 18.75/7.46 thf(func_def_2767, type, max_ext_nat: set_Pr1261947904930325089at_nat > set_Pr5488025237498180813et_nat).
% 18.75/7.46 thf(func_def_2768, type, max_ex8135407076693332796at_nat: set_Pr8693737435421807431at_nat > set_Pr4329608150637261639at_nat).
% 18.75/7.46 thf(func_def_2769, type, max_ex8833738776070432290at_nat: set_Pr5564308138774400199at_nat > set_Pr7459493094073627847at_nat).
% 18.75/7.46 thf(func_def_2770, type, max_ex4535816423174879388at_nat: set_Pr4329608150637261639at_nat > set_Pr1604112560894399303at_nat).
% 18.75/7.46 thf(func_def_2771, type, max_extp_nat: (nat > nat > $o) > set_nat > set_nat > $o).
% 18.75/7.46 thf(func_def_2772, type, max_ex4864111882549613972at_nat: (product_prod_nat_nat > product_prod_nat_nat > $o) > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o).
% 18.75/7.46 thf(func_def_2773, type, max_ex4845989503969680116at_nat: (set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o) > set_se7855581050983116737at_nat > set_se7855581050983116737at_nat > $o).
% 18.75/7.46 thf(func_def_2774, type, measure_nat: (nat > nat) > set_Pr1261947904930325089at_nat).
% 18.75/7.46 thf(func_def_2775, type, measur1827424007717751593at_nat: (set_Pr1261947904930325089at_nat > nat) > set_Pr4329608150637261639at_nat).
% 18.75/7.46 thf(func_def_2776, type, min_ex6901939911449802026at_nat: set_Pr8693737435421807431at_nat > set_Pr4329608150637261639at_nat).
% 18.75/7.46 thf(func_def_2777, type, mlex_prod_nat: (nat > nat) > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat).
% 18.75/7.46 thf(func_def_2778, type, mlex_p3502713205431853936at_nat: (set_Pr1261947904930325089at_nat > nat) > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat).
% 18.75/7.46 thf(func_def_2779, type, pred_nat: set_Pr1261947904930325089at_nat).
% 18.75/7.46 thf(func_def_2780, type, same_f6662725367016992042nt_int: ((int > option6357759511663192854e_term) > $o) > ((int > option6357759511663192854e_term) > set_Pr2560585780119916871nt_int) > set_Pr8634505666381077339nt_int).
% 18.75/7.46 thf(func_def_2781, type, same_f8038803414157382067nteger: ((produc6241069584506657477e_term > option6357759511663192854e_term) > $o) > ((produc6241069584506657477e_term > option6357759511663192854e_term) > set_Pr5052581263052047815nteger) > set_Pr1722956316086891245nteger).
% 18.75/7.46 thf(func_def_2782, type, same_f1912051055550046943et_nat: ((produc3658429121746597890et_nat > $o) > $o) > ((produc3658429121746597890et_nat > $o) > set_Pr7928877670098842301et_nat) > set_Pr3444600963470892981et_nat).
% 18.75/7.46 thf(func_def_2783, type, same_f7251492184213700963et_nat: ((produc3658429121746597890et_nat > $o) > $o) > ((produc3658429121746597890et_nat > $o) > set_Pr719794911490849221et_nat) > set_Pr7928877670098842301et_nat).
% 18.75/7.46 thf(func_def_2784, type, same_f5472592420709775776nt_int: ((produc8551481072490612790e_term > option6357759511663192854e_term) > $o) > ((produc8551481072490612790e_term > option6357759511663192854e_term) > set_Pr2560585780119916871nt_int) > set_Pr4708930517165415495nt_int).
% 18.75/7.46 thf(func_def_2785, type, same_fst_nat_nat: (nat > $o) > (nat > set_Pr1261947904930325089at_nat) > set_Pr8693737435421807431at_nat).
% 18.75/7.46 thf(func_def_2786, type, member2790140394383616496nteger: (code_integer > code_integer) > set_Co726186806682698383nteger > $o).
% 18.75/7.46 thf(func_def_2787, type, member8845023287901829240e_term: (int > option6357759511663192854e_term) > set_in3461395444621081367e_term > $o).
% 18.75/7.46 thf(func_def_2788, type, member7306185171444233115_nat_o: (int > produc7360885484439884007_nat_o) > set_in2553536192574375378_nat_o > $o).
% 18.75/7.46 thf(func_def_2789, type, member2248416676132969167nteger: (int > produc8923325533196201883nteger) > set_in2260935666578096390nteger > $o).
% 18.75/7.46 thf(func_def_2790, type, member3292482584629245920atural: (int > produc5835291356934675326atural) > set_in1345054734626228863atural > $o).
% 18.75/7.46 thf(func_def_2791, type, member254662033361028077nt_int: (int > product_prod_int_int) > set_in6154042108061588260nt_int > $o).
% 18.75/7.46 thf(func_def_2792, type, member1326526067935671339nteger: (nat > produc8923325533196201883nteger) > set_na3661387095409732706nteger > $o).
% 18.75/7.46 thf(func_def_2793, type, member528921174545443716atural: (nat > produc5835291356934675326atural) > set_na2454399383705037859atural > $o).
% 18.75/7.46 thf(func_def_2794, type, member6440191985751670089nt_int: (nat > product_prod_int_int) > set_na7251125088705586816nt_int > $o).
% 18.75/7.46 thf(func_def_2795, type, member4242434998011752849e_term: (produc6241069584506657477e_term > option6357759511663192854e_term) > set_Pr7604974323444597168e_term > $o).
% 18.75/7.46 thf(func_def_2796, type, member6576561426505652726_nat_o: (produc3658429121746597890et_nat > $o) > set_Pr4532377907799695533_nat_o > $o).
% 18.75/7.46 thf(func_def_2797, type, member3222579708246209666e_term: (produc8551481072490612790e_term > option6357759511663192854e_term) > set_Pr3642885161833720865e_term > $o).
% 18.75/7.46 thf(func_def_2798, type, member2006080708140975699_nat_o: (product_prod_nat_nat > $o) > set_Pr5582243495563764594_nat_o > $o).
% 18.75/7.46 thf(func_def_2799, type, member2837767709637065162nteger: (product_unit > produc8923325533196201883nteger) > set_Pr9591959067864425nteger > $o).
% 18.75/7.46 thf(func_def_2800, type, member4946248492122881829atural: (product_unit > produc5835291356934675326atural) > set_Pr7322412474522714716atural > $o).
% 18.75/7.46 thf(func_def_2801, type, member5541948317052402408nt_int: (product_unit > product_prod_int_int) > set_Pr3770298976803184519nt_int > $o).
% 18.75/7.46 thf(func_def_2802, type, member_o: $o > set_o > $o).
% 18.75/7.46 thf(func_def_2803, type, member_Code_integer: code_integer > set_Code_integer > $o).
% 18.75/7.46 thf(func_def_2804, type, member_Code_natural: code_natural > set_Code_natural > $o).
% 18.75/7.46 thf(func_def_2805, type, member_int: int > set_int > $o).
% 18.75/7.46 thf(func_def_2806, type, member_list_nat: list_nat > set_list_nat > $o).
% 18.75/7.46 thf(func_def_2807, type, member_nat: nat > set_nat > $o).
% 18.75/7.46 thf(func_def_2808, type, member_num: num > set_num > $o).
% 18.75/7.46 thf(func_def_2809, type, member_option_o: option_o > set_option_o > $o).
% 18.75/7.46 thf(func_def_2810, type, member_option_int: option_int > set_option_int > $o).
% 18.75/7.46 thf(func_def_2811, type, member_option_nat: option_nat > set_option_nat > $o).
% 18.75/7.46 thf(func_def_2812, type, member_option_num: option_num > set_option_num > $o).
% 18.75/7.46 thf(func_def_2813, type, member3517700364412436275it_nat: option3216581401566546698it_nat > set_op3940070208846178154it_nat > $o).
% 18.75/7.46 thf(func_def_2814, type, member3954567711264315760at_nat: option4927543243414619207at_nat > set_op4508134149509766951at_nat > $o).
% 18.75/7.46 thf(func_def_2815, type, member5596548051065438575it_nat: option8956607266484857688it_nat > set_op239864471688321678it_nat > $o).
% 18.75/7.46 thf(func_def_2816, type, member4288423094740844502at_nat: option8699557107911914541at_nat > set_op989438649584373901at_nat > $o).
% 18.75/7.46 thf(func_def_2817, type, member1378114217278917244t_unit: option_Product_unit > set_op3165557761946182707t_unit > $o).
% 18.75/7.46 thf(func_def_2818, type, member8989860449721436141et_nat: option_set_nat > set_option_set_nat > $o).
% 18.75/7.46 thf(func_def_2819, type, member6538663773838357324e_term: produc1945540942535730339e_term > set_Pr7140365069852192003e_term > $o).
% 18.75/7.46 thf(func_def_2820, type, member7034335876925520548nt_int: produc7773217078559923341nt_int > set_Pr1872883991513573699nt_int > $o).
% 18.75/7.46 thf(func_def_2821, type, member6786453453753086846e_term: produc8187290932660736981e_term > set_Pr6418322821503574069e_term > $o).
% 18.75/7.46 thf(func_def_2822, type, member4164122664394876845nteger: produc1908205239877642774nteger > set_Pr1281608226676607948nteger > $o).
% 18.75/7.46 thf(func_def_2823, type, member8781333585448626064_nat_o: produc4928098042776334183_nat_o > set_Pr2161125870931222855_nat_o > $o).
% 18.75/7.46 thf(func_def_2824, type, member6124377750444531601et_nat: produc2732055786443039994et_nat > set_Pr8536935166611901872et_nat > $o).
% 18.75/7.46 thf(func_def_2825, type, member1996754912294343701et_nat: produc3925858234332021118et_nat > set_Pr3286484037609594932et_nat > $o).
% 18.75/7.46 thf(func_def_2826, type, member8796044733138646368e_term: produc4499399687821757879e_term > set_Pr4675205556198584599e_term > $o).
% 18.75/7.46 thf(func_def_2827, type, member7618704894036264090nt_int: produc2285326912895808259nt_int > set_Pr9222295170931077689nt_int > $o).
% 18.75/7.46 thf(func_def_2828, type, member7466972457876170832od_o_o: product_prod_o_o > set_Product_prod_o_o > $o).
% 18.75/7.46 thf(func_def_2829, type, member7847949116333733898_o_int: product_prod_o_int > set_Pr8834758594704517033_o_int > $o).
% 18.75/7.46 thf(func_def_2830, type, member2802428098988154798_o_nat: product_prod_o_nat > set_Pr2101469702781467981_o_nat > $o).
% 18.75/7.46 thf(func_def_2831, type, member157494554546826820nteger: produc8923325533196201883nteger > set_Pr4811707699266497531nteger > $o).
% 18.75/7.46 thf(func_def_2832, type, member8280416476884352090atural: produc7822875418678951345atural > set_Pr7564037697178849041atural > $o).
% 18.75/7.46 thf(func_def_2833, type, member2108296798382401941atural: produc5835291356934675326atural > set_Pr2352657477744078772atural > $o).
% 18.75/7.46 thf(func_def_2834, type, member6260224972018164377et_nat: produc3658429121746597890et_nat > set_Pr3948176798113811640et_nat > $o).
% 18.75/7.46 thf(func_def_2835, type, member4489920277610959864_int_o: product_prod_int_o > set_Pr903927857289325719_int_o > $o).
% 18.75/7.46 thf(func_def_2836, type, member5262025264175285858nt_int: product_prod_int_int > set_Pr958786334691620121nt_int > $o).
% 18.75/7.46 thf(func_def_2837, type, member216504246829706758nt_nat: product_prod_int_nat > set_Pr3448869479623346877nt_nat > $o).
% 18.75/7.46 thf(func_def_2838, type, member6689249552917799696at_nat: produc4166570645942440679at_nat > set_Pr8551490117392284871at_nat > $o).
% 18.75/7.46 thf(func_def_2839, type, member6310962623043647828_nat_o: product_prod_nat_o > set_Pr3149072824959771635_nat_o > $o).
% 18.75/7.46 thf(func_def_2840, type, member4262671552274231302at_int: product_prod_nat_int > set_Pr7995236796853374141at_int > $o).
% 18.75/7.46 thf(func_def_2841, type, member8440522571783428010at_nat: product_prod_nat_nat > set_Pr1261947904930325089at_nat > $o).
% 18.75/7.46 thf(func_def_2842, type, member4085533954029916580nt_int: produc2501202720802129403nt_int > set_Pr8634505666381077339nt_int > $o).
% 18.75/7.46 thf(func_def_2843, type, member2446009503569356342nteger: produc824974754969098637nteger > set_Pr1722956316086891245nteger > $o).
% 18.75/7.46 thf(func_def_2844, type, member6341495586645257982et_nat: produc5657529347773406293et_nat > set_Pr3444600963470892981et_nat > $o).
% 18.75/7.46 thf(func_def_2845, type, member4763271486408492550et_nat: produc6830853553727218525et_nat > set_Pr7928877670098842301et_nat > $o).
% 18.75/7.46 thf(func_def_2846, type, member6582457606847315088nt_int: produc2432570611225516007nt_int > set_Pr4708930517165415495nt_int > $o).
% 18.75/7.46 thf(func_def_2847, type, member335077259223437328nteger: produc3334582477557816039nteger > set_Pr5052581263052047815nteger > $o).
% 18.75/7.46 thf(func_def_2848, type, member6099555550032318734et_nat: produc8111630337999740517et_nat > set_Pr719794911490849221et_nat > $o).
% 18.75/7.46 thf(func_def_2849, type, member8566619992076573584nt_int: produc1219242969750017639nt_int > set_Pr2560585780119916871nt_int > $o).
% 18.75/7.46 thf(func_def_2850, type, member2200362271989506215_nat_o: produc652263959640188542_nat_o > set_Pr6558897299634722526_nat_o > $o).
% 18.75/7.46 thf(func_def_2851, type, member8206827879206165904at_nat: produc859450856879609959at_nat > set_Pr8693737435421807431at_nat > $o).
% 18.75/7.46 thf(func_def_2852, type, member4107301959146914710at_nat: produc2714363965264676845at_nat > set_Pr2072254264782222413at_nat > $o).
% 18.75/7.46 thf(func_def_2853, type, member3480088626692287306at_nat: produc2087150632810049441at_nat > set_Pr5070339090747523585at_nat > $o).
% 18.75/7.46 thf(func_def_2854, type, member6009668390874684176at_nat: produc1906917888121415911at_nat > set_Pr5564308138774400199at_nat > $o).
% 18.75/7.46 thf(func_def_2855, type, member3421417852355157663it_nat: produc8664842809031399944it_nat > set_Pr1354866905816374718it_nat > $o).
% 18.75/7.46 thf(func_def_2856, type, member9116954335612470352_set_o: produc7369051934464679207_set_o > set_Pr4577759397028426247_set_o > $o).
% 18.75/7.46 thf(func_def_2857, type, member4307123515891402160nteger: produc6491284506569428743nteger > set_Pr7577011563204128103nteger > $o).
% 18.75/7.46 thf(func_def_2858, type, member2572552093476627150et_int: produc2115011035271226405et_int > set_Pr2522554150109002629et_int > $o).
% 18.75/7.46 thf(func_def_2859, type, member8277197624267554838et_nat: produc7819656566062154093et_nat > set_Pr5488025237498180813et_nat > $o).
% 18.75/7.46 thf(func_def_2860, type, member444158400953824016od_o_o: produc2934264451710624999od_o_o > set_Pr1932065953672099015od_o_o > $o).
% 18.75/7.46 thf(func_def_2861, type, member4095101504841534314at_nat: produc732395585841259969at_nat > set_Pr457366540195662369at_nat > $o).
% 18.75/7.46 thf(func_def_2862, type, member8757157785044589968at_nat: produc3843707927480180839at_nat > set_Pr4329608150637261639at_nat > $o).
% 18.75/7.46 thf(func_def_2863, type, member1466754251312161552at_nat: produc1319942482725812455at_nat > set_Pr7459493094073627847at_nat > $o).
% 18.75/7.46 thf(func_def_2864, type, member4300370950623927696at_nat: produc7299876168958306407at_nat > set_Pr1604112560894399303at_nat > $o).
% 18.75/7.46 thf(func_def_2865, type, member_Product_unit: product_unit > set_Product_unit > $o).
% 18.75/7.46 thf(func_def_2866, type, member_rat: rat > set_rat > $o).
% 18.75/7.46 thf(func_def_2867, type, member_set_o: set_o > set_set_o > $o).
% 18.75/7.46 thf(func_def_2868, type, member1834298987299537450nteger: set_Code_integer > set_set_Code_integer > $o).
% 18.75/7.46 thf(func_def_2869, type, member_set_int: set_int > set_set_int > $o).
% 18.75/7.46 thf(func_def_2870, type, member_set_list_nat: set_list_nat > set_set_list_nat > $o).
% 18.75/7.46 thf(func_def_2871, type, member_set_nat: set_nat > set_set_nat > $o).
% 18.75/7.46 thf(func_def_2872, type, member2643936169264416010at_nat: set_Pr1261947904930325089at_nat > set_se7855581050983116737at_nat > $o).
% 18.75/7.46 thf(func_def_2873, type, member5877623283571906838t_unit: set_Product_unit > set_set_Product_unit > $o).
% 18.75/7.46 thf(func_def_2874, type, h: heap_e7401611519738050253t_unit).
% 18.75/7.46 thf(func_def_2875, type, xs: list_a).
% 18.75/7.46 thf(func_def_2894, type, sP0: (option3216581401566546698it_nat > option8956607266484857688it_nat > $o) > option3216581401566546698it_nat > option8956607266484857688it_nat > $o).
% 18.75/7.46 thf(func_def_2895, type, sP1: (option3216581401566546698it_nat > option8956607266484857688it_nat > $o) > option3216581401566546698it_nat > option8956607266484857688it_nat > $o).
% 18.75/7.46 thf(func_def_2896, type, sP2: (option_num > option3216581401566546698it_nat > $o) > option3216581401566546698it_nat > option_num > $o).
% 18.75/7.46 thf(func_def_2897, type, sP3: (option_num > option3216581401566546698it_nat > $o) > option_num > option3216581401566546698it_nat > $o).
% 18.75/7.46 thf(func_def_2898, type, sP4: (option8956607266484857688it_nat > option3216581401566546698it_nat > $o) > option3216581401566546698it_nat > option8956607266484857688it_nat > $o).
% 18.75/7.46 thf(func_def_2899, type, sP5: (option8956607266484857688it_nat > option3216581401566546698it_nat > $o) > option8956607266484857688it_nat > option3216581401566546698it_nat > $o).
% 18.75/7.46 thf(func_def_2900, type, sP6: (option3216581401566546698it_nat > option3216581401566546698it_nat > $o) > option3216581401566546698it_nat > option3216581401566546698it_nat > $o).
% 18.75/7.46 thf(func_def_2901, type, sP7: (option3216581401566546698it_nat > option3216581401566546698it_nat > $o) > option3216581401566546698it_nat > option3216581401566546698it_nat > $o).
% 18.75/7.46 thf(func_def_2902, type, sP8: (option3216581401566546698it_nat > option_num > $o) > option3216581401566546698it_nat > option_num > $o).
% 18.75/7.46 thf(func_def_2903, type, sP9: (option3216581401566546698it_nat > option_num > $o) > option3216581401566546698it_nat > option_num > $o).
% 18.75/7.46 thf(func_def_2904, type, sK10: (option3216581401566546698it_nat > option8956607266484857688it_nat > $o) > option3216581401566546698it_nat > option8956607266484857688it_nat > produc6714399278180371524it_nat).
% 18.75/7.46 thf(func_def_2905, type, sK11: (option3216581401566546698it_nat > option8956607266484857688it_nat > $o) > option3216581401566546698it_nat > option8956607266484857688it_nat > produc8664842809031399944it_nat).
% 18.75/7.46 thf(func_def_2906, type, sK12: heap_T6362127782908069795rray_a > heap_e7401611519738050253t_unit > produc6653097349344004940it_nat).
% 18.75/7.46 thf(func_def_2907, type, sK13: heap_T6362127782908069795rray_a > heap_e7401611519738050253t_unit > array_a).
% 18.75/7.46 thf(func_def_2908, type, sK14: (option_num > option3216581401566546698it_nat > $o) > option3216581401566546698it_nat > option_num > produc6714399278180371524it_nat).
% 18.75/7.46 thf(func_def_2909, type, sK15: (option_num > option3216581401566546698it_nat > $o) > option3216581401566546698it_nat > option_num > num).
% 18.75/7.46 thf(func_def_2910, type, sK16: heap_T6362127782908069795rray_a > heap_e7401611519738050253t_unit > produc6653097349344004940it_nat).
% 18.75/7.46 thf(func_def_2911, type, sK17: heap_T6362127782908069795rray_a > heap_e7401611519738050253t_unit > array_a).
% 18.75/7.46 thf(func_def_2912, type, sK18: (option8956607266484857688it_nat > option3216581401566546698it_nat > $o) > option3216581401566546698it_nat > option8956607266484857688it_nat > produc6714399278180371524it_nat).
% 18.75/7.46 thf(func_def_2913, type, sK19: (option8956607266484857688it_nat > option3216581401566546698it_nat > $o) > option3216581401566546698it_nat > option8956607266484857688it_nat > produc8664842809031399944it_nat).
% 18.75/7.46 thf(func_def_2914, type, sK20: option3216581401566546698it_nat > produc6714399278180371524it_nat).
% 18.75/7.46 thf(func_def_2915, type, sK21: option3216581401566546698it_nat > produc6714399278180371524it_nat).
% 18.75/7.46 thf(func_def_2916, type, sK22: heap_T6362127782908069795rray_a > heap_T6362127782908069795rray_a > heap_e7401611519738050253t_unit).
% 18.75/7.46 thf(func_def_2917, type, sK23: (option3216581401566546698it_nat > option3216581401566546698it_nat > $o) > option3216581401566546698it_nat > option3216581401566546698it_nat > produc6714399278180371524it_nat).
% 18.75/7.46 thf(func_def_2918, type, sK24: (option3216581401566546698it_nat > option3216581401566546698it_nat > $o) > option3216581401566546698it_nat > option3216581401566546698it_nat > produc6714399278180371524it_nat).
% 18.75/7.46 thf(func_def_2919, type, sK25: (option3216581401566546698it_nat > option_num > $o) > option3216581401566546698it_nat > option_num > num).
% 18.75/7.46 thf(func_def_2920, type, sK26: (option3216581401566546698it_nat > option_num > $o) > option3216581401566546698it_nat > option_num > produc6714399278180371524it_nat).
% 18.75/7.46 thf(func_def_2921, type, sK27: option3216581401566546698it_nat > produc6714399278180371524it_nat).
% 18.75/7.46 thf(f18102,plain,(
% 18.75/7.46 $false),
% 18.75/7.46 inference(equality_resolution,[status(thm)],[f18075])).
% 18.75/7.46 thf(f18075,plain,(
% 18.75/7.46 ( ! [X0 : heap_e7401611519738050253t_unit,X1 : list_a] : (((heap_T5591663578999710211rray_a @ (array_of_list_a @ xs) @ h) != (heap_T5591663578999710211rray_a @ (array_of_list_a @ X1) @ X0))) )),
% 18.75/7.46 inference(equality_proxy_clausification,[status(thm)],[f18074])).
% 18.75/7.46 thf(f18074,plain,(
% 18.75/7.46 ( ! [X0 : heap_e7401611519738050253t_unit,X1 : list_a] : ((((heap_T5591663578999710211rray_a @ (array_of_list_a @ X1) @ X0) = (heap_T5591663578999710211rray_a @ (array_of_list_a @ xs) @ h)) = $false)) )),
% 18.75/7.46 inference(not_proxy_clausification,[status(thm)],[f18073])).
% 18.75/7.46 thf(f18073,plain,(
% 18.75/7.46 ( ! [X0 : heap_e7401611519738050253t_unit,X1 : list_a] : (($true = (~ ((heap_T5591663578999710211rray_a @ (array_of_list_a @ X1) @ X0) = (heap_T5591663578999710211rray_a @ (array_of_list_a @ xs) @ h))))) )),
% 18.75/7.46 inference(beta_eta_normalization,[status(thm)],[f18058])).
% 18.75/7.46 thf(f18058,plain,(
% 18.75/7.46 ( ! [X0 : heap_e7401611519738050253t_unit,X1 : list_a] : (($true = ((^[Y0 : heap_T6362127782908069795rray_a]: ((^[Y1 : heap_e7401611519738050253t_unit]: (~ ((heap_T5591663578999710211rray_a @ Y0 @ Y1) = (heap_T5591663578999710211rray_a @ (array_of_list_a @ xs) @ h)))))) @ (array_of_list_a @ X1) @ X0))) )),
% 18.75/7.46 inference(definition_unfolding,[status(thm)],[f18020,f18051])).
% 18.75/7.46 thf(f18051,plain,(
% 18.75/7.46 (heap_T6932021131025641745rray_a = (^[Y0 : heap_T6362127782908069795rray_a]: ((^[Y1 : heap_e7401611519738050253t_unit]: (~ ((heap_T5591663578999710211rray_a @ Y0 @ Y1) = (heap_T5591663578999710211rray_a @ (array_of_list_a @ xs) @ h)))))))),
% 18.75/7.46 inference(definition_unfolding,[status(thm)],[f18035,f18008])).
% 18.75/7.46 thf(f18008,plain,(
% 18.75/7.46 (none_P2587165478634041381it_nat = (heap_T5591663578999710211rray_a @ (array_of_list_a @ xs) @ h))),
% 18.75/7.46 inference(cnf_transformation,[status(thm)],[f17922])).
% 18.75/7.46 thf(f17922,plain,(
% 18.75/7.46 (none_P2587165478634041381it_nat = (heap_T5591663578999710211rray_a @ (array_of_list_a @ xs) @ h))),
% 18.75/7.46 inference(flattening,[status(thm)],[f8004])).
% 18.75/7.46 thf(f8004,negated_conjecture,(
% 18.75/7.46 ~(none_P2587165478634041381it_nat != (heap_T5591663578999710211rray_a @ (array_of_list_a @ xs) @ h))),
% 18.75/7.46 inference(negated_conjecture,[status(cth)],[f8003])).
% 18.75/7.46 thf(f8003,conjecture,(
% 18.75/7.46 (none_P2587165478634041381it_nat != (heap_T5591663578999710211rray_a @ (array_of_list_a @ xs) @ h))),
% 18.75/7.46 file('/export/starexec/sandbox2/tmp/tmp.rG2Hh59idJ/DTF2THF_32404.p',conj_0)).
% 18.75/7.46 thf(f18035,plain,(
% 18.75/7.46 (heap_T6932021131025641745rray_a = (^[Y0 : heap_T6362127782908069795rray_a]: ((^[Y1 : heap_e7401611519738050253t_unit]: (~ ((heap_T5591663578999710211rray_a @ Y0 @ Y1) = none_P2587165478634041381it_nat))))))),
% 18.75/7.46 inference(cnf_transformation,[status(thm)],[f12854])).
% 18.75/7.46 thf(f12854,plain,(
% 18.75/7.46 (heap_T6932021131025641745rray_a = (^[Y0 : heap_T6362127782908069795rray_a]: ((^[Y1 : heap_e7401611519738050253t_unit]: (~ ((heap_T5591663578999710211rray_a @ Y0 @ Y1) = none_P2587165478634041381it_nat))))))),
% 18.75/7.46 inference(fool_elimination,[status(thm)],[f12853])).
% 18.75/7.46 thf(f12853,plain,(
% 18.75/7.46 (heap_T6932021131025641745rray_a = (^[X0 : heap_T6362127782908069795rray_a, X1 : heap_e7401611519738050253t_unit] : (((heap_T5591663578999710211rray_a @ X0 @ X1) != none_P2587165478634041381it_nat))))),
% 18.75/7.46 inference(rectify,[status(thm)],[f13])).
% 18.75/7.46 thf(f13,axiom,(
% 18.75/7.46 (heap_T6932021131025641745rray_a = (^[X10 : heap_T6362127782908069795rray_a, X1 : heap_e7401611519738050253t_unit] : ((none_P2587165478634041381it_nat != (heap_T5591663578999710211rray_a @ X10 @ X1)))))),
% 18.75/7.46 file('/export/starexec/sandbox2/tmp/tmp.rG2Hh59idJ/DTF2THF_32404.p',fact_12_success__def)).
% 18.75/7.46 thf(f18020,plain,(
% 18.75/7.46 ( ! [X0 : heap_e7401611519738050253t_unit,X1 : list_a] : (($true = (heap_T6932021131025641745rray_a @ (array_of_list_a @ X1) @ X0))) )),
% 18.75/7.46 inference(cnf_transformation,[status(thm)],[f13216])).
% 18.75/7.46 thf(f13216,plain,(
% 18.75/7.46 ! [X0 : heap_e7401611519738050253t_unit,X1 : list_a] : ($true = (heap_T6932021131025641745rray_a @ (array_of_list_a @ X1) @ X0))),
% 18.75/7.46 inference(fool_elimination,[status(thm)],[f13215])).
% 18.75/7.46 thf(f13215,plain,(
% 18.75/7.46 ! [X0 : heap_e7401611519738050253t_unit,X1 : list_a] : (heap_T6932021131025641745rray_a @ (array_of_list_a @ X1) @ X0)),
% 18.75/7.46 inference(rectify,[status(thm)],[f46])).
% 18.75/7.46 thf(f46,axiom,(
% 18.75/7.46 ! [X8 : heap_e7401611519738050253t_unit,X17 : list_a] : (heap_T6932021131025641745rray_a @ (array_of_list_a @ X17) @ X8)),
% 18.75/7.46 file('/export/starexec/sandbox2/tmp/tmp.rG2Hh59idJ/DTF2THF_32404.p',fact_45_success__of__listI)).
% 18.75/7.46 % SZS output end Proof for DTF2THF_32404
% 18.75/7.46 % (369)------------------------------
% 18.75/7.46 % (369)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.75/7.46 % (369)Termination reason: Refutation
% 18.75/7.46
% 18.75/7.46 % (369)Memory used [KB]: 29423
% 18.75/7.46 % (369)Time elapsed: 0.441 s
% 18.75/7.46 % (369)Instructions burned: 1327 (million)
% 18.75/7.46 % (369)------------------------------
% 18.75/7.46 % (369)------------------------------
% 18.75/7.46 % (32741)Success in time 2.009 s
%------------------------------------------------------------------------------